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