diff options
Diffstat (limited to 'REORG.TODO/math/math.h')
| -rw-r--r-- | REORG.TODO/math/math.h | 786 |
1 files changed, 786 insertions, 0 deletions
diff --git a/REORG.TODO/math/math.h b/REORG.TODO/math/math.h new file mode 100644 index 0000000000..e21708045a --- /dev/null +++ b/REORG.TODO/math/math.h @@ -0,0 +1,786 @@ +/* Declarations for math functions. + Copyright (C) 1991-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* + * ISO C99 Standard: 7.12 Mathematics <math.h> + */ + +#ifndef _MATH_H +#define _MATH_H 1 + +#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION +#include <bits/libc-header-start.h> + +__BEGIN_DECLS + +/* Get definitions of __intmax_t and __uintmax_t. */ +#include <bits/types.h> + +/* Get machine-dependent vector math functions declarations. */ +#include <bits/math-vector.h> + +/* Gather machine dependent type support. */ +#include <bits/floatn.h> + +/* Get machine-dependent HUGE_VAL value (returned on overflow). + On all IEEE754 machines, this is +Infinity. */ +#include <bits/huge_val.h> + +#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT) +# include <bits/huge_val_flt128.h> +#endif + +#ifdef __USE_ISOC99 +# include <bits/huge_valf.h> +# include <bits/huge_vall.h> + +/* Get machine-dependent INFINITY value. */ +# include <bits/inf.h> + +/* Get machine-dependent NAN value (returned for some domain errors). */ +# include <bits/nan.h> +#endif /* __USE_ISOC99 */ + +#if __GLIBC_USE (IEC_60559_BFP_EXT) +/* Signaling NaN macros, if supported. */ +# if __GNUC_PREREQ (3, 3) +# define SNANF (__builtin_nansf ("")) +# define SNAN (__builtin_nans ("")) +# define SNANL (__builtin_nansl ("")) +# endif +#endif +#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT) +# define SNANF128 (__builtin_nansf128 ("")) +#endif + +/* Get __GLIBC_FLT_EVAL_METHOD. */ +#include <bits/flt-eval-method.h> + +#ifdef __USE_ISOC99 +/* Define the following typedefs. + + float_t floating-point type at least as wide as `float' used + to evaluate `float' expressions + double_t floating-point type at least as wide as `double' used + to evaluate `double' expressions +*/ +# if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16 +typedef float float_t; +typedef double double_t; +# elif __GLIBC_FLT_EVAL_METHOD == 1 +typedef double float_t; +typedef double double_t; +# elif __GLIBC_FLT_EVAL_METHOD == 2 +typedef long double float_t; +typedef long double double_t; +# elif __GLIBC_FLT_EVAL_METHOD == 32 +typedef _Float32 float_t; +typedef double double_t; +# elif __GLIBC_FLT_EVAL_METHOD == 33 +typedef _Float32x float_t; +typedef _Float32x double_t; +# elif __GLIBC_FLT_EVAL_METHOD == 64 +typedef _Float64 float_t; +typedef _Float64 double_t; +# elif __GLIBC_FLT_EVAL_METHOD == 65 +typedef _Float64x float_t; +typedef _Float64x double_t; +# elif __GLIBC_FLT_EVAL_METHOD == 128 +typedef _Float128 float_t; +typedef _Float128 double_t; +# elif __GLIBC_FLT_EVAL_METHOD == 129 +typedef _Float128x float_t; +typedef _Float128x double_t; +# else +# error "Unknown __GLIBC_FLT_EVAL_METHOD" +# endif +#endif + +/* Define macros for the return values of ilogb and llogb, based on + __FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN. + + FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. + FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. + FP_LLOGB0 Expands to a value returned by `llogb (0.0)'. + FP_LLOGBNAN Expands to a value returned by `llogb (NAN)'. + +*/ + +#include <bits/fp-logb.h> +#ifdef __USE_ISOC99 +# if __FP_LOGB0_IS_MIN +# define FP_ILOGB0 (-2147483647 - 1) +# else +# define FP_ILOGB0 (-2147483647) +# endif +# if __FP_LOGBNAN_IS_MIN +# define FP_ILOGBNAN (-2147483647 - 1) +# else +# define FP_ILOGBNAN 2147483647 +# endif +#endif +#if __GLIBC_USE (IEC_60559_BFP_EXT) +# if __WORDSIZE == 32 +# define __FP_LONG_MAX 0x7fffffffL +# else +# define __FP_LONG_MAX 0x7fffffffffffffffL +# endif +# if __FP_LOGB0_IS_MIN +# define FP_LLOGB0 (-__FP_LONG_MAX - 1) +# else +# define FP_LLOGB0 (-__FP_LONG_MAX) +# endif +# if __FP_LOGBNAN_IS_MIN +# define FP_LLOGBNAN (-__FP_LONG_MAX - 1) +# else +# define FP_LLOGBNAN __FP_LONG_MAX +# endif +#endif + +/* Get the architecture specific values describing the floating-point + evaluation. The following symbols will get defined: + + FP_FAST_FMA + FP_FAST_FMAF + FP_FAST_FMAL + If defined