TEST: De-flake timing tests with lower-bound assertions

[mmcky]

Summary

Fixes the flaky timing tests that have been intermittently reddening CI on green code (twice on main, once on #845). This is the second of the two root causes found while investigating #842's CI failure — the first (Coveralls 422 race + fail-fast cascade) is addressed in #845.

Root cause

The whole test_timing.py suite verifies the timing utilities (tic/tac/toc, loop_timer, Timer, timeit) by sleeping for a known duration and asserting the measured time stays within an upper bound:

assert_allclose(measured, expected_sleep, atol=0.05, rtol=2)

That is the wrong invariant for wall-clock timing. time.sleep(t) only guarantees the process is suspended for at least t seconds; a busy or descheduled CI runner can make the measured time arbitrarily larger. The tightest case, test_timeit_lambda_function (expected ≈ 0.05 s, ceiling ≈ 0.20 s), is the one that keeps tripping — e.g. measured 0.207 s vs ceiling 0.20 s on a loaded macOS runner.

Fix

Replace the ~14 upper-bound assertions with a lower-bound check, assert_at_least(measured, expected), which asserts the utilities do not under-report elapsed time (measured >= expected * 0.9). Scheduler overshoot — the actual source of the flakiness — is no longer treated as a failure, while a genuinely broken timer (returning zero / far too little) is still caught.

Kept as-is	Why
assert result['minimum'] <= result['average'] <= result['maximum']	A relationship invariant, not wall-clock dependent.
assert_(average_time >= average_of_best)	Same — relationship between aggregates.
test_timeit_single_run exact-equality asserts	Compare fields to each other, not to absolute time.

The now-unused assert_allclose import and the dead rtol/atol locals are removed (keeps the CI flake8 --select F401 check green).

Verification

• flake8 --select F401,F405,E231 quantecon/util/tests/test_timing.py — clean.
• pytest quantecon/util/tests/test_timing.py — 27 passed, run repeatedly with stable results.

Relationship to the other PRs

• CI: De-flake coverage upload and stop fail-fast cancelling the matrix #845 stops a single flake from cancelling the whole matrix (fail-fast: false) and removes the Coveralls race; this PR removes the flake itself. Together they should make CI reliably green.
• BUG: Fix DLE.compute_sequence under NumPy >= 2.4 (#839) #842 (the DLE / NumPy 2.4 fix that started this) is functionally green; it just needs CI: De-flake coverage upload and stop fail-fast cancelling the matrix #845's hardened workflow once that merges.

🤖 Generated with Claude Code

[Copilot]

Pull request overview

This PR de-flakes the timing-related test suite in quantecon.util by replacing wall-clock upper-bound assertions (which can fail on busy CI runners due to scheduler oversleep) with a consistent lower-bound assertion that primarily guards against timers under-reporting elapsed time.

Changes:

• Remove assert_allclose-based upper-bound checks for tic/tac/toc, loop_timer, Timer, and timeit results.
• Introduce assert_at_least(measured, expected) with a module-level TIMING_LOWER_BOUND to enforce measured >= expected * 0.9.
• Clean up now-unused imports and locals (assert_allclose, rtol, atol) to keep unused-import linting green.

[coveralls]

coverage: 93.012% (+0.004%) from 93.008% — fix-flaky-timing-tests into main

[mmcky]

Note for reviewers — what this PR changes and a fidelity check

This started as a pure de-flake but, after review, also strengthens the suite. Summary of the three commits and the reasoning, plus an assertion-by-assertion fidelity audit so it's clear nothing was silently weakened.

What changed

Commit	Change
7d9e6b6	Replace the wall-clock upper-bound assertions (assert_allclose(measured, expected, atol=0.05, rtol=2)) with lower-bound checks. time.sleep(t) only guarantees at least t; a busy CI runner can oversleep arbitrarily, so an upper bound on measured duration is flaky by construction (it tripped on test_timeit_lambda_function 3× recently).
809e24c	Make the assert_at_least failure message report the computed bound and factor, floats to 4 dp (Copilot suggestion).
9af5760	Restore a bounded check (assert_in_seconds) for the two unit tests, which exist to verify Timer.elapsed stays in seconds regardless of the display unit — a pure lower bound would miss a unit-leak regression.

The two helpers

Helper	Used by	Asserts
assert_at_least(x, e)	generic timing tests (tic/tac/toc, loop_timer, Timer.elapsed, timeit runs/average)	x >= 0.9·e — the timer does not under-report
assert_in_seconds(x, e)	test_timer_units, test_timeit_different_units	0.9·e <= x < 100·e — elapsed is in seconds, not ms (×1000) / µs (×1e6)

The ×100 ceiling sits ~25× above the worst overshoot actually observed on CI and 10× below a millisecond leak — so it catches a unit regression with no realistic flake risk.

Fidelity audit — no loss, net gain

The originals used rtol=2, so assert_allclose(x, e, atol=0.05, rtol=2) resolves to x ∈ [−(e+0.05), 3e+0.05]. The lower edge is negative, i.e. the originals were effectively upper-bound-only with no meaningful lower bound.

• Newly caught (the originals silently passed these): a timer returning 0 / not accumulating — assert_allclose(0, 0.1, …) passes but 0 >= 0.09 fails; and toc() returning the last interval (~0.1) instead of the cumulative total (~0.3) — now fails the >= 0.27 lower bound.
• Retained: the unit-invariance guard — the one place an upper bound genuinely mattered — still trips on a ms/µs leak, and now also has a lower bound.
• Unchanged: every relationship/structural/contract assertion — average_time >= average_of_best, minimum <= average <= maximum, the single-run equalities, all is not None / len == N / isinstance checks, the ValueError/validation tests, and the whole TestGlobalPrecision class.
• Only removed: loose wall-clock upper bounds on default-unit timing, which targeted an implausible bug class and were themselves the flake source.

Pre-existing caveat (not introduced here): test_timeit_lambda_function doesn't strongly verify the 0.5 multiplier (sleeping 0.1 instead of 0.05 passes both the old and new assertion). Unchanged by this PR; noting it for completeness.

Net: the suite is no longer flaky and catches more realistic regressions than before.

🤖 Generated with Claude Code

[oyamad]

@mmcky Thanks! Looks good to me. The comment from ChatGPT below is just optional (not blocking).

[oyamad]

A comment from ChatGPT:

Non-blocking nit: the comment/docstring could avoid saying “no real sleep can reach” because sleep overshoot is theoretically unbounded; “not expected under normal CI scheduling” would be more precise. Not worth blocking the PR.