# Introduction  (Page 2/2)

 Page 2 / 2

## 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 $m\in {\mathbb{N}}^{0}$ , 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;
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.

a diagram of an adult mosquito
what are white blood cells
white blood cell is part of the immune system. that help fight the infection.
MG
Mlungisi
Cells with a similar function, form a tissue. For example the nervous tissue is composed by cells:neurons and glia cells. Muscle tissue, is composed by different cells.
Anastasiya
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homogenous
Kevin
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Isala
explain if oxygen is necessary for photosynthesis
explain if oxygen is necessary for photosynthesis
Yes, the plant does need oxygen. The plant uses oxygen, water, light, and produced food. The plant use process called photosynthesis.
MG
By using the energy of sunlight, plants convert carbon dioxide and water into carbohydrates and oxygen by photosynthesis. This happens during the day and sunlight is needed.
NOBLE
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Anastasiya
yet still is it needed?
NOBLE
no. The reaction is: 6CO2+6H20+ solar energy =C6H12O6(glucose)+602. The plant requires Carbon dioxyde, light, and water Only, and produces glucose and oxygen( which is a waste).
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joining
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NOBLE
the study of non and living organism is called.
Godfrey
Is call biology
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NOBLE
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Usher
what Is ecology
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A cell is a basic structure and functional unit of life
Ndongya
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is the study of living and non living organisms
Ahmed
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Asal
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DAVID
anabolism and catabolism
Anabolism refers to the process in methabolism in which complex molecules are formed "built" and requires energy to happen. Catabolism is the opposite process: complex molecules are deconstructed releasing energy, such as during glicolysis.
Anastasiya
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draw and lable the cell
why homones are destroyed soon after completing their role
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