1 | /* Function pow 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_pow_data.h" |
21 | #include "svml_d_wrapper_impl.h" |
22 | |
23 | /* ALGORITHM DESCRIPTION: |
24 | |
25 | 1) Calculating log2|x| |
26 | Here we use the following formula. |
27 | Let |x|=2^k1*X1, where k1 is integer, 1<=X1<2. |
28 | Let C ~= 1/ln(2), |
29 | Rcp1 ~= 1/X1, X2=Rcp1*X1, |
30 | Rcp2 ~= 1/X2, X3=Rcp2*X2, |
31 | Rcp3 ~= 1/X3, Rcp3C ~= C/X3. |
32 | Then |
33 | log2|x| = k1 + log2(1/Rcp1) + log2(1/Rcp2) + log2(C/Rcp3C) + |
34 | log2(X1*Rcp1*Rcp2*Rcp3C/C), |
35 | where X1*Rcp1*Rcp2*Rcp3C = C*(1+q), q is very small. |
36 | |
37 | The values of Rcp1, log2(1/Rcp1), Rcp2, log2(1/Rcp2), |
38 | Rcp3C, log2(C/Rcp3C) are taken from tables. |
39 | Values of Rcp1, Rcp2, Rcp3C are such that RcpC=Rcp1*Rcp2*Rcp3C |
40 | is exactly represented in target precision. |
41 | |
42 | log2(X1*Rcp1*Rcp2*Rcp3C/C) = log2(1+q) = ln(1+q)/ln2 = |
43 | = 1/(ln2)*q - 1/(2ln2)*q^2 + 1/(3ln2)*q^3 - ... = |
44 | = 1/(C*ln2)*cq - 1/(2*C^2*ln2)*cq^2 + 1/(3*C^3*ln2)*cq^3 - ... = |
45 | = (1 + a1)*cq + a2*cq^2 + a3*cq^3 + ..., |
46 | where cq = X1*Rcp1*Rcp2*Rcp3C-C, |
47 | a1=1/(C*ln(2))-1 is small, |
48 | a2=1/(2*C^2*ln2), |
49 | a3=1/(3*C^3*ln2), |
50 | ... |
51 | We get 3 parts of log2 result: HH+HL+HLL ~= log2|x|. |
52 | |
53 | 2) Calculation of y*(HH+HL+HLL). |
54 | Split y into YHi+YLo. |
55 | Get high PH and medium PL parts of y*log2|x|. |
56 | Get low PLL part of y*log2|x|. |
57 | Now we have PH+PL+PLL ~= y*log2|x|. |
58 | |
59 | 3) Calculation of 2^(PH+PL+PLL). |
60 | Mathematical idea of computing 2^(PH+PL+PLL) is the following. |
61 | Let's represent PH+PL+PLL in the form N + j/2^expK + Z, |
62 | where expK=7 in this implementation, N and j are integers, |
63 | 0<=j<=2^expK-1, |Z|<2^(-expK-1). |
64 | Hence 2^(PH+PL+PLL) ~= 2^N * 2^(j/2^expK) * 2^Z, |
65 | where 2^(j/2^expK) is stored in a table, and |
66 | 2^Z ~= 1 + B1*Z + B2*Z^2 ... + B5*Z^5. |
67 | |
68 | We compute 2^(PH+PL+PLL) as follows. |
69 | Break PH into PHH + PHL, where PHH = N + j/2^expK. |
70 | Z = PHL + PL + PLL |
71 | Exp2Poly = B1*Z + B2*Z^2 ... + B5*Z^5 |
72 | Get 2^(j/2^expK) from table in the form THI+TLO. |
73 | Now we have 2^(PH+PL+PLL) ~= 2^N * (THI + TLO) * (1 + Exp2Poly). |
74 | |
75 | Get significand of 2^(PH+PL+PLL) in the form ResHi+ResLo: |
76 | ResHi := THI |
77 | ResLo := THI * Exp2Poly + TLO |
78 | |
79 | Get exponent ERes of the result: |
80 | Res := ResHi + ResLo: |
81 | Result := ex(Res) + N. */ |
82 | |
83 | .section .text.evex512, "ax" , @progbits |
84 | ENTRY (_ZGVeN8vv_pow_knl) |
85 | pushq %rbp |
86 | cfi_adjust_cfa_offset (8) |
87 | cfi_rel_offset (%rbp, 0) |
88 | movq %rsp, %rbp |
89 | cfi_def_cfa_register (%rbp) |
90 | andq $-64, %rsp |
91 | subq $1344, %rsp |
92 | vpsrlq $32, %zmm0, %zmm13 |
