{
  "abstract": "In this article, we propose an algorithmic approach to determine the integer points located near a transcendental curve. This approach is closely related to a celebrated work by Bombieri and Pila and to the so-called Coppersmith's method. We establish the underlying theoretical foundations, prove the algorithms, study their complexity and present practical experiments; we also compare our approach with previously existing ones. From a practical point of view, we focus on an instance of our general problem, called the Table Maker's Dilemma, whose solving makes it possible to evaluate a given function with correct rounding. Our experiments show a significant speedup. In particular, our results show that the development of a correctly rounded mathematical library for the binary128 format is now possible at a much smaller cost than with previously existing approaches.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.04858",
  "author_total": 2,
  "authors": [
    {
      "name": "Nicolas Brisebarre"
    },
    {
      "name": "Guillaume Hanrot"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c4kwf7rh0h4h6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.04858",
  "fulltext_url": null,
  "id": "c4kwf7rh0h4h6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.04858",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SC"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "1703|Numerical Methods and Algorithms"
    ]
  ],
  "openalex": "W7163525942",
  "pdf_url": "https://arxiv.org/pdf/2606.04858",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c4kwf7rh0h4h6.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:13Z",
      "native_id": "2606.04858",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.04858"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Integer points close to a transcendental curve: an algorithmic approach",
  "title_text": "Integer points close to a transcendental curve: an algorithmic approach",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/c4kwf7rh0h4h6",
  "venue": "arXiv",
  "versions": []
}