uClibc now has a math library. muahahahaha!

 -Erik

Makefile

@@ -29,7 +29,7 @@
 TOPDIR=./
 include Rules.mak
 
-DIRS = extra misc pwd_grp stdio string termios inet signal stdlib sysdeps unistd crypt libutil
+DIRS = extra misc pwd_grp stdio string termios inet signal stdlib sysdeps unistd crypt libutil libm
 
 ifeq ($(strip $(HAS_MMU)),true)
 	DO_SHARED=shared
@@ -60,6 +60,7 @@ shared: $(LIBNAME)
 	ln -sf $(SHARED_MAJORNAME) libc.so
 	@$(MAKE) -C crypt shared
 	@$(MAKE) -C libutil shared
+	@$(MAKE) -C libm shared
 	@$(MAKE) -C ld.so-1
 
 done: $(LIBNAME) $(DO_SHARED)
@@ -116,6 +117,7 @@ install: install_runtime install_dev install_ldso
 install_runtime:
 	@$(MAKE) -C crypt install
 	@$(MAKE) -C libutil install
+	@$(MAKE) -C libm install
 ifneq ($(DO_SHARED),)
 	install -d $(INSTALL_DIR)/lib
 	rm -rf $(INSTALL_DIR)/lib/$(SHARED_FULLNAME)
@@ -180,6 +182,16 @@ uClibc_config.h: Config
 	else \
 	    echo "#undef __UCLIBC_HAS_FLOATS__" >> uClibc_config.h ; \
 	fi
+	@if [ "$(HAS_DOUBLE)" = "true" ] ; then \
+	    echo "#define __UCLIBC_HAS_DOUBLE__ 1" >> uClibc_config.h ; \
+	else \
+	    echo "#undef __UCLIBC_HAS_DOUBLE__" >> uClibc_config.h ; \
+	fi
+	@if [ "$(HAS_LONG_DOUBLE)" = "true" ] ; then \
+	    echo "#define __UCLIBC_HAS_LONG_DOUBLE__ 1" >> uClibc_config.h ; \
+	else \
+	    echo "#undef __UCLIBC_HAS_LONG_DOUBLE__" >> uClibc_config.h ; \
+	fi
 	@if [ "$(HAS_LONG_LONG)" = "true" ] ; then \
 	    echo "#define __UCLIBC_HAS_LONG_LONG__ 1" >> uClibc_config.h ; \
 	else \

include/math.h

@@ -1,176 +1,634 @@
-#ifndef _MATH_H
-#define _MATH_H
-/*
- *   This file was automatically generated by version 1.7 of cextract.
- *   Manual editing not recommended.
+/*							mconf.h
+ * <math.h>
+ * ISO/IEC 9899:1999 -- Programming Languages C: 7.12 Mathematics 
+ * Derived from the Cephes Math Library Release 2.3
+ * Copyright 1984, 1987, 1989, 1995 by Stephen L. Moshier
  *
- *   Created: Fri Feb 23 20:31:13 1996
  *
- *   Modified (anyway) for PalmOS Feb 22, 1997, D.Jeff Dionne
+ * DESCRIPTION:
+ *
+ * The file also includes a conditional assembly definition
+ * for the type of computer arithmetic (IEEE, DEC, Motorola
+ * IEEE, or UNKnown).
+ * 
+ * For Digital Equipment PDP-11 and VAX computers, certain
+ * IBM systems, and others that use numbers with a 56-bit
+ * significand, the symbol DEC should be defined.  In this
+ * mode, most floating point constants are given as arrays
+ * of octal integers to eliminate decimal to binary conversion
+ * errors that might be introduced by the compiler.
+ *
+ * For little-endian computers, such as IBM PC, that follow the
+ * IEEE Standard for Binary Floating Point Arithmetic (ANSI/IEEE
+ * Std 754-1985), the symbol IBMPC should be defined.  These
+ * numbers have 53-bit significands.  In this mode, constants
+ * are provided as arrays of hexadecimal 16 bit integers.
+ *
+ * Big-endian IEEE format is denoted MIEEE.  On some RISC
+ * systems such as Sun SPARC, double precision constants
+ * must be stored on 8-byte address boundaries.  Since integer
+ * arrays may be aligned differently, the MIEEE configuration
+ * may fail on such machines.
+ *
+ * To accommodate other types of computer arithmetic, all
+ * constants are also provided in a normal decimal radix
+ * which one can hope are correctly converted to a suitable
+ * format by the available C language compiler.  To invoke
+ * this mode, define the symbol UNK.
+ *
+ * An important difference among these modes is a predefined
+ * set of machine arithmetic constants for each.  The numbers
+ * MACHEP (the machine roundoff error), MAXNUM (largest number
+ * represented), and several other parameters are preset by
+ * the configuration symbol.  Check the file const.c to
+ * ensure that these values are correct for your computer.
+ *
+ * Configurations NANS, INFINITIES, MINUSZERO, and DENORMAL
+ * may fail on many systems.  Verify that they are supposed
+ * to work on your computer.
+ */
+
+
+#ifndef	_MATH_H
+#define	_MATH_H	1
+
+#include <features.h>
+
+#ifndef __UCLIBC_HAS_FLOATS__
+    #define float int
+#endif
+#ifndef __UCLIBC_HAS_DOUBLE__
+    #define double int
+#endif
+#ifndef __UCLIBC_HAS_LONG_DOUBLE__
+    #define long
+    #ifndef double
+    #	define double int
+    #endif
+#endif
+
+/* Type of computer arithmetic */
+
+/* PDP-11, Pro350, VAX:
+ */
+/* #define DEC 1 */
+
+/* Intel IEEE, low order words come first:
+ */
+/* #define IBMPC 1 */
+
+/* Motorola IEEE, high order words come first
+ * (Sun 680x0 workstation):
+ */
+/* #define MIEEE 1 */
+
+/* UNKnown arithmetic, invokes coefficients given in
+ * normal decimal format.  Beware of range boundary
+ * problems (MACHEP, MAXLOG, etc. in const.c) and
+ * roundoff problems in pow.c:
+ * (Sun SPARCstation)
+ */
+#define UNK 1
+
+
+/* Define if the `long double' type works.  */
+#define HAVE_LONG_DOUBLE 1
+
+/* Define as the return type of signal handlers (int or void).  */
+#define RETSIGTYPE void
+
+/* Define if you have the ANSI C header files.  */
+#define STDC_HEADERS 1
+
+/* Define if your processor stores words with the most significant
+   byte first (like Motorola and SPARC, unlike Intel and VAX).  */
+/* #undef WORDS_BIGENDIAN */
+
+/* Define if floating point words are bigendian.  */
+/* #undef FLOAT_WORDS_BIGENDIAN */
+
+/* The number of bytes in a int.  */
+#define SIZEOF_INT 4
+
+/* Define if you have the <string.h> header file.  */
+#define HAVE_STRING_H 1
+
+
+/* Define this `volatile' if your compiler thinks
+ * that floating point arithmetic obeys the associative
+ * and distributive laws.  It will defeat some optimizations
+ * (but probably not enough of them).
+ *
+ * #define VOLATILE volatile
+ */
+#define VOLATILE
+
+/* For 12-byte long doubles on an i386, pad a 16-bit short 0
+ * to the end of real constants initialized by integer arrays.
+ *
+ * #define XPD 0,
+ *
+ * Otherwise, the type is 10 bytes long and XPD should be
+ * defined blank (e.g., Microsoft C).
+ *
+ * #define XPD
  */
+#define XPD 0,
+
+/* Define to support tiny denormal numbers, else undefine. */
+#define DENORMAL 1
+
+/* Define to ask for infinity support, else undefine. */
+#define INFINITIES 1
+
+/* Define to ask for support of numbers that are Not-a-Number,
+   else undefine.  This may automatically define INFINITIES in some files. */
+#define NANS 1
+
+/* Define to distinguish between -0.0 and +0.0.  */
+#define MINUSZERO 1
+
+/* Define 1 for ANSI C atan2() function
+   and ANSI prototypes for float arguments.
+   See atan.c and clog.c. */
+#define ANSIC 1
+#define ANSIPROT 1
+
+
+/* Constant definitions for math error conditions */
+
+#define DOMAIN		1	/* argument domain error */
+#define SING		2	/* argument singularity */
+#define OVERFLOW	3	/* overflow range error */
+#define UNDERFLOW	4	/* underflow range error */
+#define TLOSS		5	/* total loss of precision */
+#define PLOSS		6	/* partial loss of precision */
+
+#define EDOM		33
+#define ERANGE		34
+
+/* Complex numeral.  */
+typedef struct
+	{
+	double r;
+	double i;
+	} cmplx;
+
+typedef struct
+	{
+	float r;
+	float i;
+	} cmplxf;
+
+#ifdef HAVE_LONG_DOUBLE
+/* Long double complex numeral.  */
+typedef struct
+	{
+	long double r;
+	long double i;
+	} cmplxl;
+#endif
+
+
+
+/* Variable for error reporting.  See mtherr.c.  */
+extern int mtherr();
+extern int merror;
+
+
+/* If you define UNK, then be sure to set BIGENDIAN properly. */
+#include <endian.h>
+#if __BYTE_ORDER == __BIG_ENDIAN
+#  define BIGENDIAN 1
+#else /* __BYTE_ORDER == __LITTLE_ENDIAN */
+#  define BIGENDIAN 0
+#endif
+
+
+#define __USE_ISOC9X
+/* Get general and ISO C 9X specific information.  */
+#include <bits/mathdef.h>
+#undef INFINITY
+#undef DECIMAL_DIG
+#undef FP_ILOGB0
+#undef FP_ILOGBNAN
+
+/* Get the architecture specific values describing the floating-point
+   evaluation.  The following symbols will get defined:
+
+    float_t	floating-point type at least as wide as `float' used
+		to evaluate `float' expressions
+    double_t	floating-point type at least as wide as `double' used
+		to evaluate `double' expressions
+
+    FLT_EVAL_METHOD
+		Defined to
+		  0	if `float_t' is `float' and `double_t' is `double'
+		  1	if `float_t' and `double_t' are `double'
+		  2	if `float_t' and `double_t' are `long double'
+		  else	`float_t' and `double_t' are unspecified
+
+    INFINITY	representation of the infinity value of type `float'
+
+    FP_FAST_FMA
+    FP_FAST_FMAF
+    FP_FAST_FMAL
+		If defined it indicates that the `fma' function
+		generally executes about as fast as a multiply and an add.
+		This macro is defined only iff the `fma' function is
+		implemented directly with a hardware multiply-add instructions.
+
+    FP_ILOGB0	Expands to a value returned by `ilogb (0.0)'.
+    FP_ILOGBNAN	Expands to a value returned by `ilogb (NAN)'.
+
+    DECIMAL_DIG	Number of decimal digits supported by conversion between
+		decimal and all internal floating-point formats.
+
+*/
+
+/* All floating-point numbers can be put in one of these categories.  */
+enum
+  {
+    FP_NAN,
+# define FP_NAN FP_NAN
+    FP_INFINITE,
+# define FP_INFINITE FP_INFINITE
+    FP_ZERO,
+# define FP_ZERO FP_ZERO
+    FP_SUBNORMAL,
+# define FP_SUBNORMAL FP_SUBNORMAL
+    FP_NORMAL
+# define FP_NORMAL FP_NORMAL
+  };
+
+/* Return number of classification appropriate for X.  */
+# ifdef __NO_LONG_DOUBLE_MATH
+#  define fpclassify(x) \
+     (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
+# else
+#  define fpclassify(x) \
+     (sizeof (x) == sizeof (float) ?					      \
+        __fpclassifyf (x)						      \
+      : sizeof (x) == sizeof (double) ?					      \
+        __fpclassify (x) : __fpclassifyl (x))
+# endif
+
+/* Return nonzero value if sign of X is negative.  */
+int signbit(double x);
+int signbitl(long double x);
+
+/* Return nonzero value if X is not +-Inf or NaN.  */
+int isfinite(double x);
+int isfinitel(long double x);
+
+/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
+# define isnormal(x) (fpclassify (x) == FP_NORMAL)
+
+/* Return nonzero value if X is a NaN */
+int isnan(double x);
+int isnanl(long double x);
+
+/* Return nonzero value is X is positive or negative infinity.  */
+# ifdef __NO_LONG_DOUBLE_MATH
+#  define isinf(x) \
+     (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
+# else
+#  define isinf(x) \
+     (sizeof (x) == sizeof (float) ?					      \
+        __isinff (x)							      \
+      : sizeof (x) == sizeof (double) ?					      \
+        __isinf (x) : __isinfl (x))
+# endif
+
 
-typedef struct {
- double r;
- double i;
-}cmplxf;
 
 /* Some useful constants.  */
-#define M_E		2.7182818284590452354	/* e */
-#define M_LOG2E		1.4426950408889634074	/* log_2 e */
-#define M_LOG10E	0.43429448190325182765	/* log_10 e */
-#define M_LN2		0.69314718055994530942	/* log_e 2 */
-#define M_LN10		2.30258509299404568402	/* log_e 10 */
-#define M_PI		3.14159265358979323846	/* pi */
-#define M_PI_2		1.57079632679489661923	/* pi/2 */
-#define M_PI_4		0.78539816339744830962	/* pi/4 */
-#define M_1_PI		0.31830988618379067154	/* 1/pi */
-#define M_2_PI		0.63661977236758134308	/* 2/pi */
-#define M_2_SQRTPI	1.12837916709551257390	/* 2/sqrt(pi) */
-#define M_SQRT2		1.41421356237309504880	/* sqrt(2) */
-#define M_SQRT1_2	0.70710678118654752440	/* 1/sqrt(2) */
-
-
-extern double acos ( double x );
-extern double acosh ( double xx );
-extern int airy ( double xx, double *ai, double *aip, double *bi, double *bip );
-extern double asin ( double xx );
-extern double asinh ( double xx );
-extern double atan2 ( double y, double x );
-extern double atan ( double xx );
-extern double atanh ( double xx );
-extern double bdtrc ( int k, int n, double pp );
-extern double bdtr ( int k, int n, double pp );
-extern double bdtri ( int k, int n, double yy );
-extern double beta ( double aa, double bb );
-extern double cabs ( cmplxf *z );
-extern void cacos ( cmplxf *z, cmplxf *w );
-extern void cadd ( cmplxf *a, cmplxf *b, cmplxf *c );
-extern void casin ( cmplxf *z, cmplxf *w );
-extern void catan ( cmplxf *z, cmplxf *w );
-extern double cbrt ( double xx );
-extern void cchsh ( double xx, double *c, double *s );
-extern void ccos ( cmplxf *z, cmplxf *w );
-extern void ccot ( cmplxf *z, cmplxf *w );
-extern void cdiv ( cmplxf *a, cmplxf *b, cmplxf *c );
-extern double ceil ( double x );
-extern void cexp ( cmplxf *z, cmplxf *w );
-extern double chbevl ( double x, double *array, int n );
-extern double chdtrc ( double dff, double xx );
-extern double chdtr ( double dff, double xx );
-extern double chdtri ( double dff, double yy );
-#if 0
-extern void clog ( cmplxf *z, cmplxf *w );
+#if defined __USE_BSD || defined __USE_XOPEN
+# define M_E		2.7182818284590452354	/* e */
+# define M_LOG2E	1.4426950408889634074	/* log_2 e */
+# define M_LOG10E	0.43429448190325182765	/* log_10 e */
+# define M_LN2		0.69314718055994530942	/* log_e 2 */
+# define M_LN10		2.30258509299404568402	/* log_e 10 */
+# define M_PI		3.14159265358979323846	/* pi */
+# define M_PI_2		1.57079632679489661923	/* pi/2 */
+# define M_PI_4		0.78539816339744830962	/* pi/4 */
+# define M_1_PI		0.31830988618379067154	/* 1/pi */
+# define M_2_PI		0.63661977236758134308	/* 2/pi */
+# define M_2_SQRTPI	1.12837916709551257390	/* 2/sqrt(pi) */
+# define M_SQRT2	1.41421356237309504880	/* sqrt(2) */
+# define M_SQRT1_2	0.70710678118654752440	/* 1/sqrt(2) */
+#endif
+#ifdef __USE_GNU
+# define M_El		M_E
+# define M_LOG2El	M_LOG2E
+# define M_LOG10El	M_LOG10E
+# define M_LN2l		M_LN2
+# define M_LN10l	M_LN10
+# define M_PIl		M_PI
+# define M_PI_2l	M_PI_2
+# define M_PI_4l	M_PI_4
+# define M_1_PIl	M_1_PI
+# define M_2_PIl	M_2_PI
+# define M_2_SQRTPIl	M_2_SQRTPI
+# define M_SQRT2l	M_SQRT2
+# define M_SQRT1_2l	M_SQRT1_2
+#endif
+
+
+
+
+/* 7.12.4 Trigonometric functions */
+extern double acos(double x);
+extern float acosf(float x);
+extern long double acosl(long double x);
+
+extern double asin(double x);
+extern float asinf(float x);
+extern long double asinl(long double x);
+
+extern double atan(double x);
+extern float atanf(float x);
+extern long double atanl(long double x);
+
+double atan2(double y, double x);
+float atan2f(float y, float x);
+long double atan2l(long double y, long double x);
+
+double cos(double x);
+float cosf(float x);
+long double cosl(long double x);
+
+double sin(double x);
+float sinf(float x);
+long double sinl(long double x);
+
+double tan(double x);
+float tanf(float x);
+long double tanl(long double x);
+
+
+/* 7.12.5 Hyperbolic functions */
+double acosh(double x);
+float acoshf(float x);
+long double acoshl(long double x);
+
+double asinh(double x);
+float asinhf(float x);
+long double asinhl(long double x);
+
+double atanh(double x);
+float atanhf(float x);
+long double atanhl(long double x);
+
+double cosh(double x);
+float coshf(float x);
+long double coshl(long double x);
+
+double sinh(double x);
+float sinhf(float x);
+long double sinhl(long double x);
+
+double tanh(double x);
+float tanhf(float x);
+long double tanhl(long double x);
+
+
+/* 7.12.6 Exponential and logarithmic functions */
+double exp(double x);
+float expf(float x);
+long double expl(long double x);
+
+double exp2(double x);
+float exp2f(float x);
+long double exp2l(long double x);
+
+double expm1(double x);
+float expm1f(float x);
+long double expm1l(long double x);
+
+double frexp(double value, int *exp);
+float frexpf(float value, int *exp);
+long double frexpl(long double value, int *exp);
+
+int ilogb(double x);
+int ilogbf(float x);
+int ilogbl(long double x);
+
+double ldexp(double x, int exp);
+float ldexpf(float x, int exp);
+long double ldexpl(long double x, int exp);
+
+double log(double x);
+float logf(float x);
+long double logl(long double x);
+
+double log10(double x);
+float log10f(float x);
+long double log10l(long double x);
+
+double log1p(double x);
+float log1pf(float x);
+long double log1pl(long double x);
+
+double log2(double x);
+float log2f(float x);
+long double log2l(long double x);
+
+double logb(double x);
+float logbf(float x);
+long double logbl(long double x);
+
+double modf(double value, double *iptr);
+float modff(float value, float *iptr);
+long double modfl(long double value, long double *iptr);
+
+double scalbn(double x, int n);
+float scalbnf(float x, int n);
+long double scalbnl(long double x, int n);
+double scalbln(double x, long int n);
+float scalblnf(float x, long int n);
+long double scalblnl(long double x, long int n);
+
+/* 7.12.7 Power and absolute-value functions */
+double fabs(double x);
+float fabsf(float x);
+long double fabsl(long double x);
+
+double hypot(double x, double y);
+float hypotf(float x, float y);
+long double hypotl(long double x, long double y);
+
+double pow(double x, double y);
+float powf(float x, float y);
+long double powl(long double x, long double y);
+
+double sqrt(double x);
+float sqrtf(float x);
+long double sqrtl(long double x);
+
+/* 7.12.8 Error and gamma functions */
+double erf(double x);
+float erff(float x);
+long double erfl(long double x);
+
+double erfc(double x);
+float erfcf(float x);
+long double erfcl(long double x);
+
+double lgamma(double x);
+float lgammaf(float x);
+long double lgammal(long double x);
+
+double tgamma(double x);
+float tgammaf(float x);
+long double tgammal(long double x);
+
+/* 7.12.9 Nearest integer functions */
+double ceil(double x);
+float ceilf(float x);
+long double ceill(long double x);
+
+double floor(double x);
+float floorf(float x);
+long double floorl(long double x);
+
+double nearbyint(double x);
+float nearbyintf(float x);
+long double nearbyintl(long double x);
+
+double rint(double x);
+float rintf(float x);
+long double rintl(long double x);
+
+long int lrint(double x);
+long int lrintf(float x);
+long int lrintl(long double x);
+long long int llrint(double x);
+long long int llrintf(float x);
+long long int llrintl(long double x);
+
+double round(double x);
+float roundf(float x);
+long double roundl(long double x);
+
+long int lround(double x);
+long int lroundf(float x);
+long int lroundl(long double x);
+long long int llround(double x);
+long long int llroundf(float x);
+long long int llroundl(long double x);
+
+double trunc(double x);
+float truncf(float x);
+long double truncl(long double x);
+
+/* 7.12.10 Remainder functions */
+double fmod(double x, double y);
+float fmodf(float x, float y);
+long double fmodl(long double x, long double y);
+
+double remainder(double x, double y);
+float remainderf(float x, float y);
+long double remainderl(long double x, long double y);
+
+double remquo(double x, double y, int *quo);
+float remquof(float x, float y, int *quo);
+long double remquol(long double x, long double y, int *quo);
+
+/* 7.12.11 Manipulation functions */
+double copysign(double x, double y);
+float copysignf(float x, float y);
+long double copysignl(long double x, long double y);
+
+double nan(const char *tagp);
+float nanf(const char *tagp);
+long double nanl(const char *tagp);
+
+double nextafter(double x, double y);
+float nextafterf(float x, float y);
+long double nextafterl(long double x, long double y);
+
+double nexttoward(double x, long double y);
+float nexttowardf(float x, long double y);
+long double nexttowardl(long double x, long double y);
+
+/* 7.12.12 Maximum, minimum, and positive difference functions */
+double fdim(double x, double y);
+float fdimf(float x, float y);
+long double fdiml(long double x, long double y);
+
+double fmax(double x, double y);
+float fmaxf(float x, float y);
+long double fmaxl(long double x, long double y);
+
+double fmin(double x, double y);
+float fminf(float x, float y);
+long double fminl(long double x, long double y);
+
+/* 7.12.13 Floating multiply-add */
+double fma(double x, double y, double z);
+float fmaf(float x, float y, float z);
+long double fmal(long double x, long double y, long double z);
+
+/* 7.12.14 Comparison macros */
+# ifndef isgreater
+#  define isgreater(x, y) \
+  (__extension__							      \
+   ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);			      \
+      !isunordered (__x, __y) && __x > __y; }))
+# endif
+
+/* Return nonzero value if X is greater than or equal to Y.  */
+# ifndef isgreaterequal
+#  define isgreaterequal(x, y) \
+  (__extension__							      \
+   ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);			      \
+      !isunordered (__x, __y) && __x >= __y; }))
+# endif
+
+/* Return nonzero value if X is less than Y.  */
+# ifndef isless
+#  define isless(x, y) \
+  (__extension__							      \
+   ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);			      \
+      !isunordered (__x, __y) && __x < __y; }))
+# endif
+
+/* Return nonzero value if X is less than or equal to Y.  */
+# ifndef islessequal
+#  define islessequal(x, y) \
+  (__extension__							      \
+   ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);			      \
+      !isunordered (__x, __y) && __x <= __y; }))
+# endif
+
+/* Return nonzero value if either X is less than Y or Y is less than X.  */
+# ifndef islessgreater
+#  define islessgreater(x, y) \
+  (__extension__							      \
+   ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);			      \
+      !isunordered (__x, __y) && (__x < __y || __y < __x); }))
+# endif
+
+/* Return nonzero value if arguments are unordered.  */
+# ifndef isunordered
+#  define isunordered(u, v) \
+  (__extension__							      \
+   ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);			      \
+      fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
+# endif
+
+
+#ifndef __UCLIBC_HAS_FLOATS__
+    #undef float
 #endif
-extern void cmov ( short *a, short *b );
-extern void cmul ( cmplxf *a, cmplxf *b, cmplxf *c );
-extern void cneg ( cmplxf *a );
-extern double cosdg ( double xx );
-extern double cos ( double xx );
-extern double cosh ( double xx );
-extern double cotdg ( double x );
-extern double cot ( double x );
-extern void csin ( cmplxf *z, cmplxf *w );
-extern void csqrt ( cmplxf *z, cmplxf *w );
-extern void csub ( cmplxf *a, cmplxf *b, cmplxf *c );
-extern void ctan ( cmplxf *z, cmplxf *w );
-extern double ctans ( cmplxf *z );
-extern double dawsn ( double xxx );
-extern int dprec ( void );
-extern double ellie ( double phia, double ma );
-extern double ellik ( double phia, double ma );
-extern double ellpe ( double xx );
-extern int ellpj ( double uu, double mm, double *sn, double *cn, double *dn, double *ph );
-extern double ellpk ( double xx );
-extern double erfc ( double aa );
-extern double erf ( double xx );
-extern double exp10 ( double xx );
-extern double exp2 ( double xx );
-extern double exp ( double xx );
-extern double expn ( int n, double xx );
-extern double fac ( int i );
-extern double fdtrc ( int ia, int ib, double xx );
-extern double fdtr ( int ia, int ib, int xx );
-extern double fdtri ( int ia, int ib, double yy );
-extern double floor ( double x );
-extern void fresnl ( double xxa, double *ssa, double *cca );
-extern double frexp ( double x, int *pw2 );
-extern double gamma ( double xx );
-extern double gdtrc ( double aa, double bb, double xx );
-extern double gdtr ( double aa, double bb, double xx );
-extern double hyp2f0 ( double aa, double bb, double xx, int type, double *err );
-extern double hyp2f1 ( double aa, double bb, double cc, double xx );
-extern double hyperg ( double aa, double bb, double xx );
-extern double i0e ( double x );
-extern double i0 ( double x );
-extern double i1e ( double xx );
-extern double i1 ( double xx );
-extern double igamc ( double aa, double xx );
-extern double igam ( double aa, double xx );
-extern double igami ( double aa, double yy0 );
-extern double incbet ( double aaa, double bbb, double xxx );
-extern double incbi ( double aaa, double bbb, double yyy0 );
-extern double incbps ( double aa, double bb, double xx );
-extern double iv ( double v, double x );
-extern double j0 ( double xx );
-extern double j1 ( double xx );
-extern double jn ( int n, double xx );
-extern double jv ( double nn, double xx );
-extern double k0e ( double xx );
-extern double k0 ( double xx );
-extern double k1e ( double xx );
-extern double k1 ( double xx );
-extern double kn ( int nnn, double xx );
-extern double ldexp ( double x, int pw2 );
-extern int ldprec ( void );
-extern double lgam ( double xx );
-extern double log10 ( double xx );
-extern double log2 ( double xx );
-extern double log ( double xx );
-/* extern int mtherr ( char *name, int code ); */
-extern double nbdtrc ( int k, int n, double pp );
-extern double nbdtr ( int k, int n, double pp );
-extern double ndtr ( double aa );
-extern double ndtri ( double yy0 );
-extern double onef2 ( double aa, double bb, double cc, double xx, double *err );
-extern double p1evl ( double xx, double *coef, int N );
-extern double pdtrc ( int k, double mm );
-extern double pdtr ( int k, double mm );
-extern double pdtri ( int k, double yy );
-extern void poladd ( double a[], int na, double b[], int nb, double c[] );
-extern void polclr ( double *a, int n );
-extern int poldiv ( double a[], int na, double b[], int nb, double c[] );
-extern double poleva ( double *a, int na, double xx );
-extern double polevl ( double xx, double *coef, int N );
-extern void polini ( int maxdeg );
-extern void polmov ( double *a, int na, double *b );
-extern void polmul ( double a[], int na, double b[], int nb, double c[] );
-extern void polprt ( double *a, int na, int d );
-extern void polsbt ( double a[], int na, double b[], int nb, double c[] );
-extern void polsub ( double a[], int na, double b[], int nb, double c[] );
-extern double pow ( double x, double y );
-extern double powi ( double x, int nn );
-extern double psi ( double xx );
-extern double redupi ( double xx );
-extern double rgamma ( double xx );
-extern int shichi ( double xx, double *si, double *ci );
-extern int sici ( double xx, double *si, double *ci );
-extern double sindg ( double xx );
-extern double sin ( double xx );
-extern double sinh ( double xx );
-extern double spence ( double xx );
-extern int sprec ( void );
-extern double sqrt ( double xx );
-extern double stdtr ( int k, double tt );
-extern double struve ( double vv, double xx );
-extern double tandg ( double x );
-extern double tan ( double x );
-extern double tanh ( double xx );
-extern double threef0 ( double aa, double bb, double cc, double xx, double *err );
-extern double y0 ( double xx );
-extern double y1 ( double xx );
-extern double yn ( int nn, double xx );
-extern double yv ( double vv, double xx );
-extern double zetac ( double xx );
-extern double zeta ( double xx, double qq );
-
-#endif /* _MATH_H */
+#ifndef __UCLIBC_HAS_DOUBLE__
+    #undef double
+#endif
+#ifndef __UCLIBC_HAS_LONG_DOUBLE__
+    #undef long
+    #undef double
+#endif
+
+
+#endif /* math.h  */

libm/Makefile

@@ -0,0 +1,75 @@
+# Makefile for uClibc's math library
+#
+# Copyright (C) 2001 by Lineo, inc.
+#
+# This program is free software; you can redistribute it and/or modify it under
+# the terms of the GNU Library General Public License as published by the Free
+# Software Foundation; either version 2 of the License, or (at your option) any
+# later version.
+#
+# This program is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
+# details.
+#
+# You should have received a copy of the GNU Library General Public License
+# along with this program; if not, write to the Free Software Foundation, Inc.,
+# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# Derived in part from the Linux-8086 C library, the GNU C Library, and several
+# other sundry sources.  Files within this library are copyright by their
+# respective copyright holders.
+
+TOPDIR=../
+include $(TOPDIR)Rules.mak
+
+LIBM=libm.a
+LIBM_SHARED=libm.so
+TARGET_CC= $(TOPDIR)extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
+
+DIRS=
+ifeq ($(strip $(HAS_FLOATS)),true)
+	DIRS+=float
+endif
+ifeq ($(strip $(HAS_DOUBLE)),true)
+	DIRS+=double
+endif
+ifeq ($(strip $(HAS_LONG_DOUBLE)),true)
+	DIRS+=ldouble
+endif
+ALL_SUBDIRS = $(shell find * -type d -prune -name [a-z]\*)
+
+all: $(LIBM)
+
+$(LIBM): subdirs
+
+tags:
+	ctags -R
+	
+shared: $(LIBM)
+	$(TARGET_CC) $(LDFLAGS) -shared -o $(LIBM_SHARED).$(MAJOR_VERSION) \
+	    -Wl,-soname,$(LIBM_SHARED).$(MAJOR_VERSION) -Wl,--whole-archive $(LIBM) $(TOPDIR)$(SHARED_FULLNAME)
+
+install: all
+	install -d $(INSTALL_DIR)/lib
+	install -m 644 $(LIBM) $(INSTALL_DIR)/lib/
+	@if [ -f $(LIBM_SHARED).$(MAJOR_VERSION) ] ; then \
+	    install -m 644 $(LIBM_SHARED).$(MAJOR_VERSION) $(INSTALL_DIR)/lib/; \
+	    (cd $(INSTALL_DIR)/lib/;ln -sf $(LIBM_SHARED).$(MAJOR_VERSION) $(LIBM_SHARED)); \
+	fi;
+
+subdirs: $(patsubst %, _dir_%, $(DIRS))
+subdirs_clean: $(patsubst %, _dirclean_%, $(ALL_SUBDIRS))
+
+$(patsubst %, _dir_%, $(DIRS)) : dummy
+	$(MAKE) -C $(patsubst _dir_%, %, $@)
+
+$(patsubst %, _dirclean_%, $(ALL_SUBDIRS)) : dummy
+	$(MAKE) -C $(patsubst _dirclean_%, %, $@) clean
+
+clean: subdirs_clean
+	rm -f *.[oa] *~ core $(LIBM_SHARED)* $(LIBM)
+
+.PHONY: dummy
+
+

libm/README

@@ -0,0 +1,42 @@
+The actual routines included in this math library are derived almost
+exclusively from the Cephes Mathematical Library, which "is copyrighted by the
+author [and] may be used freely but ... comes with no support or guarantee"
+
+It has been ported to fit into uClibc and generally behave 
+by Erik Andersen <andersen@lineo.com>, <andersee@debian.org>
+  5 May, 2001
+
+--------------------------------------------------
+
+   Some software in this archive may be from the book _Methods and
+Programs for Mathematical Functions_ (Prentice-Hall, 1989) or
+from the Cephes Mathematical Library, a commercial product. In
+either event, it is copyrighted by the author.  What you see here
+may be used freely but it comes with no support or guarantee.
+
+   The two known misprints in the book are repaired here in the
+source listings for the gamma function and the incomplete beta
+integral.
+
+
+   Stephen L. Moshier
+   moshier@world.std.com
+
+--------------------------------------------------
+
+19 November 1992
+
+ZIP archive constructed and index compiled.
+
+To reconstruct the original directory structure, use the -d switch:
+
+	C:\CEPHES>pkunzip -d cephes
+
+This archive includes all the programs in the /netlib/cephes directory
+on research.att.com as of 17 Nov 92.  The file "index" will tell you in
+what directory and file each function can be found.  If there is
+something else mentioned in cephes.doc that you need, you can check
+research.att.com to see whether it has been added.  Failing that, you
+can contact Stephen Moshier.
+
+                                      Jim Van Zandt <jrv@mbunix.mitre.org>

libm/double/Makefile

@@ -0,0 +1,115 @@
+# Makefile for uClibc's math library
+#
+# Copyright (C) 2001 by Lineo, inc.
+#
+# This program is free software; you can redistribute it and/or modify it under
+# the terms of the GNU Library General Public License as published by the Free
+# Software Foundation; either version 2 of the License, or (at your option) any
+# later version.
+#
+# This program is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
+# details.
+#
+# You should have received a copy of the GNU Library General Public License
+# along with this program; if not, write to the Free Software Foundation, Inc.,
+# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# Derived in part from the Linux-8086 C library, the GNU C Library, and several
+# other sundry sources.  Files within this library are copyright by their
+# respective copyright holders.
+
+TOPDIR=../../
+include $(TOPDIR)Rules.mak
+
+LIBM=../libm.a
+TARGET_CC= $(TOPDIR)/extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
+
+CSRC=acosh.c airy.c asin.c asinh.c atan.c atanh.c bdtr.c beta.c \
+	btdtr.c cbrt.c chbevl.c chdtr.c clog.c cmplx.c const.c \
+	cosh.c dawsn.c ei.c ellie.c ellik.c ellpe.c ellpj.c ellpk.c \
+	exp.c exp10.c exp2.c expn.c fabs.c fac.c fdtr.c \
+	fresnl.c gamma.c gdtr.c hyp2f1.c hyperg.c i0.c i1.c igami.c incbet.c \
+	incbi.c igam.c isnan.c iv.c j0.c j1.c jn.c jv.c k0.c k1.c kn.c kolmogorov.c \
+	log.c log2.c log10.c lrand.c nbdtr.c ndtr.c ndtri.c pdtr.c planck.c \
+	polevl.c polmisc.c polylog.c polyn.c pow.c powi.c psi.c rgamma.c round.c \
+	shichi.c sici.c sin.c sindg.c sinh.c spence.c stdtr.c struve.c \
+	tan.c tandg.c tanh.c unity.c yn.c zeta.c zetac.c \
+	sqrt.c floor.c setprec.c mtherr.c
+
+COBJS=$(patsubst %.c,%.o, $(CSRC))
+
+
+OBJS=$(COBJS)
+
+all: $(OBJS) $(LIBM)
+
+$(LIBM): ar-target
+
+ar-target: $(OBJS)
+	$(AR) $(ARFLAGS) $(LIBM) $(OBJS)
+
+$(COBJS): %.o : %.c
+	$(TARGET_CC) $(CFLAGS) -c $< -o $@
+	$(STRIPTOOL) -x -R .note -R .comment $*.o
+
+$(OBJ): Makefile
+
+clean:
+	rm -f *.[oa] *~ core
+
+
+
+#-----------------------------------------
+
+#all: libmd.a mtst dtestvec monot dcalc paranoia
+
+time-it: time-it.o
+	$(CC) -o time-it time-it.o
+
+time-it.o: time-it.c
+	$(CC) -O2 -c time-it.c
+
+dcalc: dcalc.o libmd.a
+	$(CC) -o dcalc dcalc.o libmd.a
+
+mtst: mtst.o libmd.a
+	$(CC) -v -o mtst mtst.o libmd.a
+
+mtst.o: mtst.c
+	$(CC) -O2 -Wall -c mtst.c
+
+dtestvec: dtestvec.o libmd.a
+	$(CC) -o dtestvec dtestvec.o libmd.a
+
+dtestvec.o: dtestvec.c
+	$(CC) -g -c dtestvec.c
+
+monot: monot.o libmd.a
+	$(CC) -o monot monot.o libmd.a
+
+monot.o: monot.c
+	$(CC) -g -c monot.c
+
+paranoia: paranoia.o setprec.o libmd.a
+	$(CC) -o paranoia paranoia.o setprec.o libmd.a
+
+paranoia.o: paranoia.c
+	$(CC) $(CFLAGS) -Wno-implicit -c paranoia.c
+
+libmd.a: $(OBJS) $(INCS)
+	$(AR) rv libmd.a $(OBJS)
+
+#clean:
+#	rm -f *.o
+#	rm -f mtst
+#	rm -f paranoia
+#	rm -f dcalc
+#	rm -f dtestvec
+#	rm -f monot
+#	rm -f libmd.a
+#	rm -f time-it
+#	rm -f dtestvec
+
+

libm/double/README.txt

@@ -0,0 +1,5845 @@
+/*							acosh.c
+ *
+ *	Inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acosh();
+ *
+ * y = acosh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a rational approximation
+ *
+ *	sqrt(z) * P(z)/Q(z)
+ *
+ * where z = x-1, is used.  Otherwise,
+ *
+ * acosh(x)  =  log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       1,3         30000       4.2e-17     1.1e-17
+ *    IEEE      1,3         30000       4.6e-16     8.7e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * acosh domain       |x| < 1            NAN
+ *
+ */
+
+/*							airy.c
+ *
+ *	Airy function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, ai, aip, bi, bip;
+ * int airy();
+ *
+ * airy( x, _&ai, _&aip, _&bi, _&bip );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Solution of the differential equation
+ *
+ *	y"(x) = xy.
+ *
+ * The function returns the two independent solutions Ai, Bi
+ * and their first derivatives Ai'(x), Bi'(x).
+ *
+ * Evaluation is by power series summation for small x,
+ * by rational minimax approximations for large x.
+ *
+ *
+ *
+ * ACCURACY:
+ * Error criterion is absolute when function <= 1, relative
+ * when function > 1, except * denotes relative error criterion.
+ * For large negative x, the absolute error increases as x^1.5.
+ * For large positive x, the relative error increases as x^1.5.
+ *
+ * Arithmetic  domain   function  # trials      peak         rms
+ * IEEE        -10, 0     Ai        10000       1.6e-15     2.7e-16
+ * IEEE          0, 10    Ai        10000       2.3e-14*    1.8e-15*
+ * IEEE        -10, 0     Ai'       10000       4.6e-15     7.6e-16
+ * IEEE          0, 10    Ai'       10000       1.8e-14*    1.5e-15*
+ * IEEE        -10, 10    Bi        30000       4.2e-15     5.3e-16
+ * IEEE        -10, 10    Bi'       30000       4.9e-15     7.3e-16
+ * DEC         -10, 0     Ai         5000       1.7e-16     2.8e-17
+ * DEC           0, 10    Ai         5000       2.1e-15*    1.7e-16*
+ * DEC         -10, 0     Ai'        5000       4.7e-16     7.8e-17
+ * DEC           0, 10    Ai'       12000       1.8e-15*    1.5e-16*
+ * DEC         -10, 10    Bi        10000       5.5e-16     6.8e-17
+ * DEC         -10, 10    Bi'        7000       5.3e-16     8.7e-17
+ *
+ */
+
+/*							asin.c
+ *
+ *	Inverse circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asin();
+ *
+ * y = asin( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A rational function of the form x + x**3 P(x**2)/Q(x**2)
+ * is used for |x| in the interval [0, 0.5].  If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ *    asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -1, 1        40000       2.6e-17     7.1e-18
+ *    IEEE     -1, 1        10^6        1.9e-16     5.4e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * asin domain        |x| > 1           NAN
+ *
+ */
+/*							acos()
+ *
+ *	Inverse circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acos();
+ *
+ * y = acos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between 0 and pi whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x).  However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2.  Hence if x < -0.5,
+ *
+ *    acos(x) =	 pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ *    acos(x) =	 2.0 * asin(  sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -1, 1       50000       3.3e-17     8.2e-18
+ *    IEEE      -1, 1       10^6        2.2e-16     6.5e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * asin domain        |x| > 1           NAN
+ */
+
+/*							asinh.c
+ *
+ *	Inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asinh();
+ *
+ * y = asinh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic sine of argument.
+ *
+ * If |x| < 0.5, the function is approximated by a rational
+ * form  x + x**3 P(x)/Q(x).  Otherwise,
+ *
+ *     asinh(x) = log( x + sqrt(1 + x*x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -3,3         75000       4.6e-17     1.1e-17
+ *    IEEE     -1,1         30000       3.7e-16     7.8e-17
+ *    IEEE      1,3         30000       2.5e-16     6.7e-17
+ *
+ */
+
+/*							atan.c
+ *
+ *	Inverse circular tangent
+ *      (arctangent)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atan();
+ *
+ * y = atan( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose tangent
+ * is x.
+ *
+ * Range reduction is from three intervals into the interval
+ * from zero to 0.66.  The approximant uses a rational
+ * function of degree 4/5 of the form x + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10, 10     50000       2.4e-17     8.3e-18
+ *    IEEE      -10, 10      10^6       1.8e-16     5.0e-17
+ *
+ */
+/*							atan2()
+ *
+ *	Quadrant correct inverse circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, z, atan2();
+ *
+ * z = atan2( y, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle whose tangent is y/x.
+ * Define compile time symbol ANSIC = 1 for ANSI standard,
+ * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
+ * 0 to 2PI, args (x,y).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10, 10      10^6       2.5e-16     6.9e-17
+ * See atan.c.
+ *
+ */
+
+/*							atanh.c
+ *
+ *	Inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atanh();
+ *
+ * y = atanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOG to MAXLOG.
+ *
+ * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
+ * employed.  Otherwise,
+ *        atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -1,1        50000       2.4e-17     6.4e-18
+ *    IEEE      -1,1        30000       1.9e-16     5.2e-17
+ *
+ */
+
+/*							bdtr.c
+ *
+ *	Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtr();
+ *
+ * y = bdtr( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ *   k
+ *   --  ( n )   j      n-j
+ *   >   (   )  p  (1-p)
+ *   --  ( j )
+ *  j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      4.3e-15     2.6e-16
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtr domain         k < 0            0.0
+ *                     n < k
+ *                     x < 0, x > 1
+ */
+/*							bdtrc()
+ *
+ *	Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtrc();
+ *
+ * y = bdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ *   n
+ *   --  ( n )   j      n-j
+ *   >   (   )  p  (1-p)
+ *   --  ( j )
+ *  j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      6.7e-15     8.2e-16
+ *  For p between 0 and .001:
+ *    IEEE     0,100       100000      1.5e-13     2.7e-15
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtrc domain      x<0, x>1, n<k       0.0
+ */
+/*							bdtri()
+ *
+ *	Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtri();
+ *
+ * p = bdtr( k, n, y );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      2.3e-14     6.4e-16
+ *    IEEE     0,10000     100000      6.6e-12     1.2e-13
+ *  For p between 10^-6 and 0.001:
+ *    IEEE     0,100       100000      2.0e-12     1.3e-14
+ *    IEEE     0,10000     100000      1.5e-12     3.2e-14
+ * See also incbi.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtri domain     k < 0, n <= k         0.0
+ *                  x < 0, x > 1
+ */
+
+/*							beta.c
+ *
+ *	Beta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, y, beta();
+ *
+ * y = beta( a, b );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *                   -     -
+ *                  | (a) | (b)
+ * beta( a, b )  =  -----------.
+ *                     -
+ *                    | (a+b)
+ *
+ * For large arguments the logarithm of the function is
+ * evaluated using lgam(), then exponentiated.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        0,30        1700       7.7e-15     1.5e-15
+ *    IEEE       0,30       30000       8.1e-14     1.1e-14
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition          value returned
+ * beta overflow    log(beta) > MAXLOG       0.0
+ *                  a or b <0 integer        0.0
+ *
+ */
+
+/*							btdtr.c
+ *
+ *	Beta distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, btdtr();
+ *
+ * y = btdtr( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the beta density
+ * function:
+ *
+ *
+ *                          x
+ *            -             -
+ *           | (a+b)       | |  a-1      b-1
+ * P(x)  =  ----------     |   t    (1-t)    dt
+ *           -     -     | |
+ *          | (a) | (b)   -
+ *                         0
+ *
+ *
+ * This function is identical to the incomplete beta
+ * integral function incbet(a, b, x).
+ *
+ * The complemented function is
+ *
+ * 1 - P(1-x)  =  incbet( b, a, x );
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ *
+ */
+
+/*							cbrt.c
+ *
+ *	Cube root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cbrt();
+ *
+ * y = cbrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument.  A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%.  Then Newton's
+ * iteration is used three times to converge to an accurate
+ * result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        -10,10     200000      1.8e-17     6.2e-18
+ *    IEEE       0,1e308     30000      1.5e-16     5.0e-17
+ *
+ */
+
+/*							chbevl.c
+ *
+ *	Evaluate Chebyshev series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * double x, y, coef[N], chebevl();
+ *
+ * y = chbevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the series
+ *
+ *        N-1
+ *         - '
+ *  y  =   >   coef[i] T (x/2)
+ *         -            i
+ *        i=0
+ *
+ * of Chebyshev polynomials Ti at argument x/2.
+ *
+ * Coefficients are stored in reverse order, i.e. the zero
+ * order term is last in the array.  Note N is the number of
+ * coefficients, not the order.
+ *
+ * If coefficients are for the interval a to b, x must
+ * have been transformed to x -> 2(2x - b - a)/(b-a) before
+ * entering the routine.  This maps x from (a, b) to (-1, 1),
+ * over which the Chebyshev polynomials are defined.
+ *
+ * If the coefficients are for the inverted interval, in
+ * which (a, b) is mapped to (1/b, 1/a), the transformation
+ * required is x -> 2(2ab/x - b - a)/(b-a).  If b is infinity,
+ * this becomes x -> 4a/x - 1.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Taking advantage of the recurrence properties of the
+ * Chebyshev polynomials, the routine requires one more
+ * addition per loop than evaluating a nested polynomial of
+ * the same degree.
+ *
+ */
+
+/*							chdtr.c
+ *
+ *	Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double df, x, y, chdtr();
+ *
+ * y = chdtr( df, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the left hand tail (from 0 to x)
+ * of the Chi square probability density function with
+ * v degrees of freedom.
+ *
+ *
+ *                                  inf.
+ *                                    -
+ *                        1          | |  v/2-1  -t/2
+ *  P( x | v )   =   -----------     |   t      e     dt
+ *                    v/2  -       | |
+ *                   2    | (v/2)   -
+ *                                   x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ *	y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * chdtr domain   x < 0 or v < 1        0.0
+ */
+/*							chdtrc()
+ *
+ *	Complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, chdtrc();
+ *
+ * y = chdtrc( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the right hand tail (from x to
+ * infinity) of the Chi square probability density function
+ * with v degrees of freedom:
+ *
+ *
+ *                                  inf.
+ *                                    -
+ *                        1          | |  v/2-1  -t/2
+ *  P( x | v )   =   -----------     |   t      e     dt
+ *                    v/2  -       | |
+ *                   2    | (v/2)   -
+ *                                   x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ *	y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * chdtrc domain  x < 0 or v < 1        0.0
+ */
+/*							chdtri()
+ *
+ *	Inverse of complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double df, x, y, chdtri();
+ *
+ * x = chdtri( df, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Chi-square argument x such that the integral
+ * from x to infinity of the Chi-square density is equal
+ * to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ *    x/2 = igami( df/2, y );
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * chdtri domain   y < 0 or y > 1        0.0
+ *                     v < 1
+ *
+ */
+
+/*							clog.c
+ *
+ *	Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clog();
+ * cmplx z, w;
+ *
+ * clog( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ *       w = log(r) + i arctan(y/x).
+ * 
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      7000       8.5e-17     1.9e-17
+ *    IEEE      -10,+10     30000       5.0e-15     1.1e-16
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
+ * absolute error 1.0e-16.
+ */
+
+/*							cexp()
+ *
+ *	Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexp();
+ * cmplx z, w;
+ *
+ * cexp( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ *     z = x + iy,
+ *     r = exp(x),
+ *
+ * then
+ *
+ *     w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8700       3.7e-17     1.1e-17
+ *    IEEE      -10,+10     30000       3.0e-16     8.7e-17
+ *
+ */
+/*							csin()
+ *
+ *	Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csin();
+ * cmplx z, w;
+ *
+ * csin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *     w = sin x  cosh y  +  i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8400       5.3e-17     1.3e-17
+ *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
+ * Also tested by csin(casin(z)) = z.
+ *
+ */
+/*							ccos()
+ *
+ *	Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccos();
+ * cmplx z, w;
+ *
+ * ccos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *     w = cos x  cosh y  -  i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8400       4.5e-17     1.3e-17
+ *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
+ */
+/*							ctan()
+ *
+ *	Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctan();
+ * cmplx z, w;
+ *
+ * ctan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *           sin 2x  +  i sinh 2y
+ *     w  =  --------------------.
+ *            cos 2x  +  cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2.  The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5200       7.1e-17     1.6e-17
+ *    IEEE      -10,+10     30000       7.2e-16     1.2e-16
+ * Also tested by ctan * ccot = 1 and catan(ctan(z))  =  z.
+ */
+/*							ccot()
+ *
+ *	Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccot();
+ * cmplx z, w;
+ *
+ * ccot( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *           sin 2x  -  i sinh 2y
+ *     w  =  --------------------.
+ *            cosh 2y  -  cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2.  Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      3000       6.5e-17     1.6e-17
+ *    IEEE      -10,+10     30000       9.2e-16     1.2e-16
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+/*							casin()
+ *
+ *	Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casin();
+ * cmplx z, w;
+ *
+ * casin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ *                               2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10     10100       2.1e-15     3.4e-16
+ *    IEEE      -10,+10     30000       2.2e-14     2.7e-15
+ * Larger relative error can be observed for z near zero.
+ * Also tested by csin(casin(z)) = z.
+ */
+
+/*							cacos()
+ *
+ *	Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacos();
+ * cmplx z, w;
+ *
+ * cacos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z  =  PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5200      1.6e-15      2.8e-16
+ *    IEEE      -10,+10     30000      1.8e-14      2.2e-15
+ */
+/*							catan()
+ *
+ *	Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catan();
+ * cmplx z, w;
+ *
+ * catan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *          1       (    2x     )
+ * Re w  =  - arctan(-----------)  +  k PI
+ *          2       (     2    2)
+ *                  (1 - x  - y )
+ *
+ *               ( 2         2)
+ *          1    (x  +  (y+1) )
+ * Im w  =  - log(------------)
+ *          4    ( 2         2)
+ *               (x  +  (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5900       1.3e-16     7.8e-18
+ *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
+ * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
+ * had peak relative error 1.5e-16, rms relative error
+ * 2.9e-17.  See also clog().
+ */
+
+/*							cmplx.c
+ *
+ *	Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ *      double r;     real part
+ *      double i;     imaginary part
+ *     }cmplx;
+ *
+ * cmplx *a, *b, *c;
+ *
+ * cadd( a, b, c );     c = b + a
+ * csub( a, b, c );     c = b - a
+ * cmul( a, b, c );     c = b * a
+ * cdiv( a, b, c );     c = b / a
+ * cneg( c );           c = -c
+ * cmov( b, c );        c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ *    c.r  =  b.r + a.r
+ *    c.i  =  b.i + a.i
+ *
+ * Subtraction:
+ *    c.r  =  b.r - a.r
+ *    c.i  =  b.i - a.i
+ *
+ * Multiplication:
+ *    c.r  =  b.r * a.r  -  b.i * a.i
+ *    c.i  =  b.r * a.i  +  b.i * a.r
+ *
+ * Division:
+ *    d    =  a.r * a.r  +  a.i * a.i
+ *    c.r  = (b.r * a.r  + b.i * a.i)/d
+ *    c.i  = (b.i * a.r  -  b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17.  The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ *                      Relative error:
+ * arithmetic   function  # trials      peak         rms
+ *    DEC        cadd       10000       1.4e-17     3.4e-18
+ *    IEEE       cadd      100000       1.1e-16     2.7e-17
+ *    DEC        csub       10000       1.4e-17     4.5e-18
+ *    IEEE       csub      100000       1.1e-16     3.4e-17
+ *    DEC        cmul        3000       2.3e-17     8.7e-18
+ *    IEEE       cmul      100000       2.1e-16     6.9e-17
+ *    DEC        cdiv       18000       4.9e-17     1.3e-17
+ *    IEEE       cdiv      100000       3.7e-16     1.1e-16
+ */
+
+/*							cabs()
+ *
+ *	Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double cabs();
+ * cmplx z;
+ * double a;
+ *
+ * a = cabs( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ *       a = sqrt( x**2 + y**2 ).
+ * 
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring.  If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -30,+30     30000       3.2e-17     9.2e-18
+ *    IEEE      -10,+10    100000       2.7e-16     6.9e-17
+ */
+/*							csqrt()
+ *
+ *	Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrt();
+ * cmplx z, w;
+ *
+ * csqrt( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy,  r = |z|, then
+ *
+ *                       1/2
+ * Im w  =  [ (r - x)/2 ]   ,
+ *
+ * Re w  =  y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z.  The root chosen
+ * is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10     25000       3.2e-17     9.6e-18
+ *    IEEE      -10,+10    100000       3.2e-16     7.7e-17
+ *
+ *                        2
+ * Also tested by csqrt( z ) = z, and tested by arguments
+ * close to the real axis.
+ */
+
+/*							const.c
+ *
+ *	Globally declared constants
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * extern double nameofconstant;
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This file contains a number of mathematical constants and
+ * also some needed size parameters of the computer arithmetic.
+ * The values are supplied as arrays of hexadecimal integers
+ * for IEEE arithmetic; arrays of octal constants for DEC
+ * arithmetic; and in a normal decimal scientific notation for
+ * other machines.  The particular notation used is determined
+ * by a symbol (DEC, IBMPC, or UNK) defined in the include file
+ * math.h.
+ *
+ * The default size parameters are as follows.
+ *
+ * For DEC and UNK modes:
+ * MACHEP =  1.38777878078144567553E-17       2**-56
+ * MAXLOG =  8.8029691931113054295988E1       log(2**127)
+ * MINLOG = -8.872283911167299960540E1        log(2**-128)
+ * MAXNUM =  1.701411834604692317316873e38    2**127
+ *
+ * For IEEE arithmetic (IBMPC):
+ * MACHEP =  1.11022302462515654042E-16       2**-53
+ * MAXLOG =  7.09782712893383996843E2         log(2**1024)
+ * MINLOG = -7.08396418532264106224E2         log(2**-1022)
+ * MAXNUM =  1.7976931348623158E308           2**1024
+ *
+ * The global symbols for mathematical constants are
+ * PI     =  3.14159265358979323846           pi
+ * PIO2   =  1.57079632679489661923           pi/2
+ * PIO4   =  7.85398163397448309616E-1        pi/4
+ * SQRT2  =  1.41421356237309504880           sqrt(2)
+ * SQRTH  =  7.07106781186547524401E-1        sqrt(2)/2
+ * LOG2E  =  1.4426950408889634073599         1/log(2)
+ * SQ2OPI =  7.9788456080286535587989E-1      sqrt( 2/pi )
+ * LOGE2  =  6.93147180559945309417E-1        log(2)
+ * LOGSQ2 =  3.46573590279972654709E-1        log(2)/2
+ * THPIO4 =  2.35619449019234492885           3*pi/4
+ * TWOOPI =  6.36619772367581343075535E-1     2/pi
+ *
+ * These lists are subject to change.
+ */
+
+/*							cosh.c
+ *
+ *	Hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cosh();
+ *
+ * y = cosh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic cosine of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * cosh(x)  =  ( exp(x) + exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       +- 88       50000       4.0e-17     7.7e-18
+ *    IEEE     +-MAXLOG     30000       2.6e-16     5.7e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * cosh overflow    |x| > MAXLOG       MAXNUM
+ *
+ *
+ */
+
+/*							cpmul.c
+ *
+ *	Multiply two polynomials with complex coefficients
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ *		{
+ *		double r;
+ *		double i;
+ *		}cmplx;
+ *
+ * cmplx a[], b[], c[];
+ * int da, db, dc;
+ *
+ * cpmul( a, da, b, db, c, &dc );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The two argument polynomials are multiplied together, and
+ * their product is placed in c.
+ *
+ * Each polynomial is represented by its coefficients stored
+ * as an array of complex number structures (see the typedef).
+ * The degree of a is da, which must be passed to the routine
+ * as an argument; similarly the degree db of b is an argument.
+ * Array a has da + 1 elements and array b has db + 1 elements.
+ * Array c must have storage allocated for at least da + db + 1
+ * elements.  The value da + db is returned in dc; this is
+ * the degree of the product polynomial.
+ *
+ * Polynomial coefficients are stored in ascending order; i.e.,
+ * a(x) = a[0]*x**0 + a[1]*x**1 + ... + a[da]*x**da.
+ *
+ *
+ * If desired, c may be the same as either a or b, in which
+ * case the input argument array is replaced by the product
+ * array (but only up to terms of degree da + db).
+ *
+ */
+
+/*							dawsn.c
+ *
+ *	Dawson's Integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, dawsn();
+ *
+ * y = dawsn( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *                             x
+ *                             -
+ *                      2     | |        2
+ *  dawsn(x)  =  exp( -x  )   |    exp( t  ) dt
+ *                          | |
+ *                           -
+ *                           0
+ *
+ * Three different rational approximations are employed, for
+ * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,10        10000       6.9e-16     1.0e-16
+ *    DEC       0,10         6000       7.4e-17     1.4e-17
+ *
+ *
+ */
+
+/*							drand.c
+ *
+ *	Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y, drand();
+ *
+ * drand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a random number 1.0 <= y < 2.0.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used. The period, given by them, is
+ * 6953607871644.
+ *
+ * Versions invoked by the different arithmetic compile
+ * time options DEC, IBMPC, and MIEEE, produce
+ * approximately the same sequences, differing only in the
+ * least significant bits of the numbers. The UNK option
+ * implements the algorithm as recommended in the BYTE
+ * article.  It may be used on all computers. However,
+ * the low order bits of a double precision number may
+ * not be adequately random, and may vary due to arithmetic
+ * implementation details on different computers.
+ *
+ * The other compile options generate an additional random
+ * integer that overwrites the low order bits of the double
+ * precision number.  This reduces the period by a factor of
+ * two but tends to overcome the problems mentioned.
+ *
+ */
+
+/*							eigens.c
+ *
+ *	Eigenvalues and eigenvectors of a real symmetric matrix
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double A[n*(n+1)/2], EV[n*n], E[n];
+ * void eigens( A, EV, E, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The algorithm is due to J. vonNeumann.
+ *
+ * A[] is a symmetric matrix stored in lower triangular form.
+ * That is, A[ row, column ] = A[ (row*row+row)/2 + column ]
+ * or equivalently with row and column interchanged.  The
+ * indices row and column run from 0 through n-1.
+ *
+ * EV[] is the output matrix of eigenvectors stored columnwise.
+ * That is, the elements of each eigenvector appear in sequential
+ * memory order.  The jth element of the ith eigenvector is
+ * EV[ n*i+j ] = EV[i][j].
+ *
+ * E[] is the output matrix of eigenvalues.  The ith element
+ * of E corresponds to the ith eigenvector (the ith row of EV).
+ *
+ * On output, the matrix A will have been diagonalized and its
+ * orginal contents are destroyed.
+ *
+ * ACCURACY:
+ *
+ * The error is controlled by an internal parameter called RANGE
+ * which is set to 1e-10.  After diagonalization, the
+ * off-diagonal elements of A will have been reduced by
+ * this factor.
+ *
+ * ERROR MESSAGES:
+ *
+ * None.
+ *
+ */
+
+/*							ellie.c
+ *
+ *	Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double phi, m, y, ellie();
+ *
+ * y = ellie( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *                phi
+ *                 -
+ *                | |
+ *                |                   2
+ * E(phi_\m)  =    |    sqrt( 1 - m sin t ) dt
+ *                |
+ *              | |    
+ *               -
+ *                0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [-10, 10] and m in
+ * [0, 1].
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        0,2         2000       1.9e-16     3.4e-17
+ *    IEEE     -10,10      150000       3.3e-15     1.4e-16
+ *
+ *
+ */
+
+/*							ellik.c
+ *
+ *	Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double phi, m, y, ellik();
+ *
+ * y = ellik( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ *                phi
+ *                 -
+ *                | |
+ *                |           dt
+ * F(phi_\m)  =    |    ------------------
+ *                |                   2
+ *              | |    sqrt( 1 - m sin t )
+ *               -
+ *                0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with m in [0, 1] and phi as indicated.
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -10,10       200000      7.4e-16     1.0e-16
+ *
+ *
+ */
+
+/*							ellpe.c
+ *
+ *	Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double m1, y, ellpe();
+ *
+ * y = ellpe( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *            pi/2
+ *             -
+ *            | |                 2
+ * E(m)  =    |    sqrt( 1 - m sin t ) dt
+ *          | |    
+ *           -
+ *            0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ *      P(x)  -  x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        0, 1       13000       3.1e-17     9.4e-18
+ *    IEEE       0, 1       10000       2.1e-16     7.3e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * ellpe domain      x<0, x>1            0.0
+ *
+ */
+
+/*							ellpj.c
+ *
+ *	Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double u, m, sn, cn, dn, phi;
+ * int ellpj();
+ *
+ * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi).  Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-9 of 0 or 1.  In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ *            Absolute error (* = relative error):
+ * arithmetic   function   # trials      peak         rms
+ *    DEC       sn           1800       4.5e-16     8.7e-17
+ *    IEEE      phi         10000       9.2e-16*    1.4e-16*
+ *    IEEE      sn          50000       4.1e-15     4.6e-16
+ *    IEEE      cn          40000       3.6e-15     4.4e-16
+ *    IEEE      dn          10000       1.3e-12     1.8e-14
+ *
+ *  Peak error observed in consistency check using addition
+ * theorem for sn(u+v) was 4e-16 (absolute).  Also tested by
+ * the above relation to the incomplete elliptic integral.
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/*							ellpk.c
+ *
+ *	Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double m1, y, ellpk();
+ *
+ * y = ellpk( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ *            pi/2
+ *             -
+ *            | |
+ *            |           dt
+ * K(m)  =    |    ------------------
+ *            |                   2
+ *          | |    sqrt( 1 - m sin t )
+ *           -
+ *            0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ *     P(x)  -  log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        0,1        16000       3.5e-17     1.1e-17
+ *    IEEE       0,1        30000       2.5e-16     6.8e-17
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * ellpk domain       x<0, x>1           0.0
+ *
+ */
+
+/*							euclid.c
+ *
+ *	Rational arithmetic routines
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * 
+ * typedef struct
+ *      {
+ *      double n;  numerator
+ *      double d;  denominator
+ *      }fract;
+ *
+ * radd( a, b, c )      c = b + a
+ * rsub( a, b, c )      c = b - a
+ * rmul( a, b, c )      c = b * a
+ * rdiv( a, b, c )      c = b / a
+ * euclid( &n, &d )     Reduce n/d to lowest terms,
+ *                      return greatest common divisor.
+ *
+ * Arguments of the routines are pointers to the structures.
+ * The double precision numbers are assumed, without checking,
+ * to be integer valued.  Overflow conditions are reported.
+ */
+ 
+/*							exp.c
+ *
+ *	Exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp();
+ *
+ * y = exp( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ *     x    k  f
+ *    e  = 2  e.
+ *
+ * A Pade' form  1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ * of degree 2/3 is used to approximate exp(f) in the basic
+ * interval [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       +- 88       50000       2.8e-17     7.0e-18
+ *    IEEE      +- 708      40000       2.0e-16     5.6e-17
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter.  The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp underflow    x < MINLOG         0.0
+ * exp overflow     x > MAXLOG         INFINITY
+ *
+ */
+
+/*							exp10.c
+ *
+ *	Base 10 exponential function
+ *      (Common antilogarithm)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp10();
+ *
+ * y = exp10( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 10 raised to the x power.
+ *
+ * Range reduction is accomplished by expressing the argument
+ * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
+ * The Pade' form
+ *
+ *    1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ *
+ * is used to approximate 10**f.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -307,+307    30000       2.2e-16     5.5e-17
+ * Test result from an earlier version (2.1):
+ *    DEC       -38,+38     70000       3.1e-17     7.0e-18
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp10 underflow    x < -MAXL10        0.0
+ * exp10 overflow     x > MAXL10       MAXNUM
+ *
+ * DEC arithmetic: MAXL10 = 38.230809449325611792.
+ * IEEE arithmetic: MAXL10 = 308.2547155599167.
+ *
+ */
+
+/*							exp2.c
+ *
+ *	Base 2 exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp2();
+ *
+ * y = exp2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *     x    k  f
+ *    2  = 2  2.
+ *
+ * A Pade' form
+ *
+ *   1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
+ *
+ * approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE    -1022,+1024   30000       1.8e-16     5.4e-17
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp underflow    x < -MAXL2        0.0
+ * exp overflow     x > MAXL2         MAXNUM
+ *
+ * For DEC arithmetic, MAXL2 = 127.
+ * For IEEE arithmetic, MAXL2 = 1024.
+ */
+
+/*							expn.c
+ *
+ *		Exponential integral En
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double x, y, expn();
+ *
+ * y = expn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the exponential integral
+ *
+ *                 inf.
+ *                   -
+ *                  | |   -xt
+ *                  |    e
+ *      E (x)  =    |    ----  dt.
+ *       n          |      n
+ *                | |     t
+ *                 -
+ *                  1
+ *
+ *
+ * Both n and x must be nonnegative.
+ *
+ * The routine employs either a power series, a continued
+ * fraction, or an asymptotic formula depending on the
+ * relative values of n and x.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        5000       2.0e-16     4.6e-17
+ *    IEEE      0, 30       10000       1.7e-15     3.6e-16
+ *
+ */
+
+/*							fabs.c
+ *
+ *		Absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y;
+ *
+ * y = fabs( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ * 
+ * Returns the absolute value of the argument.
+ *
+ */
+
+/*							fac.c
+ *
+ *	Factorial function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y, fac();
+ * int i;
+ *
+ * y = fac( i );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns factorial of i  =  1 * 2 * 3 * ... * i.
+ * fac(0) = 1.0.
+ *
+ * Due to machine arithmetic bounds the largest value of
+ * i accepted is 33 in DEC arithmetic or 170 in IEEE
+ * arithmetic.  Greater values, or negative ones,
+ * produce an error message and return MAXNUM.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * For i < 34 the values are simply tabulated, and have
+ * full machine accuracy.  If i > 55, fac(i) = gamma(i+1);
+ * see gamma.c.
+ *
+ *                      Relative error:
+ * arithmetic   domain      peak
+ *    IEEE      0, 170    1.4e-15
+ *    DEC       0, 33      1.4e-17
+ *
+ */
+
+/*							fdtr.c
+ *
+ *	F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, y, fdtr();
+ *
+ * y = fdtr( df1, df2, x );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).  This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ *	P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x is
+ * nonnegative.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x).
+ *
+ *                x     a,b                     Relative error:
+ * arithmetic  domain  domain     # trials      peak         rms
+ *    IEEE      0,1    0,100       100000      9.8e-15     1.7e-15
+ *    IEEE      1,5    0,100       100000      6.5e-15     3.5e-16
+ *    IEEE      0,1    1,10000     100000      2.2e-11     3.3e-12
+ *    IEEE      1,5    1,10000     100000      1.1e-11     1.7e-13
+ * See also incbet.c.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * fdtr domain     a<0, b<0, x<0         0.0
+ *
+ */
+/*							fdtrc()
+ *
+ *	Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, y, fdtrc();
+ *
+ * y = fdtrc( df1, df2, x );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ *                      inf.
+ *                       -
+ *              1       | |  a-1      b-1
+ * 1-P(x)  =  ------    |   t    (1-t)    dt
+ *            B(a,b)  | |
+ *                     -
+ *                      x
+ *
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ *	P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) in the indicated intervals.
+ *                x     a,b                     Relative error:
+ * arithmetic  domain  domain     # trials      peak         rms
+ *    IEEE      0,1    1,100       100000      3.7e-14     5.9e-16
+ *    IEEE      1,5    1,100       100000      8.0e-15     1.6e-15
+ *    IEEE      0,1    1,10000     100000      1.8e-11     3.5e-13
+ *    IEEE      1,5    1,10000     100000      2.0e-11     3.0e-12
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * fdtrc domain    a<0, b<0, x<0         0.0
+ *
+ */
+/*							fdtri()
+ *
+ *	Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, p, fdtri();
+ *
+ * x = fdtri( df1, df2, p );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability p.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ *      z = incbi( df2/2, df1/2, p )
+ *      x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ *      z = incbi( df1/2, df2/2, p )
+ *      x = df2 z / (df1 (1-z)).
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ *              a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between .001 and 1:
+ *    IEEE     1,100       100000      8.3e-15     4.7e-16
+ *    IEEE     1,10000     100000      2.1e-11     1.4e-13
+ *  For p between 10^-6 and 10^-3:
+ *    IEEE     1,100        50000      1.3e-12     8.4e-15
+ *    IEEE     1,10000      50000      3.0e-12     4.8e-14
+ * See also fdtrc.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * fdtri domain   p <= 0 or p > 1       0.0
+ *                     v < 1
+ *
+ */
+
+/*							fftr.c
+ *
+ *	FFT of Real Valued Sequence
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x[], sine[];
+ * int m;
+ *
+ * fftr( x, m, sine );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the (complex valued) discrete Fourier transform of
+ * the real valued sequence x[].  The input sequence x[] contains
+ * n = 2**m samples.  The program fills array sine[k] with
+ * n/4 + 1 values of sin( 2 PI k / n ).
+ *
+ * Data format for complex valued output is real part followed
+ * by imaginary part.  The output is developed in the input
+ * array x[].
+ *
+ * The algorithm takes advantage of the fact that the FFT of an
+ * n point real sequence can be obtained from an n/2 point
+ * complex FFT.
+ *
+ * A radix 2 FFT algorithm is used.
+ *
+ * Execution time on an LSI-11/23 with floating point chip
+ * is 1.0 sec for n = 256.
+ *
+ *
+ *
+ * REFERENCE:
+ *
+ * E. Oran Brigham, The Fast Fourier Transform;
+ * Prentice-Hall, Inc., 1974
+ *
+ */
+
+/*							ceil()
+ *							floor()
+ *							frexp()
+ *							ldexp()
+ *							signbit()
+ *							isnan()
+ *							isfinite()
+ *
+ *	Floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double ceil(), floor(), frexp(), ldexp();
+ * int signbit(), isnan(), isfinite();
+ * double x, y;
+ * int expnt, n;
+ *
+ * y = floor(x);
+ * y = ceil(x);
+ * y = frexp( x, &expnt );
+ * y = ldexp( x, n );
+ * n = signbit(x);
+ * n = isnan(x);
+ * n = isfinite(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a double precision floating point
+ * result.
+ *
+ * floor() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * ceil() returns the smallest integer greater than or equal
+ * to x.  It truncates toward plus infinity.
+ *
+ * frexp() extracts the exponent from x.  It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y.  Thus  x = y * 2**expn.
+ *
+ * ldexp() multiplies x by 2**n.
+ *
+ * signbit(x) returns 1 if the sign bit of x is 1, else 0.
+ *
+ * These functions are part of the standard C run time library
+ * for many but not all C compilers.  The ones supplied are
+ * written in C for either DEC or IEEE arithmetic.  They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic.  Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+/*							fresnl.c
+ *
+ *	Fresnel integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, S, C;
+ * void fresnl();
+ *
+ * fresnl( x, _&S, _&C );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the Fresnel integrals
+ *
+ *           x
+ *           -
+ *          | |
+ * C(x) =   |   cos(pi/2 t**2) dt,
+ *        | |
+ *         -
+ *          0
+ *
+ *           x
+ *           -
+ *          | |
+ * S(x) =   |   sin(pi/2 t**2) dt.
+ *        | |
+ *         -
+ *          0
+ *
+ *
+ * The integrals are evaluated by a power series for x < 1.
+ * For x >= 1 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
+ * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *  Relative error.
+ *
+ * Arithmetic  function   domain     # trials      peak         rms
+ *   IEEE       S(x)      0, 10       10000       2.0e-15     3.2e-16
+ *   IEEE       C(x)      0, 10       10000       1.8e-15     3.3e-16
+ *   DEC        S(x)      0, 10        6000       2.2e-16     3.9e-17
+ *   DEC        C(x)      0, 10        5000       2.3e-16     3.9e-17
+ */
+
+/*							gamma.c
+ *
+ *	Gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, gamma();
+ * extern int sgngam;
+ *
+ * y = gamma( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns gamma function of the argument.  The result is
+ * correctly signed, and the sign (+1 or -1) is also
+ * returned in a global (extern) variable named sgngam.
+ * This variable is also filled in by the logarithmic gamma
+ * function lgam().
+ *
+ * Arguments |x| <= 34 are reduced by recurrence and the function
+ * approximated by a rational function of degree 6/7 in the
+ * interval (2,3).  Large arguments are handled by Stirling's
+ * formula. Large negative arguments are made positive using
+ * a reflection formula.  
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -34, 34      10000       1.3e-16     2.5e-17
+ *    IEEE    -170,-33      20000       2.3e-15     3.3e-16
+ *    IEEE     -33,  33     20000       9.4e-16     2.2e-16
+ *    IEEE      33, 171.6   20000       2.3e-15     3.2e-16
+ *
+ * Error for arguments outside the test range will be larger
+ * owing to error amplification by the exponential function.
+ *
+ */
+/*							lgam()
+ *
+ *	Natural logarithm of gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, lgam();
+ * extern int sgngam;
+ *
+ * y = lgam( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of the absolute
+ * value of the gamma function of the argument.
+ * The sign (+1 or -1) of the gamma function is returned in a
+ * global (extern) variable named sgngam.
+ *
+ * For arguments greater than 13, the logarithm of the gamma
+ * function is approximated by the logarithmic version of
+ * Stirling's formula using a polynomial approximation of
+ * degree 4. Arguments between -33 and +33 are reduced by
+ * recurrence to the interval [2,3] of a rational approximation.
+ * The cosecant reflection formula is employed for arguments
+ * less than -33.
+ *
+ * Arguments greater than MAXLGM return MAXNUM and an error
+ * message.  MAXLGM = 2.035093e36 for DEC
+ * arithmetic or 2.556348e305 for IEEE arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * arithmetic      domain        # trials     peak         rms
+ *    DEC     0, 3                  7000     5.2e-17     1.3e-17
+ *    DEC     2.718, 2.035e36       5000     3.9e-17     9.9e-18
+ *    IEEE    0, 3                 28000     5.4e-16     1.1e-16
+ *    IEEE    2.718, 2.556e305     40000     3.5e-16     8.3e-17
+ * The error criterion was relative when the function magnitude
+ * was greater than one but absolute when it was less than one.
+ *
+ * The following test used the relative error criterion, though
+ * at certain points the relative error could be much higher than
+ * indicated.
+ *    IEEE    -200, -4             10000     4.8e-16     1.3e-16
+ *
+ */
+
+/*							gdtr.c
+ *
+ *	Gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, gdtr();
+ *
+ * y = gdtr( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from zero to x of the gamma probability
+ * density function:
+ *
+ *
+ *                x
+ *        b       -
+ *       a       | |   b-1  -at
+ * y =  -----    |    t    e    dt
+ *       -     | |
+ *      | (b)   -
+ *               0
+ *
+ *  The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igam( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * gdtr domain         x < 0            0.0
+ *
+ */
+/*							gdtrc.c
+ *
+ *	Complemented gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, gdtrc();
+ *
+ * y = gdtrc( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from x to infinity of the gamma
+ * probability density function:
+ *
+ *
+ *               inf.
+ *        b       -
+ *       a       | |   b-1  -at
+ * y =  -----    |    t    e    dt
+ *       -     | |
+ *      | (b)   -
+ *               x
+ *
+ *  The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igamc( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * gdtrc domain         x < 0            0.0
+ *
+ */
+
+/*
+C
+C     ..................................................................
+C
+C        SUBROUTINE GELS
+C
+C        PURPOSE
+C           TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
+C           SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
+C           IS ASSUMED TO BE STORED COLUMNWISE.
+C
+C        USAGE
+C           CALL GELS(R,A,M,N,EPS,IER,AUX)
+C
+C        DESCRIPTION OF PARAMETERS
+C           R      - M BY N RIGHT HAND SIDE MATRIX.  (DESTROYED)
+C                    ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
+C           A      - UPPER TRIANGULAR PART OF THE SYMMETRIC
+C                    M BY M COEFFICIENT MATRIX.  (DESTROYED)
+C           M      - THE NUMBER OF EQUATIONS IN THE SYSTEM.
+C           N      - THE NUMBER OF RIGHT HAND SIDE VECTORS.
+C           EPS    - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
+C                    TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
+C           IER    - RESULTING ERROR PARAMETER CODED AS FOLLOWS
+C                    IER=0  - NO ERROR,
+C                    IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
+C                             PIVOT ELEMENT AT ANY ELIMINATION STEP
+C                             EQUAL TO 0,
+C                    IER=K  - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
+C                             CANCE INDICATED AT ELIMINATION STEP K+1,
+C                             WHERE PIVOT ELEMENT WAS LESS THAN OR
+C                             EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
+C                             ABSOLUTELY GREATEST MAIN DIAGONAL
+C                             ELEMENT OF MATRIX A.
+C           AUX    - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
+C
+C        REMARKS
+C           UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
+C           COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
+C           HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
+C           LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
+C           TOO.
+C           THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
+C           GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
+C           ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
+C           INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
+C           SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
+C           INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
+C           GIVEN IN CASE M=1.
+C           ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
+C           MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
+C           ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
+C           WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
+C
+C        SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
+C           NONE
+C
+C        METHOD
+C           SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
+C           PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
+C           SYMMETRY IN REMAINING COEFFICIENT MATRICES.
+C
+C     ..................................................................
+C
+*/
+
+/*							hyp2f1.c
+ *
+ *	Gauss hypergeometric function   F
+ *	                               2 1
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, c, x, y, hyp2f1();
+ *
+ * y = hyp2f1( a, b, c, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *  hyp2f1( a, b, c, x )  =   F ( a, b; c; x )
+ *                           2 1
+ *
+ *           inf.
+ *            -   a(a+1)...(a+k) b(b+1)...(b+k)   k+1
+ *   =  1 +   >   -----------------------------  x   .
+ *            -         c(c+1)...(c+k) (k+1)!
+ *          k = 0
+ *
+ *  Cases addressed are
+ *	Tests and escapes for negative integer a, b, or c
+ *	Linear transformation if c - a or c - b negative integer
+ *	Special case c = a or c = b
+ *	Linear transformation for  x near +1
+ *	Transformation for x < -0.5
+ *	Psi function expansion if x > 0.5 and c - a - b integer
+ *      Conditionally, a recurrence on c to make c-a-b > 0
+ *
+ * |x| > 1 is rejected.
+ *
+ * The parameters a, b, c are considered to be integer
+ * valued if they are within 1.0e-14 of the nearest integer
+ * (1.0e-13 for IEEE arithmetic).
+ *
+ * ACCURACY:
+ *
+ *
+ *               Relative error (-1 < x < 1):
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -1,7        230000      1.2e-11     5.2e-14
+ *
+ * Several special cases also tested with a, b, c in
+ * the range -7 to 7.
+ *
+ * ERROR MESSAGES:
+ *
+ * A "partial loss of precision" message is printed if
+ * the internally estimated relative error exceeds 1^-12.
+ * A "singularity" message is printed on overflow or
+ * in cases not addressed (such as x < -1).
+ */
+
+/*							hyperg.c
+ *
+ *	Confluent hypergeometric function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, hyperg();
+ *
+ * y = hyperg( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the confluent hypergeometric function
+ *
+ *                          1           2
+ *                       a x    a(a+1) x
+ *   F ( a,b;x )  =  1 + ---- + --------- + ...
+ *  1 1                  b 1!   b(b+1) 2!
+ *
+ * Many higher transcendental functions are special cases of
+ * this power series.
+ *
+ * As is evident from the formula, b must not be a negative
+ * integer or zero unless a is an integer with 0 >= a > b.
+ *
+ * The routine attempts both a direct summation of the series
+ * and an asymptotic expansion.  In each case error due to
+ * roundoff, cancellation, and nonconvergence is estimated.
+ * The result with smaller estimated error is returned.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a, b, x), all three variables
+ * ranging from 0 to 30.
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         2000       1.2e-15     1.3e-16
+ *    IEEE      0,30        30000       1.8e-14     1.1e-15
+ *
+ * Larger errors can be observed when b is near a negative
+ * integer or zero.  Certain combinations of arguments yield
+ * serious cancellation error in the power series summation
+ * and also are not in the region of near convergence of the
+ * asymptotic series.  An error message is printed if the
+ * self-estimated relative error is greater than 1.0e-12.
+ *
+ */
+
+/*							i0.c
+ *
+ *	Modified Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0();
+ *
+ * y = i0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order zero of the
+ * argument.
+ *
+ * The function is defined as i0(x) = j0( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         6000       8.2e-17     1.9e-17
+ *    IEEE      0,30        30000       5.8e-16     1.4e-16
+ *
+ */
+/*							i0e.c
+ *
+ *	Modified Bessel function of order zero,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0e();
+ *
+ * y = i0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,30        30000       5.4e-16     1.2e-16
+ * See i0().
+ *
+ */
+
+/*							i1.c
+ *
+ *	Modified Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1();
+ *
+ * y = i1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order one of the
+ * argument.
+ *
+ * The function is defined as i1(x) = -i j1( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        3400       1.2e-16     2.3e-17
+ *    IEEE      0, 30       30000       1.9e-15     2.1e-16
+ *
+ *
+ */
+/*							i1e.c
+ *
+ *	Modified Bessel function of order one,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1e();
+ *
+ * y = i1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order one of the argument.
+ *
+ * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 30       30000       2.0e-15     2.0e-16
+ * See i1().
+ *
+ */
+
+/*							igam.c
+ *
+ *	Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igam();
+ *
+ * y = igam( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *                           x
+ *                            -
+ *                   1       | |  -t  a-1
+ *  igam(a,x)  =   -----     |   e   t   dt.
+ *                  -      | |
+ *                 | (a)    -
+ *                           0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,30       200000       3.6e-14     2.9e-15
+ *    IEEE      0,100      300000       9.9e-14     1.5e-14
+ */
+/*							igamc()
+ *
+ *	Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igamc();
+ *
+ * y = igamc( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ *  igamc(a,x)   =   1 - igam(a,x)
+ *
+ *                            inf.
+ *                              -
+ *                     1       | |  -t  a-1
+ *               =   -----     |   e   t   dt.
+ *                    -      | |
+ *                   | (a)    -
+ *                             x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, x.
+ *                a         x                      Relative error:
+ * arithmetic   domain   domain     # trials      peak         rms
+ *    IEEE     0.5,100   0,100      200000       1.9e-14     1.7e-15
+ *    IEEE     0.01,0.5  0,100      200000       1.4e-13     1.6e-15
+ */
+
+/*							igami()
+ *
+ *      Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, p, igami();
+ *
+ * x = igami( a, p );
+ *
+ * DESCRIPTION:
+ *
+ * Given p, the function finds x such that
+ *
+ *  igamc( a, x ) = p.
+ *
+ * Starting with the approximate value
+ *
+ *         3
+ *  x = a t
+ *
+ *  where
+ *
+ *  t = 1 - d - ndtri(p) sqrt(d)
+ * 
+ * and
+ *
+ *  d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - p = 0.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, p in the intervals indicated.
+ *
+ *                a        p                      Relative error:
+ * arithmetic   domain   domain     # trials      peak         rms
+ *    IEEE     0.5,100   0,0.5       100000       1.0e-14     1.7e-15
+ *    IEEE     0.01,0.5  0,0.5       100000       9.0e-14     3.4e-15
+ *    IEEE    0.5,10000  0,0.5        20000       2.3e-13     3.8e-14
+ */
+
+/*							incbet.c
+ *
+ *	Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, incbet();
+ *
+ * y = incbet( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x.  The function is defined as
+ *
+ *                  x
+ *     -            -
+ *    | (a+b)      | |  a-1     b-1
+ *  -----------    |   t   (1-t)   dt.
+ *   -     -     | |
+ *  | (a) | (b)   -
+ *                 0
+ *
+ * The domain of definition is 0 <= x <= 1.  In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ *    1 - incbet( a, b, x )  =  incbet( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion
+ * or, when b*x is small, by a power series.
+ *
+ * ACCURACY:
+ *
+ * Tested at uniformly distributed random points (a,b,x) with a and b
+ * in "domain" and x between 0 and 1.
+ *                                        Relative error
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,5         10000       6.9e-15     4.5e-16
+ *    IEEE      0,85       250000       2.2e-13     1.7e-14
+ *    IEEE      0,1000      30000       5.3e-12     6.3e-13
+ *    IEEE      0,10000    250000       9.3e-11     7.1e-12
+ *    IEEE      0,100000    10000       8.7e-10     4.8e-11
+ * Outputs smaller than the IEEE gradual underflow threshold
+ * were excluded from these statistics.
+ *
+ * ERROR MESSAGES:
+ *   message         condition      value returned
+ * incbet domain      x<0, x>1          0.0
+ * incbet underflow                     0.0
+ */
+
+/*							incbi()
+ *
+ *      Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, incbi();
+ *
+ * x = incbi( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ *  incbet( a, b, x ) = y .
+ *
+ * The routine performs interval halving or Newton iterations to find the
+ * root of incbet(a,b,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ *                x     a,b
+ * arithmetic   domain  domain  # trials    peak       rms
+ *    IEEE      0,1    .5,10000   50000    5.8e-12   1.3e-13
+ *    IEEE      0,1   .25,100    100000    1.8e-13   3.9e-15
+ *    IEEE      0,1     0,5       50000    1.1e-12   5.5e-15
+ *    VAX       0,1    .5,100     25000    3.5e-14   1.1e-15
+ * With a and b constrained to half-integer or integer values:
+ *    IEEE      0,1    .5,10000   50000    5.8e-12   1.1e-13
+ *    IEEE      0,1    .5,100    100000    1.7e-14   7.9e-16
+ * With a = .5, b constrained to half-integer or integer values:
+ *    IEEE      0,1    .5,10000   10000    8.3e-11   1.0e-11
+ */
+
+/*							iv.c
+ *
+ *	Modified Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, iv();
+ *
+ * y = iv( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order v of the
+ * argument.  If x is negative, v must be integer valued.
+ *
+ * The function is defined as Iv(x) = Jv( ix ).  It is
+ * here computed in terms of the confluent hypergeometric
+ * function, according to the formula
+ *
+ *              v  -x
+ * Iv(x) = (x/2)  e   hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
+ *
+ * If v is a negative integer, then v is replaced by -v.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (v, x), with v between 0 and
+ * 30, x between 0 and 28.
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30          2000      3.1e-15     5.4e-16
+ *    IEEE      0,30         10000      1.7e-14     2.7e-15
+ *
+ * Accuracy is diminished if v is near a negative integer.
+ *
+ * See also hyperg.c.
+ *
+ */
+
+/*							j0.c
+ *
+ *	Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j0();
+ *
+ * y = j0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval the following rational
+ * approximation is used:
+ *
+ *
+ *        2         2
+ * (w - r  ) (w - r  ) P (w) / Q (w)
+ *       1         2    3       8
+ *
+ *            2
+ * where w = x  and the two r's are zeros of the function.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30       10000       4.4e-17     6.3e-18
+ *    IEEE      0, 30       60000       4.2e-16     1.1e-16
+ *
+ */
+/*							y0.c
+ *
+ *	Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y0();
+ *
+ * y = y0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *   y0(x)  = R(x)  +   2 * log(x) * j0(x) / PI.
+ * Thus a call to j0() is required.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *  Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        9400       7.0e-17     7.9e-18
+ *    IEEE      0, 30       30000       1.3e-15     1.6e-16
+ *
+ */
+
+/*							j1.c
+ *
+ *	Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j1();
+ *
+ * y = j1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 24 term Chebyshev
+ * expansion is used. In the second, the asymptotic
+ * trigonometric representation is employed using two
+ * rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC       0, 30       10000       4.0e-17     1.1e-17
+ *    IEEE      0, 30       30000       2.6e-16     1.1e-16
+ *
+ *
+ */
+/*							y1.c
+ *
+ *	Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 25 term Chebyshev
+ * expansion is used, and a call to j1() is required.
+ * In the second, the asymptotic trigonometric representation
+ * is employed using two rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC       0, 30       10000       8.6e-17     1.3e-17
+ *    IEEE      0, 30       30000       1.0e-15     1.3e-16
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+
+/*							jn.c
+ *
+ *	Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double x, y, jn();
+ *
+ * y = jn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence.  First the ratio jn/jn-1 is found by a
+ * continued fraction expansion.  Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   range      # trials      peak         rms
+ *    DEC       0, 30        5500       6.9e-17     9.3e-18
+ *    IEEE      0, 30        5000       4.4e-16     7.9e-17
+ *
+ *
+ * Not suitable for large n or x. Use jv() instead.
+ *
+ */
+
+/*							jv.c
+ *
+ *	Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, jv();
+ *
+ * y = jv( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order v of the argument,
+ * where v is real.  Negative x is allowed if v is an integer.
+ *
+ * Several expansions are included: the ascending power
+ * series, the Hankel expansion, and two transitional
+ * expansions for large v.  If v is not too large, it
+ * is reduced by recurrence to a region of best accuracy.
+ * The transitional expansions give 12D accuracy for v > 500.
+ *
+ *
+ *
+ * ACCURACY:
+ * Results for integer v are indicated by *, where x and v
+ * both vary from -125 to +125.  Otherwise,
+ * x ranges from 0 to 125, v ranges as indicated by "domain."
+ * Error criterion is absolute, except relative when |jv()| > 1.
+ *
+ * arithmetic  v domain  x domain    # trials      peak       rms
+ *    IEEE      0,125     0,125      100000      4.6e-15    2.2e-16
+ *    IEEE   -125,0       0,125       40000      5.4e-11    3.7e-13
+ *    IEEE      0,500     0,500       20000      4.4e-15    4.0e-16
+ * Integer v:
+ *    IEEE   -125,125   -125,125      50000      3.5e-15*   1.9e-16*
+ *
+ */
+
+/*							k0.c
+ *
+ *	Modified Bessel function, third kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0();
+ *
+ * y = k0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order zero of the argument.
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at 2000 random points between 0 and 8.  Peak absolute
+ * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        3100       1.3e-16     2.1e-17
+ *    IEEE      0, 30       30000       1.2e-15     1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ *  K0 domain          x <= 0          MAXNUM
+ *
+ */
+/*							k0e()
+ *
+ *	Modified Bessel function, third kind, order zero,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0e();
+ *
+ * y = k0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 30       30000       1.4e-15     1.4e-16
+ * See k0().
+ *
+ */
+
+/*							k1.c
+ *
+ *	Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1();
+ *
+ * y = k1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        3300       8.9e-17     2.2e-17
+ *    IEEE      0, 30       30000       1.2e-15     1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * k1 domain          x <= 0          MAXNUM
+ *
+ */
+/*							k1e.c
+ *
+ *	Modified Bessel function, third kind, order one,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1e();
+ *
+ * y = k1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ *      k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 30       30000       7.8e-16     1.2e-16
+ * See k1().
+ *
+ */
+
+/*							kn.c
+ *
+ *	Modified Bessel function, third kind, integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, kn();
+ * int n;
+ *
+ * y = kn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order n of the argument.
+ *
+ * The range is partitioned into the two intervals [0,9.55] and
+ * (9.55, infinity).  An ascending power series is used in the
+ * low range, and an asymptotic expansion in the high range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         3000       1.3e-9      5.8e-11
+ *    IEEE      0,30        90000       1.8e-8      3.0e-10
+ *
+ *  Error is high only near the crossover point x = 9.55
+ * between the two expansions used.
+ */
+
+
+/* Re Kolmogorov statistics, here is Birnbaum and Tingey's formula for the
+   distribution of D+, the maximum of all positive deviations between a
+   theoretical distribution function P(x) and an empirical one Sn(x)
+   from n samples.
+
+     +
+    D  =         sup        [ P(x) - Sn(x) ]
+     n     -inf < x < inf
+
+
+                  [n(1-e)]
+        +            -                    v-1              n-v
+    Pr{D   > e} =    >    C    e (e + v/n)    (1 - e - v/n)
+        n            -   n v
+                    v=0
+    [n(1-e)] is the largest integer not exceeding n(1-e).
+    nCv is the number of combinations of n things taken v at a time.
+
+ Exact Smirnov statistic, for one-sided test:
+double
+smirnov (n, e)
+     int n;
+     double e;
+
+   Kolmogorov's limiting distribution of two-sided test, returns
+   probability that sqrt(n) * max deviation > y,
+   or that max deviation > y/sqrt(n).
+   The approximation is useful for the tail of the distribution
+   when n is large.
+double
+kolmogorov (y)
+     double y;
+
+
+   Functional inverse of Smirnov distribution
+   finds e such that smirnov(n,e) = p.
+double
+smirnovi (n, p)
+     int n;
+     double p;
+
+   Functional inverse of Kolmogorov statistic for two-sided test.
+   Finds y such that kolmogorov(y) = p.
+   If e = smirnovi (n,p), then kolmogi(2 * p) / sqrt(n) should
+   be close to e.
+double
+kolmogi (p)
+     double p;
+  */
+
+/*		Levnsn.c		*/
+/* Levinson-Durbin LPC
+ *
+ * | R0 R1 R2 ... RN-1 |   | A1 |       | -R1 |
+ * | R1 R0 R1 ... RN-2 |   | A2 |       | -R2 |
+ * | R2 R1 R0 ... RN-3 |   | A3 |   =   | -R3 |
+ * |          ...      |   | ...|       | ... |
+ * | RN-1 RN-2... R0   |   | AN |       | -RN |
+ *
+ * Ref: John Makhoul, "Linear Prediction, A Tutorial Review"
+ * Proc. IEEE Vol. 63, PP 561-580 April, 1975.
+ *
+ * R is the input autocorrelation function.  R0 is the zero lag
+ * term.  A is the output array of predictor coefficients.  Note
+ * that a filter impulse response has a coefficient of 1.0 preceding
+ * A1.  E is an array of mean square error for each prediction order
+ * 1 to N.  REFL is an output array of the reflection coefficients.
+ */
+
+/*							log.c
+ *
+ *	Natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log();
+ *
+ * y = log( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting  z = 2(x-1)/x+1),
+ * 
+ *     log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0    150000      1.44e-16    5.06e-17
+ *    IEEE      +-MAXNUM    30000       1.20e-16    4.78e-17
+ *    DEC       0, 10       170000      1.8e-17     6.3e-18
+ *
+ * In the tests over the interval [+-MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOG].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity:  x = 0; returns -INFINITY
+ * log domain:       x < 0; returns NAN
+ */
+
+/*							log10.c
+ *
+ *	Common logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log10();
+ *
+ * y = log10( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns logarithm to the base 10 of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  The logarithm of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0     30000      1.5e-16     5.0e-17
+ *    IEEE      0, MAXNUM    30000      1.4e-16     4.8e-17
+ *    DEC       1, MAXNUM    50000      2.5e-17     6.0e-18
+ *
+ * In the tests over the interval [1, MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOG].
+ *
+ * ERROR MESSAGES:
+ *
+ * log10 singularity:  x = 0; returns -INFINITY
+ * log10 domain:       x < 0; returns NAN
+ */
+
+/*							log2.c
+ *
+ *	Base 2 logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log2();
+ *
+ * y = log2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the base e
+ * logarithm of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting  z = 2(x-1)/x+1),
+ * 
+ *     log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0    30000       2.0e-16     5.5e-17
+ *    IEEE      exp(+-700)  40000       1.3e-16     4.6e-17
+ *
+ * In the tests over the interval [exp(+-700)], the logarithms
+ * of the random arguments were uniformly distributed.
+ *
+ * ERROR MESSAGES:
+ *
+ * log2 singularity:  x = 0; returns -INFINITY
+ * log2 domain:       x < 0; returns NAN
+ */
+
+/*							lrand.c
+ *
+ *	Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long y, drand();
+ *
+ * drand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a long integer random number.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used. The period, given by them, is
+ * 6953607871644.
+ *
+ *
+ */
+
+/*							lsqrt.c
+ *
+ *	Integer square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long x, y;
+ * long lsqrt();
+ *
+ * y = lsqrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns a long integer square root of the long integer
+ * argument.  The computation is by binary long division.
+ *
+ * The largest possible result is lsqrt(2,147,483,647)
+ * = 46341.
+ *
+ * If x < 0, the square root of |x| is returned, and an
+ * error message is printed.
+ *
+ *
+ * ACCURACY:
+ *
+ * An extra, roundoff, bit is computed; hence the result
+ * is the nearest integer to the actual square root.
+ * NOTE: only DEC arithmetic is currently supported.
+ *
+ */
+
+/*							minv.c
+ *
+ *	Matrix inversion
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n, errcod;
+ * double A[n*n], X[n*n];
+ * double B[n];
+ * int IPS[n];
+ * int minv();
+ *
+ * errcod = minv( A, X, n, B, IPS );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the inverse of the n by n matrix A.  The result goes
+ * to X.   B and IPS are scratch pad arrays of length n.
+ * The contents of matrix A are destroyed.
+ *
+ * The routine returns nonzero on error; error messages are printed
+ * by subroutine simq().
+ *
+ */
+
+/*							mmmpy.c
+ *
+ *	Matrix multiply
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int r, c;
+ * double A[r*c], B[c*r], Y[r*r];
+ *
+ * mmmpy( r, c, A, B, Y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Y = A B
+ *              c-1
+ *              --
+ * Y[i][j]  =   >   A[i][k] B[k][j]
+ *              --
+ *              k=0
+ *
+ * Multiplies an r (rows) by c (columns) matrix A on the left
+ * by a c (rows) by r (columns) matrix B on the right
+ * to produce an r by r matrix Y.
+ *
+ *
+ */
+
+/*							mtherr.c
+ *
+ *	Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * int mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file math.h).
+ *  
+ *   Mnemonic        Value          Significance
+ *
+ *    DOMAIN            1       argument domain error
+ *    SING              2       function singularity
+ *    OVERFLOW          3       overflow range error
+ *    UNDERFLOW         4       underflow range error
+ *    TLOSS             5       total loss of precision
+ *    PLOSS             6       partial loss of precision
+ *    EDOM             33       Unix domain error code
+ *    ERANGE           34       Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition.  The display is directed to the standard
+ * output device.  The routine then returns to the calling
+ * program.  Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * math.h
+ *
+ */
+
+/*							mtransp.c
+ *
+ *	Matrix transpose
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double A[n*n], T[n*n];
+ *
+ * mtransp( n, A, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * T[r][c] = A[c][r]
+ *
+ *
+ * Transposes the n by n square matrix A and puts the result in T.
+ * The output, T, may occupy the same storage as A.
+ *
+ *
+ *
+ */
+
+/*							mvmpy.c
+ *
+ *	Matrix times vector
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int r, c;
+ * double A[r*c], V[c], Y[r];
+ *
+ * mvmpy( r, c, A, V, Y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *          c-1
+ *          --
+ * Y[j] =   >   A[j][k] V[k] ,  j = 1, ..., r
+ *          --
+ *          k=0
+ *
+ * Multiplies the r (rows) by c (columns) matrix A on the left
+ * by column vector V of dimension c on the right
+ * to produce a (column) vector Y output of dimension r.
+ *
+ *
+ *
+ *
+ */
+
+/*							nbdtr.c
+ *
+ *	Negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtr();
+ *
+ * y = nbdtr( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the negative
+ * binomial distribution:
+ *
+ *   k
+ *   --  ( n+j-1 )   n      j
+ *   >   (       )  p  (1-p)
+ *   --  (   j   )
+ *  j=0
+ *
+ * In a sequence of Bernoulli trials, this is the probability
+ * that k or fewer failures precede the nth success.
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *    IEEE     0,100       100000      1.7e-13     8.8e-15
+ * See also incbet.c.
+ *
+ */
+/*							nbdtrc.c
+ *
+ *	Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtrc();
+ *
+ * y = nbdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ *   inf
+ *   --  ( n+j-1 )   n      j
+ *   >   (       )  p  (1-p)
+ *   --  (   j   )
+ *  j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *    IEEE     0,100       100000      1.7e-13     8.8e-15
+ * See also incbet.c.
+ */
+
+/*							nbdtrc
+ *
+ *	Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtrc();
+ *
+ * y = nbdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ *   inf
+ *   --  ( n+j-1 )   n      j
+ *   >   (       )  p  (1-p)
+ *   --  (   j   )
+ *  j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ */
+/*							nbdtri
+ *
+ *	Functional inverse of negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtri();
+ *
+ * p = nbdtri( k, n, y );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the argument p such that nbdtr(k,n,p) is equal to y.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,y), with y between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *    IEEE     0,100       100000      1.5e-14     8.5e-16
+ * See also incbi.c.
+ */
+
+/*							ndtr.c
+ *
+ *	Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtr();
+ *
+ * y = ndtr( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the Gaussian probability density
+ * function, integrated from minus infinity to x:
+ *
+ *                            x
+ *                             -
+ *                   1        | |          2
+ *    ndtr(x)  = ---------    |    exp( - t /2 ) dt
+ *               sqrt(2pi)  | |
+ *                           -
+ *                          -inf.
+ *
+ *             =  ( 1 + erf(z) ) / 2
+ *             =  erfc(z) / 2
+ *
+ * where z = x/sqrt(2). Computation is via the functions
+ * erf and erfc.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -13,0         8000       2.1e-15     4.8e-16
+ *    IEEE     -13,0        30000       3.4e-14     6.7e-15
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition         value returned
+ * erfc underflow    x > 37.519379347       0.0
+ *
+ */
+/*							erf.c
+ *
+ *	Error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, erf();
+ *
+ * y = erf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The integral is
+ *
+ *                           x 
+ *                            -
+ *                 2         | |          2
+ *   erf(x)  =  --------     |    exp( - t  ) dt.
+ *              sqrt(pi)   | |
+ *                          -
+ *                           0
+ *
+ * The magnitude of x is limited to 9.231948545 for DEC
+ * arithmetic; 1 or -1 is returned outside this range.
+ *
+ * For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
+ * erf(x) = 1 - erfc(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,1         14000       4.7e-17     1.5e-17
+ *    IEEE      0,1         30000       3.7e-16     1.0e-16
+ *
+ */
+/*							erfc.c
+ *
+ *	Complementary error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, erfc();
+ *
+ * y = erfc( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *  1 - erf(x) =
+ *
+ *                           inf. 
+ *                             -
+ *                  2         | |          2
+ *   erfc(x)  =  --------     |    exp( - t  ) dt
+ *               sqrt(pi)   | |
+ *                           -
+ *                            x
+ *
+ *
+ * For small x, erfc(x) = 1 - erf(x); otherwise rational
+ * approximations are computed.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 9.2319   12000       5.1e-16     1.2e-16
+ *    IEEE      0,26.6417   30000       5.7e-14     1.5e-14
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition              value returned
+ * erfc underflow    x > 9.231948545 (DEC)       0.0
+ *
+ *
+ */
+
+/*							ndtri.c
+ *
+ *	Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtri();
+ *
+ * x = ndtri( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2.0 * log(y) );  then the approximation is
+ * x = z - log(z)/z  - (1/z) P(1/z) / Q(1/z).
+ * There are two rational functions P/Q, one for 0 < y < exp(-32)
+ * and the other for y up to exp(-2).  For larger arguments,
+ * w = y - 0.5, and  x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain        # trials      peak         rms
+ *    DEC      0.125, 1         5500       9.5e-17     2.1e-17
+ *    DEC      6e-39, 0.135     3500       5.7e-17     1.3e-17
+ *    IEEE     0.125, 1        20000       7.2e-16     1.3e-16
+ *    IEEE     3e-308, 0.135   50000       4.6e-16     9.8e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition    value returned
+ * ndtri domain       x <= 0        -MAXNUM
+ * ndtri domain       x >= 1         MAXNUM
+ *
+ */
+
+/*							pdtr.c
+ *
+ *	Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtr();
+ *
+ * y = pdtr( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the first k terms of the Poisson
+ * distribution:
+ *
+ *   k         j
+ *   --   -m  m
+ *   >   e    --
+ *   --       j!
+ *  j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the relation
+ *
+ * y = pdtr( k, m ) = igamc( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ */
+/*							pdtrc()
+ *
+ *	Complemented poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtrc();
+ *
+ * y = pdtrc( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the Poisson
+ * distribution:
+ *
+ *  inf.       j
+ *   --   -m  m
+ *   >   e    --
+ *   --       j!
+ *  j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the formula
+ *
+ * y = pdtrc( k, m ) = igam( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam.c.
+ *
+ */
+/*							pdtri()
+ *
+ *	Inverse Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtr();
+ *
+ * m = pdtri( k, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Poisson variable x such that the integral
+ * from 0 to x of the Poisson density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ *    m = igami( k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * pdtri domain    y < 0 or y >= 1       0.0
+ *                     k < 0
+ *
+ */
+
+/*							polevl.c
+ *							p1evl.c
+ *
+ *	Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * double x, y, coef[N+1], polevl[];
+ *
+ * y = polevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ *                     2          N
+ * y  =  C  + C x + C x  +...+ C x
+ *        0    1     2          N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C  , ..., coef[N] = C  .
+ *            N                   0
+ *
+ *  The function p1evl() assumes that coef[N] = 1.0 and is
+ * omitted from the array.  Its calling arguments are
+ * otherwise the same as polevl().
+ *
+ *
+ * SPEED:
+ *
+ * In the interest of speed, there are no checks for out
+ * of bounds arithmetic.  This routine is used by most of
+ * the functions in the library.  Depending on available
+ * equipment features, the user may wish to rewrite the
+ * program in microcode or assembly language.
+ *
+ */
+
+/*							polmisc.c
+ * Square root, sine, cosine, and arctangent of polynomial.
+ * See polyn.c for data structures and discussion.
+ */
+
+/*							polrt.c
+ *
+ *	Find roots of a polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ *	{
+ *	double r;
+ *	double i;
+ *	}cmplx;
+ *
+ * double xcof[], cof[];
+ * int m;
+ * cmplx root[];
+ *
+ * polrt( xcof, cof, m, root )
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Iterative determination of the roots of a polynomial of
+ * degree m whose coefficient vector is xcof[].  The
+ * coefficients are arranged in ascending order; i.e., the
+ * coefficient of x**m is xcof[m].
+ *
+ * The array cof[] is working storage the same size as xcof[].
+ * root[] is the output array containing the complex roots.
+ *
+ *
+ * ACCURACY:
+ *
+ * Termination depends on evaluation of the polynomial at
+ * the trial values of the roots.  The values of multiple roots
+ * or of roots that are nearly equal may have poor relative
+ * accuracy after the first root in the neighborhood has been
+ * found.
+ *
+ */
+
+/*							polyn.c
+ *							polyr.c
+ * Arithmetic operations on polynomials
+ *
+ * In the following descriptions a, b, c are polynomials of degree
+ * na, nb, nc respectively.  The degree of a polynomial cannot
+ * exceed a run-time value MAXPOL.  An operation that attempts
+ * to use or generate a polynomial of higher degree may produce a
+ * result that suffers truncation at degree MAXPOL.  The value of
+ * MAXPOL is set by calling the function
+ *
+ *     polini( maxpol );
+ *
+ * where maxpol is the desired maximum degree.  This must be
+ * done prior to calling any of the other functions in this module.
+ * Memory for internal temporary polynomial storage is allocated
+ * by polini().
+ *
+ * Each polynomial is represented by an array containing its
+ * coefficients, together with a separately declared integer equal
+ * to the degree of the polynomial.  The coefficients appear in
+ * ascending order; that is,
+ *
+ *                                        2                      na
+ * a(x)  =  a[0]  +  a[1] * x  +  a[2] * x   +  ...  +  a[na] * x  .
+ *
+ *
+ *
+ * sum = poleva( a, na, x );	Evaluate polynomial a(t) at t = x.
+ * polprt( a, na, D );		Print the coefficients of a to D digits.
+ * polclr( a, na );		Set a identically equal to zero, up to a[na].
+ * polmov( a, na, b );		Set b = a.
+ * poladd( a, na, b, nb, c );	c = b + a, nc = max(na,nb)
+ * polsub( a, na, b, nb, c );	c = b - a, nc = max(na,nb)
+ * polmul( a, na, b, nb, c );	c = b * a, nc = na+nb
+ *
+ *
+ * Division:
+ *
+ * i = poldiv( a, na, b, nb, c );	c = b / a, nc = MAXPOL
+ *
+ * returns i = the degree of the first nonzero coefficient of a.
+ * The computed quotient c must be divided by x^i.  An error message
+ * is printed if a is identically zero.
+ *
+ *
+ * Change of variables:
+ * If a and b are polynomials, and t = a(x), then
+ *     c(t) = b(a(x))
+ * is a polynomial found by substituting a(x) for t.  The
+ * subroutine call for this is
+ *
+ * polsbt( a, na, b, nb, c );
+ *
+ *
+ * Notes:
+ * poldiv() is an integer routine; poleva() is double.
+ * Any of the arguments a, b, c may refer to the same array.
+ *
+ */
+
+/*							pow.c
+ *
+ *	Power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, z, pow();
+ *
+ * z = pow( x, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes x raised to the yth power.  Analytically,
+ *
+ *      x**y  =  exp( y log(x) ).
+ *
+ * Following Cody and Waite, this program uses a lookup table
+ * of 2**-i/16 and pseudo extended precision arithmetic to
+ * obtain an extra three bits of accuracy in both the logarithm
+ * and the exponential.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -26,26       30000      4.2e-16      7.7e-17
+ *    DEC      -26,26       60000      4.8e-17      9.1e-18
+ * 1/26 < x < 26, with log(x) uniformly distributed.
+ * -26 < y < 26, y uniformly distributed.
+ *    IEEE     0,8700       30000      1.5e-14      2.1e-15
+ * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * pow overflow     x**y > MAXNUM      INFINITY
+ * pow underflow   x**y < 1/MAXNUM       0.0
+ * pow domain      x<0 and y noninteger  0.0
+ *
+ */
+
+/*							powi.c
+ *
+ *	Real raised to integer power
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, powi();
+ * int n;
+ *
+ * y = powi( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns argument x raised to the nth power.
+ * The routine efficiently decomposes n as a sum of powers of
+ * two. The desired power is a product of two-to-the-kth
+ * powers of x.  Thus to compute the 32767 power of x requires
+ * 28 multiplications instead of 32767 multiplications.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ *                      Relative error:
+ * arithmetic   x domain   n domain  # trials      peak         rms
+ *    DEC       .04,26     -26,26    100000       2.7e-16     4.3e-17
+ *    IEEE      .04,26     -26,26     50000       2.0e-15     3.8e-16
+ *    IEEE        1,2    -1022,1023   50000       8.6e-14     1.6e-14
+ *
+ * Returns MAXNUM on overflow, zero on underflow.
+ *
+ */
+
+/*							psi.c
+ *
+ *	Psi (digamma) function
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, psi();
+ *
+ * y = psi( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *              d      -
+ *   psi(x)  =  -- ln | (x)
+ *              dx
+ *
+ * is the logarithmic derivative of the gamma function.
+ * For integer x,
+ *                   n-1
+ *                    -
+ * psi(n) = -EUL  +   >  1/k.
+ *                    -
+ *                   k=1
+ *
+ * This formula is used for 0 < n <= 10.  If x is negative, it
+ * is transformed to a positive argument by the reflection
+ * formula  psi(1-x) = psi(x) + pi cot(pi x).
+ * For general positive x, the argument is made greater than 10
+ * using the recurrence  psi(x+1) = psi(x) + 1/x.
+ * Then the following asymptotic expansion is applied:
+ *
+ *                           inf.   B
+ *                            -      2k
+ * psi(x) = log(x) - 1/2x -   >   -------
+ *                            -        2k
+ *                           k=1   2k x
+ *
+ * where the B2k are Bernoulli numbers.
+ *
+ * ACCURACY:
+ *    Relative error (except absolute when |psi| < 1):
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         2500       1.7e-16     2.0e-17
+ *    IEEE      0,30        30000       1.3e-15     1.4e-16
+ *    IEEE      -30,0       40000       1.5e-15     2.2e-16
+ *
+ * ERROR MESSAGES:
+ *     message         condition      value returned
+ * psi singularity    x integer <=0      MAXNUM
+ */
+
+/*							revers.c
+ *
+ *	Reversion of power series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * extern int MAXPOL;
+ * int n;
+ * double x[n+1], y[n+1];
+ *
+ * polini(n);
+ * revers( y, x, n );
+ *
+ *  Note, polini() initializes the polynomial arithmetic subroutines;
+ *  see polyn.c.
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *
+ *          inf
+ *           -       i
+ *  y(x)  =  >   a  x
+ *           -    i
+ *          i=1
+ *
+ * then
+ *
+ *          inf
+ *           -       j
+ *  x(y)  =  >   A  y    ,
+ *           -    j
+ *          j=1
+ *
+ * where
+ *                   1
+ *         A    =   ---
+ *          1        a
+ *                    1
+ *
+ * etc.  The coefficients of x(y) are found by expanding
+ *
+ *          inf      inf
+ *           -        -      i
+ *  x(y)  =  >   A    >  a  x
+ *           -    j   -   i
+ *          j=1      i=1
+ *
+ *  and setting each coefficient of x , higher than the first,
+ *  to zero.
+ *
+ *
+ *
+ * RESTRICTIONS:
+ *
+ *  y[0] must be zero, and y[1] must be nonzero.
+ *
+ */
+
+/*						rgamma.c
+ *
+ *	Reciprocal gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, rgamma();
+ *
+ * y = rgamma( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns one divided by the gamma function of the argument.
+ *
+ * The function is approximated by a Chebyshev expansion in
+ * the interval [0,1].  Range reduction is by recurrence
+ * for arguments between -34.034 and +34.84425627277176174.
+ * 1/MAXNUM is returned for positive arguments outside this
+ * range.  For arguments less than -34.034 the cosecant
+ * reflection formula is applied; lograrithms are employed
+ * to avoid unnecessary overflow.
+ *
+ * The reciprocal gamma function has no singularities,
+ * but overflow and underflow may occur for large arguments.
+ * These conditions return either MAXNUM or 1/MAXNUM with
+ * appropriate sign.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -30,+30       4000       1.2e-16     1.8e-17
+ *    IEEE     -30,+30      30000       1.1e-15     2.0e-16
+ * For arguments less than -34.034 the peak error is on the
+ * order of 5e-15 (DEC), excepting overflow or underflow.
+ */
+
+/*							round.c
+ *
+ *	Round double to nearest or even integer valued double
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, round();
+ *
+ * y = round(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the nearest integer to x as a double precision
+ * floating point result.  If x ends in 0.5 exactly, the
+ * nearest even integer is chosen.
+ * 
+ *
+ *
+ * ACCURACY:
+ *
+ * If x is greater than 1/(2*MACHEP), its closest machine
+ * representation is already an integer, so rounding does
+ * not change it.
+ */
+
+/*							shichi.c
+ *
+ *	Hyperbolic sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, Chi, Shi, shichi();
+ *
+ * shichi( x, &Chi, &Shi );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integrals
+ *
+ *                            x
+ *                            -
+ *                           | |   cosh t - 1
+ *   Chi(x) = eul + ln x +   |    -----------  dt,
+ *                         | |          t
+ *                          -
+ *                          0
+ *
+ *               x
+ *               -
+ *              | |  sinh t
+ *   Shi(x) =   |    ------  dt
+ *            | |       t
+ *             -
+ *             0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are evaluated by power series for x < 8
+ * and by Chebyshev expansions for x between 8 and 88.
+ * For large x, both functions approach exp(x)/2x.
+ * Arguments greater than 88 in magnitude return MAXNUM.
+ *
+ *
+ * ACCURACY:
+ *
+ * Test interval 0 to 88.
+ *                      Relative error:
+ * arithmetic   function  # trials      peak         rms
+ *    DEC          Shi       3000       9.1e-17
+ *    IEEE         Shi      30000       6.9e-16     1.6e-16
+ *        Absolute error, except relative when |Chi| > 1:
+ *    DEC          Chi       2500       9.3e-17
+ *    IEEE         Chi      30000       8.4e-16     1.4e-16
+ */
+
+/*							sici.c
+ *
+ *	Sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, Ci, Si, sici();
+ *
+ * sici( x, &Si, &Ci );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the integrals
+ *
+ *                          x
+ *                          -
+ *                         |  cos t - 1
+ *   Ci(x) = eul + ln x +  |  --------- dt,
+ *                         |      t
+ *                        -
+ *                         0
+ *             x
+ *             -
+ *            |  sin t
+ *   Si(x) =  |  ----- dt
+ *            |    t
+ *           -
+ *            0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are approximated by rational functions.
+ * For x > 8 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * Ci(x) = f(x) sin(x) - g(x) cos(x)
+ * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
+ *
+ *
+ * ACCURACY:
+ *    Test interval = [0,50].
+ * Absolute error, except relative when > 1:
+ * arithmetic   function   # trials      peak         rms
+ *    IEEE        Si        30000       4.4e-16     7.3e-17
+ *    IEEE        Ci        30000       6.9e-16     5.1e-17
+ *    DEC         Si         5000       4.4e-17     9.0e-18
+ *    DEC         Ci         5300       7.9e-17     5.2e-18
+ */
+
+/*							simpsn.c	*/
+ * Numerical integration of function tabulated
+ * at equally spaced arguments
+ */
+
+/*							simq.c
+ *
+ *	Solution of simultaneous linear equations AX = B
+ *	by Gaussian elimination with partial pivoting
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double A[n*n], B[n], X[n];
+ * int n, flag;
+ * int IPS[];
+ * int simq();
+ *
+ * ercode = simq( A, B, X, n, flag, IPS );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * B, X, IPS are vectors of length n.
+ * A is an n x n matrix (i.e., a vector of length n*n),
+ * stored row-wise: that is, A(i,j) = A[ij],
+ * where ij = i*n + j, which is the transpose of the normal
+ * column-wise storage.
+ *
+ * The contents of matrix A are destroyed.
+ *
+ * Set flag=0 to solve.
+ * Set flag=-1 to do a new back substitution for different B vector
+ * using the same A matrix previously reduced when flag=0.
+ *
+ * The routine returns nonzero on error; messages are printed.
+ *
+ *
+ * ACCURACY:
+ *
+ * Depends on the conditioning (range of eigenvalues) of matrix A.
+ *
+ *
+ * REFERENCE:
+ *
+ * Computer Solution of Linear Algebraic Systems,
+ * by George E. Forsythe and Cleve B. Moler; Prentice-Hall, 1967.
+ *
+ */
+
+/*							sin.c
+ *
+ *	Circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sin();
+ *
+ * y = sin( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4.  The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ *      x  +  x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ *      1  -  x**2 Q(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC       0, 10       150000       3.0e-17     7.8e-18
+ *    IEEE -1.07e9,+1.07e9  130000       2.1e-16     5.4e-17
+ * 
+ * ERROR MESSAGES:
+ *
+ *   message           condition        value returned
+ * sin total loss   x > 1.073741824e9      0.0
+ *
+ * Partial loss of accuracy begins to occur at x = 2**30
+ * = 1.074e9.  The loss is not gradual, but jumps suddenly to
+ * about 1 part in 10e7.  Results may be meaningless for
+ * x > 2**49 = 5.6e14.  The routine as implemented flags a
+ * TLOSS error for x > 2**30 and returns 0.0.
+ */
+/*							cos.c
+ *
+ *	Circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cos();
+ *
+ * y = cos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4.  The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ *      1  -  x**2 Q(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ *      x  +  x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain      # trials      peak         rms
+ *    IEEE -1.07e9,+1.07e9  130000       2.1e-16     5.4e-17
+ *    DEC        0,+1.07e9   17000       3.0e-17     7.2e-18
+ */
+
+/*							sincos.c
+ *
+ *	Circular sine and cosine of argument in degrees
+ *	Table lookup and interpolation algorithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, sine, cosine, flg, sincos();
+ *
+ * sincos( x, &sine, &cosine, flg );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns both the sine and the cosine of the argument x.
+ * Several different compile time options and minimax
+ * approximations are supplied to permit tailoring the
+ * tradeoff between computation speed and accuracy.
+ * 
+ * Since range reduction is time consuming, the reduction
+ * of x modulo 360 degrees is also made optional.
+ *
+ * sin(i) is internally tabulated for 0 <= i <= 90 degrees.
+ * Approximation polynomials, ranging from linear interpolation
+ * to cubics in (x-i)**2, compute the sine and cosine
+ * of the residual x-i which is between -0.5 and +0.5 degree.
+ * In the case of the high accuracy options, the residual
+ * and the tabulated values are combined using the trigonometry
+ * formulas for sin(A+B) and cos(A+B).
+ *
+ * Compile time options are supplied for 5, 11, or 17 decimal
+ * relative accuracy (ACC5, ACC11, ACC17 respectively).
+ * A subroutine flag argument "flg" chooses betwen this
+ * accuracy and table lookup only (peak absolute error
+ * = 0.0087).
+ *
+ * If the argument flg = 1, then the tabulated value is
+ * returned for the nearest whole number of degrees. The
+ * approximation polynomials are not computed.  At
+ * x = 0.5 deg, the absolute error is then sin(0.5) = 0.0087.
+ *
+ * An intermediate speed and precision can be obtained using
+ * the compile time option LINTERP and flg = 1.  This yields
+ * a linear interpolation using a slope estimated from the sine
+ * or cosine at the nearest integer argument.  The peak absolute
+ * error with this option is 3.8e-5.  Relative error at small
+ * angles is about 1e-5.
+ *
+ * If flg = 0, then the approximation polynomials are computed
+ * and applied.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Relative speed comparisons follow for 6MHz IBM AT clone
+ * and Microsoft C version 4.0.  These figures include
+ * software overhead of do loop and function calls.
+ * Since system hardware and software vary widely, the
+ * numbers should be taken as representative only.
+ *
+ *			flg=0	flg=0	flg=1	flg=1
+ *			ACC11	ACC5	LINTERP	Lookup only
+ * In-line 8087 (/FPi)
+ * sin(), cos()		1.0	1.0	1.0	1.0
+ *
+ * In-line 8087 (/FPi)
+ * sincos()		1.1	1.4	1.9	3.0
+ *
+ * Software (/FPa)
+ * sin(), cos()		0.19	0.19	0.19	0.19
+ *
+ * Software (/FPa)
+ * sincos()		0.39	0.50	0.73	1.7
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * The accurate approximations are designed with a relative error
+ * criterion.  The absolute error is greatest at x = 0.5 degree.
+ * It decreases from a local maximum at i+0.5 degrees to full
+ * machine precision at each integer i degrees.  With the
+ * ACC5 option, the relative error of 6.3e-6 is equivalent to
+ * an absolute angular error of 0.01 arc second in the argument
+ * at x = i+0.5 degrees.  For small angles < 0.5 deg, the ACC5
+ * accuracy is 6.3e-6 (.00063%) of reading; i.e., the absolute
+ * error decreases in proportion to the argument.  This is true
+ * for both the sine and cosine approximations, since the latter
+ * is for the function 1 - cos(x).
+ *
+ * If absolute error is of most concern, use the compile time
+ * option ABSERR to obtain an absolute error of 2.7e-8 for ACC5
+ * precision.  This is about half the absolute error of the
+ * relative precision option.  In this case the relative error
+ * for small angles will increase to 9.5e-6 -- a reasonable
+ * tradeoff.
+ */
+
+/*							sindg.c
+ *
+ *	Circular sine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sindg();
+ *
+ * y = sindg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ *      x  +  x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ *      1  -  x**2 P(x**2).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC       +-1000        3100      3.3e-17      9.0e-18
+ *    IEEE      +-1000       30000      2.3e-16      5.6e-17
+ * 
+ * ERROR MESSAGES:
+ *
+ *   message           condition        value returned
+ * sindg total loss   x > 8.0e14 (DEC)      0.0
+ *                    x > 1.0e14 (IEEE)
+ *
+ */
+/*							cosdg.c
+ *
+ *	Circular cosine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cosdg();
+ *
+ * y = cosdg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ *      1  -  x**2 P(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ *      x  +  x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC      +-1000         3400       3.5e-17     9.1e-18
+ *    IEEE     +-1000        30000       2.1e-16     5.7e-17
+ *  See also sin().
+ *
+ */
+
+/*							sinh.c
+ *
+ *	Hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sinh();
+ *
+ * y = sinh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic sine of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * The range is partitioned into two segments.  If |x| <= 1, a
+ * rational function of the form x + x**3 P(x)/Q(x) is employed.
+ * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      +- 88        50000       4.0e-17     7.7e-18
+ *    IEEE     +-MAXLOG     30000       2.6e-16     5.7e-17
+ *
+ */
+
+/*							spence.c
+ *
+ *	Dilogarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, spence();
+ *
+ * y = spence( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral
+ *
+ *                    x
+ *                    -
+ *                   | | log t
+ * spence(x)  =  -   |   ----- dt
+ *                 | |   t - 1
+ *                  -
+ *                  1
+ *
+ * for x >= 0.  A rational approximation gives the integral in
+ * the interval (0.5, 1.5).  Transformation formulas for 1/x
+ * and 1-x are employed outside the basic expansion range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,4         30000       3.9e-15     5.4e-16
+ *    DEC       0,4          3000       2.5e-16     4.5e-17
+ *
+ *
+ */
+
+/*							sqrt.c
+ *
+ *	Square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sqrt();
+ *
+ * y = sqrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the square root of x.
+ *
+ * Range reduction involves isolating the power of two of the
+ * argument and using a polynomial approximation to obtain
+ * a rough value for the square root.  Then Heron's iteration
+ * is used three times to converge to an accurate value.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 10       60000       2.1e-17     7.9e-18
+ *    IEEE      0,1.7e308   30000       1.7e-16     6.3e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * sqrt domain        x < 0            0.0
+ *
+ */
+
+/*							stdtr.c
+ *
+ *	Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double t, stdtr();
+ * short k;
+ *
+ * y = stdtr( k, t );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral from minus infinity to t of the Student
+ * t distribution with integer k > 0 degrees of freedom:
+ *
+ *                                      t
+ *                                      -
+ *                                     | |
+ *              -                      |         2   -(k+1)/2
+ *             | ( (k+1)/2 )           |  (     x   )
+ *       ----------------------        |  ( 1 + --- )        dx
+ *                     -               |  (      k  )
+ *       sqrt( k pi ) | ( k/2 )        |
+ *                                   | |
+ *                                    -
+ *                                   -inf.
+ * 
+ * Relation to incomplete beta integral:
+ *
+ *        1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
+ * where
+ *        z = k/(k + t**2).
+ *
+ * For t < -2, this is the method of computation.  For higher t,
+ * a direct method is derived from integration by parts.
+ * Since the function is symmetric about t=0, the area under the
+ * right tail of the density is found by calling the function
+ * with -t instead of t.
+ * 
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 25.  The "domain" refers to t.
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -100,-2      50000       5.9e-15     1.4e-15
+ *    IEEE     -2,100      500000       2.7e-15     4.9e-17
+ */
+
+/*							stdtri.c
+ *
+ *	Functional inverse of Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double p, t, stdtri();
+ * int k;
+ *
+ * t = stdtri( k, p );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given probability p, finds the argument t such that stdtr(k,t)
+ * is equal to p.
+ * 
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 100.  The "domain" refers to p:
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE    .001,.999     25000       5.7e-15     8.0e-16
+ *    IEEE    10^-6,.001    25000       2.0e-12     2.9e-14
+ */
+
+/*							struve.c
+ *
+ *      Struve function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, struve();
+ *
+ * y = struve( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the Struve function Hv(x) of order v, argument x.
+ * Negative x is rejected unless v is an integer.
+ *
+ * This module also contains the hypergeometric functions 1F2
+ * and 3F0 and a routine for the Bessel function Yv(x) with
+ * noninteger v.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Not accurately characterized, but spot checked against tables.
+ *
+ */
+
+/*							tan.c
+ *
+ *	Circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tan();
+ *
+ * y = tan( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4.  A rational function
+ *       x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      +-1.07e9      44000      4.1e-17     1.0e-17
+ *    IEEE     +-1.07e9      30000      2.9e-16     8.1e-17
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition          value returned
+ * tan total loss   x > 1.073741824e9     0.0
+ *
+ */
+/*							cot.c
+ *
+ *	Circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cot();
+ *
+ * y = cot( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4.  A rational function
+ *       x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     +-1.07e9      30000      2.9e-16     8.2e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition          value returned
+ * cot total loss   x > 1.073741824e9       0.0
+ * cot singularity  x = 0                  INFINITY
+ *
+ */
+
+/*							tandg.c
+ *
+ *	Circular tangent of argument in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tandg();
+ *
+ * y = tandg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the argument x in degrees.
+ *
+ * Range reduction is modulo pi/4.  A rational function
+ *       x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      0,10          8000      3.4e-17      1.2e-17
+ *    IEEE     0,10         30000      3.2e-16      8.4e-17
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition          value returned
+ * tandg total loss   x > 8.0e14 (DEC)      0.0
+ *                    x > 1.0e14 (IEEE)
+ * tandg singularity  x = 180 k  +  90     MAXNUM
+ */
+/*							cotdg.c
+ *
+ *	Circular cotangent of argument in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cotdg();
+ *
+ * y = cotdg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the argument x in degrees.
+ *
+ * Range reduction is modulo pi/4.  A rational function
+ *       x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition          value returned
+ * cotdg total loss   x > 8.0e14 (DEC)      0.0
+ *                    x > 1.0e14 (IEEE)
+ * cotdg singularity  x = 180 k            MAXNUM
+ */
+
+/*							tanh.c
+ *
+ *	Hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tanh();
+ *
+ * y = tanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic tangent of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * A rational function is used for |x| < 0.625.  The form
+ * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
+ * Otherwise,
+ *    tanh(x) = sinh(x)/cosh(x) = 1  -  2/(exp(2x) + 1).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -2,2        50000       3.3e-17     6.4e-18
+ *    IEEE      -2,2        30000       2.5e-16     5.8e-17
+ *
+ */
+
+/*							unity.c
+ *
+ * Relative error approximations for function arguments near
+ * unity.
+ *
+ *    log1p(x) = log(1+x)
+ *    expm1(x) = exp(x) - 1
+ *    cosm1(x) = cos(x) - 1
+ *
+ */
+
+/*							yn.c
+ *
+ *	Bessel function of second kind of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, yn();
+ * int n;
+ *
+ * y = yn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The function is evaluated by forward recurrence on
+ * n, starting with values computed by the routines
+ * y0() and y1().
+ *
+ * If n = 0 or 1 the routine for y0 or y1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ *                      Absolute error, except relative
+ *                      when y > 1:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        2200       2.9e-16     5.3e-17
+ *    IEEE      0, 30       30000       3.4e-15     4.3e-16
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * yn singularity   x = 0              MAXNUM
+ * yn overflow                         MAXNUM
+ *
+ * Spot checked against tables for x, n between 0 and 100.
+ *
+ */
+
+/*							zeta.c
+ *
+ *	Riemann zeta function of two arguments
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, q, y, zeta();
+ *
+ * y = zeta( x, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ *                 inf.
+ *                  -        -x
+ *   zeta(x,q)  =   >   (k+q)  
+ *                  -
+ *                 k=0
+ *
+ * where x > 1 and q is not a negative integer or zero.
+ * The Euler-Maclaurin summation formula is used to obtain
+ * the expansion
+ *
+ *                n         
+ *                -       -x
+ * zeta(x,q)  =   >  (k+q)  
+ *                -         
+ *               k=1        
+ *
+ *           1-x                 inf.  B   x(x+1)...(x+2j)
+ *      (n+q)           1         -     2j
+ *  +  ---------  -  -------  +   >    --------------------
+ *        x-1              x      -                   x+2j+1
+ *                   2(n+q)      j=1       (2j)! (n+q)
+ *
+ * where the B2j are Bernoulli numbers.  Note that (see zetac.c)
+ * zeta(x,1) = zetac(x) + 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ *
+ * REFERENCE:
+ *
+ * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
+ * Series, and Products, p. 1073; Academic Press, 1980.
+ *
+ */
+
+ /*							zetac.c
+ *
+ *	Riemann zeta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, zetac();
+ *
+ * y = zetac( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ *                inf.
+ *                 -    -x
+ *   zetac(x)  =   >   k   ,   x > 1,
+ *                 -
+ *                k=2
+ *
+ * is related to the Riemann zeta function by
+ *
+ *	Riemann zeta(x) = zetac(x) + 1.
+ *
+ * Extension of the function definition for x < 1 is implemented.
+ * Zero is returned for x > log2(MAXNUM).
+ *
+ * An overflow error may occur for large negative x, due to the
+ * gamma function in the reflection formula.
+ *
+ * ACCURACY:
+ *
+ * Tabulated values have full machine accuracy.
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      1,50        10000       9.8e-16	    1.3e-16
+ *    DEC       1,50         2000       1.1e-16     1.9e-17
+ *
+ *
+ */

