Prefix sum

Common card · No. 331808

In computer science, the prefix sum, cumulative sum, inclusive scan, or simply scan of a sequence of numbers x0, x1, x2, ... is a second sequence of numbers y0, y1, y2, ..., the sums of prefixes (running totals) of the input sequence: y0 = x0 y1 = x0 + x1 y2 = x0 + x1+ x2 ... For instance, the prefix sums of the natural numbers are the triangular numbers: Prefix sums are trivial to compute in sequential models of computation, by using the formula yi = yi − 1 + xi to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, and they form the basis of the scan higher-order function in functional programming languages. Prefix sums have also been much studied in parallel algorithms, both as a test problem to be solved and as a useful primitive to be used as a subroutine in other parallel algorithms. Abstractly, a prefix sum requires only a binary associative operator ⊕, making it...

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