1 | /* Function expf vectorized with AVX-512. KNL and SKX versions. |
2 | Copyright (C) 2014-2024 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 | #include <sysdep.h> |
20 | #include "svml_s_expf_data.h" |
21 | #include "svml_s_wrapper_impl.h" |
22 | |
23 | .section .text.evex512, "ax" , @progbits |
24 | ENTRY (_ZGVeN16v_expf_knl) |
25 | /* |
26 | ALGORITHM DESCRIPTION: |
27 | |
28 | Argument representation: |
29 | M = rint(X*2^k/ln2) = 2^k*N+j |
30 | X = M*ln2/2^k + r = N*ln2 + ln2*(j/2^k) + r |
31 | then -ln2/2^(k+1) < r < ln2/2^(k+1) |
32 | Alternatively: |
33 | M = trunc(X*2^k/ln2) |
34 | then 0 < r < ln2/2^k |
35 | |
36 | Result calculation: |
37 | exp(X) = exp(N*ln2 + ln2*(j/2^k) + r) |
38 | = 2^N * 2^(j/2^k) * exp(r) |
39 | 2^N is calculated by bit manipulation |
40 | 2^(j/2^k) is computed from table lookup |
41 | exp(r) is approximated by polynomial |
42 | |
43 | The table lookup is skipped if k = 0. |
44 | For low accuracy approximation, exp(r) ~ 1 or 1+r. */ |
45 | |
46 | pushq %rbp |
47 | cfi_adjust_cfa_offset (8) |
48 | cfi_rel_offset (%rbp, 0) |
49 | movq %rsp, %rbp |
50 | cfi_def_cfa_register (%rbp) |
51 | andq $-64, %rsp |
52 | subq $1280, %rsp |
53 | movq __svml_sexp_data@GOTPCREL(%rip), %rax |
54 | |
55 | /* r = x-n*ln2_hi/2^k */ |
56 | vmovaps %zmm0, %zmm6 |
57 | |
58 | /* compare against threshold */ |
59 | movl $-1, %ecx |
60 | vmovups __sInvLn2(%rax), %zmm3 |
61 | vmovups __sLn2hi(%rax), %zmm5 |
62 | |
63 | /* m = x*2^k/ln2 + shifter */ |
64 | vfmadd213ps __sShifter(%rax), %zmm0, %zmm3 |
65 | vmovups __sPC5(%rax), %zmm9 |
66 | |
67 | /* n = m - shifter = rint(x*2^k/ln2) */ |
68 | vsubps __sShifter(%rax), %zmm3, %zmm7 |
69 | |
70 | /* remove sign of x by "and" operation */ |
71 | vpandd __iAbsMask(%rax), %zmm0, %zmm1 |
72 | vpaddd __iBias(%rax), %zmm3, %zmm4 |
73 | vpcmpgtd __iDomainRange(%rax), %zmm1, %k1 |
74 | |
75 | /* compute 2^N with "shift" */ |
76 | vpslld $23, %zmm4, %zmm8 |
77 | vfnmadd231ps %zmm7, %zmm5, %zmm6 |
78 | vpbroadcastd %ecx, %zmm2{%k1}{z} |
79 | |
80 | /* r = r-n*ln2_lo/2^k = x - n*ln2/2^k */ |
81 | vfnmadd132ps __sLn2lo(%rax), %zmm6, %zmm7 |
82 | |
83 | /* set mask for overflow/underflow */ |
84 | vptestmd %zmm2, %zmm2, %k0 |
85 | kmovw %k0, %ecx |
86 | |
87 | /* c5*r+c4 */ |
88 | vfmadd213ps __sPC4(%rax), %zmm7, %zmm9 |
89 | |
90 | /* (c5*r+c4)*r+c3 */ |
91 | vfmadd213ps __sPC3(%rax), %zmm7, %zmm9 |
92 | |
93 | /* ((c5*r+c4)*r+c3)*r+c2 */ |
