test: migrate math/base/special/falling-factorial 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 math/base/special/falling-factorial from relative tolerance testing (delta <= tol, where tol = C * EPS * abs( expected[ i ] )) to ULP difference testing using @stdlib/assert/is-almost-same-value.
• applies the migration to both test/test.js and test/test.native.js.
• removes the now unused @stdlib/math/base/special/abs and @stdlib/constants/float64/eps requires from both test files.

Each of the three fixture-based test bodies declares a single named ulps constant, and each assertion uses the t.strictEqual( isAlmostSameValue( y, expected[ i ], ulps ), true, 'returns expected value' ) shape.

The ULP bounds are the measured minimum over each full fixture set (1000 cases per fixture):

Test body	Fixture	Previous tolerance	ULP bound
evaluates the falling factorial for large x	fixtures/cpp/large.json	80.0 * EPS	116
evaluates the falling factorial for small x	fixtures/cpp/small.json	80.0 * EPS	117
evaluates the falling factorial for negative x	fixtures/cpp/negative.json	100.0 * EPS	150

Notes on how the bounds were determined:

• The minimum required ULP difference was computed for every fixture value by bisection against isAlmostSameValue, taking the per-fixture maximum.
• The bounds were measured independently for the JavaScript implementation (lib/main.js) and the native implementation (lib/native.js, built via make install-node-addons). Both implementations yield identical maxima, so test.js and test.native.js use the same values.
• Tightness was confirmed by re-running the suite with each bound decremented by one, which produces exactly one failure per test body.
• The suite was run twice at the final bounds to confirm determinism; test.js reports 3014/3014 passing and test.native.js reports 3011/3011 passing on both runs.

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.

Only the two test files are changed; no package.json or source changes were required.

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. It studied the migration idiom from previously merged conversions, applied the migration, measured the minimum ULP bounds for both the JavaScript and native implementations, and verified tightness and determinism locally.

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@stdlib-js/reviewers

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Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/falling-factorial	$\\color{red}298/322$ $\\color{green}+0.00\\%$	$\\color{red}30/35$ $\\color{green}+0.00\\%$	$\\color{green}3/3$ $\\color{green}+0.00\\%$	$\\color{red}298/322$ $\\color{green}+0.00\\%$

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