summary refs log tree commit diff
path: root/sysdeps/i386/fpu/bits/mathinline.h
blob: c6b9331f9adc2600dd4425e64e3794b1041b5bad (plain) (blame)
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
/* 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@math.ualberta.ca>, 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 _BITS_MATHINLINE_H
#define _BITS_MATHINLINE_H	1


#if defined __USE_ISOC9X && defined __GNUC__ && __GNUC__ >= 2
/* 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.  */
# define isgreater(x, y) \
     ({ int __result;							      \
	__asm__ ("fucompp; fnstsw; testb $0x45, %%ah; setz %%al;"	      \
		 "andl $0x01, %0"					      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
	__result; })

# define isgreaterequal(x, y) \
     ({ int __result;							      \
	__asm__ ("fucompp; fnstsw; testb $0x05, %%ah; setz %%al;"	      \
		 "andl $0x01, %0"					      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
	__result; })

# define isless(x, y) \
     ({ int __result;							      \
	__asm__ ("fucompp; fnstsw; xorb $0x01, %%ah; testb $0x45, %%ah;"      \
		 "setz %%al; andl $0x01, %0"				      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
	__result; })

# define islessequal(x, y) \
     ({ int __result;							      \
	__asm__ ("fucompp; fnstsw; xorb $0x01, %%ah; testb $0x05, %%ah;"      \
		 "setz %%al; andl $0x01, %0"				      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
	__result; })

# define islessgreater(x, y) \
     ({ int __result;							      \
	__asm__ ("fucompp; fnstsw; testb $0x44, %%ah; setz %%al;"	      \
		 "andl $0x01, %0"					      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
	__result; })

# define isunordered(x, y) \
     ({ int __result;							      \
	__asm__ ("fucompp; fnstsw; sahf; setp %%al; andl $0x01, %0"	      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
	__result; })
#endif


#ifdef	__GNUC__
#if !defined __NO_MATH_INLINES && defined __OPTIMIZE__

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

/* A macro to define float, double, and long double versions of various
   math functions for the ix87 FPU.  FUNC is the function name (which will
   be suffixed with f and l for the float and long double version,
   respectively).  OP is the name of the FPU operation.  */

#if defined __USE_MISC || defined __USE_ISOC9X
# define __inline_mathop(func, op) \
  __inline_mathop_ (double, func, op)					      \
  __inline_mathop_ (float, __CONCAT(func,f), op)			      \
  __inline_mathop_ (long double, __CONCAT(func,l), op)
#else
# define __inline_mathop(func, op) \
  __inline_mathop_ (double, func, op)
#endif

#define __inline_mathop_(float_type, func, op) \
  __inline_mathop_decl_ (float_type, func, op, "0" (__x))


#if defined __USE_MISC || defined __USE_ISOC9X
# define __inline_mathop_decl(func, op, params...) \
  __inline_mathop_decl_ (double, func, op, params)			      \
  __inline_mathop_decl_ (float, __CONCAT(func,f), op, params)		      \
  __inline_mathop_decl_ (long double, __CONCAT(func,l), op, params)
#else
# define __inline_mathop_decl(func, op, params...) \
  __inline_mathop_decl_ (double, func, op, params)
#endif

#define __inline_mathop_decl_(float_type, func, op, params...) \
  __MATH_INLINE float_type func (float_type);				      \
  __MATH_INLINE float_type func (float_type __x)			      \
  {									      \
    register float_type __result;					      \
    __asm __volatile__ (op : "=t" (__result) : params);			      \
    return __result;							      \
  }


#if defined __USE_MISC || defined __USE_ISOC9X
# define __inline_mathcode(func, arg, code) \
  __inline_mathcode_ (double, func, arg, code)				      \
  __inline_mathcode_ (float, __CONCAT(func,f), arg, code)		      \
  __inline_mathcode_ (long double, __CONCAT(func,l), arg, code)
#else
# define __inline_mathcode(func, arg, code) \
  __inline_mathcode_ (double, func, arg, code)
#endif

#define __inline_mathcode_(float_type, func, arg, code) \
  __MATH_INLINE float_type func (float_type);				      \
  __MATH_INLINE float_type func (float_type arg)			      \
  {									      \
    code;								      \
  }


#if defined __USE_MISC || defined __USE_ISOC9X
# define __inline_mathcode2(func, arg1, arg2, code)			      \
  __inline_mathcode2_ (double, func, arg1, arg2, code)			      \
  __inline_mathcode2_ (float, __CONCAT(func,f), arg1, arg2, code)	      \
  __inline_mathcode2_ (long double, __CONCAT(func,l), arg1, arg2, code)
#else
# define __inline_mathcode2(func, arg1, arg2, code) \
  __inline_mathcode2_ (double, func, arg1, arg2, code)
#endif

