/data/refman/pasoursint/CMSSW_6_1_1/src/JetMETCorrections/InterpolationTables/interface/HistoND.h

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#ifndef NPSTAT_HISTOND_HH_
#define NPSTAT_HISTOND_HH_

#include "JetMETCorrections/InterpolationTables/interface/ArrayND.h"
#include "JetMETCorrections/InterpolationTables/interface/HistoAxis.h"

namespace npstat {
    template <typename Numeric, class Axis=HistoAxis>
    class HistoND
    {
        template <typename Num2, class Axis2> friend class HistoND;

    public:
        typedef Numeric value_type;
        typedef Axis axis_type;

        HistoND(const std::vector<Axis>& axes, const char* title=0,
                const char* accumulatedDataLabel=0);

        HistoND(const Axis& xAxis, const char* title=0,
                const char* accumulatedDataLabel=0);

        HistoND(const Axis& xAxis, const Axis& yAxis,
                const char* title=0, const char* accumulatedDataLabel=0);

        HistoND(const Axis& xAxis, const Axis& yAxis, const Axis& zAxis,
                const char* title=0, const char* accumulatedDataLabel=0);

        HistoND(const Axis& xAxis, const Axis& yAxis,
                const Axis& zAxis, const Axis& tAxis,
                const char* title=0, const char* accumulatedDataLabel=0);

        HistoND(const Axis& xAxis, const Axis& yAxis,
                const Axis& zAxis, const Axis& tAxis, const Axis& vAxis,
                const char* title=0, const char* accumulatedDataLabel=0);

        HistoND(const ArrayShape& shape, const BoxND<double>& boundingBox,
                const char* title=0, const char* accumulatedDataLabel=0);

        template <typename Num2, class Functor>
        HistoND(const HistoND<Num2,Axis>& h, const Functor& f,
                const char* title=0, const char* accumulatedDataLabel=0);

        template <typename Num2>
        HistoND(const HistoND<Num2,Axis>& h, const unsigned *indices,
                unsigned nIndices, const char* title=0);

        template <typename Num2>
        HistoND(const HistoND<Num2,Axis>& h, const Axis& newAxis,
                unsigned newAxisNumber, const char* title=0);

        HistoND(const HistoND&);

        HistoND& operator=(const HistoND&);

        inline unsigned dim() const {return dim_;}

        inline const std::string& title() const {return title_;}

        inline const std::string& accumulatedDataLabel() const
            {return accumulatedDataLabel_;}

        inline const ArrayND<Numeric>& binContents() const {return data_;}

        inline const ArrayND<Numeric>& overflows() const {return overflow_;}

        inline const std::vector<Axis>& axes() const {return axes_;}

        inline const Axis& axis(const unsigned i) const
            {return axes_.at(i);}

        inline unsigned long nBins() const {return data_.length();}

        inline unsigned long nFillsTotal() const {return fillCount_;}

        inline unsigned long nFillsInRange() const
            {return fillCount_ - overCount_;}

        inline unsigned long nFillsOver() const {return overCount_;}

        bool isUniformlyBinned() const;

        inline void setTitle(const char* newtitle)
            {title_ = newtitle ? newtitle : ""; ++modCount_;}

        inline void setAccumulatedDataLabel(const char* newlabel)
            {accumulatedDataLabel_ = newlabel ? newlabel : ""; ++modCount_;}

        inline void setAxisLabel(const unsigned axisNum, const char* newlabel)
            {axes_.at(axisNum).setLabel(newlabel); ++modCount_;}

        double binVolume(unsigned long binNumber=0) const;

        void binCenter(unsigned long binNumber,
                       double* coords, unsigned lenCoords) const;

        template <class Point>
        void allBinCenters(std::vector<Point>* centers) const;

        void binBox(unsigned long binNumber, BoxND<double>* box) const;

        BoxND<double> boundingBox() const;

        double volume() const;

        double integral() const;

        void clear();

        void clearBinContents();

        void clearOverflows();

        bool operator==(const HistoND&) const;

        bool operator!=(const HistoND&) const;

        bool isSameData(const HistoND&) const;

        template <typename Num2>
        void fill(const double* coords, unsigned coordLength,
                  const Num2& weight);


        template <typename Num2>
        void fill(const Num2& weight);

        template <typename Num2>
        void fill(double x0, const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, double x2, const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, double x2, double x3,
                  const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, double x2, double x3, double x4,
                  const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, double x2, double x3, double x4,
                  double x5, const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, double x2, double x3, double x4,
                  double x5, double x6, const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, double x2, double x3, double x4,
                  double x5, double x6, double x7, const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, double x2, double x3, double x4,
                  double x5, double x6, double x7, double x8,
                  const Num2& weight);

        template <typename Num2>
        void fill(double x0, double x1, double x2, double x3, double x4,
                  double x5, double x6, double x7, double x8, double x9,
                  const Num2& weight);

        template <typename Num2, class Functor>
        void dispatch(const double* coords, unsigned coordLength,
                      Num2& weight, Functor& f);


        template <typename Num2, class Functor>
        void dispatch(Num2& weight, Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, Num2& weight, Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, Num2& weight, Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, double x2, Num2& weight,
                      Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, double x2, double x3,
                      Num2& weight, Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, double x2, double x3, double x4,
                      Num2& weight, Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, double x2, double x3, double x4,
                      double x5, Num2& weight, Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, double x2, double x3, double x4,
                      double x5, double x6, Num2& weight, Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, double x2, double x3, double x4,
                      double x5, double x6, double x7, Num2& weight,
                      Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, double x2, double x3, double x4,
                      double x5, double x6, double x7, double x8,
                      Num2& weight, Functor& f);

        template <typename Num2, class Functor>
        void dispatch(double x0, double x1, double x2, double x3, double x4,
                      double x5, double x6, double x7, double x8, double x9,
                      Num2& weight, Functor& f);

        const Numeric& examine(const double* coords,
                               unsigned coordLength) const;


        const Numeric& examine() const;

        const Numeric& examine(double x0) const;

        const Numeric& examine(double x0, double x1) const;

        const Numeric& examine(double x0, double x1, double x2) const;

        const Numeric& examine(double x0, double x1, double x2,
                               double x3) const;

        const Numeric& examine(double x0, double x1, double x2, double x3,
                               double x4) const;

        const Numeric& examine(double x0, double x1, double x2, double x3,
                               double x4, double x5) const;

        const Numeric& examine(double x0, double x1, double x2, double x3,
                               double x4, double x5, double x6) const;

        const Numeric& examine(double x0, double x1, double x2, double x3,
                               double x4, double x5, double x6,
                               double x7) const;

        const Numeric& examine(double x0, double x1, double x2, double x3,
                               double x4, double x5, double x6, double x7,
                               double x8) const;

        const Numeric& examine(double x0, double x1, double x2, double x3,
                               double x4, double x5, double x6, double x7,
                               double x8, double x9) const;

        const Numeric& closestBin(const double* coords,
                                  unsigned coordLength) const;


        const Numeric& closestBin() const;

        const Numeric& closestBin(double x0) const;

        const Numeric& closestBin(double x0, double x1) const;

        const Numeric& closestBin(double x0, double x1, double x2) const;

        const Numeric& closestBin(double x0, double x1, double x2,
                                  double x3) const;

        const Numeric& closestBin(double x0, double x1, double x2, double x3,
                                  double x4) const;

        const Numeric& closestBin(double x0, double x1, double x2, double x3,
                                  double x4, double x5) const;

        const Numeric& closestBin(double x0, double x1, double x2, double x3,
                                  double x4, double x5, double x6) const;

        const Numeric& closestBin(double x0, double x1, double x2, double x3,
                                  double x4, double x5, double x6,
                                  double x7) const;

        const Numeric& closestBin(double x0, double x1, double x2, double x3,
                                  double x4, double x5, double x6, double x7,
                                  double x8) const;

        const Numeric& closestBin(double x0, double x1, double x2, double x3,
                                  double x4, double x5, double x6, double x7,
                                  double x8, double x9) const;

        template <typename Num2>
        void fillC(const double* coords, unsigned coordLength,
                   const Num2& weight);


        template <typename Num2>
        void fillC(const Num2& weight);

        template <typename Num2>
        void fillC(double x0, const Num2& weight);
        
        template <typename Num2>
        void fillC(double x0, double x1, const Num2& weight);
        
        template <typename Num2>
        void fillC(double x0, double x1, double x2, const Num2& weight);
        
        template <typename Num2>
        void fillC(double x0, double x1, double x2, double x3,
                   const Num2& weight);
        
        template <typename Num2>
        void fillC(double x0, double x1, double x2, double x3, double x4,
                   const Num2& weight);
        
        template <typename Num2>
        void fillC(double x0, double x1, double x2, double x3, double x4,
                   double x5, const Num2& weight);
        
        template <typename Num2>
        void fillC(double x0, double x1, double x2, double x3, double x4,
                   double x5, double x6, const Num2& weight);
        
        template <typename Num2>
        void fillC(double x0, double x1, double x2, double x3, double x4,
                   double x5, double x6, double x7, const Num2& weight);

        template <typename Num2>
        void fillC(double x0, double x1, double x2, double x3, double x4,
                   double x5, double x6, double x7, double x8,
                   const Num2& weight);
        
        template <typename Num2>
        void fillC(double x0, double x1, double x2, double x3, double x4,
                   double x5, double x6, double x7, double x8, double x9,
                   const Num2& weight);

        template <typename Num2>
        HistoND& operator+=(const HistoND<Num2,Axis>& r);

        template <typename Num2>
        HistoND& operator-=(const HistoND<Num2,Axis>& r);


        template <typename Num2>
        void setBin(const unsigned *index, unsigned indexLen, const Num2& v);

        template <typename Num2>
        void setBin(const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, unsigned i2, const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                    const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                    unsigned i4, const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                    unsigned i4, unsigned i5, const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                    unsigned i4, unsigned i5, unsigned i6, const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                    unsigned i4, unsigned i5, unsigned i6, unsigned i7,
                    const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                    unsigned i4, unsigned i5, unsigned i6, unsigned i7,
                    unsigned i8, const Num2& v);

