/* * Copyright (C) 2013 Jared Boone, ShareBrained Technology, Inc. * * This file is part of PortaPack. * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2, or (at your option) * any later version. * * This program 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. * * You should have received a copy of the GNU General Public License * along with this program; see the file COPYING. If not, write to * the Free Software Foundation, Inc., 51 Franklin Street, * Boston, MA 02110-1301, USA. */ #ifndef __DSP_FFT_H__ #define __DSP_FFT_H__ #include <cstdint> #include <cstddef> #include <complex> #include <cmath> #include <type_traits> #include <array> #include "dsp_types.hpp" #include "complex.hpp" #include "hal.h" #include "utility.hpp" #include "sine_table_int8.hpp" namespace std { /* https://github.com/AE9RB/fftbench/blob/master/cxlr.hpp * Nice trick from AE9RB (David Turnbull) to get compiler to produce simpler * fma (fused multiply-accumulate) instead of worrying about NaN handling */ inline complex<float> operator*(const complex<float>& v1, const complex<float>& v2) { return complex<float>{ v1.real() * v2.real() - v1.imag() * v2.imag(), v1.real() * v2.imag() + v1.imag() * v2.real()}; } } /* namespace std */ template <typename T, size_t N> void fft_swap(const buffer_c16_t src, std::array<T, N>& dst) { static_assert(power_of_two(N), "only defined for N == power of two"); for (size_t i = 0; i < N; i++) { const size_t i_rev = __RBIT(i) >> (32 - log_2(N)); const auto s = src.p[i]; dst[i_rev] = { static_cast<typename T::value_type>(s.real()), static_cast<typename T::value_type>(s.imag())}; } } template <typename T, size_t N> void fft_swap(const std::array<complex16_t, N>& src, std::array<T, N>& dst) { static_assert(power_of_two(N), "only defined for N == power of two"); for (size_t i = 0; i < N; i++) { const size_t i_rev = __RBIT(i) >> (32 - log_2(N)); const auto s = src[i]; dst[i_rev] = { static_cast<typename T::value_type>(s.real()), static_cast<typename T::value_type>(s.imag())}; } } template <typename T, size_t N> void fft_swap(const std::array<T, N>& src, std::array<T, N>& dst) { static_assert(power_of_two(N), "only defined for N == power of two"); for (size_t i = 0; i < N; i++) { const size_t i_rev = __RBIT(i) >> (32 - log_2(N)); dst[i_rev] = src[i]; } } template <typename T, size_t N> void fft_swap_in_place(std::array<T, N>& data) { static_assert(power_of_two(N), "only defined for N == power of two"); for (size_t i = 0; i < N / 2; i++) { const size_t i_rev = __RBIT(i) >> (32 - log_2(N)); std::swap(data[i], data[i_rev]); } } /* http://beige.ucs.indiana.edu/B673/node14.html */ /* http://www.drdobbs.com/cpp/a-simple-and-efficient-fft-implementatio/199500857?pgno=3 */ template <typename T, size_t N> void fft_c_preswapped(std::array<T, N>& data, const size_t from, const size_t to) { static_assert(power_of_two(N), "only defined for N == power of two"); constexpr auto K = log_2(N); if ((to > K) || (from > K)) return; constexpr size_t K_max = 8; static_assert(K <= K_max, "No FFT twiddle factors for K > 8"); static constexpr std::array<std::complex<float>, K_max> wp_table{{ {-2.0f, 0.0f}, // 2 {-1.0f, -1.0f}, // 4 {-0.2928932188134524756f, -0.7071067811865475244f}, // 8 {-0.076120467488713243872f, -0.38268343236508977173f}, // 16 {-0.019214719596769550874f, -0.19509032201612826785f}, // 32 {-0.0048152733278031137552f, -0.098017140329560601994f}, // 64 {-0.0012045437948276072852f, -0.049067674327418014255f}, // 128 {-0.00030118130379577988423f, -0.024541228522912288032f}, // 256 }}; /* Provide data to this function, pre-swapped. */ for (size_t k = from; k < to; k++) { const size_t mmax = 1 << k; const auto wp = wp_table[k]; T w{1.0f, 0.0f}; for (size_t m = 0; m < mmax; ++m) { for (size_t i = m; i < N; i += mmax * 2) { const size_t j = i + mmax; const T temp = w * data[j]; data[j] = data[i] - temp; data[i] += temp; } w += w * wp; } } } /* ifft(v,N): [0] If N==1 then return. [1] For k = 0 to N/2-1, let ve[k] = v[2*k] [2] Compute ifft(ve, N/2); [3] For k = 0 to N/2-1, let vo[k] = v[2*k+1] [4] Compute ifft(vo, N/2); [5] For m = 0 to N/2-1, do [6] through [9] [6] Let w.real() = cos(2*PI*m/N) [7] Let w.imag() = sin(2*PI*m/N) [8] Let v[m] = ve[m] + w*vo[m] [9] Let v[m+N/2] = ve[m] - w*vo[m] */ template <typename T> void ifft(T* v, int n, T* tmp) { if (n > 1) { int k, m; T z, w, *vo, *ve; ve = tmp; vo = tmp + n / 2; for (k = 0; k < n / 2; k++) { ve[k] = v[2 * k]; vo[k] = v[2 * k + 1]; } ifft(ve, n / 2, v); /* FFT on even-indexed elements of v[] */ ifft(vo, n / 2, v); /* FFT on odd-indexed elements of v[] */ for (m = 0; m < n / 2; m++) { w.real(sine_table_i8[((int)(m / (double)n * 0x100 + 0x40)) & 0xFF]); w.imag(sine_table_i8[((int)(m / (double)n * 0x100)) & 0xFF]); z.real((w.real() * vo[m].real() - w.imag() * vo[m].imag()) / 127); /* Re(w*vo[m]) */ z.imag((w.real() * vo[m].imag() + w.imag() * vo[m].real()) / 127); /* Im(w*vo[m]) */ v[m].real(ve[m].real() + z.real()); v[m].imag(ve[m].imag() + z.imag()); v[m + n / 2].real(ve[m].real() - z.real()); v[m + n / 2].imag(ve[m].imag() - z.imag()); } } return; } #endif /*__DSP_FFT_H__*/