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MF		 1.file "acosl.s"
2
3
4// Copyright (c) 2001 - 2003, Intel Corporation
5// All rights reserved.
6//
7// Contributed 2001 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.
23
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// 08/28/01 New 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 acosl(long double)
49//
50// Overview of operation
51//==============================================================
52// Background
53//
54// Implementation
55//
56// For |s| in [2^{-4}, sqrt(2)/2]:
57// Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52
58// acos(s)= pi/2-asin(t)-asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e.
59// r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1)
60// asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9)
61// The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table,
62// along with the high and low parts of asin(t) (stored as two double precision
63// values)
64//
65// |s| in (sqrt(2)/2, sqrt(255/256)):
66// Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6..
67// acos(|s|)= asin(t)-asin(r)
68// acos(-|s|)=pi-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2)
69// To minimize accumulated errors, r is computed as
70// 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+
71// +(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)+
72// +ez*z'*y*(1-s^2)*(1-x),
73// where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits)
74// z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2
75//
76// |s|<2^{-4}: evaluate asin(s) as 17-degree polynomial, return pi/2-asin(s)
77// (or simply return pi/2-s, if|s|<2^{-64})
78//
79// |s| in [sqrt(255/256), 1): acos(|s|)= asin(sqrt(1-s^2))
80// acos(-|s|)= pi-asin(sqrt(1-s^2))
81// use 17-degree polynomial for asin(sqrt(1-s^2)),
82// 9-degree polynomial to evaluate sqrt(1-s^2)
83// High order term is (pi)_high-(y*(1-s^2))_high, for s<0,
84// or y*(1-s^2)_s, for s>0
85//
86
87
88
89// Registers used
90//==============================================================
91// f6-f15, f32-f36
92// r2-r3, r23-r23
93// p6, p7, p8, p12
94//
95
96
97 GR_SAVE_B0= r33
98 GR_SAVE_PFS= r34
99 GR_SAVE_GP= r35 // This reg. can safely be used
100 GR_SAVE_SP= r36
101
102 GR_Parameter_X= r37
103 GR_Parameter_Y= r38
104 GR_Parameter_RESULT= r39
105 GR_Parameter_TAG= r40
106
107 FR_X= f10
108 FR_Y= f1
109 FR_RESULT= f8
110
111
112
113RODATA
114
115.align 16
116
117LOCAL_OBJECT_START(T_table)
118
119// stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2),
120// asin(t)_high (double precision), asin(t)_low (double precision)
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335data8 0x3fcad2224cf814e0, 0x3c303de5980d071c
336data8 0x85e725e947fbee97, 0xfa4b3015e883dbfe
337data8 0x3fcb13943f7d5f80, 0x3cc29d4eefa5cb1e
338data8 0x8604b8a7144cd054, 0xfa2f90fa9883a543
339data8 0x3fcb550d625bc6a0, 0x3c9e01a746152daf
340data8 0x86229ebff69e2415, 0xfa13ad4e3dfbe1c1
341data8 0x3fcb968dc9195ea0, 0x3ccc091bd73ae518
342data8 0x8640d89acf78858c, 0xf9f784f9e5a1877b
343data8 0x3fcbd815874eb160, 0x3cb5f4b89875e187
344data8 0x865f669fe390c7f5, 0xf9db17e65944eacf
345data8 0x3fcc19a4b0a6f9c0, 0x3cc5c0bc2b0bbf14
346data8 0x867e4938df7dc45f, 0xf9be65fc1f6c2e6e
347data8 0x3fcc5b3b58e061e0, 0x3cc1ca70df8f57e7
348data8 0x869d80d0db7e4c0c, 0xf9a16f237aec427a
349data8 0x3fcc9cd993cc4040, 0x3cbae93acc85eccf
350data8 0x86bd0dd45f4f8265, 0xf98433446a806e70
351data8 0x3fccde7f754f5660, 0x3cb22f70e64568d0
352data8 0x86dcf0b16613e37a, 0xf966b246a8606170
353data8 0x3fcd202d11620fa0, 0x3c962030e5d4c849
354data8 0x86fd29d7624b3d5d, 0xf948ec11a9d4c45b
355data8 0x3fcd61e27c10c0a0, 0x3cc7083c91d59217
356data8 0x871db9b741dbe44a, 0xf92ae08c9eca4941
357data8 0x3fcda39fc97be7c0, 0x3cc9258579e57211
358data8 0x873ea0c3722d6af2, 0xf90c8f9e71633363
359data8 0x3fcde5650dd86d60, 0x3ca4755a9ea582a9
360data8 0x875fdf6fe45529e8, 0xf8edf92dc5875319
361data8 0x3fce27325d6fe520, 0x3cbc1e2b6c1954f9
362data8 0x878176321154e2bc, 0xf8cf1d20f87270b8
363data8 0x3fce6907cca0d060, 0x3cb6ca4804750830
364data8 0x87a36580fe6bccf5, 0xf8affb5e20412199
365data8 0x3fceaae56fdee040, 0x3cad6b310d6fd46c
366data8 0x87c5add5417a5cb9, 0xf89093cb0b7c0233
367data8 0x3fceeccb5bb33900, 0x3cc16e99cedadb20
368data8 0x87e84fa9057914ca, 0xf870e64d40a15036
369data8 0x3fcf2eb9a4bcb600, 0x3cc75ee47c8b09e9
370data8 0x880b4b780f02b709, 0xf850f2c9fdacdf78
371data8 0x3fcf70b05fb02e20, 0x3cad6350d379f41a
372data8 0x882ea1bfc0f228ac, 0xf830b926379e6465
373data8 0x3fcfb2afa158b8a0, 0x3cce0ccd9f829985
374data8 0x885252ff21146108, 0xf810394699fe0e8e
375data8 0x3fcff4b77e97f3e0, 0x3c9b30faa7a4c703
376data8 0x88765fb6dceebbb3, 0xf7ef730f865f6df0
377data8 0x3fd01b6406332540, 0x3cdc5772c9e0b9bd
378data8 0x88ad1f69be2cc730, 0xf7bdc59bc9cfbd97
379data8 0x3fd04cf8ad203480, 0x3caeef44fe21a74a
380data8 0x88f763f70ae2245e, 0xf77a91c868a9c54e
381data8 0x3fd08f23ce0162a0, 0x3cd6290ab3fe5889
382data8 0x89431fc7bc0c2910, 0xf73642973c91298e
383data8 0x3fd0d1610f0c1ec0, 0x3cc67401a01f08cf
384data8 0x8990573407c7738e, 0xf6f0d71d1d7a2dd6
385data8 0x3fd113b0c65d88c0, 0x3cc7aa4020fe546f
386data8 0x89df0eb108594653, 0xf6aa4e6a05cfdef2
387data8 0x3fd156134ada6fe0, 0x3cc87369da09600c
388data8 0x8a2f4ad16e0ed78a, 0xf662a78900c35249
389data8 0x3fd19888f43427a0, 0x3cc62b220f38e49c
390data8 0x8a811046373e0819, 0xf619e180181d97cc
391data8 0x3fd1db121aed7720, 0x3ca3ede7490b52f4
392data8 0x8ad463df6ea0fa2c, 0xf5cffb504190f9a2
393data8 0x3fd21daf185fa360, 0x3caafad98c1d6c1b
394data8 0x8b294a8cf0488daf, 0xf584f3f54b8604e6
395data8 0x3fd2606046bf95a0, 0x3cdb2d704eeb08fa
396data8 0x8b7fc95f35647757, 0xf538ca65c960b582
397data8 0x3fd2a32601231ec0, 0x3cc661619fa2f126
398data8 0x8bd7e588272276f8, 0xf4eb7d92ff39fccb
399data8 0x3fd2e600a3865760, 0x3c8a2a36a99aca4a
400data8 0x8c31a45bf8e9255e, 0xf49d0c68cd09b689
401data8 0x3fd328f08ad12000, 0x3cb9efaf1d7ab552
402data8 0x8c8d0b520a35eb18, 0xf44d75cd993cfad2
403data8 0x3fd36bf614dcc040, 0x3ccacbb590bef70d
404data8 0x8cea2005d068f23d, 0xf3fcb8a23ab4942b
405data8 0x3fd3af11a079a6c0, 0x3cd9775872cf037d
406data8 0x8d48e837c8cd5027, 0xf3aad3c1e2273908
407data8 0x3fd3f2438d754b40, 0x3ca03304f667109a
408data8 0x8da969ce732f3ac7, 0xf357c60202e2fd7e
409data8 0x3fd4358c3ca032e0, 0x3caecf2504ff1a9d
410data8 0x8e0baad75555e361, 0xf3038e323ae9463a
