| blob | 3e621e2c12e4aeb3fa6e496c6b61ba9297714444 |
1 .file "cbrtl.s"
4 // Copyright (c) 2000 - 2003, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
8 //
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
11 // met:
12 //
13 // * Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
15 //
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
19 //
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
22 // permission.
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 //
36 // Intel Corporation is the author of this code, and requests that all
37 // problem reports or change requests be submitted to it directly at
38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //==============================================================
42 // 04/28/00 Initial version
43 // 05/20/02 Cleaned up namespace and sf0 syntax
44 // 02/06/03 Reordered header: .section, .global, .proc, .align
45 //
46 // API
47 //==============================================================
48 // long double cbrtl(long double)
49 //
50 // Overview of operation
51 //==============================================================
52 // Background
53 //
54 // Implementation
55 //
56 // cbrt(a) = cbrt(a y) / cbrt(y)
57 // = cbrt(1 - (1 - a y)) * 1/cbrt(y)
58 //
59 // where y = frcpa(a).
60 //
61 // * cbrt(1 - (1 - a y)) is approximated by a degree-6 polynomial
62 //
63 // 1 - c_1 r - c_2 * r^2 - c_3 * r^3 - c_4 * r^4 - c_5 * r^5 - c_6 * r^6
64 //
65 // in r = 1 - a y.
66 //
67 // * The values 1/cbrt(y) are stored as two tables of constants T_hi
68 // (double-extended precision) and D (single precision) as follows:
69 //
70 // T_hi (1 + D) = 1/cbrt(y) to about 80 bits of accuracy
71 //
72 // The tables are only stored for three exponent values and are
73 // then multiplied by e/3 where e is the exponent of the input number.
74 // This computation is carried out in parallel with the polynomial
75 // evaluation:
76 //
77 // T = 2^(e/3) * T_hi
83 //===============
84 // input = x
85 // C = frcpa(x)
86 // r = C * x - 1
87 //
88 // Special values
89 //==============================================================
93 // Registers used
94 //==============================================================
95 // f6-f15
96 // r2-r3, r23-r30
97 // p6,p7,p12
101 // Data tables
102 //==============================================================
104 RODATA
106 .align 16
108 LOCAL_OBJECT_START(poly_coeffs)
110 data8 0xaaaaaaaaaaaaaab1, 0x00003ffd // C_1
111 data8 0xe38e38e38e38e3e0, 0x00003ffb // C_2
112 data8 0x3faf9add3c0be9a6, 0x3fa511e8d2b1f749 // C_3, C_4
113 data8 0x3f9ee71b2c6ebe99, 0x3f9809180fd0340c // C_5, C_6
114 LOCAL_OBJECT_END(poly_coeffs)
117 LOCAL_OBJECT_START(T_table)
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356 data8 0xc5cc5591bdbd82fa, 0xc5fa08f1ff20593c
357 data8 0xc618980a79ce6862, 0xc6373a09e34b50fa
358 data8 0xc66550a6e0baaf35, 0xc6842241926342c9
359 data8 0xc6a3070b7c93bb9e, 0xc6d18260bb84081b
360 data8 0xc6f0977c9416828b, 0xc70fc0117c641630
361 data8 0xc72efc34d7e615be, 0xc75dfb441594141e
362 data8 0xc77d68aa019bda4c, 0xc79ce9ea478dbc4f
