AMReX_FFT_R2C.H

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#ifndef AMREX_FFT_R2C_H_
#define AMREX_FFT_R2C_H_
#include <AMReX_Config.H>
 
#include <AMReX_MultiFab.H>
#include <AMReX_FFT_Helper.H>
#include <algorithm>
#include <map>
#include <numeric>
#include <tuple>
 
namespace amrex::FFT
{
 
template <typename T> class OpenBCSolver;
template <typename T> class Poisson;
template <typename T> class PoissonHybrid;
 
template <typename T = Real, FFT::Direction D = FFT::Direction::both, bool C = false>
class R2C
{
public:
    using cMF = FabArray<BaseFab<GpuComplex<T> > >;
    using MF = std::conditional_t
        <C, cMF, std::conditional_t<std::is_same_v<T,Real>,
                                    MultiFab, FabArray<BaseFab<T> > >>;
 
    template <typename U> friend class OpenBCSolver;
    template <typename U> friend class Poisson;
    template <typename U> friend class PoissonHybrid;
 
    explicit R2C (Box const& domain, Info const& info = Info{});
 
    explicit R2C (std::array<int,AMREX_SPACEDIM> const& domain_size,
                  Info const& info = Info{});
 
    ~R2C ();
 
    R2C (R2C const&) = delete;
    R2C (R2C &&) = delete;
    R2C& operator= (R2C const&) = delete;
    R2C& operator= (R2C &&) = delete;
 
    void setLocalDomain (std::array<int,AMREX_SPACEDIM> const& local_start,
                         std::array<int,AMREX_SPACEDIM> const& local_size);
 
    std::pair<std::array<int,AMREX_SPACEDIM>,std::array<int,AMREX_SPACEDIM>>
    getLocalDomain () const;
 
    void setLocalSpectralDomain (std::array<int,AMREX_SPACEDIM> const& local_start,
                                 std::array<int,AMREX_SPACEDIM> const& local_size);
 
    std::pair<std::array<int,AMREX_SPACEDIM>,std::array<int,AMREX_SPACEDIM>>
    getLocalSpectralDomain () const;
 
    template <typename F, Direction DIR=D>
    requires (DIR == Direction::both)
    void forwardThenBackward (MF const& inmf, MF& outmf, F const& post_forward,
                              int incomp = 0, int outcomp = 0)
    {
        AMREX_ALWAYS_ASSERT_WITH_MESSAGE(
            !m_info.twod_mode,
            "FFT::R2C::forwardThenBackward(post_forward) currently supports only !twod_mode");
        BL_PROFILE("FFT::R2C::forwardbackward");
        this->forward(inmf, incomp);
        this->post_forward_doit_0(post_forward);
        this->backward(outmf, outcomp);
    }
 
    template <Direction DIR=D>
    requires ((DIR == Direction::forward) || (DIR == Direction::both))
    void forward (MF const& inmf, int incomp = 0);
 
    template <Direction DIR=D>
    requires ((DIR == Direction::forward) || (DIR == Direction::both))
    void forward (MF const& inmf, cMF& outmf, int incomp = 0, int outcomp = 0);
 
    template <typename RT, typename CT, Direction DIR=D, bool CP=C>
    requires ((DIR == Direction::forward) || (DIR == Direction::both))
          && (((sizeof(RT)*2 == sizeof(CT)) && (!CP))
              || ((sizeof(RT) == sizeof(CT)) && CP))
    void forward (RT const* in, CT* out);
 
    template <Direction DIR=D>
    requires (DIR == Direction::both)
    void backward (MF& outmf, int outcomp = 0);
 
    template <Direction DIR=D>
    requires ((DIR == Direction::backward) || (DIR == Direction::both))
    void backward (cMF const& inmf, MF& outmf, int incomp = 0, int outcomp = 0);
 
    template <typename CT, typename RT, Direction DIR=D, bool CP=C>
    requires ((DIR == Direction::backward) || (DIR == Direction::both))
          && (((sizeof(RT)*2 == sizeof(CT)) && (!CP))
              || ((sizeof(RT) == sizeof(CT)) && CP))
    void backward (CT const* in, RT* out);
 
    [[nodiscard]] T scalingFactor () const;
 
    template <Direction DIR=D>
    requires ((DIR == Direction::forward) || (DIR == Direction::both))
    std::pair<cMF*,IntVect> getSpectralData () const;
 
 
    [[nodiscard]] std::pair<BoxArray,DistributionMapping> getSpectralDataLayout () const;
 
    template <typename F>
    void post_forward_doit_0 (F const& post_forward);
 
    template <typename F>
    void post_forward_doit_1 (F const& post_forward);
 
private:
 
    void prepare_openbc ();
 
    void backward_doit (MF& outmf, IntVect const& ngout = IntVect(0),
                        Periodicity const& period = Periodicity::NonPeriodic(),
                        int outcomp = 0);
 
    void backward_doit (cMF const& inmf, MF& outmf,
                        IntVect const& ngout = IntVect(0),
                        Periodicity const& period = Periodicity::NonPeriodic(),
                        int incomp = 0, int outcomp = 0);
 
    std::pair<Plan<T>,Plan<T>> make_c2c_plans (cMF& inout, int ndims) const;
 
    [[nodiscard]] MF& make_m_rx_alias (IndexType const& ix_type);
 
    [[nodiscard]] Periodicity make_m_rx_alias_periodicity (IndexType const& ix_type,
                                                           Periodicity const& period) const;
 
    static Box make_domain_x (Box const& domain)
    {
        if constexpr (C) {
            return Box(IntVect(0), IntVect(AMREX_D_DECL(domain.length(0)-1,
                                                        domain.length(1)-1,
                                                        domain.length(2)-1)),
                       domain.ixType());
        } else {
            return Box(IntVect(0), IntVect(AMREX_D_DECL(domain.length(0)/2,
                                                        domain.length(1)-1,
                                                        domain.length(2)-1)),
                       domain.ixType());
        }
    }
 
    static Box make_domain_y (Box const& domain)
    {
        if constexpr (C) {
            return Box(IntVect(0), IntVect(AMREX_D_DECL(domain.length(1)-1,
                                                        domain.length(0)-1,
                                                        domain.length(2)-1)),
                       domain.ixType());
        } else {
            return Box(IntVect(0), IntVect(AMREX_D_DECL(domain.length(1)-1,
                                                        domain.length(0)/2,
                                                        domain.length(2)-1)),
                       domain.ixType());
        }
    }
 
    static Box make_domain_z (Box const& domain)
    {
        if constexpr (C) {
            return Box(IntVect(0), IntVect(AMREX_D_DECL(domain.length(2)-1,
                                                        domain.length(0)-1,
                                                        domain.length(1)-1)),
                       domain.ixType());
        } else {
            return Box(IntVect(0), IntVect(AMREX_D_DECL(domain.length(2)-1,
                                                        domain.length(0)/2,
                                                        domain.length(1)-1)),
                       domain.ixType());
        }
    }
 
    static std::pair<BoxArray,DistributionMapping>
    make_layout_from_local_domain (std::array<int,AMREX_SPACEDIM> const& local_start,
                                   std::array<int,AMREX_SPACEDIM> const& local_size);
 
    template <typename FA, typename RT>
    std::pair<std::unique_ptr<char,DataDeleter>,std::size_t>
    install_raw_ptr (FA& fa, RT const* p);
 
