File: /usr/include/math.h
1 /* Declarations for math functions.
2 Copyright (C) 1991,92,93,95,96,97,98,99,2001 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 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.
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 Library General Public License for more details.
14
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. */
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
35 /* Get machine-dependent NAN value (returned for some domain errors). */
36 #ifdef __USE_ISOC99
37 # include <bits/nan.h>
38 #endif
39 /* Get general and ISO C99 specific information. */
40 #include <bits/mathdef.h>
41
42
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',
46 and can declare the float versions `namef' and `__namef'. */
47
48 #define __MATHCALL(function,suffix, args) \
49 __MATHDECL (_Mdouble_,function,suffix, args)
50 #define __MATHDECL(type, function,suffix, args) \
51 __MATHDECL_1(type, function,suffix, args); \
52 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
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)
58 #define __MATHDECL_1(type, function,suffix, args) \
59 extern type __MATH_PRECNAME(function,suffix) args __THROW
60
61 #define _Mdouble_ double
62 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
63 #include <bits/mathcalls.h>
64 #undef _Mdouble_
65 #undef __MATH_PRECNAME
66
67 #if defined __USE_MISC || defined __USE_ISOC99
68
69
70 /* Include the file of declarations again, this time using `float'
71 instead of `double' and appending f to each function name. */
72
73 # ifndef _Mfloat_
74 # define _Mfloat_ float
75 # endif
76 # define _Mdouble_ _Mfloat_
77 # ifdef __STDC__
78 # define __MATH_PRECNAME(name,r) name##f##r
79 # else
80 # define __MATH_PRECNAME(name,r) name/**/f/**/r
81 # endif
82 # include <bits/mathcalls.h>
83 # undef _Mdouble_
84 # undef __MATH_PRECNAME
85
86 # if (__STDC__ - 0 || __GNUC__ - 0) && !defined __NO_LONG_DOUBLE_MATH
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__ */
104
105 #endif /* Use misc or ISO C99. */
106 #undef __MATHDECL_1
107 #undef __MATHDECL
108 #undef __MATHCALL
109
110
111 #if defined __USE_MISC || defined __USE_XOPEN
112 /* This variable is used by `gamma' and `lgamma'. */
113 extern int signgam;
114 #endif
115
116
117 /* ISO C99 defines some generic macros which work on any data type. */
118 #if __USE_ISOC99
119
120 /* Get the architecture specific values describing the floating-point
121 evaluation. The following symbols will get defined:
122
123 float_t floating-point type at least as wide as `float' used
124 to evaluate `float' expressions
125 double_t floating-point type at least as wide as `double' used
126 to evaluate `double' expressions
127
128 FLT_EVAL_METHOD
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
135 INFINITY representation of the infinity value of type `float'
136
137 FP_FAST_FMA
138 FP_FAST_FMAF
139 FP_FAST_FMAL
140 If defined it indicates that the `fma' function
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
148 DECIMAL_DIG Number of decimal digits supported by conversion between
149 decimal and all internal floating-point formats.
150
151 */
152
153 /* All floating-point numbers can be put in one of these categories. */
154 enum
155 {
156 FP_NAN,
157 # define FP_NAN FP_NAN
158 FP_INFINITE,
159 # define FP_INFINITE FP_INFINITE
160 FP_ZERO,
161 # define FP_ZERO FP_ZERO
162 FP_SUBNORMAL,
163 # define FP_SUBNORMAL FP_SUBNORMAL
164 FP_NORMAL
165 # define FP_NORMAL FP_NORMAL
166 };
167
168 /* Return number of classification appropriate for X. */
169 # ifdef __NO_LONG_DOUBLE_MATH
170 # define fpclassify(x) \
171 (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
172 # else
173 # define fpclassify(x) \
174 (sizeof (x) == sizeof (float) \
175 ? __fpclassifyf (x) \
176 : sizeof (x) == sizeof (double) \
177 ? __fpclassify (x) : __fpclassifyl (x))
178 # endif
179
180 /* Return nonzero value if sign of X is negative. */
181 # ifdef __NO_LONG_DOUBLE_MATH
182 # define signbit(x) \
183 (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
184 # else
185 # define signbit(x) \
186 (sizeof (x) == sizeof (float) \
187 ? __signbitf (x) \
188 : sizeof (x) == sizeof (double) \
189 ? __signbit (x) : __signbitl (x))
190 # endif
191
192 /* Return nonzero value if X is not +-Inf or NaN. */
193 # ifdef __NO_LONG_DOUBLE_MATH
194 # define isfinite(x) \
195 (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
196 # else
197 # define isfinite(x) \
198 (sizeof (x) == sizeof (float) \
199 ? __finitef (x) \
200 : sizeof (x) == sizeof (double) \
201 ? __finite (x) : __finitel (x))
202 # endif
203
204 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
205 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
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. */
209 # ifdef __NO_LONG_DOUBLE_MATH
210 # define isnan(x) \
211 (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
212 # else
213 # define isnan(x) \
214 (sizeof (x) == sizeof (float) \
215 ? __isnanf (x) \
216 : sizeof (x) == sizeof (double) \
217 ? __isnan (x) : __isnanl (x))
218 # endif
219
220 /* Return nonzero value is X is positive or negative infinity. */
221 # ifdef __NO_LONG_DOUBLE_MATH
222 # define isinf(x) \
223 (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
224 # else
225 # define isinf(x) \
226 (sizeof (x) == sizeof (float) \
227 ? __isinff (x) \
228 : sizeof (x) == sizeof (double) \
229 ? __isinf (x) : __isinfl (x))
230 # endif
231
232 /* Bitmasks for the math_errhandling macro. */
233 # define MATH_ERRNO 1 /* errno set by math functions. */
234 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
235
236 #endif /* Use ISO C99. */
237
238 #ifdef __USE_MISC
239 /* Support for various different standard error handling behaviors. */
240 typedef enum
241 {
242 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
243 _SVID_, /* According to System V, release 4. */
244 _XOPEN_, /* Nowadays also Unix98. */
245 _POSIX_,
246 _ISOC_ /* Actually this is ISO C99. */
247 } _LIB_VERSION_TYPE;
248
249 /* This variable can be changed at run-time to any of the values above to
250 affect floating point error handling behavior (it may also be necessary
251 to change the hardware FPU exception settings). */
252 extern _LIB_VERSION_TYPE _LIB_VERSION;
253 #endif
254
255
256 #ifdef __USE_SVID
257 /* In SVID error handling, `matherr' is called with this description
258 of the exceptional condition.
