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- /* Declarations for math functions.
- Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006
- 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>
- __BEGIN_DECLS
- /* Get machine-dependent HUGE_VAL value (returned on overflow).
- On all IEEE754 machines, this is +Infinity. */
- #include <bits/huge_val.h>
- #ifdef __USE_ISOC99
- # include <bits/huge_valf.h>
- # include <bits/huge_vall.h>
- /* Get machine-dependent INFINITY value. */
- # include <bits/inf.h>
- /* Get machine-dependent NAN value (returned for some domain errors). */
- # include <bits/nan.h>
- #endif /* __USE_ISOC99 */
- /* Get general and ISO C99 specific information. */
- #include <bits/mathdef.h>
- /* 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)
- # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
- # define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
- #include <bits/mathcalls.h>
- #undef _Mdouble_
- #undef _Mdouble_BEGIN_NAMESPACE
- #undef _Mdouble_END_NAMESPACE
- #undef __MATH_PRECNAME
- #if defined __USE_MISC || defined __USE_ISOC99
- /* Include the file of declarations again, this time using `float'
- instead of `double' and appending f to each function name. */
- # 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
- # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
- # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
- # include <bits/mathcalls.h>
- # undef _Mdouble_
- # undef _Mdouble_BEGIN_NAMESPACE
- # undef _Mdouble_END_NAMESPACE
- # undef __MATH_PRECNAME
- # if (__STDC__ - 0 || __GNUC__ - 0) \
- && (!defined __NO_LONG_DOUBLE_MATH || defined __LDBL_COMPAT)
- # ifdef __LDBL_COMPAT
- # ifdef __USE_ISOC99
- extern float __nldbl_nexttowardf (float __x, long double __y)
- __THROW __attribute__ ((__const__));
- # ifdef __REDIRECT_NTH
- extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
- __nldbl_nexttowardf)
- __attribute__ ((__const__));
- extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
- nextafter) __attribute__ ((__const__));
- extern long double __REDIRECT_NTH (nexttowardl,
- (long double __x, long double __y),
- nextafter) __attribute__ ((__const__));
- # endif
- # endif
- /* Include the file of declarations again, this time using `long double'
- instead of `double' and appending l to each function name. */
- # undef __MATHDECL_1
- # define __MATHDECL_2(type, function,suffix, args, alias) \
- extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
- args, alias)
- # define __MATHDECL_1(type, function,suffix, args) \
- __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
- # endif
- # 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
- # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
- # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
- # include <bits/mathcalls.h>
- # undef _Mdouble_
- # undef _Mdouble_BEGIN_NAMESPACE
- # undef _Mdouble_END_NAMESPACE
- # 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
- /* ISO C99 defines some generic macros which work on any data type. */
- #ifdef __USE_ISOC99
- /* Get the architecture specific values describing the floating-point
- evaluation. The following symbols will get defined:
- float_t floating-point type at least as wide as `float' used
- to evaluate `float' expressions
- double_t floating-point type at least as wide as `double' used
- to evaluate `double' expressions
- FLT_EVAL_METHOD
- Defined to
- 0 if `float_t' is `float' and `double_t' is `double'
- 1 if `float_t' and `double_t' are `double'
- 2 if `float_t' and `double_t' are `long double'
- else `float_t' and `double_t' are unspecified
- INFINITY representation of the infinity value of type `float'
- FP_FAST_FMA
- FP_FAST_FMAF
- FP_FAST_FMAL
- If defined it indicates that the `fma' function
- generally executes about as fast as a multiply and an add.
- This macro is defined only iff the `fma' function is
- implemented directly with a hardware multiply-add instructions.
- FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
- FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
- DECIMAL_DIG Number of decimal digits supported by conversion between
- decimal and all internal floating-point formats.
