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63716ab270
TS 18661-1 defines libm functions that carry out an operation (+ - * / sqrt fma) on their arguments and return a result rounded to a (usually) narrower type, as if the original result were computed to infinite precision and then rounded directly to the result type without any intermediate rounding to the argument type. For example, fadd, faddl and daddl for addition. These are the last remaining TS 18661-1 functions left to be added to glibc. TS 18661-3 extends this to corresponding functions for _FloatN and _FloatNx types. As functions parametrized by two rather than one varying floating-point types, these functions require infrastructure in glibc that was not required for previous libm functions. This patch provides such infrastructure - excluding test support, and actual function implementations, which will be in subsequent patches. Declaring the functions uses a header bits/mathcalls-narrow.h, which is included many times, for each relevant pair of types. This will end up containing macro calls of the form __MATHCALL_NARROW (__MATHCALL_NAME (add), __MATHCALL_REDIR_NAME (add), 2); for each family of narrowing functions. (The structure of this macro call, with the calls to __MATHCALL_NAME and __MATHCALL_REDIR_NAME there rather than in the definition of __MATHCALL_NARROW, arises from the names such as "add" *not* themselves being reserved identifiers - meaning it's necessary to avoid any indirection that would result in a user-defined "add" macro being expanded.) Whereas for existing functions declaring long double functions is disabled if _LIBC in the case where they alias double functions, to facilitate defining the long double functions as aliases of the double ones, there is no such logic for the narrowing functions in this patch. Rather, the files defining such functions are expected to use #define to hide the original declarations of the alias names, to avoid errors about defining aliases with incompatible types. math/Makefile support is added for building the functions (listed in libm-narrow-fns, currently empty) for all relevant pairs of types. An internal header math-narrow.h is added for macros shared between multiple function implementations - currently a ROUND_TO_ODD macro to facilitate writing functions using the round-to-odd implementation approach, and alias macros to create all the required function aliases. libc_feholdexcept_setroundf128 and libc_feupdateenv_testf128 are added for use when required (only for x86_64). float128_private.h support is added for ldbl-128 narrowing functions to be used for _Float128. Certain things are specifically omitted from this patch and the immediate followups. tgmath.h support is deferred; there remain unresolved questions about how the type-generic macros for these functions are supposed to work, especially in the case of arguments of integer type. The math.h / bits/mathcalls-narrow.h logic, and the logic for determining what functions / aliases to define, will need some adjustments to support the sqrt and fma functions, where e.g. f32xsqrtf64 can just be an alias for sqrt rather than a separate function. TS 18661-1 defines FP_FAST_* macros but no support is included for defining them (they won't in general be true without architecture-specific optimized function versions). For each of the function groups (add sub mul div sqrt fma) there are always six functions present (e.g. fadd, faddl, daddl, f32addf64, f32addf32x, f32xaddf64). When _Float64x and _Float128 are supported, there are seven more (e.g. f32addf64x, f32addf128, f64addf64x, f64addf128, f32xaddf64x, f32xaddf128, f64xaddf128). In addition, in the ldbl-opt case there are function names such as __nldbl_daddl (an alias for f32xaddf64, which is not a reserved name in TS 18661-1, only in TS 18661-3), for calls to daddl to be mapped to in the -mlong-double-64 case. (Calls to faddl just get mapped to fadd, and for sqrt and fma there won't be __nldbl_* functions because dsqrtl and dfmal can just be mapped to sqrt and fma with -mlong-double-64.) While there are six or thirteen functions present in each group (plus __nldbl_* names only as an ABI, not an API), not all are distinct; they fall in various groups of aliases. There are two distinct versions built if long double has the same format as double; four if they have distinct formats but there is no _Float64x or _Float128 support; five if long double has binary128 format; seven when _Float128 is distinct from long double. Architecture-specific optimized versions are possible, but not included in my patches. For example, IA64 generally supports narrowing the result of most floating-point instructions; Power ISA 2.07 (POWER8) supports double values as arguments to float instructions, with the results narrowed as expected; Power ISA 3 (POWER9) supports round-to-odd for float128 instructions, so meaning that approach can be used without needing to set and restore the rounding mode and test "inexact". I intend to leave any such optimized versions to the architecture maintainers. Generally in such cases it would also make sense for calls to these functions to be expanded inline (given -fno-math-errno); I put a suggestion for TS 18661-1 built-in functions at <https://gcc.gnu.org/wiki/SummerOfCode>. Tested for x86_64 (this patch in isolation, as well as testing for various configurations in conjunction with further patches). * math/bits/mathcalls-narrow.h: New file. * include/bits/mathcalls-narrow.h: Likewise. * math/math-narrow.h: Likewise. * math/math.h (__MATHCALL_NARROW_ARGS_1): New macro. (__MATHCALL_NARROW_ARGS_2): Likewise. (__MATHCALL_NARROW_ARGS_3): Likewise. (__MATHCALL_NARROW_NORMAL): Likewise. (__MATHCALL_NARROW_REDIR): Likewise. (__MATHCALL_NARROW): Likewise. [__GLIBC_USE (IEC_60559_BFP_EXT)]: Repeatedly include <bits/mathcalls-narrow.h> with _Mret_, _Marg_ and __MATHCALL_NAME defined. [__GLIBC_USE (IEC_60559_TYPES_EXT)]: Likewise. * math/Makefile (headers): Add bits/mathcalls-narrow.h. (libm-narrow-fns): New variable. (libm-narrow-types-basic): Likewise. (libm-narrow-types-ldouble-yes): Likewise. (libm-narrow-types-float128-yes): Likewise. (libm-narrow-types-float128-alias-yes): Likewise. (libm-narrow-types): Likewise. (libm-routines): Add narrowing functions. * sysdeps/i386/fpu/fenv_private.h [__x86_64__] (libc_feholdexcept_setroundf128): New macro. [__x86_64__] (libc_feupdateenv_testf128): Likewise. * sysdeps/ieee754/float128/float128_private.h: Include <math/math-narrow.h>. [libc_feholdexcept_setroundf128] (libc_feholdexcept_setroundl): Undefine and redefine. [libc_feupdateenv_testf128] (libc_feupdateenv_testl): Likewise. (libm_alias_float_ldouble): Undefine and redefine. (libm_alias_double_ldouble): Likewise.
