Arbitrary Length FFT in C++ - c++

Question

I am trying to run the C++ FFT code from this web page:
https://www.nayuki.io/page/free-small-fft-in-multiple-languages
Pretty new to C++, so don't know how to run it. Essentially, I want to pass on a REAL vector and an IMAG vector to the program and generate an output of REAL and IMAG vectors.
Say my REAL_VEC = {1, 2, 3, 4, 5}
Say my IMAG_VEC = {0, 1, 0, 1, 0}
Am pasting the code that I have and its compiling. But where to give input and how to get output (for above vectors)?
//FftRealPairTest.cpp
#include <algorithm>
#include <cmath>
#include <cstdlib>
#include <iomanip>
#include <iostream>
#include <random>
#include <vector>
#include "FftRealPair.hpp"
using std::cout;
using std::endl;
using std::vector;
// Private function prototypes
static void testFft(int n);
static vector<double> randomReals(int n);
// Mutable global variable
static double maxLogError = -INFINITY;
// Random number generation
std::default_random_engine randGen((std::random_device())());
int main() {
// Test diverse size FFTs
for (int i = 0, prev = 0; i <= 4; i++) {
int n = static_cast<int>(std::lround(std::pow(1500.0, i / 100.0)));
if (n > prev) {
testFft(n);
prev = n;
}
}
cout << endl;
cout << "Max log err = " << std::setprecision(3) << maxLogError << endl;
cout << "Test " << (maxLogError < -10 ? "passed" : "failed") << endl;
return EXIT_SUCCESS;
}
static void testFft(int n) {
vector<double> inputreal(randomReals(n));
vector<double> inputimag(randomReals(n));
vector<double> actualoutreal(inputreal);
vector<double> actualoutimag(inputimag);
Fft::transform(actualoutreal, actualoutimag);
}
static vector<double> randomReals(int n) {
std::uniform_real_distribution<double> valueDist(-1.0, 1.0);
vector<double> result;
for (int i = 0; i < n; i++)
result.push_back(valueDist(randGen));
return result;
}
/////////////////
//FftRealPair.cpp
/*
* Free FFT and convolution (C++)
*
* Copyright (c) 2017 Project Nayuki. (MIT License)
* https://www.nayuki.io/page/free-small-fft-in-multiple-languages
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
* - The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
* - The Software is provided "as is", without warranty of any kind, express or
* implied, including but not limited to the warranties of merchantability,
* fitness for a particular purpose and noninfringement. In no event shall the
* authors or copyright holders be liable for any claim, damages or other
* liability, whether in an action of contract, tort or otherwise, arising from,
* out of or in connection with the Software or the use or other dealings in the
* Software.
*/
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <cstdint>
#include "FftRealPair.hpp"
using std::size_t;
using std::vector;
// Private function prototypes
static size_t reverseBits(size_t x, int n);
void Fft::transform(vector<double> &real, vector<double> &imag) {
size_t n = real.size();
if (n != imag.size())
throw "Mismatched lengths";
if (n == 0)
return;
else if ((n & (n - 1)) == 0) // Is power of 2
transformRadix2(real, imag);
else // More complicated algorithm for arbitrary sizes
transformBluestein(real, imag);
}
void Fft::inverseTransform(vector<double> &real, vector<double> &imag) {
transform(imag, real);
}
void Fft::transformRadix2(vector<double> &real, vector<double> &imag) {
// Length variables
size_t n = real.size();
if (n != imag.size())
throw "Mismatched lengths";
int levels = 0; // Compute levels = floor(log2(n))
for (size_t temp = n; temp > 1U; temp >>= 1)
levels++;
if (static_cast<size_t>(1U) << levels != n)
throw "Length is not a power of 2";
// Trignometric tables
vector<double> cosTable(n / 2);
vector<double> sinTable(n / 2);
for (size_t i = 0; i < n / 2; i++) {
cosTable[i] = std::cos(2 * M_PI * i / n);
sinTable[i] = std::sin(2 * M_PI * i / n);
}
// Bit-reversed addressing permutation
for (size_t i = 0; i < n; i++) {
size_t j = reverseBits(i, levels);
if (j > i) {
std::swap(real[i], real[j]);
std::swap(imag[i], imag[j]);
}
}
// Cooley-Tukey decimation-in-time radix-2 FFT
for (size_t size = 2; size <= n; size *= 2) {
size_t halfsize = size / 2;
size_t tablestep = n / size;
for (size_t i = 0; i < n; i += size) {
for (size_t j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
size_t l = j + halfsize;
double tpre = real[l] * cosTable[k] + imag[l] * sinTable[k];
double tpim = -real[l] * sinTable[k] + imag[l] * cosTable[k];
real[l] = real[j] - tpre;
imag[l] = imag[j] - tpim;
real[j] += tpre;
imag[j] += tpim;
}
}
if (size == n) // Prevent overflow in 'size *= 2'
break;
}
}
void Fft::transformBluestein(vector<double> &real, vector<double> &imag) {
// Find a power-of-2 convolution length m such that m >= n * 2 + 1
size_t n = real.size();
if (n != imag.size())
throw "Mismatched lengths";
size_t m = 1;
while (m / 2 <= n) {
if (m > SIZE_MAX / 2)
throw "Vector too large";
m *= 2;
}
// Trignometric tables
vector<double> cosTable(n), sinTable(n);
for (size_t i = 0; i < n; i++) {
unsigned long long temp = static_cast<unsigned long long>(i) * i;
temp %= static_cast<unsigned long long>(n) * 2;
double angle = M_PI * temp / n;
// Less accurate alternative if long long is unavailable: double angle = M_PI * i * i / n;
cosTable[i] = std::cos(angle);
sinTable[i] = std::sin(angle);
}
// Temporary vectors and preprocessing
