Polynomial Interpolation and Extrapolation
Marija Stanojevic
SI 2010/0011
Dataflow Technology
Computing with
control flow
processors
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Computing with dataflow
engines (DFEs)
Maxeler Technology
MAXELER DATAFLOW COMPUTING
One result
per clock cycle
Engine is written in Java and Host is written in C.
Minimal frequency f achieves maximal performance, thus
for a given power budget, we get Maximum Performance
Computing (MPC)!
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Neville's algorithm
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Given a set of n+1 data points (xi, yi) where no two xi are
the same, the interpolating polynomial is the polynomial p
of degree at most n with the property: p(xi) = yi for all i = 0,…,n
This polynomial exists and it is unique. Neville's algorithm evaluates this
polynomial at some point and gives value y and
error estimate dy
It is easy to work with algorithm recursively as
shown in figure in the right bottom corner
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Neville's algorithm

Algorithm is based on formula:
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It can be easily become recursive algorithm by next transformations:
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Maxeler code - Java
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Maxeler code - Java
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Maxeler code - C
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Successful
building and
running
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Results

X and Y coordinates of points were in range from 0 to 10

Algorithm complexity is N2

Interpolation is done for:
– 4 points with time of execution on Maxeler: 0.01s
– 100 points with time of execution on Maxeler: 0.14s
– 1000 points with time of execution on Maxeler: 4.68s
– 2000 points with time of execution on Maxeler: 31.09s
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Results
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Conclusion
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This project implements Neville's interpolation algorithm on Maxeler
Whole project code can be found on:
https://github.com/mstanojevic118/MaxelerProject
There are two versions of C code for Maxeler; File with NiceOutput in name
gives nicer, but less extensive output
Maxeler is practical for big amount of data, because it's fast and energy saving
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References
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Milutinovic, V., et al, Guide to DataFlow SuperComputing, Springer, 2015
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Milutinovic, V., editor, Advances in Computers: DataFlow, Elsevier, 2015
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Milutinovic, V., et al, Paradigm Shift in SuperComuting DataFlow vs ControlFlow,
Journal of Big Data, 2015
Milutinovic, V., Salom, J., Trifunovic, N., Giorgi, R., “Guide to DataFlow
SuperComputing”, Springer 2015
Press, W., Teukolsky, S., Vetterling, W., Flannery, B., Numerical Receipes in C,
Cambridge University Press, 2002
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Thank you for your attention!
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