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