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/* Function atan 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:
*
* For 0.0 <= x <= 7.0/16.0: atan(x) = atan(0.0) + atan(s), where s=(x-0.0)/(1.0+0.0*x)
* For 7.0/16.0 <= x <= 11.0/16.0: atan(x) = atan(0.5) + atan(s), where s=(x-0.5)/(1.0+0.5*x)
* For 11.0/16.0 <= x <= 19.0/16.0: atan(x) = atan(1.0) + atan(s), where s=(x-1.0)/(1.0+1.0*x)
* For 19.0/16.0 <= x <= 39.0/16.0: atan(x) = atan(1.5) + atan(s), where s=(x-1.5)/(1.0+1.5*x)
* For 39.0/16.0 <= x <= inf : atan(x) = atan(inf) + atan(s), where s=-1.0/x
* Where atan(s) ~= s+s^3*Poly11(s^2) on interval |s|<7.0/0.16.
*
*/
/* Offsets for data table __svml_datan_data_internal_avx512
*/
#define AbsMask 0
#define Shifter 64
#define MaxThreshold 128
#define MOne 192
#define One 256
#define LargeX 320
#define Zero 384
#define Tbl_H 448
#define dIndexMed 704
#define Pi2 768
#define coeff_1 832
#define coeff_2 896
#define coeff_3 960
#define coeff_4 1024
#define coeff_5 1088
#define coeff_6 1152
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN8v_atan_skx)
vmovups Shifter+__svml_datan_data_internal_avx512(%rip), %zmm4
vmovups MaxThreshold+__svml_datan_data_internal_avx512(%rip), %zmm3
vmovups One+__svml_datan_data_internal_avx512(%rip), %zmm9
/* saturate X range */
vmovups LargeX+__svml_datan_data_internal_avx512(%rip), %zmm7
vandpd __svml_datan_data_internal_avx512(%rip), %zmm0, %zmm8
/* R+Rl = DiffX/Y */
vbroadcastsd .FLT_10(%rip), %zmm15
vaddpd {rn-sae}, %zmm4, %zmm8, %zmm2
vxorpd %zmm0, %zmm8, %zmm1
vcmppd $29, {sae}, %zmm3, %zmm8, %k2
/* round to 2 bits after binary point */
vreducepd $40, {sae}, %zmm8, %zmm6
vsubpd {rn-sae}, %zmm4, %zmm2, %zmm5
/*
* if|X|>=MaxThreshold, set DiffX=-1
* VMSUB(D, DiffX, LargeMask, Zero, One);
*/
vblendmpd MOne+__svml_datan_data_internal_avx512(%rip), %zmm6, %zmm10{%k2}
vfmadd231pd {rn-sae}, %zmm8, %zmm5, %zmm9
vmovups dIndexMed+__svml_datan_data_internal_avx512(%rip), %zmm5
/* table lookup sequence */
vmovups Tbl_H+__svml_datan_data_internal_avx512(%rip), %zmm6
vgetmantpd $0, {sae}, %zmm10, %zmm14
vgetexppd {sae}, %zmm10, %zmm11
vmovups coeff_5+__svml_datan_data_internal_avx512(%rip), %zmm10
/*
* if|X|>=MaxThreshold, set Y=X
* VMADD(D, Y, LargeMask, X, Zero);
*/
vminpd {sae}, %zmm8, %zmm7, %zmm9{%k2}
vcmppd $29, {sae}, %zmm5, %zmm2, %k1
vmovups Tbl_H+128+__svml_datan_data_internal_avx512(%rip), %zmm7
vmovups coeff_1+__svml_datan_data_internal_avx512(%rip), %zmm8
vgetmantpd $0, {sae}, %zmm9, %zmm3
vgetexppd {sae}, %zmm9, %zmm12
vmovups coeff_3+__svml_datan_data_internal_avx512(%rip), %zmm9
