/*
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
// ---------------------
//
// cosh(x)=(exp(x)+exp(-x))/2
//
// Let |x|=xH+xL (upper 26 bits, lower 27 bits)
// log2(e) rounded to 26 bits (high part) plus a double precision low part is
// L2EH+L2EL (upper 26, lower 53 bits)
//
// Let xH*L2EH=k+f+r`, where (k+f)*2^7=int(xH*L2EH*2^7),
// f=0.b1 b2 ... b7, k integer
// 2^f is approximated as Tp[f]+Dp[f], and 2^{-f} as Tn[f]+Dn[f]
// Tp stores higher 53 bits, Dp stores (2^f-Tp[f]) rounded to double precision
//
// e^|x|=2^{k+f}*2^r, r=r`+xL*L2EH+|x|*L2EL, |r|<2^{-8}+2^{-14},
// for |x| in [1/8,3*2^8)
// e^{-|x|}=2^{-k-f}*2^{-r}
//
// e^|x| is approximated as 2^k*Tp+2^k*Tp*c1*r(1+c2*r+..+c5*r^4)+2^k*Dp=
// =2^k*Tp+2^k*Tp*P15+2^k*Dp
// e^{-|x|} approximated as 2^{-k}*Tn-2^{-k}*Tn*c1*r(1-c2*r+..+c5*r^4)
//
// For |x| in [1/8, 3*2^7), cosh(x) is formed as
// RN(2^k*Tp+2^{-k}*Tn)+2^k*Tp*P15+2^{-k}*Tn*P`15+2^{-k}*TnL+2^{-k}*Dn+2^k*Dp
//
// For |x| in [3*2^7, 3*2^8), (e^|x|)/2 is returned, and
// the result is checked for overflow.
//
// For |x|<1/8, a Taylor polynomial expansion is used (degree 10)
// (error bound for polynomial expansion is below 0.501 ulp)
//
// Special cases:
// cosh(NaN) = quiet NaN, and raise invalid exception
// cosh(INF) = that INF
// cosh(0)=1
// for finite argument, only cosh(0)=1 is exact
// For IEEE double
// cosh(x) overflows
// for x > 710.47586007394386342639336362481117248535156250 = MAXLOG+log(2)
//
/******************************************************************************/
#include <private/bionic_asm.h>
# -- Begin cosh
ENTRY(cosh)
# parameter 1: %xmm0
..B1.1:
..___tag_value_cosh.1:
pushq %rsi
..___tag_value_cosh.3:
..B1.2:
movsd HALFMASK(%rip), %xmm3
xorpd %xmm4, %xmm4
movsd L2E(%rip), %xmm1
movsd 8+L2E(%rip), %xmm2
movl $32768, %eax
pinsrw $3, %eax, %xmm4
movsd Shifter(%rip), %xmm6
pextrw $3, %xmm0, %ecx
andpd %xmm0, %xmm3
andnpd %xmm0, %xmm4
pshufd $68, %xmm4, %xmm5
andl $32767, %ecx
subl $16320, %ecx
cmpl $200, %ecx
jae .L_2TAG_PACKET_0.0.2
subsd %xmm3, %xmm4
mulsd %xmm1, %xmm3
mulsd %xmm5, %xmm2
cvtsd2si %xmm3, %eax
movq %xmm3, %xmm7
addsd %xmm6, %xmm3
mulsd %xmm4, %xmm1
xorpd %xmm5, %xmm5
subsd %xmm6, %xmm3
movapd cv(%rip), %xmm4
addsd %xmm1, %xmm2
movapd 16+cv(%rip), %xmm6
subsd %xmm3, %xmm7
movl $32704, %edx
pinsrw $3, %edx, %xmm5
movapd 32+cv(%rip), %xmm1
addsd %xmm7, %xmm2
movl $127, %edx
andl %eax, %edx
addl %edx, %edx
shrl $3, %eax
andl $65520, %eax
addl $16352, %eax
xorpd %xmm0, %xmm0
cmpl $184, %ecx
jae .L_2TAG_PACKET_1.0.2
pshufd $68, %xmm5, %xmm5
pinsrw $3, %eax, %xmm0
pshufd $68, %xmm0, %xmm0
psubw %xmm0, %xmm5
lea T2f(%rip), %r8
mulpd (%r8,%rdx,8), %xmm0
lea T2_neg_f(%rip), %r8
mulpd (%r8,%rdx,8), %xmm5
pshufd $68, %xmm2, %xmm3
movapd 48+cv(%rip), %xmm7
pshufd $68, %xmm2, %xmm2
mulpd %xmm3, %xmm3
mulpd %xmm2, %xmm4
mulpd %xmm2, %xmm6
mulpd 64+cv(%rip), %xmm2
mulpd %xmm3, %xmm1
mulpd %xmm3, %xmm7
mulpd %xmm3, %xmm4
mulpd %xmm3, %xmm1
addpd %xmm7, %xmm6
movq %xmm0, %xmm7
addpd %xmm1, %xmm4
shufpd $0, %xmm5, %xmm7
addpd %xmm5, %xmm0
mulpd %xmm7, %xmm2
addpd %xmm6, %xmm4
subsd %xmm0, %xmm7
mulpd %xmm2, %xmm4
pshufd $238, %xmm0, %xmm6
addsd %xmm5, %xmm7
addpd %xmm2, %xmm4
addsd %xmm6, %xmm7
pshufd $238, %xmm4, %xmm2
