// 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 ( float64) float64 {
	// special cases
	if IsNaN() ||  <= -1 ||  >= 1 {
		if  == -1 ||  == 1 {
			return Inf(int())
		}
		return NaN()
	}

	 := false
	if  < 0 {
		 = -
		 = true
	}

	var  float64
	if  <= 0.85 { // |x| <= 0.85
		 := 0.180625 - 0.25**
		 := ((((((a7*+a6)*+a5)*+a4)*+a3)*+a2)*+a1)* + a0
		 := ((((((b7*+b6)*+b5)*+b4)*+b3)*+b2)*+b1)* + b0
		 = ( * ) / 
	} else {
		var ,  float64
		 := Sqrt(Ln2 - Log(1.0-))
		if  <= 5.0 {
			 -= 1.6
			 = ((((((c7*+c6)*+c5)*+c4)*+c3)*+c2)*+c1)* + c0
			 = ((((((d7*+d6)*+d5)*+d4)*+d3)*+d2)*+d1)* + d0
		} else {
			 -= 5.0
			 = ((((((e7*+e6)*+e5)*+e4)*+e3)*+e2)*+e1)* + e0
			 = ((((((f7*+f6)*+f5)*+f4)*+f3)*+f2)*+f1)* + f0
		}
		 =  / 
	}

	if  {
		return -
	}
	return 
}

// 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 ( float64) float64 {
	return Erfinv(1 - )
}