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glibc/sysdeps/ia64/fpu/e_asinl.S
Mike Frysinger c70a4b1db0 ia64: relocate out of ports/ subdir
2014-02-16 01:12:38 -05:00

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.file "asinl.s"
// Copyright (c) 2001 - 2003, Intel Corporation
// All rights reserved.
//
// Contributed 2001 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
// 08/28/01 New version
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/06/03 Reordered header: .section, .global, .proc, .align
//
// API
//==============================================================
// long double asinl(long double)
//
// Overview of operation
//==============================================================
// Background
//
// Implementation
//
// For |s| in [2^{-4}, sqrt(2)/2]:
// Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52
// asin(s)= asin(t)+asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e.
// r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1)
// asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9)
// The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table,
// along with the high and low parts of asin(t) (stored as two double precision
// values)
//
// |s| in (sqrt(2)/2, sqrt(255/256)):
// Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6..
// asin(|s|)= pi/2-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2)
// To minimize accumulated errors, r is computed as
// 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+
// +(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)+
// +ez*z'*y*(1-s^2)*(1-x),
// where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits)
// z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2
//
// |s|<2^{-4}: evaluate as 17-degree polynomial
// (or simply return s, if|s|<2^{-64})
//
// |s| in [sqrt(255/256), 1): asin(|s|)= pi/2-asin(sqrt(1-s^2))
// use 17-degree polynomial for asin(sqrt(1-s^2)),
// 9-degree polynomial to evaluate sqrt(1-s^2)
// High order term is (pi/2)_high-(y*(1-s^2))_high
//
// Registers used
//==============================================================
// f6-f15, f32-f36
// r2-r3, r23-r23
// p6, p7, p8, p12
//
GR_SAVE_B0= r33
GR_SAVE_PFS= r34
GR_SAVE_GP= r35 // This reg. can safely be used
GR_SAVE_SP= r36
GR_Parameter_X= r37
GR_Parameter_Y= r38
GR_Parameter_RESULT= r39
GR_Parameter_TAG= r40
FR_X= f10
FR_Y= f1
FR_RESULT= f8
RODATA
.align 16
LOCAL_OBJECT_START(T_table)
// stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2),
// asin(t)_high (double precision), asin(t)_low (double precision)
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data8 0x869d80d0db7e4c0c, 0xf9a16f237aec427a
data8 0x3fcc9cd993cc4040, 0x3cbae93acc85eccf
data8 0x86bd0dd45f4f8265, 0xf98433446a806e70
data8 0x3fccde7f754f5660, 0x3cb22f70e64568d0
data8 0x86dcf0b16613e37a, 0xf966b246a8606170
data8 0x3fcd202d11620fa0, 0x3c962030e5d4c849
data8 0x86fd29d7624b3d5d, 0xf948ec11a9d4c45b
data8 0x3fcd61e27c10c0a0, 0x3cc7083c91d59217
data8 0x871db9b741dbe44a, 0xf92ae08c9eca4941
data8 0x3fcda39fc97be7c0, 0x3cc9258579e57211
data8 0x873ea0c3722d6af2, 0xf90c8f9e71633363
data8 0x3fcde5650dd86d60, 0x3ca4755a9ea582a9
data8 0x875fdf6fe45529e8, 0xf8edf92dc5875319
data8 0x3fce27325d6fe520, 0x3cbc1e2b6c1954f9
data8 0x878176321154e2bc, 0xf8cf1d20f87270b8
data8 0x3fce6907cca0d060, 0x3cb6ca4804750830
data8 0x87a36580fe6bccf5, 0xf8affb5e20412199
data8 0x3fceaae56fdee040, 0x3cad6b310d6fd46c
data8 0x87c5add5417a5cb9, 0xf89093cb0b7c0233
data8 0x3fceeccb5bb33900, 0x3cc16e99cedadb20
data8 0x87e84fa9057914ca, 0xf870e64d40a15036
data8 0x3fcf2eb9a4bcb600, 0x3cc75ee47c8b09e9
data8 0x880b4b780f02b709, 0xf850f2c9fdacdf78
data8 0x3fcf70b05fb02e20, 0x3cad6350d379f41a
data8 0x882ea1bfc0f228ac, 0xf830b926379e6465
data8 0x3fcfb2afa158b8a0, 0x3cce0ccd9f829985
data8 0x885252ff21146108, 0xf810394699fe0e8e
data8 0x3fcff4b77e97f3e0, 0x3c9b30faa7a4c703
data8 0x88765fb6dceebbb3, 0xf7ef730f865f6df0
data8 0x3fd01b6406332540, 0x3cdc5772c9e0b9bd
data8 0x88ad1f69be2cc730, 0xf7bdc59bc9cfbd97
data8 0x3fd04cf8ad203480, 0x3caeef44fe21a74a
data8 0x88f763f70ae2245e, 0xf77a91c868a9c54e
data8 0x3fd08f23ce0162a0, 0x3cd6290ab3fe5889
data8 0x89431fc7bc0c2910, 0xf73642973c91298e
data8 0x3fd0d1610f0c1ec0, 0x3cc67401a01f08cf
data8 0x8990573407c7738e, 0xf6f0d71d1d7a2dd6
data8 0x3fd113b0c65d88c0, 0x3cc7aa4020fe546f
data8 0x89df0eb108594653, 0xf6aa4e6a05cfdef2
data8 0x3fd156134ada6fe0, 0x3cc87369da09600c
data8 0x8a2f4ad16e0ed78a, 0xf662a78900c35249
data8 0x3fd19888f43427a0, 0x3cc62b220f38e49c
data8 0x8a811046373e0819, 0xf619e180181d97cc
data8 0x3fd1db121aed7720, 0x3ca3ede7490b52f4
data8 0x8ad463df6ea0fa2c, 0xf5cffb504190f9a2
data8 0x3fd21daf185fa360, 0x3caafad98c1d6c1b
data8 0x8b294a8cf0488daf, 0xf584f3f54b8604e6
data8 0x3fd2606046bf95a0, 0x3cdb2d704eeb08fa
data8 0x8b7fc95f35647757, 0xf538ca65c960b582
data8 0x3fd2a32601231ec0, 0x3cc661619fa2f126
data8 0x8bd7e588272276f8, 0xf4eb7d92ff39fccb
data8 0x3fd2e600a3865760, 0x3c8a2a36a99aca4a
data8 0x8c31a45bf8e9255e, 0xf49d0c68cd09b689
data8 0x3fd328f08ad12000, 0x3cb9efaf1d7ab552
data8 0x8c8d0b520a35eb18, 0xf44d75cd993cfad2
data8 0x3fd36bf614dcc040, 0x3ccacbb590bef70d
data8 0x8cea2005d068f23d, 0xf3fcb8a23ab4942b
data8 0x3fd3af11a079a6c0, 0x3cd9775872cf037d
data8 0x8d48e837c8cd5027, 0xf3aad3c1e2273908
