OpenCLKernels.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) 2008-2010 Stanford University and the Authors.      *
 * Authors: 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 "OpenCLKernels.h"
#include "OpenCLForceInfo.h"
#include "openmm/LangevinIntegrator.h"
#include "openmm/Context.h"
#include "openmm/internal/AndersenThermostatImpl.h"
#include "openmm/internal/CMAPTorsionForceImpl.h"
#include "openmm/internal/ContextImpl.h"
#include "openmm/internal/CustomCompoundBondForceImpl.h"
#include "openmm/internal/CustomHbondForceImpl.h"
#include "openmm/internal/NonbondedForceImpl.h"
#include "OpenCLBondedUtilities.h"
#include "OpenCLExpressionUtilities.h"
#include "OpenCLIntegrationUtilities.h"
#include "OpenCLNonbondedUtilities.h"
#include "OpenCLKernelSources.h"
#include "lepton/ExpressionTreeNode.h"
#include "lepton/Operation.h"
#include "lepton/Parser.h"
#include "lepton/ParsedExpression.h"
#include "../src/SimTKUtilities/SimTKOpenMMRealType.h"
#include "../src/SimTKUtilities/SimTKOpenMMUtilities.h"
#include <cmath>
#include <set>

using namespace OpenMM;
using namespace std;
using Lepton::ExpressionTreeNode;
using Lepton::Operation;

static string doubleToString(double value) {
    stringstream s;
    s.precision(8);
    s << scientific << value << "f";
    return s.str();
}

static string intToString(int value) {
    stringstream s;
    s << value;
    return s.str();
}

static bool isZeroExpression(const Lepton::ParsedExpression& expression) {
    const Lepton::Operation& op = expression.getRootNode().getOperation();
    if (op.getId() != Lepton::Operation::CONSTANT)
        return false;
    return (dynamic_cast<const Lepton::Operation::Constant&>(op).getValue() == 0.0);
}

static bool usesVariable(const Lepton::ExpressionTreeNode& node, const string& variable) {
    const Lepton::Operation& op = node.getOperation();
    if (op.getId() == Lepton::Operation::VARIABLE && op.getName() == variable)
        return true;
    for (int i = 0; i < (int) node.getChildren().size(); i++)
        if (usesVariable(node.getChildren()[i], variable))
            return true;
    return false;
}

static bool usesVariable(const Lepton::ParsedExpression& expression, const string& variable) {
    return usesVariable(expression.getRootNode(), variable);
}

static pair<ExpressionTreeNode, string> makeVariable(const string& name, const string& value) {
    return make_pair(ExpressionTreeNode(new Operation::Variable(name)), value);
}

void OpenCLCalcForcesAndEnergyKernel::initialize(const System& system) {
}

void OpenCLCalcForcesAndEnergyKernel::beginComputation(ContextImpl& context, bool includeForces, bool includeEnergy, int groups) {
    OpenCLNonbondedUtilities& nb = cl.getNonbondedUtilities();
    bool includeNonbonded = ((groups&(1<<nb.getForceGroup())) != 0);
    cl.setAtomsWereReordered(false);
    if (nb.getUseCutoff() && includeNonbonded && cl.getComputeForceCount()%100 == 0) {
        cl.reorderAtoms();
        nb.updateNeighborListSize();
        cl.setComputeForceCount(cl.getComputeForceCount()+1);
    }
    cl.clearAutoclearBuffers();
    if (includeNonbonded)
        nb.prepareInteractions();
}

double OpenCLCalcForcesAndEnergyKernel::finishComputation(ContextImpl& context, bool includeForces, bool includeEnergy, int groups) {
    cl.getBondedUtilities().computeInteractions(groups);
    if ((groups&(1<<cl.getNonbondedUtilities().getForceGroup())) != 0)
        cl.getNonbondedUtilities().computeInteractions();
    cl.reduceForces();
    cl.getIntegrationUtilities().distributeForcesFromVirtualSites();
    double sum = 0.0f;
    if (includeEnergy) {
        OpenCLArray<cl_float>& energy = cl.getEnergyBuffer();
        energy.download();
        for (int i = 0; i < energy.getSize(); i++)
            sum += energy[i];
    }
    return sum;
}

void OpenCLUpdateStateDataKernel::initialize(const System& system) {
}

double OpenCLUpdateStateDataKernel::getTime(const ContextImpl& context) const {
    return cl.getTime();
}

void OpenCLUpdateStateDataKernel::setTime(ContextImpl& context, double time) {
    vector<OpenCLContext*>& contexts = cl.getPlatformData().contexts;
    for (int i = 0; i < (int) contexts.size(); i++)
        contexts[i]->setTime(time);
}

void OpenCLUpdateStateDataKernel::getPositions(ContextImpl& context, vector<Vec3>& positions) {
    OpenCLArray<mm_float4>& posq = cl.getPosq();
    posq.download();
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
    positions.resize(numParticles);
    mm_float4 periodicBoxSize = cl.getPeriodicBoxSize();
    for (int i = 0; i < numParticles; ++i) {
        mm_float4 pos = posq[i];
        mm_int4 offset = cl.getPosCellOffsets()[i];
        positions[order[i]] = Vec3(pos.x-offset.x*periodicBoxSize.x, pos.y-offset.y*periodicBoxSize.y, pos.z-offset.z*periodicBoxSize.z);
    }
}

void OpenCLUpdateStateDataKernel::setPositions(ContextImpl& context, const vector<Vec3>& positions) {
    OpenCLArray<mm_float4>& posq = cl.getPosq();
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
    for (int i = 0; i < numParticles; ++i) {
        mm_float4& pos = posq[i];
        const Vec3& p = positions[order[i]];
        pos.x = (cl_float) p[0];
        pos.y = (cl_float) p[1];
        pos.z = (cl_float) p[2];
    }
    for (int i = numParticles; i < cl.getPaddedNumAtoms(); i++)
        posq[i] = mm_float4(0.0f, 0.0f, 0.0f, 0.0f);
    posq.upload();
    for (int i = 0; i < (int) cl.getPosCellOffsets().size(); i++)
        cl.getPosCellOffsets()[i] = mm_int4(0, 0, 0, 0);
}

void OpenCLUpdateStateDataKernel::getVelocities(ContextImpl& context, vector<Vec3>& velocities) {
    OpenCLArray<mm_float4>& velm = cl.getVelm();
    velm.download();
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
    velocities.resize(numParticles);
    for (int i = 0; i < numParticles; ++i) {
        mm_float4 vel = velm[i];
        velocities[order[i]] = Vec3(vel.x, vel.y, vel.z);
    }
}

void OpenCLUpdateStateDataKernel::setVelocities(ContextImpl& context, const vector<Vec3>& velocities) {
    OpenCLArray<mm_float4>& velm = cl.getVelm();
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
    for (int i = 0; i < numParticles; ++i) {
        mm_float4& vel = velm[i];
        const Vec3& p = velocities[order[i]];
        vel.x = (cl_float) p[0];
        vel.y = (cl_float) p[1];
        vel.z = (cl_float) p[2];
    }
    for (int i = numParticles; i < cl.getPaddedNumAtoms(); i++)
        velm[i] = mm_float4(0.0f, 0.0f, 0.0f, 0.0f);
    velm.upload();
}

void OpenCLUpdateStateDataKernel::getForces(ContextImpl& context, vector<Vec3>& forces) {
    OpenCLArray<mm_float4>& force = cl.getForce();
    force.download();
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
    forces.resize(numParticles);
    for (int i = 0; i < numParticles; ++i) {
        mm_float4 f = force[i];
        forces[order[i]] = Vec3(f.x, f.y, f.z);
    }
}

void OpenCLUpdateStateDataKernel::getPeriodicBoxVectors(ContextImpl& context, Vec3& a, Vec3& b, Vec3& c) const {
    mm_float4 box = cl.getPeriodicBoxSize();
    a = Vec3(box.x, 0, 0);
    b = Vec3(0, box.y, 0);
    c = Vec3(0, 0, box.z);
}

void OpenCLUpdateStateDataKernel::setPeriodicBoxVectors(ContextImpl& context, const Vec3& a, const Vec3& b, const Vec3& c) const {
    vector<OpenCLContext*>& contexts = cl.getPlatformData().contexts;
    for (int i = 0; i < (int) contexts.size(); i++)
        contexts[i]->setPeriodicBoxSize(a[0], b[1], c[2]);
}

void OpenCLUpdateStateDataKernel::createCheckpoint(ContextImpl& context, ostream& stream) {
    int version = 1;
    stream.write((char*) &version, sizeof(int));
    double time = cl.getTime();
    stream.write((char*) &time, sizeof(double));
    cl.getPosq().download();
    stream.write((char*) &cl.getPosq()[0], sizeof(mm_float4)*cl.getPosq().getSize());
    cl.getVelm().download();
    stream.write((char*) &cl.getVelm()[0], sizeof(mm_float4)*cl.getVelm().getSize());
    stream.write((char*) &cl.getAtomIndex()[0], sizeof(cl_int)*cl.getAtomIndex().getSize());
    stream.write((char*) &cl.getPosCellOffsets()[0], sizeof(mm_int4)*cl.getPosCellOffsets().size());
    mm_float4 box = cl.getPeriodicBoxSize();
    stream.write((char*) &box, sizeof(mm_float4));
    cl.getIntegrationUtilities().createCheckpoint(stream);
    SimTKOpenMMUtilities::createCheckpoint(stream);
}

void OpenCLUpdateStateDataKernel::loadCheckpoint(ContextImpl& context, istream& stream) {
    int version;
    stream.read((char*) &version, sizeof(int));
    if (version != 1)
        throw OpenMMException("Checkpoint was created with a different version of OpenMM");
    double time;
    stream.read((char*) &time, sizeof(double));
    vector<OpenCLContext*>& contexts = cl.getPlatformData().contexts;
    for (int i = 0; i < (int) contexts.size(); i++)
        contexts[i]->setTime(time);
    stream.read((char*) &cl.getPosq()[0], sizeof(mm_float4)*cl.getPosq().getSize());
    cl.getPosq().upload();
    stream.read((char*) &cl.getVelm()[0], sizeof(mm_float4)*cl.getVelm().getSize());
    cl.getVelm().upload();
    stream.read((char*) &cl.getAtomIndex()[0], sizeof(cl_int)*cl.getAtomIndex().getSize());
    cl.getAtomIndex().upload();
    stream.read((char*) &cl.getPosCellOffsets()[0], sizeof(mm_int4)*cl.getPosCellOffsets().size());
    mm_float4 box;
    stream.read((char*) &box, sizeof(mm_float4));
    for (int i = 0; i < (int) contexts.size(); i++)
        contexts[i]->setPeriodicBoxSize(box.x, box.y, box.z);
    cl.getIntegrationUtilities().loadCheckpoint(stream);
    SimTKOpenMMUtilities::loadCheckpoint(stream);
    for (int i = 0; i < cl.getReorderListeners().size(); i++)
        cl.getReorderListeners()[i]->execute();
}

void OpenCLApplyConstraintsKernel::initialize(const System& system) {
}

void OpenCLApplyConstraintsKernel::apply(ContextImpl& context, double tol) {
    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        map<string, string> defines;
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        cl::Program program = cl.createProgram(OpenCLKernelSources::constraints, defines);
        applyDeltasKernel = cl::Kernel(program, "applyPositionDeltas");
        applyDeltasKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
        applyDeltasKernel.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getPosDelta().getDeviceBuffer());
    }
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    cl.clearBuffer(integration.getPosDelta());
    integration.applyConstraints(tol);
    cl.executeKernel(applyDeltasKernel, cl.getNumAtoms());
    integration.computeVirtualSites();
}

void OpenCLVirtualSitesKernel::initialize(const System& system) {
}

void OpenCLVirtualSitesKernel::computePositions(ContextImpl& context) {
    cl.getIntegrationUtilities().computeVirtualSites();
}

class OpenCLHarmonicBondForceInfo : public OpenCLForceInfo {
public:
    OpenCLHarmonicBondForceInfo(const HarmonicBondForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumBonds();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2;
        double length, k;
        force.getBondParameters(index, particle1, particle2, length, k);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2;
        double length1, length2, k1, k2;
        force.getBondParameters(group1, particle1, particle2, length1, k1);
        force.getBondParameters(group2, particle1, particle2, length2, k2);
        return (length1 == length2 && k1 == k2);
    }
private:
    const HarmonicBondForce& force;
};

OpenCLCalcHarmonicBondForceKernel::~OpenCLCalcHarmonicBondForceKernel() {
    if (params != NULL)
        delete params;
}

void OpenCLCalcHarmonicBondForceKernel::initialize(const System& system, const HarmonicBondForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumBonds()/numContexts;
    numBonds = endIndex-startIndex;
    if (numBonds == 0)
        return;
    vector<vector<int> > atoms(numBonds, vector<int>(2));
    params = new OpenCLArray<mm_float2>(cl, numBonds, "bondParams");
    vector<mm_float2> paramVector(numBonds);
    for (int i = 0; i < numBonds; i++) {
        double length, k;
        force.getBondParameters(startIndex+i, atoms[i][0], atoms[i][1], length, k);
        paramVector[i] = mm_float2((cl_float) length, (cl_float) k);
    }
    params->upload(paramVector);
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = OpenCLKernelSources::harmonicBondForce;
    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float2");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::bondForce, replacements), force.getForceGroup());
    cl.addForce(new OpenCLHarmonicBondForceInfo(force));
}

double OpenCLCalcHarmonicBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    return 0.0;
}

class OpenCLCustomBondForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomBondForceInfo(const CustomBondForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumBonds();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2;
        vector<double> parameters;
        force.getBondParameters(index, particle1, particle2, parameters);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2;
        vector<double> parameters1, parameters2;
        force.getBondParameters(group1, particle1, particle2, parameters1);
        force.getBondParameters(group2, particle1, particle2, parameters2);
        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
        return true;
    }
private:
    const CustomBondForce& force;
};

OpenCLCalcCustomBondForceKernel::~OpenCLCalcCustomBondForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
}

void OpenCLCalcCustomBondForceKernel::initialize(const System& system, const CustomBondForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumBonds()/numContexts;
    numBonds = endIndex-startIndex;
    if (numBonds == 0)
        return;
    vector<vector<int> > atoms(numBonds, vector<int>(2));
    params = new OpenCLParameterSet(cl, force.getNumPerBondParameters(), numBonds, "customBondParams");
    vector<vector<cl_float> > paramVector(numBonds);
    for (int i = 0; i < numBonds; i++) {
        vector<double> parameters;
        force.getBondParameters(startIndex+i, atoms[i][0], atoms[i][1], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    cl.addForce(new OpenCLCustomBondForceInfo(force));

    // Record information for the expressions.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction()).optimize();
    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("r").optimize();
    map<string, Lepton::ParsedExpression> expressions;
    expressions["energy += "] = energyExpression;
    expressions["float dEdR = "] = forceExpression;

    // Create the kernels.

    map<string, string> variables;
    variables["r"] = "r";
    for (int i = 0; i < force.getNumPerBondParameters(); i++) {
        const string& name = force.getPerBondParameterName(i);
        variables[name] = "bondParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customBondGlobals", false, CL_MEM_READ_ONLY);
        globals->upload(globalParamValues);
        string argName = cl.getBondedUtilities().addArgument(globals->getDeviceBuffer(), "float");
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+intToString(i)+"]";
            variables[name] = value;
        }
    }
    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::bondForce, replacements), force.getForceGroup());
}

double OpenCLCalcCustomBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    return 0.0;
}

class OpenCLHarmonicAngleForceInfo : public OpenCLForceInfo {
public:
    OpenCLHarmonicAngleForceInfo(const HarmonicAngleForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumAngles();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3;
        double angle, k;
        force.getAngleParameters(index, particle1, particle2, particle3, angle, k);
        particles.resize(3);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3;
        double angle1, angle2, k1, k2;
        force.getAngleParameters(group1, particle1, particle2, particle3, angle1, k1);
        force.getAngleParameters(group2, particle1, particle2, particle3, angle2, k2);
        return (angle1 == angle2 && k1 == k2);
    }
private:
    const HarmonicAngleForce& force;
};

OpenCLCalcHarmonicAngleForceKernel::~OpenCLCalcHarmonicAngleForceKernel() {
    if (params != NULL)
        delete params;
}

void OpenCLCalcHarmonicAngleForceKernel::initialize(const System& system, const HarmonicAngleForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumAngles()/numContexts;
    numAngles = endIndex-startIndex;
    if (numAngles == 0)
        return;
    vector<vector<int> > atoms(numAngles, vector<int>(3));
    params = new OpenCLArray<mm_float2>(cl, numAngles, "angleParams");
    vector<mm_float2> paramVector(numAngles);
    for (int i = 0; i < numAngles; i++) {
        double angle, k;
        force.getAngleParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], angle, k);
        paramVector[i] = mm_float2((cl_float) angle, (cl_float) k);

    }
    params->upload(paramVector);
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = OpenCLKernelSources::harmonicAngleForce;
    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float2");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::angleForce, replacements), force.getForceGroup());
    cl.addForce(new OpenCLHarmonicAngleForceInfo(force));
}

double OpenCLCalcHarmonicAngleForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    return 0.0;
}

class OpenCLCustomAngleForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomAngleForceInfo(const CustomAngleForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumAngles();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3;
        vector<double> parameters;
        force.getAngleParameters(index, particle1, particle2, particle3, parameters);
        particles.resize(3);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3;
        vector<double> parameters1, parameters2;
        force.getAngleParameters(group1, particle1, particle2, particle3, parameters1);
        force.getAngleParameters(group2, particle1, particle2, particle3, parameters2);
        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
        return true;
    }
private:
    const CustomAngleForce& force;
};

OpenCLCalcCustomAngleForceKernel::~OpenCLCalcCustomAngleForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
}

void OpenCLCalcCustomAngleForceKernel::initialize(const System& system, const CustomAngleForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumAngles()/numContexts;
    numAngles = endIndex-startIndex;
    if (numAngles == 0)
        return;
    vector<vector<int> > atoms(numAngles, vector<int>(3));
    params = new OpenCLParameterSet(cl, force.getNumPerAngleParameters(), numAngles, "customAngleParams");
    vector<vector<cl_float> > paramVector(numAngles);
    for (int i = 0; i < numAngles; i++) {
        vector<double> parameters;
        force.getAngleParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    cl.addForce(new OpenCLCustomAngleForceInfo(force));

    // Record information for the expressions.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction()).optimize();
    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("theta").optimize();
    map<string, Lepton::ParsedExpression> expressions;
    expressions["energy += "] = energyExpression;
    expressions["float dEdAngle = "] = forceExpression;

    // Create the kernels.

    map<string, string> variables;
    variables["theta"] = "theta";
    for (int i = 0; i < force.getNumPerAngleParameters(); i++) {
        const string& name = force.getPerAngleParameterName(i);
        variables[name] = "angleParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customAngleGlobals", false, CL_MEM_READ_ONLY);
        globals->upload(globalParamValues);
        string argName = cl.getBondedUtilities().addArgument(globals->getDeviceBuffer(), "float");
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+intToString(i)+"]";
            variables[name] = value;
        }
    }
    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" angleParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::angleForce, replacements), force.getForceGroup());
}

double OpenCLCalcCustomAngleForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    return 0.0;
}

class OpenCLPeriodicTorsionForceInfo : public OpenCLForceInfo {
public:
    OpenCLPeriodicTorsionForceInfo(const PeriodicTorsionForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3, particle4, periodicity;
        double phase, k;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, periodicity, phase, k);
        particles.resize(4);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
        particles[3] = particle4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3, particle4, periodicity1, periodicity2;
        double phase1, phase2, k1, k2;
        force.getTorsionParameters(group1, particle1, particle2, particle3, particle4, periodicity1, phase1, k1);
        force.getTorsionParameters(group2, particle1, particle2, particle3, particle4, periodicity2, phase2, k2);
        return (periodicity1 == periodicity2 && phase1 == phase2 && k1 == k2);
    }
private:
    const PeriodicTorsionForce& force;
};

OpenCLCalcPeriodicTorsionForceKernel::~OpenCLCalcPeriodicTorsionForceKernel() {
    if (params != NULL)
        delete params;
}

void OpenCLCalcPeriodicTorsionForceKernel::initialize(const System& system, const PeriodicTorsionForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (numTorsions == 0)
        return;
    vector<vector<int> > atoms(numTorsions, vector<int>(4));
    params = new OpenCLArray<mm_float4>(cl, numTorsions, "periodicTorsionParams");
    vector<mm_float4> paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        int periodicity;
        double phase, k;
        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], periodicity, phase, k);
        paramVector[i] = mm_float4((cl_float) k, (cl_float) phase, (cl_float) periodicity, 0.0f);

    }
    params->upload(paramVector);
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = OpenCLKernelSources::periodicTorsionForce;
    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float4");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::torsionForce, replacements), force.getForceGroup());
    cl.addForce(new OpenCLPeriodicTorsionForceInfo(force));
}

double OpenCLCalcPeriodicTorsionForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    return 0.0;
}

class OpenCLRBTorsionForceInfo : public OpenCLForceInfo {
public:
    OpenCLRBTorsionForceInfo(const RBTorsionForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3, particle4;
        double c0, c1, c2, c3, c4, c5;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, c0, c1, c2, c3, c4, c5);
        particles.resize(4);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
        particles[3] = particle4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3, particle4;
        double c0a, c0b, c1a, c1b, c2a, c2b, c3a, c3b, c4a, c4b, c5a, c5b;
        force.getTorsionParameters(group1, particle1, particle2, particle3, particle4, c0a, c1a, c2a, c3a, c4a, c5a);
        force.getTorsionParameters(group2, particle1, particle2, particle3, particle4, c0b, c1b, c2b, c3b, c4b, c5b);
        return (c0a == c0b && c1a == c1b && c2a == c2b && c3a == c3b && c4a == c4b && c5a == c5b);
    }
private:
    const RBTorsionForce& force;
};

OpenCLCalcRBTorsionForceKernel::~OpenCLCalcRBTorsionForceKernel() {
    if (params != NULL)
        delete params;
}

void OpenCLCalcRBTorsionForceKernel::initialize(const System& system, const RBTorsionForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (numTorsions == 0)
        return;
    vector<vector<int> > atoms(numTorsions, vector<int>(4));
    params = new OpenCLArray<mm_float8>(cl, numTorsions, "rbTorsionParams");
    vector<mm_float8> paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        double c0, c1, c2, c3, c4, c5;
        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], c0, c1, c2, c3, c4, c5);
        paramVector[i] = mm_float8((cl_float) c0, (cl_float) c1, (cl_float) c2, (cl_float) c3, (cl_float) c4, (cl_float) c5, 0.0f, 0.0f);

    }
    params->upload(paramVector);
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = OpenCLKernelSources::rbTorsionForce;
    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float8");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::torsionForce, replacements), force.getForceGroup());
    cl.addForce(new OpenCLRBTorsionForceInfo(force));
}

double OpenCLCalcRBTorsionForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    return 0.0;
}

class OpenCLCMAPTorsionForceInfo : public OpenCLForceInfo {
public:
    OpenCLCMAPTorsionForceInfo(const CMAPTorsionForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int map, a1, a2, a3, a4, b1, b2, b3, b4;
        force.getTorsionParameters(index, map, a1, a2, a3, a4, b1, b2, b3, b4);
        particles.resize(8);
        particles[0] = a1;
        particles[1] = a2;
        particles[2] = a3;
        particles[3] = a4;
        particles[4] = b1;
        particles[5] = b2;
        particles[6] = b3;
        particles[7] = b4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int map1, map2, a1, a2, a3, a4, b1, b2, b3, b4;
        force.getTorsionParameters(group1, map1, a1, a2, a3, a4, b1, b2, b3, b4);
        force.getTorsionParameters(group2, map2, a1, a2, a3, a4, b1, b2, b3, b4);
        return (map1 == map2);
    }
private:
    const CMAPTorsionForce& force;
};

