/// <summary>
/// Performs a smaller-to-bigger summation of sequence members.
/// Works slightly slower than a simple sequential summation,
/// but as smallest values are summed up first, this method
/// significantly increases precision if the sequence doesn't non-decrease
/// monotonously and consequent values are of different degrees.
///
/// Requires a general term formula dependent on both argument and integer index (<paramref name="memberFormula"/>) as well as the current function argument.
/// Also requires a comparer allowing of knowing which sequence element is bigger and which is smaller.
/// </summary>
/// <param name="startIndex">The inclusive beginning index of sequence summation.</param>
/// <param name="endIndex">The inclusive ending index of sequence summation.</param>
/// <param name="comparer">The comparer to compare values of type <typeparamref name="T"/>. Should return a positive value if the first value is bigger than the second, zero value if they are equal, and a negative value if the first object is less.</param>
/// <param name="memberFormula">The general term formula dependent on both argument and integer index.</param>
/// <param name="argument">The current argument for the sequence.</param>
/// <returns>The result of sequential summation of the sequence starting with index <paramref name="startIndex"/> and ending with index <paramref name="endIndex"/>, both inclusive.</returns>
public T Sum_SmallerToBigger(T argument, Func <T, int, T> memberFormula, int startIndex, int endIndex, IComparer <T> comparer)
{
IPriorityQueue <T> sequence = new BinaryHeap <T>(comparer.GetReverseComparer());
if (startIndex >= endIndex)
{
for (int i = startIndex; i <= endIndex; i++)
{
sequence.Insert(memberFormula(argument, i));
}
}
else
{
for (int i = endIndex; i >= startIndex; i--)
{
sequence.Insert(memberFormula(argument, i));
}
}
T sum = this.Zero;
while (!sequence.IsEmpty)
{
sum = this.OperatorPlus(sum, sequence.Pop());
}
return(sum);
}