summaryrefslogtreecommitdiffstats
path: root/src/math/erfinv.go
diff options
context:
space:
mode:
Diffstat (limited to '')
-rw-r--r--src/math/erfinv.go129
1 files changed, 129 insertions, 0 deletions
diff --git a/src/math/erfinv.go b/src/math/erfinv.go
new file mode 100644
index 0000000..eed0feb
--- /dev/null
+++ b/src/math/erfinv.go
@@ -0,0 +1,129 @@
+// 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)
+}