Totally rework the math library, this time based on the MacOs X

math library (which is itself based on the math lib from FreeBSD).
 -Erik

include/math.h

@@ -1,212 +1,121 @@
-/*							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
- *
- *
- * 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.
+/* Declarations for math functions.
+   Copyright (C) 1991,92,93,95,96,97,98,99,2001 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library 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
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, write to the Free
+   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+   02111-1307 USA.  */
+
+/*
+ *	ISO C99 Standard: 7.12 Mathematics	<math.h>
  */
 
-
 #ifndef	_MATH_H
 #define	_MATH_H	1
 
 #include <features.h>
-#include <bits/huge_val.h>
-
-/* 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
 
+__BEGIN_DECLS
 
-/* 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
+/* Get machine-dependent HUGE_VAL value (returned on overflow).
+   On all IEEE754 machines, this is +Infinity.  */
+#include <bits/huge_val.h>
 
-/* Complex numeral.  */
-#ifdef __UCLIBC_HAS_LIBM_DOUBLE__
-typedef struct
-	{
-	double r;
-	double i;
-	} cmplx;
+/* Get machine-dependent NAN value (returned for some domain errors).  */
+#ifdef	 __USE_ISOC99
+# include <bits/nan.h>
 #endif
+/* Get general and ISO C99 specific information.  */
+#include <bits/mathdef.h>
 
-#ifdef __UCLIBC_HAS_LIBM_FLOAT__
-typedef struct
-	{
-	float r;
-	float i;
-	} cmplxf;
-#endif
 
-#ifdef __UCLIBC_HAS_LIBM_LONG_DOUBLE__
-/* Long double complex numeral.  */
-typedef struct
-	{
-	long double r;
-	long double i;
-	} cmplxl;
-#endif
+/* The file <bits/mathcalls.h> contains the prototypes for all the
+   actual math functions.  These macros are used for those prototypes,
+   so we can easily declare each function as both `name' and `__name',
+   and can declare the float versions `namef' and `__namef'.  */
 
+#define __MATHCALL(function,suffix, args)	\
+  __MATHDECL (_Mdouble_,function,suffix, args)
+#define __MATHDECL(type, function,suffix, args) \
+  __MATHDECL_1(type, function,suffix, args); \
+  __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
+#define __MATHCALLX(function,suffix, args, attrib)	\
+  __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
+#define __MATHDECLX(type, function,suffix, args, attrib) \
+  __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
+  __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
+#define __MATHDECL_1(type, function,suffix, args) \
+  extern type __MATH_PRECNAME(function,suffix) args __THROW
 
+#define _Mdouble_ 		double
+#define __MATH_PRECNAME(name,r)	__CONCAT(name,r)
+#include <bits/mathcalls.h>
+#undef	_Mdouble_
+#undef	__MATH_PRECNAME
+
+#if defined __USE_MISC || defined __USE_ISOC99
 
-/* Variable for error reporting.  See mtherr.c.  */
-__BEGIN_DECLS
-extern int mtherr(char *name, int code);
-extern int merror;
-__END_DECLS
 
+/* Include the file of declarations again, this time using `float'
+   instead of `double' and appending f to each function name.  */
 
-/* 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
+# ifndef _Mfloat_
+#  define _Mfloat_		float
+# endif
+# define _Mdouble_ 		_Mfloat_
+# ifdef __STDC__
+#  define __MATH_PRECNAME(name,r) name##f##r
+# else
+#  define __MATH_PRECNAME(name,r) name/**/f/**/r
+# endif
+# include <bits/mathcalls.h>
+# undef	_Mdouble_
+# undef	__MATH_PRECNAME
+
+# if (__STDC__ - 0 || __GNUC__ - 0) && !defined __NO_LONG_DOUBLE_MATH
+/* Include the file of declarations again, this time using `long double'
+   instead of `double' and appending l to each function name.  */
+
+#  ifndef _Mlong_double_
+#   define _Mlong_double_	long double
+#  endif
+#  define _Mdouble_ 		_Mlong_double_
+#  ifdef __STDC__
+#   define __MATH_PRECNAME(name,r) name##l##r
+#  else
+#   define __MATH_PRECNAME(name,r) name/**/l/**/r
+#  endif
+#  include <bits/mathcalls.h>
+#  undef _Mdouble_
+#  undef __MATH_PRECNAME
+
+# endif /* __STDC__ || __GNUC__ */
+
+#endif	/* Use misc or ISO C99.  */
+#undef	__MATHDECL_1
+#undef	__MATHDECL
+#undef	__MATHCALL
+
+
+#if defined __USE_MISC || defined __USE_XOPEN
+/* This variable is used by `gamma' and `lgamma'.  */
+extern int signgam;
 #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
+/* ISO C99 defines some generic macros which work on any data type.  */
+#if __USE_ISOC99
 
 /* Get the architecture specific values describing the floating-point
    evaluation.  The following symbols will get defined:
@@ -257,47 +166,139 @@ enum
   };
 