OpenCLCalcCMAPTorsionForceKernel::~OpenCLCalcCMAPTorsionForceKernel() {
    if (coefficients != NULL)
        delete coefficients;
    if (mapPositions != NULL)
        delete mapPositions;
    if (torsionMaps != NULL)
        delete torsionMaps;
}

void OpenCLCalcCMAPTorsionForceKernel::initialize(const System& system, const CMAPTorsionForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (numTorsions == 0)
        return;
    int numMaps = force.getNumMaps();
    vector<mm_float4> coeffVec;
    vector<mm_int2> mapPositionsVec(numMaps);
    vector<double> energy;
    vector<vector<double> > c;
    int currentPosition = 0;
    for (int i = 0; i < numMaps; i++) {
        int size;
        force.getMapParameters(i, size, energy);
        CMAPTorsionForceImpl::calcMapDerivatives(size, energy, c);
        mapPositionsVec[i] = mm_int2(currentPosition, size);
        currentPosition += 4*size*size;
        for (int j = 0; j < size*size; j++) {
            coeffVec.push_back(mm_float4((float) c[j][0], (float) c[j][1], (float) c[j][2], (float) c[j][3]));
            coeffVec.push_back(mm_float4((float) c[j][4], (float) c[j][5], (float) c[j][6], (float) c[j][7]));
            coeffVec.push_back(mm_float4((float) c[j][8], (float) c[j][9], (float) c[j][10], (float) c[j][11]));
            coeffVec.push_back(mm_float4((float) c[j][12], (float) c[j][13], (float) c[j][14], (float) c[j][15]));
        }
    }
    vector<vector<int> > atoms(numTorsions, vector<int>(8));
    vector<cl_int> torsionMapsVec(numTorsions);
    for (int i = 0; i < numTorsions; i++)
        force.getTorsionParameters(startIndex+i, torsionMapsVec[i], atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], atoms[i][4], atoms[i][5], atoms[i][6], atoms[i][7]);
    coefficients = new OpenCLArray<mm_float4>(cl, coeffVec.size(), "cmapTorsionCoefficients");
    mapPositions = new OpenCLArray<mm_int2>(cl, numMaps, "cmapTorsionMapPositions");
    torsionMaps = new OpenCLArray<cl_int>(cl, numTorsions, "cmapTorsionMaps");
    coefficients->upload(coeffVec);
    mapPositions->upload(mapPositionsVec);
    torsionMaps->upload(torsionMapsVec);
    map<string, string> replacements;
    replacements["COEFF"] = cl.getBondedUtilities().addArgument(coefficients->getDeviceBuffer(), "float4");
    replacements["MAP_POS"] = cl.getBondedUtilities().addArgument(mapPositions->getDeviceBuffer(), "int2");
    replacements["MAPS"] = cl.getBondedUtilities().addArgument(torsionMaps->getDeviceBuffer(), "int");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::cmapTorsionForce, replacements), force.getForceGroup());
    cl.addForce(new OpenCLCMAPTorsionForceInfo(force));
}

double OpenCLCalcCMAPTorsionForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    return 0.0;
}

class OpenCLCustomTorsionForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomTorsionForceInfo(const CustomTorsionForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3, particle4;
        vector<double> parameters;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, parameters);
        particles.resize(4);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
        particles[3] = particle4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3, particle4;
        vector<double> parameters1, parameters2;
        force.getTorsionParameters(group1, particle1, particle2, particle3, particle4, parameters1);
        force.getTorsionParameters(group2, particle1, particle2, particle3, particle4, parameters2);
        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
        return true;
    }
private:
    const CustomTorsionForce& force;
};

OpenCLCalcCustomTorsionForceKernel::~OpenCLCalcCustomTorsionForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
}

void OpenCLCalcCustomTorsionForceKernel::initialize(const System& system, const CustomTorsionForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (numTorsions == 0)
        return;
    vector<vector<int> > atoms(numTorsions, vector<int>(4));
    params = new OpenCLParameterSet(cl, force.getNumPerTorsionParameters(), numTorsions, "customTorsionParams");
    vector<vector<cl_float> > paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        vector<double> parameters;
        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    cl.addForce(new OpenCLCustomTorsionForceInfo(force));

    // Record information for the expressions.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction()).optimize();
    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("theta").optimize();
    map<string, Lepton::ParsedExpression> expressions;
    expressions["energy += "] = energyExpression;
    expressions["float dEdAngle = "] = forceExpression;

    // Create the kernels.

    map<string, string> variables;
    variables["theta"] = "theta";
    for (int i = 0; i < force.getNumPerTorsionParameters(); i++) {
        const string& name = force.getPerTorsionParameterName(i);
        variables[name] = "torsionParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customTorsionGlobals", false, CL_MEM_READ_ONLY);
        globals->upload(globalParamValues);
        string argName = cl.getBondedUtilities().addArgument(globals->getDeviceBuffer(), "float");
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+intToString(i)+"]";
            variables[name] = value;
        }
    }
    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" torsionParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::torsionForce, replacements), force.getForceGroup());
}

double OpenCLCalcCustomTorsionForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    return 0.0;
}

class OpenCLNonbondedForceInfo : public OpenCLForceInfo {
public:
    OpenCLNonbondedForceInfo(int requiredBuffers, const NonbondedForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        double charge1, charge2, sigma1, sigma2, epsilon1, epsilon2;
        force.getParticleParameters(particle1, charge1, sigma1, epsilon1);
        force.getParticleParameters(particle2, charge2, sigma2, epsilon2);
        return (charge1 == charge2 && sigma1 == sigma2 && epsilon1 == epsilon2);
    }
    int getNumParticleGroups() {
        return force.getNumExceptions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2;
        double chargeProd, sigma, epsilon;
        force.getExceptionParameters(index, particle1, particle2, chargeProd, sigma, epsilon);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2;
        double chargeProd1, chargeProd2, sigma1, sigma2, epsilon1, epsilon2;
        force.getExceptionParameters(group1, particle1, particle2, chargeProd1, sigma1, epsilon1);
        force.getExceptionParameters(group2, particle1, particle2, chargeProd2, sigma2, epsilon2);
        return (chargeProd1 == chargeProd2 && sigma1 == sigma2 && epsilon1 == epsilon2);
    }
private:
    const NonbondedForce& force;
};

OpenCLCalcNonbondedForceKernel::~OpenCLCalcNonbondedForceKernel() {
    if (sigmaEpsilon != NULL)
        delete sigmaEpsilon;
    if (exceptionParams != NULL)
        delete exceptionParams;
    if (cosSinSums != NULL)
        delete cosSinSums;
    if (pmeGrid != NULL)
        delete pmeGrid;
    if (pmeGrid2 != NULL)
        delete pmeGrid2;
    if (pmeBsplineModuliX != NULL)
        delete pmeBsplineModuliX;
    if (pmeBsplineModuliY != NULL)
        delete pmeBsplineModuliY;
    if (pmeBsplineModuliZ != NULL)
        delete pmeBsplineModuliZ;
    if (pmeBsplineTheta != NULL)
        delete pmeBsplineTheta;
    if (pmeBsplineDTheta != NULL)
        delete pmeBsplineDTheta;
    if (pmeAtomRange != NULL)
        delete pmeAtomRange;
    if (pmeAtomGridIndex != NULL)
        delete pmeAtomGridIndex;
    if (sort != NULL)
        delete sort;
    if (fft != NULL)
        delete fft;
}

void OpenCLCalcNonbondedForceKernel::initialize(const System& system, const NonbondedForce& force) {

    // Identify which exceptions are 1-4 interactions.

    vector<pair<int, int> > exclusions;
    vector<int> exceptions;
    for (int i = 0; i < force.getNumExceptions(); i++) {
        int particle1, particle2;
        double chargeProd, sigma, epsilon;
        force.getExceptionParameters(i, particle1, particle2, chargeProd, sigma, epsilon);
        exclusions.push_back(pair<int, int>(particle1, particle2));
        if (chargeProd != 0.0 || epsilon != 0.0)
            exceptions.push_back(i);
    }

    // Initialize nonbonded interactions.

    int numParticles = force.getNumParticles();
    sigmaEpsilon = new OpenCLArray<mm_float2>(cl, numParticles, "sigmaEpsilon");
    OpenCLArray<mm_float4>& posq = cl.getPosq();
    vector<mm_float2> sigmaEpsilonVector(numParticles);
    vector<vector<int> > exclusionList(numParticles);
    double sumSquaredCharges = 0.0;
    bool hasCoulomb = false;
    bool hasLJ = false;
    for (int i = 0; i < numParticles; i++) {
        double charge, sigma, epsilon;
        force.getParticleParameters(i, charge, sigma, epsilon);
        posq[i].w = (float) charge;
        sigmaEpsilonVector[i] = mm_float2((float) (0.5*sigma), (float) (2.0*sqrt(epsilon)));
        exclusionList[i].push_back(i);
        sumSquaredCharges += charge*charge;
        if (charge != 0.0)
            hasCoulomb = true;
        if (epsilon != 0.0)
            hasLJ = true;
    }
    for (int i = 0; i < (int) exclusions.size(); i++) {
        exclusionList[exclusions[i].first].push_back(exclusions[i].second);
        exclusionList[exclusions[i].second].push_back(exclusions[i].first);
    }
    posq.upload();
    sigmaEpsilon->upload(sigmaEpsilonVector);
    bool useCutoff = (force.getNonbondedMethod() != NonbondedForce::NoCutoff);
    bool usePeriodic = (force.getNonbondedMethod() != NonbondedForce::NoCutoff && force.getNonbondedMethod() != NonbondedForce::CutoffNonPeriodic);
    map<string, string> defines;
    defines["HAS_COULOMB"] = (hasCoulomb ? "1" : "0");
    defines["HAS_LENNARD_JONES"] = (hasLJ ? "1" : "0");
    if (useCutoff) {
        // Compute the reaction field constants.

        double reactionFieldK = pow(force.getCutoffDistance(), -3.0)*(force.getReactionFieldDielectric()-1.0)/(2.0*force.getReactionFieldDielectric()+1.0);
        double reactionFieldC = (1.0 / force.getCutoffDistance())*(3.0*force.getReactionFieldDielectric())/(2.0*force.getReactionFieldDielectric()+1.0);
        defines["REACTION_FIELD_K"] = doubleToString(reactionFieldK);
        defines["REACTION_FIELD_C"] = doubleToString(reactionFieldC);
    }
    if (force.getUseDispersionCorrection() && cl.getContextIndex() == 0)
        dispersionCoefficient = NonbondedForceImpl::calcDispersionCorrection(system, force);
    else
        dispersionCoefficient = 0.0;
    double alpha = 0;
    if (force.getNonbondedMethod() == NonbondedForce::Ewald) {
        // Compute the Ewald parameters.

        int kmaxx, kmaxy, kmaxz;
        NonbondedForceImpl::calcEwaldParameters(system, force, alpha, kmaxx, kmaxy, kmaxz);
        defines["EWALD_ALPHA"] = doubleToString(alpha);
        defines["TWO_OVER_SQRT_PI"] = doubleToString(2.0/sqrt(M_PI));
        defines["USE_EWALD"] = "1";
        ewaldSelfEnergy = (cl.getContextIndex() == 0 ? -ONE_4PI_EPS0*alpha*sumSquaredCharges/sqrt(M_PI) : 0.0);

        // Create the reciprocal space kernels.

        map<string, string> replacements;
        replacements["NUM_ATOMS"] = intToString(numParticles);
        replacements["KMAX_X"] = intToString(kmaxx);
        replacements["KMAX_Y"] = intToString(kmaxy);
        replacements["KMAX_Z"] = intToString(kmaxz);
        replacements["EXP_COEFFICIENT"] = doubleToString(-1.0/(4.0*alpha*alpha));
        cl::Program program = cl.createProgram(OpenCLKernelSources::ewald, replacements);
        ewaldSumsKernel = cl::Kernel(program, "calculateEwaldCosSinSums");
        ewaldForcesKernel = cl::Kernel(program, "calculateEwaldForces");
        cosSinSums = new OpenCLArray<mm_float2>(cl, (2*kmaxx-1)*(2*kmaxy-1)*(2*kmaxz-1), "cosSinSums");
    }
    else if (force.getNonbondedMethod() == NonbondedForce::PME) {
        // Compute the PME parameters.

        int gridSizeX, gridSizeY, gridSizeZ;
        NonbondedForceImpl::calcPMEParameters(system, force, alpha, gridSizeX, gridSizeY, gridSizeZ);
        gridSizeX = OpenCLFFT3D::findLegalDimension(gridSizeX);
        gridSizeY = OpenCLFFT3D::findLegalDimension(gridSizeY);
        gridSizeZ = OpenCLFFT3D::findLegalDimension(gridSizeZ);
        defines["EWALD_ALPHA"] = doubleToString(alpha);
        defines["TWO_OVER_SQRT_PI"] = doubleToString(2.0/sqrt(M_PI));
        defines["USE_EWALD"] = "1";
        ewaldSelfEnergy = (cl.getContextIndex() == 0 ? -ONE_4PI_EPS0*alpha*sumSquaredCharges/sqrt(M_PI) : 0.0);
        pmeDefines["PME_ORDER"] = intToString(PmeOrder);
        pmeDefines["NUM_ATOMS"] = intToString(numParticles);
        pmeDefines["RECIP_EXP_FACTOR"] = doubleToString(M_PI*M_PI/(alpha*alpha));
        pmeDefines["GRID_SIZE_X"] = intToString(gridSizeX);
        pmeDefines["GRID_SIZE_Y"] = intToString(gridSizeY);
        pmeDefines["GRID_SIZE_Z"] = intToString(gridSizeZ);
        pmeDefines["EPSILON_FACTOR"] = doubleToString(sqrt(ONE_4PI_EPS0));

        // Create required data structures.

        pmeGrid = new OpenCLArray<mm_float2>(cl, gridSizeX*gridSizeY*gridSizeZ, "pmeGrid");
        cl.addAutoclearBuffer(pmeGrid->getDeviceBuffer(), pmeGrid->getSize()*2);
        pmeGrid2 = new OpenCLArray<mm_float2>(cl, gridSizeX*gridSizeY*gridSizeZ, "pmeGrid2");
        pmeBsplineModuliX = new OpenCLArray<cl_float>(cl, gridSizeX, "pmeBsplineModuliX");
        pmeBsplineModuliY = new OpenCLArray<cl_float>(cl, gridSizeY, "pmeBsplineModuliY");
        pmeBsplineModuliZ = new OpenCLArray<cl_float>(cl, gridSizeZ, "pmeBsplineModuliZ");
        pmeBsplineTheta = new OpenCLArray<mm_float4>(cl, PmeOrder*numParticles, "pmeBsplineTheta");
        bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
        if (deviceIsCpu)
            pmeBsplineDTheta = new OpenCLArray<mm_float4>(cl, PmeOrder*numParticles, "pmeBsplineDTheta");
        pmeAtomRange = new OpenCLArray<cl_int>(cl, gridSizeX*gridSizeY*gridSizeZ+1, "pmeAtomRange");
        pmeAtomGridIndex = new OpenCLArray<mm_int2>(cl, numParticles, "pmeAtomGridIndex");
        sort = new OpenCLSort<SortTrait>(cl, cl.getNumAtoms());
        fft = new OpenCLFFT3D(cl, gridSizeX, gridSizeY, gridSizeZ);

        // Initialize the b-spline moduli.

        int maxSize = max(max(gridSizeX, gridSizeY), gridSizeZ);
        vector<double> data(PmeOrder);
        vector<double> ddata(PmeOrder);
        vector<double> bsplines_data(maxSize);
        data[PmeOrder-1] = 0.0;
        data[1] = 0.0;
        data[0] = 1.0;
        for (int i = 3; i < PmeOrder; 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 < PmeOrder; i++)
            ddata[i] = data[i-1]-data[i];
        double div = 1.0/(PmeOrder-1);
        data[PmeOrder-1] = 0.0;
        for (int i = 1; i < (PmeOrder-1); i++)
            data[PmeOrder-i-1] = div*(i*data[PmeOrder-i-2]+(PmeOrder-i)*data[PmeOrder-i-1]);
        data[0] = div*data[0];
        for (int i = 0; i < maxSize; i++)
            bsplines_data[i] = 0.0;
        for (int i = 1; i <= PmeOrder; 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 ? gridSizeX : dim == 1 ? gridSizeY : gridSizeZ);
            vector<cl_float> moduli(ndata);
            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);
                }
                moduli[i] = (float) (sc*sc+ss*ss);
            }
            for (int i = 0; i < ndata; i++)
            {
                if (moduli[i] < 1.0e-7)
                    moduli[i] = (moduli[i-1]+moduli[i+1])*0.5f;
            }
            if (dim == 0)
                pmeBsplineModuliX->upload(moduli);
            else if (dim == 1)
                pmeBsplineModuliY->upload(moduli);
            else
                pmeBsplineModuliZ->upload(moduli);
        }
    }
    else
        ewaldSelfEnergy = 0.0;

    // Add the interaction to the default nonbonded kernel.
    
    string source = cl.replaceStrings(OpenCLKernelSources::coulombLennardJones, defines);
    cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source, force.getForceGroup());
    if (hasLJ)
        cl.getNonbondedUtilities().addParameter(OpenCLNonbondedUtilities::ParameterInfo("sigmaEpsilon", "float", 2, sizeof(cl_float2), sigmaEpsilon->getDeviceBuffer()));

    // Initialize the exceptions.

    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*exceptions.size()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*exceptions.size()/numContexts;
    int numExceptions = endIndex-startIndex;
    if (numExceptions > 0) {
        vector<vector<int> > atoms(numExceptions, vector<int>(2));
        exceptionParams = new OpenCLArray<mm_float4>(cl, numExceptions, "exceptionParams");
        vector<mm_float4> exceptionParamsVector(numExceptions);
        for (int i = 0; i < numExceptions; i++) {
            double chargeProd, sigma, epsilon;
            force.getExceptionParameters(exceptions[startIndex+i], atoms[i][0], atoms[i][1], chargeProd, sigma, epsilon);
            exceptionParamsVector[i] = mm_float4((float) (ONE_4PI_EPS0*chargeProd), (float) sigma, (float) (4.0*epsilon), 0.0f);
        }
        exceptionParams->upload(exceptionParamsVector);
        map<string, string> replacements;
        replacements["PARAMS"] = cl.getBondedUtilities().addArgument(exceptionParams->getDeviceBuffer(), "float4");
        cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::nonbondedExceptions, replacements), force.getForceGroup());
    }
    cl.addForce(new OpenCLNonbondedForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force));
}

double OpenCLCalcNonbondedForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy, bool includeDirect, bool includeReciprocal) {
    bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        if (cosSinSums != NULL) {
            ewaldSumsKernel.setArg<cl::Buffer>(0, cl.getEnergyBuffer().getDeviceBuffer());
            ewaldSumsKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
            ewaldSumsKernel.setArg<cl::Buffer>(2, cosSinSums->getDeviceBuffer());
            ewaldForcesKernel.setArg<cl::Buffer>(0, cl.getForceBuffers().getDeviceBuffer());
            ewaldForcesKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
            ewaldForcesKernel.setArg<cl::Buffer>(2, cosSinSums->getDeviceBuffer());
        }
        if (pmeGrid != NULL) {
            string file = (deviceIsCpu ? OpenCLKernelSources::pme_cpu : OpenCLKernelSources::pme);
            cl::Program program = cl.createProgram(file, pmeDefines);
            pmeUpdateBsplinesKernel = cl::Kernel(program, "updateBsplines");
            pmeAtomRangeKernel = cl::Kernel(program, "findAtomRangeForGrid");
	    if (!deviceIsCpu)
                pmeZIndexKernel = cl::Kernel(program, "recordZIndex");
            pmeSpreadChargeKernel = cl::Kernel(program, "gridSpreadCharge");
            pmeConvolutionKernel = cl::Kernel(program, "reciprocalConvolution");
            pmeInterpolateForceKernel = cl::Kernel(program, "gridInterpolateForce");
            pmeUpdateBsplinesKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
            pmeUpdateBsplinesKernel.setArg<cl::Buffer>(1, pmeBsplineTheta->getDeviceBuffer());
            pmeUpdateBsplinesKernel.setArg(2, OpenCLContext::ThreadBlockSize*PmeOrder*sizeof(mm_float4), NULL);
            pmeUpdateBsplinesKernel.setArg<cl::Buffer>(3, pmeAtomGridIndex->getDeviceBuffer());
            if (deviceIsCpu)
                pmeUpdateBsplinesKernel.setArg<cl::Buffer>(6, pmeBsplineDTheta->getDeviceBuffer());
            pmeAtomRangeKernel.setArg<cl::Buffer>(0, pmeAtomGridIndex->getDeviceBuffer());
            pmeAtomRangeKernel.setArg<cl::Buffer>(1, pmeAtomRange->getDeviceBuffer());
            pmeAtomRangeKernel.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
	    if (!deviceIsCpu) {
                pmeZIndexKernel.setArg<cl::Buffer>(0, pmeAtomGridIndex->getDeviceBuffer());
                pmeZIndexKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
	    }
            pmeSpreadChargeKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
            pmeSpreadChargeKernel.setArg<cl::Buffer>(1, pmeAtomGridIndex->getDeviceBuffer());
            pmeSpreadChargeKernel.setArg<cl::Buffer>(2, pmeAtomRange->getDeviceBuffer());
            pmeSpreadChargeKernel.setArg<cl::Buffer>(3, pmeGrid->getDeviceBuffer());
            pmeSpreadChargeKernel.setArg<cl::Buffer>(4, pmeBsplineTheta->getDeviceBuffer());
            pmeConvolutionKernel.setArg<cl::Buffer>(0, pmeGrid2->getDeviceBuffer());
            pmeConvolutionKernel.setArg<cl::Buffer>(1, cl.getEnergyBuffer().getDeviceBuffer());
            pmeConvolutionKernel.setArg<cl::Buffer>(2, pmeBsplineModuliX->getDeviceBuffer());
            pmeConvolutionKernel.setArg<cl::Buffer>(3, pmeBsplineModuliY->getDeviceBuffer());
            pmeConvolutionKernel.setArg<cl::Buffer>(4, pmeBsplineModuliZ->getDeviceBuffer());
            interpolateForceThreads = (cl.getDevice().getInfo<CL_DEVICE_LOCAL_MEM_SIZE>() > 2*128*PmeOrder*sizeof(mm_float4) ? 128 : 64);
            pmeInterpolateForceKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
            pmeInterpolateForceKernel.setArg<cl::Buffer>(1, cl.getForceBuffers().getDeviceBuffer());
            pmeInterpolateForceKernel.setArg<cl::Buffer>(2, pmeGrid->getDeviceBuffer());
            if (deviceIsCpu) {
                pmeInterpolateForceKernel.setArg<cl::Buffer>(5, pmeBsplineTheta->getDeviceBuffer());
                pmeInterpolateForceKernel.setArg<cl::Buffer>(6, pmeBsplineDTheta->getDeviceBuffer());
            }
            else
                pmeInterpolateForceKernel.setArg(5, 2*interpolateForceThreads*PmeOrder*sizeof(mm_float4), NULL);
            if (cl.getSupports64BitGlobalAtomics()) {
                pmeFinishSpreadChargeKernel = cl::Kernel(program, "finishSpreadCharge");
                pmeFinishSpreadChargeKernel.setArg<cl::Buffer>(0, pmeGrid->getDeviceBuffer());
            }
       }
    }
    if (cosSinSums != NULL && cl.getContextIndex() == 0 && includeReciprocal) {
        mm_float4 boxSize = cl.getPeriodicBoxSize();
        mm_float4 recipBoxSize = mm_float4((float) (2*M_PI/boxSize.x), (float) (2*M_PI/boxSize.y), (float) (2*M_PI/boxSize.z), 0);
        float recipCoefficient = (float) (ONE_4PI_EPS0*4*M_PI/(boxSize.x*boxSize.y*boxSize.z));
        ewaldSumsKernel.setArg<mm_float4>(3, recipBoxSize);
        ewaldSumsKernel.setArg<cl_float>(4, recipCoefficient);
        cl.executeKernel(ewaldSumsKernel, cosSinSums->getSize());
        ewaldForcesKernel.setArg<mm_float4>(3, recipBoxSize);
        ewaldForcesKernel.setArg<cl_float>(4, recipCoefficient);
        cl.executeKernel(ewaldForcesKernel, cl.getNumAtoms());
    }
    if (pmeGrid != NULL && cl.getContextIndex() == 0 && includeReciprocal) {
        mm_float4 boxSize = cl.getPeriodicBoxSize();
        mm_float4 invBoxSize = cl.getInvPeriodicBoxSize();
        pmeUpdateBsplinesKernel.setArg<mm_float4>(4, boxSize);
        pmeUpdateBsplinesKernel.setArg<mm_float4>(5, invBoxSize);
        cl.executeKernel(pmeUpdateBsplinesKernel, cl.getNumAtoms());
        if (deviceIsCpu) {
            pmeSpreadChargeKernel.setArg<mm_float4>(5, boxSize);
            pmeSpreadChargeKernel.setArg<mm_float4>(6, invBoxSize);
            cl.executeKernel(pmeSpreadChargeKernel, 2*cl.getDevice().getInfo<CL_DEVICE_MAX_COMPUTE_UNITS>(), 1);
        }
        else {
            sort->sort(*pmeAtomGridIndex);
            pmeAtomRangeKernel.setArg<mm_float4>(3, boxSize);
            pmeAtomRangeKernel.setArg<mm_float4>(4, invBoxSize);
            cl.executeKernel(pmeAtomRangeKernel, cl.getNumAtoms());
            if (cl.getSupports64BitGlobalAtomics()) {
                pmeSpreadChargeKernel.setArg<mm_float4>(5, boxSize);
                pmeSpreadChargeKernel.setArg<mm_float4>(6, invBoxSize);
                cl.executeKernel(pmeSpreadChargeKernel, cl.getNumAtoms(), PmeOrder*PmeOrder*PmeOrder);
                cl.executeKernel(pmeFinishSpreadChargeKernel, pmeGrid->getSize());
            }
            else {
                pmeZIndexKernel.setArg<mm_float4>(2, boxSize);
                pmeZIndexKernel.setArg<mm_float4>(3, invBoxSize);
                cl.executeKernel(pmeZIndexKernel, cl.getNumAtoms());
                cl.executeKernel(pmeSpreadChargeKernel, cl.getNumAtoms());
            }
        }
        fft->execFFT(*pmeGrid, *pmeGrid2, true);
        pmeConvolutionKernel.setArg<mm_float4>(5, invBoxSize);
        pmeConvolutionKernel.setArg<cl_float>(6, (float) (1.0/(M_PI*boxSize.x*boxSize.y*boxSize.z)));
        cl.executeKernel(pmeConvolutionKernel, cl.getNumAtoms());
        fft->execFFT(*pmeGrid2, *pmeGrid, false);
        pmeInterpolateForceKernel.setArg<mm_float4>(3, boxSize);
        pmeInterpolateForceKernel.setArg<mm_float4>(4, invBoxSize);
        cl.executeKernel(pmeInterpolateForceKernel, cl.getNumAtoms(), interpolateForceThreads);
    }
    double energy = (includeReciprocal ? ewaldSelfEnergy : 0.0);
    if (dispersionCoefficient != 0.0 && includeDirect) {
        mm_float4 boxSize = cl.getPeriodicBoxSize();
        energy += dispersionCoefficient/(boxSize.x*boxSize.y*boxSize.z);
    }
    return energy;
}

class OpenCLCustomNonbondedForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomNonbondedForceInfo(int requiredBuffers, const CustomNonbondedForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        vector<double> params1;
        vector<double> params2;
        force.getParticleParameters(particle1, params1);
        force.getParticleParameters(particle2, params2);
        for (int i = 0; i < (int) params1.size(); i++)
            if (params1[i] != params2[i])
                return false;
        return true;
    }
    int getNumParticleGroups() {
        return force.getNumExclusions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2;
        force.getExclusionParticles(index, particle1, particle2);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        return true;
    }
private:
    const CustomNonbondedForce& force;
};

