| // 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(x) calculates the inverse hyperbolic tangent of x. |
| // |
| // Special cases are: |
| // Atanh(x) = NaN if x < -1 or x > 1 |
| // Atanh(1) = +Inf |
| // Atanh(-1) = -Inf |
| // Atanh(NaN) = NaN |
| func Atanh(x float64) float64 { |
| const NearZero = 1.0 / (1 << 28) // 2**-28 |
| // TODO(rsc): Remove manual inlining of IsNaN |
| // when compiler does it for us |
| // special cases |
| switch { |
| case x < -1 || x > 1 || x != x: // 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 |
| } |