1/* Function asin 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 * asin(x) = (SelMask ? (Pi/2 - 2*Poly(R)) : Poly(R))*(-1)^sign(x)
25 *
26 */
27
28/* Offsets for data table __svml_dasin_data_internal
29 */
30#define AbsMask 0
31#define OneHalf 32
32#define SmallNorm 64
33#define One 96
34#define Two 128
35#define sqrt_coeff 160
36#define poly_coeff 288
37#define Pi2H 672
38
39#include <sysdep.h>
40
41 .section .text.avx2, "ax", @progbits
42ENTRY(_ZGVdN4v_asin_avx2)
43 pushq %rbp
44 cfi_def_cfa_offset(16)
45 movq %rsp, %rbp
46 cfi_def_cfa(6, 16)
47 cfi_offset(6, -16)
48 andq $-32, %rsp
49 subq $96, %rsp
50 vmovupd __svml_dasin_data_internal(%rip), %ymm6
51 vmovupd OneHalf+__svml_dasin_data_internal(%rip), %ymm10
52 vmovupd One+__svml_dasin_data_internal(%rip), %ymm8
53 vmovapd %ymm0, %ymm5
54
55 /* x = |arg| */
56 vandpd %ymm5, %ymm6, %ymm4
57
58 /* Y = 0.5 - 0.5*x */
59 vmovapd %ymm10, %ymm15
60 vfnmadd231pd %ymm4, %ymm10, %ymm15
61
62 /* x^2 */
63 vmulpd %ymm4, %ymm4, %ymm7
64 vcmplt_oqpd %ymm4, %ymm8, %ymm9
65
66 /* S ~ -2*sqrt(Y) */
67 vcmplt_oqpd SmallNorm+__svml_dasin_data_internal(%rip), %ymm15, %ymm13
68 vminpd %ymm15, %ymm7, %ymm2
69 vaddpd %ymm15, %ymm15, %ymm7
70 vcmpnlt_uqpd %ymm10, %ymm4, %ymm1
71 vcvtpd2ps %ymm15, %xmm11
72 vmovupd poly_coeff+64+__svml_dasin_data_internal(%rip), %ymm10
73 vmulpd %ymm2, %ymm2, %ymm15
74 vrsqrtps %xmm11, %xmm12
75 vmovupd poly_coeff+192+__svml_dasin_data_internal(%rip), %ymm11
76 vfmadd213pd poly_coeff+96+__svml_dasin_data_internal(%rip), %ymm2, %ymm10
77 vcvtps2pd %xmm12, %ymm14
78 vmulpd %ymm15, %ymm15, %ymm12
79 vfmadd213pd poly_coeff+224+__svml_dasin_data_internal(%rip), %ymm2, %ymm11
80 vandnpd %ymm14, %ymm13, %ymm0
81 vandnpd %ymm5, %ymm6, %ymm3
82 vmulpd %ymm0, %ymm0, %ymm6
83 vmovupd poly_coeff+128+__svml_dasin_data_internal(%rip), %ymm13
84 vmovupd poly_coeff+256+__svml_dasin_data_internal(%rip), %ymm14
85 vfmadd213pd poly_coeff+160+__svml_dasin_data_internal(%rip), %ymm2, %ymm13
86 vfmadd213pd poly_coeff+288+__svml_dasin_data_internal(%rip), %ymm2, %ymm14
87 vfmadd213pd %ymm11, %ymm15, %ymm13
88 vmovmskpd %ymm9, %edx
89 vmulpd %ymm7, %ymm0, %ymm9
90 vfmsub213pd Two+__svml_dasin_data_internal(%rip), %ymm6, %ymm7
91
92 /* polynomial */
93 vmovupd poly_coeff+__svml_dasin_data_internal(%rip), %ymm6
94 vmovupd sqrt_coeff+__svml_dasin_data_internal(%rip), %ymm0
95 vmulpd %ymm7, %ymm9, %ymm8
96 vfmadd213pd poly_coeff+32+__svml_dasin_data_internal(%rip), %ymm2, %ymm6
97 vfmadd213pd sqrt_coeff+32+__svml_dasin_data_internal(%rip), %ymm7, %ymm0
98 vfmadd213pd %ymm10, %ymm15, %ymm6
99 vmovupd poly_coeff+320+__svml_dasin_data_internal(%rip), %ymm10
100 vfmadd213pd sqrt_coeff+64+__svml_dasin_data_internal(%rip), %ymm7, %ymm0
101 vfmadd213pd %ymm13, %ymm12, %ymm6
102 vfmadd213pd poly_coeff+352+__svml_dasin_data_internal(%rip), %ymm2, %ymm10
103 vfmadd213pd sqrt_coeff+96+__svml_dasin_data_internal(%rip), %ymm7, %ymm0
104 vfmadd213pd %ymm14, %ymm15, %ymm6
105 vfmsub213pd %ymm9, %ymm8, %ymm0
106 vfmadd213pd %ymm10, %ymm15, %ymm6
107 vblendvpd %ymm1, %ymm0, %ymm4, %ymm4
108 vmulpd %ymm6, %ymm2, %ymm2
109 vfmadd213pd %ymm4, %ymm4, %ymm2
110 vandpd Pi2H+__svml_dasin_data_internal(%rip), %ymm1, %ymm1
111 vaddpd %ymm2, %ymm1, %ymm0
112 vxorpd %ymm3, %ymm0, %ymm0
113 testl %edx, %edx
114
115 /* Go to special inputs processing branch */
116 jne L(SPECIAL_VALUES_BRANCH)
117 # LOE rbx r12 r13 r14 r15 edx ymm0 ymm5
118
119 /* Restore registers
120 * and exit the function
121 */
122
123L(EXIT):
124 movq %rbp, %rsp
125 popq %rbp
126 cfi_def_cfa(7, 8)
127 cfi_restore(6)
128 ret
129 cfi_def_cfa(6, 16)
130 cfi_offset(6, -16)
131
132 /* Branch to process
133 * special inputs
134 */
135
136L(SPECIAL_VALUES_BRANCH):
137 vmovupd %ymm5, 32(%rsp)
138 vmovupd %ymm0, 64(%rsp)
139 # LOE rbx r12 r13 r14 r15 edx ymm0
140
141 xorl %eax, %eax
142 # LOE rbx r12 r13 r14 r15 eax edx
143
144 vzeroupper
145 movq %r12, 16(%rsp)
146 /* 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) */
147 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
148 movl %eax, %r12d
149 movq %r13, 8(%rsp)
