1/* Function tanhf vectorized with AVX-512.
2 Copyright (C) 2021-2024 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 https://www.gnu.org/licenses/. */
18
19/*
20 * ALGORITHM DESCRIPTION:
21 *
22 * NOTE: Since the hyperbolic tangent function is odd
23 * (tanh(x) = -tanh(-x)), below algorithm deals with the absolute
24 * value of the argument |x|: tanh(x) = sign(x) * tanh(|x|)
25 *
26 * We use a table lookup method to compute tanh(|x|).
27 * The basic idea is to split the input range into a number of subintervals
28 * and to approximate tanh(.) with a polynomial on each of them.
29 *
30 * IEEE SPECIAL CONDITIONS:
31 * x = [+, -]0, r = [+, -]0
32 * x = +Inf, r = +1
33 * x = -Inf, r = -1
34 * x = QNaN, r = QNaN
35 * x = SNaN, r = QNaN
36 *
37 *
38 * ALGORITHM DETAILS
39 * We handle special values in a callout function, aside from main path
40 * computations. "Special" for this algorithm are:
41 * INF, NAN, |x| > HUGE_THRESHOLD
42 *
43 *
44 * Main path computations are organized as follows:
45 * Actually we split the interval [0, SATURATION_THRESHOLD)
46 * into a number of subintervals. On each subinterval we approximate tanh(.)
47 * with a minimax polynomial of pre-defined degree. Polynomial coefficients
48 * are computed beforehand and stored in table. We also use
49 *
50 * y := |x| + B,
51 *
52 * here B depends on subinterval and is used to make argument
53 * closer to zero.
54 * We also add large fake interval [SATURATION_THRESHOLD, HUGE_THRESHOLD],
55 * where 1.0 + 0.0*y + 0.0*y^2 ... coefficients are stored - just to
56 * preserve main path computation logic but return 1.0 for all arguments.
57 *
58 * Hence reconstruction looks as follows:
59 * we extract proper polynomial and range reduction coefficients
60 * (Pj and B), corresponding to subinterval, to which |x| belongs,
61 * and return
62 *
63 * r := sign(x) * (P0 + P1 * y + ... + Pn * y^n)
64 *
65 * NOTE: we use multiprecision technique to multiply and sum the first
66 * K terms of the polynomial. So Pj, j = 0..K are stored in
67 * table each as a pair of target precision numbers (Pj and PLj) to
68 * achieve wider than target precision.
69 *
70 *
71 */
72
73/* Offsets for data table __svml_stanh_data_internal_avx512. Ordered
74 by use in the function. On cold-starts this might help the
75 prefetcher. Possibly a better idea is to interleave start/end so
76 that the prefetcher is less likely to detect a stream and pull
77 irrelivant lines into cache. */
78
79/* Offsets for data table __svml_stanh_data_internal. 4 bytes each.
