1 | /* Function acosf vectorized with AVX2. |
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 32 |
34 | #define SmallNorm 64 |
35 | #define MOne 96 |
36 | #define Two 128 |
37 | #define sqrt_coeff 160 |
38 | #define poly_coeff 224 |
39 | #define Pi2H 384 |
40 | #define PiH 416 |
41 | |
42 | #include <sysdep.h> |
43 | |
44 | .section .text.avx2, "ax" , @progbits |
45 | ENTRY(_ZGVdN8v_acosf_avx2) |
46 | pushq %rbp |
47 | cfi_def_cfa_offset(16) |
48 | movq %rsp, %rbp |
49 | cfi_def_cfa(6, 16) |
50 | cfi_offset(6, -16) |
51 | andq $-32, %rsp |
52 | subq $96, %rsp |
53 | |
54 | /* |
55 | * 2*sqrt(X) ~ Sh - Sl (to 24+ bits) |
56 | * SQ ~ 2*sqrt(X) |
57 | */ |
58 | vmovups __svml_sacos_data_internal(%rip), %ymm6 |
59 | vmovups OneHalf+__svml_sacos_data_internal(%rip), %ymm7 |
60 | vmovaps %ymm0, %ymm5 |
61 | |
62 | /* x = -|arg| */ |
63 | vorps %ymm5, %ymm6, %ymm4 |
64 | |
65 | /* Y = 0.5 + 0.5*(-x) */ |
66 | vfmadd231ps %ymm4, %ymm7, %ymm7 |
67 | |
68 | /* x^2 */ |
69 | vmulps %ymm4, %ymm4, %ymm8 |
70 | |
71 | /* SQ ~ 2*sqrt(Y) */ |
72 | vmovups sqrt_coeff+__svml_sacos_data_internal(%rip), %ymm0 |
73 | vcmpnge_uqps MOne+__svml_sacos_data_internal(%rip), %ymm4, %ymm9 |
74 | vcmplt_oqps SmallNorm+__svml_sacos_data_internal(%rip), %ymm7, %ymm10 |
75 | vminps %ymm7, %ymm8, %ymm2 |
76 | vaddps %ymm7, %ymm7, %ymm14 |
77 | vrsqrtps %ymm7, %ymm11 |
78 | vmovups poly_coeff+64+__svml_sacos_data_internal(%rip), %ymm8 |
79 | vcmpnlt_uqps %ymm7, %ymm2, %ymm1 |
80 | vmulps %ymm2, %ymm2, %ymm7 |
81 | vfmadd213ps poly_coeff+96+__svml_sacos_data_internal(%rip), %ymm2, %ymm8 |
82 | vmovmskps %ymm9, %edx |
83 | |
84 | /* polynomial */ |
85 | vmovups poly_coeff+__svml_sacos_data_internal(%rip), %ymm9 |
86 | vandnps %ymm11, %ymm10, %ymm12 |
87 | vmulps %ymm12, %ymm12, %ymm13 |
88 | vfmadd213ps poly_coeff+32+__svml_sacos_data_internal(%rip), %ymm2, %ymm9 |
89 | |
90 | /* X<X^2 iff X<0 */ |
91 | vcmplt_oqps %ymm2, %ymm5, %ymm10 |
92 | vfmadd213ps %ymm8, %ymm7, %ymm9 |
93 | vandps %ymm5, %ymm6, %ymm3 |
94 | vmulps %ymm14, %ymm12, %ymm6 |
95 | vfmsub213ps Two+__svml_sacos_data_internal(%rip), %ymm13, %ymm14 |
96 | vfmadd213ps poly_coeff+128+__svml_sacos_data_internal(%rip), %ymm2, %ymm9 |
97 | vfmadd213ps sqrt_coeff+32+__svml_sacos_data_internal(%rip), %ymm14, %ymm0 |
98 | vmulps %ymm14, %ymm6, %ymm15 |
99 | vmulps %ymm9, %ymm2, %ymm14 |
100 | vfnmadd213ps %ymm6, %ymm15, %ymm0 |
101 | vblendvps %ymm1, %ymm0, %ymm4, %ymm0 |
102 | vandps PiH+__svml_sacos_data_internal(%rip), %ymm1, %ymm2 |
103 | vandnps Pi2H+__svml_sacos_data_internal(%rip), %ymm1, %ymm12 |
104 | vxorps %ymm3, %ymm0, %ymm1 |
105 | vfmadd213ps %ymm1, %ymm1, %ymm14 |
106 | vandps %ymm10, %ymm2, %ymm11 |
107 | vaddps %ymm12, %ymm11, %ymm13 |
108 | vaddps %ymm14, %ymm13, %ymm0 |
109 | testl %edx, %edx |
110 | |
111 | /* Go to special inputs processing branch */ |
112 | jne L(SPECIAL_VALUES_BRANCH) |
113 | # LOE rbx r12 r13 r14 r15 edx ymm0 ymm5 |
114 | |
115 | /* Restore registers |
116 | * and exit the function |
117 | */ |
118 | |
119 | L(EXIT): |
120 | movq %rbp, %rsp |
121 | popq %rbp |
122 | cfi_def_cfa(7, 8) |
123 | cfi_restore(6) |
124 | ret |
125 | cfi_def_cfa(6, 16) |
126 | cfi_offset(6, -16) |
127 | |
128 | /* Branch to process |
129 | * special inputs |
130 | */ |
131 | |
132 | L(SPECIAL_VALUES_BRANCH): |
133 | vmovups %ymm5, 32(%rsp) |
134 | vmovups %ymm0, 64(%rsp) |
135 | # LOE rbx r12 r13 r14 r15 edx ymm0 |
136 | |
137 | xorl %eax, %eax |
138 | # LOE rbx r12 r13 r14 r15 eax edx |
139 | |
140 | vzeroupper |
141 | movq %r12, 16(%rsp) |
142 | /* 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) */ |
143 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 |
144 | movl %eax, %r12d |
145 | movq %r13, 8(%rsp) |
146 | /* 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) */ |
147 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 |
148 | movl %edx, %r13d |
149 | movq %r14, (%rsp) |
150 | /* 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) */ |
151 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 |
152 | # LOE rbx r15 r12d r13d |
