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/* Function hypot vectorized with SSE4.
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 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 withing 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 _dHiLoMask 0
#define _dAbsMask 16
#define _dOne 32
#define _POLY_C5 48
#define _POLY_C4 64
#define _POLY_C3 80
#define _POLY_C2 96
#define _POLY_C1 112
#define _LowBoundary 128
#define _HighBoundary 144
#include <sysdep.h>
.text
.section .text.sse4,"ax",@progbits
ENTRY(_ZGVbN2vv_hypot_sse4)
subq $88, %rsp
cfi_def_cfa_offset(96)
/*
* Defines
* Implementation
* Multiprecision branch for _HA_ only
* _z = _VARG1 * _VARG1 + _VARG2 * _VARG2
*/
movaps %xmm0, %xmm10
movaps %xmm1, %xmm2
mulpd %xmm0, %xmm10
mulpd %xmm1, %xmm2
addpd %xmm2, %xmm10
/*
* _s ~ 1.0/sqrt(_z)
* _s2 ~ 1.0/(sqrt(_z)*sqrt(_z)) ~ 1.0/_z
*/
cvtpd2ps %xmm10, %xmm7
movlhps %xmm7, %xmm7
rsqrtps %xmm7, %xmm8
cvtps2pd %xmm8, %xmm11
movaps %xmm11, %xmm2
mulpd %xmm11, %xmm2
/* _e[rror] ~ (1.0/_z + O) * _z - 1.0 */
mulpd %xmm10, %xmm2
subpd _dOne+__svml_dhypot_data_internal(%rip), %xmm2
/*
* 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
*/
movups _POLY_C4+__svml_dhypot_data_internal(%rip), %xmm9
mulpd %xmm2, %xmm9
addpd _POLY_C3+__svml_dhypot_data_internal(%rip), %xmm9
mulpd %xmm2, %xmm9
addpd _POLY_C2+__svml_dhypot_data_internal(%rip), %xmm9
mulpd %xmm2, %xmm9
addpd _POLY_C1+__svml_dhypot_data_internal(%rip), %xmm9
/* result = _z * (1.0/sqrt(_z) + O) + _p * _e[rror] * _z */
mulpd %xmm9, %xmm2
mulpd %xmm11, %xmm2
mulpd %xmm10, %xmm11
mulpd %xmm10, %xmm2
/* Check _z exponent to be withing borders [3BC ; 441] else goto Callout */
movq _LowBoundary+__svml_dhypot_data_internal(%rip), %xmm5
movq _HighBoundary+__svml_dhypot_data_internal(%rip), %xmm3
pshufd $221, %xmm10, %xmm4
pcmpgtd %xmm4, %xmm5
pcmpgtd %xmm3, %xmm4
por %xmm4, %xmm5
pshufd $80, %xmm5, %xmm6
movmskpd %xmm6, %edx
addpd %xmm11, %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 $2, %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
movsd 32(%rsp,%r14,8), %xmm0
movsd 48(%rsp,%r14,8), %xmm1
call hypot@PLT
# LOE rbx rbp r14 r15 r12d r13d xmm0
movsd %xmm0, 64(%rsp,%r14,8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx rbp r15 r12d r13d
END(_ZGVbN2vv_hypot_sse4)
.section .rodata, "a"
.align 16
#ifdef __svml_dhypot_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct
{
__declspec(align(16)) VUINT32 _dHiLoMask[2][2];
__declspec(align(16)) VUINT32 _dAbsMask[2][2];
__declspec(align(16)) VUINT32 _dOne[2][2];
__declspec(align(16)) VUINT32 _POLY_C5[2][2];
__declspec(align(16)) VUINT32 _POLY_C4[2][2];
__declspec(align(16)) VUINT32 _POLY_C3[2][2];
__declspec(align(16)) VUINT32 _POLY_C2[2][2];
__declspec(align(16)) VUINT32 _POLY_C1[2][2];
__declspec(align(16)) VUINT32 _LowBoundary[4][1];
__declspec(align(16)) VUINT32 _HighBoundary[4][1];
} __svml_dhypot_data_internal;
#endif
__svml_dhypot_data_internal:
/* legacy algorithm */
.quad 0xffffc00000000000, 0xffffc00000000000 /* _dHiLoMask */
.align 16
.quad 0x7fffffffffffffff, 0x7fffffffffffffff /* _dAbsMask */
.align 16
.quad 0x3FF0000000000000, 0x3FF0000000000000 /* _dOne */
.align 16
.quad 0xBFCF800000000000, 0xBFCF800000000000 /* _POLY_C5 */
.align 16
.quad 0x3FD1800000000000, 0x3FD1800000000000 /* _POLY_C4 */
.align 16
.quad 0xBFD4000000000000, 0xBFD4000000000000 /* _POLY_C3 */
.align 16
.quad 0x3FD8000000000000, 0x3FD8000000000000 /* _POLY_C2 */
.align 16
.quad 0xBFE0000000000000, 0xBFE0000000000000 /* _POLY_C1 */
.align 16
.long 0x3BC00000, 0x3BC00000, 0x3BC00000, 0x3BC00000 /* _LowBoundary */
.align 16
.long 0x44100000, 0x44100000, 0x44100000, 0x44100000 /* _HighBoundary */
.align 16
.type __svml_dhypot_data_internal,@object
.size __svml_dhypot_data_internal,.-__svml_dhypot_data_internal
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