    Plan<T> m_fft_fwd_x{};
    Plan<T> m_fft_bwd_x{};
    Plan<T> m_fft_fwd_y{};
    Plan<T> m_fft_bwd_y{};
    Plan<T> m_fft_fwd_z{};
    Plan<T> m_fft_bwd_z{};
    Plan<T> m_fft_fwd_x_half{};
    Plan<T> m_fft_bwd_x_half{};
 
    // Comm meta-data. In the forward phase, we start with (x,y,z),
    // transpose to (y,x,z) and then (z,x,y). In the backward phase, we
    // perform inverse transpose.
    std::unique_ptr<MultiBlockCommMetaData> m_cmd_x2y; // (x,y,z) -> (y,x,z)
    std::unique_ptr<MultiBlockCommMetaData> m_cmd_y2x; // (y,x,z) -> (x,y,z)
    std::unique_ptr<MultiBlockCommMetaData> m_cmd_y2z; // (y,x,z) -> (z,x,y)
    std::unique_ptr<MultiBlockCommMetaData> m_cmd_z2y; // (z,x,y) -> (y,x,z)
    std::unique_ptr<MultiBlockCommMetaData> m_cmd_x2z; // (x,y,z) -> (z,x,y)
    std::unique_ptr<MultiBlockCommMetaData> m_cmd_z2x; // (z,x,y) -> (x,y,z)
    std::unique_ptr<MultiBlockCommMetaData> m_cmd_x2z_half; // for openbc
    std::unique_ptr<MultiBlockCommMetaData> m_cmd_z2x_half; // for openbc
    Swap01 m_dtos_x2y{};
    Swap01 m_dtos_y2x{};
    Swap02 m_dtos_y2z{};
    Swap02 m_dtos_z2y{};
    RotateFwd m_dtos_x2z{};
    RotateBwd m_dtos_z2x{};
 
    MF  m_rx;
    cMF m_cx;
    cMF m_cy;
    cMF m_cz;
 
    mutable MF m_raw_mf;
    mutable cMF m_raw_cmf;
 
    std::map<IntVect,MF> m_rx_aliases;
 
    std::unique_ptr<char,DataDeleter> m_data_1;
    std::unique_ptr<char,DataDeleter> m_data_2;
 
    Box m_real_domain;
    Box m_spectral_domain_x;
    Box m_spectral_domain_y;
    Box m_spectral_domain_z;
 
    std::unique_ptr<R2C<T,D,C>> m_r2c_sub;
    detail::SubHelper m_sub_helper;
 
    Info m_info;
 
    bool m_do_alld_fft = false;
    bool m_slab_decomp = false;
    bool m_openbc_half = false;
};
 
template <typename T, Direction D, bool C>
R2C<T,D,C>::R2C (Box const& domain, Info const& info)
    : m_real_domain(domain),
      m_spectral_domain_x(make_domain_x(domain)),
#if (AMREX_SPACEDIM >= 2)
      m_spectral_domain_y(make_domain_y(domain)),
#if (AMREX_SPACEDIM == 3)
      m_spectral_domain_z(make_domain_z(domain)),
#endif
#endif
      m_sub_helper(domain),
      m_info(info)
{
    BL_PROFILE("FFT::R2C");
 
    static_assert(std::is_same_v<float,T> || std::is_same_v<double,T>);
 
    AMREX_ALWAYS_ASSERT(m_real_domain.numPts() > 1);
#if (AMREX_SPACEDIM == 2)
    AMREX_ALWAYS_ASSERT(!m_info.twod_mode);
#else
    if (m_info.twod_mode) {
        AMREX_ALWAYS_ASSERT((int(domain.length(0) > 1) +
                             int(domain.length(1) > 1) +
                             int(domain.length(2) > 1)) >= 2);
    }
#endif
 
    {
        Box subbox = m_sub_helper.make_box(m_real_domain);
        if (subbox.size() != m_real_domain.size()) {
            m_r2c_sub = std::make_unique<R2C<T,D,C>>(subbox, m_info);
            return;
        }
    }
 
    int myproc = ParallelContext::MyProcSub();
    int nprocs = std::min(ParallelContext::NProcsSub(), m_info.nprocs);
 
#if (AMREX_SPACEDIM == 3)
    if (m_info.domain_strategy == DomainStrategy::automatic) {
        if (m_info.twod_mode) {
            m_info.domain_strategy = DomainStrategy::slab;
        } else {
            int shortside = m_real_domain.shortside();
            if (shortside < m_info.pencil_threshold*nprocs) {
                m_info.domain_strategy = DomainStrategy::pencil;
            } else {
                m_info.domain_strategy = DomainStrategy::slab;
            }
        }
    }
 
    if (!m_info.oned_mode) {
        if (m_info.twod_mode) {
            m_slab_decomp = true;
        } else if (m_info.domain_strategy == DomainStrategy::slab && (m_real_domain.length(1) > 1)) {
            m_slab_decomp = true;
        }
    }
#endif
 
    auto const ncomp = m_info.batch_size;
 
    auto bax = amrex::decompose(m_real_domain, nprocs,
                                {AMREX_D_DECL(false,!m_slab_decomp,m_real_domain.length(2)>1)}, true);
 
    DistributionMapping dmx = detail::make_iota_distromap(bax.size());
    m_rx.define(bax, dmx, ncomp, 0, MFInfo().SetAlloc(false));
 
    {
        BoxList bl = bax.boxList();
        for (auto & b : bl) {
            b.shift(-m_real_domain.smallEnd());
            b.setBig(0, m_spectral_domain_x.bigEnd(0));
        }
        BoxArray cbax(std::move(bl));
        m_cx.define(cbax, dmx, ncomp, 0, MFInfo().SetAlloc(false));
    }
 
    m_do_alld_fft = (ParallelDescriptor::NProcs() == 1) &&
                    (! m_info.twod_mode) && (! m_info.oned_mode);
 
    if (!m_do_alld_fft) // do a series of 1d or 2d ffts
    {
        //
        // make data containers
        //
 
#if (AMREX_SPACEDIM >= 2)
        DistributionMapping cdmy;
        if ((m_real_domain.length(1) > 1) && !m_slab_decomp && !m_info.oned_mode)
        {
            auto cbay = amrex::decompose(m_spectral_domain_y, nprocs,
                                         {AMREX_D_DECL(false,true,true)}, true);
            if (cbay.size() == dmx.size()) {
                cdmy = dmx;
            } else {
                cdmy = detail::make_iota_distromap(cbay.size());
            }
            m_cy.define(cbay, cdmy, ncomp, 0, MFInfo().SetAlloc(false));
        }
#endif
 
