xref: /titanic_44/usr/src/lib/libm/amd64/src/expl.s (revision a05fd0c9b9aa46cf66ddea7617e56facdf1f4aaf)
1/*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21/*
22 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
23 */
24/*
25 * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
26 * Use is subject to license terms.
27 */
28
29        .file "expl.s"
30
31#include "libm.h"
32LIBM_ANSI_PRAGMA_WEAK(expl,function)
33#include "libm_synonyms.h"
34
35	.data
36	.align	16
37ln2_hi:	.4byte	0xd1d00000, 0xb17217f7, 0x3ffe, 0x0
38ln2_lo:	.4byte	0x4c67fc0d, 0x8654361c, 0xbfce, 0x0
39
40	ENTRY(expl)
41	movl	16(%rsp),%ecx		/ cx <--sign&bexp(x)
42	andl	$0x7fff,%ecx		/ ecx <-- zero_xtnd(bexp(x))
43	cmpl	$0x3ffe,%ecx		/ Is |x| < 0.5?
44	jb	2f			/ If so, see which shortcut to take
45	je	.check_tail		/ More checking if 0.5 <= |x| < 1
46.general_case:				/ Here, |x| >= 1 or x is NaN
47	cmpl	$0x7fff,%ecx		/ bexp(|x|) = bexp(INF)?
48	je	.not_finite		/ if so, x is not finite
49	cmpl	$0x400e,%ecx		/ |x| < 32768 = 2^15?
50	jb	.finite_non_special	/ if so, proceed with argument reduction
51	fldt	8(%rsp)			/ x
52	fld1				/ 1, x
53	jmp	1f
54.finite_non_special:			/ Here, ln(2) < |x| < 2^15
55	fldt	8(%rsp)			/ x
56	fld	%st(0)			/ x, x
57	fldl2e				/ log2(e), x, x
58	fmulp				/ z := x*log2(e), x
59	frndint				/ [z], x
60	fst	%st(2)			/ [z], x, [z]
61	PIC_SETUP(1)
62	fldt	PIC_L(ln2_hi)		/ ln2_hi, [z], x, [z]
63	fmulp				/ [z]*ln2_hi, x, [z]
64	fsubrp	%st,%st(1)		/ x-[z]*ln2_hi, [z]
65	fldt	PIC_L(ln2_lo)		/ ln2_lo, x-[z]*ln2_hi, [z]
66	PIC_WRAPUP
67	fmul	%st(2),%st		/ [z]*ln2_lo, x-[z]*ln2_hi, [z]
68	fsubrp	%st,%st(1)		/ r := x-[z]*ln(2), [z]
69	fldl2e				/ log2(e), r, [z]
70	fmulp				/ f := r*log2(e), [z]
71	f2xm1				/ 2^f-1,[z]
72	fld1				/ 1, 2^f-1, [z]
73	faddp	%st,%st(1)		/ 2^f, [z]
741:
75	fscale				/ e^x, [z]
76	fstp	%st(1)
77	ret
78
792:					/ Here, |x| < 0.5
80	cmpl	$0x3fbe,%ecx		/ Is |x| >= 2^-65?
81	jae	.shortcut		/ If so, take a shortcut
82	fldt	8(%rsp)			/ x
83	fld1				/ 1, x
84	faddp	%st,%st(1)		/ 1+x (for inexact & directed rounding)
85	ret
86
87.check_tail:
88	movl	12(%rsp),%ecx		/ ecx <-- hi_32(sgnfcnd(x))
89	cmpl	$0xb17217f7,%ecx	/ Is |x| < ln(2)?
90	ja	.finite_non_special
91	jb	.shortcut
92	movl	8(%rsp),%edx		/ edx <-- lo_32(x)
93	cmpl	$0xd1cf79ab,%edx	/ Is |x| slightly < ln(2)?
94	ja	.finite_non_special	/ branch if |x| slightly > ln(2)
95.shortcut:
96	/ Here, |x| < ln(2), so |z| = |x/ln(2)| < 1,
97	/ whence z is in f2xm1's domain.
98	fldt	8(%rsp)			/ x
99	fldl2e				/ log2(e), x
100	fmulp				/ x*log2(e)
101	f2xm1				/ 2^(x*log2(e))-1 = e^x-1
102	fld1				/ 1, e^x-1
103	faddp	%st,%st(1)		/ e^x
104	ret
105
106.not_finite:
107	movl	12(%rsp),%ecx		/ ecx <-- hi_32(sgnfcnd(x))
108	cmpl	$0x80000000,%ecx	/ hi_32(|x|) = hi_32(INF)?
109	jne	.NaN_or_pinf		/ if not, x is NaN
110	movl	8(%rsp),%edx		/ edx <-- lo_32(x)
111	cmpl	$0,%edx			/ lo_32(x) = 0?
112	jne	.NaN_or_pinf		/ if not, x is NaN
113	movl	16(%rsp),%eax		/ ax <-- sign&bexp((x))
114	andl	$0x8000,%eax		/ here, x is infinite, but +/-?
115	jz	.NaN_or_pinf		/ branch if x = +INF
116	fldz				/ Here, x = -inf, so return 0
117	ret
118
119.NaN_or_pinf:
120	/ Here, x = NaN or +inf, so load x and return immediately.
121	fldt	8(%rsp)
122	fadd	%st(0),%st		/ quiet SNaN
123	ret
124	.align	16
125	SET_SIZE(expl)
126