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  3.   math.h
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/* Declarations for math functions.
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   Copyright (C) 1991-2018 Free Software Foundation, Inc.
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   This file is part of the GNU C Library.
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   The GNU C Library is free software; you can redistribute it and/or
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   modify it under the terms of the GNU Lesser General Public
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   License as published by the Free Software Foundation; either
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   version 2.1 of the License, or (at your option) any later version.
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   The GNU C Library is distributed in the hope that it will be useful,
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   but WITHOUT ANY WARRANTY; without even the implied warranty of
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   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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   Lesser General Public License for more details.
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   You should have received a copy of the GNU Lesser General Public
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   License along with the GNU C Library; if not, see
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   <http://www.gnu.org/licenses/>.  */
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/*
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 *	ISO C99 Standard: 7.12 Mathematics	<math.h>
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 */
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#ifndef	_MATH_H
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#define	_MATH_H	1
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#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
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#include <bits/libc-header-start.h>
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#if defined log && defined __GNUC__
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# warning A macro called log was already defined when <math.h> was included.
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# warning This will cause compilation problems.
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#endif
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__BEGIN_DECLS
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/* Get definitions of __intmax_t and __uintmax_t.  */
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#include <bits/types.h>
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/* Get machine-dependent vector math functions declarations.  */
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#include <bits/math-vector.h>
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/* Gather machine dependent type support.  */
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#include <bits/floatn.h>
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/* Value returned on overflow.  With IEEE 754 floating point, this is
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   +Infinity, otherwise the largest representable positive value.  */
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#if __GNUC_PREREQ (3, 3)
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# define HUGE_VAL (__builtin_huge_val ())
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#else
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/* This may provoke compiler warnings, and may not be rounded to
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   +Infinity in all IEEE 754 rounding modes, but is the best that can
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   be done in ISO C while remaining a constant expression.  10,000 is
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   greater than the maximum (decimal) exponent for all supported
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   floating-point formats and widths.  */
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# define HUGE_VAL 1e10000
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#endif
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#ifdef __USE_ISOC99
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# if __GNUC_PREREQ (3, 3)
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#  define HUGE_VALF (__builtin_huge_valf ())
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#  define HUGE_VALL (__builtin_huge_vall ())
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# else
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#  define HUGE_VALF 1e10000f
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#  define HUGE_VALL 1e10000L
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# endif
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#endif
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#if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define HUGE_VAL_F16 (__builtin_huge_valf16 ())
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#endif
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#if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define HUGE_VAL_F32 (__builtin_huge_valf32 ())
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#endif
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#if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define HUGE_VAL_F64 (__builtin_huge_valf64 ())
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#endif
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#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define HUGE_VAL_F128 (__builtin_huge_valf128 ())
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#endif
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#if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define HUGE_VAL_F32X (__builtin_huge_valf32x ())
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#endif
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#if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define HUGE_VAL_F64X (__builtin_huge_valf64x ())
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#endif
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#if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define HUGE_VAL_F128X (__builtin_huge_valf128x ())
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#endif
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#ifdef __USE_ISOC99
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/* IEEE positive infinity.  */
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# if __GNUC_PREREQ (3, 3)
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#  define INFINITY (__builtin_inff ())
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# else
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#  define INFINITY HUGE_VALF
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# endif
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/* IEEE Not A Number.  */
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# if __GNUC_PREREQ (3, 3)
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#  define NAN (__builtin_nanf (""))
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# else
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/* This will raise an "invalid" exception outside static initializers,
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   but is the best that can be done in ISO C while remaining a
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   constant expression.  */
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#  define NAN (0.0f / 0.0f)
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# endif
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#endif /* __USE_ISOC99 */
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#if __GLIBC_USE (IEC_60559_BFP_EXT)
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/* Signaling NaN macros, if supported.  */
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# if __GNUC_PREREQ (3, 3)
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#  define SNANF (__builtin_nansf (""))
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#  define SNAN (__builtin_nans (""))
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#  define SNANL (__builtin_nansl (""))
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# endif
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#endif
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#if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define SNANF16 (__builtin_nansf16 (""))
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#endif
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#if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define SNANF32 (__builtin_nansf32 (""))
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#endif
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#if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define SNANF64 (__builtin_nansf64 (""))
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#endif
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#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define SNANF128 (__builtin_nansf128 (""))
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#endif
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#if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define SNANF32X (__builtin_nansf32x (""))
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#endif
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#if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define SNANF64X (__builtin_nansf64x (""))
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#endif
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#if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define SNANF128X (__builtin_nansf128x (""))
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#endif
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/* Get __GLIBC_FLT_EVAL_METHOD.  */
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#include <bits/flt-eval-method.h>
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#ifdef __USE_ISOC99
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/* Define the following typedefs.
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    float_t	floating-point type at least as wide as `float' used
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		to evaluate `float' expressions
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    double_t	floating-point type at least as wide as `double' used
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		to evaluate `double' expressions
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*/
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# if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
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typedef float float_t;
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typedef double double_t;
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# elif __GLIBC_FLT_EVAL_METHOD == 1
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typedef double float_t;
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typedef double double_t;
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# elif __GLIBC_FLT_EVAL_METHOD == 2
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typedef long double float_t;
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typedef long double double_t;
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# elif __GLIBC_FLT_EVAL_METHOD == 32
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typedef _Float32 float_t;
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typedef double double_t;
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# elif __GLIBC_FLT_EVAL_METHOD == 33
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typedef _Float32x float_t;
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typedef _Float32x double_t;
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# elif __GLIBC_FLT_EVAL_METHOD == 64
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typedef _Float64 float_t;
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typedef _Float64 double_t;
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# elif __GLIBC_FLT_EVAL_METHOD == 65
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typedef _Float64x float_t;
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typedef _Float64x double_t;
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# elif __GLIBC_FLT_EVAL_METHOD == 128
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typedef _Float128 float_t;
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typedef _Float128 double_t;
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# elif __GLIBC_FLT_EVAL_METHOD == 129
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typedef _Float128x float_t;
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typedef _Float128x double_t;
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# else
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#  error "Unknown __GLIBC_FLT_EVAL_METHOD"
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# endif
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#endif
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/* Define macros for the return values of ilogb and llogb, based on
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   __FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.
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    FP_ILOGB0	Expands to a value returned by `ilogb (0.0)'.
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    FP_ILOGBNAN	Expands to a value returned by `ilogb (NAN)'.
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    FP_LLOGB0	Expands to a value returned by `llogb (0.0)'.
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    FP_LLOGBNAN	Expands to a value returned by `llogb (NAN)'.
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*/
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#include <bits/fp-logb.h>
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#ifdef __USE_ISOC99
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# if __FP_LOGB0_IS_MIN
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#  define FP_ILOGB0	(-2147483647 - 1)
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# else
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#  define FP_ILOGB0	(-2147483647)
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# endif
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# if __FP_LOGBNAN_IS_MIN
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#  define FP_ILOGBNAN	(-2147483647 - 1)
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# else
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#  define FP_ILOGBNAN	2147483647
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# endif
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#endif
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#if __GLIBC_USE (IEC_60559_BFP_EXT)
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# if __WORDSIZE == 32
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#  define __FP_LONG_MAX 0x7fffffffL
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# else
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#  define __FP_LONG_MAX 0x7fffffffffffffffL
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# endif
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# if __FP_LOGB0_IS_MIN
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#  define FP_LLOGB0	(-__FP_LONG_MAX - 1)
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# else
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#  define FP_LLOGB0	(-__FP_LONG_MAX)
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# endif
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# if __FP_LOGBNAN_IS_MIN
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#  define FP_LLOGBNAN	(-__FP_LONG_MAX - 1)
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# else
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#  define FP_LLOGBNAN	__FP_LONG_MAX
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# endif
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#endif
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/* Get the architecture specific values describing the floating-point
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   evaluation.  The following symbols will get defined:
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    FP_FAST_FMA
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    FP_FAST_FMAF
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    FP_FAST_FMAL
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		If defined it indicates that the `fma' function
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		generally executes about as fast as a multiply and an add.
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		This macro is defined only iff the `fma' function is
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		implemented directly with a hardware multiply-add instructions.
