Floating-point error analysis based on affine arithmetic

Abstract

During the development of floating-point signal processing systems, an efficient error analysis method is needed to guarantee the output quality. We present a novel approach to floating-point error bound analysis based on affine arithmetic. The proposed method not only provides a tighter bound than the conventional approach, but also is applicable to any arithmetic operation. The error estimation accuracy is evaluated across several different applications which cover linear operations, non-linear operations, and feedback systems. The accuracy decreases with the depth of computation path and also is affected by the linearity of the floating-point operations.