aboutsummaryrefslogtreecommitdiff
path: root/sysdeps/i386/fpu/e_pow.S
blob: a3280bf14480fa1aceaaa0ee975b5032b7e2a648 (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
/* ix87 specific implementation of pow function.
   Copyright (C) 1996-2021 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 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, see
   <https://www.gnu.org/licenses/>.  */

#include <machine/asm.h>
#include <i386-math-asm.h>
#include <libm-alias-finite.h>

	.section .rodata.cst8,"aM",@progbits,8

	.p2align 3
	.type one,@object
one:	.double 1.0
	ASM_SIZE_DIRECTIVE(one)
	.type limit,@object
limit:	.double 0.29
	ASM_SIZE_DIRECTIVE(limit)
	.type p63,@object
p63:	.byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
	ASM_SIZE_DIRECTIVE(p63)
	.type p10,@object
p10:	.byte 0, 0, 0, 0, 0, 0, 0x90, 0x40
	ASM_SIZE_DIRECTIVE(p10)

	.section .rodata.cst16,"aM",@progbits,16

	.p2align 3
	.type infinity,@object
inf_zero:
infinity:
	.byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
	ASM_SIZE_DIRECTIVE(infinity)
	.type zero,@object
zero:	.double 0.0
	ASM_SIZE_DIRECTIVE(zero)
	.type minf_mzero,@object
minf_mzero:
minfinity:
	.byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
mzero:
	.byte 0, 0, 0, 0, 0, 0, 0, 0x80
	ASM_SIZE_DIRECTIVE(minf_mzero)
DEFINE_DBL_MIN

#ifdef PIC
# define MO(op) op##@GOTOFF(%ecx)
# define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
#else
# define MO(op) op
# define MOX(op,x,f) op(,x,f)
#endif

	.text
ENTRY(__ieee754_pow)
	fldl	12(%esp)	// y
	fxam

#ifdef	PIC
	LOAD_PIC_REG (cx)
#endif

	fnstsw
	movb	%ah, %dl
	andb	$0x45, %ah
	cmpb	$0x40, %ah	// is y == 0 ?
	je	11f

	cmpb	$0x05, %ah	// is y == ±inf ?
	je	12f

	cmpb	$0x01, %ah	// is y == NaN ?
	je	30f

	fldl	4(%esp)		// x : y

	subl	$8,%esp
	cfi_adjust_cfa_offset (8)

	fxam
	fnstsw
	movb	%ah, %dh
	andb	$0x45, %ah
	cmpb	$0x40, %ah
	je	20f		// x is ±0

	cmpb	$0x05, %ah
	je	15f		// x is ±inf

	cmpb	$0x01, %ah
	je	32f		// x is NaN

	fxch			// y : x

	/* fistpll raises invalid exception for |y| >= 1L<<63.  */
	fld	%st		// y : y : x
	fabs			// |y| : y : x
	fcompl	MO(p63)		// y : x
	fnstsw
	sahf
	jnc	2f

	/* First see whether `y' is a natural number.  In this case we
	   can use a more precise algorithm.  */
	fld	%st		// y : y : x
	fistpll	(%esp)		// y : x
	fildll	(%esp)		// int(y) : y : x
	fucomp	%st(1)		// y : x
	fnstsw
	sahf
	jne	3f

	/* OK, we have an integer value for y.  If large enough that
	   errors may propagate out of the 11 bits excess precision, use
	   the algorithm for real exponent instead.  */
	fld	%st		// y : y : x
	fabs			// |y| : y : x
	fcompl	MO(p10)		// y : x
	fnstsw
	sahf
	jnc	2f
	popl	%eax
	cfi_adjust_cfa_offset (-4)
	popl	%edx
	cfi_adjust_cfa_offset (-4)
	orl	$0, %edx
	fstp	%st(0)		// x
	jns	4f		// y >= 0, jump
	fdivrl	MO(one)		// 1/x		(now referred to as x)
	negl	%eax
	adcl	$0, %edx
	negl	%edx
4:	fldl	MO(one)		// 1 : x
	fxch

	/* If y is even, take the absolute value of x.  Otherwise,
	   ensure all intermediate values that might overflow have the
	   sign of x.  */
	testb	$1, %al
	jnz	6f
	fabs

6:	shrdl	$1, %edx, %eax
	jnc	5f
	fxch
	fabs
	fmul	%st(1)		// x : ST*x
	fxch
5:	fld	%st		// x : x : ST*x
	fabs			// |x| : x : ST*x
	fmulp			// |x|*x : ST*x
	shrl	$1, %edx
	movl	%eax, %ecx
	orl	%edx, %ecx
	jnz	6b
	fstp	%st(0)		// ST*x
#ifdef	PIC
	LOAD_PIC_REG (cx)
#endif
	DBL_NARROW_EVAL_UFLOW_NONNAN
	ret

