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/* Function atan2 vectorized with SSE4.
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_datan2_data_internal
*/
#define dPI 0
#define dPIO2 16
#define dA19 32
#define dA18 48
#define dA17 64
#define dA16 80
#define dA15 96
#define dA14 112
#define dA13 128
#define dA12 144
#define dA11 160
#define dA10 176
#define dA09 192
#define dA08 208
#define dA07 224
#define dA06 240
#define dA05 256
#define dA04 272
#define dA03 288
#define dA02 304
#define dA01 320
#define dA00 336
#define dSIGN_MASK 352
#define iCHK_WORK_SUB 368
#define iCHK_WORK_CMP 384
#define dABS_MASK 400
#define dZERO 416
#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN2vv_atan2_sse4)
subq $88, %rsp
cfi_def_cfa_offset(96)
movaps %xmm1, %xmm11
/*
* #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
*/
movups dABS_MASK+__svml_datan2_data_internal(%rip), %xmm1
movaps %xmm0, %xmm10
movaps %xmm1, %xmm9
andps %xmm10, %xmm1
andps %xmm11, %xmm9
movaps %xmm1, %xmm4
cmpnltpd %xmm9, %xmm4
/* Argument signs */
movups dSIGN_MASK+__svml_datan2_data_internal(%rip), %xmm5
movaps %xmm4, %xmm0
movaps %xmm5, %xmm8
movaps %xmm5, %xmm7
/*
* 1) If y<x then a= y, b=x, PIO2=0
* 2) If y>x then a=-x, b=y, PIO2=Pi/2
*/
orps %xmm9, %xmm5
andnps %xmm1, %xmm0
andps %xmm4, %xmm5
andps %xmm11, %xmm8
movups dPIO2+__svml_datan2_data_internal(%rip), %xmm6
orps %xmm5, %xmm0
movaps %xmm4, %xmm5
andps %xmm4, %xmm6
andnps %xmm9, %xmm5
andps %xmm1, %xmm4
orps %xmm4, %xmm5
andps %xmm10, %xmm7
divpd %xmm5, %xmm0
movq iCHK_WORK_SUB+__svml_datan2_data_internal(%rip), %xmm2
xorl %edx, %edx
/* Check if y and x are on main path. */
pshufd $221, %xmm9, %xmm3
xorl %eax, %eax
pshufd $221, %xmm1, %xmm13
psubd %xmm2, %xmm3
psubd %xmm2, %xmm13
movdqa %xmm3, %xmm4
movq iCHK_WORK_CMP+__svml_datan2_data_internal(%rip), %xmm12
movdqa %xmm13, %xmm14
pcmpgtd %xmm12, %xmm4
pcmpeqd %xmm12, %xmm3
pcmpgtd %xmm12, %xmm14
pcmpeqd %xmm12, %xmm13
/* Polynomial. */
movaps %xmm0, %xmm12
por %xmm3, %xmm4
mulpd %xmm0, %xmm12
/* P = A19*R2 + A18 */
movups dA19+__svml_datan2_data_internal(%rip), %xmm15
movaps %xmm11, %xmm2
mulpd %xmm12, %xmm15
addpd dA18+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A17 */
mulpd %xmm12, %xmm15
addpd dA17+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A16 */
mulpd %xmm12, %xmm15
addpd dA16+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A15 */
mulpd %xmm12, %xmm15
addpd dA15+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A14 */
mulpd %xmm12, %xmm15
addpd dA14+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A13 */
mulpd %xmm12, %xmm15
addpd dA13+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A12 */
mulpd %xmm12, %xmm15
addpd dA12+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A11 */
mulpd %xmm12, %xmm15
addpd dA11+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A10 */
mulpd %xmm12, %xmm15
addpd dA10+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A09 */
mulpd %xmm12, %xmm15
addpd dA09+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A08 */
mulpd %xmm12, %xmm15
addpd dA08+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A07 */
mulpd %xmm12, %xmm15
addpd dA07+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A06 */
mulpd %xmm12, %xmm15
addpd dA06+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A05 */
mulpd %xmm12, %xmm15
addpd dA05+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A04 */
mulpd %xmm12, %xmm15
addpd dA04+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A03 */
mulpd %xmm12, %xmm15
addpd dA03+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A02 */
mulpd %xmm12, %xmm15
addpd dA02+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 + A01 */
mulpd %xmm12, %xmm15
addpd dA01+__svml_datan2_data_internal(%rip), %xmm15
/* P = P*R2 */
mulpd %xmm15, %xmm12
/*
* Reconstruction.
