1/* Declarations for math functions.
2 Copyright (C) 1991-2017 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <http://www.gnu.org/licenses/>. */
18
19/*
20 * ISO C99 Standard: 7.12 Mathematics <math.h>
21 */
22
23#ifndef _MATH_H
24#define _MATH_H 1
25
26#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
27#include <bits/libc-header-start.h>
28
29__BEGIN_DECLS
30
31/* Get definitions of __intmax_t and __uintmax_t. */
32#include <bits/types.h>
33
34/* Get machine-dependent vector math functions declarations. */
35#include <bits/math-vector.h>
36
37/* Gather machine dependent type support. */
38#include <bits/floatn.h>
39
40/* Get machine-dependent HUGE_VAL value (returned on overflow).
41 On all IEEE754 machines, this is +Infinity. */
42#include <bits/huge_val.h>
43
44#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
45# include <bits/huge_val_flt128.h>
46#endif
47
48#ifdef __USE_ISOC99
49# include <bits/huge_valf.h>
50# include <bits/huge_vall.h>
51
52/* Get machine-dependent INFINITY value. */
53# include <bits/inf.h>
54
55/* Get machine-dependent NAN value (returned for some domain errors). */
56# include <bits/nan.h>
57#endif /* __USE_ISOC99 */
58
59#if __GLIBC_USE (IEC_60559_BFP_EXT)
60/* Signaling NaN macros, if supported. */
61# if __GNUC_PREREQ (3, 3)
62# define SNANF (__builtin_nansf (""))
63# define SNAN (__builtin_nans (""))
64# define SNANL (__builtin_nansl (""))
65# endif
66#endif
67#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
68# define SNANF128 (__builtin_nansf128 (""))
69#endif
70
71/* Get __GLIBC_FLT_EVAL_METHOD. */
72#include <bits/flt-eval-method.h>
73
74#ifdef __USE_ISOC99
75/* Define the following typedefs.
76
77 float_t floating-point type at least as wide as `float' used
78 to evaluate `float' expressions
79 double_t floating-point type at least as wide as `double' used
80 to evaluate `double' expressions
81*/
82# if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
83typedef float float_t;
84typedef double double_t;
85# elif __GLIBC_FLT_EVAL_METHOD == 1
86typedef double float_t;
87typedef double double_t;
88# elif __GLIBC_FLT_EVAL_METHOD == 2
89typedef long double float_t;
90typedef long double double_t;
91# elif __GLIBC_FLT_EVAL_METHOD == 32
92typedef _Float32 float_t;
93typedef double double_t;
94# elif __GLIBC_FLT_EVAL_METHOD == 33
95typedef _Float32x float_t;
96typedef _Float32x double_t;
97# elif __GLIBC_FLT_EVAL_METHOD == 64
98typedef _Float64 float_t;
99typedef _Float64 double_t;
100# elif __GLIBC_FLT_EVAL_METHOD == 65
101typedef _Float64x float_t;
102typedef _Float64x double_t;
103# elif __GLIBC_FLT_EVAL_METHOD == 128
104typedef _Float128 float_t;
105typedef _Float128 double_t;
106# elif __GLIBC_FLT_EVAL_METHOD == 129
107typedef _Float128x float_t;
108typedef _Float128x double_t;
109# else
110# error "Unknown __GLIBC_FLT_EVAL_METHOD"
111# endif
112#endif
113
114/* Define macros for the return values of ilogb and llogb, based on
115 __FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.
