| blob | b5a3a7241beaeed3cc00af15acb24843f2569619 |
1 .file "asinl.s"
4 // Copyright (c) 2001 - 2003, Intel Corporation
5 // All rights reserved.
6 //
7 //
8 // Redistribution and use in source and binary forms, with or without
9 // modification, are permitted provided that the following conditions are
10 // met:
11 //
12 // * Redistributions of source code must retain the above copyright
13 // notice, this list of conditions and the following disclaimer.
14 //
15 // * Redistributions in binary form must reproduce the above copyright
16 // notice, this list of conditions and the following disclaimer in the
17 // documentation and/or other materials provided with the distribution.
18 //
19 // * The name of Intel Corporation may not be used to endorse or promote
20 // products derived from this software without specific prior written
21 // permission.
23 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
24 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
25 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
26 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
27 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
28 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
29 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
30 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
31 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
32 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
33 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
34 //
35 // Intel Corporation is the author of this code, and requests that all
36 // problem reports or change requests be submitted to it directly at
37 // http://www.intel.com/software/products/opensource/libraries/num.htm.
38 //
39 // History
40 //==============================================================
41 // 08/28/01 New version
42 // 05/20/02 Cleaned up namespace and sf0 syntax
43 // 02/06/03 Reordered header: .section, .global, .proc, .align
44 //
45 // API
46 //==============================================================
47 // long double asinl(long double)
48 //
49 // Overview of operation
50 //==============================================================
51 // Background
52 //
53 // Implementation
54 //
55 // For |s| in [2^{-4}, sqrt(2)/2]:
56 // Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52
57 // asin(s)= asin(t)+asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e.
58 // r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1)
59 // asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9)
60 // The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table,
61 // along with the high and low parts of asin(t) (stored as two double precision
62 // values)
63 //
64 // |s| in (sqrt(2)/2, sqrt(255/256)):
65 // Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6..
66 // asin(|s|)= pi/2-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2)
67 // To minimize accumulated errors, r is computed as
68 // r= (t*s)_s-t^2*y*z+z*y*(t^2-1+s^2)_s+z*y*(1-s^2)_s*x+z'*y*(1-s^2)*PS29+
69 // +(t*s-(t*s)_s)+z*y*((t^2-1-(t^2-1+s^2)_s)+s^2)+z*y*(1-s^2-(1-s^2)_s)+
70 // +ez*z'*y*(1-s^2)*(1-x),
71 // where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits)
72 // z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2
73 //
74 // |s|<2^{-4}: evaluate as 17-degree polynomial
75 // (or simply return s, if|s|<2^{-64})
76 //
77 // |s| in [sqrt(255/256), 1): asin(|s|)= pi/2-asin(sqrt(1-s^2))
78 // use 17-degree polynomial for asin(sqrt(1-s^2)),
79 // 9-degree polynomial to evaluate sqrt(1-s^2)
80 // High order term is (pi/2)_high-(y*(1-s^2))_high
81 //
85 // Registers used
86 //==============================================================
87 // f6-f15, f32-f36
88 // r2-r3, r23-r23
89 // p6, p7, p8, p12
90 //
93 GR_SAVE_B0= r33
94 GR_SAVE_PFS= r34
95 GR_SAVE_GP= r35 // This reg. can safely be used
96 GR_SAVE_SP= r36
98 GR_Parameter_X= r37
99 GR_Parameter_Y= r38
100 GR_Parameter_RESULT= r39
101 GR_Parameter_TAG= r40
103 FR_X= f10
104 FR_Y= f1
105 FR_RESULT= f8
109 RODATA
111 .align 16
115 LOCAL_OBJECT_START(T_table)
117 // stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2),
118 // asin(t)_high (double precision), asin(t)_low (double precision)
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340 data8 0x8640d89acf78858c, 0xf9f784f9e5a1877b
341 data8 0x3fcbd815874eb160, 0x3cb5f4b89875e187
342 data8 0x865f669fe390c7f5, 0xf9db17e65944eacf
343 data8 0x3fcc19a4b0a6f9c0, 0x3cc5c0bc2b0bbf14
344 data8 0x867e4938df7dc45f, 0xf9be65fc1f6c2e6e
345 data8 0x3fcc5b3b58e061e0, 0x3cc1ca70df8f57e7
346 data8 0x869d80d0db7e4c0c, 0xf9a16f237aec427a
347 data8 0x3fcc9cd993cc4040, 0x3cbae93acc85eccf
348 data8 0x86bd0dd45f4f8265, 0xf98433446a806e70
349 data8 0x3fccde7f754f5660, 0x3cb22f70e64568d0
350 data8 0x86dcf0b16613e37a, 0xf966b246a8606170
351 data8 0x3fcd202d11620fa0, 0x3c962030e5d4c849
352 data8 0x86fd29d7624b3d5d, 0xf948ec11a9d4c45b
353 data8 0x3fcd61e27c10c0a0, 0x3cc7083c91d59217
354 data8 0x871db9b741dbe44a, 0xf92ae08c9eca4941
355 data8 0x3fcda39fc97be7c0, 0x3cc9258579e57211
356 data8 0x873ea0c3722d6af2, 0xf90c8f9e71633363
357 data8 0x3fcde5650dd86d60, 0x3ca4755a9ea582a9
358 data8 0x875fdf6fe45529e8, 0xf8edf92dc5875319
359 data8 0x3fce27325d6fe520, 0x3cbc1e2b6c1954f9
360 data8 0x878176321154e2bc, 0xf8cf1d20f87270b8
361 data8 0x3fce6907cca0d060, 0x3cb6ca4804750830
362 data8 0x87a36580fe6bccf5, 0xf8affb5e20412199
363 data8 0x3fceaae56fdee040, 0x3cad6b310d6fd46c
364 data8 0x87c5add5417a5cb9, 0xf89093cb0b7c0233
365 data8 0x3fceeccb5bb33900, 0x3cc16e99cedadb20
366 data8 0x87e84fa9057914ca, 0xf870e64d40a15036
367 data8 0x3fcf2eb9a4bcb600, 0x3cc75ee47c8b09e9
368 data8 0x880b4b780f02b709, 0xf850f2c9fdacdf78
369 data8 0x3fcf70b05fb02e20, 0x3cad6350d379f41a
370 data8 0x882ea1bfc0f228ac, 0xf830b926379e6465
371 data8 0x3fcfb2afa158b8a0, 0x3cce0ccd9f829985
372 data8 0x885252ff21146108, 0xf810394699fe0e8e
373 data8 0x3fcff4b77e97f3e0, 0x3c9b30faa7a4c703
374 data8 0x88765fb6dceebbb3, 0xf7ef730f865f6df0
375 data8 0x3fd01b6406332540, 0x3cdc5772c9e0b9bd
376 data8 0x88ad1f69be2cc730, 0xf7bdc59bc9cfbd97
377 data8 0x3fd04cf8ad203480, 0x3caeef44fe21a74a
378 data8 0x88f763f70ae2245e, 0xf77a91c868a9c54e
379 data8 0x3fd08f23ce0162a0, 0x3cd6290ab3fe5889
380 data8 0x89431fc7bc0c2910, 0xf73642973c91298e
381 data8 0x3fd0d1610f0c1ec0, 0x3cc67401a01f08cf
382 data8 0x8990573407c7738e, 0xf6f0d71d1d7a2dd6
383 data8 0x3fd113b0c65d88c0, 0x3cc7aa4020fe546f
