path: root/libm/x86_64/s_tanh.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
//                     ---------------------
//
// tanh(x)=(exp(x)-exp(-x))/(exp(x)+exp(-x))=(1-exp(-2*x))/(1+exp(-2*x))
//
// 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)*2^8*2=int(xH*L2EH*2^9),
//                             f=0.b1 b2 ... b8, k integer
// 2^{-f} is approximated as Tn[f]+Dn[f]
// Tn stores the high 53 bits, Dn stores (2^{-f}-Tn[f]) rounded to double precision
//
//  r=r`+xL*L2EH+|x|*L2EL, |r|<2^{-9}+2^{-14},
//                      for |x| in [23/64,3*2^7)
// e^{-2*|x|}=2^{-k-f}*2^{-r} ~ 2^{-k}*(Tn+Dn)*(1+p)=(T0+D0)*(1+p)
//
// For |x| in [2^{-4},2^5):
//         2^{-r}-1 ~ p=c1*r+c2*r^2+..+c5*r^5
//      Let R=1/(1+T0+p*T0), truncated to 35 significant bits
//  R=1/(1+T0+D0+p*(T0+D0))*(1+eps), |eps|<2^{-33}
//  1+T0+D0+p*(T0+D0)=KH+KL, where
//       KH=(1+T0+c1*r*T0)_high (leading 17 bits)
//       KL=T0_low+D0+(c1*r*T0)_low+c1*r*D0+(c2*r^2+..c5*r^5)*T0
//  eps ~ (R*KH-1)+R*KL
//  1/(1+T0+D0+p*(T0+D0)) ~ R-R*eps
//  The result is approximated as (1-T0-D0-(T0+D0)*p)*(R-R*eps)
//  1-T0-D0-(T0+D0)*p=-((KH-2)+KL)
//    The result is formed as
//    (KH-2)*R+(-(KH-2)*R*eps+(KL*R-KL*R*eps)), with the correct sign
//                                                  set at the end
//
// For |x| in [2^{-64},2^{-4}):
//  A Taylor series expansion is used  (x+p3*x^3+..+p13*x^{13})
//
// For |x|<2^{-64}:  x is returned
//
// For |x|>=2^32: return +/-1
//
// Special cases:
//  tanh(NaN) = quiet NaN, and raise invalid exception
//  tanh(INF) = that INF
//  tanh(+/-0) = +/-0
//
/******************************************************************************/

#include <private/bionic_asm.h>
# -- Begin  tanh
ENTRY(tanh)
# parameter 1: %xmm0
..B1.1:
..___tag_value_tanh.1:
        pushq     %rsi
..___tag_value_tanh.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      $16304, %ecx
        cmpl      $144, %ecx
        jae       .L_2TAG_PACKET_0.0.1
        subsd     %xmm3, %xmm4
        mulsd     %xmm1, %xmm3
        mulsd     %xmm5, %xmm2
        cvtsd2si  %xmm3, %eax
        movq      %xmm3, %xmm7
        addsd     %xmm6, %xmm3
        mulsd     %xmm4, %xmm1
        movsd     ONEMASK(%rip), %xmm4
        subsd     %xmm6, %xmm3
        xorpd     %xmm0, %xmm0
        addsd     %xmm1, %xmm2
        subsd     %xmm3, %xmm7
        movapd    cv(%rip), %xmm6
        addsd     %xmm7, %xmm2
        movl      $255, %ecx
        andl      %eax, %ecx
        addl      %ecx, %ecx
        lea       T2_neg_f(%rip), %r8
        movapd    (%r8,%rcx,8), %xmm5
        shrl      $4, %eax
        andl      $65520, %eax
        subl      $16368, %eax
        negl      %eax
        pinsrw    $3, %eax, %xmm0
        movapd    16+cv(%rip), %xmm1
        pshufd    $68, %xmm0, %xmm0
        mulpd     %xmm5, %xmm0
        movsd     32+cv(%rip), %xmm7
        pshufd    $68, %xmm2, %xmm2
        movq      %xmm4, %xmm5
        addsd     %xmm0, %xmm4
        mulpd     %xmm2, %xmm6
        mulsd     %xmm2, %xmm7
        mulpd     %xmm2, %xmm2
        addpd     %xmm6, %xmm1
        mulsd     %xmm2, %xmm2