 /* Return number of classification appropriate for X.  */
-#ifdef __UCLIBC_HAS_LIBM_DOUBLE__
-#  define fpclassify(x) \
-     (sizeof (x) == sizeof (float) ?					      \
-        __fpclassifyf (x)						      \
-      : sizeof (x) == sizeof (double) ?					      \
-        __fpclassify (x) : __fpclassifyl (x))
-#else
+# ifdef __NO_LONG_DOUBLE_MATH
 #  define fpclassify(x) \
      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
-#endif
-
-__BEGIN_DECLS
+# else
+#  define fpclassify(x) \
+     (sizeof (x) == sizeof (float)					      \
+      ? __fpclassifyf (x)						      \
+      : sizeof (x) == sizeof (double)					      \
+      ? __fpclassify (x) : __fpclassifyl (x))
+# endif
 
-#ifdef __UCLIBC_HAS_LIBM_DOUBLE__
 /* Return nonzero value if sign of X is negative.  */
-extern int signbit(double x);
+# ifdef __NO_LONG_DOUBLE_MATH
+#  define signbit(x) \
+     (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
+# else
+#  define signbit(x) \
+     (sizeof (x) == sizeof (float)					      \
+      ? __signbitf (x)							      \
+      : sizeof (x) == sizeof (double)					      \
+      ? __signbit (x) : __signbitl (x))
+# endif
+
 /* Return nonzero value if X is not +-Inf or NaN.  */
-extern int isfinite(double x);
+# ifdef __NO_LONG_DOUBLE_MATH
+#  define isfinite(x) \
+     (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
+# else
+#  define isfinite(x) \
+     (sizeof (x) == sizeof (float)					      \
+      ? __finitef (x)							      \
+      : sizeof (x) == sizeof (double)					      \
+      ? __finite (x) : __finitel (x))
+# endif
+
 /* 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 */
-extern int isnan(double x);
-#define isinf(x) \
-     (sizeof (x) == sizeof (float) ?					      \
-        __isinff (x)							      \
-      : sizeof (x) == sizeof (double) ?					      \
-        __isinf (x) : __isinfl (x))
-#else
+
+/* Return nonzero value if X is a NaN.  We could use `fpclassify' but
+   we already have this functions `__isnan' and it is faster.  */
+# ifdef __NO_LONG_DOUBLE_MATH
+#  define isnan(x) \
+     (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
+# else
+#  define isnan(x) \
+     (sizeof (x) == sizeof (float)					      \
+      ? __isnanf (x)							      \
+      : sizeof (x) == sizeof (double)					      \
+      ? __isnan (x) : __isnanl (x))
+# endif
+
+/* 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
+
+/* Bitmasks for the math_errhandling macro.  */
+# define MATH_ERRNO	1	/* errno set by math functions.  */
+# define MATH_ERREXCEPT	2	/* Exceptions raised by math functions.  */
+
+#endif /* Use ISO C99.  */
+
+#ifdef	__USE_MISC
+/* Support for various different standard error handling behaviors.  */
+typedef enum
+{
+  _IEEE_ = -1,	/* According to IEEE 754/IEEE 854.  */
+  _SVID_,	/* According to System V, release 4.  */
+  _XOPEN_,	/* Nowadays also Unix98.  */
+  _POSIX_,
+  _ISOC_	/* Actually this is ISO C99.  */
+} _LIB_VERSION_TYPE;
+
+/* This variable can be changed at run-time to any of the values above to
+   affect floating point error handling behavior (it may also be necessary
+   to change the hardware FPU exception settings).  */
+extern _LIB_VERSION_TYPE _LIB_VERSION;
 #endif
 
 
-#ifdef __UCLIBC_HAS_LIBM_LONG_DOUBLE__
-/* Return nonzero value if sign of X is negative.  */
-extern int signbitl(long double x);
-/* Return nonzero value if X is not +-Inf or NaN.  */
-extern int isfinitel(long double x);
-/* Return nonzero value if X is a NaN */
-extern int isnanl(long double x);
-#endif
+#ifdef __USE_SVID
+/* In SVID error handling, `matherr' is called with this description
+   of the exceptional condition.
+
+   We have a problem when using C++ since `exception' is a reserved
+   name in C++.  */
+# ifdef __cplusplus
+struct __exception
+# else
+struct exception
+# endif
+  {
+    int type;
+    char *name;
+    double arg1;
+    double arg2;
+    double retval;
+  };
+
+# ifdef __cplusplus
+extern int matherr (struct __exception *__exc) throw ();
+# else
+extern int matherr (struct exception *__exc);
+# endif
+
+# define X_TLOSS	1.41484755040568800000e+16
+
+/* Types of exceptions in the `type' field.  */
+# define DOMAIN		1
+# define SING		2
+# define OVERFLOW	3
+# define UNDERFLOW	4
+# define TLOSS		5
+# define PLOSS		6
+
+/* SVID mode specifies returning this large value instead of infinity.  */
+# define HUGE		3.40282347e+38F
+
+#else	/* !SVID */
+
+# ifdef __USE_XOPEN
+/* X/Open wants another strange constant.  */
+#  define MAXFLOAT	3.40282347e+38F
+# endif
+
+#endif	/* SVID */
 
