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
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
|
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* from: @(#)fdlibm.h 5.1 93/09/24
*/
#ifndef _MATH_PRIVATE_H_
#define _MATH_PRIVATE_H_
#include <endian.h>
#include <stdint.h>
#include <sys/types.h>
/* The original fdlibm code used statements like:
n0 = ((*(int*)&one)>>29)^1; * index of high word *
ix0 = *(n0+(int*)&x); * high word of x *
ix1 = *((1-n0)+(int*)&x); * low word of x *
to dig two 32 bit words out of the 64 bit IEEE floating point
value. That is non-ANSI, and, moreover, the gcc instruction
scheduler gets it wrong. We instead use the following macros.
Unlike the original code, we determine the endianness at compile
time, not at run time; I don't see much benefit to selecting
endianness at run time. */
/* A union which permits us to convert between a double and two 32 bit
ints. */
#if __FLOAT_WORD_ORDER == BIG_ENDIAN
typedef union
{
double value;
struct
{
u_int32_t msw;
u_int32_t lsw;
} parts;
uint64_t word;
} ieee_double_shape_type;
#endif
#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN
typedef union
{
double value;
struct
{
u_int32_t lsw;
u_int32_t msw;
} parts;
uint64_t word;
} ieee_double_shape_type;
#endif
/* Get two 32 bit ints from a double. */
#define EXTRACT_WORDS(ix0,ix1,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix0) = ew_u.parts.msw; \
(ix1) = ew_u.parts.lsw; \
} while (0)
/* Get the more significant 32 bit int from a double. */
#define GET_HIGH_WORD(i,d) \
do { \
ieee_double_shape_type gh_u; \
gh_u.value = (d); \
(i) = gh_u.parts.msw; \
} while (0)
/* Get the less significant 32 bit int from a double. */
#define GET_LOW_WORD(i,d) \
do { \
ieee_double_shape_type gl_u; \
gl_u.value = (d); \
(i) = gl_u.parts.lsw; \
} while (0)
/* Get all in one, efficient on 64-bit machines. */
#define EXTRACT_WORDS64(i,d) \
do { \
ieee_double_shape_type gh_u; \
gh_u.value = (d); \
(i) = gh_u.word; \
} while (0)
/* Set a double from two 32 bit ints. */
#define INSERT_WORDS(d,ix0,ix1) \
do { \
ieee_double_shape_type iw_u; \
iw_u.parts.msw = (ix0); \
iw_u.parts.lsw = (ix1); \
(d) = iw_u.value; \
} while (0)
/* Get all in one, efficient on 64-bit machines. */
#define INSERT_WORDS64(d,i) \
do { \
ieee_double_shape_type iw_u; \
iw_u.word = (i); \
(d) = iw_u.value; \
} while (0)
/* Set the more significant 32 bits of a double from an int. */
#define SET_HIGH_WORD(d,v) \
do { \
ieee_double_shape_type sh_u; \
sh_u.value = (d); \
sh_u.parts.msw = (v); \
(d) = sh_u.value; \
} while (0)
/* Set the less significant 32 bits of a double from an int. */
#define SET_LOW_WORD(d,v) \
do { \
ieee_double_shape_type sl_u; \
sl_u.value = (d); \
sl_u.parts.lsw = (v); \
(d) = sl_u.value; \
} while (0)
/* A union which permits us to convert between a float and a 32 bit
int. */
typedef union
{
float value;
u_int32_t word;
} ieee_float_shape_type;
/* Get a 32 bit int from a float. */
#define GET_FLOAT_WORD(i,d) \
do { \
ieee_float_shape_type gf_u; \
gf_u.value = (d); \
(i) = gf_u.word; \
} while (0)
/* Set a float from a 32 bit int. */
#define SET_FLOAT_WORD(d,i) \
do { \
ieee_float_shape_type sf_u; \
sf_u.word = (i); \
(d) = sf_u.value; \
} while (0)
/* Get long double macros from a separate header. */
#include <math_ldbl.h>
/* ieee style elementary functions */
extern double __ieee754_sqrt (double);
extern double __ieee754_acos (double);
extern double __ieee754_acosh (double);
extern double __ieee754_log (double);
extern double __ieee754_atanh (double);
extern double __ieee754_asin (double);
extern double __ieee754_atan2 (double,double);
extern double __ieee754_exp (double);
extern double __ieee754_exp2 (double);
extern double __ieee754_exp10 (double);
extern double __ieee754_cosh (double);
extern double __ieee754_fmod (double,double);
extern double __ieee754_pow (double,double);
extern double __ieee754_lgamma_r (double,int *);
extern double __ieee754_gamma_r (double,int *);
extern double __ieee754_lgamma (double);
extern double __ieee754_gamma (double);
extern double __ieee754_log10 (double);
extern double __ieee754_log2 (double);
extern double __ieee754_sinh (double);
extern double __ieee754_hypot (double,double);
