1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
|
/* Function asinf vectorized with AVX2.
Copyright (C) 2021-2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
https://www.gnu.org/licenses/. */
/*
* ALGORITHM DESCRIPTION:
*
* SelMask = (|x| >= 0.5) ? 1 : 0;
* R = SelMask ? sqrt(0.5 - 0.5*|x|) : |x|
* asin(x) = (SelMask ? (Pi/2 - 2*Poly(R)) : Poly(R))*(-1)^sign(x)
*
*
*/
/* Offsets for data table __svml_sasin_data_internal
*/
#define AbsMask 0
#define OneHalf 32
#define SmallNorm 64
#define One 96
#define Two 128
#define sqrt_coeff 160
#define poly_coeff 224
#define Pi2H 384
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_asinf_avx2)
pushq %rbp
cfi_def_cfa_offset(16)
movq %rsp, %rbp
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
andq $-32, %rsp
subq $96, %rsp
vmovups __svml_sasin_data_internal(%rip), %ymm5
vmovups OneHalf+__svml_sasin_data_internal(%rip), %ymm9
vmovups One+__svml_sasin_data_internal(%rip), %ymm6
vmovaps %ymm0, %ymm4
/* x = |arg| */
vandps %ymm4, %ymm5, %ymm3
/* Y = 0.5 - 0.5*x */
vmovaps %ymm9, %ymm12
vfnmadd231ps %ymm3, %ymm9, %ymm12
/* x^2 */
vmulps %ymm3, %ymm3, %ymm7
vcmplt_oqps %ymm3, %ymm6, %ymm8
/* SQ ~ -2*sqrt(Y) */
vcmplt_oqps SmallNorm+__svml_sasin_data_internal(%rip), %ymm12, %ymm10
vminps %ymm12, %ymm7, %ymm1
vaddps %ymm12, %ymm12, %ymm15
vcmpnlt_uqps %ymm9, %ymm3, %ymm0
vrsqrtps %ymm12, %ymm11
vmovups poly_coeff+64+__svml_sasin_data_internal(%rip), %ymm7
vmulps %ymm1, %ymm1, %ymm6
vmovups sqrt_coeff+__svml_sasin_data_internal(%rip), %ymm9
vfmadd213ps poly_coeff+96+__svml_sasin_data_internal(%rip), %ymm1, %ymm7
vmovmskps %ymm8, %edx
/* polynomial */
vmovups poly_coeff+__svml_sasin_data_internal(%rip), %ymm8
vandnps %ymm11, %ymm10, %ymm13
vmulps %ymm13, %ymm13, %ymm14
vfmadd213ps poly_coeff+32+__svml_sasin_data_internal(%rip), %ymm1, %ymm8
vandnps %ymm4, %ymm5, %ymm2
vmulps %ymm15, %ymm13, %ymm5
vfmsub213ps Two+__svml_sasin_data_internal(%rip), %ymm14, %ymm15
vfmadd213ps %ymm7, %ymm6, %ymm8
vfmadd213ps sqrt_coeff+32+__svml_sasin_data_internal(%rip), %ymm15, %ymm9
vmulps %ymm15, %ymm5, %ymm15
vfmadd213ps poly_coeff+128+__svml_sasin_data_internal(%rip), %ymm1, %ymm8
vfmsub213ps %ymm5, %ymm15, %ymm9
vmulps %ymm8, %ymm1, %ymm1
vblendvps %ymm0, %ymm9, %ymm3, %ymm3
vfmadd213ps %ymm3, %ymm3, %ymm1
vandps Pi2H+__svml_sasin_data_internal(%rip), %ymm0, %ymm0
vaddps %ymm1, %ymm0, %ymm10
vxorps %ymm2, %ymm10, %ymm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm4
/* Restore registers
* and exit the function
*/
L(EXIT):
movq %rbp, %rsp
popq %rbp
cfi_def_cfa(7, 8)
cfi_restore(6)
ret
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
/* Branch to process
* special inputs
*/
L(SPECIAL_VALUES_BRANCH):
vmovups %ymm4, 32(%rsp)
vmovups %ymm0, 64(%rsp)
# LOE rbx r12 r13 r14 r15 edx ymm0
xorl %eax, %eax
# LOE rbx r12 r13 r14 r15 eax edx
vzeroupper
movq %r12, 16(%rsp)
/* 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) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
movl %eax, %r12d
movq %r13, 8(%rsp)
/* 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) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
movl %edx, %r13d
movq %r14, (%rsp)
/* 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) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
# LOE rbx r15 r12d r13d
/* Range mask
* bits check
*/
L(RANGEMASK_CHECK):
btl %r12d, %r13d
/* Call scalar math function */
jc L(SCALAR_MATH_CALL)
# LOE rbx r15 r12d r13d
/* Special inputs
* processing loop
*/
L(SPECIAL_VALUES_LOOP):
incl %r12d
cmpl $8, %r12d
/* Check bits in range mask */
jl L(RANGEMASK_CHECK)
# LOE rbx r15 r12d r13d
movq 16(%rsp), %r12
cfi_restore(12)
movq 8(%rsp), %r13
cfi_restore(13)
movq (%rsp), %r14
cfi_restore(14)
vmovups 64(%rsp), %ymm0
/* Go to exit */
jmp L(EXIT)
/* 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) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
/* 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) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
/* 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) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
# LOE rbx r12 r13 r14 r15 ymm0
/* Scalar math function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovss 32(%rsp, %r14, 4), %xmm0
call asinf@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovss %xmm0, 64(%rsp, %r14, 4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVdN8v_asinf_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_sasin_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(32)) VUINT32 AbsMask[8][1];
__declspec(align(32)) VUINT32 OneHalf[8][1];
__declspec(align(32)) VUINT32 SmallNorm[8][1];
__declspec(align(32)) VUINT32 One[8][1];
__declspec(align(32)) VUINT32 Two[8][1];
__declspec(align(32)) VUINT32 sqrt_coeff[2][8][1];
__declspec(align(32)) VUINT32 poly_coeff[5][8][1];
__declspec(align(32)) VUINT32 Pi2H[8][1];
} __svml_sasin_data_internal;
#endif
__svml_sasin_data_internal:
/* AbsMask */
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
/* OneHalf */
.align 32
.long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000
/* SmallNorm */
.align 32
.long 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000
/* One */
.align 32
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/* Two */
.align 32
.long 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000
/* sqrt_coeff[2] */
.align 32
.long 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004 /* sqrt_coeff2 */
.long 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001 /* sqrt_coeff1 */
/* poly_coeff[5] */
.align 32
.long 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07 /* poly_coeff5 */
.long 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B /* poly_coeff4 */
.long 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4 /* poly_coeff3 */
.long 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12 /* poly_coeff2 */
.long 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF /* poly_coeff1 */
/* Pi2H */
.align 32
.long 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB
.align 32
.type __svml_sasin_data_internal, @object
.size __svml_sasin_data_internal, .-__svml_sasin_data_internal
|