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glibc/sysdeps/ia64/fpu/s_tanh.S
Siddhesh Poyarekar 30891f35fa Remove "Contributed by" lines 
We stopped adding "Contributed by" or similar lines in sources in 2012
in favour of git logs and keeping the Contributors section of the
glibc manual up to date.  Removing these lines makes the license
header a bit more consistent across files and also removes the
possibility of error in attribution when license blocks or files are
copied across since the contributed-by lines don't actually reflect
reality in those cases.

Move all "Contributed by" and similar lines (Written by, Test by,
etc.) into a new file CONTRIBUTED-BY to retain record of these
contributions.  These contributors are also mentioned in
manual/contrib.texi, so we just maintain this additional record as a
courtesy to the earlier developers.

The following scripts were used to filter a list of files to edit in
place and to clean up the CONTRIBUTED-BY file respectively.  These
were not added to the glibc sources because they're not expected to be
of any use in future given that this is a one time task:

https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc
https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02

Reviewed-by: Carlos O'Donell <carlos@redhat.com>
2021-09-03 22:06:44 +05:30

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.file "tanh.s"
// Copyright (c) 2001 - 2005, Intel Corporation
// All rights reserved.
//
//
// 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
//==============================================================================
// 05/30/01 Initial version
// 12/04/01 Rewritten version with erf-like algorithm.
// Performance improved.
// 05/20/02 Cleaned up namespace and sf0 syntax
// 08/14/02 Changed mli templates to mlx
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================================
// double tanh(double)
//
// Overview of operation
//==============================================================================
//
// Algorithm description
// ---------------------
//
// There are 4 paths:
//
// 1. Special path: x = 0, Inf, NaNs, denormals
// Return tanh(x) = +/-0.0 for zeros
// Return tanh(x) = QNaN for NaNs
// Return tanh(x) = sign(x)*1.0 for Inf
// Return tanh(x) = x + x^2 for - denormals
// Return tanh(x) = x - x^2 for + denormals
//
// 2. Near zero path: 0.0 < |x| < 0.25
// Return tanh(x) = x + x^3*A3 + ... + x^19*A19
//
// 3. Main path: 0.25 <= |x| < 19.0625
// For several ranges of 0.25 <= |x| < 19.0625
// Return tanh(x) = sign(x)*(A0 + y*A1 + y^2*A2 +
// + y^3*A3 + ... + y^19*A19)
// where y = (|x|/a) - b
//
// For each range there is particular set of coefficients.
// Below is the list of ranges:
// 1/4 <= |x| < 1/2 a = 0.25, b = 1.0
// 1/2 <= |x| < 1.0 a = 0.5, b = 1.0
// 1.0 <= |x| < 2.0 a = 1.0, b = 1.0
// 2.0 <= |x| < 3.25 a = 2.0, b = 1.0
// 3.25 <= |x| < 4.0 a = 2.0, b = 2.0
// 4.0 <= |x| < 6.5 a = 4.0, b = 1.0
// 6.5 <= |x| < 8.0 a = 4.0, b = 2.0
// 8.0 <= |x| < 13.0 a = 8.0, b = 1.0
// 13.0 <= |x| < 16.0 a = 8.0, b = 2.0
// 16.0 <= |x| < 19.0625 a = 16.0, b = 1.0
// ( [3.25;4.0], [6.5;8.0], [13.0;16.0] subranges separated
// for monotonicity issues resolve )
//
// 4. Saturation path: 19.0625 <= |x| < +INF
// Return tanh(x) = sign(x)*(1.0 - tiny_value)
// (tiny_value ~ 2^(-63))
//
// Registers used
//==============================================================================
// Floating Point registers used:
// f8 = input, output
// f32 -> f64
//
// General registers used:
// r32 -> r51, r2, r3
//
// Predicate registers used:
// p6, p8, p10, p11, p12, p14, p15
// p6 arg is zero, denormal or special IEEE
// p8 to filter out case when signd(x) > 1.625
// p10 to filter out case when |x| < 0.25
// p11 to filter out case when signd(x) <= 1.625
// p12 to filter out case when |x| >= 19.0625
// p14 set to 1 for positive x
// p15 set to 1 for negative x
// Assembly macros
//==============================================================================
rDataPtr = r2
rDataPtr1 = r3
rBias = r33
rCoeffAddr3 = r34
rThreeAndQ = r35
rCoeffAddr2 = r36
rMask = r37
rArg = r38
rSignBit = r39
rAbsArg = r40
rSaturation = r41
rIndex = r42
rCoeffAddr1 = r43
rCoeffAddr4 = r44
rShiftedArg = r45
rShiftedArgMasked = r46
rBiasedExpOf4 = r47
rShiftedAbsArg = r48
rArgSgnd = r49
r1625Sgnd = r50
rTwo = r51
//==============================================================================
fA0 = f32
fA1 = f33
fA2 = f34
fA3 = f35
fA4 = f36
fA5 = f37
fA6 = f38
fA7 = f39
fA8 = f40
fA9 = f41
fA10 = f42
fA11 = f43
fA12 = f44
fA13 = f45
fA14 = f46
fA15 = f47
fA16 = f48
fA17 = f49
fA18 = f50
fA19 = f51
fArgSqr = f52
fArgAbsNorm = f53
fSignumX = f54
fRes = f55
fThreeAndQ = f56
fArgAbs = f57
fTSqr = f58
fTQuadr = f59
fTDeg3 = f60
fTDeg7 = f61
fArgAbsNormSgn = f62
fTQuadrSgn = f63
fTwo = f64
// Data tables
//==============================================================================
RODATA
.align 16
LOCAL_OBJECT_START(tanh_data)
// CAUTION: The order of these table coefficients shouldn't be changed!
