1 /*
2  * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4  *
5  * This code is free software; you can redistribute it and/or modify it
6  * under the terms of the GNU General Public License version 2 only, as
7  * published by the Free Software Foundation.  Oracle designates this
8  * particular file as subject to the "Classpath" exception as provided
9  * by Oracle in the LICENSE file that accompanied this code.
10  *
11  * This code is distributed in the hope that it will be useful, but WITHOUT
12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
14  * version 2 for more details (a copy is included in the LICENSE file that
15  * accompanied this code).
16  *
17  * You should have received a copy of the GNU General Public License version
18  * 2 along with this work; if not, write to the Free Software Foundation,
19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20  *
21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22  * or visit www.oracle.com if you need additional information or have any
23  * questions.
24  */
25 
26 /* __ieee754_sinh(x)
27  * Method :
28  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
29  *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
30  *      2.
31  *                                                  E + E/(E+1)
32  *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
33  *                                                      2
34  *
35  *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
36  *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
37  *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
38  *
39  * Special cases:
40  *      sinh(x) is |x| if x is +INF, -INF, or NaN.
41  *      only sinh(0)=0 is exact for finite x.
42  */
43 
44 #include "fdlibm.h"
45 
46 #ifdef __STDC__
47 static const double one = 1.0, shuge = 1.0e307;
48 #else
49 static double one = 1.0, shuge = 1.0e307;
50 #endif
51 
52 #ifdef __STDC__
__ieee754_sinh(double x)53         double __ieee754_sinh(double x)
54 #else
55         double __ieee754_sinh(x)
56         double x;
57 #endif
58 {
59         double t,w,h;
60         int ix,jx;
61         unsigned lx;
62 
63     /* High word of |x|. */
64         jx = __HI(x);
65         ix = jx&0x7fffffff;
66 
67     /* x is INF or NaN */
68         if(ix>=0x7ff00000) return x+x;
69 
70         h = 0.5;
71         if (jx<0) h = -h;
72     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
73         if (ix < 0x40360000) {          /* |x|<22 */
74             if (ix<0x3e300000)          /* |x|<2**-28 */
75                 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
76             t = expm1(fabs(x));
77             if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
78             return h*(t+t/(t+one));
79         }
80 
81     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
82         if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
83 
84     /* |x| in [log(maxdouble), overflowthresold] */
85         lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
86         if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
87             w = __ieee754_exp(0.5*fabs(x));
88             t = h*w;
89             return t*w;
90         }
91 
92     /* |x| > overflowthresold, sinh(x) overflow */
93         return x*shuge;
94 }
95