1 | /* Function acos vectorized with AVX2. |
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 32 |
33 | #define SmallNorm 64 |
34 | #define MOne 96 |
35 | #define Two 128 |
36 | #define sqrt_coeff 160 |
37 | #define poly_coeff 288 |
38 | #define PiH 672 |
39 | #define Pi2H 704 |
40 | |
41 | #include <sysdep.h> |
42 | |
43 | .section .text.avx2, "ax" , @progbits |
44 | ENTRY(_ZGVdN4v_acos_avx2) |
45 | pushq %rbp |
46 | cfi_def_cfa_offset(16) |
47 | movq %rsp, %rbp |
48 | cfi_def_cfa(6, 16) |
49 | cfi_offset(6, -16) |
50 | andq $-32, %rsp |
51 | subq $96, %rsp |
52 | vmovupd __svml_dacos_data_internal(%rip), %ymm6 |
53 | vmovupd OneHalf+__svml_dacos_data_internal(%rip), %ymm7 |
54 | vmovapd %ymm0, %ymm5 |
55 | |
56 | /* x = -|arg| */ |
57 | vorpd %ymm5, %ymm6, %ymm4 |
58 | |
59 | /* Y = 0.5 + 0.5*(-x) */ |
60 | vfmadd231pd %ymm4, %ymm7, %ymm7 |
61 | |
62 | /* x^2 */ |
63 | vmulpd %ymm4, %ymm4, %ymm8 |
64 | |
65 | /* S ~ 2*sqrt(Y) */ |
66 | vmovupd sqrt_coeff+__svml_dacos_data_internal(%rip), %ymm0 |
67 | vcmplt_oqpd SmallNorm+__svml_dacos_data_internal(%rip), %ymm7, %ymm12 |
68 | vminpd %ymm7, %ymm8, %ymm2 |
69 | |
70 | /* NaN processed in special branch (so wind test passed) */ |
71 | vcmpnge_uqpd MOne+__svml_dacos_data_internal(%rip), %ymm4, %ymm9 |
72 | vcvtpd2ps %ymm7, %xmm10 |
73 | vmovupd poly_coeff+64+__svml_dacos_data_internal(%rip), %ymm8 |
74 | vcmpnlt_uqpd %ymm7, %ymm2, %ymm1 |
75 | vrsqrtps %xmm10, %xmm11 |
76 | vfmadd213pd poly_coeff+96+__svml_dacos_data_internal(%rip), %ymm2, %ymm8 |
77 | vcvtps2pd %xmm11, %ymm13 |
78 | vmovupd poly_coeff+128+__svml_dacos_data_internal(%rip), %ymm11 |
79 | vandnpd %ymm13, %ymm12, %ymm14 |
80 | vmulpd %ymm14, %ymm14, %ymm15 |
81 | vfmadd213pd poly_coeff+160+__svml_dacos_data_internal(%rip), %ymm2, %ymm11 |
82 | vmulpd %ymm2, %ymm2, %ymm13 |
83 | vmovupd poly_coeff+256+__svml_dacos_data_internal(%rip), %ymm12 |
84 | vmulpd %ymm13, %ymm13, %ymm10 |
85 | vfmadd213pd poly_coeff+288+__svml_dacos_data_internal(%rip), %ymm2, %ymm12 |
86 | vandpd %ymm5, %ymm6, %ymm3 |
87 | vaddpd %ymm7, %ymm7, %ymm6 |
88 | vmulpd %ymm6, %ymm14, %ymm7 |
89 | vfmsub213pd Two+__svml_dacos_data_internal(%rip), %ymm15, %ymm6 |
90 | vmovupd poly_coeff+320+__svml_dacos_data_internal(%rip), %ymm14 |
91 | vfmadd213pd sqrt_coeff+32+__svml_dacos_data_internal(%rip), %ymm6, %ymm0 |
92 | vmulpd %ymm6, %ymm7, %ymm15 |
93 | vfmadd213pd poly_coeff+352+__svml_dacos_data_internal(%rip), %ymm2, %ymm14 |
94 | vfmadd213pd sqrt_coeff+64+__svml_dacos_data_internal(%rip), %ymm6, %ymm0 |
95 | vfmadd213pd sqrt_coeff+96+__svml_dacos_data_internal(%rip), %ymm6, %ymm0 |
96 | |
97 | /* polynomial */ |
98 | vmovupd poly_coeff+__svml_dacos_data_internal(%rip), %ymm6 |
99 | vfnmadd213pd %ymm7, %ymm15, %ymm0 |
100 | vfmadd213pd poly_coeff+32+__svml_dacos_data_internal(%rip), %ymm2, %ymm6 |
101 | vblendvpd %ymm1, %ymm0, %ymm4, %ymm0 |
102 | vfmadd213pd %ymm8, %ymm13, %ymm6 |
103 | vmovmskpd %ymm9, %edx |
104 | vmovupd poly_coeff+192+__svml_dacos_data_internal(%rip), %ymm9 |
105 | vfmadd213pd poly_coeff+224+__svml_dacos_data_internal(%rip), %ymm2, %ymm9 |
