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math.h
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/* Declarations for math functions.
Copyright (C) 1991-2022 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, see
<https://www.gnu.org/licenses/>. */
/*
* ISO C99 Standard: 7.12 Mathematics <math.h>
*/
#ifndef _MATH_H
#define _MATH_H 1
#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
#include <bits/libc-header-start.h>
#if defined log && defined __GNUC__
# warning A macro called log was already defined when <math.h> was included.
# warning This will cause compilation problems.
#endif
__BEGIN_DECLS
/* Get definitions of __intmax_t and __uintmax_t. */
#include <bits/types.h>
/* Get machine-dependent vector math functions declarations. */
#include <bits/math-vector.h>
/* Gather machine dependent type support. */
#include <bits/floatn.h>
/* Value returned on overflow. With IEEE 754 floating point, this is
+Infinity, otherwise the largest representable positive value. */
#if __GNUC_PREREQ (3, 3)
# define HUGE_VAL (__builtin_huge_val ())
#else
/* This may provoke compiler warnings, and may not be rounded to
+Infinity in all IEEE 754 rounding modes, but is the best that can
be done in ISO C while remaining a constant expression. 10,000 is
greater than the maximum (decimal) exponent for all supported
floating-point formats and widths. */
# define HUGE_VAL 1e10000
#endif
#ifdef __USE_ISOC99
# if __GNUC_PREREQ (3, 3)
# define HUGE_VALF (__builtin_huge_valf ())
# define HUGE_VALL (__builtin_huge_vall ())
# else
# define HUGE_VALF 1e10000f
# define HUGE_VALL 1e10000L
# endif
#endif
#if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F16 (__builtin_huge_valf16 ())
#endif
#if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F32 (__builtin_huge_valf32 ())
#endif
#if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F64 (__builtin_huge_valf64 ())
#endif
#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F128 (__builtin_huge_valf128 ())
#endif
#if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F32X (__builtin_huge_valf32x ())
#endif
#if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F64X (__builtin_huge_valf64x ())
#endif
#if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F128X (__builtin_huge_valf128x ())
#endif
#ifdef __USE_ISOC99
/* IEEE positive infinity. */
# if __GNUC_PREREQ (3, 3)
# define INFINITY (__builtin_inff ())
# else
# define INFINITY HUGE_VALF
# endif
/* IEEE Not A Number. */
# if __GNUC_PREREQ (3, 3)
# define NAN (__builtin_nanf (""))
# else
/* This will raise an "invalid" exception outside static initializers,
but is the best that can be done in ISO C while remaining a
constant expression. */
# define NAN (0.0f / 0.0f)
# endif
#endif /* __USE_ISOC99 */
#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Signaling NaN macros, if supported. */
# if __GNUC_PREREQ (3, 3)
# define SNANF (__builtin_nansf (""))
# define SNAN (__builtin_nans (""))
# define SNANL (__builtin_nansl (""))
# endif
#endif
#if (__HAVE_FLOAT16 \
&& __GLIBC_USE (IEC_60559_TYPES_EXT) \
&& (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
# define SNANF16 (__builtin_nansf16 (""))
#endif
#if (__HAVE_FLOAT32 \
&& __GLIBC_USE (IEC_60559_TYPES_EXT) \
&& (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
# define SNANF32 (__builtin_nansf32 (""))
#endif
#if (__HAVE_FLOAT64 \
&& __GLIBC_USE (IEC_60559_TYPES_EXT) \
&& (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
# define SNANF64 (__builtin_nansf64 (""))
#endif
#if (__HAVE_FLOAT128 \
&& __GLIBC_USE (IEC_60559_TYPES_EXT) \
&& (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
# define SNANF128 (__builtin_nansf128 (""))
#endif
#if (__HAVE_FLOAT32X \
&& __GLIBC_USE (IEC_60559_TYPES_EXT) \
&& (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
# define SNANF32X (__builtin_nansf32x (""))
#endif
#if (__HAVE_FLOAT64X \
&& __GLIBC_USE (IEC_60559_TYPES_EXT) \
&& (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
# define SNANF64X (__builtin_nansf64x (""))
#endif
#if (__HAVE_FLOAT128X \
&& __GLIBC_USE (IEC_60559_TYPES_EXT) \
&& (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
# define SNANF128X (__builtin_nansf128x (""))
#endif
/* Get __GLIBC_FLT_EVAL_METHOD. */
#include <bits/flt-eval-method.h>
#ifdef __USE_ISOC99
/* Define the following typedefs.
