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
|
/* ix87 specific implementation of arcsinh.
Copyright (C) 1996 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 Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
#include <machine/asm.h>
#ifdef __ELF__
.section .rodata
#else
.text
#endif
.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. */
ASM_TYPE_DIRECTIVE(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. */
ASM_TYPE_DIRECTIVE(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(__ieee754_acoshl)
movl 12(%esp), %ecx
cmpl $0x3fff, %ecx
jl 5f // < 1 => invalid
fldln2 // log(2)
fldt 4(%esp) // x : log(2)
cmpl $0x4020, %ecx
ja 3f // x > 2^34
#ifdef PIC
call 1f
1: popl %edx
addl $_GLOBAL_OFFSET_TABLE_+[.-1b], %edx
#endif
cmpl $0x4000, %ecx
ja 4f // x > 2
// 1 <= x <= 2 => y = log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
fsubl MO(one) // x-1 : log(2)
fld %st // x-1 : x-1 : log(2)
fmul %st(1) // (x-1)^2 : x-1 : log(2)
fadd %st(1) // x-1+(x-1)^2 : x-1 : log(2)
fadd %st(1) // 2*(x-1)+(x-1)^2 : x-1 : log(2)
fsqrt // sqrt(2*(x-1)+(x-1)^2) : x-1 : log(2)
faddp // x-1+sqrt(2*(x-1)+(x-1)^2) : log(2)
fcoml MO(limit)
fnstsw
sahf
ja 2f
fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
ret
2: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2)
fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2))
ret
// x > 2^34 => y = log(x) + log(2)
.align ALIGNARG(4)
3: fyl2x // log(x)
fldln2 // log(2) : log(x)
faddp // log(x)+log(2)
ret
// 2^34 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1)))
.align ALIGNARG(4)
4: 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)
fsubl MO(one) // x^2-1 : x : 2*x : log(2)
fsqrt // sqrt(x^2-1) : x : 2*x : log(2)
faddp // x+sqrt(x^2-1) : 2*x : log(2)
fdivrl MO(one) // 1/(x+sqrt(x^2-1)) : 2*x : log(2)
fsubrp // 2*x+1/(x+sqrt(x^2)-1) : log(2)
fyl2x // log(2*x+1/(x+sqrt(x^2-1)))
ret
// x < 1 => NaN
.align ALIGNARG(4)
5: fldz
fdiv %st, %st(0)
ret
END(__ieee754_acoshl)
|