        movsd     ONEMASK(%rip), %xmm3
        mulpd     %xmm2, %xmm1
        pshufd    $78, %xmm1, %xmm6
        addsd     %xmm6, %xmm1
        movq      %xmm1, %xmm6
        addsd     %xmm7, %xmm1
        mulsd     %xmm0, %xmm1
        addsd     %xmm4, %xmm1
        andpd     MASK3(%rip), %xmm4
        divsd     %xmm1, %xmm5
        subsd     %xmm4, %xmm3
        pshufd    $238, %xmm0, %xmm1
        addsd     %xmm0, %xmm3
        movq      %xmm4, %xmm2
        addsd     %xmm1, %xmm3
        mulsd     %xmm7, %xmm1
        mulsd     %xmm0, %xmm7
        addsd     %xmm1, %xmm3
        addsd     %xmm7, %xmm4
        movsd     RMASK(%rip), %xmm1
        mulsd     %xmm0, %xmm6
        andpd     MASK3(%rip), %xmm4
        addsd     %xmm6, %xmm3
        movq      %xmm4, %xmm6
        subsd     %xmm4, %xmm2
        addsd     %xmm7, %xmm2
        movsd     ONEMASK(%rip), %xmm7
        andpd     %xmm1, %xmm5
        addsd     %xmm2, %xmm3
        mulsd     %xmm5, %xmm4
        xorpd     %xmm2, %xmm2
        mulsd     %xmm5, %xmm3
        subsd     TWOMASK(%rip), %xmm6
        subsd     %xmm7, %xmm4
        xorl      $32768, %edx
        pinsrw    $3, %edx, %xmm2
        addsd     %xmm3, %xmm4
        mulsd     %xmm5, %xmm6
        movq      %xmm3, %xmm1
        mulsd     %xmm4, %xmm3
        movq      %xmm6, %xmm0
        mulsd     %xmm4, %xmm6
        subsd     %xmm3, %xmm1
        subsd     %xmm6, %xmm1
        addsd     %xmm1, %xmm0
        xorpd     %xmm2, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_0.0.1:
        addl      $960, %ecx
        cmpl      $1104, %ecx
        jae       .L_2TAG_PACKET_1.0.1
        movapd    pv(%rip), %xmm2
        pshufd    $68, %xmm0, %xmm1
        movapd    16+pv(%rip), %xmm3
        mulpd     %xmm1, %xmm1
        movapd    32+pv(%rip), %xmm4
        mulpd     %xmm1, %xmm2
        pshufd    $68, %xmm1, %xmm5
        addpd     %xmm3, %xmm2
        mulsd     %xmm5, %xmm5
        mulpd     %xmm1, %xmm2
        mulsd     %xmm5, %xmm5
        addpd     %xmm4, %xmm2
        mulpd     %xmm5, %xmm2
        pshufd    $238, %xmm2, %xmm5
        addsd     %xmm5, %xmm2
        mulsd     %xmm0, %xmm2
        addsd     %xmm2, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_1.0.1:
        addl      $15344, %ecx
        cmpl      $16448, %ecx
        jae       .L_2TAG_PACKET_2.0.1
        cmpl      $16, %ecx
        jb        .L_2TAG_PACKET_3.0.1
        xorpd     %xmm2, %xmm2
        movl      $17392, %eax
        pinsrw    $3, %eax, %xmm2
        mulsd     %xmm0, %xmm2
        addsd     %xmm0, %xmm2
        jmp       ..B1.4
.L_2TAG_PACKET_3.0.1:
        movq      %xmm0, %xmm2
        mulsd     %xmm2, %xmm2
        jmp       ..B1.4
.L_2TAG_PACKET_2.0.1:
        cmpl      $32752, %ecx
        jae       .L_2TAG_PACKET_4.0.1
        xorpd     %xmm2, %xmm2
        movl      $15344, %ecx
        pinsrw    $3, %ecx, %xmm2
        movq      %xmm2, %xmm3
        mulsd     %xmm2, %xmm2
        addsd     %xmm3, %xmm2
.L_2TAG_PACKET_5.0.1:
        xorpd     %xmm0, %xmm0
        orl       $16368, %edx
        pinsrw    $3, %edx, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_4.0.1:
