View Single Post
Old 2007-08-29, 11:20   #1
akruppa's Avatar
Aug 2002

2,467 Posts
Default Van Buskirk/DJB's Tangent FFT

Date: 12 Aug 2007 16:55:34 -0000
Automatic-Legal-Notices: See
From: "D. J. Bernstein" <>
Subject: The tangent FFT
Content-Disposition: inline

If you're using the complex-floating-point split-radix FFT, you can gain
a constant factor in total floating-point operations (asymptotically
more than 5%!) by switching to the tangent FFT:

The operation count is due to Van Buskirk. The algorithm in my paper has
the virtue of being simultaneously simple, in-place, and cache-friendly.

I haven't seen a serious analysis of the impact of Van Buskirk's ideas
for cost measures more complicated than counting arithmetic operations.
The Johnson-Frigo paper on the topic claims that practical performance
of FFTs is "unpredictable"; I see no justification for this claim, and
my own FFT optimization experience tells me that the opposite is true.
Has anyone tried a serious implementation of Van Buskirk's FFT?

- ---D. J. Bernstein, Professor, Mathematics, Statistics,
and Computer Science, University of Illinois at Chicago
Could this be of interest for Prime95? (Note: I have not read the paper yet.)

akruppa is offline   Reply With Quote