Home | History | Annotate | Download | only in math 
      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 
      5 package 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
     47 func Atanh(x float64) float64
     48 
     49 func atanh(x float64) float64 {
     50 	const NearZero = 1.0 / (1 << 28) // 2**-28
     51 	// special cases
     52 	switch {
     53 	case x < -1 || x > 1 || IsNaN(x):
     54 		return NaN()
     55 	case x == 1:
     56 		return Inf(1)
     57 	case x == -1:
     58 		return Inf(-1)
     59 	}
     60 	sign := false
     61 	if x < 0 {
     62 		x = -x
     63 		sign = true
     64 	}
     65 	var temp float64
     66 	switch {
     67 	case x < NearZero:
     68 		temp = x
     69 	case x < 0.5:
     70 		temp = x + x
     71 		temp = 0.5 * Log1p(temp+temp*x/(1-x))
     72 	default:
     73 		temp = 0.5 * Log1p((x+x)/(1-x))
     74 	}
     75 	if sign {
     76 		temp = -temp
     77 	}
     78 	return temp
     79 }
     80