Fix nbnxm OpenCL with cluster size 4

[gromacs.git] / src / gromacs / nbnxm / grid.cpp

/*
 * This file is part of the GROMACS molecular simulation package.
 *
 * Copyright (c) 2012,2013,2014,2015,2016,2017,2018,2019, by the GROMACS development team, led by
 * Mark Abraham, David van der Spoel, Berk Hess, and Erik Lindahl,
 * and including many others, as listed in the AUTHORS file in the
 * top-level source directory and at http://www.gromacs.org.
 *
 * GROMACS is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License
 * as published by the Free Software Foundation; either version 2.1
 * of the License, or (at your option) any later version.
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/*! \internal \file
 *
 * \brief
 * Implements the Grid class.
 *
 * \author Berk Hess <hess@kth.se>
 * \ingroup module_nbnxm
 */

#include "gmxpre.h"

#include "grid.h"

#include <cmath>
#include <cstring>

#include <algorithm>

#include "gromacs/math/utilities.h"
#include "gromacs/math/vec.h"
#include "gromacs/mdlib/gmx_omp_nthreads.h"
#include "gromacs/mdlib/updategroupscog.h"
#include "gromacs/mdtypes/forcerec.h" // only for GET_CGINFO_*
#include "gromacs/nbnxm/atomdata.h"
#include "gromacs/nbnxm/nbnxm_geometry.h"
#include "gromacs/simd/simd.h"
#include "gromacs/simd/vector_operations.h"

namespace Nbnxm
{

Grid::Geometry::Geometry(const PairlistType pairlistType) :
    isSimple(pairlistType != PairlistType::HierarchicalNxN),
    numAtomsICluster(IClusterSizePerListType[pairlistType]),
    numAtomsJCluster(JClusterSizePerListType[pairlistType]),
    numAtomsPerCell((isSimple ? 1 : c_gpuNumClusterPerCell)*numAtomsICluster),
    numAtomsICluster2Log(get_2log(numAtomsICluster))
{
}

Grid::Grid(const PairlistType pairlistType) :
    geometry_(pairlistType)
{
}

/*! \brief Returns the atom density (> 0) of a rectangular grid */
static real gridAtomDensity(int        numAtoms,
                            const rvec lowerCorner,
                            const rvec upperCorner)
{
    rvec size;

    if (numAtoms == 0)
    {
        /* To avoid zero density we use a minimum of 1 atom */
        numAtoms = 1;
    }

    rvec_sub(upperCorner, lowerCorner, size);

    return numAtoms/(size[XX]*size[YY]*size[ZZ]);
}

void Grid::setDimensions(const int           ddZone,
                         const int           numAtoms,
                         const rvec          lowerCorner,
                         const rvec          upperCorner,
                         real                atomDensity,
                         const real          maxAtomGroupRadius,
                         const bool          haveFep)
{
    /* For the home zone we compute the density when not set (=-1) or when =0 */
    if (ddZone == 0 && atomDensity <= 0)
    {
        atomDensity = gridAtomDensity(numAtoms, lowerCorner, upperCorner);
    }

    dimensions_.atomDensity        = atomDensity;
    dimensions_.maxAtomGroupRadius = maxAtomGroupRadius;

    rvec size;
    rvec_sub(upperCorner, lowerCorner, size);

    if (numAtoms > geometry_.numAtomsPerCell)
    {
        GMX_ASSERT(atomDensity > 0, "With one or more atoms, the density should be positive");

        /* target cell length */
        real tlen_x;
        real tlen_y;
        if (geometry_.isSimple)
        {
            /* To minimize the zero interactions, we should make
             * the largest of the i/j cell cubic.
             */
            int numAtomsInCell = std::max(geometry_.numAtomsICluster,
                                          geometry_.numAtomsJCluster);

            /* Approximately cubic cells */
            real tlen = std::cbrt(numAtomsInCell/atomDensity);
            tlen_x    = tlen;
            tlen_y    = tlen;
        }
        else
        {
            /* Approximately cubic sub cells */
            real tlen = std::cbrt(geometry_.numAtomsICluster/atomDensity);
            tlen_x    = tlen*c_gpuNumClusterPerCellX;
            tlen_y    = tlen*c_gpuNumClusterPerCellY;
        }
        /* We round ncx and ncy down, because we get less cell pairs
         * in the nbsist when the fixed cell dimensions (x,y) are
         * larger than the variable one (z) than the other way around.
         */
        dimensions_.numCells[XX] = std::max(1, static_cast<int>(size[XX]/tlen_x));
        dimensions_.numCells[YY] = std::max(1, static_cast<int>(size[YY]/tlen_y));
    }
    else
    {
        dimensions_.numCells[XX] = 1;
        dimensions_.numCells[YY] = 1;
    }

    for (int d = 0; d < DIM - 1; d++)
    {
        dimensions_.cellSize[d]    = size[d]/dimensions_.numCells[d];
        dimensions_.invCellSize[d] = 1/dimensions_.cellSize[d];
    }

    if (ddZone > 0)
    {
        /* This is a non-home zone, add an extra row of cells
         * for particles communicated for bonded interactions.
         * These can be beyond the cut-off. It doesn't matter where
         * they end up on the grid, but for performance it's better
         * if they don't end up in cells that can be within cut-off range.
         */
        dimensions_.numCells[XX]++;
        dimensions_.numCells[YY]++;
    }

    /* We need one additional cell entry for particles moved by DD */
    cxy_na_.resize(numColumns() + 1);
    cxy_ind_.resize(numColumns() + 2);

    /* Worst case scenario of 1 atom in each last cell */
    int maxNumCells;
    if (geometry_.numAtomsJCluster <= geometry_.numAtomsICluster)
    {
        maxNumCells = numAtoms/geometry_.numAtomsPerCell + numColumns();
    }
    else
    {
        maxNumCells = numAtoms/geometry_.numAtomsPerCell + numColumns()*geometry_.numAtomsJCluster/geometry_.numAtomsICluster;
    }

    if (!geometry_.isSimple)
    {
        numClusters_.resize(maxNumCells);
    }
    bbcz_.resize(maxNumCells);

    /* This resize also zeros the contents, this avoid possible
     * floating exceptions in SIMD with the unused bb elements.
     */
    if (geometry_.isSimple)
    {
        bb_.resize(maxNumCells);
    }
    else
    {
#if NBNXN_BBXXXX
        pbb_.resize(packedBoundingBoxesIndex(maxNumCells*c_gpuNumClusterPerCell));
#else
        bb_.resize(maxNumCells*c_gpuNumClusterPerCell);
#endif
    }

    if (geometry_.numAtomsJCluster == geometry_.numAtomsICluster)
    {
        bbj_ = bb_;
    }
    else
    {
        GMX_ASSERT(geometry_.isSimple, "Only CPU lists should have different i/j cluster sizes");

        bbjStorage_.resize(maxNumCells*geometry_.numAtomsICluster/geometry_.numAtomsJCluster);
        bbj_ = bbjStorage_;
    }

    flags_.resize(maxNumCells);
    if (haveFep)
    {
        fep_.resize(maxNumCells*geometry_.numAtomsPerCell/geometry_.numAtomsICluster);
    }

    copy_rvec(lowerCorner, dimensions_.lowerCorner);
    copy_rvec(upperCorner, dimensions_.upperCorner);
    copy_rvec(size,        dimensions_.gridSize);
}