        template <typename Num2>
        void setBin(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                    unsigned i4, unsigned i5, unsigned i6, unsigned i7,
                    unsigned i8, unsigned i9, const Num2& v);

        template <typename Num2>
        inline void setLinearBin(const unsigned long index, const Num2& v)
            {data_.linearValue(index) = v; ++modCount_;}


        template <typename Num2>
        void setBinAt(const unsigned *index, unsigned indexLen, const Num2& v);

        template <typename Num2>
        void setBinAt(const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, unsigned i2, const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                      const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                      unsigned i4, const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                      unsigned i4, unsigned i5, const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                      unsigned i4, unsigned i5, unsigned i6, const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                      unsigned i4, unsigned i5, unsigned i6, unsigned i7,
                      const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                      unsigned i4, unsigned i5, unsigned i6, unsigned i7,
                      unsigned i8, const Num2& v);

        template <typename Num2>
        void setBinAt(unsigned i0, unsigned i1, unsigned i2, unsigned i3,
                      unsigned i4, unsigned i5, unsigned i6, unsigned i7,
                      unsigned i8, unsigned i9, const Num2& v);

        template <typename Num2>
        inline void setLinearBinAt(const unsigned long index, const Num2& v)
            {data_.linearValueAt(index) = v; ++modCount_;}

        template <typename Num2>
        void setBinContents(const Num2* data, unsigned long dataLength,
                            bool clearOverflows=true);

        template <typename Num2>
        void setOverflows(const Num2* data, unsigned long dataLength);

        template <typename Num2>
        inline void setBinsToConst(const Num2& value)
            {data_.constFill(value); ++modCount_;}

        template <typename Num2>
        inline void setOverflowsToConst(const Num2& value)
            {overflow_.constFill(value); ++modCount_;}

        void recalculateNFillsFromData();


        inline void setNFillsTotal(const unsigned long i)
            {fillCount_ = i; ++modCount_;}
        inline void setNFillsOver(const unsigned long i)
            {overCount_ = i; ++modCount_;}

        template <typename Num2>
        HistoND& operator*=(const Num2& r);

        template <typename Num2>
        HistoND& operator/=(const Num2& r);


        template <typename Num2>
        void scaleBinContents(const Num2* data, unsigned long dataLength);

        template <typename Num2>
        void scaleOverflows(const Num2* data, unsigned long dataLength);


        template <typename Num2>
        void addToBinContents(const Num2& weight);

        template <typename Num2>
        void addToOverflows(const Num2& weight);


        template <typename Num2>
        void addToBinContents(const Num2* data, unsigned long dataLength);

        template <typename Num2>
        void addToOverflows(const Num2* data, unsigned long dataLength);

        template <typename Acc>
        void accumulateBinsInBox(const BoxND<double>& box, Acc* acc) const;


        template <typename Num2, typename Num3>
        void addToProjection(HistoND<Num2,Axis>* projection,
                             AbsArrayProjector<Numeric,Num3>& projector,
                             const unsigned *projectedIndices,
                             unsigned nProjectedIndices) const;

        template <typename Num2, typename Num3>
        void addToProjection(HistoND<Num2,Axis>* projection,
                             AbsVisitor<Numeric,Num3>& projector,
                             const unsigned *projectedIndices,
                             unsigned nProjectedIndices) const;

        HistoND transpose(unsigned axisNum1, unsigned axisNum2) const;

        inline unsigned long getModCount() const {return modCount_;}

        inline void incrModCount() {++modCount_;}


        inline gs::ClassId classId() const {return gs::ClassId(*this);}
        bool write(std::ostream& of) const;

        static const char* classname();
        static inline unsigned version() {return 1;}
        static HistoND* read(const gs::ClassId& id, std::istream& in);

    private:
        HistoND();

        // Special constructor which speeds up the "transpose" operation.
        // Does not do full error checking (some of it is done in transpose).
        HistoND(const HistoND& r, unsigned ax1, unsigned ax2);

        template <typename Num2>
        void fillPreservingCentroid(const Num2& weight);

        template <typename Acc>
        void accumulateBinsLoop(unsigned level, const BoxND<double>& box,
                                unsigned* idx, Acc* accumulator,
                                double overlapFraction) const;
        std::string title_;
        std::string accumulatedDataLabel_;
        ArrayND<Numeric> data_;
        ArrayND<Numeric> overflow_;
        std::vector<Axis> axes_;
        mutable std::vector<double> weightBuf_;
        mutable std::vector<unsigned> indexBuf_;
        unsigned long fillCount_;
        unsigned long overCount_;
        unsigned long modCount_;
        unsigned dim_;

    };

    template <typename Histo>
    void convertHistoToDensity(Histo* histogram, bool knownNonNegative=false);

    template <typename Histo>
    std::vector<LinearMapper1d> densityScanHistoMap(const Histo& histo);

    template <typename Histo>
    std::vector<CircularMapper1d> convolutionHistoMap(const Histo& histo,
                                                      bool doubleDataRange);
}

#include <cassert>
#include "JetMETCorrections/InterpolationTables/interface/NpstatException.h"
#include <sstream>
#include <climits>
#include <algorithm>

#include "Alignment/Geners/interface/CPP11_auto_ptr.hh"
#include "Alignment/Geners/interface/binaryIO.hh"

namespace npstat {
    namespace Private {
        template <class Axis>
        ArrayShape makeHistoShape(const std::vector<Axis>& axes)
        {
            const unsigned n = axes.size();
            ArrayShape result;
            result.reserve(n);
            for (unsigned i=0; i<n; ++i)
                result.push_back(axes[i].nBins());
            return result;
        }

        template <class Axis>
        ArrayShape makeHistoShape(const Axis& xAxis)
        {
            ArrayShape result;
            result.reserve(1U);
            result.push_back(xAxis.nBins());
            return result;
        }

        template <class Axis>
        ArrayShape makeHistoShape(const Axis& xAxis, const Axis& yAxis)
        {
            ArrayShape result;
            result.reserve(2U);
            result.push_back(xAxis.nBins());
            result.push_back(yAxis.nBins());
            return result;
        }

        template <class Axis>
        ArrayShape makeHistoShape(const Axis& xAxis,
                                  const Axis& yAxis,
                                  const Axis& zAxis)
        {
            ArrayShape result;
            result.reserve(3U);
            result.push_back(xAxis.nBins());
            result.push_back(yAxis.nBins());
            result.push_back(zAxis.nBins());
            return result;
        }

        template <class Axis>
        ArrayShape makeHistoShape(const Axis& xAxis, const Axis& yAxis,
                                  const Axis& zAxis, const Axis& tAxis)
        {
            ArrayShape result;
            result.reserve(4U);
            result.push_back(xAxis.nBins());
            result.push_back(yAxis.nBins());
            result.push_back(zAxis.nBins());
            result.push_back(tAxis.nBins());
            return result;
        }

        template <class Axis>
        ArrayShape makeHistoShape(const Axis& xAxis, const Axis& yAxis,
                                  const Axis& zAxis, const Axis& tAxis,
                                  const Axis& vAxis)
        {
            ArrayShape result;
            result.reserve(5U);
            result.push_back(xAxis.nBins());
            result.push_back(yAxis.nBins());
            result.push_back(zAxis.nBins());
            result.push_back(tAxis.nBins());
            result.push_back(vAxis.nBins());
            return result;
        }

        template <class Axis>
        std::vector<Axis> axesOfASlice(const std::vector<Axis>& axes,
                                       const unsigned *fixedIndices,
                                       const unsigned nFixedIndices)
        {
            const unsigned dim = axes.size();
            std::vector<Axis> newAxes;
            if (nFixedIndices == 0U) throw npstat::NpstatInvalidArgument(
                "In npstat::Private::axesOfASlice: "
                "at least one fixed index must be specified");
            if (nFixedIndices > dim) throw npstat::NpstatInvalidArgument(
                "In npstat::Private::axesOfASlice: too many fixed indices");
            assert(fixedIndices);
            for (unsigned i=0; i<nFixedIndices; ++i)
               if (fixedIndices[i] >= dim) throw npstat::NpstatInvalidArgument(
                  "In npstat::Private::axesOfASlice: fixed index out of range");
            newAxes.reserve(dim - nFixedIndices);
            for (unsigned i=0; i<dim; ++i)
            {
                bool fixed = false;
                for (unsigned j=0; j<nFixedIndices; ++j)
                    if (fixedIndices[j] == i)
                    {
                        fixed = true;
                        break;
                    }
                if (!fixed)
                    newAxes.push_back(axes[i]);
            }
            if (newAxes.size() != dim - nFixedIndices)
                throw npstat::NpstatInvalidArgument(
                    "In npstat::Private::axesOfASlice: duplicate fixed index");
            return newAxes;
        }

        template <class Axis>
        ArrayShape shapeOfASlice(const std::vector<Axis>& axes,
                                 const unsigned *fixedIndices,
                                 const unsigned nFixedIndices)
        {
            const unsigned dim = axes.size();
            if (nFixedIndices == 0U) throw npstat::NpstatInvalidArgument(
                "In npstat::Private::shapeOfASlice: "
                "at least one fixed index must be specified");
            if (nFixedIndices > dim) throw npstat::NpstatInvalidArgument(
                "In npstat::Private::shapeOfASlice: too many fixed indices");
            assert(fixedIndices);

            // Check that the fixed indices are within range
            for (unsigned j=0; j<nFixedIndices; ++j)
              if (fixedIndices[j] >= dim) throw npstat::NpstatInvalidArgument(
                "In npstat::Private::shapeOfASlice: fixed index out of range");

