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A moving sum calculation creates a vector B, such that bk is the sum of the elements ak-d through ak+d of an input vector A. It is shown that this procedure can be completely vectorized, resulting in substantial increases in execution speed. Timing comparisons for scalar and vector algorithms executed on both a 2-and a 4-pipe CYBER 205 are presented. Using 32-bit data on the 4-pipe version, the vector algorithm runs almost 10 times faster than the scalar does.