/* We need to sort paricles in grid columns on z-coordinate.
 * As particle are very often distributed homogeneously, we use a sorting
 * algorithm similar to pigeonhole sort. We multiply the z-coordinate
 * by a factor, cast to an int and try to store in that hole. If the hole
 * is full, we move this or another particle. A second pass is needed to make
 * contiguous elements. SORT_GRID_OVERSIZE is the ratio of holes to particles.
 * 4 is the optimal value for homogeneous particle distribution and allows
 * for an O(#particles) sort up till distributions were all particles are
 * concentrated in 1/4 of the space. No NlogN fallback is implemented,
 * as it can be expensive to detect imhomogeneous particle distributions.
 */
/*! \brief Ratio of grid cells to atoms */
static constexpr int c_sortGridRatio         = 4;
/*! \brief Maximum ratio of holes used, in the worst case all particles
 * end up in the last hole and we need num. atoms extra holes at the end.
 */
static constexpr int c_sortGridMaxSizeFactor = c_sortGridRatio + 1;

/*! \brief Sorts particle index a on coordinates x along dim.
 *
 * Backwards tells if we want decreasing iso increasing coordinates.
 * h0 is the minimum of the coordinate range.
 * invh is the 1/length of the sorting range.
 * n_per_h (>=n) is the expected average number of particles per 1/invh
 * sort is the sorting work array.
 * sort should have a size of at least n_per_h*c_sortGridRatio + n,
 * or easier, allocate at least n*c_sortGridMaxSizeFactor elements.
 */
static void sort_atoms(int dim, gmx_bool Backwards,
                       int gmx_unused dd_zone,
                       bool gmx_unused relevantAtomsAreWithinGridBounds,
                       int *a, int n,
                       gmx::ArrayRef<const gmx::RVec> x,
                       real h0, real invh, int n_per_h,
                       gmx::ArrayRef<int> sort)
{
    if (n <= 1)
    {
        /* Nothing to do */
        return;
    }

    GMX_ASSERT(n <= n_per_h, "We require n <= n_per_h");

    /* Transform the inverse range height into the inverse hole height */
    invh *= n_per_h*c_sortGridRatio;

    /* Set nsort to the maximum possible number of holes used.
     * In worst case all n elements end up in the last bin.
     */
    int nsort = n_per_h*c_sortGridRatio + n;

    /* Determine the index range used, so we can limit it for the second pass */
    int zi_min = INT_MAX;
    int zi_max = -1;

    /* Sort the particles using a simple index sort */
    for (int i = 0; i < n; i++)
    {
        /* The cast takes care of float-point rounding effects below zero.
         * This code assumes particles are less than 1/SORT_GRID_OVERSIZE
         * times the box height out of the box.
         */
        int zi = static_cast<int>((x[a[i]][dim] - h0)*invh);

#ifndef NDEBUG
        /* As we can have rounding effect, we use > iso >= here */
        if (relevantAtomsAreWithinGridBounds &&
            (zi < 0 || (dd_zone == 0 && zi > n_per_h*c_sortGridRatio)))
        {
            gmx_fatal(FARGS, "(int)((x[%d][%c]=%f - %f)*%f) = %d, not in 0 - %d*%d\n",
                      a[i], 'x'+dim, x[a[i]][dim], h0, invh, zi,
                      n_per_h, c_sortGridRatio);
        }
#endif
        if (zi < 0)
        {
            zi = 0;
        }

        /* In a non-local domain, particles communcated for bonded interactions
         * can be far beyond the grid size, which is set by the non-bonded
         * cut-off distance. We sort such particles into the last cell.
         */
        if (zi > n_per_h*c_sortGridRatio)
        {
            zi = n_per_h*c_sortGridRatio;
        }

        /* Ideally this particle should go in sort cell zi,
         * but that might already be in use,
         * in that case find the first empty cell higher up
         */
        if (sort[zi] < 0)
        {
            sort[zi] = a[i];
            zi_min   = std::min(zi_min, zi);
            zi_max   = std::max(zi_max, zi);
        }
        else
        {
            /* We have multiple atoms in the same sorting slot.
             * Sort on real z for minimal bounding box size.
             * There is an extra check for identical z to ensure
             * well-defined output order, independent of input order
             * to ensure binary reproducibility after restarts.
             */
            while (sort[zi] >= 0 && ( x[a[i]][dim] >  x[sort[zi]][dim] ||
                                      (x[a[i]][dim] == x[sort[zi]][dim] &&
                                       a[i] > sort[zi])))
            {
                zi++;
            }

            if (sort[zi] >= 0)
            {
                /* Shift all elements by one slot until we find an empty slot */
                int cp  = sort[zi];
                int zim = zi + 1;
                while (sort[zim] >= 0)
                {
                    int tmp   = sort[zim];
                    sort[zim] = cp;
                    cp        = tmp;
                    zim++;
                }
                sort[zim] = cp;
                zi_max    = std::max(zi_max, zim);
            }
            sort[zi] = a[i];
            zi_max   = std::max(zi_max, zi);
        }
    }

    int c = 0;
    if (!Backwards)
    {
        for (int zi = 0; zi < nsort; zi++)
        {
            if (sort[zi] >= 0)
            {
                a[c++]   = sort[zi];
                sort[zi] = -1;
            }
        }
    }
    else
    {
        for (int zi = zi_max; zi >= zi_min; zi--)
        {
            if (sort[zi] >= 0)
            {
                a[c++]   = sort[zi];
                sort[zi] = -1;
            }
        }
    }
    if (c < n)
    {
        gmx_incons("Lost particles while sorting");
    }
}

#if GMX_DOUBLE
//! Returns double up to one least significant float bit smaller than x
static double R2F_D(const float x)
{
    return static_cast<float>(x >= 0 ? (1 - GMX_FLOAT_EPS)*x : (1 + GMX_FLOAT_EPS)*x);
}
//! Returns double up to one least significant float bit larger than x
static double R2F_U(const float x)
{
    return static_cast<float>(x >= 0 ? (1 + GMX_FLOAT_EPS)*x : (1 - GMX_FLOAT_EPS)*x);
}
#else
//! Returns x
static float R2F_D(const float x)
{
    return x;
}
//! Returns x
static float R2F_U(const float x)
{
    return x;
}
#endif

