1 | /* Function pow 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_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 | .text |
84 | ENTRY (_ZGVeN8vv_pow_knl) |
85 | #ifndef HAVE_AVX512DQ_ASM_SUPPORT |
86 | WRAPPER_IMPL_AVX512_ff _ZGVdN4vv_pow |
87 | #else |
88 | pushq %rbp |
89 | cfi_adjust_cfa_offset (8) |
90 | cfi_rel_offset (%rbp, 0) |
91 | movq %rsp, %rbp |
92 | cfi_def_cfa_register (%rbp) |
93 | andq $-64, %rsp |
94 | subq $1344, %rsp |
95 | vpsrlq $32, %zmm0, %zmm13 |
96 | vmovaps %zmm1, %zmm12 |
97 | movq __svml_dpow_data@GOTPCREL(%rip), %rax |
98 | movl $255, %edx |
99 | vpmovqd %zmm13, %ymm10 |
100 | vpsrlq $32, %zmm12, %zmm14 |
101 | kmovw %edx, %k1 |
102 | movl $-1, %ecx |
103 | vpmovqd %zmm14, %ymm15 |
104 | |
105 | /* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ |
106 | vmovups _dbOne(%rax), %zmm6 |
107 | |
108 | /* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ |
109 | vmovaps %zmm10, %zmm5 |
110 | |
111 | /* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ |
112 | vpsubd _i3fe7fe00(%rax), %zmm10, %zmm14{%k1} |
113 | vpandd _iIndexMask(%rax), %zmm10, %zmm5{%k1} |
114 | vpsrad $20, %zmm14, %zmm14{%k1} |
115 | vpxord %zmm9, %zmm9, %zmm9 |
116 | vpaddd _HIDELTA(%rax), %zmm10, %zmm3{%k1} |
117 | vpaddd _iIndexAdd(%rax), %zmm5, %zmm5{%k1} |
118 | vpxord %zmm7, %zmm7, %zmm7 |
119 | vpaddd _i2p20_2p19(%rax), %zmm14, %zmm14{%k1} |
120 | vpcmpd $1, _LORANGE(%rax), %zmm3, %k2{%k1} |
121 | vpsrld $10, %zmm5, %zmm5{%k1} |
122 | vpandd _ABSMASK(%rax), %zmm15, %zmm2{%k1} |
123 | vpbroadcastd %ecx, %zmm1{%k2}{z} |
124 | |
125 | /* Index for reciprocal table */ |
126 | vpslld $3, %zmm5, %zmm8{%k1} |
127 | kxnorw %k2, %k2, %k2 |
128 | vgatherdpd 11712(%rax,%ymm8), %zmm9{%k2} |
129 | vpmovzxdq %ymm14, %zmm10 |
130 | |
131 | /* Index for log2 table */ |
132 | vpslld $4, %zmm5, %zmm13{%k1} |
133 | kxnorw %k2, %k2, %k2 |
134 | vpsllq $32, %zmm10, %zmm3 |
135 | vpxord %zmm8, %zmm8, %zmm8 |
136 | vpcmpd $5, _INF(%rax), %zmm2, %k3{%k1} |
137 | vpbroadcastd %ecx, %zmm4{%k3}{z} |
138 | vpternlogq $248, _iMantissaMask(%rax), %zmm0, %zmm6 |
139 | kxnorw %k3, %k3, %k3 |
140 | vpternlogq $168, _iffffffff00000000(%rax), %zmm10, %zmm3 |
141 | |
142 | /* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ |
143 | vpandq _iHighMask(%rax), %zmm6, %zmm2 |
144 | vgatherdpd 19976(%rax,%ymm13), %zmm8{%k2} |
145 | vpord %zmm4, %zmm1, %zmm11{%k1} |
146 | vsubpd _db2p20_2p19(%rax), %zmm3, %zmm1 |
147 | vsubpd %zmm2, %zmm6, %zmm5 |
148 | |
149 | /* r1 = x1*rcp1 */ |