94 | vfmadd213ps __sPC2(%rax), %zmm7, %zmm9 |
95 | |
96 | /* (((c5*r+c4)*r+c3)*r+c2)*r+c1 */ |
97 | vfmadd213ps __sPC1(%rax), %zmm7, %zmm9 |
98 | |
99 | /* exp(r) = ((((c5*r+c4)*r+c3)*r+c2)*r+c1)*r+c0 */ |
100 | vfmadd213ps __sPC0(%rax), %zmm7, %zmm9 |
101 | |
102 | /* 2^N*exp(r) */ |
103 | vmulps %zmm9, %zmm8, %zmm1 |
104 | testl %ecx, %ecx |
105 | jne .LBL_1_3 |
106 | |
107 | .LBL_1_2: |
108 | cfi_remember_state |
109 | vmovaps %zmm1, %zmm0 |
110 | movq %rbp, %rsp |
111 | cfi_def_cfa_register (%rsp) |
112 | popq %rbp |
113 | cfi_adjust_cfa_offset (-8) |
114 | cfi_restore (%rbp) |
115 | ret |
116 | |
117 | .LBL_1_3: |
118 | cfi_restore_state |
119 | vmovups %zmm0, 1152(%rsp) |
120 | vmovups %zmm1, 1216(%rsp) |
121 | je .LBL_1_2 |
122 | |
123 | xorb %dl, %dl |
124 | kmovw %k4, 1048(%rsp) |
125 | xorl %eax, %eax |
126 | kmovw %k5, 1040(%rsp) |
127 | kmovw %k6, 1032(%rsp) |
128 | kmovw %k7, 1024(%rsp) |
129 | vmovups %zmm16, 960(%rsp) |
130 | vmovups %zmm17, 896(%rsp) |
131 | vmovups %zmm18, 832(%rsp) |
132 | vmovups %zmm19, 768(%rsp) |
133 | vmovups %zmm20, 704(%rsp) |
134 | vmovups %zmm21, 640(%rsp) |
135 | vmovups %zmm22, 576(%rsp) |
136 | vmovups %zmm23, 512(%rsp) |
137 | vmovups %zmm24, 448(%rsp) |
138 | vmovups %zmm25, 384(%rsp) |
139 | vmovups %zmm26, 320(%rsp) |
140 | vmovups %zmm27, 256(%rsp) |
141 | vmovups %zmm28, 192(%rsp) |
142 | vmovups %zmm29, 128(%rsp) |
143 | vmovups %zmm30, 64(%rsp) |
144 | vmovups %zmm31, (%rsp) |
145 | movq %rsi, 1064(%rsp) |
146 | movq %rdi, 1056(%rsp) |
147 | movq %r12, 1096(%rsp) |
148 | cfi_offset_rel_rsp (12, 1096) |
149 | movb %dl, %r12b |
150 | movq %r13, 1088(%rsp) |
151 | cfi_offset_rel_rsp (13, 1088) |
152 | movl %ecx, %r13d |
153 | movq %r14, 1080(%rsp) |
154 | cfi_offset_rel_rsp (14, 1080) |
155 | movl %eax, %r14d |
156 | movq %r15, 1072(%rsp) |
157 | cfi_offset_rel_rsp (15, 1072) |
158 | cfi_remember_state |
159 | |
160 | .LBL_1_6: |
161 | btl %r14d, %r13d |
162 | jc .LBL_1_12 |
163 | |
164 | .LBL_1_7: |
165 | lea 1(%r14), %esi |
166 | btl %esi, %r13d |
167 | jc .LBL_1_10 |
168 | |
169 | .LBL_1_8: |
170 | addb $1, %r12b |
171 | addl $2, %r14d |
172 | cmpb $16, %r12b |
173 | jb .LBL_1_6 |
174 | |
175 | kmovw 1048(%rsp), %k4 |
176 | movq 1064(%rsp), %rsi |
177 | kmovw 1040(%rsp), %k5 |
178 | movq 1056(%rsp), %rdi |
179 | kmovw 1032(%rsp), %k6 |
180 | movq 1096(%rsp), %r12 |
181 | cfi_restore (%r12) |
182 | movq 1088(%rsp), %r13 |
