1 | /* Function acos vectorized with SSE4. |
2 | Copyright (C) 2021-2024 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 | /* |
20 | * ALGORITHM DESCRIPTION: |
21 | * |
22 | * SelMask = (|x| >= 0.5) ? 1 : 0; |
23 | * R = SelMask ? sqrt(0.5 - 0.5*|x|) : |x| |
24 | * acos(|x|) = SelMask ? 2*Poly(R) : (Pi/2 - Poly(R)) |
25 | * acos(x) = sign(x) ? (Pi - acos(|x|)) : acos(|x|) |
26 | * |
27 | */ |
28 | |
29 | /* Offsets for data table __svml_dacos_data_internal |
30 | */ |
31 | #define SgnBit 0 |
32 | #define OneHalf 16 |
33 | #define SmallNorm 32 |
34 | #define MOne 48 |
35 | #define Two 64 |
36 | #define sqrt_coeff 80 |
37 | #define poly_coeff 144 |
38 | #define PiH 336 |
39 | #define Pi2H 352 |
40 | |
41 | #include <sysdep.h> |
42 | |
43 | .section .text.sse4, "ax" , @progbits |
44 | ENTRY(_ZGVbN2v_acos_sse4) |
45 | subq $72, %rsp |
46 | cfi_def_cfa_offset(80) |
47 | movaps %xmm0, %xmm5 |
48 | movups __svml_dacos_data_internal(%rip), %xmm3 |
49 | movups OneHalf+__svml_dacos_data_internal(%rip), %xmm6 |
50 | |
51 | /* x = -|arg| */ |
52 | movaps %xmm3, %xmm4 |
53 | orps %xmm5, %xmm4 |
54 | |
55 | /* Y = 0.5 + 0.5*(-x) */ |
56 | movaps %xmm6, %xmm7 |
57 | mulpd %xmm4, %xmm7 |
58 | addpd %xmm7, %xmm6 |
59 | |
60 | /* S ~ 2*sqrt(Y) */ |
61 | cvtpd2ps %xmm6, %xmm9 |
62 | movlhps %xmm9, %xmm9 |
63 | |
64 | /* x^2 */ |
65 | movaps %xmm4, %xmm0 |
66 | rsqrtps %xmm9, %xmm10 |
67 | mulpd %xmm4, %xmm0 |
68 | cvtps2pd %xmm10, %xmm11 |
69 | minpd %xmm6, %xmm0 |
70 | movaps %xmm6, %xmm1 |
71 | movaps %xmm0, %xmm2 |
72 | cmpltpd SmallNorm+__svml_dacos_data_internal(%rip), %xmm1 |
73 | cmpnltpd %xmm6, %xmm2 |
74 | addpd %xmm6, %xmm6 |
75 | andnps %xmm11, %xmm1 |
76 | movaps %xmm0, %xmm11 |
77 | movaps %xmm1, %xmm12 |
78 | andps %xmm5, %xmm3 |
79 | mulpd %xmm1, %xmm12 |
80 | mulpd %xmm6, %xmm1 |
81 | mulpd %xmm12, %xmm6 |
82 | mulpd %xmm0, %xmm11 |
83 | subpd Two+__svml_dacos_data_internal(%rip), %xmm6 |
84 | movups sqrt_coeff+__svml_dacos_data_internal(%rip), %xmm13 |
85 | movaps %xmm6, %xmm14 |
86 | mulpd %xmm6, %xmm13 |
87 | mulpd %xmm1, %xmm14 |
88 | addpd sqrt_coeff+16+__svml_dacos_data_internal(%rip), %xmm13 |
89 | mulpd %xmm6, %xmm13 |
90 | addpd sqrt_coeff+32+__svml_dacos_data_internal(%rip), %xmm13 |
91 | mulpd %xmm13, %xmm6 |
92 | |
93 | /* polynomial */ |
94 | movups poly_coeff+__svml_dacos_data_internal(%rip), %xmm15 |
95 | movaps %xmm11, %xmm7 |
96 | mulpd %xmm0, %xmm15 |
97 | addpd sqrt_coeff+48+__svml_dacos_data_internal(%rip), %xmm6 |
98 | addpd poly_coeff+16+__svml_dacos_data_internal(%rip), %xmm15 |
99 | mulpd %xmm11, %xmm7 |
100 | mulpd %xmm6, %xmm14 |
101 | mulpd %xmm11, %xmm15 |
102 | subpd %xmm14, %xmm1 |
103 | movups MOne+__svml_dacos_data_internal(%rip), %xmm8 |
104 | andps %xmm2, %xmm1 |
105 | |
106 | /* NaN processed in special branch (so wind test passed) */ |
107 | cmpnlepd %xmm4, %xmm8 |
108 | movmskpd %xmm8, %edx |
109 | |
110 | /* X<X^2 iff X<0 */ |
111 | movaps %xmm5, %xmm12 |
112 | movups poly_coeff+32+__svml_dacos_data_internal(%rip), %xmm8 |
113 | movaps %xmm2, %xmm13 |
114 | movups poly_coeff+64+__svml_dacos_data_internal(%rip), %xmm6 |
115 | mulpd %xmm0, %xmm8 |
