65 lines
2.8 KiB
HTML
65 lines
2.8 KiB
HTML
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
|
||
|
|
<html>
|
||
|
|
<head><title>
|
||
|
|
FFTW FAQ - Section 4
|
||
|
|
</title>
|
||
|
|
<link rev="made" href="mailto:fftw@fftw.org">
|
||
|
|
<link rel="Contents" href="index.html">
|
||
|
|
<link rel="Start" href="index.html">
|
||
|
|
<link rel="Next" href="section5.html"><link rel="Previous" href="section3.html"><link rel="Bookmark" title="FFTW FAQ" href="index.html">
|
||
|
|
</head><body text="#000000" bgcolor="#FFFFFF"><h1>
|
||
|
|
FFTW FAQ - Section 4 <br>
|
||
|
|
Internals of FFTW
|
||
|
|
</h1>
|
||
|
|
|
||
|
|
<ul>
|
||
|
|
<li><a href="#howworks" rel=subdocument>Q4.1. How does FFTW work?</a>
|
||
|
|
<li><a href="#whyfast" rel=subdocument>Q4.2. Why is FFTW so fast?</a>
|
||
|
|
</ul><hr>
|
||
|
|
|
||
|
|
<h2><A name="howworks">
|
||
|
|
Question 4.1. How does FFTW work?
|
||
|
|
</A></h2>
|
||
|
|
|
||
|
|
The innovation (if it can be so called) in FFTW consists in having a
|
||
|
|
variety of composable <i>solvers</i>, representing different FFT algorithms and implementation strategies, whose combination into a
|
||
|
|
particular <i>plan</i> for a given size can be determined at runtime according to the characteristics of your machine/compiler.
|
||
|
|
This peculiar software architecture allows FFTW to adapt itself to
|
||
|
|
almost any machine.
|
||
|
|
<p>
|
||
|
|
For more details (albeit somewhat outdated), see the paper "FFTW:
|
||
|
|
An Adaptive Software Architecture for the FFT", by M. Frigo and
|
||
|
|
S. G. Johnson, <i>Proc. ICASSP</i> 3, 1381 (1998), also available at <A href="http://www.fftw.org">the FFTW web page</A>.
|
||
|
|
<h2><A name="whyfast">
|
||
|
|
Question 4.2. Why is FFTW so fast?
|
||
|
|
</A></h2>
|
||
|
|
|
||
|
|
This is a complex question, and there is no simple answer. In fact,
|
||
|
|
the authors do not fully know the answer, either. In addition to many
|
||
|
|
small performance hacks throughout FFTW, there are three general
|
||
|
|
reasons for FFTW's speed.
|
||
|
|
<ul>
|
||
|
|
<li> FFTW uses a variety of FFT algorithms and implementation styles
|
||
|
|
that can be arbitrarily composed to adapt itself to
|
||
|
|
a machine. See <A href="#howworks">Q4.1 `How does FFTW work?'</A>.
|
||
|
|
<li> FFTW uses a code generator to produce highly-optimized
|
||
|
|
routines for computing small transforms.
|
||
|
|
|
||
|
|
<li> FFTW uses explicit divide-and-conquer to take advantage
|
||
|
|
of the memory hierarchy.
|
||
|
|
</ul>
|
||
|
|
For more details (albeit somewhat outdated), see the paper "FFTW:
|
||
|
|
An Adaptive Software Architecture for the FFT", by M. Frigo and
|
||
|
|
S. G. Johnson, <i>Proc. ICASSP</i> 3, 1381 (1998), available along with other references at
|
||
|
|
<A href="http://www.fftw.org">the FFTW web page</A>. <hr>
|
||
|
|
Next: <a href="section5.html" rel=precedes>Known bugs</a>.<br>
|
||
|
|
Back: <a href="section3.html" rev=precedes>Using FFTW</a>.<br>
|
||
|
|
<a href="index.html" rev=subdocument>Return to contents</a>.<p>
|
||
|
|
<address>
|
||
|
|
<A href="http://www.fftw.org">Matteo Frigo and Steven G. Johnson</A> / <A href="mailto:fftw@fftw.org">fftw@fftw.org</A>
|
||
|
|
- 14 September 2021
|
||
|
|
</address><br>
|
||
|
|
Extracted from FFTW Frequently Asked Questions with Answers,
|
||
|
|
Copyright © 2021 Matteo Frigo and Massachusetts Institute of Technology.
|
||
|
|
</body></html>
|