1/* Declarations for math functions.
2 Copyright (C) 1991-2016 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#include <features.h>
27
28__BEGIN_DECLS
29
30/* Get machine-dependent vector math functions declarations. */
31#include <bits/math-vector.h>
32
33/* Get machine-dependent HUGE_VAL value (returned on overflow).
34 On all IEEE754 machines, this is +Infinity. */
35#include <bits/huge_val.h>
36#ifdef __USE_ISOC99
37# include <bits/huge_valf.h>
38# include <bits/huge_vall.h>
39
40/* Get machine-dependent INFINITY value. */
41# include <bits/inf.h>
42
43/* Get machine-dependent NAN value (returned for some domain errors). */
44# include <bits/nan.h>
45#endif /* __USE_ISOC99 */
46
47/* Get general and ISO C99 specific information. */
48#include <bits/mathdef.h>
49
50/* The file <bits/mathcalls.h> contains the prototypes for all the
51 actual math functions. These macros are used for those prototypes,
52 so we can easily declare each function as both `name' and `__name',
53 and can declare the float versions `namef' and `__namef'. */
54
55#define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
56
57#define __MATHCALL_VEC(function, suffix, args) \
58 __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
59 __MATHCALL (function, suffix, args)
60
61#define __MATHDECL_VEC(type, function,suffix, args) \
62 __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
63 __MATHDECL(type, function,suffix, args)
64
65#define __MATHCALL(function,suffix, args) \
66 __MATHDECL (_Mdouble_,function,suffix, args)
67#define __MATHDECL(type, function,suffix, args) \
68 __MATHDECL_1(type, function,suffix, args); \
69 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
70#define __MATHCALLX(function,suffix, args, attrib) \
71 __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
72#define __MATHDECLX(type, function,suffix, args, attrib) \
73 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
74 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
75#define __MATHDECL_1(type, function,suffix, args) \
76 extern type __MATH_PRECNAME(function,suffix) args __THROW
77
78#define _Mdouble_ double
79#define __MATH_PRECNAME(name,r) __CONCAT(name,r)
80#define __MATH_DECLARING_DOUBLE 1
81#define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
82#define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
83#include <bits/mathcalls.h>
84#undef _Mdouble_
85#undef _Mdouble_BEGIN_NAMESPACE
86#undef _Mdouble_END_NAMESPACE
87#undef __MATH_PRECNAME
88#undef __MATH_DECLARING_DOUBLE
89
90#ifdef __USE_ISOC99
91
92
93/* Include the file of declarations again, this time using `float'
94 instead of `double' and appending f to each function name. */
95
96# ifndef _Mfloat_
97# define _Mfloat_ float
98# endif
99# define _Mdouble_ _Mfloat_
100# define __MATH_PRECNAME(name,r) name##f##r
101# define __MATH_DECLARING_DOUBLE 0
102# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
103# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
104# include <bits/mathcalls.h>
105# undef _Mdouble_
106# undef _Mdouble_BEGIN_NAMESPACE
107# undef _Mdouble_END_NAMESPACE
108# undef __MATH_PRECNAME
109# undef __MATH_DECLARING_DOUBLE
110
111# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
112 || defined __LDBL_COMPAT \
113 || defined _LIBC_TEST
114# ifdef __LDBL_COMPAT
115
116# ifdef __USE_ISOC99
117extern float __nldbl_nexttowardf (float __x, long double __y)
118 __THROW __attribute__ ((__const__));
119# ifdef __REDIRECT_NTH
120extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
121 __nldbl_nexttowardf)
122 __attribute__ ((__const__));
123extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
124 nextafter) __attribute__ ((__const__));
125extern long double __REDIRECT_NTH (nexttowardl,
126 (long double __x, long double __y),
127 nextafter) __attribute__ ((__const__));
128# endif
129# endif
130
131# undef __MATHDECL_1
132# define __MATHDECL_2(type, function,suffix, args, alias) \
133 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
134 args, alias)
135# define __MATHDECL_1(type, function,suffix, args) \
136 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
137# endif
138
139/* Include the file of declarations again, this time using `long double'
140 instead of `double' and appending l to each function name. */
141
142# ifndef _Mlong_double_
143# define _Mlong_double_ long double
144# endif
145# define _Mdouble_ _Mlong_double_
146# define __MATH_PRECNAME(name,r) name##l##r
147# define __MATH_DECLARING_DOUBLE 0
148# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
149# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
150# define __MATH_DECLARE_LDOUBLE 1
151# include <bits/mathcalls.h>
152# undef _Mdouble_
153# undef _Mdouble_BEGIN_NAMESPACE
154# undef _Mdouble_END_NAMESPACE
155# undef __MATH_PRECNAME
156# undef __MATH_DECLARING_DOUBLE
157
158# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
159
160#endif /* Use ISO C99. */
161#undef __MATHDECL_1
162#undef __MATHDECL
163#undef __MATHCALL
164
165
166#if defined __USE_MISC || defined __USE_XOPEN
167/* This variable is used by `gamma' and `lgamma'. */
168extern int signgam;
169#endif
170
171
172/* ISO C99 defines some generic macros which work on any data type. */
173#ifdef __USE_ISOC99
174
175/* Get the architecture specific values describing the floating-point
176 evaluation. The following symbols will get defined:
177
178 float_t floating-point type at least as wide as `float' used
179 to evaluate `float' expressions
180 double_t floating-point type at least as wide as `double' used
181 to evaluate `double' expressions
182
183 FLT_EVAL_METHOD
184 Defined to
185 0 if `float_t' is `float' and `double_t' is `double'
186 1 if `float_t' and `double_t' are `double'
187 2 if `float_t' and `double_t' are `long double'
188 else `float_t' and `double_t' are unspecified
189
190 INFINITY representation of the infinity value of type `float'
191
192 FP_FAST_FMA
193 FP_FAST_FMAF
194 FP_FAST_FMAL
195 If defined it indicates that the `fma' function
196 generally executes about as fast as a multiply and an add.
197 This macro is defined only iff the `fma' function is
198 implemented directly with a hardware multiply-add instructions.
199
200 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
201 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
202
203 DECIMAL_DIG Number of decimal digits supported by conversion between
204 decimal and all internal floating-point formats.
205
206*/
207
208/* All floating-point numbers can be put in one of these categories. */
209enum
210 {
211 FP_NAN =
212# define FP_NAN 0
213 FP_NAN,
214 FP_INFINITE =
215# define FP_INFINITE 1
216 FP_INFINITE,
217 FP_ZERO =
218# define FP_ZERO 2
219 FP_ZERO,
220 FP_SUBNORMAL =
221# define FP_SUBNORMAL 3
222 FP_SUBNORMAL,
223 FP_NORMAL =
224# define FP_NORMAL 4
225 FP_NORMAL
226 };
227
228/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
229 so disable builtins if this is enabled. When fixed in a newer GCC,
230 the __SUPPORT_SNAN__ check may be skipped for those versions. */
231
232/* Return number of classification appropriate for X. */
233# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ \
234 && !defined __OPTIMIZE_SIZE__
235# define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \
236 FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
237# elif defined __NO_LONG_DOUBLE_MATH
238# define fpclassify(x) \
239 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
240# else
241# define fpclassify(x) \
242 (sizeof (x) == sizeof (float) \
243 ? __fpclassifyf (x) \
244 : sizeof (x) == sizeof (double) \
245 ? __fpclassify (x) : __fpclassifyl (x))
246# endif
247
248/* Return nonzero value if sign of X is negative. */
249# if __GNUC_PREREQ (4,0)
250# define signbit(x) \
251 (sizeof (x) == sizeof (float) \
252 ? __builtin_signbitf (x) \
253 : sizeof (x) == sizeof (double) \
254 ? __builtin_signbit (x) : __builtin_signbitl (x))
255# else
256# ifdef __NO_LONG_DOUBLE_MATH
257# define signbit(x) \
258 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
259# else
260# define signbit(x) \
261 (sizeof (x) == sizeof (float) \
262 ? __signbitf (x) \
263 : sizeof (x) == sizeof (double) \
264 ? __signbit (x) : __signbitl (x))
265# endif
266# endif
267
268/* Return nonzero value if X is not +-Inf or NaN. */
269# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
270# define isfinite(x) __builtin_isfinite (x)
271# elif defined __NO_LONG_DOUBLE_MATH
272# define isfinite(x) \
273 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
274# else
275# define isfinite(x) \
276 (sizeof (x) == sizeof (float) \
277 ? __finitef (x) \
278 : sizeof (x) == sizeof (double) \
279 ? __finite (x) : __finitel (x))
280# endif
281
282/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
283# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
284# define isnormal(x) __builtin_isnormal (x)
285# else
286# define isnormal(x) (fpclassify (x) == FP_NORMAL)
287# endif
288
