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c10b9b13 | 1 | /* Function pow vectorized with SSE4. |
d614a753 | 2 | Copyright (C) 2014-2020 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 (_ZGVbN2vv_pow_sse4) | |
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 $256, %rsp | |
92 | movq __svml_dpow_data@GOTPCREL(%rip), %rdx | |
93 | movups %xmm14, 80(%rsp) | |
94 | movups %xmm9, 176(%rsp) | |
95 | movaps %xmm1, %xmm9 | |
96 | pshufd $221, %xmm0, %xmm1 | |
97 | movq _iIndexMask(%rdx), %xmm14 | |
98 | movq _iIndexAdd(%rdx), %xmm6 | |
99 | ||
100 | /* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ | |
101 | pand %xmm1, %xmm14 | |
102 | paddd %xmm6, %xmm14 | |
103 | psrld $10, %xmm14 | |
104 | movups %xmm13, 96(%rsp) | |
105 | ||
106 | /* Index for reciprocal table */ | |
107 | movdqa %xmm14, %xmm13 | |
108 | pslld $3, %xmm13 | |
109 | ||
110 | /* Index for log2 table */ | |
111 | pslld $4, %xmm14 | |
112 | movd %xmm13, %eax | |
113 | movups %xmm10, 160(%rsp) | |
114 | movups _iMantissaMask(%rdx), %xmm10 | |
115 | movslq %eax, %rax | |
116 | ||
117 | /* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ | |
118 | andps %xmm0, %xmm10 | |
119 | pextrd $1, %xmm13, %ecx | |
120 | movslq %ecx, %rcx | |
121 | movups %xmm0, (%rsp) | |
122 | movdqa %xmm1, %xmm0 | |
123 | ||
124 | /* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ | |
125 | movq _i3fe7fe00(%rdx), %xmm6 | |
126 | psubd %xmm6, %xmm0 | |
127 | movups _iHighMask(%rdx), %xmm6 | |
128 | psrad $20, %xmm0 | |
129 | movups %xmm15, 48(%rsp) | |
130 | movups %xmm12, 112(%rsp) | |
131 | orps _dbOne(%rdx), %xmm10 | |
132 | movsd 11712(%rdx,%rax), %xmm12 | |
133 | movd %xmm14, %r8d | |
134 | movq _i2p20_2p19(%rdx), %xmm15 | |
135 | movhpd 11712(%rdx,%rcx), %xmm12 | |
136 | paddd %xmm15, %xmm0 | |
137 | pextrd $1, %xmm14, %r9d | |
138 | ||
139 | /* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ | |
140 | movaps %xmm6, %xmm14 | |
141 | andps %xmm10, %xmm14 | |
142 | movaps %xmm10, %xmm15 | |
143 | subpd %xmm14, %xmm15 | |
144 | ||
145 | /* r1 = x1*rcp1 */ | |
146 | mulpd %xmm12, %xmm10 | |
147 | ||
148 | /* E = -r1+__fence(x1Hi*rcp1) */ | |
149 | mulpd %xmm12, %xmm14 | |
150 | ||
151 | /* E=E+x1Lo*rcp1 */ | |
152 | mulpd %xmm15, %xmm12 | |
153 | subpd %xmm10, %xmm14 | |
154 | pshufd $80, %xmm0, %xmm0 | |
155 | movslq %r8d, %r8 | |
156 | andps _iffffffff00000000(%rdx), %xmm0 | |
157 | subpd _db2p20_2p19(%rdx), %xmm0 | |
158 | addpd %xmm12, %xmm14 | |
159 | movslq %r9d, %r9 | |
160 | ||
161 | /* T_Rh_Eh = T_Rh + E */ | |
162 | movaps %xmm14, %xmm15 | |