#if (AMREX_SPACEDIM == 3)
        if (!m_info.oned_mode && !m_info.twod_mode &&
            m_real_domain.length(1) > 1 &&
            m_real_domain.length(2) > 1)
        {
            auto cbaz = amrex::decompose(m_spectral_domain_z, nprocs,
                                         {false,true,true}, true);
            DistributionMapping cdmz;
            if (cbaz.size() == dmx.size()) {
                cdmz = dmx;
            } else if (cbaz.size() == cdmy.size()) {
                cdmz = cdmy;
            } else {
                cdmz = detail::make_iota_distromap(cbaz.size());
            }
            m_cz.define(cbaz, cdmz, ncomp, 0, MFInfo().SetAlloc(false));
        }
#endif
 
        if constexpr (C) {
            if (m_slab_decomp) {
                m_data_1 = detail::make_mfs_share(m_rx, m_cx);
                m_data_2 = detail::make_mfs_share(m_cz, m_cz);
            } else {
                m_data_1 = detail::make_mfs_share(m_rx, m_cz);
                m_data_2 = detail::make_mfs_share(m_cy, m_cy);
                // make m_cx an alias to m_rx
                if (myproc < m_cx.size()) {
                    Box const& box = m_cx.fabbox(myproc);
                    using FAB = typename cMF::FABType::value_type;
                    m_cx.setFab(myproc, FAB(box, ncomp, m_rx[myproc].dataPtr()));
                }
            }
        } else {
            if (m_slab_decomp) {
                m_data_1 = detail::make_mfs_share(m_rx, m_cz);
                m_data_2 = detail::make_mfs_share(m_cx, m_cx);
            } else {
                m_data_1 = detail::make_mfs_share(m_rx, m_cy);
                m_data_2 = detail::make_mfs_share(m_cx, m_cz);
            }
        }
 
        //
        // make copiers
        //
 
#if (AMREX_SPACEDIM >= 2)
        if (! m_cy.empty()) {
            // comm meta-data between x and y phases
            m_cmd_x2y = std::make_unique<MultiBlockCommMetaData>
                (m_cy, m_spectral_domain_y, m_cx, IntVect(0), m_dtos_x2y);
            m_cmd_y2x = std::make_unique<MultiBlockCommMetaData>
                (m_cx, m_spectral_domain_x, m_cy, IntVect(0), m_dtos_y2x);
        }
#endif
#if (AMREX_SPACEDIM == 3)
        if (! m_cz.empty() ) {
            if (m_slab_decomp) {
                // comm meta-data between xy and z phases
                m_cmd_x2z = std::make_unique<MultiBlockCommMetaData>
                    (m_cz, m_spectral_domain_z, m_cx, IntVect(0), m_dtos_x2z);
                m_cmd_z2x = std::make_unique<MultiBlockCommMetaData>
                    (m_cx, m_spectral_domain_x, m_cz, IntVect(0), m_dtos_z2x);
            } else {
                // comm meta-data between y and z phases
                m_cmd_y2z = std::make_unique<MultiBlockCommMetaData>
                    (m_cz, m_spectral_domain_z, m_cy, IntVect(0), m_dtos_y2z);
                m_cmd_z2y = std::make_unique<MultiBlockCommMetaData>
                    (m_cy, m_spectral_domain_y, m_cz, IntVect(0), m_dtos_z2y);
            }
        }
#endif
 
        //
        // make plans
        //
 
        if (myproc < m_rx.size())
        {
            if constexpr (C) {
                int ndims = m_slab_decomp ? 2 : 1;
                std::tie(m_fft_fwd_x, m_fft_bwd_x) = make_c2c_plans(m_cx, ndims);
            } else {
                Box const& box = m_rx.box(myproc);
                auto* pr = m_rx[myproc].dataPtr();
                auto* pc = (typename Plan<T>::VendorComplex *)m_cx[myproc].dataPtr();
#ifdef AMREX_USE_SYCL
                m_fft_fwd_x.template init_r2c<Direction::forward>(box, pr, pc, m_slab_decomp, ncomp);
                m_fft_bwd_x = m_fft_fwd_x;
#else
                if constexpr (D == Direction::both || D == Direction::forward) {
                    m_fft_fwd_x.template init_r2c<Direction::forward>(box, pr, pc, m_slab_decomp, ncomp);
                }
                if constexpr (D == Direction::both || D == Direction::backward) {
                    m_fft_bwd_x.template init_r2c<Direction::backward>(box, pr, pc, m_slab_decomp, ncomp);
                }
#endif
            }
        }
 
#if (AMREX_SPACEDIM >= 2)
        if (! m_cy.empty()) {
            std::tie(m_fft_fwd_y, m_fft_bwd_y) = make_c2c_plans(m_cy,1);
        }
#endif
#if (AMREX_SPACEDIM == 3)
        if (! m_cz.empty()) {
            std::tie(m_fft_fwd_z, m_fft_bwd_z) = make_c2c_plans(m_cz,1);
        }
#endif
    }
    else // do fft in all dimensions at the same time
    {
        if constexpr (C) {
            m_data_1 = detail::make_mfs_share(m_rx, m_cx);
            std::tie(m_fft_fwd_x, m_fft_bwd_x) = make_c2c_plans(m_cx,AMREX_SPACEDIM);
        } else {
            m_data_1 = detail::make_mfs_share(m_rx, m_rx);
            m_data_2 = detail::make_mfs_share(m_cx, m_cx);
 
            auto const& len = m_real_domain.length();
            auto* pr = (void*)m_rx[0].dataPtr();
            auto* pc = (void*)m_cx[0].dataPtr();
#ifdef AMREX_USE_SYCL
            m_fft_fwd_x.template init_r2c<Direction::forward>(len, pr, pc, false, ncomp);
            m_fft_bwd_x = m_fft_fwd_x;
#else
            if constexpr (D == Direction::both || D == Direction::forward) {
                m_fft_fwd_x.template init_r2c<Direction::forward>(len, pr, pc, false, ncomp);
            }
            if constexpr (D == Direction::both || D == Direction::backward) {
                m_fft_bwd_x.template init_r2c<Direction::backward>(len, pr, pc, false, ncomp);
            }
#endif
        }
    }
}
 
template <typename T, Direction D, bool C>
R2C<T,D,C>::R2C (std::array<int,AMREX_SPACEDIM> const& domain_size, Info const& info)
    : R2C<T,D,C>(Box(IntVect(0),IntVect(domain_size)-1), info)
{}
 
template <typename T, Direction D, bool C>
R2C<T,D,C>::~R2C ()
{
    if (m_fft_bwd_x.plan != m_fft_fwd_x.plan) {
        m_fft_bwd_x.destroy();
    }
    if (m_fft_bwd_y.plan != m_fft_fwd_y.plan) {
        m_fft_bwd_y.destroy();
    }
    if (m_fft_bwd_z.plan != m_fft_fwd_z.plan) {
        m_fft_bwd_z.destroy();
    }
    m_fft_fwd_x.destroy();
    m_fft_fwd_y.destroy();
    m_fft_fwd_z.destroy();
    if (m_fft_bwd_x_half.plan != m_fft_fwd_x_half.plan) {
        m_fft_bwd_x_half.destroy();
    }
    m_fft_fwd_x_half.destroy();
}
 
