Symmetric table addition method for accurate function approximation

Journal of VLSI Signal Processing Systems for Signal, Image, and Video Technology

Volumn 21, Issue 2, 1999, Pages 167-177

  Stine, James E ^a,b   Schulte, Michael J ^a  

^a Lehigh University   (United States)

^b LEHIGH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; PARALLEL PROCESSING SYSTEMS; TABLE LOOKUP;

MULTI-OPERAND ADDITION; SYMMETRIC TABLE ADDITION METHOD;

VLSI CIRCUITS;

EID: 0032680765     PISSN: 09225773     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008004523235     Document Type: Article

References (36)

1. V.K. Jain, G.E. Perez, and J.M. Wills, "Novel reciprocal and square-Root VLSI cell: Architecture and application to signal processing" International Conference on Acoustics, Speech and Signal Processing, Vol. 2, pp. 1201-1204, 1991.
2. V.K. Jain and L. Lin, "Square-root, reciprocal, sine/cosine, arctangent cell for signal and image processing," International Conference on Acoustics, Speech and Signal Processing, Vol. 2, pp. 521-524, 1994.
3. H. Kwan, R.L. Nelson, and E.E. Swartzlander, Jr., "Cascaded implementation of an iterative inverse-square-root algorithm with overflow lookahead," Proceedings of the 12th Symposium on Computer Arithmetic, pp. 114-123, 1995.
4. M. Zhang, S. Vassiliadis, and J.G. Delgado-Frias, "Sigmoid generators for neural computing using piecewise approximations," IEEE Transactions on Computers, Vol. 45, No. 9, pp. 1045-1050, 1996.
5. S. Mehrgardt, "Noise spectra of digital sine-generators using the table-lookup method," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 31, No. 4, pp. 1037-1039, 1983.
6. J.A. McIntosh and E.E. Swartzlander, Jr., "High-speed cosine generator," Conference record of the Twenty-Eighth Asilomar Conference on Signals, Systems and Computers, pp. 273-277, 1994.
7. J. McClellan, R. Schafer, and M. Yoder, DSP First: A Multimedia Approach, Prentice Hall, 1998.
8. D.M. Lewis, "114 MFLOPS logarithmic number system arithmetic unit for DSP applications," IEEE Journal of Solid-State Circuits, Vol. 30, No. 12, pp. 1547-1553, 1995.
9. H.-C. Shin, J.-A. Lee, and L.-S. Kim, "A minimized hardware architecture of fast Phong shader using taylor series approximation in 3D graphics," Proceedings of the International Conference on Computer Design. VLSI in Computers and Processors, pp. 286-291, 1998.
10. AltiVec Technology Programming Environments Manual. Motorola, Inc., 1998.
11. 3DNow! Technology Manual, Nov. 1998, available at http:// www.amd.com/K6/k6docs/.
12. M.J. Flynn, "On division by functional iteration," IEEE Transactions on Computers, Vol. C-19, pp. 702-706, 1970.
13. S.F. Oberman and M.J. Flynn, "Division algorithms and implementations," IEEE Transactions on Computers, Vol. C-46, pp. 833-854, 1997.
14. D.D. Sarma and D.W. Matula, ""Measuring the accuracy of ROM reciprocal tables," Proceedings of the 11th Symposium on Computer Arithmetic, pp. 95-102, July 1993.
15. C.V. Ramamoorthy and J. Goodman, "Some properties of iterative square-rooting methods using high-speed multiplication," IEEE Transactions on Computers, Vol. C-21, pp. 837-847, 1972.
16. W. Cody and W. Waite, Software Manual for the Elementary Functions, Prentice-Hall, 1980.
17. J.F. Hart et al., Computer Approximations, Wiley, 1968.
18. J.S. Walther, "A unified approach for elementary functions," Spring Joint Computer Conference, pp. 379-385, 1971.
19. J.-M. Muller, Elementary Functions: Algorithms and Implementation, Birkhauser, Boston, 1997.
20. T. Lynch, A. Ahmed, M.J. Schulte, T. Callaway, and R. Tisdale, "The K5 transcendental functions," Proceedings of the 12th Symposium on Computer Arithmetic, pp. 222-229, 1995.
21. W. Ferguson and T. Brightman, "Accurate and monotone approximations of some transcendental functions," Proceedings of the 10th Symposium on Computer Arithmetic, pp. 237-244, 1991.
22. Intel Pentium Processor Data Book, Intel Corporation, 1994.
23. M.J. Schulte and E.E. Swartzlander, Jr., "Hardware designs for exactly rounded elementary functions," IEEE Transactions on Computers, Vol. C-44, pp. 964-973, 1994.
24. P. Farmwald, "High bandwidth evaluation of elementary functions," Proceedings of the 5th Symposium on Computer Arithmetic, pp. 139-142, 1981.
25. I. Koren, Computer Arithmetic and Algorithms, Prentice Hall, 1993.
26. J.E. Volder, "The CORDIC trigonometric computing technique," IRE Transactions on Electronic Computers, Vol. EC-8, pp. 330-334, 1959.
27. G.H. Haviland and A.A. Tuszynski, "A CORDIC arithmetic processor," IEEE Transactions on Computers, Vol. C-29, pp. 68-79, 1980.
28. S.F. Hsiao and J.M. Delosme, "Householder CORIDC algorithms," IEEE Transactions on Computers, Vol. C-44, pp. 990-1000, 1995.
29. Sematech, Inc., The National Technology Roadmap for Semiconductors, 1997, available at http://notes.sematech.org/~97 pelec.htm.
30. A.R. Pelella et al., "A 2-nanosecond access, 500 MHz, 288Kb SRAM macro," Symposium on VLSI Circuits, Digest of technical papers, pp. 309-318, 1995.
31. H. Hassler and N. Takagi, "Function evaluation by table look-up and addition," Proceedings of the 12th Symposium on Computer Arithmetic, pp. 10-16, 1995.
32. D.D. Sarma and D.W. Matula, "Faithful bipartite ROM reciprocal tables," Proceedings of the 12th Symposium on Computer Arithmetic, pp. 17-29, 1995.
33. S.F. Oberman, "Floating point division and square root algorithms and implementation in the AMD-K7 microprocessor," Proceedings of the 14th Symposium on Computer Arithmetic, pp. 106-115, April 1999, in press.
34. H. Kalish and J. Isaac (Eds.), The AMD-K6 3D Processor, Abacus Software, 1998.
35. M.J. Schulte and J.E. Stine, "Symmetric bipartite tables for accurate function approximation," Proceedings of the 13th Symposium on Computer Arithmetic, pp. 175-183, 1997.
36. M.J. Schulte and J.E. Stine, "Accurate function approximations by symmetric table lookup and addition," 11th International Conference on Application-Specific Systems, Architectures, and Processors, pp. 144-153, 1997.