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b38042f514
This is a common programming error, and the cause of the problem is not always obvious. <tgmath.h> defines a log macro, but it includes <math.h> before that, so that is compatible with the warning.
829 lines
27 KiB
C++
829 lines
27 KiB
C++
/* Declarations for math functions.
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Copyright (C) 1991-2017 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_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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#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_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
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# define SNANF128 (__builtin_nansf128 (""))
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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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# ifndef _Mfloat_
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# define _Mfloat_ float
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# endif
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# define _Mdouble_ _Mfloat_
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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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# ifndef _Mlong_double_
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# define _Mlong_double_ long double
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# endif
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# define _Mdouble_ _Mlong_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 again, this time using `_Float128'
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instead of `double' and appending f128 to each function name. */
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#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)
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# ifndef _Mfloat128_
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# define _Mfloat128_ _Float128
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# endif
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# define _Mdouble_ _Mfloat128_
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# define __MATH_PRECNAME(name,r) name##f128##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_FLOAT128
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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_FLOAT128. */
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#undef __MATHDECL_1
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#undef __MATHDECL
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#undef __MATHCALL
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#if defined __USE_MISC || defined __USE_XOPEN
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/* This variable is used by `gamma' and `lgamma'. */
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extern int signgam;
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#endif
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/* Depending on the type of TG_ARG, call an appropriately suffixed
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version of FUNC with arguments (including parentheses) ARGS.
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Suffixed functions may not exist for long double if it has the same
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format as double, or for other types with the same format as float,
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double or long double. The behavior is undefined if the argument
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does not have a real floating type. The definition may use a
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conditional expression, so all suffixed versions of FUNC must
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return the same type (FUNC may include a cast if necessary rather
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than being a single identifier). */
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#ifdef __NO_LONG_DOUBLE_MATH
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# define __MATH_TG(TG_ARG, FUNC, ARGS) \
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(sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
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#elif __HAVE_DISTINCT_FLOAT128
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# if __HAVE_GENERIC_SELECTION
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# define __MATH_TG(TG_ARG, FUNC, ARGS) \
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_Generic ((TG_ARG), \
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float: FUNC ## f ARGS, \
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default: FUNC ARGS, \
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long double: FUNC ## l ARGS, \
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_Float128: FUNC ## f128 ARGS)
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# else
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# define __MATH_TG(TG_ARG, FUNC, ARGS) \
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__builtin_choose_expr \
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(__builtin_types_compatible_p (__typeof (TG_ARG), float), \
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FUNC ## f ARGS, \
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__builtin_choose_expr \
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(__builtin_types_compatible_p (__typeof (TG_ARG), double), \
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|
FUNC ARGS, \
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__builtin_choose_expr \
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|
(__builtin_types_compatible_p (__typeof (TG_ARG), long double), \
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FUNC ## l ARGS, \
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FUNC ## f128 ARGS)))
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# endif
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#else
