1// Copyright 2010 The Go Authors. All rights reserved. 2// Use of this source code is governed by a BSD-style 3// license that can be found in the LICENSE file. 4 5package math 6 7// The original C code, the long comment, and the constants 8// below are from FreeBSD's /usr/src/lib/msun/src/e_atanh.c 9// and came with this notice. The go code is a simplified 10// version of the original C. 11// 12// ==================================================== 13// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 14// 15// Developed at SunPro, a Sun Microsystems, Inc. business. 16// Permission to use, copy, modify, and distribute this 17// software is freely granted, provided that this notice 18// is preserved. 19// ==================================================== 20// 21// 22// __ieee754_atanh(x) 23// Method : 24// 1. Reduce x to positive by atanh(-x) = -atanh(x) 25// 2. For x>=0.5 26// 1 2x x 27// atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 28// 2 1 - x 1 - x 29// 30// For x<0.5 31// atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) 32// 33// Special cases: 34// atanh(x) is NaN if |x| > 1 with signal; 35// atanh(NaN) is that NaN with no signal; 36// atanh(+-1) is +-INF with signal. 37// 38 39// Atanh returns the inverse hyperbolic tangent of x. 40// 41// Special cases are: 42// Atanh(1) = +Inf 43// Atanh(±0) = ±0 44// Atanh(-1) = -Inf 45// Atanh(x) = NaN if x < -1 or x > 1 46// Atanh(NaN) = NaN 47func Atanh(x float64) float64 { 48 const NearZero = 1.0 / (1 << 28) // 2**-28 49 // special cases 50 switch { 51 case x < -1 || x > 1 || IsNaN(x): 52 return NaN() 53 case x == 1: 54 return Inf(1) 55 case x == -1: 56 return Inf(-1) 57 } 58 sign := false 59 if x < 0 { 60 x = -x 61 sign = true 62 } 63 var temp float64 64 switch { 65 case x < NearZero: 66 temp = x 67 case x < 0.5: 68 temp = x + x 69 temp = 0.5 * Log1p(temp+temp*x/(1-x)) 70 default: 71 temp = 0.5 * Log1p((x+x)/(1-x)) 72 } 73 if sign { 74 temp = -temp 75 } 76 return temp 77} 78