150 /* 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) */
151 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
152 movl %edx, %r13d
153 movq %r14, (%rsp)
154 /* 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) */
155 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
156 # LOE rbx r15 r12d r13d
157
158 /* Range mask
159 * bits check
160 */
161
162L(RANGEMASK_CHECK):
163 btl %r12d, %r13d
164
165 /* Call scalar math function */
166 jc L(SCALAR_MATH_CALL)
167 # LOE rbx r15 r12d r13d
168
169 /* Special inputs
170 * processing loop
171 */
172
173L(SPECIAL_VALUES_LOOP):
174 incl %r12d
175 cmpl $4, %r12d
176
177 /* Check bits in range mask */
178 jl L(RANGEMASK_CHECK)
179 # LOE rbx r15 r12d r13d
180
181 movq 16(%rsp), %r12
182 cfi_restore(12)
183 movq 8(%rsp), %r13
184 cfi_restore(13)
185 movq (%rsp), %r14
186 cfi_restore(14)
187 vmovupd 64(%rsp), %ymm0
188
189 /* Go to exit */
190 jmp L(EXIT)
191 /* 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) */
192 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
193 /* 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) */
194 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
195 /* 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) */
196 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
197 # LOE rbx r12 r13 r14 r15 ymm0
198
199 /* Scalar math function call
200 * to process special input
201 */
202
203L(SCALAR_MATH_CALL):
204 movl %r12d, %r14d
205 vmovsd 32(%rsp, %r14, 8), %xmm0
206 call asin@PLT
207 # LOE rbx r14 r15 r12d r13d xmm0
208
209 vmovsd %xmm0, 64(%rsp, %r14, 8)
210
211 /* Process special inputs in loop */
212 jmp L(SPECIAL_VALUES_LOOP)
213 # LOE rbx r15 r12d r13d
214END(_ZGVdN4v_asin_avx2)
215
216 .section .rodata, "a"
217 .align 32
218
219#ifdef __svml_dasin_data_internal_typedef
220typedef unsigned int VUINT32;
221typedef struct {
222 __declspec(align(32)) VUINT32 AbsMask[4][2];
223 __declspec(align(32)) VUINT32 OneHalf[4][2];
224 __declspec(align(32)) VUINT32 SmallNorm[4][2];
225 __declspec(align(32)) VUINT32 One[4][2];
226 __declspec(align(32)) VUINT32 Two[4][2];
227 __declspec(align(32)) VUINT32 sqrt_coeff[4][4][2];
228 __declspec(align(32)) VUINT32 poly_coeff[12][4][2];
229 __declspec(align(32)) VUINT32 Pi2H[4][2];
230} __svml_dasin_data_internal;
231#endif
232__svml_dasin_data_internal:
233 /* AbsMask */
234 .quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff
235 /* OneHalf */
236 .align 32
237 .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
238 /* SmallNorm */
239 .align 32
240 .quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000
241 /* One */
242 .align 32
243 .quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
244 /* Two */
245 .align 32
246 .quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000
247 /* sqrt_coeff[4] */
248 .align 32
249 .quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
250 .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
251 .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
252 .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
253 /* poly_coeff[12] */
254 .align 32
255 .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
256 .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
257 .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
258 .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
259 .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
260 .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
261 .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
262 .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
263 .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
264 .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
265 .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
266 .quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
267 /* Pi2H */
268 .align 32
269 .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18
270 .align 32
271 .type __svml_dasin_data_internal, @object
272 .size __svml_dasin_data_internal, .-__svml_dasin_data_internal
273

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_d_asin4_core_avx2.S