163 | movups %xmm8, 208(%rsp) | |
164 | movups 19968(%rdx,%r8), %xmm8 | |
165 | movups %xmm11, 144(%rsp) | |
166 | movaps %xmm8, %xmm11 | |
167 | ||
168 | /* cq = c+r1 */ | |
169 | movups _LHN(%rdx), %xmm13 | |
170 | movhpd 19968(%rdx,%r9), %xmm11 | |
171 | addpd %xmm10, %xmm13 | |
172 | ||
173 | /* T = k + L1hi */ | |
174 | addpd %xmm0, %xmm11 | |
175 | ||
176 | /* T_Rh = T + cq */ | |
177 | movaps %xmm13, %xmm12 | |
178 | addpd %xmm11, %xmm12 | |
179 | addpd %xmm12, %xmm15 | |
180 | ||
181 | /* Rl = T-T_Rh; -> -Rh */ | |
182 | subpd %xmm12, %xmm11 | |
183 | ||
184 | /* HLL = T_Rh - T_Rh_Eh; -> -Eh */ | |
185 | subpd %xmm15, %xmm12 | |
186 | ||
187 | /* Rl=Rl+cq; */ | |
188 | addpd %xmm13, %xmm11 | |
189 | ||
190 | /* cq = cq + E */ | |
191 | addpd %xmm14, %xmm13 | |
192 | ||
193 | /* HLL+=E; -> El */ | |
194 | addpd %xmm14, %xmm12 | |
195 | ||
196 | /* HLL+=Rl */ | |
197 | addpd %xmm12, %xmm11 | |
198 | unpckhpd 19968(%rdx,%r9), %xmm8 | |
199 | ||
200 | /* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ | |
201 | movaps %xmm15, %xmm14 | |
202 | ||
203 | /* HLL+=L1lo; */ | |
204 | addpd %xmm11, %xmm8 | |
205 | movups _clv_2(%rdx), %xmm11 | |
206 | ||
207 | /* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ | |
208 | movaps %xmm6, %xmm12 | |
209 | ||
210 | /* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ | |
211 | mulpd %xmm13, %xmm11 | |
212 | addpd _clv_3(%rdx), %xmm11 | |
213 | mulpd %xmm13, %xmm11 | |
214 | addpd _clv_4(%rdx), %xmm11 | |
215 | mulpd %xmm13, %xmm11 | |
216 | addpd _clv_5(%rdx), %xmm11 | |
217 | mulpd %xmm13, %xmm11 | |
218 | addpd _clv_6(%rdx), %xmm11 | |
219 | mulpd %xmm13, %xmm11 | |
220 | addpd _clv_7(%rdx), %xmm11 | |
221 | mulpd %xmm11, %xmm13 | |
222 | addpd %xmm13, %xmm8 | |
223 | addpd %xmm8, %xmm14 | |
224 | ||
225 | /* | |
226 | 2^(y*(HH+HL+HLL)) starts here: | |
227 | yH = y; Lo(yH)&=0xf8000000 | |
228 | */ | |
229 | andps %xmm9, %xmm6 | |
230 | ||
231 | /* yL = y-yH; */ | |
232 | movaps %xmm9, %xmm11 | |
233 | subpd %xmm6, %xmm11 | |
234 | andps %xmm14, %xmm12 | |
235 | ||
236 | /* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ | |
237 | movaps %xmm14, %xmm10 | |
238 | ||
239 | /* HL = T_Rh_Eh_HLLhi-HH; */ | |
240 | subpd %xmm12, %xmm14 | |
241 | subpd %xmm15, %xmm10 | |
242 | movq _HIDELTA(%rdx), %xmm2 | |
243 | ||
244 | /* pH = yH*HH; */ | |
245 | movaps %xmm6, %xmm13 | |
246 | movq _LORANGE(%rdx), %xmm3 | |
247 | paddd %xmm2, %xmm1 | |
248 | pcmpgtd %xmm1, %xmm3 | |
249 | ||
250 | /* pL=yL*HL+yH*HL; pL+=yL*HH; */ | |
251 | movaps %xmm11, %xmm1 | |
