dd931d9b48
Reviewed-on: https://go-review.googlesource.com/136435 gotools/: * Makefile.am (mostlyclean-local): Run chmod on check-go-dir to make sure it is writable. (check-go-tools): Likewise. (check-vet): Copy internal/objabi to check-vet-dir. * Makefile.in: Rebuild. From-SVN: r264546
128 lines
3.4 KiB
Go
128 lines
3.4 KiB
Go
// Copyright 2017 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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/*
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Inverse of the floating-point error function.
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*/
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// This implementation is based on the rational approximation
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// of percentage points of normal distribution available from
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// https://www.jstor.org/stable/2347330.
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const (
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// Coefficients for approximation to erf in |x| <= 0.85
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a0 = 1.1975323115670912564578e0
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a1 = 4.7072688112383978012285e1
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a2 = 6.9706266534389598238465e2
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a3 = 4.8548868893843886794648e3
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a4 = 1.6235862515167575384252e4
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a5 = 2.3782041382114385731252e4
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a6 = 1.1819493347062294404278e4
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a7 = 8.8709406962545514830200e2
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b0 = 1.0000000000000000000e0
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b1 = 4.2313330701600911252e1
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b2 = 6.8718700749205790830e2
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b3 = 5.3941960214247511077e3
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b4 = 2.1213794301586595867e4
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b5 = 3.9307895800092710610e4
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b6 = 2.8729085735721942674e4
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b7 = 5.2264952788528545610e3
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// Coefficients for approximation to erf in 0.85 < |x| <= 1-2*exp(-25)
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c0 = 1.42343711074968357734e0
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c1 = 4.63033784615654529590e0
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c2 = 5.76949722146069140550e0
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c3 = 3.64784832476320460504e0
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c4 = 1.27045825245236838258e0
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c5 = 2.41780725177450611770e-1
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c6 = 2.27238449892691845833e-2
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c7 = 7.74545014278341407640e-4
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d0 = 1.4142135623730950488016887e0
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d1 = 2.9036514445419946173133295e0
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d2 = 2.3707661626024532365971225e0
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d3 = 9.7547832001787427186894837e-1
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d4 = 2.0945065210512749128288442e-1
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d5 = 2.1494160384252876777097297e-2
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d6 = 7.7441459065157709165577218e-4
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d7 = 1.4859850019840355905497876e-9
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// Coefficients for approximation to erf in 1-2*exp(-25) < |x| < 1
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e0 = 6.65790464350110377720e0
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e1 = 5.46378491116411436990e0
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e2 = 1.78482653991729133580e0
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e3 = 2.96560571828504891230e-1
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e4 = 2.65321895265761230930e-2
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e5 = 1.24266094738807843860e-3
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e6 = 2.71155556874348757815e-5
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e7 = 2.01033439929228813265e-7
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f0 = 1.414213562373095048801689e0
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f1 = 8.482908416595164588112026e-1
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f2 = 1.936480946950659106176712e-1
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f3 = 2.103693768272068968719679e-2
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f4 = 1.112800997078859844711555e-3
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f5 = 2.611088405080593625138020e-5
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f6 = 2.010321207683943062279931e-7
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f7 = 2.891024605872965461538222e-15
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)
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// Erfinv returns the inverse error function of x.
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//
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// Special cases are:
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// Erfinv(1) = +Inf
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// Erfinv(-1) = -Inf
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// Erfinv(x) = NaN if x < -1 or x > 1
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// Erfinv(NaN) = NaN
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func Erfinv(x float64) float64 {
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// special cases
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if IsNaN(x) || x <= -1 || x >= 1 {
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if x == -1 || x == 1 {
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return Inf(int(x))
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}
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return NaN()
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}
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sign := false
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if x < 0 {
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x = -x
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sign = true
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}
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var ans float64
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if x <= 0.85 { // |x| <= 0.85
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r := 0.180625 - 0.25*x*x
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z1 := ((((((a7*r+a6)*r+a5)*r+a4)*r+a3)*r+a2)*r+a1)*r + a0
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z2 := ((((((b7*r+b6)*r+b5)*r+b4)*r+b3)*r+b2)*r+b1)*r + b0
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ans = (x * z1) / z2
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} else {
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var z1, z2 float64
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r := Sqrt(Ln2 - Log(1.0-x))
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if r <= 5.0 {
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r -= 1.6
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z1 = ((((((c7*r+c6)*r+c5)*r+c4)*r+c3)*r+c2)*r+c1)*r + c0
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z2 = ((((((d7*r+d6)*r+d5)*r+d4)*r+d3)*r+d2)*r+d1)*r + d0
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} else {
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r -= 5.0
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z1 = ((((((e7*r+e6)*r+e5)*r+e4)*r+e3)*r+e2)*r+e1)*r + e0
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z2 = ((((((f7*r+f6)*r+f5)*r+f4)*r+f3)*r+f2)*r+f1)*r + f0
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}
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ans = z1 / z2
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}
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if sign {
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return -ans
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}
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return ans
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}
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// Erfcinv returns the inverse of Erfc(x).
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//
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// Special cases are:
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// Erfcinv(0) = +Inf
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// Erfcinv(2) = -Inf
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// Erfcinv(x) = NaN if x < 0 or x > 2
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// Erfcinv(NaN) = NaN
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func Erfcinv(x float64) float64 {
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return Erfinv(1 - x)
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}
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