1 | /* Function expf vectorized with AVX-512. KNL and SKX versions. |
2 | Copyright (C) 2014-2020 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 | .text |
24 | ENTRY (_ZGVeN16v_expf_knl) |
25 | #ifndef HAVE_AVX512DQ_ASM_SUPPORT |
26 | WRAPPER_IMPL_AVX512 _ZGVdN8v_expf |
27 | #else |
28 | /* |
29 | ALGORITHM DESCRIPTION: |
30 | |
31 | Argument representation: |
32 | M = rint(X*2^k/ln2) = 2^k*N+j |
33 | X = M*ln2/2^k + r = N*ln2 + ln2*(j/2^k) + r |
34 | then -ln2/2^(k+1) < r < ln2/2^(k+1) |
35 | Alternatively: |
36 | M = trunc(X*2^k/ln2) |
37 | then 0 < r < ln2/2^k |
38 | |
39 | Result calculation: |
40 | exp(X) = exp(N*ln2 + ln2*(j/2^k) + r) |
41 | = 2^N * 2^(j/2^k) * exp(r) |
42 | 2^N is calculated by bit manipulation |
43 | 2^(j/2^k) is computed from table lookup |
44 | exp(r) is approximated by polynomial |
45 | |
46 | The table lookup is skipped if k = 0. |
47 | For low accuracy approximation, exp(r) ~ 1 or 1+r. */ |
48 | |
49 | pushq %rbp |
50 | cfi_adjust_cfa_offset (8) |
51 | cfi_rel_offset (%rbp, 0) |
52 | movq %rsp, %rbp |
53 | cfi_def_cfa_register (%rbp) |
54 | andq $-64, %rsp |
55 | subq $1280, %rsp |
56 | movq __svml_sexp_data@GOTPCREL(%rip), %rax |
57 | |
58 | /* r = x-n*ln2_hi/2^k */ |
59 | vmovaps %zmm0, %zmm6 |
60 | |
61 | /* compare against threshold */ |
62 | movl $-1, %ecx |
63 | vmovups __sInvLn2(%rax), %zmm3 |
64 | vmovups __sLn2hi(%rax), %zmm5 |
65 | |
66 | /* m = x*2^k/ln2 + shifter */ |
67 | vfmadd213ps __sShifter(%rax), %zmm0, %zmm3 |
68 | vmovups __sPC5(%rax), %zmm9 |
69 | |
70 | /* n = m - shifter = rint(x*2^k/ln2) */ |
71 | vsubps __sShifter(%rax), %zmm3, %zmm7 |
72 | |
73 | /* remove sign of x by "and" operation */ |
74 | vpandd __iAbsMask(%rax), %zmm0, %zmm1 |
75 | vpaddd __iBias(%rax), %zmm3, %zmm4 |
76 | vpcmpgtd __iDomainRange(%rax), %zmm1, %k1 |
77 | |
78 | /* compute 2^N with "shift" */ |
79 | vpslld $23, %zmm4, %zmm8 |
80 | vfnmadd231ps %zmm7, %zmm5, %zmm6 |
81 | vpbroadcastd %ecx, %zmm2{%k1}{z} |
82 | |
83 | /* r = r-n*ln2_lo/2^k = x - n*ln2/2^k */ |
84 | vfnmadd132ps __sLn2lo(%rax), %zmm6, %zmm7 |
85 | |
86 | /* set mask for overflow/underflow */ |
87 | vptestmd %zmm2, %zmm2, %k0 |
88 | kmovw %k0, %ecx |
89 | |
90 | /* c5*r+c4 */ |
91 | vfmadd213ps __sPC4(%rax), %zmm7, %zmm9 |
92 | |
93 | /* (c5*r+c4)*r+c3 */ |
94 | vfmadd213ps __sPC3(%rax), %zmm7, %zmm9 |
95 | |
96 | /* ((c5*r+c4)*r+c3)*r+c2 */ |
97 | vfmadd213ps __sPC2(%rax), %zmm7, %zmm9 |
98 | |
99 | /* (((c5*r+c4)*r+c3)*r+c2)*r+c1 */ |