384 data8 0x89df0eb108594653, 0xf6aa4e6a05cfdef2
385 data8 0x3fd156134ada6fe0, 0x3cc87369da09600c
386 data8 0x8a2f4ad16e0ed78a, 0xf662a78900c35249
387 data8 0x3fd19888f43427a0, 0x3cc62b220f38e49c
388 data8 0x8a811046373e0819, 0xf619e180181d97cc
389 data8 0x3fd1db121aed7720, 0x3ca3ede7490b52f4
390 data8 0x8ad463df6ea0fa2c, 0xf5cffb504190f9a2
391 data8 0x3fd21daf185fa360, 0x3caafad98c1d6c1b
392 data8 0x8b294a8cf0488daf, 0xf584f3f54b8604e6
393 data8 0x3fd2606046bf95a0, 0x3cdb2d704eeb08fa
394 data8 0x8b7fc95f35647757, 0xf538ca65c960b582
395 data8 0x3fd2a32601231ec0, 0x3cc661619fa2f126
396 data8 0x8bd7e588272276f8, 0xf4eb7d92ff39fccb
397 data8 0x3fd2e600a3865760, 0x3c8a2a36a99aca4a
398 data8 0x8c31a45bf8e9255e, 0xf49d0c68cd09b689
399 data8 0x3fd328f08ad12000, 0x3cb9efaf1d7ab552
400 data8 0x8c8d0b520a35eb18, 0xf44d75cd993cfad2
401 data8 0x3fd36bf614dcc040, 0x3ccacbb590bef70d
402 data8 0x8cea2005d068f23d, 0xf3fcb8a23ab4942b
403 data8 0x3fd3af11a079a6c0, 0x3cd9775872cf037d
404 data8 0x8d48e837c8cd5027, 0xf3aad3c1e2273908
405 data8 0x3fd3f2438d754b40, 0x3ca03304f667109a
406 data8 0x8da969ce732f3ac7, 0xf357c60202e2fd7e
407 data8 0x3fd4358c3ca032e0, 0x3caecf2504ff1a9d
408 data8 0x8e0baad75555e361, 0xf3038e323ae9463a
409 data8 0x3fd478ec0fd419c0, 0x3cc64bdc3d703971
410 data8 0x8e6fb18807ba877e, 0xf2ae2b1c3a6057f7
411 data8 0x3fd4bc6369fa40e0, 0x3cbb7122ec245cf2
412 data8 0x8ed5843f4bda74d5, 0xf2579b83aa556f0c
413 data8 0x3fd4fff2af11e2c0, 0x3c9cfa2dc792d394
414 data8 0x8f3d29862c861fef, 0xf1ffde2612ca1909
415 data8 0x3fd5439a4436d000, 0x3cc38d46d310526b
416 data8 0x8fa6a81128940b2d, 0xf1a6f1bac0075669
417 data8 0x3fd5875a8fa83520, 0x3cd8bf59b8153f8a
418 data8 0x901206c1686317a6, 0xf14cd4f2a730d480
419 data8 0x3fd5cb33f8cf8ac0, 0x3c9502b5c4d0e431
420 data8 0x907f4ca5fe9cf739, 0xf0f186784a125726
421 data8 0x3fd60f26e847b120, 0x3cc8a1a5e0acaa33
422 data8 0x90ee80fd34aeda5e, 0xf09504ef9a212f18
423 data8 0x3fd65333c7e43aa0, 0x3cae5b029cb1f26e
424 data8 0x915fab35e37421c6, 0xf0374ef5daab5c45
425 data8 0x3fd6975b02b8e360, 0x3cd5aa1c280c45e6
426 data8 0x91d2d2f0d894d73c, 0xefd86321822dbb51
427 data8 0x3fd6db9d05213b20, 0x3cbecf2c093ccd8b
428 data8 0x9248000249200009, 0xef7840021aca5a72
429 data8 0x3fd71ffa3cc87fc0, 0x3cb8d273f08d00d9
430 data8 0x92bf3a7351f081d2, 0xef16e42021d7cbd5
431 data8 0x3fd7647318b1ad20, 0x3cbce099d79cdc46
432 data8 0x93388a8386725713, 0xeeb44dfce6820283
433 data8 0x3fd7a908093fc1e0, 0x3ccb033ec17a30d9
434 data8 0x93b3f8aa8e653812, 0xee507c126774fa45
435 data8 0x3fd7edb9803e3c20, 0x3cc10aedb48671eb
436 data8 0x94318d99d341ade4, 0xedeb6cd32f891afb
437 data8 0x3fd83287f0e9cf80, 0x3c994c0c1505cd2a
438 data8 0x94b1523e3dedc630, 0xed851eaa3168f43c
439 data8 0x3fd87773cff956e0, 0x3cda3b7bce6a6b16
440 data8 0x95334fc20577563f, 0xed1d8ffaa2279669
441 data8 0x3fd8bc7d93a70440, 0x3cd4922edc792ce2
442 data8 0x95b78f8e8f92f274, 0xecb4bf1fd2be72da
443 data8 0x3fd901a5b3b9cf40, 0x3cd3fea1b00f9d0d
444 data8 0x963e1b4e63a87c3f, 0xec4aaa6d08694cc1
445 data8 0x3fd946eca98f2700, 0x3cdba4032d968ff1
446 data8 0x96c6fcef314074fc, 0xebdf502d53d65fea
447 data8 0x3fd98c52f024e800, 0x3cbe7be1ab8c95c9
448 data8 0x97523ea3eab028b2, 0xeb72aea36720793e
449 data8 0x3fd9d1d904239860, 0x3cd72d08a6a22b70
450 data8 0x97dfeae6f4ee4a9a, 0xeb04c4096a884e94
451 data8 0x3fda177f63e8ef00, 0x3cd818c3c1ebfac7
452 data8 0x98700c7c6d85d119, 0xea958e90cfe1efd7
453 data8 0x3fda5d468f92a540, 0x3cdf45fbfaa080fe
454 data8 0x9902ae7487a9caa1, 0xea250c6224aab21a
455 data8 0x3fdaa32f090998e0, 0x3cd715a9353cede4
456 data8 0x9997dc2e017a9550, 0xe9b33b9ce2bb7638
457 data8 0x3fdae939540d3f00, 0x3cc545c014943439
458 data8 0x9a2fa158b29b649b, 0xe9401a573f8aa706
459 data8 0x3fdb2f65f63f6c60, 0x3cd4a63c2f2ca8e2
460 data8 0x9aca09f835466186, 0xe8cba69df9f0bf35
461 data8 0x3fdb75b5773075e0, 0x3cda310ce1b217ec
462 data8 0x9b672266ab1e0136, 0xe855de74266193d4
463 data8 0x3fdbbc28606babc0, 0x3cdc84b75cca6c44
464 data8 0x9c06f7579f0b7bd5, 0xe7debfd2f98c060b
465 data8 0x3fdc02bf3d843420, 0x3cd225d967ffb922
466 data8 0x9ca995db058cabdc, 0xe76648a991511c6e
467 data8 0x3fdc497a9c224780, 0x3cde08101c5b825b
468 data8 0x9d4f0b605ce71e88, 0xe6ec76dcbc02d9a7
469 data8 0x3fdc905b0c10d420, 0x3cb1abbaa3edf120
470 data8 0x9df765b9eecad5e6, 0xe6714846bdda7318
471 data8 0x3fdcd7611f4b8a00, 0x3cbf6217ae80aadf
472 data8 0x9ea2b320350540fe, 0xe5f4bab71494cd6b
473 data8 0x3fdd1e8d6a0d56c0, 0x3cb726e048cc235c
474 data8 0x9f51023562fc5676, 0xe576cbf239235ecb
475 data8 0x3fdd65e082df5260, 0x3cd9e66872bd5250
476 data8 0xa002620915c2a2f6, 0xe4f779b15f5ec5a7
477 data8 0x3fddad5b02a82420, 0x3c89743b0b57534b
478 data8 0xa0b6e21c2caf9992, 0xe476c1a233a7873e
479 data8 0x3fddf4fd84bbe160, 0x3cbf7adea9ee3338
480 data8 0xa16e9264cc83a6b2, 0xe3f4a16696608191
481 data8 0x3fde3cc8a6ec6ee0, 0x3cce46f5a51f49c6
482 data8 0xa22983528f3d8d49, 0xe3711694552da8a8
483 data8 0x3fde84bd099a6600, 0x3cdc78f6490a2d31
484 data8 0xa2e7c5d2e2e69460, 0xe2ec1eb4e1e0a5fb
485 data8 0x3fdeccdb4fc685c0, 0x3cdd3aedb56a4825
486 data8 0xa3a96b5599bd2532, 0xe265b74506fbe1c9
487 data8 0x3fdf15241f23b3e0, 0x3cd440f3c6d65f65
488 data8 0xa46e85d1ae49d7de, 0xe1ddddb499b3606f
489 data8 0x3fdf5d98202994a0, 0x3cd6c44bd3fb745a
490 data8 0xa53727ca3e11b99e, 0xe1548f662951b00d
491 data8 0x3fdfa637fe27bf60, 0x3ca8ad1cd33054dd
492 data8 0xa6036453bdc20186, 0xe0c9c9aeabe5e481
493 data8 0x3fdfef0467599580, 0x3cc0f1ac0685d78a
494 data8 0xa6d34f1969dda338, 0xe03d89d5281e4f81
495 data8 0x3fe01bff067d6220, 0x3cc0731e8a9ef057
496 data8 0xa7a6fc62f7246ff3, 0xdfafcd125c323f54
497 data8 0x3fe04092d1ae3b40, 0x3ccabda24b59906d
498 data8 0xa87e811a861df9b9, 0xdf20909061bb9760
499 data8 0x3fe0653df0fd9fc0, 0x3ce94c8dcc722278
500 data8 0xa959f2d2dd687200, 0xde8fd16a4e5f88bd
501 data8 0x3fe08a00c1cae320, 0x3ce6b888bb60a274
502 data8 0xaa3967cdeea58bda, 0xddfd8cabd1240d22
503 data8 0x3fe0aedba3221c00, 0x3ced5941cd486e46
504 data8 0xab904fd587263c84, 0xdd1f4472e1cf64ed
505 data8 0x3fe0e651e85229c0, 0x3cdb6701042299b1
506 data8 0xad686d44dd5a74bb, 0xdbf173e1f6b46e92
507 data8 0x3fe1309cbf4cdb20, 0x3cbf1be7bb3f0ec5
508 data8 0xaf524e15640ebee4, 0xdabd54896f1029f6
509 data8 0x3fe17b4ee1641300, 0x3ce81dd055b792f1
510 data8 0xb14eca24ef7db3fa, 0xd982cb9ae2f47e41
511 data8 0x3fe1c66b9ffd6660, 0x3cd98ea31eb5ddc7
512 data8 0xb35ec807669920ce, 0xd841bd1b8291d0b6
513 data8 0x3fe211f66db3a5a0, 0x3ca480c35a27b4a2
514 data8 0xb5833e4755e04dd1, 0xd6fa0bd3150b6930
515 data8 0x3fe25df2e05b6c40, 0x3ca4bc324287a351