data8 0x3fd3f2438d754b40, 0x3ca03304f667109a
data8 0x8da969ce732f3ac7, 0xf357c60202e2fd7e
data8 0x3fd4358c3ca032e0, 0x3caecf2504ff1a9d
data8 0x8e0baad75555e361, 0xf3038e323ae9463a
data8 0x3fd478ec0fd419c0, 0x3cc64bdc3d703971
data8 0x8e6fb18807ba877e, 0xf2ae2b1c3a6057f7
data8 0x3fd4bc6369fa40e0, 0x3cbb7122ec245cf2
data8 0x8ed5843f4bda74d5, 0xf2579b83aa556f0c
data8 0x3fd4fff2af11e2c0, 0x3c9cfa2dc792d394
data8 0x8f3d29862c861fef, 0xf1ffde2612ca1909
data8 0x3fd5439a4436d000, 0x3cc38d46d310526b
data8 0x8fa6a81128940b2d, 0xf1a6f1bac0075669
data8 0x3fd5875a8fa83520, 0x3cd8bf59b8153f8a
data8 0x901206c1686317a6, 0xf14cd4f2a730d480
data8 0x3fd5cb33f8cf8ac0, 0x3c9502b5c4d0e431
data8 0x907f4ca5fe9cf739, 0xf0f186784a125726
data8 0x3fd60f26e847b120, 0x3cc8a1a5e0acaa33
data8 0x90ee80fd34aeda5e, 0xf09504ef9a212f18
data8 0x3fd65333c7e43aa0, 0x3cae5b029cb1f26e
data8 0x915fab35e37421c6, 0xf0374ef5daab5c45
data8 0x3fd6975b02b8e360, 0x3cd5aa1c280c45e6
data8 0x91d2d2f0d894d73c, 0xefd86321822dbb51
data8 0x3fd6db9d05213b20, 0x3cbecf2c093ccd8b
data8 0x9248000249200009, 0xef7840021aca5a72
data8 0x3fd71ffa3cc87fc0, 0x3cb8d273f08d00d9
data8 0x92bf3a7351f081d2, 0xef16e42021d7cbd5
data8 0x3fd7647318b1ad20, 0x3cbce099d79cdc46
data8 0x93388a8386725713, 0xeeb44dfce6820283
data8 0x3fd7a908093fc1e0, 0x3ccb033ec17a30d9
data8 0x93b3f8aa8e653812, 0xee507c126774fa45
data8 0x3fd7edb9803e3c20, 0x3cc10aedb48671eb
data8 0x94318d99d341ade4, 0xedeb6cd32f891afb
data8 0x3fd83287f0e9cf80, 0x3c994c0c1505cd2a
data8 0x94b1523e3dedc630, 0xed851eaa3168f43c
data8 0x3fd87773cff956e0, 0x3cda3b7bce6a6b16
data8 0x95334fc20577563f, 0xed1d8ffaa2279669
data8 0x3fd8bc7d93a70440, 0x3cd4922edc792ce2
data8 0x95b78f8e8f92f274, 0xecb4bf1fd2be72da
data8 0x3fd901a5b3b9cf40, 0x3cd3fea1b00f9d0d
data8 0x963e1b4e63a87c3f, 0xec4aaa6d08694cc1
data8 0x3fd946eca98f2700, 0x3cdba4032d968ff1
data8 0x96c6fcef314074fc, 0xebdf502d53d65fea
data8 0x3fd98c52f024e800, 0x3cbe7be1ab8c95c9
data8 0x97523ea3eab028b2, 0xeb72aea36720793e
data8 0x3fd9d1d904239860, 0x3cd72d08a6a22b70
data8 0x97dfeae6f4ee4a9a, 0xeb04c4096a884e94
data8 0x3fda177f63e8ef00, 0x3cd818c3c1ebfac7
data8 0x98700c7c6d85d119, 0xea958e90cfe1efd7
data8 0x3fda5d468f92a540, 0x3cdf45fbfaa080fe
data8 0x9902ae7487a9caa1, 0xea250c6224aab21a
data8 0x3fdaa32f090998e0, 0x3cd715a9353cede4
data8 0x9997dc2e017a9550, 0xe9b33b9ce2bb7638
data8 0x3fdae939540d3f00, 0x3cc545c014943439
data8 0x9a2fa158b29b649b, 0xe9401a573f8aa706
data8 0x3fdb2f65f63f6c60, 0x3cd4a63c2f2ca8e2
data8 0x9aca09f835466186, 0xe8cba69df9f0bf35
data8 0x3fdb75b5773075e0, 0x3cda310ce1b217ec
data8 0x9b672266ab1e0136, 0xe855de74266193d4
data8 0x3fdbbc28606babc0, 0x3cdc84b75cca6c44
data8 0x9c06f7579f0b7bd5, 0xe7debfd2f98c060b
data8 0x3fdc02bf3d843420, 0x3cd225d967ffb922
data8 0x9ca995db058cabdc, 0xe76648a991511c6e
data8 0x3fdc497a9c224780, 0x3cde08101c5b825b
data8 0x9d4f0b605ce71e88, 0xe6ec76dcbc02d9a7
data8 0x3fdc905b0c10d420, 0x3cb1abbaa3edf120
data8 0x9df765b9eecad5e6, 0xe6714846bdda7318
data8 0x3fdcd7611f4b8a00, 0x3cbf6217ae80aadf
data8 0x9ea2b320350540fe, 0xe5f4bab71494cd6b
data8 0x3fdd1e8d6a0d56c0, 0x3cb726e048cc235c
data8 0x9f51023562fc5676, 0xe576cbf239235ecb
data8 0x3fdd65e082df5260, 0x3cd9e66872bd5250
data8 0xa002620915c2a2f6, 0xe4f779b15f5ec5a7
data8 0x3fddad5b02a82420, 0x3c89743b0b57534b
data8 0xa0b6e21c2caf9992, 0xe476c1a233a7873e
data8 0x3fddf4fd84bbe160, 0x3cbf7adea9ee3338
data8 0xa16e9264cc83a6b2, 0xe3f4a16696608191
data8 0x3fde3cc8a6ec6ee0, 0x3cce46f5a51f49c6
data8 0xa22983528f3d8d49, 0xe3711694552da8a8
data8 0x3fde84bd099a6600, 0x3cdc78f6490a2d31
data8 0xa2e7c5d2e2e69460, 0xe2ec1eb4e1e0a5fb
data8 0x3fdeccdb4fc685c0, 0x3cdd3aedb56a4825
data8 0xa3a96b5599bd2532, 0xe265b74506fbe1c9
data8 0x3fdf15241f23b3e0, 0x3cd440f3c6d65f65
data8 0xa46e85d1ae49d7de, 0xe1ddddb499b3606f
data8 0x3fdf5d98202994a0, 0x3cd6c44bd3fb745a
data8 0xa53727ca3e11b99e, 0xe1548f662951b00d
data8 0x3fdfa637fe27bf60, 0x3ca8ad1cd33054dd
data8 0xa6036453bdc20186, 0xe0c9c9aeabe5e481
data8 0x3fdfef0467599580, 0x3cc0f1ac0685d78a
data8 0xa6d34f1969dda338, 0xe03d89d5281e4f81
data8 0x3fe01bff067d6220, 0x3cc0731e8a9ef057
data8 0xa7a6fc62f7246ff3, 0xdfafcd125c323f54
data8 0x3fe04092d1ae3b40, 0x3ccabda24b59906d
data8 0xa87e811a861df9b9, 0xdf20909061bb9760
data8 0x3fe0653df0fd9fc0, 0x3ce94c8dcc722278
data8 0xa959f2d2dd687200, 0xde8fd16a4e5f88bd
data8 0x3fe08a00c1cae320, 0x3ce6b888bb60a274
data8 0xaa3967cdeea58bda, 0xddfd8cabd1240d22
data8 0x3fe0aedba3221c00, 0x3ced5941cd486e46
data8 0xab904fd587263c84, 0xdd1f4472e1cf64ed
data8 0x3fe0e651e85229c0, 0x3cdb6701042299b1
data8 0xad686d44dd5a74bb, 0xdbf173e1f6b46e92
data8 0x3fe1309cbf4cdb20, 0x3cbf1be7bb3f0ec5
data8 0xaf524e15640ebee4, 0xdabd54896f1029f6
data8 0x3fe17b4ee1641300, 0x3ce81dd055b792f1
data8 0xb14eca24ef7db3fa, 0xd982cb9ae2f47e41
data8 0x3fe1c66b9ffd6660, 0x3cd98ea31eb5ddc7
data8 0xb35ec807669920ce, 0xd841bd1b8291d0b6
data8 0x3fe211f66db3a5a0, 0x3ca480c35a27b4a2
data8 0xb5833e4755e04dd1, 0xd6fa0bd3150b6930
data8 0x3fe25df2e05b6c40, 0x3ca4bc324287a351
data8 0xb7bd34c8000b7bd3, 0xd5ab9939a7d23aa1
data8 0x3fe2aa64b32f7780, 0x3cba67314933077c
data8 0xba0dc64d126cc135, 0xd4564563ce924481
data8 0x3fe2f74fc9289ac0, 0x3cec1a1dc0efc5ec
data8 0xbc76222cbbfa74a6, 0xd2f9eeed501125a8
data8 0x3fe344b82f859ac0, 0x3ceeef218de413ac
data8 0xbef78e31985291a9, 0xd19672e2182f78be