template <typename T, Direction D, bool C>
std::pair<BoxArray,DistributionMapping>
R2C<T,D,C>::make_layout_from_local_domain (std::array<int,AMREX_SPACEDIM> const& local_start,
                                           std::array<int,AMREX_SPACEDIM> const& local_size)
{
    IntVect lo(local_start);
    IntVect len(local_size);
    Box bx(lo, lo+len-1);
#ifdef AMREX_USE_MPI
    Vector<Box> allboxes(ParallelContext::NProcsSub());
    MPI_Allgather(&bx, 1, ParallelDescriptor::Mpi_typemap<Box>::type(),
                  allboxes.data(), 1, ParallelDescriptor::Mpi_typemap<Box>::type(),
                  ParallelContext::CommunicatorSub());
    Vector<int> pmap;
    pmap.reserve(allboxes.size());
    for (int i = 0; i < allboxes.size(); ++i) {
        if (allboxes[i].ok()) {
            pmap.push_back(ParallelContext::local_to_global_rank(i));
        }
    }
    std::erase_if(allboxes, [=] (Box const& b) { return b.isEmpty(); });
    BoxList bl(std::move(allboxes));
    return std::make_pair(BoxArray(std::move(bl)), DistributionMapping(std::move(pmap)));
#else
    return std::make_pair(BoxArray(bx), DistributionMapping(Vector<int>({0})));
#endif
}
 
template <typename T, Direction D, bool C>
void R2C<T,D,C>::setLocalDomain (std::array<int,AMREX_SPACEDIM> const& local_start,
                                 std::array<int,AMREX_SPACEDIM> const& local_size)
{
    auto const& [ba, dm] = make_layout_from_local_domain(local_start, local_size);
    m_raw_mf = MF(ba, dm, m_rx.nComp(), 0, MFInfo().SetAlloc(false));
}
 
template <typename T, Direction D, bool C>
std::pair<std::array<int,AMREX_SPACEDIM>,std::array<int,AMREX_SPACEDIM>>
R2C<T,D,C>::getLocalDomain () const
{
    m_raw_mf = MF(m_rx.boxArray(), m_rx.DistributionMap(), m_rx.nComp(), 0,
                  MFInfo{}.SetAlloc(false));
 
    auto const myproc = ParallelContext::MyProcSub();
    if (myproc < m_rx.size()) {
        Box const& box = m_rx.box(myproc);
        return std::make_pair(box.smallEnd().toArray(),
                              box.length().toArray());
    } else {
        return std::make_pair(std::array<int,AMREX_SPACEDIM>{AMREX_D_DECL(0,0,0)},
                              std::array<int,AMREX_SPACEDIM>{AMREX_D_DECL(0,0,0)});
    }
}
 
template <typename T, Direction D, bool C>
void R2C<T,D,C>::setLocalSpectralDomain (std::array<int,AMREX_SPACEDIM> const& local_start,
                                         std::array<int,AMREX_SPACEDIM> const& local_size)
{
    auto const& [ba, dm] = make_layout_from_local_domain(local_start, local_size);
    m_raw_cmf = cMF(ba, dm, m_rx.nComp(), 0, MFInfo().SetAlloc(false));
}
 
template <typename T, Direction D, bool C>
std::pair<std::array<int,AMREX_SPACEDIM>,std::array<int,AMREX_SPACEDIM>>
R2C<T,D,C>::getLocalSpectralDomain () const
{
    auto const ncomp = m_info.batch_size;
    auto const& [ba, dm] = getSpectralDataLayout();
 
    m_raw_cmf = cMF(ba, dm, ncomp, 0, MFInfo{}.SetAlloc(false));
 
    auto const myproc = ParallelContext::MyProcSub();
    if (myproc < m_raw_cmf.size()) {
        Box const& box = m_raw_cmf.box(myproc);
        return std::make_pair(box.smallEnd().toArray(), box.length().toArray());
    } else {
        return std::make_pair(std::array<int,AMREX_SPACEDIM>{AMREX_D_DECL(0,0,0)},
                              std::array<int,AMREX_SPACEDIM>{AMREX_D_DECL(0,0,0)});
    }
}
 
template <typename T, Direction D, bool C>
void R2C<T,D,C>::prepare_openbc ()
{
    if (C || m_r2c_sub) { amrex::Abort("R2C: OpenBC not supported with reduced dimensions or complex inputs"); }
 
#if (AMREX_SPACEDIM == 3)
    if (m_do_alld_fft) { return; }
 
    auto const ncomp = m_info.batch_size;
 
    if (m_slab_decomp && ! m_fft_fwd_x_half.defined) {
        auto* fab = detail::get_fab(m_rx);
        if (fab) {
            Box bottom_half = m_real_domain;
            bottom_half.growHi(2,-m_real_domain.length(2)/2);
            Box box = fab->box() & bottom_half;
            if (box.ok()) {
                auto* pr = fab->dataPtr();
                auto* pc = (typename Plan<T>::VendorComplex *)
                    detail::get_fab(m_cx)->dataPtr();
#ifdef AMREX_USE_SYCL
                m_fft_fwd_x_half.template init_r2c<Direction::forward>
                    (box, pr, pc, m_slab_decomp, ncomp);
                m_fft_bwd_x_half = m_fft_fwd_x_half;
#else
                if constexpr (D == Direction::both || D == Direction::forward) {
                    m_fft_fwd_x_half.template init_r2c<Direction::forward>
                        (box, pr, pc, m_slab_decomp, ncomp);
                }
                if constexpr (D == Direction::both || D == Direction::backward) {
                    m_fft_bwd_x_half.template init_r2c<Direction::backward>
                        (box, pr, pc, m_slab_decomp, ncomp);
                }
#endif
            }
        }
    } // else todo
 
    if (m_cmd_x2z && ! m_cmd_x2z_half) {
        Box bottom_half = m_spectral_domain_z;
        // Note that z-direction's index is 0 because we z is the
        // unit-stride direction here.
        bottom_half.growHi(0,-m_spectral_domain_z.length(0)/2);
        m_cmd_x2z_half = std::make_unique<MultiBlockCommMetaData>
            (m_cz, bottom_half, m_cx, IntVect(0), m_dtos_x2z);
    }
 
    if (m_cmd_z2x && ! m_cmd_z2x_half) {
        Box bottom_half = m_spectral_domain_x;
        bottom_half.growHi(2,-m_spectral_domain_x.length(2)/2);
        m_cmd_z2x_half = std::make_unique<MultiBlockCommMetaData>
            (m_cx, bottom_half, m_cz, IntVect(0), m_dtos_z2x);
    }
#endif
}
 
template <typename T, Direction D, bool C>
typename R2C<T,D,C>::MF&
R2C<T,D,C>::make_m_rx_alias (IndexType const& ix_type)
{
    auto const key = ix_type.ixType();
    auto it = m_rx_aliases.find(key);
    if (it != m_rx_aliases.end()) {
        return it->second;
    }
 
    BoxList bl(ix_type);
    for (auto b : m_rx.boxArray().boxList()) {
        b.setType(ix_type);
        bl.push_back(b);
    }
 
