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One way to implement a parallel prefix sum algorithm is to split the array into small blocks, independently calculate local prefix sums on them, and then do a second pass where we adjust the computed values in each block by adding the sum of all previous elements to them.
Parallel Prefix. 3.1 Parallel Prefix. An important primitive for (data) parallel computing is the scan operation, also called prefix sum which takes an associated binary operator and an ordered set [a1,,an] of n elements and returns the ordered set [a1,(a1 a2),,(a1 a2 an)].
Parallel prefix scan is a fundamental parallel computing primitive. Given a list of input elements and a binary reduction operator, a prefix scan produces a corresponding output list where each output is computed to be the reduction of the elements occurring earlier in the input.
An important primitive for (data) parallel computing is the scan operation, also called prefix sum which takes an associated binary operator and an ordered set [a1,,an] of n elements and returns the ordered set [a1,(a1 a2),,(a1 a2 an)].
Parallel scan is one of primary algorithms of parallel programming. It is meant for processing (scanning) an array in parallel to have a relative output per element or a single output as a result, without re-computing temporary parts for each next element.
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Among them, prefix adders are based on parallel prefix circuit theory which provides a solid theoretical basis for wide range of design trade-offs between delay, area and wiring complexity. This dissertation first presents an algorithm for prefix computation under the condition of non-uniform input signal arrival.
A prefix computation is a special case of a first-order recurrence in that i = i1 i. We now develop the relationship in the other direction and indicate how the first-order recurrence for the carry in Equation (5.1) can be expressed as a prefix computation. Let x1, y1, x2, and y2 be four binary signals.

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