516 data8 0xb7bd34c8000b7bd3, 0xd5ab9939a7d23aa1
517 data8 0x3fe2aa64b32f7780, 0x3cba67314933077c
518 data8 0xba0dc64d126cc135, 0xd4564563ce924481
519 data8 0x3fe2f74fc9289ac0, 0x3cec1a1dc0efc5ec
520 data8 0xbc76222cbbfa74a6, 0xd2f9eeed501125a8
521 data8 0x3fe344b82f859ac0, 0x3ceeef218de413ac
522 data8 0xbef78e31985291a9, 0xd19672e2182f78be
523 data8 0x3fe392a22087b7e0, 0x3cd2619ba201204c
524 data8 0xc19368b2b0629572, 0xd02baca5427e436a
525 data8 0x3fe3e11206694520, 0x3cb5d0b3143fe689
526 data8 0xc44b2ae8c6733e51, 0xceb975d60b6eae5d
527 data8 0x3fe4300c7e945020, 0x3cbd367143da6582
528 data8 0xc7206b894212dfef, 0xcd3fa6326ff0ac9a
529 data8 0x3fe47f965d201d60, 0x3ce797c7a4ec1d63
530 data8 0xca14e1b0622de526, 0xcbbe13773c3c5338
531 data8 0x3fe4cfb4b09d1a20, 0x3cedfadb5347143c
532 data8 0xcd2a6825eae65f82, 0xca34913d425a5ae9
533 data8 0x3fe5206cc637e000, 0x3ce2798b38e54193
534 data8 0xd06301095e1351ee, 0xc8a2f0d3679c08c0
535 data8 0x3fe571c42e3d0be0, 0x3ccd7cb9c6c2ca68
536 data8 0xd3c0d9f50057adda, 0xc70901152d59d16b
537 data8 0x3fe5c3c0c108f940, 0x3ceb6c13563180ab
538 data8 0xd74650a98cc14789, 0xc5668e3d4cbf8828
539 data8 0x3fe61668a46ffa80, 0x3caa9092e9e3c0e5
540 data8 0xdaf5f8579dcc8f8f, 0xc3bb61b3eed42d02
541 data8 0x3fe669c251ad69e0, 0x3cccf896ef3b4fee
542 data8 0xded29f9f9a6171b4, 0xc20741d7f8e8e8af
543 data8 0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d
544 data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b
545 data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321
546 data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91
547 data8 0x3fe76840418978a0, 0x3ccda46e85432c3d
548 data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3
549 data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3
550 data8 0xf049183c3f53c39b, 0xbad848720223d3a8
551 data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b
552 data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48
553 data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f
554 data8 0xfa718f05adbf2c33, 0xb70432500286b185
555 data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9
556 data8 0xfff200c3f5489608, 0xb509e6454dca33cc
557 data8 0x3fe9211b54441080, 0x3cb789cb53515688
558 // The following table entries are not used
559 //data8 0x82e138a0fac48700, 0xb3044a513a8e6132
560 //data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0
561 //data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88
562 //data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039
563 //data8 0x89377c1387d5b908, 0xaed58e9a09014d5c
564 //data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58
565 //data8 0x8cad7a2c98dec333, 0xacab929ce114d451
566 //data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f
567 //data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec
568 //data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5
569 //data8 0x9446d8191f80dd42, 0xa82ff92687235baf
570 //data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e
571 //data8 0x98758ba086e4000a, 0xa5dd497a9c184f58
572 //data8 0x3febb5f571cb0560, 0x3ce0c7774329a613
573 //data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b
574 //data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177
575 //data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03
576 //data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959
577 //data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec
578 //data8 0x3fece4f404e29b20, 0x3cea3413401132b5
579 //data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c
580 //data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276
581 //data8 0xb265c39cbd80f97a, 0x99553d969fec7beb
582 //data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2
583 //data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c
584 //data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71
585 //data8 0xbfea427678945732, 0x93d5990f9ee787af
586 //data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5
587 //data8 0xc79611399b8c90c5, 0x90f72bde80febc31
588 //data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56
589 //data8 0xcffa8425040624d7, 0x8e02b4418574ebed
590 //data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f
591 //data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024
592 //data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94
593 //data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b
594 //data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc
595 //data8 0xeea6d733421da0a6, 0x84921bbe64ae029a
596 //data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02
597 //data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6
598 //data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3
599 //data8 0x84ac1fcec4203245, 0xfb73a828893df19e
600 //data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de
601 //data8 0x8ca50621110c60e6, 0xf438a14c158d867c
602 //data8 0x3ff12d51caa6b580, 0x3ce6bce9748739b6
603 //data8 0x95b8c2062d6f8161, 0xecb3ccdd37b369da
604 //data8 0x3ff1717418520340, 0x3ca5c2732533177c
605 //data8 0xa0262917caab4ad1, 0xe4dde4ddc81fd119
606 //data8 0x3ff1b7d59dd40ba0, 0x3cc4c7c98e870ff5
607 //data8 0xac402c688b72f3f4, 0xdcae469be46d4c8d
608 //data8 0x3ff200b93cc5a540, 0x3c8dd6dc1bfe865a
609 //data8 0xba76968b9eabd9ab, 0xd41a8f3df1115f7f
610 //data8 0x3ff24c6f8f6affa0, 0x3cf1acb6d2a7eff7
611 //data8 0xcb63c87c23a71dc5, 0xcb161074c17f54ec
612 //data8 0x3ff29b5b338b7c80, 0x3ce9b5845f6ec746
613 //data8 0xdfe323b8653af367, 0xc19107d99ab27e42
614 //data8 0x3ff2edf6fac7f5a0, 0x3cf77f961925fa02
615 //data8 0xf93746caaba3e1f1, 0xb777744a9df03bff
616 //data8 0x3ff344df237486c0, 0x3cf6ddf5f6ddda43
617 //data8 0x8ca77052f6c340f0, 0xacaf476f13806648
618 //data8 0x3ff3a0dfa4bb4ae0, 0x3cfee01bbd761bff
619 //data8 0xa1a48604a81d5c62, 0xa11575d30c0aae50
620 //data8 0x3ff4030b73c55360, 0x3cf1cf0e0324d37c
621 //data8 0xbe45074b05579024, 0x9478e362a07dd287
622 //data8 0x3ff46ce4c738c4e0, 0x3ce3179555367d12
623 //data8 0xe7a08b5693d214ec, 0x8690e3575b8a7c3b
624 //data8 0x3ff4e0a887c40a80, 0x3cfbd5d46bfefe69
625 //data8 0x94503d69396d91c7, 0xedd2ce885ff04028
626 //data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b
627 //data8 0xced1d96c5bb209e6, 0xc965278083808702
628 //data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c
629 //data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd
630 //data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e
