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    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 
   44 func acosh(x float64) float64 {
   45     const (
   46         Ln2   = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
   47         Large = 1 << 28                    // 2**28
   48     )
   49     // first case is special case
   50     switch {
   51     case x < 1 || IsNaN(x):
   52         return NaN()
   53     case x == 1:
   54         return 0
   55     case x >= Large:
   56         return Log(x) + Ln2 // x > 2**28
   57     case x > 2:
   58         return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
   59     }
   60     t := x - 1
   61     return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
   62 }