OpenCLKernels.cpp 239 KB
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/* -------------------------------------------------------------------------- *
 *                                   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.               *
 *                                                                            *
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 * Portions copyright (c) 2008-2010 Stanford University and the Authors.      *
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 * 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"
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#include "OpenCLForceInfo.h"
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#include "openmm/LangevinIntegrator.h"
#include "openmm/Context.h"
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#include "openmm/internal/AndersenThermostatImpl.h"
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#include "openmm/internal/CMAPTorsionForceImpl.h"
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#include "openmm/internal/ContextImpl.h"
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#include "openmm/internal/CustomCompoundBondForceImpl.h"
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#include "openmm/internal/CustomHbondForceImpl.h"
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#include "openmm/internal/NonbondedForceImpl.h"
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#include "OpenCLBondedUtilities.h"
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#include "OpenCLExpressionUtilities.h"
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#include "OpenCLIntegrationUtilities.h"
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#include "OpenCLNonbondedUtilities.h"
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#include "OpenCLKernelSources.h"
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#include "lepton/ExpressionTreeNode.h"
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#include "lepton/Operation.h"
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#include "lepton/Parser.h"
#include "lepton/ParsedExpression.h"
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#include "../src/SimTKUtilities/SimTKOpenMMRealType.h"
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#include "../src/SimTKUtilities/SimTKOpenMMUtilities.h"
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#include <cmath>
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#include <set>
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using namespace OpenMM;
using namespace std;
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using Lepton::ExpressionTreeNode;
using Lepton::Operation;
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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();
}

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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);
}

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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);
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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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());
    mm_float4 box = cl.getPeriodicBoxSize();
    stream.write((char*) &box, sizeof(mm_float4));
    cl.getIntegrationUtilities().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));
    cl.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();
    mm_float4 box;
    stream.read((char*) &box, sizeof(mm_float4));
    cl.setPeriodicBoxSize(box.x, box.y, box.z);
    cl.getIntegrationUtilities().loadCheckpoint(stream);
}

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

void OpenCLApplyConstraintsKernel::apply(ContextImpl& context, double tol) {
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    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();
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}

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

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

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class OpenCLBondForceInfo : public OpenCLForceInfo {
public:
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    OpenCLBondForceInfo(const HarmonicBondForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumBonds();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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;
};

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

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

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double OpenCLCalcHarmonicBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    return 0.0;
}
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class OpenCLCustomBondForceInfo : public OpenCLForceInfo {
public:
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    OpenCLCustomBondForceInfo(const CustomBondForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumBonds();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumBonds()/numContexts;
    numBonds = endIndex-startIndex;
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    if (numBonds == 0)
        return;
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    vector<vector<int> > atoms(numBonds, vector<int>(2));
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    params = new OpenCLParameterSet(cl, force.getNumPerBondParameters(), numBonds, "customBondParams");
    vector<vector<cl_float> > paramVector(numBonds);
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    for (int i = 0; i < numBonds; i++) {
        vector<double> parameters;
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        force.getBondParameters(startIndex+i, atoms[i][0], atoms[i][1], parameters);
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        paramVector[i].resize(parameters.size());
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        for (int j = 0; j < (int) parameters.size(); j++)
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            paramVector[i][j] = (cl_float) parameters[j];
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    }
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    params->setParameterValues(paramVector);
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    cl.addForce(new OpenCLCustomBondForceInfo(force));
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    // 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);
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        variables[name] = "bondParams"+params->getParameterSuffix(i);
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    }
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    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;
        }
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    }
    stringstream compute;
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    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = "<<argName<<"[index];\n";
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    }
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    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
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    map<string, string> replacements;
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    replacements["COMPUTE_FORCE"] = compute.str();
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::customBondForce, replacements), force.getForceGroup());
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}

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double OpenCLCalcCustomBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (globals != NULL) {
        bool changed = false;
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        for (int i = 0; i < (int) globalParamNames.size(); i++) {
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            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;
}

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class OpenCLAngleForceInfo : public OpenCLForceInfo {
public:
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    OpenCLAngleForceInfo(const HarmonicAngleForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumAngles();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumAngles()/numContexts;
    numAngles = endIndex-startIndex;
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    if (numAngles == 0)
        return;
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    vector<vector<int> > atoms(numAngles, vector<int>(3));
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    params = new OpenCLArray<mm_float2>(cl, numAngles, "angleParams");
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    vector<mm_float2> paramVector(numAngles);
    for (int i = 0; i < numAngles; i++) {
        double angle, k;
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        force.getAngleParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], angle, k);
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        paramVector[i] = mm_float2((cl_float) angle, (cl_float) k);
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    }
    params->upload(paramVector);
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    map<string, string> replacements;
    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float2");
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::harmonicAngleForce, replacements), force.getForceGroup());
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    cl.addForce(new OpenCLAngleForceInfo(force));
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}

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

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class OpenCLCustomAngleForceInfo : public OpenCLForceInfo {
public:
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    OpenCLCustomAngleForceInfo(const CustomAngleForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumAngles();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumAngles()/numContexts;
    numAngles = endIndex-startIndex;
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    if (numAngles == 0)
        return;
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    vector<vector<int> > atoms(numAngles, vector<int>(3));
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    params = new OpenCLParameterSet(cl, force.getNumPerAngleParameters(), numAngles, "customAngleParams");
    vector<vector<cl_float> > paramVector(numAngles);
    for (int i = 0; i < numAngles; i++) {
        vector<double> parameters;
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        force.getAngleParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], parameters);
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        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
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    cl.addForce(new OpenCLCustomAngleForceInfo(force));
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    // 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;
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    expressions["float dEdAngle = "] = forceExpression;
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    // 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);
    }
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    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;
        }
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    }
    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" angleParams"<<(i+1)<<" = "<<argName<<"[index];\n";
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    }
    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::customAngleForce, replacements), force.getForceGroup());
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}

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double OpenCLCalcCustomAngleForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    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;
}

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class OpenCLPeriodicTorsionForceInfo : public OpenCLForceInfo {
public:
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    OpenCLPeriodicTorsionForceInfo(const PeriodicTorsionForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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);
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        force.getTorsionParameters(group2, particle1, particle2, particle3, particle4, periodicity2, phase2, k2);
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        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) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
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    if (numTorsions == 0)
        return;
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    vector<vector<int> > atoms(numTorsions, vector<int>(4));
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    params = new OpenCLArray<mm_float4>(cl, numTorsions, "periodicTorsionParams");
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    vector<mm_float4> paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
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        int periodicity;
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        double phase, k;
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        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], periodicity, phase, k);
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        paramVector[i] = mm_float4((cl_float) k, (cl_float) phase, (cl_float) periodicity, 0.0f);
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    }
    params->upload(paramVector);
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    map<string, string> replacements;
    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float4");
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::periodicTorsionForce, replacements), force.getForceGroup());
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    cl.addForce(new OpenCLPeriodicTorsionForceInfo(force));
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}

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

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class OpenCLRBTorsionForceInfo : public OpenCLForceInfo {
public:
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    OpenCLRBTorsionForceInfo(const RBTorsionForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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);
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        force.getTorsionParameters(group2, particle1, particle2, particle3, particle4, c0b, c1b, c2b, c3b, c4b, c5b);
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        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) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
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    if (numTorsions == 0)
        return;
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    vector<vector<int> > atoms(numTorsions, vector<int>(4));
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    params = new OpenCLArray<mm_float8>(cl, numTorsions, "rbTorsionParams");
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    vector<mm_float8> paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        double c0, c1, c2, c3, c4, c5;
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        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], c0, c1, c2, c3, c4, c5);
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        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);
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    }
    params->upload(paramVector);
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    map<string, string> replacements;
    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float8");
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::rbTorsionForce, replacements), force.getForceGroup());
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    cl.addForce(new OpenCLRBTorsionForceInfo(force));
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}

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

class OpenCLCMAPTorsionForceInfo : public OpenCLForceInfo {
public:
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    OpenCLCMAPTorsionForceInfo(const CMAPTorsionForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
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    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++) {
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            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]));
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        }
    }
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    vector<vector<int> > atoms(numTorsions, vector<int>(8));
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    vector<cl_int> torsionMapsVec(numTorsions);
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    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]);
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    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);
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    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");
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::cmapTorsionForce, replacements), force.getForceGroup());
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    cl.addForce(new OpenCLCMAPTorsionForceInfo(force));
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}

