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Add helpers for modular arithmetic

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The prime-testing techniques we will use (Miller-Rabin, Strong Lucas)
all make heavy usage of modular arithmetic.  Therefore, we lay those
foundations here, adding utilities to perform the basic arithmetic
operations robustly.

Since these are internal-only helper functions, we don't bother checking
the preconditions, although we state them clearly in the contract
comment for each utility.  After C++26, we could add contracts for
these.

Helps #509.
This commit is contained in:
Chip Hogg
2024-11-11 12:55:41 -05:00
parent 727a898141
commit 8a7483f7ea
2 changed files with 106 additions and 0 deletions
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26
test/static/prime_test.cpp
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@@ -33,6 +33,8 @@ using namespace mp_units::detail;
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...>)
{
@@ -78,4 +80,28 @@ 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);
static_assert(add_mod(MAX_U64 - 1u, MAX_U64 - 2u, MAX_U64) == MAX_U64 - 3u);
static_assert(sub_mod(2u, 1u, 5u) == 1u);
static_assert(sub_mod(1u, 2u, 5u) == 4u);
static_assert(sub_mod(MAX_U64 - 2u, MAX_U64 - 1u, MAX_U64) == MAX_U64 - 1u);
static_assert(sub_mod(1u, MAX_U64 - 1u, MAX_U64) == 2u);
static_assert(mul_mod(6u, 7u, 10u) == 2u);
static_assert(mul_mod(13u, 11u, 50u) == 43u);
static_assert(mul_mod(MAX_U64 / 2u, 10u, MAX_U64) == MAX_U64 - 5u);
static_assert(half_mod_odd(0u, 11u) == 0u);
static_assert(half_mod_odd(10u, 11u) == 5u);
static_assert(half_mod_odd(1u, 11u) == 6u);
static_assert(half_mod_odd(9u, 11u) == 10u);
static_assert(half_mod_odd(MAX_U64 - 1u, MAX_U64) == (MAX_U64 - 1u) / 2u);
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);
} // namespace