key.h

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/*
 This file is part of MADNESS.
 
 Copyright (C) 2007,2010 Oak Ridge National Laboratory
 
 This program is free software; you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation; either version 2 of the License, or
 (at your option) any later version.
 
 This program is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 GNU General Public License for more details.
 
 You should have received a copy of the GNU General Public License
 along with this program; if not, write to the Free Software
 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 
 For more information please contact:
 
 Robert J. Harrison
 Oak Ridge National Laboratory
 One Bethel Valley Road
 P.O. Box 2008, MS-6367
 
 email: harrisonrj@ornl.gov
 tel:   865-241-3937
 fax:   865-572-0680
*/
 
#ifndef MADNESS_MRA_KEY_H__INCLUDED
#define MADNESS_MRA_KEY_H__INCLUDED
 
/// \file key.h
/// \brief Multidimension Key for MRA tree and associated iterators
 
#include <madness/mra/bc.h>
#include <madness/mra/power.h>
#include <madness/tensor/tensor.h>
#include <madness/world/vector.h>
#include <madness/world/binary_fstream_archive.h>
#include <madness/world/worldhash.h>
 
#include <algorithm>
#include <climits>  // CHAR_BIT
#include <cstdint>
#include <optional>
 
namespace madness {
 
    //     // this has problems when nproc is a large-ish power of 2 such as 256
    //     // and leads to bad data distribution.
    //     static inline unsigned int sdbm(int n, const unsigned char* c, unsigned int sum=0) {
    //         for (int i=0; i<n; ++i) sum = c[i] + (sum << 6) + (sum << 16) - sum;
    //         return sum;
    //     }
 
    typedef int64_t Translation;
    typedef int Level;
 
    template<std::size_t NDIM>
    class KeyChildIterator;
 
    /// Key is the index for a node of the 2^NDIM-tree
 
    /// See KeyChildIterator for facile generation of children,
    /// and foreach_child(parent,op) for facile application of operators
    /// to child keys.
    template<std::size_t NDIM>
    class Key {
    public:
//        static const typename Vector<Translation,NDIM>::size_type static_size = Vector<Translation,NDIM>::static_size;
        static const std::size_t static_size = NDIM;
 
    private:
        friend class KeyChildIterator<NDIM> ;
        Level n = 0;
        Vector<Translation, NDIM> l = Vector<Translation, NDIM>(0);
        hashT hashval = 0;
 
 
    public:
 
        /// Default constructor makes an initialized key
        Key() : n(0), l(0), hashval(0) {}
 
        /// Constructor with given n, l
        Key(Level n, const Vector<Translation, NDIM>& l) : n(n), l(l) 
    {
            MADNESS_ASSERT(n >= 0 && size_t(n) < sizeof(Translation)*CHAR_BIT);
            rehash();
        }
 
        /// Constructor with given n and l=0
        Key(int n) : n(n), l(0) 
        {
            MADNESS_ASSERT(n >= 0 && size_t(n) < sizeof(Translation)*CHAR_BIT);
            rehash();
        }
 
        // /// easy constructor ... UGH !!!!!!!!!!!!!!!!!!!!!!
        // Key(const int n, const int l0, const int l1, const int l2) : n(n) {
        //     MADNESS_ASSERT(NDIM==3);
        //     l=Vector<Translation, NDIM>(0);
        //     l[0]=l0; l[1]=l1; l[2]=l2;
        //     rehash();
        // }
 
        /// Returns an invalid key
        static Key<NDIM>  invalid() {
          Key<NDIM> result;
          result.n = -1;
          result.l = 0;
          result.rehash();
          return result;
        }
 
        /// Checks if a key is invalid
        bool is_invalid() const {
            return n == -1;
        }
 
        /// Checks if a key is valid
        bool is_valid() const {
            return n != -1;
        }
 
        /// Equality test
        bool  operator==(const Key& other) const {
            if (hashval != other.hashval) return false;
        if (n != other.n) return false;
        for (unsigned int i=0; i<NDIM; i++)
          if (l[i] != other.l[i]) return false;
        return true; // everything is equal
        }
 
        bool operator!=(const Key& other) const {
            return !(*this == other);
        }
 
