Method and system of rounding for division or square root: eliminating remainder calculation

摘要

A method and system which provides exactly rounded division and square root results for a designated rounding mode independently of a remainder, or equivalent calculation of the relationship between the remainder and zero, for predetermined combinations of the rounding mode and the guard digit of an estimate that has several more bits of precision than the exactly rounded result, and has an error tolerance magnitude less than the weight of the least significant bit of the estimate. The estimate is generated in accordance with a quadratically converging division or square root algorithm. The method and system is described in connection with IEEE 754-1985 and IBM S/390 binary floating point architectures.