data8 0x3fe392a22087b7e0, 0x3cd2619ba201204c
data8 0xc19368b2b0629572, 0xd02baca5427e436a
data8 0x3fe3e11206694520, 0x3cb5d0b3143fe689
data8 0xc44b2ae8c6733e51, 0xceb975d60b6eae5d
data8 0x3fe4300c7e945020, 0x3cbd367143da6582
data8 0xc7206b894212dfef, 0xcd3fa6326ff0ac9a
data8 0x3fe47f965d201d60, 0x3ce797c7a4ec1d63
data8 0xca14e1b0622de526, 0xcbbe13773c3c5338
data8 0x3fe4cfb4b09d1a20, 0x3cedfadb5347143c
data8 0xcd2a6825eae65f82, 0xca34913d425a5ae9
data8 0x3fe5206cc637e000, 0x3ce2798b38e54193
data8 0xd06301095e1351ee, 0xc8a2f0d3679c08c0
data8 0x3fe571c42e3d0be0, 0x3ccd7cb9c6c2ca68
data8 0xd3c0d9f50057adda, 0xc70901152d59d16b
data8 0x3fe5c3c0c108f940, 0x3ceb6c13563180ab
data8 0xd74650a98cc14789, 0xc5668e3d4cbf8828
data8 0x3fe61668a46ffa80, 0x3caa9092e9e3c0e5
data8 0xdaf5f8579dcc8f8f, 0xc3bb61b3eed42d02
data8 0x3fe669c251ad69e0, 0x3cccf896ef3b4fee
data8 0xded29f9f9a6171b4, 0xc20741d7f8e8e8af
data8 0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d
data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b
data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321
data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91
data8 0x3fe76840418978a0, 0x3ccda46e85432c3d
data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3
data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3
data8 0xf049183c3f53c39b, 0xbad848720223d3a8
data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b
data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48
data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f
data8 0xfa718f05adbf2c33, 0xb70432500286b185
data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9
data8 0xfff200c3f5489608, 0xb509e6454dca33cc
data8 0x3fe9211b54441080, 0x3cb789cb53515688
// The following table entries are not used
//data8 0x82e138a0fac48700, 0xb3044a513a8e6132
//data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0
//data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88
//data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039
//data8 0x89377c1387d5b908, 0xaed58e9a09014d5c
//data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58
//data8 0x8cad7a2c98dec333, 0xacab929ce114d451
//data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f
//data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec
//data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5
//data8 0x9446d8191f80dd42, 0xa82ff92687235baf
//data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e
//data8 0x98758ba086e4000a, 0xa5dd497a9c184f58
//data8 0x3febb5f571cb0560, 0x3ce0c7774329a613
//data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b
//data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177
//data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03
//data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959
//data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec
//data8 0x3fece4f404e29b20, 0x3cea3413401132b5
//data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c
//data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276
//data8 0xb265c39cbd80f97a, 0x99553d969fec7beb
//data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2
//data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c
//data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71
//data8 0xbfea427678945732, 0x93d5990f9ee787af
//data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5
//data8 0xc79611399b8c90c5, 0x90f72bde80febc31
//data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56
//data8 0xcffa8425040624d7, 0x8e02b4418574ebed
//data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f
//data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024
//data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94
//data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b
//data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc
//data8 0xeea6d733421da0a6, 0x84921bbe64ae029a
//data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02
//data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6
//data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3
//data8 0x84ac1fcec4203245, 0xfb73a828893df19e
//data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de
//data8 0x8ca50621110c60e6, 0xf438a14c158d867c
//data8 0x3ff12d51caa6b580, 0x3ce6bce9748739b6
//data8 0x95b8c2062d6f8161, 0xecb3ccdd37b369da
//data8 0x3ff1717418520340, 0x3ca5c2732533177c
//data8 0xa0262917caab4ad1, 0xe4dde4ddc81fd119
//data8 0x3ff1b7d59dd40ba0, 0x3cc4c7c98e870ff5
//data8 0xac402c688b72f3f4, 0xdcae469be46d4c8d
//data8 0x3ff200b93cc5a540, 0x3c8dd6dc1bfe865a
//data8 0xba76968b9eabd9ab, 0xd41a8f3df1115f7f
//data8 0x3ff24c6f8f6affa0, 0x3cf1acb6d2a7eff7
//data8 0xcb63c87c23a71dc5, 0xcb161074c17f54ec
//data8 0x3ff29b5b338b7c80, 0x3ce9b5845f6ec746
//data8 0xdfe323b8653af367, 0xc19107d99ab27e42
//data8 0x3ff2edf6fac7f5a0, 0x3cf77f961925fa02
//data8 0xf93746caaba3e1f1, 0xb777744a9df03bff
//data8 0x3ff344df237486c0, 0x3cf6ddf5f6ddda43
//data8 0x8ca77052f6c340f0, 0xacaf476f13806648
//data8 0x3ff3a0dfa4bb4ae0, 0x3cfee01bbd761bff
//data8 0xa1a48604a81d5c62, 0xa11575d30c0aae50
//data8 0x3ff4030b73c55360, 0x3cf1cf0e0324d37c
//data8 0xbe45074b05579024, 0x9478e362a07dd287
//data8 0x3ff46ce4c738c4e0, 0x3ce3179555367d12
//data8 0xe7a08b5693d214ec, 0x8690e3575b8a7c3b
//data8 0x3ff4e0a887c40a80, 0x3cfbd5d46bfefe69
