Experiments and performance evaluation of stochastic rounding algorithms

This repository contains the source code for reproducing the results in [Sec. 7, 1] and [Sec. 8, 1].

The performance benchmarks in ./performance require the GNU MPFR Library, which in turn depends on the GNU Multiprecision Arithmetic (GMP) Library . The codes can be compiled with make all, which generates the two executables test_validation and test_performance. The former performs a validation of the functions defined in stochrnddw.c, the latter produces the data in [Table 7.1, 1]. Compiling and running both tests is as easy as:

cd performance
make all
make run_validation
make run_performance

The codes in ./numerical_experiments generate the data used for the plots in [Fig. 8.1-8.5, 1]. The folder contains the following scripts:

• test_summation_algorithms.m [Sec. 8.1-8.2, 1].
• test_summation_algorithms_double.m [Sec. 8.2, 1].
• ODE_tests.m [Sec. 8.3.1, 1].
• unit_circle_ODE.m [Sec. 8.3.2, 1].

The code for the experiment with double-precision arithmetic (test_summation_algorithms_double.m) requires the Stochastic Rounding Toolbox be in the MATLAB path.

References

[1] M. Fasi and M. Mikaitis. Algorithms for stochastically rounded elementary arithmetic operations in IEEE 754 floating-point arithmetic, IEEE Transactions on Emerging Topics in Computing. Early Access. Mar. 2021.

License

This software is distributed under the terms of the 2-clause BSD software license (see LICENSE).