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 // Copyright 2010 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package math // The original C code, the long comment, and the constants // below are from FreeBSD's /usr/src/lib/msun/src/e_acosh.c // and came with this notice. The go code is a simplified // version of the original C. // // ==================================================== // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. // // Developed at SunPro, a Sun Microsystems, Inc. business. // Permission to use, copy, modify, and distribute this // software is freely granted, provided that this notice // is preserved. // ==================================================== // // // __ieee754_acosh(x) // Method : // Based on // acosh(x) = log [ x + sqrt(x*x-1) ] // we have // acosh(x) := log(x)+ln2, if x is large; else // acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else // acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. // // Special cases: // acosh(x) is NaN with signal if x<1. // acosh(NaN) is NaN without signal. // // Acosh returns the inverse hyperbolic cosine of x. // // Special cases are: // Acosh(+Inf) = +Inf // Acosh(x) = NaN if x < 1 // Acosh(NaN) = NaN func Acosh(x float64) float64 { return libc_acosh(x) } //extern acosh func libc_acosh(float64) float64 func acosh(x float64) float64 { const Large = 1 << 28 // 2**28 // first case is special case switch { case x < 1 || IsNaN(x): return NaN() case x == 1: return 0 case x >= Large: return Log(x) + Ln2 // x > 2**28 case x > 2: return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2 } t := x - 1 return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1 }