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

[Planeshifter]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• Migrates the test suite for stats/base/dists/cauchy/logcdf from relative-tolerance (EPS-based) assertions to ULP-difference assertions, per the guidance in [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352.

• Replaces the var delta = abs( y - expected[ i ] ); var tol = <N> * EPS * abs( expected[ i ] ); t.ok( delta <= tol, ... ) pattern in test/test.logcdf.js, test/test.factory.js, and test/test.native.js with t.strictEqual( isAlmostSameValue( y, expected[ i ], <ulp> ), true, 'returns expected value' ), adding the @stdlib/assert/is-almost-same-value import to each file.

• Uses the minimum required ULP value for each fixture block, determined by measuring the actual ULP difference between computed and expected values using @stdlib/number/float64/base/ulp-difference (verified by building and running the native addon locally, and running the full suite twice to confirm determinism):

  • large_gamma fixture: 9 ULP
  • negative_median fixture: 12 ULP
  • positive_median fixture: 6 ULP

  These bounds are identical across test.logcdf.js, test.factory.js, and test.native.js, since the JS and native (C) implementations produced identical outputs in local testing.

• test/test.js was left unchanged, as it contains no tolerance-based assertions.

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.

No.

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

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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 written by Claude Code, run as an autonomous scheduled task on my account to work through the ULP migration tracking issue (#11352) one package at a time. It selected this package by scanning for the relative-tolerance idiom, studied prior converted packages (e.g., stats/base/dists/levy/logcdf, stats/base/dists/gumbel/cdf, stats/base/dists/negative-binomial/cdf) to mirror the established idiom, and empirically measured the tightest ULP bound for each fixture block rather than guessing.

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@stdlib-js/reviewers

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🤖 Generated with Claude Code

https://claude.ai/code/session_012tvj9d3aJCYgSsmTcKwDZ5

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Generated by Claude Code

[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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Generated by Claude Code

[stdlib-bot]

Thank you for working on this pull request. However, we cannot accept your contribution as the issue this pull request seeks to resolve has already been addressed in a different pull request or commit.

Thank you again for your interest in stdlib, and we look forward to reviewing your future contributions.