1/* Function hypotf 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 * 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 16 79#define _sHalf 32 80#define _LowBoundary 48 81#define _HighBoundary 64 82 83#include <sysdep.h> 84 85 .section .text.sse4, "ax", @progbits 86ENTRY(_ZGVbN4vv_hypotf_sse4) 87 subq $88, %rsp 88 cfi_def_cfa_offset(96) 89 90 /* 91 * Implementation 92 * Multiprecision branch for _HA_ only 93 * No multiprecision branch for _LA_ 94 * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 95 */ 96 movaps %xmm0, %xmm8 97 movaps %xmm1, %xmm2 98 mulps %xmm0, %xmm8 99 mulps %xmm1, %xmm2 100 101 /* 102 * Variables 103 * Defines 104 * Constants loading 105 */ 106 movups _sHalf+__svml_shypot_data_internal(%rip), %xmm5 107 addps %xmm2, %xmm8 108 109 /* _s0 ~ 1.0/sqrt(_z) */ 110 rsqrtps %xmm8, %xmm10 111 112 /* First iteration */ 113 movaps %xmm10, %xmm2 114 movaps %xmm8, %xmm3 115 mulps %xmm8, %xmm2 116 mulps %xmm5, %xmm10 117 movaps %xmm2, %xmm6 118 mulps %xmm10, %xmm6 119 120 /* Check _z exponent to be withing borders [1E3 ; 60A] else goto Callout */ 121 movdqu _LowBoundary+__svml_shypot_data_internal(%rip), %xmm4 122 subps %xmm6, %xmm5 123 124 /* Second iteration */ 125 movaps %xmm5, %xmm7 126 pcmpgtd %xmm8, %xmm4 127 mulps %xmm2, %xmm5 128 mulps %xmm10, %xmm7 129 addps %xmm5, %xmm2 130 addps %xmm7, %xmm10 131 132 /* Finish second iteration in native precision for _LA_ */ 133 movaps %xmm2, %xmm9 134 mulps %xmm2, %xmm9 135 pcmpgtd _HighBoundary+__svml_shypot_data_internal(%rip), %xmm3 136 subps %xmm8, %xmm9 137 mulps %xmm9, %xmm10 138 por %xmm3, %xmm4 139 movmskps %xmm4, %edx 140 subps %xmm10, %xmm2 141 142 /* The end of implementation */ 143 testl %edx, %edx 144 145 /* Go to special inputs processing branch */ 146 jne L(SPECIAL_VALUES_BRANCH) 147 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1 xmm2 148 149 /* Restore registers 150 * and exit the function 151 */ 152 153L(EXIT): 154 movaps %xmm2, %xmm0 155 addq $88, %rsp 156 cfi_def_cfa_offset(8) 157 ret 158 cfi_def_cfa_offset(96) 159 160 /* Branch to process 161 * special inputs 162 */ 163 164L(SPECIAL_VALUES_BRANCH): 165 movups %xmm0, 32(%rsp) 166 movups %xmm1, 48(%rsp) 167 movups %xmm2, 64(%rsp) 168 # LOE rbx rbp r12 r13 r14 r15 edx 169 170 xorl %eax, %eax 171 movq %r12, 16(%rsp) 172 cfi_offset(12, -80) 173 movl %eax, %r12d 174 movq %r13, 8(%rsp) 175 cfi_offset(13, -88) 176 movl %edx, %r13d 177 movq %r14, (%rsp) 178 cfi_offset(14, -96) 179 # LOE rbx rbp r15 r12d r13d 180 181 /* Range mask 182 * bits check 183 */ 184 185L(RANGEMASK_CHECK): 186 btl %r12d, %r13d 187 188 /* Call scalar math function */ 189 jc L(SCALAR_MATH_CALL) 190 # LOE rbx rbp r15 r12d r13d 191 192 /* Special inputs 193 * processing loop 194 */ 195 196L(SPECIAL_VALUES_LOOP): 197 incl %r12d 198 cmpl $4, %r12d 199 200 /* Check bits in range mask */ 201 jl L(RANGEMASK_CHECK) 202 # LOE rbx rbp r15 r12d r13d 203 204 movq 16(%rsp), %r12 205 cfi_restore(12) 206 movq 8(%rsp), %r13 207 cfi_restore(13) 208 movq (%rsp), %r14 209 cfi_restore(14) 210 movups 64(%rsp), %xmm2 211 212 /* Go to exit */ 213 jmp L(EXIT) 214 cfi_offset(12, -80) 215 cfi_offset(13, -88) 216 cfi_offset(14, -96) 217 # LOE rbx rbp r12 r13 r14 r15 xmm2 218 219 /* Scalar math fucntion call 220 * to process special input 221 */ 222 223L(SCALAR_MATH_CALL): 224 movl %r12d, %r14d 225 movss 32(%rsp, %r14, 4), %xmm0 226 movss 48(%rsp, %r14, 4), %xmm1 227 call hypotf@PLT 228 # LOE rbx rbp r14 r15 r12d r13d xmm0 229 230 movss %xmm0, 64(%rsp, %r14, 4) 231 232 /* Process special inputs in loop */ 233 jmp L(SPECIAL_VALUES_LOOP) 234 # LOE rbx rbp r15 r12d r13d 235END(_ZGVbN4vv_hypotf_sse4) 236 237 .section .rodata, "a" 238 .align 16 239 240#ifdef __svml_shypot_data_internal_typedef 241typedef unsigned int VUINT32; 242typedef struct { 243 __declspec(align(16)) VUINT32 _sHiLoMask[4][1]; 244 __declspec(align(16)) VUINT32 _sAbsMask[4][1]; 245 __declspec(align(16)) VUINT32 _sHalf[4][1]; 246 __declspec(align(16)) VUINT32 _LowBoundary[4][1]; 247 __declspec(align(16)) VUINT32 _HighBoundary[4][1]; 248} __svml_shypot_data_internal; 249#endif 250__svml_shypot_data_internal: 251 /* legacy algorithm */ 252 .long 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000 /* _sHiLoMask */ 253 .align 16 254 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */ 255 .align 16 256 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sHalf */ 257 .align 16 258 .long 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000 /* _LowBoundary */ 259 .align 16 260 .long 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000 /* _HighBoundary */ 261 .align 16 262 .type __svml_shypot_data_internal, @object 263 .size __svml_shypot_data_internal, .-__svml_shypot_data_internal 264