Bit-width allocation for hardware accelerators for scientific computing using SAT-modulo theory

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volumn 29, Issue 3, 2010, Pages 405-413

  Kinsman, Adam B ^a   Nicolici, Nicola ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Bit width allocation; Finite precision; Fixed point; Range analysis

Indexed keywords

ALLOCATION PROBLEMS; ANALYTICAL METHOD; BIT-WIDTH; FINITE PRECISION; HARDWARE ACCELERATORS; HARDWARE COST; MODULO THEORIES; NUMERICAL CALCULATION; RANGE ANALYSIS; SATISFIABILITY MODULO THEORIES; SCIENTIFIC APPLICATIONS; SCIENTIFIC COMPUTING;

NUMERICAL METHODS;

COMPUTER ARCHITECTURE;

EID: 77649154762     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCAD.2010.2041839     Document Type: Article

References (29)

1. 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 Integr. Syst., vol. 12, no. 3, pp. 312-324, Mar. 2004.
2. P. Belanovic and M. Rupp, "Automated floating-point to fixed-point conversion with the fixify environment," in Proc. Int. Workshop Rapid Syst. Prototyping, 2005, pp. 172-178.
3. S. Boyd and L. Vandenberghe, "Introduction" in Convex Optimization. Cambridge, U.K.: Cambridge University Press, 2004, pp. 9-11.
4. S. Boyd and L. Vandenberghe, "Geometric problems," in Convex Optimization. Cambridge, U.K.: Cambridge University Press, 2004, pp. 398-422.
5. R. N. Bracewell, "Waveforms, spectra, filters and linearity," in The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, 1999.
6. R. N. Bracewell, "The discrete Fourier transform and the FFT," in The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, 1999.
7. R. L. Burden and J. D. Faires, "Solutions of equations in one variable" in Numerical Analysis, 7th ed. Pacific Grove, CA: Brooks Cole, 2000, pp. 66-74.
8. R. Cmar, L. Rijnders, P. Schaumont, S. Vernalde, and I. Bolsens, "A methodology and design environment for DSP ASIC fixed point refinement," in Proc. IEEE/Assoc. Comput. Machinery Design Autom. Test Eur., 1999, pp. 271-276.
9. C. F. Fang, R. A. Rutenbar, and T. Chen, "Fast, accurate static analysis for fixed-point finite-precision effects in DSP designs," in Proc. Int. Conf. Comput. Aided Design, 2003, pp. 275-282.
10. M. Franzle and C. Herde, "HySAT: An efficient proof engine for bounded model checking of hybrid systems," Formal Methods Syst. Design, vol. 30, no. 3, pp. 178-198, Jun. 2007.
11. A. A. Gaffar, O. Mencer, and W. Luk, "Unifying bit-width optimization for fixed-point and floating-point designs," in Proc. IEEE Symp. Field-Program. Custom Comput. Machines, 2004, pp. 79-88.
12. H. Keding, M. Willems, M. Coors, and H. Meyr, "FRIDGE: A fixed-point design and simulation environment," in Proc. IEEE/Assoc. Comput. Machinery Design Autom. Test Eur., 1998, pp. 429-435.
13. A. B. Kinsman and N. Nicolici, "Finite precision bit-width allocation using SAT-Modulo theory," in Proc. IEEE/Assoc. Comput. Machinery Design Autom. Test Eur., 2009, pp. 1106-1111.
14. D.-U. Lee, A. A. Gaffar, O. Mencer, and W. Luk, "MiniBit: Bit-width optimization via affine arithmetic," in Proc. IEEE Design Autom. Conf., 2005, pp. 837-840.
15. 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. Comput.-Aided Design, vol. 25, no. 10, pp. 1990-2000, Oct. 2006.
16. J. A. Lopez, C. Carreras, and O. N.-Taladriz, "Improved interval-based characterization of fixed-point LTI systems with feedback loops," IEEE Trans. Comput.-Aided Design, vol. 26, no. 11, pp. 1923-1933, Nov. 2007.
17. 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," in Proc. IEEE Int. Conf. Intell. Robots Syst., 2008, p. 4187.
18. 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. Comput.-Aided Design, vol. 26, no. 3, pp. 447-455, Mar. 2007.
19. R. E. Moore, Interval Analysis, Englewood Cliffs, NJ: Prentice-Hall, 1966.
20. 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," in Proc. Int. Conf. Field Program. Logic Appl., 2007, pp. 617-620.
21. Y. Pang and K. Radecka, "Optimizing imprecise fixed-point arithmetic circuits specified by Taylor Series through arithmetic transform," in Proc. IEEE Design Autom. Conf., 2008, pp. 397-402.
22. K. Sano, T. Iizuka, and S. Yamamoto, "Systolic architecture for computational fluid dynamics on FPGAs," in Proc. Int. Symp. Field-Program. Custom Comput. Machines, 2007, pp. 107-116.
23. R. Scrofano, M. B. Gokhale, F. Trouw, and V. K. Prasanna, "Accelerating molecular dynamics simulations with reconfigurable computers," IEEE Trans. Parallel Distrib. Syst., vol. 19, no. 6, pp. 764-778, Jun. 2008.
24. R. A. Serway, R. J. Beichner, and J. W. Jewett, "Sound waves," in Physics for Scientists and Engineers, vol. 2, 5th ed. Orlando, FL: Harcourt Brace Jovanovich, 1999, pp. 531-533.
25. C. Shi and R. W. Brodersen, "An automated floating-point to fixed-point conversion methodology," in Proc. Int. Conf. Acoust. Speech Signal Process., 2003, pp. 529-532.
26. J. Stewart, "Limits and rates of change," in Calculus: Early Transcen-dentals, 6th ed. Pacific Grove, CA: Brooks Cole, 2007, pp. 121-123.
27. J. Stolfi and L. H. De Figueiredo, "Affine arithmetic," in Self-Validated Numerical Methods and Applications. Rio de Janeiro, Brazil: Brazilian Mathematics Colloquium, 1997, pp. 43-86.
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," IEE Proc. Comput. Digit. Tech., vol. 152, no. 2, pp. 193-207, Mar. 2005.
29. HySAT Download, University of Oldenburg, Oldenburg, Germany [Online]. Available: http://hysat.informatik.uni-oldenburg.de/26273.html