test: migrate blas/base/drot 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 blas/base/drot from relative tolerance testing to ULP difference testing, replacing the rtol * EPS * abs( expected ) comparisons in the isApprox helper with @stdlib/assert/is-almost-same-value. The idiom mirrors the already-migrated sibling package blas/base/drotm.

Files changed: test/test.drot.js, test/test.drot.native.js, test/test.ndarray.js, and test/test.ndarray.native.js. No non-test files are modified, and no test fixtures, expected values, or test cases were added, removed, or altered.

Each ULP constant is the measured minimum for its fixture set. Bounds were determined by computing, for every compared element, the smallest n for which isAlmostSameValue( actual, expected, n ) returns true, and taking the per-test maximum. Each bound was then verified to be minimal by confirming that the test fails at ULP - 1.

test/test.drot.js and test/test.drot.native.js:

Test	ULP	Previous rtol
applies a plane rotation (sx=1, sy=1)	5	6.0
applies a plane rotation (sx=2, sy=-2)	21	20.0
applies a plane rotation (sx=-2, sy=1)	21	20.0
applies a plane rotation (sx=-1, sy=-2)	5	4.0
supports an x stride	2	2.0
supports negative strides	21	20.0
supports complex access patterns	5	5.0

test/test.ndarray.js and test/test.ndarray.native.js:

Test	ULP	Previous rtol
applies a plane rotation (sx=1, sy=1)	5	6.0
applies a plane rotation (sx=2, sy=-2)	21	20.0
applies a plane rotation (sx=-2, sy=1)	21	20.0
applies a plane rotation (sx=-1, sy=-2)	5	4.0
supports an x stride	2	2.0
supports an x offset	2	2.0
supports a y stride	0	1.0
supports a y offset	1	1.0
supports negative strides	21	20.0
supports complex access patterns	5	5.0

Tests using exact assertions (t.deepEqual) were left unchanged.

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 21 ULP bounds are driven by a single element in each of those fixture sets. For the (sx=2, sy=-2) case, the last rotated x element is 0.8*(-0.4) + 0.6*0.5, which is subject to catastrophic cancellation: the computed value is -0.020000000000000073 against an expected literal of -0.02. The previous relative tolerance (20 * EPS * abs( expected )) permitted roughly 25 ULP at that magnitude, so 21 is a tightening rather than a relaxation, but reviewers may prefer a different treatment of that fixture.

Other

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

The bounds above were measured against the JavaScript implementations. The native test files use the same bounds, matching the convention in the already-migrated blas/base/drotm and blas/base/srotm. The native add-on could not be built locally (gfortran is unavailable in the environment used to author this change), so the native bounds are unverified locally and rely on CI. Marked as a draft for that reason.

The JavaScript test suite was run twice at the final bounds with identical results (326 assertions in test.drot.js, 360 in test.ndarray.js, all passing), confirming determinism.

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. The migration follows the idiom established in the already-migrated blas/base/drotm, and the ULP bounds were measured empirically rather than guessed.

---

@stdlib-js/reviewers

🤖 Generated with Claude Code

https://claude.ai/code/session_01JXfLRBopGnbspYy9pzBY29

---

Generated by Claude Code

[stdlib-bot]

Hello! 👋

We've noticed that you've been opening a number of PRs addressing good first issues. Thank you for your interest and enthusiasm!

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.

Not only does this ensure that other new contributors can work on things and get ramped up on all things stdlib, it also ensures that you can spend your time on more challenging problems. 🚀

For ideas for future PRs, feel free to search the codebase for TODOs and FIXMEs and be sure to check out other open issues on the issue tracker. Cheers!

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
blas/base/drot	$\\color{green}398/398$ $\\color{green}+100.00\\%$	$\\color{green}19/19$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}398/398$ $\\color{green}+100.00\\%$

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