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      1 /*
      2 Copyright (c) 2014, Intel Corporation
      3 All rights reserved.
      4 
      5 Redistribution and use in source and binary forms, with or without
      6 modification, are permitted provided that the following conditions are met:
      7 
      8     * Redistributions of source code must retain the above copyright notice,
      9     * this list of conditions and the following disclaimer.
     10 
     11     * Redistributions in binary form must reproduce the above copyright notice,
     12     * this list of conditions and the following disclaimer in the documentation
     13     * and/or other materials provided with the distribution.
     14 
     15     * Neither the name of Intel Corporation nor the names of its contributors
     16     * may be used to endorse or promote products derived from this software
     17     * without specific prior written permission.
     18 
     19 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
     20 ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
     21 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
     22 DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
     23 ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
     24 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
     25 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
     26 ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
     27 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
     28 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     29 */
     30 
     31 /******************************************************************************/
     32 //                     ALGORITHM DESCRIPTION
     33 //                     ---------------------
     34 //
     35 //   Assume x=2^{3*k+j} * 1.b1 b2 ... b5 b6 ... b52, where j = 0,1,2.
     36 //   Let r=(x*2^{-3k-j} - 1.b1 b2 ... b5 1)* rcp[b1 b2 ..b5],
     37 //   where rcp[b1 b2 .. b5]=1/(1.b1 b2 b3 b4 b5 1) in double precision
     38 //   cbrt(2^j * 1. b1 b2 .. b5 1) is approximated as T[j][b1..b5]+D[j][b1..b5]
     39 //   (T stores the high 53 bits, D stores the low order bits)
     40 //   Result=2^k*T+(2^k*T*r)*P+2^k*D
     41 //   where P=p1+p2*r+..+p8*r^7
     42 //
     43 // Special cases:
     44 //  cbrt(NaN) = quiet NaN, and raise invalid exception
     45 //  cbrt(INF) = that INF
     46 //  cbrt(+/-0) = +/-0
     47 //
     48 /******************************************************************************/
     49 
     50 #include <private/bionic_asm.h>
     51 # -- Begin  static_func
     52         .text
     53         .align __bionic_asm_align
     54         .type static_func, @function
     55 static_func:
     56 ..B1.1:
     57         call      ..L2
     58 ..L2:
     59         popl      %eax
     60         lea       _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
     61         lea       static_const_table@GOTOFF(%eax), %eax
     62         ret
     63         .size   static_func,.-static_func
     64 # -- End  static_func
     65 
     66 # -- Begin  cbrt
     67 ENTRY(cbrt)
     68 # parameter 1: 8 + %ebp
     69 ..B2.1:
     70 ..B2.2:
     71         pushl     %ebp
     72         movl      %esp, %ebp
     73         subl      $120, %esp
     74         movl      %esi, 52(%esp)
     75         call      static_func
     76         movl      %eax, %esi
     77         movsd     128(%esp), %xmm0
     78         movapd    %xmm0, %xmm7
     79         movsd     %xmm0, 8(%esp)
     80         movl      $524032, %edx
     81         movsd     64(%esi), %xmm5
     82         movsd     80(%esi), %xmm3
     83         psrlq     $44, %xmm7
     84         pextrw    $0, %xmm7, %ecx