93 | vmovaps %zmm1, %zmm12 |
94 | movq __svml_dpow_data@GOTPCREL(%rip), %rax |
95 | movl $255, %edx |
96 | vpmovqd %zmm13, %ymm10 |
97 | vpsrlq $32, %zmm12, %zmm14 |
98 | kmovw %edx, %k1 |
99 | movl $-1, %ecx |
100 | vpmovqd %zmm14, %ymm15 |
101 | |
102 | /* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ |
103 | vmovups _dbOne(%rax), %zmm6 |
104 | |
105 | /* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ |
106 | vmovaps %zmm10, %zmm5 |
107 | |
108 | /* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ |
109 | vpsubd _i3fe7fe00(%rax), %zmm10, %zmm14{%k1} |
110 | vpandd _iIndexMask(%rax), %zmm10, %zmm5{%k1} |
111 | vpsrad $20, %zmm14, %zmm14{%k1} |
112 | vpxord %zmm9, %zmm9, %zmm9 |
113 | vpaddd _HIDELTA(%rax), %zmm10, %zmm3{%k1} |
114 | vpaddd _iIndexAdd(%rax), %zmm5, %zmm5{%k1} |
115 | vpxord %zmm7, %zmm7, %zmm7 |
116 | vpaddd _i2p20_2p19(%rax), %zmm14, %zmm14{%k1} |
117 | vpcmpd $1, _LORANGE(%rax), %zmm3, %k2{%k1} |
118 | vpsrld $10, %zmm5, %zmm5{%k1} |
119 | vpandd _ABSMASK(%rax), %zmm15, %zmm2{%k1} |
120 | vpbroadcastd %ecx, %zmm1{%k2}{z} |
121 | |
122 | /* Index for reciprocal table */ |
123 | vpslld $3, %zmm5, %zmm8{%k1} |
124 | kxnorw %k2, %k2, %k2 |
125 | vgatherdpd 11712(%rax,%ymm8), %zmm9{%k2} |
126 | vpmovzxdq %ymm14, %zmm10 |
127 | |
128 | /* Index for log2 table */ |
129 | vpslld $4, %zmm5, %zmm13{%k1} |
130 | kxnorw %k2, %k2, %k2 |
131 | vpsllq $32, %zmm10, %zmm3 |
132 | vpxord %zmm8, %zmm8, %zmm8 |
133 | vpcmpd $5, _INF(%rax), %zmm2, %k3{%k1} |
134 | vpbroadcastd %ecx, %zmm4{%k3}{z} |
135 | vpternlogq $248, _iMantissaMask(%rax), %zmm0, %zmm6 |
136 | kxnorw %k3, %k3, %k3 |
137 | vpternlogq $168, _iffffffff00000000(%rax), %zmm10, %zmm3 |
138 | |
139 | /* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ |
140 | vpandq _iHighMask(%rax), %zmm6, %zmm2 |
141 | vgatherdpd 19976(%rax,%ymm13), %zmm8{%k2} |
142 | vpord %zmm4, %zmm1, %zmm11{%k1} |
143 | vsubpd _db2p20_2p19(%rax), %zmm3, %zmm1 |
144 | vsubpd %zmm2, %zmm6, %zmm5 |
145 | |
146 | /* r1 = x1*rcp1 */ |
147 | vmulpd %zmm9, %zmm6, %zmm6 |
148 | vgatherdpd 19968(%rax,%ymm13), %zmm7{%k3} |
149 | |
150 | /* cq = c+r1 */ |
151 | vaddpd _LHN(%rax), %zmm6, %zmm4 |
152 | |
153 | /* E = -r1+__fence(x1Hi*rcp1) */ |
154 | vfmsub213pd %zmm6, %zmm9, %zmm2 |
155 | |
156 | /* T = k + L1hi */ |
157 | vaddpd %zmm7, %zmm1, %zmm7 |
158 | |
159 | /* E=E+x1Lo*rcp1 */ |
160 | vfmadd213pd %zmm2, %zmm9, %zmm5 |
161 | |
162 | /* T_Rh = T + cq */ |
163 | vaddpd %zmm4, %zmm7, %zmm3 |
164 | |
165 | /* Rl = T-T_Rh; -> -Rh */ |
166 | vsubpd %zmm3, %zmm7, %zmm9 |
167 | |
168 | /* Rl=Rl+cq */ |
169 | vaddpd %zmm9, %zmm4, %zmm6 |
170 | |
171 | /* T_Rh_Eh = T_Rh + E */ |
172 | vaddpd %zmm5, %zmm3, %zmm9 |
173 | |
174 | /* HLL = T_Rh - T_Rh_Eh; -> -Eh */ |
175 | vsubpd %zmm9, %zmm3, %zmm2 |
