test: migrate stats/base/dists/weibull/skewness 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/weibull/skewness from relative tolerance assertions to ULP difference assertions using @stdlib/assert/is-almost-same-value.

Both test/test.js and test/test.native.js previously compared against a computed relative tolerance:

delta = abs( y - expected[ i ] );
tol = 1e-11 * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. ...' );

and now assert:

t.strictEqual( isAlmostSameValue( y, expected[ i ], 36208 ), true, 'returns expected value' );

ULP constant: 36208 in both test/test.js and test/test.native.js.

This is the measured minimum over the full 500-value Julia fixture set, tightened empirically:

maxULP	result
16384	4 failing
36206	1 failing
36207	1 failing
36208	514 passing, 0 failing

The JavaScript and C implementations were each measured independently against the fixtures and both peak at exactly 36208 ULP on the same input (k = 3.625597586389692, lambda = 2.9758629782847215), so a single constant is used for both test files.

The bound is larger than is typical for this migration because the Weibull skewness has a zero crossing near k ≈ 3.6. Around that root the result is computed via cancellation of same-magnitude terms

( Γ(1+3/k)·λ³ − 3·μ·σ² − μ³ ) / σ³

so the absolute error stays tiny (Δ ≈ 3.1e-17 at the worst case) while the ULP distance grows as the expected value approaches zero. The previous 1e-11 relative tolerance was approximately 45000 * EPS, so 36208 ULP is a tightening of the accepted error budget, not a loosening.

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?

No.

Other

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

Verification performed:

• make test TESTS_FILTER=".*/stats/base/dists/weibull/skewness/.*" → 514 passing in test/test.js and 514 passing in test/test.native.js.
• The native add-on was built locally (make install-node-addons NODE_ADDONS_PATTERN="stats/base/dists/weibull/skewness") so that test/test.native.js actually executes rather than being skipped.
• The full suite was run twice at the final ULP value, with identical results both times, to confirm there is no FMA/architecture-dependent flakiness.
• ESLint is clean against etc/eslint/.eslintrc.tests.js for both files.
• Only the two test files are modified.

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

This PR was authored by Claude Code running as an unattended scheduled task. It studied the already-merged conversions in this family (e.g. stats/base/dists/binomial/skewness, stats/base/dists/geometric/variance, stats/base/dists/triangular/stdev) to match the established idiom, then determined the ULP bound empirically by bisecting on the measured maximum ULP difference over the fixture set and re-running the suite to confirm minimality and determinism.

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@stdlib-js/reviewers

🤖 Generated with Claude Code

https://claude.ai/code/session_012ZDpXGX4VLAhBiWQNHMi81

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/weibull/skewness	$\\color{green}210/210$ $\\color{green}+0.00\\%$	$\\color{green}10/10$ $\\color{green}+0.00\\%$	$\\color{green}2/2$ $\\color{green}+0.00\\%$	$\\color{green}210/210$ $\\color{green}+0.00\\%$

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