1/* ix87 specific implementation of pow function.
2   Copyright (C) 1996, 1997, 1998, 1999, 2001 Free Software Foundation, Inc.
3   This file is part of the GNU C Library.
4   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
5
6   The GNU C Library is free software; you can redistribute it and/or
7   modify it under the terms of the GNU Lesser General Public
8   License as published by the Free Software Foundation; either
9   version 2.1 of the License, or (at your option) any later version.
10
11   The GNU C Library is distributed in the hope that it will be useful,
12   but WITHOUT ANY WARRANTY; without even the implied warranty of
13   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
14   Lesser General Public License for more details.
15
16   You should have received a copy of the GNU Lesser General Public
17   License along with the GNU C Library; if not, write to the Free
18   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
19   02111-1307 USA.  */
20
21#include <machine/asm.h>
22
23#ifdef __ELF__
24	.section .rodata
25#else
26	.text
27#endif
28
29	.align ALIGNARG(4)
30	ASM_TYPE_DIRECTIVE(infinity,@object)
31inf_zero:
32infinity:
33	.byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
34	ASM_SIZE_DIRECTIVE(infinity)
35	ASM_TYPE_DIRECTIVE(zero,@object)
36zero:	.double 0.0
37	ASM_SIZE_DIRECTIVE(zero)
38	ASM_TYPE_DIRECTIVE(minf_mzero,@object)
39minf_mzero:
40minfinity:
41	.byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
42mzero:
43	.byte 0, 0, 0, 0, 0, 0, 0, 0x80
44	ASM_SIZE_DIRECTIVE(minf_mzero)
45	ASM_TYPE_DIRECTIVE(one,@object)
46one:	.double 1.0
47	ASM_SIZE_DIRECTIVE(one)
48	ASM_TYPE_DIRECTIVE(limit,@object)
49limit:	.double 0.29
50	ASM_SIZE_DIRECTIVE(limit)
51
52#ifdef PIC
53#define MO(op) op##@GOTOFF(%ecx)
54#define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
55#else
56#define MO(op) op
57#define MOX(op,x,f) op(,x,f)
58#endif
59
60	.text
61ENTRY(__ieee754_pow)
62	fldl	12(%esp)	// y
63	fxam
64
65#ifdef	PIC
66	call	1f
671:	popl	%ecx
68	addl	$_GLOBAL_OFFSET_TABLE_+[.-1b], %ecx
69#endif
70
71	fnstsw
72	movb	%ah, %dl
73	andb	$0x45, %ah
74	cmpb	$0x40, %ah	// is y == 0 ?
75	je	11f
76
77	cmpb	$0x05, %ah	// is y == �inf ?
78	je	12f
79
80	cmpb	$0x01, %ah	// is y == NaN ?
81	je	30f
82
83	fldl	4(%esp)		// x : y
84
85	subl	$8,%esp
86
87	fxam
88	fnstsw
89	movb	%ah, %dh
90	andb	$0x45, %ah
91	cmpb	$0x40, %ah
92	je	20f		// x is �0
93
94	cmpb	$0x05, %ah
95	je	15f		// x is �inf
96
97	fxch			// y : x
98
99	/* First see whether `y' is a natural number.  In this case we
100	   can use a more precise algorithm.  */
101	fld	%st		// y : y : x
102	fistpll	(%esp)		// y : x
103	fildll	(%esp)		// int(y) : y : x
104	fucomp	%st(1)		// y : x
105	fnstsw
106	sahf
107	jne	2f
108
109	/* OK, we have an integer value for y.  */
110	popl	%eax
111	popl	%edx
112	orl	$0, %edx
113	fstp	%st(0)		// x
114	jns	4f		// y >= 0, jump
115	fdivrl	MO(one)		// 1/x		(now referred to as x)
116	negl	%eax
117	adcl	$0, %edx
118	negl	%edx
1194:	fldl	MO(one)		// 1 : x
120	fxch
121
1226:	shrdl	$1, %edx, %eax
123	jnc	5f
124	fxch
125	fmul	%st(1)		// x : ST*x
126	fxch
1275:	fmul	%st(0), %st	// x*x : ST*x
128	shrl	$1, %edx
129	movl	%eax, %ecx
130	orl	%edx, %ecx
131	jnz	6b
132	fstp	%st(0)		// ST*x
133	ret
134
135	/* y is �NAN */
13630:	fldl	4(%esp)		// x : y
137	fldl	MO(one)		// 1.0 : x : y
138	fucomp	%st(1)		// x : y
139	fnstsw
140	sahf
141	je	31f
142	fxch			// y : x
14331:	fstp	%st(1)
144	ret
145
146	.align ALIGNARG(4)
1472:	/* y is a real number.  */
148	fxch			// x : y
149	fldl	MO(one)		// 1.0 : x : y
150	fld	%st(1)		// x : 1.0 : x : y
151	fsub	%st(1)		// x-1 : 1.0 : x : y
152	fabs			// |x-1| : 1.0 : x : y
153	fcompl	MO(limit)	// 1.0 : x : y
154	fnstsw
155	fxch			// x : 1.0 : y
156	sahf
157	ja	7f
158	fsub	%st(1)		// x-1 : 1.0 : y
159	fyl2xp1			// log2(x) : y
160	jmp	8f
161
1627:	fyl2x			// log2(x) : y
