/* Function hypotf vectorized with AVX2. Copyright (C) 2021 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 32 #define _sHalf 64 #define _LowBoundary 96 #define _HighBoundary 128 #include .text .section .text.avx2,"ax",@progbits ENTRY(_ZGVdN8vv_hypotf_avx2) pushq %rbp cfi_def_cfa_offset(16) movq %rsp, %rbp cfi_def_cfa(6, 16) cfi_offset(6, -16) andq $-32, %rsp subq $128, %rsp /* * Implementation * Multiprecision branch for _HA_ only * No multiprecision branch for _LA_ * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 */ vmulps %ymm0, %ymm0, %ymm8 /* * Variables * Defines * Constants loading */ vmovups _sHalf+__svml_shypot_data_internal(%rip), %ymm7 /* Check _z exponent to be withing borders [1E3 ; 60A] else goto Callout */ vmovups _LowBoundary+__svml_shypot_data_internal(%rip), %ymm2 vfmadd231ps %ymm1, %ymm1, %ymm8 /* _s0 ~ 1.0/sqrt(_z) */ vrsqrtps %ymm8, %ymm6 vpcmpgtd %ymm8, %ymm2, %ymm3 /* First iteration */ vmulps %ymm8, %ymm6, %ymm9 vmulps %ymm7, %ymm6, %ymm2 vfnmadd231ps %ymm9, %ymm2, %ymm7 vfmadd213ps %ymm9, %ymm7, %ymm9 /* Second iteration */ vfmadd132ps %ymm7, %ymm2, %ymm2 vpcmpgtd _HighBoundary+__svml_shypot_data_internal(%rip), %ymm8, %ymm4 vpor %ymm4, %ymm3, %ymm5 /* Finish second iteration in native precision for _LA_ */ vfmsub231ps %ymm9, %ymm9, %ymm8 vmovmskps %ymm5, %edx vfnmadd213ps %ymm9, %ymm8, %ymm2 /* The end of implementation */ testl %edx, %edx /* Go to special inputs processing branch */ jne L(SPECIAL_VALUES_BRANCH) # LOE rbx r12 r13 r14 r15 edx ymm0 ymm1 ymm2 /* Restore registers * and exit the function */ L(EXIT): vmovaps %ymm2, %ymm0 movq %rbp, %rsp popq %rbp cfi_def_cfa(7, 8) cfi_restore(6) ret cfi_def_cfa(6, 16) cfi_offset(6, -16) /* Branch to process * special inputs */ L(SPECIAL_VALUES_BRANCH): vmovups %ymm0, 32(%rsp) vmovups %ymm1, 64(%rsp) vmovups %ymm2, 96(%rsp) # LOE rbx r12 r13 r14 r15 edx ymm2 xorl %eax, %eax # LOE rbx r12 r13 r14 r15 eax edx vzeroupper movq %r12, 16(%rsp) /* 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) */ .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22 movl %eax, %r12d movq %r13, 8(%rsp) /* 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) */ .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22 movl %edx, %r13d movq %r14, (%rsp) /* 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) */ .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22 # LOE rbx r15 r12d r13d /* Range mask * bits check */ L(RANGEMASK_CHECK): btl %r12d, %r13d /* Call scalar math function */ jc L(SCALAR_MATH_CALL) # LOE rbx r15 r12d r13d /* Special inputs * processing loop */ L(SPECIAL_VALUES_LOOP): incl %r12d cmpl $8, %r12d /* Check bits in range mask */ jl L(RANGEMASK_CHECK) # LOE rbx r15 r12d r13d movq 16(%rsp), %r12 cfi_restore(12) movq 8(%rsp), %r13 cfi_restore(13) movq (%rsp), %r14 cfi_restore(14) vmovups 96(%rsp), %ymm2 /* Go to exit */ jmp L(EXIT) /* 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) */ .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22 /* 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) */ .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22 /* 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) */ .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22 # LOE rbx r12 r13 r14 r15 ymm2 /* Scalar math fucntion call * to process special input */ L(SCALAR_MATH_CALL): movl %r12d, %r14d movss 32(%rsp,%r14,4), %xmm0 movss 64(%rsp,%r14,4), %xmm1 call hypotf@PLT # LOE rbx r14 r15 r12d r13d xmm0 movss %xmm0, 96(%rsp,%r14,4) /* Process special inputs in loop */ jmp L(SPECIAL_VALUES_LOOP) # LOE rbx r15 r12d r13d END(_ZGVdN8vv_hypotf_avx2) .section .rodata, "a" .align 32 #ifdef __svml_shypot_data_internal_typedef typedef unsigned int VUINT32; typedef struct { __declspec(align(32)) VUINT32 _sHiLoMask[8][1]; __declspec(align(32)) VUINT32 _sAbsMask[8][1]; __declspec(align(32)) VUINT32 _sHalf[8][1]; __declspec(align(32)) VUINT32 _LowBoundary[8][1]; __declspec(align(32)) VUINT32 _HighBoundary[8][1]; } __svml_shypot_data_internal; #endif __svml_shypot_data_internal: /* legacy algorithm */ .long 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000 /* _sHiLoMask */ .align 32 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */ .align 32 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sHalf */ .align 32 .long 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000 /* _LowBoundary */ .align 32 .long 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000 /* _HighBoundary */ .align 32 .type __svml_shypot_data_internal,@object .size __svml_shypot_data_internal,.-__svml_shypot_data_internal