{
  "abstract": "We implement Ozaki Scheme II (residue number system + Chinese remainder theorem), which reduces multiple-precision dense matrix multiplication to a sequence of low-precision, high-throughput integer or floating-point GEMMs on CPUs. Two backends are built on top of a shared CRT reconstruction stage: (a) exact INT8 x INT8 -> INT32 tile products on Intel AMX, and (b) binary64 DGEMM, the CPU construction of the original Ozaki Scheme II paper. On a two-socket Xeon Gold 6526Y (Emerald Rapids, 32 cores), we evaluate significand precisions of 53-2048 bits and matrix dimensions N = 256-8192. The results are always within 1 ulp of a high-precision MPFR reference (essentially correctly rounded), while running up to 167x faster than a naive MPFR matrix product, up to 588x faster than BNCmatmul's Strassen multiplication, and 9-78x faster than Ozaki Scheme I (FP64 slicing + OpenBLAS DGEMM). The break-even point between the two backends is approximately N = 2048: below it, the binary64 backend wins thanks to its smaller number of moduli; above it, the AMX-INT8 backend wins as the GEMMs dominate. We further port the implementation to AArch64 (NVIDIA GB10: Cortex-X925 x 10 + Cortex-A725 x 10). Since this machine lacks SME/SME2, the INT8 kernel uses the SMMLA matrix-product instruction of the SVE2 i8mm extension. We obtain an exact INT8 GEMM sustaining 6.5 TOPS and, still within 1 ulp across all conditions, speedups of 14-89x over BNCmatmul's Ozaki Scheme I (OpenBLAS-linked routine) and 6-19x over a fairness-adjusted OzI-best variant. The paper also includes a tutorial introduction to Ozaki Scheme II (Section \"Introduction to Ozaki Scheme II\") and a quantitative explanation of why this seemingly GPU-specific technique is fast on CPUs as well.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27831",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomonori Kouya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ckj2abspycdt9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27831",
  "fulltext_url": null,
  "id": "ckj2abspycdt9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27831",
  "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": "W7214195921",
  "pdf_url": "https://arxiv.org/pdf/2609.27831",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ckj2abspycdt9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27831",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Ozaki Scheme II Is Fast on CPUs Too: Multiple-Precision Matrix Multiplication on Intel AMX-INT8 and Arm SVE2-i8mm",
  "title_text": "Ozaki Scheme II Is Fast on CPUs Too: Multiple-Precision Matrix Multiplication on Intel AMX-INT8 and Arm SVE2-i8mm",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/ckj2abspycdt9",
  "venue": "arXiv",
  "versions": []
}