// 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 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 }