{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-computation-of-positional","title":"Efficient Computation of Positional Population Counts Using SIMD Instructions","arxiv_id":"1911.02696","date":"2019-11-07","proceeding":null,"authors":["Marcus D. R. Klarqvist","Wojciech Muła","Daniel Lemire"],"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.","url_abs":"https://arxiv.org/abs/1911.02696v6","url_pdf":"https://arxiv.org/pdf/1911.02696v6.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"efficient-computation-of-positional","repo_url":"https://github.com/lemire/pospopcnt_avx512","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}