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c10b9b13 | 1 | /* Function pow vectorized with AVX2. |
04277e02 | 2 | Copyright (C) 2014-2019 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 | |
5a82c748 | 17 | <https://www.gnu.org/licenses/>. */ |
c10b9b13 AS |
18 | |
19 | #include <sysdep.h> | |
20 | #include "svml_d_pow_data.h" | |
21 | ||
22 | .text | |
23 | ENTRY (_ZGVdN4vv_pow_avx2) | |
24 | /* | |
25 | ALGORITHM DESCRIPTION: | |
26 | ||
27 | 1) Calculating log2|x| | |
28 | Here we use the following formula. | |
29 | Let |x|=2^k1*X1, where k1 is integer, 1<=X1<2. | |
30 | Let C ~= 1/ln(2), | |
31 | Rcp1 ~= 1/X1, X2=Rcp1*X1, | |
32 | Rcp2 ~= 1/X2, X3=Rcp2*X2, | |
33 | Rcp3 ~= 1/X3, Rcp3C ~= C/X3. | |
34 | Then | |
35 | log2|x| = k1 + log2(1/Rcp1) + log2(1/Rcp2) + log2(C/Rcp3C) + | |
36 | log2(X1*Rcp1*Rcp2*Rcp3C/C), | |
37 | where X1*Rcp1*Rcp2*Rcp3C = C*(1+q), q is very small. | |
38 | ||
39 | The values of Rcp1, log2(1/Rcp1), Rcp2, log2(1/Rcp2), | |
40 | Rcp3C, log2(C/Rcp3C) are taken from tables. | |
41 | Values of Rcp1, Rcp2, Rcp3C are such that RcpC=Rcp1*Rcp2*Rcp3C | |
42 | is exactly represented in target precision. | |
43 | ||
44 | log2(X1*Rcp1*Rcp2*Rcp3C/C) = log2(1+q) = ln(1+q)/ln2 = | |
45 | = 1/(ln2)*q - 1/(2ln2)*q^2 + 1/(3ln2)*q^3 - ... = | |
46 | = 1/(C*ln2)*cq - 1/(2*C^2*ln2)*cq^2 + 1/(3*C^3*ln2)*cq^3 - ... = | |
47 | = (1 + a1)*cq + a2*cq^2 + a3*cq^3 + ..., | |
48 | where cq = X1*Rcp1*Rcp2*Rcp3C-C, | |
49 | a1=1/(C*ln(2))-1 is small, | |
50 | a2=1/(2*C^2*ln2), | |
51 | a3=1/(3*C^3*ln2), | |
52 | ... | |
53 | We get 3 parts of log2 result: HH+HL+HLL ~= log2|x|. | |
54 | ||
55 | 2) Calculation of y*(HH+HL+HLL). | |
56 | Split y into YHi+YLo. | |
57 | Get high PH and medium PL parts of y*log2|x|. | |
58 | Get low PLL part of y*log2|x|. | |
59 | Now we have PH+PL+PLL ~= y*log2|x|. | |
60 | ||
61 | 3) Calculation of 2^(PH+PL+PLL). | |
62 | Mathematical idea of computing 2^(PH+PL+PLL) is the following. | |
63 | Let's represent PH+PL+PLL in the form N + j/2^expK + Z, | |
64 | where expK=7 in this implementation, N and j are integers, | |
65 | 0<=j<=2^expK-1, |Z|<2^(-expK-1). | |
66 | Hence 2^(PH+PL+PLL) ~= 2^N * 2^(j/2^expK) * 2^Z, | |
67 | where 2^(j/2^expK) is stored in a table, and | |
68 | 2^Z ~= 1 + B1*Z + B2*Z^2 ... + B5*Z^5. | |
69 | ||
70 | We compute 2^(PH+PL+PLL) as follows. | |
71 | Break PH into PHH + PHL, where PHH = N + j/2^expK. | |
72 | Z = PHL + PL + PLL | |
73 | Exp2Poly = B1*Z + B2*Z^2 ... + B5*Z^5 | |
