3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
15 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
16 * 1. Replace x by |x| (cosh(x) = cosh(-x)).
19 * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
23 * ln2/2 <= x <= 22 : cosh(x) := -------------------
25 * 22 <= x <= lnovft : cosh(x) := exp(x)/2
26 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
27 * ln2ovft < x : cosh(x) := huge*huge (overflow)
30 * cosh(x) is |x| if x is +INF, -INF, or NaN.
31 * only cosh(0)=1 is exact for finite x.
37 #include "math_private.h"
39 static const double one = 1.0, half=0.5, huge = 1.0e300;
47 /* High word of |x|. */
52 if(ix>=0x7ff00000) return x*x;
54 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
58 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
59 return one+(t*t)/(w+w);
62 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
63 if (ix < 0x40360000) {
68 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
69 if (ix < 0x40862E42) return half*exp(fabs(x));
71 /* |x| in [log(maxdouble), overflowthresold] */
73 return __ldexp_exp(fabs(x), -1);
75 /* |x| > overflowthresold, cosh(x) overflow */
79 #if (LDBL_MANT_DIG == 53)
80 __weak_reference(cosh, coshl);