1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
|
/* Declarations for math functions.
Copyright (C) 1991, 92, 93, 95, 96, 97, 98 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
/*
* ISO C Standard: 4.5 MATHEMATICS <math.h>
*/
#ifndef _MATH_H
#define _MATH_H 1
#include <features.h>
__BEGIN_DECLS
/* Get machine-dependent HUGE_VAL value (returned on overflow).
On all IEEE754 machines, this is +Infinity. */
#include <bits/huge_val.h>
/* Get machine-dependent NAN value (returned for some domain errors). */
#ifdef __USE_GNU
# include <bits/nan.h>
#endif
/* The file <bits/mathcalls.h> contains the prototypes for all the
actual math functions. These macros are used for those prototypes,
so we can easily declare each function as both `name' and `__name',
and can declare the float versions `namef' and `__namef'. */
#define __MATHCALL(function,suffix, args) \
__MATHDECL (_Mdouble_,function,suffix, args)
#define __MATHDECL(type, function,suffix, args) \
__MATHDECL_1(type, function,suffix, args); \
__MATHDECL_1(type, __CONCAT(__,function),suffix, args)
#define __MATHCALLX(function,suffix, args, attrib) \
__MATHDECLX (_Mdouble_,function,suffix, args, attrib)
#define __MATHDECLX(type, function,suffix, args, attrib) \
__MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
__MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
#define __MATHDECL_1(type, function,suffix, args) \
extern type __MATH_PRECNAME(function,suffix) args
#define _Mdouble_ double
#define __MATH_PRECNAME(name,r) __CONCAT(name,r)
#include <bits/mathcalls.h>
#undef _Mdouble_
#undef __MATH_PRECNAME
#if defined __USE_MISC || defined __USE_ISOC9X
/* Include the file of declarations again, this time using `float'
instead of `double' and appending f to each function name. */
# ifndef _Mfloat_
# define _Mfloat_ float
# endif
# define _Mdouble_ _Mfloat_
# ifdef __STDC__
# define __MATH_PRECNAME(name,r) name##f##r
# else
# define __MATH_PRECNAME(name,r) name/**/f/**/r
# endif
# include <bits/mathcalls.h>
# undef _Mdouble_
# undef __MATH_PRECNAME
# if __STDC__ - 0 || __GNUC__ - 0
/* Include the file of declarations again, this time using `long double'
instead of `double' and appending l to each function name. */
# ifndef _Mlong_double_
# define _Mlong_double_ long double
# endif
# define _Mdouble_ _Mlong_double_
# ifdef __STDC__
# define __MATH_PRECNAME(name,r) name##l##r
# else
# define __MATH_PRECNAME(name,r) name/**/l/**/r
# endif
# include <bits/mathcalls.h>
# undef _Mdouble_
# undef __MATH_PRECNAME
# endif /* __STDC__ || __GNUC__ */
#endif /* Use misc or ISO C 9X. */
#undef __MATHDECL_1
#undef __MATHDECL
#undef __MATHCALL
#if defined __USE_MISC || defined __USE_XOPEN || defined __USE_ISOC9X
/* This variable is used by `gamma' and `lgamma'. */
extern int signgam;
#endif
/* ISO C 9X defines some generic macros which work on any data type. */
#if __USE_ISOC9X
/* Get the architecture specific values describing the floating-point
evaluation. The following symbols will get defined:
float_t floating-point type at least as wide as `float' used
to evaluate `float' expressions
double_t floating-point type at least as wide as `double' used
to evaluate `double' expressions
FLT_EVAL_METHOD
Defined to
0 if `float_t' is `float' and `double_t' is `double'
1 if `float_t' and `double_t' are `double'
2 if `float_t' and `double_t' are `long double'
else `float_t' and `double_t' are unspecified
INFINITY representation of the infinity value of type `float'
FP_FAST_FMA
FP_FAST_FMAF
FP_FAST_FMAL
If defined it indicates that the the `fma' function
generally executes about as fast as a multiply and an add.
This macro is defined only iff the `fma' function is
implemented directly with a hardware multiply-add instructions.
FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
DECIMAL_DIG Number of decimal digits supported by conversion between
decimal and all internal floating-point formats.
