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/* Function atan2 vectorized with AVX2.
Copyright (C) 2021-2022 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_datan2_data_internal
*/
#define dPI 0
#define dPIO2 32
#define dA19 64
#define dA18 96
#define dA17 128
#define dA16 160
#define dA15 192
#define dA14 224
#define dA13 256
#define dA12 288
#define dA11 320
#define dA10 352
#define dA09 384
#define dA08 416
#define dA07 448
#define dA06 480
#define dA05 512
#define dA04 544
#define dA03 576
#define dA02 608
#define dA01 640
#define dA00 672
#define dSIGN_MASK 704
#define iCHK_WORK_SUB 736
#define iCHK_WORK_CMP 768
#define dABS_MASK 800
#define dZERO 832
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN4vv_atan2_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
* Get r0~=1/B
* Cannot be replaced by VQRCP(D, dR0, dB);
* Argument Absolute values
*/
vmovupd dABS_MASK+__svml_datan2_data_internal(%rip), %ymm5
/* Argument signs */
vmovupd dSIGN_MASK+__svml_datan2_data_internal(%rip), %ymm4
vmovups iCHK_WORK_SUB+__svml_datan2_data_internal(%rip), %xmm13
vmovupd %ymm0, (%rsp)
vmovapd %ymm1, %ymm8
vandpd %ymm5, %ymm8, %ymm2
vandpd %ymm5, %ymm0, %ymm1
vcmpnlt_uqpd %ymm2, %ymm1, %ymm15
/*
* 1) If y<x then a= y, b=x, PIO2=0
* 2) If y>x then a=-x, b=y, PIO2=Pi/2
*/
vorpd %ymm4, %ymm2, %ymm6
vblendvpd %ymm15, %ymm6, %ymm1, %ymm3
vblendvpd %ymm15, %ymm1, %ymm2, %ymm6
vdivpd %ymm6, %ymm3, %ymm14
vmovups iCHK_WORK_CMP+__svml_datan2_data_internal(%rip), %xmm3
vmovupd %ymm6, 32(%rsp)
vandpd %ymm4, %ymm0, %ymm7
vandpd %ymm4, %ymm8, %ymm5
vandpd dPIO2+__svml_datan2_data_internal(%rip), %ymm15, %ymm4
/* Check if y and x are on main path. */
vextractf128 $1, %ymm2, %xmm9
vextractf128 $1, %ymm1, %xmm10
vshufps $221, %xmm9, %xmm2, %xmm11
vshufps $221, %xmm10, %xmm1, %xmm12
vpsubd %xmm13, %xmm11, %xmm0
vpsubd %xmm13, %xmm12, %xmm9
vpcmpgtd %xmm3, %xmm0, %xmm15
vpcmpeqd %xmm3, %xmm0, %xmm6
vpcmpgtd %xmm3, %xmm9, %xmm10
vpcmpeqd %xmm3, %xmm9, %xmm3
vpor %xmm6, %xmm15, %xmm11
vpor %xmm3, %xmm10, %xmm12
/* Polynomial. */
vmulpd %ymm14, %ymm14, %ymm10
vpor %xmm12, %xmm11, %xmm3
vmovupd dA18+__svml_datan2_data_internal(%rip), %ymm9
vmovupd dA17+__svml_datan2_data_internal(%rip), %ymm12
vmovupd dA16+__svml_datan2_data_internal(%rip), %ymm15
vmulpd %ymm10, %ymm10, %ymm11
/* if x<0, dPI = Pi, else dPI =0 */
vcmple_oqpd dZERO+__svml_datan2_data_internal(%rip), %ymm8, %ymm13
vmovmskps %xmm3, %eax
vmulpd %ymm11, %ymm11, %ymm0
vandpd __svml_datan2_data_internal(%rip), %ymm13, %ymm6
vmovupd dA19+__svml_datan2_data_internal(%rip), %ymm13
vfmadd213pd dA14+__svml_datan2_data_internal(%rip), %ymm0, %ymm9
vfmadd213pd dA13+__svml_datan2_data_internal(%rip), %ymm0, %ymm12
vfmadd213pd dA12+__svml_datan2_data_internal(%rip), %ymm0, %ymm15
vfmadd213pd dA15+__svml_datan2_data_internal(%rip), %ymm0, %ymm13
vfmadd213pd dA10+__svml_datan2_data_internal(%rip), %ymm0, %ymm9
vfmadd213pd dA09+__svml_datan2_data_internal(%rip), %ymm0, %ymm12
vfmadd213pd dA08+__svml_datan2_data_internal(%rip), %ymm0, %ymm15
vfmadd213pd dA11+__svml_datan2_data_internal(%rip), %ymm0, %ymm13
vfmadd213pd dA06+__svml_datan2_data_internal(%rip), %ymm0, %ymm9
vfmadd213pd dA05+__svml_datan2_data_internal(%rip), %ymm0, %ymm12
vfmadd213pd dA04+__svml_datan2_data_internal(%rip), %ymm0, %ymm15
vfmadd213pd dA07+__svml_datan2_data_internal(%rip), %ymm0, %ymm13
vfmadd213pd dA02+__svml_datan2_data_internal(%rip), %ymm0, %ymm9
vfmadd213pd dA01+__svml_datan2_data_internal(%rip), %ymm0, %ymm12
vfmadd213pd dA03+__svml_datan2_data_internal(%rip), %ymm0, %ymm13
/* A00=1.0, account for it later VQFMA(D, dP4, dP4, dR8, dA00); */
vmulpd %ymm15, %ymm0, %ymm0
vfmadd213pd %ymm9, %ymm10, %ymm13
vfmadd213pd %ymm0, %ymm10, %ymm12
vfmadd213pd %ymm12, %ymm11, %ymm13
/*
* Reconstruction.
