Method and apparatus to reduce the size of rom used in mathemati

Details Method and apparatus to reduce the size of rom used in mathemati Method and apparatus to reduce the size of rom used in mathemati

1996-06-28

1999-02-09

Elmore, Reba I.

Boots, shoes, and leggings

G06F 738

Patent

active

058703217

ABSTRACT:
A method and apparatus for implementing mathematical functions of the nature of f(x). The range of values for the value of x (e.g., from 1 to 2 when x is represented in a floating point form) is divided into two intervals. Instead of using a single memory, such as a ROM, to store values for f(x) for the range of values for x, the f(x) values are stored in two such memory devices, one for each of the two subdivided intervals of x. Because the spacing between values for x in the two intervals are different, the combined size of the two memory devices is smaller than the size of a single ROM to achieve the same precision for the value of x. A selector circuit is used to select which of the ROM outputs represents the appropriate value for f(x) based on the value of x. The value for f(x) is then supplied to an optimizing element that implements the Newton-Raphson algorithm which makes the value for f(x) more precise.

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Swokowski, Earl W., Calculus with Analytic Geometry, alternate ed., Sec. 5.2, pp. 232-237, Prindle, Weber & Schmidt, 1983.
Handbook of Applicable Mathematics, editors: Ledermann, Walter; and Vajda, Steven, Appendix C, pp. 502-504, John Wiley & Sons, 1982.

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