1/* Function powf 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_s_powf_data.h"
21
22 .section .text.sse4, "ax", @progbits
23ENTRY (_ZGVbN4vv_powf_sse4)
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 $256, %rsp
91 movaps %xmm0, %xmm3
92 movhlps %xmm0, %xmm3
93 movaps %xmm1, %xmm5
94 movups %xmm8, 112(%rsp)
95 movaps %xmm5, %xmm2
96 cvtps2pd %xmm3, %xmm8
97 cvtps2pd %xmm5, %xmm7
98 movups %xmm9, 96(%rsp)
99 movaps %xmm0, %xmm4
100 cvtps2pd %xmm0, %xmm9
101 movq __svml_spow_data@GOTPCREL(%rip), %rdx
102 movups %xmm10, 176(%rsp)
103 movups %xmm13, 48(%rsp)
104 movups _ExpMask(%rdx), %xmm6
105
106/* preserve mantissa, set input exponent to 2^(-10) */
107 movaps %xmm6, %xmm10
108 andps %xmm8, %xmm6
109 andps %xmm9, %xmm10
110
111/* exponent bits selection */
112 psrlq $20, %xmm9
113 orps _Two10(%rdx), %xmm6
114 psrlq $20, %xmm8
115 orps _Two10(%rdx), %xmm10
116
117/* reciprocal approximation good to at least 11 bits */
118 cvtpd2ps %xmm6, %xmm13
119 cvtpd2ps %xmm10, %xmm1
120 movlhps %xmm13, %xmm13
121 movhlps %xmm5, %xmm2
122 movlhps %xmm1, %xmm1
123 movups %xmm12, 208(%rsp)
124 rcpps %xmm13, %xmm12
125 movups %xmm11, 80(%rsp)
126 cvtps2pd %xmm2, %xmm11
127 rcpps %xmm1, %xmm2
128 movups %xmm14, 144(%rsp)
129 cvtps2pd %xmm12, %xmm14
130 movups %xmm15, 160(%rsp)
131 cvtps2pd %xmm2, %xmm15
132 shufps $221, %xmm8, %xmm9
133
134/* round reciprocal to nearest integer, will have 1+9 mantissa bits */
135 roundpd $0, %xmm14, %xmm14
136
137/* biased exponent in DP format */
138 pshufd $238, %xmm9, %xmm8
139 roundpd $0, %xmm15, %xmm15
140 cvtdq2pd %xmm8, %xmm1
141 mulpd %xmm15, %xmm10
142 mulpd %xmm14, %xmm6
143 cvtdq2pd %xmm9, %xmm2
144 subpd _One(%rdx), %xmm10
145 subpd _One(%rdx), %xmm6
146
147/* table lookup */
148 movaps %xmm14, %xmm8
149 movaps %xmm15, %xmm9
150 psrlq $40, %xmm8
151 psrlq $40, %xmm9
152 movd %xmm8, %r8d
153 movd %xmm9, %eax
154 psubd _NMINNORM(%rdx), %xmm4
155 movdqu _ABSMASK(%rdx), %xmm3
156 pextrd $2, %xmm8, %r9d
157 pand %xmm5, %xmm3
158 movups _Threshold(%rdx), %xmm8
159 pextrd $2, %xmm9, %ecx
160 movaps %xmm8, %xmm9
161 cmpltpd %xmm15, %xmm9
162 cmpltpd %xmm14, %xmm8
163 andps _Bias(%rdx), %xmm9
164 movaps %xmm10, %xmm14
165 andps _Bias(%rdx), %xmm8
166 movaps %xmm6, %xmm15
167 orps _Bias1(%rdx), %xmm9
168 orps _Bias1(%rdx), %xmm8
169 subpd %xmm9, %xmm2
170 subpd %xmm8, %xmm1
171 mulpd %xmm10, %xmm14
172 mulpd %xmm6, %xmm15
