#ifndef MINI_ODEINT_H_
#define MINI_ODEINT_H_

#include <array>
#include <cassert>
#include <cmath>
#include <iterator>
#include <span>

namespace mini_odeint {

template <typename T> struct DormandPrince {
  using value_type = T;
  static constexpr std::size_t stages = 7;
  static constexpr std::size_t order = 5;
  static constexpr std::size_t estimator_order = 4;
  static constexpr std::size_t dense_order = 5;

  static constexpr std::array<T, stages> c{
      0.0, 1.0 / 5.0, 3.0 / 10.0, 4.0 / 5.0, 8.0 / 9.0, 1.0, 1.0};

  static constexpr std::array<std::array<T, stages - 1>, stages> a{
      {{0.0, 0.0, 0.0, 0.0, 0.0},
       {1.0 / 5.0, 0.0, 0.0, 0.0, 0.0},
       {3.0 / 40.0, 9.0 / 40.0, 0.0, 0.0, 0.0},
       {44.0 / 45.0, -56.0 / 15.0, 32.0 / 9.0, 0.0, 0.0},
       {19372.0 / 6561.0, -25360.0 / 2187.0, 64448.0 / 6561.0, -212.0 / 729.0,
        0.0},
       {9017.0 / 3168.0, -355.0 / 33.0, 46732.0 / 5247.0, 49.0 / 176.0,
        -5103.0 / 18656.0},
       {35.0 / 384.0, 0.0, 500.0 / 1113.0, 125.0 / 192.0, -2187.0 / 6784.0,
        11.0 / 84.0}}};

  static constexpr std::array<T, stages> b_hat{
      35.0 / 384.0, 0.0, 500.0 / 1113.0, 125.0 / 192.0, -2187.0 / 6784.0,
      11.0 / 84.0,  0.0};

  static constexpr std::array<T, stages> b{5179.0 / 57600.0,    0.0,
                                           7571.0 / 16695.0,    393.0 / 640.0,
                                           -92097.0 / 339200.0, 187.0 / 2100.0,
                                           1.0 / 40.0};

  static constexpr std::array<std::array<T, dense_order>, stages> p{

      {{1.0, -32272833064.0 / 11282082432.0, 34969693132.0 / 11282082432.0,
        -13107642775.0 / 11282082432.0, 157015080.0 / 11282082432.0},
       {0.0, 0.0, 0.0, 0.0, 0.0},
       {0.0, 1323431896.0 * 100.0 / 32700410799.0,
        -2074956840.0 * 100.0 / 32700410799.0,
        914128567.0 * 100.0 / 32700410799.0,
        -15701508.0 * 100.0 / 32700410799.0},
       {0.0, -889289856.0 * 25.0 / 5641041216.0,
        2460397220.0 * 25.0 / 5641041216.0, -1518414297.0 * 25.0 / 5641041216.0,
        94209048.0 * 25.0 / 5641041216.0},
       {0.0, 259006536.0 * 2187.0 / 199316789632.0,
        -687873124.0 * 2187.0 / 199316789632.0,
        451824525.0 * 2187.0 / 199316789632.0,
        -52338360.0 * 2187.0 / 199316789632.0},
       {0.0, -361440756.0 * 11.0 / 2467955532.0,
        946554244.0 * 11.0 / 2467955532.0, -661884105.0 * 11.0 / 2467955532.0,
        106151040.0 * 11.0 / 2467955532.0},
       {0.0, 44764047.0 / 29380423.0, -127201567 / 29380423.0,
        90730570.0 / 29380423.0, -8293050.0 / 29380423.0}}};
};

template <typename E> struct OdeVector {
  using value_type = E;

  E value;

  constexpr OdeVector() = default;
  constexpr explicit OdeVector(E value) : value(std::move(value)) {}

  constexpr operator E() const { return value; }

  friend constexpr OdeVector operator+(const OdeVector &lhs,
                                       const OdeVector &rhs) {
    return OdeVector{lhs.value + rhs.value};
  }
  friend constexpr OdeVector operator*(const OdeVector &lhs,
                                       const value_type &rhs) {
    return OdeVector{lhs.value * rhs};
  }
  friend constexpr OdeVector operator*(const value_type &lhs,
                                       const OdeVector &rhs) {
    return OdeVector{lhs * rhs.value};
  }
  constexpr OdeVector &operator+=(const OdeVector &rhs) {
    value += rhs.value;
    return *this;
  }
  constexpr OdeVector &operator+=(const value_type &rhs) {
    value += rhs;
    return *this;
  }
  value_type inf_norm() const { return std::abs(value); }
};

template <typename T, std::size_t N> struct OdeVector<std::array<T, N>> {
  using array_type = std::array<T, N>;
  using value_type = T;
  std::array<T, N> value;

  constexpr OdeVector() = default;
  constexpr explicit OdeVector(std::array<T, N> value)
      : value(std::move(value)) {}

