{
  "abstract": "Stagnation in the summation of floating-point numbers occurs when the running sum, or the accumulator, does not change its value despite addends being greater than zero. Here we define different types of stagnation - commonly referred to as swamping or absorption, where one operand in an addition is nearly or completely rounded off---in floating-point summation, and propose algorithms for detecting it in numerical code that uses floating-point arithmetic. Whilst cancellation in floating-point arithmetic has been studied, for example by Lam et al. in `Dynamic floating point cancellation detection', stagnation has not been exploited as a property for detecting and reporting accuracy loss in floating-point operations. We have built prototype dynamic stagnation detection tools in two languages, MATLAB and Julia, and applied them to applications ranging from basic summation of a vector, to matrix multiplication, to a fluid flow simulation model. With this tool, users are able to identify areas of their floating-point code where stagnation occurs - in those areas of the code one may need to switch to a higher precision number format, apply stochastic rounding, or use different summation algorithms such as compensated summation. To the best of our knowledge we provide a first rigorous definition of stagnation in floating-point summation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10819",
  "author_total": 2,
  "authors": [
    {
      "name": "Mantas Mikaitis"
    },
    {
      "name": "William Woolfenden"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0j2en6qwes7xb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10819",
  "fulltext_url": null,
  "id": "0j2en6qwes7xb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10819",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1703|Numerical Methods and Algorithms"
    ]
  ],
  "openalex": "W7221181400",
  "pdf_url": "https://arxiv.org/pdf/2610.10819",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0j2en6qwes7xb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.10819",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10819"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Analysis and Detection of Stagnation in Floating-Point Summation",
  "title_text": "Analysis and Detection of Stagnation in Floating-Point Summation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/0j2en6qwes7xb",
  "venue": "arXiv",
  "versions": []
}