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
*/
# if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
typedef float float_t;
typedef double double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 1
typedef double float_t;
typedef double double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 2
typedef long double float_t;
typedef long double double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 32
typedef _Float32 float_t;
typedef double double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 33
typedef _Float32x float_t;
typedef _Float32x double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 64
typedef _Float64 float_t;
typedef _Float64 double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 65
typedef _Float64x float_t;
typedef _Float64x double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 128
typedef _Float128 float_t;
typedef _Float128 double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 129
typedef _Float128x float_t;
typedef _Float128x double_t;
# else
# error "Unknown __GLIBC_FLT_EVAL_METHOD"
# endif
#endif
/* Define macros for the return values of ilogb and llogb, based on
__FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.
FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
FP_LLOGB0 Expands to a value returned by `llogb (0.0)'.
FP_LLOGBNAN Expands to a value returned by `llogb (NAN)'.
*/
#include <bits/fp-logb.h>
#ifdef __USE_ISOC99
# if __FP_LOGB0_IS_MIN
# define FP_ILOGB0 (-2147483647 - 1)
# else
# define FP_ILOGB0 (-2147483647)
# endif
# if __FP_LOGBNAN_IS_MIN
# define FP_ILOGBNAN (-2147483647 - 1)
# else
# define FP_ILOGBNAN 2147483647
# endif
#endif
#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
# if __WORDSIZE == 32
# define __FP_LONG_MAX 0x7fffffffL
# else
# define __FP_LONG_MAX 0x7fffffffffffffffL
# endif
# if __FP_LOGB0_IS_MIN
# define FP_LLOGB0 (-__FP_LONG_MAX - 1)
# else
# define FP_LLOGB0 (-__FP_LONG_MAX)
# endif
# if __FP_LOGBNAN_IS_MIN
# define FP_LLOGBNAN (-__FP_LONG_MAX - 1)
# else
# define FP_LLOGBNAN __FP_LONG_MAX
# endif
#endif
/* Get the architecture specific values describing the floating-point
evaluation. The following symbols will get defined:
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.
*/
#include <bits/fp-fast.h>
#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
/* Rounding direction macros for fromfp functions. */
enum
{
FP_INT_UPWARD =
# define FP_INT_UPWARD 0
FP_INT_UPWARD,
FP_INT_DOWNWARD =
# define FP_INT_DOWNWARD 1
FP_INT_DOWNWARD,
FP_INT_TOWARDZERO =
# define FP_INT_TOWARDZERO 2
FP_INT_TOWARDZERO,
FP_INT_TONEARESTFROMZERO =
# define FP_INT_TONEARESTFROMZERO 3
FP_INT_TONEARESTFROMZERO,
FP_INT_TONEAREST =
# define FP_INT_TONEAREST 4
FP_INT_TONEAREST,
};
#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 __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
#define __MATHCALL_VEC(function, suffix, args) \
__SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
__MATHCALL (function, suffix, args)
#define __MATHDECL_VEC(type, function,suffix, args) \
__SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
__MATHDECL(type, function,suffix, args)
#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_IMPL(type, function, suffix, args) \
extern type __MATH_PRECNAME(function,suffix) args __THROW
#define __MATHDECL_1(type, function, suffix, args) \
__MATHDECL_1_IMPL(type, function, suffix, args)
/* Ignore the alias by default. The alias is only useful with
redirections. */
#define __MATHDECL_ALIAS(type, function, suffix, args, alias) \
__MATHDECL_1(type, function, suffix, args)
#define __MATHREDIR(type, function, suffix, args, to) \
extern type __REDIRECT_NTH (__MATH_PRECNAME (function, suffix), args, to)
#define _Mdouble_ double
#define __MATH_PRECNAME(name,r) __CONCAT(name,r)
#define __MATH_DECLARING_DOUBLE 1
#define __MATH_DECLARING_FLOATN 0
#include <bits/mathcalls-helper-functions.h>
#include <bits/mathcalls.h>
#undef _Mdouble_
#undef __MATH_PRECNAME
#undef __MATH_DECLARING_DOUBLE
#undef __MATH_DECLARING_FLOATN
#ifdef __USE_ISOC99
/* Include the file of declarations again, this time using `float'
