fix: correct Geometric::inverse_cdf against its definition

[teddytennant]

Summary

Geometric::inverse_cdf used the closed form ceil(ln1p(-x) / ln1p(-p)) alone. That quotient is only approximately integral at the step boundaries, so ceil often lands on the wrong side of the true quantile and breaks the discrete inverse definition (least k with cdf(k) >= x).

Over a sweep of 200 values of p and 400 of k, thousands of pairs failed inverse_cdf(cdf(k)) == k even though cdf separated adjacent integers.

Root cause

Floating-point evaluation of the closed form is not exact at bucket edges. Being an override, this path was also unreachable by later improvements to the default discrete inverse_cdf.

Fix

Keep the closed form as a fast candidate, then correct it against the definition:

• check candidate, candidate - 1, and candidate + 1 with two or three cdf evaluations (the usual path);
• when x is within a few ulp of 1, 1 - x loses significant bits and the closed form can be off without bound (cdf plateaus about 1/p wide), so fall back to exact integer bisection.

Test plan

• cargo test --lib geometric::
• cargo test --lib (775 passed, 2 ignored pre-existing pathological cases still marked #[ignore])
• New regressions:
  • test_inverse_cdf_round_trips_and_matches_definition
  • test_inverse_cdf_is_least_k_with_cdf_at_least_x
  • test_inverse_cdf_long_plateau

Fixes #342

[teddytennant]

The Coverage (nightly) failure here is unrelated to this change.

Recent nightly (1.99.0-nightly, 2026-08-06) started firing the deprecated lint on f64::NAN / INFINITY / NEG_INFINITY paths in the ~25 modules that do use core::f64; — the module import shadows the primitive in path resolution, so those resolve to the deprecated core::f64::* module constants rather than the associated constants. The Coverage job sets RUSTFLAGS: -D warnings, so it becomes a hard build failure.

It reproduces on a clean checkout of main (02fdab6) with nothing applied: 90 errors. This branch also produces exactly 90 — it adds no new instances. Without -D warnings it compiles fine (warnings only). Last green Coverage run on main was Jul 31.

cargo test --all-features passes on this branch: 780 passed, 0 failed.

Happy to send a separate PR swapping those paths over to the associated constants (or dropping the use core::f64; imports) if you want Coverage unblocked.

[codecov]

Codecov Report

❌ Patch coverage is 92.85714% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 95.07%. Comparing base (ccb0b26) to head (021ac1b).

Files with missing lines	Patch %	Lines
src/distribution/geometric.rs	92.85%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #431      +/-   ##
==========================================
- Coverage   95.08%   95.07%   -0.02%     
==========================================
  Files          62       62              
  Lines       14108    14191      +83     
==========================================
+ Hits        13415    13492      +77     
- Misses        693      699       +6     

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[YeungOnion]

thanks for this fix!