411data8 0x3fd478ec0fd419c0, 0x3cc64bdc3d703971
412data8 0x8e6fb18807ba877e, 0xf2ae2b1c3a6057f7
413data8 0x3fd4bc6369fa40e0, 0x3cbb7122ec245cf2
414data8 0x8ed5843f4bda74d5, 0xf2579b83aa556f0c
415data8 0x3fd4fff2af11e2c0, 0x3c9cfa2dc792d394
416data8 0x8f3d29862c861fef, 0xf1ffde2612ca1909
417data8 0x3fd5439a4436d000, 0x3cc38d46d310526b
418data8 0x8fa6a81128940b2d, 0xf1a6f1bac0075669
419data8 0x3fd5875a8fa83520, 0x3cd8bf59b8153f8a
420data8 0x901206c1686317a6, 0xf14cd4f2a730d480
421data8 0x3fd5cb33f8cf8ac0, 0x3c9502b5c4d0e431
422data8 0x907f4ca5fe9cf739, 0xf0f186784a125726
423data8 0x3fd60f26e847b120, 0x3cc8a1a5e0acaa33
424data8 0x90ee80fd34aeda5e, 0xf09504ef9a212f18
425data8 0x3fd65333c7e43aa0, 0x3cae5b029cb1f26e
426data8 0x915fab35e37421c6, 0xf0374ef5daab5c45
427data8 0x3fd6975b02b8e360, 0x3cd5aa1c280c45e6
428data8 0x91d2d2f0d894d73c, 0xefd86321822dbb51
429data8 0x3fd6db9d05213b20, 0x3cbecf2c093ccd8b
430data8 0x9248000249200009, 0xef7840021aca5a72
431data8 0x3fd71ffa3cc87fc0, 0x3cb8d273f08d00d9
432data8 0x92bf3a7351f081d2, 0xef16e42021d7cbd5
433data8 0x3fd7647318b1ad20, 0x3cbce099d79cdc46
434data8 0x93388a8386725713, 0xeeb44dfce6820283
435data8 0x3fd7a908093fc1e0, 0x3ccb033ec17a30d9
436data8 0x93b3f8aa8e653812, 0xee507c126774fa45
437data8 0x3fd7edb9803e3c20, 0x3cc10aedb48671eb
438data8 0x94318d99d341ade4, 0xedeb6cd32f891afb
439data8 0x3fd83287f0e9cf80, 0x3c994c0c1505cd2a
440data8 0x94b1523e3dedc630, 0xed851eaa3168f43c
441data8 0x3fd87773cff956e0, 0x3cda3b7bce6a6b16
442data8 0x95334fc20577563f, 0xed1d8ffaa2279669
443data8 0x3fd8bc7d93a70440, 0x3cd4922edc792ce2
444data8 0x95b78f8e8f92f274, 0xecb4bf1fd2be72da
445data8 0x3fd901a5b3b9cf40, 0x3cd3fea1b00f9d0d
446data8 0x963e1b4e63a87c3f, 0xec4aaa6d08694cc1
447data8 0x3fd946eca98f2700, 0x3cdba4032d968ff1
448data8 0x96c6fcef314074fc, 0xebdf502d53d65fea
449data8 0x3fd98c52f024e800, 0x3cbe7be1ab8c95c9
450data8 0x97523ea3eab028b2, 0xeb72aea36720793e
451data8 0x3fd9d1d904239860, 0x3cd72d08a6a22b70
452data8 0x97dfeae6f4ee4a9a, 0xeb04c4096a884e94
453data8 0x3fda177f63e8ef00, 0x3cd818c3c1ebfac7
454data8 0x98700c7c6d85d119, 0xea958e90cfe1efd7
455data8 0x3fda5d468f92a540, 0x3cdf45fbfaa080fe
456data8 0x9902ae7487a9caa1, 0xea250c6224aab21a
457data8 0x3fdaa32f090998e0, 0x3cd715a9353cede4
458data8 0x9997dc2e017a9550, 0xe9b33b9ce2bb7638
459data8 0x3fdae939540d3f00, 0x3cc545c014943439
460data8 0x9a2fa158b29b649b, 0xe9401a573f8aa706
461data8 0x3fdb2f65f63f6c60, 0x3cd4a63c2f2ca8e2
462data8 0x9aca09f835466186, 0xe8cba69df9f0bf35
463data8 0x3fdb75b5773075e0, 0x3cda310ce1b217ec
464data8 0x9b672266ab1e0136, 0xe855de74266193d4
465data8 0x3fdbbc28606babc0, 0x3cdc84b75cca6c44
466data8 0x9c06f7579f0b7bd5, 0xe7debfd2f98c060b
467data8 0x3fdc02bf3d843420, 0x3cd225d967ffb922
468data8 0x9ca995db058cabdc, 0xe76648a991511c6e
469data8 0x3fdc497a9c224780, 0x3cde08101c5b825b
470data8 0x9d4f0b605ce71e88, 0xe6ec76dcbc02d9a7
471data8 0x3fdc905b0c10d420, 0x3cb1abbaa3edf120
472data8 0x9df765b9eecad5e6, 0xe6714846bdda7318
473data8 0x3fdcd7611f4b8a00, 0x3cbf6217ae80aadf
474data8 0x9ea2b320350540fe, 0xe5f4bab71494cd6b
475data8 0x3fdd1e8d6a0d56c0, 0x3cb726e048cc235c
476data8 0x9f51023562fc5676, 0xe576cbf239235ecb
477data8 0x3fdd65e082df5260, 0x3cd9e66872bd5250
478data8 0xa002620915c2a2f6, 0xe4f779b15f5ec5a7
479data8 0x3fddad5b02a82420, 0x3c89743b0b57534b
480data8 0xa0b6e21c2caf9992, 0xe476c1a233a7873e
481data8 0x3fddf4fd84bbe160, 0x3cbf7adea9ee3338
482data8 0xa16e9264cc83a6b2, 0xe3f4a16696608191
483data8 0x3fde3cc8a6ec6ee0, 0x3cce46f5a51f49c6
484data8 0xa22983528f3d8d49, 0xe3711694552da8a8
485data8 0x3fde84bd099a6600, 0x3cdc78f6490a2d31
486data8 0xa2e7c5d2e2e69460, 0xe2ec1eb4e1e0a5fb
487data8 0x3fdeccdb4fc685c0, 0x3cdd3aedb56a4825
488data8 0xa3a96b5599bd2532, 0xe265b74506fbe1c9
489data8 0x3fdf15241f23b3e0, 0x3cd440f3c6d65f65
490data8 0xa46e85d1ae49d7de, 0xe1ddddb499b3606f
491data8 0x3fdf5d98202994a0, 0x3cd6c44bd3fb745a
492data8 0xa53727ca3e11b99e, 0xe1548f662951b00d
493data8 0x3fdfa637fe27bf60, 0x3ca8ad1cd33054dd
494data8 0xa6036453bdc20186, 0xe0c9c9aeabe5e481
495data8 0x3fdfef0467599580, 0x3cc0f1ac0685d78a
496data8 0xa6d34f1969dda338, 0xe03d89d5281e4f81
497data8 0x3fe01bff067d6220, 0x3cc0731e8a9ef057
498data8 0xa7a6fc62f7246ff3, 0xdfafcd125c323f54
499data8 0x3fe04092d1ae3b40, 0x3ccabda24b59906d
500data8 0xa87e811a861df9b9, 0xdf20909061bb9760
501data8 0x3fe0653df0fd9fc0, 0x3ce94c8dcc722278
502data8 0xa959f2d2dd687200, 0xde8fd16a4e5f88bd
503data8 0x3fe08a00c1cae320, 0x3ce6b888bb60a274
504data8 0xaa3967cdeea58bda, 0xddfd8cabd1240d22
505data8 0x3fe0aedba3221c00, 0x3ced5941cd486e46
506data8 0xab904fd587263c84, 0xdd1f4472e1cf64ed
507data8 0x3fe0e651e85229c0, 0x3cdb6701042299b1
508data8 0xad686d44dd5a74bb, 0xdbf173e1f6b46e92
509data8 0x3fe1309cbf4cdb20, 0x3cbf1be7bb3f0ec5
510data8 0xaf524e15640ebee4, 0xdabd54896f1029f6
511data8 0x3fe17b4ee1641300, 0x3ce81dd055b792f1
512data8 0xb14eca24ef7db3fa, 0xd982cb9ae2f47e41
513data8 0x3fe1c66b9ffd6660, 0x3cd98ea31eb5ddc7
514data8 0xb35ec807669920ce, 0xd841bd1b8291d0b6
515data8 0x3fe211f66db3a5a0, 0x3ca480c35a27b4a2
516data8 0xb5833e4755e04dd1, 0xd6fa0bd3150b6930
517data8 0x3fe25df2e05b6c40, 0x3ca4bc324287a351
518data8 0xb7bd34c8000b7bd3, 0xd5ab9939a7d23aa1
519data8 0x3fe2aa64b32f7780, 0x3cba67314933077c
520data8 0xba0dc64d126cc135, 0xd4564563ce924481
521data8 0x3fe2f74fc9289ac0, 0x3cec1a1dc0efc5ec
522data8 0xbc76222cbbfa74a6, 0xd2f9eeed501125a8
523data8 0x3fe344b82f859ac0, 0x3ceeef218de413ac
524data8 0xbef78e31985291a9, 0xd19672e2182f78be
525data8 0x3fe392a22087b7e0, 0x3cd2619ba201204c
526data8 0xc19368b2b0629572, 0xd02baca5427e436a
527data8 0x3fe3e11206694520, 0x3cb5d0b3143fe689
528data8 0xc44b2ae8c6733e51, 0xceb975d60b6eae5d
529data8 0x3fe4300c7e945020, 0x3cbd367143da6582
530data8 0xc7206b894212dfef, 0xcd3fa6326ff0ac9a
531data8 0x3fe47f965d201d60, 0x3ce797c7a4ec1d63
532data8 0xca14e1b0622de526, 0xcbbe13773c3c5338
533data8 0x3fe4cfb4b09d1a20, 0x3cedfadb5347143c
534data8 0xcd2a6825eae65f82, 0xca34913d425a5ae9
535data8 0x3fe5206cc637e000, 0x3ce2798b38e54193
536data8 0xd06301095e1351ee, 0xc8a2f0d3679c08c0
537data8 0x3fe571c42e3d0be0, 0x3ccd7cb9c6c2ca68
538data8 0xd3c0d9f50057adda, 0xc70901152d59d16b
539data8 0x3fe5c3c0c108f940, 0x3ceb6c13563180ab
540data8 0xd74650a98cc14789, 0xc5668e3d4cbf8828
541data8 0x3fe61668a46ffa80, 0x3caa9092e9e3c0e5
