Optimized custom precision function evaluation for embedded processors

IEEE Transactions on Computers

Volumn 58, Issue 1, 2009, Pages 46-59

  Lee, Dong U ^a   Villasenor, John D ^b  

^a Mojix   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Computer arithmetic; Elementary function approximation; Minimax approximation and algorithms; Processors; Real time and embedded systems; Simulated annealing; Spline and piecewise polynomial approximation

Indexed keywords

APPROXIMATION ALGORITHMS; AUTOMATION; CHEBYSHEV APPROXIMATION; CODES (SYMBOLS); CONFORMAL MAPPING; DIGITAL ARITHMETIC; EMBEDDED SYSTEMS; FUNCTION EVALUATION; FUNCTIONS; INTEGRATED CIRCUITS; PROBABILITY DENSITY FUNCTION; REAL TIME SYSTEMS; SIMULATED ANNEALING;

COMPUTER ARITHMETIC; ELEMENTARY FUNCTION APPROXIMATION; MINIMAX APPROXIMATION AND ALGORITHMS; PROCESSORS; REAL-TIME AND EMBEDDED SYSTEMS;

POLYNOMIAL APPROXIMATION;

EID: 57349119881     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/TC.2008.124     Document Type: Article

References (33)

1. C. Inacio and D. Ombres, "The DSP Decision: Fixed Point or Floating," IEEE Spectrum, vol. 33, no. 9, pp. 72-74, 1996.
2. "Fast Floating-Point Arithmetic Emulation on the Blackfin Processor Platforms (Engineer to Engineer Note: EE-185)," Analog Devices, 2003.
3. S. Gal and B. Bachelis, "An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard," ACM Trans. Math. Software, vol. 17, no. 1, pp. pp. 26-45, 1991.
4. "Extended-Precision Fixed-Point Arithmetic on the Blackfin Processor Platform (Engineer to Engineer Note: EE-186)," Analog Devices, 2003.
5. G. Constantinides and G. Wöginger, "The Complexity of Multiple Wordlength Assignment," Applied Math. Letters, vol. 15, no. 2, pp. 137-140, 2001.
6. V. Lefevre, J. Muller, and A. Tisserand, "Toward Correctly Rounded Transcendentals," IEEE Trans. Computers, vol. 47, no. 11, pp.1235-1243, Nov. 1998.
7. J. Muller, Elementary Functions: Algorithms and Implementation. Birkhauser Verlag, 1997.
8. P. Markstein, IA-64 and Elementary Functions: Speed and Precision. Prentice Hall, 2000.
9. R. Cheung, D. Lee, O. Mencer, W. Luk, and P. Cheung, "Automating Custom-Precision Function Evaluation for Embedded Processors," Proc. ACM/IEEE Int'l Conf. Compilers, Architecture, and Synthesis for Embedded Systems (CASES '05), pp. 22-31, 2005.
10. G. Bandera, M. Gonzalez, J. Villalba, J. Hormigo, and E. Zapata, "Evaluation of Elementary Functions Using Multimedia Features," Proc. 18th IEEE Int'l Parallel and Distributed Processing Symp. (IPDPS '04), p. 90a, 2004.
11. C. Iordache and P. Tang, "An Overview of Floating-Point Support and Math Library on the Intel XScale Architecture," Proc. 16th IEEE Symp. Computer Arithmetic (ARITH '03), pp. 122-127, 2003.
12. C. Thron, "How to Code Fast, Accurate Math Functions on DSP Parallel Devices," Embedded.com article, http://www.embedded.com/ showArticle.jhtml?articleID=47901094, 2004.
13. "C24x Fixed Point Math Library Model User's Guide," Texas Instruments, http://focus.ti.com/docs/toolsw/folders/print/sprc068. html, 2002.
