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 5package 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 39func Asinh(x float64) float64 { 40 const ( 41 Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF 42 NearZero = 1.0 / (1 << 28) // 2**-28 43 Large = 1 << 28 // 2**28 44 ) 45 // special cases 46 if IsNaN(x) || IsInf(x, 0) { 47 return x 48 } 49 sign := false 50 if x < 0 { 51 x = -x 52 sign = true 53 } 54 var temp float64 55 switch { 56 case x > Large: 57 temp = Log(x) + Ln2 // |x| > 2**28 58 case x > 2: 59 temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0 60 case x < NearZero: 61 temp = x // |x| < 2**-28 62 default: 63 temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28 64 } 65 if sign { 66 temp = -temp 67 } 68 return temp 69} 70