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Verify Miller-Rabin primality test
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#include <iostream> | |
#include <cstdint> | |
#include <array> | |
#include <ranges> | |
#include <cassert> | |
#include <bitset> | |
uint32_t pow_n(uint32_t a, uint32_t d, uint32_t n) { | |
if (d == 0) return 1; | |
if (d == 1) return a; | |
uint32_t t = pow_n(a, d / 2, n); | |
t = ((uint64_t)t * t) % n; | |
if (d % 2 == 0) { | |
return t; | |
} else { | |
return ((uint64_t)t * a) % n; | |
} | |
}; | |
bool test(uint32_t n, unsigned s, uint32_t d, uint32_t a) { | |
//std::cout << "test(n = " << n << ", s = " << s << ", d = " << d << ", a = " << a << ")\n"; | |
uint32_t x = pow_n(a ,d ,n); | |
//std::cout << " x = " << x << std::endl; | |
if (x == 1 || x == n - 1) return true; | |
for (unsigned i = 1; i < s; ++i) { | |
x = ((uint64_t)x * x) % n; | |
if (x == n - 1) return true; | |
} | |
return false; | |
} | |
bool is_prime(uint32_t n) { | |
static const std::array witnesses{2u, 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u, 29u, 31u, 37u}; | |
static const std::array bounds{ | |
2'047llu, 1'373'653llu, 25'326'001llu, 3'215'031'751llu, | |
2'152'302'898'747llu, 3'474'749'660'383llu, | |
341'550'071'728'321llu, 341'550'071'728'321llu /* no bounds for 19 */, | |
3'825'123'056'546'413'051llu, | |
3'825'123'056'546'413'051llu /* no bound for 29 */, | |
3'825'123'056'546'413'051llu /* no bound for 31 */, | |
(unsigned long long)UINT64_MAX /* off by a bit but it's the last bounds */, | |
}; | |
static_assert(witnesses.size() == bounds.size()); | |
if (n == 2) return true; // 2 is prime | |
if (n % 2 == 0) return false; // other even numbers are not | |
if (n <= witnesses.back()) { // I know the first few primes | |
return (std::ranges::find(witnesses, n) != std::end(witnesses)); | |
} | |
// write n = 2^s * d + 1 with d odd | |
unsigned s = 0; | |
uint32_t d = n - 1; | |
while (d % 2 == 0) { | |
++s; | |
d /= 2; | |
} | |
// test widtnesses until the bounds say it's a sure thing | |
auto it = bounds.cbegin(); | |
for (auto a : witnesses) { | |
//std::cout << a << " "; | |
if (!test(n, s, d, a)) return false; | |
if (n < *it++) return true; | |
} | |
return true; | |
} | |
template<std::size_t N> | |
auto composite() { | |
std::bitset<N / 2 + 1> is_composite; | |
for (uint32_t i = 3; (uint64_t)i * i < N; i += 2) { | |
if (is_composite[i / 2]) continue; | |
for (uint64_t j = i * i; j < N; j += 2 * i) is_composite[j / 2] = true; | |
} | |
return is_composite; | |
} | |
bool slow_prime(uint32_t n) { | |
static const auto is_composite = composite<UINT32_MAX + 1llu>(); | |
if (n < 2) return false; | |
if (n == 2) return true; | |
if (n % 2 == 0) return false; | |
return !is_composite.test(n / 2); | |
} | |
int main() { | |
/* | |
std::cout << "2047: "; | |
bool fast = is_prime(2047); | |
bool slow = slow_prime(2047); | |
std::cout << (fast ? "fast prime" : ""); | |
std::cout << (slow ? "slow prime" : ""); | |
std::cout << std::endl; | |
*/ | |
//std::cout << "2: prime\n"; | |
for (uint64_t i = 0; i <= UINT32_MAX; ++i) { | |
if (i % 1000000 == 1) { std::cout << "\r" << i << " "; std::cout.flush(); } | |
bool fast = is_prime(i); | |
bool slow = slow_prime(i); | |
if (fast != slow) std::cout << i << std::endl; | |
assert(fast == slow); | |
//std::cout << i << ": " << (is_prime(i) ? "prime" : "") << std::endl; | |
} | |
} |
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