//! Computes the bounding box for na coordinates in order x,y,z, bb order xyz0
static void calc_bounding_box(int na, int stride, const real *x,
                              BoundingBox *bb)
{
    int  i;
    real xl, xh, yl, yh, zl, zh;

    i  = 0;
    xl = x[i+XX];
    xh = x[i+XX];
    yl = x[i+YY];
    yh = x[i+YY];
    zl = x[i+ZZ];
    zh = x[i+ZZ];
    i += stride;
    for (int j = 1; j < na; j++)
    {
        xl = std::min(xl, x[i+XX]);
        xh = std::max(xh, x[i+XX]);
        yl = std::min(yl, x[i+YY]);
        yh = std::max(yh, x[i+YY]);
        zl = std::min(zl, x[i+ZZ]);
        zh = std::max(zh, x[i+ZZ]);
        i += stride;
    }
    /* Note: possible double to float conversion here */
    bb->lower.x = R2F_D(xl);
    bb->lower.y = R2F_D(yl);
    bb->lower.z = R2F_D(zl);
    bb->upper.x = R2F_U(xh);
    bb->upper.y = R2F_U(yh);
    bb->upper.z = R2F_U(zh);
}

/*! \brief Computes the bounding box for na packed coordinates, bb order xyz0 */
static void calc_bounding_box_x_x4(int na, const real *x,
                                   BoundingBox *bb)
{
    real xl, xh, yl, yh, zl, zh;

    xl = x[XX*c_packX4];
    xh = x[XX*c_packX4];
    yl = x[YY*c_packX4];
    yh = x[YY*c_packX4];
    zl = x[ZZ*c_packX4];
    zh = x[ZZ*c_packX4];
    for (int j = 1; j < na; j++)
    {
        xl = std::min(xl, x[j+XX*c_packX4]);
        xh = std::max(xh, x[j+XX*c_packX4]);
        yl = std::min(yl, x[j+YY*c_packX4]);
        yh = std::max(yh, x[j+YY*c_packX4]);
        zl = std::min(zl, x[j+ZZ*c_packX4]);
        zh = std::max(zh, x[j+ZZ*c_packX4]);
    }
    /* Note: possible double to float conversion here */
    bb->lower.x = R2F_D(xl);
    bb->lower.y = R2F_D(yl);
    bb->lower.z = R2F_D(zl);
    bb->upper.x = R2F_U(xh);
    bb->upper.y = R2F_U(yh);
    bb->upper.z = R2F_U(zh);
}

/*! \brief Computes the bounding box for na coordinates, bb order xyz0 */
static void calc_bounding_box_x_x8(int na, const real *x,
                                   BoundingBox *bb)
{
    real xl, xh, yl, yh, zl, zh;

    xl = x[XX*c_packX8];
    xh = x[XX*c_packX8];
    yl = x[YY*c_packX8];
    yh = x[YY*c_packX8];
    zl = x[ZZ*c_packX8];
    zh = x[ZZ*c_packX8];
    for (int j = 1; j < na; j++)
    {
        xl = std::min(xl, x[j+XX*c_packX8]);
        xh = std::max(xh, x[j+XX*c_packX8]);
        yl = std::min(yl, x[j+YY*c_packX8]);
        yh = std::max(yh, x[j+YY*c_packX8]);
        zl = std::min(zl, x[j+ZZ*c_packX8]);
        zh = std::max(zh, x[j+ZZ*c_packX8]);
    }
    /* Note: possible double to float conversion here */
    bb->lower.x = R2F_D(xl);
    bb->lower.y = R2F_D(yl);
    bb->lower.z = R2F_D(zl);
    bb->upper.x = R2F_U(xh);
    bb->upper.y = R2F_U(yh);
    bb->upper.z = R2F_U(zh);
}

/*! \brief Computes the bounding box for na packed coordinates, bb order xyz0 */
gmx_unused static void calc_bounding_box_x_x4_halves(int na, const real *x,
                                                     BoundingBox *bb,
                                                     BoundingBox *bbj)
{
    // TODO: During SIMDv2 transition only some archs use namespace (remove when done)
    using namespace gmx;

    calc_bounding_box_x_x4(std::min(na, 2), x, bbj);

    if (na > 2)
    {
        calc_bounding_box_x_x4(std::min(na-2, 2), x+(c_packX4>>1), bbj+1);
    }
    else
    {
        /* Set the "empty" bounding box to the same as the first one,
         * so we don't need to treat special cases in the rest of the code.
         */
#if NBNXN_SEARCH_BB_SIMD4
        store4(bbj[1].lower.ptr(), load4(bbj[0].lower.ptr()));
        store4(bbj[1].upper.ptr(), load4(bbj[0].upper.ptr()));
#else
        bbj[1] = bbj[0];
#endif
    }

#if NBNXN_SEARCH_BB_SIMD4
    store4(bb->lower.ptr(),
           min(load4(bbj[0].lower.ptr()), load4(bbj[1].lower.ptr())));
    store4(bb->upper.ptr(),
           max(load4(bbj[0].upper.ptr()), load4(bbj[1].upper.ptr())));
#else
    {
        bb->lower = BoundingBox::Corner::min(bbj[0].lower,
                                             bbj[1].lower);
        bb->upper = BoundingBox::Corner::max(bbj[0].upper,
                                             bbj[1].upper);
    }
#endif
}

#if NBNXN_BBXXXX

/*! \brief Computes the bounding box for na coordinates in order xyz, bb order xxxxyyyyzzzz */
static void calc_bounding_box_xxxx(int na, int stride, const real *x, float *bb)
{
    int  i;
    real xl, xh, yl, yh, zl, zh;

    i  = 0;
    xl = x[i+XX];
    xh = x[i+XX];
    yl = x[i+YY];
    yh = x[i+YY];
    zl = x[i+ZZ];
    zh = x[i+ZZ];
    i += stride;
    for (int j = 1; j < na; j++)
    {
        xl = std::min(xl, x[i+XX]);
        xh = std::max(xh, x[i+XX]);
        yl = std::min(yl, x[i+YY]);
        yh = std::max(yh, x[i+YY]);
        zl = std::min(zl, x[i+ZZ]);
        zh = std::max(zh, x[i+ZZ]);
        i += stride;
    }
    /* Note: possible double to float conversion here */
    bb[0*c_packedBoundingBoxesDimSize] = R2F_D(xl);
    bb[1*c_packedBoundingBoxesDimSize] = R2F_D(yl);
    bb[2*c_packedBoundingBoxesDimSize] = R2F_D(zl);
    bb[3*c_packedBoundingBoxesDimSize] = R2F_U(xh);
    bb[4*c_packedBoundingBoxesDimSize] = R2F_U(yh);
    bb[5*c_packedBoundingBoxesDimSize] = R2F_U(zh);
}

#endif /* NBNXN_BBXXXX */

#if NBNXN_SEARCH_SIMD4_FLOAT_X_BB

/*! \brief Computes the bounding box for na coordinates in order xyz?, bb order xyz0 */
static void calc_bounding_box_simd4(int na, const float *x,
                                    BoundingBox *bb)
{
    // TODO: During SIMDv2 transition only some archs use namespace (remove when done)
    using namespace gmx;

    static_assert(sizeof(BoundingBox::Corner) == GMX_SIMD4_WIDTH*sizeof(float),
                  "The Corner struct should hold exactly 4 floats");