        /// Comparison operator less than to enable storage in STL map
        bool operator<(const Key& other) const {
        if (hashval < other.hashval) return true;
        if (hashval > other.hashval) return false;
 
        if (n < other.n) return true;
        if (n > other.n) return false;
        
        for (unsigned int i=0; i<NDIM; i++) {
          if (l[i] < other.l[i]) return true;
          if (l[i] > other.l[i]) return false;
        }
 
        return false; // everything is equal
        }
 
        inline hashT
        hash() const {
            return hashval;
        }
 
        // template<typename Archive>
        // inline void
        // serialize(Archive& ar) {
        //     ar & archive::wrap((unsigned char*) this, sizeof(*this));
        // }
 
        Level
        level() const {
            return n;
        }
 
        const Vector<Translation, NDIM>&
        translation() const {
            return l;
        }
 
        /// const accessor to elements of this->translation()
        const Translation& operator[](std::size_t d) const {
          return l[d];
        }
 
        uint64_t
        distsq() const {
            uint64_t dist = 0;
            for (std::size_t d = 0; d < NDIM; ++d) {
                dist += l[d] * l[d];
            }
            return dist;
        }
 
        // The distance of a displacement in real space.
        double real_distsq(const madness::Tensor<double>& widths) const {
            double dist = 0;
            for (std::size_t d = 0; d < NDIM; ++d) {
                // Subtract 1 to account for the least distance between points in the boxes.
                const auto least_displacement_distance = std::max(std::abs(l[d]) - 1, static_cast<Translation>(0));
                const auto real_width = widths(d) * least_displacement_distance;
                dist += real_width * real_width;
            }
            return dist;
        }
 
        /// like distsq() but accounts for periodicity
        uint64_t distsq_bc(const array_of_bools<NDIM>& is_periodic) const {
          const Translation twonm1 = (Translation(1) << level()) >> 1;
 
          uint64_t dsq = 0;
          for (std::size_t d = 0; d < NDIM; ++d) {
            Translation la = translation()[d];
            if (is_periodic[d]) {
              if (la > twonm1) {
                la -= twonm1 * 2;
                MADNESS_ASSERT(la <= twonm1);
              }
              if (la < -twonm1) {
                la += twonm1 * 2;
                MADNESS_ASSERT(la >= -twonm1);
              }
            }
            dsq += la * la;
          }
 
          return dsq;
        }
 
        /// like real_distsq() but accounts for periodicity
        double real_distsq_bc(const array_of_bools<NDIM>& is_periodic, const Tensor<double>& widths) const {
          const Translation twonm1 = (Translation(1) << level()) >> 1;
 
          double dsq = 0;
          for (std::size_t d = 0; d < NDIM; ++d) {
            Translation la = translation()[d];
            if (is_periodic[d]) {
              if (la > twonm1) {
                la -= twonm1 * 2;
                MADNESS_ASSERT(la <= twonm1);
              }
              if (la < -twonm1) {
                la += twonm1 * 2;
                MADNESS_ASSERT(la >= -twonm1);
              }
            }
            // Subtract 1 to account for the least distance between points in the boxes.
            const auto least_displacement_distance = std::max(std::abs(la) - 1, static_cast<Translation>(0));
            const auto real_width = widths(d) * least_displacement_distance;
            dsq += real_width * real_width;
          }
 
          return dsq;
        }
 
        /// like distsq_bc() but to the nearest lattice image other than the home cell
 
        /// The rest-of-crystal kernel (OperatorInfo::images_only) at displacement l sums the free-space
        /// kernel at l + R 2^n over the lattice vectors R != 0 of the periodic axes, so it decays with this
        /// distance as an ordinary lattice-summed kernel decays with distsq_bc().
        /// @note saturates: each axis contributes at most distsq_images_axis_max(), since from level 31 on the
        ///       offset to the next-nearest image (~2^n boxes) squared does not fit; real_distsq_images() does not
        uint64_t distsq_images(const array_of_bools<NDIM>& is_periodic) const {
          return distsq_images_impl(is_periodic, [](std::size_t, Translation la) -> uint64_t {
            const uint64_t a = std::min(la < 0 ? uint64_t(0) - uint64_t(la) : uint64_t(la), distsq_images_axis_cap);
            return a * a;
          });
        }
 
        /// the largest contribution of one axis to distsq_images(); NDIM <= 6 of them sum below 2^63
        static constexpr uint64_t distsq_images_axis_max() { return distsq_images_axis_cap * distsq_images_axis_cap; }
 
