1/* Function acos vectorized with AVX-512.
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 64
33#define SmallNorm 128
34#define MOne 192
35#define Two 256
36#define sqrt_coeff_1 320
37#define sqrt_coeff_2 384
38#define sqrt_coeff_3 448
39#define sqrt_coeff_4 512
40#define poly_coeff_1 576
41#define poly_coeff_2 640
42#define poly_coeff_3 704
43#define poly_coeff_4 768
44#define poly_coeff_5 832
45#define poly_coeff_6 896
46#define poly_coeff_7 960
47#define poly_coeff_8 1024
48#define poly_coeff_9 1088
49#define poly_coeff_10 1152
50#define poly_coeff_11 1216
51#define poly_coeff_12 1280
52#define PiH 1344
53#define Pi2H 1408
54
55#include <sysdep.h>
56
57 .section .text.evex512, "ax", @progbits
58ENTRY(_ZGVeN8v_acos_skx)
59 pushq %rbp
60 cfi_def_cfa_offset(16)
61 movq %rsp, %rbp
62 cfi_def_cfa(6, 16)
63 cfi_offset(6, -16)
64 andq $-64, %rsp
65 subq $192, %rsp
66 vmovups __svml_dacos_data_internal(%rip), %zmm7
67 vmovups OneHalf+__svml_dacos_data_internal(%rip), %zmm8
68
69 /* S ~ 2*sqrt(Y) */
70 vmovups SmallNorm+__svml_dacos_data_internal(%rip), %zmm11
71 vmovups Two+__svml_dacos_data_internal(%rip), %zmm14
72 vmovups sqrt_coeff_1+__svml_dacos_data_internal(%rip), %zmm15
73 vmovups sqrt_coeff_2+__svml_dacos_data_internal(%rip), %zmm2
74 vmovups sqrt_coeff_3+__svml_dacos_data_internal(%rip), %zmm1
75 vmovups MOne+__svml_dacos_data_internal(%rip), %zmm10
76 vmovaps %zmm0, %zmm6
77
78 /* x = -|arg| */
79 vorpd %zmm6, %zmm7, %zmm5
80 vandpd %zmm6, %zmm7, %zmm4
81
82 /* Y = 0.5 + 0.5*(-x) */
83 vfmadd231pd {rn-sae}, %zmm5, %zmm8, %zmm8
84
85 /* x^2 */
86 vmulpd {rn-sae}, %zmm5, %zmm5, %zmm9
87 vrsqrt14pd %zmm8, %zmm12
88 vcmppd $17, {sae}, %zmm11, %zmm8, %k1
89 vcmppd $17, {sae}, %zmm10, %zmm5, %k0
90 vmovups poly_coeff_5+__svml_dacos_data_internal(%rip), %zmm10
91 vmovups poly_coeff_7+__svml_dacos_data_internal(%rip), %zmm11
92 vminpd {sae}, %zmm8, %zmm9, %zmm3
93 vmovups poly_coeff_3+__svml_dacos_data_internal(%rip), %zmm9
94 vxorpd %zmm12, %zmm12, %zmm12{%k1}
95 vaddpd {rn-sae}, %zmm8, %zmm8, %zmm0
96 vcmppd $21, {sae}, %zmm8, %zmm3, %k4
97
98 /* X<X^2 iff X<0 */
99 vcmppd $17, {sae}, %zmm3, %zmm6, %k2
100 vmulpd {rn-sae}, %zmm12, %zmm12, %zmm13
101 vmulpd {rn-sae}, %zmm12, %zmm0, %zmm7
102 vmovups poly_coeff_4+__svml_dacos_data_internal(%rip), %zmm12
103
104 /* polynomial */
105 vmovups poly_coeff_1+__svml_dacos_data_internal(%rip), %zmm8
106 vfmsub213pd {rn-sae}, %zmm14, %zmm13, %zmm0
107 vmovups sqrt_coeff_4+__svml_dacos_data_internal(%rip), %zmm13
108 vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm12
109 vmovups poly_coeff_11+__svml_dacos_data_internal(%rip), %zmm9
110 vfmadd231pd {rn-sae}, %zmm0, %zmm15, %zmm2
111 vmovups poly_coeff_9+__svml_dacos_data_internal(%rip), %zmm15
112 vmulpd {rn-sae}, %zmm0, %zmm7, %zmm14
113 vfmadd213pd {rn-sae}, %zmm1, %zmm0, %zmm2
114 vmovups poly_coeff_2+__svml_dacos_data_internal(%rip), %zmm1
115 kmovw %k0, %edx
116 vfmadd213pd {rn-sae}, %zmm13, %zmm0, %zmm2
117 vfmadd231pd {rn-sae}, %zmm3, %zmm8, %zmm1
118 vmovups poly_coeff_10+__svml_dacos_data_internal(%rip), %zmm8
