/*
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
// ---------------------
//
// To compute acos(s), separate schemes are used when s is in different
// intervals.
//
// |s| in [2^{-4}, sqrt(3)/2):
// Let t=2^k*1.b1 b2..b6 1, where s=2^k*1.b1 b2 .. b52
// acos(s)=pi/2-asin(t)-asin(r), where r=s*sqrt(1-t^2)-t*sqrt(1-s^2)
// asin(r)-r evaluated as 7-degree polynomial (c3*r^3+c5*r^5+c7*r^7)
// For the first degree term, r is evaluated as
// R=(s^2-t^2)/(sqrt(1-t^2)*s+sqrt(1-s^2)*t)
// (sqrt(1-t^2) read from table)
// The main source of error is still R (may still be affected by up to 3 ulps
// of rounding error). The table size must be sufficiently large, to minimize
// this effect.
//
// |s| in [sqrt(3)/2, 255/256):
// Let t=2^k*1.b1 b2..b6 1, where sqrt(1-s^2)=2^k*1.b1 b2 .. b52 (rounded)
// acos(|s|)=asin(t)-asin(r), r=s*t-sqrt(1-s^2)*sqrt(1-t^2)
// acos(-|s|)=pi-acos(|s|)
// (The -PI constant, or 0, is added to the result. The sign is set at
// the end)
// asin(r) evaluated as a polynomial (same as above)
// The first degree term is evaluated as
// r=(s^2+t^2-1)/(s*t+sqrt(1-s^2)*sqrt(1-t^2))
//
// |s|<2^{-4}: acos(s)=pi/2-asin(s)
// evaluate asin(s) as 13-degree polynomial
//
// |s| in [255/256,1): acos(|s|)=2*asin(q), where q=sqrt((1-|s|)/2)
// asin(q) is evaluated as 13-degree polynomial
// q^2=(1-|s|)/2 is obtained in advance
// 2*q*eps ~ ((1-|s|)/2-q^2)/q used for first term
// acos(-|s|)=pi-acos(|s|)
// (The -PI constant, or 0, is added to the result. The sign is set at
// the end)
//
// Special cases:
// acos(NaN) = quiet NaN, and raise invalid exception
// acos(INF) = QNaN and raise invalid exception
// acos(x) = QNaN and raise invalid exception, for |x|>1.0
// acos(1) = +0
//
/******************************************************************************/
#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 acos
ENTRY(acos)
# parameter 1: 8 + %ebp
..B2.1:
..B2.2:
pushl %ebp
movl %esp, %ebp
subl $104, %esp
movl %ebx, 48(%esp)
call static_func
movl %eax, %ebx
movsd 112(%esp), %xmm0
movsd 6048(%ebx), %xmm4
movsd 6080(%ebx), %xmm3
xorpd %xmm5, %xmm5
movsd 6064(%ebx), %xmm2
movapd %xmm0, %xmm1
movsd %xmm0, 8(%esp)
psrlq $44, %xmm0
movd %xmm0, %edx
movapd %xmm1, %xmm7
movl $8192, %ecx
pinsrw $2, %ecx, %xmm5
movapd %xmm1, %xmm0
movl $524287, %eax
andl %edx, %eax
subl $260864, %eax
cmpl $955, %eax
jae .L_2TAG_PACKET_0.0.2
mulsd %xmm1, %xmm1
andl $65535, %edx
subsd %xmm1, %xmm3
sqrtsd %xmm3, %xmm3
andpd %xmm7, %xmm2
andl $-4, %edx
subl $64256, %edx
movsd 3840(%ebx,%edx,2), %xmm1
orpd %xmm5, %xmm2
movapd (%ebx,%edx,4), %xmm4
movapd %xmm7, %xmm6
addsd %xmm2, %xmm7
subsd %xmm2, %xmm0
mulsd %xmm0, %xmm7
mulsd %xmm1, %xmm6
mulsd %xmm2, %xmm3
movapd %xmm6, %xmm1
addsd %xmm3, %xmm6
divsd %xmm6, %xmm7
movsd 5976(%ebx), %xmm0
movsd 5960(%ebx), %xmm5
subsd %xmm3, %xmm1
psrlq $63, %xmm2
movapd %xmm1, %xmm3
psllq $63, %xmm2
mulsd %xmm1, %xmm1
pshufd $68, %xmm2, %xmm2