addsd %xmm7, %xmm2
addsd %xmm4, %xmm2
addsd %xmm2, %xmm0
jmp ..B1.5
.L_2TAG_PACKET_0.0.2:
addl $16320, %ecx
cmpl $16320, %ecx
ja .L_2TAG_PACKET_2.0.2
cmpl $15952, %ecx
jae .L_2TAG_PACKET_3.0.2
addsd %xmm2, %xmm6
movq ONEMASK(%rip), %xmm0
jmp ..B1.5
.L_2TAG_PACKET_1.0.2:
subl $16352, %eax
movl %eax, %ecx
andl $32752, %eax
shrl $1, %eax
andl $65520, %eax
subl %eax, %ecx
addl $16352, %eax
pinsrw $3, %eax, %xmm0
pshufd $68, %xmm0, %xmm0
lea T2f(%rip), %r8
mulpd (%r8,%rdx,8), %xmm0
pshufd $68, %xmm2, %xmm3
movsd 48+cv(%rip), %xmm7
mulsd %xmm3, %xmm3
mulsd %xmm2, %xmm4
mulsd %xmm2, %xmm6
mulsd 64+cv(%rip), %xmm2
mulsd %xmm3, %xmm1
mulsd %xmm3, %xmm7
mulsd %xmm3, %xmm4
addl $16368, %ecx
pinsrw $3, %ecx, %xmm5
mulsd %xmm3, %xmm1
addsd %xmm7, %xmm6
addsd %xmm1, %xmm4
mulsd %xmm0, %xmm2
addsd %xmm6, %xmm4
mulsd %xmm2, %xmm4
pshufd $238, %xmm0, %xmm6
addsd %xmm6, %xmm4
addsd %xmm4, %xmm2
addsd %xmm2, %xmm0
mulsd %xmm5, %xmm0
pextrw $3, %xmm0, %eax
andl $32752, %eax
cmpl $32752, %eax
je .L_2TAG_PACKET_4.0.2
jmp ..B1.5
.L_2TAG_PACKET_3.0.2:
movapd pv(%rip), %xmm1
mulpd %xmm5, %xmm5
movapd 16+pv(%rip), %xmm2
xorpd %xmm3, %xmm3
movq %xmm5, %xmm0
mulpd %xmm5, %xmm1
movsd ONEMASK(%rip), %xmm6
mulpd %xmm5, %xmm5
movl $16352, %eax
pinsrw $3, %eax, %xmm3
addpd %xmm2, %xmm1
mulpd %xmm5, %xmm1
pshufd $238, %xmm1, %xmm2
mulsd %xmm1, %xmm5
mulsd %xmm3, %xmm0
addsd %xmm5, %xmm2
addsd %xmm2, %xmm0
addsd %xmm6, %xmm0
jmp ..B1.5
.L_2TAG_PACKET_2.0.2:
cmpl $32752, %ecx
jae .L_2TAG_PACKET_5.0.2
xorpd %xmm0, %xmm0
movl $32736, %eax
pinsrw $3, %eax, %xmm0
mulsd %xmm0, %xmm0
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_5.0.2:
mulsd %xmm0, %xmm0
jmp ..B1.5
.L_2TAG_PACKET_4.0.2:
movq %xmm0, (%rsp)
..B1.3:
movq (%rsp), %xmm0
.L_2TAG_PACKET_6.0.2:
..B1.5:
popq %rcx
..___tag_value_cosh.4:
ret
..___tag_value_cosh.5:
END(cosh)
# -- End cosh
.section .rodata, "a"
.align 16
.align 16
L2E:
.long 1610612736
.long 1080497479
.long 4166901572
.long 1053077003
.type L2E,@object
.size L2E,16
.align 16
Shifter:
.long 0
.long 1127743488
.long 0
.long 3275227136
.type Shifter,@object
.size Shifter,16
.align 16
cv:
.long 3607404736
.long 1044146952
.long 3607404736
.long 3191630600
.long 4277811695
.long 1063661122
.long 4277811695
.long 3211144770
.long 2140175755
.long 1033864261
.long 2140175755
.long 1033864261
.long 4289495988
.long 1054113747
.long 4289495988
.long 1054113747
.long 4277811695
.long 1064709698
.long 4277811695
.long 3212193346
.type cv,@object
.size cv,80
.align 16
T2f:
.long 0
.long 1072693248
.long 0
.long 0
.long 2851812149
.long 1072698941
.long 2595802551
.long 1016815913
.long 1048019041
.long 1072704666
.long 1398474845
.long 3161559171
.long 3899555717
.long 1072710421
.long 427280750
.long 3163595548
.long 3541402996
.long 1072716208
.long 2759177317
.long 1015903202
.long 702412510
.long 1072722027
.long 3803266087
.long 3163328991
.long 410360776
.long 1072727877
.long 1269990655
.long 1013024446
.long 3402036099
.long 1072733758
.long 405889334
.long 1016154232
.long 1828292879
.long 1072739672
.long 1255956747
.long 1016636974
.long 728909815
.long 1072745618
.long 383930225
.long 1016078044
.long 852742562
.long 1072751596
.long 667253586
.long 1010842135