176 | |
177 | /* cq = cq + E; */ |
178 | vaddpd %zmm5, %zmm4, %zmm4 |
179 | |
180 | /* HLL+=E; -> El */ |
181 | vaddpd %zmm2, %zmm5, %zmm1 |
182 | vmovups _clv_2(%rax), %zmm5 |
183 | |
184 | /* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ |
185 | vfmadd213pd _clv_3(%rax), %zmm4, %zmm5 |
186 | |
187 | /* HLL+=Rl */ |
188 | vaddpd %zmm6, %zmm1, %zmm7 |
189 | |
190 | /* 2^(y*(HH+HL+HLL)) starts here: |
191 | yH = y; Lo(yH)&=0xf8000000 |
192 | */ |
193 | vpandq _iHighMask(%rax), %zmm12, %zmm6 |
194 | |
195 | /* yL = y-yH */ |
196 | vsubpd %zmm6, %zmm12, %zmm2 |
197 | vfmadd213pd _clv_4(%rax), %zmm4, %zmm5 |
198 | |
199 | /* HLL+=L1lo */ |
200 | vaddpd %zmm8, %zmm7, %zmm8 |
201 | vfmadd213pd _clv_5(%rax), %zmm4, %zmm5 |
202 | vfmadd213pd _clv_6(%rax), %zmm4, %zmm5 |
203 | vfmadd213pd _clv_7(%rax), %zmm4, %zmm5 |
204 | vfmadd213pd %zmm8, %zmm4, %zmm5 |
205 | |
206 | /* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ |
207 | vaddpd %zmm5, %zmm9, %zmm13 |
208 | |
209 | /* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ |
210 | vsubpd %zmm9, %zmm13, %zmm10 |
211 | |
212 | /* HLL = HLL - HLLhi */ |
213 | vsubpd %zmm10, %zmm5, %zmm3 |
214 | |
215 | /* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ |
216 | vpandq _iHighMask(%rax), %zmm13, %zmm5 |
217 | |
218 | /* pH = yH*HH */ |
219 | vmulpd %zmm5, %zmm6, %zmm1 |
220 | |
221 | /* HL = T_Rh_Eh_HLLhi-HH */ |
222 | vsubpd %zmm5, %zmm13, %zmm4 |
223 | vpsrlq $32, %zmm1, %zmm14 |
224 | |
225 | /* pLL = y*HLL; |
226 | pHH = pH + *(double*)&db2p45_2p44 |
227 | */ |
228 | vaddpd _db2p45_2p44(%rax), %zmm1, %zmm10 |
229 | vpmovqd %zmm14, %ymm15 |
230 | vpandd _ABSMASK(%rax), %zmm15, %zmm14{%k1} |
231 | vpcmpd $5, _DOMAINRANGE(%rax), %zmm14, %k3{%k1} |
232 | |
233 | /* T1 = ((double*)exp2_tbl)[ 2*j ] */ |
234 | vpxord %zmm14, %zmm14, %zmm14 |
235 | vpbroadcastd %ecx, %zmm13{%k3}{z} |
236 | vpord %zmm13, %zmm11, %zmm11{%k1} |
237 | vptestmd %zmm11, %zmm11, %k0{%k1} |
238 | |
239 | /* pL=yL*HL+yH*HL; pL+=yL*HH */ |
240 | vmulpd %zmm4, %zmm2, %zmm11 |
241 | kmovw %k0, %ecx |
242 | vfmadd213pd %zmm11, %zmm4, %zmm6 |
243 | |
244 | /* pHH = pHH - *(double*)&db2p45_2p44 */ |
245 | vsubpd _db2p45_2p44(%rax), %zmm10, %zmm11 |
246 | vpmovqd %zmm10, %ymm4 |
247 | movzbl %cl, %ecx |
248 | |
249 | /* _n = Lo(pHH); |
250 | _n = _n & 0xffffff80; |
251 | _n = _n >> 7; |
252 | Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n |
253 | */ |
254 | vpslld $13, %zmm4, %zmm7{%k1} |
255 | |
256 | /* j = Lo(pHH)&0x0000007f */ |
257 | vpandd _jIndexMask(%rax), %zmm4, %zmm9{%k1} |
258 | vfmadd213pd %zmm6, %zmm5, %zmm2 |
259 | |
260 | /* pHL = pH - pHH */ |
261 | vsubpd %zmm11, %zmm1, %zmm1 |
262 | vpaddd _iOne(%rax), %zmm7, %zmm7{%k1} |
263 | |
264 | /* t=pL+pLL; t+=pHL */ |
265 | vfmadd231pd %zmm12, %zmm3, %zmm2 |
