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/* Function atan2f 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_satan2_data_internal
*/
#define sZERO 0
#define sONE 64
#define sSIGN_MASK 128
#define sABS_MASK 192
#define sPIO2 256
#define sPI 320
#define sPC8 384
#define sPC7 448
#define sPC6 512
#define sPC5 576
#define sPC4 640
#define sPC3 704
#define sPC2 768
#define sPC1 832
#define sPC0 896
#define iCHK_WORK_SUB 960
#define iCHK_WORK_CMP 1024
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16vv_atan2f_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
xorl %edx, %edx
/*
* #define NO_VECTOR_ZERO_ATAN2_ARGS
* Declarations
* Variables
* Constants
* The end of declarations
* Implementation
* Arguments signs
*/
vmovups sABS_MASK+__svml_satan2_data_internal(%rip), %zmm6
vmovups sONE+__svml_satan2_data_internal(%rip), %zmm3
/* Testing on working interval. */
vmovups iCHK_WORK_SUB+__svml_satan2_data_internal(%rip), %zmm9
vmovups iCHK_WORK_CMP+__svml_satan2_data_internal(%rip), %zmm14
/*
* 1) If y<x then a= y, b=x, PIO2=0
* 2) If y>x then a=-x, b=y, PIO2=Pi/2
*/
vmovups sPIO2+__svml_satan2_data_internal(%rip), %zmm4
vpternlogd $255, %zmm13, %zmm13, %zmm13
vmovaps %zmm1, %zmm8
vandps %zmm6, %zmm8, %zmm2
vandps %zmm6, %zmm0, %zmm1
vorps sSIGN_MASK+__svml_satan2_data_internal(%rip), %zmm2, %zmm5
vpsubd %zmm9, %zmm2, %zmm10
vpsubd %zmm9, %zmm1, %zmm12
vxorps %zmm2, %zmm8, %zmm7
vxorps %zmm1, %zmm0, %zmm6
vcmpps $17, {sae}, %zmm2, %zmm1, %k1
vpcmpgtd %zmm10, %zmm14, %k2
vpcmpgtd %zmm12, %zmm14, %k3
vmovups sPC6+__svml_satan2_data_internal(%rip), %zmm14
vblendmps %zmm1, %zmm5, %zmm11{%k1}
vblendmps %zmm2, %zmm1, %zmm5{%k1}
vxorps %zmm4, %zmm4, %zmm4{%k1}
/*
* Division a/b.
* Enabled when FMA is available and
* performance is better with NR iteration
*/
vrcp14ps %zmm5, %zmm15
vfnmadd231ps {rn-sae}, %zmm5, %zmm15, %zmm3
vfmadd213ps {rn-sae}, %zmm15, %zmm3, %zmm15
vmulps {rn-sae}, %zmm15, %zmm11, %zmm3
vfnmadd231ps {rn-sae}, %zmm5, %zmm3, %zmm11
vfmadd213ps {rn-sae}, %zmm3, %zmm11, %zmm15
vmovups sPC8+__svml_satan2_data_internal(%rip), %zmm11
vpternlogd $255, %zmm3, %zmm3, %zmm3
/* Polynomial. */
vmulps {rn-sae}, %zmm15, %zmm15, %zmm9
vpandnd %zmm10, %zmm10, %zmm13{%k2}
vmulps {rn-sae}, %zmm9, %zmm9, %zmm10
vfmadd231ps {rn-sae}, %zmm10, %zmm11, %zmm14
vmovups sPC5+__svml_satan2_data_internal(%rip), %zmm11
vpandnd %zmm12, %zmm12, %zmm3{%k3}
vpord %zmm3, %zmm13, %zmm3
vmovups sPC4+__svml_satan2_data_internal(%rip), %zmm13
vmovups sPC7+__svml_satan2_data_internal(%rip), %zmm12
vptestmd %zmm3, %zmm3, %k0
vfmadd213ps {rn-sae}, %zmm13, %zmm10, %zmm14
vfmadd231ps {rn-sae}, %zmm10, %zmm12, %zmm11
vmovups sPC3+__svml_satan2_data_internal(%rip), %zmm12
vmovups sPC2+__svml_satan2_data_internal(%rip), %zmm13
/* Special branch for fast (vector) processing of zero arguments */
kortestw %k0, %k0
vfmadd213ps {rn-sae}, %zmm12, %zmm10, %zmm11
vmovups sPC1+__svml_satan2_data_internal(%rip), %zmm12
vfmadd213ps {rn-sae}, %zmm13, %zmm10, %zmm14
vmovups sPC0+__svml_satan2_data_internal(%rip), %zmm13
vfmadd213ps {rn-sae}, %zmm12, %zmm10, %zmm11
vfmadd213ps {rn-sae}, %zmm13, %zmm10, %zmm14
vfmadd213ps {rn-sae}, %zmm14, %zmm9, %zmm11
/* Reconstruction. */
vfmadd213ps {rn-sae}, %zmm4, %zmm15, %zmm11
/* if x<0, sPI = Pi, else sPI =0 */
vmovups __svml_satan2_data_internal(%rip), %zmm15
vorps %zmm7, %zmm11, %zmm9
vcmpps $18, {sae}, %zmm15, %zmm8, %k4
vmovups sPI+__svml_satan2_data_internal(%rip), %zmm11
vaddps {rn-sae}, %zmm11, %zmm9, %zmm9{%k4}
vorps %zmm6, %zmm9, %zmm10
/* Go to auxiliary branch */
jne L(AUX_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm1 zmm2 zmm3 zmm4 zmm5 zmm6 zmm7 zmm8 zmm10 zmm11
/* Return from auxiliary branch
* for out of main path inputs
*/
L(AUX_BRANCH_RETURN):
/*
* Special branch for fast (vector) processing of zero arguments
* 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 zmm8 zmm10
/* Restore registers
* and exit the function
*/
L(EXIT):
vmovaps %zmm10, %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 %zmm8, 128(%rsp)
vmovups %zmm10, 192(%rsp)
# LOE rbx r12 r13 r14 r15 edx zmm10
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), %zmm10
/* 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 zmm10
/* Scalar math function 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 atan2f@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovss %xmm0, 192(%rsp, %r14, 4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
