about summary refs log tree commit diff
path: root/sysdeps/i386/fpu/bits/mathinline.h
blob: ab3b54def5368841f0519745e0cbdda29e94973e (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
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
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
/* Inline math functions for i387.
   Copyright (C) 1995,96,97,98,99,2000,2001,2003 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 Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 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
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

#ifndef _MATH_H
# error "Never use <bits/mathinline.h> directly; include <math.h> instead."
#endif

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


#if defined __USE_ISOC99 && defined __GNUC__ && __GNUC__ >= 2
# if __GNUC_PREREQ (2,97)
/* GCC 2.97 and up have builtins that actually can be used.  */
#  define isgreater(x, y) __builtin_isgreater (x, y)
#  define isgreaterequal(x, y) __builtin_isgreaterequal (x, y)
#  define isless(x, y) __builtin_isless (x, y)
#  define islessequal(x, y) __builtin_islessequal (x, y)
#  define islessgreater(x, y) __builtin_islessgreater (x, y)
#  define isunordered(x, y) __builtin_isunordered (x, y)
# else
/* ISO C99 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.  */
#  ifdef __i686__
/* For the PentiumPro and more recent processors we can provide
   better code.  */
#   define isgreater(x, y) \
     ({ register char __result;						      \
	__asm__ ("fucomip %%st(1), %%st; seta %%al"			      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");	      \
	__result; })
#   define isgreaterequal(x, y) \
     ({ register char __result;						      \
	__asm__ ("fucomip %%st(1), %%st; setae %%al"			      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");	      \
	__result; })

#   define isless(x, y) \
     ({ register char __result;						      \
	__asm__ ("fucomip %%st(1), %%st; seta %%al"			      \
		 : "=a" (__result) : "u" (x), "t" (y) : "cc", "st");	      \
	__result; })

#   define islessequal(x, y) \
     ({ register char __result;						      \
	__asm__ ("fucomip %%st(1), %%st; setae %%al"			      \
		 : "=a" (__result) : "u" (x), "t" (y) : "cc", "st");	      \
	__result; })

#   define islessgreater(x, y) \
     ({ register char __result;						      \
	__asm__ ("fucomip %%st(1), %%st; setne %%al"			      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");	      \
	__result; })

#   define isunordered(x, y) \
     ({ register char __result;						      \
	__asm__ ("fucomip %%st(1), %%st; setp %%al"			      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");	      \
	__result; })
#  else
/* This is the dumb, portable code for i386 and above.  */
#   define isgreater(x, y) \
     ({ register char __result;						      \
	__asm__ ("fucompp; fnstsw; testb $0x45, %%ah; setz %%al"	      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
	__result; })

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

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

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

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

#   define isunordered(x, y) \
     ({ register char __result;						      \
	__asm__ ("fucompp; fnstsw; sahf; setp %%al"			      \
		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
	__result; })
#  endif /* __i686__ */
# endif	/* GCC 2.97 */

/* The gcc, version 2.7 or below, has problems with all this inlining
   code.  So disable it for this version of the compiler.  */
# if __GNUC_PREREQ (2, 8)
/* Test for negative number.  Used in the signbit() macro.  */
__MATH_INLINE int
__signbitf (float __x) __THROW
{
  __extension__ union { float __f; int __i; } __u = { __f: __x };
  return __u.__i < 0;
}
__MATH_INLINE int
__signbit (double __x) __THROW
{
  __extension__ union { double __d; int __i[2]; } __u = { __d: __x };
  return __u.__i[1] < 0;
}
__MATH_INLINE int
__signbitl (long double __x) __THROW
{
  __extension__ union { long double __l; int __i[3]; } __u = { __l: __x };
  return (__u.__i[2] & 0x8000) != 0;
}
# endif
#endif


/* The gcc, version 2.7 or below, has problems with all this inlining
   code.  So disable it for this version of the compiler.  */
#if __GNUC_PREREQ (2, 8)

#if ((!defined __NO_MATH_INLINES || defined __LIBC_INTERNAL_MATH_INLINES) \
     && defined __OPTIMIZE__)

