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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>
559 lines
15 KiB
ArmAsm
559 lines
15 KiB
ArmAsm
.file "erff.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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// 08/14/01 Initial 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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// 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 erff(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 8 paths:
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// 1. x = +/-0.0
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// Return erff(x) = +/-0.0
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//
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// 2. 0.0 < |x| < 0.125
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// Return erff(x) = x *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. 0.125 <= |x| < 4.0
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// Return erff(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 0.125<=|x|< 4.0 is splitted 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 0.125 <= |x| < 0.25
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// 3.2 0.25 <= |x| < 0.5
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// 3.3 0.5 <= |x| < 1.0
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// 3.4 1.0 <= |x| < 2.0
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// 3.5 2.0 <= |x| < 4.0
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//
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// 4. 4.0 <= |x| < +INF
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// Return erff(x) = sign(x)*(1.0d - 2^(-52))
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//
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// 5. |x| = INF
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// Return erff(x) = sign(x) * 1.0
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//
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// 6. x = [S,Q]NaN
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// Return erff(x) = QNaN
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//
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// 7. x is positive denormal
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// Return erff(x) = C0*x - x^2,
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// where C0 = 2.0/sqrt(Pi)
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//
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// 8. x is negative denormal
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// Return erff(x) = C0*x + x^2,
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// where C0 = 2.0/sqrt(Pi)
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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 -> r45, r2, r3
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// Predicate registers used:
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// p0, p6 -> p12, p14, 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| < 0.125
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// p11 to filter out case when 0.125 <= |x| < 4.0
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// p12 to filter out case when |x| >= 4.0
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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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rCoeffAddr1 = r35
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rCoeffAddr2 = r36
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rOffset2 = r37
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rBias2 = r38
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rMask = r39
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rArg = r40
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rBound = r41
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rSignBit = r42
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rAbsArg = r43
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rDataPtr2 = r44
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rSaturation = r45
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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(erff_data)
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// Polynomial coefficients for the erf(x), 0.125 <= |x| < 0.25
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data8 0xBE4218BB56B49E66 // C0
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data8 0x3F7AFB8315DA322B // C1
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data8 0x3F615D6EBEE0CA32 // C2
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data8 0xBF468D71CF4F0918 // C3
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data8 0x40312115B0932F24 // D0
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data8 0xC0160D6CD0991EA3 // D1
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data8 0xBFE04A567A6DBE4A // D2
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data8 0xBF4207BC640D1509 // B0
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// Polynomial coefficients for the erf(x), 0.25 <= |x| < 0.5
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data8 0x3F90849356383F58 // C0
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data8 0x3F830BD5BA240F09 // C1
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data8 0xBF3FA4970E2BCE23 // C2
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data8 0xBF6061798E58D0FD // C3
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data8 0xBF68C0D83DD22E02 // D0
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data8 0x401C0A9EE4108F94 // D1
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data8 0xC01056F9B5E387F5 // D2
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data8 0x3F1C9744E36A5706 // B0
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// Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0
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data8 0x3F85F7D419A13DE3 // C0
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data8 0x3F791A13FF66D45A // C1
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data8 0x3F46B17B16B5929F // C2
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data8 0xBF5124947A8BF45E // C3
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data8 0x3FA1B3FD95EA9564 // D0
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data8 0x40250CECD79A020A // D1
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data8 0xC0190DC96FF66CCD // D2
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data8 0x3F4401AE28BA4DD5 // B0
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// Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0
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data8 0xBF49E07E3584C3AE // C0
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data8 0x3F3166621131445C // C1
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data8 0xBF65B7FC1EAC2099 // C2
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data8 0x3F508C6BD211D736 // C3
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data8 0xC053FABD70601067 // D0
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data8 0x404A06640EE87808 // D1
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data8 0xC0283F30817A3F08 // D2
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data8 0xBF2F6DBBF4D6257F // B0