542data8 0xdaf5f8579dcc8f8f, 0xc3bb61b3eed42d02
543data8 0x3fe669c251ad69e0, 0x3cccf896ef3b4fee
544data8 0xded29f9f9a6171b4, 0xc20741d7f8e8e8af
545data8 0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d
546data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b
547data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321
548data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91
549data8 0x3fe76840418978a0, 0x3ccda46e85432c3d
550data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3
551data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3
552data8 0xf049183c3f53c39b, 0xbad848720223d3a8
553data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b
554data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48
555data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f
556data8 0xfa718f05adbf2c33, 0xb70432500286b185
557data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9
558data8 0xfff200c3f5489608, 0xb509e6454dca33cc
559data8 0x3fe9211b54441080, 0x3cb789cb53515688
560// The following table entries are not used
561//data8 0x82e138a0fac48700, 0xb3044a513a8e6132
562//data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0
563//data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88
564//data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039
565//data8 0x89377c1387d5b908, 0xaed58e9a09014d5c
566//data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58
567//data8 0x8cad7a2c98dec333, 0xacab929ce114d451
568//data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f
569//data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec
570//data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5
571//data8 0x9446d8191f80dd42, 0xa82ff92687235baf
572//data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e
573//data8 0x98758ba086e4000a, 0xa5dd497a9c184f58
574//data8 0x3febb5f571cb0560, 0x3ce0c7774329a613
575//data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b
576//data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177
577//data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03
578//data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959
579//data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec
580//data8 0x3fece4f404e29b20, 0x3cea3413401132b5
581//data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c
582//data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276
583//data8 0xb265c39cbd80f97a, 0x99553d969fec7beb
584//data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2
585//data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c
586//data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71
587//data8 0xbfea427678945732, 0x93d5990f9ee787af
588//data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5
589//data8 0xc79611399b8c90c5, 0x90f72bde80febc31
590//data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56
591//data8 0xcffa8425040624d7, 0x8e02b4418574ebed
592//data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f
593//data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024
594//data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94
595//data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b
596//data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc
597//data8 0xeea6d733421da0a6, 0x84921bbe64ae029a
598//data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02
599//data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6
600//data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3
601//data8 0x84ac1fcec4203245, 0xfb73a828893df19e
602//data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de
603//data8 0x8ca50621110c60e6, 0xf438a14c158d867c
604//data8 0x3ff12d51caa6b580, 0x3ce6bce9748739b6
605//data8 0x95b8c2062d6f8161, 0xecb3ccdd37b369da
606//data8 0x3ff1717418520340, 0x3ca5c2732533177c
607//data8 0xa0262917caab4ad1, 0xe4dde4ddc81fd119
608//data8 0x3ff1b7d59dd40ba0, 0x3cc4c7c98e870ff5
609//data8 0xac402c688b72f3f4, 0xdcae469be46d4c8d
610//data8 0x3ff200b93cc5a540, 0x3c8dd6dc1bfe865a
611//data8 0xba76968b9eabd9ab, 0xd41a8f3df1115f7f
612//data8 0x3ff24c6f8f6affa0, 0x3cf1acb6d2a7eff7
613//data8 0xcb63c87c23a71dc5, 0xcb161074c17f54ec
614//data8 0x3ff29b5b338b7c80, 0x3ce9b5845f6ec746
615//data8 0xdfe323b8653af367, 0xc19107d99ab27e42
616//data8 0x3ff2edf6fac7f5a0, 0x3cf77f961925fa02
617//data8 0xf93746caaba3e1f1, 0xb777744a9df03bff
618//data8 0x3ff344df237486c0, 0x3cf6ddf5f6ddda43
619//data8 0x8ca77052f6c340f0, 0xacaf476f13806648
620//data8 0x3ff3a0dfa4bb4ae0, 0x3cfee01bbd761bff
621//data8 0xa1a48604a81d5c62, 0xa11575d30c0aae50
622//data8 0x3ff4030b73c55360, 0x3cf1cf0e0324d37c
623//data8 0xbe45074b05579024, 0x9478e362a07dd287
624//data8 0x3ff46ce4c738c4e0, 0x3ce3179555367d12
625//data8 0xe7a08b5693d214ec, 0x8690e3575b8a7c3b
626//data8 0x3ff4e0a887c40a80, 0x3cfbd5d46bfefe69
627//data8 0x94503d69396d91c7, 0xedd2ce885ff04028
628//data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b
629//data8 0xced1d96c5bb209e6, 0xc965278083808702
630//data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c
631//data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd
632//data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e
633//data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4
634//data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb
635LOCAL_OBJECT_END(T_table)
636
637
638
639.align 16
640
641LOCAL_OBJECT_START(poly_coeffs)
642 // C_3
643data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc
644 // C_5
645data8 0x999999999999999a, 0x0000000000003ffb
646 // C_7, C_9
647data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8
648 // pi/2 (low, high)
649data8 0x3C91A62633145C07, 0x3FF921FB54442D18
650 // C_11, C_13
651data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e
652 // C_15, C_17
653data8 0x3f8c99999999999a, 0x3f87a87878787223
654 // pi (low, high)
655data8 0x3CA1A62633145C07, 0x400921FB54442D18
656LOCAL_OBJECT_END(poly_coeffs)
657
658
659R_DBL_S = r21
660R_EXP0 = r22
661R_EXP = r15
662R_SGNMASK = r23
663R_TMP = r24
664R_TMP2 = r25
665R_INDEX = r26
666R_TMP3 = r27
667R_TMP03 = r27
668R_TMP4 = r28
669R_TMP5 = r23
670R_TMP6 = r22
671R_TMP7 = r21
672R_T = r29
673R_BIAS = r20
674
675F_T = f6
676F_1S2 = f7
677F_1S2_S = f9
678F_INV_1T2 = f10
679F_SQRT_1T2 = f11
680F_S2T2 = f12
681F_X = f13
682F_D = f14
683F_2M64 = f15
684
685F_CS2 = f32
686F_CS3 = f33
687F_CS4 = f34
