61 lines
1.7 KiB
Go
61 lines
1.7 KiB
Go
// Copyright 2010 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math
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// The original C code, the long comment, and the constants
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// below are from FreeBSD's /usr/src/lib/msun/src/e_acosh.c
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// and came with this notice. The go code is a simplified
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// version of the original C.
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//
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// ====================================================
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// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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//
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// Developed at SunPro, a Sun Microsystems, Inc. business.
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// Permission to use, copy, modify, and distribute this
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// software is freely granted, provided that this notice
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// is preserved.
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// ====================================================
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//
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//
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// __ieee754_acosh(x)
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// Method :
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// Based on
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// acosh(x) = log [ x + sqrt(x*x-1) ]
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// we have
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// acosh(x) := log(x)+ln2, if x is large; else
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// acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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// acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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//
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// Special cases:
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// acosh(x) is NaN with signal if x<1.
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// acosh(NaN) is NaN without signal.
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//
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// Acosh returns the inverse hyperbolic cosine of x.
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//
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// Special cases are:
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// Acosh(+Inf) = +Inf
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// Acosh(x) = NaN if x < 1
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// Acosh(NaN) = NaN
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func Acosh(x float64) float64 {
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const (
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Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
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Large = 1 << 28 // 2**28
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)
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// first case is special case
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switch {
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case x < 1 || IsNaN(x):
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return NaN()
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case x == 1:
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return 0
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case x >= Large:
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return Log(x) + Ln2 // x > 2**28
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case x > 2:
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return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
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}
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t := x - 1
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return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
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}
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