1 /* Declarations for math functions.
2 Copyright (C) 1991-2015 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 _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
81 #define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
82 #include <bits/mathcalls.h>
83 #undef _Mdouble_
84 #undef _Mdouble_BEGIN_NAMESPACE
85 #undef _Mdouble_END_NAMESPACE
86 #undef __MATH_PRECNAME
87
88 #ifdef __USE_ISOC99
89
90
91 /* Include the file of declarations again, this time using `float'
92 instead of `double' and appending f to each function name. */
93
94 # ifndef _Mfloat_
95 # define _Mfloat_ float
96 # endif
97 # define _Mdouble_ _Mfloat_
98 # define __MATH_PRECNAME(name,r) name##f##r
99 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
100 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
101 # include <bits/mathcalls.h>
102 # undef _Mdouble_
103 # undef _Mdouble_BEGIN_NAMESPACE
104 # undef _Mdouble_END_NAMESPACE
105 # undef __MATH_PRECNAME
106
107 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
108 || defined __LDBL_COMPAT \
109 || defined _LIBC_TEST
110 # ifdef __LDBL_COMPAT
111
112 # ifdef __USE_ISOC99
113 extern float __nldbl_nexttowardf (float __x, long double __y)
114 __THROW __attribute__ ((__const__));
115 # ifdef __REDIRECT_NTH
116 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
117 __nldbl_nexttowardf)
118 __attribute__ ((__const__));
119 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
120 nextafter) __attribute__ ((__const__));
121 extern long double __REDIRECT_NTH (nexttowardl,
122 (long double __x, long double __y),
123 nextafter) __attribute__ ((__const__));
124 # endif
125 # endif
126
127 # undef __MATHDECL_1
128 # define __MATHDECL_2(type, function,suffix, args, alias) \
129 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
130 args, alias)
131 # define __MATHDECL_1(type, function,suffix, args) \
132 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
133 # endif
134
135 /* Include the file of declarations again, this time using `long double'
136 instead of `double' and appending l to each function name. */
137
138 # ifndef _Mlong_double_
139 # define _Mlong_double_ long double
140 # endif
141 # define _Mdouble_ _Mlong_double_
142 # define __MATH_PRECNAME(name,r) name##l##r
143 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
144 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
145 # define __MATH_DECLARE_LDOUBLE 1
146 # include <bits/mathcalls.h>
147 # undef _Mdouble_
148 # undef _Mdouble_BEGIN_NAMESPACE
149 # undef _Mdouble_END_NAMESPACE
150 # undef __MATH_PRECNAME
151
152 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
153
154 #endif /* Use ISO C99. */
155 #undef __MATHDECL_1
156 #undef __MATHDECL
157 #undef __MATHCALL
158
159
160 #if defined __USE_MISC || defined __USE_XOPEN
161 /* This variable is used by `gamma' and `lgamma'. */
162 extern int signgam;
163 #endif
164
165
166 /* ISO C99 defines some generic macros which work on any data type. */
167 #ifdef __USE_ISOC99
168
169 /* Get the architecture specific values describing the floating-point
170 evaluation. The following symbols will get defined:
171
172 float_t floating-point type at least as wide as `float' used
173 to evaluate `float' expressions
174 double_t floating-point type at least as wide as `double' used
175 to evaluate `double' expressions
176
177 FLT_EVAL_METHOD
178 Defined to
179 0 if `float_t' is `float' and `double_t' is `double'
180 1 if `float_t' and `double_t' are `double'
181 2 if `float_t' and `double_t' are `long double'
182 else `float_t' and `double_t' are unspecified
183
184 INFINITY representation of the infinity value of type `float'
185
186 FP_FAST_FMA
187 FP_FAST_FMAF
188 FP_FAST_FMAL
189 If defined it indicates that the `fma' function
190 generally executes about as fast as a multiply and an add.
191 This macro is defined only iff the `fma' function is
192 implemented directly with a hardware multiply-add instructions.
193
194 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
195 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
196
197 DECIMAL_DIG Number of decimal digits supported by conversion between
198 decimal and all internal floating-point formats.
