Allow AP_SAT, AP_RND for 'maximum' precision in HLS Config

[morunner]

Description

During the development of a gravnet model for hls4ml, I found that setting rounding and saturation for the maximum allowed precision can be beneficial for increasing accuracy. Below you can see histograms and mean difference with one standard deviation when the maximum precision is ap_fixed<16,8,AP_RND,AP_SAT,0> and when rounding and saturation are not enabled (ap_fixed<16,8>).

In the current upstream main branch of hls4ml, rounding and saturation modes set through the 'maximum' field in the HLS config are ignored during precision inference (see e.g. here). I thus propose a single function _apply_max_precision_constraints to be applied where necessary in the infer_precision.py module, which adheres the following rules:

• Width/Integer: Always constrained to the minimum of inferred vs max.
• Rounding/Saturation: Inherited from max_precision ONLY if they differ from the defaults
  (meaning the user likely set them explicitly).
• Signedness: max_precision signed arg is always preferred.

We can of course discuss, what the preferred ruleset should be here.

No additional dependencies are required for this change.

Type of change

• Other (Accuracy Improvement)

Tests

Pytest

Added a new pytest module, test_max_precision.py, which tests the newly added _apply_max_precision_constraints function isolated and within the _infer_precision function, using mocks.

Conversion to HLS

Ran the full jupyter notebook for gravnet keras conversion to hls at hls4ml-gravnet (Link) to generate the below listed plots, with the proposed change enabled and disabled. The profiling section was ran with this fix applied. We currently do not provide the fully trained model open-source, since it is not finalized. @bo3z please contact me directly, also regarding the dataset, if needed.

Checklist

• I have read the guidelines for contributing.
• I have commented my code, particularly in hard-to-understand areas.
• I have made corresponding changes to the documentation. -> tbd depending on the ruleset for RND, SAT
• My changes generate no new warnings.
• I have installed and run pre-commit on the files I edited or added.
• I have added tests that prove my fix is effective or that my feature works.

GravNet plots showing accuracies and bias across layers

With rounding and saturation enabled for the maximum precision.