1/* @(#)e_cosh.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#if defined(LIBM_SCCS) && !defined(lint)
14static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $";
15#endif
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 "math.h"
39#include "math_private.h"
40
41#ifdef __STDC__
42static const double one = 1.0, half=0.5, huge = 1.0e300;
43#else
44static double one = 1.0, half=0.5, huge = 1.0e300;
45#endif
46
47#ifdef __STDC__
48	double __ieee754_cosh(double x)
49#else
50	double __ieee754_cosh(x)
51	double x;
52#endif
53{
54	double t,w;
55	int32_t ix;
56	u_int32_t lx;
57
58    /* High word of |x|. */
59	GET_HIGH_WORD(ix,x);
60	ix &= 0x7fffffff;
61
62    /* x is INF or NaN */
63	if(ix>=0x7ff00000) return x*x;
64
65    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
66	if(ix<0x3fd62e43) {
67	    t = __expm1(fabs(x));
68	    w = one+t;
69	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
70	    return one+(t*t)/(w+w);
71	}
72
73    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
74	if (ix < 0x40360000) {
75		t = __ieee754_exp(fabs(x));
76		return half*t+half/t;
77	}
78
79    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
80	if (ix < 0x40862e42)  return half*__ieee754_exp(fabs(x));
81
82    /* |x| in [log(maxdouble), overflowthresold] */
83	GET_LOW_WORD(lx,x);
84	if (ix<0x408633ce || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
85	    w = __ieee754_exp(half*fabs(x));
86	    t = half*w;
87	    return t*w;
88	}
89
90    /* |x| > overflowthresold, cosh(x) overflow */
91	return huge*huge;
92}
93