1/* Function acos vectorized with AVX-512. 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 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 fucntion 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