/*
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
// ---------------------
//
// Polynomials coefficients and other constants.
//
// Note that in this algorithm, there is a different polynomial for
// each breakpoint, so there are 32 sets of polynomial coefficients
// as well as 32 instances of the other constants.
//
// The polynomial coefficients and constants are offset from the start
// of the main block as follows:
//
// 0: c8 | c0
// 16: c9 | c1
// 32: c10 | c2
// 48: c11 | c3
// 64: c12 | c4
// 80: c13 | c5
// 96: c14 | c6
// 112: c15 | c7
// 128: T_hi
// 136: T_lo
// 144: Sigma
// 152: T_hl
// 160: Tau
// 168: Mask
// 176: (end of block)
//
// The total table size is therefore 5632 bytes.
//
// Note that c0 and c1 are always zero. We could try storing
// other constants here, and just loading the low part of the
// SIMD register in these cases, after ensuring the high part
// is zero.
//
// The higher terms of the polynomial are computed in the *low*
// part of the SIMD register. This is so we can overlap the
// multiplication by r^8 and the unpacking of the other part.
//
// The constants are:
// T_hi + T_lo = accurate constant term in power series
// Sigma + T_hl = accurate coefficient of r in power series (Sigma=1 bit)
// Tau = multiplier for the reciprocal, always -1 or 0
//
// The basic reconstruction formula using these constants is:
//
// High = tau * recip_hi + t_hi
// Med = (sgn * r + t_hl * r)_hi
// Low = (sgn * r + t_hl * r)_lo +
// tau * recip_lo + T_lo + (T_hl + sigma) * c + pol
//
// where pol = c0 + c1 * r + c2 * r^2 + ... + c15 * r^15
//
// (c0 = c1 = 0, but using them keeps SIMD regularity)
//
// We then do a compensated sum High + Med, add the low parts together
// and then do the final sum.
//
// Here recip_hi + recip_lo is an accurate reciprocal of the remainder
// modulo pi/2
//
// Special cases:
// tan(NaN) = quiet NaN, and raise invalid exception
// tan(INF) = NaN and raise invalid exception
// tan(+/-0) = +/-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 tan
ENTRY(tan)
# parameter 1: 8 + %ebp
..B2.1:
..B2.2:
pushl %ebp
movl %esp, %ebp
subl $120, %esp
movl %ebx, 56(%esp)
call static_func
movl %eax, %ebx
movsd 128(%esp), %xmm0
pextrw $3, %xmm0, %eax
andl $32767, %eax
subl $14368, %eax
cmpl $2216, %eax
ja .L_2TAG_PACKET_0.0.2
movapd 5840(%ebx), %xmm5
movapd 5856(%ebx), %xmm6
unpcklpd %xmm0, %xmm0
movapd 5712(%ebx), %xmm4
andpd %xmm0, %xmm4
movapd 5632(%ebx), %xmm1
mulpd %xmm0, %xmm1
orpd %xmm4, %xmm5
addpd %xmm5, %xmm1
movapd %xmm1, %xmm7
unpckhpd %xmm7, %xmm7
cvttsd2si %xmm7, %edx
cvttpd2dq %xmm1, %xmm1
cvtdq2pd %xmm1, %xmm1
mulpd %xmm6, %xmm1
movapd 5664(%ebx), %xmm3
movsd 5728(%ebx), %xmm5
addl $469248, %edx
movapd 5680(%ebx), %xmm4
mulpd %xmm1, %xmm3
andl $31, %edx
mulsd %xmm1, %xmm5
movl %edx, %ecx
mulpd %xmm1, %xmm4
shll $1, %ecx
subpd %xmm3, %xmm0
mulpd 5696(%ebx), %xmm1
addl %ecx, %edx
shll $2, %ecx
addl %ecx, %edx
addsd %xmm0, %xmm5
movapd %xmm0, %xmm2
subpd %xmm4, %xmm0
movsd 5744(%ebx), %xmm6
shll $4, %edx
lea (%ebx), %eax
andpd 5776(%ebx), %xmm5
movapd %xmm0, %xmm3
