Reciprocal Unit Based on Vedic Mathematics for Signal Processing Applications

Abstract

Vedic mathematics, is an ancient methodology, has a unique mathematical computation technique based on 16 sutras (formulae). High speed reciprocal unit based on such ancient mathematics is reported in this paper. Implementation methodology was adopted through sahayaks (auxiliary fraction) taken from such ancient mathematics and prototype was designed for practical signal processing applications. On account of the Vedic formulae, reciprocal approximation of a numbers is generated in fewer steps compared to Newton-Raphson's iteration based implementation with appreciable error in accuracy (~0.09%), offer high speed operation. The functionality of the algorithm was checked, and performance parameters like propagation delay, dynamic switching power consumption were calculated through spice spectre using 90nm CMOS technology. The propagation delay of the resulting 5-digit reciprocal unit was only ~3.57uS and consumes ~30.8mW power. The implementation methodology offered substantial reduction of propagation delay, and dynamic switching power consumption from earlier reported Newton-Raphson (NR) based implementation.

A new algorithm for the computation of the decimals of the inverse

“…Sahayaks (auxiliary fraction), a Sanskrit term from Vedas, is encountered to realize the reciprocal circuitry. This paper extends the previous paper of the same authors [13] and two others, where the inversion algorithm was introduced for the rst time to discuss circuit implementation of a division unit that uses this algorithm. With the help of the ancient methodology, reciprocal algorithm has been realized by algebraic transformation of the digits to smaller ones, and the overall division has been carried out through the transformed digits; thereby, circuit complexity has been reduced substantially due to reduction in propagation delay.…”

An Exhaustive Research Survey on Vedic ALU Design

“…In paper [25], P. Saha, D. Kumar, et.al, proposed a reciprocal unit using Vedic mathematics. The authors compared the proposed design with the Newton-Raphson's method to conclude that the proposed design was operating at a higher speed compared to the other.…”