        /// like real_distsq_bc() but to the nearest lattice image other than the home cell (see distsq_images())
        double real_distsq_images(const array_of_bools<NDIM>& is_periodic, const Tensor<double>& widths) const {
          return distsq_images_impl(is_periodic, [&](std::size_t d, Translation la) -> double {
            // Subtract 1 to account for the least distance between points in the boxes.
            const auto real_width = widths(d) * std::max(std::abs(la) - 1, static_cast<Translation>(0));
            return real_width * real_width;
          });
        }
 
        /// like real_distsq_images() but between the centers of the boxes
 
        /// real_distsq_images() is the least distance between points of the two boxes, which is zero for every
        /// displacement one box from an image whatever the axis. The center distance is the axis width there, so
        /// it tells those displacements apart (Displacements::sort_displacements_images breaks ties with it).
        double real_distsq_images_centers(const array_of_bools<NDIM>& is_periodic, const Tensor<double>& widths) const {
          return distsq_images_impl(is_periodic, [&](std::size_t d, Translation la) -> double {
            const double real_width = widths(static_cast<long>(d)) * static_cast<double>(la);
            return real_width * real_width;
          });
        }
 
      private:
        static constexpr uint64_t distsq_images_axis_cap = uint64_t(1) << 30;  ///< |l| in boxes at which distsq_images() saturates
 
        /// min over R != 0 of sum_d axis_distsq(d, l_d + R_d 2^n), R_d = 0 along nonperiodic axes. The sum is
        /// separable, so the minimum takes the nearest image on every axis (as distsq_bc() does) unless that is
        /// R = 0 on every periodic axis; then exactly one periodic axis moves to its next-nearest image, the
        /// one that costs least.
        template <typename F>
        auto distsq_images_impl(const array_of_bools<NDIM>& is_periodic, F&& axis_distsq) const {
          using T = decltype(axis_distsq(std::size_t(0), Translation(0)));
          const Translation twon = Translation(1) << level();
          const Translation twonm1 = twon >> 1;
          T dsq = 0;
          bool wrapped = false;
          std::optional<T> step;  // least cost of moving one periodic axis off R = 0
          for (std::size_t d = 0; d < NDIM; ++d) {
            Translation la = translation()[d];
            if (is_periodic[d]) {
              // reduce to the nearest image; one step suffices for |l| < 2^n, which is all Displacements
              // produces, the loop makes the function correct for any l
              if (la > twonm1) { do la -= twon; while (la > twonm1); wrapped = true; }
              else if (la < -twonm1) { do la += twon; while (la < -twonm1); wrapped = true; }
              else {
                const T s = axis_distsq(d, la > 0 ? la - twon : la + twon) - axis_distsq(d, la);
                if (!step || s < *step) step = s;
              }
            }
            dsq += axis_distsq(d, la);
          }
          if (!wrapped) {
            MADNESS_CHECK_THROW(step.has_value(), "Key::distsq_images: no axis is periodic, so there are no images");
            dsq += *step;
          }
          return dsq;
        }
 
      public:
        /// like "periodic" distsq() but only selects the prescribed axes
        template <std::size_t NDIM2>
        std::enable_if_t<NDIM >= NDIM2, uint64_t>
        distsq_bc(const array_of_bools<NDIM>& is_periodic, const std::array<std::size_t, NDIM2>& axes) const {
          const Translation twonm1 = (Translation(1) << level()) >> 1;
 
          uint64_t dsq = 0;
          for (std::size_t a = 0; a < NDIM2; ++a) {
            const auto d = axes[a];
            MADNESS_ASSERT(d < NDIM);
            Translation la = translation()[d];
            if (is_periodic[d]) {
              if (la > twonm1) {
                la -= twonm1 * 2;
                MADNESS_ASSERT(la <= twonm1);
              }
              if (la < -twonm1) {
                la += twonm1 * 2;
                MADNESS_ASSERT(la >= -twonm1);
              }
            }
            dsq += la * la;
          }
 
          return dsq;
        }
 
        /// Returns the key of the parent
 
        /// Default is the immediate parent (generation=1).  To get
        /// the grandparent use generation=2, and similarly for
        /// great-grandparents.
        ///
        /// !! If there is no such parent it quietly returns the
        /// closest match (which may be self if this is the top of the
        /// tree).
        Key
        parent(int generation = 1) const {
            Vector<Translation, NDIM> pl;
            if (generation > n)
                generation = n;
            for (std::size_t i = 0; i < NDIM; ++i)
                pl[i] = l[i] >> generation;
            return Key(n - generation, pl);
        }
 
 
        bool
        is_child_of(const Key& key) const {
            if (this->n < key.n) {
                return false; // I can't be child of something lower on the tree
            }
            else if (this->n == key.n) {
                return (*this == key); // I am child of myself
            }
            else {
                Level dn = this->n - key.n;
                Key mama = this->parent(dn);
                return (mama == key);
            }
        }
 
 
        bool
        is_parent_of(const Key& key) const {
            return (key.is_child_of(*this));
        }
 