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

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class OpenCLCustomTorsionForceInfo : public OpenCLForceInfo {
public:
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    OpenCLCustomTorsionForceInfo(const CustomTorsionForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        int particle1, particle2, particle3, particle4;
        vector<double> parameters;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, parameters);
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        particles.resize(4);
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        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) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
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    if (numTorsions == 0)
        return;
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    vector<vector<int> > atoms(numTorsions, vector<int>(4));
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    params = new OpenCLParameterSet(cl, force.getNumPerTorsionParameters(), numTorsions, "customTorsionParams");
    vector<vector<cl_float> > paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        vector<double> parameters;
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        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], parameters);
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        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
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    cl.addForce(new OpenCLCustomTorsionForceInfo(force));
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    // 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);
    }
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    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;
        }
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    }
    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" torsionParams"<<(i+1)<<" = "<<argName<<"[index];\n";
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    }
    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
    replacements["M_PI"] = doubleToString(M_PI);
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::customTorsionForce, replacements), force.getForceGroup());
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}

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double OpenCLCalcCustomTorsionForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    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;
}

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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();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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;
};

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

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);
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    double sumSquaredCharges = 0.0;
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    bool hasCoulomb = false;
    bool hasLJ = false;
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    for (int i = 0; i < numParticles; i++) {
        double charge, sigma, epsilon;
        force.getParticleParameters(i, charge, sigma, epsilon);
        posq[i].w = (float) charge;
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        sigmaEpsilonVector[i] = mm_float2((float) (0.5*sigma), (float) (2.0*sqrt(epsilon)));
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        exclusionList[i].push_back(i);
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        sumSquaredCharges += charge*charge;
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        if (charge != 0.0)
            hasCoulomb = true;
        if (epsilon != 0.0)
            hasLJ = true;
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    }
    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);
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    map<string, string> defines;
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    defines["HAS_COULOMB"] = (hasCoulomb ? "1" : "0");
    defines["HAS_LENNARD_JONES"] = (hasLJ ? "1" : "0");
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    if (useCutoff) {
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        // Compute the reaction field constants.

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        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);
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        defines["REACTION_FIELD_K"] = doubleToString(reactionFieldK);
        defines["REACTION_FIELD_C"] = doubleToString(reactionFieldC);
    }
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    if (force.getUseDispersionCorrection() && cl.getContextIndex() == 0)
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        dispersionCoefficient = NonbondedForceImpl::calcDispersionCorrection(system, force);
    else
        dispersionCoefficient = 0.0;
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    double alpha = 0;
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    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";
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        ewaldSelfEnergy = (cl.getContextIndex() == 0 ? -ONE_4PI_EPS0*alpha*sumSquaredCharges/sqrt(M_PI) : 0.0);
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        // 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));
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        cl::Program program = cl.createProgram(OpenCLKernelSources::ewald, replacements);
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        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");
    }
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    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";
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        ewaldSelfEnergy = (cl.getContextIndex() == 0 ? -ONE_4PI_EPS0*alpha*sumSquaredCharges/sqrt(M_PI) : 0.0);
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        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);
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        pmeDefines["EPSILON_FACTOR"] = doubleToString(sqrt(ONE_4PI_EPS0));
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        // Create required data structures.

        pmeGrid = new OpenCLArray<mm_float2>(cl, gridSizeX*gridSizeY*gridSizeZ, "pmeGrid");
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        cl.addAutoclearBuffer(pmeGrid->getDeviceBuffer(), pmeGrid->getSize()*2);
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        pmeGrid2 = new OpenCLArray<mm_float2>(cl, gridSizeX*gridSizeY*gridSizeZ, "pmeGrid2");
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        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");
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        bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
        if (deviceIsCpu)
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            pmeBsplineDTheta = new OpenCLArray<mm_float4>(cl, PmeOrder*numParticles, "pmeBsplineDTheta");
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        pmeAtomRange = new OpenCLArray<cl_int>(cl, gridSizeX*gridSizeY*gridSizeZ+1, "pmeAtomRange");
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        pmeAtomGridIndex = new OpenCLArray<mm_int2>(cl, numParticles, "pmeAtomGridIndex");
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        sort = new OpenCLSort<SortTrait>(cl, cl.getNumAtoms());
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        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);
        }
    }
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    else
        ewaldSelfEnergy = 0.0;

    // Add the interaction to the default nonbonded kernel.
    
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    string source = cl.replaceStrings(OpenCLKernelSources::coulombLennardJones, defines);
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    cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source, force.getForceGroup());
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    if (hasLJ)
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        cl.getNonbondedUtilities().addParameter(OpenCLNonbondedUtilities::ParameterInfo("sigmaEpsilon", "float", 2, sizeof(cl_float2), sigmaEpsilon->getDeviceBuffer()));
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    // Initialize the exceptions.
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    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;
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    if (numExceptions > 0) {
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        vector<vector<int> > atoms(numExceptions, vector<int>(2));
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        exceptionParams = new OpenCLArray<mm_float4>(cl, numExceptions, "exceptionParams");
        vector<mm_float4> exceptionParamsVector(numExceptions);
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        for (int i = 0; i < numExceptions; i++) {
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            double chargeProd, sigma, epsilon;
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            force.getExceptionParameters(exceptions[startIndex+i], atoms[i][0], atoms[i][1], chargeProd, sigma, epsilon);
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            exceptionParamsVector[i] = mm_float4((float) (ONE_4PI_EPS0*chargeProd), (float) sigma, (float) (4.0*epsilon), 0.0f);
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        }
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        exceptionParams->upload(exceptionParamsVector);
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        map<string, string> replacements;
        replacements["PARAMS"] = cl.getBondedUtilities().addArgument(exceptionParams->getDeviceBuffer(), "float4");
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        cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::nonbondedExceptions, replacements), force.getForceGroup());
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    }
    cl.addForce(new OpenCLNonbondedForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force));
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}

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

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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);
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        for (int i = 0; i < (int) params1.size(); i++)
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            if (params1[i] != params2[i])
                return false;
        return true;
    }
    int getNumParticleGroups() {
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        return force.getNumExclusions();
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    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        int particle1, particle2;
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        force.getExclusionParticles(index, particle1, particle2);
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        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;
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    if (tabulatedFunctionParams != NULL)
        delete tabulatedFunctionParams;
    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        delete tabulatedFunctions[i];
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}

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

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

    // 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);
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    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction(), functions).optimize();
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    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("r").optimize();
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    map<string, Lepton::ParsedExpression> forceExpressions;
    forceExpressions["tempEnergy += "] = energyExpression;
    forceExpressions["tempForce -= "] = forceExpression;
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    // Create the kernels.

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

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

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

void OpenCLCalcGBSAOBCForceKernel::initialize(const System& system, const GBSAOBCForce& force) {
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    if (cl.getPlatformData().contexts.size() > 1)
        throw OpenMMException("GBSAOBCForce does not support using multiple OpenCL devices");
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    OpenCLNonbondedUtilities& nb = cl.getNonbondedUtilities();
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    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");
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    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());
    }
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    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;
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        paramsVector[i] = mm_float2((float) radius, (float) (scalingFactor*radius));
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        posq[i].w = (float) charge;
    }
    posq.upload();
    params->upload(paramsVector);
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    prefactor = -ONE_4PI_EPS0*((1.0/force.getSoluteDielectric())-(1.0/force.getSolventDielectric()));
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    bool useCutoff = (force.getNonbondedMethod() != GBSAOBCForce::NoCutoff);
    bool usePeriodic = (force.getNonbondedMethod() != GBSAOBCForce::NoCutoff && force.getNonbondedMethod() != GBSAOBCForce::CutoffNonPeriodic);
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    string source = OpenCLKernelSources::gbsaObc2;
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    nb.addInteraction(useCutoff, usePeriodic, false, force.getCutoffDistance(), vector<vector<int> >(), source, force.getForceGroup());
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    nb.addParameter(OpenCLNonbondedUtilities::ParameterInfo("obcParams", "float", 2, sizeof(cl_float2), params->getDeviceBuffer()));;
    nb.addParameter(OpenCLNonbondedUtilities::ParameterInfo("bornForce", "float", 1, sizeof(cl_float), bornForce->getDeviceBuffer()));;
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    cl.addForce(new OpenCLGBSAOBCForceInfo(nb.getNumForceBuffers(), force));
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}