150 | vmulpd %zmm9, %zmm6, %zmm6 |
151 | vgatherdpd 19968(%rax,%ymm13), %zmm7{%k3} |
152 | |
153 | /* cq = c+r1 */ |
154 | vaddpd _LHN(%rax), %zmm6, %zmm4 |
155 | |
156 | /* E = -r1+__fence(x1Hi*rcp1) */ |
157 | vfmsub213pd %zmm6, %zmm9, %zmm2 |
158 | |
159 | /* T = k + L1hi */ |
160 | vaddpd %zmm7, %zmm1, %zmm7 |
161 | |
162 | /* E=E+x1Lo*rcp1 */ |
163 | vfmadd213pd %zmm2, %zmm9, %zmm5 |
164 | |
165 | /* T_Rh = T + cq */ |
166 | vaddpd %zmm4, %zmm7, %zmm3 |
167 | |
168 | /* Rl = T-T_Rh; -> -Rh */ |
169 | vsubpd %zmm3, %zmm7, %zmm9 |
170 | |
171 | /* Rl=Rl+cq */ |
172 | vaddpd %zmm9, %zmm4, %zmm6 |
173 | |
174 | /* T_Rh_Eh = T_Rh + E */ |
175 | vaddpd %zmm5, %zmm3, %zmm9 |
176 | |
177 | /* HLL = T_Rh - T_Rh_Eh; -> -Eh */ |
178 | vsubpd %zmm9, %zmm3, %zmm2 |
179 | |
180 | /* cq = cq + E; */ |
181 | vaddpd %zmm5, %zmm4, %zmm4 |
182 | |
183 | /* HLL+=E; -> El */ |
184 | vaddpd %zmm2, %zmm5, %zmm1 |
185 | vmovups _clv_2(%rax), %zmm5 |
186 | |
187 | /* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ |
188 | vfmadd213pd _clv_3(%rax), %zmm4, %zmm5 |
189 | |
190 | /* HLL+=Rl */ |
191 | vaddpd %zmm6, %zmm1, %zmm7 |
192 | |
193 | /* 2^(y*(HH+HL+HLL)) starts here: |
194 | yH = y; Lo(yH)&=0xf8000000 |
195 | */ |
196 | vpandq _iHighMask(%rax), %zmm12, %zmm6 |
197 | |
198 | /* yL = y-yH */ |
199 | vsubpd %zmm6, %zmm12, %zmm2 |
200 | vfmadd213pd _clv_4(%rax), %zmm4, %zmm5 |
201 | |
202 | /* HLL+=L1lo */ |
203 | vaddpd %zmm8, %zmm7, %zmm8 |
204 | vfmadd213pd _clv_5(%rax), %zmm4, %zmm5 |
205 | vfmadd213pd _clv_6(%rax), %zmm4, %zmm5 |
206 | vfmadd213pd _clv_7(%rax), %zmm4, %zmm5 |
207 | vfmadd213pd %zmm8, %zmm4, %zmm5 |
208 | |
209 | /* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ |
210 | vaddpd %zmm5, %zmm9, %zmm13 |
211 | |
212 | /* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ |
213 | vsubpd %zmm9, %zmm13, %zmm10 |
214 | |
215 | /* HLL = HLL - HLLhi */ |
216 | vsubpd %zmm10, %zmm5, %zmm3 |
217 | |
218 | /* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ |
219 | vpandq _iHighMask(%rax), %zmm13, %zmm5 |
220 | |
221 | /* pH = yH*HH */ |
222 | vmulpd %zmm5, %zmm6, %zmm1 |
223 | |
224 | /* HL = T_Rh_Eh_HLLhi-HH */ |
225 | vsubpd %zmm5, %zmm13, %zmm4 |
226 | vpsrlq $32, %zmm1, %zmm14 |
227 | |
228 | /* pLL = y*HLL; |
229 | pHH = pH + *(double*)&db2p45_2p44 |
230 | */ |
231 | vaddpd _db2p45_2p44(%rax), %zmm1, %zmm10 |
232 | vpmovqd %zmm14, %ymm15 |
233 | vpandd _ABSMASK(%rax), %zmm15, %zmm14{%k1} |
234 | vpcmpd $5, _DOMAINRANGE(%rax), %zmm14, %k3{%k1} |
235 | |
