src/fdlibm/e_sinh.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_sinh.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_sinh(x)
 * Method : 
 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
 *      1. Replace x by |x| (sinh(-x) = -sinh(x)). 
 *      2. 
 *                                                  E + E/(E+1)
 *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
 *                                                      2
 *
 *          22       <= x <= lnovft :  sinh(x) := exp(x)/2 
 *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
 *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
 *
 * Special cases:
 *      sinh(x) is |x| if x is +INF, -INF, or NaN.
 *      only sinh(0)=0 is exact for finite x.
 */

#include "fdlibm.h"

#ifdef __STDC__
static const double one = 1.0, shuge = 1.0e307;
#else
static double one = 1.0, shuge = 1.0e307;
#endif

#ifdef __STDC__
        double __ieee754_sinh(double x)
#else
        double __ieee754_sinh(x)
        double x;
#endif
{       
        fd_twoints u;
        double t,w,h;
        int ix,jx;
        unsigned lx;

    /* High word of |x|. */
        u.d = x;
        jx = __HI(u);
        ix = jx&0x7fffffff;

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

        h = 0.5;
        if (jx<0) h = -h;
    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
        if (ix < 0x40360000) {          /* |x|<22 */
            if (ix<0x3e300000)          /* |x|<2**-28 */
                if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
            t = fd_expm1(fd_fabs(x));
            if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
            return h*(t+t/(t+one));
        }

    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
        if (ix < 0x40862E42)  return h*__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(0.5*fd_fabs(x));
            t = h*w;
            return t*w;
        }

    /* |x| > overflowthresold, sinh(x) overflow */
        return x*shuge;
}
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_sinh.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_sinh(x)
53	* Method :
54	* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
55	* 1. Replace x by \|x\| (sinh(-x) = -sinh(x)).
56	* 2.
57	* E + E/(E+1)
58	* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
59	* 2
60	*
61	* 22 <= x <= lnovft : sinh(x) := exp(x)/2
62	* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
63	* ln2ovft < x : sinh(x) := x*shuge (overflow)
64	*
65	* Special cases:
66	* sinh(x) is \|x\| if x is +INF, -INF, or NaN.
67	* only sinh(0)=0 is exact for finite x.
68	*/
69
70	#include "fdlibm.h"
71
72	#ifdef __STDC__
73	static const double one = 1.0, shuge = 1.0e307;
74	#else
75	static double one = 1.0, shuge = 1.0e307;
76	#endif
77
78	#ifdef __STDC__
79	double __ieee754_sinh(double x)
80	#else
81	double __ieee754_sinh(x)
82	double x;
83	#endif
84	{
85	fd_twoints u;
86	double t,w,h;
87	int ix,jx;
88	unsigned lx;
89
90	/* High word of \|x\|. */
91	u.d = x;
92	jx = __HI(u);
93	ix = jx&0x7fffffff;
94
95	/* x is INF or NaN */
96	if(ix>=0x7ff00000) return x+x;
97
98	h = 0.5;
99	if (jx<0) h = -h;
100	/* \|x\| in [0,22], return sign(x)0.5(E+E/(E+1))) */
101	if (ix < 0x40360000) { /* \|x\|<22 */
102	if (ix<0x3e300000) /* \|x\|<2*-28 /
103	if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
104	t = fd_expm1(fd_fabs(x));
105	if(ix<0x3ff00000) return h(2.0t-t*t/(t+one));
106	return h*(t+t/(t+one));
107	}
108
109	/* \|x\| in [22, log(maxdouble)] return 0.5exp(\|x\|) /
110	if (ix < 0x40862E42) return h*__ieee754_exp(fd_fabs(x));
111
112	/* \|x\| in [log(maxdouble), overflowthresold] */
113	lx = ( ((((unsigned)&one)>>29)) + (unsigned)&x);
114	if (ix<0x408633CE \|\| (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
115	w = __ieee754_exp(0.5*fd_fabs(x));
116	t = h*w;
117	return t*w;
118	}
119
120	/* \|x\| > overflowthresold, sinh(x) overflow */
121	return x*shuge;
122	}