     85         movd      %xmm7, %eax
     86         movsd     96(%esi), %xmm1
     87         movsd     112(%esi), %xmm2
     88         movl      %ebx, 16(%esp)
     89         andl      $248, %ecx
     90         movsd     128(%ecx,%esi), %xmm4
     91         movl      %eax, %ebx
     92         andl      %eax, %edx
     93         cmpl      $0, %edx
     94         je        .L_2TAG_PACKET_0.0.2
     95         cmpl      $524032, %edx
     96         je        .L_2TAG_PACKET_1.0.2
     97         shrl      $8, %edx
     98         shrl      $8, %ebx
     99         andpd     %xmm0, %xmm2
    100         andpd     %xmm5, %xmm0
    101         orpd      %xmm2, %xmm3
    102         orpd      %xmm0, %xmm1
    103         movapd    (%esi), %xmm5
    104         movl      $5462, %eax
    105         movapd    16(%esi), %xmm6
    106         mull      %edx
    107         movl      %ebx, %edx
    108         andl      $2047, %ebx
    109         shrl      $14, %eax
    110         andl      $2048, %edx
    111         subl      %eax, %ebx
    112         subl      %eax, %ebx
    113         subl      %eax, %ebx
    114         shll      $8, %ebx
    115         addl      $682, %eax
    116         orl       %edx, %eax
    117         movd      %eax, %xmm7
    118         addl      %ebx, %ecx
    119         psllq     $52, %xmm7
    120 .L_2TAG_PACKET_2.0.2:
    121         movapd    32(%esi), %xmm2
    122         movapd    48(%esi), %xmm0
    123         subsd     %xmm3, %xmm1
    124         movq      %xmm7, %xmm3
    125         mulsd     384(%ecx,%esi), %xmm7
    126         mulsd     %xmm4, %xmm1
    127         mulsd     1152(%ecx,%esi), %xmm3
    128         movapd    %xmm1, %xmm4
    129         unpcklpd  %xmm1, %xmm1
    130         mulpd     %xmm1, %xmm5
    131         mulpd     %xmm1, %xmm6
    132         mulpd     %xmm1, %xmm1
    133         addpd     %xmm5, %xmm2
    134         addpd     %xmm6, %xmm0
    135         mulpd     %xmm1, %xmm2
    136         mulpd     %xmm1, %xmm1
    137         mulsd     %xmm7, %xmm4
    138         addpd     %xmm2, %xmm0
    139         movl      16(%esp), %ebx
    140         mulsd     %xmm0, %xmm1
    141         unpckhpd  %xmm0, %xmm0
    142         addsd     %xmm1, %xmm0
    143         mulsd     %xmm4, %xmm0
    144         addsd     %xmm3, %xmm0
    145         addsd     %xmm7, %xmm0
    146         movsd     %xmm0, (%esp)
    147         fldl      (%esp)
    148         jmp       .L_2TAG_PACKET_3.0.2
    149 .L_2TAG_PACKET_0.0.2:
    150         mulsd     1984(%esi), %xmm0
    151         movq      %xmm0, %xmm7
    152         movl      $524032, %edx
    153         psrlq     $44, %xmm7
    154         pextrw    $0, %xmm7, %ecx
    155         movd      %xmm7, %eax
    156         andl      $248, %ecx
    157         movsd     128(%ecx,%esi), %xmm4
    158         movl      %eax, %ebx
    159         andl      %eax, %edx
    160         shrl      $8, %edx
    161         shrl      $8, %ebx
    162         cmpl      $0, %edx
    163         je        .L_2TAG_PACKET_4.0.2
    164         andpd     %xmm0, %xmm2
    165         andpd     %xmm5, %xmm0
    166         orpd      %xmm2, %xmm3
    167         orpd      %xmm0, %xmm1
    168         movapd    (%esi), %xmm5
    169         movl      $5462, %eax
    170         movapd    16(%esi), %xmm6
    171         mull      %edx
    172         movl      %ebx, %edx
    173         andl      $2047, %ebx
    174         shrl      $14, %eax
    175         andl      $2048, %edx
    176         subl      %eax, %ebx
    177         subl      %eax, %ebx
    178         subl      %eax, %ebx
    179         shll      $8, %ebx
    180         addl      $661, %eax