    MF alias(BoxArray(std::move(bl)), m_rx.DistributionMap(), m_rx.nComp(),
             m_rx.nGrowVect(), MFInfo{}.SetAlloc(false));
 
    using FAB = typename MF::fab_type;
    for (MFIter mfi(alias, MFItInfo().DisableDeviceSync()); mfi.isValid(); ++mfi) {
        alias.setFab(mfi, FAB(mfi.fabbox(), m_rx.nComp(), m_rx[mfi.index()].dataPtr()));
    }
 
    auto [alias_it, inserted] = m_rx_aliases.emplace(key, std::move(alias));
    amrex::ignore_unused(inserted);
    return alias_it->second;
}
 
template <typename T, Direction D, bool C>
Periodicity
R2C<T,D,C>::make_m_rx_alias_periodicity (IndexType const& ix_type,
                                         Periodicity const& period) const
{
    IntVect per = period.intVect();
    for (int idim = 0; idim < AMREX_SPACEDIM; ++idim) {
        if (ix_type.nodeCentered(idim) && per[idim] == 0) {
            per[idim] = m_real_domain.length(idim);
        }
    }
    return Periodicity(per);
}
 
template <typename T, Direction D, bool C>
template <Direction DIR>
requires ((DIR == Direction::forward) || (DIR == Direction::both))
void R2C<T,D,C>::forward (MF const& inmf, int incomp)
{
    BL_PROFILE("FFT::R2C::forward(in)");
 
    auto const ncomp = m_info.batch_size;
 
    if (m_r2c_sub) {
        if (m_sub_helper.ghost_safe(inmf.nGrowVect())) {
            m_r2c_sub->forward(m_sub_helper.make_alias_mf(inmf), incomp);
        } else {
            MF tmp(inmf.boxArray(), inmf.DistributionMap(), ncomp, 0);
            tmp.LocalCopy(inmf, incomp, 0, ncomp, IntVect(0));
            m_r2c_sub->forward(m_sub_helper.make_alias_mf(tmp),0);
        }
        return;
    }
 
    if (&m_rx != &inmf) {
        if (m_rx.boxArray().ixType() == inmf.boxArray().ixType()) {
            m_rx.ParallelCopy(inmf, incomp, 0, ncomp);
        } else {
            MF& rx_alias = make_m_rx_alias(inmf.boxArray().ixType());
            rx_alias.ParallelCopy(inmf, incomp, 0, ncomp);
        }
    }
 
    if (m_do_alld_fft) {
        if constexpr (C) {
            m_fft_fwd_x.template compute_c2c<Direction::forward>();
        } else {
            m_fft_fwd_x.template compute_r2c<Direction::forward>();
        }
        return;
    }
 
    auto& fft_x = m_openbc_half ? m_fft_fwd_x_half : m_fft_fwd_x;
    if constexpr (C) {
        fft_x.template compute_c2c<Direction::forward>();
    } else {
        fft_x.template compute_r2c<Direction::forward>();
    }
 
    if (                          m_cmd_x2y) {
        ParallelCopy(m_cy, m_cx, *m_cmd_x2y, 0, 0, ncomp, m_dtos_x2y);
    }
    m_fft_fwd_y.template compute_c2c<Direction::forward>();
 
    if (                          m_cmd_y2z) {
        ParallelCopy(m_cz, m_cy, *m_cmd_y2z, 0, 0, ncomp, m_dtos_y2z);
    }
#if (AMREX_SPACEDIM == 3)
    else if (                     m_cmd_x2z) {
        if (m_openbc_half) {
            NonLocalBC::PackComponents components{};
            components.n_components = ncomp;
            NonLocalBC::ApplyDtosAndProjectionOnReciever packing
                {components, m_dtos_x2z};
            auto handler = ParallelCopy_nowait(m_cz, m_cx, *m_cmd_x2z_half, packing);
 
            Box upper_half = m_spectral_domain_z;
            // Note that z-direction's index is 0 because we z is the
            // unit-stride direction here.
            upper_half.growLo (0,-m_spectral_domain_z.length(0)/2);
            m_cz.setVal(0, upper_half, 0, ncomp);
 
            ParallelCopy_finish(m_cz, std::move(handler), *m_cmd_x2z_half, packing);
        } else {
            ParallelCopy(m_cz, m_cx, *m_cmd_x2z, 0, 0, ncomp, m_dtos_x2z);
        }
    }
#endif
    m_fft_fwd_z.template compute_c2c<Direction::forward>();
}
 
template <typename T, Direction D, bool C>
template <typename FA, typename RT>
std::pair<std::unique_ptr<char,DataDeleter>,std::size_t>
R2C<T,D,C>::install_raw_ptr (FA& fa, RT const* p)
{
    AMREX_ALWAYS_ASSERT(!fa.empty());
 
    using FAB = typename FA::FABType::value_type;
    using T_FAB = typename FAB::value_type;
    static_assert(sizeof(T_FAB) == sizeof(RT));
 
    auto const ncomp = m_info.batch_size;
    auto const& ia = fa.IndexArray();
 
    T_FAB* pp = nullptr;
    std::size_t sz = 0;
 
    if ( ! ia.empty() ) {
        int K = ia[0];
        Box const& box = fa.fabbox(K);
        if ((alignof(T_FAB) == alignof(RT)) || amrex::is_aligned(p,alignof(T_FAB))) {
            pp = (T_FAB*)p;
        } else {
            sz = sizeof(T_FAB) * box.numPts() * ncomp;
            pp = (T_FAB*) The_Arena()->alloc(sz);
        }
        fa.setFab(K, FAB(box,ncomp,pp));
    }
 
    if (sz == 0) {
        return std::make_pair(std::unique_ptr<char,DataDeleter>{},std::size_t(0));
    } else {
        return std::make_pair(std::unique_ptr<char,DataDeleter>
                              {(char*)pp,DataDeleter{The_Arena()}}, sz);
    }
}
 
 
template <typename T, Direction D, bool C>
template <typename RT, typename CT, Direction DIR, bool CP>
requires ((DIR == Direction::forward) || (DIR == Direction::both))
      && (((sizeof(RT)*2 == sizeof(CT)) && (!CP))
          || ((sizeof(RT) == sizeof(CT)) && CP))
void R2C<T,D,C>::forward (RT const* in, CT* out)
{
    auto [rdata, rsz] = install_raw_ptr(m_raw_mf, in);
    auto [cdata, csz] = install_raw_ptr(m_raw_cmf, out);
 
    if (rsz > 0) {
        Gpu::dtod_memcpy_async(rdata.get(),in,rsz);
        Gpu::streamSynchronize();
    }
 
    forward(m_raw_mf, m_raw_cmf);
 
    if (csz) {
        Gpu::dtod_memcpy_async(out,cdata.get(),csz);
        Gpu::streamSynchronize();
    }
}
 
template <typename T, Direction D, bool C>
template <Direction DIR>
requires (DIR == Direction::both)
void R2C<T,D,C>::backward (MF& outmf, int outcomp)
{
    backward_doit(outmf, IntVect(0), Periodicity::NonPeriodic(), outcomp);
}
 
