Finite-precision error modeling using affine arithmetic

This paper introduces a new approach for finite-precision error modeling based on affine arithmetic. The paper demonstrates that there is a common hazard in affine arithmetic-based error modeling methods described in the literature. The hazard is linked to early substitution of the signal terms that emerge in operations such as multiplication and division. The paper proposes postponed substitution combined with function maximization to address this problem. The paper also proposes a modification in the error propagation process to enhance the error modeling accuracy. An existing word length optimization method is reproduced to evaluate the efficiency of this modification. The results demonstrate that the proposed modification can improve the hardware area results by up to 7.0% at the expense of negligible complexity overhead.