631 //data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4
632 //data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb
633 LOCAL_OBJECT_END(T_table)
637 .align 16
639 LOCAL_OBJECT_START(poly_coeffs)
640 // C_3
641 data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc
642 // C_5
643 data8 0x999999999999999a, 0x0000000000003ffb
644 // C_7, C_9
645 data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8
646 // pi/2 (low, high)
647 data8 0x3C91A62633145C07, 0x3FF921FB54442D18
648 // C_11, C_13
649 data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e
650 // C_15, C_17
651 data8 0x3f8c99999999999a, 0x3f87a87878787223
652 LOCAL_OBJECT_END(poly_coeffs)
655 R_DBL_S = r21
656 R_EXP0 = r22
657 R_EXP = r15
658 R_SGNMASK = r23
659 R_TMP = r24
660 R_TMP2 = r25
661 R_INDEX = r26
662 R_TMP3 = r27
663 R_TMP03 = r27
664 R_TMP4 = r28
665 R_TMP5 = r23
666 R_TMP6 = r22
667 R_TMP7 = r21
668 R_T = r29
669 R_BIAS = r20
671 F_T = f6
672 F_1S2 = f7
673 F_1S2_S = f9
674 F_INV_1T2 = f10
675 F_SQRT_1T2 = f11
676 F_S2T2 = f12
677 F_X = f13
678 F_D = f14
679 F_2M64 = f15
681 F_CS2 = f32
682 F_CS3 = f33
683 F_CS4 = f34
684 F_CS5 = f35
685 F_CS6 = f36
686 F_CS7 = f37
687 F_CS8 = f38
688 F_CS9 = f39
689 F_S23 = f40
690 F_S45 = f41
691 F_S67 = f42
692 F_S89 = f43
693 F_S25 = f44
694 F_S69 = f45
695 F_S29 = f46
696 F_X2 = f47
697 F_X4 = f48
698 F_TSQRT = f49
699 F_DTX = f50
700 F_R = f51
701 F_R2 = f52
702 F_R3 = f53
703 F_R4 = f54
705 F_C3 = f55
706 F_C5 = f56
707 F_C7 = f57
708 F_C9 = f58
709 F_P79 = f59
710 F_P35 = f60
711 F_P39 = f61
713 F_ATHI = f62
714 F_ATLO = f63
716 F_T1 = f64
717 F_Y = f65
718 F_Y2 = f66
719 F_ANDMASK = f67
720 F_ORMASK = f68
721 F_S = f69
722 F_05 = f70
723 F_SQRT_1S2 = f71
724 F_DS = f72
725 F_Z = f73
726 F_1T2 = f74
727 F_DZ = f75
728 F_ZE = f76
729 F_YZ = f77
730 F_Y1S2 = f78
731 F_Y1S2X = f79
732 F_1X = f80
733 F_ST = f81
734 F_1T2_ST = f82
735 F_TSS = f83
736 F_Y1S2X2 = f84
737 F_DZ_TERM = f85
738 F_DTS = f86
739 F_DS2X = f87
740 F_T2 = f88
741 F_ZY1S2S = f89
742 F_Y1S2_1X = f90
743 F_TS = f91
744 F_PI2_LO = f92
745 F_PI2_HI = f93
746 F_S19 = f94
747 F_INV1T2_2 = f95
748 F_CORR = f96
749 F_DZ0 = f97
751 F_C11 = f98
752 F_C13 = f99
753 F_C15 = f100
754 F_C17 = f101
755 F_P1113 = f102
756 F_P1517 = f103
757 F_P1117 = f104
758 F_P317 = f105
759 F_R8 = f106
760 F_HI = f107
761 F_1S2_HI = f108
762 F_DS2 = f109
763 F_Y2_2 = f110
764 F_S2 = f111
765 F_S_DS2 = f112
766 F_S_1S2S = f113
767 F_XL = f114
768 F_2M128 = f115
771 .section .text
772 GLOBAL_LIBM_ENTRY(asinl)
774 {.mfi
775 // get exponent, mantissa (rounded to double precision) of s
776 getf.d R_DBL_S = f8
777 // 1-s^2
778 fnma.s1 F_1S2 = f8, f8, f1
779 // r2 = pointer to T_table
780 addl r2 = @ltoff(T_table), gp
781 }
783 {.mfi
784 // sign mask
785 mov R_SGNMASK = 0x20000
786 nop.f 0
787 // bias-63-1
788 mov R_TMP03 = 0xffff-64;;
789 }
792 {.mfi
793 // get exponent of s
794 getf.exp R_EXP = f8
795 nop.f 0
796 // R_TMP4 = 2^45
797 shl R_TMP4 = R_SGNMASK, 45-17
798 }
800 {.mlx
801 // load bias-4
802 mov R_TMP = 0xffff-4
803 // load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1)
804 movl R_TMP2 = 0x7fcd413cccfe779a;;
805 }
808 {.mfi
809 // load 2^{-64} in FP register
810 setf.exp F_2M64 = R_TMP03
811 nop.f 0
812 // index = (0x7-exponent)|b1 b2.. b6
813 extr.u R_INDEX = R_DBL_S, 46, 9
814 }
816 {.mfi
817 // get t = sign|exponent|b1 b2.. b6 1 x.. x
818 or R_T = R_DBL_S, R_TMP4
819 nop.f 0
820 // R_TMP4 = 2^45-1
821 sub R_TMP4 = R_TMP4, r0, 1;;
822 }
825 {.mfi
826 // get t = sign|exponent|b1 b2.. b6 1 0.. 0
827 andcm R_T = R_T, R_TMP4
828 nop.f 0
829 // eliminate sign from R_DBL_S (shift left by 1)
830 shl R_TMP3 = R_DBL_S, 1
831 }
833 {.mfi
834 // R_BIAS = 3*2^6
835 mov R_BIAS = 0xc0
836 nop.f 0
837 // eliminate sign from R_EXP
838 andcm R_EXP0 = R_EXP, R_SGNMASK;;
839 }
843 {.mfi
844 // load start address for T_table
845 ld8 r2 = [r2]
846 nop.f 0
847 // p8 = 1 if |s|> = sqrt(2)/2
848 cmp.geu p8, p0 = R_TMP3, R_TMP2
849 }
851 {.mlx
852 // p7 = 1 if |s|<2^{-4} (exponent of s<bias-4)
853 cmp.lt p7, p0 = R_EXP0, R_TMP
854 // sqrt coefficient cs8 = -33*13/128
855 movl R_TMP2 = 0xc0568000;;
856 }
860 {.mbb
861 // load t in FP register
862 setf.d F_T = R_T
863 // if |s|<2^{-4}, take alternate path
864 (p7) br.cond.spnt SMALL_S
865 // if |s|> = sqrt(2)/2, take alternate path
866 (p8) br.cond.sptk LARGE_S
867 }
869 {.mlx
870 // index = (4-exponent)|b1 b2.. b6
871 sub R_INDEX = R_INDEX, R_BIAS
872 // sqrt coefficient cs9 = 55*13/128
873 movl R_TMP = 0x40b2c000;;
874 }
877 {.mfi
878 // sqrt coefficient cs8 = -33*13/128
879 setf.s F_CS8 = R_TMP2
880 nop.f 0
881 // shift R_INDEX by 5
882 shl R_INDEX = R_INDEX, 5
883 }
885 {.mfi
886 // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
887 mov R_TMP4 = 0xffff - 1
888 nop.f 0
889 // sqrt coefficient cs6 = -21/16
890 mov R_TMP6 = 0xbfa8;;
891 }
894 {.mlx
895 // table index
896 add r2 = r2, R_INDEX
897 // sqrt coefficient cs7 = 33/16
898 movl R_TMP2 = 0x40040000;;
899 }
902 {.mmi
903 // load cs9 = 55*13/128
904 setf.s F_CS9 = R_TMP
905 // sqrt coefficient cs5 = 7/8
906 mov R_TMP3 = 0x3f60
907 // sqrt coefficient cs6 = 21/16
908 shl R_TMP6 = R_TMP6, 16;;
909 }
912 {.mmi
913 // load significand of 1/(1-t^2)
914 ldf8 F_INV_1T2 = [r2], 8
915 // sqrt coefficient cs7 = 33/16
916 setf.s F_CS7 = R_TMP2
917 // sqrt coefficient cs4 = -5/8
918 mov R_TMP5 = 0xbf20;;
919 }
922 {.mmi
923 // load significand of sqrt(1-t^2)
924 ldf8 F_SQRT_1T2 = [r2], 8
925 // sqrt coefficient cs6 = 21/16
926 setf.s F_CS6 = R_TMP6
927 // sqrt coefficient cs5 = 7/8
928 shl R_TMP3 = R_TMP3, 16;;
929 }
932 {.mmi
933 // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
934 setf.exp F_CS3 = R_TMP4
935 // r3 = pointer to polynomial coefficients
936 addl r3 = @ltoff(poly_coeffs), gp
937 // sqrt coefficient cs4 = -5/8
938 shl R_TMP5 = R_TMP5, 16;;
939 }
942 {.mfi
943 // sqrt coefficient cs5 = 7/8
944 setf.s F_CS5 = R_TMP3
945 // d = s-t
946 fms.s1 F_D = f8, f1, F_T
947 // set p6 = 1 if s<0, p11 = 1 if s> = 0
948 cmp.ge p6, p11 = R_EXP, R_DBL_S
949 }
951 {.mfi
952 // r3 = load start address to polynomial coefficients
953 ld8 r3 = [r3]
954 // s+t
955 fma.s1 F_S2T2 = f8, f1, F_T
956 nop.i 0;;
957 }
960 {.mfi
961 // sqrt coefficient cs4 = -5/8
962 setf.s F_CS4 = R_TMP5
963 // s^2-t^2
964 fma.s1 F_S2T2 = F_S2T2, F_D, f0
965 nop.i 0;;
966 }
969 {.mfi
970 // load C3
971 ldfe F_C3 = [r3], 16
972 // 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2))