236 | /* T1 = ((double*)exp2_tbl)[ 2*j ] */ |
237 | vpxord %zmm14, %zmm14, %zmm14 |
238 | vpbroadcastd %ecx, %zmm13{%k3}{z} |
239 | vpord %zmm13, %zmm11, %zmm11{%k1} |
240 | vptestmd %zmm11, %zmm11, %k0{%k1} |
241 | |
242 | /* pL=yL*HL+yH*HL; pL+=yL*HH */ |
243 | vmulpd %zmm4, %zmm2, %zmm11 |
244 | kmovw %k0, %ecx |
245 | vfmadd213pd %zmm11, %zmm4, %zmm6 |
246 | |
247 | /* pHH = pHH - *(double*)&db2p45_2p44 */ |
248 | vsubpd _db2p45_2p44(%rax), %zmm10, %zmm11 |
249 | vpmovqd %zmm10, %ymm4 |
250 | movzbl %cl, %ecx |
251 | |
252 | /* _n = Lo(pHH); |
253 | _n = _n & 0xffffff80; |
254 | _n = _n >> 7; |
255 | Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n |
256 | */ |
257 | vpslld $13, %zmm4, %zmm7{%k1} |
258 | |
259 | /* j = Lo(pHH)&0x0000007f */ |
260 | vpandd _jIndexMask(%rax), %zmm4, %zmm9{%k1} |
261 | vfmadd213pd %zmm6, %zmm5, %zmm2 |
262 | |
263 | /* pHL = pH - pHH */ |
264 | vsubpd %zmm11, %zmm1, %zmm1 |
265 | vpaddd _iOne(%rax), %zmm7, %zmm7{%k1} |
266 | |
267 | /* t=pL+pLL; t+=pHL */ |
268 | vfmadd231pd %zmm12, %zmm3, %zmm2 |
269 | vpslld $4, %zmm9, %zmm9{%k1} |
270 | kxnorw %k1, %k1, %k1 |
271 | vgatherdpd 36416(%rax,%ymm9), %zmm14{%k1} |
272 | vpmovzxdq %ymm7, %zmm8 |
273 | vaddpd %zmm1, %zmm2, %zmm2 |
274 | vmovups _cev_1(%rax), %zmm1 |
275 | vpsllq $32, %zmm8, %zmm13 |
276 | vpternlogq $168, _ifff0000000000000(%rax), %zmm8, %zmm13 |
277 | vfmadd213pd _cev_2(%rax), %zmm2, %zmm1 |
278 | vmulpd %zmm14, %zmm13, %zmm15 |
279 | vfmadd213pd _cev_3(%rax), %zmm2, %zmm1 |
280 | vmulpd %zmm2, %zmm15, %zmm3 |
281 | vfmadd213pd _cev_4(%rax), %zmm2, %zmm1 |
282 | vfmadd213pd _cev_5(%rax), %zmm2, %zmm1 |
283 | vfmadd213pd %zmm15, %zmm3, %zmm1 |
284 | testl %ecx, %ecx |
285 | jne .LBL_1_3 |
286 | |
287 | .LBL_1_2: |
288 | cfi_remember_state |
289 | vmovaps %zmm1, %zmm0 |
290 | movq %rbp, %rsp |
291 | cfi_def_cfa_register (%rsp) |
292 | popq %rbp |
293 | cfi_adjust_cfa_offset (-8) |
294 | cfi_restore (%rbp) |
295 | ret |
296 | |
297 | .LBL_1_3: |
298 | cfi_restore_state |
299 | vmovups %zmm0, 1152(%rsp) |
300 | vmovups %zmm12, 1216(%rsp) |
301 | vmovups %zmm1, 1280(%rsp) |
302 | je .LBL_1_2 |
303 | |
304 | xorb %dl, %dl |
305 | kmovw %k4, 1048(%rsp) |
306 | xorl %eax, %eax |
307 | kmovw %k5, 1040(%rsp) |
308 | kmovw %k6, 1032(%rsp) |
309 | kmovw %k7, 1024(%rsp) |
310 | vmovups %zmm16, 960(%rsp) |
311 | vmovups %zmm17, 896(%rsp) |
312 | vmovups %zmm18, 832(%rsp) |
313 | vmovups %zmm19, 768(%rsp) |
314 | vmovups %zmm20, 704(%rsp) |
315 | vmovups %zmm21, 640(%rsp) |
316 | vmovups %zmm22, 576(%rsp) |
