EFFICIENT AND RELIABLE METHODS FOR ROUNDED-INTERVAL ARITHMETIC

We present an efficient and reliable method for computing the unit-in- the-last-place (ulp) of a double-precision floating-point number, taki ng advantage of the standard binary representation for floating-point numbers defined by IEEE Std 754-1985. The ulp is necessary to perform software rounding for robust rounded-interval arithmetic (RIA) operati ons. Hardware rounding, using two of the standard rounding modes defin ed by IEEE-754, may be more efficient. RIA has been used to produce ro bust software systems for the solution of systems of nonlinear equatio ns, interrogation of geometric and differential properties of curves a nd surfaces, curve and surface intersections, and solid modeling. (C) 1998 Elsevier Science Ltd. All rights reserved.