[Planeshifter]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates the tests for math/base/special/bessely0 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	680.0 * EPS * abs( expected )	1127	445
large_positive	2400.0 * EPS * abs( expected )	3716	232
medium_positive	850.0 * EPS * abs( expected )	1626	217
small_positive	1000.0 * EPS * abs( expected )	1510	532
smaller	4.5 * EPS * abs( expected )	7	6
tiny_positive	10.0 * EPS * abs( expected )	2	2
subnormal	5000.0 * EPS * abs( expected )	8678	73
huge_positive	4500.0 * EPS * abs( expected )	4053	945
positive_gamut	16.0 * EPS * abs( expected )	25	18

These are the measured minima: each value above is the smallest integer for which the corresponding fixture set passes in full. I computed the exact ULP difference for every fixture point directly (via @stdlib/number/float64/base/ulp-difference) rather than searching by trial and error, so the "next largest" column shows how much headroom each bound has over the runner-up point in its set. The JavaScript and native (C) implementations agree exactly on every fixture point (I built the native add-on locally with make install-node-addons NODE_ADDONS_PATTERN="math/base/special/bessely0" and confirmed identical per-point ULP differences), 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 large_positive (3716), subnormal (8678), and huge_positive (4053) bounds are large in absolute terms, but they are strictly tighter than the relative tolerances they replace and reflect the accuracy of the current rational-approximation implementation for Y_0 in these regimes. Happy to instead round these to a nearby 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/bessely0/.*" — 41653 passing, 0 failing.
• node test/test.js and node test/test.native.js run twice each at the final bounds with identical results (41653 passing both times), 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="math/base/special/bessely0"), so the native assertions ran rather than being skipped.
• make lint-javascript-tests TESTS_FILTER=".*/math/base/special/bessely0/.*" — 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 candidate discovery (scanning the whole repo for the old tolerance idiom, then checking existing ULP-migration PRs to avoid collisions), the test migration, and the ULP bound search (computing the exact per-point ULP difference directly, then confirming determinism via repeated runs) were performed by the agent, following the idiom established in already-migrated packages in math/base/special — most directly math/base/special/bessely1 (#14344), converted just prior to this PR in the same Bessel-function family.

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Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/bessely0	$\\color{red}596/609$ $\\color{green}+97.87\\%$	$\\color{red}45/54$ $\\color{green}+83.33\\%$	$\\color{green}7/7$ $\\color{green}+100.00\\%$	$\\color{red}596/609$ $\\color{green}+97.87\\%$

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