80 */
81#define _iExpMantMask_UISA 0
82#define _iMinIdxOfsMask_UISA 4
83#define _iMaxIdxMask_UISA 8
84#define _iExpMask 12
85
86/* Offsets for data table __svml_stanh_data_internal_al64. 64 bytes
87 each. */
88#define _sC_lo 0
89#define _sC_hi 64
90#define _sP7_lo 128
91#define _sP7_hi 192
92#define _sSignMask 256
93#define _sP6_lo 320
94#define _sP6_hi 384
95#define _sP5_lo 448
96#define _sP5_hi 512
97#define _sP4_lo 576
98#define _sP4_hi 640
99#define _sP3_lo 704
100#define _sP3_hi 768
101#define _sP2_lo 832
102#define _sP2_hi 896
103#define _sP0_lo 960
104#define _sP0_hi 1024
105
106#include <sysdep.h>
107#define TANHF_DATA(x) ((x)+__svml_stanh_data_internal_al64)
108#define TANHF_DATA_UNALIGNED(x) ((x)+__svml_stanh_data_internal)
109
110 .section .text.evex512, "ax", @progbits
111ENTRY(_ZGVeN16v_tanhf_skx)
112 /* Here huge arguments, INF and NaNs are filtered out to callout. */
113 vpandd TANHF_DATA_UNALIGNED(_iExpMantMask_UISA)(%rip){1to16}, %zmm0, %zmm1
114 vpsubd TANHF_DATA_UNALIGNED(_iMinIdxOfsMask_UISA)(%rip){1to16}, %zmm1, %zmm2
115
116 /* Selection arguments between [0, 0x03e00000] into zmm3. */
117 vpxord %zmm3, %zmm3, %zmm3
118 vpmaxsd %zmm3, %zmm2, %zmm3
119 vpminsd TANHF_DATA_UNALIGNED(_iMaxIdxMask_UISA)(%rip){1to16}, %zmm3, %zmm3
120
121 /* Setup permute indices in zmm3. */
122 vpsrld $21, %zmm3, %zmm3
123
124 /* Store if there are any special cases in k1. */
125 vpcmpd $6, TANHF_DATA_UNALIGNED(_iExpMask)(%rip){1to16}, %zmm1, %k1
126
127 vmovaps TANHF_DATA(_sC_lo)(%rip), %zmm5
128 vpermt2ps TANHF_DATA(_sC_hi)(%rip), %zmm3, %zmm5
129
130 vmovaps TANHF_DATA(_sP7_lo)(%rip), %zmm2
131 vpermt2ps TANHF_DATA(_sP7_hi)(%rip), %zmm3, %zmm2
132
133 /* Store absolute values of inputs in zmm1. */
134 vmovaps TANHF_DATA(_sSignMask)(%rip), %zmm4
135 vandnps %zmm0, %zmm4, %zmm1
136 vsubps {rn-sae}, %zmm5, %zmm1, %zmm1
137
138 vmovaps TANHF_DATA(_sP6_lo)(%rip), %zmm5
139 vpermt2ps TANHF_DATA(_sP6_hi)(%rip), %zmm3, %zmm5
140
141 vmovaps TANHF_DATA(_sP5_lo)(%rip), %zmm6
142 vpermt2ps TANHF_DATA(_sP5_hi)(%rip), %zmm3, %zmm6
143
144 vfmadd213ps {rn-sae}, %zmm5, %zmm1, %zmm2
145 vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm2
146
147 vmovaps TANHF_DATA(_sP4_lo)(%rip), %zmm7
148 vpermt2ps TANHF_DATA(_sP4_hi)(%rip), %zmm3, %zmm7
149
150 vmovaps TANHF_DATA(_sP3_lo)(%rip), %zmm8
151 vpermt2ps TANHF_DATA(_sP3_hi)(%rip), %zmm3, %zmm8
152
153 vfmadd213ps {rn-sae}, %zmm7, %zmm1, %zmm2
154 vfmadd213ps {rn-sae}, %zmm8, %zmm1, %zmm2
155
156 vmovaps TANHF_DATA(_sP2_lo)(%rip), %zmm9
157 vpermt2ps TANHF_DATA(_sP2_hi)(%rip), %zmm3, %zmm9
158
159 vmovaps TANHF_DATA(_sP0_lo)(%rip), %zmm10
160 vpermt2ps TANHF_DATA(_sP0_hi)(%rip), %zmm3, %zmm10
161
162 vfmadd213ps {rn-sae}, %zmm9, %zmm1, %zmm2
163 vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm2
164
165 kmovw %k1, %edx
166 testl %edx, %edx
167
168 /* Go to special inputs processing branch. */
169 jne L(SPECIAL_VALUES_BRANCH)
170 # LOE rbx r12 r13 r14 r15 zmm0 zmm2 zmm4
171 /* Wait until after branch of write over zmm0. */
172 vpternlogd $0xec, %zmm4, %zmm2, %zmm0
173
174 /* No stack restoration on the fastpath. */
175 ret
176
177 /* Cold case. edx has 1s where there was a special value that
178 needs to be handled by a tanhf call. Optimize for code size
179 more so than speed here. */
180L(SPECIAL_VALUES_BRANCH):
181 # LOE rbx rdx r12 r13 r14 r15 zmm0 zmm2 zmm4
182 /* Use r13 to save/restore the stack. This allows us to use rbp as
183 callee save register saving code size. */
184 pushq %r13
185 cfi_adjust_cfa_offset(8)
186 cfi_offset(r13, -16)
187 /* Need to callee save registers to preserve state across tanhf calls.
