JUCE/modules/juce_dsp/frequency/juce_FFT.cpp

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

   This file is part of the JUCE 7 technical preview.
   Copyright (c) 2022 - Raw Material Software Limited

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

   For the technical preview this file cannot be licensed commercially.

   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
{
namespace dsp
{

struct FFT::Instance
{
    virtual ~Instance() = default;
    virtual void perform (const Complex<float>* input, Complex<float>* output, bool inverse) const noexcept = 0;
    virtual void performRealOnlyForwardTransform (float*, bool) const noexcept = 0;
    virtual void performRealOnlyInverseTransform (float*) const noexcept = 0;
};

struct FFT::Engine
{
    Engine (int priorityToUse) : enginePriority (priorityToUse)
    {
        auto& list = getEngines();
        list.add (this);
        std::sort (list.begin(), list.end(), [] (Engine* a, Engine* b) { return b->enginePriority < a->enginePriority; });
    }

    virtual ~Engine() = default;

    virtual FFT::Instance* create (int order) const = 0;

    //==============================================================================
    static FFT::Instance* createBestEngineForPlatform (int order)
    {
        for (auto* engine : getEngines())
            if (auto* instance = engine->create (order))
                return instance;

        jassertfalse;  // This should never happen as the fallback engine should always work!
        return nullptr;
    }

private:
    static Array<Engine*>& getEngines()
    {
        static Array<Engine*> engines;
        return engines;
    }

    int enginePriority; // used so that faster engines have priority over slower ones
};

template <typename InstanceToUse>
struct FFT::EngineImpl  : public FFT::Engine
{
    EngineImpl() : FFT::Engine (InstanceToUse::priority)        {}
    FFT::Instance* create (int order) const override            { return InstanceToUse::create (order); }
};

//==============================================================================
//==============================================================================
struct FFTFallback  : public FFT::Instance
{
    // this should have the least priority of all engines
    static constexpr int priority = -1;

    static FFTFallback* create (int order)
    {
        return new FFTFallback (order);
    }

    FFTFallback (int order)
    {
        configForward.reset (new FFTConfig (1 << order, false));
        configInverse.reset (new FFTConfig (1 << order, true));

        size = 1 << order;
    }

    void perform (const Complex<float>* input, Complex<float>* output, bool inverse) const noexcept override
    {
        if (size == 1)
        {
            *output = *input;
            return;
        }

        const SpinLock::ScopedLockType sl(processLock);

        jassert (configForward != nullptr);

        if (inverse)
        {
            configInverse->perform (input, output);

            const float scaleFactor = 1.0f / (float) size;

            for (int i = 0; i < size; ++i)
                output[i] *= scaleFactor;
        }
        else
        {
            configForward->perform (input, output);
        }
    }

    const size_t maxFFTScratchSpaceToAlloca = 256 * 1024;

    void performRealOnlyForwardTransform (float* d, bool) const noexcept override
    {
        if (size == 1)
            return;

        const size_t scratchSize = 16 + (size_t) size * sizeof (Complex<float>);

        if (scratchSize < maxFFTScratchSpaceToAlloca)
        {
            JUCE_BEGIN_IGNORE_WARNINGS_MSVC (6255)
            performRealOnlyForwardTransform (static_cast<Complex<float>*> (alloca (scratchSize)), d);
            JUCE_END_IGNORE_WARNINGS_MSVC
        }
        else
        {
            HeapBlock<char> heapSpace (scratchSize);
            performRealOnlyForwardTransform (unalignedPointerCast<Complex<float>*> (heapSpace.getData()), d);
        }
    }

    void performRealOnlyInverseTransform (float* d) const noexcept override
    {
        if (size == 1)
            return;

        const size_t scratchSize = 16 + (size_t) size * sizeof (Complex<float>);

        if (scratchSize < maxFFTScratchSpaceToAlloca)
        {
            JUCE_BEGIN_IGNORE_WARNINGS_MSVC (6255)
            performRealOnlyInverseTransform (static_cast<Complex<float>*> (alloca (scratchSize)), d);
            JUCE_END_IGNORE_WARNINGS_MSVC
        }
        else
        {
            HeapBlock<char> heapSpace (scratchSize);
            performRealOnlyInverseTransform (unalignedPointerCast<Complex<float>*> (heapSpace.getData()), d);
        }
    }