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

        hasCreatedKernels = true;
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        maxTiles = (nb.getUseCutoff() ? nb.getInteractingTiles().getSize() : 0);
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        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";
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        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());
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        defines["NUM_BLOCKS"] = OpenCLExpressionUtilities::intToString(cl.getNumAtomBlocks());
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        defines["FORCE_WORK_GROUP_SIZE"] = OpenCLExpressionUtilities::intToString(nb.getForceThreadBlockSize());
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        string platformVendor = cl::Platform(cl.getDevice().getInfo<CL_DEVICE_PLATFORM>()).getInfo<CL_PLATFORM_VENDOR>();
        if (platformVendor == "Apple")
            defines["USE_APPLE_WORKAROUND"] = "1";
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        string file;
        if (deviceIsCpu)
            file = OpenCLKernelSources::gbsaObc_cpu;
        else if (cl.getSIMDWidth() == 32)
            file = OpenCLKernelSources::gbsaObc_nvidia;
        else
            file = OpenCLKernelSources::gbsaObc_default;
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        cl::Program program = cl.createProgram(file, defines);
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        bool useLong = (cl.getSupports64BitGlobalAtomics() && !deviceIsCpu);
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        int index = 0;
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        computeBornSumKernel = cl::Kernel(program, "computeBornSum");
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        computeBornSumKernel.setArg<cl::Buffer>(index++, (useLong ? longBornSum->getDeviceBuffer() : bornSum->getDeviceBuffer()));
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        computeBornSumKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        computeBornSumKernel.setArg<cl::Buffer>(index++, params->getDeviceBuffer());
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        if (nb.getUseCutoff()) {
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            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
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            index += 2; // The periodic box size arguments are set when the kernel is executed.
            computeBornSumKernel.setArg<cl_uint>(index++, maxTiles);
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            if (cl.getSIMDWidth() == 32 || deviceIsCpu)
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                computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractionFlags().getDeviceBuffer());
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        }
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        else
            computeBornSumKernel.setArg<cl_uint>(index++, cl.getNumAtomBlocks()*(cl.getNumAtomBlocks()+1)/2);
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        if (cl.getSIMDWidth() == 32) {
            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getExclusionIndices().getDeviceBuffer());
            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getExclusionRowIndices().getDeviceBuffer());
        }
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        force1Kernel = cl::Kernel(program, "computeGBSAForce1");
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        index = 0;
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        force1Kernel.setArg<cl::Buffer>(index++, (useLong ? cl.getLongForceBuffer().getDeviceBuffer() : cl.getForceBuffers().getDeviceBuffer()));
        force1Kernel.setArg<cl::Buffer>(index++, (useLong ? longBornForce->getDeviceBuffer() : bornForce->getDeviceBuffer()));
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        force1Kernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        force1Kernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        force1Kernel.setArg<cl::Buffer>(index++, bornRadii->getDeviceBuffer());
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        if (nb.getUseCutoff()) {
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            force1Kernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            force1Kernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
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            index += 2; // The periodic box size arguments are set when the kernel is executed.
            force1Kernel.setArg<cl_uint>(index++, maxTiles);
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            if (cl.getSIMDWidth() == 32 || deviceIsCpu)
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                force1Kernel.setArg<cl::Buffer>(index++, nb.getInteractionFlags().getDeviceBuffer());
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        }
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        else
            force1Kernel.setArg<cl_uint>(index++, cl.getNumAtomBlocks()*(cl.getNumAtomBlocks()+1)/2);
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        if (cl.getSIMDWidth() == 32) {
            force1Kernel.setArg<cl::Buffer>(index++, nb.getExclusionIndices().getDeviceBuffer());
            force1Kernel.setArg<cl::Buffer>(index++, nb.getExclusionRowIndices().getDeviceBuffer());
        }
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        program = cl.createProgram(OpenCLKernelSources::gbsaObcReductions, defines);
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        reduceBornSumKernel = cl::Kernel(program, "reduceBornSum");
        reduceBornSumKernel.setArg<cl_int>(0, cl.getPaddedNumAtoms());
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        reduceBornSumKernel.setArg<cl_int>(1, nb.getNumForceBuffers());
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        reduceBornSumKernel.setArg<cl_float>(2, 1.0f);
        reduceBornSumKernel.setArg<cl_float>(3, 0.8f);
        reduceBornSumKernel.setArg<cl_float>(4, 4.85f);
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        reduceBornSumKernel.setArg<cl::Buffer>(5, (useLong ? longBornSum->getDeviceBuffer() : bornSum->getDeviceBuffer()));
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        reduceBornSumKernel.setArg<cl::Buffer>(6, params->getDeviceBuffer());
        reduceBornSumKernel.setArg<cl::Buffer>(7, bornRadii->getDeviceBuffer());
        reduceBornSumKernel.setArg<cl::Buffer>(8, obcChain->getDeviceBuffer());
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        reduceBornForceKernel = cl::Kernel(program, "reduceBornForce");
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        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());
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    }
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    if (nb.getUseCutoff()) {
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        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());
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        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
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            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);
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            if (cl.getSIMDWidth() == 32 || deviceIsCpu) {
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                computeBornSumKernel.setArg<cl::Buffer>(8, nb.getInteractionFlags().getDeviceBuffer());
                force1Kernel.setArg<cl::Buffer>(10, nb.getInteractionFlags().getDeviceBuffer());
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            }
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        }
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    }
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    cl.executeKernel(computeBornSumKernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
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    cl.executeKernel(reduceBornSumKernel, cl.getPaddedNumAtoms());
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    cl.executeKernel(force1Kernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
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    cl.executeKernel(reduceBornForceKernel, cl.getPaddedNumAtoms());
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    return 0.0;
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}
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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);
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        for (int i = 0; i < (int) params1.size(); i++)
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            if (params1[i] != params2[i])
                return false;
        return true;
    }
    int getNumParticleGroups() {
        return force.getNumExclusions();
    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        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;
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    if (energyDerivs != NULL)
        delete energyDerivs;
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    if (longEnergyDerivs != NULL)
        delete longEnergyDerivs;
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    if (globals != NULL)
        delete globals;
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    if (valueBuffers != NULL)
        delete valueBuffers;
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    if (longValueBuffers != NULL)
        delete longValueBuffers;
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    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) {
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    if (cl.getPlatformData().contexts.size() > 1)
        throw OpenMMException("CustomGBForce does not support using multiple OpenCL devices");
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    bool useExclusionsForValue = false;
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    numComputedValues = force.getNumComputedValues();
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    vector<string> computedValueNames(force.getNumComputedValues());
    vector<string> computedValueExpressions(force.getNumComputedValues());
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    if (force.getNumComputedValues() > 0) {
        CustomGBForce::ComputationType type;
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        force.getComputedValueParameters(0, computedValueNames[0], computedValueExpressions[0], type);
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        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++) {
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            force.getComputedValueParameters(i, computedValueNames[i], computedValueExpressions[i], type);
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            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");
    computedValues = new OpenCLParameterSet(cl, force.getNumComputedValues(), numParticles, "customGBComputedValues");
    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());
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        for (int j = 0; j < (int) parameters.size(); j++)
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            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());
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    stringstream tableArgs;
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    for (int i = 0; i < force.getNumFunctions(); i++) {
        string name;
        vector<double> values;
        double min, max;
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        force.getFunctionParameters(i, name, values, min, max);
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        string arrayName = prefix+"table"+intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = &fp;
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        tabulatedFunctionParamsVec[i] = mm_float4((float) min, (float) max, (float) ((values.size()-1)/(max-min)), (float) values.size()-2);
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        vector<mm_float4> f = OpenCLExpressionUtilities::computeFunctionCoefficients(values, min, max);
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        tabulatedFunctions.push_back(new OpenCLArray<mm_float4>(cl, values.size()-1, "TabulatedFunction"));
        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
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        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(arrayName, "float", 4, sizeof(cl_float4), tabulatedFunctions[tabulatedFunctions.size()-1]->getDeviceBuffer()));
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        tableArgs << ", __global const float4* restrict " << arrayName;
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    }
    if (force.getNumFunctions() > 0) {
        tabulatedFunctionParams = new OpenCLArray<mm_float4>(cl, tabulatedFunctionParamsVec.size(), "tabulatedFunctionParameters", false, CL_MEM_READ_ONLY);
        tabulatedFunctionParams->upload(tabulatedFunctionParamsVec);
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        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(prefix+"functionParams", "float", 4, sizeof(cl_float4), tabulatedFunctionParams->getDeviceBuffer()));
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        tableArgs << ", __global const float4* " << prefix << "functionParams";
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    }

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    // Record the global parameters.
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    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);
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    // Record derivatives of expressions needed for the chain rule terms.

