Floating-point error analysis based on affine arithmetic

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, nonlinear 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.