            // Build the shape for the slice
            ArrayShape sh;
            if (nFixedIndices < dim)
                sh.reserve(dim - nFixedIndices);
            for (unsigned i=0; i<dim; ++i)
            {
                bool fixed = false;
                for (unsigned j=0; j<nFixedIndices; ++j)
                    if (fixedIndices[j] == i)
                    {
                        fixed = true;
                        break;
                    }
                if (!fixed)
                    sh.push_back(axes[i].nBins());
            }
            if (sh.size() != dim - nFixedIndices)
                throw npstat::NpstatInvalidArgument(
                    "In npstat::Private::shapeOfASlice: duplicate fixed index");
            return sh;
        }

        template <class Axis>
        std::vector<Axis> addAxis(const std::vector<Axis>& axes,
                                  const Axis& newAxis,
                                  const unsigned newAxisNumber)
        {
            const unsigned dim = axes.size();
            std::vector<Axis> newAxes;
            newAxes.reserve(dim + 1U);
            unsigned iadd = 0;
            for (unsigned i=0; i<dim; ++i)
            {
                if (newAxisNumber == i)
                    newAxes.push_back(newAxis);
                else
                    newAxes.push_back(axes[iadd++]);
            }
            if (iadd == dim)
                newAxes.push_back(newAxis);
            else
                newAxes.push_back(axes[iadd]);
            return newAxes;
        }

        template <class Axis>
        ArrayShape shapeWithExtraAxis(const std::vector<Axis>& axes,
                                      const Axis& newAxis,
                                      const unsigned newAxisNumber)
        {
            const unsigned dim = axes.size();
            ArrayShape result;
            result.reserve(dim + 1U);
            unsigned iadd = 0;
            for (unsigned i=0; i<dim; ++i)
            {
                if (newAxisNumber == i)
                    result.push_back(newAxis.nBins());
                else
                    result.push_back(axes[iadd++].nBins());
            }
            if (iadd == dim)
                result.push_back(newAxis.nBins());
            else
                result.push_back(axes[iadd].nBins());
            return result;
        }

        inline void h_badargs(const char* method)
        {
            std::ostringstream os;
            os << "In npstat::HistoND::" << method << ": number of arguments"
               << " is incompatible with histogram dimensionality";
            throw npstat::NpstatInvalidArgument(os.str());
        }
    }

    template <typename Numeric, class Axis>
    template <typename Acc>
    void HistoND<Numeric,Axis>::accumulateBinsLoop(
        const unsigned level, const BoxND<double>& box,
        unsigned* idx, Acc* accumulator, const double overlapFraction) const
    {
        const Interval<double>& boxSide(box[level]);
        const Axis& axis(axes_[level]);
        const unsigned nbins = axis.nBins();
        const bool lastLevel = level == dim_ - 1U;
        for (unsigned i=0; i<nbins; ++i)
        {
            const double over = overlapFraction*
                axis.binInterval(i).overlapFraction(boxSide);
            if (over > 0.0)
            {
                idx[level] = i;
                if (lastLevel)
                    *accumulator += over*data_.value(idx, dim_);
                else
                    accumulateBinsLoop(level+1U, box, idx, accumulator, over);
            }
        }
    }

    template <typename Numeric, class Axis>
    template <typename Acc>
    void HistoND<Numeric,Axis>::accumulateBinsInBox(
        const BoxND<double>& box, Acc* accumulator) const
    {
        if (box.size() != dim_) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::accumulateBinsInBox: "
            "incompatible box dimensionality");
        assert(accumulator);
        if (dim_)
        {
            for (unsigned i=0; i<dim_; ++i)
                indexBuf_[i] = 0U;
            accumulateBinsLoop(0U, box, &indexBuf_[0], accumulator, 1.0);
        }
        else
            *accumulator += 1.0*data_();
    }

    template <typename Numeric, class Axis>
    inline void HistoND<Numeric,Axis>::clearBinContents()
    {
        data_.clear();
        fillCount_ = 0UL;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    inline void HistoND<Numeric,Axis>::clearOverflows()
    {
        overflow_.clear();
        overCount_ = 0UL;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    inline void HistoND<Numeric,Axis>::clear()
    {
        clearBinContents();
        clearOverflows();
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const std::vector<Axis>& axesIn,
                                   const char* title, const char* label)
        : title_(title ? title : ""),
          accumulatedDataLabel_(label ? label : ""),
          data_(Private::makeHistoShape(axesIn)),
          overflow_(ArrayShape(axesIn.size(), 3U)),
          axes_(axesIn),
          weightBuf_(axesIn.size()),
          indexBuf_(2U*axesIn.size()),
          modCount_(0UL),
          dim_(axesIn.size())
    {
        if (dim_ >= CHAR_BIT*sizeof(unsigned long))
            throw npstat::NpstatInvalidArgument(
                "In npstat::HistoND constructor: requested histogram "
                "dimensionality is not supported (too large)");
        clear();
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const Axis& xAxis,
                                   const char* title, const char* label)
        : title_(title ? title : ""),
          accumulatedDataLabel_(label ? label : ""),
          data_(Private::makeHistoShape(xAxis)),
          overflow_(ArrayShape(1U, 3U)),
          weightBuf_(1U),
          indexBuf_(2U*1U),
          modCount_(0UL),
          dim_(1U)
    {
        axes_.reserve(dim_);
        axes_.push_back(xAxis);
        clear();
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const Axis& xAxis, const Axis& yAxis,
                                   const char* title, const char* label)
        : title_(title ? title : ""),
          accumulatedDataLabel_(label ? label : ""),
          data_(Private::makeHistoShape(xAxis, yAxis)),
          overflow_(ArrayShape(2U, 3U)),
          weightBuf_(2U),
          indexBuf_(2U*2U),
          modCount_(0UL),
          dim_(2U)
    {
        axes_.reserve(dim_);
        axes_.push_back(xAxis);
        axes_.push_back(yAxis);
        clear();
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const Axis& xAxis, const Axis& yAxis,
                                   const Axis& zAxis, const char* title,
                                   const char* label)
        : title_(title ? title : ""),
          accumulatedDataLabel_(label ? label : ""),
          data_(Private::makeHistoShape(xAxis, yAxis, zAxis)),
          overflow_(ArrayShape(3U, 3U)),
          weightBuf_(3U),
          indexBuf_(2U*3U),
          modCount_(0UL),
          dim_(3U)
    {
        axes_.reserve(dim_);
        axes_.push_back(xAxis);
        axes_.push_back(yAxis);
        axes_.push_back(zAxis);
        clear();
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const Axis& xAxis, const Axis& yAxis,
                                   const Axis& zAxis, const Axis& tAxis,
                                   const char* title, const char* label)
        : title_(title ? title : ""),
          accumulatedDataLabel_(label ? label : ""),
          data_(Private::makeHistoShape(xAxis, yAxis, zAxis, tAxis)),
          overflow_(ArrayShape(4U, 3U)),
          weightBuf_(4U),
          indexBuf_(2U*4U),
          modCount_(0UL),
          dim_(4U)
    {
        axes_.reserve(dim_);
        axes_.push_back(xAxis);
        axes_.push_back(yAxis);
        axes_.push_back(zAxis);
        axes_.push_back(tAxis);
        clear();
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const Axis& xAxis, const Axis& yAxis,
                                   const Axis& zAxis, const Axis& tAxis,
                                   const Axis& vAxis,
                                   const char* title, const char* label)
        : title_(title ? title : ""),
          accumulatedDataLabel_(label ? label : ""),
          data_(Private::makeHistoShape(xAxis, yAxis, zAxis, tAxis, vAxis)),
          overflow_(ArrayShape(5U, 3U)),
          weightBuf_(5U),
          indexBuf_(2U*5U),
          modCount_(0UL),
          dim_(5U)
    {
        axes_.reserve(dim_);
        axes_.push_back(xAxis);
        axes_.push_back(yAxis);
        axes_.push_back(zAxis);
        axes_.push_back(tAxis);
        axes_.push_back(vAxis);
        clear();
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const ArrayShape& shape,
                                   const BoxND<double>& boundingBox,
                                   const char* title, const char* label)
        : title_(title ? title : ""),
          accumulatedDataLabel_(label ? label : ""),
          data_(shape),
          overflow_(ArrayShape(shape.size(), 3U)),
          weightBuf_(shape.size()),
          indexBuf_(2U*shape.size()),
          modCount_(0UL),
          dim_(shape.size())
    {
        if (boundingBox.size() != dim_) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND constructor: "
            "incompatible bounding box dimensionality");
        if (dim_ >= CHAR_BIT*sizeof(unsigned long))
            throw npstat::NpstatInvalidArgument(
                "In npstat::HistoND constructor: requested histogram "
                "dimensionality is not supported (too large)");
        axes_.reserve(dim_);
        for (unsigned i=0; i<dim_; ++i)
            axes_.push_back(Axis(shape[i],
                                 boundingBox[i].min(),
                                 boundingBox[i].max()));
        clear();
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    HistoND<Numeric,Axis>::HistoND(
        const HistoND<Num2,Axis>& r, const Functor& f,
        const char* title, const char* label)
        : title_(title ? title : ""),
          accumulatedDataLabel_(label ? label : ""),
          data_(r.data_, f),
          overflow_(r.overflow_, f),
          axes_(r.axes_),
          weightBuf_(r.dim_),
          indexBuf_(2U*r.dim_),
          fillCount_(r.fillCount_),
          overCount_(r.overCount_),
          modCount_(0UL),
          dim_(r.dim_)
    {
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    HistoND<Numeric,Axis>::HistoND(
        const HistoND<Num2,Axis>& h, const unsigned *indices,
        const unsigned nIndices, const char* title)
        : title_(title ? title : ""),
          accumulatedDataLabel_(h.accumulatedDataLabel_),
          data_(Private::shapeOfASlice(h.axes_, indices, nIndices)),
          overflow_(ArrayShape(data_.rank(), 3U)),
          axes_(Private::axesOfASlice(h.axes_, indices, nIndices)),
          weightBuf_(data_.rank()),
          indexBuf_(2U*data_.rank()),
          modCount_(0UL),
          dim_(data_.rank())
    {
        clear();
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    HistoND<Numeric,Axis>::HistoND(
        const HistoND<Num2,Axis>& h, const Axis& newAxis,
        const unsigned newAxisNumber, const char* title)
        : title_(title ? title : ""),
          accumulatedDataLabel_(h.accumulatedDataLabel_),
          data_(Private::shapeWithExtraAxis(h.axes_, newAxis, newAxisNumber)),
          overflow_(data_.rank(), 3U),
          axes_(Private::addAxis(h.axes_, newAxis, newAxisNumber)),
          weightBuf_(data_.rank()),
          indexBuf_(2U*data_.rank()),
          modCount_(0UL),
          dim_(data_.rank())
    {
        if (dim_ >= CHAR_BIT*sizeof(unsigned long))
            throw npstat::NpstatInvalidArgument(
                "In npstat::HistoND constructor: requested histogram "
                "dimensionality is not supported (too large)");
        clear();
    }

