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
24ENTRY (_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
234END (_ZGVeN8v_exp_knl)
235
236ENTRY (_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
448END (_ZGVeN8v_exp_skx)
449

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_d_exp8_core_avx512.S