        movq      %xmm0, %xmm2
        movd      %xmm0, %eax
        psrlq     $20, %xmm2
        movd      %xmm2, %ecx
        orl       %eax, %ecx
        cmpl      $0, %ecx
        je        .L_2TAG_PACKET_5.0.1
        addsd     %xmm0, %xmm0
        movq      %xmm0, (%rsp)
.L_2TAG_PACKET_6.0.1:
..B1.4:
        popq      %rcx
..___tag_value_tanh.4:
        ret       
..___tag_value_tanh.5:
END(tanh)
# -- End  tanh
	.section .rodata, "a"
	.align 16
	.align 16
L2E:
	.long	1610612736
	.long	1082594631
	.long	4166901572
	.long	1055174155
	.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	3884607281
	.long	3168131199
	.long	3607404735
	.long	3190582024
	.long	1874480759
	.long	1032041131
	.long	4286760334
	.long	1053736893
	.long	4277811695
	.long	3211144770
	.long	0
	.long	0
	.type	cv,@object
	.size	cv,48
	.align 16
T2_neg_f:
	.long	0
	.long	1072693248
	.long	0
	.long	0
	.long	1797923801
	.long	1072687577
	.long	1950547427
	.long	1013229059
	.long	730821105
	.long	1072681922
	.long	2523232743
	.long	1012067188
	.long	915592468
	.long	1072676282
	.long	352947894
	.long	3161024371
	.long	2174652632
	.long	1072670657
	.long	4087714590
	.long	1014450259
	.long	35929225
	.long	1072665048
	.long	2809788041
	.long	3159436968
	.long	2912730644
	.long	1072659453
	.long	3490067722
	.long	3163405074
	.long	2038973688
	.long	1072653874
	.long	892941374
	.long	1016046459
	.long	1533953344
	.long	1072648310
	.long	769171851
	.long	1015665633
	.long	1222472308
	.long	1072642761
	.long	1054357470
	.long	3161021018
	.long	929806999
	.long	1072637227
	.long	3205336643
	.long	1015259557
	.long	481706282
	.long	1072631708
	.long	1696079173
	.long	3162710528
	.long	3999357479
	.long	1072626203
	.long	2258941616
	.long	1015924724
	.long	2719515920
	.long	1072620714
	.long	2760332941
	.long	1015137933
	.long	764307441
	.long	1072615240
	.long	3021057420
	.long	3163329523
	.long	2256325230
	.long	1072609780
	.long	580117746
	.long	1015317295
	.long	2728693978
	.long	1072604335
	.long	396109971
	.long	3163462691
	.long	2009970496
	.long	1072598905
	.long	2159039665
	.long	3162572948
	.long	4224142467
	.long	1072593489
	.long	3389820386
	.long	1015207202
	.long	610758006
	.long	1072588089
	.long	1965209397
	.long	3161866232
	.long	3884662774
	.long	1072582702
	.long	2158611599
	.long	1014210185
	.long	991358482
	.long	1072577331
	.long	838715019
	.long	3163157668
	.long	351641897
	.long	1072571974
	.long	2172261526
	.long	3163010599
	.long	1796832535
	.long	1072566631
	.long	3176955716
	.long	3160585513
	.long	863738719
	.long	1072561303
	.long	1326992220
	.long	3162613197
	.long	1679558232
	.long	1072555989
	.long	2390342287
	.long	3163333970
	.long	4076975200
	.long	1072550689
	.long	2029000899
	.long	1015208535
	.long	3594158869
	.long	1072545404
	.long	2456521700
	.long	3163256561
	.long	64696965
	.long	1072540134
	.long	1768797490
	.long	1015816960
	.long	1912561781
	.long	1072534877
	.long	3147495102
	.long	1015678253
	.long	382305176
	.long	1072529635
	.long	2347622376
	.long	3162578625
	.long	3898795731
	.long	1072524406
	.long	1249994144
	.long	1011869818
	.long	3707479175
	.long	1072519192