1551 lines
52 KiB
C++
1551 lines
52 KiB
C++
/* 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
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 0
|
|
# define __MATH_DECLARE_LDOUBLE 1
|
|
# include <bits/mathcalls-helper-functions.h>
|
|
# include <bits/mathcalls.h>
|
|
# undef _Mdouble_
|
|
# undef __MATH_PRECNAME
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
|
|
# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
|
|
|
|
#endif /* Use ISO C99. */
|
|
|
|
/* Include the file of declarations for _FloatN and _FloatNx
|
|
types. */
|
|
|
|
#if __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)
|
|
# define _Mdouble_ _Float16
|
|
# define __MATH_PRECNAME(name,r) name##f16##r
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# if __HAVE_DISTINCT_FLOAT16
|
|
# include <bits/mathcalls-helper-functions.h>
|
|
# endif
|
|
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# include <bits/mathcalls.h>
|
|
# endif
|
|
# undef _Mdouble_
|
|
# undef __MATH_PRECNAME
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
#endif /* __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !_LIBC). */
|
|
|
|
#if __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)
|
|
# define _Mdouble_ _Float32
|
|
# define __MATH_PRECNAME(name,r) name##f32##r
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# if __HAVE_DISTINCT_FLOAT32
|
|
# include <bits/mathcalls-helper-functions.h>
|
|
# endif
|
|
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# include <bits/mathcalls.h>
|
|
# endif
|
|
# undef _Mdouble_
|
|
# undef __MATH_PRECNAME
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
#endif /* __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !_LIBC). */
|
|
|
|
#if __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)
|
|
# define _Mdouble_ _Float64
|
|
# define __MATH_PRECNAME(name,r) name##f64##r
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# if __HAVE_DISTINCT_FLOAT64
|
|
# include <bits/mathcalls-helper-functions.h>
|
|
# endif
|
|
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# include <bits/mathcalls.h>
|
|
# endif
|
|
# undef _Mdouble_
|
|
# undef __MATH_PRECNAME
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
#endif /* __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !_LIBC). */
|
|
|
|
#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)
|
|
# define _Mdouble_ _Float128
|
|
# define __MATH_PRECNAME(name,r) name##f128##r
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# if __HAVE_DISTINCT_FLOAT128
|
|
# include <bits/mathcalls-helper-functions.h>
|
|
# endif
|
|
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# include <bits/mathcalls.h>
|
|
# endif
|
|
# undef _Mdouble_
|
|
# undef __MATH_PRECNAME
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
#endif /* __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !_LIBC). */
|
|
|
|
#if __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)
|
|
# define _Mdouble_ _Float32x
|
|
# define __MATH_PRECNAME(name,r) name##f32x##r
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# if __HAVE_DISTINCT_FLOAT32X
|
|
# include <bits/mathcalls-helper-functions.h>
|
|
# endif
|
|
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# include <bits/mathcalls.h>
|
|
# endif
|
|
# undef _Mdouble_
|
|
# undef __MATH_PRECNAME
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
#endif /* __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !_LIBC). */
|
|
|
|
#if __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)
|
|
# define _Mdouble_ _Float64x
|
|
# define __MATH_PRECNAME(name,r) name##f64x##r
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# if __HAVE_DISTINCT_FLOAT64X
|
|
# include <bits/mathcalls-helper-functions.h>
|
|
# endif
|
|
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# include <bits/mathcalls.h>
|
|
# endif
|
|
# undef _Mdouble_
|
|
