Comparing the precision in matrix multiplication between Posits and IEEE 754 floating-points : Assessing precision improvement with emerging floating-point formats

Abstract: IEEE 754 floating-points are the current standard way to represent real values in computers, but there are alternative formats emerging. One of these emerging formats are Posits. The main characteristic of Posit is that the format allows for higher precision than IEEE 754 floats of the same bit size for numbers of magnitude close to 1, but lower precision for numbers of much smaller or bigger magnitude. This study compared the precision between IEEE 754 floating-point and Posit when it comes to matrix multiplication. Different sizes of matrices are compared, combined with different intervals which the values of the matrix elements were generated in. The results showed that Posits outperformed IEEE 754 floating-point numbers in terms of precision when the values are in an interval equal to or larger than [