template <typename T, Direction D, bool C>
void R2C<T,D,C>::backward_doit (MF& outmf, IntVect const& ngout,
                              Periodicity const& period, int outcomp)
{
    BL_PROFILE("FFT::R2C::backward(out)");
 
    auto const ncomp = m_info.batch_size;
 
    if (m_r2c_sub) {
        if (m_sub_helper.ghost_safe(outmf.nGrowVect())) {
            MF submf = m_sub_helper.make_alias_mf(outmf);
            IntVect const& subngout = m_sub_helper.make_iv(ngout);
            Periodicity const& subperiod = m_sub_helper.make_periodicity(period);
            m_r2c_sub->backward_doit(submf, subngout, subperiod, outcomp);
        } else {
            MF tmp(outmf.boxArray(), outmf.DistributionMap(), ncomp,
                   m_sub_helper.make_safe_ghost(outmf.nGrowVect()));
            this->backward_doit(tmp, ngout, period, 0);
            outmf.LocalCopy(tmp, 0, outcomp, ncomp, tmp.nGrowVect());
        }
        return;
    }
 
    if (m_do_alld_fft) {
        if constexpr (C) {
            m_fft_bwd_x.template compute_c2c<Direction::backward>();
        } else {
            m_fft_bwd_x.template compute_r2c<Direction::backward>();
        }
        auto const dst_nghost = amrex::elemwiseMin(ngout,outmf.nGrowVect());
        if (m_rx.boxArray().ixType() == outmf.boxArray().ixType()) {
            outmf.ParallelCopy(m_rx, 0, outcomp, ncomp, IntVect(0),
                               dst_nghost, period);
        } else {
            MF& rx_alias = make_m_rx_alias(outmf.boxArray().ixType());
            auto const copy_period = make_m_rx_alias_periodicity(outmf.boxArray().ixType(), period);
            outmf.ParallelCopy(rx_alias, 0, outcomp, ncomp, IntVect(0),
                               dst_nghost, copy_period);
        }
        return;
    }
 
    m_fft_bwd_z.template compute_c2c<Direction::backward>();
    if (                          m_cmd_z2y) {
        ParallelCopy(m_cy, m_cz, *m_cmd_z2y, 0, 0, ncomp, m_dtos_z2y);
    }
#if (AMREX_SPACEDIM == 3)
    else if (                     m_cmd_z2x) {
        auto const& cmd = m_openbc_half ? m_cmd_z2x_half : m_cmd_z2x;
        ParallelCopy(m_cx, m_cz, *cmd, 0, 0, ncomp, m_dtos_z2x);
    }
#endif
 
    m_fft_bwd_y.template compute_c2c<Direction::backward>();
    if (                          m_cmd_y2x) {
        ParallelCopy(m_cx, m_cy, *m_cmd_y2x, 0, 0, ncomp, m_dtos_y2x);
    }
 
    auto& fft_x = m_openbc_half ? m_fft_bwd_x_half : m_fft_bwd_x;
    if constexpr (C) {
        fft_x.template compute_c2c<Direction::backward>();
    } else {
        fft_x.template compute_r2c<Direction::backward>();
    }
    auto const dst_nghost = amrex::elemwiseMin(ngout,outmf.nGrowVect());
    if (m_rx.boxArray().ixType() == outmf.boxArray().ixType()) {
        outmf.ParallelCopy(m_rx, 0, outcomp, ncomp, IntVect(0),
                           dst_nghost, period);
    } else {
        MF& rx_alias = make_m_rx_alias(outmf.boxArray().ixType());
        auto const copy_period = make_m_rx_alias_periodicity(outmf.boxArray().ixType(), period);
        outmf.ParallelCopy(rx_alias, 0, outcomp, ncomp, IntVect(0),
                           dst_nghost, copy_period);
    }
}
 
template <typename T, Direction D, bool C>
template <typename CT, typename RT, Direction DIR, bool CP>
requires ((DIR == Direction::backward) || (DIR == Direction::both))
      && (((sizeof(RT)*2 == sizeof(CT)) && (!CP))
          || ((sizeof(RT) == sizeof(CT)) && CP))
void R2C<T,D,C>::backward (CT const* in, RT* out)
{
    auto [rdata, rsz] = install_raw_ptr(m_raw_mf, out);
    auto [cdata, csz] = install_raw_ptr(m_raw_cmf, in);
 
    if (csz) {
        Gpu::dtod_memcpy_async(cdata.get(),in,csz);
        Gpu::streamSynchronize();
    }
 
    backward(m_raw_cmf, m_raw_mf);
 
    if (rsz > 0) {
        Gpu::dtod_memcpy_async(out,rdata.get(),rsz);
        Gpu::streamSynchronize();
    }
}
 
template <typename T, Direction D, bool C>
std::pair<Plan<T>, Plan<T>>
R2C<T,D,C>::make_c2c_plans (cMF& inout, int ndims) const
{
    Plan<T> fwd;
    Plan<T> bwd;
 
    auto* fab = detail::get_fab(inout);
    if (!fab) { return {fwd, bwd};}
 
    Box const& box = fab->box();
    auto* pio = (typename Plan<T>::VendorComplex *)fab->dataPtr();
 
    auto const ncomp = m_info.batch_size;
 
#ifdef AMREX_USE_SYCL
    fwd.template init_c2c<Direction::forward>(box, pio, ncomp, ndims);
    bwd = fwd;
#else
    if constexpr (D == Direction::both || D == Direction::forward) {
        fwd.template init_c2c<Direction::forward>(box, pio, ncomp, ndims);
    }
    if constexpr (D == Direction::both || D == Direction::backward) {
        bwd.template init_c2c<Direction::backward>(box, pio, ncomp, ndims);
    }
#endif
 
    return {fwd, bwd};
}
 
namespace fft_detail {
    // The trailing int/long parameter orders these two overloads. A call
    // passing a literal 0 prefers the GpuComplex<T>& version, which is
    // called once per component of the batch, and falls back to the CellData
    // version only when the former is not viable. Without it, a functor
    // taking a generic parameter by value or by const reference would make
    // the two overloads ambiguous.
    template <typename F, typename T>
    AMREX_GPU_DEVICE AMREX_FORCE_INLINE
    auto call_post_forward (F const& f, int i, int j, int k, Array4<T> const& a,
                            int ii, int jj, int kk, int)
        noexcept -> decltype(void(f(0,0,0,a(0,0,0))))
    {
        for (int n = 0; n < a.nComp(); ++n) {
            f(i,j,k,a(ii,jj,kk,n));
        }
    }
 
    template <typename F, typename T>
    AMREX_GPU_DEVICE AMREX_FORCE_INLINE
    auto call_post_forward (F const& f, int i, int j, int k, Array4<T> const& a,
                            int ii, int jj, int kk, long)
        noexcept -> decltype(void(f(0,0,0,a.cellData(0,0,0))))
    {
        f(i,j,k,a.cellData(ii,jj,kk));
    }
}
 