289/* Return nonzero value if X is a NaN. We could use `fpclassify' but
290 we already have this functions `__isnan' and it is faster. */
291# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
292# define isnan(x) __builtin_isnan (x)
293# elif defined __NO_LONG_DOUBLE_MATH
294# define isnan(x) \
295 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
296# else
297# define isnan(x) \
298 (sizeof (x) == sizeof (float) \
299 ? __isnanf (x) \
300 : sizeof (x) == sizeof (double) \
301 ? __isnan (x) : __isnanl (x))
302# endif
303
304/* Return nonzero value if X is positive or negative infinity. */
305# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
306# define isinf(x) __builtin_isinf_sign (x)
307# elif defined __NO_LONG_DOUBLE_MATH
308# define isinf(x) \
309 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
310# else
311# define isinf(x) \
312 (sizeof (x) == sizeof (float) \
313 ? __isinff (x) \
314 : sizeof (x) == sizeof (double) \
315 ? __isinf (x) : __isinfl (x))
316# endif
317
318/* Bitmasks for the math_errhandling macro. */
319# define MATH_ERRNO 1 /* errno set by math functions. */
320# define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
321
322/* By default all functions support both errno and exception handling.
323 In gcc's fast math mode and if inline functions are defined this
324 might not be true. */
325# ifndef __FAST_MATH__
326# define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
327# endif
328
329#endif /* Use ISO C99. */
330
331#ifdef __USE_GNU
332/* Return nonzero value if X is a signaling NaN. */
333# ifdef __NO_LONG_DOUBLE_MATH
334# define issignaling(x) \
335 (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
336# else
337# define issignaling(x) \
338 (sizeof (x) == sizeof (float) \
339 ? __issignalingf (x) \
340 : sizeof (x) == sizeof (double) \
341 ? __issignaling (x) : __issignalingl (x))
342# endif
343#endif /* Use GNU. */
344
345#ifdef __USE_MISC
346/* Support for various different standard error handling behaviors. */
347typedef enum
348{
349 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
350 _SVID_, /* According to System V, release 4. */
351 _XOPEN_, /* Nowadays also Unix98. */
352 _POSIX_,
353 _ISOC_ /* Actually this is ISO C99. */
354} _LIB_VERSION_TYPE;
355
356/* This variable can be changed at run-time to any of the values above to
357 affect floating point error handling behavior (it may also be necessary
358 to change the hardware FPU exception settings). */
359extern _LIB_VERSION_TYPE _LIB_VERSION;
360#endif
361
362
363#ifdef __USE_MISC
364/* In SVID error handling, `matherr' is called with this description
365 of the exceptional condition.
366
367 We have a problem when using C++ since `exception' is a reserved
368 name in C++. */
369# ifdef __cplusplus
370struct __exception
371# else
372struct exception
373# endif
374 {
375 int type;
376 char *name;
377 double arg1;
378 double arg2;
379 double retval;
380 };
381
382# ifdef __cplusplus
383extern int matherr (struct __exception *__exc) throw ();
384# else
385extern int matherr (struct exception *__exc);
386# endif
387
388# define X_TLOSS 1.41484755040568800000e+16
389
390/* Types of exceptions in the `type' field. */
391# define DOMAIN 1
392# define SING 2
393# define OVERFLOW 3
394# define UNDERFLOW 4
395# define TLOSS 5
396# define PLOSS 6
397
398/* SVID mode specifies returning this large value instead of infinity. */
399# define HUGE 3.40282347e+38F
400
401#else /* !Misc. */
402
403# ifdef __USE_XOPEN
404/* X/Open wants another strange constant. */
405# define MAXFLOAT 3.40282347e+38F
406# endif
407
408#endif /* Misc. */
409
410
411/* Some useful constants. */
412#if defined __USE_MISC || defined __USE_XOPEN
413# define M_E 2.7182818284590452354 /* e */
414# define M_LOG2E 1.4426950408889634074 /* log_2 e */
415# define M_LOG10E 0.43429448190325182765 /* log_10 e */
416# define M_LN2 0.69314718055994530942 /* log_e 2 */
417# define M_LN10 2.30258509299404568402 /* log_e 10 */
418# define M_PI 3.14159265358979323846 /* pi */
419# define M_PI_2 1.57079632679489661923 /* pi/2 */
420# define M_PI_4 0.78539816339744830962 /* pi/4 */
421# define M_1_PI 0.31830988618379067154 /* 1/pi */
422# define M_2_PI 0.63661977236758134308 /* 2/pi */
423# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
424# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
425# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
426#endif
427
428/* The above constants are not adequate for computation using `long double's.