it indicates that the `fma' function + generally executes about as fast as a multiply and an add. + This macro is defined only iff the `fma' function is + implemented directly with a hardware multiply-add instructions. +*/ + +#include <bits/fp-fast.h> + +#if __GLIBC_USE (IEC_60559_BFP_EXT) +/* Rounding direction macros for fromfp functions. */ +enum + { + FP_INT_UPWARD = +# define FP_INT_UPWARD 0 + FP_INT_UPWARD, + FP_INT_DOWNWARD = +# define FP_INT_DOWNWARD 1 + FP_INT_DOWNWARD, + FP_INT_TOWARDZERO = +# define FP_INT_TOWARDZERO 2 + FP_INT_TOWARDZERO, + FP_INT_TONEARESTFROMZERO = +# define FP_INT_TONEARESTFROMZERO 3 + FP_INT_TONEARESTFROMZERO, + FP_INT_TONEAREST = +# define FP_INT_TONEAREST 4 + FP_INT_TONEAREST, + }; +#endif + +/* The file <bits/mathcalls.h> contains the prototypes for all the + actual math functions. These macros are used for those prototypes, + so we can easily declare each function as both `name' and `__name', + and can declare the float versions `namef' and `__namef'. */ + +#define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function) + +#define __MATHCALL_VEC(function, suffix, args) \ + __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \ + __MATHCALL (function, suffix, args) + +#define __MATHDECL_VEC(type, function,suffix, args) \ + __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \ + __MATHDECL(type, function,suffix, args) + +#define __MATHCALL(function,suffix, args) \ + __MATHDECL (_Mdouble_,function,suffix, args) +#define __MATHDECL(type, function,suffix, args) \ + __MATHDECL_1(type, function,suffix, args); \ + __MATHDECL_1(type, __CONCAT(__,function),suffix, args) +#define __MATHCALLX(function,suffix, args, attrib) \ + __MATHDECLX (_Mdouble_,function,suffix, args, attrib) +#define __MATHDECLX(type, function,suffix, args, attrib) \ + __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \ + __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib) +#define __MATHDECL_1(type, function,suffix, args) \ + extern type __MATH_PRECNAME(function,suffix) args __THROW + +#define _Mdouble_ double +#define __MATH_PRECNAME(name,r) __CONCAT(name,r) +#define __MATH_DECLARING_DOUBLE 1 +#define __MATH_DECLARING_FLOATN 0 +#include <bits/mathcalls-helper-functions.h> +#include <bits/mathcalls.h> +#undef _Mdouble_ +#undef __MATH_PRECNAME +#undef __MATH_DECLARING_DOUBLE +#undef __MATH_DECLARING_FLOATN + +#ifdef __USE_ISOC99 + + +/* Include the file of declarations again, this time using `float' + instead of `double' and appending f to each function name. */ + +# ifndef _Mfloat_ +# define _Mfloat_ float +# endif +# define _Mdouble_ _Mfloat_ +# define __MATH_PRECNAME(name,r) name##f##r +# define __MATH_DECLARING_DOUBLE 0 +# define __MATH_DECLARING_FLOATN 0 +# include <bits/mathcalls-helper-functions.h> +# include <bits/mathcalls.h> +# undef _Mdouble_ +# undef __MATH_PRECNAME +# undef __MATH_DECLARING_DOUBLE +# undef __MATH_DECLARING_FLOATN + +# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \ + || defined __LDBL_COMPAT \ + || defined _LIBC_TEST +# ifdef __LDBL_COMPAT + +# ifdef __USE_ISOC99 +extern float __nldbl_nexttowardf (float __x, long double __y) + __THROW __attribute__ ((__const__)); +# ifdef __REDIRECT_NTH +extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y), + __nldbl_nexttowardf) + __attribute__ ((__const__)); +extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y), + nextafter) __attribute__ ((__const__)); +extern long double __REDIRECT_NTH (nexttowardl, + (long double __x, long double __y), + nextafter) __attribute__ ((__const__)); +# endif +# endif + +# undef __MATHDECL_1 +# define __MATHDECL_2(type, function,suffix, args, alias) \ + extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \ + args, alias) +# define __MATHDECL_1(type, function,suffix, args) \ + __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix)) +# endif + +/* Include the file of declarations again, this time using `long double' + instead of `double' and appending l to each function name. */ + +# ifndef _Mlong_double_ +# define _Mlong_double_ long double +# endif +# define _Mdouble_ _Mlong_double_ +# 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 again, this time using `_Float128' + instead of `double' and appending f128 to each function name. */ + +#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC) +# ifndef _Mfloat128_ +# define _Mfloat128_ _Float128 +# endif +# define _Mdouble_ _Mfloat128_ +# 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. */ + +#undef __MATHDECL_1 +#undef __MATHDECL +#undef __MATHCALL + + +#if defined __USE_MISC || defined __USE_XOPEN +/* This variable is used by `gamma' and `lgamma'. */ +extern int signgam; +#endif + + +/* 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 +# 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 +# define __MATH_TG(TG_ARG, FUNC, ARGS) \ + _Generic ((TG_ARG), \ + float: FUNC ## f ARGS, \ + default: FUNC ARGS, \ + long double: FUNC ## l ARGS, \ + _Float128: FUNC ## f128 ARGS) +# else +# 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__ +# 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 __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__ + /* __builtin_isinf_sign is broken for float128 only before GCC 7.0. */ +# 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. */ +# define issignaling(x) __MATH_TG ((x), __issignaling, (x)) + +/* 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++" { +template <class __T> inline bool +iszero (__T __val) +{ +# ifdef __SUPPORT_SNAN__ + return fpclassify (__val) == FP_ZERO; +# else + return __val == 0; +# endif +} +} /* extern C++ */ +# endif /* __cplusplus */ +#endif /* Use IEC_60559_BFP_EXT. */ + +#ifdef __USE_MISC +/* Support for various different standard error handling behaviors. */ +typedef enum +{ + _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ + _SVID_, /* According to System V, release 4. */ + _XOPEN_, /* Nowadays also Unix98. */ + _POSIX_, + _ISOC_ /* Actually this is ISO C99. */ +} _LIB_VERSION_TYPE; + +/* This variable can be changed at run-time to any of the values above to + affect floating point error handling behavior (it may also be necessary + to change the hardware FPU exception settings). */ +extern _LIB_VERSION_TYPE _LIB_VERSION; +#endif + + +#ifdef __USE_MISC +/* In SVID error handling, `matherr' is called with this description + of the exceptional condition. + + We have a problem when using C++ since `exception' is a reserved + name in C++. */ +# ifdef __cplusplus +struct __exception +# else +struct exception +# endif + { + int type; + char *name; + double arg1; + double arg2; + double retval; + }; + +# ifdef __cplusplus +extern int matherr (struct __exception *__exc) throw (); +# else +extern int matherr (struct exception *__exc); +# endif + +# define X_TLOSS 1.41484755040568800000e+16 + +/* Types of exceptions in the `type' field. */ +# define DOMAIN 1 +# define SING 2 +# define OVERFLOW 3 +# define UNDERFLOW 4 +# define TLOSS 5 +# define PLOSS 6 + +/* SVID mode specifies returning this large value instead of infinity. */ +# define HUGE 3.40282347e+38F + +#else /* !Misc. */ + +# ifdef __USE_XOPEN +/* X/Open wants another strange constant. */ +# define MAXFLOAT 3.40282347e+38F +# endif + +#endif /* Misc. */ + + +/* 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_LDOUBLE 0 +# define __MATH_DECLARING_FLOATN 0 +# define _MSUF_ +# include <bits/math-finite.h> +# undef _Mdouble_ +# undef __MATH_DECLARING_DOUBLE +# undef __MATH_DECLARING_LDOUBLE +# undef __MATH_DECLARING_FLOATN +# undef _MSUF_ + +/* 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_LDOUBLE 0 +# define __MATH_DECLARING_FLOATN 0 +# define _MSUF_ f +# include <bits/math-finite.h> +# undef _Mdouble_ +# undef __MATH_DECLARING_DOUBLE +# undef __MATH_DECLARING_LDOUBLE +# undef __MATH_DECLARING_FLOATN +# undef _MSUF_ + +/* Include bits/math-finite.h for long double. */ +# ifdef __MATH_DECLARE_LDOUBLE +# define _Mdouble_ long double +# define __MATH_DECLARING_DOUBLE 0 +# define __MATH_DECLARING_LDOUBLE 1 +# define __MATH_DECLARING_FLOATN 0 +# define _MSUF_ l +# include <bits/math-finite.h> +# undef _Mdouble_ +# undef __MATH_DECLARING_DOUBLE +# undef __MATH_DECLARING_LDOUBLE +# undef __MATH_DECLARING_FLOATN +# undef _MSUF_ +# 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_LDOUBLE 0 +# define __MATH_DECLARING_FLOATN 1 +# define _MSUF_ f128 +# include <bits/math-finite.h> +# undef _Mdouble_ +# undef __MATH_DECLARING_DOUBLE +# undef __MATH_DECLARING_LDOUBLE +# undef __MATH_DECLARING_FLOATN +# undef _MSUF_ +# 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 */ |