363 data8 0xc7bc7f1ae453219d, 0xc7ec0476e15e141a
364 data8 0xc80bcbe16f1d540f, 0xc82ba78a5d349735
365 data8 0xc84b978847a06b87, 0xc86b9bf1ee817bc6
366 data8 0xc88bb4de3667cdf4, 0xc8bc00e7fe9e23a3
367 data8 0xc8dc4d7ff2d25232, 0xc8fcaeebcb40eb47
368 data8 0xc91d25431426a663, 0xc93db09d7fdb2949
369 data8 0xc95e5112e721582a, 0xc97f06bb49787677
370 data8 0xc99fd1aecd6e1b06, 0xc9d12a3e27bb1625
371 data8 0xc9f22ad82ba3d5f0, 0xca134113105e67b2
372 data8 0xca346d07b045a876, 0xca55aecf0e94bb88
373 data8 0xca77068257be9bab, 0xca98743ae1c693a8
374 data8 0xcab9f8122c99a101, 0xcadb9221e268c3b5
375 data8 0xcafd4283d8043dfd, 0xcb1f09520d37c6fb
376 data8 0xcb51ddcb9e93095e, 0xcb95f333968ad59b
377 data8 0xcbda64292d3ffd97, 0xcc1f3184af961596
378 data8 0xcc5bb1ac954d33e2, 0xcca12e9831fc6402
379 data8 0xcce70a67b64f24ad, 0xcd24794726477ea5
380 data8 0xcd6b096a0b70ee87, 0xcda9177738b15a90
381 data8 0xcdf05f2247dffab9, 0xce2f0f347f96f906
382 data8 0xce6e0be0cd551a61, 0xceb666b2c347d1de
383 data8 0xcef609b0cb874f00, 0xcf35fb5447e5c765
384 data8 0xcf763c47ee869f00, 0xcfb6cd3888d71785
385 data8 0xcff7aed4fbfbb447, 0xd038e1ce5167e3c6
386 data8 0xd07a66d7bfa0ebba, 0xd0bc3ea6b32d1b21
387 data8 0xd0f4f0e8f36c1bf8, 0xd1376458e34b037e
388 data8 0xd17a2ca133f78572, 0xd1bd4a80301c5715
389 data8 0xd1f71682b2fa4575, 0xd23ad555f773f059
390 data8 0xd2752c7039a5bf73, 0xd2b98ee008c06b59
391 data8 0xd2f4735ffd700280, 0xd32f99ed6d9ac0e1
392 data8 0xd374f0666c75d51c, 0xd3b0a7d13618e4a1
393 data8 0xd3eca2ea53bcec0c, 0xd428e23874f13a17
394 data8 0xd46f82fe293bc6d3, 0xd4ac57e9b7186420
395 data8 0xd4e972becb04e8b8, 0xd526d40a7a9b43a3
396 data8 0xd5647c5b73917370, 0xd5a26c4201bd6d13
397 data8 0xd5e0a45015350a7e, 0xd614b539c6194104
398 data8 0xd6537310e224283f, 0xd6927ab62244c917
399 data8 0xd6d1ccc1fc4ef4b7, 0xd71169cea98fdded
400 data8 0xd746a66a5bc9f6d9, 0xd786ce8f0fae5317
401 data8 0xd7bc7ff214c4e75a, 0xd7fd35467a517ed1
402 data8 0xd83e38838648d815, 0xd874a1db598b8951
403 data8 0xd8ab42205b80edaf, 0xd8ed1849d202f965
404 data8 0xd92432bd5a173685, 0xd9669ca45b03c23e
405 data8 0xd99e3327cf89574e, 0xd9d602b19b100466
406 data8 0xda0e0ba86c096841, 0xda5195fcdb1c3dce
407 data8 0xda8a1eb87a491f6c, 0xdac2e230b91c3f84
408 data8 0xdafbe0d0b66aea30, 0xdb351b04a8fafced
409 data8 0xdb6e9139e33cdd8e, 0xdba843ded7151ea1
410 data8 0xdbe2336319b61fc8, 0xdc1c60376789fa68
411 data8 0xdc56cacda82d0cd5, 0xdc917398f2797814
412 data8 0xdccc5b0d90a3e628, 0xdd0781a10469f0f2
413 data8 0xdd42e7ca0b52838f, 0xdd729ad01c69114d
414 data8 0xddae749c001fbf5e, 0xddea8f50a51c69b1
415 data8 0xde26eb69a0f0f111, 0xde576480262399bc
416 data8 0xde943789645933c8, 0xded14d58139a28af
417 data8 0xdf025c00bbf2b5c7, 0xdf3feb44d723a713
418 data8 0xdf715bc16c159be0, 0xdfaf66240e29cda8
419 data8 0xdfe139cbf6e19bdc, 0xe01fc0fe94d9fc52
420 data8 0xe051f92ffcc0bd60, 0xe090feec9c9a06ac
421 data8 0xe0c39d0c9ff862d6, 0xe0f668eeb99f188d
422 data8 0xe1362890eb663139, 0xe1695c7212aecbaa
423 data8 0xe19cbf0391bbbbe9, 0xe1d050901c531e85
424 data8 0xe2110903b4f4047a, 0xe2450559b4d80b6d
425 data8 0xe27931a231554ef3, 0xe2ad8e2ac3c5b04b