183 | cfi_restore (%r13) |
184 | kmovw 1024(%rsp), %k7 |
185 | vmovups 960(%rsp), %zmm16 |
186 | vmovups 896(%rsp), %zmm17 |
187 | vmovups 832(%rsp), %zmm18 |
188 | vmovups 768(%rsp), %zmm19 |
189 | vmovups 704(%rsp), %zmm20 |
190 | vmovups 640(%rsp), %zmm21 |
191 | vmovups 576(%rsp), %zmm22 |
192 | vmovups 512(%rsp), %zmm23 |
193 | vmovups 448(%rsp), %zmm24 |
194 | vmovups 384(%rsp), %zmm25 |
195 | vmovups 320(%rsp), %zmm26 |
196 | vmovups 256(%rsp), %zmm27 |
197 | vmovups 192(%rsp), %zmm28 |
198 | vmovups 128(%rsp), %zmm29 |
199 | vmovups 64(%rsp), %zmm30 |
200 | vmovups (%rsp), %zmm31 |
201 | movq 1080(%rsp), %r14 |
202 | cfi_restore (%r14) |
203 | movq 1072(%rsp), %r15 |
204 | cfi_restore (%r15) |
205 | vmovups 1216(%rsp), %zmm1 |
206 | jmp .LBL_1_2 |
207 | |
208 | .LBL_1_10: |
209 | cfi_restore_state |
210 | movzbl %r12b, %r15d |
211 | vmovss 1156(%rsp,%r15,8), %xmm0 |
212 | call JUMPTARGET(expf) |
213 | vmovss %xmm0, 1220(%rsp,%r15,8) |
214 | jmp .LBL_1_8 |
215 | |
216 | .LBL_1_12: |
217 | movzbl %r12b, %r15d |
218 | vmovss 1152(%rsp,%r15,8), %xmm0 |
219 | call JUMPTARGET(expf) |
220 | vmovss %xmm0, 1216(%rsp,%r15,8) |
221 | jmp .LBL_1_7 |
222 | |
223 | END (_ZGVeN16v_expf_knl) |
224 | |
225 | ENTRY (_ZGVeN16v_expf_skx) |
226 | /* |
227 | ALGORITHM DESCRIPTION: |
228 | |
229 | Argument representation: |
230 | M = rint(X*2^k/ln2) = 2^k*N+j |
231 | X = M*ln2/2^k + r = N*ln2 + ln2*(j/2^k) + r |
232 | then -ln2/2^(k+1) < r < ln2/2^(k+1) |
233 | Alternatively: |
234 | M = trunc(X*2^k/ln2) |
235 | then 0 < r < ln2/2^k |
236 | |
237 | Result calculation: |
238 | exp(X) = exp(N*ln2 + ln2*(j/2^k) + r) |
239 | = 2^N * 2^(j/2^k) * exp(r) |
240 | 2^N is calculated by bit manipulation |
241 | 2^(j/2^k) is computed from table lookup |
242 | exp(r) is approximated by polynomial |
243 | |
244 | The table lookup is skipped if k = 0. |
245 | For low accuracy approximation, exp(r) ~ 1 or 1+r. */ |
246 | |
247 | pushq %rbp |
248 | cfi_adjust_cfa_offset (8) |
249 | cfi_rel_offset (%rbp, 0) |
250 | movq %rsp, %rbp |
251 | cfi_def_cfa_register (%rbp) |
252 | andq $-64, %rsp |
253 | subq $1280, %rsp |
254 | movq __svml_sexp_data@GOTPCREL(%rip), %rax |
255 | |
256 | /* r = x-n*ln2_hi/2^k */ |
257 | vmovaps %zmm0, %zmm7 |
258 | |
259 | /* compare against threshold */ |
260 | vpternlogd $0xff, %zmm3, %zmm3, %zmm3 |
261 | vmovups __sInvLn2(%rax), %zmm4 |
262 | vmovups __sShifter(%rax), %zmm1 |
