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 |
42 | ENTRY(_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 | |
150 | L(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 | |
160 | L(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 | |
180 | L(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 | |
191 | L(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 | |
218 | L(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 |
229 | END(_ZGVbN2v_asin_sse4) |
230 | |
231 | .section .rodata, "a" |
232 | .align 16 |
233 | |
234 | #ifdef __svml_dasin_data_internal_typedef |
235 | typedef unsigned int VUINT32; |
236 | typedef 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 | |