private static BigInteger Inverse(BigInteger n)
{
n.CheckRange();
var inverse = GCD2(Crypto.FieldPrime, n).invB.Abs();
Contract.Assert((n * inverse) % Crypto.FieldPrime == 1);
return(inverse);
}
public static BigInteger RationalToWhole(BigInteger numerator, BigInteger denominator)
{
numerator.CheckRange(); denominator.CheckRange();
// Find the multiplicative inverse of the denominator over the field
var invD = Inverse(denominator);
return(numerator * invD % Crypto.FieldPrime);
}
private static BigInteger GCD(BigInteger a, BigInteger b)
{
a.CheckRange(); b.CheckRange();
if (b == 0)
{
return(a);
}
return(GCD(b, a % b));
}
public static (BigInteger numerator, BigInteger denominator) MultiplyRational(
BigInteger numeratorLhs, BigInteger denominatorLhs,
BigInteger numeratorRhs, BigInteger denominatorRhs)
{
denominatorRhs = denominatorRhs.Abs();
numeratorLhs.CheckRange(); denominatorLhs.CheckRange();
numeratorRhs.CheckRange(); denominatorRhs.CheckRange();
if (denominatorLhs == 0)
{
throw new ArgumentOutOfRangeException("LHS denominator is zero");
}
if (denominatorRhs == 0)
{
throw new ArgumentOutOfRangeException("RHS denominator is zero");
}
var numerator = (numeratorLhs * numeratorRhs) % Crypto.FieldPrime;
var denominator = (denominatorLhs * denominatorRhs) % Crypto.FieldPrime;
var gcd = GCD(numerator, denominator);
return(numerator / gcd, denominator / gcd);
}