1 | /* Function exp 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_d_exp_data.h" |
21 | #include "svml_d_wrapper_impl.h" |
22 | |
23 | .section .text.evex512, "ax" , @progbits |
24 | ENTRY (_ZGVeN8v_exp_knl) |
25 | /* |
26 | ALGORITHM DESCRIPTION: |
27 | |
28 | Argument representation: |
29 | N = rint(X*2^k/ln2) = 2^k*M+j |
30 | X = N*ln2/2^k + r = M*ln2 + ln2*(j/2^k) + r |
31 | then -ln2/2^(k+1) < r < ln2/2^(k+1) |
32 | Alternatively: |
33 | N = trunc(X*2^k/ln2) |
34 | then 0 < r < ln2/2^k |
35 | |
36 | Result calculation: |
37 | exp(X) = exp(M*ln2 + ln2*(j/2^k) + r) |
38 | = 2^M * 2^(j/2^k) * exp(r) |
39 | 2^M is calculated by bit manipulation |
40 | 2^(j/2^k) is stored in table |
41 | exp(r) is approximated by polynomial |
42 | |
43 | The table lookup is skipped if k = 0. */ |
44 | |
45 | pushq %rbp |
46 | cfi_adjust_cfa_offset (8) |
47 | cfi_rel_offset (%rbp, 0) |
48 | movq %rsp, %rbp |
49 | cfi_def_cfa_register (%rbp) |
50 | andq $-64, %rsp |
51 | subq $1280, %rsp |
52 | movq __svml_dexp_data@GOTPCREL(%rip), %rax |
53 | |
54 | /* dR = X - dN*dbLn2hi, dbLn2hi is 52-8-k hi bits of ln2/2^k */ |
55 | vmovaps %zmm0, %zmm8 |
56 | |
57 | /* iAbsX = (int)(lX>>32), lX = *(longlong*)&X */ |
58 | vpsrlq $32, %zmm0, %zmm1 |
59 | |
60 | /* iAbsX = iAbsX&iAbsMask */ |
61 | movl $255, %edx |
62 | vpmovqd %zmm1, %ymm2 |
63 | kmovw %edx, %k2 |
64 | |
65 | /* iRangeMask = (iAbsX>iDomainRange) */ |
66 | movl $-1, %ecx |
67 | |
68 | /* table lookup for dT[j] = 2^(j/2^k) */ |
69 | vpxord %zmm11, %zmm11, %zmm11 |
70 | vmovups __dbInvLn2(%rax), %zmm5 |
71 | vmovups __dbLn2hi(%rax), %zmm7 |
72 | kxnorw %k3, %k3, %k3 |
73 | |
74 | /* dM = X*dbInvLn2+dbShifter, dbInvLn2 = 2^k/Ln2 */ |
75 | vfmadd213pd __dbShifter(%rax), %zmm0, %zmm5 |
76 | vmovups __dPC2(%rax), %zmm12 |
77 | |
78 | /* dN = dM-dbShifter, dN = rint(X*2^k/Ln2) */ |
79 | vsubpd __dbShifter(%rax), %zmm5, %zmm9 |
80 | vmovups __lIndexMask(%rax), %zmm4 |
81 | vfnmadd231pd %zmm9, %zmm7, %zmm8 |
82 | vpandd __iAbsMask(%rax), %zmm2, %zmm2{%k2} |
83 | |
84 | /* lIndex = (*(longlong*)&dM)&lIndexMask, lIndex is the lower K bits of lM */ |
85 | vpandq %zmm4, %zmm5, %zmm10 |
86 | vgatherqpd (%rax,%zmm10,8), %zmm11{%k3} |
87 | vpcmpgtd __iDomainRange(%rax), %zmm2, %k1{%k2} |
88 | |
89 | /* lM = (*(longlong*)&dM)&(~lIndexMask) */ |
90 | vpandnq %zmm5, %zmm4, %zmm6 |
91 | vpbroadcastd %ecx, %zmm3{%k1}{z} |
92 | |
93 | /* lM = lM<<(52-K), 2^M */ |
94 | vpsllq $42, %zmm6, %zmm14 |
95 | |
96 | /* dR = dR - dN*dbLn2lo, dbLn2lo is 40..94 bits of lo part of ln2/2^k */ |