426 data8 0xe2e21b41b9694cce, 0xe316d93615862714
427 data8 0xe3590bd86a0d30f9, 0xe38e38e38e38e38e
428 data8 0xe3c397d1e6db7839, 0xe3f928f5953feb9e
429 data8 0xe42eeca17c62886c, 0xe464e32943446305
430 data8 0xe49b0ce15747a8a2, 0xe4d16a1eee94e9d4
431 data8 0xe4fa52107353f67d, 0xe5310a471f4d2dc3
432 data8 0xe567f6f1c2b9c224, 0xe59f18689a9e4c9a
433 data8 0xe5d66f04b8a68ecf, 0xe60dfb2005c192e9
434 data8 0xe645bd1544c7ea51, 0xe66fb21b505b20a0
435 data8 0xe6a7d32af4a7c59a, 0xe6e02b129c6a5ae4
436 data8 0xe70a9136a7403039, 0xe74349fb2d92a589
437 data8 0xe77c3a9c86ed7d42, 0xe7a713f88151518a
438 data8 0xe7e067453317ed2b, 0xe819f37a81871bb5
439 data8 0xe8454236bfaeca14, 0xe87f32f24c3fc90e
440 data8 0xe8aacd8688892ba6, 0xe8e523fd32f606f7
441 data8 0xe9110b5311407927, 0xe94bc8bf0c108fa3
442 data8 0xe977fdc439c2ca3c, 0xe9b3236528fc349e
443 data8 0xe9dfa70b745ac1b4, 0xea1b36268d0eaa38
444 data8 0xea480963fd394197, 0xea84034425f27484
445 data8 0xeab12713138dd1cc, 0xeade6db73a5e503b
446 data8 0xeb1b0268343b121b, 0xeb489b0b2bdb5f14
447 data8 0xeb765721e85f03d0, 0xebb389645f222f62
448 data8 0xebe198f090607e0c, 0xec0fcc9321024509
449 data8 0xec3e247da8b82f61, 0xec7c27d21321c9f7
450 data8 0xecaad5278824e453, 0xecd9a76d097d4e77
451 data8 0xed089ed5dcd99446, 0xed37bb95add09a1c
452 data8 0xed76c70508f904b6, 0xeda63bb05e7f93c6
453 data8 0xedd5d661daed2dc4, 0xee05974eef86b903
454 data8 0xee357ead791fc670, 0xee658cb3c134a463
455 data8 0xee95c1987f080211, 0xeec61d92d8c4314f
456 data8 0xeef6a0da64a014ac, 0xef274ba72a07c811
457 data8 0xef581e31a2c91260, 0xef8918b2bc43aec6
458 data8 0xefba3b63d89d7cbf, 0xefeb867ecffaa607
459 data8 0xf01cfa3df1b9c9fa, 0xf04e96dc05b43e2d
460 data8 0xf0805c944d827454, 0xf0b24ba285c495cb
461 data8 0xf0e46442e76f6569, 0xf116a6b2291d7896
462 data8 0xf1383fa9e9b5b381, 0xf16ac84f90083b9b
463 data8 0xf19d7b686dcb03d7, 0xf1d0593311db1757
464 data8 0xf20361ee8f1c711e, 0xf23695da7de51d3f
465 data8 0xf258d095e465cc35, 0xf28c4d0bfc982b34
466 data8 0xf2bff55eb3f0ea71, 0xf2f3c9cf9884636e
467 data8 0xf31670135ab9cc0f, 0xf34a8e9f0b54cdfb
468 data8 0xf37ed9fa6b8add3f, 0xf3a1cfe884ef6bb6
469 data8 0xf3d66689dcc8e8d3, 0xf40b2ab069d5c96a
470 data8 0xf42e718b90c8bc16, 0xf463822a0a3b4b00
471 data8 0xf498c1076015faf8, 0xf4bc5a19a33990b5
472 data8 0xf4f1e6a7d6f5425f, 0xf527a232cf6be334
473 data8 0xf54b8ecdcda90851, 0xf5819949c7ad87b4
474 data8 0xf5a5bac9213b48a9, 0xf5dc1501f324a812
475 data8 0xf6006bee86b5589e, 0xf63716b2fa067fa4
476 data8 0xf66df22fb6132b9c, 0xf6929fb98225deb1
477 data8 0xf6c9cd13021e3fea, 0xf6eeb177472cedae
478 data8 0xf713abf4cb0b3afb, 0xf74b4d5333684ef1
479 data8 0xf7707f75a72f8e94, 0xf7a874b97927af44
480 data8 0xf7cddf140aedf1d8, 0xf806291bacb7f7a9
481 data8 0xf82bcc43b92eafef, 0xf8646bf0defb759e
482 data8 0xf88a487dfc3ff5f7, 0xf8b03c2b46cdc17f
483 data8 0xf8e95541c152ae7a, 0xf90f832c2700c160
484 data8 0xf935c88e0c7f419b, 0xf96f5cd84fd86873
485 data8 0xf995dd53ebdd9d6d, 0xf9bc75a034436a41
486 data8 0xf9f686f26d5518de, 0xfa1d5b39b910a8c5
487 data8 0xfa4447acc4ecbfd2, 0xfa7ed7e51e6fdfb4
488 data8 0xfaa601394d49a1a0, 0xfacd431644ce0e40
