HyPPO: Hybrid Piece-wise Polynomial Approximation and Optimization for Hardware Efficient Designs
Lakshmi Sai Niharika Vulchi, Pranathi Valipireddy, Mahati Basavaraju, Madhav Rao · 2025
Piece-wise polynomial approximation - linear (PWL) and quadratic (PWQ) have proven to efficiently implement non-linear functions on hardware. This paper introduces Hybrid Piece-wise Polynomial Approximation (PW-Hybrid) where pieces of approximation for a function are obtained as the best combination of linear and quadratic polynomials, such that the error converges to the desired minimum. The hardware for PWL, PWQ and PW-Hybrid designs are further refined using Particle Swarm Optimization (PSO) algorithm to fine-tune the quantized bit-widths for realizing coefficients of the polynomial employed. This PSO optimised hardware design is evolved for a range of non-linear functions including i) Piece-wise polynomial linear optimized (PWLO) - Logarithmic, Hyperbolic-Tangent, Sigmoid and Softsign, and ii) Piece-wise polynomial quadratic optimized (PWQO) Exponential, and iii) Hybrid Piece-wise Polynomial optimized (HyPPO) - Sine and Sinc. The proposed design shows considerable decrease in hardware resource consumption and critical path delay, when synthesized using Cadence 45nm gpdk library. Highest improvements in HyPPO, PWLO and PWQO designs, are observed for Sine, Logarithmic and Exponential functions, with 65.06%, 24.47% and 9.67% gain in power-area-delay product (PADP) respectively, when compared with SOTA - PWL and PWQ designs. The proposed methods also exhibited minimal inference accuracy loss when tested on popular CNN architectures.