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    vector<vector<Lepton::ParsedExpression> > valueGradientExpressions(force.getNumComputedValues());
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    vector<vector<Lepton::ParsedExpression> > valueDerivExpressions(force.getNumComputedValues());
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    needParameterGradient = false;
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    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;
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         for (int j = 0; j < i; j++)
            valueDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]).optimize());
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    }
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    vector<vector<Lepton::ParsedExpression> > energyDerivExpressions(force.getNumEnergyTerms());
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    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());
            else {
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]+"1").optimize());
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]+"2").optimize());
            }
        }
    }
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    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");
    }
    else
        energyDerivs = new OpenCLParameterSet(cl, force.getNumComputedValues(), cl.getPaddedNumAtoms()*cl.getNonbondedUtilities().getNumForceBuffers(), "customGBEnergyDerivatives");
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    // Create the kernels.

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

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        vector<pair<ExpressionTreeNode, string> > variables;
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        map<string, string> rename;
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        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"));
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        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
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            variables.push_back(makeVariable(name+"1", "params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", "params"+params->getParameterSuffix(i, "2")));
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            rename[name+"1"] = name+"2";
            rename[name+"2"] = name+"1";
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        }
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+intToString(i)+"]";
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            variables.push_back(makeVariable(name, value));
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        }
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        map<string, Lepton::ParsedExpression> n2ValueExpressions;
        stringstream n2ValueSource;
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        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");
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        map<string, string> replacements;
        replacements["COMPUTE_VALUE"] = n2ValueSource.str();
        stringstream extraArgs, loadLocal1, loadLocal2, load1, load2;
        if (force.getNumGlobalParameters() > 0)
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            extraArgs << ", __global const float* globals";
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            string paramName = "params"+intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict global_" << paramName << ", __local " << buffer.getType() << "* restrict local_" << paramName;
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            loadLocal1 << "local_" << paramName << "[localAtomIndex] = " << paramName << "1;\n";
            loadLocal2 << "local_" << paramName << "[localAtomIndex] = global_" << paramName << "[j];\n";
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            load1 << buffer.getType() << " " << paramName << "1 = global_" << paramName << "[atom1];\n";
            load2 << buffer.getType() << " " << paramName << "2 = local_" << paramName << "[atom2];\n";
        }
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        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
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        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";
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        if (cl.getSIMDWidth() == 32)
            defines["WARPS_PER_GROUP"] = OpenCLExpressionUtilities::intToString(cl.getNonbondedUtilities().getForceThreadBlockSize()/OpenCLContext::TileSize);
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        defines["CUTOFF_SQUARED"] = doubleToString(force.getCutoffDistance()*force.getCutoffDistance());
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
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        defines["NUM_BLOCKS"] = OpenCLExpressionUtilities::intToString(cl.getNumAtomBlocks());
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        string file;
        if (deviceIsCpu)
            file = OpenCLKernelSources::customGBValueN2_cpu;
        else if (cl.getSIMDWidth() == 32)
            file = OpenCLKernelSources::customGBValueN2_nvidia;
        else
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            file = OpenCLKernelSources::customGBValueN2_default;
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        cl::Program program = cl.createProgram(cl.replaceStrings(file, replacements), defines);
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        pairValueKernel = cl::Kernel(program, "computeN2Value");
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        if (useExclusionsForValue)
            cl.getNonbondedUtilities().requestExclusions(exclusionList);
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    }
    {
        // Create the kernel to reduce the N2 value and calculate other values.

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

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

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        stringstream compute, extraArgs, reduce;
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        if (force.getNumGlobalParameters() > 0)
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            extraArgs << ", __global const float* globals";
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << paramName;
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        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << valueName;
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        }
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        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            string index = intToString(i+1);
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            extraArgs << ", __global " << buffer.getType() << "* restrict derivBuffers" << index;
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            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
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        if (useLong) {
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            extraArgs << ", __global const long* restrict derivBuffersIn";
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            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";
        }
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        map<string, string> variables;
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        variables["x"] = "pos.x";
        variables["y"] = "pos.y";
        variables["z"] = "pos.z";
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        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]");
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        map<string, Lepton::ParsedExpression> energyExpressions;
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        for (int i = 0; i < force.getNumEnergyTerms(); i++) {
            string expression;
            CustomGBForce::ComputationType type;
            force.getEnergyTermParameters(i, expression, type);
            if (type != CustomGBForce::SingleParticle)
                continue;
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            Lepton::ParsedExpression parsed = Lepton::Parser::parse(expression, functions).optimize();
            energyExpressions["/*"+intToString(i+1)+"*/ energy += "] = parsed;
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            for (int j = 0; j < force.getNumComputedValues(); j++)
                energyExpressions["/*"+intToString(i+1)+"*/ deriv"+energyDerivs->getParameterSuffix(j)+" += "] = energyDerivExpressions[i][j];
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            Lepton::ParsedExpression gradx = parsed.differentiate("x").optimize();
            Lepton::ParsedExpression grady = parsed.differentiate("y").optimize();
            Lepton::ParsedExpression gradz = parsed.differentiate("z").optimize();
            if (!isZeroExpression(gradx))
                energyExpressions["/*"+intToString(i+1)+"*/ force.x -= "] = gradx;
            if (!isZeroExpression(grady))
                energyExpressions["/*"+intToString(i+1)+"*/ force.y -= "] = grady;
            if (!isZeroExpression(gradz))
                energyExpressions["/*"+intToString(i+1)+"*/ force.z -= "] = gradz;
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        }
        compute << OpenCLExpressionUtilities::createExpressions(energyExpressions, variables, functionDefinitions, "temp", prefix+"functionParams");
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            string index = intToString(i+1);
            compute << "derivBuffers" << index << "[index] = deriv" << index << ";\n";
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        }
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        compute << "forceBuffers[index] = forceBuffers[index]+force;\n";
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        map<string, string> replacements;
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
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        replacements["REDUCE_DERIVATIVES"] = reduce.str();
        replacements["COMPUTE_ENERGY"] = compute.str();
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        map<string, string> defines;
        defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
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        defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
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        cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customGBEnergyPerParticle, replacements), defines);
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        perParticleEnergyKernel = cl::Kernel(program, "computePerParticleEnergy");
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    }
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    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)
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            extraArgs << ", __global const float* globals";
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << paramName;
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        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << valueName;
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        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            string index = intToString(i+1);
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            extraArgs << ", __global " << buffer.getType() << "* restrict derivBuffers" << index;
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            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++) {
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            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;
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            if (!isZeroExpression(valueGradientExpressions[i][0]))
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                gradientExpressions["dV"+is+"dR.x += "] = valueGradientExpressions[i][0];
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            if (!isZeroExpression(valueGradientExpressions[i][1]))
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                gradientExpressions["dV"+is+"dR.y += "] = valueGradientExpressions[i][1];
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            if (!isZeroExpression(valueGradientExpressions[i][2]))
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                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";
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        }
        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");
    }
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    {
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        // Create the code to calculate chain rules terms as part of the default nonbonded kernel.
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        vector<pair<ExpressionTreeNode, string> > globalVariables;
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        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+intToString(i)+"]";
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            globalVariables.push_back(makeVariable(name, prefix+value));
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        }
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        vector<pair<ExpressionTreeNode, string> > variables = globalVariables;
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        map<string, string> rename;
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        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"));
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        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
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            variables.push_back(makeVariable(name+"1", prefix+"params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", prefix+"params"+params->getParameterSuffix(i, "2")));
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            rename[name+"1"] =  name+"2";
            rename[name+"2"] =  name+"1";
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        }
        map<string, Lepton::ParsedExpression> derivExpressions;
        stringstream chainSource;
        Lepton::ParsedExpression dVdR = Lepton::Parser::parse(computedValueExpressions[0], functions).differentiate("r").optimize();
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        derivExpressions["float dV0dR1 = "] = dVdR;
        derivExpressions["float dV0dR2 = "] = dVdR.renameVariables(rename);
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        chainSource << OpenCLExpressionUtilities::createExpressions(derivExpressions, variables, functionDefinitions, prefix+"temp0_", prefix+"functionParams");
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        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";
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        variables = globalVariables;
        map<string, string> rename1;
        map<string, string> rename2;
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        variables.push_back(makeVariable("x1", "posq1.x"));
        variables.push_back(makeVariable("y1", "posq1.y"));
        variables.push_back(makeVariable("z1", "posq1.z"));
        variables.push_back(makeVariable("x2", "posq2.x"));
        variables.push_back(makeVariable("y2", "posq2.y"));
        variables.push_back(makeVariable("z2", "posq2.z"));
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        rename1["x"] = "x1";
        rename1["y"] = "y1";
        rename1["z"] = "z1";
        rename2["x"] = "x2";
        rename2["y"] = "y2";
        rename2["z"] = "z2";
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        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
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            variables.push_back(makeVariable(name+"1", prefix+"params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", prefix+"params"+params->getParameterSuffix(i, "2")));
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            rename1[name] = name+"1";
            rename2[name] = name+"2";
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        }
        for (int i = 0; i < force.getNumComputedValues(); i++) {
            const string& name = computedValueNames[i];
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            variables.push_back(makeVariable(name+"1", prefix+"values"+computedValues->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", prefix+"values"+computedValues->getParameterSuffix(i, "2")));
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            rename1[name] = name+"1";
            rename2[name] = name+"2";
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            if (i == 0)
                continue;
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            string is = intToString(i);
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            chainSource << "float dV"+is+"dR1 = 0;\n";
            chainSource << "float dV"+is+"dR2 = 0;\n";
            for (int j = 0; j < i; j++) {
                string js = intToString(j);
                Lepton::ParsedExpression dVdV = Lepton::Parser::parse(computedValueExpressions[i], functions).differentiate(computedValueNames[j]).optimize();
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                derivExpressions.clear();
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                derivExpressions["dV"+is+"dR1 += dV"+js+"dR1*"] = dVdV.renameVariables(rename1);
                derivExpressions["dV"+is+"dR2 += dV"+js+"dR2*"] = dVdV.renameVariables(rename2);
                chainSource << OpenCLExpressionUtilities::createExpressions(derivExpressions, variables, functionDefinitions, prefix+"temp"+is+"_"+js+"_", prefix+"functionParams");
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            }
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            chainSource << "tempForce -= dV"<< is << "dR1*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(i, "1") << ";\n";
            chainSource << "tempForce -= dV"<< is << "dR2*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(i, "2") << ";\n";
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        }
        map<string, string> replacements;
        replacements["COMPUTE_FORCE"] = chainSource.str();
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        string source = cl.replaceStrings(OpenCLKernelSources::customGBChainRule, replacements);
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        vector<OpenCLNonbondedUtilities::ParameterInfo> parameters;
        vector<OpenCLNonbondedUtilities::ParameterInfo> arguments;
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = prefix+"params"+intToString(i+1);
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            parameters.push_back(OpenCLNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
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        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string paramName = prefix+"values"+intToString(i+1);
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            parameters.push_back(OpenCLNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
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        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            string paramName = prefix+"dEdV"+intToString(i+1);
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            parameters.push_back(OpenCLNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
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        }
        if (globals != NULL) {
            globals->upload(globalParamValues);
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            arguments.push_back(OpenCLNonbondedUtilities::ParameterInfo(prefix+"globals", "float", 1, sizeof(cl_float), globals->getDeviceBuffer()));
        }
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        cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, force.getNumExclusions() > 0, force.getCutoffDistance(), exclusionList, source, force.getForceGroup());
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        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]);
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    }
    cl.addForce(new OpenCLCustomGBForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force));
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    if (useLong)
        cl.addAutoclearBuffer(longEnergyDerivs->getDeviceBuffer(), 2*longEnergyDerivs->getSize());
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    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));
        }
    }
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}