    Simd4Float bb_0_S = load4(x);
    Simd4Float bb_1_S = bb_0_S;

    for (int i = 1; i < na; i++)
    {
        Simd4Float x_S = load4(x + i*GMX_SIMD4_WIDTH);
        bb_0_S         = min(bb_0_S, x_S);
        bb_1_S         = max(bb_1_S, x_S);
    }

    store4(bb->lower.ptr(), bb_0_S);
    store4(bb->upper.ptr(), bb_1_S);
}

#if NBNXN_BBXXXX

/*! \brief Computes the bounding box for na coordinates in order xyz?, bb order xxxxyyyyzzzz */
static void calc_bounding_box_xxxx_simd4(int na, const float *x,
                                         BoundingBox *bb_work_aligned,
                                         real *bb)
{
    calc_bounding_box_simd4(na, x, bb_work_aligned);

    bb[0*c_packedBoundingBoxesDimSize] = bb_work_aligned->lower.x;
    bb[1*c_packedBoundingBoxesDimSize] = bb_work_aligned->lower.y;
    bb[2*c_packedBoundingBoxesDimSize] = bb_work_aligned->lower.z;
    bb[3*c_packedBoundingBoxesDimSize] = bb_work_aligned->upper.x;
    bb[4*c_packedBoundingBoxesDimSize] = bb_work_aligned->upper.y;
    bb[5*c_packedBoundingBoxesDimSize] = bb_work_aligned->upper.z;
}

#endif /* NBNXN_BBXXXX */

#endif /* NBNXN_SEARCH_SIMD4_FLOAT_X_BB */


/*! \brief Combines pairs of consecutive bounding boxes */
static void combine_bounding_box_pairs(const Grid                       &grid,
                                       gmx::ArrayRef<const BoundingBox>  bb,
                                       gmx::ArrayRef<BoundingBox>        bbj)
{
    // TODO: During SIMDv2 transition only some archs use namespace (remove when done)
    using namespace gmx;

    for (int i = 0; i < grid.numColumns(); i++)
    {
        /* Starting bb in a column is expected to be 2-aligned */
        const int sc2 = grid.firstCellInColumn(i) >> 1;
        /* For odd numbers skip the last bb here */
        const int nc2 = (grid.numAtomsInColumn(i) + 3) >> (2 + 1);
        int       c2;
        for (c2 = sc2; c2 < sc2 + nc2; c2++)
        {
#if NBNXN_SEARCH_BB_SIMD4
            Simd4Float min_S, max_S;

            min_S = min(load4(bb[c2*2+0].lower.ptr()),
                        load4(bb[c2*2+1].lower.ptr()));
            max_S = max(load4(bb[c2*2+0].upper.ptr()),
                        load4(bb[c2*2+1].upper.ptr()));
            store4(bbj[c2].lower.ptr(), min_S);
            store4(bbj[c2].upper.ptr(), max_S);
#else
            bbj[c2].lower = BoundingBox::Corner::min(bb[c2*2 + 0].lower,
                                                     bb[c2*2 + 1].lower);
            bbj[c2].upper = BoundingBox::Corner::max(bb[c2*2 + 0].upper,
                                                     bb[c2*2 + 1].upper);
#endif
        }
        if (((grid.numAtomsInColumn(i) + 3) >> 2) & 1)
        {
            /* The bb count in this column is odd: duplicate the last bb */
            bbj[c2].lower = bb[c2*2].lower;
            bbj[c2].upper = bb[c2*2].upper;
        }
    }
}


/*! \brief Prints the average bb size, used for debug output */
static void print_bbsizes_simple(FILE       *fp,
                                 const Grid &grid)
{
    dvec ba = { 0 };
    for (int c = 0; c < grid.numCells(); c++)
    {
        const BoundingBox &bb = grid.iBoundingBoxes()[c];
        ba[XX] += bb.upper.x - bb.lower.x;
        ba[YY] += bb.upper.y - bb.lower.y;
        ba[ZZ] += bb.upper.z - bb.lower.z;
    }
    dsvmul(1.0/grid.numCells(), ba, ba);

    const Grid::Dimensions &dims         = grid.dimensions();
    real                    avgCellSizeZ = (dims.atomDensity > 0 ? grid.geometry().numAtomsICluster/(dims.atomDensity*dims.cellSize[XX]*dims.cellSize[YY]) : 0.0);

    fprintf(fp, "ns bb: grid %4.2f %4.2f %4.2f abs %4.2f %4.2f %4.2f rel %4.2f %4.2f %4.2f\n",
            dims.cellSize[XX],
            dims.cellSize[YY],
            avgCellSizeZ,
            ba[XX], ba[YY], ba[ZZ],
            ba[XX]*dims.invCellSize[XX],
            ba[YY]*dims.invCellSize[YY],
            dims.atomDensity > 0 ? ba[ZZ]/avgCellSizeZ : 0.0);
}

/*! \brief Prints the average bb size, used for debug output */
static void print_bbsizes_supersub(FILE       *fp,
                                   const Grid &grid)
{
    int  ns;
    dvec ba;

    clear_dvec(ba);
    ns = 0;
    for (int c = 0; c < grid.numCells(); c++)
    {
#if NBNXN_BBXXXX
        for (int s = 0; s < grid.numClustersPerCell()[c]; s += c_packedBoundingBoxesDimSize)
        {
            int  cs_w          = (c*c_gpuNumClusterPerCell + s)/c_packedBoundingBoxesDimSize;
            auto boundingBoxes = grid.packedBoundingBoxes().subArray(cs_w*c_packedBoundingBoxesSize, c_packedBoundingBoxesSize);
            for (int i = 0; i < c_packedBoundingBoxesDimSize; i++)
            {
                for (int d = 0; d < DIM; d++)
                {
                    ba[d] +=
                        boundingBoxes[(DIM + d)*c_packedBoundingBoxesDimSize + i] -
                        boundingBoxes[(0   + d)*c_packedBoundingBoxesDimSize + i];
                }
            }
        }
#else
        for (int s = 0; s < grid.numClustersPerCell()[c]; s++)
        {
            const BoundingBox &bb = grid.iBoundingBoxes()[c*c_gpuNumClusterPerCell + s];
            ba[XX] += bb.upper.x - bb.lower.x;
            ba[YY] += bb.upper.y - bb.lower.y;
            ba[ZZ] += bb.upper.z - bb.lower.z;
        }
#endif
        ns += grid.numClustersPerCell()[c];
    }
    dsvmul(1.0/ns, ba, ba);

    const Grid::Dimensions &dims            = grid.dimensions();
    const real              avgClusterSizeZ =
        (dims.atomDensity > 0 ? grid.geometry().numAtomsPerCell/(dims.atomDensity*dims.cellSize[XX]*dims.cellSize[YY]*c_gpuNumClusterPerCellZ) : 0.0);

    fprintf(fp, "ns bb: grid %4.2f %4.2f %4.2f abs %4.2f %4.2f %4.2f rel %4.2f %4.2f %4.2f\n",
            dims.cellSize[XX]/c_gpuNumClusterPerCellX,
            dims.cellSize[YY]/c_gpuNumClusterPerCellY,
            avgClusterSizeZ,
            ba[XX], ba[YY], ba[ZZ],
            ba[XX]*c_gpuNumClusterPerCellX*dims.invCellSize[XX],
            ba[YY]*c_gpuNumClusterPerCellY*dims.invCellSize[YY],
            dims.atomDensity > 0 ? ba[ZZ]/avgClusterSizeZ : 0.0);
}