#define __inline_mathcode2_(float_type, func, arg1, arg2, code) \
  __MATH_INLINE float_type func (float_type, float_type);		      \
  __MATH_INLINE float_type func (float_type arg1, float_type arg2)	      \
  {									      \
    code;								      \
  }


/* Optimized inline implementation, sometimes with reduced precision
   and/or argument range.  */

#define __expm1_code \
  register long double __value;						      \
  register long double __exponent;					      \
  register long double __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
__inline_mathcode_ (long double, __expm1l, __x, __expm1_code)


#define __exp_code \
  register long double __value;						      \
  register long double __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
__inline_mathcode (exp, __x, __exp_code)
__inline_mathcode_ (long double, __expl, __x, __exp_code)


__inline_mathcode (tan, __x, \
  register long double __value;						      \
  register long double __value2 __attribute__ ((unused));		      \
  __asm __volatile__							      \
    ("fptan"								      \
     : "=t" (__value2), "=u" (__value) : "0" (__x));			      \
  return __value)


#define __atan2_code \
  register long double __value;						      \
  __asm __volatile__							      \
    ("fpatan\n\t"							      \
     : "=t" (__value) : "0" (__x), "u" (__y) : "st(1)");		      \
  return __value
__inline_mathcode2 (atan2, __y, __x, __atan2_code)
__inline_mathcode2_ (long double, __atan2l, __y, __x, __atan2_code)


__inline_mathcode2 (fmod, __x, __y, \
  register long double __value;						      \
  __asm __volatile__							      \
    ("1:	fprem\n\t"						      \
     "fnstsw	%%ax\n\t"						      \
     "sahf\n\t"								      \
     "jp	1b"							      \
     : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");		      \
  return __value)


__inline_mathcode2 (pow, __x, __y, \
  register long double __value;						      \
  register long double __exponent;					      \
  long int __p = (long int) __y;					      \
  if (__x == 0.0 && __y > 0.0)						      \
    return 0.0;								      \
  if (__y == (double) __p)						      \
    {									      \
      long 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__							      \
    ("fyl2x" : "=t" (__value) : "0" (__x), "u" (1.0) : "st(1)");	      \
  __asm __volatile__							      \
    ("fmul	%%st(1)		# y * log2(x)\n\t"			      \
     "fst	%%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" (__y), "1" (__value));	      \
  __value += 1.0;							      \
  __asm __volatile__							      \
    ("fscale"								      \
     : "=t" (__value) : "0" (__value), "u" (__exponent));		      \
  return __value)


__inline_mathop (sqrt, "fsqrt")
__inline_mathop_ (long double, __sqrtl, "fsqrt")

#if defined __GNUC__ && (__GNUC__ > 2 || __GNUC__ == 2 && __GNUC_MINOR__ >= 8)
__inline_mathcode_ (fabs, __x, return __builtin_fabs (__x))
__inline_mathcode_ (fabsf, __x, return __builtin_fabsf (__x))
__inline_mathcode_ (fabsl, __x, return __builtin_fabsl (__x))
__inline_mathcode_ (__fabsl, __x, return __builtin_fabsl (__x))
#else
__inline_mathop (fabs, "fabs")
__inline_mathop_ (long double, __fabsl, "fabs")
#endif

/* The argument range of this inline version is reduced.  */
__inline_mathop (sin, "fsin")
/* The argument range of this inline version is reduced.  */
__inline_mathop (cos, "fcos")

__inline_mathop (atan, "fld1; fpatan")
__inline_mathop (log, "fldln2; fxch; fyl2x")
__inline_mathop (log10, "fldlg2; fxch; fyl2x")

__inline_mathcode (asin, __x, return __atan2l (__x, __sqrtl (1.0 - __x * __x)))
__inline_mathcode (acos, __x, return __atan2l (__sqrtl (1.0 - __x * __x), __x))

__inline_mathcode_ (long double, __sgn1l, __x, return __x >= 0.0 ? 1.0 : -1.0)


/* The argument range of the inline version of sinhl is slightly reduced.  */
__inline_mathcode (sinh, __x, \
  register long double __exm1 = __expm1l (__fabsl (__x));		      \
  return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1l (__x))

__inline_mathcode (cosh, __x, \
  register long double __ex = __expl (__x);				      \
  return 0.5 * (__ex + 1.0 / __ex))

__inline_mathcode (tanh, __x, \
  register long double __exm1 = __expm1l (-__fabsl (__x + __x));	      \
  return __exm1 / (__exm1 + 2.0) * __sgn1l (-__x))


