test: migrate stats/base/dists/hypergeometric/pmf to ULP-based assertions

[kgryte]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates the tests for stats/base/dists/hypergeometric/pmf from computed relative tolerance testing (delta = abs( y - expected[i] ), tol = 1040.0 * EPS * abs( expected[i] ), t.ok( delta <= tol, ... )) to ULP difference testing using @stdlib/assert/is-almost-same-value.
• updates test/test.pmf.js, test/test.factory.js, and test/test.native.js, each of which contains one fixture loop over test/fixtures/julia/data.json. test/test.js contains no tolerance math and is unchanged.
• removes the now unused @stdlib/math/base/special/abs and @stdlib/constants/float64/eps requires from all three files (neither is used elsewhere in these files).

ULP bounds (tightened to the measured minimum over the full fixture set):

Fixture file	Test case	ULP bound	Measured maximum ULP difference
fixtures/julia/data.json	the function evaluates the pmf for x (test.pmf.js)	1967	1967
fixtures/julia/data.json	the created function evaluates the pmf for x (test.factory.js)	1967	1967
fixtures/julia/data.json	the function evaluates the pmf for x (test.native.js)	1967	1967

Notes on how the bound was determined:

• The bound is the minimum non-negative integer for which every fixture value passes. It was measured by computing, for each of the 1000 fixture values, the smallest N for which isAlmostSameValue( y, expected[i], N ) is true, and taking the maximum over the fixture set. Starting from a bound of 64 and adjusting, the suite passes at 1967 and fails at 1966 (a single failing assertion, at x: 81, N: 100, K: 87, n: 86), confirming that 1967 is tight rather than merely sufficient.
• The worst case is pmf( 81, 100, 87, 86 ), which returns 1.4708214585445427e-5 against a Julia reference value of 1.4708214585448759e-5.
• The measured maximum is identical for the main export, the factory-created function, and the C implementation, so all three files use the same bound.
• This is consistent with the previous tolerance: the old bound of 1040.0 * EPS corresponds to a relative tolerance of ~2.31e-13, while the observed worst-case relative error is ~2.27e-13. The prior tolerance was therefore already close to the observed error, and the ULP bound is of a comparable magnitude. The relatively large bound reflects the implementation, which evaluates the pmf via a sum of log-factorial terms (gammaln-based binomial coefficients) followed by exponentiation, so the argument reduction amplifies the error of the underlying kernels for large N and K.
• The native add-on was compiled locally (node-gyp rebuild), so test/test.native.js was exercised against the actual C implementation rather than skipped. The JavaScript and C implementations agree exactly on every fixture value.
• The full suite was run twice at the final bound with identical results (1027 assertions for test.pmf.js, 1031 for test.factory.js, 3 for test.js, and 1013 for test.native.js, all passing, per run), so the bound is not sensitive to FMA/contraction differences on this machine.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352

Questions

Any questions for reviewers of this pull request?

One point:

• 1967 is a much larger bound than most converted packages have needed. It is the measured minimum over the existing fixture set and is consistent with the relative tolerance it replaces, but reviewers may wish to consider whether the underlying accuracy of the implementation is itself worth a follow-up, since the ULP bound now makes the error magnitude explicit rather than hiding it behind an EPS multiplier.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

• Only the three test files are modified; no source, documentation, benchmark, or fixture files are touched.
• Verified with make test TESTS_FILTER=".*/stats/base/dists/hypergeometric/pmf/.*". Linting is clean via make lint-javascript-tests TESTS_FILTER=".*/stats/base/dists/hypergeometric/pmf/.*", which uses etc/eslint/.eslintrc.tests.js.
• The editorconfig pre-commit hook could not run in this environment, as it downloads its binary from a host this session cannot reach. The three files were instead checked against .editorconfig (LF endings, tab indentation, final newline, UTF-8, no trailing whitespace); the diff introduces no new violations.
• The idiom follows previously merged conversions, in particular stats/base/dists/chi/quantile (test: migrate stats/base/dists/chi/quantile to ULP-based assertions #14086) and stats/base/dists/lognormal/variance (test: migrate stats/base/dists/lognormal/variance to ULP-based assertions #14069), which use an inline integer ULP argument per fixture loop and the 'returns expected value' assertion message.

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

AI Assistance

When authoring the changes proposed in this PR, did you use any kind of AI assistance?

• Yes
• No

If you answered "yes" above, how did you use AI assistance?

• Code generation (e.g., when writing an implementation or fixing a bug)
• Test/benchmark generation
• Documentation (including examples)
• Research and understanding

Disclosure

If you answered "yes" to using AI assistance, please provide a short disclosure indicating how you used AI assistance. This helps reviewers determine how much scrutiny to apply when reviewing your contribution. Example disclosures: "This PR was written primarily by Claude Code." or "I consulted ChatGPT to understand the codebase, but the proposed changes were fully authored manually by myself.".

This PR was authored by Claude Code, running as an unattended scheduled task. The test migration follows the idiom established by previously merged conversions, and the ULP bound was measured empirically against both the JavaScript and compiled C implementations rather than guessed.

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/hypergeometric/pmf	$\\color{green}377/377$ $\\color{green}+100.00\\%$	$\\color{green}40/40$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}377/377$ $\\color{green}+100.00\\%$

The above coverage report was generated for the changes in this PR.