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#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A" #include "../../template.h" #include "../Prime/SieveFast.h" #include "../Prime/RabinMiller32.h" bitset<INT_MAX> all_primes; void newPrime(int p) { all_primes[p] = 1; } void solve() { srand(7777); sieve(INT_MAX, newPrime); cerr << "DONE SIEVE" << endl; for (int i = 0; i < INT_MAX; ++i) { if (rand() % 30) continue; if (all_primes[i] == 1) assert(is_prime(i)); else assert(!is_prime(i)); } cout << "Hello World\n"; }
#line 1 "Math/tests/rabin_miller_32_stress.test.cpp" #define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A" #line 1 "template.h" #include <bits/stdc++.h> using namespace std; #define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++) #define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--) #define REP(i,a) for(int i=0,_a=(a); i<_a; i++) #define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it) #define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; } #define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; } #define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; } #define sqr(x) ((x) * (x)) // For printing pair, container, etc. // Copied from https://quangloc99.github.io/2021/07/30/my-CP-debugging-template.html template<class U, class V> ostream& operator << (ostream& out, const pair<U, V>& p) { return out << '(' << p.first << ", " << p.second << ')'; } template<class Con, class = decltype(begin(declval<Con>()))> typename enable_if<!is_same<Con, string>::value, ostream&>::type operator << (ostream& out, const Con& con) { out << '{'; for (auto beg = con.begin(), it = beg; it != con.end(); it++) { out << (it == beg ? "" : ", ") << *it; } return out << '}'; } template<size_t i, class T> ostream& print_tuple_utils(ostream& out, const T& tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); } template<class ...U> ostream& operator << (ostream& out, const tuple<U...>& t) { return print_tuple_utils<0, tuple<U...>>(out, t); } mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()); long long get_rand(long long r) { return uniform_int_distribution<long long> (0, r-1)(rng); } template<typename T> vector<T> read_vector(int n) { vector<T> res(n); for (int& x : res) cin >> x; return res; } void solve(); int main() { ios::sync_with_stdio(0); cin.tie(0); solve(); return 0; } #line 1 "Math/Prime/SieveFast.h" // Tested: // - (3B+) https://oj.vnoi.info/problem/icpc22_national_c // - (1B, collect into vector of primes) https://www.spoj.com/problems/KPRIMES2/ // - (1B, print) https://www.spoj.com/problems/PRIMES2/ // // Note: // - It's possible to extract code from here to have a fast implementation // of segmented sieve for [L, R] where R is very big (e.g. 10^12) // See: https://www.spoj.com/status/SUMPRIM2,mr_invincible/ // However there are several things that need to be fixed: // 1. Initialization of small primes: // - Need to change 256 -> R^0.25 // - Change 32768 -> R^0.5 // 2. Change N_SMALL_PRIMES // 3. If R^0.5 is around 10^6, p^2 overflow int, so need to check everywhere.. // 4. si[SIEVE_SIZE] may not have enough elements to sieve small_primes.. // 5. update_sieve(offset) assumes offset is a multiple of SIEVE_SPAN. This // is not true if we sieve a segment [L, R] // 6. Maybe more issues.. // Essentially if we need to do this, either use SegmentedSieve or copy from // https://www.spoj.com/status/SUMPRIM2,mr_invincible/ which I spent like an // hour to make it work.. // Segmented sieve with wheel factorization {{{ namespace segmented_sieve_wheel { const int WHEEL = 3 * 5 * 7 * 11 * 13; const int N_SMALL_PRIMES = 6536; // cnt primes less than 2^16 const int SIEVE_SPAN = WHEEL * 64; // one iteration of segmented sieve const int SIEVE_SIZE = SIEVE_SPAN / 128 + 1; uint64_t ONES[64]; // ONES[i] = 1<<i int small_primes[N_SMALL_PRIMES]; // primes less than 2^16 // each element of sieve is a 64-bit bitmask. // Each bit (0/1) stores whether the