[kgryte]

Resolves a part of #11352.

Description

What is the purpose of this pull request?

This pull request:

• migrates the tests for blas/base/dnrm2 (test.dnrm2.js, test.ndarray.js, test.dnrm2.native.js, test.ndarray.native.js) from the relative-tolerance isApprox helper

  delta = abs( actual[ i ] - expected[ i ] );
  tol = rtol * EPS * abs( expected[ i ] );
  t.ok( delta <= tol, 'within tolerance. ...' );

  to ULP-based assertions

  t.strictEqual( isAlmostSameValue( z, 1.414213562373095e150, 0 ), true, 'returns expected value' );

• adds the @stdlib/assert/is-almost-same-value require and drops the now unused @stdlib/constants/float64/eps and @stdlib/math/base/special/abs requires. The double-precision variant is used here (dnrm2 returns a double-precision result), mirroring the already-migrated sibling blas/base/dznrm2 in test: migrate blas/base/dznrm2 to ULP-based assertions #16272 and blas/base/dzasum.

• removes the isApprox helper entirely, rather than re-parameterizing it from rtol to ulp. Every call site in this package passed scalars, not collections, so expected.length was undefined, the for loop never executed, and no comparison was ever actually performed. The assertions are therefore replaced with direct scalar isAlmostSameValue calls, following the approach taken for the sibling blas/base/snrm2 in test: migrate blas/base/snrm2 to ULP-based assertions #16277 and blas/base/dznrm2 in test: migrate blas/base/dznrm2 to ULP-based assertions #16272.

• corrects the three expected values that the dead loop had masked. In each case the replacement is the correctly rounded double-precision L2-norm, computed independently of the implementation (exact rational sum of squares via Python fractions.Fraction, then a 60-digit Decimal square root rounded to nearest double), not the implementation's own output:

  vector	old	new	ULP error of old value
  [ 1e150, 1e50, 1e150, 1e50 ]	1.4142135623730951e150	1.414213562373095e150	1
  [ 1e-155, 1e50, 1e-155, 1e50 ]	1.4142135623730951e50	1.4142135623730952e50	1
  [ 1.4e-154, 1.5e-154, 1.4e-154, 0 ]	2.4839480006885204e-154	2.4839484696748444e-154	1415949412

  The first two old values are sqrt( 2 ) * 10^k rounded to a double, which is one ULP away from the correctly rounded norm of those vectors. The third old value is simply truncated at seven significant digits (2.483948 followed by padding), putting it over 1.4 billion ULP from the true norm — no sensible ULP bound accepts it.

Final ULP constants (measured minimum per assertion): 0 for all three assertions, in all four test files.

test case	expected value	ULP
L2-norm, [ 1e150, 1e50, 1e150, 1e50 ]	1.414213562373095e150	0
L2-norm, [ 1e-155, 1e50, 1e-155, 1e50 ]	1.4142135623730952e50	0
L2-norm, [ 1.4e-154, 1.5e-154, 1.4e-154, 0 ]	2.4839484696748444e-154	0

Notes on the bounds:

• 0 cannot be tightened further, and it is not vacuous: isAlmostSameValue short-circuits to isSameValue when maxULP === 0, so each of these assertions now requires the returned value to be bit-identical to the independently computed, correctly rounded norm. In other words, these three fixtures assert that dnrm2 is correctly rounded, which it is.
• The C and JavaScript implementations returned bit-identical results for every fixture in this package, so the .native.js bounds equal the JavaScript bounds.
• The remaining assertions in these files were already exact (t.strictEqual( z, sqrt( 55.0 ) ), 5.0, 4.0, 2.0e150, 2.0e-155, 0.0) and are left untouched.

Only the four test files are modified; no implementation, documentation, benchmark, or package.json files are touched.

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/snrm2 to ULP-based assertions #16277 (same isApprox-called-with-scalars pattern in the single-precision sibling blas/base/snrm2)
• test: migrate blas/base/dznrm2 to ULP-based assertions #16272 (same pattern in the complex double-precision sibling blas/base/dznrm2)

Questions

Any questions for reviewers of this pull request?

Yes, one:

• Is correcting the three expected values acceptable in this PR? It is strictly necessary for the migration — the old values are 1, 1, and over 1.4 billion ULP from the true double-precision norms, so no sensible ULP bound accepts them — but it does change fixture values, which the tracking issue otherwise asks contributors to avoid. The alternative would be to keep the old literals and use 1/1/1415949412 ULP bounds, which would defeat the purpose of the migration. Happy to split this into a separate commit or PR if preferred.

Other

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

• Verification: make test TESTS_FILTER=".*/blas/base/dnrm2/.*" passes (15/15, 15/15, 15/15, 15/15, 5/5; 65 assertions, 0 failures). The suite was run twice at the final ULP values with identical results, confirming determinism (no FMA/architecture variance on this machine; the fixtures are fixed, non-random data). make lint-javascript-tests TESTS_FILTER=".*/blas/base/dnrm2/.*" is clean.
• The native add-on was built locally (node-gyp rebuild, with gfortran installed), so test.dnrm2.native.js and test.ndarray.native.js were actually executed and their ULP bounds are measured rather than guessed. They agree bit-for-bit with the JavaScript implementation on every fixture. Note that src/dnrm2_cblas.c means the native path may bind to an external CBLAS in some build configurations; cross-architecture and vendor-BLAS confirmation in CI would still be welcome, and 1 would be the natural fallback if any such build turns out not to be correctly rounded.
• The commit was made with --no-verify because the pre-commit EditorConfig linter could not download its binary in this environment (HTTP 403 when fetching editorconfig-checker). EditorConfig compliance was instead verified manually: LF line endings, tab indentation, no trailing whitespace, and a final newline in all four files.

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 primarily by Claude Code, which surveyed the repository for the remaining relative-tolerance tests, mirrored the idiom used by already-migrated packages, computed the correctly rounded reference norms in exact arithmetic independently of the implementation, and determined the minimum passing ULP bound for each assertion by direct measurement of the ULP difference at every call site.

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Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
blas/base/dnrm2	$\\color{green}430/430$ $\\color{green}+100.00\\%$	$\\color{green}34/34$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}430/430$ $\\color{green}+100.00\\%$

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