path: root/libm/x86/e_acos.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
//                     ---------------------
//
//  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
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	.section .note.GNU-stack, ""
# End