1/* Declarations for math functions.
2 Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006, 2009, 2011, 2012
3 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <http://www.gnu.org/licenses/>. */
19
20/*
21 * ISO C99 Standard: 7.12 Mathematics <math.h>
22 */
23
24#ifndef _MATH_H
25#define _MATH_H 1
26
27#include <features.h>
28
29__BEGIN_DECLS
30
31/* Get machine-dependent HUGE_VAL value (returned on overflow).
32 On all IEEE754 machines, this is +Infinity. */
33#include <bits/huge_val.h>
34#ifdef __USE_ISOC99
35# include <bits/huge_valf.h>
36# include <bits/huge_vall.h>
37
38/* Get machine-dependent INFINITY value. */
39# include <bits/inf.h>
40
41/* Get machine-dependent NAN value (returned for some domain errors). */
42# include <bits/nan.h>
43#endif /* __USE_ISOC99 */
44
45/* Get general and ISO C99 specific information. */
46#include <bits/mathdef.h>
47
48/* The file <bits/mathcalls.h> contains the prototypes for all the
49 actual math functions. These macros are used for those prototypes,
50 so we can easily declare each function as both `name' and `__name',
51 and can declare the float versions `namef' and `__namef'. */
52
53#define __MATHCALL(function,suffix, args) \
54 __MATHDECL (_Mdouble_,function,suffix, args)
55#define __MATHDECL(type, function,suffix, args) \
56 __MATHDECL_1(type, function,suffix, args); \
57 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
58#define __MATHCALLX(function,suffix, args, attrib) \
59 __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
60#define __MATHDECLX(type, function,suffix, args, attrib) \
61 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
62 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
63#define __MATHDECL_1(type, function,suffix, args) \
64 extern type __MATH_PRECNAME(function,suffix) args __THROW
65
66#define _Mdouble_ double
67#define __MATH_PRECNAME(name,r) __CONCAT(name,r)
68#define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
69#define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
70#include <bits/mathcalls.h>
71#undef _Mdouble_
72#undef _Mdouble_BEGIN_NAMESPACE
73#undef _Mdouble_END_NAMESPACE
74#undef __MATH_PRECNAME
75
76#if defined __USE_MISC || defined __USE_ISOC99
77
78
79/* Include the file of declarations again, this time using `float'
80 instead of `double' and appending f to each function name. */
81
82# ifndef _Mfloat_
83# define _Mfloat_ float
84# endif
85# define _Mdouble_ _Mfloat_
86# define __MATH_PRECNAME(name,r) name##f##r
87# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
88# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
89# include <bits/mathcalls.h>
90# undef _Mdouble_
91# undef _Mdouble_BEGIN_NAMESPACE
92# undef _Mdouble_END_NAMESPACE
93# undef __MATH_PRECNAME
94
95# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
96 || defined __LDBL_COMPAT
97# ifdef __LDBL_COMPAT
98
99# ifdef __USE_ISOC99
100extern float __nldbl_nexttowardf (float __x, long double __y)
101 __THROW __attribute__ ((__const__));
102# ifdef __REDIRECT_NTH
103extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
104 __nldbl_nexttowardf)
105 __attribute__ ((__const__));
106extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
107 nextafter) __attribute__ ((__const__));
108extern long double __REDIRECT_NTH (nexttowardl,
109 (long double __x, long double __y),
110 nextafter) __attribute__ ((__const__));
111# endif
112# endif
113
114# undef __MATHDECL_1
115# define __MATHDECL_2(type, function,suffix, args, alias) \
116 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
117 args, alias)
118# define __MATHDECL_1(type, function,suffix, args) \
119 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
120# endif
121
122/* Include the file of declarations again, this time using `long double'
123 instead of `double' and appending l to each function name. */
124
125# ifndef _Mlong_double_
126# define _Mlong_double_ long double
127# endif
128# define _Mdouble_ _Mlong_double_
129# define __MATH_PRECNAME(name,r) name##l##r
130# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
131# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
132# define __MATH_DECLARE_LDOUBLE 1
133# include <bits/mathcalls.h>
134# undef _Mdouble_
135# undef _Mdouble_BEGIN_NAMESPACE
136# undef _Mdouble_END_NAMESPACE
137# undef __MATH_PRECNAME
138
139# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
140
141#endif /* Use misc or ISO C99. */
142#undef __MATHDECL_1
143#undef __MATHDECL
144#undef __MATHCALL
145
146
147#if defined __USE_MISC || defined __USE_XOPEN
148/* This variable is used by `gamma' and `lgamma'. */
149extern int signgam;
150#endif
151
152
153/* ISO C99 defines some generic macros which work on any data type. */
154#ifdef __USE_ISOC99
155
156/* Get the architecture specific values describing the floating-point
157 evaluation. The following symbols will get defined:
158
159 float_t floating-point type at least as wide as `float' used
160 to evaluate `float' expressions
161 double_t floating-point type at least as wide as `double' used
162 to evaluate `double' expressions
163
164 FLT_EVAL_METHOD
165 Defined to
166 0 if `float_t' is `float' and `double_t' is `double'
167 1 if `float_t' and `double_t' are `double'
168 2 if `float_t' and `double_t' are `long double'
169 else `float_t' and `double_t' are unspecified
170
171 INFINITY representation of the infinity value of type `float'
172
173 FP_FAST_FMA
174 FP_FAST_FMAF
175 FP_FAST_FMAL
176 If defined it indicates that the `fma' function
177 generally executes about as fast as a multiply and an add.
