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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 {
+ if haveArchAtanh {
+ return archAtanh(x)
+ }
+ return atanh(x)
+}
+
+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
+}