template <typename T, Direction D, bool C>
template <typename F>
void R2C<T,D,C>::post_forward_doit_0 (F const& post_forward)
{
    if (m_info.twod_mode) {
        amrex::Abort("xxxxx todo: post_forward");
#if (AMREX_SPACEDIM > 1)
    } else if (m_r2c_sub) {
        // We need to pass the originally ordered indices to post_forward.
#if (AMREX_SPACEDIM == 2)
        // The original domain is (1,ny). The sub domain is (ny,1).
        m_r2c_sub->post_forward_doit_1
            ([=] AMREX_GPU_DEVICE (int i, int, int, auto&& sp)
                  -> decltype(void(post_forward(0,0,0,static_cast<decltype(sp)>(sp))))
             {
                 post_forward(0, i, 0, static_cast<decltype(sp)>(sp));
             });
#else
        if (m_real_domain.length(0) == 1 && m_real_domain.length(1) == 1) {
            // Original domain: (1, 1, nz). Sub domain: (nz, 1, 1)
            m_r2c_sub->post_forward_doit_1
                ([=] AMREX_GPU_DEVICE (int i, int, int, auto&& sp)
                      -> decltype(void(post_forward(0,0,0,static_cast<decltype(sp)>(sp))))
                 {
                     post_forward(0, 0, i, static_cast<decltype(sp)>(sp));
                 });
        } else if (m_real_domain.length(0) == 1 && m_real_domain.length(2) == 1) {
            // Original domain: (1, ny, 1). Sub domain: (ny, 1, 1)
            m_r2c_sub->post_forward_doit_1
                ([=] AMREX_GPU_DEVICE (int i, int, int, auto&& sp)
                          -> decltype(void(post_forward(0,0,0,static_cast<decltype(sp)>(sp))))
                     {
                         post_forward(0, i, 0, static_cast<decltype(sp)>(sp));
                     });
        } else if (m_real_domain.length(0) == 1) {
            // Original domain: (1, ny, nz). Sub domain: (ny, nz, 1)
            m_r2c_sub->post_forward_doit_1
                ([=] AMREX_GPU_DEVICE (int i, int j, int, auto&& sp)
                          -> decltype(void(post_forward(0,0,0,static_cast<decltype(sp)>(sp))))
                     {
                         post_forward(0, i, j, static_cast<decltype(sp)>(sp));
                     });
        } else if (m_real_domain.length(1) == 1) {
            // Original domain: (nx, 1, nz). Sub domain: (nx, nz, 1)
            m_r2c_sub->post_forward_doit_1
                ([=] AMREX_GPU_DEVICE (int i, int j, int, auto&& sp)
                          -> decltype(void(post_forward(0,0,0,static_cast<decltype(sp)>(sp))))
                     {
                         post_forward(i, 0, j, static_cast<decltype(sp)>(sp));
                     });
        } else {
            amrex::Abort("R2c::post_forward_doit_0: how did this happen?");
        }
#endif
#endif
    } else {
        this->post_forward_doit_1(post_forward);
    }
}
 
template <typename T, Direction D, bool C>
template <typename F>
void R2C<T,D,C>::post_forward_doit_1 (F const& post_forward)
{
    if (m_info.twod_mode) {
        amrex::Abort("xxxxx todo: post_forward");
    } else if (m_r2c_sub) {
        amrex::Abort("R2C::post_forward_doit_1: How did this happen?");
    } else {
        if (                           ! m_cz.empty()) {
            auto* spectral_fab = detail::get_fab(m_cz);
            if (spectral_fab) {
                auto const& a = spectral_fab->array(); // m_cz's ordering is z,x,y
                ParallelForOMP(spectral_fab->box(),
                [=] AMREX_GPU_DEVICE (int iz, int jx, int ky)
                {
                    fft_detail::call_post_forward(post_forward,
                                                  jx,ky,iz,a,iz,jx,ky,0);
                });
            }
        } else if (                    ! m_cy.empty()) {
            auto* spectral_fab = detail::get_fab(m_cy);
            if (spectral_fab) {
                auto const& a = spectral_fab->array(); // m_cy's ordering is y,x,z
                ParallelForOMP(spectral_fab->box(),
                [=] AMREX_GPU_DEVICE (int iy, int jx, int k)
                {
                    fft_detail::call_post_forward(post_forward,
                                                  jx,iy,k,a,iy,jx,k,0);
                });
            }
        } else {
            auto* spectral_fab = detail::get_fab(m_cx);
            if (spectral_fab) {
                auto const& a = spectral_fab->array();
                ParallelForOMP(spectral_fab->box(),
                [=] AMREX_GPU_DEVICE (int i, int j, int k)
                {
                    fft_detail::call_post_forward(post_forward,
                                                  i,j,k,a,i,j,k,0);
                });
            }
        }
    }
}
 
template <typename T, Direction D, bool C>
T R2C<T,D,C>::scalingFactor () const
{
#if (AMREX_SPACEDIM == 3)
    if (m_info.oned_mode && !m_info.twod_mode) {
        return T(1)/T(Long(m_real_domain.length(0)));
    } else if (m_info.twod_mode) {
        return T(1)/T(Long(m_real_domain.length(0)) *
                      Long(m_real_domain.length(1)));
    } else
#elif (AMREX_SPACEDIM == 2)
    if (m_info.oned_mode) {
        return T(1)/T(Long(m_real_domain.length(0)));
    } else
#endif
    {
        return T(1)/T(m_real_domain.numPts());
    }
}
 
template <typename T, Direction D, bool C>
template <Direction DIR>
requires ((DIR == Direction::forward) || (DIR == Direction::both))
std::pair<typename R2C<T,D,C>::cMF *, IntVect>
R2C<T,D,C>::getSpectralData () const
{
#if (AMREX_SPACEDIM > 1)
    if (m_r2c_sub) {
        auto [cmf, order] = m_r2c_sub->getSpectralData();
        return std::make_pair(cmf, m_sub_helper.inverse_order(order));
   } else
#endif
    if (!m_cz.empty()) {
        return std::make_pair(const_cast<cMF*>(&m_cz), IntVect{AMREX_D_DECL(2,0,1)});
    } else if (!m_cy.empty()) {
        return std::make_pair(const_cast<cMF*>(&m_cy), IntVect{AMREX_D_DECL(1,0,2)});
    } else {
        return std::make_pair(const_cast<cMF*>(&m_cx), IntVect{AMREX_D_DECL(0,1,2)});
    }
}
 
template <typename T, Direction D, bool C>
template <Direction DIR>
requires ((DIR == Direction::forward) || (DIR == Direction::both))
void R2C<T,D,C>::forward (MF const& inmf, cMF& outmf, int incomp, int outcomp)
{
    BL_PROFILE("FFT::R2C::forward(inout)");
 
    auto const ncomp = m_info.batch_size;
 
    if (m_r2c_sub)
    {
        bool inmf_safe = m_sub_helper.ghost_safe(inmf.nGrowVect());
        MF inmf_sub, inmf_tmp;
        int incomp_sub;
        if (inmf_safe) {
            inmf_sub = m_sub_helper.make_alias_mf(inmf);
            incomp_sub = incomp;
        } else {
            inmf_tmp.define(inmf.boxArray(), inmf.DistributionMap(), ncomp, 0);
            inmf_tmp.LocalCopy(inmf, incomp, 0, ncomp, IntVect(0));
            inmf_sub = m_sub_helper.make_alias_mf(inmf_tmp);
            incomp_sub = 0;
        }
 
