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
242
243
244
245
|
/* Function exp2f vectorized with AVX2.
Copyright (C) 2021 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/. */
/*
* ALGORITHM DESCRIPTION:
*
* exp2(x) = 2^n * T[j] * (1 + P(y))
* where
* x = m*(1/K) + y, y in [-1/K..1/K]
* m = n*K + j, m,n,j - signed integer, j in [-K/2..K/2]
*
* values of 2^j/K are tabulated
*
* P(y) is a minimax polynomial approximation of exp2(x)-1
* on small interval [-1/K..1/K]
*
* Special cases:
*
* exp2(NaN) = NaN
* exp2(+INF) = +INF
* exp2(-INF) = 0
* exp2(x) = 1 for subnormals
* For IEEE float
* if x >= 128.0 then exp2f(x) overflow
* if x < -151.0 then exp2f(x) underflow
*
*/
/* Offsets for data table __svml_sexp2_data_internal
*/
#define _sShifter 0
#define _sPC0 32
#define _sPC1 64
#define _sPC2 96
#define _sPC3 128
#define _sPC4 160
#define _sPC5 192
#define _sPC6 224
#define _iAbsMask 256
#define _iDomainRange 288
#include <sysdep.h>
.text
.section .text.avx2,"ax",@progbits
ENTRY(_ZGVdN8v_exp2f_avx2)
pushq %rbp
cfi_def_cfa_offset(16)
movq %rsp, %rbp
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
andq $-32, %rsp
subq $96, %rsp
vmovups __svml_sexp2_data_internal(%rip), %ymm1
/* Check for overflow\underflow */
vmovups _sPC6+__svml_sexp2_data_internal(%rip), %ymm7
/* Implementation */
vaddps %ymm1, %ymm0, %ymm6
vsubps %ymm1, %ymm6, %ymm4
/* 2^N */
vpslld $23, %ymm6, %ymm8
/* R */
vsubps %ymm4, %ymm0, %ymm5
/* Polynomial */
vfmadd213ps _sPC5+__svml_sexp2_data_internal(%rip), %ymm5, %ymm7
vfmadd213ps _sPC4+__svml_sexp2_data_internal(%rip), %ymm5, %ymm7
vfmadd213ps _sPC3+__svml_sexp2_data_internal(%rip), %ymm5, %ymm7
vfmadd213ps _sPC2+__svml_sexp2_data_internal(%rip), %ymm5, %ymm7
vfmadd213ps _sPC1+__svml_sexp2_data_internal(%rip), %ymm5, %ymm7
vfmadd213ps _sPC0+__svml_sexp2_data_internal(%rip), %ymm5, %ymm7
/* Check for overflow\underflow */
vandps _iAbsMask+__svml_sexp2_data_internal(%rip), %ymm0, %ymm2
vpcmpgtd _iDomainRange+__svml_sexp2_data_internal(%rip), %ymm2, %ymm3
vmovmskps %ymm3, %edx
/* Reconstruction */
vpaddd %ymm8, %ymm7, %ymm1
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm1
/* Restore registers
* and exit the function
*/
L(EXIT):
vmovaps %ymm1, %ymm0
movq %rbp, %rsp
popq %rbp
cfi_def_cfa(7, 8)
cfi_restore(6)
ret
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
/* Branch to process
* special inputs
*/
L(SPECIAL_VALUES_BRANCH):
vmovups %ymm0, 32(%rsp)
vmovups %ymm1, 64(%rsp)
# LOE rbx r12 r13 r14 r15 edx ymm1
xorl %eax, %eax
# LOE rbx r12 r13 r14 r15 eax edx
vzeroupper
movq %r12, 16(%rsp)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
movl %eax, %r12d
movq %r13, 8(%rsp)
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
movl %edx, %r13d
movq %r14, (%rsp)
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
# LOE rbx r15 r12d r13d
/* Range mask
* bits check
*/
L(RANGEMASK_CHECK):
btl %r12d, %r13d
/* Call scalar math function */
jc L(SCALAR_MATH_CALL)
# LOE rbx r15 r12d r13d
/* Special inputs
* processing loop
*/
L(SPECIAL_VALUES_LOOP):
incl %r12d
cmpl $8, %r12d
/* Check bits in range mask */
jl L(RANGEMASK_CHECK)
# LOE rbx r15 r12d r13d
movq 16(%rsp), %r12
cfi_restore(12)
movq 8(%rsp), %r13
cfi_restore(13)
movq (%rsp), %r14
cfi_restore(14)
vmovups 64(%rsp), %ymm1
/* Go to exit */
jmp L(EXIT)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
# LOE rbx r12 r13 r14 r15 ymm1
/* Scalar math fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movss 32(%rsp,%r14,4), %xmm0
call exp2f@PLT
# LOE rbx r14 r15 r12d r13d xmm0
movss %xmm0, 64(%rsp,%r14,4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVdN8v_exp2f_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_sexp2_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct
{
__declspec(align(32)) VUINT32 _sShifter[8][1];
__declspec(align(32)) VUINT32 _sPC0[8][1];
__declspec(align(32)) VUINT32 _sPC1[8][1];
__declspec(align(32)) VUINT32 _sPC2[8][1];
__declspec(align(32)) VUINT32 _sPC3[8][1];
__declspec(align(32)) VUINT32 _sPC4[8][1];
__declspec(align(32)) VUINT32 _sPC5[8][1];
__declspec(align(32)) VUINT32 _sPC6[8][1];
__declspec(align(32)) VUINT32 _iAbsMask[8][1];
__declspec(align(32)) VUINT32 _iDomainRange[8][1];
} __svml_sexp2_data_internal;
#endif
__svml_sexp2_data_internal:
.long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter */
.align 32
.long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 /* _sPC0 */
.align 32
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 /* _sPC1 */
.align 32
.long 0x3e75fdef, 0x3e75fdef, 0x3e75fdef, 0x3e75fdef, 0x3e75fdef, 0x3e75fdef, 0x3e75fdef, 0x3e75fdef /* _sPC2 */
.align 32
.long 0x3d6357cf, 0x3d6357cf, 0x3d6357cf, 0x3d6357cf, 0x3d6357cf, 0x3d6357cf, 0x3d6357cf, 0x3d6357cf /* _sPC3 */
.align 32
.long 0x3c1d962c, 0x3c1d962c, 0x3c1d962c, 0x3c1d962c, 0x3c1d962c, 0x3c1d962c, 0x3c1d962c, 0x3c1d962c /* _sPC4 */
.align 32
.long 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51 /* _sPC5 */
.align 32
.long 0x39213c8c, 0x39213c8c, 0x39213c8c, 0x39213c8c, 0x39213c8c, 0x39213c8c, 0x39213c8c, 0x39213c8c /* _sPC6 */
//common
.align 32
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */
.align 32
.long 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000 /* _iDomainRange=126.0 */
.align 32
.type __svml_sexp2_data_internal,@object
.size __svml_sexp2_data_internal,.-__svml_sexp2_data_internal
|