- */
- /* All floating-point numbers can be put in one of these categories. */
- enum
- {
- FP_NAN,
- # define FP_NAN FP_NAN
- FP_INFINITE,
- # define FP_INFINITE FP_INFINITE
- FP_ZERO,
- # define FP_ZERO FP_ZERO
- FP_SUBNORMAL,
- # define FP_SUBNORMAL FP_SUBNORMAL
- FP_NORMAL
- # define FP_NORMAL FP_NORMAL
- };
- /* Return number of classification appropriate for X. */
- # ifdef __NO_LONG_DOUBLE_MATH
- # define fpclassify(x) \
- (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
- # else
- # define fpclassify(x) \
- (sizeof (x) == sizeof (float) \
- ? __fpclassifyf (x) \
- : sizeof (x) == sizeof (double) \
- ? __fpclassify (x) : __fpclassifyl (x))
- # endif
- /* Return nonzero value if sign of X is negative. */
- # 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. */
- # 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. 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 __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. */
- #if defined __USE_BSD || defined __USE_XOPEN
- # define M_E 2.7182818284590452354 /* e */
- # define M_LOG2E 1.4426950408889634074 /* log_2 e */
- # define M_LOG10E 0.43429448190325182765 /* log_10 e */
- # define M_LN2 0.69314718055994530942 /* log_e 2 */
- # define M_LN10 2.30258509299404568402 /* log_e 10 */
- # define M_PI 3.14159265358979323846 /* pi */
- # define M_PI_2 1.57079632679489661923 /* pi/2 */
- # define M_PI_4 0.78539816339744830962 /* pi/4 */
- # define M_1_PI 0.31830988618379067154 /* 1/pi */
- # define M_2_PI 0.63661977236758134308 /* 2/pi */
- # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
- # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
- # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
- #endif
- /* 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 2.7182818284590452353602874713526625L /* e */
- # define M_LOG2El 1.4426950408889634073599246810018921L /* 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
- #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
- /* ISO C99 defines some macros to compare number while taking care for
- unordered numbers. Many FPUs provide special instructions to support
- these operations. Generic support in GCC for these as builtins went
- in before 3.0.0, but not all cpus added their patterns. We define
- versions that use the builtins here, and <bits/mathinline.h> will
- undef/redefine as appropriate for the specific GCC version in use. */
- # define isgreater(x, y) __builtin_isgreater(x, y)
- # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
- # define isless(x, y) __builtin_isless(x, y)
- # define islessequal(x, y) __builtin_islessequal(x, y)
- # define islessgreater(x, y) __builtin_islessgreater(x, y)
- # define isunordered(u, v) __builtin_isunordered(u, v)
- #endif
- /* Get machine-dependent inline versions (if there are any). */
- #ifdef __USE_EXTERN_INLINES
- # include <bits/mathinline.h>
- #endif
- #ifdef __USE_ISOC99
- /* If we've still got undefined comparison macros, provide defaults. */
- /* Return nonzero value if X is greater than Y. */
- # ifndef isgreater
- # define isgreater(x, y) \
- (__extension__ \
- ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
- !isunordered (__x, __y) && __x > __y; }))
- # endif
- /* Return nonzero value if X is greater than or equal to Y. */
- # ifndef isgreaterequal
- # define isgreaterequal(x, y) \
- (__extension__ \
- ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
- !isunordered (__x, __y) && __x >= __y; }))
- # endif
- /* Return nonzero value if X is less than Y. */
- # ifndef isless
- # define isless(x, y) \
- (__extension__ \
- ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
- !isunordered (__x, __y) && __x < __y; }))
- # endif
- /* Return nonzero value if X is less than or equal to Y. */
- # ifndef islessequal
- # define islessequal(x, y) \
- (__extension__ \
- ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
- !isunordered (__x, __y) && __x <= __y; }))
- # endif
- /* Return nonzero value if either X is less than Y or Y is less than X. */
- # ifndef islessgreater
- # define islessgreater(x, y) \
- (__extension__ \
- ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
- !isunordered (__x, __y) && (__x < __y || __y < __x); }))
- # endif
- /* Return nonzero value if arguments are unordered. */
- # ifndef isunordered
- # define isunordered(u, v) \
- (__extension__ \
- ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
- fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
- # endif
- #endif
- __END_DECLS
- #endif /* math.h */
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