263 | vmovups __sLn2hi(%rax), %zmm6 |
264 | vmovups __sPC5(%rax), %zmm10 |
265 | |
266 | /* m = x*2^k/ln2 + shifter */ |
267 | vfmadd213ps %zmm1, %zmm0, %zmm4 |
268 | |
269 | /* n = m - shifter = rint(x*2^k/ln2) */ |
270 | vsubps %zmm1, %zmm4, %zmm8 |
271 | vpaddd __iBias(%rax), %zmm4, %zmm5 |
272 | vfnmadd231ps %zmm8, %zmm6, %zmm7 |
273 | |
274 | /* compute 2^N with "shift" */ |
275 | vpslld $23, %zmm5, %zmm9 |
276 | |
277 | /* r = r-n*ln2_lo/2^k = x - n*ln2/2^k */ |
278 | vfnmadd132ps __sLn2lo(%rax), %zmm7, %zmm8 |
279 | |
280 | /* c5*r+c4 */ |
281 | vfmadd213ps __sPC4(%rax), %zmm8, %zmm10 |
282 | |
283 | /* (c5*r+c4)*r+c3 */ |
284 | vfmadd213ps __sPC3(%rax), %zmm8, %zmm10 |
285 | |
286 | /* ((c5*r+c4)*r+c3)*r+c2 */ |
287 | vfmadd213ps __sPC2(%rax), %zmm8, %zmm10 |
288 | |
289 | /* (((c5*r+c4)*r+c3)*r+c2)*r+c1 */ |
290 | vfmadd213ps __sPC1(%rax), %zmm8, %zmm10 |
291 | |
292 | /* exp(r) = ((((c5*r+c4)*r+c3)*r+c2)*r+c1)*r+c0 */ |
293 | vfmadd213ps __sPC0(%rax), %zmm8, %zmm10 |
294 | |
295 | /* 2^N*exp(r) */ |
296 | vmulps %zmm10, %zmm9, %zmm1 |
297 | |
298 | /* remove sign of x by "and" operation */ |
299 | vpandd __iAbsMask(%rax), %zmm0, %zmm2 |
300 | vpcmpd $2, __iDomainRange(%rax), %zmm2, %k1 |
301 | vpandnd %zmm2, %zmm2, %zmm3{%k1} |
302 | |
303 | /* set mask for overflow/underflow */ |
304 | vptestmd %zmm3, %zmm3, %k0 |
305 | kmovw %k0, %ecx |
306 | testl %ecx, %ecx |
307 | jne .LBL_2_3 |
308 | |
309 | .LBL_2_2: |
310 | cfi_remember_state |
311 | vmovaps %zmm1, %zmm0 |
312 | movq %rbp, %rsp |
313 | cfi_def_cfa_register (%rsp) |
314 | popq %rbp |
315 | cfi_adjust_cfa_offset (-8) |
316 | cfi_restore (%rbp) |
317 | ret |
318 | |
319 | .LBL_2_3: |
320 | cfi_restore_state |
321 | vmovups %zmm0, 1152(%rsp) |
322 | vmovups %zmm1, 1216(%rsp) |
323 | je .LBL_2_2 |
324 | |
325 | xorb %dl, %dl |
326 | xorl %eax, %eax |
327 | kmovw %k4, 1048(%rsp) |
328 | kmovw %k5, 1040(%rsp) |
329 | kmovw %k6, 1032(%rsp) |
330 | kmovw %k7, 1024(%rsp) |
331 | vmovups %zmm16, 960(%rsp) |
332 | vmovups %zmm17, 896(%rsp) |
333 | vmovups %zmm18, 832(%rsp) |
334 | vmovups %zmm19, 768(%rsp) |
335 | vmovups %zmm20, 704(%rsp) |
336 | vmovups %zmm21, 640(%rsp) |
337 | vmovups %zmm22, 576(%rsp) |
338 | vmovups %zmm23, 512(%rsp) |
339 | vmovups %zmm24, 448(%rsp) |
340 | vmovups %zmm25, 384(%rsp) |
341 | vmovups %zmm26, 320(%rsp) |
342 | vmovups %zmm27, 256(%rsp) |
343 | vmovups %zmm28, 192(%rsp) |