153 | |
154 | /* Range mask |
155 | * bits check |
156 | */ |
157 | |
158 | L(RANGEMASK_CHECK): |
159 | btl %r12d, %r13d |
160 | |
161 | /* Call scalar math function */ |
162 | jc L(SCALAR_MATH_CALL) |
163 | # LOE rbx r15 r12d r13d |
164 | |
165 | /* Special inputs |
166 | * processing loop |
167 | */ |
168 | |
169 | L(SPECIAL_VALUES_LOOP): |
170 | incl %r12d |
171 | cmpl $8, %r12d |
172 | |
173 | /* Check bits in range mask */ |
174 | jl L(RANGEMASK_CHECK) |
175 | # LOE rbx r15 r12d r13d |
176 | |
177 | movq 16(%rsp), %r12 |
178 | cfi_restore(12) |
179 | movq 8(%rsp), %r13 |
180 | cfi_restore(13) |
181 | movq (%rsp), %r14 |
182 | cfi_restore(14) |
183 | vmovups 64(%rsp), %ymm0 |
184 | |
185 | /* Go to exit */ |
186 | jmp L(EXIT) |
187 | /* 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) */ |
188 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 |
189 | /* 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) */ |
190 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 |
191 | /* 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) */ |
192 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 |
193 | # LOE rbx r12 r13 r14 r15 ymm0 |
194 | |
195 | /* Scalar math function call |
196 | * to process special input |
197 | */ |
198 | |
199 | L(SCALAR_MATH_CALL): |
200 | movl %r12d, %r14d |
201 | vmovss 32(%rsp, %r14, 4), %xmm0 |
202 | call acosf@PLT |
203 | # LOE rbx r14 r15 r12d r13d xmm0 |
204 | |
205 | vmovss %xmm0, 64(%rsp, %r14, 4) |
206 | |
207 | /* Process special inputs in loop */ |
208 | jmp L(SPECIAL_VALUES_LOOP) |
209 | # LOE rbx r15 r12d r13d |
210 | END(_ZGVdN8v_acosf_avx2) |
211 | |
212 | .section .rodata, "a" |
213 | .align 32 |
214 | |
215 | #ifdef __svml_sacos_data_internal_typedef |
216 | typedef unsigned int VUINT32; |
217 | typedef struct { |
218 | __declspec(align(32)) VUINT32 SgnBit[8][1]; |
219 | __declspec(align(32)) VUINT32 OneHalf[8][1]; |
220 | __declspec(align(32)) VUINT32 SmallNorm[8][1]; |
221 | __declspec(align(32)) VUINT32 MOne[8][1]; |
222 | __declspec(align(32)) VUINT32 Two[8][1]; |
223 | __declspec(align(32)) VUINT32 sqrt_coeff[2][8][1]; |
224 | __declspec(align(32)) VUINT32 poly_coeff[5][8][1]; |
225 | __declspec(align(32)) VUINT32 Pi2H[8][1]; |
226 | __declspec(align(32)) VUINT32 PiH[8][1]; |
227 | } __svml_sacos_data_internal; |
228 | #endif |
229 | __svml_sacos_data_internal: |
230 | /* SgnBit */ |
231 | .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 |
232 | /* OneHalf */ |
233 | .align 32 |
234 | .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 |
235 | /* SmallNorm */ |
236 | .align 32 |
237 | .long 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000 |
238 | /* MOne */ |
239 | .align 32 |
240 | .long 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000, 0xbf800000 |
241 | /* Two */ |
242 | .align 32 |
243 | .long 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000, 0x40000000 |
244 | /* sqrt_coeff[2] */ |
245 | .align 32 |
246 | .long 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004, 0xbdC00004 /* sqrt_coeff2 */ |
247 | .long 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001, 0x3e800001 /* sqrt_coeff1 */ |
248 | /* poly_coeff[5] */ |
249 | .align 32 |
250 | .long 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07, 0x3d2EDC07 /* poly_coeff5 */ |
251 | .long 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B, 0x3CC32A6B /* poly_coeff4 */ |
252 | .long 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4, 0x3d3A9AB4 /* poly_coeff3 */ |
253 | .long 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12, 0x3d997C12 /* poly_coeff2 */ |
254 | .long 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF, 0x3e2AAAFF /* poly_coeff1 */ |
255 | /* Pi2H */ |
256 | .align 32 |
257 | .long 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB, 0x3fc90FDB |
258 | /* PiH */ |
259 | .align 32 |
260 | .long 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB |
261 | .align 32 |
262 | .type __svml_sacos_data_internal, @object |
263 | .size __svml_sacos_data_internal, .-__svml_sacos_data_internal |
264 | |