1/* Function asin 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 * 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 16
32#define SmallNorm 32
33#define One 48
34#define Two 64
35#define sqrt_coeff 80
36#define poly_coeff 144
37#define Pi2H 336
38
39#include <sysdep.h>
40
41 .section .text.sse4, "ax", @progbits
42ENTRY(_ZGVbN2v_asin_sse4)
43 subq $72, %rsp
44 cfi_def_cfa_offset(80)
45 movaps %xmm0, %xmm5
46 movups __svml_dasin_data_internal(%rip), %xmm3
47 movups OneHalf+__svml_dasin_data_internal(%rip), %xmm8
48
49 /* x = |arg| */
50 movaps %xmm3, %xmm4
51 andps %xmm5, %xmm4
52
53 /* Y = 0.5 - 0.5*x */
54 movaps %xmm8, %xmm6
55 mulpd %xmm4, %xmm6
56 movaps %xmm8, %xmm14
57
58 /* x^2 */
59 movaps %xmm4, %xmm2
60 subpd %xmm6, %xmm14
61 mulpd %xmm4, %xmm2
62
63 /* S ~ -2*sqrt(Y) */
64 cvtpd2ps %xmm14, %xmm9
65 minpd %xmm14, %xmm2
66 movlhps %xmm9, %xmm9
67 movaps %xmm14, %xmm15
68 rsqrtps %xmm9, %xmm10
69 cmpltpd SmallNorm+__svml_dasin_data_internal(%rip), %xmm15
70 addpd %xmm14, %xmm14
71 cvtps2pd %xmm10, %xmm11
72 andnps %xmm11, %xmm15
73 movaps %xmm4, %xmm1
74 movaps %xmm15, %xmm12
75 andnps %xmm5, %xmm3
76 mulpd %xmm15, %xmm12
77 mulpd %xmm14, %xmm15
78 mulpd %xmm12, %xmm14
79 cmpnltpd %xmm8, %xmm1
80 subpd Two+__svml_dasin_data_internal(%rip), %xmm14
81
82 /* polynomial */
83 movups poly_coeff+__svml_dasin_data_internal(%rip), %xmm6
84 movaps %xmm2, %xmm12
85 mulpd %xmm2, %xmm6
86 mulpd %xmm2, %xmm12
87 addpd poly_coeff+16+__svml_dasin_data_internal(%rip), %xmm6
88 movups One+__svml_dasin_data_internal(%rip), %xmm7
89 movaps %xmm12, %xmm8
90 cmpltpd %xmm4, %xmm7
91 mulpd %xmm12, %xmm6
92 movmskpd %xmm7, %edx
93 movups poly_coeff+32+__svml_dasin_data_internal(%rip), %xmm9
94 movaps %xmm14, %xmm0
95 movups poly_coeff+64+__svml_dasin_data_internal(%rip), %xmm7
96 mulpd %xmm2, %xmm9
97 mulpd %xmm2, %xmm7
98 addpd poly_coeff+48+__svml_dasin_data_internal(%rip), %xmm9
99 addpd poly_coeff+80+__svml_dasin_data_internal(%rip), %xmm7
100 mulpd %xmm12, %xmm8
101 mulpd %xmm12, %xmm7
102 addpd %xmm6, %xmm9
103 mulpd %xmm15, %xmm0
104 mulpd %xmm8, %xmm9
105 movups poly_coeff+96+__svml_dasin_data_internal(%rip), %xmm10
106 mulpd %xmm2, %xmm10
107 movups sqrt_coeff+__svml_dasin_data_internal(%rip), %xmm13
108 mulpd %xmm14, %xmm13
109 addpd poly_coeff+112+__svml_dasin_data_internal(%rip), %xmm10
110 addpd sqrt_coeff+16+__svml_dasin_data_internal(%rip), %xmm13
111 addpd %xmm7, %xmm10
112 mulpd %xmm14, %xmm13
113 addpd %xmm9, %xmm10
114 addpd sqrt_coeff+32+__svml_dasin_data_internal(%rip), %xmm13
115 mulpd %xmm12, %xmm10
116 mulpd %xmm13, %xmm14
117 movups poly_coeff+128+__svml_dasin_data_internal(%rip), %xmm11
118 mulpd %xmm2, %xmm11
119 addpd sqrt_coeff+48+__svml_dasin_data_internal(%rip), %xmm14
120 addpd poly_coeff+144+__svml_dasin_data_internal(%rip), %xmm11
121 mulpd %xmm14, %xmm0
122 addpd %xmm10, %xmm11
123 subpd %xmm15, %xmm0
124 mulpd %xmm11, %xmm12
125 movups poly_coeff+160+__svml_dasin_data_internal(%rip), %xmm13
126 movaps %xmm1, %xmm14
127 mulpd %xmm2, %xmm13
128 addpd poly_coeff+176+__svml_dasin_data_internal(%rip), %xmm13
129 addpd %xmm12, %xmm13
130 mulpd %xmm13, %xmm2
131 andnps %xmm4, %xmm14
132 andps %xmm1, %xmm0
133 orps %xmm0, %xmm14
134 mulpd %xmm14, %xmm2
135 addpd %xmm2, %xmm14
136 movups Pi2H+__svml_dasin_data_internal(%rip), %xmm0
137 andps %xmm1, %xmm0
138 addpd %xmm14, %xmm0
139 pxor %xmm3, %xmm0
140 testl %edx, %edx
141
142 /* Go to special inputs processing branch */
143 jne L(SPECIAL_VALUES_BRANCH)
144 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm5
145
146 /* Restore registers
147 * and exit the function
148 */
149
150L(EXIT):
151 addq $72, %rsp
152 cfi_def_cfa_offset(8)
153 ret
154 cfi_def_cfa_offset(80)
155
156 /* Branch to process
157 * special inputs
158 */
159
160L(SPECIAL_VALUES_BRANCH):