173 mulpd _L2(%rdx), %xmm2
174 mulpd _L2(%rdx), %xmm1
175 movups _poly_coeff_3(%rdx), %xmm9
176 movaps %xmm9, %xmm8
177 mulpd %xmm10, %xmm8
178 mulpd %xmm6, %xmm9
179 addpd _poly_coeff_4(%rdx), %xmm8
180 addpd _poly_coeff_4(%rdx), %xmm9
181 mulpd %xmm14, %xmm8
182 mulpd %xmm15, %xmm9
183
184/* reconstruction */
185 addpd %xmm8, %xmm10
186 addpd %xmm9, %xmm6
187 movslq %eax, %rax
188 movslq %r8d, %r8
189 movslq %ecx, %rcx
190 movslq %r9d, %r9
191 movsd _Log2Rcp_lookup(%rdx,%rax), %xmm13
192 movsd _Log2Rcp_lookup(%rdx,%r8), %xmm12
193 movhpd _Log2Rcp_lookup(%rdx,%rcx), %xmm13
194 movhpd _Log2Rcp_lookup(%rdx,%r9), %xmm12
195 addpd %xmm10, %xmm13
196 addpd %xmm6, %xmm12
197 addpd %xmm13, %xmm2
198 addpd %xmm12, %xmm1
199 mulpd %xmm7, %xmm2
200 mulpd %xmm11, %xmm1
201 movups __dbInvLn2(%rdx), %xmm11
202 movdqa %xmm4, %xmm12
203 movaps %xmm11, %xmm10
204 mulpd %xmm2, %xmm10
205 mulpd %xmm1, %xmm11
206
207/* to round down; if dR is an integer we will get R = 1, which is ok */
208 movaps %xmm10, %xmm8
209 movaps %xmm11, %xmm9
210 subpd __dbHALF(%rdx), %xmm8
211 subpd __dbHALF(%rdx), %xmm9
212 addpd __dbShifter(%rdx), %xmm8
213 addpd __dbShifter(%rdx), %xmm9
214 movaps %xmm8, %xmm6
215 movaps %xmm9, %xmm7
216 subpd __dbShifter(%rdx), %xmm6
217 subpd __dbShifter(%rdx), %xmm7
218
219/* [0..1) */
220 subpd %xmm6, %xmm10
221 subpd %xmm7, %xmm11
222 mulpd __dbC1(%rdx), %xmm10
223 mulpd __dbC1(%rdx), %xmm11
224
225/* hi bits */
226 shufps $221, %xmm1, %xmm2
227 movdqu _NMAXVAL(%rdx), %xmm1
228 pcmpgtd %xmm1, %xmm12
229 pcmpeqd %xmm1, %xmm4
230 por %xmm4, %xmm12
231 movdqa %xmm3, %xmm1
232 movdqu _INF(%rdx), %xmm4
233 pcmpgtd %xmm4, %xmm1
234 pcmpeqd %xmm4, %xmm3
235
236/* iAbsX = iAbsX&iAbsMask */
237 pand __iAbsMask(%rdx), %xmm2
238 por %xmm3, %xmm1
239
240/* iRangeMask = (iAbsX>iDomainRange) */
241 pcmpgtd __iDomainRange(%rdx), %xmm2
242 por %xmm1, %xmm12
243 movups __lbLOWKBITS(%rdx), %xmm3
244 por %xmm2, %xmm12
245
246/* low K bits */
247 movaps %xmm3, %xmm2
248 andps %xmm9, %xmm3
249 andps %xmm8, %xmm2
250 psrlq $11, %xmm8
251
252/* dpP= _dbT+lJ*T_ITEM_GRAN */
253 movd %xmm2, %r10d
254 psrlq $11, %xmm9
255 movd %xmm3, %ecx
256
257/* NB : including +/- sign for the exponent!! */
258 psllq $52, %xmm8
259 psllq $52, %xmm9
260 pextrw $4, %xmm2, %r11d
261 pextrw $4, %xmm3, %r8d
262 movmskps %xmm12, %eax
263 shll $3, %r10d
264 shll $3, %ecx
265 shll $3, %r11d