OpenCLCalcCustomNonbondedForceKernel::~OpenCLCalcCustomNonbondedForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
    if (tabulatedFunctionParams != NULL)
        delete tabulatedFunctionParams;
    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        delete tabulatedFunctions[i];
}

void OpenCLCalcCustomNonbondedForceKernel::initialize(const System& system, const CustomNonbondedForce& force) {
    int forceIndex;
    for (forceIndex = 0; forceIndex < system.getNumForces() && &system.getForce(forceIndex) != &force; ++forceIndex)
        ;
    string prefix = "custom"+intToString(forceIndex)+"_";

    // Record parameters and exclusions.

    int numParticles = force.getNumParticles();
    params = new OpenCLParameterSet(cl, force.getNumPerParticleParameters(), numParticles, "customNonbondedParameters");
    if (force.getNumGlobalParameters() > 0)
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customNonbondedGlobals", false, CL_MEM_READ_ONLY);
    vector<vector<cl_float> > paramVector(numParticles);
    vector<vector<int> > exclusionList(numParticles);
    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
        force.getParticleParameters(i, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
        exclusionList[i].push_back(i);
    }
    for (int i = 0; i < force.getNumExclusions(); i++) {
        int particle1, particle2;
        force.getExclusionParticles(i, particle1, particle2);
        exclusionList[particle1].push_back(particle2);
        exclusionList[particle2].push_back(particle1);
    }
    params->setParameterValues(paramVector);

    // Record the tabulated functions.

    OpenCLExpressionUtilities::FunctionPlaceholder fp;
    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
    vector<mm_float4> tabulatedFunctionParamsVec(force.getNumFunctions());
    for (int i = 0; i < force.getNumFunctions(); i++) {
        string name;
        vector<double> values;
        double min, max;
        force.getFunctionParameters(i, name, values, min, max);
        string arrayName = prefix+"table"+intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = &fp;
        tabulatedFunctionParamsVec[i] = mm_float4((float) min, (float) max, (float) ((values.size()-1)/(max-min)), (float) values.size()-2);
        vector<mm_float4> f = OpenCLExpressionUtilities::computeFunctionCoefficients(values, min, max);
        tabulatedFunctions.push_back(new OpenCLArray<mm_float4>(cl, values.size()-1, "TabulatedFunction"));
        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(arrayName, "float", 4, sizeof(cl_float4), tabulatedFunctions[tabulatedFunctions.size()-1]->getDeviceBuffer()));
    }
    if (force.getNumFunctions() > 0) {
        tabulatedFunctionParams = new OpenCLArray<mm_float4>(cl, tabulatedFunctionParamsVec.size(), "tabulatedFunctionParameters", false, CL_MEM_READ_ONLY);
        tabulatedFunctionParams->upload(tabulatedFunctionParamsVec);
        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(prefix+"functionParams", "float", 4, sizeof(cl_float4), tabulatedFunctionParams->getDeviceBuffer()));
    }

    // Record information for the expressions.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    if (globals != NULL)
        globals->upload(globalParamValues);
    bool useCutoff = (force.getNonbondedMethod() != CustomNonbondedForce::NoCutoff);
    bool usePeriodic = (force.getNonbondedMethod() != CustomNonbondedForce::NoCutoff && force.getNonbondedMethod() != CustomNonbondedForce::CutoffNonPeriodic);
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction(), functions).optimize();
    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("r").optimize();
    map<string, Lepton::ParsedExpression> forceExpressions;
    forceExpressions["tempEnergy += "] = energyExpression;
    forceExpressions["tempForce -= "] = forceExpression;

    // Create the kernels.

    vector<pair<ExpressionTreeNode, string> > variables;
    ExpressionTreeNode rnode(new Operation::Variable("r"));
    variables.push_back(make_pair(rnode, "r"));
    variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
    variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
    for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
        const string& name = force.getPerParticleParameterName(i);
        variables.push_back(makeVariable(name+"1", prefix+"params"+params->getParameterSuffix(i, "1")));
        variables.push_back(makeVariable(name+"2", prefix+"params"+params->getParameterSuffix(i, "2")));
    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
        string value = "globals["+intToString(i)+"]";
        variables.push_back(makeVariable(name, prefix+value));
    }
    stringstream compute;
    compute << OpenCLExpressionUtilities::createExpressions(forceExpressions, variables, functionDefinitions, prefix+"temp", prefix+"functionParams");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
    string source = cl.replaceStrings(OpenCLKernelSources::customNonbonded, replacements);
    cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source, force.getForceGroup());
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        cl.getNonbondedUtilities().addParameter(OpenCLNonbondedUtilities::ParameterInfo(prefix+"params"+intToString(i+1), buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
    }
    if (globals != NULL) {
        globals->upload(globalParamValues);
        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(prefix+"globals", "float", 1, sizeof(cl_float), globals->getDeviceBuffer()));
    }
    cl.addForce(new OpenCLCustomNonbondedForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force));
}

double OpenCLCalcCustomNonbondedForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    return 0.0;
}

class OpenCLGBSAOBCForceInfo : public OpenCLForceInfo {
public:
    OpenCLGBSAOBCForceInfo(int requiredBuffers, const GBSAOBCForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        double charge1, charge2, radius1, radius2, scale1, scale2;
        force.getParticleParameters(particle1, charge1, radius1, scale1);
        force.getParticleParameters(particle2, charge2, radius2, scale2);
        return (charge1 == charge2 && radius1 == radius2 && scale1 == scale2);
    }
private:
    const GBSAOBCForce& force;
};

OpenCLCalcGBSAOBCForceKernel::~OpenCLCalcGBSAOBCForceKernel() {
    if (params != NULL)
        delete params;
    if (bornSum != NULL)
        delete bornSum;
    if (longBornSum != NULL)
        delete longBornSum;
    if (bornRadii != NULL)
        delete bornRadii;
    if (bornForce != NULL)
        delete bornForce;
    if (longBornForce != NULL)
        delete longBornForce;
    if (obcChain != NULL)
        delete obcChain;
}

void OpenCLCalcGBSAOBCForceKernel::initialize(const System& system, const GBSAOBCForce& force) {
    if (cl.getPlatformData().contexts.size() > 1)
        throw OpenMMException("GBSAOBCForce does not support using multiple OpenCL devices");
    OpenCLNonbondedUtilities& nb = cl.getNonbondedUtilities();
    params = new OpenCLArray<mm_float2>(cl, cl.getPaddedNumAtoms(), "gbsaObcParams");
    bornRadii = new OpenCLArray<cl_float>(cl, cl.getPaddedNumAtoms(), "bornRadii");
    obcChain = new OpenCLArray<cl_float>(cl, cl.getPaddedNumAtoms(), "obcChain");
    if (cl.getSupports64BitGlobalAtomics()) {
        longBornSum = new OpenCLArray<cl_long>(cl, cl.getPaddedNumAtoms(), "longBornSum");
        longBornForce = new OpenCLArray<cl_long>(cl, cl.getPaddedNumAtoms(), "longBornForce");
        bornForce = new OpenCLArray<cl_float>(cl, cl.getPaddedNumAtoms(), "bornForce");
        cl.addAutoclearBuffer(longBornSum->getDeviceBuffer(), 2*longBornSum->getSize());
        cl.addAutoclearBuffer(longBornForce->getDeviceBuffer(), 2*longBornForce->getSize());
    }
    else {
        bornSum = new OpenCLArray<cl_float>(cl, cl.getPaddedNumAtoms()*nb.getNumForceBuffers(), "bornSum");
        bornForce = new OpenCLArray<cl_float>(cl, cl.getPaddedNumAtoms()*nb.getNumForceBuffers(), "bornForce");
        cl.addAutoclearBuffer(bornSum->getDeviceBuffer(), bornSum->getSize());
        cl.addAutoclearBuffer(bornForce->getDeviceBuffer(), bornForce->getSize());
    }
    OpenCLArray<mm_float4>& posq = cl.getPosq();
    int numParticles = force.getNumParticles();
    vector<mm_float2> paramsVector(numParticles);
    const double dielectricOffset = 0.009;
    for (int i = 0; i < numParticles; i++) {
        double charge, radius, scalingFactor;
        force.getParticleParameters(i, charge, radius, scalingFactor);
        radius -= dielectricOffset;
        paramsVector[i] = mm_float2((float) radius, (float) (scalingFactor*radius));
        posq[i].w = (float) charge;
    }
    posq.upload();
    params->upload(paramsVector);
    prefactor = -ONE_4PI_EPS0*((1.0/force.getSoluteDielectric())-(1.0/force.getSolventDielectric()));
    bool useCutoff = (force.getNonbondedMethod() != GBSAOBCForce::NoCutoff);
    bool usePeriodic = (force.getNonbondedMethod() != GBSAOBCForce::NoCutoff && force.getNonbondedMethod() != GBSAOBCForce::CutoffNonPeriodic);
    string source = OpenCLKernelSources::gbsaObc2;
    nb.addInteraction(useCutoff, usePeriodic, false, force.getCutoffDistance(), vector<vector<int> >(), source, force.getForceGroup());
    nb.addParameter(OpenCLNonbondedUtilities::ParameterInfo("obcParams", "float", 2, sizeof(cl_float2), params->getDeviceBuffer()));;
    nb.addParameter(OpenCLNonbondedUtilities::ParameterInfo("bornForce", "float", 1, sizeof(cl_float), bornForce->getDeviceBuffer()));;
    cl.addForce(new OpenCLGBSAOBCForceInfo(nb.getNumForceBuffers(), force));
}

double OpenCLCalcGBSAOBCForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    OpenCLNonbondedUtilities& nb = cl.getNonbondedUtilities();
    bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
    if (!hasCreatedKernels) {
        // These Kernels cannot be created in initialize(), because the OpenCLNonbondedUtilities has not been initialized yet then.

        hasCreatedKernels = true;
        maxTiles = (nb.getUseCutoff() ? nb.getInteractingTiles().getSize() : 0);
        map<string, string> defines;
        if (nb.getForceBufferPerAtomBlock())
            defines["USE_OUTPUT_BUFFER_PER_BLOCK"] = "1";
        if (nb.getUseCutoff())
            defines["USE_CUTOFF"] = "1";
        if (nb.getUsePeriodic())
            defines["USE_PERIODIC"] = "1";
        defines["CUTOFF_SQUARED"] = doubleToString(nb.getCutoffDistance()*nb.getCutoffDistance());
        defines["PREFACTOR"] = doubleToString(prefactor);
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
        defines["NUM_BLOCKS"] = OpenCLExpressionUtilities::intToString(cl.getNumAtomBlocks());
        defines["FORCE_WORK_GROUP_SIZE"] = OpenCLExpressionUtilities::intToString(nb.getForceThreadBlockSize());
        string platformVendor = cl::Platform(cl.getDevice().getInfo<CL_DEVICE_PLATFORM>()).getInfo<CL_PLATFORM_VENDOR>();
        if (platformVendor == "Apple")
            defines["USE_APPLE_WORKAROUND"] = "1";
        string file;
        if (deviceIsCpu)
            file = OpenCLKernelSources::gbsaObc_cpu;
        else if (cl.getSIMDWidth() == 32)
            file = OpenCLKernelSources::gbsaObc_nvidia;
        else
            file = OpenCLKernelSources::gbsaObc_default;
        cl::Program program = cl.createProgram(file, defines);
        bool useLong = (cl.getSupports64BitGlobalAtomics() && !deviceIsCpu);
        int index = 0;
        computeBornSumKernel = cl::Kernel(program, "computeBornSum");
        computeBornSumKernel.setArg<cl::Buffer>(index++, (useLong ? longBornSum->getDeviceBuffer() : bornSum->getDeviceBuffer()));
        computeBornSumKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        computeBornSumKernel.setArg<cl::Buffer>(index++, params->getDeviceBuffer());
        if (nb.getUseCutoff()) {
            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
            index += 2; // The periodic box size arguments are set when the kernel is executed.
            computeBornSumKernel.setArg<cl_uint>(index++, maxTiles);
            if (cl.getSIMDWidth() == 32 || deviceIsCpu)
                computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractionFlags().getDeviceBuffer());
        }
        else
            computeBornSumKernel.setArg<cl_uint>(index++, cl.getNumAtomBlocks()*(cl.getNumAtomBlocks()+1)/2);
        if (cl.getSIMDWidth() == 32) {
            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getExclusionIndices().getDeviceBuffer());
            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getExclusionRowIndices().getDeviceBuffer());
        }
        force1Kernel = cl::Kernel(program, "computeGBSAForce1");
        index = 0;
        force1Kernel.setArg<cl::Buffer>(index++, (useLong ? cl.getLongForceBuffer().getDeviceBuffer() : cl.getForceBuffers().getDeviceBuffer()));
        force1Kernel.setArg<cl::Buffer>(index++, (useLong ? longBornForce->getDeviceBuffer() : bornForce->getDeviceBuffer()));
        force1Kernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        force1Kernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        force1Kernel.setArg<cl::Buffer>(index++, bornRadii->getDeviceBuffer());
        if (nb.getUseCutoff()) {
            force1Kernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            force1Kernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
            index += 2; // The periodic box size arguments are set when the kernel is executed.
            force1Kernel.setArg<cl_uint>(index++, maxTiles);
            if (cl.getSIMDWidth() == 32 || deviceIsCpu)
                force1Kernel.setArg<cl::Buffer>(index++, nb.getInteractionFlags().getDeviceBuffer());
        }
        else
            force1Kernel.setArg<cl_uint>(index++, cl.getNumAtomBlocks()*(cl.getNumAtomBlocks()+1)/2);
        if (cl.getSIMDWidth() == 32) {
            force1Kernel.setArg<cl::Buffer>(index++, nb.getExclusionIndices().getDeviceBuffer());
            force1Kernel.setArg<cl::Buffer>(index++, nb.getExclusionRowIndices().getDeviceBuffer());
        }
        program = cl.createProgram(OpenCLKernelSources::gbsaObcReductions, defines);
        reduceBornSumKernel = cl::Kernel(program, "reduceBornSum");
        reduceBornSumKernel.setArg<cl_int>(0, cl.getPaddedNumAtoms());
        reduceBornSumKernel.setArg<cl_int>(1, nb.getNumForceBuffers());
        reduceBornSumKernel.setArg<cl_float>(2, 1.0f);
        reduceBornSumKernel.setArg<cl_float>(3, 0.8f);
        reduceBornSumKernel.setArg<cl_float>(4, 4.85f);
        reduceBornSumKernel.setArg<cl::Buffer>(5, (useLong ? longBornSum->getDeviceBuffer() : bornSum->getDeviceBuffer()));
        reduceBornSumKernel.setArg<cl::Buffer>(6, params->getDeviceBuffer());
        reduceBornSumKernel.setArg<cl::Buffer>(7, bornRadii->getDeviceBuffer());
        reduceBornSumKernel.setArg<cl::Buffer>(8, obcChain->getDeviceBuffer());
        reduceBornForceKernel = cl::Kernel(program, "reduceBornForce");
        index = 0;
        reduceBornForceKernel.setArg<cl_int>(index++, cl.getPaddedNumAtoms());
        reduceBornForceKernel.setArg<cl_int>(index++, nb.getNumForceBuffers());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, bornForce->getDeviceBuffer());
        if (useLong)
            reduceBornForceKernel.setArg<cl::Buffer>(index++, longBornForce->getDeviceBuffer());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, params->getDeviceBuffer());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, bornRadii->getDeviceBuffer());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, obcChain->getDeviceBuffer());
    }
    if (nb.getUseCutoff()) {
        computeBornSumKernel.setArg<mm_float4>(5, cl.getPeriodicBoxSize());
        computeBornSumKernel.setArg<mm_float4>(6, cl.getInvPeriodicBoxSize());
        force1Kernel.setArg<mm_float4>(7, cl.getPeriodicBoxSize());
        force1Kernel.setArg<mm_float4>(8, cl.getInvPeriodicBoxSize());
        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
            computeBornSumKernel.setArg<cl::Buffer>(4, nb.getInteractingTiles().getDeviceBuffer());
            computeBornSumKernel.setArg<cl_uint>(7, maxTiles);
            force1Kernel.setArg<cl::Buffer>(5, nb.getInteractingTiles().getDeviceBuffer());
            force1Kernel.setArg<cl_uint>(9, maxTiles);
            if (cl.getSIMDWidth() == 32 || deviceIsCpu) {
                computeBornSumKernel.setArg<cl::Buffer>(8, nb.getInteractionFlags().getDeviceBuffer());
                force1Kernel.setArg<cl::Buffer>(10, nb.getInteractionFlags().getDeviceBuffer());
            }
        }
    }
    cl.executeKernel(computeBornSumKernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
    cl.executeKernel(reduceBornSumKernel, cl.getPaddedNumAtoms());
    cl.executeKernel(force1Kernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
    cl.executeKernel(reduceBornForceKernel, cl.getPaddedNumAtoms());
    return 0.0;
}

class OpenCLCustomGBForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomGBForceInfo(int requiredBuffers, const CustomGBForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        vector<double> params1;
        vector<double> params2;
        force.getParticleParameters(particle1, params1);
        force.getParticleParameters(particle2, params2);
        for (int i = 0; i < (int) params1.size(); i++)
            if (params1[i] != params2[i])
                return false;
        return true;
    }
    int getNumParticleGroups() {
        return force.getNumExclusions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2;
        force.getExclusionParticles(index, particle1, particle2);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        return true;
    }
private:
    const CustomGBForce& force;
};

OpenCLCalcCustomGBForceKernel::~OpenCLCalcCustomGBForceKernel() {
    if (params != NULL)
        delete params;
    if (computedValues != NULL)
        delete computedValues;
    if (energyDerivs != NULL)
        delete energyDerivs;
    if (longEnergyDerivs != NULL)
        delete longEnergyDerivs;
    if (globals != NULL)
        delete globals;
    if (valueBuffers != NULL)
        delete valueBuffers;
    if (longValueBuffers != NULL)
        delete longValueBuffers;
    if (tabulatedFunctionParams != NULL)
        delete tabulatedFunctionParams;
    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        delete tabulatedFunctions[i];
}

void OpenCLCalcCustomGBForceKernel::initialize(const System& system, const CustomGBForce& force) {
    if (cl.getPlatformData().contexts.size() > 1)
        throw OpenMMException("CustomGBForce does not support using multiple OpenCL devices");
    bool useExclusionsForValue = false;
    numComputedValues = force.getNumComputedValues();
    vector<string> computedValueNames(force.getNumComputedValues());
    vector<string> computedValueExpressions(force.getNumComputedValues());
    if (force.getNumComputedValues() > 0) {
        CustomGBForce::ComputationType type;
        force.getComputedValueParameters(0, computedValueNames[0], computedValueExpressions[0], type);
        if (type == CustomGBForce::SingleParticle)
            throw OpenMMException("OpenCLPlatform requires that the first computed value for a CustomGBForce be of type ParticlePair or ParticlePairNoExclusions.");
        useExclusionsForValue = (type == CustomGBForce::ParticlePair);
        for (int i = 1; i < force.getNumComputedValues(); i++) {
            force.getComputedValueParameters(i, computedValueNames[i], computedValueExpressions[i], type);
            if (type != CustomGBForce::SingleParticle)
                throw OpenMMException("OpenCLPlatform requires that a CustomGBForce only have one computed value of type ParticlePair or ParticlePairNoExclusions.");
        }
    }
    int forceIndex;
    for (forceIndex = 0; forceIndex < system.getNumForces() && &system.getForce(forceIndex) != &force; ++forceIndex)
        ;
    string prefix = "custom"+intToString(forceIndex)+"_";

    // Record parameters and exclusions.

    int numParticles = force.getNumParticles();
    params = new OpenCLParameterSet(cl, force.getNumPerParticleParameters(), numParticles, "customGBParameters", true);
    computedValues = new OpenCLParameterSet(cl, force.getNumComputedValues(), numParticles, "customGBComputedValues", true);
    if (force.getNumGlobalParameters() > 0)
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customGBGlobals", false, CL_MEM_READ_ONLY);
    vector<vector<cl_float> > paramVector(numParticles);
    vector<vector<int> > exclusionList(numParticles);
    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
        force.getParticleParameters(i, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
        exclusionList[i].push_back(i);
    }
    for (int i = 0; i < force.getNumExclusions(); i++) {
        int particle1, particle2;
        force.getExclusionParticles(i, particle1, particle2);
        exclusionList[particle1].push_back(particle2);
        exclusionList[particle2].push_back(particle1);
    }
    params->setParameterValues(paramVector);

    // Record the tabulated functions.