688F_CS5 = f35
689F_CS6 = f36
690F_CS7 = f37
691F_CS8 = f38
692F_CS9 = f39
0347518d
MF		 693F_S23 = f40
694F_S45 = f41
695F_S67 = f42
696F_S89 = f43
697F_S25 = f44
698F_S69 = f45
699F_S29 = f46
700F_X2 = f47
701F_X4 = f48
702F_TSQRT = f49
703F_DTX = f50
704F_R = f51
705F_R2 = f52
706F_R3 = f53
707F_R4 = f54
708
709F_C3 = f55
710F_C5 = f56
711F_C7 = f57
712F_C9 = f58
713F_P79 = f59
714F_P35 = f60
715F_P39 = f61
716
717F_ATHI = f62
718F_ATLO = f63
719
720F_T1 = f64
721F_Y = f65
722F_Y2 = f66
723F_ANDMASK = f67
724F_ORMASK = f68
725F_S = f69
726F_05 = f70
727F_SQRT_1S2 = f71
728F_DS = f72
729F_Z = f73
730F_1T2 = f74
731F_DZ = f75
732F_ZE = f76
733F_YZ = f77
734F_Y1S2 = f78
735F_Y1S2X = f79
736F_1X = f80
737F_ST = f81
738F_1T2_ST = f82
739F_TSS = f83
740F_Y1S2X2 = f84
741F_DZ_TERM = f85
742F_DTS = f86
743F_DS2X = f87
744F_T2 = f88
745F_ZY1S2S = f89
746F_Y1S2_1X = f90
d5efd131 747F_TS = f91
0347518d
MF		 748F_PI2_LO = f92
749F_PI2_HI = f93
750F_S19 = f94
751F_INV1T2_2 = f95
752F_CORR = f96
753F_DZ0 = f97
754
755F_C11 = f98
756F_C13 = f99
d5efd131
MF		 757F_C15 = f100
758F_C17 = f101
759F_P1113 = f102
760F_P1517 = f103
761F_P1117 = f104
762F_P317 = f105
763F_R8 = f106
764F_HI = f107
765F_1S2_HI = f108
766F_DS2 = f109
767F_Y2_2 = f110
768//F_S2 = f111
769//F_S_DS2 = f112
770F_S_1S2S = f113
771F_XL = f114
772F_2M128 = f115
773F_1AS = f116
774F_AS = f117
775
776
777
778.section .text
779GLOBAL_LIBM_ENTRY(acosl)
780
781{.mfi
782 // get exponent, mantissa (rounded to double precision) of s
783 getf.d R_DBL_S = f8
784 // 1-s^2
785 fnma.s1 F_1S2 = f8, f8, f1
786 // r2 = pointer to T_table
787 addl r2 = @ltoff(T_table), gp
788}
789
790{.mfi
791 // sign mask
792 mov R_SGNMASK = 0x20000
793 nop.f 0
794 // bias-63-1
795 mov R_TMP03 = 0xffff-64;;
796}
797
798
799{.mfi
800 // get exponent of s
801 getf.exp R_EXP = f8
802 nop.f 0
803 // R_TMP4 = 2^45
804 shl R_TMP4 = R_SGNMASK, 45-17
805}
806
807{.mlx
808 // load bias-4
809 mov R_TMP = 0xffff-4
810 // load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1)
811 movl R_TMP2 = 0x7fcd413cccfe779a;;
812}
813
814
815{.mfi
816 // load 2^{-64} in FP register
817 setf.exp F_2M64 = R_TMP03
818 nop.f 0
819 // index = (0x7-exponent)|b1 b2.. b6
820 extr.u R_INDEX = R_DBL_S, 46, 9
821}
822
823{.mfi
824 // get t = sign|exponent|b1 b2.. b6 1 x.. x
825 or R_T = R_DBL_S, R_TMP4
826 nop.f 0
827 // R_TMP4 = 2^45-1
828 sub R_TMP4 = R_TMP4, r0, 1;;
829}
830
831
832{.mfi
833 // get t = sign|exponent|b1 b2.. b6 1 0.. 0
834 andcm R_T = R_T, R_TMP4
835 nop.f 0
836 // eliminate sign from R_DBL_S (shift left by 1)
837 shl R_TMP3 = R_DBL_S, 1
838}
839
840{.mfi
841 // R_BIAS = 3*2^6
842 mov R_BIAS = 0xc0
843 nop.f 0
844 // eliminate sign from R_EXP
845 andcm R_EXP0 = R_EXP, R_SGNMASK;;
846}
847
848
849
850{.mfi
851 // load start address for T_table
852 ld8 r2 = [r2]
853 nop.f 0
854 // p8 = 1 if |s|> = sqrt(2)/2
855 cmp.geu p8, p0 = R_TMP3, R_TMP2
856}
857
858{.mlx
859 // p7 = 1 if |s|<2^{-4} (exponent of s<bias-4)
860 cmp.lt p7, p0 = R_EXP0, R_TMP
861 // sqrt coefficient cs8 = -33*13/128
862 movl R_TMP2 = 0xc0568000;;
863}
864
865
866
867{.mbb
868 // load t in FP register
869 setf.d F_T = R_T
870 // if |s|<2^{-4}, take alternate path
871 (p7) br.cond.spnt SMALL_S
872 // if |s|> = sqrt(2)/2, take alternate path
873 (p8) br.cond.sptk LARGE_S
874}
875
876{.mlx
877 // index = (4-exponent)|b1 b2.. b6
878 sub R_INDEX = R_INDEX, R_BIAS
879 // sqrt coefficient cs9 = 55*13/128
880 movl R_TMP = 0x40b2c000;;
881}
882
883
884{.mfi
885 // sqrt coefficient cs8 = -33*13/128
886 setf.s F_CS8 = R_TMP2
887 nop.f 0
888 // shift R_INDEX by 5
889 shl R_INDEX = R_INDEX, 5
890}
891
892{.mfi
893 // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
894 mov R_TMP4 = 0xffff - 1
895 nop.f 0
896 // sqrt coefficient cs6 = -21/16
897 mov R_TMP6 = 0xbfa8;;
898}
899
900
901{.mlx
902 // table index
903 add r2 = r2, R_INDEX
904 // sqrt coefficient cs7 = 33/16
905 movl R_TMP2 = 0x40040000;;
906}
907
908
909{.mmi
910 // load cs9 = 55*13/128
911 setf.s F_CS9 = R_TMP
912 // sqrt coefficient cs5 = 7/8
913 mov R_TMP3 = 0x3f60
914 // sqrt coefficient cs6 = 21/16
915 shl R_TMP6 = R_TMP6, 16;;
916}
917
918
919{.mmi
920 // load significand of 1/(1-t^2)
921 ldf8 F_INV_1T2 = [r2], 8
922 // sqrt coefficient cs7 = 33/16
923 setf.s F_CS7 = R_TMP2
924 // sqrt coefficient cs4 = -5/8
925 mov R_TMP5 = 0xbf20;;
926}
927
928
929{.mmi
930 // load significand of sqrt(1-t^2)
931 ldf8 F_SQRT_1T2 = [r2], 8
932 // sqrt coefficient cs6 = 21/16
933 setf.s F_CS6 = R_TMP6
934 // sqrt coefficient cs5 = 7/8
935 shl R_TMP3 = R_TMP3, 16;;
936}
937
938
939{.mmi
940 // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
941 setf.exp F_CS3 = R_TMP4
942 // r3 = pointer to polynomial coefficients
943 addl r3 = @ltoff(poly_coeffs), gp
944 // sqrt coefficient cs4 = -5/8
945 shl R_TMP5 = R_TMP5, 16;;
946}
947
948
949{.mfi
950 // sqrt coefficient cs5 = 7/8
951 setf.s F_CS5 = R_TMP3
952 // d = s-t
953 fms.s1 F_D = f8, f1, F_T
954 // set p6 = 1 if s<0, p11 = 1 if s> = 0
955 cmp.ge p6, p11 = R_EXP, R_DBL_S
956}
957
958{.mfi
959 // r3 = load start address to polynomial coefficients
960 ld8 r3 = [r3]
961 // s+t
962 fma.s1 F_S2T2 = f8, f1, F_T
963 nop.i 0;;
964}
965
966
967{.mfi
968 // sqrt coefficient cs4 = -5/8
969 setf.s F_CS4 = R_TMP5
970 // s^2-t^2
971 fma.s1 F_S2T2 = F_S2T2, F_D, f0
972 nop.i 0;;
973}
974
975
976{.mfi
977 // load C3
978 ldfe F_C3 = [r3], 16
979 // 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2))
980 fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
981 nop.i 0;;
982}
983
984{.mfi
985 // load C_5
986 ldfe F_C5 = [r3], 16
987 // set correct exponent for sqrt(1-t^2)
988 fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
989 nop.i 0;;
990}
991
992
993{.mfi
994 // load C_7, C_9
995 ldfpd F_C7, F_C9 = [r3], 16
996 // x = -(s^2-t^2)/(1-t^2)/2
997 fnma.s1 F_X = F_INV_1T2, F_S2T2, f0
998 nop.i 0;;
999}
1000
1001
1002{.mmf
1003 // load asin(t)_high, asin(t)_low
1004 ldfpd F_ATHI, F_ATLO = [r2]
1005 // load pi/2
1006 ldfpd F_PI2_LO, F_PI2_HI = [r3]
1007 // t*sqrt(1-t^2)
1008 fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0;;
1009}
1010
1011
1012{.mfi
1013 nop.m 0
1014 // cs9*x+cs8
1015 fma.s1 F_S89 = F_CS9, F_X, F_CS8
1016 nop.i 0
1017}
1018
1019{.mfi
1020 nop.m 0
1021 // cs7*x+cs6
1022 fma.s1 F_S67 = F_CS7, F_X, F_CS6