* dP=(R+R*dP) + dPIO2
*/
vfmadd213pd %ymm14, %ymm14, %ymm13
vaddpd %ymm13, %ymm4, %ymm14
vorpd %ymm5, %ymm14, %ymm0
vaddpd %ymm0, %ymm6, %ymm9
vorpd %ymm7, %ymm9, %ymm0
/* Special branch for fast (vector) processing of zero arguments */
testl %eax, %eax
/* Go to auxilary branch */
jne L(AUX_BRANCH)
# LOE rbx r12 r13 r14 r15 edx xmm3 ymm0 ymm1 ymm2 ymm4 ymm5 ymm6 ymm7 ymm8
/* Return from auxilary 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 ymm8
/* Restore registers
* and exit the function
*/
L(EXIT):
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):
vmovupd (%rsp), %ymm1
vmovupd %ymm8, 64(%rsp)
vmovupd %ymm0, 96(%rsp)
vmovupd %ymm1, 32(%rsp)
# LOE rbx r12 r13 r14 r15 edx ymm0
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 $4, %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)
vmovupd 96(%rsp), %ymm0
/* 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 ymm0
/* Scalar math fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovsd 32(%rsp, %r14, 8), %xmm0
vmovsd 64(%rsp, %r14, 8), %xmm1
call atan2@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovsd %xmm0, 96(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
cfi_restore(12)
cfi_restore(13)
cfi_restore(14)
# LOE rbx r15 r12d r13d
/* Auxilary branch
* for out of main path inputs
*/
L(AUX_BRANCH):
vmovupd (%rsp), %ymm11
/* Check if at least on of Y or Y is zero: iAXAYZERO */
vmovupd dZERO+__svml_datan2_data_internal(%rip), %ymm10
/* Check if both X & Y are not NaNs: iXYnotNAN */
vcmpordpd %ymm8, %ymm8, %ymm12
vcmpordpd %ymm11, %ymm11, %ymm13
vcmpeqpd %ymm10, %ymm2, %ymm2
vcmpeqpd %ymm10, %ymm1, %ymm1
vandpd %ymm13, %ymm12, %ymm14
vorpd %ymm1, %ymm2, %ymm2
vextractf128 $1, %ymm14, %xmm15
vextractf128 $1, %ymm2, %xmm11
vshufps $221, %xmm15, %xmm14, %xmm9
vshufps $221, %xmm11, %xmm2, %xmm12
/*
* Path for zero arguments (at least one of both)
* Check if both args are zeros (den. is zero)
*/
vcmpeqpd 32(%rsp), %ymm10, %ymm2
/* Check if at least on of Y or Y is zero and not NaN: iAXAYZEROnotNAN */
vpand %xmm9, %xmm12, %xmm1
/* Exclude from previous callout mask zero (and not NaN) arguments */
vpandn %xmm3, %xmm1, %xmm3
/* Go to callout */
vmovmskps %xmm3, %edx
/* Set sPIO2 to zero if den. is zero */
vblendvpd %ymm2, %ymm10, %ymm4, %ymm4
vorpd %ymm5, %ymm4, %ymm5
/* Res = sign(Y)*(X<0)?(PIO2+PI):PIO2 */
vextractf128 $1, %ymm10, %xmm2
vextractf128 $1, %ymm8, %xmm3
vshufps $221, %xmm2, %xmm10, %xmm4
vshufps $221, %xmm3, %xmm8, %xmm9
vpcmpgtd %xmm9, %xmm4, %xmm12
vpshufd $80, %xmm12, %xmm11
vpshufd $250, %xmm12, %xmm13
vinsertf128 $1, %xmm13, %ymm11, %ymm14
vandpd %ymm6, %ymm14, %ymm6
vaddpd %ymm6, %ymm5, %ymm2
vorpd %ymm7, %ymm2, %ymm2
/* Merge results from main and spec path */
vpshufd $80, %xmm1, %xmm7
vpshufd $250, %xmm1, %xmm1
vinsertf128 $1, %xmm1, %ymm7, %ymm3
vblendvpd %ymm3, %ymm2, %ymm0, %ymm0
/* Return to main vector processing path */
jmp L(AUX_BRANCH_RETURN)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm8
END(_ZGVdN4vv_atan2_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_datan2_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(32)) VUINT32 dPI[4][2];