# undef __MATH_PRECNAME
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
#endif /* __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !_LIBC). */
|
|
|
|
#if __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)
|
|
# define _Mdouble_ _Float128x
|
|
# define __MATH_PRECNAME(name,r) name##f128x##r
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# if __HAVE_DISTINCT_FLOAT128X
|
|
# include <bits/mathcalls-helper-functions.h>
|
|
# endif
|
|
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# include <bits/mathcalls.h>
|
|
# endif
|
|
# undef _Mdouble_
|
|
# undef __MATH_PRECNAME
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
#endif /* __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !_LIBC). */
|
|
|
|
#undef __MATHDECL_1
|
|
#undef __MATHDECL
|
|
#undef __MATHCALL
|
|
|
|
/* Declare functions returning a narrower type. */
|
|
#define __MATHCALL_NARROW_ARGS_1 (_Marg_ __x)
|
|
#define __MATHCALL_NARROW_ARGS_2 (_Marg_ __x, _Marg_ __y)
|
|
#define __MATHCALL_NARROW_ARGS_3 (_Marg_ __x, _Marg_ __y, _Marg_ __z)
|
|
#define __MATHCALL_NARROW_NORMAL(func, nargs) \
|
|
extern _Mret_ func __MATHCALL_NARROW_ARGS_ ## nargs __THROW
|
|
#define __MATHCALL_NARROW_REDIR(func, redir, nargs) \
|
|
extern _Mret_ __REDIRECT_NTH (func, __MATHCALL_NARROW_ARGS_ ## nargs, \
|
|
redir)
|
|
#define __MATHCALL_NARROW(func, redir, nargs) \
|
|
__MATHCALL_NARROW_NORMAL (func, nargs)
|
|
|
|
#if __GLIBC_USE (IEC_60559_BFP_EXT)
|
|
|
|
# define _Mret_ float
|
|
# define _Marg_ double
|
|
# define __MATHCALL_NAME(name) f ## name
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
|
|
# define _Mret_ float
|
|
# define _Marg_ long double
|
|
# define __MATHCALL_NAME(name) f ## name ## l
|
|
# ifdef __LDBL_COMPAT
|
|
# define __MATHCALL_REDIR_NAME(name) f ## name
|
|
# undef __MATHCALL_NARROW
|
|
# define __MATHCALL_NARROW(func, redir, nargs) \
|
|
__MATHCALL_NARROW_REDIR (func, redir, nargs)
|
|
# endif
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# ifdef __LDBL_COMPAT
|
|
# undef __MATHCALL_REDIR_NAME
|
|
# undef __MATHCALL_NARROW
|
|
# define __MATHCALL_NARROW(func, redir, nargs) \
|
|
__MATHCALL_NARROW_NORMAL (func, nargs)
|
|
# endif
|
|
|
|
# define _Mret_ double
|
|
# define _Marg_ long double
|
|
# define __MATHCALL_NAME(name) d ## name ## l
|
|
# ifdef __LDBL_COMPAT
|
|
# define __MATHCALL_REDIR_NAME(name) __nldbl_d ## name ## l
|
|
# undef __MATHCALL_NARROW
|
|
# define __MATHCALL_NARROW(func, redir, nargs) \
|
|
__MATHCALL_NARROW_REDIR (func, redir, nargs)
|
|
# endif
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# ifdef __LDBL_COMPAT
|
|
# undef __MATHCALL_REDIR_NAME
|
|
# undef __MATHCALL_NARROW
|
|
# define __MATHCALL_NARROW(func, redir, nargs) \
|
|
__MATHCALL_NARROW_NORMAL (func, nargs)
|
|
# endif
|
|
|
|
#endif
|
|
|
|
#if __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
|
|
# if __HAVE_FLOAT16 && __HAVE_FLOAT32
|
|
# define _Mret_ _Float16
|
|
# define _Marg_ _Float32
|
|
# define __MATHCALL_NAME(name) f16 ## name ## f32
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT16 && __HAVE_FLOAT32X
|
|
# define _Mret_ _Float16
|
|
# define _Marg_ _Float32x
|
|
# define __MATHCALL_NAME(name) f16 ## name ## f32x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT16 && __HAVE_FLOAT64
|
|
# define _Mret_ _Float16
|
|
# define _Marg_ _Float64
|
|
# define __MATHCALL_NAME(name) f16 ## name ## f64
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT16 && __HAVE_FLOAT64X
|
|
# define _Mret_ _Float16
|
|
# define _Marg_ _Float64x
|
|
# define __MATHCALL_NAME(name) f16 ## name ## f64x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT16 && __HAVE_FLOAT128
|
|
# define _Mret_ _Float16
|
|
# define _Marg_ _Float128
|
|
# define __MATHCALL_NAME(name) f16 ## name ## f128
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT16 && __HAVE_FLOAT128X
|
|
# define _Mret_ _Float16
|
|
