Verification

constfilt is verified by a layered set of GoogleTest suites that together cover the library from individual math primitives up through end-to-end filter output. The goal is to catch numerical errors and regressions at the level where they originate, without relying on any single reference being infallible.

The layers, from the inside out:

Test file	Scope
filter.test.cpp	The Filter class in isolation: stored coefficients, batch output, sample-by-sample output, state reset.
discretize.test.cpp	expm, char_poly, ss_to_tf, ZOH, Matched-Z, Tustin, each checked against closed-form analytic results.
analog_filter.test.cpp	Continuous-time transfer function to state-space conversion and stability classification; full filter output checks (coefficients, step, impulse, chirp) against Octave references for ZOH, Matched-Z, and Tustin.
butterworth.test.cpp	Full Butterworth pipeline: pole computation, state-space, discretization, filtering, lowpass and highpass, ZOH, Matched-Z, and Tustin.
elliptic.test.cpp	Full Elliptic pipeline: nome-series design, discretization, filtering, lowpass and highpass, ZOH, Matched-Z, and Tustin.

Philosophy

Octave is the primary reference. Scripts generate coefficients and filter outputs and write them to committed C++ headers, so CI needs no Octave installation and any disagreement shows up as a hard failure. See building.md for how references are regenerated.

Filter correctness is checked against step, impulse, and chirp inputs.

Because constfilt coefficients are constexpr, filter behavior must be verified at compile time as well as runtime. The batch operator() is constexpr and is exercised as such in tests; the sample-by-sample path runs at runtime and is tested separately. Both paths are also checked for bit-identical output to confirm they implement the same computation.

Tolerances

Quantity	Tolerance	Rationale
Transfer function coefficients vs. Octave	\(10^{-7}\)	High-order coefficient computation accumulates floating-point error; N=8 was observed near \(3 \times 10^{-8}\).
Step / impulse / chirp response vs. Octave	\(10^{-7}\)	Recursive filtering accumulates rounding error; this bound accommodates that without masking real discrepancies.
Analytic ZOH / Matched-Z checks	\(10^{-10}\)	Closed-form references carry no approximation error beyond double representation.
Analytic Tustin checks	\(10^{-12}\)	Reference values are exact rationals, so a tighter bound is achievable than for ZOH / Matched-Z whose references involve transcendental exp() values.
DF2T hand-trace	\(10^{-13}\) to \(10^{-14}\)	Rational inputs yield nearly exact results; tight bounds catch any arithmetic mistake.