Abstract: An initial input list in a series of sequential dependent input lists is clocked through a first sort stack and written into a first buffer as Q groups of P numbers each. The P numbers are in numerical order within each group with the smallest number in the first location of each group. The first number in each group is loaded into a second sort stack which arranges them in numerical order, causing the smallest number in the input list to form the first number in the initial output list. A replacement number is numerically sorted into the second stack from the Q groups each time the smallest remaining number is clocked out. Each replacement number is from the next location of the same Q group as the most recently clocked out number. Thus, the smallest remaining number in any of the Q groups of the first buffer is always available to the second stack and appears as the smallest remaining number in the second stack is always in the first location of the second stack.

Abstract: An input list of N numbers is clocked through a first sort stack which provides S2 groups of S1 numbers each arranged in ascending numerical order. The numbers are stored in a buffer where the first location within each group always contains the smallest number in that group. These S2 first numbers are loaded into a second sort stack which arranges them in ascending numerical order. The first location in the second stack contains the smallest number in the entire list of N numbers. This smallest number is clocked out of the second stack to form the first number in the output list. A replacement number is numerically sorted into the second stack from the S2 groups each time the smallest remaining number is clocked out. This replacement number is the next smallest number from the same group as the most recently clocked out number. Each time the smallest remaining number is clocked out, the remaining numbers in the second stack are rearranged to accommodate the replacement number for maintaining numerical order.