test: migrate stats/base/dists/triangular/cdf 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/triangular/cdf from computed relative-tolerance comparisons (delta = abs( y - expected[ i ] ) / tol = 1.0 * EPS * abs( expected[ i ] ), asserted via t.ok( delta <= tol, ... )) to ULP-difference assertions using @stdlib/assert/is-almost-same-value.
• applies the migration to test/test.cdf.js, test/test.factory.js, and test/test.native.js (three fixture blocks in each).
• removes the now-unused @stdlib/math/base/special/abs and @stdlib/constants/float64/eps requires from all three test files, along with the delta and tol variable declarations and the redundant y === expected[ i ] exact-match branch.

Only test files are changed; no implementation, fixture, or documentation changes are included.

ULP bounds

Fixture block	Fixture	Previous tolerance	ULP bound
small range b - a (test.cdf.js, test.factory.js, test.native.js)	julia/small_range.json	1.0 * EPS * abs( expected[ i ] )	0
medium range b - a (test.cdf.js, test.factory.js, test.native.js)	julia/medium_range.json	1.0 * EPS * abs( expected[ i ] )	0
large range b - a (test.cdf.js, test.factory.js, test.native.js)	julia/large_range.json	1.0 * EPS * abs( expected[ i ] )	0

0 is the minimum integer N such that isAlmostSameValue( y, expected[ i ], N ) holds for every entry in each fixture, and, being the smallest representable bound, it cannot be tightened further. Starting from a high bound and tightening, the measured maximum ULP difference over the 3000 fixture values (1000 per range) is exactly 0; both the main function and the function returned by factory reproduce all 3000 Julia reference values bit-for-bit. This was confirmed independently of the test harness by searching, for each fixture entry, for the smallest N satisfying isAlmostSameValue( y, expected[ i ], N ).

The C implementation was measured the same way and also reproduces all 3000 reference values bit-for-bit, so test.native.js uses the same bound as the JavaScript tests. In addition to the in-harness measurement, src/main.c was compiled together with its transitive C dependencies into a standalone program which was fed the fixture inputs as exact IEEE-754 bit patterns; the returned bit patterns matched the fixture expectations exactly, which additionally rules out any FMA-contraction difference on this platform.

The native add-on was built locally (make install-node-addons), so test/test.native.js executes rather than being skipped. The full suite was run twice at the final bound with identical results both times: 9049 assertions passing across test.js (3), test.cdf.js (3012), test.factory.js (3022), and test.native.js (3012); no failures and no skipped tests. make eslint-tests TESTS_FILTER=".*/stats/base/dists/triangular/cdf/.*" is clean.

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.

The resulting assertion matches the idiom used by the already-migrated sibling packages stats/base/dists/triangular/logcdf and stats/base/dists/triangular/mgf, which apply the migration across test.<name>.js, test.factory.js, and test.native.js over the same style of Julia fixtures.

One environment note: make install-node-modules fails out of the box here because npm cannot resolve es-object-atoms@^1.1.2 (a transitive dependency; the registry publishes only up to 1.1.1). The install was completed by temporarily pinning that transitive dependency via an npm overrides entry, which was reverted before committing and is not part of this diff. The pre-commit editorconfig hook could not run either, since it downloads its checker binary from GitHub and network access to that repository is not available in this environment; the three changed files were instead verified manually against .editorconfig (LF endings, UTF-8, tab indentation, no trailing whitespace, final newline present).

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

This PR was written primarily by Claude Code, running as an unattended scheduled task. It selected the package, studied previously converted packages in the same family to match the established idiom, performed the conversion, and determined the minimum passing ULP bound empirically over the full fixture set.

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@stdlib-js/reviewers

🤖 Generated with Claude Code

https://claude.ai/code/session_01QMdFi7UjR2HWqwVCypejPd

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/triangular/cdf	$\\color{green}352/352$ $\\color{green}+100.00\\%$	$\\color{green}36/36$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}352/352$ $\\color{green}+100.00\\%$

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