/*!\brief Set non-bonded interaction flags for the current cluster.
 *
 * Sorts atoms on LJ coefficients: !=0 first, ==0 at the end.
 */
static void sort_cluster_on_flag(int                 numAtomsInCluster,
                                 int                 atomStart,
                                 int                 atomEnd,
                                 const int          *atinfo,
                                 gmx::ArrayRef<int>  order,
                                 int                *flags)
{
    constexpr int c_maxNumAtomsInCluster = 8;
    int           sort1[c_maxNumAtomsInCluster];
    int           sort2[c_maxNumAtomsInCluster];

    GMX_ASSERT(numAtomsInCluster <= c_maxNumAtomsInCluster, "Need to increase c_maxNumAtomsInCluster to support larger clusters");

    *flags = 0;

    int subc = 0;
    for (int s = atomStart; s < atomEnd; s += numAtomsInCluster)
    {
        /* Make lists for this (sub-)cell on atoms with and without LJ */
        int      n1         = 0;
        int      n2         = 0;
        gmx_bool haveQ      = FALSE;
        int      a_lj_max   = -1;
        for (int a = s; a < std::min(s + numAtomsInCluster, atomEnd); a++)
        {
            haveQ = haveQ || GET_CGINFO_HAS_Q(atinfo[order[a]]);

            if (GET_CGINFO_HAS_VDW(atinfo[order[a]]))
            {
                sort1[n1++] = order[a];
                a_lj_max    = a;
            }
            else
            {
                sort2[n2++] = order[a];
            }
        }

        /* If we don't have atoms with LJ, there's nothing to sort */
        if (n1 > 0)
        {
            *flags |= NBNXN_CI_DO_LJ(subc);

            if (2*n1 <= numAtomsInCluster)
            {
                /* Only sort when strictly necessary. Ordering particles
                 * Ordering particles can lead to less accurate summation
                 * due to rounding, both for LJ and Coulomb interactions.
                 */
                if (2*(a_lj_max - s) >= numAtomsInCluster)
                {
                    for (int i = 0; i < n1; i++)
                    {
                        order[atomStart + i]      = sort1[i];
                    }
                    for (int j = 0; j < n2; j++)
                    {
                        order[atomStart + n1 + j] = sort2[j];
                    }
                }

                *flags |= NBNXN_CI_HALF_LJ(subc);
            }
        }
        if (haveQ)
        {
            *flags |= NBNXN_CI_DO_COUL(subc);
        }
        subc++;
    }
}

/*! \brief Fill a pair search cell with atoms.
 *
 * Potentially sorts atoms and sets the interaction flags.
 */
void Grid::fillCell(const GridSetData              &gridSetData,
                    nbnxn_atomdata_t               *nbat,
                    int                             atomStart,
                    int                             atomEnd,
                    const int                      *atinfo,
                    gmx::ArrayRef<const gmx::RVec>  x,
                    BoundingBox gmx_unused         *bb_work_aligned)
{
    const int                 numAtoms = atomEnd - atomStart;

    const gmx::ArrayRef<int> &cells       = gridSetData.cells;
    const gmx::ArrayRef<int> &atomIndices = gridSetData.atomIndices;

    if (geometry_.isSimple)
    {
        /* Note that non-local grids are already sorted.
         * Then sort_cluster_on_flag will only set the flags and the sorting
         * will not affect the atom order.
         */
        sort_cluster_on_flag(geometry_.numAtomsICluster, atomStart, atomEnd, atinfo, atomIndices,
                             flags_.data() + atomToCluster(atomStart) - cellOffset_);
    }

    if (gridSetData.haveFep)
    {
        /* Set the fep flag for perturbed atoms in this (sub-)cell */

        /* The grid-local cluster/(sub-)cell index */
        int cell = atomToCluster(atomStart) - cellOffset_*(geometry_.isSimple ? 1 : c_gpuNumClusterPerCell);
        fep_[cell] = 0;
        for (int at = atomStart; at < atomEnd; at++)
        {
            if (atomIndices[at] >= 0 && GET_CGINFO_FEP(atinfo[atomIndices[at]]))
            {
                fep_[cell] |= (1 << (at - atomStart));
            }
        }
    }

    /* Now we have sorted the atoms, set the cell indices */
    for (int at = atomStart; at < atomEnd; at++)
    {
        cells[atomIndices[at]] = at;
    }

    copy_rvec_to_nbat_real(atomIndices.data() + atomStart, numAtoms, geometry_.numAtomsICluster,
                           as_rvec_array(x.data()),
                           nbat->XFormat, nbat->x().data(), atomStart);

    if (nbat->XFormat == nbatX4)
    {
        /* Store the bounding boxes as xyz.xyz. */
        size_t       offset = atomToCluster(atomStart - cellOffset_*geometry_.numAtomsICluster);
        BoundingBox *bb_ptr = bb_.data() + offset;

#if GMX_SIMD && GMX_SIMD_REAL_WIDTH == 2
        if (2*geometry_.numAtomsJCluster == geometry_.numAtomsICluster)
        {
            calc_bounding_box_x_x4_halves(numAtoms, nbat->x().data() + atom_to_x_index<c_packX4>(atomStart), bb_ptr,
                                          bbj_.data() + offset*2);
        }
        else
#endif
        {
            calc_bounding_box_x_x4(numAtoms, nbat->x().data() + atom_to_x_index<c_packX4>(atomStart), bb_ptr);
        }
    }
    else if (nbat->XFormat == nbatX8)
    {
        /* Store the bounding boxes as xyz.xyz. */
        size_t       offset = atomToCluster(atomStart - cellOffset_*geometry_.numAtomsICluster);
        BoundingBox *bb_ptr = bb_.data() + offset;

        calc_bounding_box_x_x8(numAtoms, nbat->x().data() + atom_to_x_index<c_packX8>(atomStart), bb_ptr);
    }
#if NBNXN_BBXXXX
    else if (!geometry_.isSimple)
    {
        /* Store the bounding boxes in a format convenient
         * for SIMD4 calculations: xxxxyyyyzzzz...
         */
        const int clusterIndex    = ((atomStart - cellOffset_*geometry_.numAtomsPerCell) >> geometry_.numAtomsICluster2Log);
        float    *pbb_ptr         =
            pbb_.data() +
            packedBoundingBoxesIndex(clusterIndex) +
            (clusterIndex & (c_packedBoundingBoxesDimSize - 1));

