Complex Function Approximation Using Two-Dimensional Interpolation

This paper presents a new scheme for evaluating complex reciprocal and exponential functions in hardware. The proposed method utilizes a two-dimensional convolution algorithm to interpolate bivariate functions from tabulated function values in the complex domain. To reduce the memory requirements fo...

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Bibliographic Details
Published in:IEEE transactions on computers Vol. 63; no. 12; pp. 2948 - 2960
Main Authors: Wang, Dong, Ercegovac, Milos D., Xiao, Yang
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximation error
complex exponential
complex function evaluation
Complex reciprocal
Computational complexity
cubic interpolation
Function approximation
Lagrange interpolation
Lagrangian functions
linear interpolation
Personal computers
quadratic interpolation
Quadratic programming
two-dimensional interpolation
ISSN:0018-9340, 1557-9956
Online Access:Get full text
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Summary:This paper presents a new scheme for evaluating complex reciprocal and exponential functions in hardware. The proposed method utilizes a two-dimensional convolution algorithm to interpolate bivariate functions from tabulated function values in the complex domain. To reduce the memory requirements for lookup tables, the interpolation is decomposed into independent row and column computations, such that the same coefficient table can be shared. Three different interpolation kernels from degree-1 (linear) to degree-2 (quadratic Lagrange) and degree-3 (cubic Lagrange) are explored to find the optimal design parameters and the most acceptable trade-offs between performance and hardware resources. Moreover, a generic hardware architecture is designed to provide scalable implementation capabilities for computation precision and interpolation degree. To verify the proposed architecture, eight complex reciprocal and eight complex exponential design instances are implemented. The ASIC- and FPGA-based experimental results show that the proposed scheme can efficiently approximate the complex reciprocal and exponential functions with up to 16-bit precision, as well as achieve a considerable reduction of memory requirements compared with traditional bipartite and multipartite schemes. The proposed method is also applicable to other complex functions.
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2013.181