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
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
|
/* Function atanhf vectorized with AVX-512.
Copyright (C) 2021-2023 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/. */
/*
* ALGORITHM DESCRIPTION:
*
* Compute atanh(x) as 0.5 * log((1 + x)/(1 - x))
* using small lookup table that map to AVX-512 permute instructions
*
* Special cases:
*
* atanh(0) = 0
* atanh(+1) = +INF
* atanh(-1) = -INF
* atanh(x) = NaN if |x| > 1, or if x is a NaN or INF
*
*/
/* Offsets for data table __svml_satanh_data_internal_avx512 and
__svml_satanh_data_internal_avx512_al64. Ordered by use in the
function. On cold-starts this might help the prefetcher. Possibly
a better idea is to interleave start/end so that the prefetcher is
less likely to detect a stream and pull irrelivant lines into
cache. */
/* Offset into __svml_satanh_data_internal_avx512. 4-byte aligned as
the memory is broadcast to {1to16}. */
#define AbsMask 0
/* Offset into __svml_satanh_data_internal_avx512_al64. The full value
is used here. */
#define One 0
#define AddB5 64
#define RcpBitMask 128
#define Log_tbl_L_lo 192
#define Log_tbl_L_hi 256
#define Log_tbl_H_lo 320
#define Log_tbl_H_hi 384
#define L2H 448
#define L2L 512
#define poly_coeff3 576
#define poly_coeff2 640
#define poly_coeff1 704
#include <sysdep.h>
#define ATANHF_DATA(x) ((x)+__svml_satanh_data_internal_avx512_al64)
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_atanhf_skx)
vandps AbsMask+__svml_satanh_data_internal_avx512(%rip){1to16}, %zmm0, %zmm6
vmovups ATANHF_DATA(One)(%rip), %zmm4
/* 1+y */
vaddps {rn-sae}, %zmm4, %zmm6, %zmm9
/* 1-y */
vsubps {rn-sae}, %zmm6, %zmm4, %zmm8
/* round reciprocals to 1+5b mantissas */
vmovups ATANHF_DATA(AddB5)(%rip), %zmm14
vmovups ATANHF_DATA(RcpBitMask)(%rip), %zmm1
/* RcpP ~ 1/Yp */
vrcp14ps %zmm9, %zmm12
/* RcpM ~ 1/Ym */
vrcp14ps %zmm8, %zmm13
/* Yp_high */
vsubps {rn-sae}, %zmm4, %zmm9, %zmm2
/* -Ym_high */
vsubps {rn-sae}, %zmm4, %zmm8, %zmm5
/* input outside (-1, 1) ? */
vpaddd %zmm14, %zmm12, %zmm15
vpaddd %zmm14, %zmm13, %zmm12
/* Yp_low */
vsubps {rn-sae}, %zmm2, %zmm6, %zmm3
vandps %zmm1, %zmm15, %zmm7
vandps %zmm1, %zmm12, %zmm12
/* Ym_low */
vaddps {rn-sae}, %zmm5, %zmm6, %zmm5
/* Reduced argument: Rp = (RcpP*Yp - 1)+RcpP*Yp_low */
vfmsub213ps {rn-sae}, %zmm4, %zmm7, %zmm9
/* Reduced argument: Rm = (RcpM*Ym - 1)+RcpM*Ym_low */
vfmsub213ps {rn-sae}, %zmm4, %zmm12, %zmm8
vmovups ATANHF_DATA(Log_tbl_L_lo)(%rip), %zmm10
vmovups ATANHF_DATA(Log_tbl_L_hi)(%rip), %zmm13
/* exponents */
vfmadd231ps {rn-sae}, %zmm7, %zmm3, %zmm9
vgetexpps {sae}, %zmm7, %zmm15
/* Table lookups */
vfnmadd231ps {rn-sae}, %zmm12, %zmm5, %zmm8
vgetexpps {sae}, %zmm12, %zmm14
/* Prepare table index */
