| // 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(x) calculates the inverse hyperbolic sine of x. |
| // |
| // Special cases are: |
| // Asinh(+Inf) = +Inf |
| // 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 |
| ) |
| // TODO(rsc): Remove manual inlining of IsNaN, IsInf |
| // when compiler does it for us |
| // special cases |
| if x != x || x > MaxFloat64 || x < -MaxFloat64 { // 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 |
| } |