extern double __ieee754_j0 (double);
extern double __ieee754_j1 (double);
extern double __ieee754_y0 (double);
extern double __ieee754_y1 (double);
extern double __ieee754_jn (int,double);
extern double __ieee754_yn (int,double);
extern double __ieee754_remainder (double,double);
extern int32_t __ieee754_rem_pio2 (double,double*);
extern double __ieee754_scalb (double,double);
/* fdlibm kernel function */
extern double __kernel_standard (double,double,int);
extern float __kernel_standard_f (float,float,int);
extern double __kernel_sin (double,double,int);
extern double __kernel_cos (double,double);
extern double __kernel_tan (double,double,int);
extern int __kernel_rem_pio2 (double*,double*,int,int,int, const int32_t*);
/* internal functions. */
extern double __copysign (double x, double __y);
#if __GNUC_PREREQ (4, 0)
extern inline double __copysign (double x, double y)
{ return __builtin_copysign (x, y); }
#endif
/* ieee style elementary float functions */
extern float __ieee754_sqrtf (float);
extern float __ieee754_acosf (float);
extern float __ieee754_acoshf (float);
extern float __ieee754_logf (float);
extern float __ieee754_atanhf (float);
extern float __ieee754_asinf (float);
extern float __ieee754_atan2f (float,float);
extern float __ieee754_expf (float);
extern float __ieee754_exp2f (float);
extern float __ieee754_exp10f (float);
extern float __ieee754_coshf (float);
extern float __ieee754_fmodf (float,float);
extern float __ieee754_powf (float,float);
extern float __ieee754_lgammaf_r (float,int *);
extern float __ieee754_gammaf_r (float,int *);
extern float __ieee754_lgammaf (float);
extern float __ieee754_gammaf (float);
extern float __ieee754_log10f (float);
extern float __ieee754_log2f (float);
extern float __ieee754_sinhf (float);
extern float __ieee754_hypotf (float,float);
extern float __ieee754_j0f (float);
extern float __ieee754_j1f (float);
extern float __ieee754_y0f (float);
extern float __ieee754_y1f (float);
extern float __ieee754_jnf (int,float);
extern float __ieee754_ynf (int,float);
extern float __ieee754_remainderf (float,float);
extern int32_t __ieee754_rem_pio2f (float,float*);
extern float __ieee754_scalbf (float,float);
/* float versions of fdlibm kernel functions */
extern float __kernel_sinf (float,float,int);
extern float __kernel_cosf (float,float);
extern float __kernel_tanf (float,float,int);
extern int __kernel_rem_pio2f (float*,float*,int,int,int, const int32_t*);
/* internal functions. */
extern float __copysignf (float x, float __y);
#if __GNUC_PREREQ (4, 0)
extern inline float __copysignf (float x, float y)
{ return __builtin_copysignf (x, y); }
#endif
/* ieee style elementary long double functions */
extern long double __ieee754_sqrtl (long double);
extern long double __ieee754_acosl (long double);
extern long double __ieee754_acoshl (long double);
extern long double __ieee754_logl (long double);
extern long double __ieee754_atanhl (long double);
extern long double __ieee754_asinl (long double);
extern long double __ieee754_atan2l (long double,long double);
extern long double __ieee754_expl (long double);
extern long double __ieee754_exp2l (long double);
extern long double __ieee754_exp10l (long double);
extern long double __ieee754_coshl (long double);
extern long double __ieee754_fmodl (long double,long double);
extern long double __ieee754_powl (long double,long double);
extern long double __ieee754_lgammal_r (long double,int *);
extern long double __ieee754_gammal_r (long double,int *);
extern long double __ieee754_lgammal (long double);
extern long double __ieee754_gammal (long double);
extern long double __ieee754_log10l (long double);
extern long double __ieee754_log2l (long double);
extern long double __ieee754_sinhl (long double);
extern long double __ieee754_hypotl (long double,long double);
extern long double __ieee754_j0l (long double);
extern long double __ieee754_j1l (long double);
extern long double __ieee754_y0l (long double);
extern long double __ieee754_y1l (long double);
extern long double __ieee754_jnl (int,long double);
extern long double __ieee754_ynl (int,long double);
extern long double __ieee754_remainderl (long double,long double);
extern int __ieee754_rem_pio2l (long double,long double*);