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*/
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#include <bits/fp-fast.h>
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#if __GLIBC_USE (IEC_60559_BFP_EXT)
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/* Rounding direction macros for fromfp functions.  */
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enum
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  {
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    FP_INT_UPWARD =
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# define FP_INT_UPWARD 0
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      FP_INT_UPWARD,
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    FP_INT_DOWNWARD =
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# define FP_INT_DOWNWARD 1
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      FP_INT_DOWNWARD,
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    FP_INT_TOWARDZERO =
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# define FP_INT_TOWARDZERO 2
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      FP_INT_TOWARDZERO,
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    FP_INT_TONEARESTFROMZERO =
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# define FP_INT_TONEARESTFROMZERO 3
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      FP_INT_TONEARESTFROMZERO,
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    FP_INT_TONEAREST =
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# define FP_INT_TONEAREST 4
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      FP_INT_TONEAREST,
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  };
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#endif
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/* The file <bits/mathcalls.h> contains the prototypes for all the
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   actual math functions.  These macros are used for those prototypes,
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   so we can easily declare each function as both `name' and `__name',
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   and can declare the float versions `namef' and `__namef'.  */
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#define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
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#define __MATHCALL_VEC(function, suffix, args) 	\
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  __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
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  __MATHCALL (function, suffix, args)
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#define __MATHDECL_VEC(type, function,suffix, args) \
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  __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
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  __MATHDECL(type, function,suffix, args)
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#define __MATHCALL(function,suffix, args)	\
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  __MATHDECL (_Mdouble_,function,suffix, args)
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#define __MATHDECL(type, function,suffix, args) \
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  __MATHDECL_1(type, function,suffix, args); \
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  __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
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#define __MATHCALLX(function,suffix, args, attrib)	\
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  __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
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#define __MATHDECLX(type, function,suffix, args, attrib) \
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  __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
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  __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
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#define __MATHDECL_1(type, function,suffix, args) \
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  extern type __MATH_PRECNAME(function,suffix) args __THROW
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#define _Mdouble_		double
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#define __MATH_PRECNAME(name,r)	__CONCAT(name,r)
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#define __MATH_DECLARING_DOUBLE  1
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#define __MATH_DECLARING_FLOATN  0
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#include <bits/mathcalls-helper-functions.h>
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#include <bits/mathcalls.h>
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#undef	_Mdouble_
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#undef	__MATH_PRECNAME
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#undef __MATH_DECLARING_DOUBLE
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#undef __MATH_DECLARING_FLOATN
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#ifdef __USE_ISOC99
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/* Include the file of declarations again, this time using `float'
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   instead of `double' and appending f to each function name.  */
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# define _Mdouble_		float
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# define __MATH_PRECNAME(name,r) name##f##r
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# define __MATH_DECLARING_DOUBLE  0
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# define __MATH_DECLARING_FLOATN  0
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# include <bits/mathcalls-helper-functions.h>
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# include <bits/mathcalls.h>
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# undef	_Mdouble_
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# undef	__MATH_PRECNAME
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# undef __MATH_DECLARING_DOUBLE
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# undef __MATH_DECLARING_FLOATN
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# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
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     || defined __LDBL_COMPAT \
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     || defined _LIBC_TEST
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#  ifdef __LDBL_COMPAT
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#   ifdef __USE_ISOC99
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extern float __nldbl_nexttowardf (float __x, long double __y)
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				  __THROW __attribute__ ((__const__));
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#    ifdef __REDIRECT_NTH
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extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
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			     __nldbl_nexttowardf)
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     __attribute__ ((__const__));
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extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
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			      nextafter) __attribute__ ((__const__));
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extern long double __REDIRECT_NTH (nexttowardl,
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				   (long double __x, long double __y),
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				   nextafter) __attribute__ ((__const__));
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#    endif
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#   endif
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#   undef __MATHDECL_1
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#   define __MATHDECL_2(type, function,suffix, args, alias) \
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  extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
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			     args, alias)
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#   define __MATHDECL_1(type, function,suffix, args) \
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  __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
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#  endif
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/* Include the file of declarations again, this time using `long double'
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   instead of `double' and appending l to each function name.  */
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#  define _Mdouble_		long double
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#  define __MATH_PRECNAME(name,r) name##l##r
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#  define __MATH_DECLARING_DOUBLE  0
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#  define __MATH_DECLARING_FLOATN  0
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#  define __MATH_DECLARE_LDOUBLE   1
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#  include <bits/mathcalls-helper-functions.h>
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#  include <bits/mathcalls.h>
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#  undef _Mdouble_
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#  undef __MATH_PRECNAME
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#  undef __MATH_DECLARING_DOUBLE
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#  undef __MATH_DECLARING_FLOATN
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# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
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#endif	/* Use ISO C99.  */
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/* Include the file of declarations for _FloatN and _FloatNx
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   types.  */
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#if __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)
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# define _Mdouble_		_Float16
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# define __MATH_PRECNAME(name,r) name##f16##r
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# define __MATH_DECLARING_DOUBLE  0
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# define __MATH_DECLARING_FLOATN  1
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# if __HAVE_DISTINCT_FLOAT16
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#  include <bits/mathcalls-helper-functions.h>
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# endif
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# if __GLIBC_USE (IEC_60559_TYPES_EXT)
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#  include <bits/mathcalls.h>
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# endif
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# undef _Mdouble_
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# undef __MATH_PRECNAME
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# undef __MATH_DECLARING_DOUBLE
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# undef __MATH_DECLARING_FLOATN
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#endif /* __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !_LIBC).  */
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#if __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)
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# define _Mdouble_		_Float32
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# define __MATH_PRECNAME(name,r) name##f32##r
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# define __MATH_DECLARING_DOUBLE  0
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# define __MATH_DECLARING_FLOATN  1
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# if __HAVE_DISTINCT_FLOAT32
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#  include <bits/mathcalls-helper-functions.h>
Packit 6c4009 
# endif
Packit 6c4009 
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  include <bits/mathcalls.h>
Packit 6c4009 
# endif
Packit 6c4009 
# undef _Mdouble_
Packit 6c4009 
# undef __MATH_PRECNAME
Packit 6c4009 
# undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
# undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#endif /* __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !_LIBC).  */
Packit 6c4009
Packit 6c4009 
#if __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)
Packit 6c4009 
# define _Mdouble_		_Float64
Packit 6c4009 