252 | mulpd %xmm14, %xmm1 | |
253 | mulpd %xmm14, %xmm6 | |
254 | mulpd %xmm12, %xmm13 | |
255 | mulpd %xmm11, %xmm12 | |
256 | addpd %xmm6, %xmm1 | |
257 | ||
258 | /* HLL = HLL - HLLhi */ | |
259 | subpd %xmm10, %xmm8 | |
260 | addpd %xmm12, %xmm1 | |
261 | ||
262 | /* pLL = y*HLL */ | |
263 | mulpd %xmm9, %xmm8 | |
264 | movups _db2p45_2p44(%rdx), %xmm11 | |
265 | ||
266 | /* pHH = pH + *(double*)&db2p45_2p44 */ | |
267 | movaps %xmm11, %xmm12 | |
268 | addpd %xmm13, %xmm12 | |
269 | ||
270 | /* t=pL+pLL; t+=pHL */ | |
271 | addpd %xmm8, %xmm1 | |
272 | movq _ABSMASK(%rdx), %xmm5 | |
273 | pshufd $221, %xmm9, %xmm4 | |
274 | pand %xmm5, %xmm4 | |
275 | movq _INF(%rdx), %xmm7 | |
276 | movdqa %xmm4, %xmm2 | |
277 | pcmpgtd %xmm7, %xmm2 | |
278 | pcmpeqd %xmm7, %xmm4 | |
279 | pshufd $136, %xmm12, %xmm7 | |
280 | por %xmm4, %xmm2 | |
281 | ||
282 | /* pHH = pHH - *(double*)&db2p45_2p44 */ | |
283 | subpd %xmm11, %xmm12 | |
284 | pshufd $221, %xmm13, %xmm10 | |
285 | por %xmm2, %xmm3 | |
286 | ||
287 | /* pHL = pH - pHH; */ | |
288 | subpd %xmm12, %xmm13 | |
289 | pand %xmm5, %xmm10 | |
290 | movq _DOMAINRANGE(%rdx), %xmm5 | |
291 | movdqa %xmm10, %xmm4 | |
292 | addpd %xmm1, %xmm13 | |
293 | pcmpgtd %xmm5, %xmm4 | |
294 | pcmpeqd %xmm5, %xmm10 | |
295 | por %xmm10, %xmm4 | |
296 | movq _jIndexMask(%rdx), %xmm6 | |
297 | por %xmm4, %xmm3 | |
298 | movmskps %xmm3, %eax | |
299 | ||
300 | /* j = Lo(pHH)&0x0000007f */ | |
301 | pand %xmm7, %xmm6 | |
302 | movq _iOne(%rdx), %xmm3 | |
303 | ||
304 | /* _n = Lo(pHH); | |
305 | _n = _n & 0xffffff80; | |
306 | _n = _n >> 7; | |
307 | Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n | |
308 | */ | |
309 | pslld $13, %xmm7 | |
310 | paddd %xmm3, %xmm7 | |
311 | pslld $4, %xmm6 | |
312 | movups _cev_1(%rdx), %xmm3 | |
313 | movaps %xmm13, %xmm4 | |
314 | mulpd %xmm13, %xmm3 | |
315 | ||
316 | /* T1 = ((double*)exp2_tbl)[ 2*j ] */ | |
317 | movd %xmm6, %r10d | |
318 | pshufd $80, %xmm7, %xmm0 | |
319 | andps _ifff0000000000000(%rdx), %xmm0 | |
320 | addpd _cev_2(%rdx), %xmm3 | |
321 | mulpd %xmm13, %xmm3 | |
322 | addpd _cev_3(%rdx), %xmm3 | |
323 | mulpd %xmm13, %xmm3 | |
324 | movslq %r10d, %r10 | |
325 | andl $3, %eax | |
326 | pextrd $1, %xmm6, %r11d | |
327 | movslq %r11d, %r11 | |
328 | addpd _cev_4(%rdx), %xmm3 | |
329 | movsd 36416(%rdx,%r10), %xmm2 | |
330 | movhpd 36416(%rdx,%r11), %xmm2 | |
331 | mulpd %xmm2, %xmm0 | |
332 | mulpd %xmm3, %xmm13 | |
333 | mulpd %xmm0, %xmm4 | |
334 | addpd _cev_5(%rdx), %xmm13 | |
335 | mulpd %xmm4, %xmm13 | |
336 | addpd %xmm13, %xmm0 | |