/* 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.
   We define two sets of macros.  The set with the additional NP
   doesn't add a prototype declaration.  */

#if defined __USE_MISC || defined __USE_ISOC99
# 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)
# define __inline_mathopNP(func, op) \
  __inline_mathopNP_ (double, func, op)					      \
  __inline_mathopNP_ (float, __CONCAT(func,f), op)			      \
  __inline_mathopNP_ (long double, __CONCAT(func,l), op)
#else
# define __inline_mathop(func, op) \
  __inline_mathop_ (double, func, op)
# define __inline_mathopNP(func, op) \
  __inline_mathopNP_ (double, func, op)
#endif

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


#if defined __USE_MISC || defined __USE_ISOC99
# 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)
# define __inline_mathop_declNP(func, op, params...) \
  __inline_mathop_declNP_ (double, func, op, params)			      \
  __inline_mathop_declNP_ (float, __CONCAT(func,f), op, params)		      \
  __inline_mathop_declNP_ (long double, __CONCAT(func,l), op, params)
#else
# define __inline_mathop_decl(func, op, params...) \
  __inline_mathop_decl_ (double, func, op, params)
# define __inline_mathop_declNP(func, op, params...) \
  __inline_mathop_declNP_ (double, func, op, params)
#endif

#define __inline_mathop_decl_(float_type, func, op, params...) \
  __MATH_INLINE float_type func (float_type) __THROW;			      \
  __inline_mathop_declNP_ (float_type, func, op, params)

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


#if defined __USE_MISC || defined __USE_ISOC99
# 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)
# define __inline_mathcodeNP(func, arg, code) \
  __inline_mathcodeNP_ (double, func, arg, code)				      \
  __inline_mathcodeNP_ (float, __CONCAT(func,f), arg, code)		      \
  __inline_mathcodeNP_ (long double, __CONCAT(func,l), arg, code)
# 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)
# define __inline_mathcodeNP2(func, arg1, arg2, code) \
  __inline_mathcodeNP2_ (double, func, arg1, arg2, code)			      \
  __inline_mathcodeNP2_ (float, __CONCAT(func,f), arg1, arg2, code)	      \
  __inline_mathcodeNP2_ (long double, __CONCAT(func,l), arg1, arg2, code)
# define __inline_mathcode3(func, arg1, arg2, arg3, code) \
  __inline_mathcode3_ (double, func, arg1, arg2, arg3, code)		      \
  __inline_mathcode3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code)	      \
  __inline_mathcode3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)
# define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \
  __inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code)		      \
  __inline_mathcodeNP3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code)	      \
  __inline_mathcodeNP3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)
#else
# define __inline_mathcode(func, arg, code) \
  __inline_mathcode_ (double, func, (arg), code)
# define __inline_mathcodeNP(func, arg, code) \
  __inline_mathcodeNP_ (double, func, (arg), code)
# define __inline_mathcode2(func, arg1, arg2, code) \
  __inline_mathcode2_ (double, func, arg1, arg2, code)
# define __inline_mathcodeNP2(func, arg1, arg2, code) \
  __inline_mathcodeNP2_ (double, func, arg1, arg2, code)
# define __inline_mathcode3(func, arg1, arg2, arg3, code) \
  __inline_mathcode3_ (double, func, arg1, arg2, arg3, code)
# define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \
  __inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code)
#endif

#define __inline_mathcode_(float_type, func, arg, code) \
  __MATH_INLINE float_type func (float_type) __THROW;			      \
  __inline_mathcodeNP_(float_type, func, arg, code)

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


#define __inline_mathcode2_(float_type, func, arg1, arg2, code) \
  __MATH_INLINE float_type func (float_type, float_type) __THROW;	      \
  __inline_mathcodeNP2_ (float_type, func, arg1, arg2, code)

#define __inline_mathcodeNP2_(float_type, func, arg1, arg2, code) \
  __MATH_INLINE float_type func (float_type arg1, float_type arg2) __THROW    \
  {									      \
    code;								      \
  }

