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f7eac6eb | 1 | /* Declarations for math functions. |
68337808 | 2 | Copyright (C) 1991,92,93,95,96,97,98,99 Free Software Foundation, Inc. |
ba1ffaa1 | 3 | This file is part of the GNU C Library. |
28f540f4 | 4 | |
ba1ffaa1 UD |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Library General Public License as | |
7 | published by the Free Software Foundation; either version 2 of the | |
8 | License, or (at your option) any later version. | |
28f540f4 | 9 | |
ba1ffaa1 UD |
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 | Library General Public License for more details. | |
28f540f4 | 14 | |
ba1ffaa1 UD |
15 | You should have received a copy of the GNU Library General Public |
16 | License along with the GNU C Library; see the file COPYING.LIB. If not, | |
17 | write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, | |
18 | Boston, MA 02111-1307, USA. */ | |
28f540f4 RM |
19 | |
20 | /* | |
d1646309 | 21 | * ISO C99 Standard: 7.12 Mathematics <math.h> |
28f540f4 RM |
22 | */ |
23 | ||
24 | #ifndef _MATH_H | |
28f540f4 | 25 | #define _MATH_H 1 |
5107cf1d | 26 | |
28f540f4 RM |
27 | #include <features.h> |
28 | ||
29 | __BEGIN_DECLS | |
30 | ||
f7eac6eb RM |
31 | /* Get machine-dependent HUGE_VAL value (returned on overflow). |
32 | On all IEEE754 machines, this is +Infinity. */ | |
5107cf1d | 33 | #include <bits/huge_val.h> |
28f540f4 RM |
34 | |
35 | /* Get machine-dependent NAN value (returned for some domain errors). */ | |
ec751a23 | 36 | #ifdef __USE_ISOC99 |
478b92f0 | 37 | # include <bits/nan.h> |
28f540f4 | 38 | #endif |
ec751a23 | 39 | /* Get general and ISO C99 specific information. */ |
d76bd17f | 40 | #include <bits/mathdef.h> |
28f540f4 RM |
41 | |
42 | ||
5107cf1d UD |
43 | /* The file <bits/mathcalls.h> contains the prototypes for all the |
44 | actual math functions. These macros are used for those prototypes, | |
45 | so we can easily declare each function as both `name' and `__name', | |
f7eac6eb RM |
46 | and can declare the float versions `namef' and `__namef'. */ |
47 | ||
48 | #define __MATHCALL(function,suffix, args) \ | |
377a515b | 49 | __MATHDECL (_Mdouble_,function,suffix, args) |
f7eac6eb RM |
50 | #define __MATHDECL(type, function,suffix, args) \ |
51 | __MATHDECL_1(type, function,suffix, args); \ | |
377a515b | 52 | __MATHDECL_1(type, __CONCAT(__,function),suffix, args) |
3e5f5557 UD |
53 | #define __MATHCALLX(function,suffix, args, attrib) \ |
54 | __MATHDECLX (_Mdouble_,function,suffix, args, attrib) | |
55 | #define __MATHDECLX(type, function,suffix, args, attrib) \ | |
56 | __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \ | |
57 | __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib) | |
f7eac6eb | 58 | #define __MATHDECL_1(type, function,suffix, args) \ |
c1422e5b | 59 | extern type __MATH_PRECNAME(function,suffix) args __THROW |
f7eac6eb RM |
60 | |
61 | #define _Mdouble_ double | |
377a515b | 62 | #define __MATH_PRECNAME(name,r) __CONCAT(name,r) |
5107cf1d | 63 | #include <bits/mathcalls.h> |
f7eac6eb RM |
64 | #undef _Mdouble_ |
65 | #undef __MATH_PRECNAME | |
66 | ||
ec751a23 | 67 | #if defined __USE_MISC || defined __USE_ISOC99 |
76060ec0 | 68 | |
999493cb RM |
69 | |
70 | /* Include the file of declarations again, this time using `float' | |
f7eac6eb RM |
71 | instead of `double' and appending f to each function name. */ |
72 | ||
fe0ec73e UD |
73 | # ifndef _Mfloat_ |
74 | # define _Mfloat_ float | |
478b92f0 | 75 | # endif |
fe0ec73e | 76 | # define _Mdouble_ _Mfloat_ |
478b92f0 | 77 | # ifdef __STDC__ |
