1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
2  *
3  * ***** BEGIN LICENSE BLOCK *****
4  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
5  *
6  * The contents of this file are subject to the Mozilla Public License Version
7  * 1.1 (the "License"); you may not use this file except in compliance with
8  * the License. You may obtain a copy of the License at
9  * http://www.mozilla.org/MPL/
10  *
11  * Software distributed under the License is distributed on an "AS IS" basis,
12  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13  * for the specific language governing rights and limitations under the
14  * License.
15  *
16  * The Original Code is Mozilla Communicator client code, released
17  * March 31, 1998.
18  *
19  * The Initial Developer of the Original Code is
20  * Sun Microsystems, Inc.
21  * Portions created by the Initial Developer are Copyright (C) 1998
22  * the Initial Developer. All Rights Reserved.
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24  * Contributor(s):
25  *
26  * Alternatively, the contents of this file may be used under the terms of
27  * either of the GNU General Public License Version 2 or later (the "GPL"),
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38  * ***** END LICENSE BLOCK ***** */
39 
40 /* @(#)e_acosh.c 1.3 95/01/18 */
41 /*
42  * ====================================================
43  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44  *
45  * Developed at SunSoft, a Sun Microsystems, Inc. business.
46  * Permission to use, copy, modify, and distribute this
47  * software is freely granted, provided that this notice
48  * is preserved.
49  * ====================================================
50  *
51  */
52 
53 /* __ieee754_acosh(x)
54  * Method :
55  *	Based on
56  *		acosh(x) = log [ x + sqrt(x*x-1) ]
57  *	we have
58  *		acosh(x) := log(x)+ln2,	if x is large; else
59  *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
60  *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
61  *
62  * Special cases:
63  *	acosh(x) is NaN with signal if x<1.
64  *	acosh(NaN) is NaN without signal.
65  */
66 
67 #include "fdlibm.h"
68 
69 #ifdef __STDC__
70 static const double
71 #else
72 static double
73 #endif
74 one	= 1.0,
75 ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
76 
77 #ifdef __STDC__
__ieee754_acosh(double x)78 	double __ieee754_acosh(double x)
79 #else
80 	double __ieee754_acosh(x)
81 	double x;
82 #endif
83 {
84         fd_twoints u;
85 	double t;
86 	int hx;
87         u.d = x;
88 	hx = __HI(u);
89 	if(hx<0x3ff00000) {		/* x < 1 */
90 	    return (x-x)/(x-x);
91 	} else if(hx >=0x41b00000) {	/* x > 2**28 */
92 	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
93 	        return x+x;
94 	    } else
95 		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
96 	} else if(((hx-0x3ff00000)|__LO(u))==0) {
97 	    return 0.0;			/* acosh(1) = 0 */
98 	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
99 	    t=x*x;
100 	    return __ieee754_log(2.0*x-one/(x+fd_sqrt(t-one)));
101 	} else {			/* 1<x<2 */
102 	    t = x-one;
103 	    return fd_log1p(t+fd_sqrt(2.0*t+t*t));
104 	}
105 }
106