116
117 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
118 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
119 FP_LLOGB0 Expands to a value returned by `llogb (0.0)'.
120 FP_LLOGBNAN Expands to a value returned by `llogb (NAN)'.
121
122*/
123
124#include <bits/fp-logb.h>
125#ifdef __USE_ISOC99
126# if __FP_LOGB0_IS_MIN
127# define FP_ILOGB0 (-2147483647 - 1)
128# else
129# define FP_ILOGB0 (-2147483647)
130# endif
131# if __FP_LOGBNAN_IS_MIN
132# define FP_ILOGBNAN (-2147483647 - 1)
133# else
134# define FP_ILOGBNAN 2147483647
135# endif
136#endif
137#if __GLIBC_USE (IEC_60559_BFP_EXT)
138# if __WORDSIZE == 32
139# define __FP_LONG_MAX 0x7fffffffL
140# else
141# define __FP_LONG_MAX 0x7fffffffffffffffL
142# endif
143# if __FP_LOGB0_IS_MIN
144# define FP_LLOGB0 (-__FP_LONG_MAX - 1)
145# else
146# define FP_LLOGB0 (-__FP_LONG_MAX)
147# endif
148# if __FP_LOGBNAN_IS_MIN
149# define FP_LLOGBNAN (-__FP_LONG_MAX - 1)
150# else
151# define FP_LLOGBNAN __FP_LONG_MAX
152# endif
153#endif
154
155/* Get the architecture specific values describing the floating-point
156 evaluation. The following symbols will get defined:
157
158 FP_FAST_FMA
159 FP_FAST_FMAF
160 FP_FAST_FMAL
161 If defined it indicates that the `fma' function
162 generally executes about as fast as a multiply and an add.
163 This macro is defined only iff the `fma' function is
164 implemented directly with a hardware multiply-add instructions.
165*/
166
167#include <bits/fp-fast.h>
168
169#if __GLIBC_USE (IEC_60559_BFP_EXT)
170/* Rounding direction macros for fromfp functions. */
171enum
172 {
173 FP_INT_UPWARD =
174# define FP_INT_UPWARD 0
175 FP_INT_UPWARD,
176 FP_INT_DOWNWARD =
177# define FP_INT_DOWNWARD 1
178 FP_INT_DOWNWARD,
179 FP_INT_TOWARDZERO =
180# define FP_INT_TOWARDZERO 2
181 FP_INT_TOWARDZERO,
182 FP_INT_TONEARESTFROMZERO =
183# define FP_INT_TONEARESTFROMZERO 3
184 FP_INT_TONEARESTFROMZERO,
185 FP_INT_TONEAREST =
186# define FP_INT_TONEAREST 4
187 FP_INT_TONEAREST,
188 };
189#endif
190
191/* The file <bits/mathcalls.h> contains the prototypes for all the
192 actual math functions. These macros are used for those prototypes,
193 so we can easily declare each function as both `name' and `__name',
194 and can declare the float versions `namef' and `__namef'. */
195
196#define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
197
198#define __MATHCALL_VEC(function, suffix, args) \
199 __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
200 __MATHCALL (function, suffix, args)
201
202#define __MATHDECL_VEC(type, function,suffix, args) \
203 __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
204 __MATHDECL(type, function,suffix, args)
205
206#define __MATHCALL(function,suffix, args) \
207 __MATHDECL (_Mdouble_,function,suffix, args)
208#define __MATHDECL(type, function,suffix, args) \
209 __MATHDECL_1(type, function,suffix, args); \
210 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
211#define __MATHCALLX(function,suffix, args, attrib) \
212 __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
213#define __MATHDECLX(type, function,suffix, args, attrib) \
214 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
215 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
216#define __MATHDECL_1(type, function,suffix, args) \
217 extern type __MATH_PRECNAME(function,suffix) args __THROW
218
219#define _Mdouble_ double
220#define __MATH_PRECNAME(name,r) __CONCAT(name,r)
221#define __MATH_DECLARING_DOUBLE 1
222#define __MATH_DECLARING_FLOATN 0
223#include <bits/mathcalls-helper-functions.h>
