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Parallel Implementation of Cholesky LL T-Algorithm in FPGA-Based Processor

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Parallel Processing and Applied Mathematics (PPAM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4967))

Abstract

The fixed-size processor array architecture, which is intended for realization of matrix LL T-decomposition based on Cholesky algorithm, is proposed. In order to implement this architecture in modern FPGA devices, the arithmetic unit (AU) operating in the rational fraction arithmetic is designed. The AU is intended for configuring in the Xilinx Virtex4 FPGAs, and its hardware complexity is much less than the complexity of similar AUs operating with floating-point numbers.

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References

  1. Underwood, K.D., Hemmert, K.S.: Closing the Gap: CPU and FPGA Trends in Sustained Floating Point BLAS Performance. In: Proc. IEEE Symp. Field Programmable Custom Computing Machines, FCCM-(2004)

    Google Scholar 

  2. Dou, Y., Vassiliadis, S., Kuzmanov, G.K., Gaydadjiev, G.N.: 64-bit Floating Point FPGA Matrix Multiplication. In: ACM/SIGDA 13-th Int. Symp. on Field Programmable Gate Arrays, FPGA-2005, pp. 86–95 (2005)

    Google Scholar 

  3. Johnson, J., Nagvajara, P., Nwankpa, C.: High-Performance Linear Algebra Processor using FPGA. In: Proc. High Performance Embedded Computing, HPEC 2003 (2003)

    Google Scholar 

  4. El-Kurdi, Y., Gross, W.J., Giannacopoulos, D.: Sparse Matrix-Vector Multiplication for Finite Element Method Matrices on FPGAs. In: Proc. 14th IEEE Symp. on Field-Programmable Custom Computing Machines FCCM 2006 (2006)

    Google Scholar 

  5. Beauchamp, M.J., Hauck, S., Underwood, K.D., Hemmert, K.S.: Embedded Floating-Point Units in FPGAs. In: Proc. ACM Int. Symp. on Field Programmable Gate Arrays, Monterey, CA (2006)

    Google Scholar 

  6. Durbano, J.P., Ortiz, F.E., Humphrey, J.R., Prather, D.W.: FPGA-Based Acceleration of the 3D Finite-Difference Time-Domain Method. In: Proc. 12-th IEEE Symp. on Field-Programmable Custom Computing Machines FCCM 2004 (2004)

    Google Scholar 

  7. Xilinx Floating-point Operators v2.0 DS335, Xilinx (2006), http://www.xilinx.com

  8. Storaasli, O.: Scientific Applications on a NASA Reconfigurable Hypercomputer. In: Proc. 5-th MAPLD Conf. (2002)

    Google Scholar 

  9. Strenski, D.: Computational Bottlenecks and Hardware Decisions for FPGAs. FPGA and Structured ASIC Journal (14), 1–20 (2006)

    Google Scholar 

  10. Craven, S., Athanas, P.: Examining the Viability of FPGA Supercomputing. EURASIP Journal on Embedded Systems (2) (2007)

    Google Scholar 

  11. Lienhart, G., Kugel, A., Männer, R.: Using floating-point arithmetic on FPGAs to accelerate scientific n-body simulations. In: Proc. 10-th Ann. IEEE Symp. on Field-Programmable Custom Computing Machines, FCCM 2002, p. 182 (2002)

    Google Scholar 

  12. Strzodka, R., Goddeke, D.: Pipelined Mixed Precision Algorithms on FPGAs for Fast and Accurate PDE. Solvers from Low Precision Components. In: Proc. Field-Programmable Custom Computing Machines (2006)

    Google Scholar 

  13. Matousek, R., Tichy, M., Phol, Z., Kadlec, J., Softley, C., Coleman, N.: Logarithmic number systems and floating-point arithmetics on FPGA. In: Proc. 12-th Int. Conf. on Field Programmable Logic and Applications, London, pp. 627–636 (2002)

    Google Scholar 

  14. Maslennikow, O., Shevtshenko, J., Sergyienko, A.: Configurable Microprocessor Array for DSP applications. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2004. LNCS, vol. 3019, pp. 36–41. Springer, Heidelberg (2004)

    Google Scholar 

  15. Maslennikow, O., Sergyienko, A., Lepekha, V.: FPGA Implementation of the Conjugate Gradient Method. In: Wyrzykowski, R., Dongarra, J., Meyer, N., Waśniewski, J. (eds.) PPAM 2005. LNCS, vol. 3911, pp. 526–533. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Golub, G.G., Van Loan, C.F.: Matrix Computations, 2nd edn., p. 642. J. Hopkins Univ. Press, Baltimore (1989)

    MATH  Google Scholar 

  17. Irvin, M.J., Smith, D.R.: A rational arithmetic processor. In: Proc. 5-th Symp. Comput. Arithmetic, pp. 241–244 (1981)

    Google Scholar 

  18. Wyrzykowski, R., Kanevski, J., Maslennikova, N., Maslennikov, O., Ovramenko, S.: Formalized Construction Method of Array Functional Graphs for Regular Algorithms. In: Engineering Simulation, vol. 14, pp. 217–232. Gordon and Breach Science Publishers, England (1997)

    Google Scholar 

  19. Kung, S.Y.: VLSI Array Processors. Prentice-Hall, Englewood Cliffs (1988)

    Google Scholar 

  20. Moreno, J.H., Lang, T.: Matrix Computation on Systolic-Type Arrays. Kluwer Acad. Publ., Boston (1992)

    Google Scholar 

  21. Quinton, P., Robert, Y.: Systolic Algorithms and Architectures. Prentice-Hall, Engl. Cliffs (1991)

    Google Scholar 

  22. Cosnard, M., Trystram, D.: Parallel Algorithms and Architectures. Int. Thomson Computer Press, Boston (1995)

    Google Scholar 

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Roman Wyrzykowski Jack Dongarra Konrad Karczewski Jerzy Wasniewski

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Maslennikow, O., Lepekha, V., Sergiyenko, A., Tomas, A., Wyrzykowski, R. (2008). Parallel Implementation of Cholesky LL T-Algorithm in FPGA-Based Processor. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_15

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  • DOI: https://doi.org/10.1007/978-3-540-68111-3_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68105-2

  • Online ISBN: 978-3-540-68111-3

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