XiSort: Deterministic Sorting via IEEE-754 Total Ordering and Entropy Minimization

XiSort: Deterministic Sorting via IEEE-754 Total Ordering and Entropy Minimization | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 19 May 2025 V1 Latest version Share on XiSort: Deterministic Sorting via IEEE-754 Total Ordering and Entropy Minimization Author : Faruk Alpay 0009-0009-2207-6528 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.174768113.31225246/v1 171 views 146 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract XiSort is introduced as a deterministic, reproducible sorting algorithm for floating-point sequences, grounded in rigorous mathematical principles. I formalize the sorting metric minimized by XiSort, including a curved variant, and demonstrate that XiSort can be viewed as minimizing the entropy or disorder of a sequence. Leveraging the IEEE-754 total ordering relation, XiSort imposes a complete order on all floating-point values (including ±0 and NaNs), and uses information-theoretic tie-breaking to guarantee a unique sorted output. I integrate XiSort into the Alpay Algebra symbolic framework, showing that the algorithm's recursive structure, monotonic convergence, and idempotence (sorting identity) can be encoded and verified symbolically. Within Alpay Algebra, XiSort is represented as a recursive operator that preserves the closure of the state space and exhibits a convergence property under a suitable monotonic potential function. I also detail XiSort's algorithmic design and performance. Empirical results on both real-world datasets and large-scale Gaussian random data confirm that XiSort achieves competitive throughput inmemory and in external memory (out-of-core) contexts while providing bit-for-bit reproducibility. I report timing results (e.g. sorting 10 8 doubleprecision values in about 12 seconds in-memory, and 100 GB of data at ∼100 MB/s on SSD storage) alongside use cases in scientific computing and high-frequency finance. The results highlight XiSort's practical value for reproducible numerical workflows and large-scale data pipelines, ensuring consistent ordering and stable behavior across platforms and runs. Supplementary Material File (xisort__deterministic_sorting_via_ieee_754_total_ordering_and_entropy_minimization.pdf) Download 309.64 KB Information & Authors Information Version history V1 Version 1 19 May 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords alpay algebra deterministic sorting entropy entropy minimization external memory floating-point ieee-754 reproducibility scientific computing stable sorting Authors Affiliations Faruk Alpay 0009-0009-2207-6528 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 171 views 146 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Faruk Alpay. XiSort: Deterministic Sorting via IEEE-754 Total Ordering and Entropy Minimization. Authorea . 19 May 2025. DOI: https://doi.org/10.22541/au.174768113.31225246/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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