__inline_mathcode (floor, __x, \
  register long double __value;						      \
  __volatile unsigned short int __cw;					      \
  __volatile unsigned short int __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)

__inline_mathcode (ceil, __x, \
  register long double __value;						      \
  __volatile unsigned short int __cw;					      \
  __volatile unsigned short int __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)

#define __ldexp_code \
  register long double __value;						      \
  __asm __volatile__							      \
    ("fscale"								      \
     : "=t" (__value) : "0" (__x), "u" ((long double) __y));		      \
  return __value

__MATH_INLINE double ldexp (double __x, int __y);
__MATH_INLINE double
ldexp (double __x, int __y)
{
  __ldexp_code;
}


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

__inline_mathop_decl (log2, "fyl2x", "u" (1.0), "0" (__x) : "st(1)")

__inline_mathcode (expm1, __x, __expm1_code)

/* We cannot rely on M_SQRT being defined.  So we do it for ourself
   here.  */
# define __M_SQRT2	_Mldbl(1.41421356237309504880)	/* sqrt(2) */

__inline_mathcode (log1p, __x, \
  register long double __value;						      \
  if (__fabsl (__x) >= 1.0 - 0.5 * __M_SQRT2)				      \
    __value = logl (1.0 + __x);						      \
  else									      \
    __asm __volatile__							      \
      ("fldln2\n\t"							      \
       "fxch\n\t"							      \
       "fyl2xp1"							      \
       : "=t" (__value) : "0" (__x));					      \
  return __value)


/* The argument range of the inline version of asinhl is slightly reduced.  */
__inline_mathcode (asinh, __x, \
  register long double  __y = __fabsl (__x);				      \
  return (log1pl (__y * __y / (__sqrtl (__y * __y + 1.0) + 1.0) + __y)	      \
	  * __sgn1l (__x)))

__inline_mathcode (acosh, __x, \
  return logl (__x + __sqrtl (__x - 1.0) * __sqrtl (__x + 1.0)))

__inline_mathcode (atanh, __x, \
  register long double __y = __fabsl (__x);				      \
  return (-0.5 * log1pl (-(__y + __y) / (1.0 + __y)) *			      \
	  __sgn1l (__x)))


/* The argument range of the inline version of hypotl is slightly reduced.  */
__inline_mathcode2 (hypot, __x, __y, return __sqrtl (__x * __x + __y * __y))

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

__MATH_INLINE float ldexpf (float __x, int __y);
__MATH_INLINE float
ldexpf (float __x, int __y)
{
  __ldexp_code;
}

__MATH_INLINE long double ldexpl (long double __x, int __y);
__MATH_INLINE long double
ldexpl (long double __x, int __y)
{
  __ldexp_code;
}

#endif


#ifdef __USE_MISC

__inline_mathcode2 (drem, __x, __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;
}

/* Miscellaneous functions */

__inline_mathcode (__sgn, __x, \
  return __x == 0.0 ? 0.0 : (__x > 0.0 ? 1.0 : -1.0))

__inline_mathcode (__coshm1, __x, \
  register long double __exm1 = __expm1l (__fabsl (__x));		      \
  return 0.5 * (__exm1 / (__exm1 + 1.0)) * __exm1)

__inline_mathcode (__acosh1p, __x, \
  return log1pl (__x + __sqrtl (__x) * __sqrtl (__x + 2.0)))

__inline_mathcode (__pow2, __x, \
  register long double __value;						      \
  register long double __exponent;					      \
  long int __p = (long int) __x;					      \
  if (__x == (long double) __p)						      \
    return ldexpl (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)

#define __sincos_code \
  register long double __cosr;						      \
  register long double __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 void __sincos (double __x, double *__sinx, double *__cosx);
__MATH_INLINE void
__sincos (double __x, double *__sinx, double *__cosx)
{
  __sincos_code;
}

__MATH_INLINE void __sincosf (float __x, float *__sinx, float *__cosx);
__MATH_INLINE void
__sincosf (float __x, float *__sinx, float *__cosx)
{
  __sincos_code;
}

__MATH_INLINE void __sincosl (long double __x, long double *__sinx,
			      long double *__cosx);
__MATH_INLINE void
__sincosl (long double __x, long double *__sinx, long double *__cosx)
{
  __sincos_code;
}

#endif /* __USE_MISC  */

/* Undefine some of the large macros which are not used anymore.  */
#undef __expm1_code
#undef __exp_code
#undef __atan2_code
#undef __sincos_code

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

#endif /* _BITS_MATHINLINE_H  */