1023 nop.i 0;;
1024}
1025
1026{.mfi
1027 nop.m 0
1028 // cs5*x+cs4
1029 fma.s1 F_S45 = F_CS5, F_X, F_CS4
1030 nop.i 0
1031}
1032
1033{.mfi
1034 nop.m 0
1035 // x*x
1036 fma.s1 F_X2 = F_X, F_X, f0
1037 nop.i 0;;
1038}
1039
1040
1041{.mfi
1042 nop.m 0
1043 // (s-t)-t*x
1044 fnma.s1 F_DTX = F_T, F_X, F_D
1045 nop.i 0
1046}
1047
1048{.mfi
1049 nop.m 0
1050 // cs3*x+cs2 (cs2 = -0.5 = -cs3)
1051 fms.s1 F_S23 = F_CS3, F_X, F_CS3
1052 nop.i 0;;
1053}
1054
1055{.mfi
1056 nop.m 0
1057 // if sign is negative, negate table values: asin(t)_low
1058 (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0
1059 nop.i 0
1060}
1061
1062{.mfi
1063 nop.m 0
1064 // if sign is negative, negate table values: asin(t)_high
1065 (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
1066 nop.i 0;;
1067}
1068
1069
1070{.mfi
1071 nop.m 0
1072 // cs9*x^3+cs8*x^2+cs7*x+cs6
1073 fma.s1 F_S69 = F_S89, F_X2, F_S67
1074 nop.i 0
1075}
1076
1077{.mfi
1078 nop.m 0
1079 // x^4
1080 fma.s1 F_X4 = F_X2, F_X2, f0
1081 nop.i 0;;
1082}
1083
1084
1085{.mfi
1086 nop.m 0
1087 // t*sqrt(1-t^2)*x^2
1088 fma.s1 F_TSQRT = F_TSQRT, F_X2, f0
1089 nop.i 0
1090}
1091
1092{.mfi
1093 nop.m 0
1094 // cs5*x^3+cs4*x^2+cs3*x+cs2
1095 fma.s1 F_S25 = F_S45, F_X2, F_S23
1096 nop.i 0;;
1097}
1098
1099
1100{.mfi
1101 nop.m 0
1102 // ((s-t)-t*x)*sqrt(1-t^2)
1103 fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0
1104 nop.i 0;;
1105}
1106
1107{.mfi
1108 nop.m 0
1109 // (pi/2)_high - asin(t)_high
1110 fnma.s1 F_ATHI = F_ATHI, f1, F_PI2_HI
1111 nop.i 0
1112}
1113
1114{.mfi
1115 nop.m 0
1116 // asin(t)_low - (pi/2)_low
1117 fnma.s1 F_ATLO = F_PI2_LO, f1, F_ATLO
1118 nop.i 0;;
1119}
1120
1121
1122{.mfi
1123 nop.m 0
1124 // PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2
1125 fma.s1 F_S29 = F_S69, F_X4, F_S25
1126 nop.i 0;;
1127}
1128
1129
1130
1131{.mfi
1132 nop.m 0
1133 // R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29
1134 fnma.s1 F_R = F_S29, F_TSQRT, F_DTX
1135 nop.i 0;;
1136}
1137
1138
1139{.mfi
1140 nop.m 0
1141 // R^2
1142 fma.s1 F_R2 = F_R, F_R, f0
1143 nop.i 0;;
1144}
1145
1146
1147{.mfi
1148 nop.m 0
1149 // c7+c9*R^2
1150 fma.s1 F_P79 = F_C9, F_R2, F_C7
1151 nop.i 0
1152}
1153
1154{.mfi
1155 nop.m 0
1156 // c3+c5*R^2
1157 fma.s1 F_P35 = F_C5, F_R2, F_C3
1158 nop.i 0;;
1159}
1160
1161{.mfi
1162 nop.m 0
1163 // R^3
1164 fma.s1 F_R4 = F_R2, F_R2, f0
1165 nop.i 0;;
1166}
1167
1168{.mfi
1169 nop.m 0
1170 // R^3
1171 fma.s1 F_R3 = F_R2, F_R, f0
1172 nop.i 0;;
1173}
1174
1175
1176
1177{.mfi
1178 nop.m 0
1179 // c3+c5*R^2+c7*R^4+c9*R^6
1180 fma.s1 F_P39 = F_P79, F_R4, F_P35
1181 nop.i 0;;
1182}
1183
1184
1185{.mfi
1186 nop.m 0
1187 // asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1188 fma.s1 F_P39 = F_P39, F_R3, F_ATLO
1189 nop.i 0;;
1190}
1191
1192
1193{.mfi
1194 nop.m 0
1195 // R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1196 fma.s1 F_P39 = F_P39, f1, F_R
1197 nop.i 0;;
1198}
1199
1200
1201{.mfb
1202 nop.m 0
1203 // result = (pi/2)-asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1204 fnma.s0 f8 = F_P39, f1, F_ATHI
1205 // return
1206 br.ret.sptk b0;;
1207}
1208
1209
1210
1211
1212LARGE_S:
1213
1214{.mfi
1215 // bias-1
1216 mov R_TMP3 = 0xffff - 1
1217 // y ~ 1/sqrt(1-s^2)
1218 frsqrta.s1 F_Y, p7 = F_1S2
1219 // c9 = 55*13*17/128
1220 mov R_TMP4 = 0x10af7b
1221}
1222
1223{.mlx
1224 // c8 = -33*13*15/128
1225 mov R_TMP5 = 0x184923
1226 movl R_TMP2 = 0xff00000000000000;;
1227}
1228
1229{.mfi
1230 // set p6 = 1 if s<0, p11 = 1 if s>0
1231 cmp.ge p6, p11 = R_EXP, R_DBL_S
1232 // 1-s^2
1233 fnma.s1 F_1S2 = f8, f8, f1
1234 // set p9 = 1
1235 cmp.eq p9, p0 = r0, r0;;
1236}
1237
1238
1239{.mfi
1240 // load 0.5
1241 setf.exp F_05 = R_TMP3
1242 // (1-s^2) rounded to single precision
1243 fnma.s.s1 F_1S2_S = f8, f8, f1
1244 // c9 = 55*13*17/128
1245 shl R_TMP4 = R_TMP4, 10
1246}
1247
1248{.mlx
1249 // AND mask for getting t ~ sqrt(1-s^2)
1250 setf.sig F_ANDMASK = R_TMP2
1251 // OR mask
1252 movl R_TMP2 = 0x0100000000000000;;
1253}
1254
1255.pred.rel "mutex", p6, p11
1256{.mfi
1257 nop.m 0
1258 // 1-|s|
1259 (p6) fma.s1 F_1AS = f8, f1, f1
1260 nop.i 0
1261}
1262
1263{.mfi
1264 nop.m 0
1265 // 1-|s|
1266 (p11) fnma.s1 F_1AS = f8, f1, f1
1267 nop.i 0;;
1268}
1269
1270
1271{.mfi
1272 // c9 = 55*13*17/128
1273 setf.s F_CS9 = R_TMP4
1274 // |s|
1275 (p6) fnma.s1 F_AS = f8, f1, f0
1276 // c8 = -33*13*15/128
1277 shl R_TMP5 = R_TMP5, 11
1278}
1279
1280{.mfi
1281 // c7 = 33*13/16
1282 mov R_TMP4 = 0x41d68
1283 // |s|
1284 (p11) fma.s1 F_AS = f8, f1, f0
1285 nop.i 0;;
1286}
1287
1288
1289{.mfi
1290 setf.sig F_ORMASK = R_TMP2
1291 // y^2
1292 fma.s1 F_Y2 = F_Y, F_Y, f0
1293 // c7 = 33*13/16
1294 shl R_TMP4 = R_TMP4, 12
1295}
1296
1297{.mfi
1298 // c6 = -33*7/16
1299 mov R_TMP6 = 0xc1670
1300 // y' ~ sqrt(1-s^2)
1301 fma.s1 F_T1 = F_Y, F_1S2, f0
1302 // c5 = 63/8
1303 mov R_TMP7 = 0x40fc;;
1304}
1305
1306
1307{.mlx
1308 // load c8 = -33*13*15/128
1309 setf.s F_CS8 = R_TMP5
1310 // c4 = -35/8
1311 movl R_TMP5 = 0xc08c0000;;
1312}
1313
1314{.mfi
1315 // r3 = pointer to polynomial coefficients
1316 addl r3 = @ltoff(poly_coeffs), gp
1317 // 1-s-(1-s^2)_s
1318 fnma.s1 F_DS = F_1S2_S, f1, F_1AS
1319 // p9 = 0 if p7 = 1 (p9 = 1 for special cases only)
1320 (p7) cmp.ne p9, p0 = r0, r0
1321}
1322
1323{.mlx
1324 // load c7 = 33*13/16
1325 setf.s F_CS7 = R_TMP4
1326 // c3 = 5/2
1327 movl R_TMP4 = 0x40200000;;
1328}
1329
1330
1331{.mlx
1332 // load c4 = -35/8
1333 setf.s F_CS4 = R_TMP5
1334 // c2 = -3/2
1335 movl R_TMP5 = 0xbfc00000;;
1336}
1337
1338
1339{.mfi
1340 // load c3 = 5/2
1341 setf.s F_CS3 = R_TMP4
1342 // x = (1-s^2)_s*y^2-1
1343 fms.s1 F_X = F_1S2_S, F_Y2, f1
1344 // c6 = -33*7/16
1345 shl R_TMP6 = R_TMP6, 12
1346}
1347
1348{.mfi
1349 nop.m 0
1350 // y^2/2
1351 fma.s1 F_Y2_2 = F_Y2, F_05, f0
1352 nop.i 0;;
1353}
1354
1355
1356{.mfi
1357 // load c6 = -33*7/16
1358 setf.s F_CS6 = R_TMP6
1359 // eliminate lower bits from y'
1360 fand F_T = F_T1, F_ANDMASK
1361 // c5 = 63/8
1362 shl R_TMP7 = R_TMP7, 16
1363}
1364
1365
1366{.mfb
1367 // r3 = load start address to polynomial coefficients
1368 ld8 r3 = [r3]
1369 // 1-(1-s^2)_s-s^2
1370 fma.s1 F_DS = F_AS, F_1AS, F_DS
1371 // p9 = 1 if s is a special input (NaN, or |s|> = 1)
1372 (p9) br.cond.spnt acosl_SPECIAL_CASES;;
1373}
1374
1375{.mmf
1376 // get exponent, significand of y' (in single prec.)
