dexed/JuceLibraryCode/modules/juce_audio_basics/effects/juce_FFT.cpp

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

   This file is part of the JUCE library.
   Copyright (c) 2015 - ROLI Ltd.

   Permission is granted to use this software under the terms of either:
   a) the GPL v2 (or any later version)
   b) the Affero GPL v3

   Details of these licenses can be found at: www.gnu.org/licenses

   JUCE is distributed in the hope that it will be useful, but WITHOUT ANY
   WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
   A PARTICULAR PURPOSE.  See the GNU General Public License for more details.

   ------------------------------------------------------------------------------

   To release a closed-source product which uses JUCE, commercial licenses are
   available: visit www.juce.com for more information.

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

// (For the moment, we'll implement a few local operators for this complex class - one
// day we'll probably either have a juce complex class, or use the C++11 one)
static FFT::Complex operator+ (FFT::Complex a, FFT::Complex b) noexcept     { FFT::Complex c = { a.r + b.r, a.i + b.i }; return c; }
static FFT::Complex operator- (FFT::Complex a, FFT::Complex b) noexcept     { FFT::Complex c = { a.r - b.r, a.i - b.i }; return c; }
static FFT::Complex operator* (FFT::Complex a, FFT::Complex b) noexcept     { FFT::Complex c = { a.r * b.r - a.i * b.i, a.r * b.i + a.i * b.r }; return c; }
static FFT::Complex& operator+= (FFT::Complex& a, FFT::Complex b) noexcept  { a.r += b.r; a.i += b.i; return a; }

//==============================================================================
struct FFT::FFTConfig
{
    FFTConfig (int sizeOfFFT, bool isInverse)
        : fftSize (sizeOfFFT), inverse (isInverse), twiddleTable ((size_t) sizeOfFFT)
    {
        for (int i = 0; i < fftSize; ++i)
        {
            const double phase = (isInverse ? 2.0 : -2.0) * double_Pi * i / fftSize;
            twiddleTable[i].r = (float) cos (phase);
            twiddleTable[i].i = (float) sin (phase);
        }

        const int 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* input, Complex* 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> twiddleTable;

    void perform (const Complex* input, Complex* output, const int stride, const int strideIn, const Factor* facs) const noexcept
    {
        const Factor factor (*facs++);
        Complex* const originalOutput = output;
        const Complex* const 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* data, const 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;
        }

        Complex* scratch = static_cast<Complex*> (alloca (sizeof (Complex) * (size_t) factor.radix));

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

                    data[k] += scratch[q] * twiddleTable[twiddleIndex];
                }

                k += factor.length;
            }
        }
    }

    void butterfly2 (Complex* data, const int stride, const int length) const noexcept
    {
        Complex* dataEnd = data + length;
        const Complex* tw = twiddleTable;

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

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

        const Complex* twiddle1 = twiddleTable;
        const Complex* twiddle2 = twiddle1;
        const Complex* twiddle3 = twiddle1;

        for (int i = length; --i >= 0;)
        {
            const Complex s0 = data[length]   * *twiddle1;
            const Complex s1 = data[lengthX2] * *twiddle2;
            const Complex s2 = data[lengthX3] * *twiddle3;
            const Complex s3 = s0 + s2;
            const Complex s4 = s0 - s2;
            const Complex s5 = *data - s1;
            *data += s1;
            data[lengthX2] = *data - s3;
            twiddle1 += stride;
            twiddle2 += stride * 2;
            twiddle3 += stride * 3;
            *data += s3;

            if (inverse)
            {
                data[length].r   = s5.r - s4.i;
                data[length].i   = s5.i + s4.r;
                data[lengthX3].r = s5.r + s4.i;
                data[lengthX3].i = s5.i - s4.r;
            }
            else
            {
                data[length].r   = s5.r + s4.i;
                data[length].i   = s5.i - s4.r;
                data[lengthX3].r = s5.r - s4.i;
                data[lengthX3].i = s5.i + s4.r;
            }

            ++data;
        }
    }

    JUCE_DECLARE_NON_COPYABLE_WITH_LEAK_DETECTOR (FFTConfig)
};


//==============================================================================
FFT::FFT (int order, bool inverse)  : config (new FFTConfig (1 << order, inverse)), size (1 << order) {}
FFT::~FFT() {}

void FFT::perform (const Complex* const input, Complex* const output) const noexcept
{
    config->perform (input, output);
}

void FFT::performRealOnlyForwardTransform (float* d) const noexcept
{
    // This can only be called on an FFT object that was created to do forward transforms.
    jassert (! config->inverse);

    Complex* const scratch = static_cast<Complex*> (alloca (16 + sizeof (Complex) * (size_t) size));

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

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

void FFT::performRealOnlyInverseTransform (float* d) const noexcept
{
    // This can only be called on an FFT object that was created to do inverse transforms.
    jassert (config->inverse);

    Complex* const scratch = static_cast<Complex*> (alloca (16 + sizeof (Complex) * (size_t) size));

    perform (reinterpret_cast<const Complex*> (d), scratch);

    const float scaleFactor = 1.0f / size;

    for (int i = 0; i < size; ++i)
    {
        d[i]        = scratch[i].r * scaleFactor;
        d[i + size] = scratch[i].i * scaleFactor;
    }
}

void FFT::performFrequencyOnlyForwardTransform (float* d) const noexcept
{
    performRealOnlyForwardTransform (d);
    const int twiceSize = size * 2;

    for (int i = 0; i < twiceSize; i += 2)
    {
        d[i / 2] = juce_hypot (d[i], d[i + 1]);

        if (i >= size)
        {
            d[i] = 0;
            d[i + 1] = 0;
        }
    }
}