1 /* @(#)e_cosh.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
12 * $FreeBSD: src/lib/msun/src/e_cosh.c,v 1.6 1999/08/28 00:06:29 peter Exp $
13 * $DragonFly: src/lib/msun/src/Attic/e_cosh.c,v 1.2 2003/06/17 04:26:52 dillon Exp $
18 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
19 * 1. Replace x by |x| (cosh(x) = cosh(-x)).
22 * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
26 * ln2/2 <= x <= 22 : cosh(x) := -------------------
28 * 22 <= x <= lnovft : cosh(x) := exp(x)/2
29 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
30 * ln2ovft < x : cosh(x) := huge*huge (overflow)
33 * cosh(x) is |x| if x is +INF, -INF, or NaN.
34 * only cosh(0)=1 is exact for finite x.
38 #include "math_private.h"
41 static const double one = 1.0, half=0.5, huge = 1.0e300;
43 static double one = 1.0, half=0.5, huge = 1.0e300;
47 double __ieee754_cosh(double x)
49 double __ieee754_cosh(x)
57 /* High word of |x|. */
62 if(ix>=0x7ff00000) return x*x;
64 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
68 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
69 return one+(t*t)/(w+w);
72 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
73 if (ix < 0x40360000) {
74 t = __ieee754_exp(fabs(x));
78 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
79 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
81 /* |x| in [log(maxdouble), overflowthresold] */
84 ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
85 w = __ieee754_exp(half*fabs(x));
90 /* |x| > overflowthresold, cosh(x) overflow */