/// <summary>
/// Returns the composition of two linear congruential functions:
/// g(f(x)). Assumes m is the same.
/// </summary>
/// <param name="f"></param>
/// <param name="g"></param>
/// <returns></returns>
public static LCG Compose(LCG f, LCG g)
{
if (f.M != g.M)
{
throw new ArgumentException("m is not the same");
}
// g(f(x)) = g(ax + b) = c(ax + b) + d = (ca)x + (cb + d) (mod m)
return(new LCG(f.A * g.A, (f.B * g.A) + g.B, f.M));
}
public LCG GetInverse()
{
// f(x) = A*x + b (mod m)
// f^(-1)(x) =
var isInvertible = ModHelper.TryGetModInverse(A, M, out BigInteger aInverse);
if (!isInvertible)
{
throw new Exception($"{A} is not invertible mod {M}");
}
var result = new LCG(aInverse, -1 * B * aInverse, M);
return(result);
}
public override bool Equals(Object obj)
{
//Check for null and compare run-time types.
if ((obj == null) || !this.GetType().Equals(obj.GetType()))
{
return(false);
}
else
{
LCG other = (LCG)obj;
return((A == other.A) &&
(B == other.B) &&
(M == other.M));
}
}