# e_cosh.c   [plain text]

```/* @(#)e_cosh.c 5.1 93/09/24 */
/*
* ====================================================
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

#include <sys/cdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("\$NetBSD: e_cosh.c,v 1.10 1999/07/02 15:37:38 simonb Exp \$");
#endif

/* __ieee754_cosh(x)
* Method :
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
*	1. Replace x by |x| (cosh(x) = cosh(-x)).
*	2.
*		                                        [ exp(x) - 1 ]^2
*	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
*			       			           2*exp(x)
*
*		                                  exp(x) +  1/exp(x)
*	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
*			       			          2
*	    22       <= x <= lnovft :  cosh(x) := exp(x)/2
*	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
*	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
*
* Special cases:
*	cosh(x) is |x| if x is +INF, -INF, or NaN.
*	only cosh(0)=1 is exact for finite x.
*/

#include "math.h"
#include "math_private.h"

static const double one = 1.0, half=0.5, huge = 1.0e300;

#define __ieee754_exp exp

double cosh(double x)
{
double t,w;
int32_t ix;
u_int32_t lx;

/* High word of |x|. */
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;

/* x is INF or NaN */
if(ix>=0x7ff00000) return x*x;

/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e43) {
t = expm1(fabs(x));
w = one+t;
if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}

/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ix < 0x40360000) {
t = __ieee754_exp(fabs(x));
return half*t+half/t;
}

/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));

/* |x| in [log(maxdouble), overflowthresold] */
GET_LOW_WORD(lx,x);
if (ix<0x408633CE ||
((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
w = __ieee754_exp(half*fabs(x));
t = half*w;
return t*w;
}

/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
```