Fast correctly-rounding floating-point conversion

摘要

A system and method for converting bases of floating point numbers using fixed-point computation includes tables having different related spacings of exponent indices. The tables are adapted to cross-reference conversion ratios between exponent bases. The tables are characterized by bi-uniform spacings of source and target exponents and including near-unity table entries representing the conversion ratios. A source number is converted into a target number in a different radix by a sequence of reduction operations using a sequence of the tables. The reduction operations include reducing a source number exponent magnitude and accumulating a target exponent and multiplying a source number mantissa by a selected conversion ratio including a near-unity ratio of powers. A final mantissa is normalized and rounded to produce the target number in a new radix.