# define __MATH_PRECNAME(name,r) name##f64##r
Packit 6c4009 
# define __MATH_DECLARING_DOUBLE  0
Packit 6c4009 
# define __MATH_DECLARING_FLOATN  1
Packit 6c4009 
# if __HAVE_DISTINCT_FLOAT64
Packit 6c4009 
#  include <bits/mathcalls-helper-functions.h>
Packit 6c4009 
# endif
Packit 6c4009 
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  include <bits/mathcalls.h>
Packit 6c4009 
# endif
Packit 6c4009 
# undef _Mdouble_
Packit 6c4009 
# undef __MATH_PRECNAME
Packit 6c4009 
# undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
# undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#endif /* __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !_LIBC).  */
Packit 6c4009
Packit 6c4009 
#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)
Packit 6c4009 
# define _Mdouble_		_Float128
Packit 6c4009 
# define __MATH_PRECNAME(name,r) name##f128##r
Packit 6c4009 
# define __MATH_DECLARING_DOUBLE  0
Packit 6c4009 
# define __MATH_DECLARING_FLOATN  1
Packit 6c4009 
# if __HAVE_DISTINCT_FLOAT128
Packit 6c4009 
#  include <bits/mathcalls-helper-functions.h>
Packit 6c4009 
# endif
Packit 6c4009 
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  include <bits/mathcalls.h>
Packit 6c4009 
# endif
Packit 6c4009 
# undef _Mdouble_
Packit 6c4009 
# undef __MATH_PRECNAME
Packit 6c4009 
# undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
# undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#endif /* __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !_LIBC).  */
Packit 6c4009
Packit 6c4009 
#if __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)
Packit 6c4009 
# define _Mdouble_		_Float32x
Packit 6c4009 
# define __MATH_PRECNAME(name,r) name##f32x##r
Packit 6c4009 
# define __MATH_DECLARING_DOUBLE  0
Packit 6c4009 
# define __MATH_DECLARING_FLOATN  1
Packit 6c4009 
# if __HAVE_DISTINCT_FLOAT32X
Packit 6c4009 
#  include <bits/mathcalls-helper-functions.h>
Packit 6c4009 
# endif
Packit 6c4009 
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  include <bits/mathcalls.h>
Packit 6c4009 
# endif
Packit 6c4009 
# undef _Mdouble_
Packit 6c4009 
# undef __MATH_PRECNAME
Packit 6c4009 
# undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
# undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#endif /* __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !_LIBC).  */
Packit 6c4009
Packit 6c4009 
#if __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)
Packit 6c4009 
# define _Mdouble_		_Float64x
Packit 6c4009 
# define __MATH_PRECNAME(name,r) name##f64x##r
Packit 6c4009 
# define __MATH_DECLARING_DOUBLE  0
Packit 6c4009 
# define __MATH_DECLARING_FLOATN  1
Packit 6c4009 
# if __HAVE_DISTINCT_FLOAT64X
Packit 6c4009 
#  include <bits/mathcalls-helper-functions.h>
Packit 6c4009 
# endif
Packit 6c4009 
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  include <bits/mathcalls.h>
Packit 6c4009 
# endif
Packit 6c4009 
# undef _Mdouble_
Packit 6c4009 
# undef __MATH_PRECNAME
Packit 6c4009 
# undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
# undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#endif /* __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !_LIBC).  */
Packit 6c4009
Packit 6c4009 
#if __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)
Packit 6c4009 
# define _Mdouble_		_Float128x
Packit 6c4009 
# define __MATH_PRECNAME(name,r) name##f128x##r
Packit 6c4009 
# define __MATH_DECLARING_DOUBLE  0
Packit 6c4009 
# define __MATH_DECLARING_FLOATN  1
Packit 6c4009 
# if __HAVE_DISTINCT_FLOAT128X
Packit 6c4009 
#  include <bits/mathcalls-helper-functions.h>
Packit 6c4009 
# endif
Packit 6c4009 
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  include <bits/mathcalls.h>
Packit 6c4009 
# endif
Packit 6c4009 
# undef _Mdouble_
Packit 6c4009 
# undef __MATH_PRECNAME
Packit 6c4009 
# undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
# undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#endif /* __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !_LIBC).  */
Packit 6c4009
Packit 6c4009 
#undef	__MATHDECL_1
Packit 6c4009 
#undef	__MATHDECL
Packit 6c4009 
#undef	__MATHCALL
Packit 6c4009
Packit 6c4009 
/* Declare functions returning a narrower type.  */
Packit 6c4009 
#define __MATHCALL_NARROW_ARGS_1 (_Marg_ __x)
Packit 6c4009 
#define __MATHCALL_NARROW_ARGS_2 (_Marg_ __x, _Marg_ __y)
Packit 6c4009 
#define __MATHCALL_NARROW_ARGS_3 (_Marg_ __x, _Marg_ __y, _Marg_ __z)
Packit 6c4009 
#define __MATHCALL_NARROW_NORMAL(func, nargs)			\
Packit 6c4009 
  extern _Mret_ func __MATHCALL_NARROW_ARGS_ ## nargs __THROW
Packit 6c4009 
#define __MATHCALL_NARROW_REDIR(func, redir, nargs)			\
Packit 6c4009 
  extern _Mret_ __REDIRECT_NTH (func, __MATHCALL_NARROW_ARGS_ ## nargs, \
Packit 6c4009 
				redir)
Packit 6c4009 
#define __MATHCALL_NARROW(func, redir, nargs)	\
Packit 6c4009 
  __MATHCALL_NARROW_NORMAL (func, nargs)
Packit 6c4009
Packit 6c4009 
#if __GLIBC_USE (IEC_60559_BFP_EXT)
Packit 6c4009
Packit 6c4009 
# define _Mret_ float
Packit 6c4009 
# define _Marg_ double
Packit 6c4009 
# define __MATHCALL_NAME(name) f ## name
Packit 6c4009 
# include <bits/mathcalls-narrow.h>
Packit 6c4009 
# undef _Mret_
Packit 6c4009 
# undef _Marg_
Packit 6c4009 
# undef __MATHCALL_NAME
Packit 6c4009
Packit 6c4009 
# define _Mret_ float
Packit 6c4009 
# define _Marg_ long double
Packit 6c4009 
# define __MATHCALL_NAME(name) f ## name ## l
Packit 6c4009 
# ifdef __LDBL_COMPAT
Packit 6c4009 
#  define __MATHCALL_REDIR_NAME(name) f ## name
Packit 6c4009 
#  undef __MATHCALL_NARROW
Packit 6c4009 
#  define __MATHCALL_NARROW(func, redir, nargs) \
Packit 6c4009 
  __MATHCALL_NARROW_REDIR (func, redir, nargs)
Packit 6c4009 
# endif
Packit 6c4009 
# include <bits/mathcalls-narrow.h>
Packit 6c4009 
# undef _Mret_
Packit 6c4009 
# undef _Marg_
Packit 6c4009 
# undef __MATHCALL_NAME
Packit 6c4009 
# ifdef __LDBL_COMPAT
Packit 6c4009 
#  undef __MATHCALL_REDIR_NAME
Packit 6c4009 
#  undef __MATHCALL_NARROW
Packit 6c4009 
#  define __MATHCALL_NARROW(func, redir, nargs) \
Packit 6c4009 
  __MATHCALL_NARROW_NORMAL (func, nargs)
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# define _Mret_ double
Packit 6c4009 
# define _Marg_ long double
Packit 6c4009 
# define __MATHCALL_NAME(name) d ## name ## l
Packit 6c4009 
# ifdef __LDBL_COMPAT
Packit 6c4009 
#  define __MATHCALL_REDIR_NAME(name) __nldbl_d ## name ## l
Packit 6c4009 
#  undef __MATHCALL_NARROW
Packit 6c4009 
#  define __MATHCALL_NARROW(func, redir, nargs) \
Packit 6c4009 
  __MATHCALL_NARROW_REDIR (func, redir, nargs)
Packit 6c4009 
# endif
Packit 6c4009 
# include <bits/mathcalls-narrow.h>
Packit 6c4009 
# undef _Mret_
Packit 6c4009 
# undef _Marg_
Packit 6c4009 
# undef __MATHCALL_NAME
Packit 6c4009 
# ifdef __LDBL_COMPAT
Packit 6c4009 
#  undef __MATHCALL_REDIR_NAME
Packit 6c4009 
#  undef __MATHCALL_NARROW
Packit 6c4009 
#  define __MATHCALL_NARROW(func, redir, nargs) \
Packit 6c4009 
  __MATHCALL_NARROW_NORMAL (func, nargs)
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT16 && __HAVE_FLOAT32
Packit 6c4009 
#  define _Mret_ _Float16
Packit 6c4009 
#  define _Marg_ _Float32
Packit 6c4009 
#  define __MATHCALL_NAME(name) f16 ## name ## f32
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT16 && __HAVE_FLOAT32X
Packit 6c4009 
#  define _Mret_ _Float16
Packit 6c4009 
#  define _Marg_ _Float32x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f16 ## name ## f32x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT16 && __HAVE_FLOAT64
Packit 6c4009 
#  define _Mret_ _Float16
Packit 6c4009 
#  define _Marg_ _Float64
Packit 6c4009 
#  define __MATHCALL_NAME(name) f16 ## name ## f64
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT16 && __HAVE_FLOAT64X
Packit 6c4009 
#  define _Mret_ _Float16
Packit 6c4009 
#  define _Marg_ _Float64x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f16 ## name ## f64x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT16 && __HAVE_FLOAT128
Packit 6c4009 
#  define _Mret_ _Float16
Packit 6c4009 
#  define _Marg_ _Float128
Packit 6c4009 
#  define __MATHCALL_NAME(name) f16 ## name ## f128
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT16 && __HAVE_FLOAT128X
Packit 6c4009 
#  define _Mret_ _Float16
Packit 6c4009 
#  define _Marg_ _Float128x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f16 ## name ## f128x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32 && __HAVE_FLOAT32X
Packit 6c4009 
#  define _Mret_ _Float32
Packit 6c4009 
#  define _Marg_ _Float32x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32 ## name ## f32x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32 && __HAVE_FLOAT64
Packit 6c4009 
#  define _Mret_ _Float32
Packit 6c4009 
#  define _Marg_ _Float64
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32 ## name ## f64
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32 && __HAVE_FLOAT64X
Packit 6c4009 
#  define _Mret_ _Float32
Packit 6c4009 
#  define _Marg_ _Float64x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32 ## name ## f64x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32 && __HAVE_FLOAT128
Packit 6c4009 
#  define _Mret_ _Float32
Packit 6c4009 
#  define _Marg_ _Float128
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32 ## name ## f128
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32 && __HAVE_FLOAT128X
Packit 6c4009 
#  define _Mret_ _Float32
Packit 6c4009 
#  define _Marg_ _Float128x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32 ## name ## f128x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32X && __HAVE_FLOAT64
Packit 6c4009 
#  define _Mret_ _Float32x
Packit 6c4009 
#  define _Marg_ _Float64
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32x ## name ## f64
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32X && __HAVE_FLOAT64X
Packit 6c4009 
#  define _Mret_ _Float32x
Packit 6c4009 
#  define _Marg_ _Float64x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32x ## name ## f64x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32X && __HAVE_FLOAT128
Packit 6c4009 
#  define _Mret_ _Float32x
Packit 6c4009 
#  define _Marg_ _Float128
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32x ## name ## f128
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT32X && __HAVE_FLOAT128X
Packit 6c4009 
#  define _Mret_ _Float32x
Packit 6c4009 
#  define _Marg_ _Float128x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f32x ## name ## f128x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT64 && __HAVE_FLOAT64X
Packit 6c4009 
#  define _Mret_ _Float64
Packit 6c4009 
#  define _Marg_ _Float64x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f64 ## name ## f64x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT64 && __HAVE_FLOAT128
Packit 6c4009 
#  define _Mret_ _Float64
Packit 6c4009 
#  define _Marg_ _Float128
Packit 6c4009 
#  define __MATHCALL_NAME(name) f64 ## name ## f128
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT64 && __HAVE_FLOAT128X
Packit 6c4009 
#  define _Mret_ _Float64
Packit 6c4009 
#  define _Marg_ _Float128x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f64 ## name ## f128x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT64X && __HAVE_FLOAT128
Packit 6c4009 
#  define _Mret_ _Float64x
Packit 6c4009 
#  define _Marg_ _Float128
Packit 6c4009 
#  define __MATHCALL_NAME(name) f64x ## name ## f128
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT64X && __HAVE_FLOAT128X
Packit 6c4009 
#  define _Mret_ _Float64x
Packit 6c4009 
#  define _Marg_ _Float128x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f64x ## name ## f128x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if __HAVE_FLOAT128 && __HAVE_FLOAT128X
Packit 6c4009 
#  define _Mret_ _Float128
Packit 6c4009 
#  define _Marg_ _Float128x
Packit 6c4009 
#  define __MATHCALL_NAME(name) f128 ## name ## f128x
Packit 6c4009 
#  include <bits/mathcalls-narrow.h>
Packit 6c4009 
#  undef _Mret_
Packit 6c4009 
#  undef _Marg_
Packit 6c4009 
#  undef __MATHCALL_NAME
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#undef __MATHCALL_NARROW_ARGS_1
Packit 6c4009 
#undef __MATHCALL_NARROW_ARGS_2
Packit 6c4009 
#undef __MATHCALL_NARROW_ARGS_3
Packit 6c4009 
#undef __MATHCALL_NARROW_NORMAL
Packit 6c4009 
#undef __MATHCALL_NARROW_REDIR
Packit 6c4009 
#undef __MATHCALL_NARROW
Packit 6c4009
Packit 6c4009 
#if defined __USE_MISC || defined __USE_XOPEN
Packit 6c4009 
/* This variable is used by `gamma' and `lgamma'.  */
Packit 6c4009 
extern int signgam;
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if (__HAVE_DISTINCT_FLOAT16			\
Packit 6c4009 
     || __HAVE_DISTINCT_FLOAT32			\
Packit 6c4009 
     || __HAVE_DISTINCT_FLOAT64			\
Packit 6c4009 
     || __HAVE_DISTINCT_FLOAT32X		\
Packit 6c4009 
     || __HAVE_DISTINCT_FLOAT64X		\
Packit 6c4009 
     || __HAVE_DISTINCT_FLOAT128X)
