UAFEA: Unified Analytical Framework for IA/AA-Based Error Analysis of Fixed-Point Polynomial Specifications

A challenging verification and optimization problem in computer arithmetic and embedded systems is error analysis (EA) of fixed-point polynomial data-flow graphs (DFGs). This brief presents an EA framework to compute the error measure maximum mismatch of feedforward fixed-point polynomial DFGs. Our idea to reduce the overestimation keeping efficiency is introducing a unified analytical framework for the two most popular self-validated numerical methods, i.e., interval arithmetic (IA) and affine-arithmetic (AA), so that correlated arguments appear in suitable positions in the DFG. The results show that our methods can enhance error accuracy, in average, more than 24% in comparison with the state-of-the-art techniques while keeping the efficiency of IA and AA.