Kaznov / imath

C++ single-header library for fast operations on integers: factorization, prime tests and more!

imath

THIS LIBRARY IS IN AN EARLY STAGE OF DEVELOPMENT. Use with caution.

imath is an open-source C++14 library providing a set of fast operations on 32-bit and 64-bit integers.

Features

• Fast factorization - O(∜n * polylog(n))
• Fast deterministic primality test - O(log n)
• Finding the next prime after a given number
• Integer multiplication modulo ((64bit * 64bit) % 64bit)
• Efficient integer power modulo - O(log(power))
• Class for Montgomery multiplications (in development)
• Rounding to multiples of a number
• and more!

Code should be free of warnings on all major compilers, even on high warning levels -Wall and -Wextra.

Most of the functions is constexpr in C++14 on Clang and GCC, and all the functions are constexpr in C++20 for all compilers (it requires std::is_constant_evaluated()).

Some operations were tuned to use intrinsics when compiled by GCC, Clang or MSVC compilers. Note, that the library was designed to work most efficiently on x86_64 architecture, but it still should work on any machine.

Examples

Test if number is a prime

static_assert(imath::isPrime(1'000'000'007u);

Factor a number

int main() {
    auto fact_result = imath::factorize(3'851'820u);
    std::cout << "3851820 = ";
    // range-for loop also supported!
    for (size_t i = 0; i < fact_result.size() - 1; ++i) {
       auto factor = fact_result[i];
       std::cout << factor.prime << "^" << factor.power << " × ";
    }
    std::cout << fact_result.back().prime << "^"
              << fact_result.back().power;
}

Expected output: 3851820 = 2^2 × 3^3 × 5^1 × 7^1 × 1019^1

Generate a compile-time prime array

static constexpr imath::PrimeArray<8> array_of_small_primes;

int main() {
    for (auto prime : array_of_small_primes)
        std::cout << prime << " ";
}

Expected output: 2 3 5 7 11 13 17 19 Also available: imath:kSmallPrimes

Find the Greatest Common Divisor and the Least Common Multiple ot two numbers

int main() {
    std::cout << "GCD(24, 81) = " << imath::gcd(24u, 81u) << "\n";
    std::cout << "LCM(24, 81) = " << imath::lcm(24u, 81u) << "\n";
}

Test if number is a perfect square

int main() {
    std::cout << 1046528 << imath::isPerfectSquare(1046528u) ? "IS" : "IS NOT"
              << " a perfect square\n";
    std::cout << 1046529 << imath::isPerfectSquare(1046529u) ? "IS" : "IS NOT"
              << " a perfect square\n";
}

Round a number up or down to multiple of some other number

int main() {
    size_t number = 12345678;
    std::cout << number << " rounded up to thousands is "
              << imath::roundUpToMultipleOf(number, 1000) << "\n";
    std::cout << number << " rounded down to thousands is "
              << imath::roundDownToMultipleOf(number, 1000) << "\n";
}

Raise a number to given power over a modulus

int main() {
    std::cout << " (5 ^ 3) % 13 =  "
              << imath::powmod(5, 3, 13) << "\n";
    // And there is no risk of overflow!
}