489 data8 0xfaf49d96f7a75909, 0xfb2fd3c65e562fd5
490 data8 0xfb576c5762024805, 0xfb7f1debc22c4040
491 data8 0xfba6e89f32d0190a, 0xfbe2c803a0894893
492 data8 0xfc0ad1ff0ed9ecf0, 0xfc32f57bdfbcbe7f
493 data8 0xfc5b32968f99b21c, 0xfc83896bc861ab08
494 data8 0xfcabfa1861ed4815, 0xfce8d3cea7d3163e
495 data8 0xfd118595143ee273, 0xfd3a519943d4865a
496 data8 0xfd6337f8e1ae5a4b, 0xfd8c38d1c8e927eb
497 data8 0xfdb5544205095a53, 0xfdde8a67d2613531
498 data8 0xfe07db619e781611, 0xfe460768d80bf758
499 data8 0xfe6f9bfb06cd32f6, 0xfe994bcd3d14fcc2
500 data8 0xfec316fecaf3f2ab, 0xfeecfdaf33fadb80
501 data8 0xff16fffe2fa8fad6, 0xff411e0ba9db886d
502 data8 0xff6b57f7c33e4e9a, 0xff95ade2d1bd7358
503 data8 0xffc01fed60f86fb5, 0xffeaae3832b63956
504 LOCAL_OBJECT_END(T_table)
511 LOCAL_OBJECT_START(D_table)
513 data4 0x1e50f488, 0x1ebdc559, 0x1e649ec1, 0x9eed9b2c
514 data4 0x9e511c44, 0x9ec6d551, 0x9eefe248, 0x9e313854
515 data4 0x9f54ff18, 0x9d231411, 0x1ee5d63c, 0x9edf6b95
516 data4 0x9f332aaa, 0x1dc92a84, 0x1f73fb7b, 0x1e32f100
517 data4 0x9ea636f5, 0x9f6c3353, 0x9f405552, 0x1f33fd97
518 data4 0x1e975291, 0x9e59a11e, 0x1e47b0ba, 0x9d8ad33e
519 data4 0x1ea51bf6, 0x1f25d782, 0x9ecf534d, 0x1f55436f
520 data4 0x1d0975e4, 0x9f0633a1, 0x1f3e840a, 0x1f523a4c
521 data4 0x9f53cbbc, 0x9c8b5661, 0x9f6bc8eb, 0x1f4f6c7b
522 data4 0x9ed9b376, 0x9f5b30b6, 0x1f64fa5e, 0x1cbcc3e0
523 data4 0x1f343548, 0x1f62a6a2, 0x9f336abb, 0x9f1d15af
524 data4 0x1f476c83, 0x1ea86421, 0x1f33b2cf, 0x9e8f1348
525 data4 0x1f6fa829, 0x9f30ee3a, 0x9ebd6146, 0x1f2db598
526 data4 0x1ef9600d, 0x1f5b1427, 0x9edd741b, 0x1f51ef4e
527 data4 0x9f1aa57d, 0x9ee9b5e0, 0x9f17ecd7, 0x1ead71ff
528 data4 0x1f6c910e, 0x9e1837df, 0x9f0f17d9, 0x9e8350dd
529 data4 0x9d292f1b, 0x9e33b3ab, 0x9d6f0fe8, 0x9ed8c7cc
530 data4 0x9ec598c8, 0x9d56758c, 0x1e090c1e, 0x9ed4b941
531 data4 0x9f1fc4cf, 0x1f63513a, 0x9edd0abc, 0x1e3924dd
532 data4 0x1f60d56f, 0x1ea84424, 0x9e88f4fb, 0x1f205c09
533 data4 0x1ec9ae4e, 0x1d2d5738, 0x9f2c9f6d, 0x1e0765c2
534 data4 0x1e8bbdd7, 0x9f16d9f1, 0x9ea62627, 0x1f13904c
535 data4 0x1e566ab8, 0x9dca3d1a, 0x9e91f2a1, 0x9f14641c
536 data4 0x9f278946, 0x1f490c1e, 0x1f575eb6, 0x1f50b3fd
537 data4 0x9da32efb, 0x1ea95e59, 0x9e41e058, 0x9eada15f
538 data4 0x9e4fe66c, 0x1f3abc98, 0x1f1b8d1e, 0x9ece97e4
539 data4 0x1d188aed, 0x9e89b6ee, 0x1f287478, 0x9e8a161a
540 data4 0x1e4749f7, 0x9e68084a, 0x1e867f33, 0x9f462b63
541 data4 0x1db30792, 0x1f59a767, 0x9d1da4ae, 0x9f472a33
542 data4 0x1d1e91cd, 0x9f414824, 0x9f473d4f, 0x1f4b5783
543 data4 0x9f5b04b8, 0x9f5c205b, 0x1f309617, 0x9f0d6852
544 data4 0x9d96a609, 0x9f0965c2, 0x9e23f467, 0x9f089884
545 data4 0x9ec71458, 0x9ed6e955, 0x1e5e8691, 0x1f5b2bbc
546 data4 0x9f128268, 0x1ed40f5b, 0x1dc430ce, 0x1f345986
547 data4 0x1d778f72, 0x1e9b11d6, 0x9f5a40be, 0x9e07f61a
548 data4 0x9ed641a7, 0x9f334787, 0x1e952fd0, 0x1edeb5e2
549 data4 0x9e9f3eb1, 0x9e379fd9, 0x1f13102a, 0x9e5e80e1
550 data4 0x1c757944, 0x1dae2260, 0x1f183ab7, 0x1e55d576
551 data4 0x9e6bb99f, 0x9f52d7cb, 0x9e73a0f5, 0x1d4e1d14
552 data4 0x9dd05b53, 0x1f2261e4, 0x9d4ee73d, 0x1ede515e