14. F. Testa, "Floating Point Math Functions," Microchip Application Note (AN660), http://ww1.microchip.com/downloads/en/AppNotes/ 00660.pdf, 1997.
15. S. Kim, K. Kum, and W. Sung, "Fixed-Point Optimization Utility for C and C++ Based Digital Signal Processing Programs," IEEE Trans. Circuits and Systems II, vol. 45, no. 11, pp. 1455-1464, 1998.
16. H. Keding, M. Willems, M. Coors, and H. Meyr, "FRIDGE: A Fixed-Point Design and Simulation Environment," Proc. ACM/IEEE Design Automation and Test in Europe (DATE '98), pp. 429-435, 1998.
17. K. Kum, K. Kang, and W. Sung, "AUTOSCALER for C: An Optimizing Floating-Point to Integer C Program Converter for Fixed-Point Digital Signal Processors," IEEE Trans. Circuits and Systems II, vol. 47, no. 9, pp. 840-848, 2000.
18. N. Doi, T. Horiyama, M. Nakanishi, and S. Kimura, "Minimization of Fractional Wordlength on Fixed-Point Conversion for High-Level Synthesis," Proc. ACM/IEEE Asia and South Pacific Design Automation Conf. (ASP-DAC '04), pp. 80-85, 2004.
19. D. Lee, A. Abdul Gaffar, O. Mencer, and W. Luk, "MiniBit: BitWidth Optimization via Affine Arithmetic," Proc. 42nd ACM/IEEE Design Automation Conf. (DAC '05), pp. 837-840, 2005.
20. W. Cody and W. Waite, Software Manual for the Elementary Functions Prentice Hall, 1980.
21. D. Knuth, The Art of Computer Programming: Seminumerical Algorithms vol. 2, third ed. Addison-Wesley, 1997.
22. D. Lee, W. Luk, J. Villasenor, and P. Cheung, "Hierarchical Segmentation Schemes for Function Evaluation," Proc. IEEE Int'l Conf. Field-Programmable Technology (FPT '03), pp. 92-99, 2003.
23. L. de Figueiredo and J. Stolfi, "Self-Validated Numerical Methods and Applications," Brazilian Math. Colloquium Monograph, IMPA, 1997.
24. L. Ingber, "Adaptive Simulated Annealing (ASA) 25.15," http:// www.ingber.com/#ASA, 2004.
25. D. Lee, A. Abdul Gaffar, R. Cheung, O. Mencer, W. Luk, and G. Constantinides, "Accuracy-Guaranteed Bit-Width Optimization," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 25, no. 10, pp. 1990-2000, 2006.
26. "ILOG CPLEX 9.0, User's Manual," ILOG, http://www.ilog.com/products/cplex, 2003.
27. "8-Bit AVR Microcontroller with 128K Bytes In-System Programmable Flash ATmega128 Summary,"Atmel, 2004.
28. "TMS320C6000 CPU and Instruction Set Reference Guide (SPRU189F)," Texas Instruments, 2000.
29. AVR Studio 4.12, Atmel, http://www.atmel.com/dyn/products/ tools_card.asp?tool_id=2725, 2005.
30. "Code Composer Studio Development Tools v3.1 Getting Started Guide (SPRU509F)," Texas Instruments, http://focus.ti.com/lit/ug/spru509f/ spru509f.pdf, 2005.
31. B. Huber, How to Write Multiplies Correctly in C Code, Texas Instruments Application Report (SPRA683), http://focus.ti.com/lit/an/ spra683/spra683.pdf, 2000.
32. P. Kulkarni, D. Ganesan, P. Shenoy, and Q. Lu, "SensEye: A Multi-Tier Camera Sensor Network," Proc. ACM Int'l Conf. Multimedia (Multimedia '05), pp. 229-238, 2005.
33. M. Rahimi, R. Baer, O. Iroezi, J. Garcia, J. Warrior, D. Estrin, and M. Srivastava, "Cyclops: In Situ Image Sensing and Interpretation in Wireless Sensor Networks," Proc. Third ACM Conf. Embedded Networked Sensor Systems (SenSys '05), pp. 192-204, 2005.