movsd 5968(%ebx), %xmm6
mulsd %xmm1, %xmm3
mulsd %xmm1, %xmm0
xorpd %xmm2, %xmm4
mulsd %xmm3, %xmm5
subpd 5888(%ebx), %xmm4
mulsd %xmm1, %xmm3
addsd %xmm6, %xmm0
mulsd %xmm3, %xmm0
subsd %xmm4, %xmm5
pshufd $238, %xmm4, %xmm4
addsd %xmm5, %xmm0
subsd %xmm7, %xmm0
subsd %xmm4, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_0.0.2:
subl $955, %eax
cmpl $65, %eax
jae .L_2TAG_PACKET_2.0.2
psrlq $38, %xmm7
psllq $38, %xmm7
pmovmskb %xmm0, %eax
andnpd %xmm0, %xmm4
subsd %xmm7, %xmm1
movapd %xmm7, %xmm6
mulsd %xmm7, %xmm7
addsd %xmm6, %xmm0
orpd %xmm4, %xmm5
subsd %xmm7, %xmm3
mulsd %xmm1, %xmm0
movapd %xmm3, %xmm4
subsd %xmm0, %xmm3
sqrtsd %xmm3, %xmm3
andl $128, %eax
shrl $7, %eax
negl %eax
movapd %xmm3, %xmm7
andpd %xmm3, %xmm2
psllq $2, %xmm3
pextrw $3, %xmm3, %edx
orpd %xmm5, %xmm2
movd %eax, %xmm3
pshufd $0, %xmm3, %xmm3
subl $65216, %edx
addl %edx, %edx
mulsd 3840(%ebx,%edx,4), %xmm7
mulsd %xmm2, %xmm6
mulsd %xmm2, %xmm1
mulsd %xmm2, %xmm2
subsd %xmm7, %xmm6
andpd 5904(%ebx), %xmm3
addsd %xmm1, %xmm6
subsd %xmm2, %xmm4
addsd %xmm7, %xmm7
movsd 5960(%ebx), %xmm5
subsd %xmm0, %xmm4
addsd %xmm6, %xmm7
movsd 5976(%ebx), %xmm0
divsd %xmm7, %xmm4
movsd 5968(%ebx), %xmm2
addpd (%ebx,%edx,8), %xmm3
movapd %xmm6, %xmm1
mulsd %xmm6, %xmm6
mulsd %xmm6, %xmm0
mulsd %xmm6, %xmm1
mulsd %xmm1, %xmm5
mulsd %xmm6, %xmm1
addsd %xmm2, %xmm0
pxor %xmm6, %xmm6
mulsd %xmm1, %xmm0
addsd %xmm3, %xmm5
addsd %xmm5, %xmm0
andl $32768, %eax
pinsrw $3, %eax, %xmm6
movapd %xmm4, %xmm5
pshufd $238, %xmm3, %xmm3
addsd %xmm3, %xmm4
subsd %xmm4, %xmm3
addsd %xmm3, %xmm5
addsd %xmm5, %xmm0
addsd %xmm4, %xmm0
xorpd %xmm6, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_2.0.2:
addl $15291, %eax
cmpl $14336, %eax
jae .L_2TAG_PACKET_3.0.2
unpcklpd %xmm0, %xmm0
movapd 5984(%ebx), %xmm6
unpcklpd %xmm0, %xmm1
movapd 6000(%ebx), %xmm2
movapd 6016(%ebx), %xmm4
mulpd %xmm0, %xmm0
movapd 5888(%ebx), %xmm5
mulpd %xmm0, %xmm1
mulpd %xmm0, %xmm6
mulpd %xmm0, %xmm0
movapd %xmm1, %xmm3
mulsd %xmm1, %xmm1
addpd %xmm2, %xmm6
mulpd %xmm0, %xmm4
mulsd %xmm3, %xmm1
addpd %xmm4, %xmm6
pshufd $238, %xmm5, %xmm0
mulpd %xmm6, %xmm1
pshufd $238, %xmm5, %xmm6
subsd %xmm7, %xmm0
pshufd $238, %xmm1, %xmm2
subsd %xmm1, %xmm5
subsd %xmm0, %xmm6
subsd %xmm2, %xmm5
subsd %xmm6, %xmm7
subsd %xmm7, %xmm5
addsd %xmm5, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_3.0.2:
subl $15356, %eax
cmpl $4, %eax
jae .L_2TAG_PACKET_4.0.2
xorpd %xmm6, %xmm6
andpd 6048(%ebx), %xmm7
movsd 6096(%ebx), %xmm4
movapd 5984(%ebx), %xmm1
mulsd %xmm4, %xmm7
movapd 6000(%ebx), %xmm2
subsd %xmm7, %xmm4
movapd 6016(%ebx), %xmm3
pshufd $68, %xmm4, %xmm7
sqrtsd %xmm4, %xmm4
mulpd %xmm7, %xmm1
pshufd $68, %xmm7, %xmm5
pextrw $3, %xmm0, %eax
mulpd %xmm7, %xmm7
addpd %xmm1, %xmm2
movsd 5936(%ebx), %xmm1
mulpd %xmm7, %xmm3
cmpsd $1, %xmm6, %xmm0
mulsd %xmm5, %xmm7
addpd %xmm3, %xmm2
pshufd $68, %xmm0, %xmm0
mulsd %xmm7, %xmm2
andpd 5904(%ebx), %xmm0