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double OpenCLCalcCustomGBForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
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    OpenCLNonbondedUtilities& nb = cl.getNonbondedUtilities();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
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        maxTiles = (nb.getUseCutoff() ? nb.getInteractingTiles().getSize() : 0);
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        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);
        }
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        int index = 0;
        pairValueKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float4), NULL);
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        pairValueKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusions().getDeviceBuffer());
        pairValueKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionIndices().getDeviceBuffer());
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        pairValueKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionRowIndices().getDeviceBuffer());
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        pairValueKernel.setArg<cl::Buffer>(index++, useLong ? longValueBuffers->getDeviceBuffer() : valueBuffers->getDeviceBuffer());
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        pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float), NULL);
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        /// \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.
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        pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float), NULL);
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        if (nb.getUseCutoff()) {
            pairValueKernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            pairValueKernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
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            index += 2; // Periodic box size arguments are set when the kernel is executed.
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            pairValueKernel.setArg<cl_uint>(index++, maxTiles);
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            if (cl.getSIMDWidth() == 32 || deviceIsCpu)
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                pairValueKernel.setArg<cl::Buffer>(index++, nb.getInteractionFlags().getDeviceBuffer());
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        }
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        else
            pairValueKernel.setArg<cl_uint>(index++, cl.getNumAtomBlocks()*(cl.getNumAtomBlocks()+1)/2);
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        if (globals != NULL)
            pairValueKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            pairValueKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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            pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
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        }
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        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());
        }
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        index = 0;
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        perParticleValueKernel.setArg<cl_int>(index++, cl.getPaddedNumAtoms());
        perParticleValueKernel.setArg<cl_int>(index++, nb.getNumForceBuffers());
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        perParticleValueKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        perParticleValueKernel.setArg<cl::Buffer>(index++, useLong ? longValueBuffers->getDeviceBuffer() : valueBuffers->getDeviceBuffer());
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        if (globals != NULL)
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            perParticleValueKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
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        for (int i = 0; i < (int) params->getBuffers().size(); i++)
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            perParticleValueKernel.setArg<cl::Memory>(index++, params->getBuffers()[i].getMemory());
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        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++)
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            perParticleValueKernel.setArg<cl::Memory>(index++, computedValues->getBuffers()[i].getMemory());
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        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;
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        pairEnergyKernel.setArg<cl::Buffer>(index++, useLong ? cl.getLongForceBuffer().getDeviceBuffer() : cl.getForceBuffers().getDeviceBuffer());
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        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
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        pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float4), NULL);
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        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float4), NULL);
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        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusions().getDeviceBuffer());
        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionIndices().getDeviceBuffer());
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        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionRowIndices().getDeviceBuffer());
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        /// \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.
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        pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*sizeof(cl_float4), NULL);
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        if (nb.getUseCutoff()) {
            pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
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            index += 2; // Periodic box size arguments are set when the kernel is executed.
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            pairEnergyKernel.setArg<cl_uint>(index++, maxTiles);
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            if (cl.getSIMDWidth() == 32 || deviceIsCpu)
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                pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getInteractionFlags().getDeviceBuffer());
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        }
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        else
            pairEnergyKernel.setArg<cl_uint>(index++, cl.getNumAtomBlocks()*(cl.getNumAtomBlocks()+1)/2);
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        if (globals != NULL)
            pairEnergyKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            pairEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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            pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
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        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
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            pairEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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            pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
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        }
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        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);
            }
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        }
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        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());
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        perParticleEnergyKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
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        perParticleEnergyKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
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        perParticleEnergyKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        if (globals != NULL)
            perParticleEnergyKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++)
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            perParticleEnergyKernel.setArg<cl::Memory>(index++, params->getBuffers()[i].getMemory());
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        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++)
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            perParticleEnergyKernel.setArg<cl::Memory>(index++, computedValues->getBuffers()[i].getMemory());
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        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++)
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            perParticleEnergyKernel.setArg<cl::Memory>(index++, energyDerivs->getBuffers()[i].getMemory());
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        if (useLong)
            perParticleEnergyKernel.setArg<cl::Memory>(index++, longEnergyDerivs->getDeviceBuffer());
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        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());
        }
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        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());
        }
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    }
    if (globals != NULL) {
        bool changed = false;
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        for (int i = 0; i < (int) globalParamNames.size(); i++) {
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            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
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    if (nb.getUseCutoff()) {
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        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());
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        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
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            pairValueKernel.setArg<cl::Buffer>(8, nb.getInteractingTiles().getDeviceBuffer());
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            pairValueKernel.setArg<cl_uint>(12, maxTiles);
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            pairEnergyKernel.setArg<cl::Buffer>(9, nb.getInteractingTiles().getDeviceBuffer());
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            pairEnergyKernel.setArg<cl_uint>(13, maxTiles);
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            if (cl.getSIMDWidth() == 32 || deviceIsCpu) {
                pairValueKernel.setArg<cl::Buffer>(13, nb.getInteractionFlags().getDeviceBuffer());
                pairEnergyKernel.setArg<cl::Buffer>(14, nb.getInteractionFlags().getDeviceBuffer());
            }
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        }
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    }
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    cl.executeKernel(pairValueKernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
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    cl.executeKernel(perParticleValueKernel, cl.getPaddedNumAtoms());
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    cl.executeKernel(pairEnergyKernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
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    cl.executeKernel(perParticleEnergyKernel, cl.getPaddedNumAtoms());
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    if (needParameterGradient)
        cl.executeKernel(gradientChainRuleKernel, cl.getPaddedNumAtoms());
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    return 0.0;
}