106 | vfmadd213pd %ymm9, %ymm13, %ymm11 |
107 | vfmadd213pd %ymm11, %ymm10, %ymm6 |
108 | vfmadd213pd %ymm12, %ymm13, %ymm6 |
109 | vfmadd213pd %ymm14, %ymm13, %ymm6 |
110 | vmulpd %ymm6, %ymm2, %ymm9 |
111 | |
112 | /* X<X^2 iff X<0 */ |
113 | vcmplt_oqpd %ymm2, %ymm5, %ymm6 |
114 | vandpd PiH+__svml_dacos_data_internal(%rip), %ymm1, %ymm2 |
115 | vandnpd Pi2H+__svml_dacos_data_internal(%rip), %ymm1, %ymm7 |
116 | vxorpd %ymm3, %ymm0, %ymm1 |
117 | vfmadd213pd %ymm1, %ymm1, %ymm9 |
118 | vandpd %ymm6, %ymm2, %ymm2 |
119 | vaddpd %ymm7, %ymm2, %ymm8 |
120 | vaddpd %ymm9, %ymm8, %ymm0 |
121 | testl %edx, %edx |
122 | |
123 | /* Go to special inputs processing branch */ |
124 | jne L(SPECIAL_VALUES_BRANCH) |
125 | # LOE rbx r12 r13 r14 r15 edx ymm0 ymm5 |
126 | |
127 | /* Restore registers |
128 | * and exit the function |
129 | */ |
130 | |
131 | L(EXIT): |
132 | movq %rbp, %rsp |
133 | popq %rbp |
134 | cfi_def_cfa(7, 8) |
135 | cfi_restore(6) |
136 | ret |
137 | cfi_def_cfa(6, 16) |
138 | cfi_offset(6, -16) |
139 | |
140 | /* Branch to process |
141 | * special inputs |
142 | */ |
143 | |
144 | L(SPECIAL_VALUES_BRANCH): |
145 | vmovupd %ymm5, 32(%rsp) |
146 | vmovupd %ymm0, 64(%rsp) |
147 | # LOE rbx r12 r13 r14 r15 edx ymm0 |
148 | |
149 | xorl %eax, %eax |
150 | # LOE rbx r12 r13 r14 r15 eax edx |
151 | |
152 | vzeroupper |
153 | movq %r12, 16(%rsp) |
154 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */ |
155 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 |
156 | movl %eax, %r12d |
157 | movq %r13, 8(%rsp) |
158 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */ |
159 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 |
160 | movl %edx, %r13d |
161 | movq %r14, (%rsp) |
162 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */ |
163 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 |
164 | # LOE rbx r15 r12d r13d |
165 | |
166 | /* Range mask |
167 | * bits check |
168 | */ |
169 | |
170 | L(RANGEMASK_CHECK): |
171 | btl %r12d, %r13d |
172 | |
173 | /* Call scalar math function */ |
174 | jc L(SCALAR_MATH_CALL) |
175 | # LOE rbx r15 r12d r13d |
176 | |
177 | /* Special inputs |
178 | * processing loop |
179 | */ |
180 | |
181 | L(SPECIAL_VALUES_LOOP): |
182 | incl %r12d |
183 | cmpl $4, %r12d |
184 | |
185 | /* Check bits in range mask */ |
186 | jl L(RANGEMASK_CHECK) |
187 | # LOE rbx r15 r12d r13d |
188 | |
189 | movq 16(%rsp), %r12 |
190 | cfi_restore(12) |
191 | movq 8(%rsp), %r13 |
192 | cfi_restore(13) |
193 | movq (%rsp), %r14 |
194 | cfi_restore(14) |
195 | vmovupd 64(%rsp), %ymm0 |
196 | |
197 | /* Go to exit */ |
198 | jmp L(EXIT) |
199 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */ |
200 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 |
201 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */ |
202 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 |
203 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */ |
204 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 |
205 | # LOE rbx r12 r13 r14 r15 ymm0 |
206 | |
207 | /* Scalar math function call |
208 | * to process special input |
209 | */ |
210 | |