libm/double/acosh.c

@@ -0,0 +1,167 @@
+/*							acosh.c
+ *
+ *	Inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acosh();
+ *
+ * y = acosh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a rational approximation
+ *
+ *	sqrt(z) * P(z)/Q(z)
+ *
+ * where z = x-1, is used.  Otherwise,
+ *
+ * acosh(x)  =  log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       1,3         30000       4.2e-17     1.1e-17
+ *    IEEE      1,3         30000       4.6e-16     8.7e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * acosh domain       |x| < 1            NAN
+ *
+ */
+
+/*							acosh.c	*/
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+/* acosh(z) = sqrt(x) * R(x), z = x + 1, interval 0 < x < 0.5 */
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+ 1.18801130533544501356E2,
+ 3.94726656571334401102E3,
+ 3.43989375926195455866E4,
+ 1.08102874834699867335E5,
+ 1.10855947270161294369E5
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.86145380837903397292E2,
+ 4.15352677227719831579E3,
+ 2.97683430363289370382E4,
+ 8.29725251988426222434E4,
+ 7.83869920495893927727E4
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0041755,0115055,0144002,0146444,
+0043166,0132103,0155150,0150302,
+0044006,0057360,0003021,0162753,
+0044323,0021557,0175225,0056253,
+0044330,0101771,0040046,0006636
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0042072,0022467,0126670,0041232,
+0043201,0146066,0152142,0034015,
+0043750,0110257,0121165,0026100,
+0044242,0007103,0034667,0033173,
+0044231,0014576,0175573,0017472
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x59a4,0xb900,0xb345,0x405d,
+0x1a18,0x7b4d,0xd688,0x40ae,
+0x3cbd,0x00c2,0xcbde,0x40e0,
+0xab95,0xff52,0x646d,0x40fa,
+0xc1b4,0x2804,0x107f,0x40fb
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x0853,0xf5b7,0x44a6,0x4067,
+0x4702,0xda8c,0x3986,0x40b0,
+0xa588,0xf44e,0x1215,0x40dd,
+0xe6cf,0x6736,0x41c8,0x40f4,
+0x63e7,0xdf6f,0x232f,0x40f3
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x405d,0xb345,0xb900,0x59a4,
+0x40ae,0xd688,0x7b4d,0x1a18,
+0x40e0,0xcbde,0x00c2,0x3cbd,
+0x40fa,0x646d,0xff52,0xab95,
+0x40fb,0x107f,0x2804,0xc1b4
+};
+static unsigned short Q[] = {
+0x4067,0x44a6,0xf5b7,0x0853,
+0x40b0,0x3986,0xda8c,0x4702,
+0x40dd,0x1215,0xf44e,0xa588,
+0x40f4,0x41c8,0x6736,0xe6cf,
+0x40f3,0x232f,0xdf6f,0x63e7,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double log(), sqrt(), polevl(), p1evl();
+#endif
+extern double LOGE2, INFINITY, NAN;
+
+double acosh(x)
+double x;
+{
+double a, z;
+
+if( x < 1.0 )
+	{
+	mtherr( "acosh", DOMAIN );
+	return(NAN);
+	}
+
+if( x > 1.0e8 )
+	{
+#ifdef INFINITIES
+	if( x == INFINITY )
+		return( INFINITY );
+#endif
+	return( log(x) + LOGE2 );
+	}
+
+z = x - 1.0;
+
+if( z < 0.5 )
+	{
+	a = sqrt(z) * (polevl(z, P, 4) / p1evl(z, Q, 5) );
+	return( a );
+	}
+
+a = sqrt( z*(x+1.0) );
+return( log(x + a) );
+}

libm/double/airy.c

@@ -0,0 +1,965 @@
+/*							airy.c
+ *
+ *	Airy function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, ai, aip, bi, bip;
+ * int airy();
+ *
+ * airy( x, _&ai, _&aip, _&bi, _&bip );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Solution of the differential equation
+ *
+ *	y"(x) = xy.
+ *
+ * The function returns the two independent solutions Ai, Bi
+ * and their first derivatives Ai'(x), Bi'(x).
+ *
+ * Evaluation is by power series summation for small x,
+ * by rational minimax approximations for large x.
+ *
+ *
+ *
+ * ACCURACY:
+ * Error criterion is absolute when function <= 1, relative
+ * when function > 1, except * denotes relative error criterion.
+ * For large negative x, the absolute error increases as x^1.5.
+ * For large positive x, the relative error increases as x^1.5.
+ *
+ * Arithmetic  domain   function  # trials      peak         rms
+ * IEEE        -10, 0     Ai        10000       1.6e-15     2.7e-16
+ * IEEE          0, 10    Ai        10000       2.3e-14*    1.8e-15*
+ * IEEE        -10, 0     Ai'       10000       4.6e-15     7.6e-16
+ * IEEE          0, 10    Ai'       10000       1.8e-14*    1.5e-15*
+ * IEEE        -10, 10    Bi        30000       4.2e-15     5.3e-16
+ * IEEE        -10, 10    Bi'       30000       4.9e-15     7.3e-16
+ * DEC         -10, 0     Ai         5000       1.7e-16     2.8e-17
+ * DEC           0, 10    Ai         5000       2.1e-15*    1.7e-16*
+ * DEC         -10, 0     Ai'        5000       4.7e-16     7.8e-17
+ * DEC           0, 10    Ai'       12000       1.8e-15*    1.5e-16*
+ * DEC         -10, 10    Bi        10000       5.5e-16     6.8e-17
+ * DEC         -10, 10    Bi'        7000       5.3e-16     8.7e-17
+ *
+ */
+/*							airy.c */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+static double c1 = 0.35502805388781723926;
+static double c2 = 0.258819403792806798405;
+static double sqrt3 = 1.732050807568877293527;
+static double sqpii = 5.64189583547756286948E-1;
+extern double PI;
+
+extern double MAXNUM, MACHEP;
+#ifdef UNK
+#define MAXAIRY 25.77
+#endif
+#ifdef DEC
+#define MAXAIRY 25.77
+#endif
+#ifdef IBMPC
+#define MAXAIRY 103.892
+#endif
+#ifdef MIEEE
+#define MAXAIRY 103.892
+#endif
+
+
+#ifdef UNK
+static double AN[8] = {
+  3.46538101525629032477E-1,
+  1.20075952739645805542E1,
+  7.62796053615234516538E1,
+  1.68089224934630576269E2,
+  1.59756391350164413639E2,
+  7.05360906840444183113E1,
+  1.40264691163389668864E1,
+  9.99999999999999995305E-1,
+};
+static double AD[8] = {
+  5.67594532638770212846E-1,
+  1.47562562584847203173E1,
+  8.45138970141474626562E1,
+  1.77318088145400459522E2,
+  1.64234692871529701831E2,
+  7.14778400825575695274E1,
+  1.40959135607834029598E1,
+  1.00000000000000000470E0,
+};
+#endif
+#ifdef DEC
+static unsigned short AN[32] = {
+0037661,0066561,0024675,0131301,
+0041100,0017434,0034324,0101466,
+0041630,0107450,0067427,0007430,
+0042050,0013327,0071000,0034737,
+0042037,0140642,0156417,0167366,
+0041615,0011172,0075147,0051165,
+0041140,0066152,0160520,0075146,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short AD[32] = {
+0040021,0046740,0011422,0064606,
+0041154,0014640,0024631,0062450,
+0041651,0003435,0101152,0106401,
+0042061,0050556,0034605,0136602,
+0042044,0036024,0152377,0151414,
+0041616,0172247,0072216,0115374,
+0041141,0104334,0124154,0166007,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short AN[32] = {
+0xb658,0x2537,0x2dae,0x3fd6,
+0x9067,0x871a,0x03e3,0x4028,
+0xe1e3,0x0de2,0x11e5,0x4053,
+0x073c,0xee40,0x02da,0x4065,
+0xfddf,0x5ba1,0xf834,0x4063,
+0xea4f,0x4f4c,0xa24f,0x4051,
+0x0f4d,0x5c2a,0x0d8d,0x402c,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short AD[32] = {
+0x4d31,0x0262,0x29bc,0x3fe2,
+0x2ca5,0x0533,0x8334,0x402d,
+0x51a0,0xb04d,0x20e3,0x4055,
+0xb7b0,0xc730,0x2a2d,0x4066,
+0xfa61,0x9a9f,0x8782,0x4064,
+0xd35f,0xee91,0xde94,0x4051,
+0x9d81,0x950d,0x311b,0x402c,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short AN[32] = {
+0x3fd6,0x2dae,0x2537,0xb658,
+0x4028,0x03e3,0x871a,0x9067,
+0x4053,0x11e5,0x0de2,0xe1e3,
+0x4065,0x02da,0xee40,0x073c,
+0x4063,0xf834,0x5ba1,0xfddf,
+0x4051,0xa24f,0x4f4c,0xea4f,
+0x402c,0x0d8d,0x5c2a,0x0f4d,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short AD[32] = {
+0x3fe2,0x29bc,0x0262,0x4d31,
+0x402d,0x8334,0x0533,0x2ca5,
+0x4055,0x20e3,0xb04d,0x51a0,
+0x4066,0x2a2d,0xc730,0xb7b0,
+0x4064,0x8782,0x9a9f,0xfa61,
+0x4051,0xde94,0xee91,0xd35f,
+0x402c,0x311b,0x950d,0x9d81,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double APN[8] = {
+  6.13759184814035759225E-1,
+  1.47454670787755323881E1,
+  8.20584123476060982430E1,
+  1.71184781360976385540E2,
+  1.59317847137141783523E2,
+  6.99778599330103016170E1,
+  1.39470856980481566958E1,
+  1.00000000000000000550E0,
+};
+static double APD[8] = {
+  3.34203677749736953049E-1,
+  1.11810297306158156705E1,
+  7.11727352147859965283E1,
+  1.58778084372838313640E2,
+  1.53206427475809220834E2,
+  6.86752304592780337944E1,
+  1.38498634758259442477E1,
+  9.99999999999999994502E-1,
+};
+#endif
+#ifdef DEC
+static unsigned short APN[32] = {
+0040035,0017522,0065145,0054755,
+0041153,0166556,0161471,0057174,
+0041644,0016750,0034445,0046462,
+0042053,0027515,0152316,0046717,
+0042037,0050536,0067023,0023264,
+0041613,0172252,0007240,0131055,
+0041137,0023503,0052472,0002305,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short APD[32] = {
+0037653,0016276,0112106,0126625,
+0041062,0162577,0067111,0111761,
+0041616,0054160,0140004,0137455,
+0042036,0143460,0104626,0157206,
+0042031,0032330,0067131,0114260,
+0041611,0054667,0147207,0134564,
+0041135,0114412,0070653,0146015,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short APN[32] = {
+0xab3e,0x4d4c,0xa3ea,0x3fe3,
+0x2bcf,0xdc67,0x7dad,0x402d,
+0xa9a6,0x0724,0x83bd,0x4054,
+0xc9ba,0xba99,0x65e9,0x4065,
+0x64d7,0xcdc2,0xea2b,0x4063,
+0x1646,0x41d4,0x7e95,0x4051,
+0x4099,0x6aa7,0xe4e8,0x402b,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short APD[32] = {
+0xd5b3,0xd288,0x6397,0x3fd5,
+0x327e,0xedc9,0x5caf,0x4026,
+0x97e6,0x1800,0xcb0e,0x4051,
+0xdbd1,0x1132,0xd8e6,0x4063,
+0x3316,0x0dcb,0x269b,0x4063,
+0xf72f,0xf9d0,0x2b36,0x4051,
+0x7982,0x4e35,0xb321,0x402b,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short APN[32] = {
+0x3fe3,0xa3ea,0x4d4c,0xab3e,
+0x402d,0x7dad,0xdc67,0x2bcf,
+0x4054,0x83bd,0x0724,0xa9a6,
+0x4065,0x65e9,0xba99,0xc9ba,
+0x4063,0xea2b,0xcdc2,0x64d7,
+0x4051,0x7e95,0x41d4,0x1646,
+0x402b,0xe4e8,0x6aa7,0x4099,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short APD[32] = {
+0x3fd5,0x6397,0xd288,0xd5b3,
+0x4026,0x5caf,0xedc9,0x327e,
+0x4051,0xcb0e,0x1800,0x97e6,
+0x4063,0xd8e6,0x1132,0xdbd1,
+0x4063,0x269b,0x0dcb,0x3316,
+0x4051,0x2b36,0xf9d0,0xf72f,
+0x402b,0xb321,0x4e35,0x7982,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double BN16[5] = {
+-2.53240795869364152689E-1,
+ 5.75285167332467384228E-1,
+-3.29907036873225371650E-1,
+ 6.44404068948199951727E-2,
+-3.82519546641336734394E-3,
+};
+static double BD16[5] = {
+/* 1.00000000000000000000E0,*/
+-7.15685095054035237902E0,
+ 1.06039580715664694291E1,
+-5.23246636471251500874E0,
+ 9.57395864378383833152E-1,
+-5.50828147163549611107E-2,
+};
+#endif
+#ifdef DEC
+static unsigned short BN16[20] = {
+0137601,0124307,0010213,0035210,
+0040023,0042743,0101621,0016031,
+0137650,0164623,0036056,0074511,
+0037203,0174525,0000473,0142474,
+0136172,0130041,0066726,0064324,
+};
+static unsigned short BD16[20] = {
+/*0040200,0000000,0000000,0000000,*/
+0140745,0002354,0044335,0055276,
+0041051,0124717,0170130,0104013,
+0140647,0070135,0046473,0103501,
+0040165,0013745,0033324,0127766,
+0137141,0117204,0076164,0033107,
+};
+#endif
+#ifdef IBMPC
+static unsigned short BN16[20] = {
+0x6751,0xe211,0x3518,0xbfd0,
+0x2383,0x7072,0x68bc,0x3fe2,
+0xcf29,0x6785,0x1d32,0xbfd5,
+0x78a8,0xa027,0x7f2a,0x3fb0,
+0xcd1b,0x2dba,0x5604,0xbf6f,
+};
+static unsigned short BD16[20] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xab58,0x891b,0xa09d,0xc01c,
+0x1101,0xfe0b,0x3539,0x4025,
+0x70e8,0xa9a7,0xee0b,0xc014,
+0x95ff,0xa6da,0xa2fc,0x3fee,
+0x86c9,0x8f8e,0x33d0,0xbfac,
+};
+#endif
+#ifdef MIEEE
+static unsigned short BN16[20] = {
+0xbfd0,0x3518,0xe211,0x6751,
+0x3fe2,0x68bc,0x7072,0x2383,
+0xbfd5,0x1d32,0x6785,0xcf29,
+0x3fb0,0x7f2a,0xa027,0x78a8,
+0xbf6f,0x5604,0x2dba,0xcd1b,
+};
+static unsigned short BD16[20] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc01c,0xa09d,0x891b,0xab58,
+0x4025,0x3539,0xfe0b,0x1101,
+0xc014,0xee0b,0xa9a7,0x70e8,
+0x3fee,0xa2fc,0xa6da,0x95ff,
+0xbfac,0x33d0,0x8f8e,0x86c9,
+};
+#endif
+
+#ifdef UNK
+static double BPPN[5] = {
+ 4.65461162774651610328E-1,
+-1.08992173800493920734E0,
+ 6.38800117371827987759E-1,
+-1.26844349553102907034E-1,
+ 7.62487844342109852105E-3,
+};
+static double BPPD[5] = {
+/* 1.00000000000000000000E0,*/
+-8.70622787633159124240E0,
+ 1.38993162704553213172E1,
+-7.14116144616431159572E0,
+ 1.34008595960680518666E0,
+-7.84273211323341930448E-2,
+};
+#endif
+#ifdef DEC
+static unsigned short BPPN[20] = {
+0037756,0050354,0167531,0135731,
+0140213,0101216,0032767,0020375,
+0040043,0104147,0106312,0177632,
+0137401,0161574,0032015,0043714,
+0036371,0155035,0143165,0142262,
+};
+static unsigned short BPPD[20] = {
+/*0040200,0000000,0000000,0000000,*/
+0141013,0046265,0115005,0161053,
+0041136,0061631,0072445,0156131,
+0140744,0102145,0001127,0065304,
+0040253,0103757,0146453,0102513,
+0137240,0117200,0155402,0113500,
+};
+#endif
+#ifdef IBMPC
+static unsigned short BPPN[20] = {
+0x377b,0x9deb,0xca1d,0x3fdd,
+0xe420,0xc6be,0x7051,0xbff1,
+0x5ff3,0xf199,0x710c,0x3fe4,
+0xa8fa,0x8681,0x3c6f,0xbfc0,
+0xb896,0xb8ce,0x3b43,0x3f7f,
+};
+static unsigned short BPPD[20] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xbc45,0xb340,0x6996,0xc021,
+0xbb8b,0x2ea4,0xcc73,0x402b,
+0xed59,0xa04a,0x908c,0xc01c,
+0x70a9,0xf9a5,0x70fd,0x3ff5,
+0x52e8,0x1b60,0x13d0,0xbfb4,
+};
+#endif
+#ifdef MIEEE
+static unsigned short BPPN[20] = {
+0x3fdd,0xca1d,0x9deb,0x377b,
+0xbff1,0x7051,0xc6be,0xe420,
+0x3fe4,0x710c,0xf199,0x5ff3,
+0xbfc0,0x3c6f,0x8681,0xa8fa,
+0x3f7f,0x3b43,0xb8ce,0xb896,
+};
+static unsigned short BPPD[20] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc021,0x6996,0xb340,0xbc45,
+0x402b,0xcc73,0x2ea4,0xbb8b,
+0xc01c,0x908c,0xa04a,0xed59,
+0x3ff5,0x70fd,0xf9a5,0x70a9,
+0xbfb4,0x13d0,0x1b60,0x52e8,
+};
+#endif
+
+#ifdef UNK
+static double AFN[9] = {
+-1.31696323418331795333E-1,
+-6.26456544431912369773E-1,
+-6.93158036036933542233E-1,
+-2.79779981545119124951E-1,
+-4.91900132609500318020E-2,
+-4.06265923594885404393E-3,
+-1.59276496239262096340E-4,
+-2.77649108155232920844E-6,
+-1.67787698489114633780E-8,
+};
+static double AFD[9] = {
+/* 1.00000000000000000000E0,*/
+ 1.33560420706553243746E1,
+ 3.26825032795224613948E1,
+ 2.67367040941499554804E1,
+ 9.18707402907259625840E0,
+ 1.47529146771666414581E0,
+ 1.15687173795188044134E-1,
+ 4.40291641615211203805E-3,
+ 7.54720348287414296618E-5,
+ 4.51850092970580378464E-7,
+};
+#endif
+#ifdef DEC
+static unsigned short AFN[36] = {
+0137406,0155546,0124127,0033732,
+0140040,0057564,0141263,0041222,
+0140061,0071316,0013674,0175754,
+0137617,0037522,0056637,0120130,
+0137111,0075567,0121755,0166122,
+0136205,0020016,0043317,0002201,
+0135047,0001565,0075130,0002334,
+0133472,0051700,0165021,0131551,
+0131620,0020347,0132165,0013215,
+};
+static unsigned short AFD[36] = {
+/*0040200,0000000,0000000,0000000,*/
+0041125,0131131,0025627,0067623,
+0041402,0135342,0021703,0154315,
+0041325,0162305,0016671,0120175,
+0041022,0177101,0053114,0141632,
+0040274,0153131,0147364,0114306,
+0037354,0166545,0120042,0150530,
+0036220,0043127,0000727,0130273,
+0034636,0043275,0075667,0034733,
+0032762,0112715,0146250,0142474,
+};
+#endif
+#ifdef IBMPC
+static unsigned short AFN[36] = {
+0xe6fb,0xd50a,0xdb6c,0xbfc0,
+0x6852,0x9856,0x0bee,0xbfe4,
+0x9f7d,0xc2f7,0x2e59,0xbfe6,
+0xf40b,0x4bb3,0xe7ea,0xbfd1,
+0xbd8a,0xf47d,0x2f6e,0xbfa9,
+0xe090,0xc8d9,0xa401,0xbf70,
+0x009c,0xaf4b,0xe06e,0xbf24,
+0x366d,0x1d42,0x4a78,0xbec7,
+0xa2d2,0xf68e,0x041c,0xbe52,
+};
+static unsigned short AFD[36] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xedf2,0x2572,0xb64b,0x402a,
+0x7b1a,0x4478,0x575c,0x4040,
+0x3410,0xa3b7,0xbc98,0x403a,
+0x9873,0x2ac9,0x5fc8,0x4022,
+0x9319,0x39de,0x9acb,0x3ff7,
+0x5a2b,0xb404,0x9dac,0x3fbd,
+0xf617,0xe03a,0x08ca,0x3f72,
+0xe73b,0xaf76,0xc8d7,0x3f13,
+0x18a7,0xb995,0x52b9,0x3e9e,
+};
+#endif
+#ifdef MIEEE
+static unsigned short AFN[36] = {
+0xbfc0,0xdb6c,0xd50a,0xe6fb,
+0xbfe4,0x0bee,0x9856,0x6852,
+0xbfe6,0x2e59,0xc2f7,0x9f7d,
+0xbfd1,0xe7ea,0x4bb3,0xf40b,
+0xbfa9,0x2f6e,0xf47d,0xbd8a,
+0xbf70,0xa401,0xc8d9,0xe090,
+0xbf24,0xe06e,0xaf4b,0x009c,
+0xbec7,0x4a78,0x1d42,0x366d,
+0xbe52,0x041c,0xf68e,0xa2d2,
+};
+static unsigned short AFD[36] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x402a,0xb64b,0x2572,0xedf2,
+0x4040,0x575c,0x4478,0x7b1a,
+0x403a,0xbc98,0xa3b7,0x3410,
+0x4022,0x5fc8,0x2ac9,0x9873,
+0x3ff7,0x9acb,0x39de,0x9319,
+0x3fbd,0x9dac,0xb404,0x5a2b,
+0x3f72,0x08ca,0xe03a,0xf617,
+0x3f13,0xc8d7,0xaf76,0xe73b,
+0x3e9e,0x52b9,0xb995,0x18a7,
+};
+#endif
+
+#ifdef UNK
+static double AGN[11] = {
+  1.97339932091685679179E-2,
+  3.91103029615688277255E-1,
+  1.06579897599595591108E0,
+  9.39169229816650230044E-1,
+  3.51465656105547619242E-1,
+  6.33888919628925490927E-2,
+  5.85804113048388458567E-3,
+  2.82851600836737019778E-4,
+  6.98793669997260967291E-6,
+  8.11789239554389293311E-8,
+  3.41551784765923618484E-10,
+};
+static double AGD[10] = {
+/*  1.00000000000000000000E0,*/
+  9.30892908077441974853E0,
+  1.98352928718312140417E1,
+  1.55646628932864612953E1,
+  5.47686069422975497931E0,
+  9.54293611618961883998E-1,
+  8.64580826352392193095E-2,
+  4.12656523824222607191E-3,
+  1.01259085116509135510E-4,
+  1.17166733214413521882E-6,
+  4.91834570062930015649E-9,
+};
+#endif
+#ifdef DEC
+static unsigned short AGN[44] = {
+0036641,0124456,0167175,0157354,
+0037710,0037250,0001441,0136671,
+0040210,0066031,0150401,0123532,
+0040160,0066545,0003570,0153133,
+0037663,0171516,0072507,0170345,
+0037201,0151011,0007510,0045702,
+0036277,0172317,0104572,0101030,
+0035224,0045663,0000160,0136422,
+0033752,0074753,0047702,0135160,
+0032256,0052225,0156550,0107103,
+0030273,0142443,0166277,0071720,
+};
+static unsigned short AGD[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0041024,0170537,0117253,0055003,
+0041236,0127256,0003570,0143240,
+0041171,0004333,0172476,0160645,
+0040657,0041161,0055716,0157161,
+0040164,0046226,0006257,0063431,
+0037261,0010357,0065445,0047563,
+0036207,0034043,0057434,0116732,
+0034724,0055416,0130035,0026377,
+0033235,0041056,0154071,0023502,
+0031250,0177071,0167254,0047242,
+};
+#endif
+#ifdef IBMPC
+static unsigned short AGN[44] = {
+0xbbde,0xddcf,0x3525,0x3f94,
+0x37b7,0x0064,0x07d5,0x3fd9,
+0x34eb,0x3a20,0x0d83,0x3ff1,
+0x1acb,0xa0ef,0x0dac,0x3fee,
+0xfe1d,0xcea8,0x7e69,0x3fd6,
+0x0978,0x21e9,0x3a41,0x3fb0,
+0x5043,0xf12f,0xfe99,0x3f77,
+0x17a2,0x600e,0x8976,0x3f32,
+0x574e,0x69f8,0x4f3d,0x3edd,
+0x11c8,0xbbad,0xca92,0x3e75,
+0xee7a,0x7d97,0x78a4,0x3df7,
+};
+static unsigned short AGD[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6b40,0xf3d5,0x9e2b,0x4022,
+0x18d4,0xc0ef,0xd5d5,0x4033,
+0xdc35,0x7ea7,0x211b,0x402f,
+0xdbce,0x2b79,0xe84e,0x4015,
+0xece3,0xc195,0x8992,0x3fee,
+0xa9ee,0xed64,0x221d,0x3fb6,
+0x93bb,0x6be3,0xe704,0x3f70,
+0xa5a0,0xd603,0x8b61,0x3f1a,
+0x24e8,0xdb07,0xa845,0x3eb3,
+0x89d4,0x3dd5,0x1fc7,0x3e35,
+};
+#endif
+#ifdef MIEEE
+static unsigned short AGN[44] = {
+0x3f94,0x3525,0xddcf,0xbbde,
+0x3fd9,0x07d5,0x0064,0x37b7,
+0x3ff1,0x0d83,0x3a20,0x34eb,
+0x3fee,0x0dac,0xa0ef,0x1acb,
+0x3fd6,0x7e69,0xcea8,0xfe1d,
+0x3fb0,0x3a41,0x21e9,0x0978,
+0x3f77,0xfe99,0xf12f,0x5043,
+0x3f32,0x8976,0x600e,0x17a2,
+0x3edd,0x4f3d,0x69f8,0x574e,
+0x3e75,0xca92,0xbbad,0x11c8,
+0x3df7,0x78a4,0x7d97,0xee7a,
+};
+static unsigned short AGD[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4022,0x9e2b,0xf3d5,0x6b40,
+0x4033,0xd5d5,0xc0ef,0x18d4,
+0x402f,0x211b,0x7ea7,0xdc35,
+0x4015,0xe84e,0x2b79,0xdbce,
+0x3fee,0x8992,0xc195,0xece3,
+0x3fb6,0x221d,0xed64,0xa9ee,
+0x3f70,0xe704,0x6be3,0x93bb,
+0x3f1a,0x8b61,0xd603,0xa5a0,
+0x3eb3,0xa845,0xdb07,0x24e8,
+0x3e35,0x1fc7,0x3dd5,0x89d4,
+};
+#endif
+
+#ifdef UNK
+static double APFN[9] = {
+  1.85365624022535566142E-1,
+  8.86712188052584095637E-1,
+  9.87391981747398547272E-1,
+  4.01241082318003734092E-1,
+  7.10304926289631174579E-2,
+  5.90618657995661810071E-3,
+  2.33051409401776799569E-4,
+  4.08718778289035454598E-6,
+  2.48379932900442457853E-8,
+};
+static double APFD[9] = {
+/*  1.00000000000000000000E0,*/
+  1.47345854687502542552E1,
+  3.75423933435489594466E1,
+  3.14657751203046424330E1,
+  1.09969125207298778536E1,
+  1.78885054766999417817E0,
+  1.41733275753662636873E-1,
+  5.44066067017226003627E-3,
+  9.39421290654511171663E-5,
+  5.65978713036027009243E-7,
+};
+#endif
+#ifdef DEC
+static unsigned short APFN[36] = {
+0037475,0150174,0071752,0166651,
+0040142,0177621,0164246,0101757,
+0040174,0142670,0106760,0006573,
+0037715,0067570,0116274,0022404,
+0037221,0074157,0053341,0117207,
+0036301,0104257,0015075,0004777,
+0035164,0057502,0164034,0001313,
+0033611,0022254,0176000,0112565,
+0031725,0055523,0025153,0166057,
+};
+static unsigned short APFD[36] = {
+/*0040200,0000000,0000000,0000000,*/
+0041153,0140334,0130506,0061402,
+0041426,0025551,0024440,0070611,
+0041373,0134750,0047147,0176702,
+0041057,0171532,0105430,0017674,
+0040344,0174416,0001726,0047754,
+0037421,0021207,0020167,0136264,
+0036262,0043621,0151321,0124324,
+0034705,0001313,0163733,0016407,
+0033027,0166702,0150440,0170561,
+};
+#endif
+#ifdef IBMPC
+static unsigned short APFN[36] = {
+0x5db5,0x8e7d,0xba0f,0x3fc7,
+0xd07e,0x3d14,0x5ff2,0x3fec,
+0x01af,0x11be,0x98b7,0x3fef,
+0x84a1,0x1397,0xadef,0x3fd9,
+0x33d1,0xeadc,0x2f0d,0x3fb2,
+0xa140,0xe347,0x3115,0x3f78,
+0x8059,0x5d03,0x8be8,0x3f2e,
+0x12af,0x9f80,0x2495,0x3ed1,
+0x7d86,0x654d,0xab6a,0x3e5a,
+};
+static unsigned short APFD[36] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xcc60,0x9628,0x781b,0x402d,
+0x0e31,0x2524,0xc56d,0x4042,
+0xffb8,0x09cc,0x773d,0x403f,
+0x03f7,0x5163,0xfe6b,0x4025,
+0xc9fd,0xc07a,0x9f21,0x3ffc,
+0xf796,0xe40e,0x2450,0x3fc2,
+0x351a,0x3a5a,0x48f2,0x3f76,
+0x63a1,0x7cfb,0xa059,0x3f18,
+0x1e2e,0x5a24,0xfdb8,0x3ea2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short APFN[36] = {
+0x3fc7,0xba0f,0x8e7d,0x5db5,
+0x3fec,0x5ff2,0x3d14,0xd07e,
+0x3fef,0x98b7,0x11be,0x01af,
+0x3fd9,0xadef,0x1397,0x84a1,
+0x3fb2,0x2f0d,0xeadc,0x33d1,
+0x3f78,0x3115,0xe347,0xa140,
+0x3f2e,0x8be8,0x5d03,0x8059,
+0x3ed1,0x2495,0x9f80,0x12af,
+0x3e5a,0xab6a,0x654d,0x7d86,
+};
+static unsigned short APFD[36] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x402d,0x781b,0x9628,0xcc60,
+0x4042,0xc56d,0x2524,0x0e31,
+0x403f,0x773d,0x09cc,0xffb8,
+0x4025,0xfe6b,0x5163,0x03f7,
+0x3ffc,0x9f21,0xc07a,0xc9fd,
+0x3fc2,0x2450,0xe40e,0xf796,
+0x3f76,0x48f2,0x3a5a,0x351a,
+0x3f18,0xa059,0x7cfb,0x63a1,
+0x3ea2,0xfdb8,0x5a24,0x1e2e,
+};
+#endif
+
+#ifdef UNK
+static double APGN[11] = {
+-3.55615429033082288335E-2,
+-6.37311518129435504426E-1,
+-1.70856738884312371053E0,
+-1.50221872117316635393E0,
+-5.63606665822102676611E-1,
+-1.02101031120216891789E-1,
+-9.48396695961445269093E-3,
+-4.60325307486780994357E-4,
+-1.14300836484517375919E-5,
+-1.33415518685547420648E-7,
+-5.63803833958893494476E-10,
+};
+static double APGD[11] = {
+/*  1.00000000000000000000E0,*/
+  9.85865801696130355144E0,
+  2.16401867356585941885E1,
+  1.73130776389749389525E1,
+  6.17872175280828766327E0,
+  1.08848694396321495475E0,
+  9.95005543440888479402E-2,
+  4.78468199683886610842E-3,
+  1.18159633322838625562E-4,
+  1.37480673554219441465E-6,
+  5.79912514929147598821E-9,
+};
+#endif
+#ifdef DEC
+static unsigned short APGN[44] = {
+0137021,0124372,0176075,0075331,
+0140043,0023330,0177672,0161655,
+0140332,0131126,0010413,0171112,
+0140300,0044263,0175560,0054070,
+0140020,0044206,0142603,0073324,
+0137321,0015130,0066144,0144033,
+0136433,0061243,0175542,0103373,
+0135361,0053721,0020441,0053203,
+0134077,0141725,0160277,0130612,
+0132417,0040372,0100363,0060200,
+0130432,0175052,0171064,0034147,
+};
+static unsigned short APGD[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0041035,0136420,0030124,0140220,
+0041255,0017432,0034447,0162256,
+0041212,0100456,0154544,0006321,
+0040705,0134026,0127154,0123414,
+0040213,0051612,0044470,0172607,
+0037313,0143362,0053273,0157051,
+0036234,0144322,0054536,0007264,
+0034767,0146170,0054265,0170342,
+0033270,0102777,0167362,0073631,
+0031307,0040644,0167103,0021763,
+};
+#endif
+#ifdef IBMPC
+static unsigned short APGN[44] = {
+0xaf5b,0x5f87,0x351f,0xbfa2,
+0x5c76,0x1ff7,0x64db,0xbfe4,
+0x7e49,0xc221,0x564a,0xbffb,
+0x0b07,0x7f6e,0x0916,0xbff8,
+0x6edb,0xd8b0,0x0910,0xbfe2,
+0x9903,0x0d8c,0x234b,0xbfba,
+0x50df,0x7f6c,0x6c54,0xbf83,
+0x2ad0,0x2424,0x2afa,0xbf3e,
+0xf631,0xbc17,0xf87a,0xbee7,
+0x6c10,0x501e,0xe81f,0xbe81,
+0x870d,0x5e46,0x5f45,0xbe03,
+};
+static unsigned short APGD[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x9812,0x060a,0xb7a2,0x4023,
+0xfc96,0x4724,0xa3e3,0x4035,
+0x819a,0xdb2c,0x5025,0x4031,
+0x94e2,0xd5cd,0xb702,0x4018,
+0x1eb1,0x4927,0x6a71,0x3ff1,
+0x7bc5,0x4ad7,0x78de,0x3fb9,
+0xc1d7,0x4b2b,0x991a,0x3f73,
+0xbe1c,0x0b16,0xf98f,0x3f1e,
+0x4ef3,0xfdde,0x10bf,0x3eb7,
+0x647e,0x9dc8,0xe834,0x3e38,
+};
+#endif
+#ifdef MIEEE
+static unsigned short APGN[44] = {
+0xbfa2,0x351f,0x5f87,0xaf5b,
+0xbfe4,0x64db,0x1ff7,0x5c76,
+0xbffb,0x564a,0xc221,0x7e49,
+0xbff8,0x0916,0x7f6e,0x0b07,
+0xbfe2,0x0910,0xd8b0,0x6edb,
+0xbfba,0x234b,0x0d8c,0x9903,
+0xbf83,0x6c54,0x7f6c,0x50df,
+0xbf3e,0x2afa,0x2424,0x2ad0,
+0xbee7,0xf87a,0xbc17,0xf631,
+0xbe81,0xe81f,0x501e,0x6c10,
+0xbe03,0x5f45,0x5e46,0x870d,
+};
+static unsigned short APGD[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4023,0xb7a2,0x060a,0x9812,
+0x4035,0xa3e3,0x4724,0xfc96,
+0x4031,0x5025,0xdb2c,0x819a,
+0x4018,0xb702,0xd5cd,0x94e2,
+0x3ff1,0x6a71,0x4927,0x1eb1,
+0x3fb9,0x78de,0x4ad7,0x7bc5,
+0x3f73,0x991a,0x4b2b,0xc1d7,
+0x3f1e,0xf98f,0x0b16,0xbe1c,
+0x3eb7,0x10bf,0xfdde,0x4ef3,
+0x3e38,0xe834,0x9dc8,0x647e,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double exp ( double );
+extern double sqrt ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double sin ( double );
+extern double cos ( double );
+#else
+double fabs(), exp(), sqrt();
+double polevl(), p1evl(), sin(), cos();
+#endif
+
+int airy( x, ai, aip, bi, bip )
+double x, *ai, *aip, *bi, *bip;
+{
+double z, zz, t, f, g, uf, ug, k, zeta, theta;
+int domflg;
+
+domflg = 0;
+if( x > MAXAIRY )
+	{
+	*ai = 0;
+	*aip = 0;
+	*bi = MAXNUM;
+	*bip = MAXNUM;
+	return(-1);
+	}
+
+if( x < -2.09 )
+	{
+	domflg = 15;
+	t = sqrt(-x);
+	zeta = -2.0 * x * t / 3.0;
+	t = sqrt(t);
+	k = sqpii / t;
+	z = 1.0/zeta;
+	zz = z * z;
+	uf = 1.0 + zz * polevl( zz, AFN, 8 ) / p1evl( zz, AFD, 9 );
+	ug = z * polevl( zz, AGN, 10 ) / p1evl( zz, AGD, 10 );
+	theta = zeta + 0.25 * PI;
+	f = sin( theta );
+	g = cos( theta );
+	*ai = k * (f * uf - g * ug);
+	*bi = k * (g * uf + f * ug);
+	uf = 1.0 + zz * polevl( zz, APFN, 8 ) / p1evl( zz, APFD, 9 );
+	ug = z * polevl( zz, APGN, 10 ) / p1evl( zz, APGD, 10 );
+	k = sqpii * t;
+	*aip = -k * (g * uf + f * ug);
+	*bip = k * (f * uf - g * ug);
+	return(0);
+	}
+
+if( x >= 2.09 )	/* cbrt(9) */
+	{
+	domflg = 5;
+	t = sqrt(x);
+	zeta = 2.0 * x * t / 3.0;
+	g = exp( zeta );
+	t = sqrt(t);
+	k = 2.0 * t * g;
+	z = 1.0/zeta;
+	f = polevl( z, AN, 7 ) / polevl( z, AD, 7 );
+	*ai = sqpii * f / k;
+	k = -0.5 * sqpii * t / g;
+	f = polevl( z, APN, 7 ) / polevl( z, APD, 7 );
+	*aip = f * k;
+
+	if( x > 8.3203353 )	/* zeta > 16 */
+		{
+		f = z * polevl( z, BN16, 4 ) / p1evl( z, BD16, 5 );
+		k = sqpii * g;
+		*bi = k * (1.0 + f) / t;
+		f = z * polevl( z, BPPN, 4 ) / p1evl( z, BPPD, 5 );
+		*bip = k * t * (1.0 + f);
+		return(0);
+		}
+	}
+
+f = 1.0;
+g = x;
+t = 1.0;
+uf = 1.0;
+ug = x;
+k = 1.0;
+z = x * x * x;
+while( t > MACHEP )
+	{
+	uf *= z;
+	k += 1.0;
+	uf /=k;
+	ug *= z;
+	k += 1.0;
+	ug /=k;
+	uf /=k;
+	f += uf;
+	k += 1.0;
+	ug /=k;
+	g += ug;
+	t = fabs(uf/f);
+	}
+uf = c1 * f;
+ug = c2 * g;
+if( (domflg & 1) == 0 )
+	*ai = uf - ug;
+if( (domflg & 2) == 0 )
+	*bi = sqrt3 * (uf + ug);
+
+/* the deriviative of ai */
+k = 4.0;
+uf = x * x/2.0;
+ug = z/3.0;
+f = uf;
+g = 1.0 + ug;
+uf /= 3.0;
+t = 1.0;
+
+while( t > MACHEP )
+	{
+	uf *= z;
+	ug /=k;
+	k += 1.0;
+	ug *= z;
+	uf /=k;
+	f += uf;
+	k += 1.0;
+	ug /=k;
+	uf /=k;
+	g += ug;
+	k += 1.0;
+	t = fabs(ug/g);
+	}
+
+uf = c1 * f;
+ug = c2 * g;
+if( (domflg & 4) == 0 )
+	*aip = uf - ug;
+if( (domflg & 8) == 0 )
+	*bip = sqrt3 * (uf + ug);
+return(0);
+}

libm/double/arcdot.c

@@ -0,0 +1,110 @@
+/*							arcdot.c
+ *
+ *	Angle between two vectors
+ *
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double p[3], q[3], arcdot();
+ *
+ * y = arcdot( p, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * For two vectors p, q, the angle A between them is given by
+ *
+ *      p.q / (|p| |q|)  = cos A  .
+ *
+ * where "." represents inner product, "|x|" the length of vector x.
+ * If the angle is small, an expression in sin A is preferred.
+ * Set r = q - p.  Then
+ *
+ *     p.q = p.p + p.r ,
+ *
+ *     |p|^2 = p.p ,
+ *
+ *     |q|^2 = p.p + 2 p.r + r.r ,
+ *
+ *                  p.p^2 + 2 p.p p.r + p.r^2
+ *     cos^2 A  =  ----------------------------
+ *                    p.p (p.p + 2 p.r + r.r)
+ *
+ *                  p.p + 2 p.r + p.r^2 / p.p
+ *              =  --------------------------- ,
+ *                     p.p + 2 p.r + r.r
+ *
+ *     sin^2 A  =  1 - cos^2 A
+ *
+ *                   r.r - p.r^2 / p.p
+ *              =  --------------------
+ *                  p.p + 2 p.r + r.r
+ *
+ *              =   (r.r - p.r^2 / p.p) / q.q  .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -1, 1        10^6       1.7e-16     4.2e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3:  November, 1995
+Copyright 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double acos ( double );
+extern double asin ( double );
+extern double atan ( double );
+#else
+double sqrt(), acos(), asin(), atan();
+#endif
+extern double PI;
+
+double arcdot(p,q)
+double p[], q[];
+{
+double pp, pr, qq, rr, rt, pt, qt, pq;
+int i;
+
+pq = 0.0;
+qq = 0.0;
+pp = 0.0;
+pr = 0.0;
+rr = 0.0;
+for (i=0; i<3; i++)
+  {
+    pt = p[i];
+    qt = q[i];
+    pq += pt * qt;
+    qq += qt * qt;
+    pp += pt * pt;
+    rt = qt - pt;
+    pr += pt * rt;
+    rr += rt * rt;
+  }
+if (rr == 0.0 || pp == 0.0 || qq == 0.0)
+  return 0.0;
+rt = (rr - (pr * pr) / pp) / qq;
+if (rt <= 0.75)
+  {
+    rt = sqrt(rt);
+    qt = asin(rt);
+    if (pq < 0.0)
+      qt = PI - qt;
+  }
+else
+  {
+    pt = pq / sqrt(pp*qq);
+    qt = acos(pt);
+  }
+return qt;
+}

libm/double/asin.c

@@ -0,0 +1,324 @@
+/*							asin.c
+ *
+ *	Inverse circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asin();
+ *
+ * y = asin( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A rational function of the form x + x**3 P(x**2)/Q(x**2)
+ * is used for |x| in the interval [0, 0.5].  If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ *    asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -1, 1        40000       2.6e-17     7.1e-18
+ *    IEEE     -1, 1        10^6        1.9e-16     5.4e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * asin domain        |x| > 1           NAN
+ *
+ */
+/*							acos()
+ *
+ *	Inverse circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acos();
+ *
+ * y = acos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between 0 and pi whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x).  However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2.  Hence if x < -0.5,
+ *
+ *    acos(x) =	 pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ *    acos(x) =	 2.0 * asin(  sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -1, 1       50000       3.3e-17     8.2e-18
+ *    IEEE      -1, 1       10^6        2.2e-16     6.5e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * asin domain        |x| > 1           NAN
+ */
+
+/*							asin.c	*/
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* arcsin(x)  =  x + x^3 P(x^2)/Q(x^2)
+   0 <= x <= 0.625
+   Peak relative error = 1.2e-18  */
+#if UNK
+static double P[6] = {
+ 4.253011369004428248960E-3,
+-6.019598008014123785661E-1,
+ 5.444622390564711410273E0,
+-1.626247967210700244449E1,
+ 1.956261983317594739197E1,
+-8.198089802484824371615E0,
+};
+static double Q[5] = {
+/* 1.000000000000000000000E0, */
+-1.474091372988853791896E1,
+ 7.049610280856842141659E1,
+-1.471791292232726029859E2,
+ 1.395105614657485689735E2,
+-4.918853881490881290097E1,
+};
+#endif
+#if DEC
+static short P[24] = {
+0036213,0056330,0057244,0053234,
+0140032,0015011,0114762,0160255,
+0040656,0035130,0136121,0067313,
+0141202,0014616,0170474,0101731,
+0041234,0100076,0151674,0111310,
+0141003,0025540,0033165,0077246,
+};
+static short Q[20] = {
+/* 0040200,0000000,0000000,0000000, */
+0141153,0155310,0055360,0072530,
+0041614,0177001,0027764,0101237,
+0142023,0026733,0064653,0133266,
+0042013,0101264,0023775,0176351,
+0141504,0140420,0050660,0036543,
+};
+#endif
+#if IBMPC
+static short P[24] = {
+0x8ad3,0x0bd4,0x6b9b,0x3f71,
+0x5c16,0x333e,0x4341,0xbfe3,
+0x2dd9,0x178a,0xc74b,0x4015,
+0x907b,0xde27,0x4331,0xc030,
+0x9259,0xda77,0x9007,0x4033,
+0xafd5,0x06ce,0x656c,0xc020,
+};
+static short Q[20] = {
+/* 0x0000,0x0000,0x0000,0x3ff0, */
+0x0eab,0x0b5e,0x7b59,0xc02d,
+0x9054,0x25fe,0x9fc0,0x4051,
+0x76d7,0x6d35,0x65bb,0xc062,
+0xbf9d,0x84ff,0x7056,0x4061,
+0x07ac,0x0a36,0x9822,0xc048,
+};
+#endif
+#if MIEEE
+static short P[24] = {
+0x3f71,0x6b9b,0x0bd4,0x8ad3,
+0xbfe3,0x4341,0x333e,0x5c16,
+0x4015,0xc74b,0x178a,0x2dd9,
+0xc030,0x4331,0xde27,0x907b,
+0x4033,0x9007,0xda77,0x9259,
+0xc020,0x656c,0x06ce,0xafd5,
+};
+static short Q[20] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc02d,0x7b59,0x0b5e,0x0eab,
+0x4051,0x9fc0,0x25fe,0x9054,
+0xc062,0x65bb,0x6d35,0x76d7,
+0x4061,0x7056,0x84ff,0xbf9d,
+0xc048,0x9822,0x0a36,0x07ac,
+};
+#endif
+
+/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))
+   0 <= x <= 0.5
+   Peak relative error = 4.2e-18  */
+#if UNK
+static double R[5] = {
+ 2.967721961301243206100E-3,
+-5.634242780008963776856E-1,
+ 6.968710824104713396794E0,
+-2.556901049652824852289E1,
+ 2.853665548261061424989E1,
+};
+static double S[4] = {
+/* 1.000000000000000000000E0, */
+-2.194779531642920639778E1,
+ 1.470656354026814941758E2,
+-3.838770957603691357202E2,
+ 3.424398657913078477438E2,
+};
+#endif
+#if DEC
+static short R[20] = {
+0036102,0077034,0142164,0174103,
+0140020,0036222,0147711,0044173,
+0040736,0177655,0153631,0171523,
+0141314,0106525,0060015,0055474,
+0041344,0045422,0003630,0040344,
+};
+static short S[16] = {
+/* 0040200,0000000,0000000,0000000, */
+0141257,0112425,0132772,0166136,
+0042023,0010315,0075523,0175020,
+0142277,0170104,0126203,0017563,
+0042253,0034115,0102662,0022757,
+};
+#endif
+#if IBMPC
+static short R[20] = {
+0x9f08,0x988e,0x4fc3,0x3f68,
+0x290f,0x59f9,0x0792,0xbfe2,
+0x3e6a,0xbaf3,0xdff5,0x401b,
+0xab68,0xac01,0x91aa,0xc039,
+0x081d,0x40f3,0x8962,0x403c,
+};
+static short S[16] = {
+/* 0x0000,0x0000,0x0000,0x3ff0, */
+0x5d8c,0xb6bf,0xf2a2,0xc035,
+0x7f42,0xaf6a,0x6219,0x4062,
+0x63ee,0x9590,0xfe08,0xc077,
+0x44be,0xb0b6,0x6709,0x4075,
+};
+#endif
+#if MIEEE
+static short R[20] = {
+0x3f68,0x4fc3,0x988e,0x9f08,
+0xbfe2,0x0792,0x59f9,0x290f,
+0x401b,0xdff5,0xbaf3,0x3e6a,
+0xc039,0x91aa,0xac01,0xab68,
+0x403c,0x8962,0x40f3,0x081d,
+};
+static short S[16] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc035,0xf2a2,0xb6bf,0x5d8c,
+0x4062,0x6219,0xaf6a,0x7f42,
+0xc077,0xfe08,0x9590,0x63ee,
+0x4075,0x6709,0xb0b6,0x44be,
+};
+#endif
+
+/* pi/2 = PIO2 + MOREBITS.  */
+#ifdef DEC
+#define MOREBITS 5.721188726109831840122E-18
+#else
+#define MOREBITS 6.123233995736765886130E-17
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double sqrt ( double );
+double asin ( double );
+#else
+double sqrt(), polevl(), p1evl();
+double asin();
+#endif
+extern double PIO2, PIO4, NAN;
+
+double asin(x)
+double x;
+{
+double a, p, z, zz;
+short sign;
+
+if( x > 0 )
+	{
+	sign = 1;
+	a = x;
+	}
+else
+	{
+	sign = -1;
+	a = -x;
+	}
+
+if( a > 1.0 )
+	{
+	mtherr( "asin", DOMAIN );
+	return( NAN );
+	}
+
+if( a > 0.625 )
+	{
+	/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))  */
+	zz = 1.0 - a;
+	p = zz * polevl( zz, R, 4)/p1evl( zz, S, 4);
+	zz = sqrt(zz+zz);
+	z = PIO4 - zz;
+	zz = zz * p - MOREBITS;
+	z = z - zz;
+	z = z + PIO4;
+	}
+else
+	{
+	if( a < 1.0e-8 )
+		{
+		return(x);
+		}
+	zz = a * a;
+	z = zz * polevl( zz, P, 5)/p1evl( zz, Q, 5);
+	z = a * z + a;
+	}
+if( sign < 0 )
+	z = -z;
+return(z);
+}
+
+
+
+double acos(x)
+double x;
+{
+double z;
+
+if( (x < -1.0) || (x > 1.0) )
+	{
+	mtherr( "acos", DOMAIN );
+	return( NAN );
+	}
+if( x > 0.5 )
+	{
+	return( 2.0 * asin(  sqrt(0.5 - 0.5*x) ) );
+	}
+z = PIO4 - asin(x);
+z = z + MOREBITS;
+z = z + PIO4;
+return( z );
+}

libm/double/asinh.c

@@ -0,0 +1,165 @@
+/*							asinh.c
+ *
+ *	Inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asinh();
+ *
+ * y = asinh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic sine of argument.
+ *
+ * If |x| < 0.5, the function is approximated by a rational
+ * form  x + x**3 P(x)/Q(x).  Otherwise,
+ *
+ *     asinh(x) = log( x + sqrt(1 + x*x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -3,3         75000       4.6e-17     1.1e-17
+ *    IEEE     -1,1         30000       3.7e-16     7.8e-17
+ *    IEEE      1,3         30000       2.5e-16     6.7e-17
+ *
+ */
+
+/*						asinh.c	*/
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-4.33231683752342103572E-3,
+-5.91750212056387121207E-1,
+-4.37390226194356683570E0,
+-9.09030533308377316566E0,
+-5.56682227230859640450E0
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.28757002067426453537E1,
+ 4.86042483805291788324E1,
+ 6.95722521337257608734E1,
+ 3.34009336338516356383E1
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0136215,0173033,0110410,0105475,
+0140027,0076361,0020056,0164520,
+0140613,0173401,0160136,0053142,
+0141021,0070744,0000503,0176261,
+0140662,0021550,0073106,0133351
+};
+static unsigned short Q[] = {
+/* 0040200,0000000,0000000,0000000,*/
+0041116,0001336,0034120,0173054,
+0041502,0065300,0013144,0021231,
+0041613,0022376,0035516,0153063,
+0041405,0115216,0054265,0004557
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x1168,0x7221,0xbec3,0xbf71,
+0xdd2a,0x2405,0xef9e,0xbfe2,
+0xcacc,0x3c0b,0x7ee0,0xc011,
+0x7f96,0x8028,0x2e3c,0xc022,
+0xd6dd,0x0ec8,0x446d,0xc016
+};
+static unsigned short Q[] = {
+/* 0x0000,0x0000,0x0000,0x3ff0,*/
+0x1ec5,0xc70a,0xc05b,0x4029,
+0x8453,0x02cc,0x4d58,0x4048,
+0xdac6,0xc769,0x649f,0x4051,
+0xa12e,0xcb16,0xb351,0x4040
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xbf71,0xbec3,0x7221,0x1168,
+0xbfe2,0xef9e,0x2405,0xdd2a,
+0xc011,0x7ee0,0x3c0b,0xcacc,
+0xc022,0x2e3c,0x8028,0x7f96,
+0xc016,0x446d,0x0ec8,0xd6dd
+};
+static unsigned short Q[] = {
+0x4029,0xc05b,0xc70a,0x1ec5,
+0x4048,0x4d58,0x02cc,0x8453,
+0x4051,0x649f,0xc769,0xdac6,
+0x4040,0xb351,0xcb16,0xa12e
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double sqrt ( double );
+extern double log ( double );
+#else
+double log(), sqrt(), polevl(), p1evl();
+#endif
+extern double LOGE2, INFINITY;
+
+double asinh(xx)
+double xx;
+{
+double a, z, x;
+int sign;
+
+#ifdef MINUSZERO
+if( xx == 0.0 )
+  return(xx);
+#endif
+if( xx < 0.0 )
+	{
+	sign = -1;
+	x = -xx;
+	}
+else
+	{
+	sign = 1;
+	x = xx;
+	}
+
+if( x > 1.0e8 )
+	{
+#ifdef INFINITIES
+	  if( x == INFINITY )
+	    return(xx);
+#endif
+	return( sign * (log(x) + LOGE2) );
+	}
+
+z = x * x;
+if( x < 0.5 )
+	{
+	a = ( polevl(z, P, 4)/p1evl(z, Q, 4) ) * z;
+	a = a * x  +  x;
+	if( sign < 0 )
+		a = -a;
+	return(a);
+	}	
+
+a = sqrt( z + 1.0 );
+return( sign * log(x + a) );
+}

libm/double/atan.c

@@ -0,0 +1,393 @@
+/*							atan.c
+ *
+ *	Inverse circular tangent
+ *      (arctangent)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atan();
+ *
+ * y = atan( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose tangent
+ * is x.
+ *
+ * Range reduction is from three intervals into the interval
+ * from zero to 0.66.  The approximant uses a rational
+ * function of degree 4/5 of the form x + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10, 10     50000       2.4e-17     8.3e-18
+ *    IEEE      -10, 10      10^6       1.8e-16     5.0e-17
+ *
+ */
+/*							atan2()
+ *
+ *	Quadrant correct inverse circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, z, atan2();
+ *
+ * z = atan2( y, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle whose tangent is y/x.
+ * Define compile time symbol ANSIC = 1 for ANSI standard,
+ * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
+ * 0 to 2PI, args (x,y).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10, 10      10^6       2.5e-16     6.9e-17
+ * See atan.c.
+ *
+ */
+
+/*							atan.c */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+/* arctan(x)  = x + x^3 P(x^2)/Q(x^2)
+   0 <= x <= 0.66
+   Peak relative error = 2.6e-18  */
+#ifdef UNK
+static double P[5] = {
+-8.750608600031904122785E-1,
+-1.615753718733365076637E1,
+-7.500855792314704667340E1,
+-1.228866684490136173410E2,
+-6.485021904942025371773E1,
+};
+static double Q[5] = {
+/* 1.000000000000000000000E0, */
+ 2.485846490142306297962E1,
+ 1.650270098316988542046E2,
+ 4.328810604912902668951E2,
+ 4.853903996359136964868E2,
+ 1.945506571482613964425E2,
+};
+
+/* tan( 3*pi/8 ) */
+static double T3P8 = 2.41421356237309504880;
+#endif
+
+#ifdef DEC
+static short P[20] = {
+0140140,0001775,0007671,0026242,
+0141201,0041242,0155534,0001715,
+0141626,0002141,0132100,0011625,
+0141765,0142771,0064055,0150453,
+0141601,0131517,0164507,0062164,
+};
+static short Q[20] = {
+/* 0040200,0000000,0000000,0000000, */
+0041306,0157042,0154243,0000742,
+0042045,0003352,0016707,0150452,
+0042330,0070306,0113425,0170730,
+0042362,0130770,0116602,0047520,
+0042102,0106367,0156753,0013541,
+};
+
+/* tan( 3*pi/8 ) = 2.41421356237309504880 */
+static unsigned short T3P8A[] = {040432,0101171,0114774,0167462,};
+#define T3P8 *(double *)T3P8A
+#endif
+
+#ifdef IBMPC
+static short P[20] = {
+0x2594,0xa1f7,0x007f,0xbfec,
+0x807a,0x5b6b,0x2854,0xc030,
+0x0273,0x3688,0xc08c,0xc052,
+0xba25,0x2d05,0xb8bf,0xc05e,
+0xec8e,0xfd28,0x3669,0xc050,
+};
+static short Q[20] = {
+/* 0x0000,0x0000,0x0000,0x3ff0, */
+0x603c,0x5b14,0xdbc4,0x4038,
+0xfa25,0x43b8,0xa0dd,0x4064,
+0xbe3b,0xd2e2,0x0e18,0x407b,
+0x49ea,0x13b0,0x563f,0x407e,
+0x62ec,0xfbbd,0x519e,0x4068,
+};
+
+/* tan( 3*pi/8 ) = 2.41421356237309504880 */
+static unsigned short T3P8A[] = {0x9de6,0x333f,0x504f,0x4003};
+#define T3P8 *(double *)T3P8A
+#endif
+
+#ifdef MIEEE
+static short P[20] = {
+0xbfec,0x007f,0xa1f7,0x2594,
+0xc030,0x2854,0x5b6b,0x807a,
+0xc052,0xc08c,0x3688,0x0273,
+0xc05e,0xb8bf,0x2d05,0xba25,
+0xc050,0x3669,0xfd28,0xec8e,
+};
+static short Q[20] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0x4038,0xdbc4,0x5b14,0x603c,
+0x4064,0xa0dd,0x43b8,0xfa25,
+0x407b,0x0e18,0xd2e2,0xbe3b,
+0x407e,0x563f,0x13b0,0x49ea,
+0x4068,0x519e,0xfbbd,0x62ec,
+};
+
+/* tan( 3*pi/8 ) = 2.41421356237309504880 */
+static unsigned short T3P8A[] = {
+0x4003,0x504f,0x333f,0x9de6
+};
+#define T3P8 *(double *)T3P8A
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double atan ( double );
+extern double fabs ( double );
+extern int signbit ( double );
+extern int isnan ( double );
+#else
+double polevl(), p1evl(), atan(), fabs();
+//int signbit(), isnan();
+#endif
+extern double PI, PIO2, PIO4, INFINITY, NEGZERO, MAXNUM;
+
+/* pi/2 = PIO2 + MOREBITS.  */
+#ifdef DEC
+#define MOREBITS 5.721188726109831840122E-18
+#else
+#define MOREBITS 6.123233995736765886130E-17
+#endif
+
+
+double atan(x)
+double x;
+{
+double y, z;
+short sign, flag;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+	return(x);
+#endif
+#ifdef INFINITIES
+if(x == INFINITY)
+	return(PIO2);
+if(x == -INFINITY)
+	return(-PIO2);
+#endif
+/* make argument positive and save the sign */
+sign = 1;
+if( x < 0.0 )
+	{
+	sign = -1;
+	x = -x;
+	}
+/* range reduction */
+flag = 0;
+if( x > T3P8 )
+	{
+	y = PIO2;
+	flag = 1;
+	x = -( 1.0/x );
+	}
+else if( x <= 0.66 )
+	{
+	y = 0.0;
+	}
+else
+	{
+	y = PIO4;
+	flag = 2;
+	x = (x-1.0)/(x+1.0);
+	}
+z = x * x;
+z = z * polevl( z, P, 4 ) / p1evl( z, Q, 5 );
+z = x * z + x;
+if( flag == 2 )
+	z += 0.5 * MOREBITS;
+else if( flag == 1 )
+	z += MOREBITS;
+y = y + z;
+if( sign < 0 )
+	y = -y;
+return(y);
+}
+
+/*							atan2	*/
+
+#ifdef ANSIC
+double atan2( y, x )
+#else
+double atan2( x, y )
+#endif
+double x, y;
+{
+double z, w;
+short code;
+
+code = 0;
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+if( isnan(y) )
+	return(y);
+#endif
+#ifdef MINUSZERO
+if( y == 0.0 )
+	{
+	if( signbit(y) )
+		{
+		if( x > 0.0 )
+			z = y;
+		else if( x < 0.0 )
+			z = -PI;
+		else
+			{
+			if( signbit(x) )
+				z = -PI;
+			else
+				z = y;
+			}
+		}
+	else /* y is +0 */
+		{
+		if( x == 0.0 )
+			{
+			if( signbit(x) )
+				z = PI;
+			else
+				z = 0.0;
+			}
+		else if( x > 0.0 )
+			z = 0.0;
+		else
+			z = PI;
+		}
+	return z;
+	}
+if( x == 0.0 )
+	{
+	if( y > 0.0 )
+		z = PIO2;
+	else
+		z = -PIO2;
+	return z;
+	}
+#endif /* MINUSZERO */
+#ifdef INFINITIES
+if( x == INFINITY )
+	{
+	if( y == INFINITY )
+		z = 0.25 * PI;
+	else if( y == -INFINITY )
+		z = -0.25 * PI;
+	else if( y < 0.0 )
+		z = NEGZERO;
+	else
+		z = 0.0;
+	return z;
+	}
+if( x == -INFINITY )
+	{
+	if( y == INFINITY )
+		z = 0.75 * PI;
+	else if( y <= -INFINITY )
+		z = -0.75 * PI;
+	else if( y >= 0.0 )
+		z = PI;
+	else
+		z = -PI;
+	return z;
+	}
+if( y == INFINITY )
+	return( PIO2 );
+if( y == -INFINITY )
+	return( -PIO2 );
+#endif
+
+if( x < 0.0 )
+	code = 2;
+if( y < 0.0 )
+	code |= 1;
+
+#ifdef INFINITIES
+if( x == 0.0 )
+#else
+if( fabs(x) <= (fabs(y) / MAXNUM) )
+#endif
+	{
+	if( code & 1 )
+		{
+#if ANSIC
+		return( -PIO2 );
+#else
+		return( 3.0*PIO2 );
+#endif
+		}
+	if( y == 0.0 )
+		return( 0.0 );
+	return( PIO2 );
+	}
+
+if( y == 0.0 )
+	{
+	if( code & 2 )
+		return( PI );
+	return( 0.0 );
+	}
+
+
+switch( code )
+	{
+#if ANSIC
+	default:
+	case 0:
+	case 1: w = 0.0; break;
+	case 2: w = PI; break;
+	case 3: w = -PI; break;
+#else
+	default:
+	case 0: w = 0.0; break;
+	case 1: w = 2.0 * PI; break;
+	case 2:
+	case 3: w = PI; break;
+#endif
+	}
+
+z = w + atan( y/x );
+#ifdef MINUSZERO
+if( z == 0.0 && y < 0 )
+	z = NEGZERO;
+#endif
+return( z );
+}

libm/double/atanh.c

@@ -0,0 +1,156 @@
+/*							atanh.c
+ *
+ *	Inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atanh();
+ *
+ * y = atanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOG to MAXLOG.
+ *
+ * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
+ * employed.  Otherwise,
+ *        atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -1,1        50000       2.4e-17     6.4e-18
+ *    IEEE      -1,1        30000       1.9e-16     5.2e-17
+ *
+ */
+
+/*						atanh.c	*/
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright (C) 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-8.54074331929669305196E-1,
+ 1.20426861384072379242E1,
+-4.61252884198732692637E1,
+ 6.54566728676544377376E1,
+-3.09092539379866942570E1
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+-1.95638849376911654834E1,
+ 1.08938092147140262656E2,
+-2.49839401325893582852E2,
+ 2.52006675691344555838E2,
+-9.27277618139601130017E1
+};
+#endif
+#ifdef DEC
+static unsigned short P[] = {
+0140132,0122235,0105775,0130300,
+0041100,0127327,0124407,0034722,
+0141470,0100113,0115607,0130535,
+0041602,0164721,0003257,0013673,
+0141367,0043046,0166673,0045750
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0141234,0101326,0015460,0134564,
+0041731,0160115,0116451,0032045,
+0142171,0153343,0000532,0167226,
+0042174,0000665,0077604,0000310,
+0141671,0072235,0031114,0074377
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0xb618,0xb17f,0x5493,0xbfeb,
+0xe73a,0xf520,0x15da,0x4028,
+0xf62c,0x7370,0x1009,0xc047,
+0xe2f7,0x20d5,0x5d3a,0x4050,
+0x697d,0xddb7,0xe8c4,0xc03e
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x172f,0xc366,0x905a,0xc033,
+0x2685,0xb3a5,0x3c09,0x405b,
+0x5dd3,0x602b,0x3adc,0xc06f,
+0x8019,0xaff0,0x8036,0x406f,
+0x8f20,0xa649,0x2e93,0xc057
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xbfeb,0x5493,0xb17f,0xb618,
+0x4028,0x15da,0xf520,0xe73a,
+0xc047,0x1009,0x7370,0xf62c,
+0x4050,0x5d3a,0x20d5,0xe2f7,
+0xc03e,0xe8c4,0xddb7,0x697d
+};
+static unsigned short Q[] = {
+0xc033,0x905a,0xc366,0x172f,
+0x405b,0x3c09,0xb3a5,0x2685,
+0xc06f,0x3adc,0x602b,0x5dd3,
+0x406f,0x8036,0xaff0,0x8019,
+0xc057,0x2e93,0xa649,0x8f20
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double log ( double x );
+extern double polevl ( double x, void *P, int N );
+extern double p1evl ( double x, void *P, int N );
+#else
+double fabs(), log(), polevl(), p1evl();
+#endif
+extern double INFINITY, NAN;
+
+double atanh(x)
+double x;
+{
+double s, z;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+	return(x);
+#endif
+z = fabs(x);
+if( z >= 1.0 )
+	{
+	if( x == 1.0 )
+		return( INFINITY );
+	if( x == -1.0 )
+		return( -INFINITY );
+	mtherr( "atanh", DOMAIN );
+	return( NAN );
+	}
+
+if( z < 1.0e-7 )
+	return(x);
+
+if( z < 0.5 )
+	{
+	z = x * x;
+	s = x   +  x * z * (polevl(z, P, 4) / p1evl(z, Q, 5));
+	return(s);
+	}
+
+return( 0.5 * log((1.0+x)/(1.0-x)) );
+}

libm/double/bdtr.c

@@ -0,0 +1,263 @@
+/*							bdtr.c
+ *
+ *	Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtr();
+ *
+ * y = bdtr( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ *   k
+ *   --  ( n )   j      n-j
+ *   >   (   )  p  (1-p)
+ *   --  ( j )
+ *  j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      4.3e-15     2.6e-16
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtr domain         k < 0            0.0
+ *                     n < k
+ *                     x < 0, x > 1
+ */
+/*							bdtrc()
+ *
+ *	Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtrc();
+ *
+ * y = bdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ *   n
+ *   --  ( n )   j      n-j
+ *   >   (   )  p  (1-p)
+ *   --  ( j )
+ *  j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      6.7e-15     8.2e-16
+ *  For p between 0 and .001:
+ *    IEEE     0,100       100000      1.5e-13     2.7e-15
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtrc domain      x<0, x>1, n<k       0.0
+ */
+/*							bdtri()
+ *
+ *	Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtri();
+ *
+ * p = bdtr( k, n, y );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      2.3e-14     6.4e-16
+ *    IEEE     0,10000     100000      6.6e-12     1.2e-13
+ *  For p between 10^-6 and 0.001:
+ *    IEEE     0,100       100000      2.0e-12     1.3e-14
+ *    IEEE     0,10000     100000      1.5e-12     3.2e-14
+ * See also incbi.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtri domain     k < 0, n <= k         0.0
+ *                  x < 0, x > 1
+ */
+
+/*								bdtr() */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+extern double pow ( double, double );
+extern double log1p ( double );
+extern double expm1 ( double );
+#else
+double incbet(), incbi(), pow(), log1p(), expm1();
+#endif
+
+double bdtrc( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+	goto domerr;
+if( k < 0 )
+	return( 1.0 );
+
+if( n < k )
+	{
+domerr:
+	mtherr( "bdtrc", DOMAIN );
+	return( 0.0 );
+	}
+
+if( k == n )
+	return( 0.0 );
+dn = n - k;
+if( k == 0 )
+	{
+	if( p < .01 )
+		dk = -expm1( dn * log1p(-p) );
+	else
+		dk = 1.0 - pow( 1.0-p, dn );
+	}
+else
+	{
+	dk = k + 1;
+	dk = incbet( dk, dn, p );
+	}
+return( dk );
+}
+
+
+
+double bdtr( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+	goto domerr;
+if( (k < 0) || (n < k) )
+	{
+domerr:
+	mtherr( "bdtr", DOMAIN );
+	return( 0.0 );
+	}
+
+if( k == n )
+	return( 1.0 );
+
+dn = n - k;
+if( k == 0 )
+	{
+	dk = pow( 1.0-p, dn );
+	}
+else
+	{
+	dk = k + 1;
+	dk = incbet( dn, dk, 1.0 - p );
+	}
+return( dk );
+}
+
+
+double bdtri( k, n, y )
+int k, n;
+double y;
+{
+double dk, dn, p;
+
+if( (y < 0.0) || (y > 1.0) )
+	goto domerr;
+if( (k < 0) || (n <= k) )
+	{
+domerr:
+	mtherr( "bdtri", DOMAIN );
+	return( 0.0 );
+	}
+
+dn = n - k;
+if( k == 0 )
+	{
+	if( y > 0.8 )
+		p = -expm1( log1p(y-1.0) / dn );
+	else
+		p = 1.0 - pow( y, 1.0/dn );
+	}
+else
+	{
+	dk = k + 1;
+	p = incbet( dn, dk, 0.5 );
+	if( p > 0.5 )
+		p = incbi( dk, dn, 1.0-y );
+	else
+		p = 1.0 - incbi( dn, dk, y );
+	}
+return( p );
+}

libm/double/bernum.c

@@ -0,0 +1,74 @@
+/* This program computes the Bernoulli numbers.
+ * See radd.c for rational arithmetic.
+ */
+
+typedef struct{
+	double n;
+	double d;
+	}fract;
+
+#define PD 44
+fract x[PD+1] = {0.0};
+fract p[PD+1] = {0.0};
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double log10 ( double );
+#else
+double fabs(), log10();
+#endif
+extern double MACHEP;
+
+main()
+{
+int nx, np, nu;
+int i, j, k, n, sign;
+fract r, s, t;
+
+
+for(i=0; i<=PD; i++ )
+	{
+	x[i].n = 0.0;
+	x[i].d = 1.0;
+	p[i].n = 0.0;
+	p[i].d = 1.0;
+	}
+p[0].n = 1.0;
+p[0].d = 1.0;
+p[1].n = 1.0;
+p[1].d = 1.0;
+np = 1;
+x[0].n = 1.0;
+x[0].d = 1.0;
+
+for( n=1; n<PD-2; n++ )
+{
+
+/* Create line of Pascal's triangle */
+/* multiply p = u * p */
+for( k=0; k<=np; k++ )
+	{
+	radd( &p[np-k+1], &p[np-k], &p[np-k+1] );
+	}
+np += 1;
+
+/* B0 + nC1 B1 + ... + nCn-1 Bn-1 = 0 */
+s.n = 0.0;
+s.d = 1.0;
+
+for( i=0; i<n; i++ )
+	{
+	rmul( &p[i], &x[i], &t );
+	radd( &s, &t, &s );
+	}
+
+
+rdiv( &p[n], &s, &x[n] );	/* x[n] = -s/p[n] */
+x[n].n = -x[n].n;
+nx += 1;
+printf( "%2d %.15e / %.15e\n", n, x[n].n, x[n].d );
+}
+
+
+}
+

libm/double/beta.c

@@ -0,0 +1,201 @@
+/*							beta.c
+ *
+ *	Beta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, y, beta();
+ *
+ * y = beta( a, b );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *                   -     -
+ *                  | (a) | (b)
+ * beta( a, b )  =  -----------.
+ *                     -
+ *                    | (a+b)
+ *
+ * For large arguments the logarithm of the function is
+ * evaluated using lgam(), then exponentiated.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        0,30        1700       7.7e-15     1.5e-15
+ *    IEEE       0,30       30000       8.1e-14     1.1e-14
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition          value returned
+ * beta overflow    log(beta) > MAXLOG       0.0
+ *                  a or b <0 integer        0.0
+ *
+ */
+
+/*							beta.c	*/
+
+
+/*
+Cephes Math Library Release 2.0:  April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#ifdef UNK
+#define MAXGAM 34.84425627277176174
+#endif
+#ifdef DEC
+#define MAXGAM 34.84425627277176174
+#endif
+#ifdef IBMPC
+#define MAXGAM 171.624376956302725
+#endif
+#ifdef MIEEE
+#define MAXGAM 171.624376956302725
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double gamma ( double );
+extern double lgam ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double floor ( double );
+#else
+double fabs(), gamma(), lgam(), exp(), log(), floor();
+#endif
+extern double MAXLOG, MAXNUM;
+extern int sgngam;
+
+double beta( a, b )
+double a, b;
+{
+double y;
+int sign;
+
+sign = 1;
+
+if( a <= 0.0 )
+	{
+	if( a == floor(a) )
+		goto over;
+	}
+if( b <= 0.0 )
+	{
+	if( b == floor(b) )
+		goto over;
+	}
+
+
+y = a + b;
+if( fabs(y) > MAXGAM )
+	{
+	y = lgam(y);
+	sign *= sgngam; /* keep track of the sign */
+	y = lgam(b) - y;
+	sign *= sgngam;
+	y = lgam(a) + y;
+	sign *= sgngam;
+	if( y > MAXLOG )
+		{
+over:
+		mtherr( "beta", OVERFLOW );
+		return( sign * MAXNUM );
+		}
+	return( sign * exp(y) );
+	}
+
+y = gamma(y);
+if( y == 0.0 )
+	goto over;
+
+if( a > b )
+	{
+	y = gamma(a)/y;
+	y *= gamma(b);
+	}
+else
+	{
+	y = gamma(b)/y;
+	y *= gamma(a);
+	}
+
+return(y);
+}
+
+
+
+/* Natural log of |beta|.  Return the sign of beta in sgngam.  */
+
+double lbeta( a, b )
+double a, b;
+{
+double y;
+int sign;
+
+sign = 1;
+
+if( a <= 0.0 )
+	{
+	if( a == floor(a) )
+		goto over;
+	}
+if( b <= 0.0 )
+	{
+	if( b == floor(b) )
+		goto over;
+	}
+
+
+y = a + b;
+if( fabs(y) > MAXGAM )
+	{
+	y = lgam(y);
+	sign *= sgngam; /* keep track of the sign */
+	y = lgam(b) - y;
+	sign *= sgngam;
+	y = lgam(a) + y;
+	sign *= sgngam;
+	sgngam = sign;
+	return( y );
+	}
+
+y = gamma(y);
+if( y == 0.0 )
+	{
+over:
+	mtherr( "lbeta", OVERFLOW );
+	return( sign * MAXNUM );
+	}
+
+if( a > b )
+	{
+	y = gamma(a)/y;
+	y *= gamma(b);
+	}
+else
+	{
+	y = gamma(b)/y;
+	y *= gamma(a);
+	}
+
+if( y < 0 )
+  {
+    sgngam = -1;
+    y = -y;
+  }
+else
+  sgngam = 1;
+
+return( log(y) );
+}

libm/double/btdtr.c

@@ -0,0 +1,64 @@
+
+/*							btdtr.c
+ *
+ *	Beta distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, btdtr();
+ *
+ * y = btdtr( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the beta density
+ * function:
+ *
+ *
+ *                          x
+ *            -             -
+ *           | (a+b)       | |  a-1      b-1
+ * P(x)  =  ----------     |   t    (1-t)    dt
+ *           -     -     | |
+ *          | (a) | (b)   -
+ *                         0
+ *
+ *
+ * This function is identical to the incomplete beta
+ * integral function incbet(a, b, x).
+ *
+ * The complemented function is
+ *
+ * 1 - P(1-x)  =  incbet( b, a, x );
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ *
+ */
+
+/*								btdtr()	*/
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+#else
+double incbet();
+#endif
+
+double btdtr( a, b, x )
+double a, b, x;
+{
+
+return( incbet( a, b, x ) );
+}

libm/double/cbrt.c

@@ -0,0 +1,142 @@
+/*							cbrt.c
+ *
+ *	Cube root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cbrt();
+ *
+ * y = cbrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument.  A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%.  Then Newton's
+ * iteration is used three times to converge to an accurate
+ * result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        -10,10     200000      1.8e-17     6.2e-18
+ *    IEEE       0,1e308     30000      1.5e-16     5.0e-17
+ *
+ */
+/*							cbrt.c  */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1991, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+static double CBRT2  = 1.2599210498948731647672;
+static double CBRT4  = 1.5874010519681994747517;
+static double CBRT2I = 0.79370052598409973737585;
+static double CBRT4I = 0.62996052494743658238361;
+
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp();
+int isnan(), isfinite();
+#endif
+
+double cbrt(x)
+double x;
+{
+int e, rem, sign;
+double z;
+
+#ifdef NANS
+if( isnan(x) )
+  return x;
+#endif
+#ifdef INFINITIES
+if( !isfinite(x) )
+  return x;
+#endif
+if( x == 0 )
+	return( x );
+if( x > 0 )
+	sign = 1;
+else
+	{
+	sign = -1;
+	x = -x;
+	}
+
+z = x;
+/* extract power of 2, leaving
+ * mantissa between 0.5 and 1
+ */
+x = frexp( x, &e );
+
+/* Approximate cube root of number between .5 and 1,
+ * peak relative error = 9.2e-6
+ */
+x = (((-1.3466110473359520655053e-1  * x
+      + 5.4664601366395524503440e-1) * x
+      - 9.5438224771509446525043e-1) * x
+      + 1.1399983354717293273738e0 ) * x
+      + 4.0238979564544752126924e-1;
+
+/* exponent divided by 3 */
+if( e >= 0 )
+	{
+	rem = e;
+	e /= 3;
+	rem -= 3*e;
+	if( rem == 1 )
+		x *= CBRT2;
+	else if( rem == 2 )
+		x *= CBRT4;
+	}
+
+
+/* argument less than 1 */
+
+else
+	{
+	e = -e;
+	rem = e;
+	e /= 3;
+	rem -= 3*e;
+	if( rem == 1 )
+		x *= CBRT2I;
+	else if( rem == 2 )
+		x *= CBRT4I;
+	e = -e;
+	}
+
+/* multiply by power of 2 */
+x = ldexp( x, e );
+
+/* Newton iteration */
+x -= ( x - (z/(x*x)) )*0.33333333333333333333;
+#ifdef DEC
+x -= ( x - (z/(x*x)) )/3.0;
+#else
+x -= ( x - (z/(x*x)) )*0.33333333333333333333;
+#endif
+
+if( sign < 0 )
+	x = -x;
+return(x);
+}

libm/double/chbevl.c

@@ -0,0 +1,82 @@
+/*							chbevl.c
+ *
+ *	Evaluate Chebyshev series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * double x, y, coef[N], chebevl();
+ *
+ * y = chbevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the series
+ *
+ *        N-1
+ *         - '
+ *  y  =   >   coef[i] T (x/2)
+ *         -            i
+ *        i=0
+ *
+ * of Chebyshev polynomials Ti at argument x/2.
+ *
+ * Coefficients are stored in reverse order, i.e. the zero
+ * order term is last in the array.  Note N is the number of
+ * coefficients, not the order.
+ *
+ * If coefficients are for the interval a to b, x must
+ * have been transformed to x -> 2(2x - b - a)/(b-a) before
+ * entering the routine.  This maps x from (a, b) to (-1, 1),
+ * over which the Chebyshev polynomials are defined.
+ *
+ * If the coefficients are for the inverted interval, in
+ * which (a, b) is mapped to (1/b, 1/a), the transformation
+ * required is x -> 2(2ab/x - b - a)/(b-a).  If b is infinity,
+ * this becomes x -> 4a/x - 1.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Taking advantage of the recurrence properties of the
+ * Chebyshev polynomials, the routine requires one more
+ * addition per loop than evaluating a nested polynomial of
+ * the same degree.
+ *
+ */
+/*							chbevl.c	*/
+
+/*
+Cephes Math Library Release 2.0:  April, 1987
+Copyright 1985, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+double chbevl( x, array, n )
+double x;
+double array[];
+int n;
+{
+double b0, b1, b2, *p;
+int i;
+
+p = array;
+b0 = *p++;
+b1 = 0.0;
+i = n - 1;
+
+do
+	{
+	b2 = b1;
+	b1 = b0;
+	b0 = x * b1  -  b2  + *p++;
+	}
+while( --i );
+
+return( 0.5*(b0-b2) );
+}

libm/double/chdtr.c

@@ -0,0 +1,200 @@
+/*							chdtr.c
+ *
+ *	Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double df, x, y, chdtr();
+ *
+ * y = chdtr( df, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the left hand tail (from 0 to x)
+ * of the Chi square probability density function with
+ * v degrees of freedom.
+ *
+ *
+ *                                  inf.
+ *                                    -
+ *                        1          | |  v/2-1  -t/2
+ *  P( x | v )   =   -----------     |   t      e     dt
+ *                    v/2  -       | |
+ *                   2    | (v/2)   -
+ *                                   x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ *	y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * chdtr domain   x < 0 or v < 1        0.0
+ */
+/*							chdtrc()
+ *
+ *	Complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, chdtrc();
+ *
+ * y = chdtrc( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the right hand tail (from x to
+ * infinity) of the Chi square probability density function
+ * with v degrees of freedom:
+ *
+ *
+ *                                  inf.
+ *                                    -
+ *                        1          | |  v/2-1  -t/2
+ *  P( x | v )   =   -----------     |   t      e     dt
+ *                    v/2  -       | |
+ *                   2    | (v/2)   -
+ *                                   x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ *	y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * chdtrc domain  x < 0 or v < 1        0.0
+ */
+/*							chdtri()
+ *
+ *	Inverse of complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double df, x, y, chdtri();
+ *
+ * x = chdtri( df, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Chi-square argument x such that the integral
+ * from x to infinity of the Chi-square density is equal
+ * to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ *    x/2 = igami( df/2, y );
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * chdtri domain   y < 0 or y > 1        0.0
+ *                     v < 1
+ *
+ */
+
+/*								chdtr() */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double igamc ( double, double );
+extern double igam ( double, double );
+extern double igami ( double, double );
+#else
+double igamc(), igam(), igami();
+#endif
+
+double chdtrc(df,x)
+double df, x;
+{
+
+if( (x < 0.0) || (df < 1.0) )
+	{
+	mtherr( "chdtrc", DOMAIN );
+	return(0.0);
+	}
+return( igamc( df/2.0, x/2.0 ) );
+}
+
+
+
+double chdtr(df,x)
+double df, x;
+{
+
+if( (x < 0.0) || (df < 1.0) )
+	{
+	mtherr( "chdtr", DOMAIN );
+	return(0.0);
+	}
+return( igam( df/2.0, x/2.0 ) );
+}
+
+
+
+double chdtri( df, y )
+double df, y;
+{
+double x;
+
+if( (y < 0.0) || (y > 1.0) || (df < 1.0) )
+	{
+	mtherr( "chdtri", DOMAIN );
+	return(0.0);
+	}
+
+x = igami( 0.5 * df, y );
+return( 2.0 * x );
+}

libm/double/cheby.c

@@ -0,0 +1,149 @@
+/*	cheby.c
+ *
+ * Program to calculate coefficients of the Chebyshev polynomial
+ * expansion of a given input function.  The algorithm computes
+ * the discrete Fourier cosine transform of the function evaluated
+ * at unevenly spaced points.  Library routine chbevl.c uses the
+ * coefficients to calculate an approximate value of the original
+ * function.
+ *    -- S. L. Moshier
+ */
+
+extern double PI;		/* 3.14159...	*/
+extern double PIO2;
+double cosi[33] = {0.0,};	/* cosine array for Fourier transform	*/
+double func[65] = {0.0,};	/* values of the function		*/
+double cos(), log(), exp(), sqrt();
+
+main()
+{
+double c, r, s, t, x, y, z, temp;
+double low, high, dtemp;
+long n;
+int i, ii, j, n2, k, rr, invflg;
+short *p;
+char st[40];
+
+low = 0.0;		/* low end of approximation interval		*/
+high = 1.0;		/* high end					*/
+invflg = 0;		/* set to 1 if inverted interval, else zero	*/
+/* Note: inverted interval goes from 1/high to 1/low	*/
+z = 0.0;
+n = 64;			/* will find 64 coefficients			*/
+			/* but use only those greater than roundoff error */
+n2 = n/2;
+t = n;
+t = PI/t;
+
+/* calculate array of cosines */
+puts("calculating cosines");
+s = 1.0;
+cosi[0] = 1.0;
+i = 1;
+while( i < 32 )
+	{
+	y = cos( s * t );
+	cosi[i] = y;
+	s += 1.0;
+	++i;
+	}
+cosi[32] = 0.0;
+
+/*							cheby.c 2 */
+
+/* calculate function at special values of the argument */
+puts("calculating function values");
+x = low;
+y = high;
+if( invflg && (low != 0.0) )
+	{	/* inverted interval */
+	temp = 1.0/x;
+	x = 1.0/y;
+	y = temp;
+	}
+r = (x + y)/2.0;
+printf( "center %.15E  ", r);
+s = (y - x)/2.0;
+printf( "width %.15E\n", s);
+i = 0;
+while( i < 65 )
+	{
+	if( i < n2 )
+		c = cosi[i];
+	else
+		c = -cosi[64-i];
+	temp = r + s * c;
+/* if inverted interval, compute function(1/x)	*/
+	if( invflg && (temp != 0.0) )
+		temp = 1.0/temp;
+
+	printf( "%.15E  ", temp );
+
+/* insert call to function routine here:	*/
+/**********************************/
+
+	if( temp == 0.0 )
+		y = 1.0;
+	else
+		y = exp( temp * log(2.0) );
+
+/**********************************/
+	func[i] = y;
+	printf( "%.15E\n", y );
+	++i;
+	}
+
+/*							cheby.c 3 */
+
+puts( "calculating Chebyshev coefficients");
+rr = 0;
+while( rr < 65 )
+	{
+	z = func[0]/2.0;
+	j = 1;
+	while( j < 65 )
+		{
+		k = (rr * j)/n2;
+		i = rr * j - n2 * k;
+		k &= 3;
+		if( k == 0 )
+			c = cosi[i];
+		if( k == 1 )
+			{
+			i = 32-i;
+			c = -cosi[i];
+			if( i == 32 )
+				c = -c;
+			}
+		if( k == 2 )
+			{
+			c = -cosi[i];
+			}
+		if( k == 3 )
+			{
+			i = 32-i;
+			c = cosi[i];
+			}
+		if( i != 32)
+			{
+			temp = func[j];
+			temp = c * temp;
+			z += temp;
+			}
+		++j;
+		}
+
+	if( i != 32 )
+		{
+		temp /= 2.0;
+		z = z - temp;
+		}
+	z *= 2.0;
+	temp = n;
+	z /= temp;
+	dtemp = z;
+	++rr;
+	sprintf( st, "/* %.16E */", dtemp );
+	puts( st );
+	}
+}

libm/double/clog.c

@@ -0,0 +1,1043 @@
+/*							clog.c
+ *
+ *	Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clog();
+ * cmplx z, w;
+ *
+ * clog( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ *       w = log(r) + i arctan(y/x).
+ * 
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      7000       8.5e-17     1.9e-17
+ *    IEEE      -10,+10     30000       5.0e-15     1.1e-16
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
+ * absolute error 1.0e-16.
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#ifdef ANSIPROT
+static void cchsh ( double x, double *c, double *s );
+static double redupi ( double x );
+static double ctans ( cmplx *z );
+/* These are supposed to be in some standard place. */
+double fabs (double);
+double sqrt (double);
+double pow (double, double);
+double log (double);
+double exp (double);
+double atan2 (double, double);
+double cosh (double);
+double sinh (double);
+double asin (double);
+double sin (double);
+double cos (double);
+double cabs (cmplx *);
+void cadd ( cmplx *, cmplx *, cmplx * );
+void cmul ( cmplx *, cmplx *, cmplx * );
+void csqrt ( cmplx *, cmplx * );
+static void cchsh ( double, double *, double * );
+static double redupi ( double );
+static double ctans ( cmplx * );
+void clog ( cmplx *, cmplx * );
+void casin ( cmplx *, cmplx * );
+void cacos ( cmplx *, cmplx * );
+void catan ( cmplx *, cmplx * );
+#else
+static void cchsh();
+static double redupi();
+static double ctans();
+double cabs(), fabs(), sqrt(), pow();
+double log(), exp(), atan2(), cosh(), sinh();
+double asin(), sin(), cos();
+void cadd(), cmul(), csqrt();
+void clog(), casin(), cacos(), catan();
+#endif
+
+
+extern double MAXNUM, MACHEP, PI, PIO2;
+
+void clog( z, w )
+register cmplx *z, *w;
+{
+double p, rr;
+
+/*rr = sqrt( z->r * z->r  +  z->i * z->i );*/
+rr = cabs(z);
+p = log(rr);
+#if ANSIC
+rr = atan2( z->i, z->r );
+#else
+rr = atan2( z->r, z->i );
+if( rr > PI )
+	rr -= PI + PI;
+#endif
+w->i = rr;
+w->r = p;
+}
+/*							cexp()
+ *
+ *	Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexp();
+ * cmplx z, w;
+ *
+ * cexp( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ *     z = x + iy,
+ *     r = exp(x),
+ *
+ * then
+ *
+ *     w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8700       3.7e-17     1.1e-17
+ *    IEEE      -10,+10     30000       3.0e-16     8.7e-17
+ *
+ */
+
+void cexp( z, w )
+register cmplx *z, *w;
+{
+double r;
+
+r = exp( z->r );
+w->r = r * cos( z->i );
+w->i = r * sin( z->i );
+}
+/*							csin()
+ *
+ *	Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csin();
+ * cmplx z, w;
+ *
+ * csin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *     w = sin x  cosh y  +  i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8400       5.3e-17     1.3e-17
+ *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
+ * Also tested by csin(casin(z)) = z.
+ *
+ */
+
+void csin( z, w )
+register cmplx *z, *w;
+{
+double ch, sh;
+
+cchsh( z->i, &ch, &sh );
+w->r = sin( z->r ) * ch;
+w->i = cos( z->r ) * sh;
+}
+
+
+
+/* calculate cosh and sinh */
+
+static void cchsh( x, c, s )
+double x, *c, *s;
+{
+double e, ei;
+
+if( fabs(x) <= 0.5 )
+	{
+	*c = cosh(x);
+	*s = sinh(x);
+	}
+else
+	{
+	e = exp(x);
+	ei = 0.5/e;
+	e = 0.5 * e;
+	*s = e - ei;
+	*c = e + ei;
+	}
+}
+
+/*							ccos()
+ *
+ *	Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccos();
+ * cmplx z, w;
+ *
+ * ccos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *     w = cos x  cosh y  -  i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8400       4.5e-17     1.3e-17
+ *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
+ */
+
+void ccos( z, w )
+register cmplx *z, *w;
+{
+double ch, sh;
+
+cchsh( z->i, &ch, &sh );
+w->r = cos( z->r ) * ch;
+w->i = -sin( z->r ) * sh;
+}
+/*							ctan()
+ *
+ *	Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctan();
+ * cmplx z, w;
+ *
+ * ctan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *           sin 2x  +  i sinh 2y
+ *     w  =  --------------------.
+ *            cos 2x  +  cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2.  The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5200       7.1e-17     1.6e-17
+ *    IEEE      -10,+10     30000       7.2e-16     1.2e-16
+ * Also tested by ctan * ccot = 1 and catan(ctan(z))  =  z.
+ */
+
+void ctan( z, w )
+register cmplx *z, *w;
+{
+double d;
+
+d = cos( 2.0 * z->r ) + cosh( 2.0 * z->i );
+
+if( fabs(d) < 0.25 )
+	d = ctans(z);
+
+if( d == 0.0 )
+	{
+	mtherr( "ctan", OVERFLOW );
+	w->r = MAXNUM;
+	w->i = MAXNUM;
+	return;
+	}
+
+w->r = sin( 2.0 * z->r ) / d;
+w->i = sinh( 2.0 * z->i ) / d;
+}
+/*							ccot()
+ *
+ *	Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccot();
+ * cmplx z, w;
+ *
+ * ccot( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *           sin 2x  -  i sinh 2y
+ *     w  =  --------------------.
+ *            cosh 2y  -  cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2.  Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      3000       6.5e-17     1.6e-17
+ *    IEEE      -10,+10     30000       9.2e-16     1.2e-16
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+
+void ccot( z, w )
+register cmplx *z, *w;
+{
+double d;
+
+d = cosh(2.0 * z->i) - cos(2.0 * z->r);
+
+if( fabs(d) < 0.25 )
+	d = ctans(z);
+
+if( d == 0.0 )
+	{
+	mtherr( "ccot", OVERFLOW );
+	w->r = MAXNUM;
+	w->i = MAXNUM;
+	return;
+	}
+
+w->r = sin( 2.0 * z->r ) / d;
+w->i = -sinh( 2.0 * z->i ) / d;
+}
+
+/* Program to subtract nearest integer multiple of PI */
+/* extended precision value of PI: */
+#ifdef UNK
+static double DP1 = 3.14159265160560607910E0;
+static double DP2 = 1.98418714791870343106E-9;
+static double DP3 = 1.14423774522196636802E-17;
+#endif
+
+#ifdef DEC
+static unsigned short P1[] = {0040511,0007732,0120000,0000000,};
+static unsigned short P2[] = {0031010,0055060,0100000,0000000,};
+static unsigned short P3[] = {0022123,0011431,0105056,0001560,};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef IBMPC
+static unsigned short P1[] = {0x0000,0x5400,0x21fb,0x4009};
+static unsigned short P2[] = {0x0000,0x1000,0x0b46,0x3e21};
+static unsigned short P3[] = {0xc06e,0x3145,0x6263,0x3c6a};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef MIEEE
+static unsigned short P1[] = {
+0x4009,0x21fb,0x5400,0x0000
+};
+static unsigned short P2[] = {
+0x3e21,0x0b46,0x1000,0x0000
+};
+static unsigned short P3[] = {
+0x3c6a,0x6263,0x3145,0xc06e
+};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+static double redupi(x)
+double x;
+{
+double t;
+long i;
+
+t = x/PI;
+if( t >= 0.0 )
+	t += 0.5;
+else
+	t -= 0.5;
+
+i = t;	/* the multiple */
+t = i;
+t = ((x - t * DP1) - t * DP2) - t * DP3;
+return(t);
+}
+
+/*  Taylor series expansion for cosh(2y) - cos(2x)	*/
+
+static double ctans(z)
+cmplx *z;
+{
+double f, x, x2, y, y2, rn, t;
+double d;
+
+x = fabs( 2.0 * z->r );
+y = fabs( 2.0 * z->i );
+
+x = redupi(x);
+
+x = x * x;
+y = y * y;
+x2 = 1.0;
+y2 = 1.0;
+f = 1.0;
+rn = 0.0;
+d = 0.0;
+do
+	{
+	rn += 1.0;
+	f *= rn;
+	rn += 1.0;
+	f *= rn;
+	x2 *= x;
+	y2 *= y;
+	t = y2 + x2;
+	t /= f;
+	d += t;
+
+	rn += 1.0;
+	f *= rn;
+	rn += 1.0;
+	f *= rn;
+	x2 *= x;
+	y2 *= y;
+	t = y2 - x2;
+	t /= f;
+	d += t;
+	}
+while( fabs(t/d) > MACHEP );
+return(d);
+}
+/*							casin()
+ *
+ *	Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casin();
+ * cmplx z, w;
+ *
+ * casin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ *                               2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10     10100       2.1e-15     3.4e-16
+ *    IEEE      -10,+10     30000       2.2e-14     2.7e-15
+ * Larger relative error can be observed for z near zero.
+ * Also tested by csin(casin(z)) = z.
+ */
+
+void casin( z, w )
+cmplx *z, *w;
+{
+static cmplx ca, ct, zz, z2;
+double x, y;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0 )
+	{
+	if( fabs(x) > 1.0 )
+		{
+		w->r = PIO2;
+		w->i = 0.0;
+		mtherr( "casin", DOMAIN );
+		}
+	else
+		{
+		w->r = asin(x);
+		w->i = 0.0;
+		}
+	return;
+	}
+
+/* Power series expansion */
+/*
+b = cabs(z);
+if( b < 0.125 )
+{
+z2.r = (x - y) * (x + y);
+z2.i = 2.0 * x * y;
+
+cn = 1.0;
+n = 1.0;
+ca.r = x;
+ca.i = y;
+sum.r = x;
+sum.i = y;
+do
+	{
+	ct.r = z2.r * ca.r  -  z2.i * ca.i;
+	ct.i = z2.r * ca.i  +  z2.i * ca.r;
+	ca.r = ct.r;
+	ca.i = ct.i;
+
+	cn *= n;
+	n += 1.0;
+	cn /= n;
+	n += 1.0;
+	b = cn/n;
+
+	ct.r *= b;
+	ct.i *= b;
+	sum.r += ct.r;
+	sum.i += ct.i;
+	b = fabs(ct.r) + fabs(ct.i);
+	}
+while( b > MACHEP );
+w->r = sum.r;
+w->i = sum.i;
+return;
+}
+*/
+
+
+ca.r = x;
+ca.i = y;
+
+ct.r = -ca.i;	/* iz */
+ct.i = ca.r;
+
+	/* sqrt( 1 - z*z) */
+/* cmul( &ca, &ca, &zz ) */
+zz.r = (ca.r - ca.i) * (ca.r + ca.i);	/*x * x  -  y * y */
+zz.i = 2.0 * ca.r * ca.i;
+
+zz.r = 1.0 - zz.r;
+zz.i = -zz.i;
+csqrt( &zz, &z2 );
+
+cadd( &z2, &ct, &zz );
+clog( &zz, &zz );
+w->r = zz.i;	/* mult by 1/i = -i */
+w->i = -zz.r;
+return;
+}
+/*							cacos()
+ *
+ *	Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacos();
+ * cmplx z, w;
+ *
+ * cacos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z  =  PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5200      1.6e-15      2.8e-16
+ *    IEEE      -10,+10     30000      1.8e-14      2.2e-15
+ */
+
+void cacos( z, w )
+cmplx *z, *w;
+{
+
+casin( z, w );
+w->r = PIO2  -  w->r;
+w->i = -w->i;
+}
+/*							catan()
+ *
+ *	Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catan();
+ * cmplx z, w;
+ *
+ * catan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *          1       (    2x     )
+ * Re w  =  - arctan(-----------)  +  k PI
+ *          2       (     2    2)
+ *                  (1 - x  - y )
+ *
+ *               ( 2         2)
+ *          1    (x  +  (y+1) )
+ * Im w  =  - log(------------)
+ *          4    ( 2         2)
+ *               (x  +  (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5900       1.3e-16     7.8e-18
+ *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
+ * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
+ * had peak relative error 1.5e-16, rms relative error
+ * 2.9e-17.  See also clog().
+ */
+
+void catan( z, w )
+cmplx *z, *w;
+{
+double a, t, x, x2, y;
+
+x = z->r;
+y = z->i;
+
+if( (x == 0.0) && (y > 1.0) )
+	goto ovrf;
+
+x2 = x * x;
+a = 1.0 - x2 - (y * y);
+if( a == 0.0 )
+	goto ovrf;
+
+#if ANSIC
+t = atan2( 2.0 * x, a )/2.0;
+#else
+t = atan2( a, 2.0 * x )/2.0;
+#endif
+w->r = redupi( t );
+
+t = y - 1.0;
+a = x2 + (t * t);
+if( a == 0.0 )
+	goto ovrf;
+
+t = y + 1.0;
+a = (x2 + (t * t))/a;
+w->i = log(a)/4.0;
+return;
+
+ovrf:
+mtherr( "catan", OVERFLOW );
+w->r = MAXNUM;
+w->i = MAXNUM;
+}
+
+
+/*							csinh
+ *
+ *	Complex hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csinh();
+ * cmplx z, w;
+ *
+ * csinh( &z, &w );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * csinh z = (cexp(z) - cexp(-z))/2
+ *         = sinh x * cos y  +  i cosh x * sin y .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       3.1e-16     8.2e-17
+ *
+ */
+
+void
+csinh (z, w)
+     cmplx *z, *w;
+{
+  double x, y;
+
+  x = z->r;
+  y = z->i;
+  w->r = sinh (x) * cos (y);
+  w->i = cosh (x) * sin (y);
+}
+
+
+/*							casinh
+ *
+ *	Complex inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casinh();
+ * cmplx z, w;
+ *
+ * casinh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * casinh z = -i casin iz .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       1.8e-14     2.6e-15
+ *
+ */
+
+void
+casinh (z, w)
+     cmplx *z, *w;
+{
+  cmplx u;
+
+  u.r = 0.0;
+  u.i = 1.0;
+  cmul( z, &u, &u );
+  casin( &u, w );
+  u.r = 0.0;
+  u.i = -1.0;
+  cmul( &u, w, w );
+}
+
+/*							ccosh
+ *
+ *	Complex hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccosh();
+ * cmplx z, w;
+ *
+ * ccosh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * ccosh(z) = cosh x  cos y + i sinh x sin y .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       2.9e-16     8.1e-17
+ *
+ */
+
+void
+ccosh (z, w)
+     cmplx *z, *w;
+{
+  double x, y;
+
+  x = z->r;
+  y = z->i;
+  w->r = cosh (x) * cos (y);
+  w->i = sinh (x) * sin (y);
+}
+
+
+/*							cacosh
+ *
+ *	Complex inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacosh();
+ * cmplx z, w;
+ *
+ * cacosh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * acosh z = i acos z .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       1.6e-14     2.1e-15
+ *
+ */
+
+void
+cacosh (z, w)
+     cmplx *z, *w;
+{
+  cmplx u;
+
+  cacos( z, w );
+  u.r = 0.0;
+  u.i = 1.0;
+  cmul( &u, w, w );
+}
+
+
+/*							ctanh
+ *
+ *	Complex hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctanh();
+ * cmplx z, w;
+ *
+ * ctanh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * tanh z = (sinh 2x  +  i sin 2y) / (cosh 2x + cos 2y) .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       1.7e-14     2.4e-16
+ *
+ */
+
+/* 5.253E-02,1.550E+00 1.643E+01,6.553E+00 1.729E-14  21355  */
+
+void
+ctanh (z, w)
+     cmplx *z, *w;
+{
+  double x, y, d;
+
+  x = z->r;
+  y = z->i;
+  d = cosh (2.0 * x) + cos (2.0 * y);
+  w->r = sinh (2.0 * x) / d;
+  w->i = sin (2.0 * y) / d;
+  return;
+}
+
+
+/*							catanh
+ *
+ *	Complex inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catanh();
+ * cmplx z, w;
+ *
+ * catanh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse tanh, equal to  -i catan (iz);
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       2.3e-16     6.2e-17
+ *
+ */
+
+void
+catanh (z, w)
+     cmplx *z, *w;
+{
+  cmplx u;
+
+  u.r = 0.0;
+  u.i = 1.0;
+  cmul (z, &u, &u);  /* i z */
+  catan (&u, w);
+  u.r = 0.0;
+  u.i = -1.0;
+  cmul (&u, w, w);  /* -i catan iz */
+  return;
+}
+
+
+/*							cpow
+ *
+ *	Complex power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cpow();
+ * cmplx a, z, w;
+ *
+ * cpow (&a, &z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Raises complex A to the complex Zth power.
+ * Definition is per AMS55 # 4.2.8,
+ * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
+ *
+ */
+
+
+void
+cpow (a, z, w)
+     cmplx *a, *z, *w;
+{
+  double x, y, r, theta, absa, arga;
+
+  x = z->r;
+  y = z->i;
+  absa = cabs (a);
+  if (absa == 0.0)
+    {
+      w->r = 0.0;
+      w->i = 0.0;
+      return;
+    }
+  arga = atan2 (a->i, a->r);
+  r = pow (absa, x);
+  theta = x * arga;
+  if (y != 0.0)
+    {
+      r = r * exp (-y * arga);
+      theta = theta + y * log (absa);
+    }
+  w->r = r * cos (theta);
+  w->i = r * sin (theta);
+  return;
+}

