Closure and Precision in Level-Index Arithmetic

Abstract

First it is proved that two recently introduced systems of computer arithmetic, the level-index (li) and symmetric level-index (sli) systems are closed under the four basic arithmetic operations, provided that division by zero is excluded and the operations are executed in finite precision. In consequence, the li and sli systems are free from the defects of overflow and underflow. Second, measures of precision are discussed and compared. Third, the ranges and local precisions of numbers stored in the li and sli systems are compared with corresponding ranges and local precisions of numbers stored in the floating-point system.