    OpenCLExpressionUtilities::FunctionPlaceholder fp;
    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
    vector<mm_float4> tabulatedFunctionParamsVec(force.getNumFunctions());
    stringstream tableArgs;
    for (int i = 0; i < force.getNumFunctions(); i++) {
        string name;
        vector<double> values;
        double min, max;
        force.getFunctionParameters(i, name, values, min, max);
        string arrayName = prefix+"table"+intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = &fp;
        tabulatedFunctionParamsVec[i] = mm_float4((float) min, (float) max, (float) ((values.size()-1)/(max-min)), (float) values.size()-2);
        vector<mm_float4> f = OpenCLExpressionUtilities::computeFunctionCoefficients(values, min, max);
        tabulatedFunctions.push_back(new OpenCLArray<mm_float4>(cl, values.size()-1, "TabulatedFunction"));
        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(arrayName, "float", 4, sizeof(cl_float4), tabulatedFunctions[tabulatedFunctions.size()-1]->getDeviceBuffer()));
        tableArgs << ", __global const float4* restrict " << arrayName;
    }
    if (force.getNumFunctions() > 0) {
        tabulatedFunctionParams = new OpenCLArray<mm_float4>(cl, tabulatedFunctionParamsVec.size(), "tabulatedFunctionParameters", false, CL_MEM_READ_ONLY);
        tabulatedFunctionParams->upload(tabulatedFunctionParamsVec);
        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(prefix+"functionParams", "float", 4, sizeof(cl_float4), tabulatedFunctionParams->getDeviceBuffer()));
        tableArgs << ", __global const float4* " << prefix << "functionParams";
    }

    // Record the global parameters.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    if (globals != NULL)
        globals->upload(globalParamValues);

    // Record derivatives of expressions needed for the chain rule terms.

    vector<vector<Lepton::ParsedExpression> > valueGradientExpressions(force.getNumComputedValues());
    vector<vector<Lepton::ParsedExpression> > valueDerivExpressions(force.getNumComputedValues());
    needParameterGradient = false;
    for (int i = 1; i < force.getNumComputedValues(); i++) {
        Lepton::ParsedExpression ex = Lepton::Parser::parse(computedValueExpressions[i], functions).optimize();
        valueGradientExpressions[i].push_back(ex.differentiate("x").optimize());
        valueGradientExpressions[i].push_back(ex.differentiate("y").optimize());
        valueGradientExpressions[i].push_back(ex.differentiate("z").optimize());
        if (!isZeroExpression(valueGradientExpressions[i][0]) || !isZeroExpression(valueGradientExpressions[i][1]) || !isZeroExpression(valueGradientExpressions[i][2]))
            needParameterGradient = true;
         for (int j = 0; j < i; j++)
            valueDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]).optimize());
    }
    vector<vector<Lepton::ParsedExpression> > energyDerivExpressions(force.getNumEnergyTerms());
    vector<bool> needChainForValue(force.getNumComputedValues(), false);
    for (int i = 0; i < force.getNumEnergyTerms(); i++) {
        string expression;
        CustomGBForce::ComputationType type;
        force.getEnergyTermParameters(i, expression, type);
        Lepton::ParsedExpression ex = Lepton::Parser::parse(expression, functions).optimize();
        for (int j = 0; j < force.getNumComputedValues(); j++) {
            if (type == CustomGBForce::SingleParticle) {
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]).optimize());
                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
            }
            else {
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]+"1").optimize());
                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]+"2").optimize());
                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
            }
        }
    }
    bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
    bool useLong = (cl.getSupports64BitGlobalAtomics() && !deviceIsCpu);
    if (useLong) {
        longEnergyDerivs = new OpenCLArray<cl_long>(cl, force.getNumComputedValues()*cl.getPaddedNumAtoms(), "customGBLongEnergyDerivatives");
        energyDerivs = new OpenCLParameterSet(cl, force.getNumComputedValues(), cl.getPaddedNumAtoms(), "customGBEnergyDerivatives", true);
    }
    else
        energyDerivs = new OpenCLParameterSet(cl, force.getNumComputedValues(), cl.getPaddedNumAtoms()*cl.getNonbondedUtilities().getNumForceBuffers(), "customGBEnergyDerivatives", true);
 
    // Create the kernels.

    bool useCutoff = (force.getNonbondedMethod() != CustomGBForce::NoCutoff);
    bool usePeriodic = (force.getNonbondedMethod() != CustomGBForce::NoCutoff && force.getNonbondedMethod() != CustomGBForce::CutoffNonPeriodic);
    {
        // Create the N2 value kernel.

        vector<pair<ExpressionTreeNode, string> > variables;
        map<string, string> rename;
        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
            variables.push_back(makeVariable(name+"1", "params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", "params"+params->getParameterSuffix(i, "2")));
            rename[name+"1"] = name+"2";
            rename[name+"2"] = name+"1";
        }
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+intToString(i)+"]";
            variables.push_back(makeVariable(name, value));
        }
        map<string, Lepton::ParsedExpression> n2ValueExpressions;
        stringstream n2ValueSource;
        Lepton::ParsedExpression ex = Lepton::Parser::parse(computedValueExpressions[0], functions).optimize();
        n2ValueExpressions["tempValue1 = "] = ex;
        n2ValueExpressions["tempValue2 = "] = ex.renameVariables(rename);
        n2ValueSource << OpenCLExpressionUtilities::createExpressions(n2ValueExpressions, variables, functionDefinitions, "temp", prefix+"functionParams");
        map<string, string> replacements;
        string n2ValueStr = n2ValueSource.str();
        replacements["COMPUTE_VALUE"] = n2ValueStr;
        stringstream extraArgs, loadLocal1, loadLocal2, load1, load2;
        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", __global const float* globals";
        pairValueUsesParam.resize(params->getBuffers().size(), false);
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
            if (n2ValueStr.find(paramName+"1") != n2ValueStr.npos || n2ValueStr.find(paramName+"2") != n2ValueStr.npos) {
                extraArgs << ", __global const " << buffer.getType() << "* restrict global_" << paramName << ", __local " << buffer.getType() << "* restrict local_" << paramName;
                loadLocal1 << "local_" << paramName << "[localAtomIndex] = " << paramName << "1;\n";
                loadLocal2 << "local_" << paramName << "[localAtomIndex] = global_" << paramName << "[j];\n";
                load1 << buffer.getType() << " " << paramName << "1 = global_" << paramName << "[atom1];\n";
                load2 << buffer.getType() << " " << paramName << "2 = local_" << paramName << "[atom2];\n";
                pairValueUsesParam[i] = true;
            }
        }
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
        replacements["LOAD_LOCAL_PARAMETERS_FROM_1"] = loadLocal1.str();
        replacements["LOAD_LOCAL_PARAMETERS_FROM_GLOBAL"] = loadLocal2.str();
        replacements["LOAD_ATOM1_PARAMETERS"] = load1.str();
        replacements["LOAD_ATOM2_PARAMETERS"] = load2.str();
        map<string, string> defines;
        if (cl.getNonbondedUtilities().getForceBufferPerAtomBlock())
            defines["USE_OUTPUT_BUFFER_PER_BLOCK"] = "1";
        if (useCutoff)
            defines["USE_CUTOFF"] = "1";
        if (usePeriodic)
            defines["USE_PERIODIC"] = "1";
        if (useExclusionsForValue)
            defines["USE_EXCLUSIONS"] = "1";
        if (cl.getSIMDWidth() == 32)
            defines["WARPS_PER_GROUP"] = OpenCLExpressionUtilities::intToString(cl.getNonbondedUtilities().getForceThreadBlockSize()/OpenCLContext::TileSize);
        defines["CUTOFF_SQUARED"] = doubleToString(force.getCutoffDistance()*force.getCutoffDistance());
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
        defines["NUM_BLOCKS"] = OpenCLExpressionUtilities::intToString(cl.getNumAtomBlocks());
        string file;
        if (deviceIsCpu)
            file = OpenCLKernelSources::customGBValueN2_cpu;
        else if (cl.getSIMDWidth() == 32)
            file = OpenCLKernelSources::customGBValueN2_nvidia;
        else
            file = OpenCLKernelSources::customGBValueN2_default;
        cl::Program program = cl.createProgram(cl.replaceStrings(file, replacements), defines);
        pairValueKernel = cl::Kernel(program, "computeN2Value");
        if (useExclusionsForValue)
            cl.getNonbondedUtilities().requestExclusions(exclusionList);
    }
    {
        // Create the kernel to reduce the N2 value and calculate other values.

        stringstream reductionSource, extraArgs;
        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", __global const float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
            extraArgs << ", __global const " << buffer.getType() << "* restrict " << paramName;
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* restrict global_" << valueName;
            reductionSource << buffer.getType() << " local_" << valueName << ";\n";
        }
        reductionSource << "local_values" << computedValues->getParameterSuffix(0) << " = sum;\n";
        map<string, string> variables;
        variables["x"] = "pos.x";
        variables["y"] = "pos.y";
        variables["z"] = "pos.z";
        for (int i = 0; i < force.getNumPerParticleParameters(); i++)
            variables[force.getPerParticleParameterName(i)] = "params"+params->getParameterSuffix(i, "[index]");
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables[force.getGlobalParameterName(i)] = "globals["+intToString(i)+"]";
        for (int i = 1; i < force.getNumComputedValues(); i++) {
            variables[computedValueNames[i-1]] = "local_values"+computedValues->getParameterSuffix(i-1);
            map<string, Lepton::ParsedExpression> valueExpressions;
            valueExpressions["local_values"+computedValues->getParameterSuffix(i)+" = "] = Lepton::Parser::parse(computedValueExpressions[i], functions).optimize();
            reductionSource << OpenCLExpressionUtilities::createExpressions(valueExpressions, variables, functionDefinitions, "value"+intToString(i)+"_temp", prefix+"functionParams");
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            string valueName = "values"+intToString(i+1);
            reductionSource << "global_" << valueName << "[index] = local_" << valueName << ";\n";
        }
        map<string, string> replacements;
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
        replacements["COMPUTE_VALUES"] = reductionSource.str();
        map<string, string> defines;
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customGBValuePerParticle, replacements), defines);
        perParticleValueKernel = cl::Kernel(program, "computePerParticleValues");
    }
    {
        // Create the N2 energy kernel.

        vector<pair<ExpressionTreeNode, string> > variables;
        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
            variables.push_back(makeVariable(name+"1", "params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", "params"+params->getParameterSuffix(i, "2")));
        }
        for (int i = 0; i < force.getNumComputedValues(); i++) {
            variables.push_back(makeVariable(computedValueNames[i]+"1", "values"+computedValues->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(computedValueNames[i]+"2", "values"+computedValues->getParameterSuffix(i, "2")));
        }
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables.push_back(makeVariable(force.getGlobalParameterName(i), "globals["+intToString(i)+"]"));
        stringstream n2EnergySource;
        bool anyExclusions = (force.getNumExclusions() > 0);
        for (int i = 0; i < force.getNumEnergyTerms(); i++) {
            string expression;
            CustomGBForce::ComputationType type;
            force.getEnergyTermParameters(i, expression, type);
            if (type == CustomGBForce::SingleParticle)
                continue;
            bool exclude = (anyExclusions && type == CustomGBForce::ParticlePair);
            map<string, Lepton::ParsedExpression> n2EnergyExpressions;
            n2EnergyExpressions["tempEnergy += "] = Lepton::Parser::parse(expression, functions).optimize();
            n2EnergyExpressions["dEdR += "] = Lepton::Parser::parse(expression, functions).differentiate("r").optimize();
            if (useLong) {
                for (int j = 0; j < force.getNumComputedValues(); j++) {
                    if (needChainForValue[j]) {
                        string index = intToString(j+1);
                        n2EnergyExpressions["/*"+intToString(i+1)+"*/ deriv"+index+"_1 += "] = energyDerivExpressions[i][2*j];
                        n2EnergyExpressions["/*"+intToString(i+1)+"*/ deriv"+index+"_2 += "] = energyDerivExpressions[i][2*j+1];
                    }
                }
            }
            else {
                for (int j = 0; j < force.getNumComputedValues(); j++) {
                    if (needChainForValue[j]) {
                        n2EnergyExpressions["/*"+intToString(i+1)+"*/ deriv"+energyDerivs->getParameterSuffix(j, "_1")+" += "] = energyDerivExpressions[i][2*j];
                        n2EnergyExpressions["/*"+intToString(i+1)+"*/ deriv"+energyDerivs->getParameterSuffix(j, "_2")+" += "] = energyDerivExpressions[i][2*j+1];
                    }
                }
            }
            if (exclude)
                n2EnergySource << "if (!isExcluded) {\n";
            n2EnergySource << OpenCLExpressionUtilities::createExpressions(n2EnergyExpressions, variables, functionDefinitions, "temp", prefix+"functionParams");
            if (exclude)
                n2EnergySource << "}\n";
        }
        map<string, string> replacements;
        string n2EnergyStr = n2EnergySource.str();
        replacements["COMPUTE_INTERACTION"] = n2EnergyStr;
        stringstream extraArgs, loadLocal1, loadLocal2, clearLocal, load1, load2, declare1, recordDeriv, storeDerivs1, storeDerivs2, declareTemps, setTemps;
        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", __global const float* globals";
        pairEnergyUsesParam.resize(params->getBuffers().size(), false);
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
            if (n2EnergyStr.find(paramName+"1") != n2EnergyStr.npos || n2EnergyStr.find(paramName+"2") != n2EnergyStr.npos) {
                extraArgs << ", __global const " << buffer.getType() << "* restrict global_" << paramName << ", __local " << buffer.getType() << "* restrict local_" << paramName;
                loadLocal1 << "local_" << paramName << "[localAtomIndex] = " << paramName << "1;\n";
                loadLocal2 << "local_" << paramName << "[localAtomIndex] = global_" << paramName << "[j];\n";
                load1 << buffer.getType() << " " << paramName << "1 = global_" << paramName << "[atom1];\n";
                load2 << buffer.getType() << " " << paramName << "2 = local_" << paramName << "[atom2];\n";
                pairEnergyUsesParam[i] = true;
            }
        }
        pairEnergyUsesValue.resize(computedValues->getBuffers().size(), false);
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+intToString(i+1);
            if (n2EnergyStr.find(valueName+"1") != n2EnergyStr.npos || n2EnergyStr.find(valueName+"2") != n2EnergyStr.npos) {
                extraArgs << ", __global const " << buffer.getType() << "* restrict global_" << valueName << ", __local " << buffer.getType() << "* restrict local_" << valueName;
                loadLocal1 << "local_" << valueName << "[localAtomIndex] = " << valueName << "1;\n";
                loadLocal2 << "local_" << valueName << "[localAtomIndex] = global_" << valueName << "[j];\n";
                load1 << buffer.getType() << " " << valueName << "1 = global_" << valueName << "[atom1];\n";
                load2 << buffer.getType() << " " << valueName << "2 = local_" << valueName << "[atom2];\n";
                pairEnergyUsesValue[i] = true;
            }
        }
        if (useLong) {
            extraArgs << ", __global long* restrict derivBuffers";
            for (int i = 0; i < force.getNumComputedValues(); i++) {
                string index = intToString(i+1);
                extraArgs << ", __local float* restrict local_deriv" << index;
                clearLocal << "local_deriv" << index << "[localAtomIndex] = 0.0f;\n";
                declare1 << "float deriv" << index << "_1 = 0.0f;\n";
                load2 << "float deriv" << index << "_2 = 0.0f;\n";
                recordDeriv << "local_deriv" << index << "[atom2] += deriv" << index << "_2;\n";
                storeDerivs1 << "STORE_DERIVATIVE_1(" << index << ")\n";
                storeDerivs2 << "STORE_DERIVATIVE_2(" << index << ")\n";
                declareTemps << "__local float tempDerivBuffer" << index << "[64];\n";
                setTemps << "tempDerivBuffer" << index << "[get_local_id(0)] = deriv" << index << "_1;\n";
            }
        }
        else {
            for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
                string index = intToString(i+1);
                extraArgs << ", __global " << buffer.getType() << "* restrict derivBuffers" << index << ", __local " << buffer.getType() << "* restrict local_deriv" << index;
                clearLocal << "local_deriv" << index << "[localAtomIndex] = 0.0f;\n";
                declare1 << buffer.getType() << " deriv" << index << "_1 = 0.0f;\n";
                load2 << buffer.getType() << " deriv" << index << "_2 = 0.0f;\n";
                recordDeriv << "local_deriv" << index << "[atom2] += deriv" << index << "_2;\n";
                storeDerivs1 << "STORE_DERIVATIVE_1(" << index << ")\n";
                storeDerivs2 << "STORE_DERIVATIVE_2(" << index << ")\n";
                declareTemps << "__local " << buffer.getType() << " tempDerivBuffer" << index << "[64];\n";
                setTemps << "tempDerivBuffer" << index << "[get_local_id(0)] = deriv" << index << "_1;\n";
            }
        }
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
        replacements["LOAD_LOCAL_PARAMETERS_FROM_1"] = loadLocal1.str();
        replacements["LOAD_LOCAL_PARAMETERS_FROM_GLOBAL"] = loadLocal2.str();
        replacements["CLEAR_LOCAL_DERIVATIVES"] = clearLocal.str();
        replacements["LOAD_ATOM1_PARAMETERS"] = load1.str();
        replacements["LOAD_ATOM2_PARAMETERS"] = load2.str();
        replacements["DECLARE_ATOM1_DERIVATIVES"] = declare1.str();
        replacements["RECORD_DERIVATIVE_2"] = recordDeriv.str();
        replacements["STORE_DERIVATIVES_1"] = storeDerivs1.str();
        replacements["STORE_DERIVATIVES_2"] = storeDerivs2.str();
        replacements["DECLARE_TEMP_BUFFERS"] = declareTemps.str();
        replacements["SET_TEMP_BUFFERS"] = setTemps.str();
        map<string, string> defines;
        if (cl.getNonbondedUtilities().getForceBufferPerAtomBlock())
            defines["USE_OUTPUT_BUFFER_PER_BLOCK"] = "1";
        if (useCutoff)
            defines["USE_CUTOFF"] = "1";
        if (usePeriodic)
            defines["USE_PERIODIC"] = "1";
        if (anyExclusions)
            defines["USE_EXCLUSIONS"] = "1";
        if (cl.getSIMDWidth() == 32)
            defines["WARPS_PER_GROUP"] = OpenCLExpressionUtilities::intToString(cl.getNonbondedUtilities().getForceThreadBlockSize()/OpenCLContext::TileSize);
        defines["CUTOFF_SQUARED"] = doubleToString(force.getCutoffDistance()*force.getCutoffDistance());
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
        defines["NUM_BLOCKS"] = OpenCLExpressionUtilities::intToString(cl.getNumAtomBlocks());
        string file;
        if (deviceIsCpu)
            file = OpenCLKernelSources::customGBEnergyN2_cpu;
        else if (cl.getSIMDWidth() == 32)
            file = OpenCLKernelSources::customGBEnergyN2_nvidia;
        else
            file = OpenCLKernelSources::customGBEnergyN2_default;
        cl::Program program = cl.createProgram(cl.replaceStrings(file, replacements), defines);
        pairEnergyKernel = cl::Kernel(program, "computeN2Energy");
    }
    {
        // Create the kernel to reduce the derivatives and calculate per-particle energy terms.

        stringstream compute, extraArgs, reduce;
        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", __global const float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
            extraArgs << ", __global const " << buffer.getType() << "* restrict " << paramName;
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+intToString(i+1);
            extraArgs << ", __global const " << buffer.getType() << "* restrict " << valueName;
        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            string index = intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* restrict derivBuffers" << index;
            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
        if (useLong) {
            extraArgs << ", __global const long* restrict derivBuffersIn";
            for (int i = 0; i < energyDerivs->getNumParameters(); ++i)
                reduce << "derivBuffers" << energyDerivs->getParameterSuffix(i, "[index]") <<
                        " = (1.0f/0xFFFFFFFF)*derivBuffersIn[index+PADDED_NUM_ATOMS*" << intToString(i) << "];\n";
        }
        else {
            for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++)
                reduce << "REDUCE_VALUE(derivBuffers" << intToString(i+1) << ", " << energyDerivs->getBuffers()[i].getType() << ")\n";
        }
        
        // Compute the various expressions.
        
        map<string, string> variables;
        variables["x"] = "pos.x";
        variables["y"] = "pos.y";
        variables["z"] = "pos.z";
        for (int i = 0; i < force.getNumPerParticleParameters(); i++)
            variables[force.getPerParticleParameterName(i)] = "params"+params->getParameterSuffix(i, "[index]");
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables[force.getGlobalParameterName(i)] = "globals["+intToString(i)+"]";
        for (int i = 0; i < force.getNumComputedValues(); i++)
            variables[computedValueNames[i]] = "values"+computedValues->getParameterSuffix(i, "[index]");
        map<string, Lepton::ParsedExpression> expressions;
        for (int i = 0; i < force.getNumEnergyTerms(); i++) {
            string expression;
            CustomGBForce::ComputationType type;
            force.getEnergyTermParameters(i, expression, type);
            if (type != CustomGBForce::SingleParticle)
                continue;
            Lepton::ParsedExpression parsed = Lepton::Parser::parse(expression, functions).optimize();
            expressions["/*"+intToString(i+1)+"*/ energy += "] = parsed;
            for (int j = 0; j < force.getNumComputedValues(); j++)
                expressions["/*"+intToString(i+1)+"*/ deriv"+energyDerivs->getParameterSuffix(j)+" += "] = energyDerivExpressions[i][j];
            Lepton::ParsedExpression gradx = parsed.differentiate("x").optimize();
            Lepton::ParsedExpression grady = parsed.differentiate("y").optimize();
            Lepton::ParsedExpression gradz = parsed.differentiate("z").optimize();
            if (!isZeroExpression(gradx))
                expressions["/*"+intToString(i+1)+"*/ force.x -= "] = gradx;
            if (!isZeroExpression(grady))
                expressions["/*"+intToString(i+1)+"*/ force.y -= "] = grady;
            if (!isZeroExpression(gradz))
                expressions["/*"+intToString(i+1)+"*/ force.z -= "] = gradz;
        }
        for (int i = 1; i < force.getNumComputedValues(); i++)
            for (int j = 0; j < i; j++)
                expressions["float dV"+intToString(i)+"dV"+intToString(j)+" = "] = valueDerivExpressions[i][j];
        compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functionDefinitions, "temp", prefix+"functionParams");
        
        // Record values.
        
        compute << "forceBuffers[index] = forceBuffers[index]+force;\n";
        for (int i = 1; i < force.getNumComputedValues(); i++) {
            compute << "float totalDeriv"<<i<<" = dV"<<i<<"dV0";
            for (int j = 1; j < i; j++)
                compute << " + totalDeriv"<<j<<"*dV"<<i<<"dV"<<j;
            compute << ";\n";
            compute << "deriv"<<(i+1)<<" *= totalDeriv"<<i<<";\n";
        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            string index = intToString(i+1);
            compute << "derivBuffers" << index << "[index] = deriv" << index << ";\n";
        }
        map<string, string> replacements;
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
        replacements["REDUCE_DERIVATIVES"] = reduce.str();
        replacements["COMPUTE_ENERGY"] = compute.str();
        map<string, string> defines;
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
        cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customGBEnergyPerParticle, replacements), defines);
        perParticleEnergyKernel = cl::Kernel(program, "computePerParticleEnergy");
    }
    if (needParameterGradient) {
        // Create the kernel to compute chain rule terms for computed values that depend explicitly on particle coordinates.

        stringstream compute, extraArgs;
        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", __global const float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
            extraArgs << ", __global const " << buffer.getType() << "* restrict " << paramName;
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+intToString(i+1);
            extraArgs << ", __global const " << buffer.getType() << "* restrict " << valueName;
        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            string index = intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* restrict derivBuffers" << index;
            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
        map<string, string> variables;
        variables["x"] = "pos.x";
        variables["y"] = "pos.y";
        variables["z"] = "pos.z";
        for (int i = 0; i < force.getNumPerParticleParameters(); i++)
            variables[force.getPerParticleParameterName(i)] = "params"+params->getParameterSuffix(i, "[index]");
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables[force.getGlobalParameterName(i)] = "globals["+intToString(i)+"]";
        for (int i = 0; i < force.getNumComputedValues(); i++)
            variables[computedValueNames[i]] = "values"+computedValues->getParameterSuffix(i, "[index]");
        for (int i = 1; i < force.getNumComputedValues(); i++) {
            string is = intToString(i);
            compute << "float4 dV"<<is<<"dR = (float4) 0;\n";
            for (int j = 1; j < i; j++) {
                if (!isZeroExpression(valueDerivExpressions[i][j])) {
                    map<string, Lepton::ParsedExpression> derivExpressions;
                    string js = intToString(j);
                    derivExpressions["float dV"+is+"dV"+js+" = "] = valueDerivExpressions[i][j];
                    compute << OpenCLExpressionUtilities::createExpressions(derivExpressions, variables, functionDefinitions, "temp_"+is+"_"+js, prefix+"functionParams");
                    compute << "dV"<<is<<"dR += dV"<<is<<"dV"<<js<<"*dV"<<js<<"dR;\n";
                }
            }
            map<string, Lepton::ParsedExpression> gradientExpressions;
            if (!isZeroExpression(valueGradientExpressions[i][0]))
                gradientExpressions["dV"+is+"dR.x += "] = valueGradientExpressions[i][0];
            if (!isZeroExpression(valueGradientExpressions[i][1]))
                gradientExpressions["dV"+is+"dR.y += "] = valueGradientExpressions[i][1];
            if (!isZeroExpression(valueGradientExpressions[i][2]))
                gradientExpressions["dV"+is+"dR.z += "] = valueGradientExpressions[i][2];
            compute << OpenCLExpressionUtilities::createExpressions(gradientExpressions, variables, functionDefinitions, "temp", prefix+"functionParams");
        }
        for (int i = 1; i < force.getNumComputedValues(); i++) {
            string is = intToString(i);
            compute << "force -= deriv"<<energyDerivs->getParameterSuffix(i)<<"*dV"<<is<<"dR;\n";
        }
        map<string, string> replacements;
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
        replacements["COMPUTE_FORCES"] = compute.str();
        map<string, string> defines;
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customGBGradientChainRule, replacements), defines);
        gradientChainRuleKernel = cl::Kernel(program, "computeGradientChainRuleTerms");
    }
    {
        // Create the code to calculate chain rules terms as part of the default nonbonded kernel.