	/* y is ±NAN */
30:	fldl	4(%esp)		// x : y
	fldl	MO(one)		// 1.0 : x : y
	fucomp	%st(1)		// x : y
	fnstsw
	sahf
	je	31f
	fxch			// y : x
31:	fstp	%st(1)
	ret

	cfi_adjust_cfa_offset (8)
32:	addl	$8, %esp
	cfi_adjust_cfa_offset (-8)
	fstp	%st(1)
	ret

	cfi_adjust_cfa_offset (8)
	.align ALIGNARG(4)
2:	// y is a large integer (absolute value at least 1L<<10), but
	// may be odd unless at least 1L<<64.  So it may be necessary
	// to adjust the sign of a negative result afterwards.
	fxch			// x : y
	fabs			// |x| : y
	fxch			// y : x
	.align ALIGNARG(4)
3:	/* y is a real number.  */
	fxch			// x : y
	fldl	MO(one)		// 1.0 : x : y
	fldl	MO(limit)	// 0.29 : 1.0 : x : y
	fld	%st(2)		// x : 0.29 : 1.0 : x : y
	fsub	%st(2)		// x-1 : 0.29 : 1.0 : x : y
	fabs			// |x-1| : 0.29 : 1.0 : x : y
	fucompp			// 1.0 : x : y
	fnstsw
	fxch			// x : 1.0 : y
	sahf
	ja	7f
	fsub	%st(1)		// x-1 : 1.0 : y
	fyl2xp1			// log2(x) : y
	jmp	8f

7:	fyl2x			// log2(x) : y
8:	fmul	%st(1)		// y*log2(x) : y
	fst	%st(1)		// y*log2(x) : y*log2(x)
	frndint			// int(y*log2(x)) : y*log2(x)
	fsubr	%st, %st(1)	// int(y*log2(x)) : fract(y*log2(x))
	fxch			// fract(y*log2(x)) : int(y*log2(x))
	f2xm1			// 2^fract(y*log2(x))-1 : int(y*log2(x))
	faddl	MO(one)		// 2^fract(y*log2(x)) : int(y*log2(x))

	// Before scaling, we must negate if x is negative and y is an
	// odd integer.
	testb	$2, %dh
	jz	291f
	// x is negative.  If y is an odd integer, negate the result.
	fldl	20(%esp)	// y : 2^fract(y*log2(x)) : int(y*log2(x))
	fld	%st		// y : y : 2^fract(y*log2(x)) : int(y*log2(x))
	fabs			// |y| : y : 2^fract(y*log2(x)) : int(y*log2(x))
	fcompl	MO(p63)		// y : 2^fract(y*log2(x)) : int(y*log2(x))
	fnstsw
	sahf
	jnc	290f

	// We must find out whether y is an odd integer.
	fld	%st		// y : y : 2^fract(y*log2(x)) : int(y*log2(x))
	fistpll	(%esp)		// y : 2^fract(y*log2(x)) : int(y*log2(x))
	fildll	(%esp)		// int(y) : y : 2^fract(y*log2(x)) : int(y*log2(x))
	fucompp			// 2^fract(y*log2(x)) : int(y*log2(x))
	fnstsw
	sahf
	jne	291f

	// OK, the value is an integer, but is it odd?
	popl	%eax
	cfi_adjust_cfa_offset (-4)
	popl	%edx
	cfi_adjust_cfa_offset (-4)
	andb	$1, %al
	jz	292f		// jump if not odd
	// It's an odd integer.
	fchs
	jmp	292f

	cfi_adjust_cfa_offset (8)
290:	fstp	%st(0)		// 2^fract(y*log2(x)) : int(y*log2(x))
291:	addl	$8, %esp
	cfi_adjust_cfa_offset (-8)
292:	fscale			// +/- 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
	fstp	%st(1)		// +/- 2^fract(y*log2(x))*2^int(y*log2(x))
	DBL_NARROW_EVAL_UFLOW_NONNAN
	ret


	// pow(x,±0) = 1
	.align ALIGNARG(4)
11:	fstp	%st(0)		// pop y
	fldl	MO(one)
	ret

	// y == ±inf
	.align ALIGNARG(4)
12:	fstp	%st(0)		// pop y
	fldl	MO(one)		// 1
	fldl	4(%esp)		// x : 1
	fabs			// abs(x) : 1
	fucompp			// < 1, == 1, or > 1
	fnstsw
	andb	$0x45, %ah
	cmpb	$0x45, %ah
	je	13f		// jump if x is NaN

	cmpb	$0x40, %ah
	je	14f		// jump if |x| == 1

	shlb	$1, %ah
	xorb	%ah, %dl
	andl	$2, %edx
	fldl	MOX(inf_zero, %edx, 4)
	ret

	.align ALIGNARG(4)
14:	fldl	MO(one)
	ret

	.align ALIGNARG(4)
13:	fldl	4(%esp)		// load x == NaN
	ret

	cfi_adjust_cfa_offset (8)
	.align ALIGNARG(4)
	// x is ±inf
15:	fstp	%st(0)		// y
	testb	$2, %dh
	jz	16f		// jump if x == +inf