.long 2952712987
.long 1072757606
.long 3293494651
.long 3161168877
.long 3490863953
.long 1072763649
.long 960797498
.long 3163997456
.long 3228316108
.long 1072769725
.long 3010241991
.long 3159471380
.long 2930322912
.long 1072775834
.long 2599499422
.long 3163762623
.long 3366293073
.long 1072781976
.long 3119426314
.long 1015169130
.long 1014845819
.long 1072788152
.long 3117910646
.long 3162607681
.long 948735466
.long 1072794361
.long 3516338028
.long 3163623459
.long 3949972341
.long 1072800603
.long 2068408548
.long 1015962444
.long 2214878420
.long 1072806880
.long 892270087
.long 3164164998
.long 828946858
.long 1072813191
.long 10642492
.long 1016988014
.long 586995997
.long 1072819536
.long 41662348
.long 3163676568
.long 2288159958
.long 1072825915
.long 2169144469
.long 1015924597
.long 2440944790
.long 1072832329
.long 2492769774
.long 1015196030
.long 1853186616
.long 1072838778
.long 3066496371
.long 1016705150
.long 1337108031
.long 1072845262
.long 3203724452
.long 1015726421
.long 1709341917
.long 1072851781
.long 2571168217
.long 1015201075
.long 3790955393
.long 1072858335
.long 2352942462
.long 3164228666
.long 4112506593
.long 1072864925
.long 2947355221
.long 1015419624
.long 3504003472
.long 1072871551
.long 3594001060
.long 3158379228
.long 2799960843
.long 1072878213
.long 1423655381
.long 1016070727
.long 2839424854
.long 1072884911
.long 1171596163
.long 1014090255
.long 171030293
.long 1072891646
.long 3526460132
.long 1015477354
.long 4232894513
.long 1072898416
.long 2383938684
.long 1015717095
.long 2992903935
.long 1072905224
.long 2218154406
.long 1016276769
.long 1603444721
.long 1072912069
.long 1548633640
.long 3163249902
.long 926591435
.long 1072918951
.long 3208833762
.long 3163962090
.long 1829099622
.long 1072925870
.long 1016661181
.long 3164509581
.long 887463927
.long 1072932827
.long 3596744163
.long 3161842742
.long 3272845541
.long 1072939821
.long 928852419
.long 3164536824
.long 1276261410
.long 1072946854
.long 300981948
.long 1015732745
.long 78413852
.long 1072953925
.long 4183226867
.long 3164065827
.long 569847338
.long 1072961034
.long 472945272
.long 3160339305
.long 3645941911
.long 1072968181
.long 3814685081
.long 3162621917
.long 1617004845
.long 1072975368
.long 82804944
.long 1011391354
.long 3978100823
.long 1072982593
.long 3513027190
.long 1016894539
.long 3049340112
.long 1072989858
.long 3062915824
.long 1014219171
.long 4040676318
.long 1072997162
.long 4090609238
.long 1016712034
.long 3577096743
.long 1073004506
.long 2951496418
.long 1014842263
.long 2583551245
.long 1073011890
.long 3161094195
.long 1016655067
.long 1990012071
.long 1073019314
.long 3529070563
.long 3163861769
.long 2731501122
.long 1073026778
.long 1774031855
.long 3163518597
.long 1453150082
.long 1073034283
.long 498154669
.long 3162536638
.long 3395129871
.long 1073041828
.long 4025345435
.long 3163383964
.long 917841882
.long 1073049415
.long 18715565
.long 1016707884
.long 3566716925
.long 1073057042
.long 1536826856
.long 1015191009
.long 3712504873
.long 1073064711
.long 88491949
.long 1016476236
.long 2321106615
.long 1073072422
.long 2171176610
.long 1010584347
.long 363667784
.long 1073080175
.long 813753950
