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8aa92022 | 1 | /* Function powf vectorized with AVX2. |
04277e02 | 2 | Copyright (C) 2014-2019 Free Software Foundation, Inc. |
8aa92022 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/>. */ |
8aa92022 AS |
18 | |
19 | #include <sysdep.h> | |
20 | #include "svml_s_powf_data.h" | |
21 | ||
22 | .text | |
23 | ENTRY(_ZGVdN8vv_powf_avx2) | |
24 | /* | |
25 | ALGORITHM DESCRIPTION: | |
26 | ||
27 | We are using the next identity : pow(x,y) = 2^(y * log2(x)). | |
28 | ||
29 | 1) log2(x) calculation | |
30 | Here we use the following formula. | |
31 | Let |x|=2^k1*X1, where k1 is integer, 1<=X1<2. | |
32 | Let C ~= 1/ln(2), | |
33 | Rcp1 ~= 1/X1, X2=Rcp1*X1, | |
34 | Rcp2 ~= 1/X2, X3=Rcp2*X2, | |
35 | Rcp3 ~= 1/X3, Rcp3C ~= C/X3. | |
36 | Then | |
37 | log2|x| = k1 + log2(1/Rcp1) + log2(1/Rcp2) + log2(C/Rcp3C) + | |
38 | log2(X1*Rcp1*Rcp2*Rcp3C/C), | |
39 | where X1*Rcp1*Rcp2*Rcp3C = C*(1+q), q is very small. | |
40 | ||
41 | The values of Rcp1, log2(1/Rcp1), Rcp2, log2(1/Rcp2), | |
42 | Rcp3C, log2(C/Rcp3C) are taken from tables. | |
43 | Values of Rcp1, Rcp2, Rcp3C are such that RcpC=Rcp1*Rcp2*Rcp3C | |
44 | is exactly represented in target precision. | |
45 | ||
46 | log2(X1*Rcp1*Rcp2*Rcp3C/C) = log2(1+q) = ln(1+q)/ln2 = | |
47 | = 1/(ln2)*q - 1/(2ln2)*q^2 + 1/(3ln2)*q^3 - ... = | |
48 | = 1/(C*ln2)*cq - 1/(2*C^2*ln2)*cq^2 + 1/(3*C^3*ln2)*cq^3 - ... = | |
49 | = (1 + a1)*cq + a2*cq^2 + a3*cq^3 + ..., | |
50 | where | |
51 | cq=X1*Rcp1*Rcp2*Rcp3C-C, | |
52 | a1=1/(C*ln(2))-1 is small, | |
53 | a2=1/(2*C^2*ln2), | |
54 | a3=1/(3*C^3*ln2), | |
55 | ... | |
56 | Log2 result is split by three parts: HH+HL+HLL | |
57 | ||
58 | 2) Calculation of y*log2(x) | |
59 | Split y into YHi+YLo. | |
60 | Get high PH and medium PL parts of y*log2|x|. | |
61 | Get low PLL part of y*log2|x|. | |
62 | Now we have PH+PL+PLL ~= y*log2|x|. | |
63 | ||
64 | 3) Calculation of 2^(y*log2(x)) | |
65 | Let's represent PH+PL+PLL in the form N + j/2^expK + Z, | |
66 | where expK=7 in this implementation, N and j are integers, | |
67 | 0<=j<=2^expK-1, |Z|<2^(-expK-1). Hence | |
68 | 2^(PH+PL+PLL) ~= 2^N * 2^(j/2^expK) * 2^Z, | |
69 | where 2^(j/2^expK) is stored in a table, and | |
70 | 2^Z ~= 1 + B1*Z + B2*Z^2 ... + B5*Z^5. | |
71 | We compute 2^(PH+PL+PLL) as follows: | |
72 | Break PH into PHH + PHL, where PHH = N + j/2^expK. | |