	.long	3613079303
	.long	1014164738
	.long	3939148246
	.long	1072513992
	.long	3210352148
	.long	1015274323
	.long	135105010
	.long	1072508807
	.long	1906148728
	.long	3163375739
	.long	721996136
	.long	1072503635
	.long	563754734
	.long	1015371318
	.long	1242007932
	.long	1072498477
	.long	1132034716
	.long	3163339831
	.long	1532734324
	.long	1072493333
	.long	3094216535
	.long	3163162857
	.long	1432208378
	.long	1072488203
	.long	1401068914
	.long	3162363963
	.long	778901109
	.long	1072483087
	.long	2248183955
	.long	3161268751
	.long	3706687593
	.long	1072477984
	.long	3521726940
	.long	1013253067
	.long	1464976603
	.long	1072472896
	.long	3507292405
	.long	3161977534
	.long	2483480501
	.long	1072467821
	.long	1216371780
	.long	1013034172
	.long	2307442995
	.long	1072462760
	.long	3190117721
	.long	3162404539
	.long	777507147
	.long	1072457713
	.long	4282924205
	.long	1015187533
	.long	2029714210
	.long	1072452679
	.long	613660079
	.long	1015099143
	.long	1610600570
	.long	1072447659
	.long	3766732298
	.long	1015760183
	.long	3657065772
	.long	1072442652
	.long	399025623
	.long	3162957078
	.long	3716502172
	.long	1072437659
	.long	2303740125
	.long	1014042725
	.long	1631695677
	.long	1072432680
	.long	2717633076
	.long	3162344026
	.long	1540824585
	.long	1072427714
	.long	1064017011
	.long	3163487690
	.long	3287523847
	.long	1072422761
	.long	1625971539
	.long	3157009955
	.long	2420883922
	.long	1072417822
	.long	2049810052
	.long	1014119888
	.long	3080351519
	.long	1072412896
	.long	3379126788
	.long	3157218001
	.long	815859274
	.long	1072407984
	.long	240396590
	.long	3163487443
	.long	4062661092
	.long	1072403084
	.long	1422616006
	.long	3163255318
	.long	4076559943
	.long	1072398198
	.long	2119478331
	.long	3160758351
	.long	703710506
	.long	1072393326
	.long	1384660846
	.long	1015195891
	.long	2380618042
	.long	1072388466
	.long	3149557219
	.long	3163320799
	.long	364333489
	.long	1072383620
	.long	3923737744
	.long	3161421373
	.long	3092190715
	.long	1072378786
	.long	814012168
	.long	3159523422
	.long	1822067026
	.long	1072373966
	.long	1241994956
	.long	1015340290
	.long	697153126
	.long	1072369159
	.long	1283515429
	.long	3163283189
	.long	3861050111
	.long	1072364364
	.long	254893773
	.long	3162813180
	.long	2572866477
	.long	1072359583
	.long	878562433
	.long	1015521741
	.long	977020788
	.long	1072354815
	.long	3065100517
	.long	1015541563
	.long	3218338682
	.long	1072350059
	.long	3404164304
	.long	3162477108
	.long	557149882
	.long	1072345317
	.long	3672720709
	.long	1014537265
	.long	1434058175
	.long	1072340587
	.long	251133233
	.long	1015085769
	.long	1405169241
	.long	1072335870
	.long	2998539689
	.long	3162830951
	.long	321958744
	.long	1072331166
	.long	3401933767
	.long	1015794558
	.long	2331271250
	.long	1072326474
	.long	812057446
	.long	1012207446
	.long	2990417245
	.long	1072321795
	.long	3683467745
	.long	3163369326
	.long	2152073944
	.long	1072317129
	.long	1486860576
	.long	3163203456
	.long	3964284211
	.long	1072312475
	.long	2111583915
	.long	1015427164
	.long	3985553595
	.long	1072307834
	.long	4002146062
	.long	1015834136
	.long	2069751141
