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
|
/* Copyright (C) 1991, 1992, 1993 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, 1992 Free Software Foundation, Inc., 675 Mass Ave,
Cambridge, MA 02139, USA. */
/*
* ANSI Standard: 4.5 MATHEMATICS <math.h>
*/
#ifndef _MATH_H
#define _MATH_H 1
#include <features.h>
__BEGIN_DECLS
#define __need_Emath
#include <errno.h>
/* Get machine-dependent HUGE_VAL value (returned on overflow). */
#include <huge_val.h>
/* Get machine-dependent NAN value (returned for some domain errors). */
#ifdef __USE_GNU
#include <nan.h>
#endif
/* Trigonometric functions. */
/* Arc cosine of X. */
extern double acos __P ((double __x)) __attribute__ ((__const__));
/* Arc sine of X. */
extern double asin __P ((double __x)) __attribute__ ((__const__));
/* Arc tangent of X. */
extern double atan __P ((double __x)) __attribute__ ((__const__));
/* Arc tangent of Y/X. */
extern double atan2 __P ((double __y, double __x)) __attribute__ ((__const__));
/* Cosine of X. */
extern double cos __P ((double __x)) __attribute__ ((__const__));
/* Sine of X. */
extern double sin __P ((double __x)) __attribute__ ((__const__));
/* Tangent of X. */
extern double tan __P ((double __x)) __attribute__ ((__const__));
/* Hyperbolic functions. */
/* Hyperbolic cosine of X. */
extern double cosh __P ((double __x)) __attribute__ ((__const__));
/* Hyperbolic sine of X. */
extern double sinh __P ((double __x)) __attribute__ ((__const__));
/* Hyperbolic tangent of X. */
extern double tanh __P ((double __x)) __attribute__ ((__const__));
#ifdef __USE_MISC
/* Hyperbolic arc cosine of X. */
extern double acosh __P ((double __x)) __attribute__ ((__const__));
/* Hyperbolic arc sine of X. */
extern double asinh __P ((double __x)) __attribute__ ((__const__));
/* Hyperbolic arc tangent of X. */
extern double atanh __P ((double __x)) __attribute__ ((__const__));
#endif
/* Exponential and logarithmic functions. */
/* Exponentional function of X. */
extern double exp __P ((double __x)) __attribute__ ((__const__));
/* Break VALUE into a normalized fraction and an integral power of 2. */
extern double frexp __P ((double __value, int *__exp));
/* X times (two to the EXP power). */
extern double ldexp __P ((double __x, int __exp)) __attribute__ ((__const__));
/* Natural logarithm of X. */
extern double log __P ((double __x)) __attribute__ ((__const__));
/* Base-ten logarithm of X. */
extern double log10 __P ((double __x)) __attribute__ ((__const__));
#ifdef __USE_MISC
/* Return exp(X) - 1. */
extern double __expm1 __P ((double __x)) __attribute__ ((__const__));
extern double expm1 __P ((double __x)) __attribute__ ((__const__));
/* Return log(1 + X). */
extern double log1p __P ((double __x)) __attribute__ ((__const__));
#endif
/* Break VALUE into integral and fractional parts. */
extern double modf __P ((double __value, double *__iptr));
/* Power functions. */
/* Return X to the Y power. */
extern double pow __P ((double __x, double __y)) __attribute__ ((__const__));
/* Return the square root of X. */
extern double sqrt __P ((double __x)) __attribute__ ((__const__));
#ifdef __USE_MISC
/* Return the cube root of X. */
extern double cbrt __P ((double __x)) __attribute__ ((__const__));
#endif
/* Nearest integer, absolute value, and remainder functions. */
/* Smallest integral value not less than X. */
extern double ceil __P ((double __x)) __attribute__ ((__const__));
/* Absolute value of X. */
extern double fabs __P ((double __x)) __attribute__ ((__const__));
/* Largest integer not greater than X. */
extern double floor __P ((double __x)) __attribute__ ((__const__));
/* Floating-point modulo remainder of X/Y. */
extern double fmod __P ((double __x, double __y)) __attribute__ ((__const__));
/* Return 0 if VALUE is finite or NaN, +1 if it
is +Infinity, -1 if it is -Infinity. */
extern int __isinf __P ((double __value)) __attribute__ ((__const__));
/* Return nonzero if VALUE is not a number. */
extern int __isnan __P ((double __value)) __attribute__ ((__const__));
/* Return nonzero if VALUE is finite and not NaN. */
extern int __finite __P ((double __value)) __attribute__ ((__const__));
#ifdef __OPTIMIZE__
#define __finite(value) (!__isinf(value))
#endif
/* Deal with an infinite or NaN result.
If ERROR is ERANGE, result is +Inf;
if ERROR is - ERANGE, result is -Inf;
otherwise result is NaN.
