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/* Declarations for math functions.
Copyright (C) 1991-1993,1995-1999,2001,2002 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>
/* 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>
/* 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. */
#if __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 1.4426950408889634073599246810018922L /* 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
/* Get machine-dependent inline versions (if there are any). */
#ifdef __USE_EXTERN_INLINES
# include <bits/mathinline.h>
#endif
#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__ \
({ __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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