97 | vfnmadd132pd __dbLn2lo(%rax), %zmm8, %zmm9 |
98 | |
99 | /* Mask = iRangeMask?1:0, set mask for overflow/underflow */ |
100 | vptestmd %zmm3, %zmm3, %k0{%k2} |
101 | |
102 | /* exp(r) = b0+r*(b0+r*(b1+r*b2)) */ |
103 | vfmadd213pd __dPC1(%rax), %zmm9, %zmm12 |
104 | kmovw %k0, %ecx |
105 | movzbl %cl, %ecx |
106 | vfmadd213pd __dPC0(%rax), %zmm9, %zmm12 |
107 | vfmadd213pd __dPC0(%rax), %zmm9, %zmm12 |
108 | |
109 | /* 2^(j/2^k) * exp(r) */ |
110 | vmulpd %zmm12, %zmm11, %zmm13 |
111 | |
112 | /* multiply by 2^M through integer add */ |
113 | vpaddq %zmm14, %zmm13, %zmm1 |
114 | testl %ecx, %ecx |
115 | jne .LBL_1_3 |
116 | |
117 | .LBL_1_2: |
118 | cfi_remember_state |
119 | vmovaps %zmm1, %zmm0 |
120 | movq %rbp, %rsp |
121 | cfi_def_cfa_register (%rsp) |
122 | popq %rbp |
123 | cfi_adjust_cfa_offset (-8) |
124 | cfi_restore (%rbp) |
125 | ret |
126 | |
127 | .LBL_1_3: |
128 | cfi_restore_state |
129 | vmovups %zmm0, 1152(%rsp) |
130 | vmovups %zmm1, 1216(%rsp) |
131 | je .LBL_1_2 |
132 | |
133 | xorb %dl, %dl |
134 | kmovw %k4, 1048(%rsp) |
135 | xorl %eax, %eax |
136 | kmovw %k5, 1040(%rsp) |
137 | kmovw %k6, 1032(%rsp) |
138 | kmovw %k7, 1024(%rsp) |
139 | vmovups %zmm16, 960(%rsp) |
140 | vmovups %zmm17, 896(%rsp) |
141 | vmovups %zmm18, 832(%rsp) |
142 | vmovups %zmm19, 768(%rsp) |
143 | vmovups %zmm20, 704(%rsp) |
144 | vmovups %zmm21, 640(%rsp) |
145 | vmovups %zmm22, 576(%rsp) |
146 | vmovups %zmm23, 512(%rsp) |
147 | vmovups %zmm24, 448(%rsp) |
148 | vmovups %zmm25, 384(%rsp) |
149 | vmovups %zmm26, 320(%rsp) |
150 | vmovups %zmm27, 256(%rsp) |
151 | vmovups %zmm28, 192(%rsp) |
152 | vmovups %zmm29, 128(%rsp) |
153 | vmovups %zmm30, 64(%rsp) |
154 | vmovups %zmm31, (%rsp) |
155 | movq %rsi, 1064(%rsp) |
156 | movq %rdi, 1056(%rsp) |
157 | movq %r12, 1096(%rsp) |
158 | cfi_offset_rel_rsp (12, 1096) |
159 | movb %dl, %r12b |
160 | movq %r13, 1088(%rsp) |
161 | cfi_offset_rel_rsp (13, 1088) |
162 | movl %ecx, %r13d |
163 | movq %r14, 1080(%rsp) |
164 | cfi_offset_rel_rsp (14, 1080) |
165 | movl %eax, %r14d |
166 | movq %r15, 1072(%rsp) |
167 | cfi_offset_rel_rsp (15, 1072) |
168 | cfi_remember_state |
169 | |
170 | .LBL_1_6: |
171 | btl %r14d, %r13d |
172 | jc .LBL_1_12 |
173 | |
174 | .LBL_1_7: |
175 | lea 1(%r14), %esi |
176 | btl %esi, %r13d |
177 | jc .LBL_1_10 |
178 | |
179 | .LBL_1_8: |
180 | addb $1, %r12b |
181 | addl $2, %r14d |
182 | cmpb $16, %r12b |
183 | jb .LBL_1_6 |
184 | |
185 | kmovw 1048(%rsp), %k4 |
186 | movq 1064(%rsp), %rsi |
187 | kmovw 1040(%rsp), %k5 |
188 | movq 1056(%rsp), %rdi |
189 | kmovw 1032(%rsp), %k6 |
