Exact accumulation of floating-point numbers

Abstract

The authors present a new idea for designing a chip which computes the exact sum of arbitrarily many floating-point numbers, i.e. it can accumulate the floating-point numbers without cancellation. Such a chip is needed to provide a fast implementation of Kulisch arithmetic. This is a new theory of floating-point arithmetic which makes it possible to compute least significant bit accurate solutions to even ill-conditioned numerical problems. The proposed approach avoids the disadvantages of previously suggested designs which are too large, too slow, or consume too much power. The crucial point is a technique for a fast carry resolution in a long accumulator. It can also be implemented in software.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>