        vector<pair<ExpressionTreeNode, string> > globalVariables;
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+intToString(i)+"]";
            globalVariables.push_back(makeVariable(name, prefix+value));
        }
        vector<pair<ExpressionTreeNode, string> > variables = globalVariables;
        map<string, string> rename;
        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
            variables.push_back(makeVariable(name+"1", prefix+"params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", prefix+"params"+params->getParameterSuffix(i, "2")));
            rename[name+"1"] = name+"2";
            rename[name+"2"] = name+"1";
        }
        map<string, Lepton::ParsedExpression> derivExpressions;
        stringstream chainSource;
        Lepton::ParsedExpression dVdR = Lepton::Parser::parse(computedValueExpressions[0], functions).differentiate("r").optimize();
        derivExpressions["float dV0dR1 = "] = dVdR;
        derivExpressions["float dV0dR2 = "] = dVdR.renameVariables(rename);
        chainSource << OpenCLExpressionUtilities::createExpressions(derivExpressions, variables, functionDefinitions, prefix+"temp0_", prefix+"functionParams");
        if (needChainForValue[0]) {
            if (useExclusionsForValue)
                chainSource << "if (!isExcluded) {\n";
            chainSource << "tempForce -= dV0dR1*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(0, "1") << ";\n";
            chainSource << "tempForce -= dV0dR2*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(0, "2") << ";\n";
            if (useExclusionsForValue)
                chainSource << "}\n";
        }
        for (int i = 1; i < force.getNumComputedValues(); i++) {
            if (needChainForValue[i]) {
                chainSource << "tempForce -= dV0dR1*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(i, "1") << ";\n";
                chainSource << "tempForce -= dV0dR2*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(i, "2") << ";\n";
            }
        }
        map<string, string> replacements;
        string chainStr = chainSource.str();
        replacements["COMPUTE_FORCE"] = chainStr;
        string source = cl.replaceStrings(OpenCLKernelSources::customGBChainRule, replacements);
        vector<OpenCLNonbondedUtilities::ParameterInfo> parameters;
        vector<OpenCLNonbondedUtilities::ParameterInfo> arguments;
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = prefix+"params"+intToString(i+1);
            if (chainStr.find(paramName+"1") != chainStr.npos || chainStr.find(paramName+"2") != chainStr.npos)
                parameters.push_back(OpenCLNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string paramName = prefix+"values"+intToString(i+1);
            if (chainStr.find(paramName+"1") != chainStr.npos || chainStr.find(paramName+"2") != chainStr.npos)
                parameters.push_back(OpenCLNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            if (needChainForValue[i]) { 
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
                string paramName = prefix+"dEdV"+intToString(i+1);
                parameters.push_back(OpenCLNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
            }
        }
        if (globals != NULL) {
            globals->upload(globalParamValues);
            arguments.push_back(OpenCLNonbondedUtilities::ParameterInfo(prefix+"globals", "float", 1, sizeof(cl_float), globals->getDeviceBuffer()));
        }
        cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, force.getNumExclusions() > 0, force.getCutoffDistance(), exclusionList, source, force.getForceGroup());
        for (int i = 0; i < (int) parameters.size(); i++)
            cl.getNonbondedUtilities().addParameter(parameters[i]);
        for (int i = 0; i < (int) arguments.size(); i++)
            cl.getNonbondedUtilities().addArgument(arguments[i]);
    }
    cl.addForce(new OpenCLCustomGBForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force));
    if (useLong)
        cl.addAutoclearBuffer(longEnergyDerivs->getDeviceBuffer(), 2*longEnergyDerivs->getSize());
    else {
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            cl.addAutoclearBuffer(buffer.getMemory(), buffer.getSize()*energyDerivs->getNumObjects()/sizeof(cl_float));
        }
    }
}

double OpenCLCalcCustomGBForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
    OpenCLNonbondedUtilities& nb = cl.getNonbondedUtilities();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        maxTiles = (nb.getUseCutoff() ? nb.getInteractingTiles().getSize() : 0);
        bool useLong = (cl.getSupports64BitGlobalAtomics() && !deviceIsCpu);
        if (useLong) {
            longValueBuffers = new OpenCLArray<cl_long>(cl, cl.getPaddedNumAtoms(), "customGBLongValueBuffers");
            cl.addAutoclearBuffer(longValueBuffers->getDeviceBuffer(), 2*longValueBuffers->getSize());
            cl.clearBuffer(longValueBuffers->getDeviceBuffer(), 2*longValueBuffers->getSize());
        }
        else {
            valueBuffers = new OpenCLArray<cl_float>(cl, cl.getPaddedNumAtoms()*nb.getNumForceBuffers(), "customGBValueBuffers");
            cl.addAutoclearBuffer(valueBuffers->getDeviceBuffer(), valueBuffers->getSize());
            cl.clearBuffer(*valueBuffers);
        }
        int index = 0;
        pairValueKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float4), NULL);
        pairValueKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusions().getDeviceBuffer());
        pairValueKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionIndices().getDeviceBuffer());
        pairValueKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionRowIndices().getDeviceBuffer());
        pairValueKernel.setArg<cl::Buffer>(index++, useLong ? longValueBuffers->getDeviceBuffer() : valueBuffers->getDeviceBuffer());
        pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float), NULL);
        /// \todo Eliminate this argument and make local to the kernel. For *_default.cl kernel can actually make it TileSize rather than getForceThreadBlockSize as only half the workgroup stores to it as was done with nonbonded_default.cl.
        /// \todo Also make the previous __local argument local as was done with nonbonded_default.cl.
        pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float), NULL);
        if (nb.getUseCutoff()) {
            pairValueKernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            pairValueKernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
            index += 2; // Periodic box size arguments are set when the kernel is executed.
            pairValueKernel.setArg<cl_uint>(index++, maxTiles);
            if (cl.getSIMDWidth() == 32 || deviceIsCpu)
                pairValueKernel.setArg<cl::Buffer>(index++, nb.getInteractionFlags().getDeviceBuffer());
        }
        else
            pairValueKernel.setArg<cl_uint>(index++, cl.getNumAtomBlocks()*(cl.getNumAtomBlocks()+1)/2);
        if (globals != NULL)
            pairValueKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            if (pairValueUsesParam[i]) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
                pairValueKernel.setArg<cl::Memory>(index++, buffer.getMemory());
                pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
            }
        }
        if (tabulatedFunctionParams != NULL) {
            for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
                pairValueKernel.setArg<cl::Buffer>(index++, tabulatedFunctions[i]->getDeviceBuffer());
            pairValueKernel.setArg<cl::Buffer>(index++, tabulatedFunctionParams->getDeviceBuffer());
        }
        index = 0;
        perParticleValueKernel.setArg<cl_int>(index++, cl.getPaddedNumAtoms());
        perParticleValueKernel.setArg<cl_int>(index++, nb.getNumForceBuffers());
        perParticleValueKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        perParticleValueKernel.setArg<cl::Buffer>(index++, useLong ? longValueBuffers->getDeviceBuffer() : valueBuffers->getDeviceBuffer());
        if (globals != NULL)
            perParticleValueKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++)
            perParticleValueKernel.setArg<cl::Memory>(index++, params->getBuffers()[i].getMemory());
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++)
            perParticleValueKernel.setArg<cl::Memory>(index++, computedValues->getBuffers()[i].getMemory());
        if (tabulatedFunctionParams != NULL) {
            for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
                perParticleValueKernel.setArg<cl::Buffer>(index++, tabulatedFunctions[i]->getDeviceBuffer());
            perParticleValueKernel.setArg<cl::Buffer>(index++, tabulatedFunctionParams->getDeviceBuffer());
        }
        index = 0;
        pairEnergyKernel.setArg<cl::Buffer>(index++, useLong ? cl.getLongForceBuffer().getDeviceBuffer() : cl.getForceBuffers().getDeviceBuffer());
        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float4), NULL);
        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float4), NULL);
        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusions().getDeviceBuffer());
        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionIndices().getDeviceBuffer());
        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionRowIndices().getDeviceBuffer());
        /// \todo Eliminate this argument and make local to the kernel. For *_default.cl kernel can actually make it TileSize rather than getForceThreadBlockSize as only half the workgroup stores to it as was done with nonbonded_default.cl.
        /// \todo Also make the previous __local argument local as was done with nonbonded_default.cl.
        pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float4), NULL);
        if (nb.getUseCutoff()) {
            pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
            index += 2; // Periodic box size arguments are set when the kernel is executed.
            pairEnergyKernel.setArg<cl_uint>(index++, maxTiles);
            if (cl.getSIMDWidth() == 32 || deviceIsCpu)
                pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getInteractionFlags().getDeviceBuffer());
        }
        else
            pairEnergyKernel.setArg<cl_uint>(index++, cl.getNumAtomBlocks()*(cl.getNumAtomBlocks()+1)/2);
        if (globals != NULL)
            pairEnergyKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            if (pairEnergyUsesParam[i]) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
                pairEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
                pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
            }
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            if (pairEnergyUsesValue[i]) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
                pairEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
                pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
            }
        }
        if (useLong) {
            pairEnergyKernel.setArg<cl::Memory>(index++, longEnergyDerivs->getDeviceBuffer());
            for (int i = 0; i < numComputedValues; ++i)
                pairEnergyKernel.setArg(index++, nb.getForceThreadBlockSize()*sizeof(cl_float), NULL);
        }
        else {
            for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
                pairEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
                pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
            }
        }
        if (tabulatedFunctionParams != NULL) {
            for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
                pairEnergyKernel.setArg<cl::Buffer>(index++, tabulatedFunctions[i]->getDeviceBuffer());
            pairEnergyKernel.setArg<cl::Buffer>(index++, tabulatedFunctionParams->getDeviceBuffer());
        }
        index = 0;
        perParticleEnergyKernel.setArg<cl_int>(index++, cl.getPaddedNumAtoms());
        perParticleEnergyKernel.setArg<cl_int>(index++, nb.getNumForceBuffers());
        perParticleEnergyKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
        perParticleEnergyKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        perParticleEnergyKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        if (globals != NULL)
            perParticleEnergyKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++)
            perParticleEnergyKernel.setArg<cl::Memory>(index++, params->getBuffers()[i].getMemory());
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++)
            perParticleEnergyKernel.setArg<cl::Memory>(index++, computedValues->getBuffers()[i].getMemory());
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++)
            perParticleEnergyKernel.setArg<cl::Memory>(index++, energyDerivs->getBuffers()[i].getMemory());
        if (useLong)
            perParticleEnergyKernel.setArg<cl::Memory>(index++, longEnergyDerivs->getDeviceBuffer());
        if (tabulatedFunctionParams != NULL) {
            for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
                perParticleEnergyKernel.setArg<cl::Buffer>(index++, tabulatedFunctions[i]->getDeviceBuffer());
            perParticleEnergyKernel.setArg<cl::Buffer>(index++, tabulatedFunctionParams->getDeviceBuffer());
        }
        if (needParameterGradient) {
            index = 0;
            gradientChainRuleKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
            gradientChainRuleKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
            if (globals != NULL)
                gradientChainRuleKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
            for (int i = 0; i < (int) params->getBuffers().size(); i++)
                gradientChainRuleKernel.setArg<cl::Memory>(index++, params->getBuffers()[i].getMemory());
            for (int i = 0; i < (int) computedValues->getBuffers().size(); i++)
                gradientChainRuleKernel.setArg<cl::Memory>(index++, computedValues->getBuffers()[i].getMemory());
            for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++)
                gradientChainRuleKernel.setArg<cl::Memory>(index++, energyDerivs->getBuffers()[i].getMemory());
        }
    }
    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    if (nb.getUseCutoff()) {
        pairValueKernel.setArg<mm_float4>(10, cl.getPeriodicBoxSize());
        pairValueKernel.setArg<mm_float4>(11, cl.getInvPeriodicBoxSize());
        pairEnergyKernel.setArg<mm_float4>(11, cl.getPeriodicBoxSize());
        pairEnergyKernel.setArg<mm_float4>(12, cl.getInvPeriodicBoxSize());
        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
            pairValueKernel.setArg<cl::Buffer>(8, nb.getInteractingTiles().getDeviceBuffer());
            pairValueKernel.setArg<cl_uint>(12, maxTiles);
            pairEnergyKernel.setArg<cl::Buffer>(9, nb.getInteractingTiles().getDeviceBuffer());
            pairEnergyKernel.setArg<cl_uint>(13, maxTiles);
            if (cl.getSIMDWidth() == 32 || deviceIsCpu) {
                pairValueKernel.setArg<cl::Buffer>(13, nb.getInteractionFlags().getDeviceBuffer());
                pairEnergyKernel.setArg<cl::Buffer>(14, nb.getInteractionFlags().getDeviceBuffer());
            }
        }
    }
    cl.executeKernel(pairValueKernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
    cl.executeKernel(perParticleValueKernel, cl.getPaddedNumAtoms());
    cl.executeKernel(pairEnergyKernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
    cl.executeKernel(perParticleEnergyKernel, cl.getPaddedNumAtoms());
    if (needParameterGradient)
        cl.executeKernel(gradientChainRuleKernel, cl.getPaddedNumAtoms());
    return 0.0;
}

class OpenCLCustomExternalForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomExternalForceInfo(const CustomExternalForce& force, int numParticles) : OpenCLForceInfo(0), force(force), indices(numParticles, -1) {
        vector<double> params;
        for (int i = 0; i < force.getNumParticles(); i++) {
            int particle;
            force.getParticleParameters(i, particle, params);
            indices[particle] = i;
        }
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        particle1 = indices[particle1];
        particle2 = indices[particle2];
        if (particle1 == -1 && particle2 == -1)
            return true;
        if (particle1 == -1 || particle2 == -1)
            return false;
        int temp;
        vector<double> params1;
        vector<double> params2;
        force.getParticleParameters(particle1, temp, params1);
        force.getParticleParameters(particle2, temp, params2);
        for (int i = 0; i < (int) params1.size(); i++)
            if (params1[i] != params2[i])
                return false;
        return true;
    }
private:
    const CustomExternalForce& force;
    vector<int> indices;
};

OpenCLCalcCustomExternalForceKernel::~OpenCLCalcCustomExternalForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
}

void OpenCLCalcCustomExternalForceKernel::initialize(const System& system, const CustomExternalForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumParticles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumParticles()/numContexts;
    numParticles = endIndex-startIndex;
    if (numParticles == 0)
        return;
    vector<vector<int> > atoms(numParticles, vector<int>(1));
    params = new OpenCLParameterSet(cl, force.getNumPerParticleParameters(), numParticles, "customExternalParams");
    vector<vector<cl_float> > paramVector(numParticles);
    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
        force.getParticleParameters(startIndex+i, atoms[i][0], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    cl.addForce(new OpenCLCustomExternalForceInfo(force, system.getNumParticles()));

    // Record information for the expressions.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction()).optimize();
    Lepton::ParsedExpression forceExpressionX = energyExpression.differentiate("x").optimize();
    Lepton::ParsedExpression forceExpressionY = energyExpression.differentiate("y").optimize();
    Lepton::ParsedExpression forceExpressionZ = energyExpression.differentiate("z").optimize();
    map<string, Lepton::ParsedExpression> expressions;
    expressions["energy += "] = energyExpression;
    expressions["float dEdX = "] = forceExpressionX;
    expressions["float dEdY = "] = forceExpressionY;
    expressions["float dEdZ = "] = forceExpressionZ;

    // Create the kernels.

    map<string, string> variables;
    variables["x"] = "pos1.x";
    variables["y"] = "pos1.y";
    variables["z"] = "pos1.z";
    for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
        const string& name = force.getPerParticleParameterName(i);
        variables[name] = "particleParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customExternalGlobals", false, CL_MEM_READ_ONLY);
        globals->upload(globalParamValues);
        string argName = cl.getBondedUtilities().addArgument(globals->getDeviceBuffer(), "float");
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+intToString(i)+"]";
            variables[name] = value;
        }
    }
    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" particleParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::customExternalForce, replacements), force.getForceGroup());
}

double OpenCLCalcCustomExternalForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    return 0.0;
}

class OpenCLCustomHbondForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomHbondForceInfo(int requiredBuffers, const CustomHbondForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        return true;
    }
    int getNumParticleGroups() {
        return force.getNumDonors()+force.getNumAcceptors()+force.getNumExclusions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int p1, p2, p3;
        vector<double> parameters;
        if (index < force.getNumDonors()) {
            force.getDonorParameters(index, p1, p2, p3, parameters);
            particles.clear();
            particles.push_back(p1);
            if (p2 > -1)
                particles.push_back(p2);
            if (p3 > -1)
                particles.push_back(p3);
            return;
        }
        index -= force.getNumDonors();
        if (index < force.getNumAcceptors()) {
            force.getAcceptorParameters(index, p1, p2, p3, parameters);
            particles.clear();
            particles.push_back(p1);
            if (p2 > -1)
                particles.push_back(p2);
            if (p3 > -1)
                particles.push_back(p3);
            return;
        }
        index -= force.getNumAcceptors();
        int donor, acceptor;
        force.getExclusionParticles(index, donor, acceptor);
        particles.clear();
        force.getDonorParameters(donor, p1, p2, p3, parameters);
        particles.push_back(p1);
        if (p2 > -1)
            particles.push_back(p2);
        if (p3 > -1)
            particles.push_back(p3);
        force.getAcceptorParameters(acceptor, p1, p2, p3, parameters);
        particles.push_back(p1);
        if (p2 > -1)
            particles.push_back(p2);
        if (p3 > -1)
            particles.push_back(p3);
    }
    bool areGroupsIdentical(int group1, int group2) {
        int p1, p2, p3;
        vector<double> params1, params2;
        if (group1 < force.getNumDonors() && group2 < force.getNumDonors()) {
            force.getDonorParameters(group1, p1, p2, p3, params1);
            force.getDonorParameters(group2, p1, p2, p3, params2);
            return (params1 == params2 && params1 == params2);
        }
        if (group1 < force.getNumDonors() || group2 < force.getNumDonors())
            return false;
        group1 -= force.getNumDonors();
        group2 -= force.getNumDonors();
        if (group1 < force.getNumAcceptors() && group2 < force.getNumAcceptors()) {
            force.getAcceptorParameters(group1, p1, p2, p3, params1);
            force.getAcceptorParameters(group2, p1, p2, p3, params2);
            return (params1 == params2 && params1 == params2);
        }
        if (group1 < force.getNumAcceptors() || group2 < force.getNumAcceptors())
            return false;
        return true;
    }
private:
    const CustomHbondForce& force;
};

OpenCLCalcCustomHbondForceKernel::~OpenCLCalcCustomHbondForceKernel() {
    if (donorParams != NULL)
        delete donorParams;
    if (acceptorParams != NULL)
        delete acceptorParams;
    if (donors != NULL)
        delete donors;
    if (acceptors != NULL)
        delete acceptors;
    if (donorBufferIndices != NULL)
        delete donorBufferIndices;
    if (acceptorBufferIndices != NULL)
        delete acceptorBufferIndices;
    if (globals != NULL)
        delete globals;
    if (donorExclusions != NULL)
        delete donorExclusions;
    if (acceptorExclusions != NULL)
        delete acceptorExclusions;
    if (tabulatedFunctionParams != NULL)
        delete tabulatedFunctionParams;
    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        delete tabulatedFunctions[i];
}

static void addDonorAndAcceptorCode(stringstream& computeDonor, stringstream& computeAcceptor, const string& value) {
    computeDonor << value;
    computeAcceptor << value;
}

static void applyDonorAndAcceptorForces(stringstream& applyToDonor, stringstream& applyToAcceptor, int atom, const string& value) {
    string forceNames[] = {"f1", "f2", "f3"};
    if (atom < 3)
        applyToAcceptor << forceNames[atom]<<".xyz += "<<value<<";\n";
    else
        applyToDonor << forceNames[atom-3]<<".xyz += "<<value<<";\n";
}

void OpenCLCalcCustomHbondForceKernel::initialize(const System& system, const CustomHbondForce& force) {
    // Record the lists of donors and acceptors, and the parameters for each one.

    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumDonors()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumDonors()/numContexts;
    numDonors = endIndex-startIndex;
    numAcceptors = force.getNumAcceptors();
    if (numDonors == 0 || numAcceptors == 0)
        return;
    int numParticles = system.getNumParticles();
    donors = new OpenCLArray<mm_int4>(cl, numDonors, "customHbondDonors");
    acceptors = new OpenCLArray<mm_int4>(cl, numAcceptors, "customHbondAcceptors");
    donorParams = new OpenCLParameterSet(cl, force.getNumPerDonorParameters(), numDonors, "customHbondDonorParameters");
    acceptorParams = new OpenCLParameterSet(cl, force.getNumPerAcceptorParameters(), numAcceptors, "customHbondAcceptorParameters");
    if (force.getNumGlobalParameters() > 0)
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customHbondGlobals", false, CL_MEM_READ_ONLY);
    vector<vector<cl_float> > donorParamVector(numDonors);
    vector<mm_int4> donorVector(numDonors);
    for (int i = 0; i < numDonors; i++) {
        vector<double> parameters;
        force.getDonorParameters(startIndex+i, donorVector[i].x, donorVector[i].y, donorVector[i].z, parameters);
        donorParamVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            donorParamVector[i][j] = (cl_float) parameters[j];
    }
    donors->upload(donorVector);
    donorParams->setParameterValues(donorParamVector);
    vector<vector<cl_float> > acceptorParamVector(numAcceptors);
    vector<mm_int4> acceptorVector(numAcceptors);
    for (int i = 0; i < numAcceptors; i++) {
        vector<double> parameters;
        force.getAcceptorParameters(i, acceptorVector[i].x, acceptorVector[i].y, acceptorVector[i].z, parameters);
        acceptorParamVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            acceptorParamVector[i][j] = (cl_float) parameters[j];
    }
    acceptors->upload(acceptorVector);
    acceptorParams->setParameterValues(acceptorParamVector);

    // Select an output buffer index for each donor and acceptor.

    donorBufferIndices = new OpenCLArray<mm_int4>(cl, numDonors, "customHbondDonorBuffers");
    acceptorBufferIndices = new OpenCLArray<mm_int4>(cl, numAcceptors, "customHbondAcceptorBuffers");
    vector<mm_int4> donorBufferVector(numDonors);
    vector<mm_int4> acceptorBufferVector(numAcceptors);
    vector<int> donorBufferCounter(numParticles, 0);
    for (int i = 0; i < numDonors; i++)
        donorBufferVector[i] = mm_int4(donorVector[i].x > -1 ? donorBufferCounter[donorVector[i].x]++ : 0,
                                       donorVector[i].y > -1 ? donorBufferCounter[donorVector[i].y]++ : 0,
                                       donorVector[i].z > -1 ? donorBufferCounter[donorVector[i].z]++ : 0, 0);
    vector<int> acceptorBufferCounter(numParticles, 0);
    for (int i = 0; i < numAcceptors; i++)
        acceptorBufferVector[i] = mm_int4(acceptorVector[i].x > -1 ? acceptorBufferCounter[acceptorVector[i].x]++ : 0,
                                       acceptorVector[i].y > -1 ? acceptorBufferCounter[acceptorVector[i].y]++ : 0,
                                       acceptorVector[i].z > -1 ? acceptorBufferCounter[acceptorVector[i].z]++ : 0, 0);
    donorBufferIndices->upload(donorBufferVector);
    acceptorBufferIndices->upload(acceptorBufferVector);
    int maxBuffers = 1;
    for (int i = 0; i < (int) donorBufferCounter.size(); i++)
        maxBuffers = max(maxBuffers, donorBufferCounter[i]);
    for (int i = 0; i < (int) acceptorBufferCounter.size(); i++)
        maxBuffers = max(maxBuffers, acceptorBufferCounter[i]);
    cl.addForce(new OpenCLCustomHbondForceInfo(maxBuffers, force));

    // Record exclusions.

    vector<mm_int4> donorExclusionVector(numDonors, mm_int4(-1, -1, -1, -1));
    vector<mm_int4> acceptorExclusionVector(numAcceptors, mm_int4(-1, -1, -1, -1));
    for (int i = 0; i < force.getNumExclusions(); i++) {
        int donor, acceptor;
        force.getExclusionParticles(i, donor, acceptor);
        if (donor < startIndex || donor >= endIndex)
            continue;
        donor -= startIndex;
        if (donorExclusionVector[donor].x == -1)
            donorExclusionVector[donor].x = acceptor;
        else if (donorExclusionVector[donor].y == -1)
            donorExclusionVector[donor].y = acceptor;
        else if (donorExclusionVector[donor].z == -1)
            donorExclusionVector[donor].z = acceptor;
        else if (donorExclusionVector[donor].w == -1)
            donorExclusionVector[donor].w = acceptor;
        else
            throw OpenMMException("CustomHbondForce: OpenCLPlatform does not support more than four exclusions per donor");
        if (acceptorExclusionVector[acceptor].x == -1)
            acceptorExclusionVector[acceptor].x = donor;
        else if (acceptorExclusionVector[acceptor].y == -1)
            acceptorExclusionVector[acceptor].y = donor;
        else if (acceptorExclusionVector[acceptor].z == -1)
            acceptorExclusionVector[acceptor].z = donor;
        else if (acceptorExclusionVector[acceptor].w == -1)
            acceptorExclusionVector[acceptor].w = donor;
        else
            throw OpenMMException("CustomHbondForce: OpenCLPlatform does not support more than four exclusions per acceptor");
    }
    donorExclusions = new OpenCLArray<mm_int4>(cl, numDonors, "customHbondDonorExclusions");
    acceptorExclusions = new OpenCLArray<mm_int4>(cl, numDonors, "customHbondAcceptorExclusions");
    donorExclusions->upload(donorExclusionVector);
    acceptorExclusions->upload(acceptorExclusionVector);

    // Record the tabulated functions.

