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Scope

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] .

Contributions

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.

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:

  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

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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