1377 getf.s R_TMP = F_T1
1378 // load c3 = -3/2
1379 setf.s F_CS2 = R_TMP5
1380 // y*(1-s^2)
1381 fma.s1 F_Y1S2 = F_Y, F_1S2, f0;;
1382}
1383
1384
1385
1386{.mfi
1387 nop.m 0
1388 // if s<0, set s = -s
1389 (p6) fnma.s1 f8 = f8, f1, f0
1390 nop.i 0;;
1391}
1392
1393
1394{.mfi
1395 // load c5 = 63/8
1396 setf.s F_CS5 = R_TMP7
1397 // x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2
1398 fma.s1 F_X = F_DS, F_Y2, F_X
1399 // for t = 2^k*1.b1 b2.., get 7-k|b1.. b6
1400 extr.u R_INDEX = R_TMP, 17, 9;;
1401}
1402
1403
1404{.mmi
1405 // index = (4-exponent)|b1 b2.. b6
1406 sub R_INDEX = R_INDEX, R_BIAS
1407 nop.m 0
1408 // get exponent of y
1409 shr.u R_TMP2 = R_TMP, 23;;
1410}
1411
1412{.mmi
1413 // load C3
1414 ldfe F_C3 = [r3], 16
1415 // set p8 = 1 if y'<2^{-4}
1416 cmp.gt p8, p0 = 0x7b, R_TMP2
1417 // shift R_INDEX by 5
1418 shl R_INDEX = R_INDEX, 5;;
1419}
1420
1421
1422{.mfb
1423 // get table index for sqrt(1-t^2)
1424 add r2 = r2, R_INDEX
1425 // get t = 2^k*1.b1 b2.. b7 1
1426 for F_T = F_T, F_ORMASK
1427 (p8) br.cond.spnt VERY_LARGE_INPUT;;
1428}
1429
1430
1431
1432{.mmf
1433 // load C5
1434 ldfe F_C5 = [r3], 16
1435 // load 1/(1-t^2)
1436 ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16
1437 // x = ((1-s^2)*y^2-1)/2
1438 fma.s1 F_X = F_X, F_05, f0;;
1439}
1440
1441
1442
1443{.mmf
1444 nop.m 0
1445 // C7, C9
1446 ldfpd F_C7, F_C9 = [r3], 16
1447 // set correct exponent for t
1448 fmerge.se F_T = F_T1, F_T;;
1449}
1450
1451
1452
1453{.mfi
1454 // get address for loading pi
1455 add r3 = 48, r3
1456 // c9*x+c8
1457 fma.s1 F_S89 = F_X, F_CS9, F_CS8
1458 nop.i 0
1459}
1460
1461{.mfi
1462 nop.m 0
1463 // x^2
1464 fma.s1 F_X2 = F_X, F_X, f0
1465 nop.i 0;;
1466}
1467
1468
1469{.mfi
1470 // pi (low, high)
1471 ldfpd F_PI2_LO, F_PI2_HI = [r3]
1472 // y*(1-s^2)*x
1473 fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
1474 nop.i 0
1475}
1476
1477{.mfi
1478 nop.m 0
1479 // c7*x+c6
1480 fma.s1 F_S67 = F_X, F_CS7, F_CS6
1481 nop.i 0;;
1482}
1483
1484
1485{.mfi
1486 nop.m 0
1487 // 1-x
1488 fnma.s1 F_1X = F_X, f1, f1
1489 nop.i 0
1490}
1491
1492{.mfi
1493 nop.m 0
1494 // c3*x+c2
1495 fma.s1 F_S23 = F_X, F_CS3, F_CS2
1496 nop.i 0;;
1497}
1498
1499
1500{.mfi
1501 nop.m 0
1502 // 1-t^2
1503 fnma.s1 F_1T2 = F_T, F_T, f1
1504 nop.i 0
1505}
1506
1507{.mfi
1508 // load asin(t)_high, asin(t)_low
1509 ldfpd F_ATHI, F_ATLO = [r2]
1510 // c5*x+c4
1511 fma.s1 F_S45 = F_X, F_CS5, F_CS4
1512 nop.i 0;;
1513}
1514
1515
1516
1517{.mfi
1518 nop.m 0
1519 // t*s
1520 fma.s1 F_TS = F_T, f8, f0
1521 nop.i 0
1522}
1523
1524{.mfi
1525 nop.m 0
1526 // 0.5/(1-t^2)
1527 fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
1528 nop.i 0;;
1529}
1530
1531{.mfi
1532 nop.m 0
1533 // z~sqrt(1-t^2), rounded to 24 significant bits
1534 fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0
1535 nop.i 0
1536}
1537
1538{.mfi
1539 nop.m 0
1540 // sqrt(1-t^2)
1541 fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
1542 nop.i 0;;
1543}
1544
1545
1546{.mfi
1547 nop.m 0
1548 // y*(1-s^2)*x^2
1549 fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
1550 nop.i 0
1551}
1552
1553{.mfi
1554 nop.m 0
1555 // x^4
1556 fma.s1 F_X4 = F_X2, F_X2, f0
1557 nop.i 0;;
1558}
1559
1560
1561{.mfi
1562 nop.m 0
1563 // s*t rounded to 24 significant bits
1564 fma.s.s1 F_TSS = F_T, f8, f0
1565 nop.i 0
1566}
1567
1568{.mfi
1569 nop.m 0
1570 // c9*x^3+..+c6
1571 fma.s1 F_S69 = F_X2, F_S89, F_S67
1572 nop.i 0;;
1573}
1574
1575
1576{.mfi
1577 nop.m 0
1578 // ST = (t^2-1+s^2) rounded to 24 significant bits
1579 fms.s.s1 F_ST = f8, f8, F_1T2
1580 nop.i 0
1581}
1582
1583{.mfi
1584 nop.m 0
1585 // c5*x^3+..+c2
1586 fma.s1 F_S25 = F_X2, F_S45, F_S23
1587 nop.i 0;;
1588}
1589
1590
1591{.mfi
1592 nop.m 0
1593 // 0.25/(1-t^2)
1594 fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0
1595 nop.i 0
1596}
1597
1598{.mfi
1599 nop.m 0
1600 // t*s-sqrt(1-t^2)*(1-s^2)*y
1601 fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS
1602 nop.i 0;;
1603}
1604
1605
1606{.mfi
1607 nop.m 0
1608 // z*0.5/(1-t^2)
1609 fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0
1610 nop.i 0
1611}
1612
1613{.mfi
1614 nop.m 0
1615 // z^2+t^2-1
1616 fms.s1 F_DZ0 = F_Z, F_Z, F_1T2
1617 nop.i 0;;
1618}
1619
1620
1621{.mfi
1622 nop.m 0
1623 // (1-s^2-(1-s^2)_s)*x
1624 fma.s1 F_DS2X = F_X, F_DS, f0
1625 nop.i 0;;
1626}
1627
1628
1629{.mfi
1630 nop.m 0
1631 // t*s-(t*s)_s
1632 fms.s1 F_DTS = F_T, f8, F_TSS
1633 nop.i 0
1634}
1635
1636{.mfi
1637 nop.m 0
1638 // c9*x^7+..+c2
1639 fma.s1 F_S29 = F_X4, F_S69, F_S25
1640 nop.i 0;;
1641}
1642
1643
1644{.mfi
1645 nop.m 0
1646 // y*z
1647 fma.s1 F_YZ = F_Z, F_Y, f0
1648 nop.i 0
1649}
1650
1651{.mfi
1652 nop.m 0
1653 // t^2
1654 fma.s1 F_T2 = F_T, F_T, f0
1655 nop.i 0;;
1656}
1657
1658
1659{.mfi
1660 nop.m 0
1661 // 1-t^2+ST
1662 fma.s1 F_1T2_ST = F_ST, f1, F_1T2
1663 nop.i 0;;
1664}
1665
1666
1667{.mfi
1668 nop.m 0
1669 // y*(1-s^2)(1-x)
1670 fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0
1671 nop.i 0
1672}
1673
1674{.mfi
1675 nop.m 0
1676 // dz ~ sqrt(1-t^2)-z
1677 fma.s1 F_DZ = F_DZ0, F_ZE, f0
1678 nop.i 0;;
1679}
1680
1681
1682{.mfi
1683 nop.m 0
1684 // -1+correction for sqrt(1-t^2)-z
1685 fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0
1686 nop.i 0;;
1687}
1688
1689
1690{.mfi
1691 nop.m 0
1692 // (PS29*x^2+x)*y*(1-s^2)
1693 fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
1694 nop.i 0;;
1695}
1696
1697{.mfi
1698 nop.m 0
1699 // z*y*(1-s^2)_s
1700 fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0
1701 nop.i 0
1702}
1703
1704{.mfi
1705 nop.m 0
1706 // s^2-(1-t^2+ST)
1707 fms.s1 F_1T2_ST = f8, f8, F_1T2_ST
1708 nop.i 0;;
1709}
1710
1711
1712{.mfi
1713 nop.m 0
1714 // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x
1715 fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS
1716 nop.i 0
1717}
1718
1719{.mfi
1720 nop.m 0
1721 // dz*y*(1-s^2)*(1-x)
1722 fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0
1723 nop.i 0;;
1724}
1725
1726
1727{.mfi
1728 nop.m 0
1729 // R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19
1730 // (used for polynomial evaluation)
1731 fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS
1732 nop.i 0;;
1733}
1734
1735
1736{.mfi
1737 nop.m 0
1738 // (PS29*x^2)*y*(1-s^2)
1739 fma.s1 F_S29 = F_Y1S2X2, F_S29, f0
1740 nop.i 0
1741}
1742
1743{.mfi
1744 nop.m 0
1745 // apply correction to dz*y*(1-s^2)*(1-x)
1746 fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM
1747 nop.i 0;;
1748}
1749
1750
1751{.mfi
1752 nop.m 0
1753 // R^2
1754 fma.s1 F_R2 = F_R, F_R, f0
1755 nop.i 0;;
1756}
1757
1758
1759{.mfi
1760 nop.m 0
1761 // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x)
1762 fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS
1763 nop.i 0;;
1764}
1765
1766
1767{.mfi
1768 nop.m 0
1769 // c7+c9*R^2
1770 fma.s1 F_P79 = F_C9, F_R2, F_C7
1771 nop.i 0
1772}
1773
1774{.mfi
1775 nop.m 0
1776 // c3+c5*R^2
1777 fma.s1 F_P35 = F_C5, F_R2, F_C3
1778 nop.i 0;;
1779}
1780
1781{.mfi
1782 nop.m 0
1783 // asin(t)_low-(pi)_low (if s<0)