libm/double/cmplx.c

@@ -0,0 +1,461 @@
+/*							cmplx.c
+ *
+ *	Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ *      double r;     real part
+ *      double i;     imaginary part
+ *     }cmplx;
+ *
+ * cmplx *a, *b, *c;
+ *
+ * cadd( a, b, c );     c = b + a
+ * csub( a, b, c );     c = b - a
+ * cmul( a, b, c );     c = b * a
+ * cdiv( a, b, c );     c = b / a
+ * cneg( c );           c = -c
+ * cmov( b, c );        c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ *    c.r  =  b.r + a.r
+ *    c.i  =  b.i + a.i
+ *
+ * Subtraction:
+ *    c.r  =  b.r - a.r
+ *    c.i  =  b.i - a.i
+ *
+ * Multiplication:
+ *    c.r  =  b.r * a.r  -  b.i * a.i
+ *    c.i  =  b.r * a.i  +  b.i * a.r
+ *
+ * Division:
+ *    d    =  a.r * a.r  +  a.i * a.i
+ *    c.r  = (b.r * a.r  + b.i * a.i)/d
+ *    c.i  = (b.i * a.r  -  b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17.  The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ *                      Relative error:
+ * arithmetic   function  # trials      peak         rms
+ *    DEC        cadd       10000       1.4e-17     3.4e-18
+ *    IEEE       cadd      100000       1.1e-16     2.7e-17
+ *    DEC        csub       10000       1.4e-17     4.5e-18
+ *    IEEE       csub      100000       1.1e-16     3.4e-17
+ *    DEC        cmul        3000       2.3e-17     8.7e-18
+ *    IEEE       cmul      100000       2.1e-16     6.9e-17
+ *    DEC        cdiv       18000       4.9e-17     1.3e-17
+ *    IEEE       cdiv      100000       3.7e-16     1.1e-16
+ */
+/*				cmplx.c
+ * complex number arithmetic
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double cabs ( cmplx * );
+extern double sqrt ( double );
+extern double atan2 ( double, double );
+extern double cos ( double );
+extern double sin ( double );
+extern double sqrt ( double );
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+int isnan ( double );
+void cdiv ( cmplx *, cmplx *, cmplx * );
+void cadd ( cmplx *, cmplx *, cmplx * );
+#else
+double fabs(), cabs(), sqrt(), atan2(), cos(), sin();
+double sqrt(), frexp(), ldexp();
+int isnan();
+void cdiv(), cadd();
+#endif
+
+extern double MAXNUM, MACHEP, PI, PIO2, INFINITY, NAN;
+/*
+typedef struct
+	{
+	double r;
+	double i;
+	}cmplx;
+*/
+cmplx czero = {0.0, 0.0};
+extern cmplx czero;
+cmplx cone = {1.0, 0.0};
+extern cmplx cone;
+
+/*	c = b + a	*/
+
+void cadd( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+
+c->r = b->r + a->r;
+c->i = b->i + a->i;
+}
+
+
+/*	c = b - a	*/
+
+void csub( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+
+c->r = b->r - a->r;
+c->i = b->i - a->i;
+}
+
+/*	c = b * a */
+
+void cmul( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+double y;
+
+y    = b->r * a->r  -  b->i * a->i;
+c->i = b->r * a->i  +  b->i * a->r;
+c->r = y;
+}
+
+
+
+/*	c = b / a */
+
+void cdiv( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+double y, p, q, w;
+
+
+y = a->r * a->r  +  a->i * a->i;
+p = b->r * a->r  +  b->i * a->i;
+q = b->i * a->r  -  b->r * a->i;
+
+if( y < 1.0 )
+	{
+	w = MAXNUM * y;
+	if( (fabs(p) > w) || (fabs(q) > w) || (y == 0.0) )
+		{
+		c->r = MAXNUM;
+		c->i = MAXNUM;
+		mtherr( "cdiv", OVERFLOW );
+		return;
+		}
+	}
+c->r = p/y;
+c->i = q/y;
+}
+
+
+/*	b = a
+   Caution, a `short' is assumed to be 16 bits wide.  */
+
+void cmov( a, b )
+void *a, *b;
+{
+register short *pa, *pb;
+int i;
+
+pa = (short *) a;
+pb = (short *) b;
+i = 8;
+do
+	*pb++ = *pa++;
+while( --i );
+}
+
+
+void cneg( a )
+register cmplx *a;
+{
+
+a->r = -a->r;
+a->i = -a->i;
+}
+
+/*							cabs()
+ *
+ *	Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double cabs();
+ * cmplx z;
+ * double a;
+ *
+ * a = cabs( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ *       a = sqrt( x**2 + y**2 ).
+ * 
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring.  If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -30,+30     30000       3.2e-17     9.2e-18
+ *    IEEE      -10,+10    100000       2.7e-16     6.9e-17
+ */
+
+
+/*
+Cephes Math Library Release 2.1:  January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/*
+typedef struct
+	{
+	double r;
+	double i;
+	}cmplx;
+*/
+
+#ifdef UNK
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+#ifdef DEC
+#define PREC 29
+#define MAXEXP 128
+#define MINEXP -128
+#endif
+#ifdef IBMPC
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+#ifdef MIEEE
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+
+
+double cabs( z )
+register cmplx *z;
+{
+double x, y, b, re, im;
+int ex, ey, e;
+
+#ifdef INFINITIES
+/* Note, cabs(INFINITY,NAN) = INFINITY. */
+if( z->r == INFINITY || z->i == INFINITY
+   || z->r == -INFINITY || z->i == -INFINITY )
+  return( INFINITY );
+#endif
+
+#ifdef NANS
+if( isnan(z->r) )
+  return(z->r);
+if( isnan(z->i) )
+  return(z->i);
+#endif
+
+re = fabs( z->r );
+im = fabs( z->i );
+
+if( re == 0.0 )
+	return( im );
+if( im == 0.0 )
+	return( re );
+
+/* Get the exponents of the numbers */
+x = frexp( re, &ex );
+y = frexp( im, &ey );
+
+/* Check if one number is tiny compared to the other */
+e = ex - ey;
+if( e > PREC )
+	return( re );
+if( e < -PREC )
+	return( im );
+
+/* Find approximate exponent e of the geometric mean. */
+e = (ex + ey) >> 1;
+
+/* Rescale so mean is about 1 */
+x = ldexp( re, -e );
+y = ldexp( im, -e );
+		
+/* Hypotenuse of the right triangle */
+b = sqrt( x * x  +  y * y );
+
+/* Compute the exponent of the answer. */
+y = frexp( b, &ey );
+ey = e + ey;
+
+/* Check it for overflow and underflow. */
+if( ey > MAXEXP )
+	{
+	mtherr( "cabs", OVERFLOW );
+	return( INFINITY );
+	}
+if( ey < MINEXP )
+	return(0.0);
+
+/* Undo the scaling */
+b = ldexp( b, e );
+return( b );
+}
+/*							csqrt()
+ *
+ *	Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrt();
+ * cmplx z, w;
+ *
+ * csqrt( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy,  r = |z|, then
+ *
+ *                       1/2
+ * Im w  =  [ (r - x)/2 ]   ,
+ *
+ * Re w  =  y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z.  The root chosen
+ * is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10     25000       3.2e-17     9.6e-18
+ *    IEEE      -10,+10    100000       3.2e-16     7.7e-17
+ *
+ *                        2
+ * Also tested by csqrt( z ) = z, and tested by arguments
+ * close to the real axis.
+ */
+
+
+void csqrt( z, w )
+cmplx *z, *w;
+{
+cmplx q, s;
+double x, y, r, t;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0 )
+	{
+	if( x < 0.0 )
+		{
+		w->r = 0.0;
+		w->i = sqrt(-x);
+		return;
+		}
+	else
+		{
+		w->r = sqrt(x);
+		w->i = 0.0;
+		return;
+		}
+	}
+
+
+if( x == 0.0 )
+	{
+	r = fabs(y);
+	r = sqrt(0.5*r);
+	if( y > 0 )
+		w->r = r;
+	else
+		w->r = -r;
+	w->i = r;
+	return;
+	}
+
+/* Approximate  sqrt(x^2+y^2) - x  =  y^2/2x - y^4/24x^3 + ... .
+ * The relative error in the first term is approximately y^2/12x^2 .
+ */
+if( (fabs(y) < 2.e-4 * fabs(x))
+   && (x > 0) )
+	{
+	t = 0.25*y*(y/x);
+	}
+else
+	{
+	r = cabs(z);
+	t = 0.5*(r - x);
+	}
+
+r = sqrt(t);
+q.i = r;
+q.r = y/(2.0*r);
+/* Heron iteration in complex arithmetic */
+cdiv( &q, z, &s );
+cadd( &q, &s, w );
+w->r *= 0.5;
+w->i *= 0.5;
+}
+
+
+double hypot( x, y )
+double x, y;
+{
+cmplx z;
+
+z.r = x;
+z.i = y;
+return( cabs(&z) );
+}

libm/double/coil.c

@@ -0,0 +1,63 @@
+/* Program to calculate the inductance of a coil
+ *
+ * Reference: E. Jahnke and F. Emde, _Tables of Functions_,
+ * 4th edition, Dover, 1945, pp 86-89.
+ */
+
+double sin(), cos(), atan(), ellpe(), ellpk();
+
+double d;
+double l;
+double N;
+
+/* double PI = 3.14159265358979323846; */
+extern double PI;
+
+main()
+{
+double a, f, tana, sina, K, E, m, L, t;
+
+printf( "Self inductance of circular solenoidal coil\n" );
+
+loop:
+getnum( "diameter in centimeters", &d );
+if( d < 0.0 )
+	exit(0);  /* escape gracefully */
+getnum( "length in centimeters", &l );
+if( d < 0.0 )
+	exit(0);
+getnum( "total number of turns", &N );
+if( d < 0.0 )
+	exit(0);
+tana = d/l;        /* form factor */
+a = atan( tana );
+sina = sin(a);     /* modulus of the elliptic functions (k) */
+m = cos(a);        /* subroutine argument = 1 - k^2 */
+m = m * m;
+K = ellpk(m);
+E = ellpe(m);
+tana = tana * tana;  /* square of tan(a) */
+
+f = ((K + (tana - 1.0) * E)/sina  -  tana)/3.0;
+L = 4.e-9 * PI * N * N * d * f;
+printf( "L = %.4e Henries\n", L );
+goto loop;
+}
+
+
+/* Get value entered on keyboard
+ */
+getnum( str, pd )
+char *str;
+double *pd;
+{
+char s[40];
+
+printf( "%s (%.10e) ? ", str, *pd );
+gets(s);
+if( s[0] != '\0' )
+	{
+	sscanf( s, "%lf", pd );
+	printf( "%.10e\n", *pd );
+	}
+}

libm/double/const.c

@@ -0,0 +1,252 @@
+/*							const.c
+ *
+ *	Globally declared constants
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * extern double nameofconstant;
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This file contains a number of mathematical constants and
+ * also some needed size parameters of the computer arithmetic.
+ * The values are supplied as arrays of hexadecimal integers
+ * for IEEE arithmetic; arrays of octal constants for DEC
+ * arithmetic; and in a normal decimal scientific notation for
+ * other machines.  The particular notation used is determined
+ * by a symbol (DEC, IBMPC, or UNK) defined in the include file
+ * math.h.
+ *
+ * The default size parameters are as follows.
+ *
+ * For DEC and UNK modes:
+ * MACHEP =  1.38777878078144567553E-17       2**-56
+ * MAXLOG =  8.8029691931113054295988E1       log(2**127)
+ * MINLOG = -8.872283911167299960540E1        log(2**-128)
+ * MAXNUM =  1.701411834604692317316873e38    2**127
+ *
+ * For IEEE arithmetic (IBMPC):
+ * MACHEP =  1.11022302462515654042E-16       2**-53
+ * MAXLOG =  7.09782712893383996843E2         log(2**1024)
+ * MINLOG = -7.08396418532264106224E2         log(2**-1022)
+ * MAXNUM =  1.7976931348623158E308           2**1024
+ *
+ * The global symbols for mathematical constants are
+ * PI     =  3.14159265358979323846           pi
+ * PIO2   =  1.57079632679489661923           pi/2
+ * PIO4   =  7.85398163397448309616E-1        pi/4
+ * SQRT2  =  1.41421356237309504880           sqrt(2)
+ * SQRTH  =  7.07106781186547524401E-1        sqrt(2)/2
+ * LOG2E  =  1.4426950408889634073599         1/log(2)
+ * SQ2OPI =  7.9788456080286535587989E-1      sqrt( 2/pi )
+ * LOGE2  =  6.93147180559945309417E-1        log(2)
+ * LOGSQ2 =  3.46573590279972654709E-1        log(2)/2
+ * THPIO4 =  2.35619449019234492885           3*pi/4
+ * TWOOPI =  6.36619772367581343075535E-1     2/pi
+ *
+ * These lists are subject to change.
+ */
+
+/*							const.c */
+
+/*
+Cephes Math Library Release 2.3:  March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+#if 1
+double MACHEP =  1.11022302462515654042E-16;   /* 2**-53 */
+#else
+double MACHEP =  1.38777878078144567553E-17;   /* 2**-56 */
+#endif
+double UFLOWTHRESH =  2.22507385850720138309E-308; /* 2**-1022 */
+#ifdef DENORMAL
+double MAXLOG =  7.09782712893383996732E2;     /* log(MAXNUM) */
+/* double MINLOG = -7.44440071921381262314E2; */     /* log(2**-1074) */
+double MINLOG = -7.451332191019412076235E2;     /* log(2**-1075) */
+#else
+double MAXLOG =  7.08396418532264106224E2;     /* log 2**1022 */
+double MINLOG = -7.08396418532264106224E2;     /* log 2**-1022 */
+#endif
+double MAXNUM =  1.79769313486231570815E308;    /* 2**1024*(1-MACHEP) */
+double PI     =  3.14159265358979323846;       /* pi */
+double PIO2   =  1.57079632679489661923;       /* pi/2 */
+double PIO4   =  7.85398163397448309616E-1;    /* pi/4 */
+double SQRT2  =  1.41421356237309504880;       /* sqrt(2) */
+double SQRTH  =  7.07106781186547524401E-1;    /* sqrt(2)/2 */
+double LOG2E  =  1.4426950408889634073599;     /* 1/log(2) */
+double SQ2OPI =  7.9788456080286535587989E-1;  /* sqrt( 2/pi ) */
+double LOGE2  =  6.93147180559945309417E-1;    /* log(2) */
+double LOGSQ2 =  3.46573590279972654709E-1;    /* log(2)/2 */
+double THPIO4 =  2.35619449019234492885;       /* 3*pi/4 */
+double TWOOPI =  6.36619772367581343075535E-1; /* 2/pi */
+#ifdef INFINITIES
+double INFINITY = 1.0/0.0;  /* 99e999; */
+#else
+double INFINITY =  1.79769313486231570815E308;    /* 2**1024*(1-MACHEP) */
+#endif
+#ifdef NANS
+double NAN = 1.0/0.0 - 1.0/0.0;
+#else
+double NAN = 0.0;
+#endif
+#ifdef MINUSZERO
+double NEGZERO = -0.0;
+#else
+double NEGZERO = 0.0;
+#endif
+#endif
+
+#ifdef IBMPC
+			/* 2**-53 =  1.11022302462515654042E-16 */
+unsigned short MACHEP[4] = {0x0000,0x0000,0x0000,0x3ca0};
+unsigned short UFLOWTHRESH[4] = {0x0000,0x0000,0x0000,0x0010};
+#ifdef DENORMAL
+			/* log(MAXNUM) =  7.09782712893383996732224E2 */
+unsigned short MAXLOG[4] = {0x39ef,0xfefa,0x2e42,0x4086};
+			/* log(2**-1074) = - -7.44440071921381262314E2 */
+/*unsigned short MINLOG[4] = {0x71c3,0x446d,0x4385,0xc087};*/
+unsigned short MINLOG[4] = {0x3052,0xd52d,0x4910,0xc087};
+#else
+			/* log(2**1022) =   7.08396418532264106224E2 */
+unsigned short MAXLOG[4] = {0xbcd2,0xdd7a,0x232b,0x4086};
+			/* log(2**-1022) = - 7.08396418532264106224E2 */
+unsigned short MINLOG[4] = {0xbcd2,0xdd7a,0x232b,0xc086};
+#endif
+			/* 2**1024*(1-MACHEP) =  1.7976931348623158E308 */
+unsigned short MAXNUM[4] = {0xffff,0xffff,0xffff,0x7fef};
+unsigned short PI[4]     = {0x2d18,0x5444,0x21fb,0x4009};
+unsigned short PIO2[4]   = {0x2d18,0x5444,0x21fb,0x3ff9};
+unsigned short PIO4[4]   = {0x2d18,0x5444,0x21fb,0x3fe9};
+unsigned short SQRT2[4]  = {0x3bcd,0x667f,0xa09e,0x3ff6};
+unsigned short SQRTH[4]  = {0x3bcd,0x667f,0xa09e,0x3fe6};
+unsigned short LOG2E[4]  = {0x82fe,0x652b,0x1547,0x3ff7};
+unsigned short SQ2OPI[4] = {0x3651,0x33d4,0x8845,0x3fe9};
+unsigned short LOGE2[4]  = {0x39ef,0xfefa,0x2e42,0x3fe6};
+unsigned short LOGSQ2[4] = {0x39ef,0xfefa,0x2e42,0x3fd6};
+unsigned short THPIO4[4] = {0x21d2,0x7f33,0xd97c,0x4002};
+unsigned short TWOOPI[4] = {0xc883,0x6dc9,0x5f30,0x3fe4};
+#ifdef INFINITIES
+unsigned short INFINITY[4] = {0x0000,0x0000,0x0000,0x7ff0};
+#else
+unsigned short INFINITY[4] = {0xffff,0xffff,0xffff,0x7fef};
+#endif
+#ifdef NANS
+unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x7ffc};
+#else
+unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
+#endif
+#ifdef MINUSZERO
+unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x8000};
+#else
+unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
+#endif
+#endif
+
+#ifdef MIEEE
+			/* 2**-53 =  1.11022302462515654042E-16 */
+unsigned short MACHEP[4] = {0x3ca0,0x0000,0x0000,0x0000};
+unsigned short UFLOWTHRESH[4] = {0x0010,0x0000,0x0000,0x0000};
+#ifdef DENORMAL
+			/* log(2**1024) =   7.09782712893383996843E2 */
+unsigned short MAXLOG[4] = {0x4086,0x2e42,0xfefa,0x39ef};
+			/* log(2**-1074) = - -7.44440071921381262314E2 */
+/* unsigned short MINLOG[4] = {0xc087,0x4385,0x446d,0x71c3}; */
+unsigned short MINLOG[4] = {0xc087,0x4910,0xd52d,0x3052};
+#else
+			/* log(2**1022) =  7.08396418532264106224E2 */
+unsigned short MAXLOG[4] = {0x4086,0x232b,0xdd7a,0xbcd2};
+			/* log(2**-1022) = - 7.08396418532264106224E2 */
+unsigned short MINLOG[4] = {0xc086,0x232b,0xdd7a,0xbcd2};
+#endif
+			/* 2**1024*(1-MACHEP) =  1.7976931348623158E308 */
+unsigned short MAXNUM[4] = {0x7fef,0xffff,0xffff,0xffff};
+unsigned short PI[4]     = {0x4009,0x21fb,0x5444,0x2d18};
+unsigned short PIO2[4]   = {0x3ff9,0x21fb,0x5444,0x2d18};
+unsigned short PIO4[4]   = {0x3fe9,0x21fb,0x5444,0x2d18};
+unsigned short SQRT2[4]  = {0x3ff6,0xa09e,0x667f,0x3bcd};
+unsigned short SQRTH[4]  = {0x3fe6,0xa09e,0x667f,0x3bcd};
+unsigned short LOG2E[4]  = {0x3ff7,0x1547,0x652b,0x82fe};
+unsigned short SQ2OPI[4] = {0x3fe9,0x8845,0x33d4,0x3651};
+unsigned short LOGE2[4]  = {0x3fe6,0x2e42,0xfefa,0x39ef};
+unsigned short LOGSQ2[4] = {0x3fd6,0x2e42,0xfefa,0x39ef};
+unsigned short THPIO4[4] = {0x4002,0xd97c,0x7f33,0x21d2};
+unsigned short TWOOPI[4] = {0x3fe4,0x5f30,0x6dc9,0xc883};
+#ifdef INFINITIES
+unsigned short INFINITY[4] = {0x7ff0,0x0000,0x0000,0x0000};
+#else
+unsigned short INFINITY[4] = {0x7fef,0xffff,0xffff,0xffff};
+#endif
+#ifdef NANS
+unsigned short NAN[4] = {0x7ff8,0x0000,0x0000,0x0000};
+#else
+unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
+#endif
+#ifdef MINUSZERO
+unsigned short NEGZERO[4] = {0x8000,0x0000,0x0000,0x0000};
+#else
+unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
+#endif
+#endif
+
+#ifdef DEC
+			/* 2**-56 =  1.38777878078144567553E-17 */
+unsigned short MACHEP[4] = {0022200,0000000,0000000,0000000};
+unsigned short UFLOWTHRESH[4] = {0x0080,0x0000,0x0000,0x0000};
+			/* log 2**127 = 88.029691931113054295988 */
+unsigned short MAXLOG[4] = {041660,007463,0143742,025733,};
+			/* log 2**-128 = -88.72283911167299960540 */
+unsigned short MINLOG[4] = {0141661,071027,0173721,0147572,};
+			/* 2**127 = 1.701411834604692317316873e38 */
+unsigned short MAXNUM[4] = {077777,0177777,0177777,0177777,};
+unsigned short PI[4]     = {040511,007732,0121041,064302,};
+unsigned short PIO2[4]   = {040311,007732,0121041,064302,};
+unsigned short PIO4[4]   = {040111,007732,0121041,064302,};
+unsigned short SQRT2[4]  = {040265,002363,031771,0157145,};
+unsigned short SQRTH[4]  = {040065,002363,031771,0157144,};
+unsigned short LOG2E[4]  = {040270,0125073,024534,013761,};
+unsigned short SQ2OPI[4] = {040114,041051,0117241,0131204,};
+unsigned short LOGE2[4]  = {040061,071027,0173721,0147572,};
+unsigned short LOGSQ2[4] = {037661,071027,0173721,0147572,};
+unsigned short THPIO4[4] = {040426,0145743,0174631,007222,};
+unsigned short TWOOPI[4] = {040042,0174603,067116,042025,};
+/* Approximate infinity by MAXNUM.  */
+unsigned short INFINITY[4] = {077777,0177777,0177777,0177777,};
+unsigned short NAN[4] = {0000000,0000000,0000000,0000000};
+#ifdef MINUSZERO
+unsigned short NEGZERO[4] = {0000000,0000000,0000000,0100000};
+#else
+unsigned short NEGZERO[4] = {0000000,0000000,0000000,0000000};
+#endif
+#endif
+
+#ifndef UNK
+extern unsigned short MACHEP[];
+extern unsigned short UFLOWTHRESH[];
+extern unsigned short MAXLOG[];
+extern unsigned short UNDLOG[];
+extern unsigned short MINLOG[];
+extern unsigned short MAXNUM[];
+extern unsigned short PI[];
+extern unsigned short PIO2[];
+extern unsigned short PIO4[];
+extern unsigned short SQRT2[];
+extern unsigned short SQRTH[];
+extern unsigned short LOG2E[];
+extern unsigned short SQ2OPI[];
+extern unsigned short LOGE2[];
+extern unsigned short LOGSQ2[];
+extern unsigned short THPIO4[];
+extern unsigned short TWOOPI[];
+extern unsigned short INFINITY[];
+extern unsigned short NAN[];
+extern unsigned short NEGZERO[];
+#endif

libm/double/cosh.c

@@ -0,0 +1,83 @@
+/*							cosh.c
+ *
+ *	Hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cosh();
+ *
+ * y = cosh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic cosine of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * cosh(x)  =  ( exp(x) + exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       +- 88       50000       4.0e-17     7.7e-18
+ *    IEEE     +-MAXLOG     30000       2.6e-16     5.7e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * cosh overflow    |x| > MAXLOG       MAXNUM
+ *
+ *
+ */
+
+/*							cosh.c */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1985, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double exp ( double );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double exp();
+int isnan(), isfinite();
+#endif
+extern double MAXLOG, INFINITY, LOGE2;
+
+double cosh(x)
+double x;
+{
+double y;
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+if( x < 0 )
+	x = -x;
+if( x > (MAXLOG + LOGE2) )
+	{
+	mtherr( "cosh", OVERFLOW );
+	return( INFINITY );
+	}	
+if( x >= (MAXLOG - LOGE2) )
+	{
+	y = exp(0.5 * x);
+	y = (0.5 * y) * y;
+	return(y);
+	}
+y = exp(x);
+y = 0.5 * (y + 1.0 / y);
+return( y );
+}

libm/double/cpmul.c

@@ -0,0 +1,104 @@
+/*							cpmul.c
+ *
+ *	Multiply two polynomials with complex coefficients
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ *		{
+ *		double r;
+ *		double i;
+ *		}cmplx;
+ *
+ * cmplx a[], b[], c[];
+ * int da, db, dc;
+ *
+ * cpmul( a, da, b, db, c, &dc );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The two argument polynomials are multiplied together, and
+ * their product is placed in c.
+ *
+ * Each polynomial is represented by its coefficients stored
+ * as an array of complex number structures (see the typedef).
+ * The degree of a is da, which must be passed to the routine
+ * as an argument; similarly the degree db of b is an argument.
+ * Array a has da + 1 elements and array b has db + 1 elements.
+ * Array c must have storage allocated for at least da + db + 1
+ * elements.  The value da + db is returned in dc; this is
+ * the degree of the product polynomial.
+ *
+ * Polynomial coefficients are stored in ascending order; i.e.,
+ * a(x) = a[0]*x**0 + a[1]*x**1 + ... + a[da]*x**da.
+ *
+ *
+ * If desired, c may be the same as either a or b, in which
+ * case the input argument array is replaced by the product
+ * array (but only up to terms of degree da + db).
+ *
+ */
+
+/*							cpmul	*/
+
+typedef struct
+	{
+	double r;
+	double i;
+	}cmplx;
+
+int cpmul( a, da, b, db, c, dc )
+cmplx *a, *b, *c;
+int da, db;
+int *dc;
+{
+int i, j, k;
+cmplx y;
+register cmplx *pa, *pb, *pc;
+
+if( da > db )	/* Know which polynomial has higher degree */
+	{
+	i = da;	/* Swapping is OK because args are on the stack */
+	da = db;
+	db = i;
+	pa = a;
+	a = b;
+	b = pa;
+	}
+	
+k = da + db;
+*dc = k;		/* Output the degree of the product */
+pc = &c[db+1];
+for( i=db+1; i<=k; i++ )	/* Clear high order terms of output */
+	{
+	pc->r = 0;
+	pc->i = 0;
+	pc++;
+	}
+/* To permit replacement of input, work backward from highest degree */
+pb = &b[db];
+for( j=0; j<=db; j++ )
+	{
+	pa = &a[da];
+	pc = &c[k-j];
+	for( i=0; i<da; i++ )
+		{
+		y.r = pa->r * pb->r  -  pa->i * pb->i;	/* cmpx multiply */
+		y.i = pa->r * pb->i  +  pa->i * pb->r;
+		pc->r += y.r;	/* accumulate partial product */
+		pc->i += y.i;
+		pa--;
+		pc--;
+		}
+	y.r = pa->r * pb->r  -  pa->i * pb->i;	/* replace last term,	*/
+	y.i = pa->r * pb->i  +  pa->i * pb->r;	/* ...do not accumulate	*/
+	pc->r = y.r;
+	pc->i = y.i;
+	pb--;
+	}
+  return 0;
+}

libm/double/dawsn.c

@@ -0,0 +1,392 @@
+/*							dawsn.c
+ *
+ *	Dawson's Integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, dawsn();
+ *
+ * y = dawsn( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *                             x
+ *                             -
+ *                      2     | |        2
+ *  dawsn(x)  =  exp( -x  )   |    exp( t  ) dt
+ *                          | |
+ *                           -
+ *                           0
+ *
+ * Three different rational approximations are employed, for
+ * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,10        10000       6.9e-16     1.0e-16
+ *    DEC       0,10         6000       7.4e-17     1.4e-17
+ *
+ *
+ */
+
+/*							dawsn.c */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+/* Dawson's integral, interval 0 to 3.25 */
+#ifdef UNK
+static double AN[10] = {
+ 1.13681498971755972054E-11,
+ 8.49262267667473811108E-10,
+ 1.94434204175553054283E-8,
+ 9.53151741254484363489E-7,
+ 3.07828309874913200438E-6,
+ 3.52513368520288738649E-4,
+-8.50149846724410912031E-4,
+ 4.22618223005546594270E-2,
+-9.17480371773452345351E-2,
+ 9.99999999999999994612E-1,
+};
+static double AD[11] = {
+ 2.40372073066762605484E-11,
+ 1.48864681368493396752E-9,
+ 5.21265281010541664570E-8,
+ 1.27258478273186970203E-6,
+ 2.32490249820789513991E-5,
+ 3.25524741826057911661E-4,
+ 3.48805814657162590916E-3,
+ 2.79448531198828973716E-2,
+ 1.58874241960120565368E-1,
+ 5.74918629489320327824E-1,
+ 1.00000000000000000539E0,
+};
+#endif
+#ifdef DEC
+static unsigned short AN[40] = {
+0027107,0176630,0075752,0107612,
+0030551,0070604,0166707,0127727,
+0031647,0002210,0117120,0056376,
+0033177,0156026,0141275,0140627,
+0033516,0112200,0037035,0165515,
+0035270,0150613,0016423,0105634,
+0135536,0156227,0023515,0044413,
+0037055,0015273,0105147,0064025,
+0137273,0163145,0014460,0166465,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short AD[44] = {
+0027323,0067372,0115566,0131320,
+0030714,0114432,0074206,0006637,
+0032137,0160671,0044203,0026344,
+0033252,0146656,0020247,0100231,
+0034303,0003346,0123260,0022433,
+0035252,0125460,0173041,0155415,
+0036144,0113747,0125203,0124617,
+0036744,0166232,0143671,0133670,
+0037442,0127755,0162625,0000100,
+0040023,0026736,0003604,0106265,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short AN[40] = {
+0x51f1,0x0f7d,0xffb3,0x3da8,
+0xf5fb,0x9db8,0x2e30,0x3e0d,
+0x0ba0,0x13ca,0xe091,0x3e54,
+0xb833,0xd857,0xfb82,0x3eaf,
+0xbd6a,0x07c3,0xd290,0x3ec9,
+0x7174,0x63a2,0x1a31,0x3f37,
+0xa921,0xe4e9,0xdb92,0xbf4b,
+0xed03,0x714c,0xa357,0x3fa5,
+0x1da7,0xa326,0x7ccc,0xbfb7,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short AD[44] = {
+0xd65a,0x536e,0x6ddf,0x3dba,
+0xc1b4,0x4f10,0x9323,0x3e19,
+0x659c,0x2910,0xfc37,0x3e6b,
+0xf013,0xc414,0x59b5,0x3eb5,
+0x04a3,0xd4d6,0x60dc,0x3ef8,
+0x3b62,0x1ec4,0x5566,0x3f35,
+0x7532,0xf550,0x92fc,0x3f6c,
+0x36f7,0x58f7,0x9d93,0x3f9c,
+0xa008,0xbcb2,0x55fd,0x3fc4,
+0x9197,0xc0f0,0x65bb,0x3fe2,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short AN[40] = {
+0x3da8,0xffb3,0x0f7d,0x51f1,
+0x3e0d,0x2e30,0x9db8,0xf5fb,
+0x3e54,0xe091,0x13ca,0x0ba0,
+0x3eaf,0xfb82,0xd857,0xb833,
+0x3ec9,0xd290,0x07c3,0xbd6a,
+0x3f37,0x1a31,0x63a2,0x7174,
+0xbf4b,0xdb92,0xe4e9,0xa921,
+0x3fa5,0xa357,0x714c,0xed03,
+0xbfb7,0x7ccc,0xa326,0x1da7,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short AD[44] = {
+0x3dba,0x6ddf,0x536e,0xd65a,
+0x3e19,0x9323,0x4f10,0xc1b4,
+0x3e6b,0xfc37,0x2910,0x659c,
+0x3eb5,0x59b5,0xc414,0xf013,
+0x3ef8,0x60dc,0xd4d6,0x04a3,
+0x3f35,0x5566,0x1ec4,0x3b62,
+0x3f6c,0x92fc,0xf550,0x7532,
+0x3f9c,0x9d93,0x58f7,0x36f7,
+0x3fc4,0x55fd,0xbcb2,0xa008,
+0x3fe2,0x65bb,0xc0f0,0x9197,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+/* interval 3.25 to 6.25 */
+#ifdef UNK
+static double BN[11] = {
+ 5.08955156417900903354E-1,
+-2.44754418142697847934E-1,
+ 9.41512335303534411857E-2,
+-2.18711255142039025206E-2,
+ 3.66207612329569181322E-3,
+-4.23209114460388756528E-4,
+ 3.59641304793896631888E-5,
+-2.14640351719968974225E-6,
+ 9.10010780076391431042E-8,
+-2.40274520828250956942E-9,
+ 3.59233385440928410398E-11,
+};
+static double BD[10] = {
+/*  1.00000000000000000000E0,*/
+-6.31839869873368190192E-1,
+ 2.36706788228248691528E-1,
+-5.31806367003223277662E-2,
+ 8.48041718586295374409E-3,
+-9.47996768486665330168E-4,
+ 7.81025592944552338085E-5,
+-4.55875153252442634831E-6,
+ 1.89100358111421846170E-7,
+-4.91324691331920606875E-9,
+ 7.18466403235734541950E-11,
+};
+#endif
+#ifdef DEC
+static unsigned short BN[44] = {
+0040002,0045342,0113762,0004360,
+0137572,0120346,0172745,0144046,
+0037300,0151134,0123440,0117047,
+0136663,0025423,0014755,0046026,
+0036157,0177561,0027535,0046744,
+0135335,0161052,0071243,0146535,
+0034426,0154060,0164506,0135625,
+0133420,0005356,0100017,0151334,
+0032303,0066137,0024013,0046212,
+0131045,0016612,0066270,0047574,
+0027435,0177025,0060625,0116363,
+};
+static unsigned short BD[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0140041,0140101,0174552,0037073,
+0037562,0061503,0124271,0160756,
+0137131,0151760,0073210,0110534,
+0036412,0170562,0117017,0155377,
+0135570,0101374,0074056,0037276,
+0034643,0145376,0001516,0060636,
+0133630,0173540,0121344,0155231,
+0032513,0005602,0134516,0007144,
+0131250,0150540,0075747,0105341,
+0027635,0177020,0012465,0125402,
+};
+#endif
+#ifdef IBMPC
+static unsigned short BN[44] = {
+0x411e,0x52fe,0x495c,0x3fe0,
+0xb905,0xdebc,0x541c,0xbfcf,
+0x13c5,0x94e4,0x1a4b,0x3fb8,
+0xa983,0x633d,0x6562,0xbf96,
+0xa9bd,0x25eb,0xffee,0x3f6d,
+0x79ac,0x4e54,0xbc45,0xbf3b,
+0xd773,0x1d28,0xdb06,0x3f02,
+0xfa5b,0xd001,0x015d,0xbec2,
+0x6991,0xe501,0x6d8b,0x3e78,
+0x09f0,0x4d97,0xa3b1,0xbe24,
+0xb39e,0xac32,0xbfc2,0x3dc3,
+};
+static unsigned short BD[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x47c7,0x3f2d,0x3808,0xbfe4,
+0x3c3e,0x7517,0x4c68,0x3fce,
+0x122b,0x0ed1,0x3a7e,0xbfab,
+0xfb60,0x53c1,0x5e2e,0x3f81,
+0xc7d8,0x8f05,0x105f,0xbf4f,
+0xcc34,0xc069,0x795f,0x3f14,
+0x9b53,0x145c,0x1eec,0xbed3,
+0xc1cd,0x5729,0x6170,0x3e89,
+0xf15c,0x0f7c,0x1a2c,0xbe35,
+0xb560,0x02a6,0xbfc2,0x3dd3,
+};
+#endif
+#ifdef MIEEE
+static unsigned short BN[44] = {
+0x3fe0,0x495c,0x52fe,0x411e,
+0xbfcf,0x541c,0xdebc,0xb905,
+0x3fb8,0x1a4b,0x94e4,0x13c5,
+0xbf96,0x6562,0x633d,0xa983,
+0x3f6d,0xffee,0x25eb,0xa9bd,
+0xbf3b,0xbc45,0x4e54,0x79ac,
+0x3f02,0xdb06,0x1d28,0xd773,
+0xbec2,0x015d,0xd001,0xfa5b,
+0x3e78,0x6d8b,0xe501,0x6991,
+0xbe24,0xa3b1,0x4d97,0x09f0,
+0x3dc3,0xbfc2,0xac32,0xb39e,
+};
+static unsigned short BD[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xbfe4,0x3808,0x3f2d,0x47c7,
+0x3fce,0x4c68,0x7517,0x3c3e,
+0xbfab,0x3a7e,0x0ed1,0x122b,
+0x3f81,0x5e2e,0x53c1,0xfb60,
+0xbf4f,0x105f,0x8f05,0xc7d8,
+0x3f14,0x795f,0xc069,0xcc34,
+0xbed3,0x1eec,0x145c,0x9b53,
+0x3e89,0x6170,0x5729,0xc1cd,
+0xbe35,0x1a2c,0x0f7c,0xf15c,
+0x3dd3,0xbfc2,0x02a6,0xb560,
+};
+#endif
+
+/* 6.25 to infinity */
+#ifdef UNK
+static double CN[5] = {
+-5.90592860534773254987E-1,
+ 6.29235242724368800674E-1,
+-1.72858975380388136411E-1,
+ 1.64837047825189632310E-2,
+-4.86827613020462700845E-4,
+};
+static double CD[5] = {
+/* 1.00000000000000000000E0,*/
+-2.69820057197544900361E0,
+ 1.73270799045947845857E0,
+-3.93708582281939493482E-1,
+ 3.44278924041233391079E-2,
+-9.73655226040941223894E-4,
+};
+#endif
+#ifdef DEC
+static unsigned short CN[20] = {
+0140027,0030427,0176477,0074402,
+0040041,0012617,0112375,0162657,
+0137461,0000761,0074120,0135160,
+0036607,0004325,0117246,0115525,
+0135377,0036345,0064750,0047732,
+};
+static unsigned short CD[20] = {
+/*0040200,0000000,0000000,0000000,*/
+0140454,0127521,0071653,0133415,
+0040335,0144540,0016105,0045241,
+0137711,0112053,0155034,0062237,
+0037015,0002102,0177442,0074546,
+0135577,0036345,0064750,0052152,
+};
+#endif
+#ifdef IBMPC
+static unsigned short CN[20] = {
+0xef20,0xffa7,0xe622,0xbfe2,
+0xbcb6,0xf29f,0x22b1,0x3fe4,
+0x174e,0x2f0a,0x203e,0xbfc6,
+0xd36b,0xb3d4,0xe11a,0x3f90,
+0x09fb,0xad3d,0xe79c,0xbf3f,
+};
+static unsigned short CD[20] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x76e2,0x2e75,0x95ea,0xc005,
+0xa954,0x0388,0xb92c,0x3ffb,
+0x8c94,0x7b43,0x3285,0xbfd9,
+0x4f2d,0x5fe4,0xa088,0x3fa1,
+0x0a8d,0xad3d,0xe79c,0xbf4f,
+};
+#endif
+#ifdef MIEEE
+static unsigned short CN[20] = {
+0xbfe2,0xe622,0xffa7,0xef20,
+0x3fe4,0x22b1,0xf29f,0xbcb6,
+0xbfc6,0x203e,0x2f0a,0x174e,
+0x3f90,0xe11a,0xb3d4,0xd36b,
+0xbf3f,0xe79c,0xad3d,0x09fb,
+};
+static unsigned short CD[20] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc005,0x95ea,0x2e75,0x76e2,
+0x3ffb,0xb92c,0x0388,0xa954,
+0xbfd9,0x3285,0x7b43,0x8c94,
+0x3fa1,0xa088,0x5fe4,0x4f2d,
+0xbf4f,0xe79c,0xad3d,0x0a8d,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+double chbevl(), sqrt(), fabs(), polevl(), p1evl();
+#endif
+extern double PI, MACHEP;
+
+double dawsn( xx )
+double xx;
+{
+double x, y;
+int sign;
+
+
+sign = 1;
+if( xx < 0.0 )
+	{
+	sign = -1;
+	xx = -xx;
+	}
+
+if( xx < 3.25 )
+{
+x = xx*xx;
+y = xx * polevl( x, AN, 9 )/polevl( x, AD, 10 );
+return( sign * y );
+}
+
+
+x = 1.0/(xx*xx);
+
+if( xx < 6.25 )
+	{
+	y = 1.0/xx + x * polevl( x, BN, 10) / (p1evl( x, BD, 10) * xx);
+	return( sign * 0.5 * y );
+	}
+
+
+if( xx > 1.0e9 )
+	return( (sign * 0.5)/xx );
+
+/* 6.25 to infinity */
+y = 1.0/xx + x * polevl( x, CN, 4) / (p1evl( x, CD, 5) * xx);
+return( sign * 0.5 * y );
+}

libm/double/dcalc.c

@@ -0,0 +1,1512 @@
+/* calc.c */
+/* Keyboard command interpreter	*/
+/* by Stephen L. Moshier */
+
+
+/* length of command line: */
+#define LINLEN 128
+
+#define XON 0x11
+#define XOFF 0x13
+
+#define SALONE 1
+#define DECPDP 0
+#define INTLOGIN 0
+#define INTHELP 1
+#ifndef TRUE
+#define TRUE 1
+#endif
+
+/* Initialize squirrel printf: */
+#define INIPRINTF 0
+
+#if DECPDP
+#define TRUE 1
+#endif
+
+#include <stdio.h>
+#include <string.h>
+
+static char idterp[] = {
+"\n\nSteve Moshier's command interpreter V1.3\n"};
+#define ISLOWER(c) ((c >= 'a') && (c <= 'z'))
+#define ISUPPER(c) ((c >= 'A') && (c <= 'Z'))
+#define ISALPHA(c) (ISLOWER(c) || ISUPPER(c))
+#define ISDIGIT(c) ((c >= '0') && (c <= '9'))
+#define ISATF(c) (((c >= 'a')&&(c <= 'f')) || ((c >= 'A')&&(c <= 'F')))
+#define ISXDIGIT(c) (ISDIGIT(c) || ISATF(c))
+#define ISOCTAL(c) ((c >= '0') && (c < '8'))
+#define ISALNUM(c) (ISALPHA(c) || (ISDIGIT(c))
+FILE *fopen();
+
+#include "dcalc.h"
+/* #include "ehead.h" */
+#include <math.h>
+/* int strlen(), strcmp(); */
+int system();
+
+/* space for working precision numbers */
+static double vs[22];
+
+/*	the symbol table of temporary variables: */
+
+#define NTEMP 4
+struct varent temp[NTEMP] = {
+{"T",	OPR | TEMP, &vs[14]},
+{"T",	OPR | TEMP, &vs[15]},
+{"T",	OPR | TEMP, &vs[16]},
+{"\0",	OPR | TEMP, &vs[17]}
+};
+
+/*	the symbol table of operators		*/
+/* EOL is interpreted on null, newline, or ;	*/
+struct symbol oprtbl[] = {
+{"BOL",		OPR | BOL,	0},
+{"EOL",		OPR | EOL,	0},
+{"-",		OPR | UMINUS,	8},
+/*"~",		OPR | COMP,	8,*/
+{",",		OPR | EOE,	1},
+{"=",		OPR | EQU,	2},
+/*"|",		OPR | LOR,	3,*/
+/*"^",		OPR | LXOR,	4,*/
+/*"&",		OPR | LAND,	5,*/
+{"+",		OPR | PLUS,	6},
+{"-",		OPR | MINUS, 6},
+{"*",		OPR | MULT,	7},
+{"/",		OPR | DIV,	7},
+/*"%",		OPR | MOD,	7,*/
+{"(",		OPR | LPAREN,	11},
+{")",		OPR | RPAREN,	11},
+{"\0",		ILLEG, 0}
+};
+
+#define NOPR 8
+
+/*	the symbol table of indirect variables: */
+extern double PI;
+struct varent indtbl[] = {
+{"t",		VAR | IND,	&vs[21]},
+{"u",		VAR | IND,	&vs[20]},	
+{"v",		VAR | IND,	&vs[19]},
+{"w",		VAR | IND,	&vs[18]},	
+{"x",		VAR | IND,	&vs[10]},
+{"y",		VAR | IND,	&vs[11]},
+{"z",		VAR | IND,	&vs[12]},
+{"pi",		VAR | IND,	&PI},
+{"\0",		ILLEG,		0}
+};
+
+/*	the symbol table of constants:	*/
+
+#define NCONST 10
+struct varent contbl[NCONST] = {
+{"C",CONST,&vs[0]},
+{"C",CONST,&vs[1]},
+{"C",CONST,&vs[2]},
+{"C",CONST,&vs[3]},
+{"C",CONST,&vs[4]},
+{"C",CONST,&vs[5]},
+{"C",CONST,&vs[6]},
+{"C",CONST,&vs[7]},
+{"C",CONST,&vs[8]},
+{"\0",CONST,&vs[9]}
+};
+
+/* the symbol table of string variables: */
+
+static char strngs[160] = {0};
+
+#define NSTRNG 5
+struct strent strtbl[NSTRNG] = {
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{"\0",ILLEG,0},
+};
+
+
+/* Help messages */
+#if INTHELP
+static char *intmsg[] = {
+"?",
+"Unkown symbol",
+"Expression ends in illegal operator",
+"Precede ( by operator",
+")( is illegal",
+"Unmatched )",
+"Missing )",
+"Illegal left hand side",
+"Missing symbol",
+"Must assign to a variable",
+"Divide by zero",
+"Missing symbol",
+"Missing operator",
+"Precede quantity by operator",
+"Quantity preceded by )",
+"Function syntax",
+"Too many function args",
+"No more temps",
+"Arg list"
+};
+#endif
+
+#ifdef ANSIPROT
+double floor ( double );
+int dprec ( void );
+#else
+double floor();
+int dprec();
+#endif
+/*	the symbol table of functions:	*/
+#if SALONE
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double log ( double );
+extern double pow ( double, double );
+extern double sqrt ( double );
+extern double tanh ( double );
+extern double exp ( double );
+extern double fabs ( double );
+extern double hypot ( double, double );
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+extern double sin ( double );
+extern double cos ( double );
+extern double atan ( double );
+extern double atan2 ( double, double );
+extern double gamma ( double );
+extern double lgam ( double );
+double zfrexp ( double );
+double zldexp ( double, double );
+double makenan ( double );
+double makeinfinity ( double );
+double hex ( double );
+double hexinput ( double, double );
+double cmdh ( void );
+double cmdhlp ( void );
+double init ( void );
+double cmddm ( void );
+double cmdtm ( void );
+double cmdem ( double );
+double take ( char * );
+double mxit ( void );
+double bits ( double );
+double csys ( char * );
+double cmddig ( double );
+double prhlst ( void * );
+double abmac ( void );
+double ifrac ( double );
+double xcmpl ( double, double );
+void exit ( int );
+#else
+void exit();
+double hex(), hexinput(), cmdh(), cmdhlp(), init();
+double cmddm(), cmdtm(), cmdem();
+double take(), mxit(), bits(), csys();
+double cmddig(), prhlst(), abmac();
+double ifrac(), xcmpl();
+double floor(), log(), pow(), sqrt(), tanh(), exp(), fabs(), hypot();
+double frexp(), zfrexp(), ldexp(), zldexp(), makenan(), makeinfinity();
+double incbet(), incbi(), sin(), cos(), atan(), atan2(), gamma(), lgam();
+#define GLIBC2 0
+#if GLIBC2
+double lgamma();
+#endif
+#endif /* not ANSIPROT */
+struct funent funtbl[] = {
+{"h",		OPR | FUNC, cmdh},
+{"help",	OPR | FUNC, cmdhlp},
+{"hex",		OPR | FUNC, hex},
+{"hexinput",		OPR | FUNC, hexinput},
+/*"view",		OPR | FUNC, view,*/
+{"exp",		OPR | FUNC, exp},
+{"floor",	OPR | FUNC, floor},
+{"log",		OPR | FUNC, log},
+{"pow",		OPR | FUNC, pow},
+{"sqrt",	OPR | FUNC, sqrt},
+{"tanh",	OPR | FUNC, tanh},
+{"sin",		OPR | FUNC, sin},
+{"cos",		OPR | FUNC, cos},
+{"atan",	OPR | FUNC, atan},
+{"atantwo",	OPR | FUNC, atan2},
+{"tanh",	OPR | FUNC, tanh},
+{"gamma",	OPR | FUNC, gamma},
+#if GLIBC2
+{"lgamma",	OPR | FUNC, lgamma},
+#else
+{"lgam",	OPR | FUNC, lgam},
+#endif
+{"incbet",	OPR | FUNC, incbet},
+{"incbi",	OPR | FUNC, incbi},
+{"fabs",	OPR | FUNC, fabs},
+{"hypot",	OPR | FUNC, hypot},
+{"ldexp",	OPR | FUNC, zldexp},
+{"frexp",	OPR | FUNC, zfrexp},
+{"nan",	        OPR | FUNC, makenan},
+{"infinity",	OPR | FUNC, makeinfinity},
+{"ifrac",	OPR | FUNC, ifrac},
+{"cmp",		OPR | FUNC, xcmpl},
+{"bits",	OPR | FUNC, bits},
+{"digits",	OPR | FUNC, cmddig},
+{"dm",		OPR | FUNC, cmddm},
+{"tm",		OPR | FUNC, cmdtm},
+{"em",		OPR | FUNC, cmdem},
+{"take",	OPR | FUNC | COMMAN, take},
+{"system",	OPR | FUNC | COMMAN, csys},
+{"exit",	OPR | FUNC, mxit},
+/*
+"remain",	OPR | FUNC, eremain,
+*/
+{"\0",		OPR | FUNC,	0}
+};
+
+/*	the symbol table of key words */
+struct funent keytbl[] = {
+{"\0",		ILLEG,	0}
+};
+#endif
+
+void zgets();
+
+/* Number of decimals to display */
+#define DEFDIS 70
+static int ndigits = DEFDIS;
+
+/* Menu stack */
+struct funent *menstk[5] = {&funtbl[0], NULL, NULL, NULL, NULL};
+int menptr = 0;
+
+/* Take file stack */
+FILE *takstk[10] = {0};
+int takptr = -1;
+
+/* size of the expression scan list: */
+#define NSCAN 20
+
+/* previous token, saved for syntax checking: */
+struct symbol *lastok = 0;
+
+/*	variables used by parser: */
+static char str[128] = {0};
+int uposs = 0;		/* possible unary operator */
+static double qnc;
+char lc[40] = { '\n' };	/*	ASCII string of token	symbol	*/
+static char line[LINLEN] = { '\n','\0' };	/* input command line */
+static char maclin[LINLEN] = { '\n','\0' };	/* macro command */
+char *interl = line;		/* pointer into line */
+extern char *interl;
+static int maccnt = 0;	/* number of times to execute macro command */
+static int comptr = 0;	/* comma stack pointer */
+static double comstk[5];	/* comma argument stack */
+static int narptr = 0;	/* pointer to number of args */
+static int narstk[5] = {0};	/* stack of number of function args */
+
+/*							main()		*/
+
+/*	Entire program starts here	*/
+
+int main()
+{
+
+/*	the scan table:			*/
+
+/*	array of pointers to symbols which have been parsed:	*/
+struct symbol *ascsym[NSCAN];
+
+/*	current place in ascsym:			*/
+register struct symbol **as;
+
+/*	array of attributes of operators parsed:		*/
+int ascopr[NSCAN];
+
+/*	current place in ascopr:			*/
+register int *ao;
+
+#if LARGEMEM
+/*	array of precedence levels of operators:		*/
+long asclev[NSCAN];
+/*	current place in asclev:			*/
+long *al;
+long symval;	/* value of symbol just parsed */
+#else
+int asclev[NSCAN];
+int *al;
+int symval;
+#endif
+
+double acc;	/* the accumulator, for arithmetic */
+int accflg;	/* flags accumulator in use	*/
+double val;	/* value to be combined into accumulator */
+register struct symbol *psym;	/* pointer to symbol just parsed */
+struct varent *pvar;	/* pointer to an indirect variable symbol */
+struct funent *pfun;	/* pointer to a function symbol */
+struct strent *pstr;	/* pointer to a string symbol */
+int att;	/* attributes of symbol just parsed */
+int i;		/* counter	*/
+int offset;	/* parenthesis level */
+int lhsflg;	/* kluge to detect illegal assignments */
+struct symbol *parser();	/* parser returns pointer to symbol */
+int errcod;	/* for syntax error printout */
+
+
+/* Perform general initialization */
+
+init();
+
+menstk[0] = &funtbl[0];
+menptr = 0;
+cmdhlp();		/* print out list of symbols */
+
+
+/*	Return here to get next command line to execute	*/
+getcmd:
+
+/* initialize registers and mutable symbols */
+
+accflg = 0;	/* Accumulator not in use				*/
+acc = 0.0;	/* Clear the accumulator				*/
+offset = 0;	/* Parenthesis level zero				*/
+comptr = 0;	/* Start of comma stack					*/
+narptr = -1;	/* Start of function arg counter stack	*/
+
+psym = (struct symbol *)&contbl[0];
+for( i=0; i<NCONST; i++ )
+	{
+	psym->attrib = CONST;	/* clearing the busy bit */
+	++psym;
+	}
+psym = (struct symbol *)&temp[0];
+for( i=0; i<NTEMP; i++ )
+	{
+	psym->attrib = VAR | TEMP;	/* clearing the busy bit */
+	++psym;
+	}
+
+pstr = &strtbl[0];
+for( i=0; i<NSTRNG; i++ )
+	{
+	pstr->spel = &strngs[ 40*i ];
+	pstr->attrib = STRING | VAR;
+	pstr->string = &strngs[ 40*i ];
+	++pstr;
+	}
+
+/*	List of scanned symbols is empty:	*/
+as = &ascsym[0];
+*as = 0;
+--as;
+/*	First item in scan list is Beginning of Line operator	*/
+ao = &ascopr[0];
+*ao = oprtbl[0].attrib & 0xf;	/* BOL */
+/*	value of first item: */
+al = &asclev[0];
+*al = oprtbl[0].sym;
+
+lhsflg = 0;		/* illegal left hand side flag */
+psym = &oprtbl[0];	/* pointer to current token */
+
+/*	get next token from input string	*/
+
+gettok:
+lastok = psym;		/* last token = current token */
+psym = parser();	/* get a new current token */
+/*printf( "%s attrib %7o value %7o\n", psym->spel, psym->attrib & 0xffff,
+		psym->sym );*/
+
+/* Examine attributes of the symbol returned by the parser	*/
+att = psym->attrib;
+if( att == ILLEG )
+	{
+	errcod = 1;
+	goto synerr;
+	}
+
+/*	Push functions onto scan list without analyzing further */
+if( att & FUNC )
+	{
+	/* A command is a function whose argument is
+	 * a pointer to the rest of the input line.
+	 * A second argument is also passed: the address
+	 * of the last token parsed.
+	 */
+	if( att & COMMAN )
+		{
+		pfun = (struct funent *)psym;
+		( *(pfun->fun))( interl, lastok );
+		abmac();	/* scrub the input line */
+		goto getcmd;	/* and ask for more input */
+		}
+	++narptr;	/* offset to number of args */
+	narstk[narptr] = 0;
+	i = lastok->attrib & 0xffff; /* attrib=short, i=int */
+	if( ((i & OPR) == 0)
+			|| (i == (OPR | RPAREN))
+			|| (i == (OPR | FUNC)) )
+		{
+		errcod = 15;
+		goto synerr;
+		}
+
+	++lhsflg;
+	++as;
+	*as = psym;
+	++ao;
+	*ao = FUNC;
+	++al;
+	*al = offset + UMINUS;
+	goto gettok;
+	}
+
+/* deal with operators */
+if( att & OPR )
+	{
+	att &= 0xf;
+	/* expression cannot end with an operator other than
+	 * (, ), BOL, or a function
+	 */
+	if( (att == RPAREN) || (att == EOL) || (att == EOE))
+		{
+		i = lastok->attrib & 0xffff; /* attrib=short, i=int */
+		if( (i & OPR) 
+			&& (i != (OPR | RPAREN))
+			&& (i != (OPR | LPAREN))
+			&& (i != (OPR | FUNC))
+			&& (i != (OPR | BOL)) )
+				{
+				errcod = 2;
+				goto synerr;
+				}
+		}
+	++lhsflg;	/* any operator but ( and = is not a legal lhs */
+
+/*	operator processing, continued */
+
+	switch( att )
+		{
+ 	case EOE:
+		lhsflg = 0;
+		break; 
+	case LPAREN:
+		/* ( must be preceded by an operator of some sort. */
+		if( ((lastok->attrib & OPR) == 0) )
+			{
+			errcod = 3;
+			goto synerr;
+			}
+		/* also, a preceding ) is illegal */
+		if( (unsigned short )lastok->attrib == (OPR|RPAREN))
+			{
+			errcod = 4;
+			goto synerr;
+			}
+		/* Begin looking for illegal left hand sides: */
+		lhsflg = 0;
+		offset += RPAREN;	/* new parenthesis level */
+		goto gettok;
+	case RPAREN:
+		offset -= RPAREN;	/* parenthesis level */
+		if( offset < 0 )
+			{
+			errcod = 5;	/* parenthesis error */
+			goto synerr;
+			}
+		goto gettok;
+	case EOL:
+		if( offset != 0 )
+			{
+			errcod = 6;	/* parenthesis error */
+			goto synerr;
+			}
+		break;
+	case EQU:
+		if( --lhsflg )	/* was incremented before switch{} */
+			{
+			errcod = 7;
+			goto synerr;
+			}
+	case UMINUS:
+	case COMP:
+		goto pshopr;	/* evaluate right to left */
+	default:	;
+		}
+
+
+/*	evaluate expression whenever precedence is not increasing	*/
+
+symval = psym->sym + offset;
+
+while( symval <= *al )
+	{
+	/* if just starting, must fill accumulator with last
+	 * thing on the line
+	 */
+	if( (accflg == 0) && (as >= ascsym) && (((*as)->attrib & FUNC) == 0 ))
+		{
+		pvar = (struct varent *)*as;
+/*
+		if( pvar->attrib & STRING )
+			strcpy( (char *)&acc, (char *)pvar->value );
+		else
+*/
+			acc = *pvar->value;
+		--as;
+		accflg = 1;
+		}
+
+/* handle beginning of line type cases, where the symbol
+ * list ascsym[] may be empty.
+ */
+	switch( *ao )
+		{
+	case BOL:	
+		printf( "%.16e\n", acc );
+#if 0
+#if NE == 6
+		e64toasc( &acc, str, 100 );
+#else
+		e113toasc( &acc, str, 100 );
+#endif
+#endif
+		printf( "%s\n", str );
+		goto getcmd;	/* all finished */
+	case UMINUS:
+		acc = -acc;
+		goto nochg;
+/*
+	case COMP:
+		acc = ~acc;
+		goto nochg;
+*/
+	default:	;
+		}
+/* Now it is illegal for symbol list to be empty,
+ * because we are going to need a symbol below.
+ */
+	if( as < &ascsym[0] )
+		{
+		errcod = 8;
+		goto synerr;
+		}
+/* get attributes and value of current symbol */
+	att = (*as)->attrib;
+	pvar = (struct varent *)*as;
+	if( att & FUNC )
+		val = 0.0;
+	else
+		{
+/*
+		if( att & STRING )
+			strcpy( (char *)&val, (char *)pvar->value );
+		else
+*/
+			val = *pvar->value;
+		}
+
+/* Expression evaluation, continued. */
+
+	switch( *ao )
+		{
+	case FUNC:
+		pfun = (struct funent *)*as;
+	/* Call the function with appropriate number of args */
+	i = narstk[ narptr ];
+	--narptr;
+	switch(i)
+			{
+			case 0:
+			acc = ( *(pfun->fun) )(acc);
+			break;
+			case 1:
+			acc = ( *(pfun->fun) )(acc, comstk[comptr-1]);
+			break;
+			case 2:
+			acc = ( *(pfun->fun) )(acc, comstk[comptr-2],
+				comstk[comptr-1]);
+			break;
+			case 3:
+			acc = ( *(pfun->fun) )(acc, comstk[comptr-3],
+				comstk[comptr-2], comstk[comptr-1]);
+			break;
+			default:
+			errcod = 16;
+			goto synerr;
+			}
+		comptr -= i;
+		accflg = 1;	/* in case at end of line */
+		break;
+	case EQU:
+		if( ( att & TEMP) || ((att & VAR) == 0) || (att & STRING) )
+			{
+			errcod = 9;
+			goto synerr;	/* can only assign to a variable */
+			}
+		pvar = (struct varent *)*as;
+		*pvar->value = acc;
+		break;
+	case PLUS:
+		acc = acc + val;	break;
+	case MINUS:
+		acc = val - acc;	break;
+	case MULT:
+		acc = acc * val;	break;
+	case DIV:
+		if( acc == 0.0 )
+			{
+/*
+divzer:
+*/
+			errcod = 10;
+			goto synerr;
+			}
+		acc = val / acc;	break;
+/*
+	case MOD:
+		if( acc == 0 )
+			goto divzer;
+		acc = val % acc;	break;
+	case LOR:
+		acc |= val;		break;
+	case LXOR:
+		acc ^= val;		break;
+	case LAND:
+		acc &= val;		break;
+*/
+	case EOE:
+		if( narptr < 0 )
+			{
+			errcod = 18;
+			goto synerr;
+			}
+		narstk[narptr] += 1;
+		comstk[comptr++] = acc;
+/*	printf( "\ncomptr: %d narptr: %d %d\n", comptr, narptr, acc );*/
+		acc = val;
+		break;
+		}
+
+
+/*	expression evaluation, continued		*/
+
+/* Pop evaluated tokens from scan list:		*/
+	/* make temporary variable not busy	*/
+	if( att & TEMP )
+		(*as)->attrib &= ~BUSY;
+	if( as < &ascsym[0] )	/* can this happen? */
+		{
+		errcod = 11;
+		goto synerr;
+		}
+	--as;
+nochg:
+	--ao;
+	--al;
+	if( ao < &ascopr[0] )	/* can this happen? */
+		{
+		errcod = 12;
+		goto synerr;
+		}
+/* If precedence level will now increase, then			*/
+/* save accumulator in a temporary location			*/
+	if( symval > *al )
+		{
+		/* find a free temp location */
+		pvar = &temp[0];
+		for( i=0; i<NTEMP; i++ )
+			{
+			if( (pvar->attrib & BUSY) == 0)
+				goto temfnd;
+			++pvar;
+			}
+		errcod = 17;
+		printf( "no more temps\n" );
+		pvar = &temp[0];
+		goto synerr;
+
+	temfnd:
+		pvar->attrib |= BUSY;
+		*pvar->value = acc;
+		/*printf( "temp %d\n", acc );*/
+		accflg = 0;
+		++as;	/* push the temp onto the scan list */
+		*as = (struct symbol *)pvar;
+		}
+	}	/* End of evaluation loop */
+
+
+/*	Push operator onto scan list when precedence increases	*/
+
+pshopr:
+	++ao;
+	*ao = psym->attrib & 0xf;
+	++al;
+	*al = psym->sym + offset;
+	goto gettok;
+	}	/* end of OPR processing */
+
+
+/* Token was not an operator.  Push symbol onto scan list.	*/
+if( (lastok->attrib & OPR) == 0 )
+	{
+	errcod = 13;
+	goto synerr;	/* quantities must be preceded by an operator */
+	}
+if( (unsigned short )lastok->attrib == (OPR | RPAREN) )	/* ...but not by ) */
+	{
+	errcod = 14;
+	goto synerr;
+	}
+++as;
+*as = psym;
+goto gettok;
+
+synerr:
+
+#if INTHELP
+printf( "%s ", intmsg[errcod] );
+#endif
+printf( " error %d\n", errcod );
+abmac();	/* flush the command line */
+goto getcmd;
+}	/* end of program */
+
+/*						parser()	*/
+
+/* Get token from input string and identify it.		*/
+
+
+static char number[128];
+
+struct symbol *parser( )
+{
+register struct symbol *psym;
+register char *pline;
+struct varent *pvar;
+struct strent *pstr;
+char *cp, *plc, *pn;
+long lnc;
+int i;
+double tem;
+
+/* reference for old Whitesmiths compiler: */
+/*
+ *extern FILE *stdout;
+ */
+
+pline = interl;		/* get current location in command string	*/
+
+
+/*	If at beginning of string, must ask for more input	*/
+if( pline == line )
+	{
+
+	if( maccnt > 0 )
+		{
+		--maccnt;
+		cp = maclin;
+		plc = pline;
+		while( (*plc++ = *cp++) != 0 )
+			;
+		goto mstart;
+		}
+	if( takptr < 0 )
+		{	/* no take file active: prompt keyboard input */
+		printf("* ");
+		}
+/* 	Various ways of typing in a command line. */
+
+/*
+ * Old Whitesmiths call to print "*" immediately
+ * use RT11 .GTLIN to get command string
+ * from command file or terminal
+ */
+
+/*
+ *	fflush(stdout);
+ *	gtlin(line);
+ */
+
+ 
+	zgets( line, TRUE );	/* keyboard input for other systems: */
+
+
+mstart:
+	uposs = 1;	/* unary operators possible at start of line */
+	}
+
+ignore:
+/* Skip over spaces */
+while( *pline == ' ' )
+	++pline;
+
+/* unary minus after operator */
+if( uposs && (*pline == '-') )
+	{
+	psym = &oprtbl[2];	/* UMINUS */
+	++pline;
+	goto pdon3;
+	}
+	/* COMP */
+/*
+if( uposs && (*pline == '~') )
+	{
+	psym = &oprtbl[3];
+	++pline;
+	goto pdon3;
+	}
+*/
+if( uposs && (*pline == '+') )	/* ignore leading plus sign */
+	{
+	++pline;
+	goto ignore;
+	}
+
+/* end of null terminated input */
+if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
+	{
+	pline = line;
+	goto endlin;
+	}
+if( *pline == ';' )
+	{
+	++pline;
+endlin:
+	psym = &oprtbl[1];	/* EOL */
+	goto pdon2;
+	}
+
+
+/*						parser()	*/
+
+
+/* Test for numeric input */
+if( (ISDIGIT(*pline)) || (*pline == '.') )
+	{
+	lnc = 0;	/* initialize numeric input to zero */
+	qnc = 0.0;
+	if( *pline == '0' )
+		{ /* leading "0" may mean octal or hex radix */
+		++pline;
+		if( *pline == '.' )
+			goto decimal; /* 0.ddd */
+		/* leading "0x" means hexadecimal radix */
+		if( (*pline == 'x') || (*pline == 'X') )
+			{
+			++pline;
+			while( ISXDIGIT(*pline) )
+				{
+				i = *pline++ & 0xff;
+				if( i >= 'a' )
+					i -= 047;
+				if( i >= 'A' )
+					i -= 07;
+				i -= 060;
+				lnc = (lnc << 4) + i;
+				qnc = lnc;
+				}
+			goto numdon;
+			}
+		else
+			{
+			while( ISOCTAL( *pline ) )
+				{
+				i = ((*pline++) & 0xff) - 060;
+				lnc = (lnc << 3) + i;
+				qnc = lnc;
+				}
+			goto numdon;
+			}
+		}
+	else
+		{
+		/* no leading "0" means decimal radix */
+/******/
+decimal:
+		pn = number;
+		while( (ISDIGIT(*pline)) || (*pline == '.') )
+			*pn++ = *pline++;
+/* get possible exponent field */
+		if( (*pline == 'e') || (*pline == 'E') )
+			*pn++ = *pline++;
+		else
+			goto numcvt;
+		if( (*pline == '-') || (*pline == '+') )
+			*pn++ = *pline++;
+		while( ISDIGIT(*pline) )
+			*pn++ = *pline++;
+numcvt:
+		*pn++ = ' ';
+		*pn++ = 0;
+#if 0
+#if NE == 6
+		asctoe64( number, &qnc );
+#else
+		asctoe113( number, &qnc );
+#endif
+#endif
+		sscanf( number, "%le", &qnc );
+		}
+/* output the number	*/
+numdon:
+	/* search the symbol table of constants 	*/
+	pvar = &contbl[0];
+	for( i=0; i<NCONST; i++ )
+		{
+		if( (pvar->attrib & BUSY) == 0 )
+			goto confnd;
+		tem = *pvar->value;
+		if( tem == qnc )
+			{
+			psym = (struct symbol *)pvar;
+			goto pdon2;
+			}
+		++pvar;
+		}
+	printf( "no room for constant\n" );
+	psym = (struct symbol *)&contbl[0];
+	goto pdon2;
+
+confnd:
+	pvar->spel= contbl[0].spel;
+	pvar->attrib = CONST | BUSY;
+	*pvar->value = qnc;
+	psym = (struct symbol *)pvar;
+	goto pdon2;
+	}
+
+/* check for operators */
+psym = &oprtbl[3];
+for( i=0; i<NOPR; i++ )
+	{
+	if( *pline == *(psym->spel) )
+		goto pdon1;
+	++psym;
+	}
+
+/* if quoted, it is a string variable */
+if( *pline == '"' )
+	{
+	/* find an empty slot for the string */
+	pstr = strtbl;	/* string table	*/
+	for( i=0; i<NSTRNG-1; i++ ) 
+		{
+		if( (pstr->attrib & BUSY) == 0 )
+			goto fndstr;
+		++pstr;
+		}
+	printf( "No room for string\n" );
+	pstr->attrib |= ILLEG;
+	psym = (struct symbol *)pstr;
+	goto pdon0;
+
+fndstr:
+	pstr->attrib |= BUSY;
+	plc = pstr->string;
+	++pline;
+	for( i=0; i<39; i++ )
+		{
+		*plc++ = *pline;
+		if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
+			{
+illstr:
+			pstr = &strtbl[NSTRNG-1];
+			pstr->attrib |= ILLEG;
+			printf( "Missing string terminator\n" );
+			psym = (struct symbol *)pstr;
+			goto pdon0;
+			}
+		if( *pline++ == '"' )
+			goto finstr;
+		}
+
+	goto illstr;	/* no terminator found */
+
+finstr:
+	--plc;
+	*plc = '\0';
+	psym = (struct symbol *)pstr;
+	goto pdon2;
+	}
+/* If none of the above, search function and symbol tables:	*/
+
+/* copy character string to array lc[] */
+plc = &lc[0];
+while( ISALPHA(*pline) )
+	{
+	/* convert to lower case characters */
+	if( ISUPPER( *pline ) )
+		*pline += 040;
+	*plc++ = *pline++;
+	}
+*plc = 0;	/* Null terminate the output string */
+
+/*						parser()	*/
+
+psym = (struct symbol *)menstk[menptr];	/* function table	*/
+plc = &lc[0];
+cp = psym->spel;
+do
+	{
+	if( strcmp( plc, cp ) == 0 )
+		goto pdon3;	/* following unary minus is possible */
+	++psym;
+	cp = psym->spel;
+	}
+while( *cp != '\0' );
+
+psym = (struct symbol *)&indtbl[0];	/* indirect symbol table */
+plc = &lc[0];
+cp = psym->spel;
+do
+	{
+	if( strcmp( plc, cp ) == 0 )
+		goto pdon2;
+	++psym;
+	cp = psym->spel;
+	}
+while( *cp != '\0' );
+
+pdon0:
+pline = line;	/* scrub line if illegal symbol */
+goto pdon2;
+
+pdon1:
+++pline;
+if( (psym->attrib & 0xf) == RPAREN )
+pdon2:	uposs = 0;
+else
+pdon3:	uposs = 1;
+
+interl = pline;
+return( psym );
+}		/* end of parser */
+
+/*	exit from current menu */
+
+double cmdex()
+{
+
+if( menptr == 0 )
+	{
+	printf( "Main menu is active.\n" );
+	}
+else
+	--menptr;
+
+cmdh();
+return(0.0);
+}
+
+
+/*			gets()		*/
+
+void zgets( gline, echo )
+char *gline;
+int echo;
+{
+register char *pline;
+register int i;
+
+
+scrub:
+pline = gline;
+getsl:
+	if( (pline - gline) >= LINLEN )
+		{
+		printf( "\nLine too long\n *" );
+		goto scrub;
+		}
+	if( takptr < 0 )
+		{	/* get character from keyboard */
+/*
+if DECPDP
+		gtlin( gline );
+		return(0);
+else
+*/
+		*pline = getchar();
+/*endif*/
+		}
+	else
+		{	/* get a character from take file */
+		i = fgetc( takstk[takptr] );
+		if( i == -1 )
+			{	/* end of take file */
+			if( takptr >= 0 )
+				{	/* close file and bump take stack */
+				fclose( takstk[takptr] );
+				takptr -= 1;
+				}
+			if( takptr < 0 )	/* no more take files:   */
+				printf( "*" ); /* prompt keyboard input */
+			goto scrub;	/* start a new input line */
+			}
+		*pline = i;
+		}
+
+	*pline &= 0x7f;
+	/* xon or xoff characters need filtering out. */
+	if ( *pline == XON || *pline == XOFF )
+		goto getsl;
+
+	/*	control U or control C	*/
+	if( (*pline == 025) || (*pline == 03) )
+		{
+		printf( "\n" );
+		goto scrub;
+		}
+
+	/*  Backspace or rubout */
+	if( (*pline == 010) || (*pline == 0177) )
+		{
+		pline -= 1;
+		if( pline >= gline )
+			{
+			if ( echo )
+				printf( "\010\040\010" );
+			goto getsl;
+			}
+		else
+			goto scrub;
+		}
+	if ( echo )
+		printf( "%c", *pline );
+	if( (*pline != '\n') && (*pline != '\r') )
+		{
+		++pline;
+		goto getsl;
+		}
+	*pline = 0;
+	if ( echo )
+		printf( "%c", '\n' );	/* \r already echoed */
+}
+
+
+/*		help function  */
+double cmdhlp()
+{
+
+printf( "%s", idterp );
+printf( "\nFunctions:\n" );
+prhlst( &funtbl[0] );
+printf( "\nVariables:\n" );
+prhlst( &indtbl[0] );
+printf( "\nOperators:\n" );
+prhlst( &oprtbl[2] );
+printf("\n");
+return(0.0);
+}
+
+
+double cmdh()
+{
+
+prhlst( menstk[menptr] );
+printf( "\n" );
+return(0.0);
+}
+
+/* print keyword spellings */
+
+double prhlst(vps)
+void *vps;
+{
+register int j, k;
+int m;
+register struct symbol *ps = vps;
+
+j = 0;
+while( *(ps->spel) != '\0' )
+	{
+	k = strlen( ps->spel )  -  1;
+/* size of a tab field is 2**3 chars */
+	m = ((k >> 3) + 1) << 3;
+	j += m;
+	if( j > 72 )
+		{
+		printf( "\n" );
+		j = m;
+		}
+	printf( "%s\t", ps->spel );
+	++ps;
+	}
+return(0.0);
+}
+
+
+#if SALONE
+double init()
+{
+/* Set coprocessor to double precision. */
+dprec();
+return 0.0;
+}
+#endif
+
+
+/*	macro commands */
+
+/*	define macro */
+double cmddm()
+{
+
+zgets( maclin, TRUE );
+return(0.0);
+}
+
+/*	type (i.e., display) macro */
+double cmdtm()
+{
+
+printf( "%s\n", maclin );
+return 0.0;
+}
+
+/*	execute macro # times */
+double cmdem( arg )
+double arg;
+{
+double f;
+long n;
+
+f = floor(arg);
+n = f;
+if( n <= 0 )
+	n = 1;
+maccnt = n;
+return(0.0);
+}
+
+
+/* open a take file */
+
+double take( fname )
+char *fname;
+{
+FILE *f;
+
+while( *fname == ' ' )
+	fname += 1;
+f = fopen( fname, "r" );
+
+if( f == 0 )
+	{
+	printf( "Can't open take file %s\n", fname );
+	takptr = -1;	/* terminate all take file input */
+	return 0.0;
+	}
+takptr += 1;
+takstk[ takptr ]  =  f;
+printf( "Running %s\n", fname );
+return(0.0);
+}
+
+
+/*	abort macro execution */
+double abmac()
+{
+
+maccnt = 0;
+interl = line;
+return(0.0);
+}
+
+
+/* display integer part in hex, octal, and decimal
+ */
+double hex(qx)
+double qx;
+{
+double f;
+long z;
+
+f = floor(qx);
+z = f;
+printf( "0%lo  0x%lx  %ld.\n", z, z, z );
+return(qx);
+}
+
+#define NASC 16
+
+double bits( x )
+double x;
+{
+union
+  {
+    double d;
+    short i[4];
+  } du;
+union
+  {
+    float f;
+    short i[2];
+  } df;
+int i;
+
+du.d = x;
+printf( "double: " );
+for( i=0; i<4; i++ )
+	printf( "0x%04x,", du.i[i] & 0xffff );
+printf( "\n" );
+
+df.f = (float) x;
+printf( "float: " );
+for( i=0; i<2; i++ )
+	printf( "0x%04x,", df.i[i] & 0xffff );
+printf( "\n" );
+return(x);
+}
+
+
+/* Exit to monitor. */
+double mxit()
+{
+
+exit(0);
+return(0.0);
+}
+
+
+double cmddig( x )
+double x;
+{
+double f;
+long lx;
+
+f = floor(x);
+lx = f;
+ndigits = lx;
+if( ndigits <= 0 )
+	ndigits = DEFDIS;
+return(f);
+}
+
+
+double csys(x)
+char *x;
+{
+
+system( x+1 );
+cmdh();
+return(0.0);
+}
+
+
+double ifrac(x)
+double x;
+{
+unsigned long lx;
+long double y, z;
+
+z = floor(x);
+lx = z;
+y = x - z;
+printf( " int = %lx\n", lx );
+return(y);
+}
+
+double xcmpl(x,y)
+double x,y;
+{
+double ans;
+
+ans = -2.0;
+if( x == y )
+	{
+	printf( "x == y " );
+	ans = 0.0;
+	}
+if( x < y )
+	{
+	printf( "x < y" );
+	ans = -1.0;
+	}
+if( x > y )
+	{
+	printf( "x > y" );
+	ans = 1.0;
+	}
+return( ans );
+}
+
+extern double INFINITY, NAN;
+
+double makenan(x)
+double x;
+{
+return(NAN);
+}
+
+double makeinfinity(x)
+double x;
+{
+return(INFINITY);
+}
+
+double zfrexp(x)
+double x;
+{
+double y;
+int e;
+y = frexp(x, &e);
+printf("exponent = %d, significand = ", e );
+return(y);
+}
+
+double zldexp(x,e)
+double x, e;
+{
+double y;
+int i;
+
+i = e;
+y = ldexp(x,i);
+return(y);
+}
+
+double hexinput(a, b)
+double a,b;
+{
+union
+  {
+    double d;
+    unsigned short i[4];
+  } u;
+unsigned long l;
+
+#ifdef IBMPC
+l = a;
+u.i[3] = l >> 16;
+u.i[2] = l;
+l = b;
+u.i[1] = l >> 16;
+u.i[0] = l;
+#endif
+#ifdef DEC
+l = a;
+u.i[3] = l >> 16;
+u.i[2] = l;
+l = b;
+u.i[1] = l >> 16;
+u.i[0] = l;
+#endif
+#ifdef MIEEE
+l = a;
+u.i[0] = l >> 16;
+u.i[1] = l;
+l = b;
+u.i[2] = l >> 16;
+u.i[3] = l;
+#endif
+#ifdef UNK
+l = a;
+u.i[0] = l >> 16;
+u.i[1] = l;
+l = b;
+u.i[2] = l >> 16;
+u.i[3] = l;
+#endif
+return(u.d);
+}

libm/double/dcalc.h

@@ -0,0 +1,77 @@
+/*		calc.h
+ * include file for calc.c
+ */
+ 
+/* 32 bit memory addresses: */
+#define LARGEMEM 1
+
+/* data structure of symbol table */
+struct symbol
+	{
+	char *spel;
+	short attrib;
+#if LARGEMEM
+	long sym;
+#else
+	short sym;
+#endif
+	};
+
+struct funent
+	{
+	char *spel;
+	short attrib;
+	double (*fun )();
+	};
+
+struct varent
+        {
+	char *spel;
+	short attrib;
+	double *value;
+        };
+
+struct strent
+	{
+	char *spel;
+	short attrib;
+	char *string;
+	};
+
+
+/*	general symbol attributes:	*/
+#define OPR 0x8000
+#define	VAR 0x4000
+#define CONST 0x2000
+#define FUNC 0x1000
+#define ILLEG 0x800
+#define BUSY 0x400
+#define TEMP 0x200
+#define STRING 0x100
+#define COMMAN 0x80
+#define IND 0x1
+
+/* attributes of operators (ordered by precedence): */
+#define BOL 1
+#define EOL 2
+/* end of expression (comma): */
+#define EOE 3
+#define EQU 4
+#define PLUS 5
+#define MINUS 6
+#define MULT 7
+#define DIV 8
+#define UMINUS 9
+#define LPAREN 10
+#define RPAREN 11
+#define COMP 12
+#define MOD 13
+#define LAND 14
+#define LOR 15
+#define LXOR 16
+
+
+extern struct funent funtbl[];
+/*extern struct symbol symtbl[];*/
+extern struct varent indtbl[];
+

libm/double/dtestvec.c

@@ -0,0 +1,543 @@
+
+/* Test vectors for math functions.
+   See C9X section F.9.  */
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1998, 2000 by Stephen L. Moshier
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+int isfinite (double);
+
+/* C9X spells lgam lgamma.  */
+#define GLIBC2 0
+
+extern double PI;
+static double MPI, PIO2, MPIO2, PIO4, MPIO4, THPIO4, MTHPIO4;
+
+#if 0
+#define PI 3.141592653589793238463E0
+#define PIO2 1.570796326794896619231E0
+#define PIO4 7.853981633974483096157E-1
+#define THPIO4 2.35619449019234492884698
+#define SQRT2 1.414213562373095048802E0
+#define SQRTH 7.071067811865475244008E-1
+#define INF (1.0/0.0)
+#define MINF (-1.0/0.0)
+#endif
+
+extern double MACHEP, SQRTH, SQRT2;
+extern double NAN, INFINITY, NEGZERO;
+static double INF, MINF;
+static double ZERO, MZERO, HALF, MHALF, ONE, MONE, TWO, MTWO, THREE, MTHREE;
+/* #define NAN (1.0/0.0 - 1.0/0.0) */
+
+/* Functions of one variable.  */
+double log (double);
+double exp ( double);
+double atan (double);
+double sin (double);
+double cos (double);
+double tan (double);
+double acos (double);
+double asin (double);
+double acosh (double);
+double asinh (double);
+double atanh (double);
+double sinh (double);
+double cosh (double);
+double tanh (double);
+double exp2 (double);
+double expm1 (double);
+double log10 (double);
+double log1p (double);
+double log2 (double);
+double fabs (double);
+double erf (double);
+double erfc (double);
+double gamma (double);
+double floor (double);
+double ceil (double);
+double cbrt (double);
+#if GLIBC2
+double lgamma (double);
+#else
+double lgam (double);
+#endif
+
+struct oneargument
+  {
+    char *name;			/* Name of the function. */
+    double (*func) (double);
+    double *arg1;
+    double *answer;
+    int thresh;			/* Error report threshold. */
+  };
+
+struct oneargument test1[] =
+{
+  {"atan", atan, &ONE, &PIO4, 0},
+  {"sin", sin, &PIO2, &ONE, 0},
+#if 0
+  {"cos", cos, &PIO4, &SQRTH, 0},
+  {"sin", sin, 32767., 1.8750655394138942394239E-1, 0},
+  {"cos", cos, 32767., 9.8226335176928229845654E-1, 0},
+  {"tan", tan, 32767., 1.9089234430221485740826E-1, 0},
+  {"sin", sin, 8388607., 9.9234509376961249835628E-1, 0},
+  {"cos", cos, 8388607., -1.2349580912475928183718E-1, 0},
+  {"tan", tan, 8388607., -8.0354556223613614748329E0, 0},
+  /*
+  {"sin", sin, 2147483647., -7.2491655514455639054829E-1, 0},
+  {"cos", cos, 2147483647., -6.8883669187794383467976E-1, 0},
+  {"tan", tan, 2147483647., 1.0523779637351339136698E0, 0},
+  */
+  {"cos", cos, &PIO2, 6.1232339957367574e-17, 1},
+  {"sin", sin, &PIO4, &SQRTH, 1},
+#endif
+  {"acos", acos, &NAN, &NAN, 0},
+  {"acos", acos, &ONE, &ZERO, 0},
+  {"acos", acos, &TWO, &NAN, 0},
+  {"acos", acos, &MTWO, &NAN, 0},
+  {"asin", asin, &NAN, &NAN, 0},
+  {"asin", asin, &ZERO, &ZERO, 0},
+  {"asin", asin, &MZERO, &MZERO, 0},
+  {"asin", asin, &TWO, &NAN, 0},
+  {"asin", asin, &MTWO, &NAN, 0},
+  {"atan", atan, &NAN, &NAN, 0},
+  {"atan", atan, &ZERO, &ZERO, 0},
+  {"atan", atan, &MZERO, &MZERO, 0},
+  {"atan", atan, &INF, &PIO2, 0},
+  {"atan", atan, &MINF, &MPIO2, 0},
+  {"cos", cos, &NAN, &NAN, 0},
+  {"cos", cos, &ZERO, &ONE, 0},
+  {"cos", cos, &MZERO, &ONE, 0},
+  {"cos", cos, &INF, &NAN, 0},
+  {"cos", cos, &MINF, &NAN, 0},
+  {"sin", sin, &NAN, &NAN, 0},
+  {"sin", sin, &MZERO, &MZERO, 0},
+  {"sin", sin, &ZERO, &ZERO, 0},
+  {"sin", sin, &INF, &NAN, 0},
+  {"sin", sin, &MINF, &NAN, 0},
+  {"tan", tan, &NAN, &NAN, 0},
+  {"tan", tan, &ZERO, &ZERO, 0},
+  {"tan", tan, &MZERO, &MZERO, 0},
+  {"tan", tan, &INF, &NAN, 0},
+  {"tan", tan, &MINF, &NAN, 0},
+  {"acosh", acosh, &NAN, &NAN, 0},
+  {"acosh", acosh, &ONE, &ZERO, 0},
+  {"acosh", acosh, &INF, &INF, 0},
+  {"acosh", acosh, &HALF, &NAN, 0},
+  {"acosh", acosh, &MONE, &NAN, 0},
+  {"asinh", asinh, &NAN, &NAN, 0},
+  {"asinh", asinh, &ZERO, &ZERO, 0},
+  {"asinh", asinh, &MZERO, &MZERO, 0},
+  {"asinh", asinh, &INF, &INF, 0},
+  {"asinh", asinh, &MINF, &MINF, 0},
+  {"atanh", atanh, &NAN, &NAN, 0},
+  {"atanh", atanh, &ZERO, &ZERO, 0},
+  {"atanh", atanh, &MZERO, &MZERO, 0},
+  {"atanh", atanh, &ONE, &INF, 0},
+  {"atanh", atanh, &MONE, &MINF, 0},
+  {"atanh", atanh, &TWO, &NAN, 0},
+  {"atanh", atanh, &MTWO, &NAN, 0},
+  {"cosh", cosh, &NAN, &NAN, 0},
+  {"cosh", cosh, &ZERO, &ONE, 0},
+  {"cosh", cosh, &MZERO, &ONE, 0},
+  {"cosh", cosh, &INF, &INF, 0},
+  {"cosh", cosh, &MINF, &INF, 0},
+  {"sinh", sinh, &NAN, &NAN, 0},
+  {"sinh", sinh, &ZERO, &ZERO, 0},
+  {"sinh", sinh, &MZERO, &MZERO, 0},
+  {"sinh", sinh, &INF, &INF, 0},
+  {"sinh", sinh, &MINF, &MINF, 0},
+  {"tanh", tanh, &NAN, &NAN, 0},
+  {"tanh", tanh, &ZERO, &ZERO, 0},
+  {"tanh", tanh, &MZERO, &MZERO, 0},
+  {"tanh", tanh, &INF, &ONE, 0},
+  {"tanh", tanh, &MINF, &MONE, 0},
+  {"exp", exp, &NAN, &NAN, 0},
+  {"exp", exp, &ZERO, &ONE, 0},
+  {"exp", exp, &MZERO, &ONE, 0},
+  {"exp", exp, &INF, &INF, 0},
+  {"exp", exp, &MINF, &ZERO, 0},
+#if !GLIBC2
+  {"exp2", exp2, &NAN, &NAN, 0},
+  {"exp2", exp2, &ZERO, &ONE, 0},
+  {"exp2", exp2, &MZERO, &ONE, 0},
+  {"exp2", exp2, &INF, &INF, 0},
+  {"exp2", exp2, &MINF, &ZERO, 0},
+#endif
+  {"expm1", expm1, &NAN, &NAN, 0},
+  {"expm1", expm1, &ZERO, &ZERO, 0},
+  {"expm1", expm1, &MZERO, &MZERO, 0},
+  {"expm1", expm1, &INF, &INF, 0},
+  {"expm1", expm1, &MINF, &MONE, 0},
+  {"log", log, &NAN, &NAN, 0},
+  {"log", log, &ZERO, &MINF, 0},
+  {"log", log, &MZERO, &MINF, 0},
+  {"log", log, &ONE, &ZERO, 0},
+  {"log", log, &MONE, &NAN, 0},
+  {"log", log, &INF, &INF, 0},
+  {"log10", log10, &NAN, &NAN, 0},
+  {"log10", log10, &ZERO, &MINF, 0},
+  {"log10", log10, &MZERO, &MINF, 0},
+  {"log10", log10, &ONE, &ZERO, 0},
+  {"log10", log10, &MONE, &NAN, 0},
+  {"log10", log10, &INF, &INF, 0},
+  {"log1p", log1p, &NAN, &NAN, 0},
+  {"log1p", log1p, &ZERO, &ZERO, 0},
+  {"log1p", log1p, &MZERO, &MZERO, 0},
+  {"log1p", log1p, &MONE, &MINF, 0},
+  {"log1p", log1p, &MTWO, &NAN, 0},
+  {"log1p", log1p, &INF, &INF, 0},
+#if !GLIBC2
+  {"log2", log2, &NAN, &NAN, 0},
+  {"log2", log2, &ZERO, &MINF, 0},
+  {"log2", log2, &MZERO, &MINF, 0},
+  {"log2", log2, &MONE, &NAN, 0},
+  {"log2", log2, &INF, &INF, 0},
+#endif
+  /*  {"fabs", fabs, NAN, NAN, 0}, */
+  {"fabs", fabs, &ONE, &ONE, 0},
+  {"fabs", fabs, &MONE, &ONE, 0},
+  {"fabs", fabs, &ZERO, &ZERO, 0},
+  {"fabs", fabs, &MZERO, &ZERO, 0},
+  {"fabs", fabs, &INF, &INF, 0},
+  {"fabs", fabs, &MINF, &INF, 0},
+  {"cbrt", cbrt, &NAN, &NAN, 0},
+  {"cbrt", cbrt, &ZERO, &ZERO, 0},
+  {"cbrt", cbrt, &MZERO, &MZERO, 0},
+  {"cbrt", cbrt, &INF, &INF, 0},
+  {"cbrt", cbrt, &MINF, &MINF, 0},
+  {"erf", erf, &NAN, &NAN, 0},
+  {"erf", erf, &ZERO, &ZERO, 0},
+  {"erf", erf, &MZERO, &MZERO, 0},
+  {"erf", erf, &INF, &ONE, 0},
+  {"erf", erf, &MINF, &MONE, 0},
+  {"erfc", erfc, &NAN, &NAN, 0},
+  {"erfc", erfc, &INF, &ZERO, 0},
+  {"erfc", erfc, &MINF, &TWO, 0},
+  {"gamma", gamma, &NAN, &NAN, 0},
+  {"gamma", gamma, &INF, &INF, 0},
+  {"gamma", gamma, &MONE, &NAN, 0},
+  {"gamma", gamma, &ZERO, &NAN, 0},
+  {"gamma", gamma, &MINF, &NAN, 0},
+#if GLIBC2
+  {"lgamma", lgamma, &NAN, &NAN, 0},
+  {"lgamma", lgamma, &INF, &INF, 0},
+  {"lgamma", lgamma, &MONE, &INF, 0},
+  {"lgamma", lgamma, &ZERO, &INF, 0},
+  {"lgamma", lgamma, &MINF, &INF, 0},
+#else
+  {"lgam", lgam, &NAN, &NAN, 0},
+  {"lgam", lgam, &INF, &INF, 0},
+  {"lgam", lgam, &MONE, &INF, 0},
+  {"lgam", lgam, &ZERO, &INF, 0},
+  {"lgam", lgam, &MINF, &INF, 0},
+#endif
+  {"ceil", ceil, &NAN, &NAN, 0},
+  {"ceil", ceil, &ZERO, &ZERO, 0},
+  {"ceil", ceil, &MZERO, &MZERO, 0},
+  {"ceil", ceil, &INF, &INF, 0},
+  {"ceil", ceil, &MINF, &MINF, 0},
+  {"floor", floor, &NAN, &NAN, 0},
+  {"floor", floor, &ZERO, &ZERO, 0},
+  {"floor", floor, &MZERO, &MZERO, 0},
+  {"floor", floor, &INF, &INF, 0},
+  {"floor", floor, &MINF, &MINF, 0},
+  {"null", NULL, &ZERO, &ZERO, 0},
+};
+
+/* Functions of two variables.  */
+double atan2 (double, double);
+double pow (double, double);
+
+struct twoarguments
+  {
+    char *name;			/* Name of the function. */
+    double (*func) (double, double);
+    double *arg1;
+    double *arg2;
+    double *answer;
+    int thresh;
+  };
+
+struct twoarguments test2[] =
+{
+  {"atan2", atan2, &ZERO, &ONE, &ZERO, 0},
+  {"atan2", atan2, &MZERO, &ONE, &MZERO, 0},
+  {"atan2", atan2, &ZERO, &ZERO, &ZERO, 0},
+  {"atan2", atan2, &MZERO, &ZERO, &MZERO, 0},
+  {"atan2", atan2, &ZERO, &MONE, &PI, 0},
+  {"atan2", atan2, &MZERO, &MONE, &MPI, 0},
+  {"atan2", atan2, &ZERO, &MZERO, &PI, 0},
+  {"atan2", atan2, &MZERO, &MZERO, &MPI, 0},
+  {"atan2", atan2, &ONE, &ZERO, &PIO2, 0},
+  {"atan2", atan2, &ONE, &MZERO, &PIO2, 0},
+  {"atan2", atan2, &MONE, &ZERO, &MPIO2, 0},
+  {"atan2", atan2, &MONE, &MZERO, &MPIO2, 0},
+  {"atan2", atan2, &ONE, &INF, &ZERO, 0},
+  {"atan2", atan2, &MONE, &INF, &MZERO, 0},
+  {"atan2", atan2, &INF, &ONE, &PIO2, 0},
+  {"atan2", atan2, &INF, &MONE, &PIO2, 0},
+  {"atan2", atan2, &MINF, &ONE, &MPIO2, 0},
+  {"atan2", atan2, &MINF, &MONE, &MPIO2, 0},
+  {"atan2", atan2, &ONE, &MINF, &PI, 0},
+  {"atan2", atan2, &MONE, &MINF, &MPI, 0},
+  {"atan2", atan2, &INF, &INF, &PIO4, 0},
+  {"atan2", atan2, &MINF, &INF, &MPIO4, 0},
+  {"atan2", atan2, &INF, &MINF, &THPIO4, 0},
+  {"atan2", atan2, &MINF, &MINF, &MTHPIO4, 0},
+  {"atan2", atan2, &ONE, &ONE, &PIO4, 0},
+  {"atan2", atan2, &NAN, &ONE, &NAN, 0},
+  {"atan2", atan2, &ONE, &NAN, &NAN, 0},
+  {"atan2", atan2, &NAN, &NAN, &NAN, 0},
+  {"pow", pow, &ONE, &ZERO, &ONE, 0},
+  {"pow", pow, &ONE, &MZERO, &ONE, 0},
+  {"pow", pow, &MONE, &ZERO, &ONE, 0},
+  {"pow", pow, &MONE, &MZERO, &ONE, 0},
+  {"pow", pow, &INF, &ZERO, &ONE, 0},
+  {"pow", pow, &INF, &MZERO, &ONE, 0},
+  {"pow", pow, &NAN, &ZERO, &ONE, 0},
+  {"pow", pow, &NAN, &MZERO, &ONE, 0},
+  {"pow", pow, &TWO, &INF, &INF, 0},
+  {"pow", pow, &MTWO, &INF, &INF, 0},
+  {"pow", pow, &HALF, &INF, &ZERO, 0},
+  {"pow", pow, &MHALF, &INF, &ZERO, 0},
+  {"pow", pow, &TWO, &MINF, &ZERO, 0},
+  {"pow", pow, &MTWO, &MINF, &ZERO, 0},
+  {"pow", pow, &HALF, &MINF, &INF, 0},
+  {"pow", pow, &MHALF, &MINF, &INF, 0},
+  {"pow", pow, &INF, &HALF, &INF, 0},
+  {"pow", pow, &INF, &TWO, &INF, 0},
+  {"pow", pow, &INF, &MHALF, &ZERO, 0},
+  {"pow", pow, &INF, &MTWO, &ZERO, 0},
+  {"pow", pow, &MINF, &THREE, &MINF, 0},
+  {"pow", pow, &MINF, &TWO, &INF, 0},
+  {"pow", pow, &MINF, &MTHREE, &MZERO, 0},
+  {"pow", pow, &MINF, &MTWO, &ZERO, 0},
+  {"pow", pow, &NAN, &ONE, &NAN, 0},
+  {"pow", pow, &ONE, &NAN, &NAN, 0},
+  {"pow", pow, &NAN, &NAN, &NAN, 0},
+  {"pow", pow, &ONE, &INF, &NAN, 0},
+  {"pow", pow, &MONE, &INF, &NAN, 0},
+  {"pow", pow, &ONE, &MINF, &NAN, 0},
+  {"pow", pow, &MONE, &MINF, &NAN, 0},
+  {"pow", pow, &MTWO, &HALF, &NAN, 0},
+  {"pow", pow, &ZERO, &MTHREE, &INF, 0},
+  {"pow", pow, &MZERO, &MTHREE, &MINF, 0},
+  {"pow", pow, &ZERO, &MHALF, &INF, 0},
+  {"pow", pow, &MZERO, &MHALF, &INF, 0},
+  {"pow", pow, &ZERO, &THREE, &ZERO, 0},
+  {"pow", pow, &MZERO, &THREE, &MZERO, 0},
+  {"pow", pow, &ZERO, &HALF, &ZERO, 0},
+  {"pow", pow, &MZERO, &HALF, &ZERO, 0},
+  {"null", NULL, &ZERO, &ZERO, &ZERO, 0},
+};
+
+/* Integer functions of one variable.  */
+
+int isnan (double);
+int signbit (double);
+
+struct intans
+  {
+    char *name;			/* Name of the function. */
+    int (*func) (double);
+    double *arg1;
+    int ianswer;
+  };
+
+struct intans test3[] =
+{
+  {"isfinite", isfinite, &ZERO, 1},
+  {"isfinite", isfinite, &INF, 0},
+  {"isfinite", isfinite, &MINF, 0},
+  {"isnan", isnan, &NAN, 1},
+  {"isnan", isnan, &INF, 0},
+  {"isnan", isnan, &ZERO, 0},
+  {"isnan", isnan, &MZERO, 0},
+  {"signbit", signbit, &MZERO, 1},
+  {"signbit", signbit, &MONE, 1},
+  {"signbit", signbit, &ZERO, 0},
+  {"signbit", signbit, &ONE, 0},
+  {"signbit", signbit, &MINF, 1},
+  {"signbit", signbit, &INF, 0},
+  {"null", NULL, &ZERO, 0},
+};
+
+static volatile double x1;
+static volatile double x2;
+static volatile double y;
+static volatile double answer;
+
+void
+pvec(x)
+double x;
+{
+  union
+  {
+    double d;
+    unsigned short s[4];
+  } u;
+  int i;
+
+  u.d = x;
+  for (i = 0; i < 4; i++)
+    printf ("0x%04x ", u.s[i]);
+  printf ("\n");
+}
+
+
+int
+main ()
+{
+  int i, nerrors, k, ianswer, ntests;
+  double (*fun1) (double);
+  double (*fun2) (double, double);
+  int (*fun3) (double);
+  double e;
+  union
+    {
+      double d;
+      char c[8];
+    } u, v;
+
+  ZERO = 0.0;
+  MZERO = NEGZERO;
+  HALF = 0.5;
+  MHALF = -HALF;
+  ONE = 1.0;
+  MONE = -ONE;
+  TWO = 2.0;
+  MTWO = -TWO;
+  THREE = 3.0;
+  MTHREE = -THREE;
+  INF = INFINITY;
+  MINF = -INFINITY;
+  MPI = -PI;
+  PIO2 = 0.5 * PI;
+  MPIO2 = -PIO2;
+  PIO4 = 0.5 * PIO2;
+  MPIO4 = -PIO4;
+  THPIO4 = 3.0 * PIO4;
+  MTHPIO4 = -THPIO4;
+
+  nerrors = 0;
+  ntests = 0;
+  i = 0;
+  for (;;)
+    {
+      fun1 = test1[i].func;
+      if (fun1 == NULL)
+	break;
+      x1 = *(test1[i].arg1);
+      y = (*(fun1)) (x1);
+      answer = *(test1[i].answer);
+      if (test1[i].thresh == 0)
+	{
+	  v.d = answer;
+	  u.d = y;
+	  if (memcmp(u.c, v.c, 8) != 0)
+	    {
+	      if( isnan(v.d) && isnan(u.d) )
+		goto nxttest1;
+	      goto wrongone;
+	    }
+	  else
+	    goto nxttest1;
+	}
+      if (y != answer)
+	{
+	  e = y - answer;
+	  if (answer != 0.0)
+	    e = e / answer;
+	  if (e < 0)
+	    e = -e;
+	  if (e > test1[i].thresh * MACHEP)
+	    {
+wrongone:
+	      printf ("%s (%.16e) = %.16e\n    should be %.16e\n",
+		      test1[i].name, x1, y, answer);
+	      nerrors += 1;
+	    }
+	}
+nxttest1:
+      ntests += 1;
+      i += 1;
+    }
+
+  i = 0;
+  for (;;)
+    {
+      fun2 = test2[i].func;
+      if (fun2 == NULL)
+	break;
+      x1 = *(test2[i].arg1);
+      x2 = *(test2[i].arg2);
+      y = (*(fun2)) (x1, x2);
+      answer = *(test2[i].answer);
+      if (test2[i].thresh == 0)
+	{
+	  v.d = answer;
+	  u.d = y;
+	  if (memcmp(u.c, v.c, 8) != 0)
+	    {
+	      if( isnan(v.d) && isnan(u.d) )
+		goto nxttest2;
+#if 0
+	      if( isnan(v.d) )
+		pvec(v.d);
+	      if( isnan(u.d) )
+		pvec(u.d);
+#endif
+	    goto wrongtwo;
+	    }
+	  else
+	    goto nxttest2;
+	}
+      if (y != answer)
+	{
+	  e = y - answer;
+	  if (answer != 0.0)
+	    e = e / answer;
+	  if (e < 0)
+	    e = -e;
+	  if (e > test2[i].thresh * MACHEP)
+	    {
+wrongtwo:
+	      printf ("%s (%.16e, %.16e) = %.16e\n    should be %.16e\n",
+		      test2[i].name, x1, x2, y, answer);
+	      nerrors += 1;
+	    }
+	}
+nxttest2:
+      ntests += 1;
+      i += 1;
+    }
+
+
+  i = 0;
+  for (;;)
+    {
+      fun3 = test3[i].func;
+      if (fun3 == NULL)
+	break;
+      x1 = *(test3[i].arg1);
+      k = (*(fun3)) (x1);
+      ianswer = test3[i].ianswer;
+      if (k != ianswer)
+	{
+	  printf ("%s (%.16e) = %d\n    should be. %d\n",
+		  test3[i].name, x1, k, ianswer);
+	  nerrors += 1;
+	}
+      ntests += 1;
+      i += 1;
+    }
+
+  printf ("testvect: %d errors in %d tests\n", nerrors, ntests);
+  exit (0);
+}

