test: migrate stats/base/dists/invgamma/mode 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/invgamma/mode 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 = 2.0 * EPS * abs( expected[ i ] );
t.ok( delta <= tol, 'within tolerance. ...' );

and now assert:

t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );

ULP constant: 0 in both test/test.js and test/test.native.js.

This is the measured minimum over the full 200-value Julia fixture set. Measuring the ULP distance between each computed value and its reference value directly:

implementation	fixtures	exact (SameValue) matches	max ULP difference
JavaScript (lib/main.js)	200	200	0
C (src/main.c, via lib/native.js)	200	200	0

0 is the tightest representable bound, so no further tightening is possible.

Exact agreement is expected here rather than fortuitous: both implementations evaluate the mode as a single IEEE-754 division,

beta / ( alpha + 1.0 )

so each result is correctly rounded and there is no accumulation, no transcendental evaluation, and no opportunity for FMA contraction to change the result. Note that at maxULP === 0 isAlmostSameValue falls back to the SameValue algorithm, which is strictly stronger than the previous y === expected[ i ] fast path (it distinguishes -0 from +0).

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:

• test/test.js → 214 passing, 0 failing.
• test/test.native.js → 214 passing, 0 failing. The native add-on was built locally (node-gyp configure build in the package directory) so that test/test.native.js actually executes rather than being skipped; the assertion count confirms the tests were not skipped.
• Both files were 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.

One environment note for reviewers: make install-node-modules currently fails in a clean container with ETARGET: No matching version found for es-object-atoms@^1.1.2 (requested by array-includes@3.2.0, pulled in transitively via eslint-plugin-import). The published versions of es-object-atoms top out at 1.1.1. This is unrelated to the changes in this PR, but it meant the test and lint runs above were performed against a locally assembled dependency set rather than via make test / make lint.

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/invgamma/entropy, stats/base/dists/weibull/skewness, stats/base/dists/geometric/mean) to match the established idiom, then determined the ULP bound empirically by measuring the maximum ULP difference over the fixture set for both the JavaScript and C implementations 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_01LRbc6joCcUqZmp2X4Va3wh

---

Generated by Claude Code

[stdlib-bot]

Hello! 👋

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Now that you've made a few contributions, we suggest no longer working on good first issues. Instead, we encourage you to prioritize cleaning up any PRs which have yet to be merged and then proceed to work on more involved tasks.

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/invgamma/mode	$\\color{green}195/195$ $\\color{green}+0.00\\%$	$\\color{green}10/10$ $\\color{green}+0.00\\%$	$\\color{green}2/2$ $\\color{green}+0.00\\%$	$\\color{green}195/195$ $\\color{green}+0.00\\%$

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