summaryrefslogtreecommitdiff
path: root/sysdeps/i386/fpu/__math.h
blob: d5945e8ca2e641307faea78247f4deff26bea8ec (plain)
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
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
/* Inline math functions for i387.
   Copyright (C) 1995, 1996, 1997 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by John C. Bowman <bowman@ipp-garching.mpg.de>, 1995.

   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.  */

#ifndef __MATH_H
#define __MATH_H	1

#if defined __GNUG__ && \
    (__GNUC__ < 2 || (__GNUC__ == 2 && __GNUC_MINOR__ <= 7))
/* gcc 2.7.2 and 2.7.2.1 have problems with inlining `long double'
   functions so we disable this now.  */
#undef __NO_MATH_INLINES
#define __NO_MATH_INLINES
#endif

#ifdef	__GNUC__
#ifndef __NO_MATH_INLINES

#ifdef __cplusplus
#define	__MATH_INLINE __inline
#else
#define	__MATH_INLINE extern __inline
#endif

__MATH_INLINE double cos (double);
__MATH_INLINE double sin (double);


__MATH_INLINE double __expm1 (double __x);
__MATH_INLINE double
__expm1 (double __x)
{
  register double __value, __exponent, __temp;
  __asm __volatile__
    ("fldl2e			# e^x - 1 = 2^(x * log2(e)) - 1\n\t"
     "fmul	%%st(1)		# x * log2(e)\n\t"
     "fstl	%%st(1)\n\t"
     "frndint			# int(x * log2(e))\n\t"
     "fxch\n\t"
     "fsub	%%st(1)		# fract(x * log2(e))\n\t"
     "f2xm1			# 2^(fract(x * log2(e))) - 1\n\t"
     "fscale			# 2^(x * log2(e)) - 2^(int(x * log2(e)))\n\t"
     : "=t" (__value), "=u" (__exponent) : "0" (__x));
  __asm __volatile__
    ("fscale			# 2^int(x * log2(e))\n\t"
     : "=t" (__temp) : "0" (1.0), "u" (__exponent));
  __temp -= 1.0;

  return __temp + __value;
}

__MATH_INLINE double __sgn1 (double __x);
__MATH_INLINE double
__sgn1 (double __x)
{
  return __x >= 0.0 ? 1.0 : -1.0;
}

__MATH_INLINE double sqrt (double __x);
__MATH_INLINE double
sqrt (double __x)
{
  register double __value;
  __asm __volatile__
    ("fsqrt"
     : "=t" (__value) : "0" (__x));

  return __value;
}

__MATH_INLINE double fabs (double __x);
__MATH_INLINE double
fabs (double __x)
{
  register double __value;
  __asm __volatile__
    ("fabs"
     : "=t" (__value) : "0" (__x));

  return __value;
}

/* The argument range of this inline version is limited.  */
__MATH_INLINE double sin (double __x);
__MATH_INLINE double
sin (double __x)
{
  register double __value;
  __asm __volatile__
    ("fsin"
     : "=t" (__value) : "0" (__x));

  return __value;
}

/* The argument range of this inline version is limited.  */
__MATH_INLINE double cos (double __x);
__MATH_INLINE double
cos (double __x)
{
  register double __value;
  __asm __volatile__
    ("fcos"
     : "=t" (__value): "0" (__x));

  return __value;
}

__MATH_INLINE double tan (double __x);
__MATH_INLINE double
tan (double __x)
{
  register double __value;
  register double __value2 __attribute__ ((unused));
  __asm __volatile__
    ("fptan"
     : "=t" (__value2), "=u" (__value) : "0" (__x));

  return __value;
}

__MATH_INLINE double atan2 (double __y, double __x);
__MATH_INLINE double
atan2 (double __y, double __x)
{
  register double __value;
  __asm __volatile__
    ("fpatan\n\t"
     "fldl %%st(0)"
     : "=t" (__value) : "0" (__x), "u" (__y));

  return __value;
}

__MATH_INLINE double asin (double __x);
__MATH_INLINE double
asin (double __x)
{
  return atan2 (__x, sqrt (1.0 - __x * __x));
}

__MATH_INLINE double acos (double __x);
__MATH_INLINE double
acos (double __x)
{
  return atan2 (sqrt (1.0 - __x * __x), __x);
}