973 fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
974 nop.i 0;;
975 }
977 {.mfi
978 // load C_5
979 ldfe F_C5 = [r3], 16
980 // set correct exponent for sqrt(1-t^2)
981 fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
982 nop.i 0;;
983 }
986 {.mfi
987 // load C_7, C_9
988 ldfpd F_C7, F_C9 = [r3]
989 // x = -(s^2-t^2)/(1-t^2)/2
990 fnma.s1 F_X = F_INV_1T2, F_S2T2, f0
991 nop.i 0;;
992 }
995 {.mfi
996 // load asin(t)_high, asin(t)_low
997 ldfpd F_ATHI, F_ATLO = [r2]
998 // t*sqrt(1-t^2)
999 fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0
1000 nop.i 0;;
1001 }
1004 {.mfi
1005 nop.m 0
1006 // cs9*x+cs8
1007 fma.s1 F_S89 = F_CS9, F_X, F_CS8
1008 nop.i 0
1009 }
1011 {.mfi
1012 nop.m 0
1013 // cs7*x+cs6
1014 fma.s1 F_S67 = F_CS7, F_X, F_CS6
1015 nop.i 0;;
1016 }
1018 {.mfi
1019 nop.m 0
1020 // cs5*x+cs4
1021 fma.s1 F_S45 = F_CS5, F_X, F_CS4
1022 nop.i 0
1023 }
1025 {.mfi
1026 nop.m 0
1027 // x*x
1028 fma.s1 F_X2 = F_X, F_X, f0
1029 nop.i 0;;
1030 }
1033 {.mfi
1034 nop.m 0
1035 // (s-t)-t*x
1036 fnma.s1 F_DTX = F_T, F_X, F_D
1037 nop.i 0
1038 }
1040 {.mfi
1041 nop.m 0
1042 // cs3*x+cs2 (cs2 = -0.5 = -cs3)
1043 fms.s1 F_S23 = F_CS3, F_X, F_CS3
1044 nop.i 0;;
1045 }
1048 {.mfi
1049 nop.m 0
1050 // cs9*x^3+cs8*x^2+cs7*x+cs6
1051 fma.s1 F_S69 = F_S89, F_X2, F_S67
1052 nop.i 0
1053 }
1055 {.mfi
1056 nop.m 0
1057 // x^4
1058 fma.s1 F_X4 = F_X2, F_X2, f0
1059 nop.i 0;;
1060 }
1063 {.mfi
1064 nop.m 0
1065 // t*sqrt(1-t^2)*x^2
1066 fma.s1 F_TSQRT = F_TSQRT, F_X2, f0
1067 nop.i 0
1068 }
1070 {.mfi
1071 nop.m 0
1072 // cs5*x^3+cs4*x^2+cs3*x+cs2
1073 fma.s1 F_S25 = F_S45, F_X2, F_S23
1074 nop.i 0;;
1075 }
1078 {.mfi
1079 nop.m 0
1080 // ((s-t)-t*x)*sqrt(1-t^2)
1081 fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0
1082 nop.i 0;;
1083 }
1086 {.mfi
1087 nop.m 0
1088 // if sign is negative, negate table values: asin(t)_low
1089 (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0
1090 nop.i 0
1091 }
1093 {.mfi
1094 nop.m 0
1095 // PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2
1096 fma.s1 F_S29 = F_S69, F_X4, F_S25
1097 nop.i 0;;
1098 }
1101 {.mfi
1102 nop.m 0
1103 // if sign is negative, negate table values: asin(t)_high
1104 (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
1105 nop.i 0
1106 }
1108 {.mfi
1109 nop.m 0
1110 // R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29
1111 fnma.s1 F_R = F_S29, F_TSQRT, F_DTX
1112 nop.i 0;;
1113 }
1116 {.mfi
1117 nop.m 0
1118 // R^2
1119 fma.s1 F_R2 = F_R, F_R, f0
1120 nop.i 0;;
1121 }
1124 {.mfi
1125 nop.m 0
1126 // c7+c9*R^2
1127 fma.s1 F_P79 = F_C9, F_R2, F_C7
1128 nop.i 0
1129 }
1131 {.mfi
1132 nop.m 0
1133 // c3+c5*R^2
1134 fma.s1 F_P35 = F_C5, F_R2, F_C3
1135 nop.i 0;;
1136 }
1138 {.mfi
1139 nop.m 0
1140 // R^3
1141 fma.s1 F_R4 = F_R2, F_R2, f0
1142 nop.i 0;;
1143 }
1145 {.mfi
1146 nop.m 0
1147 // R^3
1148 fma.s1 F_R3 = F_R2, F_R, f0
1149 nop.i 0;;
1150 }
1154 {.mfi
1155 nop.m 0
1156 // c3+c5*R^2+c7*R^4+c9*R^6
1157 fma.s1 F_P39 = F_P79, F_R4, F_P35
1158 nop.i 0;;
1159 }
1162 {.mfi
1163 nop.m 0
1164 // asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1165 fma.s1 F_P39 = F_P39, F_R3, F_ATLO
1166 nop.i 0;;
1167 }
1170 {.mfi
1171 nop.m 0
1172 // R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1173 fma.s1 F_P39 = F_P39, f1, F_R
1174 nop.i 0;;
1175 }
1178 {.mfb
1179 nop.m 0
1180 // result = asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1181 fma.s0 f8 = F_ATHI, f1, F_P39
1182 // return
1183 br.ret.sptk b0;;
1184 }
1189 LARGE_S:
1191 {.mfi
1192 // bias-1
1193 mov R_TMP3 = 0xffff - 1
1194 // y ~ 1/sqrt(1-s^2)
1195 frsqrta.s1 F_Y, p7 = F_1S2
1196 // c9 = 55*13*17/128
1197 mov R_TMP4 = 0x10af7b
1198 }
1200 {.mlx
1201 // c8 = -33*13*15/128
1202 mov R_TMP5 = 0x184923
1203 movl R_TMP2 = 0xff00000000000000;;
1204 }
1206 {.mfi
1207 // set p6 = 1 if s<0, p11 = 1 if s>0
1208 cmp.ge p6, p11 = R_EXP, R_DBL_S
1209 // 1-s^2
1210 fnma.s1 F_1S2 = f8, f8, f1
1211 // set p9 = 1
1212 cmp.eq p9, p0 = r0, r0;;
1213 }
1216 {.mfi
1217 // load 0.5
1218 setf.exp F_05 = R_TMP3
1219 // (1-s^2) rounded to single precision
1220 fnma.s.s1 F_1S2_S = f8, f8, f1
1221 // c9 = 55*13*17/128
1222 shl R_TMP4 = R_TMP4, 10
1223 }
1225 {.mlx
1226 // AND mask for getting t ~ sqrt(1-s^2)
1227 setf.sig F_ANDMASK = R_TMP2
1228 // OR mask
1229 movl R_TMP2 = 0x0100000000000000;;
1230 }
1233 {.mfi
1234 nop.m 0
1235 // (s^2)_s
1236 fma.s.s1 F_S2 = f8, f8, f0
1237 nop.i 0;;
1238 }
1241 {.mmi
1242 // c9 = 55*13*17/128
1243 setf.s F_CS9 = R_TMP4
1244 // c7 = 33*13/16
1245 mov R_TMP4 = 0x41d68
1246 // c8 = -33*13*15/128
1247 shl R_TMP5 = R_TMP5, 11;;
1248 }
1251 {.mfi
1252 setf.sig F_ORMASK = R_TMP2
1253 // y^2
1254 fma.s1 F_Y2 = F_Y, F_Y, f0
1255 // c7 = 33*13/16
1256 shl R_TMP4 = R_TMP4, 12
1257 }
1259 {.mfi
1260 // c6 = -33*7/16
1261 mov R_TMP6 = 0xc1670
1262 // y' ~ sqrt(1-s^2)
1263 fma.s1 F_T1 = F_Y, F_1S2, f0
1264 // c5 = 63/8
1265 mov R_TMP7 = 0x40fc;;
1266 }
1269 {.mlx
1270 // load c8 = -33*13*15/128
1271 setf.s F_CS8 = R_TMP5
1272 // c4 = -35/8
1273 movl R_TMP5 = 0xc08c0000;;
1274 }
1276 {.mfi
1277 // r3 = pointer to polynomial coefficients
1278 addl r3 = @ltoff(poly_coeffs), gp
1279 // 1-(1-s^2)_s
1280 fnma.s1 F_DS = F_1S2_S, f1, f1
1281 // p9 = 0 if p7 = 1 (p9 = 1 for special cases only)
1282 (p7) cmp.ne p9, p0 = r0, r0
1283 }
1285 {.mlx
1286 // load c7 = 33*13/16
1287 setf.s F_CS7 = R_TMP4
1288 // c3 = 5/2
1289 movl R_TMP4 = 0x40200000;;
1290 }
1293 {.mfi
1294 nop.m 0
1295 // 1-(s^2)_s
1296 fnma.s1 F_S_1S2S = F_S2, f1, f1
1297 nop.i 0
1298 }
1300 {.mlx
1301 // load c4 = -35/8
1302 setf.s F_CS4 = R_TMP5
1303 // c2 = -3/2
1304 movl R_TMP5 = 0xbfc00000;;
1305 }
1308 {.mfi
1309 // load c3 = 5/2
1310 setf.s F_CS3 = R_TMP4
1311 // x = (1-s^2)_s*y^2-1
1312 fms.s1 F_X = F_1S2_S, F_Y2, f1
1313 // c6 = -33*7/16
1314 shl R_TMP6 = R_TMP6, 12
1315 }
1317 {.mfi
1318 nop.m 0
1319 // y^2/2
1320 fma.s1 F_Y2_2 = F_Y2, F_05, f0
1321 nop.i 0;;
1322 }
1325 {.mfi
1326 // load c6 = -33*7/16
1327 setf.s F_CS6 = R_TMP6
1328 // eliminate lower bits from y'
1329 fand F_T = F_T1, F_ANDMASK
1330 // c5 = 63/8
1331 shl R_TMP7 = R_TMP7, 16
1332 }
1334 {.mfb
1335 // r3 = load start address to polynomial coefficients
1336 ld8 r3 = [r3]
1337 // 1-(1-s^2)_s-s^2
1338 fnma.s1 F_DS = f8, f8, F_DS
1339 // p9 = 1 if s is a special input (NaN, or |s|> = 1)
1340 (p9) br.cond.spnt ASINL_SPECIAL_CASES;;
1341 }
1343 {.mmf
1344 // get exponent, significand of y' (in single prec.)