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class OpenCLCustomExternalForceInfo : public OpenCLForceInfo {
public:
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    OpenCLCustomExternalForceInfo(const CustomExternalForce& force, int numParticles) : OpenCLForceInfo(0), force(force), indices(numParticles, -1) {
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        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);
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        for (int i = 0; i < (int) params1.size(); i++)
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            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) {
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    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;
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    vector<vector<int> > atoms(numParticles, vector<int>(1));
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    params = new OpenCLParameterSet(cl, force.getNumPerParticleParameters(), numParticles, "customExternalParams");
    vector<vector<cl_float> > paramVector(numParticles);
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    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
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        force.getParticleParameters(startIndex+i, atoms[i][0], parameters);
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        paramVector[i].resize(parameters.size());
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        for (int j = 0; j < (int) parameters.size(); j++)
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            paramVector[i][j] = (cl_float) parameters[j];
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    }
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    params->setParameterValues(paramVector);
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    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;
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    variables["x"] = "pos1.x";
    variables["y"] = "pos1.y";
    variables["z"] = "pos1.z";
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    for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
        const string& name = force.getPerParticleParameterName(i);
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        variables[name] = "particleParams"+params->getParameterSuffix(i);
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    }
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    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;
        }
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    }
    stringstream compute;
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    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" particleParams"<<(i+1)<<" = "<<argName<<"[index];\n";
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    }
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    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
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    map<string, string> replacements;
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    replacements["COMPUTE_FORCE"] = compute.str();
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::customExternalForce, replacements), force.getForceGroup());
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}

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double OpenCLCalcCustomExternalForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (globals != NULL) {
        bool changed = false;
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        for (int i = 0; i < (int) globalParamNames.size(); i++) {
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            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;
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}
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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();
    }
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Peter Eastman committed
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        int p1, p2, p3;
        vector<double> parameters;
        if (index < force.getNumDonors()) {
            force.getDonorParameters(index, p1, p2, p3, parameters);
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            particles.clear();
            particles.push_back(p1);
            if (p2 > -1)
                particles.push_back(p2);
            if (p3 > -1)
                particles.push_back(p3);
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            return;
        }
        index -= force.getNumDonors();
        if (index < force.getNumAcceptors()) {
            force.getAcceptorParameters(index, p1, p2, p3, parameters);
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            particles.clear();
            particles.push_back(p1);
            if (p2 > -1)
                particles.push_back(p2);
            if (p3 > -1)
                particles.push_back(p3);
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            return;
        }
        index -= force.getNumAcceptors();
        int donor, acceptor;
        force.getExclusionParticles(index, donor, acceptor);
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        particles.clear();
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        force.getDonorParameters(donor, p1, p2, p3, parameters);
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        particles.push_back(p1);
        if (p2 > -1)
            particles.push_back(p2);
        if (p3 > -1)
            particles.push_back(p3);
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        force.getAcceptorParameters(acceptor, p1, p2, p3, parameters);
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        particles.push_back(p1);
        if (p2 > -1)
            particles.push_back(p2);
        if (p3 > -1)
            particles.push_back(p3);
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    }
    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;
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    if (donorExclusions != NULL)
        delete donorExclusions;
    if (acceptorExclusions != NULL)
        delete acceptorExclusions;
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    if (tabulatedFunctionParams != NULL)
        delete tabulatedFunctionParams;
    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        delete tabulatedFunctions[i];
}

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

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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumDonors()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumDonors()/numContexts;
    numDonors = endIndex-startIndex;
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    numAcceptors = force.getNumAcceptors();
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    if (numDonors == 0 || numAcceptors == 0)
        return;
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    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;
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        force.getDonorParameters(startIndex+i, donorVector[i].x, donorVector[i].y, donorVector[i].z, parameters);
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        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);

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    // Select an output buffer index for each donor and acceptor.
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    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);
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    vector<int> donorBufferCounter(numParticles, 0);
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    for (int i = 0; i < numDonors; i++)
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        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);
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    vector<int> acceptorBufferCounter(numParticles, 0);
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    for (int i = 0; i < numAcceptors; i++)
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        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);
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    donorBufferIndices->upload(donorBufferVector);
    acceptorBufferIndices->upload(acceptorBufferVector);
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    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));
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    // Record exclusions.

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    vector<mm_int4> donorExclusionVector(numDonors, mm_int4(-1, -1, -1, -1));
    vector<mm_int4> acceptorExclusionVector(numAcceptors, mm_int4(-1, -1, -1, -1));
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    for (int i = 0; i < force.getNumExclusions(); i++) {
        int donor, acceptor;
        force.getExclusionParticles(i, donor, acceptor);
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        if (donor < startIndex || donor >= endIndex)
            continue;
        donor -= startIndex;
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        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");
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    }
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    donorExclusions = new OpenCLArray<mm_int4>(cl, numDonors, "customHbondDonorExclusions");
    acceptorExclusions = new OpenCLArray<mm_int4>(cl, numDonors, "customHbondAcceptorExclusions");
    donorExclusions->upload(donorExclusionVector);
    acceptorExclusions->upload(acceptorExclusionVector);
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    // 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;
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        force.getFunctionParameters(i, name, values, min, max);
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        string arrayName = "table"+intToString(i);
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        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = &fp;
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        tabulatedFunctionParamsVec[i] = mm_float4((float) min, (float) max, (float) ((values.size()-1)/(max-min)), (float) values.size()-2);
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        vector<mm_float4> f = OpenCLExpressionUtilities::computeFunctionCoefficients(values, min, max);
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        tabulatedFunctions.push_back(new OpenCLArray<mm_float4>(cl, values.size()-1, "TabulatedFunction"));
        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
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        tableArgs << ", __global const float4* restrict " << arrayName;
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    }
    if (force.getNumFunctions() > 0) {
        tabulatedFunctionParams = new OpenCLArray<mm_float4>(cl, tabulatedFunctionParamsVec.size(), "tabulatedFunctionParameters", false, CL_MEM_READ_ONLY);
        tabulatedFunctionParams->upload(tabulatedFunctionParamsVec);
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        tableArgs << ", __global const float4* restrict functionParams";
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    }

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    // Record information about parameters.
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    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)+"]";
    }
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    // 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.

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

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

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double OpenCLCalcCustomHbondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numDonors == 0 || numAcceptors == 0)
        return 0.0;
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    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;
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        donorKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        donorKernel.setArg<cl::Buffer>(index++, donorExclusions->getDeviceBuffer());
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        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);
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        index += 2; // Periodic box size arguments are set when the kernel is executed.
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        if (globals != NULL)
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            donorKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
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        for (int i = 0; i < (int) donorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = donorParams->getBuffers()[i];
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            donorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        }
        for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
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            donorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        }
        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());
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        acceptorKernel.setArg<cl::Buffer>(index++, acceptorExclusions->getDeviceBuffer());
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        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);
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        index += 2; // Periodic box size arguments are set when the kernel is executed.
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        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];
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            acceptorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        }
        for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
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            acceptorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        }
        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());
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        }
    }
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    donorKernel.setArg<mm_float4>(8, cl.getPeriodicBoxSize());
    donorKernel.setArg<mm_float4>(9, cl.getInvPeriodicBoxSize());
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    cl.executeKernel(donorKernel, max(numDonors, numAcceptors));
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    acceptorKernel.setArg<mm_float4>(8, cl.getPeriodicBoxSize());
    acceptorKernel.setArg<mm_float4>(9, cl.getInvPeriodicBoxSize());
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    cl.executeKernel(acceptorKernel, max(numDonors, numAcceptors));
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    return 0.0;
}

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class OpenCLCustomCompoundBondForceInfo : public OpenCLForceInfo {
public:
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    OpenCLCustomCompoundBondForceInfo(const CustomCompoundBondForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    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;
}

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OpenCLIntegrateVerletStepKernel::~OpenCLIntegrateVerletStepKernel() {
}

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

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

    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

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    integration.applyConstraints(integrator.getConstraintTolerance());
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    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
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    integration.computeVirtualSites();
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    // Update the time and step count.

