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Diffstat (limited to 'src/math/acosh.go')
-rw-r--r-- | src/math/acosh.go | 65 |
1 files changed, 65 insertions, 0 deletions
diff --git a/src/math/acosh.go b/src/math/acosh.go new file mode 100644 index 0000000..a85d003 --- /dev/null +++ b/src/math/acosh.go @@ -0,0 +1,65 @@ +// 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 { + if haveArchAcosh { + return archAcosh(x) + } + return acosh(x) +} + +func acosh(x float64) float64 { + const 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 +} |