190 | movq 1096(%rsp), %r12 |
191 | cfi_restore (%r12) |
192 | movq 1088(%rsp), %r13 |
193 | cfi_restore (%r13) |
194 | kmovw 1024(%rsp), %k7 |
195 | vmovups 960(%rsp), %zmm16 |
196 | vmovups 896(%rsp), %zmm17 |
197 | vmovups 832(%rsp), %zmm18 |
198 | vmovups 768(%rsp), %zmm19 |
199 | vmovups 704(%rsp), %zmm20 |
200 | vmovups 640(%rsp), %zmm21 |
201 | vmovups 576(%rsp), %zmm22 |
202 | vmovups 512(%rsp), %zmm23 |
203 | vmovups 448(%rsp), %zmm24 |
204 | vmovups 384(%rsp), %zmm25 |
205 | vmovups 320(%rsp), %zmm26 |
206 | vmovups 256(%rsp), %zmm27 |
207 | vmovups 192(%rsp), %zmm28 |
208 | vmovups 128(%rsp), %zmm29 |
209 | vmovups 64(%rsp), %zmm30 |
210 | vmovups (%rsp), %zmm31 |
211 | movq 1080(%rsp), %r14 |
212 | cfi_restore (%r14) |
213 | movq 1072(%rsp), %r15 |
214 | cfi_restore (%r15) |
215 | vmovups 1216(%rsp), %zmm1 |
216 | jmp .LBL_1_2 |
217 | |
218 | .LBL_1_10: |
219 | cfi_restore_state |
220 | movzbl %r12b, %r15d |
221 | shlq $4, %r15 |
222 | vmovsd 1160(%rsp,%r15), %xmm0 |
223 | call JUMPTARGET(exp) |
224 | vmovsd %xmm0, 1224(%rsp,%r15) |
225 | jmp .LBL_1_8 |
226 | |
227 | .LBL_1_12: |
228 | movzbl %r12b, %r15d |
229 | shlq $4, %r15 |
230 | vmovsd 1152(%rsp,%r15), %xmm0 |
231 | call JUMPTARGET(exp) |
232 | vmovsd %xmm0, 1216(%rsp,%r15) |
233 | jmp .LBL_1_7 |
234 | END (_ZGVeN8v_exp_knl) |
235 | |
236 | ENTRY (_ZGVeN8v_exp_skx) |
237 | /* |
238 | ALGORITHM DESCRIPTION: |
239 | |
240 | Argument representation: |
241 | N = rint(X*2^k/ln2) = 2^k*M+j |
242 | X = N*ln2/2^k + r = M*ln2 + ln2*(j/2^k) + r |
243 | then -ln2/2^(k+1) < r < ln2/2^(k+1) |
244 | Alternatively: |
245 | N = trunc(X*2^k/ln2) |
246 | then 0 < r < ln2/2^k |
247 | |
248 | Result calculation: |
249 | exp(X) = exp(M*ln2 + ln2*(j/2^k) + r) |
250 | = 2^M * 2^(j/2^k) * exp(r) |
251 | 2^M is calculated by bit manipulation |
252 | 2^(j/2^k) is stored in table |
253 | exp(r) is approximated by polynomial |
254 | |
255 | The table lookup is skipped if k = 0. */ |
256 | |
257 | pushq %rbp |
258 | cfi_adjust_cfa_offset (8) |
259 | cfi_rel_offset (%rbp, 0) |
260 | movq %rsp, %rbp |
261 | cfi_def_cfa_register (%rbp) |
262 | andq $-64, %rsp |
263 | subq $1280, %rsp |
264 | movq __svml_dexp_data@GOTPCREL(%rip), %rax |
265 | |
266 | /* table lookup for dT[j] = 2^(j/2^k) */ |
267 | kxnorw %k1, %k1, %k1 |
268 | |
269 | /* iAbsX = (int)(lX>>32), lX = *(longlong*)&X */ |
270 | vpsrlq $32, %zmm0, %zmm1 |
271 | vmovups __dbInvLn2(%rax), %zmm7 |
272 | vmovups __dbShifter(%rax), %zmm5 |
273 | vmovups __lIndexMask(%rax), %zmm6 |
274 | vmovups __dbLn2hi(%rax), %zmm9 |
