vd conv(vd a, vd b) {
int s = max(sz(a),sz(b)), L = get(s), n = 1<<L;
if (s <= 0) return {};
a.resize(n); a = fwht(a);
b.resize(n); b = fwht(b);
F0R(i,n) a[i] = a[i]*b[i];
a = fwht_rev(a);
return a;
}
/*
* we expect correct parameter size and preallocated out. Last 3 parameters are
* used as a cache - just supply the same vectors everytime when you're doing
* this multiple times.
*/
void fwht_dyadic_multiply (const bvector& a, const bvector& b, bvector& out,
std::vector<int>&t,
std::vector<int>&A,
std::vector<int>&B)
{
uint i;
//lift everyting to Z.
for (i = 0; i < a.size(); ++i) t[i] = a[i];
fwht (t, A);
for (i = 0; i < b.size(); ++i) t[i] = b[i];
fwht (t, B);
//multiply diagonals to A
for (i = 0; i < A.size(); ++i) A[i] *= B[i];
fwht (A, t);
uint bitpos = a.size(); //no problem as a.size() == 1<<m == 2^m
for (i = 0; i < t.size(); ++i) out[i] = (t[i] & bitpos) ? 1 : 0;
}
void mfwht(double data[], int *nrow, int *ncol){
for(int i=0; i < *ncol; i++){ fwht(data+(i * *nrow), nrow);}
}
vd fwht_rev(vd& a) {
vd res = fwht(a);
F0R(i,sz(res)) res[i] /= a.size();
return res;
}