 
 /* Some useful constants.  */
@@ -316,257 +317,48 @@ extern int isnanl(long double x);
 # define M_SQRT2	1.41421356237309504880	/* sqrt(2) */
 # define M_SQRT1_2	0.70710678118654752440	/* 1/sqrt(2) */
 #endif
+
+/* The above constants are not adequate for computation using `long double's.
+   Therefore we provide as an extension constants with similar names as a
+   GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 #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
+# define M_El		2.7182818284590452353602874713526625L  /* e */
+# define M_LOG2El	1.4426950408889634073599246810018922L  /* log_2 e */
+# define M_LOG10El	0.4342944819032518276511289189166051L  /* log_10 e */
+# define M_LN2l		0.6931471805599453094172321214581766L  /* log_e 2 */
+# define M_LN10l	2.3025850929940456840179914546843642L  /* log_e 10 */
+# define M_PIl		3.1415926535897932384626433832795029L  /* pi */
+# define M_PI_2l	1.5707963267948966192313216916397514L  /* pi/2 */
+# define M_PI_4l	0.7853981633974483096156608458198757L  /* pi/4 */
+# define M_1_PIl	0.3183098861837906715377675267450287L  /* 1/pi */
+# define M_2_PIl	0.6366197723675813430755350534900574L  /* 2/pi */
+# define M_2_SQRTPIl	1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
+# define M_SQRT2l	1.4142135623730950488016887242096981L  /* sqrt(2) */
+# define M_SQRT1_2l	0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 #endif
 
 
+/* When compiling in strict ISO C compatible mode we must not use the
+   inline functions since they, among other things, do not set the
+   `errno' variable correctly.  */
+#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
+# define __NO_MATH_INLINES	1
+#endif
 