__MATH_INLINE double atan (double __x);
__MATH_INLINE double
atan (double __x)
{
  register double __value;
  __asm __volatile__
    ("fld1\n\t"
     "fpatan"
     : "=t" (__value) : "0" (__x));

  return __value;
}

__MATH_INLINE double exp (double __x);
__MATH_INLINE double
exp (double __x)
{
  register double __value, __exponent;
  __asm __volatile__
    ("fldl2e			# e^x = 2^(x * log2(e))\n\t"
     "fmul	%%st(1)		# x * log2(e)\n\t"
     "fstl	%%st(1)\n\t"
     "frndint			# int(x * log2(e))\n\t"
     "fxch\n\t"
     "fsub	%%st(1)		# fract(x * log2(e))\n\t"
     "f2xm1			# 2^(fract(x * log2(e))) - 1\n\t"
     : "=t" (__value), "=u" (__exponent) : "0" (__x));
  __value += 1.0;
  __asm __volatile__
    ("fscale"
     : "=t" (__value) : "0" (__value), "u" (__exponent));

  return __value;
}

__MATH_INLINE double sinh (double __x);
__MATH_INLINE double
sinh (double __x)
{
  register double __exm1 = __expm1 (fabs (__x));

  return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1 (__x);
}

__MATH_INLINE double cosh (double __x);
__MATH_INLINE double
cosh (double __x)
{
  register double __ex = exp (__x);

  return 0.5 * (__ex + 1.0 / __ex);
}

__MATH_INLINE double tanh (double __x);
__MATH_INLINE double
tanh (double __x)
{
  register double __exm1 = __expm1 (-fabs (__x + __x));

  return __exm1 / (__exm1 + 2.0) * __sgn1 (-__x);
}

__MATH_INLINE double log (double __x);
__MATH_INLINE double
log (double __x)
{
  register double __value;
  __asm __volatile__
    ("fldln2\n\t"
     "fxch\n\t"
     "fyl2x"
     : "=t" (__value) : "0" (__x));

  return __value;
}

__MATH_INLINE double log10 (double __x);
__MATH_INLINE double
log10 (double __x)
{
  register double __value;
  __asm __volatile__
    ("fldlg2\n\t"
     "fxch\n\t"
     "fyl2x"
     : "=t" (__value) : "0" (__x));

  return __value;
}

__MATH_INLINE double __log2 (double __x);
__MATH_INLINE double
__log2 (double __x)
{
  register double __value;
  __asm __volatile__
    ("fld1\n\t"
     "fxch\n\t"
     "fyl2x"
     : "=t" (__value) : "0" (__x));

  return __value;
}

__MATH_INLINE double fmod (double __x, double __y);
__MATH_INLINE double
fmod (double __x, double __y)
{
  register double __value;
  __asm __volatile__
    ("1:	fprem\n\t"
     "fstsw	%%ax\n\t"
     "sahf\n\t"
     "jp	1b"
     : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");

  return __value;
}

__MATH_INLINE double ldexp (double __x, int __y);
__MATH_INLINE double
ldexp (double __x, int __y)
{
  register double __value;
  __asm __volatile__
    ("fscale"
     : "=t" (__value) : "0" (__x), "u" ((double) __y));

  return __value;
}

__MATH_INLINE double pow (double __x, double __y);
__MATH_INLINE double
pow (double __x, double __y)
{
  register double __value, __exponent;
  long __p = (long) __y;

  if (__x == 0.0 && __y > 0.0)
    return 0.0;
  if (__y == (double) __p)
    {
      double __r = 1.0;
      if (__p == 0)
	return 1.0;
      if (__p < 0)
	{
	  __p = -__p;
	  __x = 1.0 / __x;
	}
      while (1)
	{
	  if (__p & 1)
	    __r *= __x;
	  __p >>= 1;
	  if (__p == 0)
	    return __r;
	  __x *= __x;
	}
      /* NOTREACHED */
    }
  __asm __volatile__
    ("fmul	%%st(1)		# y * log2(x)\n\t"
     "fstl	%%st(1)\n\t"
     "frndint			# int(y * log2(x))\n\t"
     "fxch\n\t"
     "fsub	%%st(1)		# fract(y * log2(x))\n\t"
     "f2xm1			# 2^(fract(y * log2(x))) - 1\n\t"
     : "=t" (__value), "=u" (__exponent) :  "0" (__log2 (__x)), "1" (__y));
  __value += 1.0;
  __asm __volatile__
    ("fscale"
     : "=t" (__value) : "0" (__value), "u" (__exponent));

  return __value;
}

__MATH_INLINE double floor (double __x);
__MATH_INLINE double
floor (double __x)
{
  register double __value;
  __volatile unsigned short int __cw, __cwtmp;

