Assessing Differences in Precision with Posit Floating Point Format compared to IEEE 754
Abstract: Choosing the correct floating point representation can greatly impact the performance and precision of floating point operations. The current floating point representation standard is IEEE 754. A recent floating point representation which seems to yield a greater precision for the same number of bits is called Posit. In this thesis, we have conducted a study on the comparison of precision of using matrix multiplication on square dense matrices with Posit compared to IEEE 754. Our method for the study included auto-generating random matrices of different sizes, and performing identical multiplications with Posit, float and double data-types. By calculating the euclidean relative error for the pairs (Posit, double), and (float, double), we were able to analyze differences in precision for Posit and IEEE 754. The results show that Posit outperforms IEEE 754 within certain matrix element intervals. The greatest improvement for Posit arose around the interval [-1; 1], where the error was decreased by around 93 percent compared to IEEE 754. When increasing or decreasing the range further, the precision improvement yielded lower results and IEEE 754 was in general more precise for larger and smaller values. Increasing matrix size also decreased the ranges of which Posit was more precise. Thus, Posit seems to have an inherent advantage in applications where the numbers are distributed around 1 and -1.
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