-#ifdef __UCLIBC_HAS_LIBM_DOUBLE__
-/* 7.12.4 Trigonometric functions */
-extern double acos(double x);
-extern double asin(double x);
-extern double atan(double x);
-extern double atan2(double y, double x);
-extern double cos(double x);
-extern double sin(double x);
-extern double tan(double x);
-
-/* 7.12.5 Hyperbolic functions */
-extern double acosh(double x);
-extern double asinh(double x);
-extern double atanh(double x);
-extern double cosh(double x);
-extern double sinh(double x);
-extern double tanh(double x);
-
-/* 7.12.6 Exponential and logarithmic functions */
-extern double exp(double x);
-extern double exp2(double x);
-extern double expm1(double x);
-extern double frexp(double value, int *ex);
-extern int ilogb(double x);
-extern double ldexp(double x, int ex);
-extern double log(double x);
-extern double log10(double x);
-extern double log1p(double x);
-extern double log2(double x);
-extern double logb(double x);
-extern double modf(double value, double *iptr);
-extern double scalbn(double x, int n);
-extern double scalbln(double x, long int n);
-
-/* 7.12.7 Power and absolute-value functions */
-extern double fabs(double x);
-extern double hypot(double x, double y);
-extern double pow(double x, double y);
-extern double sqrt(double x);
-
-/* 7.12.8 Error and gamma functions */
-extern double erf(double x);
-extern double erfc(double x);
-extern double lgamma(double x);
-extern double tgamma(double x);
-
-/* 7.12.9 Nearest integer functions */
-extern double ceil(double x);
-extern double floor(double x);
-extern double nearbyint(double x);
-extern double rint(double x);
-extern long int lrint(double x);
-extern long long int llrint(double x);
-extern double round(double x);
-extern long int lround(double x);
-extern long long int llround(double x);
-extern double trunc(double x);
-
-/* 7.12.10 Remainder functions */
-extern double fmod(double x, double y);
-extern double remainder(double x, double y);
-extern double remquo(double x, double y, int *quo);
-
-/* 7.12.11 Manipulation functions */
-extern double copysign(double x, double y);
-extern double nan(const char *tagp);
-extern double nextafter(double x, double y);
-
-/* 7.12.12 Maximum, minimum, and positive difference functions */
-extern double fdim(double x, double y);
-extern double fmax(double x, double y);
-extern double fmin(double x, double y);
-
-/* 7.12.13 Floating multiply-add */
-extern double fma(double x, double y, double z);
-#endif	
-
-#ifdef __UCLIBC_HAS_LIBM_FLOAT__
-/* 7.12.4 Trigonometric functions */
-extern float acosf(float x);
-extern float asinf(float x);
-extern float atanf(float x);
-extern float atan2f(float y, float x);
-extern float cosf(float x);
-extern float sinf(float x);
-extern float tanf(float x);
-
-/* 7.12.5 Hyperbolic functions */
-extern float acoshf(float x);
-extern float asinhf(float x);
-extern float atanhf(float x);
-extern float coshf(float x);
-extern float sinhf(float x);
-extern float tanhf(float x);
-
-/* 7.12.6 Exponential and logarithmic functions */
-extern float expf(float x);
-extern float exp2f(float x);
-extern float expm1f(float x);
-extern float frexpf(float value, int *ex);
-extern int ilogbf(float x);
-extern float ldexpf(float x, int ex);
-extern float logf(float x);
-extern float log10f(float x);
-extern float log1pf(float x);
-extern float log2f(float x);
-extern float logbf(float x);
-extern float modff(float value, float *iptr);
-extern float scalbnf(float x, int n);
-extern float scalblnf(float x, long int n);
-
-/* 7.12.7 Power and absolute-value functions */
-extern float fabsf(float x);
-extern float hypotf(float x, float y);
-extern float powf(float x, float y);
-extern float sqrtf(float x);
-
-/* 7.12.8 Error and gamma functions */
-extern float erff(float x);
-extern float erfcf(float x);
-extern float lgammaf(float x);
-extern float tgammaf(float x);
-
-/* 7.12.9 Nearest integer functions */
-extern float ceilf(float x);
-extern float floorf(float x);
-extern float nearbyintf(float x);
-extern float rintf(float x);
-extern long int lrintf(float x);
-extern long long int llrintf(float x);
-extern float roundf(float x);
-extern long int lroundf(float x);
-extern long long int llroundf(float x);
-extern float truncf(float x);
-
-/* 7.12.10 Remainder functions */
-extern float fmodf(float x, float y);
-extern float remainderf(float x, float y);
-extern float remquof(float x, float y, int *quo);
-
-/* 7.12.11 Manipulation functions */
-extern float copysignf(float x, float y);
-extern float nanf(const char *tagp);
-extern float nextafterf(float x, float y);
-
-/* 7.12.12 Maximum, minimum, and positive difference functions */
-extern float fdimf(float x, float y);
-extern float fmaxf(float x, float y);
-extern float fminf(float x, float y);
-
-/* 7.12.13 Floating multiply-add */
-extern float fmaf(float x, float y, float z);
-#endif	
-
-#ifdef __UCLIBC_HAS_LIBM_LONG_DOUBLE__
-/* 7.12.4 Trigonometric functions */
-extern long double acosl(long double x);
-extern long double asinl(long double x);
-extern long double atanl(long double x);
-extern long double atan2l(long double y, long double x);
-extern long double cosl(long double x);
-extern long double sinl(long double x);
-extern long double tanl(long double x);
-
-/* 7.12.5 Hyperbolic functions */
-extern long double acoshl(long double x);
-extern long double asinhl(long double x);
-extern long double atanhl(long double x);
-extern long double coshl(long double x);
-extern long double sinhl(long double x);
-extern long double tanhl(long double x);
-
-/* 7.12.6 Exponential and logarithmic functions */
-extern long double expl(long double x);
-extern long double exp2l(long double x);
-extern long double expm1l(long double x);
-extern long double frexpl(long double value, int *ex);
-extern int ilogbl(long double x);
-extern long double ldexpl(long double x, int ex);
-extern long double logl(long double x);
-extern long double log10l(long double x);
-extern long double log1pl(long double x);
-extern long double log2l(long double x);
-extern long double logbl(long double x);
-extern long double modfl(long double value, long double *iptr);
-extern long double scalbnl(long double x, int n);
-extern long double scalblnl(long double x, long int n);
-
-/* 7.12.7 Power and absolute-value functions */
-extern long double fabsl(long double x);
-extern long double hypotl(long double x, long double y);
-extern long double powl(long double x, long double y);
-extern long double sqrtl(long double x);
-
-/* 7.12.8 Error and gamma functions */
-extern long double erfl(long double x);
-extern long double erfcl(long double x);
-extern long double lgammal(long double x);
-extern long double tgammal(long double x);
-
-/* 7.12.9 Nearest integer functions */
-extern long double ceill(long double x);
-extern long double floorl(long double x);
-extern long double nearbyintl(long double x);
-extern long double rintl(long double x);
-extern long int lrintl(long double x);
-extern long long int llrintl(long double x);
-extern long double roundl(long double x);
-extern long int lroundl(long double x);
-extern long long int llroundl(long double x);
-extern long double truncl(long double x);
-
-/* 7.12.10 Remainder functions */
-extern long double fmodl(long double x, long double y);
-extern long double remainderl(long double x, long double y);
-extern long double remquol(long double x, long double y, int *quo);
-
-/* 7.12.11 Manipulation functions */
-extern long double copysignl(long double x, long double y);
-extern long double nanl(const char *tagp);
-extern long double nextafterl(long double x, long double y);
-extern long double nexttowardl(long double x, long double y);
-
-/* 7.12.12 Maximum, minimum, and positive difference functions */
-extern long double fdiml(long double x, long double y);
-extern long double fmaxl(long double x, long double y);
-extern long double fminl(long double x, long double y);
-
-/* 7.12.13 Floating multiply-add */
-extern long double fmal(long double x, long double y, long double z);
+/* Get machine-dependent inline versions (if there are any).  */
+#ifdef __USE_EXTERN_INLINES
+# include <bits/mathinline.h>
 #endif
 
-/* 7.12.14 Comparison macros */
+
+#if __USE_ISOC99
+/* ISO C99 defines some macros to compare number while taking care
+   for unordered numbers.  Since many FPUs provide special
+   instructions to support these operations and these tests are
+   defined in <bits/mathinline.h>, we define the generic macros at
+   this late point and only if they are not defined yet.  */
+
+/* Return nonzero value if X is greater than Y.  */
 # ifndef isgreater
 #  define isgreater(x, y) \
   (__extension__							      \
@@ -614,6 +406,9 @@ extern long double fmal(long double x, long double y, long double z);
       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 # endif
 
+#endif
+
 __END_DECLS
 
+
 #endif /* math.h  */

libm/Makefile

@@ -25,31 +25,43 @@ include $(TOPDIR)Rules.mak
 LIBM=libm.a
 LIBM_SHARED=libm.so
 LIBM_SHARED_FULLNAME=libm-$(MAJOR_VERSION).$(MINOR_VERSION).so
+TARGET_CC= $(TOPDIR)extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
+TARGET_CFLAGS+=-D_IEEE_LIBM -D_ISOC99_SOURCE -D_SVID_SOURCE
 