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

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

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

void OpenCLIntegrateLangevinStepKernel::execute(ContextImpl& context, const LangevinIntegrator& integrator) {
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    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
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    int numAtoms = cl.getNumAtoms();
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    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
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        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());
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        kernel1.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
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        kernel2.setArg<cl::Buffer>(1, integration.getPosDelta().getDeviceBuffer());
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        kernel2.setArg<cl::Buffer>(2, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, integration.getStepSize().getDeviceBuffer());
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    }
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    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;
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        double vscale = exp(-stepSize/tau);
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        double fscale = (1-vscale)*tau;
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        double noisescale = sqrt(2*kT/tau)*sqrt(0.5*(1-vscale*vscale)*tau);
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        vector<cl_float> p(params->getSize());
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        p[0] = (cl_float) vscale;
        p[1] = (cl_float) fscale;
        p[2] = (cl_float) noisescale;
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        params->upload(p);
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        integration.getStepSize()[0].y = (cl_float) stepSize;
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        integration.getStepSize().upload();
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        prevTemp = temperature;
        prevFriction = friction;
        prevStepSize = stepSize;
    }

    // Call the first integration kernel.

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

    // Apply constraints.

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    integration.applyConstraints(integrator.getConstraintTolerance());
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    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
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    integration.computeVirtualSites();
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    // Update the time and step count.

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
}
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OpenCLIntegrateBrownianStepKernel::~OpenCLIntegrateBrownianStepKernel() {
}

void OpenCLIntegrateBrownianStepKernel::initialize(const System& system, const BrownianIntegrator& integrator) {
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    cl.getPlatformData().initializeContexts(system);
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    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
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    cl::Program program = cl.createProgram(OpenCLKernelSources::brownian, defines, "");
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    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());
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        kernel1.setArg<cl::Buffer>(4, cl.getVelm().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
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        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.

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

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
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    integration.computeVirtualSites();
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    // Update the time and step count.

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
}
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OpenCLIntegrateVariableVerletStepKernel::~OpenCLIntegrateVariableVerletStepKernel() {
}

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

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double OpenCLIntegrateVariableVerletStepKernel::execute(ContextImpl& context, const VariableVerletIntegrator& integrator, double maxTime) {
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    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
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    int numAtoms = cl.getNumAtoms();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl_int>(0, numAtoms);
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        kernel1.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
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        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);
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        kernel2.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
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        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);
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        selectSizeKernel.setArg<cl::Buffer>(3, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
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        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);
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    selectSizeKernel.setArg<cl_float>(2, (cl_float) integrator.getErrorTolerance());
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    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);
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    integration.computeVirtualSites();
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    // Update the time and step count.

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

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

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

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double OpenCLIntegrateVariableLangevinStepKernel::execute(ContextImpl& context, const VariableLangevinIntegrator& integrator, double maxTime) {
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    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
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    int numAtoms = cl.getNumAtoms();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
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        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());
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        kernel1.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
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        kernel2.setArg<cl::Buffer>(1, integration.getPosDelta().getDeviceBuffer());
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        kernel2.setArg<cl::Buffer>(2, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, integration.getStepSize().getDeviceBuffer());
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        selectSizeKernel.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
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        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);
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    }

    // Select the step size to use.

    float maxStepSize = (float)(maxTime-cl.getTime());
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    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()));
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    cl.executeKernel(selectSizeKernel, blockSize, blockSize);

    // Call the first integration kernel.

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

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
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    integration.computeVirtualSites();
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    // Update the time and step count.

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

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class OpenCLIntegrateCustomStepKernel::ReorderListener : public OpenCLContext::ReorderListener {
public:
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    ReorderListener(OpenCLContext& cl, OpenCLParameterSet& perDofValues, vector<vector<cl_float> >& localPerDofValues, bool& deviceValuesAreCurrent) :
            cl(cl), perDofValues(perDofValues), localPerDofValues(localPerDofValues), deviceValuesAreCurrent(deviceValuesAreCurrent) {
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        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.

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        if (perDofValues.getNumParameters() == 0)
            return;
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        int numAtoms = cl.getNumAtoms();
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        if (deviceValuesAreCurrent)
            perDofValues.getParameterValues(localPerDofValues);
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        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];
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        deviceValuesAreCurrent = true;
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    }
private:
    OpenCLContext& cl;
    OpenCLParameterSet& perDofValues;
    vector<vector<cl_float> >& localPerDofValues;
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    bool& deviceValuesAreCurrent;
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    vector<int> lastAtomOrder;
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};

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OpenCLIntegrateCustomStepKernel::~OpenCLIntegrateCustomStepKernel() {
    if (globalValues != NULL)
        delete globalValues;
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    if (contextParameterValues != NULL)
        delete contextParameterValues;
    if (sumBuffer != NULL)
        delete sumBuffer;
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    if (energy != NULL)
        delete energy;
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    if (uniformRandoms != NULL)
        delete uniformRandoms;
    if (randomSeed != NULL)
        delete randomSeed;
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    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);
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    sumBuffer = new OpenCLArray<cl_float>(cl, 3*system.getNumParticles(), "sumBuffer");
    energy = new OpenCLArray<cl_float>(cl, 1, "energy");
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    perDofValues = new OpenCLParameterSet(cl, integrator.getNumPerDofVariables(), 3*system.getNumParticles(), "perDofVariables");
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    cl.addReorderListener(new ReorderListener(cl, *perDofValues, localPerDofValues, deviceValuesAreCurrent));
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    prevStepSize = -1.0;
    SimTKOpenMMUtilities::setRandomNumberSeed(integrator.getRandomNumberSeed());
}

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

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

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;
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        // 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();
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        kernels.resize(integrator.getNumComputations());
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        requiredGaussian.resize(integrator.getNumComputations(), 0);
        requiredUniform.resize(integrator.getNumComputations(), 0);
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        needsForces.resize(numSteps, false);
        needsEnergy.resize(numSteps, false);
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        forceGroup.resize(numSteps, -2);
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        invalidatesForces.resize(numSteps, false);
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        merged.resize(numSteps, false);
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        modifiesParameters = false;
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        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());
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        // 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);
        }
        
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        // Record information about all the computation steps.
        
        stepType.resize(numSteps);
        vector<string> variable(numSteps);
        vector<Lepton::ParsedExpression> expression(numSteps);
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        vector<string> forceGroupName;
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        vector<string> energyGroupName;
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        for (int i = 0; i < 32; i++) {
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            stringstream fname;
            fname << "f" << i;
            forceGroupName.push_back(fname.str());
            stringstream ename;
            ename << "energy" << i;
            energyGroupName.push_back(ename.str());
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        }
        vector<string> forceName(numSteps, "f");
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        vector<string> energyName(numSteps, "energy");
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        for (int step = 0; step < numSteps; step++) {
            string expr;
            integrator.getComputationStep(step, stepType[step], variable[step], expr);
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            if (expr.size() > 0) {
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                expression[step] = Lepton::Parser::parse(expr).optimize();
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                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];
                    }
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                    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];
                    }
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                }
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            }
            invalidatesForces[step] = (stepType[step] == CustomIntegrator::ConstrainPositions || affectsForce.find(variable[step]) != affectsForce.end());
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            if (forceGroup[step] == -2 && step > 0)
                forceGroup[step] = forceGroup[step-1];
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        }
        
        // 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;
        }
        
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        // Identify steps that can be merged into a single kernel.
        
        for (int step = 1; step < numSteps; step++) {
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            if (needsForces[step] || needsEnergy[step])
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                continue;
            if (stepType[step-1] == CustomIntegrator::ComputeGlobal && stepType[step] == CustomIntegrator::ComputeGlobal)
                merged[step] = true;
            if (stepType[step-1] == CustomIntegrator::ComputePerDof && stepType[step] == CustomIntegrator::ComputePerDof &&
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                    !usesVariable(expression[step], "uniform"))
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                merged[step] = true;
        }
        
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        // Loop over all steps and create the kernels for them.
        
