1/* Function acos 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 * 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 16
33#define SmallNorm 32
34#define MOne 48
35#define Two 64
36#define sqrt_coeff 80
37#define poly_coeff 144
38#define PiH 336
39#define Pi2H 352
40
41#include <sysdep.h>
42
43 .section .text.sse4, "ax", @progbits
44ENTRY(_ZGVbN2v_acos_sse4)
45 subq $72, %rsp
46 cfi_def_cfa_offset(80)
47 movaps %xmm0, %xmm5
48 movups __svml_dacos_data_internal(%rip), %xmm3
49 movups OneHalf+__svml_dacos_data_internal(%rip), %xmm6
50
51 /* x = -|arg| */
52 movaps %xmm3, %xmm4
53 orps %xmm5, %xmm4
54
55 /* Y = 0.5 + 0.5*(-x) */
56 movaps %xmm6, %xmm7
57 mulpd %xmm4, %xmm7
58 addpd %xmm7, %xmm6
59
60 /* S ~ 2*sqrt(Y) */
61 cvtpd2ps %xmm6, %xmm9
62 movlhps %xmm9, %xmm9
63
64 /* x^2 */
65 movaps %xmm4, %xmm0
66 rsqrtps %xmm9, %xmm10
67 mulpd %xmm4, %xmm0
68 cvtps2pd %xmm10, %xmm11
69 minpd %xmm6, %xmm0
70 movaps %xmm6, %xmm1
71 movaps %xmm0, %xmm2
72 cmpltpd SmallNorm+__svml_dacos_data_internal(%rip), %xmm1
73 cmpnltpd %xmm6, %xmm2
74 addpd %xmm6, %xmm6
75 andnps %xmm11, %xmm1
76 movaps %xmm0, %xmm11
77 movaps %xmm1, %xmm12
78 andps %xmm5, %xmm3
79 mulpd %xmm1, %xmm12
80 mulpd %xmm6, %xmm1
81 mulpd %xmm12, %xmm6
82 mulpd %xmm0, %xmm11
83 subpd Two+__svml_dacos_data_internal(%rip), %xmm6
84 movups sqrt_coeff+__svml_dacos_data_internal(%rip), %xmm13
85 movaps %xmm6, %xmm14
86 mulpd %xmm6, %xmm13
87 mulpd %xmm1, %xmm14
88 addpd sqrt_coeff+16+__svml_dacos_data_internal(%rip), %xmm13
89 mulpd %xmm6, %xmm13
90 addpd sqrt_coeff+32+__svml_dacos_data_internal(%rip), %xmm13
91 mulpd %xmm13, %xmm6
92
93 /* polynomial */
94 movups poly_coeff+__svml_dacos_data_internal(%rip), %xmm15
95 movaps %xmm11, %xmm7
96 mulpd %xmm0, %xmm15
97 addpd sqrt_coeff+48+__svml_dacos_data_internal(%rip), %xmm6
98 addpd poly_coeff+16+__svml_dacos_data_internal(%rip), %xmm15
99 mulpd %xmm11, %xmm7
100 mulpd %xmm6, %xmm14
101 mulpd %xmm11, %xmm15
102 subpd %xmm14, %xmm1
103 movups MOne+__svml_dacos_data_internal(%rip), %xmm8
104 andps %xmm2, %xmm1
105
106 /* NaN processed in special branch (so wind test passed) */
107 cmpnlepd %xmm4, %xmm8
108 movmskpd %xmm8, %edx
109
110 /* X<X^2 iff X<0 */
111 movaps %xmm5, %xmm12
112 movups poly_coeff+32+__svml_dacos_data_internal(%rip), %xmm8
113 movaps %xmm2, %xmm13
114 movups poly_coeff+64+__svml_dacos_data_internal(%rip), %xmm6
115 mulpd %xmm0, %xmm8
116 mulpd %xmm0, %xmm6
117 addpd poly_coeff+48+__svml_dacos_data_internal(%rip), %xmm8
118 addpd poly_coeff+80+__svml_dacos_data_internal(%rip), %xmm6
119 cmpltpd %xmm0, %xmm12
120 addpd %xmm15, %xmm8
121 mulpd %xmm11, %xmm6
122 mulpd %xmm7, %xmm8
123 movups poly_coeff+96+__svml_dacos_data_internal(%rip), %xmm9
124 mulpd %xmm0, %xmm9
125 addpd poly_coeff+112+__svml_dacos_data_internal(%rip), %xmm9
126 addpd %xmm6, %xmm9
127 movups poly_coeff+128+__svml_dacos_data_internal(%rip), %xmm10
128 movaps %xmm2, %xmm6
129 mulpd %xmm0, %xmm10
130 addpd %xmm8, %xmm9
131 addpd poly_coeff+144+__svml_dacos_data_internal(%rip), %xmm10
132 mulpd %xmm11, %xmm9
133 movups poly_coeff+160+__svml_dacos_data_internal(%rip), %xmm14
134 andnps %xmm4, %xmm6
135 addpd %xmm9, %xmm10
136 mulpd %xmm0, %xmm14
137 mulpd %xmm10, %xmm11
138 addpd poly_coeff+176+__svml_dacos_data_internal(%rip), %xmm14
139 addpd %xmm11, %xmm14
140 mulpd %xmm0, %xmm14
141 orps %xmm1, %xmm6
142 pxor %xmm3, %xmm6
143 mulpd %xmm6, %xmm14
144 movups PiH+__svml_dacos_data_internal(%rip), %xmm0
145 andps %xmm2, %xmm0
146 andnps Pi2H+__svml_dacos_data_internal(%rip), %xmm13
147 andps %xmm12, %xmm0
148 addpd %xmm13, %xmm0
149 addpd %xmm14, %xmm6
150 addpd %xmm6, %xmm0
151 testl %edx, %edx
152
153 /* Go to special inputs processing branch */
154 jne L(SPECIAL_VALUES_BRANCH)
155 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm5
156
157 /* Restore registers
158 * and exit the function
159 */
160
161L(EXIT):
162 addq $72, %rsp
163 cfi_def_cfa_offset(8)
164 ret
165 cfi_def_cfa_offset(80)
166
