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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
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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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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