1. Polynomial Interpolation and Extrapolation1
Polynomial Interpolation and Extrapolation
Marija Stanojevic
SI 2010/0011

2. Dataflow Technology Computing with dataflow engines (DFEs)
Computing with control flow processors

3. Maxeler Technology MAXELER DATAFLOW COMPUTING One result3
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)! 3
/16

4. Neville's algorithm
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

5. Neville's algorithm Algorithm is based on formula:
It can be easily become recursive algorithm by next transformations:

6. Maxeler code - Java

7. Maxeler code - Java

8. Maxeler code - C

9. Successful building and running

10. 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

11. Results

12. Conclusion
This project implements Neville's interpolation algorithm on Maxeler
Whole project code can be found on:
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

13. References
Milutinovic V., Rakocevic G., Stojanovic S., Sustran Z., Mencer O., Pell O., Flynn M., Korolija N., DataFlow ExaScale SuperComputing: Revisiting the Paradigm and the Algorithms, mare_nostrum/hpc-events/hpcac _maxeler.pdf
Selected MaxCompiler Examples, Sustran Z., Stojanovic S., home.etf.rs/~vm/tutorial/Berlin/11.%20Maxeler-examples.pptx
Press W., Teukolsky S., Vetterling W., Flannery B., Numerical Receipes in C, Cambridge University Press, 2002
Neville's algorithm,

14. Thank you for your attention!