src/fdlibm/e_acosh.c

/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 *
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is Mozilla Communicator client code, released
 * March 31, 1998.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 1998
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either of the GNU General Public License Version 2 or later (the "GPL"),
 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

/* @(#)e_acosh.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, 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.
 */

#include "fdlibm.h"

#ifdef __STDC__
static const double 
#else
static double 
#endif
one     = 1.0,
ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */

#ifdef __STDC__
        double __ieee754_acosh(double x)
#else
        double __ieee754_acosh(x)
        double x;
#endif
{       
        fd_twoints u;
        double t;
        int hx;
        u.d = x;
        hx = __HI(u);
        if(hx<0x3ff00000) {             /* x < 1 */
            return (x-x)/(x-x);
        } else if(hx >=0x41b00000) {    /* x > 2**28 */
            if(hx >=0x7ff00000) {       /* x is inf of NaN */
                return x+x;
            } else 
                return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */
        } else if(((hx-0x3ff00000)|__LO(u))==0) {
            return 0.0;                 /* acosh(1) = 0 */
        } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
            t=x*x;
            return __ieee754_log(2.0*x-one/(x+fd_sqrt(t-one)));
        } else {                        /* 1<x<2 */
            t = x-one;
            return fd_log1p(t+fd_sqrt(2.0*t+t*t));
        }
}
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.
23	*
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"),
28	* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29	* in which case the provisions of the GPL or the LGPL are applicable instead
30	* of those above. If you wish to allow use of your version of this file only
31	* under the terms of either the GPL or the LGPL, and not to allow others to
32	* use your version of this file under the terms of the MPL, indicate your
33	* decision by deleting the provisions above and replace them with the notice
34	* and other provisions required by the GPL or the LGPL. If you do not delete
35	* the provisions above, a recipient may use your version of this file under
36	* the terms of any one of the MPL, the GPL or the LGPL.
37	*
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(2.0t+tt)); 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__
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(2.0t+tt));
104	}
105	}