  __asm __volatile ("fnstcw %0" : "=m" (__cw));
  __cwtmp = (__cw & 0xf3ff) | 0x0400; /* rounding down */
  __asm __volatile ("fldcw %0" : : "m" (__cwtmp));
  __asm __volatile ("frndint" : "=t" (__value) : "0" (__x));
  __asm __volatile ("fldcw %0" : : "m" (__cw));

  return __value;
}

__MATH_INLINE double ceil (double __x);
__MATH_INLINE double
ceil (double __x)
{
  register double __value;
  __volatile unsigned short int __cw, __cwtmp;

  __asm __volatile ("fnstcw %0" : "=m" (__cw));
  __cwtmp = (__cw & 0xf3ff) | 0x0800; /* rounding up */
  __asm __volatile ("fldcw %0" : : "m" (__cwtmp));
  __asm __volatile ("frndint" : "=t" (__value) : "0" (__x));
  __asm __volatile ("fldcw %0" : : "m" (__cw));

  return __value;
}


/* Optimized versions for some non-standardized functions.  */
#if defined __USE_ISOC9X || defined __USE_MISC

__MATH_INLINE double hypot (double __x, double __y);
__MATH_INLINE double
hypot (double __x, double __y)
{
  return sqrt (__x * __x + __y * __y);
}

__MATH_INLINE double log1p (double __x);
__MATH_INLINE double
log1p (double __x)
{
  register double __value;

  if (fabs (__x) >= 1.0 - 0.5 * M_SQRT2)
    __value = log (1.0 + __x);
  else
    __asm __volatile__
      ("fldln2\n\t"
       "fxch\n\t"
       "fyl2xp1"
       : "=t" (__value) : "0" (__x));

  return __value;
}

__MATH_INLINE double asinh (double __x);
__MATH_INLINE double
asinh (double __x)
{
  register double __y = fabs (__x);

  return log1p ((__y * __y / (sqrt (__y * __y + 1.0) + 1.0) + __y)
		* __sgn1 (__x));
}

__MATH_INLINE double acosh (double __x);
__MATH_INLINE double
acosh (double __x)
{
  return log (__x + sqrt (__x - 1.0) * sqrt (__x + 1.0));
}

__MATH_INLINE double atanh (double __x);
__MATH_INLINE double
atanh (double __x)
{
  register double __y = fabs (__x);

  return -0.5 * __log1p (-(__y + __y) / (1.0 + __y)) * __sgn1 (__x);
}

__MATH_INLINE double logb (double __x);
__MATH_INLINE double
logb (double __x)
{
  register double __value, __junk;
  __asm __volatile__
    ("fxtract\n\t"
     : "=t" (__junk), "=u" (__value) : "0" (__x));

  return __value;
}

__MATH_INLINE double drem (double __x, double __y);
__MATH_INLINE double
drem (double __x, double __y)
{
  register double __value;
  __asm __volatile__
    ("1:	fprem1\n\t"
     "fstsw	%%ax\n\t"
     "sahf\n\t"
     "jp	1b"
     : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");

  return __value;
}

/* This function is used in the `isfinite' macro.  */
__MATH_INLINE int __finite (double __x);
__MATH_INLINE int
__finite (double __x)
{
  register int __result;
  __asm__ __volatile__
    ("orl	$0x800fffff, %0\n\t"
     "incl	%0\n\t"
     "shrl	$31, %0"
     : "=q" (__result) : "0" (((int *) &__x)[1]));
  return __result;
}


/* ISO C 9X defines some macros to perform unordered comparisons.  The
   ix87 FPU supports this with special opcodes and we should use them.
   These must not be inline functions since we have to be able to handle
   all floating-point types.  */
#undef isgreater
#define isgreater(x, y) \
     ({ int result;							      \
	__asm__ ("fucompp; fnstsw; andb $0x45, %%ah; setz %%al;"	      \
		 "andl $0xff, %0"					      \
		 : "=a" (result) : "t" (x), "u" (y) : "cc");		      \
	result; })

