1 | /* Function acos vectorized with AVX-512. |
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 64 |
33 | #define SmallNorm 128 |
34 | #define MOne 192 |
35 | #define Two 256 |
36 | #define sqrt_coeff_1 320 |
37 | #define sqrt_coeff_2 384 |
38 | #define sqrt_coeff_3 448 |
39 | #define sqrt_coeff_4 512 |
40 | #define poly_coeff_1 576 |
41 | #define poly_coeff_2 640 |
42 | #define poly_coeff_3 704 |
43 | #define poly_coeff_4 768 |
44 | #define poly_coeff_5 832 |
45 | #define poly_coeff_6 896 |
46 | #define poly_coeff_7 960 |
47 | #define poly_coeff_8 1024 |
48 | #define poly_coeff_9 1088 |
49 | #define poly_coeff_10 1152 |
50 | #define poly_coeff_11 1216 |
51 | #define poly_coeff_12 1280 |
52 | #define PiH 1344 |
53 | #define Pi2H 1408 |
54 | |
55 | #include <sysdep.h> |
56 | |
57 | .section .text.evex512, "ax" , @progbits |
58 | ENTRY(_ZGVeN8v_acos_skx) |
59 | pushq %rbp |
60 | cfi_def_cfa_offset(16) |
61 | movq %rsp, %rbp |
62 | cfi_def_cfa(6, 16) |
63 | cfi_offset(6, -16) |
64 | andq $-64, %rsp |
65 | subq $192, %rsp |
66 | vmovups __svml_dacos_data_internal(%rip), %zmm7 |
67 | vmovups OneHalf+__svml_dacos_data_internal(%rip), %zmm8 |
68 | |
69 | /* S ~ 2*sqrt(Y) */ |
70 | vmovups SmallNorm+__svml_dacos_data_internal(%rip), %zmm11 |
71 | vmovups Two+__svml_dacos_data_internal(%rip), %zmm14 |
72 | vmovups sqrt_coeff_1+__svml_dacos_data_internal(%rip), %zmm15 |
73 | vmovups sqrt_coeff_2+__svml_dacos_data_internal(%rip), %zmm2 |
74 | vmovups sqrt_coeff_3+__svml_dacos_data_internal(%rip), %zmm1 |
75 | vmovups MOne+__svml_dacos_data_internal(%rip), %zmm10 |
76 | vmovaps %zmm0, %zmm6 |
77 | |
78 | /* x = -|arg| */ |
79 | vorpd %zmm6, %zmm7, %zmm5 |
80 | vandpd %zmm6, %zmm7, %zmm4 |
81 | |
82 | /* Y = 0.5 + 0.5*(-x) */ |
83 | vfmadd231pd {rn-sae}, %zmm5, %zmm8, %zmm8 |
84 | |
85 | /* x^2 */ |
86 | vmulpd {rn-sae}, %zmm5, %zmm5, %zmm9 |
87 | vrsqrt14pd %zmm8, %zmm12 |
88 | vcmppd $17, {sae}, %zmm11, %zmm8, %k1 |
89 | vcmppd $17, {sae}, %zmm10, %zmm5, %k0 |
90 | vmovups poly_coeff_5+__svml_dacos_data_internal(%rip), %zmm10 |
91 | vmovups poly_coeff_7+__svml_dacos_data_internal(%rip), %zmm11 |
92 | vminpd {sae}, %zmm8, %zmm9, %zmm3 |
93 | vmovups poly_coeff_3+__svml_dacos_data_internal(%rip), %zmm9 |
94 | vxorpd %zmm12, %zmm12, %zmm12{%k1} |
95 | vaddpd {rn-sae}, %zmm8, %zmm8, %zmm0 |
96 | vcmppd $21, {sae}, %zmm8, %zmm3, %k4 |
97 | |
98 | /* X<X^2 iff X<0 */ |
99 | vcmppd $17, {sae}, %zmm3, %zmm6, %k2 |
100 | vmulpd {rn-sae}, %zmm12, %zmm12, %zmm13 |
101 | vmulpd {rn-sae}, %zmm12, %zmm0, %zmm7 |
102 | vmovups poly_coeff_4+__svml_dacos_data_internal(%rip), %zmm12 |
103 | |
104 | /* polynomial */ |
105 | vmovups poly_coeff_1+__svml_dacos_data_internal(%rip), %zmm8 |
106 | vfmsub213pd {rn-sae}, %zmm14, %zmm13, %zmm0 |
107 | vmovups sqrt_coeff_4+__svml_dacos_data_internal(%rip), %zmm13 |
108 | vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm12 |
109 | vmovups poly_coeff_11+__svml_dacos_data_internal(%rip), %zmm9 |
110 | vfmadd231pd {rn-sae}, %zmm0, %zmm15, %zmm2 |
111 | vmovups poly_coeff_9+__svml_dacos_data_internal(%rip), %zmm15 |
112 | vmulpd {rn-sae}, %zmm0, %zmm7, %zmm14 |
113 | vfmadd213pd {rn-sae}, %zmm1, %zmm0, %zmm2 |
114 | vmovups poly_coeff_2+__svml_dacos_data_internal(%rip), %zmm1 |
115 | kmovw %k0, %edx |
116 | vfmadd213pd {rn-sae}, %zmm13, %zmm0, %zmm2 |
117 | vfmadd231pd {rn-sae}, %zmm3, %zmm8, %zmm1 |
118 | vmovups poly_coeff_10+__svml_dacos_data_internal(%rip), %zmm8 |
