  The study addresses the problem of precision in floating-point (FP)
computations. A method for estimating the errors which affect intermediate and
final results is proposed and a summary of many software simulations is
discussed. The basic idea consists of representing FP numbers by means of a
data structure collecting value and estimated error information. Under certain
constraints, the estimate of the absolute error is accurate and has a compact
statistical distribution. By monitoring the estimated relative error during a
computation (an ad-hoc definition of relative error has been used), the
validity of results can be ensured. The error estimate enables the
implementation of robust algorithms, and the detection of ill-conditioned
problems. A dynamic extension of number precision, under the control of error
estimates, is advocated, in order to compute results within given error bounds.
A reduced time penalty could be achieved by a specialized FP processor. The
realization of a hardwired processor incorporating the method, with current
technology, should not be anymore a problem and would make the practical
adoption of the method feasible for most applications.
