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As necessary, math functions were structured to use stubs, so that they can
be accelerated with assembly on any platform.
Technique used was minimax polynomial approximation using tables of
polynomial coefficients, with argument range reduction.
Benchmark New Old Speedup
BenchmarkAcos 12.2 47.5 3.89
BenchmarkAcosh 18.5 56.2 3.04
BenchmarkAsin 13.1 40.6 3.10
BenchmarkAsinh 19.4 62.8 3.24
BenchmarkAtan 10.1 23 2.28
BenchmarkAtanh 19.1 53.2 2.79
BenchmarkAtan2 16.5 33.9 2.05
BenchmarkCbrt 14.8 58 3.92
BenchmarkErf 10.8 20.1 1.86
BenchmarkErfc 11.2 23.5 2.10
BenchmarkExp 8.77 53.8 6.13
BenchmarkExpm1 10.1 38.3 3.79
BenchmarkLog 13.1 40.1 3.06
BenchmarkLog1p 12.7 38.3 3.02
BenchmarkPowInt 31.7 40.5 1.28
BenchmarkPowFrac 33.1 141 4.26
BenchmarkTan 11.5 30 2.61
Accuracy was tested against a high precision
reference function to determine maximum error.
Note: ulperr is error in "units in the last place"
max
ulperr
Acos 1.15
Acosh 1.07
Asin 2.22
Asinh 1.72
Atan 1.41
Atanh 3.00
Atan2 1.45
Cbrt 1.18
Erf 1.29
Erfc 4.82
Exp 1.00
Expm1 2.26
Log 0.94
Log1p 2.39
Tan 3.14
Pow will have 99.99% correctly rounded results with reasonable inputs
producing numeric (non Inf or NaN) results
Change-Id: I850e8cf7b70426e8b54ec49d74acd4cddc8c6cb2
Reviewed-on: https://go-review.googlesource.com/38585
Reviewed-by: Michael Munday <munday@ca.ibm.com>
Run-TryBot: Michael Munday <munday@ca.ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
32 lines
732 B
Go
32 lines
732 B
Go
// Copyright 2016 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math
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// Export internal functions and variable for testing.
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var Log10NoVec = log10
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var CosNoVec = cos
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var CoshNoVec = cosh
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var SinNoVec = sin
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var SinhNoVec = sinh
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var TanhNoVec = tanh
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var Log1pNovec = log1p
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var AtanhNovec = atanh
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var AcosNovec = acos
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var AcoshNovec = acosh
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var AsinNovec = asin
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var AsinhNovec = asinh
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var ErfNovec = erf
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var ErfcNovec = erfc
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var AtanNovec = atan
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var Atan2Novec = atan2
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var CbrtNovec = cbrt
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var LogNovec = log
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var TanNovec = tan
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var ExpNovec = exp
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var Expm1Novec = expm1
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var PowNovec = pow
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var HypotNovec = hypot
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var HasVX = hasVX
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