100 | vfmadd213ps __sPC1(%rax), %zmm7, %zmm9 |
101 | |
102 | /* exp(r) = ((((c5*r+c4)*r+c3)*r+c2)*r+c1)*r+c0 */ |
103 | vfmadd213ps __sPC0(%rax), %zmm7, %zmm9 |
104 | |
105 | /* 2^N*exp(r) */ |
106 | vmulps %zmm9, %zmm8, %zmm1 |
107 | testl %ecx, %ecx |
108 | jne .LBL_1_3 |
109 | |
110 | .LBL_1_2: |
111 | cfi_remember_state |
112 | vmovaps %zmm1, %zmm0 |
113 | movq %rbp, %rsp |
114 | cfi_def_cfa_register (%rsp) |
115 | popq %rbp |
116 | cfi_adjust_cfa_offset (-8) |
117 | cfi_restore (%rbp) |
118 | ret |
119 | |
120 | .LBL_1_3: |
121 | cfi_restore_state |
122 | vmovups %zmm0, 1152(%rsp) |
123 | vmovups %zmm1, 1216(%rsp) |
124 | je .LBL_1_2 |
125 | |
126 | xorb %dl, %dl |
127 | kmovw %k4, 1048(%rsp) |
128 | xorl %eax, %eax |
129 | kmovw %k5, 1040(%rsp) |
130 | kmovw %k6, 1032(%rsp) |
131 | kmovw %k7, 1024(%rsp) |
132 | vmovups %zmm16, 960(%rsp) |
133 | vmovups %zmm17, 896(%rsp) |
134 | vmovups %zmm18, 832(%rsp) |
135 | vmovups %zmm19, 768(%rsp) |
136 | vmovups %zmm20, 704(%rsp) |
137 | vmovups %zmm21, 640(%rsp) |
138 | vmovups %zmm22, 576(%rsp) |
139 | vmovups %zmm23, 512(%rsp) |
140 | vmovups %zmm24, 448(%rsp) |
141 | vmovups %zmm25, 384(%rsp) |
142 | vmovups %zmm26, 320(%rsp) |
143 | vmovups %zmm27, 256(%rsp) |
144 | vmovups %zmm28, 192(%rsp) |
145 | vmovups %zmm29, 128(%rsp) |
146 | vmovups %zmm30, 64(%rsp) |
147 | vmovups %zmm31, (%rsp) |
148 | movq %rsi, 1064(%rsp) |
149 | movq %rdi, 1056(%rsp) |
150 | movq %r12, 1096(%rsp) |
151 | cfi_offset_rel_rsp (12, 1096) |
152 | movb %dl, %r12b |
153 | movq %r13, 1088(%rsp) |
154 | cfi_offset_rel_rsp (13, 1088) |
155 | movl %ecx, %r13d |
156 | movq %r14, 1080(%rsp) |
157 | cfi_offset_rel_rsp (14, 1080) |
158 | movl %eax, %r14d |
159 | movq %r15, 1072(%rsp) |
160 | cfi_offset_rel_rsp (15, 1072) |
161 | cfi_remember_state |
162 | |
163 | .LBL_1_6: |
164 | btl %r14d, %r13d |
165 | jc .LBL_1_12 |
166 | |
167 | .LBL_1_7: |
168 | lea 1(%r14), %esi |
169 | btl %esi, %r13d |
170 | jc .LBL_1_10 |
171 | |
172 | .LBL_1_8: |
173 | addb $1, %r12b |
174 | addl $2, %r14d |
175 | cmpb $16, %r12b |
176 | jb .LBL_1_6 |
177 | |
178 | kmovw 1048(%rsp), %k4 |
179 | movq 1064(%rsp), %rsi |
180 | kmovw 1040(%rsp), %k5 |
181 | movq 1056(%rsp), %rdi |
182 | kmovw 1032(%rsp), %k6 |
183 | movq 1096(%rsp), %r12 |
184 | cfi_restore (%r12) |
185 | movq 1088(%rsp), %r13 |
186 | cfi_restore (%r13) |
187 | kmovw 1024(%rsp), %k7 |
188 | vmovups 960(%rsp), %zmm16 |
189 | vmovups 896(%rsp), %zmm17 |
190 | vmovups 832(%rsp), %zmm18 |
