High Quality Content by WIKIPEDIA articles! The prefix sum (also known as the scan, prefix reduction, or partial sum) is an operation on lists in which each element in the result list is obtained from the sum of the elements in the operand list up to its index. There are two types of prefix sum, inclusive prefix sum and exclusive prefix sum: in the inclusive prefix sum, all the operand elements are used; whereas in the exclusive prefix sum, the first element in the result list is the identity element (0 for add operation) and the last element of the operand list is not used. Prefix scans are used extensively in data-parallel programming. Some of the diverse uses of prefix scan include sorting, parsing, combinator reduction, and region labeling. A technique used by many data-parallel algorithms is to apply an exclusive prefix sum to an array of 0s and 1s.

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