    void performRealOnlyForwardTransform (Complex<float>* scratch, float* d) const noexcept
    {
        for (int i = 0; i < size; ++i)
            scratch[i] = { d[i], 0 };

        perform (scratch, reinterpret_cast<Complex<float>*> (d), false);
    }

    void performRealOnlyInverseTransform (Complex<float>* scratch, float* d) const noexcept
    {
        auto* input = reinterpret_cast<Complex<float>*> (d);

        for (int i = size >> 1; i < size; ++i)
            input[i] = std::conj (input[size - i]);

        perform (input, scratch, true);

        for (int i = 0; i < size; ++i)
        {
            d[i] = scratch[i].real();
            d[i + size] = scratch[i].imag();
        }
    }

    //==============================================================================
    struct FFTConfig
    {
        FFTConfig (int sizeOfFFT, bool isInverse)
            : fftSize (sizeOfFFT), inverse (isInverse), twiddleTable ((size_t) sizeOfFFT)
        {
            auto inverseFactor = (inverse ? 2.0 : -2.0) * MathConstants<double>::pi / (double) fftSize;

            if (fftSize <= 4)
            {
                for (int i = 0; i < fftSize; ++i)
                {
                    auto phase = i * inverseFactor;

                    twiddleTable[i] = { (float) std::cos (phase),
                                        (float) std::sin (phase) };
                }
            }
            else
            {
                for (int i = 0; i < fftSize / 4; ++i)
                {
                    auto phase = i * inverseFactor;

                    twiddleTable[i] = { (float) std::cos (phase),
                                        (float) std::sin (phase) };
                }

                for (int i = fftSize / 4; i < fftSize / 2; ++i)
                {
                    auto other = twiddleTable[i - fftSize / 4];

                    twiddleTable[i] = { inverse ? -other.imag() :  other.imag(),
                                        inverse ?  other.real() : -other.real() };
                }

                twiddleTable[fftSize / 2].real (-1.0f);
                twiddleTable[fftSize / 2].imag (0.0f);

                for (int i = fftSize / 2; i < fftSize; ++i)
                {
                    auto index = fftSize / 2 - (i - fftSize / 2);
                    twiddleTable[i] = conj(twiddleTable[index]);
                }
            }

            auto root = (int) std::sqrt ((double) fftSize);
            int divisor = 4, n = fftSize;

            for (int i = 0; i < numElementsInArray (factors); ++i)
            {
                while ((n % divisor) != 0)
                {
                    if (divisor == 2)       divisor = 3;
                    else if (divisor == 4)  divisor = 2;
                    else                    divisor += 2;

                    if (divisor > root)
                        divisor = n;
                }

                n /= divisor;

                jassert (divisor == 1 || divisor == 2 || divisor == 4);
                factors[i].radix = divisor;
                factors[i].length = n;
            }
        }

        void perform (const Complex<float>* input, Complex<float>* output) const noexcept
        {
            perform (input, output, 1, 1, factors);
        }

        const int fftSize;
        const bool inverse;

        struct Factor { int radix, length; };
        Factor factors[32];
        HeapBlock<Complex<float>> twiddleTable;

        void perform (const Complex<float>* input, Complex<float>* output, int stride, int strideIn, const Factor* facs) const noexcept
        {
            auto factor = *facs++;
            auto* originalOutput = output;
            auto* outputEnd = output + factor.radix * factor.length;

            if (stride == 1 && factor.radix <= 5)
            {
                for (int i = 0; i < factor.radix; ++i)
                    perform (input + stride * strideIn * i, output + i * factor.length, stride * factor.radix, strideIn, facs);

                butterfly (factor, output, stride);
                return;
            }

            if (factor.length == 1)
            {
                do
                {
                    *output++ = *input;
                    input += stride * strideIn;
                }
                while (output < outputEnd);
            }
            else
            {
                do
                {
                    perform (input, output, stride * factor.radix, strideIn, facs);
                    input += stride * strideIn;
                    output += factor.length;
                }
                while (output < outputEnd);
            }

            butterfly (factor, originalOutput, stride);
        }

        void butterfly (const Factor factor, Complex<float>* data, int stride) const noexcept
        {
            switch (factor.radix)
            {
                case 1:   break;
                case 2:   butterfly2 (data, stride, factor.length); return;
                case 4:   butterfly4 (data, stride, factor.length); return;
                default:  jassertfalse; break;
            }

