gpu.cpp

/* -------------------------------------------------------------------------- *
 *                                   OpenMM                                   *
 * -------------------------------------------------------------------------- *
 * This is part of the OpenMM molecular simulation toolkit originating from   *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org.               *
 *                                                                            *
 * Portions copyright (c) 2009 Stanford University and the Authors.           *
 * Authors: Scott Le Grand, Peter Eastman                                     *
 * Contributors:                                                              *
 *                                                                            *
 * This program 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 3 of the License, or       *
 * (at your option) any later version.                                        *
 *                                                                            *
 * This program is distributed in the hope that it will be useful,            *
 * but WITHOUT ANY WARRANTY; without even the implied warranty of             *
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the              *
 * GNU Lesser General Public License for more details.                        *
 *                                                                            *
 * You should have received a copy of the GNU Lesser General Public License   *
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.      *
 * -------------------------------------------------------------------------- */

#include <stdio.h>
#include <string.h>
#include <cuda.h>
#include <vector_functions.h>
#include <cstdlib>
#include <string>
#include <iostream>
#include <fstream>
#include <sstream>
#include <cmath>
#include <map>
#include <set>
#include <algorithm>
#ifdef WIN32
  #define _USE_MATH_DEFINES /* M_PI */
  #include <math.h>
  #include <windows.h>
#else
  #include <stdint.h>
#endif
using namespace std;

#include "gputypes.h"
#include "cudaKernels.h"
#include "hilbert.h"
#include "openmm/OpenMMException.h"
#include "quern.h"
#include "Lepton.h"

// In case we're using some primitive version of Visual Studio this will
// make sure that erf() and erfc() are defined.
#include "openmm/internal/MSVC_erfc.h"

using OpenMM::OpenMMException;
using Lepton::Operation;

struct ShakeCluster {
    int centralID;
    int peripheralID[3];
    int size;
    bool valid;
    float distance;
    float centralInvMass, peripheralInvMass;
    ShakeCluster() : valid(true) {
    }
    ShakeCluster(int centralID, float invMass) : centralID(centralID), centralInvMass(invMass), size(0), valid(true) {
    }
    void addAtom(int id, float dist, float invMass) {
        if (size == 3 || (size > 0 && dist != distance) || (size > 0 && invMass != peripheralInvMass))
            valid = false;
        else {
            peripheralID[size++] = id;
            distance = dist;
            peripheralInvMass = invMass;
        }
    }
};

struct Constraint
{
    Constraint(int atom1, int atom2, float distance2) : atom1(atom1), atom2(atom2), distance2(distance2) {
    }
    int atom1, atom2;
    float distance2;
};

struct ConstraintOrderer : public binary_function<int, int, bool> {
    const vector<int>& atom1;
    const vector<int>& atom2;
    ConstraintOrderer(const vector<int>& atom1, const vector<int>& atom2) : atom1(atom1), atom2(atom2) {
    }
    bool operator()(int x, int y) {
        if (atom1[x] != atom1[y])
            return atom1[x] < atom1[y];
        return atom2[x] < atom2[y];
    }
};

struct Molecule {
    vector<int> atoms;
    vector<int> bonds;
    vector<int> angles;
    vector<int> periodicTorsions;
    vector<int> rbTorsions;
    vector<int> constraints;
    vector<int> lj14s;
};

static const float dielectricOffset         =    0.009f;
static const float probeRadius              =    0.14f;
static const float forceConversionFactor    =    0.4184f;

//static const float surfaceAreaFactor        =   -6.0f * 0.06786f * forceConversionFactor * 1000.0f;  // PI * 4.0f * 0.0049f * 1000.0f;
//static const float surfaceAreaFactor        =   -6.0f * PI * 4.0f * 0.0049f * 1000.0f;
static const float surfaceAreaFactor        = -6.0f*PI*0.0216f*1000.0f*0.4184f;
//static const float surfaceAreaFactor        = -1.7035573959e+001;
//static const float surfaceAreaFactor        = -166.02691f;
//static const float surfaceAreaFactor        = 1.0f;

static const float alphaOBC                 =    1.0f;
static const float betaOBC                  =    0.8f;
static const float gammaOBC                 =    4.85f;
static const float kcalMolTokJNM            =   -0.4184f;
static const float electricConstant         = -166.02691f;
static const float defaultInnerDielectric   =    1.0f;
static const float defaultSolventDielectric =   78.3f;
static const float KILO                     =    1e3;                      // Thousand
static const float BOLTZMANN                =    1.380658e-23f;            // (J/K)    
static const float AVOGADRO                 =    6.0221367e23f;            // ()        
static const float RGAS                     =    BOLTZMANN * AVOGADRO;     // (J/(mol K))
static const float BOLTZ                    =    (RGAS / KILO);            // (kJ/(mol K)) 

#define DUMP_PARAMETERS 0

template <int SIZE>
static Expression<SIZE> createExpression(gpuContext gpu, const string& expression, const Lepton::ExpressionProgram& program, const vector<string>& variables,
        const vector<string>& globalParamNames, unsigned int& maxStackSize) {
    Expression<SIZE> exp;
    if (program.getNumOperations() > SIZE)
        throw OpenMMException("Expression contains too many operations: "+expression);
    exp.length = program.getNumOperations();
    exp.stackSize = program.getStackSize();
    if (exp.stackSize > maxStackSize)
        maxStackSize = exp.stackSize;
    for (int i = 0; i < program.getNumOperations(); i++) {
        const Operation& op = program.getOperation(i);
        switch (op.getId()) {
            case Operation::CONSTANT:
                exp.op[i] = CONSTANT;
                exp.arg[i] = dynamic_cast<const Operation::Constant*>(&op)->getValue();
                break;
            case Operation::VARIABLE:
                if (variables.size() > 0 && op.getName() == variables[0])
                    exp.op[i] = VARIABLE0;
                else if (variables.size() > 1 && op.getName() == variables[1])
                    exp.op[i] = VARIABLE1;
                else if (variables.size() > 2 && op.getName() == variables[2])
                    exp.op[i] = VARIABLE2;
                else if (variables.size() > 3 && op.getName() == variables[3])
                    exp.op[i] = VARIABLE3;
                else if (variables.size() > 4 && op.getName() == variables[4])
                    exp.op[i] = VARIABLE4;
                else if (variables.size() > 5 && op.getName() == variables[5])
                    exp.op[i] = VARIABLE5;
                else if (variables.size() > 6 && op.getName() == variables[6])
                    exp.op[i] = VARIABLE6;
                else if (variables.size() > 7 && op.getName() == variables[7])
                    exp.op[i] = VARIABLE7;
                else {
                    int j;
                    for (j = 0; j < globalParamNames.size() && op.getName() != globalParamNames[j]; j++);
                    if (j == globalParamNames.size())
                        throw OpenMMException("Unknown variable '"+op.getName()+"' in expression: "+expression);
                    exp.op[i] = GLOBAL;
                    exp.arg[i] = j;
                }
                break;
            case Operation::CUSTOM:
                exp.op[i] = dynamic_cast<const Operation::Custom*>(&op)->getDerivOrder()[0] == 0 ? CUSTOM : CUSTOM_DERIV;
                for (int j = 0; j < MAX_TABULATED_FUNCTIONS; j++)
                    if (op.getName() == gpu->tabulatedFunctions[j].name) {
                        exp.arg[i] = j;
                        break;
                    }
                break;
            case Operation::ADD:
                exp.op[i] = ADD;
                break;
            case Operation::SUBTRACT:
                exp.op[i] = SUBTRACT;
                break;
            case Operation::MULTIPLY:
                exp.op[i] = MULTIPLY;
                break;
            case Operation::DIVIDE:
                exp.op[i] = DIVIDE;
                break;
            case Operation::POWER:
                exp.op[i] = POWER;
                break;
            case Operation::NEGATE:
                exp.op[i] = NEGATE;
                break;
            case Operation::SQRT:
                exp.op[i] = SQRT;
                break;
            case Operation::EXP:
                exp.op[i] = EXP;
                break;
            case Operation::LOG:
                exp.op[i] = LOG;
                break;
            case Operation::SIN:
                exp.op[i] = SIN;
                break;
            case Operation::COS:
                exp.op[i] = COS;
                break;
            case Operation::SEC:
                exp.op[i] = SEC;
                break;
            case Operation::CSC:
                exp.op[i] = CSC;
                break;
            case Operation::TAN:
                exp.op[i] = TAN;
                break;
            case Operation::COT:
                exp.op[i] = COT;
                break;
            case Operation::ASIN:
                exp.op[i] = ASIN;
                break;
            case Operation::ACOS:
                exp.op[i] = ACOS;
                break;
            case Operation::ATAN:
                exp.op[i] = ATAN;
                break;
            case Operation::SINH:
                exp.op[i] = SINH;
                break;
            case Operation::COSH:
                exp.op[i] = COSH;
                break;
            case Operation::TANH:
                exp.op[i] = TANH;
                break;
            case Operation::SQUARE:
                exp.op[i] = SQUARE;
                break;
            case Operation::CUBE:
                exp.op[i] = CUBE;
                break;
            case Operation::RECIPROCAL:
                exp.op[i] = RECIPROCAL;
                break;
            case Operation::ADD_CONSTANT:
                exp.op[i] = ADD_CONSTANT;
                exp.arg[i] = dynamic_cast<const Operation::AddConstant*>(&op)->getValue();
                break;
            case Operation::MULTIPLY_CONSTANT:
                exp.op[i] = MULTIPLY_CONSTANT;
                exp.arg[i] = dynamic_cast<const Operation::MultiplyConstant*>(&op)->getValue();
                break;
            case Operation::POWER_CONSTANT:
                exp.op[i] = POWER_CONSTANT;
                exp.arg[i] = dynamic_cast<const Operation::PowerConstant*>(&op)->getValue();
                break;
        }
    }
    return exp;
}

extern "C"
void gpuSetBondParameters(gpuContext gpu, const vector<int>& atom1, const vector<int>& atom2, const vector<float>& length, const vector<float>& k)
{
    int bonds = atom1.size();
    gpu->sim.bonds                              = bonds;
    CUDAStream<int4>* psBondID                  = new CUDAStream<int4>(bonds, 1, "BondID");
    gpu->psBondID                               = psBondID;
    gpu->sim.pBondID                            = psBondID->_pDevStream[0];
    CUDAStream<float2>* psBondParameter         = new CUDAStream<float2>(bonds, 1, "BondParameter");
    gpu->psBondParameter                        = psBondParameter;
    gpu->sim.pBondParameter                     = psBondParameter->_pDevStream[0];
    for (int i = 0; i < bonds; i++)
    {
        (*psBondID)[i].x = atom1[i];
        (*psBondID)[i].y = atom2[i];
        (*psBondParameter)[i].x = length[i];
        (*psBondParameter)[i].y = k[i];
        psBondID->_pSysData[i].z = gpu->pOutputBufferCounter[psBondID->_pSysData[i].x]++;
        psBondID->_pSysData[i].w = gpu->pOutputBufferCounter[psBondID->_pSysData[i].y]++;
#if (DUMP_PARAMETERS == 1)                
        cout << 
            i << " " << 
            (*psBondID)[i].x << " " <<
            (*psBondID)[i].y << " " <<
            (*psBondID)[i].z << " " <<
            (*psBondID)[i].w << " " <<
            (*psBondParameter)[i].x << " " <<
            (*psBondParameter)[i].y <<
            endl;
#endif
    }
    psBondID->Upload();
    psBondParameter->Upload();
}

extern "C"
void gpuSetBondAngleParameters(gpuContext gpu, const vector<int>& atom1, const vector<int>& atom2, const vector<int>& atom3,
        const vector<float>& angle, const vector<float>& k)
{
    int bond_angles = atom1.size();
    gpu->sim.bond_angles                        = bond_angles;
    CUDAStream<int4>* psBondAngleID1            = new CUDAStream<int4>(bond_angles, 1, "BondAngleID1");
    gpu->psBondAngleID1                         = psBondAngleID1;
    gpu->sim.pBondAngleID1                      = psBondAngleID1->_pDevStream[0];
    CUDAStream<int2>* psBondAngleID2            = new CUDAStream<int2>(bond_angles, 1, "BondAngleID2");
    gpu->psBondAngleID2                         = psBondAngleID2;
    gpu->sim.pBondAngleID2                      = psBondAngleID2->_pDevStream[0];
    CUDAStream<float2>* psBondAngleParameter    = new CUDAStream<float2>(bond_angles, 1, "BondAngleParameter");
    gpu->psBondAngleParameter                   = psBondAngleParameter;
    gpu->sim.pBondAngleParameter                = psBondAngleParameter->_pDevStream[0];        

    for (int i = 0; i < bond_angles; i++)
    {
        (*psBondAngleID1)[i].x = atom1[i];
        (*psBondAngleID1)[i].y = atom2[i];
        (*psBondAngleID1)[i].z = atom3[i];
        (*psBondAngleParameter)[i].x = angle[i];
        (*psBondAngleParameter)[i].y = k[i];
        psBondAngleID1->_pSysData[i].w = gpu->pOutputBufferCounter[psBondAngleID1->_pSysData[i].x]++;
        psBondAngleID2->_pSysData[i].x = gpu->pOutputBufferCounter[psBondAngleID1->_pSysData[i].y]++;
        psBondAngleID2->_pSysData[i].y = gpu->pOutputBufferCounter[psBondAngleID1->_pSysData[i].z]++;
#if (DUMP_PARAMETERS == 1)
         cout << 
            i << " " << 
            (*psBondAngleID1)[i].x << " " <<
            (*psBondAngleID1)[i].y << " " <<
            (*psBondAngleID1)[i].z << " " <<
            (*psBondAngleID1)[i].w << " " <<
            (*psBondAngleID2)[i].x << " " <<
            (*psBondAngleID2)[i].y << " " <<
            (*psBondAngleParameter)[i].x << " " <<
            (*psBondAngleParameter)[i].y <<
            endl;
#endif
    }
    psBondAngleID1->Upload();
    psBondAngleID2->Upload();
    psBondAngleParameter->Upload();
}

extern "C"
void gpuSetDihedralParameters(gpuContext gpu, const vector<int>& atom1, const vector<int>& atom2, const vector<int>& atom3, const vector<int>& atom4,
        const vector<float>& k, const vector<float>& phase, const vector<int>& periodicity)
{
        int dihedrals = atom1.size();
        gpu->sim.dihedrals = dihedrals;
        CUDAStream<int4>* psDihedralID1             = new CUDAStream<int4>(dihedrals, 1, "DihedralID1");
        gpu->psDihedralID1                          = psDihedralID1;
        gpu->sim.pDihedralID1                       = psDihedralID1->_pDevStream[0];
        CUDAStream<int4>* psDihedralID2             = new CUDAStream<int4>(dihedrals, 1, "DihedralID2");
        gpu->psDihedralID2                          = psDihedralID2;
        gpu->sim.pDihedralID2                       = psDihedralID2->_pDevStream[0];
        CUDAStream<float4>* psDihedralParameter     = new CUDAStream<float4>(dihedrals, 1, "DihedralParameter");
        gpu->psDihedralParameter                    = psDihedralParameter;
        gpu->sim.pDihedralParameter                 = psDihedralParameter->_pDevStream[0];
        for (int i = 0; i < dihedrals; i++)
        {
            (*psDihedralID1)[i].x = atom1[i];
            (*psDihedralID1)[i].y = atom2[i];
            (*psDihedralID1)[i].z = atom3[i];
            (*psDihedralID1)[i].w = atom4[i];
            (*psDihedralParameter)[i].x = k[i];
            (*psDihedralParameter)[i].y = phase[i];
            (*psDihedralParameter)[i].z = (float) periodicity[i];
            psDihedralID2->_pSysData[i].x = gpu->pOutputBufferCounter[psDihedralID1->_pSysData[i].x]++;
            psDihedralID2->_pSysData[i].y = gpu->pOutputBufferCounter[psDihedralID1->_pSysData[i].y]++;
            psDihedralID2->_pSysData[i].z = gpu->pOutputBufferCounter[psDihedralID1->_pSysData[i].z]++;
            psDihedralID2->_pSysData[i].w = gpu->pOutputBufferCounter[psDihedralID1->_pSysData[i].w]++;
#if (DUMP_PARAMETERS == 1)
            cout << 
                i << " " << 
                (*psDihedralID1)[i].x << " " <<
                (*psDihedralID1)[i].y << " " <<
                (*psDihedralID1)[i].z << " " <<
                (*psDihedralID1)[i].w << " " <<
                (*psDihedralID2)[i].x << " " <<
                (*psDihedralID2)[i].y << " " <<
                (*psDihedralID2)[i].z << " " <<
                (*psDihedralID2)[i].w << " " <<
                (*psDihedralParameter)[i].x << " " <<
                (*psDihedralParameter)[i].y << " " <<
                (*psDihedralParameter)[i].z << endl;
#endif
        }
        psDihedralID1->Upload();
        psDihedralID2->Upload();
        psDihedralParameter->Upload();
}

