posits

Posits are a family of floating-point number formats proposed as an alternative to IEEE 754 representations. They were introduced by John L. Gustafson and colleagues with the aim of delivering more accurate results and a wider effective range for the same number of bits, while providing simpler and more predictable handling of exceptional conditions. Posits have been explored in numerical analysis, high-performance computing, and machine learning research, but they have not achieved broad standardization or widespread hardware adoption.

A posits value is defined by a compact, self-describing structure consisting of a sign, a regime, an exponent, and a fraction. In this scheme the regime encodes a scale factor using a run-length of identical bits, which allows the format to adapt its precision and range dynamically within a fixed total bit width. The exponent and fraction provide the remaining precision, and there is a Not a Real (NaR) value used for invalid or undefined results, rather than a collection of NaN patterns. The total bit width and the maximum exponent size are denoted as P(n, es), where n is the number of bits and es is the exponent size.

Compared with IEEE 754, posits often offer higher accuracy for many common computations at the same bit width, improved numerical stability for certain operations, and a more consistent treatment of zeros and exceptional cases. However, implementing posits requires specialized software or hardware support, and the lack of standardization has limited their practical adoption. Software libraries and experimental hardware projects have demonstrated posit arithmetic, but mainstream mainstream architectures remain IEEE 754–dominant.