-DIRS=
-ifeq ($(strip $(HAS_LIBM_FLOAT)),true)
-	DIRS+=float
+ifeq ($(strip $(DO_C89_ONLY)),true)
+CSRC =   FIXME
+else
+CSRC =   e_acos.c e_acosh.c e_asin.c e_atan2.c e_atanh.c e_cosh.c\
+         e_exp.c e_fmod.c e_gamma.c e_gamma_r.c e_hypot.c e_j0.c\
+         e_j1.c e_jn.c e_lgamma.c e_lgamma_r.c e_log.c e_log10.c\
+         e_pow.c e_remainder.c e_rem_pio2.c e_scalb.c e_sinh.c\
+         e_sqrt.c k_cos.c k_rem_pio2.c k_sin.c k_standard.c k_tan.c\
+         s_asinh.c s_atan.c s_cbrt.c s_ceil.c s_copysign.c s_cos.c\
+         s_erf.c s_expm1.c s_fabs.c s_finite.c s_floor.c s_frexp.c\
+         s_ilogb.c s_ldexp.c s_lib_version.c s_log1p.c s_logb.c\
+         s_matherr.c s_modf.c s_nextafter.c s_rint.c s_scalbn.c\
+         s_signgam.c s_significand.c s_sin.c s_tan.c s_tanh.c\
+         w_acos.c w_acosh.c w_asin.c w_atan2.c w_atanh.c w_cabs.c\
+         w_cosh.c w_drem.c w_exp.c w_fmod.c w_gamma.c w_gamma_r.c\
+         w_hypot.c w_j0.c w_j1.c w_jn.c w_lgamma.c w_lgamma_r.c\
+         w_log.c w_log10.c w_pow.c w_remainder.c w_scalb.c w_sinh.c\
+         w_sqrt.c ceilfloor.c fpmacros.c frexpldexp.c logb.c rndint.c\
+         scalb.c sign.c
 endif
-ifeq ($(strip $(HAS_LIBM_DOUBLE)),true)
-	DIRS+=double
-endif
-ifeq ($(strip $(HAS_LIBM_LONG_DOUBLE)),true)
-	DIRS+=ldouble
-endif
-ALL_SUBDIRS = float double ldouble
+COBJS=$(patsubst %.c,%.o, $(CSRC))
+OBJS=$(COBJS)
+
 
-all: $(LIBM)
 
-$(LIBM): subdirs
+all: $(OBJS) $(LIBM)
+
+$(LIBM): ar-target
 	@if [ -f $(LIBM) ] ; then \
 		install -d $(TOPDIR)lib; \
 		rm -f $(TOPDIR)lib/$(LIBM); \
 		install -m 644 $(LIBM) $(TOPDIR)lib; \
 	fi;
 
-tags:
-	ctags -R
-
 shared: all
 	if [ -f $(LIBM) ] ; then \
 	    $(TARGET_CC) $(TARGET_LDFLAGS) -nostdlib -shared -o $(LIBM_SHARED_FULLNAME) \
@@ -61,18 +73,18 @@ shared: all
 	    (cd $(TOPDIR)lib; ln -sf $(LIBM_SHARED_FULLNAME) $(LIBM_SHARED).$(MAJOR_VERSION)); \
 	fi;
 
-subdirs: $(patsubst %, _dir_%, $(DIRS))
-subdirs_clean: $(patsubst %, _dirclean_%, $(ALL_SUBDIRS))
-
-$(patsubst %, _dir_%, $(DIRS)) : dummy
-	$(MAKE) -C $(patsubst _dir_%, %, $@)
+ar-target: $(OBJS)
+	$(AR) $(ARFLAGS) $(LIBM) $(OBJS)
 
-$(patsubst %, _dirclean_%, $(ALL_SUBDIRS)) : dummy
-	$(MAKE) -C $(patsubst _dirclean_%, %, $@) clean
+$(COBJS): %.o : %.c
+	$(TARGET_CC) $(TARGET_CFLAGS) -c $< -o $@
+	$(STRIPTOOL) -x -R .note -R .comment $*.o
 
-clean: subdirs_clean
-	rm -f *.[oa] *~ core $(LIBM_SHARED)* $(LIBM_SHARED_FULLNAME)*
+$(OBJ): Makefile
 
-.PHONY: dummy
+tags:
+	ctags -R
 
+clean: 
+	rm -f *.[oa] *~ core $(LIBM_SHARED)* $(LIBM_SHARED_FULLNAME)*
 

libm/README

@@ -1,42 +1,16 @@
-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"
+The routines included in this math library are derived from the
+math library for Apple's MacOS X/Darwin math library, which was
+itself swiped from FreeBSD.  The original copyright information
+is as follows:
 
-It has been ported to fit into uClibc and generally behave 
-by Erik Andersen <andersen@lineo.com>, <andersee@debian.org>
-  5 May, 2001
+	Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 
---------------------------------------------------
+	Developed at SunPro, a Sun Microsystems, Inc. business.
+	Permission to use, copy, modify, and distribute this
+	software is freely granted, provided that this notice 
+	is preserved.
 