            JUCE_BEGIN_IGNORE_WARNINGS_MSVC (6255)
            auto* scratch = static_cast<Complex<float>*> (alloca ((size_t) factor.radix * sizeof (Complex<float>)));
            JUCE_END_IGNORE_WARNINGS_MSVC

            for (int i = 0; i < factor.length; ++i)
            {
                for (int k = i, q1 = 0; q1 < factor.radix; ++q1)
                {
                    JUCE_BEGIN_IGNORE_WARNINGS_MSVC (6386)
                    scratch[q1] = data[k];
                    JUCE_END_IGNORE_WARNINGS_MSVC
                    k += factor.length;
                }

                for (int k = i, q1 = 0; q1 < factor.radix; ++q1)
                {
                    int twiddleIndex = 0;
                    data[k] = scratch[0];

                    for (int q = 1; q < factor.radix; ++q)
                    {
                        twiddleIndex += stride * k;

                        if (twiddleIndex >= fftSize)
                            twiddleIndex -= fftSize;

                        JUCE_BEGIN_IGNORE_WARNINGS_MSVC (6385)
                        data[k] += scratch[q] * twiddleTable[twiddleIndex];
                        JUCE_END_IGNORE_WARNINGS_MSVC
                    }

                    k += factor.length;
                }
            }
        }

        void butterfly2 (Complex<float>* data, const int stride, const int length) const noexcept
        {
            auto* dataEnd = data + length;
            auto* tw = twiddleTable.getData();

            for (int i = length; --i >= 0;)
            {
                auto s = *dataEnd;
                s *= (*tw);
                tw += stride;
                *dataEnd++ = *data - s;
                *data++ += s;
            }
        }

        void butterfly4 (Complex<float>* data, const int stride, const int length) const noexcept
        {
            auto lengthX2 = length * 2;
            auto lengthX3 = length * 3;

            auto strideX2 = stride * 2;
            auto strideX3 = stride * 3;

            auto* twiddle1 = twiddleTable.getData();
            auto* twiddle2 = twiddle1;
            auto* twiddle3 = twiddle1;

            for (int i = length; --i >= 0;)
            {
                auto s0 = data[length]   * *twiddle1;
                auto s1 = data[lengthX2] * *twiddle2;
                auto s2 = data[lengthX3] * *twiddle3;
                auto s3 = s0;             s3 += s2;
                auto s4 = s0;             s4 -= s2;
                auto s5 = *data;          s5 -= s1;

                *data += s1;
                data[lengthX2] = *data;
                data[lengthX2] -= s3;
                twiddle1 += stride;
                twiddle2 += strideX2;
                twiddle3 += strideX3;
                *data += s3;

                if (inverse)
                {
                    data[length] = { s5.real() - s4.imag(),
                                     s5.imag() + s4.real() };

                    data[lengthX3] = { s5.real() + s4.imag(),
                                       s5.imag() - s4.real() };
                }
                else
                {
                    data[length] = { s5.real() + s4.imag(),
                                     s5.imag() - s4.real() };

                    data[lengthX3] = { s5.real() - s4.imag(),
                                       s5.imag() + s4.real() };
                }

                ++data;
            }
        }

        JUCE_DECLARE_NON_COPYABLE_WITH_LEAK_DETECTOR (FFTConfig)
    };

    //==============================================================================
    SpinLock processLock;
    std::unique_ptr<FFTConfig> configForward, configInverse;
    int size;
};

FFT::EngineImpl<FFTFallback> fftFallback;

//==============================================================================
//==============================================================================
#if (JUCE_MAC || JUCE_IOS) && JUCE_USE_VDSP_FRAMEWORK
struct AppleFFT  : public FFT::Instance
{
    static constexpr int priority = 5;

    static AppleFFT* create (int order)
    {
        return new AppleFFT (order);
    }

    AppleFFT (int orderToUse)
        : order (static_cast<vDSP_Length> (orderToUse)),
          fftSetup (vDSP_create_fftsetup (order, 2)),
          forwardNormalisation (0.5f),
          inverseNormalisation (1.0f / static_cast<float> (1 << order))
    {}

