atanh.go

     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  //
    43  //	Atanh(1) = +Inf
    44  //	Atanh(±0) = ±0
    45  //	Atanh(-1) = -Inf
    46  //	Atanh(x) = NaN if x < -1 or x > 1
    47  //	Atanh(NaN) = NaN
    48  func Atanh(x float64) float64 {
    49  	if haveArchAtanh {
    50  		return archAtanh(x)
    51  	}
    52  	return atanh(x)
    53  }
    54  
    55  func atanh(x float64) float64 {
    56  	const NearZero = 1.0 / (1 << 28) // 2**-28
    57  	// special cases
    58  	switch {
    59  	case x < -1 || x > 1 || IsNaN(x):
    60  		return NaN()
    61  	case x == 1:
    62  		return Inf(1)
    63  	case x == -1:
    64  		return Inf(-1)
    65  	}
    66  	sign := false
    67  	if x < 0 {
    68  		x = -x
    69  		sign = true
    70  	}
    71  	var temp float64
    72  	switch {
    73  	case x < NearZero:
    74  		temp = x
    75  	case x < 0.5:
    76  		temp = x + x
    77  		temp = 0.5 * Log1p(temp+temp*x/(1-x))
    78  	default:
    79  		temp = 0.5 * Log1p((x+x)/(1-x))
    80  	}
    81  	if sign {
    82  		temp = -temp
    83  	}
    84  	return temp
    85  }
    86
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