-   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.
+It has been ported to work with uClibc and generally behave 
+by Erik Andersen <andersen@codepoet.org>
+  22 May, 2001
 
-   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/ceilfloor.c

@@ -0,0 +1,179 @@
+#if defined(__ppc__)
+/*******************************************************************************
+*                                                                              *
+*      File ceilfloor.c,                                                       *
+*      Function ceil(x) and floor(x),                                          *
+*      Implementation of ceil and floor for the PowerPC.                       *
+*                                                                              *
+*      Copyright © 1991 Apple Computer, Inc.  All rights reserved.             *
+*                                                                              *
+*      Written by Ali Sazegari, started on November 1991,                      *
+*                                                                              *
+*      based on math.h, library code for Macintoshes with a 68881/68882        *
+*      by Jim Thomas.                                                          *
+*                                                                              *
+*      W A R N I N G:  This routine expects a 64 bit double model.             *
+*                                                                              *
+*      December 03 1992: first rs6000 port.                                    *
+*      July     14 1993: comment changes and addition of #pragma fenv_access.  *
+*	 May      06 1997: port of the ibm/taligent ceil and floor routines.     *
+*	 April    11 2001: first port to os x using gcc.				 *
+*	 June	    13 2001: replaced __setflm with in-line assembly			 *
+*                                                                              *
+*******************************************************************************/
+
+#if !defined(__ppc__)
+#define asm(x)
+#endif
+
+static const double        twoTo52  = 4503599627370496.0;
+static const unsigned long signMask = 0x80000000ul;
+
+typedef union
+      {
+      struct {
+#if defined(__BIG_ENDIAN__)
+	unsigned long int hi;
+	unsigned long int lo;
+#else
+	unsigned long int lo;
+	unsigned long int hi;
+#endif
+      } words;
+      double dbl;
+      } DblInHex;
+
+/*******************************************************************************
+*            Functions needed for the computation.                             *
+*******************************************************************************/
+
+/*******************************************************************************
+*      Ceil(x) returns the smallest integer not less than x.                   *
+*******************************************************************************/
+
+double ceil ( double x )
+	{
+	DblInHex xInHex,OldEnvironment;
+	register double y;
+	register unsigned long int xhi;
+	register int target;
+	
+	xInHex.dbl = x;
+	xhi = xInHex.words.hi & 0x7fffffffUL;	  // xhi is the high half of |x|
+	target = ( xInHex.words.hi < signMask );
+	
+	if ( xhi < 0x43300000ul ) 
+/*******************************************************************************
+*      Is |x| < 2.0^52?                                                        *
+*******************************************************************************/
+		{
+		if ( xhi < 0x3ff00000ul ) 
+/*******************************************************************************
+*      Is |x| < 1.0?                                                           *
+*******************************************************************************/
+			{
+			if ( ( xhi | xInHex.words.lo ) == 0ul )  // zero x is exact case
+				return ( x );
+			else 
+				{			                // inexact case
+				asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+				OldEnvironment.words.lo |= 0x02000000ul;
+				asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+				if ( target )
+					return ( 1.0 );
+				else
+					return ( -0.0 );
+				}
+			}
+/*******************************************************************************
+*      Is 1.0 < |x| < 2.0^52?                                                  *
+*******************************************************************************/
+		if ( target ) 
+			{
+			y = ( x + twoTo52 ) - twoTo52;          // round at binary pt.
+			if ( y < x )
+				return ( y + 1.0 );
+			else
+				return ( y );
+			}
+		
+		else 
+			{
+			y = ( x - twoTo52 ) + twoTo52;          // round at binary pt.
+			if ( y < x )
+				return ( y + 1.0 );
+			else
+				return ( y );
+			}
+		}
+/*******************************************************************************
+*      |x| >= 2.0^52 or x is a NaN.                                            *
+*******************************************************************************/
+	return ( x );
+	}
+
+/*******************************************************************************
+*      Floor(x) returns the largest integer not greater than x.                *
+*******************************************************************************/
+
+double floor ( double x )
+	{
+	DblInHex xInHex,OldEnvironment;
+	register double y;
+	register unsigned long int xhi;
+	register long int target;
+	
+	xInHex.dbl = x;
+	xhi = xInHex.words.hi & 0x7fffffffUL;	  // xhi is the high half of |x|
+	target = ( xInHex.words.hi < signMask );
+	
+	if ( xhi < 0x43300000ul ) 
+/*******************************************************************************
+*      Is |x| < 2.0^52?                                                        *
+*******************************************************************************/
+		{
+		if ( xhi < 0x3ff00000ul ) 
+/*******************************************************************************
+*      Is |x| < 1.0?                                                           *
+*******************************************************************************/
+			{
+			if ( ( xhi | xInHex.words.lo ) == 0ul )  // zero x is exact case
+				return ( x );
+			else 
+				{			                // inexact case
+				asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+				OldEnvironment.words.lo |= 0x02000000ul;
+				asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+				if ( target )
+					return ( 0.0 );
+				else
+					return ( -1.0 );
+				}
+			}
+/*******************************************************************************
+*      Is 1.0 < |x| < 2.0^52?                                                  *
+*******************************************************************************/
+		if ( target ) 
+			{
+			y = ( x + twoTo52 ) - twoTo52;          // round at binary pt.
+			if ( y > x )
+				return ( y - 1.0 );
+			else
+				return ( y );
+			}
+		
+		else 
+			{
+			y = ( x - twoTo52 ) + twoTo52;          // round at binary pt.
+			if ( y > x )
+				return ( y - 1.0 );
+			else
+				return ( y );
+			}
+		}
+/*******************************************************************************
+*      |x| >= 2.0^52 or x is a NaN.                                            *
+*******************************************************************************/
+	return ( x );
+	}
+#endif /* __ppc__ */

