timmylindh / positeval

Comparative tool for comparing IEEE 754 and Posit32 floating point precision with Matrix Multiplication

This project provides a tool for comparing the IEEE 754 and Posit32 floating point precision in regards to Matrix Multiplication. The tool generates a set of matrices and calculates the Euclidian error compared to the double IEEE 754 64-bit format.

As can be observed, Posit outperforms IEEE 754 (which is the current standard used for floating points in most modern computers) in a specific range of interval for numbers. We therefore hypothesize that Posit may be a viable format for computers specialized in deep learning or machine learning tasks, where many of the calculations are on probabilities, thus centering between 0 and 1.

Compilation

To compile the nessecary binaries and libraries, issue the following command in matrix_multiplication/:

make compile

Running

To run the automated mean error calculations, issue:

make all RANGE=xx SIZE=yy NUM=zz

This will create NUM randomly generated matrices of size SIZE x SIZE, where each matrix entry is a value between -RANGE and RANGE in the matrices/in folder. Each matrix is then multiplied with another, and the resulting matrix is stored in out/32, out/64 and out/posit.

An error is then calculated by comparing the matrices generated in the 32-bit IEEE 754 format and the 32-bit Posit format, to the double precision IEEE 754 64-bit format. The error is calculated as the Euclidian norm. The final result is the average of the Euclidian norms for all the matrices.