fe0ec73e | 78 | # define __MATH_PRECNAME(name,r) name##f##r |
478b92f0 | 79 | # else |
fe0ec73e | 80 | # define __MATH_PRECNAME(name,r) name/**/f/**/r |
478b92f0 UD |
81 | # endif |
82 | # include <bits/mathcalls.h> | |
83 | # undef _Mdouble_ | |
84 | # undef __MATH_PRECNAME | |
76060ec0 | 85 | |
48252123 | 86 | # if (__STDC__ - 0 || __GNUC__ - 0) && !defined __NO_LONG_DOUBLE_MATH |
fe0ec73e UD |
87 | /* Include the file of declarations again, this time using `long double' |
88 | instead of `double' and appending l to each function name. */ | |
89 | ||
90 | # ifndef _Mlong_double_ | |
91 | # define _Mlong_double_ long double | |
92 | # endif | |
93 | # define _Mdouble_ _Mlong_double_ | |
94 | # ifdef __STDC__ | |
95 | # define __MATH_PRECNAME(name,r) name##l##r | |
96 | # else | |
97 | # define __MATH_PRECNAME(name,r) name/**/l/**/r | |
98 | # endif | |
99 | # include <bits/mathcalls.h> | |
100 | # undef _Mdouble_ | |
101 | # undef __MATH_PRECNAME | |
102 | ||
103 | # endif /* __STDC__ || __GNUC__ */ | |
377a515b | 104 | |
ec751a23 | 105 | #endif /* Use misc or ISO C99. */ |
4cca6b86 UD |
106 | #undef __MATHDECL_1 |
107 | #undef __MATHDECL | |
108 | #undef __MATHCALL | |
109 | ||
110 | ||
00d8bc81 | 111 | #if defined __USE_MISC || defined __USE_XOPEN |
4cca6b86 UD |
112 | /* This variable is used by `gamma' and `lgamma'. */ |
113 | extern int signgam; | |
114 | #endif | |
377a515b UD |
115 | |
116 | ||
ec751a23 UD |
117 | /* ISO C99 defines some generic macros which work on any data type. */ |
118 | #if __USE_ISOC99 | |
377a515b | 119 | |
63551311 UD |
120 | /* Get the architecture specific values describing the floating-point |
121 | evaluation. The following symbols will get defined: | |
122 | ||
fe0ec73e | 123 | float_t floating-point type at least as wide as `float' used |
63551311 | 124 | to evaluate `float' expressions |
fe0ec73e | 125 | double_t floating-point type at least as wide as `double' used |
63551311 UD |
126 | to evaluate `double' expressions |
127 | ||
fe0ec73e | 128 | FLT_EVAL_METHOD |
63551311 UD |
129 | Defined to |
130 | 0 if `float_t' is `float' and `double_t' is `double' | |
131 | 1 if `float_t' and `double_t' are `double' | |
132 | 2 if `float_t' and `double_t' are `long double' | |
133 | else `float_t' and `double_t' are unspecified | |
134 | ||
fe0ec73e | 135 | INFINITY representation of the infinity value of type `float' |
dfd2257a | 136 | |
fe0ec73e UD |
137 | FP_FAST_FMA |
138 | FP_FAST_FMAF | |
139 | FP_FAST_FMAL | |
3081378b | 140 | If defined it indicates that the `fma' function |
dfd2257a UD |
141 | generally executes about as fast as a multiply and an add. |
142 | This macro is defined only iff the `fma' function is | |
143 | implemented directly with a hardware multiply-add instructions. | |
144 | ||
145 | FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. | |
146 | FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. | |
147 | ||
fe0ec73e UD |
148 | DECIMAL_DIG Number of decimal digits supported by conversion between |
149 | decimal and all internal floating-point formats. | |
150 | ||
63551311 | 151 | */ |
63551311 | 152 | |
377a515b UD |
153 | /* All floating-point numbers can be put in one of these categories. */ |
154 | enum | |
155 | { | |
156 | FP_NAN, | |
478b92f0 | 157 | # define FP_NAN FP_NAN |
377a515b | 158 | FP_INFINITE, |
478b92f0 | 159 | # define FP_INFINITE FP_INFINITE |
377a515b | 160 | FP_ZERO, |
478b92f0 | 161 | # define FP_ZERO FP_ZERO |
377a515b | 162 | FP_SUBNORMAL, |
478b92f0 | 163 | # define FP_SUBNORMAL FP_SUBNORMAL |
377a515b | 164 | FP_NORMAL |
478b92f0 | 165 | # define FP_NORMAL FP_NORMAL |
377a515b UD |
166 | }; |
