Posit Number System

Post date: Aug 07, 2018 4:33:55 AM

Posit numbers are a new way to represent real numbers for computers, an alternative to the standard IEEE floating point formats. The primary advantage of posits is the ability to get more precision or dynamic range out of a given number of bits.

A conventional floating point number (IEEE 754) has a sign bit, a set of bits to represent the exponent, and a set of bits called the significand (formerly called the mantissa). For a given size number, the lengths of the various parts are fixed. A 64-bit floating point number, for example, has 1 sign bit, 11 exponent bits, and 52 bits for the significand.

A posit adds an additional category of bits, known as the regime. A posit has four parts

• 1. sign bit

  2. regime

  3. exponent

  4. fraction

Unlike IEEE numbers, the exponent and fraction parts of a posit do not have fixed length. The sign and regime bits have first priority. Next, the remaining bits, if any, go into the exponent. If there are still bits left after the exponent, the rest go into the fraction

Generic format

An example.

Advantages of posit over IEEE 754:

• Simpler, smaller, faster circuits

• Superior accuracy, dynamic range, closure

• Better answers with same number of bits or equally good answers with fewer bits

Who will be the first to produce a chip with posit arithmetic?

• • John D. Cook, Anatomy of a floating point number. 6 April 2009.

  • John D. Cook, Anatomy of a posit number. 11 April 2018.

  • John D. Cook, Comparing range and precision of IEEE and posit. 14 April 2018.

  • John L. Gustafson and Isaac Yonemoto., Beating Floating Point at its Own Game: Posit Arithmetic. Supercomputing Frontiers and Innovations,  VOL 4, NO 2 (2017). DOI: 10.14529/jsfi170206.

  • John L. Gustafson, Beyond Floating Point: Next-Generation Computer Arithmetic, https://web.stanford.edu/class/ee380/Abstracts/170201-slides.pdf