c++ - Highly Factorized Sieve of Eratosthenes -

just fun, i'm trying implement pseudocode this stackoverflow answer highly factorized sieve of eratosthenes in c++. can't figure out why code returns both prime , non-prime numbers. implementing these loops incorrectly? should using while loops instead? suspect i'm not incrementing loops properly. appreciated. i've spent several hours trying hunt down flaw.

gordonbgood's pseudocode inserted comments, , i've used same variable names.

#include <iostream> #include <vector> #include <cmath>  const int limit = 1000000000; const std::vector<int> r {23,29,31,37,41,43,47,53, 59,61,67,71,73,79,83, //positions + 19                       89,97,101,103,107,109,113,121,127, 131,137,139,                       143,149,151,157,163,167,169,173,179,181,187,191,193,                        197,199,209,211,221,223,227,229};  int main() { // array of length 11 times 13 times 17 times 19 = 46189 wheels initialized // doesn't contain multiples of large wheel primes // n n ← 210 × w + x w ∈ {0,...46189}, x in r: // //    if (n mod cp) not equal 0 cp ∈ {11,13,17,19}: // no 2,3,5,7 //        mstr(n) ← true else mstr(n) ← false                // factors   std::vector<bool> mstr(limit);   int n;   (int w=0; w <= 46189; ++w) {     (auto x = begin(r); x != end(r); ++x) {       n = 210*w + *x;       if (n % 11 != 0 && n % 13 != 0 && n % 17 != 0 && n % 19 != 0)         mstr[n]=true;       else         mstr[n]=false;      }   }  // initialize sieve array of smaller wheels // enough wheels include representation limit // n n ← 210 × w + x, w ∈ {0,...(limit - 19) ÷ 210}, x in r: //    sieve(n) ← mstr(n mod (210 × 46189))    // init pre-culled primes.   std::vector<bool> sieve(limit+1000);   (int w=0; w <= (limit-19)/210; ++w) {     (auto x = begin(r); x != end(r); ++x) {       n = 210*w + *x;       sieve[n] = mstr[(n % (210*46189))];     }   }  // eliminate composites sieving, occurrences on // wheel using wheel factorization version of sieve of eratosthenes // n² ≤ limit when n ← 210 × k + x k ∈ {0..}, x in r //    if sieve(n): //        // n prime, cull multiples //        s ← n² - n × (x - 23)     // zero'th modulo cull start position //        while c0 ≤ limit when c0 ← s + n × m m in r: //            c0d ← (c0 - 23) ÷ 210, cm ← (c0 - 23) mod 210 + 23 //means cm in r //            while c ≤ limit c ← 210 × (c0d + n × j) + cm //                    j ∈ {0,...}: //                sieve(c) ← false       // cull composites of prime     int s, c, c0, c0d, cm, j;   ( auto x = begin(r); x != end(r); ++x) {     ( int k=0; (n=210*k + (*x)) <= sqrt(limit); ++k){       if (sieve[n]) {         s = n*n - n*((*x)-23);         ( auto m = begin(r); (c0=s+n*(*m)) <= limit &&  m != end(r); ++m) {       c0d = (c0-23)/210;       cm  = (c0-23)%210 + 23;       ( int j=0; (c=210*(c0d+n*j)+cm) <= limit; ++j) {         sieve[c] = false;           }         }        }      }    }   // output 2, 3, 5, 7, 11, 13, 17, 19, // n ≤ limit when n ← 210 × k + x k ∈ {0..}, x in r: //     if sieve(n): output n     std::cout << "2\n3\n5\n7\n11\n13\n17\n19\n";   ( auto x = begin(r); x != end(r); ++x) {     ( int k = 0; (n=210*k + (*x)) <= limit; ++k) {       if (sieve[n]);     std::cout << n << std::endl;     }   }   std::cout << std::endl;    return 0; }