/*
Copyright (c) 2014, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/******************************************************************************/
// ALGORITHM DESCRIPTION
// ---------------------
//
//
//1. The method is based on the relationship of atan2(Y,X) to atan(|Y/X|)
// as follows.
// / sign(Y) atan(|Y/X|) if X > 0
// atan2(Y,X) =
// \ sign(Y)*pi - sign(Y)*atan(|Y/X|) if X < 0
//
// Thus, atan2(Y,X) is of the form atan2(Y,X) = PI + sgn*atan(|Y/X|)
// where PI and sgn can be determined by the four possible combinations of
// of the pair (sign(X),sign(Y)). We concentrate on the numerical method
// for atan(|Y/X|).
//
//2. For |Y/X| < 2^(-64), atan(|Y/X|) ~=~ |Y/X|. Hence, atan2(Y,X) is Y/X
// if X > 0, and sign(Y)*pi otherwise.
//3. For |Y/X| >= 2^(65), atan(|Y/X|) ~=~ pi/2. Hence atan2(Y,X) is sign(Y)pi/2.
//4. For 2^(-64) <= |Y/X| < 2^(-5), atan(|Y/X|) is approximated by a polynomial
// of the form Z + Z*E*polynomial(E), where Z = |Y/X| and E = Z*Z.
//5. For |Y/X| > 2^(5), atan(|Y/X|) = pi/2 + atan(-|X/Y|), and atan(-|X/Y|) is
// calculated using the polynomial in 4 above.
//6. For 2^(-5) <= |Y/X| <= 2^(5), we employ a table lookup method. First,
// we obtain B = 2^k * 1.b1 b2 b3 b4 = 2^k * (1+k/16) that approximate
// |Y/X| to approximately 5 significant bits. Hence, atan(|Y/X|) is
//
// atan(|Y/X|) = atan(B) + atan(Z), where Z = (|Y|-B|X|)/(|X|+B|Y|).
// ~=~ tau + Z + Z*E*polynomial(E), where E = Z*Z.
//
// B has the range from 2^(-6)*(1+14/16) to 2^5 = 2^(5)*(1+0/16), totally
// 163 possible values. These values are calculated beforehand and stored
// in a table. The polynomial is the one used in 4.
//
// Special cases:
// atan2(+-0, +0) = +-0
// atan2(+-0, -0) = +-pi
// atan2(+-0, x) = +-0, for x > 0, and +-pi, for x < 0
// atan2(y, +-0) = +pi/2 for y > 0, and -pi/2 for y < 0
// atan2(+-y, +INF) = +-0, for finite y > 0
// atan2(+-y, -INF) = +-pi, for finite y > 0
// atan2(+-INF, x) = +-pi/2, for finite x
// atan2(+-INF, +INF) = +-pi/4
// atan2(+-INF, -INF) = +-3*pi/4
//
/******************************************************************************/
#include <private/bionic_asm.h>
# -- Begin static_func
.text
.align __bionic_asm_align
.type static_func, @function
static_func:
..B1.1:
call ..L2
..L2:
popl %eax
lea _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
lea static_const_table@GOTOFF(%eax), %eax
ret
.size static_func,.-static_func
# -- End static_func
# -- Begin atan2
ENTRY(atan2)
# parameter 1: 8 + %ebp
# parameter 2: 16 + %ebp
..B2.1:
..B2.2:
pushl %ebp
movl %esp, %ebp
subl $120, %esp
movl %ebx, 64(%esp)
call static_func
movl %eax, %ebx
movsd 136(%esp), %xmm1
movsd 128(%esp), %xmm0
pextrw $3, %xmm0, %eax
movq %xmm0, 8(%esp)
andl $32752, %eax
movq %xmm1, 16(%esp)
subl $14448, %eax
cmpl $3840, %eax
ja .L_2TAG_PACKET_0.0.2
pextrw $3, %xmm1, %eax
