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- Computing the fast fourier
- Computing the fast fourier
- Introduction
Scope
In investigating the hypotheses, the scope of this work has been limited in several ways:
- It is limited to single-threaded complex 1D FFTs, because
multi-dimensional, multi-threaded or multi-processor FFTs (or anycombination thereof) are ultimately decomposed into 1D components running on
a single core, and all other things being equal, it is the performance ofthese 1D components running on a single microprocessor core that determines
the overall performance of a given multi-threaded implementation;
- It is limited to transforms that operate on vectors of length
where
, because these are the easiest to compute on
machines, and consequently the most often used by applications. This excludesthe prime-factor algorithm
[link] ,
[link] ,
and the Radar
[link] and
Bluestein
[link] ,
[link] ,
[link] algorithms for prime sizes;
- It is limited to the
split-radix
[link] ,
[link] ,
[link] ,
[link] ,
[link] and
conjugate-pair
[link] ,
[link] ,
[link] ,
[link] algorithms. The Winograd
algorithm
[link] ,
[link] ,
[link] ,
[link] is excluded because of its low performance on systems where multiplication
costs about the same as addition;
- It is limited to out-of-place transforms, because they are generally
faster than in-place transforms, except at the boundaries of thecache
[link] ;
- The benchmark experiments are limited to the Intel x86 and ARM
machines, because it is estimated that 92% of the microprocessors in therapidly expanding mobile market are ARM devices
[link] , while
Intel's share of the worldwide PC and mobile PC microprocessors markets isestimated to be 79.3% and 84.4%,
respectively
[link] .
Contributions
The contributions of this work are summarized as follows:
- Three methods of computing the conjugate-pair algorithm on SIMD
microprocessors are described in
Streaming FFT ;
- The source code for the high-performance SIMD FFT library
developed in this thesis is publicly available under a permissive open sourcelicence
on github.
Organization
This work is divided into two parts. The first part,
Chapters 1-4, encompasses therelevant background, while the second part,
Chapters 5-8, is concerned withcontributions that challenge the state of the art.
A brief overview of the contents of each chapter:
-
Algorithms provides an overview of FFT algorithms from the mathematical perspective;
-
Implementation details complements the mathematical perspective
of the previous chapter with a more focused view of the low level detailsthat are relevant to efficient implementation on SIMD microprocessors;
-
Existing libraries reviews existing state of the art libraries,
with reference to algorithms and implementation details of the previouschapters;
-
Streaming FFT describes SFFT, a library for
SIMD microprocessors that is, in many cases, faster than the state ofthe art FFT libraries reviewed in
Existing libraries ;
-
Benchmark methods describes the benchmarking methods used to
evaluate performance and accuracy of various FFT implementations throughoutthis work;
-
Results and discussion presents the results of benchmarks on 18
different machines, as well as the results of model-based optimizationexperiments, with reference to earlier chapters and other related work;
-
Conclusions and future work concludes the work with a review of
the hypotheses, a summary of the contributions, and some idea for directionsthat future work might take.
Questions & Answers
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Misack
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Wine
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list any five characteristics of the blood cells
Shaker
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advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
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Yamosa
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Hilary
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Source:
OpenStax, Computing the fast fourier transform on simd microprocessors. OpenStax CNX. Jul 15, 2012 Download for free at http://cnx.org/content/col11438/1.2
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