lfold

lfold, short for locality-aware fold, is a conceptual operation in computer science and functional programming that generalizes the classical fold (reduce) by applying the fold locally on blocks of data before combining the results. The central idea is to exploit data locality and parallelism by dividing input into chunks that can be processed independently, then merging partial results in a final fold step. The term appears in a subset of literature and talks on memory-hierarchy optimization and streaming computation, where improving cache efficiency and parallel throughput is important.

In its simplest form, lfold partitions a data structure into blocks, computes a block-local fold on each block, and then performs a secondary fold on the set of block results. Variants differ in how blocks are chosen, how partial results are merged, and whether multiple levels of locality are used. The operation typically requires the folding operator to be associative and to have a well-defined neutral element so that partial results can be combined in any order without changing the end result.

A common example is summing a large array: divide the array into B blocks, compute the sum of each block independently, then sum the B block results to obtain the final total. Lfold can yield improvements in cache performance and parallelism on multi-core CPUs and GPUs, especially for large data streams or matrices.

Limitations include the need for operator associativity, overhead from block management, and potential inefficiencies if data locality is already optimal or block boundaries misalign with hardware caches. See also fold, monoid, map-reduce, and data locality.