# define _Marg_ _Float128x
|
|
# define __MATHCALL_NAME(name) f16 ## name ## f128x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32 && __HAVE_FLOAT32X
|
|
# define _Mret_ _Float32
|
|
# define _Marg_ _Float32x
|
|
# define __MATHCALL_NAME(name) f32 ## name ## f32x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32 && __HAVE_FLOAT64
|
|
# define _Mret_ _Float32
|
|
# define _Marg_ _Float64
|
|
# define __MATHCALL_NAME(name) f32 ## name ## f64
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32 && __HAVE_FLOAT64X
|
|
# define _Mret_ _Float32
|
|
# define _Marg_ _Float64x
|
|
# define __MATHCALL_NAME(name) f32 ## name ## f64x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32 && __HAVE_FLOAT128
|
|
# define _Mret_ _Float32
|
|
# define _Marg_ _Float128
|
|
# define __MATHCALL_NAME(name) f32 ## name ## f128
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32 && __HAVE_FLOAT128X
|
|
# define _Mret_ _Float32
|
|
# define _Marg_ _Float128x
|
|
# define __MATHCALL_NAME(name) f32 ## name ## f128x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32X && __HAVE_FLOAT64
|
|
# define _Mret_ _Float32x
|
|
# define _Marg_ _Float64
|
|
# define __MATHCALL_NAME(name) f32x ## name ## f64
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32X && __HAVE_FLOAT64X
|
|
# define _Mret_ _Float32x
|
|
# define _Marg_ _Float64x
|
|
# define __MATHCALL_NAME(name) f32x ## name ## f64x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32X && __HAVE_FLOAT128
|
|
# define _Mret_ _Float32x
|
|
# define _Marg_ _Float128
|
|
# define __MATHCALL_NAME(name) f32x ## name ## f128
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT32X && __HAVE_FLOAT128X
|
|
# define _Mret_ _Float32x
|
|
# define _Marg_ _Float128x
|
|
# define __MATHCALL_NAME(name) f32x ## name ## f128x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT64 && __HAVE_FLOAT64X
|
|
# define _Mret_ _Float64
|
|
# define _Marg_ _Float64x
|
|
# define __MATHCALL_NAME(name) f64 ## name ## f64x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT64 && __HAVE_FLOAT128
|
|
# define _Mret_ _Float64
|
|
# define _Marg_ _Float128
|
|
# define __MATHCALL_NAME(name) f64 ## name ## f128
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT64 && __HAVE_FLOAT128X
|
|
# define _Mret_ _Float64
|
|
# define _Marg_ _Float128x
|
|
# define __MATHCALL_NAME(name) f64 ## name ## f128x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT64X && __HAVE_FLOAT128
|
|
# define _Mret_ _Float64x
|
|
# define _Marg_ _Float128
|
|
# define __MATHCALL_NAME(name) f64x ## name ## f128
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT64X && __HAVE_FLOAT128X
|
|
# define _Mret_ _Float64x
|
|
# define _Marg_ _Float128x
|
|
# define __MATHCALL_NAME(name) f64x ## name ## f128x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
# if __HAVE_FLOAT128 && __HAVE_FLOAT128X
|
|
# define _Mret_ _Float128
|
|
# define _Marg_ _Float128x
|
|
# define __MATHCALL_NAME(name) f128 ## name ## f128x
|
|
# include <bits/mathcalls-narrow.h>
|
|
# undef _Mret_
|
|
# undef _Marg_
|
|
# undef __MATHCALL_NAME
|
|
# endif
|
|
|
|
#endif
|
|
|
|
#undef __MATHCALL_NARROW_ARGS_1
|
|
#undef __MATHCALL_NARROW_ARGS_2
|
|
#undef __MATHCALL_NARROW_ARGS_3
|
|
#undef __MATHCALL_NARROW_NORMAL
|
|
#undef __MATHCALL_NARROW_REDIR
|
|
#undef __MATHCALL_NARROW
|
|
|
|
#if defined __USE_MISC || defined __USE_XOPEN
|
|
/* This variable is used by `gamma' and `lgamma'. */
|
|
extern int signgam;
|
|
#endif
|
|
|
|
#if (__HAVE_DISTINCT_FLOAT16 \
|
|
|| __HAVE_DISTINCT_FLOAT32 \
|
|
|| __HAVE_DISTINCT_FLOAT64 \
|
|
|| __HAVE_DISTINCT_FLOAT32X \
|
|
|| __HAVE_DISTINCT_FLOAT64X \
|
|
|| __HAVE_DISTINCT_FLOAT128X)
|
|
# error "Unsupported _FloatN or _FloatNx types for <math.h>."
|
|
#endif
|
|
|
|
/* Depending on the type of TG_ARG, call an appropriately suffixed
|
|
version of FUNC with arguments (including parentheses) ARGS.