//data8 0x94503d69396d91c7, 0xedd2ce885ff04028
//data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b
//data8 0xced1d96c5bb209e6, 0xc965278083808702
//data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c
//data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd
//data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e
//data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4
//data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb
LOCAL_OBJECT_END(T_table)
.align 16
LOCAL_OBJECT_START(poly_coeffs)
// C_3
data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc
// C_5
data8 0x999999999999999a, 0x0000000000003ffb
// C_7, C_9
data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8
// pi/2 (low, high)
data8 0x3C91A62633145C07, 0x3FF921FB54442D18
// C_11, C_13
data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e
// C_15, C_17
data8 0x3f8c99999999999a, 0x3f87a87878787223
LOCAL_OBJECT_END(poly_coeffs)
R_DBL_S = r21
R_EXP0 = r22
R_EXP = r15
R_SGNMASK = r23
R_TMP = r24
R_TMP2 = r25
R_INDEX = r26
R_TMP3 = r27
R_TMP03 = r27
R_TMP4 = r28
R_TMP5 = r23
R_TMP6 = r22
R_TMP7 = r21
R_T = r29
R_BIAS = r20
F_T = f6
F_1S2 = f7
F_1S2_S = f9
F_INV_1T2 = f10
F_SQRT_1T2 = f11
F_S2T2 = f12
F_X = f13
F_D = f14
F_2M64 = f15
F_CS2 = f32
F_CS3 = f33
F_CS4 = f34
F_CS5 = f35
F_CS6 = f36
F_CS7 = f37
F_CS8 = f38
F_CS9 = f39
F_S23 = f40
F_S45 = f41
F_S67 = f42
F_S89 = f43
F_S25 = f44
F_S69 = f45
F_S29 = f46
F_X2 = f47
F_X4 = f48
F_TSQRT = f49
F_DTX = f50
F_R = f51
F_R2 = f52
F_R3 = f53
F_R4 = f54
F_C3 = f55
F_C5 = f56
F_C7 = f57
F_C9 = f58
F_P79 = f59
F_P35 = f60
F_P39 = f61
F_ATHI = f62
F_ATLO = f63
F_T1 = f64
F_Y = f65
F_Y2 = f66
F_ANDMASK = f67
F_ORMASK = f68
F_S = f69
F_05 = f70
F_SQRT_1S2 = f71
F_DS = f72
F_Z = f73
F_1T2 = f74
F_DZ = f75
F_ZE = f76
F_YZ = f77
F_Y1S2 = f78
F_Y1S2X = f79
F_1X = f80
F_ST = f81
F_1T2_ST = f82
F_TSS = f83
F_Y1S2X2 = f84
F_DZ_TERM = f85
F_DTS = f86
F_DS2X = f87
F_T2 = f88
F_ZY1S2S = f89
F_Y1S2_1X = f90
F_TS = f91
F_PI2_LO = f92
F_PI2_HI = f93
F_S19 = f94
F_INV1T2_2 = f95
F_CORR = f96
F_DZ0 = f97
F_C11 = f98
F_C13 = f99
F_C15 = f100
F_C17 = f101
F_P1113 = f102
F_P1517 = f103
F_P1117 = f104
F_P317 = f105
F_R8 = f106
F_HI = f107
F_1S2_HI = f108
F_DS2 = f109
F_Y2_2 = f110
F_S2 = f111
F_S_DS2 = f112
F_S_1S2S = f113
F_XL = f114
F_2M128 = f115
.section .text
GLOBAL_LIBM_ENTRY(asinl)
{.mfi
// get exponent, mantissa (rounded to double precision) of s
getf.d R_DBL_S = f8
// 1-s^2
fnma.s1 F_1S2 = f8, f8, f1
// r2 = pointer to T_table
addl r2 = @ltoff(T_table), gp
}
{.mfi
// sign mask
mov R_SGNMASK = 0x20000
nop.f 0
// bias-63-1
mov R_TMP03 = 0xffff-64;;
}
{.mfi
// get exponent of s
getf.exp R_EXP = f8
nop.f 0
// R_TMP4 = 2^45
shl R_TMP4 = R_SGNMASK, 45-17
}
{.mlx
// load bias-4
mov R_TMP = 0xffff-4
// load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1)
movl R_TMP2 = 0x7fcd413cccfe779a;;
}
{.mfi
// load 2^{-64} in FP register
setf.exp F_2M64 = R_TMP03
nop.f 0
// index = (0x7-exponent)|b1 b2.. b6
extr.u R_INDEX = R_DBL_S, 46, 9
}
{.mfi
// get t = sign|exponent|b1 b2.. b6 1 x.. x
or R_T = R_DBL_S, R_TMP4
nop.f 0
// R_TMP4 = 2^45-1
sub R_TMP4 = R_TMP4, r0, 1;;
}
{.mfi
// get t = sign|exponent|b1 b2.. b6 1 0.. 0
andcm R_T = R_T, R_TMP4
nop.f 0
// eliminate sign from R_DBL_S (shift left by 1)
shl R_TMP3 = R_DBL_S, 1
}
{.mfi
// R_BIAS = 3*2^6
mov R_BIAS = 0xc0
nop.f 0
// eliminate sign from R_EXP
andcm R_EXP0 = R_EXP, R_SGNMASK;;
}
{.mfi
// load start address for T_table
ld8 r2 = [r2]
nop.f 0
// p8 = 1 if |s|> = sqrt(2)/2
cmp.geu p8, p0 = R_TMP3, R_TMP2
}
{.mlx
// p7 = 1 if |s|<2^{-4} (exponent of s<bias-4)
cmp.lt p7, p0 = R_EXP0, R_TMP
// sqrt coefficient cs8 = -33*13/128
movl R_TMP2 = 0xc0568000;;
}
{.mbb
// load t in FP register
setf.d F_T = R_T
// if |s|<2^{-4}, take alternate path
(p7) br.cond.spnt SMALL_S
// if |s|> = sqrt(2)/2, take alternate path
(p8) br.cond.sptk LARGE_S
}
{.mlx
// index = (4-exponent)|b1 b2.. b6
sub R_INDEX = R_INDEX, R_BIAS
// sqrt coefficient cs9 = 55*13/128
movl R_TMP = 0x40b2c000;;
}
{.mfi
// sqrt coefficient cs8 = -33*13/128
setf.s F_CS8 = R_TMP2
nop.f 0
// shift R_INDEX by 5
shl R_INDEX = R_INDEX, 5
}
{.mfi
// sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
mov R_TMP4 = 0xffff - 1
nop.f 0
// sqrt coefficient cs6 = -21/16
mov R_TMP6 = 0xbfa8;;
}
{.mlx
// table index
add r2 = r2, R_INDEX
// sqrt coefficient cs7 = 33/16
movl R_TMP2 = 0x40040000;;
}
{.mmi
// load cs9 = 55*13/128
setf.s F_CS9 = R_TMP
// sqrt coefficient cs5 = 7/8
mov R_TMP3 = 0x3f60
// sqrt coefficient cs6 = 21/16
shl R_TMP6 = R_TMP6, 16;;
}
{.mmi
// load significand of 1/(1-t^2)
ldf8 F_INV_1T2 = [r2], 8
// sqrt coefficient cs7 = 33/16
setf.s F_CS7 = R_TMP2
// sqrt coefficient cs4 = -5/8
mov R_TMP5 = 0xbf20;;
}
{.mmi
// load significand of sqrt(1-t^2)
ldf8 F_SQRT_1T2 = [r2], 8
// sqrt coefficient cs6 = 21/16
setf.s F_CS6 = R_TMP6
// sqrt coefficient cs5 = 7/8
shl R_TMP3 = R_TMP3, 16;;
}
{.mmi
// sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
setf.exp F_CS3 = R_TMP4
// r3 = pointer to polynomial coefficients
addl r3 = @ltoff(poly_coeffs), gp
// sqrt coefficient cs4 = -5/8
shl R_TMP5 = R_TMP5, 16;;
}
{.mfi
// sqrt coefficient cs5 = 7/8
setf.s F_CS5 = R_TMP3
// d = s-t
fms.s1 F_D = f8, f1, F_T
// set p6 = 1 if s<0, p11 = 1 if s> = 0
