Optimize bit rate permutation search about acl HOT 1 OPEN

As it turns out, due to floating point rounding, once the error tapers off near its lowest value, adding more bits can sometimes cause the error to rise slightly. This can occur due to floating point rounding/noise. As such, our data is near but not quite sorted.

Perhaps we can leverage this in some other way. The error tapers typically when little accuracy is added which is when the noise creeps. For most joints, we would stop iterating and skip those permutations long before we reach them. This would be an issue only when the error tapers above our threshold.

We could perhaps search for a decent guess of the error by starting in the middle. We can then binary search to find our best permutation guess. It might not be the best one due to the issue above but once we have this permutation size and its error, we can search exhaustively more quickly by discarding most permutations at the first sample: most permutations that are larger will use fewer bits and yield a higher error. We could cache which permutations we tested and their error to avoid performing repeated work during the exhaustive search.

from acl.