.long 1016833785
.long 3111574537
.long 1073087969
.long 2606161479
.long 3163808322
.long 2956612997
.long 1073095806
.long 2118169751
.long 3163784129
.long 885834528
.long 1073103686
.long 1973258547
.long 3163310140
.long 2186617381
.long 1073111608
.long 2270764084
.long 3164321289
.long 3561793907
.long 1073119573
.long 1157054053
.long 1012938926
.long 1719614413
.long 1073127582
.long 330458198
.long 3164331316
.long 1963711167
.long 1073135634
.long 1744767757
.long 3161622870
.long 1013258799
.long 1073143730
.long 1748797611
.long 3161177658
.long 4182873220
.long 1073151869
.long 629542646
.long 3163044879
.long 3907805044
.long 1073160053
.long 2257091225
.long 3162598983
.long 1218806132
.long 1073168282
.long 1818613052
.long 3163597017
.long 1447192521
.long 1073176555
.long 1462857171
.long 3163563097
.long 1339972927
.long 1073184873
.long 167908909
.long 1016620728
.long 1944781191
.long 1073193236
.long 3993278767
.long 3162772855
.long 19972402
.long 1073201645
.long 3507899862
.long 1017057868
.long 919555682
.long 1073210099
.long 3121969534
.long 1013996802
.long 1413356050
.long 1073218599
.long 1651349291
.long 3163716742
.long 2571947539
.long 1073227145
.long 3558159064
.long 3164425245
.long 1176749997
.long 1073235738
.long 2738998779
.long 3163084420
.long 2604962541
.long 1073244377
.long 2614425274
.long 3164587768
.long 3649726105
.long 1073253063
.long 4085036346
.long 1016698050
.long 1110089947
.long 1073261797
.long 1451641639
.long 1016523249
.long 380978316
.long 1073270578
.long 854188970
.long 3161511262
.long 2568320822
.long 1073279406
.long 2732824428
.long 1015401491
.long 194117574
.long 1073288283
.long 777528612
.long 3164460665
.long 2966275557
.long 1073297207
.long 2176155324
.long 3160891335
.long 3418903055
.long 1073306180
.long 2527457337
.long 3161869180
.long 2682146384
.long 1073315202
.long 2082178513
.long 3164411995
.long 1892288442
.long 1073324273
.long 2446255666
.long 3163648957
.long 2191782032
.long 1073333393
.long 2960257726
.long 1014791238
.long 434316067
.long 1073342563
.long 2028358766
.long 1014506698
.long 2069751141
.long 1073351782
.long 1562170675
.long 3163773257
.long 3964284211
.long 1073361051
.long 2111583915
.long 1016475740
.long 2990417245
.long 1073370371
.long 3683467745
.long 3164417902
.long 321958744
.long 1073379742
.long 3401933767
.long 1016843134
.long 1434058175
.long 1073389163
.long 251133233
.long 1016134345
.long 3218338682
.long 1073398635
.long 3404164304
.long 3163525684
.long 2572866477
.long 1073408159
.long 878562433
.long 1016570317
.long 697153126
.long 1073417735
.long 1283515429
.long 3164331765
.long 3092190715
.long 1073427362
.long 814012168
.long 3160571998
.long 2380618042
.long 1073437042
.long 3149557219
.long 3164369375
.long 4076559943
.long 1073446774
.long 2119478331
.long 3161806927
.long 815859274
.long 1073456560
.long 240396590
.long 3164536019
.long 2420883922
.long 1073466398
.long 2049810052
.long 1015168464
.long 1540824585
.long 1073476290
.long 1064017011
.long 3164536266
.long 3716502172
.long 1073486235
.long 2303740125
.long 1015091301
.long 1610600570
.long 1073496235
.long 3766732298
.long 1016808759
.long 777507147
