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
44ENTRY(_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
131L(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
144L(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
170L(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
181L(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
211L(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
222END(_ZGVdN4v_acos_avx2)
223
224 .section .rodata, "a"
225 .align 32
226
227#ifdef __svml_dacos_data_internal_typedef
228typedef unsigned int VUINT32;
229typedef 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

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_d_acos4_core_avx2.S