[AUD-023][Medium] Validate zero-divisor constructor parameters

[gabrielsantosphilips]

Audit finding

• ID: AUD-023
• Status: Verified defect cluster
• Severity: Medium
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

Three public constructors accept values that immediately become divisors:

• RecursiveLeastSquares(forgettingFactor=0) produces NaN covariance after one update.
• GoertzelAlgorithm(blockLength=0) performs four divisions by zero and reports ready before any sample.
• AlphaBetaFilter(..., Ts=0) stores an infinite velocity gain.

Sources:

• numerical-toolbox-cpp/numerical/estimators/online/RecursiveLeastSquares.hpp

  Lines 52 to 67 in 2f47932

  	RecursiveLeastSquares<T, Features>::RecursiveLeastSquares(T forgettingFactor)
  	: covariance(DesignMatrix::Identity())
  	, lambda(forgettingFactor)
  	, lambdaInverse(T(1) / lambda)
  	{
  	}
  	template<typename T, std::size_t Features>
  	RecursiveLeastSquares<T, Features>::RecursiveLeastSquares(T initialCovariance, T forgettingFactor)
  	: covariance(DesignMatrix::Identity() * initialCovariance)
  	, lambda(forgettingFactor)
  	, lambdaInverse(T(1) / lambda)
  	{
  	}
  	template<typename T, std::size_t Features>

• numerical-toolbox-cpp/numerical/analysis/GoertzelAlgorithm.hpp

  Lines 42 to 55 in 2f47932

  	template<typename T>
  	GoertzelAlgorithm<T>::GoertzelAlgorithm(std::size_t k, std::size_t blockLength)
  	: coeff{ T{ 2 } * math::Cos(T{ 2 } * std::numbers::pi_v<T> * static_cast<T>(k) / static_cast<T>(blockLength)) }
  	, cosine{ math::Cos(T{ 2 } * std::numbers::pi_v<T> * static_cast<T>(k) / static_cast<T>(blockLength)) }
  	, sine{ math::Sin(T{ 2 } * std::numbers::pi_v<T> * static_cast<T>(k) / static_cast<T>(blockLength)) }
  	, blockSize{ blockLength }
  	{}
  	template<typename T>
  	GoertzelAlgorithm<T>::GoertzelAlgorithm(T targetHz, T sampleHz, std::size_t blockLength)
  	: GoertzelAlgorithm(
  	static_cast<std::size_t>(targetHz / sampleHz * static_cast<T>(blockLength) + T{ 0.5 }),
  	blockLength)

• numerical-toolbox-cpp/numerical/filters/active/AlphaBetaFilter.hpp

  Lines 56 to 75 in 2f47932

  	AlphaBetaFilter<T, Order>::AlphaBetaFilter(T alpha, T beta, T Ts)
  	requires(Order == 2)
  	: samplePeriod{ Ts }
  	, gainAlpha{ alpha }
  	, gainBeta{ beta }
  	, betaOverTs{ beta / Ts }
  	{}
  	template<typename T, std::size_t Order>
  	AlphaBetaFilter<T, Order>::AlphaBetaFilter(T alpha, T beta, T gamma, T Ts)
  	requires(Order == 3)
  	: samplePeriod{ Ts }
  	, gainAlpha{ alpha }
  	, gainBeta{ beta }
  	, gainGamma{ gamma }
  	, betaOverTs{ beta / Ts }
  	, twoGammaOverTs2{ T{ 2 } * gamma / (Ts * Ts) }
  	{}
  	template<typename T, std::size_t Order>

Acceptance criteria

• Enforce finite documented domains before division.
• Use status factories where runtime values can be invalid.
• Add one float-only TEST_F failure case per constructor.
• No NaN/Inf state is stored for rejected input.