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
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
|
/* Compute cubic root of float value.
Copyright (C) 1997-2020 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
Ulrich Drepper <drepper@cygnus.com>, 1997.
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 <machine/asm.h>
#include <libm-alias-float.h>
.section .rodata
.align ALIGNARG(4)
.type f3,@object
f3: .double 0.191502161678719066
ASM_SIZE_DIRECTIVE(f3)
.type f2,@object
f2: .double 0.697570460207922770
ASM_SIZE_DIRECTIVE(f2)
.type f1,@object
f1: .double 0.492659620528969547
ASM_SIZE_DIRECTIVE(f1)
#define CBRT2 1.2599210498948731648
#define ONE_CBRT2 0.793700525984099737355196796584
#define SQR_CBRT2 1.5874010519681994748
#define ONE_SQR_CBRT2 0.629960524947436582364439673883
.type factor,@object
.align ALIGNARG(4)
factor: .double ONE_SQR_CBRT2
.double ONE_CBRT2
.double 1.0
.double CBRT2
.double SQR_CBRT2
ASM_SIZE_DIRECTIVE(factor)
.type two25,@object
two25: .byte 0, 0, 0, 0x4c
ASM_SIZE_DIRECTIVE(two25)
#ifdef PIC
#define MO(op) op##@GOTOFF(%ebx)
#define MOX(op,x) op##@GOTOFF(%ebx,x,1)
#else
#define MO(op) op
#define MOX(op,x) op(x)
#endif
.text
ENTRY(__cbrtf)
movl 4(%esp), %eax
xorl %ecx, %ecx
movl %eax, %edx
andl $0x7fffffff, %eax
jz 1f
cmpl $0x7f800000, %eax
jae 1f
#ifdef PIC
pushl %ebx
cfi_adjust_cfa_offset (4)
cfi_rel_offset (ebx, 0)
LOAD_PIC_REG (bx)
#endif
cmpl $0x00800000, %eax
jae 2f
#ifdef PIC
flds 8(%esp)
#else
flds 4(%esp)
#endif
fmuls MO(two25)
movl $-25, %ecx
#ifdef PIC
fstps 8(%esp)
movl 8(%esp), %eax
#else
fstps 4(%esp)
movl 4(%esp), %eax
#endif
movl %eax, %edx
andl $0x7fffffff, %eax
2: shrl $23, %eax
andl $0x807fffff, %edx
subl $126, %eax
orl $0x3f000000, %edx
addl %eax, %ecx
#ifdef PIC
movl %edx, 8(%esp)
flds 8(%esp) /* xm */
#else
movl %edx, 4(%esp)
flds 4(%esp) /* xm */
#endif
fabs
/* The following code has two tracks:
a) compute the normalized cbrt value
b) compute xe/3 and xe%3
The right track computes the value for b) and this is done
in an optimized way by avoiding division.
But why two tracks at all? Very easy: efficiency. Some FP
instruction can overlap with a certain amount of integer (and
FP) instructions. So we get (except for the imull) all
instructions for free. */
fld %st(0) /* xm : xm */
fmull MO(f3) /* f3*xm : xm */
movl $1431655766, %eax
fsubrl MO(f2) /* f2-f3*xm : xm */
imull %ecx
fmul %st(1) /* (f2-f3*xm)*xm : xm */
movl %ecx, %eax
faddl MO(f1) /* u:=f1+(f2-f3*xm)*xm : xm */
sarl $31, %eax
fld %st /* u : u : xm */
subl %eax, %edx
fmul %st(1) /* u*u : u : xm */
fld %st(2) /* xm : u*u : u : xm */
fadd %st /* 2*xm : u*u : u : xm */
fxch %st(1) /* u*u : 2*xm : u : xm */
fmul %st(2) /* t2:=u*u*u : 2*xm : u : xm */
movl %edx, %eax
fadd %st, %st(1) /* t2 : t2+2*xm : u : xm */
leal (%edx,%edx,2),%edx
fadd %st(0) /* 2*t2 : t2+2*xm : u : xm */
subl %edx, %ecx
faddp %st, %st(3) /* t2+2*xm : u : 2*t2+xm */
shll $3, %ecx
fmulp /* u*(t2+2*xm) : 2*t2+xm */
fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */
fmull MOX(16+factor,%ecx) /* u*(t2+2*xm)/(2*t2+xm)*FACT */
pushl %eax
cfi_adjust_cfa_offset (4)
fildl (%esp) /* xe/3 : u*(t2+2*xm)/(2*t2+xm)*FACT */
fxch /* u*(t2+2*xm)/(2*t2+xm)*FACT : xe/3 */
fscale /* u*(t2+2*xm)/(2*t2+xm)*FACT*2^xe/3 */
popl %edx
cfi_adjust_cfa_offset (-4)
#ifdef PIC
movl 8(%esp), %eax
popl %ebx
cfi_adjust_cfa_offset (-4)
cfi_restore (ebx)
#else
movl 4(%esp), %eax
#endif
testl %eax, %eax
fstp %st(1)
jns 4f
fchs
4: ret
/* Return the argument. */
1: flds 4(%esp)
ret
END(__cbrtf)
libm_alias_float (__cbrt, cbrt)
|