cmp.ge p6, p11 = R_EXP, R_DBL_S
}
{.mfi
// r3 = load start address to polynomial coefficients
ld8 r3 = [r3]
// s+t
fma.s1 F_S2T2 = f8, f1, F_T
nop.i 0;;
}
{.mfi
// sqrt coefficient cs4 = -5/8
setf.s F_CS4 = R_TMP5
// s^2-t^2
fma.s1 F_S2T2 = F_S2T2, F_D, f0
nop.i 0;;
}
{.mfi
// load C3
ldfe F_C3 = [r3], 16
// 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2))
fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
nop.i 0;;
}
{.mfi
// load C_5
ldfe F_C5 = [r3], 16
// set correct exponent for sqrt(1-t^2)
fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
nop.i 0;;
}
{.mfi
// load C_7, C_9
ldfpd F_C7, F_C9 = [r3]
// x = -(s^2-t^2)/(1-t^2)/2
fnma.s1 F_X = F_INV_1T2, F_S2T2, f0
nop.i 0;;
}
{.mfi
// load asin(t)_high, asin(t)_low
ldfpd F_ATHI, F_ATLO = [r2]
// t*sqrt(1-t^2)
fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0
nop.i 0;;
}
{.mfi
nop.m 0
// cs9*x+cs8
fma.s1 F_S89 = F_CS9, F_X, F_CS8
nop.i 0
}
{.mfi
nop.m 0
// cs7*x+cs6
fma.s1 F_S67 = F_CS7, F_X, F_CS6
nop.i 0;;
}
{.mfi
nop.m 0
// cs5*x+cs4
fma.s1 F_S45 = F_CS5, F_X, F_CS4
nop.i 0
}
{.mfi
nop.m 0
// x*x
fma.s1 F_X2 = F_X, F_X, f0
nop.i 0;;
}
{.mfi
nop.m 0
// (s-t)-t*x
fnma.s1 F_DTX = F_T, F_X, F_D
nop.i 0
}
{.mfi
nop.m 0
// cs3*x+cs2 (cs2 = -0.5 = -cs3)
fms.s1 F_S23 = F_CS3, F_X, F_CS3
nop.i 0;;
}
{.mfi
nop.m 0
// cs9*x^3+cs8*x^2+cs7*x+cs6
fma.s1 F_S69 = F_S89, F_X2, F_S67
nop.i 0
}
{.mfi
nop.m 0
// x^4
fma.s1 F_X4 = F_X2, F_X2, f0
nop.i 0;;
}
{.mfi
nop.m 0
// t*sqrt(1-t^2)*x^2
fma.s1 F_TSQRT = F_TSQRT, F_X2, f0
nop.i 0
}
{.mfi
nop.m 0
// cs5*x^3+cs4*x^2+cs3*x+cs2
fma.s1 F_S25 = F_S45, F_X2, F_S23
nop.i 0;;
}
{.mfi
nop.m 0
// ((s-t)-t*x)*sqrt(1-t^2)
fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0
nop.i 0;;
}
{.mfi
nop.m 0
// if sign is negative, negate table values: asin(t)_low
(p6) fnma.s1 F_ATLO = F_ATLO, f1, f0
nop.i 0
}
{.mfi
nop.m 0
// PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2
fma.s1 F_S29 = F_S69, F_X4, F_S25
nop.i 0;;
}
{.mfi
nop.m 0
// if sign is negative, negate table values: asin(t)_high
(p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
nop.i 0
}
{.mfi
nop.m 0
// R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29
fnma.s1 F_R = F_S29, F_TSQRT, F_DTX
nop.i 0;;
}
{.mfi
nop.m 0
// R^2
fma.s1 F_R2 = F_R, F_R, f0
nop.i 0;;
}
{.mfi
nop.m 0
// c7+c9*R^2
fma.s1 F_P79 = F_C9, F_R2, F_C7
nop.i 0
}
{.mfi
nop.m 0
// c3+c5*R^2
fma.s1 F_P35 = F_C5, F_R2, F_C3
nop.i 0;;
}
{.mfi
nop.m 0
// R^3
fma.s1 F_R4 = F_R2, F_R2, f0
nop.i 0;;
}
{.mfi
nop.m 0
// R^3
fma.s1 F_R3 = F_R2, F_R, f0
nop.i 0;;
}
{.mfi
nop.m 0
// c3+c5*R^2+c7*R^4+c9*R^6
fma.s1 F_P39 = F_P79, F_R4, F_P35
nop.i 0;;
}
{.mfi
nop.m 0
// asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
fma.s1 F_P39 = F_P39, F_R3, F_ATLO
nop.i 0;;
}
{.mfi
nop.m 0
// R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
fma.s1 F_P39 = F_P39, f1, F_R
nop.i 0;;
}
{.mfb
nop.m 0
// result = asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
fma.s0 f8 = F_ATHI, f1, F_P39
// return
br.ret.sptk b0;;
}
LARGE_S:
{.mfi
// bias-1
mov R_TMP3 = 0xffff - 1
// y ~ 1/sqrt(1-s^2)
frsqrta.s1 F_Y, p7 = F_1S2
// c9 = 55*13*17/128
mov R_TMP4 = 0x10af7b
}
{.mlx
// c8 = -33*13*15/128
mov R_TMP5 = 0x184923
movl R_TMP2 = 0xff00000000000000;;
}
{.mfi
// set p6 = 1 if s<0, p11 = 1 if s>0
cmp.ge p6, p11 = R_EXP, R_DBL_S
// 1-s^2
fnma.s1 F_1S2 = f8, f8, f1
// set p9 = 1
cmp.eq p9, p0 = r0, r0;;
}
{.mfi
// load 0.5
setf.exp F_05 = R_TMP3
// (1-s^2) rounded to single precision
fnma.s.s1 F_1S2_S = f8, f8, f1
// c9 = 55*13*17/128
shl R_TMP4 = R_TMP4, 10
}
{.mlx
// AND mask for getting t ~ sqrt(1-s^2)
setf.sig F_ANDMASK = R_TMP2
// OR mask
movl R_TMP2 = 0x0100000000000000;;
}
{.mfi
nop.m 0
// (s^2)_s
fma.s.s1 F_S2 = f8, f8, f0
nop.i 0;;
}
{.mmi
// c9 = 55*13*17/128
setf.s F_CS9 = R_TMP4
// c7 = 33*13/16
mov R_TMP4 = 0x41d68
// c8 = -33*13*15/128
shl R_TMP5 = R_TMP5, 11;;
}
{.mfi
setf.sig F_ORMASK = R_TMP2
// y^2
fma.s1 F_Y2 = F_Y, F_Y, f0
// c7 = 33*13/16
shl R_TMP4 = R_TMP4, 12
}
{.mfi
// c6 = -33*7/16
mov R_TMP6 = 0xc1670
// y' ~ sqrt(1-s^2)
fma.s1 F_T1 = F_Y, F_1S2, f0
// c5 = 63/8
mov R_TMP7 = 0x40fc;;
}
{.mlx
// load c8 = -33*13*15/128
setf.s F_CS8 = R_TMP5
// c4 = -35/8
movl R_TMP5 = 0xc08c0000;;
}
{.mfi
// r3 = pointer to polynomial coefficients
addl r3 = @ltoff(poly_coeffs), gp
// 1-(1-s^2)_s
fnma.s1 F_DS = F_1S2_S, f1, f1
// p9 = 0 if p7 = 1 (p9 = 1 for special cases only)
(p7) cmp.ne p9, p0 = r0, r0
}
{.mlx
// load c7 = 33*13/16
setf.s F_CS7 = R_TMP4
// c3 = 5/2
movl R_TMP4 = 0x40200000;;
}
{.mfi
nop.m 0
// 1-(s^2)_s
fnma.s1 F_S_1S2S = F_S2, f1, f1
nop.i 0
}
{.mlx
// load c4 = -35/8
setf.s F_CS4 = R_TMP5
// c2 = -3/2
movl R_TMP5 = 0xbfc00000;;
}
{.mfi
// load c3 = 5/2
setf.s F_CS3 = R_TMP4
// x = (1-s^2)_s*y^2-1
fms.s1 F_X = F_1S2_S, F_Y2, f1
// c6 = -33*7/16
shl R_TMP6 = R_TMP6, 12
}
{.mfi
nop.m 0
// y^2/2
fma.s1 F_Y2_2 = F_Y2, F_05, f0
nop.i 0;;
}
{.mfi
// load c6 = -33*7/16
setf.s F_CS6 = R_TMP6
// eliminate lower bits from y'
fand F_T = F_T1, F_ANDMASK
// c5 = 63/8
shl R_TMP7 = R_TMP7, 16
}
{.mfb
// r3 = load start address to polynomial coefficients
ld8 r3 = [r3]
// 1-(1-s^2)_s-s^2
fnma.s1 F_DS = f8, f8, F_DS
// p9 = 1 if s is a special input (NaN, or |s|> = 1)
(p9) br.cond.spnt ASINL_SPECIAL_CASES;;
}
{.mmf
// get exponent, significand of y' (in single prec.)
