FLOATING-POINT NUMBERS WITH ERROR-ESTIMATES

The study addresses the problem of precision in floating-point computations. A method for estimating the errors which affect intermediate and final results is presented, and a synthesis of many software simulations is discussed. The basic idea is to represent floating-point numbers by means of a data-structure collecting value and estimated error information. It has been found that, under certain circumstances, the estimate of the absolute error is accurate and has a compact statistical distribution. It is also shown that, by monitoring the estimated relative error during a computation (an ad hoc definition of relative error is used), the validity of results can be ensured. The error estimates enable robust algorithms to be implemented and ill conditioned problems to be detected. A hardware implementation of the method by means of a special floating-point processor is outlined. A dynamic extension of number precision, under the control of error estimates, is also advocated, in order to compute results within given error bounds.