|
|
Suffixed functions may not exist for long double if it has the same
|
|
format as double, or for other types with the same format as float,
|
|
double or long double. The behavior is undefined if the argument
|
|
does not have a real floating type. The definition may use a
|
|
conditional expression, so all suffixed versions of FUNC must
|
|
return the same type (FUNC may include a cast if necessary rather
|
|
than being a single identifier). */
|
|
#ifdef __NO_LONG_DOUBLE_MATH
|
|
# if __HAVE_DISTINCT_FLOAT128
|
|
# error "Distinct _Float128 without distinct long double not supported."
|
|
# endif
|
|
# define __MATH_TG(TG_ARG, FUNC, ARGS) \
|
|
(sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
|
|
#elif __HAVE_DISTINCT_FLOAT128
|
|
# if __HAVE_GENERIC_SELECTION
|
|
# if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT32
|
|
# define __MATH_TG_F32(FUNC, ARGS) _Float32: FUNC ## f ARGS,
|
|
# else
|
|
# define __MATH_TG_F32(FUNC, ARGS)
|
|
# endif
|
|
# if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT64X
|
|
# if __HAVE_FLOAT64X_LONG_DOUBLE
|
|
# define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## l ARGS,
|
|
# else
|
|
# define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## f128 ARGS,
|
|
# endif
|
|
# else
|
|
# define __MATH_TG_F64X(FUNC, ARGS)
|
|
# endif
|
|
# define __MATH_TG(TG_ARG, FUNC, ARGS) \
|
|
_Generic ((TG_ARG), \
|
|
float: FUNC ## f ARGS, \
|
|
__MATH_TG_F32 (FUNC, ARGS) \
|
|
default: FUNC ARGS, \
|
|
long double: FUNC ## l ARGS, \
|
|
__MATH_TG_F64X (FUNC, ARGS) \
|
|
_Float128: FUNC ## f128 ARGS)
|
|
# else
|
|
# if __HAVE_FLOATN_NOT_TYPEDEF
|
|
# error "Non-typedef _FloatN but no _Generic."
|
|
# endif
|
|
# define __MATH_TG(TG_ARG, FUNC, ARGS) \
|
|
__builtin_choose_expr \
|
|
(__builtin_types_compatible_p (__typeof (TG_ARG), float), \
|
|
FUNC ## f ARGS, \
|
|
__builtin_choose_expr \
|
|
(__builtin_types_compatible_p (__typeof (TG_ARG), double), \
|
|
FUNC ARGS, \
|
|
__builtin_choose_expr \
|
|
(__builtin_types_compatible_p (__typeof (TG_ARG), long double), \
|
|
FUNC ## l ARGS, \
|
|
FUNC ## f128 ARGS)))
|
|
# endif
|
|
#else
|
|
# define __MATH_TG(TG_ARG, FUNC, ARGS) \
|
|
(sizeof (TG_ARG) == sizeof (float) \
|
|
? FUNC ## f ARGS \
|
|
: sizeof (TG_ARG) == sizeof (double) \
|
|
? FUNC ARGS \
|
|
: FUNC ## l ARGS)
|
|
#endif
|
|
|
|
/* ISO C99 defines some generic macros which work on any data type. */
|
|
#ifdef __USE_ISOC99
|
|
|
|
/* All floating-point numbers can be put in one of these categories. */
|
|
enum
|
|
{
|
|
FP_NAN =
|
|
# define FP_NAN 0
|
|
FP_NAN,
|
|
FP_INFINITE =
|
|
# define FP_INFINITE 1
|
|
FP_INFINITE,
|
|
FP_ZERO =
|
|
# define FP_ZERO 2
|
|
FP_ZERO,
|
|
FP_SUBNORMAL =
|
|
# define FP_SUBNORMAL 3
|
|
FP_SUBNORMAL,
|
|
FP_NORMAL =
|
|
# define FP_NORMAL 4
|
|
FP_NORMAL
|
|
};
|
|
|
|
/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
|
|
so disable builtins if this is enabled. When fixed in a newer GCC,
|
|
the __SUPPORT_SNAN__ check may be skipped for those versions. */
|
|
|
|
/* Return number of classification appropriate for X. */
|
|
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ \
|
|
&& (!defined __OPTIMIZE_SIZE__ || defined __cplusplus)