211 | L(SCALAR_MATH_CALL): |
212 | movl %r12d, %r14d |
213 | vmovsd 32(%rsp, %r14, 8), %xmm0 |
214 | call acos@PLT |
215 | # LOE rbx r14 r15 r12d r13d xmm0 |
216 | |
217 | vmovsd %xmm0, 64(%rsp, %r14, 8) |
218 | |
219 | /* Process special inputs in loop */ |
220 | jmp L(SPECIAL_VALUES_LOOP) |
221 | # LOE rbx r15 r12d r13d |
222 | END(_ZGVdN4v_acos_avx2) |
223 | |
224 | .section .rodata, "a" |
225 | .align 32 |
226 | |
227 | #ifdef __svml_dacos_data_internal_typedef |
228 | typedef unsigned int VUINT32; |
229 | typedef struct { |
230 | __declspec(align(32)) VUINT32 SgnBit[4][2]; |
231 | __declspec(align(32)) VUINT32 OneHalf[4][2]; |
232 | __declspec(align(32)) VUINT32 SmallNorm[4][2]; |
233 | __declspec(align(32)) VUINT32 MOne[4][2]; |
234 | __declspec(align(32)) VUINT32 Two[4][2]; |
235 | __declspec(align(32)) VUINT32 sqrt_coeff[4][4][2]; |
236 | __declspec(align(32)) VUINT32 poly_coeff[12][4][2]; |
237 | __declspec(align(32)) VUINT32 PiH[4][2]; |
238 | __declspec(align(32)) VUINT32 Pi2H[4][2]; |
239 | } __svml_dacos_data_internal; |
240 | #endif |
241 | __svml_dacos_data_internal: |
242 | /* SgnBit */ |
243 | .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000 |
244 | /* OneHalf */ |
245 | .align 32 |
246 | .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000 |
247 | /* SmallNorm */ |
248 | .align 32 |
249 | .quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000 |
250 | /* MOne */ |
251 | .align 32 |
252 | .quad 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000 |
253 | /* Two */ |
254 | .align 32 |
255 | .quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000 |
256 | /* sqrt_coeff[4] */ |
257 | .align 32 |
258 | .quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */ |
259 | .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */ |
260 | .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */ |
261 | .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */ |
262 | /* poly_coeff[12] */ |
263 | .align 32 |
264 | .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */ |
265 | .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */ |
266 | .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */ |
267 | .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */ |
268 | .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */ |
269 | .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */ |
270 | .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */ |
271 | .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */ |
272 | .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */ |
273 | .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */ |
274 | .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */ |
275 | .quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */ |
276 | /* PiH */ |
277 | .align 32 |
278 | .quad 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18 |
279 | /* Pi2H */ |
280 | .align 32 |
281 | .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18 |
282 | .align 32 |
283 | .type __svml_dacos_data_internal, @object |
284 | .size __svml_dacos_data_internal, .-__svml_dacos_data_internal |
285 | |