We prove that prefix sums of n integers of at most b bits can be found on a COMMON CRCW PRAM in [Formula: see text] time with a linear time-processor product. The algorithm is optimally fast, for any polynomial number of processors. In particular, if [Formula: see text] the time taken is [Formula: see text]. This is a generalisation of previous result. The previous [Formula: see text] time algorithm was valid only for O(log n)-bit numbers. Application of this algorithm to r-way parallel merge sort algorithm is also considered. We also consider a more realistic PRAM variant, in which the word size, m, may be smaller than b (m≥log n). On this model, prefix sums can be found in [Formula: see text] optimal time.
A sound and complete abstraction for reasoning about parallel prefix sums
