acosh.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_acosh.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_acosh(x)
    23  // Method :
    24  //	Based on
    25  //	        acosh(x) = log [ x + sqrt(x*x-1) ]
    26  //	we have
    27  //	        acosh(x) := log(x)+ln2,	if x is large; else
    28  //	        acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
    29  //	        acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
    30  //
    31  // Special cases:
    32  //	acosh(x) is NaN with signal if x<1.
    33  //	acosh(NaN) is NaN without signal.
    34  //
    35  
    36  // Acosh returns the inverse hyperbolic cosine of x.
    37  //
    38  // Special cases are:
    39  //	Acosh(+Inf) = +Inf
    40  //	Acosh(x) = NaN if x < 1
    41  //	Acosh(NaN) = NaN
    42  func Acosh(x float64) float64 {
    43  	if haveArchAcosh {
    44  		return archAcosh(x)
    45  	}
    46  	return acosh(x)
    47  }
    48  
    49  func acosh(x float64) float64 {
    50  	const Large = 1 << 28 // 2**28
    51  	// first case is special case
    52  	switch {
    53  	case x < 1 || IsNaN(x):
    54  		return NaN()
    55  	case x == 1:
    56  		return 0
    57  	case x >= Large:
    58  		return Log(x) + Ln2 // x > 2**28
    59  	case x > 2:
    60  		return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
    61  	}
    62  	t := x - 1
    63  	return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
    64  }
    65
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