Source file src/pkg/math/asinh.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/s_asinh.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	// asinh(x)
    23	// Method :
    24	//	Based on
    25	//	        asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
    26	//	we have
    27	//	asinh(x) := x  if  1+x*x=1,
    28	//	         := sign(x)*(log(x)+ln2)) for large |x|, else
    29	//	         := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
    30	//	         := sign(x)*log1p(|x| + x**2/(1 + sqrt(1+x**2)))
    31	//
    32	
    33	// Asinh(x) calculates the inverse hyperbolic sine of x.
    34	//
    35	// Special cases are:
    36	//	Asinh(±0) = ±0
    37	//	Asinh(±Inf) = ±Inf
    38	//	Asinh(NaN) = NaN
    39	func Asinh(x float64) float64 {
    40		const (
    41			Ln2      = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
    42			NearZero = 1.0 / (1 << 28)            // 2**-28
    43			Large    = 1 << 28                    // 2**28
    44		)
    45		// special cases
    46		if IsNaN(x) || IsInf(x, 0) {
    47			return x
    48		}
    49		sign := false
    50		if x < 0 {
    51			x = -x
    52			sign = true
    53		}
    54		var temp float64
    55		switch {
    56		case x > Large:
    57			temp = Log(x) + Ln2 // |x| > 2**28
    58		case x > 2:
    59			temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0
    60		case x < NearZero:
    61			temp = x // |x| < 2**-28
    62		default:
    63			temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28
    64		}
    65		if sign {
    66			temp = -temp
    67		}
    68		return temp
    69	}