vpermt2pd Tbl_H+64+__svml_datan_data_internal_avx512(%rip), %zmm2, %zmm6
vsubpd {rn-sae}, %zmm12, %zmm11, %zmm4
vpermt2pd Tbl_H+192+__svml_datan_data_internal_avx512(%rip), %zmm2, %zmm7
vrcp14pd %zmm3, %zmm13
vmovups coeff_4+__svml_datan_data_internal_avx512(%rip), %zmm12
vmovups coeff_6+__svml_datan_data_internal_avx512(%rip), %zmm11
vblendmpd %zmm7, %zmm6, %zmm2{%k1}
vmulpd {rn-sae}, %zmm13, %zmm14, %zmm0
vfnmadd231pd {rn-sae}, %zmm3, %zmm13, %zmm15
vfnmadd213pd {rn-sae}, %zmm14, %zmm0, %zmm3
vfmadd213pd {rn-sae}, %zmm15, %zmm15, %zmm15
vfmadd213pd {rn-sae}, %zmm13, %zmm13, %zmm15
vfmadd213pd {rn-sae}, %zmm0, %zmm15, %zmm3
vscalefpd {rn-sae}, %zmm4, %zmm3, %zmm0
/* set table value to Pi/2 for large X */
vblendmpd Pi2+__svml_datan_data_internal_avx512(%rip), %zmm2, %zmm3{%k2}
vmovups coeff_2+__svml_datan_data_internal_avx512(%rip), %zmm2
/* polynomial evaluation */
vmulpd {rn-sae}, %zmm0, %zmm0, %zmm14
vmulpd {rn-sae}, %zmm14, %zmm14, %zmm13
vmulpd {rn-sae}, %zmm0, %zmm14, %zmm15
vfmadd231pd {rn-sae}, %zmm14, %zmm8, %zmm2
vfmadd231pd {rn-sae}, %zmm14, %zmm9, %zmm12
vfmadd213pd {rn-sae}, %zmm11, %zmm10, %zmm14
vfmadd213pd {rn-sae}, %zmm12, %zmm13, %zmm2
vfmadd213pd {rn-sae}, %zmm14, %zmm13, %zmm2
vfmadd213pd {rn-sae}, %zmm0, %zmm15, %zmm2
vaddpd {rn-sae}, %zmm3, %zmm2, %zmm0
vxorpd %zmm1, %zmm0, %zmm0
ret
END(_ZGVeN8v_atan_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_datan_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 AbsMask[8][2];
__declspec(align(64)) VUINT32 Shifter[8][2];
__declspec(align(64)) VUINT32 MaxThreshold[8][2];
__declspec(align(64)) VUINT32 MOne[8][2];
__declspec(align(64)) VUINT32 One[8][2];
__declspec(align(64)) VUINT32 LargeX[8][2];
__declspec(align(64)) VUINT32 Zero[8][2];
__declspec(align(64)) VUINT32 Tbl_H[32][2];
__declspec(align(64)) VUINT32 dIndexMed[8][2];
__declspec(align(64)) VUINT32 Pi2[8][2];
__declspec(align(64)) VUINT32 coeff[6][8][2];
} __svml_datan_data_internal_avx512;
#endif
__svml_datan_data_internal_avx512:
/* AbsMask */
.quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff
/* Shifter */
.align 64
.quad 0x4318000000000000, 0x4318000000000000, 0x4318000000000000, 0x4318000000000000, 0x4318000000000000, 0x4318000000000000, 0x4318000000000000, 0x4318000000000000
/* MaxThreshold */
.align 64
.quad 0x401f800000000000, 0x401f800000000000, 0x401f800000000000, 0x401f800000000000, 0x401f800000000000, 0x401f800000000000, 0x401f800000000000, 0x401f800000000000
/* MOne */
.align 64
.quad 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000
/* One */
.align 64
.quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