* dP=(R+R*dP) + dPIO2
*/
mulpd %xmm0, %xmm12
addpd %xmm12, %xmm0
/* if x<0, dPI = Pi, else dPI =0 */
movups dZERO+__svml_datan2_data_internal(%rip), %xmm3
por %xmm13, %xmm14
cmplepd %xmm3, %xmm2
addpd %xmm6, %xmm0
andps __svml_datan2_data_internal(%rip), %xmm2
orps %xmm8, %xmm0
addpd %xmm2, %xmm0
por %xmm14, %xmm4
orps %xmm7, %xmm0
movmskps %xmm4, %ecx
/* Special branch for fast (vector) processing of zero arguments */
testb $3, %cl
/* Go to auxiliary branch */
jne L(AUX_BRANCH)
# LOE rbx rbp r12 r13 r14 r15 eax edx xmm0 xmm1 xmm2 xmm3 xmm4 xmm5 xmm6 xmm7 xmm8 xmm9 xmm10 xmm11
/* 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 rbp r12 r13 r14 r15 eax edx xmm0 xmm10 xmm11
/* Restore registers
* and exit the function
*/
L(EXIT):
addq $88, %rsp
cfi_def_cfa_offset(8)
ret
cfi_def_cfa_offset(96)
/* Branch to process
* special inputs
*/
L(SPECIAL_VALUES_BRANCH):
movups %xmm10, 32(%rsp)
movups %xmm11, 48(%rsp)
movups %xmm0, 64(%rsp)
# LOE rbx rbp r12 r13 r14 r15 eax edx xmm0
movq %r12, 16(%rsp)
cfi_offset(12, -80)
movl %eax, %r12d
movq %r13, 8(%rsp)
cfi_offset(13, -88)
movl %edx, %r13d
movq %r14, (%rsp)
cfi_offset(14, -96)
# LOE rbx rbp r15 r12d r13d
/* Range mask
* bits check
*/
L(RANGEMASK_CHECK):
btl %r12d, %r13d
/* Call scalar math function */
jc L(SCALAR_MATH_CALL)
# LOE rbx rbp r15 r12d r13d
/* Special inputs
* processing loop
*/
L(SPECIAL_VALUES_LOOP):
incl %r12d
cmpl $2, %r12d
/* Check bits in range mask */
jl L(RANGEMASK_CHECK)
# LOE rbx rbp r15 r12d r13d
movq 16(%rsp), %r12
cfi_restore(12)
movq 8(%rsp), %r13
cfi_restore(13)
movq (%rsp), %r14
cfi_restore(14)
movups 64(%rsp), %xmm0
/* Go to exit */
jmp L(EXIT)
cfi_offset(12, -80)
cfi_offset(13, -88)
cfi_offset(14, -96)
# LOE rbx rbp r12 r13 r14 r15 xmm0
/* Scalar math function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movsd 32(%rsp, %r14, 8), %xmm0
movsd 48(%rsp, %r14, 8), %xmm1
call atan2@PLT
# LOE rbx rbp r14 r15 r12d r13d xmm0
movsd %xmm0, 64(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
cfi_restore(12)
cfi_restore(13)
cfi_restore(14)
# LOE rbx rbp r15 r12d r13d
/* Auxiliary branch
* for out of main path inputs
*/
L(AUX_BRANCH):
/* Check if both X & Y are not NaNs: iXYnotNAN */
movaps %xmm11, %xmm13
movaps %xmm10, %xmm12
cmpordpd %xmm11, %xmm13
cmpordpd %xmm10, %xmm12
/* Check if at least on of Y or Y is zero: iAXAYZERO */
cmpeqpd %xmm3, %xmm9
cmpeqpd %xmm3, %xmm1
/*
* Path for zero arguments (at least one of both)
* Check if both args are zeros (den. is zero)
*/
cmpeqpd %xmm3, %xmm5
andps %xmm12, %xmm13
orps %xmm1, %xmm9
pshufd $221, %xmm9, %xmm1
pshufd $221, %xmm13, %xmm9
/* Check if at least on of Y or Y is zero and not NaN: iAXAYZEROnotNAN */
pand %xmm9, %xmm1
/* Exclude from previous callout mask zero (and not NaN) arguments */
movdqa %xmm1, %xmm14
pandn %xmm4, %xmm14
/* Set sPIO2 to zero if den. is zero */
movaps %xmm5, %xmm4
andnps %xmm6, %xmm4
andps %xmm3, %xmm5
/* Res = sign(Y)*(X<0)?(PIO2+PI):PIO2 */
pshufd $221, %xmm3, %xmm3
orps %xmm5, %xmm4
pshufd $221, %xmm11, %xmm5
orps %xmm8, %xmm4
pcmpgtd %xmm5, %xmm3
pshufd $80, %xmm3, %xmm6
andps %xmm2, %xmm6
addpd %xmm6, %xmm4
/* Go to callout */
movmskps %xmm14, %edx
/* Merge results from main and spec path */
pshufd $80, %xmm1, %xmm2
orps %xmm7, %xmm4
movdqa %xmm2, %xmm7
andps %xmm2, %xmm4
andnps %xmm0, %xmm7
andl $3, %edx
movaps %xmm7, %xmm0
orps %xmm4, %xmm0
/* Return to main vector processing path */
jmp L(AUX_BRANCH_RETURN)