266 | vpslld $4, %zmm9, %zmm9{%k1} |
267 | kxnorw %k1, %k1, %k1 |
268 | vgatherdpd 36416(%rax,%ymm9), %zmm14{%k1} |
269 | vpmovzxdq %ymm7, %zmm8 |
270 | vaddpd %zmm1, %zmm2, %zmm2 |
271 | vmovups _cev_1(%rax), %zmm1 |
272 | vpsllq $32, %zmm8, %zmm13 |
273 | vpternlogq $168, _ifff0000000000000(%rax), %zmm8, %zmm13 |
274 | vfmadd213pd _cev_2(%rax), %zmm2, %zmm1 |
275 | vmulpd %zmm14, %zmm13, %zmm15 |
276 | vfmadd213pd _cev_3(%rax), %zmm2, %zmm1 |
277 | vmulpd %zmm2, %zmm15, %zmm3 |
278 | vfmadd213pd _cev_4(%rax), %zmm2, %zmm1 |
279 | vfmadd213pd _cev_5(%rax), %zmm2, %zmm1 |
280 | vfmadd213pd %zmm15, %zmm3, %zmm1 |
281 | testl %ecx, %ecx |
282 | jne .LBL_1_3 |
283 | |
284 | .LBL_1_2: |
285 | cfi_remember_state |
286 | vmovaps %zmm1, %zmm0 |
287 | movq %rbp, %rsp |
288 | cfi_def_cfa_register (%rsp) |
289 | popq %rbp |
290 | cfi_adjust_cfa_offset (-8) |
291 | cfi_restore (%rbp) |
292 | ret |
293 | |
294 | .LBL_1_3: |
295 | cfi_restore_state |
296 | vmovups %zmm0, 1152(%rsp) |
297 | vmovups %zmm12, 1216(%rsp) |
298 | vmovups %zmm1, 1280(%rsp) |
299 | je .LBL_1_2 |
300 | |
301 | xorb %dl, %dl |
302 | kmovw %k4, 1048(%rsp) |
303 | xorl %eax, %eax |
304 | kmovw %k5, 1040(%rsp) |
305 | kmovw %k6, 1032(%rsp) |
306 | kmovw %k7, 1024(%rsp) |
307 | vmovups %zmm16, 960(%rsp) |
308 | vmovups %zmm17, 896(%rsp) |
309 | vmovups %zmm18, 832(%rsp) |
310 | vmovups %zmm19, 768(%rsp) |
311 | vmovups %zmm20, 704(%rsp) |
312 | vmovups %zmm21, 640(%rsp) |
313 | vmovups %zmm22, 576(%rsp) |
314 | vmovups %zmm23, 512(%rsp) |
315 | vmovups %zmm24, 448(%rsp) |
316 | vmovups %zmm25, 384(%rsp) |
317 | vmovups %zmm26, 320(%rsp) |
318 | vmovups %zmm27, 256(%rsp) |
319 | vmovups %zmm28, 192(%rsp) |
320 | vmovups %zmm29, 128(%rsp) |
321 | vmovups %zmm30, 64(%rsp) |
322 | vmovups %zmm31, (%rsp) |
323 | movq %rsi, 1064(%rsp) |
324 | movq %rdi, 1056(%rsp) |
325 | movq %r12, 1096(%rsp) |
326 | cfi_offset_rel_rsp (12, 1096) |
327 | movb %dl, %r12b |
328 | movq %r13, 1088(%rsp) |
329 | cfi_offset_rel_rsp (13, 1088) |
330 | movl %ecx, %r13d |
331 | movq %r14, 1080(%rsp) |
332 | cfi_offset_rel_rsp (14, 1080) |
333 | movl %eax, %r14d |
334 | movq %r15, 1072(%rsp) |
335 | cfi_offset_rel_rsp (15, 1072) |
336 | cfi_remember_state |
337 | |
338 | .LBL_1_6: |
339 | btl %r14d, %r13d |
340 | jc .LBL_1_12 |
341 | |
342 | .LBL_1_7: |
343 | lea 1(%r14), %esi |
344 | btl %esi, %r13d |
345 | jc .LBL_1_10 |
346 | |
347 | .LBL_1_8: |
348 | addb $1, %r12b |
349 | addl $2, %r14d |
350 | cmpb $16, %r12b |
351 | jb .LBL_1_6 |
352 | |
353 | kmovw 1048(%rsp), %k4 |
354 | movq 1064(%rsp), %rsi |
355 | kmovw 1040(%rsp), %k5 |
356 | movq 1056(%rsp), %rdi |
357 | kmovw 1032(%rsp), %k6 |
358 | movq 1096(%rsp), %r12 |
359 | cfi_restore (%r12) |
360 | movq 1088(%rsp), %r13 |
361 | cfi_restore (%r13) |
