1/* Function acos vectorized with AVX2. 2 Copyright (C) 2021-2022 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 32 33#define SmallNorm 64 34#define MOne 96 35#define Two 128 36#define sqrt_coeff 160 37#define poly_coeff 288 38#define PiH 672 39#define Pi2H 704 40 41#include <sysdep.h> 42 43 .section .text.avx2, "ax", @progbits 44ENTRY(_ZGVdN4v_acos_avx2) 45 pushq %rbp 46 cfi_def_cfa_offset(16) 47 movq %rsp, %rbp 48 cfi_def_cfa(6, 16) 49 cfi_offset(6, -16) 50 andq $-32, %rsp 51 subq $96, %rsp 52 vmovupd __svml_dacos_data_internal(%rip), %ymm6 53 vmovupd OneHalf+__svml_dacos_data_internal(%rip), %ymm7 54 vmovapd %ymm0, %ymm5 55 56 /* x = -|arg| */ 57 vorpd %ymm5, %ymm6, %ymm4 58 59 /* Y = 0.5 + 0.5*(-x) */ 60 vfmadd231pd %ymm4, %ymm7, %ymm7 61 62 /* x^2 */ 63 vmulpd %ymm4, %ymm4, %ymm8 64 65 /* S ~ 2*sqrt(Y) */ 66 vmovupd sqrt_coeff+__svml_dacos_data_internal(%rip), %ymm0 67 vcmplt_oqpd SmallNorm+__svml_dacos_data_internal(%rip), %ymm7, %ymm12 68 vminpd %ymm7, %ymm8, %ymm2 69 70 /* NaN processed in special branch (so wind test passed) */ 71 vcmpnge_uqpd MOne+__svml_dacos_data_internal(%rip), %ymm4, %ymm9 72 vcvtpd2ps %ymm7, %xmm10 73 vmovupd poly_coeff+64+__svml_dacos_data_internal(%rip), %ymm8 74 vcmpnlt_uqpd %ymm7, %ymm2, %ymm1 75 vrsqrtps %xmm10, %xmm11 76 vfmadd213pd poly_coeff+96+__svml_dacos_data_internal(%rip), %ymm2, %ymm8 77 vcvtps2pd %xmm11, %ymm13 78 vmovupd poly_coeff+128+__svml_dacos_data_internal(%rip), %ymm11 79 vandnpd %ymm13, %ymm12, %ymm14 80 vmulpd %ymm14, %ymm14, %ymm15 81 vfmadd213pd poly_coeff+160+__svml_dacos_data_internal(%rip), %ymm2, %ymm11 82 vmulpd %ymm2, %ymm2, %ymm13 83 vmovupd poly_coeff+256+__svml_dacos_data_internal(%rip), %ymm12 84 vmulpd %ymm13, %ymm13, %ymm10 85 vfmadd213pd poly_coeff+288+__svml_dacos_data_internal(%rip), %ymm2, %ymm12 86 vandpd %ymm5, %ymm6, %ymm3 87 vaddpd %ymm7, %ymm7, %ymm6 88 vmulpd %ymm6, %ymm14, %ymm7 89 vfmsub213pd Two+__svml_dacos_data_internal(%rip), %ymm15, %ymm6 90 vmovupd poly_coeff+320+__svml_dacos_data_internal(%rip), %ymm14 91 vfmadd213pd sqrt_coeff+32+__svml_dacos_data_internal(%rip), %ymm6, %ymm0 92 vmulpd %ymm6, %ymm7, %ymm15 93 vfmadd213pd poly_coeff+352+__svml_dacos_data_internal(%rip), %ymm2, %ymm14 94 vfmadd213pd sqrt_coeff+64+__svml_dacos_data_internal(%rip), %ymm6, %ymm0 95 vfmadd213pd sqrt_coeff+96+__svml_dacos_data_internal(%rip), %ymm6, %ymm0 96 97 /* polynomial */ 98 vmovupd poly_coeff+__svml_dacos_data_internal(%rip), %ymm6 99 vfnmadd213pd %ymm7, %ymm15, %ymm0 100 vfmadd213pd poly_coeff+32+__svml_dacos_data_internal(%rip), %ymm2, %ymm6 101 vblendvpd %ymm1, %ymm0, %ymm4, %ymm0 102 vfmadd213pd %ymm8, %ymm13, %ymm6 103 vmovmskpd %ymm9, %edx 104 vmovupd poly_coeff+192+__svml_dacos_data_internal(%rip), %ymm9 105 vfmadd213pd poly_coeff+224+__svml_dacos_data_internal(%rip), %ymm2, %ymm9 106 vfmadd213pd %ymm9, %ymm13, %ymm11 107 vfmadd213pd %ymm11, %ymm10, %ymm6 108 vfmadd213pd %ymm12, %ymm13, %ymm6 109 vfmadd213pd %ymm14, %ymm13, %ymm6 110 vmulpd %ymm6, %ymm2, %ymm9 111 112 /* X<X^2 iff X<0 */ 113 vcmplt_oqpd %ymm2, %ymm5, %ymm6 114 vandpd PiH+__svml_dacos_data_internal(%rip), %ymm1, %ymm2 115 vandnpd Pi2H+__svml_dacos_data_internal(%rip), %ymm1, %ymm7 116 vxorpd %ymm3, %ymm0, %ymm1 117 vfmadd213pd %ymm1, %ymm1, %ymm9 118 vandpd %ymm6, %ymm2, %ymm2 119 vaddpd %ymm7, %ymm2, %ymm8 120 vaddpd %ymm9, %ymm8, %ymm0 121 testl %edx, %edx 122 123 /* Go to special inputs processing branch */ 124 jne L(SPECIAL_VALUES_BRANCH) 125 # LOE rbx r12 r13 r14 r15 edx ymm0 ymm5 126 127 /* Restore registers 128 * and exit the function 129 */ 130 131L(EXIT): 132 movq %rbp, %rsp 133 popq %rbp 134 cfi_def_cfa(7, 8) 135 cfi_restore(6) 136 ret 137 cfi_def_cfa(6, 16) 138 cfi_offset(6, -16) 139 140 /* Branch to process 141 * special inputs 142 */ 143 144L(SPECIAL_VALUES_BRANCH): 145 vmovupd %ymm5, 32(%rsp) 146 vmovupd %ymm0, 64(%rsp) 147 # LOE rbx r12 r13 r14 r15 edx ymm0 148 149 xorl %eax, %eax 150 # LOE rbx r12 r13 r14 r15 eax edx 151 152 vzeroupper 153 movq %r12, 16(%rsp) 154 /* 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) */ 155 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 156 movl %eax, %r12d 157 movq %r13, 8(%rsp) 158 /* 