224#include <bits/mathcalls.h>
225#undef _Mdouble_
226#undef __MATH_PRECNAME
227#undef __MATH_DECLARING_DOUBLE
228#undef __MATH_DECLARING_FLOATN
229
230#ifdef __USE_ISOC99
231
232
233/* Include the file of declarations again, this time using `float'
234 instead of `double' and appending f to each function name. */
235
236# ifndef _Mfloat_
237# define _Mfloat_ float
238# endif
239# define _Mdouble_ _Mfloat_
240# define __MATH_PRECNAME(name,r) name##f##r
241# define __MATH_DECLARING_DOUBLE 0
242# define __MATH_DECLARING_FLOATN 0
243# include <bits/mathcalls-helper-functions.h>
244# include <bits/mathcalls.h>
245# undef _Mdouble_
246# undef __MATH_PRECNAME
247# undef __MATH_DECLARING_DOUBLE
248# undef __MATH_DECLARING_FLOATN
249
250# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
251 || defined __LDBL_COMPAT \
252 || defined _LIBC_TEST
253# ifdef __LDBL_COMPAT
254
255# ifdef __USE_ISOC99
256extern float __nldbl_nexttowardf (float __x, long double __y)
257 __THROW __attribute__ ((__const__));
258# ifdef __REDIRECT_NTH
259extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
260 __nldbl_nexttowardf)
261 __attribute__ ((__const__));
262extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
263 nextafter) __attribute__ ((__const__));
264extern long double __REDIRECT_NTH (nexttowardl,
265 (long double __x, long double __y),
266 nextafter) __attribute__ ((__const__));
267# endif
268# endif
269
270# undef __MATHDECL_1
271# define __MATHDECL_2(type, function,suffix, args, alias) \
272 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
273 args, alias)
274# define __MATHDECL_1(type, function,suffix, args) \
275 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
276# endif
277
278/* Include the file of declarations again, this time using `long double'
279 instead of `double' and appending l to each function name. */
280
281# ifndef _Mlong_double_
282# define _Mlong_double_ long double
283# endif
284# define _Mdouble_ _Mlong_double_
285# define __MATH_PRECNAME(name,r) name##l##r
286# define __MATH_DECLARING_DOUBLE 0
287# define __MATH_DECLARING_FLOATN 0
288# define __MATH_DECLARE_LDOUBLE 1
289# include <bits/mathcalls-helper-functions.h>
290# include <bits/mathcalls.h>
291# undef _Mdouble_
292# undef __MATH_PRECNAME
293# undef __MATH_DECLARING_DOUBLE
294# undef __MATH_DECLARING_FLOATN
295
296# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
297
298#endif /* Use ISO C99. */
299
300/* Include the file of declarations again, this time using `_Float128'
301 instead of `double' and appending f128 to each function name. */
302
303#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)
304# ifndef _Mfloat128_
305# define _Mfloat128_ _Float128
306# endif
307# define _Mdouble_ _Mfloat128_
308# define __MATH_PRECNAME(name,r) name##f128##r
309# define __MATH_DECLARING_DOUBLE 0
310# define __MATH_DECLARING_FLOATN 1
311# if __HAVE_DISTINCT_FLOAT128
312# include <bits/mathcalls-helper-functions.h>
313# endif
314# if __GLIBC_USE (IEC_60559_TYPES_EXT)
315# include <bits/mathcalls.h>
316# endif
317# undef _Mdouble_
318# undef __MATH_PRECNAME
319# undef __MATH_DECLARING_DOUBLE
320# undef __MATH_DECLARING_FLOATN
321#endif /* __HAVE_DISTINCT_FLOAT128. */
322
323#undef __MATHDECL_1
324#undef __MATHDECL
325#undef __MATHCALL
326
327
328#if defined __USE_MISC || defined __USE_XOPEN
329/* This variable is used by `gamma' and `lgamma'. */
330extern int signgam;
331#endif
332
333
334/* Depending on the type of TG_ARG, call an appropriately suffixed
335 version of FUNC with arguments (including parentheses) ARGS.