libm/double/Makefile

@@ -1,114 +0,0 @@
-# Makefile for uClibc's math library
-# Copyright (C) 2001 by Lineo, inc.
-#
-# This math library is derived primarily from the Cephes Math Library,
-# copyright by Stephen L. Moshier <moshier@world.std.com>
-#
-# 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
-#
-
-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 noncephes.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) $(TARGET_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
-	$(TARGET_CC) -o time-it time-it.o
-
-time-it.o: time-it.c
-	$(TARGET_CC) -O2 -c time-it.c
-
-dcalc: dcalc.o libmd.a
-	$(TARGET_CC) -o dcalc dcalc.o libmd.a
-
-mtst: mtst.o libmd.a
-	$(TARGET_CC) -v -o mtst mtst.o libmd.a
-
-mtst.o: mtst.c
-	$(TARGET_CC) -O2 -Wall -c mtst.c
-
-dtestvec: dtestvec.o libmd.a
-	$(TARGET_CC) -o dtestvec dtestvec.o libmd.a
-
-dtestvec.o: dtestvec.c
-	$(TARGET_CC) -g -c dtestvec.c
-
-monot: monot.o libmd.a
-	$(TARGET_CC) -o monot monot.o libmd.a
-
-monot.o: monot.c
-	$(TARGET_CC) -g -c monot.c
-
-paranoia: paranoia.o setprec.o libmd.a
-	$(TARGET_CC) -o paranoia paranoia.o setprec.o libmd.a
-
-paranoia.o: paranoia.c
-	$(TARGET_CC) $(TARGET_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

@@ -1,5845 +0,0 @@
-/*							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/acos.c

@@ -1,58 +0,0 @@
-/*							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
- */
-
-#define __USE_BSD
-#include <math.h>
-
-double acos(double x)
-{
-    if (x < -0.5) {
-	return (M_PI - 2.0 * asin( sqrt((1+x)/2) ));
-    }
-    if (x > 0.5) {
-	return (2.0 * asin(  sqrt((1-x)/2) ));
-    }
-
-    return(M_PI_2 - asin(x));
-}

libm/double/acosh.c

@@ -1,167 +0,0 @@
-/*							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

@@ -1,965 +0,0 @@
-/*							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

@@ -1,110 +0,0 @@
-/*							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

@@ -1,324 +0,0 @@
-/*							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

@@ -1,165 +0,0 @@
-/*							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

@@ -1,393 +0,0 @@
-/*							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

@@ -1,156 +0,0 @@
-/*							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

@@ -1,263 +0,0 @@
-/*							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

@@ -1,74 +0,0 @@
-/* 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

@@ -1,201 +0,0 @@
-/*							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

@@ -1,64 +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.
- *
- */
-
-/*								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

@@ -1,142 +0,0 @@
-/*							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

@@ -1,82 +0,0 @@
-/*							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

@@ -1,200 +0,0 @@
-/*							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

@@ -1,149 +0,0 @@
-/*	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

@@ -1,1043 +0,0 @@
-/*							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

@@ -1,461 +0,0 @@
-/*							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

@@ -1,63 +0,0 @@
-/* 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

@@ -1,252 +0,0 @@
-/*							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

@@ -1,83 +0,0 @@
-/*							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

@@ -1,104 +0,0 @@
-/*							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

@@ -1,392 +0,0 @@
-/*							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

@@ -1,1512 +0,0 @@
-/* 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

@@ -1,77 +0,0 @@
-/*		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

@@ -1,543 +0,0 @@
-
-/* 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

@@ -1,1062 +0,0 @@
-/*							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

@@ -1,181 +0,0 @@
-/*							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

@@ -1,148 +0,0 @@
-/*							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

@@ -1,148 +0,0 @@
-/*							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

@@ -1,195 +0,0 @@
-/*							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

@@ -1,171 +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.
- *
- */
-
-/*							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

@@ -1,234 +0,0 @@
-/*							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

@@ -1,37 +0,0 @@
-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

@@ -1,251 +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.
- */
- 
-
-#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

@@ -1,203 +0,0 @@
-/*							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

@@ -1,223 +0,0 @@
-/*							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

@@ -1,183 +0,0 @@
-/*							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

@@ -1,208 +0,0 @@
-/*							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

@@ -1,56 +0,0 @@
-/*							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

@@ -1,263 +0,0 @@
-/*							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

@@ -1,237 +0,0 @@
-/*							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

@@ -1,237 +0,0 @@
-/*							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

@@ -1,531 +0,0 @@
-/*							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);
-	}
-}
-
-/**********************************************************************/
-/*
- * trunc is just a slightly modified version of floor above.
- */
-
-double trunc(double x)
-{
-	union {
-		double y;
-		unsigned short sh[4];
-	} u;
-	unsigned short *p;
-	int e;
-
-#ifdef UNK
-	mtherr( "trunc", 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 )
-		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];
-
-	return(u.y);
-}

libm/double/fltest.c

@@ -1,272 +0,0 @@
-/* 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

@@ -1,18 +0,0 @@
-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

@@ -1,259 +0,0 @@
-/* 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

@@ -1,515 +0,0 @@
-/*							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