#define __inline_mathcode3_(float_type, func, arg1, arg2, arg3, code) \
  __MATH_INLINE float_type func (float_type, float_type, float_type) __THROW; \
  __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code)

#define __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code) \
  __MATH_INLINE float_type func (float_type arg1, float_type arg2,	      \
				 float_type arg3) __THROW		      \
  {									      \
    code;								      \
  }
#endif


#if !defined __NO_MATH_INLINES && defined __OPTIMIZE__
/* Miscellaneous functions */

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

/* __FAST_MATH__ is defined by gcc -ffast-math.  */
#ifdef __FAST_MATH__
__inline_mathcode (__pow2, __x, \
  register long double __value;						      \
  register long double __exponent;					      \
  __extension__ long long int __p = (long long int) __x;		      \
  if (__x == (long double) __p)						      \
    {									      \
      __asm __volatile__						      \
	("fscale"							      \
	 : "=t" (__value) : "0" (1.0), "u" (__x));			      \
      return __value;							      \
    }									      \
  __asm __volatile__							      \
    ("fld	%%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)

# ifdef __USE_GNU
#  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) __THROW
{
  __sincos_code;
}

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

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


/* 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"			      \
     "fst	%%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;							      \
  __temp += __value;							      \
  return __temp ? __temp : __x
__inline_mathcodeNP_ (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"			      \
     "fst	%%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_mathcodeNP (exp, __x, __exp_code)
__inline_mathcodeNP_ (long double, __expl, __x, __exp_code)


__inline_mathcodeNP (tan, __x, \
  register long double __value;						      \
  register long double __value2 __attribute__ ((__unused__));		      \
  __asm __volatile__							      \
    ("fptan"								      \
     : "=t" (__value2), "=u" (__value) : "0" (__x));			      \
  return __value)
#endif /* __FAST_MATH__ */


#define __atan2_code \
  register long double __value;						      \
  __asm __volatile__							      \
    ("fpatan"								      \
     : "=t" (__value) : "0" (__x), "u" (__y) : "st(1)");		      \
  return __value
__inline_mathcodeNP2 (atan2, __y, __x, __atan2_code)
__inline_mathcodeNP2_ (long double, __atan2l, __y, __x, __atan2_code)


__inline_mathcodeNP2 (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)


#ifdef __FAST_MATH__
# if !__GNUC_PREREQ (3,3)
__inline_mathopNP (sqrt, "fsqrt")
__inline_mathopNP_ (long double, __sqrtl, "fsqrt")
#  define __libc_sqrtl(n) __sqrtl (n)
# else
#  define __libc_sqrtl(n) __builtin_sqrtl (n)
# endif
#endif

#if __GNUC_PREREQ (2, 8)
__inline_mathcodeNP_ (double, fabs, __x, return __builtin_fabs (__x))
__inline_mathcodeNP_ (float, fabsf, __x, return __builtin_fabsf (__x))
__inline_mathcodeNP_ (long double, fabsl, __x, return __builtin_fabsl (__x))
__inline_mathcodeNP_ (long double, __fabsl, __x, return __builtin_fabsl (__x))
#else
__inline_mathop (fabs, "fabs")
__inline_mathop_ (long double, __fabsl, "fabs")
#endif

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

__inline_mathop_declNP (log, "fldln2; fxch; fyl2x", "0" (__x) : "st(1)")
__inline_mathop_declNP (log10, "fldlg2; fxch; fyl2x", "0" (__x) : "st(1)")

__inline_mathcodeNP (asin, __x, return __atan2l (__x, __libc_sqrtl (1.0 - __x * __x)))
__inline_mathcodeNP (acos, __x, return __atan2l (__libc_sqrtl (1.0 - __x * __x), __x))
#endif /* __FAST_MATH__ */

__inline_mathop_declNP (atan, "fld1; fpatan", "0" (__x) : "st(1)")

__inline_mathcode_ (long double, __sgn1l, __x, \
  __extension__ union { long double __xld; unsigned int __xi[3]; } __n =      \
    { __xld: __x };							      \
  __n.__xi[2] = (__n.__xi[2] & 0x8000) | 0x3fff;			      \
  __n.__xi[1] = 0x80000000;						      \
  __n.__xi[0] = 0;							      \
  return __n.__xld)


