NDLI: An interpolating memory unit for function evaluation: analysis and design

Content Provider	IEEE Xplore Digital Library
Author	Noetzel, A.S.
Copyright Year	1968
Abstract	A technique for the evaluation of a general continuous function f(x) is presented, and the design of an interpolating memory as an implementation of the technique is described. The technique partitions the domain of f(x) into segments and defines an interpolating (or approximating) function for each. The implementation is a memory subsystem that holds the parameters of the approximating functions and yields an interpolated function value on each read reference. Polynomial interpolating functions are considered in particular. Hardware requirements (memory and computational logic) are analyzed in terms of the required precision. It is shown that as long as f(x) has d+1 derivatives, where d is the degree of the interpolating polynomial, d+1 additional bits of precision of the computed f(x) are obtained for each additional address bit used in the interpolating memory. This establishes a tradeoff between memory and computational logic, which can be exploited in the design of a unit for a specific function, for any precision requirement. Furthermore, a single unit can be designed for any class of functions that have the required derivatives. Two examples of implementations for particular functions are presented.<>
Sponsorship	IEEE Computer Society Technical Committee on Distributed Process IEEE Computer Society Technical Committee on VLSI IEEE Technical Committee on Computer Architecture IEEE Computer Society
Starting Page	377
Ending Page	384
Page Count	8
File Size	776442
File Format	PDF
ISSN	00189340
Volume Number	38
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1989-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Hardware Piecewise linear approximation Logic design Polynomials Arithmetic Interpolation Computer applications Signal processing Linear approximation Computer errors
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Software Hardware and Architecture

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