instead of `double' and appending f to each function name. */
# define _Mdouble_ float
# define __MATH_PRECNAME(name,r) name##f##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 0
# include <bits/mathcalls-helper-functions.h>
# include <bits/mathcalls.h>
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
|| defined __LDBL_COMPAT \
|| defined _LIBC_TEST
# 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
# undef __MATHDECL_1
# define __MATHDECL_1(type, function,suffix, args) \
__MATHREDIR(type, function, suffix, args, __CONCAT(function,suffix))
# elif __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
# ifdef __REDIRECT_NTH
# ifdef __USE_ISOC99
extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
__nexttowardf_to_ieee128)
__attribute__ ((__const__));
extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
__nexttoward_to_ieee128)
__attribute__ ((__const__));
#define __dremieee128 __remainderieee128
#define __gammaieee128 __lgammaieee128
# endif
# endif
# undef __MATHDECL_1
# undef __MATHDECL_ALIAS
# define __REDIRTO(function, suffix) \
__ ## function ## ieee128 ## suffix
# define __REDIRTO_ALT(function, suffix) \
__ ## function ## f128 ## suffix
# define __MATHDECL_1(type, function, suffix, args) \
__MATHREDIR (type, function, suffix, args, __REDIRTO (function, suffix))
# define __MATHDECL_ALIAS(type, function, suffix, args, alias) \
__MATHREDIR (type, function, suffix, args, __REDIRTO_ALT (alias, suffix))
# endif
/* Include the file of declarations again, this time using `long double'
instead of `double' and appending l to each function name. */
# define _Mdouble_ long double
# define __MATH_PRECNAME(name,r) name##l##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 0
# define __MATH_DECLARE_LDOUBLE 1
# include <bits/mathcalls-helper-functions.h>
# include <bits/mathcalls.h>
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
# if defined __LDBL_COMPAT \
|| __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
# undef __REDIRTO
# undef __REDIRTO_ALT
# undef __MATHDECL_1
# undef __MATHDECL_ALIAS
# define __MATHDECL_1(type, function, suffix, args) \
__MATHDECL_1_IMPL(type, function, suffix, args)
# define __MATHDECL_ALIAS(type, function, suffix, args, alias) \
__MATHDECL_1(type, function, suffix, args)
# endif
# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
#endif /* Use ISO C99. */
/* Include the file of declarations for _FloatN and _FloatNx
types. */
#if __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)
# define _Mdouble_ _Float16
# define __MATH_PRECNAME(name,r) name##f16##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 1
# if __HAVE_DISTINCT_FLOAT16
# include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
# include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !_LIBC). */
#if __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)
# define _Mdouble_ _Float32
# define __MATH_PRECNAME(name,r) name##f32##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 1
# if __HAVE_DISTINCT_FLOAT32
# include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
# include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !_LIBC). */
#if __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)
# define _Mdouble_ _Float64
# define __MATH_PRECNAME(name,r) name##f64##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 1
# if __HAVE_DISTINCT_FLOAT64
# include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
# include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !_LIBC). */
#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)
# define _Mdouble_ _Float128
# define __MATH_PRECNAME(name,r) name##f128##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 1
# if __HAVE_DISTINCT_FLOAT128
# include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
# include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !_LIBC). */
#if __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)
# define _Mdouble_ _Float32x
# define __MATH_PRECNAME(name,r) name##f32x##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 1
# if __HAVE_DISTINCT_FLOAT32X
# include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
# include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !_LIBC). */
#if __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)