1345 getf.s R_TMP = F_T1
1346 // load c3 = -3/2
1347 setf.s F_CS2 = R_TMP5
1348 // y*(1-s^2)
1349 fma.s1 F_Y1S2 = F_Y, F_1S2, f0;;
1350 }
1353 {.mfi
1354 nop.m 0
1355 // x' = (y^2/2)*(1-(s^2)_s)-0.5
1356 fms.s1 F_XL = F_Y2_2, F_S_1S2S, F_05
1357 nop.i 0
1358 }
1360 {.mfi
1361 nop.m 0
1362 // s^2-(s^2)_s
1363 fms.s1 F_S_DS2 = f8, f8, F_S2
1364 nop.i 0;;
1365 }
1368 {.mfi
1369 nop.m 0
1370 // if s<0, set s = -s
1371 (p6) fnma.s1 f8 = f8, f1, f0
1372 nop.i 0;;
1373 }
1375 {.mfi
1376 // load c5 = 63/8
1377 setf.s F_CS5 = R_TMP7
1378 // x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2
1379 fma.s1 F_X = F_DS, F_Y2, F_X
1380 // for t = 2^k*1.b1 b2.., get 7-k|b1.. b6
1381 extr.u R_INDEX = R_TMP, 17, 9;;
1382 }
1385 {.mmi
1386 // index = (4-exponent)|b1 b2.. b6
1387 sub R_INDEX = R_INDEX, R_BIAS
1388 nop.m 0
1389 // get exponent of y
1390 shr.u R_TMP2 = R_TMP, 23;;
1391 }
1393 {.mmi
1394 // load C3
1395 ldfe F_C3 = [r3], 16
1396 // set p8 = 1 if y'<2^{-4}
1397 cmp.gt p8, p0 = 0x7b, R_TMP2
1398 // shift R_INDEX by 5
1399 shl R_INDEX = R_INDEX, 5;;
1400 }
1403 {.mfb
1404 // get table index for sqrt(1-t^2)
1405 add r2 = r2, R_INDEX
1406 // get t = 2^k*1.b1 b2.. b7 1
1407 for F_T = F_T, F_ORMASK
1408 (p8) br.cond.spnt VERY_LARGE_INPUT;;
1409 }
1413 {.mmf
1414 // load C5
1415 ldfe F_C5 = [r3], 16
1416 // load 1/(1-t^2)
1417 ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16
1418 // x = ((1-s^2)*y^2-1)/2
1419 fma.s1 F_X = F_X, F_05, f0;;
1420 }
1424 {.mmf
1425 nop.m 0
1426 // C7, C9
1427 ldfpd F_C7, F_C9 = [r3], 16
1428 // set correct exponent for t
1429 fmerge.se F_T = F_T1, F_T;;
1430 }
1434 {.mfi
1435 // pi/2 (low, high)
1436 ldfpd F_PI2_LO, F_PI2_HI = [r3]
1437 // c9*x+c8
1438 fma.s1 F_S89 = F_X, F_CS9, F_CS8
1439 nop.i 0
1440 }
1442 {.mfi
1443 nop.m 0
1444 // x^2
1445 fma.s1 F_X2 = F_X, F_X, f0
1446 nop.i 0;;
1447 }
1450 {.mfi
1451 nop.m 0
1452 // y*(1-s^2)*x
1453 fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
1454 nop.i 0
1455 }
1457 {.mfi
1458 nop.m 0
1459 // c7*x+c6
1460 fma.s1 F_S67 = F_X, F_CS7, F_CS6
1461 nop.i 0;;
1462 }
1465 {.mfi
1466 nop.m 0
1467 // 1-x
1468 fnma.s1 F_1X = F_X, f1, f1
1469 nop.i 0
1470 }
1472 {.mfi
1473 nop.m 0
1474 // c3*x+c2
1475 fma.s1 F_S23 = F_X, F_CS3, F_CS2
1476 nop.i 0;;
1477 }
1480 {.mfi
1481 nop.m 0
1482 // 1-t^2
1483 fnma.s1 F_1T2 = F_T, F_T, f1
1484 nop.i 0
1485 }
1487 {.mfi
1488 // load asin(t)_high, asin(t)_low
1489 ldfpd F_ATHI, F_ATLO = [r2]
1490 // c5*x+c4
1491 fma.s1 F_S45 = F_X, F_CS5, F_CS4
1492 nop.i 0;;
1493 }
1497 {.mfi
1498 nop.m 0
1499 // t*s
1500 fma.s1 F_TS = F_T, f8, f0
1501 nop.i 0
1502 }
1504 {.mfi
1505 nop.m 0
1506 // 0.5/(1-t^2)
1507 fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
1508 nop.i 0;;
1509 }
1511 {.mfi
1512 nop.m 0
1513 // z~sqrt(1-t^2), rounded to 24 significant bits
1514 fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0
1515 nop.i 0
1516 }
1518 {.mfi
1519 nop.m 0
1520 // sqrt(1-t^2)
1521 fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
1522 nop.i 0;;
1523 }
1526 {.mfi
1527 nop.m 0
1528 // y*(1-s^2)*x^2
1529 fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
1530 nop.i 0
1531 }
1533 {.mfi
1534 nop.m 0
1535 // x^4
1536 fma.s1 F_X4 = F_X2, F_X2, f0
1537 nop.i 0;;
1538 }
1541 {.mfi
1542 nop.m 0
1543 // s*t rounded to 24 significant bits
1544 fma.s.s1 F_TSS = F_T, f8, f0
1545 nop.i 0
1546 }
1548 {.mfi
1549 nop.m 0
1550 // c9*x^3+..+c6
1551 fma.s1 F_S69 = F_X2, F_S89, F_S67
1552 nop.i 0;;
1553 }
1556 {.mfi
1557 nop.m 0
1558 // ST = (t^2-1+s^2) rounded to 24 significant bits
1559 fms.s.s1 F_ST = f8, f8, F_1T2
1560 nop.i 0
1561 }
1563 {.mfi
1564 nop.m 0
1565 // c5*x^3+..+c2
1566 fma.s1 F_S25 = F_X2, F_S45, F_S23
1567 nop.i 0;;
1568 }
1571 {.mfi
1572 nop.m 0
1573 // 0.25/(1-t^2)
1574 fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0
1575 nop.i 0
1576 }
1578 {.mfi
1579 nop.m 0
1580 // t*s-sqrt(1-t^2)*(1-s^2)*y
1581 fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS
1582 nop.i 0;;
1583 }
1586 {.mfi
1587 nop.m 0
1588 // z*0.5/(1-t^2)
1589 fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0
1590 nop.i 0
1591 }
1593 {.mfi
1594 nop.m 0
1595 // z^2+t^2-1
1596 fms.s1 F_DZ0 = F_Z, F_Z, F_1T2
1597 nop.i 0;;
1598 }
1601 {.mfi
1602 nop.m 0
1603 // (1-s^2-(1-s^2)_s)*x
1604 fma.s1 F_DS2X = F_X, F_DS, f0
1605 nop.i 0;;
1606 }
1609 {.mfi
1610 nop.m 0
1611 // t*s-(t*s)_s
1612 fms.s1 F_DTS = F_T, f8, F_TSS
1613 nop.i 0
1614 }
1616 {.mfi
1617 nop.m 0
1618 // c9*x^7+..+c2
1619 fma.s1 F_S29 = F_X4, F_S69, F_S25
1620 nop.i 0;;
1621 }
1624 {.mfi
1625 nop.m 0
1626 // y*z
1627 fma.s1 F_YZ = F_Z, F_Y, f0
1628 nop.i 0
1629 }
1631 {.mfi
1632 nop.m 0
1633 // t^2
1634 fma.s1 F_T2 = F_T, F_T, f0
1635 nop.i 0;;
1636 }
1639 {.mfi
1640 nop.m 0
1641 // 1-t^2+ST
1642 fma.s1 F_1T2_ST = F_ST, f1, F_1T2
1643 nop.i 0;;
1644 }
1647 {.mfi
1648 nop.m 0
1649 // y*(1-s^2)(1-x)
1650 fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0
1651 nop.i 0
1652 }
1654 {.mfi
1655 nop.m 0
1656 // dz ~ sqrt(1-t^2)-z
1657 fma.s1 F_DZ = F_DZ0, F_ZE, f0
1658 nop.i 0;;
1659 }
1662 {.mfi
1663 nop.m 0
1664 // -1+correction for sqrt(1-t^2)-z
1665 fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0
1666 nop.i 0;;
1667 }
1670 {.mfi
1671 nop.m 0
1672 // (PS29*x^2+x)*y*(1-s^2)
1673 fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
1674 nop.i 0;;
1675 }
1678 {.mfi
1679 nop.m 0
1680 // z*y*(1-s^2)_s
1681 fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0
1682 nop.i 0
1683 }
1685 {.mfi
1686 nop.m 0
1687 // s^2-(1-t^2+ST)
1688 fms.s1 F_1T2_ST = f8, f8, F_1T2_ST
1689 nop.i 0;;
1690 }
1693 {.mfi
1694 nop.m 0
1695 // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x
1696 fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS
1697 nop.i 0
1698 }
1700 {.mfi
1701 nop.m 0
1702 // dz*y*(1-s^2)*(1-x)
1703 fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0
1704 nop.i 0;;
1705 }
1708 {.mfi
1709 nop.m 0
1710 // R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19
1711 // (used for polynomial evaluation)
1712 fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS
1713 nop.i 0;;
1714 }
1717 {.mfi
1718 nop.m 0
1719 // (PS29*x^2)*y*(1-s^2)
1720 fma.s1 F_S29 = F_Y1S2X2, F_S29, f0
1721 nop.i 0
1722 }
1724 {.mfi
1725 nop.m 0
1726 // apply correction to dz*y*(1-s^2)*(1-x)
1727 fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM
1728 nop.i 0;;
1729 }
1732 {.mfi
1733 nop.m 0
1734 // R^2
1735 fma.s1 F_R2 = F_R, F_R, f0
1736 nop.i 0;;
1737 }
1740 {.mfi
1741 nop.m 0
1742 // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x)
1743 fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS
1744 nop.i 0;;
1745 }