259
260 We have a problem when using C++ since `exception' is a reserved
261 name in C++. */
262 # ifdef __cplusplus
263 struct __exception
264 # else
265 struct exception
266 # endif
267 {
268 int type;
269 char *name;
270 double arg1;
271 double arg2;
272 double retval;
273 };
274
275 # ifdef __cplusplus
276 extern int matherr (struct __exception *__exc) throw ();
277 # else
278 extern int matherr (struct exception *__exc);
279 # endif
280
281 # define X_TLOSS 1.41484755040568800000e+16
282
283 /* Types of exceptions in the `type' field. */
284 # define DOMAIN 1
285 # define SING 2
286 # define OVERFLOW 3
287 # define UNDERFLOW 4
288 # define TLOSS 5
289 # define PLOSS 6
290
291 /* SVID mode specifies returning this large value instead of infinity. */
292 # define HUGE 3.40282347e+38F
293
294 #else /* !SVID */
295
296 # ifdef __USE_XOPEN
297 /* X/Open wants another strange constant. */
298 # define MAXFLOAT 3.40282347e+38F
299 # endif
300
301 #endif /* SVID */
302
303
304 /* Some useful constants. */
305 #if defined __USE_BSD || defined __USE_XOPEN
306 # define M_E 2.7182818284590452354 /* e */
307 # define M_LOG2E 1.4426950408889634074 /* log_2 e */
308 # define M_LOG10E 0.43429448190325182765 /* log_10 e */
309 # define M_LN2 0.69314718055994530942 /* log_e 2 */
310 # define M_LN10 2.30258509299404568402 /* log_e 10 */
311 # define M_PI 3.14159265358979323846 /* pi */
312 # define M_PI_2 1.57079632679489661923 /* pi/2 */
313 # define M_PI_4 0.78539816339744830962 /* pi/4 */
314 # define M_1_PI 0.31830988618379067154 /* 1/pi */
315 # define M_2_PI 0.63661977236758134308 /* 2/pi */
316 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
317 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
318 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
319 #endif
320
321 /* The above constants are not adequate for computation using `long double's.
322 Therefore we provide as an extension constants with similar names as a
323 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
324 #ifdef __USE_GNU
325 # define M_El 2.7182818284590452353602874713526625L /* e */
326 # define M_LOG2El 1.4426950408889634073599246810018922L /* log_2 e */
327 # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
328 # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
329 # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
330 # define M_PIl 3.1415926535897932384626433832795029L /* pi */
331 # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
332 # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
333 # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
334 # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
335 # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
336 # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
337 # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
338 #endif
339
340
341 /* When compiling in strict ISO C compatible mode we must not use the
342 inline functions since they, among other things, do not set the
343 `errno' variable correctly. */
344 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
345 # define __NO_MATH_INLINES 1
346 #endif
347
348 /* Get machine-dependent inline versions (if there are any). */
349 #ifdef __USE_EXTERN_INLINES
350 # include <bits/mathinline.h>
351 #endif
352
353
354 #if __USE_ISOC99
355 /* ISO C99 defines some macros to compare number while taking care
356 for unordered numbers. Since many FPUs provide special
357 instructions to support these operations and these tests are
358 defined in <bits/mathinline.h>, we define the generic macros at
359 this late point and only if they are not defined yet. */
360
361 /* Return nonzero value if X is greater than Y. */
362 # ifndef isgreater
363 # define isgreater(x, y) \
364 (__extension__ \
365 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
366 !isunordered (__x, __y) && __x > __y; }))
367 # endif
368
369 /* Return nonzero value if X is greater than or equal to Y. */
370 # ifndef isgreaterequal
371 # define isgreaterequal(x, y) \
372 (__extension__ \
373 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
374 !isunordered (__x, __y) && __x >= __y; }))
375 # endif
376
377 /* Return nonzero value if X is less than Y. */
378 # ifndef isless
379 # define isless(x, y) \
380 (__extension__ \
381 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
382 !isunordered (__x, __y) && __x < __y; }))
383 # endif
384
385 /* Return nonzero value if X is less than or equal to Y. */
386 # ifndef islessequal
387 # define islessequal(x, y) \
388 (__extension__ \
389 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
390 !isunordered (__x, __y) && __x <= __y; }))
391 # endif
392
393 /* Return nonzero value if either X is less than Y or Y is less than X. */
394 # ifndef islessgreater
395 # define islessgreater(x, y) \
396 (__extension__ \
397 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
398 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
399 # endif
400
401 /* Return nonzero value if arguments are unordered. */
402 # ifndef isunordered
403 # define isunordered(u, v) \
404 (__extension__ \
405 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
406 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
407 # endif
408
409 #endif
410
411 __END_DECLS
412
413
414 #endif /* math.h */
415