# define _Mdouble_ _Float64x
# define __MATH_PRECNAME(name,r) name##f64x##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 1
# if __HAVE_DISTINCT_FLOAT64X
# include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
# include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !_LIBC). */
#if __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)
# define _Mdouble_ _Float128x
# define __MATH_PRECNAME(name,r) name##f128x##r
# define __MATH_DECLARING_DOUBLE 0
# define __MATH_DECLARING_FLOATN 1
# if __HAVE_DISTINCT_FLOAT128X
# include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
# include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !_LIBC). */
#undef __MATHDECL_1_IMPL
#undef __MATHDECL_1
#undef __MATHDECL_ALIAS
#undef __MATHDECL
#undef __MATHCALL
/* Declare functions returning a narrower type. */
#define __MATHCALL_NARROW_ARGS_1 (_Marg_ __x)
#define __MATHCALL_NARROW_ARGS_2 (_Marg_ __x, _Marg_ __y)
#define __MATHCALL_NARROW_ARGS_3 (_Marg_ __x, _Marg_ __y, _Marg_ __z)
#define __MATHCALL_NARROW_NORMAL(func, nargs) \
extern _Mret_ func __MATHCALL_NARROW_ARGS_ ## nargs __THROW
#define __MATHCALL_NARROW_REDIR(func, redir, nargs) \
extern _Mret_ __REDIRECT_NTH (func, __MATHCALL_NARROW_ARGS_ ## nargs, \
redir)
#define __MATHCALL_NARROW(func, redir, nargs) \
__MATHCALL_NARROW_NORMAL (func, nargs)
#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
# define _Mret_ float
# define _Marg_ double
# define __MATHCALL_NAME(name) f ## name
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# define _Mret_ float
# define _Marg_ long double
# define __MATHCALL_NAME(name) f ## name ## l
# ifdef __LDBL_COMPAT
# define __MATHCALL_REDIR_NAME(name) f ## name
# define __MATHCALL_REDIR_NAME2(name) f ## name
# undef __MATHCALL_NARROW
# define __MATHCALL_NARROW(func, redir, nargs) \
__MATHCALL_NARROW_REDIR (func, redir, nargs)
# elif __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
# define __MATHCALL_REDIR_NAME(name) __ ## f32 ## name ## ieee128
# define __MATHCALL_REDIR_NAME2(name) __ ## f32 ## name ## ieee128
# undef __MATHCALL_NARROW
# define __MATHCALL_NARROW(func, redir, nargs) \
__MATHCALL_NARROW_REDIR (func, redir, nargs)
# endif
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# if defined __LDBL_COMPAT \
|| __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
# undef __MATHCALL_REDIR_NAME
# undef __MATHCALL_REDIR_NAME2
# undef __MATHCALL_NARROW
# define __MATHCALL_NARROW(func, redir, nargs) \
__MATHCALL_NARROW_NORMAL (func, nargs)
# endif
# define _Mret_ double
# define _Marg_ long double
# define __MATHCALL_NAME(name) d ## name ## l
# ifdef __LDBL_COMPAT
# define __MATHCALL_REDIR_NAME(name) __nldbl_d ## name ## l
# define __MATHCALL_REDIR_NAME2(name) name
# undef __MATHCALL_NARROW
# define __MATHCALL_NARROW(func, redir, nargs) \
__MATHCALL_NARROW_REDIR (func, redir, nargs)
# elif __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
# define __MATHCALL_REDIR_NAME(name) __ ## f64 ## name ## ieee128
# define __MATHCALL_REDIR_NAME2(name) __ ## f64 ## name ## ieee128
# undef __MATHCALL_NARROW
# define __MATHCALL_NARROW(func, redir, nargs) \
__MATHCALL_NARROW_REDIR (func, redir, nargs)
# endif
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# if defined __LDBL_COMPAT \
|| __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
# undef __MATHCALL_REDIR_NAME
# undef __MATHCALL_REDIR_NAME2
# undef __MATHCALL_NARROW
# define __MATHCALL_NARROW(func, redir, nargs) \
__MATHCALL_NARROW_NORMAL (func, nargs)
# endif
#endif
#if __GLIBC_USE (IEC_60559_TYPES_EXT)
# if __HAVE_FLOAT16 && __HAVE_FLOAT32
# define _Mret_ _Float16
# define _Marg_ _Float32
# define __MATHCALL_NAME(name) f16 ## name ## f32
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT16 && __HAVE_FLOAT32X
# define _Mret_ _Float16
# define _Marg_ _Float32x
# define __MATHCALL_NAME(name) f16 ## name ## f32x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT16 && __HAVE_FLOAT64
# define _Mret_ _Float16
# define _Marg_ _Float64
# define __MATHCALL_NAME(name) f16 ## name ## f64
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT16 && __HAVE_FLOAT64X
