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prime.hpp
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prime.hpp
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#ifndef PRIME_HPP
#define PRIME_HPP
#include <cmath>
#include <numeric>
template<class U>
class prime_enumerator {
using value_type = U;
value_type current = 1;
std::vector<value_type> previous;
public:
static value_type is_prime(value_type x) {
if (x < 2) return false;
for (value_type i = 2; true; ++i) {
const std::size_t q = x / i;
if (q < i) return true;
if (x % i == 0) return false;
}
return true;
}
value_type operator()() {
while(true) {
++current;
bool has_div = false;
for(value_type p : previous) {
const value_type q = current / p;
// simpler sqrt check
if( q < p ) break;
// dont use modulo
if(current == q * p) {
has_div = true;
break;
}
}
if(!has_div) {
previous.emplace_back(current);
return current;
}
}
}
};
template<class U>
static U gcd(U a, U b) {
// vanilla euclid's algorithm
U res;
while(U r = a % b) {
a = b;
b = r;
res = r;
}
return res;
}
template<class U, class T>
static void bezout(U a, U b, T* s, T* t) {
// bezout decomposition
T s_prev = 1, t_prev = 0;
T s_curr = 0, t_curr = 1;
while(U r = a % b) {
const U q = a / b;
const T s_next = s_prev - q * s_curr;
const T t_next = t_prev - q * t_curr;
s_prev = s_curr;
s_curr = s_next;
t_prev = t_curr;
t_curr = t_next;
a = b;
b = r;
}
*s = s_curr;
*t = t_curr;
}
template<class U>
static U modular_inverse(U x, U n) {
// note: x and n must be coprime
U t_prev = 0, t = 1;
U a = n, b = x;
while(true) {
const U q = a / b;
const U r = a - b * q;
if(!r) {
assert(b == 1 && "arguments must be coprime");
assert((x * t) % n == 1);
return t;
}
// keep the modular inverse modulo n
const U t_next = (t_prev + t * (n - q)) % n;
t_prev = t;
t = t_next;
a = b;
b = r;
}
}
template<class U>
static U chinese_remainders(const U* a, const U* n, std::size_t size) {
// let's be cautious
using uint = unsigned long;
using sint = long;
//
const uint prod = std::accumulate(n, n + size, uint(1), std::multiplies<uint>());
uint x = 0;
for(std::size_t i = 0; i < size; ++i) {
assert(a[i] < n[i]);
// TODO assemble m modulo n[i] to avoid overflowing
const uint m = prod / n[i];
const uint ei = m * modular_inverse<uint>(m % n[i], n[i]);
x += a[i] * ei;
x %= prod;
}
// for(std::size_t i = 0; i < size; ++i) {
// assert( x % n[i] == a[i] );
// }
// for(std::size_t j = 0; j < prod; ++j) {
// uint y = x + j * size;
// std::clog << "j: " << j << " prod: " << prod << " y: " << y << std::endl;
// for(std::size_t i = 0; i < size; ++i) {
// uint q = j % n[i];
// std::clog << " qi: " << q << std::endl;
// std::clog << " test: " << ((a[i] + size * q) < n[i]) << std::endl;
// std::clog << " test2: " << ((size * q) < n[i]) << std::endl;
// assert( (y % n[i]) % size == a[i] );
// }
// }
return x;
}
#endif