#undef isgreaterequal
#define isgreaterequal(x, y) \
     ({ int result;							      \
	__asm__ ("fucompp; fnstsw; testb $0x05, %%ah; setz %%al;"	      \
		 "andl $0xff, %0"					      \
		 : "=a" (result) : "t" (x), "u" (y) : "cc");		      \
	result; })

#undef isless
#define isless(x, y) \
     ({ int result;							      \
	__asm__ ("fucompp; fnstsw; xorb $0x01, %%ah; testb $0x45, %%ah;"      \
		 "setz %%al; andl $0xff, %0"				      \
		 : "=a" (result) : "t" (x), "u" (y) : "cc");		      \
	result; })

#undef islessequal
#define islessequal(x, y) \
     ({ int result;							      \
	__asm__ ("fucompp; fnstsw; xorb $0x01, %%ah; testb $0x05, %%ah;"      \
		 "setz %%al; andl $0xff, %0"				      \
		 : "=a" (result) : "t" (x), "u" (y) : "cc");		      \
	result; })

#undef islessgreater
#define islessgreater(x, y) \
     ({ int result;							      \
	__asm__ ("fucompp; fnstsw; testb $0x44, %%ah; setz %%al;"	      \
		 "andl $0xff, %0"					      \
		 : "=a" (result) : "t" (x), "u" (y) : "cc");		      \
	result; })

#undef isunordered
#define isunordered(x, y) \
     ({ int result;							      \
	__asm__ ("fucompp; fnstsw; sahf; setp %%al; andl $0xff, %0"	      \
		 : "=a" (result) : "t" (x), "u" (y) : "cc");		      \
	result; })
#endif


#ifdef __USE_MISC
__MATH_INLINE double coshm1 (double __x);
__MATH_INLINE double
coshm1 (double __x)
{
  register double __exm1 = __expm1 (fabs (__x));

  return 0.5 * (__exm1 / (__exm1 + 1.0)) * __exm1;
}

__MATH_INLINE double acosh1p (double __x);
__MATH_INLINE double
acosh1p (double __x)
{
  return __log1p (__x + sqrt (__x) * sqrt (__x + 2.0));
}

__MATH_INLINE void sincos (double __x, double *__sinx, double *__cosx);
__MATH_INLINE void
sincos (double __x, double *__sinx, double *__cosx)
{
  register double __cosr, __sinr;
  __asm __volatile__
    ("fsincos\n\t"
     "fnstsw	%%ax\n\t"
     "testl	$0x400, %%eax\n\t"
     "jz	1f\n\t"
     "fldpi\n\t"
     "fadd	%%st(0)\n\t"
     "fxch	%%st(1)\n\t"
     "2: fprem1\n\t"
     "fnstsw	%%ax\n\t"
     "testl	$0x400, %%eax\n\t"
     "jnz	2b\n\t"
     "fstp	%%st(1)\n\t"
     "fsincos\n\t"
     "1:"
     : "=t" (__cosr), "=u" (__sinr) : "0" (__x));

  *__sinx = __sinr;
  *__cosx = __cosr;
}

__MATH_INLINE double sgn (double __x);
__MATH_INLINE double
sgn (double __x)
{
  return __x == 0.0 ? 0.0 : (__x > 0.0 ? 1.0 : -1.0);
}

__MATH_INLINE double pow2 (double __x);
__MATH_INLINE double
pow2 (double __x)
{
  register double __value, __exponent;
  long __p = (long) __x;

  if (__x == (double) __p)
    return ldexp (1.0, __p);

  __asm __volatile__
    ("fldl	%%st(0)\n\t"
     "frndint			# int(x)\n\t"
     "fxch\n\t"
     "fsub	%%st(1)		# fract(x)\n\t"
     "f2xm1			# 2^(fract(x)) - 1\n\t"
     : "=t" (__value), "=u" (__exponent) : "0" (__x));
  __value += 1.0;
  __asm __volatile__
    ("fscale"
     : "=t" (__value) : "0" (__value), "u" (__exponent));

  return __value;
}

#endif /* __USE_MISC  */

#endif /* __NO_MATH_INLINES  */
#endif /* __GNUC__  */

#endif /* __MATH_H  */