[kgryte]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates the tests for blas/base/dznrm2 from relative tolerance assertions to ULP-based assertions, following the same approach as the sibling migration for blas/base/scnrm2 (test: migrate blas/base/scnrm2 to ULP-based assertions #16261).

• removes the local isApprox test helper (along with the @stdlib/constants/float64/eps and @stdlib/math/base/special/abs imports) and replaces each call site with t.strictEqual( isAlmostSameValue( actual, expected, <ulp> ), true, 'returns expected value' );, using @stdlib/assert/is-almost-same-value.

• tightens four truncated reference values so that the ULP comparison is meaningful. The removed helper iterated over expected.length, but every call site passed a scalar return value, so the loop body never executed and the numeric results were effectively unasserted. As a result, several reference values had only been recorded to ~6 significant digits. The replacements are the correctly rounded double-precision values of the exact L2 norms and agree with the previously recorded digits:

  • 14.1 → 14.106735979665885 (sqrt(199))
  • 2.82842e+150 → 2.82842712474619e+150 (sqrt(8)*1e150)
  • 2.82843e-155 → 2.82842712474619e-155 (sqrt(8)*1e-155)
  • 3.51283e-154 → 3.512833614050059e-154

  Each was computed independently at 80 decimal digits of precision and then correctly rounded to the nearest float64, so the expectations remain independent references rather than a recording of implementation output.

ULP bounds

Bounds were measured by instrumenting each assertion with @stdlib/number/float64/base/ulp-difference over every test case and then tightened to the minimum passing integer:

File	ULP
test/test.dznrm2.js	0
test/test.ndarray.js	0
test/test.dznrm2.native.js	1
test/test.ndarray.native.js	1

The measured minimum for the JavaScript implementation is 0 ULP at every call site: against correctly rounded references, dznrm2 returns exactly the expected value. This is expected, since the scaled sum-of-squares accumulation only scales by powers of two (exact) before a correctly rounded sqrt.

The native bounds could not be measured locally because the native add-on is not built in this environment (those tests skip), so they are set to a conservative 1, matching how the corresponding native test files were handled in #16261.

The full package test suite was run twice at the final bounds to confirm determinism; both runs were green (test.dznrm2.js: 9 passing, test.ndarray.js: 14 passing, test.js: 5 passing, native files skipped). make eslint-tests TESTS_FILTER=".*/blas/base/dznrm2/.*" is clean, and only test files are changed.

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
• test: migrate blas/base/scnrm2 to ULP-based assertions #16261

Questions

Any questions for reviewers of this pull request?

• Is updating the four truncated reference values in scope here? Without it, the ULP comparison would require bounds on the order of 1e12, which would defeat the purpose of the migration. test: migrate blas/base/scnrm2 to ULP-based assertions #16261 made the equivalent change for 14.1 → 14.106736183166504, so this follows that precedent, but it is a larger set of values and worth a second look.
• Should the native test files use 0 to match the JavaScript files instead of the conservative 1? They were left at 1 since the bound could not be verified against a built add-on here.

Other

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

Opened as a draft pending reviewer input on the two questions above.

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 authored by Claude Code running as an unattended scheduled task: it selected the package, studied the prior art in #11352 and #16261, applied the migration, measured the ULP bounds, and wrote this description.

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@stdlib-js/reviewers

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Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
blas/base/dznrm2	$\\color{green}452/452$ $\\color{green}+100.00\\%$	$\\color{green}37/37$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}452/452$ $\\color{green}+100.00\\%$

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