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
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
|
/* Function exp10f vectorized with AVX-512.
Copyright (C) 2021-2022 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/. */
/*
* ALGORITHM DESCRIPTION:
* Typical exp10() implementation, except that:
* - tables are small (16 elements), allowing for fast gathers
* - all arguments processed in the main path
* - final VSCALEF assists branch-free design (correct overflow/underflow and special case responses)
* - a VAND is used to ensure the reduced argument |R|<2, even for large inputs
* - RZ mode used to avoid oveflow to +/-Inf for x*log2(e); helps with special case handling
* - SAE used to avoid spurious flag settings
*
*/
/* Offsets for data table __svml_sexp10_data_internal_avx512
*/
#define Exp_tbl_L 0
#define Exp_tbl_H 128
#define L2E 256
#define Shifter 320
#define L2H 384
#define L2L 448
#define EMask 512
#define AbsMask 576
#define Threshold 640
#define poly_coeff2 704
#define poly_coeff1 768
#include <sysdep.h>
.section .text.exex512, "ax", @progbits
ENTRY(_ZGVeN16v_exp10f_skx)
pushq %rbp
cfi_def_cfa_offset(16)
movq %rsp, %rbp
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
andq $-64, %rsp
subq $192, %rsp
vmovups L2E+__svml_sexp10_data_internal_avx512(%rip), %zmm2
vmovups Shifter+__svml_sexp10_data_internal_avx512(%rip), %zmm1
vmovups L2H+__svml_sexp10_data_internal_avx512(%rip), %zmm5
vmovups L2L+__svml_sexp10_data_internal_avx512(%rip), %zmm4
/* ensure |R|<2 even for special cases */
vmovups EMask+__svml_sexp10_data_internal_avx512(%rip), %zmm6
vmovups poly_coeff2+__svml_sexp10_data_internal_avx512(%rip), %zmm9
/* 2^(52-4)*1.5 + x * log2(e) */
vfmadd213ps {rz-sae}, %zmm1, %zmm0, %zmm2
vmovups poly_coeff1+__svml_sexp10_data_internal_avx512(%rip), %zmm10
vmovups __svml_sexp10_data_internal_avx512(%rip), %zmm8
vmovups Exp_tbl_H+__svml_sexp10_data_internal_avx512(%rip), %zmm15
vmovups Threshold+__svml_sexp10_data_internal_avx512(%rip), %zmm13
vpsrld $5, %zmm2, %zmm3
/* Z0 ~ x*log2(e), rounded down to 6 fractional bits */
vsubps {rn-sae}, %zmm1, %zmm2, %zmm1
vpermt2ps Exp_tbl_L+64+__svml_sexp10_data_internal_avx512(%rip), %zmm2, %zmm8
vpermt2ps Exp_tbl_H+64+__svml_sexp10_data_internal_avx512(%rip), %zmm3, %zmm15
vandps AbsMask+__svml_sexp10_data_internal_avx512(%rip), %zmm0, %zmm12
/* R = x - Z0*log(2) */
vfnmadd213ps {rn-sae}, %zmm0, %zmm1, %zmm5
vcmpps $29, {sae}, %zmm13, %zmm12, %k0
vfnmadd231ps {rn-sae}, %zmm1, %zmm4, %zmm5
kmovw %k0, %edx
vrangeps $2, {sae}, %zmm6, %zmm5, %zmm11
vfmadd231ps {rn-sae}, %zmm11, %zmm9, %zmm10
vmulps {rn-sae}, %zmm11, %zmm10, %zmm14
/* x!=0? */
vpxord %zmm7, %zmm7, %zmm7
vcmpps $4, {sae}, %zmm7, %zmm0, %k1
/* Th*Tl */
vmulps {rn-sae}, %zmm8, %zmm15, %zmm15{%k1}
vfmadd213ps {rn-sae}, %zmm15, %zmm14, %zmm15
vscalefps {rn-sae}, %zmm1, %zmm15, %zmm1
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm1
/* Restore registers
* and exit the function
*/
L(EXIT):
vmovaps %zmm1, %zmm0
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 %zmm0, 64(%rsp)
vmovups %zmm1, 128(%rsp)
# LOE rbx r12 r13 r14 r15 edx zmm1
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: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 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: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