extern "C"
void gpuSetRbDihedralParameters(gpuContext gpu, const vector<int>& atom1, const vector<int>& atom2, const vector<int>& atom3, const vector<int>& atom4,
        const vector<float>& c0, const vector<float>& c1, const vector<float>& c2, const vector<float>& c3, const vector<float>& c4, const vector<float>& c5)
{
    int rb_dihedrals = atom1.size();
    gpu->sim.rb_dihedrals = rb_dihedrals;
    CUDAStream<int4>* psRbDihedralID1           = new CUDAStream<int4>(rb_dihedrals, 1, "RbDihedralID1");
    gpu->psRbDihedralID1                        = psRbDihedralID1;
    gpu->sim.pRbDihedralID1                     = psRbDihedralID1->_pDevStream[0];
    CUDAStream<int4>* psRbDihedralID2           = new CUDAStream<int4>(rb_dihedrals, 1, "RbDihedralID2");
    gpu->psRbDihedralID2                        = psRbDihedralID2;
    gpu->sim.pRbDihedralID2                     = psRbDihedralID2->_pDevStream[0];
    CUDAStream<float4>* psRbDihedralParameter1  = new CUDAStream<float4>(rb_dihedrals, 1, "RbDihedralParameter1");
    gpu->psRbDihedralParameter1                 = psRbDihedralParameter1;
    gpu->sim.pRbDihedralParameter1              = psRbDihedralParameter1->_pDevStream[0];
    CUDAStream<float2>* psRbDihedralParameter2  = new CUDAStream<float2>(rb_dihedrals, 1, "RbDihedralParameter2");
    gpu->psRbDihedralParameter2                 = psRbDihedralParameter2;
    gpu->sim.pRbDihedralParameter2              = psRbDihedralParameter2->_pDevStream[0];

    for (int i = 0; i < rb_dihedrals; i++)
    {
        (*psRbDihedralID1)[i].x = atom1[i];
        (*psRbDihedralID1)[i].y = atom2[i];
        (*psRbDihedralID1)[i].z = atom3[i];
        (*psRbDihedralID1)[i].w = atom4[i];
        (*psRbDihedralParameter1)[i].x = c0[i];
        (*psRbDihedralParameter1)[i].y = c1[i];
        (*psRbDihedralParameter1)[i].z = c2[i];
        (*psRbDihedralParameter1)[i].w = c3[i];
        (*psRbDihedralParameter2)[i].x = c4[i];
        (*psRbDihedralParameter2)[i].y = c5[i];
        psRbDihedralID2->_pSysData[i].x = gpu->pOutputBufferCounter[psRbDihedralID1->_pSysData[i].x]++;
        psRbDihedralID2->_pSysData[i].y = gpu->pOutputBufferCounter[psRbDihedralID1->_pSysData[i].y]++;
        psRbDihedralID2->_pSysData[i].z = gpu->pOutputBufferCounter[psRbDihedralID1->_pSysData[i].z]++;
        psRbDihedralID2->_pSysData[i].w = gpu->pOutputBufferCounter[psRbDihedralID1->_pSysData[i].w]++;
#if (DUMP_PARAMETERS == 1)
        cout << 
            i << " " << 
            (*psRbDihedralID1)[i].x << " " <<
            (*psRbDihedralID1)[i].y << " " <<
            (*psRbDihedralID1)[i].z << " " <<
            (*psRbDihedralID1)[i].w <<" " <<
            (*psRbDihedralID2)[i].x << " " <<
            (*psRbDihedralID2)[i].y << " " <<
            (*psRbDihedralID2)[i].z << " " <<
            (*psRbDihedralID2)[i].w <<" " <<
            (*psRbDihedralParameter1)[i].x << " " <<
            (*psRbDihedralParameter1)[i].y << " " <<
            (*psRbDihedralParameter1)[i].z << " " <<
            (*psRbDihedralParameter1)[i].w << " " <<
            (*psRbDihedralParameter2)[i].x << " " <<
            (*psRbDihedralParameter2)[i].y <<
            endl;
#endif
    }
    psRbDihedralID1->Upload();
    psRbDihedralID2->Upload();
    psRbDihedralParameter1->Upload();
    psRbDihedralParameter2->Upload();
}

extern "C"
void gpuSetLJ14Parameters(gpuContext gpu, float epsfac, float fudge, const vector<int>& atom1, const vector<int>& atom2,
        const vector<float>& c6, const vector<float>& c12, const vector<float>& q1, const vector<float>& q2)
{
    int LJ14s = atom1.size();
    float scale = epsfac * fudge;

    gpu->sim.LJ14s                              = LJ14s;
    CUDAStream<int4>* psLJ14ID                  = new CUDAStream<int4>(LJ14s, 1, "LJ14ID");
    gpu->psLJ14ID                               = psLJ14ID;
    gpu->sim.pLJ14ID                            = psLJ14ID->_pDevStream[0];
    CUDAStream<float4>* psLJ14Parameter         = new CUDAStream<float4>(LJ14s, 1, "LJ14Parameter");
    gpu->psLJ14Parameter                        = psLJ14Parameter;
    gpu->sim.pLJ14Parameter                     = psLJ14Parameter->_pDevStream[0];

    for (int i = 0; i < LJ14s; i++)
    {
        (*psLJ14ID)[i].x = atom1[i];
        (*psLJ14ID)[i].y = atom2[i];
        psLJ14ID->_pSysData[i].z = gpu->pOutputBufferCounter[psLJ14ID->_pSysData[i].x]++;
        psLJ14ID->_pSysData[i].w = gpu->pOutputBufferCounter[psLJ14ID->_pSysData[i].y]++;
        float p0, p1, p2;
        if (c12[i] == 0.0f)
        {
            p0 = 0.0f;
            p1 = 1.0f;
        }
        else
        {
            p0 = c6[i] * c6[i] / c12[i];
            p1 = pow(c12[i] / c6[i], 1.0f / 6.0f);
        }
        p2 = scale * q1[i] * q2[i];
        (*psLJ14Parameter)[i].x = p0;
        (*psLJ14Parameter)[i].y = p1;
        (*psLJ14Parameter)[i].z = p2;
    }
#if (DUMP_PARAMETERS == 1)
        cout << 
            i << " " <<
            (*psLJ14ID)[i].x << " " <<
            (*psLJ14ID)[i].y << " " <<
            (*psLJ14ID)[i].z << " " <<
            (*psLJ14ID)[i].w << " " <<
            (*psLJ14Parameter)[i].x << " " <<
            (*psLJ14Parameter)[i].y << " " <<
            (*psLJ14Parameter)[i].z << " " <<
            p0 << " " << 
            p1 << " " << 
            p2 << " " << 
            endl;
#endif
    psLJ14ID->Upload();
    psLJ14Parameter->Upload();
}

static void setExclusions(gpuContext gpu, const vector<vector<int> >& exclusions) {
    if (gpu->exclusions.size() > 0) {
        bool ok = (exclusions.size() == gpu->exclusions.size());
        for (int i = 0; i < exclusions.size() && ok; i++) {
            if (exclusions[i].size() != gpu->exclusions[i].size())
                ok = false;
            else {
                for (int j = 0; j < exclusions[i].size(); j++)
                    if (find(gpu->exclusions[i].begin(), gpu->exclusions[i].end(), exclusions[i][j]) == gpu->exclusions[i].end())
                        ok = false;
            }
        }
        if (!ok)
            throw OpenMMException("All nonbonded forces must have identical sets of exceptions");
    }
    gpu->exclusions = exclusions;
}

extern "C"
void gpuSetCoulombParameters(gpuContext gpu, float epsfac, const vector<int>& atom, const vector<float>& c6, const vector<float>& c12, const vector<float>& q,
        const vector<char>& symbol, const vector<vector<int> >& exclusions, CudaNonbondedMethod method)
{
    unsigned int coulombs = c6.size();
    gpu->sim.epsfac = epsfac;
    gpu->sim.nonbondedMethod = method;
    if (coulombs > 0)
        setExclusions(gpu, exclusions);
    
    for (unsigned int i = 0; i < coulombs; i++)
    {
            float p0 = q[i];
            float p1 = 0.5f, p2 = 0.0f;               
            if ((c6[i] > 0.0f) && (c12[i] > 0.0f))
            {
                p1 = 0.5f * pow(c12[i] / c6[i], 1.0f / 6.0f);
                p2 = c6[i] * sqrt(1.0f / c12[i]);
            }
            if (symbol.size() > 0)
                gpu->pAtomSymbol[i] = symbol[i];
            (*gpu->psPosq4)[i].w = p0;
            (*gpu->psSigEps2)[i].x = p1;
            (*gpu->psSigEps2)[i].y = p2;
    }

    // Dummy out extra atom data
    for (unsigned int i = coulombs; i < gpu->sim.paddedNumberOfAtoms; i++)
    {
        (*gpu->psPosq4)[i].x       = 100000.0f + i * 10.0f;
        (*gpu->psPosq4)[i].y       = 100000.0f + i * 10.0f;
        (*gpu->psPosq4)[i].z       = 100000.0f + i * 10.0f;
        (*gpu->psPosq4)[i].w       = 0.0f;
        (*gpu->psSigEps2)[i].x     = 0.0f;
        (*gpu->psSigEps2)[i].y     = 0.0f;
    }

    gpu->psPosq4->Upload();
    gpu->psSigEps2->Upload();
}

extern "C"
void gpuSetNonbondedCutoff(gpuContext gpu, float cutoffDistance, float solventDielectric)
{
    if (gpu->sim.nonbondedCutoff != 0.0f && gpu->sim.nonbondedCutoff != cutoffDistance)
        throw OpenMMException("All nonbonded forces must use the same cutoff");
    gpu->sim.nonbondedCutoff = cutoffDistance;
    gpu->sim.nonbondedCutoffSqr = cutoffDistance*cutoffDistance;
    gpu->sim.reactionFieldK = pow(cutoffDistance, -3.0f)*(solventDielectric-1.0f)/(2.0f*solventDielectric+1.0f);
    gpu->sim.reactionFieldC = (1.0f / cutoffDistance)*(3.0f*solventDielectric)/(2.0f*solventDielectric+1.0f);
}

extern "C"
void gpuSetTabulatedFunction(gpuContext gpu, int index, const string& name, const vector<double>& values, double min, double max, bool interpolating)
{
    if (index < 0 || index >= MAX_TABULATED_FUNCTIONS) {
        stringstream str;
        str << "Only " << MAX_TABULATED_FUNCTIONS << " tabulated functions are supported";
        throw OpenMMException(str.str());
    }
    if (gpu->tabulatedFunctions[index].coefficients != NULL)
        delete gpu->tabulatedFunctions[index].coefficients;
    CUDAStream<float4>* coeff = new CUDAStream<float4>((int) values.size()-1, 1, "TabulatedFunction");
    gpu->tabulatedFunctions[index].coefficients = coeff;
    gpu->sim.pTabulatedFunctionCoefficients[index] = coeff->_pDevData;
    gpu->tabulatedFunctions[index].name = name;
    gpu->tabulatedFunctions[index].min = min;
    gpu->tabulatedFunctions[index].max = max;
    gpu->tabulatedFunctionsChanged = true;

    // First create a padded set of function values.

    vector<double> padded(values.size()+2);
    padded[0] = 2*values[0]-values[1];
    for (int i = 0; i < (int) values.size(); i++)
        padded[i+1] = values[i];
    padded[padded.size()-1] = 2*values[values.size()-1]-values[values.size()-2];

    // Now compute the spline coefficients.

    for (int i = 0; i < (int) values.size()-1; i++) {
        float4 c;
        if (interpolating) {
            c.x = padded[i+1];
            c.y = 0.5*(-padded[i]+padded[i+2]);
            c.z = 0.5*(2.0*padded[i]-5.0*padded[i+1]+4.0*padded[i+2]-padded[i+3]);
            c.w = 0.5*(-padded[i]+3.0*padded[i+1]-3.0*padded[i+2]+padded[i+3]);
        }
        else {
            c.x = (padded[i]+4.0*padded[i+1]+padded[i+2])/6.0;
            c.y = (-3.0*padded[i]+3.0*padded[i+2])/6.0;
            c.z = (3.0*padded[i]-6.0*padded[i+1]+3.0*padded[i+2])/6.0;
            c.w = (-padded[i]+3.0*padded[i+1]-3.0*padded[i+2]+padded[i+3])/6.0;
        }
        (*coeff)[i] = c;
    }
    coeff->Upload();
}

extern "C"
void gpuSetCustomNonbondedParameters(gpuContext gpu, const vector<vector<double> >& parameters, const vector<vector<int> >& exclusions,
            const vector<int>& exceptionAtom1, const vector<int>& exceptionAtom2, const vector<vector<double> >& exceptionParams,
            CudaNonbondedMethod method, float cutoffDistance, const string& energyExp, const vector<string>& combiningRules,
            const vector<string>& paramNames, const vector<string>& globalParamNames)
{
    if (gpu->sim.nonbondedCutoff != 0.0f && gpu->sim.nonbondedCutoff != cutoffDistance)
        throw OpenMMException("All nonbonded forces must use the same cutoff");
    if (paramNames.size() > 4)
        throw OpenMMException("CudaPlatform only supports four per-atom parameters for custom nonbonded forces");
    if (globalParamNames.size() > 8)
        throw OpenMMException("CudaPlatform only supports eight global parameters for custom nonbonded forces");
    gpu->sim.nonbondedCutoff = cutoffDistance;
    gpu->sim.nonbondedCutoffSqr = cutoffDistance*cutoffDistance;
    gpu->sim.customNonbondedMethod = method;
    gpu->sim.customExceptions = exceptionAtom1.size();
    gpu->sim.customParameters = paramNames.size();
    gpu->sim.custom_exception_threads_per_block = (gpu->sim.customExceptions+gpu->sim.blocks-1)/gpu->sim.blocks;
    if (gpu->sim.custom_exception_threads_per_block < 1)
        gpu->sim.custom_exception_threads_per_block = 1;
    if (gpu->sim.custom_exception_threads_per_block > gpu->sim.max_localForces_threads_per_block)
        gpu->sim.custom_exception_threads_per_block = gpu->sim.max_localForces_threads_per_block;
    setExclusions(gpu, exclusions);
    gpu->psCustomParams = new CUDAStream<float4>(gpu->sim.paddedNumberOfAtoms, 1, "CustomParams");
    gpu->sim.pCustomParams = gpu->psCustomParams->_pDevData;
    gpu->psCustomExceptionID = new CUDAStream<int4>(gpu->sim.customExceptions, 1, "CustomExceptionId");
    gpu->sim.pCustomExceptionID = gpu->psCustomExceptionID->_pDevData;
    gpu->psCustomExceptionParams = new CUDAStream<float4>(gpu->sim.customExceptions, 1, "CustomExceptionParams");
    gpu->sim.pCustomExceptionParams = gpu->psCustomExceptionParams->_pDevData;
    for (int i = 0; i < (int) parameters.size(); i++) {
        if (parameters[i].size() > 0)
            (*gpu->psCustomParams)[i].x = (float) parameters[i][0];
        if (parameters[i].size() > 1)
            (*gpu->psCustomParams)[i].y = (float) parameters[i][1];
        if (parameters[i].size() > 2)
            (*gpu->psCustomParams)[i].z = (float) parameters[i][2];
        if (parameters[i].size() > 3)
            (*gpu->psCustomParams)[i].w = (float) parameters[i][3];
    }
    for (int i = 0; i < (int) exceptionAtom1.size(); i++) {
        (*gpu->psCustomExceptionID)[i].x = exceptionAtom1[i];
        (*gpu->psCustomExceptionID)[i].y = exceptionAtom2[i];
        (*gpu->psCustomExceptionID)[i].z = gpu->pOutputBufferCounter[exceptionAtom1[i]]++;
        (*gpu->psCustomExceptionID)[i].w = gpu->pOutputBufferCounter[exceptionAtom2[i]]++;
        if (exceptionParams[i].size() > 0)
            (*gpu->psCustomExceptionParams)[i].x = exceptionParams[i][0];
        if (exceptionParams[i].size() > 1)
            (*gpu->psCustomExceptionParams)[i].y = exceptionParams[i][1];
        if (exceptionParams[i].size() > 2)
            (*gpu->psCustomExceptionParams)[i].z = exceptionParams[i][2];
        if (exceptionParams[i].size() > 3)
            (*gpu->psCustomExceptionParams)[i].w = exceptionParams[i][3];
    }
    gpu->psCustomParams->Upload();
    gpu->psCustomExceptionID->Upload();
    gpu->psCustomExceptionParams->Upload();

    // This class serves as a placeholder for custom functions in expressions.

    class FunctionPlaceholder : public Lepton::CustomFunction {
    public:
        int getNumArguments() const {
            return 1;
        }
        double evaluate(const double* arguments) const {
            return 0.0;
        }
        double evaluateDerivative(const double* arguments, const int* derivOrder) const {
            return 0.0;
        }
        CustomFunction* clone() const {
            return new FunctionPlaceholder();
        }
    };

    // Record the tabulated functions, which were previously set with calls to gpuSetTabulatedFunction().