__declspec(align(32)) VUINT32 dPIO2[4][2];
__declspec(align(32)) VUINT32 dA19[4][2];
__declspec(align(32)) VUINT32 dA18[4][2];
__declspec(align(32)) VUINT32 dA17[4][2];
__declspec(align(32)) VUINT32 dA16[4][2];
__declspec(align(32)) VUINT32 dA15[4][2];
__declspec(align(32)) VUINT32 dA14[4][2];
__declspec(align(32)) VUINT32 dA13[4][2];
__declspec(align(32)) VUINT32 dA12[4][2];
__declspec(align(32)) VUINT32 dA11[4][2];
__declspec(align(32)) VUINT32 dA10[4][2];
__declspec(align(32)) VUINT32 dA09[4][2];
__declspec(align(32)) VUINT32 dA08[4][2];
__declspec(align(32)) VUINT32 dA07[4][2];
__declspec(align(32)) VUINT32 dA06[4][2];
__declspec(align(32)) VUINT32 dA05[4][2];
__declspec(align(32)) VUINT32 dA04[4][2];
__declspec(align(32)) VUINT32 dA03[4][2];
__declspec(align(32)) VUINT32 dA02[4][2];
__declspec(align(32)) VUINT32 dA01[4][2];
__declspec(align(32)) VUINT32 dA00[4][2];
__declspec(align(32)) VUINT32 dSIGN_MASK[4][2];
__declspec(align(32)) VUINT32 iCHK_WORK_SUB[8][1];
__declspec(align(32)) VUINT32 iCHK_WORK_CMP[8][1];
__declspec(align(32)) VUINT32 dABS_MASK[4][2];
__declspec(align(32)) VUINT32 dZERO[4][2];
} __svml_datan2_data_internal;
#endif
__svml_datan2_data_internal:
.quad 0x400921FB54442D18, 0x400921FB54442D18, 0x400921FB54442D18, 0x400921FB54442D18 // dPI
.align 32
.quad 0x3FF921FB54442D18, 0x3FF921FB54442D18, 0x3FF921FB54442D18, 0x3FF921FB54442D18 // dPIO2
.align 32
.quad 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3 // dA19
.align 32
.quad 0x3F2CED0A36665209, 0x3F2CED0A36665209, 0x3F2CED0A36665209, 0x3F2CED0A36665209 // dA18
.align 32
.quad 0xBF52E67C93954C23, 0xBF52E67C93954C23, 0xBF52E67C93954C23, 0xBF52E67C93954C23 // dA17
.align 32
.quad 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3 // dA16
.align 32
.quad 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD // dA15
.align 32
.quad 0x3F914F4C661116A5, 0x3F914F4C661116A5, 0x3F914F4C661116A5, 0x3F914F4C661116A5 // dA14
.align 32
.quad 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C // dA13
.align 32
.quad 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F // dA12
.align 32
.quad 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC // dA11
.align 32
.quad 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B // dA10
.align 32
.quad 0xBFAAD261EAA09954, 0xBFAAD261EAA09954, 0xBFAAD261EAA09954, 0xBFAAD261EAA09954 // dA09
.align 32
.quad 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF // dA08
.align 32
.quad 0xBFB11084009435E0, 0xBFB11084009435E0, 0xBFB11084009435E0, 0xBFB11084009435E0 // dA07
.align 32
.quad 0x3FB3B12A49295651, 0x3FB3B12A49295651, 0x3FB3B12A49295651, 0x3FB3B12A49295651 // dA06
.align 32
.quad 0xBFB745D009BADA94, 0xBFB745D009BADA94, 0xBFB745D009BADA94, 0xBFB745D009BADA94 // dA05
.align 32
.quad 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5 // dA04
.align 32
.quad 0xBFC2492491EE55C7, 0xBFC2492491EE55C7, 0xBFC2492491EE55C7, 0xBFC2492491EE55C7 // dA03
.align 32
.quad 0x3FC999999997EE34, 0x3FC999999997EE34, 0x3FC999999997EE34, 0x3FC999999997EE34 // dA02
.align 32
.quad 0xBFD55555555553C5, 0xBFD55555555553C5, 0xBFD55555555553C5, 0xBFD55555555553C5 // dA01
.align 32
.quad 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000 // dA00
.align 32
.quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000 // dSIGN_MASK
.align 32
.long 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000 // iCHK_WORK_SUB
.align 32
.long 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000 // iCHK_WORK_CMP
.align 32
.quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff // dABS_MASK
.align 32
.quad 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000 // dZERO
.align 32
.type __svml_datan2_data_internal, @object
.size __svml_datan2_data_internal, .-__svml_datan2_data_internal
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