Study of the posit number system: a practical approach

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) has been for decades the standard for floating-point arithmetic and is implemented in a vast majority of modern computer systems. Recently, a new number representation format called posit (Type III unum) introduced by John L. Gustafson – who claims this new format can provide higher accuracy using equal or less number of bits and simpler hardware than current standard – is proposed as an alternative to the now omnipresent IEEE 754 arithmetic. In this Bachelor dissertation, the novel posit number format, its characteristics and properties – presented in literature – are analyzed and compared with the standard for floating-point numbers (floats). Based on the literature assertions, we focus on determining whether posits would be a good “drop-in replacement” for floats. With the help of Wolfram Mathematica and Python, different environments are created to compare the performance of IEEE 754 floating-point standard with Type III unum: posits. In order to get a more practical approach, first, we propose different numerical problems to compare the accuracy of both formats, including algebraic problems and numerical methods. Then, we focus on the possible use of posits in Deep Learning problems, such as training artificial Neural Networks or preforming low-precision inference on Convolutional Neural Networks. To conclude this work, we propose a low-level design for posit arithmetic multiplier using the FloPoCo tool to generate synthesizable VHDL code.