119 | vmulpd {rn-sae}, %zmm3, %zmm3, %zmm0 |
120 | vfnmadd213pd {rn-sae}, %zmm7, %zmm14, %zmm2 |
121 | vmovups poly_coeff_6+__svml_dacos_data_internal(%rip), %zmm7 |
122 | vfmadd231pd {rn-sae}, %zmm3, %zmm15, %zmm8 |
123 | vfmadd213pd {rn-sae}, %zmm12, %zmm0, %zmm1 |
124 | vblendmpd %zmm2, %zmm5, %zmm2{%k4} |
125 | vfmadd231pd {rn-sae}, %zmm3, %zmm10, %zmm7 |
126 | vmovups poly_coeff_8+__svml_dacos_data_internal(%rip), %zmm10 |
127 | vfmadd231pd {rn-sae}, %zmm3, %zmm11, %zmm10 |
128 | vmovups poly_coeff_12+__svml_dacos_data_internal(%rip), %zmm11 |
129 | kandw %k4, %k2, %k3 |
130 | vfmadd213pd {rn-sae}, %zmm10, %zmm0, %zmm7 |
131 | vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm11 |
132 | vmulpd {rn-sae}, %zmm0, %zmm0, %zmm10 |
133 | vfmadd213pd {rn-sae}, %zmm7, %zmm10, %zmm1 |
134 | vfmadd213pd {rn-sae}, %zmm8, %zmm0, %zmm1 |
135 | vfmadd213pd {rn-sae}, %zmm11, %zmm0, %zmm1 |
136 | vmovups Pi2H+__svml_dacos_data_internal(%rip), %zmm0 |
137 | vmulpd {rn-sae}, %zmm3, %zmm1, %zmm1 |
138 | vxorpd %zmm4, %zmm2, %zmm3 |
139 | vxorpd %zmm0, %zmm0, %zmm0{%k4} |
140 | vfmadd213pd {rn-sae}, %zmm3, %zmm3, %zmm1 |
141 | vorpd PiH+__svml_dacos_data_internal(%rip), %zmm0, %zmm0{%k3} |
142 | vaddpd {rn-sae}, %zmm1, %zmm0, %zmm0 |
143 | testl %edx, %edx |
144 | |
145 | /* Go to special inputs processing branch */ |
146 | jne L(SPECIAL_VALUES_BRANCH) |
147 | # LOE rbx r12 r13 r14 r15 edx zmm0 zmm6 |
148 | |
149 | /* Restore registers |
150 | * and exit the function |
151 | */ |
152 | |
153 | L(EXIT): |
154 | movq %rbp, %rsp |
155 | popq %rbp |
156 | cfi_def_cfa(7, 8) |
157 | cfi_restore(6) |
158 | ret |
159 | cfi_def_cfa(6, 16) |
160 | cfi_offset(6, -16) |
161 | |
162 | /* Branch to process |
163 | * special inputs |
164 | */ |
165 | |
166 | L(SPECIAL_VALUES_BRANCH): |
167 | vmovups %zmm6, 64(%rsp) |
168 | vmovups %zmm0, 128(%rsp) |
169 | # LOE rbx r12 r13 r14 r15 edx zmm0 |
170 | |
171 | xorl %eax, %eax |
172 | # LOE rbx r12 r13 r14 r15 eax edx |
173 | |
174 | vzeroupper |
175 | movq %r12, 16(%rsp) |
176 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */ |
177 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 |
178 | movl %eax, %r12d |
179 | movq %r13, 8(%rsp) |
180 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */ |
181 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 |
182 | movl %edx, %r13d |
183 | movq %r14, (%rsp) |
184 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */ |
185 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 |
186 | # LOE rbx r15 r12d r13d |
187 | |
188 | /* Range mask |
189 | * bits check |
190 | */ |
191 | |
192 | L(RANGEMASK_CHECK): |
193 | btl %r12d, %r13d |
194 | |
195 | /* Call scalar math function */ |
196 | jc L(SCALAR_MATH_CALL) |
197 | # LOE rbx r15 r12d r13d |
198 | |
199 | /* Special inputs |
200 | * processing loop |
201 | */ |
202 | |
203 | L(SPECIAL_VALUES_LOOP): |
204 | incl %r12d |
205 | cmpl $8, %r12d |
206 | |
207 | /* Check bits in range mask */ |
208 | jl L(RANGEMASK_CHECK) |
209 | # LOE rbx r15 r12d r13d |
210 | |
211 | movq 16(%rsp), %r12 |
212 | cfi_restore(12) |
213 | movq 8(%rsp), %r13 |
214 | cfi_restore(13) |
215 | movq (%rsp), %r14 |
216 | cfi_restore(14) |
217 | vmovups 128(%rsp), %zmm0 |
218 | |
219 | /* Go to exit */ |
220 | jmp L(EXIT) |
221 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */ |
222 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 |
223 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */ |
224 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 |
225 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */ |
226 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 |
227 | # LOE rbx r12 r13 r14 r15 zmm0 |
228 | |
229 | /* Scalar math function call |
230 | * to process special input |
231 | */ |
232 | |
233 | L(SCALAR_MATH_CALL): |
234 | movl %r12d, %r14d |
235 | vmovsd 64(%rsp, %r14, 8), %xmm0 |
236 | call acos@PLT |
237 | # LOE rbx r14 r15 r12d r13d xmm0 |
238 | |
239 | vmovsd %xmm0, 128(%rsp, %r14, 8) |
240 | |
241 | /* Process special inputs in loop */ |
242 | jmp L(SPECIAL_VALUES_LOOP) |
243 | # LOE rbx r15 r12d r13d |
244 | END(_ZGVeN8v_acos_skx) |
245 | |
246 | .section .rodata, "a" |
247 | .align 64 |
248 | |
249 | #ifdef __svml_dacos_data_internal_typedef |
250 | typedef unsigned int VUINT32; |
251 | typedef struct { |
252 | __declspec(align(64)) VUINT32 SgnBit[8][2]; |
253 | __declspec(align(64)) VUINT32 OneHalf[8][2]; |
254 | __declspec(align(64)) VUINT32 SmallNorm[8][2]; |
255 | __declspec(align(64)) VUINT32 MOne[8][2]; |
256 | __declspec(align(64)) VUINT32 Two[8][2]; |
257 | __declspec(align(64)) VUINT32 sqrt_coeff[4][8][2]; |
258 | __declspec(align(64)) VUINT32 poly_coeff[12][8][2]; |
259 | __declspec(align(64)) VUINT32 PiH[8][2]; |
260 | __declspec(align(64)) VUINT32 Pi2H[8][2]; |
261 | } __svml_dacos_data_internal; |
262 | #endif |
263 | __svml_dacos_data_internal: |
264 | /* SgnBit */ |
265 | .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000 |
266 | /* OneHalf */ |
267 | .align 64 |
268 | .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000 |
269 | /* SmallNorm */ |
270 | .align 64 |
271 | .quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000 |
272 | /* MOne */ |
273 | .align 64 |
274 | .quad 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000 |
275 | /* Two */ |
276 | .align 64 |
277 | .quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000 |
278 | /* sqrt_coeff[4] */ |
279 | .align 64 |
280 | .quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */ |
281 | .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */ |
282 | .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */ |
283 | .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */ |
284 | /* poly_coeff[12] */ |
285 | .align 64 |
286 | .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */ |
287 | .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */ |
288 | .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */ |
289 | .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */ |
290 | .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */ |
291 | .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */ |
292 | .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */ |
293 | .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */ |
294 | .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */ |
295 | .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */ |
296 | .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */ |
297 | .quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */ |
298 | /* PiH */ |
299 | .align 64 |
300 | .quad 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18 |
301 | /* Pi2H */ |
302 | .align 64 |
303 | .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18 |
304 | .align 64 |
305 | .type __svml_dacos_data_internal, @object |
306 | .size __svml_dacos_data_internal, .-__svml_dacos_data_internal |
307 | |