275 | vmovups __dPC0(%rax), %zmm12 |
276 | |
277 | /* dM = X*dbInvLn2+dbShifter, dbInvLn2 = 2^k/Ln2 */ |
278 | vfmadd213pd %zmm5, %zmm0, %zmm7 |
279 | vpmovqd %zmm1, %ymm2 |
280 | |
281 | /* dN = dM-dbShifter, dN = rint(X*2^k/Ln2) */ |
282 | vsubpd %zmm5, %zmm7, %zmm11 |
283 | |
284 | /* iAbsX = iAbsX&iAbsMask */ |
285 | vpand __iAbsMask(%rax), %ymm2, %ymm3 |
286 | |
287 | /* dR = X - dN*dbLn2hi, dbLn2hi is 52-8-k hi bits of ln2/2^k */ |
288 | vmovaps %zmm0, %zmm10 |
289 | vfnmadd231pd %zmm11, %zmm9, %zmm10 |
290 | vmovups __dPC2(%rax), %zmm9 |
291 | |
292 | /* dR = dR - dN*dbLn2lo, dbLn2lo is 40..94 bits of lo part of ln2/2^k */ |
293 | vfnmadd132pd __dbLn2lo(%rax), %zmm10, %zmm11 |
294 | |
295 | /* exp(r) = b0+r*(b0+r*(b1+r*b2)) */ |
296 | vfmadd213pd __dPC1(%rax), %zmm11, %zmm9 |
297 | vfmadd213pd %zmm12, %zmm11, %zmm9 |
298 | vfmadd213pd %zmm12, %zmm11, %zmm9 |
299 | |
300 | /* iRangeMask = (iAbsX>iDomainRange) */ |
301 | vpcmpgtd __iDomainRange(%rax), %ymm3, %ymm4 |
302 | |
303 | /* Mask = iRangeMask?1:0, set mask for overflow/underflow */ |
304 | vmovmskps %ymm4, %ecx |
305 | |
306 | /* lIndex = (*(longlong*)&dM)&lIndexMask, lIndex is the lower K bits of lM */ |
307 | vpandq %zmm6, %zmm7, %zmm13 |
308 | vpmovqd %zmm13, %ymm14 |
309 | vpxord %zmm15, %zmm15, %zmm15 |
310 | vgatherdpd (%rax,%ymm14,8), %zmm15{%k1} |
311 | |
312 | /* 2^(j/2^k) * exp(r) */ |
313 | vmulpd %zmm9, %zmm15, %zmm10 |
314 | |
315 | /* lM = (*(longlong*)&dM)&(~lIndexMask) */ |
316 | vpandnq %zmm7, %zmm6, %zmm8 |
317 | |
318 | /* lM = lM<<(52-K), 2^M */ |
319 | vpsllq $42, %zmm8, %zmm1 |
320 | |
321 | /* multiply by 2^M through integer add */ |
322 | vpaddq %zmm1, %zmm10, %zmm1 |
323 | testl %ecx, %ecx |
324 | jne .LBL_2_3 |
325 | |
326 | .LBL_2_2: |
327 | cfi_remember_state |
328 | vmovaps %zmm1, %zmm0 |
329 | movq %rbp, %rsp |
330 | cfi_def_cfa_register (%rsp) |
331 | popq %rbp |
332 | cfi_adjust_cfa_offset (-8) |
333 | cfi_restore (%rbp) |
334 | ret |
335 | |
336 | .LBL_2_3: |
337 | cfi_restore_state |
338 | vmovups %zmm0, 1152(%rsp) |
339 | vmovups %zmm1, 1216(%rsp) |
340 | je .LBL_2_2 |
341 | |
342 | xorb %dl, %dl |
343 | xorl %eax, %eax |
344 | kmovw %k4, 1048(%rsp) |
345 | kmovw %k5, 1040(%rsp) |
346 | kmovw %k6, 1032(%rsp) |
347 | kmovw %k7, 1024(%rsp) |
348 | vmovups %zmm16, 960(%rsp) |
349 | vmovups %zmm17, 896(%rsp) |
350 | vmovups %zmm18, 832(%rsp) |
351 | vmovups %zmm19, 768(%rsp) |
352 | vmovups %zmm20, 704(%rsp) |
353 | vmovups %zmm21, 640(%rsp) |
354 | vmovups %zmm22, 576(%rsp) |
355 | vmovups %zmm23, 512(%rsp) |
356 | vmovups %zmm24, 448(%rsp) |
