1 | /* Function pow vectorized with SSE4. |
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 | |
22 | .section .text.sse4, "ax" , @progbits |
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 | |
416 | call JUMPTARGET(pow) |
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 | |
427 | call JUMPTARGET(pow) |
428 | |
429 | movsd %xmm0, 192(%rsp,%r15) |
430 | jmp .LBL_1_7 |
431 | |
432 | END (_ZGVbN2vv_pow_sse4) |
433 | |