    template <typename Numeric, class Axis>
    bool HistoND<Numeric,Axis>::isUniformlyBinned() const
    {
        for (unsigned i=0; i<dim_; ++i)
            if (!axes_[i].isUniform())
                return false;
        return true;
    }

    template <typename Numeric, class Axis>
    double HistoND<Numeric,Axis>::integral() const
    {
        typedef typename PreciseType<Numeric>::type Precise;

        if (dim_ == 0U)
            return 0.0;
        if (isUniformlyBinned())
        {
            Precise sum = data_.template sum<Precise>();
            return static_cast<double>(sum)*binVolume();
        }
        else
        {
            Precise sum = Precise();
            const Numeric* data = data_.data();
            const unsigned long len = data_.length();
            for (unsigned long i=0; i<len; ++i)
                sum += data[i]*binVolume(i);
            return static_cast<double>(sum);
        }
    }

    template <typename Numeric, class Axis>
    BoxND<double> HistoND<Numeric,Axis>::boundingBox() const
    {
        BoxND<double> box;
        if (dim_)
        {
            box.reserve(dim_);
            const Axis* ax = &axes_[0];
            for (unsigned i=0; i<dim_; ++i)
                box.push_back(ax[i].interval());
        }
        return box;
    }

    template <typename Numeric, class Axis>
    void HistoND<Numeric,Axis>::binCenter(
        const unsigned long binNumber,
        double* coords, const unsigned lenCoords) const
    {
        if (dim_ != lenCoords) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::binCenter: "
            "incompatible input point dimensionality");
        if (dim_)
        {
            assert(coords);
            data_.convertLinearIndex(binNumber, &indexBuf_[0], dim_);
            const Axis* ax = &axes_[0];
            for (unsigned i=0; i<dim_; ++i)
                coords[i] = ax[i].binCenter(indexBuf_[i]);
        }
    }

    template <typename Numeric, class Axis>
    template <class Point>
    void HistoND<Numeric,Axis>::allBinCenters(
        std::vector<Point>* centers) const
    {
        assert(centers);
        centers->clear();
        const unsigned long len = data_.length();
        centers->reserve(len);
        unsigned* ibuf = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        Point center;
        if (center.size() < dim_) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::allBinCenters: "
            "incompatible point dimensionality (too small)");
        typename Point::value_type* cdat = &center[0];

        for (unsigned long i=0; i<len; ++i)
        {
            data_.convertLinearIndex(i, ibuf, dim_);
            for (unsigned idim=0; idim<dim_; ++idim)
                cdat[idim] = ax[idim].binCenter(ibuf[idim]);
            centers->push_back(center);
        }
    }

    template <typename Numeric, class Axis>
    void HistoND<Numeric,Axis>::binBox(const unsigned long binNumber,
                                       BoxND<double>* box) const
    {
        assert(box);
        box->clear();
        if (dim_)
        {
            box->reserve(dim_);
            data_.convertLinearIndex(binNumber, &indexBuf_[0], dim_);
            const Axis* ax = &axes_[0];
            for (unsigned i=0; i<dim_; ++i)
                box->push_back(ax[i].binInterval(indexBuf_[i]));
        }
    }

    template <typename Numeric, class Axis>
    inline bool HistoND<Numeric,Axis>::isSameData(const HistoND& r) const
    {
        return dim_ == r.dim_ &&
               overflow_ == r.overflow_ &&
               data_ == r.data_;
    }

    template <typename Numeric, class Axis>
    inline bool HistoND<Numeric,Axis>::operator==(const HistoND& r) const
    {
        return dim_ == r.dim_ &&
               fillCount_ == r.fillCount_ &&
               overCount_ == r.overCount_ &&
               title_ == r.title_ &&
               accumulatedDataLabel_ == r.accumulatedDataLabel_ &&
               axes_ == r.axes_ &&
               overflow_ == r.overflow_ &&
               data_ == r.data_;
    }

    template <typename Numeric, class Axis>
    inline bool HistoND<Numeric,Axis>::operator!=(const HistoND& r) const
    {
        return !(*this == r);
    }

    template <typename Numeric, class Axis>
    double HistoND<Numeric,Axis>::binVolume(
        const unsigned long binNumber) const
    {
        double v = 1.0;
        if (dim_)
        {
            data_.convertLinearIndex(binNumber, &indexBuf_[0], dim_);
            const Axis* ax = &axes_[0];
            for (unsigned i=0; i<dim_; ++i)
                v *= ax[i].binWidth(indexBuf_[i]);
        }
        return v;
    }

    template <typename Numeric, class Axis>
    double HistoND<Numeric,Axis>::volume() const
    {
        double v = 1.0;
        if (dim_)
        {
            const Axis* ax = &axes_[0];
            for (unsigned i=0; i<dim_; ++i)
                v *= (ax[i].max() - ax[i].min());
        }
        return v;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(
        const double* coords, const unsigned coordLength, const Num2& w)
    {
        if (coordLength != dim_) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::fill: "
            "incompatible input point dimensionality");
        if (coordLength)
        {
            assert(coords);
            unsigned* idx = &indexBuf_[0];
            unsigned* over = idx + dim_;
            const Axis* ax = &axes_[0];
            unsigned overflown = 0U;
            for (unsigned i=0; i<dim_; ++i)
            {
                over[i] = ax[i].overflowIndex(coords[i], idx + i);
                overflown |= (over[i] - 1U);
            }
            if (overflown)
            {
                overflow_.value(over, dim_) += w;
                ++overCount_;
            }
            else
                data_.value(idx, dim_) += w;
        }
        else
            data_() += w;
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(
        const double* coords, const unsigned coordLength, Num2& w, Functor& f)
    {
        if (coordLength != dim_) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::dispatch: "
            "incompatible input point dimensionality");
        if (coordLength)
        {
            assert(coords);
            unsigned* idx = &indexBuf_[0];
            unsigned* over = idx + dim_;
            const Axis* ax = &axes_[0];
            unsigned overflown = 0U;
            for (unsigned i=0; i<dim_; ++i)
            {
                over[i] = ax[i].overflowIndex(coords[i], idx + i);
                overflown |= (over[i] - 1U);
            }
            if (overflown)
                f(overflow_.value(over, dim_), w);
            else
                f(data_.value(idx, dim_), w);
        }
        else
            f(data_(), w);
         ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(
        const double* coords, const unsigned coordLength) const
    {
        if (coordLength != dim_) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::examine: "
            "incompatible input point dimensionality");
        if (coordLength)
        {
            assert(coords);
            unsigned* idx = &indexBuf_[0];
            unsigned* over = idx + dim_;
            const Axis* ax = &axes_[0];
            unsigned overflown = 0U;
            for (unsigned i=0; i<dim_; ++i)
            {
                over[i] = ax[i].overflowIndex(coords[i], idx + i);
                overflown |= (over[i] - 1U);
            }
            if (overflown)
                return overflow_.value(over, dim_);
            else
                return data_.value(idx, dim_);
        }
        else
            return data_();
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(
        const double* coords, const unsigned coordLength) const
    {
        if (coordLength != dim_) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::closestBin: "
            "incompatible input point dimensionality");
        if (coordLength)
        {
            assert(coords);
            unsigned* idx = &indexBuf_[0];
            const Axis* ax = &axes_[0];
            for (unsigned i=0; i<dim_; ++i)
                idx[i] = ax[i].closestValidBin(coords[i]);
            return data_.value(idx, dim_);
        }
        else
            return data_();
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillPreservingCentroid(const Num2& value)
    {
        const double* weights = &weightBuf_[0];
        const unsigned* cell = &indexBuf_[0];
        const unsigned long* strides = data_.strides();
        const unsigned long maxcycle = 1UL << dim_;
        for (unsigned long icycle=0; icycle<maxcycle; ++icycle)
        {
            double w = 1.0;
            unsigned long icell = 0UL;
            for (unsigned i=0; i<dim_; ++i)
            {
                if (icycle & (1UL << i))
                {
                    w *= (1.0 - weights[i]);
                    icell += strides[i]*(cell[i] + 1U);
                }
                else
                {
                    w *= weights[i];
                    icell += strides[i]*cell[i];
                }
            }
            data_.linearValue(icell) += (value * w);
        }
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(
        const double* coords, const unsigned coordLength, const Num2& w)
    {
        if (coordLength != dim_) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::fillC: "
            "incompatible input point dimensionality");
        if (coordLength)
        {
            assert(coords);
            double* wg = &weightBuf_[0];
            unsigned* idx = &indexBuf_[0];
            unsigned* over = idx + dim_;
            const Axis* ax = &axes_[0];
            unsigned overflown = 0U;
            for (unsigned i=0; i<dim_; ++i)
            {
                over[i] = ax[i].overflowIndexWeighted(coords[i], idx+i, wg+i);
                overflown |= (over[i] - 1U);
            }
            if (overflown)
            {
                overflow_.value(over, dim_) += w;
                ++overCount_;
            }
            else
                fillPreservingCentroid(w);
        }
        else
            data_() += w;
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::fill(const Num2& w)
    {
        if (dim_) Private::h_badargs("fill");
        data_() += w;
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    inline void HistoND<Numeric,Axis>::dispatch(Num2& w, Functor& f)
    {
        if (dim_) Private::h_badargs("dispatch");
        f(data_(), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::fillC(const Num2& w)
    {
        if (dim_) Private::h_badargs("fillC");
        data_() += w;
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    inline const Numeric& HistoND<Numeric,Axis>::examine() const
    {
        if (dim_) Private::h_badargs("examine");
        return data_();
    }

