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// Copyright 2010 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
// The original C code, the long comment, and the constants
// below are from FreeBSD's /usr/src/lib/msun/src/e_atanh.c
// and came with this notice. The go code is a simplified
// version of the original C.
//
// ====================================================
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
//
// Developed at SunPro, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
//
//
// __ieee754_atanh(x)
// Method :
// 1. Reduce x to positive by atanh(-x) = -atanh(x)
// 2. For x>=0.5
// 1 2x x
// atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
// 2 1 - x 1 - x
//
// For x<0.5
// atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
//
// Special cases:
// atanh(x) is NaN if |x| > 1 with signal;
// atanh(NaN) is that NaN with no signal;
// atanh(+-1) is +-INF with signal.
//
// Atanh returns the inverse hyperbolic tangent of x.
//
// Special cases are:
// Atanh(1) = +Inf
// Atanh(±0) = ±0
// Atanh(-1) = -Inf
// Atanh(x) = NaN if x < -1 or x > 1
// Atanh(NaN) = NaN
func Atanh(x float64) float64 {
const NearZero = 1.0 / (1 << 28) // 2**-28
// special cases
switch {
case x < -1 || x > 1 || IsNaN(x):
return NaN()
case x == 1:
return Inf(1)
case x == -1:
return Inf(-1)
}
sign := false
if x < 0 {
x = -x
sign = true
}
var temp float64
switch {
case x < NearZero:
temp = x
case x < 0.5:
temp = x + x
temp = 0.5 * Log1p(temp+temp*x/(1-x))
default:
temp = 0.5 * Log1p((x+x)/(1-x))
}
if sign {
temp = -temp
}
return temp
}
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