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

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

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

__inline_mathcodeNP (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_mathcodeNP (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)

#ifdef __FAST_MATH__
# 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) __THROW
{
  __ldexp_code;
}
#endif


/* Optimized versions for some non-standardized functions.  */
#if defined __USE_ISOC99 || defined __USE_MISC

# ifdef __FAST_MATH__
__inline_mathcodeNP (expm1, __x, __expm1_code)

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

__inline_mathcodeNP (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) : "st(1)");				      \
  return __value)


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

__inline_mathcodeNP (acosh, __x, \
  return logl (__x + __libc_sqrtl (__x - 1.0) * __libc_sqrtl (__x + 1.0)))

__inline_mathcodeNP (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_mathcodeNP2 (hypot, __x, __y,
		      return __libc_sqrtl (__x * __x + __y * __y))

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

# endif
#endif

#ifdef __USE_ISOC99
#ifdef __FAST_MATH__
__inline_mathop_declNP (log2, "fld1; fxch; fyl2x", "0" (__x) : "st(1)")

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

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

__inline_mathcodeNP3 (fma, __x, __y, __z, return (__x * __y) + __z)

__inline_mathopNP (rint, "frndint")
#endif /* __FAST_MATH__ */

#define __lrint_code \
  long int __lrintres;							      \
  __asm__ __volatile__							      \
    ("fistpl %0"							      \
     : "=m" (__lrintres) : "t" (__x) : "st");				      \
  return __lrintres
__MATH_INLINE long int
lrintf (float __x) __THROW
{
  __lrint_code;
}
__MATH_INLINE long int
lrint (double __x) __THROW
{
  __lrint_code;
}
__MATH_INLINE long int
lrintl (long double __x) __THROW
{
  __lrint_code;
}
#undef __lrint_code

#define __llrint_code \
  long long int __llrintres;						      \
  __asm__ __volatile__							      \
    ("fistpll %0"							      \
     : "=m" (__llrintres) : "t" (__x) : "st");				      \
  return __llrintres
__MATH_INLINE long long int
llrintf (float __x) __THROW
{
  __llrint_code;
}
__MATH_INLINE long long int
llrint (double __x) __THROW
{
  __llrint_code;
}
__MATH_INLINE long long int
llrintl (long double __x) __THROW
{
  __llrint_code;
}
#undef __llrint_code

#endif


#ifdef __USE_MISC

__inline_mathcodeNP2 (drem, __x, __y, \
  register double __value;						      \
  register int __clobbered;						      \
  __asm __volatile__							      \
    ("1:	fprem1\n\t"						      \
     "fstsw	%%ax\n\t"						      \
     "sahf\n\t"								      \
     "jp	1b"							      \
     : "=t" (__value), "=&a" (__clobbered) : "0" (__x), "u" (__y) : "cc");    \
  return __value)


/* This function is used in the `isfinite' macro.  */
__MATH_INLINE int
__finite (double __x) __THROW
{
  return (__extension__
	  (((((union { double __d; int __i[2]; }) {__d: __x}).__i[1]
	     | 0x800fffffu) + 1) >> 31));
}

/* Miscellaneous functions */
#ifdef __FAST_MATH__
__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 + __libc_sqrtl (__x) * __libc_sqrtl (__x + 2.0)))

#endif /* __FAST_MATH__ */
#endif /* __USE_MISC  */

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

#endif /* __NO_MATH_INLINES  */


/* This code is used internally in the GNU libc.  */
#ifdef __LIBC_INTERNAL_MATH_INLINES
__inline_mathop (__ieee754_sqrt, "fsqrt")
__inline_mathcode2 (__ieee754_atan2, __y, __x,
		    register long double __value;
		    __asm __volatile__ ("fpatan\n\t"
					: "=t" (__value)
					: "0" (__x), "u" (__y) : "st(1)");
		    return __value;)
#endif

#endif /* __GNUC__  */