357 | vmovups %zmm25, 384(%rsp) |
358 | vmovups %zmm26, 320(%rsp) |
359 | vmovups %zmm27, 256(%rsp) |
360 | vmovups %zmm28, 192(%rsp) |
361 | vmovups %zmm29, 128(%rsp) |
362 | vmovups %zmm30, 64(%rsp) |
363 | vmovups %zmm31, (%rsp) |
364 | movq %rsi, 1064(%rsp) |
365 | movq %rdi, 1056(%rsp) |
366 | movq %r12, 1096(%rsp) |
367 | cfi_offset_rel_rsp (12, 1096) |
368 | movb %dl, %r12b |
369 | movq %r13, 1088(%rsp) |
370 | cfi_offset_rel_rsp (13, 1088) |
371 | movl %ecx, %r13d |
372 | movq %r14, 1080(%rsp) |
373 | cfi_offset_rel_rsp (14, 1080) |
374 | movl %eax, %r14d |
375 | movq %r15, 1072(%rsp) |
376 | cfi_offset_rel_rsp (15, 1072) |
377 | cfi_remember_state |
378 | |
379 | .LBL_2_6: |
380 | btl %r14d, %r13d |
381 | jc .LBL_2_12 |
382 | |
383 | .LBL_2_7: |
384 | lea 1(%r14), %esi |
385 | btl %esi, %r13d |
386 | jc .LBL_2_10 |
387 | |
388 | .LBL_2_8: |
389 | incb %r12b |
390 | addl $2, %r14d |
391 | cmpb $16, %r12b |
392 | jb .LBL_2_6 |
393 | |
394 | kmovw 1048(%rsp), %k4 |
395 | kmovw 1040(%rsp), %k5 |
396 | kmovw 1032(%rsp), %k6 |
397 | kmovw 1024(%rsp), %k7 |
398 | vmovups 960(%rsp), %zmm16 |
399 | vmovups 896(%rsp), %zmm17 |
400 | vmovups 832(%rsp), %zmm18 |
401 | vmovups 768(%rsp), %zmm19 |
402 | vmovups 704(%rsp), %zmm20 |
403 | vmovups 640(%rsp), %zmm21 |
404 | vmovups 576(%rsp), %zmm22 |
405 | vmovups 512(%rsp), %zmm23 |
406 | vmovups 448(%rsp), %zmm24 |
407 | vmovups 384(%rsp), %zmm25 |
408 | vmovups 320(%rsp), %zmm26 |
409 | vmovups 256(%rsp), %zmm27 |
410 | vmovups 192(%rsp), %zmm28 |
411 | vmovups 128(%rsp), %zmm29 |
412 | vmovups 64(%rsp), %zmm30 |
413 | vmovups (%rsp), %zmm31 |
414 | vmovups 1216(%rsp), %zmm1 |
415 | movq 1064(%rsp), %rsi |
416 | movq 1056(%rsp), %rdi |
417 | movq 1096(%rsp), %r12 |
418 | cfi_restore (%r12) |
419 | movq 1088(%rsp), %r13 |
420 | cfi_restore (%r13) |
421 | movq 1080(%rsp), %r14 |
422 | cfi_restore (%r14) |
423 | movq 1072(%rsp), %r15 |
424 | cfi_restore (%r15) |
425 | jmp .LBL_2_2 |
426 | |
427 | .LBL_2_10: |
428 | cfi_restore_state |
429 | movzbl %r12b, %r15d |
430 | shlq $4, %r15 |
431 | vmovsd 1160(%rsp,%r15), %xmm0 |
432 | vzeroupper |
433 | vmovsd 1160(%rsp,%r15), %xmm0 |
434 | call JUMPTARGET(exp) |
435 | vmovsd %xmm0, 1224(%rsp,%r15) |
436 | jmp .LBL_2_8 |
437 | |
438 | .LBL_2_12: |
439 | movzbl %r12b, %r15d |
440 | shlq $4, %r15 |
441 | vmovsd 1152(%rsp,%r15), %xmm0 |
442 | vzeroupper |
443 | vmovsd 1152(%rsp,%r15), %xmm0 |
444 | call JUMPTARGET(exp) |
445 | vmovsd %xmm0, 1216(%rsp,%r15) |
446 | jmp .LBL_2_7 |
447 | |
448 | END (_ZGVeN8v_exp_skx) |
449 | |