1748 {.mfi
1749 nop.m 0
1750 // c7+c9*R^2
1751 fma.s1 F_P79 = F_C9, F_R2, F_C7
1752 nop.i 0
1753 }
1755 {.mfi
1756 nop.m 0
1757 // c3+c5*R^2
1758 fma.s1 F_P35 = F_C5, F_R2, F_C3
1759 nop.i 0;;
1760 }
1762 {.mfi
1763 nop.m 0
1764 // asin(t)_low-(pi/2)_low
1765 fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO
1766 nop.i 0
1767 }
1769 {.mfi
1770 nop.m 0
1771 // R^4
1772 fma.s1 F_R4 = F_R2, F_R2, f0
1773 nop.i 0;;
1774 }
1776 {.mfi
1777 nop.m 0
1778 // R^3
1779 fma.s1 F_R3 = F_R2, F_R, f0
1780 nop.i 0;;
1781 }
1784 {.mfi
1785 nop.m 0
1786 // (t*s)_s-t^2*y*z
1787 fnma.s1 F_TSS = F_T2, F_YZ, F_TSS
1788 nop.i 0
1789 }
1791 {.mfi
1792 nop.m 0
1793 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)
1794 fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM
1795 nop.i 0;;
1796 }
1799 {.mfi
1800 nop.m 0
1801 // (pi/2)_hi-asin(t)_hi
1802 fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI
1803 nop.i 0
1804 }
1806 {.mfi
1807 nop.m 0
1808 // c3+c5*R^2+c7*R^4+c9*R^6
1809 fma.s1 F_P39 = F_P79, F_R4, F_P35
1810 nop.i 0;;
1811 }
1814 {.mfi
1815 nop.m 0
1816 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+
1817 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29
1818 fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM
1819 nop.i 0;;
1820 }
1823 {.mfi
1824 nop.m 0
1825 // (t*s)_s-t^2*y*z+z*y*ST
1826 fma.s1 F_TSS = F_YZ, F_ST, F_TSS
1827 nop.i 0
1828 }
1830 {.mfi
1831 nop.m 0
1832 // -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1833 fms.s1 F_P39 = F_P39, F_R3, F_ATLO
1834 nop.i 0;;
1835 }
1838 {.mfi
1839 nop.m 0
1840 // if s<0, change sign of F_ATHI
1841 (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
1842 nop.i 0
1843 }
1845 {.mfi
1846 nop.m 0
1847 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1848 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 +
1849 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1850 fma.s1 F_DZ_TERM = F_P39, f1, F_DZ_TERM
1851 nop.i 0;;
1852 }
1855 {.mfi
1856 nop.m 0
1857 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1858 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
1859 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1860 fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM
1861 nop.i 0;;
1862 }
1865 {.mfi
1866 nop.m 0
1867 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1868 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
1869 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) +
1870 // + (t*s)_s-t^2*y*z+z*y*ST
1871 fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM
1872 nop.i 0;;
1873 }
1876 .pred.rel "mutex", p6, p11
1877 {.mfi
1878 nop.m 0
1879 // result: add high part of pi/2-table value
1880 // s>0 in this case
1881 (p11) fma.s0 f8 = F_DZ_TERM, f1, F_ATHI
1882 nop.i 0
1883 }
1885 {.mfb
1886 nop.m 0
1887 // result: add high part of pi/2-table value
1888 // if s<0
1889 (p6) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI
1890 br.ret.sptk b0;;
1891 }
1898 SMALL_S:
1900 // use 15-term polynomial approximation
1902 {.mmi
1903 // r3 = pointer to polynomial coefficients
1904 addl r3 = @ltoff(poly_coeffs), gp;;
1905 // load start address for coefficients
1906 ld8 r3 = [r3]
1907 mov R_TMP = 0x3fbf;;
1908 }
1911 {.mmi
1912 add r2 = 64, r3
1913 ldfe F_C3 = [r3], 16
1914 // p7 = 1 if |s|<2^{-64} (exponent of s<bias-64)
1915 cmp.lt p7, p0 = R_EXP0, R_TMP;;
1916 }
1918 {.mmf
1919 ldfe F_C5 = [r3], 16
1920 ldfpd F_C11, F_C13 = [r2], 16
1921 // 2^{-128}
1922 fma.s1 F_2M128 = F_2M64, F_2M64, f0;;
1923 }
1925 {.mmf
1926 ldfpd F_C7, F_C9 = [r3]
1927 ldfpd F_C15, F_C17 = [r2]
1928 // if |s|<2^{-64}, return s+2^{-128}*s
1929 (p7) fma.s0 f8 = f8, F_2M128, f8;;
1930 }
1934 {.mfb
1935 nop.m 0
1936 // s^2
1937 fma.s1 F_R2 = f8, f8, f0
1938 // if |s|<2^{-64}, return s
1939 (p7) br.ret.spnt b0;;
1940 }
1943 {.mfi
1944 nop.m 0
1945 // s^3
1946 fma.s1 F_R3 = f8, F_R2, f0
1947 nop.i 0
1948 }
1950 {.mfi
1951 nop.m 0
1952 // s^4
1953 fma.s1 F_R4 = F_R2, F_R2, f0
1954 nop.i 0;;
1955 }
1958 {.mfi
1959 nop.m 0
1960 // c3+c5*s^2
1961 fma.s1 F_P35 = F_C5, F_R2, F_C3
1962 nop.i 0
1963 }
1965 {.mfi
1966 nop.m 0
1967 // c11+c13*s^2
1968 fma.s1 F_P1113 = F_C13, F_R2, F_C11
1969 nop.i 0;;
1970 }
1973 {.mfi
1974 nop.m 0
1975 // c7+c9*s^2
1976 fma.s1 F_P79 = F_C9, F_R2, F_C7
1977 nop.i 0
1978 }
1980 {.mfi
1981 nop.m 0
1982 // c15+c17*s^2
1983 fma.s1 F_P1517 = F_C17, F_R2, F_C15
1984 nop.i 0;;
1985 }
1988 {.mfi
1989 nop.m 0
1990 // s^8
1991 fma.s1 F_R8 = F_R4, F_R4, f0
1992 nop.i 0;;
1993 }
1996 {.mfi
1997 nop.m 0
1998 // c3+c5*s^2+c7*s^4+c9*s^6
1999 fma.s1 F_P39 = F_P79, F_R4, F_P35
2000 nop.i 0
2001 }
2003 {.mfi
2004 nop.m 0
2005 // c11+c13*s^2+c15*s^4+c17*s^6
2006 fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
2007 nop.i 0;;
2008 }
2011 {.mfi
2012 nop.m 0
2013 // c3+..+c17*s^14
2014 fma.s1 F_P317 = F_R8, F_P1117, F_P39
2015 nop.i 0;;
2016 }
2019 {.mfb
2020 nop.m 0
2021 // result
2022 fma.s0 f8 = F_P317, F_R3, f8
2023 br.ret.sptk b0;;
2024 }
2027 {.mfb
2028 nop.m 0
2029 fma.s0 f8 = F_P317, F_R3, f0//F_P317, F_R3, F_S29
2030 // nop.f 0//fma.s0 f8 = f13, f6, f0
2031 br.ret.sptk b0;;
2032 }
2038 VERY_LARGE_INPUT:
2040 {.mfi
2041 nop.m 0
2042 // s rounded to 24 significant bits
2043 fma.s.s1 F_S = f8, f1, f0
2044 nop.i 0
2045 }
2047 {.mfi
2048 // load C5
2049 ldfe F_C5 = [r3], 16
2050 // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2
2051 fnma.s1 F_X = F_S_DS2, F_Y2_2, F_XL
2052 nop.i 0;;
2053 }
2057 {.mmf
2058 nop.m 0
2059 // C7, C9
2060 ldfpd F_C7, F_C9 = [r3], 16
2061 nop.f 0;;
2062 }
2066 {.mfi
2067 // pi/2 (low, high)
2068 ldfpd F_PI2_LO, F_PI2_HI = [r3], 16
2069 // c9*x+c8
2070 fma.s1 F_S89 = F_X, F_CS9, F_CS8
2071 nop.i 0
2072 }
2074 {.mfi
2075 nop.m 0
2076 // x^2
2077 fma.s1 F_X2 = F_X, F_X, f0
2078 nop.i 0;;
2079 }
2082 {.mfi
2083 nop.m 0
2084 // y*(1-s^2)*x
2085 fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
2086 nop.i 0
2087 }
2089 {.mfi
2090 // C11, C13
2091 ldfpd F_C11, F_C13 = [r3], 16
2092 // c7*x+c6
2093 fma.s1 F_S67 = F_X, F_CS7, F_CS6
2094 nop.i 0;;
2095 }
2098 {.mfi
2099 // C15, C17
2100 ldfpd F_C15, F_C17 = [r3], 16
2101 // c3*x+c2
2102 fma.s1 F_S23 = F_X, F_CS3, F_CS2
2103 nop.i 0;;
2104 }
2107 {.mfi
2108 nop.m 0
2109 // c5*x+c4
2110 fma.s1 F_S45 = F_X, F_CS5, F_CS4
2111 nop.i 0;;
2112 }
2115 {.mfi
2116 nop.m 0
2117 // (s_s)^2
2118 fma.s1 F_DS = F_S, F_S, f0
2119 nop.i 0
2120 }
2122 {.mfi
2123 nop.m 0
2124 // 1-(s_s)^2
2125 fnma.s1 F_1S2_S = F_S, F_S, f1
2126 nop.i 0;;
2127 }
2130 {.mfi
2131 nop.m 0
2132 // y*(1-s^2)*x^2
2133 fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
2134 nop.i 0
2135 }
2137 {.mfi
2138 nop.m 0
2139 // x^4