andl $32752, %eax
subl $14448, %eax
cmpl $3840, %eax
ja .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_2.0.2:
unpcklpd %xmm1, %xmm0
xorpd %xmm5, %xmm5
xorpd %xmm3, %xmm3
movl $2048, %eax
pinsrw $3, %eax, %xmm5
paddw %xmm1, %xmm5
psrlq $29, %xmm5
rcpss %xmm5, %xmm3
xorpd %xmm4, %xmm4
movl $14336, %ecx
pinsrw $3, %ecx, %xmm4
psllq $29, %xmm3
paddw %xmm4, %xmm3
mulsd %xmm0, %xmm3
xorpd %xmm2, %xmm2
xorpd %xmm6, %xmm6
xorpd %xmm7, %xmm7
movl $32768, %eax
pinsrw $2, %eax, %xmm6
movl $32767, %ecx
pinsrw $3, %ecx, %xmm7
paddd %xmm6, %xmm3
andpd %xmm7, %xmm3
movapd %xmm3, %xmm5
pextrw $3, %xmm3, %eax
movl $16448, %ecx
pinsrw $3, %ecx, %xmm2
minsd %xmm2, %xmm3
movmskpd %xmm0, %edx
psllq $1, %xmm0
psrlq $1, %xmm0
cmpsd $2, %xmm2, %xmm5
psllq $1, %xmm1
psrlq $1, %xmm1
movapd %xmm1, %xmm6
movapd %xmm1, %xmm7
movapd %xmm0, %xmm2
movl $0, %ecx
pinsrw $0, %ecx, %xmm6
subsd %xmm6, %xmm7
movapd %xmm0, %xmm4
mulsd %xmm3, %xmm6
mulsd %xmm3, %xmm4
mulsd %xmm3, %xmm7
andpd %xmm5, %xmm0
subsd %xmm6, %xmm0
andpd %xmm5, %xmm1
addsd %xmm1, %xmm4
subsd %xmm7, %xmm0
andl $32752, %eax
subl $16286, %eax
cmpl $1121, %eax
ja .L_2TAG_PACKET_3.0.2
divsd %xmm4, %xmm0
pextrw $3, %xmm3, %ecx
movsd 2944(%ebx), %xmm2
movsd 2960(%ebx), %xmm3
pextrw $0, %xmm5, %eax
addl %edx, %edx
movapd 2688(%ebx,%edx,8), %xmm6
movapd 2752(%ebx,%edx,8), %xmm1
subl $16286, %ecx
notl %eax
andl $1, %eax
addl %eax, %ecx
addl %ecx, %ecx
movapd (%ebx,%ecx,8), %xmm5
xorpd %xmm1, %xmm5
addpd %xmm6, %xmm5
movapd %xmm5, %xmm6
unpckhpd %xmm5, %xmm5
xorpd %xmm0, %xmm1
movapd %xmm1, %xmm4
mulsd %xmm0, %xmm0
mulsd %xmm0, %xmm2
addsd %xmm0, %xmm3
addsd %xmm6, %xmm1
subsd %xmm1, %xmm6
addsd %xmm4, %xmm6
addsd 2952(%ebx), %xmm2
mulsd %xmm0, %xmm3
mulsd %xmm0, %xmm4
addsd %xmm5, %xmm6
mulsd %xmm4, %xmm2
addsd 2968(%ebx), %xmm3
mulsd %xmm3, %xmm2
addsd %xmm6, %xmm2
addsd %xmm2, %xmm1
movsd %xmm1, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_3.0.2:
addl $942, %eax
cmpl $942, %eax
ja .L_2TAG_PACKET_5.0.2
xorpd %xmm4, %xmm4
movl $16368, %ecx
pinsrw $3, %ecx, %xmm4
divsd %xmm1, %xmm4
addl %edx, %edx
movapd 2752(%ebx,%edx,8), %xmm6
unpcklpd %xmm3, %xmm3
xorpd %xmm6, %xmm0
xorpd %xmm6, %xmm2
xorpd %xmm6, %xmm3
movapd 2816(%ebx,%edx,8), %xmm7
movsd 2944(%ebx), %xmm1
movsd 2960(%ebx), %xmm5
andpd 2880(%ebx,%edx,8), %xmm3
mulsd %xmm4, %xmm2
mulsd %xmm4, %xmm0
movapd %xmm2, %xmm6
mulsd %xmm2, %xmm2
mulsd %xmm2, %xmm1
addsd %xmm2, %xmm5
mulsd %xmm2, %xmm6
addsd 2952(%ebx), %xmm1
mulsd %xmm2, %xmm5
addsd %xmm0, %xmm7
addpd %xmm3, %xmm7
mulsd %xmm6, %xmm1
addsd 2968(%ebx), %xmm5
mulsd %xmm1, %xmm5
addsd %xmm7, %xmm5
unpckhpd %xmm7, %xmm7
addsd %xmm7, %xmm5
movsd %xmm5, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_5.0.2:
movsd 16(%esp), %xmm1
movsd 8(%esp), %xmm0
pextrw $3, %xmm1, %eax
andl $32752, %eax
pextrw $3, %xmm0, %ecx
andl $32752, %ecx