    181         orl       %edx, %eax
    182         movd      %eax, %xmm7
    183         addl      %ebx, %ecx
    184         psllq     $52, %xmm7
    185         jmp       .L_2TAG_PACKET_2.0.2
    186 .L_2TAG_PACKET_4.0.2:
    187         cmpl      $0, %ebx
    188         jne       .L_2TAG_PACKET_5.0.2
    189         movl      16(%esp), %ebx
    190         fldl      1952(%esi)
    191         jmp       .L_2TAG_PACKET_3.0.2
    192 .L_2TAG_PACKET_5.0.2:
    193         movl      16(%esp), %ebx
    194         fldl      1968(%esi)
    195         jmp       .L_2TAG_PACKET_3.0.2
    196 .L_2TAG_PACKET_1.0.2:
    197         movl      16(%esp), %ebx
    198         movl      132(%esp), %eax
    199         movl      128(%esp), %edx
    200         movl      %eax, %ecx
    201         andl      $2147483647, %ecx
    202         cmpl      $2146435072, %ecx
    203         ja        .L_2TAG_PACKET_6.0.2
    204         cmpl      $0, %edx
    205         jne       .L_2TAG_PACKET_6.0.2
    206         cmpl      $2146435072, %eax
    207         jne       .L_2TAG_PACKET_7.0.2
    208         fldl      1920(%esi)
    209         jmp       .L_2TAG_PACKET_3.0.2
    210 .L_2TAG_PACKET_7.0.2:
    211         fldl      1936(%esi)
    212         jmp       .L_2TAG_PACKET_3.0.2
    213 .L_2TAG_PACKET_6.0.2:
    214         movsd     8(%esp), %xmm0
    215         addsd     %xmm0, %xmm0
    216         movsd     %xmm0, (%esp)
    217         fldl      (%esp)
    218 .L_2TAG_PACKET_3.0.2:
    219         movl      52(%esp), %esi
    220         movl      %ebp, %esp
    221         popl      %ebp
    222         ret
    223 ..B2.3:
    224 END(cbrt)
    225 # -- End  cbrt
    226 
    227 # Start file scope ASM
    228 ALIAS_SYMBOL(cbrtl, cbrt);
    229 # End file scope ASM
    230 	.section .rodata, "a"
    231 	.align 16
    232 	.align 16
    233 static_const_table:
    234 	.long	1553778919
    235 	.long	3213899486
    236 	.long	3534952507
    237 	.long	3215266280
    238 	.long	1646371399
    239 	.long	3214412045
    240 	.long	477218588
    241 	.long	3216798151
    242 	.long	3582521621
    243 	.long	1066628362
    244 	.long	1007461464
    245 	.long	1068473053
    246 	.long	889629714
    247 	.long	1067378449
    248 	.long	1431655765
    249 	.long	1070945621
    250 	.long	4294967295
    251 	.long	1048575
    252 	.long	0
    253 	.long	0
    254 	.long	0
    255 	.long	3220193280
    256 	.long	0
    257 	.long	0
    258 	.long	0
    259 	.long	3220176896
    260 	.long	0
    261 	.long	0
    262 	.long	0
    263 	.long	1032192
    264 	.long	0
    265 	.long	0
    266 	.long	528611360
    267 	.long	3220144632
    268 	.long	2884679527
    269 	.long	3220082993
    270 	.long	1991868891
    271 	.long	3220024928
    272 	.long	2298714891
    273 	.long	3219970134
    274 	.long	58835168
    275 	.long	3219918343
    276 	.long	3035110223
    277 	.long	3219869313
    278 	.long	1617585086
    279 	.long	3219822831
    280 	.long	2500867033
    281 	.long	3219778702
    282 	.long	4241943008
    283 	.long	3219736752
    284 	.long	258732970
    285 	.long	3219696825
    286 	.long	404232216
    287 	.long	3219658776
    288 	.long	2172167368
    289 	.long	3219622476
    290 	.long	1544257904
    291 	.long	3219587808
    292 	.long	377579543
    293 	.long	3219554664
    294 	.long	1616385542
    295 	.long	3219522945
    296 	.long	813783277
    297 	.long	3219492562
    298 	.long	3940743189
    299 	.long	3219463431
    300 	.long	2689777499
    301 	.long	3219435478
    302 	.long	1700977147
    303 	.long	3219408632
    304 	.long	3169102082
    305 	.long	3219382828
    306 	.long	327235604
    307 	.long	3219358008
    308 	.long	1244336319
    309 	.long	3219334115
