private static T GetSimplifiedRational <T>(IValueHelper <T> valueHelper, T n, T d, out T denominator)
where T : struct, IComparable, IFormattable, IConvertible, IComparable <T>, IEquatable <T>
{
if (d.Equals(valueHelper.Zero))
{
throw new DivideByZeroException();
}
if (n.Equals(valueHelper.Zero))
{
denominator = valueHelper.PositiveOne;
return(valueHelper.Zero);
}
if (n.Equals(d))
{
denominator = valueHelper.PositiveOne;
return(valueHelper.PositiveOne);
}
if (d.CompareTo(valueHelper.Zero) < 0)
{
d = valueHelper.Multiply(d, valueHelper.NegativeOne);
n = valueHelper.Multiply(n, valueHelper.NegativeOne);
}
T gcd = GetGCD <T>(valueHelper, n, d);
denominator = valueHelper.Divide(d, gcd);
return(valueHelper.Divide(n, gcd));
}
private static T GetNormalizedRational <T>(IValueHelper <T> valueHelper, T w, T n, T d, out T numerator, out T denominator)
where T : struct, IComparable, IFormattable, IConvertible, IComparable <T>, IEquatable <T>
{
n = GetSimplifiedRational <T>(valueHelper, n, d, out denominator);
if (n.Equals(valueHelper.Zero))
{
numerator = n;
return(w);
}
if (denominator.Equals(valueHelper.PositiveOne))
{
numerator = valueHelper.Zero;
return(valueHelper.Add(w, n));
}
if (n.CompareTo(denominator) > 0)
{
numerator = valueHelper.Modulus(n, denominator);
if (w.CompareTo(valueHelper.Zero) < 0)
{
w = valueHelper.Subtract(w, valueHelper.Divide(valueHelper.Subtract(n, numerator), denominator));
}
else
{
w = valueHelper.Add(w, valueHelper.Divide(valueHelper.Subtract(n, numerator), denominator));
}
numerator = GetSimplifiedRational <T>(valueHelper, numerator, denominator, out denominator);
}
else
{
numerator = n;
}
if (w.Equals(valueHelper.Zero))
{
return(w);
}
if (numerator.CompareTo(valueHelper.Zero) < 0)
{
if (w.CompareTo(valueHelper.Zero) < 0)
{
w = valueHelper.Add(w, valueHelper.PositiveOne);
}
else
{
w = valueHelper.Subtract(w, valueHelper.PositiveOne);
}
numerator = valueHelper.Add(numerator, denominator);
}
return(w);
}
private static T GetLCM <T>(IValueHelper <T> valueHelper, T d1, T d2, out T secondMultiplier)
where T : struct, IComparable, IFormattable, IConvertible, IComparable <T>, IEquatable <T>
{
T zero = default(T);
if (d1.CompareTo(zero) < 0)
{
return(GetLCM <T>(valueHelper, valueHelper.Abs(d1), d2, out secondMultiplier));
}
if (d2.CompareTo(zero) < 0)
{
return(GetLCM <T>(valueHelper, d1, valueHelper.Abs(d2), out secondMultiplier));
}
if (d1.Equals(d2))
{
secondMultiplier = valueHelper.PositiveOne;
return(secondMultiplier);
}
if (d1.CompareTo(d2) < 0)
{
secondMultiplier = GetLCM <T>(valueHelper, d2, d1, out d1);
return(d1);
}
secondMultiplier = d1;
while (!valueHelper.Modulus(secondMultiplier, d2).Equals(zero))
{
secondMultiplier = valueHelper.Add(secondMultiplier, d1);
}
return(GetSimplifiedRational <T>(valueHelper, valueHelper.Divide(secondMultiplier, d1), secondMultiplier, out secondMultiplier));
}