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
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
|
/* Compute cubic root of long double value.
Copyright (C) 1997-2023 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 f8,@object
f8: .quad 0xa57ef3d83a542839 /* 0.161617097923756032 */
.short 0x3ffc
ASM_SIZE_DIRECTIVE(f8)
.align ALIGNARG(4)
.type f7,@object
f7: .quad 0xfd11da7820029014 /* -0.988553671195413709 */
.short 0xbffe
ASM_SIZE_DIRECTIVE(f7)
.align ALIGNARG(4)
.type f6,@object
f6: .quad 0xa9ca93fcade3b4ad /* 2.65298938441952296 */
.short 0x4000
ASM_SIZE_DIRECTIVE(f6)
.align ALIGNARG(4)
.type f5,@object
f5: .quad 0x839186562c931c34 /* -4.11151425200350531 */
.short 0xc001
ASM_SIZE_DIRECTIVE(f5)
.align ALIGNARG(4)
.type f4,@object
f4: .quad 0x830f25c9ee304594 /* 4.09559907378707839 */
.short 0x4001
ASM_SIZE_DIRECTIVE(f4)
.align ALIGNARG(4)
.type f3,@object
f3: .quad 0xb4bedd1d5fa2f0c6 /* -2.82414939754975962 */
.short 0xc000
ASM_SIZE_DIRECTIVE(f3)
.align ALIGNARG(4)
.type f2,@object
f2: .quad 0xd685a163b08586e3 /* 1.67595307700780102 */
.short 0x3fff
ASM_SIZE_DIRECTIVE(f2)
.align ALIGNARG(4)
.type f1,@object
f1: .quad 0xad16073ed4ec3b45 /* 0.338058687610520237 */
.short 0x3ffd
ASM_SIZE_DIRECTIVE(f1)
/* We make the entries in the following table all 16 bytes
wide to avoid having to implement a multiplication by 10. */
.type factor,@object
.align ALIGNARG(4)
factor: /* 1.0 / cbrt (2.0) ^ 2 = 0.629960524947436582364439673883 */
.quad 0xa14517cc6b945711
.short 0x3ffe
.byte 0, 0, 0, 0, 0, 0
/* 1.0 / cbrt (2.0) = 0.793700525984099737355196796584 */
.quad 0xcb2ff529eb71e415
.short 0x3ffe
.byte 0, 0, 0, 0, 0, 0
/* 1.0L */
.quad 0x8000000000000000
.short 0x3fff
.byte 0, 0, 0, 0, 0, 0
/* cbrt (2.0) = 1.2599210498948731648 */
.quad 0xa14517cc6b945711
.short 0x3fff
.byte 0, 0, 0, 0, 0, 0
/* cbrt (2.0) ^ 2 = 1.5874010519681994748 */
.quad 0xcb2ff529eb71e416
.short 0x3fff
ASM_SIZE_DIRECTIVE(factor)
.type two64,@object
.align ALIGNARG(4)
two64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
ASM_SIZE_DIRECTIVE(two64)
#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(__cbrtl)
movl 4(%esp), %ecx
movl 12(%esp), %eax
orl 8(%esp), %ecx
movl %eax, %edx
andl $0x7fff, %eax
orl %eax, %ecx
jz 1f
xorl %ecx, %ecx
cmpl $0x7fff, %eax
je 1f
#ifdef PIC
pushl %ebx
cfi_adjust_cfa_offset (4)
cfi_rel_offset (ebx, 0)
LOAD_PIC_REG (bx)
#endif
cmpl $0, %eax
jne 2f
#ifdef PIC
fldt 8(%esp)
#else
fldt 4(%esp)
#endif
fmull MO(two64)
movl $-64, %ecx
#ifdef PIC
fstpt 8(%esp)
movl 16(%esp), %eax
#else
fstpt 4(%esp)
movl 12(%esp), %eax
#endif
movl %eax, %edx
andl $0x7fff, %eax
2: andl $0x8000, %edx
subl $16382, %eax
orl $0x3ffe, %edx
addl %eax, %ecx
#ifdef PIC
movl %edx, 16(%esp)
fldt 8(%esp) /* xm */
#else
movl %edx, 12(%esp)
fldt 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. */
fldt MO(f8) /* f8 : xm */
fmul %st(1) /* f8*xm : xm */
fldt MO(f7)
faddp /* f7+f8*xm : xm */
fmul %st(1) /* (f7+f8*xm)*xm : xm */
movl $1431655766, %eax
fldt MO(f6)
faddp /* f6+(f7+f8*xm)*xm : xm */
imull %ecx
fmul %st(1) /* (f6+(f7+f8*xm)*xm)*xm : xm */
movl %ecx, %eax
fldt MO(f5)
faddp /* f5+(f6+(f7+f8*xm)*xm)*xm : xm */
sarl $31, %eax
fmul %st(1) /* (f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */
subl %eax, %edx
fldt MO(f4)
faddp /* f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */
fmul %st(1) /* (f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */
fldt MO(f3)
faddp /* f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */
fmul %st(1) /* (f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */
fldt MO(f2)
faddp /* f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */
fmul %st(1) /* (f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm)*xm : xm */
fldt MO(f1)
faddp /* u:=f1+(f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm)*xm : xm */
fld %st /* u : u : xm */
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 $4, %ecx
fmulp /* u*(t2+2*xm) : 2*t2+xm */
fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */
fldt MOX(32+factor,%ecx)
fmulp /* 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 16(%esp), %eax
popl %ebx
cfi_adjust_cfa_offset (-4)
cfi_restore (ebx)
#else
movl 12(%esp), %eax
#endif
testl $0x8000, %eax
fstp %st(1)
jz 4f
fchs
4: ret
/* Return the argument. */
1: fldt 4(%esp)
fadd %st
ret
END(__cbrtl)
libm_alias_ldouble (__cbrt, cbrt)
|
