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/* Function hypot vectorized with AVX-512.
Copyright (C) 2021-2023 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 error = z*(rsqrt(z)*rsqrt(z)) - 1
* Calculate fixing part p with polynom
* Fix answer with sqrt(z) = z * rsqrt(z) + error * p * z
*
* 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 within borders [3BC ; 441] else goto Callout
*
* _s ~ 1.0/sqrt(_z)
* _s2 ~ 1.0/(sqrt(_z)*sqrt(_z)) ~ 1.0/_z = (1.0/_z + O)
* _e[rror] = (1.0/_z + O) * _z - 1.0
* calculate fixing part _p
* _p = (((_POLY_C5*_e + _POLY_C4)*_e +_POLY_C3)*_e +_POLY_C2)*_e + _POLY_C1
* some parts of polynom are skipped for lower flav
*
* result = _z * (1.0/sqrt(_z) + O) + _p * _e[rror] * _z
*
*
*/
/* Offsets for data table __svml_dhypot_data_internal
*/
#define _dAbsMask 0
#define _lExpBound_uisa 64
#define _lExpBound 128
#define _dHalf 192
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN8vv_hypot_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
vgetexppd {sae}, %zmm0, %zmm2
vgetexppd {sae}, %zmm1, %zmm3
vmovups _dHalf+__svml_dhypot_data_internal(%rip), %zmm9
vmaxpd {sae}, %zmm3, %zmm2, %zmm4
vmulpd {rn-sae}, %zmm0, %zmm0, %zmm2
vandpd _dAbsMask+__svml_dhypot_data_internal(%rip), %zmm4, %zmm5
vfmadd231pd {rn-sae}, %zmm1, %zmm1, %zmm2
/* Select exponent bound so that no scaling is needed */
vpcmpq $5, _lExpBound_uisa+__svml_dhypot_data_internal(%rip), %zmm5, %k0
vrsqrt14pd %zmm2, %zmm6
kmovw %k0, %edx
vmulpd {rn-sae}, %zmm6, %zmm2, %zmm7
vmulpd {rn-sae}, %zmm6, %zmm9, %zmm8
vfnmadd231pd {rn-sae}, %zmm7, %zmm8, %zmm9
vfmadd231pd {rn-sae}, %zmm9, %zmm8, %zmm8
vfmadd213pd {rn-sae}, %zmm7, %zmm7, %zmm9
vfnmadd231pd {rn-sae}, %zmm9, %zmm9, %zmm2
vfmadd213pd {rn-sae}, %zmm9, %zmm8, %zmm2
/* 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 $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 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 function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovsd 64(%rsp, %r14, 8), %xmm0
vmovsd 128(%rsp, %r14, 8), %xmm1
call hypot@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovsd %xmm0, 192(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN8vv_hypot_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_dhypot_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 _dAbsMask[8][2];
__declspec(align(64)) VUINT32 _lExpBound_uisa[8][2];
__declspec(align(64)) VUINT32 _lExpBound[8][2];
__declspec(align(64)) VUINT32 _dHalf[8][2];
} __svml_dhypot_data_internal;
#endif
__svml_dhypot_data_internal:
/* legacy algorithm */
.quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff /* _dAbsMask */
/* fma based algorithm*/
.align 64
.quad 0x407ff00000000000, 0x407ff00000000000, 0x407ff00000000000, 0x407ff00000000000, 0x407ff00000000000, 0x407ff00000000000, 0x407ff00000000000, 0x407ff00000000000 /* _lExpBound_uisa */
.align 64
.quad 0x404f800000000000, 0x404f800000000000, 0x404f800000000000, 0x404f800000000000, 0x404f800000000000, 0x404f800000000000, 0x404f800000000000, 0x404f800000000000 /* _lExpBound */
.align 64
.quad 0x3FE0000000000000, 0x3FE0000000000000, 0x3FE0000000000000, 0x3FE0000000000000, 0x3FE0000000000000, 0x3FE0000000000000, 0x3FE0000000000000, 0x3FE0000000000000 /* _dHalf */
.align 64
.type __svml_dhypot_data_internal, @object
.size __svml_dhypot_data_internal, .-__svml_dhypot_data_internal
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