#include <array>
#include <cstdint>
#include <iostream>
#include <tuple>
#include <type_traits>

#include "dpf.hpp"

// (K,N) Shamir. The secret is the constant term of a degree K-1 polynomial.
// Party i holds that polynomial at x = i+1. Any K shares open it. (2,3) is
// shamir_share: make_shamir_shares(secret, slope) is deal<T, 2, 3>.
// fp61 and gf2n both open. For gf2n, N must be less than 2^k.
//
//   c++ -std=c++17 -march=native -I include -I thirdparty examples/mwe/shamir.cpp

int main()
{
    using F = dpf::fp61;
    const F secret{10};
    // p(x) = 10 + 2x + 3x^2. Parties 0, 2, and 4 are enough.
    const std::array<F, 2> coeff{{F{2}, F{3}}};
    auto shares = dpf::make_shamir_shares<3, 5>(secret, coeff);
    const F opened = dpf::shamir::reconstruct(
        std::get<0>(shares), std::get<2>(shares), std::get<4>(shares));

    const F slope{3};
    auto [s0, s1, s2] = dpf::make_shamir_shares(secret, slope);
    static_assert(std::is_same_v<decltype(s0), dpf::shamir::share<F, 0, 2, 3>>);
    const F opened23 = dpf::reconstruct(s1, s2);
    const bool on_line = s0.raw() == secret + slope * F{1}
        && s2.raw() == secret + slope * F{3};

    using G = dpf::gf28;
    auto [g0, g1, g2] = dpf::make_shamir_shares(G{0x1b}, G{0x5a});
    const G gopen = dpf::reconstruct(g0, g2);
    const G gopen13 = dpf::reconstruct(g1, g2);

    std::cout << opened.raw() << " " << opened23.raw() << " "
        << static_cast<unsigned>(gopen.raw()) << "\n";
    return (opened == secret && opened23 == secret && on_line
        && gopen == G{0x1b} && gopen13 == G{0x1b})
        ? 0 : 1;
}