test: migrate stats/base/dists/cauchy/logcdf 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/cauchy/logcdf from relative tolerance testing to ULP difference testing, per [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352.

Only test files are changed (test/test.logcdf.js, test/test.factory.js, test/test.native.js); test/test.js contains no tolerance-based assertions and is left untouched. The implementation is unchanged.

Per fixture set, the ULP constants were tightened to the measured minimum over the full 1000-element fixture:

Fixture	Previous tolerance	ULP constant	Measured minimum
large_gamma.json	7.0 * EPS * abs( expected[i] )	9	9 (fails at 8)
negative_median.json	7.0 * EPS * abs( expected[i] ) (JS), 300.0 * EPS * ... (native)	12	12 (fails at 11)
positive_median.json	7.0 * EPS * abs( expected[i] ) (JS), 220.0 * EPS * ... (native)	6	6 (fails at 5)

The same constants are used in all three test files.

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, concerning test/test.native.js.

The native add-on is not built in the environment used to author this PR, so test/test.native.js is skipped there and the C implementation could not be exercised through the add-on. To avoid guessing, src/main.c was compiled standalone together with its resolved C dependency closure (math/base/special/atan2, math/base/special/ln, etc.) and evaluated against the same fixtures. That C implementation reproduced the JavaScript ULP profile exactly — 9 / 12 / 6, identical worst-case indices, and stable across -O0, -O2, and -O3 — so the native test uses the same constants as the JavaScript tests.

Note that this tightens the native assertions considerably relative to the previous 300.0 * EPS and 220.0 * EPS tolerances (roughly 300–600 ULP). The measurement suggests those tolerances were loose padding rather than evidence of real JS/C divergence, but a reviewer with a built add-on may wish to confirm on their own platform before this is merged.

Other

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

Verification performed:

• test.logcdf.js (3014 assertions) and test.factory.js (3018 assertions) pass; test.js (3 assertions) is unchanged and passes.
• The full suite was run twice at the final constants with identical results, to rule out FMA/architecture-dependent flakiness.
• Minimality was confirmed programmatically: at N-1, large_gamma and negative_median each produce one failure and positive_median produces three, for both the main export and the factory-generated function.
• ESLint is clean for the changed files under both .eslintrc.js and etc/eslint/.eslintrc.tests.js.

Marked as a draft pending the native add-on question above.

Checklist

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

• Read, understood, and followed the contributing guidelines.

AI Assistance

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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. It selected the package, mirrored the conversion idiom from the already-migrated sibling package stats/base/dists/cauchy/logpdf, measured the minimum ULP bounds against the fixtures, and ran the verification described above.

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/cauchy/logcdf	$\\color{green}289/289$ $\\color{green}+100.00\\%$	$\\color{green}19/19$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}289/289$ $\\color{green}+100.00\\%$

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

[Planeshifter]

⚠️ Issue Reference Review

An automated check found potentially unrelated issue/PR references in this PR:

Reference	Assessment	Reasoning
#11352	suspicious	Issue #11352 is an RFC explicitly scoped to migrating math/base/special packages from relative-tolerance to ULP-based testing (its own instructions say to search for a package "in math/base/special"). This PR migrates tests for stats/base/dists/cauchy/logcdf, which is outside the issue's stated scope.

Why this matters: GitHub automatically closes issues referenced with
closing keywords (Resolves, Closes, Fixes) when the PR is merged. Incorrect
references can accidentally close unrelated issues.

What to do:

• If the reference is correct, no action needed. This check may produce
  false positives.
• If the reference is incorrect, please update your PR description.

This assessment was generated by an AI model and is informational only.

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