191 | vmovups 768(%rsp), %zmm19 |
192 | vmovups 704(%rsp), %zmm20 |
193 | vmovups 640(%rsp), %zmm21 |
194 | vmovups 576(%rsp), %zmm22 |
195 | vmovups 512(%rsp), %zmm23 |
196 | vmovups 448(%rsp), %zmm24 |
197 | vmovups 384(%rsp), %zmm25 |
198 | vmovups 320(%rsp), %zmm26 |
199 | vmovups 256(%rsp), %zmm27 |
200 | vmovups 192(%rsp), %zmm28 |
201 | vmovups 128(%rsp), %zmm29 |
202 | vmovups 64(%rsp), %zmm30 |
203 | vmovups (%rsp), %zmm31 |
204 | movq 1080(%rsp), %r14 |
205 | cfi_restore (%r14) |
206 | movq 1072(%rsp), %r15 |
207 | cfi_restore (%r15) |
208 | vmovups 1216(%rsp), %zmm1 |
209 | jmp .LBL_1_2 |
210 | |
211 | .LBL_1_10: |
212 | cfi_restore_state |
213 | movzbl %r12b, %r15d |
214 | vmovss 1156(%rsp,%r15,8), %xmm0 |
215 | call JUMPTARGET(expf) |
216 | vmovss %xmm0, 1220(%rsp,%r15,8) |
217 | jmp .LBL_1_8 |
218 | |
219 | .LBL_1_12: |
220 | movzbl %r12b, %r15d |
221 | vmovss 1152(%rsp,%r15,8), %xmm0 |
222 | call JUMPTARGET(expf) |
223 | vmovss %xmm0, 1216(%rsp,%r15,8) |
224 | jmp .LBL_1_7 |
225 | |
226 | #endif |
227 | END (_ZGVeN16v_expf_knl) |
228 | |
229 | ENTRY (_ZGVeN16v_expf_skx) |
230 | #ifndef HAVE_AVX512DQ_ASM_SUPPORT |
231 | WRAPPER_IMPL_AVX512 _ZGVdN8v_expf |
232 | #else |
233 | /* |
234 | ALGORITHM DESCRIPTION: |
235 | |
236 | Argument representation: |
237 | M = rint(X*2^k/ln2) = 2^k*N+j |
238 | X = M*ln2/2^k + r = N*ln2 + ln2*(j/2^k) + r |
239 | then -ln2/2^(k+1) < r < ln2/2^(k+1) |
240 | Alternatively: |
241 | M = trunc(X*2^k/ln2) |
242 | then 0 < r < ln2/2^k |
243 | |
244 | Result calculation: |
245 | exp(X) = exp(N*ln2 + ln2*(j/2^k) + r) |
246 | = 2^N * 2^(j/2^k) * exp(r) |
247 | 2^N is calculated by bit manipulation |
248 | 2^(j/2^k) is computed from table lookup |
249 | exp(r) is approximated by polynomial |
250 | |
251 | The table lookup is skipped if k = 0. |
252 | For low accuracy approximation, exp(r) ~ 1 or 1+r. */ |
253 | |
254 | pushq %rbp |
255 | cfi_adjust_cfa_offset (8) |
256 | cfi_rel_offset (%rbp, 0) |
257 | movq %rsp, %rbp |
258 | cfi_def_cfa_register (%rbp) |
259 | andq $-64, %rsp |
260 | subq $1280, %rsp |
261 | movq __svml_sexp_data@GOTPCREL(%rip), %rax |
262 | |
263 | /* r = x-n*ln2_hi/2^k */ |
264 | vmovaps %zmm0, %zmm7 |
265 | |
266 | /* compare against threshold */ |
267 | vmovups .L_2il0floatpacket.13(%rip), %zmm3 |
268 | vmovups __sInvLn2(%rax), %zmm4 |
269 | vmovups __sShifter(%rax), %zmm1 |
270 | vmovups __sLn2hi(%rax), %zmm6 |
271 | vmovups __sPC5(%rax), %zmm10 |
272 | |