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) */ 159 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 160 movl %edx, %r13d 161 movq %r14, (%rsp) 162 /* 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) */ 163 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 164 # LOE rbx r15 r12d r13d 165 166 /* Range mask 167 * bits check 168 */ 169 170L(RANGEMASK_CHECK): 171 btl %r12d, %r13d 172 173 /* Call scalar math function */ 174 jc L(SCALAR_MATH_CALL) 175 # LOE rbx r15 r12d r13d 176 177 /* Special inputs 178 * processing loop 179 */ 180 181L(SPECIAL_VALUES_LOOP): 182 incl %r12d 183 cmpl $4, %r12d 184 185 /* Check bits in range mask */ 186 jl L(RANGEMASK_CHECK) 187 # LOE rbx r15 r12d r13d 188 189 movq 16(%rsp), %r12 190 cfi_restore(12) 191 movq 8(%rsp), %r13 192 cfi_restore(13) 193 movq (%rsp), %r14 194 cfi_restore(14) 195 vmovupd 64(%rsp), %ymm0 196 197 /* Go to exit */ 198 jmp L(EXIT) 199 /* 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) */ 200 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 201 /* 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) */ 202 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 203 /* 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) */ 204 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 205 # LOE rbx r12 r13 r14 r15 ymm0 206 207 /* Scalar math fucntion call 208 * to process special input 209 */ 210 211L(SCALAR_MATH_CALL): 212 movl %r12d, %r14d 213 vmovsd 32(%rsp, %r14, 8), %xmm0 214 call acos@PLT 215 # LOE rbx r14 r15 r12d r13d xmm0 216 217 vmovsd %xmm0, 64(%rsp, %r14, 8) 218 219 /* Process special inputs in loop */ 220 jmp L(SPECIAL_VALUES_LOOP) 221 # LOE rbx r15 r12d r13d 222END(_ZGVdN4v_acos_avx2) 223 224 .section .rodata, "a" 225 .align 32 226 227#ifdef __svml_dacos_data_internal_typedef 228typedef unsigned int VUINT32; 229typedef struct { 230 __declspec(align(32)) VUINT32 SgnBit[4][2]; 231 __declspec(align(32)) VUINT32 OneHalf[4][2]; 232 __declspec(align(32)) VUINT32 SmallNorm[4][2]; 233 __declspec(align(32)) VUINT32 MOne[4][2]; 234 __declspec(align(32)) VUINT32 Two[4][2]; 235 __declspec(align(32)) VUINT32 sqrt_coeff[4][4][2]; 236 __declspec(align(32)) VUINT32 poly_coeff[12][4][2]; 237 __declspec(align(32)) VUINT32 PiH[4][2]; 238 __declspec(align(32)) VUINT32 Pi2H[4][2]; 239} __svml_dacos_data_internal; 240#endif 241__svml_dacos_data_internal: 242 /* SgnBit */ 243 .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000 244 /* OneHalf */ 245 .align 32 246 .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000 247 /* SmallNorm */ 248 .align 32 249 .quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000 250 /* MOne */ 251 .align 32 252 .quad 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000 253 /* Two */ 254 .align 32 255 .quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000 256 /* sqrt_coeff[4] */ 257 .align 32 258 .quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */ 259 .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */ 260 .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */ 261 .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */ 262 /* poly_coeff[12] */ 263 .align 32 264 .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */ 265 .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */ 266 .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */ 267 .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */ 268 .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */ 269 .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */ 270 .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */ 271 .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */ 272 .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */ 273 .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */ 274 .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */ 275 .quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */ 276 /* PiH */ 277 .align 32 278 .quad 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18 279 /* Pi2H */ 280 .align 32 281 .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18 282 .align 32 283 .type __svml_dacos_data_internal, @object 284 .size __svml_dacos_data_internal, .-__svml_dacos_data_internal 285