vector<double> areal(m), aimag(m);
for (size_t i = 0; i < n; i++) {
areal[i] = real[i] * cosTable[i] + imag[i] * sinTable[i];
aimag[i] = -real[i] * sinTable[i] + imag[i] * cosTable[i];
}
vector<double> breal(m), bimag(m);
breal[0] = cosTable[0];
bimag[0] = sinTable[0];
for (size_t i = 1; i < n; i++) {
breal[i] = breal[m - i] = cosTable[i];
bimag[i] = bimag[m - i] = sinTable[i];
}
// Convolution
vector<double> creal(m), cimag(m);
convolve(areal, aimag, breal, bimag, creal, cimag);
// Postprocessing
for (size_t i = 0; i < n; i++) {
real[i] = creal[i] * cosTable[i] + cimag[i] * sinTable[i];
imag[i] = -creal[i] * sinTable[i] + cimag[i] * cosTable[i];
}
}
void Fft::convolve(const vector<double> &x, const vector<double> &y, vector<double> &out) {
size_t n = x.size();
if (n != y.size() || n != out.size())
throw "Mismatched lengths";
vector<double> outimag(n);
convolve(x, vector<double>(n), y, vector<double>(n), out, outimag);
}
void Fft::convolve(
const vector<double> &xreal, const vector<double> &ximag,
const vector<double> &yreal, const vector<double> &yimag,
vector<double> &outreal, vector<double> &outimag) {
size_t n = xreal.size();
if (n != ximag.size() || n != yreal.size() || n != yimag.size()
|| n != outreal.size() || n != outimag.size())
throw "Mismatched lengths";
vector<double> xr(xreal);
vector<double> xi(ximag);
vector<double> yr(yreal);
vector<double> yi(yimag);
transform(xr, xi);
transform(yr, yi);
for (size_t i = 0; i < n; i++) {
double temp = xr[i] * yr[i] - xi[i] * yi[i];
xi[i] = xi[i] * yr[i] + xr[i] * yi[i];
xr[i] = temp;
}
inverseTransform(xr, xi);
for (size_t i = 0; i < n; i++) { // Scaling (because this FFT implementation omits it)
outreal[i] = xr[i] / n;
outimag[i] = xi[i] / n;
}
}
static size_t reverseBits(size_t x, int n) {
size_t result = 0;
for (int i = 0; i < n; i++, x >>= 1)
result = (result << 1) | (x & 1U);
return result;
}
///////////
//FftRealPair.hpp
/*
* Free FFT and convolution (C++)
*
* Copyright (c) 2017 Project Nayuki. (MIT License)
* https://www.nayuki.io/page/free-small-fft-in-multiple-languages
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
* - The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
* - The Software is provided "as is", without warranty of any kind, express or
* implied, including but not limited to the warranties of merchantability,
* fitness for a particular purpose and noninfringement. In no event shall the
* authors or copyright holders be liable for any claim, damages or other
* liability, whether in an action of contract, tort or otherwise, arising from,
* out of or in connection with the Software or the use or other dealings in the
* Software.
*/
#pragma once
#include <vector>
namespace Fft {
/*
* Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
* The vector can have any length. This is a wrapper function.
*/
void transform(std::vector<double> &real, std::vector<double> &imag);
/*
* Computes the inverse discrete Fourier transform (IDFT) of the given complex vector, storing the result back into the vector.
* The vector can have any length. This is a wrapper function. This transform does not perform scaling, so the inverse is not a true inverse.
*/
void inverseTransform(std::vector<double> &real, std::vector<double> &imag);
/*
* Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
* The vector's length must be a power of 2. Uses the Cooley-Tukey decimation-in-time radix-2 algorithm.
*/
void transformRadix2(std::vector<double> &real, std::vector<double> &imag);
/*
* Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
* The vector can have any length. This requires the convolution function, which in turn requires the radix-2 FFT function.
* Uses Bluestein's chirp z-transform algorithm.
*/
void transformBluestein(std::vector<double> &real, std::vector<double> &imag);
/*
* Computes the circular convolution of the given real vectors. Each vector's length must be the same.
*/
void convolve(const std::vector<double> &x, const std::vector<double> &y, std::vector<double> &out);
/*
* Computes the circular convolution of the given complex vectors. Each vector's length must be the same.
*/
void convolve(
const std::vector<double> &xreal, const std::vector<double> &ximag,
const std::vector<double> &yreal, const std::vector<double> &yimag,
std::vector<double> &outreal, std::vector<double> &outimag);
}

Answer 1

If you look at the .hpp file that you posted, the first function transform() takes two inputs: your real and imaginary vectors. The FFT is done 'in place' so the result is returned in the same vectors.
If you want to give a try, you may look at the testFft() and initialize
inputReal and inputImag with your data. The vectors are then copied in actualOutReal and actualOutImag (to avoid overwriting the original data) and passed to transform.
After that you should have your output in the same vectors (actualOutReal and actualOutImag).

Answer 2

This code does precisely what you want (requires C++11):
#include <cstddef>
#include <vector>
#include "FftRealPair.hpp"
int main() {
// Declare input
std::vector<double> real{1, 2, 3, 4, 5};
std::vector<double> imag{0, 1, 0, 1, 0};
// Do FFT
Fft::transform(real, imag);
// Print result
for (std::size_t i = 0; i < real.size(); i++) {
std::cout << real[i] << " " << imag[i] << std::endl;
}
return 0;
}