Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Rapid Multiplication Modulo the Sum and Difference of Highly Composite Numbers

Colin Percival
Mathematics of Computation
Vol. 72, No. 241 (Jan., 2003), pp. 387-395
Stable URL: http://www.jstor.org/stable/4099997
Page Count: 9
  • Read Online (Free)
  • Download ($34.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Rapid Multiplication Modulo the Sum and Difference of Highly Composite Numbers
Preview not available

Abstract

We extend the work of Richard Crandall et al. to demonstrate how the Discrete Weighted Transform (DWT) can be applied to speed up multiplication modulo any number of the form $a \pm b$ where $\prod_{p\vert ab}p$ is small. In particular this allows rapid computation modulo numbers of the form $k \cdot 2^{n}\pm 1$. In addition, we prove tight bounds on the rounding errors which naturally occur in floating-point implementations of FFT and DWT multiplications. This makes it possible for FFT multiplications to be used in situations where correctness is essential, for example in computer algebra packages.

Page Thumbnails

  • Thumbnail: Page 
387
    387
  • Thumbnail: Page 
388
    388
  • Thumbnail: Page 
389
    389
  • Thumbnail: Page 
390
    390
  • Thumbnail: Page 
391
    391
  • Thumbnail: Page 
392
    392
  • Thumbnail: Page 
393
    393
  • Thumbnail: Page 
394
    394
  • Thumbnail: Page 
395
    395