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 if haveArchAsinh { 41 return archAsinh(x) 42 } 43 return asinh(x) 44 } 45 46 func asinh(x float64) float64 { 47 const ( 48 Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF 49 NearZero = 1.0 / (1 << 28) // 2**-28 50 Large = 1 << 28 // 2**28 51 ) 52 // special cases 53 if IsNaN(x) || IsInf(x, 0) { 54 return x 55 } 56 sign := false 57 if x < 0 { 58 x = -x 59 sign = true 60 } 61 var temp float64 62 switch { 63 case x > Large: 64 temp = Log(x) + Ln2 // |x| > 2**28 65 case x > 2: 66 temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0 67 case x < NearZero: 68 temp = x // |x| < 2**-28 69 default: 70 temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28 71 } 72 if sign { 73 temp = -temp 74 } 75 return temp 76 } 77