path: root/libm/x86_64/e_sinh.S

/*
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
//                     ---------------------
//
//  sinh(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 the high 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 [23/64,3*2^7)
//  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)+2^{-k}*Dn
//
//  For |x| in [1/8, 3*2^7), sinh(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), sign(x)*(e^|x|)/2 is returned, and
//  the result is checked for overflow.
//
//  For |x|<23/64, a Taylor polynomial expansion is used (degree 13)
//  To reduce rounding errors, the p3*x^3 term is computed as
//     (p3*xh^3)_high+[(p3*xl*(3*x*xh+xl^2))+(p3*xh^3)_low],
//  where x=xh+xl, (xh are the leading 17 bits of x), and
//     (p3*xh^3)_high=RN(x+p3*xh^3)-x
//  (error bound for polynomial expansion is below 0.51 ulp)
//
// Special cases:
//  sinh(NaN) = quiet NaN, and raise invalid exception
//  sinh(+/-INF) = +/-INF
//  sinh(x) = x for subnormals
//  for finite argument, only sinh(0)=0 is exact
//  For IEEE double
//    sinh(x) overflows  for x > 
//    710.47586007394386342639336362481117248535156250 = MAXLOG+log(2)
//
/******************************************************************************/

#include <private/bionic_asm.h>
# -- Begin  sinh
ENTRY(sinh)
# parameter 1: %xmm0
..B1.1:
..___tag_value_sinh.1:
        pushq     %rsi
..___tag_value_sinh.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
        movl      $32768, %edx
        andl      %ecx, %edx
        andl      $32767, %ecx
        subl      $16343, %ecx
        cmpl      $177, %ecx
        jae       .L_2TAG_PACKET_0.0.2
        subsd     %xmm3, %xmm4
        mulsd     %xmm1, %xmm3
        mulsd     %xmm5, %xmm2
        cvtsd2si  %xmm3, %eax
        shll      $3, %edx
        orl       %edx, %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      $161, %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
        subpd     %xmm5, %xmm0
        mulpd     %xmm7, %xmm2
        addpd     %xmm6, %xmm4
        subsd     %xmm0, %xmm7
        mulpd     %xmm2, %xmm4
        pshufd    $238, %xmm0, %xmm6
        subsd     %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_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
        movl      $127, %edx
        cmpl      $32752, %eax
        je        .L_2TAG_PACKET_2.0.2
        jmp       ..B1.5
.L_2TAG_PACKET_0.0.2:
        addl      $16343, %ecx
        cmpl      $16343, %ecx
        ja        .L_2TAG_PACKET_3.0.2
        cmpl      $15856, %ecx
        jb        .L_2TAG_PACKET_4.0.2
        movapd    pv(%rip), %xmm1
        pshufd    $68, %xmm0, %xmm6
        mulpd     %xmm5, %xmm5
        movapd    16+pv(%rip), %xmm2
        pshufd    $68, %xmm0, %xmm7
        movapd    32+pv(%rip), %xmm3
        pshufd    $68, %xmm0, %xmm4
        andpd     MASK3(%rip), %xmm6
        mulpd     %xmm5, %xmm1
        mulsd     %xmm5, %xmm2
        subpd     %xmm6, %xmm4
        mulpd     %xmm5, %xmm7
        addpd     %xmm3, %xmm1
        pshufd    $68, %xmm6, %xmm3
        mulpd     %xmm5, %xmm5
        mulsd     %xmm7, %xmm2
        mulpd     %xmm7, %xmm1
        pshufd    $68, %xmm0, %xmm7
        mulsd     %xmm6, %xmm6
