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In investigating the hypotheses, the scope of this work has been limited in several ways:

  1. 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;
  2. It is limited to transforms that operate on vectors of length 2 m where m N 0 , 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;
  3. 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;
  4. It is limited to out-of-place transforms, because they are generally faster than in-place transforms, except at the boundaries of thecache  [link] ;
  5. 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] .


The contributions of this work are summarized as follows:

  1. Three methods of computing the conjugate-pair algorithm on SIMD microprocessors are described in Streaming FFT ;
  2. The source code for the high-performance SIMD FFT library developed in this thesis is publicly available under a permissive open sourcelicence on github.


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:

  1. Algorithms provides an overview of FFT algorithms from the mathematical perspective;
  2. 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;
  3. Existing libraries reviews existing state of the art libraries, with reference to algorithms and implementation details of the previouschapters;
  4. 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 ;
  5. Benchmark methods describes the benchmarking methods used to evaluate performance and accuracy of various FFT implementations throughoutthis work;
  6. 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;
  7. 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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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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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