Our implementation of GLST uses double-precision variables for atom positions, cubature nodes and weights, structure factors, as well as forces and energies. However, as an optimization for speed, we use single-precision trigonometric functions as this provides a speedup of 14% for our benchmark system containing 197,159 atoms (c.f. Tab. I). The single-precision trigonometric functions can lead to additional roundoff error, as evident by the asymptotic behavior of the error for increasing target accuracy threshold (Fig. ) and by the broader peaks in the single-precision error histograms when compared to the double-precision histograms (Figs. ). This round off error can lead to the system having small net forces, that can be removed using Gram-Schmidt orthogonalization. If GLST were to be used for MD simulations, these small net forces could be removed each step before integration.