317 | vmovups %zmm23, 512(%rsp) |
318 | vmovups %zmm24, 448(%rsp) |
319 | vmovups %zmm25, 384(%rsp) |
320 | vmovups %zmm26, 320(%rsp) |
321 | vmovups %zmm27, 256(%rsp) |
322 | vmovups %zmm28, 192(%rsp) |
323 | vmovups %zmm29, 128(%rsp) |
324 | vmovups %zmm30, 64(%rsp) |
325 | vmovups %zmm31, (%rsp) |
326 | movq %rsi, 1064(%rsp) |
327 | movq %rdi, 1056(%rsp) |
328 | movq %r12, 1096(%rsp) |
329 | cfi_offset_rel_rsp (12, 1096) |
330 | movb %dl, %r12b |
331 | movq %r13, 1088(%rsp) |
332 | cfi_offset_rel_rsp (13, 1088) |
333 | movl %ecx, %r13d |
334 | movq %r14, 1080(%rsp) |
335 | cfi_offset_rel_rsp (14, 1080) |
336 | movl %eax, %r14d |
337 | movq %r15, 1072(%rsp) |
338 | cfi_offset_rel_rsp (15, 1072) |
339 | cfi_remember_state |
340 | |
341 | .LBL_1_6: |
342 | btl %r14d, %r13d |
343 | jc .LBL_1_12 |
344 | |
345 | .LBL_1_7: |
346 | lea 1(%r14), %esi |
347 | btl %esi, %r13d |
348 | jc .LBL_1_10 |
349 | |
350 | .LBL_1_8: |
351 | addb $1, %r12b |
352 | addl $2, %r14d |
353 | cmpb $16, %r12b |
354 | jb .LBL_1_6 |
355 | |
356 | kmovw 1048(%rsp), %k4 |
357 | movq 1064(%rsp), %rsi |
358 | kmovw 1040(%rsp), %k5 |
359 | movq 1056(%rsp), %rdi |
360 | kmovw 1032(%rsp), %k6 |
361 | movq 1096(%rsp), %r12 |
362 | cfi_restore (%r12) |
363 | movq 1088(%rsp), %r13 |
364 | cfi_restore (%r13) |
365 | kmovw 1024(%rsp), %k7 |
366 | vmovups 960(%rsp), %zmm16 |
367 | vmovups 896(%rsp), %zmm17 |
368 | vmovups 832(%rsp), %zmm18 |
369 | vmovups 768(%rsp), %zmm19 |
370 | vmovups 704(%rsp), %zmm20 |
371 | vmovups 640(%rsp), %zmm21 |
372 | vmovups 576(%rsp), %zmm22 |
373 | vmovups 512(%rsp), %zmm23 |
374 | vmovups 448(%rsp), %zmm24 |
375 | vmovups 384(%rsp), %zmm25 |
376 | vmovups 320(%rsp), %zmm26 |
377 | vmovups 256(%rsp), %zmm27 |
378 | vmovups 192(%rsp), %zmm28 |
379 | vmovups 128(%rsp), %zmm29 |
380 | vmovups 64(%rsp), %zmm30 |
381 | vmovups (%rsp), %zmm31 |
382 | movq 1080(%rsp), %r14 |
383 | cfi_restore (%r14) |
384 | movq 1072(%rsp), %r15 |
385 | cfi_restore (%r15) |
386 | vmovups 1280(%rsp), %zmm1 |
387 | jmp .LBL_1_2 |
388 | |
389 | .LBL_1_10: |
390 | cfi_restore_state |
391 | movzbl %r12b, %r15d |
392 | shlq $4, %r15 |
393 | vmovsd 1160(%rsp,%r15), %xmm0 |
394 | vmovsd 1224(%rsp,%r15), %xmm1 |
395 | call JUMPTARGET(pow) |
396 | vmovsd %xmm0, 1288(%rsp,%r15) |
397 | jmp .LBL_1_8 |
398 | |
399 | .LBL_1_12: |
400 | movzbl %r12b, %r15d |
401 | shlq $4, %r15 |
402 | vmovsd 1152(%rsp,%r15), %xmm0 |
403 | vmovsd 1216(%rsp,%r15), %xmm1 |
404 | call JUMPTARGET(pow) |
405 | vmovsd %xmm0, 1280(%rsp,%r15) |
