A circuit for exact summation of floating-point numbers

In recent years methods for solving numerical problems have been developed which in contrast to traditional numerical methods compute intervals which are proven to contain the true solution of the given problem (cf. [10,11]). These methods rely on an exact evaluation of inner product expressions in order to obtain good (i.e. small) enclosure intervals. Practical experience has shown that using these methods even ill conditioned problems can often be solved with maximum accuracy. Since the exact inner product computation is a basic operation for these methods we developed a circuit to support the difficult part of the inner product computation: the accurate accumulation of the partial products.