vpsrld $18, %zmm7, %zmm3
vpsrld $18, %zmm12, %zmm2
vmovups ATANHF_DATA(Log_tbl_H_lo)(%rip), %zmm11
vmovups ATANHF_DATA(Log_tbl_H_hi)(%rip), %zmm7
/* Km-Kp */
vmovaps %zmm3, %zmm5
vpermi2ps %zmm13, %zmm10, %zmm3
vpermt2ps %zmm13, %zmm2, %zmm10
vpermi2ps %zmm7, %zmm11, %zmm5
vpermt2ps %zmm7, %zmm2, %zmm11
vsubps {rn-sae}, %zmm15, %zmm14, %zmm1
vsubps {rn-sae}, %zmm3, %zmm10, %zmm7
/* K*L2H + Th */
vmovups ATANHF_DATA(L2H)(%rip), %zmm2
/* K*L2L + Tl */
vmovups ATANHF_DATA(L2L)(%rip), %zmm3
/* table values */
vsubps {rn-sae}, %zmm5, %zmm11, %zmm5
vfmadd231ps {rn-sae}, %zmm1, %zmm2, %zmm5
vfmadd213ps {rn-sae}, %zmm7, %zmm3, %zmm1
/* polynomials */
vmovups ATANHF_DATA(poly_coeff3)(%rip), %zmm7
vmovups ATANHF_DATA(poly_coeff2)(%rip), %zmm10
vmovaps %zmm10, %zmm14
vfmadd231ps {rn-sae}, %zmm9, %zmm7, %zmm10
vfmadd231ps {rn-sae}, %zmm8, %zmm7, %zmm14
vmovups ATANHF_DATA(poly_coeff1)(%rip), %zmm12
vfmadd213ps {rn-sae}, %zmm12, %zmm9, %zmm10
vfmadd213ps {rn-sae}, %zmm12, %zmm8, %zmm14
vfmadd213ps {rn-sae}, %zmm4, %zmm9, %zmm10
vfmadd213ps {rn-sae}, %zmm4, %zmm8, %zmm14
/* (K*L2L + Tl) + Rp*PolyP */
vfmadd213ps {rn-sae}, %zmm1, %zmm9, %zmm10
/* zmm12 = zmm12 & (zmm4 | zmm0). */
vpternlogq $0xe0, %zmm0, %zmm4, %zmm12
/* (K*L2L + Tl) + Rp*PolyP -Rm*PolyM */
vfnmadd213ps {rn-sae}, %zmm5, %zmm8, %zmm14
vaddps {rn-sae}, %zmm14, %zmm10, %zmm8
vcmpps $21, {sae}, %zmm4, %zmm6, %k0
kmovw %k0, %edx
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 zmm0 zmm8 zmm12
vmulps {rn-sae}, %zmm12, %zmm8, %zmm0
/* No register to restore on fast path. */
ret
/* Cold case. edx has 1s where there was a special value that
needs to be handled by a atanhf call. Optimize for code size
more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
# LOE rbx rdx r12 r13 r14 r15 zmm0 zmm8 zmm12
/* Use r13 to save/restore the stack. This allows us to use rbp as
callee save register saving code size. */
pushq %r13
cfi_adjust_cfa_offset(8)
cfi_offset(r13, -16)
/* Need to callee save registers to preserve state across tanhf calls.
*/
pushq %rbx
cfi_adjust_cfa_offset(8)
cfi_offset(rbx, -24)
pushq %rbp
cfi_adjust_cfa_offset(8)
cfi_offset(rbp, -32)
movq %rsp, %r13
cfi_def_cfa_register(r13)
/* Align stack and make room for 2x zmm vectors. */
andq $-64, %rsp
addq $-128, %rsp
vmulps {rn-sae}, %zmm12, %zmm8, %zmm1
vmovaps %zmm1, (%rsp)
vmovaps %zmm0, 64(%rsp)
vzeroupper
/* edx has 1s where there was a special value that needs to be handled
by a atanhf call. */
movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
# LOE rbx rbp r12 r13 r14 r15
/* use rbp as index for special value that is saved across calls to
atanhf. We technically don't need a callee save register here as offset
to rsp is always [0, 56] so we can restore rsp by realigning to 64.
Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
in the loop. Realigning also costs more code size. */
xorl %ebp, %ebp
tzcntl %ebx, %ebp
/* Scalar math function call to process special input. */
vmovss 64(%rsp, %rbp, 4), %xmm0
call atanhf@PLT
/* No good way to avoid the store-forwarding fault this will cause on
return. `lfence` avoids the SF fault but at greater cost as it
serialized stack/callee save restoration. */
vmovss %xmm0, (%rsp, %rbp, 4)
blsrl %ebx, %ebx
jnz L(SPECIAL_VALUES_LOOP)
# LOE r12 r13 r14 r15
/* All results have been written to (%rsp). */
vmovaps (%rsp), %zmm0
/* Restore rsp. */
movq %r13, %rsp
cfi_def_cfa_register(rsp)
/* Restore callee save registers. */
popq %rbp
cfi_adjust_cfa_offset(-8)
cfi_restore(rbp)
popq %rbx
cfi_adjust_cfa_offset(-8)
cfi_restore(rbp)
popq %r13
cfi_adjust_cfa_offset(-8)
cfi_restore(r13)
ret
END(_ZGVeN16v_atanhf_skx)
.section .rodata, "a"
.align 4
#ifdef __svml_satanh_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct{
__declspec(align(4)) VUINT32 AbsMask[1][1];
__declspec(align(64)) VUINT32 One[16][1];
__declspec(align(64)) VUINT32 AddB5[16][1];
__declspec(align(64)) VUINT32 RcpBitMask[16][1];
__declspec(align(64)) VUINT32 Log_tbl_L_lo[16][1];
__declspec(align(64)) VUINT32 Log_tbl_L_hi[16][1];
__declspec(align(64)) VUINT32 Log_tbl_H_lo[16][1];
__declspec(align(64)) VUINT32 Log_tbl_H_hi[16][1];
__declspec(align(64)) VUINT32 L2H[16][1];
__declspec(align(64)) VUINT32 L2L[16][1];
__declspec(align(64)) VUINT32 poly_coeff3[16][1];
__declspec(align(64)) VUINT32 poly_coeff2[16][1];
__declspec(align(64)) VUINT32 poly_coeff1[16][1];
} __svml_satanh_data_internal_avx512;
#endif
__svml_satanh_data_internal_avx512:
/* Leave this at front so we can potentially save space due to
smaller alignment constraint. */
.align 4
/* AbsMask */
.long 0x7fffffff
.align 64
__svml_satanh_data_internal_avx512_al64:
/* One */
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/* AddB5 */
.align 64
.long 0x00020000, 0x00020000, 0x00020000, 0x00020000
.long 0x00020000, 0x00020000, 0x00020000, 0x00020000
.long 0x00020000, 0x00020000, 0x00020000, 0x00020000
.long 0x00020000, 0x00020000, 0x00020000, 0x00020000
/* RcpBitMask */
.align 64
.long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
.long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
.long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
.long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
/* Log_tbl_L_lo */
.align 64
.long 0x00000000
.long 0x3726c39e
.long 0x38a30c01
.long 0x37528ae5
.long 0x38e0edc5
.long 0xb8ab41f8
.long 0xb7cf8f58
.long 0x3896a73d
.long 0xb5838656
.long 0x380c36af
.long 0xb8235454
.long 0x3862bae1
.long 0x38c5e10e
.long 0x38dedfac
.long 0x38ebfb5e
.long 0xb8e63c9f
/* Log_tbl_L_hi */
.align 64
.long 0xb85c1340
.long 0x38777bcd
.long 0xb6038656
.long 0x37d40984
.long 0xb8b85028
.long 0xb8ad5a5a
.long 0x3865c84a
.long 0x38c3d2f5
.long 0x383ebce1
.long 0xb8a1ed76
.long 0xb7a332c4
.long 0xb779654f
.long 0xb8602f73
.long 0x38f85db0
.long 0x37b4996f
.long 0xb8bfb3ca
/* Log_tbl_H_lo */
.align 64
.long 0x00000000
.long 0x3cfc0000
.long 0x3d780000
.long 0x3db78000
.long 0x3df10000
.long 0x3e14c000
.long 0x3e300000
.long 0x3e4a8000
.long 0x3e648000
.long 0x3e7dc000
.long 0x3e8b4000
.long 0x3e974000
.long 0x3ea30000
.long 0x3eae8000
.long 0x3eb9c000
.long 0x3ec4e000
/* Log_tbl_H_hi */
.align 64
.long 0x3ecfa000
.long 0x3eda2000
.long 0x3ee48000
.long 0x3eeea000
.long 0x3ef8a000
.long 0x3f013000
.long 0x3f05f000
.long 0x3f0aa000
.long 0x3f0f4000
.long 0x3f13d000
.long 0x3f184000
.long 0x3f1ca000
.long 0x3f20f000
.long 0x3f252000
.long 0x3f295000
.long 0x3f2d7000
/* L2H = log(2)_high */
.align 64
.long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
.long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
.long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
.long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
/* L2L = log(2)_low */
.align 64
.long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
.long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
.long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
.long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
/* poly_coeff3 */
.align 64
.long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
.long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
.long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
.long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
/* poly_coeff2 */
.align 64
.long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
.long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
.long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
.long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
/* poly_coeff1 */
.align 64
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
.align 64
.type __svml_satanh_data_internal_avx512_al64, @object
.size __svml_satanh_data_internal_avx512_al64, .-__svml_satanh_data_internal_avx512_al64
.type __svml_satanh_data_internal_avx512, @object
.size __svml_satanh_data_internal_avx512, .-__svml_satanh_data_internal_avx512
|