167 | ||
168 | /* Return number of classification appropriate for X. */ | |
68337808 UD |
169 | # ifdef __NO_LONG_DOUBLE_MATH |
170 | # define fpclassify(x) \ | |
48252123 | 171 | (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x)) |
68337808 UD |
172 | # else |
173 | # define fpclassify(x) \ | |
15daa639 UD |
174 | (sizeof (x) == sizeof (float) \ |
175 | ? __fpclassifyf (x) \ | |
176 | : sizeof (x) == sizeof (double) \ | |
177 | ? __fpclassify (x) : __fpclassifyl (x)) | |
68337808 | 178 | # endif |
377a515b UD |
179 | |
180 | /* Return nonzero value if sign of X is negative. */ | |
68337808 UD |
181 | # ifdef __NO_LONG_DOUBLE_MATH |
182 | # define signbit(x) \ | |
48252123 | 183 | (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x)) |
68337808 UD |
184 | # else |
185 | # define signbit(x) \ | |
15daa639 UD |
186 | (sizeof (x) == sizeof (float) \ |
187 | ? __signbitf (x) \ | |
188 | : sizeof (x) == sizeof (double) \ | |
189 | ? __signbit (x) : __signbitl (x)) | |
68337808 | 190 | # endif |
377a515b UD |
191 | |
192 | /* Return nonzero value if X is not +-Inf or NaN. */ | |
68337808 UD |
193 | # ifdef __NO_LONG_DOUBLE_MATH |
194 | # define isfinite(x) \ | |
48252123 | 195 | (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x)) |
68337808 UD |
196 | # else |
197 | # define isfinite(x) \ | |
15daa639 UD |
198 | (sizeof (x) == sizeof (float) \ |
199 | ? __finitef (x) \ | |
200 | : sizeof (x) == sizeof (double) \ | |
201 | ? __finite (x) : __finitel (x)) | |
68337808 | 202 | # endif |
377a515b UD |
203 | |
204 | /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ | |
478b92f0 | 205 | # define isnormal(x) (fpclassify (x) == FP_NORMAL) |
377a515b UD |
206 | |
207 | /* Return nonzero value if X is a NaN. We could use `fpclassify' but | |
208 | we already have this functions `__isnan' and it is faster. */ | |
68337808 UD |
209 | # ifdef __NO_LONG_DOUBLE_MATH |
210 | # define isnan(x) \ | |
48252123 | 211 | (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x)) |
68337808 UD |
212 | # else |
213 | # define isnan(x) \ | |
15daa639 UD |
214 | (sizeof (x) == sizeof (float) \ |
215 | ? __isnanf (x) \ | |
216 | : sizeof (x) == sizeof (double) \ | |
217 | ? __isnan (x) : __isnanl (x)) | |
68337808 | 218 | # endif |
28f540f4 | 219 | |
bfce746a | 220 | /* Return nonzero value is X is positive or negative infinity. */ |
68337808 UD |
221 | # ifdef __NO_LONG_DOUBLE_MATH |
222 | # define isinf(x) \ | |
48252123 | 223 | (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x)) |
68337808 UD |
224 | # else |
225 | # define isinf(x) \ | |
15daa639 UD |
226 | (sizeof (x) == sizeof (float) \ |
227 | ? __isinff (x) \ | |
228 | : sizeof (x) == sizeof (double) \ | |
229 | ? __isinf (x) : __isinfl (x)) | |
68337808 | 230 | # endif |
bfce746a | 231 | |
ec751a23 | 232 | #endif /* Use ISO C99. */ |
377a515b | 233 | |
28f540f4 | 234 | #ifdef __USE_MISC |
f7eac6eb | 235 | /* Support for various different standard error handling behaviors. */ |
b9337b6a UD |
236 | typedef enum |
237 | { | |
238 | _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ | |
239 | _SVID_, /* According to System V, release 4. */ | |
240 | _XOPEN_, /* Nowadays also Unix98. */ | |
241 | _POSIX_, | |
ec751a23 | 242 | _ISOC_ /* Actually this is ISO C99. */ |
b9337b6a | 243 | } _LIB_VERSION_TYPE; |
28f540f4 | 244 | |
f7eac6eb RM |
245 | /* This variable can be changed at run-time to any of the values above to |
246 | affect floating point error handling behavior (it may also be necessary | |
247 | to change the hardware FPU exception settings). */ | |
248 | extern _LIB_VERSION_TYPE _LIB_VERSION; | |