// Main path coefficients:
// Coefficients ##0..15 ("main" coefficient tables)
// Polynomial coefficients for the tanh(x), 0.25 <= |x| < 0.5
data8 0xE9D218BC9A3FB55A, 0x00003FC7 //A19
data8 0xC8C0D38687F36EBA, 0x00003FCE //A18
data8 0xA2663E519FAC8A43, 0x0000BFD2 //A17
data8 0xD913F0490674B0DF, 0x00003FD3 //A16
data8 0xF75D84789DE0AE52, 0x00003FD6 //A15
data8 0xACB3C40EEF3A06F0, 0x0000BFD9 //A14
data8 0xEBD7F5DC02CFD5BA, 0x0000BFDB //A13
data8 0x8B52CDF66D709E2A, 0x00003FDF //A12
data8 0x9EC21F28E05C4A3E, 0x00003FE0 //A11
data8 0xC412B44D0176F3ED, 0x0000BFE4 //A10
data8 0x97BF35A34DD1EA4C, 0x0000BFE0 //A9
data8 0xF89F5B39E3A3AA36, 0x00003FE9 //A8
data8 0xF2BA654BCEEBA433, 0x0000BFEA //A7
data8 0x8E1C15876AA589AD, 0x0000BFEF //A6
data8 0x942226246A8C2A86, 0x00003FF1 //A5
data8 0x8F06D9FF7DB47261, 0x00003FF4 //A4
//
// Polynomial coefficients for the tanh(x), 0.5 <= |x| < 1.0
data8 0xC4A7B8FB672A8520, 0x00003FDC //A19
data8 0xA20724B847E13499, 0x0000BFE0 //A18
data8 0xE17DB53F02E4D340, 0x00003FE2 //A17
data8 0x90264A1012F4CA6F, 0x0000BFE4 //A16
data8 0xEBEC9F776F0BF415, 0x0000BFE0 //A15
data8 0x89AF912B305B45A4, 0x00003FE7 //A14
data8 0xB4A960B81F5EC36A, 0x0000BFE7 //A13
data8 0x969A4E95B2DA86B5, 0x0000BFEA //A12
data8 0x8A3FC0EC082305CB, 0x00003FEC //A11
data8 0x83D7795BCBE24373, 0x00003FEC //A10
data8 0xDCBF42AEB82932EC, 0x0000BFEF //A9
data8 0x83318E61ECAFD804, 0x00003FF0 //A8
data8 0xEA4DE5746975A914, 0x00003FF2 //A7
data8 0xCE63E8FA6B96480B, 0x0000BFF4 //A6
data8 0xDF017BE0D4FE45D8, 0x0000BFF4 //A5
data8 0xA8A0C6E2226DF3CD, 0x00003FF8 //A4
//
// Polynomial coefficients for the tanh(x), 1.0 <= |x| < 2.0
data8 0x8E89D2EBFDAA160B, 0x00003FE9 //A19
data8 0xDD9226310A272046, 0x0000BFEC //A18
data8 0xA038042D28B0D665, 0x00003FEF //A17
data8 0x8C04796F03516306, 0x0000BFF1 //A16
data8 0x9CD6A9CB4E90A2FD, 0x00003FF2 //A15
data8 0xC8980E166F5A84FD, 0x0000BFF2 //A14
data8 0x9ADFE65F56B7BCFD, 0x00003FED //A13
data8 0x8B11FDFB5D0A7B96, 0x00003FF4 //A12
data8 0x8209A125E829CBFA, 0x0000BFF5 //A11
data8 0xCF38AAC17B85BD76, 0x00003FF1 //A10
data8 0xD5C2E248D8AB99AB, 0x00003FF6 //A9
data8 0xE12BE2785727F2D6, 0x0000BFF7 //A8
data8 0x9FC9EF90F87BF1E2, 0x00003FF6 //A7
data8 0x9B02FE0DAF42C08F, 0x00003FF9 //A6
data8 0xBDACE06F531D9491, 0x0000BFFA //A5
data8 0xE3048AD1DB2F648C, 0x00003FF9 //A4
//
// Polynomial coefficients for the tanh(x), 2.0 <= |x| < 3.25
data8 0x856EC3B0330A385A, 0x00003FEB //A19
data8 0xC641D69DAE2D429C, 0x0000BFF2 //A18
data8 0xC683EB0BE1343FFF, 0x00003FF5 //A17
data8 0xC358954224E4E823, 0x0000BFF7 //A16
data8 0xF813A8D6D396BC5F, 0x00003FF8 //A15
data8 0xE0ECDFED078D37D6, 0x0000BFF9 //A14