    OpenCLExpressionUtilities::FunctionPlaceholder fp;
    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
    vector<mm_float4> tabulatedFunctionParamsVec(force.getNumFunctions());
    stringstream tableArgs;
    for (int i = 0; i < force.getNumFunctions(); i++) {
        string name;
        vector<double> values;
        double min, max;
        force.getFunctionParameters(i, name, values, min, max);
        string arrayName = "table"+intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = &fp;
        tabulatedFunctionParamsVec[i] = mm_float4((float) min, (float) max, (float) ((values.size()-1)/(max-min)), (float) values.size()-2);
        vector<mm_float4> f = OpenCLExpressionUtilities::computeFunctionCoefficients(values, min, max);
        tabulatedFunctions.push_back(new OpenCLArray<mm_float4>(cl, values.size()-1, "TabulatedFunction"));
        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
        tableArgs << ", __global const float4* restrict " << arrayName;
    }
    if (force.getNumFunctions() > 0) {
        tabulatedFunctionParams = new OpenCLArray<mm_float4>(cl, tabulatedFunctionParamsVec.size(), "tabulatedFunctionParameters", false, CL_MEM_READ_ONLY);
        tabulatedFunctionParams->upload(tabulatedFunctionParamsVec);
        tableArgs << ", __global const float4* restrict functionParams";
    }

    // Record information about parameters.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    if (globals != NULL)
        globals->upload(globalParamValues);
    map<string, string> variables;
    for (int i = 0; i < force.getNumPerDonorParameters(); i++) {
        const string& name = force.getPerDonorParameterName(i);
        variables[name] = "donorParams"+donorParams->getParameterSuffix(i);
    }
    for (int i = 0; i < force.getNumPerAcceptorParameters(); i++) {
        const string& name = force.getPerAcceptorParameterName(i);
        variables[name] = "acceptorParams"+acceptorParams->getParameterSuffix(i);
    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
        variables[name] = "globals["+intToString(i)+"]";
    }

    // Now to generate the kernel.  First, it needs to calculate all distances, angles,
    // and dihedrals the expression depends on.

    map<string, vector<int> > distances;
    map<string, vector<int> > angles;
    map<string, vector<int> > dihedrals;
    Lepton::ParsedExpression energyExpression = CustomHbondForceImpl::prepareExpression(force, functions, distances, angles, dihedrals);
    map<string, Lepton::ParsedExpression> forceExpressions;
    set<string> computedDeltas;
    computedDeltas.insert("D1A1");
    string atomNames[] = {"A1", "A2", "A3", "D1", "D2", "D3"};
    string atomNamesLower[] = {"a1", "a2", "a3", "d1", "d2", "d3"};
    stringstream computeDonor, computeAcceptor, extraArgs;
    int index = 0;
    for (map<string, vector<int> >::const_iterator iter = distances.begin(); iter != distances.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
        if (computedDeltas.count(deltaName) == 0) {
            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 delta"+deltaName+" = delta("+atomNamesLower[atoms[0]]+", "+atomNamesLower[atoms[1]]+");\n");
            computedDeltas.insert(deltaName);
        }
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float r_"+deltaName+" = sqrt(delta"+deltaName+".w);\n");
        variables[iter->first] = "r_"+deltaName;
        forceExpressions["float dEdDistance"+intToString(index)+" = "] = energyExpression.differentiate(iter->first).optimize();
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = angles.begin(); iter != angles.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName1 = atomNames[atoms[1]]+atomNames[atoms[0]];
        string deltaName2 = atomNames[atoms[1]]+atomNames[atoms[2]];
        string angleName = "angle_"+atomNames[atoms[0]]+atomNames[atoms[1]]+atomNames[atoms[2]];
        if (computedDeltas.count(deltaName1) == 0) {
            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 delta"+deltaName1+" = delta("+atomNamesLower[atoms[1]]+", "+atomNamesLower[atoms[0]]+");\n");
            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 delta"+deltaName2+" = delta("+atomNamesLower[atoms[1]]+", "+atomNamesLower[atoms[2]]+");\n");
            computedDeltas.insert(deltaName2);
        }
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float "+angleName+" = computeAngle(delta"+deltaName1+", delta"+deltaName2+");\n");
        variables[iter->first] = angleName;
        forceExpressions["float dEdAngle"+intToString(index)+" = "] = energyExpression.differentiate(iter->first).optimize();
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = dihedrals.begin(); iter != dihedrals.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName1 = atomNames[atoms[0]]+atomNames[atoms[1]];
        string deltaName2 = atomNames[atoms[2]]+atomNames[atoms[1]];
        string deltaName3 = atomNames[atoms[2]]+atomNames[atoms[3]];
        string crossName1 = "cross_"+deltaName1+"_"+deltaName2;
        string crossName2 = "cross_"+deltaName2+"_"+deltaName3;
        string dihedralName = "dihedral_"+atomNames[atoms[0]]+atomNames[atoms[1]]+atomNames[atoms[2]]+atomNames[atoms[3]];
        if (computedDeltas.count(deltaName1) == 0) {
            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 delta"+deltaName1+" = delta("+atomNamesLower[atoms[0]]+", "+atomNamesLower[atoms[1]]+");\n");
            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 delta"+deltaName2+" = delta("+atomNamesLower[atoms[2]]+", "+atomNamesLower[atoms[1]]+");\n");
            computedDeltas.insert(deltaName2);
        }
        if (computedDeltas.count(deltaName3) == 0) {
            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 delta"+deltaName3+" = delta("+atomNamesLower[atoms[2]]+", "+atomNamesLower[atoms[3]]+");\n");
            computedDeltas.insert(deltaName3);
        }
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 "+crossName1+" = computeCross(delta"+deltaName1+", delta"+deltaName2+");\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 "+crossName2+" = computeCross(delta"+deltaName2+", delta"+deltaName3+");\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float "+dihedralName+" = computeAngle("+crossName1+", "+crossName2+");\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, dihedralName+" *= (delta"+deltaName1+".x*"+crossName2+".x + delta"+deltaName1+".y*"+crossName2+".y + delta"+deltaName1+".z*"+crossName2+".z < 0 ? -1 : 1);\n");
        variables[iter->first] = dihedralName;
        forceExpressions["float dEdDihedral"+intToString(index)+" = "] = energyExpression.differentiate(iter->first).optimize();
    }

    // Next it needs to load parameters from global memory.

    if (force.getNumGlobalParameters() > 0)
        extraArgs << ", __global const float* restrict globals";
    for (int i = 0; i < (int) donorParams->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = donorParams->getBuffers()[i];
        extraArgs << ", __global const "+buffer.getType()+"* restrict donor"+buffer.getName();
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, buffer.getType()+" donorParams"+intToString(i+1)+" = donor"+buffer.getName()+"[index];\n");
    }
    for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
        extraArgs << ", __global const "+buffer.getType()+"* restrict acceptor"+buffer.getName();
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, buffer.getType()+" acceptorParams"+intToString(i+1)+" = acceptor"+buffer.getName()+"[index];\n");
    }

    // Now evaluate the expressions.

    computeAcceptor << OpenCLExpressionUtilities::createExpressions(forceExpressions, variables, functionDefinitions, "temp", "functionParams");
    forceExpressions["energy += "] = energyExpression;
    computeDonor << OpenCLExpressionUtilities::createExpressions(forceExpressions, variables, functionDefinitions, "temp", "functionParams");

    // Finally, apply forces to atoms.

    index = 0;
    for (map<string, vector<int> >::const_iterator iter = distances.begin(); iter != distances.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
        string value = "(dEdDistance"+intToString(index)+"/r_"+deltaName+")*delta"+deltaName+".xyz";
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[0], "-"+value);
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[1], value);
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = angles.begin(); iter != angles.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName1 = atomNames[atoms[1]]+atomNames[atoms[0]];
        string deltaName2 = atomNames[atoms[1]]+atomNames[atoms[2]];
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "{\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 crossProd = cross(delta"+deltaName2+", delta"+deltaName1+");\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float lengthCross = max(length(crossProd), 1e-6f);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 deltaCross0 = -cross(delta"+deltaName1+", crossProd)*dEdAngle"+intToString(index)+"/(delta"+deltaName1+".w*lengthCross);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 deltaCross2 = cross(delta"+deltaName2+", crossProd)*dEdAngle"+intToString(index)+"/(delta"+deltaName2+".w*lengthCross);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 deltaCross1 = -(deltaCross0+deltaCross2);\n");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[0], "deltaCross0.xyz");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[1], "deltaCross1.xyz");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[2], "deltaCross2.xyz");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "}\n");
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = dihedrals.begin(); iter != dihedrals.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName1 = atomNames[atoms[0]]+atomNames[atoms[1]];
        string deltaName2 = atomNames[atoms[2]]+atomNames[atoms[1]];
        string deltaName3 = atomNames[atoms[2]]+atomNames[atoms[3]];
        string crossName1 = "cross_"+deltaName1+"_"+deltaName2;
        string crossName2 = "cross_"+deltaName2+"_"+deltaName3;
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "{\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float r = sqrt(delta"+deltaName2+".w);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 ff;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.x = (-dEdDihedral"+intToString(index)+"*r)/"+crossName1+".w;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.y = (delta"+deltaName1+".x*delta"+deltaName2+".x + delta"+deltaName1+".y*delta"+deltaName2+".y + delta"+deltaName1+".z*delta"+deltaName2+".z)/delta"+deltaName2+".w;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.z = (delta"+deltaName3+".x*delta"+deltaName2+".x + delta"+deltaName3+".y*delta"+deltaName2+".y + delta"+deltaName3+".z*delta"+deltaName2+".z)/delta"+deltaName2+".w;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.w = (dEdDihedral"+intToString(index)+"*r)/"+crossName2+".w;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 internalF0 = ff.x*"+crossName1+";\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 internalF3 = ff.w*"+crossName2+";\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "float4 s = ff.y*internalF0 - ff.z*internalF3;\n");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[0], "internalF0.xyz");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[1], "s.xyz-internalF0.xyz");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[2], "-s.xyz-internalF3.xyz");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[3], "internalF3.xyz");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "}\n");
    }

    // Generate the kernels.

    map<string, string> replacements;
    replacements["COMPUTE_DONOR_FORCE"] = computeDonor.str();
    replacements["COMPUTE_ACCEPTOR_FORCE"] = computeAcceptor.str();
    replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
    map<string, string> defines;
    defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
    defines["NUM_DONORS"] = intToString(numDonors);
    defines["NUM_ACCEPTORS"] = intToString(numAcceptors);
    defines["M_PI"] = doubleToString(M_PI);
    if (force.getNonbondedMethod() != CustomHbondForce::NoCutoff) {
        defines["USE_CUTOFF"] = "1";
        defines["CUTOFF_SQUARED"] = doubleToString(force.getCutoffDistance()*force.getCutoffDistance());
    }
    if (force.getNonbondedMethod() != CustomHbondForce::NoCutoff && force.getNonbondedMethod() != CustomHbondForce::CutoffNonPeriodic)
        defines["USE_PERIODIC"] = "1";
    if (force.getNumExclusions() > 0)
        defines["USE_EXCLUSIONS"] = "1";
    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customHbondForce, replacements), defines);
    donorKernel = cl::Kernel(program, "computeDonorForces");
    acceptorKernel = cl::Kernel(program, "computeAcceptorForces");
}

double OpenCLCalcCustomHbondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (numDonors == 0 || numAcceptors == 0)
        return 0.0;
    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        int index = 0;
        donorKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, donorExclusions->getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, donors->getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, acceptors->getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, donorBufferIndices->getDeviceBuffer());
        donorKernel.setArg(index++, 3*OpenCLContext::ThreadBlockSize*sizeof(mm_float4), NULL);
        index += 2; // Periodic box size arguments are set when the kernel is executed.
        if (globals != NULL)
            donorKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) donorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = donorParams->getBuffers()[i];
            donorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
        }
        for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
            donorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
        }
        if (tabulatedFunctionParams != NULL) {
            for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
                donorKernel.setArg<cl::Buffer>(index++, tabulatedFunctions[i]->getDeviceBuffer());
            donorKernel.setArg<cl::Buffer>(index++, tabulatedFunctionParams->getDeviceBuffer());
        }
        index = 0;
        acceptorKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, acceptorExclusions->getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, donors->getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, acceptors->getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, acceptorBufferIndices->getDeviceBuffer());
        acceptorKernel.setArg(index++, 3*OpenCLContext::ThreadBlockSize*sizeof(mm_float4), NULL);
        index += 2; // Periodic box size arguments are set when the kernel is executed.
        if (globals != NULL)
            acceptorKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) donorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = donorParams->getBuffers()[i];
            acceptorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
        }
        for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
            acceptorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
        }
        if (tabulatedFunctionParams != NULL) {
            for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
                acceptorKernel.setArg<cl::Buffer>(index++, tabulatedFunctions[i]->getDeviceBuffer());
            acceptorKernel.setArg<cl::Buffer>(index++, tabulatedFunctionParams->getDeviceBuffer());
        }
    }
    donorKernel.setArg<mm_float4>(8, cl.getPeriodicBoxSize());
    donorKernel.setArg<mm_float4>(9, cl.getInvPeriodicBoxSize());
    cl.executeKernel(donorKernel, max(numDonors, numAcceptors));
    acceptorKernel.setArg<mm_float4>(8, cl.getPeriodicBoxSize());
    acceptorKernel.setArg<mm_float4>(9, cl.getInvPeriodicBoxSize());
    cl.executeKernel(acceptorKernel, max(numDonors, numAcceptors));
    return 0.0;
}

class OpenCLCustomCompoundBondForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomCompoundBondForceInfo(const CustomCompoundBondForce& force) : OpenCLForceInfo(0), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumBonds();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        vector<double> parameters;
        force.getBondParameters(index, particles, parameters);
    }
    bool areGroupsIdentical(int group1, int group2) {
        vector<int> particles;
        vector<double> parameters1, parameters2;
        force.getBondParameters(group1, particles, parameters1);
        force.getBondParameters(group2, particles, parameters2);
        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
        return true;
    }
private:
    const CustomCompoundBondForce& force;
};

OpenCLCalcCustomCompoundBondForceKernel::~OpenCLCalcCustomCompoundBondForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
    if (tabulatedFunctionParams != NULL)
        delete tabulatedFunctionParams;
    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        delete tabulatedFunctions[i];
}

void OpenCLCalcCustomCompoundBondForceKernel::initialize(const System& system, const CustomCompoundBondForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumBonds()/numContexts;
    numBonds = endIndex-startIndex;
    if (numBonds == 0)
        return;
    int particlesPerBond = force.getNumParticlesPerBond();
    vector<vector<int> > atoms(numBonds, vector<int>(particlesPerBond));
    params = new OpenCLParameterSet(cl, force.getNumPerBondParameters(), numBonds, "customCompoundBondParams");
    vector<vector<cl_float> > paramVector(numBonds);
    for (int i = 0; i < numBonds; i++) {
        vector<double> parameters;
        force.getBondParameters(startIndex+i, atoms[i], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    cl.addForce(new OpenCLCustomCompoundBondForceInfo(force));

    // Record the tabulated functions.

    OpenCLExpressionUtilities::FunctionPlaceholder fp;
    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
    vector<mm_float4> tabulatedFunctionParamsVec(force.getNumFunctions());
    stringstream tableArgs;
    for (int i = 0; i < force.getNumFunctions(); i++) {
        string name;
        vector<double> values;
        double min, max;
        force.getFunctionParameters(i, name, values, min, max);
        functions[name] = &fp;
        tabulatedFunctionParamsVec[i] = mm_float4((float) min, (float) max, (float) ((values.size()-1)/(max-min)), (float) values.size()-2);
        vector<mm_float4> f = OpenCLExpressionUtilities::computeFunctionCoefficients(values, min, max);
        OpenCLArray<mm_float4>* array = new OpenCLArray<mm_float4>(cl, values.size()-1, "TabulatedFunction");
        tabulatedFunctions.push_back(array);
        array->upload(f);
        string arrayName = cl.getBondedUtilities().addArgument(array->getDeviceBuffer(), "float4");
        functionDefinitions.push_back(make_pair(name, arrayName));
    }
    string functionParamsName;
    if (force.getNumFunctions() > 0) {
        tabulatedFunctionParams = new OpenCLArray<mm_float4>(cl, tabulatedFunctionParamsVec.size(), "tabulatedFunctionParameters", false, CL_MEM_READ_ONLY);
        tabulatedFunctionParams->upload(tabulatedFunctionParamsVec);
        functionParamsName = cl.getBondedUtilities().addArgument(tabulatedFunctionParams->getDeviceBuffer(), "float4");
    }
    
    // Record information about parameters.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    map<string, string> variables;
    for (int i = 0; i < particlesPerBond; i++) {
        string index = intToString(i+1);
        variables["x"+index] = "pos"+index+".x";
        variables["y"+index] = "pos"+index+".y";
        variables["z"+index] = "pos"+index+".z";
    }
    for (int i = 0; i < force.getNumPerBondParameters(); i++) {
        const string& name = force.getPerBondParameterName(i);
        variables[name] = "bondParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customCompoundBondGlobals", false, CL_MEM_READ_ONLY);
        globals->upload(globalParamValues);
        string argName = cl.getBondedUtilities().addArgument(globals->getDeviceBuffer(), "float");
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+intToString(i)+"]";
            variables[name] = value;
        }
    }

    // Now to generate the kernel.  First, it needs to calculate all distances, angles,
    // and dihedrals the expression depends on.

    map<string, vector<int> > distances;
    map<string, vector<int> > angles;
    map<string, vector<int> > dihedrals;
    Lepton::ParsedExpression energyExpression = CustomCompoundBondForceImpl::prepareExpression(force, functions, distances, angles, dihedrals);
    map<string, Lepton::ParsedExpression> forceExpressions;
    set<string> computedDeltas;
    vector<string> atomNames, posNames;
    for (int i = 0; i < particlesPerBond; i++) {
        string index = intToString(i+1);
        atomNames.push_back("P"+index);
        posNames.push_back("pos"+index);
    }
    stringstream compute;
    int index = 0;
    for (map<string, vector<int> >::const_iterator iter = distances.begin(); iter != distances.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
        if (computedDeltas.count(deltaName) == 0) {
            compute<<"float4 delta"<<deltaName<<" = ccb_delta("<<posNames[atoms[0]]<<", "<<posNames[atoms[1]]<<");\n";
            computedDeltas.insert(deltaName);
        }
        compute<<"float r_"<<deltaName<<" = sqrt(delta"<<deltaName<<".w);\n";
        variables[iter->first] = "r_"+deltaName;
        forceExpressions["float dEdDistance"+intToString(index)+" = "] = energyExpression.differentiate(iter->first).optimize();
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = angles.begin(); iter != angles.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName1 = atomNames[atoms[1]]+atomNames[atoms[0]];
        string deltaName2 = atomNames[atoms[1]]+atomNames[atoms[2]];
        string angleName = "angle_"+atomNames[atoms[0]]+atomNames[atoms[1]]+atomNames[atoms[2]];
        if (computedDeltas.count(deltaName1) == 0) {
            compute<<"float4 delta"<<deltaName1<<" = ccb_delta("<<posNames[atoms[1]]<<", "<<posNames[atoms[0]]<<");\n";
            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
            compute<<"float4 delta"<<deltaName2<<" = ccb_delta("<<posNames[atoms[1]]<<", "<<posNames[atoms[2]]<<");\n";
            computedDeltas.insert(deltaName2);
        }
        compute<<"float "<<angleName<<" = ccb_computeAngle(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
        variables[iter->first] = angleName;
        forceExpressions["float dEdAngle"+intToString(index)+" = "] = energyExpression.differentiate(iter->first).optimize();
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = dihedrals.begin(); iter != dihedrals.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName1 = atomNames[atoms[0]]+atomNames[atoms[1]];
        string deltaName2 = atomNames[atoms[2]]+atomNames[atoms[1]];
        string deltaName3 = atomNames[atoms[2]]+atomNames[atoms[3]];
        string crossName1 = "cross_"+deltaName1+"_"+deltaName2;
        string crossName2 = "cross_"+deltaName2+"_"+deltaName3;
        string dihedralName = "dihedral_"+atomNames[atoms[0]]+atomNames[atoms[1]]+atomNames[atoms[2]]+atomNames[atoms[3]];
        if (computedDeltas.count(deltaName1) == 0) {
            compute<<"float4 delta"<<deltaName1<<" = ccb_delta("<<posNames[atoms[0]]<<", "<<posNames[atoms[1]]<<");\n";
            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
            compute<<"float4 delta"<<deltaName2<<" = ccb_delta("<<posNames[atoms[2]]<<", "<<posNames[atoms[1]]<<");\n";
            computedDeltas.insert(deltaName2);
        }
        if (computedDeltas.count(deltaName3) == 0) {
            compute<<"float4 delta"<<deltaName3<<" = ccb_delta("<<posNames[atoms[2]]<<", "<<posNames[atoms[3]]<<");\n";
            computedDeltas.insert(deltaName3);
        }
        compute<<"float4 "<<crossName1<<" = ccb_computeCross(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
        compute<<"float4 "<<crossName2<<" = ccb_computeCross(delta"<<deltaName2<<", delta"<<deltaName3<<");\n";
        compute<<"float "<<dihedralName<<" = ccb_computeAngle("<<crossName1<<", "<<crossName2<<");\n";
        compute<<dihedralName<<" *= (delta"<<deltaName1<<".x*"<<crossName2<<".x + delta"<<deltaName1<<".y*"<<crossName2<<".y + delta"<<deltaName1<<".z*"<<crossName2<<".z < 0 ? -1 : 1);\n";
        variables[iter->first] = dihedralName;
        forceExpressions["float dEdDihedral"+intToString(index)+" = "] = energyExpression.differentiate(iter->first).optimize();
    }

    // Now evaluate the expressions.