Packit 6c4009 
# error "Unsupported _FloatN or _FloatNx types for <math.h>."
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
/* Depending on the type of TG_ARG, call an appropriately suffixed
Packit 6c4009 
   version of FUNC with arguments (including parentheses) ARGS.
Packit 6c4009 
   Suffixed functions may not exist for long double if it has the same
Packit 6c4009 
   format as double, or for other types with the same format as float,
Packit 6c4009 
   double or long double.  The behavior is undefined if the argument
Packit 6c4009 
   does not have a real floating type.  The definition may use a
Packit 6c4009 
   conditional expression, so all suffixed versions of FUNC must
Packit 6c4009 
   return the same type (FUNC may include a cast if necessary rather
Packit 6c4009 
   than being a single identifier).  */
Packit 6c4009 
#ifdef __NO_LONG_DOUBLE_MATH
Packit 6c4009 
# if __HAVE_DISTINCT_FLOAT128
Packit 6c4009 
#  error "Distinct _Float128 without distinct long double not supported."
Packit 6c4009 
# endif
Packit 6c4009 
# define __MATH_TG(TG_ARG, FUNC, ARGS)					\
Packit 6c4009 
  (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
Packit 6c4009 
#elif __HAVE_DISTINCT_FLOAT128
Packit 6c4009 
# if __HAVE_GENERIC_SELECTION
Packit 6c4009 
#  if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT32
Packit 6c4009 
#   define __MATH_TG_F32(FUNC, ARGS) _Float32: FUNC ## f ARGS,
Packit 6c4009 
#  else
Packit 6c4009 
#   define __MATH_TG_F32(FUNC, ARGS)
Packit 6c4009 
#  endif
Packit 6c4009 
#  if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT64X
Packit 6c4009 
#   if __HAVE_FLOAT64X_LONG_DOUBLE
Packit 6c4009 
#    define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## l ARGS,
Packit 6c4009 
#   else
Packit 6c4009 
#    define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## f128 ARGS,
Packit 6c4009 
#   endif
Packit 6c4009 
#  else
Packit 6c4009 
#   define __MATH_TG_F64X(FUNC, ARGS)
Packit 6c4009 
#  endif
Packit 6c4009 
#  define __MATH_TG(TG_ARG, FUNC, ARGS)	\
Packit 6c4009 
     _Generic ((TG_ARG),			\
Packit 6c4009 
	       float: FUNC ## f ARGS,		\
Packit 6c4009 
	       __MATH_TG_F32 (FUNC, ARGS)	\
Packit 6c4009 
	       default: FUNC ARGS,		\
Packit 6c4009 
	       long double: FUNC ## l ARGS,	\
Packit 6c4009 
	       __MATH_TG_F64X (FUNC, ARGS)	\
Packit 6c4009 
	       _Float128: FUNC ## f128 ARGS)
Packit 6c4009 
# else
Packit 6c4009 
#  if __HAVE_FLOATN_NOT_TYPEDEF
Packit 6c4009 
#   error "Non-typedef _FloatN but no _Generic."
Packit 6c4009 
#  endif
Packit 6c4009 
#  define __MATH_TG(TG_ARG, FUNC, ARGS)					\
Packit 6c4009 
     __builtin_choose_expr						\
Packit 6c4009 
     (__builtin_types_compatible_p (__typeof (TG_ARG), float),		\
Packit 6c4009 
      FUNC ## f ARGS,							\
Packit 6c4009 
      __builtin_choose_expr						\
Packit 6c4009 
      (__builtin_types_compatible_p (__typeof (TG_ARG), double),	\
Packit 6c4009 
       FUNC ARGS,							\
Packit 6c4009 
       __builtin_choose_expr						\
Packit 6c4009 
       (__builtin_types_compatible_p (__typeof (TG_ARG), long double),	\
Packit 6c4009 
	FUNC ## l ARGS,							\
Packit 6c4009 
	FUNC ## f128 ARGS)))
Packit 6c4009 
# endif
Packit 6c4009 
#else
Packit 6c4009 
# define __MATH_TG(TG_ARG, FUNC, ARGS)		\
Packit 6c4009 
  (sizeof (TG_ARG) == sizeof (float)		\
Packit 6c4009 
   ? FUNC ## f ARGS				\
Packit 6c4009 
   : sizeof (TG_ARG) == sizeof (double)		\
Packit 6c4009 
   ? FUNC ARGS					\
Packit 6c4009 
   : FUNC ## l ARGS)
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
/* ISO C99 defines some generic macros which work on any data type.  */
Packit 6c4009 
#ifdef __USE_ISOC99
Packit 6c4009
Packit 6c4009 
/* All floating-point numbers can be put in one of these categories.  */
Packit 6c4009 
enum
Packit 6c4009 
  {
Packit 6c4009 
    FP_NAN =
Packit 6c4009 
# define FP_NAN 0
Packit 6c4009 
      FP_NAN,
Packit 6c4009 
    FP_INFINITE =
Packit 6c4009 
# define FP_INFINITE 1
Packit 6c4009 
      FP_INFINITE,
Packit 6c4009 
    FP_ZERO =
Packit 6c4009 
# define FP_ZERO 2
Packit 6c4009 
      FP_ZERO,
Packit 6c4009 
    FP_SUBNORMAL =
Packit 6c4009 
# define FP_SUBNORMAL 3
Packit 6c4009 
      FP_SUBNORMAL,
Packit 6c4009 
    FP_NORMAL =
Packit 6c4009 
# define FP_NORMAL 4
Packit 6c4009 
      FP_NORMAL
Packit 6c4009 
  };
Packit 6c4009
Packit 6c4009 
/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
Packit 6c4009 
   so disable builtins if this is enabled.  When fixed in a newer GCC,
Packit 6c4009 
   the __SUPPORT_SNAN__ check may be skipped for those versions.  */
Packit 6c4009
Packit 6c4009 
/* Return number of classification appropriate for X.  */
Packit Service 72659b 
# if ((__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__)		      \
Packit Service 72659b 
      || __glibc_clang_prereq (2,8))					      \
Packit 6c4009 
     && (!defined __OPTIMIZE_SIZE__ || defined __cplusplus)
