PT-Float: A Floating-Point Unit with Dynamically Varying Exponent and Fraction Sizes

This paper introduces Precision Trade-Off Floats (PT-Floats). This number system uses the concept of Tapered Precision, a concept introduced by R. Morris in 1971 and later exploited in the Unum formats, most notably by the Posit number system. The idea is to trade off exponent bits with fraction bits according to the application domain. In general, the numbers having an absolute value close to 1 are given more fraction bits and fewer exponent bits, and the numbers with very small or extensive magnitudes are given more exponent bits and fewer fraction bits. This way, near-unit values are kept at high precision while the other values span a vast dynamic range. This work proposes a solution to the problem of redundant representations in the Unum I system. This solution allows the exponent size to be stored as an unsigned binary number, using much less space than Posit’s es field plus regime bits. Our experimental results indicate that the new format reduces hardware resources and energy consumption. We showcase examples where half-size PT-Float units have enough precision, accuracy, and dynamic range to replace full-size IEEE-754 units.