data8 0x950E4E619855E316, 0x00003FFA //A13
data8 0x8453B8F93370FB58, 0x0000BFFA //A12
data8 0xFDBA28430AEC95BA, 0x00003FF7 //A11
data8 0x9371AAC1FDB1E664, 0x00003FFA //A10
data8 0xAC972DA97782D88A, 0x0000BFFB //A9
data8 0xE18F47B10B9CE1BC, 0x00003FFB //A8
data8 0xAB7C81230BF13BC6, 0x0000BFFB //A7
data8 0xA6CAAD4A3E31A7D5, 0x0000BFF8 //A6
data8 0x9CABD76D1D5C3878, 0x00003FFC //A5
data8 0x92906D077941CAA9, 0x0000BFFD //A4
//
// Polynomial coefficients for the tanh(x), 4.0 <= |x| < 6.5
data8 0x9232D19F71709AC9, 0x0000BFF5 //A19
data8 0x819E31323F5DD3F8, 0x00003FF8 //A18
data8 0xDA8E1CDB8D23DC29, 0x0000BFF9 //A17
data8 0xE97C7CD8FC0486D8, 0x00003FFA //A16
data8 0xB0C4AD234D88C9F2, 0x0000BFFB //A15
data8 0xC5989BFB28FDE267, 0x00003FFB //A14
data8 0x9B26520EC4EFEE8E, 0x0000BFFB //A13
data8 0xC4B6F758AD21E574, 0x00003FF9 //A12
data8 0xCC36E3FFA10D2CFF, 0x00003FFA //A11
data8 0x8738696FB06A5CED, 0x0000BFFC //A10
data8 0xD31981825BF39228, 0x00003FFC //A9
data8 0x82C58FB9BEE43992, 0x0000BFFD //A8
data8 0x88D5AAE49164B6F3, 0x00003FFD //A7
data8 0xF4CA0B968AF2DDE2, 0x0000BFFC //A6
data8 0xB99874B482BD17EE, 0x00003FFC //A5
data8 0xE93FB2F99431DC1D, 0x0000BFFB //A4
//
// Polynomial coefficients for the tanh(x), 8.0 <= |x| < 13.0
data8 0xAAA9EB7EADA85CEC, 0x00003FF5 //A19
data8 0x980C80EE05A6BE78, 0x0000BFF8 //A18
data8 0x818DA9F5396390A5, 0x00003FFA //A17
data8 0x8D8CC21E23D8A6A2, 0x0000BFFB //A16
data8 0xE0EC19E55A886765, 0x00003FFB //A15
data8 0x8C11197A7E6244C5, 0x0000BFFC //A14
data8 0x901D2BF203C2F7F3, 0x00003FFC //A13
data8 0xFEACAEE66EE803E5, 0x0000BFFB //A12
data8 0xC684E4925E318C3F, 0x00003FFB //A11
data8 0x8A9D8A970565F28D, 0x0000BFFB //A10
data8 0xAE34C61DE5CEA4D4, 0x00003FFA //A9
data8 0xC44C5714BD6208A0, 0x0000BFF9 //A8
data8 0xC4612F7D6C8BDB79, 0x00003FF8 //A7
data8 0xABD91DCE40D5EECB, 0x0000BFF7 //A6
data8 0x80E375C1B847B72F, 0x00003FF6 //A5
data8 0xA11C7DD978CF700A, 0x0000BFF4 //A4
//
// Polynomial coefficients for the tanh(x), 16.0 <= |x| < 19.0625
data8 0xE29D17C510F86F6B, 0x00003FF3 //A19
data8 0x88FE52EB39A3A98C, 0x0000BFF5 //A18
data8 0xA406547E50360693, 0x00003FF5 //A17
data8 0x83E6260B71C6D7DE, 0x0000BFF5 //A16
data8 0xA36AB5B0CBC97B85, 0x00003FF4 //A15
data8 0xA94931E0B7BA6C14, 0x0000BFF3 //A14
data8 0x9A4596DAF350AD63, 0x00003FF2 //A13
data8 0xFE47643F375AECA5, 0x0000BFF0 //A12
data8 0xBF8433C5ABEE63B1, 0x00003FEF //A11
data8 0x83CEE05D7AE90A0A, 0x0000BFEE //A10
data8 0xA4CC45480BCEB02D, 0x00003FEC //A9
data8 0xB967CBDCBC16CB10, 0x0000BFEA //A8
data8 0xB9681B214EDC098D, 0x00003FE8 //A7
data8 0xA23B20D87B80DFA8, 0x0000BFE6 //A6
data8 0xF358B2C46F10CBAF, 0x00003FE3 //A5