        /// Assuming keys are at the same level, returns true if displaced by no more than 1 in any direction
 
        /// Assumes key and this are at the same level
        bool
        is_neighbor_of(const Key& key, const array_of_bools<NDIM>& bperiodic) const {
          Translation dist = 0;
          Translation TWON1 = (Translation(1)<<n) - 1;
            for (std::size_t i=0; i<NDIM; ++i)
            {
              Translation ll = std::abs(l[i] - key.l[i]);
              if (bperiodic[i] && ll==TWON1) ll=1;
              dist = std::max(dist, ll);
            }
            return (dist <= 1);
        }
 
        /// True iff this box is a neighbor of a point in simulation coordinates
 
        /// Geometrically: this box's closure overlaps the closed box of
        /// half-width 1 (one box-width at this level) centered on `simpt`.
        /// Equivalently, the Chebyshev distance from this box to `simpt`
        /// (measured in box-widths) is at most 1.
        ///
        /// This is the point-argument analogue of the key-vs-key overload
        /// `is_neighbor_of(Key, bperiodic)`; both express "within one
        /// box-width" adjacency. It supersedes the legacy idiom
        /// `simpt2key(simpt, n).is_neighbor_of(*this, ...)`, which was
        /// asymmetric for points lying on box boundaries because
        /// `simpt2key` truncates to a single key. The new test reports
        /// face-, edge-, and corner-coincident points as contained in
        /// *every* box that shares the face/edge/corner — and therefore
        /// every neighbor of those boxes is correctly flagged too.
        ///
        /// @param[in] simpt point in simulation coordinates
        ///                  (in [0,1]^NDIM, modulo 1 in periodic dimensions)
        /// @param[in] bperiodic per-dimension periodic-boundary flags
        template <typename T>
        bool
        is_neighbor_of(const Vector<T, NDIM>& simpt,
                       const array_of_bools<NDIM>& bperiodic) const {
            const double twon = std::ldexp(1.0, n);  // 2^n
            const double period = twon;              // sim domain has unit length
            // round-off in d = twon*simpt - l is ~ period * eps; pad by a few
            // ULPs so points within machine noise of an edge deterministically
            // count as on it.
            const double tol = 8.0 * period * std::numeric_limits<double>::epsilon();
            for (std::size_t i = 0; i < NDIM; ++i) {
                // signed distance from this box's lower edge, in box-widths
                double d = twon * static_cast<double>(simpt[i]) - static_cast<double>(l[i]);
                if (bperiodic[i]) {
                    // fold to the nearest periodic image: d ∈ [-period/2, period/2)
                    d -= period * std::floor((d + 0.5 * period) / period);
                }
                if (d < -1.0 - tol || d > 2.0 + tol)
                    return false;
            }
            return true;
        }
 
        /// given a displacement, generate a neighbor key; ignore boundary conditions and disp's level
 
        /// @param[in]  disp    the displacement
        /// @return     a new key
        Key neighbor(const Key<NDIM>& disp) const {
            Vector<Translation,NDIM> l = this->translation()+disp.translation();
            return Key(this->level(),l);
        }
 
        /// given a displacement, generate a neighbor key; ignore boundary conditions and disp's level
 
        /// @param[in]  disp    the displacement
        /// @return     a new key
        Key neighbor(const Vector<Translation,NDIM>& disp) const {
          Vector<Translation,NDIM> l = this->translation()+disp;
          return Key(this->level(),l);
        }
 
 
        /// check if this MultiIndex contains point x, disregarding these two dimensions
        bool thisKeyContains(const Vector<double,NDIM>& x, const unsigned int& dim0,
                const unsigned int& dim1) const {
 
            // it's sufficient if one single dimension is out
            bool contains=true;
            const double twotoN = std::pow(2.0,double(n));
            MADNESS_ASSERT(dim0<NDIM and dim1<NDIM);
 
            for (unsigned int i=0; i<NDIM; i++ ) {
 
                // check bounds
                MADNESS_ASSERT((x[i]>=0.0) and (x[i]<=1.0));
 