    template <typename Numeric, class Axis>
    inline const Numeric& HistoND<Numeric,Axis>::closestBin() const
    {
        if (dim_) Private::h_badargs("closestBin");
        return data_();
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const Num2& w)
    {
        if (dim_ != 1U) Private::h_badargs("fill");
        unsigned i0;
        const unsigned ov0 = axes_[0].overflowIndex(x0, &i0);
        if (ov0 == 1U)
            data_(i0) += w;
        else
        {
            overflow_(ov0) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, Num2& w, Functor& f)
    {
        if (dim_ != 1U) Private::h_badargs("dispatch");
        unsigned i0;
        const unsigned ov0 = axes_[0].overflowIndex(x0, &i0);
        if (ov0 == 1U)
            f(data_(i0), w);
        else
            f(overflow_(ov0), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const Num2& w)
    {
        if (dim_ != 1U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const unsigned ov0 = axes_[0].overflowIndexWeighted(x0, idx, wg);
        if (ov0 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(ov0) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    inline const Numeric& HistoND<Numeric,Axis>::examine(const double x0) const
    {
        if (dim_ != 1U) Private::h_badargs("examine");
        unsigned i0;
        const unsigned ov0 = axes_[0].overflowIndex(x0, &i0);
        if (ov0 == 1U)
            return data_(i0);
        else
            return overflow_(ov0);
    }

    template <typename Numeric, class Axis>
    inline const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0) const
    {
        if (dim_ != 1U) Private::h_badargs("closestBin");
        const unsigned i0 = axes_[0].closestValidBin(x0);
        return data_(i0);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const Num2& w)
    {
        if (dim_ != 2U) Private::h_badargs("fill");
        unsigned i0, i1;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        if (o0 == 1U && o1 == 1U)
            data_(i0, i1) += w;
        else
        {
            overflow_(o0, o1) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         Num2& w, Functor& f)
    {
        if (dim_ != 2U) Private::h_badargs("dispatch");
        unsigned i0, i1;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        if (o0 == 1U && o1 == 1U)
            f(data_(i0, i1), w);
        else
            f(overflow_(o0, o1), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                      const Num2& w)
    {
        if (dim_ != 2U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        if (o0 == 1U && o1 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(const double x0,
                                                  const double x1) const
    {
        if (dim_ != 2U) Private::h_badargs("examine");
        unsigned i0, i1;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        if (o0 == 1U && o1 == 1U)
            return data_(i0, i1);
        else
            return overflow_(o0, o1);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1) const
    {
        if (dim_ != 2U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        return data_(i0, i1);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const double x2, const Num2& w)
    {
        if (dim_ != 3U) Private::h_badargs("fill");
        unsigned i0, i1, i2;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        if (o0 == 1U && o1 == 1U && o2 == 1U)
            data_(i0, i1, i2) += w;
        else
        {
            overflow_(o0, o1, o2) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         const double x2, Num2& w, Functor& f)
    {
        if (dim_ != 3U) Private::h_badargs("dispatch");
        unsigned i0, i1, i2;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        if (o0 == 1U && o1 == 1U && o2 == 1U)
            f(data_(i0, i1, i2), w);
        else
            f(overflow_(o0, o1, o2), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                 const double x2, const Num2& w)
    {
        if (dim_ != 3U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        const unsigned o2 = ax[2].overflowIndexWeighted(x2, idx+2, wg+2);
        if (o0 == 1U && o1 == 1U && o2 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1, o2) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(const double x0,
                                                  const double x1,
                                                  const double x2) const
    {
        if (dim_ != 3U) Private::h_badargs("examine");
        unsigned i0, i1, i2;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        if (o0 == 1U && o1 == 1U && o2 == 1U)
            return data_(i0, i1, i2);
        else
            return overflow_(o0, o1, o2);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1,
                                                     const double x2) const
    {
        if (dim_ != 3U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        const unsigned i2 = ax[2].closestValidBin(x2);
        return data_(i0, i1, i2);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const double x2, const double x3,
                                     const Num2& w)
    {
        if (dim_ != 4U) Private::h_badargs("fill");
        unsigned i0, i1, i2, i3;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U)
            data_(i0, i1, i2, i3) += w;
        else
        {
            overflow_(o0, o1, o2, o3) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         const double x2, const double x3,
                                         Num2& w, Functor& f)
    {
        if (dim_ != 4U) Private::h_badargs("dispatch");
        unsigned i0, i1, i2, i3;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U)
            f(data_(i0, i1, i2, i3), w);
        else
            f(overflow_(o0, o1, o2, o3), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                      const double x2, const double x3,
                                      const Num2& w)
    {
        if (dim_ != 4U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        const unsigned o2 = ax[2].overflowIndexWeighted(x2, idx+2, wg+2);
        const unsigned o3 = ax[3].overflowIndexWeighted(x3, idx+3, wg+3);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1, o2, o3) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(const double x0,
                                                  const double x1,
                                                  const double x2,
                                                  const double x3) const
    {
        if (dim_ != 4U) Private::h_badargs("examine");
        unsigned i0, i1, i2, i3;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U)
            return data_(i0, i1, i2, i3);
        else
            return overflow_(o0, o1, o2, o3);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1,
                                                     const double x2,
                                                     const double x3) const
    {
        if (dim_ != 4U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        const unsigned i2 = ax[2].closestValidBin(x2);
        const unsigned i3 = ax[3].closestValidBin(x3);
        return data_(i0, i1, i2, i3);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const double x2, const double x3,
                                     const double x4, const Num2& w)
    {
        if (dim_ != 5U) Private::h_badargs("fill");
        unsigned i0, i1, i2, i3, i4;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U)
            data_(i0, i1, i2, i3, i4) += w;
        else
        {
            overflow_(o0, o1, o2, o3, o4) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         const double x2, const double x3,
                                         const double x4, Num2& w, Functor& f)
    {
        if (dim_ != 5U) Private::h_badargs("dispatch");
        unsigned i0, i1, i2, i3, i4;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U)
            f(data_(i0, i1, i2, i3, i4), w);
        else
            f(overflow_(o0, o1, o2, o3, o4), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                      const double x2, const double x3,
                                      const double x4, const Num2& w)
    {
        if (dim_ != 5U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        const unsigned o2 = ax[2].overflowIndexWeighted(x2, idx+2, wg+2);
        const unsigned o3 = ax[3].overflowIndexWeighted(x3, idx+3, wg+3);
        const unsigned o4 = ax[4].overflowIndexWeighted(x4, idx+4, wg+4);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1, o2, o3, o4) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(
        const double x0, const double x1,
        const double x2, const double x3,
        const double x4) const
    {
        if (dim_ != 5U) Private::h_badargs("examine");
        unsigned i0, i1, i2, i3, i4;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U)
            return data_(i0, i1, i2, i3, i4);
        else
            return overflow_(o0, o1, o2, o3, o4);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1,
                                                     const double x2,
                                                     const double x3,
                                                     const double x4) const
    {
        if (dim_ != 5U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        const unsigned i2 = ax[2].closestValidBin(x2);
        const unsigned i3 = ax[3].closestValidBin(x3);
        const unsigned i4 = ax[4].closestValidBin(x4);
        return data_(i0, i1, i2, i3, i4);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const double x2, const double x3,
                                     const double x4, const double x5,
                                     const Num2& w)
    {
        if (dim_ != 6U) Private::h_badargs("fill");
        unsigned i0, i1, i2, i3, i4, i5;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        if (o0 == 1U && o1 == 1U && o2 == 1U &&
            o3 == 1U && o4 == 1U && o5 == 1U)
            data_(i0, i1, i2, i3, i4, i5) += w;
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }
    
    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         const double x2, const double x3,
                                         const double x4, const double x5,
                                         Num2& w, Functor& f)
    {
        if (dim_ != 6U) Private::h_badargs("dispatch");
        unsigned i0, i1, i2, i3, i4, i5;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        if (o0 == 1U && o1 == 1U && o2 == 1U &&
            o3 == 1U && o4 == 1U && o5 == 1U)
            f(data_(i0, i1, i2, i3, i4, i5), w);
        else
            f(overflow_(o0, o1, o2, o3, o4, o5), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                      const double x2, const double x3,
                                      const double x4, const double x5,
                                      const Num2& w)
    {
        if (dim_ != 6U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        const unsigned o2 = ax[2].overflowIndexWeighted(x2, idx+2, wg+2);
        const unsigned o3 = ax[3].overflowIndexWeighted(x3, idx+3, wg+3);
        const unsigned o4 = ax[4].overflowIndexWeighted(x4, idx+4, wg+4);
        const unsigned o5 = ax[5].overflowIndexWeighted(x5, idx+5, wg+5);
        if (o0 == 1U && o1 == 1U && o2 == 1U &&
            o3 == 1U && o4 == 1U && o5 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }
    