data8 0x98176FD06229A385, 0x0000BFE1 //A4
//
// Binary subranges
// Polynomial coefficients for the tanh(x), 3.25 <= |x| < 4.0
data8 0xEF2EE841288F6706, 0x00003FE9 //A19
data8 0xE65D5B74B85F82A6, 0x00003FEB //A18
data8 0xE495FC21E42A79FF, 0x00003FEA //A17
data8 0xF99B267A913CF3E5, 0x00003FEC //A16
data8 0xFE3D700F4A0A0FDE, 0x0000BFEC //A15
data8 0x8F91BB4EE4E4EA52, 0x00003FEE //A14
data8 0xBCA9F41A5C6EF8BA, 0x0000BFEE //A13
data8 0xF93E00884027A9CF, 0x00003FED //A12
data8 0xC4D4036A61BABC2F, 0x00003FEF //A11
data8 0x86CC2AD1AD47C7D5, 0x0000BFF2 //A10
data8 0xD3065DEF4CE9AD32, 0x00003FF3 //A9
data8 0x82C44125F568D54E, 0x0000BFF5 //A8
data8 0x88D588729BAF14CA, 0x00003FF6 //A7
data8 0xF4CA0661307243C7, 0x0000BFF6 //A6
data8 0xB998746D57061F74, 0x00003FF7 //A5
data8 0xE93FB2F482327C19, 0x0000BFF7 //A4
//
// Polynomial coefficients for the tanh(x), 6.5 <= |x| < 8.0
data8 0xEB189B71ADC40BE2, 0x00003FEA //A19
data8 0xA60B46F9FF6DC2DF, 0x00003FEA //A18
data8 0xBB061CDD9F368B9D, 0x00003FEC //A17
data8 0x841E08BDF5429991, 0x0000BFEC //A16
data8 0xDD33990B433F25BE, 0x00003FED //A15
data8 0xBA5DE6B870F0A2BB, 0x0000BFEE //A14
data8 0xA71D489AAA6DACF0, 0x00003FEF //A13
data8 0x874CCB2B8F3FBC0E, 0x0000BFF0 //A12
data8 0xCB1D2E9754EA534A, 0x00003FF0 //A11
data8 0x8BA5ABB53BA6ABCF, 0x0000BFF1 //A10
data8 0xAE91FD1C2391A32B, 0x00003FF1 //A9
data8 0xC465A74B798E5761, 0x0000BFF1 //A8
data8 0xC4666152397D15C1, 0x00003FF1 //A7
data8 0xABD9E63CA575B950, 0x0000BFF1 //A6
data8 0x80E38B18E8D0F460, 0x00003FF1 //A5
data8 0xA11C80E20AAFDD3C, 0x0000BFF0 //A4
//
// Polynomial coefficients for the tanh(x), 13.0 <= |x| < 16.0
data8 0xBECD0AF7E22E5594, 0x00003FE9 //A19
data8 0xE2834E2D68C1128C, 0x00003FEA //A18
data8 0x97B117611B317379, 0x00003FEB //A17
data8 0xEE91A0D39A772F6B, 0x00003FEA //A16
data8 0x92F6EC377DCADA4F, 0x00003FEA //A15
data8 0xD8FCCD6A3277FAB7, 0x00003FE8 //A14
data8 0xC15AB9CB0C3DCFE0, 0x00003FE7 //A13
data8 0xC3C659704A7147CD, 0x00003FE2 //A12
data8 0xFA17F09D27C97912, 0x00003FE4 //A11
data8 0xF664147182B94788, 0x0000BFE3 //A10
data8 0xA6C89FA741464DA1, 0x00003FE3 //A9
data8 0xB90FE464A825EFA8, 0x0000BFE2 //A8
data8 0xB973AE0FD86EC024, 0x00003FE1 //A7
data8 0xA23A087F96846951, 0x0000BFE0 //A6
data8 0xF358D8A7FC012D5D, 0x00003FDE //A5
data8 0x98176E2309B7C73A, 0x0000BFDD //A4
//
// Coefficients ##16..19 ("tail" coefficient tables)
// Polynomial coefficients for the tanh(x), 0.25 <= |x| < 0.5
data8 0x838F209ABB9BA7B3, 0x0000BFF7 //A3
data8 0xEBC0AC78DA4FC500, 0x0000BFF8 //A2
data8 0xF0A4D02960B60E69, 0x00003FFC //A1
data8 0xFACBF534D0E42F8A, 0x00003FFC //A0
//
// Polynomial coefficients for the tanh(x), 0.5 <= |x| < 1.0