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// Polynomial coefficients for the erf(x), 2.0 <= |x| < 4.0
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data8 0xBF849855D67E9407 // C0
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data8 0x3F5ECA5FEC01C70C // C1
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data8 0xBF483110C30FABA4 // C2
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data8 0x3F1618DA72860403 // C3
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data8 0xC08A5C9D5FE8B9F6 // D0
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data8 0x406EFF5F088CEC4B // D1
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data8 0xC03A5743DF38FDE0 // D2
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data8 0xBEE397A9FA5686A2 // B0
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// Polynomial coefficients for the erf(x), -0.125 < x < 0.125
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data8 0x3FF20DD7504270CB // C0
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data8 0xBFD8127465AFE719 // C1
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data8 0x3FBCE2D77791DD77 // C2
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data8 0xBF9B582755CDF345 // C3
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// Polynomial coefficients for the erf(x), 0.125 <= |x| < 0.25
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data8 0xBD54E7E451AF0E36 // A0
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data8 0x3FF20DD75043FE20 // A1
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data8 0xBE05680ACF8280E4 // A2
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data8 0xBFD812745E92C3D3 // A3
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// Polynomial coefficients for the erf(x), 0.25 <= |x| < 0.5
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data8 0xBE1ACEC2859CB55F // A0
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data8 0x3FF20DD75E8D2B64 // A1
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data8 0xBEABC6A83208FCFC // A2
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data8 0xBFD81253E42E7B99 // A3
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// Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0
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data8 0x3EABD5A2482B4979 // A0
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data8 0x3FF20DCAA52085D5 // A1
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data8 0x3F13A994A348795B // A2
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data8 0xBFD8167B2DFCDE44 // A3
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// Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0
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data8 0xBF5BA377DDAB4E17 // A0
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data8 0x3FF2397F1D8FC0ED // A1
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data8 0xBF9945BFC1915C21 // A2
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data8 0xBFD747AAABB690D8 // A3
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// Polynomial coefficients for the erf(x), 2.0 <= |x| < 4.0
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data8 0x3FF0E2920E0391AF // A0
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data8 0xC00D249D1A95A5AE // A1
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data8 0x40233905061C3803 // A2
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data8 0xC027560B851F7690 // A3
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//
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data8 0x3FEFFFFFFFFFFFFF // 1.0 - epsilon
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data8 0x3FF20DD750429B6D // C0 = 2.0/sqrt(Pi)
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LOCAL_OBJECT_END(erff_data)
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.section .text
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GLOBAL_LIBM_ENTRY(erff)
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{ .mfi
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alloc r32 = ar.pfs, 0, 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(erff_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 = 0x1F0, r0
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}
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;;
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{ .mfi
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nop.m 0
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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 = 0x3E0, r0
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nop.f 0
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adds rSaturation = 0x408, 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 // 0.125f 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 erff_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| < 0.125?
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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, 20// 4.0 in GR (saturation bound)
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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| < 4.0?
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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 = 512, 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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nop.i 0
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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 erff_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 erff_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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{ .mfi
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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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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 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
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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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// sign(x)*(|x|^7 + D2*x^6)
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fma.s1 fPolDTmp = fArg6Sgn, fD2, fArg7Sgn
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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 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 0.125 <=|x|< 4.0
|
|
};;
|
|
|
|
|
|
// Here if |x| < 0.125
|
|
erff_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*(C3*x^6 + C2*x^4 + C1*x^2 + C0)
|
|
fma.s.s0 f8 = fPolC, f8, f0
|
|
br.ret.sptk b0 // Exit for |x| < 0.125
|
|
};;
|
|
|
|
// Here if 4.0 <= |x| < +inf
|
|
erff_saturation:
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0d - 2^(-52))
|
|
// Exit for 4.0 <= |x| < +inf
|
|
br.ret.sptk b0 // Exit for 4.0 <=|x|< +inf
|
|
}
|
|
;;
|
|
|
|
// Here if x is single precision denormal
|
|
erff_denormal:
|
|
{ .mfi
|
|
adds rDataPtr = 520, rDataPtr // address of C0
|
|
fclass.m p7,p8 = f8, 0x0a // is x -denormal ?
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfd fC0 = [rDataPtr] // C0
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fC0 = fC0,f8,f0 // C0*x
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.s.s0 f8 = f8,f8,fC0 // -denormal
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p8) fnma.s.s0 f8 = f8,f8,fC0 // +denormal
|
|
br.ret.sptk b0 // Exit for denormal
|
|
}
|
|
;;
|
|
|
|
GLOBAL_LIBM_END(erff)
|
|
libm_alias_float_other (erf, erf)
|