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Issue No.11 - November (2011 vol.60)
pp: 1652-1663
Adam B. Kinsman , McMaster University, Hamilton
Nicola Nicolici , McMaster University, Hamilton,
As interest mounts in using hardware accelerators to speed up numerical scientific calculations, automation tool support is required to aid designers in mapping applications to custom hardware. One key step in designing this custom hardware is bit-width allocation where the known-art faces challenges when dealing with applications from the scientific computing domain, thus motivating the use of computational methods based on Satisfiability-Modulo Theory. Many real-life applications are, however, specified in terms of vectors and matrices which are of sufficient size to make expansion into scalar equations infeasible. The proposed vector-magnitude method and its extension via block vectors enable computational methods to be leveraged in tackling calculations of practically relevant complexity. Application to case studies confirms that through a more compact computational instance, search efficiency is improved leading to tighter bounds and thus smaller bit-widths.
Bit-width allocation, hardware accelerators.
Adam B. Kinsman, Nicola Nicolici, "Computational Vector-Magnitude-Based Range Determination for Scientific Abstract Data Types", IEEE Transactions on Computers, vol.60, no. 11, pp. 1652-1663, November 2011, doi:10.1109/TC.2010.266
[1] G. Arfken, Mathematical Methods for Physicists, third ed. Academic Press, 1985.
[2] P. Banerjee, M. Haldar, A. Nayak, V. Kim, V. Saxena, S. Parkes, D. Bagchi, S. Pal, N. Tripathi, D. Zaretsky, R. Anderson, and J.R. Uribe, “Overview of a Compiler for Synthesizing MATLAB Programs onto FPGAs,” IEEE Trans. Very Large Scale Integration Systems, vol. 12, no. 3, pp. 312-324, Mar. 2004.
[3] P. Belanovic and M. Rupp, “Automated Floating-Point to Fixed-Point Conversion with the Fixify Environment,” Proc. Int'l Workshop Rapid System Prototyping, pp. 172-178, 2005.
[4] A. Benedetti and P. Perona, “Bit-Width Optimization for Configurable DSP's by Multi-Interval Analysis,” Proc. Asilomar Conf. Signals, Systems and Computers, vol. 1, pp. 355-359, 2000.
[5] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge Univ. Press, 2004.
[6] C.F. Fang, R.A. Rutenbar, and T. Chen, “Fast, Accurate Static Analysis for Fixed-Point Finite-Precision Effects in DSP Designs,” Proc. Int'l Conf. Computer Aided Design (ICCAD), pp. 275-282, 2003.
[7] M. Franzle and C. Herde, “HySAT: An Efficient Proof Engine for Bounded Model Checking of Hybrid Systems,” Formal Methods in System Design, vol. 30, no. 3, pp. 178-198, June 2007.
[8] D. Goldberg, “What Every Computer Scientist Should Know about Floating Point Arithmetic,” ACM Computing Surveys, vol. 23, no. 1, pp. 5-48, 1991.
[9] G.H. Golub and C.F. Van Loan, Matrix Computations, third ed. John Hopkins Univ. Press, 1996.
[10] W. Kahan, “The Improbability of Probabilistic Error Analyses for Numerical Computations,” technical report, EECS Dept., Univ. of California, 1998.
[11] H. Keding, M. Willems, M. Coors, and H. Meyr, “FRIDGE: A Fixed-Point Design and Simulation Environment,” Proc. IEEE/ACM Design Automation and Test in Europe (DATE), pp. 429-435, 1998.
[12] A.B. Kinsman and N. Nicolici, “Bit-Width Allocation for Hardware Accelerators for Scientific Computing Using SAT-Modulo Theory,” IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 29, no. 3, pp. 405-413, Mar. 2010.
[13] D.-U. Lee, A.A. Gaffar, R.C.C. Cheung, O. Mencer, W. Luk, and G.A. Constantinides, “Accuracy-Guaranteed Bit-Width Optimization,” IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 25, no. 10, pp. 1990-2000, Oct. 2006.