188 */
189 pushq %rbx
190 cfi_adjust_cfa_offset(8)
191 cfi_offset(rbx, -24)
192 pushq %rbp
193 cfi_adjust_cfa_offset(8)
194 cfi_offset(rbp, -32)
195 movq %rsp, %r13
196 cfi_def_cfa_register(r13)
197
198 /* Align stack and make room for 2x zmm vectors. */
199 andq $-64, %rsp
200 addq $-128, %rsp
201
202 /* Save original input (zmm0 unchanged up to this point). */
203 vmovaps %zmm0, 64(%rsp)
204 /* Save all already computed inputs. */
205 vpternlogd $0xec, %zmm4, %zmm2, %zmm0
206 vmovaps %zmm0, (%rsp)
207
208 vzeroupper
209
210 /* edx has 1s where there was a special value that needs to be handled
211 by a tanhf call. */
212 movl %edx, %ebx
213L(SPECIAL_VALUES_LOOP):
214 # LOE rbx rbp r12 r13 r14 r15
215 /* use rbp as index for special value that is saved across calls to
216 tanhf. We technically don't need a callee save register here as offset
217 to rsp is always [0, 56] so we can restore rsp by realigning to 64.
218 Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
219 in the loop. Realigning also costs more code size. */
220 xorl %ebp, %ebp
221 tzcntl %ebx, %ebp
222
223 /* Scalar math function call to process special input. */
224 vmovss 64(%rsp, %rbp, 4), %xmm0
225 call tanhf@PLT
226
227 /* No good way to avoid the store-forwarding fault this will cause on
228 return. `lfence` avoids the SF fault but at greater cost as it
229 serialized stack/callee save restoration. */
230 vmovss %xmm0, (%rsp, %rbp, 4)
231
232 blsrl %ebx, %ebx
233 jnz L(SPECIAL_VALUES_LOOP)
234 # LOE r12 r13 r14 r15
235
236 /* All results have been written to (%rsp). */
237 vmovaps (%rsp), %zmm0
238 /* Restore rsp. */
239 movq %r13, %rsp
240 cfi_def_cfa_register(rsp)
241 /* Restore callee save registers. */
242 popq %rbp
243 cfi_adjust_cfa_offset(-8)
244 cfi_restore(rbp)
245 popq %rbx
246 cfi_adjust_cfa_offset(-8)
247 cfi_restore(rbp)
248 popq %r13
249 cfi_adjust_cfa_offset(-8)
250 cfi_restore(r13)
251 ret
252END(_ZGVeN16v_tanhf_skx)
253
254 .section .rodata, "a"
255 .align 16
256#ifdef __svml_stanh_data_internal_typedef
257typedef unsigned int VUINT32;
258typedef struct
259 {
260 __declspec(align(4)) VUINT32 _iExpMantMask_UISA[1][1];
261 __declspec(align(4)) VUINT32 _iMinIdxOfsMask_UISA[1][1];
262 __declspec(align(4)) VUINT32 _iMaxIdxMask_UISA[1][1];
263 __declspec(align(4)) VUINT32 _iExpMask[1][1];
264 __declspec(align(64)) VUINT32 _sC_lo[16][1];
265 __declspec(align(64)) VUINT32 _sC_hi[16][1];
266 __declspec(align(64)) VUINT32 _sP7_lo[16][1];
267 __declspec(align(64)) VUINT32 _sP7_hi[16][1];
268 __declspec(align(64)) VUINT32 _sSignMask[16][1];
269 __declspec(align(64)) VUINT32 _sP6_lo[16][1];
270 __declspec(align(64)) VUINT32 _sP6_hi[16][1];
271 __declspec(align(64)) VUINT32 _sP5_lo[16][1];
272 __declspec(align(64)) VUINT32 _sP5_hi[16][1];
273 __declspec(align(64)) VUINT32 _sP4_lo[16][1];
274 __declspec(align(64)) VUINT32 _sP4_hi[16][1];
275 __declspec(align(64)) VUINT32 _sP3_lo[16][1];
276 __declspec(align(64)) VUINT32 _sP3_hi[16][1];
277 __declspec(align(64)) VUINT32 _sP2_lo[16][1];
278 __declspec(align(64)) VUINT32 _sP2_hi[16][1];
279 __declspec(align(64)) VUINT32 _sP0_lo[16][1];
280 __declspec(align(64)) VUINT32 _sP0_hi[16][1];
281} __svml_stanh_data_internal;
282#endif
283
284__svml_stanh_data_internal:
285 .align 4
286 /* _iExpMantMask_UISA */
287 .long 0x7fe00000
288
289 .align 4
290 /* _iMinIdxOfsMask_UISA */
291 .long 0x3d400000
292
293 .align 4
294 /* _iMaxIdxMask_UISA */
295 .long 0x03e00000
296
297 .align 4
298 /* _iExpMask */
299 .long 0x7f000000
300
301 .align 64
302__svml_stanh_data_internal_al64:
303 .align 64
304 /* _sC_lo */
305 .long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
306 .long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
307 .long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
308 .long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
309
310 .align 64
311 /* _sC_hi */
312 .long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
313 .long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
314 .long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
315 .long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
316
317 .align 64
318 /* _sP7_lo */
319 .long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
320 .long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
321 .long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
322 .long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
