Table-Lookup/Interpolation Function Generation for Fixed-Point Digital Computations

Aus, H. M.; Korn, Granino A.

doi:10.1109/t-c.1969.222758

Cited by 20 publications

(5 citation statements)

References 4 publications

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“…One of the earliest examinations of digital interpolation was performed by Aus and Korn [22] in the 1960s, who examined software routines for degree-1 interpolations for sine and cosine functions on the DEC PDP-9 platform. Lewis [11] described an interleaved memory architecture for interpolation and its application to evaluating the addition/subtraction functions in logarithmic number systems.…”

Section: Related Workmentioning

confidence: 99%

Hardware Implementation Trade-Offs of Polynomial Approximations and Interpolations

Lee¹,

Cheung

Luk

et al. 2008

IEEE Trans. Comput.

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Abstract-This paper examines the hardware implementation trade-offs when evaluating functions via piecewise polynomial approximations and interpolations for precisions of up to 24 bits. In polynomial approximations, polynomials are evaluated using stored coefficients. Polynomial interpolations, however, require the coefficients to be computed on-the-fly by using stored function values. Although it is known that interpolations require less memory than approximations, but at the expense of additional computations, the trade-offs in memory, area, delay, and power consumption between the two approaches have not been examined in detail. This work quantitatively analyzes these trade-offs for optimized approximations and interpolations across different functions and target precisions. Hardware architectures for degree-1 and degree-2 approximations and interpolations are described. The results show that the extent of memory savings realized by using interpolation is significantly lower than what is commonly believed. Furthermore, experimental results on a field-programmable gate array (FPGA) show that, for high output precision, degree-1 interpolations offer considerable area and power savings over degree-1 approximations, but similar savings are not realized when degree-2 interpolations and approximations are compared. The availability of both interpolation-based and approximation-based designs offers a richer set of design trade-offs than what is available using either interpolation or approximation alone.

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Section: Related Workmentioning

confidence: 99%

Hardware Implementation Trade-Offs of Polynomial Approximations and Interpolations

Lee¹,

Cheung

Luk

et al. 2008

IEEE Trans. Comput.

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“…Typically, this selection is made empirically, since there is a lack of systematic techniques either to evaluate the LUT accuracy or to generate it. Most of the existing methods are constrained to single input and output LUTs [35][36][37] and cannot be extended to multiple inputs and outputs LUTs [38].…”

Section: Introductionmentioning

confidence: 99%

On the generation of enhanced lookup tables for wheel-rail contact models

Marques

Magalhães

Liu

et al. 2019

Wear

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In railway dynamics, the interpolation of lookup tables (LUTs) is a procedure to reduce the computational effort when computing the wheel-rail interaction forces. However, the generation of LUTs with multiple inputs and multiple outputs is a challenging task for which issues such as their minimal size and uniform accuracy over the LUT domain have not been systematically addressed before. This work presents a comprehensive methodology for a detailed analysis of general LUTs, identifying ways to improve them. First, an analysis of the variation of the input parameters is made and the interpolation error is assessed on the cells and edges of the original table. From this analysis, two enhanced LUTs are proposed. One is approximately 5 times smaller than the original but holds similar accuracy. The other table exhibits half of the maximum interpolation error of the original LUT but holds an identical size. This methodology is demonstrated here using the recently published Kalker Book of Tables for Non-Hertzian contact (KBTNH) but it can be used by any other LUT approach in order to improve accuracy and/or to reduce size.

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“…Here, we extend that algorithm to multivariable functions defined on rectangular grids and sketch a hardware implementation for generating functions of two variables. Aus and Korn [5] describe a fast algorithm for function generation with fixed-point variables. Bilinear interpolation, described in Rubin [6], is a traditional method for generating functions of two variables in aerospace simulations.…”

Section: Introductionmentioning

confidence: 99%

Hardware Support for Multivariable Floating Point Function Generation

O'Grady

Young²

1999

SIMULATION

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A method suited for hardware implementation as sists in evaluating a multivariable, floating-point function F(X,Y,...Z) defined on an N-dimensional rectangular grid. A preprocessing stage analyzes the function's breakpoints for each dimension. It determines a subinterval range that includes the breakpoint range for that dimension and subdivides the subinterval range into equal-sized subintervals in a procedure that enables easy identification of the breakpoint interval containing a subinterval. The method's run-time stage processes the N com ponents of the input argument in parallel to iden tify the N-dimensional rectangular cell containing the input argument. At run time, two additions and a multiplication convert each component of the input argument to an index identifying the sub intervat containing it. Then two table lookups iden tify the breakpoint interval containing the sub interval. An implementation of a two-variable function generator that uses bilinear interpolation is sketched to illustrate application of the cell-iden tification method.

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Table-Lookup/Interpolation Function Generation for Fixed-Point Digital Computations

Cited by 20 publications

References 4 publications

Hardware Implementation Trade-Offs of Polynomial Approximations and Interpolations

Hardware Implementation Trade-Offs of Polynomial Approximations and Interpolations

On the generation of enhanced lookup tables for wheel-rail contact models

Hardware Support for Multivariable Floating Point Function Generation

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