442 lines
14 KiB
C
442 lines
14 KiB
C
/* Declarations for math functions.
|
|
Copyright (C) 1991-1993,1995-1999,2001,2002,2004 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
|
|
/* 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
|
|
# 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 */
|