cfi_restore(12)
cfi_restore(13)
cfi_restore(14)
# LOE rbx r15 r12d r13d
/* Auxiliary branch
* for out of main path inputs
*/
L(AUX_BRANCH):
/* Check if at least on of Y or Y is zero: iAXAYZERO */
vmovups __svml_satan2_data_internal(%rip), %zmm9
/* Check if both X & Y are not NaNs: iXYnotNAN */
vcmpps $3, {sae}, %zmm8, %zmm8, %k1
vcmpps $3, {sae}, %zmm0, %zmm0, %k2
vpcmpd $4, %zmm9, %zmm2, %k3
vpcmpd $4, %zmm9, %zmm1, %k4
/*
* Path for zero arguments (at least one of both)
* Check if both args are zeros (den. is zero)
*/
vcmpps $4, {sae}, %zmm9, %zmm5, %k5
/* Res = sign(Y)*(X<0)?(PIO2+PI):PIO2 */
vpcmpgtd %zmm8, %zmm9, %k6
vpternlogd $255, %zmm14, %zmm14, %zmm14
vpternlogd $255, %zmm12, %zmm12, %zmm12
vpternlogd $255, %zmm13, %zmm13, %zmm13
vpandnd %zmm2, %zmm2, %zmm14{%k3}
vpternlogd $255, %zmm2, %zmm2, %zmm2
vpandnd %zmm1, %zmm1, %zmm2{%k4}
vpord %zmm2, %zmm14, %zmm15
vpternlogd $255, %zmm2, %zmm2, %zmm2
vpandnd %zmm5, %zmm5, %zmm2{%k5}
/* Set sPIO2 to zero if den. is zero */
vpandnd %zmm4, %zmm2, %zmm4
vpandd %zmm2, %zmm9, %zmm5
vpord %zmm5, %zmm4, %zmm2
vorps %zmm7, %zmm2, %zmm7
vaddps {rn-sae}, %zmm11, %zmm7, %zmm7{%k6}
vorps %zmm6, %zmm7, %zmm6
vpandnd %zmm8, %zmm8, %zmm12{%k1}
vpandnd %zmm0, %zmm0, %zmm13{%k2}
vandps %zmm13, %zmm12, %zmm12
/* Check if at least on of Y or Y is zero and not NaN: iAXAYZEROnotNAN */
vpandd %zmm12, %zmm15, %zmm1
/* Exclude from previous callout mask zero (and not NaN) arguments */
vpandnd %zmm3, %zmm1, %zmm3
/* Go to callout */
vptestmd %zmm3, %zmm3, %k0
kmovw %k0, %edx
/* Merge results from main and spec path */
vpandnd %zmm10, %zmm1, %zmm10
vpandd %zmm1, %zmm6, %zmm11
vpord %zmm11, %zmm10, %zmm10
/* Return to main vector processing path */
jmp L(AUX_BRANCH_RETURN)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm8 zmm10
END(_ZGVeN16vv_atan2f_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_satan2_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 sZERO[16][1];
__declspec(align(64)) VUINT32 sONE[16][1];
__declspec(align(64)) VUINT32 sSIGN_MASK[16][1];
__declspec(align(64)) VUINT32 sABS_MASK[16][1];
__declspec(align(64)) VUINT32 sPIO2[16][1];
__declspec(align(64)) VUINT32 sPI[16][1];
__declspec(align(64)) VUINT32 sPC8[16][1];
__declspec(align(64)) VUINT32 sPC7[16][1];
__declspec(align(64)) VUINT32 sPC6[16][1];
__declspec(align(64)) VUINT32 sPC5[16][1];
__declspec(align(64)) VUINT32 sPC4[16][1];
__declspec(align(64)) VUINT32 sPC3[16][1];
__declspec(align(64)) VUINT32 sPC2[16][1];
__declspec(align(64)) VUINT32 sPC1[16][1];
__declspec(align(64)) VUINT32 sPC0[16][1];
__declspec(align(64)) VUINT32 iCHK_WORK_SUB[16][1];
__declspec(align(64)) VUINT32 iCHK_WORK_CMP[16][1];
} __svml_satan2_data_internal;
#endif
__svml_satan2_data_internal:
.long 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000 // sZERO
.align 64
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 // sONE
.align 64
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 // sSIGN_MASK
.align 64
.long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF // sABS_MASK
.align 64
.long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB // sPIO2
.align 64
.long 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB // sPI
.align 64
.long 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0 // sA08
.align 64
.long 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631 // sA07
.align 64
.long 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384 // sA06
.align 64
.long 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629 // sA05
.align 64
.long 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474 // sA04
.align 64
.long 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8 // sA03
.align 64
.long 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F // sA02
.align 64
.long 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49 // sA01
.align 64
.long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 // sA00
.align 64
.long 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000 // iCHK_WORK_SUB
.align 64
.long 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000 // iCHK_WORK_CMP
.align 64
.type __svml_satan2_data_internal, @object
.size __svml_satan2_data_internal, .-__svml_satan2_data_internal
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