336 Suffixed functions may not exist for long double if it has the same
337 format as double, or for other types with the same format as float,
338 double or long double. The behavior is undefined if the argument
339 does not have a real floating type. The definition may use a
340 conditional expression, so all suffixed versions of FUNC must
341 return the same type (FUNC may include a cast if necessary rather
342 than being a single identifier). */
343#ifdef __NO_LONG_DOUBLE_MATH
344# define __MATH_TG(TG_ARG, FUNC, ARGS) \
345 (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
346#elif __HAVE_DISTINCT_FLOAT128
347# if __HAVE_GENERIC_SELECTION
348# define __MATH_TG(TG_ARG, FUNC, ARGS) \
349 _Generic ((TG_ARG), \
350 float: FUNC ## f ARGS, \
351 default: FUNC ARGS, \
352 long double: FUNC ## l ARGS, \
353 _Float128: FUNC ## f128 ARGS)
354# else
355# define __MATH_TG(TG_ARG, FUNC, ARGS) \
356 __builtin_choose_expr \
357 (__builtin_types_compatible_p (__typeof (TG_ARG), float), \
358 FUNC ## f ARGS, \
359 __builtin_choose_expr \
360 (__builtin_types_compatible_p (__typeof (TG_ARG), double), \
361 FUNC ARGS, \
362 __builtin_choose_expr \
363 (__builtin_types_compatible_p (__typeof (TG_ARG), long double), \
364 FUNC ## l ARGS, \
365 FUNC ## f128 ARGS)))
366# endif
367#else
368# define __MATH_TG(TG_ARG, FUNC, ARGS) \
369 (sizeof (TG_ARG) == sizeof (float) \
370 ? FUNC ## f ARGS \
371 : sizeof (TG_ARG) == sizeof (double) \
372 ? FUNC ARGS \
373 : FUNC ## l ARGS)
374#endif
375
376/* ISO C99 defines some generic macros which work on any data type. */
377#ifdef __USE_ISOC99
378
379/* All floating-point numbers can be put in one of these categories. */
380enum
381 {
382 FP_NAN =
383# define FP_NAN 0
384 FP_NAN,
385 FP_INFINITE =
386# define FP_INFINITE 1
387 FP_INFINITE,
388 FP_ZERO =
389# define FP_ZERO 2
390 FP_ZERO,
391 FP_SUBNORMAL =
392# define FP_SUBNORMAL 3
393 FP_SUBNORMAL,
394 FP_NORMAL =
395# define FP_NORMAL 4
396 FP_NORMAL
397 };
398
399/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
400 so disable builtins if this is enabled. When fixed in a newer GCC,
401 the __SUPPORT_SNAN__ check may be skipped for those versions. */
402
403/* Return number of classification appropriate for X. */
404# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ \
405 && !defined __OPTIMIZE_SIZE__
406# define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \
407 FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
408# else
409# define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
410# endif
411
412/* Return nonzero value if sign of X is negative. */
413# if __GNUC_PREREQ (6,0)
414# define signbit(x) __builtin_signbit (x)
415# elif __GNUC_PREREQ (4,0)
416# define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
417# else
418# define signbit(x) __MATH_TG ((x), __signbit, (x))
419# endif
420
421/* Return nonzero value if X is not +-Inf or NaN. */
422# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
423# define isfinite(x) __builtin_isfinite (x)
424# else
425# define isfinite(x) __MATH_TG ((x), __finite, (x))
426# endif
427
428/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
429# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
430# define isnormal(x) __builtin_isnormal (x)
431# else
432# define isnormal(x) (fpclassify (x) == FP_NORMAL)
433# endif
434
435/* Return nonzero value if X is a NaN. We could use `fpclassify' but
436 we already have this functions `__isnan' and it is faster. */
437# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
438# define isnan(x) __builtin_isnan (x)
439# else
440# define isnan(x) __MATH_TG ((x), __isnan, (x))
441# endif
442
443/* Return nonzero value if X is positive or negative infinity. */
444# if __HAVE_DISTINCT_FLOAT128 && !__GNUC_PREREQ (7,0) \
445 && !defined __SUPPORT_SNAN__
446 /* __builtin_isinf_sign is broken for float128 only before GCC 7.0. */
447# define isinf(x) \
448 (__builtin_types_compatible_p (__typeof (x), _Float128) \
449 ? __isinff128 (x) : __builtin_isinf_sign (x))
450# elif __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
451# define isinf(x) __builtin_isinf_sign (x)
452# else
453# define isinf(x) __MATH_TG ((x), __isinf, (x))
454# endif
455
456/* Bitmasks for the math_errhandling macro. */
457# define MATH_ERRNO 1 /* errno set by math functions. */
458# define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
459
460/* By default all functions support both errno and exception handling.