    ~AppleFFT() override
    {
        if (fftSetup != nullptr)
        {
            vDSP_destroy_fftsetup (fftSetup);
            fftSetup = nullptr;
        }
    }

    void perform (const Complex<float>* input, Complex<float>* output, bool inverse) const noexcept override
    {
        auto size = (1 << order);

        DSPSplitComplex splitInput  (toSplitComplex (const_cast<Complex<float>*> (input)));
        DSPSplitComplex splitOutput (toSplitComplex (output));

        vDSP_fft_zop (fftSetup, &splitInput,  2, &splitOutput, 2,
                      order, inverse ?  kFFTDirection_Inverse : kFFTDirection_Forward);

        float factor = (inverse ? inverseNormalisation : forwardNormalisation * 2.0f);
        vDSP_vsmul ((float*) output, 1, &factor, (float*) output, 1, static_cast<size_t> (size << 1));
    }

    void performRealOnlyForwardTransform (float* inoutData, bool ignoreNegativeFreqs) const noexcept override
    {
        auto size = (1 << order);
        auto* inout = reinterpret_cast<Complex<float>*> (inoutData);
        auto splitInOut (toSplitComplex (inout));

        inoutData[size] = 0.0f;
        vDSP_fft_zrip (fftSetup, &splitInOut, 2, order, kFFTDirection_Forward);
        vDSP_vsmul (inoutData, 1, &forwardNormalisation, inoutData, 1, static_cast<size_t> (size << 1));

        mirrorResult (inout, ignoreNegativeFreqs);
    }

    void performRealOnlyInverseTransform (float* inoutData) const noexcept override
    {
        auto* inout = reinterpret_cast<Complex<float>*> (inoutData);
        auto size = (1 << order);
        auto splitInOut (toSplitComplex (inout));

        // Imaginary part of nyquist and DC frequencies are always zero
        // so Apple uses the imaginary part of the DC frequency to store
        // the real part of the nyquist frequency
        if (size != 1)
            inout[0] = Complex<float> (inout[0].real(), inout[size >> 1].real());

        vDSP_fft_zrip (fftSetup, &splitInOut, 2, order, kFFTDirection_Inverse);
        vDSP_vsmul (inoutData, 1, &inverseNormalisation, inoutData, 1, static_cast<size_t> (size << 1));
        vDSP_vclr (inoutData + size, 1, static_cast<size_t> (size));
    }

private:
    //==============================================================================
    void mirrorResult (Complex<float>* out, bool ignoreNegativeFreqs) const noexcept
    {
        auto size = (1 << order);
        auto i = size >> 1;

        // Imaginary part of nyquist and DC frequencies are always zero
        // so Apple uses the imaginary part of the DC frequency to store
        // the real part of the nyquist frequency
        out[i++] = { out[0].imag(), 0.0 };
        out[0]   = { out[0].real(), 0.0 };

        if (! ignoreNegativeFreqs)
            for (; i < size; ++i)
                out[i] = std::conj (out[size - i]);
    }

    static DSPSplitComplex toSplitComplex (Complex<float>* data) noexcept
    {
        // this assumes that Complex interleaves real and imaginary parts
        // and is tightly packed.
        return { reinterpret_cast<float*> (data),
                 reinterpret_cast<float*> (data) + 1};
    }

    //==============================================================================
    vDSP_Length order;
    FFTSetup fftSetup;
    float forwardNormalisation, inverseNormalisation;
};

FFT::EngineImpl<AppleFFT> appleFFT;
#endif

//==============================================================================
//==============================================================================
#if JUCE_DSP_USE_SHARED_FFTW || JUCE_DSP_USE_STATIC_FFTW