cmpl %eax, %ecx
jg .L_2TAG_PACKET_6.0.2
pextrw $3, %xmm1, %ecx
cmpl $32767, %ecx
jg .L_2TAG_PACKET_7.0.2
divsd %xmm1, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_7.0.2:
andpd 2672(%ebx), %xmm0
movsd 2640(%ebx), %xmm2
xorpd %xmm2, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_6.0.2:
andpd 2672(%ebx), %xmm0
movsd 2624(%ebx), %xmm2
xorpd %xmm2, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_0.0.2:
.L_2TAG_PACKET_1.0.2:
pextrw $3, %xmm0, %ecx
andl $32752, %ecx
pextrw $3, %xmm1, %eax
andl $32752, %eax
cmpl $32752, %ecx
je .L_2TAG_PACKET_8.0.2
cmpl $32752, %eax
je .L_2TAG_PACKET_9.0.2
movsd 2992(%ebx), %xmm3
movl $1024, %edx
movsd 2976(%ebx), %xmm4
xorpd %xmm6, %xmm6
movsd 3008(%ebx), %xmm7
cmpl $0, %ecx
je .L_2TAG_PACKET_10.0.2
.L_2TAG_PACKET_11.0.2:
cmpl $0, %eax
je .L_2TAG_PACKET_12.0.2
.L_2TAG_PACKET_13.0.2:
addl %ecx, %edx
subl %eax, %edx
cmpl $2048, %edx
ja .L_2TAG_PACKET_5.0.2
addl $15344, %edx
pinsrw $3, %edx, %xmm6
andpd %xmm4, %xmm0
andpd %xmm4, %xmm1
orpd %xmm6, %xmm0
orpd %xmm7, %xmm1
jmp .L_2TAG_PACKET_2.0.2
.L_2TAG_PACKET_10.0.2:
subl $880, %edx
mulsd %xmm3, %xmm0
pextrw $3, %xmm0, %ecx
andl $32752, %ecx
cmpl $0, %ecx
je .L_2TAG_PACKET_14.0.2
jmp .L_2TAG_PACKET_11.0.2
.L_2TAG_PACKET_12.0.2:
addl $880, %edx
mulsd %xmm3, %xmm1
pextrw $3, %xmm1, %eax
andl $32752, %eax
cmpl $0, %eax
je .L_2TAG_PACKET_15.0.2
jmp .L_2TAG_PACKET_13.0.2
.L_2TAG_PACKET_8.0.2:
movd %xmm0, %edx
movapd %xmm0, %xmm2
psrlq $32, %xmm2
movd %xmm2, %ecx
andl $1048575, %ecx
orl %edx, %ecx
cmpl $0, %ecx
jne .L_2TAG_PACKET_16.0.2
psrlq $63, %xmm0
psllq $63, %xmm0
cmpl $32752, %eax
jae .L_2TAG_PACKET_17.0.2
movapd 2624(%ebx), %xmm5
pshufd $238, %xmm5, %xmm4
addsd %xmm4, %xmm5
orpd %xmm5, %xmm0
.L_2TAG_PACKET_18.0.2:
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_16.0.2:
addsd %xmm1, %xmm0
jmp .L_2TAG_PACKET_18.0.2
.L_2TAG_PACKET_17.0.2:
movd %xmm1, %eax
movapd %xmm1, %xmm2
psrlq $32, %xmm2
movd %xmm2, %ecx
movl $-2147483648, %edx
andl %ecx, %edx
andl $1048575, %ecx
orl %eax, %ecx
cmpl $0, %ecx
jne .L_2TAG_PACKET_19.0.2
cmpl $0, %edx
jne .L_2TAG_PACKET_20.0.2
movapd 2656(%ebx), %xmm5
pshufd $238, %xmm5, %xmm4
addsd %xmm4, %xmm5
orpd %xmm5, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_19.0.2:
movapd %xmm1, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_20.0.2:
movapd 2656(%ebx), %xmm5
movapd 2624(%ebx), %xmm6
addpd %xmm6, %xmm5
pshufd $238, %xmm5, %xmm6
addpd %xmm6, %xmm5
orpd %xmm5, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_9.0.2:
movd %xmm1, %eax
movapd %xmm1, %xmm2
psrlq $32, %xmm2
movd %xmm2, %ecx
movl $-2147483648, %edx
andl %ecx, %edx
andl $1048575, %ecx
orl %eax, %ecx
cmpl $0, %ecx
jne .L_2TAG_PACKET_19.0.2
psrlq $63, %xmm0
psllq $63, %xmm0
cmpl $0, %edx
jne .L_2TAG_PACKET_21.0.2
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_21.0.2:
