/** 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());
}
}
/** Converts an integral double (such as a toInt result) to an IntNum. */
public static IntNum toExactInt(double value)
{
if (Double.IsInfinity(value) || Double.IsNaN(value))
{
throw new ArithmeticException("cannot convert " + value + " to exact integer");
}
long bits = BitConverter.DoubleToInt64Bits(value);
bool neg = bits < 0;
int exp = (int)(bits >> 52) & 0x7FF;
bits &= 0xfffffffffffffL;
if (exp == 0)
{
bits <<= 1;
}
else
{
bits |= 0x10000000000000L;
}
if (exp <= 1075)
{
int rshift = 1075 - exp;
if (rshift > 53)
{
return(IntNum.zero());
}
bits >>= rshift;
return(IntNum.make(neg ? -bits : bits));
}
return(IntNum.shift(IntNum.make(neg ? -bits : bits), exp - 1075));
}
/** Do one the the 16 possible bit-wise operations of two IntNums. */
public static IntNum bitOp(int op, IntNum x, IntNum y)
{
switch (op)
{
case 0: return(IntNum.zero());
case 1: return(and(x, y));
case 3: return(x);
case 5: return(y);
case 15: return(IntNum.minusOne());
}
IntNum result = new IntNum();
setBitOp(result, op, x, y);
return(result.canonicalize());
}
/** Return the logical (bit-wise) negation of an IntNum. */
public static IntNum not(IntNum x)
{
return(bitOp(12, x, IntNum.zero()));
}
/** Return exact "rational" infinity.
* @param sign either 1 or -1 for positive or negative infinity */
public static RatNum infinity(int sign)
{
return(new IntFraction(IntNum.make(sign), IntNum.zero()));
}
public override RealNum im()
{
return(IntNum.zero());
}