178 This macro is defined only iff the `fma' function is
179 implemented directly with a hardware multiply-add instructions.
180
181 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
182 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
183
184 DECIMAL_DIG Number of decimal digits supported by conversion between
185 decimal and all internal floating-point formats.
186
187*/
188
189/* All floating-point numbers can be put in one of these categories. */
190enum
191 {
192 FP_NAN,
193# define FP_NAN FP_NAN
194 FP_INFINITE,
195# define FP_INFINITE FP_INFINITE
196 FP_ZERO,
197# define FP_ZERO FP_ZERO
198 FP_SUBNORMAL,
199# define FP_SUBNORMAL FP_SUBNORMAL
200 FP_NORMAL
201# define FP_NORMAL FP_NORMAL
202 };
203
204/* Return number of classification appropriate for X. */
205# ifdef __NO_LONG_DOUBLE_MATH
206# define fpclassify(x) \
207 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
208# else
209# define fpclassify(x) \
210 (sizeof (x) == sizeof (float) \
211 ? __fpclassifyf (x) \
212 : sizeof (x) == sizeof (double) \
213 ? __fpclassify (x) : __fpclassifyl (x))
214# endif
215
216/* Return nonzero value if sign of X is negative. */
217# ifdef __NO_LONG_DOUBLE_MATH
218# define signbit(x) \
219 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
220# else
221# define signbit(x) \
222 (sizeof (x) == sizeof (float) \
223 ? __signbitf (x) \
224 : sizeof (x) == sizeof (double) \
225 ? __signbit (x) : __signbitl (x))
226# endif
227
228/* Return nonzero value if X is not +-Inf or NaN. */
229# ifdef __NO_LONG_DOUBLE_MATH
230# define isfinite(x) \
231 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
232# else
233# define isfinite(x) \
234 (sizeof (x) == sizeof (float) \
235 ? __finitef (x) \
236 : sizeof (x) == sizeof (double) \
237 ? __finite (x) : __finitel (x))
238# endif
239
240/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
241# define isnormal(x) (fpclassify (x) == FP_NORMAL)
242
243/* Return nonzero value if X is a NaN. We could use `fpclassify' but
244 we already have this functions `__isnan' and it is faster. */
245# ifdef __NO_LONG_DOUBLE_MATH
246# define isnan(x) \
247 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
248# else
249# define isnan(x) \
250 (sizeof (x) == sizeof (float) \
251 ? __isnanf (x) \
252 : sizeof (x) == sizeof (double) \
253 ? __isnan (x) : __isnanl (x))
254# endif
255
256/* Return nonzero value if X is positive or negative infinity. */
257# ifdef __NO_LONG_DOUBLE_MATH
258# define isinf(x) \
259 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
260# else
261# define isinf(x) \
262 (sizeof (x) == sizeof (float) \
263 ? __isinff (x) \
264 : sizeof (x) == sizeof (double) \
265 ? __isinf (x) : __isinfl (x))
266# endif
267
268/* Bitmasks for the math_errhandling macro. */
269# define MATH_ERRNO 1 /* errno set by math functions. */
270# define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
271
272/* By default all functions support both errno and exception handling.
273 In gcc's fast math mode and if inline functions are defined this
274 might not be true. */
275# ifndef __FAST_MATH__
276# define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
277# endif
278
279#endif /* Use ISO C99. */
280
281#ifdef __USE_MISC
282/* Support for various different standard error handling behaviors. */
283typedef enum
284{
285 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
286 _SVID_, /* According to System V, release 4. */
287 _XOPEN_, /* Nowadays also Unix98. */
288 _POSIX_,
289 _ISOC_ /* Actually this is ISO C99. */
290} _LIB_VERSION_TYPE;
291
292/* This variable can be changed at run-time to any of the values above to
293 affect floating point error handling behavior (it may also be necessary
294 to change the hardware FPU exception settings). */
295extern _LIB_VERSION_TYPE _LIB_VERSION;
296#endif
297
298
299#ifdef __USE_SVID
300/* In SVID error handling, `matherr' is called with this description
301 of the exceptional condition.
