Overflow/underflow-free floating-point number representations with self-delimiting variable-length exponent field

Abstract

A class of new floating-point representations of real numbers, based on representations of the integers, is described. In the class, every representation uses a self-delimiting representation of the integers as a variable length field of the exponent, and neither overflow nor underflow appears in practice. The adopted representations of the integers are defined systematically, so that representation's of numbers greater than one have both exponent-significant and integer-fraction interpretations. Since representation errors are characterized by the length function of an underlying representation of the integers, superior systems in precision can be easily selected from the proposed class. >