74 | Get 2^(j/2^expK) from table in the form THI+TLO. | |
75 | Now we have 2^(PH+PL+PLL) ~= 2^N * (THI + TLO) * (1 + Exp2Poly). | |
76 | ||
77 | Get significand of 2^(PH+PL+PLL) in the form ResHi+ResLo: | |
78 | ResHi := THI | |
79 | ResLo := THI * Exp2Poly + TLO | |
80 | ||
81 | Get exponent ERes of the result: | |
82 | Res := ResHi + ResLo: | |
83 | Result := ex(Res) + N. */ | |
84 | ||
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 $448, %rsp | |
92 | movq __svml_dpow_data@GOTPCREL(%rip), %rax | |
93 | vmovups %ymm11, 160(%rsp) | |
94 | vmovups %ymm8, 224(%rsp) | |
95 | vmovups %ymm10, 352(%rsp) | |
96 | vmovups %ymm9, 384(%rsp) | |
97 | vmovups %ymm13, 288(%rsp) | |
98 | vmovapd %ymm1, %ymm11 | |
99 | vxorpd %ymm1, %ymm1, %ymm1 | |
100 | vextracti128 $1, %ymm0, %xmm5 | |
101 | vshufps $221, %xmm5, %xmm0, %xmm5 | |
102 | ||
103 | /* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ | |
104 | vandps _iIndexMask(%rax), %xmm5, %xmm3 | |
105 | vpaddd _iIndexAdd(%rax), %xmm3, %xmm6 | |
106 | vpsrld $10, %xmm6, %xmm8 | |
107 | ||
108 | /* Index for reciprocal table */ | |
109 | vpslld $3, %xmm8, %xmm9 | |
110 | ||
111 | /* Index for log2 table */ | |
112 | vpslld $4, %xmm8, %xmm6 | |
113 | ||
114 | /* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ | |
115 | vandpd _iMantissaMask(%rax), %ymm0, %ymm4 | |
116 | vorpd _dbOne(%rax), %ymm4, %ymm13 | |
117 | vpcmpeqd %ymm4, %ymm4, %ymm4 | |
118 | vpcmpeqd %ymm8, %ymm8, %ymm8 | |
119 | ||
120 | /* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ | |
121 | vpsubd _i3fe7fe00(%rax), %xmm5, %xmm3 | |
122 | vpaddd _HIDELTA(%rax), %xmm5, %xmm5 | |
123 | vextracti128 $1, %ymm11, %xmm7 | |
124 | vshufps $221, %xmm7, %xmm11, %xmm2 | |
125 | vpand _ABSMASK(%rax), %xmm2, %xmm10 | |
126 | vpcmpeqd %ymm2, %ymm2, %ymm2 | |
127 | vgatherdpd %ymm2, 11712(%rax,%xmm9), %ymm1 | |
128 | vmovups _LORANGE(%rax), %xmm7 | |
129 | vxorpd %ymm2, %ymm2, %ymm2 | |
130 | vgatherdpd %ymm4, 19968(%rax,%xmm6), %ymm2 | |
131 | vxorpd %ymm4, %ymm4, %ymm4 | |
132 | vgatherdpd %ymm8, 19976(%rax,%xmm6), %ymm4 | |
133 | vpsrad $20, %xmm3, %xmm6 | |
134 | vpaddd _i2p20_2p19(%rax), %xmm6, %xmm9 | |
135 | vpshufd $80, %xmm9, %xmm8 | |
136 | vpshufd $250, %xmm9, %xmm3 | |
137 | ||
138 | /* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ | |
139 | vandpd _iHighMask(%rax), %ymm13, %ymm9 | |
140 | vinserti128 $1, %xmm3, %ymm8, %ymm6 | |
141 | vandpd _iffffffff00000000(%rax), %ymm6, %ymm8 | |
142 | ||
143 | /* r1 = x1*rcp1 */ | |