119 vmulpd {rn-sae}, %zmm3, %zmm3, %zmm0
120 vfnmadd213pd {rn-sae}, %zmm7, %zmm14, %zmm2
121 vmovups poly_coeff_6+__svml_dacos_data_internal(%rip), %zmm7
122 vfmadd231pd {rn-sae}, %zmm3, %zmm15, %zmm8
123 vfmadd213pd {rn-sae}, %zmm12, %zmm0, %zmm1
124 vblendmpd %zmm2, %zmm5, %zmm2{%k4}
125 vfmadd231pd {rn-sae}, %zmm3, %zmm10, %zmm7
126 vmovups poly_coeff_8+__svml_dacos_data_internal(%rip), %zmm10
127 vfmadd231pd {rn-sae}, %zmm3, %zmm11, %zmm10
128 vmovups poly_coeff_12+__svml_dacos_data_internal(%rip), %zmm11
129 kandw %k4, %k2, %k3
130 vfmadd213pd {rn-sae}, %zmm10, %zmm0, %zmm7
131 vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm11
132 vmulpd {rn-sae}, %zmm0, %zmm0, %zmm10
133 vfmadd213pd {rn-sae}, %zmm7, %zmm10, %zmm1
134 vfmadd213pd {rn-sae}, %zmm8, %zmm0, %zmm1
135 vfmadd213pd {rn-sae}, %zmm11, %zmm0, %zmm1
136 vmovups Pi2H+__svml_dacos_data_internal(%rip), %zmm0
137 vmulpd {rn-sae}, %zmm3, %zmm1, %zmm1
138 vxorpd %zmm4, %zmm2, %zmm3
139 vxorpd %zmm0, %zmm0, %zmm0{%k4}
140 vfmadd213pd {rn-sae}, %zmm3, %zmm3, %zmm1
141 vorpd PiH+__svml_dacos_data_internal(%rip), %zmm0, %zmm0{%k3}
142 vaddpd {rn-sae}, %zmm1, %zmm0, %zmm0
143 testl %edx, %edx
144
145 /* Go to special inputs processing branch */
146 jne L(SPECIAL_VALUES_BRANCH)
147 # LOE rbx r12 r13 r14 r15 edx zmm0 zmm6
148
149 /* Restore registers
150 * and exit the function
151 */
152
153L(EXIT):
154 movq %rbp, %rsp
155 popq %rbp
156 cfi_def_cfa(7, 8)
157 cfi_restore(6)
158 ret
159 cfi_def_cfa(6, 16)
160 cfi_offset(6, -16)
161
162 /* Branch to process
163 * special inputs
164 */
165
166L(SPECIAL_VALUES_BRANCH):
167 vmovups %zmm6, 64(%rsp)
168 vmovups %zmm0, 128(%rsp)
169 # LOE rbx r12 r13 r14 r15 edx zmm0
170
171 xorl %eax, %eax
172 # LOE rbx r12 r13 r14 r15 eax edx
173
174 vzeroupper
175 movq %r12, 16(%rsp)
176 /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
177 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
178 movl %eax, %r12d
179 movq %r13, 8(%rsp)
180 /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
181 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
182 movl %edx, %r13d
183 movq %r14, (%rsp)
184 /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
185 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
186 # LOE rbx r15 r12d r13d
187
188 /* Range mask
189 * bits check
190 */
191
192L(RANGEMASK_CHECK):
193 btl %r12d, %r13d
194
195 /* Call scalar math function */
196 jc L(SCALAR_MATH_CALL)
197 # LOE rbx r15 r12d r13d
198
199 /* Special inputs
200 * processing loop
201 */
202
203L(SPECIAL_VALUES_LOOP):
204 incl %r12d
205 cmpl $8, %r12d
206
207 /* Check bits in range mask */
208 jl L(RANGEMASK_CHECK)
209 # LOE rbx r15 r12d r13d
210
211 movq 16(%rsp), %r12
212 cfi_restore(12)
213 movq 8(%rsp), %r13
214 cfi_restore(13)
215 movq (%rsp), %r14
216 cfi_restore(14)
217 vmovups 128(%rsp), %zmm0
218
219 /* Go to exit */
220 jmp L(EXIT)
221 /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
222 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
223 /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
224 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
