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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>
582 lines
16 KiB
ArmAsm
582 lines
16 KiB
ArmAsm
.file "tanhf.s"
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// Copyright (c) 2001 - 2005, Intel Corporation
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// All rights reserved.
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//
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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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// 05/30/01 Initial version
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/10/03 Reordered header: .section, .global, .proc, .align
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// 03/31/05 Reformatted delimiters between data tables
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//
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// API
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//==============================================================
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// float tanhf(float)
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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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//
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// There are 9 paths:
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// 1. x = +/-0.0
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// Return tanhf(x) = +/-0.0
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//
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// 2. 0.0 < |x| < 0.3125
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// Return tanhf(x) = x + x^3*Pol3(x^2),
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// where Pol3(x^2) = C3*x^6 + C2*x^4 + C1*x^2 + C0
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//
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// 3. 0.3125 <= |x| < 8.0
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// Return tanhf(x) = sign(x)*PolD(x)*PolC(|x|) + sign(x)*PolA(|x|),
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// where sign(x)*PolD(x) = sign(x)*(|x|^7 + D2*x^6 + D1*|x|^5 + D0*x^4),
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// PolC(|x|) = B0*x^4 + C3*|x|^3 + C2*|x|^2 + C1*|x| + C0,
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// PolA(|x|) = A3|x|^3 + A2*x^2 + A1*|x| + A0
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//
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// Actually range 0.3125<=|x|< 8.0 is split to 5 subranges.
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// For each subrange there is particular set of coefficients.
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// Below is the list of subranges:
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// 3.1 0.3125 <= |x| < 0.5
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// 3.2 0.5 <= |x| < 1.0
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// 3.3 1.0 <= |x| < 2.0
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// 3.4 2.0 <= |x| < 4.0
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// 3.5 4.0 <= |x| < 8.0
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//
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// 4. 8.0 <= |x| < 9.125
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// Return tanhf(x) = sign(x)*(A3|x|^3 + A2*x^2 + A1*|x| + A0)
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//
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// 5. 9.125 <= |x| < +INF
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// Return tanhf(x) = sign(x)*(1.0d - 2^(-52))
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//
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// 6. |x| = INF
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// Return tanhf(x) = sign(x) * 1.0
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//
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// 7. x = [S,Q]NaN
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// Return tanhf(x) = QNaN
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//
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// 8. x is positive denormal
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// Return tanhf(x) = x - x^2
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//
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// 9. x is negative denormal
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// Return tanhf(x) = x + x^2
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//
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// Registers used
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//==============================================================
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// Floating Point registers used:
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// f8, input
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// f32 -> f59
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// General registers used:
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// r32 -> r46, r2, r3
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// Predicate registers used:
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// p0, p6 -> p15
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// p6 to filter out case when x = [Q,S]NaN or +/-0
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// p7 to filter out case when x = denormal
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// p8 set if |x| >= 0.3125, used also to process denormal input
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// p9 to filter out case when |x| = inf
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// p10 to filter out case when |x| < 0.3125
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// p11 to filter out case when 0.3125 <= |x| < 9.125
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// p12 to filter out case when |x| >= 9.125
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// p13 to filter out case when 8.0 <= |x| < 9.125
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// p14 set to 1 for positive x
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// p15 set to 1 for negative x
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// Assembly macros
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//==============================================================
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rDataPtr = r2
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rDataPtr1 = r3
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rBias = r33
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rCoeffAddr3 = r34
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rNearSaturation = r35
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rCoeffAddr1 = r36
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rCoeffAddr2 = r37
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rOffset2 = r38
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rBias2 = r39
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rMask = r40
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rArg = r41
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rBound = r42
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rSignBit = r43
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rAbsArg = r44
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rDataPtr2 = r45
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rSaturation = r46
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//==============================================================
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fA0 = f32
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fA1 = f33
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fA2 = f34
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fA3 = f35
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fC0 = f36
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fC1 = f37
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fC2 = f38
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fC3 = f39
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fD0 = f40
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fD1 = f41
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fD2 = f42
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fB0 = f43
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fArgSqr = f44
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fAbsArg = f45
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fSignumX = f46
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fArg4 = f47
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fArg4Sgn = f48
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fArg3 = f49
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fArg3Sgn = f50
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fArg7Sgn = f51
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fArg6Sgn = f52
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fPolC = f53
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fPolCTmp = f54