/* LargeX */
.align 64
.quad 0x47f0000000000000, 0x47f0000000000000, 0x47f0000000000000, 0x47f0000000000000, 0x47f0000000000000, 0x47f0000000000000, 0x47f0000000000000, 0x47f0000000000000
/* Zero */
.align 64
.quad 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000
/* Tbl_H */
.align 64
.quad 0x0000000000000000, 0x3fcf5b75f92c80dd
.quad 0x3fddac670561bb4f, 0x3fe4978fa3269ee1
.quad 0x3fe921fb54442d18, 0x3fecac7c57846f9e
.quad 0x3fef730bd281f69b, 0x3ff0d38f2c5ba09f
.quad 0x3ff1b6e192ebbe44, 0x3ff270ef55a53a25
.quad 0x3ff30b6d796a4da8, 0x3ff38d6a6ce13353
.quad 0x3ff3fc176b7a8560, 0x3ff45b54837351a0
.quad 0x3ff4ae10fc6589a5, 0x3ff4f68dea672617
.quad 0x3ff5368c951e9cfd, 0x3ff56f6f33a3e6a7
.quad 0x3ff5a25052114e60, 0x3ff5d013c41adabd
.quad 0x3ff5f97315254857, 0x3ff61f06c6a92b89
.quad 0x3ff6414d44094c7c, 0x3ff660b02c736a06
.quad 0x3ff67d8863bc99bd, 0x3ff698213a9d5053
.quad 0x3ff6b0bae830c070, 0x3ff6c78c7edeb195
.quad 0x3ff6dcc57bb565fd, 0x3ff6f08f07435fec
.quad 0x3ff7030cf9403197, 0x3ff7145eac2088a4
/* dIndexMed */
.align 64
.quad 0x4318000000000010, 0x4318000000000010, 0x4318000000000010, 0x4318000000000010, 0x4318000000000010, 0x4318000000000010, 0x4318000000000010, 0x4318000000000010
/* Pi2 */
.align 64
.quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18
/* coeff6 */
.align 64
.quad 0x3fb2e9b9f5c4fe97, 0x3fb2e9b9f5c4fe97, 0x3fb2e9b9f5c4fe97, 0x3fb2e9b9f5c4fe97, 0x3fb2e9b9f5c4fe97, 0x3fb2e9b9f5c4fe97, 0x3fb2e9b9f5c4fe97, 0x3fb2e9b9f5c4fe97
.quad 0xbfb74257c46790cc, 0xbfb74257c46790cc, 0xbfb74257c46790cc, 0xbfb74257c46790cc, 0xbfb74257c46790cc, 0xbfb74257c46790cc, 0xbfb74257c46790cc, 0xbfb74257c46790cc
.quad 0x3fbc71bfeff916a0, 0x3fbc71bfeff916a0, 0x3fbc71bfeff916a0, 0x3fbc71bfeff916a0, 0x3fbc71bfeff916a0, 0x3fbc71bfeff916a0, 0x3fbc71bfeff916a0, 0x3fbc71bfeff916a0
.quad 0xbfc249248eef04da, 0xbfc249248eef04da, 0xbfc249248eef04da, 0xbfc249248eef04da, 0xbfc249248eef04da, 0xbfc249248eef04da, 0xbfc249248eef04da, 0xbfc249248eef04da
.quad 0x3fc999999998741e, 0x3fc999999998741e, 0x3fc999999998741e, 0x3fc999999998741e, 0x3fc999999998741e, 0x3fc999999998741e, 0x3fc999999998741e, 0x3fc999999998741e
.quad 0xbfd555555555554d, 0xbfd555555555554d, 0xbfd555555555554d, 0xbfd555555555554d, 0xbfd555555555554d, 0xbfd555555555554d, 0xbfd555555555554d, 0xbfd555555555554d
.align 64
.type __svml_datan_data_internal_avx512, @object
.size __svml_datan_data_internal_avx512, .-__svml_datan_data_internal_avx512
.align 8
.FLT_10:
.long 0x00000000, 0x3ff00000
.type .FLT_10, @object
.size .FLT_10, 8
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