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Source file src/math/atanh.go

Documentation: math

  // 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 {
  	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
  }
  

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