161 movups %xmm5, 32(%rsp)
162 movups %xmm0, 48(%rsp)
163 # LOE rbx rbp r12 r13 r14 r15 edx
164
165 xorl %eax, %eax
166 movq %r12, 16(%rsp)
167 cfi_offset(12, -64)
168 movl %eax, %r12d
169 movq %r13, 8(%rsp)
170 cfi_offset(13, -72)
171 movl %edx, %r13d
172 movq %r14, (%rsp)
173 cfi_offset(14, -80)
174 # LOE rbx rbp r15 r12d r13d
175
176 /* Range mask
177 * bits check
178 */
179
180L(RANGEMASK_CHECK):
181 btl %r12d, %r13d
182
183 /* Call scalar math function */
184 jc L(SCALAR_MATH_CALL)
185 # LOE rbx rbp r15 r12d r13d
186
187 /* Special inputs
188 * processing loop
189 */
190
191L(SPECIAL_VALUES_LOOP):
192 incl %r12d
193 cmpl $2, %r12d
194
195 /* Check bits in range mask */
196 jl L(RANGEMASK_CHECK)
197 # LOE rbx rbp r15 r12d r13d
198
199 movq 16(%rsp), %r12
200 cfi_restore(12)
201 movq 8(%rsp), %r13
202 cfi_restore(13)
203 movq (%rsp), %r14
204 cfi_restore(14)
205 movups 48(%rsp), %xmm0
206
207 /* Go to exit */
208 jmp L(EXIT)
209 cfi_offset(12, -64)
210 cfi_offset(13, -72)
211 cfi_offset(14, -80)
212 # LOE rbx rbp r12 r13 r14 r15 xmm0
213
214 /* Scalar math function call
215 * to process special input
216 */
217
218L(SCALAR_MATH_CALL):
219 movl %r12d, %r14d
220 movsd 32(%rsp, %r14, 8), %xmm0
221 call asin@PLT
222 # LOE rbx rbp r14 r15 r12d r13d xmm0
223
224 movsd %xmm0, 48(%rsp, %r14, 8)
225
226 /* Process special inputs in loop */
227 jmp L(SPECIAL_VALUES_LOOP)
228 # LOE rbx rbp r15 r12d r13d
229END(_ZGVbN2v_asin_sse4)
230
231 .section .rodata, "a"
232 .align 16
233
234#ifdef __svml_dasin_data_internal_typedef
235typedef unsigned int VUINT32;
236typedef struct {
237 __declspec(align(16)) VUINT32 AbsMask[2][2];
238 __declspec(align(16)) VUINT32 OneHalf[2][2];
239 __declspec(align(16)) VUINT32 SmallNorm[2][2];
240 __declspec(align(16)) VUINT32 One[2][2];
241 __declspec(align(16)) VUINT32 Two[2][2];
242 __declspec(align(16)) VUINT32 sqrt_coeff[4][2][2];
243 __declspec(align(16)) VUINT32 poly_coeff[12][2][2];
244 __declspec(align(16)) VUINT32 Pi2H[2][2];
245} __svml_dasin_data_internal;
246#endif
247__svml_dasin_data_internal:
248 /* AbsMask */
249 .quad 0x7fffffffffffffff, 0x7fffffffffffffff
250 /* OneHalf */
251 .align 16
252 .quad 0x3fe0000000000000, 0x3fe0000000000000
253 /* SmallNorm */
254 .align 16
255 .quad 0x3000000000000000, 0x3000000000000000
256 /* One */
257 .align 16
258 .quad 0x3ff0000000000000, 0x3ff0000000000000
259 /* Two */
260 .align 16
261 .quad 0x4000000000000000, 0x4000000000000000
262 /* sqrt_coeff[4] */
263 .align 16
264 .quad 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
265 .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
266 .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
267 .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
268 /* poly_coeff[12] */
269 .align 16
270 .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
271 .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
272 .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
273 .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
274 .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
275 .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
276 .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
277 .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
278 .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
279 .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
280 .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
281 .quad 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
282 /* Pi2H */
283 .align 16
284 .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18
285 .align 16
286 .type __svml_dasin_data_internal, @object
287 .size __svml_dasin_data_internal, .-__svml_dasin_data_internal
288

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_d_asin2_core_sse4.S