461 In gcc's fast math mode and if inline functions are defined this
462 might not be true. */
463# ifndef __FAST_MATH__
464# define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
465# endif
466
467#endif /* Use ISO C99. */
468
469#if __GLIBC_USE (IEC_60559_BFP_EXT)
470# include <bits/iscanonical.h>
471
472/* Return nonzero value if X is a signaling NaN. */
473# define issignaling(x) __MATH_TG ((x), __issignaling, (x))
474
475/* Return nonzero value if X is subnormal. */
476# define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
477
478/* Return nonzero value if X is zero. */
479# ifndef __cplusplus
480# ifdef __SUPPORT_SNAN__
481# define iszero(x) (fpclassify (x) == FP_ZERO)
482# else
483# define iszero(x) (((__typeof (x)) (x)) == 0)
484# endif
485# else /* __cplusplus */
486extern "C++" {
487template <class __T> inline bool
488iszero (__T __val)
489{
490# ifdef __SUPPORT_SNAN__
491 return fpclassify (__val) == FP_ZERO;
492# else
493 return __val == 0;
494# endif
495}
496} /* extern C++ */
497# endif /* __cplusplus */
498#endif /* Use IEC_60559_BFP_EXT. */
499
500#ifdef __USE_MISC
501/* Support for various different standard error handling behaviors. */
502typedef enum
503{
504 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
505 _SVID_, /* According to System V, release 4. */
506 _XOPEN_, /* Nowadays also Unix98. */
507 _POSIX_,
508 _ISOC_ /* Actually this is ISO C99. */
509} _LIB_VERSION_TYPE;
510
511/* This variable can be changed at run-time to any of the values above to
512 affect floating point error handling behavior (it may also be necessary
513 to change the hardware FPU exception settings). */
514extern _LIB_VERSION_TYPE _LIB_VERSION;
515#endif
516
517
518#ifdef __USE_MISC
519/* In SVID error handling, `matherr' is called with this description
520 of the exceptional condition.
521
522 We have a problem when using C++ since `exception' is a reserved
523 name in C++. */
524# ifdef __cplusplus
525struct __exception
526# else
527struct exception
528# endif
529 {
530 int type;
531 char *name;
532 double arg1;
533 double arg2;
534 double retval;
535 };
536
537# ifdef __cplusplus
538extern int matherr (struct __exception *__exc) throw ();
539# else
540extern int matherr (struct exception *__exc);
541# endif
542
543# define X_TLOSS 1.41484755040568800000e+16
544
545/* Types of exceptions in the `type' field. */
546# define DOMAIN 1
547# define SING 2
548# define OVERFLOW 3
549# define UNDERFLOW 4
550# define TLOSS 5
551# define PLOSS 6
552
553/* SVID mode specifies returning this large value instead of infinity. */
554# define HUGE 3.40282347e+38F
555
556#else /* !Misc. */
557
558# ifdef __USE_XOPEN
559/* X/Open wants another strange constant. */
560# define MAXFLOAT 3.40282347e+38F
561# endif
562
563#endif /* Misc. */
564
565
566/* Some useful constants. */
567#if defined __USE_MISC || defined __USE_XOPEN
568# define M_E 2.7182818284590452354 /* e */
569# define M_LOG2E 1.4426950408889634074 /* log_2 e */
570# define M_LOG10E 0.43429448190325182765 /* log_10 e */
571# define M_LN2 0.69314718055994530942 /* log_e 2 */
572# define M_LN10 2.30258509299404568402 /* log_e 10 */
573# define M_PI 3.14159265358979323846 /* pi */
574# define M_PI_2 1.57079632679489661923 /* pi/2 */
575# define M_PI_4 0.78539816339744830962 /* pi/4 */
576# define M_1_PI 0.31830988618379067154 /* 1/pi */
577# define M_2_PI 0.63661977236758134308 /* 2/pi */
578# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
579# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
580# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
581#endif
582
583/* The above constants are not adequate for computation using `long double's.