    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(const double x0,
                                                  const double x1,
                                                  const double x2,
                                                  const double x3,
                                                  const double x4,
                                                  const double x5) const
    {
        if (dim_ != 6U) Private::h_badargs("examine");
        unsigned i0, i1, i2, i3, i4, i5;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        if (o0 == 1U && o1 == 1U && o2 == 1U &&
            o3 == 1U && o4 == 1U && o5 == 1U)
            return data_(i0, i1, i2, i3, i4, i5);
        else
            return overflow_(o0, o1, o2, o3, o4, o5);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1,
                                                     const double x2,
                                                     const double x3,
                                                     const double x4,
                                                     const double x5) const
    {
        if (dim_ != 6U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        const unsigned i2 = ax[2].closestValidBin(x2);
        const unsigned i3 = ax[3].closestValidBin(x3);
        const unsigned i4 = ax[4].closestValidBin(x4);
        const unsigned i5 = ax[5].closestValidBin(x5);
        return data_(i0, i1, i2, i3, i4, i5);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const double x2, const double x3,
                                     const double x4, const double x5,
                                     const double x6, const Num2& w)
    {
        if (dim_ != 7U) Private::h_badargs("fill");
        unsigned i0, i1, i2, i3, i4, i5, i6;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        if (o0 == 1U && o1 == 1U && o2 == 1U &&
            o3 == 1U && o4 == 1U && o5 == 1U && o6 == 1U)
            data_(i0, i1, i2, i3, i4, i5, i6) += w;
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5, o6) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         const double x2, const double x3,
                                         const double x4, const double x5,
                                         const double x6, Num2& w, Functor& f)
    {
        if (dim_ != 7U) Private::h_badargs("dispatch");
        unsigned i0, i1, i2, i3, i4, i5, i6;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        if (o0 == 1U && o1 == 1U && o2 == 1U &&
            o3 == 1U && o4 == 1U && o5 == 1U && o6 == 1U)
            f(data_(i0, i1, i2, i3, i4, i5, i6), w);
        else
            f(overflow_(o0, o1, o2, o3, o4, o5, o6), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                      const double x2, const double x3,
                                      const double x4, const double x5,
                                      const double x6, const Num2& w)
    {
        if (dim_ != 7U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        const unsigned o2 = ax[2].overflowIndexWeighted(x2, idx+2, wg+2);
        const unsigned o3 = ax[3].overflowIndexWeighted(x3, idx+3, wg+3);
        const unsigned o4 = ax[4].overflowIndexWeighted(x4, idx+4, wg+4);
        const unsigned o5 = ax[5].overflowIndexWeighted(x5, idx+5, wg+5);
        const unsigned o6 = ax[6].overflowIndexWeighted(x6, idx+6, wg+6);
        if (o0 == 1U && o1 == 1U && o2 == 1U &&
            o3 == 1U && o4 == 1U && o5 == 1U && o6 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5, o6) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(
        const double x0, const double x1,
        const double x2, const double x3,
        const double x4, const double x5,
        const double x6) const
    {
        if (dim_ != 7U) Private::h_badargs("examine");
        unsigned i0, i1, i2, i3, i4, i5, i6;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        if (o0 == 1U && o1 == 1U && o2 == 1U &&
            o3 == 1U && o4 == 1U && o5 == 1U && o6 == 1U)
            return data_(i0, i1, i2, i3, i4, i5, i6);
        else
            return overflow_(o0, o1, o2, o3, o4, o5, o6);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1,
                                                     const double x2,
                                                     const double x3,
                                                     const double x4,
                                                     const double x5,
                                                     const double x6) const
    {
        if (dim_ != 7U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        const unsigned i2 = ax[2].closestValidBin(x2);
        const unsigned i3 = ax[3].closestValidBin(x3);
        const unsigned i4 = ax[4].closestValidBin(x4);
        const unsigned i5 = ax[5].closestValidBin(x5);
        const unsigned i6 = ax[6].closestValidBin(x6);
        return data_(i0, i1, i2, i3, i4, i5, i6);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const double x2, const double x3,
                                     const double x4, const double x5,
                                     const double x6, const double x7,
                                     const Num2& w)
    {
        if (dim_ != 8U) Private::h_badargs("fill");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U &&
            o4 == 1U && o5 == 1U && o6 == 1U && o7 == 1U)
            data_(i0, i1, i2, i3, i4, i5, i6, i7) += w;
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5, o6, o7) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         const double x2, const double x3,
                                         const double x4, const double x5,
                                         const double x6, const double x7,
                                         Num2& w, Functor& f)
    {
        if (dim_ != 8U) Private::h_badargs("dispatch");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U &&
            o4 == 1U && o5 == 1U && o6 == 1U && o7 == 1U)
            f(data_(i0, i1, i2, i3, i4, i5, i6, i7), w);
        else
            f(overflow_(o0, o1, o2, o3, o4, o5, o6, o7), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                      const double x2, const double x3,
                                      const double x4, const double x5,
                                      const double x6, const double x7,
                                      const Num2& w)
    {
        if (dim_ != 8U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        const unsigned o2 = ax[2].overflowIndexWeighted(x2, idx+2, wg+2);
        const unsigned o3 = ax[3].overflowIndexWeighted(x3, idx+3, wg+3);
        const unsigned o4 = ax[4].overflowIndexWeighted(x4, idx+4, wg+4);
        const unsigned o5 = ax[5].overflowIndexWeighted(x5, idx+5, wg+5);
        const unsigned o6 = ax[6].overflowIndexWeighted(x6, idx+6, wg+6);
        const unsigned o7 = ax[7].overflowIndexWeighted(x7, idx+7, wg+7);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U &&
            o4 == 1U && o5 == 1U && o6 == 1U && o7 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5, o6, o7) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(
        const double x0, const double x1,
        const double x2, const double x3,
        const double x4, const double x5,
        const double x6,
        const double x7) const
    {
        if (dim_ != 8U) Private::h_badargs("examine");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U &&
            o4 == 1U && o5 == 1U && o6 == 1U && o7 == 1U)
            return data_(i0, i1, i2, i3, i4, i5, i6, i7);
        else
            return overflow_(o0, o1, o2, o3, o4, o5, o6, o7);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1,
                                                     const double x2,
                                                     const double x3,
                                                     const double x4,
                                                     const double x5,
                                                     const double x6,
                                                     const double x7) const
    {
        if (dim_ != 8U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        const unsigned i2 = ax[2].closestValidBin(x2);
        const unsigned i3 = ax[3].closestValidBin(x3);
        const unsigned i4 = ax[4].closestValidBin(x4);
        const unsigned i5 = ax[5].closestValidBin(x5);
        const unsigned i6 = ax[6].closestValidBin(x6);
        const unsigned i7 = ax[7].closestValidBin(x7);
        return data_(i0, i1, i2, i3, i4, i5, i6, i7);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const double x2, const double x3,
                                     const double x4, const double x5,
                                     const double x6, const double x7,
                                     const double x8, const Num2& w)
    {
        if (dim_ != 9U) Private::h_badargs("fill");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7, i8;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        const unsigned o8 = ax[8].overflowIndex(x8, &i8);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U &&
            o5 == 1U && o6 == 1U && o7 == 1U && o8 == 1U)
            data_(i0, i1, i2, i3, i4, i5, i6, i7, i8) += w;
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5, o6, o7, o8) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         const double x2, const double x3,
                                         const double x4, const double x5,
                                         const double x6, const double x7,
                                         const double x8, Num2& w, Functor& f)
    {
        if (dim_ != 9U) Private::h_badargs("dispatch");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7, i8;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        const unsigned o8 = ax[8].overflowIndex(x8, &i8);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U &&
            o5 == 1U && o6 == 1U && o7 == 1U && o8 == 1U)
            f(data_(i0, i1, i2, i3, i4, i5, i6, i7, i8), w);
        else
            f(overflow_(o0, o1, o2, o3, o4, o5, o6, o7, o8), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                      const double x2, const double x3,
                                      const double x4, const double x5,
                                      const double x6, const double x7,
                                      const double x8, const Num2& w)
    {
        if (dim_ != 9U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        const unsigned o2 = ax[2].overflowIndexWeighted(x2, idx+2, wg+2);
        const unsigned o3 = ax[3].overflowIndexWeighted(x3, idx+3, wg+3);
        const unsigned o4 = ax[4].overflowIndexWeighted(x4, idx+4, wg+4);
        const unsigned o5 = ax[5].overflowIndexWeighted(x5, idx+5, wg+5);
        const unsigned o6 = ax[6].overflowIndexWeighted(x6, idx+6, wg+6);
        const unsigned o7 = ax[7].overflowIndexWeighted(x7, idx+7, wg+7);
        const unsigned o8 = ax[8].overflowIndexWeighted(x8, idx+8, wg+8);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U &&
            o5 == 1U && o6 == 1U && o7 == 1U && o8 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5, o6, o7, o8) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(
        const double x0, const double x1,
        const double x2, const double x3,
        const double x4, const double x5,
        const double x6, const double x7,
        const double x8) const
    {
        if (dim_ != 9U) Private::h_badargs("examine");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7, i8;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        const unsigned o8 = ax[8].overflowIndex(x8, &i8);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U &&
            o5 == 1U && o6 == 1U && o7 == 1U && o8 == 1U)
            return data_(i0, i1, i2, i3, i4, i5, i6, i7, i8);
        else
            return overflow_(o0, o1, o2, o3, o4, o5, o6, o7, o8);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1,
                                                     const double x2,
                                                     const double x3,
                                                     const double x4,
                                                     const double x5,
                                                     const double x6,
                                                     const double x7,
                                                     const double x8) const
    {
        if (dim_ != 9U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        const unsigned i2 = ax[2].closestValidBin(x2);
        const unsigned i3 = ax[3].closestValidBin(x3);
        const unsigned i4 = ax[4].closestValidBin(x4);
        const unsigned i5 = ax[5].closestValidBin(x5);
        const unsigned i6 = ax[6].closestValidBin(x6);
        const unsigned i7 = ax[7].closestValidBin(x7);
        const unsigned i8 = ax[8].closestValidBin(x8);
        return data_(i0, i1, i2, i3, i4, i5, i6, i7, i8);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fill(const double x0, const double x1,
                                     const double x2, const double x3,
                                     const double x4, const double x5,
                                     const double x6, const double x7,
                                     const double x8, const double x9,
                                     const Num2& w)
    {
        if (dim_ != 10U) Private::h_badargs("fill");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7, i8, i9;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        const unsigned o8 = ax[8].overflowIndex(x8, &i8);
        const unsigned o9 = ax[9].overflowIndex(x9, &i9);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U &&
            o5 == 1U && o6 == 1U && o7 == 1U && o8 == 1U && o9 == 1U)
            data_(i0, i1, i2, i3, i4, i5, i6, i7, i8, i9) += w;
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5, o6, o7, o8, o9) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, class Functor>
    void HistoND<Numeric,Axis>::dispatch(const double x0, const double x1,
                                         const double x2, const double x3,
                                         const double x4, const double x5,
                                         const double x6, const double x7,
                                         const double x8, const double x9,
                                         Num2& w, Functor& f)
    {
        if (dim_ != 10U) Private::h_badargs("dispatch");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7, i8, i9;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        const unsigned o8 = ax[8].overflowIndex(x8, &i8);
        const unsigned o9 = ax[9].overflowIndex(x9, &i9);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U &&
            o5 == 1U && o6 == 1U && o7 == 1U && o8 == 1U && o9 == 1U)
            f(data_(i0, i1, i2, i3, i4, i5, i6, i7, i8, i9), w);
        else
            f(overflow_(o0, o1, o2, o3, o4, o5, o6, o7, o8, o9), w);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::fillC(const double x0, const double x1,
                                      const double x2, const double x3,
                                      const double x4, const double x5,
                                      const double x6, const double x7,
                                      const double x8, const double x9,
                                      const Num2& w)
    {
        if (dim_ != 10U) Private::h_badargs("fillC");
        double* wg = &weightBuf_[0];
        unsigned* idx = &indexBuf_[0];
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndexWeighted(x0, idx+0, wg+0);
        const unsigned o1 = ax[1].overflowIndexWeighted(x1, idx+1, wg+1);
        const unsigned o2 = ax[2].overflowIndexWeighted(x2, idx+2, wg+2);
        const unsigned o3 = ax[3].overflowIndexWeighted(x3, idx+3, wg+3);
        const unsigned o4 = ax[4].overflowIndexWeighted(x4, idx+4, wg+4);
        const unsigned o5 = ax[5].overflowIndexWeighted(x5, idx+5, wg+5);
        const unsigned o6 = ax[6].overflowIndexWeighted(x6, idx+6, wg+6);
        const unsigned o7 = ax[7].overflowIndexWeighted(x7, idx+7, wg+7);
        const unsigned o8 = ax[8].overflowIndexWeighted(x8, idx+8, wg+8);
        const unsigned o9 = ax[9].overflowIndexWeighted(x9, idx+9, wg+9);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U &&
            o5 == 1U && o6 == 1U && o7 == 1U && o8 == 1U && o9 == 1U)
            fillPreservingCentroid(w);
        else
        {
            overflow_(o0, o1, o2, o3, o4, o5, o6, o7, o8, o9) += w;
            ++overCount_;
        }
        ++fillCount_; ++modCount_;
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::examine(
        const double x0, const double x1,
        const double x2, const double x3,
        const double x4, const double x5,
        const double x6, const double x7,
        const double x8,
        const double x9) const
    {
        if (dim_ != 10U) Private::h_badargs("examine");
        unsigned i0, i1, i2, i3, i4, i5, i6, i7, i8, i9;
        const Axis* ax = &axes_[0];
        const unsigned o0 = ax[0].overflowIndex(x0, &i0);
        const unsigned o1 = ax[1].overflowIndex(x1, &i1);
        const unsigned o2 = ax[2].overflowIndex(x2, &i2);
        const unsigned o3 = ax[3].overflowIndex(x3, &i3);
        const unsigned o4 = ax[4].overflowIndex(x4, &i4);
        const unsigned o5 = ax[5].overflowIndex(x5, &i5);
        const unsigned o6 = ax[6].overflowIndex(x6, &i6);
        const unsigned o7 = ax[7].overflowIndex(x7, &i7);
        const unsigned o8 = ax[8].overflowIndex(x8, &i8);
        const unsigned o9 = ax[9].overflowIndex(x9, &i9);
        if (o0 == 1U && o1 == 1U && o2 == 1U && o3 == 1U && o4 == 1U &&
            o5 == 1U && o6 == 1U && o7 == 1U && o8 == 1U && o9 == 1U)
            return data_(i0, i1, i2, i3, i4, i5, i6, i7, i8, i9);
        else
            return overflow_(o0, o1, o2, o3, o4, o5, o6, o7, o8, o9);
    }

