mayhem-firmware/firmware/common/dsp_fft.hpp

/*
 * 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__*/