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1 - Introduction

Published online by Cambridge University Press:  03 May 2010

Ryan Kastner ,
Anup Hosangadi  and
Farzan Fallah
Ryan Kastner
Affiliation:
University of California, San Diego
Anup Hosangadi
Affiliation:
University of California, Santa Barbara
Farzan Fallah
Affiliation:
Stanford University, California
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Summary

Overview

Arithmetic is one of the old topics in computing. It dates back to the many early civilizations that used the abacus to perform arithmetic operations. The seventeenth and eighteenth centuries brought many advances with the invention of mechanical counting machines like the slide rule, Schickard's Calculating Clock, Leibniz's Stepped Reckoner, the Pascaline, and Babbage's Difference and Analytical Engines. The vacuum tube computers of the early twentieth century were the first programmable, digital, electronic, computing devices. The introduction of the integrated circuit in the 1950s heralded the present era where the complexity of computing resources is growing exponentially. Today's computers perform extremely advanced operations such as wireless communication and audio, image, and video processing, and are capable of performing over 1015 operations per second.

Owing to the fact that computer arithmetic is a well-studied field, it should come as no surprise that there are many books on the various subtopics of computer arithmetic. This book provides a focused view on the optimization of polynomial functions and linear systems. The book discusses optimizations that are applicable to both software and hardware design flows; e.g., it describes the best way to implement arithmetic operations when your target computational device is a digital signal processor (DSP), a field programmable gate array (FPGA) or an application specific integrated circuit (ASIC).

Polynomials are among the most important functions in mathematics and are used in algebraic number theory, geometry, and applied analysis.

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Arithmetic Optimization Techniques for Hardware and Software Design , pp. 1 - 8
Publisher: Cambridge University Press
Print publication year: 2010

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References

Shi, C. and Brodersen, R. W., An automated floating-point to fixed-point conversion methodology, IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Washington, DC: IEEE Computer Society, 2003.Google Scholar
Fang, C. F., Rutenbar, R. A., and Chen, T., Fast, accurate static analysis for fixed-point finite-precision effects in DSP designs, International Conference on Computer Aided Design (ICCAD), San Jose, 2003. Washington, DC: IEEE Computer Society, 2003.Google Scholar
Menard, D. and Sentieys, O., Automatic evaluation of the accuracy of fixed-point algorithms, Design, Automation and Test in Europe Conference and Exhibition, 2002. Washington, DC: IEEE Computer Society, 2002.Google Scholar
Micheli, G. D., Synthesis and optimization of digital circuits, New York, NY: McGraw-Hill, 1994.Google Scholar
Potkonjak, M., Srivastava, M. B., and Chandrakasan, A. P., Multiple constant multiplications: efficient and versatile framework and algorithms for exploring common subexpression elimination, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, 15(2), 151–65, 1996.CrossRefGoogle Scholar
Pasko, R., Schaumont, P., Derudder, V., Vernalde, V., and Durackova, D., A new algorithm for elimination of common subexpressions, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, 18(1), 58–68, 1999.CrossRefGoogle Scholar
Pasko, R., Schaumont, P., Derudder, V., and Durackova, D., Optimization method for broadband modem FIR filter design using common subexpression elimination, International Symposium on System Synthesis, 1997. Washington, DC: IEEE Computer Society, 1997.Google Scholar
Hosangadi, A., Fallah, F., and Kastner, R., Common subexpression elimination involving multiple variables for linear DSP synthesis, IEEE International Conference on Application-Specific Architectures and Processors, 2004. Washington, DC: IEEE Computer Society, 2004.Google Scholar
Chatterjee, A., Roy, R. K., and D'Abreu, M. A., Greedy hardware optimization for linear digital circuits using number splitting and refactorization, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 1(4), 423–31, 1993.CrossRefGoogle Scholar
Nguyen, H. T. and Chatterjee, A., Number-splitting with shift-and-add decomposition for power and hardware optimization in linear DSP synthesis, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 8, 419–24, 2000.CrossRefGoogle Scholar
Puschel, M., Singer, B., Xiong, J., et al., SPIRAL: a generator for platform-adapted libraries of signal processing algorithms, Journal of High Performance Computing and Applications, 18, 21–45, 2004.CrossRefGoogle Scholar
Kastner, R., Ogrenci-Memik, S., Bozorgzadeh, E., and Sarrafzadeh, M., Instruction generation for hybrid reconfigurable systems, International Conference on Computer Aided Design. New York, NY: ACM, 2001.Google Scholar
Peymandoust, A., Pozzi, L., Ienne, P., and Micheli, G., Automatic instruction set extension and utilization for embedded processors, IEEE International Conference on Application-Specific Systems, Architectures, and Processors, 2003. Washington, DC: IEEE Computer Society, 2003.Google Scholar
,Tensilica Inc., http://www.tensilica.com.
Muchnick, S. S., Advanced Compiler Design and Implementation, San Francisco, CA: Morgan Kaufmann Publishers, 1997.Google Scholar
Deschamps, J. P., Bioul, G. J. A., and Sutter, G. D., Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems, New York, NY: Wiley-Interscience (2006).Google Scholar
Meyer-Baese, U., Digital Signal Processing with Field Programmable Gate Arrays, third edition. Springer, 2007.Google Scholar
Fang, C. Fang, Rutenbar, R. A., Puschel, M., and Chen, T., Toward efficient static analysis of Finite-Precision effects in DSP applications via affine arithmetic modeling, Design Automation Conference. New York, NY: ACM, 2003.Google Scholar

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  • Introduction
  • Ryan Kastner, University of California, San Diego, Anup Hosangadi, University of California, Santa Barbara, Farzan Fallah, Stanford University, California
  • Book: Arithmetic Optimization Techniques for Hardware and Software Design
  • Online publication: 03 May 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511712180.002
Available formats
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Save book to Dropbox

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  • Introduction
  • Ryan Kastner, University of California, San Diego, Anup Hosangadi, University of California, Santa Barbara, Farzan Fallah, Stanford University, California
  • Book: Arithmetic Optimization Techniques for Hardware and Software Design
  • Online publication: 03 May 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511712180.002
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Introduction
  • Ryan Kastner, University of California, San Diego, Anup Hosangadi, University of California, Santa Barbara, Farzan Fallah, Stanford University, California
  • Book: Arithmetic Optimization Techniques for Hardware and Software Design
  • Online publication: 03 May 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511712180.002
Available formats
×