test(@stdlib/stats/incr/mpcorr): add absolute tolerance floor near zero

[Planeshifter]

Resolves .

Description

What is the purpose of this pull request?

This pull request:

• Fixes a flaky assertion in lib/node_modules/@stdlib/stats/incr/mpcorr/test/test.js that has failed the scheduled linux_test workflow (Node.js v12/v14/v16 jobs) on every run against develop for the past ~30 days (e.g. https://github.com/stdlib-js/stdlib/actions/runs/31582982055). The test "the accumulator function computes a moving sample Pearson product-moment correlation coefficient incrementally" fails intermittently, e.g. dataset: 1. window: 77. expected: 0.00001111149059682119. actual: 0.00001111149059554248. tol: 1.2336232698496807e-15. delta: 1.2787097362952984e-15.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• None.

Questions

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No.

Other

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Root cause: tol = 5.0e5 * EPS * abs( expected ); is purely relative to expected. Over a window of W=10 independent random values, expected (a Pearson correlation coefficient) is frequently near zero. As expected approaches zero, the tolerance collapses toward zero and ordinary incremental-vs-batch floating-point noise (~1e-16 to 1e-15) exceeds it. This is not evidence of an unstable accumulator; no growing or unstable drift was found in the accumulator itself. Distinct from the bug fixed in the sibling mpcorrdist PR (#13152), where r itself lands slightly outside [-1, 1]; here expected is a small, valid, in-range value.

Fix: both occurrences of tol = 5.0e5 * EPS * abs( expected ); (unknown-means and known-means test variants, ~lines 370 and 418) changed to tol = ( 5.0e5 * EPS * abs( expected ) ) + ( 10.0 * EPS );, adding a small absolute floor. The 10.0 * EPS constant matches the existing absolute-floor constant already used for the analogous expected === 0.0 case in lib/node_modules/@stdlib/stats/incr/mpcorrdist/test/test.js (line 384). No change to lib/main.js; accumulator runtime behavior is unchanged, this is test-only.

Validation: ran the package's full test suite (2422 assertions) 16 times locally against freshly-randomized data (test has no fixed seed); 100% pass. Three independent automated reviews (correctness, regression scope, style/conventions) returned approve with no blocking findings. One reviewer additionally ran an empirical simulation (2500 runs / 4.27M comparisons): old tolerance fails ~1% of runs, new tolerance fails 0/2500. A closed-form estimate puts residual per-run failure probability at ~1.2e-4, down from ~2.7e-2 (~230x reduction) — not full elimination, since the fix targets the near-zero regime without changing relative-noise magnitude at larger values.

Non-blocking notes for reviewers: (1) a larger absolute floor (30-50 * EPS) would be essentially free, since r is bounded to [-1, 1] and extra tolerance loses no meaningful test power, and would further shrink the residual failure probability; not applied here to keep the diff matching the existing reviewed constant exactly. (2) the same purely-relative-tolerance pattern (tol = 5.0e5 * EPS * abs( expected )) exists in sibling packages mpcorr2, nanmpcorr, nanmpcorr2, mapcorr, nanmapcorr — same latent flake risk, out of scope for this fix.

Checklist

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• Read, understood, and followed the contributing guidelines.

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This PR was written by an automated CI-failure triage routine running Claude Code, as part of a scheduled job that reviews GitHub Actions failures on develop. The routine identified the failure cluster from live job logs, investigated root cause via a dedicated sub-agent, applied the fix, validated it by running the full package test suite 16 times against freshly-randomized data, and required approval from three independent automated reviewers (correctness, regression scope, style/conventions) before committing.

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/incr/mpcorr	$\\color{green}590/590$ $\\color{green}+100.00\\%$	$\\color{green}61/61$ $\\color{green}+100.00\\%$	$\\color{green}3/3$ $\\color{green}+100.00\\%$	$\\color{green}590/590$ $\\color{green}+100.00\\%$

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