553 data4 0x1f22a573, 0x9ecac348, 0x1e6a2ac0, 0x1e2787d2
554 data4 0x9eb64b87, 0x1f0c69c6, 0x9f470a01, 0x9d7c1686
555 data4 0x1e468ebe, 0x9f21ee2f, 0x9ee52116, 0x9e20f715
556 data4 0x1ed18533, 0x9f005b38, 0x9f20cb95, 0x1da72967
557 data4 0x1f1ba5d7, 0x1e2f8b16, 0x9c794f96, 0x9ca74ea3
558 data4 0x1f410555, 0x9eff2b96, 0x1ce8f0b1, 0x1f0cee77
559 data4 0x1f191edd, 0x9ed5fcbc, 0x1f30f242, 0x9e0ad369
560 data4 0x1ed8f3c8, 0x1f52bb0e, 0x9e9ce408, 0x1f18907f
561 data4 0x9ecdad40, 0x9e8af91d, 0x1d46698a, 0x9f4b93d6
562 data4 0x9f3f5d33, 0x1e2e52f7, 0x9f13aeec, 0x9f3b1969
563 data4 0x1f0996f4, 0x9f2a03df, 0x1e264767, 0x1f3ab1fb
564 data4 0x9f3193c9, 0x9f21ce22, 0x9eab624c, 0x9ecd8fb1
565 data4 0x1eaf9a85, 0x1f0c6a2c, 0x1eecbe61, 0x1f3fead9
566 data4 0x1f1d3a29, 0x1e9099ce, 0x1eadd875, 0x1e4dbfb8
567 data4 0x9dc640d2, 0x1f413680, 0x9f3f57b3, 0x1dfa1553
568 data4 0x1ec71c6b, 0x1e00cc00, 0x9f271e55, 0x1e5a88bb
569 data4 0x1f46cc2b, 0x1ee80ff9, 0x9e29c6f3, 0x1f15e229
570 data4 0x9ea83d66, 0x1f37408e, 0x9dacb66e, 0x1e6f6259
571 data4 0x9f106973, 0x1dd4e5ac, 0x1cbfdcc8, 0x9f231c9f
572 data4 0x9e8677e4, 0x9e9e695a, 0x1efd782b, 0x9dd26959
573 data4 0x9e80af69, 0x1f386fb3, 0x1f022e8c, 0x9e839967
574 data4 0x1ce6796f, 0x1e4c22c2, 0x1e57ef24, 0x1e919804
575 data4 0x9d7ea090, 0x1e40140a, 0x1f261b46, 0x1db75be2
576 data4 0x1f145019, 0x9e3102b9, 0x9e22507b, 0x1eae813c
577 data4 0x1f117e97, 0x1f282296, 0x1f3814b3, 0x1e17977b
578 data4 0x1f39d6ff, 0x9f1c81b9, 0x9eb5bcad, 0x1f0f596e
579 data4 0x1e757fd5, 0x9f090daa, 0x9f2532fc, 0x9eebafbb
580 data4 0x1f086556, 0x9eeedde8, 0x9f32e174, 0x1e33c030
581 data4 0x1f1f145a, 0x1e6e556c, 0x1e419ffb, 0x9eb6019a
582 data4 0x9e872a2e, 0x1e113136, 0x1e93096f, 0x1f39be40
583 data4 0x1f1665ad, 0x9db81d7d, 0x9cd29091, 0x1e3f4af7
584 data4 0x9f23176c, 0x9eccf9b3, 0x1f34fc6c, 0x9ed36894
585 data4 0x1ef08e06, 0x9f3b46bb, 0x9f2c850b, 0x1f1565a4
586 data4 0x1e887bc3, 0x1e92629c, 0x9f11ac9e, 0x9e5579f3
587 data4 0x1e4d5790, 0x9ee1c3d1, 0x9e916aec, 0x9eb8d9b8
588 data4 0x1db46105, 0x1e168663, 0x1f26a942, 0x9f0f0383
589 data4 0x9f079032, 0x9ecae1d8, 0x1ed3b34c, 0x9edc5ee6
590 data4 0x9e8a75a7, 0x1f3c3de2, 0x9ee5041e, 0x1f08c727
591 data4 0x1d02d7ae, 0x9f36adda, 0x9ef9a857, 0x9ef5cb3a
592 data4 0x9eee73da, 0x9da5d629, 0x1e0e99be, 0x1e5159b9
593 data4 0x1f2eac89, 0x9e8eedc5, 0x1dd0ec90, 0x1f229aff
594 data4 0x1ed9c3e6, 0x1e95c55a, 0x9f0c24e4, 0x1e8afed6
595 data4 0x1e599a96, 0x1e881b21, 0x1eab84b9, 0x9ba2bb0e
596 data4 0x9e33ab10, 0x1f1710b5, 0x1ebfa271, 0x9e90bbc5
597 data4 0x9f32515b, 0x9b32aae8, 0x1eda455c, 0x1da8186e
598 data4 0x9e8917ff, 0x1ec4d08e, 0x1c90069d, 0x9f2f1d29
599 data4 0x9ecee86d, 0x9f234d1f, 0x1f370724, 0x1da87496
600 data4 0x1e7959f0, 0x9e8ada34, 0x1f1c7f6f, 0x1edd576b
601 data4 0x9de91e8b, 0x1ec4ef89, 0x1f32078a, 0x1e9925e2
602 data4 0x9d8eeccb, 0x9ea3d011, 0x1f231fdf, 0x9f1dbdfa
603 data4 0x1e7507a3, 0x1ec42614, 0x9e8693cb, 0x9ec68398
604 data4 0x1d5b05fb, 0x1de32119, 0x9f003429, 0x9ec16d92
605 data4 0x9f095315, 0x9f119d2c, 0x9ed0c984, 0x9f090662
606 data4 0x9e59aa1f, 0x9ed4e64a, 0x9f2798a7, 0x9f23624d
