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/* Function cbrt vectorized with AVX-512.
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:
*
* x=2^{3*k+j} * 1.b1 b2 ... b5 b6 ... b52
* Let r=(x*2^{-3k-j} - 1.b1 b2 ... b5 1)* rcp[b1 b2 ..b5],
* where rcp[b1 b2 .. b5]=1/(1.b1 b2 b3 b4 b5 1) in double precision
* cbrt(2^j * 1. b1 b2 .. b5 1) is approximated as T[j][b1..b5]+D[j][b1..b5]
* (T stores the high 53 bits, D stores the low order bits)
* Result=2^k*T+(2^k*T*r)*P+2^k*D
* where P=p1+p2*r+..+p8*r^7
*
*/
/* Offsets for data table __svml_dcbrt_data_internal_avx512
*/
#define etbl_H 0
#define etbl_L 64
#define cbrt_tbl_H 128
#define BiasL 256
#define SZero 320
#define OneThird 384
#define Bias3 448
#define Three 512
#define One 576
#define poly_coeff10 640
#define poly_coeff9 704
#define poly_coeff8 768
#define poly_coeff7 832
#define poly_coeff6 896
#define poly_coeff5 960
#define poly_coeff4 1024
#define poly_coeff3 1088
#define poly_coeff2 1152
#define poly_coeff1 1216
#include <sysdep.h>
.text
.section .text.evex512,"ax",@progbits
ENTRY(_ZGVeN8v_cbrt_skx)
vgetmantpd $0, {sae}, %zmm0, %zmm14
/* GetExp(x) */
vgetexppd {sae}, %zmm0, %zmm7
vmovups BiasL+__svml_dcbrt_data_internal_avx512(%rip), %zmm8
/* exponent/3 */
vmovups OneThird+__svml_dcbrt_data_internal_avx512(%rip), %zmm9
vmovups Bias3+__svml_dcbrt_data_internal_avx512(%rip), %zmm10
/* Reduced argument: R = DblRcp*Mantissa - 1 */
vmovups One+__svml_dcbrt_data_internal_avx512(%rip), %zmm2
/* exponent%3 (to be used as index) */
vmovups Three+__svml_dcbrt_data_internal_avx512(%rip), %zmm11
/* DblRcp ~ 1/Mantissa */
vrcp14pd %zmm14, %zmm13
vaddpd {rn-sae}, %zmm8, %zmm7, %zmm12
vandpd SZero+__svml_dcbrt_data_internal_avx512(%rip), %zmm0, %zmm6
/* round DblRcp to 3 fractional bits (RN mode, no Precision exception) */
vrndscalepd $72, {sae}, %zmm13, %zmm15
vfmsub231pd {rn-sae}, %zmm12, %zmm9, %zmm10
/* polynomial */
vmovups poly_coeff10+__svml_dcbrt_data_internal_avx512(%rip), %zmm0
vmovups poly_coeff8+__svml_dcbrt_data_internal_avx512(%rip), %zmm7
vmovups poly_coeff7+__svml_dcbrt_data_internal_avx512(%rip), %zmm9
vfmsub231pd {rn-sae}, %zmm15, %zmm14, %zmm2
vrndscalepd $9, {sae}, %zmm10, %zmm5
/* Table lookup */
vmovups cbrt_tbl_H+__svml_dcbrt_data_internal_avx512(%rip), %zmm10
vmovups poly_coeff6+__svml_dcbrt_data_internal_avx512(%rip), %zmm8
vmovups poly_coeff3+__svml_dcbrt_data_internal_avx512(%rip), %zmm13
vfmadd231pd {rn-sae}, %zmm2, %zmm7, %zmm9
vfnmadd231pd {rn-sae}, %zmm5, %zmm11, %zmm12
vmovups poly_coeff5+__svml_dcbrt_data_internal_avx512(%rip), %zmm11
vmovups poly_coeff1+__svml_dcbrt_data_internal_avx512(%rip), %zmm14
/* Prepare table index */
vpsrlq $49, %zmm15, %zmm1
/* Table lookup: 2^(exponent%3) */
vpermpd __svml_dcbrt_data_internal_avx512(%rip), %zmm12, %zmm4
vpermpd etbl_L+__svml_dcbrt_data_internal_avx512(%rip), %zmm12, %zmm3
vpermt2pd cbrt_tbl_H+64+__svml_dcbrt_data_internal_avx512(%rip), %zmm1, %zmm10
