#include <getopt.h>
#include <vector>
#include <array>
#include <cmath>
#include <iostream>

using Real = double;

class Point : public std::array<Real, 2> {
public:
  Real τ() const {
    return front();
  }
  Real C() const {
    return back();
  }
};

unsigned p = 2;

Real f(Real q) {
  return 0.5 * pow(q, p);
}

Real df(Real q) {
  return 0.5 * p * pow(q, p - 1);
}

Real ddf(Real q) {
  return 0.5 * p * (p - 1) * pow(q, p - 2);
}

Real integrate(const std::vector<Point>& Cₜ, double τ₀) {
  Real I = 0;
#pragma omp parallel for reduction(+:I)
  for (unsigned i = 0; i < Cₜ.size() - 1; i++) {
    unsigned j = Cₜ.size() - 1 - i;
    Real Δτ = Cₜ[i + 1].τ() - Cₜ[i].τ();
    Real C = (Cₜ[j].C() + Cₜ[j - 1].C()) / 2;
    Real dC = (Cₜ[i + 1].C() - Cₜ[i].C()) / Δτ;

    Real dddC = 0;
    if (i > 4 && i < Cₜ.size() && Cₜ.size() > 4) {
      dddC += (Cₜ[j].C() - 3 * Cₜ[j+1].C() + 3 * Cₜ[j+2].C() - Cₜ[j+3].C()) / pow(Δτ, 3);
      dddC += (Cₜ[j+1].C() - 3 * Cₜ[j+2].C() + 3 * Cₜ[j+3].C() - Cₜ[j+4].C()) / pow(Δτ, 3);
      dddC /= 2;
    }
    I += Δτ * df(C) * (dC - pow(τ₀, 2) * dddC);
  }
  return I;
}

Real energy(const std::vector<Point>& Ct, Real τ₀) {
  Real I = 0;
  for (unsigned i = 0; i < Ct.size() - 1; i++) {
    Real Δτ = Ct[i + 1].τ() - Ct[i].τ();
    Real C = (Ct[i].C() + Ct[i + 1].C()) / 2;
    Real dC = (Ct[i + 1].C() - Ct[i].C()) / Δτ;

    Real dddC = 0;
    if (i > 1 && i < Ct.size() - 2 && Ct.size() > 3) {
      dddC = (Ct[i+1].C() - 3 * Ct[i].C() + 3 * Ct[i-1].C() - Ct[i-2].C()) / pow(Δτ, 3);
    }
    I += Δτ * df(C) * (dC - pow(τ₀, 2) * dddC);
  }
  return I;
}

int main(int argc, char* argv[]) {
  Real Δτ = 1e-3;
  Real τₘₐₓ = 1e3;
  Real τ₀ = 0;
  Real y = 0.5;

  int opt;

  while ((opt = getopt(argc, argv, "d:T:t:y:")) != -1) {
    switch (opt) {
    case 'd':
      Δτ = atof(optarg);
      break;
    case 'T':
      τₘₐₓ = atof(optarg);
      break;
    case 't':
      τ₀ = atof(optarg);
      break;
    case 'y':
      y = atof(optarg);
      break;
    default:
      exit(1);
    }
  }

  Real z = (sqrt(1 + 2 * τ₀) - 1) / (2 * τ₀);

  std::vector<Point> Cₜ;
  Cₜ.reserve(τₘₐₓ / Δτ + 1);

  Cₜ.push_back({0, 1});

  while (Cₜ.back().τ() < τₘₐₓ) {
    Real dC = -z * Cₜ.back().C() - 2 * pow(y, 2) * integrate(Cₜ, τ₀);
    Cₜ.push_back({Cₜ.back().τ() + Δτ, Cₜ.back().C() + Δτ * dC});
    std::cout << Cₜ.back().τ() << " " << Cₜ.back().C() << std::endl;
  }

  std::cerr << - 2 * y * energy(Cₜ, τ₀) << std::endl;

  return 0;
}