1/* Function asin vectorized with SSE4. 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 * 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 42ENTRY(_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 150L(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 160L(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 180L(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 191L(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 fucntion call 215 * to process special input 216 */ 217 218L(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 229END(_ZGVbN2v_asin_sse4) 230 231 .section .rodata, "a" 232 .align 16 233 234#ifdef __svml_dasin_data_internal_typedef 235typedef unsigned int VUINT32; 236typedef 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