# sinh_freeBSD.c   [plain text]

```
/* @(#)e_sinh.c 1.3 95/01/18 */
/*
* ====================================================
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

#ifndef lint
static char rcsid[] = "\$FreeBSD: src/lib/msun/src/e_sinh.c,v 1.9 2005/02/04 18:26:06 das Exp \$";
#endif

/* sinh(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
*	1. Replace x by |x| (sinh(-x) = -sinh(x)).
*	2.
*		                                    E + E/(E+1)
*	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
*			       			        2
*
*	    22       <= x <= lnovft :  sinh(x) := exp(x)/2
*	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
*	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
*
* Special cases:
*	sinh(x) is |x| if x is +INF, -INF, or NaN.
*	only sinh(0)=0 is exact for finite x.
*/

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

static const double one = 1.0, shuge = 1.0e307;

double
sinh(double x)
{
double t,w,h;
int32_t ix,jx;
u_int32_t lx;

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

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

h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x40360000) {		/* |x|<22 */
if (ix<0x3e300000) 		/* |x|<2**-28 */
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
t = expm1(fabs(x));
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
return h*(t+t/(t+one));
}

/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862E42)  return h*exp(fabs(x));

/* |x| in [log(maxdouble), overflowthresold] */
GET_LOW_WORD(lx,x);
if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
w = exp(0.5*fabs(x));
t = h*w;
return t*w;
}

/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
```