bool find_init_composite_pos(int prime, int residue, int& pos1, int& pos2){
int rd2 = residue;
if(residue > prime || residue < 0) rd2 = residue % prime;
if(rd2 < 0) rd2 +=prime;
i64 nonres = find_non_residue(prime);
i64 r = Tonelli_Shanks(prime, nonres, rd2);
i64 r2 = prime - r;
if( r == NOT_FOUND) return false;
int coeff = simpleEq( r, prime) ;
assert((coeff * prime + r )%10 ==0);
pos1 = (coeff * prime + r)/ 10;
if(100LL*pos1*pos1 + prime - residue == prime)
pos1 += prime;
coeff = simpleEq( r2, prime);
assert((coeff * prime + r2 )%10 ==0);
pos2 = (coeff * prime + r2)/ 10;
if(100LL*pos2*pos2 + prime - residue == prime)
pos2 += prime;
return true;
}
void Sieve::CalculateOffsets2(void)
{
if (factorbase.size() == 0) return;
if (Q(0) % 2 == 0)
{
OffsetValue off2(0, 2, std::log(2.0));
offsets.push_back(off2);
CalculateOffsetsRec(0, 2, 2, std::log(2.0));
}
else
{
OffsetValue off2(1, 2, std::log(2.0));
offsets.push_back(off2);
CalculateOffsetsRec(1, 2, 2, std::log(2.0));
}
for (std::vector<unsigned long int>::iterator it = factorbase.begin() + 1;
it != factorbase.end(); ++it)
{
mpz_class retv = Tonelli_Shanks(*it, N);
mpz_class cof = *it - retv;
retv = (retv - N_sqrt) % *it;
if (retv < 0)
retv += *it;
cof = (cof - N_sqrt) % *it;
if (cof < 0)
cof += *it;
if (retv < SIEVESIZE && retv >= 0)
{
OffsetValue off(retv.get_ui(), *it, std::log((float)*it));
offsets.push_back(off);
CalculateOffsetsRec(retv.get_ui(), *it, *it, std::log((float)*it));
}
if (cof < SIEVESIZE && cof >= 0)
{
OffsetValue off(cof.get_ui(), *it, std::log((float)*it));
offsets.push_back(off);
CalculateOffsetsRec(cof.get_ui(), *it, *it, std::log((float)*it));
}
}
}