#if NBNXN_SEARCH_SIMD4_FLOAT_X_BB
        if (nbat->XFormat == nbatXYZQ)
        {
            calc_bounding_box_xxxx_simd4(numAtoms, nbat->x().data() + atomStart*nbat->xstride,
                                         bb_work_aligned, pbb_ptr);
        }
        else
#endif
        {
            calc_bounding_box_xxxx(numAtoms, nbat->xstride, nbat->x().data() + atomStart*nbat->xstride,
                                   pbb_ptr);
        }
        if (gmx_debug_at)
        {
            fprintf(debug, "cell %4d bb %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f\n",
                    atomToCluster(atomStart),
                    pbb_ptr[0*c_packedBoundingBoxesDimSize], pbb_ptr[3*c_packedBoundingBoxesDimSize],
                    pbb_ptr[1*c_packedBoundingBoxesDimSize], pbb_ptr[4*c_packedBoundingBoxesDimSize],
                    pbb_ptr[2*c_packedBoundingBoxesDimSize], pbb_ptr[5*c_packedBoundingBoxesDimSize]);
        }
    }
#endif
    else
    {
        /* Store the bounding boxes as xyz.xyz. */
        BoundingBox *bb_ptr = bb_.data() + atomToCluster(atomStart - cellOffset_*geometry_.numAtomsPerCell);

        calc_bounding_box(numAtoms, nbat->xstride, nbat->x().data() + atomStart*nbat->xstride,
                          bb_ptr);

        if (gmx_debug_at)
        {
            int bbo = atomToCluster(atomStart - cellOffset_*geometry_.numAtomsPerCell);
            fprintf(debug, "cell %4d bb %5.2f %5.2f %5.2f %5.2f %5.2f %5.2f\n",
                    atomToCluster(atomStart),
                    bb_[bbo].lower.x,
                    bb_[bbo].lower.y,
                    bb_[bbo].lower.z,
                    bb_[bbo].upper.x,
                    bb_[bbo].upper.y,
                    bb_[bbo].upper.z);
        }
    }
}

void Grid::sortColumnsCpuGeometry(const GridSetData &gridSetData,
                                  int dd_zone,
                                  int atomStart, int atomEnd,
                                  const int *atinfo,
                                  gmx::ArrayRef<const gmx::RVec> x,
                                  nbnxn_atomdata_t *nbat,
                                  int cxy_start, int cxy_end,
                                  gmx::ArrayRef<int> sort_work)
{
    if (debug)
    {
        fprintf(debug, "cell_offset %d sorting columns %d - %d, atoms %d - %d\n",
                cellOffset_, cxy_start, cxy_end, atomStart, atomEnd);
    }

    const bool relevantAtomsAreWithinGridBounds = (dimensions_.maxAtomGroupRadius == 0);

    const int  numAtomsPerCell = geometry_.numAtomsPerCell;

    /* Sort the atoms within each x,y column in 3 dimensions */
    for (int cxy = cxy_start; cxy < cxy_end; cxy++)
    {
        const int numAtoms   = numAtomsInColumn(cxy);
        const int numCellsZ  = cxy_ind_[cxy + 1] - cxy_ind_[cxy];
        const int atomOffset = firstAtomInColumn(cxy);

        /* Sort the atoms within each x,y column on z coordinate */
        sort_atoms(ZZ, FALSE, dd_zone,
                   relevantAtomsAreWithinGridBounds,
                   gridSetData.atomIndices.data() + atomOffset, numAtoms, x,
                   dimensions_.lowerCorner[ZZ],
                   1.0/dimensions_.gridSize[ZZ], numCellsZ*numAtomsPerCell,
                   sort_work);

        /* Fill the ncz cells in this column */
        const int firstCell  = firstCellInColumn(cxy);
        int       cellFilled = firstCell;
        for (int cellZ = 0; cellZ < numCellsZ; cellZ++)
        {
            const int cell           = firstCell + cellZ;

            const int atomOffsetCell = atomOffset + cellZ*numAtomsPerCell;
            const int numAtomsCell   = std::min(numAtomsPerCell, numAtoms - (atomOffsetCell - atomOffset));

            fillCell(gridSetData, nbat,
                     atomOffsetCell, atomOffsetCell + numAtomsCell, atinfo, x,
                     nullptr);

            /* This copy to bbcz is not really necessary.
             * But it allows to use the same grid search code
             * for the simple and supersub cell setups.
             */
            if (numAtomsCell > 0)
            {
                cellFilled = cell;
            }
            bbcz_[cell].lower = bb_[cellFilled].lower.z;
            bbcz_[cell].upper = bb_[cellFilled].upper.z;
        }

        /* Set the unused atom indices to -1 */
        for (int ind = numAtoms; ind < numCellsZ*numAtomsPerCell; ind++)
        {
            gridSetData.atomIndices[atomOffset + ind] = -1;
        }
    }
}

/* Spatially sort the atoms within one grid column */
void Grid::sortColumnsGpuGeometry(const GridSetData &gridSetData,
                                  int dd_zone,
                                  int atomStart, int atomEnd,
                                  const int *atinfo,
                                  gmx::ArrayRef<const gmx::RVec> x,
                                  nbnxn_atomdata_t *nbat,
                                  int cxy_start, int cxy_end,
                                  gmx::ArrayRef<int> sort_work)
{
    BoundingBox  bb_work_array[2];
    BoundingBox *bb_work_aligned = reinterpret_cast<BoundingBox *>((reinterpret_cast<std::size_t>(bb_work_array + 1)) & (~(static_cast<std::size_t>(15))));

    if (debug)
    {
        fprintf(debug, "cell_offset %d sorting columns %d - %d, atoms %d - %d\n",
                cellOffset_, cxy_start, cxy_end, atomStart, atomEnd);
    }

    const bool relevantAtomsAreWithinGridBounds = (dimensions_.maxAtomGroupRadius == 0);

    const int  numAtomsPerCell = geometry_.numAtomsPerCell;

    const int  subdiv_x = geometry_.numAtomsICluster;
    const int  subdiv_y = c_gpuNumClusterPerCellX*subdiv_x;
    const int  subdiv_z = c_gpuNumClusterPerCellY*subdiv_y;

    /* Extract the atom index array that will be filled here */
    const gmx::ArrayRef<int> &atomIndices = gridSetData.atomIndices;

    /* Sort the atoms within each x,y column in 3 dimensions.
     * Loop over all columns on the x/y grid.
     */
    for (int cxy = cxy_start; cxy < cxy_end; cxy++)
    {
        const int gridX            = cxy/dimensions_.numCells[YY];
        const int gridY            = cxy - gridX*dimensions_.numCells[YY];

        const int numAtomsInColumn = cxy_na_[cxy];
        const int numCellsInColumn = cxy_ind_[cxy + 1] - cxy_ind_[cxy];
        const int atomOffset       = firstAtomInColumn(cxy);

        /* Sort the atoms within each x,y column on z coordinate */
        sort_atoms(ZZ, FALSE, dd_zone,
                   relevantAtomsAreWithinGridBounds,
                   atomIndices.data() + atomOffset, numAtomsInColumn, x,
                   dimensions_.lowerCorner[ZZ],
                   1.0/dimensions_.gridSize[ZZ], numCellsInColumn*numAtomsPerCell,
                   sort_work);

