1/* Function acosf 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
30/* Offsets for data table __svml_sacos_data_internal
31 */
32#define SgnBit 0
33#define OneHalf 16
34#define SmallNorm 32
35#define MOne 48
36#define Two 64
37#define sqrt_coeff 80
38#define poly_coeff 112
39#define Pi2H 192
40#define PiH 208
41
42#include <sysdep.h>
43
44 .section .text.sse4, "ax", @progbits
45ENTRY(_ZGVbN4v_acosf_sse4)
46 subq $72, %rsp
47 cfi_def_cfa_offset(80)
48
49 /* X<X^2 iff X<0 */
50 movaps %xmm0, %xmm14
51
52 /*
53 * 2*sqrt(X) ~ Sh - Sl (to 24+ bits)
54 * SQ ~ 2*sqrt(X)
55 */
56 movups __svml_sacos_data_internal(%rip), %xmm3
57 movups OneHalf+__svml_sacos_data_internal(%rip), %xmm5
58
59 /* x = -|arg| */
60 movaps %xmm3, %xmm4
61 orps %xmm0, %xmm4
62
63 /* Y = 0.5 + 0.5*(-x) */
64 movaps %xmm5, %xmm6
65 mulps %xmm4, %xmm6
66
67 /* x^2 */
68 movaps %xmm4, %xmm13
69 mulps %xmm4, %xmm13
70 addps %xmm6, %xmm5
71
72 /* SQ ~ 2*sqrt(Y) */
73 rsqrtps %xmm5, %xmm8
74 minps %xmm5, %xmm13
75 movaps %xmm5, %xmm2
76 movaps %xmm13, %xmm1
77 cmpltps SmallNorm+__svml_sacos_data_internal(%rip), %xmm2
78 cmpnltps %xmm5, %xmm1
79 cmpltps %xmm13, %xmm14
80 addps %xmm5, %xmm5
81 andnps %xmm8, %xmm2
82 movaps %xmm13, %xmm11
83 movaps %xmm2, %xmm9
84 movaps %xmm1, %xmm6
85 mulps %xmm2, %xmm9
86 andnps %xmm4, %xmm6
87 mulps %xmm5, %xmm2
88 mulps %xmm13, %xmm11
89 mulps %xmm9, %xmm5
90 movups sqrt_coeff+__svml_sacos_data_internal(%rip), %xmm10
91 andps %xmm0, %xmm3
92
93 /* polynomial */
94 movups poly_coeff+__svml_sacos_data_internal(%rip), %xmm12
95 movaps %xmm1, %xmm15
96 mulps %xmm13, %xmm12
97 subps Two+__svml_sacos_data_internal(%rip), %xmm5
98 mulps %xmm5, %xmm10
99 addps poly_coeff+16+__svml_sacos_data_internal(%rip), %xmm12
100 mulps %xmm2, %xmm5
101 mulps %xmm11, %xmm12
102 addps sqrt_coeff+16+__svml_sacos_data_internal(%rip), %xmm10
103 mulps %xmm5, %xmm10
104 movups poly_coeff+32+__svml_sacos_data_internal(%rip), %xmm5
105 subps %xmm10, %xmm2
106 mulps %xmm13, %xmm5
107 movups MOne+__svml_sacos_data_internal(%rip), %xmm7
108 andps %xmm1, %xmm2
109 cmpnleps %xmm4, %xmm7
110 addps poly_coeff+48+__svml_sacos_data_internal(%rip), %xmm5
111 movmskps %xmm7, %edx
112 orps %xmm2, %xmm6
113 addps %xmm12, %xmm5
114 mulps %xmm13, %xmm5
115 pxor %xmm3, %xmm6
116 movups PiH+__svml_sacos_data_internal(%rip), %xmm7
117 andps %xmm1, %xmm7
118 addps poly_coeff+64+__svml_sacos_data_internal(%rip), %xmm5
119 mulps %xmm13, %xmm5
120 andps %xmm14, %xmm7
121 mulps %xmm6, %xmm5
122 andnps Pi2H+__svml_sacos_data_internal(%rip), %xmm15
123 addps %xmm5, %xmm6
124 addps %xmm15, %xmm7
125 addps %xmm6, %xmm7
126 testl %edx, %edx
127
128 /* Go to special inputs processing branch */
129 jne L(SPECIAL_VALUES_BRANCH)
130 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm7
131
132 /* Restore registers
133 * and exit the function
134 */
135
136L(EXIT):
137 movaps %xmm7, %xmm0
138 addq $72, %rsp
139 cfi_def_cfa_offset(8)
140 ret
141 cfi_def_cfa_offset(80)
142
143 /* Branch to process
144 * special inputs
145 */
146
147L(SPECIAL_VALUES_BRANCH):
148 movups %xmm0, 32(%rsp)
149 movups %xmm7, 48(%rsp)
150 # LOE rbx rbp r12 r13 r14 r15 edx
151
152 xorl %eax, %eax
153 movq %r12, 16(%rsp)
154 cfi_offset(12, -64)
155 movl %eax, %r12d
156 movq %r13, 8(%rsp)
157 cfi_offset(13, -72)
158 movl %edx, %r13d
159 movq %r14, (%rsp)