movapd 2640(%ebx), %xmm5
pshufd $238, %xmm5, %xmm4
addsd %xmm4, %xmm5
orpd %xmm5, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_14.0.2:
pextrw $3, %xmm1, %edx
andl $32768, %edx
cmpl $0, %edx
je .L_2TAG_PACKET_22.0.2
movapd 2640(%ebx), %xmm5
pshufd $238, %xmm5, %xmm4
addsd %xmm4, %xmm5
comisd %xmm0, %xmm1
orpd %xmm5, %xmm0
jne .L_2TAG_PACKET_23.0.2
.L_2TAG_PACKET_24.0.2:
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_23.0.2:
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_22.0.2:
comisd %xmm0, %xmm1
jne .L_2TAG_PACKET_23.0.2
je .L_2TAG_PACKET_24.0.2
.L_2TAG_PACKET_15.0.2:
movapd 2624(%ebx), %xmm5
psrlq $63, %xmm0
psllq $63, %xmm0
pshufd $238, %xmm5, %xmm4
addsd %xmm4, %xmm5
orpd %xmm5, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
.L_2TAG_PACKET_4.0.2:
movl 64(%esp), %ebx
movl %ebp, %esp
popl %ebp
ret
..B2.3:
END(atan2)
# -- End atan2
# Start file scope ASM
ALIAS_SYMBOL(atan2l, atan2);
# End file scope ASM
.section .rodata, "a"
.align 16
.align 16
static_const_table:
.long 3390881280
.long 1067318733
.long 1411116779
.long 1018950063
.long 2985987840
.long 1067384211
.long 2088903695
.long 1018086027
.long 3148445184
.long 1067449685
.long 2044163806
.long 1017271335
.long 3667629184
.long 1067515494
.long 2353092775
.long 1019967309
.long 1546568832
.long 1067580954
.long 611991315
.long 1017602584
.long 3815996800
.long 1067646404
.long 466038598
.long 1019686426
.long 4050241920
.long 1067711845
.long 3265026328
.long 1019626952
.long 120454912
.long 1067777277
.long 1542207696
.long 1020155608
.long 2784639744
.long 1067842697
.long 3883834623
.long 1018602870
.long 1328010624
.long 1067908107
.long 1791097456
.long 1019053126
.long 2217794048
.long 1067973505
.long 551619938
.long 1018494194
.long 3333520000
.long 1068038891
.long 2390331823
.long 1019033022
.long 2557052032
.long 1068104265
.long 2423976108
.long 1019728674
.long 2067649536
.long 1068169626
.long 3757397745
.long 1018672362
.long 4047094784
.long 1068234973
.long 481613184
.long 1019275104
.long 2089853184
.long 1068300307
.long 1733914374
.long 1020124677
.long 2678003840
.long 1068365626
.long 1373600282
.long 1013935474
.long 3706496128
.long 1068430930
.long 1000610902
.long 1019673285
.long 3073179008
.long 1068496219
.long 1497143008
.long 1019900342
.long 2803716736
.long 1068562846
.long 1476677416
.long 1019444094
.long 3204984128
.long 1068628077
.long 1192335905
.long 1018748628
.long 831146624
.long 1068693273
.long 2733586224
.long 1018823295
.long 243029376
.long 1068758431
.long 950106081
.long 1019046675
.long 1735561920
.long 1068823549
.long 3546440856
.long 1020104712
.long 1339217792
.long 1068888626
.long 3028812387
.long 1019818321
.long 3706342144
.long 1068953659
.long 3814564029
.long 1017763871
.long 637726976
.long 1069018648
.long 3584007699
.long 1017976868