data8 0xC0ECBDC0A0D133A6, 0x0000BFF8 //A3
data8 0xBA13A076BF8E812F, 0x0000BFFB //A2
data8 0xC954A37D1A1CA070, 0x00003FFD //A1
data8 0xEC9A9EBAB4579B29, 0x00003FFD //A0
//
// Polynomial coefficients for the tanh(x), 1.0 <= |x| < 2.0
data8 0xD42E9175A6EA1397, 0x00003FFB //A3
data8 0xA3C361378A55CF56, 0x0000BFFD //A2
data8 0xD706E07CC8622983, 0x00003FFD //A1
data8 0xC2F7D5A8A79CA2AC, 0x00003FFE //A0
//
// Polynomial coefficients for the tanh(x), 2.0 <= |x| < 3.25
data8 0xAC7A7F8776817C7E, 0x00003FFD //A3
data8 0x8B7CE95E69FCFE9A, 0x0000BFFD //A2
data8 0x90B161317028D995, 0x00003FFC //A1
data8 0xF6CA82F0DE1E9E9A, 0x00003FFE //A0
//
// Polynomial coefficients for the tanh(x), 4.0 <= |x| < 6.5
data8 0xE9E072407BC22DC6, 0x00003FFA //A3
data8 0xAFA4A913D8E6BB4A, 0x0000BFF9 //A2
data8 0xAFC2D6A885BAA875, 0x00003FF7 //A1
data8 0xFFD40B84505A10B2, 0x00003FFE //A0
//
// Polynomial coefficients for the tanh(x), 8.0 <= |x| < 13.0
data8 0xA11C8A1FED168CD5, 0x00003FF2 //A3
data8 0xF1AAD6B02063A5F5, 0x0000BFEF //A2
data8 0xF1AADA46AD341C34, 0x00003FEC //A1
data8 0xFFFFFC39548FC34B, 0x00003FFE //A0
//
// Polynomial coefficients for the tanh(x), 16.0 <= |x| < 19.0625
data8 0x98176FD1F0950C16, 0x00003FDE //A3
data8 0xE42327BB09C8B2A5, 0x0000BFDA //A2
data8 0xE42327BB0B154F13, 0x00003FD6 //A1
data8 0xFFFFFFFFFFF8DEE7, 0x00003FFE //A0
//
// Binary subranges
// Polynomial coefficients for the tanh(x), 3.25 <= |x| < 4.0
data8 0xE9E072404329293B, 0x00003FF7 //A3
data8 0xAFA4A913D798300B, 0x0000BFF7 //A2
data8 0xAFC2D6A885B48567, 0x00003FF6 //A1
data8 0xFFD40B84505A10B4, 0x00003FFE //A0
//
// Polynomial coefficients for the tanh(x), 6.5 <= |x| < 8.0
data8 0xA11C8A63815F7A28, 0x00003FEF //A3
data8 0xF1AAD6B65B0EBF53, 0x0000BFED //A2
data8 0xF1AADA46E799831F, 0x00003FEB //A1
data8 0xFFFFFC39548FC348, 0x00003FFE //A0
//
// Polynomial coefficients for the tanh(x), 13.0 <= |x| < 16.0
data8 0x98176FE982140A59, 0x00003FDB //A3
data8 0xE42327B9B0D7202F, 0x0000BFD8 //A2
data8 0xE42327BB13076BD6, 0x00003FD5 //A1
data8 0xFFFFFFFFFFF8DEE7, 0x00003FFE //A0
//
// Polynomial coefficients for the tanh(x), 0.0 <= |x| < 0.25
// ('tanh_near_zero' path)
data8 0xBF2BA5D26E479D0C //A9
data8 0x3F4336D96F81EE26 //A8
data8 0xBF8226E34AE197B0 //A5
data8 0x3F9664F488148657 //A4
data8 0xAAAAAAAAAAAAAA99, 0x0000BFFD //A1
data8 0xBF57D91925BB5EE2 //A7
data8 0x3F6D6D36C3D5B7A1 //A6
data8 0xBFABA1BA1BA19D32 //A3
data8 0x3FC1111111111108 //A2
//
// 1.0 - 2^(-63)
// ('tanh_saturation' path)
data8 0xFFFFFFFFFFFFFFFF, 0x00003FFE
LOCAL_OBJECT_END(tanh_data)
// CAUTION: The order of table coefficients shouldn't be changed!