addl %edx, %eax
subpd %xmm0, %xmm2
unpckhpd %xmm0, %xmm0
divsd %xmm5, %xmm6
subpd %xmm4, %xmm2
movapd 16(%eax), %xmm7
subsd %xmm5, %xmm3
mulpd %xmm0, %xmm7
subpd %xmm1, %xmm2
movapd 48(%eax), %xmm1
mulpd %xmm0, %xmm1
movapd 96(%eax), %xmm4
mulpd %xmm0, %xmm4
addsd %xmm3, %xmm2
movapd %xmm0, %xmm3
mulpd %xmm0, %xmm0
addpd (%eax), %xmm7
addpd 32(%eax), %xmm1
mulpd %xmm0, %xmm1
addpd 80(%eax), %xmm4
addpd %xmm1, %xmm7
movapd 112(%eax), %xmm1
mulpd %xmm0, %xmm1
mulpd %xmm0, %xmm0
addpd %xmm1, %xmm4
movapd 64(%eax), %xmm1
mulpd %xmm0, %xmm1
addpd %xmm1, %xmm7
movapd %xmm3, %xmm1
mulpd %xmm0, %xmm3
mulsd %xmm0, %xmm0
mulpd 144(%eax), %xmm1
mulpd %xmm3, %xmm4
movapd %xmm1, %xmm3
addpd %xmm4, %xmm7
movapd %xmm1, %xmm4
mulsd %xmm7, %xmm0
unpckhpd %xmm7, %xmm7
addsd %xmm7, %xmm0
unpckhpd %xmm1, %xmm1
addsd %xmm1, %xmm3
subsd %xmm3, %xmm4
addsd %xmm4, %xmm1
movapd %xmm2, %xmm4
movsd 144(%eax), %xmm7
unpckhpd %xmm2, %xmm2
addsd 152(%eax), %xmm7
mulsd %xmm2, %xmm7
addsd 136(%eax), %xmm7
addsd %xmm1, %xmm7
addsd %xmm7, %xmm0
movsd 5744(%ebx), %xmm7
mulsd %xmm6, %xmm4
movsd 168(%eax), %xmm2
andpd %xmm6, %xmm2
mulsd %xmm2, %xmm5
mulsd 160(%eax), %xmm6
subsd %xmm5, %xmm7
subsd 128(%eax), %xmm2
subsd %xmm4, %xmm7
mulsd %xmm6, %xmm7
movapd %xmm3, %xmm4
subsd %xmm2, %xmm3
addsd %xmm3, %xmm2
subsd %xmm2, %xmm4
addsd %xmm4, %xmm0
subsd %xmm7, %xmm0
addsd %xmm3, %xmm0
movsd %xmm0, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_0.0.2:
jg .L_2TAG_PACKET_2.0.2
shrl $4, %eax
cmpl $268434558, %eax
jne .L_2TAG_PACKET_3.0.2
movapd %xmm0, %xmm3
mulsd 5808(%ebx), %xmm3
.L_2TAG_PACKET_3.0.2:
movsd 5792(%ebx), %xmm3
mulsd %xmm0, %xmm3
addsd %xmm0, %xmm3
mulsd 5808(%ebx), %xmm3
movsd %xmm3, (%esp)
fldl (%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_2.0.2:
movq 5712(%ebx), %xmm7
andpd %xmm0, %xmm7
xorpd %xmm0, %xmm7
ucomisd 5760(%ebx), %xmm7
je .L_2TAG_PACKET_4.0.2
subl $32, %esp
movsd %xmm0, (%esp)
lea 40(%esp), %eax
movl %eax, 8(%esp)
movl $2, %eax
movl %eax, 12(%esp)
call __libm_tancot_huge
addl $32, %esp
fldl 8(%esp)
jmp .L_2TAG_PACKET_1.0.2
.L_2TAG_PACKET_4.0.2:
movq %xmm0, (%esp)
fldl (%esp)
fsubl (%esp)
.L_2TAG_PACKET_1.0.2:
movl 56(%esp), %ebx
movl %ebp, %esp
popl %ebp
ret
..B2.3:
END(tan)
# -- End tan
# Start file scope ASM
ALIAS_SYMBOL(tanl, tan);
# End file scope ASM
.section .rodata, "a"
.align 16
.align 16
static_const_table:
.long 0
.long 0
.long 0
.long 0
.long 2284589306
.long 1066820852
.long 0
.long 0
.long 0
.long 0
.long 0
.long 0
.long 1441186365
.long 1065494243
.long 1431655765
.long 1070945621
.long 0
.long 0
.long 0
.long 0
.long 236289504
.long 1064135997
.long 286331153
.long 1069617425
.long 0
.long 0
.long 0
.long 0
.long 1160476131
.long 1062722102
.long 463583772
.long 1068212666
.long 0
.long 0
.long 0
.long 0
.long 0
.long 1072693248
.long 0
.long 0
.long 0
.long 0
.long 0
.long 0
.long 1313038235
.long 1066745731
.long 0
.long 0
.long 1013878342
.long 1067152618
.long 0
.long 0
.long 3663426833
.long 1065725283
.long 3693284251
.long 1069118808
.long 650852232
.long 1065882376
.long 1996245381
.long 1071000265
.long 2008746170