Packit 6c4009 
     /* The check for __cplusplus allows the use of the builtin, even
Packit 6c4009 
	when optimization for size is on.  This is provided for
Packit 6c4009 
	libstdc++, only to let its configure test work when it is built
Packit 6c4009 
	with -Os.  No further use of this definition of fpclassify is
Packit 6c4009 
	expected in C++ mode, since libstdc++ provides its own version
Packit 6c4009 
	of fpclassify in cmath (which undefines fpclassify).  */
Packit 6c4009 
#  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,	      \
Packit 6c4009 
     FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
Packit 6c4009 
# else
Packit 6c4009 
#  define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
/* Return nonzero value if sign of X is negative.  */
Packit Service 72659b 
# if __GNUC_PREREQ (6,0) || __glibc_clang_prereq (3,3)
Packit 6c4009 
#  define signbit(x) __builtin_signbit (x)
Packit 6c4009 
# elif defined __cplusplus
Packit 6c4009 
  /* In C++ mode, __MATH_TG cannot be used, because it relies on
Packit 6c4009 
     __builtin_types_compatible_p, which is a C-only builtin.
Packit 6c4009 
     The check for __cplusplus allows the use of the builtin instead of
Packit 6c4009 
     __MATH_TG. This is provided for libstdc++, only to let its configure
Packit 6c4009 
     test work. No further use of this definition of signbit is expected
Packit 6c4009 
     in C++ mode, since libstdc++ provides its own version of signbit
Packit 6c4009 
     in cmath (which undefines signbit). */
Packit 6c4009 
#  define signbit(x) __builtin_signbitl (x)
Packit 6c4009 
# elif __GNUC_PREREQ (4,0)
Packit 6c4009 
#  define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
Packit 6c4009 
# else
Packit 6c4009 
#  define signbit(x) __MATH_TG ((x), __signbit, (x))
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
/* Return nonzero value if X is not +-Inf or NaN.  */
Packit Service 72659b 
# if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
Packit Service 72659b 
     || __glibc_clang_prereq (2,8)
Packit 6c4009 
#  define isfinite(x) __builtin_isfinite (x)
Packit 6c4009 
# else
Packit 6c4009 
#  define isfinite(x) __MATH_TG ((x), __finite, (x))
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
Packit Service 72659b 
# if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
Packit Service 72659b 
     || __glibc_clang_prereq (2,8)
Packit 6c4009 
#  define isnormal(x) __builtin_isnormal (x)
Packit 6c4009 
# else
Packit 6c4009 
#  define isnormal(x) (fpclassify (x) == FP_NORMAL)
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
/* Return nonzero value if X is a NaN.  We could use `fpclassify' but
Packit 6c4009 
   we already have this functions `__isnan' and it is faster.  */
Packit Service 72659b 
# if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
Packit Service 72659b 
     || __glibc_clang_prereq (2,8)
Packit 6c4009 
#  define isnan(x) __builtin_isnan (x)
Packit 6c4009 
# else
Packit 6c4009 
#  define isnan(x) __MATH_TG ((x), __isnan, (x))
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
/* Return nonzero value if X is positive or negative infinity.  */
Packit 6c4009 
# if __HAVE_DISTINCT_FLOAT128 && !__GNUC_PREREQ (7,0) \
Packit 6c4009 
     && !defined __SUPPORT_SNAN__ && !defined __cplusplus
Packit 6c4009 
   /* Since __builtin_isinf_sign is broken for float128 before GCC 7.0,
Packit 6c4009 
      use the helper function, __isinff128, with older compilers.  This is
Packit 6c4009 
      only provided for C mode, because in C++ mode, GCC has no support
Packit 6c4009 
      for __builtin_types_compatible_p (and when in C++ mode, this macro is
Packit 6c4009 
      not used anyway, because libstdc++ headers undefine it).  */
Packit 6c4009 
#  define isinf(x) \
Packit 6c4009 
    (__builtin_types_compatible_p (__typeof (x), _Float128) \
Packit 6c4009 
     ? __isinff128 (x) : __builtin_isinf_sign (x))
Packit Service 72659b 
# elif (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
Packit Service 72659b 
       || __glibc_clang_prereq (3,7)
Packit 6c4009 
#  define isinf(x) __builtin_isinf_sign (x)
Packit 6c4009 
# else
Packit 6c4009 
#  define isinf(x) __MATH_TG ((x), __isinf, (x))
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
/* Bitmasks for the math_errhandling macro.  */
Packit 6c4009 
# define MATH_ERRNO	1	/* errno set by math functions.  */
Packit 6c4009 
# define MATH_ERREXCEPT	2	/* Exceptions raised by math functions.  */
Packit 6c4009
Packit 6c4009 
/* By default all math functions support both errno and exception handling
Packit 6c4009 
   (except for soft floating point implementations which may only support
Packit 6c4009 
   errno handling).  If errno handling is disabled, exceptions are still
Packit 6c4009 
   supported by GLIBC.  Set math_errhandling to 0 with -ffast-math (this is
Packit 6c4009 
   nonconforming but it is more useful than leaving it undefined).  */
Packit 6c4009 
# ifdef __FAST_MATH__
Packit 6c4009 
#  define math_errhandling	0
Packit 6c4009 
# elif defined __NO_MATH_ERRNO__
Packit 6c4009 
#  define math_errhandling	(MATH_ERREXCEPT)
Packit 6c4009 
# else
Packit 6c4009 
#  define math_errhandling	(MATH_ERRNO | MATH_ERREXCEPT)
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
#endif /* Use ISO C99.  */
Packit 6c4009
Packit 6c4009 
#if __GLIBC_USE (IEC_60559_BFP_EXT)
Packit 6c4009 
# include <bits/iscanonical.h>
Packit 6c4009
Packit 6c4009 
/* Return nonzero value if X is a signaling NaN.  */
Packit 6c4009 
# ifndef __cplusplus
Packit 6c4009 
#  define issignaling(x) __MATH_TG ((x), __issignaling, (x))
Packit 6c4009 
# else
Packit 6c4009 
   /* In C++ mode, __MATH_TG cannot be used, because it relies on
Packit 6c4009 
      __builtin_types_compatible_p, which is a C-only builtin.  On the
Packit 6c4009 
      other hand, overloading provides the means to distinguish between
Packit 6c4009 
      the floating-point types.  The overloading resolution will match
Packit 6c4009 
      the correct parameter (regardless of type qualifiers (i.e.: const
Packit 6c4009 
      and volatile)).  */
Packit 6c4009 
extern "C++" {
Packit 6c4009 
inline int issignaling (float __val) { return __issignalingf (__val); }
Packit 6c4009 
inline int issignaling (double __val) { return __issignaling (__val); }
Packit 6c4009 
inline int
Packit 6c4009 
issignaling (long double __val)
Packit 6c4009 
{
Packit 6c4009 
#  ifdef __NO_LONG_DOUBLE_MATH
Packit 6c4009 
  return __issignaling (__val);
Packit 6c4009 
#  else
Packit 6c4009 
  return __issignalingl (__val);
Packit 6c4009 
#  endif
Packit 6c4009 
}
Packit 6c4009 
#  if __HAVE_FLOAT128_UNLIKE_LDBL
Packit 6c4009 
/* When using an IEEE 128-bit long double, _Float128 is defined as long double
Packit 6c4009 
   in C++.  */
Packit 6c4009 
inline int issignaling (_Float128 __val) { return __issignalingf128 (__val); }
Packit 6c4009 
#  endif
Packit 6c4009 
} /* extern C++ */
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
/* Return nonzero value if X is subnormal.  */
Packit 6c4009 
# define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
Packit 6c4009
Packit 6c4009 
/* Return nonzero value if X is zero.  */
Packit 6c4009 
# ifndef __cplusplus
Packit 6c4009 
#  ifdef __SUPPORT_SNAN__
Packit 6c4009 
#   define iszero(x) (fpclassify (x) == FP_ZERO)
Packit 6c4009 
#  else
Packit 6c4009 
#   define iszero(x) (((__typeof (x)) (x)) == 0)
Packit 6c4009 
#  endif
Packit 6c4009 
# else	/* __cplusplus */
Packit 6c4009 
extern "C++" {
Packit 6c4009 
#  ifdef __SUPPORT_SNAN__
Packit 6c4009 
inline int
Packit 6c4009 
iszero (float __val)
Packit 6c4009 
{
Packit 6c4009 
  return __fpclassifyf (__val) == FP_ZERO;
Packit 6c4009 
}
Packit 6c4009 
inline int
Packit 6c4009 
iszero (double __val)
Packit 6c4009 
{
Packit 6c4009 
  return __fpclassify (__val) == FP_ZERO;
Packit 6c4009 
}
Packit 6c4009 
inline int
Packit 6c4009 
iszero (long double __val)
Packit 6c4009 
{
Packit 6c4009 
#   ifdef __NO_LONG_DOUBLE_MATH
Packit 6c4009 
  return __fpclassify (__val) == FP_ZERO;
Packit 6c4009 
#   else
Packit 6c4009 
  return __fpclassifyl (__val) == FP_ZERO;
Packit 6c4009 
#   endif
Packit 6c4009 
}
Packit 6c4009 
#   if __HAVE_FLOAT128_UNLIKE_LDBL
Packit 6c4009 
  /* When using an IEEE 128-bit long double, _Float128 is defined as long double
Packit 6c4009 
     in C++.  */
Packit 6c4009 
inline int
Packit 6c4009 
iszero (_Float128 __val)
Packit 6c4009 
{
Packit 6c4009 
  return __fpclassifyf128 (__val) == FP_ZERO;
Packit 6c4009 
}
Packit 6c4009 
#   endif
Packit 6c4009 
#  else
Packit 6c4009 
template <class __T> inline bool
Packit 6c4009 
iszero (__T __val)
Packit 6c4009 
{
Packit 6c4009 
  return __val == 0;
Packit 6c4009 
}
Packit 6c4009 
#  endif
Packit 6c4009 
} /* extern C++ */
Packit 6c4009 
# endif	/* __cplusplus */
Packit 6c4009 
#endif /* Use IEC_60559_BFP_EXT.  */
Packit 6c4009
Packit 6c4009 
#ifdef __USE_XOPEN
Packit 6c4009 
/* X/Open wants another strange constant.  */
Packit 6c4009 
# define MAXFLOAT	3.40282347e+38F
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009
Packit 6c4009 
/* Some useful constants.  */
Packit 6c4009 
#if defined __USE_MISC || defined __USE_XOPEN
Packit 6c4009 
# define M_E		2.7182818284590452354	/* e */
Packit 6c4009 
# define M_LOG2E	1.4426950408889634074	/* log_2 e */
Packit 6c4009 
# define M_LOG10E	0.43429448190325182765	/* log_10 e */
Packit 6c4009 
# define M_LN2		0.69314718055994530942	/* log_e 2 */
Packit 6c4009 
# define M_LN10		2.30258509299404568402	/* log_e 10 */
Packit 6c4009 
# define M_PI		3.14159265358979323846	/* pi */
Packit 6c4009 
# define M_PI_2		1.57079632679489661923	/* pi/2 */
Packit 6c4009 
# define M_PI_4		0.78539816339744830962	/* pi/4 */
Packit 6c4009 
# define M_1_PI		0.31830988618379067154	/* 1/pi */
Packit 6c4009 
# define M_2_PI		0.63661977236758134308	/* 2/pi */
Packit 6c4009 
# define M_2_SQRTPI	1.12837916709551257390	/* 2/sqrt(pi) */
Packit 6c4009 
# define M_SQRT2	1.41421356237309504880	/* sqrt(2) */
Packit 6c4009 
# define M_SQRT1_2	0.70710678118654752440	/* 1/sqrt(2) */
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
/* The above constants are not adequate for computation using `long double's.
