https://arxiv.org/abs/2501.08889

Skip to main content
Cornell University
We gratefully acknowledge support from the Simons Foundation, member
institutions, and all contributors. Donate
 
arxiv logo > cs > arXiv:2501.08889
[                    ]

Help | Advanced Search

[All fields        ]
Search
arXiv logo
Cornell University Logo
[                    ] GO
quick links

  * Login
  * Help Pages
  * About

Computer Science > Hardware Architecture

arXiv:2501.08889 (cs)
[Submitted on 15 Jan 2025]

Title:Karatsuba Matrix Multiplication and its Efficient Custom
Hardware Implementations

Authors:Trevor E. Pogue, Nicola Nicolici
View a PDF of the paper titled Karatsuba Matrix Multiplication and
its Efficient Custom Hardware Implementations, by Trevor E. Pogue and
1 other authors
View PDF HTML (experimental)

    Abstract:While the Karatsuba algorithm reduces the complexity of
    large integer multiplication, the extra additions required
    minimize its benefits for smaller integers of more commonly-used
    bitwidths. In this work, we propose the extension of the scalar
    Karatsuba multiplication algorithm to matrix multiplication,
    showing how this maintains the reduction in multiplication
    complexity of the original Karatsuba algorithm while reducing the
    complexity of the extra additions. Furthermore, we propose new
    matrix multiplication hardware architectures for efficiently
    exploiting this extension of the Karatsuba algorithm in custom
    hardware. We show that the proposed algorithm and hardware
    architectures can provide real area or execution time
    improvements for integer matrix multiplication compared to scalar
    Karatsuba or conventional matrix multiplication algorithms, while
    also supporting implementation through proven systolic array and
    conventional multiplier architectures at the core. We provide a
    complexity analysis of the algorithm and architectures and
    evaluate the proposed designs both in isolation and in an
    end-to-end deep learning accelerator system compared to baseline
    designs and prior state-of-the-art works implemented on the same
    type of compute platform, demonstrating their ability to increase
    the performance-per-area of matrix multiplication hardware.

          Accepted for publication in IEEE Transactions on Computers;
Comments: Associated source code available on github at this https
          URL
Subjects: Hardware Architecture (cs.AR); Artificial Intelligence
          (cs.AI); Performance (cs.PF)
Cite as:  arXiv:2501.08889 [cs.AR]
          (or arXiv:2501.08889v1 [cs.AR] for this version)
          https://doi.org/10.48550/arXiv.2501.08889
          Focus to learn more
          arXiv-issued DOI via DataCite
Related   https://doi.org/10.1109/TC.2025.3525606
DOI:      Focus to learn more
          DOI(s) linking to related resources

Submission history

From: Trevor Pogue [view email]
[v1] Wed, 15 Jan 2025 16:00:43 UTC (2,925 KB)
Full-text links:

Access Paper:

    View a PDF of the paper titled Karatsuba Matrix Multiplication
    and its Efficient Custom Hardware Implementations, by Trevor E.
    Pogue and 1 other authors
  * View PDF
  * HTML (experimental)
  * TeX Source
  * Other Formats

view license
Current browse context:
cs.AR
< prev   |   next >
new | recent | 2025-01
Change to browse by:
cs
cs.AI
cs.PF

References & Citations

  * NASA ADS
  * Google Scholar
  * Semantic Scholar

a export BibTeX citation Loading...

BibTeX formatted citation

x
[loading...          ]
Data provided by:

Bookmark

BibSonomy logo Reddit logo
(*) Bibliographic Tools

Bibliographic and Citation Tools

[ ] Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
[ ] Connected Papers Toggle
Connected Papers (What is Connected Papers?)
[ ] Litmaps Toggle
Litmaps (What is Litmaps?)
[ ] scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
( ) Code, Data, Media

Code, Data and Media Associated with this Article

[ ] alphaXiv Toggle
alphaXiv (What is alphaXiv?)
[ ] Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
[ ] DagsHub Toggle
DagsHub (What is DagsHub?)
[ ] GotitPub Toggle
Gotit.pub (What is GotitPub?)
[ ] Huggingface Toggle
Hugging Face (What is Huggingface?)
[ ] Links to Code Toggle
Papers with Code (What is Papers with Code?)
[ ] ScienceCast Toggle
ScienceCast (What is ScienceCast?)
( ) Demos

Demos

[ ] Replicate Toggle
Replicate (What is Replicate?)
[ ] Spaces Toggle
Hugging Face Spaces (What is Spaces?)
[ ] Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
( ) Related Papers

Recommenders and Search Tools

[ ] Link to Influence Flower
Influence Flower (What are Influence Flowers?)
[ ] Core recommender toggle
CORE Recommender (What is CORE?)

  * Author
  * Venue
  * Institution
  * Topic

( ) About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and
share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have
embraced and accepted our values of openness, community, excellence,
and user data privacy. arXiv is committed to these values and only
works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community?
Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is
MathJax?)

  * About
  * Help

  * Click here to contact arXiv Contact
  * Click here to subscribe Subscribe

  * Copyright
  * Privacy Policy

  * Web Accessibility Assistance
  * arXiv Operational Status
    Get status notifications via email or slack