199
200 */
201
202 /* All floating-point numbers can be put in one of these categories. */
203 enum
204 {
205 FP_NAN =
206 # define FP_NAN 0
207 FP_NAN,
208 FP_INFINITE =
209 # define FP_INFINITE 1
210 FP_INFINITE,
211 FP_ZERO =
212 # define FP_ZERO 2
213 FP_ZERO,
214 FP_SUBNORMAL =
215 # define FP_SUBNORMAL 3
216 FP_SUBNORMAL,
217 FP_NORMAL =
218 # define FP_NORMAL 4
219 FP_NORMAL
220 };
221
222 /* Return number of classification appropriate for X. */
223 # ifdef __NO_LONG_DOUBLE_MATH
224 # define fpclassify(x) \
225 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
226 # else
227 # define fpclassify(x) \
228 (sizeof (x) == sizeof (float) \
229 ? __fpclassifyf (x) \
230 : sizeof (x) == sizeof (double) \
231 ? __fpclassify (x) : __fpclassifyl (x))
232 # endif
233
234 /* Return nonzero value if sign of X is negative. */
235 # ifdef __NO_LONG_DOUBLE_MATH
236 # define signbit(x) \
237 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
238 # else
239 # define signbit(x) \
240 (sizeof (x) == sizeof (float) \
241 ? __signbitf (x) \
242 : sizeof (x) == sizeof (double) \
243 ? __signbit (x) : __signbitl (x))
244 # endif
245
246 /* Return nonzero value if X is not +-Inf or NaN. */
247 # ifdef __NO_LONG_DOUBLE_MATH
248 # define isfinite(x) \
249 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
250 # else
251 # define isfinite(x) \
252 (sizeof (x) == sizeof (float) \
253 ? __finitef (x) \
254 : sizeof (x) == sizeof (double) \
255 ? __finite (x) : __finitel (x))
256 # endif
257
258 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
259 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
260
261 /* Return nonzero value if X is a NaN. We could use `fpclassify' but
262 we already have this functions `__isnan' and it is faster. */
263 # ifdef __NO_LONG_DOUBLE_MATH
264 # define isnan(x) \
265 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
266 # else
267 # define isnan(x) \
268 (sizeof (x) == sizeof (float) \
269 ? __isnanf (x) \
270 : sizeof (x) == sizeof (double) \
271 ? __isnan (x) : __isnanl (x))
272 # endif
273
274 /* Return nonzero value if X is positive or negative infinity. */
275 # ifdef __NO_LONG_DOUBLE_MATH
276 # define isinf(x) \
277 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
278 # else
279 # define isinf(x) \
280 (sizeof (x) == sizeof (float) \
281 ? __isinff (x) \
282 : sizeof (x) == sizeof (double) \
283 ? __isinf (x) : __isinfl (x))
284 # endif
285
286 /* Bitmasks for the math_errhandling macro. */
287 # define MATH_ERRNO 1 /* errno set by math functions. */
288 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
289
290 /* By default all functions support both errno and exception handling.
291 In gcc's fast math mode and if inline functions are defined this
292 might not be true. */
293 # ifndef __FAST_MATH__
294 # define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
295 # endif
296
297 #endif /* Use ISO C99. */
298
299 #ifdef __USE_GNU
300 /* Return nonzero value if X is a signaling NaN. */
301 # ifdef __NO_LONG_DOUBLE_MATH
302 # define issignaling(x) \
303 (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
304 # else
305 # define issignaling(x) \
306 (sizeof (x) == sizeof (float) \
307 ? __issignalingf (x) \
308 : sizeof (x) == sizeof (double) \
309 ? __issignaling (x) : __issignalingl (x))
310 # endif
311 #endif /* Use GNU. */
312
313 #ifdef __USE_MISC
314 /* Support for various different standard error handling behaviors. */
315 typedef enum
316 {
317 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
318 _SVID_, /* According to System V, release 4. */
319 _XOPEN_, /* Nowadays also Unix98. */
320 _POSIX_,
321 _ISOC_ /* Actually this is ISO C99. */
322 } _LIB_VERSION_TYPE;
323
324 /* This variable can be changed at run-time to any of the values above to
325 affect floating point error handling behavior (it may also be necessary
326 to change the hardware FPU exception settings). */
327 extern _LIB_VERSION_TYPE _LIB_VERSION;
328 #endif
329
330
331 #ifdef __USE_MISC
332 /* In SVID error handling, `matherr' is called with this description
333 of the exceptional condition.
