public static BigInt Gcd(BigInt x, BigInt y) {
cnt++;
if( y == 0 ) return x;
if( y == 1 ) return y;
return Gcd( y, (BigInt)(x % y) );
}
public BigRational(String num, int nBase)
{
// the algo to convert from a float into a rational isn't that complicated:
// 1. Get the non-integer part of the number
// 2. Assuming it's base 10, then:
// 2.1 ...the numerator is the non-integer part converted to an integer, and the
// 2.2 ...the denominator is an integer equal to 10^(length of non-integer part)
// 2.3 ...then just normalise it
// 3. Then you need to add the integer part back
// HACK: String processing to get numbers: baaaaad
int radixIdx = num.IndexOf('.');
if( radixIdx == -1 ) {
_num = new BigInt( num );
_den = new BigInt(1);
return;
}
String intPart = num.Substring(0, radixIdx);
String fltPart = num.Substring( radixIdx );
BigInt tempNumerator = new BigInt( fltPart );
BigInt tempDenominator = new BigInt( (int)Math.Pow( nBase, fltPart.Length ) );
Normalise( tempNumerator, tempDenominator, out tempNumerator, out tempDenominator );
// then add back the integer part
BigRational intPortion = new BigRational( intPart );
BigRational fltPortion = new BigRational( tempNumerator, tempDenominator );
BigRational result = (BigRational)(intPortion + fltPortion);
this._num = result._num;
this._den = result._den;
}
public static BigInt Factorial(BigInt num) {
// HACK: Is there a more efficient implementation?
// I know there is a way to cache and use earlier results, but not much more
// also, note this function fails if num is non-integer. This should be the Gamma function instead
BigInt one = (BigInt)BigIntFactory.Instance.Unity;
if(num.IsZero) return one;
if(num < num.Factory.Zero) throw new ArgumentException("Argument must be greater than or equal to zero", "num");
return (BigInt)( num * Factorial( (BigInt)(num - one) ) );
}
private BigInt(BigInt copyThis)
{
_v = new IntX( copyThis._v );
_v.Normalize();
}
private BigRational(BigInt num, BigInt den)
{
_num = num;
_den = den;
}
private static void Normalise(BigInt oldNum, BigInt oldDen, out BigInt newNum, out BigInt newDen)
{
// TODO: Maybe also ensure that the denominator is positive, only the numerator can be negative
// find the GCD of oldNum and oldDen, then apply it to find and return newNum and newDen
BigInt gcd = (BigInt)BigMath.Gcd( oldNum, oldDen );
newNum = (BigInt)(oldNum / gcd);
newDen = (BigInt)(oldDen / gcd);
}
public BigRational(BigInt num)
{
// an integer is represented by a fraction integer/1
_num = num;
_den = new BigInt(1);
}