#if JUCE_DSP_USE_STATIC_FFTW
extern "C"
{
    void* fftwf_plan_dft_1d     (int, void*, void*, int, int);
    void* fftwf_plan_dft_r2c_1d (int, void*, void*, int);
    void* fftwf_plan_dft_c2r_1d (int, void*, void*, int);
    void fftwf_destroy_plan     (void*);
    void fftwf_execute_dft      (void*, void*, void*);
    void fftwf_execute_dft_r2c  (void*, void*, void*);
    void fftwf_execute_dft_c2r  (void*, void*, void*);
}
#endif

struct FFTWImpl  : public FFT::Instance
{
   #if JUCE_DSP_USE_STATIC_FFTW
    // if the JUCE developer has gone through the hassle of statically
    // linking in fftw, they probably want to use it
    static constexpr int priority = 10;
   #else
    static constexpr int priority = 3;
   #endif

    struct FFTWPlan;
    using FFTWPlanRef = FFTWPlan*;

    enum
    {
        measure   = 0,
        unaligned = (1 << 1),
        estimate  = (1 << 6)
    };

    struct Symbols
    {
        FFTWPlanRef (*plan_dft_fftw) (unsigned, Complex<float>*, Complex<float>*, int, unsigned);
        FFTWPlanRef (*plan_r2c_fftw) (unsigned, float*, Complex<float>*, unsigned);
        FFTWPlanRef (*plan_c2r_fftw) (unsigned, Complex<float>*, float*, unsigned);
        void (*destroy_fftw) (FFTWPlanRef);

        void (*execute_dft_fftw) (FFTWPlanRef, const Complex<float>*, Complex<float>*);
        void (*execute_r2c_fftw) (FFTWPlanRef, float*, Complex<float>*);
        void (*execute_c2r_fftw) (FFTWPlanRef, Complex<float>*, float*);

       #if JUCE_DSP_USE_STATIC_FFTW
        template <typename FuncPtr, typename ActualSymbolType>
        static bool symbol (FuncPtr& dst, ActualSymbolType sym)
        {
            dst = reinterpret_cast<FuncPtr> (sym);
            return true;
        }
       #else
        template <typename FuncPtr>
        static bool symbol (DynamicLibrary& lib, FuncPtr& dst, const char* name)
        {
            dst = reinterpret_cast<FuncPtr> (lib.getFunction (name));
            return (dst != nullptr);
        }
       #endif
    };

    static FFTWImpl* create (int order)
    {
        DynamicLibrary lib;

      #if ! JUCE_DSP_USE_STATIC_FFTW
       #if JUCE_MAC
        auto libName = "libfftw3f.dylib";
       #elif JUCE_WINDOWS
        auto libName = "libfftw3f.dll";
       #else
        auto libName = "libfftw3f.so";
       #endif

        if (lib.open (libName))
      #endif
        {
            Symbols symbols;

           #if JUCE_DSP_USE_STATIC_FFTW
            if (! Symbols::symbol (symbols.plan_dft_fftw, fftwf_plan_dft_1d))     return nullptr;
            if (! Symbols::symbol (symbols.plan_r2c_fftw, fftwf_plan_dft_r2c_1d)) return nullptr;
            if (! Symbols::symbol (symbols.plan_c2r_fftw, fftwf_plan_dft_c2r_1d)) return nullptr;
            if (! Symbols::symbol (symbols.destroy_fftw,  fftwf_destroy_plan))    return nullptr;

            if (! Symbols::symbol (symbols.execute_dft_fftw, fftwf_execute_dft))     return nullptr;
            if (! Symbols::symbol (symbols.execute_r2c_fftw, fftwf_execute_dft_r2c)) return nullptr;
            if (! Symbols::symbol (symbols.execute_c2r_fftw, fftwf_execute_dft_c2r)) return nullptr;
           #else
            if (! Symbols::symbol (lib, symbols.plan_dft_fftw, "fftwf_plan_dft_1d"))     return nullptr;
            if (! Symbols::symbol (lib, symbols.plan_r2c_fftw, "fftwf_plan_dft_r2c_1d")) return nullptr;
            if (! Symbols::symbol (lib, symbols.plan_c2r_fftw, "fftwf_plan_dft_c2r_1d")) return nullptr;
            if (! Symbols::symbol (lib, symbols.destroy_fftw,  "fftwf_destroy_plan"))    return nullptr;

            if (! Symbols::symbol (lib, symbols.execute_dft_fftw, "fftwf_execute_dft"))     return nullptr;
            if (! Symbols::symbol (lib, symbols.execute_r2c_fftw, "fftwf_execute_dft_r2c")) return nullptr;
            if (! Symbols::symbol (lib, symbols.execute_c2r_fftw, "fftwf_execute_dft_c2r")) return nullptr;
           #endif

            return new FFTWImpl (static_cast<size_t> (order), std::move (lib), symbols);
        }