    310 	.long	1300311200
    311 	.long	3219311099
    312 	.long	3095471925
    313 	.long	3219288912
    314 	.long	2166487928
    315 	.long	3219267511
    316 	.long	2913108253
    317 	.long	3219246854
    318 	.long	293672978
    319 	.long	3219226904
    320 	.long	288737297
    321 	.long	3219207624
    322 	.long	1810275472
    323 	.long	3219188981
    324 	.long	174592167
    325 	.long	3219170945
    326 	.long	3539053052
    327 	.long	3219153485
    328 	.long	2164392968
    329 	.long	3219136576
    330 	.long	572345495
    331 	.long	1072698681
    332 	.long	1998204467
    333 	.long	1072709382
    334 	.long	3861501553
    335 	.long	1072719872
    336 	.long	2268192434
    337 	.long	1072730162
    338 	.long	2981979308
    339 	.long	1072740260
    340 	.long	270859143
    341 	.long	1072750176
    342 	.long	2958651392
    343 	.long	1072759916
    344 	.long	313113243
    345 	.long	1072769490
    346 	.long	919449400
    347 	.long	1072778903
    348 	.long	2809328903
    349 	.long	1072788162
    350 	.long	2222981587
    351 	.long	1072797274
    352 	.long	2352530781
    353 	.long	1072806244
    354 	.long	594152517
    355 	.long	1072815078
    356 	.long	1555767199
    357 	.long	1072823780
    358 	.long	4282421314
    359 	.long	1072832355
    360 	.long	2355578597
    361 	.long	1072840809
    362 	.long	1162590619
    363 	.long	1072849145
    364 	.long	797864051
    365 	.long	1072857367
    366 	.long	431273680
    367 	.long	1072865479
    368 	.long	2669831148
    369 	.long	1072873484
    370 	.long	733477752
    371 	.long	1072881387
    372 	.long	4280220604
    373 	.long	1072889189
    374 	.long	801961634
    375 	.long	1072896896
    376 	.long	2915370760
    377 	.long	1072904508
    378 	.long	1159613482
    379 	.long	1072912030
    380 	.long	2689944798
    381 	.long	1072919463
    382 	.long	1248687822
    383 	.long	1072926811
    384 	.long	2967951030
    385 	.long	1072934075
    386 	.long	630170432
    387 	.long	1072941259
    388 	.long	3760898254
    389 	.long	1072948363
    390 	.long	0
    391 	.long	1072955392
    392 	.long	2370273294
    393 	.long	1072962345
    394 	.long	1261754802
    395 	.long	1072972640
    396 	.long	546334065
    397 	.long	1072986123
    398 	.long	1054893830
    399 	.long	1072999340
    400 	.long	1571187597
    401 	.long	1073012304
    402 	.long	1107975175
    403 	.long	1073025027
    404 	.long	3606909377
    405 	.long	1073037519
    406 	.long	1113616747
    407 	.long	1073049792
    408 	.long	4154744632
    409 	.long	1073061853
    410 	.long	3358931423
    411 	.long	1073073713
    412 	.long	4060702372
    413 	.long	1073085379
    414 	.long	747576176
    415 	.long	1073096860
    416 	.long	3023138255
    417 	.long	1073108161
    418 	.long	1419988548
    419 	.long	1073119291
    420 	.long	1914185305
    421 	.long	1073130255
    422 	.long	294389948
    423 	.long	1073141060
    424 	.long	3761802570
    425 	.long	1073151710
    426 	.long	978281566
    427 	.long	1073162213
    428 	.long	823148820
    429 	.long	1073172572
    430 	.long	2420954441
    431 	.long	1073182792
    432 	.long	3815449908
    433 	.long	1073192878
    434 	.long	2046058587
    435 	.long	1073202835
    436 	.long	1807524753
    437 	.long	1073212666
    438 	.long	2628681401
    439 	.long	1073222375
    440 	.long	3225667357
    441 	.long	1073231966
    442 	.long	1555307421
    443 	.long	1073241443
    444 	.long	3454043099
    445 	.long	1073250808
    446 	.long	1208137896
    447 	.long	1073260066
    448 	.long	3659916772
    449 	.long	1073269218
    450 	.long	1886261264
    451 	.long	1073278269
    452 	.long	3593647839
    453 	.long	1073287220
    454 	.long	3086012205