libm/double/ei.c

@@ -0,0 +1,1062 @@
+/*							ei.c
+ *
+ *	Exponential integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ei();
+ *
+ * y = ei( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *               x
+ *                -     t
+ *               | |   e
+ *    Ei(x) =   -|-   ---  dt .
+ *             | |     t
+ *              -
+ *             -inf
+ * 
+ * Not defined for x <= 0.
+ * See also expn.c.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE       0,100       50000      8.6e-16     1.3e-16
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  May, 1999
+Copyright 1999 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double log ( double );
+extern double exp ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+extern double log(), exp(), polevl(), p1evl();
+#endif
+
+#define EUL 5.772156649015328606065e-1
+
+/* 0 < x <= 2
+   Ei(x) - EUL - ln(x) = x A(x)/B(x)
+   Theoretical peak relative error 9.73e-18  */
+#if UNK
+static double A[6] = {
+-5.350447357812542947283E0,
+ 2.185049168816613393830E2,
+-4.176572384826693777058E3,
+ 5.541176756393557601232E4,
+-3.313381331178144034309E5,
+ 1.592627163384945414220E6,
+};
+static double B[6] = {
+  /*  1.000000000000000000000E0, */
+-5.250547959112862969197E1,
+ 1.259616186786790571525E3,
+-1.756549581973534652631E4,
+ 1.493062117002725991967E5,
+-7.294949239640527645655E5,
+ 1.592627163384945429726E6,
+};
+#endif
+#if DEC
+static short A[24] = {
+0140653,0033335,0060230,0144217,
+0042132,0100502,0035625,0167413,
+0143202,0102224,0037176,0175403,
+0044130,0071704,0077421,0170343,
+0144641,0144504,0041200,0045154,
+0045302,0064631,0047234,0142052,
+};
+static short B[24] = {
+  /* 0040200,0000000,0000000,0000000, */
+0141522,0002634,0070442,0142614,
+0042635,0071667,0146532,0027705,
+0143611,0035375,0156025,0114015,
+0044421,0147215,0106177,0046330,
+0145062,0014556,0144216,0103725,
+0045302,0064631,0047234,0142052,
+};
+#endif
+#if IBMPC
+static short A[24] = {
+0x1912,0xac13,0x66db,0xc015,
+0xbde1,0x4772,0x5028,0x406b,
+0xdf60,0x87cf,0x5092,0xc0b0,
+0x3e1c,0x8fe2,0x0e78,0x40eb,
+0x094e,0x8850,0x3928,0xc114,
+0x9885,0x29d3,0x4d33,0x4138,
+};
+static short B[24] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0x58b1,0x8e24,0x40b3,0xc04a,
+0x45f9,0xf9ab,0xae76,0x4093,
+0xb302,0xbb82,0x275f,0xc0d1,
+0xe99b,0xb18f,0x39d1,0x4102,
+0xd0fb,0xd911,0x432d,0xc126,
+0x9885,0x29d3,0x4d33,0x4138,
+};
+#endif
+#if MIEEE
+static short A[24] = {
+0xc015,0x66db,0xac13,0x1912,
+0x406b,0x5028,0x4772,0xbde1,
+0xc0b0,0x5092,0x87cf,0xdf60,
+0x40eb,0x0e78,0x8fe2,0x3e1c,
+0xc114,0x3928,0x8850,0x094e,
+0x4138,0x4d33,0x29d3,0x9885,
+};
+static short B[24] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc04a,0x40b3,0x8e24,0x58b1,
+0x4093,0xae76,0xf9ab,0x45f9,
+0xc0d1,0x275f,0xbb82,0xb302,
+0x4102,0x39d1,0xb18f,0xe99b,
+0xc126,0x432d,0xd911,0xd0fb,
+0x4138,0x4d33,0x29d3,0x9885,
+};
+#endif
+
+#if 0
+/* 0 < x <= 4
+   Ei(x) - EUL - ln(x) = x A(x)/B(x)
+   Theoretical peak relative error 4.75e-17  */
+#if UNK
+static double A[7] = {
+-6.831869820732773831942E0,
+ 2.920190530726774500309E2,
+-1.195883839286649567993E4,
+ 1.761045255472548975666E5,
+-2.623034438354006526979E6,
+ 1.472430336917880803157E7,
+-8.205359388213261174960E7,
+};
+static double B[7] = {
+  /* 1.000000000000000000000E0, */
+-7.731946237840033971071E1,
+ 2.751808700543578450827E3,
+-5.829268609072186897994E4,
+ 7.916610857961870631379E5,
+-6.873926904825733094076E6,
+ 3.523770183971164032710E7,
+-8.205359388213260785363E7,
+};
+#endif
+#if DEC
+static short A[28] = {
+0140732,0117255,0072522,0071743,
+0042222,0001160,0052302,0002334,
+0143472,0155532,0101650,0155462,
+0044453,0175041,0121220,0172022,
+0145440,0014351,0140337,0157550,
+0046140,0126317,0057202,0100233,
+0146634,0100473,0036072,0067054,
+};
+static short B[28] = {
+  /* 0040200,0000000,0000000,0000000, */
+0141632,0121620,0111247,0010115,
+0043053,0176360,0067773,0027324,
+0144143,0132257,0121644,0036204,
+0045101,0043321,0057553,0151231,
+0145721,0143215,0147505,0050610,
+0046406,0065721,0072675,0152744,
+0146634,0100473,0036072,0067052,
+};
+#endif
+#if IBMPC
+static short A[28] = {
+0x4e7c,0xaeaa,0x53d5,0xc01b,
+0x409b,0x0a98,0x404e,0x4072,
+0x1b66,0x5075,0x5b6b,0xc0c7,
+0x1e82,0x3452,0x7f44,0x4105,
+0xfbed,0x381b,0x031d,0xc144,
+0x5013,0xebd0,0x1599,0x416c,
+0x4dc5,0x6787,0x9027,0xc193,
+};
+static short B[28] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xe20a,0x1254,0x5472,0xc053,
+0x65db,0x0dff,0x7f9e,0x40a5,
+0x8791,0xf474,0x7695,0xc0ec,
+0x7a53,0x2bed,0x28da,0x4128,
+0xaa31,0xb9e8,0x38d1,0xc15a,
+0xbabd,0x2eb7,0xcd7a,0x4180,
+0x4dc5,0x6787,0x9027,0xc193,
+};
+#endif
+#if MIEEE
+static short A[28] = {
+0xc01b,0x53d5,0xaeaa,0x4e7c,
+0x4072,0x404e,0x0a98,0x409b,
+0xc0c7,0x5b6b,0x5075,0x1b66,
+0x4105,0x7f44,0x3452,0x1e82,
+0xc144,0x031d,0x381b,0xfbed,
+0x416c,0x1599,0xebd0,0x5013,
+0xc193,0x9027,0x6787,0x4dc5,
+};
+static short B[28] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc053,0x5472,0x1254,0xe20a,
+0x40a5,0x7f9e,0x0dff,0x65db,
+0xc0ec,0x7695,0xf474,0x8791,
+0x4128,0x28da,0x2bed,0x7a53,
+0xc15a,0x38d1,0xb9e8,0xaa31,
+0x4180,0xcd7a,0x2eb7,0xbabd,
+0xc193,0x9027,0x6787,0x4dc5,
+};
+#endif
+#endif /* 0 */
+
+#if 0
+/* 0 < x <= 8
+   Ei(x) - EUL - ln(x) = x A(x)/B(x)
+   Theoretical peak relative error 2.14e-17  */
+
+#if UNK
+static double A[9] = {
+-1.111230942210860450145E1,
+ 3.688203982071386319616E2,
+-4.924786153494029574350E4,
+ 1.050677503345557903241E6,
+-3.626713709916703688968E7,
+ 4.353499908839918635414E8,
+-6.454613717232006895409E9,
+ 3.408243056457762907071E10,
+-1.995466674647028468613E11,
+};
+static double B[9] = {
+  /*  1.000000000000000000000E0, */
+-1.356757648138514017969E2,
+ 8.562181317107341736606E3,
+-3.298257180413775117555E5,
+ 8.543534058481435917210E6,
+-1.542380618535140055068E8,
+ 1.939251779195993632028E9,
+-1.636096210465615015435E10,
+ 8.396909743075306970605E10,
+-1.995466674647028425886E11,
+};
+#endif
+#if DEC
+static short A[36] = {
+0141061,0146004,0173357,0151553,
+0042270,0064402,0147366,0126701,
+0144100,0057734,0106615,0144356,
+0045200,0040654,0003332,0004456,
+0146412,0054440,0043130,0140263,
+0047317,0113517,0033422,0065123,
+0150300,0056313,0065235,0131147,
+0050775,0167423,0146222,0075760,
+0151471,0153642,0003442,0147667,
+};
+static short B[36] = {
+  /* 0040200,0000000,0000000,0000000, */
+0142007,0126376,0166077,0043600,
+0043405,0144271,0125461,0014364,
+0144641,0006066,0175061,0164463,
+0046002,0056456,0007370,0121657,
+0147023,0013706,0156647,0177115,
+0047747,0026504,0103144,0054507,
+0150563,0146036,0007051,0177135,
+0051234,0063625,0173266,0003111,
+0151471,0153642,0003442,0147666,
+};
+#endif
+#if IBMPC
+static short A[36] = {
+0xfa6d,0x9edd,0x3980,0xc026,
+0xd5b8,0x59de,0x0d20,0x4077,
+0xb91e,0x91b1,0x0bfb,0xc0e8,
+0x4126,0x80db,0x0835,0x4130,
+0x1816,0x08cb,0x4b24,0xc181,
+0x4d4a,0xe6e2,0xf2e9,0x41b9,
+0xb64d,0x6d53,0x0b99,0xc1f8,
+0x4f7e,0x7992,0xbde2,0x421f,
+0x59f7,0x40e4,0x3af4,0xc247,
+};
+static short B[36] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xe8f0,0xdd87,0xf59f,0xc060,
+0x231e,0x3566,0xb917,0x40c0,
+0x3d26,0xdf46,0x2186,0xc114,
+0x1476,0xc1df,0x4ba5,0x4160,
+0xffca,0xdbb4,0x62f8,0xc1a2,
+0x8b29,0x90cc,0xe5a8,0x41dc,
+0x3fcc,0xc1c5,0x7983,0xc20e,
+0xc0c9,0xbed6,0x8cf2,0x4233,
+0x59f7,0x40e4,0x3af4,0xc247,
+};
+#endif
+#if MIEEE
+static short A[36] = {
+0xc026,0x3980,0x9edd,0xfa6d,
+0x4077,0x0d20,0x59de,0xd5b8,
+0xc0e8,0x0bfb,0x91b1,0xb91e,
+0x4130,0x0835,0x80db,0x4126,
+0xc181,0x4b24,0x08cb,0x1816,
+0x41b9,0xf2e9,0xe6e2,0x4d4a,
+0xc1f8,0x0b99,0x6d53,0xb64d,
+0x421f,0xbde2,0x7992,0x4f7e,
+0xc247,0x3af4,0x40e4,0x59f7,
+};
+static short B[36] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc060,0xf59f,0xdd87,0xe8f0,
+0x40c0,0xb917,0x3566,0x231e,
+0xc114,0x2186,0xdf46,0x3d26,
+0x4160,0x4ba5,0xc1df,0x1476,
+0xc1a2,0x62f8,0xdbb4,0xffca,
+0x41dc,0xe5a8,0x90cc,0x8b29,
+0xc20e,0x7983,0xc1c5,0x3fcc,
+0x4233,0x8cf2,0xbed6,0xc0c9,
+0xc247,0x3af4,0x40e4,0x59f7,
+};
+#endif
+#endif /* 0 */
+
+/* 8 <= x <= 20
+   x exp(-x) Ei(x) - 1 = 1/x R(1/x)
+   Theoretical peak absolute error = 1.07e-17  */
+#if UNK
+static double A2[10] = {
+-2.106934601691916512584E0,
+ 1.732733869664688041885E0,
+-2.423619178935841904839E-1,
+ 2.322724180937565842585E-2,
+ 2.372880440493179832059E-4,
+-8.343219561192552752335E-5,
+ 1.363408795605250394881E-5,
+-3.655412321999253963714E-7,
+ 1.464941733975961318456E-8,
+ 6.176407863710360207074E-10,
+};
+static double B2[9] = {
+  /* 1.000000000000000000000E0, */
+-2.298062239901678075778E-1,
+ 1.105077041474037862347E-1,
+-1.566542966630792353556E-2,
+ 2.761106850817352773874E-3,
+-2.089148012284048449115E-4,
+ 1.708528938807675304186E-5,
+-4.459311796356686423199E-7,
+ 1.394634930353847498145E-8,
+ 6.150865933977338354138E-10,
+};
+#endif
+#if DEC
+static short A2[40] = {
+0140406,0154004,0035104,0173336,
+0040335,0145071,0031560,0150165,
+0137570,0026670,0176230,0055040,
+0036676,0043416,0077122,0054476,
+0035170,0150206,0034407,0175571,
+0134656,0174121,0123231,0021751,
+0034144,0136766,0036746,0121115,
+0132704,0037632,0135077,0107300,
+0031573,0126321,0117076,0004314,
+0030451,0143233,0041352,0172464,
+};
+static short B2[36] = {
+  /* 0040200,0000000,0000000,0000000, */
+0137553,0051122,0120721,0170437,
+0037342,0050734,0175047,0032132,
+0136600,0052311,0101406,0147050,
+0036064,0171657,0120001,0071165,
+0135133,0010043,0151244,0066340,
+0034217,0051141,0026115,0043305,
+0132757,0064120,0106341,0051217,
+0031557,0114261,0060663,0135017,
+0030451,0011337,0001344,0175542,
+};
+#endif
+#if IBMPC
+static short A2[40] = {
+0x9edc,0x8748,0xdb00,0xc000,
+0x1a0f,0x266e,0xb947,0x3ffb,
+0x0b44,0x1f93,0x05b7,0xbfcf,
+0x4b28,0xcfca,0xc8e1,0x3f97,
+0xff6f,0xc720,0x1a10,0x3f2f,
+0x247d,0x34d3,0xdf0a,0xbf15,
+0xd44a,0xc7bc,0x97be,0x3eec,
+0xf1d8,0x5747,0x87f3,0xbe98,
+0xc119,0x33c7,0x759a,0x3e4f,
+0x5ea6,0x685d,0x38d3,0x3e05,
+};
+static short B2[36] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0x3e24,0x543a,0x6a4a,0xbfcd,
+0xe68b,0x9f44,0x4a3b,0x3fbc,
+0xd9c5,0x3060,0x0a99,0xbf90,
+0x2e4f,0xf400,0x9e75,0x3f66,
+0x8d9c,0x7a54,0x6204,0xbf2b,
+0xa8d9,0x2589,0xea4c,0x3ef1,
+0x2a52,0x119c,0xed0a,0xbe9d,
+0x7742,0x2c36,0xf316,0x3e4d,
+0x9f6c,0xe05c,0x225b,0x3e05,
+};
+#endif
+#if MIEEE
+static short A2[40] = {
+0xc000,0xdb00,0x8748,0x9edc,
+0x3ffb,0xb947,0x266e,0x1a0f,
+0xbfcf,0x05b7,0x1f93,0x0b44,
+0x3f97,0xc8e1,0xcfca,0x4b28,
+0x3f2f,0x1a10,0xc720,0xff6f,
+0xbf15,0xdf0a,0x34d3,0x247d,
+0x3eec,0x97be,0xc7bc,0xd44a,
+0xbe98,0x87f3,0x5747,0xf1d8,
+0x3e4f,0x759a,0x33c7,0xc119,
+0x3e05,0x38d3,0x685d,0x5ea6,
+};
+static short B2[36] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbfcd,0x6a4a,0x543a,0x3e24,
+0x3fbc,0x4a3b,0x9f44,0xe68b,
+0xbf90,0x0a99,0x3060,0xd9c5,
+0x3f66,0x9e75,0xf400,0x2e4f,
+0xbf2b,0x6204,0x7a54,0x8d9c,
+0x3ef1,0xea4c,0x2589,0xa8d9,
+0xbe9d,0xed0a,0x119c,0x2a52,
+0x3e4d,0xf316,0x2c36,0x7742,
+0x3e05,0x225b,0xe05c,0x9f6c,
+};
+#endif
+
+/* x > 20
+   x exp(-x) Ei(x) - 1  =  1/x A3(1/x)/B3(1/x)
+   Theoretical absolute error = 6.15e-17  */
+#if UNK
+static double A3[9] = {
+-7.657847078286127362028E-1,
+ 6.886192415566705051750E-1,
+-2.132598113545206124553E-1,
+ 3.346107552384193813594E-2,
+-3.076541477344756050249E-3,
+ 1.747119316454907477380E-4,
+-6.103711682274170530369E-6,
+ 1.218032765428652199087E-7,
+-1.086076102793290233007E-9,
+};
+static double B3[9] = {
+  /* 1.000000000000000000000E0, */
+-1.888802868662308731041E0,
+ 1.066691687211408896850E0,
+-2.751915982306380647738E-1,
+ 3.930852688233823569726E-2,
+-3.414684558602365085394E-3,
+ 1.866844370703555398195E-4,
+-6.345146083130515357861E-6,
+ 1.239754287483206878024E-7,
+-1.086076102793126632978E-9,
+};
+#endif
+#if DEC
+static short A3[36] = {
+0140104,0005167,0071746,0115510,
+0040060,0044531,0140741,0154556,
+0137532,0060307,0126506,0071123,
+0037011,0007173,0010405,0127224,
+0136111,0117715,0003654,0175577,
+0035067,0031340,0102657,0147714,
+0133714,0147173,0167473,0136640,
+0032402,0144407,0115547,0060114,
+0130625,0042347,0156431,0113425,
+};
+static short B3[36] = {
+  /* 0040200,0000000,0000000,0000000, */
+0140361,0142112,0155277,0067714,
+0040210,0104532,0065676,0074326,
+0137614,0162751,0142421,0131033,
+0037041,0000772,0053236,0002632,
+0136137,0144346,0100536,0153136,
+0035103,0140270,0152211,0166215,
+0133724,0164143,0145763,0021153,
+0032405,0017033,0035333,0025736,
+0130625,0042347,0156431,0077134,
+};
+#endif
+#if IBMPC
+static short A3[36] = {
+0xd369,0xee7c,0x814e,0xbfe8,
+0x3b2e,0x383c,0x092b,0x3fe6,
+0xce4a,0xf5a8,0x4c18,0xbfcb,
+0xb5d2,0x6220,0x21cf,0x3fa1,
+0x9f70,0xa0f5,0x33f9,0xbf69,
+0xf9f9,0x10b5,0xe65c,0x3f26,
+0x77b4,0x7de7,0x99cf,0xbed9,
+0xec09,0xf36c,0x5920,0x3e80,
+0x32e3,0xfba3,0xa89c,0xbe12,
+};
+static short B3[36] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xedf9,0x5b57,0x3889,0xbffe,
+0xcf1b,0x4d77,0x112b,0x3ff1,
+0x3643,0x38a2,0x9cbd,0xbfd1,
+0xc0b3,0x4ad3,0x203f,0x3fa4,
+0xdacc,0xd02b,0xf91c,0xbf6b,
+0x3d92,0x1a91,0x7817,0x3f28,
+0x644d,0x797e,0x9d0c,0xbeda,
+0x657c,0x675b,0xa3c3,0x3e80,
+0x2fcb,0xfba3,0xa89c,0xbe12,
+};
+#endif
+#if MIEEE
+static short A3[36] = {
+0xbfe8,0x814e,0xee7c,0xd369,
+0x3fe6,0x092b,0x383c,0x3b2e,
+0xbfcb,0x4c18,0xf5a8,0xce4a,
+0x3fa1,0x21cf,0x6220,0xb5d2,
+0xbf69,0x33f9,0xa0f5,0x9f70,
+0x3f26,0xe65c,0x10b5,0xf9f9,
+0xbed9,0x99cf,0x7de7,0x77b4,
+0x3e80,0x5920,0xf36c,0xec09,
+0xbe12,0xa89c,0xfba3,0x32e3,
+};
+static short B3[36] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbffe,0x3889,0x5b57,0xedf9,
+0x3ff1,0x112b,0x4d77,0xcf1b,
+0xbfd1,0x9cbd,0x38a2,0x3643,
+0x3fa4,0x203f,0x4ad3,0xc0b3,
+0xbf6b,0xf91c,0xd02b,0xdacc,
+0x3f28,0x7817,0x1a91,0x3d92,
+0xbeda,0x9d0c,0x797e,0x644d,
+0x3e80,0xa3c3,0x675b,0x657c,
+0xbe12,0xa89c,0xfba3,0x2fcb,
+};
+#endif
+
+/* 16 <= x <= 32
+   x exp(-x) Ei(x) - 1  =  1/x A4(1/x) / B4(1/x)
+   Theoretical absolute error = 1.22e-17  */
+#if UNK
+static double A4[8] = {
+-2.458119367674020323359E-1,
+-1.483382253322077687183E-1,
+ 7.248291795735551591813E-2,
+-1.348315687380940523823E-2,
+ 1.342775069788636972294E-3,
+-7.942465637159712264564E-5,
+ 2.644179518984235952241E-6,
+-4.239473659313765177195E-8,
+};
+static double B4[8] = {
+  /* 1.000000000000000000000E0, */
+-1.044225908443871106315E-1,
+-2.676453128101402655055E-1,
+ 9.695000254621984627876E-2,
+-1.601745692712991078208E-2,
+ 1.496414899205908021882E-3,
+-8.462452563778485013756E-5,
+ 2.728938403476726394024E-6,
+-4.239462431819542051337E-8,
+};
+#endif
+#if DEC
+static short A4[32] = {
+0137573,0133037,0152607,0113356,
+0137427,0162771,0145061,0126345,
+0037224,0070754,0110451,0174104,
+0136534,0164165,0072170,0063753,
+0035660,0000016,0002560,0147751,
+0134646,0110311,0123316,0047432,
+0033461,0071250,0101031,0075202,
+0132066,0012601,0077305,0170177,
+};
+static short B4[32] = {
+  /* 0040200,0000000,0000000,0000000, */
+0137325,0155602,0162437,0030710,
+0137611,0004316,0071344,0176361,
+0037306,0106671,0011103,0155053,
+0136603,0033412,0132530,0175171,
+0035704,0021532,0015516,0166130,
+0134661,0074162,0036741,0073466,
+0033467,0021316,0003100,0171325,
+0132066,0012541,0162202,0150160,
+};
+#endif
+#if IBMPC
+static short A4[] = {
+0xf2de,0xfab0,0x76c3,0xbfcf,
+0x359d,0x3946,0xfcbf,0xbfc2,
+0x3f09,0x9225,0x8e3d,0x3fb2,
+0x0cfd,0xae8f,0x9d0e,0xbf8b,
+0x19fd,0xc0ae,0x0001,0x3f56,
+0xc9e3,0x34d9,0xd219,0xbf14,
+0x2f50,0x1043,0x2e55,0x3ec6,
+0xbe10,0x2fd8,0xc2b0,0xbe66,
+};
+static short B4[] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xe639,0x5ca3,0xbb70,0xbfba,
+0x9f9e,0xce5c,0x2119,0xbfd1,
+0x7b45,0x2248,0xd1b7,0x3fb8,
+0x1f4f,0x56ab,0x66e1,0xbf90,
+0xdd8b,0x4369,0x846b,0x3f58,
+0x2ee7,0x47bc,0x2f0e,0xbf16,
+0x1e5b,0xc0c8,0xe459,0x3ec6,
+0x5a0e,0x3c90,0xc2ac,0xbe66,
+};
+#endif
+#if MIEEE
+static short A4[32] = {
+0xbfcf,0x76c3,0xfab0,0xf2de,
+0xbfc2,0xfcbf,0x3946,0x359d,
+0x3fb2,0x8e3d,0x9225,0x3f09,
+0xbf8b,0x9d0e,0xae8f,0x0cfd,
+0x3f56,0x0001,0xc0ae,0x19fd,
+0xbf14,0xd219,0x34d9,0xc9e3,
+0x3ec6,0x2e55,0x1043,0x2f50,
+0xbe66,0xc2b0,0x2fd8,0xbe10,
+};
+static short B4[32] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbfba,0xbb70,0x5ca3,0xe639,
+0xbfd1,0x2119,0xce5c,0x9f9e,
+0x3fb8,0xd1b7,0x2248,0x7b45,
+0xbf90,0x66e1,0x56ab,0x1f4f,
+0x3f58,0x846b,0x4369,0xdd8b,
+0xbf16,0x2f0e,0x47bc,0x2ee7,
+0x3ec6,0xe459,0xc0c8,0x1e5b,
+0xbe66,0xc2ac,0x3c90,0x5a0e,
+};
+#endif
+
+
+#if 0
+/* 20 <= x <= 40
+   x exp(-x) Ei(x) - 1  =  1/x A4(1/x) / B4(1/x)
+   Theoretical absolute error = 1.78e-17  */
+#if UNK
+static double A4[8] = {
+ 2.067245813525780707978E-1,
+-5.153749551345223645670E-1,
+ 1.928289589546695033096E-1,
+-3.124468842857260044075E-2,
+ 2.740283734277352539912E-3,
+-1.377775664366875175601E-4,
+ 3.803788980664744242323E-6,
+-4.611038277393688031154E-8,
+};
+static double B4[8] = {
+  /*  1.000000000000000000000E0, */
+-8.544436025219516861531E-1,
+ 2.507436807692907385181E-1,
+-3.647688090228423114064E-2,
+ 3.008576950332041388892E-3,
+-1.452926405348421286334E-4,
+ 3.896007735260115431965E-6,
+-4.611037642697098234083E-8,
+};
+#endif
+#if DEC
+static short A4[32] = {
+0037523,0127633,0150301,0022031,
+0140003,0167634,0170572,0170420,
+0037505,0072364,0060672,0063220,
+0136777,0172334,0057456,0102640,
+0036063,0113125,0002476,0047251,
+0135020,0074142,0042600,0043630,
+0033577,0042230,0155372,0136105,
+0132106,0005346,0165333,0114541,
+};
+static short B4[28] = {
+  /* 0040200,0000000,0000000,0000000, */
+0140132,0136320,0160433,0131535,
+0037600,0060571,0144452,0060214,
+0137025,0064310,0024220,0176472,
+0036105,0025613,0115762,0166605,
+0135030,0054662,0035454,0061763,
+0033602,0135163,0116430,0000066,
+0132106,0005345,0020602,0137133,
+};
+#endif
+#if IBMPC
+static short A4[32] = {
+0x2483,0x7a18,0x75f3,0x3fca,
+0x5e22,0x9e2f,0x7df3,0xbfe0,
+0x4cd2,0x8c37,0xae9e,0x3fc8,
+0xd0b4,0x8be5,0xfe9b,0xbf9f,
+0xc9d5,0xa0a7,0x72ca,0x3f66,
+0x08f3,0x48b0,0x0f0c,0xbf22,
+0x5789,0x1b5f,0xe893,0x3ecf,
+0x732c,0xdd5b,0xc15c,0xbe68,
+};
+static short B4[28] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0x766c,0x1c23,0x579a,0xbfeb,
+0x4c11,0x3925,0x0c2f,0x3fd0,
+0x1fa7,0x0512,0xad19,0xbfa2,
+0x5db1,0x737e,0xa571,0x3f68,
+0x8c7e,0x4765,0x0b36,0xbf23,
+0x0007,0x73a3,0x574e,0x3ed0,
+0x57cb,0xa430,0xc15c,0xbe68,
+};
+#endif
+#if MIEEE
+static short A4[32] = {
+0x3fca,0x75f3,0x7a18,0x2483,
+0xbfe0,0x7df3,0x9e2f,0x5e22,
+0x3fc8,0xae9e,0x8c37,0x4cd2,
+0xbf9f,0xfe9b,0x8be5,0xd0b4,
+0x3f66,0x72ca,0xa0a7,0xc9d5,
+0xbf22,0x0f0c,0x48b0,0x08f3,
+0x3ecf,0xe893,0x1b5f,0x5789,
+0xbe68,0xc15c,0xdd5b,0x732c,
+};
+static short B4[28] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbfeb,0x579a,0x1c23,0x766c,
+0x3fd0,0x0c2f,0x3925,0x4c11,
+0xbfa2,0xad19,0x0512,0x1fa7,
+0x3f68,0xa571,0x737e,0x5db1,
+0xbf23,0x0b36,0x4765,0x8c7e,
+0x3ed0,0x574e,0x73a3,0x0007,
+0xbe68,0xc15c,0xa430,0x57cb,
+};
+#endif
+#endif /* 0 */
+
+/* 4 <= x <= 8
+   x exp(-x) Ei(x) - 1  =  1/x A5(1/x) / B5(1/x)
+   Theoretical absolute error = 2.20e-17  */
+#if UNK
+static double A5[8] = {
+-1.373215375871208729803E0,
+-7.084559133740838761406E-1,
+ 1.580806855547941010501E0,
+-2.601500427425622944234E-1,
+ 2.994674694113713763365E-2,
+-1.038086040188744005513E-3,
+ 4.371064420753005429514E-5,
+ 2.141783679522602903795E-6,
+};
+static double B5[8] = {
+  /* 1.000000000000000000000E0, */
+ 8.585231423622028380768E-1,
+ 4.483285822873995129957E-1,
+ 7.687932158124475434091E-2,
+ 2.449868241021887685904E-2,
+ 8.832165941927796567926E-4,
+ 4.590952299511353531215E-4,
+-4.729848351866523044863E-6,
+ 2.665195537390710170105E-6,
+};
+#endif
+#if DEC
+static short A5[32] = {
+0140257,0142605,0076335,0113632,
+0140065,0056535,0161231,0074311,
+0040312,0053741,0004357,0076405,
+0137605,0031142,0165503,0136705,
+0036765,0051341,0053573,0007602,
+0135610,0010143,0027643,0110522,
+0034467,0052762,0062024,0120161,
+0033417,0135620,0036500,0062647,
+};
+static short B[32] = {
+  /* 0040200,0000000,0000000,0000000, */
+0040133,0144054,0031516,0004100,
+0037745,0105522,0166622,0123146,
+0037235,0071347,0157560,0157464,
+0036710,0130565,0173747,0041670,
+0035547,0103651,0106243,0101240,
+0035360,0131267,0176263,0140257,
+0133636,0132426,0102537,0102531,
+0033462,0155665,0167503,0176350,
+};
+#endif
+#if IBMPC
+static short A5[32] = {
+0xb2f3,0xaf9b,0xf8b0,0xbff5,
+0x2f19,0xbc53,0xabab,0xbfe6,
+0xefa1,0x211d,0x4afc,0x3ff9,
+0x77b9,0x5d68,0xa64c,0xbfd0,
+0x61f0,0x2aef,0xaa5c,0x3f9e,
+0x722a,0x65f4,0x020c,0xbf51,
+0x940e,0x4c82,0xeabe,0x3f06,
+0x0cb5,0x07a8,0xf772,0x3ec1,
+};
+static short B5[32] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xc108,0x8669,0x7905,0x3feb,
+0x54cd,0x5db2,0xb16a,0x3fdc,
+0x1be7,0xfbee,0xae5c,0x3fb3,
+0xe877,0xbefc,0x162e,0x3f99,
+0x7054,0x3194,0xf0f5,0x3f4c,
+0x7816,0xff96,0x1656,0x3f3e,
+0xf0ab,0xd0ab,0xd6a2,0xbed3,
+0x7f9d,0xbde8,0x5b76,0x3ec6,
+};
+#endif
+#if MIEEE
+static short A5[32] = {
+0xbff5,0xf8b0,0xaf9b,0xb2f3,
+0xbfe6,0xabab,0xbc53,0x2f19,
+0x3ff9,0x4afc,0x211d,0xefa1,
+0xbfd0,0xa64c,0x5d68,0x77b9,
+0x3f9e,0xaa5c,0x2aef,0x61f0,
+0xbf51,0x020c,0x65f4,0x722a,
+0x3f06,0xeabe,0x4c82,0x940e,
+0x3ec1,0xf772,0x07a8,0x0cb5,
+};
+static short B5[32] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0x3feb,0x7905,0x8669,0xc108,
+0x3fdc,0xb16a,0x5db2,0x54cd,
+0x3fb3,0xae5c,0xfbee,0x1be7,
+0x3f99,0x162e,0xbefc,0xe877,
+0x3f4c,0xf0f5,0x3194,0x7054,
+0x3f3e,0x1656,0xff96,0x7816,
+0xbed3,0xd6a2,0xd0ab,0xf0ab,
+0x3ec6,0x5b76,0xbde8,0x7f9d,
+};
+#endif
+/* 2 <= x <= 4
+   x exp(-x) Ei(x) - 1  =  1/x A6(1/x) / B6(1/x)
+   Theoretical absolute error = 4.89e-17  */
+#if UNK
+static double A6[8] = {
+ 1.981808503259689673238E-2,
+-1.271645625984917501326E0,
+-2.088160335681228318920E0,
+ 2.755544509187936721172E0,
+-4.409507048701600257171E-1,
+ 4.665623805935891391017E-2,
+-1.545042679673485262580E-3,
+ 7.059980605299617478514E-5,
+};
+static double B6[7] = {
+  /* 1.000000000000000000000E0, */
+ 1.476498670914921440652E0,
+ 5.629177174822436244827E-1,
+ 1.699017897879307263248E-1,
+ 2.291647179034212017463E-2,
+ 4.450150439728752875043E-3,
+ 1.727439612206521482874E-4,
+ 3.953167195549672482304E-5,
+};
+#endif
+#if DEC
+static short A6[32] = {
+0036642,0054611,0061263,0000140,
+0140242,0142510,0125732,0072035,
+0140405,0122153,0037643,0104527,
+0040460,0055327,0055550,0116240,
+0137741,0142112,0070441,0103510,
+0037077,0015234,0104750,0146765,
+0135712,0101407,0107554,0020253,
+0034624,0007373,0072621,0063735,
+};
+static short B6[28] = {
+  /* 0040200,0000000,0000000,0000000, */
+0040274,0176750,0110025,0061006,
+0040020,0015540,0021354,0155050,
+0037455,0175274,0015257,0021112,
+0036673,0135523,0016042,0117203,
+0036221,0151221,0046352,0144174,
+0035065,0021232,0117727,0152432,
+0034445,0147317,0037300,0067123,
+};
+#endif
+#if IBMPC
+static short A6[32] = {
+0x600c,0x2c56,0x4b31,0x3f94,
+0x4e84,0x157b,0x58a9,0xbff4,
+0x712b,0x67f4,0xb48d,0xc000,
+0x1394,0xeb6d,0x0b5a,0x4006,
+0x30e9,0x4e24,0x3889,0xbfdc,
+0x19bf,0x913d,0xe353,0x3fa7,
+0x8415,0xf1ed,0x5060,0xbf59,
+0x2cfc,0x6eb2,0x81df,0x3f12,
+};
+static short B6[28] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xac41,0x1202,0x9fbd,0x3ff7,
+0x9b45,0x045d,0x036c,0x3fe2,
+0xe449,0x8355,0xbf57,0x3fc5,
+0x53d0,0x6384,0x776a,0x3f97,
+0x590f,0x299d,0x3a52,0x3f72,
+0xfaa3,0x53fa,0xa453,0x3f26,
+0x0dca,0xe7d8,0xb9d9,0x3f04,
+};
+#endif
+#if MIEEE
+static short A6[32] = {
+0x3f94,0x4b31,0x2c56,0x600c,
+0xbff4,0x58a9,0x157b,0x4e84,
+0xc000,0xb48d,0x67f4,0x712b,
+0x4006,0x0b5a,0xeb6d,0x1394,
+0xbfdc,0x3889,0x4e24,0x30e9,
+0x3fa7,0xe353,0x913d,0x19bf,
+0xbf59,0x5060,0xf1ed,0x8415,
+0x3f12,0x81df,0x6eb2,0x2cfc,
+};
+static short B6[28] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0x3ff7,0x9fbd,0x1202,0xac41,
+0x3fe2,0x036c,0x045d,0x9b45,
+0x3fc5,0xbf57,0x8355,0xe449,
+0x3f97,0x776a,0x6384,0x53d0,
+0x3f72,0x3a52,0x299d,0x590f,
+0x3f26,0xa453,0x53fa,0xfaa3,
+0x3f04,0xb9d9,0xe7d8,0x0dca,
+};
+#endif
+/* 32 <= x <= 64
+   x exp(-x) Ei(x) - 1  =  1/x A7(1/x) / B7(1/x)
+   Theoretical absolute error = 7.71e-18  */
+#if UNK
+static double A7[6] = {
+ 1.212561118105456670844E-1,
+-5.823133179043894485122E-1,
+ 2.348887314557016779211E-1,
+-3.040034318113248237280E-2,
+ 1.510082146865190661777E-3,
+-2.523137095499571377122E-5,
+};
+static double B7[5] = {
+  /* 1.000000000000000000000E0, */
+-1.002252150365854016662E0,
+ 2.928709694872224144953E-1,
+-3.337004338674007801307E-2,
+ 1.560544881127388842819E-3,
+-2.523137093603234562648E-5,
+};
+#endif
+#if DEC
+static short A7[24] = {
+0037370,0052437,0152524,0150125,
+0140025,0011174,0050154,0131330,
+0037560,0103253,0167464,0062245,
+0136771,0005043,0174001,0023345,
+0035705,0166762,0157300,0016451,
+0134323,0123764,0157767,0134477,
+};
+static short B7[20] = {
+  /* 0040200,0000000,0000000,0000000, */
+0140200,0044714,0064025,0060324,
+0037625,0171457,0003712,0073131,
+0137010,0127406,0150061,0141746,
+0035714,0105462,0072356,0103712,
+0134323,0123764,0156514,0077414,
+};
+#endif
+#if IBMPC
+static short A7[24] = {
+0x9a0b,0xfaaa,0x0aa3,0x3fbf,
+0x965b,0x8a0d,0xa24f,0xbfe2,
+0x8c95,0x7de6,0x10d5,0x3fce,
+0x24dd,0x7f00,0x2144,0xbf9f,
+0x03a5,0x5bd8,0xbdbe,0x3f58,
+0xf728,0x9bfe,0x74fe,0xbefa,
+};
+static short B7[20] = {
+  /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xac1a,0x8d02,0x0939,0xbff0,
+0x4ecb,0xe0f9,0xbe65,0x3fd2,
+0x387d,0xda06,0x15e0,0xbfa1,
+0xd0f9,0x4e9d,0x9166,0x3f59,
+0x8fe2,0x9ba9,0x74fe,0xbefa,
+};
+#endif
+#if MIEEE
+static short A7[24] = {
+0x3fbf,0x0aa3,0xfaaa,0x9a0b,
+0xbfe2,0xa24f,0x8a0d,0x965b,
+0x3fce,0x10d5,0x7de6,0x8c95,
+0xbf9f,0x2144,0x7f00,0x24dd,
+0x3f58,0xbdbe,0x5bd8,0x03a5,
+0xbefa,0x74fe,0x9bfe,0xf728,
+};
+static short B7[20] = {
+  /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbff0,0x0939,0x8d02,0xac1a,
+0x3fd2,0xbe65,0xe0f9,0x4ecb,
+0xbfa1,0x15e0,0xda06,0x387d,
+0x3f59,0x9166,0x4e9d,0xd0f9,
+0xbefa,0x74fe,0x9ba9,0x8fe2,
+};
+#endif
+
+double ei (x)
+double x;
+{
+  double f, w;
+
+  if (x <= 0.0)
+    {
+      mtherr("ei", DOMAIN);
+      return 0.0;
+    }
+  else if (x < 2.0)
+    {
+  /* Power series.
+                            inf    n
+                             -    x
+     Ei(x) = EUL + ln x  +   >   ----
+                             -   n n!
+                            n=1
+  */
+      f = polevl(x,A,5) / p1evl(x,B,6);
+      /*      f = polevl(x,A,6) / p1evl(x,B,7); */
+      /*      f = polevl(x,A,8) / p1evl(x,B,9); */
+      return (EUL + log(x) + x * f);
+    }
+  else if (x < 4.0)
+    {
+  /* Asymptotic expansion.
+                            1       2       6
+    x exp(-x) Ei(x) =  1 + ---  +  ---  +  ---- + ...
+                            x        2       3
+                                    x       x
+  */
+      w = 1.0/x;
+      f = polevl(w,A6,7) / p1evl(w,B6,7);
+      return (exp(x) * w * (1.0 + w * f));
+    }
+  else if (x < 8.0)
+    {
+      w = 1.0/x;
+      f = polevl(w,A5,7) / p1evl(w,B5,8);
+      return (exp(x) * w * (1.0 + w * f));
+    }
+  else if (x < 16.0)
+    {
+      w = 1.0/x;
+      f = polevl(w,A2,9) / p1evl(w,B2,9);
+      return (exp(x) * w * (1.0 + w * f));
+    }
+  else if (x < 32.0)
+    {
+      w = 1.0/x;
+      f = polevl(w,A4,7) / p1evl(w,B4,8);
+      return (exp(x) * w * (1.0 + w * f));
+    }
+  else if (x < 64.0)
+    {
+      w = 1.0/x;
+      f = polevl(w,A7,5) / p1evl(w,B7,5);
+      return (exp(x) * w * (1.0 + w * f));
+    }
+  else
+    {
+      w = 1.0/x;
+      f = polevl(w,A3,8) / p1evl(w,B3,9);
+      return (exp(x) * w * (1.0 + w * f));
+    }
+}

libm/double/eigens.c

@@ -0,0 +1,181 @@
+/*							eigens.c
+ *
+ *	Eigenvalues and eigenvectors of a real symmetric matrix
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double A[n*(n+1)/2], EV[n*n], E[n];
+ * void eigens( A, EV, E, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The algorithm is due to J. vonNeumann.
+ *
+ * A[] is a symmetric matrix stored in lower triangular form.
+ * That is, A[ row, column ] = A[ (row*row+row)/2 + column ]
+ * or equivalently with row and column interchanged.  The
+ * indices row and column run from 0 through n-1.
+ *
+ * EV[] is the output matrix of eigenvectors stored columnwise.
+ * That is, the elements of each eigenvector appear in sequential
+ * memory order.  The jth element of the ith eigenvector is
+ * EV[ n*i+j ] = EV[i][j].
+ *
+ * E[] is the output matrix of eigenvalues.  The ith element
+ * of E corresponds to the ith eigenvector (the ith row of EV).
+ *
+ * On output, the matrix A will have been diagonalized and its
+ * orginal contents are destroyed.
+ *
+ * ACCURACY:
+ *
+ * The error is controlled by an internal parameter called RANGE
+ * which is set to 1e-10.  After diagonalization, the
+ * off-diagonal elements of A will have been reduced by
+ * this factor.
+ *
+ * ERROR MESSAGES:
+ *
+ * None.
+ *
+ */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double fabs ( double );
+#else
+double sqrt(), fabs();
+#endif
+
+void eigens( A, RR, E, N )
+double A[], RR[], E[];
+int N;
+{
+int IND, L, LL, LM, M, MM, MQ, I, J, IA, LQ;
+int IQ, IM, IL, NLI, NMI;
+double ANORM, ANORMX, AIA, THR, ALM, ALL, AMM, X, Y;
+double SINX, SINX2, COSX, COSX2, SINCS, AIL, AIM;
+double RLI, RMI;
+static double RANGE = 1.0e-10; /*3.0517578e-5;*/
+
+
+/* Initialize identity matrix in RR[] */
+for( J=0; J<N*N; J++ )
+	RR[J] = 0.0;
+MM = 0;
+for( J=0; J<N; J++ )
+	{
+	RR[MM + J] = 1.0;
+	MM += N;
+	}
+
+ANORM=0.0;
+for( I=0; I<N; I++ )
+	{
+	for( J=0; J<N; J++ )
+		{
+		if( I != J )
+			{
+			IA = I + (J*J+J)/2;
+			AIA = A[IA];
+			ANORM += AIA * AIA;
+			}
+		}
+	}
+if( ANORM <= 0.0 )
+	goto done;
+ANORM = sqrt( ANORM + ANORM );
+ANORMX = ANORM * RANGE / N;
+THR = ANORM;
+
+while( THR > ANORMX )
+{
+THR=THR/N;
+
+do
+{ /* while IND != 0 */
+IND = 0;
+
+for( L=0; L<N-1; L++ )
+	{
+
+for( M=L+1; M<N; M++ )
+	{
+	MQ=(M*M+M)/2;
+	LM=L+MQ;
+	ALM=A[LM];
+	if( fabs(ALM) < THR )
+		continue;
+
+	IND=1;
+	LQ=(L*L+L)/2;
+	LL=L+LQ;
+	MM=M+MQ;
+	ALL=A[LL];
+	AMM=A[MM];
+	X=(ALL-AMM)/2.0;
+	Y=-ALM/sqrt(ALM*ALM+X*X);
+	if(X < 0.0)
+		Y=-Y;
+	SINX = Y / sqrt( 2.0 * (1.0 + sqrt( 1.0-Y*Y)) );
+	SINX2=SINX*SINX;
+	COSX=sqrt(1.0-SINX2);
+	COSX2=COSX*COSX;
+	SINCS=SINX*COSX;
+
+/*	   ROTATE L AND M COLUMNS */
+for( I=0; I<N; I++ )
+	{
+	IQ=(I*I+I)/2;
+	if( (I != M) && (I != L) )
+		{
+		if(I > M)
+			IM=M+IQ;
+		else
+			IM=I+MQ;
+		if(I >= L)
+			IL=L+IQ;
+		else
+			IL=I+LQ;
+		AIL=A[IL];
+		AIM=A[IM];
+		X=AIL*COSX-AIM*SINX;
+		A[IM]=AIL*SINX+AIM*COSX;
+		A[IL]=X;
+		}
+	NLI = N*L + I;
+	NMI = N*M + I;
+	RLI = RR[ NLI ];
+	RMI = RR[ NMI ];
+	RR[NLI]=RLI*COSX-RMI*SINX;
+	RR[NMI]=RLI*SINX+RMI*COSX;
+	}
+
+	X=2.0*ALM*SINCS;
+	A[LL]=ALL*COSX2+AMM*SINX2-X;
+	A[MM]=ALL*SINX2+AMM*COSX2+X;
+	A[LM]=(ALL-AMM)*SINCS+ALM*(COSX2-SINX2);
+	} /* for M=L+1 to N-1 */
+	} /* for L=0 to N-2 */
+
+	}
+while( IND != 0 );
+
+} /* while THR > ANORMX */
+
+done:	;
+
+/* Extract eigenvalues from the reduced matrix */
+L=0;
+for( J=1; J<=N; J++ )
+	{
+	L=L+J;
+	E[J-1]=A[L-1];
+	}
+}

libm/double/ellie.c

@@ -0,0 +1,148 @@
+/*							ellie.c
+ *
+ *	Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double phi, m, y, ellie();
+ *
+ * y = ellie( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *                phi
+ *                 -
+ *                | |
+ *                |                   2
+ * E(phi_\m)  =    |    sqrt( 1 - m sin t ) dt
+ *                |
+ *              | |    
+ *               -
+ *                0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [-10, 10] and m in
+ * [0, 1].
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        0,2         2000       1.9e-16     3.4e-17
+ *    IEEE     -10,10      150000       3.3e-15     1.4e-16
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1993, 2000 by Stephen L. Moshier
+*/
+
+/*	Incomplete elliptic integral of second kind	*/
+#include <math.h>
+extern double PI, PIO2, MACHEP;
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double log ( double );
+extern double sin ( double x );
+extern double tan ( double x );
+extern double atan ( double );
+extern double floor ( double );
+extern double ellpe ( double );
+extern double ellpk ( double );
+double ellie ( double, double );
+#else
+double sqrt(), fabs(), log(), sin(), tan(), atan(), floor();
+double ellpe(), ellpk(), ellie();
+#endif
+
+double ellie( phi, m )
+double phi, m;
+{
+double a, b, c, e, temp;
+double lphi, t, E;
+int d, mod, npio2, sign;
+
+if( m == 0.0 )
+	return( phi );
+lphi = phi;
+npio2 = floor( lphi/PIO2 );
+if( npio2 & 1 )
+	npio2 += 1;
+lphi = lphi - npio2 * PIO2;
+if( lphi < 0.0 )
+	{
+	lphi = -lphi;
+	sign = -1;
+	}
+else
+	{
+	sign = 1;
+	}
+a = 1.0 - m;
+E = ellpe( a );
+if( a == 0.0 )
+	{
+	temp = sin( lphi );
+	goto done;
+	}
+t = tan( lphi );
+b = sqrt(a);
+/* Thanks to Brian Fitzgerald <fitzgb@mml0.meche.rpi.edu>
+   for pointing out an instability near odd multiples of pi/2.  */
+if( fabs(t) > 10.0 )
+	{
+	/* Transform the amplitude */
+	e = 1.0/(b*t);
+	/* ... but avoid multiple recursions.  */
+	if( fabs(e) < 10.0 )
+		{
+		e = atan(e);
+		temp = E + m * sin( lphi ) * sin( e ) - ellie( e, m );
+		goto done;
+		}
+	}
+c = sqrt(m);
+a = 1.0;
+d = 1;
+e = 0.0;
+mod = 0;
+
+while( fabs(c/a) > MACHEP )
+	{
+	temp = b/a;
+	lphi = lphi + atan(t*temp) + mod * PI;
+	mod = (lphi + PIO2)/PI;
+	t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
+	c = ( a - b )/2.0;
+	temp = sqrt( a * b );
+	a = ( a + b )/2.0;
+	b = temp;
+	d += d;
+	e += c * sin(lphi);
+	}
+
+temp = E / ellpk( 1.0 - m );
+temp *= (atan(t) + mod * PI)/(d * a);
+temp += e;
+
+done:
+
+if( sign < 0 )
+	temp = -temp;
+temp += npio2 * E;
+return( temp );
+}

libm/double/ellik.c

@@ -0,0 +1,148 @@
+/*							ellik.c
+ *
+ *	Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double phi, m, y, ellik();
+ *
+ * y = ellik( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ *                phi
+ *                 -
+ *                | |
+ *                |           dt
+ * F(phi_\m)  =    |    ------------------
+ *                |                   2
+ *              | |    sqrt( 1 - m sin t )
+ *               -
+ *                0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with m in [0, 1] and phi as indicated.
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -10,10       200000      7.4e-16     1.0e-16
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+/*	Incomplete elliptic integral of first kind	*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double log ( double );
+extern double tan ( double );
+extern double atan ( double );
+extern double floor ( double );
+extern double ellpk ( double );
+double ellik ( double, double );
+#else
+double sqrt(), fabs(), log(), tan(), atan(), floor(), ellpk();
+double ellik();
+#endif
+extern double PI, PIO2, MACHEP, MAXNUM;
+
+double ellik( phi, m )
+double phi, m;
+{
+double a, b, c, e, temp, t, K;
+int d, mod, sign, npio2;
+
+if( m == 0.0 )
+	return( phi );
+a = 1.0 - m;
+if( a == 0.0 )
+	{
+	if( fabs(phi) >= PIO2 )
+		{
+		mtherr( "ellik", SING );
+		return( MAXNUM );
+		}
+	return(  log(  tan( (PIO2 + phi)/2.0 )  )   );
+	}
+npio2 = floor( phi/PIO2 );
+if( npio2 & 1 )
+	npio2 += 1;
+if( npio2 )
+	{
+	K = ellpk( a );
+	phi = phi - npio2 * PIO2;
+	}
+else
+	K = 0.0;
+if( phi < 0.0 )
+	{
+	phi = -phi;
+	sign = -1;
+	}
+else
+	sign = 0;
+b = sqrt(a);
+t = tan( phi );
+if( fabs(t) > 10.0 )
+	{
+	/* Transform the amplitude */
+	e = 1.0/(b*t);
+	/* ... but avoid multiple recursions.  */
+	if( fabs(e) < 10.0 )
+		{
+		e = atan(e);
+		if( npio2 == 0 )
+			K = ellpk( a );
+		temp = K - ellik( e, m );
+		goto done;
+		}
+	}
+a = 1.0;
+c = sqrt(m);
+d = 1;
+mod = 0;
+
+while( fabs(c/a) > MACHEP )
+	{
+	temp = b/a;
+	phi = phi + atan(t*temp) + mod * PI;
+	mod = (phi + PIO2)/PI;
+	t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
+	c = ( a - b )/2.0;
+	temp = sqrt( a * b );
+	a = ( a + b )/2.0;
+	b = temp;
+	d += d;
+	}
+
+temp = (atan(t) + mod * PI)/(d * a);
+
+done:
+if( sign < 0 )
+	temp = -temp;
+temp += npio2 * K;
+return( temp );
+}

libm/double/ellpe.c

@@ -0,0 +1,195 @@
+/*							ellpe.c
+ *
+ *	Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double m1, y, ellpe();
+ *
+ * y = ellpe( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *            pi/2
+ *             -
+ *            | |                 2
+ * E(m)  =    |    sqrt( 1 - m sin t ) dt
+ *          | |    
+ *           -
+ *            0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ *      P(x)  -  x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        0, 1       13000       3.1e-17     9.4e-18
+ *    IEEE       0, 1       10000       2.1e-16     7.3e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * ellpe domain      x<0, x>1            0.0
+ *
+ */
+
+/*							ellpe.c		*/
+
+/* Elliptic integral of second kind */
+
+/*
+Cephes Math Library, Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+  1.53552577301013293365E-4,
+  2.50888492163602060990E-3,
+  8.68786816565889628429E-3,
+  1.07350949056076193403E-2,
+  7.77395492516787092951E-3,
+  7.58395289413514708519E-3,
+  1.15688436810574127319E-2,
+  2.18317996015557253103E-2,
+  5.68051945617860553470E-2,
+  4.43147180560990850618E-1,
+  1.00000000000000000299E0
+};
+static double Q[] = {
+  3.27954898576485872656E-5,
+  1.00962792679356715133E-3,
+  6.50609489976927491433E-3,
+  1.68862163993311317300E-2,
+  2.61769742454493659583E-2,
+  3.34833904888224918614E-2,
+  4.27180926518931511717E-2,
+  5.85936634471101055642E-2,
+  9.37499997197644278445E-2,
+  2.49999999999888314361E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0035041,0001364,0141572,0117555,
+0036044,0066032,0130027,0033404,
+0036416,0053617,0064456,0102632,
+0036457,0161100,0061177,0122612,
+0036376,0136251,0012403,0124162,
+0036370,0101316,0151715,0131613,
+0036475,0105477,0050317,0133272,
+0036662,0154232,0024645,0171552,
+0037150,0126220,0047054,0030064,
+0037742,0162057,0167645,0165612,
+0040200,0000000,0000000,0000000
+};
+static unsigned short Q[] = {
+0034411,0106743,0115771,0055462,
+0035604,0052575,0155171,0045540,
+0036325,0030424,0064332,0167756,
+0036612,0052366,0063006,0115175,
+0036726,0070430,0004533,0124654,
+0037011,0022741,0030675,0030711,
+0037056,0174452,0127062,0132122,
+0037157,0177750,0142041,0072523,
+0037277,0177777,0173137,0002627,
+0037577,0177777,0177777,0101101
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x53ee,0x986f,0x205e,0x3f24,
+0xe6e0,0x5602,0x8d83,0x3f64,
+0xd0b3,0xed25,0xcaf1,0x3f81,
+0xf4b1,0x0c4f,0xfc48,0x3f85,
+0x750e,0x22a0,0xd795,0x3f7f,
+0xb671,0xda79,0x1059,0x3f7f,
+0xf6d7,0xea19,0xb167,0x3f87,
+0xbe6d,0x4534,0x5b13,0x3f96,
+0x8607,0x09c5,0x1592,0x3fad,
+0xbd71,0xfdf4,0x5c85,0x3fdc,
+0x0000,0x0000,0x0000,0x3ff0
+};
+static unsigned short Q[] = {
+0x2b66,0x737f,0x31bc,0x3f01,
+0x296c,0xbb4f,0x8aaf,0x3f50,
+0x5dfe,0x8d1b,0xa622,0x3f7a,
+0xd350,0xccc0,0x4a9e,0x3f91,
+0x7535,0x012b,0xce23,0x3f9a,
+0xa639,0x2637,0x24bc,0x3fa1,
+0x568a,0x55c6,0xdf25,0x3fa5,
+0x2eaa,0x1884,0xfffd,0x3fad,
+0xe0b3,0xfecb,0xffff,0x3fb7,
+0xf048,0xffff,0xffff,0x3fcf
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f24,0x205e,0x986f,0x53ee,
+0x3f64,0x8d83,0x5602,0xe6e0,
+0x3f81,0xcaf1,0xed25,0xd0b3,
+0x3f85,0xfc48,0x0c4f,0xf4b1,
+0x3f7f,0xd795,0x22a0,0x750e,
+0x3f7f,0x1059,0xda79,0xb671,
+0x3f87,0xb167,0xea19,0xf6d7,
+0x3f96,0x5b13,0x4534,0xbe6d,
+0x3fad,0x1592,0x09c5,0x8607,
+0x3fdc,0x5c85,0xfdf4,0xbd71,
+0x3ff0,0x0000,0x0000,0x0000
+};
+static unsigned short Q[] = {
+0x3f01,0x31bc,0x737f,0x2b66,
+0x3f50,0x8aaf,0xbb4f,0x296c,
+0x3f7a,0xa622,0x8d1b,0x5dfe,
+0x3f91,0x4a9e,0xccc0,0xd350,
+0x3f9a,0xce23,0x012b,0x7535,
+0x3fa1,0x24bc,0x2637,0xa639,
+0x3fa5,0xdf25,0x55c6,0x568a,
+0x3fad,0xfffd,0x1884,0x2eaa,
+0x3fb7,0xffff,0xfecb,0xe0b3,
+0x3fcf,0xffff,0xffff,0xf048
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double log ( double );
+#else
+double polevl(), log();
+#endif
+
+double ellpe(x)
+double x;
+{
+
+if( (x <= 0.0) || (x > 1.0) )
+	{
+	if( x == 0.0 )
+		return( 1.0 );
+	mtherr( "ellpe", DOMAIN );
+	return( 0.0 );
+	}
+return( polevl(x,P,10) - log(x) * (x * polevl(x,Q,9)) );
+}

libm/double/ellpj.c

@@ -0,0 +1,171 @@
+/*							ellpj.c
+ *
+ *	Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double u, m, sn, cn, dn, phi;
+ * int ellpj();
+ *
+ * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi).  Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-9 of 0 or 1.  In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ *            Absolute error (* = relative error):
+ * arithmetic   function   # trials      peak         rms
+ *    DEC       sn           1800       4.5e-16     8.7e-17
+ *    IEEE      phi         10000       9.2e-16*    1.4e-16*
+ *    IEEE      sn          50000       4.1e-15     4.6e-16
+ *    IEEE      cn          40000       3.6e-15     4.4e-16
+ *    IEEE      dn          10000       1.3e-12     1.8e-14
+ *
+ *  Peak error observed in consistency check using addition
+ * theorem for sn(u+v) was 4e-16 (absolute).  Also tested by
+ * the above relation to the incomplete elliptic integral.
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/*							ellpj.c		*/
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double asin ( double );
+extern double tanh ( double );
+extern double sinh ( double );
+extern double cosh ( double );
+extern double atan ( double );
+extern double exp ( double );
+#else
+double sqrt(), fabs(), sin(), cos(), asin(), tanh();
+double sinh(), cosh(), atan(), exp();
+#endif
+extern double PIO2, MACHEP;
+
+int ellpj( u, m, sn, cn, dn, ph )
+double u, m;
+double *sn, *cn, *dn, *ph;
+{
+double ai, b, phi, t, twon;
+double a[9], c[9];
+int i;
+
+
+/* Check for special cases */
+
+if( m < 0.0 || m > 1.0 )
+	{
+	mtherr( "ellpj", DOMAIN );
+	*sn = 0.0;
+	*cn = 0.0;
+	*ph = 0.0;
+	*dn = 0.0;
+	return(-1);
+	}
+if( m < 1.0e-9 )
+	{
+	t = sin(u);
+	b = cos(u);
+	ai = 0.25 * m * (u - t*b);
+	*sn = t - ai*b;
+	*cn = b + ai*t;
+	*ph = u - ai;
+	*dn = 1.0 - 0.5*m*t*t;
+	return(0);
+	}
+
+if( m >= 0.9999999999 )
+	{
+	ai = 0.25 * (1.0-m);
+	b = cosh(u);
+	t = tanh(u);
+	phi = 1.0/b;
+	twon = b * sinh(u);
+	*sn = t + ai * (twon - u)/(b*b);
+	*ph = 2.0*atan(exp(u)) - PIO2 + ai*(twon - u)/b;
+	ai *= t * phi;
+	*cn = phi - ai * (twon - u);
+	*dn = phi + ai * (twon + u);
+	return(0);
+	}
+
+
+/*	A. G. M. scale		*/
+a[0] = 1.0;
+b = sqrt(1.0 - m);
+c[0] = sqrt(m);
+twon = 1.0;
+i = 0;
+
+while( fabs(c[i]/a[i]) > MACHEP )
+	{
+	if( i > 7 )
+		{
+		mtherr( "ellpj", OVERFLOW );
+		goto done;
+		}
+	ai = a[i];
+	++i;
+	c[i] = ( ai - b )/2.0;
+	t = sqrt( ai * b );
+	a[i] = ( ai + b )/2.0;
+	b = t;
+	twon *= 2.0;
+	}
+
+done:
+
+/* backward recurrence */
+phi = twon * a[i] * u;
+do
+	{
+	t = c[i] * sin(phi) / a[i];
+	b = phi;
+	phi = (asin(t) + phi)/2.0;
+	}
+while( --i );
+
+*sn = sin(phi);
+t = cos(phi);
+*cn = t;
+*dn = t/cos(phi-b);
+*ph = phi;
+return(0);
+}

libm/double/ellpk.c

@@ -0,0 +1,234 @@
+/*							ellpk.c
+ *
+ *	Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double m1, y, ellpk();
+ *
+ * y = ellpk( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ *            pi/2
+ *             -
+ *            | |
+ *            |           dt
+ * K(m)  =    |    ------------------
+ *            |                   2
+ *          | |    sqrt( 1 - m sin t )
+ *           -
+ *            0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ *     P(x)  -  log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC        0,1        16000       3.5e-17     1.1e-17
+ *    IEEE       0,1        30000       2.5e-16     6.8e-17
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * ellpk domain       x<0, x>1           0.0
+ *
+ */
+
+/*							ellpk.c */
+
+
+/*
+Cephes Math Library, Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef DEC
+static unsigned short P[] =
+{
+0035020,0127576,0040430,0051544,
+0036025,0070136,0042703,0153716,
+0036402,0122614,0062555,0077777,
+0036441,0102130,0072334,0025172,
+0036341,0043320,0117242,0172076,
+0036312,0146456,0077242,0154141,
+0036420,0003467,0013727,0035407,
+0036564,0137263,0110651,0020237,
+0036775,0001330,0144056,0020305,
+0037305,0144137,0157521,0141734,
+0040261,0071027,0173721,0147572
+};
+static unsigned short Q[] =
+{
+0034366,0130371,0103453,0077633,
+0035557,0122745,0173515,0113016,
+0036302,0124470,0167304,0074473,
+0036575,0132403,0117226,0117576,
+0036703,0156271,0047124,0147733,
+0036766,0137465,0002053,0157312,
+0037031,0014423,0154274,0176515,
+0037107,0177747,0143216,0016145,
+0037217,0177777,0172621,0074000,
+0037377,0177777,0177776,0156435,
+0040000,0000000,0000000,0000000
+};
+static unsigned short ac1[] = {0040261,0071027,0173721,0147572};
+#define C1 (*(double *)ac1)
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] =
+{
+0x0a6d,0xc823,0x15ef,0x3f22,
+0x7afa,0xc8b8,0xae0b,0x3f62,
+0xb000,0x8cad,0x54b1,0x3f80,
+0x854f,0x0e9b,0x308b,0x3f84,
+0x5e88,0x13d4,0x28da,0x3f7c,
+0x5b0c,0xcfd4,0x59a5,0x3f79,
+0xe761,0xe2fa,0x00e6,0x3f82,
+0x2414,0x7235,0x97d6,0x3f8e,
+0xc419,0x1905,0xa05b,0x3f9f,
+0x387c,0xfbea,0xb90b,0x3fb8,
+0x39ef,0xfefa,0x2e42,0x3ff6
+};
+static unsigned short Q[] =
+{
+0x6ff3,0x30e5,0xd61f,0x3efe,
+0xb2c2,0xbee9,0xf4bc,0x3f4d,
+0x8f27,0x1dd8,0x5527,0x3f78,
+0xd3f0,0x73d2,0xb6a0,0x3f8f,
+0x99fb,0x29ca,0x7b97,0x3f98,
+0x7bd9,0xa085,0xd7e6,0x3f9e,
+0x9faa,0x7b17,0x2322,0x3fa3,
+0xc38d,0xf8d1,0xfffc,0x3fa8,
+0x2f00,0xfeb2,0xffff,0x3fb1,
+0xdba4,0xffff,0xffff,0x3fbf,
+0x0000,0x0000,0x0000,0x3fe0
+};
+static unsigned short ac1[] = {0x39ef,0xfefa,0x2e42,0x3ff6};
+#define C1 (*(double *)ac1)
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] =
+{
+0x3f22,0x15ef,0xc823,0x0a6d,
+0x3f62,0xae0b,0xc8b8,0x7afa,
+0x3f80,0x54b1,0x8cad,0xb000,
+0x3f84,0x308b,0x0e9b,0x854f,
+0x3f7c,0x28da,0x13d4,0x5e88,
+0x3f79,0x59a5,0xcfd4,0x5b0c,
+0x3f82,0x00e6,0xe2fa,0xe761,
+0x3f8e,0x97d6,0x7235,0x2414,
+0x3f9f,0xa05b,0x1905,0xc419,
+0x3fb8,0xb90b,0xfbea,0x387c,
+0x3ff6,0x2e42,0xfefa,0x39ef
+};
+static unsigned short Q[] =
+{
+0x3efe,0xd61f,0x30e5,0x6ff3,
+0x3f4d,0xf4bc,0xbee9,0xb2c2,
+0x3f78,0x5527,0x1dd8,0x8f27,
+0x3f8f,0xb6a0,0x73d2,0xd3f0,
+0x3f98,0x7b97,0x29ca,0x99fb,
+0x3f9e,0xd7e6,0xa085,0x7bd9,
+0x3fa3,0x2322,0x7b17,0x9faa,
+0x3fa8,0xfffc,0xf8d1,0xc38d,
+0x3fb1,0xffff,0xfeb2,0x2f00,
+0x3fbf,0xffff,0xffff,0xdba4,
+0x3fe0,0x0000,0x0000,0x0000
+};
+static unsigned short ac1[] = {
+0x3ff6,0x2e42,0xfefa,0x39ef
+};
+#define C1 (*(double *)ac1)
+#endif
+
+#ifdef UNK
+static double P[] =
+{
+ 1.37982864606273237150E-4,
+ 2.28025724005875567385E-3,
+ 7.97404013220415179367E-3,
+ 9.85821379021226008714E-3,
+ 6.87489687449949877925E-3,
+ 6.18901033637687613229E-3,
+ 8.79078273952743772254E-3,
+ 1.49380448916805252718E-2,
+ 3.08851465246711995998E-2,
+ 9.65735902811690126535E-2,
+ 1.38629436111989062502E0
+};
+
+static double Q[] =
+{
+ 2.94078955048598507511E-5,
+ 9.14184723865917226571E-4,
+ 5.94058303753167793257E-3,
+ 1.54850516649762399335E-2,
+ 2.39089602715924892727E-2,
+ 3.01204715227604046988E-2,
+ 3.73774314173823228969E-2,
+ 4.88280347570998239232E-2,
+ 7.03124996963957469739E-2,
+ 1.24999999999870820058E-1,
+ 4.99999999999999999821E-1
+};
+static double C1 = 1.3862943611198906188E0; /* log(4) */
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+#else
+double polevl(), p1evl(), log();
+#endif
+extern double MACHEP, MAXNUM;
+
+double ellpk(x)
+double x;
+{
+
+if( (x < 0.0) || (x > 1.0) )
+	{
+	mtherr( "ellpk", DOMAIN );
+	return( 0.0 );
+	}
+
+if( x > MACHEP )
+	{
+	return( polevl(x,P,10) - log(x) * polevl(x,Q,10) );
+	}
+else
+	{
+	if( x == 0.0 )
+		{
+		mtherr( "ellpk", SING );
+		return( MAXNUM );
+		}
+	else
+		{
+		return( C1 - 0.5 * log(x) );
+		}
+	}
+}

libm/double/eltst.c

@@ -0,0 +1,37 @@
+extern double MACHEP, PIO2, PI;
+double ellie(), ellpe(), floor(), fabs();
+double ellie2();
+
+main()
+{
+double y, m, phi, e, E, phipi, y1;
+int i, j, npi;
+
+/* dprec();  */
+m = 0.9;
+E = ellpe(0.1);
+for( j=-10; j<=10; j++ )
+  {
+    printf( "%d * PIO2\n", j );
+    for( i=-2; i<=2; i++ )
+      {
+	phi = PIO2 * j + 50 * MACHEP * i;
+	npi = floor(phi/PIO2);
+	if( npi & 1 )
+		npi += 1;
+	phipi = phi - npi * PIO2;
+	npi = floor(phi/PIO2);
+	if( npi & 1 )
+		npi += 1;
+	phipi = phi - npi * PIO2;
+	printf( "phi %.9e npi %d ", phi, npi );
+	y1 = E * npi + ellie(phipi,m);
+	y = ellie2( phi, m );
+	printf( "y %.9e ", y );
+	e = fabs(y - y1);
+	if( y1 != 0.0 )
+	  e /= y1;
+	printf( "e %.4e\n", e );
+      }
+  }
+}

libm/double/euclid.c

@@ -0,0 +1,251 @@
+/*							euclid.c
+ *
+ *	Rational arithmetic routines
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * 
+ * typedef struct
+ *      {
+ *      double n;  numerator
+ *      double d;  denominator
+ *      }fract;
+ *
+ * radd( a, b, c )      c = b + a
+ * rsub( a, b, c )      c = b - a
+ * rmul( a, b, c )      c = b * a
+ * rdiv( a, b, c )      c = b / a
+ * euclid( &n, &d )     Reduce n/d to lowest terms,
+ *                      return greatest common divisor.
+ *
+ * Arguments of the routines are pointers to the structures.
+ * The double precision numbers are assumed, without checking,
+ * to be integer valued.  Overflow conditions are reported.
+ */
+ 
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double floor ( double );
+double euclid( double *, double * );
+#else
+double fabs(), floor(), euclid();
+#endif
+
+extern double MACHEP;
+#define BIG (1.0/MACHEP)
+
+typedef struct
+	{
+	double n; /* numerator */
+	double d; /* denominator */
+	}fract;
+
+/* Add fractions. */
+
+void radd( f1, f2, f3 )
+fract *f1, *f2, *f3;
+{
+double gcd, d1, d2, gcn, n1, n2;
+
+n1 = f1->n;
+d1 = f1->d;
+n2 = f2->n;
+d2 = f2->d;
+if( n1 == 0.0 )
+	{
+	f3->n = n2;
+	f3->d = d2;
+	return;
+	}
+if( n2 == 0.0 )
+	{
+	f3->n = n1;
+	f3->d = d1;
+	return;
+	}
+
+gcd = euclid( &d1, &d2 ); /* common divisors of denominators */
+gcn = euclid( &n1, &n2 ); /* common divisors of numerators */
+/* Note, factoring the numerators
+ * makes overflow slightly less likely.
+ */
+f3->n = ( n1 * d2 + n2 * d1) * gcn;
+f3->d = d1 * d2 * gcd;
+euclid( &f3->n, &f3->d );
+}
+
+
+/* Subtract fractions. */
+
+void rsub( f1, f2, f3 )
+fract *f1, *f2, *f3;
+{
+double gcd, d1, d2, gcn, n1, n2;
+
+n1 = f1->n;
+d1 = f1->d;
+n2 = f2->n;
+d2 = f2->d;
+if( n1 == 0.0 )
+	{
+	f3->n = n2;
+	f3->d = d2;
+	return;
+	}
+if( n2 == 0.0 )
+	{
+	f3->n = -n1;
+	f3->d = d1;
+	return;
+	}
+
+gcd = euclid( &d1, &d2 );
+gcn = euclid( &n1, &n2 );
+f3->n = (n2 * d1 - n1 * d2) * gcn;
+f3->d = d1 * d2 * gcd;
+euclid( &f3->n, &f3->d );
+}
+
+
+
+
+/* Multiply fractions. */
+
+void rmul( ff1, ff2, ff3 )
+fract *ff1, *ff2, *ff3;
+{
+double d1, d2, n1, n2;
+
+n1 = ff1->n;
+d1 = ff1->d;
+n2 = ff2->n;
+d2 = ff2->d;
+
+if( (n1 == 0.0) || (n2 == 0.0) )
+	{
+	ff3->n = 0.0;
+	ff3->d = 1.0;
+	return;
+	}
+euclid( &n1, &d2 ); /* cross cancel common divisors */
+euclid( &n2, &d1 );
+ff3->n = n1 * n2;
+ff3->d = d1 * d2;
+/* Report overflow. */
+if( (fabs(ff3->n) >= BIG) || (fabs(ff3->d) >= BIG) )
+	{
+	mtherr( "rmul", OVERFLOW );
+	return;
+	}
+/* euclid( &ff3->n, &ff3->d );*/
+}
+
+
+
+/* Divide fractions. */
+
+void rdiv( ff1, ff2, ff3 )
+fract *ff1, *ff2, *ff3;
+{
+double d1, d2, n1, n2;
+
+n1 = ff1->d;	/* Invert ff1, then multiply */
+d1 = ff1->n;
+if( d1 < 0.0 )
+	{ /* keep denominator positive */
+	n1 = -n1;
+	d1 = -d1;
+	}
+n2 = ff2->n;
+d2 = ff2->d;
+if( (n1 == 0.0) || (n2 == 0.0) )
+	{
+	ff3->n = 0.0;
+	ff3->d = 1.0;
+	return;
+	}
+
+euclid( &n1, &d2 ); /* cross cancel any common divisors */
+euclid( &n2, &d1 );
+ff3->n = n1 * n2;
+ff3->d = d1 * d2;
+/* Report overflow. */
+if( (fabs(ff3->n) >= BIG) || (fabs(ff3->d) >= BIG) )
+	{
+	mtherr( "rdiv", OVERFLOW );
+	return;
+	}
+/* euclid( &ff3->n, &ff3->d );*/
+}
+
+
+
+
+
+/* Euclidean algorithm
+ *   reduces fraction to lowest terms,
+ *   returns greatest common divisor.
+ */
+
+
+double euclid( num, den )
+double *num, *den;
+{
+double n, d, q, r;
+
+n = *num; /* Numerator. */
+d = *den; /* Denominator. */
+
+/* Make numbers positive, locally. */
+if( n < 0.0 )
+	n = -n;
+if( d < 0.0 )
+	d = -d;
+
+/* Abort if numbers are too big for integer arithmetic. */
+if( (n >= BIG) || (d >= BIG) )
+	{
+	mtherr( "euclid", OVERFLOW );
+	return(1.0);
+	}
+
+/* Divide by zero, gcd = 1. */
+if(d == 0.0)
+	return( 1.0 );
+
+/* Zero. Return 0/1, gcd = denominator. */
+if(n == 0.0)
+	{
+/*
+	if( *den < 0.0 )
+		*den = -1.0;
+	else
+		*den = 1.0;
+*/
+	*den = 1.0;
+	return( d );
+	}
+
+while( d > 0.5 )
+	{
+/* Find integer part of n divided by d. */
+	q = floor( n/d );
+/* Find remainder after dividing n by d. */
+	r = n - d * q;
+/* The next fraction is d/r. */
+	n = d;
+	d = r;
+	}
+
+if( n < 0.0 )
+	mtherr( "euclid", UNDERFLOW );
+
+*num /= n;
+*den /= n;
+return( n );
+}
+

libm/double/exp.c

@@ -0,0 +1,203 @@
+/*							exp.c
+ *
+ *	Exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp();
+ *
+ * y = exp( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ *     x    k  f
+ *    e  = 2  e.
+ *
+ * A Pade' form  1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ * of degree 2/3 is used to approximate exp(f) in the basic
+ * interval [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       +- 88       50000       2.8e-17     7.0e-18
+ *    IEEE      +- 708      40000       2.0e-16     5.6e-17
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter.  The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp underflow    x < MINLOG         0.0
+ * exp overflow     x > MAXLOG         INFINITY
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+/*	Exponential function	*/
+
+#include <math.h>
+
+#ifdef UNK
+
+static double P[] = {
+ 1.26177193074810590878E-4,
+ 3.02994407707441961300E-2,
+ 9.99999999999999999910E-1,
+};
+static double Q[] = {
+ 3.00198505138664455042E-6,
+ 2.52448340349684104192E-3,
+ 2.27265548208155028766E-1,
+ 2.00000000000000000009E0,
+};
+static double C1 = 6.93145751953125E-1;
+static double C2 = 1.42860682030941723212E-6;
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0035004,0047156,0127442,0057502,
+0036770,0033210,0063121,0061764,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short Q[] = {
+0033511,0072665,0160662,0176377,
+0036045,0070715,0124105,0132777,
+0037550,0134114,0142077,0001637,
+0040400,0000000,0000000,0000000,
+};
+static unsigned short sc1[] = {0040061,0071000,0000000,0000000};
+#define C1 (*(double *)sc1)
+static unsigned short sc2[] = {0033277,0137216,0075715,0057117};
+#define C2 (*(double *)sc2)
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x4be8,0xd5e4,0x89cd,0x3f20,
+0x2c7e,0x0cca,0x06d1,0x3f9f,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short Q[] = {
+0x5fa0,0xbc36,0x2eb6,0x3ec9,
+0xb6c0,0xb508,0xae39,0x3f64,
+0xe074,0x9887,0x1709,0x3fcd,
+0x0000,0x0000,0x0000,0x4000,
+};
+static unsigned short sc1[] = {0x0000,0x0000,0x2e40,0x3fe6};
+#define C1 (*(double *)sc1)
+static unsigned short sc2[] = {0xabca,0xcf79,0xf7d1,0x3eb7};
+#define C2 (*(double *)sc2)
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f20,0x89cd,0xd5e4,0x4be8,
+0x3f9f,0x06d1,0x0cca,0x2c7e,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short Q[] = {
+0x3ec9,0x2eb6,0xbc36,0x5fa0,
+0x3f64,0xae39,0xb508,0xb6c0,
+0x3fcd,0x1709,0x9887,0xe074,
+0x4000,0x0000,0x0000,0x0000,
+};
+static unsigned short sc1[] = {0x3fe6,0x2e40,0x0000,0x0000};
+#define C1 (*(double *)sc1)
+static unsigned short sc2[] = {0x3eb7,0xf7d1,0xcf79,0xabca};
+#define C2 (*(double *)sc2)
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double polevl(), p1evl(), floor(), ldexp();
+int isnan(), isfinite();
+#endif
+extern double LOGE2, LOG2E, MAXLOG, MINLOG, MAXNUM;
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+
+double exp(x)
+double x;
+{
+double px, xx;
+int n;
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+if( x > MAXLOG)
+	{
+#ifdef INFINITIES
+	return( INFINITY );
+#else
+	mtherr( "exp", OVERFLOW );
+	return( MAXNUM );
+#endif
+	}
+
+if( x < MINLOG )
+	{
+#ifndef INFINITIES
+	mtherr( "exp", UNDERFLOW );
+#endif
+	return(0.0);
+	}
+
+/* Express e**x = e**g 2**n
+ *   = e**g e**( n loge(2) )
+ *   = e**( g + n loge(2) )
+ */
+px = floor( LOG2E * x + 0.5 ); /* floor() truncates toward -infinity. */
+n = px;
+x -= px * C1;
+x -= px * C2;
+
+/* rational approximation for exponential
+ * of the fractional part:
+ * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+xx = x * x;
+px = x * polevl( xx, P, 2 );
+x =  px/( polevl( xx, Q, 3 ) - px );
+x = 1.0 + 2.0 * x;
+
+/* multiply by power of 2 */
+x = ldexp( x, n );
+return(x);
+}

libm/double/exp10.c

@@ -0,0 +1,223 @@
+/*							exp10.c
+ *
+ *	Base 10 exponential function
+ *      (Common antilogarithm)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp10();
+ *
+ * y = exp10( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 10 raised to the x power.
+ *
+ * Range reduction is accomplished by expressing the argument
+ * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
+ * The Pade' form
+ *
+ *    1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ *
+ * is used to approximate 10**f.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -307,+307    30000       2.2e-16     5.5e-17
+ * Test result from an earlier version (2.1):
+ *    DEC       -38,+38     70000       3.1e-17     7.0e-18
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp10 underflow    x < -MAXL10        0.0
+ * exp10 overflow     x > MAXL10       MAXNUM
+ *
+ * DEC arithmetic: MAXL10 = 38.230809449325611792.
+ * IEEE arithmetic: MAXL10 = 308.2547155599167.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1991, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+ 4.09962519798587023075E-2,
+ 1.17452732554344059015E1,
+ 4.06717289936872725516E2,
+ 2.39423741207388267439E3,
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 8.50936160849306532625E1,
+ 1.27209271178345121210E3,
+ 2.07960819286001865907E3,
+};
+/* static double LOG102 = 3.01029995663981195214e-1; */
+static double LOG210 = 3.32192809488736234787e0;
+static double LG102A = 3.01025390625000000000E-1;
+static double LG102B = 4.60503898119521373889E-6;
+/* static double MAXL10 = 38.230809449325611792; */
+static double MAXL10 = 308.2547155599167;
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0037047,0165657,0114061,0067234,
+0041073,0166243,0123052,0144643,
+0042313,0055720,0024032,0047443,
+0043025,0121714,0070232,0050007,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041652,0027756,0071216,0050075,
+0042637,0001367,0077263,0136017,
+0043001,0174673,0024157,0133416,
+};
+/*
+static unsigned short L102[] = {0037632,0020232,0102373,0147770};
+#define LOG102 *(double *)L102
+*/
+static unsigned short L210[] = {0040524,0115170,0045715,0015613};
+#define LOG210 *(double *)L210
+static unsigned short L102A[] = {0037632,0020000,0000000,0000000,};
+#define LG102A *(double *)L102A
+static unsigned short L102B[] = {0033632,0102373,0147767,0114220,};
+#define LG102B *(double *)L102B
+static unsigned short MXL[] = {0041430,0166131,0047761,0154130,};
+#define MAXL10 ( *(double *)MXL )
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x2dd4,0xf306,0xfd75,0x3fa4,
+0x5934,0x74c5,0x7d94,0x4027,
+0x49e4,0x0503,0x6b7a,0x4079,
+0x4a01,0x8e13,0xb479,0x40a2,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xca08,0xce51,0x45fd,0x4055,
+0x7782,0xefd6,0xe05e,0x4093,
+0xf6e2,0x650d,0x3f37,0x40a0,
+};
+/*
+static unsigned short L102[] = {0x79ff,0x509f,0x4413,0x3fd3};
+#define LOG102 *(double *)L102
+*/
+static unsigned short L210[] = {0xa371,0x0979,0x934f,0x400a};
+#define LOG210 *(double *)L210
+static unsigned short L102A[] = {0x0000,0x0000,0x4400,0x3fd3,};
+#define LG102A *(double *)L102A
+static unsigned short L102B[] = {0xf312,0x79fe,0x509f,0x3ed3,};
+#define LG102B *(double *)L102B
+static double MAXL10 = 308.2547155599167;
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3fa4,0xfd75,0xf306,0x2dd4,
+0x4027,0x7d94,0x74c5,0x5934,
+0x4079,0x6b7a,0x0503,0x49e4,
+0x40a2,0xb479,0x8e13,0x4a01,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4055,0x45fd,0xce51,0xca08,
+0x4093,0xe05e,0xefd6,0x7782,
+0x40a0,0x3f37,0x650d,0xf6e2,
+};
+/*
+static unsigned short L102[] = {0x3fd3,0x4413,0x509f,0x79ff};
+#define LOG102 *(double *)L102
+*/
+static unsigned short L210[] = {0x400a,0x934f,0x0979,0xa371};
+#define LOG210 *(double *)L210
+static unsigned short L102A[] = {0x3fd3,0x4400,0x0000,0x0000,};
+#define LG102A *(double *)L102A
+static unsigned short L102B[] = {0x3ed3,0x509f,0x79fe,0xf312,};
+#define LG102B *(double *)L102B
+static double MAXL10 = 308.2547155599167;
+#endif
+
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double floor(), ldexp(), polevl(), p1evl();
+int isnan(), isfinite();
+#endif
+extern double MAXNUM;
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+
+double exp10(x)
+double x;
+{
+double px, xx;
+short n;
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+if( x > MAXL10 )
+	{
+#ifdef INFINITIES
+	return( INFINITY );
+#else
+	mtherr( "exp10", OVERFLOW );
+	return( MAXNUM );
+#endif
+	}
+
+if( x < -MAXL10 )	/* Would like to use MINLOG but can't */
+	{
+#ifndef INFINITIES
+	mtherr( "exp10", UNDERFLOW );
+#endif
+	return(0.0);
+	}
+
+/* Express 10**x = 10**g 2**n
+ *   = 10**g 10**( n log10(2) )
+ *   = 10**( g + n log10(2) )
+ */
+px = floor( LOG210 * x + 0.5 );
+n = px;
+x -= px * LG102A;
+x -= px * LG102B;
+
+/* rational approximation for exponential
+ * of the fractional part:
+ * 10**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+xx = x * x;
+px = x * polevl( xx, P, 3 );
+x =  px/( p1evl( xx, Q, 3 ) - px );
+x = 1.0 + ldexp( x, 1 );
+
+/* multiply by power of 2 */
+x = ldexp( x, n );
+
+return(x);
+}

libm/double/exp2.c

@@ -0,0 +1,183 @@
+/*							exp2.c
+ *
+ *	Base 2 exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp2();
+ *
+ * y = exp2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *     x    k  f
+ *    2  = 2  2.
+ *
+ * A Pade' form
+ *
+ *   1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
+ *
+ * approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE    -1022,+1024   30000       1.8e-16     5.4e-17
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp underflow    x < -MAXL2        0.0
+ * exp overflow     x > MAXL2         MAXNUM
+ *
+ * For DEC arithmetic, MAXL2 = 127.
+ * For IEEE arithmetic, MAXL2 = 1024.
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+ 2.30933477057345225087E-2,
+ 2.02020656693165307700E1,
+ 1.51390680115615096133E3,
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 2.33184211722314911771E2,
+ 4.36821166879210612817E3,
+};
+#define MAXL2 1024.0
+#define MINL2 -1024.0
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0036675,0027102,0122327,0053227,
+0041241,0116724,0115412,0157355,
+0042675,0036404,0101733,0132226,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0042151,0027450,0077732,0160744,
+0043210,0100661,0077550,0056560,
+};
+#define MAXL2 127.0
+#define MINL2 -127.0
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0xead3,0x549a,0xa5c8,0x3f97,
+0x5bde,0x9361,0x33ba,0x4034,
+0x7693,0x907b,0xa7a0,0x4097,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x5c3c,0x0ffb,0x25e5,0x406d,
+0x0bae,0x2fed,0x1036,0x40b1,
+};
+#define MAXL2 1024.0
+#define MINL2 -1022.0
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f97,0xa5c8,0x549a,0xead3,
+0x4034,0x33ba,0x9361,0x5bde,
+0x4097,0xa7a0,0x907b,0x7693,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x406d,0x25e5,0x0ffb,0x5c3c,
+0x40b1,0x1036,0x2fed,0x0bae,
+};
+#define MAXL2 1024.0
+#define MINL2 -1022.0
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double polevl(), p1evl(), floor(), ldexp();
+int isnan(), isfinite();
+#endif
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+extern double MAXNUM;
+
+double exp2(x)
+double x;
+{
+double px, xx;
+short n;
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+if( x > MAXL2)
+	{
+#ifdef INFINITIES
+	return( INFINITY );
+#else
+	mtherr( "exp2", OVERFLOW );
+	return( MAXNUM );
+#endif
+	}
+
+if( x < MINL2 )
+	{
+#ifndef INFINITIES
+	mtherr( "exp2", UNDERFLOW );
+#endif
+	return(0.0);
+	}
+
+xx = x;	/* save x */
+/* separate into integer and fractional parts */
+px = floor(x+0.5);
+n = px;
+x = x - px;
+
+/* rational approximation
+ * exp2(x) = 1 +  2xP(xx)/(Q(xx) - P(xx))
+ * where xx = x**2
+ */
+xx = x * x;
+px = x * polevl( xx, P, 2 );
+x =  px / ( p1evl( xx, Q, 2 ) - px );
+x = 1.0 + ldexp( x, 1 );
+
+/* scale by power of 2 */
+x = ldexp( x, n );
+return(x);
+}

libm/double/expn.c

@@ -0,0 +1,208 @@
+/*							expn.c
+ *
+ *		Exponential integral En
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double x, y, expn();
+ *
+ * y = expn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the exponential integral
+ *
+ *                 inf.
+ *                   -
+ *                  | |   -xt
+ *                  |    e
+ *      E (x)  =    |    ----  dt.
+ *       n          |      n
+ *                | |     t
+ *                 -
+ *                  1
+ *
+ *
+ * Both n and x must be nonnegative.
+ *
+ * The routine employs either a power series, a continued
+ * fraction, or an asymptotic formula depending on the
+ * relative values of n and x.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        5000       2.0e-16     4.6e-17
+ *    IEEE      0, 30       10000       1.7e-15     3.6e-16
+ *
+ */
+
+/*							expn.c	*/
+
+/* Cephes Math Library Release 2.8:  June, 2000
+   Copyright 1985, 2000 by Stephen L. Moshier */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double pow ( double, double );
+extern double gamma ( double );
+extern double log ( double );
+extern double exp ( double );
+extern double fabs ( double );
+#else
+double pow(), gamma(), log(), exp(), fabs();
+#endif
+#define EUL 0.57721566490153286060
+#define BIG  1.44115188075855872E+17
+extern double MAXNUM, MACHEP, MAXLOG;
+
+double expn( n, x )
+int n;
+double x;
+{
+double ans, r, t, yk, xk;
+double pk, pkm1, pkm2, qk, qkm1, qkm2;
+double psi, z;
+int i, k;
+static double big = BIG;
+
+if( n < 0 )
+	goto domerr;
+
+if( x < 0 )
+	{
+domerr:	mtherr( "expn", DOMAIN );
+	return( MAXNUM );
+	}
+
+if( x > MAXLOG )
+	return( 0.0 );
+
+if( x == 0.0 )
+	{
+	if( n < 2 )
+		{
+		mtherr( "expn", SING );
+		return( MAXNUM );
+		}
+	else
+		return( 1.0/(n-1.0) );
+	}
+
+if( n == 0 )
+	return( exp(-x)/x );
+
+/*							expn.c	*/
+/*		Expansion for large n		*/
+
+if( n > 5000 )
+	{
+	xk = x + n;
+	yk = 1.0 / (xk * xk);
+	t = n;
+	ans = yk * t * (6.0 * x * x  -  8.0 * t * x  +  t * t);
+	ans = yk * (ans + t * (t  -  2.0 * x));
+	ans = yk * (ans + t);
+	ans = (ans + 1.0) * exp( -x ) / xk;
+	goto done;
+	}
+
+if( x > 1.0 )
+	goto cfrac;
+
+/*							expn.c	*/
+
+/*		Power series expansion		*/
+
+psi = -EUL - log(x);
+for( i=1; i<n; i++ )
+	psi = psi + 1.0/i;
+
+z = -x;
+xk = 0.0;
+yk = 1.0;
+pk = 1.0 - n;
+if( n == 1 )
+	ans = 0.0;
+else
+	ans = 1.0/pk;
+do
+	{
+	xk += 1.0;
+	yk *= z/xk;
+	pk += 1.0;
+	if( pk != 0.0 )
+		{
+		ans += yk/pk;
+		}
+	if( ans != 0.0 )
+		t = fabs(yk/ans);
+	else
+		t = 1.0;
+	}
+while( t > MACHEP );
+k = xk;
+t = n;
+r = n - 1;
+ans = (pow(z, r) * psi / gamma(t)) - ans;
+goto done;
+
+/*							expn.c	*/
+/*		continued fraction		*/
+cfrac:
+k = 1;
+pkm2 = 1.0;
+qkm2 = x;
+pkm1 = 1.0;
+qkm1 = x + n;
+ans = pkm1/qkm1;
+
+do
+	{
+	k += 1;
+	if( k & 1 )
+		{
+		yk = 1.0;
+		xk = n + (k-1)/2;
+		}
+	else
+		{
+		yk = x;
+		xk = k/2;
+		}
+	pk = pkm1 * yk  +  pkm2 * xk;
+	qk = qkm1 * yk  +  qkm2 * xk;
+	if( qk != 0 )
+		{
+		r = pk/qk;
+		t = fabs( (ans - r)/r );
+		ans = r;
+		}
+	else
+		t = 1.0;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+if( fabs(pk) > big )
+		{
+		pkm2 /= big;
+		pkm1 /= big;
+		qkm2 /= big;
+		qkm1 /= big;
+		}
+	}
+while( t > MACHEP );
+
+ans *= exp( -x );
+
+done:
+return( ans );
+}
+

libm/double/fabs.c

@@ -0,0 +1,56 @@
+/*							fabs.c
+ *
+ *		Absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y;
+ *
+ * y = fabs( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ * 
+ * Returns the absolute value of the argument.
+ *
+ */
+
+
+#include <math.h>
+/* Avoid using UNK if possible.  */
+#ifdef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+double fabs(x)
+double x;
+{
+union
+  {
+    double d;
+    short i[4];
+  } u;
+
+u.d = x;
+#ifdef IBMPC
+    u.i[3] &= 0x7fff;
+#endif
+#ifdef MIEEE
+    u.i[0] &= 0x7fff;
+#endif
+#ifdef DEC
+    u.i[3] &= 0x7fff;
+#endif
+#ifdef UNK
+if( u.d < 0 )
+   u.d = -u.d;
+#endif
+return( u.d );
+}

libm/double/fac.c

@@ -0,0 +1,263 @@
+/*							fac.c
+ *
+ *	Factorial function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y, fac();
+ * int i;
+ *
+ * y = fac( i );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns factorial of i  =  1 * 2 * 3 * ... * i.
+ * fac(0) = 1.0.
+ *
+ * Due to machine arithmetic bounds the largest value of
+ * i accepted is 33 in DEC arithmetic or 170 in IEEE
+ * arithmetic.  Greater values, or negative ones,
+ * produce an error message and return MAXNUM.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * For i < 34 the values are simply tabulated, and have
+ * full machine accuracy.  If i > 55, fac(i) = gamma(i+1);
+ * see gamma.c.
+ *
+ *                      Relative error:
+ * arithmetic   domain      peak
+ *    IEEE      0, 170    1.4e-15
+ *    DEC       0, 33      1.4e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Factorials of integers from 0 through 33 */
+#ifdef UNK
+static double factbl[] = {
+  1.00000000000000000000E0,
+  1.00000000000000000000E0,
+  2.00000000000000000000E0,
+  6.00000000000000000000E0,
+  2.40000000000000000000E1,
+  1.20000000000000000000E2,
+  7.20000000000000000000E2,
+  5.04000000000000000000E3,
+  4.03200000000000000000E4,
+  3.62880000000000000000E5,
+  3.62880000000000000000E6,
+  3.99168000000000000000E7,
+  4.79001600000000000000E8,
+  6.22702080000000000000E9,
+  8.71782912000000000000E10,
+  1.30767436800000000000E12,
+  2.09227898880000000000E13,
+  3.55687428096000000000E14,
+  6.40237370572800000000E15,
+  1.21645100408832000000E17,
+  2.43290200817664000000E18,
+  5.10909421717094400000E19,
+  1.12400072777760768000E21,
+  2.58520167388849766400E22,
+  6.20448401733239439360E23,
+  1.55112100433309859840E25,
+  4.03291461126605635584E26,
+  1.0888869450418352160768E28,
+  3.04888344611713860501504E29,
+  8.841761993739701954543616E30,
+  2.6525285981219105863630848E32,
+  8.22283865417792281772556288E33,
+  2.6313083693369353016721801216E35,
+  8.68331761881188649551819440128E36
+};
+#define MAXFAC 33
+#endif
+
+#ifdef DEC
+static unsigned short factbl[] = {
+0040200,0000000,0000000,0000000,
+0040200,0000000,0000000,0000000,
+0040400,0000000,0000000,0000000,
+0040700,0000000,0000000,0000000,
+0041300,0000000,0000000,0000000,
+0041760,0000000,0000000,0000000,
+0042464,0000000,0000000,0000000,
+0043235,0100000,0000000,0000000,
+0044035,0100000,0000000,0000000,
+0044661,0030000,0000000,0000000,
+0045535,0076000,0000000,0000000,
+0046430,0042500,0000000,0000000,
+0047344,0063740,0000000,0000000,
+0050271,0112146,0000000,0000000,
+0051242,0060731,0040000,0000000,
+0052230,0035673,0126000,0000000,
+0053230,0035673,0126000,0000000,
+0054241,0137567,0063300,0000000,
+0055265,0173546,0051630,0000000,
+0056330,0012711,0101504,0100000,
+0057407,0006635,0171012,0150000,
+0060461,0040737,0046656,0030400,
+0061563,0135223,0005317,0101540,
+0062657,0027031,0127705,0023155,
+0064003,0061223,0041723,0156322,
+0065115,0045006,0014773,0004410,
+0066246,0146044,0172433,0173526,
+0067414,0136077,0027317,0114261,
+0070566,0044556,0110753,0045465,
+0071737,0031214,0032075,0036050,
+0073121,0037543,0070371,0064146,
+0074312,0132550,0052561,0116443,
+0075512,0132550,0052561,0116443,
+0076721,0005423,0114035,0025014
+};
+#define MAXFAC 33
+#endif
+
+#ifdef IBMPC
+static unsigned short factbl[] = {
+0x0000,0x0000,0x0000,0x3ff0,
+0x0000,0x0000,0x0000,0x3ff0,
+0x0000,0x0000,0x0000,0x4000,
+0x0000,0x0000,0x0000,0x4018,
+0x0000,0x0000,0x0000,0x4038,
+0x0000,0x0000,0x0000,0x405e,
+0x0000,0x0000,0x8000,0x4086,
+0x0000,0x0000,0xb000,0x40b3,
+0x0000,0x0000,0xb000,0x40e3,
+0x0000,0x0000,0x2600,0x4116,
+0x0000,0x0000,0xaf80,0x414b,
+0x0000,0x0000,0x08a8,0x4183,
+0x0000,0x0000,0x8cfc,0x41bc,
+0x0000,0xc000,0x328c,0x41f7,
+0x0000,0x2800,0x4c3b,0x4234,
+0x0000,0x7580,0x0777,0x4273,
+0x0000,0x7580,0x0777,0x42b3,
+0x0000,0xecd8,0x37ee,0x42f4,
+0x0000,0xca73,0xbeec,0x4336,
+0x9000,0x3068,0x02b9,0x437b,
+0x5a00,0xbe41,0xe1b3,0x43c0,
+0xc620,0xe9b5,0x283b,0x4406,
+0xf06c,0x6159,0x7752,0x444e,
+0xa4ce,0x35f8,0xe5c3,0x4495,
+0x7b9a,0x687a,0x6c52,0x44e0,
+0x6121,0xc33f,0xa940,0x4529,
+0x7eeb,0x9ea3,0xd984,0x4574,
+0xf316,0xe5d9,0x9787,0x45c1,
+0x6967,0xd23d,0xc92d,0x460e,
+0xa785,0x8687,0xe651,0x465b,
+0x2d0d,0x6e1f,0x27ec,0x46aa,
+0x33a4,0x0aae,0x56ad,0x46f9,
+0x33a4,0x0aae,0x56ad,0x4749,
+0xa541,0x7303,0x2162,0x479a
+};
+#define MAXFAC 170
+#endif
+
+#ifdef MIEEE
+static unsigned short factbl[] = {
+0x3ff0,0x0000,0x0000,0x0000,
+0x3ff0,0x0000,0x0000,0x0000,
+0x4000,0x0000,0x0000,0x0000,
+0x4018,0x0000,0x0000,0x0000,
+0x4038,0x0000,0x0000,0x0000,
+0x405e,0x0000,0x0000,0x0000,
+0x4086,0x8000,0x0000,0x0000,
+0x40b3,0xb000,0x0000,0x0000,
+0x40e3,0xb000,0x0000,0x0000,
+0x4116,0x2600,0x0000,0x0000,
+0x414b,0xaf80,0x0000,0x0000,
+0x4183,0x08a8,0x0000,0x0000,
+0x41bc,0x8cfc,0x0000,0x0000,
+0x41f7,0x328c,0xc000,0x0000,
+0x4234,0x4c3b,0x2800,0x0000,
+0x4273,0x0777,0x7580,0x0000,
+0x42b3,0x0777,0x7580,0x0000,
+0x42f4,0x37ee,0xecd8,0x0000,
+0x4336,0xbeec,0xca73,0x0000,
+0x437b,0x02b9,0x3068,0x9000,
+0x43c0,0xe1b3,0xbe41,0x5a00,
+0x4406,0x283b,0xe9b5,0xc620,
+0x444e,0x7752,0x6159,0xf06c,
+0x4495,0xe5c3,0x35f8,0xa4ce,
+0x44e0,0x6c52,0x687a,0x7b9a,
+0x4529,0xa940,0xc33f,0x6121,
+0x4574,0xd984,0x9ea3,0x7eeb,
+0x45c1,0x9787,0xe5d9,0xf316,
+0x460e,0xc92d,0xd23d,0x6967,
+0x465b,0xe651,0x8687,0xa785,
+0x46aa,0x27ec,0x6e1f,0x2d0d,
+0x46f9,0x56ad,0x0aae,0x33a4,
+0x4749,0x56ad,0x0aae,0x33a4,
+0x479a,0x2162,0x7303,0xa541
+};
+#define MAXFAC 170
+#endif
+
+#ifdef ANSIPROT
+double gamma ( double );
+#else
+double gamma();
+#endif
+extern double MAXNUM;
+
+double fac(i)
+int i;
+{
+double x, f, n;
+int j;
+
+if( i < 0 )
+	{
+	mtherr( "fac", SING );
+	return( MAXNUM );
+	}
+
+if( i > MAXFAC )
+	{
+	mtherr( "fac", OVERFLOW );
+	return( MAXNUM );
+	}
+
+/* Get answer from table for small i. */
+if( i < 34 )
+	{
+#ifdef UNK
+	return( factbl[i] );
+#else
+	return( *(double *)(&factbl[4*i]) );
+#endif
+	}
+/* Use gamma function for large i. */
+if( i > 55 )
+	{
+	x = i + 1;
+	return( gamma(x) );
+	}
+/* Compute directly for intermediate i. */
+n = 34.0;
+f = 34.0;
+for( j=35; j<=i; j++ )
+	{
+	n += 1.0;
+	f *= n;
+	}
+#ifdef UNK
+	f *= factbl[33];
+#else
+	f *= *(double *)(&factbl[4*33]);
+#endif
+return( f );
+}

libm/double/fdtr.c

@@ -0,0 +1,237 @@
+/*							fdtr.c
+ *
+ *	F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, y, fdtr();
+ *
+ * y = fdtr( df1, df2, x );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).  This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ *	P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x is
+ * nonnegative.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x).
+ *
+ *                x     a,b                     Relative error:
+ * arithmetic  domain  domain     # trials      peak         rms
+ *    IEEE      0,1    0,100       100000      9.8e-15     1.7e-15
+ *    IEEE      1,5    0,100       100000      6.5e-15     3.5e-16
+ *    IEEE      0,1    1,10000     100000      2.2e-11     3.3e-12
+ *    IEEE      1,5    1,10000     100000      1.1e-11     1.7e-13
+ * See also incbet.c.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * fdtr domain     a<0, b<0, x<0         0.0
+ *
+ */
+/*							fdtrc()
+ *
+ *	Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, y, fdtrc();
+ *
+ * y = fdtrc( df1, df2, x );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ *                      inf.
+ *                       -
+ *              1       | |  a-1      b-1
+ * 1-P(x)  =  ------    |   t    (1-t)    dt
+ *            B(a,b)  | |
+ *                     -
+ *                      x
+ *
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ *	P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) in the indicated intervals.
+ *                x     a,b                     Relative error:
+ * arithmetic  domain  domain     # trials      peak         rms
+ *    IEEE      0,1    1,100       100000      3.7e-14     5.9e-16
+ *    IEEE      1,5    1,100       100000      8.0e-15     1.6e-15
+ *    IEEE      0,1    1,10000     100000      1.8e-11     3.5e-13
+ *    IEEE      1,5    1,10000     100000      2.0e-11     3.0e-12
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * fdtrc domain    a<0, b<0, x<0         0.0
+ *
+ */
+/*							fdtri()
+ *
+ *	Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, p, fdtri();
+ *
+ * x = fdtri( df1, df2, p );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability p.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ *      z = incbi( df2/2, df1/2, p )
+ *      x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ *      z = incbi( df1/2, df2/2, p )
+ *      x = df2 z / (df1 (1-z)).
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ *              a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between .001 and 1:
+ *    IEEE     1,100       100000      8.3e-15     4.7e-16
+ *    IEEE     1,10000     100000      2.1e-11     1.4e-13
+ *  For p between 10^-6 and 10^-3:
+ *    IEEE     1,100        50000      1.3e-12     8.4e-15
+ *    IEEE     1,10000      50000      3.0e-12     4.8e-14
+ * See also fdtrc.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * fdtri domain   p <= 0 or p > 1       0.0
+ *                     v < 1
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+#else
+double incbet(), incbi();
+#endif
+
+double fdtrc( ia, ib, x )
+int ia, ib;
+double x;
+{
+double a, b, w;
+
+if( (ia < 1) || (ib < 1) || (x < 0.0) )
+	{
+	mtherr( "fdtrc", DOMAIN );
+	return( 0.0 );
+	}
+a = ia;
+b = ib;
+w = b / (b + a * x);
+return( incbet( 0.5*b, 0.5*a, w ) );
+}
+
+
+
+double fdtr( ia, ib, x )
+int ia, ib;
+double x;
+{
+double a, b, w;
+
+if( (ia < 1) || (ib < 1) || (x < 0.0) )
+	{
+	mtherr( "fdtr", DOMAIN );
+	return( 0.0 );
+	}
+a = ia;
+b = ib;
+w = a * x;
+w = w / (b + w);
+return( incbet(0.5*a, 0.5*b, w) );
+}
+
+
+double fdtri( ia, ib, y )
+int ia, ib;
+double y;
+{
+double a, b, w, x;
+
+if( (ia < 1) || (ib < 1) || (y <= 0.0) || (y > 1.0) )
+	{
+	mtherr( "fdtri", DOMAIN );
+	return( 0.0 );
+	}
+a = ia;
+b = ib;
+/* Compute probability for x = 0.5.  */
+w = incbet( 0.5*b, 0.5*a, 0.5 );
+/* If that is greater than y, then the solution w < .5.
+   Otherwise, solve at 1-y to remove cancellation in (b - b*w).  */
+if( w > y || y < 0.001)
+	{
+	w = incbi( 0.5*b, 0.5*a, y );
+	x = (b - b*w)/(a*w);
+	}
+else
+	{
+	w = incbi( 0.5*a, 0.5*b, 1.0-y );
+	x = b*w/(a*(1.0-w));
+	}
+return(x);
+}

libm/double/fftr.c

@@ -0,0 +1,237 @@
+/*							fftr.c
+ *
+ *	FFT of Real Valued Sequence
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x[], sine[];
+ * int m;
+ *
+ * fftr( x, m, sine );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the (complex valued) discrete Fourier transform of
+ * the real valued sequence x[].  The input sequence x[] contains
+ * n = 2**m samples.  The program fills array sine[k] with
+ * n/4 + 1 values of sin( 2 PI k / n ).
+ *
+ * Data format for complex valued output is real part followed
+ * by imaginary part.  The output is developed in the input
+ * array x[].
+ *
+ * The algorithm takes advantage of the fact that the FFT of an
+ * n point real sequence can be obtained from an n/2 point
+ * complex FFT.
+ *
+ * A radix 2 FFT algorithm is used.
+ *
+ * Execution time on an LSI-11/23 with floating point chip
+ * is 1.0 sec for n = 256.
+ *
+ *
+ *
+ * REFERENCE:
+ *
+ * E. Oran Brigham, The Fast Fourier Transform;
+ * Prentice-Hall, Inc., 1974
+ *
+ */
+
+
+#include <math.h>
+
+static short n0 = 0;
+static short n4 = 0;
+static short msav = 0;
+
+extern double PI;
+
+#ifdef ANSIPROT
+extern double sin ( double );
+static int bitrv(int, int);
+#else
+double sin();
+static int bitrv();
+#endif
+
+fftr( x, m0, sine )
+double x[];
+int m0;
+double sine[];
+{
+int th, nd, pth, nj, dth, m;
+int n, n2, j, k, l, r;
+double xr, xi, tr, ti, co, si;
+double a, b, c, d, bc, cs, bs, cc;
+double *p, *q;
+
+/* Array x assumed filled with real-valued data */
+/* m0 = log2(n0)			*/
+/* n0 is the number of real data samples */
+
+if( m0 != msav )
+	{
+	msav = m0;
+
+	/* Find n0 = 2**m0	*/
+	n0 = 1;
+	for( j=0; j<m0; j++ )
+		n0 <<= 1;
+
+	n4 = n0 >> 2;
+
+	/* Calculate array of sines */
+	xr = 2.0 * PI / n0;
+	for( j=0; j<=n4; j++ )
+		sine[j] = sin( j * xr );
+	}
+
+n = n0 >> 1;	/* doing half length transform */
+m = m0 - 1;
+
+
+/*							fftr.c	*/
+
+/*  Complex Fourier Transform of n Complex Data Points */
+
+/*	First, bit reverse the input data	*/
+
+for( k=0; k<n; k++ )
+	{
+	j = bitrv( k, m );
+	if( j > k )
+		{ /* executed approx. n/2 times */
+		p = &x[2*k];
+		tr = *p++;
+		ti = *p;
+		q = &x[2*j+1];
+		*p = *q;
+		*(--p) = *(--q);
+		*q++ = tr;
+		*q = ti;
+		}
+	}
+	
+/*							fftr.c	*/
+/*			Radix 2 Complex FFT			*/
+n2 = n/2;
+nj = 1;
+pth = 1;
+dth = 0;
+th = 0;
+
+for( l=0; l<m; l++ )
+	{	/* executed log2(n) times, total */
+	j = 0;
+	do
+		{	/* executed n-1 times, total */
+		r = th << 1;
+		si = sine[r];
+		co = sine[ n4 - r ];
+		if( j >= pth )
+			{
+			th -= dth;
+			co = -co;
+			}
+		else
+			th += dth;
+
+		nd = j;
+
+		do
+			{ /* executed n/2 log2(n) times, total */
+			r = (nd << 1) + (nj << 1);
+			p = &x[ r ];
+			xr = *p++;
+			xi = *p;
+			tr = xr * co + xi * si;
+			ti = xi * co - xr * si;
+			r = nd << 1;
+			q = &x[ r ];
+			xr = *q++;
+			xi = *q;
+			*p = xi - ti;
+			*(--p) = xr - tr;
+			*q = xi + ti;
+			*(--q) = xr + tr;
+			nd += nj << 1;
+			}
+		while( nd < n );
+		}
+	while( ++j < nj );
+
+	n2 >>= 1;
+	dth = n2;
+	pth = nj;
+	nj <<= 1;
+	}
+
+/*							fftr.c	*/
+
+/*	Special trick algorithm			*/
+/*	converts to spectrum of real series	*/
+
+/* Highest frequency term; add space to input array if wanted */
+/*
+x[2*n] = x[0] - x[1];
+x[2*n+1] = 0.0;
+*/
+
+/* Zero frequency term */
+x[0] = x[0] + x[1];
+x[1] = 0.0;
+n2 = n/2;
+
+for( j=1; j<=n2; j++ )
+	{	/* executed n/2 times */
+	si = sine[j];
+	co = sine[ n4 - j ];
+	p = &x[ 2*j ];
+	xr = *p++;
+	xi = *p;
+	q = &x[ 2*(n-j) ];
+	tr = *q++;
+	ti = *q;
+	a = xr + tr;
+	b = xi + ti;
+	c = xr - tr;
+	d = xi - ti;
+	bc = b * co;
+	cs = c * si;
+	bs = b * si;
+	cc = c * co;
+	*p = ( d - bs - cc )/2.0;
+	*(--p) = ( a + bc - cs )/2.0;
+	*q = -( d + bs + cc )/2.0;
+	*(--q) = ( a - bc + cs )/2.0;
+	}
+
+return(0);
+}
+
+/*							fftr.c	*/
+
+/*	Bit reverser	*/
+
+int bitrv( j, m )
+int j, m;
+{
+register int j1, ans;
+short k;
+
+ans = 0;
+j1 = j;
+
+for( k=0; k<m; k++ )
+	{
+	ans = (ans << 1) + (j1 & 1);
+	j1 >>= 1;
+	}
+
+return( ans );
+}

libm/double/floor.c

@@ -0,0 +1,453 @@
+/*							ceil()
+ *							floor()
+ *							frexp()
+ *							ldexp()
+ *							signbit()
+ *							isnan()
+ *							isfinite()
+ *
+ *	Floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double ceil(), floor(), frexp(), ldexp();
+ * int signbit(), isnan(), isfinite();
+ * double x, y;
+ * int expnt, n;
+ *
+ * y = floor(x);
+ * y = ceil(x);
+ * y = frexp( x, &expnt );
+ * y = ldexp( x, n );
+ * n = signbit(x);
+ * n = isnan(x);
+ * n = isfinite(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a double precision floating point
+ * result.
+ *
+ * floor() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * ceil() returns the smallest integer greater than or equal
+ * to x.  It truncates toward plus infinity.
+ *
+ * frexp() extracts the exponent from x.  It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y.  Thus  x = y * 2**expn.
+ *
+ * ldexp() multiplies x by 2**n.
+ *
+ * signbit(x) returns 1 if the sign bit of x is 1, else 0.
+ *
+ * These functions are part of the standard C run time library
+ * for many but not all C compilers.  The ones supplied are
+ * written in C for either DEC or IEEE arithmetic.  They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic.  Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+/* ceil(), floor(), frexp(), ldexp() may need to be rewritten. */
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+#ifdef DEC
+#define EXPMSK 0x807f
+#define MEXP 255
+#define NBITS 56
+#endif
+
+#ifdef IBMPC
+#define EXPMSK 0x800f
+#define MEXP 0x7ff
+#define NBITS 53
+#endif
+
+#ifdef MIEEE
+#define EXPMSK 0x800f
+#define MEXP 0x7ff
+#define NBITS 53
+#endif
+
+extern double MAXNUM, NEGZERO;
+#ifdef ANSIPROT
+double floor ( double );
+int isnan ( double );
+int isfinite ( double );
+double ldexp ( double, int );
+#else
+double floor();
+int isnan(), isfinite();
+double ldexp();
+#endif
+
+double ceil(x)
+double x;
+{
+double y;
+
+#ifdef UNK
+mtherr( "ceil", DOMAIN );
+return(0.0);
+#endif
+#ifdef NANS
+if( isnan(x) )
+	return( x );
+#endif
+#ifdef INFINITIES
+if(!isfinite(x))
+	return(x);
+#endif
+
+y = floor(x);
+if( y < x )
+	y += 1.0;
+#ifdef MINUSZERO
+if( y == 0.0 && x < 0.0 )
+	return( NEGZERO );
+#endif
+return(y);
+}
+
+
+
+
+/* Bit clearing masks: */
+
+static unsigned short bmask[] = {
+0xffff,
+0xfffe,
+0xfffc,
+0xfff8,
+0xfff0,
+0xffe0,
+0xffc0,
+0xff80,
+0xff00,
+0xfe00,
+0xfc00,
+0xf800,
+0xf000,
+0xe000,
+0xc000,
+0x8000,
+0x0000,
+};
+
+
+
+
+
+double floor(x)
+double x;
+{
+union
+	{
+	double y;
+	unsigned short sh[4];
+	} u;
+unsigned short *p;
+int e;
+
+#ifdef UNK
+mtherr( "floor", DOMAIN );
+return(0.0);
+#endif
+#ifdef NANS
+if( isnan(x) )
+	return( x );
+#endif
+#ifdef INFINITIES
+if(!isfinite(x))
+	return(x);
+#endif
+#ifdef MINUSZERO
+if(x == 0.0L)
+	return(x);
+#endif
+u.y = x;
+/* find the exponent (power of 2) */
+#ifdef DEC
+p = (unsigned short *)&u.sh[0];
+e = (( *p  >> 7) & 0377) - 0201;
+p += 3;
+#endif
+
+#ifdef IBMPC
+p = (unsigned short *)&u.sh[3];
+e = (( *p >> 4) & 0x7ff) - 0x3ff;
+p -= 3;
+#endif
+
+#ifdef MIEEE
+p = (unsigned short *)&u.sh[0];
+e = (( *p >> 4) & 0x7ff) - 0x3ff;
+p += 3;
+#endif
+
+if( e < 0 )
+	{
+	if( u.y < 0.0 )
+		return( -1.0 );
+	else
+		return( 0.0 );
+	}
+
+e = (NBITS -1) - e;
+/* clean out 16 bits at a time */
+while( e >= 16 )
+	{
+#ifdef IBMPC
+	*p++ = 0;
+#endif
+
+#ifdef DEC
+	*p-- = 0;
+#endif
+
+#ifdef MIEEE
+	*p-- = 0;
+#endif
+	e -= 16;
+	}
+
+/* clear the remaining bits */
+if( e > 0 )
+	*p &= bmask[e];
+
+if( (x < 0) && (u.y != x) )
+	u.y -= 1.0;
+
+return(u.y);
+}
+
+
+
+
+double frexp( x, pw2 )
+double x;
+int *pw2;
+{
+union
+	{
+	double y;
+	unsigned short sh[4];
+	} u;
+int i;
+#ifdef DENORMAL
+int k;
+#endif
+short *q;
+
+u.y = x;
+
+#ifdef UNK
+mtherr( "frexp", DOMAIN );
+return(0.0);
+#endif
+
+#ifdef IBMPC
+q = (short *)&u.sh[3];
+#endif
+
+#ifdef DEC
+q = (short *)&u.sh[0];
+#endif
+
+#ifdef MIEEE
+q = (short *)&u.sh[0];
+#endif
+
+/* find the exponent (power of 2) */
+#ifdef DEC
+i  = ( *q >> 7) & 0377;
+if( i == 0 )
+	{
+	*pw2 = 0;
+	return(0.0);
+	}
+i -= 0200;
+*pw2 = i;
+*q &= 0x807f;	/* strip all exponent bits */
+*q |= 040000;	/* mantissa between 0.5 and 1 */
+return(u.y);
+#endif
+
+#ifdef IBMPC
+i  = ( *q >> 4) & 0x7ff;
+if( i != 0 )
+	goto ieeedon;
+#endif
+
+#ifdef MIEEE
+i  =  *q >> 4;
+i &= 0x7ff;
+if( i != 0 )
+	goto ieeedon;
+#ifdef DENORMAL
+
+#else
+*pw2 = 0;
+return(0.0);
+#endif
+
+#endif
+
+
+#ifndef DEC
+/* Number is denormal or zero */
+#ifdef DENORMAL
+if( u.y == 0.0 )
+	{
+	*pw2 = 0;
+	return( 0.0 );
+	}
+
+
+/* Handle denormal number. */
+do
+	{
+	u.y *= 2.0;
+	i -= 1;
+	k  = ( *q >> 4) & 0x7ff;
+	}
+while( k == 0 );
+i = i + k;
+#endif /* DENORMAL */
+
+ieeedon:
+
+i -= 0x3fe;
+*pw2 = i;
+*q &= 0x800f;
+*q |= 0x3fe0;
+return( u.y );
+#endif
+}
+
+
+
+
+
+
+
+double ldexp( x, pw2 )
+double x;
+int pw2;
+{
+union
+	{
+	double y;
+	unsigned short sh[4];
+	} u;
+short *q;
+int e;
+
+#ifdef UNK
+mtherr( "ldexp", DOMAIN );
+return(0.0);
+#endif
+
+u.y = x;
+#ifdef DEC
+q = (short *)&u.sh[0];
+e  = ( *q >> 7) & 0377;
+if( e == 0 )
+	return(0.0);
+#else
+
+#ifdef IBMPC
+q = (short *)&u.sh[3];
+#endif
+#ifdef MIEEE
+q = (short *)&u.sh[0];
+#endif
+while( (e = (*q & 0x7ff0) >> 4) == 0 )
+	{
+	if( u.y == 0.0 )
+		{
+		return( 0.0 );
+		}
+/* Input is denormal. */
+	if( pw2 > 0 )
+		{
+		u.y *= 2.0;
+		pw2 -= 1;
+		}
+	if( pw2 < 0 )
+		{
+		if( pw2 < -53 )
+			return(0.0);
+		u.y /= 2.0;
+		pw2 += 1;
+		}
+	if( pw2 == 0 )
+		return(u.y);
+	}
+#endif /* not DEC */
+
+e += pw2;
+
+/* Handle overflow */
+#ifdef DEC
+if( e > MEXP )
+	return( MAXNUM );
+#else
+if( e >= MEXP )
+	return( 2.0*MAXNUM );
+#endif
+
+/* Handle denormalized results */
+if( e < 1 )
+	{
+#ifdef DENORMAL
+	if( e < -53 )
+		return(0.0);
+	*q &= 0x800f;
+	*q |= 0x10;
+	/* For denormals, significant bits may be lost even
+	   when dividing by 2.  Construct 2^-(1-e) so the result
+	   is obtained with only one multiplication.  */
+	u.y *= ldexp(1.0, e-1);
+	return(u.y);
+#else
+	return(0.0);
+#endif
+	}
+else
+	{
+#ifdef DEC
+	*q &= 0x807f;	/* strip all exponent bits */
+	*q |= (e & 0xff) << 7;
+#else
+	*q &= 0x800f;
+	*q |= (e & 0x7ff) << 4;
+#endif
+	return(u.y);
+	}
+}

libm/double/fltest.c

@@ -0,0 +1,272 @@
+/* fltest.c
+ * Test program for floor(), frexp(), ldexp()
+ */
+
+/*
+Cephes Math Library Release 2.1:  December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+
+#include <math.h>
+extern double MACHEP;
+#define UTH -1023
+
+main()
+{
+double x, y, y0, z, f, x00, y00;
+int i, j, k, e, e0;
+int errfr, errld, errfl, underexp, err, errth, e00;
+double frexp(), ldexp(), floor();
+
+
+/*
+if( 1 )
+	goto flrtst;
+*/
+
+printf( "Testing frexp() and ldexp().\n" );
+errfr = 0;
+errld = 0;
+underexp = 0;
+f = 1.0;
+x00 = 2.0;
+y00 = 0.5;
+e00 = 2;
+
+for( j=0; j<20; j++ )
+{
+if( j == 10 )
+	{
+	f = 1.0;
+	x00 = 2.0;
+	e00 = 1;
+/* Find 2**(2**10) / 2 */
+#ifdef DEC
+	for( i=0; i<5; i++ )
+#else
+	for( i=0; i<9; i++ )
+#endif
+		{
+		x00 *= x00;
+		e00 += e00;
+		}
+	y00 = x00/2.0;
+	x00 = x00 * y00;
+	e00 += e00;
+	y00 = 0.5;
+	}
+x = x00 * f;
+y0 = y00 * f;
+e0 = e00;
+for( i=0; i<2200; i++ )
+	{
+	x /= 2.0;
+	e0 -= 1;
+	if( x == 0.0 )
+		{
+		if( f == 1.0 )
+			underexp = e0;
+		y0 = 0.0;
+		e0 = 0;
+		}
+	y = frexp( x, &e );
+	if( (e0 < -1023) && (e != e0) )
+		{
+		if( e == (e0 - 1) )
+			{
+			e += 1;
+			y /= 2.0;
+			}
+		if( e == (e0 + 1) )
+			{
+			e -= 1;
+			y *= 2.0;
+			}
+		}
+	err = y - y0;
+	if( y0 != 0.0 )
+		err /= y0;
+	if( err < 0.0 )
+		err = -err;
+	if( e0 > -1023 )
+		errth = 0.0;
+	else
+		{/* Denormal numbers may have rounding errors */
+		if( e0 == -1023 )
+			{
+			errth = 2.0 * MACHEP;
+			}
+		else
+			{
+			errth *= 2.0;
+			}
+		}
+
+	if( (x != 0.0) && ((err > errth) || (e != e0)) )
+		{
+		printf( "Test %d: ", j+1 );
+		printf( " frexp( %.15e) =?= %.15e * 2**%d;", x, y, e );
+		printf( " should be %.15e * 2**%d\n", y0, e0 );
+		errfr += 1;
+		}
+	y = ldexp( x, 1-e0 );
+	err = y - 1.0;
+	if( err < 0.0 )
+		err = -err;
+	if( (err > errth) && ((x == 0.0) && (y != 0.0)) )
+		{
+		printf( "Test %d: ", j+1 );
+		printf( "ldexp( %.15e, %d ) =?= %.15e;", x, 1-e0, y );
+		if( x != 0.0 )
+			printf( " should be %.15e\n", f );
+		else
+			printf( " should be %.15e\n", 0.0 );
+		errld += 1;
+		}
+	if( x == 0.0 )
+		{
+		break;
+		}
+	}
+f = f * 1.08005973889;
+}
+
+
+x = 2.22507385850720138309e-308;
+for (i = 0; i < 52; i++)
+  {
+    y = ldexp (x, -i);
+    z = ldexp (y, i);
+    if (x != z)
+      {
+	printf ("x %.16e, i %d, y %.16e, z %.16e\n", x, i, y, z);
+	errld += 1;
+      }
+  }
+
+
+if( (errld == 0) && (errfr == 0) )
+	{
+	printf( "No errors found.\n" );
+	}
+
+flrtst:
+
+printf( "Testing floor().\n" );
+errfl = 0;
+
+f = 1.0/MACHEP;
+x00 = 1.0;
+for( j=0; j<57; j++ )
+{
+x = x00 - 1.0;
+for( i=0; i<128; i++ )
+	{
+	y = floor(x);
+	if( y != x )
+		{
+		flierr( x, y, j );
+		errfl += 1;
+		}
+/* Warning! the if() statement is compiler dependent,
+ * since x-0.49 may be held in extra precision accumulator
+ * so would never compare equal to x!  The subroutine call
+ * y = floor() forces z to be stored as a double and reloaded
+ * for the if() statement.
+ */
+	z = x - 0.49;
+	y = floor(z);
+	if( z == x )
+		break;
+	if( y != (x - 1.0) )
+		{
+		flierr( z, y, j );
+		errfl += 1;
+		}
+
+	z = x + 0.49;
+	y = floor(z);
+	if( z != x )
+		{
+		if( y != x )
+			{
+			flierr( z, y, j );
+			errfl += 1;
+			}
+		}
+	x = -x;
+	y = floor(x);
+	if( z != x )
+		{
+		if( y != x )
+			{
+			flierr( x, y, j );
+			errfl += 1;
+			}
+		}
+	z = x + 0.49;
+	y = floor(z);
+	if( z != x )
+		{
+		if( y != x )
+			{
+			flierr( z, y, j );
+			errfl += 1;
+			}
+		}
+	z = x - 0.49;
+	y = floor(z);
+	if( z != x )
+		{
+		if( y != (x - 1.0) )
+			{
+			flierr( z, y, j );
+			errfl += 1;
+			}
+		}
+	x = -x;
+	x += 1.0;
+	}
+x00 = x00 + x00;
+}
+y = floor(0.0);
+if( y != 0.0 )
+	{
+	flierr( 0.0, y, 57 );
+	errfl += 1;
+	}
+y = floor(-0.0);
+if( y != 0.0 )
+	{
+	flierr( -0.0, y, 58 );
+	errfl += 1;
+	}
+y = floor(-1.0);
+if( y != -1.0 )
+	{
+	flierr( -1.0, y, 59 );
+	errfl += 1;
+	}
+y = floor(-0.1);
+if( y != -1.0 )
+	{
+	flierr( -0.1, y, 60 );
+	errfl += 1;
+	}
+
+if( errfl == 0 )
+	printf( "No errors found in floor().\n" );
+
+}
+
+
+flierr( x, y, k )
+double x, y;
+int k;
+{
+printf( "Test %d: ", k+1 );
+printf( "floor(%.15e) =?= %.15e\n", x, y );
+}

libm/double/fltest2.c

@@ -0,0 +1,18 @@
+int drand();
+double exp(), frexp(), ldexp();
+volatile double x, y, z;
+
+main()
+{
+int i, e;
+
+for( i=0; i<100000; i++ )
+  {
+    drand(&x);
+    x = exp( 10.0*(x - 1.5) );
+    y = frexp( x, &e );
+    z = ldexp( y, e );
+    if( z != x )
+      abort();
+  }
+}

libm/double/fltest3.c

@@ -0,0 +1,259 @@
+/* fltest.c
+ * Test program for floor(), frexp(), ldexp()
+ */
+
+/*
+Cephes Math Library Release 2.1:  December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+
+#include <math.h>
+/*extern double MACHEP;*/
+#define MACHEP  2.3e-16
+#define UTH -1023
+
+main()
+{
+double x, y, y0, z, f, x00, y00;
+int i, j, k, e, e0;
+int errfr, errld, errfl, underexp, err, errth, e00;
+double frexp(), ldexp(), floor();
+
+
+/*
+if( 1 )
+	goto flrtst;
+*/
+
+printf( "Testing frexp() and ldexp().\n" );
+errfr = 0;
+errld = 0;
+underexp = 0;
+f = 1.0;
+x00 = 2.0;
+y00 = 0.5;
+e00 = 2;
+
+for( j=0; j<20; j++ )
+{
+if( j == 10 )
+	{
+	f = 1.0;
+	x00 = 2.0;
+	e00 = 1;
+/* Find 2**(2**10) / 2 */
+#ifdef DEC
+	for( i=0; i<5; i++ )
+#else
+	for( i=0; i<9; i++ )
+#endif
+		{
+		x00 *= x00;
+		e00 += e00;
+		}
+	y00 = x00/2.0;
+	x00 = x00 * y00;
+	e00 += e00;
+	y00 = 0.5;
+	}
+x = x00 * f;
+y0 = y00 * f;
+e0 = e00;
+for( i=0; i<2200; i++ )
+	{
+	x /= 2.0;
+	e0 -= 1;
+	if( x == 0.0 )
+		{
+		if( f == 1.0 )
+			underexp = e0;
+		y0 = 0.0;
+		e0 = 0;
+		}
+	y = frexp( x, &e );
+	if( (e0 < -1023) && (e != e0) )
+		{
+		if( e == (e0 - 1) )
+			{
+			e += 1;
+			y /= 2.0;
+			}
+		if( e == (e0 + 1) )
+			{
+			e -= 1;
+			y *= 2.0;
+			}
+		}
+	err = y - y0;
+	if( y0 != 0.0 )
+		err /= y0;
+	if( err < 0.0 )
+		err = -err;
+	if( e0 > -1023 )
+		errth = 0.0;
+	else
+		{/* Denormal numbers may have rounding errors */
+		if( e0 == -1023 )
+			{
+			errth = 2.0 * MACHEP;
+			}
+		else
+			{
+			errth *= 2.0;
+			}
+		}
+
+	if( (x != 0.0) && ((err > errth) || (e != e0)) )
+		{
+		printf( "Test %d: ", j+1 );
+		printf( " frexp( %.15e) =?= %.15e * 2**%d;", x, y, e );
+		printf( " should be %.15e * 2**%d\n", y0, e0 );
+		errfr += 1;
+		}
+	y = ldexp( x, 1-e0 );
+	err = y - 1.0;
+	if( err < 0.0 )
+		err = -err;
+	if( (err > errth) && ((x == 0.0) && (y != 0.0)) )
+		{
+		printf( "Test %d: ", j+1 );
+		printf( "ldexp( %.15e, %d ) =?= %.15e;", x, 1-e0, y );
+		if( x != 0.0 )
+			printf( " should be %.15e\n", f );
+		else
+			printf( " should be %.15e\n", 0.0 );
+		errld += 1;
+		}
+	if( x == 0.0 )
+		{
+		break;
+		}
+	}
+f = f * 1.08005973889;
+}
+
+if( (errld == 0) && (errfr == 0) )
+	{
+	printf( "No errors found.\n" );
+	}
+
+flrtst:
+
+printf( "Testing floor().\n" );
+errfl = 0;
+
+f = 1.0/MACHEP;
+x00 = 1.0;
+for( j=0; j<57; j++ )
+{
+x = x00 - 1.0;
+for( i=0; i<128; i++ )
+	{
+	y = floor(x);
+	if( y != x )
+		{
+		flierr( x, y, j );
+		errfl += 1;
+		}
+/* Warning! the if() statement is compiler dependent,
+ * since x-0.49 may be held in extra precision accumulator
+ * so would never compare equal to x!  The subroutine call
+ * y = floor() forces z to be stored as a double and reloaded
+ * for the if() statement.
+ */
+	z = x - 0.49;
+	y = floor(z);
+	if( z == x )
+		break;
+	if( y != (x - 1.0) )
+		{
+		flierr( z, y, j );
+		errfl += 1;
+		}
+
+	z = x + 0.49;
+	y = floor(z);
+	if( z != x )
+		{
+		if( y != x )
+			{
+			flierr( z, y, j );
+			errfl += 1;
+			}
+		}
+	x = -x;
+	y = floor(x);
+	if( z != x )
+		{
+		if( y != x )
+			{
+			flierr( x, y, j );
+			errfl += 1;
+			}
+		}
+	z = x + 0.49;
+	y = floor(z);
+	if( z != x )
+		{
+		if( y != x )
+			{
+			flierr( z, y, j );
+			errfl += 1;
+			}
+		}
+	z = x - 0.49;
+	y = floor(z);
+	if( z != x )
+		{
+		if( y != (x - 1.0) )
+			{
+			flierr( z, y, j );
+			errfl += 1;
+			}
+		}
+	x = -x;
+	x += 1.0;
+	}
+x00 = x00 + x00;
+}
+y = floor(0.0);
+if( y != 0.0 )
+	{
+	flierr( 0.0, y, 57 );
+	errfl += 1;
+	}
+y = floor(-0.0);
+if( y != 0.0 )
+	{
+	flierr( -0.0, y, 58 );
+	errfl += 1;
+	}
+y = floor(-1.0);
+if( y != -1.0 )
+	{
+	flierr( -1.0, y, 59 );
+	errfl += 1;
+	}
+y = floor(-0.1);
+if( y != -1.0 )
+	{
+	flierr( -0.1, y, 60 );
+	errfl += 1;
+	}
+
+if( errfl == 0 )
+	printf( "No errors found in floor().\n" );
+
+}
+
+
+flierr( x, y, k )
+double x, y;
+int k;
+{
+printf( "Test %d: ", k+1 );
+printf( "floor(%.15e) =?= %.15e\n", x, y );
+}