.section .text
GLOBAL_LIBM_ENTRY(tanh)
{ .mfi
alloc r32 = ar.pfs, 0, 20, 0, 0
fmerge.se fArgAbsNorm = f1, f8 // normalized x
adds rSignBit = 0x1, r0 // Bit for sign removing
}
{ .mfi
addl rDataPtr = @ltoff(tanh_data), gp // Data pointer
fma.s1 fTwo = f1, f1, f1 // 2.0 construct
addl rArgSgnd = 0xfff, r0 // mask for exponent
};;
{ .mfi
getf.d rArg = f8 // x in GR
fclass.m p6,p0 = f8, 0xEF // Filter 0, denormals and specials
// 0xEF = @qnan|@snan|@pos|@neg|@zero|@unorm|@inf
shl rArgSgnd = rArgSgnd, 52 // mask for exponent
}
{ .mlx
ld8 rDataPtr = [rDataPtr] // Real data pointer
movl r1625Sgnd = 0xA000000000000 // 1.625 signd
// 1.625 significand used to filter values greater than 3.25, 6.5, 13.0
// to enter binary subranges
};;
{ .mfi
addl rBias = 0x3FD00, r0 // bias of 0.25 << 8
fma.s1 fArgSqr = f8, f8, f0 // x^2
shl rSignBit = rSignBit, 63 // mask for sign bit
}
{ .mlx
addl rMask = 0x7FF00, r0 // Mask for index bits
movl rTwo = 0x4000000000000000 // 2.0
};;
{ .mfi
andcm rArgSgnd = rArg, rArgSgnd // Remove exponent
nop.f 0
shr.u rShiftedArg = rArg, 44 // Select only necessary bits of arg
}
{ .mfb
andcm rAbsArg = rArg, rSignBit // Remove sign
nop.f 0
(p6) br.cond.spnt _tanh_spec // Branch to zero, denorm & specs
};;
{ .mfi
and rShiftedArgMasked = rShiftedArg, rMask // bias of x << 8
fmerge.s fArgAbs = f1, f8 // |x|
shr rShiftedAbsArg = rAbsArg, 44 // Select only necessary
// bits of absolute arg
}
{ .mfi
cmp.gt p8, p11 = rArgSgnd, r1625Sgnd // p8 = 1 if
// signd(x) > 1.625 - to filter values greater than 3.25, 6.5, 13.0
nop.f 0
nop.i 0
};;
{ .mfi
sub rIndex = rShiftedArgMasked, rBias // index << 8
nop.f 0
cmp.lt p10, p0 = rShiftedArgMasked, rBias // p10=1 if |x|<0.25
}
{ .mfb
(p8) cmp.gt p8, p11 = rAbsArg, rTwo // If arg is greater than 2.0?
// (then we should use binary subranges)
nop.f 0
(p10) br.cond.spnt tanh_near_zero // branch out if |x| < 0.25
};;
.pred.rel "mutex",p8,p11
{ .mfi
(p8) add rIndex = 0x400, rIndex // Make pointer to binary
// subranges
(p11) fms.s1 fArgAbsNorm = fArgAbsNorm, f1, f1 // |x|/b - 1.0
addl rSaturation = 0x40331, r0 // shifted bits of 19.0625
}
{ .mfi
nop.m 0
(p8) fms.s1 fArgAbsNorm = fArgAbsNorm, f1, fTwo // |x|/b - 2.0
// this is only for binary subranges [3.25;4], [6.5;8], [13.0;16]
nop.i 0
}
;;
{ .mfi
add rCoeffAddr1 = rDataPtr, rIndex// coeff. ##0,2,..14
nop.f 0
nop.i 0
};;
{ .mfi
adds rCoeffAddr2 = 16, rCoeffAddr1 // Shifted pointer to coeffs
fmerge.s fSignumX = f8, f1 // signum(x)
nop.i 0
}
{ .mfb
cmp.le p12, p0 = rSaturation, rShiftedAbsArg // |x|>=19.0625?
