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Implement Baillie-PSW

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Chip Hogg
2024-11-14 21:27:09 -05:00
parent ec914986d1
commit 3b586a685f
2 changed files with 46 additions and 0 deletions
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22
src/core/include/mp-units/ext/prime.h
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@ -379,6 +379,28 @@ struct LucasSequenceElement {
return false;
}
// The Baillie-PSW test is technically a "probable prime" test. However, it is known to be correct for all
// 64-bit integers, and no counterexample of any size has ever been found. Thus, for this library's purposes,
// we can treat it as deterministic... probably.
[[nodiscard]] consteval bool baillie_psw_probable_prime(uint64_t n)
{
if (n < 2u) {
return false;
}
if (n < 4u) {
return true;
}
if (n % 2u == 0u) {
return false;
}
if (!miller_rabin_probable_prime(2u, n)) {
return false;
}
return strong_lucas_probable_prime(n);
}
[[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)) {

24
test/static/prime_test.cpp
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@ -197,4 +197,28 @@ static_assert(strong_lucas_probable_prime(9'007'199'254'740'881u), "Large known
static_assert(strong_lucas_probable_prime(18'446'744'073'709'551'557u), "Largest 64-bit prime");
// Tests for Baillie-PSW, which is known to be correct for all 64-bit integers.
static_assert(baillie_psw_probable_prime(3u), "Known small prime");
static_assert(baillie_psw_probable_prime(5u), "Known small prime");
static_assert(baillie_psw_probable_prime(7u), "Known small prime");
static_assert(!baillie_psw_probable_prime(9u), "Known small composite");
// Test some Miller-Rabin pseudoprimes (https://oeis.org/A001262), which should NOT be marked prime.
static_assert(!baillie_psw_probable_prime(2047u), "Miller-Rabin pseudoprime");
static_assert(!baillie_psw_probable_prime(3277u), "Miller-Rabin pseudoprime");
static_assert(!baillie_psw_probable_prime(486737u), "Miller-Rabin pseudoprime");
// Test some Strong Lucas pseudoprimes (https://oeis.org/A217255), which should NOT be marked prime.
static_assert(!baillie_psw_probable_prime(5459u), "Strong Lucas pseudoprime");
static_assert(!baillie_psw_probable_prime(5777u), "Strong Lucas pseudoprime");
static_assert(!baillie_psw_probable_prime(10877u), "Strong Lucas pseudoprime");
static_assert(!baillie_psw_probable_prime(324899u), "Strong Lucas pseudoprime");
// Test some actual primes
static_assert(baillie_psw_probable_prime(225'653'407'801u), "Large known prime");
static_assert(baillie_psw_probable_prime(334'524'384'739u), "Large known prime");
static_assert(baillie_psw_probable_prime(9'007'199'254'740'881u), "Large known prime");
static_assert(baillie_psw_probable_prime(18'446'744'073'709'551'557u), "Largest 64-bit prime");
} // namespace