116 | mulpd %xmm0, %xmm6 |
117 | addpd poly_coeff+48+__svml_dacos_data_internal(%rip), %xmm8 |
118 | addpd poly_coeff+80+__svml_dacos_data_internal(%rip), %xmm6 |
119 | cmpltpd %xmm0, %xmm12 |
120 | addpd %xmm15, %xmm8 |
121 | mulpd %xmm11, %xmm6 |
122 | mulpd %xmm7, %xmm8 |
123 | movups poly_coeff+96+__svml_dacos_data_internal(%rip), %xmm9 |
124 | mulpd %xmm0, %xmm9 |
125 | addpd poly_coeff+112+__svml_dacos_data_internal(%rip), %xmm9 |
126 | addpd %xmm6, %xmm9 |
127 | movups poly_coeff+128+__svml_dacos_data_internal(%rip), %xmm10 |
128 | movaps %xmm2, %xmm6 |
129 | mulpd %xmm0, %xmm10 |
130 | addpd %xmm8, %xmm9 |
131 | addpd poly_coeff+144+__svml_dacos_data_internal(%rip), %xmm10 |
132 | mulpd %xmm11, %xmm9 |
133 | movups poly_coeff+160+__svml_dacos_data_internal(%rip), %xmm14 |
134 | andnps %xmm4, %xmm6 |
135 | addpd %xmm9, %xmm10 |
136 | mulpd %xmm0, %xmm14 |
137 | mulpd %xmm10, %xmm11 |
138 | addpd poly_coeff+176+__svml_dacos_data_internal(%rip), %xmm14 |
139 | addpd %xmm11, %xmm14 |
140 | mulpd %xmm0, %xmm14 |
141 | orps %xmm1, %xmm6 |
142 | pxor %xmm3, %xmm6 |
143 | mulpd %xmm6, %xmm14 |
144 | movups PiH+__svml_dacos_data_internal(%rip), %xmm0 |
145 | andps %xmm2, %xmm0 |
146 | andnps Pi2H+__svml_dacos_data_internal(%rip), %xmm13 |
147 | andps %xmm12, %xmm0 |
148 | addpd %xmm13, %xmm0 |
149 | addpd %xmm14, %xmm6 |
150 | addpd %xmm6, %xmm0 |
151 | testl %edx, %edx |
152 | |
153 | /* Go to special inputs processing branch */ |
154 | jne L(SPECIAL_VALUES_BRANCH) |
155 | # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm5 |
156 | |
157 | /* Restore registers |
158 | * and exit the function |
159 | */ |
160 | |
161 | L(EXIT): |
162 | addq $72, %rsp |
163 | cfi_def_cfa_offset(8) |
164 | ret |
165 | cfi_def_cfa_offset(80) |
166 | |
167 | /* Branch to process |
168 | * special inputs |
169 | */ |
170 | |
171 | L(SPECIAL_VALUES_BRANCH): |
172 | movups %xmm5, 32(%rsp) |
173 | movups %xmm0, 48(%rsp) |
174 | # LOE rbx rbp r12 r13 r14 r15 edx |
175 | |
176 | xorl %eax, %eax |
177 | movq %r12, 16(%rsp) |
178 | cfi_offset(12, -64) |
179 | movl %eax, %r12d |
180 | movq %r13, 8(%rsp) |
181 | cfi_offset(13, -72) |
182 | movl %edx, %r13d |
183 | movq %r14, (%rsp) |
184 | cfi_offset(14, -80) |
185 | # LOE rbx rbp r15 r12d r13d |
186 | |
187 | /* Range mask |
188 | * bits check |
189 | */ |
190 | |
191 | L(RANGEMASK_CHECK): |
192 | btl %r12d, %r13d |
193 | |
194 | /* Call scalar math function */ |
195 | jc L(SCALAR_MATH_CALL) |
196 | # LOE rbx rbp r15 r12d r13d |
197 | |
198 | /* Special inputs |
199 | * processing loop |
200 | */ |
201 | |
202 | L(SPECIAL_VALUES_LOOP): |
203 | incl %r12d |
204 | cmpl $2, %r12d |
205 | |
206 | /* Check bits in range mask */ |
207 | jl L(RANGEMASK_CHECK) |
208 | # LOE rbx rbp r15 r12d r13d |
209 | |
210 | movq 16(%rsp), %r12 |
211 | cfi_restore(12) |
212 | movq 8(%rsp), %r13 |
213 | cfi_restore(13) |
214 | movq (%rsp), %r14 |
215 | cfi_restore(14) |
216 | movups 48(%rsp), %xmm0 |
217 | |
218 | /* Go to exit */ |
219 | jmp L(EXIT) |
220 | cfi_offset(12, -64) |
221 | cfi_offset(13, -72) |
222 | cfi_offset(14, -80) |
223 | # LOE rbx rbp r12 r13 r14 r15 xmm0 |