406 | jmp .LBL_1_7 |
407 | |
408 | #endif |
409 | END (_ZGVeN8vv_pow_knl) |
410 | |
411 | ENTRY (_ZGVeN8vv_pow_skx) |
412 | #ifndef HAVE_AVX512DQ_ASM_SUPPORT |
413 | WRAPPER_IMPL_AVX512_ff _ZGVdN4vv_pow |
414 | #else |
415 | pushq %rbp |
416 | cfi_adjust_cfa_offset (8) |
417 | cfi_rel_offset (%rbp, 0) |
418 | movq %rsp, %rbp |
419 | cfi_def_cfa_register (%rbp) |
420 | andq $-64, %rsp |
421 | subq $1344, %rsp |
422 | vpsrlq $32, %zmm0, %zmm10 |
423 | kxnorw %k1, %k1, %k1 |
424 | kxnorw %k2, %k2, %k2 |
425 | kxnorw %k3, %k3, %k3 |
426 | vpmovqd %zmm10, %ymm7 |
427 | movq __svml_dpow_data@GOTPCREL(%rip), %rax |
428 | vmovaps %zmm1, %zmm6 |
429 | vpsrlq $32, %zmm6, %zmm13 |
430 | |
431 | /* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ |
432 | vpand _iIndexMask(%rax), %ymm7, %ymm15 |
433 | vpaddd _HIDELTA(%rax), %ymm7, %ymm2 |
434 | |
435 | /* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ |
436 | vpsubd _i3fe7fe00(%rax), %ymm7, %ymm7 |
437 | vmovdqu _ABSMASK(%rax), %ymm4 |
438 | vmovdqu _LORANGE(%rax), %ymm3 |
439 | |
440 | /* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ |
441 | vmovups _dbOne(%rax), %zmm11 |
442 | vmovdqu _INF(%rax), %ymm5 |
443 | vpaddd _iIndexAdd(%rax), %ymm15, %ymm12 |
444 | vpmovqd %zmm13, %ymm14 |
445 | vpternlogq $248, _iMantissaMask(%rax), %zmm0, %zmm11 |
446 | vpsrld $10, %ymm12, %ymm10 |
447 | vpsrad $20, %ymm7, %ymm13 |
448 | |
449 | /* Index for reciprocal table */ |
450 | vpslld $3, %ymm10, %ymm8 |
451 | |
452 | /* Index for log2 table */ |
453 | vpslld $4, %ymm10, %ymm1 |
454 | vpcmpgtd %ymm2, %ymm3, %ymm3 |
455 | vpand %ymm4, %ymm14, %ymm2 |
456 | vpaddd _i2p20_2p19(%rax), %ymm13, %ymm14 |
457 | vpmovzxdq %ymm14, %zmm15 |
458 | vpsllq $32, %zmm15, %zmm7 |
459 | vpternlogq $168, _iffffffff00000000(%rax), %zmm15, %zmm7 |
460 | vsubpd _db2p20_2p19(%rax), %zmm7, %zmm13 |
461 | vpxord %zmm9, %zmm9, %zmm9 |
462 | vgatherdpd 11712(%rax,%ymm8), %zmm9{%k1} |
463 | |
464 | /* T1 = ((double*)exp2_tbl)[ 2*j ] */ |
465 | kxnorw %k1, %k1, %k1 |
466 | vpxord %zmm12, %zmm12, %zmm12 |
467 | vpxord %zmm8, %zmm8, %zmm8 |
468 | vgatherdpd 19968(%rax,%ymm1), %zmm12{%k2} |
469 | vgatherdpd 19976(%rax,%ymm1), %zmm8{%k3} |
470 | vmovups _iHighMask(%rax), %zmm1 |
471 | |
472 | /* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ |
473 | vandpd %zmm1, %zmm11, %zmm10 |
474 | vsubpd %zmm10, %zmm11, %zmm15 |
475 | |
476 | /* r1 = x1*rcp1 */ |
477 | vmulpd %zmm9, %zmm11, %zmm11 |
478 | |
479 | /* E = -r1+__fence(x1Hi*rcp1) */ |