        bool outmf_safe = m_sub_helper.ghost_safe(outmf.nGrowVect());
        cMF outmf_sub, outmf_tmp;
        int outcomp_sub;
        if (outmf_safe) {
            outmf_sub = m_sub_helper.make_alias_mf(outmf);
            outcomp_sub = outcomp;
        } else {
            outmf_tmp.define(outmf.boxArray(), outmf.DistributionMap(), ncomp, 0);
            outmf_sub = m_sub_helper.make_alias_mf(outmf_tmp);
            outcomp_sub = 0;
        }
 
        m_r2c_sub->forward(inmf_sub, outmf_sub, incomp_sub, outcomp_sub);
 
        if (!outmf_safe) {
            outmf.LocalCopy(outmf_tmp, 0, outcomp, ncomp, IntVect(0));
        }
    }
    else
    {
        forward(inmf, incomp);
        if (!m_cz.empty()) { // m_cz's order (z,x,y) -> (x,y,z)
            RotateBwd dtos{};
            MultiBlockCommMetaData cmd
                (outmf, m_spectral_domain_x, m_cz, IntVect(0), dtos);
            ParallelCopy(outmf, m_cz, cmd, 0, outcomp, ncomp, dtos);
        } else if (!m_cy.empty()) { // m_cy's order (y,x,z) -> (x,y,z)
            MultiBlockCommMetaData cmd
                (outmf, m_spectral_domain_x, m_cy, IntVect(0), m_dtos_y2x);
            ParallelCopy(outmf, m_cy, cmd, 0, outcomp, ncomp, m_dtos_y2x);
        } else {
            outmf.ParallelCopy(m_cx, 0, outcomp, ncomp);
        }
    }
}
 
template <typename T, Direction D, bool C>
template <Direction DIR>
requires ((DIR == Direction::backward) || (DIR == Direction::both))
void R2C<T,D,C>::backward (cMF const& inmf, MF& outmf, int incomp, int outcomp)
{
    backward_doit(inmf, outmf, IntVect(0), Periodicity::NonPeriodic(), incomp, outcomp);
}
 
template <typename T, Direction D, bool C>
void R2C<T,D,C>::backward_doit (cMF const& inmf, MF& outmf, IntVect const& ngout,
                              Periodicity const& period, int incomp, int outcomp)
{
    BL_PROFILE("FFT::R2C::backward(inout)");
 
    auto const ncomp = m_info.batch_size;
 
    if (m_r2c_sub)
    {
        bool inmf_safe = m_sub_helper.ghost_safe(inmf.nGrowVect());
        cMF inmf_sub, inmf_tmp;
        int incomp_sub;
        if (inmf_safe) {
            inmf_sub = m_sub_helper.make_alias_mf(inmf);
            incomp_sub = incomp;
        } else {
            inmf_tmp.define(inmf.boxArray(), inmf.DistributionMap(), ncomp, 0);
            inmf_tmp.LocalCopy(inmf, incomp, 0, ncomp, IntVect(0));
            inmf_sub = m_sub_helper.make_alias_mf(inmf_tmp);
            incomp_sub = 0;
        }
 
        bool outmf_safe = m_sub_helper.ghost_safe(outmf.nGrowVect());
        MF outmf_sub, outmf_tmp;
        int outcomp_sub;
        if (outmf_safe) {
            outmf_sub = m_sub_helper.make_alias_mf(outmf);
            outcomp_sub = outcomp;
        } else {
            IntVect const& ngtmp = m_sub_helper.make_safe_ghost(outmf.nGrowVect());
            outmf_tmp.define(outmf.boxArray(), outmf.DistributionMap(), ncomp, ngtmp);
            outmf_sub = m_sub_helper.make_alias_mf(outmf_tmp);
            outcomp_sub = 0;
        }
 
        IntVect const& subngout = m_sub_helper.make_iv(ngout);
        Periodicity const& subperiod = m_sub_helper.make_periodicity(period);
        m_r2c_sub->backward_doit(inmf_sub, outmf_sub, subngout, subperiod, incomp_sub, outcomp_sub);
 
        if (!outmf_safe) {
            outmf.LocalCopy(outmf_tmp, 0, outcomp, ncomp, outmf_tmp.nGrowVect());
        }
    }
    else
    {
        if (!m_cz.empty()) { // (x,y,z) -> m_cz's order (z,x,y)
            RotateFwd dtos{};
            MultiBlockCommMetaData cmd
                (m_cz, m_spectral_domain_z, inmf, IntVect(0), dtos);
            ParallelCopy(m_cz, inmf, cmd, incomp, 0, ncomp, dtos);
        } else if (!m_cy.empty()) { // (x,y,z) -> m_cy's ordering (y,x,z)
            MultiBlockCommMetaData cmd
                (m_cy, m_spectral_domain_y, inmf, IntVect(0), m_dtos_x2y);
            ParallelCopy(m_cy, inmf, cmd, incomp, 0, ncomp, m_dtos_x2y);
        } else {
            m_cx.ParallelCopy(inmf, incomp, 0, ncomp);
        }
        backward_doit(outmf, ngout, period, outcomp);
    }
}
 
template <typename T, Direction D, bool C>
std::pair<BoxArray,DistributionMapping>
R2C<T,D,C>::getSpectralDataLayout () const
{
#if (AMREX_SPACEDIM > 1)
    if (m_r2c_sub) {
        auto const& [ba, dm] = m_r2c_sub->getSpectralDataLayout();
        return std::make_pair(m_sub_helper.inverse_boxarray(ba), dm);
    }
#endif
 
#if (AMREX_SPACEDIM == 3)
    if (!m_cz.empty()) {
        BoxList bl = m_cz.boxArray().boxList();
        for (auto& b : bl) {
            auto lo = b.smallEnd();
            auto hi = b.bigEnd();
            std::swap(lo[0], lo[1]);
            std::swap(lo[1], lo[2]);
            std::swap(hi[0], hi[1]);
            std::swap(hi[1], hi[2]);
            b.setSmall(lo);
            b.setBig(hi);
        }
        return std::make_pair(BoxArray(std::move(bl)), m_cz.DistributionMap());
    } else
#endif
#if (AMREX_SPACEDIM >= 2)
    if (!m_cy.empty()) {
        BoxList bl = m_cy.boxArray().boxList();
        for (auto& b : bl) {
            auto lo = b.smallEnd();
            auto hi = b.bigEnd();
            std::swap(lo[0], lo[1]);
            std::swap(hi[0], hi[1]);
            b.setSmall(lo);
            b.setBig(hi);
        }
        return std::make_pair(BoxArray(std::move(bl)), m_cy.DistributionMap());
    } else
#endif
    {
        return std::make_pair(m_cx.boxArray(), m_cx.DistributionMap());
    }
}
 
template <typename T = Real, FFT::Direction D = FFT::Direction::both>
using C2C = R2C<T, D, true>;
 
}
 
#endif