  operator std::array<T, N>() const { return value; }

  friend constexpr OdeVector operator+(const OdeVector &lhs,
                                       const OdeVector &rhs) {
    OdeVector result{lhs};
    for (std::size_t i = 0; i < N; ++i) {
      result.value[i] += rhs.value[i];
    }
    return result;
  }
  friend constexpr OdeVector operator*(const OdeVector &lhs,
                                       const value_type &rhs) {
    OdeVector result{lhs};
    for (std::size_t i = 0; i < N; ++i) {
      result.value[i] *= rhs;
    }
    return result;
  }
  friend constexpr OdeVector operator*(const value_type &lhs,
                                       const OdeVector &rhs) {
    OdeVector result{rhs};
    for (std::size_t i = 0; i < N; ++i) {
      result.value[i] *= lhs;
    }
    return result;
  }
  constexpr OdeVector &operator+=(const OdeVector &rhs) {
    for (std::size_t i = 0; i < N; ++i) {
      value[i] += rhs.value[i];
    }
    return *this;
  }

  constexpr OdeVector &operator+=(const value_type &rhs) {
    for (std::size_t i = 0; i < N; ++i) {
      value[i] += rhs;
    }
    return *this;
  }

  value_type inf_norm() const {
    auto max = std::abs(value[0]);
    for (std::size_t i = 1; i < N; ++i) {
      max = std::max(max, std::abs(value[i]));
    }
    return max;
  }
};

template <typename Vector, typename Scalar = std::iter_value_t<Vector>,
          typename Tableau = DormandPrince<Scalar>>
  requires std::same_as<Scalar, std::iter_value_t<Tableau>>

inline std::size_t explicitRungeKutta(std::span<Vector> ys,
                                      std::span<Scalar const> ts, Vector y0,
                                      Scalar tol, auto &&dydx)
  requires requires(decltype(dydx) f) {
    { f(Vector{}, Scalar{}) } -> std::same_as<Vector>;
  }
{
  const auto stages = Tableau::stages;
  const auto dense_order = Tableau::dense_order;
  const auto order = Tableau::order;
  const auto &a = Tableau::a;
  const auto &p = Tableau::p;
  const auto &c = Tableau::c;
  const auto &b = Tableau::b;
  const auto &b_hat = Tableau::b_hat;

  static_assert(Tableau::c.back() == 1.0, "last c value must be 1.0");

  auto y_hat_n = y0;
  ys[0] = y0;

  std::size_t it = 1;

  std::array<Vector, stages> k;

  const auto N = ts.size();
  if (!N) {
    return 0;
  }

  auto t_n = ts[0];
  auto h_n = ts[N - 1] - t_n;

  int step_count = 0;

  k[stages - 1] = dydx(y0, t_n);

  while (t_n < ts[N - 1]) {
    auto step_rejected = true;
    while (step_rejected) {
      // reuse last k (we have asserted that the last c value is 1.0)
      const auto last_k_store = k[stages - 1];
      k[0] = k[stages - 1];
      for (std::size_t i = 1; i < stages; ++i) {
        OdeVector<Vector> sum_ak{};
        for (std::size_t j = 0; j < i; ++j) {
          sum_ak += a[i][j] * k[j];
        }
        k[i] = dydx(y_hat_n + h_n * sum_ak, t_n + c[i] * h_n);
      }

      // calculate final value and error
      OdeVector<Vector> error{};
      OdeVector<Vector> sum_bk{};
      for (std::size_t i = 0; i < stages; ++i) {
        sum_bk += b_hat[i] * k[i];
        error += (b_hat[i] - b[i]) * k[i];
      }
      const auto y_hat_np1 = y_hat_n + h_n * sum_bk;

      // check if step is successful, ie error is within tolerance
      const auto E_hp1 = (h_n * error).inf_norm();
      if (E_hp1 < tol) {
        // if moved over any requested times then interpolate their values
        const auto t_np1 = t_n + h_n;
        while (it < N && t_np1 >= ts[it]) {
          const auto sigma = (ts[it] - t_n) / h_n;
          OdeVector<Vector> Phi{};
          for (std::size_t i = 0; i < stages; ++i) {
            auto term = sigma;
            auto b_i = term * p[i][0];
            for (std::size_t j = 1; j < dense_order; ++j) {
              term *= sigma;
              b_i += term * p[i][j];
            }
            Phi += b_i * k[i];
          }
          ys[it] = y_hat_n + h_n * Phi;
          ++it;
        }

        // move to next step
        step_rejected = false;
        y_hat_n = y_hat_np1;
        t_n = t_np1;
        ++step_count;
      } else {
        // failed step, reset last k back to stored value
        k[stages - 1] = last_k_store;
      }

      // adapt step size
      h_n *= 0.9 * std::pow(tol / E_hp1, 1.0 / (order + 1.0));
    }
  }

  assert(it == N);
  return it;
}

} // namespace mini_odeint

#include <vector>

#include <iostream>

int main() {
  using namespace mini_odeint;
  // make vector of doubles from 0.0 to 1.0 by 0.001
  std::vector<float> times;
  times.reserve(1001);
  for (int i = 0; i < 1000; ++i) {
    times.push_back(i / 1000.0);
  }

  std::vector<std::array<float, 2>> ys(times.size());

  explicitRungeKutta(
      std::span(ys), std::span<const float>(times),
      std::array<float, 2>{1.0, 2.0}, float(1e-6),
      [](auto y, auto t) { return std::array<float, 2>{-y[0], -y[1]}; });

  for (const auto &v : ys) {
    std::cout << v[0] << v[1] << '\n';
  }
}

#endif // MINI_ODEINT_H_