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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/e_acosh.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.
+// ====================================================
+//
+//
+// __ieee754_acosh(x)
+// Method :
+// Based on
+// acosh(x) = log [ x + sqrt(x*x-1) ]
+// we have
+// acosh(x) := log(x)+ln2, if x is large; else
+// acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+// acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+//
+// Special cases:
+// acosh(x) is NaN with signal if x<1.
+// acosh(NaN) is NaN without signal.
+//
+
+// Acosh returns the inverse hyperbolic cosine of x.
+//
+// Special cases are:
+// Acosh(+Inf) = +Inf
+// Acosh(x) = NaN if x < 1
+// Acosh(NaN) = NaN
+func Acosh(x float64) float64 {
+ const (
+ Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
+ Large = 1 << 28 // 2**28
+ )
+ // first case is special case
+ switch {
+ case x < 1 || IsNaN(x):
+ return NaN()
+ case x == 1:
+ return 0
+ case x >= Large:
+ return Log(x) + Ln2 // x > 2**28
+ case x > 2:
+ return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
+ }
+ t := x - 1
+ return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
+}