    455 	.long	1073296075
    456 	.long	2769796922
    457 	.long	1073304836
    458 	.long	888716057
    459 	.long	1073317807
    460 	.long	2201465623
    461 	.long	1073334794
    462 	.long	164369365
    463 	.long	1073351447
    464 	.long	3462666733
    465 	.long	1073367780
    466 	.long	2773905457
    467 	.long	1073383810
    468 	.long	1342879088
    469 	.long	1073399550
    470 	.long	2543933975
    471 	.long	1073415012
    472 	.long	1684477781
    473 	.long	1073430209
    474 	.long	3532178543
    475 	.long	1073445151
    476 	.long	1147747300
    477 	.long	1073459850
    478 	.long	1928031793
    479 	.long	1073474314
    480 	.long	2079717015
    481 	.long	1073488553
    482 	.long	4016765315
    483 	.long	1073502575
    484 	.long	3670431139
    485 	.long	1073516389
    486 	.long	3549227225
    487 	.long	1073530002
    488 	.long	11637607
    489 	.long	1073543422
    490 	.long	588220169
    491 	.long	1073556654
    492 	.long	2635407503
    493 	.long	1073569705
    494 	.long	2042029317
    495 	.long	1073582582
    496 	.long	1925128962
    497 	.long	1073595290
    498 	.long	4136375664
    499 	.long	1073607834
    500 	.long	759964600
    501 	.long	1073620221
    502 	.long	4257606771
    503 	.long	1073632453
    504 	.long	297278907
    505 	.long	1073644538
    506 	.long	3655053093
    507 	.long	1073656477
    508 	.long	2442253172
    509 	.long	1073668277
    510 	.long	1111876799
    511 	.long	1073679941
    512 	.long	3330973139
    513 	.long	1073691472
    514 	.long	3438879452
    515 	.long	1073702875
    516 	.long	3671565478
    517 	.long	1073714153
    518 	.long	1317849547
    519 	.long	1073725310
    520 	.long	1642364115
    521 	.long	1073736348
    522 	.long	4050900474
    523 	.long	1014427190
    524 	.long	1157977860
    525 	.long	1016444461
    526 	.long	1374568199
    527 	.long	1017271387
    528 	.long	2809163288
    529 	.long	1016882676
    530 	.long	3742377377
    531 	.long	1013168191
    532 	.long	3101606597
    533 	.long	1017541672
    534 	.long	65224358
    535 	.long	1017217597
    536 	.long	2691591250
    537 	.long	1017266643
    538 	.long	4020758549
    539 	.long	1017689313
    540 	.long	1316310992
    541 	.long	1018030788
    542 	.long	1031537856
    543 	.long	1014090882
    544 	.long	3261395239
    545 	.long	1016413641
    546 	.long	886424999
    547 	.long	1016313335
    548 	.long	3114776834
    549 	.long	1014195875
    550 	.long	1681120620
    551 	.long	1017825416
    552 	.long	1329600273
    553 	.long	1016625740
    554 	.long	465474623
    555 	.long	1017097119
    556 	.long	4251633980
    557 	.long	1017169077
    558 	.long	1986990133
    559 	.long	1017710645
    560 	.long	752958613
    561 	.long	1017159641
    562 	.long	2216216792
    563 	.long	1018020163
    564 	.long	4282860129
    565 	.long	1015924861
    566 	.long	1557627859
    567 	.long	1016039538
    568 	.long	3889219754
    569 	.long	1018086237
    570 	.long	3684996408
    571 	.long	1017353275
    572 	.long	723532103
    573 	.long	1017717141
    574 	.long	2951149676
    575 	.long	1012528470
    576 	.long	831890937
    577 	.long	1017830553
    578 	.long	1031212645
    579 	.long	1017387331
    580 	.long	2741737450
    581 	.long	1017604974
    582 	.long	2863311531
    583 	.long	1003776682
    584 	.long	4276736099
    585 	.long	1013153088
    586 	.long	4111778382
    587 	.long	1015673686
    588 	.long	1728065769
    589 	.long	1016413986
    590 	.long	2708718031
    591 	.long	1018078833
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    734 	.type	static_const_table,@object
    735 	.size	static_const_table,2000
    736 	.data
    737 	.section .note.GNU-stack, ""
    738 # End
    739