{"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/the-fast-loaded-dice-roller-a-near-optimal","title":"The Fast Loaded Dice Roller: A Near-Optimal Exact Sampler for Discrete Probability Distributions","arxiv_id":"2003.03830","date":"2020-03-08","proceeding":null,"authors":["Feras A. Saad","Cameron E. Freer","Martin C. Rinard","Vikash K. Mansinghka"],"abstract":"This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we call the Fast Loaded Dice Roller (FLDR), is highly efficient in both space and time: (i) the size of the sampler is guaranteed to be linear in the number of bits needed to encode the input distribution; and (ii) the expected number of bits of entropy it consumes per sample is at most 6 bits more than the information-theoretically optimal rate. We present fast implementations of the linear-time preprocessing and near-optimal sampling algorithms using unsigned integer arithmetic. Empirical evaluations on a broad set of probability distributions establish that FLDR is 2x-10x faster in both preprocessing and sampling than multiple baseline algorithms, including the widely-used alias and interval samplers. It also uses up to 10000x less space than the information-theoretically optimal sampler, at the expense of less than 1.5x runtime overhead.","url_abs":"https://arxiv.org/abs/2003.03830v2","url_pdf":"https://arxiv.org/pdf/2003.03830v2.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":"the-fast-loaded-dice-roller-a-near-optimal","repo_url":"https://github.com/probcomp/fast-loaded-dice-roller","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"the-fast-loaded-dice-roller-a-near-optimal","repo_url":"https://github.com/probsys/randomness-recycling","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}