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CarpetX: a Cactus driver for the Einstein Toolkit based on AMReX 
#ifndef PROLONGATE_3D_RF2_HXX
#define PROLONGATE_3D_RF2_HXX

#include "driver.hxx"

#include <AMReX_Interpolater.H>

#include <cassert>

namespace CarpetX {
using namespace std;

constexpr int VC = 0;        // vertex centering
constexpr int CC = 1;        // cell centering
constexpr bool POLY = false; // polynomial interpolation (non-conservative)
constexpr bool CONS = true;  // conservative

template <int CENTI, int CENTJ, int CENTK, bool CONSI, bool CONSJ, bool CONSK,
          int ORDERI, int ORDERJ, int ORDERK>
class prolongate_3d_rf2 final : public amrex::Interpolater {

  // Centering must be vertex (0) or cell (1)
  static_assert(CENTI == 0 || CENTI == 1, "");
  static_assert(CENTJ == 0 || CENTJ == 1, "");
  static_assert(CENTK == 0 || CENTK == 1, "");

  // Order must be nonnegative
  static_assert(ORDERI >= 0, "");
  static_assert(ORDERJ >= 0, "");
  static_assert(ORDERK >= 0, "");

  static constexpr array<int, dim> indextype() { return {CENTI, CENTJ, CENTK}; }
  static constexpr array<bool, dim> conservative() {
    return {CONSI, CONSJ, CONSK};
  }
  static constexpr array<int, dim> order() { return {ORDERI, ORDERJ, ORDERK}; }

public:
  virtual ~prolongate_3d_rf2() override;

  virtual amrex::Box CoarseBox(const amrex::Box &fine, int ratio) override;
  virtual amrex::Box CoarseBox(const amrex::Box &fine,
                               const amrex::IntVect &ratio) override;

  virtual void interp(const amrex::FArrayBox &crse, int crse_comp,
                      amrex::FArrayBox &fine, int fine_comp, int ncomp,
                      const amrex::Box &fine_region,
                      const amrex::IntVect &ratio,
                      const amrex::Geometry &crse_geom,
                      const amrex::Geometry &fine_geom,
                      amrex::Vector<amrex::BCRec> const &bcr, int actual_comp,
                      int actual_state, amrex::RunOn gpu_or_cpu) override;
};

////////////////////////////////////////////////////////////////////////////////

extern prolongate_3d_rf2<VC, VC, VC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_3d_rf2_c000_o1;
extern prolongate_3d_rf2<VC, VC, CC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_3d_rf2_c001_o1;
extern prolongate_3d_rf2<VC, CC, VC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_3d_rf2_c010_o1;
extern prolongate_3d_rf2<VC, CC, CC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_3d_rf2_c011_o1;
extern prolongate_3d_rf2<CC, VC, VC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_3d_rf2_c100_o1;
extern prolongate_3d_rf2<CC, VC, CC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_3d_rf2_c101_o1;
extern prolongate_3d_rf2<CC, CC, VC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_3d_rf2_c110_o1;
extern prolongate_3d_rf2<CC, CC, CC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_3d_rf2_c111_o1;

extern prolongate_3d_rf2<VC, VC, VC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_3d_rf2_c000_o3;
extern prolongate_3d_rf2<VC, VC, CC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_3d_rf2_c001_o3;
extern prolongate_3d_rf2<VC, CC, VC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_3d_rf2_c010_o3;
extern prolongate_3d_rf2<VC, CC, CC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_3d_rf2_c011_o3;
extern prolongate_3d_rf2<CC, VC, VC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_3d_rf2_c100_o3;
extern prolongate_3d_rf2<CC, VC, CC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_3d_rf2_c101_o3;
extern prolongate_3d_rf2<CC, CC, VC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_3d_rf2_c110_o3;
extern prolongate_3d_rf2<CC, CC, CC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_3d_rf2_c111_o3;

extern prolongate_3d_rf2<VC, VC, VC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_cons_3d_rf2_c000_o0;
extern prolongate_3d_rf2<VC, VC, CC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_cons_3d_rf2_c001_o0;
extern prolongate_3d_rf2<VC, CC, VC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_cons_3d_rf2_c010_o0;
extern prolongate_3d_rf2<VC, CC, CC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_cons_3d_rf2_c011_o0;
extern prolongate_3d_rf2<CC, VC, VC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_cons_3d_rf2_c100_o0;
extern prolongate_3d_rf2<CC, VC, CC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_cons_3d_rf2_c101_o0;
extern prolongate_3d_rf2<CC, CC, VC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_cons_3d_rf2_c110_o0;
extern prolongate_3d_rf2<CC, CC, CC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_cons_3d_rf2_c111_o0;

extern prolongate_3d_rf2<VC, VC, VC, CONS, CONS, CONS, 1, 1, 1>
    prolongate_cons_3d_rf2_c000_o1;
extern prolongate_3d_rf2<VC, VC, CC, CONS, CONS, CONS, 1, 1, 2>
    prolongate_cons_3d_rf2_c001_o1;
extern prolongate_3d_rf2<VC, CC, VC, CONS, CONS, CONS, 1, 2, 1>
    prolongate_cons_3d_rf2_c010_o1;
extern prolongate_3d_rf2<VC, CC, CC, CONS, CONS, CONS, 1, 2, 2>
    prolongate_cons_3d_rf2_c011_o1;
extern prolongate_3d_rf2<CC, VC, VC, CONS, CONS, CONS, 2, 1, 1>
    prolongate_cons_3d_rf2_c100_o1;
extern prolongate_3d_rf2<CC, VC, CC, CONS, CONS, CONS, 2, 1, 2>
    prolongate_cons_3d_rf2_c101_o1;
extern prolongate_3d_rf2<CC, CC, VC, CONS, CONS, CONS, 2, 2, 1>
    prolongate_cons_3d_rf2_c110_o1;
extern prolongate_3d_rf2<CC, CC, CC, CONS, CONS, CONS, 2, 2, 2>
    prolongate_cons_3d_rf2_c111_o1;

