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 } 63