144 | vmulpd %ymm1, %ymm13, %ymm6 | |
145 | vsubpd %ymm9, %ymm13, %ymm3 | |
146 | vsubpd _db2p20_2p19(%rax), %ymm8, %ymm8 | |
147 | ||
148 | /* cq = c+r1 */ | |
149 | vaddpd _LHN(%rax), %ymm6, %ymm13 | |
150 | ||
151 | /* E = -r1+__fence(x1Hi*rcp1) */ | |
152 | vfmsub213pd %ymm6, %ymm1, %ymm9 | |
153 | ||
154 | /* E=E+x1Lo*rcp1 */ | |
155 | vfmadd213pd %ymm9, %ymm1, %ymm3 | |
156 | ||
157 | /* T = k + L1hi */ | |
158 | vaddpd %ymm2, %ymm8, %ymm1 | |
159 | ||
160 | /* T_Rh = T + cq */ | |
161 | vaddpd %ymm13, %ymm1, %ymm8 | |
162 | ||
163 | /* Rl = T-T_Rh; -> -Rh */ | |
164 | vsubpd %ymm8, %ymm1, %ymm6 | |
165 | ||
166 | /* Rl=Rl+cq */ | |
167 | vaddpd %ymm6, %ymm13, %ymm1 | |
168 | ||
169 | /* T_Rh_Eh = T_Rh + E */ | |
170 | vaddpd %ymm3, %ymm8, %ymm6 | |
171 | ||
172 | /* cq = cq + E */ | |
173 | vaddpd %ymm3, %ymm13, %ymm13 | |
174 | ||
175 | /* HLL = T_Rh - T_Rh_Eh; -> -Eh */ | |
176 | vsubpd %ymm6, %ymm8, %ymm9 | |
177 | ||
178 | /* HLL+=E; -> El */ | |
179 | vaddpd %ymm9, %ymm3, %ymm2 | |
180 | ||
181 | /* HLL+=Rl */ | |
182 | vaddpd %ymm1, %ymm2, %ymm8 | |
183 | ||
184 | /* HLL+=L1lo */ | |
185 | vaddpd %ymm4, %ymm8, %ymm4 | |
186 | vmovupd _clv_2(%rax), %ymm8 | |
187 | ||
188 | /* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ | |
189 | vfmadd213pd _clv_3(%rax), %ymm13, %ymm8 | |
190 | vfmadd213pd _clv_4(%rax), %ymm13, %ymm8 | |
191 | vfmadd213pd _clv_5(%rax), %ymm13, %ymm8 | |
192 | vfmadd213pd _clv_6(%rax), %ymm13, %ymm8 | |
193 | vfmadd213pd _clv_7(%rax), %ymm13, %ymm8 | |
194 | vfmadd213pd %ymm4, %ymm13, %ymm8 | |
195 | ||
196 | /* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ | |
197 | vaddpd %ymm8, %ymm6, %ymm9 | |
198 | ||
199 | /* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ | |
200 | vandpd _iHighMask(%rax), %ymm9, %ymm2 | |
201 | ||
202 | /* | |
203 | 2^(y*(HH+HL+HLL)) starts here: | |
204 | yH = y; Lo(yH)&=0xf8000000; | |
205 | */ | |
206 | vandpd _iHighMask(%rax), %ymm11, %ymm1 | |
207 | ||
208 | /* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ | |
209 | vsubpd %ymm6, %ymm9, %ymm13 | |
210 | ||
211 | /* HL = T_Rh_Eh_HLLhi-HH */ | |
212 | vsubpd %ymm2, %ymm9, %ymm4 | |
213 | ||
214 | /* pH = yH*HH */ | |
215 | vmulpd %ymm2, %ymm1, %ymm9 | |
216 | ||
217 | /* HLL = HLL - HLLhi */ | |
218 | vsubpd %ymm13, %ymm8, %ymm6 | |
219 | ||
220 | /* yL = y-yH */ | |
221 | vsubpd %ymm1, %ymm11, %ymm8 | |
222 | vextracti128 $1, %ymm9, %xmm3 | |
223 | vshufps $221, %xmm3, %xmm9, %xmm13 | |
224 | vpand _ABSMASK(%rax), %xmm13, %xmm3 | |
