|
/* @(#)e_sinh.c 1.3 95/01/18 */
|
/*
|
* ====================================================
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
*
|
* 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.
|
* ====================================================
|
*/
|
|
/* __ieee754_sinh(x)
|
* Method :
|
* mathematically ieee_sinh(x) if defined to be (ieee_exp(x)-ieee_exp(-x))/2
|
* 1. Replace x by |x| (ieee_sinh(-x) = -ieee_sinh(x)).
|
* 2.
|
* E + E/(E+1)
|
* 0 <= x <= 22 : ieee_sinh(x) := --------------, E=ieee_expm1(x)
|
* 2
|
*
|
* 22 <= x <= lnovft : ieee_sinh(x) := ieee_exp(x)/2
|
* lnovft <= x <= ln2ovft: ieee_sinh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2)
|
* ln2ovft < x : ieee_sinh(x) := x*shuge (overflow)
|
*
|
* Special cases:
|
* sinh(x) is |x| if x is +INF, -INF, or NaN.
|
* only ieee_sinh(0)=0 is exact for finite x.
|
*/
|
|
#include "fdlibm.h"
|
|
#ifdef __STDC__
|
static const double one = 1.0, shuge = 1.0e307;
|
#else
|
static double one = 1.0, shuge = 1.0e307;
|
#endif
|
|
#ifdef __STDC__
|
double __ieee754_sinh(double x)
|
#else
|
double __ieee754_sinh(x)
|
double x;
|
#endif
|
{
|
double t,w,h;
|
int ix,jx;
|
unsigned lx;
|
|
/* High word of |x|. */
|
jx = __HI(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;/* ieee_sinh(tiny) = tiny with inexact */
|
t = ieee_expm1(ieee_fabs(x));
|
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
|
return h*(t+t/(t+one));
|
}
|
|
/* |x| in [22, ieee_log(maxdouble)] return 0.5*ieee_exp(|x|) */
|
if (ix < 0x40862E42) return h*__ieee754_exp(ieee_fabs(x));
|
|
/* |x| in [log(maxdouble), overflowthresold] */
|
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
|
if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
|
w = __ieee754_exp(0.5*ieee_fabs(x));
|
t = h*w;
|
return t*w;
|
}
|
|
/* |x| > overflowthresold, ieee_sinh(x) overflow */
|
return x*shuge;
|
}
|