    FunctionPlaceholder* fp = new FunctionPlaceholder();
    map<string, Lepton::CustomFunction*> functions;
    gpu->psTabulatedFunctionParams = new CUDAStream<float4>(MAX_TABULATED_FUNCTIONS, 1, "TabulatedFunctionRange");
    gpu->sim.pTabulatedFunctionParams = gpu->psTabulatedFunctionParams->_pDevData;
    for (int i = 0; i < MAX_TABULATED_FUNCTIONS; i++) {
        gpuTabulatedFunction& func = gpu->tabulatedFunctions[i];
        if (func.coefficients != NULL) {
            (*gpu->psTabulatedFunctionParams)[i] = make_float4((float) func.min, (float) func.max, (float) (func.coefficients->_length/(func.max-func.min)), 0.0f);
            functions[func.name] = fp;
        }
    }
    gpu->psTabulatedFunctionParams->Upload();

    // Create the Expressions.

    vector<string> variables;
    variables.push_back("r");
    for (int i = 0; i < (int) paramNames.size(); i++)
        variables.push_back(paramNames[i]);
    gpu->sim.customExpressionStackSize = 0;
    SetCustomNonbondedEnergyExpression(createExpression<128>(gpu, energyExp, Lepton::Parser::parse(energyExp, functions).optimize().createProgram(), variables, globalParamNames, gpu->sim.customExpressionStackSize));
    SetCustomNonbondedForceExpression(createExpression<128>(gpu, energyExp, Lepton::Parser::parse(energyExp, functions).differentiate("r").optimize().createProgram(), variables, globalParamNames, gpu->sim.customExpressionStackSize));
    Expression<64> paramExpressions[4];
    vector<string> combiningRuleParams;
    for (int j = 1; j < 3; j++) {
        for (int i = 0; i < (int) paramNames.size(); i++) {
            stringstream name;
            name << paramNames[i] << j;
            combiningRuleParams.push_back(name.str());
        }
        for (int i = paramNames.size(); i < 4; i++)
            combiningRuleParams.push_back("");
    }
    for (int i = 0; i < (int) paramNames.size(); i++)
        paramExpressions[i] = createExpression<64>(gpu, combiningRules[i], Lepton::Parser::parse(combiningRules[i], functions).optimize().createProgram(), combiningRuleParams, globalParamNames, gpu->sim.customExpressionStackSize);
    SetCustomNonbondedCombiningRules(paramExpressions);
    delete fp;
}

static void tabulateErfc(gpuContext gpu)
{
    int tableSize = 2048;
    gpu->sim.tabulatedErfcSize = tableSize;
    gpu->sim.tabulatedErfcScale = tableSize/(gpu->sim.alphaEwald*gpu->sim.nonbondedCutoff);
    gpu->psTabulatedErfc = new CUDAStream<float>(tableSize, 1, "TabulatedErfc");
    gpu->sim.pTabulatedErfc = gpu->psTabulatedErfc->_pDevData;
    for (int i = 0; i < tableSize; ++i)
        (*gpu->psTabulatedErfc)[i] = erfc(i*(gpu->sim.alphaEwald*gpu->sim.nonbondedCutoff)/tableSize);
    gpu->psTabulatedErfc->Upload();
}

extern "C"
void gpuSetEwaldParameters(gpuContext gpu, float alpha, int kmaxx, int kmaxy, int kmaxz)
{
    gpu->sim.alphaEwald         = alpha;
    gpu->sim.factorEwald        = -1 / (4*alpha*alpha);
    gpu->sim.kmaxX              = kmaxx;
    gpu->sim.kmaxY              = kmaxy;
    gpu->sim.kmaxZ              = kmaxz;
    gpu->psEwaldCosSinSum       = new CUDAStream<float2>((gpu->sim.kmaxX*2-1) * (gpu->sim.kmaxY*2-1) * (gpu->sim.kmaxZ*2-1), 1, "EwaldCosSinSum");
    gpu->sim.pEwaldCosSinSum    = gpu->psEwaldCosSinSum->_pDevStream[0];
    tabulateErfc(gpu);
}

extern "C"
void gpuSetPMEParameters(gpuContext gpu, float alpha, int gridSizeX, int gridSizeY, int gridSizeZ)
{
    gpu->sim.alphaEwald         = alpha;
    int3 gridSize = make_int3(gridSizeX, gridSizeY, gridSizeZ);
    gpu->sim.pmeGridSize = gridSize;
    int3 groupSize = make_int3(2, 4, 4);
    gpu->sim.pmeGroupSize = groupSize;
    const int3 numGroups = make_int3((gridSize.x+groupSize.x-1)/groupSize.x, (gridSize.y+groupSize.y-1)/groupSize.y, (gridSize.z+groupSize.z-1)/groupSize.z);
    const unsigned int totalGroups = numGroups.x*numGroups.y*numGroups.z;
    cufftPlan3d(&gpu->fftplan, gridSize.x, gridSize.y, gridSize.z, CUFFT_C2C);
    gpu->psPmeGrid = new CUDAStream<cufftComplex>(gridSize.x*gridSize.y*gridSize.z, 1, "PmeGrid");
    gpu->sim.pPmeGrid = gpu->psPmeGrid->_pDevData;
    gpu->psPmeBsplineModuli[0] = new CUDAStream<float>(gridSize.x, 1, "PmeBsplineModuli0");
    gpu->sim.pPmeBsplineModuli[0] = gpu->psPmeBsplineModuli[0]->_pDevData;
    gpu->psPmeBsplineModuli[1] = new CUDAStream<float>(gridSize.y, 1, "PmeBsplineModuli1");
    gpu->sim.pPmeBsplineModuli[1] = gpu->psPmeBsplineModuli[1]->_pDevData;
    gpu->psPmeBsplineModuli[2] = new CUDAStream<float>(gridSize.z, 1, "PmeBsplineModuli2");
    gpu->sim.pPmeBsplineModuli[2] = gpu->psPmeBsplineModuli[2]->_pDevData;
    gpu->psPmeBsplineTheta = new CUDAStream<float4>(PME_ORDER*gpu->natoms, 1, "PmeBsplineTheta");
    gpu->sim.pPmeBsplineTheta = gpu->psPmeBsplineTheta->_pDevData;
    gpu->psPmeBsplineDtheta = new CUDAStream<float4>(PME_ORDER*gpu->natoms, 1, "PmeBsplineDtheta");
    gpu->sim.pPmeBsplineDtheta = gpu->psPmeBsplineDtheta->_pDevData;
    gpu->psPmeAtomRange = new CUDAStream<int>(gridSize.x*gridSize.y*gridSize.z+1, 1, "PmeAtomRange");
    gpu->sim.pPmeAtomRange = gpu->psPmeAtomRange->_pDevData;
    gpu->psPmeAtomGridIndex = new CUDAStream<float2>(gpu->natoms, 1, "PmeAtomGridIndex");
    gpu->sim.pPmeAtomGridIndex = gpu->psPmeAtomGridIndex->_pDevData;
    tabulateErfc(gpu);

    // Initialize the b-spline moduli.

    int maxSize = max(max(gridSize.x, gridSize.y), gridSize.z);
    vector<double> data(PME_ORDER);
    vector<double> ddata(PME_ORDER);
    vector<double> bsplines_data(maxSize);
    data[PME_ORDER-1] = 0.0;
    data[1] = 0.0;
    data[0] = 1.0;
    for (int i = 3; i < PME_ORDER; i++)
    {
        double div = 1.0/(i-1.0);
        data[i-1] = 0.0;
        for (int j = 1; j < (i-1); j++)
            data[i-j-1] = div*(j*data[i-j-2]+(i-j)*data[i-j-1]);
        data[0] = div*data[0];
    }

    // Differentiate.

    ddata[0] = -data[0];
    for (int i = 1; i < PME_ORDER; i++)
        ddata[i] = data[i-1]-data[i];
    double div = 1.0/(PME_ORDER-1);
    data[PME_ORDER-1] = 0.0;
    for (int i = 1; i < (PME_ORDER-1); i++)
        data[PME_ORDER-i-1] = div*(i*data[PME_ORDER-i-2]+(PME_ORDER-i)*data[PME_ORDER-i-1]);
    data[0] = div*data[0];
    for (int i = 0; i < maxSize; i++)
        bsplines_data[i] = 0.0;
    for (int i = 1; i <= PME_ORDER; i++)
        bsplines_data[i] = data[i-1];

    // Evaluate the actual bspline moduli for X/Y/Z.

    for(int dim = 0; dim < 3; dim++)
    {
        int ndata = (dim == 0 ? gridSize.x : dim == 1 ? gridSize.y : gridSize.z);
        for (int i = 0; i < ndata; i++)
        {
            double sc = 0.0;
            double ss = 0.0;
            for (int j = 0; j < ndata; j++)
            {
                double arg = (2.0*M_PI*i*j)/ndata;
                sc += bsplines_data[j]*cos(arg);
                ss += bsplines_data[j]*sin(arg);
            }
            (*gpu->psPmeBsplineModuli[dim])[i] = (float) (sc*sc+ss*ss);
        }
        for (int i = 0; i < ndata; i++)
        {
            if ((*gpu->psPmeBsplineModuli[dim])[i] < 1.0e-7)
                (*gpu->psPmeBsplineModuli[dim])[i] = ((*gpu->psPmeBsplineModuli[dim])[i-1]+(*gpu->psPmeBsplineModuli[dim])[i+1])*0.5f;
        }
        gpu->psPmeBsplineModuli[dim]->Upload();
    }
}

extern "C"
void gpuSetPeriodicBoxSize(gpuContext gpu, float xsize, float ysize, float zsize)
{
    gpu->sim.periodicBoxSizeX = xsize;
    gpu->sim.periodicBoxSizeY = ysize;
    gpu->sim.periodicBoxSizeZ = zsize;
    gpu->sim.recipBoxSizeX = 2.0f*PI/gpu->sim.periodicBoxSizeX;
    gpu->sim.recipBoxSizeY = 2.0f*PI/gpu->sim.periodicBoxSizeY;
    gpu->sim.recipBoxSizeZ = 2.0f*PI/gpu->sim.periodicBoxSizeZ;
    gpu->sim.cellVolume = gpu->sim.periodicBoxSizeX*gpu->sim.periodicBoxSizeY*gpu->sim.periodicBoxSizeZ;
}

extern "C"
void gpuSetObcParameters(gpuContext gpu, float innerDielectric, float solventDielectric, const vector<float>& radius, const vector<float>& scale, const vector<float>& charge)
{
    unsigned int atoms = radius.size();

    gpu->bIncludeGBSA = true;
    for (unsigned int i = 0; i < atoms; i++)
    {
            (*gpu->psObcData)[i].x = radius[i] - dielectricOffset;
            (*gpu->psObcData)[i].y = scale[i] * (*gpu->psObcData)[i].x;
            (*gpu->psPosq4)[i].w = charge[i];

#if (DUMP_PARAMETERS == 1)
        cout << 
            i << " " << 
            (*gpu->psObcData)[i].x << " " <<
            (*gpu->psObcData)[i].y;
#endif
    }

    // Dummy out extra atom data
    for (unsigned int i = atoms; i < gpu->sim.paddedNumberOfAtoms; i++)
    {
        (*gpu->psBornRadii)[i]     = 0.2f;
        (*gpu->psObcData)[i].x     = 0.01f;
        (*gpu->psObcData)[i].y     = 0.01f;
    }

    gpu->psBornRadii->Upload();
    gpu->psObcData->Upload();
    gpu->psPosq4->Upload();
    gpu->sim.preFactor = 2.0f*electricConstant*((1.0f/innerDielectric)-(1.0f/solventDielectric))*gpu->sim.forceConversionFactor;
}

static void markShakeClusterInvalid(ShakeCluster& cluster, map<int, ShakeCluster>& allClusters, vector<bool>& invalidForShake)
{
    cluster.valid = false;
    invalidForShake[cluster.centralID] = true;
    for (int i = 0; i < cluster.size; i++) {
        invalidForShake[cluster.peripheralID[i]] = true;
        map<int, ShakeCluster>::iterator otherCluster = allClusters.find(cluster.peripheralID[i]);
        if (otherCluster != allClusters.end() && otherCluster->second.valid)
            markShakeClusterInvalid(otherCluster->second, allClusters, invalidForShake);
    }
}

extern "C"
void gpuSetConstraintParameters(gpuContext gpu, const vector<int>& atom1, const vector<int>& atom2, const vector<float>& distance,
        const vector<float>& invMass1, const vector<float>& invMass2, float constraintTolerance)
{
    // Create a vector for recording which atoms are handled by SHAKE (or SETTLE).

    vector<bool> isShakeAtom(gpu->natoms, false);

    // Find how many constraints each atom is involved in.
    
    vector<int> constraintCount(gpu->natoms, 0);
    for (int i = 0; i < (int)atom1.size(); i++) {
        constraintCount[atom1[i]]++;
        constraintCount[atom2[i]]++;
    }

    // Identify clusters of three atoms that can be treated with SETTLE.  First, for every
    // atom that might be part of such a cluster, make a list of the two other atoms it is
    // connected to.

    vector<map<int, float> > settleConstraints(gpu->natoms);
    for (int i = 0; i < (int)atom1.size(); i++) {
        if (constraintCount[atom1[i]] == 2 && constraintCount[atom2[i]] == 2) {
            settleConstraints[atom1[i]][atom2[i]] = distance[i];
            settleConstraints[atom2[i]][atom1[i]] = distance[i];
        }
    }

    // Now remove the ones that don't actually form closed loops of three atoms.

    vector<int> settleClusters;
    for (int i = 0; i < (int)settleConstraints.size(); i++) {
        if (settleConstraints[i].size() == 2) {
            int partner1 = settleConstraints[i].begin()->first;
            int partner2 = (++settleConstraints[i].begin())->first;
            if (settleConstraints[partner1].size() != 2 || settleConstraints[partner2].size() != 2 ||
                    settleConstraints[partner1].find(partner2) == settleConstraints[partner1].end())
                settleConstraints[i].clear();
            else if (i < partner1 && i < partner2)
                settleClusters.push_back(i);
        }
        else
            settleConstraints[i].clear();
    }

    // Record the actual SETTLE clusters.

    CUDAStream<int4>* psSettleID          = new CUDAStream<int4>((int) settleClusters.size(), 1, "SettleID");
    gpu->psSettleID                       = psSettleID;
    gpu->sim.pSettleID                    = psSettleID->_pDevStream[0];
    CUDAStream<float2>* psSettleParameter = new CUDAStream<float2>((int) settleClusters.size(), 1, "SettleParameter");
    gpu->psSettleParameter                = psSettleParameter;
    gpu->sim.pSettleParameter             = psSettleParameter->_pDevStream[0];
    gpu->sim.settleConstraints            = settleClusters.size();
      for (int i = 0; i < (int)settleClusters.size(); i++) {
        int atom1 = settleClusters[i];
        int atom2 = settleConstraints[atom1].begin()->first;
        int atom3 = (++settleConstraints[atom1].begin())->first;
        float dist12 = settleConstraints[atom1].find(atom2)->second;
        float dist13 = settleConstraints[atom1].find(atom3)->second;
        float dist23 = settleConstraints[atom2].find(atom3)->second;
        if (dist12 == dist13) { // atom1 is the central atom
            (*psSettleID)[i].x = atom1;
            (*psSettleID)[i].y = atom2;
            (*psSettleID)[i].z = atom3;
            (*psSettleParameter)[i].x = dist12;
            (*psSettleParameter)[i].y = dist23;
        }
        else if (dist12 == dist23) { // atom2 is the central atom
            (*psSettleID)[i].x = atom2;
            (*psSettleID)[i].y = atom1;
            (*psSettleID)[i].z = atom3;
            (*psSettleParameter)[i].x = dist12;
            (*psSettleParameter)[i].y = dist13;
        }
        else if (dist13 == dist23) { // atom3 is the central atom
            (*psSettleID)[i].x = atom3;
            (*psSettleID)[i].y = atom1;
            (*psSettleID)[i].z = atom2;
            (*psSettleParameter)[i].x = dist13;
            (*psSettleParameter)[i].y = dist12;
        }
        else
            throw OpenMMException("Two of the three distances constrained with SETTLE must be the same.");
        isShakeAtom[atom1] = true;
        isShakeAtom[atom2] = true;
        isShakeAtom[atom3] = true;
    }
    psSettleID->Upload();
    psSettleParameter->Upload();
    gpu->sim.settle_threads_per_block     = (gpu->sim.settleConstraints + gpu->sim.blocks - 1) / gpu->sim.blocks;
    if (gpu->sim.settle_threads_per_block > gpu->sim.max_shake_threads_per_block)
        gpu->sim.settle_threads_per_block = gpu->sim.max_shake_threads_per_block;
    if (gpu->sim.settle_threads_per_block < 1)
        gpu->sim.settle_threads_per_block = 1;

    // Find clusters consisting of a central atom with up to three peripheral atoms.

    map<int, ShakeCluster> clusters;
    vector<bool> invalidForShake(gpu->natoms, false);
    for (int i = 0; i < (int)atom1.size(); i++) {
        if (isShakeAtom[atom1[i]])
            continue; // This is being taken care of with SETTLE.