[14] J.A. Lopez, C. Carreras, and O. Nieto-Taladriz, “Improved Interval-Based Characterization of Fixed-Point LTI Systems with Feedback Loops,” IEEE Trans. Computer Aided Design, vol. 26, no. 11, pp. 1923-1933, Nov. 2007.
[15] R. Mafi, S. Sirouspour, B. Moody, B. Mahdavikhah, K. Elizeh, A.B. Kinsman, N. Nicolici, M. Fotoohi, and D. Madill, “Hardware-Based Parallel Computing for Real-Time Haptic Rendering of Deformable Objects,” Proc. IEEE Int'l Conf. Intelligent Robots and Systems (IROS), p. 4187, 2008.
[16] A. Mallik, D. Sinha, P. Banerjee, and H. Zhou, “Low-Power Optimization by Smart Bit-Width Allocation in a SystemC-Based ASIC Design Environment,” IEEE Trans. Computer-Aided Design, vol. 26, no. 3, pp. 447-455, Mar. 2007.
[17] R.E. Moore, Interval Analysis. Prentice Hall, 1966.
[18] J. Nocedal and S.J. Wright, Numerical Optimization. Springer-Verlag, 1999.
[19] W.G. Osborne, R.C.C. Cheung, J.G.F. Coutinho, W. Luk, and O. Mencer, “Automatic Accuracy-Guaranteed Bit-Width Optimization for Fixed and Floating-Point Systems,” Proc. Int'l Conf. Field Programmable Logic and Applications (FPL), pp. 617-620, 2007.
[20] W.G. Osborne, J.G.F. Coutinho, R.C.C. Cheung, W. Luk, and O. Mencer, “Instrumented Multi-Stage Word-Length Optimization,” Proc. Int'l Conf. Field-Programmable Technology, pp. 89-96, Dec. 2007.
[21] Y. Pang and K. Radecka, “Optimizing Imprecise Fixed-Point Arithmetic Circuits Specified by Taylor Series through Arithmetic Transform,” Proc. IEEE/ACM Design Automation Conf., pp. 397-402, 2008.
[22] Y. Pu and Y. Ha, “An Automated, Efficient and Static Bit-Width Optimization Methodology towards Maximum Bit-Width-to-Error Tradeoff with Affine Arithmetic Model,” Proc. IEEE/ACM Asia and South Pacific Conf. Design Automation, p. 6, Jan. 2006.
[23] Ruey-Yuan Han, “Fast Fourier Transform Correlation Tracking Algorithm with Background Correction,” US Patent Number: 6970577, Nov. 2005.
[24] K. Sano, T. Iizuka, and S. Yamamoto, “Systolic Architecture for Computational Fluid Dynamics on FPGAs,” Proc. IEEE Ann. Int'l Symp. Field-Programmable Custom Computing Machines, pp. 107-116, 2007.
[25] R. Scrofano, M.B. Gokhale, F. Trouw, and V.K. Prasanna, “Accelerating Molecular Dynamics Simulations with Reconfigurable Computers,” IEEE Trans. Parallel and Distributed Systems, vol. 19, no. 6, pp. 764-778, June 2008.
[26] C. Shi and R.W. Brodersen, “An Automated Floating-Point to Fixed-Point Conversion Methodology,” Proc. Int'l Conf. Acoustics, Speech, and Signal Processing (ICASSP), pp. 529-532, 2003.
[27] J. Stolfi and L. de Figueiredo, “Self-Validated Numerical Methods and Applications,” Proc. Brazilian Math. Colloquium Monograph, 1997.
[28] T.J. Todman, G.A. Constantinides, S.J.E. Wilton, O. Mencer, W. Luk, and P.Y.K. Cheung, “Reconfigurable Computing: Architectures and Design Methods,” Proc. IEE-Computer and Digital Techniques, vol. 152, no. 2, pp. 193-207, Mar. 2005.
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