73 | Z = PHL + PL + PLL | |
74 | Exp2Poly = B1*Z + B2*Z^2 ... + B5*Z^5 | |
75 | Get 2^(j/2^expK) from table in the form THI+TLO. | |
76 | Now we have 2^(PH+PL+PLL) ~= 2^N * (THI + TLO) * (1 + Exp2Poly). | |
77 | Get significand of 2^(PH+PL+PLL) in the form ResHi+ResLo: | |
78 | ResHi := THI | |
79 | ResLo := THI * Exp2Poly + TLO | |
80 | Get exponent ERes of the result: | |
81 | Res := ResHi + ResLo: | |
82 | Result := ex(Res) + N. */ | |
83 | ||
84 | pushq %rbp | |
85 | cfi_adjust_cfa_offset (8) | |
86 | cfi_rel_offset (%rbp, 0) | |
87 | movq %rsp, %rbp | |
88 | cfi_def_cfa_register (%rbp) | |
89 | andq $-64, %rsp | |
90 | subq $448, %rsp | |
91 | lea __VPACK_ODD_ind.6357.0.1(%rip), %rcx | |
92 | vmovups %ymm14, 320(%rsp) | |
93 | ||
94 | /* hi bits */ | |
95 | lea __VPACK_ODD_ind.6358.0.1(%rip), %rax | |
96 | vmovups %ymm12, 256(%rsp) | |
97 | vmovups %ymm9, 96(%rsp) | |
98 | vmovups %ymm13, 224(%rsp) | |
99 | vmovups %ymm15, 352(%rsp) | |
100 | vmovups %ymm11, 384(%rsp) | |
101 | vmovups %ymm10, 288(%rsp) | |
102 | vmovups (%rcx), %ymm10 | |
103 | vmovups %ymm8, 160(%rsp) | |
104 | vmovdqa %ymm1, %ymm9 | |
105 | movq __svml_spow_data@GOTPCREL(%rip), %rdx | |
106 | vextractf128 $1, %ymm0, %xmm7 | |
107 | vcvtps2pd %xmm0, %ymm14 | |
108 | vcvtps2pd %xmm7, %ymm12 | |
109 | vpsubd _NMINNORM(%rdx), %ymm0, %ymm7 | |
110 | ||
111 | /* preserve mantissa, set input exponent to 2^(-10) */ | |
112 | vandpd _ExpMask(%rdx), %ymm14, %ymm3 | |
113 | vandpd _ExpMask(%rdx), %ymm12, %ymm13 | |
114 | ||
115 | /* exponent bits selection */ | |
116 | vpsrlq $20, %ymm12, %ymm12 | |
117 | vpsrlq $20, %ymm14, %ymm14 | |
118 | vextractf128 $1, %ymm9, %xmm2 | |
119 | vcvtps2pd %xmm9, %ymm1 | |
120 | vpand _ABSMASK(%rdx), %ymm9, %ymm8 | |
121 | vcvtps2pd %xmm2, %ymm6 | |
122 | vorpd _Two10(%rdx), %ymm3, %ymm2 | |
123 | vorpd _Two10(%rdx), %ymm13, %ymm3 | |
124 | ||
125 | /* reciprocal approximation good to at least 11 bits */ | |
126 | vcvtpd2ps %ymm2, %xmm5 | |
127 | vcvtpd2ps %ymm3, %xmm15 | |
128 | vrcpps %xmm5, %xmm4 | |
129 | vrcpps %xmm15, %xmm11 | |
130 | vcvtps2pd %xmm4, %ymm13 | |
131 | vcvtps2pd %xmm11, %ymm4 | |
132 | vpermps %ymm12, %ymm10, %ymm11 | |
133 | ||
134 | /* round reciprocal to nearest integer, will have 1+9 mantissa bits */ | |
135 | vroundpd $0, %ymm13, %ymm12 | |
136 | vpermps %ymm14, %ymm10, %ymm5 | |