.long 1148779264
.long 1069083589
.long 2282532133
.long 1019483954
.long 1406131392
.long 1069148481
.long 1547359113
.long 1019786342
.long 1908875904
.long 1069213322
.long 1315508410
.long 1020009473
.long 3194947520
.long 1069278110
.long 3845393201
.long 1015803761
.long 1547487744
.long 1069342844
.long 3863107865
.long 1019810104
.long 1881061952
.long 1069407521
.long 4288343548
.long 1019687581
.long 563086336
.long 1069472140
.long 2582230241
.long 1020099350
.long 2594975552
.long 1069536698
.long 2306443764
.long 1019667244
.long 3438545024
.long 1069606573
.long 957455549
.long 1015587735
.long 4211357472
.long 1069670906
.long 2611778754
.long 1017877214
.long 3002835424
.long 1069735101
.long 235580458
.long 1020211685
.long 3905315424
.long 1069799150
.long 3630647617
.long 1018736849
.long 2849656576
.long 1069863047
.long 2412165062
.long 1019693004
.long 507429472
.long 1069926785
.long 1397750723
.long 1018412717
.long 2307470272
.long 1069990356
.long 1796470904
.long 1019796181
.long 1271814912
.long 1070053755
.long 189761565
.long 1016149115
.long 3800538144
.long 1070116974
.long 2524871582
.long 1018263353
.long 3916203552
.long 1070180008
.long 127848658
.long 1017672664
.long 457192032
.long 1070242851
.long 4020400938
.long 1019823010
.long 1385324704
.long 1070305495
.long 564511179
.long 1016079094
.long 2322869856
.long 1070367935
.long 2347103319
.long 1018927760
.long 3743438624
.long 1070430165
.long 877973862
.long 1019638162
.long 2392255552
.long 1070492180
.long 2432782267
.long 1018872629
.long 4180443328
.long 1070553973
.long 3102990015
.long 1020093101
.long 2547540832
.long 1070636485
.long 3877738253
.long 1017300424
.long 2735468912
.long 1070697461
.long 2446470256
.long 1019235378
.long 542633792
.long 1070757943
.long 583606328
.long 1018624131
.long 923265984
.long 1070817911
.long 1793926708
.long 1019714161
.long 918728448
.long 1070877348
.long 3726463586
.long 1019433296
.long 2572275008
.long 1070936237
.long 1845354238
.long 1019459238
.long 50974688
.long 1070994564
.long 983808064
.long 1016685418
.long 1105518320
.long 1071052313
.long 2357496692
.long 1015139882
.long 1264825328
.long 1071109472
.long 2244129354
.long 1019046344
.long 961157920
.long 1071166029
.long 3124185339
.long 1018541776
.long 1162701584
.long 1071221973
.long 1279780948
.long 1019268918
.long 3284935664
.long 1071277294
.long 2670033472
.long 1019833744
.long 497441888
.long 1071331985
.long 1032737410
.long 1019795212
.long 3377383904
.long 1071386036
.long 2356897182
.long 1020205553
.long 1126962000
.long 1071439443
.long 3723724586
.long 1015212418
.long 90291008
.long 1071492199
.long 4178672431
.long 1020186971
.long 190059536
.long 1071595741
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.section .note.GNU-stack, ""
# End