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/*
* TinyFFT.cpp
* -----------
* Purpose: A simple FFT implementation for power-of-two FFTs
* Notes : This is a C++ adaption of Ryuhei Mori's BSD 2-clause licensed TinyFFT
* available from https://github.com/ryuhei-mori/tinyfft
* Authors: Ryuhei Mori
* OpenMPT Devs
* The OpenMPT source code is released under the BSD license. Read LICENSE for more details.
*/
#include "stdafx.h"
#include "TinyFFT.h"
OPENMPT_NAMESPACE_BEGIN
void TinyFFT::GenerateTwiddleFactors(uint32 i, uint32 b, std::complex<double> z)
{
if(b == 0)
w[i] = z;
else
{
GenerateTwiddleFactors(i, b >> 1, z);
GenerateTwiddleFactors(i | b, b >> 1, z * w[b]);
}
}
TinyFFT::TinyFFT(const uint32 fftSize)
: w(std::size_t(1) << (fftSize - 1))
, k(fftSize)
{
const uint32 m = 1 << k;
constexpr double PI2_ = 6.28318530717958647692;
const double arg = -PI2_ / m;
for(uint32 i = 1, j = m / 4; j; i <<= 1, j >>= 1)
{
w[i] = std::exp(I * (arg * j));
}
GenerateTwiddleFactors(0, m / 4, 1);
}
uint32 TinyFFT::Size() const noexcept
{
return 1 << k;
}
// Computes in-place FFT of size 2^k of A, result is in bit-reversed order.
void TinyFFT::FFT(std::vector<std::complex<double>> &A) const
{
MPT_ASSERT(A.size() == (std::size_t(1) << k));
const uint32 m = 1 << k;
uint32 u = 1;
uint32 v = m / 4;
if(k & 1)
{
for(uint32 j = 0; j < m / 2; j++)
{
auto Ajv = A[j + (m / 2)];
A[j + (m / 2)] = A[j] - Ajv;
A[j] += Ajv;
}
u <<= 1;
v >>= 1;
}
for(uint32 i = k & ~1; i > 0; i -= 2)
{
for(uint32 jh = 0; jh < u; jh++)
{
auto wj = w[jh << 1];
auto wj2 = w[jh];
auto wj3 = wj2 * wj;
for(uint32 j = jh << i, je = j + v; j < je; j++)
{
auto tmp0 = A[j];
auto tmp1 = wj * A[j + v];
auto tmp2 = wj2 * A[j + 2 * v];
auto tmp3 = wj3 * A[j + 3 * v];
auto ttmp0 = tmp0 + tmp2;
auto ttmp2 = tmp0 - tmp2;
auto ttmp1 = tmp1 + tmp3;
auto ttmp3 = -I * (tmp1 - tmp3);
A[j] = ttmp0 + ttmp1;
A[j + v] = ttmp0 - ttmp1;
A[j + 2 * v] = ttmp2 + ttmp3;
A[j + 3 * v] = ttmp2 - ttmp3;
}
}
u <<= 2;
v >>= 2;
}
}
// Computes in-place IFFT of size 2^k of A, input is expected to be in bit-reversed order.
void TinyFFT::IFFT(std::vector<std::complex<double>> &A) const
{
MPT_ASSERT(A.size() == (std::size_t(1) << k));
const uint32 m = 1 << k;
uint32 u = m / 4;
uint32 v = 1;
for(uint32 i = 2; i <= k; i += 2)
{
for(uint32 jh = 0; jh < u; jh++)
{
auto wj = std::conj(w[jh << 1]);
auto wj2 = std::conj(w[jh]);
auto wj3 = wj2 * wj;
for(uint32 j = jh << i, je = j + v; j < je; j++)
{
auto tmp0 = A[j];
auto tmp1 = A[j + v];
auto tmp2 = A[j + 2 * v];
auto tmp3 = A[j + 3 * v];
auto ttmp0 = tmp0 + tmp1;
auto ttmp1 = tmp0 - tmp1;
auto ttmp2 = tmp2 + tmp3;
auto ttmp3 = I * (tmp2 - tmp3);
A[j] = ttmp0 + ttmp2;
A[j + v] = wj * (ttmp1 + ttmp3);
A[j + 2 * v] = wj2 * (ttmp0 - ttmp2);
A[j + 3 * v] = wj3 * (ttmp1 - ttmp3);
}
}
u >>= 2;
v <<= 2;
}
if(k & 1)
{
for(uint32 j = 0; j < m / 2; j++)
{
auto Ajv = A[j + (m / 2)];
A[j + (m / 2)] = A[j] - Ajv;
A[j] += Ajv;
}
}
}
void TinyFFT::Normalize(std::vector<std::complex<double>> &data)
{
const double s = static_cast<double>(data.size());
for(auto &v : data)
v /= s;
}
OPENMPT_NAMESPACE_END
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