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
|
/* Function atanhf vectorized with AVX2.
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))
*
* 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. Ordered
by use in the function. On cold-starts this might hhelp 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. */
#define SgnMask 0
#define sOne 32
#define sTopMask12 64
#define TinyRange 96
#define iBrkValue 128
#define iOffExpoMask 160
#define sPoly 192
#define sLn2 448
#define sHalf 480
#include <sysdep.h>
#define ATANHF_DATA(x) ((x)+__svml_satanh_data_internal)
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_atanhf_avx2)
/* Strip off the sign, so treat X as positive until right at the end */
vmovaps ATANHF_DATA(SgnMask)(%rip), %ymm2
vandps %ymm2, %ymm0, %ymm3
/* Load constants including One = 1 */
vmovups ATANHF_DATA(sOne)(%rip), %ymm5
vsubps %ymm3, %ymm5, %ymm1
vmovups ATANHF_DATA(sTopMask12)(%rip), %ymm4
vrcpps %ymm1, %ymm7
vsubps %ymm1, %ymm5, %ymm9
vandps %ymm4, %ymm7, %ymm6
vsubps %ymm3, %ymm9, %ymm7
/* No need to split sU when FMA is available */
vfnmadd213ps %ymm5, %ymm6, %ymm1
vmovaps %ymm0, %ymm8
vfmadd213ps %ymm0, %ymm0, %ymm0
vfnmadd231ps %ymm6, %ymm7, %ymm1
/*
* Check whether |X| < 1, in which case we use the main function.
* Otherwise set the rangemask so that the callout will get used.
* Note that this will also use the callout for NaNs since not(NaN < 1).
*/
vcmpnlt_uqps %ymm5, %ymm3, %ymm14
vcmplt_oqps ATANHF_DATA(TinyRange)(%rip), %ymm3, %ymm15
/*
* Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
* the upper part UHi being <= 12 bits long. Then we have
* atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)).
*/
vaddps %ymm3, %ymm3, %ymm3
/*
* Split V as well into upper 12 bits and lower part, so that we can get
* a preliminary quotient estimate without rounding error.
*/
vandps %ymm4, %ymm3, %ymm4
vsubps %ymm4, %ymm3, %ymm7
/* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
vmulps %ymm4, %ymm6, %ymm4
/* Compute D = E + E^2 */
vfmadd213ps %ymm1, %ymm1, %ymm1
/* Record the sign for eventual reincorporation. */
vandnps %ymm8, %ymm2, %ymm3
/* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
vorps %ymm3, %ymm0, %ymm13
vmulps %ymm7, %ymm6, %ymm2
/*
* Compute R * (VHi + VLo) * (1 + E + E^2)
* = R * (VHi + VLo) * (1 + D)
* = QHi + (QHi * D + QLo + QLo * D)
*/
/*
* If less precision is acceptable the `vmulps %ymm1, %ymm4, %ymm9;
* vaddps %ymm1, %ymm9, %ymm1` can be replaced with
* `vfmadd231ps %ymm1, %ymm4, %ymm4`.
*/
vmulps %ymm1, %ymm4, %ymm6
vfmadd213ps %ymm2, %ymm2, %ymm1
vaddps %ymm1, %ymm6, %ymm1
/*
* Now finally accumulate the high and low parts of the
* argument to log1p, H + L, with a final compensated summation.
*/
vaddps %ymm1, %ymm4, %ymm2
/* reduction: compute r, n */
vmovups ATANHF_DATA(iBrkValue)(%rip), %ymm9
/*
* Now we feed into the log1p code, using H in place of _VARG1 and
* later incorporating L into the reduced argument.