225 | vpcmpgtd %xmm5, %xmm7, %xmm13 | |
226 | vpcmpgtd _INF(%rax), %xmm10, %xmm7 | |
227 | vpcmpeqd _INF(%rax), %xmm10, %xmm10 | |
228 | vpor %xmm10, %xmm7, %xmm7 | |
229 | vpor %xmm7, %xmm13, %xmm5 | |
230 | ||
231 | /* pL=yL*HL+yH*HL; pL+=yL*HH */ | |
232 | vmulpd %ymm4, %ymm8, %ymm7 | |
233 | vpcmpgtd _DOMAINRANGE(%rax), %xmm3, %xmm13 | |
234 | vpcmpeqd _DOMAINRANGE(%rax), %xmm3, %xmm10 | |
235 | vpor %xmm10, %xmm13, %xmm3 | |
236 | vpor %xmm3, %xmm5, %xmm13 | |
237 | vfmadd213pd %ymm7, %ymm4, %ymm1 | |
238 | ||
239 | /* pLL = y*HLL; | |
240 | pHH = pH + *(double*)&db2p45_2p44 | |
241 | */ | |
242 | vaddpd _db2p45_2p44(%rax), %ymm9, %ymm7 | |
243 | vmovmskps %xmm13, %ecx | |
244 | vfmadd213pd %ymm1, %ymm2, %ymm8 | |
245 | ||
246 | /* t=pL+pLL; t+=pHL */ | |
247 | vfmadd231pd %ymm11, %ymm6, %ymm8 | |
248 | vextracti128 $1, %ymm7, %xmm1 | |
249 | vshufps $136, %xmm1, %xmm7, %xmm10 | |
250 | ||
251 | /* _n = Lo(pHH); | |
252 | _n = _n & 0xffffff80; | |
253 | _n = _n >> 7; | |
254 | Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n | |
255 | */ | |
256 | vpslld $13, %xmm10, %xmm2 | |
257 | vpaddd _iOne(%rax), %xmm2, %xmm13 | |
258 | vpshufd $80, %xmm13, %xmm4 | |
259 | vpshufd $250, %xmm13, %xmm1 | |
260 | ||
261 | /* j = Lo(pHH)&0x0000007f */ | |
262 | vandps _jIndexMask(%rax), %xmm10, %xmm3 | |
263 | ||
264 | /* T1 = ((double*)exp2_tbl)[ 2*j ] */ | |
265 | vpcmpeqd %ymm10, %ymm10, %ymm10 | |
266 | vpslld $4, %xmm3, %xmm5 | |
267 | ||
268 | /* pHH = pHH - *(double*)&db2p45_2p44 */ | |
269 | vsubpd _db2p45_2p44(%rax), %ymm7, %ymm7 | |
270 | ||
271 | /* pHL = pH - pHH */ | |
272 | vsubpd %ymm7, %ymm9, %ymm9 | |
273 | vaddpd %ymm9, %ymm8, %ymm6 | |
274 | vinserti128 $1, %xmm1, %ymm4, %ymm2 | |
275 | vxorpd %ymm1, %ymm1, %ymm1 | |
276 | vgatherdpd %ymm10, 36416(%rax,%xmm5), %ymm1 | |
277 | vandpd _ifff0000000000000(%rax), %ymm2, %ymm13 | |
278 | vmovupd _cev_1(%rax), %ymm2 | |
279 | vmulpd %ymm1, %ymm13, %ymm1 | |
280 | vfmadd213pd _cev_2(%rax), %ymm6, %ymm2 | |
281 | vmulpd %ymm6, %ymm1, %ymm8 | |
282 | vfmadd213pd _cev_3(%rax), %ymm6, %ymm2 | |
283 | vfmadd213pd _cev_4(%rax), %ymm6, %ymm2 | |
284 | vfmadd213pd _cev_5(%rax), %ymm6, %ymm2 | |
285 | vfmadd213pd %ymm1, %ymm8, %ymm2 | |
286 | testl %ecx, %ecx | |
287 | jne .LBL_1_3 | |
288 | ||
289 | .LBL_1_2: | |
290 | cfi_remember_state | |
291 | vmovups 224(%rsp), %ymm8 | |
292 | vmovups 384(%rsp), %ymm9 | |
293 | vmovups 352(%rsp), %ymm10 | |
294 | vmovups 160(%rsp), %ymm11 | |
295 | vmovups 288(%rsp), %ymm13 | |
