Efficient Computation of Positional Population Counts Using SIMD Instructions [r-libre/2236]

Klarqvist, Marcus D. R.; Muła, Wojciech, & Lemire, Daniel (2021). Efficient Computation of Positional Population Counts Using SIMD Instructions. Concurrency and Computation: Practice and Experience, 33 (17). https://doi.org/10.1002/cpe.6304

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Item Type:	Journal Articles
Refereed:	Yes
Status:	Published
Abstract:	In several fields such as statistics, machine learning, and bioinformatics, categorical variables are frequently represented as one-hot encoded vectors. For example, given 8 distinct values, we map each value to a byte where only a single bit has been set. We are motivated to quickly compute statistics over such encodings. Given a stream of k-bit words, we seek to compute k distinct sums corresponding to bit values at indexes 0, 1, 2, ..., k-1. If the k-bit words are one-hot encoded then the sums correspond to a frequency histogram. This multiple-sum problem is a generalization of the population-count problem where we seek the sum of all bit values. Accordingly, we refer to the multiple-sum problem as a positional population-count. Using SIMD (Single Instruction, Multiple Data) instructions from recent Intel processors, we describe algorithms for computing the 16-bit position population count using less than half of a CPU cycle per 16-bit word. Our best approach uses up to 400 times fewer instructions and is up to 50 times faster than baseline code using only regular (non-SIMD) instructions, for sufficiently large inputs.
Depositor:	Lemire, Daniel
Owner / Manager:	Daniel Lemire
Deposited:	19 Mar 2021 12:54
Last Modified:	18 Aug 2021 13:48

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