2012-04-17 02:02:27 +00:00
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.file "asinl.s"
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// Copyright (c) 2001 - 2003, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2001 by the Intel Numerics Group, Intel Corporation
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//==============================================================
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// 08/28/01 New version
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/06/03 Reordered header: .section, .global, .proc, .align
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//
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// API
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//==============================================================
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// long double asinl(long double)
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//
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// Overview of operation
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//==============================================================
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// Background
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//
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// Implementation
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//
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// For |s| in [2^{-4}, sqrt(2)/2]:
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// Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52
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// asin(s)= asin(t)+asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e.
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// r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1)
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// asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9)
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// The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table,
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// along with the high and low parts of asin(t) (stored as two double precision
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// values)
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//
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// |s| in (sqrt(2)/2, sqrt(255/256)):
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// Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6..
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// asin(|s|)= pi/2-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2)
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// To minimize accumulated errors, r is computed as
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// 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+
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// +(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)+
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// +ez*z'*y*(1-s^2)*(1-x),
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// where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits)
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// z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2
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//
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// |s|<2^{-4}: evaluate as 17-degree polynomial
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// (or simply return s, if|s|<2^{-64})
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//
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// |s| in [sqrt(255/256), 1): asin(|s|)= pi/2-asin(sqrt(1-s^2))
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// use 17-degree polynomial for asin(sqrt(1-s^2)),
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// 9-degree polynomial to evaluate sqrt(1-s^2)
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// High order term is (pi/2)_high-(y*(1-s^2))_high
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//
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// Registers used
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//==============================================================
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// f6-f15, f32-f36
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// r2-r3, r23-r23
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// p6, p7, p8, p12
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//
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GR_SAVE_B0= r33
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GR_SAVE_PFS= r34
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GR_SAVE_GP= r35 // This reg. can safely be used
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GR_SAVE_SP= r36
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GR_Parameter_X= r37
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GR_Parameter_Y= r38
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GR_Parameter_RESULT= r39
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GR_Parameter_TAG= r40
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FR_X= f10
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FR_Y= f1
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FR_RESULT= f8
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RODATA
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.align 16
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LOCAL_OBJECT_START(T_table)
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// stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2),
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// asin(t)_high (double precision), asin(t)_low (double precision)
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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
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|
|
|
//data8 0x94503d69396d91c7, 0xedd2ce885ff04028
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|
|
//data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b
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|
|
//data8 0xced1d96c5bb209e6, 0xc965278083808702
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|
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|
|
//data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c
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|
|
//data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd
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|
|
//data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e
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|
|
//data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4
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|
|
//data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb
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|
|
LOCAL_OBJECT_END(T_table)
|
|
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|
|
.align 16
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|
|
|
LOCAL_OBJECT_START(poly_coeffs)
|
|
|
|
|
// C_3
|
|
|
|
|
data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc
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|
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|
|
// C_5
|
|
|
|
|
data8 0x999999999999999a, 0x0000000000003ffb
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|
|
|
// C_7, C_9
|
|
|
|
|
data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8
|
|
|
|
|
// pi/2 (low, high)
|
|
|
|
|
data8 0x3C91A62633145C07, 0x3FF921FB54442D18
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|
|
// C_11, C_13
|
|
|
|
|
data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e
|
|
|
|
|
// C_15, C_17
|
|
|
|
|
data8 0x3f8c99999999999a, 0x3f87a87878787223
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|
|
LOCAL_OBJECT_END(poly_coeffs)
|
|
|
|
|
|
|
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|
|
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
|
|
|
|
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|
|
F_T = f6
|
|
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|
|
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
|
|
|
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|
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|
|
F_CS2 = f32
|
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|
|
F_CS3 = f33
|
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|
|
F_CS4 = f34
|
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|
|
F_CS5 = f35
|
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|
|
F_CS6 = f36
|
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|
|
F_CS7 = f37
|
|
|
|
|
F_CS8 = f38
|
|
|
|
|
F_CS9 = f39
|
2012-04-17 02:08:04 +00:00
|
|
|
F_S23 = f40
|
|
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|
|
F_S45 = f41
|
|
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|
|
F_S67 = f42
|
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|
|
F_S89 = f43
|
|
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|
|
F_S25 = f44
|
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|
|
F_S69 = f45
|
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|
|
F_S29 = f46
|
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|
|
F_X2 = f47
|
|
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|
|
F_X4 = f48
|
|
|
|
|
F_TSQRT = f49
|
|
|
|
|
F_DTX = f50
|
|
|
|
|
F_R = f51
|
|
|
|
|
F_R2 = f52
|
|
|
|
|
F_R3 = f53
|
|
|
|
|
F_R4 = f54
|
2012-04-17 02:02:27 +00:00
|
|
|
|
2012-04-17 02:08:04 +00:00
|
|
|
F_C3 = f55
|
|
|
|
|
F_C5 = f56
|
|
|
|
|
F_C7 = f57
|
|
|
|
|
F_C9 = f58
|
|
|
|
|
F_P79 = f59
|
|
|
|
|
F_P35 = f60
|
|
|
|
|
F_P39 = f61
|
2012-04-17 02:02:27 +00:00
|
|
|
|
2012-04-17 02:08:04 +00:00
|
|
|
F_ATHI = f62
|
|
|
|
|
F_ATLO = f63
|
2012-04-17 02:02:27 +00:00
|
|
|
|
2012-04-17 02:08:04 +00:00
|
|
|
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
|
2012-04-17 02:02:27 +00:00
|
|
|
F_TS = f91
|
2012-04-17 02:08:04 +00:00
|
|
|
F_PI2_LO = f92
|
|
|
|
|
F_PI2_HI = f93
|
|
|
|
|
F_S19 = f94
|
|
|
|
|
F_INV1T2_2 = f95
|
|
|
|
|
F_CORR = f96
|
|
|
|
|
F_DZ0 = f97
|
2012-04-17 02:02:27 +00:00
|
|
|
|
2012-04-17 02:08:04 +00:00
|
|
|
F_C11 = f98
|
|
|
|
|
F_C13 = f99
|
2012-04-17 02:02:27 +00:00
|
|
|
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#
|