|
|
/* The check for __cplusplus allows the use of the builtin, even
|
|
when optimization for size is on. This is provided for
|
|
libstdc++, only to let its configure test work when it is built
|
|
with -Os. No further use of this definition of fpclassify is
|
|
expected in C++ mode, since libstdc++ provides its own version
|
|
of fpclassify in cmath (which undefines fpclassify). */
|
|
# define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \
|
|
FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
|
|
# else
|
|
# define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
|
|
# endif
|
|
|
|
/* Return nonzero value if sign of X is negative. */
|
|
# if __GNUC_PREREQ (6,0)
|
|
# define signbit(x) __builtin_signbit (x)
|
|
# elif defined __cplusplus
|
|
/* In C++ mode, __MATH_TG cannot be used, because it relies on
|
|
__builtin_types_compatible_p, which is a C-only builtin.
|
|
The check for __cplusplus allows the use of the builtin instead of
|
|
__MATH_TG. This is provided for libstdc++, only to let its configure
|
|
test work. No further use of this definition of signbit is expected
|
|
in C++ mode, since libstdc++ provides its own version of signbit
|
|
in cmath (which undefines signbit). */
|
|
# define signbit(x) __builtin_signbitl (x)
|
|
# elif __GNUC_PREREQ (4,0)
|
|
# define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
|
|
# else
|
|
# define signbit(x) __MATH_TG ((x), __signbit, (x))
|
|
# endif
|
|
|
|
/* Return nonzero value if X is not +-Inf or NaN. */
|
|
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
|
|
# define isfinite(x) __builtin_isfinite (x)
|
|
# else
|
|
# define isfinite(x) __MATH_TG ((x), __finite, (x))
|
|
# endif
|
|
|
|
/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
|
|
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
|
|
# 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 math functions support both errno and exception handling
|
|
(except for soft floating point implementations which may only support
|
|
errno handling). If errno handling is disabled, exceptions are still
|
|
supported by GLIBC. Set math_errhandling to 0 with -ffast-math (this is
|
|
nonconforming but it is more useful than leaving it undefined). */
|
|
# ifdef __FAST_MATH__
|
|
# define math_errhandling 0
|
|
# elif defined __NO_MATH_ERRNO__
|
|
# define math_errhandling (MATH_ERREXCEPT)
|
|
# else
|
|
# 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_FLOAT16 && defined __USE_GNU
|
|
# define M_Ef16 __f16 (2.718281828459045235360287471352662498) /* e */
|
|
# define M_LOG2Ef16 __f16 (1.442695040888963407359924681001892137) /* log_2 e */
|
|
# define M_LOG10Ef16 __f16 (0.434294481903251827651128918916605082) /* log_10 e */
|
|
# define M_LN2f16 __f16 (0.693147180559945309417232121458176568) /* log_e 2 */
|
|
# define M_LN10f16 __f16 (2.302585092994045684017991454684364208) /* log_e 10 */
|
|
# define M_PIf16 __f16 (3.141592653589793238462643383279502884) /* pi */
|
|
# define M_PI_2f16 __f16 (1.570796326794896619231321691639751442) /* pi/2 */
|
|
# define M_PI_4f16 __f16 (0.785398163397448309615660845819875721) /* pi/4 */
|
|
# define M_1_PIf16 __f16 (0.318309886183790671537767526745028724) /* 1/pi */
|
|
# define M_2_PIf16 __f16 (0.636619772367581343075535053490057448) /* 2/pi */
|
|
# define M_2_SQRTPIf16 __f16 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
|
|
# define M_SQRT2f16 __f16 (1.414213562373095048801688724209698079) /* sqrt(2) */
|
|
# define M_SQRT1_2f16 __f16 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
|
|
#endif
|
|
|
|
#if __HAVE_FLOAT32 && defined __USE_GNU
|
|
# define M_Ef32 __f32 (2.718281828459045235360287471352662498) /* e */
|
|
# define M_LOG2Ef32 __f32 (1.442695040888963407359924681001892137) /* log_2 e */
|
|
# define M_LOG10Ef32 __f32 (0.434294481903251827651128918916605082) /* log_10 e */
|
|
# define M_LN2f32 __f32 (0.693147180559945309417232121458176568) /* log_e 2 */
|
|
# define M_LN10f32 __f32 (2.302585092994045684017991454684364208) /* log_e 10 */
|
|
# define M_PIf32 __f32 (3.141592653589793238462643383279502884) /* pi */
|
|
# define M_PI_2f32 __f32 (1.570796326794896619231321691639751442) /* pi/2 */
|
|
# define M_PI_4f32 __f32 (0.785398163397448309615660845819875721) /* pi/4 */
|
|
# define M_1_PIf32 __f32 (0.318309886183790671537767526745028724) /* 1/pi */
|
|
# define M_2_PIf32 __f32 (0.636619772367581343075535053490057448) /* 2/pi */
|
|
# define M_2_SQRTPIf32 __f32 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
|
|
# define M_SQRT2f32 __f32 (1.414213562373095048801688724209698079) /* sqrt(2) */
|
|
# define M_SQRT1_2f32 __f32 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
|
|
#endif
|
|
|
|
#if __HAVE_FLOAT64 && defined __USE_GNU
|
|
# define M_Ef64 __f64 (2.718281828459045235360287471352662498) /* e */
|
|
# define M_LOG2Ef64 __f64 (1.442695040888963407359924681001892137) /* log_2 e */
|
|
# define M_LOG10Ef64 __f64 (0.434294481903251827651128918916605082) /* log_10 e */
|
|
# define M_LN2f64 __f64 (0.693147180559945309417232121458176568) /* log_e 2 */
|
|
# define M_LN10f64 __f64 (2.302585092994045684017991454684364208) /* log_e 10 */
|
