Semi-logarithmic number systems

IEEE Transactions on Computers

Volumn 47, Issue 2, 1998, Pages 145-161

  Muller, Jean Michel ^a,b   Scherbyna, Alexandre ^c   Tisserand, Arnaud ^b  

^a IEEE   (France)

^b UNIVERSITÉ DE LYON   (France)

^c State Technical University   (Ukraine)

Author keywords

Floating point arithmetic; Logarithmic number systems

Indexed keywords

ALGORITHMS; DIGITAL ARITHMETIC;

SEMI LOGARITHMIC NUMBER SYSTEMS;

NUMBER THEORY;

EID: 0031999568     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/12.663760     Document Type: Article

References (28)

1. S.F. Anderson, J.G. Earle, R.E. Goldschmidt, and D.M. Powers, "The IBM 360/370 Model 91: Floating-Point Execution Unit," IBM J. Research and Development, Jan. 1967.
2. Reprinted in E.E. Swartzlander, Computer Arithmetic, vol. 1. IEEE CS Press Tutorial, 1990.
3. M.G. Arnold, T.A. Bailey, J.R. Cowles, and J.J. Cupal, "Redundant Logarithmic Number Systems," Proc. Ninth Symp. Computer Arithmetic, M.D. Ercegovac and E.E. Swartzlander, eds., pp. 144-151, Santa Monica, Calif., Sept. 1989.
4. M.G. Arnold, T.A. Bailey, J.R. Cowles, and M.D. Winkel, "Applying Features of IEEE 754 to Sign/Logarithm Arithmetic," IEEE Trans. Computers, vol. 41, no. 8, pp. 1,040-1,050, Aug.1992.
5. J.L. Barlow and E.H. Bareiss, "On Roundoff Error Distributions in Floating-Point and Logarithmic Arithmetic," Computing, vol. 34, pp. 324-347, 1985.
6. W.J. Cody, "Static and Dynamic Numerical Characteristics of Floating-Point Arithmetic," IEEE Trans. Computers, vol. 22, no. 6, pp. 598-601, June 1973.
7. D. Goldberg, "What Every Computer Scientist Should Know About Floating-Point Arithmetic," ACM Computing Surveys, vol. 23, no. 1, pp. 5-47, Mar. 1991.
8. R.W. Hamming, "On the Distribution of Numbers," Bell Systems Technical J., vol. 49, pp. 1,609-1,625, 1970.
9. Reprinted in E.E. Swartzlander, Computer Arithmetic, vol. 1. IEEE CS Press Tutorial, 1990.
10. H. Henkel, "Improved Addition for the Logarithmic Number Systems," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 37, pp. 301-303, 1989.
11. N.G. Kingsbury and P.J.W. Rayner, "Digital Filtering Using Logarithmic Arithmetic," Electronic Letters, vol. 7, pp. 56-58, 1971.
12. Reprinted in E.E. Swartzlander, Computer Arithmetic, vol. 1. IEEE CS Press Tutorial, 1990.
13. D.M. Lewis, "An Accurate LNS Arithmetic Using Interleaved Memory Function Interpolator," Proc. 11th Symp. Computer Arithmetic, M.J. Irwin, E.E. Swartzlander, and G. Jullien, eds., pp. 2-9, June 1993.
14. D.W. Matula and P. Kornerup, "Finite Precision Rational Arithmetic: Slash Number Systems," IEEE Trans. Computers, vol. 34, no. 1, pp. 3-18, Jan. 1985.
15. S. Matsui and M. Iri, "An Overflow/Underflow Free Floating-Point Representation of Numbers," J. Information Processing, vol. 4, no. 3, pp. 123-133, 1981.
16. Reprinted in E.E. Swartzlander, Computer Arithmetic, vol. 2. IEEE CS Press Tutorial, 1990.
17. F.W.J. Olver, "A Closed Computer Arithmetic," Proc. Eighth IEEE Symp. Computer Arithmetic, May 1987.
18. Reprinted in E.E. Swartzlander, Computer Arithmetic, vol. 2. IEEE CS Press Tutorial, 1990.
19. T. Stouraitis and F.J. Taylor, "Floating-Point to Logarithmic Encoder Error Analysis," IEEE Trans. Computers, vol. 37, pp. 858-863, 1988.
20. E.E. Swartzlander and A.G. Alexpoulos, "The Sign-Logarithm Number System," IEEE Trans. Computers, Dec. 1975.
21. Reprinted in E.E. Swartzlander, Computer Arithmetic, vol. 1, IEEE CS Press Tutorial, 1990.
22. F.J. Taylor, "An Extended Precision Logarithmic number System," IEEE Trans. Acoustics, Speech, Signal Processing, vol. 31, p. 231, 1983.
23. F.J. Taylor, R. Gill, J. Joseph, and J. Radke, "A 20 bit Logarithmic Number System Processor," IEEE Trans. Computers, vol. 37, no. 2, pp. 190-200, Feb. 1988.
24. P.R. Turner, "The Distribution of Leading Significant Digits," IMA J. Numerical Analysis, vol. 2, pp. 407-412, 1982.
25. P.R. Turner, "Further Revelations on LSD," IMA J. Numerical Analysis, vol. 4, pp. 225-231, 1984.
26. P.R. Turner, "Implementation and Analysis of Extended SLI Operations," Proc. 10th IEEE Symp. Computer Arithmetic, P. Kornerup and D. Matula, eds., pp. 118-126, June 1991.
27. P.R. Turner, "Complex SLI Arithmetic: Representation, Algorithms, and Analysis," Proc. 11th Symp. Computer Arithmetic, M.J. Irwin, E.E. Swartzlander, and G. Jullien, eds., pp. 18-25, June 1993.
28. H. Yokoo, "Overflow/Underflow-Free Floating-Point Number Representations with Self-Delimiting Variable-Length Exponent Fields," IEEE Trans. Computers, vol. 41, no. 8, pp. 1,033-1,039, Aug. 1992.