        // Determine which is the central atom.

        bool firstIsCentral;
        if (constraintCount[atom1[i]] > 1)
            firstIsCentral = true;
        else if (constraintCount[atom2[i]] > 1)
            firstIsCentral = false;
        else if (atom1[i] < atom2[i])
            firstIsCentral = true;
        else
            firstIsCentral = false;
        int centralID, peripheralID;
        float centralInvMass, peripheralInvMass;
        if (firstIsCentral) {
            centralID = atom1[i];
            peripheralID = atom2[i];
            centralInvMass = invMass1[i];
            peripheralInvMass = invMass2[i];
        }
        else {
            centralID = atom2[i];
            peripheralID = atom1[i];
            centralInvMass = invMass2[i];
            peripheralInvMass = invMass1[i];
        }

        // Add it to the cluster.

        if (clusters.find(centralID) == clusters.end()) {
            clusters[centralID] = ShakeCluster(centralID, centralInvMass);
        }
        ShakeCluster& cluster = clusters[centralID];
        cluster.addAtom(peripheralID, distance[i], peripheralInvMass);
        if (constraintCount[peripheralID] != 1 || invalidForShake[atom1[i]] || invalidForShake[atom2[i]]) {
            markShakeClusterInvalid(cluster, clusters, invalidForShake);
            map<int, ShakeCluster>::iterator otherCluster = clusters.find(peripheralID);
            if (otherCluster != clusters.end() && otherCluster->second.valid)
                markShakeClusterInvalid(otherCluster->second, clusters, invalidForShake);
        }
    }
    int validShakeClusters = 0;
    for (map<int, ShakeCluster>::iterator iter = clusters.begin(); iter != clusters.end(); ++iter) {
        ShakeCluster& cluster = iter->second;
        if (cluster.valid) {
            cluster.valid = !invalidForShake[cluster.centralID];
            for (int i = 0; i < cluster.size; i++)
                if (invalidForShake[cluster.peripheralID[i]])
                    cluster.valid = false;
            if (cluster.valid)
                ++validShakeClusters;
        }
    }

    // Fill in the Cuda streams.

    CUDAStream<int4>* psShakeID             = new CUDAStream<int4>(validShakeClusters, 1, "ShakeID");
    gpu->psShakeID                          = psShakeID;
    gpu->sim.pShakeID                       = psShakeID->_pDevStream[0];
    CUDAStream<float4>* psShakeParameter    = new CUDAStream<float4>(validShakeClusters, 1, "ShakeParameter");
    gpu->psShakeParameter                   = psShakeParameter;
    gpu->sim.pShakeParameter                = psShakeParameter->_pDevStream[0];
    gpu->sim.ShakeConstraints               = validShakeClusters;
    int index = 0;
    for (map<int, ShakeCluster>::const_iterator iter = clusters.begin(); iter != clusters.end(); ++iter) {
        const ShakeCluster& cluster = iter->second;
        if (!cluster.valid)
            continue;
        (*psShakeID)[index].x = cluster.centralID;
        (*psShakeID)[index].y = cluster.peripheralID[0];
        (*psShakeID)[index].z = cluster.size > 1 ? cluster.peripheralID[1] : -1;
        (*psShakeID)[index].w = cluster.size > 2 ? cluster.peripheralID[2] : -1;
        (*psShakeParameter)[index].x = cluster.centralInvMass;
        (*psShakeParameter)[index].y = 0.5f/(cluster.centralInvMass+cluster.peripheralInvMass);
        (*psShakeParameter)[index].z = cluster.distance*cluster.distance;
        (*psShakeParameter)[index].w = cluster.peripheralInvMass;
        isShakeAtom[cluster.centralID] = true;
        isShakeAtom[cluster.peripheralID[0]] = true;
        if (cluster.size > 1)
            isShakeAtom[cluster.peripheralID[1]] = true;
        if (cluster.size > 2)
            isShakeAtom[cluster.peripheralID[2]] = true;
        ++index;
    }
    psShakeID->Upload();
    psShakeParameter->Upload();
    gpu->sim.shakeTolerance = constraintTolerance;
    gpu->sim.shake_threads_per_block     = (gpu->sim.ShakeConstraints + gpu->sim.blocks - 1) / gpu->sim.blocks;
    if (gpu->sim.shake_threads_per_block > gpu->sim.max_shake_threads_per_block)
        gpu->sim.shake_threads_per_block = gpu->sim.max_shake_threads_per_block;
    if (gpu->sim.shake_threads_per_block < 1)
        gpu->sim.shake_threads_per_block = 1;

    // Find connected constraints for CCMA.

    vector<int> ccmaConstraints;
    for (unsigned i = 0; i < atom1.size(); i++)
        if (!isShakeAtom[atom1[i]])
            ccmaConstraints.push_back(i);

    // Record the connections between constraints.

    int numCCMA = (int) ccmaConstraints.size();
    vector<vector<int> > atomConstraints(gpu->natoms);
    for (int i = 0; i < numCCMA; i++) {
        atomConstraints[atom1[ccmaConstraints[i]]].push_back(i);
        atomConstraints[atom2[ccmaConstraints[i]]].push_back(i);
    }
    vector<vector<int> > linkedConstraints(numCCMA);
    for (unsigned atom = 0; atom < atomConstraints.size(); atom++) {
        for (unsigned i = 0; i < atomConstraints[atom].size(); i++)
            for (unsigned j = 0; j < i; j++) {
                int c1 = atomConstraints[atom][i];
                int c2 = atomConstraints[atom][j];
                linkedConstraints[c1].push_back(c2);
                linkedConstraints[c2].push_back(c1);
            }
    }
    int maxLinks = 0;
    for (unsigned i = 0; i < linkedConstraints.size(); i++)
        maxLinks = max(maxLinks, (int) linkedConstraints[i].size());
    int maxAtomConstraints = 0;
    for (unsigned i = 0; i < atomConstraints.size(); i++)
        maxAtomConstraints = max(maxAtomConstraints, (int) atomConstraints[i].size());

    // Compute the constraint coupling matrix

    vector<vector<int> > atomAngles(gpu->natoms);
    for (int i = 0; i < (int) gpu->sim.bond_angles; i++)
        atomAngles[(*gpu->psBondAngleID1)[i].y].push_back(i);
    vector<vector<pair<int, double> > > matrix(numCCMA);
    if (numCCMA > 0) {
        for (int j = 0; j < numCCMA; j++) {
            for (int k = 0; k < numCCMA; k++) {
                if (j == k) {
                    matrix[j].push_back(pair<int, double>(j, 1.0));
                    continue;
                }
                double scale;
                int cj = ccmaConstraints[j];
                int ck = ccmaConstraints[k];
                int atomj0 = atom1[cj];
                int atomj1 = atom2[cj];
                int atomk0 = atom1[ck];
                int atomk1 = atom2[ck];
                int atoma, atomb, atomc;
                if (atomj0 == atomk0) {
                    atoma = atomj1;
                    atomb = atomj0;
                    atomc = atomk1;
                    scale = invMass1[cj]/(invMass1[cj]+invMass2[cj]);
                }
                else if (atomj1 == atomk1) {
                    atoma = atomj0;
                    atomb = atomj1;
                    atomc = atomk0;
                    scale = invMass2[cj]/(invMass1[cj]+invMass2[cj]);
                }
                else if (atomj0 == atomk1) {
                    atoma = atomj1;
                    atomb = atomj0;
                    atomc = atomk0;
                    scale = invMass1[cj]/(invMass1[cj]+invMass2[cj]);
                }
                else if (atomj1 == atomk0) {
                    atoma = atomj0;
                    atomb = atomj1;
                    atomc = atomk1;
                    scale = invMass2[cj]/(invMass1[cj]+invMass2[cj]);
                }
                else
                    continue; // These constraints are not connected.

                // Look for a third constraint forming a triangle with these two.

                bool foundConstraint = false;
                for (int other = 0; other < numCCMA; other++) {
                    if ((atom1[other] == atoma && atom2[other] == atomc) || (atom1[other] == atomc && atom2[other] == atoma)) {
                        double d1 = distance[cj];
                        double d2 = distance[ck];
                        double d3 = distance[other];
                        matrix[j].push_back(pair<int, double>(k, scale*(d1*d1+d2*d2-d3*d3)/(2.0*d1*d2)));
                        foundConstraint = true;
                        break;
                    }
                }
                if (!foundConstraint) {
                    // We didn't find one, so look for an angle force field term.

                    const vector<int>& angleCandidates = atomAngles[atomb];
                    for (vector<int>::const_iterator iter = angleCandidates.begin(); iter != angleCandidates.end(); iter++) {
                        int4 atoms = (*gpu->psBondAngleID1)[*iter];
                        if ((atoms.x == atoma && atoms.z == atomc) || (atoms.z == atoma && atoms.x == atomc)) {
                            double angle = (*gpu->psBondAngleParameter)[*iter].x;
                            matrix[j].push_back(pair<int, double>(k, scale*cos(angle*PI/180.0)));
                            break;
                        }
                    }
                }
            }
        }

        // Invert it using QR.

        vector<int> matrixRowStart;
        vector<int> matrixColIndex;
        vector<double> matrixValue;
        for (int i = 0; i < numCCMA; i++) {
            matrixRowStart.push_back(matrixValue.size());
            for (int j = 0; j < (int) matrix[i].size(); j++) {
                pair<int, double> element = matrix[i][j];
                matrixColIndex.push_back(element.first);
                matrixValue.push_back(element.second);
            }
        }
        matrixRowStart.push_back(matrixValue.size());
        int *qRowStart, *qColIndex, *rRowStart, *rColIndex;
        double *qValue, *rValue;
        int result = QUERN_compute_qr(numCCMA, numCCMA, &matrixRowStart[0], &matrixColIndex[0], &matrixValue[0], NULL,
                &qRowStart, &qColIndex, &qValue, &rRowStart, &rColIndex, &rValue);
        vector<double> rhs(numCCMA);
        matrix.clear();
        matrix.resize(numCCMA);
        for (int i = 0; i < numCCMA; i++) {
            // Extract column i of the inverse matrix.

            for (int j = 0; j < numCCMA; j++)
                rhs[j] = (i == j ? 1.0 : 0.0);
            result = QUERN_multiply_with_q_transpose(numCCMA, qRowStart, qColIndex, qValue, &rhs[0]);
            result = QUERN_solve_with_r(numCCMA, rRowStart, rColIndex, rValue, &rhs[0], &rhs[0]);
            for (int j = 0; j < numCCMA; j++) {
                double value = rhs[j]*distance[ccmaConstraints[i]]/distance[ccmaConstraints[j]];
                if (abs(value) > 0.1)
                    matrix[j].push_back(pair<int, double>(i, value));
            }
        }
        QUERN_free_result(qRowStart, qColIndex, qValue);
        QUERN_free_result(rRowStart, rColIndex, rValue);
    }
    int maxRowElements = 0;
    for (unsigned i = 0; i < matrix.size(); i++)
        maxRowElements = max(maxRowElements, (int) matrix[i].size());
    maxRowElements++;

    // Sort the constraints.

    vector<int> constraintOrder(numCCMA);
    for (int i = 0; i < numCCMA; ++i)
        constraintOrder[i] = i;
    sort(constraintOrder.begin(), constraintOrder.end(), ConstraintOrderer(atom1, atom2));
    vector<int> inverseOrder(numCCMA);
    for (int i = 0; i < numCCMA; ++i)
        inverseOrder[constraintOrder[i]] = i;
    for (int i = 0; i < (int)matrix.size(); ++i)
        for (int j = 0; j < (int)matrix[i].size(); ++j)
            matrix[i][j].first = inverseOrder[matrix[i][j].first];

    // Fill in the CUDA streams.

    CUDAStream<int2>* psCcmaAtoms = new CUDAStream<int2>(numCCMA, 1, "CcmaAtoms");
    gpu->psCcmaAtoms              = psCcmaAtoms;
    gpu->sim.pCcmaAtoms           = psCcmaAtoms->_pDevData;
    CUDAStream<float4>* psCcmaDistance = new CUDAStream<float4>(numCCMA, 1, "CcmaDistance");
    gpu->psCcmaDistance                = psCcmaDistance;
    gpu->sim.pCcmaDistance             = psCcmaDistance->_pDevData;
    CUDAStream<int>* psCcmaAtomConstraints = new CUDAStream<int>(gpu->natoms*maxAtomConstraints, 1, "CcmaAtomConstraints");
    gpu->psCcmaAtomConstraints             = psCcmaAtomConstraints;
    gpu->sim.pCcmaAtomConstraints          = psCcmaAtomConstraints->_pDevData;
    CUDAStream<int>* psCcmaNumAtomConstraints = new CUDAStream<int>(gpu->natoms, 1, "CcmaAtomConstraintsIndex");
    gpu->psCcmaNumAtomConstraints             = psCcmaNumAtomConstraints;
    gpu->sim.pCcmaNumAtomConstraints          = psCcmaNumAtomConstraints->_pDevData;
    CUDAStream<float>* psCcmaDelta1 = new CUDAStream<float>(numCCMA, 1, "CcmaDelta1");
    gpu->psCcmaDelta1             = psCcmaDelta1;
    gpu->sim.pCcmaDelta1          = psCcmaDelta1->_pDevData;
    CUDAStream<float>* psCcmaDelta2 = new CUDAStream<float>(numCCMA, 1, "CcmaDelta2");
    gpu->psCcmaDelta2             = psCcmaDelta2;
    gpu->sim.pCcmaDelta2          = psCcmaDelta2->_pDevData;
    CUDAStream<short>* psSyncCounter = new CUDAStream<short>(3*gpu->sim.blocks, 1, "SyncCounter");
    gpu->psSyncCounter               = psSyncCounter;
    gpu->sim.pSyncCounter            = psSyncCounter->_pDevData;
    CUDAStream<unsigned int>* psRequiredIterations = new CUDAStream<unsigned int>(1, 1, "RequiredIterations");
    gpu->psRequiredIterations               = psRequiredIterations;
    gpu->sim.pRequiredIterations            = psRequiredIterations->_pDevData;
    CUDAStream<float>* psCcmaReducedMass = new CUDAStream<float>(numCCMA, 1, "CcmaReducedMass");
    gpu->psCcmaReducedMass             = psCcmaReducedMass;
    gpu->sim.pCcmaReducedMass          = psCcmaReducedMass->_pDevData;
    CUDAStream<unsigned int>* psConstraintMatrixColumn = new CUDAStream<unsigned int>(numCCMA*maxRowElements, 1, "ConstraintMatrixColumn");
    gpu->psConstraintMatrixColumn               = psConstraintMatrixColumn;
    gpu->sim.pConstraintMatrixColumn            = psConstraintMatrixColumn->_pDevData;
    CUDAStream<float>* psConstraintMatrixValue = new CUDAStream<float>(numCCMA*maxRowElements, 1, "ConstraintMatrixValue");
    gpu->psConstraintMatrixValue             = psConstraintMatrixValue;
    gpu->sim.pConstraintMatrixValue          = psConstraintMatrixValue->_pDevData;
    gpu->sim.ccmaConstraints = numCCMA;
    for (int i = 0; i < numCCMA; i++) {
        int index = constraintOrder[i];
        int c = ccmaConstraints[index];
        (*psCcmaAtoms)[i].x = atom1[c];
        (*psCcmaAtoms)[i].y = atom2[c];
        (*psCcmaDistance)[i].w = distance[c];
        (*psCcmaReducedMass)[i] = 0.5f/(invMass1[c]+invMass2[c]);
        for (unsigned int j = 0; j < matrix[index].size(); j++) {
            (*psConstraintMatrixColumn)[i+j*numCCMA] = matrix[index][j].first;
            (*psConstraintMatrixValue)[i+j*numCCMA] = (float) matrix[index][j].second;
        }
        (*psConstraintMatrixColumn)[i+matrix[index].size()*numCCMA] = numCCMA;
    }
    for (unsigned int i = 0; i < psSyncCounter->_length; i++)
        (*psSyncCounter)[i] = -1;
    for (unsigned int i = 0; i < atomConstraints.size(); i++) {
        (*psCcmaNumAtomConstraints)[i] = atomConstraints[i].size();
        for (unsigned int j = 0; j < atomConstraints[i].size(); j++) {
            bool forward = (atom1[ccmaConstraints[atomConstraints[i][j]]] == i);
            (*psCcmaAtomConstraints)[i+j*gpu->natoms] = (forward ? inverseOrder[atomConstraints[i][j]]+1 : -inverseOrder[atomConstraints[i][j]]-1);
        }
    }
    psCcmaAtoms->Upload();
    psCcmaDistance->Upload();
    psCcmaReducedMass->Upload();
    psCcmaAtomConstraints->Upload();
    psCcmaNumAtomConstraints->Upload();
    psSyncCounter->Upload();
    psConstraintMatrixColumn->Upload();
    psConstraintMatrixValue->Upload();
    gpu->sim.ccma_threads_per_block = (gpu->sim.ccmaConstraints + gpu->sim.blocks - 1) / gpu->sim.blocks;
    if (gpu->sim.ccma_threads_per_block > gpu->sim.threads_per_block)
        gpu->sim.ccma_threads_per_block = gpu->sim.threads_per_block;
    if (gpu->sim.ccma_threads_per_block < gpu->sim.blocks)
        gpu->sim.ccma_threads_per_block = gpu->sim.blocks;