vmovups poly_coeff9+__svml_dcbrt_data_internal_avx512(%rip), %zmm1
vfmadd231pd {rn-sae}, %zmm2, %zmm8, %zmm11
vmovups poly_coeff2+__svml_dcbrt_data_internal_avx512(%rip), %zmm12
vscalefpd {rn-sae}, %zmm5, %zmm10, %zmm15
vfmadd231pd {rn-sae}, %zmm2, %zmm0, %zmm1
vmovups poly_coeff4+__svml_dcbrt_data_internal_avx512(%rip), %zmm5
vfmadd231pd {rn-sae}, %zmm2, %zmm12, %zmm14
vmulpd {rn-sae}, %zmm2, %zmm2, %zmm0
vfmadd231pd {rn-sae}, %zmm2, %zmm5, %zmm13
/* Sh*R */
vmulpd {rn-sae}, %zmm2, %zmm4, %zmm2
vfmadd213pd {rn-sae}, %zmm9, %zmm0, %zmm1
vfmadd213pd {rn-sae}, %zmm11, %zmm0, %zmm1
vfmadd213pd {rn-sae}, %zmm13, %zmm0, %zmm1
vfmadd213pd {rn-sae}, %zmm14, %zmm0, %zmm1
/* Sl + (Sh*R)*Poly */
vfmadd213pd {rn-sae}, %zmm3, %zmm1, %zmm2
/*
* branch-free
* scaled_Th*(Sh+Sl+Sh*R*Poly)
*/
vaddpd {rn-sae}, %zmm4, %zmm2, %zmm3
vmulpd {rn-sae}, %zmm15, %zmm3, %zmm4
vorpd %zmm6, %zmm4, %zmm0
ret
END(_ZGVeN8v_cbrt_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_dcbrt_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 etbl_H[8][2];
__declspec(align(64)) VUINT32 etbl_L[8][2];
__declspec(align(64)) VUINT32 cbrt_tbl_H[16][2];
__declspec(align(64)) VUINT32 BiasL[8][2];
__declspec(align(64)) VUINT32 SZero[8][2];
__declspec(align(64)) VUINT32 OneThird[8][2];
__declspec(align(64)) VUINT32 Bias3[8][2];
__declspec(align(64)) VUINT32 Three[8][2];
__declspec(align(64)) VUINT32 One[8][2];
__declspec(align(64)) VUINT32 poly_coeff10[8][2];
__declspec(align(64)) VUINT32 poly_coeff9[8][2];
__declspec(align(64)) VUINT32 poly_coeff8[8][2];
__declspec(align(64)) VUINT32 poly_coeff7[8][2];
__declspec(align(64)) VUINT32 poly_coeff6[8][2];
__declspec(align(64)) VUINT32 poly_coeff5[8][2];
__declspec(align(64)) VUINT32 poly_coeff4[8][2];
__declspec(align(64)) VUINT32 poly_coeff3[8][2];
__declspec(align(64)) VUINT32 poly_coeff2[8][2];
__declspec(align(64)) VUINT32 poly_coeff1[8][2];
} __svml_dcbrt_data_internal_avx512;
#endif
__svml_dcbrt_data_internal_avx512:
/*== etbl_H ==*/
.quad 0x3ff0000000000000
.quad 0x3ff428a2f98d728b
.quad 0x3ff965fea53d6e3d
.quad 0x0000000000000000
.quad 0xbff0000000000000
.quad 0xbff428a2f98d728b
.quad 0xbff965fea53d6e3d
.quad 0x0000000000000000
/*== etbl_L ==*/
.align 64
.quad 0x0000000000000000
.quad 0xbc7ddc22548ea41e
.quad 0xbc9f53e999952f09
.quad 0x0000000000000000
.quad 0x0000000000000000
.quad 0x3c7ddc22548ea41e
.quad 0x3c9f53e999952f09
.quad 0x0000000000000000
/*== cbrt_tbl_H ==*/
.align 64
.quad 0x3ff428a2f98d728b
.quad 0x3ff361f35ca116ff
.quad 0x3ff2b6b5edf6b54a
.quad 0x3ff220e6dd675180
.quad 0x3ff19c3b38e975a8
.quad 0x3ff12589c21fb842
.quad 0x3ff0ba6ee5f9aad4
.quad 0x3ff059123d3a9848
.quad 0x3ff0000000000000
.quad 0x0000000000000000
.quad 0x0000000000000000
.quad 0x0000000000000000
.quad 0x0000000000000000
.quad 0x0000000000000000
.quad 0x0000000000000000
.quad 0x0000000000000000
/*== BiasL ==*/
.align 64