        return nullptr;
    }

    FFTWImpl (size_t orderToUse, DynamicLibrary&& libraryToUse, const Symbols& symbols)
        : fftwLibrary (std::move (libraryToUse)), fftw (symbols), order (static_cast<size_t> (orderToUse))
    {
        ScopedLock lock (getFFTWPlanLock());

        auto n = (1u << order);
        HeapBlock<Complex<float>> in (n), out (n);

        c2cForward = fftw.plan_dft_fftw (n, in.getData(), out.getData(), -1, unaligned | estimate);
        c2cInverse = fftw.plan_dft_fftw (n, in.getData(), out.getData(), +1, unaligned | estimate);

        r2c = fftw.plan_r2c_fftw (n, (float*) in.getData(), in.getData(), unaligned | estimate);
        c2r = fftw.plan_c2r_fftw (n, in.getData(), (float*) in.getData(), unaligned | estimate);
    }

    ~FFTWImpl() override
    {
        ScopedLock lock (getFFTWPlanLock());

        fftw.destroy_fftw (c2cForward);
        fftw.destroy_fftw (c2cInverse);
        fftw.destroy_fftw (r2c);
        fftw.destroy_fftw (c2r);
    }

    void perform (const Complex<float>* input, Complex<float>* output, bool inverse) const noexcept override
    {
        if (inverse)
        {
            auto n = (1u << order);
            fftw.execute_dft_fftw (c2cInverse, input, output);
            FloatVectorOperations::multiply ((float*) output, 1.0f / static_cast<float> (n), (int) n << 1);
        }
        else
        {
            fftw.execute_dft_fftw (c2cForward, input, output);
        }
    }

    void performRealOnlyForwardTransform (float* inputOutputData, bool ignoreNegativeFreqs) const noexcept override
    {
        if (order == 0)
            return;

        auto* out = reinterpret_cast<Complex<float>*> (inputOutputData);

        fftw.execute_r2c_fftw (r2c, inputOutputData, out);

        auto size = (1 << order);

        if (! ignoreNegativeFreqs)
            for (int i = size >> 1; i < size; ++i)
                out[i] = std::conj (out[size - i]);
    }

    void performRealOnlyInverseTransform (float* inputOutputData) const noexcept override
    {
        auto n = (1u << order);

        fftw.execute_c2r_fftw (c2r, (Complex<float>*) inputOutputData, inputOutputData);
        FloatVectorOperations::multiply ((float*) inputOutputData, 1.0f / static_cast<float> (n), (int) n);
    }

    //==============================================================================
    // fftw's plan_* and destroy_* methods are NOT thread safe. So we need to share
    // a lock between all instances of FFTWImpl
    static CriticalSection& getFFTWPlanLock() noexcept
    {
        static CriticalSection cs;
        return cs;
    }

    //==============================================================================
    DynamicLibrary fftwLibrary;
    Symbols fftw;
    size_t order;

    FFTWPlanRef c2cForward, c2cInverse, r2c, c2r;
};

FFT::EngineImpl<FFTWImpl> fftwEngine;
#endif

//==============================================================================
//==============================================================================
#if JUCE_DSP_USE_INTEL_MKL
struct IntelFFT  : public FFT::Instance
{
    static constexpr int priority = 8;

    static bool succeeded (MKL_LONG status) noexcept        { return status == 0; }

    static IntelFFT* create (int orderToUse)
    {
        DFTI_DESCRIPTOR_HANDLE mklc2c, mklc2r;

        if (DftiCreateDescriptor (&mklc2c, DFTI_SINGLE, DFTI_COMPLEX, 1, 1 << orderToUse) == 0)
        {
            if (succeeded (DftiSetValue (mklc2c, DFTI_PLACEMENT, DFTI_NOT_INPLACE))
                 && succeeded (DftiSetValue (mklc2c, DFTI_BACKWARD_SCALE, 1.0f / static_cast<float> (1 << orderToUse)))
                 && succeeded (DftiCommitDescriptor (mklc2c)))
            {
                if (succeeded (DftiCreateDescriptor (&mklc2r, DFTI_SINGLE, DFTI_REAL, 1, 1 << orderToUse)))
                {
                    if (succeeded (DftiSetValue (mklc2r, DFTI_PLACEMENT, DFTI_INPLACE))
                         && succeeded (DftiSetValue (mklc2r, DFTI_BACKWARD_SCALE, 1.0f / static_cast<float> (1 << orderToUse)))
                         && succeeded (DftiCommitDescriptor (mklc2r)))
                    {
                        return new IntelFFT (static_cast<size_t> (orderToUse), mklc2c, mklc2r);
                    }

