Implementation of 2-x function using polynomial approximation
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Date
2022-10
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G. B. Pant University of Agriculture and Technology, Pantnagar
Abstract
The primary building block of arithmetic circuits is the implementation of elementary functions. Commonly utilised building blocks in sophisticated algorithms include elementary functions like logarithms, exponentials, trigonometric functions, square roots, and inverse square roots. With a limited amount of arithmetic operations, it is impossible to compute elementary functions precisely, only an approximation of these functions is obtainable. The aim of the proposed work is to implement one of the elementary functions i.e., ‘2-X’ which is a frequently used function in digital signal processing, machine learning, artificial intelligence and is frequently utilised in a variety of scientific application. So, we proposed to design an architecture of a polynomial approximation based 2-X function using polynomial approximation. This architecture is implemented with hybrid method and curve fitting techniques with linear and quadratic polynomial approximation method. Further, in the proposed architecture number of segments are increased to reduce error characteristics and to improve accuracy. The designed architecture is simulated using Verilog Xilinx ISE Design Suite software with Isim simulator and MATLAB simulation tools. The results show that both the architecture design methods provide the flexibility that one may choose either the linear approximation for shorter latency or the quadratic approximation for relative high accuracy result. The maximum error of proposed architecture is reduced in comparision to the previously described architecture. So, proposed architecture has better accuracy than previous architecture at the cost of small increase in memory.