	.long	1072303206
	.long	1562170675
	.long	3162724681
	.long	2366108318
	.long	1072298590
	.long	2867985102
	.long	3161762254
	.long	434316067
	.long	1072293987
	.long	2028358766
	.long	1013458122
	.long	424392917
	.long	1072289396
	.long	2749202995
	.long	3162838718
	.long	2191782032
	.long	1072284817
	.long	2960257726
	.long	1013742662
	.long	1297350157
	.long	1072280251
	.long	1308022040
	.long	3163412558
	.long	1892288442
	.long	1072275697
	.long	2446255666
	.long	3162600381
	.long	3833209506
	.long	1072271155
	.long	2722920684
	.long	1013754842
	.long	2682146384
	.long	1072266626
	.long	2082178513
	.long	3163363419
	.long	2591453363
	.long	1072262109
	.long	2132396182
	.long	3159074198
	.long	3418903055
	.long	1072257604
	.long	2527457337
	.long	3160820604
	.long	727685349
	.long	1072253112
	.long	2038246809
	.long	3162358742
	.long	2966275557
	.long	1072248631
	.long	2176155324
	.long	3159842759
	.long	1403662306
	.long	1072244163
	.long	2788809599
	.long	3161671007
	.long	194117574
	.long	1072239707
	.long	777528612
	.long	3163412089
	.long	3492293770
	.long	1072235262
	.long	2248032210
	.long	1015386826
	.long	2568320822
	.long	1072230830
	.long	2732824428
	.long	1014352915
	.long	1577608921
	.long	1072226410
	.long	1875489510
	.long	3162968394
	.long	380978316
	.long	1072222002
	.long	854188970
	.long	3160462686
	.long	3134592888
	.long	1072217605
	.long	4232266862
	.long	1015991134
	.long	1110089947
	.long	1072213221
	.long	1451641639
	.long	1015474673
	.long	2759350287
	.long	1072208848
	.long	1148526634
	.long	1015894933
	.long	3649726105
	.long	1072204487
	.long	4085036346
	.long	1015649474
	.long	3643909174
	.long	1072200138
	.long	3537586109
	.long	1014354647
	.long	2604962541
	.long	1072195801
	.long	2614425274
	.long	3163539192
	.long	396319521
	.long	1072191476
	.long	4172420816
	.long	3159074632
	.long	1176749997
	.long	1072187162
	.long	2738998779
	.long	3162035844
	.long	515457527
	.long	1072182860
	.long	836709333
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	.type	T2_neg_f,@object
	.size	T2_neg_f,4096
	.space 512, 0x00 	# pad
	.align 16
MASK3:
	.long	0
	.long	4294967280
	.long	0
	.long	4294967280
	.type	MASK3,@object
	.size	MASK3,16
	.align 16
RMASK:
	.long	4294705152
	.long	4294967295
	.long	4294705152
	.long	4294967295
	.type	RMASK,@object
	.size	RMASK,16
	.align 16
pv:
	.long	236289503
	.long	1064135997
	.long	463583772
	.long	3215696314
	.long	1441186365
	.long	3212977891
	.long	286331153
	.long	1069617425
	.long	2284589306
	.long	1066820852
	.long	1431655765
	.long	3218429269
	.type	pv,@object
	.size	pv,48
	.align 4
HALFMASK:
	.long	4160749568
	.long	2147483647
	.type	HALFMASK,@object
	.size	HALFMASK,8
	.align 4
ONEMASK:
	.long	0
	.long	1072693248
	.type	ONEMASK,@object
	.size	ONEMASK,8
	.align 4
TWOMASK:
	.long	0
	.long	1073741824
	.type	TWOMASK,@object
	.size	TWOMASK,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_tanh.1-.
	.4byte ..___tag_value_tanh.5-..___tag_value_tanh.1
	.2byte 0x0400
	.4byte ..___tag_value_tanh.3-..___tag_value_tanh.1
	.2byte 0x100e
	.byte 0x04
	.4byte ..___tag_value_tanh.4-..___tag_value_tanh.3
	.2byte 0x080e
	.byte 0x00
# End