                // leave these two dimensions out
                if ((i==dim0) or (i==dim1)) continue;
 
                const int ll=int (x[i]*twotoN);
                if (not (l[i]==ll)) contains=false;
            }
            return contains;
        }
 
        /// break key into two low-dimensional keys
        template<std::size_t LDIM, std::size_t KDIM>
        void break_apart(Key<LDIM>& key1, Key<KDIM>& key2) const {
 
            // if LDIM==NDIM the 2nd key will be constructed empty
            // static_assert((LDIM+KDIM==NDIM) or (LDIM==NDIM));
            Vector<Translation, LDIM> l1;
            Vector<Translation, KDIM> l2;
            if constexpr((LDIM+KDIM==NDIM) or (LDIM==NDIM)) {
                for (size_t i=0; i<LDIM; ++i) {
                    l1[i]=l[i];
                }
                for (size_t i=LDIM; i<NDIM; ++i) {
                    l2[i-LDIM]=l[i];
                }
 
                key1=Key<LDIM>(n,l1);
                key2=Key<KDIM>(n,l2);
            } else {
                MADNESS_EXCEPTION("Key::break_apart: LDIM+KDIM must equal NDIM or LDIM==NDIM",1);
            }
        }
 
        /// extract a new key consisting of first VDIM dimensions of this
        template<std::size_t VDIM>
        Key<VDIM> extract_front() const {
          static_assert(VDIM <= NDIM, "VDIM must be less than or equal to NDIM");
          Vector<Translation, VDIM> t;
          for (size_t i = 0; i < VDIM; ++i) t[i] = this->translation()[i];
          return Key<VDIM>(this->level(),t);
        }
 
        /// extract a new key consisting of last VDIM dimensions of this
        template<std::size_t VDIM>
        Key<VDIM> extract_back() const {
          static_assert(VDIM <= NDIM, "VDIM must be less than or equal to NDIM");
          Vector<Translation, VDIM> t;
          for (size_t i = 0; i < VDIM; ++i) t[i] = this->translation()[NDIM-VDIM+i];
          return Key<VDIM>(this->level(),t);
        }
 
        /// extract a new key with the Translations indicated in the v array
        template<std::size_t VDIM>
        Key<VDIM> extract_key(const std::array<int,VDIM>& v) const {
            Vector<Translation, VDIM> t;
            for (size_t i = 0; i < VDIM; ++i) t[i] = this->translation()[v[i]];
            return Key<VDIM>(this->level(),t);
        };
 
        /// extract a new key with the Translations complementary to the ones indicated in the v array
        template<std::size_t VDIM>
        Key<NDIM-VDIM> extract_complement_key(const std::array<int,VDIM>& v) const {
 
            // return the complement of v, e.g. v={0,1}, v_complement={2,3,4} if NDIM==5
            // v must be contiguous and ascending (i.e. 1,2,3 or 2,3,4)
            auto v_complement = [](const std::array<int, VDIM>& v) {
                std::array<int, NDIM - VDIM> result;
                for (std::size_t i = 0; i < NDIM - VDIM; i++) result[i] = (v.back() + i + 1) % NDIM;
                return result;
            };
            return extract_key(v_complement(v));
        };
 
        /// merge with other key (ie concatenate), use level of rhs, not of this
        template<std::size_t LDIM>
        Key<NDIM+LDIM> merge_with(const Key<LDIM>& rhs) const {
            Vector<Translation,NDIM+LDIM> t;
            if constexpr (NDIM > 0) for (size_t i=0; i<NDIM; ++i) t[i]     =this->l[i];
            if constexpr (LDIM > 0) for (size_t i=0; i<LDIM; ++i) t[NDIM+i]=rhs.translation()[i];
            return Key<NDIM+LDIM>(rhs.level(),t);
        }
 
        /// return if the other key is pointing in the same direction and is farther out
 
        /// unlike in distsq() the direction is taken into account, and other must be
        /// longer than this in each dimension
        /// @param[in]  other   a key
        /// @return     if other is farther out
        bool is_farther_out_than(const Key<NDIM>& other) const {
            for (size_t i=0; i<NDIM; ++i) {
                if ((other.translation()[i]>0) and (other.translation()[i]>l[i])) return false;
                if ((other.translation()[i]<0) and (other.translation()[i]<l[i])) return false;
            }
            return true;
        }
 