    template <typename Numeric, class Axis>
    const Numeric& HistoND<Numeric,Axis>::closestBin(const double x0,
                                                     const double x1,
                                                     const double x2,
                                                     const double x3,
                                                     const double x4,
                                                     const double x5,
                                                     const double x6,
                                                     const double x7,
                                                     const double x8,
                                                     const double x9) const
    {
        if (dim_ != 10U) Private::h_badargs("closestBin");
        const Axis* ax = &axes_[0];
        const unsigned i0 = ax[0].closestValidBin(x0);
        const unsigned i1 = ax[1].closestValidBin(x1);
        const unsigned i2 = ax[2].closestValidBin(x2);
        const unsigned i3 = ax[3].closestValidBin(x3);
        const unsigned i4 = ax[4].closestValidBin(x4);
        const unsigned i5 = ax[5].closestValidBin(x5);
        const unsigned i6 = ax[6].closestValidBin(x6);
        const unsigned i7 = ax[7].closestValidBin(x7);
        const unsigned i8 = ax[8].closestValidBin(x8);
        const unsigned i9 = ax[9].closestValidBin(x9);
        return data_(i0, i1, i2, i3, i4, i5, i6, i7, i8, i9);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned *index,
                                              const unsigned indexLen,
                                              const Num2& v)
    {
        data_.value(index, indexLen) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned *index,
                                                const unsigned indexLen,
                                                const Num2& v)
    {
        data_.valueAt(index, indexLen) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const Num2& v)
    {
        data_() = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const Num2& v)
    {
        data_.at() = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(
        const unsigned i0, const Num2& v)
    {
        data_(i0) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(
        const unsigned i0, const Num2& v)
    {
        data_.at(i0) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const Num2& v)
    {
        data_(i0, i1) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const Num2& v)
    {
        data_.at(i0, i1) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const unsigned i2,
                                              const Num2& v)
    {
        data_(i0, i1, i2) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const unsigned i2,
                                              const unsigned i3,
                                              const Num2& v)
    {
        data_(i0, i1, i2, i3) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const unsigned i2,
                                              const unsigned i3,
                                              const unsigned i4,
                                              const Num2& v)
    {
        data_(i0, i1, i2, i3, i4) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const unsigned i2,
                                              const unsigned i3,
                                              const unsigned i4,
                                              const unsigned i5,
                                              const Num2& v)
    {
        data_(i0, i1, i2, i3, i4, i5) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const unsigned i2,
                                              const unsigned i3,
                                              const unsigned i4,
                                              const unsigned i5,
                                              const unsigned i6,
                                              const Num2& v)
    {
        data_(i0, i1, i2, i3, i4, i5, i6) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const unsigned i2,
                                              const unsigned i3,
                                              const unsigned i4,
                                              const unsigned i5,
                                              const unsigned i6,
                                              const unsigned i7,
                                              const Num2& v)
    {
        data_(i0, i1, i2, i3, i4, i5, i6, i7) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const unsigned i2,
                                              const unsigned i3,
                                              const unsigned i4,
                                              const unsigned i5,
                                              const unsigned i6,
                                              const unsigned i7,
                                              const unsigned i8,
                                              const Num2& v)
    {
        data_(i0, i1, i2, i3, i4, i5, i6, i7, i8) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBin(const unsigned i0,
                                              const unsigned i1,
                                              const unsigned i2,
                                              const unsigned i3,
                                              const unsigned i4,
                                              const unsigned i5,
                                              const unsigned i6,
                                              const unsigned i7,
                                              const unsigned i8,
                                              const unsigned i9,
                                              const Num2& v)
    {
        data_(i0, i1, i2, i3, i4, i5, i6, i7, i8, i9) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const unsigned i2,
                                                const Num2& v)
    {
        data_.at(i0, i1, i2) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const unsigned i2,
                                                const unsigned i3,
                                                const Num2& v)
    {
        data_.at(i0, i1, i2, i3) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const unsigned i2,
                                                const unsigned i3,
                                                const unsigned i4,
                                                const Num2& v)
    {
        data_.at(i0, i1, i2, i3, i4) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const unsigned i2,
                                                const unsigned i3,
                                                const unsigned i4,
                                                const unsigned i5,
                                                const Num2& v)
    {
        data_.at(i0, i1, i2, i3, i4, i5) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const unsigned i2,
                                                const unsigned i3,
                                                const unsigned i4,
                                                const unsigned i5,
                                                const unsigned i6,
                                                const Num2& v)
    {
        data_.at(i0, i1, i2, i3, i4, i5, i6) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const unsigned i2,
                                                const unsigned i3,
                                                const unsigned i4,
                                                const unsigned i5,
                                                const unsigned i6,
                                                const unsigned i7,
                                                const Num2& v)
    {
        data_.at(i0, i1, i2, i3, i4, i5, i6, i7) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const unsigned i2,
                                                const unsigned i3,
                                                const unsigned i4,
                                                const unsigned i5,
                                                const unsigned i6,
                                                const unsigned i7,
                                                const unsigned i8,
                                                const Num2& v)
    {
        data_.at(i0, i1, i2, i3, i4, i5, i6, i7, i8) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinAt(const unsigned i0,
                                                const unsigned i1,
                                                const unsigned i2,
                                                const unsigned i3,
                                                const unsigned i4,
                                                const unsigned i5,
                                                const unsigned i6,
                                                const unsigned i7,
                                                const unsigned i8,
                                                const unsigned i9,
                                                const Num2& v)
    {
        data_.at(i0, i1, i2, i3, i4, i5, i6, i7, i8, i9) = v;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline HistoND<Numeric,Axis>& HistoND<Numeric,Axis>::operator+=(
        const HistoND<Num2,Axis>& r)
    {
        data_ += r.data_;
        overflow_ += r.overflow_;
        fillCount_ += r.fillCount_;
        overCount_ += r.overCount_;
        ++modCount_;
        return *this;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline HistoND<Numeric,Axis>& HistoND<Numeric,Axis>::operator-=(
        const HistoND<Num2,Axis>& r)
    {
        data_ -= r.data_;
        overflow_ -= r.overflow_;

