2 /* @(#)e_cosh.c 1.3 95/01/18 */
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
11 * ====================================================
17 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
18 * 1. Replace x by |x| (cosh(x) = cosh(-x)).
21 * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
25 * ln2/2 <= x <= 22 : cosh(x) := -------------------
27 * 22 <= x <= lnovft : cosh(x) := exp(x)/2
28 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
29 * ln2ovft < x : cosh(x) := huge*huge (overflow)
32 * cosh(x) is |x| if x is +INF, -INF, or NaN.
33 * only cosh(0)=1 is exact for finite x.
39 #include "math_private.h"
41 static const double one = 1.0, half=0.5, huge = 1.0e300;
44 __ieee754_cosh(double x)
49 /* High word of |x|. */
54 if(ix>=0x7ff00000) return x*x;
56 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
60 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
61 return one+(t*t)/(w+w);
64 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
65 if (ix < 0x40360000) {
66 t = __ieee754_exp(fabs(x));
70 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
71 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
73 /* |x| in [log(maxdouble), overflowthresold] */
75 return __ldexp_exp(fabs(x), -1);
77 /* |x| > overflowthresold, cosh(x) overflow */
81 #if (LDBL_MANT_DIG == 53)
82 __weak_reference(cosh, coshl);