Iterated Log Coding: A Novel Floating-Point Encoding Format
This article introduces a novel real number encoding format—iterated log coding. Unlike traditional floating-point representations, this format uses a sequence of sign bits to represent numbers, each sign bit indicating the positivity or negativity of the number within a specific range. This approach allows for a remarkably wide range of representable numbers, including extremely large or small values that are beyond the capabilities of traditional floating-point formats. It features a unique lexicographic ordering property. While the precision distribution is non-uniform, the method offers advantages in representing numbers within certain ranges, particularly where extremely large or small values are involved and precision requirements are less stringent.