584 Therefore we provide as an extension constants with similar names as a
585 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
586#ifdef __USE_GNU
587# define M_El 2.718281828459045235360287471352662498L /* e */
588# define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
589# define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
590# define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
591# define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
592# define M_PIl 3.141592653589793238462643383279502884L /* pi */
593# define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
594# define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
595# define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
596# define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
597# define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
598# define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
599# define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
600#endif
601
602#if __HAVE_FLOAT128 && defined __USE_GNU
603# define M_Ef128 __f128 (2.718281828459045235360287471352662498) /* e */
604# define M_LOG2Ef128 __f128 (1.442695040888963407359924681001892137) /* log_2 e */
605# define M_LOG10Ef128 __f128 (0.434294481903251827651128918916605082) /* log_10 e */
606# define M_LN2f128 __f128 (0.693147180559945309417232121458176568) /* log_e 2 */
607# define M_LN10f128 __f128 (2.302585092994045684017991454684364208) /* log_e 10 */
608# define M_PIf128 __f128 (3.141592653589793238462643383279502884) /* pi */
609# define M_PI_2f128 __f128 (1.570796326794896619231321691639751442) /* pi/2 */
610# define M_PI_4f128 __f128 (0.785398163397448309615660845819875721) /* pi/4 */
611# define M_1_PIf128 __f128 (0.318309886183790671537767526745028724) /* 1/pi */
612# define M_2_PIf128 __f128 (0.636619772367581343075535053490057448) /* 2/pi */
613# define M_2_SQRTPIf128 __f128 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
614# define M_SQRT2f128 __f128 (1.414213562373095048801688724209698079) /* sqrt(2) */
615# define M_SQRT1_2f128 __f128 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
616#endif
617
618/* When compiling in strict ISO C compatible mode we must not use the
619 inline functions since they, among other things, do not set the
620 `errno' variable correctly. */
621#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
622# define __NO_MATH_INLINES 1
623#endif
624
625#if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
626/* ISO C99 defines some macros to compare number while taking care for
627 unordered numbers. Many FPUs provide special instructions to support
628 these operations. Generic support in GCC for these as builtins went
629 in before 3.0.0, but not all cpus added their patterns. We define
630 versions that use the builtins here, and <bits/mathinline.h> will
631 undef/redefine as appropriate for the specific GCC version in use. */
632# define isgreater(x, y) __builtin_isgreater(x, y)
633# define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
634# define isless(x, y) __builtin_isless(x, y)
635# define islessequal(x, y) __builtin_islessequal(x, y)
636# define islessgreater(x, y) __builtin_islessgreater(x, y)
637# define isunordered(u, v) __builtin_isunordered(u, v)
638#endif
639
640/* Get machine-dependent inline versions (if there are any). */
641#ifdef __USE_EXTERN_INLINES
642# include <bits/mathinline.h>
643#endif
644
645/* Define special entry points to use when the compiler got told to
646 only expect finite results. */
647#if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
648
649/* Include bits/math-finite.h for double. */
650# define _Mdouble_ double
651# define __MATH_DECLARING_DOUBLE 1
652# define __MATH_DECLARING_LDOUBLE 0
653# define __MATH_DECLARING_FLOATN 0
654# define _MSUF_
655# include <bits/math-finite.h>
656# undef _Mdouble_
657# undef __MATH_DECLARING_DOUBLE
658# undef __MATH_DECLARING_LDOUBLE
659# undef __MATH_DECLARING_FLOATN
660# undef _MSUF_
