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Replace old factoring with Baillie-PSW

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Chip Hogg
2024-11-15 13:30:05 -05:00
parent 3b586a685f
commit de68b3a9f1
5 changed files with 29 additions and 177 deletions
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test/static/prime_test.cpp
-45
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@@ -35,51 +35,6 @@ namespace {
inline constexpr auto MAX_U64 = std::numeric_limits<std::uint64_t>::max();
template<std::size_t BasisSize, std::size_t... Is>
constexpr bool check_primes(std::index_sequence<Is...>)
{
return ((Is < 2 || wheel_factorizer<BasisSize>::is_prime(Is) == is_prime_by_trial_division(Is)) && ...);
}
static_assert(check_primes<2>(std::make_index_sequence<122>{}));
// This is the smallest number that can catch the bug where we use only _prime_ numbers in the first wheel, rather than
// numbers which are _coprime to the basis_.
//
// The basis for N = 4 is {2, 3, 5, 7}, so the wheel size is 210. 11 * 11 = 121 is within the first wheel. It is
// coprime with every element of the basis, but it is _not_ prime. If we keep only prime numbers, then we will neglect
// using numbers of the form (210 * n + 121) as trial divisors, which is a problem if any are prime. For n = 1, we have
// a divisor of (210 + 121 = 331), which happens to be prime but will not be used. Thus, (331 * 331 = 109561) is a
// composite number which could wrongly appear prime if we skip over 331.
static_assert(wheel_factorizer<4>::is_prime(109'561) == is_prime_by_trial_division(109'561));
static_assert(wheel_factorizer<1>::coprimes_in_first_wheel.size() == 1);
static_assert(wheel_factorizer<2>::coprimes_in_first_wheel.size() == 2);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel.size() == 8);
static_assert(wheel_factorizer<4>::coprimes_in_first_wheel.size() == 48);
static_assert(wheel_factorizer<5>::coprimes_in_first_wheel.size() == 480);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[0] == 1);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[1] == 7);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[2] == 11);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[3] == 13);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[4] == 17);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[5] == 19);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[6] == 23);
static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[7] == 29);
static_assert(!wheel_factorizer<1>::is_prime(0));
static_assert(!wheel_factorizer<1>::is_prime(1));
static_assert(wheel_factorizer<1>::is_prime(2));
static_assert(!wheel_factorizer<2>::is_prime(0));
static_assert(!wheel_factorizer<2>::is_prime(1));
static_assert(wheel_factorizer<2>::is_prime(2));
static_assert(!wheel_factorizer<3>::is_prime(0));
static_assert(!wheel_factorizer<3>::is_prime(1));
static_assert(wheel_factorizer<3>::is_prime(2));
// Modular arithmetic.
static_assert(add_mod(1u, 2u, 5u) == 3u);
static_assert(add_mod(4u, 4u, 5u) == 3u);