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/* Function atan2f vectorized with AVX2.
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 sSIGN_MASK 32
#define sABS_MASK 64
#define sPIO2 96
#define sPI 128
#define sPC8 160
#define sPC7 192
#define sPC6 224
#define sPC5 256
#define sPC4 288
#define sPC3 320
#define sPC2 352
#define sPC1 384
#define sPC0 416
#define iCHK_WORK_SUB 448
#define iCHK_WORK_CMP 480
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8vv_atan2f_avx2)
pushq %rbp
cfi_def_cfa_offset(16)
movq %rsp, %rbp
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
andq $-32, %rsp
subq $128, %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), %ymm2
/* Testing on working interval. */
vmovups iCHK_WORK_SUB+__svml_satan2_data_internal(%rip), %ymm15
vmovups iCHK_WORK_CMP+__svml_satan2_data_internal(%rip), %ymm9
/* if x<0, sPI = Pi, else sPI =0 */
vmovups __svml_satan2_data_internal(%rip), %ymm5
vmovaps %ymm1, %ymm7
vandps %ymm2, %ymm7, %ymm13
vandps %ymm2, %ymm0, %ymm12
vcmplt_oqps %ymm13, %ymm12, %ymm4
vcmple_oqps %ymm5, %ymm7, %ymm6
vpsubd %ymm15, %ymm13, %ymm10
vpsubd %ymm15, %ymm12, %ymm8
/*
* 1) If y<x then a= y, b=x, PIO2=0
* 2) If y>x then a=-x, b=y, PIO2=Pi/2
*/
vorps sSIGN_MASK+__svml_satan2_data_internal(%rip), %ymm13, %ymm3
vblendvps %ymm4, %ymm12, %ymm3, %ymm14
vblendvps %ymm4, %ymm13, %ymm12, %ymm3
/* Division a/b. */
vdivps %ymm3, %ymm14, %ymm11
vpcmpgtd %ymm9, %ymm10, %ymm14
vpcmpeqd %ymm9, %ymm10, %ymm15
vpor %ymm15, %ymm14, %ymm10
vmovups sPC7+__svml_satan2_data_internal(%rip), %ymm15
vpcmpgtd %ymm9, %ymm8, %ymm14
vpcmpeqd %ymm9, %ymm8, %ymm8
vpor %ymm8, %ymm14, %ymm9
vmovups sPC8+__svml_satan2_data_internal(%rip), %ymm14
vpor %ymm9, %ymm10, %ymm10
/* Polynomial. */
vmulps %ymm11, %ymm11, %ymm9
vmulps %ymm9, %ymm9, %ymm8
vfmadd213ps sPC6+__svml_satan2_data_internal(%rip), %ymm8, %ymm14
vfmadd213ps sPC5+__svml_satan2_data_internal(%rip), %ymm8, %ymm15
vfmadd213ps sPC4+__svml_satan2_data_internal(%rip), %ymm8, %ymm14
vfmadd213ps sPC3+__svml_satan2_data_internal(%rip), %ymm8, %ymm15
vfmadd213ps sPC2+__svml_satan2_data_internal(%rip), %ymm8, %ymm14
vfmadd213ps sPC1+__svml_satan2_data_internal(%rip), %ymm8, %ymm15
vfmadd213ps sPC0+__svml_satan2_data_internal(%rip), %ymm8, %ymm14
vfmadd213ps %ymm14, %ymm9, %ymm15
vandnps sPIO2+__svml_satan2_data_internal(%rip), %ymm4, %ymm4
/* Reconstruction. */
vfmadd213ps %ymm4, %ymm11, %ymm15
vxorps %ymm13, %ymm7, %ymm1
vandps sPI+__svml_satan2_data_internal(%rip), %ymm6, %ymm6
vorps %ymm1, %ymm15, %ymm11
vaddps %ymm11, %ymm6, %ymm8
vmovmskps %ymm10, %eax
vxorps %ymm12, %ymm0, %ymm2
vorps %ymm2, %ymm8, %ymm9
/* Special branch for fast (vector) processing of zero arguments */
testl %eax, %eax
/* Go to auxiliary branch */
jne L(AUX_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm1 ymm2 ymm3 ymm4 ymm5 ymm6 ymm7 ymm9 ymm10 ymm12 ymm13
/* 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 ymm0 ymm7 ymm9
/* Restore registers
* and exit the function
*/
L(EXIT):
vmovaps %ymm9, %ymm0
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 %ymm0, 32(%rsp)
vmovups %ymm7, 64(%rsp)
vmovups %ymm9, 96(%rsp)
# LOE rbx r12 r13 r14 r15 edx ymm9
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: -32; DW_OP_and; DW_OP_const4s: -112; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 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: -32; DW_OP_and; DW_OP_const4s: -120; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22
movl %edx, %r13d
movq %r14, (%rsp)
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -128; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 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 96(%rsp), %ymm9
/* Go to exit */
jmp L(EXIT)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -112; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -120; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -128; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22