nop.f 0
(p12) br.cond.spnt tanh_saturation // branch out if x |x| >= 19.0625
};;
{.mfi
ldfe fA19 = [rCoeffAddr1], 32 // Load A19
nop.f 0
nop.i 0
}
{.mfi
ldfe fA18 = [rCoeffAddr2], 32 // Load A18
nop.f 0
adds rCoeffAddr3 = 0xA00, rDataPtr // Pointer to "tail"
// coefficients tables
};;
{.mfi
ldfe fA17 = [rCoeffAddr1], 32 // Load A17
nop.f 0
nop.i 0
}
{.mfi
ldfe fA16 = [rCoeffAddr2], 32 // Load A16
nop.f 0
nop.i 0
};;
{.mfi
ldfe fA15 = [rCoeffAddr1], 32 // Load A15
fma.s1 fTSqr = fArgAbsNorm, fArgAbsNorm, f0 // x^2
shr.u rIndex = rIndex, 2 // Index for "tail" tables
}
{.mfi
ldfe fA14 = [rCoeffAddr2], 32 // Load A14
nop.f 0
adds rCoeffAddr4 = 16, r0 // Shifter pointer
// to "tail" tables
};;
{.mfi
ldfe fA13 = [rCoeffAddr1], 32 // Load A13
nop.f 0
add rCoeffAddr3 = rCoeffAddr3, rIndex // "tail" coeffs to load
// ##16..23
}
{.mfi
ldfe fA12 = [rCoeffAddr2], 32 // Load A12
nop.f 0
cmp.lt p15, p14 = rArg, r0 // Arg positive (p14)
// or negative (p15)?
};;
{.mfi
ldfe fA11 = [rCoeffAddr1], 32 // Load A11
nop.f 0
add rCoeffAddr4 = rCoeffAddr3, rCoeffAddr4 // shifted "tail"
// coeffs to load
}
{.mfi
ldfe fA10 = [rCoeffAddr2], 32 // Load A10
nop.f 0
nop.i 0
};;
{.mfi
ldfe fA9 = [rCoeffAddr1], 32 // Load A9
nop.f 0
nop.i 0
}
{.mfi
ldfe fA8 = [rCoeffAddr2], 32 // Load A8
nop.f 0
nop.i 0
};;
{.mfi
ldfe fA7 = [rCoeffAddr1], 32 // Load A7
nop.f 0
nop.i 0
}
{.mfi
ldfe fA6 = [rCoeffAddr2], 32 // Load A6
nop.f 0
nop.i 0
};;
{.mfi
ldfe fA5 = [rCoeffAddr1], 32 // Load A5
fma.s1 fTDeg3 = fArgAbsNorm, fTSqr, f0 // x^3
nop.i 0
}
{.mfi
ldfe fA4 = [rCoeffAddr2], 32 // Load A4
fma.s1 fTQuadr = fTSqr, fTSqr, f0 // x^4
nop.i 0
};;
// Path #3 Polynomial Pol19(y) computation; y = fArgAbsNorm
{.mfi
ldfe fA3 = [rCoeffAddr3], 32 // Load A3
fma.s1 fArgAbsNormSgn = fArgAbsNorm, fSignumX, f0 // sign(x)*x
nop.i 0
}
{.mfi
ldfe fA2 = [rCoeffAddr4], 32 // Load A2
nop.f 0
nop.i 0
};;
{.mfi
ldfe fA1 = [rCoeffAddr3], 32 // Load A1
fma.s1 fRes = fA19, fArgAbsNorm, fA18 // Polynomial
nop.i 0
}
{.mfi
ldfe fA0 = [rCoeffAddr4], 32 // Load A0
nop.f 0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA17 = fA17, fArgAbsNorm, fA16 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA15 = fA15, fArgAbsNorm, fA14 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fTDeg7 = fTDeg3, fTQuadr, f0 // Polynomial
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA13 = fA13, fArgAbsNorm, fA12 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA11 = fA11, fArgAbsNorm, fA10 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA9 = fA9, fArgAbsNorm, fA8 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fRes = fRes, fTSqr, fA17 // Polynomial
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA7 = fA7, fArgAbsNorm, fA6 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA5 = fA5, fArgAbsNorm, f0 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA15 = fA15, fTSqr, fA13 // Polynomial
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA4 = fA4, fArgAbsNorm, fA3 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA2 = fA2, fArgAbsNorm, fA1 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA11 = fA11, fTSqr, fA9 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA7 = fA7, fTSqr, fA5 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fRes = fRes, fTQuadr, fA15 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA4 = fA4, fTSqr, fA2 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fRes = fRes, fTQuadr, fA11 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA4 = fA7, fTDeg3, fA4 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fRes = fRes, fTDeg7, fA4 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