607 data4 0x1e0467d9, 0x1f22e7e7, 0x1e915256, 0x9cb4df70
608 data4 0x9e6f687c, 0x9e3c35e5, 0x9e5757ab, 0x9f031fa1
609 data4 0x1f25bff7, 0x1f0e58c2, 0x1ef3ce04, 0x1f002ecb
610 data4 0x9ebdc836, 0x9ed657dd, 0x9f149441, 0x9e8544b2
611 data4 0x1cd8ff1e, 0x1e9bb463, 0x1eaa1c5c, 0x1f200c1a
612 data4 0x1edbfbaf, 0x1f18724d, 0x9ed63c22, 0x9f08e045
613 data4 0x1f13ad07, 0x9e949311, 0x9f0c50d4, 0x1e824516
614 data4 0x1d5e52ba, 0x1d583fbd, 0x1e3b60a9, 0x9effe6d3
615 data4 0x1f0d0508, 0x1f00be77, 0x9e404bfa, 0x9e1ca381
616 data4 0x9f084dd8, 0x9e6db85d, 0x1db698e4, 0x9ebd1871
617 data4 0x9ecc2679, 0x1ee68442, 0x1edb1050, 0x9dbc96a4
618 data4 0x9f27c1f4, 0x1c99b756, 0x1eb4400a, 0x9f24390a
619 data4 0x1d927875, 0x9f074faa, 0x1e9dc2c3, 0x1f13c0d2
620 data4 0x1e3c9685, 0x9e6b6f75, 0x9db9cb31, 0x1ea5f3aa
621 data4 0x9d992c61, 0x1f1015e4, 0x1f194f70, 0x9e19d2b3
622 data4 0x9d89116c, 0x1f23cd35, 0x1e33d3a2, 0x1ee331b8
623 data4 0x1d5ba7ec, 0x9f273788, 0x9e6907f4, 0x9ed5f912
624 data4 0x9edd458d, 0x1e2ca7b2, 0x1ef81fe4, 0x1dc7ade6
625 data4 0x1e876e51, 0x9f04ec89, 0x1f1da63a, 0x1ec02bd0
626 data4 0x9e71326f, 0x1e7847b4, 0x1f0de618, 0x9e036cb6
627 data4 0x1eec61e2, 0x1ef1758b, 0x9ee880a3, 0x1ed269d7
628 data4 0x1e27edd3, 0x9e8a81a1, 0x1eacb84d, 0x9e1aad37
629 data4 0x1f1aa8f7, 0x1e9bbd90, 0x1ea1b61f, 0x9ed41c2f
630 data4 0x1dbb5dd6, 0x1f0ec733, 0x9df06b1b, 0x1e06fef1
631 data4 0x9edede3a, 0x1edeb5e2, 0x1f0e63ee, 0x9db316bb
632 data4 0x9efc1ad3, 0x1f01fbb5, 0x9cc0d078, 0x1ea28b36
633 data4 0x9e9dd205, 0x9e791534, 0x1da1c8d5, 0x9e8195cc
634 data4 0x1f0681a4, 0x1eeaf1e2, 0x9ef83b37, 0x9f22a92b
635 data4 0x1eabc4ce, 0x1f10eefb, 0x1e06d9aa, 0x1e7cacd5
636 data4 0x1f1ea087, 0x1eb21983, 0x9f100c78, 0x1e840abe
637 data4 0x9efab66c, 0x1f183fa8, 0x9e84ee68, 0x9eea083d
638 data4 0x9ee23a74, 0x1f1351d7, 0x9ec5d42a, 0x9f071f57
639 data4 0x9ef578d9, 0x9f1aa7e7, 0x1eb02044, 0x1f151a2e
640 data4 0x9c0dc8b2, 0x9ef4087a, 0x1ec12b93, 0x1c1a946b
641 data4 0x1e89946f, 0x9dafe8c3, 0x1d295288, 0x9e8497ab
642 data4 0x1ec000c6, 0x1e102f29, 0x1e542256, 0x1e67d44d
643 data4 0x1ef688d8, 0x1f0e0f29, 0x1e67861f, 0x1e869748
644 data4 0x1ee6aa6e, 0x9e4d228b, 0x9e50be5b, 0x1e9fe225
645 data4 0x9ea34102, 0x9e628a3b, 0x9ed9fd83, 0x1ecd7109
646 data4 0x1f1864ff, 0x1ea19b76, 0x1db0d1c9, 0x9dff519b
647 data4 0x1e8fea71, 0x9ee82e9a, 0x9f08919b, 0x9ef5c8ae
648 data4 0x9ee446a4, 0x1ea59444, 0x1eb74230, 0x1ea13fbf
649 data4 0x9ea6a3ea, 0x1e5f2797, 0x9e0adb07, 0x9d3adadd
650 data4 0x1ebf2ee2, 0x1da19bfa, 0x1e8dea6d, 0x1ec4fea9
651 data4 0x1e669f22, 0x1dc5f919, 0x9ed25caa, 0x1ee475b1
652 data4 0x1ed0603e, 0x9eacb35c, 0x1dc00b27, 0x1e2f9991
653 data4 0x1e7b0406, 0x1eaa3387, 0x9d865bde, 0x1eb78a48
654 data4 0x1c40ae2e, 0x1ee9838b, 0x9f0f0d7f, 0x1e3e5d26
655 data4 0x1e99e7a6, 0x9e681ccf, 0x9e93ed65, 0x9eeb6a66
656 data4 0x1e29e9af, 0x9e96f923, 0x9e74f11d, 0x9f1474da
657 data4 0x1eec2ea7, 0x1ebf7aa3, 0x9c25dcca, 0x9f0553c2
658 data4 0x9e599efd, 0x1d2ab490, 0x1e95d7cd, 0x9ee4b20e
659 data4 0x9d988ce5, 0x9ef9787e, 0x9dbbba5b, 0x9f12c304
660 data4 0x1e3b9d70, 0x1e7bcae8, 0x9d98bb6e, 0x9e8e6b01