        /* This loop goes over the cells and clusters along z at once */
        for (int sub_z = 0; sub_z < numCellsInColumn*c_gpuNumClusterPerCellZ; sub_z++)
        {
            const int atomOffsetZ = atomOffset + sub_z*subdiv_z;
            const int numAtomsZ   = std::min(subdiv_z, numAtomsInColumn - (atomOffsetZ - atomOffset));
            int       cz          = -1;
            /* We have already sorted on z */

            if (sub_z % c_gpuNumClusterPerCellZ == 0)
            {
                cz = sub_z/c_gpuNumClusterPerCellZ;
                const int cell = cxy_ind_[cxy] + cz;

                /* The number of atoms in this cell/super-cluster */
                const int numAtoms = std::min(numAtomsPerCell, numAtomsInColumn - (atomOffsetZ - atomOffset));

                numClusters_[cell] = std::min(c_gpuNumClusterPerCell,
                                              (numAtoms + geometry_.numAtomsICluster - 1)/ geometry_.numAtomsICluster);

                /* Store the z-boundaries of the bounding box of the cell */
                bbcz_[cell].lower = x[atomIndices[atomOffsetZ]][ZZ];
                bbcz_[cell].upper = x[atomIndices[atomOffsetZ + numAtoms - 1]][ZZ];
            }

            if (c_gpuNumClusterPerCellY > 1)
            {
                /* Sort the atoms along y */
                sort_atoms(YY, (sub_z & 1) != 0, dd_zone,
                           relevantAtomsAreWithinGridBounds,
                           atomIndices.data() + atomOffsetZ, numAtomsZ, x,
                           dimensions_.lowerCorner[YY] + gridY*dimensions_.cellSize[YY],
                           dimensions_.invCellSize[YY], subdiv_z,
                           sort_work);
            }

            for (int sub_y = 0; sub_y < c_gpuNumClusterPerCellY; sub_y++)
            {
                const int atomOffsetY = atomOffsetZ + sub_y*subdiv_y;
                const int numAtomsY   = std::min(subdiv_y, numAtomsInColumn - (atomOffsetY - atomOffset));

                if (c_gpuNumClusterPerCellX > 1)
                {
                    /* Sort the atoms along x */
                    sort_atoms(XX, ((cz*c_gpuNumClusterPerCellY + sub_y) & 1) != 0, dd_zone,
                               relevantAtomsAreWithinGridBounds,
                               atomIndices.data() + atomOffsetY, numAtomsY, x,
                               dimensions_.lowerCorner[XX] + gridX*dimensions_.cellSize[XX],
                               dimensions_.invCellSize[XX], subdiv_y,
                               sort_work);
                }

                for (int sub_x = 0; sub_x < c_gpuNumClusterPerCellX; sub_x++)
                {
                    const int atomOffsetX = atomOffsetY + sub_x*subdiv_x;
                    const int numAtomsX   = std::min(subdiv_x, numAtomsInColumn - (atomOffsetX - atomOffset));

                    fillCell(gridSetData, nbat,
                             atomOffsetX, atomOffsetX + numAtomsX, atinfo, x,
                             bb_work_aligned);
                }
            }
        }

        /* Set the unused atom indices to -1 */
        for (int ind = numAtomsInColumn; ind < numCellsInColumn*numAtomsPerCell; ind++)
        {
            atomIndices[atomOffset + ind] = -1;
        }
    }
}

/*! \brief Sets the cell index in the cell array for atom \p atomIndex and increments the atom count for the grid column */
static void setCellAndAtomCount(gmx::ArrayRef<int>  cell,
                                int                 cellIndex,
                                gmx::ArrayRef<int>  cxy_na,
                                int                 atomIndex)
{
    cell[atomIndex]    = cellIndex;
    cxy_na[cellIndex] += 1;
}

void Grid::calcColumnIndices(const Grid::Dimensions         &gridDims,
                             const gmx::UpdateGroupsCog     *updateGroupsCog,
                             const int                       atomStart,
                             const int                       atomEnd,
                             gmx::ArrayRef<const gmx::RVec>  x,
                             const int                       dd_zone,
                             const int                      *move,
                             const int                       thread,
                             const int                       nthread,
                             gmx::ArrayRef<int>              cell,
                             gmx::ArrayRef<int>              cxy_na)
{
    const int numColumns = gridDims.numCells[XX]*gridDims.numCells[YY];

    /* We add one extra cell for particles which moved during DD */
    for (int i = 0; i < numColumns; i++)
    {
        cxy_na[i] = 0;
    }

    int taskAtomStart = atomStart + static_cast<int>((thread + 0)*(atomEnd - atomStart))/nthread;
    int taskAtomEnd   = atomStart + static_cast<int>((thread + 1)*(atomEnd - atomStart))/nthread;

    if (dd_zone == 0)
    {
        /* Home zone */
        for (int i = taskAtomStart; i < taskAtomEnd; i++)
        {
            if (move == nullptr || move[i] >= 0)
            {

                const gmx::RVec &coord = (updateGroupsCog ? updateGroupsCog->cogForAtom(i) : x[i]);

                /* We need to be careful with rounding,
                 * particles might be a few bits outside the local zone.
                 * The int cast takes care of the lower bound,
                 * we will explicitly take care of the upper bound.
                 */
                int cx = static_cast<int>((coord[XX] - gridDims.lowerCorner[XX])*gridDims.invCellSize[XX]);
                int cy = static_cast<int>((coord[YY] - gridDims.lowerCorner[YY])*gridDims.invCellSize[YY]);

#ifndef NDEBUG
                if (cx < 0 || cx > gridDims.numCells[XX] ||
                    cy < 0 || cy > gridDims.numCells[YY])
                {
                    gmx_fatal(FARGS,
                              "grid cell cx %d cy %d out of range (max %d %d)\n"
                              "atom %f %f %f, grid->c0 %f %f",
                              cx, cy,
                              gridDims.numCells[XX],
                              gridDims.numCells[YY],
                              x[i][XX], x[i][YY], x[i][ZZ],
                              gridDims.lowerCorner[XX],
                              gridDims.lowerCorner[YY]);
                }
#endif
                /* Take care of potential rouding issues */
                cx = std::min(cx, gridDims.numCells[XX] - 1);
                cy = std::min(cy, gridDims.numCells[YY] - 1);

                /* For the moment cell will contain only the, grid local,
                 * x and y indices, not z.
                 */
                setCellAndAtomCount(cell, cx*gridDims.numCells[YY] + cy, cxy_na, i);
            }
            else
            {
                /* Put this moved particle after the end of the grid,
                 * so we can process it later without using conditionals.
                 */
                setCellAndAtomCount(cell, numColumns, cxy_na, i);
            }
        }
    }
    else
    {
        /* Non-home zone */
        for (int i = taskAtomStart; i < taskAtomEnd; i++)
        {
            int cx = static_cast<int>((x[i][XX] - gridDims.lowerCorner[XX])*gridDims.invCellSize[XX]);
            int cy = static_cast<int>((x[i][YY] - gridDims.lowerCorner[YY])*gridDims.invCellSize[YY]);

            /* For non-home zones there could be particles outside
             * the non-bonded cut-off range, which have been communicated
             * for bonded interactions only. For the result it doesn't
             * matter where these end up on the grid. For performance
             * we put them in an extra row at the border.
             */
            cx = std::max(cx, 0);
            cx = std::min(cx, gridDims.numCells[XX] - 1);
            cy = std::max(cy, 0);
            cy = std::min(cy, gridDims.numCells[YY] - 1);