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fPolA = f55
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fPolATmp = f56
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fPolD = f57
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fPolDTmp = f58
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fArgSqrSgn = f59
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// Data tables
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//==============================================================
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RODATA
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.align 16
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LOCAL_OBJECT_START(tanhf_data)
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// Polynomial coefficients for the tanh(x), 0.3125 <= |x| < 0.5
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data8 0x3F9BEEDFDD177D7B // C0
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data8 0x3F970D10C7F32458 // C1
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data8 0x3F766D6B051F3A38 // C2
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data8 0xBF732F2001B23402 // C3
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data8 0xBF854BE1CE1ED499 // D0
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data8 0x4013C944F3999A16 // D1
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data8 0xC01106C6975222C0 // D2
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data8 0x3F783D5ACCF9EBE8 // B0
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// Polynomial coefficients for the tanh(x), 0.5 <= |x| < 1.0
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data8 0xBF5D631440786869 // C0
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data8 0xBF575D79A0D52069 // C1
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data8 0xBF7E2237B7EFC705 // C2
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data8 0x3F6A7ACBC273041F // C3
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data8 0xC040E32EA52D91EB // D0
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data8 0x403D19463E5DB4D7 // D1
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data8 0xC02216F61F759F39 // D2
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data8 0xBF55B4EA0B844BE7 // B0
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// Polynomial coefficients for the tanh(x), 1.0 <= |x| < 2.0
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data8 0x3F8637DBE5B3E690 // C0
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data8 0xBF7F7FEC158C07F5 // C1
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data8 0x3F711C586706838A // C2
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data8 0xBF50EF7EF605554E // C3
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data8 0xC054D45448354E25 // D0
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data8 0x404ADFEEA282E730 // D1
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data8 0xC028AEE456D59549 // D2
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data8 0x3F25232D1BED59A8 // B0
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// Polynomial coefficients for the tanh(x), 2.0 <= |x| < 4.0
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data8 0xBF52602285F2D06C // C0
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data8 0x3F2E57C298FFE1E0 // C1
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data8 0xBF15ED575DB3C811 // C2
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data8 0x3EE428878A08525C // C3
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data8 0xC0895A26849039C1 // D0
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data8 0x406E3C60BBFBB575 // D1
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data8 0xC03A06F62867C75A // D2
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data8 0xBEB114C70F1C723E // B0
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// Polynomial coefficients for the tanh(x), 4.0 <= |x| < 8.0
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data8 0x3EF4B22BD17039A3 // C0
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data8 0xBEB704ADC040C57F // C1
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data8 0x3E937A98288AFE1A // C2
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data8 0xBE4F33B2C9FFE7E7 // C3
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data8 0xC0BE48CFADE2431E // D0
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data8 0x4090E74249760FDD // D1
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data8 0xC04B6F537FCF2F1E // D2
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data8 0x3E0DCD879C91ADEA // B0
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// Polynomial coefficients for the tanh(x), -0.3125 < x < 0.3125
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data8 0xBFD555551E8245B7 // A0
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data8 0x3FC110E63F52E689 // A1
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data8 0xBFAB8CD6A5B7BAFA // A2
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data8 0x3F945D467FCEB553 // A3
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// Polynomial coefficients for the tanh(x), 0.3125 <= |x| < 0.5
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data8 0xBE3DCC92FCAECBB6 // A0
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data8 0x3FF0000043B7D267 // A1
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data8 0xBED18BF28ACFC4B1 // A2
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data8 0xBFD554A56F82837E // A3
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// Polynomial coefficients for the tanh(x), 0.5 <= |x| < 1.0
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data8 0x3EFD6054758539F9 // A0
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data8 0x3FEFFBFC77198EBE // A1
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data8 0x3F700327CA98D237 // A2
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data8 0xBFD68955F5BB2FA1 // A3
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// Polynomial coefficients for the tanh(x), 1.0 <= |x| < 2.0
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data8 0xBF71A53F229DF01B // A0
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data8 0x3FF0AECFD730DE50 // A1
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data8 0xBFC882F88E5DF3BA // A2
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data8 0x3FC6EDF212CA2A8D // A3
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// Polynomial coefficients for the tanh(x), 2.0 <= |x| < 4.0
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data8 0xBFAF0B712E9EDA47 // A0
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data8 0x3FF1C208080BEA64 // A1
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data8 0x3FC3D29B20C8946E // A2
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data8 0xBFF04514ED900A6A // A3
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// Polynomial coefficients for the tanh(x), 4.0 <= |x| < 8.0
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data8 0xBFB1DEA49A831CBC // A0
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data8 0x3FFA729FC7085674 // A1
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data8 0xBFF2F44D923A8FA4 // A2
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data8 0x3FE092FC5712227E // A3
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// Polynomial coefficients for the tanh(x), 8.0 <= |x| <= 9.125
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data8 0x3FEFFF5769EE3041 // A0
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data8 0x3EFBBF148D850891 // A1
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data8 0xBEC86BCEF0F5C2FE // A2
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data8 0x3E7CBA4F3A885A5C // A3
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//
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data8 0x3FEFFFFFFFFFFFFF // 1.0 - epsilon
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LOCAL_OBJECT_END(tanhf_data)
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.section .text
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GLOBAL_LIBM_ENTRY(tanhf)
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{ .mfi
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alloc r32 = ar.pfs, 1, 14, 0, 0
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fmerge.s fAbsArg = f1, f8 // |x|
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addl rMask = 0x806, r0
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}
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{ .mfi
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addl rDataPtr = @ltoff(tanhf_data), gp
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fma.s1 fArgSqr = f8, f8, f0 // x^2
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adds rSignBit = 0x1, r0
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}
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;;
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{ .mfi
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getf.s rArg = f8 // x in GR
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fclass.m p7,p0 = f8, 0x0b // is x denormal ?