344 | vmovups %zmm29, 128(%rsp) |
345 | vmovups %zmm30, 64(%rsp) |
346 | vmovups %zmm31, (%rsp) |
347 | movq %rsi, 1064(%rsp) |
348 | movq %rdi, 1056(%rsp) |
349 | movq %r12, 1096(%rsp) |
350 | cfi_offset_rel_rsp (12, 1096) |
351 | movb %dl, %r12b |
352 | movq %r13, 1088(%rsp) |
353 | cfi_offset_rel_rsp (13, 1088) |
354 | movl %ecx, %r13d |
355 | movq %r14, 1080(%rsp) |
356 | cfi_offset_rel_rsp (14, 1080) |
357 | movl %eax, %r14d |
358 | movq %r15, 1072(%rsp) |
359 | cfi_offset_rel_rsp (15, 1072) |
360 | cfi_remember_state |
361 | |
362 | |
363 | .LBL_2_6: |
364 | btl %r14d, %r13d |
365 | jc .LBL_2_12 |
366 | |
367 | .LBL_2_7: |
368 | lea 1(%r14), %esi |
369 | btl %esi, %r13d |
370 | jc .LBL_2_10 |
371 | |
372 | .LBL_2_8: |
373 | incb %r12b |
374 | addl $2, %r14d |
375 | cmpb $16, %r12b |
376 | jb .LBL_2_6 |
377 | |
378 | kmovw 1048(%rsp), %k4 |
379 | kmovw 1040(%rsp), %k5 |
380 | kmovw 1032(%rsp), %k6 |
381 | kmovw 1024(%rsp), %k7 |
382 | vmovups 960(%rsp), %zmm16 |
383 | vmovups 896(%rsp), %zmm17 |
384 | vmovups 832(%rsp), %zmm18 |
385 | vmovups 768(%rsp), %zmm19 |
386 | vmovups 704(%rsp), %zmm20 |
387 | vmovups 640(%rsp), %zmm21 |
388 | vmovups 576(%rsp), %zmm22 |
389 | vmovups 512(%rsp), %zmm23 |
390 | vmovups 448(%rsp), %zmm24 |
391 | vmovups 384(%rsp), %zmm25 |
392 | vmovups 320(%rsp), %zmm26 |
393 | vmovups 256(%rsp), %zmm27 |
394 | vmovups 192(%rsp), %zmm28 |
395 | vmovups 128(%rsp), %zmm29 |
396 | vmovups 64(%rsp), %zmm30 |
397 | vmovups (%rsp), %zmm31 |
398 | vmovups 1216(%rsp), %zmm1 |
399 | movq 1064(%rsp), %rsi |
400 | movq 1056(%rsp), %rdi |
401 | movq 1096(%rsp), %r12 |
402 | cfi_restore (%r12) |
403 | movq 1088(%rsp), %r13 |
404 | cfi_restore (%r13) |
405 | movq 1080(%rsp), %r14 |
406 | cfi_restore (%r14) |
407 | movq 1072(%rsp), %r15 |
408 | cfi_restore (%r15) |
409 | jmp .LBL_2_2 |
410 | |
411 | .LBL_2_10: |
412 | cfi_restore_state |
413 | movzbl %r12b, %r15d |
414 | vmovss 1156(%rsp,%r15,8), %xmm0 |
415 | vzeroupper |
416 | vmovss 1156(%rsp,%r15,8), %xmm0 |
417 | |
418 | call JUMPTARGET(expf) |
419 | |
420 | vmovss %xmm0, 1220(%rsp,%r15,8) |
421 | jmp .LBL_2_8 |
422 | |
423 | .LBL_2_12: |
424 | movzbl %r12b, %r15d |
425 | vmovss 1152(%rsp,%r15,8), %xmm0 |
426 | vzeroupper |
427 | vmovss 1152(%rsp,%r15,8), %xmm0 |
428 | |
429 | call JUMPTARGET(expf) |
430 | |
431 | vmovss %xmm0, 1216(%rsp,%r15,8) |
432 | jmp .LBL_2_7 |
433 | |
434 | END (_ZGVeN16v_expf_skx) |
435 | |