libm/double/fresnl.c

@@ -0,0 +1,515 @@
+/*							fresnl.c
+ *
+ *	Fresnel integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, S, C;
+ * void fresnl();
+ *
+ * fresnl( x, _&S, _&C );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the Fresnel integrals
+ *
+ *           x
+ *           -
+ *          | |
+ * C(x) =   |   cos(pi/2 t**2) dt,
+ *        | |
+ *         -
+ *          0
+ *
+ *           x
+ *           -
+ *          | |
+ * S(x) =   |   sin(pi/2 t**2) dt.
+ *        | |
+ *         -
+ *          0
+ *
+ *
+ * The integrals are evaluated by a power series for x < 1.
+ * For x >= 1 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
+ * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *  Relative error.
+ *
+ * Arithmetic  function   domain     # trials      peak         rms
+ *   IEEE       S(x)      0, 10       10000       2.0e-15     3.2e-16
+ *   IEEE       C(x)      0, 10       10000       1.8e-15     3.3e-16
+ *   DEC        S(x)      0, 10        6000       2.2e-16     3.9e-17
+ *   DEC        C(x)      0, 10        5000       2.3e-16     3.9e-17
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* S(x) for small x */
+#ifdef UNK
+static double sn[6] = {
+-2.99181919401019853726E3,
+ 7.08840045257738576863E5,
+-6.29741486205862506537E7,
+ 2.54890880573376359104E9,
+-4.42979518059697779103E10,
+ 3.18016297876567817986E11,
+};
+static double sd[6] = {
+/* 1.00000000000000000000E0,*/
+ 2.81376268889994315696E2,
+ 4.55847810806532581675E4,
+ 5.17343888770096400730E6,
+ 4.19320245898111231129E8,
+ 2.24411795645340920940E10,
+ 6.07366389490084639049E11,
+};
+#endif
+#ifdef DEC
+static unsigned short sn[24] = {
+0143072,0176433,0065455,0127034,
+0045055,0007200,0134540,0026661,
+0146560,0035061,0023667,0127545,
+0050027,0166503,0002673,0153756,
+0151045,0002721,0121737,0102066,
+0051624,0013177,0033451,0021271,
+};
+static unsigned short sd[24] = {
+/*0040200,0000000,0000000,0000000,*/
+0042214,0130051,0112070,0101617,
+0044062,0010307,0172346,0152510,
+0045635,0160575,0143200,0136642,
+0047307,0171215,0127457,0052361,
+0050647,0031447,0032621,0013510,
+0052015,0064733,0117362,0012653,
+};
+#endif
+#ifdef IBMPC
+static unsigned short sn[24] = {
+0xb5c3,0x6d65,0x5fa3,0xc0a7,
+0x05b6,0x172c,0xa1d0,0x4125,
+0xf5ed,0x24f6,0x0746,0xc18e,
+0x7afe,0x60b7,0xfda8,0x41e2,
+0xf087,0x347b,0xa0ba,0xc224,
+0x2457,0xe6e5,0x82cf,0x4252,
+};
+static unsigned short sd[24] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x1072,0x3287,0x9605,0x4071,
+0xdaa9,0xfe9c,0x4218,0x40e6,
+0x17b4,0xb8d0,0xbc2f,0x4153,
+0xea9e,0xb5e5,0xfe51,0x41b8,
+0x22e9,0xe6b2,0xe664,0x4214,
+0x42b5,0x73de,0xad3b,0x4261,
+};
+#endif
+#ifdef MIEEE
+static unsigned short sn[24] = {
+0xc0a7,0x5fa3,0x6d65,0xb5c3,
+0x4125,0xa1d0,0x172c,0x05b6,
+0xc18e,0x0746,0x24f6,0xf5ed,
+0x41e2,0xfda8,0x60b7,0x7afe,
+0xc224,0xa0ba,0x347b,0xf087,
+0x4252,0x82cf,0xe6e5,0x2457,
+};
+static unsigned short sd[24] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4071,0x9605,0x3287,0x1072,
+0x40e6,0x4218,0xfe9c,0xdaa9,
+0x4153,0xbc2f,0xb8d0,0x17b4,
+0x41b8,0xfe51,0xb5e5,0xea9e,
+0x4214,0xe664,0xe6b2,0x22e9,
+0x4261,0xad3b,0x73de,0x42b5,
+};
+#endif
+
+/* C(x) for small x */
+#ifdef UNK
+static double cn[6] = {
+-4.98843114573573548651E-8,
+ 9.50428062829859605134E-6,
+-6.45191435683965050962E-4,
+ 1.88843319396703850064E-2,
+-2.05525900955013891793E-1,
+ 9.99999999999999998822E-1,
+};
+static double cd[7] = {
+ 3.99982968972495980367E-12,
+ 9.15439215774657478799E-10,
+ 1.25001862479598821474E-7,
+ 1.22262789024179030997E-5,
+ 8.68029542941784300606E-4,
+ 4.12142090722199792936E-2,
+ 1.00000000000000000118E0,
+};
+#endif
+#ifdef DEC
+static unsigned short cn[24] = {
+0132126,0040141,0063733,0013231,
+0034037,0072223,0010200,0075637,
+0135451,0021020,0073264,0036057,
+0036632,0131520,0101316,0060233,
+0137522,0072541,0136124,0132202,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short cd[28] = {
+0026614,0135503,0051776,0032631,
+0030573,0121116,0154033,0126712,
+0032406,0034100,0012442,0106212,
+0034115,0017567,0150520,0164623,
+0035543,0106171,0177336,0146351,
+0037050,0150073,0000607,0171635,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short cn[24] = {
+0x62d3,0x2cfb,0xc80c,0xbe6a,
+0x0f74,0x6210,0xee92,0x3ee3,
+0x8786,0x0ed6,0x2442,0xbf45,
+0xcc13,0x1059,0x566a,0x3f93,
+0x9690,0x378a,0x4eac,0xbfca,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short cd[28] = {
+0xc6b3,0x6a7f,0x9768,0x3d91,
+0x75b9,0xdb03,0x7449,0x3e0f,
+0x5191,0x02a4,0xc708,0x3e80,
+0x1d32,0xfa2a,0xa3ee,0x3ee9,
+0xd99d,0x3fdb,0x718f,0x3f4c,
+0xfe74,0x6030,0x1a07,0x3fa5,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short cn[24] = {
+0xbe6a,0xc80c,0x2cfb,0x62d3,
+0x3ee3,0xee92,0x6210,0x0f74,
+0xbf45,0x2442,0x0ed6,0x8786,
+0x3f93,0x566a,0x1059,0xcc13,
+0xbfca,0x4eac,0x378a,0x9690,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short cd[28] = {
+0x3d91,0x9768,0x6a7f,0xc6b3,
+0x3e0f,0x7449,0xdb03,0x75b9,
+0x3e80,0xc708,0x02a4,0x5191,
+0x3ee9,0xa3ee,0xfa2a,0x1d32,
+0x3f4c,0x718f,0x3fdb,0xd99d,
+0x3fa5,0x1a07,0x6030,0xfe74,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+/* Auxiliary function f(x) */
+#ifdef UNK
+static double fn[10] = {
+  4.21543555043677546506E-1,
+  1.43407919780758885261E-1,
+  1.15220955073585758835E-2,
+  3.45017939782574027900E-4,
+  4.63613749287867322088E-6,
+  3.05568983790257605827E-8,
+  1.02304514164907233465E-10,
+  1.72010743268161828879E-13,
+  1.34283276233062758925E-16,
+  3.76329711269987889006E-20,
+};
+static double fd[10] = {
+/*  1.00000000000000000000E0,*/
+  7.51586398353378947175E-1,
+  1.16888925859191382142E-1,
+  6.44051526508858611005E-3,
+  1.55934409164153020873E-4,
+  1.84627567348930545870E-6,
+  1.12699224763999035261E-8,
+  3.60140029589371370404E-11,
+  5.88754533621578410010E-14,
+  4.52001434074129701496E-17,
+  1.25443237090011264384E-20,
+};
+#endif
+#ifdef DEC
+static unsigned short fn[40] = {
+0037727,0152216,0106601,0016214,
+0037422,0154606,0112710,0071355,
+0036474,0143453,0154253,0166545,
+0035264,0161606,0022250,0073743,
+0033633,0110036,0024653,0136246,
+0032003,0036652,0041164,0036413,
+0027740,0174122,0046305,0036726,
+0025501,0125270,0121317,0167667,
+0023032,0150555,0076175,0047443,
+0020061,0133570,0070130,0027657,
+};
+static unsigned short fd[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0040100,0063767,0054413,0151452,
+0037357,0061566,0007243,0065754,
+0036323,0005365,0033552,0133625,
+0035043,0101123,0000275,0165402,
+0033367,0146614,0110623,0023647,
+0031501,0116644,0125222,0144263,
+0027436,0062051,0117235,0001411,
+0025204,0111543,0056370,0036201,
+0022520,0071351,0015227,0122144,
+0017554,0172240,0112713,0005006,
+};
+#endif
+#ifdef IBMPC
+static unsigned short fn[40] = {
+0x2391,0xd1b0,0xfa91,0x3fda,
+0x0e5e,0xd2b9,0x5b30,0x3fc2,
+0x7dad,0x7b15,0x98e5,0x3f87,
+0x0efc,0xc495,0x9c70,0x3f36,
+0x7795,0xc535,0x7203,0x3ed3,
+0x87a1,0x484e,0x67b5,0x3e60,
+0xa7bb,0x4998,0x1f0a,0x3ddc,
+0xfdf7,0x1459,0x3557,0x3d48,
+0xa9e4,0xaf8f,0x5a2d,0x3ca3,
+0x05f6,0x0e0b,0x36ef,0x3be6,
+};
+static unsigned short fd[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x7a65,0xeb21,0x0cfe,0x3fe8,
+0x6d7d,0xc1d4,0xec6e,0x3fbd,
+0x56f3,0xa6ed,0x615e,0x3f7a,
+0xbd60,0x6017,0x704a,0x3f24,
+0x64f5,0x9232,0xf9b1,0x3ebe,
+0x5916,0x9552,0x33b4,0x3e48,
+0xa061,0x33d3,0xcc85,0x3dc3,
+0x0790,0x6b9f,0x926c,0x3d30,
+0xf48d,0x2352,0x0e5d,0x3c8a,
+0x6141,0x12b9,0x9e94,0x3bcd,
+};
+#endif
+#ifdef MIEEE
+static unsigned short fn[40] = {
+0x3fda,0xfa91,0xd1b0,0x2391,
+0x3fc2,0x5b30,0xd2b9,0x0e5e,
+0x3f87,0x98e5,0x7b15,0x7dad,
+0x3f36,0x9c70,0xc495,0x0efc,
+0x3ed3,0x7203,0xc535,0x7795,
+0x3e60,0x67b5,0x484e,0x87a1,
+0x3ddc,0x1f0a,0x4998,0xa7bb,
+0x3d48,0x3557,0x1459,0xfdf7,
+0x3ca3,0x5a2d,0xaf8f,0xa9e4,
+0x3be6,0x36ef,0x0e0b,0x05f6,
+};
+static unsigned short fd[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3fe8,0x0cfe,0xeb21,0x7a65,
+0x3fbd,0xec6e,0xc1d4,0x6d7d,
+0x3f7a,0x615e,0xa6ed,0x56f3,
+0x3f24,0x704a,0x6017,0xbd60,
+0x3ebe,0xf9b1,0x9232,0x64f5,
+0x3e48,0x33b4,0x9552,0x5916,
+0x3dc3,0xcc85,0x33d3,0xa061,
+0x3d30,0x926c,0x6b9f,0x0790,
+0x3c8a,0x0e5d,0x2352,0xf48d,
+0x3bcd,0x9e94,0x12b9,0x6141,
+};
+#endif
+
+
+/* Auxiliary function g(x) */
+#ifdef UNK
+static double gn[11] = {
+  5.04442073643383265887E-1,
+  1.97102833525523411709E-1,
+  1.87648584092575249293E-2,
+  6.84079380915393090172E-4,
+  1.15138826111884280931E-5,
+  9.82852443688422223854E-8,
+  4.45344415861750144738E-10,
+  1.08268041139020870318E-12,
+  1.37555460633261799868E-15,
+  8.36354435630677421531E-19,
+  1.86958710162783235106E-22,
+};
+static double gd[11] = {
+/*  1.00000000000000000000E0,*/
+  1.47495759925128324529E0,
+  3.37748989120019970451E-1,
+  2.53603741420338795122E-2,
+  8.14679107184306179049E-4,
+  1.27545075667729118702E-5,
+  1.04314589657571990585E-7,
+  4.60680728146520428211E-10,
+  1.10273215066240270757E-12,
+  1.38796531259578871258E-15,
+  8.39158816283118707363E-19,
+  1.86958710162783236342E-22,
+};
+#endif
+#ifdef DEC
+static unsigned short gn[44] = {
+0040001,0021435,0120406,0053123,
+0037511,0152523,0037703,0122011,
+0036631,0134302,0122721,0110235,
+0035463,0051712,0043215,0114732,
+0034101,0025677,0147725,0057630,
+0032323,0010342,0067523,0002206,
+0030364,0152247,0110007,0054107,
+0026230,0057654,0035464,0047124,
+0023706,0036401,0167705,0045440,
+0021166,0154447,0105632,0142461,
+0016142,0002353,0011175,0170530,
+};
+static unsigned short gd[44] = {
+/*0040200,0000000,0000000,0000000,*/
+0040274,0145551,0016742,0127005,
+0037654,0166557,0076416,0015165,
+0036717,0140217,0030675,0050111,
+0035525,0110060,0076405,0070502,
+0034125,0176061,0060120,0031730,
+0032340,0001615,0054343,0120501,
+0030375,0041414,0070747,0107060,
+0026233,0031034,0160757,0074526,
+0023710,0003341,0137100,0144664,
+0021167,0126414,0023774,0015435,
+0016142,0002353,0011175,0170530,
+};
+#endif
+#ifdef IBMPC
+static unsigned short gn[44] = {
+0xcaca,0xb420,0x2463,0x3fe0,
+0x7481,0x67f8,0x3aaa,0x3fc9,
+0x3214,0x54ba,0x3718,0x3f93,
+0xb33b,0x48d1,0x6a79,0x3f46,
+0xabf3,0xf9fa,0x2577,0x3ee8,
+0x6091,0x4dea,0x621c,0x3e7a,
+0xeb09,0xf200,0x9a94,0x3dfe,
+0x89cb,0x8766,0x0bf5,0x3d73,
+0xa964,0x3df8,0xc7a0,0x3cd8,
+0x58a6,0xf173,0xdb24,0x3c2e,
+0xbe2b,0x624f,0x409d,0x3b6c,
+};
+static unsigned short gd[44] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x55c1,0x23bc,0x996d,0x3ff7,
+0xc34f,0xefa1,0x9dad,0x3fd5,
+0xaa09,0xe637,0xf811,0x3f99,
+0xae28,0x0fa0,0xb206,0x3f4a,
+0x067b,0x2c0a,0xbf86,0x3eea,
+0x7428,0xab1c,0x0071,0x3e7c,
+0xf1c6,0x8e3c,0xa861,0x3dff,
+0xef2b,0x9c3d,0x6643,0x3d73,
+0x1936,0x37c8,0x00dc,0x3cd9,
+0x8364,0x84ff,0xf5a1,0x3c2e,
+0xbe2b,0x624f,0x409d,0x3b6c,
+};
+#endif
+#ifdef MIEEE
+static unsigned short gn[44] = {
+0x3fe0,0x2463,0xb420,0xcaca,
+0x3fc9,0x3aaa,0x67f8,0x7481,
+0x3f93,0x3718,0x54ba,0x3214,
+0x3f46,0x6a79,0x48d1,0xb33b,
+0x3ee8,0x2577,0xf9fa,0xabf3,
+0x3e7a,0x621c,0x4dea,0x6091,
+0x3dfe,0x9a94,0xf200,0xeb09,
+0x3d73,0x0bf5,0x8766,0x89cb,
+0x3cd8,0xc7a0,0x3df8,0xa964,
+0x3c2e,0xdb24,0xf173,0x58a6,
+0x3b6c,0x409d,0x624f,0xbe2b,
+};
+static unsigned short gd[44] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3ff7,0x996d,0x23bc,0x55c1,
+0x3fd5,0x9dad,0xefa1,0xc34f,
+0x3f99,0xf811,0xe637,0xaa09,
+0x3f4a,0xb206,0x0fa0,0xae28,
+0x3eea,0xbf86,0x2c0a,0x067b,
+0x3e7c,0x0071,0xab1c,0x7428,
+0x3dff,0xa861,0x8e3c,0xf1c6,
+0x3d73,0x6643,0x9c3d,0xef2b,
+0x3cd9,0x00dc,0x37c8,0x1936,
+0x3c2e,0xf5a1,0x84ff,0x8364,
+0x3b6c,0x409d,0x624f,0xbe2b,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double cos ( double );
+extern double sin ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+double fabs(), cos(), sin(), polevl(), p1evl();
+#endif
+extern double PI, PIO2, MACHEP;
+
+int fresnl( xxa, ssa, cca )
+double xxa, *ssa, *cca;
+{
+double f, g, cc, ss, c, s, t, u;
+double x, x2;
+
+x = fabs(xxa);
+x2 = x * x;
+if( x2 < 2.5625 )
+	{
+	t = x2 * x2;
+	ss = x * x2 * polevl( t, sn, 5)/p1evl( t, sd, 6 );
+	cc = x * polevl( t, cn, 5)/polevl(t, cd, 6 );
+	goto done;
+	}
+
+
+
+
+
+
+if( x > 36974.0 )
+	{
+	cc = 0.5;
+	ss = 0.5;
+	goto done;
+	}
+
+
+/*		Asymptotic power series auxiliary functions
+ *		for large argument
+ */
+	x2 = x * x;
+	t = PI * x2;
+	u = 1.0/(t * t);
+	t = 1.0/t;
+	f = 1.0 - u * polevl( u, fn, 9)/p1evl(u, fd, 10);
+	g = t * polevl( u, gn, 10)/p1evl(u, gd, 11);
+
+	t = PIO2 * x2;
+	c = cos(t);
+	s = sin(t);
+	t = PI * x;
+	cc = 0.5  +  (f * s  -  g * c)/t;
+	ss = 0.5  -  (f * c  +  g * s)/t;
+
+done:
+if( xxa < 0.0 )
+	{
+	cc = -cc;
+	ss = -ss;
+	}
+
+*cca = cc;
+*ssa = ss;
+return(0);
+}

libm/double/gamma.c

@@ -0,0 +1,685 @@
+/*							gamma.c
+ *
+ *	Gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, gamma();
+ * extern int sgngam;
+ *
+ * y = gamma( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns gamma function of the argument.  The result is
+ * correctly signed, and the sign (+1 or -1) is also
+ * returned in a global (extern) variable named sgngam.
+ * This variable is also filled in by the logarithmic gamma
+ * function lgam().
+ *
+ * Arguments |x| <= 34 are reduced by recurrence and the function
+ * approximated by a rational function of degree 6/7 in the
+ * interval (2,3).  Large arguments are handled by Stirling's
+ * formula. Large negative arguments are made positive using
+ * a reflection formula.  
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -34, 34      10000       1.3e-16     2.5e-17
+ *    IEEE    -170,-33      20000       2.3e-15     3.3e-16
+ *    IEEE     -33,  33     20000       9.4e-16     2.2e-16
+ *    IEEE      33, 171.6   20000       2.3e-15     3.2e-16
+ *
+ * Error for arguments outside the test range will be larger
+ * owing to error amplification by the exponential function.
+ *
+ */
+/*							lgam()
+ *
+ *	Natural logarithm of gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, lgam();
+ * extern int sgngam;
+ *
+ * y = lgam( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of the absolute
+ * value of the gamma function of the argument.
+ * The sign (+1 or -1) of the gamma function is returned in a
+ * global (extern) variable named sgngam.
+ *
+ * For arguments greater than 13, the logarithm of the gamma
+ * function is approximated by the logarithmic version of
+ * Stirling's formula using a polynomial approximation of
+ * degree 4. Arguments between -33 and +33 are reduced by
+ * recurrence to the interval [2,3] of a rational approximation.
+ * The cosecant reflection formula is employed for arguments
+ * less than -33.
+ *
+ * Arguments greater than MAXLGM return MAXNUM and an error
+ * message.  MAXLGM = 2.035093e36 for DEC
+ * arithmetic or 2.556348e305 for IEEE arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * arithmetic      domain        # trials     peak         rms
+ *    DEC     0, 3                  7000     5.2e-17     1.3e-17
+ *    DEC     2.718, 2.035e36       5000     3.9e-17     9.9e-18
+ *    IEEE    0, 3                 28000     5.4e-16     1.1e-16
+ *    IEEE    2.718, 2.556e305     40000     3.5e-16     8.3e-17
+ * The error criterion was relative when the function magnitude
+ * was greater than one but absolute when it was less than one.
+ *
+ * The following test used the relative error criterion, though
+ * at certain points the relative error could be much higher than
+ * indicated.
+ *    IEEE    -200, -4             10000     4.8e-16     1.3e-16
+ *
+ */
+
+/*							gamma.c	*/
+/*	gamma function	*/
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+  1.60119522476751861407E-4,
+  1.19135147006586384913E-3,
+  1.04213797561761569935E-2,
+  4.76367800457137231464E-2,
+  2.07448227648435975150E-1,
+  4.94214826801497100753E-1,
+  9.99999999999999996796E-1
+};
+static double Q[] = {
+-2.31581873324120129819E-5,
+ 5.39605580493303397842E-4,
+-4.45641913851797240494E-3,
+ 1.18139785222060435552E-2,
+ 3.58236398605498653373E-2,
+-2.34591795718243348568E-1,
+ 7.14304917030273074085E-2,
+ 1.00000000000000000320E0
+};
+#define MAXGAM 171.624376956302725
+static double LOGPI = 1.14472988584940017414;
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0035047,0162701,0146301,0005234,
+0035634,0023437,0032065,0176530,
+0036452,0137157,0047330,0122574,
+0037103,0017310,0143041,0017232,
+0037524,0066516,0162563,0164605,
+0037775,0004671,0146237,0014222,
+0040200,0000000,0000000,0000000
+};
+static unsigned short Q[] = {
+0134302,0041724,0020006,0116565,
+0035415,0072121,0044251,0025634,
+0136222,0003447,0035205,0121114,
+0036501,0107552,0154335,0104271,
+0037022,0135717,0014776,0171471,
+0137560,0034324,0165024,0037021,
+0037222,0045046,0047151,0161213,
+0040200,0000000,0000000,0000000
+};
+#define MAXGAM 34.84425627277176174
+static unsigned short LPI[4] = {
+0040222,0103202,0043475,0006750,
+};
+#define LOGPI *(double *)LPI
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x2153,0x3998,0xfcb8,0x3f24,
+0xbfab,0xe686,0x84e3,0x3f53,
+0x14b0,0xe9db,0x57cd,0x3f85,
+0x23d3,0x18c4,0x63d9,0x3fa8,
+0x7d31,0xdcae,0x8da9,0x3fca,
+0xe312,0x3993,0xa137,0x3fdf,
+0x0000,0x0000,0x0000,0x3ff0
+};
+static unsigned short Q[] = {
+0xd3af,0x8400,0x487a,0xbef8,
+0x2573,0x2915,0xae8a,0x3f41,
+0xb44a,0xe750,0x40e4,0xbf72,
+0xb117,0x5b1b,0x31ed,0x3f88,
+0xde67,0xe33f,0x5779,0x3fa2,
+0x87c2,0x9d42,0x071a,0xbfce,
+0x3c51,0xc9cd,0x4944,0x3fb2,
+0x0000,0x0000,0x0000,0x3ff0
+};
+#define MAXGAM 171.624376956302725
+static unsigned short LPI[4] = {
+0xa1bd,0x48e7,0x50d0,0x3ff2,
+};
+#define LOGPI *(double *)LPI
+#endif 
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f24,0xfcb8,0x3998,0x2153,
+0x3f53,0x84e3,0xe686,0xbfab,
+0x3f85,0x57cd,0xe9db,0x14b0,
+0x3fa8,0x63d9,0x18c4,0x23d3,
+0x3fca,0x8da9,0xdcae,0x7d31,
+0x3fdf,0xa137,0x3993,0xe312,
+0x3ff0,0x0000,0x0000,0x0000
+};
+static unsigned short Q[] = {
+0xbef8,0x487a,0x8400,0xd3af,
+0x3f41,0xae8a,0x2915,0x2573,
+0xbf72,0x40e4,0xe750,0xb44a,
+0x3f88,0x31ed,0x5b1b,0xb117,
+0x3fa2,0x5779,0xe33f,0xde67,
+0xbfce,0x071a,0x9d42,0x87c2,
+0x3fb2,0x4944,0xc9cd,0x3c51,
+0x3ff0,0x0000,0x0000,0x0000
+};
+#define MAXGAM 171.624376956302725
+static unsigned short LPI[4] = {
+0x3ff2,0x50d0,0x48e7,0xa1bd,
+};
+#define LOGPI *(double *)LPI
+#endif 
+
+/* Stirling's formula for the gamma function */
+#if UNK
+static double STIR[5] = {
+ 7.87311395793093628397E-4,
+-2.29549961613378126380E-4,
+-2.68132617805781232825E-3,
+ 3.47222221605458667310E-3,
+ 8.33333333333482257126E-2,
+};
+#define MAXSTIR 143.01608
+static double SQTPI = 2.50662827463100050242E0;
+#endif
+#if DEC
+static unsigned short STIR[20] = {
+0035516,0061622,0144553,0112224,
+0135160,0131531,0037460,0165740,
+0136057,0134460,0037242,0077270,
+0036143,0107070,0156306,0027751,
+0037252,0125252,0125252,0146064,
+};
+#define MAXSTIR 26.77
+static unsigned short SQT[4] = {
+0040440,0066230,0177661,0034055,
+};
+#define SQTPI *(double *)SQT
+#endif
+#if IBMPC
+static unsigned short STIR[20] = {
+0x7293,0x592d,0xcc72,0x3f49,
+0x1d7c,0x27e6,0x166b,0xbf2e,
+0x4fd7,0x07d4,0xf726,0xbf65,
+0xc5fd,0x1b98,0x71c7,0x3f6c,
+0x5986,0x5555,0x5555,0x3fb5,
+};
+#define MAXSTIR 143.01608
+static unsigned short SQT[4] = {
+0x2706,0x1ff6,0x0d93,0x4004,
+};
+#define SQTPI *(double *)SQT
+#endif
+#if MIEEE
+static unsigned short STIR[20] = {
+0x3f49,0xcc72,0x592d,0x7293,
+0xbf2e,0x166b,0x27e6,0x1d7c,
+0xbf65,0xf726,0x07d4,0x4fd7,
+0x3f6c,0x71c7,0x1b98,0xc5fd,
+0x3fb5,0x5555,0x5555,0x5986,
+};
+#define MAXSTIR 143.01608
+static unsigned short SQT[4] = {
+0x4004,0x0d93,0x1ff6,0x2706,
+};
+#define SQTPI *(double *)SQT
+#endif
+
+int sgngam = 0;
+extern int sgngam;
+extern double MAXLOG, MAXNUM, PI;
+#ifdef ANSIPROT
+extern double pow ( double, double );
+extern double log ( double );
+extern double exp ( double );
+extern double sin ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double fabs ( double );
+extern int isnan ( double );
+extern int isfinite ( double );
+static double stirf ( double );
+double lgam ( double );
+#else
+double pow(), log(), exp(), sin(), polevl(), p1evl(), floor(), fabs();
+int isnan(), isfinite();
+static double stirf();
+double lgam();
+#endif
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+#ifdef NANS
+extern double NAN;
+#endif
+
+/* Gamma function computed by Stirling's formula.
+ * The polynomial STIR is valid for 33 <= x <= 172.
+ */
+static double stirf(x)
+double x;
+{
+double y, w, v;
+
+w = 1.0/x;
+w = 1.0 + w * polevl( w, STIR, 4 );
+y = exp(x);
+if( x > MAXSTIR )
+	{ /* Avoid overflow in pow() */
+	v = pow( x, 0.5 * x - 0.25 );
+	y = v * (v / y);
+	}
+else
+	{
+	y = pow( x, x - 0.5 ) / y;
+	}
+y = SQTPI * y * w;
+return( y );
+}
+
+
+
+double gamma(x)
+double x;
+{
+double p, q, z;
+int i;
+
+sgngam = 1;
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+#ifdef INFINITIES
+#ifdef NANS
+if( x == INFINITY )
+	return(x);
+if( x == -INFINITY )
+	return(NAN);
+#else
+if( !isfinite(x) )
+	return(x);
+#endif
+#endif
+q = fabs(x);
+
+if( q > 33.0 )
+	{
+	if( x < 0.0 )
+		{
+		p = floor(q);
+		if( p == q )
+			{
+#ifdef NANS
+gamnan:
+			mtherr( "gamma", DOMAIN );
+			return (NAN);
+#else
+			goto goverf;
+#endif
+			}
+		i = p;
+		if( (i & 1) == 0 )
+			sgngam = -1;
+		z = q - p;
+		if( z > 0.5 )
+			{
+			p += 1.0;
+			z = q - p;
+			}
+		z = q * sin( PI * z );
+		if( z == 0.0 )
+			{
+#ifdef INFINITIES
+			return( sgngam * INFINITY);
+#else
+goverf:
+			mtherr( "gamma", OVERFLOW );
+			return( sgngam * MAXNUM);
+#endif
+			}
+		z = fabs(z);
+		z = PI/(z * stirf(q) );
+		}
+	else
+		{
+		z = stirf(x);
+		}
+	return( sgngam * z );
+	}
+
+z = 1.0;
+while( x >= 3.0 )
+	{
+	x -= 1.0;
+	z *= x;
+	}
+
+while( x < 0.0 )
+	{
+	if( x > -1.E-9 )
+		goto small;
+	z /= x;
+	x += 1.0;
+	}
+
+while( x < 2.0 )
+	{
+	if( x < 1.e-9 )
+		goto small;
+	z /= x;
+	x += 1.0;
+	}
+
+if( x == 2.0 )
+	return(z);
+
+x -= 2.0;
+p = polevl( x, P, 6 );
+q = polevl( x, Q, 7 );
+return( z * p / q );
+
+small:
+if( x == 0.0 )
+	{
+#ifdef INFINITIES
+#ifdef NANS
+	  goto gamnan;
+#else
+	  return( INFINITY );
+#endif
+#else
+	mtherr( "gamma", SING );
+	return( MAXNUM );
+#endif
+	}
+else
+	return( z/((1.0 + 0.5772156649015329 * x) * x) );
+}
+
+
+
+/* A[]: Stirling's formula expansion of log gamma
+ * B[], C[]: log gamma function between 2 and 3
+ */
+#ifdef UNK
+static double A[] = {
+ 8.11614167470508450300E-4,
+-5.95061904284301438324E-4,
+ 7.93650340457716943945E-4,
+-2.77777777730099687205E-3,
+ 8.33333333333331927722E-2
+};
+static double B[] = {
+-1.37825152569120859100E3,
+-3.88016315134637840924E4,
+-3.31612992738871184744E5,
+-1.16237097492762307383E6,
+-1.72173700820839662146E6,
+-8.53555664245765465627E5
+};
+static double C[] = {
+/* 1.00000000000000000000E0, */
+-3.51815701436523470549E2,
+-1.70642106651881159223E4,
+-2.20528590553854454839E5,
+-1.13933444367982507207E6,
+-2.53252307177582951285E6,
+-2.01889141433532773231E6
+};
+/* log( sqrt( 2*pi ) ) */
+static double LS2PI  =  0.91893853320467274178;
+#define MAXLGM 2.556348e305
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0035524,0141201,0034633,0031405,
+0135433,0176755,0126007,0045030,
+0035520,0006371,0003342,0172730,
+0136066,0005540,0132605,0026407,
+0037252,0125252,0125252,0125132
+};
+static unsigned short B[] = {
+0142654,0044014,0077633,0035410,
+0144027,0110641,0125335,0144760,
+0144641,0165637,0142204,0047447,
+0145215,0162027,0146246,0155211,
+0145322,0026110,0010317,0110130,
+0145120,0061472,0120300,0025363
+};
+static unsigned short C[] = {
+/*0040200,0000000,0000000,0000000*/
+0142257,0164150,0163630,0112622,
+0143605,0050153,0156116,0135272,
+0144527,0056045,0145642,0062332,
+0145213,0012063,0106250,0001025,
+0145432,0111254,0044577,0115142,
+0145366,0071133,0050217,0005122
+};
+/* log( sqrt( 2*pi ) ) */
+static unsigned short LS2P[] = {040153,037616,041445,0172645,};
+#define LS2PI *(double *)LS2P
+#define MAXLGM 2.035093e36
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0x6661,0x2733,0x9850,0x3f4a,
+0xe943,0xb580,0x7fbd,0xbf43,
+0x5ebb,0x20dc,0x019f,0x3f4a,
+0xa5a1,0x16b0,0xc16c,0xbf66,
+0x554b,0x5555,0x5555,0x3fb5
+};
+static unsigned short B[] = {
+0x6761,0x8ff3,0x8901,0xc095,
+0xb93e,0x355b,0xf234,0xc0e2,
+0x89e5,0xf890,0x3d73,0xc114,
+0xdb51,0xf994,0xbc82,0xc131,
+0xf20b,0x0219,0x4589,0xc13a,
+0x055e,0x5418,0x0c67,0xc12a
+};
+static unsigned short C[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x12b2,0x1cf3,0xfd0d,0xc075,
+0xd757,0x7b89,0xaa0d,0xc0d0,
+0x4c9b,0xb974,0xeb84,0xc10a,
+0x0043,0x7195,0x6286,0xc131,
+0xf34c,0x892f,0x5255,0xc143,
+0xe14a,0x6a11,0xce4b,0xc13e
+};
+/* log( sqrt( 2*pi ) ) */
+static unsigned short LS2P[] = {
+0xbeb5,0xc864,0x67f1,0x3fed
+};
+#define LS2PI *(double *)LS2P
+#define MAXLGM 2.556348e305
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0x3f4a,0x9850,0x2733,0x6661,
+0xbf43,0x7fbd,0xb580,0xe943,
+0x3f4a,0x019f,0x20dc,0x5ebb,
+0xbf66,0xc16c,0x16b0,0xa5a1,
+0x3fb5,0x5555,0x5555,0x554b
+};
+static unsigned short B[] = {
+0xc095,0x8901,0x8ff3,0x6761,
+0xc0e2,0xf234,0x355b,0xb93e,
+0xc114,0x3d73,0xf890,0x89e5,
+0xc131,0xbc82,0xf994,0xdb51,
+0xc13a,0x4589,0x0219,0xf20b,
+0xc12a,0x0c67,0x5418,0x055e
+};
+static unsigned short C[] = {
+0xc075,0xfd0d,0x1cf3,0x12b2,
+0xc0d0,0xaa0d,0x7b89,0xd757,
+0xc10a,0xeb84,0xb974,0x4c9b,
+0xc131,0x6286,0x7195,0x0043,
+0xc143,0x5255,0x892f,0xf34c,
+0xc13e,0xce4b,0x6a11,0xe14a
+};
+/* log( sqrt( 2*pi ) ) */
+static unsigned short LS2P[] = {
+0x3fed,0x67f1,0xc864,0xbeb5
+};
+#define LS2PI *(double *)LS2P
+#define MAXLGM 2.556348e305
+#endif
+
+
+/* Logarithm of gamma function */
+
+
+double lgam(x)
+double x;
+{
+double p, q, u, w, z;
+int i;
+
+sgngam = 1;
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+
+#ifdef INFINITIES
+if( !isfinite(x) )
+	return(INFINITY);
+#endif
+
+if( x < -34.0 )
+	{
+	q = -x;
+	w = lgam(q); /* note this modifies sgngam! */
+	p = floor(q);
+	if( p == q )
+		{
+lgsing:
+#ifdef INFINITIES
+		mtherr( "lgam", SING );
+		return (INFINITY);
+#else
+		goto loverf;
+#endif
+		}
+	i = p;
+	if( (i & 1) == 0 )
+		sgngam = -1;
+	else
+		sgngam = 1;
+	z = q - p;
+	if( z > 0.5 )
+		{
+		p += 1.0;
+		z = p - q;
+		}
+	z = q * sin( PI * z );
+	if( z == 0.0 )
+		goto lgsing;
+/*	z = log(PI) - log( z ) - w;*/
+	z = LOGPI - log( z ) - w;
+	return( z );
+	}
+
+if( x < 13.0 )
+	{
+	z = 1.0;
+	p = 0.0;
+	u = x;
+	while( u >= 3.0 )
+		{
+		p -= 1.0;
+		u = x + p;
+		z *= u;
+		}
+	while( u < 2.0 )
+		{
+		if( u == 0.0 )
+			goto lgsing;
+		z /= u;
+		p += 1.0;
+		u = x + p;
+		}
+	if( z < 0.0 )
+		{
+		sgngam = -1;
+		z = -z;
+		}
+	else
+		sgngam = 1;
+	if( u == 2.0 )
+		return( log(z) );
+	p -= 2.0;
+	x = x + p;
+	p = x * polevl( x, B, 5 ) / p1evl( x, C, 6);
+	return( log(z) + p );
+	}
+
+if( x > MAXLGM )
+	{
+#ifdef INFINITIES
+	return( sgngam * INFINITY );
+#else
+loverf:
+	mtherr( "lgam", OVERFLOW );
+	return( sgngam * MAXNUM );
+#endif
+	}
+
+q = ( x - 0.5 ) * log(x) - x + LS2PI;
+if( x > 1.0e8 )
+	return( q );
+
+p = 1.0/(x*x);
+if( x >= 1000.0 )
+	q += ((   7.9365079365079365079365e-4 * p
+		- 2.7777777777777777777778e-3) *p
+		+ 0.0833333333333333333333) / x;
+else
+	q += polevl( p, A, 4 ) / x;
+return( q );
+}

libm/double/gdtr.c

@@ -0,0 +1,130 @@
+/*							gdtr.c
+ *
+ *	Gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, gdtr();
+ *
+ * y = gdtr( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from zero to x of the gamma probability
+ * density function:
+ *
+ *
+ *                x
+ *        b       -
+ *       a       | |   b-1  -at
+ * y =  -----    |    t    e    dt
+ *       -     | |
+ *      | (b)   -
+ *               0
+ *
+ *  The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igam( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * gdtr domain         x < 0            0.0
+ *
+ */
+/*							gdtrc.c
+ *
+ *	Complemented gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, gdtrc();
+ *
+ * y = gdtrc( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from x to infinity of the gamma
+ * probability density function:
+ *
+ *
+ *               inf.
+ *        b       -
+ *       a       | |   b-1  -at
+ * y =  -----    |    t    e    dt
+ *       -     | |
+ *      | (b)   -
+ *               x
+ *
+ *  The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igamc( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * gdtrc domain         x < 0            0.0
+ *
+ */
+
+/*							gdtr()  */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double igam ( double, double );
+extern double igamc ( double, double );
+#else
+double igam(), igamc();
+#endif
+
+double gdtr( a, b, x )
+double a, b, x;
+{
+
+if( x < 0.0 )
+	{
+	mtherr( "gdtr", DOMAIN );
+	return( 0.0 );
+	}
+return(  igam( b, a * x )  );
+}
+
+
+
+double gdtrc( a, b, x )
+double a, b, x;
+{
+
+if( x < 0.0 )
+	{
+	mtherr( "gdtrc", DOMAIN );
+	return( 0.0 );
+	}
+return(  igamc( b, a * x )  );
+}

libm/double/gels.c

@@ -0,0 +1,232 @@
+/*
+C
+C     ..................................................................
+C
+C        SUBROUTINE GELS
+C
+C        PURPOSE
+C           TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
+C           SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
+C           IS ASSUMED TO BE STORED COLUMNWISE.
+C
+C        USAGE
+C           CALL GELS(R,A,M,N,EPS,IER,AUX)
+C
+C        DESCRIPTION OF PARAMETERS
+C           R      - M BY N RIGHT HAND SIDE MATRIX.  (DESTROYED)
+C                    ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
+C           A      - UPPER TRIANGULAR PART OF THE SYMMETRIC
+C                    M BY M COEFFICIENT MATRIX.  (DESTROYED)
+C           M      - THE NUMBER OF EQUATIONS IN THE SYSTEM.
+C           N      - THE NUMBER OF RIGHT HAND SIDE VECTORS.
+C           EPS    - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
+C                    TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
+C           IER    - RESULTING ERROR PARAMETER CODED AS FOLLOWS
+C                    IER=0  - NO ERROR,
+C                    IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
+C                             PIVOT ELEMENT AT ANY ELIMINATION STEP
+C                             EQUAL TO 0,
+C                    IER=K  - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
+C                             CANCE INDICATED AT ELIMINATION STEP K+1,
+C                             WHERE PIVOT ELEMENT WAS LESS THAN OR
+C                             EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
+C                             ABSOLUTELY GREATEST MAIN DIAGONAL
+C                             ELEMENT OF MATRIX A.
+C           AUX    - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
+C
+C        REMARKS
+C           UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
+C           COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
+C           HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
+C           LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
+C           TOO.
+C           THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
+C           GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
+C           ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
+C           INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
+C           SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
+C           INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
+C           GIVEN IN CASE M=1.
+C           ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
+C           MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
+C           ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
+C           WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
+C
+C        SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
+C           NONE
+C
+C        METHOD
+C           SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
+C           PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
+C           SYMMETRY IN REMAINING COEFFICIENT MATRICES.
+C
+C     ..................................................................
+C
+*/
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+#else
+double fabs();
+#endif
+
+gels( A, R, M, EPS, AUX )
+double A[],R[];
+int M;
+double EPS;
+double AUX[];
+{
+int I, J, K, L, IER;
+int II, LL, LLD, LR, LT, LST, LLST, LEND;
+double tb, piv, tol, pivi;
+
+if( M <= 0 )
+	{
+fatal:
+	IER = -1;
+	goto done;
+	}
+/* SEARCH FOR GREATEST MAIN DIAGONAL ELEMENT */
+
+/*  Diagonal elements are at A(i,i) = 1, 3, 6, 10, ...
+ *  A(i,j) = A( i(i-1)/2 + j )
+ */
+IER = 0;
+piv = 0.0;
+L = 0;
+for( K=1; K<=M; K++ )
+	{
+	L += K;
+	tb = fabs( A[L-1] );
+	if( tb > piv )
+		{
+		piv = tb;
+		I = L;
+		J = K;
+		}
+	}
+tol = EPS * piv;
+
+/*
+C     MAIN DIAGONAL ELEMENT A(I)=A(J,J) IS FIRST PIVOT ELEMENT.
+C     PIV CONTAINS THE ABSOLUTE VALUE OF A(I).
+*/
+
+/*     START ELIMINATION LOOP */
+LST = 0;
+LEND = M - 1;
+for( K=1; K<=M; K++ )
+	{
+/*     TEST ON USEFULNESS OF SYMMETRIC ALGORITHM */
+	if( piv <= 0.0 )
+		goto fatal;
+	if( IER == 0 )
+		{
+		if( piv <= tol )
+			{
+			IER = K - 1;
+			}
+		}
+	LT = J - K;
+	LST += K;
+
+/*  PIVOT ROW REDUCTION AND ROW INTERCHANGE IN RIGHT HAND SIDE R */
+	pivi = 1.0 / A[I-1];
+	L = K;
+	LL = L + LT;
+	tb = pivi * R[LL-1];
+	R[LL-1] = R[L-1];
+	R[L-1] = tb;
+/* IS ELIMINATION TERMINATED */
+	if( K >= M )
+		break;
+/*
+C     ROW AND COLUMN INTERCHANGE AND PIVOT ROW REDUCTION IN MATRIX A.
+C     ELEMENTS OF PIVOT COLUMN ARE SAVED IN AUXILIARY VECTOR AUX.
+*/
+	LR = LST + (LT*(K+J-1))/2;
+	LL = LR;
+	L=LST;
+	for( II=K; II<=LEND; II++ )
+		{
+		L += II;
+		LL += 1;
+		if( L == LR )
+			{
+			A[LL-1] = A[LST-1];
+			tb = A[L-1];
+			goto lab13;
+			}
+		if( L > LR )
+			LL = L + LT;
+
+		tb = A[LL-1];
+		A[LL-1] = A[L-1];
+lab13:
+		AUX[II-1] = tb;
+		A[L-1] = pivi * tb;
+		}
+/* SAVE COLUMN INTERCHANGE INFORMATION */
+	A[LST-1] = LT;
+/* ELEMENT REDUCTION AND SEARCH FOR NEXT PIVOT */
+	piv = 0.0;
+	LLST = LST;
+	LT = 0;
+	for( II=K; II<=LEND; II++ )
+		{
+		pivi = -AUX[II-1];
+		LL = LLST;
+		LT += 1;
+		for( LLD=II; LLD<=LEND; LLD++ )
+			{
+			LL += LLD;
+			L = LL + LT;
+			A[L-1] += pivi * A[LL-1];
+			}
+		LLST += II;
+		LR = LLST + LT;
+		tb =fabs( A[LR-1] );
+		if( tb > piv )
+			{
+			piv = tb;
+			I = LR;
+			J = II + 1;
+			}
+		LR = K;
+		LL = LR + LT;
+		R[LL-1] += pivi * R[LR-1];
+		}
+	}
+/* END OF ELIMINATION LOOP */
+
+/* BACK SUBSTITUTION AND BACK INTERCHANGE */
+
+if( LEND <= 0 )
+	{
+	if( LEND < 0 )
+		goto fatal;
+	goto done;
+	}
+II = M;
+for( I=2; I<=M; I++ )
+	{
+	LST -= II;
+	II -= 1;
+	L = A[LST-1] + 0.5;
+	J = II;
+	tb = R[J-1];
+	LL = J;
+	K = LST;
+	for( LT=II; LT<=LEND; LT++ )
+		{
+		LL += 1;
+		K += LT;
+		tb -= A[K-1] * R[LL-1];
+		}
+	K = J + L;
+	R[J-1] = R[K-1];
+	R[K-1] = tb;
+	}
+done:
+return( IER );
+}

libm/double/hyp2f1.c

@@ -0,0 +1,460 @@
+/*							hyp2f1.c
+ *
+ *	Gauss hypergeometric function   F
+ *	                               2 1
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, c, x, y, hyp2f1();
+ *
+ * y = hyp2f1( a, b, c, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *  hyp2f1( a, b, c, x )  =   F ( a, b; c; x )
+ *                           2 1
+ *
+ *           inf.
+ *            -   a(a+1)...(a+k) b(b+1)...(b+k)   k+1
+ *   =  1 +   >   -----------------------------  x   .
+ *            -         c(c+1)...(c+k) (k+1)!
+ *          k = 0
+ *
+ *  Cases addressed are
+ *	Tests and escapes for negative integer a, b, or c
+ *	Linear transformation if c - a or c - b negative integer
+ *	Special case c = a or c = b
+ *	Linear transformation for  x near +1
+ *	Transformation for x < -0.5
+ *	Psi function expansion if x > 0.5 and c - a - b integer
+ *      Conditionally, a recurrence on c to make c-a-b > 0
+ *
+ * |x| > 1 is rejected.
+ *
+ * The parameters a, b, c are considered to be integer
+ * valued if they are within 1.0e-14 of the nearest integer
+ * (1.0e-13 for IEEE arithmetic).
+ *
+ * ACCURACY:
+ *
+ *
+ *               Relative error (-1 < x < 1):
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -1,7        230000      1.2e-11     5.2e-14
+ *
+ * Several special cases also tested with a, b, c in
+ * the range -7 to 7.
+ *
+ * ERROR MESSAGES:
+ *
+ * A "partial loss of precision" message is printed if
+ * the internally estimated relative error exceeds 1^-12.
+ * A "singularity" message is printed on overflow or
+ * in cases not addressed (such as x < -1).
+ */
+
+/*							hyp2f1	*/
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef DEC
+#define EPS 1.0e-14
+#define EPS2 1.0e-11
+#endif
+
+#ifdef IBMPC
+#define EPS 1.0e-13
+#define EPS2 1.0e-10
+#endif
+
+#ifdef MIEEE
+#define EPS 1.0e-13
+#define EPS2 1.0e-10
+#endif
+
+#ifdef UNK
+#define EPS 1.0e-13
+#define EPS2 1.0e-10
+#endif
+
+#define ETHRESH 1.0e-12
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double pow ( double, double );
+extern double round ( double );
+extern double gamma ( double );
+extern double log ( double );
+extern double exp ( double );
+extern double psi ( double );
+static double hyt2f1(double, double, double, double, double *);
+static double hys2f1(double, double, double, double, double *);
+double hyp2f1(double, double, double, double);
+#else
+double fabs(), pow(), round(), gamma(), log(), exp(), psi();
+static double hyt2f1();
+static double hys2f1();
+double hyp2f1();
+#endif
+extern double MAXNUM, MACHEP;
+
+double hyp2f1( a, b, c, x )
+double a, b, c, x;
+{
+double d, d1, d2, e;
+double p, q, r, s, y, ax;
+double ia, ib, ic, id, err;
+int flag, i, aid;
+
+err = 0.0;
+ax = fabs(x);
+s = 1.0 - x;
+flag = 0;
+ia = round(a); /* nearest integer to a */
+ib = round(b);
+
+if( a <= 0 )
+	{
+	if( fabs(a-ia) < EPS )		/* a is a negative integer */
+		flag |= 1;
+	}
+
+if( b <= 0 )
+	{
+	if( fabs(b-ib) < EPS )		/* b is a negative integer */
+		flag |= 2;
+	}
+
+if( ax < 1.0 )
+	{
+	if( fabs(b-c) < EPS )		/* b = c */
+		{
+		y = pow( s, -a );	/* s to the -a power */
+		goto hypdon;
+		}
+	if( fabs(a-c) < EPS )		/* a = c */
+		{
+		y = pow( s, -b );	/* s to the -b power */
+		goto hypdon;
+		}
+	}
+
+
+
+if( c <= 0.0 )
+	{
+	ic = round(c); 	/* nearest integer to c */
+	if( fabs(c-ic) < EPS )		/* c is a negative integer */
+		{
+		/* check if termination before explosion */
+		if( (flag & 1) && (ia > ic) )
+			goto hypok;
+		if( (flag & 2) && (ib > ic) )
+			goto hypok;
+		goto hypdiv;
+		}
+	}
+
+if( flag )			/* function is a polynomial */
+	goto hypok;
+
+if( ax > 1.0 )			/* series diverges	*/
+	goto hypdiv;
+
+p = c - a;
+ia = round(p); /* nearest integer to c-a */
+if( (ia <= 0.0) && (fabs(p-ia) < EPS) )	/* negative int c - a */
+	flag |= 4;
+
+r = c - b;
+ib = round(r); /* nearest integer to c-b */
+if( (ib <= 0.0) && (fabs(r-ib) < EPS) )	/* negative int c - b */
+	flag |= 8;
+
+d = c - a - b;
+id = round(d); /* nearest integer to d */
+q = fabs(d-id);
+
+/* Thanks to Christian Burger <BURGER@DMRHRZ11.HRZ.Uni-Marburg.DE>
+ * for reporting a bug here.  */
+if( fabs(ax-1.0) < EPS )			/* |x| == 1.0	*/
+	{
+	if( x > 0.0 )
+		{
+		if( flag & 12 ) /* negative int c-a or c-b */
+			{
+			if( d >= 0.0 )
+				goto hypf;
+			else
+				goto hypdiv;
+			}
+		if( d <= 0.0 )
+			goto hypdiv;
+		y = gamma(c)*gamma(d)/(gamma(p)*gamma(r));
+		goto hypdon;
+		}
+
+	if( d <= -1.0 )
+		goto hypdiv;
+
+	}
+
+/* Conditionally make d > 0 by recurrence on c
+ * AMS55 #15.2.27
+ */
+if( d < 0.0 )
+	{
+/* Try the power series first */
+	y = hyt2f1( a, b, c, x, &err );
+	if( err < ETHRESH )
+		goto hypdon;
+/* Apply the recurrence if power series fails */
+	err = 0.0;
+	aid = 2 - id;
+	e = c + aid;
+	d2 = hyp2f1(a,b,e,x);
+	d1 = hyp2f1(a,b,e+1.0,x);
+	q = a + b + 1.0;
+	for( i=0; i<aid; i++ )
+		{
+		r = e - 1.0;
+		y = (e*(r-(2.0*e-q)*x)*d2 + (e-a)*(e-b)*x*d1)/(e*r*s);
+		e = r;
+		d1 = d2;
+		d2 = y;
+		}
+	goto hypdon;
+	}
+
+
+if( flag & 12 )
+	goto hypf; /* negative integer c-a or c-b */
+
+hypok:
+y = hyt2f1( a, b, c, x, &err );
+
+
+hypdon:
+if( err > ETHRESH )
+	{
+	mtherr( "hyp2f1", PLOSS );
+/*	printf( "Estimated err = %.2e\n", err ); */
+	}
+return(y);
+
+/* The transformation for c-a or c-b negative integer
+ * AMS55 #15.3.3
+ */
+hypf:
+y = pow( s, d ) * hys2f1( c-a, c-b, c, x, &err );
+goto hypdon;
+
+/* The alarm exit */
+hypdiv:
+mtherr( "hyp2f1", OVERFLOW );
+return( MAXNUM );
+}
+
+
+
+
+
+
+/* Apply transformations for |x| near 1
+ * then call the power series
+ */
+static double hyt2f1( a, b, c, x, loss )
+double a, b, c, x;
+double *loss;
+{
+double p, q, r, s, t, y, d, err, err1;
+double ax, id, d1, d2, e, y1;
+int i, aid;
+
+err = 0.0;
+s = 1.0 - x;
+if( x < -0.5 )
+	{
+	if( b > a )
+		y = pow( s, -a ) * hys2f1( a, c-b, c, -x/s, &err );
+
+	else
+		y = pow( s, -b ) * hys2f1( c-a, b, c, -x/s, &err );
+
+	goto done;
+	}
+
+d = c - a - b;
+id = round(d);	/* nearest integer to d */
+
+if( x > 0.9 )
+{
+if( fabs(d-id) > EPS ) /* test for integer c-a-b */
+	{
+/* Try the power series first */
+	y = hys2f1( a, b, c, x, &err );
+	if( err < ETHRESH )
+		goto done;
+/* If power series fails, then apply AMS55 #15.3.6 */
+	q = hys2f1( a, b, 1.0-d, s, &err );	
+	q *= gamma(d) /(gamma(c-a) * gamma(c-b));
+	r = pow(s,d) * hys2f1( c-a, c-b, d+1.0, s, &err1 );
+	r *= gamma(-d)/(gamma(a) * gamma(b));
+	y = q + r;
+
+	q = fabs(q); /* estimate cancellation error */
+	r = fabs(r);
+	if( q > r )
+		r = q;
+	err += err1 + (MACHEP*r)/y;
+
+	y *= gamma(c);
+	goto done;
+	}
+else
+	{
+/* Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12 */
+	if( id >= 0.0 )
+		{
+		e = d;
+		d1 = d;
+		d2 = 0.0;
+		aid = id;
+		}
+	else
+		{
+		e = -d;
+		d1 = 0.0;
+		d2 = d;
+		aid = -id;
+		}
+
+	ax = log(s);
+
+	/* sum for t = 0 */
+	y = psi(1.0) + psi(1.0+e) - psi(a+d1) - psi(b+d1) - ax;
+	y /= gamma(e+1.0);
+
+	p = (a+d1) * (b+d1) * s / gamma(e+2.0);	/* Poch for t=1 */
+	t = 1.0;
+	do
+		{
+		r = psi(1.0+t) + psi(1.0+t+e) - psi(a+t+d1)
+			- psi(b+t+d1) - ax;
+		q = p * r;
+		y += q;
+		p *= s * (a+t+d1) / (t+1.0);
+		p *= (b+t+d1) / (t+1.0+e);
+		t += 1.0;
+		}
+	while( fabs(q/y) > EPS );
+
+
+	if( id == 0.0 )
+		{
+		y *= gamma(c)/(gamma(a)*gamma(b));
+		goto psidon;
+		}
+
+	y1 = 1.0;
+
+	if( aid == 1 )
+		goto nosum;
+
+	t = 0.0;
+	p = 1.0;
+	for( i=1; i<aid; i++ )
+		{
+		r = 1.0-e+t;
+		p *= s * (a+t+d2) * (b+t+d2) / r;
+		t += 1.0;
+		p /= t;
+		y1 += p;
+		}
+nosum:
+	p = gamma(c);
+	y1 *= gamma(e) * p / (gamma(a+d1) * gamma(b+d1));
+
+	y *= p / (gamma(a+d2) * gamma(b+d2));
+	if( (aid & 1) != 0 )
+		y = -y;
+
+	q = pow( s, id );	/* s to the id power */
+	if( id > 0.0 )
+		y *= q;
+	else
+		y1 *= q;
+
+	y += y1;
+psidon:
+	goto done;
+	}
+
+}
+
+/* Use defining power series if no special cases */
+y = hys2f1( a, b, c, x, &err );
+
+done:
+*loss = err;
+return(y);
+}
+
+
+
+
+
+/* Defining power series expansion of Gauss hypergeometric function */
+
+static double hys2f1( a, b, c, x, loss )
+double a, b, c, x;
+double *loss; /* estimates loss of significance */
+{
+double f, g, h, k, m, s, u, umax;
+int i;
+
+i = 0;
+umax = 0.0;
+f = a;
+g = b;
+h = c;
+s = 1.0;
+u = 1.0;
+k = 0.0;
+do
+	{
+	if( fabs(h) < EPS )
+		{
+		*loss = 1.0;
+		return( MAXNUM );
+		}
+	m = k + 1.0;
+	u = u * ((f+k) * (g+k) * x / ((h+k) * m));
+	s += u;
+	k = fabs(u);  /* remember largest term summed */
+	if( k > umax )
+		umax = k;
+	k = m;
+	if( ++i > 10000 ) /* should never happen */
+		{
+		*loss = 1.0;
+		return(s);
+		}
+	}
+while( fabs(u/s) > MACHEP );
+
+/* return estimated relative error */
+*loss = (MACHEP*umax)/fabs(s) + (MACHEP*i);
+
+return(s);
+}

libm/double/hyperg.c

@@ -0,0 +1,386 @@
+/*							hyperg.c
+ *
+ *	Confluent hypergeometric function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, hyperg();
+ *
+ * y = hyperg( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the confluent hypergeometric function
+ *
+ *                          1           2
+ *                       a x    a(a+1) x
+ *   F ( a,b;x )  =  1 + ---- + --------- + ...
+ *  1 1                  b 1!   b(b+1) 2!
+ *
+ * Many higher transcendental functions are special cases of
+ * this power series.
+ *
+ * As is evident from the formula, b must not be a negative
+ * integer or zero unless a is an integer with 0 >= a > b.
+ *
+ * The routine attempts both a direct summation of the series
+ * and an asymptotic expansion.  In each case error due to
+ * roundoff, cancellation, and nonconvergence is estimated.
+ * The result with smaller estimated error is returned.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a, b, x), all three variables
+ * ranging from 0 to 30.
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         2000       1.2e-15     1.3e-16
+ qtst1:
+ 21800   max =  1.4200E-14   rms =  1.0841E-15  ave = -5.3640E-17 
+ ltstd:
+ 25500   max = 1.2759e-14   rms = 3.7155e-16  ave = 1.5384e-18 
+ *    IEEE      0,30        30000       1.8e-14     1.1e-15
+ *
+ * Larger errors can be observed when b is near a negative
+ * integer or zero.  Certain combinations of arguments yield
+ * serious cancellation error in the power series summation
+ * and also are not in the region of near convergence of the
+ * asymptotic series.  An error message is printed if the
+ * self-estimated relative error is greater than 1.0e-12.
+ *
+ */
+
+/*							hyperg.c */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef ANSIPROT
+extern double exp ( double );
+extern double log ( double );
+extern double gamma ( double );
+extern double lgam ( double );
+extern double fabs ( double );
+double hyp2f0 ( double, double, double, int, double * );
+static double hy1f1p(double, double, double, double *);
+static double hy1f1a(double, double, double, double *);
+double hyperg (double, double, double);
+#else
+double exp(), log(), gamma(), lgam(), fabs(), hyp2f0();
+static double hy1f1p();
+static double hy1f1a();
+double hyperg();
+#endif
+extern double MAXNUM, MACHEP;
+
+double hyperg( a, b, x)
+double a, b, x;
+{
+double asum, psum, acanc, pcanc, temp;
+
+/* See if a Kummer transformation will help */
+temp = b - a;
+if( fabs(temp) < 0.001 * fabs(a) )
+	return( exp(x) * hyperg( temp, b, -x )  );
+
+
+psum = hy1f1p( a, b, x, &pcanc );
+if( pcanc < 1.0e-15 )
+	goto done;
+
+
+/* try asymptotic series */
+
+asum = hy1f1a( a, b, x, &acanc );
+
+
+/* Pick the result with less estimated error */
+
+if( acanc < pcanc )
+	{
+	pcanc = acanc;
+	psum = asum;
+	}
+
+done:
+if( pcanc > 1.0e-12 )
+	mtherr( "hyperg", PLOSS );
+
+return( psum );
+}
+
+
+
+
+/* Power series summation for confluent hypergeometric function		*/
+
+
+static double hy1f1p( a, b, x, err )
+double a, b, x;
+double *err;
+{
+double n, a0, sum, t, u, temp;
+double an, bn, maxt, pcanc;
+
+
+/* set up for power series summation */
+an = a;
+bn = b;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+maxt = 0.0;
+
+
+while( t > MACHEP )
+	{
+	if( bn == 0 )			/* check bn first since if both	*/
+		{
+		mtherr( "hyperg", SING );
+		return( MAXNUM );	/* an and bn are zero it is	*/
+		}
+	if( an == 0 )			/* a singularity		*/
+		return( sum );
+	if( n > 200 )
+		goto pdone;
+	u = x * ( an / (bn * n) );
+
+	/* check for blowup */
+	temp = fabs(u);
+	if( (temp > 1.0 ) && (maxt > (MAXNUM/temp)) )
+		{
+		pcanc = 1.0;	/* estimate 100% error */
+		goto blowup;
+		}
+
+	a0 *= u;
+	sum += a0;
+	t = fabs(a0);
+	if( t > maxt )
+		maxt = t;
+/*
+	if( (maxt/fabs(sum)) > 1.0e17 )
+		{
+		pcanc = 1.0;
+		goto blowup;
+		}
+*/
+	an += 1.0;
+	bn += 1.0;
+	n += 1.0;
+	}
+
+pdone:
+
+/* estimate error due to roundoff and cancellation */
+if( sum != 0.0 )
+	maxt /= fabs(sum);
+maxt *= MACHEP; 	/* this way avoids multiply overflow */
+pcanc = fabs( MACHEP * n  +  maxt );
+
+blowup:
+
+*err = pcanc;
+
+return( sum );
+}
+
+
+/*							hy1f1a()	*/
+/* asymptotic formula for hypergeometric function:
+ *
+ *        (    -a                         
+ *  --    ( |z|                           
+ * |  (b) ( -------- 2f0( a, 1+a-b, -1/x )
+ *        (  --                           
+ *        ( |  (b-a)                      
+ *
+ *
+ *                                x    a-b                     )
+ *                               e  |x|                        )
+ *                             + -------- 2f0( b-a, 1-a, 1/x ) )
+ *                                --                           )
+ *                               |  (a)                        )
+ */
+
+static double hy1f1a( a, b, x, err )
+double a, b, x;
+double *err;
+{
+double h1, h2, t, u, temp, acanc, asum, err1, err2;
+
+if( x == 0 )
+	{
+	acanc = 1.0;
+	asum = MAXNUM;
+	goto adone;
+	}
+temp = log( fabs(x) );
+t = x + temp * (a-b);
+u = -temp * a;
+
+if( b > 0 )
+	{
+	temp = lgam(b);
+	t += temp;
+	u += temp;
+	}
+
+h1 = hyp2f0( a, a-b+1, -1.0/x, 1, &err1 );
+
+temp = exp(u) / gamma(b-a);
+h1 *= temp;
+err1 *= temp;
+
+h2 = hyp2f0( b-a, 1.0-a, 1.0/x, 2, &err2 );
+
+if( a < 0 )
+	temp = exp(t) / gamma(a);
+else
+	temp = exp( t - lgam(a) );
+
+h2 *= temp;
+err2 *= temp;
+
+if( x < 0.0 )
+	asum = h1;
+else
+	asum = h2;
+
+acanc = fabs(err1) + fabs(err2);
+
+
+if( b < 0 )
+	{
+	temp = gamma(b);
+	asum *= temp;
+	acanc *= fabs(temp);
+	}
+
+
+if( asum != 0.0 )
+	acanc /= fabs(asum);
+
+acanc *= 30.0;	/* fudge factor, since error of asymptotic formula
+		 * often seems this much larger than advertised */
+
+adone:
+
+
+*err = acanc;
+return( asum );
+}
+
+/*							hyp2f0()	*/
+
+double hyp2f0( a, b, x, type, err )
+double a, b, x;
+int type;	/* determines what converging factor to use */
+double *err;
+{
+double a0, alast, t, tlast, maxt;
+double n, an, bn, u, sum, temp;
+
+an = a;
+bn = b;
+a0 = 1.0e0;
+alast = 1.0e0;
+sum = 0.0;
+n = 1.0e0;
+t = 1.0e0;
+tlast = 1.0e9;
+maxt = 0.0;
+
+do
+	{
+	if( an == 0 )
+		goto pdone;
+	if( bn == 0 )
+		goto pdone;
+
+	u = an * (bn * x / n);
+
+	/* check for blowup */
+	temp = fabs(u);
+	if( (temp > 1.0 ) && (maxt > (MAXNUM/temp)) )
+		goto error;
+
+	a0 *= u;
+	t = fabs(a0);
+
+	/* terminating condition for asymptotic series */
+	if( t > tlast )
+		goto ndone;
+
+	tlast = t;
+	sum += alast;	/* the sum is one term behind */
+	alast = a0;
+
+	if( n > 200 )
+		goto ndone;
+
+	an += 1.0e0;
+	bn += 1.0e0;
+	n += 1.0e0;
+	if( t > maxt )
+		maxt = t;
+	}
+while( t > MACHEP );
+
+
+pdone:	/* series converged! */
+
+/* estimate error due to roundoff and cancellation */
+*err = fabs(  MACHEP * (n + maxt)  );
+
+alast = a0;
+goto done;
+
+ndone:	/* series did not converge */
+
+/* The following "Converging factors" are supposed to improve accuracy,
+ * but do not actually seem to accomplish very much. */
+
+n -= 1.0;
+x = 1.0/x;
+
+switch( type )	/* "type" given as subroutine argument */
+{
+case 1:
+	alast *= ( 0.5 + (0.125 + 0.25*b - 0.5*a + 0.25*x - 0.25*n)/x );
+	break;
+
+case 2:
+	alast *= 2.0/3.0 - b + 2.0*a + x - n;
+	break;
+
+default:
+	;
+}
+
+/* estimate error due to roundoff, cancellation, and nonconvergence */
+*err = MACHEP * (n + maxt)  +  fabs ( a0 );
+
+
+done:
+sum += alast;
+return( sum );
+
+/* series blew up: */
+error:
+*err = MAXNUM;
+mtherr( "hyperg", TLOSS );
+return( sum );
+}

libm/double/i0.c

@@ -0,0 +1,397 @@
+/*							i0.c
+ *
+ *	Modified Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0();
+ *
+ * y = i0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order zero of the
+ * argument.
+ *
+ * The function is defined as i0(x) = j0( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         6000       8.2e-17     1.9e-17
+ *    IEEE      0,30        30000       5.8e-16     1.4e-16
+ *
+ */
+/*							i0e.c
+ *
+ *	Modified Bessel function of order zero,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0e();
+ *
+ * y = i0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,30        30000       5.4e-16     1.2e-16
+ * See i0().
+ *
+ */
+
+/*							i0.c		*/
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for exp(-x) I0(x)
+ * in the interval [0,8].
+ *
+ * lim(x->0){ exp(-x) I0(x) } = 1.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+-4.41534164647933937950E-18,
+ 3.33079451882223809783E-17,
+-2.43127984654795469359E-16,
+ 1.71539128555513303061E-15,
+-1.16853328779934516808E-14,
+ 7.67618549860493561688E-14,
+-4.85644678311192946090E-13,
+ 2.95505266312963983461E-12,
+-1.72682629144155570723E-11,
+ 9.67580903537323691224E-11,
+-5.18979560163526290666E-10,
+ 2.65982372468238665035E-9,
+-1.30002500998624804212E-8,
+ 6.04699502254191894932E-8,
+-2.67079385394061173391E-7,
+ 1.11738753912010371815E-6,
+-4.41673835845875056359E-6,
+ 1.64484480707288970893E-5,
+-5.75419501008210370398E-5,
+ 1.88502885095841655729E-4,
+-5.76375574538582365885E-4,
+ 1.63947561694133579842E-3,
+-4.32430999505057594430E-3,
+ 1.05464603945949983183E-2,
+-2.37374148058994688156E-2,
+ 4.93052842396707084878E-2,
+-9.49010970480476444210E-2,
+ 1.71620901522208775349E-1,
+-3.04682672343198398683E-1,
+ 6.76795274409476084995E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0121642,0162671,0004646,0103567,
+0022431,0115424,0135755,0026104,
+0123214,0023533,0110365,0156635,
+0023767,0033304,0117662,0172716,
+0124522,0100426,0012277,0157531,
+0025254,0155062,0054461,0030465,
+0126010,0131143,0013560,0153604,
+0026517,0170577,0006336,0114437,
+0127227,0162253,0152243,0052734,
+0027724,0142766,0061641,0160200,
+0130416,0123760,0116564,0125262,
+0031066,0144035,0021246,0054641,
+0131537,0053664,0060131,0102530,
+0032201,0155664,0165153,0020652,
+0132617,0061434,0074423,0176145,
+0033225,0174444,0136147,0122542,
+0133624,0031576,0056453,0020470,
+0034211,0175305,0172321,0041314,
+0134561,0054462,0147040,0165315,
+0035105,0124333,0120203,0162532,
+0135427,0013750,0174257,0055221,
+0035726,0161654,0050220,0100162,
+0136215,0131361,0000325,0041110,
+0036454,0145417,0117357,0017352,
+0136702,0072367,0104415,0133574,
+0037111,0172126,0072505,0014544,
+0137302,0055601,0120550,0033523,
+0037457,0136543,0136544,0043002,
+0137633,0177536,0001276,0066150,
+0040055,0041164,0100655,0010521
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0xd0ef,0x2134,0x5cb7,0xbc54,
+0xa589,0x977d,0x3362,0x3c83,
+0xbbb4,0x721e,0x84eb,0xbcb1,
+0x5eba,0x93f6,0xe6d8,0x3cde,
+0xfbeb,0xc297,0x5022,0xbd0a,
+0x2627,0x4b26,0x9b46,0x3d35,
+0x1af0,0x62ee,0x164c,0xbd61,
+0xd324,0xe19b,0xfe2f,0x3d89,
+0x6abc,0x7a94,0xfc95,0xbdb2,
+0x3c10,0xcc74,0x98be,0x3dda,
+0x9556,0x13ae,0xd4fe,0xbe01,
+0xcb34,0xa454,0xd903,0x3e26,
+0x30ab,0x8c0b,0xeaf6,0xbe4b,
+0x6435,0x9d4d,0x3b76,0x3e70,
+0x7f8d,0x8f22,0xec63,0xbe91,
+0xf4ac,0x978c,0xbf24,0x3eb2,
+0x6427,0xcba5,0x866f,0xbed2,
+0x2859,0xbe9a,0x3f58,0x3ef1,
+0x1d5a,0x59c4,0x2b26,0xbf0e,
+0x7cab,0x7410,0xb51b,0x3f28,
+0xeb52,0x1f15,0xe2fd,0xbf42,
+0x100e,0x8a12,0xdc75,0x3f5a,
+0xa849,0x201a,0xb65e,0xbf71,
+0xe3dd,0xf3dd,0x9961,0x3f85,
+0xb6f0,0xf121,0x4e9e,0xbf98,
+0xa32d,0xcea8,0x3e8a,0x3fa9,
+0x06ea,0x342d,0x4b70,0xbfb8,
+0x88c0,0x77ac,0xf7ac,0x3fc5,
+0xcd8d,0xc057,0x7feb,0xbfd3,
+0xa22a,0x9035,0xa84e,0x3fe5,
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0xbc54,0x5cb7,0x2134,0xd0ef,
+0x3c83,0x3362,0x977d,0xa589,
+0xbcb1,0x84eb,0x721e,0xbbb4,
+0x3cde,0xe6d8,0x93f6,0x5eba,
+0xbd0a,0x5022,0xc297,0xfbeb,
+0x3d35,0x9b46,0x4b26,0x2627,
+0xbd61,0x164c,0x62ee,0x1af0,
+0x3d89,0xfe2f,0xe19b,0xd324,
+0xbdb2,0xfc95,0x7a94,0x6abc,
+0x3dda,0x98be,0xcc74,0x3c10,
+0xbe01,0xd4fe,0x13ae,0x9556,
+0x3e26,0xd903,0xa454,0xcb34,
+0xbe4b,0xeaf6,0x8c0b,0x30ab,
+0x3e70,0x3b76,0x9d4d,0x6435,
+0xbe91,0xec63,0x8f22,0x7f8d,
+0x3eb2,0xbf24,0x978c,0xf4ac,
+0xbed2,0x866f,0xcba5,0x6427,
+0x3ef1,0x3f58,0xbe9a,0x2859,
+0xbf0e,0x2b26,0x59c4,0x1d5a,
+0x3f28,0xb51b,0x7410,0x7cab,
+0xbf42,0xe2fd,0x1f15,0xeb52,
+0x3f5a,0xdc75,0x8a12,0x100e,
+0xbf71,0xb65e,0x201a,0xa849,
+0x3f85,0x9961,0xf3dd,0xe3dd,
+0xbf98,0x4e9e,0xf121,0xb6f0,
+0x3fa9,0x3e8a,0xcea8,0xa32d,
+0xbfb8,0x4b70,0x342d,0x06ea,
+0x3fc5,0xf7ac,0x77ac,0x88c0,
+0xbfd3,0x7feb,0xc057,0xcd8d,
+0x3fe5,0xa84e,0x9035,0xa22a
+};
+#endif
+
+
+/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
+ * in the inverted interval [8,infinity].
+ *
+ * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
+ */
+
+#ifdef UNK
+static double B[] =
+{
+-7.23318048787475395456E-18,
+-4.83050448594418207126E-18,
+ 4.46562142029675999901E-17,
+ 3.46122286769746109310E-17,
+-2.82762398051658348494E-16,
+-3.42548561967721913462E-16,
+ 1.77256013305652638360E-15,
+ 3.81168066935262242075E-15,
+-9.55484669882830764870E-15,
+-4.15056934728722208663E-14,
+ 1.54008621752140982691E-14,
+ 3.85277838274214270114E-13,
+ 7.18012445138366623367E-13,
+-1.79417853150680611778E-12,
+-1.32158118404477131188E-11,
+-3.14991652796324136454E-11,
+ 1.18891471078464383424E-11,
+ 4.94060238822496958910E-10,
+ 3.39623202570838634515E-9,
+ 2.26666899049817806459E-8,
+ 2.04891858946906374183E-7,
+ 2.89137052083475648297E-6,
+ 6.88975834691682398426E-5,
+ 3.36911647825569408990E-3,
+ 8.04490411014108831608E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0122005,0066672,0123124,0054311,
+0121662,0033323,0030214,0104602,
+0022515,0170300,0113314,0020413,
+0022437,0117350,0035402,0007146,
+0123243,0000135,0057220,0177435,
+0123305,0073476,0144106,0170702,
+0023777,0071755,0017527,0154373,
+0024211,0052214,0102247,0033270,
+0124454,0017763,0171453,0012322,
+0125072,0166316,0075505,0154616,
+0024612,0133770,0065376,0025045,
+0025730,0162143,0056036,0001632,
+0026112,0015077,0150464,0063542,
+0126374,0101030,0014274,0065457,
+0127150,0077271,0125763,0157617,
+0127412,0104350,0040713,0120445,
+0027121,0023765,0057500,0001165,
+0030407,0147146,0003643,0075644,
+0031151,0061445,0044422,0156065,
+0031702,0132224,0003266,0125551,
+0032534,0000076,0147153,0005555,
+0033502,0004536,0004016,0026055,
+0034620,0076433,0142314,0171215,
+0036134,0146145,0013454,0101104,
+0040115,0171425,0062500,0047133
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0x8b19,0x54ca,0xadb7,0xbc60,
+0x9130,0x6611,0x46da,0xbc56,
+0x8421,0x12d9,0xbe18,0x3c89,
+0x41cd,0x0760,0xf3dd,0x3c83,
+0x1fe4,0xabd2,0x600b,0xbcb4,
+0xde38,0xd908,0xaee7,0xbcb8,
+0xfb1f,0xa3ea,0xee7d,0x3cdf,
+0xe6d7,0x9094,0x2a91,0x3cf1,
+0x629a,0x7e65,0x83fe,0xbd05,
+0xbb32,0xcf68,0x5d99,0xbd27,
+0xc545,0x0d5f,0x56ff,0x3d11,
+0xc073,0x6b83,0x1c8c,0x3d5b,
+0x8cec,0xfa26,0x4347,0x3d69,
+0x8d66,0x0317,0x9043,0xbd7f,
+0x7bf2,0x357e,0x0fd7,0xbdad,
+0x7425,0x0839,0x511d,0xbdc1,
+0x004f,0xabe8,0x24fe,0x3daa,
+0x6f75,0xc0f4,0xf9cc,0x3e00,
+0x5b87,0xa922,0x2c64,0x3e2d,
+0xd56d,0x80d6,0x5692,0x3e58,
+0x616e,0xd9cd,0x8007,0x3e8b,
+0xc586,0xc101,0x412b,0x3ec8,
+0x9e52,0x7899,0x0fa3,0x3f12,
+0x9049,0xa2e5,0x998c,0x3f6b,
+0x09cb,0xaca8,0xbe62,0x3fe9
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0xbc60,0xadb7,0x54ca,0x8b19,
+0xbc56,0x46da,0x6611,0x9130,
+0x3c89,0xbe18,0x12d9,0x8421,
+0x3c83,0xf3dd,0x0760,0x41cd,
+0xbcb4,0x600b,0xabd2,0x1fe4,
+0xbcb8,0xaee7,0xd908,0xde38,
+0x3cdf,0xee7d,0xa3ea,0xfb1f,
+0x3cf1,0x2a91,0x9094,0xe6d7,
+0xbd05,0x83fe,0x7e65,0x629a,
+0xbd27,0x5d99,0xcf68,0xbb32,
+0x3d11,0x56ff,0x0d5f,0xc545,
+0x3d5b,0x1c8c,0x6b83,0xc073,
+0x3d69,0x4347,0xfa26,0x8cec,
+0xbd7f,0x9043,0x0317,0x8d66,
+0xbdad,0x0fd7,0x357e,0x7bf2,
+0xbdc1,0x511d,0x0839,0x7425,
+0x3daa,0x24fe,0xabe8,0x004f,
+0x3e00,0xf9cc,0xc0f4,0x6f75,
+0x3e2d,0x2c64,0xa922,0x5b87,
+0x3e58,0x5692,0x80d6,0xd56d,
+0x3e8b,0x8007,0xd9cd,0x616e,
+0x3ec8,0x412b,0xc101,0xc586,
+0x3f12,0x0fa3,0x7899,0x9e52,
+0x3f6b,0x998c,0xa2e5,0x9049,
+0x3fe9,0xbe62,0xaca8,0x09cb
+};
+#endif
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double sqrt ( double );
+#else
+double chbevl(), exp(), sqrt();
+#endif
+
+double i0(x)
+double x;
+{
+double y;
+
+if( x < 0 )
+	x = -x;
+if( x <= 8.0 )
+	{
+	y = (x/2.0) - 2.0;
+	return( exp(x) * chbevl( y, A, 30 ) );
+	}
+
+return(  exp(x) * chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
+
+}
+
+
+
+
+double i0e( x )
+double x;
+{
+double y;
+
+if( x < 0 )
+	x = -x;
+if( x <= 8.0 )
+	{
+	y = (x/2.0) - 2.0;
+	return( chbevl( y, A, 30 ) );
+	}
+
+return(  chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
+
+}

libm/double/i1.c

@@ -0,0 +1,402 @@
+/*							i1.c
+ *
+ *	Modified Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1();
+ *
+ * y = i1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order one of the
+ * argument.
+ *
+ * The function is defined as i1(x) = -i j1( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        3400       1.2e-16     2.3e-17
+ *    IEEE      0, 30       30000       1.9e-15     2.1e-16
+ *
+ *
+ */
+/*							i1e.c
+ *
+ *	Modified Bessel function of order one,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1e();
+ *
+ * y = i1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order one of the argument.
+ *
+ * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 30       30000       2.0e-15     2.0e-16
+ * See i1().
+ *
+ */
+
+/*							i1.c 2		*/
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1985, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for exp(-x) I1(x) / x
+ * in the interval [0,8].
+ *
+ * lim(x->0){ exp(-x) I1(x) / x } = 1/2.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+ 2.77791411276104639959E-18,
+-2.11142121435816608115E-17,
+ 1.55363195773620046921E-16,
+-1.10559694773538630805E-15,
+ 7.60068429473540693410E-15,
+-5.04218550472791168711E-14,
+ 3.22379336594557470981E-13,
+-1.98397439776494371520E-12,
+ 1.17361862988909016308E-11,
+-6.66348972350202774223E-11,
+ 3.62559028155211703701E-10,
+-1.88724975172282928790E-9,
+ 9.38153738649577178388E-9,
+-4.44505912879632808065E-8,
+ 2.00329475355213526229E-7,
+-8.56872026469545474066E-7,
+ 3.47025130813767847674E-6,
+-1.32731636560394358279E-5,
+ 4.78156510755005422638E-5,
+-1.61760815825896745588E-4,
+ 5.12285956168575772895E-4,
+-1.51357245063125314899E-3,
+ 4.15642294431288815669E-3,
+-1.05640848946261981558E-2,
+ 2.47264490306265168283E-2,
+-5.29459812080949914269E-2,
+ 1.02643658689847095384E-1,
+-1.76416518357834055153E-1,
+ 2.52587186443633654823E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0021514,0174520,0060742,0000241,
+0122302,0137206,0016120,0025663,
+0023063,0017437,0026235,0176536,
+0123637,0052523,0170150,0125632,
+0024410,0165770,0030251,0044134,
+0125143,0012160,0162170,0054727,
+0025665,0075702,0035716,0145247,
+0126413,0116032,0176670,0015462,
+0027116,0073425,0110351,0105242,
+0127622,0104034,0137530,0037364,
+0030307,0050645,0120776,0175535,
+0131001,0130331,0043523,0037455,
+0031441,0026160,0010712,0100174,
+0132076,0164761,0022706,0017500,
+0032527,0015045,0115076,0104076,
+0133146,0001714,0015434,0144520,
+0033550,0161166,0124215,0077050,
+0134136,0127715,0143365,0157170,
+0034510,0106652,0013070,0064130,
+0135051,0117126,0117264,0123761,
+0035406,0045355,0133066,0175751,
+0135706,0061420,0054746,0122440,
+0036210,0031232,0047235,0006640,
+0136455,0012373,0144235,0011523,
+0036712,0107437,0036731,0015111,
+0137130,0156742,0115744,0172743,
+0037322,0033326,0124667,0124740,
+0137464,0123210,0021510,0144556,
+0037601,0051433,0111123,0177721
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0x4014,0x0c3c,0x9f2a,0x3c49,
+0x0576,0xc38a,0x57d0,0xbc78,
+0xbfac,0xe593,0x63e3,0x3ca6,
+0x1573,0x7e0d,0xeaaa,0xbcd3,
+0x290c,0x0615,0x1d7f,0x3d01,
+0x0b3b,0x1c8f,0x628e,0xbd2c,
+0xd955,0x4779,0xaf78,0x3d56,
+0x0366,0x5fb7,0x7383,0xbd81,
+0x3154,0xb21d,0xcee2,0x3da9,
+0x07de,0x97eb,0x5103,0xbdd2,
+0xdf6c,0xb43f,0xea34,0x3df8,
+0x67e6,0x28ea,0x361b,0xbe20,
+0x5010,0x0239,0x258e,0x3e44,
+0xc3e8,0x24b8,0xdd3e,0xbe67,
+0xd108,0xb347,0xe344,0x3e8a,
+0x992a,0x8363,0xc079,0xbeac,
+0xafc5,0xd511,0x1c4e,0x3ecd,
+0xbbcf,0xb8de,0xd5f9,0xbeeb,
+0x0d0b,0x42c7,0x11b5,0x3f09,
+0x94fe,0xd3d6,0x33ca,0xbf25,
+0xdf7d,0xb6c6,0xc95d,0x3f40,
+0xd4a4,0x0b3c,0xcc62,0xbf58,
+0xa1b4,0x49d3,0x0653,0x3f71,
+0xa26a,0x7913,0xa29f,0xbf85,
+0x2349,0xe7bb,0x51e3,0x3f99,
+0x9ebc,0x537c,0x1bbc,0xbfab,
+0xf53c,0xd536,0x46da,0x3fba,
+0x192e,0x0469,0x94d1,0xbfc6,
+0x7ffa,0x724a,0x2a63,0x3fd0
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0x3c49,0x9f2a,0x0c3c,0x4014,
+0xbc78,0x57d0,0xc38a,0x0576,
+0x3ca6,0x63e3,0xe593,0xbfac,
+0xbcd3,0xeaaa,0x7e0d,0x1573,
+0x3d01,0x1d7f,0x0615,0x290c,
+0xbd2c,0x628e,0x1c8f,0x0b3b,
+0x3d56,0xaf78,0x4779,0xd955,
+0xbd81,0x7383,0x5fb7,0x0366,
+0x3da9,0xcee2,0xb21d,0x3154,
+0xbdd2,0x5103,0x97eb,0x07de,
+0x3df8,0xea34,0xb43f,0xdf6c,
+0xbe20,0x361b,0x28ea,0x67e6,
+0x3e44,0x258e,0x0239,0x5010,
+0xbe67,0xdd3e,0x24b8,0xc3e8,
+0x3e8a,0xe344,0xb347,0xd108,
+0xbeac,0xc079,0x8363,0x992a,
+0x3ecd,0x1c4e,0xd511,0xafc5,
+0xbeeb,0xd5f9,0xb8de,0xbbcf,
+0x3f09,0x11b5,0x42c7,0x0d0b,
+0xbf25,0x33ca,0xd3d6,0x94fe,
+0x3f40,0xc95d,0xb6c6,0xdf7d,
+0xbf58,0xcc62,0x0b3c,0xd4a4,
+0x3f71,0x0653,0x49d3,0xa1b4,
+0xbf85,0xa29f,0x7913,0xa26a,
+0x3f99,0x51e3,0xe7bb,0x2349,
+0xbfab,0x1bbc,0x537c,0x9ebc,
+0x3fba,0x46da,0xd536,0xf53c,
+0xbfc6,0x94d1,0x0469,0x192e,
+0x3fd0,0x2a63,0x724a,0x7ffa
+};
+#endif
+
+/*							i1.c	*/
+
+/* Chebyshev coefficients for exp(-x) sqrt(x) I1(x)
+ * in the inverted interval [8,infinity].
+ *
+ * lim(x->inf){ exp(-x) sqrt(x) I1(x) } = 1/sqrt(2pi).
+ */
+
+#ifdef UNK
+static double B[] =
+{
+ 7.51729631084210481353E-18,
+ 4.41434832307170791151E-18,
+-4.65030536848935832153E-17,
+-3.20952592199342395980E-17,
+ 2.96262899764595013876E-16,
+ 3.30820231092092828324E-16,
+-1.88035477551078244854E-15,
+-3.81440307243700780478E-15,
+ 1.04202769841288027642E-14,
+ 4.27244001671195135429E-14,
+-2.10154184277266431302E-14,
+-4.08355111109219731823E-13,
+-7.19855177624590851209E-13,
+ 2.03562854414708950722E-12,
+ 1.41258074366137813316E-11,
+ 3.25260358301548823856E-11,
+-1.89749581235054123450E-11,
+-5.58974346219658380687E-10,
+-3.83538038596423702205E-9,
+-2.63146884688951950684E-8,
+-2.51223623787020892529E-7,
+-3.88256480887769039346E-6,
+-1.10588938762623716291E-4,
+-9.76109749136146840777E-3,
+ 7.78576235018280120474E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0022012,0125555,0115227,0043456,
+0021642,0156127,0052075,0145203,
+0122526,0072435,0111231,0011664,
+0122424,0001544,0161671,0114403,
+0023252,0144257,0163532,0142121,
+0023276,0132162,0174045,0013204,
+0124007,0077154,0057046,0110517,
+0124211,0066650,0116127,0157073,
+0024473,0133413,0130551,0107504,
+0025100,0064741,0032631,0040364,
+0124675,0045101,0071551,0012400,
+0125745,0161054,0071637,0011247,
+0126112,0117410,0035525,0122231,
+0026417,0037237,0131034,0176427,
+0027170,0100373,0024742,0025725,
+0027417,0006417,0105303,0141446,
+0127246,0163716,0121202,0060137,
+0130431,0123122,0120436,0166000,
+0131203,0144134,0153251,0124500,
+0131742,0005234,0122732,0033006,
+0132606,0157751,0072362,0121031,
+0133602,0043372,0047120,0015626,
+0134747,0165774,0001125,0046462,
+0136437,0166402,0117746,0155137,
+0040107,0050305,0125330,0124241
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0xe8e6,0xb352,0x556d,0x3c61,
+0xb950,0xea87,0x5b8a,0x3c54,
+0x2277,0xb253,0xcea3,0xbc8a,
+0x3320,0x9c77,0x806c,0xbc82,
+0x588a,0xfceb,0x5915,0x3cb5,
+0xa2d1,0x5f04,0xd68e,0x3cb7,
+0xd22a,0x8bc4,0xefcd,0xbce0,
+0xfbc7,0x138a,0x2db5,0xbcf1,
+0x31e8,0x762d,0x76e1,0x3d07,
+0x281e,0x26b3,0x0d3c,0x3d28,
+0x22a0,0x2e6d,0xa948,0xbd17,
+0xe255,0x8e73,0xbc45,0xbd5c,
+0xb493,0x076a,0x53e1,0xbd69,
+0x9fa3,0xf643,0xe7d3,0x3d81,
+0x457b,0x653c,0x101f,0x3daf,
+0x7865,0xf158,0xe1a1,0x3dc1,
+0x4c0c,0xd450,0xdcf9,0xbdb4,
+0xdd80,0x5423,0x34ca,0xbe03,
+0x3528,0x9ad5,0x790b,0xbe30,
+0x46c1,0x94bb,0x4153,0xbe5c,
+0x5443,0x2e9e,0xdbfd,0xbe90,
+0x0373,0x49ca,0x48df,0xbed0,
+0xa9a6,0x804a,0xfd7f,0xbf1c,
+0xdb4c,0x53fc,0xfda0,0xbf83,
+0x1514,0xb55b,0xea18,0x3fe8
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0x3c61,0x556d,0xb352,0xe8e6,
+0x3c54,0x5b8a,0xea87,0xb950,
+0xbc8a,0xcea3,0xb253,0x2277,
+0xbc82,0x806c,0x9c77,0x3320,
+0x3cb5,0x5915,0xfceb,0x588a,
+0x3cb7,0xd68e,0x5f04,0xa2d1,
+0xbce0,0xefcd,0x8bc4,0xd22a,
+0xbcf1,0x2db5,0x138a,0xfbc7,
+0x3d07,0x76e1,0x762d,0x31e8,
+0x3d28,0x0d3c,0x26b3,0x281e,
+0xbd17,0xa948,0x2e6d,0x22a0,
+0xbd5c,0xbc45,0x8e73,0xe255,
+0xbd69,0x53e1,0x076a,0xb493,
+0x3d81,0xe7d3,0xf643,0x9fa3,
+0x3daf,0x101f,0x653c,0x457b,
+0x3dc1,0xe1a1,0xf158,0x7865,
+0xbdb4,0xdcf9,0xd450,0x4c0c,
+0xbe03,0x34ca,0x5423,0xdd80,
+0xbe30,0x790b,0x9ad5,0x3528,
+0xbe5c,0x4153,0x94bb,0x46c1,
+0xbe90,0xdbfd,0x2e9e,0x5443,
+0xbed0,0x48df,0x49ca,0x0373,
+0xbf1c,0xfd7f,0x804a,0xa9a6,
+0xbf83,0xfda0,0x53fc,0xdb4c,
+0x3fe8,0xea18,0xb55b,0x1514
+};
+#endif
+
+/*							i1.c	*/
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double sqrt ( double );
+extern double fabs ( double );
+#else
+double chbevl(), exp(), sqrt(), fabs();
+#endif
+
+double i1(x)
+double x;
+{ 
+double y, z;
+
+z = fabs(x);
+if( z <= 8.0 )
+	{
+	y = (z/2.0) - 2.0;
+	z = chbevl( y, A, 29 ) * z * exp(z);
+	}
+else
+	{
+	z = exp(z) * chbevl( 32.0/z - 2.0, B, 25 ) / sqrt(z);
+	}
+if( x < 0.0 )
+	z = -z;
+return( z );
+}
+
+/*							i1e()	*/
+
+double i1e( x )
+double x;
+{ 
+double y, z;
+
+z = fabs(x);
+if( z <= 8.0 )
+	{
+	y = (z/2.0) - 2.0;
+	z = chbevl( y, A, 29 ) * z;
+	}
+else
+	{
+	z = chbevl( 32.0/z - 2.0, B, 25 ) / sqrt(z);
+	}
+if( x < 0.0 )
+	z = -z;
+return( z );
+}

libm/double/igam.c

@@ -0,0 +1,210 @@
+/*							igam.c
+ *
+ *	Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igam();
+ *
+ * y = igam( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *                           x
+ *                            -
+ *                   1       | |  -t  a-1
+ *  igam(a,x)  =   -----     |   e   t   dt.
+ *                  -      | |
+ *                 | (a)    -
+ *                           0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,30       200000       3.6e-14     2.9e-15
+ *    IEEE      0,100      300000       9.9e-14     1.5e-14
+ */
+/*							igamc()
+ *
+ *	Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igamc();
+ *
+ * y = igamc( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ *  igamc(a,x)   =   1 - igam(a,x)
+ *
+ *                            inf.
+ *                              -
+ *                     1       | |  -t  a-1
+ *               =   -----     |   e   t   dt.
+ *                    -      | |
+ *                   | (a)    -
+ *                             x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, x.
+ *                a         x                      Relative error:
+ * arithmetic   domain   domain     # trials      peak         rms
+ *    IEEE     0.5,100   0,100      200000       1.9e-14     1.7e-15
+ *    IEEE     0.01,0.5  0,100      200000       1.4e-13     1.6e-15
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1985, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double lgam ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double fabs ( double );
+extern double igam ( double, double );
+extern double igamc ( double, double );
+#else
+double lgam(), exp(), log(), fabs(), igam(), igamc();
+#endif
+
+extern double MACHEP, MAXLOG;
+static double big = 4.503599627370496e15;
+static double biginv =  2.22044604925031308085e-16;
+
+double igamc( a, x )
+double a, x;
+{
+double ans, ax, c, yc, r, t, y, z;
+double pk, pkm1, pkm2, qk, qkm1, qkm2;
+
+if( (x <= 0) || ( a <= 0) )
+	return( 1.0 );
+
+if( (x < 1.0) || (x < a) )
+	return( 1.0 - igam(a,x) );
+
+ax = a * log(x) - x - lgam(a);
+if( ax < -MAXLOG )
+	{
+	mtherr( "igamc", UNDERFLOW );
+	return( 0.0 );
+	}
+ax = exp(ax);
+
+/* continued fraction */
+y = 1.0 - a;
+z = x + y + 1.0;
+c = 0.0;
+pkm2 = 1.0;
+qkm2 = x;
+pkm1 = x + 1.0;
+qkm1 = z * x;
+ans = pkm1/qkm1;
+
+do
+	{
+	c += 1.0;
+	y += 1.0;
+	z += 2.0;
+	yc = y * c;
+	pk = pkm1 * z  -  pkm2 * yc;
+	qk = qkm1 * z  -  qkm2 * yc;
+	if( qk != 0 )
+		{
+		r = pk/qk;
+		t = fabs( (ans - r)/r );
+		ans = r;
+		}
+	else
+		t = 1.0;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+	if( fabs(pk) > big )
+		{
+		pkm2 *= biginv;
+		pkm1 *= biginv;
+		qkm2 *= biginv;
+		qkm1 *= biginv;
+		}
+	}
+while( t > MACHEP );
+
+return( ans * ax );
+}
+
+
+
+/* left tail of incomplete gamma function:
+ *
+ *          inf.      k
+ *   a  -x   -       x
+ *  x  e     >   ----------
+ *           -     -
+ *          k=0   | (a+k+1)
+ *
+ */
+
+double igam( a, x )
+double a, x;
+{
+double ans, ax, c, r;
+
+if( (x <= 0) || ( a <= 0) )
+	return( 0.0 );
+
+if( (x > 1.0) && (x > a ) )
+	return( 1.0 - igamc(a,x) );
+
+/* Compute  x**a * exp(-x) / gamma(a)  */
+ax = a * log(x) - x - lgam(a);
+if( ax < -MAXLOG )
+	{
+	mtherr( "igam", UNDERFLOW );
+	return( 0.0 );
+	}
+ax = exp(ax);
+
+/* power series */
+r = a;
+c = 1.0;
+ans = 1.0;
+
+do
+	{
+	r += 1.0;
+	c *= x/r;
+	ans += c;
+	}
+while( c/ans > MACHEP );
+
+return( ans * ax/a );
+}

libm/double/igami.c

@@ -0,0 +1,187 @@
+/*							igami()
+ *
+ *      Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, p, igami();
+ *
+ * x = igami( a, p );
+ *
+ * DESCRIPTION:
+ *
+ * Given p, the function finds x such that
+ *
+ *  igamc( a, x ) = p.
+ *
+ * Starting with the approximate value
+ *
+ *         3
+ *  x = a t
+ *
+ *  where
+ *
+ *  t = 1 - d - ndtri(p) sqrt(d)
+ * 
+ * and
+ *
+ *  d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - p = 0.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, p in the intervals indicated.
+ *
+ *                a        p                      Relative error:
+ * arithmetic   domain   domain     # trials      peak         rms
+ *    IEEE     0.5,100   0,0.5       100000       1.0e-14     1.7e-15
+ *    IEEE     0.01,0.5  0,0.5       100000       9.0e-14     3.4e-15
+ *    IEEE    0.5,10000  0,0.5        20000       2.3e-13     3.8e-14
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
+#ifdef ANSIPROT
+extern double igamc ( double, double );
+extern double ndtri ( double );
+extern double exp ( double );
+extern double fabs ( double );
+extern double log ( double );
+extern double sqrt ( double );
+extern double lgam ( double );
+#else
+double igamc(), ndtri(), exp(), fabs(), log(), sqrt(), lgam();
+#endif
+
+double igami( a, y0 )
+double a, y0;
+{
+double x0, x1, x, yl, yh, y, d, lgm, dithresh;
+int i, dir;
+
+/* bound the solution */
+x0 = MAXNUM;
+yl = 0;
+x1 = 0;
+yh = 1.0;
+dithresh = 5.0 * MACHEP;
+
+/* approximation to inverse function */
+d = 1.0/(9.0*a);
+y = ( 1.0 - d - ndtri(y0) * sqrt(d) );
+x = a * y * y * y;
+
+lgm = lgam(a);
+
+for( i=0; i<10; i++ )
+	{
+	if( x > x0 || x < x1 )
+		goto ihalve;
+	y = igamc(a,x);
+	if( y < yl || y > yh )
+		goto ihalve;
+	if( y < y0 )
+		{
+		x0 = x;
+		yl = y;
+		}
+	else
+		{
+		x1 = x;
+		yh = y;
+		}
+/* compute the derivative of the function at this point */
+	d = (a - 1.0) * log(x) - x - lgm;
+	if( d < -MAXLOG )
+		goto ihalve;
+	d = -exp(d);
+/* compute the step to the next approximation of x */
+	d = (y - y0)/d;
+	if( fabs(d/x) < MACHEP )
+		goto done;
+	x = x - d;
+	}
+
+/* Resort to interval halving if Newton iteration did not converge. */
+ihalve:
+
+d = 0.0625;
+if( x0 == MAXNUM )
+	{
+	if( x <= 0.0 )
+		x = 1.0;
+	while( x0 == MAXNUM )
+		{
+		x = (1.0 + d) * x;
+		y = igamc( a, x );
+		if( y < y0 )
+			{
+			x0 = x;
+			yl = y;
+			break;
+			}
+		d = d + d;
+		}
+	}
+d = 0.5;
+dir = 0;
+
+for( i=0; i<400; i++ )
+	{
+	x = x1  +  d * (x0 - x1);
+	y = igamc( a, x );
+	lgm = (x0 - x1)/(x1 + x0);
+	if( fabs(lgm) < dithresh )
+		break;
+	lgm = (y - y0)/y0;
+	if( fabs(lgm) < dithresh )
+		break;
+	if( x <= 0.0 )
+		break;
+	if( y >= y0 )
+		{
+		x1 = x;
+		yh = y;
+		if( dir < 0 )
+			{
+			dir = 0;
+			d = 0.5;
+			}
+		else if( dir > 1 )
+			d = 0.5 * d + 0.5; 
+		else
+			d = (y0 - yl)/(yh - yl);
+		dir += 1;
+		}
+	else
+		{
+		x0 = x;
+		yl = y;
+		if( dir > 0 )
+			{
+			dir = 0;
+			d = 0.5;
+			}
+		else if( dir < -1 )
+			d = 0.5 * d;
+		else
+			d = (y0 - yl)/(yh - yl);
+		dir -= 1;
+		}
+	}
+if( x == 0.0 )
+	mtherr( "igami", UNDERFLOW );
+
+done:
+return( x );
+}

libm/double/incbet.c

@@ -0,0 +1,409 @@
+/*							incbet.c
+ *
+ *	Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, incbet();
+ *
+ * y = incbet( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x.  The function is defined as
+ *
+ *                  x
+ *     -            -
+ *    | (a+b)      | |  a-1     b-1
+ *  -----------    |   t   (1-t)   dt.
+ *   -     -     | |
+ *  | (a) | (b)   -
+ *                 0
+ *
+ * The domain of definition is 0 <= x <= 1.  In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ *    1 - incbet( a, b, x )  =  incbet( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion
+ * or, when b*x is small, by a power series.
+ *
+ * ACCURACY:
+ *
+ * Tested at uniformly distributed random points (a,b,x) with a and b
+ * in "domain" and x between 0 and 1.
+ *                                        Relative error
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,5         10000       6.9e-15     4.5e-16
+ *    IEEE      0,85       250000       2.2e-13     1.7e-14
+ *    IEEE      0,1000      30000       5.3e-12     6.3e-13
+ *    IEEE      0,10000    250000       9.3e-11     7.1e-12
+ *    IEEE      0,100000    10000       8.7e-10     4.8e-11
+ * Outputs smaller than the IEEE gradual underflow threshold
+ * were excluded from these statistics.
+ *
+ * ERROR MESSAGES:
+ *   message         condition      value returned
+ * incbet domain      x<0, x>1          0.0
+ * incbet underflow                     0.0
+ */
+
+
+/*
+Cephes Math Library, Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef DEC
+#define MAXGAM 34.84425627277176174
+#else
+#define MAXGAM 171.624376956302725
+#endif
+
+extern double MACHEP, MINLOG, MAXLOG;
+#ifdef ANSIPROT
+extern double gamma ( double );
+extern double lgam ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double pow ( double, double );
+extern double fabs ( double );
+static double incbcf(double, double, double);
+static double incbd(double, double, double);
+static double pseries(double, double, double);
+#else
+double gamma(), lgam(), exp(), log(), pow(), fabs();
+static double incbcf(), incbd(), pseries();
+#endif
+
+static double big = 4.503599627370496e15;
+static double biginv =  2.22044604925031308085e-16;
+
+
+double incbet( aa, bb, xx )
+double aa, bb, xx;
+{
+double a, b, t, x, xc, w, y;
+int flag;
+
+if( aa <= 0.0 || bb <= 0.0 )
+	goto domerr;
+
+if( (xx <= 0.0) || ( xx >= 1.0) )
+	{
+	if( xx == 0.0 )
+		return(0.0);
+	if( xx == 1.0 )
+		return( 1.0 );
+domerr:
+	mtherr( "incbet", DOMAIN );
+	return( 0.0 );
+	}
+
+flag = 0;
+if( (bb * xx) <= 1.0 && xx <= 0.95)
+	{
+	t = pseries(aa, bb, xx);
+		goto done;
+	}
+
+w = 1.0 - xx;
+
+/* Reverse a and b if x is greater than the mean. */
+if( xx > (aa/(aa+bb)) )
+	{
+	flag = 1;
+	a = bb;
+	b = aa;
+	xc = xx;
+	x = w;
+	}
+else
+	{
+	a = aa;
+	b = bb;
+	xc = w;
+	x = xx;
+	}
+
+if( flag == 1 && (b * x) <= 1.0 && x <= 0.95)
+	{
+	t = pseries(a, b, x);
+	goto done;
+	}
+
+/* Choose expansion for better convergence. */
+y = x * (a+b-2.0) - (a-1.0);
+if( y < 0.0 )
+	w = incbcf( a, b, x );
+else
+	w = incbd( a, b, x ) / xc;
+
+/* Multiply w by the factor
+     a      b   _             _     _
+    x  (1-x)   | (a+b) / ( a | (a) | (b) ) .   */
+
+y = a * log(x);
+t = b * log(xc);
+if( (a+b) < MAXGAM && fabs(y) < MAXLOG && fabs(t) < MAXLOG )
+	{
+	t = pow(xc,b);
+	t *= pow(x,a);
+	t /= a;
+	t *= w;
+	t *= gamma(a+b) / (gamma(a) * gamma(b));
+	goto done;
+	}
+/* Resort to logarithms.  */
+y += t + lgam(a+b) - lgam(a) - lgam(b);
+y += log(w/a);
+if( y < MINLOG )
+	t = 0.0;
+else
+	t = exp(y);
+
+done:
+
+if( flag == 1 )
+	{
+	if( t <= MACHEP )
+		t = 1.0 - MACHEP;
+	else
+		t = 1.0 - t;
+	}
+return( t );
+}
+
+/* Continued fraction expansion #1
+ * for incomplete beta integral
+ */
+
+static double incbcf( a, b, x )
+double a, b, x;
+{
+double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+double k1, k2, k3, k4, k5, k6, k7, k8;
+double r, t, ans, thresh;
+int n;
+
+k1 = a;
+k2 = a + b;
+k3 = a;
+k4 = a + 1.0;
+k5 = 1.0;
+k6 = b - 1.0;
+k7 = k4;
+k8 = a + 2.0;
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = 1.0;
+qkm1 = 1.0;
+ans = 1.0;
+r = 1.0;
+n = 0;
+thresh = 3.0 * MACHEP;
+do
+	{
+	
+	xk = -( x * k1 * k2 )/( k3 * k4 );
+	pk = pkm1 +  pkm2 * xk;
+	qk = qkm1 +  qkm2 * xk;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+
+	xk = ( x * k5 * k6 )/( k7 * k8 );
+	pk = pkm1 +  pkm2 * xk;
+	qk = qkm1 +  qkm2 * xk;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+
+	if( qk != 0 )
+		r = pk/qk;
+	if( r != 0 )
+		{
+		t = fabs( (ans - r)/r );
+		ans = r;
+		}
+	else
+		t = 1.0;
+
+	if( t < thresh )
+		goto cdone;
+
+	k1 += 1.0;
+	k2 += 1.0;
+	k3 += 2.0;
+	k4 += 2.0;
+	k5 += 1.0;
+	k6 -= 1.0;
+	k7 += 2.0;
+	k8 += 2.0;
+
+	if( (fabs(qk) + fabs(pk)) > big )
+		{
+		pkm2 *= biginv;
+		pkm1 *= biginv;
+		qkm2 *= biginv;
+		qkm1 *= biginv;
+		}
+	if( (fabs(qk) < biginv) || (fabs(pk) < biginv) )
+		{
+		pkm2 *= big;
+		pkm1 *= big;
+		qkm2 *= big;
+		qkm1 *= big;
+		}
+	}
+while( ++n < 300 );
+
+cdone:
+return(ans);
+}
+
+
+/* Continued fraction expansion #2
+ * for incomplete beta integral
+ */
+
+static double incbd( a, b, x )
+double a, b, x;
+{
+double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+double k1, k2, k3, k4, k5, k6, k7, k8;
+double r, t, ans, z, thresh;
+int n;
+
+k1 = a;
+k2 = b - 1.0;
+k3 = a;
+k4 = a + 1.0;
+k5 = 1.0;
+k6 = a + b;
+k7 = a + 1.0;;
+k8 = a + 2.0;
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = 1.0;
+qkm1 = 1.0;
+z = x / (1.0-x);
+ans = 1.0;
+r = 1.0;
+n = 0;
+thresh = 3.0 * MACHEP;
+do
+	{
+	
+	xk = -( z * k1 * k2 )/( k3 * k4 );
+	pk = pkm1 +  pkm2 * xk;
+	qk = qkm1 +  qkm2 * xk;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+
+	xk = ( z * k5 * k6 )/( k7 * k8 );
+	pk = pkm1 +  pkm2 * xk;
+	qk = qkm1 +  qkm2 * xk;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+
+	if( qk != 0 )
+		r = pk/qk;
+	if( r != 0 )
+		{
+		t = fabs( (ans - r)/r );
+		ans = r;
+		}
+	else
+		t = 1.0;
+
+	if( t < thresh )
+		goto cdone;
+
+	k1 += 1.0;
+	k2 -= 1.0;
+	k3 += 2.0;
+	k4 += 2.0;
+	k5 += 1.0;
+	k6 += 1.0;
+	k7 += 2.0;
+	k8 += 2.0;
+
+	if( (fabs(qk) + fabs(pk)) > big )
+		{
+		pkm2 *= biginv;
+		pkm1 *= biginv;
+		qkm2 *= biginv;
+		qkm1 *= biginv;
+		}
+	if( (fabs(qk) < biginv) || (fabs(pk) < biginv) )
+		{
+		pkm2 *= big;
+		pkm1 *= big;
+		qkm2 *= big;
+		qkm1 *= big;
+		}
+	}
+while( ++n < 300 );
+cdone:
+return(ans);
+}
+
+/* Power series for incomplete beta integral.
+   Use when b*x is small and x not too close to 1.  */
+
+static double pseries( a, b, x )
+double a, b, x;
+{
+double s, t, u, v, n, t1, z, ai;
+
+ai = 1.0 / a;
+u = (1.0 - b) * x;
+v = u / (a + 1.0);
+t1 = v;
+t = u;
+n = 2.0;
+s = 0.0;
+z = MACHEP * ai;
+while( fabs(v) > z )
+	{
+	u = (n - b) * x / n;
+	t *= u;
+	v = t / (a + n);
+	s += v; 
+	n += 1.0;
+	}
+s += t1;
+s += ai;
+
+u = a * log(x);
+if( (a+b) < MAXGAM && fabs(u) < MAXLOG )
+	{
+	t = gamma(a+b)/(gamma(a)*gamma(b));
+	s = s * t * pow(x,a);
+	}
+else
+	{
+	t = lgam(a+b) - lgam(a) - lgam(b) + u + log(s);
+	if( t < MINLOG )
+		s = 0.0;
+	else
+	s = exp(t);
+	}
+return(s);
+}

libm/double/incbi.c

@@ -0,0 +1,313 @@
+/*							incbi()
+ *
+ *      Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, incbi();
+ *
+ * x = incbi( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ *  incbet( a, b, x ) = y .
+ *
+ * The routine performs interval halving or Newton iterations to find the
+ * root of incbet(a,b,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ *                x     a,b
+ * arithmetic   domain  domain  # trials    peak       rms
+ *    IEEE      0,1    .5,10000   50000    5.8e-12   1.3e-13
+ *    IEEE      0,1   .25,100    100000    1.8e-13   3.9e-15
+ *    IEEE      0,1     0,5       50000    1.1e-12   5.5e-15
+ *    VAX       0,1    .5,100     25000    3.5e-14   1.1e-15
+ * With a and b constrained to half-integer or integer values:
+ *    IEEE      0,1    .5,10000   50000    5.8e-12   1.1e-13
+ *    IEEE      0,1    .5,100    100000    1.7e-14   7.9e-16
+ * With a = .5, b constrained to half-integer or integer values:
+ *    IEEE      0,1    .5,10000   10000    8.3e-11   1.0e-11
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1996, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
+#ifdef ANSIPROT
+extern double ndtri ( double );
+extern double exp ( double );
+extern double fabs ( double );
+extern double log ( double );
+extern double sqrt ( double );
+extern double lgam ( double );
+extern double incbet ( double, double, double );
+#else
+double ndtri(), exp(), fabs(), log(), sqrt(), lgam(), incbet();
+#endif
+
+double incbi( aa, bb, yy0 )
+double aa, bb, yy0;
+{
+double a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt;
+int i, rflg, dir, nflg;
+
+
+i = 0;
+if( yy0 <= 0 )
+	return(0.0);
+if( yy0 >= 1.0 )
+	return(1.0);
+x0 = 0.0;
+yl = 0.0;
+x1 = 1.0;
+yh = 1.0;
+nflg = 0;
+
+if( aa <= 1.0 || bb <= 1.0 )
+	{
+	dithresh = 1.0e-6;
+	rflg = 0;
+	a = aa;
+	b = bb;
+	y0 = yy0;
+	x = a/(a+b);
+	y = incbet( a, b, x );
+	goto ihalve;
+	}
+else
+	{
+	dithresh = 1.0e-4;
+	}
+/* approximation to inverse function */
+
+yp = -ndtri(yy0);
+
+if( yy0 > 0.5 )
+	{
+	rflg = 1;
+	a = bb;
+	b = aa;
+	y0 = 1.0 - yy0;
+	yp = -yp;
+	}
+else
+	{
+	rflg = 0;
+	a = aa;
+	b = bb;
+	y0 = yy0;
+	}
+
+lgm = (yp * yp - 3.0)/6.0;
+x = 2.0/( 1.0/(2.0*a-1.0)  +  1.0/(2.0*b-1.0) );
+d = yp * sqrt( x + lgm ) / x
+	- ( 1.0/(2.0*b-1.0) - 1.0/(2.0*a-1.0) )
+	* (lgm + 5.0/6.0 - 2.0/(3.0*x));
+d = 2.0 * d;
+if( d < MINLOG )
+	{
+	x = 1.0;
+	goto under;
+	}
+x = a/( a + b * exp(d) );
+y = incbet( a, b, x );
+yp = (y - y0)/y0;
+if( fabs(yp) < 0.2 )
+	goto newt;
+
+/* Resort to interval halving if not close enough. */
+ihalve:
+
+dir = 0;
+di = 0.5;
+for( i=0; i<100; i++ )
+	{
+	if( i != 0 )
+		{
+		x = x0  +  di * (x1 - x0);
+		if( x == 1.0 )
+			x = 1.0 - MACHEP;
+		if( x == 0.0 )
+			{
+			di = 0.5;
+			x = x0  +  di * (x1 - x0);
+			if( x == 0.0 )
+				goto under;
+			}
+		y = incbet( a, b, x );
+		yp = (x1 - x0)/(x1 + x0);
+		if( fabs(yp) < dithresh )
+			goto newt;
+		yp = (y-y0)/y0;
+		if( fabs(yp) < dithresh )
+			goto newt;
+		}
+	if( y < y0 )
+		{
+		x0 = x;
+		yl = y;
+		if( dir < 0 )
+			{
+			dir = 0;
+			di = 0.5;
+			}
+		else if( dir > 3 )
+			di = 1.0 - (1.0 - di) * (1.0 - di);
+		else if( dir > 1 )
+			di = 0.5 * di + 0.5; 
+		else
+			di = (y0 - y)/(yh - yl);
+		dir += 1;
+		if( x0 > 0.75 )
+			{
+			if( rflg == 1 )
+				{
+				rflg = 0;
+				a = aa;
+				b = bb;
+				y0 = yy0;
+				}
+			else
+				{
+				rflg = 1;
+				a = bb;
+				b = aa;
+				y0 = 1.0 - yy0;
+				}
+			x = 1.0 - x;
+			y = incbet( a, b, x );
+			x0 = 0.0;
+			yl = 0.0;
+			x1 = 1.0;
+			yh = 1.0;
+			goto ihalve;
+			}
+		}
+	else
+		{
+		x1 = x;
+		if( rflg == 1 && x1 < MACHEP )
+			{
+			x = 0.0;
+			goto done;
+			}
+		yh = y;
+		if( dir > 0 )
+			{
+			dir = 0;
+			di = 0.5;
+			}
+		else if( dir < -3 )
+			di = di * di;
+		else if( dir < -1 )
+			di = 0.5 * di;
+		else
+			di = (y - y0)/(yh - yl);
+		dir -= 1;
+		}
+	}
+mtherr( "incbi", PLOSS );
+if( x0 >= 1.0 )
+	{
+	x = 1.0 - MACHEP;
+	goto done;
+	}
+if( x <= 0.0 )
+	{
+under:
+	mtherr( "incbi", UNDERFLOW );
+	x = 0.0;
+	goto done;
+	}
+
+newt:
+
+if( nflg )
+	goto done;
+nflg = 1;
+lgm = lgam(a+b) - lgam(a) - lgam(b);
+
+for( i=0; i<8; i++ )
+	{
+	/* Compute the function at this point. */
+	if( i != 0 )
+		y = incbet(a,b,x);
+	if( y < yl )
+		{
+		x = x0;
+		y = yl;
+		}
+	else if( y > yh )
+		{
+		x = x1;
+		y = yh;
+		}
+	else if( y < y0 )
+		{
+		x0 = x;
+		yl = y;
+		}
+	else
+		{
+		x1 = x;
+		yh = y;
+		}
+	if( x == 1.0 || x == 0.0 )
+		break;
+	/* Compute the derivative of the function at this point. */
+	d = (a - 1.0) * log(x) + (b - 1.0) * log(1.0-x) + lgm;
+	if( d < MINLOG )
+		goto done;
+	if( d > MAXLOG )
+		break;
+	d = exp(d);
+	/* Compute the step to the next approximation of x. */
+	d = (y - y0)/d;
+	xt = x - d;
+	if( xt <= x0 )
+		{
+		y = (x - x0) / (x1 - x0);
+		xt = x0 + 0.5 * y * (x - x0);
+		if( xt <= 0.0 )
+			break;
+		}
+	if( xt >= x1 )
+		{
+		y = (x1 - x) / (x1 - x0);
+		xt = x1 - 0.5 * y * (x1 - x);
+		if( xt >= 1.0 )
+			break;
+		}
+	x = xt;
+	if( fabs(d/x) < 128.0 * MACHEP )
+		goto done;
+	}
+/* Did not converge.  */
+dithresh = 256.0 * MACHEP;
+goto ihalve;
+
+done:
+
+if( rflg )
+	{
+	if( x <= MACHEP )
+		x = 1.0 - MACHEP;
+	else
+		x = 1.0 - x;
+	}
+return( x );
+}

libm/double/isnan.c

@@ -0,0 +1,237 @@
+/*							isnan()
+ *							signbit()
+ *							isfinite()
+ *
+ *	Floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double ceil(), floor(), frexp(), ldexp();
+ * int signbit(), isnan(), isfinite();
+ * double x, y;
+ * int expnt, n;
+ *
+ * y = floor(x);
+ * y = ceil(x);
+ * y = frexp( x, &expnt );
+ * y = ldexp( x, n );
+ * n = signbit(x);
+ * n = isnan(x);
+ * n = isfinite(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a double precision floating point
+ * result.
+ *
+ * floor() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * ceil() returns the smallest integer greater than or equal
+ * to x.  It truncates toward plus infinity.
+ *
+ * frexp() extracts the exponent from x.  It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y.  Thus  x = y * 2**expn.
+ *
+ * ldexp() multiplies x by 2**n.
+ *
+ * signbit(x) returns 1 if the sign bit of x is 1, else 0.
+ *
+ * These functions are part of the standard C run time library
+ * for many but not all C compilers.  The ones supplied are
+ * written in C for either DEC or IEEE arithmetic.  They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic.  Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+
+/*
+Cephes Math Library Release 2.3:  March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+/* ceil(), floor(), frexp(), ldexp() may need to be rewritten. */
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+
+/* Return 1 if the sign bit of x is 1, else 0.  */
+
+int signbit(x)
+double x;
+{
+union
+	{
+	double d;
+	short s[4];
+	int i[2];
+	} u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+	{
+#ifdef IBMPC
+	return( u.i[1] < 0 );
+#endif
+#ifdef DEC
+	return( u.s[3] < 0 );
+#endif
+#ifdef MIEEE
+	return( u.i[0] < 0 );
+#endif
+	}
+else
+	{
+#ifdef IBMPC
+	return( u.s[3] < 0 );
+#endif
+#ifdef DEC
+	return( u.s[3] < 0 );
+#endif
+#ifdef MIEEE
+	return( u.s[0] < 0 );
+#endif
+	}
+}
+
+
+/* Return 1 if x is a number that is Not a Number, else return 0.  */
+
+int isnan(x)
+double x;
+{
+#ifdef NANS
+union
+	{
+	double d;
+	unsigned short s[4];
+	unsigned int i[2];
+	} u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+	{
+#ifdef IBMPC
+	if( ((u.i[1] & 0x7ff00000) == 0x7ff00000)
+	    && (((u.i[1] & 0x000fffff) != 0) || (u.i[0] != 0)))
+		return 1;
+#endif
+#ifdef DEC
+	if( (u.s[1] & 0x7fff) == 0)
+		{
+		if( (u.s[2] | u.s[1] | u.s[0]) != 0 )
+			return(1);
+		}
+#endif
+#ifdef MIEEE
+	if( ((u.i[0] & 0x7ff00000) == 0x7ff00000)
+	    && (((u.i[0] & 0x000fffff) != 0) || (u.i[1] != 0)))
+		return 1;
+#endif
+	return(0);
+	}
+else
+	{ /* size int not 4 */
+#ifdef IBMPC
+	if( (u.s[3] & 0x7ff0) == 0x7ff0)
+		{
+		if( ((u.s[3] & 0x000f) | u.s[2] | u.s[1] | u.s[0]) != 0 )
+			return(1);
+		}
+#endif
+#ifdef DEC
+	if( (u.s[3] & 0x7fff) == 0)
+		{
+		if( (u.s[2] | u.s[1] | u.s[0]) != 0 )
+			return(1);
+		}
+#endif
+#ifdef MIEEE
+	if( (u.s[0] & 0x7ff0) == 0x7ff0)
+		{
+		if( ((u.s[0] & 0x000f) | u.s[1] | u.s[2] | u.s[3]) != 0 )
+			return(1);
+		}
+#endif
+	return(0);
+	} /* size int not 4 */
+
+#else
+/* No NANS.  */
+return(0);
+#endif
+}
+
+
+/* Return 1 if x is not infinite and is not a NaN.  */
+
+int isfinite(x)
+double x;
+{
+#ifdef INFINITIES
+union
+	{
+	double d;
+	unsigned short s[4];
+	unsigned int i[2];
+	} u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+	{
+#ifdef IBMPC
+	if( (u.i[1] & 0x7ff00000) != 0x7ff00000)
+		return 1;
+#endif
+#ifdef DEC
+	if( (u.s[3] & 0x7fff) != 0)
+		return 1;
+#endif
+#ifdef MIEEE
+	if( (u.i[0] & 0x7ff00000) != 0x7ff00000)
+		return 1;
+#endif
+	return(0);
+	}
+else
+	{
+#ifdef IBMPC
+	if( (u.s[3] & 0x7ff0) != 0x7ff0)
+		return 1;
+#endif
+#ifdef DEC
+	if( (u.s[3] & 0x7fff) != 0)
+		return 1;
+#endif
+#ifdef MIEEE
+	if( (u.s[0] & 0x7ff0) != 0x7ff0)
+		return 1;
+#endif
+	return(0);
+	}
+#else
+/* No INFINITY.  */
+return(1);
+#endif
+}