* compute 1+x as high, low parts
*/
vmaxps %ymm2, %ymm5, %ymm0
vminps %ymm2, %ymm5, %ymm6
/* This is needed for rounding (see `vaddps %ymm1, %ymm4, %ymm2`). */
vsubps %ymm2, %ymm4, %ymm2
vaddps %ymm6, %ymm0, %ymm4
vpsubd %ymm9, %ymm4, %ymm7
vsubps %ymm4, %ymm0, %ymm4
vaddps %ymm2, %ymm1, %ymm2
vmovaps ATANHF_DATA(iOffExpoMask)(%rip), %ymm1
vandps %ymm1, %ymm7, %ymm0
vaddps %ymm4, %ymm6, %ymm4
vandnps %ymm7, %ymm1, %ymm6
vmovups ATANHF_DATA(sPoly+0)(%rip), %ymm1
vpaddd %ymm9, %ymm0, %ymm0
vaddps %ymm4, %ymm2, %ymm4
vpsubd %ymm6, %ymm5, %ymm6
/* polynomial evaluation */
vsubps %ymm5, %ymm0, %ymm2
vfmadd231ps %ymm4, %ymm6, %ymm2
vfmadd213ps ATANHF_DATA(sPoly+32)(%rip), %ymm2, %ymm1
vfmadd213ps ATANHF_DATA(sPoly+64)(%rip), %ymm2, %ymm1
vfmadd213ps ATANHF_DATA(sPoly+96)(%rip), %ymm2, %ymm1
vfmadd213ps ATANHF_DATA(sPoly+128)(%rip), %ymm2, %ymm1
vfmadd213ps ATANHF_DATA(sPoly+160)(%rip), %ymm2, %ymm1
vfmadd213ps ATANHF_DATA(sPoly+192)(%rip), %ymm2, %ymm1
vfmadd213ps ATANHF_DATA(sPoly+224)(%rip), %ymm2, %ymm1
vmulps %ymm1, %ymm2, %ymm1
vfmadd213ps %ymm2, %ymm2, %ymm1
/* final reconstruction */
vpsrad $23, %ymm7, %ymm6
vcvtdq2ps %ymm6, %ymm2
vfmadd132ps ATANHF_DATA(sLn2)(%rip), %ymm1, %ymm2
/* Finally, halve the result and reincorporate the sign */
vxorps ATANHF_DATA(sHalf)(%rip), %ymm3, %ymm3
vmulps %ymm2, %ymm3, %ymm2
vmovmskps %ymm14, %edx
testl %edx, %edx
vblendvps %ymm15, %ymm13, %ymm2, %ymm0
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx rdx r12 r13 r14 r15 ymm0
/* No registers 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 ymm0 ymm8
/* 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 ymm vectors. */
andq $-32, %rsp
addq $-64, %rsp
/* Save all already computed inputs. */
vmovups %ymm0, (%rsp)
/* Save original input (ymm8 unchanged up to this point). */
vmovups %ymm8, 32(%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, 28] 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 fucntion call to process special input. */
vmovss 32(%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). */
vmovups (%rsp), %ymm0
/* 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(_ZGVdN8v_atanhf_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_satanh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct{
__declspec(align(32)) VUINT32 SgnMask[8][1];
__declspec(align(32)) VUINT32 sOne[8][1];
__declspec(align(32)) VUINT32 sTopMask12[8][1];
__declspec(align(32)) VUINT32 TinyRange[8][1];
__declspec(align(32)) VUINT32 iBrkValue[8][1];
__declspec(align(32)) VUINT32 iOffExpoMask[8][1];
__declspec(align(32)) VUINT32 sPoly[8][8][1];
__declspec(align(32)) VUINT32 sLn2[8][1];
__declspec(align(32)) VUINT32 sHalf[8][1];
} __svml_satanh_data_internal;
#endif
__svml_satanh_data_internal:
/* SgnMask */
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
/* sOne = SP 1.0 */
.align 32
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/* sTopMask12 */
.align 32
.long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
.long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
/* TinyRange */
.align 32
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
/* iBrkValue = SP 2/3 */
.align 32
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
/* iOffExpoMask = SP significand mask */
.align 32
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
/* sPoly[] = SP polynomial */
.align 32
.long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed
.long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
.long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3
.long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
.long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12
.long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
.long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37
.long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
.long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190
.long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
.long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e
.long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
.long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94
.long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
/* sLn2 = SP ln(2) */
.align 32
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
/* sHalf */
.align 32
.long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
.long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
.align 32
.type __svml_satanh_data_internal, @object
.size __svml_satanh_data_internal, .-__svml_satanh_data_internal
|
