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
|
/* ix87 specific implementation of arcsinh.
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 <libm-alias-ldouble.h>
#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)
fadd %st
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
cmpl $0x0001, %eax
jae 8f
fld %st(0)
fmul %st(0)
fstp %st(0)
8: 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)
libm_alias_ldouble (__asinh, asinh)
|