337 | jne .LBL_1_3 | |
338 | ||
339 | .LBL_1_2: | |
340 | cfi_remember_state | |
341 | movups 208(%rsp), %xmm8 | |
342 | movups 176(%rsp), %xmm9 | |
343 | movups 160(%rsp), %xmm10 | |
344 | movups 144(%rsp), %xmm11 | |
345 | movups 112(%rsp), %xmm12 | |
346 | movups 96(%rsp), %xmm13 | |
347 | movups 80(%rsp), %xmm14 | |
348 | movups 48(%rsp), %xmm15 | |
349 | movq %rbp, %rsp | |
350 | cfi_def_cfa_register (%rsp) | |
351 | popq %rbp | |
352 | cfi_adjust_cfa_offset (-8) | |
353 | cfi_restore (%rbp) | |
354 | ret | |
355 | ||
356 | .LBL_1_3: | |
357 | cfi_restore_state | |
358 | movups (%rsp), %xmm1 | |
359 | movups %xmm1, 64(%rsp) | |
360 | movups %xmm9, 128(%rsp) | |
361 | movups %xmm0, 192(%rsp) | |
362 | je .LBL_1_2 | |
363 | ||
364 | xorb %cl, %cl | |
365 | xorl %edx, %edx | |
366 | movq %rsi, 8(%rsp) | |
367 | movq %rdi, (%rsp) | |
368 | movq %r12, 40(%rsp) | |
369 | cfi_offset_rel_rsp (12, 40) | |
370 | movb %cl, %r12b | |
371 | movq %r13, 32(%rsp) | |
372 | cfi_offset_rel_rsp (13, 32) | |
373 | movl %eax, %r13d | |
374 | movq %r14, 24(%rsp) | |
375 | cfi_offset_rel_rsp (14, 24) | |
376 | movl %edx, %r14d | |
377 | movq %r15, 16(%rsp) | |
378 | cfi_offset_rel_rsp (15, 16) | |
379 | cfi_remember_state | |
380 | ||
381 | .LBL_1_6: | |
382 | btl %r14d, %r13d | |
383 | jc .LBL_1_12 | |
384 | ||
385 | .LBL_1_7: | |
386 | lea 1(%r14), %esi | |
387 | btl %esi, %r13d | |
388 | jc .LBL_1_10 | |
389 | ||
390 | .LBL_1_8: | |
391 | incb %r12b | |
392 | addl $2, %r14d | |
393 | cmpb $16, %r12b | |
394 | jb .LBL_1_6 | |
395 | ||
396 | movq 8(%rsp), %rsi | |
397 | movq (%rsp), %rdi | |
398 | movq 40(%rsp), %r12 | |
399 | cfi_restore (%r12) | |
400 | movq 32(%rsp), %r13 | |
401 | cfi_restore (%r13) | |
402 | movq 24(%rsp), %r14 | |
403 | cfi_restore (%r14) | |
404 | movq 16(%rsp), %r15 | |
405 | cfi_restore (%r15) | |
406 | movups 192(%rsp), %xmm0 | |
407 | jmp .LBL_1_2 | |
408 | ||
409 | .LBL_1_10: | |
410 | cfi_restore_state | |
411 | movzbl %r12b, %r15d | |
412 | shlq $4, %r15 | |
413 | movsd 72(%rsp,%r15), %xmm0 | |
414 | movsd 136(%rsp,%r15), %xmm1 | |
415 | ||
d0007dc5 | 416 | call JUMPTARGET(pow) |
c10b9b13 AS |
417 | |
418 | movsd %xmm0, 200(%rsp,%r15) | |
419 | jmp .LBL_1_8 | |
420 | ||
421 | .LBL_1_12: | |
422 | movzbl %r12b, %r15d | |
423 | shlq $4, %r15 | |
424 | movsd 64(%rsp,%r15), %xmm0 | |
425 | movsd 128(%rsp,%r15), %xmm1 | |
426 | ||
d0007dc5 | 427 | call JUMPTARGET(pow) |
c10b9b13 AS |
428 | |
429 | movsd %xmm0, 192(%rsp,%r15) | |
430 | jmp .LBL_1_7 | |
431 | ||
432 | END (_ZGVbN2vv_pow_sse4) |