Abstract
Interpolation is a useful technique for storage of complex functions on limited memory space: some few sampling values are stored on a memory bank, and the function values in between are calculated by interpolation. This paper presents a programmable Look-Up Table-based interpolator, which uses a reconfigurable nonuniform sampling scheme: the sampled points are not uniformly spaced. Their distribution can also be reconfigured to minimize the approximation error on specific portions of the interpolated function’s domain. Switching from one set of configuration parameters to another set, selected on the fly from a variety of precomputed parameters, and using different sampling schemes allow for the interpolation of a plethora of functions, achieving memory saving and minimum approximation error. As a study case, the proposed interpolator was used as the core of a programmable noise generator—output signals drawn from different Probability Density Functions were produced for testing FPGA implementations of chaotic encryption algorithms. As a result of the proposed method, the interpolation of a specific transformation function on a Gaussian noise generator reduced the memory usage to 2.71% when compared to the traditional uniform sampling scheme method, while keeping the approximation error below a threshold equal to 0.000030518.
Highlights
A Programmable Look-Up Table-Based Interpolator with Nonuniform Sampling SchemeElvio Carlos Dutra e Silva Junior, Leandro Soares Indrusiak, Weiler Alves Finamore, and Manfred Glesner
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Precise Inferior Limit (PIL) and the Corrected Superior Limit (CSL) of each partition n are calculated by (2) and (3) which use a constant binary decimal point position (d = 14), the function signal Sg(a), which outputs the values −1 or +1 according to the signal negative or positive of a given argument a (notice that for a null argument, Sg(0) = 0), and the function round R(b/c), which calculates the maximum multiple of the argument c, less or equal to them the argument b (note that the symbol / used on the representation of the function round R(b/c) has no relation to the division operation)
Summary
Elvio Carlos Dutra e Silva Junior, Leandro Soares Indrusiak, Weiler Alves Finamore, and Manfred Glesner. This paper presents a programmable LookUp Table-based interpolator, which uses a reconfigurable nonuniform sampling scheme: the sampled points are not uniformly spaced. Their distribution can be reconfigured to minimize the approximation error on specific portions of the interpolated function’s domain. Switching from one set of configuration parameters to another set, selected on the fly from a variety of precomputed parameters, and using different sampling schemes allow for the interpolation of a plethora of functions, achieving memory saving and minimum approximation error. As a result of the proposed method, the interpolation of a specific transformation function on a Gaussian noise generator reduced the memory usage to 2.71% when compared to the traditional uniform sampling scheme method, while keeping the approximation error below a threshold equal to 0.000030518
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