225 /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
226 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
227 # LOE rbx r12 r13 r14 r15 zmm0
228
229 /* Scalar math function call
230 * to process special input
231 */
232
233L(SCALAR_MATH_CALL):
234 movl %r12d, %r14d
235 vmovsd 64(%rsp, %r14, 8), %xmm0
236 call acos@PLT
237 # LOE rbx r14 r15 r12d r13d xmm0
238
239 vmovsd %xmm0, 128(%rsp, %r14, 8)
240
241 /* Process special inputs in loop */
242 jmp L(SPECIAL_VALUES_LOOP)
243 # LOE rbx r15 r12d r13d
244END(_ZGVeN8v_acos_skx)
245
246 .section .rodata, "a"
247 .align 64
248
249#ifdef __svml_dacos_data_internal_typedef
250typedef unsigned int VUINT32;
251typedef struct {
252 __declspec(align(64)) VUINT32 SgnBit[8][2];
253 __declspec(align(64)) VUINT32 OneHalf[8][2];
254 __declspec(align(64)) VUINT32 SmallNorm[8][2];
255 __declspec(align(64)) VUINT32 MOne[8][2];
256 __declspec(align(64)) VUINT32 Two[8][2];
257 __declspec(align(64)) VUINT32 sqrt_coeff[4][8][2];
258 __declspec(align(64)) VUINT32 poly_coeff[12][8][2];
259 __declspec(align(64)) VUINT32 PiH[8][2];
260 __declspec(align(64)) VUINT32 Pi2H[8][2];
261} __svml_dacos_data_internal;
262#endif
263__svml_dacos_data_internal:
264 /* SgnBit */
265 .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000
266 /* OneHalf */
267 .align 64
268 .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
269 /* SmallNorm */
270 .align 64
271 .quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000
272 /* MOne */
273 .align 64
274 .quad 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000
275 /* Two */
276 .align 64
277 .quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000
278 /* sqrt_coeff[4] */
279 .align 64
280 .quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
281 .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
282 .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
283 .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
284 /* poly_coeff[12] */
285 .align 64
286 .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
287 .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
288 .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
289 .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
290 .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
291 .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
292 .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
293 .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
294 .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
295 .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
296 .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
297 .quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
298 /* PiH */
299 .align 64
300 .quad 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18
301 /* Pi2H */
302 .align 64
303 .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18
304 .align 64
305 .type __svml_dacos_data_internal, @object
306 .size __svml_dacos_data_internal, .-__svml_dacos_data_internal
307

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_d_acos8_core_avx512.S