1/* Function hypotf 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 * HIGH LEVEL OVERVIEW 23 * 24 * Calculate z = (x*x+y*y) 25 * Calculate reciplicle sqrt (z) 26 * Calculate make two NR iterations 27 * 28 * ALGORITHM DETAILS 29 * 30 * Multiprecision branch for _HA_ only 31 * Remove sigm from both arguments 32 * Find maximum (_x) and minimum (_y) (by abs value) between arguments 33 * Split _x int _a and _b for multiprecision 34 * If _x >> _y we will we will not split _y for multiprecision 35 * all _y will be put into lower part (_d) and higher part (_c = 0) 36 * Fixing _hilo_mask for the case _x >> _y 37 * Split _y into _c and _d for multiprecision with fixed mask 38 * 39 * compute Hi and Lo parts of _z = _x*_x + _y*_y 40 * 41 * _zHi = _a*_a + _c*_c 42 * _zLo = (_x + _a)*_b + _d*_y + _d*_c 43 * _z = _zHi + _zLo 44 * 45 * No multiprecision branch for _LA_ and _EP_ 46 * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 47 * 48 * Check _z exponent to be withing borders [1E3 ; 60A] else goto Callout 49 * 50 * Compute resciplicle sqrt s0 ~ 1.0/sqrt(_z), 51 * that multiplied by _z, is final result for _EP_ version. 52 * 53 * First iteration (or zero iteration): 54 * s = z * s0 55 * h = .5 * s0 56 * d = s * h - .5 57 * 58 * Second iteration: 59 * h = d * h + h 60 * s = s * d + s 61 * d = s * s - z (in multiprecision for _HA_) 62 * 63 * result = s - h * d 64 * 65 * EP version of the function can be implemented as y[i]=sqrt(a[i]^2+b[i]^2) 66 * with all intermediate operations done in target precision for i=1, .., n. 67 * It can return result y[i]=0 in case a[i]^2 and b[i]^2 underflow in target 68 * precision (for some i). It can return result y[i]=NAN in case 69 * a[i]^2+b[i]^2 overflow in target precision, for some i. It can return 70 * result y[i]=NAN in case a[i] or b[i] is infinite, for some i. 71 * 72 * 73 */ 74 75/* Offsets for data table __svml_shypot_data_internal 76 */ 77#define _sHiLoMask 0 78#define _sAbsMask 32 79#define _sHalf 64 80#define _LowBoundary 96 81#define _HighBoundary 128 82 83#include <sysdep.h> 84 85 .section .text.avx2, "ax", @progbits 86ENTRY(_ZGVdN8vv_hypotf_avx2) 87 pushq %rbp 88 cfi_def_cfa_offset(16) 89 movq %rsp, %rbp 90 cfi_def_cfa(6, 16) 91 cfi_offset(6, -16) 92 andq $-32, %rsp 93 subq $128, %rsp 94 95 /* 96 * Implementation 97 * Multiprecision branch for _HA_ only 98 * No multiprecision branch for _LA_ 99 * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 100 */ 101 vmulps %ymm0, %ymm0, %ymm8 102 103 /* 104 * Variables 105 * Defines 106 * Constants loading 107 */ 108 vmovups _sHalf+__svml_shypot_data_internal(%rip), %ymm7 109 110 /* Check _z exponent to be withing borders [1E3 ; 60A] else goto Callout */ 111 vmovups _LowBoundary+__svml_shypot_data_internal(%rip), %ymm2 112 vfmadd231ps %ymm1, %ymm1, %ymm8 113 114 /* _s0 ~ 1.0/sqrt(_z) */ 115 vrsqrtps %ymm8, %ymm6 116 vpcmpgtd %ymm8, %ymm2, %ymm3 117 118 /* First iteration */ 119 vmulps %ymm8, %ymm6, %ymm9 120 vmulps %ymm7, %ymm6, %ymm2 121 vfnmadd231ps %ymm9, %ymm2, %ymm7 122 vfmadd213ps %ymm9, %ymm7, %ymm9 123 124 /* Second iteration */ 125 vfmadd132ps %ymm7, %ymm2, %ymm2 126 vpcmpgtd _HighBoundary+__svml_shypot_data_internal(%rip), %ymm8, %ymm4 127 vpor %ymm4, %ymm3, %ymm5 128 129 /* Finish second iteration in native precision for _LA_ */ 130 vfmsub231ps %ymm9, %ymm9, %ymm8 131 vmovmskps %ymm5, %edx 132 vfnmadd213ps %ymm9, %ymm8, %ymm2 133 134 /* The end of implementation */ 135 testl %edx, %edx 136 137 /* Go to special inputs processing branch */ 138 jne L(SPECIAL_VALUES_BRANCH) 139 # LOE rbx r12 r13 r14 r15 edx ymm0 ymm1 ymm2 140 141 /* Restore registers 142 * and exit the function 143 */ 144 145L(EXIT): 146 vmovaps %ymm2, %ymm0 147 movq %rbp, %rsp 148 popq %rbp 149 cfi_def_cfa(7, 8) 150 cfi_restore(6) 151 ret 152 cfi_def_cfa(6, 16) 153 cfi_offset(6, -16) 154 155 /* Branch to process 156 * special inputs 157 */ 158 159L(SPECIAL_VALUES_BRANCH): 160 vmovups %ymm0, 32(%rsp) 161 vmovups %ymm1, 64(%rsp) 162 vmovups %ymm2, 96(%rsp) 163 # LOE rbx r12 r13 r14 r15 edx ymm2 164 165 xorl %eax, %eax 166 # LOE rbx r12 r13 r14 r15 eax edx 167 168 vzeroupper 169 movq %r12, 16(%rsp) 170 /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -112; DW_OP_plus) */ 171 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22 172 movl %eax, %r12d 173 movq %r13, 8(%rsp) 174 /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -120; DW_OP_plus) */ 175 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22 176 movl %edx, %r13d 177 movq %r14, (%rsp) 178 /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -128; DW_OP_plus) */ 179 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22 180 # LOE rbx r15 r12d r13d 181 182 /* Range mask 183 * bits check 184 */ 185 186L(RANGEMASK_CHECK): 187 btl %r12d, %r13d 188 189 /* Call scalar math function */ 190 jc L(SCALAR_MATH_CALL) 191 # LOE rbx r15 r12d r13d 192 193 /* Special inputs 194 * processing loop 195 */ 196 197L(SPECIAL_VALUES_LOOP): 198 incl %r12d 199 cmpl $8, %r12d 200 201 /* Check bits in range mask */ 202 jl L(RANGEMASK_CHECK) 203 # LOE rbx r15 r12d r13d 204 205 movq 16(%rsp), %r12 206 cfi_restore(12) 207 movq 8(%rsp), %r13 208 cfi_restore(13) 209 movq (%rsp), %r14 210 cfi_restore(14) 211 vmovups 96(%rsp), %ymm2 212 213 /* Go to exit */ 214 jmp L(EXIT) 215 /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -112; DW_OP_plus) */ 216 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22 217 /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -120; DW_OP_plus) */ 218 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22 219 /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -128; DW_OP_plus) */ 220 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22 221 # LOE rbx r12 r13 r14 r15 ymm2 222 223 /* Scalar math fucntion call 224 * to process special input 225 */ 226 227L(SCALAR_MATH_CALL): 228 movl %r12d, %r14d 229 vmovss 32(%rsp, %r14, 4), %xmm0 230 vmovss 64(%rsp, %r14, 4), %xmm1 231 call hypotf@PLT 232 # LOE rbx r14 r15 r12d r13d xmm0 233 234 vmovss %xmm0, 96(%rsp, %r14, 4) 235 236 /* Process special inputs in loop */ 237 jmp L(SPECIAL_VALUES_LOOP) 238 # LOE rbx r15 r12d r13d 239END(_ZGVdN8vv_hypotf_avx2) 240 241 .section .rodata, "a" 242 .align 32 243 244#ifdef __svml_shypot_data_internal_typedef 245typedef unsigned int VUINT32; 246typedef struct { 247 __declspec(align(32)) VUINT32 _sHiLoMask[8][1]; 248 __declspec(align(32)) VUINT32 _sAbsMask[8][1]; 249 __declspec(align(32)) VUINT32 _sHalf[8][1]; 250 __declspec(align(32)) VUINT32 _LowBoundary[8][1]; 251 __declspec(align(32)) VUINT32 _HighBoundary[8][1]; 252} __svml_shypot_data_internal; 253#endif 254__svml_shypot_data_internal: 255 /* legacy algorithm */ 256 .long 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000 /* _sHiLoMask */ 257 .align 32 258 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */ 259 .align 32 260 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sHalf */ 261 .align 32 262 .long 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000 /* _LowBoundary */ 263 .align 32 264 .long 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000 /* _HighBoundary */ 265 .align 32 266 .type __svml_shypot_data_internal, @object 267 .size __svml_shypot_data_internal, .-__svml_shypot_data_internal 268