Actas de congresos
Optimized Math Functions For A Fixed-point Dsp Architecture
Registro en:
9780769530147
Proceedings - Symposium On Computer Architecture And High Performance Computing. , v. , n. , p. 125 - 132, 2007.
15506533
10.1109/SBAC-PAD.2007.33
2-s2.0-47249120791
Autor
Lenzi K.G.
Saotome O.
Institución
Resumen
This paper presents a method for implementing several high-performance math functions through polynomial approximation on the fixed-point Blackfin ADSP-BF533 architecture. We present a strategy to overcome the performance given by the Blackfin's C library using a fast emulated floating-point format. We also discuss the methods applied to generate the polynomial approximation for the sine, logarithmic, and exponential functions, as well as the optimization schemes used to implement these functions. This work contributed to a maximum cycle reduction of 85% over the standard math library. © 2007 IEEE.
125 132 Cullen, K.B., Guenole, C.M., Hurley, N.J., Simulation Tools For Fixed Point DSP Algorithms and Architectures (2004) International Journal of Digital Signal Processing, 1 (3) Berkeley Design Technology Inc. (2007) A Survey of Mainstream DSP Processors, Inside DSP Articles at http://www.insidedsp.com/Articles/ tabid/64/PageID/297/Arti cleID/202/articleType/Article View/Default, aspxTrombetta, R., O'Gara, T., (2005) Floating Point Implementations on Fixed Point DSP Architectures, , http://www.ecnmag.com/article.aspx?id=133162, at Katz, D., Gentile, R., Lukasiak, T., (2003) Floating-Point Emulation on Fixed-Point DSPs is Becoming Practical, , http://www.reedelectronics.com/ecnmag/index.asp?layout=article&artic leid=CA267186, at Menard, D., Charot, F., Automatic Floating-point to Fixed-point Convertion for DSP Code Generation (2002) ACM Proceedings of the 2002 International Conference on Compilers, Architecture, and Synthesis for Embedded Systems Iordache, C., Tang, P.T.P., An Overview of Floating-Point Support and Math Library on the Intel Xscale Architecture (2003) IEEE Proceedings of 16th Symposium on Computer Arithmetic Franz, G., Simar, R., (2004) Comparing Fixed- and Floating-Point DSPs, , White Paper, Texas Instruments (2006) Programa de Satélites Universitários, , http://www.itasat.ita.br, ITASAT, at Analog Devices, ADSP-BF533 Blackfin Processor Hardware Reference, Analog Devices, 2003(2006) Intel Micro Signal Architecture, , http://www.intel.com/design/msa, at (2007) A BDTI Analysis of the Analog Devices ADSP-BF5xx, , http://www.bdti.com/articles/blackfin_summary_report.pdf, Berkeley Design Technology Inc, at IEEE Standard for Binary Floating Point Arithmetic (1985) ANSI/IEEE Std, pp. 754-1985. , IEEE, Institute of Electrical and Electronics Engineers Goldberg, D., What Every Computer Scientist Should Know About Floating-Point Arithmetic (1991) ACM Computing Surveys, 23 (1). , March Kahan, W., (1997) Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic, , http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.pdf, at Analog Devices, EE-185: Fast Floating-Point Arithmetic Emulation on the Blackfin Processor Platform, Application Notes, Analog Devices, 2003Analog Devices, ADSP-BF533 Blackfin Processor Instruction Set, Analog Devices, 2003Brisebarre, N., Muller, J.-M., Tisserand, A., Computing Machine-Efficient Polynomial Approximation (2006) ACM Transactions on Mathematical Software, , June Rivlin, T.J., (1990) Chebyshev polynomials. From approximation theory to algebra (Second edition), , Pure and Applied Mathematics. John Wiley & Sons, New York Li, R.C., Near Optimality of Chebyshev Interpolation for Elementary Function Computation (2004) IEEE Transactions on Computers, 53 (6). , June Parks, T.W., McClellan, J.H., Chebyshev approximation for nonrecursive digital filters with linear phase (1972) IEEE Trans. Circuit Theory, CT-19 (2) Brisebarre, N., Defour, D., Kornerup, P., Muller, J.M., Revol, N., A New Range-Reduction Algorithm (2005) IEEE Transactions on Computers, , March Li, R.C., Boldo, S., Daumas, M., Theorems on Efficient Argument Reduction (2003) Proceedings of the 16th IEEE Symposium on Computer Arithmetic Payne, M., Hanek, R., Radian Reduction for Trigonometric Functions (1983) SIGNUM Newsletter Testa, F.J., AN660 - Floating-Point Math Functions (1997), Microchip Application NotesTang, P.T.P., Table-driven implementation of the exponential function in IEEE floating-point arithmetic (1989) ACM Transactions on Mathematical Software, , TOMS Bessalah, H., Anane, N., Anane, M., (2003) Multifunction Generator Using Horner Scheme And Small Tables, , ICM, Cairo, Egypt Cody, W.J., (1980) Software Manual for the Elementary Functions, , Prentice-Hall, New Jersey Compiler, VisualDSP++4.0 C/C++ Compiler and Library Manual for Blackfin Processors, Blackfin Manuals, Analog Devices, 2005Tang, P.T.P., Table-lookup algorithms for elementary functions and their error analysis (1991) Proceedings, 10th IEEE Symposium on Computer Arithmetic Muller, J.M., (2006) Elementary Functions: Algorithms and implementation, , Birkhauser, 2nd Ed Yang, M., Wang, J., Wang, Y., Zheng, S.Q., Optimized Parallel Implementation of Polynomial Approximation Math Functions on a DSP Processor (2001) Proceedings of the 44th IEEE Midwest Symposium on Circuits and Systems