// Prolongation operators for discrete differential forms:
// interpolating (non-conservative) for vertex centred directions,
// conservative for cell centred directions. We use linear
// interpolation for vertex centred and constant interpolation for
// cell centred directions.
extern prolongate_3d_rf2<VC, VC, VC, POLY, POLY, POLY, 1, 1, 1>
    prolongate_ddf_3d_rf2_c000_o1;
extern prolongate_3d_rf2<VC, VC, CC, POLY, POLY, CONS, 1, 1, 0>
    prolongate_ddf_3d_rf2_c001_o1;
extern prolongate_3d_rf2<VC, CC, VC, POLY, CONS, POLY, 1, 0, 1>
    prolongate_ddf_3d_rf2_c010_o1;
extern prolongate_3d_rf2<VC, CC, CC, POLY, CONS, CONS, 1, 0, 0>
    prolongate_ddf_3d_rf2_c011_o1;
extern prolongate_3d_rf2<CC, VC, VC, CONS, POLY, POLY, 0, 1, 1>
    prolongate_ddf_3d_rf2_c100_o1;
extern prolongate_3d_rf2<CC, VC, CC, CONS, POLY, CONS, 0, 1, 0>
    prolongate_ddf_3d_rf2_c101_o1;
extern prolongate_3d_rf2<CC, CC, VC, CONS, CONS, POLY, 0, 0, 1>
    prolongate_ddf_3d_rf2_c110_o1;
extern prolongate_3d_rf2<CC, CC, CC, CONS, CONS, CONS, 0, 0, 0>
    prolongate_ddf_3d_rf2_c111_o1;

extern prolongate_3d_rf2<VC, VC, VC, POLY, POLY, POLY, 3, 3, 3>
    prolongate_ddf_3d_rf2_c000_o3;
extern prolongate_3d_rf2<VC, VC, CC, POLY, POLY, CONS, 3, 3, 2>
    prolongate_ddf_3d_rf2_c001_o3;
extern prolongate_3d_rf2<VC, CC, VC, POLY, CONS, POLY, 3, 2, 3>
    prolongate_ddf_3d_rf2_c010_o3;
extern prolongate_3d_rf2<VC, CC, CC, POLY, CONS, CONS, 3, 2, 2>
    prolongate_ddf_3d_rf2_c011_o3;
extern prolongate_3d_rf2<CC, VC, VC, CONS, POLY, POLY, 2, 3, 3>
    prolongate_ddf_3d_rf2_c100_o3;
extern prolongate_3d_rf2<CC, VC, CC, CONS, POLY, CONS, 2, 3, 2>
    prolongate_ddf_3d_rf2_c101_o3;
extern prolongate_3d_rf2<CC, CC, VC, CONS, CONS, POLY, 2, 2, 3>
    prolongate_ddf_3d_rf2_c110_o3;
extern prolongate_3d_rf2<CC, CC, CC, CONS, CONS, CONS, 2, 2, 2>
    prolongate_ddf_3d_rf2_c111_o3;

extern prolongate_3d_rf2<VC, VC, VC, POLY, POLY, POLY, 5, 5, 5>
    prolongate_ddf_3d_rf2_c000_o5;
extern prolongate_3d_rf2<VC, VC, CC, POLY, POLY, CONS, 5, 5, 4>
    prolongate_ddf_3d_rf2_c001_o5;
extern prolongate_3d_rf2<VC, CC, VC, POLY, CONS, POLY, 5, 4, 5>
    prolongate_ddf_3d_rf2_c010_o5;
extern prolongate_3d_rf2<VC, CC, CC, POLY, CONS, CONS, 5, 4, 4>
    prolongate_ddf_3d_rf2_c011_o5;
extern prolongate_3d_rf2<CC, VC, VC, CONS, POLY, POLY, 4, 5, 5>
    prolongate_ddf_3d_rf2_c100_o5;
extern prolongate_3d_rf2<CC, VC, CC, CONS, POLY, CONS, 4, 5, 4>
    prolongate_ddf_3d_rf2_c101_o5;
extern prolongate_3d_rf2<CC, CC, VC, CONS, CONS, POLY, 4, 4, 5>
    prolongate_ddf_3d_rf2_c110_o5;
extern prolongate_3d_rf2<CC, CC, CC, CONS, CONS, CONS, 4, 4, 4>
    prolongate_ddf_3d_rf2_c111_o5;

} // namespace CarpetX

#endif // #ifndef PROLONGATE_3D_RF2_HXX