Math/tests/rabin_miller_32_stress.test.cpp

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Last update: 2022-12-26 20:01:50+08:00
Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A

Depends on

Code

#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";
}