1 /* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */
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 * ====================================================
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.
35 #include <math_private.h>
37 static const double one
= 1.0, half
=0.5, huge
= 1.0e300
;
40 __ieee754_cosh (double x
)
46 /* High word of |x|. */
51 if (ix
< 0x40360000) {
52 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
56 if (ix
<0x3c800000) return w
; /* cosh(tiny) = 1 */
57 return one
+(t
*t
)/(w
+w
);
60 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
61 t
= __ieee754_exp(fabs(x
));
65 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
66 if (ix
< 0x40862e42) return half
*__ieee754_exp(fabs(x
));
68 /* |x| in [log(maxdouble), overflowthresold] */
70 if (ix
<0x408633ce || ((ix
==0x408633ce)&&(lx
<=(u_int32_t
)0x8fb9f87d))) {
71 w
= __ieee754_exp(half
*fabs(x
));
77 if(ix
>=0x7ff00000) return x
*x
;
79 /* |x| > overflowthresold, cosh(x) overflow */
82 strong_alias (__ieee754_cosh
, __cosh_finite
)