661 data4 0x9f07d03b, 0x9d67c822, 0x9f0ef69e, 0x1c7c0fe3
662 data4 0x9e9bfbb9, 0x9e83b84b, 0x1efbf15e, 0x9ecfa6a6
663 data4 0x9c91158e, 0x9ecf6770, 0x1ee1e3a8, 0x9dc95ec0
664 data4 0x1ef603f7, 0x1d5e52ba, 0x1c477d1b, 0x9e955cd8
665 data4 0x1ed665b0, 0x9e8376c4, 0x9c0ee88e, 0x1e8c989e
666 data4 0x1ea2df29, 0x9d961e5c, 0x1e101813, 0x1e7fffff
667 data4 0x9e5abff4, 0x1dbddd71, 0x1eb69100, 0x1e71f114
668 data4 0x1e9ca798, 0x1ef62c8d, 0x9db4e55a, 0x1dbe69ce
669 data4 0x9ef1c01f, 0x1f044a2a, 0x9eb9e0d7, 0x9ee59745
670 data4 0x9e874803, 0x1ea0b418, 0x9e13572a, 0x1ddbb3a2
671 data4 0x9ec0e391, 0x1e89fba1, 0x1ee8b261, 0x9e5d25f0
672 data4 0x9ef222cb, 0x9ef135ec, 0x1ea04b9a, 0x9f04291f
673 data4 0x9e969254, 0x9ee32f08, 0x9ed909d3, 0x9e362640
674 data4 0x9ec20735, 0x1e50131b, 0x9ed4e049, 0x1ee8e817
675 data4 0x1e1e09c0, 0x9ea643c5, 0x9e5a1ab6, 0x9e389059
676 data4 0x1e560947, 0x1d02b877, 0x1e4475ab, 0x9ea9aaf6
677 data4 0x1e95bc5e, 0x1eaf6afd, 0x1d43067d, 0x9d043821
678 data4 0x9e97baa9, 0x1de5c4f9, 0x9e9a0069, 0x9e1b9944
679 data4 0x1eb13686, 0x9eb907eb, 0x1e059589, 0x1cbd0f93
680 data4 0x9eb7e6ae, 0x1e9fa175, 0x1ee5bdf4, 0x1e8052f7
681 data4 0x9c80d1e3, 0x1bfbe28e, 0x9e672b3b, 0x9ecacf19
682 data4 0x9e3c04be, 0x1dfe8c5c, 0x1e1ba9cb, 0x1eb40b1e
683 data4 0x1ec7e7f6, 0x9d0d45b3, 0x1ef0113b, 0x9a155fa3
684 data4 0x1e28ec3b, 0x1e7ca8df, 0x9d2f91b4, 0x1eccd9ed
685 data4 0x9ed943bc, 0x9ccaab19, 0x9e8a5c58, 0x1ec3bca8
686 data4 0x1ed78dc7, 0x9ed391a8, 0x9e938f6e, 0x9ec4a030
687 data4 0x9e80346e, 0x1e7a4686, 0x9e284315, 0x9e39584c
688 data4 0x1ebdc9b4, 0x9e9cfce5, 0x9ef55c65, 0x1e2941e7
689 data4 0x9efbe59f, 0x1d87c41b, 0x1e40befc, 0x1e3d05b5
690 data4 0x1de9ea67, 0x1ec9a21c, 0x1decb69a, 0x1df6e75a
691 data4 0x9e8030ab, 0x9db20540, 0x9ef1e977, 0x1e3cdc43
692 data4 0x1e0492b0, 0x9e91d872, 0x1e775346, 0x9e939978
693 data4 0x1eb2714e, 0x1e49a203, 0x9e10195a, 0x1ef1ffc3
694 data4 0x9ea8b709, 0x9e832e27, 0x1ed5ac3b, 0x1edb20a6
695 data4 0x1e4dbd4e, 0x1efbb932, 0x1d8170ec, 0x1e6c4849
696 data4 0x1f008e17, 0x1e8000c4, 0x1d855ecf, 0x9e37cb85
697 data4 0x1ecffdf5, 0x1eba6519, 0x9edbe600, 0x1ea3e5e7
698 data4 0x1ed4fb39, 0x1f00be77, 0x1e6f4484, 0x9e9e7107
699 data4 0x9e30b29d, 0x9ee6e174, 0x1e3a2656, 0x9dd72f3f
700 data4 0x9ee12138, 0x1ed16fed, 0x9ece8a02, 0x9ca5b249
701 data4 0x9eafd508, 0x9ef0e9fc, 0x1d1307ac, 0x1eecee20
702 data4 0x1cf60c6f, 0x9d556216, 0x9eaed175, 0x9ec919f4
703 data4 0x1ec2c988, 0x1cd82772, 0x9dc99456, 0x1eab0467
704 data4 0x1e89b36f, 0x1c757944, 0x1eef9abd, 0x9e98664d
705 LOCAL_OBJECT_END(D_table)
708 .section .text
709 GLOBAL_LIBM_ENTRY(cbrtl)
711 { .mfi
712 getf.sig r3=f8
713 // will continue only for normal/denormal numbers
714 fclass.nm.unc p12,p7 = f8, 0x1b
715 // r2 = pointer to C_1...C_6 followed by T_table
716 addl r2 = @ltoff(poly_coeffs), gp;;
717 }
718 {.mfi
719 // r29=2/3*bias -63=0xaaaa-0x3f=0xaa6b
720 mov r29=0xaa6b
721 // normalize a
722 fma.s1 f14=f8,f1,f0
723 // r27 = pointer to D table
724 addl r27 = @ltoff(D_table), gp;;
725 }
726 {.mib
727 nop.m 0
728 (p7) cmp.eq p12,p0=r3,r0
729 nop.b 0;;
730 }