323
324 .align 64
325 /* _sP7_hi */
326 .long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
327 .long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
328 .long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
329 .long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
330
331 .align 64
332 /* _sSignMask */
333 .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
334 .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
335 .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
336 .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
337
338 .align 64
339 /* _sP6_lo */
340 .long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
341 .long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
342 .long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
343 .long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
344
345 .align 64
346 /* _sP6_hi */
347 .long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
348 .long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
349 .long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
350 .long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
351
352 .align 64
353 /* _sP5_lo */
354 .long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
355 .long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
356 .long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
357 .long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
358
359 .align 64
360 /* _sP5_hi */
361 .long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
362 .long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
363 .long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
364 .long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
365
366 .align 64
367 /* _sP4_lo */
368 .long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
369 .long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
370 .long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
371 .long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
372
373 .align 64
374 /* _sP4_hi */
375 .long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
376 .long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
377 .long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
378 .long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
379
380 .align 64
381 /* _sP3_lo */
382 .long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
383 .long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
384 .long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
385 .long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
386
387 .align 64
388 /* _sP3_hi */
389 .long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
390 .long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
391 .long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
392 .long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
393
394 .align 64
395 /* _sP2_lo */
396 .long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
397 .long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
398 .long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
399 .long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
400
401 .align 64
402 /* _sP2_hi */
403 .long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
404 .long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
405 .long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
406 .long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
407
408 .align 64
409 /* _sP0_lo */
410 .long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
411 .long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
412 .long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
413 .long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
414
415 .align 64
416 /* _sP0_hi */
417 .long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
418 .long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
419 .long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
420 .long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
421
422 .align 64
423 .type __svml_stanh_data_internal_al64, @object
424 .size __svml_stanh_data_internal_al64, .-__svml_stanh_data_internal_al64
425 .type __svml_stanh_data_internal, @object
426 .size __svml_stanh_data_internal, .-__svml_stanh_data_internal
427

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf16_core_avx512.S