273 | /* m = x*2^k/ln2 + shifter */ |
274 | vfmadd213ps %zmm1, %zmm0, %zmm4 |
275 | |
276 | /* n = m - shifter = rint(x*2^k/ln2) */ |
277 | vsubps %zmm1, %zmm4, %zmm8 |
278 | vpaddd __iBias(%rax), %zmm4, %zmm5 |
279 | vfnmadd231ps %zmm8, %zmm6, %zmm7 |
280 | |
281 | /* compute 2^N with "shift" */ |
282 | vpslld $23, %zmm5, %zmm9 |
283 | |
284 | /* r = r-n*ln2_lo/2^k = x - n*ln2/2^k */ |
285 | vfnmadd132ps __sLn2lo(%rax), %zmm7, %zmm8 |
286 | |
287 | /* c5*r+c4 */ |
288 | vfmadd213ps __sPC4(%rax), %zmm8, %zmm10 |
289 | |
290 | /* (c5*r+c4)*r+c3 */ |
291 | vfmadd213ps __sPC3(%rax), %zmm8, %zmm10 |
292 | |
293 | /* ((c5*r+c4)*r+c3)*r+c2 */ |
294 | vfmadd213ps __sPC2(%rax), %zmm8, %zmm10 |
295 | |
296 | /* (((c5*r+c4)*r+c3)*r+c2)*r+c1 */ |
297 | vfmadd213ps __sPC1(%rax), %zmm8, %zmm10 |
298 | |
299 | /* exp(r) = ((((c5*r+c4)*r+c3)*r+c2)*r+c1)*r+c0 */ |
300 | vfmadd213ps __sPC0(%rax), %zmm8, %zmm10 |
301 | |
302 | /* 2^N*exp(r) */ |
303 | vmulps %zmm10, %zmm9, %zmm1 |
304 | |
305 | /* remove sign of x by "and" operation */ |
306 | vpandd __iAbsMask(%rax), %zmm0, %zmm2 |
307 | vpcmpd $2, __iDomainRange(%rax), %zmm2, %k1 |
308 | vpandnd %zmm2, %zmm2, %zmm3{%k1} |
309 | |
310 | /* set mask for overflow/underflow */ |
311 | vptestmd %zmm3, %zmm3, %k0 |
312 | kmovw %k0, %ecx |
313 | testl %ecx, %ecx |
314 | jne .LBL_2_3 |
315 | |
316 | .LBL_2_2: |
317 | cfi_remember_state |
318 | vmovaps %zmm1, %zmm0 |
319 | movq %rbp, %rsp |
320 | cfi_def_cfa_register (%rsp) |
321 | popq %rbp |
322 | cfi_adjust_cfa_offset (-8) |
323 | cfi_restore (%rbp) |
324 | ret |
325 | |
326 | .LBL_2_3: |
327 | cfi_restore_state |
328 | vmovups %zmm0, 1152(%rsp) |
329 | vmovups %zmm1, 1216(%rsp) |
330 | je .LBL_2_2 |
331 | |
332 | xorb %dl, %dl |
333 | xorl %eax, %eax |
334 | kmovw %k4, 1048(%rsp) |
335 | kmovw %k5, 1040(%rsp) |
336 | kmovw %k6, 1032(%rsp) |
337 | kmovw %k7, 1024(%rsp) |
338 | vmovups %zmm16, 960(%rsp) |
339 | vmovups %zmm17, 896(%rsp) |
340 | vmovups %zmm18, 832(%rsp) |
341 | vmovups %zmm19, 768(%rsp) |
342 | vmovups %zmm20, 704(%rsp) |
343 | vmovups %zmm21, 640(%rsp) |
344 | vmovups %zmm22, 576(%rsp) |
345 | vmovups %zmm23, 512(%rsp) |
346 | vmovups %zmm24, 448(%rsp) |
347 | vmovups %zmm25, 384(%rsp) |
348 | vmovups %zmm26, 320(%rsp) |
349 | vmovups %zmm27, 256(%rsp) |
350 | vmovups %zmm28, 192(%rsp) |
351 | vmovups %zmm29, 128(%rsp) |
352 | vmovups %zmm30, 64(%rsp) |
353 | vmovups %zmm31, (%rsp) |
354 | movq %rsi, 1064(%rsp) |
355 | movq %rdi, 1056(%rsp) |
