Methods and apparatus for determining approximating...

Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed

Reexamination Certificate

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Reexamination Certificate

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07325022

ABSTRACT:
Methods and apparatus for determining approximating polynomials using instruction-embedded coefficients are disclosed. In particular, the methods and apparatus use a plurality of coefficient values stored in a plurality of instructions. The coefficient values are associated with a runtime approximating polynomial of a K-th root family function. The coefficient values and the instructions stored in an instruction memory enable the processor system to determine a K-th root family function approximation value based on the runtime approximating polynomial.

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M.J.D. Powell. “Approximation Theory and Methods.” Cambridge University Press, May 1981. pp. 85-95. ISBN: 0521295149.
“IEEE Standard for Floating-point Arithmetic.” ANSI/IEEE Standard 754-1985. Published by The Institute of Electrical and Electronics Engineers, Inc., New York, New York. 1985.
Ping Tak Peter Tang. “Table-lookup Algorithms for Elementary Functions and Their Error Analysis.” Proceedings of the 10thSymposium on Computer Architecture, pp. 232-236. Grenoble, 1991.
Cornea-Hasegan, M; Norin B. “IA-64 Floating-poing Operations and the IEEE Standard for Binary Floating-point Arithmetic.” Intel Technology Journal Q4, 1999. http://www.intel.com/technology/itj/q41999/pdf/ia64fpbf.pdf.

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