Method and apparatus for exponential/logarithmic computation

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G06F 738

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active

051970244

ABSTRACT:
A method and apparatus for use in or with a general-purpose computing environment employs particularly efficient exponential and logarithmic function generation in combination with a logarithmic data format, herein called an exponential/logarithmic (E/L) or exponential floating-point (E-FLP) computational system, to attain general-purpose exponential floating-point (E-FLP) numerical processing comparable in effectiveness to conventional floating-point (C-FLP) processing of similiar precision and dynamic range. An E/L (or E-FLP) quantity according to the invention has an exponential floating-point (E-FLP) value that is inferred from its logarithmic fixed-point (L-FXP) representation or "format" value which when employed with exponential and logarithmic transformations according to the invention yields rapid and precise computational results. [Direct combinatorial construction provides increased speed in microprogrammed embodiments and provides pipe-lined operation in embodiments routing operands in close sequence.] E-FLP computations and their associated L-FXP implementations are disclosed, including the elementary transcendental functions (exponential, logarithm, sine, cosine, tangent and their inverses, etc.). E-FLP computations are characterized by fast multiplication-oriented arithmetic and particularly fast logarithms, exponentials, powers and roots.

REFERENCES:
patent: 3099742 (1963-07-01), Bryne et al.
patent: 3194951 (1965-07-01), Shaefer
patent: 3402285 (1964-09-01), Wang
patent: 3436533 (1969-04-01), Moore et al.
patent: 4046999 (1977-09-01), Katsuoka et al.
patent: 4062014 (1977-12-01), Rothgordt et al.
patent: 4063082 (1977-12-01), Nussbaumer
patent: 4158889 (1979-06-01), Monden
patent: 4583180 (1986-04-01), Kmetz
patent: 4720809 (1988-01-01), Taylor
patent: 4727508 (1988-02-01), Williams
patent: 4747067 (1988-05-01), Jagodnik, Jr. et al.
patent: 4823301 (1989-04-01), Knierim
patent: 4839846 (1989-06-01), Hirose et al.
Combet et al., "Computation of the Base Two Logarithm of Binary Numbers", IEEE Transactions on Electronic Computers, pp. 863-867, 1965.
Swartzlander, Jr. et al., "The Sign/Logarithm Number System", IEEE Transactions on Computers, pp. 1238-1242, 1978 (Dec.).
Lee et al., "The Focus Number System", IEEE Transactions on Computers, pp. 1167-1170, Nov. 1970.
Edgar et al., "Focus Micro-Computer Number System", Communications of the ACM, vol. 22, No. 3, Mar. 1979, pp. 166-177.
Lo et al., "A Hardwired Generalized Algorithm for Generating the Logarithm Base-K by Iteration", IEEE Transactions on Computers, vol. 36, No. 11, Nov. 1987, pp. 1363-1367.
N. G. Kingsbury and P. J. W. Rayner, "Digital Filtering Using Logarithmic Arithmetic", Electronic Letters, Jan. 28, 1971, 56-58.
"Integrated-Circuit Logarithmic Arithmetic Units", IEEE Computer Transactions, May 1985, 475-483, J. H. Lang et al.
"A 20-Bit Logarithmic Number Processor", IEEE Computer Transactions, Feb., 1988, 190-200, F. J. Taylor et al.
T. Stouraitis and F. J. Taylor, "Analysis of Logarithmic Number System Processors", Transactions on Circuits and Systems, May, 1988, 519-527.
"A Simple but Realistic Model of Floating-Point Computation", W. S. Brown, ACM Transactions on Mathematical Software, vol. 7, No. 4, Dec., 1981.
"Handbook of Mathemical Functions with Formulas, Graphs, and Mathematical Tables", Edited by Milton Abramowitz and Irene A. Stegun, National Bureau of Standards Applied Mathematics Series 55, Issued Jun., 1964.
"The Implementation of Logarithmic Arithmetic", by A. Bechtosheim and T. Gross, Computer Systems Laboratory, Stanford University Dec. 1, 1980.
"A Parallel Search Table for Logarithmic Arithmetic", by A. Bechtosheim and T. Gross, Computer Systems Laboratory, Stanford University, Mar. 15, 1980.
"Redundant Logarithmic Arithmetic", IEEE Transactions on Computer, vol. 39, No. 8, Aug. 1990, 1077-1086, by M. G. Arnold, T. A. Bailey, J. R. Cowles and J. J. Cupal.
"Extending the Precision of the Sign Logarithm Number System" (M. S. Thesis) M. G. Arnold, University of Wyoming, Laramie, Wyoming, Jul. 1982.
"A Class of Algorithms for Automatic Evaluation of Certain Elementary Functions in a Binary Computer", Thesis by Bruce Gene DeLugish, 1970 (pp. 49-56; 7-15; 25-37).
The TTL Data Book vol. 2, 1985, Texas Instruments, pp. 3-357/366, 3-377/383, 3-577/581, 3-709/720, 3-851/855, 3-857/861, 3-895/898, 3-917/921 and 3-922/925.
1956 edition of Webster's New Collegiate Dictionary by G. & C. Merriam Co., pp. 22, 529, 575, 672-673 and 787.
1983 edition of Webster's New Universal Unabridged Dictionary by Simon & Shuster, pp. 45, 1134, 1227-1228, 1434 and 1688.
"A 10-ns Hybrid Number System Data Execution Unit for Digital Signal Processing Systems", IEEE Journal of Solid-State Circuits, vol. 26, Bi, 4, Apr. 1991, pp. 590-599, by F. Lai.
IBM Research Report RC 14521 (#64941), Mar. 22, 1989 entitled "A Hybrid Number System Processor with Geometric and Complex Arithmetic Capabilities", by F. Lai et al.
Article entitled "Uncalculated Art", Science, May 24, 1991, p. 1185.

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