362 | kmovw 1024(%rsp), %k7 |
363 | vmovups 960(%rsp), %zmm16 |
364 | vmovups 896(%rsp), %zmm17 |
365 | vmovups 832(%rsp), %zmm18 |
366 | vmovups 768(%rsp), %zmm19 |
367 | vmovups 704(%rsp), %zmm20 |
368 | vmovups 640(%rsp), %zmm21 |
369 | vmovups 576(%rsp), %zmm22 |
370 | vmovups 512(%rsp), %zmm23 |
371 | vmovups 448(%rsp), %zmm24 |
372 | vmovups 384(%rsp), %zmm25 |
373 | vmovups 320(%rsp), %zmm26 |
374 | vmovups 256(%rsp), %zmm27 |
375 | vmovups 192(%rsp), %zmm28 |
376 | vmovups 128(%rsp), %zmm29 |
377 | vmovups 64(%rsp), %zmm30 |
378 | vmovups (%rsp), %zmm31 |
379 | movq 1080(%rsp), %r14 |
380 | cfi_restore (%r14) |
381 | movq 1072(%rsp), %r15 |
382 | cfi_restore (%r15) |
383 | vmovups 1280(%rsp), %zmm1 |
384 | jmp .LBL_1_2 |
385 | |
386 | .LBL_1_10: |
387 | cfi_restore_state |
388 | movzbl %r12b, %r15d |
389 | shlq $4, %r15 |
390 | vmovsd 1160(%rsp,%r15), %xmm0 |
391 | vmovsd 1224(%rsp,%r15), %xmm1 |
392 | call JUMPTARGET(pow) |
393 | vmovsd %xmm0, 1288(%rsp,%r15) |
394 | jmp .LBL_1_8 |
395 | |
396 | .LBL_1_12: |
397 | movzbl %r12b, %r15d |
398 | shlq $4, %r15 |
399 | vmovsd 1152(%rsp,%r15), %xmm0 |
400 | vmovsd 1216(%rsp,%r15), %xmm1 |
401 | call JUMPTARGET(pow) |
402 | vmovsd %xmm0, 1280(%rsp,%r15) |
403 | jmp .LBL_1_7 |
404 | |
405 | END (_ZGVeN8vv_pow_knl) |
406 | |
407 | ENTRY (_ZGVeN8vv_pow_skx) |
408 | pushq %rbp |
409 | cfi_adjust_cfa_offset (8) |
410 | cfi_rel_offset (%rbp, 0) |
411 | movq %rsp, %rbp |
412 | cfi_def_cfa_register (%rbp) |
413 | andq $-64, %rsp |
414 | subq $1344, %rsp |
415 | vpsrlq $32, %zmm0, %zmm10 |
416 | kxnorw %k1, %k1, %k1 |
417 | kxnorw %k2, %k2, %k2 |
418 | kxnorw %k3, %k3, %k3 |
419 | vpmovqd %zmm10, %ymm7 |
420 | movq __svml_dpow_data@GOTPCREL(%rip), %rax |
421 | vmovaps %zmm1, %zmm6 |
422 | vpsrlq $32, %zmm6, %zmm13 |
423 | |
424 | /* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ |
425 | vpand _iIndexMask(%rax), %ymm7, %ymm15 |
426 | vpaddd _HIDELTA(%rax), %ymm7, %ymm2 |
427 | |
428 | /* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ |
429 | vpsubd _i3fe7fe00(%rax), %ymm7, %ymm7 |
430 | vmovdqu _ABSMASK(%rax), %ymm4 |
431 | vmovdqu _LORANGE(%rax), %ymm3 |
432 | |
433 | /* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ |
434 | vmovups _dbOne(%rax), %zmm11 |
435 | vmovdqu _INF(%rax), %ymm5 |
436 | vpaddd _iIndexAdd(%rax), %ymm15, %ymm12 |
437 | vpmovqd %zmm13, %ymm14 |
438 | vpternlogq $248, _iMantissaMask(%rax), %zmm0, %zmm11 |
439 | vpsrld $10, %ymm12, %ymm10 |
440 | vpsrad $20, %ymm7, %ymm13 |
441 | |
442 | /* Index for reciprocal table */ |
443 | vpslld $3, %ymm10, %ymm8 |
444 | |
445 | /* Index for log2 table */ |
446 | vpslld $4, %ymm10, %ymm1 |
447 | vpcmpgtd %ymm2, %ymm3, %ymm3 |
448 | vpand %ymm4, %ymm14, %ymm2 |
449 | vpaddd _i2p20_2p19(%rax), %ymm13, %ymm14 |
450 | vpmovzxdq %ymm14, %zmm15 |
