xref: /freebsd/lib/msun/src/e_sinh.c (revision 1e413cf93298b5b97441a21d9a50fdcd0ee9945e)
1 
2 /* @(#)e_sinh.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  */
13 
14 #ifndef lint
15 static char rcsid[] = "$FreeBSD$";
16 #endif
17 
18 /* __ieee754_sinh(x)
19  * Method :
20  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
21  *	1. Replace x by |x| (sinh(-x) = -sinh(x)).
22  *	2.
23  *		                                    E + E/(E+1)
24  *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
25  *			       			        2
26  *
27  *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2
28  *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
29  *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
30  *
31  * Special cases:
32  *	sinh(x) is |x| if x is +INF, -INF, or NaN.
33  *	only sinh(0)=0 is exact for finite x.
34  */
35 
36 #include "math.h"
37 #include "math_private.h"
38 
39 static const double one = 1.0, shuge = 1.0e307;
40 
41 double
42 __ieee754_sinh(double x)
43 {
44 	double t,w,h;
45 	int32_t ix,jx;
46 	u_int32_t lx;
47 
48     /* High word of |x|. */
49 	GET_HIGH_WORD(jx,x);
50 	ix = jx&0x7fffffff;
51 
52     /* x is INF or NaN */
53 	if(ix>=0x7ff00000) return x+x;
54 
55 	h = 0.5;
56 	if (jx<0) h = -h;
57     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
58 	if (ix < 0x40360000) {		/* |x|<22 */
59 	    if (ix<0x3e300000) 		/* |x|<2**-28 */
60 		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
61 	    t = expm1(fabs(x));
62 	    if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
63 	    return h*(t+t/(t+one));
64 	}
65 
66     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
67 	if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
68 
69     /* |x| in [log(maxdouble), overflowthresold] */
70 	GET_LOW_WORD(lx,x);
71 	if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
72 	    w = __ieee754_exp(0.5*fabs(x));
73 	    t = h*w;
74 	    return t*w;
75 	}
76 
77     /* |x| > overflowthresold, sinh(x) overflow */
78 	return x*shuge;
79 }
80