                    DftiFreeDescriptor (&mklc2r);
                }
            }

            DftiFreeDescriptor (&mklc2c);
        }

        return {};
    }

    IntelFFT (size_t orderToUse, DFTI_DESCRIPTOR_HANDLE c2cToUse, DFTI_DESCRIPTOR_HANDLE cr2ToUse)
        : order (orderToUse), c2c (c2cToUse), c2r (cr2ToUse)
    {}

    ~IntelFFT() override
    {
        DftiFreeDescriptor (&c2c);
        DftiFreeDescriptor (&c2r);
    }

    void perform (const Complex<float>* input, Complex<float>* output, bool inverse) const noexcept override
    {
        if (inverse)
            DftiComputeBackward (c2c, (void*) input, output);
        else
            DftiComputeForward (c2c, (void*) input, output);
    }

    void performRealOnlyForwardTransform (float* inputOutputData, bool ignoreNegativeFreqs) const noexcept override
    {
        if (order == 0)
            return;

        DftiComputeForward (c2r, inputOutputData);

        auto* out = reinterpret_cast<Complex<float>*> (inputOutputData);
        auto size = (1 << order);

        if (! ignoreNegativeFreqs)
            for (int i = size >> 1; i < size; ++i)
                out[i] = std::conj (out[size - i]);
    }

    void performRealOnlyInverseTransform (float* inputOutputData) const noexcept override
    {
        DftiComputeBackward (c2r, inputOutputData);
    }

    size_t order;
    DFTI_DESCRIPTOR_HANDLE c2c, c2r;
};

FFT::EngineImpl<IntelFFT> fftwEngine;
#endif

//==============================================================================
//==============================================================================
// Visual Studio should define no more than one of these, depending on the
// setting at 'Project' > 'Properties' > 'Configuration Properties' > 'Intel
// Performance Libraries' > 'Use Intel(R) IPP'
#if _IPP_SEQUENTIAL_STATIC || _IPP_SEQUENTIAL_DYNAMIC || _IPP_PARALLEL_STATIC || _IPP_PARALLEL_DYNAMIC
class IntelPerformancePrimitivesFFT : public FFT::Instance
{
public:
    static constexpr auto priority = 9;

    static IntelPerformancePrimitivesFFT* create (const int order)
    {
        auto complexContext = Context<ComplexTraits>::create (order);
        auto realContext    = Context<RealTraits>   ::create (order);

        if (complexContext.isValid() && realContext.isValid())
            return new IntelPerformancePrimitivesFFT (std::move (complexContext), std::move (realContext), order);

        return {};
    }

    void perform (const Complex<float>* input, Complex<float>* output, bool inverse) const noexcept override
    {
        if (inverse)
        {
            ippsFFTInv_CToC_32fc (reinterpret_cast<const Ipp32fc*> (input),
                                  reinterpret_cast<Ipp32fc*> (output),
                                  cplx.specPtr,
                                  cplx.workBuf.get());
        }
        else
        {
            ippsFFTFwd_CToC_32fc (reinterpret_cast<const Ipp32fc*> (input),
                                  reinterpret_cast<Ipp32fc*> (output),
                                  cplx.specPtr,
                                  cplx.workBuf.get());
        }
    }

    void performRealOnlyForwardTransform (float* inoutData, bool ignoreNegativeFreqs) const noexcept override
    {
        ippsFFTFwd_RToCCS_32f_I (inoutData, real.specPtr, real.workBuf.get());

        if (order == 0)
            return;

        auto* out = reinterpret_cast<Complex<float>*> (inoutData);
        const auto size = (1 << order);

        if (! ignoreNegativeFreqs)
            for (auto i = size >> 1; i < size; ++i)
                out[i] = std::conj (out[size - i]);
    }

    void performRealOnlyInverseTransform (float* inoutData) const noexcept override
    {
        ippsFFTInv_CCSToR_32f_I (inoutData, real.specPtr, real.workBuf.get());
    }

