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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 {
+ if haveArchAsinh {
+ return archAsinh(x)
+ }
+ return asinh(x)
+}
+
+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
+}