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 returns 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  	if haveArchAsinh {
    41  		return archAsinh(x)
    42  	}
    43  	return asinh(x)
    44  }
    45  
    46  func asinh(x float64) float64 {
    47  	const (
    48  		Ln2      = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
    49  		NearZero = 1.0 / (1 << 28)            // 2**-28
    50  		Large    = 1 << 28                    // 2**28
    51  	)
    52  	// special cases
    53  	if IsNaN(x) || IsInf(x, 0) {
    54  		return x
    55  	}
    56  	sign := false
    57  	if x < 0 {
    58  		x = -x
    59  		sign = true
    60  	}
    61  	var temp float64
    62  	switch {
    63  	case x > Large:
    64  		temp = Log(x) + Ln2 // |x| > 2**28
    65  	case x > 2:
    66  		temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0
    67  	case x < NearZero:
    68  		temp = x // |x| < 2**-28
    69  	default:
    70  		temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28
    71  	}
    72  	if sign {
    73  		temp = -temp
    74  	}
    75  	return temp
    76  }
    77
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