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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/s_asinh.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. // ==================================================== // // // asinh(x) // Method : // Based on // asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] // we have // asinh(x) := x if 1+x*x=1, // := sign(x)*(log(x)+ln2)) for large |x|, else // := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else // := sign(x)*log1p(|x| + x**2/(1 + sqrt(1+x**2))) // // Asinh returns the inverse hyperbolic sine of x. // // Special cases are: // Asinh(±0) = ±0 // Asinh(±Inf) = ±Inf // Asinh(NaN) = NaN func Asinh(x float64) float64 { const ( Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF NearZero = 1.0 / (1 << 28) // 2**-28 Large = 1 << 28 // 2**28 ) // special cases if IsNaN(x) || IsInf(x, 0) { return x } sign := false if x < 0 { x = -x sign = true } var temp float64 switch { case x > Large: temp = Log(x) + Ln2 // |x| > 2**28 case x > 2: temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0 case x < NearZero: temp = x // |x| < 2**-28 default: temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28 } if sign { temp = -temp } return temp }