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// sign bit and 2 most bits in significand
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shl rMask = rMask, 20
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}
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{ .mfi
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ld8 rDataPtr = [rDataPtr]
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nop.f 0
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adds rBias2 = 0x1F4, r0
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}
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;;
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{ .mfi
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adds rNearSaturation = 0x14, r0
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fmerge.s fSignumX = f8, f1 // signum(x)
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shl rSignBit = rSignBit, 31 // mask for sign bit
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}
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{ .mfi
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adds rBound = 0x3EA, r0
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nop.f 0
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addl rSaturation = 0x4112, r0
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}
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;;
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{ .mfi
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andcm rOffset2 = rArg, rMask
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fclass.m p6,p0 = f8, 0xc7 // is x [S,Q]NaN or +/-0 ?
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shl rBound = rBound, 20 // 1.0f in GR
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}
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{ .mfb
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andcm rAbsArg = rArg, rSignBit // |x| in GR
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nop.f 0
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(p7) br.cond.spnt tanhf_denormal // branch out if x is denormal
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}
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;;
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{ .mfi
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adds rCoeffAddr2 = 352, rDataPtr
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fclass.m p9,p0 = f8, 0x23 // is x +/- inf?
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shr rOffset2 = rOffset2, 21
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}
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{ .mfi
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cmp.lt p10, p8 = rAbsArg, rBound // |x| < 0.3125?
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nop.f 0
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adds rCoeffAddr3 = 16, rDataPtr
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}
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;;
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{ .mfi
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(p8) sub rBias = rOffset2, rBias2
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fma.s1 fArg4 = fArgSqr, fArgSqr, f0 // x^4
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shl rSaturation = rSaturation, 16
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}
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{ .mfb
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(p10) adds rBias = 0x14, r0
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(p6) fma.s.s0 f8 = f8,f1,f8 // NaN or +/-0
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(p6) br.ret.spnt b0 // exit for x = NaN or +/-0
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}
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;;
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{ .mfi
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shladd rCoeffAddr1 = rBias, 4, rDataPtr
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fma.s1 fArg3Sgn = fArgSqr, f8, f0 // sign(x)*|x|^3
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// is |x| < 9.125?
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cmp.lt p11, p12 = rAbsArg, rSaturation
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}
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{ .mfi
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shladd rCoeffAddr3 = rBias, 4, rCoeffAddr3
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fma.s1 fArg3 = fArgSqr, fAbsArg, f0 // |x|^3
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shladd rCoeffAddr2 = rBias, 3, rCoeffAddr2
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}
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;;
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{ .mfi
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(p11) ldfpd fC0, fC1 = [rCoeffAddr1]
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(p9) fmerge.s f8 = f8,f1 // +/- inf
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(p12) adds rDataPtr = 544, rDataPtr
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}
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{ .mfb
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(p11) ldfpd fC2, fC3 = [rCoeffAddr3], 16
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nop.f 0
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(p9) br.ret.spnt b0 // exit for x = +/- inf
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}
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;;
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{ .mfi
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(p11) ldfpd fA0, fA1 = [rCoeffAddr2], 16
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nop.f 0
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(p8) cmp.eq.unc p13, p0 = rBias, rNearSaturation
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}
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{ .mfi
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add rCoeffAddr1 = 48, rCoeffAddr1
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nop.f 0
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nop.i 0
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}
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;;
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{ .mfi
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(p11) ldfpd fD0, fD1 = [rCoeffAddr3]