        // Subtraction does not make much sense for fill counts.
        // We will assume that what we want should be equivalent
        // to the in-place multiplication of the other histogram
        // by -1 and then adding.
        //
        fillCount_ += r.fillCount_;
        overCount_ += r.overCount_;

        ++modCount_;
        return *this;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline HistoND<Numeric,Axis>&
    HistoND<Numeric,Axis>::operator*=(const Num2& r)
    {
        data_ *= r;
        overflow_ *= r;
        ++modCount_;
        return *this;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline HistoND<Numeric,Axis>&
    HistoND<Numeric,Axis>::operator/=(const Num2& r)
    {
        data_ /= r;
        overflow_ /= r;
        ++modCount_;
        return *this;
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const HistoND& r,
                                   const unsigned ax1,
                                   const unsigned ax2)
        : title_(r.title_),
          accumulatedDataLabel_(r.accumulatedDataLabel_),
          data_(r.data_.transpose(ax1, ax2)),
          overflow_(r.overflow_.transpose(ax1, ax2)),
          axes_(r.axes_),
          weightBuf_(r.weightBuf_),
          indexBuf_(r.indexBuf_),
          fillCount_(r.fillCount_),
          overCount_(r.overCount_),
          modCount_(0UL),
          dim_(r.dim_)
    {
        std::swap(axes_[ax1], axes_[ax2]);
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>::HistoND(const HistoND& r)
        : title_(r.title_),
          accumulatedDataLabel_(r.accumulatedDataLabel_),
          data_(r.data_),
          overflow_(r.overflow_),
          axes_(r.axes_),
          weightBuf_(r.weightBuf_),
          indexBuf_(r.indexBuf_),
          fillCount_(r.fillCount_),
          overCount_(r.overCount_),
          modCount_(0UL),
          dim_(r.dim_)
    {
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis>& HistoND<Numeric,Axis>::operator=(const HistoND& r)
    {
        if (&r != this)
        {
            title_ = r.title_;
            accumulatedDataLabel_ = r.accumulatedDataLabel_;
            data_.uninitialize();
            data_ = r.data_;
            overflow_.uninitialize();
            overflow_ = r.overflow_;
            axes_ = r.axes_;
            weightBuf_ = r.weightBuf_;
            indexBuf_ = r.indexBuf_;
            fillCount_ = r.fillCount_;
            overCount_ = r.overCount_;
            dim_ = r.dim_;
            ++modCount_;
        }
        return *this;
    }

    template <typename Numeric, class Axis>
    HistoND<Numeric,Axis> HistoND<Numeric,Axis>::transpose(
        const unsigned axisNum1, const unsigned axisNum2) const
    {
        if (axisNum1 >= dim_ || axisNum2 >= dim_)
            throw npstat::NpstatOutOfRange("In npstat::HistoND::transpose: "
                                    "axis number is out of range");
        if (axisNum1 == axisNum2)
            // Just make a copy
            return *this;
        else
            return HistoND(*this, axisNum1, axisNum2);
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::addToBinContents(const Num2& weight)
    {
        const unsigned long nDat = data_.length();
        Numeric* data = const_cast<Numeric*>(data_.data());
        for (unsigned long i=0; i<nDat; ++i)
            data[i] += weight;
        fillCount_ += nDat;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::addToOverflows(const Num2& weight)
    {
        const unsigned long nOver = overflow_.length();
        Numeric* data = const_cast<Numeric*>(overflow_.data());
        for (unsigned long i=0; i<nOver; ++i)
            data[i] += weight;
        overCount_ += nOver;
        fillCount_ += nOver;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::addToBinContents(
        const Num2* data, const unsigned long dataLength)
    {
        if (dataLength != data_.length()) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::addToBinContents: incompatible data length");
        assert(data);
        Numeric* dat = const_cast<Numeric*>(data_.data());
        for (unsigned long i=0; i<dataLength; ++i)
            dat[i] += data[i];
        fillCount_ += dataLength;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::addToOverflows(
        const Num2* data, const unsigned long dataLength)
    {
        if (dataLength != overflow_.length()) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::addToOverflows: incompatible data length");
        assert(data);
        Numeric* dat = const_cast<Numeric*>(overflow_.data());
        for (unsigned long i=0; i<dataLength; ++i)
            dat[i] += data[i];
        overCount_ += dataLength;
        fillCount_ += dataLength;
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::scaleBinContents(
        const Num2* data, const unsigned long dataLength)
    {
        if (dataLength != data_.length()) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::scaleBinContents: incompatible data length");
        assert(data);
        Numeric* dat = const_cast<Numeric*>(data_.data());
        for (unsigned long i=0; i<dataLength; ++i)
            dat[i] *= data[i];
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    void HistoND<Numeric,Axis>::scaleOverflows(
        const Num2* data, const unsigned long dataLength)
    {
        if (dataLength != overflow_.length()) throw npstat::NpstatInvalidArgument(
            "In npstat::HistoND::scaleOverflows: incompatible data length");
        assert(data);
        Numeric* dat = const_cast<Numeric*>(overflow_.data());
        for (unsigned long i=0; i<dataLength; ++i)
            dat[i] *= data[i];
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setBinContents(
        const Num2* data, const unsigned long dataLength,
        const bool clearOverflowsNow)
    {
        data_.setData(data, dataLength);
        if (clearOverflowsNow)
            clearOverflows();
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2>
    inline void HistoND<Numeric,Axis>::setOverflows(
        const Num2* data, const unsigned long dataLength)
    {
        overflow_.setData(data, dataLength);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    inline void HistoND<Numeric,Axis>::recalculateNFillsFromData()
    {
        const long double nOver = overflow_.template sum<long double>();
        const long double nData = data_.template sum<long double>();
        overCount_ = static_cast<unsigned long>(nOver);
        fillCount_ = static_cast<unsigned long>(nData + nOver);
        ++modCount_;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, typename Num3>
    inline void HistoND<Numeric,Axis>::addToProjection(
        HistoND<Num2,Axis>* projection,
        AbsArrayProjector<Numeric,Num3>& projector,
        const unsigned *projectedIndices,
        const unsigned nProjectedIndices) const
    {
        assert(projection);
        data_.addToProjection(&projection->data_, projector,
                              projectedIndices, nProjectedIndices);
        projection->fillCount_ += projection->nBins();
        projection->modCount_++;
    }

    template <typename Numeric, class Axis>
    template <typename Num2, typename Num3>
    inline void HistoND<Numeric,Axis>::addToProjection(
        HistoND<Num2,Axis>* projection,
        AbsVisitor<Numeric,Num3>& projector,
        const unsigned *projectedIndices,
        const unsigned nProjectedIndices) const
    {
        assert(projection);
        data_.addToProjection(&projection->data_, projector,
                              projectedIndices, nProjectedIndices);
        projection->fillCount_ += projection->nBins();
        projection->modCount_++;
    }

    template <typename Numeric, class Axis>
    const char* HistoND<Numeric,Axis>::classname()
    {
        static const std::string myClass(gs::template_class_name<Numeric,Axis>(
                                             "npstat::HistoND"));
        return myClass.c_str();
    }

    template<typename Numeric, class Axis>
    bool HistoND<Numeric,Axis>::write(std::ostream& of) const
    {
        gs::write_pod(of, title_);
        gs::write_pod(of, accumulatedDataLabel_);
        gs::write_pod(of, fillCount_);
        gs::write_pod(of, overCount_);

        return !of.fail() &&
            gs::write_obj_vector(of, axes_) && 
            data_.classId().write(of) &&
            data_.write(of) &&
            overflow_.write(of);
    }

    template<typename Numeric, class Axis>
    HistoND<Numeric,Axis>* HistoND<Numeric,Axis>::read(const gs::ClassId& id,
                                                       std::istream& in)
    {
        static const gs::ClassId current(
            gs::ClassId::makeId<HistoND<Numeric,Axis> >());
        current.ensureSameId(id);

        std::string title;
        gs::read_pod(in, &title);

        std::string accumulatedDataLabel;
        gs::read_pod(in, &accumulatedDataLabel);

        unsigned long fillCount = 0, overCount = 0;
        gs::read_pod(in, &fillCount);
        gs::read_pod(in, &overCount);
        if (in.fail()) throw gs::IOReadFailure(
            "In npstat::HistoND::read: input stream failure");

        std::vector<Axis> axes;
        gs::read_heap_obj_vector_as_placed(in, &axes);
        gs::ClassId ida(in, 1);
        ArrayND<Numeric> data, over;
        ArrayND<Numeric>::restore(ida, in, &data);
        ArrayND<Numeric>::restore(ida, in, &over);
        CPP11_auto_ptr<HistoND<Numeric,Axis> > result(
            new HistoND<Numeric,Axis>(axes, title.c_str(),
                                      accumulatedDataLabel.c_str()));
        result->data_ = data;
        result->overflow_ = over;
        result->fillCount_ = fillCount;
        result->overCount_ = overCount;
        return result.release();
    }

    template <typename Histo>
    void convertHistoToDensity(Histo* h, const bool knownNonNegative)
    {
        assert(h);
        if (!knownNonNegative)
            (const_cast<ArrayND<typename 
                Histo::value_type>&>(h->binContents())).makeNonNegative();
        const double integ = h->integral();
        *h /= integ;
    }

    template <typename Histo>
    std::vector<LinearMapper1d> densityScanHistoMap(const Histo& histo)
    {
        std::vector<LinearMapper1d> result;
        const unsigned d = histo.dim();
        result.reserve(d);
        for (unsigned i=0; i<d; ++i)
        {
            const LinearMapper1d& m = histo.axis(i).binNumberMapper(false);
            result.push_back(m.inverse());
        }
        return result;
    }

    template <typename Histo>
    std::vector<CircularMapper1d> convolutionHistoMap(
        const Histo& histo, const bool doubleRange)
    {
        std::vector<CircularMapper1d> result;
        const unsigned d = histo.dim();
        result.reserve(d);
        for (unsigned i=0; i<d; ++i)
            result.push_back(histo.axis(i).kernelScanMapper(doubleRange));
        return result;
    }
}


#endif // NPSTAT_HISTOND_HH_