334
335 We have a problem when using C++ since `exception' is a reserved
336 name in C++. */
337 # ifdef __cplusplus
338 struct __exception
339 # else
340 struct exception
341 # endif
342 {
343 int type;
344 char *name;
345 double arg1;
346 double arg2;
347 double retval;
348 };
349
350 # ifdef __cplusplus
351 extern int matherr (struct __exception *__exc) throw ();
352 # else
353 extern int matherr (struct exception *__exc);
354 # endif
355
356 # define X_TLOSS 1.41484755040568800000e+16
357
358 /* Types of exceptions in the `type' field. */
359 # define DOMAIN 1
360 # define SING 2
361 # define OVERFLOW 3
362 # define UNDERFLOW 4
363 # define TLOSS 5
364 # define PLOSS 6
365
366 /* SVID mode specifies returning this large value instead of infinity. */
367 # define HUGE 3.40282347e+38F
368
369 #else /* !Misc. */
370
371 # ifdef __USE_XOPEN
372 /* X/Open wants another strange constant. */
373 # define MAXFLOAT 3.40282347e+38F
374 # endif
375
376 #endif /* Misc. */
377
378
379 /* Some useful constants. */
380 #if defined __USE_MISC || defined __USE_XOPEN
381 # define M_E 2.7182818284590452354 /* e */
382 # define M_LOG2E 1.4426950408889634074 /* log_2 e */
383 # define M_LOG10E 0.43429448190325182765 /* log_10 e */
384 # define M_LN2 0.69314718055994530942 /* log_e 2 */
385 # define M_LN10 2.30258509299404568402 /* log_e 10 */
386 # define M_PI 3.14159265358979323846 /* pi */
387 # define M_PI_2 1.57079632679489661923 /* pi/2 */
388 # define M_PI_4 0.78539816339744830962 /* pi/4 */
389 # define M_1_PI 0.31830988618379067154 /* 1/pi */
390 # define M_2_PI 0.63661977236758134308 /* 2/pi */
391 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
392 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
393 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
394 #endif
395
396 /* The above constants are not adequate for computation using `long double's.
397 Therefore we provide as an extension constants with similar names as a
398 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
399 #ifdef __USE_GNU
400 # define M_El 2.718281828459045235360287471352662498L /* e */
401 # define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
402 # define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
403 # define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
404 # define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
405 # define M_PIl 3.141592653589793238462643383279502884L /* pi */
406 # define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
407 # define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
408 # define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
409 # define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
410 # define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
411 # define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
412 # define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
413 #endif
414
415
416 /* When compiling in strict ISO C compatible mode we must not use the
417 inline functions since they, among other things, do not set the
418 `errno' variable correctly. */
419 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
420 # define __NO_MATH_INLINES 1
421 #endif
422
423 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
424 /* ISO C99 defines some macros to compare number while taking care for
425 unordered numbers. Many FPUs provide special instructions to support
426 these operations. Generic support in GCC for these as builtins went
427 in before 3.0.0, but not all cpus added their patterns. We define
428 versions that use the builtins here, and <bits/mathinline.h> will
429 undef/redefine as appropriate for the specific GCC version in use. */
430 # define isgreater(x, y) __builtin_isgreater(x, y)
431 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
432 # define isless(x, y) __builtin_isless(x, y)
433 # define islessequal(x, y) __builtin_islessequal(x, y)
434 # define islessgreater(x, y) __builtin_islessgreater(x, y)
435 # define isunordered(u, v) __builtin_isunordered(u, v)
436 #endif
437
438 /* Get machine-dependent inline versions (if there are any). */
439 #ifdef __USE_EXTERN_INLINES
440 # include <bits/mathinline.h>
441 #endif
442
443 /* Define special entry points to use when the compiler got told to
444 only expect finite results. */
445 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
446 # include <bits/math-finite.h>
447 #endif
448
449 #ifdef __USE_ISOC99
450 /* If we've still got undefined comparison macros, provide defaults. */
451
452 /* Return nonzero value if X is greater than Y. */
453 # ifndef isgreater
454 # define isgreater(x, y) \
455 (__extension__ \
456 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
457 !isunordered (__x, __y) && __x > __y; }))
458 # endif
459
460 /* Return nonzero value if X is greater than or equal to Y. */
461 # ifndef isgreaterequal
462 # define isgreaterequal(x, y) \
463 (__extension__ \
464 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
465 !isunordered (__x, __y) && __x >= __y; }))
466 # endif
467
468 /* Return nonzero value if X is less than Y. */
469 # ifndef isless
470 # define isless(x, y) \
471 (__extension__ \
472 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
473 !isunordered (__x, __y) && __x < __y; }))
474 # endif
475
476 /* Return nonzero value if X is less than or equal to Y. */
477 # ifndef islessequal
478 # define islessequal(x, y) \
479 (__extension__ \
480 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
481 !isunordered (__x, __y) && __x <= __y; }))
482 # endif
483
484 /* Return nonzero value if either X is less than Y or Y is less than X. */
485 # ifndef islessgreater
486 # define islessgreater(x, y) \
487 (__extension__ \
488 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
489 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
490 # endif
491
492 /* Return nonzero value if arguments are unordered. */
493 # ifndef isunordered
494 # define isunordered(u, v) \
495 (__extension__ \
496 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
497 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
498 # endif
499
500 #endif
501
502 __END_DECLS
503
504
505 #endif /* math.h */
506