.quad 0x4338000000000000, 0x4338000000000000, 0x4338000000000000, 0x4338000000000000, 0x4338000000000000, 0x4338000000000000, 0x4338000000000000, 0x4338000000000000
/*== Zero ==*/
.align 64
.quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000
/*== OneThird ==*/
.align 64
.quad 0x3fd5555555555556, 0x3fd5555555555556, 0x3fd5555555555556, 0x3fd5555555555556, 0x3fd5555555555556, 0x3fd5555555555556, 0x3fd5555555555556, 0x3fd5555555555556
/*== Bias3 ==*/
.align 64
.quad 0x4320000000000000, 0x4320000000000000, 0x4320000000000000, 0x4320000000000000, 0x4320000000000000, 0x4320000000000000, 0x4320000000000000, 0x4320000000000000
/*== Three ==*/
.align 64
.quad 0x4008000000000000, 0x4008000000000000, 0x4008000000000000, 0x4008000000000000, 0x4008000000000000, 0x4008000000000000, 0x4008000000000000, 0x4008000000000000
/*==One ==*/
.align 64
.quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
/*== poly_coeff10 ==*/
.align 64
.quad 0xbf882e3b6adeca62, 0xbf882e3b6adeca62, 0xbf882e3b6adeca62, 0xbf882e3b6adeca62, 0xbf882e3b6adeca62, 0xbf882e3b6adeca62, 0xbf882e3b6adeca62, 0xbf882e3b6adeca62
/*== poly_coeff9 ==*/
.align 64
.quad 0x3f8bda24bae48875, 0x3f8bda24bae48875, 0x3f8bda24bae48875, 0x3f8bda24bae48875, 0x3f8bda24bae48875, 0x3f8bda24bae48875, 0x3f8bda24bae48875, 0x3f8bda24bae48875
/*== poly_coeff8 ==*/
.align 64
.quad 0xbf9036b87c71d55f, 0xbf9036b87c71d55f, 0xbf9036b87c71d55f, 0xbf9036b87c71d55f, 0xbf9036b87c71d55f, 0xbf9036b87c71d55f, 0xbf9036b87c71d55f, 0xbf9036b87c71d55f
/*== poly_coeff7 ==*/
.align 64
.quad 0x3f9374ed9398b914, 0x3f9374ed9398b914, 0x3f9374ed9398b914, 0x3f9374ed9398b914, 0x3f9374ed9398b914, 0x3f9374ed9398b914, 0x3f9374ed9398b914, 0x3f9374ed9398b914
/*== poly_coeff6 ==*/
.align 64
.quad 0xbf98090d77f2468e, 0xbf98090d77f2468e, 0xbf98090d77f2468e, 0xbf98090d77f2468e, 0xbf98090d77f2468e, 0xbf98090d77f2468e, 0xbf98090d77f2468e, 0xbf98090d77f2468e
/*== poly_coeff5 ==*/
.align 64
.quad 0x3f9ee71141dcf569, 0x3f9ee71141dcf569, 0x3f9ee71141dcf569, 0x3f9ee71141dcf569, 0x3f9ee71141dcf569, 0x3f9ee71141dcf569, 0x3f9ee71141dcf569, 0x3f9ee71141dcf569
/*== poly_coeff4 ==*/
.align 64
.quad 0xbfa511e8d2b0363e, 0xbfa511e8d2b0363e, 0xbfa511e8d2b0363e, 0xbfa511e8d2b0363e, 0xbfa511e8d2b0363e, 0xbfa511e8d2b0363e, 0xbfa511e8d2b0363e, 0xbfa511e8d2b0363e
/*== poly_coeff3 ==*/
.align 64
.quad 0x3faf9add3c0b7e31, 0x3faf9add3c0b7e31, 0x3faf9add3c0b7e31, 0x3faf9add3c0b7e31, 0x3faf9add3c0b7e31, 0x3faf9add3c0b7e31, 0x3faf9add3c0b7e31, 0x3faf9add3c0b7e31
/*== poly_coeff2 ==*/
.align 64
.quad 0xbfbc71c71c71c741, 0xbfbc71c71c71c741, 0xbfbc71c71c71c741, 0xbfbc71c71c71c741, 0xbfbc71c71c71c741, 0xbfbc71c71c71c741, 0xbfbc71c71c71c741, 0xbfbc71c71c71c741
/*== poly_coeff1 ==*/
.align 64
.quad 0x3fd5555555555557, 0x3fd5555555555557, 0x3fd5555555555557, 0x3fd5555555555557, 0x3fd5555555555557, 0x3fd5555555555557, 0x3fd5555555555557, 0x3fd5555555555557
.align 64
.type __svml_dcbrt_data_internal_avx512,@object
.size __svml_dcbrt_data_internal_avx512,.-__svml_dcbrt_data_internal_avx512
|
