1 | /* Function powf vectorized with AVX2. |
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_s_powf_data.h" |
21 | |
22 | .section .text.avx2, "ax" , @progbits |
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 | |
320 | call JUMPTARGET(powf) |
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 | |
331 | call JUMPTARGET(powf) |
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 |
358 | |