            /* For the moment cell will contain only the, grid local,
             * x and y indices, not z.
             */
            setCellAndAtomCount(cell, cx*gridDims.numCells[YY] + cy, cxy_na, i);
        }
    }
}

/*! \brief Resizes grid and atom data which depend on the number of cells */
static void resizeForNumberOfCells(const int           numNbnxnAtoms,
                                   const int           numAtomsMoved,
                                   GridSetData        *gridSetData,
                                   nbnxn_atomdata_t   *nbat)
{
    /* Note: gridSetData->cellIndices was already resized before */

    /* To avoid conditionals we store the moved particles at the end of a,
     * make sure we have enough space.
     */
    gridSetData->atomIndices.resize(numNbnxnAtoms + numAtomsMoved);

    /* Make space in nbat for storing the atom coordinates */
    nbat->resizeCoordinateBuffer(numNbnxnAtoms);
}

void Grid::setCellIndices(int                             ddZone,
                          int                             cellOffset,
                          GridSetData                    *gridSetData,
                          gmx::ArrayRef<GridWork>         gridWork,
                          int                             atomStart,
                          int                             atomEnd,
                          const int                      *atinfo,
                          gmx::ArrayRef<const gmx::RVec>  x,
                          const int                       numAtomsMoved,
                          nbnxn_atomdata_t               *nbat)
{
    cellOffset_ = cellOffset;

    const int nthread = gmx_omp_nthreads_get(emntPairsearch);

    const int numAtomsPerCell = geometry_.numAtomsPerCell;

    /* Make the cell index as a function of x and y */
    int ncz_max      = 0;
    int ncz          = 0;
    cxy_ind_[0]      = 0;
    for (int i = 0; i < numColumns() + 1; i++)
    {
        /* We set ncz_max at the beginning of the loop iso at the end
         * to skip i=grid->ncx*grid->numCells[YY] which are moved particles
         * that do not need to be ordered on the grid.
         */
        if (ncz > ncz_max)
        {
            ncz_max = ncz;
        }
        int cxy_na_i = gridWork[0].numAtomsPerColumn[i];
        for (int thread = 1; thread < nthread; thread++)
        {
            cxy_na_i += gridWork[thread].numAtomsPerColumn[i];
        }
        ncz = (cxy_na_i + numAtomsPerCell - 1)/numAtomsPerCell;
        if (nbat->XFormat == nbatX8)
        {
            /* Make the number of cell a multiple of 2 */
            ncz = (ncz + 1) & ~1;
        }
        cxy_ind_[i+1] = cxy_ind_[i] + ncz;
        /* Clear cxy_na_, so we can reuse the array below */
        cxy_na_[i] = 0;
    }
    numCellsTotal_ = cxy_ind_[numColumns()] - cxy_ind_[0];

    /* Resize grid and atom data which depend on the number of cells */
    resizeForNumberOfCells(atomIndexEnd(), numAtomsMoved, gridSetData, nbat);

    if (debug)
    {
        fprintf(debug, "ns na_sc %d na_c %d super-cells: %d x %d y %d z %.1f maxz %d\n",
                numAtomsPerCell, geometry_.numAtomsICluster, numCellsTotal_,
                dimensions_.numCells[XX], dimensions_.numCells[YY],
                numCellsTotal_/(static_cast<double>(numColumns())),
                ncz_max);
        if (gmx_debug_at)
        {
            int i = 0;
            for (int cy = 0; cy < dimensions_.numCells[YY]; cy++)
            {
                for (int cx = 0; cx < dimensions_.numCells[XX]; cx++)
                {
                    fprintf(debug, " %2d", cxy_ind_[i + 1] - cxy_ind_[i]);
                    i++;
                }
                fprintf(debug, "\n");
            }
        }
    }

    /* Make sure the work array for sorting is large enough */
    const int worstCaseSortBufferSize = ncz_max*numAtomsPerCell*c_sortGridMaxSizeFactor;
    if (worstCaseSortBufferSize > gmx::index(gridWork[0].sortBuffer.size()))
    {
        for (GridWork &work : gridWork)
        {
            /* Elements not in use should be -1 */
            work.sortBuffer.resize(worstCaseSortBufferSize, -1);
        }
    }

    /* Now we know the dimensions we can fill the grid.
     * This is the first, unsorted fill. We sort the columns after this.
     */
    gmx::ArrayRef<int> cells       = gridSetData->cells;
    gmx::ArrayRef<int> atomIndices = gridSetData->atomIndices;
    for (int i = atomStart; i < atomEnd; i++)
    {
        /* At this point nbs->cell contains the local grid x,y indices */
        const int cxy = cells[i];
        atomIndices[firstAtomInColumn(cxy) + cxy_na_[cxy]++] = i;
    }

    if (ddZone == 0)
    {
        /* Set the cell indices for the moved particles */
        int n0 = numCellsTotal_*numAtomsPerCell;
        int n1 = numCellsTotal_*numAtomsPerCell + cxy_na_[numColumns()];
        if (ddZone == 0)
        {
            for (int i = n0; i < n1; i++)
            {
                cells[atomIndices[i]] = i;
            }
        }
    }

    /* Sort the super-cell columns along z into the sub-cells. */
#pragma omp parallel for num_threads(nthread) schedule(static)
    for (int thread = 0; thread < nthread; thread++)
    {
        try
        {
            int columnStart = ((thread + 0)*numColumns())/nthread;
            int columnEnd   = ((thread + 1)*numColumns())/nthread;
            if (geometry_.isSimple)
            {
                sortColumnsCpuGeometry(*gridSetData, ddZone,
                                       atomStart, atomEnd, atinfo, x, nbat,
                                       columnStart, columnEnd,
                                       gridWork[thread].sortBuffer);
            }
            else
            {
                sortColumnsGpuGeometry(*gridSetData, ddZone,
                                       atomStart, atomEnd, atinfo, x, nbat,
                                       columnStart, columnEnd,
                                       gridWork[thread].sortBuffer);
            }
        }
        GMX_CATCH_ALL_AND_EXIT_WITH_FATAL_ERROR;
    }

    if (geometry_.isSimple && nbat->XFormat == nbatX8)
    {
        combine_bounding_box_pairs(*this, bb_, bbj_);
    }

    if (!geometry_.isSimple)
    {
        numClustersTotal_ = 0;
        for (int i = 0; i < numCellsTotal_; i++)
        {
            numClustersTotal_ += numClusters_[i];
        }
    }

    if (debug)
    {
        if (geometry_.isSimple)
        {
            print_bbsizes_simple(debug, *this);
        }
        else
        {
            fprintf(debug, "ns non-zero sub-cells: %d average atoms %.2f\n",
                    numClustersTotal_,
                    (atomEnd - atomStart)/static_cast<double>(numClustersTotal_));

            print_bbsizes_supersub(debug, *this);
        }
    }
}

} // namespace Nbnxm