mulpd %xmm5, %xmm2
andpd %xmm4, %xmm1
pshufd $68, %xmm4, %xmm3
subsd %xmm1, %xmm4
addsd %xmm3, %xmm3
mulsd %xmm1, %xmm1
subsd %xmm4, %xmm3
subsd %xmm1, %xmm5
mulsd %xmm3, %xmm4
pshufd $238, %xmm3, %xmm3
subsd %xmm4, %xmm5
divsd %xmm3, %xmm5
addpd %xmm3, %xmm3
mulpd %xmm3, %xmm2
pshufd $238, %xmm2, %xmm4
addsd %xmm0, %xmm2
andl $32768, %eax
pinsrw $3, %eax, %xmm6
pshufd $238, %xmm0, %xmm0
addsd %xmm4, %xmm2
addsd %xmm5, %xmm2
addsd %xmm3, %xmm2
addsd %xmm2, %xmm0
xorpd %xmm6, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_4.0.2:
addl $261884, %eax
cmpl $261888, %eax
jb .L_2TAG_PACKET_5.0.2
movd %xmm7, %ecx
psrlq $32, %xmm7
movd %xmm7, %edx
andl $2147483647, %edx
movl $1072693248, %eax
subl %edx, %eax
orl %ecx, %eax
cmpl $0, %eax
je .L_2TAG_PACKET_6.0.2
movq 8(%esp), %xmm2
movd %xmm2, %edx
psrlq $32, %xmm2
movd %xmm2, %ecx
andl $2147483647, %ecx
subl $1, %edx
sbbl $2146435072, %ecx
cmpl $0, %ecx
jge .L_2TAG_PACKET_7.0.2
xorpd %xmm1, %xmm1
xorpd %xmm0, %xmm0
movl $32752, %edx
pinsrw $3, %edx, %xmm1
mulsd %xmm1, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_6.0.2:
pextrw $1, %xmm7, %edx
shrl $15, %edx
negl %edx
movd %edx, %xmm7
pshufd $0, %xmm7, %xmm7
movsd 5920(%ebx), %xmm2
movsd 5928(%ebx), %xmm0
andpd %xmm7, %xmm2
andpd %xmm7, %xmm0
addsd %xmm2, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_5.0.2:
movsd 5888(%ebx), %xmm2
movsd 5896(%ebx), %xmm0
addsd %xmm2, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_7.0.2:
xorpd %xmm6, %xmm6
addsd %xmm6, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
.L_2TAG_PACKET_1.0.2:
movl 48(%esp), %ebx
movl %ebp, %esp
popl %ebp
ret
..B2.3:
END(acos)
# -- End acos
# Start file scope ASM
ALIAS_SYMBOL(acosl, acos);
# End file scope ASM
.section .rodata, "a"
.align 16
.align 16
static_const_table:
.long 3822952792
.long 1021639372
.long 182792448
.long 1068507836
.long 2264213271
.long 1019558908
.long 649052928
.long 1068524253
.long 1797139609
.long 1022295143
.long 1243095296
.long 1068540671
.long 1415938756
.long 1021439537
.long 2033294592
.long 1068557090
.long 2356809978
.long 1021777916
.long 3088063744
.long 1068573510
.long 2669055318
.long 1022124482
.long 180888576
.long 1068589932
.long 3566445325
.long 1021358712
.long 1970196992
.long 1068606354
.long 896980323
.long 1021319659
.long 4229555456
.long 1068622777
.long 436049712
.long 1021319758
.long 2732572160
.long 1068639202
.long 583123209
.long 1020797960
.long 1842831872
.long 1068655628
.long 1370449804
.long 1021429270
.long 1628994560
.long 1068672055
.long 2411391464
.long 1021057980
.long 2159763712
.long 1068688483
.long 1208692749
.long 1021943903
.long 3503886336
.long 1068704912
.long 538793309
.long 1019744063
.long 1435187200
.long 1068721343
.long 4085087612
.long 1020608419
.long 317469952
.long 1068737775
.long 144386942
.long 1021440732
.long 219617280
.long 1068754208
.long 2940088361
.long 1019981122
.long 1210558208
