public EccPoint Add(EccPoint pointA, EccPoint pointB)
{
// Any point added to infinity is itself
if (pointA.Infinity)
{
return(pointB);
}
// Any point added to infinity is itself
if (pointB.Infinity)
{
return(pointA);
}
// Any point added to its inverse is infinity
if (pointA.Equals(Negate(pointB)))
{
return(new EccPoint("infinity"));
}
// Cannot add two identical points, use Double instead
if (pointA.Equals(pointB))
{
return(Double(pointA));
}
var numerator = _operator.Subtract(pointB.Y, pointA.Y);
var denominator = _operator.Subtract(pointB.X, pointA.X);
var lambda = _operator.Divide(numerator, denominator);
var x = _operator.Subtract(_operator.Subtract(_operator.Multiply(lambda, lambda), pointA.X), pointB.X);
var y = _operator.Subtract(_operator.Multiply(_operator.Subtract(pointA.X, x), lambda), pointA.Y);
return(new EccPoint(x, y));
}
public EdPoint Add(EdPoint pointA, EdPoint pointB)
{
var numeratorX = _operator.Add(_operator.Multiply(pointA.X, pointB.Y), _operator.Multiply(pointA.Y, pointB.X));
var numeratorY = _operator.Subtract(_operator.Multiply(pointA.Y, pointB.Y), _operator.Multiply(CoefficientA, _operator.Multiply(pointA.X, pointB.X)));
var denominatorMult = _operator.Multiply(CoefficientD, _operator.Multiply(_operator.Multiply(pointA.X, pointB.X), _operator.Multiply(pointA.Y, pointB.Y)));
var denominatorX = _operator.Add(1, denominatorMult);
var denominatorY = _operator.Subtract(1, denominatorMult);
var x = _operator.Divide(numeratorX, denominatorX);
var y = _operator.Divide(numeratorY, denominatorY);
return(new EdPoint(x, y));
}