451 | vpsllq $32, %zmm15, %zmm7 |
452 | vpternlogq $168, _iffffffff00000000(%rax), %zmm15, %zmm7 |
453 | vsubpd _db2p20_2p19(%rax), %zmm7, %zmm13 |
454 | vpxord %zmm9, %zmm9, %zmm9 |
455 | vgatherdpd 11712(%rax,%ymm8), %zmm9{%k1} |
456 | |
457 | /* T1 = ((double*)exp2_tbl)[ 2*j ] */ |
458 | kxnorw %k1, %k1, %k1 |
459 | vpxord %zmm12, %zmm12, %zmm12 |
460 | vpxord %zmm8, %zmm8, %zmm8 |
461 | vgatherdpd 19968(%rax,%ymm1), %zmm12{%k2} |
462 | vgatherdpd 19976(%rax,%ymm1), %zmm8{%k3} |
463 | vmovups _iHighMask(%rax), %zmm1 |
464 | |
465 | /* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ |
466 | vandpd %zmm1, %zmm11, %zmm10 |
467 | vsubpd %zmm10, %zmm11, %zmm15 |
468 | |
469 | /* r1 = x1*rcp1 */ |
470 | vmulpd %zmm9, %zmm11, %zmm11 |
471 | |
472 | /* E = -r1+__fence(x1Hi*rcp1) */ |
473 | vfmsub213pd %zmm11, %zmm9, %zmm10 |
474 | |
475 | /* cq = c+r1 */ |
476 | vaddpd _LHN(%rax), %zmm11, %zmm14 |
477 | |
478 | /* E=E+x1Lo*rcp1 */ |
479 | vfmadd213pd %zmm10, %zmm9, %zmm15 |
480 | |
481 | /* T = k + L1hi */ |
482 | vaddpd %zmm12, %zmm13, %zmm9 |
483 | |
484 | /* T_Rh = T + cq */ |
485 | vaddpd %zmm14, %zmm9, %zmm11 |
486 | |
487 | /* T_Rh_Eh = T_Rh + E */ |
488 | vaddpd %zmm15, %zmm11, %zmm13 |
489 | |
490 | /* Rl = T-T_Rh; -> -Rh */ |
491 | vsubpd %zmm11, %zmm9, %zmm12 |
492 | |
493 | /* HLL = T_Rh - T_Rh_Eh; -> -Eh */ |
494 | vsubpd %zmm13, %zmm11, %zmm9 |
495 | |
496 | /* Rl=Rl+cq */ |
497 | vaddpd %zmm12, %zmm14, %zmm10 |
498 | |
499 | /* HLL+=E; -> El */ |
500 | vaddpd %zmm9, %zmm15, %zmm7 |
501 | |
502 | /* HLL+=Rl */ |
503 | vaddpd %zmm10, %zmm7, %zmm12 |
504 | |
505 | /* 2^(y*(HH+HL+HLL)) starts here: |
506 | yH = y; Lo(yH)&=0xf8000000 |
507 | */ |
508 | vandpd %zmm1, %zmm6, %zmm7 |
509 | |
510 | /* HLL+=L1lo */ |
511 | vaddpd %zmm8, %zmm12, %zmm12 |
512 | |
513 | /* cq = cq + E */ |
514 | vaddpd %zmm15, %zmm14, %zmm8 |
515 | vmovups _clv_2(%rax), %zmm14 |
516 | |
517 | /* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ |
518 | vfmadd213pd _clv_3(%rax), %zmm8, %zmm14 |
519 | vfmadd213pd _clv_4(%rax), %zmm8, %zmm14 |
520 | vfmadd213pd _clv_5(%rax), %zmm8, %zmm14 |
521 | vfmadd213pd _clv_6(%rax), %zmm8, %zmm14 |
522 | vfmadd213pd _clv_7(%rax), %zmm8, %zmm14 |
523 | vfmadd213pd %zmm12, %zmm8, %zmm14 |
524 | |
525 | /* yL = y-yH */ |
526 | vsubpd %zmm7, %zmm6, %zmm8 |
527 | |
528 | /* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ |
529 | vaddpd %zmm14, %zmm13, %zmm15 |
530 | |
531 | /* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ |
532 | vandpd %zmm1, %zmm15, %zmm11 |
533 | |
534 | /* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ |
535 | vsubpd %zmm13, %zmm15, %zmm13 |
536 | |
537 | /* pH = yH*HH */ |
538 | vmulpd %zmm11, %zmm7, %zmm9 |
539 | |
540 | /* HLL = HLL - HLLhi */ |
541 | vsubpd %zmm13, %zmm14, %zmm12 |
