[kgryte]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates the tests for math/base/special/bessely1 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.
• replaces the delta/tol computation and the y === expected special case in test/test.js and test/test.native.js with a single t.strictEqual( isAlmostSameValue( y, expected[ i ], N ), true, 'returns expected value' ); assertion.
• removes the now-unused @stdlib/math/base/special/abs require and adds @stdlib/assert/is-almost-same-value. The @stdlib/constants/float64/eps require is retained, as EPS is still used when generating negative inputs.

ULP bounds (per fixture set, identical for test/test.js and test/test.native.js):

Fixture set	Previous tolerance	ULP bound	Next largest ULP difference in set
very_large_positive	300.0 * EPS * abs( expected )	254	251
large_positive	600.0 * EPS * abs( expected )	689	494
medium_positive	300.0 * EPS * abs( expected )	395	288
small_positive	1800.0 * EPS * abs( expected )	2338	1774
smaller	4.5 * EPS * abs( expected )	5	4
tiny_positive	8.0 * EPS * abs( expected )	1	0
huge_positive	4500.0 * EPS * abs( expected )	1200	248
positive_gamut	16.0 * EPS * abs( expected )	27	25

These are the measured minima. Starting from a high bound and tightening, each value above is the smallest integer for which the corresponding fixture set passes in full: decrementing every bound by one fails 1934 of 41646 assertions (exactly one point per set, except tiny_positive, where a bound of 0 degrades to exact equality and fails 1927 points). The JavaScript and native (C) implementations agree exactly on every fixture point, so the same bounds apply to both test files.

Only the two test files are changed; no source, documentation, or package.json changes are included.

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?

The small_positive (2338) and huge_positive (1200) bounds are large in absolute terms, but they are strictly tighter than the relative tolerances they replace and reflect the accuracy of the current implementation near the zeros of Y_1. Happy to instead round these to the nearest convenient value if reviewers prefer some headroom over the measured minimum.

Other

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

Verification performed locally:

• make test TESTS_FILTER=".*/math/base/special/bessely1/.*" — test/test.js 41646 passing, 0 failing; test/test.native.js 41646 passing, 0 failing. Run twice at the final bounds with identical results, so the bounds are not sensitive to FMA/arch variation on this machine.
• test/test.native.js was exercised against a locally built addon (make install-node-addons NODE_ADDONS_PATTERN="bessely1"), so the native assertions ran rather than being skipped.
• Tightness check: lowering every bound by one produced 39712 passing / 1934 failing, confirming the reported minima.
• make lint-javascript-tests TESTS_FILTER=".*/math/base/special/bessely1/.*" — clean.

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 running as an unattended scheduled task. The test migration and the ULP bound search (start high, tighten to the minimum that still passes, then re-run to confirm determinism) were performed by the agent, following the idiom established in already-migrated packages in math/base/special.

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@stdlib-js/reviewers

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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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Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/bessely1	$\\color{red}527/535$ $\\color{green}+98.50\\%$	$\\color{red}41/47$ $\\color{green}+87.23\\%$	$\\color{green}6/6$ $\\color{green}+100.00\\%$	$\\color{red}527/535$ $\\color{green}+98.50\\%$

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