summary refs log tree commit diff
path: root/sysdeps/i386/fpu/s_asinhl.S
blob: 759af3d6848e94dbe2d822d5e068234ad26339ca (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
/* ix87 specific implementation of arcsinh.
   Copyright (C) 1996-2013 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.

   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
   <http://www.gnu.org/licenses/>.  */

#include <machine/asm.h>

	.section .rodata

	.align ALIGNARG(4)
	.type huge,@object
huge:	.tfloat 1e+4930
	ASM_SIZE_DIRECTIVE(huge)
	.align ALIGNARG(4)
	/* Please note that we use double value for 1.0.  This number
	   has an exact representation and so we don't get accuracy
	   problems.  The advantage is that the code is simpler.  */
	.type one,@object
one:	.double 1.0
	ASM_SIZE_DIRECTIVE(one)
	/* It is not important that this constant is precise.  It is only
	   a value which is known to be on the safe side for using the
	   fyl2xp1 instruction.  */
	.type limit,@object
limit:	.double 0.29
	ASM_SIZE_DIRECTIVE(limit)

#ifdef PIC
#define MO(op) op##@GOTOFF(%edx)
#else
#define MO(op) op
#endif

	.text
ENTRY(__asinhl)
	movl	12(%esp), %ecx
	movl	$0x7fff, %eax
	andl	%ecx, %eax
	andl	$0x8000, %ecx
	movl	%eax, %edx
	orl	$0xffff8000, %edx
	incl	%edx
	jz	7f			// x in ±Inf or NaN
	xorl	%ecx, 12(%esp)
	fldt	4(%esp)			// |x|
	cmpl	$0x3fde, %eax
	jb	2f			// |x| < 2^-34
	fldln2				// log(2) : |x|
	cmpl	$0x4020, %eax
	fxch				// |x| : log(2)
	ja	3f			// |x| > 2^34
#ifdef	PIC
	LOAD_PIC_REG (dx)
#endif
	cmpl	$0x4000, %eax
	ja	5f			// |x| > 2

	// 2^-34 <= |x| <= 2 => y = sign(x)*log1p(|x|+|x|^2/(1+sqrt(1+|x|^2)))
	fld	%st			// |x| : |x| : log(2)
	fmul	%st(1)			// |x|^2 : |x| : log(2)
	fld	%st			// |x|^2 : |x|^2 : |x| : log(2)
	faddl	MO(one)			// 1+|x|^2 : |x|^2 : |x| : log(2)
	fsqrt				// sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
	faddl	MO(one)			// 1+sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
	fdivrp				// |x|^2/(1+sqrt(1+|x|^2)) : |x| : log(2)
	faddp				// |x|+|x|^2/(1+sqrt(1+|x|^2)) : log(2)
	fcoml	MO(limit)
	fnstsw
	sahf
	ja	6f
	fyl2xp1
	jecxz	4f
	fchs
4:	ret

7:	fldt	4(%esp)
	ret

6:	faddl	MO(one)
	fyl2x
	jecxz	4f
	fchs
4:	ret

	// |x| < 2^-34 => y = x (inexact iff |x| != 0.0)
	.align ALIGNARG(4)
2:
#ifdef	PIC
	LOAD_PIC_REG (dx)
#endif
	jecxz	4f
	fchs				// x
4:	fld	%st			// x : x
	fldt	MO(huge)		// huge : x : x
	faddp				// huge+x : x
	fstp	%st(0)			// x
	ret

	// |x| > 2^34 => y = sign(x) * (log(|x|) + log(2))
	.align ALIGNARG(4)
3:	fyl2x				// log(|x|)
	fldln2				// log(2) : log(|x|)
	faddp				// log(|x|)+log(2)
	jecxz	4f
	fchs
4:	ret

	// |x| > 2 => y = sign(x) * log(2*|x| + 1/(|x|+sqrt(x*x+1)))
	.align ALIGNARG(4)
5:	fld	%st			// |x| : |x| : log(2)
	fadd	%st, %st(1)		// |x| : 2*|x| : log(2)
	fld	%st			// |x| : |x| : 2*|x| : log(2)
	fmul	%st(1)			// |x|^2 : |x| : 2*|x| : log(2)
	faddl	MO(one)			// 1+|x|^2 : |x| : 2*|x| : log(2)
	fsqrt				// sqrt(1+|x|^2) : |x| : 2*|x| : log(2)
	faddp				// |x|+sqrt(1+|x|^2) : 2*|x| : log(2)
	fdivrl	MO(one)			// 1/(|x|+sqrt(1+|x|^2)) : 2*|x| : log(2)
	faddp				// 2*|x|+1/(|x|+sqrt(1+|x|^2)) : log(2)
	fyl2x				// log(2*|x|+1/(|x|+sqrt(1+|x|^2)))
	jecxz	4f
	fchs
4:	ret
END(__asinhl)
weak_alias (__asinhl, asinhl)