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# define __MATH_TG(TG_ARG, FUNC, ARGS) \
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(sizeof (TG_ARG) == sizeof (float) \
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? FUNC ## f ARGS \
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: sizeof (TG_ARG) == sizeof (double) \
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? FUNC ARGS \
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: FUNC ## l ARGS)
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#endif
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/* ISO C99 defines some generic macros which work on any data type. */
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#ifdef __USE_ISOC99
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/* All floating-point numbers can be put in one of these categories. */
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enum
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{
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FP_NAN =
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# define FP_NAN 0
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FP_NAN,
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FP_INFINITE =
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# define FP_INFINITE 1
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FP_INFINITE,
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FP_ZERO =
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# define FP_ZERO 2
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FP_ZERO,
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FP_SUBNORMAL =
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|
# define FP_SUBNORMAL 3
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FP_SUBNORMAL,
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FP_NORMAL =
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|
# define FP_NORMAL 4
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FP_NORMAL
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|
};
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|
/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
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|
so disable builtins if this is enabled. When fixed in a newer GCC,
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|
the __SUPPORT_SNAN__ check may be skipped for those versions. */
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|
/* Return number of classification appropriate for X. */
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|
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ \
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|
&& !defined __OPTIMIZE_SIZE__
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|
# define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \
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FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
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# else
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|
# define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
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# endif
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/* Return nonzero value if sign of X is negative. */
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|
# if __GNUC_PREREQ (6,0)
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# define signbit(x) __builtin_signbit (x)
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# elif __GNUC_PREREQ (4,0)
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# define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
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# else
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# define signbit(x) __MATH_TG ((x), __signbit, (x))
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# endif
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|
/* Return nonzero value if X is not +-Inf or NaN. */
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|
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
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|
# define isfinite(x) __builtin_isfinite (x)
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# else
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|
# define isfinite(x) __MATH_TG ((x), __finite, (x))
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|
# endif
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|
|
/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
|
|
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
|
|
# define isnormal(x) __builtin_isnormal (x)
|
|
# else
|
|
# define isnormal(x) (fpclassify (x) == FP_NORMAL)
|
|
# endif
|
|
|
|
/* Return nonzero value if X is a NaN. We could use `fpclassify' but
|
|
we already have this functions `__isnan' and it is faster. */
|
|
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
|
|
# define isnan(x) __builtin_isnan (x)
|
|
# else
|
|
# define isnan(x) __MATH_TG ((x), __isnan, (x))
|
|
# endif
|
|
|
|
/* Return nonzero value if X is positive or negative infinity. */
|
|
# if __HAVE_DISTINCT_FLOAT128 && !__GNUC_PREREQ (7,0) \
|
|
&& !defined __SUPPORT_SNAN__ && !defined __cplusplus
|
|
/* Since __builtin_isinf_sign is broken for float128 before GCC 7.0,
|
|
use the helper function, __isinff128, with older compilers. This is
|
|
only provided for C mode, because in C++ mode, GCC has no support
|
|
for __builtin_types_compatible_p (and when in C++ mode, this macro is
|
|
not used anyway, because libstdc++ headers undefine it). */
|
|
# define isinf(x) \
|
|
(__builtin_types_compatible_p (__typeof (x), _Float128) \
|
|
? __isinff128 (x) : __builtin_isinf_sign (x))
|
|
# elif __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
|
|
# define isinf(x) __builtin_isinf_sign (x)
|
|
# else
|
|
# define isinf(x) __MATH_TG ((x), __isinf, (x))
|
|
# endif
|
|
|
|
/* Bitmasks for the math_errhandling macro. */
|
|
# define MATH_ERRNO 1 /* errno set by math functions. */
|
|
# define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
|
|
|
|
/* By default all functions support both errno and exception handling.