    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
    forceExpressions["energy += "] = energyExpression;
    compute << OpenCLExpressionUtilities::createExpressions(forceExpressions, variables, functionDefinitions, "temp", functionParamsName);

    // Finally, apply forces to atoms.

    vector<string> forceNames;
    for (int i = 0; i < particlesPerBond; i++) {
        string istr = intToString(i+1);
        string forceName = "force"+istr;
        forceNames.push_back(forceName);
        compute<<"float4 "<<forceName<<" = (float4) (0.0f, 0.0f, 0.0f, 0.0f);\n";
        compute<<"{\n";
        Lepton::ParsedExpression forceExpressionX = energyExpression.differentiate("x"+istr).optimize();
        Lepton::ParsedExpression forceExpressionY = energyExpression.differentiate("y"+istr).optimize();
        Lepton::ParsedExpression forceExpressionZ = energyExpression.differentiate("z"+istr).optimize();
        map<string, Lepton::ParsedExpression> expressions;
        if (!isZeroExpression(forceExpressionX))
            expressions[forceName+".x -= "] = forceExpressionX;
        if (!isZeroExpression(forceExpressionY))
            expressions[forceName+".y -= "] = forceExpressionY;
        if (!isZeroExpression(forceExpressionZ))
            expressions[forceName+".z -= "] = forceExpressionZ;
        if (expressions.size() > 0)
            compute<<OpenCLExpressionUtilities::createExpressions(expressions, variables, functionDefinitions, "coordtemp", functionParamsName);
        compute<<"}\n";
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = distances.begin(); iter != distances.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
        string value = "(dEdDistance"+intToString(index)+"/r_"+deltaName+")*delta"+deltaName+".xyz";
        compute<<forceNames[atoms[0]]<<".xyz += "<<"-"<<value<<";\n";
        compute<<forceNames[atoms[1]]<<".xyz += "<<value<<";\n";
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = angles.begin(); iter != angles.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName1 = atomNames[atoms[1]]+atomNames[atoms[0]];
        string deltaName2 = atomNames[atoms[1]]+atomNames[atoms[2]];
        compute<<"{\n";
        compute<<"float4 crossProd = cross(delta"<<deltaName2<<", delta"<<deltaName1<<");\n";
        compute<<"float lengthCross = max(length(crossProd), 1e-6f);\n";
        compute<<"float4 deltaCross0 = -cross(delta"<<deltaName1<<", crossProd)*dEdAngle"<<intToString(index)<<"/(delta"<<deltaName1<<".w*lengthCross);\n";
        compute<<"float4 deltaCross2 = cross(delta"<<deltaName2<<", crossProd)*dEdAngle"<<intToString(index)<<"/(delta"<<deltaName2<<".w*lengthCross);\n";
        compute<<"float4 deltaCross1 = -(deltaCross0+deltaCross2);\n";
        compute<<forceNames[atoms[0]]<<".xyz += deltaCross0.xyz;\n";
        compute<<forceNames[atoms[1]]<<".xyz += deltaCross1.xyz;\n";
        compute<<forceNames[atoms[2]]<<".xyz += deltaCross2.xyz;\n";
        compute<<"}\n";
    }
    index = 0;
    for (map<string, vector<int> >::const_iterator iter = dihedrals.begin(); iter != dihedrals.end(); ++iter, ++index) {
        const vector<int>& atoms = iter->second;
        string deltaName1 = atomNames[atoms[0]]+atomNames[atoms[1]];
        string deltaName2 = atomNames[atoms[2]]+atomNames[atoms[1]];
        string deltaName3 = atomNames[atoms[2]]+atomNames[atoms[3]];
        string crossName1 = "cross_"+deltaName1+"_"+deltaName2;
        string crossName2 = "cross_"+deltaName2+"_"+deltaName3;
        compute<<"{\n";
        compute<<"float r = sqrt(delta"<<deltaName2<<".w);\n";
        compute<<"float4 ff;\n";
        compute<<"ff.x = (-dEdDihedral"<<intToString(index)<<"*r)/"<<crossName1<<".w;\n";
        compute<<"ff.y = (delta"<<deltaName1<<".x*delta"<<deltaName2<<".x + delta"<<deltaName1<<".y*delta"<<deltaName2<<".y + delta"<<deltaName1<<".z*delta"<<deltaName2<<".z)/delta"<<deltaName2<<".w;\n";
        compute<<"ff.z = (delta"<<deltaName3<<".x*delta"<<deltaName2<<".x + delta"<<deltaName3<<".y*delta"<<deltaName2<<".y + delta"<<deltaName3<<".z*delta"<<deltaName2<<".z)/delta"<<deltaName2<<".w;\n";
        compute<<"ff.w = (dEdDihedral"<<intToString(index)<<"*r)/"<<crossName2<<".w;\n";
        compute<<"float4 internalF0 = ff.x*"<<crossName1<<";\n";
        compute<<"float4 internalF3 = ff.w*"<<crossName2<<";\n";
        compute<<"float4 s = ff.y*internalF0 - ff.z*internalF3;\n";
        compute<<forceNames[atoms[0]]<<".xyz += internalF0.xyz;\n";
        compute<<forceNames[atoms[1]]<<".xyz += s.xyz-internalF0.xyz;\n";
        compute<<forceNames[atoms[2]]<<".xyz += -s.xyz-internalF3.xyz;\n";
        compute<<forceNames[atoms[3]]<<".xyz += internalF3.xyz;\n";
        compute<<"}\n";
    }
    cl.getBondedUtilities().addInteraction(atoms, compute.str(), force.getForceGroup());
    map<string, string> replacements;
    replacements["M_PI"] = doubleToString(M_PI);
    cl.getBondedUtilities().addPrefixCode(cl.replaceStrings(OpenCLKernelSources::customCompoundBond, replacements));;
}

double OpenCLCalcCustomCompoundBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    return 0.0;
}

OpenCLIntegrateVerletStepKernel::~OpenCLIntegrateVerletStepKernel() {
}

void OpenCLIntegrateVerletStepKernel::initialize(const System& system, const VerletIntegrator& integrator) {
    cl.getPlatformData().initializeContexts(system);
    cl::Program program = cl.createProgram(OpenCLKernelSources::verlet, "");
    kernel1 = cl::Kernel(program, "integrateVerletPart1");
    kernel2 = cl::Kernel(program, "integrateVerletPart2");
    prevStepSize = -1.0;
}

void OpenCLIntegrateVerletStepKernel::execute(ContextImpl& context, const VerletIntegrator& integrator) {
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    int numAtoms = cl.getNumAtoms();
    double dt = integrator.getStepSize();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl_int>(0, numAtoms);
        kernel1.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(3, cl.getVelm().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(4, cl.getForce().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getPosDelta().getDeviceBuffer());
        kernel2.setArg<cl_int>(0, numAtoms);
        kernel2.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(4, integration.getPosDelta().getDeviceBuffer());
    }
    if (dt != prevStepSize) {
        vector<mm_float2> stepSizeVec(1);
        stepSizeVec[0] = mm_float2((cl_float) dt, (cl_float) dt);
        cl.getIntegrationUtilities().getStepSize().upload(stepSizeVec);
        prevStepSize = dt;
    }

    // Call the first integration kernel.

    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
    integration.computeVirtualSites();

    // Update the time and step count.

    cl.setTime(cl.getTime()+dt);
    cl.setStepCount(cl.getStepCount()+1);
}

OpenCLIntegrateLangevinStepKernel::~OpenCLIntegrateLangevinStepKernel() {
    if (params != NULL)
        delete params;
}

void OpenCLIntegrateLangevinStepKernel::initialize(const System& system, const LangevinIntegrator& integrator) {
    cl.getPlatformData().initializeContexts(system);
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
    defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
    cl::Program program = cl.createProgram(OpenCLKernelSources::langevin, defines, "");
    kernel1 = cl::Kernel(program, "integrateLangevinPart1");
    kernel2 = cl::Kernel(program, "integrateLangevinPart2");
    params = new OpenCLArray<cl_float>(cl, 3, "langevinParams");
    prevStepSize = -1.0;
}

void OpenCLIntegrateLangevinStepKernel::execute(ContextImpl& context, const LangevinIntegrator& integrator) {
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    int numAtoms = cl.getNumAtoms();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl::Buffer>(0, cl.getVelm().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(1, cl.getForce().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(2, integration.getPosDelta().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(3, params->getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(1, integration.getPosDelta().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(2, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, integration.getStepSize().getDeviceBuffer());
    }
    double temperature = integrator.getTemperature();
    double friction = integrator.getFriction();
    double stepSize = integrator.getStepSize();
    if (temperature != prevTemp || friction != prevFriction || stepSize != prevStepSize) {
        // Calculate the integration parameters.

        double tau = (friction == 0.0 ? 0.0 : 1.0/friction);
        double kT = BOLTZ*temperature;
        double vscale = exp(-stepSize/tau);
        double fscale = (1-vscale)*tau;
        double noisescale = sqrt(2*kT/tau)*sqrt(0.5*(1-vscale*vscale)*tau);
        vector<cl_float> p(params->getSize());
        p[0] = (cl_float) vscale;
        p[1] = (cl_float) fscale;
        p[2] = (cl_float) noisescale;
        params->upload(p);
        integration.getStepSize()[0].y = (cl_float) stepSize;
        integration.getStepSize().upload();
        prevTemp = temperature;
        prevFriction = friction;
        prevStepSize = stepSize;
    }

    // Call the first integration kernel.

    kernel1.setArg<cl_uint>(6, integration.prepareRandomNumbers(cl.getPaddedNumAtoms()));
    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
    integration.computeVirtualSites();

    // Update the time and step count.

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
}

OpenCLIntegrateBrownianStepKernel::~OpenCLIntegrateBrownianStepKernel() {
}

void OpenCLIntegrateBrownianStepKernel::initialize(const System& system, const BrownianIntegrator& integrator) {
    cl.getPlatformData().initializeContexts(system);
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
    cl::Program program = cl.createProgram(OpenCLKernelSources::brownian, defines, "");
    kernel1 = cl::Kernel(program, "integrateBrownianPart1");
    kernel2 = cl::Kernel(program, "integrateBrownianPart2");
    prevStepSize = -1.0;
}

void OpenCLIntegrateBrownianStepKernel::execute(ContextImpl& context, const BrownianIntegrator& integrator) {
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    int numAtoms = cl.getNumAtoms();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl::Buffer>(2, cl.getForce().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(3, integration.getPosDelta().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(4, cl.getVelm().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(2, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, integration.getPosDelta().getDeviceBuffer());
    }
    double temperature = integrator.getTemperature();
    double friction = integrator.getFriction();
    double stepSize = integrator.getStepSize();
    if (temperature != prevTemp || friction != prevFriction || stepSize != prevStepSize) {
        double tau = (friction == 0.0 ? 0.0 : 1.0/friction);
        kernel1.setArg<cl_float>(0, (cl_float) (tau*stepSize));
        kernel1.setArg<cl_float>(1, (cl_float) (sqrt(2.0f*BOLTZ*temperature*stepSize*tau)));
        kernel2.setArg<cl_float>(0, (cl_float) (1.0/stepSize));
        prevTemp = temperature;
        prevFriction = friction;
        prevStepSize = stepSize;
    }

    // Call the first integration kernel.

    kernel1.setArg<cl_uint>(6, integration.prepareRandomNumbers(cl.getPaddedNumAtoms()));
    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
    integration.computeVirtualSites();

    // Update the time and step count.

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
}

OpenCLIntegrateVariableVerletStepKernel::~OpenCLIntegrateVariableVerletStepKernel() {
}

void OpenCLIntegrateVariableVerletStepKernel::initialize(const System& system, const VariableVerletIntegrator& integrator) {
    cl.getPlatformData().initializeContexts(system);
    cl::Program program = cl.createProgram(OpenCLKernelSources::verlet, "");
    kernel1 = cl::Kernel(program, "integrateVerletPart1");
    kernel2 = cl::Kernel(program, "integrateVerletPart2");
    selectSizeKernel = cl::Kernel(program, "selectVerletStepSize");
    blockSize = min(min(256, system.getNumParticles()), (int) cl.getDevice().getInfo<CL_DEVICE_MAX_WORK_GROUP_SIZE>());
}

double OpenCLIntegrateVariableVerletStepKernel::execute(ContextImpl& context, const VariableVerletIntegrator& integrator, double maxTime) {
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    int numAtoms = cl.getNumAtoms();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl_int>(0, numAtoms);
        kernel1.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(3, cl.getVelm().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(4, cl.getForce().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getPosDelta().getDeviceBuffer());
        kernel2.setArg<cl_int>(0, numAtoms);
        kernel2.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(4, integration.getPosDelta().getDeviceBuffer());
        selectSizeKernel.setArg<cl_int>(0, numAtoms);
        selectSizeKernel.setArg<cl::Buffer>(3, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
        selectSizeKernel.setArg<cl::Buffer>(4, cl.getVelm().getDeviceBuffer());
        selectSizeKernel.setArg<cl::Buffer>(5, cl.getForce().getDeviceBuffer());
        selectSizeKernel.setArg(6, blockSize*sizeof(cl_float), NULL);
    }

    // Select the step size to use.

    float maxStepSize = (float)(maxTime-cl.getTime());
    selectSizeKernel.setArg<cl_float>(1, maxStepSize);
    selectSizeKernel.setArg<cl_float>(2, (cl_float) integrator.getErrorTolerance());
    cl.executeKernel(selectSizeKernel, blockSize, blockSize);

    // Call the first integration kernel.

    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
    integration.computeVirtualSites();

    // Update the time and step count.

    cl.getIntegrationUtilities().getStepSize().download();
    double dt = cl.getIntegrationUtilities().getStepSize()[0].y;
    double time = cl.getTime()+dt;
    if (dt == maxStepSize)
        time = maxTime; // Avoid round-off error
    cl.setTime(time);
    cl.setStepCount(cl.getStepCount()+1);
    return dt;
}

OpenCLIntegrateVariableLangevinStepKernel::~OpenCLIntegrateVariableLangevinStepKernel() {
    if (params != NULL)
        delete params;
}

void OpenCLIntegrateVariableLangevinStepKernel::initialize(const System& system, const VariableLangevinIntegrator& integrator) {
    cl.getPlatformData().initializeContexts(system);
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
    defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
    cl::Program program = cl.createProgram(OpenCLKernelSources::langevin, defines, "");
    kernel1 = cl::Kernel(program, "integrateLangevinPart1");
    kernel2 = cl::Kernel(program, "integrateLangevinPart2");
    selectSizeKernel = cl::Kernel(program, "selectLangevinStepSize");
    params = new OpenCLArray<cl_float>(cl, 3, "langevinParams");
    blockSize = min(256, system.getNumParticles());
    blockSize = max(blockSize, params->getSize());
    blockSize = min(blockSize, (int) cl.getDevice().getInfo<CL_DEVICE_MAX_WORK_GROUP_SIZE>());
}

double OpenCLIntegrateVariableLangevinStepKernel::execute(ContextImpl& context, const VariableLangevinIntegrator& integrator, double maxTime) {
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    int numAtoms = cl.getNumAtoms();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl::Buffer>(0, cl.getVelm().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(1, cl.getForce().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(2, integration.getPosDelta().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(3, params->getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(1, integration.getPosDelta().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(2, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, integration.getStepSize().getDeviceBuffer());
        selectSizeKernel.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
        selectSizeKernel.setArg<cl::Buffer>(5, cl.getVelm().getDeviceBuffer());
        selectSizeKernel.setArg<cl::Buffer>(6, cl.getForce().getDeviceBuffer());
        selectSizeKernel.setArg<cl::Buffer>(7, params->getDeviceBuffer());
        selectSizeKernel.setArg(8, params->getSize()*sizeof(cl_float), NULL);
        selectSizeKernel.setArg(9, blockSize*sizeof(cl_float), NULL);
    }

    // Select the step size to use.

    float maxStepSize = (float)(maxTime-cl.getTime());
    selectSizeKernel.setArg<cl_float>(0, maxStepSize);
    selectSizeKernel.setArg<cl_float>(1, (cl_float) integrator.getErrorTolerance());
    selectSizeKernel.setArg<cl_float>(2, (cl_float) (integrator.getFriction() == 0.0 ? 0.0 : 1.0/integrator.getFriction()));
    selectSizeKernel.setArg<cl_float>(3, (cl_float) (BOLTZ*integrator.getTemperature()));
    cl.executeKernel(selectSizeKernel, blockSize, blockSize);

    // Call the first integration kernel.

    kernel1.setArg<cl_uint>(6, integration.prepareRandomNumbers(cl.getPaddedNumAtoms()));
    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
    integration.computeVirtualSites();

    // Update the time and step count.

    cl.getIntegrationUtilities().getStepSize().download();
    double dt = cl.getIntegrationUtilities().getStepSize()[0].y;
    double time = cl.getTime()+dt;
    if (dt == maxStepSize)
        time = maxTime; // Avoid round-off error
    cl.setTime(time);
    cl.setStepCount(cl.getStepCount()+1);
    return dt;
}

class OpenCLIntegrateCustomStepKernel::ReorderListener : public OpenCLContext::ReorderListener {
public:
    ReorderListener(OpenCLContext& cl, OpenCLParameterSet& perDofValues, vector<vector<cl_float> >& localPerDofValues, bool& deviceValuesAreCurrent) :
            cl(cl), perDofValues(perDofValues), localPerDofValues(localPerDofValues), deviceValuesAreCurrent(deviceValuesAreCurrent) {
        int numAtoms = cl.getNumAtoms();
        lastAtomOrder.resize(numAtoms);
        for (int i = 0; i < numAtoms; i++)
            lastAtomOrder[i] = cl.getAtomIndex()[i];
    }
    void execute() {
        // Reorder the per-DOF variables to reflect the new atom order.

        if (perDofValues.getNumParameters() == 0)
            return;
        int numAtoms = cl.getNumAtoms();
        if (deviceValuesAreCurrent)
            perDofValues.getParameterValues(localPerDofValues);
        vector<vector<cl_float> > swap(3*numAtoms);
        for (int i = 0; i < numAtoms; i++) {
            swap[3*lastAtomOrder[i]] = localPerDofValues[3*i];
            swap[3*lastAtomOrder[i]+1] = localPerDofValues[3*i+1];
            swap[3*lastAtomOrder[i]+2] = localPerDofValues[3*i+2];
        }
        OpenCLArray<cl_int>& order = cl.getAtomIndex();
        for (int i = 0; i < numAtoms; i++) {
            localPerDofValues[3*i] = swap[3*order[i]];
            localPerDofValues[3*i+1] = swap[3*order[i]+1];
            localPerDofValues[3*i+2] = swap[3*order[i]+2];
        }
        perDofValues.setParameterValues(localPerDofValues);
        for (int i = 0; i < numAtoms; i++)
            lastAtomOrder[i] = order[i];
        deviceValuesAreCurrent = true;
    }
private:
    OpenCLContext& cl;
    OpenCLParameterSet& perDofValues;
    vector<vector<cl_float> >& localPerDofValues;
    bool& deviceValuesAreCurrent;
    vector<int> lastAtomOrder;
};

OpenCLIntegrateCustomStepKernel::~OpenCLIntegrateCustomStepKernel() {
    if (globalValues != NULL)
        delete globalValues;
    if (contextParameterValues != NULL)
        delete contextParameterValues;
    if (sumBuffer != NULL)
        delete sumBuffer;
    if (energy != NULL)
        delete energy;
    if (uniformRandoms != NULL)
        delete uniformRandoms;
    if (randomSeed != NULL)
        delete randomSeed;
    if (perDofValues != NULL)
        delete perDofValues;
}

void OpenCLIntegrateCustomStepKernel::initialize(const System& system, const CustomIntegrator& integrator) {
    cl.getPlatformData().initializeContexts(system);
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    numGlobalVariables = integrator.getNumGlobalVariables();
    globalValues = new OpenCLArray<cl_float>(cl, max(1, numGlobalVariables), "globalVariables", true);
    sumBuffer = new OpenCLArray<cl_float>(cl, 3*system.getNumParticles(), "sumBuffer");
    energy = new OpenCLArray<cl_float>(cl, 1, "energy");
    perDofValues = new OpenCLParameterSet(cl, integrator.getNumPerDofVariables(), 3*system.getNumParticles(), "perDofVariables");
    cl.addReorderListener(new ReorderListener(cl, *perDofValues, localPerDofValues, deviceValuesAreCurrent));
    prevStepSize = -1.0;
    SimTKOpenMMUtilities::setRandomNumberSeed(integrator.getRandomNumberSeed());
}

string OpenCLIntegrateCustomStepKernel::createGlobalComputation(const string& variable, const Lepton::ParsedExpression& expr, CustomIntegrator& integrator, const string& energyName) {
    map<string, Lepton::ParsedExpression> expressions;
    if (variable == "dt")
        expressions["dt[0].y = "] = expr;
    else {
        for (int i = 0; i < integrator.getNumGlobalVariables(); i++)
            if (variable == integrator.getGlobalVariableName(i))
                expressions["globals["+intToString(i)+"] = "] = expr;
        for (int i = 0; i < (int) parameterNames.size(); i++)
            if (variable == parameterNames[i]) {
                expressions["params["+intToString(i)+"] = "] = expr;
                modifiesParameters = true;
            }
    }
    if (expressions.size() == 0)
        throw OpenMMException("Unknown global variable: "+variable);
    map<string, string> variables;
    variables["dt"] = "dt[0].y";
    variables["uniform"] = "uniform";
    variables["gaussian"] = "gaussian";
    variables[energyName] = "energy[0]";
    for (int i = 0; i < integrator.getNumGlobalVariables(); i++)
        variables[integrator.getGlobalVariableName(i)] = "globals["+intToString(i)+"]";
    for (int i = 0; i < (int) parameterNames.size(); i++)
        variables[parameterNames[i]] = "params["+intToString(i)+"]";
    vector<pair<string, string> > functions;
    return OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
}

string OpenCLIntegrateCustomStepKernel::createPerDofComputation(const string& variable, const Lepton::ParsedExpression& expr, int component, CustomIntegrator& integrator, const string& forceName, const string& energyName) {
    const string suffixes[] = {".x", ".y", ".z"};
    string suffix = suffixes[component];
    map<string, Lepton::ParsedExpression> expressions;
    if (variable == "x")
        expressions["position"+suffix+" = "] = expr;
    else if (variable == "v")
        expressions["velocity"+suffix+" = "] = expr;
    else if (variable == "")
        expressions["sum[3*index+"+intToString(component)+"] = "] = expr;
    else {
        for (int i = 0; i < integrator.getNumPerDofVariables(); i++)
            if (variable == integrator.getPerDofVariableName(i))
                expressions["perDof"+suffix.substr(1)+perDofValues->getParameterSuffix(i)+" = "] = expr;
    }
    if (expressions.size() == 0)
        throw OpenMMException("Unknown per-DOF variable: "+variable);
    map<string, string> variables;
    variables["x"] = "position"+suffix;
    variables["v"] = "velocity"+suffix;
    variables[forceName] = "f"+suffix;
    variables["gaussian"] = "gaussian"+suffix;
    variables["uniform"] = "uniform"+suffix;
    variables["m"] = "mass";
    variables["dt"] = "stepSize";
    variables[energyName] = "energy[0]";
    for (int i = 0; i < integrator.getNumGlobalVariables(); i++)
        variables[integrator.getGlobalVariableName(i)] = "globals["+intToString(i)+"]";
    for (int i = 0; i < integrator.getNumPerDofVariables(); i++)
        variables[integrator.getPerDofVariableName(i)] = "perDof"+suffix.substr(1)+perDofValues->getParameterSuffix(i);
    for (int i = 0; i < (int) parameterNames.size(); i++)
        variables[parameterNames[i]] = "params["+intToString(i)+"]";
    vector<pair<string, string> > functions;
    string tempType = (cl.getSupportsDoublePrecision() ? "double" : "float");
    return OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp"+intToString(component)+"_", "", tempType);
}

void OpenCLIntegrateCustomStepKernel::execute(ContextImpl& context, CustomIntegrator& integrator, bool& forcesAreValid) {
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    int numAtoms = cl.getNumAtoms();
    int numSteps = integrator.getNumComputations();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        
        // Initialize various data structures.
        
        const map<string, double>& params = context.getParameters();
        contextParameterValues = new OpenCLArray<cl_float>(cl, max(1, (int) params.size()), "contextParameters", true);
        for (map<string, double>::const_iterator iter = params.begin(); iter != params.end(); ++iter) {
            contextParameterValues->set(parameterNames.size(), (float) iter->second);
            parameterNames.push_back(iter->first);
        }
        contextParameterValues->upload();
        kernels.resize(integrator.getNumComputations());
        requiredGaussian.resize(integrator.getNumComputations(), 0);
        requiredUniform.resize(integrator.getNumComputations(), 0);
        needsForces.resize(numSteps, false);
        needsEnergy.resize(numSteps, false);
        forceGroup.resize(numSteps, -2);
        invalidatesForces.resize(numSteps, false);
        merged.resize(numSteps, false);
        modifiesParameters = false;
        map<string, string> defines;
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        defines["WORK_GROUP_SIZE"] = intToString(OpenCLContext::ThreadBlockSize);
        
        // Initialize the random number generator.
        
        uniformRandoms = new OpenCLArray<mm_float4>(cl, cl.getNumAtoms(), "uniformRandoms");
        randomSeed = new OpenCLArray<mm_int4>(cl, cl.getNumThreadBlocks()*OpenCLContext::ThreadBlockSize, "randomSeed");
        vector<mm_int4> seed(randomSeed->getSize());
        unsigned int r = integrator.getRandomNumberSeed()+1;
        for (int i = 0; i < randomSeed->getSize(); i++) {
            seed[i].x = r = (1664525*r + 1013904223) & 0xFFFFFFFF;
            seed[i].y = r = (1664525*r + 1013904223) & 0xFFFFFFFF;
            seed[i].z = r = (1664525*r + 1013904223) & 0xFFFFFFFF;
            seed[i].w = r = (1664525*r + 1013904223) & 0xFFFFFFFF;
        }
        randomSeed->upload(seed);
        cl::Program randomProgram = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
        randomKernel = cl::Kernel(randomProgram, "generateRandomNumbers");
        randomKernel.setArg<cl::Buffer>(0, uniformRandoms->getDeviceBuffer());
        randomKernel.setArg<cl::Buffer>(1, randomSeed->getDeviceBuffer());
        
