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Merge pull request #638 from chiphogg/chiphogg/miller-rabin#509

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Add Miller-Rabin probable prime test
This commit is contained in:
Mateusz Pusz
2024-11-14 08:27:31 +01:00
committed by GitHub
parent e4bccad75c cfd9ddb675
commit 7e1baf65fa
2 changed files with 63 additions and 0 deletions
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45
src/core/include/mp-units/ext/prime.h
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@ -138,6 +138,51 @@ namespace mp_units::detail {
return result;
}
// Decompose a positive integer by factoring out all powers of 2.
struct NumberDecomposition {
std::uint64_t power_of_two;
std::uint64_t odd_remainder;
};
// Express any positive `n` as `(2^s * d)`, where `d` is odd.
[[nodiscard]] consteval NumberDecomposition decompose(std::uint64_t n)
{
NumberDecomposition result{0u, n};
while (result.odd_remainder % 2u == 0u) {
result.odd_remainder /= 2u;
++result.power_of_two;
}
return result;
}
// Perform a Miller-Rabin primality test on `n` using base `a`.
//
// Precondition: (a >= 2).
// Precondition: (n >= a + 2).
// Precondition: (n % 2 == 1).
[[nodiscard]] consteval bool miller_rabin_probable_prime(std::uint64_t a, std::uint64_t n)
{
MP_UNITS_EXPECTS_DEBUG(a >= 2u);
MP_UNITS_EXPECTS_DEBUG(n >= a + 2u);
MP_UNITS_EXPECTS_DEBUG(n % 2u == 1u);
const auto [s, d] = decompose(n - 1u);
auto x = pow_mod(a, d, n);
if (x == 1u) {
return true;
}
const auto minus_one = n - 1u;
for (auto r = 0u; r < s; ++r) {
if (x == minus_one) {
return true;
}
x = mul_mod(x, x, n);
}
return false;
}
[[nodiscard]] consteval bool is_prime_by_trial_division(std::uintmax_t n)
{
for (std::uintmax_t f = 2; f * f <= n; f += 1 + (f % 2)) {

18
test/static/prime_test.cpp
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@ -104,4 +104,22 @@ static_assert(half_mod_odd(MAX_U64 - 2u, MAX_U64) == MAX_U64 - 1u);
static_assert(pow_mod(5u, 8u, 9u) == ((5u * 5u * 5u * 5u) * (5u * 5u * 5u * 5u)) % 9u);
static_assert(pow_mod(2u, 64u, MAX_U64) == 1u);
// Miller-Rabin primality testing.
static_assert(miller_rabin_probable_prime(2u, 5u));
static_assert(miller_rabin_probable_prime(2u, 7u));
static_assert(!miller_rabin_probable_prime(2u, 9u));
static_assert(miller_rabin_probable_prime(2u, 11u));
static_assert(miller_rabin_probable_prime(2u, 2047u), "Known base 2 pseudoprime");
static_assert(miller_rabin_probable_prime(2u, 3277u), "Known base 2 pseudoprime");
static_assert(miller_rabin_probable_prime(3u, 121u), "Known base 3 pseudoprime");
static_assert(miller_rabin_probable_prime(3u, 703u), "Known base 3 pseudoprime");
static_assert(miller_rabin_probable_prime(2u, 225'653'407'801u), "Large known prime");
static_assert(miller_rabin_probable_prime(2u, 334'524'384'739u), "Large known prime");
static_assert(miller_rabin_probable_prime(2u, 9'007'199'254'740'881u), "Large known prime");
static_assert(miller_rabin_probable_prime(2u, 18'446'744'073'709'551'557u), "Largest 64-bit prime");
} // namespace