Packit 6c4009 
   Therefore we provide as an extension constants with similar names as a
Packit 6c4009 
   GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
Packit 6c4009 
#ifdef __USE_GNU
Packit 6c4009 
# define M_El		2.718281828459045235360287471352662498L /* e */
Packit 6c4009 
# define M_LOG2El	1.442695040888963407359924681001892137L /* log_2 e */
Packit 6c4009 
# define M_LOG10El	0.434294481903251827651128918916605082L /* log_10 e */
Packit 6c4009 
# define M_LN2l		0.693147180559945309417232121458176568L /* log_e 2 */
Packit 6c4009 
# define M_LN10l	2.302585092994045684017991454684364208L /* log_e 10 */
Packit 6c4009 
# define M_PIl		3.141592653589793238462643383279502884L /* pi */
Packit 6c4009 
# define M_PI_2l	1.570796326794896619231321691639751442L /* pi/2 */
Packit 6c4009 
# define M_PI_4l	0.785398163397448309615660845819875721L /* pi/4 */
Packit 6c4009 
# define M_1_PIl	0.318309886183790671537767526745028724L /* 1/pi */
Packit 6c4009 
# define M_2_PIl	0.636619772367581343075535053490057448L /* 2/pi */
Packit 6c4009 
# define M_2_SQRTPIl	1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
Packit 6c4009 
# define M_SQRT2l	1.414213562373095048801688724209698079L /* sqrt(2) */
Packit 6c4009 
# define M_SQRT1_2l	0.707106781186547524400844362104849039L /* 1/sqrt(2) */
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if __HAVE_FLOAT16 && defined __USE_GNU
Packit 6c4009 
# define M_Ef16		__f16 (2.718281828459045235360287471352662498) /* e */
Packit 6c4009 
# define M_LOG2Ef16	__f16 (1.442695040888963407359924681001892137) /* log_2 e */
Packit 6c4009 
# define M_LOG10Ef16	__f16 (0.434294481903251827651128918916605082) /* log_10 e */
Packit 6c4009 
# define M_LN2f16	__f16 (0.693147180559945309417232121458176568) /* log_e 2 */
Packit 6c4009 
# define M_LN10f16	__f16 (2.302585092994045684017991454684364208) /* log_e 10 */
Packit 6c4009 
# define M_PIf16	__f16 (3.141592653589793238462643383279502884) /* pi */
Packit 6c4009 
# define M_PI_2f16	__f16 (1.570796326794896619231321691639751442) /* pi/2 */
Packit 6c4009 
# define M_PI_4f16	__f16 (0.785398163397448309615660845819875721) /* pi/4 */
Packit 6c4009 
# define M_1_PIf16	__f16 (0.318309886183790671537767526745028724) /* 1/pi */
Packit 6c4009 
# define M_2_PIf16	__f16 (0.636619772367581343075535053490057448) /* 2/pi */
Packit 6c4009 
# define M_2_SQRTPIf16	__f16 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
Packit 6c4009 
# define M_SQRT2f16	__f16 (1.414213562373095048801688724209698079) /* sqrt(2) */
Packit 6c4009 
# define M_SQRT1_2f16	__f16 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if __HAVE_FLOAT32 && defined __USE_GNU
Packit 6c4009 
# define M_Ef32		__f32 (2.718281828459045235360287471352662498) /* e */
Packit 6c4009 
# define M_LOG2Ef32	__f32 (1.442695040888963407359924681001892137) /* log_2 e */
Packit 6c4009 
# define M_LOG10Ef32	__f32 (0.434294481903251827651128918916605082) /* log_10 e */
Packit 6c4009 
# define M_LN2f32	__f32 (0.693147180559945309417232121458176568) /* log_e 2 */
Packit 6c4009 
# define M_LN10f32	__f32 (2.302585092994045684017991454684364208) /* log_e 10 */
Packit 6c4009 
# define M_PIf32	__f32 (3.141592653589793238462643383279502884) /* pi */
Packit 6c4009 
# define M_PI_2f32	__f32 (1.570796326794896619231321691639751442) /* pi/2 */
Packit 6c4009 
# define M_PI_4f32	__f32 (0.785398163397448309615660845819875721) /* pi/4 */
Packit 6c4009 
# define M_1_PIf32	__f32 (0.318309886183790671537767526745028724) /* 1/pi */
Packit 6c4009 
# define M_2_PIf32	__f32 (0.636619772367581343075535053490057448) /* 2/pi */
Packit 6c4009 
# define M_2_SQRTPIf32	__f32 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
Packit 6c4009 
# define M_SQRT2f32	__f32 (1.414213562373095048801688724209698079) /* sqrt(2) */
Packit 6c4009 
# define M_SQRT1_2f32	__f32 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if __HAVE_FLOAT64 && defined __USE_GNU
Packit 6c4009 
# define M_Ef64		__f64 (2.718281828459045235360287471352662498) /* e */
Packit 6c4009 
# define M_LOG2Ef64	__f64 (1.442695040888963407359924681001892137) /* log_2 e */
Packit 6c4009 
# define M_LOG10Ef64	__f64 (0.434294481903251827651128918916605082) /* log_10 e */
Packit 6c4009 
# define M_LN2f64	__f64 (0.693147180559945309417232121458176568) /* log_e 2 */
Packit 6c4009 
# define M_LN10f64	__f64 (2.302585092994045684017991454684364208) /* log_e 10 */
Packit 6c4009 
# define M_PIf64	__f64 (3.141592653589793238462643383279502884) /* pi */
Packit 6c4009 
# define M_PI_2f64	__f64 (1.570796326794896619231321691639751442) /* pi/2 */
Packit 6c4009 
# define M_PI_4f64	__f64 (0.785398163397448309615660845819875721) /* pi/4 */
Packit 6c4009 
# define M_1_PIf64	__f64 (0.318309886183790671537767526745028724) /* 1/pi */
Packit 6c4009 
# define M_2_PIf64	__f64 (0.636619772367581343075535053490057448) /* 2/pi */
Packit 6c4009 
# define M_2_SQRTPIf64	__f64 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
Packit 6c4009 
# define M_SQRT2f64	__f64 (1.414213562373095048801688724209698079) /* sqrt(2) */
Packit 6c4009 
# define M_SQRT1_2f64	__f64 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if __HAVE_FLOAT128 && defined __USE_GNU
Packit 6c4009 
# define M_Ef128	__f128 (2.718281828459045235360287471352662498) /* e */
Packit 6c4009 
# define M_LOG2Ef128	__f128 (1.442695040888963407359924681001892137) /* log_2 e */
Packit 6c4009 
# define M_LOG10Ef128	__f128 (0.434294481903251827651128918916605082) /* log_10 e */
Packit 6c4009 
# define M_LN2f128	__f128 (0.693147180559945309417232121458176568) /* log_e 2 */
Packit 6c4009 
# define M_LN10f128	__f128 (2.302585092994045684017991454684364208) /* log_e 10 */
Packit 6c4009 
# define M_PIf128	__f128 (3.141592653589793238462643383279502884) /* pi */
Packit 6c4009 
# define M_PI_2f128	__f128 (1.570796326794896619231321691639751442) /* pi/2 */
Packit 6c4009 
# define M_PI_4f128	__f128 (0.785398163397448309615660845819875721) /* pi/4 */
Packit 6c4009 
# define M_1_PIf128	__f128 (0.318309886183790671537767526745028724) /* 1/pi */
Packit 6c4009 
# define M_2_PIf128	__f128 (0.636619772367581343075535053490057448) /* 2/pi */
Packit 6c4009 
# define M_2_SQRTPIf128	__f128 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
Packit 6c4009 
# define M_SQRT2f128	__f128 (1.414213562373095048801688724209698079) /* sqrt(2) */
Packit 6c4009 
# define M_SQRT1_2f128	__f128 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if __HAVE_FLOAT32X && defined __USE_GNU
Packit 6c4009 
# define M_Ef32x	__f32x (2.718281828459045235360287471352662498) /* e */
Packit 6c4009 
# define M_LOG2Ef32x	__f32x (1.442695040888963407359924681001892137) /* log_2 e */
Packit 6c4009 
# define M_LOG10Ef32x	__f32x (0.434294481903251827651128918916605082) /* log_10 e */
Packit 6c4009 
# define M_LN2f32x	__f32x (0.693147180559945309417232121458176568) /* log_e 2 */
Packit 6c4009 
# define M_LN10f32x	__f32x (2.302585092994045684017991454684364208) /* log_e 10 */
Packit 6c4009 
# define M_PIf32x	__f32x (3.141592653589793238462643383279502884) /* pi */
Packit 6c4009 
# define M_PI_2f32x	__f32x (1.570796326794896619231321691639751442) /* pi/2 */
Packit 6c4009 
# define M_PI_4f32x	__f32x (0.785398163397448309615660845819875721) /* pi/4 */
Packit 6c4009 
# define M_1_PIf32x	__f32x (0.318309886183790671537767526745028724) /* 1/pi */
Packit 6c4009 
# define M_2_PIf32x	__f32x (0.636619772367581343075535053490057448) /* 2/pi */
Packit 6c4009 
# define M_2_SQRTPIf32x	__f32x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
Packit 6c4009 
# define M_SQRT2f32x	__f32x (1.414213562373095048801688724209698079) /* sqrt(2) */
Packit 6c4009 
# define M_SQRT1_2f32x	__f32x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if __HAVE_FLOAT64X && defined __USE_GNU
Packit 6c4009 
# define M_Ef64x	__f64x (2.718281828459045235360287471352662498) /* e */
Packit 6c4009 
# define M_LOG2Ef64x	__f64x (1.442695040888963407359924681001892137) /* log_2 e */
Packit 6c4009 
# define M_LOG10Ef64x	__f64x (0.434294481903251827651128918916605082) /* log_10 e */
Packit 6c4009 
# define M_LN2f64x	__f64x (0.693147180559945309417232121458176568) /* log_e 2 */
Packit 6c4009 
# define M_LN10f64x	__f64x (2.302585092994045684017991454684364208) /* log_e 10 */
Packit 6c4009 
# define M_PIf64x	__f64x (3.141592653589793238462643383279502884) /* pi */
Packit 6c4009 
# define M_PI_2f64x	__f64x (1.570796326794896619231321691639751442) /* pi/2 */
Packit 6c4009 
# define M_PI_4f64x	__f64x (0.785398163397448309615660845819875721) /* pi/4 */
Packit 6c4009 
# define M_1_PIf64x	__f64x (0.318309886183790671537767526745028724) /* 1/pi */
Packit 6c4009 
# define M_2_PIf64x	__f64x (0.636619772367581343075535053490057448) /* 2/pi */
Packit 6c4009 
# define M_2_SQRTPIf64x	__f64x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
Packit 6c4009 
# define M_SQRT2f64x	__f64x (1.414213562373095048801688724209698079) /* sqrt(2) */
Packit 6c4009 
# define M_SQRT1_2f64x	__f64x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#if __HAVE_FLOAT128X && defined __USE_GNU
Packit 6c4009 
# error "M_* values needed for _Float128x"
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
/* When compiling in strict ISO C compatible mode we must not use the
Packit 6c4009 
   inline functions since they, among other things, do not set the
Packit 6c4009 
   `errno' variable correctly.  */
Packit 6c4009 
#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
Packit 6c4009 
# define __NO_MATH_INLINES	1
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
#ifdef __USE_ISOC99
Packit 6c4009 
# if __GNUC_PREREQ (3, 1)
Packit 6c4009 
/* ISO C99 defines some macros to compare number while taking care for
Packit 6c4009 
   unordered numbers.  Many FPUs provide special instructions to support
Packit 6c4009 
   these operations.  Generic support in GCC for these as builtins went
Packit 6c4009 
   in 2.97, but not all cpus added their patterns until 3.1.  Therefore
Packit 6c4009 
   we enable the builtins from 3.1 onwards and use a generic implementation
Packit 6c4009 
   othwerwise.  */
Packit 6c4009 