1784 (p6) fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO
1785 nop.i 0
1786}
1787
1788{.mfi
1789 nop.m 0
1790 // R^4
1791 fma.s1 F_R4 = F_R2, F_R2, f0
1792 nop.i 0;;
1793}
1794
1795{.mfi
1796 nop.m 0
1797 // R^3
1798 fma.s1 F_R3 = F_R2, F_R, f0
1799 nop.i 0;;
1800}
1801
1802
1803{.mfi
1804 nop.m 0
1805 // (t*s)_s-t^2*y*z
1806 fnma.s1 F_TSS = F_T2, F_YZ, F_TSS
1807 nop.i 0
1808}
1809
1810{.mfi
1811 nop.m 0
1812 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)
1813 fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM
1814 nop.i 0;;
1815}
1816
1817
1818{.mfi
1819 nop.m 0
1820 // (pi)_hi-asin(t)_hi (if s<0)
1821 (p6) fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI
1822 nop.i 0
1823}
1824
1825{.mfi
1826 nop.m 0
1827 // c3+c5*R^2+c7*R^4+c9*R^6
1828 fma.s1 F_P39 = F_P79, F_R4, F_P35
1829 nop.i 0;;
1830}
1831
1832
1833{.mfi
1834 nop.m 0
1835 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+
1836 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29
1837 fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM
1838 nop.i 0;;
1839}
1840
1841
1842{.mfi
1843 nop.m 0
1844 // (t*s)_s-t^2*y*z+z*y*ST
1845 fma.s1 F_TSS = F_YZ, F_ST, F_TSS
1846 nop.i 0
1847}
1848
1849{.mfi
1850 nop.m 0
1851 // -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1852 fms.s1 F_P39 = F_P39, F_R3, F_ATLO
1853 nop.i 0;;
1854}
1855
1856
1857{.mfi
1858 nop.m 0
1859 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1860 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 +
1861 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1862 fma.s1 F_DZ_TERM = F_P39, f1, F_DZ_TERM
1863 nop.i 0;;
1864}
1865
1866
1867{.mfi
1868 nop.m 0
1869 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1870 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
1871 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1872 fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM
1873 nop.i 0;;
1874}
1875
1876
1877{.mfi
1878 nop.m 0
1879 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1880 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
1881 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) +
1882 // + (t*s)_s-t^2*y*z+z*y*ST
1883 fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM
1884 nop.i 0;;
1885}
1886
1887
1888.pred.rel "mutex", p6, p11
1889{.mfi
1890 nop.m 0
1891 // result: add high part of table value
1892 // s>0 in this case
1893 (p11) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI
1894 nop.i 0
1895}
1896
1897{.mfb
1898 nop.m 0
1899 // result: add high part of pi-table value
1900 // if s<0
1901 (p6) fma.s0 f8 = F_DZ_TERM, f1, F_ATHI
1902 br.ret.sptk b0;;
1903}
1904
1905
1906
1907
1908
1909
1910SMALL_S:
1911
1912 // use 15-term polynomial approximation
1913
1914{.mmi
1915 // r3 = pointer to polynomial coefficients
1916 addl r3 = @ltoff(poly_coeffs), gp;;
1917 // load start address for coefficients
1918 ld8 r3 = [r3]
1919 mov R_TMP = 0x3fbf;;
1920}
1921
1922
1923{.mmi
1924 add r2 = 64, r3
1925 ldfe F_C3 = [r3], 16
1926 // p7 = 1 if |s|<2^{-64} (exponent of s<bias-64)
1927 cmp.lt p7, p0 = R_EXP0, R_TMP;;
1928}
1929
1930{.mmf
1931 ldfe F_C5 = [r3], 16
1932 ldfpd F_C11, F_C13 = [r2], 16
1933 nop.f 0;;
1934}
1935
1936{.mmf
1937 ldfpd F_C7, F_C9 = [r3], 16
1938 ldfpd F_C15, F_C17 = [r2]
1939 nop.f 0;;
1940}
1941
1942
1943
1944{.mfb
1945 // load pi/2
1946 ldfpd F_PI2_LO, F_PI2_HI = [r3]
1947 // s^2
1948 fma.s1 F_R2 = f8, f8, f0
1949 // |s|<2^{-64}
1950 (p7) br.cond.spnt RETURN_PI2;;
1951}
1952
1953
1954{.mfi
1955 nop.m 0
1956 // s^3
1957 fma.s1 F_R3 = f8, F_R2, f0
1958 nop.i 0
1959}
1960
1961{.mfi
1962 nop.m 0
1963 // s^4
1964 fma.s1 F_R4 = F_R2, F_R2, f0
1965 nop.i 0;;
1966}
1967
1968
1969{.mfi
1970 nop.m 0
1971 // c3+c5*s^2
1972 fma.s1 F_P35 = F_C5, F_R2, F_C3
1973 nop.i 0
1974}
1975
1976{.mfi
1977 nop.m 0
1978 // c11+c13*s^2
1979 fma.s1 F_P1113 = F_C13, F_R2, F_C11
1980 nop.i 0;;
1981}
1982
1983
1984{.mfi
1985 nop.m 0
1986 // c7+c9*s^2
1987 fma.s1 F_P79 = F_C9, F_R2, F_C7
1988 nop.i 0
1989}
1990
1991{.mfi
1992 nop.m 0
1993 // c15+c17*s^2
1994 fma.s1 F_P1517 = F_C17, F_R2, F_C15
1995 nop.i 0;;
1996}
1997
1998{.mfi
1999 nop.m 0
2000 // (pi/2)_high-s_high
2001 fnma.s1 F_T = f8, f1, F_PI2_HI
2002 nop.i 0
2003}
2004{.mfi
2005 nop.m 0
2006 // s^8
2007 fma.s1 F_R8 = F_R4, F_R4, f0
2008 nop.i 0;;
2009}
2010
2011
2012{.mfi
2013 nop.m 0
2014 // c3+c5*s^2+c7*s^4+c9*s^6
2015 fma.s1 F_P39 = F_P79, F_R4, F_P35
2016 nop.i 0
2017}
2018
2019{.mfi
2020 nop.m 0
2021 // c11+c13*s^2+c15*s^4+c17*s^6
2022 fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
2023 nop.i 0;;
2024}
2025
2026{.mfi
2027 nop.m 0
2028 // -s_high
2029 fms.s1 F_S = F_T, f1, F_PI2_HI
2030 nop.i 0;;
2031}
2032
2033{.mfi
2034 nop.m 0
2035 // c3+..+c17*s^14
2036 fma.s1 F_P317 = F_R8, F_P1117, F_P39
2037 nop.i 0;;
2038}
2039
2040{.mfi
2041 nop.m 0
2042 // s_low
2043 fma.s1 F_DS = f8, f1, F_S
2044 nop.i 0;;
2045}
2046
2047{.mfi
2048 nop.m 0
2049 // (pi/2)_low-s^3*(c3+..+c17*s^14)
2050 fnma.s0 F_P317 = F_P317, F_R3, F_PI2_LO
2051 nop.i 0;;
2052}
2053
2054{.mfi
2055 nop.m 0
2056 // (pi/2)_low-s_low-s^3*(c3+..+c17*s^14)
2057 fms.s1 F_P317 = F_P317, f1, F_DS
2058 nop.i 0;;
2059}
2060
2061{.mfb
2062 nop.m 0
2063 // result: pi/2-s-c3*s^3-..-c17*s^17
2064 fma.s0 f8 = F_T, f1, F_P317
2065 br.ret.sptk b0;;
2066}
2067
2068
2069
2070
2071
2072RETURN_PI2:
2073
2074{.mfi
2075 nop.m 0
2076 // (pi/2)_low-s
2077 fms.s0 F_PI2_LO = F_PI2_LO, f1, f8
2078 nop.i 0;;
2079}
2080
2081{.mfb
2082 nop.m 0
2083 // (pi/2)-s
2084 fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
2085 br.ret.sptk b0;;
2086}
2087
2088
2089
2090
2091
2092VERY_LARGE_INPUT:
2093
2094
2095{.mmf
2096 // pointer to pi_low, pi_high
2097 add r2 = 80, r3
2098 // load C5
2099 ldfe F_C5 = [r3], 16
2100 // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2
2101 fma.s1 F_X = F_X, F_05, f0;;
2102}
2103
2104.pred.rel "mutex", p6, p11
2105{.mmf
2106 // load pi (low, high), if s<0
2107 (p6) ldfpd F_PI2_LO, F_PI2_HI = [r2]
2108 // C7, C9
2109 ldfpd F_C7, F_C9 = [r3], 16
2110 // if s>0, set F_PI2_LO=0
2111 (p11) fma.s1 F_PI2_HI = f0, f0, f0;;
2112}
2113
2114{.mfi
2115 nop.m 0
2116 (p11) fma.s1 F_PI2_LO = f0, f0, f0
2117 nop.i 0;;
2118}
2119
2120{.mfi
2121 // adjust address for C_11
2122 add r3 = 16, r3
2123 // c9*x+c8
2124 fma.s1 F_S89 = F_X, F_CS9, F_CS8
2125 nop.i 0
2126}
2127
2128{.mfi
2129 nop.m 0
2130 // x^2
2131 fma.s1 F_X2 = F_X, F_X, f0
2132 nop.i 0;;
2133}
2134
2135
2136{.mfi
2137 nop.m 0
2138 // y*(1-s^2)*x
2139 fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
2140 nop.i 0
2141}
2142
2143{.mfi
2144 // C11, C13
2145 ldfpd F_C11, F_C13 = [r3], 16
2146 // c7*x+c6
2147 fma.s1 F_S67 = F_X, F_CS7, F_CS6
2148 nop.i 0;;
2149}
2150
2151
2152{.mfi
2153 // C15, C17
2154 ldfpd F_C15, F_C17 = [r3], 16
2155 // c3*x+c2
2156 fma.s1 F_S23 = F_X, F_CS3, F_CS2
2157 nop.i 0;;
2158}
2159
2160
2161{.mfi
2162 nop.m 0
2163 // c5*x+c4
2164 fma.s1 F_S45 = F_X, F_CS5, F_CS4
2165 nop.i 0;;
2166}
2167
2168
2169
2170
2171{.mfi
2172 nop.m 0
