test: migrate stats/base/dists/cauchy/pdf to ULP-based assertions

[kgryte]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates stats/base/dists/cauchy/pdf 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/test.factory.js carried the relative-tolerance idiom (delta/tol/EPS with t.ok( delta <= tol, ... )), across the three fixture loops. Those assertions are replaced with isAlmostSameValue, and the now-unused @stdlib/math/base/special/abs and @stdlib/constants/float64/eps requires are removed in favor of @stdlib/assert/is-almost-same-value.

test/test.pdf.js and test/test.native.js already asserted exact equality via t.strictEqual and are intentionally left unchanged.

Final ULP constant: 0 (all three fixture loops).

This is the measured minimum. All 3000 fixture values — 1000 each across large_gamma, negative_median, and positive_median — compare bit-for-bit identical to the expected values, for both the factory and main entry points, so no nonzero ULP budget is required. This is consistent with test.pdf.js/test.native.js already relying on exact comparison, and matches the , 0 ) bound used by previously migrated packages in this family.

The bound was measured by exponential-then-binary search for the minimal passing N per fixture point, and the suite was then run three times at the final bound to confirm determinism (no FMA/arch variation).

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 notes:

• test/test.js, test/test.pdf.js, and test/test.factory.js all pass (3018 assertions in the migrated file); test/test.native.js skips, as the native add-on is not built in this environment.
• ESLint is clean on the changed file under the repository's test lint configuration, via the pre-commit hook.
• The only changed file is test/test.factory.js.

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 as part of a batch migration of relative-tolerance tests to ULP-based assertions, mirroring the idiom established in previously merged packages in this family (e.g. stats/base/dists/cauchy/cdf). The ULP bound was measured rather than guessed.

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Generated by Claude Code

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/cauchy/pdf	$\\color{green}293/293$ $\\color{green}+100.00\\%$	$\\color{green}19/19$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}293/293$ $\\color{green}+100.00\\%$

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