429 Therefore we provide as an extension constants with similar names as a
430 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
431#ifdef __USE_GNU
432# define M_El 2.718281828459045235360287471352662498L /* e */
433# define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
434# define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
435# define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
436# define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
437# define M_PIl 3.141592653589793238462643383279502884L /* pi */
438# define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
439# define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
440# define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
441# define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
442# define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
443# define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
444# define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
445#endif
446
447
448/* When compiling in strict ISO C compatible mode we must not use the
449 inline functions since they, among other things, do not set the
450 `errno' variable correctly. */
451#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
452# define __NO_MATH_INLINES 1
453#endif
454
455#if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
456/* ISO C99 defines some macros to compare number while taking care for
457 unordered numbers. Many FPUs provide special instructions to support
458 these operations. Generic support in GCC for these as builtins went
459 in before 3.0.0, but not all cpus added their patterns. We define
460 versions that use the builtins here, and <bits/mathinline.h> will
461 undef/redefine as appropriate for the specific GCC version in use. */
462# define isgreater(x, y) __builtin_isgreater(x, y)
463# define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
464# define isless(x, y) __builtin_isless(x, y)
465# define islessequal(x, y) __builtin_islessequal(x, y)
466# define islessgreater(x, y) __builtin_islessgreater(x, y)
467# define isunordered(u, v) __builtin_isunordered(u, v)
468#endif
469
470/* Get machine-dependent inline versions (if there are any). */
471#ifdef __USE_EXTERN_INLINES
472# include <bits/mathinline.h>
473#endif
474
475/* Define special entry points to use when the compiler got told to
476 only expect finite results. */
477#if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
478# include <bits/math-finite.h>
479#endif
480
481#ifdef __USE_ISOC99
482/* If we've still got undefined comparison macros, provide defaults. */
483
484/* Return nonzero value if X is greater than Y. */
485# ifndef isgreater
486# define isgreater(x, y) \
487 (__extension__ \
488 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
489 !isunordered (__x, __y) && __x > __y; }))
490# endif
491
492/* Return nonzero value if X is greater than or equal to Y. */
493# ifndef isgreaterequal
494# define isgreaterequal(x, y) \
495 (__extension__ \
496 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
497 !isunordered (__x, __y) && __x >= __y; }))
498# endif
499
500/* Return nonzero value if X is less than Y. */
501# ifndef isless
502# define isless(x, y) \
503 (__extension__ \
504 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
505 !isunordered (__x, __y) && __x < __y; }))
506# endif
507
508/* Return nonzero value if X is less than or equal to Y. */
509# ifndef islessequal
510# define islessequal(x, y) \
511 (__extension__ \
512 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
513 !isunordered (__x, __y) && __x <= __y; }))
514# endif
515
516/* Return nonzero value if either X is less than Y or Y is less than X. */
517# ifndef islessgreater
518# define islessgreater(x, y) \
519 (__extension__ \
520 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
521 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
522# endif
523
524/* Return nonzero value if arguments are unordered. */
525# ifndef isunordered
526# define isunordered(u, v) \
527 (__extension__ \
528 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
529 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
530# endif
531
532#endif
533
534__END_DECLS
535
536
537#endif /* math.h */
538