137 | vroundpd $0, %ymm4, %ymm14 | |
138 | vmovupd _One(%rdx), %ymm4 | |
139 | ||
140 | /* table lookup */ | |
141 | vpsrlq $40, %ymm12, %ymm10 | |
142 | vfmsub213pd %ymm4, %ymm12, %ymm2 | |
143 | vfmsub213pd %ymm4, %ymm14, %ymm3 | |
144 | vcmpgt_oqpd _Threshold(%rdx), %ymm12, %ymm12 | |
145 | vxorpd %ymm4, %ymm4, %ymm4 | |
146 | vandpd _Bias(%rdx), %ymm12, %ymm12 | |
147 | ||
148 | /* biased exponent in DP format */ | |
149 | vcvtdq2pd %xmm11, %ymm13 | |
150 | vpcmpeqd %ymm11, %ymm11, %ymm11 | |
151 | vgatherqpd %ymm11, _Log2Rcp_lookup(%rdx,%ymm10), %ymm4 | |
152 | vpsrlq $40, %ymm14, %ymm10 | |
153 | vcmpgt_oqpd _Threshold(%rdx), %ymm14, %ymm14 | |
154 | vpcmpeqd %ymm11, %ymm11, %ymm11 | |
155 | vandpd _Bias(%rdx), %ymm14, %ymm14 | |
156 | vcvtdq2pd %xmm5, %ymm15 | |
157 | vxorpd %ymm5, %ymm5, %ymm5 | |
158 | vgatherqpd %ymm11, _Log2Rcp_lookup(%rdx,%ymm10), %ymm5 | |
159 | vorpd _Bias1(%rdx), %ymm12, %ymm11 | |
160 | vorpd _Bias1(%rdx), %ymm14, %ymm10 | |
161 | vsubpd %ymm11, %ymm15, %ymm11 | |
162 | vsubpd %ymm10, %ymm13, %ymm14 | |
163 | vmovupd _poly_coeff_4(%rdx), %ymm15 | |
164 | vmovupd _poly_coeff_3(%rdx), %ymm13 | |
165 | vmulpd %ymm3, %ymm3, %ymm10 | |
166 | vfmadd213pd %ymm15, %ymm3, %ymm13 | |
167 | vmovdqa %ymm15, %ymm12 | |
168 | vfmadd231pd _poly_coeff_3(%rdx), %ymm2, %ymm12 | |
169 | vmulpd %ymm2, %ymm2, %ymm15 | |
170 | ||
171 | /* reconstruction */ | |
172 | vfmadd213pd %ymm3, %ymm10, %ymm13 | |
173 | vfmadd213pd %ymm2, %ymm15, %ymm12 | |
174 | vaddpd %ymm5, %ymm13, %ymm13 | |
175 | vaddpd %ymm4, %ymm12, %ymm2 | |
176 | vfmadd231pd _L2(%rdx), %ymm14, %ymm13 | |
177 | vfmadd132pd _L2(%rdx), %ymm2, %ymm11 | |
178 | vmulpd %ymm6, %ymm13, %ymm2 | |
179 | vmulpd %ymm1, %ymm11, %ymm10 | |
180 | vmulpd __dbInvLn2(%rdx), %ymm2, %ymm6 | |
181 | vmulpd __dbInvLn2(%rdx), %ymm10, %ymm15 | |
182 | ||
183 | /* to round down; if dR is an integer we will get R = 1, which is ok */ | |
184 | vsubpd __dbHALF(%rdx), %ymm6, %ymm3 | |
185 | vsubpd __dbHALF(%rdx), %ymm15, %ymm1 | |
186 | vaddpd __dbShifter(%rdx), %ymm3, %ymm13 | |
187 | vaddpd __dbShifter(%rdx), %ymm1, %ymm14 | |
188 | vsubpd __dbShifter(%rdx), %ymm13, %ymm12 | |
189 | vmovups (%rax), %ymm1 | |
190 | vsubpd __dbShifter(%rdx), %ymm14, %ymm11 | |
191 | ||
192 | /* [0..1) */ | |
193 | vsubpd %ymm12, %ymm6, %ymm6 | |
194 | vpermps %ymm10, %ymm1, %ymm3 | |
195 | vpermps %ymm2, %ymm1, %ymm10 | |