2173 // y*(1-s^2)*x^2
2174 fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
2175 nop.i 0
2176}
2177
2178{.mfi
2179 nop.m 0
2180 // x^4
2181 fma.s1 F_X4 = F_X2, F_X2, f0
2182 nop.i 0;;
2183}
2184
2185
2186{.mfi
2187 nop.m 0
2188 // c9*x^3+..+c6
2189 fma.s1 F_S69 = F_X2, F_S89, F_S67
2190 nop.i 0;;
2191}
2192
2193
2194{.mfi
2195 nop.m 0
2196 // c5*x^3+..+c2
2197 fma.s1 F_S25 = F_X2, F_S45, F_S23
2198 nop.i 0;;
2199}
2200
2201
2202
2203{.mfi
2204 nop.m 0
2205 // (pi)_high-y*(1-s^2)_s
2206 fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI
2207 nop.i 0;;
2208}
2209
2210
2211{.mfi
2212 nop.m 0
2213 // c9*x^7+..+c2
2214 fma.s1 F_S29 = F_X4, F_S69, F_S25
2215 nop.i 0;;
2216}
2217
2218
2219{.mfi
2220 nop.m 0
2221 // -(y*(1-s^2)_s)_high
2222 fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI
2223 nop.i 0;;
2224}
2225
2226
2227{.mfi
2228 nop.m 0
2229 // (PS29*x^2+x)*y*(1-s^2)
2230 fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
2231 nop.i 0;;
2232}
2233
2234
2235{.mfi
2236 nop.m 0
2237 // y*(1-s^2)_s-(y*(1-s^2))_high
2238 fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI
2239 nop.i 0;;
2240}
2241
2242
2243
2244{.mfi
2245 nop.m 0
2246 // R ~ sqrt(1-s^2)
2247 // (used for polynomial evaluation)
2248 fnma.s1 F_R = F_S19, f1, F_Y1S2
2249 nop.i 0;;
2250}
2251
2252
2253{.mfi
2254 nop.m 0
2255 // y*(1-s^2)-(y*(1-s^2))_high
2256 fma.s1 F_DS2 = F_Y, F_DS, F_DS2
2257 nop.i 0
2258}
2259
2260{.mfi
2261 nop.m 0
2262 // (pi)_low+(PS29*x^2)*y*(1-s^2)
2263 fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO
2264 nop.i 0;;
2265}
2266
2267
2268{.mfi
2269 nop.m 0
2270 // R^2
2271 fma.s1 F_R2 = F_R, F_R, f0
2272 nop.i 0;;
2273}
2274
2275
2276{.mfi
2277 nop.m 0
2278 // if s<0
2279 // (pi)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)
2280 fms.s1 F_S29 = F_S29, f1, F_DS2
2281 nop.i 0;;
2282}
2283
2284
2285{.mfi
2286 nop.m 0
2287 // c7+c9*R^2
2288 fma.s1 F_P79 = F_C9, F_R2, F_C7
2289 nop.i 0
2290}
2291
2292{.mfi
2293 nop.m 0
2294 // c3+c5*R^2
2295 fma.s1 F_P35 = F_C5, F_R2, F_C3
2296 nop.i 0;;
2297}
2298
2299
2300
2301{.mfi
2302 nop.m 0
2303 // R^4
2304 fma.s1 F_R4 = F_R2, F_R2, f0
2305 nop.i 0
2306}
2307
2308{.mfi
2309 nop.m 0
2310 // R^3
2311 fma.s1 F_R3 = F_R2, F_R, f0
2312 nop.i 0;;
2313}
2314
2315
2316{.mfi
2317 nop.m 0
2318 // c11+c13*R^2
2319 fma.s1 F_P1113 = F_C13, F_R2, F_C11
2320 nop.i 0
2321}
2322
2323{.mfi
2324 nop.m 0
2325 // c15+c17*R^2
2326 fma.s1 F_P1517 = F_C17, F_R2, F_C15
2327 nop.i 0;;
2328}
2329
2330
2331{.mfi
2332 nop.m 0
2333 // (pi)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x
2334 fma.s1 F_S29 = F_Y1S2, F_X, F_S29
2335 nop.i 0;;
2336}
2337
2338
2339{.mfi
2340 nop.m 0
2341 // c11+c13*R^2+c15*R^4+c17*R^6
2342 fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
2343 nop.i 0
2344}
2345
2346{.mfi
2347 nop.m 0
2348 // c3+c5*R^2+c7*R^4+c9*R^6
2349 fma.s1 F_P39 = F_P79, F_R4, F_P35
2350 nop.i 0;;
2351}
2352
2353
2354
2355{.mfi
2356 nop.m 0
2357 // R^8
2358 fma.s1 F_R8 = F_R4, F_R4, f0
2359 nop.i 0;;
2360}
2361
2362
2363{.mfi
2364 nop.m 0
2365 // c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14
2366 fma.s1 F_P317 = F_P1117, F_R8, F_P39
2367 nop.i 0;;
2368}
2369
2370
2371{.mfi
2372 nop.m 0
2373 // (pi)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
2374 // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
2375 fnma.s1 F_S29 = F_P317, F_R3, F_S29
2376 nop.i 0;;
2377}
2378
2379.pred.rel "mutex", p6, p11
2380{.mfi
2381 nop.m 0
2382 // Result (if s<0):
2383 // (pi)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
2384 // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
2385 // +(pi)_high-(y*(1-s^2))_high
2386 (p6) fma.s0 f8 = F_S29, f1, F_HI
2387 nop.i 0
2388}
2389
2390{.mfb
2391 nop.m 0
2392 // Result (if s>0):
2393 // (PS29*x^2)*y*(1-s^2)-
2394 // -y*(1-s^2)*x + P3, 17
2395 // +(y*(1-s^2))
2396 (p11) fms.s0 f8 = F_Y, F_1S2_S, F_S29
2397 br.ret.sptk b0;;
2398}
2399
2400
2401
2402
2403
2404
2405acosl_SPECIAL_CASES:
2406
2407{.mfi
2408 alloc r32 = ar.pfs, 1, 4, 4, 0
2409 // check if the input is a NaN, or unsupported format
2410 // (i.e. not infinity or normal/denormal)
2411 fclass.nm p7, p8 = f8, 0x3f
2412 // pointer to pi/2
2413 add r3 = 96, r3;;
2414}
2415
2416
2417{.mfi
2418 // load pi/2
2419 ldfpd F_PI2_HI, F_PI2_LO = [r3]
2420 // get |s|
2421 fmerge.s F_S = f0, f8
2422 nop.i 0
2423}
2424
2425{.mfb
2426 nop.m 0
2427 // if NaN, quietize it, and return
2428 (p7) fma.s0 f8 = f8, f1, f0
2429 (p7) br.ret.spnt b0;;
2430}
2431
2432
2433{.mfi
2434 nop.m 0
2435 // |s| = 1 ?
2436 fcmp.eq.s0 p9, p10 = F_S, f1
2437 nop.i 0
2438}
2439
2440{.mfi
2441 nop.m 0
2442 // load FR_X
2443 fma.s1 FR_X = f8, f1, f0
2444 // load error tag
2445 mov GR_Parameter_TAG = 57;;
2446}
2447
2448
2449{.mfi
2450 nop.m 0
2451 // if s = 1, result is 0
2452 (p9) fma.s0 f8 = f0, f0, f0
2453 // set p6=0 for |s|>1
2454 (p10) cmp.ne p6, p0 = r0, r0;;
2455}
2456
2457
2458{.mfb
2459 nop.m 0
2460 // if s = -1, result is pi
2461 (p6) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
2462 // return if |s| = 1
2463 (p9) br.ret.sptk b0;;
2464}
2465
2466
2467{.mfi
2468 nop.m 0
2469 // get Infinity
2470 frcpa.s1 FR_RESULT, p0 = f1, f0
2471 nop.i 0;;
2472}
2473
2474
2475{.mfb
2476 nop.m 0
2477 // return QNaN indefinite (0*Infinity)
2478 fma.s0 FR_RESULT = f0, FR_RESULT, f0
2479 nop.b 0;;
2480}
2481
2482
2483GLOBAL_LIBM_END(acosl)
2484
2485
2486LOCAL_LIBM_ENTRY(__libm_error_region)
2487.prologue
2488// (1)
2489{ .mfi
2490 add GR_Parameter_Y=-32,sp // Parameter 2 value
2491 nop.f 0
2492.save ar.pfs,GR_SAVE_PFS
2493 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
2494}
2495{ .mfi
2496.fframe 64
2497 add sp=-64,sp // Create new stack
2498 nop.f 0
2499 mov GR_SAVE_GP=gp // Save gp
2500};;
2501
2502
2503// (2)
2504{ .mmi
2505 stfe [GR_Parameter_Y] = f1,16 // Store Parameter 2 on stack
2506 add GR_Parameter_X = 16,sp // Parameter 1 address
2507.save b0, GR_SAVE_B0
2508 mov GR_SAVE_B0=b0 // Save b0
2509};;
2510
2511.body
2512// (3)
2513{ .mib
2514 stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
2515 add GR_Parameter_RESULT = 0,GR_Parameter_Y
2516 nop.b 0 // Parameter 3 address
2517}
2518{ .mib
2519 stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
2520 add GR_Parameter_Y = -16,GR_Parameter_Y
2521 br.call.sptk b0=__libm_error_support# // Call error handling function
2522};;
2523{ .mmi
2524 nop.m 0
2525 nop.m 0
2526 add GR_Parameter_RESULT = 48,sp
2527};;
2528
2529// (4)
2530{ .mmi
2531 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
2532.restore sp
2533 add sp = 64,sp // Restore stack pointer
2534 mov b0 = GR_SAVE_B0 // Restore return address
2535};;
2536
2537{ .mib
2538 mov gp = GR_SAVE_GP // Restore gp
2539 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
2540 br.ret.sptk b0 // Return
2541};;
2542
2543LOCAL_LIBM_END(__libm_error_region)
2544
2545.type __libm_error_support#,@function
2546.global __libm_error_support#
2547
2548
2549
2550
2551
2552
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