160 cfi_offset(14, -80)
161 # LOE rbx rbp r15 r12d r13d
162
163 /* Range mask
164 * bits check
165 */
166
167L(RANGEMASK_CHECK):
168 btl %r12d, %r13d
169
170 /* Call scalar math function */
171 jc L(SCALAR_MATH_CALL)
172 # LOE rbx rbp r15 r12d r13d
173
174 /* Special inputs
175 * processing loop
176 */
177
178L(SPECIAL_VALUES_LOOP):
179 incl %r12d
180 cmpl $4, %r12d
181
182 /* Check bits in range mask */
183 jl L(RANGEMASK_CHECK)
184 # LOE rbx rbp r15 r12d r13d
185
186 movq 16(%rsp), %r12
187 cfi_restore(12)
188 movq 8(%rsp), %r13
189 cfi_restore(13)
190 movq (%rsp), %r14
191 cfi_restore(14)
192 movups 48(%rsp), %xmm7
193
194 /* Go to exit */
195 jmp L(EXIT)
196 cfi_offset(12, -64)
197 cfi_offset(13, -72)
198 cfi_offset(14, -80)
199 # LOE rbx rbp r12 r13 r14 r15 xmm7
200
201 /* Scalar math function call
202 * to process special input
203 */
204
205L(SCALAR_MATH_CALL):
206 movl %r12d, %r14d
207 movss 32(%rsp, %r14, 4), %xmm0
208 call acosf@PLT
209 # LOE rbx rbp r14 r15 r12d r13d xmm0
210
211 movss %xmm0, 48(%rsp, %r14, 4)
212
213 /* Process special inputs in loop */
214 jmp L(SPECIAL_VALUES_LOOP)
215 # LOE rbx rbp r15 r12d r13d
216END(_ZGVbN4v_acosf_sse4)
217
218 .section .rodata, "a"
219 .align 16
220
221#ifdef __svml_sacos_data_internal_typedef
222typedef unsigned int VUINT32;
223typedef struct {
224 __declspec(align(16)) VUINT32 SgnBit[4][1];
225 __declspec(align(16)) VUINT32 OneHalf[4][1];
226 __declspec(align(16)) VUINT32 SmallNorm[4][1];
227 __declspec(align(16)) VUINT32 MOne[4][1];
228 __declspec(align(16)) VUINT32 Two[4][1];
229 __declspec(align(16)) VUINT32 sqrt_coeff[2][4][1];
230 __declspec(align(16)) VUINT32 poly_coeff[5][4][1];
231 __declspec(align(16)) VUINT32 Pi2H[4][1];
232 __declspec(align(16)) VUINT32 PiH[4][1];
233} __svml_sacos_data_internal;
234#endif
235__svml_sacos_data_internal:
236 /* SgnBit */
237 .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
238 /* OneHalf */
239 .align 16
240 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000
241 /* SmallNorm */
242 .align 16
243 .long 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000
244 /* MOne */
245 .align 16
246 .long 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000
247 /* Two */
248 .align 16
249 .long 0x40000000, 0x40000000, 0x40000000, 0x40000000
250 /* sqrt_coeff[2] */
251 .align 16
252 .long 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004 /* sqrt_coeff2 */
253 .long 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001 /* sqrt_coeff1 */
254 /* poly_coeff[5] */
255 .align 16
256 .long 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07 /* poly_coeff5 */
257 .long 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B /* poly_coeff4 */
258 .long 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4 /* poly_coeff3 */
259 .long 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12 /* poly_coeff2 */
260 .long 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF /* poly_coeff1 */
261 /* Pi2H */
262 .align 16
263 .long 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB
264 /* PiH */
265 .align 16
266 .long 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB
267 .align 16
268 .type __svml_sacos_data_internal, @object
269 .size __svml_sacos_data_internal, .-__svml_sacos_data_internal
270

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_acosf4_core_sse4.S