    // count number of atoms w/o constraint

    int count = 0;
    for (int i = 0; i < gpu->natoms; i++)
       if (!isShakeAtom[i])
          count++;

    // Allocate NonShake parameters

    gpu->sim.NonShakeConstraints                  = count;
    if( count || true ){

       CUDAStream<int>* psNonShakeID              = new CUDAStream<int>(count, 1, "NonShakeID");
       gpu->psNonShakeID                          = psNonShakeID;
       gpu->sim.pNonShakeID                       = psNonShakeID->_pDevStream[0];

       gpu->sim.nonshake_threads_per_block        = (count + gpu->sim.blocks - 1) / gpu->sim.blocks;

       if (gpu->sim.nonshake_threads_per_block > gpu->sim.max_shake_threads_per_block)
           gpu->sim.nonshake_threads_per_block = gpu->sim.max_shake_threads_per_block;

       if (gpu->sim.nonshake_threads_per_block < 1)
               gpu->sim.nonshake_threads_per_block = 1;

       // load indices

       count = 0;
       for (int i = 0; i < gpu->natoms; i++){
          if (!isShakeAtom[i]){
             (*psNonShakeID)[count++] = i;
          }
       }
       psNonShakeID->Upload();

    } else {
       gpu->sim.nonshake_threads_per_block           = 0;
    }
}

extern "C"
int gpuAllocateInitialBuffers(gpuContext gpu)
{
    gpu->sim.atoms                      = gpu->natoms;
    gpu->sim.paddedNumberOfAtoms        = ((gpu->sim.atoms + GRID - 1) >> GRIDBITS) << GRIDBITS;
    gpu->sim.degreesOfFreedom           = 3 * gpu->sim.atoms - 6;
    gpu->gpAtomTable                    = NULL;
    gpu->gAtomTypes                     = 0;
    gpu->psPosq4                        = new CUDAStream<float4>(gpu->sim.paddedNumberOfAtoms, 1, "Posq");
    gpu->sim.stride                     = gpu->psPosq4->_stride;
    gpu->sim.stride2                    = gpu->sim.stride * 2;
    gpu->sim.stride3                    = gpu->sim.stride * 3;
    gpu->sim.stride4                    = gpu->sim.stride * 4;
    gpu->sim.pPosq                      = gpu->psPosq4->_pDevStream[0];
    gpu->sim.stride                     = gpu->psPosq4->_stride;
    gpu->sim.stride2                    = 2 * gpu->sim.stride;
    gpu->sim.stride3                    = 3 * gpu->sim.stride;
    gpu->sim.stride4                    = 4 * gpu->sim.stride;
    gpu->psPosqP4                       = new CUDAStream<float4>(gpu->sim.paddedNumberOfAtoms, 1, "PosqP");
    gpu->sim.pPosqP                     = gpu->psPosqP4->_pDevStream[0];
    gpu->psOldPosq4                     = new CUDAStream<float4>(gpu->sim.paddedNumberOfAtoms, 1, "OldPosq");
    gpu->sim.pOldPosq                   = gpu->psOldPosq4->_pDevStream[0];
    gpu->psVelm4                        = new CUDAStream<float4>(gpu->sim.paddedNumberOfAtoms, 1, "Velm");
    gpu->sim.pVelm4                     = gpu->psVelm4->_pDevStream[0];
    gpu->psvVector4                     = new CUDAStream<float4>(gpu->sim.paddedNumberOfAtoms, 1, "vVector");
    gpu->sim.pvVector4                  = gpu->psvVector4->_pDevStream[0];
    gpu->psxVector4                     = new CUDAStream<float4>(gpu->sim.paddedNumberOfAtoms, 1, "xVector");
    gpu->sim.pxVector4                  = gpu->psxVector4->_pDevStream[0];
    gpu->psBornRadii                    = new CUDAStream<float>(gpu->sim.paddedNumberOfAtoms, 1, "BornRadii");
    gpu->sim.pBornRadii                 = gpu->psBornRadii->_pDevStream[0];
    gpu->psObcChain                     = new CUDAStream<float>(gpu->sim.paddedNumberOfAtoms, 1, "ObcChain");
    gpu->sim.pObcChain                  = gpu->psObcChain->_pDevStream[0];
    gpu->psSigEps2                      = new CUDAStream<float2>(gpu->sim.paddedNumberOfAtoms, 1, "SigEps2");
    gpu->sim.pAttr                      = gpu->psSigEps2->_pDevStream[0];
    gpu->psObcData                      = new CUDAStream<float2>(gpu->sim.paddedNumberOfAtoms, 1, "ObcData");
    gpu->sim.pObcData                   = gpu->psObcData->_pDevStream[0];
    gpu->psStepSize                     = new CUDAStream<float2>(1, 1, "StepSize");
    gpu->sim.pStepSize                  = gpu->psStepSize->_pDevStream[0];
    (*gpu->psStepSize)[0] = make_float2(0.0f, 0.0f);
    gpu->psStepSize->Upload();
    gpu->psLangevinParameters           = new CUDAStream<float>(11, 1, "LangevinParameters");
    gpu->sim.pLangevinParameters        = gpu->psLangevinParameters->_pDevStream[0];
    gpu->pAtomSymbol                    = new unsigned char[gpu->natoms];
    gpu->psAtomIndex                    = new CUDAStream<int>(gpu->sim.paddedNumberOfAtoms, 1, "AtomIndex");
    gpu->sim.pAtomIndex                 = gpu->psAtomIndex->_pDevStream[0];
    for (int i = 0; i < (int) gpu->sim.paddedNumberOfAtoms; i++)
        (*gpu->psAtomIndex)[i] = i;
    gpu->psAtomIndex->Upload();
    gpu->posCellOffsets.resize(gpu->natoms, make_int3(0, 0, 0));
    // Determine randoms
    gpu->seed                           = 1;
    gpu->sim.randomFrames               = 20;
    gpu->sim.randomIterations           = gpu->sim.randomFrames;
    gpu->sim.randoms                    = gpu->sim.randomFrames * gpu->sim.paddedNumberOfAtoms;
    gpu->sim.totalRandoms               = gpu->sim.randoms + gpu->sim.paddedNumberOfAtoms;
    gpu->sim.totalRandomsTimesTwo       = gpu->sim.totalRandoms * 2;
    gpu->psRandom4                      = new CUDAStream<float4>(gpu->sim.totalRandomsTimesTwo, 1, "Random4");
    gpu->psRandom2                      = new CUDAStream<float2>(gpu->sim.totalRandomsTimesTwo, 1, "Random2");
    gpu->psRandomPosition               = new CUDAStream<int>(gpu->sim.blocks, 1, "RandomPosition");
    gpu->psRandomSeed                   = new CUDAStream<uint4>(gpu->sim.blocks * gpu->sim.random_threads_per_block, 1, "RandomSeed");
    gpu->sim.pRandom4a                  = gpu->psRandom4->_pDevStream[0];
    gpu->sim.pRandom2a                  = gpu->psRandom2->_pDevStream[0];
    gpu->sim.pRandom4b                  = gpu->psRandom4->_pDevStream[0] + gpu->sim.totalRandoms;
    gpu->sim.pRandom2b                  = gpu->psRandom2->_pDevStream[0] + gpu->sim.totalRandoms;
    gpu->sim.pRandomPosition            = gpu->psRandomPosition->_pDevStream[0];
    gpu->sim.pRandomSeed                = gpu->psRandomSeed->_pDevStream[0];

    // Allocate and clear linear momentum buffer
    gpu->psLinearMomentum = new CUDAStream<float4>(gpu->sim.blocks, 1, "LinearMomentum");
    gpu->sim.pLinearMomentum = gpu->psLinearMomentum->_pDevStream[0];
    for (int i = 0; i < (int) gpu->sim.blocks; i++)
    {
        (*gpu->psLinearMomentum)[i].x = 0.0f;
        (*gpu->psLinearMomentum)[i].y = 0.0f;
        (*gpu->psLinearMomentum)[i].z = 0.0f;
        (*gpu->psLinearMomentum)[i].w = 0.0f;
    }
    gpu->psLinearMomentum->Upload();

    return 1;
}

extern "C"
void gpuSetPositions(gpuContext gpu, const vector<float>& x, const vector<float>& y, const vector<float>& z)
{
    for (int i = 0; i < gpu->natoms; i++)
    {
        (*gpu->psPosq4)[i].x = x[i];
        (*gpu->psPosq4)[i].y = y[i];
        (*gpu->psPosq4)[i].z = z[i];
    }
    gpu->psPosq4->Upload();

	 // set flag to recalculate Born radii

	 gpu->bRecalculateBornRadii = true;
} 

extern "C"
void gpuSetVelocities(gpuContext gpu, const vector<float>& x, const vector<float>& y, const vector<float>& z)
{
    for (int i = 0; i < gpu->natoms; i++)
    {
        (*gpu->psVelm4)[i].x = x[i];
        (*gpu->psVelm4)[i].y = y[i];
        (*gpu->psVelm4)[i].z = z[i];
    }
    gpu->psVelm4->Upload();
} 

extern "C"
void gpuSetMass(gpuContext gpu, const vector<float>& mass)
{
    float totalMass = 0.0f;
    for (int i = 0; i < gpu->natoms; i++)
    {
        (*gpu->psVelm4)[i].w = 1.0f/mass[i];
        totalMass += mass[i];
    }
    gpu->sim.inverseTotalMass = 1.0f / totalMass;
    gpu->psVelm4->Upload();
} 

extern "C"
void gpuInitializeRandoms(gpuContext gpu)
{
    for (int i = 0; i < (int) gpu->sim.blocks; i++)
    {
        (*gpu->psRandomPosition)[i] = 0;
    }
    int seed = gpu->seed | ((gpu->seed ^ 0xffffffff) << 16);
    srand(seed);
    for (int i = 0; i < (int) (gpu->sim.blocks * gpu->sim.random_threads_per_block); i++)
    {
        (*gpu->psRandomSeed)[i].x = rand();
        (*gpu->psRandomSeed)[i].y = rand();
        (*gpu->psRandomSeed)[i].z = rand();
        (*gpu->psRandomSeed)[i].w = rand();
    }
    gpu->psRandomPosition->Upload();
    gpu->psRandomSeed->Upload();
    gpuSetConstants(gpu);
    kGenerateRandoms(gpu);
    return;
}

extern "C"
bool gpuIsAvailable()
{
    int deviceCount;
    cudaGetDeviceCount(&deviceCount);
    return (deviceCount > 0);
}

extern "C"
void* gpuInit(int numAtoms, unsigned int device, bool useBlockingSync)
{
    gpuContext gpu = new _gpuContext;
    int LRFSize = 0;
    int SMCount = 0;
    int SMMajor = 0;
    int SMMinor = 0;

    // Select which device to use
    int currentDevice;
    cudaError_t status = cudaGetDevice(&currentDevice);
    RTERROR(status, "Error getting CUDA device")
    if (device != currentDevice)
        cudaSetDevice(device); // Ignore errors
    status = cudaGetDevice(&gpu->device);
    RTERROR(status, "Error getting CUDA device")
    status = cudaSetDeviceFlags(useBlockingSync ? cudaDeviceBlockingSync : cudaDeviceScheduleAuto);
    RTERROR(status, "Error setting device flags")
    gpu->useBlockingSync = useBlockingSync;

    // Determine kernel call configuration
    cudaDeviceProp deviceProp;
    cudaGetDeviceProperties(&deviceProp, currentDevice);

    // Determine SM version
    if (deviceProp.major == 1)
    {
        switch (deviceProp.minor)
        {
        case 0:
        case 1:
            gpu->sm_version = SM_10;
            gpu->sim.workUnitsPerSM = G8X_NONBOND_WORKUNITS_PER_SM;
            break;

        default:
            gpu->sm_version = SM_12;
            gpu->sim.workUnitsPerSM = GT2XX_NONBOND_WORKUNITS_PER_SM;
            break;
        }
    }

    gpu->sim.nonbond_blocks = deviceProp.multiProcessorCount;
    gpu->sim.bornForce2_blocks = deviceProp.multiProcessorCount;
    gpu->sim.blocks = deviceProp.multiProcessorCount;
    if (deviceProp.regsPerBlock == 8192)
    {
        gpu->sim.nonbond_threads_per_block          = G8X_NONBOND_THREADS_PER_BLOCK;
        gpu->sim.bornForce2_threads_per_block       = G8X_BORNFORCE2_THREADS_PER_BLOCK;
        gpu->sim.max_shake_threads_per_block        = G8X_SHAKE_THREADS_PER_BLOCK;
        gpu->sim.max_update_threads_per_block       = G8X_UPDATE_THREADS_PER_BLOCK;
        gpu->sim.max_localForces_threads_per_block  = G8X_LOCALFORCES_THREADS_PER_BLOCK;
        gpu->sim.threads_per_block                  = G8X_THREADS_PER_BLOCK;
        gpu->sim.random_threads_per_block           = G8X_RANDOM_THREADS_PER_BLOCK;
    }
    else
    {
        gpu->sim.nonbond_threads_per_block          = GT2XX_NONBOND_THREADS_PER_BLOCK;
        gpu->sim.bornForce2_threads_per_block       = GT2XX_BORNFORCE2_THREADS_PER_BLOCK;
        gpu->sim.max_shake_threads_per_block        = GT2XX_SHAKE_THREADS_PER_BLOCK;
        gpu->sim.max_update_threads_per_block       = GT2XX_UPDATE_THREADS_PER_BLOCK;
        gpu->sim.max_localForces_threads_per_block  = GT2XX_LOCALFORCES_THREADS_PER_BLOCK;
        gpu->sim.threads_per_block                  = GT2XX_NONBOND_THREADS_PER_BLOCK;
        gpu->sim.random_threads_per_block           = GT2XX_RANDOM_THREADS_PER_BLOCK;
    }
    gpu->sim.shake_threads_per_block                = gpu->sim.max_shake_threads_per_block;
    gpu->sim.localForces_threads_per_block          = gpu->sim.max_localForces_threads_per_block;

    gpu->natoms = numAtoms;
    gpuAllocateInitialBuffers(gpu);
    for (int i = 0; i < gpu->natoms; i++)
    {
        (*gpu->psxVector4)[i].x = 0.0f;
        (*gpu->psxVector4)[i].y = 0.0f;
        (*gpu->psxVector4)[i].z = 0.0f;
        (*gpu->psxVector4)[i].w = 0.0f;
    }
    gpu->psxVector4->Upload();

    gpu->iterations = 0;
    gpu->sim.update_threads_per_block               = (gpu->natoms + gpu->sim.blocks - 1) / gpu->sim.blocks;
    if (gpu->sim.update_threads_per_block > gpu->sim.max_update_threads_per_block)
        gpu->sim.update_threads_per_block = gpu->sim.max_update_threads_per_block;
    if (gpu->sim.update_threads_per_block < gpu->psLangevinParameters->_length)
            gpu->sim.update_threads_per_block = gpu->psLangevinParameters->_length;
    gpu->sim.bf_reduce_threads_per_block = gpu->sim.update_threads_per_block;
    gpu->sim.bsf_reduce_threads_per_block = (gpu->sim.stride4 + gpu->natoms + gpu->sim.blocks - 1) / gpu->sim.blocks;
    gpu->sim.bsf_reduce_threads_per_block = ((gpu->sim.bsf_reduce_threads_per_block + (GRID - 1)) / GRID) * GRID;
    if (gpu->sim.bsf_reduce_threads_per_block > gpu->sim.threads_per_block)
        gpu->sim.bsf_reduce_threads_per_block = gpu->sim.threads_per_block;
    if (gpu->sim.bsf_reduce_threads_per_block < 1)
        gpu->sim.bsf_reduce_threads_per_block = 1;