# LOE rbx r12 r13 r14 r15 ymm9
/* Scalar math function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovss 32(%rsp, %r14, 4), %xmm0
vmovss 64(%rsp, %r14, 4), %xmm1
call atan2f@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovss %xmm0, 96(%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 */
vpcmpeqd %ymm5, %ymm13, %ymm13
vpcmpeqd %ymm5, %ymm12, %ymm12
/* Check if both X & Y are not NaNs: iXYnotNAN */
vcmpordps %ymm7, %ymm7, %ymm11
vcmpordps %ymm0, %ymm0, %ymm14
/*
* Path for zero arguments (at least one of both)
* Check if both args are zeros (den. is zero)
*/
vcmpeqps %ymm5, %ymm3, %ymm3
vpor %ymm12, %ymm13, %ymm15
/* Set sPIO2 to zero if den. is zero */
vblendvps %ymm3, %ymm5, %ymm4, %ymm4
vandps %ymm14, %ymm11, %ymm8
/* Check if at least on of Y or Y is zero and not NaN: iAXAYZEROnotNAN */
vpand %ymm8, %ymm15, %ymm8
/* Res = sign(Y)*(X<0)?(PIO2+PI):PIO2 */
vpcmpgtd %ymm7, %ymm5, %ymm5
vorps %ymm1, %ymm4, %ymm1
vandps %ymm6, %ymm5, %ymm6
vaddps %ymm6, %ymm1, %ymm1
/* Exclude from previous callout mask zero (and not NaN) arguments */
vpandn %ymm10, %ymm8, %ymm10
vorps %ymm2, %ymm1, %ymm2
/* Go to callout */
vmovmskps %ymm10, %edx
/* Merge results from main and spec path */
vblendvps %ymm8, %ymm2, %ymm9, %ymm9
/* Return to main vector processing path */
jmp L(AUX_BRANCH_RETURN)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm7 ymm9
END(_ZGVdN8vv_atan2f_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_satan2_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(32)) VUINT32 sZERO[8][1];
__declspec(align(32)) VUINT32 sSIGN_MASK[8][1];
__declspec(align(32)) VUINT32 sABS_MASK[8][1];
__declspec(align(32)) VUINT32 sPIO2[8][1];
__declspec(align(32)) VUINT32 sPI[8][1];
__declspec(align(32)) VUINT32 sPC8[8][1];
__declspec(align(32)) VUINT32 sPC7[8][1];
__declspec(align(32)) VUINT32 sPC6[8][1];
__declspec(align(32)) VUINT32 sPC5[8][1];
__declspec(align(32)) VUINT32 sPC4[8][1];
__declspec(align(32)) VUINT32 sPC3[8][1];
__declspec(align(32)) VUINT32 sPC2[8][1];
__declspec(align(32)) VUINT32 sPC1[8][1];
__declspec(align(32)) VUINT32 sPC0[8][1];
__declspec(align(32)) VUINT32 iCHK_WORK_SUB[8][1];
__declspec(align(32)) VUINT32 iCHK_WORK_CMP[8][1];
} __svml_satan2_data_internal;
#endif
__svml_satan2_data_internal:
.long 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000 // sZERO
.align 32
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 // sSIGN_MASK
.align 32
.long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF // sABS_MASK
.align 32
.long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB // sPIO2
.align 32
.long 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB // sPI
.align 32
.long 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0 // sA08
.align 32
.long 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631 // sA07
.align 32
.long 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384 // sA06
.align 32
.long 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629 // sA05
.align 32
.long 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474 // sA04
.align 32
.long 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8 // sA03
.align 32
.long 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F // sA02
.align 32
.long 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49 // sA01
.align 32
.long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 // sA00
.align 32
.long 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000 // iCHK_WORK_SUB
.align 32
.long 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000 // iCHK_WORK_CMP
.align 32
.type __svml_satan2_data_internal, @object
.size __svml_satan2_data_internal, .-__svml_satan2_data_internal
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