224 | |
225 | /* Scalar math function call |
226 | * to process special input |
227 | */ |
228 | |
229 | L(SCALAR_MATH_CALL): |
230 | movl %r12d, %r14d |
231 | movsd 32(%rsp, %r14, 8), %xmm0 |
232 | call acos@PLT |
233 | # LOE rbx rbp r14 r15 r12d r13d xmm0 |
234 | |
235 | movsd %xmm0, 48(%rsp, %r14, 8) |
236 | |
237 | /* Process special inputs in loop */ |
238 | jmp L(SPECIAL_VALUES_LOOP) |
239 | # LOE rbx rbp r15 r12d r13d |
240 | END(_ZGVbN2v_acos_sse4) |
241 | |
242 | .section .rodata, "a" |
243 | .align 16 |
244 | |
245 | #ifdef __svml_dacos_data_internal_typedef |
246 | typedef unsigned int VUINT32; |
247 | typedef struct { |
248 | __declspec(align(16)) VUINT32 SgnBit[2][2]; |
249 | __declspec(align(16)) VUINT32 OneHalf[2][2]; |
250 | __declspec(align(16)) VUINT32 SmallNorm[2][2]; |
251 | __declspec(align(16)) VUINT32 MOne[2][2]; |
252 | __declspec(align(16)) VUINT32 Two[2][2]; |
253 | __declspec(align(16)) VUINT32 sqrt_coeff[4][2][2]; |
254 | __declspec(align(16)) VUINT32 poly_coeff[12][2][2]; |
255 | __declspec(align(16)) VUINT32 PiH[2][2]; |
256 | __declspec(align(16)) VUINT32 Pi2H[2][2]; |
257 | } __svml_dacos_data_internal; |
258 | #endif |
259 | __svml_dacos_data_internal: |
260 | /* SgnBit */ |
261 | .quad 0x8000000000000000, 0x8000000000000000 |
262 | /* OneHalf */ |
263 | .align 16 |
264 | .quad 0x3fe0000000000000, 0x3fe0000000000000 |
265 | /* SmallNorm */ |
266 | .align 16 |
267 | .quad 0x3000000000000000, 0x3000000000000000 |
268 | /* MOne */ |
269 | .align 16 |
270 | .quad 0xbff0000000000000, 0xbff0000000000000 |
271 | /* Two */ |
272 | .align 16 |
273 | .quad 0x4000000000000000, 0x4000000000000000 |
274 | /* sqrt_coeff[4] */ |
275 | .align 16 |
276 | .quad 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */ |
277 | .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */ |
278 | .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */ |
279 | .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */ |
280 | /* poly_coeff[12] */ |
281 | .align 16 |
282 | .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */ |
283 | .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */ |
284 | .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */ |
285 | .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */ |
286 | .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */ |
287 | .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */ |
288 | .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */ |
289 | .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */ |
290 | .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */ |
291 | .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */ |
292 | .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */ |
293 | .quad 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */ |
294 | /* PiH */ |
295 | .align 16 |
296 | .quad 0x400921fb54442d18, 0x400921fb54442d18 |
297 | /* Pi2H */ |
298 | .align 16 |
299 | .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18 |
300 | .align 16 |
301 | .type __svml_dacos_data_internal, @object |
302 | .size __svml_dacos_data_internal, .-__svml_dacos_data_internal |
303 | |