corresponding element is a prime number. // We only need to store odd numbers // -> 1st bitmask stores 3, 5, 7, 9, ... uint64_t si[SIEVE_SIZE]; // for each 'wheel', we store the sieve pattern (i.e. what numbers cannot // be primes) uint64_t pattern[WHEEL]; inline void mark(uint64_t* s, int o) { s[o >> 6] |= ONES[o & 63]; } inline int test(uint64_t* s, int o) { return (s[o >> 6] & ONES[o & 63]) == 0; } // update_sieve {{{ void update_sieve(uint32_t offset) { // copy each wheel pattern to sieve for (int i = 0, k; i < SIEVE_SIZE; i += k) { k = std::min(WHEEL, SIEVE_SIZE - i); memcpy(si + i, pattern, sizeof(*pattern) * k); } // Correctly mark 1, 3, 5, 7, 11, 13 as not prime / primes if (offset == 0) { si[0] |= ONES[0]; si[0] &= ~(ONES[1] | ONES[2] | ONES[3] | ONES[5] | ONES[6]); } // sieve for primes >= 17 (stored in `small_primes`) for (int i = 0; i < N_SMALL_PRIMES; ++i) { uint32_t j = small_primes[i] * (uint32_t) small_primes[i]; if (j > offset + SIEVE_SPAN - 1) break; if (j > offset) j = (j - offset) >> 1; else { j = small_primes[i] - offset % small_primes[i]; if ((j & 1) == 0) j += small_primes[i]; j >>= 1; } while (j < SIEVE_SPAN / 2) { mark(si, j); j += small_primes[i]; } } } // }}} template<typename F> void sieve(uint32_t MAX, F func) { // init small primes {{{ for (int i = 0; i < 64; ++i) ONES[i] = 1ULL << i; // sieve to find small primes for (int i = 3; i < 256; i += 2) { if (test(si, i >> 1)) { for (int j = i*i / 2; j < 32768; j += i) mark(si, j); } } // store primes >= 17 in `small_primes` (we will sieve differently // for primes 2, 3, 5, 7, 11, 13) { int m = 0; for (int i = 8; i < 32768; ++i) { if (test(si, i)) small_primes[m++] = i*2 + 1; } assert(m == N_SMALL_PRIMES); } // }}} // For primes 3, 5, 7, 11, 13: we initialize wheel pattern.. for (int i = 1; i < WHEEL * 64; i += 3) mark(pattern, i); for (int i = 2; i < WHEEL * 64; i += 5) mark(pattern, i); for (int i = 3; i < WHEEL * 64; i += 7) mark(pattern, i); for (int i = 5; i < WHEEL * 64; i += 11) mark(pattern, i); for (int i = 6; i < WHEEL * 64; i += 13) mark(pattern, i); // Segmented sieve if (2 <= MAX) func(2); for (uint32_t offset = 0; offset < MAX; offset += SIEVE_SPAN) { update_sieve(offset); for (uint32_t j = 0; j < SIEVE_SIZE; j++){ uint64_t x = ~si[j]; while (x){ uint32_t p = offset + (j << 7) + (__builtin_ctzll(x) << 1) + 1; if (p > offset + SIEVE_SPAN - 1) break; if (p <= MAX) { func(p); } x ^= (-x & x); } } } } } using segmented_sieve_wheel::sieve; // }}} #line 1 "Math/Prime/RabinMiller32.h" // Tested: // - https://www.spoj.com/problems/PRIC/ #line 5 "Math/Prime/RabinMiller32.h" // Rabin Miller for 32-bit numbers {{{ inline unsigned mod_mult(unsigned a, unsigned b, unsigned m) { return (uint64_t)a*b%m; } unsigned mod_pow(unsigned a, uint64_t b, unsigned m) { unsigned ret = 1; for(;;) { if (b&1) ret = mod_mult(ret, a, m); if (!(b>>=1)) return ret; a = mod_mult(a, a, m); } } bool is_prime(unsigned n) { if (n <= 3) return (n >= 2); static const unsigned small[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, }; for (size_t i = 0; i < sizeof(small)/sizeof(unsigned); i++) { if (n%small[i] == 0) return n == small[i]; } // Jaeschke93 showed that 2,7,61 suffice for n < 4,759,123,141. static const unsigned millerrabin[] = {2, 7, 61}; unsigned s = n-1, r = 0; while (s%2 == 0) {s /= 2; r++;} for (size_t i = 0, j; i < sizeof(millerrabin)/sizeof(unsigned); i++) { unsigned md = mod_pow(millerrabin[i], s, n); if (md == 1) continue; for (j = 1; j < r; j++) { if (md == n-1) break; md = mod_mult(md, md, n); } if (md != n-1) return false; } return true; } // }}} #line 6 "Math/tests/rabin_miller_32_stress.test.cpp" bitset<INT_MAX> all_primes; void newPrime(int p) { all_primes[p] = 1; } void solve() { srand(7777); sieve(INT_MAX, newPrime); cerr << "DONE SIEVE" << endl; for (int i = 0; i < INT_MAX; ++i) { if (rand() % 30) continue; if (all_primes[i] == 1) assert(is_prime(i)); else assert(!is_prime(i)); } cout << "Hello World\n"; }