# define _Mret_ _Float16
# define _Marg_ _Float64x
# define __MATHCALL_NAME(name) f16 ## name ## f64x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT16 && __HAVE_FLOAT128
# define _Mret_ _Float16
# define _Marg_ _Float128
# define __MATHCALL_NAME(name) f16 ## name ## f128
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT16 && __HAVE_FLOAT128X
# define _Mret_ _Float16
# define _Marg_ _Float128x
# define __MATHCALL_NAME(name) f16 ## name ## f128x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32 && __HAVE_FLOAT32X
# define _Mret_ _Float32
# define _Marg_ _Float32x
# define __MATHCALL_NAME(name) f32 ## name ## f32x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32 && __HAVE_FLOAT64
# define _Mret_ _Float32
# define _Marg_ _Float64
# define __MATHCALL_NAME(name) f32 ## name ## f64
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32 && __HAVE_FLOAT64X
# define _Mret_ _Float32
# define _Marg_ _Float64x
# define __MATHCALL_NAME(name) f32 ## name ## f64x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32 && __HAVE_FLOAT128
# define _Mret_ _Float32
# define _Marg_ _Float128
# define __MATHCALL_NAME(name) f32 ## name ## f128
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32 && __HAVE_FLOAT128X
# define _Mret_ _Float32
# define _Marg_ _Float128x
# define __MATHCALL_NAME(name) f32 ## name ## f128x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32X && __HAVE_FLOAT64
# define _Mret_ _Float32x
# define _Marg_ _Float64
# define __MATHCALL_NAME(name) f32x ## name ## f64
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32X && __HAVE_FLOAT64X
# define _Mret_ _Float32x
# define _Marg_ _Float64x
# define __MATHCALL_NAME(name) f32x ## name ## f64x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32X && __HAVE_FLOAT128
# define _Mret_ _Float32x
# define _Marg_ _Float128
# define __MATHCALL_NAME(name) f32x ## name ## f128
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT32X && __HAVE_FLOAT128X
# define _Mret_ _Float32x
# define _Marg_ _Float128x
# define __MATHCALL_NAME(name) f32x ## name ## f128x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT64 && __HAVE_FLOAT64X
# define _Mret_ _Float64
# define _Marg_ _Float64x
# define __MATHCALL_NAME(name) f64 ## name ## f64x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT64 && __HAVE_FLOAT128
# define _Mret_ _Float64
# define _Marg_ _Float128
# define __MATHCALL_NAME(name) f64 ## name ## f128
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT64 && __HAVE_FLOAT128X
# define _Mret_ _Float64
# define _Marg_ _Float128x
# define __MATHCALL_NAME(name) f64 ## name ## f128x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT64X && __HAVE_FLOAT128
# define _Mret_ _Float64x
# define _Marg_ _Float128
# define __MATHCALL_NAME(name) f64x ## name ## f128
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT64X && __HAVE_FLOAT128X
# define _Mret_ _Float64x
# define _Marg_ _Float128x
# define __MATHCALL_NAME(name) f64x ## name ## f128x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
# if __HAVE_FLOAT128 && __HAVE_FLOAT128X
# define _Mret_ _Float128
# define _Marg_ _Float128x
# define __MATHCALL_NAME(name) f128 ## name ## f128x
# include <bits/mathcalls-narrow.h>
# undef _Mret_
# undef _Marg_
# undef __MATHCALL_NAME
# endif
#endif
#undef __MATHCALL_NARROW_ARGS_1
#undef __MATHCALL_NARROW_ARGS_2
#undef __MATHCALL_NARROW_ARGS_3
#undef __MATHCALL_NARROW_NORMAL
#undef __MATHCALL_NARROW_REDIR
#undef __MATHCALL_NARROW
#if defined __USE_MISC || defined __USE_XOPEN
/* This variable is used by `gamma' and `lgamma'. */
extern int signgam;
#endif
#if (__HAVE_DISTINCT_FLOAT16 \
|| __HAVE_DISTINCT_FLOAT32 \
|| __HAVE_DISTINCT_FLOAT64 \
|| __HAVE_DISTINCT_FLOAT32X \
|| __HAVE_DISTINCT_FLOAT64X \
|| __HAVE_DISTINCT_FLOAT128X)
# error "Unsupported _FloatN or _FloatNx types for <math.h>."
#endif
/* Depending on the type of TG_ARG, call an appropriately suffixed
version of FUNC with arguments (including parentheses) ARGS.
