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
|
/* Function exp vectorized with SSE4.
Copyright (C) 2014-2016 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
<http://www.gnu.org/licenses/>. */
#include <sysdep.h>
#include "svml_d_exp_data.h"
.text
ENTRY (_ZGVbN2v_exp_sse4)
/*
ALGORITHM DESCRIPTION:
Argument representation:
N = rint(X*2^k/ln2) = 2^k*M+j
X = N*ln2/2^k + r = M*ln2 + ln2*(j/2^k) + r
then -ln2/2^(k+1) < r < ln2/2^(k+1)
Alternatively:
N = trunc(X*2^k/ln2)
then 0 < r < ln2/2^k
Result calculation:
exp(X) = exp(M*ln2 + ln2*(j/2^k) + r)
= 2^M * 2^(j/2^k) * exp(r)
2^M is calculated by bit manipulation
2^(j/2^k) is stored in table
exp(r) is approximated by polynomial.
The table lookup is skipped if k = 0. */
pushq %rbp
cfi_adjust_cfa_offset (8)
cfi_rel_offset (%rbp, 0)
movq %rsp, %rbp
cfi_def_cfa_register (%rbp)
andq $-64, %rsp
subq $320, %rsp
movaps %xmm0, %xmm3
movq __svml_dexp_data@GOTPCREL(%rip), %r8
/* iAbsX = (int)(lX>>32), lX = *(longlong*)&X */
pshufd $221, %xmm3, %xmm7
movups __dbInvLn2(%r8), %xmm0
/* dK = X*dbInvLn2 */
mulpd %xmm3, %xmm0
movq __iAbsMask(%r8), %xmm5
movq __iDomainRange(%r8), %xmm6
/* iAbsX = iAbsX&iAbsMask */
pand %xmm5, %xmm7
/* iRangeMask = (iAbsX>iDomainRange) */
pcmpgtd %xmm6, %xmm7
/* Mask = iRangeMask?1:0, set mask for overflow/underflow */
movmskps %xmm7, %eax
/* dN = rint(X*2^k/Ln2) */
xorps %xmm7, %xmm7
movups __dbLn2hi(%r8), %xmm5
movups __dbLn2lo(%r8), %xmm6
roundpd $0, %xmm0, %xmm7
/* dR = X - dN*dbLn2hi, dbLn2hi is 52-8-k hi bits of ln2/2^k */
mulpd %xmm7, %xmm5
/* dR = dR - dN*dbLn2lo, dbLn2lo is 40..94 bits of lo part of ln2/2^k */
mulpd %xmm6, %xmm7
movups __dbShifter(%r8), %xmm4
/* dM = X*dbInvLn2+dbShifter */
addpd %xmm0, %xmm4
movaps %xmm3, %xmm0
subpd %xmm5, %xmm0
subpd %xmm7, %xmm0
movups __dPC2(%r8), %xmm5
/* exp(r) = b0+r*(b0+r*(b1+r*b2)) */
mulpd %xmm0, %xmm5
addpd __dPC1(%r8), %xmm5
mulpd %xmm0, %xmm5
movups __dPC0(%r8), %xmm6
addpd %xmm6, %xmm5
mulpd %xmm5, %xmm0
movdqu __lIndexMask(%r8), %xmm2
/* lIndex = (*(longlong*)&dM)&lIndexMask, lIndex is the lower K bits of lM */
movdqa %xmm2, %xmm1
/* lM = (*(longlong*)&dM)&(~lIndexMask) */
pandn %xmm4, %xmm2
pand %xmm4, %xmm1
/* lM = lM<<(52-K), 2^M */
psllq $42, %xmm2
/* table lookup for dT[j] = 2^(j/2^k) */
movd %xmm1, %edx
pextrw $4, %xmm1, %ecx
addpd %xmm0, %xmm6
shll $3, %edx
shll $3, %ecx
movq (%r8,%rdx), %xmm0
andl $3, %eax
movhpd (%r8,%rcx), %xmm0
/* 2^(j/2^k) * exp(r) */
mulpd %xmm6, %xmm0
/* multiply by 2^M through integer add */
paddq %xmm2, %xmm0
jne .LBL_1_3
.LBL_1_2:
cfi_remember_state
movq %rbp, %rsp
cfi_def_cfa_register (%rsp)
popq %rbp
cfi_adjust_cfa_offset (-8)
cfi_restore (%rbp)
ret
.LBL_1_3:
cfi_restore_state
movups %xmm3, 192(%rsp)
movups %xmm0, 256(%rsp)
je .LBL_1_2
xorb %cl, %cl
xorl %edx, %edx
movups %xmm8, 112(%rsp)
movups %xmm9, 96(%rsp)
movups %xmm10, 80(%rsp)
movups %xmm11, 64(%rsp)
movups %xmm12, 48(%rsp)
movups %xmm13, 32(%rsp)
movups %xmm14, 16(%rsp)
movups %xmm15, (%rsp)
movq %rsi, 136(%rsp)
movq %rdi, 128(%rsp)
movq %r12, 168(%rsp)
cfi_offset_rel_rsp (12, 168)
movb %cl, %r12b
movq %r13, 160(%rsp)
cfi_offset_rel_rsp (13, 160)
movl %eax, %r13d
movq %r14, 152(%rsp)
cfi_offset_rel_rsp (14, 152)
movl %edx, %r14d
movq %r15, 144(%rsp)
cfi_offset_rel_rsp (15, 144)
cfi_remember_state
.LBL_1_6:
btl %r14d, %r13d
jc .LBL_1_12
.LBL_1_7:
lea 1(%r14), %esi
btl %esi, %r13d
jc .LBL_1_10
.LBL_1_8:
incb %r12b
addl $2, %r14d
cmpb $16, %r12b
jb .LBL_1_6
movups 112(%rsp), %xmm8
movups 96(%rsp), %xmm9
movups 80(%rsp), %xmm10
movups 64(%rsp), %xmm11
movups 48(%rsp), %xmm12
movups 32(%rsp), %xmm13
movups 16(%rsp), %xmm14
movups (%rsp), %xmm15
movq 136(%rsp), %rsi
movq 128(%rsp), %rdi
movq 168(%rsp), %r12
cfi_restore (%r12)
movq 160(%rsp), %r13
cfi_restore (%r13)
movq 152(%rsp), %r14
cfi_restore (%r14)
movq 144(%rsp), %r15
cfi_restore (%r15)
movups 256(%rsp), %xmm0
jmp .LBL_1_2
.LBL_1_10:
cfi_restore_state
movzbl %r12b, %r15d
shlq $4, %r15
movsd 200(%rsp,%r15), %xmm0
call JUMPTARGET(exp)
movsd %xmm0, 264(%rsp,%r15)
jmp .LBL_1_8
.LBL_1_12:
movzbl %r12b, %r15d
shlq $4, %r15
movsd 192(%rsp,%r15), %xmm0
call JUMPTARGET(exp)
movsd %xmm0, 256(%rsp,%r15)
jmp .LBL_1_7
END (_ZGVbN2v_exp_sse4)
|