302
303 We have a problem when using C++ since `exception' is a reserved
304 name in C++. */
305# ifdef __cplusplus
306struct __exception
307# else
308struct exception
309# endif
310 {
311 int type;
312 char *name;
313 double arg1;
314 double arg2;
315 double retval;
316 };
317
318# ifdef __cplusplus
319extern int matherr (struct __exception *__exc) throw ();
320# else
321extern int matherr (struct exception *__exc);
322# endif
323
324# define X_TLOSS 1.41484755040568800000e+16
325
326/* Types of exceptions in the `type' field. */
327# define DOMAIN 1
328# define SING 2
329# define OVERFLOW 3
330# define UNDERFLOW 4
331# define TLOSS 5
332# define PLOSS 6
333
334/* SVID mode specifies returning this large value instead of infinity. */
335# define HUGE 3.40282347e+38F
336
337#else /* !SVID */
338
339# ifdef __USE_XOPEN
340/* X/Open wants another strange constant. */
341# define MAXFLOAT 3.40282347e+38F
342# endif
343
344#endif /* SVID */
345
346
347/* Some useful constants. */
348#if defined __USE_BSD || defined __USE_XOPEN
349# define M_E 2.7182818284590452354 /* e */
350# define M_LOG2E 1.4426950408889634074 /* log_2 e */
351# define M_LOG10E 0.43429448190325182765 /* log_10 e */
352# define M_LN2 0.69314718055994530942 /* log_e 2 */
353# define M_LN10 2.30258509299404568402 /* log_e 10 */
354# define M_PI 3.14159265358979323846 /* pi */
355# define M_PI_2 1.57079632679489661923 /* pi/2 */
356# define M_PI_4 0.78539816339744830962 /* pi/4 */
357# define M_1_PI 0.31830988618379067154 /* 1/pi */
358# define M_2_PI 0.63661977236758134308 /* 2/pi */
359# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
360# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
361# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
362#endif
363
364/* The above constants are not adequate for computation using `long double's.
365 Therefore we provide as an extension constants with similar names as a
366 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
367#ifdef __USE_GNU
368# define M_El 2.718281828459045235360287471352662498L /* e */
369# define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
370# define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
371# define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
372# define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
373# define M_PIl 3.141592653589793238462643383279502884L /* pi */
374# define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
375# define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
376# define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
377# define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
378# define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
379# define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
380# define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
381#endif
382
383
384/* When compiling in strict ISO C compatible mode we must not use the
385 inline functions since they, among other things, do not set the
386 `errno' variable correctly. */
387#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
388# define __NO_MATH_INLINES 1
389#endif
390
391#if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
392/* ISO C99 defines some macros to compare number while taking care for
393 unordered numbers. Many FPUs provide special instructions to support
394 these operations. Generic support in GCC for these as builtins went
395 in before 3.0.0, but not all cpus added their patterns. We define
396 versions that use the builtins here, and <bits/mathinline.h> will
397 undef/redefine as appropriate for the specific GCC version in use. */
398# define isgreater(x, y) __builtin_isgreater(x, y)
399# define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
400# define isless(x, y) __builtin_isless(x, y)
401# define islessequal(x, y) __builtin_islessequal(x, y)
402# define islessgreater(x, y) __builtin_islessgreater(x, y)
403# define isunordered(u, v) __builtin_isunordered(u, v)
404#endif
405
406/* Get machine-dependent inline versions (if there are any). */
407#ifdef __USE_EXTERN_INLINES
408# include <bits/mathinline.h>
409#endif
410
411/* Define special entry points to use when the compiler got told to
412 only expect finite results. */
413#if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
414# include <bits/math-finite.h>
415#endif
416
417#ifdef __USE_ISOC99
418/* If we've still got undefined comparison macros, provide defaults. */
419
420/* Return nonzero value if X is greater than Y. */
421# ifndef isgreater
422# define isgreater(x, y) \
423 (__extension__ \
424 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
425 !isunordered (__x, __y) && __x > __y; }))
426# endif
427
428/* Return nonzero value if X is greater than or equal to Y. */
429# ifndef isgreaterequal
430# define isgreaterequal(x, y) \
431 (__extension__ \
432 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
433 !isunordered (__x, __y) && __x >= __y; }))
434# endif
435
436/* Return nonzero value if X is less than Y. */
437# ifndef isless
438# define isless(x, y) \
439 (__extension__ \
440 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
441 !isunordered (__x, __y) && __x < __y; }))
442# endif
443
444/* Return nonzero value if X is less than or equal to Y. */
445# ifndef islessequal
446# define islessequal(x, y) \
447 (__extension__ \
448 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
449 !isunordered (__x, __y) && __x <= __y; }))
450# endif
451
452/* Return nonzero value if either X is less than Y or Y is less than X. */
453# ifndef islessgreater
454# define islessgreater(x, y) \
455 (__extension__ \
456 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
457 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
458# endif
459
460/* Return nonzero value if arguments are unordered. */
461# ifndef isunordered
462# define isunordered(u, v) \
463 (__extension__ \
464 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
465 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
466# endif
467
468#endif
469
470__END_DECLS
471
472
473#endif /* math.h */
474