Suffixed functions may not exist for long double if it has the same
format as double, or for other types with the same format as float,
double or long double. The behavior is undefined if the argument
does not have a real floating type. The definition may use a
conditional expression, so all suffixed versions of FUNC must
return the same type (FUNC may include a cast if necessary rather
than being a single identifier). */
#ifdef __NO_LONG_DOUBLE_MATH
# if __HAVE_DISTINCT_FLOAT128
# error "Distinct _Float128 without distinct long double not supported."
# endif
# define __MATH_TG(TG_ARG, FUNC, ARGS) \
(sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
#elif __HAVE_DISTINCT_FLOAT128
# if __HAVE_GENERIC_SELECTION
# if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT32
# define __MATH_TG_F32(FUNC, ARGS) _Float32: FUNC ## f ARGS,
# else
# define __MATH_TG_F32(FUNC, ARGS)
# endif
# if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT64X
# if __HAVE_FLOAT64X_LONG_DOUBLE
# define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## l ARGS,
# else
# define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## f128 ARGS,
# endif
# else
# define __MATH_TG_F64X(FUNC, ARGS)
# endif
# define __MATH_TG(TG_ARG, FUNC, ARGS) \
_Generic ((TG_ARG), \
float: FUNC ## f ARGS, \
__MATH_TG_F32 (FUNC, ARGS) \
default: FUNC ARGS, \
long double: FUNC ## l ARGS, \
__MATH_TG_F64X (FUNC, ARGS) \
_Float128: FUNC ## f128 ARGS)
# else
# if __HAVE_FLOATN_NOT_TYPEDEF
# error "Non-typedef _FloatN but no _Generic."
# endif
# define __MATH_TG(TG_ARG, FUNC, ARGS) \
__builtin_choose_expr \
(__builtin_types_compatible_p (__typeof (TG_ARG), float), \
FUNC ## f ARGS, \
__builtin_choose_expr \
(__builtin_types_compatible_p (__typeof (TG_ARG), double), \
FUNC ARGS, \
__builtin_choose_expr \
(__builtin_types_compatible_p (__typeof (TG_ARG), long double), \
FUNC ## l ARGS, \
FUNC ## f128 ARGS)))
# endif
#else
# define __MATH_TG(TG_ARG, FUNC, ARGS) \
(sizeof (TG_ARG) == sizeof (float) \
? FUNC ## f ARGS \
: sizeof (TG_ARG) == sizeof (double) \
? FUNC ARGS \
: FUNC ## l ARGS)
#endif
/* ISO C99 defines some generic macros which work on any data type. */
#ifdef __USE_ISOC99
/* All floating-point numbers can be put in one of these categories. */
enum
{
FP_NAN =
# define FP_NAN 0
FP_NAN,
FP_INFINITE =
# define FP_INFINITE 1
FP_INFINITE,
FP_ZERO =
# define FP_ZERO 2
FP_ZERO,
FP_SUBNORMAL =
# define FP_SUBNORMAL 3
FP_SUBNORMAL,
FP_NORMAL =
# define FP_NORMAL 4
FP_NORMAL
};
/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
so disable builtins if this is enabled. When fixed in a newer GCC,
the __SUPPORT_SNAN__ check may be skipped for those versions. */
/* Return number of classification appropriate for X. */
# if ((__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
|| __glibc_clang_prereq (2,8)) \
&& (!defined __OPTIMIZE_SIZE__ || defined __cplusplus)
/* The check for __cplusplus allows the use of the builtin, even
when optimization for size is on. This is provided for
libstdc++, only to let its configure test work when it is built
with -Os. No further use of this definition of fpclassify is
expected in C++ mode, since libstdc++ provides its own version
of fpclassify in cmath (which undefines fpclassify). */
# define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \
FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
# else
# define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
# endif
/* Return nonzero value if sign of X is negative. */
# if __GNUC_PREREQ (6,0) || __glibc_clang_prereq (3,3)
# define signbit(x) __builtin_signbit (x)
# elif defined __cplusplus
/* In C++ mode, __MATH_TG cannot be used, because it relies on
__builtin_types_compatible_p, which is a C-only builtin.
The check for __cplusplus allows the use of the builtin instead of
__MATH_TG. This is provided for libstdc++, only to let its configure
test work. No further use of this definition of signbit is expected
in C++ mode, since libstdc++ provides its own version of signbit
in cmath (which undefines signbit). */
# define signbit(x) __builtin_signbitl (x)
# elif __GNUC_PREREQ (4,0)
# define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
# else
# define signbit(x) __MATH_TG ((x), __signbit, (x))
# endif
/* Return nonzero value if X is not +-Inf or NaN. */
# if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
|| __glibc_clang_prereq (2,8)
# define isfinite(x) __builtin_isfinite (x)
# else
# define isfinite(x) __MATH_TG ((x), __finite, (x))
# endif
/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
# if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \