/// <summary>
/// Performs modulus inversion on an Integer.
/// </summary>
/// <param name="value">The Integer to inverse.</param>
/// <param name="modulus">The Integer by which to divide.</param>
/// <returns>The result of inversing the Integer; if any.</returns>
public static Integer ModInv(this Integer value, Integer modulus)
{
if (modulus < 1)
{
throw new ArgumentOutOfRangeException(nameof(modulus));
}
if (Abs(value) >= modulus)
{
value = value % modulus;
}
if (value < 0)
{
value = value + modulus;
var result = Lehmer.Inv(modulus, value);
if (result != 0)
{
result = result - modulus;
}
return(result);
}
return(Lehmer.Inv(modulus, value));
}
/// <summary>
/// Finds the greatest common divisor of two Integers.
/// </summary>
/// <param name="left">The first value.</param>
/// <param name="right">The second value.</param>
/// <returns>The greatest common divisor of left and right.</returns>
public static Integer Gcd(this Integer left, Integer right)
{
var a = Abs(left);
var b = Abs(right);
if (a < b)
{
return(Lehmer.Gcd(b, a));
}
return(Lehmer.Gcd(a, b));
}