356 | movq %r12, 1096(%rsp) |
357 | cfi_offset_rel_rsp (12, 1096) |
358 | movb %dl, %r12b |
359 | movq %r13, 1088(%rsp) |
360 | cfi_offset_rel_rsp (13, 1088) |
361 | movl %ecx, %r13d |
362 | movq %r14, 1080(%rsp) |
363 | cfi_offset_rel_rsp (14, 1080) |
364 | movl %eax, %r14d |
365 | movq %r15, 1072(%rsp) |
366 | cfi_offset_rel_rsp (15, 1072) |
367 | cfi_remember_state |
368 | |
369 | |
370 | .LBL_2_6: |
371 | btl %r14d, %r13d |
372 | jc .LBL_2_12 |
373 | |
374 | .LBL_2_7: |
375 | lea 1(%r14), %esi |
376 | btl %esi, %r13d |
377 | jc .LBL_2_10 |
378 | |
379 | .LBL_2_8: |
380 | incb %r12b |
381 | addl $2, %r14d |
382 | cmpb $16, %r12b |
383 | jb .LBL_2_6 |
384 | |
385 | kmovw 1048(%rsp), %k4 |
386 | kmovw 1040(%rsp), %k5 |
387 | kmovw 1032(%rsp), %k6 |
388 | kmovw 1024(%rsp), %k7 |
389 | vmovups 960(%rsp), %zmm16 |
390 | vmovups 896(%rsp), %zmm17 |
391 | vmovups 832(%rsp), %zmm18 |
392 | vmovups 768(%rsp), %zmm19 |
393 | vmovups 704(%rsp), %zmm20 |
394 | vmovups 640(%rsp), %zmm21 |
395 | vmovups 576(%rsp), %zmm22 |
396 | vmovups 512(%rsp), %zmm23 |
397 | vmovups 448(%rsp), %zmm24 |
398 | vmovups 384(%rsp), %zmm25 |
399 | vmovups 320(%rsp), %zmm26 |
400 | vmovups 256(%rsp), %zmm27 |
401 | vmovups 192(%rsp), %zmm28 |
402 | vmovups 128(%rsp), %zmm29 |
403 | vmovups 64(%rsp), %zmm30 |
404 | vmovups (%rsp), %zmm31 |
405 | vmovups 1216(%rsp), %zmm1 |
406 | movq 1064(%rsp), %rsi |
407 | movq 1056(%rsp), %rdi |
408 | movq 1096(%rsp), %r12 |
409 | cfi_restore (%r12) |
410 | movq 1088(%rsp), %r13 |
411 | cfi_restore (%r13) |
412 | movq 1080(%rsp), %r14 |
413 | cfi_restore (%r14) |
414 | movq 1072(%rsp), %r15 |
415 | cfi_restore (%r15) |
416 | jmp .LBL_2_2 |
417 | |
418 | .LBL_2_10: |
419 | cfi_restore_state |
420 | movzbl %r12b, %r15d |
421 | vmovss 1156(%rsp,%r15,8), %xmm0 |
422 | vzeroupper |
423 | vmovss 1156(%rsp,%r15,8), %xmm0 |
424 | |
425 | call JUMPTARGET(expf) |
426 | |
427 | vmovss %xmm0, 1220(%rsp,%r15,8) |
428 | jmp .LBL_2_8 |
429 | |
430 | .LBL_2_12: |
431 | movzbl %r12b, %r15d |
432 | vmovss 1152(%rsp,%r15,8), %xmm0 |
433 | vzeroupper |
434 | vmovss 1152(%rsp,%r15,8), %xmm0 |
435 | |
436 | call JUMPTARGET(expf) |
437 | |
438 | vmovss %xmm0, 1216(%rsp,%r15,8) |
439 | jmp .LBL_2_7 |
440 | |
441 | #endif |
442 | END (_ZGVeN16v_expf_skx) |
443 | |
444 | .section .rodata, "a" |
445 | .L_2il0floatpacket.13: |
446 | .long 0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff |
447 | .type .L_2il0floatpacket.13,@object |
448 | |