480 | vfmsub213pd %zmm11, %zmm9, %zmm10 |
481 | |
482 | /* cq = c+r1 */ |
483 | vaddpd _LHN(%rax), %zmm11, %zmm14 |
484 | |
485 | /* E=E+x1Lo*rcp1 */ |
486 | vfmadd213pd %zmm10, %zmm9, %zmm15 |
487 | |
488 | /* T = k + L1hi */ |
489 | vaddpd %zmm12, %zmm13, %zmm9 |
490 | |
491 | /* T_Rh = T + cq */ |
492 | vaddpd %zmm14, %zmm9, %zmm11 |
493 | |
494 | /* T_Rh_Eh = T_Rh + E */ |
495 | vaddpd %zmm15, %zmm11, %zmm13 |
496 | |
497 | /* Rl = T-T_Rh; -> -Rh */ |
498 | vsubpd %zmm11, %zmm9, %zmm12 |
499 | |
500 | /* HLL = T_Rh - T_Rh_Eh; -> -Eh */ |
501 | vsubpd %zmm13, %zmm11, %zmm9 |
502 | |
503 | /* Rl=Rl+cq */ |
504 | vaddpd %zmm12, %zmm14, %zmm10 |
505 | |
506 | /* HLL+=E; -> El */ |
507 | vaddpd %zmm9, %zmm15, %zmm7 |
508 | |
509 | /* HLL+=Rl */ |
510 | vaddpd %zmm10, %zmm7, %zmm12 |
511 | |
512 | /* 2^(y*(HH+HL+HLL)) starts here: |
513 | yH = y; Lo(yH)&=0xf8000000 |
514 | */ |
515 | vandpd %zmm1, %zmm6, %zmm7 |
516 | |
517 | /* HLL+=L1lo */ |
518 | vaddpd %zmm8, %zmm12, %zmm12 |
519 | |
520 | /* cq = cq + E */ |
521 | vaddpd %zmm15, %zmm14, %zmm8 |
522 | vmovups _clv_2(%rax), %zmm14 |
523 | |
524 | /* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ |
525 | vfmadd213pd _clv_3(%rax), %zmm8, %zmm14 |
526 | vfmadd213pd _clv_4(%rax), %zmm8, %zmm14 |
527 | vfmadd213pd _clv_5(%rax), %zmm8, %zmm14 |
528 | vfmadd213pd _clv_6(%rax), %zmm8, %zmm14 |
529 | vfmadd213pd _clv_7(%rax), %zmm8, %zmm14 |
530 | vfmadd213pd %zmm12, %zmm8, %zmm14 |
531 | |
532 | /* yL = y-yH */ |
533 | vsubpd %zmm7, %zmm6, %zmm8 |
534 | |
535 | /* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ |
536 | vaddpd %zmm14, %zmm13, %zmm15 |
537 | |
538 | /* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ |
539 | vandpd %zmm1, %zmm15, %zmm11 |
540 | |
541 | /* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ |
542 | vsubpd %zmm13, %zmm15, %zmm13 |
543 | |
544 | /* pH = yH*HH */ |
545 | vmulpd %zmm11, %zmm7, %zmm9 |
546 | |
547 | /* HLL = HLL - HLLhi */ |
548 | vsubpd %zmm13, %zmm14, %zmm12 |
549 | |
550 | /* HL = T_Rh_Eh_HLLhi-HH */ |
551 | vsubpd %zmm11, %zmm15, %zmm10 |
552 | vpsrlq $32, %zmm9, %zmm1 |
553 | vmovdqu _DOMAINRANGE(%rax), %ymm13 |
554 | vpmovqd %zmm1, %ymm1 |
555 | vpand %ymm4, %ymm1, %ymm1 |
556 | vpcmpgtd %ymm5, %ymm2, %ymm4 |
557 | vpcmpeqd %ymm5, %ymm2, %ymm5 |
558 | vpternlogd $254, %ymm5, %ymm4, %ymm3 |
559 | vpcmpgtd %ymm13, %ymm1, %ymm2 |
560 | vpcmpeqd %ymm13, %ymm1, %ymm4 |
561 | vpternlogd $254, %ymm4, %ymm2, %ymm3 |
562 | |
563 | /* pLL = y*HLL */ |
564 | vmovups _db2p45_2p44(%rax), %zmm2 |