|
|
In gcc's fast math mode and if inline functions are defined this
|
|
might not be true. */
|
|
# ifndef __FAST_MATH__
|
|
# define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
|
|
# endif
|
|
|
|
#endif /* Use ISO C99. */
|
|
|
|
#if __GLIBC_USE (IEC_60559_BFP_EXT)
|
|
# include <bits/iscanonical.h>
|
|
|
|
/* Return nonzero value if X is a signaling NaN. */
|
|
# ifndef __cplusplus
|
|
# define issignaling(x) __MATH_TG ((x), __issignaling, (x))
|
|
# else
|
|
/* In C++ mode, __MATH_TG cannot be used, because it relies on
|
|
__builtin_types_compatible_p, which is a C-only builtin. On the
|
|
other hand, overloading provides the means to distinguish between
|
|
the floating-point types. The overloading resolution will match
|
|
the correct parameter (regardless of type qualifiers (i.e.: const
|
|
and volatile). */
|
|
extern "C++" {
|
|
inline int issignaling (float __val) { return __issignalingf (__val); }
|
|
inline int issignaling (double __val) { return __issignaling (__val); }
|
|
inline int
|
|
issignaling (long double __val)
|
|
{
|
|
# ifdef __NO_LONG_DOUBLE_MATH
|
|
return __issignaling (__val);
|
|
# else
|
|
return __issignalingl (__val);
|
|
# endif
|
|
}
|
|
# if __HAVE_DISTINCT_FLOAT128
|
|
inline int issignaling (_Float128 __val) { return __issignalingf128 (__val); }
|
|
# endif
|
|
} /* extern C++ */
|
|
# endif
|
|
|
|
/* Return nonzero value if X is subnormal. */
|
|
# define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
|
|
|
|
/* Return nonzero value if X is zero. */
|
|
# ifndef __cplusplus
|
|
# ifdef __SUPPORT_SNAN__
|
|
# define iszero(x) (fpclassify (x) == FP_ZERO)
|
|
# else
|
|
# define iszero(x) (((__typeof (x)) (x)) == 0)
|
|
# endif
|
|
# else /* __cplusplus */
|
|
extern "C++" {
|
|
# ifdef __SUPPORT_SNAN__
|
|
inline int
|
|
iszero (float __val)
|
|
{
|
|
return __fpclassifyf (__val) == FP_ZERO;
|
|
}
|
|
inline int
|
|
iszero (double __val)
|
|
{
|
|
return __fpclassify (__val) == FP_ZERO;
|
|
}
|
|
inline int
|
|
iszero (long double __val)
|
|
{
|
|
# ifdef __NO_LONG_DOUBLE_MATH
|
|
return __fpclassify (__val) == FP_ZERO;
|
|
# else
|
|
return __fpclassifyl (__val) == FP_ZERO;
|
|
# endif
|
|
}
|
|
# if __HAVE_DISTINCT_FLOAT128
|
|
inline int
|
|
iszero (_Float128 __val)
|
|
{
|
|
return __fpclassifyf128 (__val) == FP_ZERO;
|
|
}
|
|
# endif
|
|
# else
|
|
template <class __T> inline bool
|
|
iszero (__T __val)
|
|
{
|
|
return __val == 0;
|
|
}
|
|
# endif
|
|
} /* extern C++ */
|
|
# endif /* __cplusplus */
|
|
#endif /* Use IEC_60559_BFP_EXT. */
|
|
|
|
#ifdef __USE_XOPEN
|
|
/* X/Open wants another strange constant. */
|
|
# define MAXFLOAT 3.40282347e+38F
|
|
#endif
|
|
|
|
|
|
/* Some useful constants. */
|
|
#if defined __USE_MISC || defined __USE_XOPEN
|
|
# define M_E 2.7182818284590452354 /* e */
|
|
# define M_LOG2E 1.4426950408889634074 /* log_2 e */
|
|
# define M_LOG10E 0.43429448190325182765 /* log_10 e */
|
|
# define M_LN2 0.69314718055994530942 /* log_e 2 */
|
|
# define M_LN10 2.30258509299404568402 /* log_e 10 */
|
|
# define M_PI 3.14159265358979323846 /* pi */
|
|
# define M_PI_2 1.57079632679489661923 /* pi/2 */
|
|
# define M_PI_4 0.78539816339744830962 /* pi/4 */
|
|
# define M_1_PI 0.31830988618379067154 /* 1/pi */
|
|
# define M_2_PI 0.63661977236758134308 /* 2/pi */
|
|
# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
|
|
# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
|
|
# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
|
|
#endif
|
|
|
|
/* The above constants are not adequate for computation using `long double's.
