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/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 39 func 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
