Case Studies for Augmented Floating-Point

Much of scientific computat ion involves operations with higher data types such as vectors, matrices, complex quantities, and intervals of these. A well implemented conventional computer ari thmetic gives good results with floating-point numbers taken two at time. However , using this ari thmetic to implement computat ions with the higher data types can return arbi t rar i ly bad results. Kulisch and Miranker [4] have proposed a computer ari thmetic that furnishes an optimal accuracy for the dyadic ari thmetic operations for all of these higher data types. Its implementation is based on the int roduct ion of an accurate inner product to the s tandard floating-point ar i thmetic operat ion set.