#  define isgreater(x, y)	__builtin_isgreater(x, y)
Packit 6c4009 
#  define isgreaterequal(x, y)	__builtin_isgreaterequal(x, y)
Packit 6c4009 
#  define isless(x, y)		__builtin_isless(x, y)
Packit 6c4009 
#  define islessequal(x, y)	__builtin_islessequal(x, y)
Packit 6c4009 
#  define islessgreater(x, y)	__builtin_islessgreater(x, y)
Packit 6c4009 
#  define isunordered(x, y)	__builtin_isunordered(x, y)
Packit 6c4009 
# else
Packit 6c4009 
#  define isgreater(x, y) \
Packit 6c4009 
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
Packit 6c4009 
		    !isunordered (__x, __y) && __x > __y; }))
Packit 6c4009 
#  define isgreaterequal(x, y) \
Packit 6c4009 
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
Packit 6c4009 
		    !isunordered (__x, __y) && __x >= __y; }))
Packit 6c4009 
#  define isless(x, y) \
Packit 6c4009 
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
Packit 6c4009 
		    !isunordered (__x, __y) && __x < __y; }))
Packit 6c4009 
#  define islessequal(x, y) \
Packit 6c4009 
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
Packit 6c4009 
		    !isunordered (__x, __y) && __x <= __y; }))
Packit 6c4009 
#  define islessgreater(x, y) \
Packit 6c4009 
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
Packit 6c4009 
		    !isunordered (__x, __y) && __x != __y; }))
Packit 6c4009 
/* isunordered must always check both operands first for signaling NaNs.  */
Packit 6c4009 
#  define isunordered(x, y) \
Packit 6c4009 
  (__extension__ ({ __typeof__ (x) __u = (x); __typeof__ (y) __v = (y); \
Packit 6c4009 
		    __u != __v && (__u != __u || __v != __v); }))
Packit 6c4009 
# endif
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
/* Get machine-dependent inline versions (if there are any).  */
Packit 6c4009 
#ifdef __USE_EXTERN_INLINES
Packit 6c4009 
# include <bits/mathinline.h>
Packit 6c4009 
#endif
Packit 6c4009
Packit 6c4009 
/* Define special entry points to use when the compiler got told to
Packit 6c4009 
   only expect finite results.  */
Packit 6c4009 
#if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
Packit 6c4009
Packit 6c4009 
/* Include bits/math-finite.h for double.  */
Packit 6c4009 
# define _Mdouble_ double
Packit 6c4009 
# define __MATH_DECLARING_DOUBLE 1
Packit 6c4009 
# define __MATH_DECLARING_FLOATN 0
Packit 6c4009 
# define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## reentrant
Packit 6c4009 
# define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## reentrant ## _finite
Packit 6c4009 
# include <bits/math-finite.h>
Packit 6c4009 
# undef _Mdouble_
Packit 6c4009 
# undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
# undef __MATH_DECLARING_FLOATN
Packit 6c4009 
# undef __REDIRFROM_X
Packit 6c4009 
# undef __REDIRTO_X
Packit 6c4009
Packit 6c4009 
/* When __USE_ISOC99 is defined, include math-finite for float and
Packit 6c4009 
   long double, as well.  */
Packit 6c4009 
# ifdef __USE_ISOC99
Packit 6c4009
Packit 6c4009 
/* Include bits/math-finite.h for float.  */
Packit 6c4009 
#  define _Mdouble_ float
Packit 6c4009 
#  define __MATH_DECLARING_DOUBLE 0
Packit 6c4009 
#  define __MATH_DECLARING_FLOATN 0
Packit 6c4009 
#  define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## f ## reentrant
Packit 6c4009 
#  define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## f ## reentrant ## _finite
Packit 6c4009 
#  include <bits/math-finite.h>
Packit 6c4009 
#  undef _Mdouble_
Packit 6c4009 
#  undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
#  undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#  undef __REDIRFROM_X
Packit 6c4009 
#  undef __REDIRTO_X
Packit 6c4009
Packit 6c4009 
/* Include bits/math-finite.h for long double.  */
Packit 6c4009 
#  ifdef __MATH_DECLARE_LDOUBLE
Packit 6c4009 
#   define _Mdouble_ long double
Packit 6c4009 
#   define __MATH_DECLARING_DOUBLE 0
Packit 6c4009 
#   define __MATH_DECLARING_FLOATN 0
Packit 6c4009 
#   define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## l ## reentrant
Packit 6c4009 
#   ifdef __NO_LONG_DOUBLE_MATH
Packit 6c4009 
#    define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## reentrant ## _finite
Packit 6c4009 
#   else
Packit 6c4009 
#    define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## l ## reentrant ## _finite
Packit 6c4009 
#   endif
Packit 6c4009 
#   include <bits/math-finite.h>
Packit 6c4009 
#   undef _Mdouble_
Packit 6c4009 
#   undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
#   undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#   undef __REDIRFROM_X
Packit 6c4009 
#   undef __REDIRTO_X
Packit 6c4009 
#  endif
Packit 6c4009
Packit 6c4009 
# endif /* __USE_ISOC99.  */
Packit 6c4009
Packit 6c4009 
/* Include bits/math-finite.h for _FloatN and _FloatNx.  */
Packit 6c4009
Packit 6c4009 
# if (__HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC))	\
Packit 6c4009 
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  define _Mdouble_ _Float16
Packit 6c4009 
#  define __MATH_DECLARING_DOUBLE 0
Packit 6c4009 
#  define __MATH_DECLARING_FLOATN 1
Packit 6c4009 
#  define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## f16 ## reentrant
Packit 6c4009 
#  if __HAVE_DISTINCT_FLOAT16
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## f16 ## reentrant ## _finite
Packit 6c4009 
#  else
Packit 6c4009 
#   error "non-disinct _Float16"
Packit 6c4009 
#  endif
Packit 6c4009 
#  include <bits/math-finite.h>
Packit 6c4009 
#  undef _Mdouble_
Packit 6c4009 
#  undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
#  undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#  undef __REDIRFROM_X
Packit 6c4009 
#  undef __REDIRTO_X
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if (__HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC))	\
Packit 6c4009 
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  define _Mdouble_ _Float32
Packit 6c4009 
#  define __MATH_DECLARING_DOUBLE 0
Packit 6c4009 
#  define __MATH_DECLARING_FLOATN 1
Packit 6c4009 
#  define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## f32 ## reentrant
Packit 6c4009 
#  if __HAVE_DISTINCT_FLOAT32
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## f32 ## reentrant ## _finite
Packit 6c4009 
#  else
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## f ## reentrant ## _finite
Packit 6c4009 
#  endif
Packit 6c4009 
#  include <bits/math-finite.h>
Packit 6c4009 
#  undef _Mdouble_
Packit 6c4009 
#  undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
#  undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#  undef __REDIRFROM_X
Packit 6c4009 
#  undef __REDIRTO_X
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if (__HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC))	\
Packit 6c4009 
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  define _Mdouble_ _Float64
Packit 6c4009 
#  define __MATH_DECLARING_DOUBLE 0
Packit 6c4009 
#  define __MATH_DECLARING_FLOATN 1
Packit 6c4009 
#  define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## f64 ## reentrant
Packit 6c4009 
#  if __HAVE_DISTINCT_FLOAT64
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## f64 ## reentrant ## _finite
Packit 6c4009 
#  else
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## reentrant ## _finite
Packit 6c4009 
#  endif
Packit 6c4009 
#  include <bits/math-finite.h>
Packit 6c4009 
#  undef _Mdouble_
Packit 6c4009 
#  undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
#  undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#  undef __REDIRFROM_X
Packit 6c4009 
#  undef __REDIRTO_X
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if (__HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC))	\
Packit 6c4009 
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  define _Mdouble_ _Float128
Packit 6c4009 
#  define __MATH_DECLARING_DOUBLE 0
Packit 6c4009 
#  define __MATH_DECLARING_FLOATN 1
Packit 6c4009 
#  define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## f128 ## reentrant
Packit 6c4009 
#  if __HAVE_DISTINCT_FLOAT128
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## f128 ## reentrant ## _finite
Packit 6c4009 
#  else
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## l ## reentrant ## _finite
Packit 6c4009 
#  endif
Packit 6c4009 
#  include <bits/math-finite.h>
Packit 6c4009 
#  undef _Mdouble_
Packit 6c4009 
#  undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
#  undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#  undef __REDIRFROM_X
Packit 6c4009 
#  undef __REDIRTO_X
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if (__HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC))	\
Packit 6c4009 
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  define _Mdouble_ _Float32x
Packit 6c4009 
#  define __MATH_DECLARING_DOUBLE 0
Packit 6c4009 
#  define __MATH_DECLARING_FLOATN 1
Packit 6c4009 
#  define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## f32x ## reentrant
Packit 6c4009 
#  if __HAVE_DISTINCT_FLOAT32X
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## f32x ## reentrant ## _finite
Packit 6c4009 
#  else
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## reentrant ## _finite
Packit 6c4009 
#  endif
Packit 6c4009 
#  include <bits/math-finite.h>
Packit 6c4009 
#  undef _Mdouble_
Packit 6c4009 
#  undef __MATH_DECLARING_DOUBLE
Packit 6c4009 
#  undef __MATH_DECLARING_FLOATN
Packit 6c4009 
#  undef __REDIRFROM_X
Packit 6c4009 
#  undef __REDIRTO_X
Packit 6c4009 
# endif
Packit 6c4009
Packit 6c4009 
# if (__HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC))	\
Packit 6c4009 
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
Packit 6c4009 
#  define _Mdouble_ _Float64x
Packit 6c4009 
#  define __MATH_DECLARING_DOUBLE 0
Packit 6c4009 
#  define __MATH_DECLARING_FLOATN 1
Packit 6c4009 
#  define __REDIRFROM_X(function, reentrant) \
Packit 6c4009 
  function ## f64x ## reentrant
Packit 6c4009 
#  if __HAVE_DISTINCT_FLOAT64X
Packit 6c4009 
#   define __REDIRTO_X(function, reentrant) \
Packit 6c4009 
   __ ## function ## f64x ## reentrant ## _finite
Packit 6c4009 
