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/* __ieee754_cosh(x)
15 * Method :
16 * mathematically ieee_cosh(x) if defined to be (ieee_exp(x)+ieee_exp(-x))/2
17 *	1. Replace x by |x| (ieee_cosh(x) = ieee_cosh(-x)).
18 *	2.
19 *		                                        [ ieee_exp(x) - 1 ]^2
20 *	    0        <= x <= ln2/2  :  ieee_cosh(x) := 1 + -------------------
21 *			       			           2*ieee_exp(x)
22 *
23 *		                                  ieee_exp(x) +  1/ieee_exp(x)
24 *	    ln2/2    <= x <= 22     :  ieee_cosh(x) := -------------------
25 *			       			          2
26 *	    22       <= x <= lnovft :  ieee_cosh(x) := ieee_exp(x)/2
27 *	    lnovft   <= x <= ln2ovft:  ieee_cosh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2)
28 *	    ln2ovft  <  x	    :  ieee_cosh(x) := huge*huge (overflow)
29 *
30 * Special cases:
31 *	cosh(x) is |x| if x is +INF, -INF, or NaN.
32 *	only ieee_cosh(0)=1 is exact for finite x.
33 */
34
35#include "fdlibm.h"
36
37#ifdef __STDC__
38static const double one = 1.0, half=0.5, huge = 1.0e300;
39#else
40static double one = 1.0, half=0.5, huge = 1.0e300;
41#endif
42
43#ifdef __STDC__
44	double __ieee754_cosh(double x)
45#else
46	double __ieee754_cosh(x)
47	double x;
48#endif
49{
50	double t,w;
51	int ix;
52	unsigned lx;
53
54    /* High word of |x|. */
55	ix = __HI(x);
56	ix &= 0x7fffffff;
57
58    /* x is INF or NaN */
59	if(ix>=0x7ff00000) return x*x;
60
61    /* |x| in [0,0.5*ln2], return 1+ieee_expm1(|x|)^2/(2*ieee_exp(|x|)) */
62	if(ix<0x3fd62e43) {
63	    t = ieee_expm1(ieee_fabs(x));
64	    w = one+t;
65	    if (ix<0x3c800000) return w;	/* ieee_cosh(tiny) = 1 */
66	    return one+(t*t)/(w+w);
67	}
68
69    /* |x| in [0.5*ln2,22], return (ieee_exp(|x|)+1/ieee_exp(|x|)/2; */
70	if (ix < 0x40360000) {
71		t = __ieee754_exp(ieee_fabs(x));
72		return half*t+half/t;
73	}
74
75    /* |x| in [22, ieee_log(maxdouble)] return half*ieee_exp(|x|) */
76	if (ix < 0x40862E42)  return half*__ieee754_exp(ieee_fabs(x));
77
78    /* |x| in [log(maxdouble), overflowthresold] */
79	lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
80	if (ix<0x408633CE ||
81	      (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
82	    w = __ieee754_exp(half*ieee_fabs(x));
83	    t = half*w;
84	    return t*w;
85	}
86
87    /* |x| > overflowthresold, ieee_cosh(x) overflow */
88	return huge*huge;
89}
90