getf.s R_TMP = F_T1
// load c3 = -3/2
setf.s F_CS2 = R_TMP5
// y*(1-s^2)
fma.s1 F_Y1S2 = F_Y, F_1S2, f0;;
}
{.mfi
nop.m 0
// x' = (y^2/2)*(1-(s^2)_s)-0.5
fms.s1 F_XL = F_Y2_2, F_S_1S2S, F_05
nop.i 0
}
{.mfi
nop.m 0
// s^2-(s^2)_s
fms.s1 F_S_DS2 = f8, f8, F_S2
nop.i 0;;
}
{.mfi
nop.m 0
// if s<0, set s = -s
(p6) fnma.s1 f8 = f8, f1, f0
nop.i 0;;
}
{.mfi
// load c5 = 63/8
setf.s F_CS5 = R_TMP7
// x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2
fma.s1 F_X = F_DS, F_Y2, F_X
// for t = 2^k*1.b1 b2.., get 7-k|b1.. b6
extr.u R_INDEX = R_TMP, 17, 9;;
}
{.mmi
// index = (4-exponent)|b1 b2.. b6
sub R_INDEX = R_INDEX, R_BIAS
nop.m 0
// get exponent of y
shr.u R_TMP2 = R_TMP, 23;;
}
{.mmi
// load C3
ldfe F_C3 = [r3], 16
// set p8 = 1 if y'<2^{-4}
cmp.gt p8, p0 = 0x7b, R_TMP2
// shift R_INDEX by 5
shl R_INDEX = R_INDEX, 5;;
}
{.mfb
// get table index for sqrt(1-t^2)
add r2 = r2, R_INDEX
// get t = 2^k*1.b1 b2.. b7 1
for F_T = F_T, F_ORMASK
(p8) br.cond.spnt VERY_LARGE_INPUT;;
}
{.mmf
// load C5
ldfe F_C5 = [r3], 16
// load 1/(1-t^2)
ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16
// x = ((1-s^2)*y^2-1)/2
fma.s1 F_X = F_X, F_05, f0;;
}
{.mmf
nop.m 0
// C7, C9
ldfpd F_C7, F_C9 = [r3], 16
// set correct exponent for t
fmerge.se F_T = F_T1, F_T;;
}
{.mfi
// pi/2 (low, high)
ldfpd F_PI2_LO, F_PI2_HI = [r3]
// c9*x+c8
fma.s1 F_S89 = F_X, F_CS9, F_CS8
nop.i 0
}
{.mfi
nop.m 0
// x^2
fma.s1 F_X2 = F_X, F_X, f0
nop.i 0;;
}
{.mfi
nop.m 0
// y*(1-s^2)*x
fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
nop.i 0
}
{.mfi
nop.m 0
// c7*x+c6
fma.s1 F_S67 = F_X, F_CS7, F_CS6
nop.i 0;;
}
{.mfi
nop.m 0
// 1-x
fnma.s1 F_1X = F_X, f1, f1
nop.i 0
}
{.mfi
nop.m 0
// c3*x+c2
fma.s1 F_S23 = F_X, F_CS3, F_CS2
nop.i 0;;
}
{.mfi
nop.m 0
// 1-t^2
fnma.s1 F_1T2 = F_T, F_T, f1
nop.i 0
}
{.mfi
// load asin(t)_high, asin(t)_low
ldfpd F_ATHI, F_ATLO = [r2]
// c5*x+c4
fma.s1 F_S45 = F_X, F_CS5, F_CS4
nop.i 0;;
}
{.mfi
nop.m 0
// t*s
fma.s1 F_TS = F_T, f8, f0
nop.i 0
}
{.mfi
nop.m 0
// 0.5/(1-t^2)
fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
nop.i 0;;
}
{.mfi
nop.m 0
// z~sqrt(1-t^2), rounded to 24 significant bits
fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0
nop.i 0
}
{.mfi
nop.m 0
// sqrt(1-t^2)
fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
nop.i 0;;
}
{.mfi
nop.m 0
// y*(1-s^2)*x^2
fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
nop.i 0
}
{.mfi
nop.m 0
// x^4
fma.s1 F_X4 = F_X2, F_X2, f0
nop.i 0;;
}
{.mfi
nop.m 0
// s*t rounded to 24 significant bits
fma.s.s1 F_TSS = F_T, f8, f0
nop.i 0
}
{.mfi
nop.m 0
// c9*x^3+..+c6
fma.s1 F_S69 = F_X2, F_S89, F_S67
nop.i 0;;
}
{.mfi
nop.m 0
// ST = (t^2-1+s^2) rounded to 24 significant bits
fms.s.s1 F_ST = f8, f8, F_1T2
nop.i 0
}
{.mfi
nop.m 0
// c5*x^3+..+c2
fma.s1 F_S25 = F_X2, F_S45, F_S23
nop.i 0;;
}
{.mfi
nop.m 0
// 0.25/(1-t^2)
fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0
nop.i 0
}
{.mfi
nop.m 0
// t*s-sqrt(1-t^2)*(1-s^2)*y
fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS
nop.i 0;;
}
{.mfi
nop.m 0
// z*0.5/(1-t^2)
fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0
nop.i 0
}
{.mfi
nop.m 0
// z^2+t^2-1
fms.s1 F_DZ0 = F_Z, F_Z, F_1T2
nop.i 0;;
}
{.mfi
nop.m 0
// (1-s^2-(1-s^2)_s)*x
fma.s1 F_DS2X = F_X, F_DS, f0
nop.i 0;;
}
{.mfi
nop.m 0
// t*s-(t*s)_s
fms.s1 F_DTS = F_T, f8, F_TSS
nop.i 0
}
{.mfi
nop.m 0
// c9*x^7+..+c2
fma.s1 F_S29 = F_X4, F_S69, F_S25
nop.i 0;;
}
{.mfi
nop.m 0
// y*z
fma.s1 F_YZ = F_Z, F_Y, f0
nop.i 0
}
{.mfi
nop.m 0
// t^2
fma.s1 F_T2 = F_T, F_T, f0
nop.i 0;;
}
{.mfi
nop.m 0
// 1-t^2+ST
fma.s1 F_1T2_ST = F_ST, f1, F_1T2
nop.i 0;;
}
{.mfi
nop.m 0
// y*(1-s^2)(1-x)
fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0
nop.i 0
}
{.mfi
nop.m 0
// dz ~ sqrt(1-t^2)-z
fma.s1 F_DZ = F_DZ0, F_ZE, f0
nop.i 0;;
}
{.mfi
nop.m 0
// -1+correction for sqrt(1-t^2)-z
fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0
nop.i 0;;
}
{.mfi
nop.m 0
// (PS29*x^2+x)*y*(1-s^2)
fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
nop.i 0;;
}
{.mfi
nop.m 0
// z*y*(1-s^2)_s
fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0
nop.i 0
}
{.mfi
nop.m 0
// s^2-(1-t^2+ST)
fms.s1 F_1T2_ST = f8, f8, F_1T2_ST
nop.i 0;;
}
{.mfi
nop.m 0
// (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x
fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS
nop.i 0
}
{.mfi
nop.m 0
// dz*y*(1-s^2)*(1-x)
fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0
nop.i 0;;
}
{.mfi
nop.m 0
// R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19
// (used for polynomial evaluation)
fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS
nop.i 0;;
}
{.mfi
nop.m 0
// (PS29*x^2)*y*(1-s^2)
fma.s1 F_S29 = F_Y1S2X2, F_S29, f0
nop.i 0
}
{.mfi
nop.m 0
// apply correction to dz*y*(1-s^2)*(1-x)
fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM
nop.i 0;;
}
{.mfi
nop.m 0
// R^2
fma.s1 F_R2 = F_R, F_R, f0
nop.i 0;;
}
{.mfi
nop.m 0
// (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x)
fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS
nop.i 0;;
}
{.mfi
nop.m 0
// c7+c9*R^2
fma.s1 F_P79 = F_C9, F_R2, F_C7
nop.i 0
}
{.mfi
nop.m 0
// c3+c5*R^2
fma.s1 F_P35 = F_C5, F_R2, F_C3
nop.i 0;;
}
{.mfi
nop.m 0
// asin(t)_low-(pi/2)_low
fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO
nop.i 0
}
{.mfi
nop.m 0
// R^4
fma.s1 F_R4 = F_R2, F_R2, f0
nop.i 0;;
}
{.mfi
nop.m 0
// R^3
fma.s1 F_R3 = F_R2, F_R, f0
nop.i 0;;
}
{.mfi
nop.m 0
// (t*s)_s-t^2*y*z
fnma.s1 F_TSS = F_T2, F_YZ, F_TSS
nop.i 0
}
{.mfi
nop.m 0
// d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)
fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM
nop.i 0;;
}
{.mfi
nop.m 0
// (pi/2)_hi-asin(t)_hi
fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI
nop.i 0
}
{.mfi
nop.m 0
// c3+c5*R^2+c7*R^4+c9*R^6
fma.s1 F_P39 = F_P79, F_R4, F_P35
nop.i 0;;
}
{.mfi
nop.m 0
// d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+
// + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29
fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM
nop.i 0;;
}
{.mfi
nop.m 0
// (t*s)_s-t^2*y*z+z*y*ST
fma.s1 F_TSS = F_YZ, F_ST, F_TSS
nop.i 0
}
{.mfi
nop.m 0
// -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
fms.s1 F_P39 = F_P39, F_R3, F_ATLO
nop.i 0;;
}
{.mfi
nop.m 0
// if s<0, change sign of F_ATHI
(p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
nop.i 0
}
{.mfi
nop.m 0
// d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
// + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 +
// - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
fma.s1 F_DZ_TERM = F_P39, f1, F_DZ_TERM
nop.i 0;;
}
{.mfi
nop.m 0
// d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
// + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
// - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM
nop.i 0;;
}
{.mfi
nop.m 0
// d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
// + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
// - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) +
// + (t*s)_s-t^2*y*z+z*y*ST
fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM
nop.i 0;;
}
.pred.rel "mutex", p6, p11
{.mfi
nop.m 0
// result: add high part of pi/2-table value
// s>0 in this case
(p11) fma.s0 f8 = F_DZ_TERM, f1, F_ATHI
nop.i 0
}
{.mfb
nop.m 0
// result: add high part of pi/2-table value
// if s<0
(p6) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI
br.ret.sptk b0;;
}
SMALL_S:
// use 15-term polynomial approximation
{.mmi
// r3 = pointer to polynomial coefficients
addl r3 = @ltoff(poly_coeffs), gp;;
// load start address for coefficients
ld8 r3 = [r3]
mov R_TMP = 0x3fbf;;
}
{.mmi
add r2 = 64, r3
ldfe F_C3 = [r3], 16
// p7 = 1 if |s|<2^{-64} (exponent of s<bias-64)
cmp.lt p7, p0 = R_EXP0, R_TMP;;
}
{.mmf
ldfe F_C5 = [r3], 16
ldfpd F_C11, F_C13 = [r2], 16
// 2^{-128}
fma.s1 F_2M128 = F_2M64, F_2M64, f0;;
}
{.mmf
ldfpd F_C7, F_C9 = [r3]
ldfpd F_C15, F_C17 = [r2]
// if |s|<2^{-64}, return s+2^{-128}*s
(p7) fma.s0 f8 = f8, F_2M128, f8;;
}
{.mfb
nop.m 0
// s^2
fma.s1 F_R2 = f8, f8, f0
// if |s|<2^{-64}, return s
(p7) br.ret.spnt b0;;
}
{.mfi
nop.m 0
// s^3
fma.s1 F_R3 = f8, F_R2, f0
nop.i 0
}
{.mfi
nop.m 0
// s^4
fma.s1 F_R4 = F_R2, F_R2, f0
nop.i 0;;
}
{.mfi
nop.m 0
// c3+c5*s^2
fma.s1 F_P35 = F_C5, F_R2, F_C3
nop.i 0
}
{.mfi
nop.m 0
// c11+c13*s^2
fma.s1 F_P1113 = F_C13, F_R2, F_C11
nop.i 0;;
}
{.mfi
nop.m 0
// c7+c9*s^2
fma.s1 F_P79 = F_C9, F_R2, F_C7
nop.i 0
}
{.mfi
nop.m 0
// c15+c17*s^2
fma.s1 F_P1517 = F_C17, F_R2, F_C15
nop.i 0;;
}
{.mfi
nop.m 0
// s^8
fma.s1 F_R8 = F_R4, F_R4, f0
nop.i 0;;
}
{.mfi
nop.m 0
// c3+c5*s^2+c7*s^4+c9*s^6
fma.s1 F_P39 = F_P79, F_R4, F_P35
nop.i 0
}
{.mfi
nop.m 0
// c11+c13*s^2+c15*s^4+c17*s^6
fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
nop.i 0;;
}
{.mfi
nop.m 0
// c3+..+c17*s^14
fma.s1 F_P317 = F_R8, F_P1117, F_P39
nop.i 0;;
}
{.mfb
nop.m 0
// result
fma.s0 f8 = F_P317, F_R3, f8
br.ret.sptk b0;;
}
{.mfb
nop.m 0
fma.s0 f8 = F_P317, F_R3, f0//F_P317, F_R3, F_S29
// nop.f 0//fma.s0 f8 = f13, f6, f0
br.ret.sptk b0;;
}
VERY_LARGE_INPUT:
{.mfi
nop.m 0
// s rounded to 24 significant bits
fma.s.s1 F_S = f8, f1, f0
nop.i 0
}
{.mfi
// load C5
ldfe F_C5 = [r3], 16
// x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2
fnma.s1 F_X = F_S_DS2, F_Y2_2, F_XL
nop.i 0;;
}
{.mmf
nop.m 0
// C7, C9
ldfpd F_C7, F_C9 = [r3], 16
nop.f 0;;
}
{.mfi
// pi/2 (low, high)
ldfpd F_PI2_LO, F_PI2_HI = [r3], 16
// c9*x+c8
fma.s1 F_S89 = F_X, F_CS9, F_CS8
nop.i 0
}
{.mfi
nop.m 0
// x^2
fma.s1 F_X2 = F_X, F_X, f0
nop.i 0;;
}
{.mfi
nop.m 0
// y*(1-s^2)*x
fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
nop.i 0
}
{.mfi
// C11, C13
ldfpd F_C11, F_C13 = [r3], 16
// c7*x+c6
fma.s1 F_S67 = F_X, F_CS7, F_CS6
nop.i 0;;
}
{.mfi
// C15, C17
ldfpd F_C15, F_C17 = [r3], 16
// c3*x+c2
fma.s1 F_S23 = F_X, F_CS3, F_CS2
nop.i 0;;
}
{.mfi
nop.m 0
// c5*x+c4
fma.s1 F_S45 = F_X, F_CS5, F_CS4
nop.i 0;;
}
{.mfi
nop.m 0
// (s_s)^2
fma.s1 F_DS = F_S, F_S, f0
nop.i 0
