/* Function hypotf vectorized with SSE4. Copyright (C) 2021-2022 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see https://www.gnu.org/licenses/. */ /* * ALGORITHM DESCRIPTION: * * HIGH LEVEL OVERVIEW * * Calculate z = (x*x+y*y) * Calculate reciplicle sqrt (z) * Calculate make two NR iterations * * ALGORITHM DETAILS * * Multiprecision branch for _HA_ only * Remove sigm from both arguments * Find maximum (_x) and minimum (_y) (by abs value) between arguments * Split _x int _a and _b for multiprecision * If _x >> _y we will we will not split _y for multiprecision * all _y will be put into lower part (_d) and higher part (_c = 0) * Fixing _hilo_mask for the case _x >> _y * Split _y into _c and _d for multiprecision with fixed mask * * compute Hi and Lo parts of _z = _x*_x + _y*_y * * _zHi = _a*_a + _c*_c * _zLo = (_x + _a)*_b + _d*_y + _d*_c * _z = _zHi + _zLo * * No multiprecision branch for _LA_ and _EP_ * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 * * Check _z exponent to be withing borders [1E3 ; 60A] else goto Callout * * Compute resciplicle sqrt s0 ~ 1.0/sqrt(_z), * that multiplied by _z, is final result for _EP_ version. * * First iteration (or zero iteration): * s = z * s0 * h = .5 * s0 * d = s * h - .5 * * Second iteration: * h = d * h + h * s = s * d + s * d = s * s - z (in multiprecision for _HA_) * * result = s - h * d * * EP version of the function can be implemented as y[i]=sqrt(a[i]^2+b[i]^2) * with all intermediate operations done in target precision for i=1, .., n. * It can return result y[i]=0 in case a[i]^2 and b[i]^2 underflow in target * precision (for some i). It can return result y[i]=NAN in case * a[i]^2+b[i]^2 overflow in target precision, for some i. It can return * result y[i]=NAN in case a[i] or b[i] is infinite, for some i. * * */ /* Offsets for data table __svml_shypot_data_internal */ #define _sHiLoMask 0 #define _sAbsMask 16 #define _sHalf 32 #define _LowBoundary 48 #define _HighBoundary 64 #include .section .text.sse4, "ax", @progbits ENTRY(_ZGVbN4vv_hypotf_sse4) subq $88, %rsp cfi_def_cfa_offset(96) /* * Implementation * Multiprecision branch for _HA_ only * No multiprecision branch for _LA_ * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 */ movaps %xmm0, %xmm8 movaps %xmm1, %xmm2 mulps %xmm0, %xmm8 mulps %xmm1, %xmm2 /* * Variables * Defines * Constants loading */ movups _sHalf+__svml_shypot_data_internal(%rip), %xmm5 addps %xmm2, %xmm8 /* _s0 ~ 1.0/sqrt(_z) */ rsqrtps %xmm8, %xmm10 /* First iteration */ movaps %xmm10, %xmm2 movaps %xmm8, %xmm3 mulps %xmm8, %xmm2 mulps %xmm5, %xmm10 movaps %xmm2, %xmm6 mulps %xmm10, %xmm6 /* Check _z exponent to be withing borders [1E3 ; 60A] else goto Callout */ movdqu _LowBoundary+__svml_shypot_data_internal(%rip), %xmm4 subps %xmm6, %xmm5 /* Second iteration */ movaps %xmm5, %xmm7 pcmpgtd %xmm8, %xmm4 mulps %xmm2, %xmm5 mulps %xmm10, %xmm7 addps %xmm5, %xmm2 addps %xmm7, %xmm10 /* Finish second iteration in native precision for _LA_ */ movaps %xmm2, %xmm9 mulps %xmm2, %xmm9 pcmpgtd _HighBoundary+__svml_shypot_data_internal(%rip), %xmm3 subps %xmm8, %xmm9 mulps %xmm9, %xmm10 por %xmm3, %xmm4 movmskps %xmm4, %edx subps %xmm10, %xmm2 /* The end of implementation */ testl %edx, %edx /* Go to special inputs processing branch */ jne L(SPECIAL_VALUES_BRANCH) # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1 xmm2 /* Restore registers * and exit the function */ L(EXIT): movaps %xmm2, %xmm0 addq $88, %rsp cfi_def_cfa_offset(8) ret cfi_def_cfa_offset(96) /* Branch to process * special inputs */ L(SPECIAL_VALUES_BRANCH): movups %xmm0, 32(%rsp) movups %xmm1, 48(%rsp) movups %xmm2, 64(%rsp) # LOE rbx rbp r12 r13 r14 r15 edx xorl %eax, %eax movq %r12, 16(%rsp) cfi_offset(12, -80) movl %eax, %r12d movq %r13, 8(%rsp) cfi_offset(13, -88) movl %edx, %r13d movq %r14, (%rsp) cfi_offset(14, -96) # LOE rbx rbp r15 r12d r13d /* Range mask * bits check */ L(RANGEMASK_CHECK): btl %r12d, %r13d /* Call scalar math function */ jc L(SCALAR_MATH_CALL) # LOE rbx rbp r15 r12d r13d /* Special inputs * processing loop */ L(SPECIAL_VALUES_LOOP): incl %r12d cmpl $4, %r12d /* Check bits in range mask */ jl L(RANGEMASK_CHECK) # LOE rbx rbp r15 r12d r13d movq 16(%rsp), %r12 cfi_restore(12) movq 8(%rsp), %r13 cfi_restore(13) movq (%rsp), %r14 cfi_restore(14) movups 64(%rsp), %xmm2 /* Go to exit */ jmp L(EXIT) cfi_offset(12, -80) cfi_offset(13, -88) cfi_offset(14, -96) # LOE rbx rbp r12 r13 r14 r15 xmm2 /* Scalar math fucntion call * to process special input */ L(SCALAR_MATH_CALL): movl %r12d, %r14d movss 32(%rsp, %r14, 4), %xmm0 movss 48(%rsp, %r14, 4), %xmm1 call hypotf@PLT # LOE rbx rbp r14 r15 r12d r13d xmm0 movss %xmm0, 64(%rsp, %r14, 4) /* Process special inputs in loop */ jmp L(SPECIAL_VALUES_LOOP) # LOE rbx rbp r15 r12d r13d END(_ZGVbN4vv_hypotf_sse4) .section .rodata, "a" .align 16 #ifdef __svml_shypot_data_internal_typedef typedef unsigned int VUINT32; typedef struct { __declspec(align(16)) VUINT32 _sHiLoMask[4][1]; __declspec(align(16)) VUINT32 _sAbsMask[4][1]; __declspec(align(16)) VUINT32 _sHalf[4][1]; __declspec(align(16)) VUINT32 _LowBoundary[4][1]; __declspec(align(16)) VUINT32 _HighBoundary[4][1]; } __svml_shypot_data_internal; #endif __svml_shypot_data_internal: /* legacy algorithm */ .long 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000 /* _sHiLoMask */ .align 16 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */ .align 16 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sHalf */ .align 16 .long 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000 /* _LowBoundary */ .align 16 .long 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000 /* _HighBoundary */ .align 16 .type __svml_shypot_data_internal, @object .size __svml_shypot_data_internal, .-__svml_shypot_data_internal