test: migrate math/base/special/cscd to ULP-based assertions - #14313

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates the tests for math/base/special/cscd from relative tolerance testing (delta <= tol, where tol = 1.4 * EPS * abs( expected[ i ] )) to ULP difference testing using @stdlib/assert/is-almost-same-value.

Both test/test.js and test/test.native.js are updated. In each file, the two fixture loops (negative and positive values) now assert

t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );

The now-unused @stdlib/constants/float64/eps and @stdlib/math/base/special/abs requires are removed, and the @stdlib/assert/is-almost-same-value require is added. The pre-existing expected[ i ] === null branches (which assert exact -Infinity/+Infinity returns at multiples of 180) are left unchanged, as those are exact comparisons rather than tolerance-based ones.

ULP constant

The measured minimum ULP value is 2, used in all four converted fixture loops:

The bound was tightened by measuring the exact worst-case ULP difference over the full Julia fixture sets (999 non-null cases per set): the maximum observed difference is exactly 2 ULP in both the negative and positive sets, and the suite fails at 1 ULP. The test suite was run twice at the final value to confirm determinism (2009 passing assertions, no failures, 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?

test/test.native.js uses the same 2 ULP bound as test/test.js. The native addon was not built in the environment used to author this change, so those tests were skipped locally and the C implementation's ULP behavior was not measured directly. The bound mirrors the JavaScript measurement on the grounds that both implementations are the same expression (1.0 / sind( x ) in lib/main.js and stdlib_base_cscd in src/main.c). Happy to adjust if reviewers would prefer a separately measured value for the native tests.

Other

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

The conversion mirrors the idiom already used by the sibling package math/base/special/cotd, which has the same fixture structure, including the null special-case branches.

Verification performed:

• make test TESTS_FILTER=".*/math/base/special/cscd/.*" — passing (run twice)
• make eslint-tests TESTS_FILTER=".*/math/base/special/cscd/.*" — clean
• only the two test files are modified

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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Disclosure

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This PR was written by Claude Code running as an unattended scheduled task. The tolerance-to-ULP conversion, the ULP bound search, and the local verification runs were all performed by the agent.

@stdlib-js/reviewers

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