266 shll $3, %r8d
267 movq 13952(%rdx,%r10), %xmm6
268 movq 13952(%rdx,%rcx), %xmm7
269 movhpd 13952(%rdx,%r11), %xmm6
270 movhpd 13952(%rdx,%r8), %xmm7
271 mulpd %xmm6, %xmm10
272 mulpd %xmm7, %xmm11
273 addpd %xmm10, %xmm6
274 addpd %xmm11, %xmm7
275 paddq %xmm8, %xmm6
276 paddq %xmm9, %xmm7
277 cvtpd2ps %xmm6, %xmm1
278 cvtpd2ps %xmm7, %xmm4
279 movlhps %xmm4, %xmm1
280 testl %eax, %eax
281 jne .LBL_1_3
282
283.LBL_1_2:
284 cfi_remember_state
285 movups 112(%rsp), %xmm8
286 movaps %xmm1, %xmm0
287 movups 96(%rsp), %xmm9
288 movups 176(%rsp), %xmm10
289 movups 80(%rsp), %xmm11
290 movups 208(%rsp), %xmm12
291 movups 48(%rsp), %xmm13
292 movups 144(%rsp), %xmm14
293 movups 160(%rsp), %xmm15
294 movq %rbp, %rsp
295 cfi_def_cfa_register (%rsp)
296 popq %rbp
297 cfi_adjust_cfa_offset (-8)
298 cfi_restore (%rbp)
299 ret
300
301.LBL_1_3:
302 cfi_restore_state
303 movups %xmm0, 64(%rsp)
304 movups %xmm5, 128(%rsp)
305 movups %xmm1, 192(%rsp)
306 je .LBL_1_2
307
308 xorb %cl, %cl
309 xorl %edx, %edx
310 movq %rsi, 8(%rsp)
311 movq %rdi, (%rsp)
312 movq %r12, 40(%rsp)
313 cfi_offset_rel_rsp (12, 40)
314 movb %cl, %r12b
315 movq %r13, 32(%rsp)
316 cfi_offset_rel_rsp (13, 32)
317 movl %eax, %r13d
318 movq %r14, 24(%rsp)
319 cfi_offset_rel_rsp (14, 24)
320 movl %edx, %r14d
321 movq %r15, 16(%rsp)
322 cfi_offset_rel_rsp (15, 16)
323 cfi_remember_state
324
325.LBL_1_6:
326 btl %r14d, %r13d
327 jc .LBL_1_12
328
329.LBL_1_7:
330 lea 1(%r14), %esi
331 btl %esi, %r13d
332 jc .LBL_1_10
333
334.LBL_1_8:
335 incb %r12b
336 addl $2, %r14d
337 cmpb $16, %r12b
338 jb .LBL_1_6
339
340 movq 8(%rsp), %rsi
341 movq (%rsp), %rdi
342 movq 40(%rsp), %r12
343 cfi_restore (%r12)
344 movq 32(%rsp), %r13
345 cfi_restore (%r13)
346 movq 24(%rsp), %r14
347 cfi_restore (%r14)
348 movq 16(%rsp), %r15
349 cfi_restore (%r15)
350 movups 192(%rsp), %xmm1
351 jmp .LBL_1_2
352
353.LBL_1_10:
354 cfi_restore_state
355 movzbl %r12b, %r15d
356 movss 68(%rsp,%r15,8), %xmm0
357 movss 132(%rsp,%r15,8), %xmm1
358
359 call JUMPTARGET(powf)
360
361 movss %xmm0, 196(%rsp,%r15,8)
362 jmp .LBL_1_8
363
364.LBL_1_12:
365 movzbl %r12b, %r15d
366 movss 64(%rsp,%r15,8), %xmm0
367 movss 128(%rsp,%r15,8), %xmm1
368
369 call JUMPTARGET(powf)
370
371 movss %xmm0, 192(%rsp,%r15,8)
372 jmp .LBL_1_7
373
374END (_ZGVbN4vv_powf_sse4)
375

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_powf4_core_sse4.S