JUCE/modules/juce_dsp/frequency/juce_FFT_test.cpp

/*
  ==============================================================================

   This file is part of the JUCE library.
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   licensing.

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   Or: You may also use this code under the terms of the GPL v3 (see
   www.gnu.org/licenses).

   JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
   EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
   DISCLAIMED.

  ==============================================================================
*/

namespace juce::dsp
{

struct FFTUnitTest  : public UnitTest
{
    FFTUnitTest()
        : UnitTest ("FFT", UnitTestCategories::dsp)
    {}

    static void fillRandom (Random& random, Complex<float>* buffer, size_t n)
    {
        for (size_t i = 0; i < n; ++i)
            buffer[i] = Complex<float> ((2.0f * random.nextFloat()) - 1.0f,
                                             (2.0f * random.nextFloat()) - 1.0f);
    }

    static void fillRandom (Random& random, float* buffer, size_t n)
    {
        for (size_t i = 0; i < n; ++i)
            buffer[i] = (2.0f * random.nextFloat()) - 1.0f;
    }

    static Complex<float> freqConvolution (const Complex<float>* in, float freq, size_t n)
    {
        Complex<float> sum (0.0, 0.0);
        for (size_t i = 0; i < n; ++i)
            sum += in[i] * exp (Complex<float> (0, static_cast<float> (i) * freq));

        return sum;
    }

    static void performReferenceFourier (const Complex<float>* in, Complex<float>* out,
                                         size_t n, bool reverse)
    {
        auto base_freq = static_cast<float> (((reverse ? 1.0 : -1.0) * MathConstants<double>::twoPi)
                                               / static_cast<float> (n));

        for (size_t i = 0; i < n; ++i)
            out[i] = freqConvolution (in, static_cast<float> (i) * base_freq, n);
    }

    static void performReferenceFourier (const float* in, Complex<float>* out,
                                         size_t n, bool reverse)
    {
        HeapBlock<Complex<float>> buffer (n);

        for (size_t i = 0; i < n; ++i)
            buffer.getData()[i] = Complex<float> (in[i], 0.0f);

        float base_freq = static_cast<float> (((reverse ? 1.0 : -1.0) * MathConstants<double>::twoPi)
                                                / static_cast<float> (n));

        for (size_t i = 0; i < n; ++i)
            out[i] = freqConvolution (buffer.getData(), static_cast<float> (i) * base_freq, n);
    }


    //==============================================================================
    template <typename Type>
    static bool checkArrayIsSimilar (Type* a, Type* b, size_t n) noexcept
    {
        for (size_t i = 0; i < n; ++i)
            if (std::abs (a[i] - b[i]) > 1e-3f)
                return false;

        return true;
    }

    struct RealTest
    {
        static void run (FFTUnitTest& u)
        {
            Random random (378272);

            for (size_t order = 0; order <= 8; ++order)
            {
                auto n = (1u << order);

                FFT fft ((int) order);

                HeapBlock<float> input (n);
                HeapBlock<Complex<float>> reference (n), output (n);

                fillRandom (random, input.getData(), n);
                performReferenceFourier (input.getData(), reference.getData(), n, false);

                // fill only first half with real numbers
                zeromem (output.getData(), n * sizeof (Complex<float>));
                memcpy (reinterpret_cast<float*> (output.getData()), input.getData(), n * sizeof (float));

                fft.performRealOnlyForwardTransform ((float*) output.getData());
                u.expect (checkArrayIsSimilar (reference.getData(), output.getData(), n));

                // fill only first half with real numbers
                zeromem (output.getData(), n * sizeof (Complex<float>));
                memcpy (reinterpret_cast<float*> (output.getData()), input.getData(), n * sizeof (float));

                fft.performRealOnlyForwardTransform ((float*) output.getData(), true);
                std::fill (reference.getData() + ((n >> 1) + 1), reference.getData() + n, std::complex<float> (0.0f));
                u.expect (checkArrayIsSimilar (reference.getData(), output.getData(), (n >> 1) + 1));

                memcpy (output.getData(), reference.getData(), n * sizeof (Complex<float>));
                fft.performRealOnlyInverseTransform ((float*) output.getData());
                u.expect (checkArrayIsSimilar ((float*) output.getData(), input.getData(), n));
            }
        }
    };

    struct FrequencyOnlyTest
    {
        static void run (FFTUnitTest& u)
        {
            Random random (378272);
            for (size_t order = 0; order <= 8; ++order)
            {
                auto n = (1u << order);

                FFT fft ((int) order);

                std::vector<float> inout ((size_t) n << 1), reference ((size_t) n << 1);
                std::vector<Complex<float>> frequency (n);

                fillRandom (random, inout.data(), n);
                zeromem (reference.data(), sizeof (float) * ((size_t) n << 1));
                performReferenceFourier (inout.data(), frequency.data(), n, false);

                for (size_t i = 0; i < n; ++i)
                    reference[i] = std::abs (frequency[i]);

                for (auto ignoreNegative : { false, true })
                {
                    auto inoutCopy = inout;
                    fft.performFrequencyOnlyForwardTransform (inoutCopy.data(), ignoreNegative);
                    auto numMatching = ignoreNegative ? (n / 2) + 1 : n;
                    u.expect (checkArrayIsSimilar (inoutCopy.data(), reference.data(), numMatching));
                }
            }
        }
    };

    struct ComplexTest
    {
        static void run (FFTUnitTest& u)
        {
            Random random (378272);

            for (size_t order = 0; order <= 7; ++order)
            {
                auto n = (1u << order);

                FFT fft ((int) order);

                HeapBlock<Complex<float>> input (n), buffer (n), output (n), reference (n);

                fillRandom (random, input.getData(), n);
                performReferenceFourier (input.getData(), reference.getData(), n, false);

                memcpy (buffer.getData(), input.getData(), sizeof (Complex<float>) * n);
                fft.perform (buffer.getData(), output.getData(), false);

                u.expect (checkArrayIsSimilar (output.getData(), reference.getData(), n));

                memcpy (buffer.getData(), reference.getData(), sizeof (Complex<float>) * n);
                fft.perform (buffer.getData(), output.getData(), true);


                u.expect (checkArrayIsSimilar (output.getData(), input.getData(), n));
            }
        }
    };

    template <class TheTest>
    void runTestForAllTypes (const char* unitTestName)
    {
        beginTest (unitTestName);

        TheTest::run (*this);
    }

    void runTest() override
    {
        runTestForAllTypes<RealTest> ("Real input numbers Test");
        runTestForAllTypes<FrequencyOnlyTest> ("Frequency only Test");
        runTestForAllTypes<ComplexTest> ("Complex input numbers Test");
    }
};

static FFTUnitTest fftUnitTest;

} // namespace juce::dsp