}
{.mfi
nop.m 0
// 1-(s_s)^2
fnma.s1 F_1S2_S = F_S, F_S, f1
nop.i 0;;
}
{.mfi
nop.m 0
// y*(1-s^2)*x^2
fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
nop.i 0
}
{.mfi
nop.m 0
// x^4
fma.s1 F_X4 = F_X2, F_X2, f0
nop.i 0;;
}
{.mfi
nop.m 0
// c9*x^3+..+c6
fma.s1 F_S69 = F_X2, F_S89, F_S67
nop.i 0;;
}
{.mfi
nop.m 0
// c5*x^3+..+c2
fma.s1 F_S25 = F_X2, F_S45, F_S23
nop.i 0;;
}
{.mfi
nop.m 0
// ((s_s)^2-s^2)
fnma.s1 F_DS = f8, f8, F_DS
nop.i 0
}
{.mfi
nop.m 0
// (pi/2)_high-y*(1-(s_s)^2)
fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI
nop.i 0;;
}
{.mfi
nop.m 0
// c9*x^7+..+c2
fma.s1 F_S29 = F_X4, F_S69, F_S25
nop.i 0;;
}
{.mfi
nop.m 0
// -(y*(1-(s_s)^2))_high
fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI
nop.i 0;;
}
{.mfi
nop.m 0
// (PS29*x^2+x)*y*(1-s^2)
fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
nop.i 0;;
}
{.mfi
nop.m 0
// y*(1-(s_s)^2)-(y*(1-s^2))_high
fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI
nop.i 0;;
}
{.mfi
nop.m 0
// R ~ sqrt(1-s^2)
// (used for polynomial evaluation)
fnma.s1 F_R = F_S19, f1, F_Y1S2
nop.i 0;;
}
{.mfi
nop.m 0
// y*(1-s^2)-(y*(1-s^2))_high
fma.s1 F_DS2 = F_Y, F_DS, F_DS2
nop.i 0
}
{.mfi
nop.m 0
// (pi/2)_low+(PS29*x^2)*y*(1-s^2)
fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO
nop.i 0;;
}
{.mfi
nop.m 0
// R^2
fma.s1 F_R2 = F_R, F_R, f0
nop.i 0;;
}
{.mfi
nop.m 0
// (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)
fms.s1 F_S29 = F_S29, f1, F_DS2
nop.i 0;;
}
{.mfi
nop.m 0
// c7+c9*R^2
fma.s1 F_P79 = F_C9, F_R2, F_C7
nop.i 0
}
{.mfi
nop.m 0
// c3+c5*R^2
fma.s1 F_P35 = F_C5, F_R2, F_C3
nop.i 0;;
}
{.mfi
nop.m 0
// R^4
fma.s1 F_R4 = F_R2, F_R2, f0
nop.i 0
}
{.mfi
nop.m 0
// R^3
fma.s1 F_R3 = F_R2, F_R, f0
nop.i 0;;
}
{.mfi
nop.m 0
// c11+c13*R^2
fma.s1 F_P1113 = F_C13, F_R2, F_C11
nop.i 0
}
{.mfi
nop.m 0
// c15+c17*R^2
fma.s1 F_P1517 = F_C17, F_R2, F_C15
nop.i 0;;
}
{.mfi
nop.m 0
// (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x
fma.s1 F_S29 = F_Y1S2, F_X, F_S29
nop.i 0;;
}
{.mfi
nop.m 0
// c11+c13*R^2+c15*R^4+c17*R^6
fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
nop.i 0
}
{.mfi
nop.m 0
// c3+c5*R^2+c7*R^4+c9*R^6
fma.s1 F_P39 = F_P79, F_R4, F_P35
nop.i 0;;
}
{.mfi
nop.m 0
// R^8
fma.s1 F_R8 = F_R4, F_R4, f0
nop.i 0;;
}
{.mfi
nop.m 0
// c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14
fma.s1 F_P317 = F_P1117, F_R8, F_P39
nop.i 0;;
}
{.mfi
nop.m 0
// (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
// -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
fnma.s1 F_S29 = F_P317, F_R3, F_S29
nop.i 0;;
}
{.mfi
nop.m 0
// set sign
(p6) fnma.s1 F_S29 = F_S29, f1, f0
nop.i 0
}
{.mfi
nop.m 0
(p6) fnma.s1 F_HI = F_HI, f1, f0
nop.i 0;;
}
{.mfb
nop.m 0
// Result:
// (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
// -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
// +(pi/2)_high-(y*(1-s^2))_high
fma.s0 f8 = F_S29, f1, F_HI
br.ret.sptk b0;;
}
ASINL_SPECIAL_CASES:
{.mfi
alloc r32 = ar.pfs, 1, 4, 4, 0
// check if the input is a NaN, or unsupported format
// (i.e. not infinity or normal/denormal)
fclass.nm p7, p8 = f8, 0x3f
// pointer to pi/2
add r3 = 48, r3;;
}
{.mfi
// load pi/2
ldfpd F_PI2_HI, F_PI2_LO = [r3]
// get |s|
fmerge.s F_S = f0, f8
nop.i 0
}
{.mfb
nop.m 0
// if NaN, quietize it, and return
(p7) fma.s0 f8 = f8, f1, f0
(p7) br.ret.spnt b0;;
}
{.mfi
nop.m 0
// |s| = 1 ?
fcmp.eq.s0 p9, p0 = F_S, f1
nop.i 0
}
{.mfi
nop.m 0
// load FR_X
fma.s1 FR_X = f8, f1, f0
// load error tag
mov GR_Parameter_TAG = 60;;
}
{.mfb
nop.m 0
// change sign if s = -1
(p6) fnma.s1 F_PI2_HI = F_PI2_HI, f1, f0
nop.b 0
}
{.mfb
nop.m 0
// change sign if s = -1
(p6) fnma.s1 F_PI2_LO = F_PI2_LO, f1, f0
nop.b 0;;
}
{.mfb
nop.m 0
// if s = 1, result is pi/2
(p9) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
// return if |s| = 1
(p9) br.ret.sptk b0;;
}
{.mfi
nop.m 0
// get Infinity
frcpa.s1 FR_RESULT, p0 = f1, f0
nop.i 0;;
}
{.mfi
nop.m 0
// return QNaN indefinite (0*Infinity)
fma.s0 FR_RESULT = f0, FR_RESULT, f0
nop.i 0;;
}
GLOBAL_LIBM_END(asinl)
LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
// (1)
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
add sp=-64,sp // Create new stack
nop.f 0
mov GR_SAVE_GP=gp // Save gp
};;
// (2)
{ .mmi
stfe [GR_Parameter_Y] = f1,16 // Store Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
// (3)
{ .mib
stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y
nop.b 0 // Parameter 3 address
}
{ .mib
stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
nop.m 0
nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
// (4)
{ .mmi
ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
add sp = 64,sp // Restore stack pointer
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mib
mov gp = GR_SAVE_GP // Restore gp
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
br.ret.sptk b0 // Return
};;
LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
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