Source file src/pkg/math/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(x) calculates 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		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	}