.long 1064664197
.long 3055842593
.long 1068578846
.long 1495406348
.long 1064652437
.long 2269530157
.long 1069711235
.long 285563696
.long 1063576465
.long 1046897440
.long 1067705865
.long 233429731
.long 1063453151
.long 522045958
.long 1068476590
.long 2354785698
.long 1069102779
.long 1317599141
.long 1012432133
.long 0
.long 1072693248
.long 2828230105
.long 1065606626
.long 0
.long 0
.long 0
.long 0
.long 1512545955
.long 1068119047
.long 0
.long 0
.long 1127048698
.long 1067909459
.long 0
.long 0
.long 2300200450
.long 1067254767
.long 3593250296
.long 1070233561
.long 3009365544
.long 1066902117
.long 1127373050
.long 1071173457
.long 3046103305
.long 1066371299
.long 24583402
.long 1069723988
.long 4082511758
.long 1065914199
.long 3223889699
.long 1070020367
.long 548927984
.long 1065415756
.long 558065897
.long 1068949418
.long 680073315
.long 1064940726
.long 388873200
.long 1068944270
.long 3763679576
.long 1070167541
.long 1497360404
.long 1009710547
.long 0
.long 1072693248
.long 64931152
.long 1067729411
.long 0
.long 0
.long 0
.long 0
.long 2467582782
.long 1069256389
.long 0
.long 0
.long 162150096
.long 1068946420
.long 0
.long 0
.long 3702794237
.long 1068579152
.long 3631919291
.long 1070936926
.long 3456821413
.long 1068217218
.long 2031366438
.long 1071495745
.long 1596664020
.long 1067799281
.long 1509038701
.long 1070601643
.long 583171477
.long 1067510148
.long 3785344682
.long 1070618476
.long 2402036048
.long 1067075736
.long 3233018412
.long 1069913186
.long 411280568
.long 1066710556
.long 1065584192
.long 1069747896
.long 895247324
.long 1070819848
.long 500078909
.long 3161288781
.long 0
.long 1072693248
.long 729983843
.long 1068994194
.long 0
.long 0
.long 0
.long 0
.long 1458794562
.long 1070398550
.long 0
.long 0
.long 2857777489
.long 1070137637
.long 0
.long 0
.long 1024359517
.long 1069876531
.long 2616040238
.long 1071582937
.long 1609024636
.long 1069675088
.long 2529240549
.long 1071836633
.long 1510128600
.long 1069440113
.long 2251697184
.long 1071253687
.long 1262761453
.long 1069142850
.long 1263091857
.long 1071190461
.long 3043383486
.long 1068885191
.long 2476932470
.long 1070842002
.long 3659995028
.long 1068669200
.long 855891755
.long 1070696894
.long 2583490354
.long 1071284857
.long 3062633575
.long 1014008623
.long 0
.long 1072693248
.long 2550940471
.long 1069938201
.long 0
.long 0
.long 0
.long 0
.long 3422807297
.long 1071640847
.long 0
.long 0
.long 1151658053
.long 1071494715
.long 0
.long 0
.long 929607071
.long 1071346340
.long 1037049034
.long 1072037305
.long 2786928657
.long 1071215282
.long 1447406859
.long 1072265209
.long 3490952107
.long 1071090851
.long 3205232916
.long 1071968658
.long 1297344304
.long 1070977120
.long 1066110976
.long 1071946035
.long 3803721480
.long 1070871082
.long 1496754229
.long 1071807201
.long 2982550683
.long 1070773243
.long 4014441989
.long 1071736222
.long 419968236
.long 1071717047
.long 3451266538
.long 3163444811
.long 0
.long 1072693248
.long 2960267235
.long 1070745841
.long 0
.long 0
.long 0
.long 0
.long 724322768
