void BigIntegerStrassen::FastFourierTransform(vcomp &vect, bool invert){
//static long double PI = 3.14159265358979323846;
static long double PI = 3.14159265358979323846264338327950288419716939937510L;
ll n = (ll)vect.size();
if (n == 1) return;
vcomp vect0(n / 2), vect1(n / 2);
for (ll i = 0, j = 0; i<n; i += 2, ++j){
vect0[j] = vect[i];
vect1[j] = vect[i + 1];
}
FastFourierTransform(vect0, invert);
FastFourierTransform(vect1, invert);
long double ang = 2 * PI / n * (invert ? -1 : 1);
std::complex<long double> w(1), wn(cos(ang), sin(ang));
for (ll i = 0; i < n / 2; ++i) {
vect[i] = vect0[i] + w * vect1[i];
vect[i + n / 2] = vect0[i] - w * vect1[i];
if (invert){
vect[i] /= 2;
vect[i + n / 2] /= 2;
}
w *= wn;
}
}
void BigIntegerStrassen::Multiply(const BigIntegerStrassen &right_number){
vcomp fa(number.begin(), number.end());
auto right_arr = right_number.ToArray();
vcomp fb(right_arr.begin(), right_arr.end());
ll n = 1;
while (n < std::max(number.size(), right_arr.size())) n <<= 1;
n <<= 1;
fa.resize(n);
fb.resize(n);
FastFourierTransform(fa, false);
FastFourierTransform(fb, false);
for (ll i = 0; i < n; i++) fa[i] *= fb[i];
FastFourierTransform(fa, true);
number.resize(n);
ll carry = 0;
for (ll i = 0; i < n; i++){
carry += ll(fa[i].real() + 0.5);
number[i] = carry % base;
carry /= base;
}
while (number.size() && number.back() == 0) number.pop_back();
}
void FastFourierTransform(ComplexNumber x[], ComplexNumber X[], int N, int s) {
ComplexNumber t;
ComplexNumber intermediate_complex_number, intermediate_product;
if (N == 1) {
X[0] = x[0];
}
else {
FastFourierTransform(x, X, N / 2, 2 * s);
FastFourierTransform(x + s, X + N / 2, N / 2, 2 * s);
for (int k = 0; k < N / 2; k++) {
t = X[k];
intermediate_complex_number = NewComplexNumber(1.0, -2.0 * PI * (float)k / (float) N, 1);
intermediate_product = MultiplyComplexNumbers(intermediate_complex_number, X[k + N/2]);
X[k] = AddComplexNumbers(t, intermediate_product);
X[k + N/2] = SubtractComplexNumbers(t, intermediate_product);
}
}
}
TEST( FastFourierTransformTest, Inversible ) {
Polynomial<std::complex<double>> p = { { 1, 0 }, { 2, 3 }, { 4, 5 }, { 3, 5 } };
auto q = FastFourierTransform( p, false );
auto r = FastFourierTransform( q, true );
EXPECT_EQ( p, r );
}
