/* Function hypotf vectorized with AVX-512. 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 _sAbsMask 0 #define _sHalf 64 #define _iExpBound 128 #include .section .text.evex512, "ax", @progbits ENTRY(_ZGVeN16vv_hypotf_skx) pushq %rbp cfi_def_cfa_offset(16) movq %rsp, %rbp cfi_def_cfa(6, 16) cfi_offset(6, -16) andq $-64, %rsp subq $256, %rsp vgetexpps {sae}, %zmm0, %zmm2 vgetexpps {sae}, %zmm1, %zmm3 vmovups _sHalf+__svml_shypot_data_internal(%rip), %zmm6 vmaxps {sae}, %zmm3, %zmm2, %zmm4 vmulps {rn-sae}, %zmm0, %zmm0, %zmm2 vandps _sAbsMask+__svml_shypot_data_internal(%rip), %zmm4, %zmm5 vfmadd231ps {rn-sae}, %zmm1, %zmm1, %zmm2 vpcmpd $5, _iExpBound+__svml_shypot_data_internal(%rip), %zmm5, %k0 vrsqrt14ps %zmm2, %zmm7 kmovw %k0, %edx vmulps {rn-sae}, %zmm7, %zmm2, %zmm9 vmulps {rn-sae}, %zmm7, %zmm6, %zmm8 vfnmadd231ps {rn-sae}, %zmm9, %zmm9, %zmm2 vfmadd213ps {rn-sae}, %zmm9, %zmm8, %zmm2 /* * VSCALEF( S, _VRES1, _VRES1, sExp ); * 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 zmm0 zmm1 zmm2 /* Restore registers * and exit the function */ L(EXIT): vmovaps %zmm2, %zmm0 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 %zmm0, 64(%rsp) vmovups %zmm1, 128(%rsp) vmovups %zmm2, 192(%rsp) # LOE rbx r12 r13 r14 r15 edx zmm2 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: -64; DW_OP_and; DW_OP_const4s: -240; DW_OP_plus) */ .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x10, 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: -64; DW_OP_and; DW_OP_const4s: -248; DW_OP_plus) */ .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x08, 0xff, 0xff, 0xff, 0x22 movl %edx, %r13d movq %r14, (%rsp) /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -256; DW_OP_plus) */ .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x00, 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 $16, %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 192(%rsp), %zmm2 /* Go to exit */ jmp L(EXIT) /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -240; DW_OP_plus) */ .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x10, 0xff, 0xff, 0xff, 0x22 /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -248; DW_OP_plus) */ .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x08, 0xff, 0xff, 0xff, 0x22 /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -256; DW_OP_plus) */ .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x00, 0xff, 0xff, 0xff, 0x22 # LOE rbx r12 r13 r14 r15 zmm2 /* Scalar math fucntion call * to process special input */ L(SCALAR_MATH_CALL): movl %r12d, %r14d vmovss 64(%rsp, %r14, 4), %xmm0 vmovss 128(%rsp, %r14, 4), %xmm1 call hypotf@PLT # LOE rbx r14 r15 r12d r13d xmm0 vmovss %xmm0, 192(%rsp, %r14, 4) /* Process special inputs in loop */ jmp L(SPECIAL_VALUES_LOOP) # LOE rbx r15 r12d r13d END(_ZGVeN16vv_hypotf_skx) .section .rodata, "a" .align 64 #ifdef __svml_shypot_data_internal_typedef typedef unsigned int VUINT32; typedef struct { __declspec(align(64)) VUINT32 _sAbsMask[16][1]; __declspec(align(64)) VUINT32 _sHalf[16][1]; __declspec(align(64)) VUINT32 _iExpBound[16][1]; } __svml_shypot_data_internal; #endif __svml_shypot_data_internal: .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */ .align 64 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sHalf */ /* fma based algorithm*/ .align 64 .long 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000 /* _iExpBound */ .align 64 .type __svml_shypot_data_internal, @object .size __svml_shypot_data_internal, .-__svml_shypot_data_internal