    // Initialize constants to reasonable values
    gpu->sim.probeRadius            = probeRadius;
    gpu->sim.surfaceAreaFactor      = surfaceAreaFactor;
    gpu->sim.electricConstant       = electricConstant;
    gpu->sim.nonbondedMethod        = NO_CUTOFF;
    gpu->sim.nonbondedCutoff        = 0.0f;
    gpu->sim.nonbondedCutoffSqr     = 0.0f;

    gpu->sim.bigFloat               = 99999999.0f;
    gpu->sim.forceConversionFactor  = forceConversionFactor;
    gpu->sim.preFactor              = 2.0f*electricConstant*((1.0f/defaultInnerDielectric)-(1.0f/defaultSolventDielectric))*gpu->sim.forceConversionFactor;
    gpu->sim.dielectricOffset       = dielectricOffset;
    gpu->sim.alphaOBC               = alphaOBC;
    gpu->sim.betaOBC                = betaOBC;
    gpu->sim.gammaOBC               = gammaOBC;
    gpuSetLangevinIntegrationParameters(gpu, 1.0f, 2.0e-3f, 300.0f, 0.0f);
    gpu->sim.maxShakeIterations     = 15;
    gpu->sim.shakeTolerance         = 1.0e-04f * 2.0f;
    gpu->sim.InvMassJ               = 9.920635e-001f;
    gpu->grid                       = GRID;
    gpu->bCalculateCM               = false;
    gpu->bRemoveCM                  = false;
    gpu->bRecalculateBornRadii      = true;
    gpu->bIncludeGBSA               = false;
    gpuInitializeRandoms(gpu);

    // To be determined later
    gpu->psLJ14ID                   = NULL;
    gpu->psForce4                   = NULL;
    gpu->psEnergy                   = NULL;
    gpu->sim.pForce4                = NULL;
    gpu->sim.pForce4a               = NULL;
    gpu->sim.pForce4b               = NULL;
    gpu->psBornForce                = NULL;
    gpu->sim.pBornForce             = NULL;
    gpu->psBornSum                  = NULL;
    gpu->sim.pBornSum               = NULL;
    gpu->psBondID                   = NULL;
    gpu->psBondParameter            = NULL;
    gpu->psBondAngleID1             = NULL;
    gpu->psBondAngleID2             = NULL;
    gpu->psBondAngleParameter       = NULL;
    gpu->psDihedralID1              = NULL;
    gpu->psDihedralID2              = NULL;
    gpu->psDihedralParameter        = NULL;
    gpu->psRbDihedralID1            = NULL;
    gpu->psRbDihedralID2            = NULL;
    gpu->psRbDihedralParameter1     = NULL;
    gpu->psRbDihedralParameter2     = NULL;
    gpu->psLJ14ID                   = NULL;
    gpu->psLJ14Parameter            = NULL;
    gpu->psCustomParams             = NULL;
    gpu->psCustomExceptionID        = NULL;
    gpu->psCustomExceptionParams    = NULL;
    gpu->psEwaldCosSinSum           = NULL;
    gpu->psTabulatedErfc            = NULL;
    gpu->psPmeGrid                  = NULL;
    gpu->psPmeBsplineModuli[0]      = NULL;
    gpu->psPmeBsplineModuli[1]      = NULL;
    gpu->psPmeBsplineModuli[2]      = NULL;
    gpu->psPmeBsplineTheta          = NULL;
    gpu->psPmeBsplineDtheta         = NULL;
    gpu->psPmeAtomRange             = NULL;
    gpu->psPmeAtomGridIndex         = NULL;
    gpu->psShakeID                  = NULL;
    gpu->psShakeParameter           = NULL;
    gpu->psSettleID                 = NULL;
    gpu->psSettleParameter          = NULL;
    gpu->psExclusion                = NULL;
    gpu->psExclusionIndex           = NULL;
    gpu->psWorkUnit                 = NULL;
    gpu->psInteractingWorkUnit      = NULL;
    gpu->psInteractionFlag          = NULL;
    gpu->psInteractionCount         = NULL;
    gpu->psGridBoundingBox          = NULL;
    gpu->psGridCenter               = NULL;
    gpu->psCcmaAtoms                = NULL;
    gpu->psCcmaDistance             = NULL;
    gpu->psCcmaAtomConstraints      = NULL;
    gpu->psCcmaNumAtomConstraints   = NULL;
    gpu->psCcmaDelta1               = NULL;
    gpu->psCcmaDelta2               = NULL;
    gpu->psSyncCounter              = NULL;
    gpu->psRequiredIterations       = NULL;
    gpu->psCcmaReducedMass          = NULL;
    gpu->psConstraintMatrixColumn   = NULL;
    gpu->psConstraintMatrixValue    = NULL;
    gpu->psTabulatedFunctionParams  = NULL;
    for (int i = 0; i < MAX_TABULATED_FUNCTIONS; i++)
        gpu->tabulatedFunctions[i].coefficients = NULL;

    // Initialize output buffer before reading parameters
    gpu->pOutputBufferCounter       = new unsigned int[gpu->sim.paddedNumberOfAtoms];
    memset(gpu->pOutputBufferCounter, 0, gpu->sim.paddedNumberOfAtoms * sizeof(unsigned int));

    return (void*)gpu;
}

extern "C"
void gpuSetLangevinIntegrationParameters(gpuContext gpu, float tau, float deltaT, float temperature, float errorTol) {
    gpu->sim.deltaT                 = deltaT;
    gpu->sim.oneOverDeltaT          = 1.0f/deltaT;
    gpu->sim.errorTol               = errorTol;
    gpu->sim.tau                    = tau;
    gpu->sim.T                      = temperature;
    gpu->sim.kT                     = BOLTZ * gpu->sim.T;
    double GDT                       = gpu->sim.deltaT / gpu->sim.tau;
    double EPH                       = exp(0.5 * GDT);
    double EMH                       = exp(-0.5 * GDT);
    double EP                        = exp(GDT);
    double EM                        = exp(-GDT);
    double B, C, D;
    if (GDT >= 0.1)
    {
        double term1 = EPH - 1.0;
        term1                      *= term1;
        B                           = GDT * (EP - 1.0) - 4.0 * term1;
        C                           = GDT - 3.0 + 4.0 * EMH - EM;
        D                           = 2.0 - EPH - EMH;
    }
    else
    {
        double term1                 = 0.5 * GDT;
        double term2                 = term1 * term1;
        double term4                 = term2 * term2;

        double third                 = 1.0 / 3.0;
        double o7_9                  = 7.0 / 9.0;
        double o1_12                 = 1.0 / 12.0;
        double o17_90                = 17.0 / 90.0;
        double o7_30                 = 7.0 / 30.0;
        double o31_1260              = 31.0 / 1260.0;
        double o_360                 = 1.0 / 360.0;

        B                           = term4 * (third + term1 * (third + term1 * (o17_90 + term1 * o7_9)));
        C                           = term2 * term1 * (2.0 * third + term1 * (-0.5 + term1 * (o7_30 + term1 * (-o1_12 + term1 * o31_1260))));
        D                           = term2 * (-1.0 + term2 * (-o1_12 - term2 * o_360));
    }
    double DOverTauC                 = D / (gpu->sim.tau * C);
    double TauOneMinusEM             = gpu->sim.tau * (1.0-EM);
    double TauDOverEMMinusOne        = gpu->sim.tau * D / (EM - 1.0);
    double fix1                      = gpu->sim.tau * (EPH - EMH);
    if (fix1 == 0.0)
        fix1 = deltaT;
    double oneOverFix1               = 1.0 / fix1;
    double V                         = sqrt(gpu->sim.kT * (1.0 - EM));
    double X                         = gpu->sim.tau * sqrt(gpu->sim.kT * C);
    double Yv                        = sqrt(gpu->sim.kT * B / C);
    double Yx                        = gpu->sim.tau * sqrt(gpu->sim.kT * B / (1.0 - EM));
    (*gpu->psLangevinParameters)[0] = (float) EM;
    (*gpu->psLangevinParameters)[1] = (float) EM;
    (*gpu->psLangevinParameters)[2] = (float) DOverTauC;
    (*gpu->psLangevinParameters)[3] = (float) TauOneMinusEM;
    (*gpu->psLangevinParameters)[4] = (float) TauDOverEMMinusOne;
    (*gpu->psLangevinParameters)[5] = (float) V;
    (*gpu->psLangevinParameters)[6] = (float) X;
    (*gpu->psLangevinParameters)[7] = (float) Yv;
    (*gpu->psLangevinParameters)[8] = (float) Yx;
    (*gpu->psLangevinParameters)[9] = (float) fix1;
    (*gpu->psLangevinParameters)[10] = (float) oneOverFix1;
    gpu->psLangevinParameters->Upload();
    gpu->psStepSize->Download();
    (*gpu->psStepSize)[0].y = deltaT;
    gpu->psStepSize->Upload();
}

extern "C"
void gpuSetVerletIntegrationParameters(gpuContext gpu, float deltaT, float errorTol) {
    gpu->sim.deltaT                 = deltaT;
    gpu->sim.oneOverDeltaT          = 1.0f/deltaT;
    gpu->sim.errorTol               = errorTol;
    gpu->psStepSize->Download();
    (*gpu->psStepSize)[0].y = deltaT;
    gpu->psStepSize->Upload();
}

extern "C"
void gpuSetBrownianIntegrationParameters(gpuContext gpu, float tau, float deltaT, float temperature) {
    gpu->sim.deltaT                 = deltaT;
    gpu->sim.oneOverDeltaT          = 1.0f/deltaT;
    gpu->sim.tau                    = tau;
    gpu->sim.tauDeltaT              = gpu->sim.deltaT * gpu->sim.tau;
    gpu->sim.T                      = temperature;
    gpu->sim.kT                     = BOLTZ * gpu->sim.T;
    gpu->sim.noiseAmplitude         = sqrt(2.0f*gpu->sim.kT*deltaT*tau);
    gpu->psStepSize->Download();
    (*gpu->psStepSize)[0].y = deltaT;
    gpu->psStepSize->Upload();
}

extern "C"
void gpuSetAndersenThermostatParameters(gpuContext gpu, float temperature, float collisionFrequency) {
    gpu->sim.T                      = temperature;
    gpu->sim.kT                     = BOLTZ * gpu->sim.T;
    gpu->sim.collisionFrequency     = collisionFrequency;
}

extern "C"
void gpuShutDown(gpuContext gpu)
{
    // Delete sysmem pointers
    delete[] gpu->pOutputBufferCounter;
    delete[] gpu->gpAtomTable;
    delete[] gpu->pAtomSymbol;

    // Delete device pointers
    delete gpu->psPosq4;
    delete gpu->psPosqP4;
    delete gpu->psOldPosq4;
    delete gpu->psVelm4;
    delete gpu->psForce4;
    delete gpu->psEnergy;
    delete gpu->psxVector4;
    delete gpu->psvVector4;
    delete gpu->psSigEps2;
    if (gpu->psCustomParams != NULL) {
        delete gpu->psCustomParams;
        delete gpu->psCustomExceptionID;
        delete gpu->psCustomExceptionParams;
    }
    if (gpu->psEwaldCosSinSum != NULL)
        delete gpu->psEwaldCosSinSum;
    if (gpu->psPmeGrid != NULL) {
        delete gpu->psPmeGrid;
        delete gpu->psPmeBsplineModuli[0];
        delete gpu->psPmeBsplineModuli[1];
        delete gpu->psPmeBsplineModuli[2];
        delete gpu->psPmeBsplineTheta;
        delete gpu->psPmeBsplineDtheta;
        delete gpu->psPmeAtomRange;
        delete gpu->psPmeAtomGridIndex;
        cufftDestroy(gpu->fftplan);
    }
    if (gpu->psTabulatedErfc != NULL)
        delete gpu->psTabulatedErfc;
    delete gpu->psObcData;
    delete gpu->psObcChain;
    delete gpu->psBornForce;
    delete gpu->psBornRadii;
    delete gpu->psBornSum;
    delete gpu->psBondID;
    delete gpu->psBondParameter;
    delete gpu->psBondAngleID1;
    delete gpu->psBondAngleID2;
    delete gpu->psBondAngleParameter;
    delete gpu->psDihedralID1;
    delete gpu->psDihedralID2;
    delete gpu->psDihedralParameter;
    delete gpu->psRbDihedralID1;
    delete gpu->psRbDihedralID2;
    delete gpu->psRbDihedralParameter1;
    delete gpu->psRbDihedralParameter2;
    delete gpu->psLJ14ID;
    delete gpu->psLJ14Parameter;
    delete gpu->psShakeID;
    delete gpu->psShakeParameter;
    delete gpu->psSettleID;
    delete gpu->psSettleParameter;
    delete gpu->psNonShakeID;
    delete gpu->psExclusion;
    delete gpu->psExclusionIndex;
    delete gpu->psWorkUnit;
    delete gpu->psInteractingWorkUnit;
    delete gpu->psInteractionFlag;
    delete gpu->psInteractionCount;
    delete gpu->psStepSize;
    delete gpu->psLangevinParameters;
    delete gpu->psRandom4;
    delete gpu->psRandom2;
    delete gpu->psRandomPosition;    
    delete gpu->psRandomSeed;
    delete gpu->psLinearMomentum;
    delete gpu->psAtomIndex;
    delete gpu->psGridBoundingBox;
    delete gpu->psGridCenter;
    delete gpu->psCcmaAtoms;
    delete gpu->psCcmaDistance;
    delete gpu->psCcmaAtomConstraints;
    delete gpu->psCcmaNumAtomConstraints;
    delete gpu->psCcmaDelta1;
    delete gpu->psCcmaDelta2;
    delete gpu->psSyncCounter;
    delete gpu->psRequiredIterations;
    delete gpu->psCcmaReducedMass;
    delete gpu->psConstraintMatrixColumn;
    delete gpu->psConstraintMatrixValue;
    delete gpu->psTabulatedFunctionParams;
    for (int i = 0; i < MAX_TABULATED_FUNCTIONS; i++)
        if (gpu->tabulatedFunctions[i].coefficients != NULL)
            delete gpu->tabulatedFunctions[i].coefficients;
    if (gpu->compactPlan.valid)
        destroyCompactionPlan(gpu->compactPlan);

    // Wrap up
    delete gpu;
    return;
}

extern "C"
int gpuBuildOutputBuffers(gpuContext gpu)
{
    // Select the number of output buffer to use.
    gpu->bOutputBufferPerWarp           = true;
    gpu->sim.nonbondOutputBuffers       = gpu->sim.nonbond_blocks * gpu->sim.nonbond_threads_per_block / GRID;
    if (gpu->sim.nonbondOutputBuffers >= gpu->sim.paddedNumberOfAtoms/GRID)
    {
        // For small systems, it is more efficient to have one output buffer per block of 32 atoms instead of one per warp.
        gpu->bOutputBufferPerWarp           = false;
        gpu->sim.nonbondOutputBuffers       = gpu->sim.paddedNumberOfAtoms / GRID;
    }
    gpu->sim.totalNonbondOutputBuffers  = (gpu->bIncludeGBSA ? 2 * gpu->sim.nonbondOutputBuffers : gpu->sim.nonbondOutputBuffers);
    gpu->sim.outputBuffers              = gpu->sim.totalNonbondOutputBuffers;


    unsigned int outputBuffers = gpu->sim.totalNonbondOutputBuffers;
    for (unsigned int i = 0; i < gpu->sim.paddedNumberOfAtoms; i++)
    {
        if (outputBuffers < gpu->pOutputBufferCounter[i])
        {
            outputBuffers = gpu->pOutputBufferCounter[i];
        }
    }    
    gpu->sim.outputBuffers      = outputBuffers;
    gpu->sim.energyOutputBuffers = max(gpu->sim.nonbond_threads_per_block, gpu->sim.localForces_threads_per_block)*gpu->sim.blocks;
    gpu->psForce4               = new CUDAStream<float4>(gpu->sim.paddedNumberOfAtoms, outputBuffers, "Force");
    gpu->psEnergy               = new CUDAStream<float>(gpu->sim.energyOutputBuffers, 1, "Energy");
    gpu->psBornForce            = new CUDAStream<float>(gpu->sim.paddedNumberOfAtoms, gpu->sim.nonbondOutputBuffers, "BornForce");
    gpu->psBornSum              = new CUDAStream<float>(gpu->sim.paddedNumberOfAtoms, gpu->sim.nonbondOutputBuffers, "BornSum");
    gpu->sim.pForce4            = gpu->psForce4->_pDevStream[0];
    gpu->sim.pForce4a           = gpu->sim.pForce4;
    gpu->sim.pForce4b           = gpu->sim.pForce4 + 1 * gpu->sim.nonbondOutputBuffers * gpu->sim.stride;
    gpu->sim.pEnergy            = gpu->psEnergy->_pDevStream[0];
    gpu->sim.pBornForce         = gpu->psBornForce->_pDevStream[0];
    gpu->sim.pBornSum           = gpu->psBornSum->_pDevStream[0];