.long 1072881308
.long 0
.long 0
.long 643153048
.long 1072905816
.long 0
.long 0
.long 4285079458
.long 1072928558
.long 3912524733
.long 1072622983
.long 118362272
.long 1072952754
.long 4107767972
.long 1072827408
.long 2689502883
.long 1072976922
.long 946523347
.long 1072772766
.long 573204189
.long 1073001761
.long 581531518
.long 1072826391
.long 1386236526
.long 1073026959
.long 3718905905
.long 1072832823
.long 1145558140
.long 1073052673
.long 513572637
.long 1072861969
.long 716700048
.long 1071997368
.long 547126769
.long 1015523525
.long 0
.long 1072693248
.long 1097907398
.long 1071420120
.long 0
.long 0
.long 0
.long 0
.long 3349892442
.long 1074290212
.long 0
.long 0
.long 3913197405
.long 1074501181
.long 0
.long 0
.long 2494034522
.long 1074739170
.long 1264738763
.long 1073084804
.long 1520293906
.long 1074899632
.long 1958936600
.long 1073411493
.long 2133649635
.long 1075052171
.long 4270740730
.long 1073574708
.long 1728930189
.long 1075224844
.long 1303998552
.long 1073799186
.long 618611933
.long 1075420255
.long 1769828046
.long 1073938542
.long 2200537986
.long 1075641421
.long 433361110
.long 1074105369
.long 719595600
.long 1072317184
.long 294527206
.long 3162140088
.long 0
.long 1073741824
.long 3811788216
.long 3218400550
.long 0
.long 0
.long 0
.long 0
.long 1704352102
.long 1075943001
.long 0
.long 0
.long 2284589306
.long 1076258036
.long 0
.long 0
.long 2211264291
.long 1076659010
.long 0
.long 1073741824
.long 1441186365
.long 1077028579
.long 1431655765
.long 1074091349
.long 876943673
.long 1077353622
.long 2863311531
.long 1074440874
.long 236289504
.long 1077767485
.long 286331153
.long 1074860305
.long 2805473311
.long 1078115278
.long 95443718
.long 1075163227
.long 1160476131
.long 1078450742
.long 463583772
.long 1075552698
.long 0
.long 1072693248
.long 0
.long 0
.long 0
.long 1073741824
.long 0
.long 0
.long 0
.long 0
.long 0
.long 0
.long 1330165971
.long 3207850745
.long 0
.long 0
.long 217536623
.long 1059109098
.long 0
.long 0
.long 3492120849
.long 3205151475
.long 602185705
.long 3215678092
.long 760422958
.long 1056312597
.long 555127889
.long 1067545266
.long 3139784124
.long 3202470837
.long 3690544014
.long 3213150171
.long 95707915
.long 1053635428
.long 4003114407
.long 1064581412
.long 2034926231
.long 3199711161
.long 3759536023
.long 3210559989
.long 3826928214
.long 1050893819
.long 3837960785
.long 1061790379
.long 1526325248
.long 3217967566
.long 2356426521
.long 1025423456
.long 0
.long 0
.long 457728975
.long 1071088276
.long 0
.long 1072693248
.long 0
.long 4294967288
.long 1398462608
.long 3207303968
.long 0
.long 0
.long 26205983
.long 1058461213
.long 0
.long 0
.long 56226238
.long 3204528612
.long 2754706541
.long 3215359511
.long 2187799823
.long 1055634437
.long 790323742
.long 1067402587
.long 1372385848
.long 3201651479
.long 4097292716
.long 3212856302
.long 3348210357
.long 1052830099
.long 2442796466
.long 1064337602
.long 862608142
.long 3198830754
.long 170296152
.long 3210060867
.long 3755571428
.long 1049933343
.long 3614866008
.long 1061361670
