test: migrate stats/base/dists/beta/stdev 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/beta/stdev from relative tolerance testing to ULP difference testing.
• replaces the delta/tol comparisons in test/test.js and test/test.native.js with @stdlib/assert/is-almost-same-value, adds the corresponding require, and removes the now-unused @stdlib/math/base/special/abs and @stdlib/constants/float64/eps imports.
• uses a ULP bound of 2 in both test/test.js and test/test.native.js. This is the measured minimum over the full 1000-case Python fixture set: a bound of 1 fails for one case (alpha: 7.512224992944586, beta: 16.738584643513867), while 2 passes for all cases. The suite was run twice at the final bound to confirm determinism.
• makes no changes outside of the two test files.

Note on the native tests: the JavaScript and C implementations perform an identical sequence of operations (sqrt( ( alpha * beta ) / ( alpha + beta + 1.0 ) ) / ( alpha + beta )) with a correctly rounded sqrt, and the compiled C implementation was verified to return bit-identical results to the JavaScript implementation across all 1000 fixture cases, giving the same measured minimum of 2.

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.

No.

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 written by Claude Code, which selected the package, mirrored the conversion idiom used in already-migrated packages, and measured the minimum passing ULP bound.

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https://claude.ai/code/session_017Yzm1pYd69FheDzXXPPnR4

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/beta/stdev	$\\color{green}201/201$ $\\color{green}+100.00\\%$	$\\color{green}10/10$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}201/201$ $\\color{green}+100.00\\%$

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