296 | vmovdqa %ymm2, %ymm0 | |
297 | movq %rbp, %rsp | |
298 | cfi_def_cfa_register (%rsp) | |
299 | popq %rbp | |
300 | cfi_adjust_cfa_offset (-8) | |
301 | cfi_restore (%rbp) | |
302 | ret | |
303 | ||
304 | .LBL_1_3: | |
305 | cfi_restore_state | |
306 | vmovupd %ymm0, 192(%rsp) | |
307 | vmovupd %ymm11, 256(%rsp) | |
308 | vmovupd %ymm2, 320(%rsp) | |
309 | je .LBL_1_2 | |
310 | ||
311 | xorb %dl, %dl | |
312 | xorl %eax, %eax | |
313 | vmovups %ymm12, 64(%rsp) | |
314 | vmovups %ymm14, 32(%rsp) | |
315 | vmovups %ymm15, (%rsp) | |
316 | movq %rsi, 104(%rsp) | |
317 | movq %rdi, 96(%rsp) | |
318 | movq %r12, 136(%rsp) | |
319 | cfi_offset_rel_rsp (12, 136) | |
320 | movb %dl, %r12b | |
321 | movq %r13, 128(%rsp) | |
322 | cfi_offset_rel_rsp (13, 128) | |
323 | movl %ecx, %r13d | |
324 | movq %r14, 120(%rsp) | |
325 | cfi_offset_rel_rsp (14, 120) | |
326 | movl %eax, %r14d | |
327 | movq %r15, 112(%rsp) | |
328 | cfi_offset_rel_rsp (15, 112) | |
329 | cfi_remember_state | |
330 | ||
331 | .LBL_1_6: | |
332 | btl %r14d, %r13d | |
333 | jc .LBL_1_12 | |
334 | ||
335 | .LBL_1_7: | |
336 | lea 1(%r14), %esi | |
337 | btl %esi, %r13d | |
338 | jc .LBL_1_10 | |
339 | ||
340 | .LBL_1_8: | |
341 | incb %r12b | |
342 | addl $2, %r14d | |
343 | cmpb $16, %r12b | |
344 | jb .LBL_1_6 | |
345 | ||
346 | vmovups 64(%rsp), %ymm12 | |
347 | vmovups 32(%rsp), %ymm14 | |
348 | vmovups (%rsp), %ymm15 | |
349 | vmovupd 320(%rsp), %ymm2 | |
350 | movq 104(%rsp), %rsi | |
351 | movq 96(%rsp), %rdi | |
352 | movq 136(%rsp), %r12 | |
353 | cfi_restore (%r12) | |
354 | movq 128(%rsp), %r13 | |
355 | cfi_restore (%r13) | |
356 | movq 120(%rsp), %r14 | |
357 | cfi_restore (%r14) | |
358 | movq 112(%rsp), %r15 | |
359 | cfi_restore (%r15) | |
360 | jmp .LBL_1_2 | |
361 | ||
362 | .LBL_1_10: | |
363 | cfi_restore_state | |
364 | movzbl %r12b, %r15d | |
365 | shlq $4, %r15 | |
366 | vmovsd 200(%rsp,%r15), %xmm0 | |
367 | vmovsd 264(%rsp,%r15), %xmm1 | |
368 | vzeroupper | |
369 | ||
533f9beb | 370 | call JUMPTARGET(__pow_finite) |
c10b9b13 AS |
371 | |
372 | vmovsd %xmm0, 328(%rsp,%r15) | |
373 | jmp .LBL_1_8 | |
374 | ||
375 | .LBL_1_12: | |
376 | movzbl %r12b, %r15d | |
377 | shlq $4, %r15 | |
378 | vmovsd 192(%rsp,%r15), %xmm0 | |
379 | vmovsd 256(%rsp,%r15), %xmm1 | |
380 | vzeroupper | |
381 | ||
533f9beb | 382 | call JUMPTARGET(__pow_finite) |
c10b9b13 AS |
383 | |
384 | vmovsd %xmm0, 320(%rsp,%r15) | |
385 | jmp .LBL_1_7 | |
386 | ||
387 | END (_ZGVdN4vv_pow_avx2) |