.long 1073506289
.long 4282924205
.long 1016236109
.long 2483480501
.long 1073516397
.long 1216371780
.long 1014082748
.long 3706687593
.long 1073526560
.long 3521726940
.long 1014301643
.long 1432208378
.long 1073536779
.long 1401068914
.long 3163412539
.long 1242007932
.long 1073547053
.long 1132034716
.long 3164388407
.long 135105010
.long 1073557383
.long 1906148728
.long 3164424315
.long 3707479175
.long 1073567768
.long 3613079303
.long 1015213314
.long 382305176
.long 1073578211
.long 2347622376
.long 3163627201
.long 64696965
.long 1073588710
.long 1768797490
.long 1016865536
.long 4076975200
.long 1073599265
.long 2029000899
.long 1016257111
.long 863738719
.long 1073609879
.long 1326992220
.long 3163661773
.long 351641897
.long 1073620550
.long 2172261526
.long 3164059175
.long 3884662774
.long 1073631278
.long 2158611599
.long 1015258761
.long 4224142467
.long 1073642065
.long 3389820386
.long 1016255778
.long 2728693978
.long 1073652911
.long 396109971
.long 3164511267
.long 764307441
.long 1073663816
.long 3021057420
.long 3164378099
.long 3999357479
.long 1073674779
.long 2258941616
.long 1016973300
.long 929806999
.long 1073685803
.long 3205336643
.long 1016308133
.long 1533953344
.long 1073696886
.long 769171851
.long 1016714209
.long 2912730644
.long 1073708029
.long 3490067722
.long 3164453650
.long 2174652632
.long 1073719233
.long 4087714590
.long 1015498835
.long 730821105
.long 1073730498
.long 2523232743
.long 1013115764
.type T2f,@object
.size T2f,2048
.align 16
T2_neg_f:
.long 0
.long 1072693248
.long 0
.long 0
.long 730821105
.long 1072681922
.long 2523232743
.long 1012067188
.long 2174652632
.long 1072670657
.long 4087714590
.long 1014450259
.long 2912730644
.long 1072659453
.long 3490067722
.long 3163405074
.long 1533953344
.long 1072648310
.long 769171851
.long 1015665633
.long 929806999
.long 1072637227
.long 3205336643
.long 1015259557
.long 3999357479
.long 1072626203
.long 2258941616
.long 1015924724
.long 764307441
.long 1072615240
.long 3021057420
.long 3163329523
.long 2728693978
.long 1072604335
.long 396109971
.long 3163462691
.long 4224142467
.long 1072593489
.long 3389820386
.long 1015207202
.long 3884662774
.long 1072582702
.long 2158611599
.long 1014210185
.long 351641897
.long 1072571974
.long 2172261526
.long 3163010599
.long 863738719
.long 1072561303
.long 1326992220
.long 3162613197
.long 4076975200
.long 1072550689
.long 2029000899
.long 1015208535
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pv:
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HALFMASK:
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ONEMASK:
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.data
.section .note.GNU-stack, ""
// -- Begin DWARF2 SEGMENT .eh_frame
.section .eh_frame,"a",@progbits
.eh_frame_seg:
.align 1
.4byte 0x00000014
.8byte 0x00527a0100000000
.8byte 0x08070c1b01107801
.4byte 0x00000190
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.4byte 0x0000001c
.4byte ..___tag_value_cosh.1-.
.4byte ..___tag_value_cosh.5-..___tag_value_cosh.1
.2byte 0x0400
.4byte ..___tag_value_cosh.3-..___tag_value_cosh.1
.2byte 0x100e
.byte 0x04
.4byte ..___tag_value_cosh.4-..___tag_value_cosh.3
.2byte 0x080e
.byte 0x00
# End