|
|
Therefore we provide as an extension constants with similar names as a
|
|
GNU extension. Provide enough digits for the 128-bit IEEE quad. */
|
|
#ifdef __USE_GNU
|
|
# define M_El 2.718281828459045235360287471352662498L /* e */
|
|
# define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
|
|
# define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
|
|
# define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
|
|
# define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
|
|
# define M_PIl 3.141592653589793238462643383279502884L /* pi */
|
|
# define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
|
|
# define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
|
|
# define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
|
|
# define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
|
|
# define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
|
|
# define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
|
|
# define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
|
|
#endif
|
|
|
|
#if __HAVE_FLOAT128 && defined __USE_GNU
|
|
# define M_Ef128 __f128 (2.718281828459045235360287471352662498) /* e */
|
|
# define M_LOG2Ef128 __f128 (1.442695040888963407359924681001892137) /* log_2 e */
|
|
# define M_LOG10Ef128 __f128 (0.434294481903251827651128918916605082) /* log_10 e */
|
|
# define M_LN2f128 __f128 (0.693147180559945309417232121458176568) /* log_e 2 */
|
|
# define M_LN10f128 __f128 (2.302585092994045684017991454684364208) /* log_e 10 */
|
|
# define M_PIf128 __f128 (3.141592653589793238462643383279502884) /* pi */
|
|
# define M_PI_2f128 __f128 (1.570796326794896619231321691639751442) /* pi/2 */
|
|
# define M_PI_4f128 __f128 (0.785398163397448309615660845819875721) /* pi/4 */
|
|
# define M_1_PIf128 __f128 (0.318309886183790671537767526745028724) /* 1/pi */
|
|
# define M_2_PIf128 __f128 (0.636619772367581343075535053490057448) /* 2/pi */
|
|
# define M_2_SQRTPIf128 __f128 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
|
|
# define M_SQRT2f128 __f128 (1.414213562373095048801688724209698079) /* sqrt(2) */
|
|
# define M_SQRT1_2f128 __f128 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
|
|
#endif
|
|
|
|
/* When compiling in strict ISO C compatible mode we must not use the
|
|
inline functions since they, among other things, do not set the
|
|
`errno' variable correctly. */
|
|
#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
|
|
# define __NO_MATH_INLINES 1
|
|
#endif
|
|
|
|
#if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
|
|
/* ISO C99 defines some macros to compare number while taking care for
|
|
unordered numbers. Many FPUs provide special instructions to support
|
|
these operations. Generic support in GCC for these as builtins went
|
|
in before 3.0.0, but not all cpus added their patterns. We define
|
|
versions that use the builtins here, and <bits/mathinline.h> will
|
|
undef/redefine as appropriate for the specific GCC version in use. */
|
|
# define isgreater(x, y) __builtin_isgreater(x, y)
|
|
# define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
|
|
# define isless(x, y) __builtin_isless(x, y)
|
|
# define islessequal(x, y) __builtin_islessequal(x, y)
|
|
# define islessgreater(x, y) __builtin_islessgreater(x, y)
|
|
# define isunordered(u, v) __builtin_isunordered(u, v)
|
|
#endif
|
|
|
|
/* Get machine-dependent inline versions (if there are any). */
|
|
#ifdef __USE_EXTERN_INLINES
|
|
# include <bits/mathinline.h>
|
|
#endif
|
|
|
|
/* Define special entry points to use when the compiler got told to
|
|
only expect finite results. */
|
|
#if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
|
|
|
|
/* Include bits/math-finite.h for double. */
|
|
# define _Mdouble_ double
|
|
# define __MATH_DECLARING_DOUBLE 1
|
|
# define __MATH_DECLARING_FLOATN 0
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## reentrant
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## reentrant ## _finite
|
|
# include <bits/math-finite.h>
|
|
# undef _Mdouble_
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
# undef __REDIRFROM_X
|
|
# undef __REDIRTO_X
|
|
|
|
/* When __USE_ISOC99 is defined, include math-finite for float and
|
|
long double, as well. */
|
|
# ifdef __USE_ISOC99
|
|
|
|