// result for negative argument
(p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA0 // Polynomial
nop.i 0
}
{ .mfb
nop.m 0
// result for positive argument
(p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA0 // Polynomial
br.ret.sptk b0
};;
// |x| < 0.25 Path /////////////////////////////////////////////////////////////
.align 32
tanh_near_zero:
{ .mfi
adds rCoeffAddr1 = 0xC80, rDataPtr // address of A9
fma.s0 fTSqr = fArgSqr, fArgSqr, f0 // x^4
nop.i 0
}
{ .mfi
adds rCoeffAddr2 = 0xCB0, rDataPtr // address of A7
nop.f 0
nop.i 0
};;
{ .mfi
ldfpd fA9, fA8 = [rCoeffAddr1], 16 // Load A9, A8
nop.f 0
nop.i 0
}
{ .mfi
ldfpd fA7, fA6 = [rCoeffAddr2], 16 // Load A7, A6
nop.f 0
nop.i 0
};;
{ .mfi
ldfpd fA5, fA4 = [rCoeffAddr1], 16 // Load A5, A4
nop.f 0
nop.i 0
}
{ .mfi
ldfpd fA3, fA2 = [rCoeffAddr2], 16 // Load A3, A2
nop.f 0
nop.i 0
};;
{ .mfi
ldfe fA1 = [rCoeffAddr1] // Load A1
nop.f 0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fTQuadr = fTSqr, fTSqr, f0 // x^4
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fRes = fA9, fArgSqr, fA8 // Polynomial
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA7 = fA7, fArgSqr, fA6 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA3 = fA3, fArgSqr, fA2 // Polynomial
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA5 = fA5, fArgSqr, fA4 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA1 = fA1, fArgSqr, f0 // Polynomial
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fTQuadrSgn = fTQuadr, f8, f0 // x^4 * x
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fRes = fRes, fTSqr, fA7 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fA1 = fA3, fTSqr, fA1 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fRes = fRes, fTSqr, fA5 // Polynomial
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 fRes = fRes, fTQuadr, fA1 // Polynomial
nop.i 0
};;
{ .mfb
nop.m 0
fma.d.s0 f8 = fRes, f8, f8 // x+x*Polynomial
br.ret.sptk b0 // Exit for |x| < 0.25
};;
// 19.0625 <= |x| < +inf Saturation path ///////////////////////////////////////
.align 32
tanh_saturation:
{ .mfi
adds rDataPtr = 0xCD0, rDataPtr // address of A0
nop.f 0
nop.i 0
};;
{ .mfi
ldfe fA0 = [rDataPtr] // Load A0 = 2^(-63)
nop.f 0
nop.i 0
};;
{ .mfb
nop.m 0
fma.d.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0-2^(-63))
br.ret.sptk b0 // Exit for 19.0625 <=|x|< +inf
};;
// 0, denormals and special IEEE numbers path /////////////////////////////////
_tanh_spec:
{ .mfi
cmp.lt p15, p14 = rArg, r0 // Is arg negative (p15)
// or positive p14)
fclass.m p6,p0 = f8, 0x23 // To filter infinities
// 0x23 = @pos|@neg|@inf
nop.i 0
};;
{ .mfi
nop.m 0
fclass.m p7,p0 = f8, 0xC7 // To filter NaNs & Zeros
// 0xC7 = @pos|@neg|@zero|@qnan|@snan
nop.i 0
};;
{ .mfb
nop.m 0
(p6) fmerge.s f8 = f8, f1 // +/-1 for INF args
(p6) br.ret.spnt b0 // exit for x = INF
};;
{ .mfb
nop.m 0
(p7) fma.d.s0 f8 = f8, f1, f8 // +/-0 for 0 args
// and NaNs for NaNs
(p7) br.ret.spnt b0 // exit for x = NaN or +/-0
};;
{ .mfi
nop.m 0
fnorm.s0 f8 = f8 // Normalize arg
nop.i 0
};;
.pred.rel "mutex",p14,p15
{ .mfi
nop.m 0
(p14) fnma.d.s0 f8 = f8, f8, f8 // res = r-r^2
nop.i 0
}
{ .mfb
nop.m 0
(p15) fma.d.s0 f8 = f8, f8, f8 // res = r+r^2
br.ret.sptk b0 // 0, denormals, specials return
};;
GLOBAL_LIBM_END(tanh)
libm_alias_double_other (tanh, tanh)
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