*/
# include <bits/mathdef.h>
/* All floating-point numbers can be put in one of these categories. */
enum
{
FP_NAN,
# define FP_NAN FP_NAN
FP_INFINITE,
# define FP_INFINITE FP_INFINITE
FP_ZERO,
# define FP_ZERO FP_ZERO
FP_SUBNORMAL,
# define FP_SUBNORMAL FP_SUBNORMAL
FP_NORMAL
# define FP_NORMAL FP_NORMAL
};
/* Return number of classification appropriate for X. */
# define fpclassify(x) \
(sizeof (x) == sizeof (float) ? \
__fpclassifyf (x) \
: sizeof (x) == sizeof (double) ? \
__fpclassify (x) : __fpclassifyl (x))
/* Return nonzero value if sign of X is negative. */
# define signbit(x) \
(sizeof (x) == sizeof (float) ? \
__signbitf (x) \
: sizeof (x) == sizeof (double) ? \
__signbit (x) : __signbitl (x))
/* Return nonzero value if X is not +-Inf or NaN. */
# define isfinite(x) \
(sizeof (x) == sizeof (float) ? \
__finitef (x) \
: sizeof (x) == sizeof (double) ? \
__finite (x) : __finitel (x))
/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
# define isnormal(x) (fpclassify (x) == FP_NORMAL)
/* Return nonzero value if X is a NaN. We could use `fpclassify' but
we already have this functions `__isnan' and it is faster. */
# define isnan(x) \
(sizeof (x) == sizeof (float) ? \
__isnanf (x) \
: sizeof (x) == sizeof (double) ? \
__isnan (x) : __isnanl (x))
#endif /* Use ISO C 9X. */
#ifdef __USE_MISC
/* Support for various different standard error handling behaviors. */
typedef enum { _IEEE_ = -1, _SVID_, _XOPEN_, _POSIX_ } _LIB_VERSION_TYPE;
/* This variable can be changed at run-time to any of the values above to
affect floating point error handling behavior (it may also be necessary
to change the hardware FPU exception settings). */
extern _LIB_VERSION_TYPE _LIB_VERSION;
#endif
#ifdef __USE_SVID
/* In SVID error handling, `matherr' is called with this description
of the exceptional condition.
We have a problem when using C++ since `exception' is a reserved
name in C++. */
# ifdef __cplusplus
struct __exception
# else
struct exception
# endif
{
int type;
char *name;
double arg1;
double arg2;
double retval;
};
# ifdef __cplusplus
extern int __matherr __P ((struct __exception *__exc));
extern int matherr __P ((struct __exception *__exc));
# else
extern int __matherr __P ((struct exception *__exc));
extern int matherr __P ((struct exception *__exc));
# endif
# define X_TLOSS 1.41484755040568800000e+16
/* Types of exceptions in the `type' field. */
# define DOMAIN 1
# define SING 2
# define OVERFLOW 3
# define UNDERFLOW 4
# define TLOSS 5
# define PLOSS 6
/* SVID mode specifies returning this large value instead of infinity. */
# define HUGE FLT_MAX
# include <float.h> /* Defines FLT_MAX. */
#else /* !SVID */
# ifdef __USE_XOPEN
/* X/Open wants another strange constant. */
# define MAXFLOAT FLT_MAX
# include <float.h>
# endif
#endif /* SVID */
/* Some useful constants. */
#if defined __USE_BSD || defined __USE_UNIX98
# define M_E 2.7182818284590452354 /* e */
# define M_LOG2E 1.4426950408889634074 /* log_2 e */
# define M_LOG10E 0.43429448190325182765 /* log_10 e */
# define M_LN2 0.69314718055994530942 /* log_e 2 */
# define M_LN10 2.30258509299404568402 /* log_e 10 */
# define M_PI 3.14159265358979323846 /* pi */
# define M_PI_2 1.57079632679489661923 /* pi/2 */
# define M_PI_4 0.78539816339744830962 /* pi/4 */
# define M_1_PI 0.31830988618379067154 /* 1/pi */
# define M_2_PI 0.63661977236758134308 /* 2/pi */
# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
#endif
/* The above constants are not adequate for computation using `long double's.
Therefore we provide as an extension constants with similar names as a
GNU extension. Provide enough digits for the 128-bit IEEE quad. */
#ifdef __USE_GNU
# define M_El 2.7182818284590452353602874713526625L /* e */
# define M_LOG2El 1.4426950408889634073599246810018922L /* log_2 e */
# define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
# define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
# define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
# define M_PIl 3.1415926535897932384626433832795029L /* pi */
# define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
# define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
# define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
# define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
# define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
# define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
# define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
#endif
/* Get machine-dependent inline versions (if there are any). */
#ifdef __OPTIMIZE__
# include <bits/mathinline.h>
#endif
#if __USE_ISOC9X
/* ISO C 9X defines some macros to compare number while taking care
for unordered numbers. Since many FPUs provide special
instructions to support these operations and these tests are
defined in <bits/mathinline.h>, we define the generic macros at
this late point and only if they are not defined yet. */
/* Return nonzero value if X is greater than Y. */
# ifndef isgreater
# define isgreater(x, y) \
(__extension__ \
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
!isunordered (__x, __y) && __x > __y; }))
# endif
/* Return nonzero value if X is greater than or equal to Y. */
# ifndef isgreaterequal
# define isgreaterequal(x, y) \
(__extension__ \
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
!isunordered (__x, __y) && __x >= __y; }))
# endif
/* Return nonzero value if X is less than Y. */
# ifndef isless
# define isless(x, y) \
(__extension__ \
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
!isunordered (__x, __y) && __x < __y; }))
# endif
/* Return nonzero value if X is less than or equal to Y. */
# ifndef islessequal
# define islessequal(x, y) \
(__extension__ \
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
!isunordered (__x, __y) && __x <= __y; }))
# endif
/* Return nonzero value if either X is less than Y or Y is less than X. */
# ifndef islessgreater
# define islessgreater(x, y) \
(__extension__ \
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
!isunordered (__x, __y) && (__x < __y || __y < __x); }))
# endif
/* Return nonzero value if arguments are unordered. */
# ifndef isunordered
# define isunordered(u, v) \
(__extension__ \
({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
# endif
#endif
__END_DECLS
#endif /* math.h */
|
