These choices lead to all the standard variations of DSTs and also discrete cosine transforms (DCTs). Each boundary can be either even or odd (2 choices per boundary) and can be symmetric about a data point or the point halfway between two data points (2 choices per boundary), for a total of formula_5 possibilities. Half of these possibilities, those where the "left" boundary is odd, correspond to the 8 types of DST; the other half are the 8 types of DCT.