    // Determine local energy paramter offsets for bonded interactions
    gpu->sim.bond_offset        =                                  gpu->psBondParameter->_stride;
    gpu->sim.bond_angle_offset  = gpu->sim.bond_offset           + gpu->psBondAngleParameter->_stride;
    gpu->sim.dihedral_offset    = gpu->sim.bond_angle_offset     + gpu->psDihedralParameter->_stride;
    gpu->sim.rb_dihedral_offset = gpu->sim.dihedral_offset       + gpu->psRbDihedralParameter1->_stride;
    gpu->sim.LJ14_offset        = gpu->sim.rb_dihedral_offset    + gpu->psLJ14Parameter->_stride;
    gpu->sim.localForces_threads_per_block  = (gpu->sim.LJ14_offset / gpu->sim.blocks + 15) & 0xfffffff0;
    if (gpu->sim.localForces_threads_per_block > gpu->sim.max_localForces_threads_per_block)
        gpu->sim.localForces_threads_per_block = gpu->sim.max_localForces_threads_per_block;
    if (gpu->sim.localForces_threads_per_block < 1)
        gpu->sim.localForces_threads_per_block = 1;

    // Flip local force output buffers
    int flip = outputBuffers - 1;
    for (int i = 0; i < (int) gpu->sim.bonds; i++)
    {
        (*gpu->psBondID)[i].z = flip - (*gpu->psBondID)[i].z;
        (*gpu->psBondID)[i].w = flip - (*gpu->psBondID)[i].w;
    }
    for (int i = 0; i < (int) gpu->sim.bond_angles; i++)
    {
        (*gpu->psBondAngleID1)[i].w = flip - (*gpu->psBondAngleID1)[i].w;
        (*gpu->psBondAngleID2)[i].x = flip - (*gpu->psBondAngleID2)[i].x;
        (*gpu->psBondAngleID2)[i].y = flip - (*gpu->psBondAngleID2)[i].y;
    }
    for (int i = 0; i < (int) gpu->sim.dihedrals; i++)
    {
        (*gpu->psDihedralID2)[i].x = flip - (*gpu->psDihedralID2)[i].x;
        (*gpu->psDihedralID2)[i].y = flip - (*gpu->psDihedralID2)[i].y;
        (*gpu->psDihedralID2)[i].z = flip - (*gpu->psDihedralID2)[i].z;
        (*gpu->psDihedralID2)[i].w = flip - (*gpu->psDihedralID2)[i].w;
    }
    for (int i = 0; i < (int) gpu->sim.rb_dihedrals; i++)
    {
        (*gpu->psRbDihedralID2)[i].x = flip - (*gpu->psRbDihedralID2)[i].x;
        (*gpu->psRbDihedralID2)[i].y = flip - (*gpu->psRbDihedralID2)[i].y;
        (*gpu->psRbDihedralID2)[i].z = flip - (*gpu->psRbDihedralID2)[i].z;
        (*gpu->psRbDihedralID2)[i].w = flip - (*gpu->psRbDihedralID2)[i].w;
    }
    for (int i = 0; i < (int) gpu->sim.LJ14s; i++)
    {
        (*gpu->psLJ14ID)[i].z = flip - (*gpu->psLJ14ID)[i].z;
        (*gpu->psLJ14ID)[i].w = flip - (*gpu->psLJ14ID)[i].w;
    }
    gpu->psBondID->Upload();
    gpu->psBondAngleID1->Upload();
    gpu->psBondAngleID2->Upload();
    gpu->psDihedralID2->Upload();
    gpu->psRbDihedralID2->Upload();
    gpu->psLJ14ID->Upload();

    return 1;
}

extern "C"
int gpuBuildThreadBlockWorkList(gpuContext gpu)
{
    const unsigned int atoms = gpu->sim.paddedNumberOfAtoms;
    const unsigned int grid = gpu->grid;
    const unsigned int dim = (atoms + (grid - 1)) / grid;
    const unsigned int cells = dim * (dim + 1) / 2;
    CUDAStream<unsigned int>* psWorkUnit = new CUDAStream<unsigned int>(cells, 1u, "WorkUnit");
    unsigned int* pWorkList = psWorkUnit->_pSysData;
    gpu->psWorkUnit = psWorkUnit;
    gpu->sim.pWorkUnit = psWorkUnit->_pDevStream[0];
    CUDAStream<unsigned int>* psInteractingWorkUnit = new CUDAStream<unsigned int>(cells, 1u, "InteractingWorkUnit");
    gpu->psInteractingWorkUnit = psInteractingWorkUnit;
    gpu->sim.pInteractingWorkUnit = psInteractingWorkUnit->_pDevStream[0];
    CUDAStream<unsigned int>* psInteractionFlag = new CUDAStream<unsigned int>(cells, 1u, "InteractionFlag");
    gpu->psInteractionFlag = psInteractionFlag;
    gpu->sim.pInteractionFlag = psInteractionFlag->_pDevStream[0];
    CUDAStream<size_t>* psInteractionCount = new CUDAStream<size_t>(1, 1u, "InteractionCount");
    gpu->psInteractionCount = psInteractionCount;
    gpu->sim.pInteractionCount = psInteractionCount->_pDevStream[0];
    CUDAStream<float4>* psGridBoundingBox = new CUDAStream<float4>(dim, 1u, "GridBoundingBox");
    gpu->psGridBoundingBox = psGridBoundingBox;
    gpu->sim.pGridBoundingBox = psGridBoundingBox->_pDevStream[0];
    CUDAStream<float4>* psGridCenter = new CUDAStream<float4>(dim, 1u, "GridCenter");
    gpu->psGridCenter = psGridCenter;
    gpu->sim.pGridCenter = psGridCenter->_pDevStream[0];
    gpu->sim.nonbond_workBlock      = gpu->sim.nonbond_threads_per_block / GRID;
    gpu->sim.bornForce2_workBlock   = gpu->sim.bornForce2_threads_per_block / GRID;
    gpu->sim.workUnits = cells;

    // Initialize the plan for doing stream compaction.
    planCompaction(gpu->compactPlan);

    // Increase block count if necessary for extra large molecules that would
    // otherwise overflow the SM workunit buffers
//    int minimumBlocks = (cells + gpu->sim.workUnitsPerSM - 1) / gpu->sim.workUnitsPerSM;
//    if ((int) gpu->sim.nonbond_blocks < minimumBlocks)
//    {
//        gpu->sim.nonbond_blocks = gpu->sim.nonbond_blocks * ((minimumBlocks + gpu->sim.nonbond_blocks - 1) / gpu->sim.nonbond_blocks);
//    }
//    if ((int) gpu->sim.bornForce2_blocks < minimumBlocks)
//    {
//        gpu->sim.bornForce2_blocks = gpu->sim.bornForce2_blocks * ((minimumBlocks + gpu->sim.bornForce2_blocks - 1) / gpu->sim.bornForce2_blocks);
//    }
    gpu->sim.nbWorkUnitsPerBlock            = cells / gpu->sim.nonbond_blocks;
    gpu->sim.nbWorkUnitsPerBlockRemainder   = cells - gpu->sim.nonbond_blocks * gpu->sim.nbWorkUnitsPerBlock;
    gpu->sim.bf2WorkUnitsPerBlock           = cells / gpu->sim.bornForce2_blocks;
    gpu->sim.bf2WorkUnitsPerBlockRemainder  = cells - gpu->sim.bornForce2_blocks * gpu->sim.bf2WorkUnitsPerBlock;
    gpu->sim.interaction_threads_per_block = 64;
    gpu->sim.interaction_blocks = (gpu->sim.workUnits + gpu->sim.interaction_threads_per_block - 1) / gpu->sim.interaction_threads_per_block;
    if (gpu->sim.interaction_blocks > 8*gpu->sim.blocks)
        gpu->sim.interaction_blocks = 8*gpu->sim.blocks;

    // Decrease thread count for extra small molecules to spread computation
    // across entire chip
    int activeWorkUnits = gpu->sim.nonbond_blocks * gpu->sim.nonbond_workBlock;
    if (activeWorkUnits > (int) cells)
    {
        int balancedWorkBlock                   = (cells + gpu->sim.nonbond_blocks - 1) / gpu->sim.nonbond_blocks;
        gpu->sim.nonbond_threads_per_block      = balancedWorkBlock * GRID;
        gpu->sim.nonbond_workBlock              = balancedWorkBlock;
    }
    activeWorkUnits = gpu->sim.bornForce2_blocks * gpu->sim.bornForce2_workBlock;
    if (activeWorkUnits > (int) cells)
    {
        int balancedWorkBlock                   = (cells + gpu->sim.bornForce2_blocks - 1) / gpu->sim.bornForce2_blocks;
        gpu->sim.bornForce2_threads_per_block   = balancedWorkBlock * GRID;
        gpu->sim.bornForce2_workBlock           = balancedWorkBlock;
    }

    unsigned int count = 0;
    for (unsigned int y = 0; y < dim; y++)
    {
        for (unsigned int x = y; x < dim; x++)
        {
            pWorkList[count] = (x << 17) | (y << 2);
            count++;
        }
    }
    (*gpu->psInteractionCount)[0] = gpu->sim.workUnits;

    gpu->psInteractionCount->Upload();
    psWorkUnit->Upload();
    gpuSetConstants(gpu);
    return cells;
}

extern "C"
void gpuBuildExclusionList(gpuContext gpu)
{
    const unsigned int atoms = gpu->sim.paddedNumberOfAtoms;
    const unsigned int grid = gpu->grid;
    const unsigned int dim = atoms/grid;
    unsigned int* pWorkList = gpu->psWorkUnit->_pSysData;

    // Mark which work units have exclusions.

    for (int atom1 = 0; atom1 < (int)gpu->exclusions.size(); ++atom1)
    {
        int x = atom1/grid;
        for (int j = 0; j < (int)gpu->exclusions[atom1].size(); ++j)
        {
            int atom2 = gpu->exclusions[atom1][j];
            int y = atom2/grid;
            int cell = (x > y ? x+y*dim-y*(y+1)/2 : y+x*dim-x*(x+1)/2);
            pWorkList[cell] |= 1;
        }
    }
    if ((int)gpu->sim.paddedNumberOfAtoms > gpu->natoms)
    {
        int lastBlock = gpu->natoms/grid;
        for (int i = 0; i < (int)gpu->sim.workUnits; ++i)
        {
            int x = pWorkList[i]>>17;
            int y = (pWorkList[i]>>2)&0x7FFF;
            if (x == lastBlock || y == lastBlock)
                pWorkList[i] |= 1;
        }
    }

    // Build a list of indexes for the work units with exclusions.

    CUDAStream<unsigned int>* psExclusionIndex = new CUDAStream<unsigned int>(gpu->sim.workUnits, 1u, "ExclusionIndex");
    gpu->psExclusionIndex = psExclusionIndex;
    unsigned int* pExclusionIndex = psExclusionIndex->_pSysData;
    gpu->sim.pExclusionIndex = psExclusionIndex->_pDevData;
    int numWithExclusions = 0;
    for (int i = 0; i < (int)psExclusionIndex->_length; ++i)
        if ((pWorkList[i]&1) == 1)
            pExclusionIndex[i] = (numWithExclusions++)*grid;

    // Record the exclusion data.

    CUDAStream<unsigned int>* psExclusion = new CUDAStream<unsigned int>(numWithExclusions*grid, 1u, "Exclusion");
    gpu->psExclusion = psExclusion;
    unsigned int* pExclusion = psExclusion->_pSysData;
    gpu->sim.pExclusion = psExclusion->_pDevData;
    for (int i = 0; i < (int)psExclusion->_length; ++i)
        pExclusion[i] = 0xFFFFFFFF;
    for (int atom1 = 0; atom1 < (int)gpu->exclusions.size(); ++atom1)
    {
        int x = atom1/grid;
        int offset1 = atom1-x*grid;
        for (int j = 0; j < (int)gpu->exclusions[atom1].size(); ++j)
        {
            int atom2 = gpu->exclusions[atom1][j];
            int y = atom2/grid;
            int offset2 = atom2-y*grid;
            if (x > y)
            {
                int cell = x+y*dim-y*(y+1)/2;
                pExclusion[pExclusionIndex[cell]+offset1] &= 0xFFFFFFFF-(1<<offset2);
            }
            else
            {
                int cell = y+x*dim-x*(x+1)/2;
                pExclusion[pExclusionIndex[cell]+offset2] &= 0xFFFFFFFF-(1<<offset1);
            }
        }
    }

    // Mark all interactions that involve a padding atom as being excluded.

    for (int atom1 = gpu->natoms; atom1 < (int)atoms; ++atom1)
    {
        int x = atom1/grid;
        int offset1 = atom1-x*grid;
        for (int atom2 = 0; atom2 < (int)atoms; ++atom2)
        {
            int y = atom2/grid;
            int offset2 = atom2-y*grid;
            if (x >= y)
            {
                int cell = x+y*dim-y*(y+1)/2;
                pExclusion[pExclusionIndex[cell]+offset1] &= 0xFFFFFFFF-(1<<offset2);
            }
            if (y >= x)
            {
                int cell = y+x*dim-x*(x+1)/2;
                pExclusion[pExclusionIndex[cell]+offset2] &= 0xFFFFFFFF-(1<<offset1);
            }
        }
    }
    
    psExclusion->Upload();
    psExclusionIndex->Upload();
    gpu->psWorkUnit->Upload();
    gpuSetConstants(gpu);
}

extern "C"
int gpuSetConstants(gpuContext gpu)
{
    SetCalculateCDLJForcesSim(gpu);
    SetCalculateCDLJObcGbsaForces1Sim(gpu);
    SetCalculateCustomNonbondedForcesSim(gpu);
    SetCalculateLocalForcesSim(gpu);
    SetCalculateObcGbsaBornSumSim(gpu);
    SetCalculateObcGbsaForces2Sim(gpu);
    SetCalculateAndersenThermostatSim(gpu);
    SetCalculatePMESim(gpu);
    SetForcesSim(gpu);
    SetShakeHSim(gpu);
    SetLangevinUpdateSim(gpu);
    SetVerletUpdateSim(gpu);
    SetBrownianUpdateSim(gpu);
    SetSettleSim(gpu);
    SetCCMASim(gpu);
    SetRandomSim(gpu);
    return 1;
}

static void tagAtomsInMolecule(int atom, int molecule, vector<int>& atomMolecule, vector<vector<int> >& atomBonds)
{
    // Recursively tag atoms as belonging to a particular molecule.

    atomMolecule[atom] = molecule;
    for (int i = 0; i < (int)atomBonds[atom].size(); i++)
        if (atomMolecule[atomBonds[atom][i]] == -1)
            tagAtomsInMolecule(atomBonds[atom][i], molecule, atomMolecule, atomBonds);
}

static void findMoleculeGroups(gpuContext gpu)
{
    // First make a list of constraints for future use.

    vector<Constraint> constraints;
    for (int i = 0; i < (int)gpu->sim.ShakeConstraints; i++)
    {
        int atom1 = (*gpu->psShakeID)[i].x;
        int atom2 = (*gpu->psShakeID)[i].y;
        int atom3 = (*gpu->psShakeID)[i].z;
        int atom4 = (*gpu->psShakeID)[i].w;
        float distance2 = (*gpu->psShakeParameter)[i].z;
        constraints.push_back(Constraint(atom1, atom2, distance2));
        if (atom3 != -1)
            constraints.push_back(Constraint(atom1, atom3, distance2));
        if (atom4 != -1)
            constraints.push_back(Constraint(atom1, atom4, distance2));
    }
    for (int i = 0; i < (int)gpu->sim.settleConstraints; i++)
    {
        int atom1 = (*gpu->psSettleID)[i].x;
        int atom2 = (*gpu->psSettleID)[i].y;
        int atom3 = (*gpu->psSettleID)[i].z;
        float distance12 = (*gpu->psSettleParameter)[i].x;
        float distance23 = (*gpu->psSettleParameter)[i].y;
        constraints.push_back(Constraint(atom1, atom2, distance12*distance12));
        constraints.push_back(Constraint(atom1, atom3, distance12*distance12));
        constraints.push_back(Constraint(atom2, atom3, distance23*distance23));
    }
    for (int i = 0; i < (int)gpu->sim.ccmaConstraints; i++)
    {
        int atom1 = (*gpu->psCcmaAtoms)[i].x;
        int atom2 = (*gpu->psCcmaAtoms)[i].y;
        float distance2 = (*gpu->psCcmaDistance)[i].w;
        constraints.push_back(Constraint(atom1, atom2, distance2));
    }

    // First make a list of every other atom to which each atom is connect by a bond, constraint, or exclusion.