 
        /// Recomputes hashval ... presently only done when reading from external storage
        void
        rehash() {
            //hashval = sdbm(sizeof(n)+sizeof(l), (unsigned char*)(&n));
            // default hash is still best
 
      hashval = hash_value(l);
      hash_combine(hashval, n);
        }
    };
 
    template<std::size_t NDIM>
    std::ostream&
    operator<<(std::ostream& s, const Key<NDIM>& key) {
        s << "(" << key.level() << "," << key.translation() << ")";
        return s;
    }
 
    /// given a source and a target, return the displacement in translation
 
    /// @param[in]  source  the source key
    /// @param[in]  target  the target key
    /// @return     disp    such that target = source + disp
    template<size_t NDIM>
    Key<NDIM> displacement(const Key<NDIM>& source, const Key<NDIM>& target) {
        MADNESS_ASSERT(source.level()==target.level());
        const Vector<Translation,NDIM> l = target.translation()-source.translation();
        return Key<NDIM>(source.level(),l);
    }
 
 
 
    /// Iterates in lexical order thru all children of a key
 
    /// Example usage:
    /// \code
    ///    for (KeyChildIterator<NDIM> it(key); it; ++it) print(it.key());
    /// \endcode
    template<std::size_t NDIM>
    class KeyChildIterator {
        Key<NDIM> parent;
        Key<NDIM> child;
        Vector<Translation, NDIM> p;
        bool finished;
 
    public:
        KeyChildIterator() :
                p(0), finished(true) {
        }
 
        KeyChildIterator(const Key<NDIM>& parent) :
                parent(parent), child(parent.n + 1, parent.l * 2), p(0),
                finished(false) {
        }
 
        /// Pre-increment of an iterator (i.e., ++it)
        KeyChildIterator&
        operator++() {
            if (finished)
                return *this;
            std::size_t i;
            for (i = 0; i < NDIM; ++i) {
                if (p[i] == 0) {
                    ++(p[i]);
                    ++(child.l[i]);
                    for (std::size_t j = 0; j < i; ++j) {
                        --(p[j]);
                        --(child.l[j]);
                    }
                    break;
                }
            }
            finished = (i == NDIM);
            child.rehash();
            return *this;
        }
 
        /// True if iterator is not at end
        operator bool() const {
            return !finished;
        }
 
        template<typename Archive>
        inline void
        serialize(Archive& ar) {
            ar & archive::wrap((unsigned char*) this, sizeof(*this));
        }
 
        /// Returns the key of the child
        inline const Key<NDIM>&
        key() const {
            return child;
        }
    };
 
    /// Applies op(key) to each child key of parent
    template<std::size_t NDIM, typename opT>
    inline void
    foreach_child(const Key<NDIM>& parent, opT& op) {
        for (KeyChildIterator<NDIM>
                it(parent); it; ++it)
            op(it.key());
    }
 
    /// Applies member function of obj to each child key of parent
    template<std::size_t NDIM, typename objT>
    inline void
    foreach_child(const Key<NDIM>& parent, objT* obj, void
                  (objT::*memfun)(const Key<NDIM>&)) {
        for (KeyChildIterator<NDIM>
                it(parent); it; ++it)
            (obj ->* memfun)(it.key());
    }
 
    namespace archive {
 
        // For efficiency serialize opaque so is just one memcpy, but
        // when reading from external storage rehash() so that we
        // can read data even if hash algorithm/function has changed.
 
        template <class Archive, std::size_t NDIM>
        struct ArchiveLoadImpl< Archive, Key<NDIM> > {
            static void load(const Archive& ar, Key<NDIM>& t) {
                ar & archive::wrap((unsigned char*) &t, sizeof(t));
            }
        };
 
        template <std::size_t NDIM>
        struct ArchiveLoadImpl< BinaryFstreamInputArchive, Key<NDIM> > {
            static void load(const BinaryFstreamInputArchive& ar, Key<NDIM>& t) {
                ar & archive::wrap((unsigned char*) &t, sizeof(t));
                t.rehash(); // <<<<<<<<<< This is the point
            }
        };
 
        template <class Archive, std::size_t NDIM>
        struct ArchiveStoreImpl< Archive, Key<NDIM> > {
            static void store(const Archive& ar, const Key<NDIM>& t) {
                ar & archive::wrap((unsigned char*) &t, sizeof(t));
            }
        };
    }
 
}
 
#endif // MADNESS_MRA_KEY_H__INCLUDED