Even with non-integer sample rates, the error of the old algorithm is less than the typical error of the internal crystal, but there are some specialized applications where the improvement could matter.

For example, HackRF One was used as a part of this time transfer system that achieved better than 40 ns precision: https://arxiv.org/abs/2406.13596

Clock generator precision was a significant limiting factor in this system, so I think that 256 times less error would result in a huge improvement overall.

The new #Si5351 implementation in HackRF is an even better improvement than I realized at first because the old, vendor-recommended algorithm introduces error by not rounding properly. The mean error of the old algorithm is approximately 256 times the mean error of the new one.

I think this is pretty great, but in practice this should rarely matter to HackRF users. The most commonly used sample rates are error-free integer divisions of the 800 MHz clock generator VCO.

The sequel article investigates jitter and explains how Si5351 achieves much better spectral purity than one might expect of such a clock generator.

When Jared and I chose the part for HackRF One back in 2012, we were very pleasantly surprised by its performance. Since then it has become a popular choice for all sorts of radio projects for good reason. It's nice to finally understand the internals well enough to see why it works so well for our application.