@@ -1,685 +0,0 @@
-/*							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

@@ -1,130 +0,0 @@
-/*							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

@@ -1,232 +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
-*/
-#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

@@ -1,460 +0,0 @@
-/*							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

@@ -1,386 +0,0 @@
-/*							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

@@ -1,397 +0,0 @@
-/*							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

@@ -1,402 +0,0 @@
-/*							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

@@ -1,210 +0,0 @@
-/*							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

@@ -1,187 +0,0 @@
-/*							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

@@ -1,409 +0,0 @@
-/*							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

@@ -1,313 +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
- */
-
-
-/*
-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

@@ -1,237 +0,0 @@
-/*							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

@@ -1,116 +0,0 @@
-/*							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

@@ -1,543 +0,0 @@
-/*							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

@@ -1,515 +0,0 @@
-/*							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

@@ -1,133 +0,0 @@
-/*							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

@@ -1,884 +0,0 @@
-/*							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

@@ -1,333 +0,0 @@
-/*							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

@@ -1,335 +0,0 @@
-/*							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

@@ -1,255 +0,0 @@
-/*							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

@@ -1,243 +0,0 @@
-
-/* 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

@@ -1,82 +0,0 @@
-/*		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

@@ -1,341 +0,0 @@
-/*							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

@@ -1,250 +0,0 @@
-/*							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

@@ -1,348 +0,0 @@
-/*							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

@@ -1,86 +0,0 @@
-/*							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

@@ -1,85 +0,0 @@
-/*							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

@@ -1,469 +0,0 @@
-/*							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

@@ -1,61 +0,0 @@
-/*							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

@@ -1,122 +0,0 @@
-/* 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

@@ -1,308 +0,0 @@
-
-/* 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

@@ -1,102 +0,0 @@
-/*							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

@@ -1,61 +0,0 @@
-/*							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

@@ -1,464 +0,0 @@
-/*   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

@@ -1,222 +0,0 @@
-/*							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

@@ -1,481 +0,0 @@
-/*							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

@@ -1,417 +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
- *
- */
-
-
-/*
-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/noncephes.c

@@ -1,127 +0,0 @@
-/*
- * This file contains math functions missing from the Cephes library.
- *
- * May 22, 2001         Manuel Novoa III
- *
- *    Added modf and fmod.
- *
- * TODO:
- *    Break out functions into seperate object files as is done
- *       by (for example) stdio.  Also do this with cephes files.
- */
-
-#include <math.h>
-#include <errno.h>
-
-#undef UNK
-
-/* Set this to nonzero to enable a couple of shortcut tests in fmod. */
-#define SPEED_OVER_SIZE 0
-
-/**********************************************************************/
-
-double modf(double x, double *iptr)
-{
-	double y;
-
-#ifdef UNK
-	mtherr( "modf", DOMAIN );
-	*iptr = NAN;
-	return NAN;
-#endif
-
-#ifdef NANS
-	if( isnan(x) ) {
-		*iptr = x;
-		return x;
-	}
-#endif
-
-#ifdef INFINITIES
-	if(!isfinite(x)) {
-		*iptr = x;				/* Matches glibc, but returning NAN */
-		return 0;				/* makes more sense to me... */
-	}
-#endif
-
-	if (x < 0) {				/* Round towards 0. */
-		y = ceil(x);
-	} else {
-		y = floor(x);
-	}
-
-	*iptr = y;
-	return x - y;
-}
-
-/**********************************************************************/
-
-extern double NAN;
-
-double fmod(double x, double y)
-{
-	double z;
-	int negative, ex, ey;
-
-#ifdef UNK
-	mtherr( "fmod", DOMAIN );
-	return NAN;
-#endif
-
-#ifdef NANS
-	if( isnan(x) || isnan(y) ) {
-		errno = EDOM;
-		return NAN; 
-	}
-#endif
-
-	if (y == 0) {
-		errno = EDOM;
-		return NAN; 
-	}
-
-#ifdef INFINITIES
-	if(!isfinite(x)) {
-		errno = EDOM;
-		return NAN;
-	}
-
-#if SPEED_OVER_SIZE
-	if(!isfinite(y)) {
-		return x;
-	}
-#endif
-#endif
-
-#if SPEED_OVER_SIZE
-	if (x == 0) {
-		return 0;
-	}
-#endif
-
-	negative = 0;
-	if (x < 0) {
-		negative = 1;
-		x = -x;
-	}
-
-	if (y < 0) {
-		y = -y;
-	}
-
-	frexp(y,&ey);
-	while (x >= y) {
-		frexp(x,&ex);
-		z = ldexp(y,ex-ey);
-		if (z > x) {
-			z /= 2;
-		}
-		x -= z;
-	}
-
-	if (negative) {
-		return -x;
-	} else {
-		return x;
-	}
-}

libm/double/paranoia.c

@@ -1,2156 +0,0 @@
-/*	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

@@ -1,184 +0,0 @@
-/*							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

@@ -1,223 +0,0 @@
-/*							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

@@ -1,97 +0,0 @@
-/*							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.
- *
- */
-
-
-/*
-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

@@ -1,309 +0,0 @@
-
-/* 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

@@ -1,227 +0,0 @@
-/*							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

@@ -1,467 +0,0 @@
-/*							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

@@ -1,471 +0,0 @@
-/*							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);
-}
-