{
  "abstract": "Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a uniformly quantized random variable. Our approximation uncovers a different quantity that provides this link for floating-point quantization. Additionally, we prove that the entropy of a floating-point quantized random variable is approximately unchanged under scaling. Closed-form expressions for the floating-point entropy of common distributions are provided and compared to exact results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.11546",
  "author_total": 4,
  "authors": [
    {
      "name": "Sultan M. Daniels"
    },
    {
      "name": "Samuel H. D'Ambrosia"
    },
    {
      "name": "Michael R. DeWeese"
    },
    {
      "name": "Anant Sahai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06gg8gv55q7q8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.11546",
  "fulltext_url": null,
  "id": "06gg8gv55q7q8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.11546",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1703|Numerical Methods and Algorithms"
    ]
  ],
  "openalex": "W7161068793",
  "pdf_url": "https://arxiv.org/pdf/2605.11546",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06gg8gv55q7q8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2605.11546",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.11546"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "The Entropy of Floating-Point Numbers",
  "title_text": "The Entropy of Floating-Point Numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/06gg8gv55q7q8",
  "venue": "arXiv",
  "versions": []
}