731 {.mfb
732 // load start address for C_1...C_6 followed by T_table
733 ld8 r2=[r2]
734 (p12) fma.s0 f8=f8,f1,f0
735 (p12) br.ret.spnt b0;;
736 }
737 {.mmf
738 // load C_1
739 ldfe f7=[r2],16
740 // load start address of D table
741 ld8 r27=[r27]
742 // y=frcpa(a)
743 frcpa.s0 f8,p6=f1,f8;;
744 }
745 {.mmi
746 // load C_2
747 ldfe f9=[r2],16;;
748 // load C_3, C_4
749 ldfpd f10,f11=[r2],16
750 nop.i 0;;
751 }
752 {.mmi
753 // get normalized significand
754 getf.sig r23=f14
755 // get exponent
756 getf.exp r24=f14
757 mov r25=0x20000;;
758 }
759 {.mii
760 // get r26=sign
761 and r26=r24,r25
762 // eliminate leading 1 from r23=2nd table index
763 shl r23=r23,1
764 // eliminate sign from exponent (r25)
765 andcm r25=r24,r25;;
766 }
767 {.mfi
768 // load C_5,C_6
769 (p6) ldfpd f12,f13=[r2],16
770 // r=1-a*y
771 (p6) fnma.s1 f6=f8,f14,f1
772 // 1: exponent*=5; // (2^{16}-1)/3=0x5555
773 shladd r24=r25,2,r25;;
774 }
775 {.mib
776 // r30=(5*expon)*16
777 shladd r30=r24,4,r0
778 // r28=3*exponent
779 shladd r28=r25,1,r25
780 nop.b 0;;
781 }
782 {.mmi
783 // r28=6*exponent
784 shladd r28=r28,1,r0
785 // r24=17*expon
786 add r24=r24,r30
787 // r23=2nd table index (8 bits)
788 shr.u r23=r23,56;;
789 }
790 {.mmi
791 // adjust T_table pointer by 2nd index
792 shladd r2=r23,3,r2
793 // adjust D_table pointer by 2nd index
794 shladd r27=r23,2,r27
795 // r30=(17*expon)*16^2
796 shl r30=r24,8;;
797 }
798 {.mmi
799 // r24=expon*(2^16-1)/3
800 add r24=r24,r30;;
801 // r24=expon*(2^20+2)/3=expon*0x55556
802 shladd r24=r24,4,r28
803 nop.i 0;;
804 }
805 {.mii
806 nop.m 0
807 // r24=floor(expon/3)
808 shr.u r24=r24,20
809 nop.i 0;;
810 }
811 {.mmi
812 nop.m 0
813 // r28=3*exponent
814 shladd r28=r24,1,r24
815 // bias exponent
816 add r24=r29,r24;;
817 }
818 {.mmi
819 // get remainder of exponent/3
820 sub r25=r25,r28;;
821 // add sign to exponent
822 or r24=r24,r26
823 // remainder <<=8
824 shl r25=r25,8;;
825 }
826 {.mfi
827 // adjust D_table pointer by 1st index
828 shladd r27=r25,2,r27
829 // P_1=C_1+C_2*r
830 (p6) fma.s1 f7=f9,f6,f7
831 // adjust T_table pointer by 1st index
832 shladd r2=r25,3,r2
833 }
834 {.mfi
835 // f14=sign*2^{exponent/3}
836 (p6) setf.exp f14=r24
837 // r2=r*r
838 (p6) fma.s1 f9=f6,f6,f0
839 nop.i 0;;
840 }
841 {.mfi
842 // load D
843 (p6) ldfs f15=[r27]
844 // P_2=C_3+C_4*r
845 (p6) fma.s1 f10=f11,f6,f10
846 nop.i 0
847 }
848 {.mfi
849 // load T
850 (p6) ldf8 f8=[r2]
851 // P_3=C_5+C_6*r
852 (p6) fma.s1 f12=f13,f6,f12
853 nop.i 0;;
854 }
855 {.mfi
856 nop.m 0
857 // P_4=D-r*P_1
858 (p6) fnma.s1 f15=f6,f7,f15
859 nop.i 0
860 }
861 {.mfi
862 nop.m 0
863 // r3=r*r2
864 (p6) fma.s1 f6=f6,f9,f0
865 nop.i 0;;
866 }
867 {.mfi
868 nop.m 0
869 // P_5=P_2+r2*P_3
870 (p6) fma.s1 f10=f9,f12,f10
871 nop.i 0;;
872 }
873 {.mfi
874 nop.m 0
875 // T=T*(sign*2^{exponent/3})
876 (p6) fma.s1 f8=f8,f14,f0
877 nop.i 0
878 }
879 {.mfi
880 nop.m 0
881 // P=P_4-r3*P_5
882 (p6) fnma.s1 f6=f6,f10,f15
883 nop.i 0;;
884 }
885 {.mfb
886 nop.m 0
887 // result=T+T*p
888 (p6) fma.s0 f8=f8,f6,f8
889 br.ret.sptk b0;;
890 }
891 GLOBAL_LIBM_END(cbrtl)