extern long double __ieee754_scalbl (long double,long double);
/* long double versions of fdlibm kernel functions */
extern long double __kernel_sinl (long double,long double,int);
extern long double __kernel_cosl (long double,long double);
extern long double __kernel_tanl (long double,long double,int);
extern void __kernel_sincosl (long double,long double,
long double *,long double *, int);
extern int __kernel_rem_pio2l (long double*,long double*,int,int,
int,const int*);
#ifndef NO_LONG_DOUBLE
/* prototypes required to compile the ldbl-96 support without warnings */
extern int __finitel (long double);
extern int __ilogbl (long double);
extern int __isinfl (long double);
extern int __isnanl (long double);
extern long double __atanl (long double);
extern long double __copysignl (long double, long double);
extern long double __expm1l (long double);
extern long double __floorl (long double);
extern long double __frexpl (long double, int *);
extern long double __ldexpl (long double, int);
extern long double __log1pl (long double);
extern long double __nanl (const char *);
extern long double __rintl (long double);
extern long double __scalbnl (long double, int);
extern long double __sqrtl (long double x);
extern long double fabsl (long double x);
extern void __sincosl (long double, long double *, long double *);
extern long double __logbl (long double x);
extern long double __significandl (long double x);
#if __GNUC_PREREQ (4, 0)
extern inline long double __copysignl (long double x, long double y)
{ return __builtin_copysignl (x, y); }
#endif
#endif
/* Prototypes for functions of the IBM Accurate Mathematical Library. */
extern double __exp1 (double __x, double __xx, double __error);
extern double __sin (double __x);
extern double __cos (double __x);
extern int __branred (double __x, double *__a, double *__aa);
extern void __doasin (double __x, double __dx, double __v[]);
extern void __dubsin (double __x, double __dx, double __v[]);
extern void __dubcos (double __x, double __dx, double __v[]);
extern double __halfulp (double __x, double __y);
extern double __sin32 (double __x, double __res, double __res1);
extern double __cos32 (double __x, double __res, double __res1);
extern double __mpsin (double __x, double __dx);
extern double __mpcos (double __x, double __dx);
extern double __mpsin1 (double __x);
extern double __mpcos1 (double __x);
extern double __slowexp (double __x);
extern double __slowpow (double __x, double __y, double __z);
extern void __docos (double __x, double __dx, double __v[]);
#ifndef math_opt_barrier
# define math_opt_barrier(x) \
({ __typeof (x) __x = (x); __asm ("" : "+m" (__x)); __x; })
# define math_force_eval(x) \
({ __typeof (x) __x = (x); __asm __volatile__ ("" : : "m" (__x)); })
#endif
/* The standards only specify one variant of the fenv.h interfaces.
But at least for some architectures we can be more efficient if we
know what operations are going to be performed. Therefore we
define additional interfaces. By default they refer to the normal
interfaces. */
#define libc_feholdexcept(e) (void) feholdexcept (e)
#define libc_feholdexceptf(e) (void) feholdexcept (e)
#define libc_feholdexceptl(e) (void) feholdexcept (e)
#define libc_feholdexcept_setround(e, r) \
do { feholdexcept (e); fesetround (r); } while (0)
#define libc_feholdexcept_setroundf(e, r) \
do { feholdexcept (e); fesetround (r); } while (0)
#define libc_feholdexcept_setroundl(e, r) \
do { feholdexcept (e); fesetround (r); } while (0)
#define libc_fetestexcept(e) fetestexcept (e)
#define libc_fetestexceptf(e) fetestexcept (e)
#define libc_fetestexceptl(e) fetestexcept (e)
#define libc_fesetenv(e) (void) fesetenv (e)
#define libc_fesetenvf(e) (void) fesetenv (e)
#define libc_fesetenvl(e) (void) fesetenv (e)
#define libc_feupdateenv(e) (void) feupdateenv (e)
#define libc_feupdateenvf(e) (void) feupdateenv (e)
#define libc_feupdateenvl(e) (void) feupdateenv (e)
#define __nan(str) \
(__builtin_constant_p (str) && str[0] == '\0' ? NAN : __nan (str))
#define __nanf(str) \
(__builtin_constant_p (str) && str[0] == '\0' ? NAN : __nan (str))
#define __nanl(str) \
(__builtin_constant_p (str) && str[0] == '\0' ? NAN : __nan (str))
#endif /* _MATH_PRIVATE_H_ */
|