565 | |
566 | /* pHH = pH + *(double*)&db2p45_2p44 */ |
567 | vaddpd %zmm2, %zmm9, %zmm1 |
568 | vpmovqd %zmm1, %ymm5 |
569 | |
570 | /* j = Lo(pHH)&0x0000007f */ |
571 | vpand _jIndexMask(%rax), %ymm5, %ymm14 |
572 | vpslld $4, %ymm14, %ymm15 |
573 | vmovmskps %ymm3, %ecx |
574 | |
575 | /* pL=yL*HL+yH*HL; pL+=yL*HH */ |
576 | vmulpd %zmm10, %zmm8, %zmm3 |
577 | vfmadd213pd %zmm3, %zmm10, %zmm7 |
578 | vfmadd213pd %zmm7, %zmm11, %zmm8 |
579 | |
580 | /* _n = Lo(pHH) |
581 | _n = _n & 0xffffff80 |
582 | _n = _n >> 7 |
583 | Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n |
584 | */ |
585 | vpslld $13, %ymm5, %ymm7 |
586 | |
587 | /* t=pL+pLL; t+=pHL */ |
588 | vfmadd231pd %zmm6, %zmm12, %zmm8 |
589 | vpaddd _iOne(%rax), %ymm7, %ymm10 |
590 | vpmovzxdq %ymm10, %zmm11 |
591 | vpsllq $32, %zmm11, %zmm3 |
592 | vpternlogq $168, _ifff0000000000000(%rax), %zmm11, %zmm3 |
593 | |
594 | /* pHH = pHH - *(double*)&db2p45_2p44 */ |
595 | vsubpd %zmm2, %zmm1, %zmm11 |
596 | vmovups _cev_1(%rax), %zmm2 |
597 | |
598 | /* pHL = pH - pHH */ |
599 | vsubpd %zmm11, %zmm9, %zmm9 |
600 | vaddpd %zmm9, %zmm8, %zmm8 |
601 | vfmadd213pd _cev_2(%rax), %zmm8, %zmm2 |
602 | vfmadd213pd _cev_3(%rax), %zmm8, %zmm2 |
603 | vfmadd213pd _cev_4(%rax), %zmm8, %zmm2 |
604 | vfmadd213pd _cev_5(%rax), %zmm8, %zmm2 |
605 | vpxord %zmm4, %zmm4, %zmm4 |
606 | vgatherdpd 36416(%rax,%ymm15), %zmm4{%k1} |
607 | vmulpd %zmm4, %zmm3, %zmm1 |
608 | vmulpd %zmm8, %zmm1, %zmm12 |
609 | vfmadd213pd %zmm1, %zmm12, %zmm2 |
610 | testl %ecx, %ecx |
611 | jne .LBL_2_3 |
612 | |
613 | .LBL_2_2: |
614 | cfi_remember_state |
615 | vmovaps %zmm2, %zmm0 |
616 | movq %rbp, %rsp |
617 | cfi_def_cfa_register (%rsp) |
618 | popq %rbp |
619 | cfi_adjust_cfa_offset (-8) |
620 | cfi_restore (%rbp) |
621 | ret |
622 | |
623 | .LBL_2_3: |
624 | cfi_restore_state |
625 | vmovups %zmm0, 1152(%rsp) |
626 | vmovups %zmm6, 1216(%rsp) |
627 | vmovups %zmm2, 1280(%rsp) |
628 | je .LBL_2_2 |
629 | |
630 | xorb %dl, %dl |
631 | xorl %eax, %eax |
632 | kmovw %k4, 1048(%rsp) |
633 | kmovw %k5, 1040(%rsp) |
634 | kmovw %k6, 1032(%rsp) |
635 | kmovw %k7, 1024(%rsp) |
636 | vmovups %zmm16, 960(%rsp) |
637 | vmovups %zmm17, 896(%rsp) |
638 | vmovups %zmm18, 832(%rsp) |
639 | vmovups %zmm19, 768(%rsp) |
640 | vmovups %zmm20, 704(%rsp) |
641 | vmovups %zmm21, 640(%rsp) |
642 | vmovups %zmm22, 576(%rsp) |
643 | vmovups %zmm23, 512(%rsp) |
644 | vmovups %zmm24, 448(%rsp) |
645 | vmovups %zmm25, 384(%rsp) |
646 | vmovups %zmm26, 320(%rsp) |