libm/double/iv.c

@@ -0,0 +1,116 @@
+/*							iv.c
+ *
+ *	Modified Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, iv();
+ *
+ * y = iv( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order v of the
+ * argument.  If x is negative, v must be integer valued.
+ *
+ * The function is defined as Iv(x) = Jv( ix ).  It is
+ * here computed in terms of the confluent hypergeometric
+ * function, according to the formula
+ *
+ *              v  -x
+ * Iv(x) = (x/2)  e   hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
+ *
+ * If v is a negative integer, then v is replaced by -v.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (v, x), with v between 0 and
+ * 30, x between 0 and 28.
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30          2000      3.1e-15     5.4e-16
+ *    IEEE      0,30         10000      1.7e-14     2.7e-15
+ *
+ * Accuracy is diminished if v is near a negative integer.
+ *
+ * See also hyperg.c.
+ *
+ */
+/*							iv.c	*/
+/*	Modified Bessel function of noninteger order		*/
+/* If x < 0, then v must be an integer. */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double hyperg ( double, double, double );
+extern double exp ( double );
+extern double gamma ( double );
+extern double log ( double );
+extern double fabs ( double );
+extern double floor ( double );
+#else
+double hyperg(), exp(), gamma(), log(), fabs(), floor();
+#endif
+extern double MACHEP, MAXNUM;
+
+double iv( v, x )
+double v, x;
+{
+int sign;
+double t, ax;
+
+/* If v is a negative integer, invoke symmetry */
+t = floor(v);
+if( v < 0.0 )
+	{
+	if( t == v )
+		{
+		v = -v;	/* symmetry */
+		t = -t;
+		}
+	}
+/* If x is negative, require v to be an integer */
+sign = 1;
+if( x < 0.0 )
+	{
+	if( t != v )
+		{
+		mtherr( "iv", DOMAIN );
+		return( 0.0 );
+		}
+	if( v != 2.0 * floor(v/2.0) )
+		sign = -1;
+	}
+
+/* Avoid logarithm singularity */
+if( x == 0.0 )
+	{
+	if( v == 0.0 )
+		return( 1.0 );
+	if( v < 0.0 )
+		{
+		mtherr( "iv", OVERFLOW );
+		return( MAXNUM );
+		}
+	else
+		return( 0.0 );
+	}
+
+ax = fabs(x);
+t = v * log( 0.5 * ax )  -  x;
+t = sign * exp(t) / gamma( v + 1.0 );
+ax = v + 0.5;
+return( t * hyperg( ax,  2.0 * ax,  2.0 * x ) );
+}

libm/double/j0.c

@@ -0,0 +1,543 @@
+/*							j0.c
+ *
+ *	Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j0();
+ *
+ * y = j0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval the following rational
+ * approximation is used:
+ *
+ *
+ *        2         2
+ * (w - r  ) (w - r  ) P (w) / Q (w)
+ *       1         2    3       8
+ *
+ *            2
+ * where w = x  and the two r's are zeros of the function.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30       10000       4.4e-17     6.3e-18
+ *    IEEE      0, 30       60000       4.2e-16     1.1e-16
+ *
+ */
+/*							y0.c
+ *
+ *	Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y0();
+ *
+ * y = y0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *   y0(x)  = R(x)  +   2 * log(x) * j0(x) / PI.
+ * Thus a call to j0() is required.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *  Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        9400       7.0e-17     7.9e-18
+ *    IEEE      0, 30       30000       1.3e-15     1.6e-16
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+/* Note: all coefficients satisfy the relative error criterion
+ * except YP, YQ which are designed for absolute error. */
+
+#include <math.h>
+
+#ifdef UNK
+static double PP[7] = {
+  7.96936729297347051624E-4,
+  8.28352392107440799803E-2,
+  1.23953371646414299388E0,
+  5.44725003058768775090E0,
+  8.74716500199817011941E0,
+  5.30324038235394892183E0,
+  9.99999999999999997821E-1,
+};
+static double PQ[7] = {
+  9.24408810558863637013E-4,
+  8.56288474354474431428E-2,
+  1.25352743901058953537E0,
+  5.47097740330417105182E0,
+  8.76190883237069594232E0,
+  5.30605288235394617618E0,
+  1.00000000000000000218E0,
+};
+#endif
+#ifdef DEC
+static unsigned short PP[28] = {
+0035520,0164604,0140733,0054470,
+0037251,0122605,0115356,0107170,
+0040236,0124412,0071500,0056303,
+0040656,0047737,0045720,0045263,
+0041013,0172143,0045004,0142103,
+0040651,0132045,0026241,0026406,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short PQ[28] = {
+0035562,0052006,0070034,0134666,
+0037257,0057055,0055242,0123424,
+0040240,0071626,0046630,0032371,
+0040657,0011077,0032013,0012731,
+0041014,0030307,0050331,0006414,
+0040651,0145457,0065021,0150304,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short PP[28] = {
+0x6b27,0x983b,0x1d30,0x3f4a,
+0xd1cf,0xb35d,0x34b0,0x3fb5,
+0x0b98,0x4e68,0xd521,0x3ff3,
+0x0956,0xe97a,0xc9fb,0x4015,
+0x9888,0x6940,0x7e8c,0x4021,
+0x25a1,0xa594,0x3684,0x4015,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short PQ[28] = {
+0x9737,0xce03,0x4a80,0x3f4e,
+0x54e3,0xab54,0xebc5,0x3fb5,
+0x069f,0xc9b3,0x0e72,0x3ff4,
+0x62bb,0xe681,0xe247,0x4015,
+0x21a1,0xea1b,0x8618,0x4021,
+0x3a19,0xed42,0x3965,0x4015,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short PP[28] = {
+0x3f4a,0x1d30,0x983b,0x6b27,
+0x3fb5,0x34b0,0xb35d,0xd1cf,
+0x3ff3,0xd521,0x4e68,0x0b98,
+0x4015,0xc9fb,0xe97a,0x0956,
+0x4021,0x7e8c,0x6940,0x9888,
+0x4015,0x3684,0xa594,0x25a1,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short PQ[28] = {
+0x3f4e,0x4a80,0xce03,0x9737,
+0x3fb5,0xebc5,0xab54,0x54e3,
+0x3ff4,0x0e72,0xc9b3,0x069f,
+0x4015,0xe247,0xe681,0x62bb,
+0x4021,0x8618,0xea1b,0x21a1,
+0x4015,0x3965,0xed42,0x3a19,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double QP[8] = {
+-1.13663838898469149931E-2,
+-1.28252718670509318512E0,
+-1.95539544257735972385E1,
+-9.32060152123768231369E1,
+-1.77681167980488050595E2,
+-1.47077505154951170175E2,
+-5.14105326766599330220E1,
+-6.05014350600728481186E0,
+};
+static double QQ[7] = {
+/*  1.00000000000000000000E0,*/
+  6.43178256118178023184E1,
+  8.56430025976980587198E2,
+  3.88240183605401609683E3,
+  7.24046774195652478189E3,
+  5.93072701187316984827E3,
+  2.06209331660327847417E3,
+  2.42005740240291393179E2,
+};
+#endif
+#ifdef DEC
+static unsigned short QP[32] = {
+0136472,0035021,0142451,0141115,
+0140244,0024731,0150620,0105642,
+0141234,0067177,0124161,0060141,
+0141672,0064572,0151557,0043036,
+0142061,0127141,0003127,0043517,
+0142023,0011727,0060271,0144544,
+0141515,0122142,0126620,0143150,
+0140701,0115306,0106715,0007344,
+};
+static unsigned short QQ[28] = {
+/*0040200,0000000,0000000,0000000,*/
+0041600,0121272,0004741,0026544,
+0042526,0015605,0105654,0161771,
+0043162,0123155,0165644,0062645,
+0043342,0041675,0167576,0130756,
+0043271,0052720,0165631,0154214,
+0043000,0160576,0034614,0172024,
+0042162,0000570,0030500,0051235,
+};
+#endif
+#ifdef IBMPC
+static unsigned short QP[32] = {
+0x384a,0x38a5,0x4742,0xbf87,
+0x1174,0x3a32,0x853b,0xbff4,
+0x2c0c,0xf50e,0x8dcf,0xc033,
+0xe8c4,0x5a6d,0x4d2f,0xc057,
+0xe8ea,0x20ca,0x35cc,0xc066,
+0x392d,0xec17,0x627a,0xc062,
+0x18cd,0x55b2,0xb48c,0xc049,
+0xa1dd,0xd1b9,0x3358,0xc018,
+};
+static unsigned short QQ[28] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x25ac,0x413c,0x1457,0x4050,
+0x9c7f,0xb175,0xc370,0x408a,
+0x8cb5,0xbd74,0x54cd,0x40ae,
+0xd63e,0xbdef,0x4877,0x40bc,
+0x3b11,0x1d73,0x2aba,0x40b7,
+0x9e82,0xc731,0x1c2f,0x40a0,
+0x0a54,0x0628,0x402f,0x406e,
+};
+#endif
+#ifdef MIEEE
+static unsigned short QP[32] = {
+0xbf87,0x4742,0x38a5,0x384a,
+0xbff4,0x853b,0x3a32,0x1174,
+0xc033,0x8dcf,0xf50e,0x2c0c,
+0xc057,0x4d2f,0x5a6d,0xe8c4,
+0xc066,0x35cc,0x20ca,0xe8ea,
+0xc062,0x627a,0xec17,0x392d,
+0xc049,0xb48c,0x55b2,0x18cd,
+0xc018,0x3358,0xd1b9,0xa1dd,
+};
+static unsigned short QQ[28] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4050,0x1457,0x413c,0x25ac,
+0x408a,0xc370,0xb175,0x9c7f,
+0x40ae,0x54cd,0xbd74,0x8cb5,
+0x40bc,0x4877,0xbdef,0xd63e,
+0x40b7,0x2aba,0x1d73,0x3b11,
+0x40a0,0x1c2f,0xc731,0x9e82,
+0x406e,0x402f,0x0628,0x0a54,
+};
+#endif
+
+
+#ifdef UNK
+static double YP[8] = {
+ 1.55924367855235737965E4,
+-1.46639295903971606143E7,
+ 5.43526477051876500413E9,
+-9.82136065717911466409E11,
+ 8.75906394395366999549E13,
+-3.46628303384729719441E15,
+ 4.42733268572569800351E16,
+-1.84950800436986690637E16,
+};
+static double YQ[7] = {
+/* 1.00000000000000000000E0,*/
+ 1.04128353664259848412E3,
+ 6.26107330137134956842E5,
+ 2.68919633393814121987E8,
+ 8.64002487103935000337E10,
+ 2.02979612750105546709E13,
+ 3.17157752842975028269E15,
+ 2.50596256172653059228E17,
+};
+#endif
+#ifdef DEC
+static unsigned short YP[32] = {
+0043563,0120677,0042264,0046166,
+0146137,0140371,0113444,0042260,
+0050241,0175707,0100502,0063344,
+0152144,0125737,0007265,0164526,
+0053637,0051621,0163035,0060546,
+0155105,0004416,0107306,0060023,
+0056035,0045133,0030132,0000024,
+0155603,0065132,0144061,0131732,
+};
+static unsigned short YQ[28] = {
+/*0040200,0000000,0000000,0000000,*/
+0042602,0024422,0135557,0162663,
+0045030,0155665,0044075,0160135,
+0047200,0035432,0105446,0104005,
+0051240,0167331,0056063,0022743,
+0053223,0127746,0025764,0012160,
+0055064,0044206,0177532,0145545,
+0056536,0111375,0163715,0127201,
+};
+#endif
+#ifdef IBMPC
+static unsigned short YP[32] = {
+0x898f,0xe896,0x7437,0x40ce,
+0x8896,0x32e4,0xf81f,0xc16b,
+0x4cdd,0xf028,0x3f78,0x41f4,
+0xbd2b,0xe1d6,0x957b,0xc26c,
+0xac2d,0x3cc3,0xea72,0x42d3,
+0xcc02,0xd1d8,0xa121,0xc328,
+0x4003,0x660b,0xa94b,0x4363,
+0x367b,0x5906,0x6d4b,0xc350,
+};
+static unsigned short YQ[28] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xfcb6,0x576d,0x4522,0x4090,
+0xbc0c,0xa907,0x1b76,0x4123,
+0xd101,0x5164,0x0763,0x41b0,
+0x64bc,0x2b86,0x1ddb,0x4234,
+0x828e,0xc57e,0x75fc,0x42b2,
+0x596d,0xdfeb,0x8910,0x4326,
+0xb5d0,0xbcf9,0xd25f,0x438b,
+};
+#endif
+#ifdef MIEEE
+static unsigned short YP[32] = {
+0x40ce,0x7437,0xe896,0x898f,
+0xc16b,0xf81f,0x32e4,0x8896,
+0x41f4,0x3f78,0xf028,0x4cdd,
+0xc26c,0x957b,0xe1d6,0xbd2b,
+0x42d3,0xea72,0x3cc3,0xac2d,
+0xc328,0xa121,0xd1d8,0xcc02,
+0x4363,0xa94b,0x660b,0x4003,
+0xc350,0x6d4b,0x5906,0x367b,
+};
+static unsigned short YQ[28] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4090,0x4522,0x576d,0xfcb6,
+0x4123,0x1b76,0xa907,0xbc0c,
+0x41b0,0x0763,0x5164,0xd101,
+0x4234,0x1ddb,0x2b86,0x64bc,
+0x42b2,0x75fc,0xc57e,0x828e,
+0x4326,0x8910,0xdfeb,0x596d,
+0x438b,0xd25f,0xbcf9,0xb5d0,
+};
+#endif
+
+#ifdef UNK
+/*  5.783185962946784521175995758455807035071 */
+static double DR1 = 5.78318596294678452118E0;
+/* 30.47126234366208639907816317502275584842 */
+static double DR2 = 3.04712623436620863991E1;
+#endif
+
+#ifdef DEC
+static unsigned short R1[] = {0040671,0007734,0001061,0056734};
+#define DR1 *(double *)R1
+static unsigned short R2[] = {0041363,0142445,0030416,0165567};
+#define DR2 *(double *)R2
+#endif
+
+#ifdef IBMPC
+static unsigned short R1[] = {0x2bbb,0x8046,0x21fb,0x4017};
+#define DR1 *(double *)R1
+static unsigned short R2[] = {0xdd6f,0xa621,0x78a4,0x403e};
+#define DR2 *(double *)R2
+#endif
+
+#ifdef MIEEE
+static unsigned short R1[] = {0x4017,0x21fb,0x8046,0x2bbb};
+#define DR1 *(double *)R1
+static unsigned short R2[] = {0x403e,0x78a4,0xa621,0xdd6f};
+#define DR2 *(double *)R2
+#endif
+
+#ifdef UNK
+static double RP[4] = {
+-4.79443220978201773821E9,
+ 1.95617491946556577543E12,
+-2.49248344360967716204E14,
+ 9.70862251047306323952E15,
+};
+static double RQ[8] = {
+/* 1.00000000000000000000E0,*/
+ 4.99563147152651017219E2,
+ 1.73785401676374683123E5,
+ 4.84409658339962045305E7,
+ 1.11855537045356834862E10,
+ 2.11277520115489217587E12,
+ 3.10518229857422583814E14,
+ 3.18121955943204943306E16,
+ 1.71086294081043136091E18,
+};
+#endif
+#ifdef DEC
+static unsigned short RP[16] = {
+0150216,0161235,0064344,0014450,
+0052343,0135216,0035624,0144153,
+0154142,0130247,0003310,0003667,
+0055411,0173703,0047772,0176635,
+};
+static unsigned short RQ[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0042371,0144025,0032265,0136137,
+0044451,0133131,0132420,0151466,
+0046470,0144641,0072540,0030636,
+0050446,0126600,0045042,0044243,
+0052365,0172633,0110301,0071063,
+0054215,0032424,0062272,0043513,
+0055742,0005013,0171731,0072335,
+0057275,0170646,0036663,0013134,
+};
+#endif
+#ifdef IBMPC
+static unsigned short RP[16] = {
+0x8325,0xad1c,0xdc53,0xc1f1,
+0x990d,0xc772,0x7751,0x427c,
+0x00f7,0xe0d9,0x5614,0xc2ec,
+0x5fb4,0x69ff,0x3ef8,0x4341,
+};
+static unsigned short RQ[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xb78c,0xa696,0x3902,0x407f,
+0x1a67,0x36a2,0x36cb,0x4105,
+0x0634,0x2eac,0x1934,0x4187,
+0x4914,0x0944,0xd5b0,0x4204,
+0x2e46,0x7218,0xbeb3,0x427e,
+0x48e9,0x8c97,0xa6a2,0x42f1,
+0x2e9c,0x7e7b,0x4141,0x435c,
+0x62cc,0xc7b6,0xbe34,0x43b7,
+};
+#endif
+#ifdef MIEEE
+static unsigned short RP[16] = {
+0xc1f1,0xdc53,0xad1c,0x8325,
+0x427c,0x7751,0xc772,0x990d,
+0xc2ec,0x5614,0xe0d9,0x00f7,
+0x4341,0x3ef8,0x69ff,0x5fb4,
+};
+static unsigned short RQ[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x407f,0x3902,0xa696,0xb78c,
+0x4105,0x36cb,0x36a2,0x1a67,
+0x4187,0x1934,0x2eac,0x0634,
+0x4204,0xd5b0,0x0944,0x4914,
+0x427e,0xbeb3,0x7218,0x2e46,
+0x42f1,0xa6a2,0x8c97,0x48e9,
+0x435c,0x4141,0x7e7b,0x2e9c,
+0x43b7,0xbe34,0xc7b6,0x62cc,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double sqrt ( double );
+double j0 ( double );
+#else
+double polevl(), p1evl(), log(), sin(), cos(), sqrt();
+double j0();
+#endif
+extern double TWOOPI, SQ2OPI, PIO4;
+
+double j0(x)
+double x;
+{
+double w, z, p, q, xn;
+
+if( x < 0 )
+	x = -x;
+
+if( x <= 5.0 )
+	{
+	z = x * x;
+	if( x < 1.0e-5 )
+		return( 1.0 - z/4.0 );
+
+	p = (z - DR1) * (z - DR2);
+	p = p * polevl( z, RP, 3)/p1evl( z, RQ, 8 );
+	return( p );
+	}
+
+w = 5.0/x;
+q = 25.0/(x*x);
+p = polevl( q, PP, 6)/polevl( q, PQ, 6 );
+q = polevl( q, QP, 7)/p1evl( q, QQ, 7 );
+xn = x - PIO4;
+p = p * cos(xn) - w * q * sin(xn);
+return( p * SQ2OPI / sqrt(x) );
+}
+
+/*							y0() 2	*/
+/* Bessel function of second kind, order zero	*/
+
+/* Rational approximation coefficients YP[], YQ[] are used here.
+ * The function computed is  y0(x)  -  2 * log(x) * j0(x) / PI,
+ * whose value at x = 0 is  2 * ( log(0.5) + EUL ) / PI
+ * = 0.073804295108687225.
+ */
+
+/*
+#define PIO4 .78539816339744830962
+#define SQ2OPI .79788456080286535588
+*/
+extern double MAXNUM;
+
+double y0(x)
+double x;
+{
+double w, z, p, q, xn;
+
+if( x <= 5.0 )
+	{
+	if( x <= 0.0 )
+		{
+		mtherr( "y0", DOMAIN );
+		return( -MAXNUM );
+		}
+	z = x * x;
+	w = polevl( z, YP, 7) / p1evl( z, YQ, 7 );
+	w += TWOOPI * log(x) * j0(x);
+	return( w );
+	}
+
+w = 5.0/x;
+z = 25.0 / (x * x);
+p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
+q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
+xn = x - PIO4;
+p = p * sin(xn) + w * q * cos(xn);
+return( p * SQ2OPI / sqrt(x) );
+}

libm/double/j1.c

@@ -0,0 +1,515 @@
+/*							j1.c
+ *
+ *	Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j1();
+ *
+ * y = j1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 24 term Chebyshev
+ * expansion is used. In the second, the asymptotic
+ * trigonometric representation is employed using two
+ * rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC       0, 30       10000       4.0e-17     1.1e-17
+ *    IEEE      0, 30       30000       2.6e-16     1.1e-16
+ *
+ *
+ */
+/*							y1.c
+ *
+ *	Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 25 term Chebyshev
+ * expansion is used, and a call to j1() is required.
+ * In the second, the asymptotic trigonometric representation
+ * is employed using two rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain      # trials      peak         rms
+ *    DEC       0, 30       10000       8.6e-17     1.3e-17
+ *    IEEE      0, 30       30000       1.0e-15     1.3e-16
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+/*
+#define PIO4 .78539816339744830962
+#define THPIO4 2.35619449019234492885
+#define SQ2OPI .79788456080286535588
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double RP[4] = {
+-8.99971225705559398224E8,
+ 4.52228297998194034323E11,
+-7.27494245221818276015E13,
+ 3.68295732863852883286E15,
+};
+static double RQ[8] = {
+/* 1.00000000000000000000E0,*/
+ 6.20836478118054335476E2,
+ 2.56987256757748830383E5,
+ 8.35146791431949253037E7,
+ 2.21511595479792499675E10,
+ 4.74914122079991414898E12,
+ 7.84369607876235854894E14,
+ 8.95222336184627338078E16,
+ 5.32278620332680085395E18,
+};
+#endif
+#ifdef DEC
+static unsigned short RP[16] = {
+0147526,0110742,0063322,0077052,
+0051722,0112720,0065034,0061530,
+0153604,0052227,0033147,0105650,
+0055121,0055025,0032276,0022015,
+};
+static unsigned short RQ[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0042433,0032610,0155604,0033473,
+0044572,0173320,0067270,0006616,
+0046637,0045246,0162225,0006606,
+0050645,0004773,0157577,0053004,
+0052612,0033734,0001667,0176501,
+0054462,0054121,0173147,0121367,
+0056237,0002777,0121451,0176007,
+0057623,0136253,0131601,0044710,
+};
+#endif
+#ifdef IBMPC
+static unsigned short RP[16] = {
+0x4fc5,0x4cda,0xd23c,0xc1ca,
+0x8c6b,0x0d43,0x52ba,0x425a,
+0xf175,0xe6cc,0x8a92,0xc2d0,
+0xc482,0xa697,0x2b42,0x432a,
+};
+static unsigned short RQ[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x86e7,0x1b70,0x66b1,0x4083,
+0x01b2,0x0dd7,0x5eda,0x410f,
+0xa1b1,0xdc92,0xe954,0x4193,
+0xeac1,0x7bef,0xa13f,0x4214,
+0xffa8,0x8076,0x46fb,0x4291,
+0xf45f,0x3ecc,0x4b0a,0x4306,
+0x3f81,0xf465,0xe0bf,0x4373,
+0x2939,0x7670,0x7795,0x43d2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short RP[16] = {
+0xc1ca,0xd23c,0x4cda,0x4fc5,
+0x425a,0x52ba,0x0d43,0x8c6b,
+0xc2d0,0x8a92,0xe6cc,0xf175,
+0x432a,0x2b42,0xa697,0xc482,
+};
+static unsigned short RQ[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4083,0x66b1,0x1b70,0x86e7,
+0x410f,0x5eda,0x0dd7,0x01b2,
+0x4193,0xe954,0xdc92,0xa1b1,
+0x4214,0xa13f,0x7bef,0xeac1,
+0x4291,0x46fb,0x8076,0xffa8,
+0x4306,0x4b0a,0x3ecc,0xf45f,
+0x4373,0xe0bf,0xf465,0x3f81,
+0x43d2,0x7795,0x7670,0x2939,
+};
+#endif
+
+#ifdef UNK
+static double PP[7] = {
+ 7.62125616208173112003E-4,
+ 7.31397056940917570436E-2,
+ 1.12719608129684925192E0,
+ 5.11207951146807644818E0,
+ 8.42404590141772420927E0,
+ 5.21451598682361504063E0,
+ 1.00000000000000000254E0,
+};
+static double PQ[7] = {
+ 5.71323128072548699714E-4,
+ 6.88455908754495404082E-2,
+ 1.10514232634061696926E0,
+ 5.07386386128601488557E0,
+ 8.39985554327604159757E0,
+ 5.20982848682361821619E0,
+ 9.99999999999999997461E-1,
+};
+#endif
+#ifdef DEC
+static unsigned short PP[28] = {
+0035507,0144542,0061543,0024326,
+0037225,0145105,0017766,0022661,
+0040220,0043766,0010254,0133255,
+0040643,0113047,0142611,0151521,
+0041006,0144344,0055351,0074261,
+0040646,0156520,0120574,0006416,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short PQ[28] = {
+0035425,0142330,0115041,0165514,
+0037214,0177352,0145105,0052026,
+0040215,0072515,0141207,0073255,
+0040642,0056427,0137222,0106405,
+0041006,0062716,0166427,0165450,
+0040646,0133352,0035425,0123304,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short PP[28] = {
+0x651b,0x4c6c,0xf92c,0x3f48,
+0xc4b6,0xa3fe,0xb948,0x3fb2,
+0x96d6,0xc215,0x08fe,0x3ff2,
+0x3a6a,0xf8b1,0x72c4,0x4014,
+0x2f16,0x8b5d,0xd91c,0x4020,
+0x81a2,0x142f,0xdbaa,0x4014,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short PQ[28] = {
+0x3d69,0x1344,0xb89b,0x3f42,
+0xaa83,0x5948,0x9fdd,0x3fb1,
+0xeed6,0xb850,0xaea9,0x3ff1,
+0x51a1,0xf7d2,0x4ba2,0x4014,
+0xfd65,0xdda2,0xccb9,0x4020,
+0xb4d9,0x4762,0xd6dd,0x4014,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short PP[28] = {
+0x3f48,0xf92c,0x4c6c,0x651b,
+0x3fb2,0xb948,0xa3fe,0xc4b6,
+0x3ff2,0x08fe,0xc215,0x96d6,
+0x4014,0x72c4,0xf8b1,0x3a6a,
+0x4020,0xd91c,0x8b5d,0x2f16,
+0x4014,0xdbaa,0x142f,0x81a2,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short PQ[28] = {
+0x3f42,0xb89b,0x1344,0x3d69,
+0x3fb1,0x9fdd,0x5948,0xaa83,
+0x3ff1,0xaea9,0xb850,0xeed6,
+0x4014,0x4ba2,0xf7d2,0x51a1,
+0x4020,0xccb9,0xdda2,0xfd65,
+0x4014,0xd6dd,0x4762,0xb4d9,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double QP[8] = {
+ 5.10862594750176621635E-2,
+ 4.98213872951233449420E0,
+ 7.58238284132545283818E1,
+ 3.66779609360150777800E2,
+ 7.10856304998926107277E2,
+ 5.97489612400613639965E2,
+ 2.11688757100572135698E2,
+ 2.52070205858023719784E1,
+};
+static double QQ[7] = {
+/* 1.00000000000000000000E0,*/
+ 7.42373277035675149943E1,
+ 1.05644886038262816351E3,
+ 4.98641058337653607651E3,
+ 9.56231892404756170795E3,
+ 7.99704160447350683650E3,
+ 2.82619278517639096600E3,
+ 3.36093607810698293419E2,
+};
+#endif
+#ifdef DEC
+static unsigned short QP[32] = {
+0037121,0037723,0055605,0151004,
+0040637,0066656,0031554,0077264,
+0041627,0122714,0153170,0161466,
+0042267,0061712,0036520,0140145,
+0042461,0133315,0131573,0071176,
+0042425,0057525,0147500,0013201,
+0042123,0130122,0061245,0154131,
+0041311,0123772,0064254,0172650,
+};
+static unsigned short QQ[28] = {
+/*0040200,0000000,0000000,0000000,*/
+0041624,0074603,0002112,0101670,
+0042604,0007135,0010162,0175565,
+0043233,0151510,0157757,0172010,
+0043425,0064506,0112006,0104276,
+0043371,0164125,0032271,0164242,
+0043060,0121425,0122750,0136013,
+0042250,0005773,0053472,0146267,
+};
+#endif
+#ifdef IBMPC
+static unsigned short QP[32] = {
+0xba40,0x6b70,0x27fa,0x3faa,
+0x8fd6,0xc66d,0xedb5,0x4013,
+0x1c67,0x9acf,0xf4b9,0x4052,
+0x180d,0x47aa,0xec79,0x4076,
+0x6e50,0xb66f,0x36d9,0x4086,
+0x02d0,0xb9e8,0xabea,0x4082,
+0xbb0b,0x4c54,0x760a,0x406a,
+0x9eb5,0x4d15,0x34ff,0x4039,
+};
+static unsigned short QQ[28] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x5077,0x6089,0x8f30,0x4052,
+0x5f6f,0xa20e,0x81cb,0x4090,
+0xfe81,0x1bfd,0x7a69,0x40b3,
+0xd118,0xd280,0xad28,0x40c2,
+0x3d14,0xa697,0x3d0a,0x40bf,
+0x1781,0xb4bd,0x1462,0x40a6,
+0x5997,0x6ae7,0x017f,0x4075,
+};
+#endif
+#ifdef MIEEE
+static unsigned short QP[32] = {
+0x3faa,0x27fa,0x6b70,0xba40,
+0x4013,0xedb5,0xc66d,0x8fd6,
+0x4052,0xf4b9,0x9acf,0x1c67,
+0x4076,0xec79,0x47aa,0x180d,
+0x4086,0x36d9,0xb66f,0x6e50,
+0x4082,0xabea,0xb9e8,0x02d0,
+0x406a,0x760a,0x4c54,0xbb0b,
+0x4039,0x34ff,0x4d15,0x9eb5,
+};
+static unsigned short QQ[28] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4052,0x8f30,0x6089,0x5077,
+0x4090,0x81cb,0xa20e,0x5f6f,
+0x40b3,0x7a69,0x1bfd,0xfe81,
+0x40c2,0xad28,0xd280,0xd118,
+0x40bf,0x3d0a,0xa697,0x3d14,
+0x40a6,0x1462,0xb4bd,0x1781,
+0x4075,0x017f,0x6ae7,0x5997,
+};
+#endif
+
+#ifdef UNK
+static double YP[6] = {
+ 1.26320474790178026440E9,
+-6.47355876379160291031E11,
+ 1.14509511541823727583E14,
+-8.12770255501325109621E15,
+ 2.02439475713594898196E17,
+-7.78877196265950026825E17,
+};
+static double YQ[8] = {
+/* 1.00000000000000000000E0,*/
+ 5.94301592346128195359E2,
+ 2.35564092943068577943E5,
+ 7.34811944459721705660E7,
+ 1.87601316108706159478E10,
+ 3.88231277496238566008E12,
+ 6.20557727146953693363E14,
+ 6.87141087355300489866E16,
+ 3.97270608116560655612E18,
+};
+#endif
+#ifdef DEC
+static unsigned short YP[24] = {
+0047626,0112763,0013715,0133045,
+0152026,0134552,0142033,0024411,
+0053720,0045245,0102210,0077565,
+0155347,0000321,0136415,0102031,
+0056463,0146550,0055633,0032605,
+0157054,0171012,0167361,0054265,
+};
+static unsigned short YQ[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0042424,0111515,0044773,0153014,
+0044546,0005405,0171307,0075774,
+0046614,0023575,0047105,0063556,
+0050613,0143034,0101533,0156026,
+0052541,0175367,0166514,0114257,
+0054415,0014466,0134350,0171154,
+0056164,0017436,0025075,0022101,
+0057534,0103614,0103663,0121772,
+};
+#endif
+#ifdef IBMPC
+static unsigned short YP[24] = {
+0xb6c5,0x62f9,0xd2be,0x41d2,
+0x6521,0x5883,0xd72d,0xc262,
+0x0fef,0xb091,0x0954,0x42da,
+0xb083,0x37a1,0xe01a,0xc33c,
+0x66b1,0x0b73,0x79ad,0x4386,
+0x2b17,0x5dde,0x9e41,0xc3a5,
+};
+static unsigned short YQ[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x7ac2,0xa93f,0x9269,0x4082,
+0xef7f,0xbe58,0xc160,0x410c,
+0xacee,0xa9c8,0x84ef,0x4191,
+0x7b83,0x906b,0x78c3,0x4211,
+0x9316,0xfda9,0x3f5e,0x428c,
+0x1e4e,0xd71d,0xa326,0x4301,
+0xa488,0xc547,0x83e3,0x436e,
+0x747f,0x90f6,0x90f1,0x43cb,
+};
+#endif
+#ifdef MIEEE
+static unsigned short YP[24] = {
+0x41d2,0xd2be,0x62f9,0xb6c5,
+0xc262,0xd72d,0x5883,0x6521,
+0x42da,0x0954,0xb091,0x0fef,
+0xc33c,0xe01a,0x37a1,0xb083,
+0x4386,0x79ad,0x0b73,0x66b1,
+0xc3a5,0x9e41,0x5dde,0x2b17,
+};
+static unsigned short YQ[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4082,0x9269,0xa93f,0x7ac2,
+0x410c,0xc160,0xbe58,0xef7f,
+0x4191,0x84ef,0xa9c8,0xacee,
+0x4211,0x78c3,0x906b,0x7b83,
+0x428c,0x3f5e,0xfda9,0x9316,
+0x4301,0xa326,0xd71d,0x1e4e,
+0x436e,0x83e3,0xc547,0xa488,
+0x43cb,0x90f1,0x90f6,0x747f,
+};
+#endif
+
+
+#ifdef UNK
+static double Z1 = 1.46819706421238932572E1;
+static double Z2 = 4.92184563216946036703E1;
+#endif
+
+#ifdef DEC
+static unsigned short DZ1[] = {0041152,0164532,0006114,0010540};
+static unsigned short DZ2[] = {0041504,0157663,0001625,0020621};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef IBMPC
+static unsigned short DZ1[] = {0x822c,0x4189,0x5d2b,0x402d};
+static unsigned short DZ2[] = {0xa432,0x6072,0x9bf6,0x4048};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef MIEEE
+static unsigned short DZ1[] = {0x402d,0x5d2b,0x4189,0x822c};
+static unsigned short DZ2[] = {0x4048,0x9bf6,0x6072,0xa432};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double sqrt ( double );
+double j1 ( double );
+#else
+double polevl(), p1evl(), log(), sin(), cos(), sqrt();
+double j1();
+#endif
+extern double TWOOPI, THPIO4, SQ2OPI;
+
+double j1(x)
+double x;
+{
+double w, z, p, q, xn;
+
+w = x;
+if( x < 0 )
+	w = -x;
+
+if( w <= 5.0 )
+	{
+	z = x * x;	
+	w = polevl( z, RP, 3 ) / p1evl( z, RQ, 8 );
+	w = w * x * (z - Z1) * (z - Z2);
+	return( w );
+	}
+
+w = 5.0/x;
+z = w * w;
+p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
+q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
+xn = x - THPIO4;
+p = p * cos(xn) - w * q * sin(xn);
+return( p * SQ2OPI / sqrt(x) );
+}
+
+
+extern double MAXNUM;
+
+double y1(x)
+double x;
+{
+double w, z, p, q, xn;
+
+if( x <= 5.0 )
+	{
+	if( x <= 0.0 )
+		{
+		mtherr( "y1", DOMAIN );
+		return( -MAXNUM );
+		}
+	z = x * x;
+	w = x * (polevl( z, YP, 5 ) / p1evl( z, YQ, 8 ));
+	w += TWOOPI * ( j1(x) * log(x)  -  1.0/x );
+	return( w );
+	}
+
+w = 5.0/x;
+z = w * w;
+p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
+q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
+xn = x - THPIO4;
+p = p * sin(xn) + w * q * cos(xn);
+return( p * SQ2OPI / sqrt(x) );
+}

libm/double/jn.c

@@ -0,0 +1,133 @@
+/*							jn.c
+ *
+ *	Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double x, y, jn();
+ *
+ * y = jn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence.  First the ratio jn/jn-1 is found by a
+ * continued fraction expansion.  Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   range      # trials      peak         rms
+ *    DEC       0, 30        5500       6.9e-17     9.3e-18
+ *    IEEE      0, 30        5000       4.4e-16     7.9e-17
+ *
+ *
+ * Not suitable for large n or x. Use jv() instead.
+ *
+ */
+
+/*							jn.c
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double j0 ( double );
+extern double j1 ( double );
+#else
+double fabs(), j0(), j1();
+#endif
+extern double MACHEP;
+
+double jn( n, x )
+int n;
+double x;
+{
+double pkm2, pkm1, pk, xk, r, ans;
+int k, sign;
+
+if( n < 0 )
+	{
+	n = -n;
+	if( (n & 1) == 0 )	/* -1**n */
+		sign = 1;
+	else
+		sign = -1;
+	}
+else
+	sign = 1;
+
+if( x < 0.0 )
+	{
+	if( n & 1 )
+		sign = -sign;
+	x = -x;
+	}
+
+if( n == 0 )
+	return( sign * j0(x) );
+if( n == 1 )
+	return( sign * j1(x) );
+if( n == 2 )
+	return( sign * (2.0 * j1(x) / x  -  j0(x)) );
+
+if( x < MACHEP )
+	return( 0.0 );
+
+/* continued fraction */
+#ifdef DEC
+k = 56;
+#else
+k = 53;
+#endif
+
+pk = 2 * (n + k);
+ans = pk;
+xk = x * x;
+
+do
+	{
+	pk -= 2.0;
+	ans = pk - (xk/ans);
+	}
+while( --k > 0 );
+ans = x/ans;
+
+/* backward recurrence */
+
+pk = 1.0;
+pkm1 = 1.0/ans;
+k = n-1;
+r = 2 * k;
+
+do
+	{
+	pkm2 = (pkm1 * r  -  pk * x) / x;
+	pk = pkm1;
+	pkm1 = pkm2;
+	r -= 2.0;
+	}
+while( --k > 0 );
+
+if( fabs(pk) > fabs(pkm1) )
+	ans = j1(x)/pk;
+else
+	ans = j0(x)/pkm1;
+return( sign * ans );
+}

libm/double/jv.c

@@ -0,0 +1,884 @@
+/*							jv.c
+ *
+ *	Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, jv();
+ *
+ * y = jv( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order v of the argument,
+ * where v is real.  Negative x is allowed if v is an integer.
+ *
+ * Several expansions are included: the ascending power
+ * series, the Hankel expansion, and two transitional
+ * expansions for large v.  If v is not too large, it
+ * is reduced by recurrence to a region of best accuracy.
+ * The transitional expansions give 12D accuracy for v > 500.
+ *
+ *
+ *
+ * ACCURACY:
+ * Results for integer v are indicated by *, where x and v
+ * both vary from -125 to +125.  Otherwise,
+ * x ranges from 0 to 125, v ranges as indicated by "domain."
+ * Error criterion is absolute, except relative when |jv()| > 1.
+ *
+ * arithmetic  v domain  x domain    # trials      peak       rms
+ *    IEEE      0,125     0,125      100000      4.6e-15    2.2e-16
+ *    IEEE   -125,0       0,125       40000      5.4e-11    3.7e-13
+ *    IEEE      0,500     0,500       20000      4.4e-15    4.0e-16
+ * Integer v:
+ *    IEEE   -125,125   -125,125      50000      3.5e-15*   1.9e-16*
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+#define DEBUG 0
+
+#ifdef DEC
+#define MAXGAM 34.84425627277176174
+#else
+#define MAXGAM 171.624376956302725
+#endif
+
+#ifdef ANSIPROT
+extern int airy ( double, double *, double *, double *, double * );
+extern double fabs ( double );
+extern double floor ( double );
+extern double frexp ( double, int * );
+extern double polevl ( double, void *, int );
+extern double j0 ( double );
+extern double j1 ( double );
+extern double sqrt ( double );
+extern double cbrt ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double acos ( double );
+extern double pow ( double, double );
+extern double gamma ( double );
+extern double lgam ( double );
+static double recur(double *, double, double *, int);
+static double jvs(double, double);
+static double hankel(double, double);
+static double jnx(double, double);
+static double jnt(double, double);
+#else
+int airy();
+double fabs(), floor(), frexp(), polevl(), j0(), j1(), sqrt(), cbrt();
+double exp(), log(), sin(), cos(), acos(), pow(), gamma(), lgam();
+static double recur(), jvs(), hankel(), jnx(), jnt();
+#endif
+
+extern double MAXNUM, MACHEP, MINLOG, MAXLOG;
+#define BIG  1.44115188075855872E+17
+
+double jv( n, x )
+double n, x;
+{
+double k, q, t, y, an;
+int i, sign, nint;
+
+nint = 0;	/* Flag for integer n */
+sign = 1;	/* Flag for sign inversion */
+an = fabs( n );
+y = floor( an );
+if( y == an )
+	{
+	nint = 1;
+	i = an - 16384.0 * floor( an/16384.0 );
+	if( n < 0.0 )
+		{
+		if( i & 1 )
+			sign = -sign;
+		n = an;
+		}
+	if( x < 0.0 )
+		{
+		if( i & 1 )
+			sign = -sign;
+		x = -x;
+		}
+	if( n == 0.0 )
+		return( j0(x) );
+	if( n == 1.0 )
+		return( sign * j1(x) );
+	}
+
+if( (x < 0.0) && (y != an) )
+	{
+	mtherr( "Jv", DOMAIN );
+	y = 0.0;
+	goto done;
+ 	}
+
+y = fabs(x);
+
+if( y < MACHEP )
+	goto underf;
+
+k = 3.6 * sqrt(y);
+t = 3.6 * sqrt(an);
+if( (y < t) && (an > 21.0) )
+	return( sign * jvs(n,x) );
+if( (an < k) && (y > 21.0) )
+	return( sign * hankel(n,x) );
+
+if( an < 500.0 )
+	{
+/* Note: if x is too large, the continued
+ * fraction will fail; but then the
+ * Hankel expansion can be used.
+ */
+	if( nint != 0 )
+		{
+		k = 0.0;
+		q = recur( &n, x, &k, 1 );
+		if( k == 0.0 )
+			{
+			y = j0(x)/q;
+			goto done;
+			}
+		if( k == 1.0 )
+			{
+			y = j1(x)/q;
+			goto done;
+			}
+		}
+
+if( an > 2.0 * y )
+	goto rlarger;
+
+	if( (n >= 0.0) && (n < 20.0)
+		&& (y > 6.0) && (y < 20.0) )
+		{
+/* Recur backwards from a larger value of n
+ */
+rlarger:
+		k = n;
+
+		y = y + an + 1.0;
+		if( y < 30.0 )
+			y = 30.0;
+		y = n + floor(y-n);
+		q = recur( &y, x, &k, 0 );
+		y = jvs(y,x) * q;
+		goto done;
+		}
+
+	if( k <= 30.0 )
+		{
+		k = 2.0;
+		}
+	else if( k < 90.0 )
+		{
+		k = (3*k)/4;
+		}
+	if( an > (k + 3.0) )
+		{
+		if( n < 0.0 )
+			k = -k;
+		q = n - floor(n);
+		k = floor(k) + q;
+		if( n > 0.0 )
+			q = recur( &n, x, &k, 1 );
+		else
+			{
+			t = k;
+			k = n;
+			q = recur( &t, x, &k, 1 );
+			k = t;
+			}
+		if( q == 0.0 )
+			{
+underf:
+			y = 0.0;
+			goto done;
+			}
+		}
+	else
+		{
+		k = n;
+		q = 1.0;
+		}
+
+/* boundary between convergence of
+ * power series and Hankel expansion
+ */
+	y = fabs(k);
+	if( y < 26.0 )
+		t = (0.0083*y + 0.09)*y + 12.9;
+	else
+		t = 0.9 * y;
+
+	if( x > t )
+		y = hankel(k,x);
+	else
+		y = jvs(k,x);
+#if DEBUG
+printf( "y = %.16e, recur q = %.16e\n", y, q );
+#endif
+	if( n > 0.0 )
+		y /= q;
+	else
+		y *= q;
+	}
+
+else
+	{
+/* For large n, use the uniform expansion
+ * or the transitional expansion.
+ * But if x is of the order of n**2,
+ * these may blow up, whereas the
+ * Hankel expansion will then work.
+ */
+	if( n < 0.0 )
+		{
+		mtherr( "Jv", TLOSS );
+		y = 0.0;
+		goto done;
+		}
+	t = x/n;
+	t /= n;
+	if( t > 0.3 )
+		y = hankel(n,x);
+	else
+		y = jnx(n,x);
+	}
+
+done:	return( sign * y);
+}
+
+/* Reduce the order by backward recurrence.
+ * AMS55 #9.1.27 and 9.1.73.
+ */
+
+static double recur( n, x, newn, cancel )
+double *n;
+double x;
+double *newn;
+int cancel;
+{
+double pkm2, pkm1, pk, qkm2, qkm1;
+/* double pkp1; */
+double k, ans, qk, xk, yk, r, t, kf;
+static double big = BIG;
+int nflag, ctr;
+
+/* continued fraction for Jn(x)/Jn-1(x)  */
+if( *n < 0.0 )
+	nflag = 1;
+else
+	nflag = 0;
+
+fstart:
+
+#if DEBUG
+printf( "recur: n = %.6e, newn = %.6e, cfrac = ", *n, *newn );
+#endif
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = x;
+qkm1 = *n + *n;
+xk = -x * x;
+yk = qkm1;
+ans = 1.0;
+ctr = 0;
+do
+	{
+	yk += 2.0;
+	pk = pkm1 * yk +  pkm2 * xk;
+	qk = qkm1 * yk +  qkm2 * xk;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+	if( qk != 0 )
+		r = pk/qk;
+	else
+		r = 0.0;
+	if( r != 0 )
+		{
+		t = fabs( (ans - r)/r );
+		ans = r;
+		}
+	else
+		t = 1.0;
+
+	if( ++ctr > 1000 )
+		{
+		mtherr( "jv", UNDERFLOW );
+		goto done;
+		}
+	if( t < MACHEP )
+		goto done;
+
+	if( fabs(pk) > big )
+		{
+		pkm2 /= big;
+		pkm1 /= big;
+		qkm2 /= big;
+		qkm1 /= big;
+		}
+	}
+while( t > MACHEP );
+
+done:
+
+#if DEBUG
+printf( "%.6e\n", ans );
+#endif
+
+/* Change n to n-1 if n < 0 and the continued fraction is small
+ */
+if( nflag > 0 )
+	{
+	if( fabs(ans) < 0.125 )
+		{
+		nflag = -1;
+		*n = *n - 1.0;
+		goto fstart;
+		}
+	}
+
+
+kf = *newn;
+
+/* backward recurrence
+ *              2k
+ *  J   (x)  =  --- J (x)  -  J   (x)
+ *   k-1         x   k         k+1
+ */
+
+pk = 1.0;
+pkm1 = 1.0/ans;
+k = *n - 1.0;
+r = 2 * k;
+do
+	{
+	pkm2 = (pkm1 * r  -  pk * x) / x;
+	/*	pkp1 = pk; */
+	pk = pkm1;
+	pkm1 = pkm2;
+	r -= 2.0;
+/*
+	t = fabs(pkp1) + fabs(pk);
+	if( (k > (kf + 2.5)) && (fabs(pkm1) < 0.25*t) )
+		{
+		k -= 1.0;
+		t = x*x;
+		pkm2 = ( (r*(r+2.0)-t)*pk - r*x*pkp1 )/t;
+		pkp1 = pk;
+		pk = pkm1;
+		pkm1 = pkm2;
+		r -= 2.0;
+		}
+*/
+	k -= 1.0;
+	}
+while( k > (kf + 0.5) );
+
+/* Take the larger of the last two iterates
+ * on the theory that it may have less cancellation error.
+ */
+
+if( cancel )
+	{
+	if( (kf >= 0.0) && (fabs(pk) > fabs(pkm1)) )
+		{
+		k += 1.0;
+		pkm2 = pk;
+		}
+	}
+*newn = k;
+#if DEBUG
+printf( "newn %.6e rans %.6e\n", k, pkm2 );
+#endif
+return( pkm2 );
+}
+
+
+
+/* Ascending power series for Jv(x).
+ * AMS55 #9.1.10.
+ */
+
+extern double PI;
+extern int sgngam;
+
+static double jvs( n, x )
+double n, x;
+{
+double t, u, y, z, k;
+int ex;
+
+z = -x * x / 4.0;
+u = 1.0;
+y = u;
+k = 1.0;
+t = 1.0;
+
+while( t > MACHEP )
+	{
+	u *= z / (k * (n+k));
+	y += u;
+	k += 1.0;
+	if( y != 0 )
+		t = fabs( u/y );
+	}
+#if DEBUG
+printf( "power series=%.5e ", y );
+#endif
+t = frexp( 0.5*x, &ex );
+ex = ex * n;
+if(  (ex > -1023)
+  && (ex < 1023) 
+  && (n > 0.0)
+  && (n < (MAXGAM-1.0)) )
+	{
+	t = pow( 0.5*x, n ) / gamma( n + 1.0 );
+#if DEBUG
+printf( "pow(.5*x, %.4e)/gamma(n+1)=%.5e\n", n, t );
+#endif
+	y *= t;
+	}
+else
+	{
+#if DEBUG
+	z = n * log(0.5*x);
+	k = lgam( n+1.0 );
+	t = z - k;
+	printf( "log pow=%.5e, lgam(%.4e)=%.5e\n", z, n+1.0, k );
+#else
+	t = n * log(0.5*x) - lgam(n + 1.0);
+#endif
+	if( y < 0 )
+		{
+		sgngam = -sgngam;
+		y = -y;
+		}
+	t += log(y);
+#if DEBUG
+printf( "log y=%.5e\n", log(y) );
+#endif
+	if( t < -MAXLOG )
+		{
+		return( 0.0 );
+		}
+	if( t > MAXLOG )
+		{
+		mtherr( "Jv", OVERFLOW );
+		return( MAXNUM );
+		}
+	y = sgngam * exp( t );
+	}
+return(y);
+}
+
+/* Hankel's asymptotic expansion
+ * for large x.
+ * AMS55 #9.2.5.
+ */
+
+static double hankel( n, x )
+double n, x;
+{
+double t, u, z, k, sign, conv;
+double p, q, j, m, pp, qq;
+int flag;
+
+m = 4.0*n*n;
+j = 1.0;
+z = 8.0 * x;
+k = 1.0;
+p = 1.0;
+u = (m - 1.0)/z;
+q = u;
+sign = 1.0;
+conv = 1.0;
+flag = 0;
+t = 1.0;
+pp = 1.0e38;
+qq = 1.0e38;
+
+while( t > MACHEP )
+	{
+	k += 2.0;
+	j += 1.0;
+	sign = -sign;
+	u *= (m - k * k)/(j * z);
+	p += sign * u;
+	k += 2.0;
+	j += 1.0;
+	u *= (m - k * k)/(j * z);
+	q += sign * u;
+	t = fabs(u/p);
+	if( t < conv )
+		{
+		conv = t;
+		qq = q;
+		pp = p;
+		flag = 1;
+		}
+/* stop if the terms start getting larger */
+	if( (flag != 0) && (t > conv) )
+		{
+#if DEBUG
+		printf( "Hankel: convergence to %.4E\n", conv );
+#endif
+		goto hank1;
+		}
+	}	
+
+hank1:
+u = x - (0.5*n + 0.25) * PI;
+t = sqrt( 2.0/(PI*x) ) * ( pp * cos(u) - qq * sin(u) );
+#if DEBUG
+printf( "hank: %.6e\n", t );
+#endif
+return( t );
+}
+
+
+/* Asymptotic expansion for large n.
+ * AMS55 #9.3.35.
+ */
+
+static double lambda[] = {
+  1.0,
+  1.041666666666666666666667E-1,
+  8.355034722222222222222222E-2,
+  1.282265745563271604938272E-1,
+  2.918490264641404642489712E-1,
+  8.816272674437576524187671E-1,
+  3.321408281862767544702647E+0,
+  1.499576298686255465867237E+1,
+  7.892301301158651813848139E+1,
+  4.744515388682643231611949E+2,
+  3.207490090890661934704328E+3
+};
+static double mu[] = {
+  1.0,
+ -1.458333333333333333333333E-1,
+ -9.874131944444444444444444E-2,
+ -1.433120539158950617283951E-1,
+ -3.172272026784135480967078E-1,
+ -9.424291479571202491373028E-1,
+ -3.511203040826354261542798E+0,
+ -1.572726362036804512982712E+1,
+ -8.228143909718594444224656E+1,
+ -4.923553705236705240352022E+2,
+ -3.316218568547972508762102E+3
+};
+static double P1[] = {
+ -2.083333333333333333333333E-1,
+  1.250000000000000000000000E-1
+};
+static double P2[] = {
+  3.342013888888888888888889E-1,
+ -4.010416666666666666666667E-1,
+  7.031250000000000000000000E-2
+};
+static double P3[] = {
+ -1.025812596450617283950617E+0,
+  1.846462673611111111111111E+0,
+ -8.912109375000000000000000E-1,
+  7.324218750000000000000000E-2
+};
+static double P4[] = {
+  4.669584423426247427983539E+0,
+ -1.120700261622299382716049E+1,
+  8.789123535156250000000000E+0,
+ -2.364086914062500000000000E+0,
+  1.121520996093750000000000E-1
+};
+static double P5[] = {
+ -2.8212072558200244877E1,
+  8.4636217674600734632E1,
+ -9.1818241543240017361E1,
+  4.2534998745388454861E1,
+ -7.3687943594796316964E0,
+  2.27108001708984375E-1
+};
+static double P6[] = {
+  2.1257013003921712286E2,
+ -7.6525246814118164230E2,
+  1.0599904525279998779E3,
+ -6.9957962737613254123E2,
+  2.1819051174421159048E2,
+ -2.6491430486951555525E1,
+  5.7250142097473144531E-1
+};
+static double P7[] = {
+ -1.9194576623184069963E3,
+  8.0617221817373093845E3,
+ -1.3586550006434137439E4,
+  1.1655393336864533248E4,
+ -5.3056469786134031084E3,
+  1.2009029132163524628E3,
+ -1.0809091978839465550E2,
+  1.7277275025844573975E0
+};
+
+
+static double jnx( n, x )
+double n, x;
+{
+double zeta, sqz, zz, zp, np;
+double cbn, n23, t, z, sz;
+double pp, qq, z32i, zzi;
+double ak, bk, akl, bkl;
+int sign, doa, dob, nflg, k, s, tk, tkp1, m;
+static double u[8];
+static double ai, aip, bi, bip;
+
+/* Test for x very close to n.
+ * Use expansion for transition region if so.
+ */
+cbn = cbrt(n);
+z = (x - n)/cbn;
+if( fabs(z) <= 0.7 )
+	return( jnt(n,x) );
+
+z = x/n;
+zz = 1.0 - z*z;
+if( zz == 0.0 )
+	return(0.0);
+
+if( zz > 0.0 )
+	{
+	sz = sqrt( zz );
+	t = 1.5 * (log( (1.0+sz)/z ) - sz );	/* zeta ** 3/2		*/
+	zeta = cbrt( t * t );
+	nflg = 1;
+	}
+else
+	{
+	sz = sqrt(-zz);
+	t = 1.5 * (sz - acos(1.0/z));
+	zeta = -cbrt( t * t );
+	nflg = -1;
+	}
+z32i = fabs(1.0/t);
+sqz = cbrt(t);
+
+/* Airy function */
+n23 = cbrt( n * n );
+t = n23 * zeta;
+
+#if DEBUG
+printf("zeta %.5E, Airy(%.5E)\n", zeta, t );
+#endif
+airy( t, &ai, &aip, &bi, &bip );
+
+/* polynomials in expansion */
+u[0] = 1.0;
+zzi = 1.0/zz;
+u[1] = polevl( zzi, P1, 1 )/sz;
+u[2] = polevl( zzi, P2, 2 )/zz;
+u[3] = polevl( zzi, P3, 3 )/(sz*zz);
+pp = zz*zz;
+u[4] = polevl( zzi, P4, 4 )/pp;
+u[5] = polevl( zzi, P5, 5 )/(pp*sz);
+pp *= zz;
+u[6] = polevl( zzi, P6, 6 )/pp;
+u[7] = polevl( zzi, P7, 7 )/(pp*sz);
+
+#if DEBUG
+for( k=0; k<=7; k++ )
+	printf( "u[%d] = %.5E\n", k, u[k] );
+#endif
+
+pp = 0.0;
+qq = 0.0;
+np = 1.0;
+/* flags to stop when terms get larger */
+doa = 1;
+dob = 1;
+akl = MAXNUM;
+bkl = MAXNUM;
+
+for( k=0; k<=3; k++ )
+	{
+	tk = 2 * k;
+	tkp1 = tk + 1;
+	zp = 1.0;
+	ak = 0.0;
+	bk = 0.0;
+	for( s=0; s<=tk; s++ )
+		{
+		if( doa )
+			{
+			if( (s & 3) > 1 )
+				sign = nflg;
+			else
+				sign = 1;
+			ak += sign * mu[s] * zp * u[tk-s];
+			}
+
+		if( dob )
+			{
+			m = tkp1 - s;
+			if( ((m+1) & 3) > 1 )
+				sign = nflg;
+			else
+				sign = 1;
+			bk += sign * lambda[s] * zp * u[m];
+			}
+		zp *= z32i;
+		}
+
+	if( doa )
+		{
+		ak *= np;
+		t = fabs(ak);
+		if( t < akl )
+			{
+			akl = t;
+			pp += ak;
+			}
+		else
+			doa = 0;
+		}
+
+	if( dob )
+		{
+		bk += lambda[tkp1] * zp * u[0];
+		bk *= -np/sqz;
+		t = fabs(bk);
+		if( t < bkl )
+			{
+			bkl = t;
+			qq += bk;
+			}
+		else
+			dob = 0;
+		}
+#if DEBUG
+	printf("a[%d] %.5E, b[%d] %.5E\n", k, ak, k, bk );
+#endif
+	if( np < MACHEP )
+		break;
+	np /= n*n;
+	}
+
+/* normalizing factor ( 4*zeta/(1 - z**2) )**1/4	*/
+t = 4.0 * zeta/zz;
+t = sqrt( sqrt(t) );
+
+t *= ai*pp/cbrt(n)  +  aip*qq/(n23*n);
+return(t);
+}
+
+/* Asymptotic expansion for transition region,
+ * n large and x close to n.
+ * AMS55 #9.3.23.
+ */
+
+static double PF2[] = {
+ -9.0000000000000000000e-2,
+  8.5714285714285714286e-2
+};
+static double PF3[] = {
+  1.3671428571428571429e-1,
+ -5.4920634920634920635e-2,
+ -4.4444444444444444444e-3
+};
+static double PF4[] = {
+  1.3500000000000000000e-3,
+ -1.6036054421768707483e-1,
+  4.2590187590187590188e-2,
+  2.7330447330447330447e-3
+};
+static double PG1[] = {
+ -2.4285714285714285714e-1,
+  1.4285714285714285714e-2
+};
+static double PG2[] = {
+ -9.0000000000000000000e-3,
+  1.9396825396825396825e-1,
+ -1.1746031746031746032e-2
+};
+static double PG3[] = {
+  1.9607142857142857143e-2,
+ -1.5983694083694083694e-1,
+  6.3838383838383838384e-3
+};
+
+
+static double jnt( n, x )
+double n, x;
+{
+double z, zz, z3;
+double cbn, n23, cbtwo;
+double ai, aip, bi, bip;	/* Airy functions */
+double nk, fk, gk, pp, qq;
+double F[5], G[4];
+int k;
+
+cbn = cbrt(n);
+z = (x - n)/cbn;
+cbtwo = cbrt( 2.0 );
+
+/* Airy function */
+zz = -cbtwo * z;
+airy( zz, &ai, &aip, &bi, &bip );
+
+/* polynomials in expansion */
+zz = z * z;
+z3 = zz * z;
+F[0] = 1.0;
+F[1] = -z/5.0;
+F[2] = polevl( z3, PF2, 1 ) * zz;
+F[3] = polevl( z3, PF3, 2 );
+F[4] = polevl( z3, PF4, 3 ) * z;
+G[0] = 0.3 * zz;
+G[1] = polevl( z3, PG1, 1 );
+G[2] = polevl( z3, PG2, 2 ) * z;
+G[3] = polevl( z3, PG3, 2 ) * zz;
+#if DEBUG
+for( k=0; k<=4; k++ )
+	printf( "F[%d] = %.5E\n", k, F[k] );
+for( k=0; k<=3; k++ )
+	printf( "G[%d] = %.5E\n", k, G[k] );
+#endif
+pp = 0.0;
+qq = 0.0;
+nk = 1.0;
+n23 = cbrt( n * n );
+
+for( k=0; k<=4; k++ )
+	{
+	fk = F[k]*nk;
+	pp += fk;
+	if( k != 4 )
+		{
+		gk = G[k]*nk;
+		qq += gk;
+		}
+#if DEBUG
+	printf("fk[%d] %.5E, gk[%d] %.5E\n", k, fk, k, gk );
+#endif
+	nk /= n23;
+	}
+
+fk = cbtwo * ai * pp/cbn  +  cbrt(4.0) * aip * qq/n;
+return(fk);
+}

libm/double/k0.c

@@ -0,0 +1,333 @@
+/*							k0.c
+ *
+ *	Modified Bessel function, third kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0();
+ *
+ * y = k0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order zero of the argument.
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at 2000 random points between 0 and 8.  Peak absolute
+ * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        3100       1.3e-16     2.1e-17
+ *    IEEE      0, 30       30000       1.2e-15     1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ *  K0 domain          x <= 0          MAXNUM
+ *
+ */
+/*							k0e()
+ *
+ *	Modified Bessel function, third kind, order zero,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0e();
+ *
+ * y = k0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 30       30000       1.4e-15     1.4e-16
+ * See k0().
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for K0(x) + log(x/2) I0(x)
+ * in the interval [0,2].  The odd order coefficients are all
+ * zero; only the even order coefficients are listed.
+ * 
+ * lim(x->0){ K0(x) + log(x/2) I0(x) } = -EUL.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+ 1.37446543561352307156E-16,
+ 4.25981614279661018399E-14,
+ 1.03496952576338420167E-11,
+ 1.90451637722020886025E-9,
+ 2.53479107902614945675E-7,
+ 2.28621210311945178607E-5,
+ 1.26461541144692592338E-3,
+ 3.59799365153615016266E-2,
+ 3.44289899924628486886E-1,
+-5.35327393233902768720E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0023036,0073417,0032477,0165673,
+0025077,0154126,0016046,0012517,
+0027066,0011342,0035211,0005041,
+0031002,0160233,0037454,0050224,
+0032610,0012747,0037712,0173741,
+0034277,0144007,0172147,0162375,
+0035645,0140563,0125431,0165626,
+0037023,0057662,0125124,0102051,
+0037660,0043304,0004411,0166707,
+0140011,0005467,0047227,0130370
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0xfd77,0xe6a7,0xcee1,0x3ca3,
+0xc2aa,0xc384,0xfb0a,0x3d27,
+0x2144,0x4751,0xc25c,0x3da6,
+0x8a13,0x67e5,0x5c13,0x3e20,
+0x5efc,0xe7f9,0x02bc,0x3e91,
+0xfca0,0xfe8c,0xf900,0x3ef7,
+0x3d73,0x7563,0xb82e,0x3f54,
+0x9085,0x554a,0x6bf6,0x3fa2,
+0x3db9,0x8121,0x08d8,0x3fd6,
+0xf61f,0xe9d2,0x2166,0xbfe1
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0x3ca3,0xcee1,0xe6a7,0xfd77,
+0x3d27,0xfb0a,0xc384,0xc2aa,
+0x3da6,0xc25c,0x4751,0x2144,
+0x3e20,0x5c13,0x67e5,0x8a13,
+0x3e91,0x02bc,0xe7f9,0x5efc,
+0x3ef7,0xf900,0xfe8c,0xfca0,
+0x3f54,0xb82e,0x7563,0x3d73,
+0x3fa2,0x6bf6,0x554a,0x9085,
+0x3fd6,0x08d8,0x8121,0x3db9,
+0xbfe1,0x2166,0xe9d2,0xf61f
+};
+#endif
+
+
+
+/* Chebyshev coefficients for exp(x) sqrt(x) K0(x)
+ * in the inverted interval [2,infinity].
+ * 
+ * lim(x->inf){ exp(x) sqrt(x) K0(x) } = sqrt(pi/2).
+ */
+
+#ifdef UNK
+static double B[] = {
+ 5.30043377268626276149E-18,
+-1.64758043015242134646E-17,
+ 5.21039150503902756861E-17,
+-1.67823109680541210385E-16,
+ 5.51205597852431940784E-16,
+-1.84859337734377901440E-15,
+ 6.34007647740507060557E-15,
+-2.22751332699166985548E-14,
+ 8.03289077536357521100E-14,
+-2.98009692317273043925E-13,
+ 1.14034058820847496303E-12,
+-4.51459788337394416547E-12,
+ 1.85594911495471785253E-11,
+-7.95748924447710747776E-11,
+ 3.57739728140030116597E-10,
+-1.69753450938905987466E-9,
+ 8.57403401741422608519E-9,
+-4.66048989768794782956E-8,
+ 2.76681363944501510342E-7,
+-1.83175552271911948767E-6,
+ 1.39498137188764993662E-5,
+-1.28495495816278026384E-4,
+ 1.56988388573005337491E-3,
+-3.14481013119645005427E-2,
+ 2.44030308206595545468E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0021703,0106456,0076144,0173406,
+0122227,0173144,0116011,0030033,
+0022560,0044562,0006506,0067642,
+0123101,0076243,0123273,0131013,
+0023436,0157713,0056243,0141331,
+0124005,0032207,0063726,0164664,
+0024344,0066342,0051756,0162300,
+0124710,0121365,0154053,0077022,
+0025264,0161166,0066246,0077420,
+0125647,0141671,0006443,0103212,
+0026240,0076431,0077147,0160445,
+0126636,0153741,0174002,0105031,
+0027243,0040102,0035375,0163073,
+0127656,0176256,0113476,0044653,
+0030304,0125544,0006377,0130104,
+0130751,0047257,0110537,0127324,
+0031423,0046400,0014772,0012164,
+0132110,0025240,0155247,0112570,
+0032624,0105314,0007437,0021574,
+0133365,0155243,0174306,0116506,
+0034152,0004776,0061643,0102504,
+0135006,0136277,0036104,0175023,
+0035715,0142217,0162474,0115022,
+0137000,0147671,0065177,0134356,
+0040434,0026754,0175163,0044070
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0x9ee1,0xcf8c,0x71a5,0x3c58,
+0x2603,0x9381,0xfecc,0xbc72,
+0xcdf4,0x41a8,0x092e,0x3c8e,
+0x7641,0x74d7,0x2f94,0xbca8,
+0x785b,0x6b94,0xdbf9,0x3cc3,
+0xdd36,0xecfa,0xa690,0xbce0,
+0xdc98,0x4a7d,0x8d9c,0x3cfc,
+0x6fc2,0xbb05,0x145e,0xbd19,
+0xcfe2,0xcd94,0x9c4e,0x3d36,
+0x70d1,0x21a4,0xf877,0xbd54,
+0xfc25,0x2fcc,0x0fa3,0x3d74,
+0x5143,0x3f00,0xdafc,0xbd93,
+0xbcc7,0x475f,0x6808,0x3db4,
+0xc935,0xd2e7,0xdf95,0xbdd5,
+0xf608,0x819f,0x956c,0x3df8,
+0xf5db,0xf22b,0x29d5,0xbe1d,
+0x428e,0x033f,0x69a0,0x3e42,
+0xf2af,0x1b54,0x0554,0xbe69,
+0xe46f,0x81e3,0x9159,0x3e92,
+0xd3a9,0x7f18,0xbb54,0xbebe,
+0x70a9,0xcc74,0x413f,0x3eed,
+0x9f42,0xe788,0xd797,0xbf20,
+0x9342,0xfca7,0xb891,0x3f59,
+0xf71e,0x2d4f,0x19f7,0xbfa0,
+0x6907,0x9f4e,0x85bd,0x4003
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0x3c58,0x71a5,0xcf8c,0x9ee1,
+0xbc72,0xfecc,0x9381,0x2603,
+0x3c8e,0x092e,0x41a8,0xcdf4,
+0xbca8,0x2f94,0x74d7,0x7641,
+0x3cc3,0xdbf9,0x6b94,0x785b,
+0xbce0,0xa690,0xecfa,0xdd36,
+0x3cfc,0x8d9c,0x4a7d,0xdc98,
+0xbd19,0x145e,0xbb05,0x6fc2,
+0x3d36,0x9c4e,0xcd94,0xcfe2,
+0xbd54,0xf877,0x21a4,0x70d1,
+0x3d74,0x0fa3,0x2fcc,0xfc25,
+0xbd93,0xdafc,0x3f00,0x5143,
+0x3db4,0x6808,0x475f,0xbcc7,
+0xbdd5,0xdf95,0xd2e7,0xc935,
+0x3df8,0x956c,0x819f,0xf608,
+0xbe1d,0x29d5,0xf22b,0xf5db,
+0x3e42,0x69a0,0x033f,0x428e,
+0xbe69,0x0554,0x1b54,0xf2af,
+0x3e92,0x9159,0x81e3,0xe46f,
+0xbebe,0xbb54,0x7f18,0xd3a9,
+0x3eed,0x413f,0xcc74,0x70a9,
+0xbf20,0xd797,0xe788,0x9f42,
+0x3f59,0xb891,0xfca7,0x9342,
+0xbfa0,0x19f7,0x2d4f,0xf71e,
+0x4003,0x85bd,0x9f4e,0x6907
+};
+#endif
+
+/*							k0.c	*/
+#ifdef ANSIPROT 
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double i0 ( double );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double chbevl(), exp(), i0(), log(), sqrt();
+#endif
+extern double PI;
+extern double MAXNUM;
+
+double k0(x)
+double x;
+{
+double y, z;
+
+if( x <= 0.0 )
+	{
+	mtherr( "k0", DOMAIN );
+	return( MAXNUM );
+	}
+
+if( x <= 2.0 )
+	{
+	y = x * x - 2.0;
+	y = chbevl( y, A, 10 ) - log( 0.5 * x ) * i0(x);
+	return( y );
+	}
+z = 8.0/x - 2.0;
+y = exp(-x) * chbevl( z, B, 25 ) / sqrt(x);
+return(y);
+}
+
+
+
+
+double k0e( x )
+double x;
+{
+double y;
+
+if( x <= 0.0 )
+	{
+	mtherr( "k0e", DOMAIN );
+	return( MAXNUM );
+	}
+
+if( x <= 2.0 )
+	{
+	y = x * x - 2.0;
+	y = chbevl( y, A, 10 ) - log( 0.5 * x ) * i0(x);
+	return( y * exp(x) );
+	}
+
+y = chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x);
+return(y);
+}

libm/double/k1.c

@@ -0,0 +1,335 @@
+/*							k1.c
+ *
+ *	Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1();
+ *
+ * y = k1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity).  Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 30        3300       8.9e-17     2.2e-17
+ *    IEEE      0, 30       30000       1.2e-15     1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * k1 domain          x <= 0          MAXNUM
+ *
+ */
+/*							k1e.c
+ *
+ *	Modified Bessel function, third kind, order one,
+ *	exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1e();
+ *
+ * y = k1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ *      k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 30       30000       7.8e-16     1.2e-16
+ * See k1().
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for x(K1(x) - log(x/2) I1(x))
+ * in the interval [0,2].
+ * 
+ * lim(x->0){ x(K1(x) - log(x/2) I1(x)) } = 1.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+-7.02386347938628759343E-18,
+-2.42744985051936593393E-15,
+-6.66690169419932900609E-13,
+-1.41148839263352776110E-10,
+-2.21338763073472585583E-8,
+-2.43340614156596823496E-6,
+-1.73028895751305206302E-4,
+-6.97572385963986435018E-3,
+-1.22611180822657148235E-1,
+-3.53155960776544875667E-1,
+ 1.52530022733894777053E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0122001,0110501,0164746,0151255,
+0124056,0165213,0150034,0147377,
+0126073,0124026,0167207,0001044,
+0130033,0030735,0141061,0033116,
+0131676,0020350,0121341,0107175,
+0133443,0046631,0062031,0070716,
+0135065,0067427,0026435,0164022,
+0136344,0112234,0165752,0006222,
+0137373,0015622,0017016,0155636,
+0137664,0150333,0125730,0067240,
+0040303,0036411,0130200,0043120
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0xda56,0x3d3c,0x3228,0xbc60,
+0x99e0,0x7a03,0xdd51,0xbce5,
+0xe045,0xddd0,0x7502,0xbd67,
+0x26ca,0xb846,0x663b,0xbde3,
+0x31d0,0x145c,0xc41d,0xbe57,
+0x2e3a,0x2c83,0x69b3,0xbec4,
+0xbd02,0xe5a3,0xade2,0xbf26,
+0x4192,0x9d7d,0x9293,0xbf7c,
+0xdb74,0x43c1,0x6372,0xbfbf,
+0x0dd4,0x757b,0x9a1b,0xbfd6,
+0x08ca,0x3610,0x67a1,0x3ff8
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0xbc60,0x3228,0x3d3c,0xda56,
+0xbce5,0xdd51,0x7a03,0x99e0,
+0xbd67,0x7502,0xddd0,0xe045,
+0xbde3,0x663b,0xb846,0x26ca,
+0xbe57,0xc41d,0x145c,0x31d0,
+0xbec4,0x69b3,0x2c83,0x2e3a,
+0xbf26,0xade2,0xe5a3,0xbd02,
+0xbf7c,0x9293,0x9d7d,0x4192,
+0xbfbf,0x6372,0x43c1,0xdb74,
+0xbfd6,0x9a1b,0x757b,0x0dd4,
+0x3ff8,0x67a1,0x3610,0x08ca
+};
+#endif
+
+
+
+/* Chebyshev coefficients for exp(x) sqrt(x) K1(x)
+ * in the interval [2,infinity].
+ *
+ * lim(x->inf){ exp(x) sqrt(x) K1(x) } = sqrt(pi/2).
+ */
+
+#ifdef UNK
+static double B[] =
+{
+-5.75674448366501715755E-18,
+ 1.79405087314755922667E-17,
+-5.68946255844285935196E-17,
+ 1.83809354436663880070E-16,
+-6.05704724837331885336E-16,
+ 2.03870316562433424052E-15,
+-7.01983709041831346144E-15,
+ 2.47715442448130437068E-14,
+-8.97670518232499435011E-14,
+ 3.34841966607842919884E-13,
+-1.28917396095102890680E-12,
+ 5.13963967348173025100E-12,
+-2.12996783842756842877E-11,
+ 9.21831518760500529508E-11,
+-4.19035475934189648750E-10,
+ 2.01504975519703286596E-9,
+-1.03457624656780970260E-8,
+ 5.74108412545004946722E-8,
+-3.50196060308781257119E-7,
+ 2.40648494783721712015E-6,
+-1.93619797416608296024E-5,
+ 1.95215518471351631108E-4,
+-2.85781685962277938680E-3,
+ 1.03923736576817238437E-1,
+ 2.72062619048444266945E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0121724,0061352,0013041,0150076,
+0022245,0074324,0016172,0173232,
+0122603,0030250,0135670,0165221,
+0023123,0165362,0023561,0060124,
+0123456,0112436,0141654,0073623,
+0024022,0163557,0077564,0006753,
+0124374,0165221,0131014,0026524,
+0024737,0017512,0144250,0175451,
+0125312,0021456,0123136,0076633,
+0025674,0077720,0020125,0102607,
+0126265,0067543,0007744,0043701,
+0026664,0152702,0033002,0074202,
+0127273,0055234,0120016,0071733,
+0027712,0133200,0042441,0075515,
+0130346,0057000,0015456,0074470,
+0031012,0074441,0051636,0111155,
+0131461,0136444,0177417,0002101,
+0032166,0111743,0032176,0021410,
+0132674,0001224,0076555,0027060,
+0033441,0077430,0135226,0106663,
+0134242,0065610,0167155,0113447,
+0035114,0131304,0043664,0102163,
+0136073,0045065,0171465,0122123,
+0037324,0152767,0147401,0017732,
+0040456,0017275,0050061,0062120,
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0x3a08,0x42c4,0x8c5d,0xbc5a,
+0x5ed3,0x838f,0xaf1a,0x3c74,
+0x1d52,0x1777,0x6615,0xbc90,
+0x2c0b,0x44ee,0x7d5e,0x3caa,
+0x8ef2,0xd875,0xd2a3,0xbcc5,
+0x81bd,0xefee,0x5ced,0x3ce2,
+0x85ab,0x3641,0x9d52,0xbcff,
+0x1f65,0x5915,0xe3e9,0x3d1b,
+0xcfb3,0xd4cb,0x4465,0xbd39,
+0xb0b1,0x040a,0x8ffa,0x3d57,
+0x88f8,0x61fc,0xadec,0xbd76,
+0x4f10,0x46c0,0x9ab8,0x3d96,
+0xce7b,0x9401,0x6b53,0xbdb7,
+0x2f6a,0x08a4,0x56d0,0x3dd9,
+0xcf27,0x0365,0xcbc0,0xbdfc,
+0xd24e,0x2a73,0x4f24,0x3e21,
+0xe088,0x9fe1,0x37a4,0xbe46,
+0xc461,0x668f,0xd27c,0x3e6e,
+0xa5c6,0x8fad,0x8052,0xbe97,
+0xd1b6,0x1752,0x2fe3,0x3ec4,
+0xb2e5,0x1dcd,0x4d71,0xbef4,
+0x908e,0x88f6,0x9658,0x3f29,
+0xb48a,0xbe66,0x6946,0xbf67,
+0x23fb,0xf9e0,0x9abe,0x3fba,
+0x2c8a,0xaa06,0xc3d7,0x4005
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0xbc5a,0x8c5d,0x42c4,0x3a08,
+0x3c74,0xaf1a,0x838f,0x5ed3,
+0xbc90,0x6615,0x1777,0x1d52,
+0x3caa,0x7d5e,0x44ee,0x2c0b,
+0xbcc5,0xd2a3,0xd875,0x8ef2,
+0x3ce2,0x5ced,0xefee,0x81bd,
+0xbcff,0x9d52,0x3641,0x85ab,
+0x3d1b,0xe3e9,0x5915,0x1f65,
+0xbd39,0x4465,0xd4cb,0xcfb3,
+0x3d57,0x8ffa,0x040a,0xb0b1,
+0xbd76,0xadec,0x61fc,0x88f8,
+0x3d96,0x9ab8,0x46c0,0x4f10,
+0xbdb7,0x6b53,0x9401,0xce7b,
+0x3dd9,0x56d0,0x08a4,0x2f6a,
+0xbdfc,0xcbc0,0x0365,0xcf27,
+0x3e21,0x4f24,0x2a73,0xd24e,
+0xbe46,0x37a4,0x9fe1,0xe088,
+0x3e6e,0xd27c,0x668f,0xc461,
+0xbe97,0x8052,0x8fad,0xa5c6,
+0x3ec4,0x2fe3,0x1752,0xd1b6,
+0xbef4,0x4d71,0x1dcd,0xb2e5,
+0x3f29,0x9658,0x88f6,0x908e,
+0xbf67,0x6946,0xbe66,0xb48a,
+0x3fba,0x9abe,0xf9e0,0x23fb,
+0x4005,0xc3d7,0xaa06,0x2c8a
+};
+#endif
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double i1 ( double );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double chbevl(), exp(), i1(), log(), sqrt();
+#endif
+extern double PI;
+extern double MINLOG, MAXNUM;
+
+double k1(x)
+double x;
+{
+double y, z;
+
+z = 0.5 * x;
+if( z <= 0.0 )
+	{
+	mtherr( "k1", DOMAIN );
+	return( MAXNUM );
+	}
+
+if( x <= 2.0 )
+	{
+	y = x * x - 2.0;
+	y =  log(z) * i1(x)  +  chbevl( y, A, 11 ) / x;
+	return( y );
+	}
+
+return(  exp(-x) * chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) );
+}
+
+
+
+
+double k1e( x )
+double x;
+{
+double y;
+
+if( x <= 0.0 )
+	{
+	mtherr( "k1e", DOMAIN );
+	return( MAXNUM );
+	}
+
+if( x <= 2.0 )
+	{
+	y = x * x - 2.0;
+	y =  log( 0.5 * x ) * i1(x)  +  chbevl( y, A, 11 ) / x;
+	return( y * exp(x) );
+	}
+
+return(  chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) );
+}

libm/double/kn.c

@@ -0,0 +1,255 @@
+/*							kn.c
+ *
+ *	Modified Bessel function, third kind, integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, kn();
+ * int n;
+ *
+ * y = kn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order n of the argument.
+ *
+ * The range is partitioned into the two intervals [0,9.55] and
+ * (9.55, infinity).  An ascending power series is used in the
+ * low range, and an asymptotic expansion in the high range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         3000       1.3e-9      5.8e-11
+ *    IEEE      0,30        90000       1.8e-8      3.0e-10
+ *
+ *  Error is high only near the crossover point x = 9.55
+ * between the two expansions used.
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+
+/*
+Algorithm for Kn.
+                       n-1 
+                   -n   -  (n-k-1)!    2   k
+K (x)  =  0.5 (x/2)     >  -------- (-x /4)
+ n                      -     k!
+                       k=0
+
+                    inf.                                   2   k
+       n         n   -                                   (x /4)
+ + (-1)  0.5(x/2)    >  {p(k+1) + p(n+k+1) - 2log(x/2)} ---------
+                     -                                  k! (n+k)!
+                    k=0
+
+where  p(m) is the psi function: p(1) = -EUL and
+
+                      m-1
+                       -
+      p(m)  =  -EUL +  >  1/k
+                       -
+                      k=1
+
+For large x,
+                                         2        2     2
+                                      u-1     (u-1 )(u-3 )
+K (z)  =  sqrt(pi/2z) exp(-z) { 1 + ------- + ------------ + ...}
+ v                                        1            2
+                                    1! (8z)     2! (8z)
+asymptotically, where
+
+           2
+    u = 4 v .
+
+*/
+
+#include <math.h>
+
+#define EUL 5.772156649015328606065e-1
+#define MAXFAC 31
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double fabs(), exp(), log(), sqrt();
+#endif
+extern double MACHEP, MAXNUM, MAXLOG, PI;
+
+double kn( nn, x )
+int nn;
+double x;
+{
+double k, kf, nk1f, nkf, zn, t, s, z0, z;
+double ans, fn, pn, pk, zmn, tlg, tox;
+int i, n;
+
+if( nn < 0 )
+	n = -nn;
+else
+	n = nn;
+
+if( n > MAXFAC )
+	{
+overf:
+	mtherr( "kn", OVERFLOW );
+	return( MAXNUM );
+	}
+
+if( x <= 0.0 )
+	{
+	if( x < 0.0 )
+		mtherr( "kn", DOMAIN );
+	else
+		mtherr( "kn", SING );
+	return( MAXNUM );
+	}
+
+
+if( x > 9.55 )
+	goto asymp;
+
+ans = 0.0;
+z0 = 0.25 * x * x;
+fn = 1.0;
+pn = 0.0;
+zmn = 1.0;
+tox = 2.0/x;
+
+if( n > 0 )
+	{
+	/* compute factorial of n and psi(n) */
+	pn = -EUL;
+	k = 1.0;
+	for( i=1; i<n; i++ )
+		{
+		pn += 1.0/k;
+		k += 1.0;
+		fn *= k;
+		}
+
+	zmn = tox;
+
+	if( n == 1 )
+		{
+		ans = 1.0/x;
+		}
+	else
+		{
+		nk1f = fn/n;
+		kf = 1.0;
+		s = nk1f;
+		z = -z0;
+		zn = 1.0;
+		for( i=1; i<n; i++ )
+			{
+			nk1f = nk1f/(n-i);
+			kf = kf * i;
+			zn *= z;
+			t = nk1f * zn / kf;
+			s += t;   
+			if( (MAXNUM - fabs(t)) < fabs(s) )
+				goto overf;
+			if( (tox > 1.0) && ((MAXNUM/tox) < zmn) )
+				goto overf;
+			zmn *= tox;
+			}
+		s *= 0.5;
+		t = fabs(s);
+		if( (zmn > 1.0) && ((MAXNUM/zmn) < t) )
+			goto overf;
+		if( (t > 1.0) && ((MAXNUM/t) < zmn) )
+			goto overf;
+		ans = s * zmn;
+		}
+	}
+
+
+tlg = 2.0 * log( 0.5 * x );
+pk = -EUL;
+if( n == 0 )
+	{
+	pn = pk;
+	t = 1.0;
+	}
+else
+	{
+	pn = pn + 1.0/n;
+	t = 1.0/fn;
+	}
+s = (pk+pn-tlg)*t;
+k = 1.0;
+do
+	{
+	t *= z0 / (k * (k+n));
+	pk += 1.0/k;
+	pn += 1.0/(k+n);
+	s += (pk+pn-tlg)*t;
+	k += 1.0;
+	}
+while( fabs(t/s) > MACHEP );
+
+s = 0.5 * s / zmn;
+if( n & 1 )
+	s = -s;
+ans += s;
+
+return(ans);
+
+
+
+/* Asymptotic expansion for Kn(x) */
+/* Converges to 1.4e-17 for x > 18.4 */
+
+asymp:
+
+if( x > MAXLOG )
+	{
+	mtherr( "kn", UNDERFLOW );
+	return(0.0);
+	}
+k = n;
+pn = 4.0 * k * k;
+pk = 1.0;
+z0 = 8.0 * x;
+fn = 1.0;
+t = 1.0;
+s = t;
+nkf = MAXNUM;
+i = 0;
+do
+	{
+	z = pn - pk * pk;
+	t = t * z /(fn * z0);
+	nk1f = fabs(t);
+	if( (i >= n) && (nk1f > nkf) )
+		{
+		goto adone;
+		}
+	nkf = nk1f;
+	s += t;
+	fn += 1.0;
+	pk += 2.0;
+	i += 1;
+	}
+while( fabs(t/s) > MACHEP );
+
+adone:
+ans = exp(-x) * sqrt( PI/(2.0*x) ) * s;
+return(ans);
+}

libm/double/kolmogorov.c

@@ -0,0 +1,243 @@
+
+/* Re Kolmogorov statistics, here is Birnbaum and Tingey's formula for the
+   distribution of D+, the maximum of all positive deviations between a
+   theoretical distribution function P(x) and an empirical one Sn(x)
+   from n samples.
+
+     +
+    D  =         sup     [P(x) - S (x)]
+     n     -inf < x < inf         n
+
+
+                  [n(1-e)]
+        +            -                    v-1              n-v
+    Pr{D   > e} =    >    C    e (e + v/n)    (1 - e - v/n)
+        n            -   n v
+                    v=0
+
+    [n(1-e)] is the largest integer not exceeding n(1-e).
+    nCv is the number of combinations of n things taken v at a time.  */
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double pow ( double, double );
+extern double floor ( double );
+extern double lgam ( double );
+extern double exp ( double );
+extern double sqrt ( double );
+extern double log ( double );
+extern double fabs ( double );
+double smirnov ( int, double );
+double kolmogorov ( double );
+#else
+double pow (), floor (), lgam (), exp (), sqrt (), log (), fabs ();
+double smirnov (), kolmogorov ();
+#endif
+extern double MAXLOG;
+
+/* Exact Smirnov statistic, for one-sided test.  */
+double
+smirnov (n, e)
+     int n;
+     double e;
+{
+  int v, nn;
+  double evn, omevn, p, t, c, lgamnp1;
+
+  if (n <= 0 || e < 0.0 || e > 1.0)
+    return (-1.0);
+  nn = floor ((double) n * (1.0 - e));
+  p = 0.0;
+  if (n < 1013)
+    {
+      c = 1.0;
+      for (v = 0; v <= nn; v++)
+	{
+	  evn = e + ((double) v) / n;
+	  p += c * pow (evn, (double) (v - 1))
+	    * pow (1.0 - evn, (double) (n - v));
+	  /* Next combinatorial term; worst case error = 4e-15.  */
+	  c *= ((double) (n - v)) / (v + 1);
+	}
+    }
+  else
+    {
+      lgamnp1 = lgam ((double) (n + 1));
+      for (v = 0; v <= nn; v++)
+	{
+	  evn = e + ((double) v) / n;
+	  omevn = 1.0 - evn;
+	  if (fabs (omevn) > 0.0)
+	    {
+	      t = lgamnp1
+		- lgam ((double) (v + 1))
+		- lgam ((double) (n - v + 1))
+		+ (v - 1) * log (evn)
+		+ (n - v) * log (omevn);
+	      if (t > -MAXLOG)
+		p += exp (t);
+	    }
+	}
+    }
+  return (p * e);
+}
+
+
+/* Kolmogorov's limiting distribution of two-sided test, returns
+   probability that sqrt(n) * max deviation > y,
+   or that max deviation > y/sqrt(n).
+   The approximation is useful for the tail of the distribution
+   when n is large.  */
+double
+kolmogorov (y)
+     double y;
+{
+  double p, t, r, sign, x;
+
+  x = -2.0 * y * y;
+  sign = 1.0;
+  p = 0.0;
+  r = 1.0;
+  do
+    {
+      t = exp (x * r * r);
+      p += sign * t;
+      if (t == 0.0)
+	break;
+      r += 1.0;
+      sign = -sign;
+    }
+  while ((t / p) > 1.1e-16);
+  return (p + p);
+}
+
+/* Functional inverse of Smirnov distribution
+   finds e such that smirnov(n,e) = p.  */
+double
+smirnovi (n, p)
+     int n;
+     double p;
+{
+  double e, t, dpde;
+
+  if (p <= 0.0 || p > 1.0)
+    {
+      mtherr ("smirnovi", DOMAIN);
+      return 0.0;
+    }
+  /* Start with approximation p = exp(-2 n e^2).  */
+  e = sqrt (-log (p) / (2.0 * n));
+  do
+    {
+      /* Use approximate derivative in Newton iteration. */
+      t = -2.0 * n * e;
+      dpde = 2.0 * t * exp (t * e);
+      if (fabs (dpde) > 0.0)
+	t = (p - smirnov (n, e)) / dpde;
+      else
+	{
+	  mtherr ("smirnovi", UNDERFLOW);
+	  return 0.0;
+	}
+      e = e + t;
+      if (e >= 1.0 || e <= 0.0)
+	{
+	  mtherr ("smirnovi", OVERFLOW);
+	  return 0.0;
+	}
+    }
+  while (fabs (t / e) > 1e-10);
+  return (e);
+}
+
+
+/* Functional inverse of Kolmogorov statistic for two-sided test.
+   Finds y such that kolmogorov(y) = p.
+   If e = smirnovi (n,p), then kolmogi(2 * p) / sqrt(n) should
+   be close to e.  */
+double
+kolmogi (p)
+     double p;
+{
+  double y, t, dpdy;
+
+  if (p <= 0.0 || p > 1.0)
+    {
+      mtherr ("kolmogi", DOMAIN);
+      return 0.0;
+    }
+  /* Start with approximation p = 2 exp(-2 y^2).  */
+  y = sqrt (-0.5 * log (0.5 * p));
+  do
+    {
+      /* Use approximate derivative in Newton iteration. */
+      t = -2.0 * y;
+      dpdy = 4.0 * t * exp (t * y);
+      if (fabs (dpdy) > 0.0)
+	t = (p - kolmogorov (y)) / dpdy;
+      else
+	{
+	  mtherr ("kolmogi", UNDERFLOW);
+	  return 0.0;
+	}
+      y = y + t;
+    }
+  while (fabs (t / y) > 1e-10);
+  return (y);
+}
+
+
+#ifdef SALONE
+/* Type in a number.  */
+void
+getnum (s, px)
+     char *s;
+     double *px;
+{
+  char str[30];
+
+  printf (" %s (%.15e) ? ", s, *px);
+  gets (str);
+  if (str[0] == '\0' || str[0] == '\n')
+    return;
+  sscanf (str, "%lf", px);
+  printf ("%.15e\n", *px);
+}
+
+/* Type in values, get answers.  */
+void
+main ()
+{
+  int n;
+  double e, p, ps, pk, ek, y;
+
+  n = 5;
+  e = 0.0;
+  p = 0.1;
+loop:
+  ps = n;
+  getnum ("n", &ps);
+  n = ps;
+  if (n <= 0)
+    {
+      printf ("? Operator error.\n");
+      goto loop;
+    }
+  /*
+  getnum ("e", &e);
+  ps = smirnov (n, e);
+  y = sqrt ((double) n) * e;
+  printf ("y = %.4e\n", y);
+  pk = kolmogorov (y);
+  printf ("Smirnov = %.15e, Kolmogorov/2 = %.15e\n", ps, pk / 2.0);
+*/
+  getnum ("p", &p);
+  e = smirnovi (n, p);
+  printf ("Smirnov e = %.15e\n", e);
+  y = kolmogi (2.0 * p);
+  ek = y / sqrt ((double) n);
+  printf ("Kolmogorov e = %.15e\n", ek);
+  goto loop;
+}
+#endif

libm/double/levnsn.c

@@ -0,0 +1,82 @@
+/*		Levnsn.c		*/
+/* Levinson-Durbin LPC
+ *
+ * | R0 R1 R2 ... RN-1 |   | A1 |       | -R1 |
+ * | R1 R0 R1 ... RN-2 |   | A2 |       | -R2 |
+ * | R2 R1 R0 ... RN-3 |   | A3 |   =   | -R3 |
+ * |          ...      |   | ...|       | ... |
+ * | RN-1 RN-2... R0   |   | AN |       | -RN |
+ *
+ * Ref: John Makhoul, "Linear Prediction, A Tutorial Review"
+ * Proc. IEEE Vol. 63, PP 561-580 April, 1975.
+ *
+ * R is the input autocorrelation function.  R0 is the zero lag
+ * term.  A is the output array of predictor coefficients.  Note
+ * that a filter impulse response has a coefficient of 1.0 preceding
+ * A1.  E is an array of mean square error for each prediction order
+ * 1 to N.  REFL is an output array of the reflection coefficients.
+ */
+
+#define abs(x) ( (x) < 0 ? -(x) : (x) )
+
+int levnsn( n, r, a, e, refl )
+int n;
+double r[], a[], e[], refl[];
+{
+int k, km1, i, kmi, j;
+double ai, akk, err, err1, r0, t, akmi;
+double *pa, *pr;
+
+for( i=0; i<n; i++ )
+	{
+	a[i] = 0.0;
+	e[i] = 0.0;
+	refl[i] = 0.0;
+	}
+r0 = r[0];
+e[0] = r0;
+err = r0;
+
+akk = -r[1]/err;
+err = (1.0 - akk*akk) * err;
+e[1] = err;
+a[1] = akk;
+refl[1] = akk;
+
+if( err < 1.0e-2 )
+	return 0;
+
+for( k=2; k<n; k++ )
+	{
+	t = 0.0;
+	pa = &a[1];
+	pr = &r[k-1];
+	for( j=1; j<k; j++ )
+		t += *pa++ * *pr--;
+	akk = -( r[k] + t )/err;
+	refl[k] = akk;
+	km1 = k/2;
+	for( j=1; j<=km1; j++ )
+		{
+		kmi = k-j;
+		ai = a[j];
+		akmi = a[kmi];
+		a[j] = ai + akk*akmi;
+		if( i == kmi )
+			goto nxtk;
+		a[kmi] = akmi + akk*ai;
+		}
+nxtk:
+	a[k] = akk;
+	err1 = (1.0 - akk*akk)*err;
+	e[k] = err1;
+	if( err1 < 0 )
+		err1 = -err1;
+/*	err1 = abs(err1);*/
+/*	if( (err1 < 1.0e-2) || (err1 >= err) )*/
+	if( err1 < 1.0e-2 )
+		return 0;
+	err = err1;
+	}
+  return 0;
+}

libm/double/log.c

@@ -0,0 +1,341 @@
+/*							log.c
+ *
+ *	Natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log();
+ *
+ * y = log( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting  z = 2(x-1)/x+1),
+ * 
+ *     log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0    150000      1.44e-16    5.06e-17
+ *    IEEE      +-MAXNUM    30000       1.20e-16    4.78e-17
+ *    DEC       0, 10       170000      1.8e-17     6.3e-18
+ *
+ * In the tests over the interval [+-MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOG].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity:  x = 0; returns -INFINITY
+ * log domain:       x < 0; returns NAN
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+static char fname[] = {"log"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+#ifdef UNK
+static double P[] = {
+ 1.01875663804580931796E-4,
+ 4.97494994976747001425E-1,
+ 4.70579119878881725854E0,
+ 1.44989225341610930846E1,
+ 1.79368678507819816313E1,
+ 7.70838733755885391666E0,
+};
+static double Q[] = {
+/* 1.00000000000000000000E0, */
+ 1.12873587189167450590E1,
+ 4.52279145837532221105E1,
+ 8.29875266912776603211E1,
+ 7.11544750618563894466E1,
+ 2.31251620126765340583E1,
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0037777,0127270,0162547,0057274,
+0041001,0054665,0164317,0005341,
+0041451,0034104,0031640,0105773,
+0041677,0011276,0123617,0160135,
+0041701,0126603,0053215,0117250,
+0041420,0115777,0135206,0030232,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041220,0144332,0045272,0174241,
+0041742,0164566,0035720,0130431,
+0042246,0126327,0166065,0116357,
+0042372,0033420,0157525,0124560,
+0042271,0167002,0066537,0172303,
+0041730,0164777,0113711,0044407,
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x1bb0,0x93c3,0xb4c2,0x3f1a,
+0x52f2,0x3f56,0xd6f5,0x3fdf,
+0x6911,0xed92,0xd2ba,0x4012,
+0xeb2e,0xc63e,0xff72,0x402c,
+0xc84d,0x924b,0xefd6,0x4031,
+0xdcf8,0x7d7e,0xd563,0x401e,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xef8e,0xae97,0x9320,0x4026,
+0xc033,0x4e19,0x9d2c,0x4046,
+0xbdbd,0xa326,0xbf33,0x4054,
+0xae21,0xeb5e,0xc9e2,0x4051,
+0x25b2,0x9e1f,0x200a,0x4037,
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f1a,0xb4c2,0x93c3,0x1bb0,
+0x3fdf,0xd6f5,0x3f56,0x52f2,
+0x4012,0xd2ba,0xed92,0x6911,
+0x402c,0xff72,0xc63e,0xeb2e,
+0x4031,0xefd6,0x924b,0xc84d,
+0x401e,0xd563,0x7d7e,0xdcf8,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4026,0x9320,0xae97,0xef8e,
+0x4046,0x9d2c,0x4e19,0xc033,
+0x4054,0xbf33,0xa326,0xbdbd,
+0x4051,0xc9e2,0xeb5e,0xae21,
+0x4037,0x200a,0x9e1f,0x25b2,
+};
+#endif
+
+/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+
+#ifdef UNK
+static double R[3] = {
+-7.89580278884799154124E-1,
+ 1.63866645699558079767E1,
+-6.41409952958715622951E1,
+};
+static double S[3] = {
+/* 1.00000000000000000000E0,*/
+-3.56722798256324312549E1,
+ 3.12093766372244180303E2,
+-7.69691943550460008604E2,
+};
+#endif
+#ifdef DEC
+static unsigned short R[12] = {
+0140112,0020756,0161540,0072035,
+0041203,0013743,0114023,0155527,
+0141600,0044060,0104421,0050400,
+};
+static unsigned short S[12] = {
+/*0040200,0000000,0000000,0000000,*/
+0141416,0130152,0017543,0064122,
+0042234,0006000,0104527,0020155,
+0142500,0066110,0146631,0174731,
+};
+#endif
+#ifdef IBMPC
+static unsigned short R[12] = {
+0x0e84,0xdc6c,0x443d,0xbfe9,
+0x7b6b,0x7302,0x62fc,0x4030,
+0x2a20,0x1122,0x0906,0xc050,
+};
+static unsigned short S[12] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6d0a,0x43ec,0xd60d,0xc041,
+0xe40e,0x112a,0x8180,0x4073,
+0x3f3b,0x19b3,0x0d89,0xc088,
+};
+#endif
+#ifdef MIEEE
+static unsigned short R[12] = {
+0xbfe9,0x443d,0xdc6c,0x0e84,
+0x4030,0x62fc,0x7302,0x7b6b,
+0xc050,0x0906,0x1122,0x2a20,
+};
+static unsigned short S[12] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc041,0xd60d,0x43ec,0x6d0a,
+0x4073,0x8180,0x112a,0xe40e,
+0xc088,0x0d89,0x19b3,0x3f3b,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp(), polevl(), p1evl();
+int isnan(), isfinite();
+#endif
+#define SQRTH 0.70710678118654752440
+extern double INFINITY, NAN;
+
+double log(x)
+double x;
+{
+int e;
+#ifdef DEC
+short *q;
+#endif
+double y, z;
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITY )
+	return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0 )
+	{
+	if( x == 0.0 )
+	        {
+		mtherr( fname, SING );
+		return( -INFINITY );
+	        }
+	else
+	        {
+		mtherr( fname, DOMAIN );
+		return( NAN );
+	        }
+	}
+
+/* separate mantissa from exponent */
+
+#ifdef DEC
+q = (short *)&x;
+e = *q;			/* short containing exponent */
+e = ((e >> 7) & 0377) - 0200;	/* the exponent */
+*q &= 0177;	/* strip exponent from x */
+*q |= 040000;	/* x now between 0.5 and 1 */
+#endif
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+#ifdef IBMPC
+x = frexp( x, &e );
+/*
+q = (short *)&x;
+q += 3;
+e = *q;
+e = ((e >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x0f;
+*q |= 0x3fe0;
+*/
+#endif
+
+/* Equivalent C language standard library function: */
+#ifdef UNK
+x = frexp( x, &e );
+#endif
+
+#ifdef MIEEE
+x = frexp( x, &e );
+#endif
+
+
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+
+if( (e > 2) || (e < -2) )
+{
+if( x < SQRTH )
+	{ /* 2( 2x-1 )/( 2x+1 ) */
+	e -= 1;
+	z = x - 0.5;
+	y = 0.5 * z + 0.5;
+	}	
+else
+	{ /*  2 (x-1)/(x+1)   */
+	z = x - 0.5;
+	z -= 0.5;
+	y = 0.5 * x  + 0.5;
+	}
+
+x = z / y;
+
+
+/* rational form */
+z = x*x;
+z = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
+y = e;
+z = z - y * 2.121944400546905827679e-4;
+z = z + x;
+z = z + e * 0.693359375;
+goto ldone;
+}
+
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+	{
+	e -= 1;
+	x = ldexp( x, 1 ) - 1.0; /*  2x - 1  */
+	}	
+else
+	{
+	x = x - 1.0;
+	}
+
+
+/* rational form */
+z = x*x;
+#if DEC
+y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) );
+#else
+y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
+#endif
+if( e )
+	y = y - e * 2.121944400546905827679e-4;
+y = y - ldexp( z, -1 );   /*  y - 0.5 * z  */
+z = x + y;
+if( e )
+	z = z + e * 0.693359375;
+
+ldone:
+
+return( z );
+}

libm/double/log10.c

@@ -0,0 +1,250 @@
+/*							log10.c
+ *
+ *	Common logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log10();
+ *
+ * y = log10( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns logarithm to the base 10 of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  The logarithm of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0     30000      1.5e-16     5.0e-17
+ *    IEEE      0, MAXNUM    30000      1.4e-16     4.8e-17
+ *    DEC       1, MAXNUM    50000      2.5e-17     6.0e-18
+ *
+ * In the tests over the interval [1, MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOG].
+ *
+ * ERROR MESSAGES:
+ *
+ * log10 singularity:  x = 0; returns -INFINITY
+ * log10 domain:       x < 0; returns NAN
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+static char fname[] = {"log10"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+#ifdef UNK
+static double P[] = {
+  4.58482948458143443514E-5,
+  4.98531067254050724270E-1,
+  6.56312093769992875930E0,
+  2.97877425097986925891E1,
+  6.06127134467767258030E1,
+  5.67349287391754285487E1,
+  1.98892446572874072159E1
+};
+static double Q[] = {
+/* 1.00000000000000000000E0, */
+  1.50314182634250003249E1,
+  8.27410449222435217021E1,
+  2.20664384982121929218E2,
+  3.07254189979530058263E2,
+  2.14955586696422947765E2,
+  5.96677339718622216300E1
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0034500,0046473,0051374,0135174,
+0037777,0037566,0145712,0150321,
+0040722,0002426,0031543,0123107,
+0041356,0046513,0170752,0004346,
+0041562,0071553,0023536,0163343,
+0041542,0170221,0024316,0114216,
+0041237,0016454,0046611,0104602
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041160,0100260,0067736,0102424,
+0041645,0075552,0036563,0147072,
+0042134,0125025,0021132,0025320,
+0042231,0120211,0046030,0103271,
+0042126,0172241,0052151,0120426,
+0041556,0125702,0072116,0047103
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x974f,0x6a5f,0x09a7,0x3f08,
+0x5a1a,0xd979,0xe7ee,0x3fdf,
+0x74c9,0xc66c,0x40a2,0x401a,
+0x411d,0x7e3d,0xc9a9,0x403d,
+0xdcdc,0x64eb,0x4e6d,0x404e,
+0xd312,0x2519,0x5e12,0x404c,
+0x3130,0x89b1,0xe3a5,0x4033
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xd0a2,0x0dfb,0x1016,0x402e,
+0x79c7,0x47ae,0xaf6d,0x4054,
+0x455a,0xa44b,0x9542,0x406b,
+0x10d7,0x2983,0x3411,0x4073,
+0x3423,0x2a8d,0xde94,0x406a,
+0xc9c8,0x4e89,0xd578,0x404d
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f08,0x09a7,0x6a5f,0x974f,
+0x3fdf,0xe7ee,0xd979,0x5a1a,
+0x401a,0x40a2,0xc66c,0x74c9,
+0x403d,0xc9a9,0x7e3d,0x411d,
+0x404e,0x4e6d,0x64eb,0xdcdc,
+0x404c,0x5e12,0x2519,0xd312,
+0x4033,0xe3a5,0x89b1,0x3130
+};
+static unsigned short Q[] = {
+0x402e,0x1016,0x0dfb,0xd0a2,
+0x4054,0xaf6d,0x47ae,0x79c7,
+0x406b,0x9542,0xa44b,0x455a,
+0x4073,0x3411,0x2983,0x10d7,
+0x406a,0xde94,0x2a8d,0x3423,
+0x404d,0xd578,0x4e89,0xc9c8
+};
+#endif
+
+#define SQRTH 0.70710678118654752440
+#define L102A 3.0078125E-1
+#define L102B 2.48745663981195213739E-4
+#define L10EA 4.3359375E-1
+#define L10EB 7.00731903251827651129E-4
+
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp(), polevl(), p1evl();
+int isnan(), isfinite();
+#endif
+extern double LOGE2, SQRT2, INFINITY, NAN;
+
+double log10(x)
+double x;
+{
+VOLATILE double z;
+double y;
+#ifdef DEC
+short *q;
+#endif
+int e;
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITY )
+	return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0 )
+	{
+	if( x == 0.0 )
+	        {
+		mtherr( fname, SING );
+		return( -INFINITY );
+	        }
+	else
+	        {
+		mtherr( fname, DOMAIN );
+		return( NAN );
+	        }
+	}
+
+/* separate mantissa from exponent */
+
+#ifdef DEC
+q = (short *)&x;
+e = *q;			/* short containing exponent */
+e = ((e >> 7) & 0377) - 0200;	/* the exponent */
+*q &= 0177;	/* strip exponent from x */
+*q |= 040000;	/* x now between 0.5 and 1 */
+#endif
+
+#ifdef IBMPC
+x = frexp( x, &e );
+/*
+q = (short *)&x;
+q += 3;
+e = *q;
+e = ((e >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x0f;
+*q |= 0x3fe0;
+*/
+#endif
+
+/* Equivalent C language standard library function: */
+#ifdef UNK
+x = frexp( x, &e );
+#endif
+
+#ifdef MIEEE
+x = frexp( x, &e );
+#endif
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+	{
+	e -= 1;
+	x = ldexp( x, 1 ) - 1.0; /*  2x - 1  */
+	}	
+else
+	{
+	x = x - 1.0;
+	}
+
+
+/* rational form */
+z = x*x;
+y = x * ( z * polevl( x, P, 6 ) / p1evl( x, Q, 6 ) );
+y = y - ldexp( z, -1 );   /*  y - 0.5 * x**2  */
+
+/* multiply log of fraction by log10(e)
+ * and base 2 exponent by log10(2)
+ */
+z = (x + y) * L10EB;  /* accumulate terms in order of size */
+z += y * L10EA;
+z += x * L10EA;
+z += e * L102B;
+z += e * L102A;
+
+
+return( z );
+}

libm/double/log2.c

@@ -0,0 +1,348 @@
+/*							log2.c
+ *
+ *	Base 2 logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log2();
+ *
+ * y = log2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the base e
+ * logarithm of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting  z = 2(x-1)/x+1),
+ * 
+ *     log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0    30000       2.0e-16     5.5e-17
+ *    IEEE      exp(+-700)  40000       1.3e-16     4.6e-17
+ *
+ * In the tests over the interval [exp(+-700)], the logarithms
+ * of the random arguments were uniformly distributed.
+ *
+ * ERROR MESSAGES:
+ *
+ * log2 singularity:  x = 0; returns -INFINITY
+ * log2 domain:       x < 0; returns NAN
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+static char fname[] = {"log2"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+#ifdef UNK
+static double P[] = {
+ 1.01875663804580931796E-4,
+ 4.97494994976747001425E-1,
+ 4.70579119878881725854E0,
+ 1.44989225341610930846E1,
+ 1.79368678507819816313E1,
+ 7.70838733755885391666E0,
+};
+static double Q[] = {
+/* 1.00000000000000000000E0, */
+ 1.12873587189167450590E1,
+ 4.52279145837532221105E1,
+ 8.29875266912776603211E1,
+ 7.11544750618563894466E1,
+ 2.31251620126765340583E1,
+};
+#define LOG2EA 0.44269504088896340735992
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0037777,0127270,0162547,0057274,
+0041001,0054665,0164317,0005341,
+0041451,0034104,0031640,0105773,
+0041677,0011276,0123617,0160135,
+0041701,0126603,0053215,0117250,
+0041420,0115777,0135206,0030232,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041220,0144332,0045272,0174241,
+0041742,0164566,0035720,0130431,
+0042246,0126327,0166065,0116357,
+0042372,0033420,0157525,0124560,
+0042271,0167002,0066537,0172303,
+0041730,0164777,0113711,0044407,
+};
+static unsigned short L[5] = {0037742,0124354,0122560,0057703};
+#define LOG2EA (*(double *)(&L[0]))
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x1bb0,0x93c3,0xb4c2,0x3f1a,
+0x52f2,0x3f56,0xd6f5,0x3fdf,
+0x6911,0xed92,0xd2ba,0x4012,
+0xeb2e,0xc63e,0xff72,0x402c,
+0xc84d,0x924b,0xefd6,0x4031,
+0xdcf8,0x7d7e,0xd563,0x401e,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xef8e,0xae97,0x9320,0x4026,
+0xc033,0x4e19,0x9d2c,0x4046,
+0xbdbd,0xa326,0xbf33,0x4054,
+0xae21,0xeb5e,0xc9e2,0x4051,
+0x25b2,0x9e1f,0x200a,0x4037,
+};
+static unsigned short L[5] = {0x0bf8,0x94ae,0x551d,0x3fdc};
+#define LOG2EA (*(double *)(&L[0]))
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f1a,0xb4c2,0x93c3,0x1bb0,
+0x3fdf,0xd6f5,0x3f56,0x52f2,
+0x4012,0xd2ba,0xed92,0x6911,
+0x402c,0xff72,0xc63e,0xeb2e,
+0x4031,0xefd6,0x924b,0xc84d,
+0x401e,0xd563,0x7d7e,0xdcf8,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4026,0x9320,0xae97,0xef8e,
+0x4046,0x9d2c,0x4e19,0xc033,
+0x4054,0xbf33,0xa326,0xbdbd,
+0x4051,0xc9e2,0xeb5e,0xae21,
+0x4037,0x200a,0x9e1f,0x25b2,
+};
+static unsigned short L[5] = {0x3fdc,0x551d,0x94ae,0x0bf8};
+#define LOG2EA (*(double *)(&L[0]))
+#endif
+
+/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+
+#ifdef UNK
+static double R[3] = {
+-7.89580278884799154124E-1,
+ 1.63866645699558079767E1,
+-6.41409952958715622951E1,
+};
+static double S[3] = {
+/* 1.00000000000000000000E0,*/
+-3.56722798256324312549E1,
+ 3.12093766372244180303E2,
+-7.69691943550460008604E2,
+};
+/* log2(e) - 1 */
+#define LOG2EA 0.44269504088896340735992
+#endif
+#ifdef DEC
+static unsigned short R[12] = {
+0140112,0020756,0161540,0072035,
+0041203,0013743,0114023,0155527,
+0141600,0044060,0104421,0050400,
+};
+static unsigned short S[12] = {
+/*0040200,0000000,0000000,0000000,*/
+0141416,0130152,0017543,0064122,
+0042234,0006000,0104527,0020155,
+0142500,0066110,0146631,0174731,
+};
+/* log2(e) - 1 */
+#define LOG2EA 0.44269504088896340735992L
+#endif
+#ifdef IBMPC
+static unsigned short R[12] = {
+0x0e84,0xdc6c,0x443d,0xbfe9,
+0x7b6b,0x7302,0x62fc,0x4030,
+0x2a20,0x1122,0x0906,0xc050,
+};
+static unsigned short S[12] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6d0a,0x43ec,0xd60d,0xc041,
+0xe40e,0x112a,0x8180,0x4073,
+0x3f3b,0x19b3,0x0d89,0xc088,
+};
+#endif
+#ifdef MIEEE
+static unsigned short R[12] = {
+0xbfe9,0x443d,0xdc6c,0x0e84,
+0x4030,0x62fc,0x7302,0x7b6b,
+0xc050,0x0906,0x1122,0x2a20,
+};
+static unsigned short S[12] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc041,0xd60d,0x43ec,0x6d0a,
+0x4073,0x8180,0x112a,0xe40e,
+0xc088,0x0d89,0x19b3,0x3f3b,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp(), polevl(), p1evl();
+int isnan(), isfinite();
+#endif
+#define SQRTH 0.70710678118654752440
+extern double LOGE2, INFINITY, NAN;
+
+double log2(x)
+double x;
+{
+int e;
+double y;
+VOLATILE double z;
+#ifdef DEC
+short *q;
+#endif
+
+#ifdef NANS
+if( isnan(x) )
+	return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITY )
+	return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0 )
+	{
+	if( x == 0.0 )
+	        {
+		mtherr( fname, SING );
+		return( -INFINITY );
+	        }
+	else
+	        {
+		mtherr( fname, DOMAIN );
+		return( NAN );
+	        }
+	}
+
+/* separate mantissa from exponent */
+
+#ifdef DEC
+q = (short *)&x;
+e = *q;			/* short containing exponent */
+e = ((e >> 7) & 0377) - 0200;	/* the exponent */
+*q &= 0177;	/* strip exponent from x */
+*q |= 040000;	/* x now between 0.5 and 1 */
+#endif
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+#ifdef IBMPC
+x = frexp( x, &e );
+/*
+q = (short *)&x;
+q += 3;
+e = *q;
+e = ((e >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x0f;
+*q |= 0x3fe0;
+*/
+#endif
+
+/* Equivalent C language standard library function: */
+#ifdef UNK
+x = frexp( x, &e );
+#endif
+
+#ifdef MIEEE
+x = frexp( x, &e );
+#endif
+
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+
+if( (e > 2) || (e < -2) )
+{
+if( x < SQRTH )
+	{ /* 2( 2x-1 )/( 2x+1 ) */
+	e -= 1;
+	z = x - 0.5;
+	y = 0.5 * z + 0.5;
+	}	
+else
+	{ /*  2 (x-1)/(x+1)   */
+	z = x - 0.5;
+	z -= 0.5;
+	y = 0.5 * x  + 0.5;
+	}
+
+x = z / y;
+z = x*x;
+y = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
+goto ldone;
+}
+
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+	{
+	e -= 1;
+	x = ldexp( x, 1 ) - 1.0; /*  2x - 1  */
+	}	
+else
+	{
+	x = x - 1.0;
+	}
+
+z = x*x;
+#if DEC
+y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) ) - ldexp( z, -1 );
+#else
+y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) ) - ldexp( z, -1 );
+#endif
+
+ldone:
+
+/* Multiply log of fraction by log2(e)
+ * and base 2 exponent by 1
+ *
+ * ***CAUTION***
+ *
+ * This sequence of operations is critical and it may
+ * be horribly defeated by some compiler optimizers.
+ */
+z = y * LOG2EA;
+z += x * LOG2EA;
+z += y;
+z += x;
+z += e;
+return( z );
+}

libm/double/lrand.c

@@ -0,0 +1,86 @@
+/*							lrand.c
+ *
+ *	Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long y, drand();
+ *
+ * drand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a long integer random number.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used. The period, given by them, is
+ * 6953607871644.
+ *
+ *
+ */
+
+
+
+#include <math.h>
+
+
+/*  Three-generator random number algorithm
+ * of Brian Wichmann and David Hill
+ * BYTE magazine, March, 1987 pp 127-8
+ *
+ * The period, given by them, is (p-1)(q-1)(r-1)/4 = 6.95e12.
+ */
+
+static int sx = 1;
+static int sy = 10000;
+static int sz = 3000;
+
+/* This function implements the three
+ * congruential generators.
+ */
+ 
+long lrand()
+{
+int r, s;
+unsigned long ans;
+
+/*
+if( arg )
+	{
+	sx = 1;
+	sy = 10000;
+	sz = 3000;
+	}
+*/
+
+/*  sx = sx * 171 mod 30269 */
+r = sx/177;
+s = sx - 177 * r;
+sx = 171 * s - 2 * r;
+if( sx < 0 )
+	sx += 30269;
+
+
+/* sy = sy * 172 mod 30307 */
+r = sy/176;
+s = sy - 176 * r;
+sy = 172 * s - 35 * r;
+if( sy < 0 )
+	sy += 30307;
+
+/* sz = 170 * sz mod 30323 */
+r = sz/178;
+s = sz - 178 * r;
+sz = 170 * s - 63 * r;
+if( sz < 0 )
+	sz += 30323;
+
+ans = sx * sy * sz;
+return(ans);
+}
+