.long 1068770642
.long 2176850347
.long 1018373705
.long 3359268352
.long 1068787077
.long 2395611454
.long 1021889042
.long 2439803648
.long 1068803514
.long 1650705253
.long 1020227966
.long 2816203520
.long 1068819952
.long 3702166386
.long 1019379914
.long 262620672
.long 1068836392
.long 1855649370
.long 1020453124
.long 3438159616
.long 1068852832
.long 923063860
.long 1019273834
.long 3822105856
.long 1068869274
.long 4289947947
.long 1019434249
.long 1483729920
.long 1068885718
.long 787455814
.long 1020738379
.long 787321088
.long 1068902163
.long 3321653337
.long 1021842569
.long 1802253312
.long 1068918609
.long 2653633526
.long 1021821525
.long 302985984
.long 1068935057
.long 161272028
.long 1021655149
.long 653966080
.long 1068951506
.long 2566098667
.long 1020066219
.long 2924727296
.long 1068967956
.long 3646493722
.long 1014292285
.long 2889890304
.long 1068984408
.long 1081009196
.long 1022189620
.long 619098112
.long 1069000862
.long 4011643355
.long 1021773297
.long 477017600
.long 1069017317
.long 4030305534
.long 1021292252
.long 2533403904
.long 1069033773
.long 2645187591
.long 1019527099
.long 2563102208
.long 1069050231
.long 3857293792
.long 1022311697
.long 635982336
.long 1069066691
.long 3625936637
.long 1017511744
.long 1116940800
.long 1069083152
.long 3653872993
.long 1022016631
.long 4075964160
.long 1069099614
.long 2468900271
.long 1021769532
.long 993165568
.long 1069116079
.long 1358104224
.long 1021199776
.long 528586752
.long 1069132545
.long 2200950332
.long 1022024872
.long 2752395776
.long 1069149012
.long 3197072454
.long 1017751319
.long 3439855616
.long 1069165481
.long 1651081806
.long 1020809338
.long 2661257728
.long 1069181952
.long 539032752
.long 1021728805
.long 486957312
.long 1069198425
.long 3136045149
.long 1016888671
.long 1282340352
.long 1069214899
.long 2593963259
.long 1018956103
.long 822921728
.long 1069231375
.long 2146032737
.long 1022306465
.long 3474216192
.long 1069247852
.long 3976811625
.long 1021350207
.long 716902656
.long 1069264332
.long 718267222
.long 1018624727
.long 1211594496
.long 1069280813
.long 1485641389
.long 1018447451
.long 734070272
.long 1069297296
.long 354455128
.long 1021341291
.long 3650110720
.long 1069313780
.long 682185947
.long 1021651853
.long 1440663040
.long 1069330267
.long 3558574550
.long 1021615110
.long 2766612224
.long 1069346755
.long 874607978
.long 1017746872
.long 3404011008
.long 1069363245
.long 4154988502
.long 1021439906
.long 3423949056
.long 1069379737
.long 2263202309
.long 1021479615
.long 2897587712
.long 1069396231
.long 2562065031
.long 1022090363
.long 1896159232
.long 1069412727
.long 3836237663
.long 1019867288
.long 490968576
.long 1069429225
.long 3322056743
.long 1006752762
.long 3048360192
.long 1069445724
.long 1152314833
.long 1013122252
.long 1049850624
.long 1069462226
.long 3601590727
.long 1022214610
.long 3156899584
