REALM: Reduced-Error Approximate Log-based Integer Multiplier
Hassaan Saadat1,a, Haris Javaid2, Aleksandar Ignjatovic1,b and Sri Parameswaran1,c
1The University of New South Wales, Sydney, Australia
ah.saadat@unsw.edu.au
ba.ignjatovic@unsw.edu.au
csri.parameswaran@unsw.edu.au
2Xilinx Inc., Singapore
harisj@xilinx.com
ABSTRACT
We propose a new error-configurable approximate unsigned integer multiplier named REALM. It incorporates a novel error-reduction method into the classical approximate log-based multiplier. Each power-of-two-interval of the input operands is partitioned into M×M segments, and an errorreduction factor for each segment is analytically determined. These error-reduction factors can be used across any powerof- two-interval, so we quantize only M2 factors and store them in the form of read-only hardwired lookup tables to keep the resource overhead to a minimum. Error characterization of REALM shows that it achieves very low error bias (mostly ≤0.05%), along with lower mean error (from 0.4% to 1.6%), and lower peak error (from 2.08% to 7.4%) than the classical approximate log-based multiplier and its state-of-the-art derivatives (mean errors ≥2.6% and peak errors ≥7.8%). Synthesis results using TSMC 45nm standard-cell library show that REALM enables significant power-efficiency (66% to 86% reduction) and area-efficiency (50% to 76% reduction) when compared with the accurate integer multiplier. We show that REALM produces Pareto optimal design trade-offs in the design space of state-of-the-art approximate multipliers. Application-level evaluation of REALM demonstrates that it has negligible effect on the output quality.