661
662/* When __USE_ISOC99 is defined, include math-finite for float and
663 long double, as well. */
664# ifdef __USE_ISOC99
665
666/* Include bits/math-finite.h for float. */
667# define _Mdouble_ float
668# define __MATH_DECLARING_DOUBLE 0
669# define __MATH_DECLARING_LDOUBLE 0
670# define __MATH_DECLARING_FLOATN 0
671# define _MSUF_ f
672# include <bits/math-finite.h>
673# undef _Mdouble_
674# undef __MATH_DECLARING_DOUBLE
675# undef __MATH_DECLARING_LDOUBLE
676# undef __MATH_DECLARING_FLOATN
677# undef _MSUF_
678
679/* Include bits/math-finite.h for long double. */
680# ifdef __MATH_DECLARE_LDOUBLE
681# define _Mdouble_ long double
682# define __MATH_DECLARING_DOUBLE 0
683# define __MATH_DECLARING_LDOUBLE 1
684# define __MATH_DECLARING_FLOATN 0
685# define _MSUF_ l
686# include <bits/math-finite.h>
687# undef _Mdouble_
688# undef __MATH_DECLARING_DOUBLE
689# undef __MATH_DECLARING_LDOUBLE
690# undef __MATH_DECLARING_FLOATN
691# undef _MSUF_
692# endif
693
694# endif /* __USE_ISOC99. */
695
696/* Include bits/math-finite.h for float128. */
697# if (__HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)) \
698 && __GLIBC_USE (IEC_60559_TYPES_EXT)
699# define _Mdouble_ _Float128
700# define __MATH_DECLARING_DOUBLE 0
701# define __MATH_DECLARING_LDOUBLE 0
702# define __MATH_DECLARING_FLOATN 1
703# define _MSUF_ f128
704# include <bits/math-finite.h>
705# undef _Mdouble_
706# undef __MATH_DECLARING_DOUBLE
707# undef __MATH_DECLARING_LDOUBLE
708# undef __MATH_DECLARING_FLOATN
709# undef _MSUF_
710# endif
711#endif /* __FINITE_MATH_ONLY__ > 0. */
712
713#ifdef __USE_ISOC99
714/* If we've still got undefined comparison macros, provide defaults. */
715
716/* Return nonzero value if X is greater than Y. */
717# ifndef isgreater
718# define isgreater(x, y) \
719 (__extension__ \
720 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
721 !isunordered (__x, __y) && __x > __y; }))
722# endif
723
724/* Return nonzero value if X is greater than or equal to Y. */
725# ifndef isgreaterequal
726# define isgreaterequal(x, y) \
727 (__extension__ \
728 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
729 !isunordered (__x, __y) && __x >= __y; }))
730# endif
731
732/* Return nonzero value if X is less than Y. */
733# ifndef isless
734# define isless(x, y) \
735 (__extension__ \
736 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
737 !isunordered (__x, __y) && __x < __y; }))
738# endif
739
740/* Return nonzero value if X is less than or equal to Y. */
741# ifndef islessequal
742# define islessequal(x, y) \
743 (__extension__ \
744 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
745 !isunordered (__x, __y) && __x <= __y; }))
746# endif
747
748/* Return nonzero value if either X is less than Y or Y is less than X. */
749# ifndef islessgreater
750# define islessgreater(x, y) \
751 (__extension__ \
752 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
753 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
754# endif
755
756/* Return nonzero value if arguments are unordered. */
757# ifndef isunordered
758# define isunordered(u, v) \
759 (__extension__ \
760 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
761 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
762# endif
763
764#endif
765
766#if __GLIBC_USE (IEC_60559_BFP_EXT)
767/* An expression whose type has the widest of the evaluation formats
768 of X and Y (which are of floating-point types). */
769# if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
770# define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
771# elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
772# define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
773# else
774# define __MATH_EVAL_FMT2(x, y) ((x) + (y))
775# endif
776
777/* Return X == Y but raising "invalid" and setting errno if X or Y is
778 a NaN. */
779# define iseqsig(x, y) \
780 __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
781#endif
782
783__END_DECLS
784
785
786#endif /* math.h */
787