|
# define M_PIf64 __f64 (3.141592653589793238462643383279502884) /* pi */
|
|
# define M_PI_2f64 __f64 (1.570796326794896619231321691639751442) /* pi/2 */
|
|
# define M_PI_4f64 __f64 (0.785398163397448309615660845819875721) /* pi/4 */
|
|
# define M_1_PIf64 __f64 (0.318309886183790671537767526745028724) /* 1/pi */
|
|
# define M_2_PIf64 __f64 (0.636619772367581343075535053490057448) /* 2/pi */
|
|
# define M_2_SQRTPIf64 __f64 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
|
|
# define M_SQRT2f64 __f64 (1.414213562373095048801688724209698079) /* sqrt(2) */
|
|
# define M_SQRT1_2f64 __f64 (0.707106781186547524400844362104849039) /* 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
|
|
|
|
#if __HAVE_FLOAT32X && defined __USE_GNU
|
|
# define M_Ef32x __f32x (2.718281828459045235360287471352662498) /* e */
|
|
# define M_LOG2Ef32x __f32x (1.442695040888963407359924681001892137) /* log_2 e */
|
|
# define M_LOG10Ef32x __f32x (0.434294481903251827651128918916605082) /* log_10 e */
|
|
# define M_LN2f32x __f32x (0.693147180559945309417232121458176568) /* log_e 2 */
|
|
# define M_LN10f32x __f32x (2.302585092994045684017991454684364208) /* log_e 10 */
|
|
# define M_PIf32x __f32x (3.141592653589793238462643383279502884) /* pi */
|
|
# define M_PI_2f32x __f32x (1.570796326794896619231321691639751442) /* pi/2 */
|
|
# define M_PI_4f32x __f32x (0.785398163397448309615660845819875721) /* pi/4 */
|
|
# define M_1_PIf32x __f32x (0.318309886183790671537767526745028724) /* 1/pi */
|
|
# define M_2_PIf32x __f32x (0.636619772367581343075535053490057448) /* 2/pi */
|
|
# define M_2_SQRTPIf32x __f32x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
|
|
# define M_SQRT2f32x __f32x (1.414213562373095048801688724209698079) /* sqrt(2) */
|
|
# define M_SQRT1_2f32x __f32x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
|
|
#endif
|
|
|
|
#if __HAVE_FLOAT64X && defined __USE_GNU
|
|
# define M_Ef64x __f64x (2.718281828459045235360287471352662498) /* e */
|
|
# define M_LOG2Ef64x __f64x (1.442695040888963407359924681001892137) /* log_2 e */
|
|
# define M_LOG10Ef64x __f64x (0.434294481903251827651128918916605082) /* log_10 e */
|
|
# define M_LN2f64x __f64x (0.693147180559945309417232121458176568) /* log_e 2 */
|
|
# define M_LN10f64x __f64x (2.302585092994045684017991454684364208) /* log_e 10 */
|
|
# define M_PIf64x __f64x (3.141592653589793238462643383279502884) /* pi */
|
|
# define M_PI_2f64x __f64x (1.570796326794896619231321691639751442) /* pi/2 */
|
|
# define M_PI_4f64x __f64x (0.785398163397448309615660845819875721) /* pi/4 */
|
|
# define M_1_PIf64x __f64x (0.318309886183790671537767526745028724) /* 1/pi */
|
|
# define M_2_PIf64x __f64x (0.636619772367581343075535053490057448) /* 2/pi */
|
|
# define M_2_SQRTPIf64x __f64x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
|
|
# define M_SQRT2f64x __f64x (1.414213562373095048801688724209698079) /* sqrt(2) */
|
|
# define M_SQRT1_2f64x __f64x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
|
|
#endif
|
|
|
|
#if __HAVE_FLOAT128X && defined __USE_GNU
|
|
# error "M_* values needed for _Float128x"
|
|
#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
|
|
|
|
#ifdef __USE_ISOC99
|
|
# if __GNUC_PREREQ (3, 1)
|
|
/* 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 2.97, but not all cpus added their patterns until 3.1. Therefore
|
|
we enable the builtins from 3.1 onwards and use a generic implementation
|
|
othwerwise. */
|
|
# 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(x, y) __builtin_isunordered(x, y)
|
|
# else
|
|
# define isgreater(x, y) \
|
|
(__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
|
|
!isunordered (__x, __y) && __x > __y; }))
|
|
# define isgreaterequal(x, y) \
|
|
(__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
|
|
!isunordered (__x, __y) && __x >= __y; }))
|
|
# define isless(x, y) \
|
|
(__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
|
|
!isunordered (__x, __y) && __x < __y; }))
|
|
# define islessequal(x, y) \
|
|
(__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
|
|
!isunordered (__x, __y) && __x <= __y; }))
|
|
# define islessgreater(x, y) \
|
|
(__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
|
|
!isunordered (__x, __y) && __x != __y; }))
|
|
/* isunordered must always check both operands first for signaling NaNs. */
|
|
# define isunordered(x, y) \
|
|
(__extension__ ({ __typeof__ (x) __u = (x); __typeof__ (y) __v = (y); \
|
|
__u != __v && (__u != __u || __v != __v); }))
|
|
# endif
|
|
#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 _FloatN and _FloatNx. */
|
|
|
|
# if (__HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)) \
|
|
&& __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# define _Mdouble_ _Float16
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## f16 ## reentrant
|
|
# if __HAVE_DISTINCT_FLOAT16
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f16 ## reentrant ## _finite
|
|
# else
|
|
# error "non-disinct _Float16"
|
|
# endif
|
|
# include <bits/math-finite.h>
|
|
# undef _Mdouble_
|
|
# undef __MATH_DECLARING_DOUBLE
|
|
# undef __MATH_DECLARING_FLOATN
|
|
