This paper presents an arithmetic module generator based on an arithmetic description language called ARITH. The use of ARITH makes it possible to describe a wide variety of arithmetic algorithms in a unified manner. The ARITH descriptions are formally verified in the generator even if the arithmetic algorithms include unconventional number systems for operands or internal variables. The proposed generator also optimizes arithmetic algorithms by using performance profiles derived from the previous generation. From these features, we can obtain high-performance arithmetic modules whose functions are completely verified at the algorithm level. In this paper, we demonstrate that the optimal prefix adders improved the performance of generated arithmetic modules such as multipliers in comparison with the standard prefix adders.