# LOE rbx rbp r12 r13 r14 r15 eax edx xmm0 xmm10 xmm11
END(_ZGVbN2vv_atan2_sse4)
.section .rodata, "a"
.align 16
#ifdef __svml_datan2_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(16)) VUINT32 dPI[2][2];
__declspec(align(16)) VUINT32 dPIO2[2][2];
__declspec(align(16)) VUINT32 dA19[2][2];
__declspec(align(16)) VUINT32 dA18[2][2];
__declspec(align(16)) VUINT32 dA17[2][2];
__declspec(align(16)) VUINT32 dA16[2][2];
__declspec(align(16)) VUINT32 dA15[2][2];
__declspec(align(16)) VUINT32 dA14[2][2];
__declspec(align(16)) VUINT32 dA13[2][2];
__declspec(align(16)) VUINT32 dA12[2][2];
__declspec(align(16)) VUINT32 dA11[2][2];
__declspec(align(16)) VUINT32 dA10[2][2];
__declspec(align(16)) VUINT32 dA09[2][2];
__declspec(align(16)) VUINT32 dA08[2][2];
__declspec(align(16)) VUINT32 dA07[2][2];
__declspec(align(16)) VUINT32 dA06[2][2];
__declspec(align(16)) VUINT32 dA05[2][2];
__declspec(align(16)) VUINT32 dA04[2][2];
__declspec(align(16)) VUINT32 dA03[2][2];
__declspec(align(16)) VUINT32 dA02[2][2];
__declspec(align(16)) VUINT32 dA01[2][2];
__declspec(align(16)) VUINT32 dA00[2][2];
__declspec(align(16)) VUINT32 dSIGN_MASK[2][2];
__declspec(align(16)) VUINT32 iCHK_WORK_SUB[4][1];
__declspec(align(16)) VUINT32 iCHK_WORK_CMP[4][1];
__declspec(align(16)) VUINT32 dABS_MASK[2][2];
__declspec(align(16)) VUINT32 dZERO[2][2];
} __svml_datan2_data_internal;
#endif
__svml_datan2_data_internal:
.quad 0x400921FB54442D18, 0x400921FB54442D18 // dPI
.align 16
.quad 0x3FF921FB54442D18, 0x3FF921FB54442D18 // dPIO2
.align 16
.quad 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3 // dA19
.align 16
.quad 0x3F2CED0A36665209, 0x3F2CED0A36665209 // dA18
.align 16
.quad 0xBF52E67C93954C23, 0xBF52E67C93954C23 // dA17
.align 16
.quad 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3 // dA16
.align 16
.quad 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD // dA15
.align 16
.quad 0x3F914F4C661116A5, 0x3F914F4C661116A5 // dA14
.align 16
.quad 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C // dA13
.align 16
.quad 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F // dA12
.align 16
.quad 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC // dA11
.align 16
.quad 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B // dA10
.align 16
.quad 0xBFAAD261EAA09954, 0xBFAAD261EAA09954 // dA09
.align 16
.quad 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF // dA08
.align 16
.quad 0xBFB11084009435E0, 0xBFB11084009435E0 // dA07
.align 16
.quad 0x3FB3B12A49295651, 0x3FB3B12A49295651 // dA06
.align 16
.quad 0xBFB745D009BADA94, 0xBFB745D009BADA94 // dA05
.align 16
.quad 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5 // dA04
.align 16
.quad 0xBFC2492491EE55C7, 0xBFC2492491EE55C7 // dA03
.align 16
.quad 0x3FC999999997EE34, 0x3FC999999997EE34 // dA02
.align 16
.quad 0xBFD55555555553C5, 0xBFD55555555553C5 // dA01
.align 16
.quad 0x3FF0000000000000, 0x3FF0000000000000 // dA00
.align 16
.quad 0x8000000000000000, 0x8000000000000000 // dSIGN_MASK
.align 16
.long 0x80300000, 0x80300000, 0x80300000, 0x80300000 // iCHK_WORK_SUB
.align 16
.long 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000 // iCHK_WORK_CMP
.align 16
.quad 0x7fffffffffffffff, 0x7fffffffffffffff // dABS_MASK
.align 16
.quad 0x0000000000000000, 0x0000000000000000 // dZERO
.align 16
.type __svml_datan2_data_internal, @object
.size __svml_datan2_data_internal, .-__svml_datan2_data_internal
|
