rseng-numerical-accuracy

# Numerical accuracy in research code Floating-point numbers are approximations with well-defined rules, and research conclusions can hinge on respecting them. The two recurring failures: treating floats as exact (== comparisons, accumulating error blindly) and treating all differences as noise (tolerances loosened until tests pass). Both are avoidable with a small set of habits - and both matter more in research than elsewhere, because the numbers ARE the result. ## The ground rules - Never compare floats with == (except against an exactly representable sentinel like 0.0 you assigned yourself). Use tolerance-based comparison: `math.isclose`, `numpy.isclose`, or the testing helpers below. - Decimal literals are usually not representable: 0.1 is stored as the nearest binary fraction, which is why 0.1 + 0.2 != 0.3. Format-rounding for display hides this; arithmetic does not. - NaN propagates and never equals anything, including itself; test with isnan, and decide explicitly whether NaN in data means missing, invalid or bug (rseng-data-management's missing-data discipline). Silent NaN propagation into published numbers is the classic silent failure. - Precision-degrading operations (subtracting nearly equal numbers - catastrophic cancellation; summing numbers of very different magnitude) lose precision structurally; restructure the formula (e.g. use expm1/log1p, two-pass variance algorithms) rather than adding digits. ## Tolerances: choose, do not t...