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nop.f 0
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nop.i 0
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}
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{ .mfb
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(p11) ldfpd fD2, fB0 = [rCoeffAddr1]
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// sign(x)*|x|^2
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fma.s1 fArgSqrSgn = fArgSqr, fSignumX, f0
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(p10) br.cond.spnt tanhf_near_zero
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}
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;;
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{ .mfi
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(p11) ldfpd fA2, fA3 = [rCoeffAddr2], 16
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fcmp.lt.s1 p15, p14 = f8,f0
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nop.i 0
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}
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{ .mfb
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(p12) ldfd fA0 = [rDataPtr]
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fma.s1 fArg4Sgn = fArg4, fSignumX, f0 // sign(x)*|x|^4
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(p12) br.cond.spnt tanhf_saturation
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}
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;;
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{ .mfi
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nop.m 0
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fma.s1 fArg7Sgn = fArg4, fArg3Sgn, f0 // sign(x)*|x|^7
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nop.i 0
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}
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{ .mfb
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nop.m 0
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fma.s1 fArg6Sgn = fArg3, fArg3Sgn, f0 // sign(x)*|x|^6
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(p13) br.cond.spnt tanhf_close_to_saturation
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}
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;;
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{ .mfi
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nop.m 0
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fma.s1 fPolC = fC3, fAbsArg, fC2 // C3*|x| + C2
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nop.i 0
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}
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{ .mfi
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nop.m 0
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fma.s1 fPolCTmp = fC1, fAbsArg, fC0 // C1*|x| + C0
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nop.i 0
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};;
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{ .mfi
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nop.m 0
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fma.s1 fPolA = fA1, fAbsArg, fA0 // A1*|x| + A0
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nop.i 0
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}
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;;
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{ .mfi
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nop.m 0
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fma.s1 fPolD = fD1, fAbsArg, fD0 // D1*|x| + D0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// sign(x)*(|x|^7 + D2*x^6)
|
|
fma.s1 fPolDTmp = fArg6Sgn, fD2, fArg7Sgn
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolATmp = fA3, fAbsArg, fA2 // A3*|x| + A2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB0 = fB0, fArg4, f0 // B0*x^4
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// C3*|x|^3 + C2*x^2 + C1*|x| + C0
|
|
fma.s1 fPolC = fPolC, fArgSqr, fPolCTmp
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// PolD = sign(x)*(|x|^7 + D2*x^6 + D1*|x|^5 + D0*x^4)
|
|
fma.d.s1 fPolD = fPolD, fArg4Sgn, fPolDTmp
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// PolA = A3|x|^3 + A2*x^2 + A1*|x| + A0
|
|
fma.d.s1 fPolA = fPolATmp, fArgSqr, fPolA
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// PolC = B0*x^4 + C3*|x|^3 + C2*|x|^2 + C1*|x| + C0
|
|
fma.d.s1 fPolC = fPolC, f1, fB0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p14) fma.s.s0 f8 = fPolC, fPolD, fPolA // for positive x
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p15) fms.s.s0 f8 = fPolC, fPolD, fPolA // for negative x
|
|
br.ret.sptk b0 // Exit for 0.3125 <=|x|< 8.0
|
|
};;
|
|
|
|
|
|
// Here if |x| < 0.3125
|
|
tanhf_near_zero:
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolC = fC3, fArgSqr, fC2 // C3*x^2 + C2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolCTmp = fC1, fArgSqr, fC0 // C1*x^2 + C0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolC = fPolC, fArg4, fPolCTmp // C3*x^6 + C2*x^4 + C1*x^2 + C0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
// x + x^3*(C3*x^6 + C2*x^4 + C1*x^2 + C0)
|
|
fma.s.s0 f8 = fPolC, fArg3Sgn, f8
|
|
br.ret.sptk b0 // Exit for |x| < 0.3125
|
|
};;
|
|
|
|
// Here if 9.125 <= |x| < +inf
|
|
tanhf_saturation:
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0d - 2^(-52))
|
|
// Exit for 9.125 <= |x| < +inf
|
|
br.ret.sptk b0 // Exit for 9.125 <=|x|< +inf
|
|
}
|
|
;;
|
|
|
|
// Here if 8.0 <= |x| < 9.125
|
|
tanhf_close_to_saturation:
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolATmp = fA1, fAbsArg, fA0 // A1*|x| + A0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fPolA = fA3, fAbsArg, fA2 // A3*|x| + A2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.pred.rel "mutex", p14, p15
|
|
{ .mfi
|
|
nop.m 0
|
|
// for positive x
|
|
(p14) fma.s.s0 f8 = fPolA, fArgSqr, fPolATmp
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
// for negative x
|
|
(p15) fms.s.s0 f8 = fPolA, fArgSqrSgn, fPolATmp
|
|
br.ret.sptk b0 // Exit for 8.0 <=|x|< 9.125
|
|
};;
|
|
|
|
// Here if x is single precision denormal
|
|
tanhf_denormal:
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m p7,p8 = f8, 0x0a // is x -denormal ?
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.s.s0 f8 = f8,f8,f8 // -denormal
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p8) fnma.s.s0 f8 = f8,f8,f8 // +denormal
|
|
br.ret.sptk b0 // Exit for denormal
|
|
}
|
|
;;
|
|
|
|
GLOBAL_LIBM_END(tanhf)
|
|
libm_alias_float_other (tanh, tanh)
|