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c10b9b13 | 1 | /* Function pow vectorized with AVX-512. KNL and SKX versions. |
bfff8b1b | 2 | Copyright (C) 2014-2017 Free Software Foundation, Inc. |
c10b9b13 AS |
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 | <http://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) | |
f43cb35c | 85 | #ifndef HAVE_AVX512DQ_ASM_SUPPORT |
c10b9b13 AS |
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 | |
533f9beb | 395 | call JUMPTARGET(__pow_finite) |
c10b9b13 AS |
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 | |
533f9beb | 404 | call JUMPTARGET(__pow_finite) |
c10b9b13 AS |
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) | |
f43cb35c | 412 | #ifndef HAVE_AVX512DQ_ASM_SUPPORT |
c10b9b13 AS |
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 | ||
533f9beb | 723 | call JUMPTARGET(__pow_finite) |
c10b9b13 AS |
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 | ||
533f9beb | 735 | call JUMPTARGET(__pow_finite) |
c10b9b13 AS |
736 | |
737 | vmovsd %xmm0, 1280(%rsp,%r15) | |
738 | jmp .LBL_2_7 | |
739 | ||
740 | #endif | |
741 | END (_ZGVeN8vv_pow_skx) |