/* Include bits/math-finite.h for float. */
|
|
# define _Mdouble_ float
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 0
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## f ## reentrant
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f ## reentrant ## _finite
|
|
# include <bits/math-finite.h>
|
|
# undef _Mdouble_
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
# undef __REDIRFROM_X
|
|
# undef __REDIRTO_X
|
|
|
|
/* Include bits/math-finite.h for long double. */
|
|
# ifdef __MATH_DECLARE_LDOUBLE
|
|
# define _Mdouble_ long double
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 0
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## l ## reentrant
|
|
# ifdef __NO_LONG_DOUBLE_MATH
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## reentrant ## _finite
|
|
# else
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## l ## reentrant ## _finite
|
|
# endif
|
|
# include <bits/math-finite.h>
|
|
# undef _Mdouble_
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
# undef __REDIRFROM_X
|
|
# undef __REDIRTO_X
|
|
# endif
|
|
|
|
# endif /* __USE_ISOC99. */
|
|
|
|
/* Include bits/math-finite.h for float128. */
|
|
# if (__HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)) \
|
|
&& __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# define _Mdouble_ _Float128
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## f128 ## reentrant
|
|
# if __HAVE_DISTINCT_FLOAT128
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f128 ## reentrant ## _finite
|
|
# else
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## l ## reentrant ## _finite
|
|
# endif
|
|
# include <bits/math-finite.h>
|
|
# undef _Mdouble_
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
# undef __REDIRFROM_X
|
|
# undef __REDIRTO_X
|
|
# endif
|
|
#endif /* __FINITE_MATH_ONLY__ > 0. */
|
|
|
|
#ifdef __USE_ISOC99
|
|
/* If we've still got undefined comparison macros, provide defaults. */
|
|
|
|
/* Return nonzero value if X is greater than Y. */
|
|
# ifndef isgreater
|
|
# define isgreater(x, y) \
|
|
(__extension__ \
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
|
!isunordered (__x, __y) && __x > __y; }))
|
|
# endif
|
|
|
|
/* Return nonzero value if X is greater than or equal to Y. */
|
|
# ifndef isgreaterequal
|
|
# define isgreaterequal(x, y) \
|
|
(__extension__ \
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
|
!isunordered (__x, __y) && __x >= __y; }))
|
|
# endif
|
|
|
|
/* Return nonzero value if X is less than Y. */
|
|
# ifndef isless
|
|
# define isless(x, y) \
|
|
(__extension__ \
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
|
!isunordered (__x, __y) && __x < __y; }))
|
|
# endif
|
|
|
|
/* Return nonzero value if X is less than or equal to Y. */
|
|
# ifndef islessequal
|
|
# define islessequal(x, y) \
|
|
(__extension__ \
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
|
!isunordered (__x, __y) && __x <= __y; }))
|
|
# endif
|
|
|
|
/* Return nonzero value if either X is less than Y or Y is less than X. */
|
|
# ifndef islessgreater
|
|
# define islessgreater(x, y) \
|
|
(__extension__ \
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
|
!isunordered (__x, __y) && (__x < __y || __y < __x); }))
|
|
# endif
|
|
|
|
/* Return nonzero value if arguments are unordered. */
|
|
# ifndef isunordered
|
|
# define isunordered(u, v) \
|
|
(__extension__ \
|
|
({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
|
|
fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
|
|
# endif
|
|
|
|
#endif
|
|
|
|
#if __GLIBC_USE (IEC_60559_BFP_EXT)
|
|
/* An expression whose type has the widest of the evaluation formats
|
|
of X and Y (which are of floating-point types). */
|
|
# if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
|
|
# define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
|
|
# elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
|
|
# define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
|
|
# else
|
|
# define __MATH_EVAL_FMT2(x, y) ((x) + (y))
|
|
# endif
|
|
|
|
/* Return X == Y but raising "invalid" and setting errno if X or Y is
|
|
a NaN. */
|
|
# define iseqsig(x, y) \
|
|
__MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
|
|
#endif
|
|
|
|
__END_DECLS
|
|
|
|
|
|
#endif /* math.h */
|