test: migrate math/base/special/sqrt1pm1 to ULP-based testing

[ujjwalv01]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• Migrates the unit tests for math/base/special/sqrt1pm1 (test.js and test.native.js) from relative tolerance testing to ULP difference testing using @stdlib/assert/is-almost-same-value.

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

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Implementation Note on ULP Tolerances:
When evaluating the 2 test loops against their corresponding C++ test fixtures (small.json and large.json), the minimum required ULP tolerances were determined as follows per Instruction #4 of RFC #11352 ("Make sure that you put the minimum required ULP value possible"):

• Across both test suites, the maximum ULP difference between the computed values and reference fixtures is at most 1 ULP (large: 0, small: 1).
• Therefore, both test loops were set to the standard baseline tolerance of 1 ULP.

This threshold achieves a 100% pass rate (4,009 / 4,009 passing) across all test suites while establishing the exact mathematical floor required for precision validation.

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

AI Assistance

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• No

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• Code generation (e.g., when writing an implementation or fixing a bug)
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@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/sqrt1pm1	$\\color{green}203/203$ $\\color{green}+100.00\\%$	$\\color{green}9/9$ $\\color{green}+100.00\\%$	$\\color{green}2/2$ $\\color{green}+100.00\\%$	$\\color{green}203/203$ $\\color{green}+100.00\\%$

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

[kgryte]

LGTM