        // Build a list of all variables that affect the forces, so we can tell which
        // steps invalidate them.
        
        set<string> affectsForce;
        affectsForce.insert("x");
        for (vector<ForceImpl*>::const_iterator iter = context.getForceImpls().begin(); iter != context.getForceImpls().end(); ++iter) {
            const map<string, double> params = (*iter)->getDefaultParameters();
            for (map<string, double>::const_iterator param = params.begin(); param != params.end(); ++param)
                affectsForce.insert(param->first);
        }
        
        // Record information about all the computation steps.
        
        stepType.resize(numSteps);
        vector<string> variable(numSteps);
        vector<Lepton::ParsedExpression> expression(numSteps);
        vector<string> forceGroupName;
        vector<string> energyGroupName;
        for (int i = 0; i < 32; i++) {
            stringstream fname;
            fname << "f" << i;
            forceGroupName.push_back(fname.str());
            stringstream ename;
            ename << "energy" << i;
            energyGroupName.push_back(ename.str());
        }
        vector<string> forceName(numSteps, "f");
        vector<string> energyName(numSteps, "energy");
        for (int step = 0; step < numSteps; step++) {
            string expr;
            integrator.getComputationStep(step, stepType[step], variable[step], expr);
            if (expr.size() > 0) {
                expression[step] = Lepton::Parser::parse(expr).optimize();
                if (usesVariable(expression[step], "f")) {
                    needsForces[step] = true;
                    forceGroup[step] = -1;
                }
                if (usesVariable(expression[step], "energy")) {
                    needsEnergy[step] = true;
                    forceGroup[step] = -1;
                }
                for (int i = 0; i < 32; i++) {
                    if (usesVariable(expression[step], forceGroupName[i])) {
                        if (forceGroup[step] != -2)
                            throw OpenMMException("A single computation step cannot depend on multiple force groups");
                        needsForces[step] = true;
                        forceGroup[step] = 1<<i;
                        forceName[step] = forceGroupName[i];
                    }
                    if (usesVariable(expression[step], energyGroupName[i])) {
                        if (forceGroup[step] != -2)
                            throw OpenMMException("A single computation step cannot depend on multiple force groups");
                        needsEnergy[step] = true;
                        forceGroup[step] = 1<<i;
                        energyName[step] = energyGroupName[i];
                    }
                }
            }
            invalidatesForces[step] = (stepType[step] == CustomIntegrator::ConstrainPositions || affectsForce.find(variable[step]) != affectsForce.end());
            if (forceGroup[step] == -2 && step > 0)
                forceGroup[step] = forceGroup[step-1];
        }
        
        // Determine how each step will represent the position (as just a value, or a value plus a delta).
        
        vector<bool> storePosAsDelta(numSteps, false);
        vector<bool> loadPosAsDelta(numSteps, false);
        bool beforeConstrain = false;
        for (int step = numSteps-1; step >= 0; step--) {
            if (stepType[step] == CustomIntegrator::ConstrainPositions)
                beforeConstrain = true;
            else if (stepType[step] == CustomIntegrator::ComputePerDof && variable[step] == "x" && beforeConstrain)
                storePosAsDelta[step] = true;
        }
        bool storedAsDelta = false;
        for (int step = 0; step < numSteps; step++) {
            loadPosAsDelta[step] = storedAsDelta;
            if (storePosAsDelta[step] == true)
                storedAsDelta = true;
            if (stepType[step] == CustomIntegrator::ConstrainPositions)
                storedAsDelta = false;
        }
        
        // Identify steps that can be merged into a single kernel.
        
        for (int step = 1; step < numSteps; step++) {
            if (needsForces[step] || needsEnergy[step])
                continue;
            if (stepType[step-1] == CustomIntegrator::ComputeGlobal && stepType[step] == CustomIntegrator::ComputeGlobal)
                merged[step] = true;
            if (stepType[step-1] == CustomIntegrator::ComputePerDof && stepType[step] == CustomIntegrator::ComputePerDof &&
                    !usesVariable(expression[step], "uniform"))
                merged[step] = true;
        }
        
        // Loop over all steps and create the kernels for them.
        
        for (int step = 0; step < numSteps; step++) {
            if ((stepType[step] == CustomIntegrator::ComputePerDof || stepType[step] == CustomIntegrator::ComputeSum) && !merged[step]) {
                // Compute a per-DOF value.
                
                stringstream compute;
                for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++) {
                    const OpenCLNonbondedUtilities::ParameterInfo& buffer = perDofValues->getBuffers()[i];
                    compute << buffer.getType()<<" perDofx"<<intToString(i+1)<<" = perDofValues"<<intToString(i+1)<<"[3*index];\n";
                    compute << buffer.getType()<<" perDofy"<<intToString(i+1)<<" = perDofValues"<<intToString(i+1)<<"[3*index+1];\n";
                    compute << buffer.getType()<<" perDofz"<<intToString(i+1)<<" = perDofValues"<<intToString(i+1)<<"[3*index+2];\n";
                }
                string convert = (cl.getSupportsDoublePrecision() ? "convert_float4(" : "(");
                int numGaussian = 0, numUniform = 0;
                for (int j = step; j < numSteps && (j == step || merged[j]); j++) {
                    compute << "{\n";
                    for (int i = 0; i < 3; i++)
                        compute << createPerDofComputation(stepType[j] == CustomIntegrator::ComputePerDof ? variable[j] : "", expression[j], i, integrator, forceName[j], energyName[j]);
                    if (variable[j] == "x") {
                        if (storePosAsDelta[j]) {
                            if (cl.getSupportsDoublePrecision())
                                compute << "posDelta[index] = convert_float4(position-convert_double4(posq[index]));\n";
                            else
                                compute << "posDelta[index] = position-posq[index];\n";
                        }
                        else
                            compute << "posq[index] = " << convert << "position);\n";
                    }
                    else if (variable[j] == "v")
                        compute << "velm[index] = " << convert << "velocity);\n";
                    else {
                        for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++) {
                            const OpenCLNonbondedUtilities::ParameterInfo& buffer = perDofValues->getBuffers()[i];
                            compute << "perDofValues"<<intToString(i+1)<<"[3*index] = perDofx"<<intToString(i+1)<<";\n";
                            compute << "perDofValues"<<intToString(i+1)<<"[3*index+1] = perDofy"<<intToString(i+1)<<";\n";
                            compute << "perDofValues"<<intToString(i+1)<<"[3*index+2] = perDofz"<<intToString(i+1)<<";\n";
                        }
                    }
                    compute << "}\n";
                    numGaussian += numAtoms*usesVariable(expression[j], "gaussian");
                    numUniform += numAtoms*usesVariable(expression[j], "uniform");
                }
                map<string, string> replacements;
                replacements["COMPUTE_STEP"] = compute.str();
                stringstream args;
                for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++) {
                    const OpenCLNonbondedUtilities::ParameterInfo& buffer = perDofValues->getBuffers()[i];
                    string valueName = "perDofValues"+intToString(i+1);
                    args << ", __global " << buffer.getType() << "* restrict " << valueName;
                }
                replacements["PARAMETER_ARGUMENTS"] = args.str();
                if (loadPosAsDelta[step])
                    defines["LOAD_POS_AS_DELTA"] = "1";
                else if (defines.find("LOAD_POS_AS_DELTA") != defines.end())
                    defines.erase("LOAD_POS_AS_DELTA");
                cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customIntegratorPerDof, replacements), defines);
                cl::Kernel kernel = cl::Kernel(program, "computePerDof");
                kernels[step].push_back(kernel);
                requiredGaussian[step] = numGaussian;
                requiredUniform[step] = numUniform;
                int index = 0;
                kernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, integration.getPosDelta().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, cl.getVelm().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, cl.getForce().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, integration.getStepSize().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, globalValues->getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, contextParameterValues->getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, sumBuffer->getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, integration.getRandom().getDeviceBuffer());
                index++;
                kernel.setArg<cl::Buffer>(index++, uniformRandoms->getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, energy->getDeviceBuffer());
                for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++)
                    kernel.setArg<cl::Memory>(index++, perDofValues->getBuffers()[i].getMemory());
                if (stepType[step] == CustomIntegrator::ComputeSum) {
                    // Create a second kernel for this step that sums the values.

                    program = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
                    kernel = cl::Kernel(program, "computeSum");
                    kernels[step].push_back(kernel);
                    index = 0;
                    kernel.setArg<cl::Buffer>(index++, sumBuffer->getDeviceBuffer());
                    bool found = false;
                    for (int j = 0; j < integrator.getNumGlobalVariables() && !found; j++)
                        if (variable[step] == integrator.getGlobalVariableName(j)) {
                            kernel.setArg<cl::Buffer>(index++, globalValues->getDeviceBuffer());
                            kernel.setArg<cl_uint>(index++, j);
                            found = true;
                        }
                    for (int j = 0; j < (int) parameterNames.size() && !found; j++)
                        if (variable[step] == parameterNames[j]) {
                            kernel.setArg<cl::Buffer>(index++, contextParameterValues->getDeviceBuffer());
                            kernel.setArg<cl_uint>(index++, j);
                            found = true;
                            modifiesParameters = true;
                        }
                    if (!found)
                        throw OpenMMException("Unknown global variable: "+variable[step]);
                    kernel.setArg<cl_int>(index++, 3*numAtoms);
                }
            }
            else if (stepType[step] == CustomIntegrator::ComputeGlobal && !merged[step]) {
                // Compute a global value.

                stringstream compute;
                for (int i = step; i < numSteps && (i == step || merged[i]); i++)
                    compute << "{\n" << createGlobalComputation(variable[i], expression[i], integrator, energyName[i]) << "}\n";
                map<string, string> replacements;
                replacements["COMPUTE_STEP"] = compute.str();
                cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customIntegratorGlobal, replacements), defines);
                cl::Kernel kernel = cl::Kernel(program, "computeGlobal");
                kernels[step].push_back(kernel);
                int index = 0;
                kernel.setArg<cl::Buffer>(index++, integration.getStepSize().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, globalValues->getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, contextParameterValues->getDeviceBuffer());
                index += 2;
                kernel.setArg<cl::Buffer>(index++, energy->getDeviceBuffer());
            }
            else if (stepType[step] == CustomIntegrator::ConstrainPositions) {
                // Apply position constraints.

                cl::Program program = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
                cl::Kernel kernel = cl::Kernel(program, "applyPositionDeltas");
                kernels[step].push_back(kernel);
                int index = 0;
                kernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, integration.getPosDelta().getDeviceBuffer());
            }
        }
        
        // Create the kernel for summing energy.

        cl::Program program = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
        sumEnergyKernel = cl::Kernel(program, "computeSum");
        int index = 0;
        sumEnergyKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        sumEnergyKernel.setArg<cl::Buffer>(index++, energy->getDeviceBuffer());
        sumEnergyKernel.setArg<cl_int>(index++, 0);
        sumEnergyKernel.setArg<cl_int>(index++, cl.getEnergyBuffer().getSize());
    }
    
    // Make sure all values (variables, parameters, etc.) stored on the device are up to date.
    
    if (!deviceValuesAreCurrent) {
        perDofValues->setParameterValues(localPerDofValues);
        deviceValuesAreCurrent = true;
    }
    localValuesAreCurrent = false;
    double stepSize = integrator.getStepSize();
    if (stepSize != prevStepSize) {
        integration.getStepSize()[0].y = (cl_float) stepSize;
        integration.getStepSize().upload();
        prevStepSize = stepSize;
    }
    bool paramsChanged = false;
    for (int i = 0; i < (int) parameterNames.size(); i++) {
        float value = (float) context.getParameter(parameterNames[i]);
        if (value != contextParameterValues->get(i)) {
            contextParameterValues->set(i, value);
            paramsChanged = true;
        }
    }
    if (paramsChanged)
        contextParameterValues->upload();

    // Loop over computation steps in the integrator and execute them.

    for (int i = 0; i < numSteps; i++) {
        if ((needsForces[i] || needsEnergy[i]) && (!forcesAreValid || context.getLastForceGroups() != forceGroup[i])) {
            // Recompute forces and/or energy.  Figure out what is actually needed
            // between now and the next time they get invalidated again.
            
            bool computeForce = false, computeEnergy = false;
            for (int j = i; ; j++) {
                if (needsForces[j])
                    computeForce = true;
                if (needsEnergy[j])
                    computeEnergy = true;
                if (invalidatesForces[j])
                    break;
                if (j == numSteps-1)
                    j = -1;
                if (j == i-1)
                    break;
            }
            recordChangedParameters(context);
            context.calcForcesAndEnergy(computeForce, computeEnergy, forceGroup[i]);
            if (computeEnergy)
                cl.executeKernel(sumEnergyKernel, OpenCLContext::ThreadBlockSize, OpenCLContext::ThreadBlockSize);
            forcesAreValid = true;
        }
        if (stepType[i] == CustomIntegrator::ComputePerDof && !merged[i]) {
            kernels[i][0].setArg<cl_uint>(9, integration.prepareRandomNumbers(requiredGaussian[i]));
            if (requiredUniform[i] > 0)
                cl.executeKernel(randomKernel, numAtoms);
            cl.executeKernel(kernels[i][0], numAtoms);
        }
        else if (stepType[i] == CustomIntegrator::ComputeGlobal && !merged[i]) {
            kernels[i][0].setArg<cl_float>(3, SimTKOpenMMUtilities::getUniformlyDistributedRandomNumber());
            kernels[i][0].setArg<cl_float>(4, SimTKOpenMMUtilities::getNormallyDistributedRandomNumber());
            cl.executeKernel(kernels[i][0], 1, 1);
        }
        else if (stepType[i] == CustomIntegrator::ComputeSum) {
            kernels[i][0].setArg<cl_uint>(9, integration.prepareRandomNumbers(requiredGaussian[i]));
            if (requiredUniform[i] > 0)
                cl.executeKernel(randomKernel, numAtoms);
            cl.executeKernel(kernels[i][0], numAtoms);
            cl.executeKernel(kernels[i][1], OpenCLContext::ThreadBlockSize, OpenCLContext::ThreadBlockSize);
        }
        else if (stepType[i] == CustomIntegrator::UpdateContextState) {
            recordChangedParameters(context);
            context.updateContextState();
        }
        else if (stepType[i] == CustomIntegrator::ConstrainPositions) {
            cl.getIntegrationUtilities().applyConstraints(integrator.getConstraintTolerance());
            cl.executeKernel(kernels[i][0], numAtoms);
            cl.getIntegrationUtilities().computeVirtualSites();
        }
        else if (stepType[i] == CustomIntegrator::ConstrainVelocities) {
            cl.getIntegrationUtilities().applyVelocityConstraints(integrator.getConstraintTolerance());
        }
        if (invalidatesForces[i])
            forcesAreValid = false;
    }
    recordChangedParameters(context);

    // Update the time and step count.

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
}

void OpenCLIntegrateCustomStepKernel::recordChangedParameters(ContextImpl& context) {
    if (!modifiesParameters)
        return;
    contextParameterValues->download();
    for (int i = 0; i < (int) parameterNames.size(); i++) {
        float value = (float) context.getParameter(parameterNames[i]);
        if (value != contextParameterValues->get(i))
            context.setParameter(parameterNames[i], contextParameterValues->get(i));
    }
}

void OpenCLIntegrateCustomStepKernel::getGlobalVariables(ContextImpl& context, vector<double>& values) const {
    globalValues->download();
    values.resize(numGlobalVariables);
    for (int i = 0; i < numGlobalVariables; i++)
        values[i] = globalValues->get(i);
}

void OpenCLIntegrateCustomStepKernel::setGlobalVariables(ContextImpl& context, const vector<double>& values) {
    for (int i = 0; i < numGlobalVariables; i++)
        globalValues->set(i, (float) values[i]);
    globalValues->upload();
}

void OpenCLIntegrateCustomStepKernel::getPerDofVariable(ContextImpl& context, int variable, vector<Vec3>& values) const {
    if (!localValuesAreCurrent) {
        perDofValues->getParameterValues(localPerDofValues);
        localValuesAreCurrent = true;
    }
    values.resize(perDofValues->getNumObjects()/3);
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
    for (int i = 0; i < (int) values.size(); i++)
        for (int j = 0; j < 3; j++)
            values[order[i]][j] = localPerDofValues[3*i+j][variable];
}

void OpenCLIntegrateCustomStepKernel::setPerDofVariable(ContextImpl& context, int variable, const vector<Vec3>& values) {
    if (!localValuesAreCurrent) {
        perDofValues->getParameterValues(localPerDofValues);
        localValuesAreCurrent = true;
    }
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
    for (int i = 0; i < (int) values.size(); i++)
        for (int j = 0; j < 3; j++)
            localPerDofValues[3*i+j][variable] = (float) values[order[i]][j];
    deviceValuesAreCurrent = false;
}

OpenCLApplyAndersenThermostatKernel::~OpenCLApplyAndersenThermostatKernel() {
    if (atomGroups != NULL)
        delete atomGroups;
}

void OpenCLApplyAndersenThermostatKernel::initialize(const System& system, const AndersenThermostat& thermostat) {
    randomSeed = thermostat.getRandomNumberSeed();
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
    cl::Program program = cl.createProgram(OpenCLKernelSources::andersenThermostat, defines);
    kernel = cl::Kernel(program, "applyAndersenThermostat");
    cl.getIntegrationUtilities().initRandomNumberGenerator(randomSeed);

    // Create the arrays with the group definitions.

    vector<vector<int> > groups = AndersenThermostatImpl::calcParticleGroups(system);
    atomGroups = new OpenCLArray<int>(cl, cl.getNumAtoms(), "atomGroups");
    vector<int> atoms(atomGroups->getSize());
    for (int i = 0; i < (int) groups.size(); i++) {
        for (int j = 0; j < (int) groups[i].size(); j++)
            atoms[groups[i][j]] = i;
    }
    atomGroups->upload(atoms);
}

void OpenCLApplyAndersenThermostatKernel::execute(ContextImpl& context) {
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel.setArg<cl::Buffer>(2, cl.getVelm().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(3, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(4, cl.getIntegrationUtilities().getRandom().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(6, atomGroups->getDeviceBuffer());
    }
    kernel.setArg<cl_float>(0, (cl_float) context.getParameter(AndersenThermostat::CollisionFrequency()));
    kernel.setArg<cl_float>(1, (cl_float) (BOLTZ*context.getParameter(AndersenThermostat::Temperature())));
    kernel.setArg<cl_uint>(5, cl.getIntegrationUtilities().prepareRandomNumbers(cl.getPaddedNumAtoms()));
    cl.executeKernel(kernel, cl.getNumAtoms());
}

OpenCLApplyMonteCarloBarostatKernel::~OpenCLApplyMonteCarloBarostatKernel() {
    if (savedPositions != NULL)
        delete savedPositions;
    if (moleculeAtoms != NULL)
        delete moleculeAtoms;
    if (moleculeStartIndex != NULL)
        delete moleculeStartIndex;
}

void OpenCLApplyMonteCarloBarostatKernel::initialize(const System& system, const MonteCarloBarostat& thermostat) {
    savedPositions = new OpenCLArray<mm_float4>(cl, cl.getPaddedNumAtoms(), "savedPositions");
    cl::Program program = cl.createProgram(OpenCLKernelSources::monteCarloBarostat);
    kernel = cl::Kernel(program, "scalePositions");
}

void OpenCLApplyMonteCarloBarostatKernel::scaleCoordinates(ContextImpl& context, double scale) {
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;

        // Create the arrays with the molecule definitions.

        vector<vector<int> > molecules = context.getMolecules();
        numMolecules = molecules.size();
        moleculeAtoms = new OpenCLArray<int>(cl, cl.getNumAtoms(), "moleculeAtoms");
        moleculeStartIndex = new OpenCLArray<int>(cl, numMolecules+1, "moleculeStartIndex");
        vector<int> atoms(moleculeAtoms->getSize());
        vector<int> startIndex(moleculeStartIndex->getSize());
        int index = 0;
        for (int i = 0; i < numMolecules; i++) {
            startIndex[i] = index;
            for (int j = 0; j < (int) molecules[i].size(); j++)
                atoms[index++] = molecules[i][j];
        }
        startIndex[numMolecules] = index;
        moleculeAtoms->upload(atoms);
        moleculeStartIndex->upload(startIndex);

        // Initialize the kernel arguments.
        
        kernel.setArg<cl_int>(1, numMolecules);
        kernel.setArg<cl::Buffer>(4, cl.getPosq().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(5, moleculeAtoms->getDeviceBuffer());
        kernel.setArg<cl::Buffer>(6, moleculeStartIndex->getDeviceBuffer());
    }
    cl.getQueue().enqueueCopyBuffer(cl.getPosq().getDeviceBuffer(), savedPositions->getDeviceBuffer(), 0, 0, cl.getPosq().getSize()*sizeof(mm_float4));
    kernel.setArg<cl_float>(0, (cl_float) scale);
    kernel.setArg<mm_float4>(2, cl.getPeriodicBoxSize());
    kernel.setArg<mm_float4>(3, cl.getInvPeriodicBoxSize());
    cl.executeKernel(kernel, cl.getNumAtoms());
    for (int i = 0; i < (int) cl.getPosCellOffsets().size(); i++)
        cl.getPosCellOffsets()[i] = mm_int4(0, 0, 0, 0);
}

void OpenCLApplyMonteCarloBarostatKernel::restoreCoordinates(ContextImpl& context) {
    cl.getQueue().enqueueCopyBuffer(savedPositions->getDeviceBuffer(), cl.getPosq().getDeviceBuffer(), 0, 0, cl.getPosq().getSize()*sizeof(mm_float4));
}

void OpenCLCalcKineticEnergyKernel::initialize(const System& system) {
    int numParticles = system.getNumParticles();
    masses.resize(numParticles);
    for (int i = 0; i < numParticles; ++i)
        masses[i] = system.getParticleMass(i);
}

double OpenCLCalcKineticEnergyKernel::execute(ContextImpl& context) {
    // We don't currently have a GPU kernel to do this, so we retrieve the velocities and calculate the energy
    // on the CPU.

    OpenCLArray<mm_float4>& velm = cl.getVelm();
    velm.download();
    double energy = 0.0;
    for (size_t i = 0; i < masses.size(); ++i) {
        mm_float4 v = velm[i];
        energy += masses[i]*(v.x*v.x+v.y*v.y+v.z*v.z);
    }
    return 0.5*energy;
}

OpenCLRemoveCMMotionKernel::~OpenCLRemoveCMMotionKernel() {
    if (cmMomentum != NULL)
        delete cmMomentum;
}

void OpenCLRemoveCMMotionKernel::initialize(const System& system, const CMMotionRemover& force) {
    frequency = force.getFrequency();
    int numAtoms = cl.getNumAtoms();
    cmMomentum = new OpenCLArray<mm_float4>(cl, (numAtoms+OpenCLContext::ThreadBlockSize-1)/OpenCLContext::ThreadBlockSize, "cmMomentum");
    double totalMass = 0.0;
    for (int i = 0; i < numAtoms; i++)
        totalMass += system.getParticleMass(i);
    map<string, string> defines;
    defines["INVERSE_TOTAL_MASS"] = doubleToString(1.0/totalMass);
    cl::Program program = cl.createProgram(OpenCLKernelSources::removeCM, defines);
    kernel1 = cl::Kernel(program, "calcCenterOfMassMomentum");
    kernel1.setArg<cl_int>(0, numAtoms);
    kernel1.setArg<cl::Buffer>(1, cl.getVelm().getDeviceBuffer());
    kernel1.setArg<cl::Buffer>(2, cmMomentum->getDeviceBuffer());
    kernel1.setArg(3, OpenCLContext::ThreadBlockSize*sizeof(mm_float4), NULL);
    kernel2 = cl::Kernel(program, "removeCenterOfMassMomentum");
    kernel2.setArg<cl_int>(0, numAtoms);
    kernel2.setArg<cl::Buffer>(1, cl.getVelm().getDeviceBuffer());
    kernel2.setArg<cl::Buffer>(2, cmMomentum->getDeviceBuffer());
    kernel2.setArg(3, OpenCLContext::ThreadBlockSize*sizeof(mm_float4), NULL);
}

void OpenCLRemoveCMMotionKernel::execute(ContextImpl& context) {
    cl.executeKernel(kernel1, cl.getNumAtoms());
    cl.executeKernel(kernel2, cl.getNumAtoms());
}