542 | |
543 | /* HL = T_Rh_Eh_HLLhi-HH */ |
544 | vsubpd %zmm11, %zmm15, %zmm10 |
545 | vpsrlq $32, %zmm9, %zmm1 |
546 | vmovdqu _DOMAINRANGE(%rax), %ymm13 |
547 | vpmovqd %zmm1, %ymm1 |
548 | vpand %ymm4, %ymm1, %ymm1 |
549 | vpcmpgtd %ymm5, %ymm2, %ymm4 |
550 | vpcmpeqd %ymm5, %ymm2, %ymm5 |
551 | vpternlogd $254, %ymm5, %ymm4, %ymm3 |
552 | vpcmpgtd %ymm13, %ymm1, %ymm2 |
553 | vpcmpeqd %ymm13, %ymm1, %ymm4 |
554 | vpternlogd $254, %ymm4, %ymm2, %ymm3 |
555 | |
556 | /* pLL = y*HLL */ |
557 | vmovups _db2p45_2p44(%rax), %zmm2 |
558 | |
559 | /* pHH = pH + *(double*)&db2p45_2p44 */ |
560 | vaddpd %zmm2, %zmm9, %zmm1 |
561 | vpmovqd %zmm1, %ymm5 |
562 | |
563 | /* j = Lo(pHH)&0x0000007f */ |
564 | vpand _jIndexMask(%rax), %ymm5, %ymm14 |
565 | vpslld $4, %ymm14, %ymm15 |
566 | vmovmskps %ymm3, %ecx |
567 | |
568 | /* pL=yL*HL+yH*HL; pL+=yL*HH */ |
569 | vmulpd %zmm10, %zmm8, %zmm3 |
570 | vfmadd213pd %zmm3, %zmm10, %zmm7 |
571 | vfmadd213pd %zmm7, %zmm11, %zmm8 |
572 | |
573 | /* _n = Lo(pHH) |
574 | _n = _n & 0xffffff80 |
575 | _n = _n >> 7 |
576 | Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n |
577 | */ |
578 | vpslld $13, %ymm5, %ymm7 |
579 | |
580 | /* t=pL+pLL; t+=pHL */ |
581 | vfmadd231pd %zmm6, %zmm12, %zmm8 |
582 | vpaddd _iOne(%rax), %ymm7, %ymm10 |
583 | vpmovzxdq %ymm10, %zmm11 |
584 | vpsllq $32, %zmm11, %zmm3 |
585 | vpternlogq $168, _ifff0000000000000(%rax), %zmm11, %zmm3 |
586 | |
587 | /* pHH = pHH - *(double*)&db2p45_2p44 */ |
588 | vsubpd %zmm2, %zmm1, %zmm11 |
589 | vmovups _cev_1(%rax), %zmm2 |
590 | |
591 | /* pHL = pH - pHH */ |
592 | vsubpd %zmm11, %zmm9, %zmm9 |
593 | vaddpd %zmm9, %zmm8, %zmm8 |
594 | vfmadd213pd _cev_2(%rax), %zmm8, %zmm2 |
595 | vfmadd213pd _cev_3(%rax), %zmm8, %zmm2 |
596 | vfmadd213pd _cev_4(%rax), %zmm8, %zmm2 |
597 | vfmadd213pd _cev_5(%rax), %zmm8, %zmm2 |
598 | vpxord %zmm4, %zmm4, %zmm4 |
599 | vgatherdpd 36416(%rax,%ymm15), %zmm4{%k1} |
600 | vmulpd %zmm4, %zmm3, %zmm1 |
601 | vmulpd %zmm8, %zmm1, %zmm12 |
602 | vfmadd213pd %zmm1, %zmm12, %zmm2 |
603 | testl %ecx, %ecx |
604 | jne .LBL_2_3 |
605 | |
606 | .LBL_2_2: |
607 | cfi_remember_state |
608 | vmovaps %zmm2, %zmm0 |
609 | movq %rbp, %rsp |
610 | cfi_def_cfa_register (%rsp) |
611 | popq %rbp |
612 | cfi_adjust_cfa_offset (-8) |
613 | cfi_restore (%rbp) |
614 | ret |
615 | |
616 | .LBL_2_3: |
617 | cfi_restore_state |
618 | vmovups %zmm0, 1152(%rsp) |
619 | vmovups %zmm6, 1216(%rsp) |
620 | vmovups %zmm2, 1280(%rsp) |
621 | je .LBL_2_2 |
622 | |
623 | xorb %dl, %dl |
624 | xorl %eax, %eax |
625 | kmovw %k4, 1048(%rsp) |
626 | kmovw %k5, 1040(%rsp) |
627 | kmovw %k6, 1032(%rsp) |
628 | kmovw %k7, 1024(%rsp) |
629 | vmovups %zmm16, 960(%rsp) |
630 | vmovups %zmm17, 896(%rsp) |
631 | vmovups %zmm18, 832(%rsp) |
