/** Calcaulte the simplest rational between two reals. */
public static RealNum rationalize(RealNum x, RealNum y)
{
// This algorithm is by Alan Bawden. It has been transcribed
// with permission from C-Gambit, copyright Marc Feeley.
if (x.grt(y))
{
return(simplest_rational2(y, x));
}
else if (!(y.grt(x)))
{
return(x);
}
else if (x.sign() > 0)
{
return(simplest_rational2(x, y));
}
else if (y.isNegative())
{
return((RealNum)(simplest_rational2((RealNum)y.neg(),
(RealNum)x.neg())).neg());
}
else
{
return(IntNum.zero());
}
}
/** Calcaulte the simplest rational between two reals. */
public static RealNum rationalize(RealNum x, RealNum y)
{
// This algorithm is by Alan Bawden. It has been transcribed
// with permission from C-Gambit, copyright Marc Feeley.
if (x.grt (y))
return simplest_rational2 (y, x);
else if (! (y.grt(x)))
return x;
else if (x.sign() > 0)
return simplest_rational2 (x, y);
else if (y.isNegative ())
return (RealNum) (simplest_rational2 ((RealNum)y.neg(),
(RealNum)x.neg())).neg();
else
return IntNum.zero ();
}
private static RealNum simplest_rational2(RealNum x, RealNum y)
{
RealNum fx = x.toInt(FLOOR);
RealNum fy = y.toInt(FLOOR);
if (!x.grt(fx))
{
return(fx);
}
else if (fx.Equals(fy))
{
RealNum n = (RealNum)IntNum.one().div(y.sub(fy));
RealNum d = (RealNum)IntNum.one().div(x.sub(fx));
return((RealNum)fx.add(IntNum.one().div(simplest_rational2(n, d)),
1));
}
else
{
return((RealNum)fx.add(IntNum.one(), 1));
}
}
private static RealNum simplest_rational2(RealNum x, RealNum y)
{
RealNum fx = x.toInt (FLOOR);
RealNum fy = y.toInt (FLOOR);
if (! x.grt(fx))
return fx;
else if (fx.Equals(fy))
{
RealNum n = (RealNum) IntNum.one().div(y.sub(fy));
RealNum d = (RealNum) IntNum.one().div(x.sub(fx));
return (RealNum) fx.add(IntNum.one().div(simplest_rational2 (n, d)),
1);
}
else
return (RealNum) fx.add(IntNum.one(), 1);
}
