test: migrate blas/base/zaxpy 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 blas/base/zaxpy from relative tolerance testing to ULP difference testing.
• replaces the isApprox test helper's delta/tol computation (rtol * EPS * abs( expected[ i ] )) with isAlmostSameValue( actual[ i ], expected[ i ], ulp ) from @stdlib/assert/is-almost-same-value, dropping the now unused @stdlib/constants/float64/eps and @stdlib/math/base/special/abs imports and normalizing all assertion messages to 'returns expected value'.
• replaces the previous blanket rtol of 14.0 at every call site with the minimum required ULP bound for that call site.

The migration mirrors the idiom already used by the single-precision sibling package blas/base/caxpy, which passes a per-call-site integer ULP bound to the same isApprox helper shape.

Files changed (test files only):

• test/test.zaxpy.js
• test/test.zaxpy.native.js
• test/test.ndarray.js
• test/test.ndarray.native.js

Measured ULP bounds

Each bound below is the measured minimum: the suite passes at the stated value and fails at the value minus one. Bounds were determined by instrumenting isApprox with @stdlib/number/float64/base/ulp-difference to record the maximum observed ULP difference per call site, and then independently confirmed by re-running each call site at N-1.

test/test.zaxpy.js and test/test.zaxpy.native.js (identical bounds):

Test case	ULP
scales elements from x by alpha and adds the result to y	24
supports an x stride	8
supports a y stride	6
supports negative x strides	24
supports negative y strides	8
supports complex access patterns	6
supports view offsets	24

test/test.ndarray.js and test/test.ndarray.native.js (identical bounds; the native file additionally covers dcabs1( alpha ) === 0.0):

Test case	ULP
scales elements from x by alpha and adds the result to y	24
dcabs1( alpha ) === 0.0 returns the second input array unchanged (native only)	0
supports an x stride	8
supports an x offset	11
supports a y stride	6
supports a y offset	1
supports a negative x stride	24
supports a negative y stride	8
supports complex access patterns	6

The maximum bound (24 ULP) is driven by the hand-written decimal expected fixtures rather than by the implementation; the same effect is visible in blas/base/caxpy, whose corresponding cases converted to 15 ULP.

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?

The native test files were exercised against a locally built addon, and their measured bounds came out identical to the JavaScript ones, so the JS and native files carry the same values. Happy to adjust if a different convention is preferred for the 0 ULP case in test/test.ndarray.native.js, where isAlmostSameValue falls back to exact SameValue comparison.

Other

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

Verification performed:

• make test TESTS_FILTER=".*/blas/base/zaxpy/.*" — 496 assertions passing across all five test files (test.js, test.zaxpy.js, test.zaxpy.native.js, test.ndarray.js, test.ndarray.native.js), run three times with identical results to rule out arch/FMA nondeterminism.
• make lint-javascript-tests TESTS_FILTER=".*/blas/base/zaxpy/.*" — clean.
• The native tests were run against an addon built locally (node-gyp rebuild), so the native bounds are measured rather than inferred.
• Only the four test files listed above are modified; no source, documentation, or benchmark files are touched.

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 task: it selected the package, studied the already-converted sibling packages (blas/base/caxpy, blas/base/zdrot) to match the established idiom, performed the migration, and measured and minimized each ULP bound.

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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/zaxpy	$\\color{green}417/417$ $\\color{green}+100.00\\%$	$\\color{green}18/18$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}417/417$ $\\color{green}+100.00\\%$

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