/// <summary>
/// Runs the EEA on two BigIntegers
/// </summary>
/// <param name="A">Quotient A</param>
/// <param name="B">Quotient B</param>
/// <returns>Return a BigIntEuclidean object that contains the result in the variables X, Y, and GCD</returns>
///
/// <remarks>
/// Implemented from pseudocode on <a href="http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm"/>Wikipedia
/// </remarks>
public static BigIntEuclidean Calculate(BigInteger A, BigInteger B)
{
BigInteger x = BigInteger.Zero;
BigInteger lastX = BigInteger.One;
BigInteger y = BigInteger.One;
BigInteger lastY = BigInteger.Zero;
while (!B.Equals(BigInteger.Zero))
{
BigInteger[] quotientAndRemainder = A.DivideAndRemainder(B);
BigInteger quotient = quotientAndRemainder[0];
BigInteger temp = A;
A = B;
B = quotientAndRemainder[1];
temp = x;
x = lastX.Subtract(quotient.Multiply(x));
lastX = temp;
temp = y;
y = lastY.Subtract(quotient.Multiply(y));
lastY = temp;
}
BigIntEuclidean result = new BigIntEuclidean();
result.X = lastX;
result.Y = lastY;
result.GCD = A;
return result;
}
/// <summary>
/// Runs the EEA on two BigIntegers
/// </summary>
/// <param name="A">Quotient A</param>
/// <param name="B">Quotient B</param>
/// <returns>Return a BigIntEuclidean object that contains the result in the variables X, Y, and GCD</returns>
///
/// <remarks>
/// Implemented from pseudocode on <a href="http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm"/>Wikipedia
/// </remarks>
public static BigIntEuclidean Calculate(BigInteger A, BigInteger B)
{
BigInteger x = BigInteger.Zero;
BigInteger lastX = BigInteger.One;
BigInteger y = BigInteger.One;
BigInteger lastY = BigInteger.Zero;
while (!B.Equals(BigInteger.Zero))
{
BigInteger[] quotientAndRemainder = A.DivideAndRemainder(B);
BigInteger quotient = quotientAndRemainder[0];
BigInteger temp = A;
A = B;
B = quotientAndRemainder[1];
temp = x;
x = lastX.Subtract(quotient.Multiply(x));
lastX = temp;
temp = y;
y = lastY.Subtract(quotient.Multiply(y));
lastY = temp;
}
BigIntEuclidean result = new BigIntEuclidean();
result.X = lastX;
result.Y = lastY;
result.GCD = A;
return(result);
}