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 exp(x)-1.
Copyright (C) 1996-2022 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/>. */
/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
#include <sysdep.h>
#include <machine/asm.h>
#include <i386-math-asm.h>
#include <libm-alias-float.h>
.section .rodata
.align ALIGNARG(4)
.type minus1,@object
minus1: .double -1.0
ASM_SIZE_DIRECTIVE(minus1)
.type one,@object
one: .double 1.0
ASM_SIZE_DIRECTIVE(one)
.type l2e,@object
l2e: .tfloat 1.442695040888963407359924681002
ASM_SIZE_DIRECTIVE(l2e)
DEFINE_FLT_MIN
#ifdef PIC
#define MO(op) op##@GOTOFF(%edx)
#else
#define MO(op) op
#endif
.text
ENTRY(__expm1f)
movzwl 4+2(%esp), %eax
xorb $0x80, %ah // invert sign bit (now 1 is "positive")
cmpl $0xc2b1, %eax // is num >= 88.5?
jae HIDDEN_JUMPTARGET (__expf)
flds 4(%esp) // x
fxam // Is NaN, +-Inf or +-0?
xorb $0x80, %ah
cmpl $0xc190, %eax // is num <= -18.0?
fstsw %ax
movb $0x45, %ch
jb 4f
// Below -18.0 (may be -NaN or -Inf).
andb %ah, %ch
#ifdef PIC
LOAD_PIC_REG (dx)
#endif
cmpb $0x01, %ch
je 5f // If -NaN, jump.
jmp 2f // -large, possibly -Inf.
4: // In range -18.0 to 88.5 (may be +-0 but not NaN or +-Inf).
andb %ah, %ch
cmpb $0x40, %ch
je 3f // If +-0, jump.
#ifdef PIC
LOAD_PIC_REG (dx)
#endif
5: fldt MO(l2e) // log2(e) : x
fmulp // log2(e)*x
fld %st // log2(e)*x : log2(e)*x
// Set round-to-nearest temporarily.
subl $8, %esp
cfi_adjust_cfa_offset (8)
fstcw 4(%esp)
movl $0xf3ff, %ecx
andl 4(%esp), %ecx
movl %ecx, (%esp)
fldcw (%esp)
frndint // int(log2(e)*x) : log2(e)*x
fldcw 4(%esp)
addl $8, %esp
cfi_adjust_cfa_offset (-8)
fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x)
fxch // fract(log2(e)*x) : int(log2(e)*x)
f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x)
fscale // 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
fxch // int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fldl MO(one) // 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fscale // 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fsubrl MO(one) // 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fstp %st(1) // 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fsubrp %st, %st(1) // 2^(log2(e)*x)
FLT_CHECK_FORCE_UFLOW
ret
2: fstp %st
fldl MO(minus1) // Set result to -1.0.
3: ret
END(__expm1f)
libm_alias_float (__expm1, expm1)
|