196 | vpcmpgtd _NMAXVAL(%rdx), %ymm7, %ymm4 | |
197 | vpcmpgtd _INF(%rdx), %ymm8, %ymm1 | |
198 | vpcmpeqd _NMAXVAL(%rdx), %ymm7, %ymm7 | |
199 | vpcmpeqd _INF(%rdx), %ymm8, %ymm8 | |
200 | vpor %ymm7, %ymm4, %ymm2 | |
201 | vpor %ymm8, %ymm1, %ymm1 | |
202 | vsubpd %ymm11, %ymm15, %ymm7 | |
203 | vinsertf128 $1, %xmm10, %ymm3, %ymm10 | |
204 | vpor %ymm1, %ymm2, %ymm3 | |
205 | ||
206 | /* iAbsX = iAbsX&iAbsMask */ | |
207 | vandps __iAbsMask(%rdx), %ymm10, %ymm10 | |
208 | ||
209 | /* iRangeMask = (iAbsX>iDomainRange) */ | |
210 | vpcmpgtd __iDomainRange(%rdx), %ymm10, %ymm4 | |
211 | vpor %ymm4, %ymm3, %ymm5 | |
212 | vmulpd __dbC1(%rdx), %ymm7, %ymm4 | |
213 | vmovmskps %ymm5, %ecx | |
214 | vmulpd __dbC1(%rdx), %ymm6, %ymm5 | |
215 | ||
216 | /* low K bits */ | |
217 | vandps __lbLOWKBITS(%rdx), %ymm14, %ymm6 | |
218 | ||
219 | /* dpP= _dbT+lJ*T_ITEM_GRAN */ | |
220 | vxorpd %ymm7, %ymm7, %ymm7 | |
221 | vpcmpeqd %ymm1, %ymm1, %ymm1 | |
222 | vandps __lbLOWKBITS(%rdx), %ymm13, %ymm2 | |
223 | vxorpd %ymm10, %ymm10, %ymm10 | |
224 | vpcmpeqd %ymm3, %ymm3, %ymm3 | |
225 | vgatherqpd %ymm1, 13952(%rdx,%ymm6,8), %ymm7 | |
226 | vgatherqpd %ymm3, 13952(%rdx,%ymm2,8), %ymm10 | |
227 | vpsrlq $11, %ymm14, %ymm14 | |
228 | vpsrlq $11, %ymm13, %ymm13 | |
229 | vfmadd213pd %ymm7, %ymm4, %ymm7 | |
230 | vfmadd213pd %ymm10, %ymm5, %ymm10 | |
231 | ||
232 | /* NB : including +/- sign for the exponent!! */ | |
233 | vpsllq $52, %ymm14, %ymm8 | |
234 | vpsllq $52, %ymm13, %ymm11 | |
235 | vpaddq %ymm8, %ymm7, %ymm12 | |
236 | vpaddq %ymm11, %ymm10, %ymm1 | |
237 | vcvtpd2ps %ymm12, %xmm15 | |
238 | vcvtpd2ps %ymm1, %xmm2 | |
239 | vinsertf128 $1, %xmm2, %ymm15, %ymm1 | |
240 | testl %ecx, %ecx | |
241 | jne .LBL_1_3 | |
242 | ||
243 | .LBL_1_2: | |
244 | cfi_remember_state | |
245 | vmovups 160(%rsp), %ymm8 | |
246 | vmovups 96(%rsp), %ymm9 | |
247 | vmovups 288(%rsp), %ymm10 | |
248 | vmovups 384(%rsp), %ymm11 | |
249 | vmovups 256(%rsp), %ymm12 | |
250 | vmovups 224(%rsp), %ymm13 | |
251 | vmovups 320(%rsp), %ymm14 | |
252 | vmovups 352(%rsp), %ymm15 | |
253 | vmovdqa %ymm1, %ymm0 | |
254 | movq %rbp, %rsp | |
255 | cfi_def_cfa_register (%rsp) | |
256 | popq %rbp | |
257 | cfi_adjust_cfa_offset (-8) | |
258 | cfi_restore (%rbp) | |
259 | ret | |
260 | ||
261 | .LBL_1_3: | |
262 | cfi_restore_state | |
263 | vmovups %ymm0, 64(%rsp) | |
