Round-off noise estimation of fixed-point algorithms using Modified Affine Arithmetic and Legendre Polynomials

The implementation of algorithms in fixed-point format causes the apparition of Round-Off Noise which propagates through the different functional units of the system. This issue causes the Signal-to-Noise Ratio of the outputs is degraded. Given an algorithm, it is essential to estimate the integer and fractional bit-widths of all the variables and operations to comply with the Signal-to-Noise Ratio requirements. In this context, Affine Arithmetic can obtain fast and accurate estimations of the bit-widths for linear systems. However, for non-linear systems, Affine Arithmetic loses the temporal correlation of the variables. Other existing frameworks are either time consuming or lead to inaccurate bound estimations. In this paper, a Modified Affine Arithmetic framework with Legendre polynomials is used to obtain fast and accurate bound estimations also for non-linear systems. Moreover, the approach proposed in this paper obtains speedups in the range of 7 to 100 compared to Monte-Carlo simulations.