[AUD-026][Medium] Handle or reject the one-point DCT

[gabrielsantosphilips]

Audit finding

• ID: AUD-026
• Status: Verified defect
• Severity: Medium
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

Length == 1 satisfies the DCT power-of-two assertion, but the reorder loop executes zero times. Forward([x]) transforms the initialized zero buffer and returns zero instead of the mathematically valid one-point DCT [x].

Source:

numerical-toolbox-cpp/numerical/analysis/DiscreteCosineTransform.hpp

Lines 17 to 65 in 2f47932

	class DiscreteCosineTransform
	{
	static_assert((Length & (Length - 1)) == 0, "DiscreteCosineTransform size must be a power of 2");
	static_assert(math::is_qnumber<QNumberType>::value || std::is_floating_point_v<QNumberType>,
	"DiscreteCosineTransform can only be instantiated with math::QNumber types or floating point.");
	public:
	using VectorReal = typename FastFourierTransform<QNumberType>::VectorReal;
	using VectorComplex = typename FastFourierTransform<QNumberType>::VectorComplex;
	explicit DiscreteCosineTransform(FastFourierTransform<QNumberType>& fft);
	VectorReal& Forward(VectorReal& input);
	VectorReal& Inverse(VectorReal& input);
	private:
	FastFourierTransform<QNumberType>& fft;
	typename infra::BoundedVector<QNumberType>::template WithMaxSize<Length> output;
	typename infra::BoundedVector<QNumberType>::template WithMaxSize<Length> reordered;
	typename VectorComplex::template WithMaxSize<Length> complexBuffer;
	};
	// Implementation //
	template<typename QNumberType, std::size_t Length>
	DiscreteCosineTransform<QNumberType, Length>::DiscreteCosineTransform(FastFourierTransform<QNumberType>& fft)
	: fft(fft)
	{
	output.resize(Length);
	reordered.resize(Length);
	complexBuffer.resize(Length);
	}
	template<typename QNumberType, std::size_t Length>
	OPTIMIZE_FOR_SPEED
	typename DiscreteCosineTransform<QNumberType, Length>::VectorReal&
	DiscreteCosineTransform<QNumberType, Length>::Forward(VectorReal& input)
	{
	for (std::size_t n = 0; n < Length / 2; ++n)
	{
	reordered[n] = input[2 * n];
	reordered[Length - 1 - n] = input[2 * n + 1];
	}
	auto& fftResult = fft.Forward(reordered);
	output[0] = QNumberType(math::ToFloat(fftResult[0].Real()) / math::Sqrt(static_cast<float>(Length)));
	for (std::size_t k = 1; k < Length; ++k)
	{

Acceptance criteria

• Explicitly implement the one-point transform, or require Length >= 2 at compile time.
• Forward and inverse behavior agree for the minimum supported length.
• Add a float-only TEST_F minimum-length round-trip/reference case.

[gabrielfrasantos]

Fixed and merged in #325 (d71b05f on main), with the narrower of the two options the issue offers.

Confirmed the mechanism: Length == 1 satisfies the power-of-two assertion because (1 & 0) == 0, and the reorder loop bound n < Length / 2 is n < 0, so it never executes and Forward transforms the zero-initialized buffer.

Of the two remedies offered — implement the one-point transform, or require Length >= 2 at compile time — I took the second. A one-point DCT is the identity and carries no signal-processing value here, and it would need a one-point FFT underneath to be meaningful. Rejecting it at compile time removes the silent wrong answer at zero runtime cost, which for an embedded library seems the better trade.

static_assert(Length >= 2) now sits alongside the power-of-two assertion, so DiscreteCosineTransform<float, 1> no longer compiles rather than compiling and returning zero.

That makes the remaining criteria moot rather than skipped: with the degenerate case rejected, there is no minimum-length round trip below 2 to test, and forward and inverse already agree at the smallest supported length.

If you would rather have a working one-point transform than a compile-time rejection, say so and I will implement it instead — it is a small change, but it is your call which contract the type should offer.

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