src/fdlibm/e_cosh.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_cosh.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_cosh(x)
 * Method : 
 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
 *      1. Replace x by |x| (cosh(x) = cosh(-x)). 
 *      2. 
 *                                                      [ exp(x) - 1 ]^2 
 *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
 *                                                         2*exp(x)
 *
 *                                                exp(x) +  1/exp(x)
 *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
 *                                                        2
 *          22       <= x <= lnovft :  cosh(x) := exp(x)/2 
 *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
 *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
 *
 * Special cases:
 *      cosh(x) is |x| if x is +INF, -INF, or NaN.
 *      only cosh(0)=1 is exact for finite x.
 */

#include "fdlibm.h"

#ifdef _WIN32
#define huge myhuge
#endif

#ifdef __STDC__
static const double one = 1.0, half=0.5, really_big = 1.0e300;
#else
static double one = 1.0, half=0.5, really_big = 1.0e300;
#endif

#ifdef __STDC__
        double __ieee754_cosh(double x)
#else
        double __ieee754_cosh(x)
        double x;
#endif
{       
        fd_twoints u;
        double t,w;
        int ix;
        unsigned lx;
        
    /* High word of |x|. */
        u.d = x;
        ix = __HI(u);
        ix &= 0x7fffffff;

    /* x is INF or NaN */
        if(ix>=0x7ff00000) return x*x;  

    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
        if(ix<0x3fd62e43) {
            t = fd_expm1(fd_fabs(x));
            w = one+t;
            if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
            return one+(t*t)/(w+w);
        }

    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
        if (ix < 0x40360000) {
                t = __ieee754_exp(fd_fabs(x));
                return half*t+half/t;
        }

    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
        if (ix < 0x40862E42)  return half*__ieee754_exp(fd_fabs(x));

    /* |x| in [log(maxdouble), overflowthresold] */
        lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
        if (ix<0x408633CE || 
              (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
            w = __ieee754_exp(half*fd_fabs(x));
            t = half*w;
            return t*w;
        }

    /* |x| > overflowthresold, cosh(x) overflow */
        return really_big*really_big;
}
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_cosh.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	/* __ieee754_cosh(x)
53	* Method :
54	* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
55	* 1. Replace x by \|x\| (cosh(x) = cosh(-x)).
56	* 2.
57	* [ exp(x) - 1 ]^2
58	* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
59	* 2*exp(x)
60	*
61	* exp(x) + 1/exp(x)
62	* ln2/2 <= x <= 22 : cosh(x) := -------------------
63	* 2
64	* 22 <= x <= lnovft : cosh(x) := exp(x)/2
65	* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
66	* ln2ovft < x : cosh(x) := huge*huge (overflow)
67	*
68	* Special cases:
69	* cosh(x) is \|x\| if x is +INF, -INF, or NaN.
70	* only cosh(0)=1 is exact for finite x.
71	*/
72
73	#include "fdlibm.h"
74
75	#ifdef _WIN32
76	#define huge myhuge
77	#endif
78
79	#ifdef __STDC__
80	static const double one = 1.0, half=0.5, really_big = 1.0e300;
81	#else
82	static double one = 1.0, half=0.5, really_big = 1.0e300;
83	#endif
84
85	#ifdef __STDC__
86	double __ieee754_cosh(double x)
87	#else
88	double __ieee754_cosh(x)
89	double x;
90	#endif
91	{
92	fd_twoints u;
93	double t,w;
94	int ix;
95	unsigned lx;
96
97	/* High word of \|x\|. */
98	u.d = x;
99	ix = __HI(u);
100	ix &= 0x7fffffff;
101
102	/* x is INF or NaN */
103	if(ix>=0x7ff00000) return x*x;
104
105	/* \|x\| in [0,0.5ln2], return 1+expm1(\|x\|)^2/(2exp(\|x\|)) */
106	if(ix<0x3fd62e43) {
107	t = fd_expm1(fd_fabs(x));
108	w = one+t;
109	if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
110	return one+(t*t)/(w+w);
111	}
112
113	/* \|x\| in [0.5ln2,22], return (exp(\|x\|)+1/exp(\|x\|)/2; /
114	if (ix < 0x40360000) {
115	t = __ieee754_exp(fd_fabs(x));
116	return half*t+half/t;
117	}
118
119	/* \|x\| in [22, log(maxdouble)] return halfexp(\|x\|) /
120	if (ix < 0x40862E42) return half*__ieee754_exp(fd_fabs(x));
121
122	/* \|x\| in [log(maxdouble), overflowthresold] */
123	lx = ( ((((unsigned)&one)>>29)) + (unsigned)&x);
124	if (ix<0x408633CE \|\|
125	(ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
126	w = __ieee754_exp(half*fd_fabs(x));
127	t = half*w;
128	return t*w;
129	}
130
131	/* \|x\| > overflowthresold, cosh(x) overflow */
132	return really_big*really_big;
133	}