1 
2 /* @(#)e_cosh.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 #include <sys/cdefs.h>
15 __FBSDID("$FreeBSD$");
16 
17 /* __ieee754_cosh(x)
18  * Method :
19  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
20  *	1. Replace x by |x| (cosh(x) = cosh(-x)).
21  *	2.
22  *		                                        [ exp(x) - 1 ]^2
23  *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
24  *			       			           2*exp(x)
25  *
26  *		                                  exp(x) +  1/exp(x)
27  *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
28  *			       			          2
29  *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2
30  *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
31  *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
32  *
33  * Special cases:
34  *	cosh(x) is |x| if x is +INF, -INF, or NaN.
35  *	only cosh(0)=1 is exact for finite x.
36  */
37 
38 #include <float.h>
39 
40 #include "math.h"
41 #include "math_private.h"
42 
43 static const double one = 1.0, half=0.5, huge = 1.0e300;
44 
45 double
__ieee754_cosh(double x)46 __ieee754_cosh(double x)
47 {
48 	double t,w;
49 	int32_t ix;
50 
51     /* High word of |x|. */
52 	GET_HIGH_WORD(ix,x);
53 	ix &= 0x7fffffff;
54 
55     /* x is INF or NaN */
56 	if(ix>=0x7ff00000) return x*x;
57 
58     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
59 	if(ix<0x3fd62e43) {
60 	    t = expm1(fabs(x));
61 	    w = one+t;
62 	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
63 	    return one+(t*t)/(w+w);
64 	}
65 
66     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
67 	if (ix < 0x40360000) {
68 		t = __ieee754_exp(fabs(x));
69 		return half*t+half/t;
70 	}
71 
72     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
73 	if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
74 
75     /* |x| in [log(maxdouble), overflowthresold] */
76 	if (ix<=0x408633CE)
77 	    return __ldexp_exp(fabs(x), -1);
78 
79     /* |x| > overflowthresold, cosh(x) overflow */
80 	return huge*huge;
81 }
82 
83 #if (LDBL_MANT_DIG == 53)
84 __weak_reference(cosh, coshl);
85 #endif
86