    int numAtoms = gpu->natoms;
    vector<vector<int> > atomBonds(numAtoms);
    for (int i = 0; i < (int)gpu->sim.bonds; i++)
    {
        int atom1 = (*gpu->psBondID)[i].x;
        int atom2 = (*gpu->psBondID)[i].y;
        atomBonds[atom1].push_back(atom2);
        atomBonds[atom2].push_back(atom1);
    }
    for (int i = 0; i < (int)constraints.size(); i++)
    {
        int atom1 = constraints[i].atom1;
        int atom2 = constraints[i].atom2;
        atomBonds[atom1].push_back(atom2);
        atomBonds[atom2].push_back(atom1);
    }
    for (int i = 0; i < (int)gpu->exclusions.size(); i++)
        for (int j = 0; j < (int)gpu->exclusions[i].size(); j++)
            atomBonds[i].push_back(gpu->exclusions[i][j]);

    // Now tag atoms by which molecule they belong to.

    vector<int> atomMolecule(numAtoms, -1);
    int numMolecules = 0;
    for (int i = 0; i < numAtoms; i++)
        if (atomMolecule[i] == -1)
            tagAtomsInMolecule(i, numMolecules++, atomMolecule, atomBonds);
    vector<vector<int> > atomIndices(numMolecules);
    for (int i = 0; i < numAtoms; i++)
        atomIndices[atomMolecule[i]].push_back(i);

    // Construct a description of each molecule.

    vector<Molecule> molecules(numMolecules);
    for (int i = 0; i < numMolecules; i++)
        molecules[i].atoms = atomIndices[i];
    for (int i = 0; i < (int)gpu->sim.bonds; i++)
    {
        int atom1 = (*gpu->psBondID)[i].x;
        molecules[atomMolecule[atom1]].bonds.push_back(i);
    }
    for (int i = 0; i < (int)gpu->sim.bond_angles; i++)
    {
        int atom1 = (*gpu->psBondAngleID1)[i].x;
        molecules[atomMolecule[atom1]].angles.push_back(i);
    }
    for (int i = 0; i < (int)gpu->sim.dihedrals; i++)
    {
        int atom1 = (*gpu->psDihedralID1)[i].x;
        molecules[atomMolecule[atom1]].periodicTorsions.push_back(i);
    }
    for (int i = 0; i < (int)gpu->sim.rb_dihedrals; i++)
    {
        int atom1 = (*gpu->psRbDihedralID1)[i].x;
        molecules[atomMolecule[atom1]].rbTorsions.push_back(i);
    }
    for (int i = 0; i < (int)constraints.size(); i++)
    {
        molecules[atomMolecule[constraints[i].atom1]].constraints.push_back(i);
    }
    for (int i = 0; i < (int)gpu->sim.LJ14s; i++)
    {
        int atom1 = (*gpu->psLJ14ID)[i].x;
        molecules[atomMolecule[atom1]].lj14s.push_back(i);
    }

    // Sort them into groups of identical molecules.

    vector<Molecule> uniqueMolecules;
    vector<vector<int> > moleculeInstances;
    for (int molIndex = 0; molIndex < (int)molecules.size(); molIndex++)
    {
        Molecule& mol = molecules[molIndex];

        // See if it is identical to another molecule.

        bool isNew = true;
        for (int j = 0; j < (int)uniqueMolecules.size() && isNew; j++)
        {
            Molecule& mol2 = uniqueMolecules[j];
            bool identical = true;
            if (mol.atoms.size() != mol2.atoms.size() || mol.bonds.size() != mol2.bonds.size()
                    || mol.angles.size() != mol2.angles.size() || mol.periodicTorsions.size() != mol2.periodicTorsions.size()
                    || mol.rbTorsions.size() != mol2.rbTorsions.size() || mol.constraints.size() != mol2.constraints.size()
                    || mol.lj14s.size() != mol2.lj14s.size())
                identical = false;
            int atomOffset = mol2.atoms[0]-mol.atoms[0];
            float4* posq = gpu->psPosq4->_pSysData;
            float4* velm = gpu->psVelm4->_pSysData;
            float2* sigeps = gpu->psSigEps2->_pSysData;
            for (int i = 0; i < (int)mol.atoms.size() && identical; i++)
                if (mol.atoms[i] != mol2.atoms[i]-atomOffset || posq[mol.atoms[i]].w != posq[mol2.atoms[i]].w ||
                        velm[mol.atoms[i]].w != velm[mol2.atoms[i]].w || sigeps[mol.atoms[i]].x != sigeps[mol2.atoms[i]].x ||
                        sigeps[mol.atoms[i]].y != sigeps[mol2.atoms[i]].y)
                    identical = false;
            int4* bondID = gpu->psBondID->_pSysData;
            float2* bondParam = gpu->psBondParameter->_pSysData;
            for (int i = 0; i < (int)mol.bonds.size() && identical; i++)
                if (bondID[mol.bonds[i]].x != bondID[mol2.bonds[i]].x-atomOffset || bondID[mol.bonds[i]].y != bondID[mol2.bonds[i]].y-atomOffset ||
                        bondParam[mol.bonds[i]].x != bondParam[mol2.bonds[i]].x || bondParam[mol.bonds[i]].y != bondParam[mol2.bonds[i]].y)
                    identical = false;
            int4* angleID = gpu->psBondAngleID1->_pSysData;
            float2* angleParam = gpu->psBondAngleParameter->_pSysData;
            for (int i = 0; i < (int)mol.angles.size() && identical; i++)
                if (angleID[mol.angles[i]].x != angleID[mol2.angles[i]].x-atomOffset ||
                        angleID[mol.angles[i]].y != angleID[mol2.angles[i]].y-atomOffset ||
                        angleID[mol.angles[i]].z != angleID[mol2.angles[i]].z-atomOffset ||
                        angleParam[mol.angles[i]].x != angleParam[mol2.angles[i]].x ||
                        angleParam[mol.angles[i]].y != angleParam[mol2.angles[i]].y)
                    identical = false;
            int4* periodicID = gpu->psDihedralID1->_pSysData;
            float4* periodicParam = gpu->psDihedralParameter->_pSysData;
            for (int i = 0; i < (int)mol.periodicTorsions.size() && identical; i++)
                if (periodicID[mol.periodicTorsions[i]].x != periodicID[mol2.periodicTorsions[i]].x-atomOffset ||
                        periodicID[mol.periodicTorsions[i]].y != periodicID[mol2.periodicTorsions[i]].y-atomOffset ||
                        periodicID[mol.periodicTorsions[i]].z != periodicID[mol2.periodicTorsions[i]].z-atomOffset ||
                        periodicID[mol.periodicTorsions[i]].w != periodicID[mol2.periodicTorsions[i]].w-atomOffset ||
                        periodicParam[mol.periodicTorsions[i]].x != periodicParam[mol2.periodicTorsions[i]].x ||
                        periodicParam[mol.periodicTorsions[i]].y != periodicParam[mol2.periodicTorsions[i]].y ||
                        periodicParam[mol.periodicTorsions[i]].z != periodicParam[mol2.periodicTorsions[i]].z)
                    identical = false;
            int4* rbID = gpu->psRbDihedralID1->_pSysData;
            float4* rbParam1 = gpu->psRbDihedralParameter1->_pSysData;
            float2* rbParam2 = gpu->psRbDihedralParameter2->_pSysData;
            for (int i = 0; i < (int)mol.rbTorsions.size() && identical; i++)
                if (rbID[mol.rbTorsions[i]].x != rbID[mol2.rbTorsions[i]].x-atomOffset ||
                        rbID[mol.rbTorsions[i]].y != rbID[mol2.rbTorsions[i]].y-atomOffset ||
                        rbID[mol.rbTorsions[i]].z != rbID[mol2.rbTorsions[i]].z-atomOffset ||
                        rbID[mol.rbTorsions[i]].w != rbID[mol2.rbTorsions[i]].w-atomOffset ||
                        rbParam1[mol.rbTorsions[i]].x != rbParam1[mol2.rbTorsions[i]].x ||
                        rbParam1[mol.rbTorsions[i]].y != rbParam1[mol2.rbTorsions[i]].y ||
                        rbParam1[mol.rbTorsions[i]].z != rbParam1[mol2.rbTorsions[i]].z ||
                        rbParam1[mol.rbTorsions[i]].w != rbParam1[mol2.rbTorsions[i]].w ||
                        rbParam2[mol.rbTorsions[i]].x != rbParam2[mol2.rbTorsions[i]].x ||
                        rbParam2[mol.rbTorsions[i]].y != rbParam2[mol2.rbTorsions[i]].y)
                    identical = false;
            for (int i = 0; i < (int)mol.constraints.size() && identical; i++)
                if (constraints[mol.constraints[i]].atom1 != constraints[mol2.constraints[i]].atom1-atomOffset ||
                        constraints[mol.constraints[i]].atom2 != constraints[mol2.constraints[i]].atom2-atomOffset ||
                        constraints[mol.constraints[i]].distance2 != constraints[mol2.constraints[i]].distance2)
                    identical = false;
            int4* lj14ID = gpu->psLJ14ID->_pSysData;
            float4* lj14Param = gpu->psLJ14Parameter->_pSysData;
            for (int i = 0; i < (int)mol.lj14s.size() && identical; i++)
                if (lj14ID[mol.lj14s[i]].x != lj14ID[mol2.lj14s[i]].x-atomOffset || lj14ID[mol.lj14s[i]].y != lj14ID[mol2.lj14s[i]].y-atomOffset ||
                        lj14Param[mol.lj14s[i]].x != lj14Param[mol2.lj14s[i]].x || lj14Param[mol.lj14s[i]].y != lj14Param[mol2.lj14s[i]].y ||
                        lj14Param[mol.lj14s[i]].z != lj14Param[mol2.lj14s[i]].z)
                    identical = false;
            if (identical)
            {
                moleculeInstances[j].push_back(mol.atoms[0]);
                isNew = false;
            }
        }
        if (isNew)
        {
            uniqueMolecules.push_back(mol);
            moleculeInstances.push_back(vector<int>());
            moleculeInstances[moleculeInstances.size()-1].push_back(mol.atoms[0]);
        }
    }
    gpu->moleculeGroups.resize(moleculeInstances.size());
    for (int i = 0; i < (int)moleculeInstances.size(); i++)
    {
        gpu->moleculeGroups[i].instances = moleculeInstances[i];
        vector<int>& atoms = uniqueMolecules[i].atoms;
        gpu->moleculeGroups[i].atoms.resize(atoms.size());
        for (int j = 0; j < (int)atoms.size(); j++)
            gpu->moleculeGroups[i].atoms[j] = atoms[j]-atoms[0];
    }
}

extern "C"
void gpuReorderAtoms(gpuContext gpu)
{
    if (gpu->natoms == 0 || gpu->sim.nonbondedCutoffSqr == 0.0)
        return;
    if (gpu->moleculeGroups.size() == 0)
        findMoleculeGroups(gpu);

    // Find the range of positions and the number of bins along each axis.

    int numAtoms = gpu->natoms;
    gpu->psPosq4->Download();
    gpu->psVelm4->Download();
    float4* posq = gpu->psPosq4->_pSysData;
    float4* velm = gpu->psVelm4->_pSysData;
    float minx = posq[0].x, maxx = posq[0].x;
    float miny = posq[0].y, maxy = posq[0].y;
    float minz = posq[0].z, maxz = posq[0].z;
    if (gpu->sim.nonbondedMethod == PERIODIC || gpu->sim.nonbondedMethod == EWALD || gpu->sim.nonbondedMethod == PARTICLE_MESH_EWALD)
    {
        minx = miny = minz = 0.0;
        maxx = gpu->sim.periodicBoxSizeX;
        maxy = gpu->sim.periodicBoxSizeY;
        maxz = gpu->sim.periodicBoxSizeZ;
    }
    else
    {
        for (int i = 1; i < numAtoms; i++)
        {
            minx = min(minx, posq[i].x);
            maxx = max(maxx, posq[i].x);
            miny = min(miny, posq[i].y);
            maxy = max(maxy, posq[i].y);
            minz = min(minz, posq[i].z);
            maxz = max(maxz, posq[i].z);
        }
    }

    // Loop over each group of identical molecules and reorder them.

    vector<int> originalIndex(numAtoms);
    vector<float4> newPosq(numAtoms);
    vector<float4> newVelm(numAtoms);
    vector<int3> newCellOffsets(numAtoms);
    for (int group = 0; group < (int)gpu->moleculeGroups.size(); group++)
    {
        // Find the center of each molecule.

        gpuMoleculeGroup& mol = gpu->moleculeGroups[group];
        int numMolecules = mol.instances.size();
        vector<int>& atoms = mol.atoms;
        vector<float3> molPos(numMolecules);
        for (int i = 0; i < numMolecules; i++)
        {
            molPos[i].x = 0.0f;
            molPos[i].y = 0.0f;
            molPos[i].z = 0.0f;
            for (int j = 0; j < (int)atoms.size(); j++)
            {
                int atom = atoms[j]+mol.instances[i];
                molPos[i].x += posq[atom].x;
                molPos[i].y += posq[atom].y;
                molPos[i].z += posq[atom].z;
            }
            molPos[i].x /= atoms.size();
            molPos[i].y /= atoms.size();
            molPos[i].z /= atoms.size();
        }
        if (gpu->sim.nonbondedMethod == PERIODIC || gpu->sim.nonbondedMethod == EWALD || gpu->sim.nonbondedMethod == PARTICLE_MESH_EWALD)
        {
            // Move each molecule position into the same box.

            for (int i = 0; i < numMolecules; i++)
            {
                int xcell = (int) floor(molPos[i].x/gpu->sim.periodicBoxSizeX);
                int ycell = (int) floor(molPos[i].y/gpu->sim.periodicBoxSizeY);
                int zcell = (int) floor(molPos[i].z/gpu->sim.periodicBoxSizeZ);
                float dx = xcell*gpu->sim.periodicBoxSizeX;
                float dy = ycell*gpu->sim.periodicBoxSizeY;
                float dz = zcell*gpu->sim.periodicBoxSizeZ;
                if (dx != 0.0f || dy != 0.0f || dz != 0.0f)
                {
                    molPos[i].x -= dx;
                    molPos[i].y -= dy;
                    molPos[i].z -= dz;
                    for (int j = 0; j < (int)atoms.size(); j++)
                    {
                        int atom = atoms[j]+mol.instances[i];
                        posq[atom].x -= dx;
                        posq[atom].y -= dy;
                        posq[atom].z -= dz;
                        gpu->posCellOffsets[atom].x -= xcell;
                        gpu->posCellOffsets[atom].y -= ycell;
                        gpu->posCellOffsets[atom].z -= zcell;
                    }
                }
            }
        }

        // Select a bin for each molecule, then sort them by bin.

        bool useHilbert = (numMolecules > 5000 || atoms.size() > 8); // For small systems, a simple zigzag curve works better than a Hilbert curve.
        float binWidth;
        if (useHilbert)
            binWidth = (float)(max(max(maxx-minx, maxy-miny), maxz-minz)/255.0);
        else
            binWidth = (float)(0.2*sqrt(gpu->sim.nonbondedCutoffSqr));
        int xbins = 1 + (int) ((maxx-minx)/binWidth);
        int ybins = 1 + (int) ((maxy-miny)/binWidth);
        vector<pair<int, int> > molBins(numMolecules);
        bitmask_t coords[3];
        for (int i = 0; i < numMolecules; i++)
        {
            int x = (int) ((molPos[i].x-minx)/binWidth);
            int y = (int) ((molPos[i].y-miny)/binWidth);
            int z = (int) ((molPos[i].z-minz)/binWidth);
            int bin;
            if (useHilbert)
            {
                coords[0] = x;
                coords[1] = y;
                coords[2] = z;
                bin = (int) hilbert_c2i(3, 8, coords);
            }
            else
            {
                int yodd = y&1;
                int zodd = z&1;
                bin = z*xbins*ybins;
                bin += (zodd ? ybins-y : y)*xbins;
                bin += (yodd ? xbins-x : x);
            }
            molBins[i] = pair<int, int>(bin, i);
        }
        sort(molBins.begin(), molBins.end());

        // Reorder the atoms.

        for (int i = 0; i < numMolecules; i++)
        {
            for (int j = 0; j < (int)atoms.size(); j++)
            {
                int oldIndex = mol.instances[molBins[i].second]+atoms[j];
                int newIndex = mol.instances[i]+atoms[j];
                originalIndex[newIndex] = (*gpu->psAtomIndex)[oldIndex];
                newPosq[newIndex] = posq[oldIndex];
                newVelm[newIndex] = velm[oldIndex];
                newCellOffsets[newIndex] = gpu->posCellOffsets[oldIndex];
            }
        }
    }

    // Update the streams.

    for (int i = 0; i < numAtoms; i++) {
        posq[i] = newPosq[i];
        velm[i] = newVelm[i];
        (*gpu->psAtomIndex)[i] = originalIndex[i];
        gpu->posCellOffsets[i] = newCellOffsets[i];
    }
    gpu->psPosq4->Upload();
    gpu->psVelm4->Upload();
    gpu->psAtomIndex->Upload();
}