.long 719978496
.long 3217669096
.long 1998842465
.long 3174703977
.long 0
.long 0
.long 3749156607
.long 1071048258
.long 0
.long 1072693248
.long 0
.long 4294967288
.long 3120498638
.long 3206749304
.long 0
.long 0
.long 2773578114
.long 1058009312
.long 0
.long 0
.long 2030783676
.long 3203817873
.long 2223654598
.long 3215071936
.long 2976134650
.long 1054987244
.long 706390066
.long 1067217386
.long 4258437615
.long 3200900378
.long 1066252975
.long 3212391267
.long 815777514
.long 1051989462
.long 3202745457
.long 1064010682
.long 2493556375
.long 3198004753
.long 1046243251
.long 3209678971
.long 2593078846
.long 1049017717
.long 2763962276
.long 1060970161
.long 701480960
.long 3217377742
.long 3205862232
.long 3174660915
.long 0
.long 0
.long 2267016812
.long 1071015664
.long 0
.long 1072693248
.long 0
.long 4294967288
.long 2107155798
.long 3206166872
.long 0
.long 0
.long 2642992129
.long 1057424578
.long 0
.long 0
.long 1936992811
.long 3203204426
.long 1485063559
.long 3214682643
.long 1432914553
.long 1054319398
.long 3996381654
.long 1067075828
.long 2833029256
.long 3200223545
.long 2866066872
.long 3211982662
.long 2432888737
.long 1051234178
.long 3669764559
.long 1063748136
.long 2458496952
.long 3197170774
.long 1948234989
.long 3209098147
.long 2843698787
.long 1048163519
.long 3398041407
.long 1060559728
.long 2829230080
.long 3217092115
.long 1034046433
.long 3174271903
.long 0
.long 0
.long 298675305
.long 1070989821
.long 0
.long 1072693248
.long 0
.long 4294967288
.long 437603223
.long 3205589761
.long 0
.long 0
.long 759330352
.long 1057048511
.long 0
.long 0
.long 3107463368
.long 3202507988
.long 3144465176
.long 3214191500
.long 2290961810
.long 1053841035
.long 1618153340
.long 1066971547
.long 3836869393
.long 3199400272
.long 584032116
.long 3211469261
.long 1245704358
.long 1050626462
.long 4247487438
.long 1063561943
.long 1669034927
.long 3196274812
.long 3844233498
.long 3208626322
.long 2706958524
.long 1047411374
.long 3857199098
.long 1060281647
.long 3593904128
.long 3216590719
.long 3267547836
.long 3172163321
.long 0
.long 0
.long 4076712227
.long 1070970214
.long 0
.long 1072693248
.long 0
.long 4294967288
.long 3290090340
.long 3204793485
.long 0
.long 0
.long 3685760367
.long 1056668370
.long 0
.long 0
.long 2655163949
.long 3201674917
.long 628750575
.long 3213566872
.long 680140505
.long 1053299777
.long 2954464709
.long 1066900026
.long 803201619
.long 3198516435
.long 1466315631
.long 3210837162
.long 1611220163
.long 1049972438
.long 2766187256
.long 1063437894
.long 1804579484
.long 3195331491
.long 3695969289
.long 3207854418
.long 2617238373
.long 1046675948
.long 3095830084
.long 1060095334
.long 3789570048
.long 3216034914
.long 23826559
.long 3172048060
.long 0
.long 0
.long 3870939386
.long 1070956467
.long 0
.long 1072693248
.long 0
.long 4294967288
.long 1571758758
.long 3203672535
.long 0
.long 0
.long 113026373
.long 1056416381
.long 0
.long 0
.long 1913766298
.long 3200523326
.long 2507068734
.long 3212502004
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# End