.long 1069478729
.long 1855169970
.long 1019487271
.long 851173376
.long 1069495235
.long 312649594
.long 1020868604
.long 2794281728
.long 1069511742
.long 1093490181
.long 1020777577
.long 468042496
.long 1069528252
.long 1152540679
.long 1021403732
.long 2534219264
.long 1069544763
.long 2292126035
.long 1021872430
.long 1376146432
.long 1069558527
.long 3293753641
.long 1020500454
.long 4175442432
.long 1069575044
.long 3626347564
.long 1021610969
.long 3523113472
.long 1069591566
.long 339956500
.long 1021119039
.long 4003350528
.long 1069608092
.long 3429333082
.long 1022813542
.long 1611067392
.long 1069624623
.long 2298017544
.long 1021977587
.long 931782144
.long 1069641158
.long 2164684743
.long 1021250988
.long 2256725504
.long 1069657697
.long 1138762335
.long 1021443776
.long 1582853120
.long 1069674241
.long 1084010382
.long 1022994693
.long 3497758720
.long 1069690789
.long 406366244
.long 1022713586
.long 3999816960
.long 1069707342
.long 1488723042
.long 1023381290
.long 3383096064
.long 1069723900
.long 2541558953
.long 1019137887
.long 1942403584
.long 1069740463
.long 1879620343
.long 1022653642
.long 4268263680
.long 1069757030
.long 3039077047
.long 1022252545
.long 2067062272
.long 1069773603
.long 4190670677
.long 1020725863
.long 4225828096
.long 1069790180
.long 1998567321
.long 1022014385
.long 2452507136
.long 1069806763
.long 1511628873
.long 1021900300
.long 1340746240
.long 1069823351
.long 788367341
.long 1022726208
.long 1190035456
.long 1069839944
.long 3856337230
.long 1021834118
.long 2300688384
.long 1069856542
.long 3211396579
.long 1022621365
.long 678886400
.long 1069873146
.long 4001011887
.long 1022042646
.long 921594112
.long 1069889755
.long 557811968
.long 1023065533
.long 3331668992
.long 1069906369
.long 1877060679
.long 1022419742
.long 3917875200
.long 1069922989
.long 1181055171
.long 1022752712
.long 2984829696
.long 1069939615
.long 4294526932
.long 1021499988
.long 838049024
.long 1069956247
.long 3658081878
.long 1022957952
.long 2078928384
.long 1069972884
.long 820353701
.long 1019391107
.long 2719854336
.long 1069989527
.long 1644022489
.long 1023378240
.long 3069117696
.long 1070006176
.long 2771393702
.long 1019319954
.long 3435962368
.long 1070022831
.long 3876394145
.long 1023024433
.long 4130595328
.long 1070039492
.long 1630447748
.long 1021465882
.long 1169236224
.long 1070056160
.long 2828355997
.long 1020458120
.long 3453997312
.long 1070072833
.long 164091641
.long 1020388279
.long 2708127744
.long 1070089513
.long 3036550223
.long 1023328684
.long 3540797696
.long 1070106199
.long 3710949463
.long 1022568805
.long 1972276736
.long 1070122892
.long 3885277950
.long 1019761674
.long 2613815552
.long 1070139591
.long 2764165077
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.type static_const_table,@object
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.data
.section .note.GNU-stack, ""
# End