movl %edx, %r13d
movq %r14, (%rsp)
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 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 $16, %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 128(%rsp), %zmm1
/* Go to exit */
jmp L(EXIT)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
# LOE rbx r12 r13 r14 r15 zmm1
/* Scalar math fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movss 64(%rsp, %r14, 4), %xmm0
call exp10f@PLT
# LOE rbx r14 r15 r12d r13d xmm0
movss %xmm0, 128(%rsp, %r14, 4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN16v_exp10f_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_sexp10_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Exp_tbl_L[32][1];
__declspec(align(64)) VUINT32 Exp_tbl_H[32][1];
__declspec(align(64)) VUINT32 L2E[16][1];
__declspec(align(64)) VUINT32 Shifter[16][1];
__declspec(align(64)) VUINT32 L2H[16][1];
__declspec(align(64)) VUINT32 L2L[16][1];
__declspec(align(64)) VUINT32 EMask[16][1];
__declspec(align(64)) VUINT32 AbsMask[16][1];
__declspec(align(64)) VUINT32 Threshold[16][1];
__declspec(align(64)) VUINT32 poly_coeff2[16][1];
__declspec(align(64)) VUINT32 poly_coeff1[16][1];
} __svml_sexp10_data_internal_avx512;
#endif
__svml_sexp10_data_internal_avx512:
/* Exp_tbl_L */
.long 0x3f800001, 0x3f801631, 0x3f802c65, 0x3f80429d
.long 0x3f8058d9, 0x3f806f18, 0x3f80855c, 0x3f809ba3
.long 0x3f80b1ee, 0x3f80c83d, 0x3f80de90, 0x3f80f4e7
.long 0x3f810b42, 0x3f8121a0, 0x3f813803, 0x3f814e69
.long 0x3f8164d3, 0x3f817b41, 0x3f8191b3, 0x3f81a829
.long 0x3f81bea2, 0x3f81d520, 0x3f81eba2, 0x3f820227
.long 0x3f8218b0, 0x3f822f3d, 0x3f8245cf, 0x3f825c64
.long 0x3f8272fd, 0x3f828999, 0x3f82a03a, 0x3f82b6df
/* Exp_tbl_H */
.align 64
.long 0x3f800000, 0x3f82cd87, 0x3f85aac3, 0x3f88980f
.long 0x3f8b95c2, 0x3f8ea43a, 0x3f91c3d3, 0x3f94f4f0
.long 0x3f9837f0, 0x3f9b8d3a, 0x3f9ef532, 0x3fa27043
.long 0x3fa5fed7, 0x3fa9a15b, 0x3fad583f, 0x3fb123f6
.long 0x3fb504f3, 0x3fb8fbaf, 0x3fbd08a4, 0x3fc12c4d
.long 0x3fc5672a, 0x3fc9b9be, 0x3fce248c, 0x3fd2a81e
.long 0x3fd744fd, 0x3fdbfbb8, 0x3fe0ccdf, 0x3fe5b907
.long 0x3feac0c7, 0x3fefe4ba, 0x3ff5257d, 0x3ffa83b3
/* log2(10) */
.align 64
.long 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78, 0x40549A78
/* Shifter=2^(23-10)*1.5 */
.align 64
.long 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000, 0x46400000
/* L2H = log(2)_high */
.align 64
.long 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b, 0x3e9a209b
/* L2L = log(2)_low */
.align 64
.long 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860, 0xb2760860
/* EMask */
.align 64
.long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000
/* AbsMask */
.align 64
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
/* Threshold */
.align 64
.long 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818, 0x4217B818
/* poly_coeff2 */
.align 64
.long 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA, 0x4029B7DA
/* poly_coeff1 */
.align 64
.long 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D, 0x40135D8D
.align 64
.type __svml_sexp10_data_internal_avx512, @object
.size __svml_sexp10_data_internal_avx512, .-__svml_sexp10_data_internal_avx512
|