	// fistpll raises invalid exception for |y| >= 1L<<63, so test
	// that (in which case y is certainly even) before testing
	// whether y is odd.
	fld	%st		// y : y
	fabs			// |y| : y
	fcompl	MO(p63)		// y
	fnstsw
	sahf
	jnc	16f

	// We must find out whether y is an odd integer.
	fld	%st		// y : y
	fistpll	(%esp)		// y
	fildll	(%esp)		// int(y) : y
	fucompp			// <empty>
	fnstsw
	sahf
	jne	17f

	// OK, the value is an integer.
	popl	%eax
	cfi_adjust_cfa_offset (-4)
	popl	%edx
	cfi_adjust_cfa_offset (-4)
	andb	$1, %al
	jz	18f		// jump if not odd
	// It's an odd integer.
	shrl	$31, %edx
	fldl	MOX(minf_mzero, %edx, 8)
	ret

	cfi_adjust_cfa_offset (8)
	.align ALIGNARG(4)
16:	fcompl	MO(zero)
	addl	$8, %esp
	cfi_adjust_cfa_offset (-8)
	fnstsw
	shrl	$5, %eax
	andl	$8, %eax
	fldl	MOX(inf_zero, %eax, 1)
	ret

	cfi_adjust_cfa_offset (8)
	.align ALIGNARG(4)
17:	shll	$30, %edx	// sign bit for y in right position
	addl	$8, %esp
	cfi_adjust_cfa_offset (-8)
18:	shrl	$31, %edx
	fldl	MOX(inf_zero, %edx, 8)
	ret

	cfi_adjust_cfa_offset (8)
	.align ALIGNARG(4)
	// x is ±0
20:	fstp	%st(0)		// y
	testb	$2, %dl
	jz	21f		// y > 0

	// x is ±0 and y is < 0.  We must find out whether y is an odd integer.
	testb	$2, %dh
	jz	25f

	// fistpll raises invalid exception for |y| >= 1L<<63, so test
	// that (in which case y is certainly even) before testing
	// whether y is odd.
	fld	%st		// y : y
	fabs			// |y| : y
	fcompl	MO(p63)		// y
	fnstsw
	sahf
	jnc	25f

	fld	%st		// y : y
	fistpll	(%esp)		// y
	fildll	(%esp)		// int(y) : y
	fucompp			// <empty>
	fnstsw
	sahf
	jne	26f

	// OK, the value is an integer.
	popl	%eax
	cfi_adjust_cfa_offset (-4)
	popl	%edx
	cfi_adjust_cfa_offset (-4)
	andb	$1, %al
	jz	27f		// jump if not odd
	// It's an odd integer.
	// Raise divide-by-zero exception and get minus infinity value.
	fldl	MO(one)
	fdivl	MO(zero)
	fchs
	ret

	cfi_adjust_cfa_offset (8)
25:	fstp	%st(0)
26:	addl	$8, %esp
	cfi_adjust_cfa_offset (-8)
27:	// Raise divide-by-zero exception and get infinity value.
	fldl	MO(one)
	fdivl	MO(zero)
	ret

	cfi_adjust_cfa_offset (8)
	.align ALIGNARG(4)
	// x is ±0 and y is > 0.  We must find out whether y is an odd integer.
21:	testb	$2, %dh
	jz	22f

	// fistpll raises invalid exception for |y| >= 1L<<63, so test
	// that (in which case y is certainly even) before testing
	// whether y is odd.
	fcoml	MO(p63)		// y
	fnstsw
	sahf
	jnc	22f

	fld	%st		// y : y
	fistpll	(%esp)		// y
	fildll	(%esp)		// int(y) : y
	fucompp			// <empty>
	fnstsw
	sahf
	jne	23f

	// OK, the value is an integer.
	popl	%eax
	cfi_adjust_cfa_offset (-4)
	popl	%edx
	cfi_adjust_cfa_offset (-4)
	andb	$1, %al
	jz	24f		// jump if not odd
	// It's an odd integer.
	fldl	MO(mzero)
	ret

	cfi_adjust_cfa_offset (8)
22:	fstp	%st(0)
23:	addl	$8, %esp	// Don't use 2 x pop
	cfi_adjust_cfa_offset (-8)
24:	fldl	MO(zero)
	ret

END(__ieee754_pow)
libm_alias_finite (__ieee754_pow, __pow)