        addsd     %xmm7, %xmm7
        mulsd     %xmm4, %xmm4
        mulpd     %xmm5, %xmm1
        addsd     %xmm0, %xmm7
        mulsd     %xmm3, %xmm6
        mulsd     %xmm3, %xmm7
        pshufd    $238, %xmm1, %xmm3
        mulsd     %xmm5, %xmm1
        pshufd    $238, %xmm4, %xmm5
        addsd     %xmm2, %xmm3
        pshufd    $238, %xmm2, %xmm2
        addsd     %xmm4, %xmm7
        movq      %xmm0, %xmm4
        mulsd     %xmm2, %xmm6
        mulsd     %xmm5, %xmm7
        addsd     %xmm6, %xmm0
        mulsd     %xmm2, %xmm7
        subsd     %xmm0, %xmm4
        addsd     %xmm7, %xmm1
        addsd     %xmm4, %xmm6
        addsd     %xmm3, %xmm1
        addsd     %xmm6, %xmm1
        addsd     %xmm1, %xmm0
        jmp       ..B1.5
.L_2TAG_PACKET_4.0.2:
        cmpl      $16, %ecx
        jae       .L_2TAG_PACKET_5.0.2
        movq      %xmm0, %xmm1
        mulsd     %xmm1, %xmm1
        jmp       ..B1.5
.L_2TAG_PACKET_5.0.2:
        xorpd     %xmm2, %xmm2
        movl      $17392, %ecx
        pinsrw    $3, %ecx, %xmm2
        xorpd     %xmm3, %xmm3
        movl      $15344, %edx
        pinsrw    $3, %edx, %xmm3
        mulsd     %xmm0, %xmm2
        addsd     %xmm2, %xmm0
        mulsd     %xmm3, %xmm0
        jmp       ..B1.5
.L_2TAG_PACKET_3.0.2:
        cmpl      $32752, %ecx
        jae       .L_2TAG_PACKET_6.0.2
        xorpd     %xmm0, %xmm0
        movl      $32736, %eax
        pinsrw    $3, %eax, %xmm0
        orl       %edx, %eax
        pinsrw    $3, %eax, %xmm1
        mulsd     %xmm1, %xmm0
        jmp       .L_2TAG_PACKET_2.0.2
.L_2TAG_PACKET_6.0.2:
        xorpd     %xmm1, %xmm1
        movl      $32768, %eax
        pinsrw    $3, %eax, %xmm1
        andnpd    %xmm0, %xmm1
        mulsd     %xmm1, %xmm0
        jmp       ..B1.5
.L_2TAG_PACKET_2.0.2:
        movq      %xmm0, (%rsp)
..B1.3:
        movq      (%rsp), %xmm0
.L_2TAG_PACKET_7.0.2:
..B1.5:
        popq      %rcx
..___tag_value_sinh.4:
        ret       
..___tag_value_sinh.5:
END(sinh)
# -- End  sinh
	.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	1064709698
	.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
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	.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
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	.type	T2_neg_f,@object
	.size	T2_neg_f,2048
	.align 16
pv:
	.long	329805064
	.long	1038488134
	.long	2773927730
	.long	1053236707
	.long	286331153
	.long	1065423121
	.long	1431655765
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	.long	1744127201
	.long	1046144581
	.long	436314137
	.long	1059717536
	.type	pv,@object
	.size	pv,48
	.align 16
MASK3:
	.long	0
	.long	4294967280
	.long	0
	.long	4294967280
	.type	MASK3,@object
	.size	MASK3,16
	.align 8
HALFMASK:
	.long	4160749568
	.long	2147483647
	.type	HALFMASK,@object
	.size	HALFMASK,8
	.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
	.4byte 0x0000001c
	.4byte 0x0000001c
	.4byte ..___tag_value_sinh.1-.
	.4byte ..___tag_value_sinh.5-..___tag_value_sinh.1
	.2byte 0x0400
	.4byte ..___tag_value_sinh.3-..___tag_value_sinh.1
	.2byte 0x100e
	.byte 0x04
	.4byte ..___tag_value_sinh.4-..___tag_value_sinh.3
	.2byte 0x080e
	.byte 0x00
# End