libm/double/lsqrt.c

@@ -0,0 +1,85 @@
+/*							lsqrt.c
+ *
+ *	Integer square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long x, y;
+ * long lsqrt();
+ *
+ * y = lsqrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns a long integer square root of the long integer
+ * argument.  The computation is by binary long division.
+ *
+ * The largest possible result is lsqrt(2,147,483,647)
+ * = 46341.
+ *
+ * If x < 0, the square root of |x| is returned, and an
+ * error message is printed.
+ *
+ *
+ * ACCURACY:
+ *
+ * An extra, roundoff, bit is computed; hence the result
+ * is the nearest integer to the actual square root.
+ * NOTE: only DEC arithmetic is currently supported.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0:  April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+long lsqrt(x)
+long x;
+{
+long num, sq;
+long temp;
+int i, j, k, n;
+
+if( x < 0 )
+	{
+	mtherr( "lsqrt", DOMAIN );
+	x = -x;
+	}
+
+num = 0;
+sq = 0;
+k = 24;
+n = 4;
+
+for( j=0; j<4; j++ )
+	{
+	num |= (x >> k) & 0xff;	/* bring in next byte of arg */
+	if( j == 3 )		/* do roundoff bit at end */
+		n = 5;
+	for( i=0; i<n; i++ )
+		{
+		num <<= 2;		/* next 2 bits of arg */
+		sq <<= 1;		/* shift up answer */
+		temp = (sq << 1) + 256;	/* trial divisor */
+		temp = num - temp;
+		if( temp >= 0 )
+			{
+			num = temp;	/* it went in */
+			sq += 256;	/* answer bit = 1 */
+			}
+		}
+	k -= 8;	/* shift count to get next byte of arg */
+	}
+
+sq += 256;	/* add roundoff bit */
+sq >>= 9;	/* truncate */
+return( sq );
+}

libm/double/ltstd.c

@@ -0,0 +1,469 @@
+/*							ltstd.c		*/
+/*  Function test routine.
+ *  Requires long double type check routine and double precision function
+ *  under test.  Indicate function name and range in #define statements
+ *  below.  Modifications for two argument functions and absolute
+ *  rather than relative accuracy report are indicated.
+ */
+
+#include <stdio.h>
+/* int printf(), gets(), sscanf(); */
+
+#include <math.h>
+#ifdef ANSIPROT
+int drand ( void );
+int dprec ( void );
+int ldprec ( void );
+double exp ( double );
+double sqrt ( double );
+double fabs ( double );
+double floor ( double );
+long double sqrtl ( long double );
+long double fabsl ( long double );
+#else
+int drand();
+int dprec(), ldprec();
+double exp(), sqrt(), fabs(), floor();
+long double sqrtl(), fabsl();
+#endif
+
+#define RELERR 1
+#define ONEARG 0
+#define ONEINT 0
+#define TWOARG 0
+#define TWOINT 0
+#define THREEARG 1
+#define THREEINT 0
+#define FOURARG 0
+#define VECARG 0
+#define FOURANS 0
+#define TWOANS 0
+#define PROB 0
+#define EXPSCALE 0
+#define EXPSC2 0
+/* insert function to be tested here: */
+#define FUNC hyperg
+double FUNC();
+#define QFUNC hypergl
+long double QFUNC();
+/*extern int aiconf;*/
+
+extern double MAXLOG;
+extern double MINLOG;
+extern double MAXNUM;
+#define LTS 3.258096538
+/* insert low end and width of test interval */
+#define LOW 0.0
+#define WIDTH 30.0
+#define LOWA  0.0
+#define WIDTHA 30.0
+/* 1.073741824e9 */
+/* 2.147483648e9 */
+long double qone = 1.0L;
+static long double q1, q2, q3, qa, qb, qc, qz, qy1, qy2, qy3, qy4;
+static double y2, y3, y4, a, b, c, x, y, z, e;
+static long double qe, qmax, qrmsa, qave;
+volatile double v;
+static long double lp[3], lq[3];
+static double dp[3], dq[3];
+
+char strave[20];
+char strrms[20];
+char strmax[20];
+double underthresh =  2.22507385850720138309E-308; /* 2^-1022 */
+
+void main()
+{
+char s[80];
+int i, j, k;
+long m, n;
+
+merror = 0;
+ldprec();   /* set up coprocessor.  */
+/*aiconf = -1;*/	/* configure Airy function */
+x = 1.0;
+z = x * x;
+qmax = 0.0L;
+sprintf(strmax, "%.4Le", qmax );
+qrmsa = 0.0L;
+qave = 0.0L;
+
+#if 1
+printf(" Start at random number #:" );
+gets( s );
+sscanf( s, "%ld", &n );
+printf("%ld\n", n );
+#else
+n = 0;
+#endif
+
+for( m=0; m<n; m++ )
+	drand( &x );
+n = 0;
+m = 0;
+x = floor( x );
+
+loop:
+
+for( i=0; i<500; i++ )
+{
+n++;
+m++;
+
+#if ONEARG || TWOARG || THREEARG || FOURARG
+/*ldprec();*/	/* set up floating point coprocessor */
+/* make random number in desired range */
+drand( &x );
+x = WIDTH *  ( x - 1.0 )  +  LOW;
+#if EXPSCALE
+x = exp(x);
+drand( &a );
+a = 1.0e-13 * x * a;
+if( x > 0.0 )
+	x -= a;
+else
+	x += a;
+#endif
+#if ONEINT
+k = x;
+x = k;
+#endif
+v = x;
+q1 = v;		/* double number to q type */
+#endif
+
+/* do again if second argument required */
+
+#if TWOARG || THREEARG || FOURARG
+drand( &a );
+a = WIDTHA *  ( a - 1.0 )  +  LOWA;
+/*a /= 50.0;*/
+#if EXPSC2
+a = exp(a);
+drand( &y2 );
+y2 = 1.0e-13 * y2 * a;
+if( a > 0.0 )
+	a -= y2;
+else
+	a += y2;
+#endif
+#if TWOINT || THREEINT
+k = a + 0.25;
+a = k;
+#endif
+v = a;
+qy4 = v;
+#endif
+
+#if THREEARG || FOURARG
+drand( &b );
+#if PROB
+/*
+b = b - 1.0;
+b = a * b;
+*/
+#if 1
+/* This makes b <= a, for bdtr.  */
+b = (a - LOWA) *  ( b - 1.0 )  +  LOWA;
+if( b > 1.0 && a > 1.0 )
+  b -= 1.0;
+else
+  {
+    a += 1.0;
+    k = a;
+    a = k;
+    v = a;
+    qy4 = v;
+  }
+#else
+b = WIDTHA *  ( b - 1.0 )  +  LOWA;
+#endif
+
+/* Half-integer a and b */
+/*
+a = 0.5*floor(2.0*a+1.0);
+b = 0.5*floor(2.0*b+1.0);
+*/
+v = a;
+qy4 = v;
+/*x = (a / (a+b));*/
+
+#else
+b = WIDTHA *  ( b - 1.0 )  +  LOWA;
+#endif
+#if THREEINT
+j = b + 0.25;
+b = j;
+#endif
+v = b;
+qb = v;
+#endif
+
+#if FOURARG
+drand( &c );
+c = WIDTHA *  ( c - 1.0 )  +  LOWA;
+/* for hyp2f1 to ensure c-a-b > -1 */
+/*
+z = c-a-b;
+if( z < -1.0 )
+	c -= 1.6 * z;
+*/
+v = c;
+qc = v;
+#endif
+
+#if VECARG
+for( j=0; j<3; j++)
+  {
+    drand( &x );
+    x = WIDTH *  ( x - 1.0 )  +  LOW;
+    v = x;
+    dp[j] = v;
+    q1 = v;		/* double number to q type */
+    lp[j] = q1;
+    drand( &x );
+    x = WIDTH *  ( x - 1.0 )  +  LOW;
+    v = x;
+    dq[j] = v;
+    q1 = v;		/* double number to q type */
+    lq[j] = q1;
+  }
+#endif /* VECARG */
+
+/*printf("%.16E %.16E\n", a, x);*/
+/* compute function under test */
+/* Set to double precision */
+/*dprec();*/
+#if ONEARG
+#if FOURANS
+/*FUNC( x, &z, &y2, &y3, &y4 );*/
+FUNC( x, &y4, &y2, &y3, &z );
+#else
+#if TWOANS
+FUNC( x, &z, &y2 );
+/*FUNC( x, &y2, &z );*/
+#else
+#if ONEINT
+z = FUNC( k );
+#else
+z = FUNC( x );
+#endif
+#endif
+#endif
+#endif
+
+#if TWOARG
+#if TWOINT
+z = FUNC( k, x );
+/*z = FUNC( x, k );*/
+/*z = FUNC( a, x );*/
+#else
+#if FOURANS
+FUNC( a, x, &z, &y2, &y3, &y4 );
+#else
+z = FUNC( a, x );
+#endif
+#endif
+#endif
+
+#if THREEARG
+#if THREEINT
+z = FUNC( j, k, x );
+#else
+z = FUNC( a, b, x );
+#endif
+#endif
+
+#if FOURARG
+z = FUNC( a, b, c, x );
+#endif
+
+#if VECARG
+z = FUNC( dp, dq );
+#endif
+
+q2 = z;
+/* handle detected overflow */
+if( (z == MAXNUM) || (z == -MAXNUM) )
+	{
+	printf("detected overflow ");
+#if FOURARG
+	printf("%.4E %.4E %.4E %.4E %.4E %6ld \n",
+		a, b, c, x, y, n);
+#else
+	printf("%.16E %.4E %.4E %6ld \n", x, a, z, n);
+#endif
+	e = 0.0;
+	m -= 1;
+	goto endlup;
+	}
+/* Skip high precision if underflow.  */
+if( merror == UNDERFLOW )
+  goto underf;
+
+/* compute high precision function */
+/*ldprec();*/
+#if ONEARG
+#if FOURANS
+/*qy4 = QFUNC( q1, qz, qy2, qy3 );*/
+qz = QFUNC( q1, qy4, qy2, qy3 );
+#else
+#if TWOANS
+qy2 = QFUNC( q1, qz );
+/*qz = QFUNC( q1, qy2 );*/
+#else
+/* qy4 = 0.0L;*/
+/* qy4 = 1.0L;*/
+/*qz = QFUNC( qy4, q1 );*/
+/*qz = QFUNC( 1, q1 );*/
+qz = QFUNC( q1 );  /* normal */
+#endif
+#endif
+#endif
+
+#if TWOARG
+#if TWOINT
+qz = QFUNC( k, q1 );
+/*qz = QFUNC( q1, qy4 );*/
+/*qz = QFUNC( qy4, q1 );*/
+#else
+#if FOURANS
+qc = QFUNC( qy4, q1, qz, qy2, qy3 );
+#else
+/*qy4 = 0.0L;;*/
+/*qy4 = 1.0L );*/
+qz = QFUNC( qy4, q1 );
+#endif
+#endif
+#endif
+
+#if THREEARG
+#if THREEINT
+qz = QFUNC( j, k, q1 );
+#else
+qz = QFUNC( qy4, qb, q1 );
+#endif
+#endif
+
+#if FOURARG
+qz = QFUNC( qy4, qb, qc, q1 );
+#endif
+
+#if VECARG
+qz = QFUNC( lp, lq );
+#endif
+
+y = qz; /* correct answer, in double precision */
+
+/* get absolute error, in extended precision */
+qe = q2 - qz;
+e = qe; /* the error in double precision */
+
+/*  handle function result equal to zero
+    or underflowed. */
+if( qz == 0.0L || merror == UNDERFLOW || fabs(z) < underthresh )
+	{
+underf:
+	  merror = 0;
+/* Don't bother to print anything.  */
+#if 0
+	printf("ans 0 ");
+#if ONEARG
+	printf("%.8E %.8E %.4E %6ld \n", x, y, e, n);
+#endif
+
+#if TWOARG
+#if TWOINT
+	printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, e, n);
+#else
+	printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, e, n);
+#endif
+#endif
+
+#if THREEARG
+	printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, e, n);
+#endif
+
+#if FOURARG
+	printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
+		a, b, c, x, y, e, n);
+#endif
+#endif /* 0 */
+	  qe = 0.0L;
+	e = 0.0;
+	m -= 1;
+	goto endlup;
+	}
+
+else
+
+/*	relative error	*/
+
+/* comment out the following two lines if absolute accuracy report */
+
+#if RELERR
+  qe = qe / qz;
+#else
+	{
+	  q2 = qz;
+	  q2 = fabsl(q2);
+	  if( q2 > 1.0L )
+	    qe = qe / qz;
+	}
+#endif
+
+qave = qave + qe;
+/* absolute value of error */
+qe = fabs(qe);
+
+/* peak detect the error */
+if( qe > qmax )
+	{
+	  qmax = qe;
+	  sprintf(strmax, "%.4Le", qmax );
+#if ONEARG
+	printf("%.8E %.8E %s %6ld \n", x, y, strmax, n);
+#endif
+#if TWOARG
+#if TWOINT
+	printf("%d %.8E %.8E %s %6ld \n", k, x, y, strmax, n);
+#else
+	printf("%.6E %.6E %.6E %s %6ld \n", a, x, y, strmax, n);
+#endif
+#endif
+#if THREEARG
+	printf("%.6E %.6E %.6E %.6E %s %6ld \n", a, b, x, y, strmax, n);
+#endif
+#if FOURARG
+	printf("%.4E %.4E %.4E %.4E %.4E %s %6ld \n",
+		a, b, c, x, y, strmax, n);
+#endif
+#if VECARG
+	printf("%.8E %s %6ld \n", y, strmax, n);
+#endif
+	}
+
+/* accumulate rms error	*/
+/* rmsa += e * e;  accumulate the square of the error */
+q2 = qe * qe;
+qrmsa = qrmsa + q2;
+endlup:   ;
+/*ldprec();*/
+}
+
+/* report every 500 trials */
+/* rms = sqrt( rmsa/m ); */
+q1 = m;
+q2 = qrmsa / q1;
+q2 = sqrtl(q2);
+sprintf(strrms, "%.4Le", q2 );
+
+q2 = qave / q1;
+sprintf(strave, "%.4Le", q2 );
+/*
+printf("%6ld   max = %s   rms = %s  ave = %s \n", m, strmax, strrms, strave );
+*/
+printf("%6ld   max = %s   rms = %s  ave = %s \r", m, strmax, strrms, strave );
+fflush(stdout);
+goto loop;
+}

libm/double/minv.c

@@ -0,0 +1,61 @@
+/*							minv.c
+ *
+ *	Matrix inversion
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n, errcod;
+ * double A[n*n], X[n*n];
+ * double B[n];
+ * int IPS[n];
+ * int minv();
+ *
+ * errcod = minv( A, X, n, B, IPS );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the inverse of the n by n matrix A.  The result goes
+ * to X.   B and IPS are scratch pad arrays of length n.
+ * The contents of matrix A are destroyed.
+ *
+ * The routine returns nonzero on error; error messages are printed
+ * by subroutine simq().
+ *
+ */
+
+minv( A, X, n, B, IPS )
+double A[], X[];
+int n;
+double B[];
+int IPS[];
+{
+double *pX;
+int i, j, k;
+
+for( i=1; i<n; i++ )
+	B[i] = 0.0;
+B[0] = 1.0;
+/* Reduce the matrix and solve for first right hand side vector */
+pX = X;
+k = simq( A, B, pX, n, 1, IPS );
+if( k )
+	return(-1);
+/* Solve for the remaining right hand side vectors */
+for( i=1; i<n; i++ )
+	{
+	B[i-1] = 0.0;
+	B[i] = 1.0;
+	pX += n;
+	k = simq( A, B, pX, n, -1, IPS );
+	if( k )
+		return(-1);
+	}
+/* Transpose the array of solution vectors */
+mtransp( n, X, X );
+return(0);
+}
+

libm/double/mod2pi.c

@@ -0,0 +1,122 @@
+/* Program to test range reduction of trigonometry functions
+ *
+ * -- Steve Moshier
+ */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern double sin ( double );
+#else
+double floor(), ldexp(), sin();
+#endif
+
+#define TPI 6.283185307179586476925
+
+main()
+{
+char s[40];
+double a, n, t, x, y, z;
+int lflg;
+
+x = TPI/4.0;
+t = 1.0;
+
+loop:
+
+t = 2.0 * t;
+
+/* Stop testing at a point beyond which the integer part of
+ * x/2pi cannot be represented exactly by a double precision number.
+ * The library trigonometry functions will probably give up long before
+ * this point is reached.
+ */
+if( t > 1.0e16 )
+	exit(0);
+
+/* Adjust the following to choose a nontrivial x
+ * where test function(x) has a slope of about 1 or more.
+ */
+x = TPI * t  + 0.5;
+
+z = x;
+lflg = 0;
+
+inlup:
+
+/* floor() returns the largest integer less than its argument.
+ * If you do not have this, or AINT(), then you may convert x/TPI
+ * to a long integer and then back to double; but in that case
+ * x will be limited to the largest value that will fit into a
+ * long integer.
+ */
+n = floor( z/TPI );
+
+/* Carefully subtract 2 pi n from x.
+ * This is done by subtracting n * 2**k in such a way that there
+ * is no arithmetic cancellation error at any step.  The k are the
+ * bits in the number 2 pi.
+ *
+ * If you do not have ldexp(), then you may multiply or
+ * divide n by an appropriate power of 2 after each step.
+ * For example:
+ *  a = z - 4*n;
+ *  a -= 2*n;
+ *  n /= 4;
+ *  a -= n;   n/4
+ *  n /= 8;
+ *  a -= n;   n/32
+ * etc.
+ * This will only work if division by a power of 2 is exact.
+ */
+
+a = z - ldexp(n, 2);	/* 4n */
+a -= ldexp( n, 1);	/* 2n */
+a -= ldexp( n, -2 );	/* n/4 */
+a -= ldexp( n, -5 );	/* n/32 */
+a -= ldexp( n, -9 );	/* n/512 */
+a += ldexp( n, -15 );	/* add n/32768 */
+a -= ldexp( n, -17 );	/* n/131072 */
+a -= ldexp( n, -18 );
+a -= ldexp( n, -20 );
+a -= ldexp( n, -22 );
+a -= ldexp( n, -24 );
+a -= ldexp( n, -28 );
+a -= ldexp( n, -32 );
+a -= ldexp( n, -37 );
+a -= ldexp( n, -39 );
+a -= ldexp( n, -40 );
+a -= ldexp( n, -42 );
+a -= ldexp( n, -46 );
+a -= ldexp( n, -47 );
+
+/* Subtract what is left of 2 pi n after all the above reductions.
+ */
+a -= 2.44929359829470635445e-16 * n;
+
+/* If the test is extended too far, it is possible
+ * to have chosen the wrong value of n.  The following
+ * will fix that, but at some reduction in accuracy.
+ */
+if( (a > TPI) || (a < -1e-11) )
+	{
+	z = a;
+	lflg += 1;
+	printf( "Warning! Reduction failed on first try.\n" );
+	goto inlup;
+	}
+if( a < 0.0 )
+	{
+	printf( "Warning! Reduced value < 0\n" );
+	a += TPI;
+	}
+
+/* Compute the test function at x and at a = x mod 2 pi.
+ */
+y = sin(x);
+z = sin(a);
+printf( "sin(%.15e) error = %.3e\n", x, y-z );
+goto loop;
+}
+

libm/double/monot.c

@@ -0,0 +1,308 @@
+
+/* monot.c
+   Floating point function test vectors.
+
+   Arguments and function values are synthesized for NPTS points in
+   the vicinity of each given tabulated test point.  The points are
+   chosen to be near and on either side of the likely function algorithm
+   domain boundaries.  Since the function programs change their methods
+   at these points, major coding errors or monotonicity failures might be
+   detected.
+
+   August, 1998
+   S. L. Moshier  */
+
+
+#include <stdio.h>
+
+/* Avoid including math.h.  */
+double frexp (double, int *);
+double ldexp (double, int);
+
+/* Number of test points to generate on each side of tabulated point.  */
+#define NPTS 100
+
+/* Functions of one variable.  */
+double exp (double);
+double log (double);
+double sin (double);
+double cos (double);
+double tan (double);
+double atan (double);
+double asin (double);
+double acos (double);
+double sinh (double);
+double cosh (double);
+double tanh (double);
+double asinh (double);
+double acosh (double);
+double atanh (double);
+double gamma (double);
+double fabs (double);
+double floor (double);
+
+struct oneargument
+  {
+    char *name;			/* Name of the function. */
+    double (*func) (double);
+    double arg1;		/* Function argument, assumed exact.  */
+    double answer1;		/* Exact, close to function value.  */
+    double answer2;		/* answer1 + answer2 has extended precision. */
+    double derivative;		/* dy/dx evaluated at x = arg1. */
+    int thresh;			/* Error report threshold. 2 = 1 ULP approx. */
+  };
+
+/* Add this to error threshold test[i].thresh.  */
+#define OKERROR 0
+
+/* Unit of relative error in test[i].thresh.  */
+static double MACHEP = 1.1102230246251565404e-16;
+/* extern double MACHEP; */
+
+
+struct oneargument test1[] =
+{
+  {"exp", exp, 1.0, 2.7182769775390625,
+   4.85091998273536028747e-6, 2.71828182845904523536, 2},
+  {"exp", exp, -1.0, 3.678741455078125e-1,
+    5.29566362982159552377e-6, 3.678794411714423215955e-1, 2},
+  {"exp", exp, 0.5, 1.648712158203125,
+    9.1124970031468486507878e-6, 1.64872127070012814684865, 2},
+  {"exp", exp, -0.5, 6.065216064453125e-1,
+    9.0532673209236037995e-6, 6.0653065971263342360e-1, 2},
+  {"exp", exp, 2.0, 7.3890533447265625,
+    2.75420408772723042746e-6, 7.38905609893065022723, 2},
+  {"exp", exp, -2.0, 1.353302001953125e-1,
+    5.08304130019189399949e-6, 1.3533528323661269189e-1, 2},
+  {"log", log, 1.41421356237309492343, 3.465728759765625e-1,
+   7.1430341006605745676897e-7, 7.0710678118654758708668e-1, 2},
+  {"log", log, 7.07106781186547461715e-1, -3.46588134765625e-1,
+   1.45444856522566402246e-5, 1.41421356237309517417, 2},
+  {"sin", sin, 7.85398163397448278999e-1, 7.0709228515625e-1,
+   1.4496030297502751942956e-5, 7.071067811865475460497e-1, 2},
+  {"sin", sin, -7.85398163397448501044e-1, -7.071075439453125e-1,
+   7.62758764840238811175e-7, 7.07106781186547389040e-1, 2},
+  {"sin", sin, 1.570796326794896558, 9.999847412109375e-1,
+   1.52587890625e-5, 6.12323399573676588613e-17, 2},
+  {"sin", sin, -1.57079632679489678004, -1.0,
+   1.29302922820150306903e-32, -1.60812264967663649223e-16, 2},
+  {"sin", sin, 4.712388980384689674, -1.0,
+   1.68722975549458979398e-32, -1.83697019872102976584e-16, 2},
+  {"sin", sin, -4.71238898038468989604, 9.999847412109375e-1,
+   1.52587890625e-5, 3.83475850529283315008e-17, 2},
+  {"cos", cos, 3.92699081698724139500E-1, 9.23873901367187500000E-1,
+   5.63114409926198633370E-6, -3.82683432365089757586E-1, 2},
+  {"cos", cos, 7.85398163397448278999E-1, 7.07092285156250000000E-1,
+   1.44960302975460497458E-5, -7.07106781186547502752E-1, 2},
+  {"cos", cos, 1.17809724509617241850E0, 3.82675170898437500000E-1,
+   8.26146665231415693919E-6, -9.23879532511286738554E-1, 2},
+  {"cos", cos, 1.96349540849362069750E0, -3.82690429687500000000E-1,
+   6.99732241029898567203E-6, -9.23879532511286785419E-1, 2},
+  {"cos", cos, 2.35619449019234483700E0, -7.07107543945312500000E-1,
+   7.62758765040545859856E-7, -7.07106781186547589348E-1, 2},
+  {"cos", cos, 2.74889357189106897650E0, -9.23889160156250000000E-1,
+   9.62764496328487887036E-6, -3.82683432365089870728E-1, 2},
+  {"cos", cos, 3.14159265358979311600E0, -1.00000000000000000000E0,
+   7.49879891330928797323E-33, -1.22464679914735317723E-16, 2},
+  {"tan", tan, 7.85398163397448278999E-1, 9.999847412109375e-1,
+   1.52587890624387676600E-5, 1.99999999999999987754E0, 2},
+  {"tan", tan, 1.17809724509617241850E0, 2.41419982910156250000E0,
+   1.37332715322352112604E-5, 6.82842712474618858345E0, 2},
+  {"tan", tan, 1.96349540849362069750E0, -2.41421508789062500000E0,
+   1.52551752942854759743E-6, 6.82842712474619262118E0, 2},
+  {"tan", tan, 2.35619449019234483700E0, -1.00001525878906250000E0,
+   1.52587890623163029801E-5, 2.00000000000000036739E0, 2},
+  {"tan", tan, 2.74889357189106897650E0, -4.14215087890625000000E-1,
+   1.52551752982565655126E-6, 1.17157287525381000640E0, 2},
+  {"atan", atan, 4.14213562373094923430E-1, 3.92684936523437500000E-1,
+   1.41451752865477964149E-5, 8.53553390593273837869E-1, 2},
+  {"atan", atan, 1.0, 7.85385131835937500000E-1,
+   1.30315615108096156608E-5, 0.5, 2},
+  {"atan", atan, 2.41421356237309492343E0, 1.17808532714843750000E0,
+   1.19179477349460632350E-5, 1.46446609406726250782E-1, 2},
+  {"atan", atan, -2.41421356237309514547E0, -1.17810058593750000000E0,
+   3.34084132752141908545E-6, 1.46446609406726227789E-1, 2},
+  {"atan", atan, -1.0, -7.85400390625000000000E-1,
+   2.22722755169038433915E-6, 0.5, 2},
+  {"atan", atan, -4.14213562373095145475E-1, -3.92700195312500000000E-1,
+   1.11361377576267665972E-6, 8.53553390593273703853E-1, 2},
+  {"asin", asin, 3.82683432365089615246E-1, 3.92684936523437500000E-1,
+   1.41451752864854321970E-5, 1.08239220029239389286E0, 2},
+  {"asin", asin, 0.5, 5.23590087890625000000E-1,
+   8.68770767387307710723E-6, 1.15470053837925152902E0, 2},
+  {"asin", asin, 7.07106781186547461715E-1, 7.85385131835937500000E-1,
+   1.30315615107209645016E-5, 1.41421356237309492343E0, 2},
+  {"asin", asin, 9.23879532511286738483E-1, 1.17808532714843750000E0,
+   1.19179477349183147612E-5, 2.61312592975275276483E0, 2},
+  {"asin", asin, -0.5, -5.23605346679687500000E-1,
+   6.57108138862692289277E-6, 1.15470053837925152902E0, 2},
+  {"acos", acos, 1.95090322016128192573E-1, 1.37443542480468750000E0,
+   1.13611408471185777914E-5, -1.01959115820831832232E0, 2},
+  {"acos", acos, 3.82683432365089615246E-1, 1.17808532714843750000E0,
+   1.19179477351337991247E-5, -1.08239220029239389286E0, 2},
+  {"acos", acos, 0.5, 1.04719543457031250000E0,
+   2.11662628524615421446E-6, -1.15470053837925152902E0, 2},
+  {"acos", acos, 7.07106781186547461715E-1, 7.85385131835937500000E-1,
+   1.30315615108982668201E-5, -1.41421356237309492343E0, 2},
+  {"acos", acos, 9.23879532511286738483E-1, 3.92684936523437500000E-1,
+   1.41451752867009165605E-5, -2.61312592975275276483E0, 2},
+  {"acos", acos, 9.80785280403230430579E-1, 1.96334838867187500000E-1,
+   1.47019821746724723933E-5, -5.12583089548300990774E0, 2},
+  {"acos", acos, -0.5, 2.09439086914062500000E0,
+   4.23325257049230842892E-6, -1.15470053837925152902E0, 2},
+  {"sinh", sinh, 1.0, 1.17518615722656250000E0,
+   1.50364172389568823819E-5, 1.54308063481524377848E0, 2},
+  {"sinh", sinh, 7.09089565712818057364E2, 4.49423283712885057274E307,
+   4.25947714184369757620E208, 4.49423283712885057274E307, 2},
+  {"sinh", sinh, 2.22044604925031308085E-16, 0.00000000000000000000E0,
+   2.22044604925031308085E-16, 1.00000000000000000000E0, 2},
+  {"cosh", cosh, 7.09089565712818057364E2, 4.49423283712885057274E307,
+   4.25947714184369757620E208, 4.49423283712885057274E307, 2},
+  {"cosh", cosh, 1.0, 1.54307556152343750000E0,
+   5.07329180627847790562E-6, 1.17520119364380145688E0, 2},
+  {"cosh", cosh, 0.5, 1.12762451171875000000E0,
+   1.45348763078522622516E-6, 5.21095305493747361622E-1, 2},
+  {"tanh", tanh, 0.5, 4.62112426757812500000E-1,
+   4.73050219725850231848E-6, 7.86447732965927410150E-1, 2},
+  {"tanh", tanh, 5.49306144334054780032E-1, 4.99984741210937500000E-1,
+   1.52587890624507506378E-5, 7.50000000000000049249E-1, 2},
+  {"tanh", tanh, 0.625, 5.54595947265625000000E-1,
+   3.77508375729399903910E-6, 6.92419147969988069631E-1, 2},
+  {"asinh", asinh, 0.5, 4.81201171875000000000E-1,
+   1.06531846034474977589E-5, 8.94427190999915878564E-1, 2},
+  {"asinh", asinh, 1.0, 8.81362915039062500000E-1,
+   1.06719804805252326093E-5, 7.07106781186547524401E-1, 2},
+  {"asinh", asinh, 2.0, 1.44363403320312500000E0,
+   1.44197568534249327674E-6, 4.47213595499957939282E-1, 2},
+  {"acosh", acosh, 2.0, 1.31695556640625000000E0,
+   2.33051856670862504635E-6, 5.77350269189625764509E-1, 2},
+  {"acosh", acosh, 1.5, 9.62417602539062500000E-1,
+   6.04758014439499551783E-6, 8.94427190999915878564E-1, 2},
+  {"acosh", acosh, 1.03125, 2.49343872070312500000E-1,
+   9.62177257298785143908E-6, 3.96911150685467059809E0, 2},
+  {"atanh", atanh, 0.5, 5.49301147460937500000E-1,
+   4.99687311734569762262E-6, 1.33333333333333333333E0, 2},
+#if 0
+  {"gamma", gamma, 1.0, 1.0,
+   0.0, -5.772156649015328606e-1, 2},
+  {"gamma", gamma, 2.0, 1.0,
+   0.0, 4.2278433509846713939e-1, 2},
+  {"gamma", gamma, 3.0, 2.0,
+   0.0, 1.845568670196934279, 2},
+  {"gamma", gamma, 4.0, 6.0,
+   0.0, 7.536706010590802836, 2},
+#endif
+  {"null", NULL, 0.0, 0.0, 0.0, 2},
+};
+
+/* These take care of extra-precise floating point register problems.  */
+volatile double volat1;
+volatile double volat2;
+
+
+/* Return the next nearest floating point value to X
+   in the direction of UPDOWN (+1 or -1).
+   (Fails if X is denormalized.)  */
+
+double
+nextval (x, updown)
+     double x;
+     int updown;
+{
+  double m;
+  int i;
+
+  volat1 = x;
+  m = 0.25 * MACHEP * volat1 * updown;
+  volat2 = volat1 + m;
+  if (volat2 != volat1)
+    printf ("successor failed\n");
+
+  for (i = 2; i < 10; i++)
+    {
+      volat2 = volat1 + i * m;
+      if (volat1 != volat2)
+	return volat2;
+    }
+
+  printf ("nextval failed\n");
+  return volat1;
+}
+
+
+
+
+int
+main ()
+{
+  double (*fun1) (double);
+  int i, j, errs, tests;
+  double x, x0, y, dy, err;
+
+  /* Set math coprocessor to double precision.  */
+  /*  dprec (); */
+  errs = 0;
+  tests = 0;
+  i = 0;
+
+  for (;;)
+    {
+      fun1 = test1[i].func;
+      if (fun1 == NULL)
+	break;
+      volat1 = test1[i].arg1;
+      x0 = volat1;
+      x = volat1;
+      for (j = 0; j <= NPTS; j++)
+	{
+	  volat1 = x - x0;
+	  dy = volat1 * test1[i].derivative;
+	  dy = test1[i].answer2 + dy;
+	  volat1 = test1[i].answer1 + dy;
+	  volat2 = (*(fun1)) (x);
+	  if (volat2 != volat1)
+	    {
+	      /* Report difference between program result
+		 and extended precision function value.  */
+	      err = volat2 - test1[i].answer1;
+	      err = err - dy;
+	      err = err / volat1;
+	      if (fabs (err) > ((OKERROR + test1[i].thresh) * MACHEP))
+		{
+		  printf ("%d %s(%.16e) = %.16e, rel err = %.3e\n",
+			  j, test1[i].name, x, volat2, err);
+		  errs += 1;
+		}
+	    }
+	  x = nextval (x, 1);
+	  tests += 1;
+	}
+
+      x = x0;
+      x = nextval (x, -1);
+      for (j = 1; j < NPTS; j++)
+	{
+	  volat1 = x - x0;
+	  dy = volat1 * test1[i].derivative;
+	  dy = test1[i].answer2 + dy;
+	  volat1 = test1[i].answer1 + dy;
+	  volat2 = (*(fun1)) (x);
+	  if (volat2 != volat1)
+	    {
+	      err = volat2 - test1[i].answer1;
+	      err = err - dy;
+	      err = err / volat1;
+	      if (fabs (err) > ((OKERROR + test1[i].thresh) * MACHEP))
+		{
+		  printf ("%d %s(%.16e) = %.16e, rel err = %.3e\n",
+			  j, test1[i].name, x, volat2, err);
+		  errs += 1;
+		}
+	    }
+	  x = nextval (x, -1);
+	  tests += 1;
+	}
+      i += 1;
+    }
+  printf ("%d errors in %d tests\n", errs, tests);
+}

libm/double/mtherr.c

@@ -0,0 +1,102 @@
+/*							mtherr.c
+ *
+ *	Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * int mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file math.h).
+ *  
+ *   Mnemonic        Value          Significance
+ *
+ *    DOMAIN            1       argument domain error
+ *    SING              2       function singularity
+ *    OVERFLOW          3       overflow range error
+ *    UNDERFLOW         4       underflow range error
+ *    TLOSS             5       total loss of precision
+ *    PLOSS             6       partial loss of precision
+ *    EDOM             33       Unix domain error code
+ *    ERANGE           34       Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition.  The display is directed to the standard
+ * output device.  The routine then returns to the calling
+ * program.  Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * math.h
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0:  April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <stdio.h>
+#include <math.h>
+
+int merror = 0;
+
+/* Notice: the order of appearance of the following
+ * messages is bound to the error codes defined
+ * in math.h.
+ */
+static char *ermsg[7] = {
+"unknown",      /* error code 0 */
+"domain",       /* error code 1 */
+"singularity",  /* et seq.      */
+"overflow",
+"underflow",
+"total loss of precision",
+"partial loss of precision"
+};
+
+
+int mtherr( name, code )
+char *name;
+int code;
+{
+
+/* Display string passed by calling program,
+ * which is supposed to be the name of the
+ * function in which the error occurred:
+ */
+printf( "\n%s ", name );
+
+/* Set global error message word */
+merror = code;
+
+/* Display error message defined
+ * by the code argument.
+ */
+if( (code <= 0) || (code >= 7) )
+	code = 0;
+printf( "%s error\n", ermsg[code] );
+
+/* Return to calling
+ * program
+ */
+return( 0 );
+}

libm/double/mtransp.c

@@ -0,0 +1,61 @@
+/*							mtransp.c
+ *
+ *	Matrix transpose
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double A[n*n], T[n*n];
+ *
+ * mtransp( n, A, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * T[r][c] = A[c][r]
+ *
+ *
+ * Transposes the n by n square matrix A and puts the result in T.
+ * The output, T, may occupy the same storage as A.
+ *
+ *
+ *
+ */
+
+
+mtransp( n, A, T )
+int n;
+double *A, *T;
+{
+int i, j, np1;
+double *pAc, *pAr, *pTc, *pTr, *pA0, *pT0;
+double x, y;
+
+np1 = n+1;
+pA0 = A;
+pT0 = T;
+for( i=0; i<n-1; i++ ) /* row index */
+	{
+	pAc = pA0; /* next diagonal element of input */
+	pAr = pAc + n; /* next row down underneath the diagonal element */
+	pTc = pT0; /* next diagonal element of the output */
+	pTr = pTc + n; /* next row underneath */
+	*pTc++ = *pAc++; /* copy the diagonal element */
+	for( j=i+1; j<n; j++ ) /* column index */
+		{
+		x = *pAr;
+		*pTr = *pAc++;
+		*pTc++ = x;
+		pAr += n;
+		pTr += n;
+		}
+	pA0 += np1; /* &A[n*i+i] for next i */
+	pT0 += np1; /* &T[n*i+i] for next i */
+	}
+*pT0 = *pA0; /* copy the diagonal element */
+}
+

libm/double/mtst.c

@@ -0,0 +1,464 @@
+/*   mtst.c
+ Consistency tests for math functions.
+ To get strict rounding rules on a 386 or 68000 computer,
+ define SETPREC to 1.
+
+ With NTRIALS=10000, the following are typical results for
+ IEEE double precision arithmetic.
+
+Consistency test of math functions.
+Max and rms relative errors for 10000 random arguments.
+x =   cbrt(   cube(x) ):  max = 0.00E+00   rms = 0.00E+00
+x =   atan(    tan(x) ):  max = 2.21E-16   rms = 3.27E-17
+x =    sin(   asin(x) ):  max = 2.13E-16   rms = 2.95E-17
+x =   sqrt( square(x) ):  max = 0.00E+00   rms = 0.00E+00
+x =    log(    exp(x) ):  max = 1.11E-16 A rms = 4.35E-18 A
+x =   tanh(  atanh(x) ):  max = 2.22E-16   rms = 2.43E-17
+x =  asinh(   sinh(x) ):  max = 2.05E-16   rms = 3.49E-18
+x =  acosh(   cosh(x) ):  max = 1.43E-15 A rms = 1.54E-17 A
+x =  log10(  exp10(x) ):  max = 5.55E-17 A rms = 1.27E-18 A
+x = pow( pow(x,a),1/a ):  max = 7.60E-14   rms = 1.05E-15
+x =    cos(   acos(x) ):  max = 2.22E-16 A rms = 6.90E-17 A
+*/
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#ifndef NTRIALS
+#define NTRIALS 10000
+#endif
+
+#define SETPREC 1
+#define STRTST 0
+
+#define WTRIALS (NTRIALS/5)
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double sqrt ( double );
+extern double cbrt ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double exp10 ( double );
+extern double log10 ( double );
+extern double tan ( double );
+extern double atan ( double );
+extern double sin ( double );
+extern double asin ( double );
+extern double cos ( double );
+extern double acos ( double );
+extern double pow ( double, double );
+extern double tanh ( double );
+extern double atanh ( double );
+extern double sinh ( double );
+extern double asinh ( double x );
+extern double cosh ( double );
+extern double acosh ( double );
+extern double gamma ( double );
+extern double lgam ( double );
+#else
+double fabs(), sqrt(), cbrt(), exp(), log();
+double exp10(), log10(), tan(), atan();
+double sin(), asin(), cos(), acos(), pow();
+double tanh(), atanh(), sinh(), asinh(), cosh(), acosh();
+double gamma(), lgam();
+#endif
+
+/* C9X spells lgam lgamma.  */
+#define GLIBC2 0
+#if GLIBC2
+double lgamma (double);
+#endif
+
+#if SETPREC
+int dprec();
+#endif
+
+int drand();
+/* void exit(); */
+/* int printf(); */
+
+
+/* Provide inverses for square root and cube root: */
+double square(x)
+double x;
+{
+return( x * x );
+}
+
+double cube(x)
+double x;
+{
+return( x * x * x );
+}
+
+/* lookup table for each function */
+struct fundef
+	{
+	char *nam1;		/* the function */
+	double (*name )();
+	char *nam2;		/* its inverse  */
+	double (*inv )();
+	int nargs;		/* number of function arguments */
+	int tstyp;		/* type code of the function */
+	long ctrl;		/* relative error flag */
+	double arg1w;		/* width of domain for 1st arg */
+	double arg1l;		/* lower bound domain 1st arg */
+	long arg1f;		/* flags, e.g. integer arg */
+	double arg2w;		/* same info for args 2, 3, 4 */
+	double arg2l;
+	long arg2f;
+/*
+	double arg3w;
+	double arg3l;
+	long arg3f;
+	double arg4w;
+	double arg4l;
+	long arg4f;
+*/
+	};
+
+
+/* fundef.ctrl bits: */
+#define RELERR 1
+
+/* fundef.tstyp  test types: */
+#define POWER 1 
+#define ELLIP 2 
+#define GAMMA 3
+#define WRONK1 4
+#define WRONK2 5
+#define WRONK3 6
+
+/* fundef.argNf  argument flag bits: */
+#define INT 2
+#define EXPSCAL 4
+
+extern double MINLOG;
+extern double MAXLOG;
+extern double PI;
+extern double PIO2;
+/*
+define MINLOG -170.0
+define MAXLOG +170.0
+define PI 3.14159265358979323846
+define PIO2 1.570796326794896619
+*/
+
+#define NTESTS 12
+struct fundef defs[NTESTS] = {
+{"  cube",   cube,   "  cbrt",   cbrt, 1, 0, 1, 2002.0, -1001.0, 0,
+0.0, 0.0, 0},
+{"   tan",    tan,   "  atan",   atan, 1, 0, 1,    0.0,     0.0,  0,
+0.0, 0.0, 0},
+{"  asin",   asin,   "   sin",    sin, 1, 0, 1,   2.0,      -1.0,  0,
+0.0, 0.0, 0},
+{"square", square,   "  sqrt",   sqrt, 1, 0, 1, 170.0,    -85.0, EXPSCAL,
+0.0, 0.0, 0},
+{"   exp",    exp,   "   log",    log, 1, 0, 0, 340.0,    -170.0,  0,
+0.0, 0.0, 0},
+{" atanh",  atanh,   "  tanh",   tanh, 1, 0, 1,    2.0,    -1.0,  0,
+0.0, 0.0, 0},
+{"  sinh",   sinh,   " asinh",  asinh, 1, 0, 1, 340.0,   0.0,  0,
+0.0, 0.0, 0},
+{"  cosh",   cosh,   " acosh",  acosh, 1, 0, 0, 340.0,      0.0,  0,
+0.0, 0.0, 0},
+{" exp10",  exp10,   " log10",  log10, 1, 0, 0, 340.0,    -170.0,  0,
+0.0, 0.0, 0},
+{"pow",       pow,      "pow",    pow, 2, POWER, 1, 21.0, 0.0,   0,
+42.0, -21.0, 0},
+{"  acos",   acos,   "   cos",    cos, 1, 0, 0,   2.0,      -1.0,  0,
+0.0, 0.0, 0},
+#if GLIBC2
+{ "gamma",  gamma,     "lgamma",   lgamma, 1, GAMMA, 0, 34.0, 0.0,   0,
+0.0, 0.0, 0},
+#else
+{ "gamma",  gamma,     "lgam",   lgam, 1, GAMMA, 0, 34.0, 0.0,   0,
+0.0, 0.0, 0},
+#endif
+};
+
+static char *headrs[] = {
+"x = %s( %s(x) ): ",
+"x = %s( %s(x,a),1/a ): ",	/* power */
+"Legendre %s, %s: ",		/* ellip */
+"%s(x) = log(%s(x)): ",		/* gamma */
+"Wronksian of %s, %s: ",
+"Wronksian of %s, %s: ",
+"Wronksian of %s, %s: "
+};
+ 
+static double yy1 = 0.0;
+static double y2 = 0.0;
+static double y3 = 0.0;
+static double y4 = 0.0;
+static double a = 0.0;
+static double x = 0.0;
+static double y = 0.0;
+static double z = 0.0;
+static double e = 0.0;
+static double max = 0.0;
+static double rmsa = 0.0;
+static double rms = 0.0;
+static double ave = 0.0;
+
+
+int main()
+{
+double (*fun )();
+double (*ifun )();
+struct fundef *d;
+int i, k, itst;
+int m, ntr;
+
+#if SETPREC
+dprec();  /* set coprocessor precision */
+#endif
+ntr = NTRIALS;
+printf( "Consistency test of math functions.\n" );
+printf( "Max and rms relative errors for %d random arguments.\n",
+	ntr );
+
+/* Initialize machine dependent parameters: */
+defs[1].arg1w = PI;
+defs[1].arg1l = -PI/2.0;
+/* Microsoft C has trouble with denormal numbers. */
+#if 0
+defs[3].arg1w = MAXLOG;
+defs[3].arg1l = -MAXLOG/2.0;
+defs[4].arg1w = 2*MAXLOG;
+defs[4].arg1l = -MAXLOG;
+#endif
+defs[6].arg1w = 2.0*MAXLOG;
+defs[6].arg1l = -MAXLOG;
+defs[7].arg1w = MAXLOG;
+defs[7].arg1l = 0.0;
+
+
+/* Outer loop, on the test number: */
+
+for( itst=STRTST; itst<NTESTS; itst++ )
+{
+d = &defs[itst];
+k = 0;
+m = 0;
+max = 0.0;
+rmsa = 0.0;
+ave = 0.0;
+fun = d->name;
+ifun = d->inv;
+
+/* Absolute error criterion starts with gamma function
+ * (put all such at end of table)
+ */
+if( d->tstyp == GAMMA )
+	printf( "Absolute error criterion (but relative if >1):\n" );
+
+/* Smaller number of trials for Wronksians
+ * (put them at end of list)
+ */
+if( d->tstyp == WRONK1 )
+	{
+	ntr = WTRIALS;
+	printf( "Absolute error and only %d trials:\n", ntr );
+	}
+
+printf( headrs[d->tstyp], d->nam2, d->nam1 );
+
+for( i=0; i<ntr; i++ )
+{
+m++;
+
+/* make random number(s) in desired range(s) */
+switch( d->nargs )
+{
+
+default:
+goto illegn;
+	
+case 2:
+drand( &a );
+a = d->arg2w *  ( a - 1.0 )  +  d->arg2l;
+if( d->arg2f & EXPSCAL )
+	{
+	a = exp(a);
+	drand( &y2 );
+	a -= 1.0e-13 * a * y2;
+	}
+if( d->arg2f & INT )
+	{
+	k = a + 0.25;
+	a = k;
+	}
+
+case 1:
+drand( &x );
+x = d->arg1w *  ( x - 1.0 )  +  d->arg1l;
+if( d->arg1f & EXPSCAL )
+	{
+	x = exp(x);
+	drand( &a );
+	x += 1.0e-13 * x * a;
+	}
+}
+
+
+/* compute function under test */
+switch( d->nargs )
+	{
+	case 1:
+	switch( d->tstyp )
+		{
+		case ELLIP:
+		yy1 = ( *(fun) )(x);
+		y2 = ( *(fun) )(1.0-x);
+		y3 = ( *(ifun) )(x);
+		y4 = ( *(ifun) )(1.0-x);
+		break;
+
+#if 1
+		case GAMMA:
+#if GLIBC2
+		y = lgamma(x);
+#else
+		y = lgam(x);
+#endif
+		x = log( gamma(x) );
+		break;
+#endif
+		default:
+		z = ( *(fun) )(x);
+		y = ( *(ifun) )(z);
+		}
+	break;
+	
+	case 2:
+	if( d->arg2f & INT )
+		{
+		switch( d->tstyp )
+			{
+			case WRONK1:
+			yy1 = (*fun)( k, x ); /* jn */
+			y2 = (*fun)( k+1, x );
+			y3 = (*ifun)( k, x ); /* yn */
+			y4 = (*ifun)( k+1, x );	
+			break;
+
+			case WRONK2:
+			yy1 = (*fun)( a, x ); /* iv */
+			y2 = (*fun)( a+1.0, x );
+			y3 = (*ifun)( k, x ); /* kn */	
+			y4 = (*ifun)( k+1, x );	
+			break;
+
+			default:
+			z = (*fun)( k, x );
+			y = (*ifun)( k, z );
+			}
+		}
+	else
+		{
+		if( d->tstyp == POWER )
+			{
+			z = (*fun)( x, a );
+			y = (*ifun)( z, 1.0/a );
+			}
+		else
+			{
+			z = (*fun)( a, x );
+			y = (*ifun)( a, z );
+			}
+		}
+	break;
+
+
+	default:
+illegn:
+	printf( "Illegal nargs= %d", d->nargs );
+	exit(1);
+	}	
+
+switch( d->tstyp )
+	{
+	case WRONK1:
+	e = (y2*y3 - yy1*y4) - 2.0/(PI*x); /* Jn, Yn */
+	break;
+
+	case WRONK2:
+	e = (y2*y3 + yy1*y4) - 1.0/x; /* In, Kn */
+	break;
+	
+	case ELLIP:
+	e = (yy1-y3)*y4 + y3*y2 - PIO2;
+	break;
+
+	default:
+	e = y - x;
+	break;
+	}
+
+if( d->ctrl & RELERR )
+	e /= x;
+else
+	{
+	if( fabs(x) > 1.0 )
+		e /= x;
+	}
+
+ave += e;
+/* absolute value of error */
+if( e < 0 )
+	e = -e;
+
+/* peak detect the error */
+if( e > max )
+	{
+	max = e;
+
+	if( e > 1.0e-10 )
+		{
+		printf("x %.6E z %.6E y %.6E max %.4E\n",
+		 x, z, y, max);
+		if( d->tstyp == POWER )
+			{
+			printf( "a %.6E\n", a );
+			}
+		if( d->tstyp >= WRONK1 )
+			{
+		printf( "yy1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
+		 yy1, y2, y3, y4, k, x );
+			}
+		}
+
+/*
+	printf("%.8E %.8E %.4E %6ld \n", x, y, max, n);
+	printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, max, n);
+	printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, max, n);
+	printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, max, n);
+	printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
+		a, b, c, x, y, max, n);
+*/
+	}
+
+/* accumulate rms error	*/
+e *= 1.0e16;	/* adjust range */
+rmsa += e * e;	/* accumulate the square of the error */
+}
+
+/* report after NTRIALS trials */
+rms = 1.0e-16 * sqrt( rmsa/m );
+if(d->ctrl & RELERR)
+	printf(" max = %.2E   rms = %.2E\n", max, rms );
+else
+	printf(" max = %.2E A rms = %.2E A\n", max, rms );
+} /* loop on itst */
+
+exit(0);
+}

libm/double/nbdtr.c

@@ -0,0 +1,222 @@
+/*							nbdtr.c
+ *
+ *	Negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtr();
+ *
+ * y = nbdtr( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the negative
+ * binomial distribution:
+ *
+ *   k
+ *   --  ( n+j-1 )   n      j
+ *   >   (       )  p  (1-p)
+ *   --  (   j   )
+ *  j=0
+ *
+ * In a sequence of Bernoulli trials, this is the probability
+ * that k or fewer failures precede the nth success.
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *    IEEE     0,100       100000      1.7e-13     8.8e-15
+ * See also incbet.c.
+ *
+ */
+/*							nbdtrc.c
+ *
+ *	Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtrc();
+ *
+ * y = nbdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ *   inf
+ *   --  ( n+j-1 )   n      j
+ *   >   (       )  p  (1-p)
+ *   --  (   j   )
+ *  j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *    IEEE     0,100       100000      1.7e-13     8.8e-15
+ * See also incbet.c.
+ */
+
+/*							nbdtrc
+ *
+ *	Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtrc();
+ *
+ * y = nbdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ *   inf
+ *   --  ( n+j-1 )   n      j
+ *   >   (       )  p  (1-p)
+ *   --  (   j   )
+ *  j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ */
+/*							nbdtri
+ *
+ *	Functional inverse of negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtri();
+ *
+ * p = nbdtri( k, n, y );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the argument p such that nbdtr(k,n,p) is equal to y.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,y), with y between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *    IEEE     0,100       100000      1.5e-14     8.5e-16
+ * See also incbi.c.
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+#else
+double incbet(), incbi();
+#endif
+
+double nbdtrc( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+	goto domerr;
+if( k < 0 )
+	{
+domerr:
+	mtherr( "nbdtr", DOMAIN );
+	return( 0.0 );
+	}
+
+dk = k+1;
+dn = n;
+return( incbet( dk, dn, 1.0 - p ) );
+}
+
+
+
+double nbdtr( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+	goto domerr;
+if( k < 0 )
+	{
+domerr:
+	mtherr( "nbdtr", DOMAIN );
+	return( 0.0 );
+	}
+dk = k+1;
+dn = n;
+return( incbet( dn, dk, p ) );
+}
+
+
+
+double nbdtri( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn, w;
+
+if( (p < 0.0) || (p > 1.0) )
+	goto domerr;
+if( k < 0 )
+	{
+domerr:
+	mtherr( "nbdtri", DOMAIN );
+	return( 0.0 );
+	}
+dk = k+1;
+dn = n;
+w = incbi( dn, dk, p );
+return( w );
+}

libm/double/ndtr.c

@@ -0,0 +1,481 @@
+/*							ndtr.c
+ *
+ *	Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtr();
+ *
+ * y = ndtr( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the Gaussian probability density
+ * function, integrated from minus infinity to x:
+ *
+ *                            x
+ *                             -
+ *                   1        | |          2
+ *    ndtr(x)  = ---------    |    exp( - t /2 ) dt
+ *               sqrt(2pi)  | |
+ *                           -
+ *                          -inf.
+ *
+ *             =  ( 1 + erf(z) ) / 2
+ *             =  erfc(z) / 2
+ *
+ * where z = x/sqrt(2). Computation is via the functions
+ * erf and erfc.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC      -13,0         8000       2.1e-15     4.8e-16
+ *    IEEE     -13,0        30000       3.4e-14     6.7e-15
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition         value returned
+ * erfc underflow    x > 37.519379347       0.0
+ *
+ */
+/*							erf.c
+ *
+ *	Error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, erf();
+ *
+ * y = erf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The integral is
+ *
+ *                           x 
+ *                            -
+ *                 2         | |          2
+ *   erf(x)  =  --------     |    exp( - t  ) dt.
+ *              sqrt(pi)   | |
+ *                          -
+ *                           0
+ *
+ * The magnitude of x is limited to 9.231948545 for DEC
+ * arithmetic; 1 or -1 is returned outside this range.
+ *
+ * For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
+ * erf(x) = 1 - erfc(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,1         14000       4.7e-17     1.5e-17
+ *    IEEE      0,1         30000       3.7e-16     1.0e-16
+ *
+ */
+/*							erfc.c
+ *
+ *	Complementary error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, erfc();
+ *
+ * y = erfc( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *  1 - erf(x) =
+ *
+ *                           inf. 
+ *                             -
+ *                  2         | |          2
+ *   erfc(x)  =  --------     |    exp( - t  ) dt
+ *               sqrt(pi)   | |
+ *                           -
+ *                            x
+ *
+ *
+ * For small x, erfc(x) = 1 - erf(x); otherwise rational
+ * approximations are computed.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0, 9.2319   12000       5.1e-16     1.2e-16
+ *    IEEE      0,26.6417   30000       5.7e-14     1.5e-14
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition              value returned
+ * erfc underflow    x > 9.231948545 (DEC)       0.0
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+extern double SQRTH;
+extern double MAXLOG;
+
+
+#ifdef UNK
+static double P[] = {
+ 2.46196981473530512524E-10,
+ 5.64189564831068821977E-1,
+ 7.46321056442269912687E0,
+ 4.86371970985681366614E1,
+ 1.96520832956077098242E2,
+ 5.26445194995477358631E2,
+ 9.34528527171957607540E2,
+ 1.02755188689515710272E3,
+ 5.57535335369399327526E2
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.32281951154744992508E1,
+ 8.67072140885989742329E1,
+ 3.54937778887819891062E2,
+ 9.75708501743205489753E2,
+ 1.82390916687909736289E3,
+ 2.24633760818710981792E3,
+ 1.65666309194161350182E3,
+ 5.57535340817727675546E2
+};
+static double R[] = {
+ 5.64189583547755073984E-1,
+ 1.27536670759978104416E0,
+ 5.01905042251180477414E0,
+ 6.16021097993053585195E0,
+ 7.40974269950448939160E0,
+ 2.97886665372100240670E0
+};
+static double S[] = {
+/* 1.00000000000000000000E0,*/
+ 2.26052863220117276590E0,
+ 9.39603524938001434673E0,
+ 1.20489539808096656605E1,
+ 1.70814450747565897222E1,
+ 9.60896809063285878198E0,
+ 3.36907645100081516050E0
+};
+static double T[] = {
+ 9.60497373987051638749E0,
+ 9.00260197203842689217E1,
+ 2.23200534594684319226E3,
+ 7.00332514112805075473E3,
+ 5.55923013010394962768E4
+};
+static double U[] = {
+/* 1.00000000000000000000E0,*/
+ 3.35617141647503099647E1,
+ 5.21357949780152679795E2,
+ 4.59432382970980127987E3,
+ 2.26290000613890934246E4,
+ 4.92673942608635921086E4
+};
+
+#define UTHRESH 37.519379347
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0030207,0054445,0011173,0021706,
+0040020,0067272,0030661,0122075,
+0040756,0151236,0173053,0067042,
+0041502,0106175,0062555,0151457,
+0042104,0102525,0047401,0003667,
+0042403,0116176,0011446,0075303,
+0042551,0120723,0061641,0123275,
+0042600,0070651,0007264,0134516,
+0042413,0061102,0167507,0176625
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041123,0123257,0165741,0017142,
+0041655,0065027,0173413,0115450,
+0042261,0074011,0021573,0004150,
+0042563,0166530,0013662,0007200,
+0042743,0176427,0162443,0105214,
+0043014,0062546,0153727,0123772,
+0042717,0012470,0006227,0067424,
+0042413,0061103,0003042,0013254
+};
+static unsigned short R[] = {
+0040020,0067272,0101024,0155421,
+0040243,0037467,0056706,0026462,
+0040640,0116017,0120665,0034315,
+0040705,0020162,0143350,0060137,
+0040755,0016234,0134304,0130157,
+0040476,0122700,0051070,0015473
+};
+static unsigned short S[] = {
+/*0040200,0000000,0000000,0000000,*/
+0040420,0126200,0044276,0070413,
+0041026,0053051,0007302,0063746,
+0041100,0144203,0174051,0061151,
+0041210,0123314,0126343,0177646,
+0041031,0137125,0051431,0033011,
+0040527,0117362,0152661,0066201
+};
+static unsigned short T[] = {
+0041031,0126770,0170672,0166101,
+0041664,0006522,0072360,0031770,
+0043013,0100025,0162641,0126671,
+0043332,0155231,0161627,0076200,
+0044131,0024115,0021020,0117343
+};
+static unsigned short U[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041406,0037461,0177575,0032714,
+0042402,0053350,0123061,0153557,
+0043217,0111227,0032007,0164217,
+0043660,0145000,0004013,0160114,
+0044100,0071544,0167107,0125471
+};
+#define UTHRESH 14.0
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x6479,0xa24f,0xeb24,0x3df0,
+0x3488,0x4636,0x0dd7,0x3fe2,
+0x6dc4,0xdec5,0xda53,0x401d,
+0xba66,0xacad,0x518f,0x4048,
+0x20f7,0xa9e0,0x90aa,0x4068,
+0xcf58,0xc264,0x738f,0x4080,
+0x34d8,0x6c74,0x343a,0x408d,
+0x972a,0x21d6,0x0e35,0x4090,
+0xffb3,0x5de8,0x6c48,0x4081
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x23cc,0xfd7c,0x74d5,0x402a,
+0x7365,0xfee1,0xad42,0x4055,
+0x610d,0x246f,0x2f01,0x4076,
+0x41d0,0x02f6,0x7dab,0x408e,
+0x7151,0xfca4,0x7fa2,0x409c,
+0xf4ff,0xdafa,0x8cac,0x40a1,
+0xede2,0x0192,0xe2a7,0x4099,
+0x42d6,0x60c4,0x6c48,0x4081
+};
+static unsigned short R[] = {
+0x9b62,0x5042,0x0dd7,0x3fe2,
+0xc5a6,0xebb8,0x67e6,0x3ff4,
+0xa71a,0xf436,0x1381,0x4014,
+0x0c0c,0x58dd,0xa40e,0x4018,
+0x960e,0x9718,0xa393,0x401d,
+0x0367,0x0a47,0xd4b8,0x4007
+};
+static unsigned short S[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xce21,0x0917,0x1590,0x4002,
+0x4cfd,0x21d8,0xcac5,0x4022,
+0x2c4d,0x7f05,0x1910,0x4028,
+0x7ff5,0x959c,0x14d9,0x4031,
+0x26c1,0xaa63,0x37ca,0x4023,
+0x2d90,0x5ab6,0xf3de,0x400a
+};
+static unsigned short T[] = {
+0x5d88,0x1e37,0x35bf,0x4023,
+0x067f,0x4e9e,0x81aa,0x4056,
+0x35b7,0xbcb4,0x7002,0x40a1,
+0xef90,0x3c72,0x5b53,0x40bb,
+0x13dc,0xa442,0x2509,0x40eb
+};
+static unsigned short U[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xa6ba,0x3fef,0xc7e6,0x4040,
+0x3aee,0x14c6,0x4add,0x4080,
+0xfd12,0xe680,0xf252,0x40b1,
+0x7c0a,0x0101,0x1940,0x40d6,
+0xf567,0x9dc8,0x0e6c,0x40e8
+};
+#define UTHRESH 37.519379347
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3df0,0xeb24,0xa24f,0x6479,
+0x3fe2,0x0dd7,0x4636,0x3488,
+0x401d,0xda53,0xdec5,0x6dc4,
+0x4048,0x518f,0xacad,0xba66,
+0x4068,0x90aa,0xa9e0,0x20f7,
+0x4080,0x738f,0xc264,0xcf58,
+0x408d,0x343a,0x6c74,0x34d8,
+0x4090,0x0e35,0x21d6,0x972a,
+0x4081,0x6c48,0x5de8,0xffb3
+};
+static unsigned short Q[] = {
+0x402a,0x74d5,0xfd7c,0x23cc,
+0x4055,0xad42,0xfee1,0x7365,
+0x4076,0x2f01,0x246f,0x610d,
+0x408e,0x7dab,0x02f6,0x41d0,
+0x409c,0x7fa2,0xfca4,0x7151,
+0x40a1,0x8cac,0xdafa,0xf4ff,
+0x4099,0xe2a7,0x0192,0xede2,
+0x4081,0x6c48,0x60c4,0x42d6
+};
+static unsigned short R[] = {
+0x3fe2,0x0dd7,0x5042,0x9b62,
+0x3ff4,0x67e6,0xebb8,0xc5a6,
+0x4014,0x1381,0xf436,0xa71a,
+0x4018,0xa40e,0x58dd,0x0c0c,
+0x401d,0xa393,0x9718,0x960e,
+0x4007,0xd4b8,0x0a47,0x0367
+};
+static unsigned short S[] = {
+0x4002,0x1590,0x0917,0xce21,
+0x4022,0xcac5,0x21d8,0x4cfd,
+0x4028,0x1910,0x7f05,0x2c4d,
+0x4031,0x14d9,0x959c,0x7ff5,
+0x4023,0x37ca,0xaa63,0x26c1,
+0x400a,0xf3de,0x5ab6,0x2d90
+};
+static unsigned short T[] = {
+0x4023,0x35bf,0x1e37,0x5d88,
+0x4056,0x81aa,0x4e9e,0x067f,
+0x40a1,0x7002,0xbcb4,0x35b7,
+0x40bb,0x5b53,0x3c72,0xef90,
+0x40eb,0x2509,0xa442,0x13dc
+};
+static unsigned short U[] = {
+0x4040,0xc7e6,0x3fef,0xa6ba,
+0x4080,0x4add,0x14c6,0x3aee,
+0x40b1,0xf252,0xe680,0xfd12,
+0x40d6,0x1940,0x0101,0x7c0a,
+0x40e8,0x0e6c,0x9dc8,0xf567
+};
+#define UTHRESH 37.519379347
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double exp ( double );
+extern double log ( double );
+extern double fabs ( double );
+double erf ( double );
+double erfc ( double );
+#else
+double polevl(), p1evl(), exp(), log(), fabs();
+double erf(), erfc();
+#endif
+
+double ndtr(a)
+double a;
+{
+double x, y, z;
+
+x = a * SQRTH;
+z = fabs(x);
+
+if( z < SQRTH )
+	y = 0.5 + 0.5 * erf(x);
+
+else
+	{
+	y = 0.5 * erfc(z);
+
+	if( x > 0 )
+		y = 1.0 - y;
+	}
+
+return(y);
+}
+
+
+double erfc(a)
+double a;
+{
+double p,q,x,y,z;
+
+
+if( a < 0.0 )
+	x = -a;
+else
+	x = a;
+
+if( x < 1.0 )
+	return( 1.0 - erf(a) );
+
+z = -a * a;
+
+if( z < -MAXLOG )
+	{
+under:
+	mtherr( "erfc", UNDERFLOW );
+	if( a < 0 )
+		return( 2.0 );
+	else
+		return( 0.0 );
+	}
+
+z = exp(z);
+
+if( x < 8.0 )
+	{
+	p = polevl( x, P, 8 );
+	q = p1evl( x, Q, 8 );
+	}
+else
+	{
+	p = polevl( x, R, 5 );
+	q = p1evl( x, S, 6 );
+	}
+y = (z * p)/q;
+
+if( a < 0 )
+	y = 2.0 - y;
+
+if( y == 0.0 )
+	goto under;
+
+return(y);
+}
+
+
+
+double erf(x)
+double x;
+{
+double y, z;
+
+if( fabs(x) > 1.0 )
+	return( 1.0 - erfc(x) );
+z = x * x;
+y = x * polevl( z, T, 4 ) / p1evl( z, U, 5 );
+return( y );
+
+}

libm/double/ndtri.c

@@ -0,0 +1,417 @@
+/*							ndtri.c
+ *
+ *	Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtri();
+ *
+ * x = ndtri( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2.0 * log(y) );  then the approximation is
+ * x = z - log(z)/z  - (1/z) P(1/z) / Q(1/z).
+ * There are two rational functions P/Q, one for 0 < y < exp(-32)
+ * and the other for y up to exp(-2).  For larger arguments,
+ * w = y - 0.5, and  x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain        # trials      peak         rms
+ *    DEC      0.125, 1         5500       9.5e-17     2.1e-17
+ *    DEC      6e-39, 0.135     3500       5.7e-17     1.3e-17
+ *    IEEE     0.125, 1        20000       7.2e-16     1.3e-16
+ *    IEEE     3e-308, 0.135   50000       4.6e-16     9.8e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition    value returned
+ * ndtri domain       x <= 0        -MAXNUM
+ * ndtri domain       x >= 1         MAXNUM
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+extern double MAXNUM;
+
+#ifdef UNK
+/* sqrt(2pi) */
+static double s2pi = 2.50662827463100050242E0;
+#endif
+
+#ifdef DEC
+static unsigned short s2p[] = {0040440,0066230,0177661,0034055};
+#define s2pi *(double *)s2p
+#endif
+
+#ifdef IBMPC
+static unsigned short s2p[] = {0x2706,0x1ff6,0x0d93,0x4004};
+#define s2pi *(double *)s2p
+#endif
+
+#ifdef MIEEE
+static unsigned short s2p[] = {
+0x4004,0x0d93,0x1ff6,0x2706
+};
+#define s2pi *(double *)s2p
+#endif
+
+/* approximation for 0 <= |y - 0.5| <= 3/8 */
+#ifdef UNK
+static double P0[5] = {
+-5.99633501014107895267E1,
+ 9.80010754185999661536E1,
+-5.66762857469070293439E1,
+ 1.39312609387279679503E1,
+-1.23916583867381258016E0,
+};
+static double Q0[8] = {
+/* 1.00000000000000000000E0,*/
+ 1.95448858338141759834E0,
+ 4.67627912898881538453E0,
+ 8.63602421390890590575E1,
+-2.25462687854119370527E2,
+ 2.00260212380060660359E2,
+-8.20372256168333339912E1,
+ 1.59056225126211695515E1,
+-1.18331621121330003142E0,
+};
+#endif
+#ifdef DEC
+static unsigned short P0[20] = {
+0141557,0155170,0071360,0120550,
+0041704,0000214,0172417,0067307,
+0141542,0132204,0040066,0156723,
+0041136,0163161,0157276,0007747,
+0140236,0116374,0073666,0051764,
+};
+static unsigned short Q0[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0040372,0026256,0110403,0123707,
+0040625,0122024,0020277,0026661,
+0041654,0134161,0124134,0007244,
+0142141,0073162,0133021,0131371,
+0042110,0041235,0043516,0057767,
+0141644,0011417,0036155,0137305,
+0041176,0076556,0004043,0125430,
+0140227,0073347,0152776,0067251,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P0[20] = {
+0x142d,0x0e5e,0xfb4f,0xc04d,
+0xedd9,0x9ea1,0x8011,0x4058,
+0xdbba,0x8806,0x5690,0xc04c,
+0xc1fd,0x3bd7,0xdcce,0x402b,
+0xca7e,0x8ef6,0xd39f,0xbff3,
+};
+static unsigned short Q0[36] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x74f9,0xd220,0x4595,0x3fff,
+0xe5b6,0x8417,0xb482,0x4012,
+0x81d4,0x350b,0x970e,0x4055,
+0x365f,0x56c2,0x2ece,0xc06c,
+0xcbff,0xa8e9,0x0853,0x4069,
+0xb7d9,0xe78d,0x8261,0xc054,
+0x7563,0xc104,0xcfad,0x402f,
+0xcdd5,0xfabf,0xeedc,0xbff2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P0[20] = {
+0xc04d,0xfb4f,0x0e5e,0x142d,
+0x4058,0x8011,0x9ea1,0xedd9,
+0xc04c,0x5690,0x8806,0xdbba,
+0x402b,0xdcce,0x3bd7,0xc1fd,
+0xbff3,0xd39f,0x8ef6,0xca7e,
+};
+static unsigned short Q0[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3fff,0x4595,0xd220,0x74f9,
+0x4012,0xb482,0x8417,0xe5b6,
+0x4055,0x970e,0x350b,0x81d4,
+0xc06c,0x2ece,0x56c2,0x365f,
+0x4069,0x0853,0xa8e9,0xcbff,
+0xc054,0x8261,0xe78d,0xb7d9,
+0x402f,0xcfad,0xc104,0x7563,
+0xbff2,0xeedc,0xfabf,0xcdd5,
+};
+#endif
+
+
+/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
+ * i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
+ */
+#ifdef UNK
+static double P1[9] = {
+ 4.05544892305962419923E0,
+ 3.15251094599893866154E1,
+ 5.71628192246421288162E1,
+ 4.40805073893200834700E1,
+ 1.46849561928858024014E1,
+ 2.18663306850790267539E0,
+-1.40256079171354495875E-1,
+-3.50424626827848203418E-2,
+-8.57456785154685413611E-4,
+};
+static double Q1[8] = {
+/*  1.00000000000000000000E0,*/
+ 1.57799883256466749731E1,
+ 4.53907635128879210584E1,
+ 4.13172038254672030440E1,
+ 1.50425385692907503408E1,
+ 2.50464946208309415979E0,
+-1.42182922854787788574E-1,
+-3.80806407691578277194E-2,
+-9.33259480895457427372E-4,
+};
+#endif
+#ifdef DEC
+static unsigned short P1[36] = {
+0040601,0143074,0150744,0073326,
+0041374,0031554,0113253,0146016,
+0041544,0123272,0012463,0176771,
+0041460,0051160,0103560,0156511,
+0041152,0172624,0117772,0030755,
+0040413,0170713,0151545,0176413,
+0137417,0117512,0022154,0131671,
+0137017,0104257,0071432,0007072,
+0135540,0143363,0063137,0036166,
+};
+static unsigned short Q1[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0041174,0075325,0004736,0120326,
+0041465,0110044,0047561,0045567,
+0041445,0042321,0012142,0030340,
+0041160,0127074,0166076,0141051,
+0040440,0046055,0040745,0150400,
+0137421,0114146,0067330,0010621,
+0137033,0175162,0025555,0114351,
+0135564,0122773,0145750,0030357,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P1[36] = {
+0x8edb,0x9a3c,0x38c7,0x4010,
+0x7982,0x92d5,0x866d,0x403f,
+0x7fbf,0x42a6,0x94d7,0x404c,
+0x1ba9,0x10ee,0x0a4e,0x4046,
+0x463e,0x93ff,0x5eb2,0x402d,
+0xbfa1,0x7a6c,0x7e39,0x4001,
+0x9677,0x448d,0xf3e9,0xbfc1,
+0x41c7,0xee63,0xf115,0xbfa1,
+0xe78f,0x6ccb,0x18de,0xbf4c,
+};
+static unsigned short Q1[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xd41b,0xa13b,0x8f5a,0x402f,
+0x296f,0x89ee,0xb204,0x4046,
+0x461c,0x228c,0xa89a,0x4044,
+0xd845,0x9d87,0x15c7,0x402e,
+0xba20,0xa83c,0x0985,0x4004,
+0x0232,0xcddb,0x330c,0xbfc2,
+0xb31d,0x456d,0x7f4e,0xbfa3,
+0x061e,0x797d,0x94bf,0xbf4e,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P1[36] = {
+0x4010,0x38c7,0x9a3c,0x8edb,
+0x403f,0x866d,0x92d5,0x7982,
+0x404c,0x94d7,0x42a6,0x7fbf,
+0x4046,0x0a4e,0x10ee,0x1ba9,
+0x402d,0x5eb2,0x93ff,0x463e,
+0x4001,0x7e39,0x7a6c,0xbfa1,
+0xbfc1,0xf3e9,0x448d,0x9677,
+0xbfa1,0xf115,0xee63,0x41c7,
+0xbf4c,0x18de,0x6ccb,0xe78f,
+};
+static unsigned short Q1[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x402f,0x8f5a,0xa13b,0xd41b,
+0x4046,0xb204,0x89ee,0x296f,
+0x4044,0xa89a,0x228c,0x461c,
+0x402e,0x15c7,0x9d87,0xd845,
+0x4004,0x0985,0xa83c,0xba20,
+0xbfc2,0x330c,0xcddb,0x0232,
+0xbfa3,0x7f4e,0x456d,0xb31d,
+0xbf4e,0x94bf,0x797d,0x061e,
+};
+#endif
+
+/* Approximation for interval z = sqrt(-2 log y ) between 8 and 64
+ * i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
+ */
+
+#ifdef UNK
+static double P2[9] = {
+  3.23774891776946035970E0,
+  6.91522889068984211695E0,
+  3.93881025292474443415E0,
+  1.33303460815807542389E0,
+  2.01485389549179081538E-1,
+  1.23716634817820021358E-2,
+  3.01581553508235416007E-4,
+  2.65806974686737550832E-6,
+  6.23974539184983293730E-9,
+};
+static double Q2[8] = {
+/*  1.00000000000000000000E0,*/
+  6.02427039364742014255E0,
+  3.67983563856160859403E0,
+  1.37702099489081330271E0,
+  2.16236993594496635890E-1,
+  1.34204006088543189037E-2,
+  3.28014464682127739104E-4,
+  2.89247864745380683936E-6,
+  6.79019408009981274425E-9,
+};
+#endif
+#ifdef DEC
+static unsigned short P2[36] = {
+0040517,0033507,0036236,0125641,
+0040735,0044616,0014473,0140133,
+0040574,0012567,0114535,0102541,
+0040252,0120340,0143474,0150135,
+0037516,0051057,0115361,0031211,
+0036512,0131204,0101511,0125144,
+0035236,0016627,0043160,0140216,
+0033462,0060512,0060141,0010641,
+0031326,0062541,0101304,0077706,
+};
+static unsigned short Q2[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0040700,0143322,0132137,0040501,
+0040553,0101155,0053221,0140257,
+0040260,0041071,0052573,0010004,
+0037535,0066472,0177261,0162330,
+0036533,0160475,0066666,0036132,
+0035253,0174533,0027771,0044027,
+0033502,0016147,0117666,0063671,
+0031351,0047455,0141663,0054751,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P2[36] = {
+0xd574,0xe793,0xe6e8,0x4009,
+0x780b,0xc327,0xa931,0x401b,
+0xb0ac,0xf32b,0x82ae,0x400f,
+0x9a0c,0x18e7,0x541c,0x3ff5,
+0x2651,0xf35e,0xca45,0x3fc9,
+0x354d,0x9069,0x5650,0x3f89,
+0x1812,0xe8ce,0xc3b2,0x3f33,
+0x2234,0x4c0c,0x4c29,0x3ec6,
+0x8ff9,0x3058,0xccac,0x3e3a,
+};
+static unsigned short Q2[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xe828,0x568b,0x18da,0x4018,
+0x3816,0xaad2,0x704d,0x400d,
+0x6200,0x2aaf,0x0847,0x3ff6,
+0x3c9b,0x5fd6,0xada7,0x3fcb,
+0xc78b,0xadb6,0x7c27,0x3f8b,
+0x2903,0x65ff,0x7f2b,0x3f35,
+0xccf7,0xf3f6,0x438c,0x3ec8,
+0x6b3d,0xb876,0x29e5,0x3e3d,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P2[36] = {
+0x4009,0xe6e8,0xe793,0xd574,
+0x401b,0xa931,0xc327,0x780b,
+0x400f,0x82ae,0xf32b,0xb0ac,
+0x3ff5,0x541c,0x18e7,0x9a0c,
+0x3fc9,0xca45,0xf35e,0x2651,
+0x3f89,0x5650,0x9069,0x354d,
+0x3f33,0xc3b2,0xe8ce,0x1812,
+0x3ec6,0x4c29,0x4c0c,0x2234,
+0x3e3a,0xccac,0x3058,0x8ff9,
+};
+static unsigned short Q2[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4018,0x18da,0x568b,0xe828,
+0x400d,0x704d,0xaad2,0x3816,
+0x3ff6,0x0847,0x2aaf,0x6200,
+0x3fcb,0xada7,0x5fd6,0x3c9b,
+0x3f8b,0x7c27,0xadb6,0xc78b,
+0x3f35,0x7f2b,0x65ff,0x2903,
+0x3ec8,0x438c,0xf3f6,0xccf7,
+0x3e3d,0x29e5,0xb876,0x6b3d,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double polevl(), p1evl(), log(), sqrt();
+#endif
+
+double ndtri(y0)
+double y0;
+{
+double x, y, z, y2, x0, x1;
+int code;
+
+if( y0 <= 0.0 )
+	{
+	mtherr( "ndtri", DOMAIN );
+	return( -MAXNUM );
+	}
+if( y0 >= 1.0 )
+	{
+	mtherr( "ndtri", DOMAIN );
+	return( MAXNUM );
+	}
+code = 1;
+y = y0;
+if( y > (1.0 - 0.13533528323661269189) ) /* 0.135... = exp(-2) */
+	{
+	y = 1.0 - y;
+	code = 0;
+	}
+
+if( y > 0.13533528323661269189 )
+	{
+	y = y - 0.5;
+	y2 = y * y;
+	x = y + y * (y2 * polevl( y2, P0, 4)/p1evl( y2, Q0, 8 ));
+	x = x * s2pi; 
+	return(x);
+	}
+
+x = sqrt( -2.0 * log(y) );
+x0 = x - log(x)/x;
+
+z = 1.0/x;
+if( x < 8.0 ) /* y > exp(-32) = 1.2664165549e-14 */
+	x1 = z * polevl( z, P1, 8 )/p1evl( z, Q1, 8 );
+else
+	x1 = z * polevl( z, P2, 8 )/p1evl( z, Q2, 8 );
+x = x0 - x1;
+if( code != 0 )
+	x = -x;
+return( x );
+}

libm/double/paranoia.c

@@ -0,0 +1,2156 @@
+/*	A C version of Kahan's Floating Point Test "Paranoia"
+
+			Thos Sumner, UCSF, Feb. 1985
+			David Gay, BTL, Jan. 1986
+
+	This is a rewrite from the Pascal version by
+
+			B. A. Wichmann, 18 Jan. 1985
+
+	(and does NOT exhibit good C programming style).
+
+(C) Apr 19 1983 in BASIC version by:
+	Professor W. M. Kahan,
+	567 Evans Hall
+	Electrical Engineering & Computer Science Dept.
+	University of California
+	Berkeley, California 94720
+	USA
+
+converted to Pascal by:
+	B. A. Wichmann
+	National Physical Laboratory
+	Teddington Middx
+	TW11 OLW
+	UK
+
+converted to C by:
+
+	David M. Gay		and	Thos Sumner
+	AT&T Bell Labs			Computer Center, Rm. U-76
+	600 Mountainn Avenue		University of California
+	Murray Hill, NJ 07974		San Francisco, CA 94143
+	USA				USA
+
+with simultaneous corrections to the Pascal source (reflected
+in the Pascal source available over netlib).
+
+Reports of results on various systems from all the versions
+of Paranoia are being collected by Richard Karpinski at the
+same address as Thos Sumner.  This includes sample outputs,
+bug reports, and criticisms.
+
+You may copy this program freely if you acknowledge its source.
+Comments on the Pascal version to NPL, please.
+
+
+The C version catches signals from floating-point exceptions.
+If signal(SIGFPE,...) is unavailable in your environment, you may
+#define NOSIGNAL to comment out the invocations of signal.
+
+This source file is too big for some C compilers, but may be split
+into pieces.  Comments containing "SPLIT" suggest convenient places
+for this splitting.  At the end of these comments is an "ed script"
+(for the UNIX(tm) editor ed) that will do this splitting.
+
+By #defining Single when you compile this source, you may obtain
+a single-precision C version of Paranoia.
+
+
+The following is from the introductory commentary from Wichmann's work:
+
+The BASIC program of Kahan is written in Microsoft BASIC using many
+facilities which have no exact analogy in Pascal.  The Pascal
+version below cannot therefore be exactly the same.  Rather than be
+a minimal transcription of the BASIC program, the Pascal coding
+follows the conventional style of block-structured languages.  Hence
+the Pascal version could be useful in producing versions in other
+structured languages.
+
+Rather than use identifiers of minimal length (which therefore have
+little mnemonic significance), the Pascal version uses meaningful
+identifiers as follows [Note: A few changes have been made for C]:
+
+
+BASIC   C               BASIC   C               BASIC   C               
+
+   A                       J                       S    StickyBit
+   A1   AInverse           J0   NoErrors           T
+   B    Radix                    [Failure]         T0   Underflow
+   B1   BInverse           J1   NoErrors           T2   ThirtyTwo
+   B2   RadixD2                  [SeriousDefect]   T5   OneAndHalf
+   B9   BMinusU2           J2   NoErrors           T7   TwentySeven
+   C                             [Defect]          T8   TwoForty
+   C1   CInverse           J3   NoErrors           U    OneUlp
+   D                             [Flaw]            U0   UnderflowThreshold
+   D4   FourD              K    PageNo             U1
+   E0                      L    Milestone          U2
+   E1                      M                       V
+   E2   Exp2               N                       V0
+   E3                      N1                      V8
+   E5   MinSqEr            O    Zero               V9
+   E6   SqEr               O1   One                W
+   E7   MaxSqEr            O2   Two                X
+   E8                      O3   Three              X1
+   E9                      O4   Four               X8
+   F1   MinusOne           O5   Five               X9   Random1
+   F2   Half               O8   Eight              Y
+   F3   Third              O9   Nine               Y1
+   F6                      P    Precision          Y2
+   F9                      Q                       Y9   Random2
+   G1   GMult              Q8                      Z
+   G2   GDiv               Q9                      Z0   PseudoZero
+   G3   GAddSub            R                       Z1
+   H                       R1   RMult              Z2
+   H1   HInverse           R2   RDiv               Z9
+   I                       R3   RAddSub
+   IO   NoTrials           R4   RSqrt
+   I3   IEEE               R9   Random9
+
+   SqRWrng
+
+All the variables in BASIC are true variables and in consequence,
+the program is more difficult to follow since the "constants" must
+be determined (the glossary is very helpful).  The Pascal version
+uses Real constants, but checks are added to ensure that the values
+are correctly converted by the compiler.
+
+The major textual change to the Pascal version apart from the
+identifiersis that named procedures are used, inserting parameters
+wherehelpful.  New procedures are also introduced.  The
+correspondence is as follows:
+
+
+BASIC       Pascal
+lines 
+
+  90- 140   Pause
+ 170- 250   Instructions
+ 380- 460   Heading
+ 480- 670   Characteristics
+ 690- 870   History
+2940-2950   Random
+3710-3740   NewD
+4040-4080   DoesYequalX
+4090-4110   PrintIfNPositive
+4640-4850   TestPartialUnderflow
+
+=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=
+
+Below is an "ed script" that splits para.c into 10 files
+of the form part[1-8].c, subs.c, and msgs.c, plus a header
+file, paranoia.h, that these files require.
+r paranoia.c
+$
+?SPLIT
++,$w msgs.c
+.,$d
+?SPLIT
+.d
++d
+-,$w subs.c
+-,$d
+?part8
++d
+?include
+.,$w part8.c
+.,$d
+-d
+?part7
++d
+?include
+.,$w part7.c
+.,$d
+-d
+?part6
++d
+?include
+.,$w part6.c
+.,$d
+-d
+?part5
++d
+?include
+.,$w part5.c
+.,$d
+-d
+?part4
++d
+?include
+.,$w part4.c
+.,$d
+-d
+?part3
++d
+?include
+.,$w part3.c
+.,$d
+-d
+?part2
++d
+?include
+.,$w part2.c
+.,$d
+?SPLIT
+.d
+1,/^#include/-1d
+1,$w part1.c
+/Computed constants/,$d
+1,$s/^int/extern &/
+1,$s/^FLOAT/extern &/
+1,$s! = .*!;!
+/^Guard/,/^Round/s/^/extern /
+/^jmp_buf/s/^/extern /
+/^Sig_type/s/^/extern /
+a
+extern int sigfpe();
+.
+w paranoia.h
+q
+
+*/
+
+#include <stdio.h>
+#ifndef NOSIGNAL
+#include <signal.h>
+#endif
+#include <setjmp.h>
+
+extern double fabs(), floor(), log(), pow(), sqrt();
+
+#ifdef Single
+#define FLOAT float
+#define FABS(x) (float)fabs((double)(x))
+#define FLOOR(x) (float)floor((double)(x))
+#define LOG(x) (float)log((double)(x))
+#define POW(x,y) (float)pow((double)(x),(double)(y))
+#define SQRT(x) (float)sqrt((double)(x))
+#else
+#define FLOAT double
+#define FABS(x) fabs(x)
+#define FLOOR(x) floor(x)
+#define LOG(x) log(x)
+#define POW(x,y) pow(x,y)
+#define SQRT(x) sqrt(x)
+#endif
+
+jmp_buf ovfl_buf;
+typedef int (*Sig_type)();
+Sig_type sigsave;
+
+#define KEYBOARD 0
+
+FLOAT Radix, BInvrse, RadixD2, BMinusU2;
+FLOAT Sign(), Random();
+
+/*Small floating point constants.*/
+FLOAT Zero = 0.0;
+FLOAT Half = 0.5;
+FLOAT One = 1.0;
+FLOAT Two = 2.0;
+FLOAT Three = 3.0;
+FLOAT Four = 4.0;
+FLOAT Five = 5.0;
+FLOAT Eight = 8.0;
+FLOAT Nine = 9.0;
+FLOAT TwentySeven = 27.0;
+FLOAT ThirtyTwo = 32.0;
+FLOAT TwoForty = 240.0;
+FLOAT MinusOne = -1.0;
+FLOAT OneAndHalf = 1.5;
+/*Integer constants*/
+int NoTrials = 20; /*Number of tests for commutativity. */
+#define False 0
+#define True 1
+
+/* Definitions for declared types 
+	Guard == (Yes, No);
+	Rounding == (Chopped, Rounded, Other);
+	Message == packed array [1..40] of char;
+	Class == (Flaw, Defect, Serious, Failure);
+	  */
+#define Yes 1
+#define No  0
+#define Chopped 2
+#define Rounded 1
+#define Other   0
+#define Flaw    3
+#define Defect  2
+#define Serious 1
+#define Failure 0
+typedef int Guard, Rounding, Class;
+typedef char Message;
+
+/* Declarations of Variables */
+int Indx;
+char ch[8];
+FLOAT AInvrse, A1;
+FLOAT C, CInvrse;
+FLOAT D, FourD;
+FLOAT E0, E1, Exp2, E3, MinSqEr;
+FLOAT SqEr, MaxSqEr, E9;
+FLOAT Third;
+FLOAT F6, F9;
+FLOAT H, HInvrse;
+int I;
+FLOAT StickyBit, J;
+FLOAT MyZero;
+FLOAT Precision;
+FLOAT Q, Q9;
+FLOAT R, Random9;
+FLOAT T, Underflow, S;
+FLOAT OneUlp, UfThold, U1, U2;
+FLOAT V, V0, V9;
+FLOAT W;
+FLOAT X, X1, X2, X8, Random1;
+FLOAT Y, Y1, Y2, Random2;
+FLOAT Z, PseudoZero, Z1, Z2, Z9;
+volatile FLOAT VV;
+int ErrCnt[4];
+int fpecount;
+int Milestone;
+int PageNo;
+int M, N, N1;
+Guard GMult, GDiv, GAddSub;
+Rounding RMult, RDiv, RAddSub, RSqrt;
+int Break, Done, NotMonot, Monot, Anomaly, IEEE,
+		SqRWrng, UfNGrad;
+/* Computed constants. */
+/*U1  gap below 1.0, i.e, 1.0-U1 is next number below 1.0 */
+/*U2  gap above 1.0, i.e, 1.0+U2 is next number above 1.0 */
+
+/* floating point exception receiver */
+sigfpe()
+{
+	fpecount++;
+	printf("\n* * * FLOATING-POINT ERROR * * *\n");
+	fflush(stdout);
+	if (sigsave) {
+#ifndef NOSIGNAL
+		signal(SIGFPE, sigsave);
+#endif
+		sigsave = 0;
+		longjmp(ovfl_buf, 1);
+		}
+	abort();
+}
+
+main()
+{
+ /* Set coprocessor to double precision, no arith traps. */
+  /* __setfpucw(0x127f);*/
+  dprec();
+	/* First two assignments use integer right-hand sides. */
+	Zero = 0;
+	One = 1;
+	Two = One + One;
+	Three = Two + One;
+	Four = Three + One;
+	Five = Four + One;
+	Eight = Four + Four;
+	Nine = Three * Three;
+	TwentySeven = Nine * Three;
+	ThirtyTwo = Four * Eight;
+	TwoForty = Four * Five * Three * Four;
+	MinusOne = -One;
+	Half = One / Two;
+	OneAndHalf = One + Half;
+	ErrCnt[Failure] = 0;
+	ErrCnt[Serious] = 0;
+	ErrCnt[Defect] = 0;
+	ErrCnt[Flaw] = 0;
+	PageNo = 1;
+	/*=============================================*/
+	Milestone = 0;
+	/*=============================================*/
+#ifndef NOSIGNAL
+	signal(SIGFPE, sigfpe);
+#endif
+	Instructions();
+	Pause();
+	Heading();
+	Pause();
+	Characteristics();
+	Pause();
+	History();
+	Pause();
+	/*=============================================*/
+	Milestone = 7;
+	/*=============================================*/
+	printf("Program is now RUNNING tests on small integers:\n");
+	
+	TstCond (Failure, (Zero + Zero == Zero) && (One - One == Zero)
+		   && (One > Zero) && (One + One == Two),
+			"0+0 != 0, 1-1 != 0, 1 <= 0, or 1+1 != 2");
+	Z = - Zero;
+	if (Z == 0.0) {
+		U1 = 0.001;
+		Radix = 1;
+		TstPtUf();
+		}
+	else {
+		ErrCnt[Failure] = ErrCnt[Failure] + 1;
+		printf("Comparison alleges that -0.0 is Non-zero!\n");
+		}
+	TstCond (Failure, (Three == Two + One) && (Four == Three + One)
+		   && (Four + Two * (- Two) == Zero)
+		   && (Four - Three - One == Zero),
+		   "3 != 2+1, 4 != 3+1, 4+2*(-2) != 0, or 4-3-1 != 0");
+	TstCond (Failure, (MinusOne == (0 - One))
+		   && (MinusOne + One == Zero ) && (One + MinusOne == Zero)
+		   && (MinusOne + FABS(One) == Zero)
+		   && (MinusOne + MinusOne * MinusOne == Zero),
+		   "-1+1 != 0, (-1)+abs(1) != 0, or -1+(-1)*(-1) != 0");
+	TstCond (Failure, Half + MinusOne + Half == Zero,
+		  "1/2 + (-1) + 1/2 != 0");
+	/*=============================================*/
+	/*SPLIT
+	part2();
+	part3();
+	part4();
+	part5();
+	part6();
+	part7();
+	part8();
+	}
+#include "paranoia.h"
+part2(){
+*/
+	Milestone = 10;
+	/*=============================================*/
+	TstCond (Failure, (Nine == Three * Three)
+		   && (TwentySeven == Nine * Three) && (Eight == Four + Four)
+		   && (ThirtyTwo == Eight * Four)
+		   && (ThirtyTwo - TwentySeven - Four - One == Zero),
+		   "9 != 3*3, 27 != 9*3, 32 != 8*4, or 32-27-4-1 != 0");
+	TstCond (Failure, (Five == Four + One) &&
+			(TwoForty == Four * Five * Three * Four)
+		   && (TwoForty / Three - Four * Four * Five == Zero)
+		   && ( TwoForty / Four - Five * Three * Four == Zero)
+		   && ( TwoForty / Five - Four * Three * Four == Zero),
+		  "5 != 4+1, 240/3 != 80, 240/4 != 60, or 240/5 != 48");
+	if (ErrCnt[Failure] == 0) {
+		printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n");
+		printf("\n");
+		}
+	printf("Searching for Radix and Precision.\n");
+	W = One;
+	do  {
+		W = W + W;
+		Y = W + One;
+		Z = Y - W;
+		Y = Z - One;
+		} while (MinusOne + FABS(Y) < Zero);
+	/*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
+	Precision = Zero;
+	Y = One;
+	do  {
+		Radix = W + Y;
+		Y = Y + Y;
+		Radix = Radix - W;
+		} while ( Radix == Zero);
+	if (Radix < Two) Radix = One;
+	printf("Radix = %f .\n", Radix);
+	if (Radix != 1) {
+		W = One;
+		do  {
+			Precision = Precision + One;
+			W = W * Radix;
+			Y = W + One;
+			} while ((Y - W) == One);
+		}
+	/*... now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1
+			                              ...*/
+	U1 = One / W;
+	U2 = Radix * U1;
+	printf("Closest relative separation found is U1 = %.7e .\n\n", U1);
+	printf("Recalculating radix and precision.");
+	
+	/*save old values*/
+	E0 = Radix;
+	E1 = U1;
+	E9 = U2;
+	E3 = Precision;
+	
+	X = Four / Three;
+	Third = X - One;
+	F6 = Half - Third;
+	X = F6 + F6;
+	X = FABS(X - Third);
+	if (X < U2) X = U2;
+	
+	/*... now X = (unknown no.) ulps of 1+...*/
+	do  {
+		U2 = X;
+		Y = Half * U2 + ThirtyTwo * U2 * U2;
+		Y = One + Y;
+		X = Y - One;
+		} while ( ! ((U2 <= X) || (X <= Zero)));
+	
+	/*... now U2 == 1 ulp of 1 + ... */
+	X = Two / Three;
+	F6 = X - Half;
+	Third = F6 + F6;
+	X = Third - Half;
+	X = FABS(X + F6);
+	if (X < U1) X = U1;
+	
+	/*... now  X == (unknown no.) ulps of 1 -... */
+	do  {
+		U1 = X;
+		Y = Half * U1 + ThirtyTwo * U1 * U1;
+		Y = Half - Y;
+		X = Half + Y;
+		Y = Half - X;
+		X = Half + Y;
+		} while ( ! ((U1 <= X) || (X <= Zero)));
+	/*... now U1 == 1 ulp of 1 - ... */
+	if (U1 == E1) printf("confirms closest relative separation U1 .\n");
+	else printf("gets better closest relative separation U1 = %.7e .\n", U1);
+	W = One / U1;
+	F9 = (Half - U1) + Half;
+	Radix = FLOOR(0.01 + U2 / U1);
+	if (Radix == E0) printf("Radix confirmed.\n");
+	else printf("MYSTERY: recalculated Radix = %.7e .\n", Radix);
+	TstCond (Defect, Radix <= Eight + Eight,
+		   "Radix is too big: roundoff problems");
+	TstCond (Flaw, (Radix == Two) || (Radix == 10)
+		   || (Radix == One), "Radix is not as good as 2 or 10");
+	/*=============================================*/
+	Milestone = 20;
+	/*=============================================*/
+	TstCond (Failure, F9 - Half < Half,
+		   "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?");
+	X = F9;
+	I = 1;
+	Y = X - Half;
+	Z = Y - Half;
+	TstCond (Failure, (X != One)
+		   || (Z == Zero), "Comparison is fuzzy,X=1 but X-1/2-1/2 != 0");
+	X = One + U2;
+	I = 0;
+	/*=============================================*/
+	Milestone = 25;
+	/*=============================================*/
+	/*... BMinusU2 = nextafter(Radix, 0) */
+	BMinusU2 = Radix - One;
+	BMinusU2 = (BMinusU2 - U2) + One;
+	/* Purify Integers */
+	if (Radix != One)  {
+		X = - TwoForty * LOG(U1) / LOG(Radix);
+		Y = FLOOR(Half + X);
+		if (FABS(X - Y) * Four < One) X = Y;
+		Precision = X / TwoForty;
+		Y = FLOOR(Half + Precision);
+		if (FABS(Precision - Y) * TwoForty < Half) Precision = Y;
+		}
+	if ((Precision != FLOOR(Precision)) || (Radix == One)) {
+		printf("Precision cannot be characterized by an Integer number\n");
+		printf("of significant digits but, by itself, this is a minor flaw.\n");
+		}
+	if (Radix == One) 
+		printf("logarithmic encoding has precision characterized solely by U1.\n");
+	else printf("The number of significant digits of the Radix is %f .\n",
+			Precision);
+	TstCond (Serious, U2 * Nine * Nine * TwoForty < One,
+		   "Precision worse than 5 decimal figures  ");
+	/*=============================================*/
+	Milestone = 30;
+	/*=============================================*/
+	/* Test for extra-precise subepressions */
+	X = FABS(((Four / Three - One) - One / Four) * Three - One / Four);
+	do  {
+		Z2 = X;
+		X = (One + (Half * Z2 + ThirtyTwo * Z2 * Z2)) - One;
+		} while ( ! ((Z2 <= X) || (X <= Zero)));
+	X = Y = Z = FABS((Three / Four - Two / Three) * Three - One / Four);
+	do  {
+		Z1 = Z;
+		Z = (One / Two - ((One / Two - (Half * Z1 + ThirtyTwo * Z1 * Z1))
+			+ One / Two)) + One / Two;
+		} while ( ! ((Z1 <= Z) || (Z <= Zero)));
+	do  {
+		do  {
+			Y1 = Y;
+			Y = (Half - ((Half - (Half * Y1 + ThirtyTwo * Y1 * Y1)) + Half
+				)) + Half;
+			} while ( ! ((Y1 <= Y) || (Y <= Zero)));
+		X1 = X;
+		X = ((Half * X1 + ThirtyTwo * X1 * X1) - F9) + F9;
+		} while ( ! ((X1 <= X) || (X <= Zero)));
+	if ((X1 != Y1) || (X1 != Z1)) {
+		BadCond(Serious, "Disagreements among the values X1, Y1, Z1,\n");
+		printf("respectively  %.7e,  %.7e,  %.7e,\n", X1, Y1, Z1);
+		printf("are symptoms of inconsistencies introduced\n");
+		printf("by extra-precise evaluation of arithmetic subexpressions.\n");
+		notify("Possibly some part of this");
+		if ((X1 == U1) || (Y1 == U1) || (Z1 == U1))  printf(
+			"That feature is not tested further by this program.\n") ;
+		}
+	else  {
+		if ((Z1 != U1) || (Z2 != U2)) {
+			if ((Z1 >= U1) || (Z2 >= U2)) {
+				BadCond(Failure, "");
+				notify("Precision");
+				printf("\tU1 = %.7e, Z1 - U1 = %.7e\n",U1,Z1-U1);
+				printf("\tU2 = %.7e, Z2 - U2 = %.7e\n",U2,Z2-U2);
+				}
+			else {
+				if ((Z1 <= Zero) || (Z2 <= Zero)) {
+					printf("Because of unusual Radix = %f", Radix);
+					printf(", or exact rational arithmetic a result\n");
+					printf("Z1 = %.7e, or Z2 = %.7e ", Z1, Z2);
+					notify("of an\nextra-precision");
+					}
+				if (Z1 != Z2 || Z1 > Zero) {
+					X = Z1 / U1;
+					Y = Z2 / U2;
+					if (Y > X) X = Y;
+					Q = - LOG(X);
+					printf("Some subexpressions appear to be calculated extra\n");
+					printf("precisely with about %g extra B-digits, i.e.\n",
+						(Q / LOG(Radix)));
+					printf("roughly %g extra significant decimals.\n",
+						Q / LOG(10.));
+					}
+				printf("That feature is not tested further by this program.\n");
+				}
+			}
+		}
+	Pause();
+	/*=============================================*/
+	/*SPLIT
+	}
+#include "paranoia.h"
+part3(){
+*/
+	Milestone = 35;
+	/*=============================================*/
+	if (Radix >= Two) {
+		X = W / (Radix * Radix);
+		Y = X + One;
+		Z = Y - X;
+		T = Z + U2;
+		X = T - Z;
+		TstCond (Failure, X == U2,
+			"Subtraction is not normalized X=Y,X+Z != Y+Z!");
+		if (X == U2) printf(
+			"Subtraction appears to be normalized, as it should be.");
+		}
+	printf("\nChecking for guard digit in *, /, and -.\n");
+	Y = F9 * One;
+	Z = One * F9;
+	X = F9 - Half;
+	Y = (Y - Half) - X;
+	Z = (Z - Half) - X;
+	X = One + U2;
+	T = X * Radix;
+	R = Radix * X;
+	X = T - Radix;
+	X = X - Radix * U2;
+	T = R - Radix;
+	T = T - Radix * U2;
+	X = X * (Radix - One);
+	T = T * (Radix - One);
+	if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)) GMult = Yes;
+	else {
+		GMult = No;
+		TstCond (Serious, False,
+			"* lacks a Guard Digit, so 1*X != X");
+		}
+	Z = Radix * U2;
+	X = One + Z;
+	Y = FABS((X + Z) - X * X) - U2;
+	X = One - U2;
+	Z = FABS((X - U2) - X * X) - U1;
+	TstCond (Failure, (Y <= Zero)
+		   && (Z <= Zero), "* gets too many final digits wrong.\n");
+	Y = One - U2;
+	X = One + U2;
+	Z = One / Y;
+	Y = Z - X;
+	X = One / Three;
+	Z = Three / Nine;
+	X = X - Z;
+	T = Nine / TwentySeven;
+	Z = Z - T;
+	TstCond(Defect, X == Zero && Y == Zero && Z == Zero,
+		"Division lacks a Guard Digit, so error can exceed 1 ulp\n\
+or  1/3  and  3/9  and  9/27 may disagree");
+	Y = F9 / One;
+	X = F9 - Half;
+	Y = (Y - Half) - X;
+	X = One + U2;
+	T = X / One;
+	X = T - X;
+	if ((X == Zero) && (Y == Zero) && (Z == Zero)) GDiv = Yes;
+	else {
+		GDiv = No;
+		TstCond (Serious, False,
+			"Division lacks a Guard Digit, so X/1 != X");
+		}
+	X = One / (One + U2);
+	Y = X - Half - Half;
+	TstCond (Serious, Y < Zero,
+		   "Computed value of 1/1.000..1 >= 1");
+	X = One - U2;
+	Y = One + Radix * U2;
+	Z = X * Radix;
+	T = Y * Radix;
+	R = Z / Radix;
+	StickyBit = T / Radix;
+	X = R - X;
+	Y = StickyBit - Y;
+	TstCond (Failure, X == Zero && Y == Zero,
+			"* and/or / gets too many last digits wrong");
+	Y = One - U1;
+	X = One - F9;
+	Y = One - Y;
+	T = Radix - U2;
+	Z = Radix - BMinusU2;
+	T = Radix - T;
+	if ((X == U1) && (Y == U1) && (Z == U2) && (T == U2)) GAddSub = Yes;
+	else {
+		GAddSub = No;
+		TstCond (Serious, False,
+			"- lacks Guard Digit, so cancellation is obscured");
+		}
+	if (F9 != One && F9 - One >= Zero) {
+		BadCond(Serious, "comparison alleges  (1-U1) < 1  although\n");
+		printf("  subtration yields  (1-U1) - 1 = 0 , thereby vitiating\n");
+		printf("  such precautions against division by zero as\n");
+		printf("  ...  if (X == 1.0) {.....} else {.../(X-1.0)...}\n");
+		}
+	if (GMult == Yes && GDiv == Yes && GAddSub == Yes) printf(
+		"     *, /, and - appear to have guard digits, as they should.\n");
+	/*=============================================*/
+	Milestone = 40;
+	/*=============================================*/
+	Pause();
+	printf("Checking rounding on multiply, divide and add/subtract.\n");
+	RMult = Other;
+	RDiv = Other;
+	RAddSub = Other;
+	RadixD2 = Radix / Two;
+	A1 = Two;
+	Done = False;
+	do  {
+		AInvrse = Radix;
+		do  {
+			X = AInvrse;
+			AInvrse = AInvrse / A1;
+			} while ( ! (FLOOR(AInvrse) != AInvrse));
+		Done = (X == One) || (A1 > Three);
+		if (! Done) A1 = Nine + One;
+		} while ( ! (Done));
+	if (X == One) A1 = Radix;
+	AInvrse = One / A1;
+	X = A1;
+	Y = AInvrse;
+	Done = False;
+	do  {
+		Z = X * Y - Half;
+		TstCond (Failure, Z == Half,
+			"X * (1/X) differs from 1");
+		Done = X == Radix;
+		X = Radix;
+		Y = One / X;
+		} while ( ! (Done));
+	Y2 = One + U2;
+	Y1 = One - U2;
+	X = OneAndHalf - U2;
+	Y = OneAndHalf + U2;
+	Z = (X - U2) * Y2;
+	T = Y * Y1;
+	Z = Z - X;
+	T = T - X;
+	X = X * Y2;
+	Y = (Y + U2) * Y1;
+	X = X - OneAndHalf;
+	Y = Y - OneAndHalf;
+	if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T <= Zero)) {
+		X = (OneAndHalf + U2) * Y2;
+		Y = OneAndHalf - U2 - U2;
+		Z = OneAndHalf + U2 + U2;
+		T = (OneAndHalf - U2) * Y1;
+		X = X - (Z + U2);
+		StickyBit = Y * Y1;
+		S = Z * Y2;
+		T = T - Y;
+		Y = (U2 - Y) + StickyBit;
+		Z = S - (Z + U2 + U2);
+		StickyBit = (Y2 + U2) * Y1;
+		Y1 = Y2 * Y1;
+		StickyBit = StickyBit - Y2;
+		Y1 = Y1 - Half;
+		if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
+			&& ( StickyBit == Zero) && (Y1 == Half)) {
+			RMult = Rounded;
+			printf("Multiplication appears to round correctly.\n");
+			}
+		else	if ((X + U2 == Zero) && (Y < Zero) && (Z + U2 == Zero)
+				&& (T < Zero) && (StickyBit + U2 == Zero)
+				&& (Y1 < Half)) {
+				RMult = Chopped;
+				printf("Multiplication appears to chop.\n");
+				}
+			else printf("* is neither chopped nor correctly rounded.\n");
+		if ((RMult == Rounded) && (GMult == No)) notify("Multiplication");
+		}
+	else printf("* is neither chopped nor correctly rounded.\n");
+	/*=============================================*/
+	Milestone = 45;
+	/*=============================================*/
+	Y2 = One + U2;
+	Y1 = One - U2;
+	Z = OneAndHalf + U2 + U2;
+	X = Z / Y2;
+	T = OneAndHalf - U2 - U2;
+	Y = (T - U2) / Y1;
+	Z = (Z + U2) / Y2;
+	X = X - OneAndHalf;
+	Y = Y - T;
+	T = T / Y1;
+	Z = Z - (OneAndHalf + U2);
+	T = (U2 - OneAndHalf) + T;
+	if (! ((X > Zero) || (Y > Zero) || (Z > Zero) || (T > Zero))) {
+		X = OneAndHalf / Y2;
+		Y = OneAndHalf - U2;
+		Z = OneAndHalf + U2;
+		X = X - Y;
+		T = OneAndHalf / Y1;
+		Y = Y / Y1;
+		T = T - (Z + U2);
+		Y = Y - Z;
+		Z = Z / Y2;
+		Y1 = (Y2 + U2) / Y2;
+		Z = Z - OneAndHalf;
+		Y2 = Y1 - Y2;
+		Y1 = (F9 - U1) / F9;
+		if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
+			&& (Y2 == Zero) && (Y2 == Zero)
+			&& (Y1 - Half == F9 - Half )) {
+			RDiv = Rounded;
+			printf("Division appears to round correctly.\n");
+			if (GDiv == No) notify("Division");
+			}
+		else if ((X < Zero) && (Y < Zero) && (Z < Zero) && (T < Zero)
+			&& (Y2 < Zero) && (Y1 - Half < F9 - Half)) {
+			RDiv = Chopped;
+			printf("Division appears to chop.\n");
+			}
+		}
+	if (RDiv == Other) printf("/ is neither chopped nor correctly rounded.\n");
+	BInvrse = One / Radix;
+	TstCond (Failure, (BInvrse * Radix - Half == Half),
+		   "Radix * ( 1 / Radix ) differs from 1");
+	/*=============================================*/
+	/*SPLIT
+	}
+#include "paranoia.h"
+part4(){
+*/
+	Milestone = 50;
+	/*=============================================*/
+	TstCond (Failure, ((F9 + U1) - Half == Half)
+		   && ((BMinusU2 + U2 ) - One == Radix - One),
+		   "Incomplete carry-propagation in Addition");
+	X = One - U1 * U1;
+	Y = One + U2 * (One - U2);
+	Z = F9 - Half;
+	X = (X - Half) - Z;
+	Y = Y - One;
+	if ((X == Zero) && (Y == Zero)) {
+		RAddSub = Chopped;
+		printf("Add/Subtract appears to be chopped.\n");
+		}
+	if (GAddSub == Yes) {
+		X = (Half + U2) * U2;
+		Y = (Half - U2) * U2;
+		X = One + X;
+		Y = One + Y;
+		X = (One + U2) - X;
+		Y = One - Y;
+		if ((X == Zero) && (Y == Zero)) {
+			X = (Half + U2) * U1;
+			Y = (Half - U2) * U1;
+			X = One - X;
+			Y = One - Y;
+			X = F9 - X;
+			Y = One - Y;
+			if ((X == Zero) && (Y == Zero)) {
+				RAddSub = Rounded;
+				printf("Addition/Subtraction appears to round correctly.\n");
+				if (GAddSub == No) notify("Add/Subtract");
+				}
+			else printf("Addition/Subtraction neither rounds nor chops.\n");
+			}
+		else printf("Addition/Subtraction neither rounds nor chops.\n");
+		}
+	else printf("Addition/Subtraction neither rounds nor chops.\n");
+	S = One;
+	X = One + Half * (One + Half);
+	Y = (One + U2) * Half;
+	Z = X - Y;
+	T = Y - X;
+	StickyBit = Z + T;
+	if (StickyBit != Zero) {
+		S = Zero;
+		BadCond(Flaw, "(X - Y) + (Y - X) is non zero!\n");
+		}
+	StickyBit = Zero;
+	if ((GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
+		&& (RMult == Rounded) && (RDiv == Rounded)
+		&& (RAddSub == Rounded) && (FLOOR(RadixD2) == RadixD2)) {
+		printf("Checking for sticky bit.\n");
+		X = (Half + U1) * U2;
+		Y = Half * U2;
+		Z = One + Y;
+		T = One + X;
+		if ((Z - One <= Zero) && (T - One >= U2)) {
+			Z = T + Y;
+			Y = Z - X;
+			if ((Z - T >= U2) && (Y - T == Zero)) {
+				X = (Half + U1) * U1;
+				Y = Half * U1;
+				Z = One - Y;
+				T = One - X;
+				if ((Z - One == Zero) && (T - F9 == Zero)) {
+					Z = (Half - U1) * U1;
+					T = F9 - Z;
+					Q = F9 - Y;
+					if ((T - F9 == Zero) && (F9 - U1 - Q == Zero)) {
+						Z = (One + U2) * OneAndHalf;
+						T = (OneAndHalf + U2) - Z + U2;
+						X = One + Half / Radix;
+						Y = One + Radix * U2;
+						Z = X * Y;
+						if (T == Zero && X + Radix * U2 - Z == Zero) {
+							if (Radix != Two) {
+								X = Two + U2;
+								Y = X / Two;
+								if ((Y - One == Zero)) StickyBit = S;
+								}
+							else StickyBit = S;
+							}
+						}
+					}
+				}
+			}
+		}
+	if (StickyBit == One) printf("Sticky bit apparently used correctly.\n");
+	else printf("Sticky bit used incorrectly or not at all.\n");
+	TstCond (Flaw, !(GMult == No || GDiv == No || GAddSub == No ||
+			RMult == Other || RDiv == Other || RAddSub == Other),
+		"lack(s) of guard digits or failure(s) to correctly round or chop\n\
+(noted above) count as one flaw in the final tally below");
+	/*=============================================*/
+	Milestone = 60;
+	/*=============================================*/
+	printf("\n");
+	printf("Does Multiplication commute?  ");
+	printf("Testing on %d random pairs.\n", NoTrials);
+	Random9 = SQRT(3.0);
+	Random1 = Third;
+	I = 1;
+	do  {
+		X = Random();
+		Y = Random();
+		Z9 = Y * X;
+		Z = X * Y;
+		Z9 = Z - Z9;
+		I = I + 1;
+		} while ( ! ((I > NoTrials) || (Z9 != Zero)));
+	if (I == NoTrials) {
+		Random1 = One + Half / Three;
+		Random2 = (U2 + U1) + One;
+		Z = Random1 * Random2;
+		Y = Random2 * Random1;
+		Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
+			Three) * ((U2 + U1) + One);
+		}
+	if (! ((I == NoTrials) || (Z9 == Zero)))
+		BadCond(Defect, "X * Y == Y * X trial fails.\n");
+	else printf("     No failures found in %d integer pairs.\n", NoTrials);
+	/*=============================================*/
+	Milestone = 70;
+	/*=============================================*/
+	printf("\nRunning test of square root(x).\n");
+	TstCond (Failure, (Zero == SQRT(Zero))
+		   && (- Zero == SQRT(- Zero))
+		   && (One == SQRT(One)), "Square root of 0.0, -0.0 or 1.0 wrong");
+	MinSqEr = Zero;
+	MaxSqEr = Zero;
+	J = Zero;
+	X = Radix;
+	OneUlp = U2;
+	SqXMinX (Serious);
+	X = BInvrse;
+	OneUlp = BInvrse * U1;
+	SqXMinX (Serious);
+	X = U1;
+	OneUlp = U1 * U1;
+	SqXMinX (Serious);
+	if (J != Zero) Pause();
+	printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
+	J = Zero;
+	X = Two;
+	Y = Radix;
+	if ((Radix != One)) do  {
+		X = Y;
+		Y = Radix * Y;
+		} while ( ! ((Y - X >= NoTrials)));
+	OneUlp = X * U2;
+	I = 1;
+	while (I < 10) {
+		X = X + One;
+		SqXMinX (Defect);
+		if (J > Zero) break;
+		I = I + 1;
+		}
+	printf("Test for sqrt monotonicity.\n");
+	I = - 1;
+	X = BMinusU2;
+	Y = Radix;
+	Z = Radix + Radix * U2;
+	NotMonot = False;
+	Monot = False;
+	while ( ! (NotMonot || Monot)) {
+		I = I + 1;
+		X = SQRT(X);
+		Q = SQRT(Y);
+		Z = SQRT(Z);
+		if ((X > Q) || (Q > Z)) NotMonot = True;
+		else {
+			Q = FLOOR(Q + Half);
+			if ((I > 0) || (Radix == Q * Q)) Monot = True;
+			else if (I > 0) {
+			if (I > 1) Monot = True;
+			else {
+				Y = Y * BInvrse;
+				X = Y - U1;
+				Z = Y + U1;
+				}
+			}
+			else {
+				Y = Q;
+				X = Y - U2;
+				Z = Y + U2;
+				}
+			}
+		}
+	if (Monot) printf("sqrt has passed a test for Monotonicity.\n");
+	else {
+		BadCond(Defect, "");
+		printf("sqrt(X) is non-monotonic for X near %.7e .\n", Y);
+		}
+	/*=============================================*/
+	/*SPLIT
+	}
+#include "paranoia.h"
+part5(){
+*/
+	Milestone = 80;
+	/*=============================================*/
+	MinSqEr = MinSqEr + Half;
+	MaxSqEr = MaxSqEr - Half;
+	Y = (SQRT(One + U2) - One) / U2;
+	SqEr = (Y - One) + U2 / Eight;
+	if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+	SqEr = Y + U2 / Eight;
+	if (SqEr < MinSqEr) MinSqEr = SqEr;
+	Y = ((SQRT(F9) - U2) - (One - U2)) / U1;
+	SqEr = Y + U1 / Eight;
+	if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+	SqEr = (Y + One) + U1 / Eight;
+	if (SqEr < MinSqEr) MinSqEr = SqEr;
+	OneUlp = U2;
+	X = OneUlp;
+	for( Indx = 1; Indx <= 3; ++Indx) {
+		Y = SQRT((X + U1 + X) + F9);
+		Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;
+		Z = ((U1 - X) + F9) * Half * X * X / OneUlp;
+		SqEr = (Y + Half) + Z;
+		if (SqEr < MinSqEr) MinSqEr = SqEr;
+		SqEr = (Y - Half) + Z;
+		if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+		if (((Indx == 1) || (Indx == 3))) 
+			X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));
+		else {
+			OneUlp = U1;
+			X = - OneUlp;
+			}
+		}
+	/*=============================================*/
+	Milestone = 85;
+	/*=============================================*/
+	SqRWrng = False;
+	Anomaly = False;
+	if (Radix != One) {
+		printf("Testing whether sqrt is rounded or chopped.\n");
+		D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));
+	/* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
+		X = D / Radix;
+		Y = D / A1;
+		if ((X != FLOOR(X)) || (Y != FLOOR(Y))) {
+			Anomaly = True;
+			}
+		else {
+			X = Zero;
+			Z2 = X;
+			Y = One;
+			Y2 = Y;
+			Z1 = Radix - One;
+			FourD = Four * D;
+			do  {
+				if (Y2 > Z2) {
+					Q = Radix;
+					Y1 = Y;
+					do  {
+						X1 = FABS(Q + FLOOR(Half - Q / Y1) * Y1);
+						Q = Y1;
+						Y1 = X1;
+						} while ( ! (X1 <= Zero));
+					if (Q <= One) {
+						Z2 = Y2;
+						Z = Y;
+						}
+					}
+				Y = Y + Two;
+				X = X + Eight;
+				Y2 = Y2 + X;
+				if (Y2 >= FourD) Y2 = Y2 - FourD;
+				} while ( ! (Y >= D));
+			X8 = FourD - Z2;
+			Q = (X8 + Z * Z) / FourD;
+			X8 = X8 / Eight;
+			if (Q != FLOOR(Q)) Anomaly = True;
+			else {
+				Break = False;
+				do  {
+					X = Z1 * Z;
+					X = X - FLOOR(X / Radix) * Radix;
+					if (X == One) 
+						Break = True;
+					else
+						Z1 = Z1 - One;
+					} while ( ! (Break || (Z1 <= Zero)));
+				if ((Z1 <= Zero) && (! Break)) Anomaly = True;
+				else {
+					if (Z1 > RadixD2) Z1 = Z1 - Radix;
+					do  {
+						NewD();
+						} while ( ! (U2 * D >= F9));
+					if (D * Radix - D != W - D) Anomaly = True;
+					else {
+						Z2 = D;
+						I = 0;
+						Y = D + (One + Z) * Half;
+						X = D + Z + Q;
+						SR3750();
+						Y = D + (One - Z) * Half + D;
+						X = D - Z + D;
+						X = X + Q + X;
+						SR3750();
+						NewD();
+						if (D - Z2 != W - Z2) Anomaly = True;
+						else {
+							Y = (D - Z2) + (Z2 + (One - Z) * Half);
+							X = (D - Z2) + (Z2 - Z + Q);
+							SR3750();
+							Y = (One + Z) * Half;
+							X = Q;
+							SR3750();
+							if (I == 0) Anomaly = True;
+							}
+						}
+					}
+				}
+			}
+		if ((I == 0) || Anomaly) {
+			BadCond(Failure, "Anomalous arithmetic with Integer < ");
+			printf("Radix^Precision = %.7e\n", W);
+			printf(" fails test whether sqrt rounds or chops.\n");
+			SqRWrng = True;
+			}
+		}
+	if (! Anomaly) {
+		if (! ((MinSqEr < Zero) || (MaxSqEr > Zero))) {
+			RSqrt = Rounded;
+			printf("Square root appears to be correctly rounded.\n");
+			}
+		else  {
+			if ((MaxSqEr + U2 > U2 - Half) || (MinSqEr > Half)
+				|| (MinSqEr + Radix < Half)) SqRWrng = True;
+			else {
+				RSqrt = Chopped;
+				printf("Square root appears to be chopped.\n");
+				}
+			}
+		}
+	if (SqRWrng) {
+		printf("Square root is neither chopped nor correctly rounded.\n");
+		printf("Observed errors run from %.7e ", MinSqEr - Half);
+		printf("to %.7e ulps.\n", Half + MaxSqEr);
+		TstCond (Serious, MaxSqEr - MinSqEr < Radix * Radix,
+			"sqrt gets too many last digits wrong");
+		}
+	/*=============================================*/
+	Milestone = 90;
+	/*=============================================*/
+	Pause();
+	printf("Testing powers Z^i for small Integers Z and i.\n");
+	N = 0;
+	/* ... test powers of zero. */
+	I = 0;
+	Z = -Zero;
+	M = 3.0;
+	Break = False;
+	do  {
+		X = One;
+		SR3980();
+		if (I <= 10) {
+			I = 1023;
+			SR3980();
+			}
+		if (Z == MinusOne) Break = True;
+		else {
+			Z = MinusOne;
+			PrintIfNPositive();
+			N = 0;
+			/* .. if(-1)^N is invalid, replace MinusOne by One. */
+			I = - 4;
+			}
+		} while ( ! Break);
+	PrintIfNPositive();
+	N1 = N;
+	N = 0;
+	Z = A1;
+	M = FLOOR(Two * LOG(W) / LOG(A1));
+	Break = False;
+	do  {
+		X = Z;
+		I = 1;
+		SR3980();
+		if (Z == AInvrse) Break = True;
+		else Z = AInvrse;
+		} while ( ! (Break));
+	/*=============================================*/
+		Milestone = 100;
+	/*=============================================*/
+	/*  Powers of Radix have been tested, */
+	/*         next try a few primes     */
+	M = NoTrials;
+	Z = Three;
+	do  {
+		X = Z;
+		I = 1;
+		SR3980();
+		do  {
+			Z = Z + Two;
+			} while ( Three * FLOOR(Z / Three) == Z );
+		} while ( Z < Eight * Three );
+	if (N > 0) {
+		printf("Errors like this may invalidate financial calculations\n");
+		printf("\tinvolving interest rates.\n");
+		}
+	PrintIfNPositive();
+	N += N1;
+	if (N == 0) printf("... no discrepancis found.\n");
+	if (N > 0) Pause();
+	else printf("\n");
+	/*=============================================*/
+	/*SPLIT
+	}
+#include "paranoia.h"
+part6(){
+*/
+	Milestone = 110;
+	/*=============================================*/
+	printf("Seeking Underflow thresholds UfThold and E0.\n");
+	D = U1;
+	if (Precision != FLOOR(Precision)) {
+		D = BInvrse;
+		X = Precision;
+		do  {
+			D = D * BInvrse;
+			X = X - One;
+			} while ( X > Zero);
+		}
+	Y = One;
+	Z = D;
+	/* ... D is power of 1/Radix < 1. */
+	do  {
+		C = Y;
+		Y = Z;
+		Z = Y * Y;
+		VV = Z;
+		} while ((Y > Z) && (VV + VV > VV));
+	Y = C;
+	Z = Y * D;
+	do  {
+		C = Y;
+		Y = Z;
+		Z = Y * D;
+		VV = Z;
+		} while ((Y > Z) && (VV + VV > VV));
+	if (Radix < Two) HInvrse = Two;
+	else HInvrse = Radix;
+	H = One / HInvrse;
+	/* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
+	CInvrse = One / C;
+	E0 = C;
+	Z = E0 * H;
+	/* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
+	do  {
+		Y = E0;
+		E0 = Z;
+		Z = E0 * H;
+		VV = Z;
+		} while ((E0 > VV) && (VV + VV > VV));
+	UfThold = E0;
+	E1 = Zero;
+	Q = Zero;
+	E9 = U2;
+	S = One + E9;
+	D = C * S;
+	if (D <= C) {
+		E9 = Radix * U2;
+		S = One + E9;
+		D = C * S;
+		if (D <= C) {
+			BadCond(Failure, "multiplication gets too many last digits wrong.\n");
+			Underflow = E0;
+			Y1 = Zero;
+			PseudoZero = Z;
+			Pause();
+			}
+		}
+	else {
+		Underflow = D;
+		PseudoZero = Underflow * H;
+		UfThold = Zero;
+		do  {
+			Y1 = Underflow;
+			Underflow = PseudoZero;
+			if (E1 + E1 <= E1) {
+				Y2 = Underflow * HInvrse;
+				E1 = FABS(Y1 - Y2);
+				Q = Y1;
+				if ((UfThold == Zero) && (Y1 != Y2)) UfThold = Y1;
+				}
+			PseudoZero = PseudoZero * H;
+			VV = PseudoZero;
+			} while ((Underflow > VV)
+				&& (VV + VV > VV));
+		}
+	/* Comment line 4530 .. 4560 */
+	if (PseudoZero != Zero) {
+		printf("\n");
+		Z = PseudoZero;
+	/* ... Test PseudoZero for "phoney- zero" violates */
+	/* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
+		   ... */
+		if (PseudoZero <= Zero) {
+			BadCond(Failure, "Positive expressions can underflow to an\n");
+			printf("allegedly negative value\n");
+			printf("PseudoZero that prints out as: %g .\n", PseudoZero);
+			X = - PseudoZero;
+			if (X <= Zero) {
+				printf("But -PseudoZero, which should be\n");
+				printf("positive, isn't; it prints out as  %g .\n", X);
+				}
+			}
+		else {
+			BadCond(Flaw, "Underflow can stick at an allegedly positive\n");
+			printf("value PseudoZero that prints out as %g .\n", PseudoZero);
+			}
+		TstPtUf();
+		}
+	/*=============================================*/
+	Milestone = 120;
+	/*=============================================*/
+	if (CInvrse * Y > CInvrse * Y1) {
+		S = H * S;
+		E0 = Underflow;
+		}
+	if (! ((E1 == Zero) || (E1 == E0))) {
+		BadCond(Defect, "");
+		if (E1 < E0) {
+			printf("Products underflow at a higher");
+			printf(" threshold than differences.\n");
+			if (PseudoZero == Zero) 
+			E0 = E1;
+			}
+		else {
+			printf("Difference underflows at a higher");
+			printf(" threshold than products.\n");
+			}
+		}
+	printf("Smallest strictly positive number found is E0 = %g .\n", E0);
+	Z = E0;
+	TstPtUf();
+	Underflow = E0;
+	if (N == 1) Underflow = Y;
+	I = 4;
+	if (E1 == Zero) I = 3;
+	if (UfThold == Zero) I = I - 2;
+	UfNGrad = True;
+	switch (I)  {
+		case	1:
+		UfThold = Underflow;
+		if ((CInvrse * Q) != ((CInvrse * Y) * S)) {
+			UfThold = Y;
+			BadCond(Failure, "Either accuracy deteriorates as numbers\n");
+			printf("approach a threshold = %.17e\n", UfThold);;
+			printf(" coming down from %.17e\n", C);
+			printf(" or else multiplication gets too many last digits wrong.\n");
+			}
+		Pause();
+		break;
+	
+		case	2:
+		BadCond(Failure, "Underflow confuses Comparison which alleges that\n");
+		printf("Q == Y while denying that |Q - Y| == 0; these values\n");
+		printf("print out as Q = %.17e, Y = %.17e .\n", Q, Y);
+		printf ("|Q - Y| = %.17e .\n" , FABS(Q - Y2));
+		UfThold = Q;
+		break;
+	
+		case	3:
+		X = X;
+		break;
+	
+		case	4:
+		if ((Q == UfThold) && (E1 == E0)
+			&& (FABS( UfThold - E1 / E9) <= E1)) {
+			UfNGrad = False;
+			printf("Underflow is gradual; it incurs Absolute Error =\n");
+			printf("(roundoff in UfThold) < E0.\n");
+			Y = E0 * CInvrse;
+			Y = Y * (OneAndHalf + U2);
+			X = CInvrse * (One + U2);
+			Y = Y / X;
+			IEEE = (Y == E0);
+			}
+		}
+	if (UfNGrad) {
+		printf("\n");
+		R = SQRT(Underflow / UfThold);
+		if (R <= H) {
+			Z = R * UfThold;
+			X = Z * (One + R * H * (One + H));
+			}
+		else {
+			Z = UfThold;
+			X = Z * (One + H * H * (One + H));
+			}
+		if (! ((X == Z) || (X - Z != Zero))) {
+			BadCond(Flaw, "");
+			printf("X = %.17e\n\tis not equal to Z = %.17e .\n", X, Z);
+			Z9 = X - Z;
+			printf("yet X - Z yields %.17e .\n", Z9);
+			printf("    Should this NOT signal Underflow, ");
+			printf("this is a SERIOUS DEFECT\nthat causes ");
+			printf("confusion when innocent statements like\n");;
+			printf("    if (X == Z)  ...  else");
+			printf("  ... (f(X) - f(Z)) / (X - Z) ...\n");
+			printf("encounter Division by Zero although actually\n");
+			printf("X / Z = 1 + %g .\n", (X / Z - Half) - Half);
+			}
+		}
+	printf("The Underflow threshold is %.17e, %s\n", UfThold,
+		   " below which");
+	printf("calculation may suffer larger Relative error than ");
+	printf("merely roundoff.\n");
+	Y2 = U1 * U1;
+	Y = Y2 * Y2;
+	Y2 = Y * U1;
+	if (Y2 <= UfThold) {
+		if (Y > E0) {
+			BadCond(Defect, "");
+			I = 5;
+			}
+		else {
+			BadCond(Serious, "");
+			I = 4;
+			}
+		printf("Range is too narrow; U1^%d Underflows.\n", I);
+		}
+	/*=============================================*/
+	/*SPLIT
+	}
+#include "paranoia.h"
+part7(){
+*/
+	Milestone = 130;
+	/*=============================================*/
+	Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;
+	Y2 = Y + Y;
+	printf("Since underflow occurs below the threshold\n");
+	printf("UfThold = (%.17e) ^ (%.17e)\nonly underflow ", HInvrse, Y);
+	printf("should afflict the expression\n\t(%.17e) ^ (%.17e);\n", HInvrse, Y);
+	V9 = POW(HInvrse, Y2);
+	printf("actually calculating yields: %.17e .\n", V9);
+	if (! ((V9 >= Zero) && (V9 <= (Radix + Radix + E9) * UfThold))) {
+		BadCond(Serious, "this is not between 0 and underflow\n");
+		printf("   threshold = %.17e .\n", UfThold);
+		}
+	else if (! (V9 > UfThold * (One + E9)))
+		printf("This computed value is O.K.\n");
+	else {
+		BadCond(Defect, "this is not between 0 and underflow\n");
+		printf("   threshold = %.17e .\n", UfThold);
+		}
+	/*=============================================*/
+	Milestone = 140;
+	/*=============================================*/
+	printf("\n");
+	/* ...calculate Exp2 == exp(2) == 7.389056099... */
+	X = Zero;
+	I = 2;
+	Y = Two * Three;
+	Q = Zero;
+	N = 0;
+	do  {
+		Z = X;
+		I = I + 1;
+		Y = Y / (I + I);
+		R = Y + Q;
+		X = Z + R;
+		Q = (Z - X) + R;
+		} while(X > Z);
+	Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);
+	X = Z * Z;
+	Exp2 = X * X;
+	X = F9;
+	Y = X - U1;
+	printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = %.17e as X -> 1.\n",
+		Exp2);
+	for(I = 1;;) {
+		Z = X - BInvrse;
+		Z = (X + One) / (Z - (One - BInvrse));
+		Q = POW(X, Z) - Exp2;
+		if (FABS(Q) > TwoForty * U2) {
+			N = 1;
+	 		V9 = (X - BInvrse) - (One - BInvrse);
+			BadCond(Defect, "Calculated");
+			printf(" %.17e for\n", POW(X,Z));
+			printf("\t(1 + (%.17e) ^ (%.17e);\n", V9, Z);
+			printf("\tdiffers from correct value by %.17e .\n", Q);
+			printf("\tThis much error may spoil financial\n");
+			printf("\tcalculations involving tiny interest rates.\n");
+			break;
+			}
+		else {
+			Z = (Y - X) * Two + Y;
+			X = Y;
+			Y = Z;
+			Z = One + (X - F9)*(X - F9);
+			if (Z > One && I < NoTrials) I++;
+			else  {
+				if (X > One) {
+					if (N == 0)
+					   printf("Accuracy seems adequate.\n");
+					break;
+					}
+				else {
+					X = One + U2;
+					Y = U2 + U2;
+					Y += X;
+					I = 1;
+					}
+				}
+			}
+		}
+	/*=============================================*/
+	Milestone = 150;
+	/*=============================================*/
+	printf("Testing powers Z^Q at four nearly extreme values.\n");
+	N = 0;
+	Z = A1;
+	Q = FLOOR(Half - LOG(C) / LOG(A1));
+	Break = False;
+	do  {
+		X = CInvrse;
+		Y = POW(Z, Q);
+		IsYeqX();
+		Q = - Q;
+		X = C;
+		Y = POW(Z, Q);
+		IsYeqX();
+		if (Z < One) Break = True;
+		else Z = AInvrse;
+		} while ( ! (Break));
+	PrintIfNPositive();
+	if (N == 0) printf(" ... no discrepancies found.\n");
+	printf("\n");
+	
+	/*=============================================*/
+	Milestone = 160;
+	/*=============================================*/
+	Pause();
+	printf("Searching for Overflow threshold:\n");
+	printf("This may generate an error.\n");
+	sigsave = sigfpe;
+	I = 0;
+	Y = - CInvrse;
+	V9 = HInvrse * Y;
+	if (setjmp(ovfl_buf)) goto overflow;
+	do {
+		V = Y;
+		Y = V9;
+		V9 = HInvrse * Y;
+		} while(V9 < Y);
+	I = 1;
+overflow:
+	Z = V9;
+	printf("Can `Z = -Y' overflow?\n");
+	printf("Trying it on Y = %.17e .\n", Y);
+	V9 = - Y;
+	V0 = V9;
+	if (V - Y == V + V0) printf("Seems O.K.\n");
+	else {
+		printf("finds a ");
+		BadCond(Flaw, "-(-Y) differs from Y.\n");
+		}
+	if (Z != Y) {
+		BadCond(Serious, "");
+		printf("overflow past %.17e\n\tshrinks to %.17e .\n", Y, Z);
+		}
+	Y = V * (HInvrse * U2 - HInvrse);
+	Z = Y + ((One - HInvrse) * U2) * V;
+	if (Z < V0) Y = Z;
+	if (Y < V0) V = Y;
+	if (V0 - V < V0) V = V0;
+	printf("Overflow threshold is V  = %.17e .\n", V);
+	if (I) printf("Overflow saturates at V0 = %.17e .\n", V0);
+	else printf("There is no saturation value because \
+the system traps on overflow.\n");
+	V9 = V * One;
+	printf("No Overflow should be signaled for V * 1 = %.17e\n", V9);
+	V9 = V / One;
+	printf("                           nor for V / 1 = %.17e .\n", V9);
+	printf("Any overflow signal separating this * from the one\n");
+	printf("above is a DEFECT.\n");
+	/*=============================================*/
+	Milestone = 170;
+	/*=============================================*/
+	if (!(-V < V && -V0 < V0 && -UfThold < V && UfThold < V)) {
+		BadCond(Failure, "Comparisons involving ");
+		printf("+-%g, +-%g\nand +-%g are confused by Overflow.",
+			V, V0, UfThold);
+		}
+	/*=============================================*/
+	Milestone = 175;
+	/*=============================================*/
+	printf("\n");
+	for(Indx = 1; Indx <= 3; ++Indx) {
+		switch (Indx)  {
+			case 1: Z = UfThold; break;
+			case 2: Z = E0; break;
+			case 3: Z = PseudoZero; break;
+			}
+		if (Z != Zero) {
+			V9 = SQRT(Z);
+			Y = V9 * V9;
+			if (Y / (One - Radix * E9) < Z
+			   || Y > (One + Radix + E9) * Z) {
+				if (V9 > U1) BadCond(Serious, "");
+				else BadCond(Defect, "");
+				printf("Comparison alleges that what prints as Z = %.17e\n", Z);
+				printf(" is too far from sqrt(Z) ^ 2 = %.17e .\n", Y);
+				}
+			}
+		}
+	/*=============================================*/
+	Milestone = 180;
+	/*=============================================*/
+	for(Indx = 1; Indx <= 2; ++Indx) {
+		if (Indx == 1) Z = V;
+		else Z = V0;
+		V9 = SQRT(Z);
+		X = (One - Radix * E9) * V9;
+		V9 = V9 * X;
+		if (((V9 < (One - Two * Radix * E9) * Z) || (V9 > Z))) {
+			Y = V9;
+			if (X < W) BadCond(Serious, "");
+			else BadCond(Defect, "");
+			printf("Comparison alleges that Z = %17e\n", Z);
+			printf(" is too far from sqrt(Z) ^ 2 (%.17e) .\n", Y);
+			}
+		}
+	/*=============================================*/
+	/*SPLIT
+	}
+#include "paranoia.h"
+part8(){
+*/
+	Milestone = 190;
+	/*=============================================*/
+	Pause();
+	X = UfThold * V;
+	Y = Radix * Radix;
+	if (X*Y < One || X > Y) {
+		if (X * Y < U1 || X > Y/U1) BadCond(Defect, "Badly");
+		else BadCond(Flaw, "");
+			
+		printf(" unbalanced range; UfThold * V = %.17e\n\t%s\n",
+			X, "is too far from 1.\n");
+		}
+	/*=============================================*/
+	Milestone = 200;
+	/*=============================================*/
+	for (Indx = 1; Indx <= 5; ++Indx)  {
+		X = F9;
+		switch (Indx)  {
+			case 2: X = One + U2; break;
+			case 3: X = V; break;
+			case 4: X = UfThold; break;
+			case 5: X = Radix;
+			}
+		Y = X;
+		sigsave = sigfpe;
+		if (setjmp(ovfl_buf))
+			printf("  X / X  traps when X = %g\n", X);
+		else {
+			V9 = (Y / X - Half) - Half;
+			if (V9 == Zero) continue;
+			if (V9 == - U1 && Indx < 5) BadCond(Flaw, "");
+			else BadCond(Serious, "");
+			printf("  X / X differs from 1 when X = %.17e\n", X);
+			printf("  instead, X / X - 1/2 - 1/2 = %.17e .\n", V9);
+			}
+		}
+	/*=============================================*/
+	Milestone = 210;
+	/*=============================================*/
+	MyZero = Zero;
+	printf("\n");
+	printf("What message and/or values does Division by Zero produce?\n") ;
+#ifndef NOPAUSE
+	printf("This can interupt your program.  You can ");
+	printf("skip this part if you wish.\n");
+	printf("Do you wish to compute 1 / 0? ");
+	fflush(stdout);
+	read (KEYBOARD, ch, 8);
+	if ((ch[0] == 'Y') || (ch[0] == 'y')) {
+#endif
+		sigsave = sigfpe;
+		printf("    Trying to compute 1 / 0 produces ...");
+		if (!setjmp(ovfl_buf)) printf("  %.7e .\n", One / MyZero);
+#ifndef NOPAUSE
+		}
+	else printf("O.K.\n");
+	printf("\nDo you wish to compute 0 / 0? ");
+	fflush(stdout);
+	read (KEYBOARD, ch, 80);
+	if ((ch[0] == 'Y') || (ch[0] == 'y')) {
+#endif
+		sigsave = sigfpe;
+		printf("\n    Trying to compute 0 / 0 produces ...");
+		if (!setjmp(ovfl_buf)) printf("  %.7e .\n", Zero / MyZero);
+#ifndef NOPAUSE
+		}
+	else printf("O.K.\n");
+#endif
+	/*=============================================*/
+	Milestone = 220;
+	/*=============================================*/
+	Pause();
+	printf("\n");
+	{
+		static char *msg[] = {
+			"FAILUREs  encountered =",
+			"SERIOUS DEFECTs  discovered =",
+			"DEFECTs  discovered =",
+			"FLAWs  discovered =" };
+		int i;
+		for(i = 0; i < 4; i++) if (ErrCnt[i])
+			printf("The number of  %-29s %d.\n",
+				msg[i], ErrCnt[i]);
+		}
+	printf("\n");
+	if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect]
+			+ ErrCnt[Flaw]) > 0) {
+		if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[
+			Defect] == 0) && (ErrCnt[Flaw] > 0)) {
+			printf("The arithmetic diagnosed seems ");
+			printf("satisfactory though flawed.\n");
+			}
+		if ((ErrCnt[Failure] + ErrCnt[Serious] == 0)
+			&& ( ErrCnt[Defect] > 0)) {
+			printf("The arithmetic diagnosed may be acceptable\n");
+			printf("despite inconvenient Defects.\n");
+			}
+		if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) {
+			printf("The arithmetic diagnosed has ");
+			printf("unacceptable serious defects.\n");
+			}
+		if (ErrCnt[Failure] > 0) {
+			printf("Fatal FAILURE may have spoiled this");
+			printf(" program's subsequent diagnoses.\n");
+			}
+		}
+	else {
+		printf("No failures, defects nor flaws have been discovered.\n");
+		if (! ((RMult == Rounded) && (RDiv == Rounded)
+			&& (RAddSub == Rounded) && (RSqrt == Rounded))) 
+			printf("The arithmetic diagnosed seems satisfactory.\n");
+		else {
+			if (StickyBit >= One &&
+				(Radix - Two) * (Radix - Nine - One) == Zero) {
+				printf("Rounding appears to conform to ");
+				printf("the proposed IEEE standard P");
+				if ((Radix == Two) &&
+					 ((Precision - Four * Three * Two) *
+					  ( Precision - TwentySeven -
+					   TwentySeven + One) == Zero)) 
+					printf("754");
+				else printf("854");
+				if (IEEE) printf(".\n");
+				else {
+					printf(",\nexcept for possibly Double Rounding");
+					printf(" during Gradual Underflow.\n");
+					}
+				}
+			printf("The arithmetic diagnosed appears to be excellent!\n");
+			}
+		}
+	if (fpecount)
+		printf("\nA total of %d floating point exceptions were registered.\n",
+			fpecount);
+	printf("END OF TEST.\n");
+	}
+
+/*SPLIT subs.c
+#include "paranoia.h"
+*/
+
+/* Sign */
+
+FLOAT Sign (X)
+FLOAT X;
+{ return X >= 0. ? 1.0 : -1.0; }
+
+/* Pause */
+
+Pause()
+{
+	char ch[8];
+	
+#ifndef NOPAUSE
+	printf("\nTo continue, press RETURN");
+	fflush(stdout);
+	read(KEYBOARD, ch, 8);
+#endif
+	printf("\nDiagnosis resumes after milestone Number %d", Milestone);
+	printf("          Page: %d\n\n", PageNo);
+	++Milestone;
+	++PageNo;
+	}
+
+ /* TstCond */
+
+TstCond (K, Valid, T)
+int K, Valid;
+char *T;
+{ if (! Valid) { BadCond(K,T); printf(".\n"); } }
+
+BadCond(K, T)
+int K;
+char *T;
+{
+	static char *msg[] = { "FAILURE", "SERIOUS DEFECT", "DEFECT", "FLAW" };
+
+	ErrCnt [K] = ErrCnt [K] + 1;
+	printf("%s:  %s", msg[K], T);
+	}
+
+/* Random */
+/*  Random computes
+     X = (Random1 + Random9)^5
+     Random1 = X - FLOOR(X) + 0.000005 * X;
+   and returns the new value of Random1
+*/
+
+FLOAT Random()
+{
+	FLOAT X, Y;
+	
+	X = Random1 + Random9;
+	Y = X * X;
+	Y = Y * Y;
+	X = X * Y;
+	Y = X - FLOOR(X);
+	Random1 = Y + X * 0.000005;
+	return(Random1);
+	}
+
+/* SqXMinX */
+
+SqXMinX (ErrKind)
+int ErrKind;
+{
+	FLOAT XA, XB;
+	
+	XB = X * BInvrse;
+	XA = X - XB;
+	SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;
+	if (SqEr != Zero) {
+		if (SqEr < MinSqEr) MinSqEr = SqEr;
+		if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+		J = J + 1.0;
+		BadCond(ErrKind, "\n");
+		printf("sqrt( %.17e) - %.17e  = %.17e\n", X * X, X, OneUlp * SqEr);
+		printf("\tinstead of correct value 0 .\n");
+		}
+	}
+
+/* NewD */
+
+NewD()
+{
+	X = Z1 * Q;
+	X = FLOOR(Half - X / Radix) * Radix + X;
+	Q = (Q - X * Z) / Radix + X * X * (D / Radix);
+	Z = Z - Two * X * D;
+	if (Z <= Zero) {
+		Z = - Z;
+		Z1 = - Z1;
+		}
+	D = Radix * D;
+	}
+
+/* SR3750 */
+
+SR3750()
+{
+	if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {
+		I = I + 1;
+		X2 = SQRT(X * D);
+		Y2 = (X2 - Z2) - (Y - Z2);
+		X2 = X8 / (Y - Half);
+		X2 = X2 - Half * X2 * X2;
+		SqEr = (Y2 + Half) + (Half - X2);
+		if (SqEr < MinSqEr) MinSqEr = SqEr;
+		SqEr = Y2 - X2;
+		if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+		}
+	}
+
+/* IsYeqX */
+
+IsYeqX()
+{
+	if (Y != X) {
+		if (N <= 0) {
+			if (Z == Zero && Q <= Zero)
+				printf("WARNING:  computing\n");
+			else BadCond(Defect, "computing\n");
+			printf("\t(%.17e) ^ (%.17e)\n", Z, Q);
+			printf("\tyielded %.17e;\n", Y);
+			printf("\twhich compared unequal to correct %.17e ;\n",
+				X);
+			printf("\t\tthey differ by %.17e .\n", Y - X);
+			}
+		N = N + 1; /* ... count discrepancies. */
+		}
+	}
+
+/* SR3980 */
+
+SR3980()
+{
+	do {
+		Q = (FLOAT) I;
+		Y = POW(Z, Q);
+		IsYeqX();
+		if (++I > M) break;
+		X = Z * X;
+		} while ( X < W );
+	}
+
+/* PrintIfNPositive */
+
+PrintIfNPositive()
+{
+	if (N > 0) printf("Similar discrepancies have occurred %d times.\n", N);
+	}
+
+/* TstPtUf */
+
+TstPtUf()
+{
+	N = 0;
+	if (Z != Zero) {
+		printf("Since comparison denies Z = 0, evaluating ");
+		printf("(Z + Z) / Z should be safe.\n");
+		sigsave = sigfpe;
+		if (setjmp(ovfl_buf)) goto very_serious;
+		Q9 = (Z + Z) / Z;
+		printf("What the machine gets for (Z + Z) / Z is  %.17e .\n",
+			Q9);
+		if (FABS(Q9 - Two) < Radix * U2) {
+			printf("This is O.K., provided Over/Underflow");
+			printf(" has NOT just been signaled.\n");
+			}
+		else {
+			if ((Q9 < One) || (Q9 > Two)) {
+very_serious:
+				N = 1;
+				ErrCnt [Serious] = ErrCnt [Serious] + 1;
+				printf("This is a VERY SERIOUS DEFECT!\n");
+				}
+			else {
+				N = 1;
+				ErrCnt [Defect] = ErrCnt [Defect] + 1;
+				printf("This is a DEFECT!\n");
+				}
+			}
+		V9 = Z * One;
+		Random1 = V9;
+		V9 = One * Z;
+		Random2 = V9;
+		V9 = Z / One;
+		if ((Z == Random1) && (Z == Random2) && (Z == V9)) {
+			if (N > 0) Pause();
+			}
+		else {
+			N = 1;
+			BadCond(Defect, "What prints as Z = ");
+			printf("%.17e\n\tcompares different from  ", Z);
+			if (Z != Random1) printf("Z * 1 = %.17e ", Random1);
+			if (! ((Z == Random2)
+				|| (Random2 == Random1)))
+				printf("1 * Z == %g\n", Random2);
+			if (! (Z == V9)) printf("Z / 1 = %.17e\n", V9);
+			if (Random2 != Random1) {
+				ErrCnt [Defect] = ErrCnt [Defect] + 1;
+				BadCond(Defect, "Multiplication does not commute!\n");
+				printf("\tComparison alleges that 1 * Z = %.17e\n",
+					Random2);
+				printf("\tdiffers from Z * 1 = %.17e\n", Random1);
+				}
+			Pause();
+			}
+		}
+	}
+
+notify(s)
+char *s;
+{
+	printf("%s test appears to be inconsistent...\n", s);
+	printf("   PLEASE NOTIFY KARPINKSI!\n");
+	}
+
+/*SPLIT msgs.c */
+
+/* Instructions */
+
+msglist(s)
+char **s;
+{ while(*s) printf("%s\n", *s++); }
+
+Instructions()
+{
+  static char *instr[] = {
+	"Lest this program stop prematurely, i.e. before displaying\n",
+	"    `END OF TEST',\n",
+	"try to persuade the computer NOT to terminate execution when an",
+	"error like Over/Underflow or Division by Zero occurs, but rather",
+	"to persevere with a surrogate value after, perhaps, displaying some",
+	"warning.  If persuasion avails naught, don't despair but run this",
+	"program anyway to see how many milestones it passes, and then",
+	"amend it to make further progress.\n",
+	"Answer questions with Y, y, N or n (unless otherwise indicated).\n",
+	0};
+
+	msglist(instr);
+	}
+
+/* Heading */
+
+Heading()
+{
+  static char *head[] = {
+	"Users are invited to help debug and augment this program so it will",
+	"cope with unanticipated and newly uncovered arithmetic pathologies.\n",
+	"Please send suggestions and interesting results to",
+	"\tRichard Karpinski",
+	"\tComputer Center U-76",
+	"\tUniversity of California",
+	"\tSan Francisco, CA 94143-0704, USA\n",
+	"In doing so, please include the following information:",
+#ifdef Single
+	"\tPrecision:\tsingle;",
+#else
+	"\tPrecision:\tdouble;",
+#endif
+	"\tVersion:\t27 January 1986;",
+	"\tComputer:\n",
+	"\tCompiler:\n",
+	"\tOptimization level:\n",
+	"\tOther relevant compiler options:",
+	0};
+
+	msglist(head);
+	}
+
+/* Characteristics */
+
+Characteristics()
+{
+	static char *chars[] = {
+	 "Running this program should reveal these characteristics:",
+	"     Radix = 1, 2, 4, 8, 10, 16, 100, 256 ...",
+	"     Precision = number of significant digits carried.",
+	"     U2 = Radix/Radix^Precision = One Ulp",
+	"\t(OneUlpnit in the Last Place) of 1.000xxx .",
+	"     U1 = 1/Radix^Precision = One Ulp of numbers a little less than 1.0 .",
+	"     Adequacy of guard digits for Mult., Div. and Subt.",
+	"     Whether arithmetic is chopped, correctly rounded, or something else",
+	"\tfor Mult., Div., Add/Subt. and Sqrt.",
+	"     Whether a Sticky Bit used correctly for rounding.",
+	"     UnderflowThreshold = an underflow threshold.",
+	"     E0 and PseudoZero tell whether underflow is abrupt, gradual, or fuzzy.",
+	"     V = an overflow threshold, roughly.",
+	"     V0  tells, roughly, whether  Infinity  is represented.",
+	"     Comparisions are checked for consistency with subtraction",
+	"\tand for contamination with pseudo-zeros.",
+	"     Sqrt is tested.  Y^X is not tested.",
+	"     Extra-precise subexpressions are revealed but NOT YET tested.",
+	"     Decimal-Binary conversion is NOT YET tested for accuracy.",
+	0};
+
+	msglist(chars);
+	}
+
+History()
+
+{ /* History */
+ /* Converted from Brian Wichmann's Pascal version to C by Thos Sumner,
+	with further massaging by David M. Gay. */
+
+  static char *hist[] = {
+	"The program attempts to discriminate among",
+	"   FLAWs, like lack of a sticky bit,",
+	"   Serious DEFECTs, like lack of a guard digit, and",
+	"   FAILUREs, like 2+2 == 5 .",
+	"Failures may confound subsequent diagnoses.\n",
+	"The diagnostic capabilities of this program go beyond an earlier",
+	"program called `MACHAR', which can be found at the end of the",
+	"book  `Software Manual for the Elementary Functions' (1980) by",
+	"W. J. Cody and W. Waite. Although both programs try to discover",
+	"the Radix, Precision and range (over/underflow thresholds)",
+	"of the arithmetic, this program tries to cope with a wider variety",
+	"of pathologies, and to say how well the arithmetic is implemented.",
+	"\nThe program is based upon a conventional radix representation for",
+	"floating-point numbers, but also allows logarithmic encoding",
+	"as used by certain early WANG machines.\n",
+	"BASIC version of this program (C) 1983 by Prof. W. M. Kahan;",
+	"see source comments for more history.",
+	0};
+
+	msglist(hist);
+	}