1638:	fmul	%st(1)		// y*log2(x) : y
164	fst	%st(1)		// y*log2(x) : y*log2(x)
165	frndint			// int(y*log2(x)) : y*log2(x)
166	fsubr	%st, %st(1)	// int(y*log2(x)) : fract(y*log2(x))
167	fxch			// fract(y*log2(x)) : int(y*log2(x))
168	f2xm1			// 2^fract(y*log2(x))-1 : int(y*log2(x))
169	faddl	MO(one)		// 2^fract(y*log2(x)) : int(y*log2(x))
170	fscale			// 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
171	addl	$8, %esp
172	fstp	%st(1)		// 2^fract(y*log2(x))*2^int(y*log2(x))
173	ret
174
175
176	// pow(x,�0) = 1
177	.align ALIGNARG(4)
17811:	fstp	%st(0)		// pop y
179	fldl	MO(one)
180	ret
181
182	// y == �inf
183	.align ALIGNARG(4)
18412:	fstp	%st(0)		// pop y
185	fldl	4(%esp)		// x
186	fabs
187	fcompl	MO(one)		// < 1, == 1, or > 1
188	fnstsw
189	andb	$0x45, %ah
190	cmpb	$0x45, %ah
191	je	13f		// jump if x is NaN
192
193	cmpb	$0x40, %ah
194	je	14f		// jump if |x| == 1
195
196	shlb	$1, %ah
197	xorb	%ah, %dl
198	andl	$2, %edx
199	fldl	MOX(inf_zero, %edx, 4)
200	ret
201
202	.align ALIGNARG(4)
20314:	fldl	MO(one)
204	ret
205
206	.align ALIGNARG(4)
20713:	fldl	4(%esp)		// load x == NaN
208	ret
209
210	.align ALIGNARG(4)
211	// x is �inf
21215:	fstp	%st(0)		// y
213	testb	$2, %dh
214	jz	16f		// jump if x == +inf
215
216	// We must find out whether y is an odd integer.
217	fld	%st		// y : y
218	fistpll	(%esp)		// y
219	fildll	(%esp)		// int(y) : y
220	fucompp			// <empty>
221	fnstsw
222	sahf
223	jne	17f
224
225	// OK, the value is an integer, but is the number of bits small
226	// enough so that all are coming from the mantissa?
227	popl	%eax
228	popl	%edx
229	andb	$1, %al
230	jz	18f		// jump if not odd
231	movl	%edx, %eax
232	orl	%edx, %edx
233	jns	155f
234	negl	%eax
235155:	cmpl	$0x00200000, %eax
236	ja	18f		// does not fit in mantissa bits
237	// It's an odd integer.
238	shrl	$31, %edx
239	fldl	MOX(minf_mzero, %edx, 8)
240	ret
241
242	.align ALIGNARG(4)
24316:	fcompl	MO(zero)
244	addl	$8, %esp
245	fnstsw
246	shrl	$5, %eax
247	andl	$8, %eax
248	fldl	MOX(inf_zero, %eax, 1)
249	ret
250
251	.align ALIGNARG(4)
25217:	shll	$30, %edx	// sign bit for y in right position
253	addl	$8, %esp
25418:	shrl	$31, %edx
255	fldl	MOX(inf_zero, %edx, 8)
256	ret
257
258	.align ALIGNARG(4)
259	// x is �0
26020:	fstp	%st(0)		// y
261	testb	$2, %dl
262	jz	21f		// y > 0
263
264	// x is �0 and y is < 0.  We must find out whether y is an odd integer.
265	testb	$2, %dh
266	jz	25f
267
268	fld	%st		// y : y
269	fistpll	(%esp)		// y
270	fildll	(%esp)		// int(y) : y
271	fucompp			// <empty>
272	fnstsw
273	sahf
274	jne	26f
275
276	// OK, the value is an integer, but is the number of bits small
277	// enough so that all are coming from the mantissa?
278	popl	%eax
279	popl	%edx
280	andb	$1, %al
281	jz	27f		// jump if not odd
282	cmpl	$0xffe00000, %edx
283	jbe	27f		// does not fit in mantissa bits
284	// It's an odd integer.
285	// Raise divide-by-zero exception and get minus infinity value.
286	fldl	MO(one)
287	fdivl	MO(zero)
288	fchs
289	ret
290
29125:	fstp	%st(0)
29226:	addl	$8, %esp
29327:	// Raise divide-by-zero exception and get infinity value.
294	fldl	MO(one)
295	fdivl	MO(zero)
296	ret
297
298	.align ALIGNARG(4)
299	// x is �0 and y is > 0.  We must find out whether y is an odd integer.
30021:	testb	$2, %dh
301	jz	22f
302
303	fld	%st		// y : y
304	fistpll	(%esp)		// y
305	fildll	(%esp)		// int(y) : y
306	fucompp			// <empty>
307	fnstsw
308	sahf
309	jne	23f
310
311	// OK, the value is an integer, but is the number of bits small
312	// enough so that all are coming from the mantissa?
313	popl	%eax
314	popl	%edx
315	andb	$1, %al
316	jz	24f		// jump if not odd
317	cmpl	$0xffe00000, %edx
318	jae	24f		// does not fit in mantissa bits
319	// It's an odd integer.
320	fldl	MO(mzero)
321	ret
322
32322:	fstp	%st(0)
32423:	addl	$8, %esp	// Don't use 2 x pop
32524:	fldl	MO(zero)
326	ret
327
328END(__ieee754_pow)
329