28f540f4 RM |
249 | #endif |
250 | ||
251 | ||
ceb2d9aa | 252 | #ifdef __USE_SVID |
f7eac6eb | 253 | /* In SVID error handling, `matherr' is called with this description |
2f6d1f1b UD |
254 | of the exceptional condition. |
255 | ||
fe0ec73e UD |
256 | We have a problem when using C++ since `exception' is a reserved |
257 | name in C++. */ | |
478b92f0 | 258 | # ifdef __cplusplus |
ceb2d9aa | 259 | struct __exception |
478b92f0 | 260 | # else |
f7eac6eb | 261 | struct exception |
478b92f0 | 262 | # endif |
f7eac6eb RM |
263 | { |
264 | int type; | |
265 | char *name; | |
266 | double arg1; | |
267 | double arg2; | |
268 | double retval; | |
269 | }; | |
28f540f4 | 270 | |
478b92f0 | 271 | # ifdef __cplusplus |
c1422e5b | 272 | extern int matherr (struct __exception *__exc) throw (); |
478b92f0 | 273 | # else |
c1422e5b | 274 | extern int matherr (struct exception *__exc); |
478b92f0 | 275 | # endif |
28f540f4 | 276 | |
478b92f0 | 277 | # define X_TLOSS 1.41484755040568800000e+16 |
28f540f4 | 278 | |
f7eac6eb | 279 | /* Types of exceptions in the `type' field. */ |
478b92f0 UD |
280 | # define DOMAIN 1 |
281 | # define SING 2 | |
282 | # define OVERFLOW 3 | |
283 | # define UNDERFLOW 4 | |
284 | # define TLOSS 5 | |
285 | # define PLOSS 6 | |
28f540f4 | 286 | |
f7eac6eb | 287 | /* SVID mode specifies returning this large value instead of infinity. */ |
478b92f0 UD |
288 | # define HUGE FLT_MAX |
289 | # include <float.h> /* Defines FLT_MAX. */ | |
28f540f4 | 290 | |
377a515b UD |
291 | #else /* !SVID */ |
292 | ||
478b92f0 | 293 | # ifdef __USE_XOPEN |
377a515b | 294 | /* X/Open wants another strange constant. */ |
478b92f0 UD |
295 | # define MAXFLOAT FLT_MAX |
296 | # include <float.h> | |
297 | # endif | |
377a515b | 298 | |
ceb2d9aa | 299 | #endif /* SVID */ |
28f540f4 | 300 | |
28f540f4 | 301 | |
28f540f4 | 302 | /* Some useful constants. */ |
e918a7fe | 303 | #if defined __USE_BSD || defined __USE_XOPEN |
0a614877 UD |
304 | # define M_E 2.7182818284590452354 /* e */ |
305 | # define M_LOG2E 1.4426950408889634074 /* log_2 e */ | |
306 | # define M_LOG10E 0.43429448190325182765 /* log_10 e */ | |
307 | # define M_LN2 0.69314718055994530942 /* log_e 2 */ | |
308 | # define M_LN10 2.30258509299404568402 /* log_e 10 */ | |
309 | # define M_PI 3.14159265358979323846 /* pi */ | |
310 | # define M_PI_2 1.57079632679489661923 /* pi/2 */ | |
311 | # define M_PI_4 0.78539816339744830962 /* pi/4 */ | |
312 | # define M_1_PI 0.31830988618379067154 /* 1/pi */ | |
313 | # define M_2_PI 0.63661977236758134308 /* 2/pi */ | |
314 | # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ | |
315 | # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ | |
316 | # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ | |
714a562f UD |
317 | #endif |
318 | ||
0a614877 UD |
319 | /* The above constants are not adequate for computation using `long double's. |
320 | Therefore we provide as an extension constants with similar names as a | |
9a24f906 | 321 | GNU extension. Provide enough digits for the 128-bit IEEE quad. */ |
0a614877 | 322 | #ifdef __USE_GNU |
9a24f906 UD |
323 | # define M_El 2.7182818284590452353602874713526625L /* e */ |
324 | # define M_LOG2El 1.4426950408889634073599246810018922L /* log_2 e */ | |
325 | # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */ | |
326 | # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */ | |
327 | # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */ | |
328 | # define M_PIl 3.1415926535897932384626433832795029L /* pi */ | |
329 | # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */ | |
330 | # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */ | |
331 | # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */ | |
332 | # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */ | |
333 | # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */ | |
334 | # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */ | |
335 | # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */ | |
0a614877 | 336 | #endif |
710f7bab | 337 | |
28f540f4 | 338 | |
00bc5db0 UD |
339 | /* When compiling in strict ISO C compatible mode we must not use the |
340 | inline functions since they, among other things, do not set the | |
341 | `errno' variable correctly. */ | |
342 | #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES | |
343 | # define __NO_MATH_INLINES 1 | |
344 | #endif | |
345 | ||
4d585333 | 346 | /* Get machine-dependent inline versions (if there are any). */ |
0c6cee5d | 347 | #ifdef __USE_EXTERN_INLINES |
478b92f0 | 348 | # include <bits/mathinline.h> |
4d585333 RM |
349 | #endif |
350 | ||
351 | ||
ec751a23 UD |
352 | #if __USE_ISOC99 |
353 | /* ISO C99 defines some macros to compare number while taking care | |
ae1025be | 354 | for unordered numbers. Since many FPUs provide special |
907a1bac UD |
355 | instructions to support these operations and these tests are |
356 | defined in <bits/mathinline.h>, we define the generic macros at | |
fe0ec73e | 357 | this late point and only if they are not defined yet. */ |
ae1025be UD |
358 | |
359 | /* Return nonzero value if X is greater than Y. */ | |
360 | # ifndef isgreater | |
55c14926 UD |
361 | # define isgreater(x, y) \ |
362 | (__extension__ \ | |
363 | ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ | |
364 | !isunordered (__x, __y) && __x > __y; })) | |
ae1025be UD |
365 | # endif |
366 | ||
367 | /* Return nonzero value if X is greater than or equal to Y. */ | |
368 | # ifndef isgreaterequal | |
55c14926 UD |
369 | # define isgreaterequal(x, y) \ |
370 | (__extension__ \ | |
371 | ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ | |
372 | !isunordered (__x, __y) && __x >= __y; })) | |
ae1025be UD |
373 | # endif |
374 | ||
375 | /* Return nonzero value if X is less than Y. */ | |
376 | # ifndef isless | |
55c14926 UD |
377 | # define isless(x, y) \ |
378 | (__extension__ \ | |
379 | ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ | |
380 | !isunordered (__x, __y) && __x < __y; })) | |
ae1025be UD |
381 | # endif |
382 | ||
383 | /* Return nonzero value if X is less than or equal to Y. */ | |
384 | # ifndef islessequal | |
55c14926 UD |
385 | # define islessequal(x, y) \ |
386 | (__extension__ \ | |
387 | ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ | |
388 | !isunordered (__x, __y) && __x <= __y; })) | |
ae1025be UD |
389 | # endif |
390 | ||
391 | /* Return nonzero value if either X is less than Y or Y is less than X. */ | |
392 | # ifndef islessgreater | |
393 | # define islessgreater(x, y) \ | |
55c14926 UD |
394 | (__extension__ \ |
395 | ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ | |
396 | !isunordered (__x, __y) && (__x < __y || __y < __x); })) | |
ae1025be UD |
397 | # endif |
398 | ||
399 | /* Return nonzero value if arguments are unordered. */ | |
400 | # ifndef isunordered | |
d111572f | 401 | # define isunordered(u, v) \ |
55c14926 | 402 | (__extension__ \ |
d111572f UD |
403 | ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ |
404 | fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) | |
ae1025be UD |
405 | # endif |
406 | ||
407 | #endif | |
408 | ||
4d585333 RM |
409 | __END_DECLS |
410 | ||
411 | ||
28f540f4 | 412 | #endif /* math.h */ |