libm/double/pdtr.c

@@ -0,0 +1,184 @@
+/*							pdtr.c
+ *
+ *	Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtr();
+ *
+ * y = pdtr( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the first k terms of the Poisson
+ * distribution:
+ *
+ *   k         j
+ *   --   -m  m
+ *   >   e    --
+ *   --       j!
+ *  j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the relation
+ *
+ * y = pdtr( k, m ) = igamc( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ */
+/*							pdtrc()
+ *
+ *	Complemented poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtrc();
+ *
+ * y = pdtrc( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the Poisson
+ * distribution:
+ *
+ *  inf.       j
+ *   --   -m  m
+ *   >   e    --
+ *   --       j!
+ *  j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the formula
+ *
+ * y = pdtrc( k, m ) = igam( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam.c.
+ *
+ */
+/*							pdtri()
+ *
+ *	Inverse Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtr();
+ *
+ * m = pdtri( k, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Poisson variable x such that the integral
+ * from 0 to x of the Poisson density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ *    m = igami( k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * pdtri domain    y < 0 or y >= 1       0.0
+ *                     k < 0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double igam ( double, double );
+extern double igamc ( double, double );
+extern double igami ( double, double );
+#else
+double igam(), igamc(), igami();
+#endif
+
+double pdtrc( k, m )
+int k;
+double m;
+{
+double v;
+
+if( (k < 0) || (m <= 0.0) )
+	{
+	mtherr( "pdtrc", DOMAIN );
+	return( 0.0 );
+	}
+v = k+1;
+return( igam( v, m ) );
+}
+
+
+
+double pdtr( k, m )
+int k;
+double m;
+{
+double v;
+
+if( (k < 0) || (m <= 0.0) )
+	{
+	mtherr( "pdtr", DOMAIN );
+	return( 0.0 );
+	}
+v = k+1;
+return( igamc( v, m ) );
+}
+
+
+double pdtri( k, y )
+int k;
+double y;
+{
+double v;
+
+if( (k < 0) || (y < 0.0) || (y >= 1.0) )
+	{
+	mtherr( "pdtri", DOMAIN );
+	return( 0.0 );
+	}
+v = k+1;
+v = igami( v, y );
+return( v );
+}

libm/double/planck.c

@@ -0,0 +1,223 @@
+/*							planck.c
+ *
+ *	Integral of Planck's black body radiation formula
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double lambda, T, y, plancki();
+ *
+ * y = plancki( lambda, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *  Evaluates the definite integral, from wavelength 0 to lambda,
+ *  of Planck's radiation formula
+ *                      -5
+ *            c1  lambda
+ *     E =  ------------------
+ *            c2/(lambda T)
+ *           e             - 1
+ *
+ * Physical constants c1 = 3.7417749e-16 and c2 = 0.01438769 are built in
+ * to the function program.  They are scaled to provide a result
+ * in watts per square meter.  Argument T represents temperature in degrees
+ * Kelvin; lambda is wavelength in meters.
+ *
+ * The integral is expressed in closed form, in terms of polylogarithms
+ * (see polylog.c).
+ *
+ * The total area under the curve is
+ *      (-1/8) (42 zeta(4) - 12 pi^2 zeta(2) + pi^4 ) c1 (T/c2)^4
+ *       = (pi^4 / 15)  c1 (T/c2)^4
+ *       =  5.6705032e-8 T^4
+ * where sigma = 5.6705032e-8 W m^2 K^-4 is the Stefan-Boltzmann constant.
+ *
+ *
+ * ACCURACY:
+ *
+ * The left tail of the function experiences some relative error
+ * amplification in computing the dominant term exp(-c2/(lambda T)).
+ * For the right-hand tail see planckc, below.
+ *
+ *                      Relative error.
+ *   The domain refers to lambda T / c2.
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.1, 10      50000      7.1e-15     5.4e-16
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  July, 1999
+Copyright 1999 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double polylog (int, double);
+extern double exp (double);
+extern double log1p (double); /* log(1+x) */
+extern double expm1 (double); /* exp(x) - 1 */
+double planckc(double, double);
+double plancki(double, double);
+#else
+double polylog(), exp(), log1p(), expm1();
+double planckc(), plancki();
+#endif
+
+/*  NIST value (1999): 2 pi h c^2 = 3.741 7749(22) �× 10-16 W m2  */
+double planck_c1 = 3.7417749e-16;
+/*  NIST value (1999):  h c / k  = 0.014 387 69 m K */
+double planck_c2 = 0.01438769;
+
+
+double
+plancki(w, T)
+  double w, T;
+{
+  double b, h, y, bw;
+
+  b = T / planck_c2;
+  bw = b * w;
+
+  if (bw > 0.59375)
+    {
+      y = b * b;
+      h = y * y;
+      /* Right tail.  */
+      y = planckc (w, T);
+      /* pi^4 / 15  */
+      y =  6.493939402266829149096 * planck_c1 * h  -  y;
+      return y;
+    }
+
+  h = exp(-planck_c2/(w*T));
+  y =      6. * polylog (4, h)  * bw;
+  y = (y + 6. * polylog (3, h)) * bw;
+  y = (y + 3. * polylog (2, h)) * bw;
+  y = (y          - log1p (-h)) * bw;
+  h = w * w;
+  h = h * h;
+  y = y * (planck_c1 / h);
+  return y;
+}
+
+/*							planckc
+ *
+ *	Complemented Planck radiation integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double lambda, T, y, planckc();
+ *
+ * y = planckc( lambda, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *  Integral from w to infinity (area under right hand tail)
+ *  of Planck's radiation formula.
+ *
+ *  The program for large lambda uses an asymptotic series in inverse
+ *  powers of the wavelength.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error.
+ *   The domain refers to lambda T / c2.
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.6, 10      50000      1.1e-15     2.2e-16
+ *
+ */
+
+double
+planckc (w, T)
+     double w;
+     double T;
+{
+  double b, d, p, u, y;
+
+  b = T / planck_c2;
+  d = b*w;
+  if (d <= 0.59375)
+    {
+      y =  6.493939402266829149096 * planck_c1 * b*b*b*b;
+      return (y - plancki(w,T));
+    }
+  u = 1.0/d;
+  p = u * u;
+#if 0
+  y = 236364091.*p/365866013534056632601804800000.;
+  y = (y - 15458917./475677107995483570176000000.)*p;
+  y = (y + 174611./123104841613737984000000.)*p;
+  y = (y - 43867./643745871363538944000.)*p;
+  y = ((y + 3617./1081289781411840000.)*p - 1./5928123801600.)*p;
+  y = ((y + 691./78460462080000.)*p - 1./2075673600.)*p;
+  y = ((((y + 1./35481600.)*p - 1.0/544320.)*p + 1.0/6720.)*p -  1./40.)*p;
+  y = y + log(d * expm1(u));
+  y = y - 5.*u/8. + 1./3.;
+#else
+  y = -236364091.*p/45733251691757079075225600000.;
+  y = (y + 77683./352527500984795136000000.)*p;
+  y = (y - 174611./18465726242060697600000.)*p;
+  y = (y + 43867./107290978560589824000.)*p;
+  y = ((y - 3617./202741834014720000.)*p + 1./1270312243200.)*p;
+  y = ((y - 691./19615115520000.)*p + 1./622702080.)*p;
+  y = ((((y - 1./13305600.)*p + 1./272160.)*p - 1./5040.)*p + 1./60.)*p;
+  y = y - 0.125*u + 1./3.;
+#endif
+  y = y * planck_c1 * b / (w*w*w);
+  return y;
+}
+
+
+/*							planckd
+ *
+ *	Planck's black body radiation formula
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double lambda, T, y, planckd();
+ *
+ * y = planckd( lambda, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *  Evaluates Planck's radiation formula
+ *                      -5
+ *            c1  lambda
+ *     E =  ------------------
+ *            c2/(lambda T)
+ *           e             - 1
+ *
+ */
+
+double
+planckd(w, T)
+  double w, T;
+{
+   return (planck_c2 / ((w*w*w*w*w) * (exp(planck_c2/(w*T)) - 1.0)));
+}
+
+
+/* Wavelength, w, of maximum radiation at given temperature T.
+   c2/wT = constant
+   Wein displacement law.
+  */
+double
+planckw(T)
+  double T;
+{
+  return (planck_c2 / (4.96511423174427630 * T));
+}

libm/double/polevl.c

@@ -0,0 +1,97 @@
+/*							polevl.c
+ *							p1evl.c
+ *
+ *	Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * double x, y, coef[N+1], polevl[];
+ *
+ * y = polevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ *                     2          N
+ * y  =  C  + C x + C x  +...+ C x
+ *        0    1     2          N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C  , ..., coef[N] = C  .
+ *            N                   0
+ *
+ *  The function p1evl() assumes that coef[N] = 1.0 and is
+ * omitted from the array.  Its calling arguments are
+ * otherwise the same as polevl().
+ *
+ *
+ * SPEED:
+ *
+ * In the interest of speed, there are no checks for out
+ * of bounds arithmetic.  This routine is used by most of
+ * the functions in the library.  Depending on available
+ * equipment features, the user may wish to rewrite the
+ * program in microcode or assembly language.
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.1:  December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+double polevl( x, coef, N )
+double x;
+double coef[];
+int N;
+{
+double ans;
+int i;
+double *p;
+
+p = coef;
+ans = *p++;
+i = N;
+
+do
+	ans = ans * x  +  *p++;
+while( --i );
+
+return( ans );
+}
+
+/*							p1evl()	*/
+/*                                          N
+ * Evaluate polynomial when coefficient of x  is 1.0.
+ * Otherwise same as polevl.
+ */
+
+double p1evl( x, coef, N )
+double x;
+double coef[];
+int N;
+{
+double ans;
+double *p;
+int i;
+
+p = coef;
+ans = x + *p++;
+i = N-1;
+
+do
+	ans = ans * x  + *p++;
+while( --i );
+
+return( ans );
+}

libm/double/polmisc.c

@@ -0,0 +1,309 @@
+
+/* Square root, sine, cosine, and arctangent of polynomial.
+ * See polyn.c for data structures and discussion.
+ */
+
+#include <stdio.h>
+#include <math.h>
+#ifdef ANSIPROT
+extern double atan2 ( double, double );
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern void polclr ( double *a, int n );
+extern void polmov ( double *a, int na, double *b );
+extern void polmul ( double a[], int na, double b[], int nb, double c[] );
+extern void poladd ( double a[], int na, double b[], int nb, double c[] );
+extern void polsub ( double a[], int na, double b[], int nb, double c[] );
+extern int poldiv ( double a[], int na, double b[], int nb, double c[] );
+extern void polsbt ( double a[], int na, double b[], int nb, double c[] );
+extern void * malloc ( long );
+extern void free ( void * );
+#else
+double atan2(), sqrt(), fabs(), sin(), cos();
+void polclr(), polmov(), polsbt(), poladd(), polsub(), polmul();
+int poldiv();
+void * malloc();
+void free ();
+#endif
+
+/* Highest degree of polynomial to be handled
+   by the polyn.c subroutine package.  */
+#define N 16
+/* Highest degree actually initialized at runtime.  */
+extern int MAXPOL;
+
+/* Taylor series coefficients for various functions
+ */
+double patan[N+1] = {
+  0.0,     1.0,      0.0, -1.0/3.0,     0.0,
+  1.0/5.0, 0.0, -1.0/7.0,      0.0, 1.0/9.0, 0.0, -1.0/11.0,
+  0.0, 1.0/13.0, 0.0, -1.0/15.0, 0.0 };
+
+double psin[N+1] = {
+  0.0, 1.0, 0.0,   -1.0/6.0,  0.0, 1.0/120.0,  0.0,
+  -1.0/5040.0, 0.0, 1.0/362880.0, 0.0, -1.0/39916800.0,
+  0.0, 1.0/6227020800.0, 0.0, -1.0/1.307674368e12, 0.0};
+
+double pcos[N+1] = {
+  1.0, 0.0,   -1.0/2.0,  0.0, 1.0/24.0,  0.0,
+  -1.0/720.0, 0.0, 1.0/40320.0, 0.0, -1.0/3628800.0, 0.0,
+  1.0/479001600.0, 0.0, -1.0/8.7179291e10, 0.0, 1.0/2.0922789888e13};
+
+double pasin[N+1] = {
+  0.0,     1.0,  0.0, 1.0/6.0,  0.0,
+  3.0/40.0, 0.0, 15.0/336.0, 0.0, 105.0/3456.0, 0.0, 945.0/42240.0,
+  0.0, 10395.0/599040.0 , 0.0, 135135.0/9676800.0 , 0.0
+};
+
+/* Square root of 1 + x.  */
+double psqrt[N+1] = {
+  1.0, 1./2., -1./8., 1./16., -5./128., 7./256., -21./1024., 33./2048.,
+  -429./32768., 715./65536., -2431./262144., 4199./524288., -29393./4194304.,
+  52003./8388608., -185725./33554432., 334305./67108864.,
+  -9694845./2147483648.};
+
+/* Arctangent of the ratio num/den of two polynomials.
+ */
+void
+polatn( num, den, ans, nn )
+     double num[], den[], ans[];
+     int nn;
+{
+  double a, t;
+  double *polq, *polu, *polt;
+  int i;
+
+  if (nn > N)
+    {
+      mtherr ("polatn", OVERFLOW);
+      return;
+    }
+  /* arctan( a + b ) = arctan(a) + arctan( b/(1 + ab + a**2) ) */
+  t = num[0];
+  a = den[0];
+  if( (t == 0.0) && (a == 0.0 ) )
+    {
+      t = num[1];
+      a = den[1];
+    }
+  t = atan2( t, a );  /* arctan(num/den), the ANSI argument order */
+  polq = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  polu = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  polt = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  polclr( polq, MAXPOL );
+  i = poldiv( den, nn, num, nn, polq );
+  a = polq[0]; /* a */
+  polq[0] = 0.0; /* b */
+  polmov( polq, nn, polu ); /* b */
+  /* Form the polynomial
+     1 + ab + a**2
+     where a is a scalar.  */
+  for( i=0; i<=nn; i++ )
+    polu[i] *= a;
+  polu[0] += 1.0 + a * a;
+  poldiv( polu, nn, polq, nn, polt ); /* divide into b */
+  polsbt( polt, nn, patan, nn, polu ); /* arctan(b)  */
+  polu[0] += t; /* plus arctan(a) */
+  polmov( polu, nn, ans );
+  free( polt );
+  free( polu );
+  free( polq );
+}
+
+
+
+/* Square root of a polynomial.
+ * Assumes the lowest degree nonzero term is dominant
+ * and of even degree.  An error message is given
+ * if the Newton iteration does not converge.
+ */
+void
+polsqt( pol, ans, nn )
+     double pol[], ans[];
+     int nn;
+{
+  double t;
+  double *x, *y;
+  int i, n;
+#if 0
+  double z[N+1];
+  double u;
+#endif
+
+  if (nn > N)
+    {
+      mtherr ("polatn", OVERFLOW);
+      return;
+    }
+  x = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  y = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  polmov( pol, nn, x );
+  polclr( y, MAXPOL );
+
+  /* Find lowest degree nonzero term.  */
+  t = 0.0;
+  for( n=0; n<nn; n++ )
+    {
+      if( x[n] != 0.0 )
+	goto nzero;
+    }
+  polmov( y, nn, ans );
+  return;
+
+nzero:
+
+  if( n > 0 )
+    {
+      if (n & 1)
+        {
+	  printf("error, sqrt of odd polynomial\n");
+	  return;
+	}
+      /* Divide by x^n.  */
+      y[n] = x[n];
+      poldiv (y, nn, pol, N, x);
+    }
+
+  t = x[0];
+  for( i=1; i<=nn; i++ )
+    x[i] /= t;
+  x[0] = 0.0;
+  /* series development sqrt(1+x) = 1  +  x / 2  -  x**2 / 8  +  x**3 / 16
+     hopes that first (constant) term is greater than what follows   */
+  polsbt( x, nn, psqrt, nn, y);
+  t = sqrt( t );
+  for( i=0; i<=nn; i++ )
+    y[i] *= t;
+
+  /* If first nonzero coefficient was at degree n > 0, multiply by
+     x^(n/2).  */
+  if (n > 0)
+    {
+      polclr (x, MAXPOL);
+      x[n/2] = 1.0;
+      polmul (x, nn, y, nn, y);
+    }
+#if 0
+/* Newton iterations */
+for( n=0; n<10; n++ )
+	{
+	poldiv( y, nn, pol, nn, z );
+	poladd( y, nn, z, nn, y );
+	for( i=0; i<=nn; i++ )
+		y[i] *= 0.5;
+	for( i=0; i<=nn; i++ )
+		{
+		u = fabs( y[i] - z[i] );
+		if( u > 1.0e-15 )
+			goto more;
+		}
+	goto done;
+more:	;
+	}
+printf( "square root did not converge\n" );
+done:
+#endif /* 0 */
+
+polmov( y, nn, ans );
+free( y );
+free( x );
+}
+
+
+
+/* Sine of a polynomial.
+ * The computation uses
+ *     sin(a+b) = sin(a) cos(b) + cos(a) sin(b)
+ * where a is the constant term of the polynomial and
+ * b is the sum of the rest of the terms.
+ * Since sin(b) and cos(b) are computed by series expansions,
+ * the value of b should be small.
+ */
+void
+polsin( x, y, nn )
+     double x[], y[];
+     int nn;
+{
+  double a, sc;
+  double *w, *c;
+  int i;
+
+  if (nn > N)
+    {
+      mtherr ("polatn", OVERFLOW);
+      return;
+    }
+  w = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  c = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  polmov( x, nn, w );
+  polclr( c, MAXPOL );
+  polclr( y, nn );
+  /* a, in the description, is x[0].  b is the polynomial x - x[0].  */
+  a = w[0];
+  /* c = cos (b) */
+  w[0] = 0.0;
+  polsbt( w, nn, pcos, nn, c );
+  sc = sin(a);
+  /* sin(a) cos (b) */
+  for( i=0; i<=nn; i++ )
+    c[i] *= sc;
+  /* y = sin (b)  */
+  polsbt( w, nn, psin, nn, y );
+  sc = cos(a);
+  /* cos(a) sin(b) */
+  for( i=0; i<=nn; i++ )
+    y[i] *= sc;
+  poladd( c, nn, y, nn, y );
+  free( c );
+  free( w );
+}
+
+
+/* Cosine of a polynomial.
+ * The computation uses
+ *     cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
+ * where a is the constant term of the polynomial and
+ * b is the sum of the rest of the terms.
+ * Since sin(b) and cos(b) are computed by series expansions,
+ * the value of b should be small.
+ */
+void
+polcos( x, y, nn )
+     double x[], y[];
+     int nn;
+{
+  double a, sc;
+  double *w, *c;
+  int i;
+  double sin(), cos();
+
+  if (nn > N)
+    {
+      mtherr ("polatn", OVERFLOW);
+      return;
+    }
+  w = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  c = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+  polmov( x, nn, w );
+  polclr( c, MAXPOL );
+  polclr( y, nn );
+  a = w[0];
+  w[0] = 0.0;
+  /* c = cos(b)  */
+  polsbt( w, nn, pcos, nn, c );
+  sc = cos(a);
+  /* cos(a) cos(b)  */
+  for( i=0; i<=nn; i++ )
+    c[i] *= sc;
+  /* y = sin(b) */
+  polsbt( w, nn, psin, nn, y );
+  sc = sin(a);
+  /* sin(a) sin(b) */
+  for( i=0; i<=nn; i++ )
+    y[i] *= sc;
+  polsub( y, nn, c, nn, y );
+  free( c );
+  free( w );
+}

libm/double/polrt.c

@@ -0,0 +1,227 @@
+/*							polrt.c
+ *
+ *	Find roots of a polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ *	{
+ *	double r;
+ *	double i;
+ *	}cmplx;
+ *
+ * double xcof[], cof[];
+ * int m;
+ * cmplx root[];
+ *
+ * polrt( xcof, cof, m, root )
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Iterative determination of the roots of a polynomial of
+ * degree m whose coefficient vector is xcof[].  The
+ * coefficients are arranged in ascending order; i.e., the
+ * coefficient of x**m is xcof[m].
+ *
+ * The array cof[] is working storage the same size as xcof[].
+ * root[] is the output array containing the complex roots.
+ *
+ *
+ * ACCURACY:
+ *
+ * Termination depends on evaluation of the polynomial at
+ * the trial values of the roots.  The values of multiple roots
+ * or of roots that are nearly equal may have poor relative
+ * accuracy after the first root in the neighborhood has been
+ * found.
+ *
+ */
+
+/*							polrt	*/
+/* Complex roots of real polynomial */
+/* number of coefficients is m + 1 ( i.e., m is degree of polynomial) */
+
+#include <math.h>
+/*
+typedef struct
+	{
+	double r;
+	double i;
+	}cmplx;
+*/
+#ifdef ANSIPROT
+extern double fabs ( double );
+#else
+double fabs();
+#endif
+
+int polrt( xcof, cof, m, root )
+double xcof[], cof[];
+int m;
+cmplx root[];
+{
+register double *p, *q;
+int i, j, nsav, n, n1, n2, nroot, iter, retry;
+int final;
+double mag, cofj;
+cmplx x0, x, xsav, dx, t, t1, u, ud;
+
+final = 0;
+n = m;
+if( n <= 0 )
+	return(1);
+if( n > 36 )
+	return(2);
+if( xcof[m] == 0.0 )
+	return(4);
+
+n1 = n;
+n2 = n;
+nroot = 0;
+nsav = n;
+q = &xcof[0];
+p = &cof[n];
+for( j=0; j<=nsav; j++ )
+	*p-- = *q++;	/*	cof[ n-j ] = xcof[j];*/
+xsav.r = 0.0;
+xsav.i = 0.0;
+
+nxtrut:
+x0.r = 0.00500101;
+x0.i = 0.01000101;
+retry = 0;
+
+tryagn:
+retry += 1;
+x.r = x0.r;
+
+x0.r = -10.0 * x0.i;
+x0.i = -10.0 * x.r;
+
+x.r = x0.r;
+x.i = x0.i;
+
+finitr:
+iter = 0;
+
+while( iter < 500 )
+{
+u.r = cof[n];
+if( u.r == 0.0 )
+	{		/* this root is zero */
+	x.r = 0;
+	n1 -= 1;
+	n2 -= 1;
+	goto zerrut;
+	}
+u.i = 0;
+ud.r = 0;
+ud.i = 0;
+t.r = 1.0;
+t.i = 0;
+p = &cof[n-1];
+for( i=0; i<n; i++ )
+	{
+	t1.r = x.r * t.r  -  x.i * t.i;
+	t1.i = x.r * t.i  +  x.i * t.r;
+	cofj = *p--;		/* evaluate polynomial */
+	u.r += cofj * t1.r;
+	u.i += cofj * t1.i;
+	cofj = cofj * (i+1);	/* derivative */
+	ud.r += cofj * t.r;
+	ud.i -= cofj * t.i;
+	t.r = t1.r;
+	t.i = t1.i;
+	}
+
+mag = ud.r * ud.r  +  ud.i * ud.i;
+if( mag == 0.0 )
+	{
+	if( !final )
+		goto tryagn;
+	x.r = xsav.r;
+	x.i = xsav.i;
+	goto findon;
+	}
+dx.r = (u.i * ud.i  -  u.r * ud.r)/mag;
+x.r += dx.r;
+dx.i = -(u.r * ud.i  +  u.i * ud.r)/mag;
+x.i += dx.i;
+if( (fabs(dx.i) + fabs(dx.r)) < 1.0e-6 )
+	goto lupdon;
+iter += 1;
+}	/* while iter < 500 */
+
+if( final )
+	goto lupdon;
+if( retry < 5 )
+	goto tryagn;
+return(3);
+
+lupdon:
+/* Swap original and reduced polynomials */
+q = &xcof[nsav];
+p = &cof[0];
+for( j=0; j<=n2; j++ )
+	{
+	cofj = *q;
+	*q-- = *p;
+	*p++ = cofj;
+	}
+i = n;
+n = n1;
+n1 = i;
+
+if( !final )
+	{
+	final = 1;
+	if( fabs(x.i/x.r) < 1.0e-4 )
+		x.i = 0.0;
+	xsav.r = x.r;
+	xsav.i = x.i;
+	goto finitr;	/* do final iteration on original polynomial */
+	}
+
+findon:
+final = 0;
+if( fabs(x.i/x.r) >= 1.0e-5 )
+	{
+	cofj = x.r + x.r;
+	mag = x.r * x.r  +  x.i * x.i;
+	n -= 2;
+	}
+else
+	{		/* root is real */
+zerrut:
+	x.i = 0;
+	cofj = x.r;
+	mag = 0;
+	n -= 1;
+	}
+/* divide working polynomial cof(z) by z - x */
+p = &cof[1];
+*p += cofj * *(p-1);
+for( j=1; j<n; j++ )
+	{
+	*(p+1) += cofj * *p  -  mag * *(p-1);
+	p++;
+	}
+
+setrut:
+root[nroot].r = x.r;
+root[nroot].i = x.i;
+nroot += 1;
+if( mag != 0.0 )
+	{
+	x.i = -x.i;
+	mag = 0;
+	goto setrut;	/* fill in the complex conjugate root */
+	}
+if( n > 0 )
+	goto nxtrut;
+return(0);
+}

libm/double/polylog.c

@@ -0,0 +1,467 @@
+/*							polylog.c
+ *
+ *	Polylogarithms
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, polylog();
+ * int n;
+ *
+ * y = polylog( n, x );
+ *
+ *
+ * The polylogarithm of order n is defined by the series
+ *
+ *
+ *              inf   k
+ *               -   x
+ *  Li (x)  =    >   ---  .
+ *    n          -     n
+ *              k=1   k
+ *
+ *
+ *  For x = 1,
+ *
+ *               inf
+ *                -    1
+ *   Li (1)  =    >   ---   =  Riemann zeta function (n)  .
+ *     n          -     n
+ *               k=1   k
+ *
+ *
+ *  When n = 2, the function is the dilogarithm, related to Spence's integral:
+ *
+ *                 x                      1-x
+ *                 -                        -
+ *                | |  -ln(1-t)            | |  ln t
+ *   Li (x)  =    |    -------- dt    =    |    ------ dt    =   spence(1-x) .
+ *     2        | |       t              | |    1 - t
+ *               -                        -
+ *                0                        1
+ *
+ *
+ *  See also the program cpolylog.c for the complex polylogarithm,
+ *  whose definition is extended to x > 1.
+ *
+ *  References:
+ *
+ *  Lewin, L., _Polylogarithms and Associated Functions_,
+ *  North Holland, 1981.
+ *
+ *  Lewin, L., ed., _Structural Properties of Polylogarithms_,
+ *  American Mathematical Society, 1991.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain   n   # trials      peak         rms
+ *    IEEE      0, 1     2     50000      6.2e-16     8.0e-17
+ *    IEEE      0, 1     3    100000      2.5e-16     6.6e-17
+ *    IEEE      0, 1     4     30000      1.7e-16     4.9e-17
+ *    IEEE      0, 1     5     30000      5.1e-16     7.8e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  July, 1999
+Copyright 1999 by Stephen L. Moshier
+*/
+
+#include <math.h>
+extern double PI;
+
+/* polylog(4, 1-x) = zeta(4) - x zeta(3) + x^2 A4(x)/B4(x)
+   0 <= x <= 0.125
+   Theoretical peak absolute error 4.5e-18  */
+#if UNK
+static double A4[13] = {
+ 3.056144922089490701751E-2,
+ 3.243086484162581557457E-1,
+ 2.877847281461875922565E-1,
+ 7.091267785886180663385E-2,
+ 6.466460072456621248630E-3,
+ 2.450233019296542883275E-4,
+ 4.031655364627704957049E-6,
+ 2.884169163909467997099E-8,
+ 8.680067002466594858347E-11,
+ 1.025983405866370985438E-13,
+ 4.233468313538272640380E-17,
+ 4.959422035066206902317E-21,
+ 1.059365867585275714599E-25,
+};
+static double B4[12] = {
+  /* 1.000000000000000000000E0, */
+ 2.821262403600310974875E0,
+ 1.780221124881327022033E0,
+ 3.778888211867875721773E-1,
+ 3.193887040074337940323E-2,
+ 1.161252418498096498304E-3,
+ 1.867362374829870620091E-5,
+ 1.319022779715294371091E-7,
+ 3.942755256555603046095E-10,
+ 4.644326968986396928092E-13,
+ 1.913336021014307074861E-16,
+ 2.240041814626069927477E-20,
+ 4.784036597230791011855E-25,
+};
+#endif
+#if DEC
+static short A4[52] = {
+0036772,0056001,0016601,0164507,
+0037646,0005710,0076603,0176456,
+0037623,0054205,0013532,0026476,
+0037221,0035252,0101064,0065407,
+0036323,0162231,0042033,0107244,
+0035200,0073170,0106141,0136543,
+0033607,0043647,0163672,0055340,
+0031767,0137614,0173376,0072313,
+0027676,0160156,0161276,0034203,
+0025347,0003752,0123106,0064266,
+0022503,0035770,0160173,0177501,
+0017273,0056226,0033704,0132530,
+0013403,0022244,0175205,0052161,
+};
+static short B4[48] = {
+  /*0040200,0000000,0000000,0000000, */
+0040464,0107620,0027471,0071672,
+0040343,0157111,0025601,0137255,
+0037701,0075244,0140412,0160220,
+0037002,0151125,0036572,0057163,
+0035630,0032452,0050727,0161653,
+0034234,0122515,0034323,0172615,
+0032415,0120405,0123660,0003160,
+0030330,0140530,0161045,0150177,
+0026002,0134747,0014542,0002510,
+0023134,0113666,0035730,0035732,
+0017723,0110343,0041217,0007764,
+0014024,0007412,0175575,0160230,
+};
+#endif
+#if IBMPC
+static short A4[52] = {
+0x3d29,0x23b0,0x4b80,0x3f9f,
+0x7fa6,0x0fb0,0xc179,0x3fd4,
+0x45a8,0xa2eb,0x6b10,0x3fd2,
+0x8d61,0x5046,0x2755,0x3fb2,
+0x71d4,0x2883,0x7c93,0x3f7a,
+0x37ac,0x118c,0x0ecf,0x3f30,
+0x4b5c,0xfcf7,0xe8f4,0x3ed0,
+0xce99,0x9edf,0xf7f1,0x3e5e,
+0xc710,0xdc57,0xdc0d,0x3dd7,
+0xcd17,0x54c8,0xe0fd,0x3d3c,
+0x7fe8,0x1c0f,0x677f,0x3c88,
+0x96ab,0xc6f8,0x6b92,0x3bb7,
+0xaa8e,0x9f50,0x6494,0x3ac0,
+};
+static short B4[48] = {
+  /*0x0000,0x0000,0x0000,0x3ff0,*/
+0x2e77,0x05e7,0x91f2,0x4006,
+0x37d6,0x2570,0x7bc9,0x3ffc,
+0x5c12,0x9821,0x2f54,0x3fd8,
+0x4bce,0xa7af,0x5a4a,0x3fa0,
+0xfc75,0x4a3a,0x06a5,0x3f53,
+0x7eb2,0xa71a,0x94a9,0x3ef3,
+0x00ce,0xb4f6,0xb420,0x3e81,
+0xba10,0x1c44,0x182b,0x3dfb,
+0x40a9,0xe32c,0x573c,0x3d60,
+0x077b,0xc77b,0x92f6,0x3cab,
+0xe1fe,0x6851,0x721c,0x3bda,
+0xbc13,0x5f6f,0x81e1,0x3ae2,
+};
+#endif
+#if MIEEE
+static short A4[52] = {
+0x3f9f,0x4b80,0x23b0,0x3d29,
+0x3fd4,0xc179,0x0fb0,0x7fa6,
+0x3fd2,0x6b10,0xa2eb,0x45a8,
+0x3fb2,0x2755,0x5046,0x8d61,
+0x3f7a,0x7c93,0x2883,0x71d4,
+0x3f30,0x0ecf,0x118c,0x37ac,
+0x3ed0,0xe8f4,0xfcf7,0x4b5c,
+0x3e5e,0xf7f1,0x9edf,0xce99,
+0x3dd7,0xdc0d,0xdc57,0xc710,
+0x3d3c,0xe0fd,0x54c8,0xcd17,
+0x3c88,0x677f,0x1c0f,0x7fe8,
+0x3bb7,0x6b92,0xc6f8,0x96ab,
+0x3ac0,0x6494,0x9f50,0xaa8e,
+};
+static short B4[48] = {
+  /*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4006,0x91f2,0x05e7,0x2e77,
+0x3ffc,0x7bc9,0x2570,0x37d6,
+0x3fd8,0x2f54,0x9821,0x5c12,
+0x3fa0,0x5a4a,0xa7af,0x4bce,
+0x3f53,0x06a5,0x4a3a,0xfc75,
+0x3ef3,0x94a9,0xa71a,0x7eb2,
+0x3e81,0xb420,0xb4f6,0x00ce,
+0x3dfb,0x182b,0x1c44,0xba10,
+0x3d60,0x573c,0xe32c,0x40a9,
+0x3cab,0x92f6,0xc77b,0x077b,
+0x3bda,0x721c,0x6851,0xe1fe,
+0x3ae2,0x81e1,0x5f6f,0xbc13,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double spence ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double zetac ( double );
+extern double pow ( double, double );
+extern double powi ( double, int );
+extern double log ( double );
+extern double fac ( int i );
+extern double fabs (double);
+double polylog (int, double);
+#else
+extern double spence(), polevl(), p1evl(), zetac();
+extern double pow(), powi(), log();
+extern double fac(); /* factorial */
+extern double fabs();
+double polylog();
+#endif
+extern double MACHEP;
+
+double
+polylog (n, x)
+     int n;
+     double x;
+{
+  double h, k, p, s, t, u, xc, z;
+  int i, j;
+
+/*  This recurrence provides formulas for n < 2.
+
+    d                 1
+    --   Li (x)  =   ---  Li   (x)  .
+    dx     n          x     n-1
+
+*/
+
+  if (n == -1)
+    {
+      p  = 1.0 - x;
+      u = x / p;
+      s = u * u + u;
+      return s;
+    }
+
+  if (n == 0)
+    {
+      s = x / (1.0 - x);
+      return s;
+    }
+
+  /* Not implemented for n < -1.
+     Not defined for x > 1.  Use cpolylog if you need that.  */
+  if (x > 1.0 || n < -1)
+    {
+      mtherr("polylog", DOMAIN);
+      return 0.0;
+    }
+
+  if (n == 1)
+    {
+      s = -log (1.0 - x);
+      return s;
+    }
+
+  /* Argument +1 */
+  if (x == 1.0 && n > 1)
+    {
+      s = zetac ((double) n) + 1.0;
+      return s;
+    }
+
+  /* Argument -1.
+                        1-n
+     Li (-z)  = - (1 - 2   ) Li (z)
+       n                       n
+   */
+  if (x == -1.0 && n > 1)
+    {
+      /* Li_n(1) = zeta(n) */
+      s = zetac ((double) n) + 1.0;
+      s = s * (powi (2.0, 1 - n) - 1.0);
+      return s;
+    }
+
+/*  Inversion formula:
+ *                                                   [n/2]   n-2r
+ *                n                  1     n           -  log    (z)
+ *  Li (-z) + (-1)  Li (-1/z)  =  - --- log (z)  +  2  >  ----------- Li  (-1)
+ *    n               n              n!                -   (n - 2r)!    2r
+ *                                                    r=1
+ */
+  if (x < -1.0 && n > 1)
+    {
+      double q, w;
+      int r;
+
+      w = log (-x);
+      s = 0.0;
+      for (r = 1; r <= n / 2; r++)
+	{
+	  j = 2 * r;
+	  p = polylog (j, -1.0);
+	  j = n - j;
+	  if (j == 0)
+	    {
+	      s = s + p;
+	      break;
+	    }
+	  q = (double) j;
+	  q = pow (w, q) * p / fac (j);
+	  s = s + q;
+	}
+      s = 2.0 * s;
+      q = polylog (n, 1.0 / x);
+      if (n & 1)
+	q = -q;
+      s = s - q;
+      s = s - pow (w, (double) n) / fac (n);
+      return s;
+    }
+
+  if (n == 2)
+    {
+      if (x < 0.0 || x > 1.0)
+	return (spence (1.0 - x));
+    }
+
+
+
+  /*  The power series converges slowly when x is near 1.  For n = 3, this
+      identity helps:
+
+      Li (-x/(1-x)) + Li (1-x) + Li (x)
+        3               3          3
+                     2                               2                 3
+       = Li (1) + (pi /6) log(1-x) - (1/2) log(x) log (1-x) + (1/6) log (1-x)
+           3
+  */
+
+  if (n == 3)
+    {
+      p = x * x * x;
+      if (x > 0.8)
+	{
+	  u = log(x);
+	  s = p / 6.0;
+	  xc = 1.0 - x;
+	  s = s - 0.5 * u * u * log(xc);
+          s = s + PI * PI * u / 6.0;
+          s = s - polylog (3, -xc/x);
+	  s = s - polylog (3, xc);
+	  s = s + zetac(3.0);
+	  s = s + 1.0;
+	  return s;
+	}
+      /* Power series  */
+      t = p / 27.0;
+      t = t + .125 * x * x;
+      t = t + x;
+
+      s = 0.0;
+      k = 4.0;
+      do
+	{
+	  p = p * x;
+	  h = p / (k * k * k);
+	  s = s + h;
+	  k += 1.0;
+	}
+      while (fabs(h/s) > 1.1e-16);
+      return (s + t);
+    }
+
+if (n == 4)
+  {
+    if (x >= 0.875)
+      {
+	u = 1.0 - x;
+	s = polevl(u, A4, 12) / p1evl(u, B4, 12);
+	s =  s * u * u - 1.202056903159594285400 * u;
+	s +=  1.0823232337111381915160;
+	return s;
+      }
+    goto pseries;
+  }
+
+
+  if (x < 0.75)
+    goto pseries;
+
+
+/*  This expansion in powers of log(x) is especially useful when
+    x is near 1.
+
+    See also the pari gp calculator.
+
+                      inf                  j
+                       -    z(n-j) (log(x))
+    polylog(n,x)  =    >   -----------------
+                       -           j!
+                      j=0
+
+      where
+
+      z(j) = Riemann zeta function (j), j != 1
+
+                              n-1
+                               -
+      z(1) =  -log(-log(x)) +  >  1/k
+                               -
+                              k=1
+  */
+
+  z = log(x);
+  h = -log(-z);
+  for (i = 1; i < n; i++)
+    h = h + 1.0/i;
+  p = 1.0;
+  s = zetac((double)n) + 1.0;
+  for (j=1; j<=n+1; j++)
+  {
+    p = p * z / j;
+    if (j == n-1)
+      s = s + h * p;
+    else
+      s = s + (zetac((double)(n-j)) + 1.0) * p;
+  }
+  j = n + 3;
+  z = z * z;
+  for(;;)
+    {
+      p = p * z / ((j-1)*j);
+      h = (zetac((double)(n-j)) + 1.0);
+      h = h * p;
+      s = s + h;
+      if (fabs(h/s) < MACHEP)
+	break;
+      j += 2;
+    }
+  return s;
+
+
+pseries:
+
+  p = x * x * x;
+  k = 3.0;
+  s = 0.0;
+  do
+    {
+      p = p * x;
+      k += 1.0;
+      h = p / powi(k, n);
+      s = s + h;
+    }
+  while (fabs(h/s) > MACHEP);
+  s += x * x * x / powi(3.0,n);
+  s += x * x / powi(2.0,n);
+  s += x;
+  return s;
+}

libm/double/polyn.c

@@ -0,0 +1,471 @@
+/*							polyn.c
+ *							polyr.c
+ * Arithmetic operations on polynomials
+ *
+ * In the following descriptions a, b, c are polynomials of degree
+ * na, nb, nc respectively.  The degree of a polynomial cannot
+ * exceed a run-time value MAXPOL.  An operation that attempts
+ * to use or generate a polynomial of higher degree may produce a
+ * result that suffers truncation at degree MAXPOL.  The value of
+ * MAXPOL is set by calling the function
+ *
+ *     polini( maxpol );
+ *
+ * where maxpol is the desired maximum degree.  This must be
+ * done prior to calling any of the other functions in this module.
+ * Memory for internal temporary polynomial storage is allocated
+ * by polini().
+ *
+ * Each polynomial is represented by an array containing its
+ * coefficients, together with a separately declared integer equal
+ * to the degree of the polynomial.  The coefficients appear in
+ * ascending order; that is,
+ *
+ *                                        2                      na
+ * a(x)  =  a[0]  +  a[1] * x  +  a[2] * x   +  ...  +  a[na] * x  .
+ *
+ *
+ *
+ * sum = poleva( a, na, x );	Evaluate polynomial a(t) at t = x.
+ * polprt( a, na, D );		Print the coefficients of a to D digits.
+ * polclr( a, na );		Set a identically equal to zero, up to a[na].
+ * polmov( a, na, b );		Set b = a.
+ * poladd( a, na, b, nb, c );	c = b + a, nc = max(na,nb)
+ * polsub( a, na, b, nb, c );	c = b - a, nc = max(na,nb)
+ * polmul( a, na, b, nb, c );	c = b * a, nc = na+nb
+ *
+ *
+ * Division:
+ *
+ * i = poldiv( a, na, b, nb, c );	c = b / a, nc = MAXPOL
+ *
+ * returns i = the degree of the first nonzero coefficient of a.
+ * The computed quotient c must be divided by x^i.  An error message
+ * is printed if a is identically zero.
+ *
+ *
+ * Change of variables:
+ * If a and b are polynomials, and t = a(x), then
+ *     c(t) = b(a(x))
+ * is a polynomial found by substituting a(x) for t.  The
+ * subroutine call for this is
+ *
+ * polsbt( a, na, b, nb, c );
+ *
+ *
+ * Notes:
+ * poldiv() is an integer routine; poleva() is double.
+ * Any of the arguments a, b, c may refer to the same array.
+ *
+ */
+
+#include <stdio.h>
+#include <math.h>
+#if ANSIPROT
+void exit (int);
+extern void * malloc ( long );
+extern void free ( void * );
+void polclr ( double *, int );
+void polmov ( double *, int, double * );
+void polmul ( double *, int, double *, int, double * );
+int poldiv ( double *, int, double *, int, double * );
+#else
+void exit();
+void * malloc();
+void free ();
+void polclr(), polmov(), poldiv(), polmul();
+#endif
+#ifndef NULL
+#define NULL 0
+#endif
+
+/* near pointer version of malloc() */
+/*
+#define malloc _nmalloc
+#define free _nfree
+*/
+
+/* Pointers to internal arrays.  Note poldiv() allocates
+ * and deallocates some temporary arrays every time it is called.
+ */
+static double *pt1 = 0;
+static double *pt2 = 0;
+static double *pt3 = 0;
+
+/* Maximum degree of polynomial. */
+int MAXPOL = 0;
+extern int MAXPOL;
+
+/* Number of bytes (chars) in maximum size polynomial. */
+static int psize = 0;
+
+
+/* Initialize max degree of polynomials
+ * and allocate temporary storage.
+ */
+void polini( maxdeg )
+int maxdeg;
+{
+
+MAXPOL = maxdeg;
+psize = (maxdeg + 1) * sizeof(double);
+
+/* Release previously allocated memory, if any. */
+if( pt3 )
+	free(pt3);
+if( pt2 )
+	free(pt2);
+if( pt1 )
+	free(pt1);
+
+/* Allocate new arrays */
+pt1 = (double * )malloc(psize); /* used by polsbt */
+pt2 = (double * )malloc(psize); /* used by polsbt */
+pt3 = (double * )malloc(psize); /* used by polmul */
+
+/* Report if failure */
+if( (pt1 == NULL) || (pt2 == NULL) || (pt3 == NULL) )
+	{
+	mtherr( "polini", ERANGE );
+	exit(1);
+	}
+}
+
+
+
+/* Print the coefficients of a, with d decimal precision.
+ */
+static char *form = "abcdefghijk";
+
+void polprt( a, na, d )
+double a[];
+int na, d;
+{
+int i, j, d1;
+char *p;
+
+/* Create format descriptor string for the printout.
+ * Do this partly by hand, since sprintf() may be too
+ * bug-ridden to accomplish this feat by itself.
+ */
+p = form;
+*p++ = '%';
+d1 = d + 8;
+sprintf( p, "%d ", d1 );
+p += 1;
+if( d1 >= 10 )
+	p += 1;
+*p++ = '.';
+sprintf( p, "%d ", d );
+p += 1;
+if( d >= 10 )
+	p += 1;
+*p++ = 'e';
+*p++ = ' ';
+*p++ = '\0';
+
+
+/* Now do the printing.
+ */
+d1 += 1;
+j = 0;
+for( i=0; i<=na; i++ )
+	{
+/* Detect end of available line */
+	j += d1;
+	if( j >= 78 )
+		{
+		printf( "\n" );
+		j = d1;
+		}
+	printf( form, a[i] );
+	}
+printf( "\n" );
+}
+
+
+
+/* Set a = 0.
+ */
+void polclr( a, n )
+register double *a;
+int n;
+{
+int i;
+
+if( n > MAXPOL )
+	n = MAXPOL;
+for( i=0; i<=n; i++ )
+	*a++ = 0.0;
+}
+
+
+
+/* Set b = a.
+ */
+void polmov( a, na, b )
+register double *a, *b;
+int na;
+{
+int i;
+
+if( na > MAXPOL )
+	na = MAXPOL;
+
+for( i=0; i<= na; i++ )
+	{
+	*b++ = *a++;
+	}
+}
+
+
+/* c = b * a.
+ */
+void polmul( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+int i, j, k, nc;
+double x;
+
+nc = na + nb;
+polclr( pt3, MAXPOL );
+
+for( i=0; i<=na; i++ )
+	{
+	x = a[i];
+	for( j=0; j<=nb; j++ )
+		{
+		k = i + j;
+		if( k > MAXPOL )
+			break;
+		pt3[k] += x * b[j];
+		}
+	}
+
+if( nc > MAXPOL )
+	nc = MAXPOL;
+for( i=0; i<=nc; i++ )
+	c[i] = pt3[i];
+}
+
+
+
+ 
+/* c = b + a.
+ */
+void poladd( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+int i, n;
+
+
+if( na > nb )
+	n = na;
+else
+	n = nb;
+
+if( n > MAXPOL )
+	n = MAXPOL;
+
+for( i=0; i<=n; i++ )
+	{
+	if( i > na )
+		c[i] = b[i];
+	else if( i > nb )
+		c[i] = a[i];
+	else
+		c[i] = b[i] + a[i];
+	}
+}
+
+/* c = b - a.
+ */
+void polsub( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+int i, n;
+
+
+if( na > nb )
+	n = na;
+else
+	n = nb;
+
+if( n > MAXPOL )
+	n = MAXPOL;
+
+for( i=0; i<=n; i++ )
+	{
+	if( i > na )
+		c[i] = b[i];
+	else if( i > nb )
+		c[i] = -a[i];
+	else
+		c[i] = b[i] - a[i];
+	}
+}
+
+
+
+/* c = b/a
+ */
+int poldiv( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+double quot;
+double *ta, *tb, *tq;
+int i, j, k, sing;
+
+sing = 0;
+
+/* Allocate temporary arrays.  This would be quicker
+ * if done automatically on the stack, but stack space
+ * may be hard to obtain on a small computer.
+ */
+ta = (double * )malloc( psize );
+polclr( ta, MAXPOL );
+polmov( a, na, ta );
+
+tb = (double * )malloc( psize );
+polclr( tb, MAXPOL );
+polmov( b, nb, tb );
+
+tq = (double * )malloc( psize );
+polclr( tq, MAXPOL );
+
+/* What to do if leading (constant) coefficient
+ * of denominator is zero.
+ */
+if( a[0] == 0.0 )
+	{
+	for( i=0; i<=na; i++ )
+		{
+		if( ta[i] != 0.0 )
+			goto nzero;
+		}
+	mtherr( "poldiv", SING );
+	goto done;
+
+nzero:
+/* Reduce the degree of the denominator. */
+	for( i=0; i<na; i++ )
+		ta[i] = ta[i+1];
+	ta[na] = 0.0;
+
+	if( b[0] != 0.0 )
+		{
+/* Optional message:
+		printf( "poldiv singularity, divide quotient by x\n" );
+*/
+		sing += 1;
+		}
+	else
+		{
+/* Reduce degree of numerator. */
+		for( i=0; i<nb; i++ )
+			tb[i] = tb[i+1];
+		tb[nb] = 0.0;
+		}
+/* Call self, using reduced polynomials. */
+	sing += poldiv( ta, na, tb, nb, c );
+	goto done;
+	}
+
+/* Long division algorithm.  ta[0] is nonzero.
+ */
+for( i=0; i<=MAXPOL; i++ )
+	{
+	quot = tb[i]/ta[0];
+	for( j=0; j<=MAXPOL; j++ )
+		{
+		k = j + i;
+		if( k > MAXPOL )
+			break;
+		tb[k] -= quot * ta[j];
+		}
+	tq[i] = quot;
+	}
+/* Send quotient to output array. */
+polmov( tq, MAXPOL, c );
+
+done:
+
+/* Restore allocated memory. */
+free(tq);
+free(tb);
+free(ta);
+return( sing );
+}
+
+
+
+
+/* Change of variables
+ * Substitute a(y) for the variable x in b(x).
+ * x = a(y)
+ * c(x) = b(x) = b(a(y)).
+ */
+
+void polsbt( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+int i, j, k, n2;
+double x;
+
+/* 0th degree term:
+ */
+polclr( pt1, MAXPOL );
+pt1[0] = b[0];
+
+polclr( pt2, MAXPOL );
+pt2[0] = 1.0;
+n2 = 0;
+
+for( i=1; i<=nb; i++ )
+	{
+/* Form ith power of a. */
+	polmul( a, na, pt2, n2, pt2 );
+	n2 += na;
+	x = b[i];
+/* Add the ith coefficient of b times the ith power of a. */
+	for( j=0; j<=n2; j++ )
+		{
+		if( j > MAXPOL )
+			break;
+		pt1[j] += x * pt2[j];
+		}
+	}
+
+k = n2 + nb;
+if( k > MAXPOL )
+	k = MAXPOL;
+for( i=0; i<=k; i++ )
+	c[i] = pt1[i];
+}
+
+
+
+
+/* Evaluate polynomial a(t) at t = x.
+ */
+double poleva( a, na, x )
+double a[];
+int na;
+double x;
+{
+double s;
+int i;
+
+s = a[na];
+for( i=na-1; i>=0; i-- )
+	{
+	s = s * x + a[i];
+	}
+return(s);
+}
+

libm/double/polyr.c

@@ -0,0 +1,533 @@
+
+/* Arithmetic operations on polynomials with rational coefficients
+ *
+ * In the following descriptions a, b, c are polynomials of degree
+ * na, nb, nc respectively.  The degree of a polynomial cannot
+ * exceed a run-time value MAXPOL.  An operation that attempts
+ * to use or generate a polynomial of higher degree may produce a
+ * result that suffers truncation at degree MAXPOL.  The value of
+ * MAXPOL is set by calling the function
+ *
+ *     polini( maxpol );
+ *
+ * where maxpol is the desired maximum degree.  This must be
+ * done prior to calling any of the other functions in this module.
+ * Memory for internal temporary polynomial storage is allocated
+ * by polini().
+ *
+ * Each polynomial is represented by an array containing its
+ * coefficients, together with a separately declared integer equal
+ * to the degree of the polynomial.  The coefficients appear in
+ * ascending order; that is,
+ *
+ *                                        2                      na
+ * a(x)  =  a[0]  +  a[1] * x  +  a[2] * x   +  ...  +  a[na] * x  .
+ *
+ *
+ *
+ * `a', `b', `c' are arrays of fracts.
+ * poleva( a, na, &x, &sum );	Evaluate polynomial a(t) at t = x.
+ * polprt( a, na, D );		Print the coefficients of a to D digits.
+ * polclr( a, na );		Set a identically equal to zero, up to a[na].
+ * polmov( a, na, b );		Set b = a.
+ * poladd( a, na, b, nb, c );	c = b + a, nc = max(na,nb)
+ * polsub( a, na, b, nb, c );	c = b - a, nc = max(na,nb)
+ * polmul( a, na, b, nb, c );	c = b * a, nc = na+nb
+ *
+ *
+ * Division:
+ *
+ * i = poldiv( a, na, b, nb, c );	c = b / a, nc = MAXPOL
+ *
+ * returns i = the degree of the first nonzero coefficient of a.
+ * The computed quotient c must be divided by x^i.  An error message
+ * is printed if a is identically zero.
+ *
+ *
+ * Change of variables:
+ * If a and b are polynomials, and t = a(x), then
+ *     c(t) = b(a(x))
+ * is a polynomial found by substituting a(x) for t.  The
+ * subroutine call for this is
+ *
+ * polsbt( a, na, b, nb, c );
+ *
+ *
+ * Notes:
+ * poldiv() is an integer routine; poleva() is double.
+ * Any of the arguments a, b, c may refer to the same array.
+ *
+ */
+
+#include <stdio.h>
+#include <math.h>
+#ifndef NULL
+#define NULL 0
+#endif
+typedef struct{
+	double n;
+	double d;
+	}fract;
+
+#ifdef ANSIPROT
+extern void radd ( fract *, fract *, fract * );
+extern void rsub ( fract *, fract *, fract * );
+extern void rmul ( fract *, fract *, fract * );
+extern void rdiv ( fract *, fract *, fract * );
+void polmov ( fract *, int, fract * );
+void polmul ( fract *, int, fract *, int, fract * );
+int poldiv ( fract *, int, fract *, int, fract * );
+void * malloc ( long );
+void free ( void * );
+#else
+void radd(), rsub(), rmul(), rdiv();
+void polmov(), polmul();
+int poldiv();
+void * malloc();
+void free ();
+#endif
+
+/* near pointer version of malloc() */
+/*
+#define malloc _nmalloc
+#define free _nfree
+*/
+/* Pointers to internal arrays.  Note poldiv() allocates
+ * and deallocates some temporary arrays every time it is called.
+ */
+static fract *pt1 = 0;
+static fract *pt2 = 0;
+static fract *pt3 = 0;
+
+/* Maximum degree of polynomial. */
+int MAXPOL = 0;
+extern int MAXPOL;
+
+/* Number of bytes (chars) in maximum size polynomial. */
+static int psize = 0;
+
+
+/* Initialize max degree of polynomials
+ * and allocate temporary storage.
+ */
+void polini( maxdeg )
+int maxdeg;
+{
+
+MAXPOL = maxdeg;
+psize = (maxdeg + 1) * sizeof(fract);
+
+/* Release previously allocated memory, if any. */
+if( pt3 )
+	free(pt3);
+if( pt2 )
+	free(pt2);
+if( pt1 )
+	free(pt1);
+
+/* Allocate new arrays */
+pt1 = (fract * )malloc(psize); /* used by polsbt */
+pt2 = (fract * )malloc(psize); /* used by polsbt */
+pt3 = (fract * )malloc(psize); /* used by polmul */
+
+/* Report if failure */
+if( (pt1 == NULL) || (pt2 == NULL) || (pt3 == NULL) )
+	{
+	mtherr( "polini", ERANGE );
+	exit(1);
+	}
+}
+
+
+
+/* Print the coefficients of a, with d decimal precision.
+ */
+static char *form = "abcdefghijk";
+
+void polprt( a, na, d )
+fract a[];
+int na, d;
+{
+int i, j, d1;
+char *p;
+
+/* Create format descriptor string for the printout.
+ * Do this partly by hand, since sprintf() may be too
+ * bug-ridden to accomplish this feat by itself.
+ */
+p = form;
+*p++ = '%';
+d1 = d + 8;
+sprintf( p, "%d ", d1 );
+p += 1;
+if( d1 >= 10 )
+	p += 1;
+*p++ = '.';
+sprintf( p, "%d ", d );
+p += 1;
+if( d >= 10 )
+	p += 1;
+*p++ = 'e';
+*p++ = ' ';
+*p++ = '\0';
+
+
+/* Now do the printing.
+ */
+d1 += 1;
+j = 0;
+for( i=0; i<=na; i++ )
+	{
+/* Detect end of available line */
+	j += d1;
+	if( j >= 78 )
+		{
+		printf( "\n" );
+		j = d1;
+		}
+	printf( form, a[i].n );
+	j += d1;
+	if( j >= 78 )
+		{
+		printf( "\n" );
+		j = d1;
+		}
+	printf( form, a[i].d );
+	}
+printf( "\n" );
+}
+
+
+
+/* Set a = 0.
+ */
+void polclr( a, n )
+fract a[];
+int n;
+{
+int i;
+
+if( n > MAXPOL )
+	n = MAXPOL;
+for( i=0; i<=n; i++ )
+	{
+	a[i].n = 0.0;
+	a[i].d = 1.0;
+	}
+}
+
+
+
+/* Set b = a.
+ */
+void polmov( a, na, b )
+fract a[], b[];
+int na;
+{
+int i;
+
+if( na > MAXPOL )
+	na = MAXPOL;
+
+for( i=0; i<= na; i++ )
+	{
+	b[i].n = a[i].n;
+	b[i].d = a[i].d;
+	}
+}
+
+
+/* c = b * a.
+ */
+void polmul( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+int i, j, k, nc;
+fract temp;
+fract *p;
+
+nc = na + nb;
+polclr( pt3, MAXPOL );
+
+p = &a[0];
+for( i=0; i<=na; i++ )
+	{
+	for( j=0; j<=nb; j++ )
+		{
+		k = i + j;
+		if( k > MAXPOL )
+			break;
+		rmul( p, &b[j], &temp ); /*pt3[k] += a[i] * b[j];*/
+		radd( &temp, &pt3[k], &pt3[k] );
+		}
+	++p;
+	}
+
+if( nc > MAXPOL )
+	nc = MAXPOL;
+for( i=0; i<=nc; i++ )
+	{
+	c[i].n = pt3[i].n;
+	c[i].d = pt3[i].d;
+	}
+}
+
+
+
+ 
+/* c = b + a.
+ */
+void poladd( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+int i, n;
+
+
+if( na > nb )
+	n = na;
+else
+	n = nb;
+
+if( n > MAXPOL )
+	n = MAXPOL;
+
+for( i=0; i<=n; i++ )
+	{
+	if( i > na )
+		{
+		c[i].n = b[i].n;
+		c[i].d = b[i].d;
+		}
+	else if( i > nb )
+		{
+		c[i].n = a[i].n;
+		c[i].d = a[i].d;
+		}
+	else
+		{
+		radd( &a[i], &b[i], &c[i] ); /*c[i] = b[i] + a[i];*/
+		}
+	}
+}
+
+/* c = b - a.
+ */
+void polsub( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+int i, n;
+
+
+if( na > nb )
+	n = na;
+else
+	n = nb;
+
+if( n > MAXPOL )
+	n = MAXPOL;
+
+for( i=0; i<=n; i++ )
+	{
+	if( i > na )
+		{
+		c[i].n = b[i].n;
+		c[i].d = b[i].d;
+		}
+	else if( i > nb )
+		{
+		c[i].n = -a[i].n;
+		c[i].d = a[i].d;
+		}
+	else
+		{
+		rsub( &a[i], &b[i], &c[i] ); /*c[i] = b[i] - a[i];*/
+		}
+	}
+}
+
+
+
+/* c = b/a
+ */
+int poldiv( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+fract *ta, *tb, *tq;
+fract quot;
+fract temp;
+int i, j, k, sing;
+
+sing = 0;
+
+/* Allocate temporary arrays.  This would be quicker
+ * if done automatically on the stack, but stack space
+ * may be hard to obtain on a small computer.
+ */
+ta = (fract * )malloc( psize );
+polclr( ta, MAXPOL );
+polmov( a, na, ta );
+
+tb = (fract * )malloc( psize );
+polclr( tb, MAXPOL );
+polmov( b, nb, tb );
+
+tq = (fract * )malloc( psize );
+polclr( tq, MAXPOL );
+
+/* What to do if leading (constant) coefficient
+ * of denominator is zero.
+ */
+if( a[0].n == 0.0 )
+	{
+	for( i=0; i<=na; i++ )
+		{
+		if( ta[i].n != 0.0 )
+			goto nzero;
+		}
+	mtherr( "poldiv", SING );
+	goto done;
+
+nzero:
+/* Reduce the degree of the denominator. */
+	for( i=0; i<na; i++ )
+		{
+		ta[i].n = ta[i+1].n;
+		ta[i].d = ta[i+1].d;
+		}
+	ta[na].n = 0.0;
+	ta[na].d = 1.0;
+
+	if( b[0].n != 0.0 )
+		{
+/* Optional message:
+		printf( "poldiv singularity, divide quotient by x\n" );
+*/
+		sing += 1;
+		}
+	else
+		{
+/* Reduce degree of numerator. */
+		for( i=0; i<nb; i++ )
+			{
+			tb[i].n = tb[i+1].n;
+			tb[i].d = tb[i+1].d;
+			}
+		tb[nb].n = 0.0;
+		tb[nb].d = 1.0;
+		}
+/* Call self, using reduced polynomials. */
+	sing += poldiv( ta, na, tb, nb, c );
+	goto done;
+	}
+
+/* Long division algorithm.  ta[0] is nonzero.
+ */
+for( i=0; i<=MAXPOL; i++ )
+	{
+	rdiv( &ta[0], &tb[i], &quot ); /*quot = tb[i]/ta[0];*/
+	for( j=0; j<=MAXPOL; j++ )
+		{
+		k = j + i;
+		if( k > MAXPOL )
+			break;
+
+		rmul( &ta[j], &quot, &temp ); /*tb[k] -= quot * ta[j];*/
+		rsub( &temp, &tb[k], &tb[k] );
+		}
+	tq[i].n = quot.n;
+	tq[i].d = quot.d;
+	}
+/* Send quotient to output array. */
+polmov( tq, MAXPOL, c );
+
+done:
+
+/* Restore allocated memory. */
+free(tq);
+free(tb);
+free(ta);
+return( sing );
+}
+
+
+
+
+/* Change of variables
+ * Substitute a(y) for the variable x in b(x).
+ * x = a(y)
+ * c(x) = b(x) = b(a(y)).
+ */
+
+void polsbt( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+int i, j, k, n2;
+fract temp;
+fract *p;
+
+/* 0th degree term:
+ */
+polclr( pt1, MAXPOL );
+pt1[0].n = b[0].n;
+pt1[0].d = b[0].d;
+
+polclr( pt2, MAXPOL );
+pt2[0].n = 1.0;
+pt2[0].d = 1.0;
+n2 = 0;
+p = &b[1];
+
+for( i=1; i<=nb; i++ )
+	{
+/* Form ith power of a. */
+	polmul( a, na, pt2, n2, pt2 );
+	n2 += na;
+/* Add the ith coefficient of b times the ith power of a. */
+	for( j=0; j<=n2; j++ )
+		{
+		if( j > MAXPOL )
+			break;
+		rmul( &pt2[j], p, &temp ); /*pt1[j] += b[i] * pt2[j];*/
+		radd( &temp, &pt1[j], &pt1[j] );
+		}
+	++p;
+	}
+
+k = n2 + nb;
+if( k > MAXPOL )
+	k = MAXPOL;
+for( i=0; i<=k; i++ )
+	{
+	c[i].n = pt1[i].n;
+	c[i].d = pt1[i].d;
+	}
+}
+
+
+
+
+/* Evaluate polynomial a(t) at t = x.
+ */
+void poleva( a, na, x, s )
+fract a[];
+int na;
+fract *x;
+fract *s;
+{
+int i;
+fract temp;
+
+s->n = a[na].n;
+s->d = a[na].d;
+for( i=na-1; i>=0; i-- )
+	{
+	rmul( s, x, &temp ); /*s = s * x + a[i];*/
+	radd( &a[i], &temp, s );
+	}
+}
+

libm/double/pow.c

@@ -0,0 +1,756 @@
+/*							pow.c
+ *
+ *	Power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, z, pow();
+ *
+ * z = pow( x, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes x raised to the yth power.  Analytically,
+ *
+ *      x**y  =  exp( y log(x) ).
+ *
+ * Following Cody and Waite, this program uses a lookup table
+ * of 2**-i/16 and pseudo extended precision arithmetic to
+ * obtain an extra three bits of accuracy in both the logarithm
+ * and the exponential.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -26,26       30000      4.2e-16      7.7e-17
+ *    DEC      -26,26       60000      4.8e-17      9.1e-18
+ * 1/26 < x < 26, with log(x) uniformly distributed.
+ * -26 < y < 26, y uniformly distributed.
+ *    IEEE     0,8700       30000      1.5e-14      2.1e-15
+ * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * pow overflow     x**y > MAXNUM      INFINITY
+ * pow underflow   x**y < 1/MAXNUM       0.0
+ * pow domain      x<0 and y noninteger  0.0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+static char fname[] = {"pow"};
+
+#define SQRTH 0.70710678118654752440
+
+#ifdef UNK
+static double P[] = {
+  4.97778295871696322025E-1,
+  3.73336776063286838734E0,
+  7.69994162726912503298E0,
+  4.66651806774358464979E0
+};
+static double Q[] = {
+/* 1.00000000000000000000E0, */
+  9.33340916416696166113E0,
+  2.79999886606328401649E1,
+  3.35994905342304405431E1,
+  1.39995542032307539578E1
+};
+/* 2^(-i/16), IEEE precision */
+static double A[] = {
+  1.00000000000000000000E0,
+  9.57603280698573700036E-1,
+  9.17004043204671215328E-1,
+  8.78126080186649726755E-1,
+  8.40896415253714502036E-1,
+  8.05245165974627141736E-1,
+  7.71105412703970372057E-1,
+  7.38413072969749673113E-1,
+  7.07106781186547572737E-1,
+  6.77127773468446325644E-1,
+  6.48419777325504820276E-1,
+  6.20928906036742001007E-1,
+  5.94603557501360513449E-1,
+  5.69394317378345782288E-1,
+  5.45253866332628844837E-1,
+  5.22136891213706877402E-1,
+  5.00000000000000000000E-1
+};
+static double B[] = {
+ 0.00000000000000000000E0,
+ 1.64155361212281360176E-17,
+ 4.09950501029074826006E-17,
+ 3.97491740484881042808E-17,
+-4.83364665672645672553E-17,
+ 1.26912513974441574796E-17,
+ 1.99100761573282305549E-17,
+-1.52339103990623557348E-17,
+ 0.00000000000000000000E0
+};
+static double R[] = {
+ 1.49664108433729301083E-5,
+ 1.54010762792771901396E-4,
+ 1.33335476964097721140E-3,
+ 9.61812908476554225149E-3,
+ 5.55041086645832347466E-2,
+ 2.40226506959099779976E-1,
+ 6.93147180559945308821E-1
+};
+
+#define douba(k) A[k]
+#define doubb(k) B[k]
+#define MEXP 16383.0
+#ifdef DENORMAL
+#define MNEXP -17183.0
+#else
+#define MNEXP -16383.0
+#endif
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0037776,0156313,0175332,0163602,
+0040556,0167577,0052366,0174245,
+0040766,0062753,0175707,0055564,
+0040625,0052035,0131344,0155636,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041025,0052644,0154404,0105155,
+0041337,0177772,0007016,0047646,
+0041406,0062740,0154273,0020020,
+0041137,0177054,0106127,0044555,
+};
+static unsigned short A[] = {
+0040200,0000000,0000000,0000000,
+0040165,0022575,0012444,0103314,
+0040152,0140306,0163735,0022071,
+0040140,0146336,0166052,0112341,
+0040127,0042374,0145326,0116553,
+0040116,0022214,0012437,0102201,
+0040105,0063452,0010525,0003333,
+0040075,0004243,0117530,0006067,
+0040065,0002363,0031771,0157145,
+0040055,0054076,0165102,0120513,
+0040045,0177326,0124661,0050471,
+0040036,0172462,0060221,0120422,
+0040030,0033760,0050615,0134251,
+0040021,0141723,0071653,0010703,
+0040013,0112701,0161752,0105727,
+0040005,0125303,0063714,0044173,
+0040000,0000000,0000000,0000000
+};
+static unsigned short B[] = {
+0000000,0000000,0000000,0000000,
+0021473,0040265,0153315,0140671,
+0121074,0062627,0042146,0176454,
+0121413,0003524,0136332,0066212,
+0121767,0046404,0166231,0012553,
+0121257,0015024,0002357,0043574,
+0021736,0106532,0043060,0056206,
+0121310,0020334,0165705,0035326,
+0000000,0000000,0000000,0000000
+};
+
+static unsigned short R[] = {
+0034173,0014076,0137624,0115771,
+0035041,0076763,0003744,0111311,
+0035656,0141766,0041127,0074351,
+0036435,0112533,0073611,0116664,
+0037143,0054106,0134040,0152223,
+0037565,0176757,0176026,0025551,
+0040061,0071027,0173721,0147572
+};
+
+/*
+static double R[] = {
+0.14928852680595608186e-4,
+0.15400290440989764601e-3,
+0.13333541313585784703e-2,
+0.96181290595172416964e-2,
+0.55504108664085595326e-1,
+0.24022650695909537056e0,
+0.69314718055994529629e0
+};
+*/
+#define douba(k) (*(double *)&A[(k)<<2])
+#define doubb(k) (*(double *)&B[(k)<<2])
+#define MEXP 2031.0
+#define MNEXP -2031.0
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x5cf0,0x7f5b,0xdb99,0x3fdf,
+0xdf15,0xea9e,0xddef,0x400d,
+0xeb6f,0x7f78,0xccbd,0x401e,
+0x9b74,0xb65c,0xaa83,0x4012,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x914e,0x9b20,0xaab4,0x4022,
+0xc9f5,0x41c1,0xffff,0x403b,
+0x6402,0x1b17,0xccbc,0x4040,
+0xe92e,0x918a,0xffc5,0x402b,
+};
+static unsigned short A[] = {
+0x0000,0x0000,0x0000,0x3ff0,
+0x90da,0xa2a4,0xa4af,0x3fee,
+0xa487,0xdcfb,0x5818,0x3fed,
+0x529c,0xdd85,0x199b,0x3fec,
+0xd3ad,0x995a,0xe89f,0x3fea,
+0xf090,0x82a3,0xc491,0x3fe9,
+0xa0db,0x422a,0xace5,0x3fe8,
+0x0187,0x73eb,0xa114,0x3fe7,
+0x3bcd,0x667f,0xa09e,0x3fe6,
+0x5429,0xdd48,0xab07,0x3fe5,
+0x2a27,0xd536,0xbfda,0x3fe4,
+0x3422,0x4c12,0xdea6,0x3fe3,
+0xb715,0x0a31,0x06fe,0x3fe3,
+0x6238,0x6e75,0x387a,0x3fe2,
+0x517b,0x3c7d,0x72b8,0x3fe1,
+0x890f,0x6cf9,0xb558,0x3fe0,
+0x0000,0x0000,0x0000,0x3fe0
+};
+static unsigned short B[] = {
+0x0000,0x0000,0x0000,0x0000,
+0x3707,0xd75b,0xed02,0x3c72,
+0xcc81,0x345d,0xa1cd,0x3c87,
+0x4b27,0x5686,0xe9f1,0x3c86,
+0x6456,0x13b2,0xdd34,0xbc8b,
+0x42e2,0xafec,0x4397,0x3c6d,
+0x82e4,0xd231,0xf46a,0x3c76,
+0x8a76,0xb9d7,0x9041,0xbc71,
+0x0000,0x0000,0x0000,0x0000
+};
+static unsigned short R[] = {
+0x937f,0xd7f2,0x6307,0x3eef,
+0x9259,0x60fc,0x2fbe,0x3f24,
+0xef1d,0xc84a,0xd87e,0x3f55,
+0x33b7,0x6ef1,0xb2ab,0x3f83,
+0x1a92,0xd704,0x6b08,0x3fac,
+0xc56d,0xff82,0xbfbd,0x3fce,
+0x39ef,0xfefa,0x2e42,0x3fe6
+};
+
+#define douba(k) (*(double *)&A[(k)<<2])
+#define doubb(k) (*(double *)&B[(k)<<2])
+#define MEXP 16383.0
+#ifdef DENORMAL
+#define MNEXP -17183.0
+#else
+#define MNEXP -16383.0
+#endif
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3fdf,0xdb99,0x7f5b,0x5cf0,
+0x400d,0xddef,0xea9e,0xdf15,
+0x401e,0xccbd,0x7f78,0xeb6f,
+0x4012,0xaa83,0xb65c,0x9b74
+};
+static unsigned short Q[] = {
+0x4022,0xaab4,0x9b20,0x914e,
+0x403b,0xffff,0x41c1,0xc9f5,
+0x4040,0xccbc,0x1b17,0x6402,
+0x402b,0xffc5,0x918a,0xe92e
+};
+static unsigned short A[] = {
+0x3ff0,0x0000,0x0000,0x0000,
+0x3fee,0xa4af,0xa2a4,0x90da,
+0x3fed,0x5818,0xdcfb,0xa487,
+0x3fec,0x199b,0xdd85,0x529c,
+0x3fea,0xe89f,0x995a,0xd3ad,
+0x3fe9,0xc491,0x82a3,0xf090,
+0x3fe8,0xace5,0x422a,0xa0db,
+0x3fe7,0xa114,0x73eb,0x0187,
+0x3fe6,0xa09e,0x667f,0x3bcd,
+0x3fe5,0xab07,0xdd48,0x5429,
+0x3fe4,0xbfda,0xd536,0x2a27,
+0x3fe3,0xdea6,0x4c12,0x3422,
+0x3fe3,0x06fe,0x0a31,0xb715,
+0x3fe2,0x387a,0x6e75,0x6238,
+0x3fe1,0x72b8,0x3c7d,0x517b,
+0x3fe0,0xb558,0x6cf9,0x890f,
+0x3fe0,0x0000,0x0000,0x0000
+};
+static unsigned short B[] = {
+0x0000,0x0000,0x0000,0x0000,
+0x3c72,0xed02,0xd75b,0x3707,
+0x3c87,0xa1cd,0x345d,0xcc81,
+0x3c86,0xe9f1,0x5686,0x4b27,
+0xbc8b,0xdd34,0x13b2,0x6456,
+0x3c6d,0x4397,0xafec,0x42e2,
+0x3c76,0xf46a,0xd231,0x82e4,
+0xbc71,0x9041,0xb9d7,0x8a76,
+0x0000,0x0000,0x0000,0x0000
+};
+static unsigned short R[] = {
+0x3eef,0x6307,0xd7f2,0x937f,
+0x3f24,0x2fbe,0x60fc,0x9259,
+0x3f55,0xd87e,0xc84a,0xef1d,
+0x3f83,0xb2ab,0x6ef1,0x33b7,
+0x3fac,0x6b08,0xd704,0x1a92,
+0x3fce,0xbfbd,0xff82,0xc56d,
+0x3fe6,0x2e42,0xfefa,0x39ef
+};
+
+#define douba(k) (*(double *)&A[(k)<<2])
+#define doubb(k) (*(double *)&B[(k)<<2])
+#define MEXP 16383.0
+#ifdef DENORMAL
+#define MNEXP -17183.0
+#else
+#define MNEXP -16383.0
+#endif
+#endif
+
+/* log2(e) - 1 */
+#define LOG2EA 0.44269504088896340736
+
+#define F W
+#define Fa Wa
+#define Fb Wb
+#define G W
+#define Ga Wa
+#define Gb u
+#define H W
+#define Ha Wb
+#define Hb Wb
+
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double fabs ( double );
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double powi ( double, int );
+extern int signbit ( double );
+extern int isnan ( double );
+extern int isfinite ( double );
+static double reduc ( double );
+#else
+double floor(), fabs(), frexp(), ldexp();
+double polevl(), p1evl(), powi();
+int signbit(), isnan(), isfinite();
+static double reduc();
+#endif
+extern double MAXNUM;
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+#ifdef NANS
+extern double NAN;
+#endif
+#ifdef MINUSZERO
+extern double NEGZERO;
+#endif
+
+double pow( x, y )
+double x, y;
+{
+double w, z, W, Wa, Wb, ya, yb, u;
+/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
+double aw, ay, wy;
+int e, i, nflg, iyflg, yoddint;
+
+if( y == 0.0 )
+	return( 1.0 );
+#ifdef NANS
+if( isnan(x) )
+	return( x );
+if( isnan(y) )
+	return( y );
+#endif
+if( y == 1.0 )
+	return( x );
+
+
+#ifdef INFINITIES
+if( !isfinite(y) && (x == 1.0 || x == -1.0) )
+	{
+	mtherr( "pow", DOMAIN );
+#ifdef NANS
+	return( NAN );
+#else
+	return( INFINITY );
+#endif
+	}
+#endif
+
+if( x == 1.0 )
+	return( 1.0 );
+
+if( y >= MAXNUM )
+	{
+#ifdef INFINITIES
+	if( x > 1.0 )
+		return( INFINITY );
+#else
+	if( x > 1.0 )
+		return( MAXNUM );
+#endif
+	if( x > 0.0 && x < 1.0 )
+		return( 0.0);
+	if( x < -1.0 )
+		{
+#ifdef INFINITIES
+		return( INFINITY );
+#else
+		return( MAXNUM );
+#endif
+		}
+	if( x > -1.0 && x < 0.0 )
+		return( 0.0 );
+	}
+if( y <= -MAXNUM )
+	{
+	if( x > 1.0 )
+		return( 0.0 );
+#ifdef INFINITIES
+	if( x > 0.0 && x < 1.0 )
+		return( INFINITY );
+#else
+	if( x > 0.0 && x < 1.0 )
+		return( MAXNUM );
+#endif
+	if( x < -1.0 )
+		return( 0.0 );
+#ifdef INFINITIES
+	if( x > -1.0 && x < 0.0 )
+		return( INFINITY );
+#else
+	if( x > -1.0 && x < 0.0 )
+		return( MAXNUM );
+#endif
+	}
+if( x >= MAXNUM )
+	{
+#if INFINITIES
+	if( y > 0.0 )
+		return( INFINITY );
+#else
+	if( y > 0.0 )
+		return( MAXNUM );
+#endif
+	return(0.0);
+	}
+/* Set iyflg to 1 if y is an integer.  */
+iyflg = 0;
+w = floor(y);
+if( w == y )
+	iyflg = 1;
+
+/* Test for odd integer y.  */
+yoddint = 0;
+if( iyflg )
+	{
+	ya = fabs(y);
+	ya = floor(0.5 * ya);
+	yb = 0.5 * fabs(w);
+	if( ya != yb )
+		yoddint = 1;
+	}
+
+if( x <= -MAXNUM )
+	{
+	if( y > 0.0 )
+		{
+#ifdef INFINITIES
+		if( yoddint )
+			return( -INFINITY );
+		return( INFINITY );
+#else
+		if( yoddint )
+			return( -MAXNUM );
+		return( MAXNUM );
+#endif
+		}
+	if( y < 0.0 )
+		{
+#ifdef MINUSZERO
+		if( yoddint )
+			return( NEGZERO );
+#endif
+		return( 0.0 );
+		}
+ 	}
+
+nflg = 0;	/* flag = 1 if x<0 raised to integer power */
+if( x <= 0.0 )
+	{
+	if( x == 0.0 )
+		{
+		if( y < 0.0 )
+			{
+#ifdef MINUSZERO
+			if( signbit(x) && yoddint )
+				return( -INFINITY );
+#endif
+#ifdef INFINITIES
+			return( INFINITY );
+#else
+			return( MAXNUM );
+#endif
+			}
+		if( y > 0.0 )
+			{
+#ifdef MINUSZERO
+			if( signbit(x) && yoddint )
+				return( NEGZERO );
+#endif
+			return( 0.0 );
+			}
+		return( 1.0 );
+		}
+	else
+		{
+		if( iyflg == 0 )
+			{ /* noninteger power of negative number */
+			mtherr( fname, DOMAIN );
+#ifdef NANS
+			return(NAN);
+#else
+			return(0.0L);
+#endif
+			}
+		nflg = 1;
+		}
+	}
+
+/* Integer power of an integer.  */
+
+if( iyflg )
+	{
+	i = w;
+	w = floor(x);
+	if( (w == x) && (fabs(y) < 32768.0) )
+		{
+		w = powi( x, (int) y );
+		return( w );
+		}
+	}
+
+if( nflg )
+	x = fabs(x);
+
+/* For results close to 1, use a series expansion.  */
+w = x - 1.0;
+aw = fabs(w);
+ay = fabs(y);
+wy = w * y;
+ya = fabs(wy);
+if((aw <= 1.0e-3 && ay <= 1.0)
+   || (ya <= 1.0e-3 && ay >= 1.0))
+	{
+	z = (((((w*(y-5.)/720. + 1./120.)*w*(y-4.) + 1./24.)*w*(y-3.)
+		+ 1./6.)*w*(y-2.) + 0.5)*w*(y-1.) )*wy + wy + 1.;
+	goto done;
+	}
+/* These are probably too much trouble.  */
+#if 0
+w = y * log(x);
+if (aw > 1.0e-3 && fabs(w) < 1.0e-3)
+  {
+    z = ((((((
+    w/7. + 1.)*w/6. + 1.)*w/5. + 1.)*w/4. + 1.)*w/3. + 1.)*w/2. + 1.)*w + 1.;
+    goto done;
+  }
+
+if(ya <= 1.0e-3 && aw <= 1.0e-4)
+  {
+    z = (((((
+	     wy*1./720.
+	     + (-w*1./48. + 1./120.) )*wy
+	    + ((w*17./144. - 1./12.)*w + 1./24.) )*wy
+	   + (((-w*5./16. + 7./24.)*w - 1./4.)*w + 1./6.) )*wy
+	  + ((((w*137./360. - 5./12.)*w + 11./24.)*w - 1./2.)*w + 1./2.) )*wy
+	 + (((((-w*1./6. + 1./5.)*w - 1./4)*w + 1./3.)*w -1./2.)*w ) )*wy
+	   + wy + 1.0;
+    goto done;
+  }
+#endif
+
+/* separate significand from exponent */
+x = frexp( x, &e );
+
+#if 0
+/* For debugging, check for gross overflow. */
+if( (e * y)  > (MEXP + 1024) )
+	goto overflow;
+#endif
+
+/* Find significand of x in antilog table A[]. */
+i = 1;
+if( x <= douba(9) )
+	i = 9;
+if( x <= douba(i+4) )
+	i += 4;
+if( x <= douba(i+2) )
+	i += 2;
+if( x >= douba(1) )
+	i = -1;
+i += 1;
+
+
+/* Find (x - A[i])/A[i]
+ * in order to compute log(x/A[i]):
+ *
+ * log(x) = log( a x/a ) = log(a) + log(x/a)
+ *
+ * log(x/a) = log(1+v),  v = x/a - 1 = (x-a)/a
+ */
+x -= douba(i);
+x -= doubb(i/2);
+x /= douba(i);
+
+
+/* rational approximation for log(1+v):
+ *
+ * log(1+v)  =  v  -  v**2/2  +  v**3 P(v) / Q(v)
+ */
+z = x*x;
+w = x * ( z * polevl( x, P, 3 ) / p1evl( x, Q, 4 ) );
+w = w - ldexp( z, -1 );   /*  w - 0.5 * z  */
+
+/* Convert to base 2 logarithm:
+ * multiply by log2(e)
+ */
+w = w + LOG2EA * w;
+/* Note x was not yet added in
+ * to above rational approximation,
+ * so do it now, while multiplying
+ * by log2(e).
+ */
+z = w + LOG2EA * x;
+z = z + x;
+
+/* Compute exponent term of the base 2 logarithm. */
+w = -i;
+w = ldexp( w, -4 );	/* divide by 16 */
+w += e;
+/* Now base 2 log of x is w + z. */
+
+/* Multiply base 2 log by y, in extended precision. */
+
+/* separate y into large part ya
+ * and small part yb less than 1/16
+ */
+ya = reduc(y);
+yb = y - ya;
+
+
+F = z * y  +  w * yb;
+Fa = reduc(F);
+Fb = F - Fa;
+
+G = Fa + w * ya;
+Ga = reduc(G);
+Gb = G - Ga;
+
+H = Fb + Gb;
+Ha = reduc(H);
+w = ldexp( Ga+Ha, 4 );
+
+/* Test the power of 2 for overflow */
+if( w > MEXP )
+	{
+#ifndef INFINITIES
+	mtherr( fname, OVERFLOW );
+#endif
+#ifdef INFINITIES
+	if( nflg && yoddint )
+	  return( -INFINITY );
+	return( INFINITY );
+#else
+	if( nflg && yoddint )
+	  return( -MAXNUM );
+	return( MAXNUM );
+#endif
+	}
+
+if( w < (MNEXP - 1) )
+	{
+#ifndef DENORMAL
+	mtherr( fname, UNDERFLOW );
+#endif
+#ifdef MINUSZERO
+	if( nflg && yoddint )
+	  return( NEGZERO );
+#endif
+	return( 0.0 );
+	}
+
+e = w;
+Hb = H - Ha;
+
+if( Hb > 0.0 )
+	{
+	e += 1;
+	Hb -= 0.0625;
+	}
+
+/* Now the product y * log2(x)  =  Hb + e/16.0.
+ *
+ * Compute base 2 exponential of Hb,
+ * where -0.0625 <= Hb <= 0.
+ */
+z = Hb * polevl( Hb, R, 6 );  /*    z  =  2**Hb - 1    */
+
+/* Express e/16 as an integer plus a negative number of 16ths.
+ * Find lookup table entry for the fractional power of 2.
+ */
+if( e < 0 )
+	i = 0;
+else
+	i = 1;
+i = e/16 + i;
+e = 16*i - e;
+w = douba( e );
+z = w + w * z;      /*    2**-e * ( 1 + (2**Hb-1) )    */
+z = ldexp( z, i );  /* multiply by integer power of 2 */
+
+done:
+
+/* Negate if odd integer power of negative number */
+if( nflg && yoddint )
+	{
+#ifdef MINUSZERO
+	if( z == 0.0 )
+		z = NEGZERO;
+	else
+#endif
+		z = -z;
+	}
+return( z );
+}
+
+
+/* Find a multiple of 1/16 that is within 1/16 of x. */
+static double reduc(x)
+double x;
+{
+double t;
+
+t = ldexp( x, 4 );
+t = floor( t );
+t = ldexp( t, -4 );
+return(t);
+}