#  elif __HAVE_FLOAT64X_LONG_DOUBLE
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#   define __REDIRTO_X(function, reentrant) \
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   __ ## function ## l ## reentrant ## _finite
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#  else
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#   define __REDIRTO_X(function, reentrant) \
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   __ ## function ## f128 ## reentrant ## _finite
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#  endif
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#  include <bits/math-finite.h>
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#  undef _Mdouble_
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#  undef __MATH_DECLARING_DOUBLE
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#  undef __MATH_DECLARING_FLOATN
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#  undef __REDIRFROM_X
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#  undef __REDIRTO_X
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# endif
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# if (__HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)) \
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      && __GLIBC_USE (IEC_60559_TYPES_EXT)
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#  define _Mdouble_ _Float128x
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#  define __MATH_DECLARING_DOUBLE 0
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#  define __MATH_DECLARING_FLOATN 1
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#  define __REDIRFROM_X(function, reentrant) \
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  function ## f128x ## reentrant
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#  if __HAVE_DISTINCT_FLOAT128X
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#   define __REDIRTO_X(function, reentrant) \
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   __ ## function ## f128x ## reentrant ## _finite
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#  else
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#   error "non-disinct _Float128x"
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#  endif
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#  include <bits/math-finite.h>
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#  undef _Mdouble_
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#  undef __MATH_DECLARING_DOUBLE
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#  undef __MATH_DECLARING_FLOATN
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#  undef __REDIRFROM_X
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#  undef __REDIRTO_X
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# endif
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#endif /* __FINITE_MATH_ONLY__ > 0.  */
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#if __GLIBC_USE (IEC_60559_BFP_EXT)
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/* An expression whose type has the widest of the evaluation formats
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   of X and Y (which are of floating-point types).  */
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# if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
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#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
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# elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
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#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
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# elif __FLT_EVAL_METHOD__ == 0 || __FLT_EVAL_METHOD__ == 32
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#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0f)
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# else
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#  define __MATH_EVAL_FMT2(x, y) ((x) + (y))
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# endif
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/* Return X == Y but raising "invalid" and setting errno if X or Y is
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   a NaN.  */
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# if !defined __cplusplus || (__cplusplus < 201103L && !defined __GNUC__)
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#  define iseqsig(x, y) \
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   __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
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# else
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/* In C++ mode, __MATH_TG cannot be used, because it relies on
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   __builtin_types_compatible_p, which is a C-only builtin.  Moreover,
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   the comparison macros from ISO C take two floating-point arguments,
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   which need not have the same type.  Choosing what underlying function
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   to call requires evaluating the formats of the arguments, then
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   selecting which is wider.  The macro __MATH_EVAL_FMT2 provides this
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   information, however, only the type of the macro expansion is
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   relevant (actually evaluating the expression would be incorrect).
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   Thus, the type is used as a template parameter for __iseqsig_type,
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   which calls the appropriate underlying function.  */
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extern "C++" {
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template<typename> struct __iseqsig_type;
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template<> struct __iseqsig_type<float>
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{
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  static int __call (float __x, float __y) throw ()
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  {
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    return __iseqsigf (__x, __y);
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  }
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};
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template<> struct __iseqsig_type<double>
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{
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  static int __call (double __x, double __y) throw ()
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  {
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    return __iseqsig (__x, __y);
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  }
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};
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template<> struct __iseqsig_type<long double>
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{
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  static int __call (long double __x, long double __y) throw ()
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  {
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#  ifndef __NO_LONG_DOUBLE_MATH
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    return __iseqsigl (__x, __y);
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#  else
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    return __iseqsig (__x, __y);
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#  endif
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  }
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};
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#  if __HAVE_FLOAT128_UNLIKE_LDBL
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  /* When using an IEEE 128-bit long double, _Float128 is defined as long double
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     in C++.  */
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template<> struct __iseqsig_type<_Float128>
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{
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  static int __call (_Float128 __x, _Float128 __y) throw ()
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  {
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    return __iseqsigf128 (__x, __y);
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  }
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};
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#  endif
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template<typename _T1, typename _T2>
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inline int
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iseqsig (_T1 __x, _T2 __y) throw ()
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{
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#  if __cplusplus >= 201103L
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  typedef decltype (__MATH_EVAL_FMT2 (__x, __y)) _T3;
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#  else
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  typedef __typeof (__MATH_EVAL_FMT2 (__x, __y)) _T3;
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#  endif
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  return __iseqsig_type<_T3>::__call (__x, __y);
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}
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} /* extern "C++" */
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# endif /* __cplusplus */
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#endif
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__END_DECLS
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#endif /* math.h  */

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