void Test::test_PolyMult_works() {
srand(time(0));
int n = 4;
int randMin = -100, randMax = 100;
Vector<Complex> P(n), Q(n);
for(int i = 0; i < n; ++i) {
double real = rand()%(randMax-randMin)+randMin;
double imaginary = rand()%(randMax-randMin)+randMin;
P[i] = Complex(real, imaginary);
Q[i] = Complex(real, imaginary);
}
FFT fft;
fft.preComputeOmega(n);
Vector<Complex> resultsR = fft.polyMultR(P, Q, n);
fft.preComputeRBS(n);
Vector<Complex> resultsD = fft.polyMultD(P, Q, n);
for(int i = 0; i < n; ++i) {
if(resultsD[i] != resultsR[i])
std::cout << "*** Failed ***" << std::endl;
std::cout << resultsR[i] << " " << resultsD[i] << std::endl;
}
}
void Test::test_PolyMult_dynamic() {
int n = 2;
Vector<Complex> P(n),Q(n);
P[0] = Complex(2,0);
P[1] = Complex(2,0);
Q[0] = Complex(2,0);
Q[1] = Complex(2,0);
FFT fft;
fft.preComputeOmega(n);
fft.preComputeRBS(n);
Vector<Complex> results = fft.polyMultD(P, Q, n);
for(Complex c : results) {
std::cout << c << std::endl;
}
}
void Test::test_FFT_works() {
srand(time(0));
int n = 4;
Vector<Complex> P(n);
int randMin = -100, randMax = 100;
for(int i = 0; i < n; ++i) {
double real = rand()%(randMax-randMin)+randMin;
double imaginary = rand()%(randMax-randMin)+randMin;
P[i] = Complex(real, imaginary);
}
// P[0] = Complex(2,0);
// P[1] = Complex(2,0);
// P[2] = Complex(2,0);
// P[3] = Complex(2,0);
Vector<Complex> x = Vector<Complex> (n);
for(int i = 0; i < n; i++) {
x[i] = Complex(cos(2*PI/n * i), sin(2*PI/n * i));
}
FFT fft;
fft.preComputeRBS(n);
Vector<Complex> algebraic = fft.algebraic(P, n, x);
Vector<Complex> recursive = fft.recursive(P, n, x, 1);
Vector<Complex> dynamic = fft.dynamic(P, n, x);
for(int i = 0; i < n; ++i) {
std::cout << "A(" << i << "): " << algebraic[i] << std::endl;
std::cout << "R(" << i << "): " << recursive[i] << std::endl;
std::cout << "D(" << i << "): " << dynamic[i] << std::endl;
std::cout << std::endl;
}
}
void Test::run_FFT_dynamic() {
int minN = 32, maxN = 20000000;
std::cout << "FFT dynamic" << std::endl
<< "N" << '\t' << "Time" << std::endl;
for(int n = minN; n <= maxN; n*=2) {
FFT fft;
fft.preComputeRBS(n);
fft.preComputeOmega(n);
int runTime = averageRuntime([&](){
Vector<Complex> P = fft.makeRandomVector(n, -1, 1);
Vector<Complex> Q = fft.makeRandomVector(n, -1, 1);
Vector<Complex> result = fft.polyMultD(P, Q, n);
}, RUNS);
std::cout << n << '\t' << runTime << std::endl;
}
}
void Test::test_FFT_vs_previous_approaches() {
std::cout << "Simple Test" << std::endl;
{
int n = 2;
double p[] = {3,5};
double q[] = {2,1};
Vector<double> P(p, p+n);
Vector<double> Q(q, q+n);
Vector<Complex> PFFT (P.begin(), P.end());
Vector<Complex> QFFT (Q.begin(), Q.end());
PolyMult polyMultSB;
Vector<double> pqActualSB = polyMultSB.schoolBook(n, P, Q);
PolyMult polyMultDnC4;
std::vector<double> pqActualDnC4 = polyMultDnC4.divideAndConquer4(n, P, Q);
PolyMult polyMultDnC3;
std::vector<double> pqActualDnC3 = polyMultDnC3.divideAndConquer3(n, P, Q);
FFT fft;
fft.preComputeOmega(n);
Vector<Complex> pqActualFFTR = fft.polyMultR(PFFT, QFFT, n);
fft.preComputeRBS(n);
Vector<Complex> pqActualFFTD = fft.polyMultD(PFFT, QFFT, n);
double pqExpected[] = {6,13,5};
int w1 = 10;
std::cout << std::setw(w1) << "Expected"
<< std::setw(w1) << "SB"
<< std::setw(w1) << "DnC 4"
<< std::setw(w1) << "DnC 3"
<< std::setw(w1) << "FFT R"
<< std::setw(w1) << "FFT D"
<< std::endl;
std::cout << std::right;
for(int index = 0; index < 2*n-1; ++index) {
std::cout << std::setw(w1) << pqExpected[index]
<< std::setw(w1) << pqActualSB[index]
<< std::setw(w1) << pqActualDnC4[index]
<< std::setw(w1) << pqActualDnC3[index]
<< std::setw(w1) << pqActualFFTR[index].real()
<< std::setw(w1) << pqActualFFTD[index].real()
<< std::endl;
}
}
std::cout << std::endl
<< "Random Test" << std::endl;
{
srand(time(0));
int n = 8;
int randMin = 0, randMax = 100;
Vector<double> P(n), Q(n);
Vector<Complex> PFFT(n), QFFT(n);
for(int i = 0; i < n; ++i) {
double randomP = rand()%(randMax-randMin)+randMin;
double randomQ = rand()%(randMax-randMin)+randMin;
P[i] = randomP;
Q[i] = randomQ;
PFFT[i] = Complex(randomP, 0);
QFFT[i] = Complex(randomQ, 0);
}
PolyMult polyMultSB;
Vector<double> pqActualSB = polyMultSB.schoolBook(n, P, Q);
PolyMult polyMultDnC4;
std::vector<double> pqActualDnC4 = polyMultDnC4.divideAndConquer4(n, P, Q);
PolyMult polyMultDnC3;
std::vector<double> pqActualDnC3 = polyMultDnC3.divideAndConquer3(n, P, Q);
FFT fft;
fft.preComputeOmega(n);
Vector<Complex> pqActualFFTR = fft.polyMultR(PFFT, QFFT, n);
fft.preComputeRBS(n);
Vector<Complex> pqActualFFTD = fft.polyMultD(PFFT, QFFT, n);
int w1 = 10;
std::cout << std::setw(w1) << "SB"
<< std::setw(w1) << "DnC 4"
<< std::setw(w1) << "DnC 3"
<< std::setw(w1) << "FFT R"
<< std::setw(w1) << "FFT D"
<< std::endl;
std::cout << std::right << std::fixed;
for(int index = 0; index < 2*n-1; ++index) {
std::cout << std::setprecision(0) << std::setw(w1) << pqActualSB[index]
<< std::setprecision(0) << std::setw(w1) << pqActualDnC4[index]
<< std::setprecision(0) << std::setw(w1) << pqActualDnC3[index]
<< std::setprecision(0) << std::setw(w1) << pqActualFFTR[index].real()
<< std::setprecision(0) << std::setw(w1) << pqActualFFTD[index].real()
<< std::endl;
}
}
}