This will set `errno' to either ERANGE or EDOM,
and may return an infinity or NaN, or may do something else. */
extern double __infnan __P ((int __error));
/* Return X with its signed changed to Y's. */
extern double __copysign __P ((double __x, double __y))
__attribute__ ((__const__));
/* Return X times (2 to the Nth power). */
extern double __scalb __P ((double __x, int __n))
__attribute__ ((__const__));
#ifdef __OPTIMIZE__
#define __scalb(x, n) ldexp ((x), (n))
#endif
/* Return the remainder of X/Y. */
extern double __drem __P ((double __x, double __y))
__attribute__ ((__const__));
/* Return the base 2 signed integral exponent of X. */
extern double __logb __P ((double __x)) __attribute__ ((__const__));
#ifdef __USE_MISC
/* Return the integer nearest X in the direction of the
prevailing rounding mode. */
extern double __rint __P ((double __x)) __attribute__ ((__const__));
extern double rint __P ((double __x)) __attribute__ ((__const__));
/* Return `sqrt(X*X + Y*Y)'. */
extern double hypot __P ((double __x, double __y)) __attribute__ ((__const__));
struct __cabs_complex
{
double __x, __y;
};
/* Return `sqrt(X*X + Y*Y)'. */
extern double cabs __P ((struct __cabs_complex)) __attribute__ ((__const__));
extern int isinf __P ((double __value)) __attribute__ ((__const__));
extern int isnan __P ((double __value)) __attribute__ ((__const__));
extern int finite __P ((double __value)) __attribute__ ((__const__));
extern double infnan __P ((int __error)) __attribute__ ((__const__));
extern double copysign __P ((double __x, double __y))
__attribute__ ((__const__));
extern double scalb __P ((double __x, int __n)) __attribute__ ((__const__));
extern double drem __P ((double __x, double __y)) __attribute__ ((__const__));
extern double logb __P ((double __x)) __attribute__ ((__const__));
#ifdef __OPTIMIZE__
#define isinf(value) __isinf(value)
#define isnan(value) __isnan(value)
#define infnan(error) __infnan(error)
#define finite(value) __finite(value)
#define copysign(x, y) __copysign((x), (y))
#define scalb(x, n) __scalb((x), (n))
#define drem(x, y) __drem((x), (y))
#define logb(x) __logb(x)
#endif /* Optimizing. */
#endif /* Use misc. */
#if 0
/* The "Future Library Directions" section of the
ANSI Standard reserves these as `float' and
`long double' versions of the above functions. */
extern float acosf __P ((float __x)) __attribute__ ((__const__));
extern float asinf __P ((float __x)) __attribute__ ((__const__));
extern float atanf __P ((float __x)) __attribute__ ((__const__));
extern float atan2f __P ((float __y, float __x)) __attribute__ ((__const__));
extern float cosf __P ((float __x)) __attribute__ ((__const__));
extern float sinf __P ((float __x)) __attribute__ ((__const__));
extern float tanf __P ((float __x)) __attribute__ ((__const__));
extern float coshf __P ((float __x)) __attribute__ ((__const__));
extern float sinhf __P ((float __x)) __attribute__ ((__const__));
extern float tanhf __P ((float __x)) __attribute__ ((__const__));
extern float expf __P ((float __x)) __attribute__ ((__const__));
extern float frexpf __P ((float __value, int *__exp));
extern float ldexpf __P ((float __x, int __exp)) __attribute__ ((__const__));
extern float logf __P ((float __x)) __attribute__ ((__const__));
extern float log10f __P ((float __x)) __attribute__ ((__const__));
extern float modff __P ((float __value, float *__iptr));
extern float powf __P ((float __x, float __y)) __attribute__ ((__const__));
extern float sqrtf __P ((float __x)) __attribute__ ((__const__));
extern float ceilf __P ((float __x)) __attribute__ ((__const__));
extern float fabsf __P ((float __x)) __attribute__ ((__const__));
extern float floorf __P ((float __x)) __attribute__ ((__const__));
extern float fmodf __P ((float __x, float __y)) __attribute__ ((__const__));
extern __long_double_t acosl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t asinl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t atanl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t atan2l __P ((__long_double_t __y, __long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t cosl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t sinl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t tanl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t coshl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t sinhl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t tanhl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t expl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t frexpl __P ((__long_double_t __value, int *__exp));
extern __long_double_t ldexpl __P ((__long_double_t __x, int __exp))
__attribute__ ((__const__));
extern __long_double_t logl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t log10l __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t modfl __P ((__long_double_t __value,
__long_double_t *__ip));
extern __long_double_t powl __P ((__long_double_t __x, __long_double_t __y))
__attribute__ ((__const__));
extern __long_double_t sqrtl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t ceill __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t fabsl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t floorl __P ((__long_double_t __x))
__attribute__ ((__const__));
extern __long_double_t fmodl __P ((__long_double_t __x, __long_double_t __y))
__attribute__ ((__const__));
#endif /* 0 */
/* Get machine-dependent inline versions (if there are any). */
#include <__math.h>
__END_DECLS
#ifdef __USE_BSD
/* Some useful constants. */
#define M_E 2.7182818284590452354 /* e */
#define M_LOG2E 1.4426950408889634074 /* log 2e */
#define M_LOG10E 0.43429448190325182765 /* log 10e */
#define M_LN2 0.69314718055994530942 /* log e2 */
#define M_LN10 2.30258509299404568402 /* log e10 */
#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
#endif /* math.h */
|