167 /* Branch to process
168 * special inputs
169 */
170
171L(SPECIAL_VALUES_BRANCH):
172 movups %xmm5, 32(%rsp)
173 movups %xmm0, 48(%rsp)
174 # LOE rbx rbp r12 r13 r14 r15 edx
175
176 xorl %eax, %eax
177 movq %r12, 16(%rsp)
178 cfi_offset(12, -64)
179 movl %eax, %r12d
180 movq %r13, 8(%rsp)
181 cfi_offset(13, -72)
182 movl %edx, %r13d
183 movq %r14, (%rsp)
184 cfi_offset(14, -80)
185 # LOE rbx rbp r15 r12d r13d
186
187 /* Range mask
188 * bits check
189 */
190
191L(RANGEMASK_CHECK):
192 btl %r12d, %r13d
193
194 /* Call scalar math function */
195 jc L(SCALAR_MATH_CALL)
196 # LOE rbx rbp r15 r12d r13d
197
198 /* Special inputs
199 * processing loop
200 */
201
202L(SPECIAL_VALUES_LOOP):
203 incl %r12d
204 cmpl $2, %r12d
205
206 /* Check bits in range mask */
207 jl L(RANGEMASK_CHECK)
208 # LOE rbx rbp r15 r12d r13d
209
210 movq 16(%rsp), %r12
211 cfi_restore(12)
212 movq 8(%rsp), %r13
213 cfi_restore(13)
214 movq (%rsp), %r14
215 cfi_restore(14)
216 movups 48(%rsp), %xmm0
217
218 /* Go to exit */
219 jmp L(EXIT)
220 cfi_offset(12, -64)
221 cfi_offset(13, -72)
222 cfi_offset(14, -80)
223 # LOE rbx rbp r12 r13 r14 r15 xmm0
224
225 /* Scalar math function call
226 * to process special input
227 */
228
229L(SCALAR_MATH_CALL):
230 movl %r12d, %r14d
231 movsd 32(%rsp, %r14, 8), %xmm0
232 call acos@PLT
233 # LOE rbx rbp r14 r15 r12d r13d xmm0
234
235 movsd %xmm0, 48(%rsp, %r14, 8)
236
237 /* Process special inputs in loop */
238 jmp L(SPECIAL_VALUES_LOOP)
239 # LOE rbx rbp r15 r12d r13d
240END(_ZGVbN2v_acos_sse4)
241
242 .section .rodata, "a"
243 .align 16
244
245#ifdef __svml_dacos_data_internal_typedef
246typedef unsigned int VUINT32;
247typedef struct {
248 __declspec(align(16)) VUINT32 SgnBit[2][2];
249 __declspec(align(16)) VUINT32 OneHalf[2][2];
250 __declspec(align(16)) VUINT32 SmallNorm[2][2];
251 __declspec(align(16)) VUINT32 MOne[2][2];
252 __declspec(align(16)) VUINT32 Two[2][2];
253 __declspec(align(16)) VUINT32 sqrt_coeff[4][2][2];
254 __declspec(align(16)) VUINT32 poly_coeff[12][2][2];
255 __declspec(align(16)) VUINT32 PiH[2][2];
256 __declspec(align(16)) VUINT32 Pi2H[2][2];
257} __svml_dacos_data_internal;
258#endif
259__svml_dacos_data_internal:
260 /* SgnBit */
261 .quad 0x8000000000000000, 0x8000000000000000
262 /* OneHalf */
263 .align 16
264 .quad 0x3fe0000000000000, 0x3fe0000000000000
265 /* SmallNorm */
266 .align 16
267 .quad 0x3000000000000000, 0x3000000000000000
268 /* MOne */
269 .align 16
270 .quad 0xbff0000000000000, 0xbff0000000000000
271 /* Two */
272 .align 16
273 .quad 0x4000000000000000, 0x4000000000000000
274 /* sqrt_coeff[4] */
275 .align 16
276 .quad 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
277 .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
278 .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
279 .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
280 /* poly_coeff[12] */
281 .align 16
282 .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
283 .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
284 .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
285 .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
286 .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
287 .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
288 .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
289 .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
290 .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
291 .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
292 .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
293 .quad 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
294 /* PiH */
295 .align 16
296 .quad 0x400921fb54442d18, 0x400921fb54442d18
297 /* Pi2H */
298 .align 16
299 .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18
300 .align 16
301 .type __svml_dacos_data_internal, @object
302 .size __svml_dacos_data_internal, .-__svml_dacos_data_internal
303

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_d_acos2_core_sse4.S