# undef __REDIRFROM_X
|
|
# undef __REDIRTO_X
|
|
# endif
|
|
|
|
# if (__HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)) \
|
|
&& __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# define _Mdouble_ _Float32
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## f32 ## reentrant
|
|
# if __HAVE_DISTINCT_FLOAT32
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f32 ## reentrant ## _finite
|
|
# else
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f ## 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
|
|
|
|
# if (__HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)) \
|
|
&& __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# define _Mdouble_ _Float64
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## f64 ## reentrant
|
|
# if __HAVE_DISTINCT_FLOAT64
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f64 ## reentrant ## _finite
|
|
# else
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## 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
|
|
|
|
# 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
|
|
|
|
# if (__HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)) \
|
|
&& __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# define _Mdouble_ _Float32x
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## f32x ## reentrant
|
|
# if __HAVE_DISTINCT_FLOAT32X
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f32x ## reentrant ## _finite
|
|
# else
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## 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
|
|
|
|
# if (__HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)) \
|
|
&& __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# define _Mdouble_ _Float64x
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## f64x ## reentrant
|
|
# if __HAVE_DISTINCT_FLOAT64X
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f64x ## reentrant ## _finite
|
|
# elif __HAVE_FLOAT64X_LONG_DOUBLE
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## l ## reentrant ## _finite
|
|
# else
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f128 ## 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
|
|
|
|
# if (__HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)) \
|
|
&& __GLIBC_USE (IEC_60559_TYPES_EXT)
|
|
# define _Mdouble_ _Float128x
|
|
# define __MATH_DECLARING_DOUBLE 0
|
|
# define __MATH_DECLARING_FLOATN 1
|
|
# define __REDIRFROM_X(function, reentrant) \
|
|
function ## f128x ## reentrant
|
|
# if __HAVE_DISTINCT_FLOAT128X
|
|
# define __REDIRTO_X(function, reentrant) \
|
|
__ ## function ## f128x ## reentrant ## _finite
|
|
# else
|
|
# error "non-disinct _Float128x"
|
|
# 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. */
|
|
|
|
#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)
|
|
# elif __FLT_EVAL_METHOD__ == 0 || __FLT_EVAL_METHOD__ == 32
|
|
# define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0f)
|
|
# 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. */
|
|
# if !defined __cplusplus || (__cplusplus < 201103L && !defined __GNUC__)
|
|
# define iseqsig(x, y) \
|
|
__MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
|
|
# else
|
|
/* In C++ mode, __MATH_TG cannot be used, because it relies on
|
|
__builtin_types_compatible_p, which is a C-only builtin. Moreover,
|
|
the comparison macros from ISO C take two floating-point arguments,
|
|
which need not have the same type. Choosing what underlying function
|
|
to call requires evaluating the formats of the arguments, then
|
|
selecting which is wider. The macro __MATH_EVAL_FMT2 provides this
|
|
information, however, only the type of the macro expansion is
|
|
relevant (actually evaluating the expression would be incorrect).
|
|
Thus, the type is used as a template parameter for __iseqsig_type,
|
|
which calls the appropriate underlying function. */
|
|
extern "C++" {
|
|
template<typename> struct __iseqsig_type;
|
|
|
|
template<> struct __iseqsig_type<float>
|
|
{
|
|
static int __call (float __x, float __y) throw ()
|
|
{
|
|
return __iseqsigf (__x, __y);
|
|
}
|
|
};
|
|
|
|
template<> struct __iseqsig_type<double>
|
|
{
|
|
static int __call (double __x, double __y) throw ()
|
|
{
|
|
return __iseqsig (__x, __y);
|
|
}
|
|
};
|
|
|
|
template<> struct __iseqsig_type<long double>
|
|
{
|
|
static int __call (double __x, double __y) throw ()
|
|
{
|
|
# ifndef __NO_LONG_DOUBLE_MATH
|
|
return __iseqsigl (__x, __y);
|
|
# else
|
|
return __iseqsig (__x, __y);
|
|
# endif
|
|
}
|
|
};
|
|
|
|
# if __HAVE_DISTINCT_FLOAT128
|
|
template<> struct __iseqsig_type<_Float128>
|
|
{
|
|
static int __call (_Float128 __x, _Float128 __y) throw ()
|
|
{
|
|
return __iseqsigf128 (__x, __y);
|
|
}
|
|
};
|
|
# endif
|
|
|
|
template<typename _T1, typename _T2>
|
|
inline int
|
|
iseqsig (_T1 __x, _T2 __y) throw ()
|
|
{
|
|
# if __cplusplus >= 201103L
|
|
typedef decltype (__MATH_EVAL_FMT2 (__x, __y)) _T3;
|
|
# else
|
|
typedef __typeof (__MATH_EVAL_FMT2 (__x, __y)) _T3;
|
|
# endif
|
|
return __iseqsig_type<_T3>::__call (__x, __y);
|
|
}
|
|
|
|
} /* extern "C++" */
|
|
# endif /* __cplusplus */
|
|
|
|
#endif
|
|
|
|
__END_DECLS
|
|
|
|
|
|
#endif /* math.h */
|