2140 fma.s1 F_X4 = F_X2, F_X2, f0
2141 nop.i 0;;
2142 }
2145 {.mfi
2146 nop.m 0
2147 // c9*x^3+..+c6
2148 fma.s1 F_S69 = F_X2, F_S89, F_S67
2149 nop.i 0;;
2150 }
2153 {.mfi
2154 nop.m 0
2155 // c5*x^3+..+c2
2156 fma.s1 F_S25 = F_X2, F_S45, F_S23
2157 nop.i 0;;
2158 }
2161 {.mfi
2162 nop.m 0
2163 // ((s_s)^2-s^2)
2164 fnma.s1 F_DS = f8, f8, F_DS
2165 nop.i 0
2166 }
2168 {.mfi
2169 nop.m 0
2170 // (pi/2)_high-y*(1-(s_s)^2)
2171 fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI
2172 nop.i 0;;
2173 }
2176 {.mfi
2177 nop.m 0
2178 // c9*x^7+..+c2
2179 fma.s1 F_S29 = F_X4, F_S69, F_S25
2180 nop.i 0;;
2181 }
2184 {.mfi
2185 nop.m 0
2186 // -(y*(1-(s_s)^2))_high
2187 fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI
2188 nop.i 0;;
2189 }
2192 {.mfi
2193 nop.m 0
2194 // (PS29*x^2+x)*y*(1-s^2)
2195 fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
2196 nop.i 0;;
2197 }
2200 {.mfi
2201 nop.m 0
2202 // y*(1-(s_s)^2)-(y*(1-s^2))_high
2203 fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI
2204 nop.i 0;;
2205 }
2209 {.mfi
2210 nop.m 0
2211 // R ~ sqrt(1-s^2)
2212 // (used for polynomial evaluation)
2213 fnma.s1 F_R = F_S19, f1, F_Y1S2
2214 nop.i 0;;
2215 }
2218 {.mfi
2219 nop.m 0
2220 // y*(1-s^2)-(y*(1-s^2))_high
2221 fma.s1 F_DS2 = F_Y, F_DS, F_DS2
2222 nop.i 0
2223 }
2225 {.mfi
2226 nop.m 0
2227 // (pi/2)_low+(PS29*x^2)*y*(1-s^2)
2228 fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO
2229 nop.i 0;;
2230 }
2234 {.mfi
2235 nop.m 0
2236 // R^2
2237 fma.s1 F_R2 = F_R, F_R, f0
2238 nop.i 0;;
2239 }
2242 {.mfi
2243 nop.m 0
2244 // (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)
2245 fms.s1 F_S29 = F_S29, f1, F_DS2
2246 nop.i 0;;
2247 }
2250 {.mfi
2251 nop.m 0
2252 // c7+c9*R^2
2253 fma.s1 F_P79 = F_C9, F_R2, F_C7
2254 nop.i 0
2255 }
2257 {.mfi
2258 nop.m 0
2259 // c3+c5*R^2
2260 fma.s1 F_P35 = F_C5, F_R2, F_C3
2261 nop.i 0;;
2262 }
2266 {.mfi
2267 nop.m 0
2268 // R^4
2269 fma.s1 F_R4 = F_R2, F_R2, f0
2270 nop.i 0
2271 }
2273 {.mfi
2274 nop.m 0
2275 // R^3
2276 fma.s1 F_R3 = F_R2, F_R, f0
2277 nop.i 0;;
2278 }
2281 {.mfi
2282 nop.m 0
2283 // c11+c13*R^2
2284 fma.s1 F_P1113 = F_C13, F_R2, F_C11
2285 nop.i 0
2286 }
2288 {.mfi
2289 nop.m 0
2290 // c15+c17*R^2
2291 fma.s1 F_P1517 = F_C17, F_R2, F_C15
2292 nop.i 0;;
2293 }
2296 {.mfi
2297 nop.m 0
2298 // (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x
2299 fma.s1 F_S29 = F_Y1S2, F_X, F_S29
2300 nop.i 0;;
2301 }
2304 {.mfi
2305 nop.m 0
2306 // c11+c13*R^2+c15*R^4+c17*R^6
2307 fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
2308 nop.i 0
2309 }
2311 {.mfi
2312 nop.m 0
2313 // c3+c5*R^2+c7*R^4+c9*R^6
2314 fma.s1 F_P39 = F_P79, F_R4, F_P35
2315 nop.i 0;;
2316 }
2319 {.mfi
2320 nop.m 0
2321 // R^8
2322 fma.s1 F_R8 = F_R4, F_R4, f0
2323 nop.i 0;;
2324 }
2327 {.mfi
2328 nop.m 0
2329 // c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14
2330 fma.s1 F_P317 = F_P1117, F_R8, F_P39
2331 nop.i 0;;
2332 }
2335 {.mfi
2336 nop.m 0
2337 // (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
2338 // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
2339 fnma.s1 F_S29 = F_P317, F_R3, F_S29
2340 nop.i 0;;
2341 }
2343 {.mfi
2344 nop.m 0
2345 // set sign
2346 (p6) fnma.s1 F_S29 = F_S29, f1, f0
2347 nop.i 0
2348 }
2350 {.mfi
2351 nop.m 0
2352 (p6) fnma.s1 F_HI = F_HI, f1, f0
2353 nop.i 0;;
2354 }
2357 {.mfb
2358 nop.m 0
2359 // Result:
2360 // (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
2361 // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
2362 // +(pi/2)_high-(y*(1-s^2))_high
2363 fma.s0 f8 = F_S29, f1, F_HI
2364 br.ret.sptk b0;;
2365 }
2375 ASINL_SPECIAL_CASES:
2377 {.mfi
2378 alloc r32 = ar.pfs, 1, 4, 4, 0
2379 // check if the input is a NaN, or unsupported format
2380 // (i.e. not infinity or normal/denormal)
2381 fclass.nm p7, p8 = f8, 0x3f
2382 // pointer to pi/2
2383 add r3 = 48, r3;;
2384 }
2387 {.mfi
2388 // load pi/2
2389 ldfpd F_PI2_HI, F_PI2_LO = [r3]
2390 // get |s|
2391 fmerge.s F_S = f0, f8
2392 nop.i 0
2393 }
2395 {.mfb
2396 nop.m 0
2397 // if NaN, quietize it, and return
2398 (p7) fma.s0 f8 = f8, f1, f0
2399 (p7) br.ret.spnt b0;;
2400 }
2403 {.mfi
2404 nop.m 0
2405 // |s| = 1 ?
2406 fcmp.eq.s0 p9, p0 = F_S, f1
2407 nop.i 0
2408 }
2410 {.mfi
2411 nop.m 0
2412 // load FR_X
2413 fma.s1 FR_X = f8, f1, f0
2414 // load error tag
2415 mov GR_Parameter_TAG = 60;;
2416 }
2419 {.mfb
2420 nop.m 0
2421 // change sign if s = -1
2422 (p6) fnma.s1 F_PI2_HI = F_PI2_HI, f1, f0
2423 nop.b 0
2424 }
2426 {.mfb
2427 nop.m 0
2428 // change sign if s = -1
2429 (p6) fnma.s1 F_PI2_LO = F_PI2_LO, f1, f0
2430 nop.b 0;;
2431 }
2433 {.mfb
2434 nop.m 0
2435 // if s = 1, result is pi/2
2436 (p9) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
2437 // return if |s| = 1
2438 (p9) br.ret.sptk b0;;
2439 }
2442 {.mfi
2443 nop.m 0
2444 // get Infinity
2445 frcpa.s1 FR_RESULT, p0 = f1, f0
2446 nop.i 0;;
2447 }
2450 {.mfi
2451 nop.m 0
2452 // return QNaN indefinite (0*Infinity)
2453 fma.s0 FR_RESULT = f0, FR_RESULT, f0
2454 nop.i 0;;
2455 }
2458 GLOBAL_LIBM_END(asinl)
2459 libm_alias_ldouble_other (asin, asin)
2463 LOCAL_LIBM_ENTRY(__libm_error_region)
2464 .prologue
2465 // (1)
2466 { .mfi
2467 add GR_Parameter_Y=-32,sp // Parameter 2 value
2468 nop.f 0
2469 .save ar.pfs,GR_SAVE_PFS
2470 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
2471 }
2472 { .mfi
2473 .fframe 64
2474 add sp=-64,sp // Create new stack
2475 nop.f 0
2476 mov GR_SAVE_GP=gp // Save gp
2477 };;
2480 // (2)
2481 { .mmi
2482 stfe [GR_Parameter_Y] = f1,16 // Store Parameter 2 on stack
2483 add GR_Parameter_X = 16,sp // Parameter 1 address
2484 .save b0, GR_SAVE_B0
2485 mov GR_SAVE_B0=b0 // Save b0
2486 };;
2488 .body
2489 // (3)
2490 { .mib
2491 stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
2492 add GR_Parameter_RESULT = 0,GR_Parameter_Y
2493 nop.b 0 // Parameter 3 address
2494 }
2495 { .mib
2496 stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
2497 add GR_Parameter_Y = -16,GR_Parameter_Y
2498 br.call.sptk b0=__libm_error_support# // Call error handling function
2499 };;
2500 { .mmi
2501 nop.m 0
2502 nop.m 0
2503 add GR_Parameter_RESULT = 48,sp
2504 };;
2506 // (4)
2507 { .mmi
2508 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
2509 .restore sp
2510 add sp = 64,sp // Restore stack pointer
2511 mov b0 = GR_SAVE_B0 // Restore return address
2512 };;
2514 { .mib
2515 mov gp = GR_SAVE_GP // Restore gp
2516 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
2517 br.ret.sptk b0 // Return
2518 };;
2520 LOCAL_LIBM_END(__libm_error_region)
2522 .type __libm_error_support#,@function
2523 .global __libm_error_support#