libdpf/examples/grotto/jet_and_ring.cpp

#include <cstdint>
#include <iostream>
#include <vector>

#include "grotto.hpp"

/// Binomial jet readouts and an exact ring switch from one public offset.
int main()
{
    //! [jet-and-ring]
    // --- Binomial jet -------------------------------------------------------
    // After eta opens, the jet is the binomial basis at the wrapped
    // center+kappa. Degree 3 leaves room for a degree-2 hockey-stick prefix.
    const std::uint8_t center = 12;
    const std::uint8_t eta = 3;
    const std::uint8_t point = static_cast<std::uint8_t>(center + eta);  // 15
    const std::size_t degree = 3;
    auto jet_keys = grotto::make_offset_jet_keys<std::uint8_t>(center, degree);
    // f(t) = 4 + 2 C(t,1) + C(t,2)  (padded to degree 3).
    const std::vector<std::uint64_t> poly{4, 2, 1};
    std::vector<std::uint64_t> coeff = poly;
    coeff.push_back(0);
    const std::vector<std::uint8_t> knots{0};

    const auto j0 = grotto::offset_jet_shares<0>(jet_keys, knots, eta);
    const auto j1 = grotto::offset_jet_shares<1>(jet_keys, knots, eta);
    std::vector<std::uint64_t> jet(degree + 1);
    for (std::size_t k = 0; k <= degree; ++k)
        jet[k] = j0[k] + j1[k];

    const std::uint64_t value = grotto::offset_jet_dot(coeff, jet);
    const std::uint64_t diff = grotto::offset_jet_dot(
        grotto::offset_jet_difference_coeff(coeff), jet);
    const std::uint64_t prefix = grotto::offset_jet_dot(
        grotto::offset_jet_prefix_coeff(poly), jet);

    // Padé / Newton are public dots against the same jet, then one reciprocal
    // after the shares are opened. For a seed p(t)/p'(t):
    //   auto num = offset_jet_dot(coeff, jet);
    //   auto den = offset_jet_dot(offset_jet_difference_coeff(coeff), jet);
    //   // open num, den; one masked reciprocal; Newton: t - num/den.

    // --- Exact ring switch --------------------------------------------------
    // Same public-offset pattern: eta = x - r, then x lands in the residue.
    const std::uint8_t r = 200;
    const std::uint8_t x = 44;
    const std::uint8_t ring_eta = static_cast<std::uint8_t>(x - r);  // 100, wraps
    using Z = grotto::zn64<1009>;
    auto ring = grotto::make_ring_switch_keys<Z>(r);
    const Z x_mod = grotto::ring_switch_eval<0>(ring, ring_eta)
        + grotto::ring_switch_eval<1>(ring, ring_eta);

    auto field = grotto::make_ring_switch_keys<dpf::field128>(r);
    const dpf::field128 x_field = grotto::ring_switch_eval<0>(field, ring_eta)
        + grotto::ring_switch_eval<1>(field, ring_eta);
    //! [jet-and-ring]

    auto c = [](std::uint64_t t, unsigned k) {
        return grotto::offset_jet_binom(t, k);
    };
    const std::uint64_t expect_v =
        4 + 2 * c(point, 1) + c(point, 2);
    if (value != expect_v)
    {
        std::cerr << "jet value\n";
        return 1;
    }
    const std::uint64_t expect_fx1 =
        4 + 2 * c(static_cast<std::uint8_t>(point + 1), 1)
          + c(static_cast<std::uint8_t>(point + 1), 2);
    if (diff != expect_fx1 - expect_v)
    {
        std::cerr << "jet difference\n";
        return 1;
    }
    std::uint64_t expect_p = 0;
    for (std::uint8_t i = 0; i < point; ++i)
        expect_p += 4 + 2 * c(i, 1) + c(i, 2);
    if (prefix != expect_p)
    {
        std::cerr << "jet prefix\n";
        return 1;
    }
    if (x_mod.raw() != static_cast<std::uint64_t>(x) % 1009)
    {
        std::cerr << "ring zn64\n";
        return 1;
    }
    if (x_field != dpf::field128{x})
    {
        std::cerr << "ring field128\n";
        return 1;
    }

    std::cout << value << " " << diff << " " << prefix << " "
              << x_mod.raw() << "\n";
    return 0;
}