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Code Editor : erfinv.go
// Copyright 2017 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package math /* Inverse of the floating-point error function. */ // This implementation is based on the rational approximation // of percentage points of normal distribution available from // https://www.jstor.org/stable/2347330. const ( // Coefficients for approximation to erf in |x| <= 0.85 a0 = 1.1975323115670912564578e0 a1 = 4.7072688112383978012285e1 a2 = 6.9706266534389598238465e2 a3 = 4.8548868893843886794648e3 a4 = 1.6235862515167575384252e4 a5 = 2.3782041382114385731252e4 a6 = 1.1819493347062294404278e4 a7 = 8.8709406962545514830200e2 b0 = 1.0000000000000000000e0 b1 = 4.2313330701600911252e1 b2 = 6.8718700749205790830e2 b3 = 5.3941960214247511077e3 b4 = 2.1213794301586595867e4 b5 = 3.9307895800092710610e4 b6 = 2.8729085735721942674e4 b7 = 5.2264952788528545610e3 // Coefficients for approximation to erf in 0.85 < |x| <= 1-2*exp(-25) c0 = 1.42343711074968357734e0 c1 = 4.63033784615654529590e0 c2 = 5.76949722146069140550e0 c3 = 3.64784832476320460504e0 c4 = 1.27045825245236838258e0 c5 = 2.41780725177450611770e-1 c6 = 2.27238449892691845833e-2 c7 = 7.74545014278341407640e-4 d0 = 1.4142135623730950488016887e0 d1 = 2.9036514445419946173133295e0 d2 = 2.3707661626024532365971225e0 d3 = 9.7547832001787427186894837e-1 d4 = 2.0945065210512749128288442e-1 d5 = 2.1494160384252876777097297e-2 d6 = 7.7441459065157709165577218e-4 d7 = 1.4859850019840355905497876e-9 // Coefficients for approximation to erf in 1-2*exp(-25) < |x| < 1 e0 = 6.65790464350110377720e0 e1 = 5.46378491116411436990e0 e2 = 1.78482653991729133580e0 e3 = 2.96560571828504891230e-1 e4 = 2.65321895265761230930e-2 e5 = 1.24266094738807843860e-3 e6 = 2.71155556874348757815e-5 e7 = 2.01033439929228813265e-7 f0 = 1.414213562373095048801689e0 f1 = 8.482908416595164588112026e-1 f2 = 1.936480946950659106176712e-1 f3 = 2.103693768272068968719679e-2 f4 = 1.112800997078859844711555e-3 f5 = 2.611088405080593625138020e-5 f6 = 2.010321207683943062279931e-7 f7 = 2.891024605872965461538222e-15 ) // Erfinv returns the inverse error function of x. // // Special cases are: // Erfinv(1) = +Inf // Erfinv(-1) = -Inf // Erfinv(x) = NaN if x < -1 or x > 1 // Erfinv(NaN) = NaN func Erfinv(x float64) float64 { // special cases if IsNaN(x) || x <= -1 || x >= 1 { if x == -1 || x == 1 { return Inf(int(x)) } return NaN() } sign := false if x < 0 { x = -x sign = true } var ans float64 if x <= 0.85 { // |x| <= 0.85 r := 0.180625 - 0.25*x*x z1 := ((((((a7*r+a6)*r+a5)*r+a4)*r+a3)*r+a2)*r+a1)*r + a0 z2 := ((((((b7*r+b6)*r+b5)*r+b4)*r+b3)*r+b2)*r+b1)*r + b0 ans = (x * z1) / z2 } else { var z1, z2 float64 r := Sqrt(Ln2 - Log(1.0-x)) if r <= 5.0 { r -= 1.6 z1 = ((((((c7*r+c6)*r+c5)*r+c4)*r+c3)*r+c2)*r+c1)*r + c0 z2 = ((((((d7*r+d6)*r+d5)*r+d4)*r+d3)*r+d2)*r+d1)*r + d0 } else { r -= 5.0 z1 = ((((((e7*r+e6)*r+e5)*r+e4)*r+e3)*r+e2)*r+e1)*r + e0 z2 = ((((((f7*r+f6)*r+f5)*r+f4)*r+f3)*r+f2)*r+f1)*r + f0 } ans = z1 / z2 } if sign { return -ans } return ans } // Erfcinv returns the inverse of Erfc(x). // // Special cases are: // Erfcinv(0) = +Inf // Erfcinv(2) = -Inf // Erfcinv(x) = NaN if x < 0 or x > 2 // Erfcinv(NaN) = NaN func Erfcinv(x float64) float64 { return Erfinv(1 - x) }
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