private:
    static constexpr auto flag = IPP_FFT_DIV_INV_BY_N;
    static constexpr auto hint = ippAlgHintFast;

    struct IppFree
    {
        template <typename Ptr>
        void operator() (Ptr* ptr) const noexcept { ippsFree (ptr); }
    };

    using IppPtr = std::unique_ptr<Ipp8u[], IppFree>;

    template <typename Traits>
    struct Context
    {
        using SpecPtr = typename Traits::Spec*;

        static Context create (const int order)
        {
            int specSize = 0, initSize = 0, workSize = 0;

            if (Traits::getSize (order, flag, hint, &specSize, &initSize, &workSize) != ippStsNoErr)
                return {};

            const auto initBuf = IppPtr (ippsMalloc_8u (initSize));
            auto specBuf       = IppPtr (ippsMalloc_8u (specSize));
            SpecPtr specPtr = nullptr;

            if (Traits::init (&specPtr, order, flag, hint, specBuf.get(), initBuf.get()) != ippStsNoErr)
                return {};

            return { std::move (specBuf), IppPtr (ippsMalloc_8u (workSize)), specPtr };
        }

        Context() noexcept = default;

        Context (IppPtr&& spec, IppPtr&& work, typename Traits::Spec* ptr) noexcept
            : specBuf (std::move (spec)), workBuf (std::move (work)), specPtr (ptr)
        {}

        bool isValid() const noexcept { return specPtr != nullptr; }

        IppPtr specBuf, workBuf;
        SpecPtr specPtr = nullptr;
    };

    struct ComplexTraits
    {
        static constexpr auto getSize = ippsFFTGetSize_C_32fc;
        static constexpr auto init = ippsFFTInit_C_32fc;
        using Spec = IppsFFTSpec_C_32fc;
    };

    struct RealTraits
    {
        static constexpr auto getSize = ippsFFTGetSize_R_32f;
        static constexpr auto init = ippsFFTInit_R_32f;
        using Spec = IppsFFTSpec_R_32f;
    };

    IntelPerformancePrimitivesFFT (Context<ComplexTraits>&& complexToUse,
                                   Context<RealTraits>&& realToUse,
                                   const int orderToUse)
        : cplx (std::move (complexToUse)),
          real (std::move (realToUse)),
          order (orderToUse)
    {}

    Context<ComplexTraits> cplx;
    Context<RealTraits> real;
    int order = 0;
};

FFT::EngineImpl<IntelPerformancePrimitivesFFT> intelPerformancePrimitivesFFT;
#endif

//==============================================================================
//==============================================================================
FFT::FFT (int order)
    : engine (FFT::Engine::createBestEngineForPlatform (order)),
      size (1 << order)
{
}

FFT::FFT (FFT&&) noexcept = default;

FFT& FFT::operator= (FFT&&) noexcept = default;

FFT::~FFT() = default;

void FFT::perform (const Complex<float>* input, Complex<float>* output, bool inverse) const noexcept
{
    if (engine != nullptr)
        engine->perform (input, output, inverse);
}

void FFT::performRealOnlyForwardTransform (float* inputOutputData, bool ignoreNegativeFreqs) const noexcept
{
    if (engine != nullptr)
        engine->performRealOnlyForwardTransform (inputOutputData, ignoreNegativeFreqs);
}

void FFT::performRealOnlyInverseTransform (float* inputOutputData) const noexcept
{
    if (engine != nullptr)
        engine->performRealOnlyInverseTransform (inputOutputData);
}

void FFT::performFrequencyOnlyForwardTransform (float* inputOutputData, bool ignoreNegativeFreqs) const noexcept
{
    if (size == 1)
        return;

    performRealOnlyForwardTransform (inputOutputData, ignoreNegativeFreqs);
    auto* out = reinterpret_cast<Complex<float>*> (inputOutputData);

    const auto limit = ignoreNegativeFreqs ? (size / 2) + 1 : size;

    for (int i = 0; i < limit; ++i)
        inputOutputData[i] = std::abs (out[i]);

    zeromem (inputOutputData + limit, static_cast<size_t> (size * 2 - limit) * sizeof (float));
}

} // namespace dsp
} // namespace juce