[JackieTien97]

Finite samples can produce NaN in Akima interpolation because the weighted slope products overflow before division. For example, with x = {0, 2, 4, 6, 8} and y = {0, 1e200, 0, 1e200, 0}, evaluating the interpolant at 3 returns NaN instead of approximately 5e199.

Preserve the existing calculation when the intermediate sums are finite and at least one weighted product is nonzero. Otherwise, normalize the two weights before forming the convex combination of slopes. Keeping the existing arithmetic for representable products preserves small contributions when the weights have very different magnitudes; unconditionally normalizing those weights can itself underflow a weight.

Add regression coverage for:

• Large finite samples in both original and modified Akima interpolation.
• Scale invariance at 1e200, -1e200, and 1e-200 in both modes.
• Highly unbalanced weights: y = {1e-200, 0, 0, 1e200, 1e200} must retain the value -1.875e-201 at x = 3 in both modes.

Also add a release-note entry.

Validation:

• The four new overflow/scale regressions fail on the unmodified base revision.
• Full mvn clean verify passes: 3,828 tests reported, 33 skipped, no failures or errors.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.21%. Comparing base (f554608) to head (c6ced52).
⚠️ Report is 412 commits behind head on master.

Additional details and impacted files

@@             Coverage Diff              @@
##             master     #351      +/-   ##
============================================
+ Coverage     86.54%   87.21%   +0.67%     
+ Complexity     9787       91    -9696     
============================================
  Files           532      499      -33     
  Lines         35516    33535    -1981     
  Branches       6194     5853     -341     
============================================
- Hits          30738    29249    -1489     
+ Misses         3518     3160     -358     
+ Partials       1260     1126     -134     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[aherbert]

Thanks for the fix. I would suggest also raising an exception if the differences overflow and there are regions in the interpolator that will not work.

[aherbert]

Note that prior to this step the computation of the computation of the differences can also overflow. Feel free to investigate if that can be recovered. Otherwise I suggest raising an exception for an interpolator that will not work.