632 | vmovups %zmm19, 768(%rsp) |
633 | vmovups %zmm20, 704(%rsp) |
634 | vmovups %zmm21, 640(%rsp) |
635 | vmovups %zmm22, 576(%rsp) |
636 | vmovups %zmm23, 512(%rsp) |
637 | vmovups %zmm24, 448(%rsp) |
638 | vmovups %zmm25, 384(%rsp) |
639 | vmovups %zmm26, 320(%rsp) |
640 | vmovups %zmm27, 256(%rsp) |
641 | vmovups %zmm28, 192(%rsp) |
642 | vmovups %zmm29, 128(%rsp) |
643 | vmovups %zmm30, 64(%rsp) |
644 | vmovups %zmm31, (%rsp) |
645 | movq %rsi, 1064(%rsp) |
646 | movq %rdi, 1056(%rsp) |
647 | movq %r12, 1096(%rsp) |
648 | cfi_offset_rel_rsp (12, 1096) |
649 | movb %dl, %r12b |
650 | movq %r13, 1088(%rsp) |
651 | cfi_offset_rel_rsp (13, 1088) |
652 | movl %ecx, %r13d |
653 | movq %r14, 1080(%rsp) |
654 | cfi_offset_rel_rsp (14, 1080) |
655 | movl %eax, %r14d |
656 | movq %r15, 1072(%rsp) |
657 | cfi_offset_rel_rsp (15, 1072) |
658 | cfi_remember_state |
659 | |
660 | .LBL_2_6: |
661 | btl %r14d, %r13d |
662 | jc .LBL_2_12 |
663 | |
664 | .LBL_2_7: |
665 | lea 1(%r14), %esi |
666 | btl %esi, %r13d |
667 | jc .LBL_2_10 |
668 | |
669 | .LBL_2_8: |
670 | incb %r12b |
671 | addl $2, %r14d |
672 | cmpb $16, %r12b |
673 | jb .LBL_2_6 |
674 | |
675 | kmovw 1048(%rsp), %k4 |
676 | kmovw 1040(%rsp), %k5 |
677 | kmovw 1032(%rsp), %k6 |
678 | kmovw 1024(%rsp), %k7 |
679 | vmovups 960(%rsp), %zmm16 |
680 | vmovups 896(%rsp), %zmm17 |
681 | vmovups 832(%rsp), %zmm18 |
682 | vmovups 768(%rsp), %zmm19 |
683 | vmovups 704(%rsp), %zmm20 |
684 | vmovups 640(%rsp), %zmm21 |
685 | vmovups 576(%rsp), %zmm22 |
686 | vmovups 512(%rsp), %zmm23 |
687 | vmovups 448(%rsp), %zmm24 |
688 | vmovups 384(%rsp), %zmm25 |
689 | vmovups 320(%rsp), %zmm26 |
690 | vmovups 256(%rsp), %zmm27 |
691 | vmovups 192(%rsp), %zmm28 |
692 | vmovups 128(%rsp), %zmm29 |
693 | vmovups 64(%rsp), %zmm30 |
694 | vmovups (%rsp), %zmm31 |
695 | vmovups 1280(%rsp), %zmm2 |
696 | movq 1064(%rsp), %rsi |
697 | movq 1056(%rsp), %rdi |
698 | movq 1096(%rsp), %r12 |
699 | cfi_restore (%r12) |
700 | movq 1088(%rsp), %r13 |
701 | cfi_restore (%r13) |
702 | movq 1080(%rsp), %r14 |
703 | cfi_restore (%r14) |
704 | movq 1072(%rsp), %r15 |
705 | cfi_restore (%r15) |
706 | jmp .LBL_2_2 |
707 | |
708 | .LBL_2_10: |
709 | cfi_restore_state |
710 | movzbl %r12b, %r15d |
711 | shlq $4, %r15 |
712 | vmovsd 1224(%rsp,%r15), %xmm1 |
713 | vzeroupper |
714 | vmovsd 1160(%rsp,%r15), %xmm0 |
715 | |
716 | call JUMPTARGET(pow) |
717 | |
718 | vmovsd %xmm0, 1288(%rsp,%r15) |
719 | jmp .LBL_2_8 |
720 | |
721 | .LBL_2_12: |
722 | movzbl %r12b, %r15d |
723 | shlq $4, %r15 |
724 | vmovsd 1216(%rsp,%r15), %xmm1 |
725 | vzeroupper |
726 | vmovsd 1152(%rsp,%r15), %xmm0 |
727 | |
728 | call JUMPTARGET(pow) |
729 | |
730 | vmovsd %xmm0, 1280(%rsp,%r15) |
731 | jmp .LBL_2_7 |
732 | |
733 | END (_ZGVeN8vv_pow_skx) |
734 | |