647 | vmovups %zmm27, 256(%rsp) |
648 | vmovups %zmm28, 192(%rsp) |
649 | vmovups %zmm29, 128(%rsp) |
650 | vmovups %zmm30, 64(%rsp) |
651 | vmovups %zmm31, (%rsp) |
652 | movq %rsi, 1064(%rsp) |
653 | movq %rdi, 1056(%rsp) |
654 | movq %r12, 1096(%rsp) |
655 | cfi_offset_rel_rsp (12, 1096) |
656 | movb %dl, %r12b |
657 | movq %r13, 1088(%rsp) |
658 | cfi_offset_rel_rsp (13, 1088) |
659 | movl %ecx, %r13d |
660 | movq %r14, 1080(%rsp) |
661 | cfi_offset_rel_rsp (14, 1080) |
662 | movl %eax, %r14d |
663 | movq %r15, 1072(%rsp) |
664 | cfi_offset_rel_rsp (15, 1072) |
665 | cfi_remember_state |
666 | |
667 | .LBL_2_6: |
668 | btl %r14d, %r13d |
669 | jc .LBL_2_12 |
670 | |
671 | .LBL_2_7: |
672 | lea 1(%r14), %esi |
673 | btl %esi, %r13d |
674 | jc .LBL_2_10 |
675 | |
676 | .LBL_2_8: |
677 | incb %r12b |
678 | addl $2, %r14d |
679 | cmpb $16, %r12b |
680 | jb .LBL_2_6 |
681 | |
682 | kmovw 1048(%rsp), %k4 |
683 | kmovw 1040(%rsp), %k5 |
684 | kmovw 1032(%rsp), %k6 |
685 | kmovw 1024(%rsp), %k7 |
686 | vmovups 960(%rsp), %zmm16 |
687 | vmovups 896(%rsp), %zmm17 |
688 | vmovups 832(%rsp), %zmm18 |
689 | vmovups 768(%rsp), %zmm19 |
690 | vmovups 704(%rsp), %zmm20 |
691 | vmovups 640(%rsp), %zmm21 |
692 | vmovups 576(%rsp), %zmm22 |
693 | vmovups 512(%rsp), %zmm23 |
694 | vmovups 448(%rsp), %zmm24 |
695 | vmovups 384(%rsp), %zmm25 |
696 | vmovups 320(%rsp), %zmm26 |
697 | vmovups 256(%rsp), %zmm27 |
698 | vmovups 192(%rsp), %zmm28 |
699 | vmovups 128(%rsp), %zmm29 |
700 | vmovups 64(%rsp), %zmm30 |
701 | vmovups (%rsp), %zmm31 |
702 | vmovups 1280(%rsp), %zmm2 |
703 | movq 1064(%rsp), %rsi |
704 | movq 1056(%rsp), %rdi |
705 | movq 1096(%rsp), %r12 |
706 | cfi_restore (%r12) |
707 | movq 1088(%rsp), %r13 |
708 | cfi_restore (%r13) |
709 | movq 1080(%rsp), %r14 |
710 | cfi_restore (%r14) |
711 | movq 1072(%rsp), %r15 |
712 | cfi_restore (%r15) |
713 | jmp .LBL_2_2 |
714 | |
715 | .LBL_2_10: |
716 | cfi_restore_state |
717 | movzbl %r12b, %r15d |
718 | shlq $4, %r15 |
719 | vmovsd 1224(%rsp,%r15), %xmm1 |
720 | vzeroupper |
721 | vmovsd 1160(%rsp,%r15), %xmm0 |
722 | |
723 | call JUMPTARGET(pow) |
724 | |
725 | vmovsd %xmm0, 1288(%rsp,%r15) |
726 | jmp .LBL_2_8 |
727 | |
728 | .LBL_2_12: |
729 | movzbl %r12b, %r15d |
730 | shlq $4, %r15 |
731 | vmovsd 1216(%rsp,%r15), %xmm1 |
732 | vzeroupper |
733 | vmovsd 1152(%rsp,%r15), %xmm0 |
734 | |
735 | call JUMPTARGET(pow) |
736 | |
737 | vmovsd %xmm0, 1280(%rsp,%r15) |
738 | jmp .LBL_2_7 |
739 | |
740 | #endif |
741 | END (_ZGVeN8vv_pow_skx) |
742 | |