264 | vmovups %ymm9, 128(%rsp) | |
265 | vmovups %ymm1, 192(%rsp) | |
266 | je .LBL_1_2 | |
267 | ||
268 | xorb %dl, %dl | |
269 | xorl %eax, %eax | |
270 | movq %rsi, 8(%rsp) | |
271 | movq %rdi, (%rsp) | |
272 | movq %r12, 40(%rsp) | |
273 | cfi_offset_rel_rsp (12, 40) | |
274 | movb %dl, %r12b | |
275 | movq %r13, 32(%rsp) | |
276 | cfi_offset_rel_rsp (13, 32) | |
277 | movl %ecx, %r13d | |
278 | movq %r14, 24(%rsp) | |
279 | cfi_offset_rel_rsp (14, 24) | |
280 | movl %eax, %r14d | |
281 | movq %r15, 16(%rsp) | |
282 | cfi_offset_rel_rsp (15, 16) | |
283 | cfi_remember_state | |
284 | ||
285 | .LBL_1_6: | |
286 | btl %r14d, %r13d | |
287 | jc .LBL_1_12 | |
288 | ||
289 | .LBL_1_7: | |
290 | lea 1(%r14), %esi | |
291 | btl %esi, %r13d | |
292 | jc .LBL_1_10 | |
293 | ||
294 | .LBL_1_8: | |
295 | incb %r12b | |
296 | addl $2, %r14d | |
297 | cmpb $16, %r12b | |
298 | jb .LBL_1_6 | |
299 | ||
300 | movq 8(%rsp), %rsi | |
301 | movq (%rsp), %rdi | |
302 | movq 40(%rsp), %r12 | |
303 | cfi_restore (%r12) | |
304 | movq 32(%rsp), %r13 | |
305 | cfi_restore (%r13) | |
306 | movq 24(%rsp), %r14 | |
307 | cfi_restore (%r14) | |
308 | movq 16(%rsp), %r15 | |
309 | cfi_restore (%r15) | |
310 | vmovups 192(%rsp), %ymm1 | |
311 | jmp .LBL_1_2 | |
312 | ||
313 | .LBL_1_10: | |
314 | cfi_restore_state | |
315 | movzbl %r12b, %r15d | |
316 | vmovss 68(%rsp,%r15,8), %xmm0 | |
317 | vmovss 132(%rsp,%r15,8), %xmm1 | |
318 | vzeroupper | |
319 | ||
533f9beb | 320 | call JUMPTARGET(__powf_finite) |
8aa92022 AS |
321 | |
322 | vmovss %xmm0, 196(%rsp,%r15,8) | |
323 | jmp .LBL_1_8 | |
324 | ||
325 | .LBL_1_12: | |
326 | movzbl %r12b, %r15d | |
327 | vmovss 64(%rsp,%r15,8), %xmm0 | |
328 | vmovss 128(%rsp,%r15,8), %xmm1 | |
329 | vzeroupper | |
330 | ||
533f9beb | 331 | call JUMPTARGET(__powf_finite) |
8aa92022 AS |
332 | |
333 | vmovss %xmm0, 192(%rsp,%r15,8) | |
334 | jmp .LBL_1_7 | |
335 | ||
336 | END(_ZGVdN8vv_powf_avx2) | |
337 | ||
338 | .section .rodata, "a" | |
339 | __VPACK_ODD_ind.6357.0.1: | |
340 | .long 1 | |
341 | .long 3 | |
342 | .long 5 | |
343 | .long 7 | |
344 | .long 0 | |
345 | .long 0 | |
346 | .long 0 | |
347 | .long 0 | |
348 | .space 32, 0x00 | |
349 | __VPACK_ODD_ind.6358.0.1: | |
350 | .long 1 | |
351 | .long 3 | |
352 | .long 5 | |
353 | .long 7 | |
354 | .long 0 | |
355 | .long 0 | |
356 | .long 0 | |
357 | .long 0 |