        for (int step = 0; step < numSteps; step++) {
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            if ((stepType[step] == CustomIntegrator::ComputePerDof || stepType[step] == CustomIntegrator::ComputeSum) && !merged[step]) {
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                // 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";
                }
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                string convert = (cl.getSupportsDoublePrecision() ? "convert_float4(" : "(");
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                int numGaussian = 0, numUniform = 0;
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                for (int j = step; j < numSteps && (j == step || merged[j]); j++) {
                    compute << "{\n";
                    for (int i = 0; i < 3; i++)
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                        compute << createPerDofComputation(stepType[j] == CustomIntegrator::ComputePerDof ? variable[j] : "", expression[j], i, integrator, forceName[j], energyName[j]);
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                    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";
                        }
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                        else
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                            compute << "posq[index] = " << convert << "position);\n";
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                    }
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                    else if (variable[j] == "v")
                        compute << "velm[index] = " << convert << "velocity);\n";
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                    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";
                        }
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                    }
                    compute << "}\n";
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                    numGaussian += numAtoms*usesVariable(expression[j], "gaussian");
                    numUniform += numAtoms*usesVariable(expression[j], "uniform");
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                }
                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();
4194
4195
4196
4197
                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");
4198
4199
4200
                cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customIntegratorPerDof, replacements), defines);
                cl::Kernel kernel = cl::Kernel(program, "computePerDof");
                kernels[step].push_back(kernel);
4201
4202
                requiredGaussian[step] = numGaussian;
                requiredUniform[step] = numUniform;
4203
4204
4205
4206
4207
4208
4209
                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());
4210
4211
                kernel.setArg<cl::Buffer>(index++, contextParameterValues->getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, sumBuffer->getDeviceBuffer());
4212
                kernel.setArg<cl::Buffer>(index++, integration.getRandom().getDeviceBuffer());
4213
                index++;
4214
                kernel.setArg<cl::Buffer>(index++, uniformRandoms->getDeviceBuffer());
4215
                kernel.setArg<cl::Buffer>(index++, energy->getDeviceBuffer());
4216
4217
                for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++)
                    kernel.setArg<cl::Memory>(index++, perDofValues->getBuffers()[i].getMemory());
4218
                if (stepType[step] == CustomIntegrator::ComputeSum) {
4219
4220
                    // Create a second kernel for this step that sums the values.

4221
                    program = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
4222
4223
4224
4225
4226
4227
                    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++)
4228
                        if (variable[step] == integrator.getGlobalVariableName(j)) {
4229
4230
4231
4232
4233
                            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++)
4234
                        if (variable[step] == parameterNames[j]) {
4235
4236
4237
4238
4239
4240
                            kernel.setArg<cl::Buffer>(index++, contextParameterValues->getDeviceBuffer());
                            kernel.setArg<cl_uint>(index++, j);
                            found = true;
                            modifiesParameters = true;
                        }
                    if (!found)
4241
                        throw OpenMMException("Unknown global variable: "+variable[step]);
4242
                    kernel.setArg<cl_int>(index++, 3*numAtoms);
4243
                }
4244
            }
4245
            else if (stepType[step] == CustomIntegrator::ComputeGlobal && !merged[step]) {
4246
4247
4248
                // Compute a global value.

                stringstream compute;
4249
                for (int i = step; i < numSteps && (i == step || merged[i]); i++)
4250
                    compute << "{\n" << createGlobalComputation(variable[i], expression[i], integrator, energyName[i]) << "}\n";
4251
4252
4253
4254
4255
4256
4257
4258
                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());
4259
                kernel.setArg<cl::Buffer>(index++, contextParameterValues->getDeviceBuffer());
4260
4261
                index += 2;
                kernel.setArg<cl::Buffer>(index++, energy->getDeviceBuffer());
4262
            }
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
            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());
            }
4273
        }
4274
4275
4276
4277
4278
4279
4280
4281
        
        // 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());
4282
4283
        sumEnergyKernel.setArg<cl_int>(index++, 0);
        sumEnergyKernel.setArg<cl_int>(index++, cl.getEnergyBuffer().getSize());
4284
    }
4285
4286
4287
    
    // Make sure all values (variables, parameters, etc.) stored on the device are up to date.
    
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
    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;
    }
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
    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();
4309
4310
4311
4312

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

    for (int i = 0; i < numSteps; i++) {
4313
        if ((needsForces[i] || needsEnergy[i]) && (!forcesAreValid || context.getLastForceGroups() != forceGroup[i])) {
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
            // 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;
            }
4330
            recordChangedParameters(context);
4331
            context.calcForcesAndEnergy(computeForce, computeEnergy, forceGroup[i]);
4332
            if (computeEnergy)
4333
                cl.executeKernel(sumEnergyKernel, OpenCLContext::ThreadBlockSize, OpenCLContext::ThreadBlockSize);
4334
4335
            forcesAreValid = true;
        }
4336
        if (stepType[i] == CustomIntegrator::ComputePerDof && !merged[i]) {
4337
4338
4339
            kernels[i][0].setArg<cl_uint>(9, integration.prepareRandomNumbers(requiredGaussian[i]));
            if (requiredUniform[i] > 0)
                cl.executeKernel(randomKernel, numAtoms);
4340
4341
            cl.executeKernel(kernels[i][0], numAtoms);
        }
4342
        else if (stepType[i] == CustomIntegrator::ComputeGlobal && !merged[i]) {
4343
4344
            kernels[i][0].setArg<cl_float>(3, SimTKOpenMMUtilities::getUniformlyDistributedRandomNumber());
            kernels[i][0].setArg<cl_float>(4, SimTKOpenMMUtilities::getNormallyDistributedRandomNumber());
4345
            cl.executeKernel(kernels[i][0], 1, 1);
4346
        }
4347
        else if (stepType[i] == CustomIntegrator::ComputeSum) {
4348
4349
4350
            kernels[i][0].setArg<cl_uint>(9, integration.prepareRandomNumbers(requiredGaussian[i]));
            if (requiredUniform[i] > 0)
                cl.executeKernel(randomKernel, numAtoms);
4351
4352
4353
4354
4355
            cl.executeKernel(kernels[i][0], numAtoms);
            cl.executeKernel(kernels[i][1], OpenCLContext::ThreadBlockSize, OpenCLContext::ThreadBlockSize);
        }
        else if (stepType[i] == CustomIntegrator::UpdateContextState) {
            recordChangedParameters(context);
4356
            context.updateContextState();
4357
        }
4358
4359
4360
        else if (stepType[i] == CustomIntegrator::ConstrainPositions) {
            cl.getIntegrationUtilities().applyConstraints(integrator.getConstraintTolerance());
            cl.executeKernel(kernels[i][0], numAtoms);
4361
            cl.getIntegrationUtilities().computeVirtualSites();
4362
        }
4363
4364
4365
        else if (stepType[i] == CustomIntegrator::ConstrainVelocities) {
            cl.getIntegrationUtilities().applyVelocityConstraints(integrator.getConstraintTolerance());
        }
4366
4367
4368
        if (invalidatesForces[i])
            forcesAreValid = false;
    }
4369
    recordChangedParameters(context);
4370
4371
4372
4373
4374
4375
4376

    // Update the time and step count.

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

4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
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));
    }
}

4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
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);
4407
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
4408
4409
    for (int i = 0; i < (int) values.size(); i++)
        for (int j = 0; j < 3; j++)
4410
            values[order[i]][j] = localPerDofValues[3*i+j][variable];
4411
4412
4413
4414
4415
4416
4417
}

void OpenCLIntegrateCustomStepKernel::setPerDofVariable(ContextImpl& context, int variable, const vector<Vec3>& values) {
    if (!localValuesAreCurrent) {
        perDofValues->getParameterValues(localPerDofValues);
        localValuesAreCurrent = true;
    }
4418
    OpenCLArray<cl_int>& order = cl.getAtomIndex();
4419
4420
    for (int i = 0; i < (int) values.size(); i++)
        for (int j = 0; j < 3; j++)
4421
            localPerDofValues[3*i+j][variable] = (float) values[order[i]][j];
4422
4423
4424
    deviceValuesAreCurrent = false;
}

4425
OpenCLApplyAndersenThermostatKernel::~OpenCLApplyAndersenThermostatKernel() {
4426
4427
    if (atomGroups != NULL)
        delete atomGroups;
4428
4429
4430
4431
4432
4433
}

void OpenCLApplyAndersenThermostatKernel::initialize(const System& system, const AndersenThermostat& thermostat) {
    randomSeed = thermostat.getRandomNumberSeed();
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
4434
    cl::Program program = cl.createProgram(OpenCLKernelSources::andersenThermostat, defines);
4435
    kernel = cl::Kernel(program, "applyAndersenThermostat");
4436
4437
4438
4439
4440
4441
4442
4443
4444
4445
4446

    // 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);
4447
4448
4449
4450
4451
4452
4453
4454
4455
}

void OpenCLApplyAndersenThermostatKernel::execute(ContextImpl& context) {
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        cl.getIntegrationUtilities().initRandomNumberGenerator(randomSeed);
        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());
4456
        kernel.setArg<cl::Buffer>(6, atomGroups->getDeviceBuffer());
4457
4458
4459
4460
4461
4462
4463
    }
    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());
}

4464
4465
4466
4467
4468
4469
4470
4471
4472
4473
4474
4475
4476
4477
4478
4479
4480
4481
4482
4483
4484
4485
4486
4487
4488
4489
4490
4491
4492
4493
4494
4495
4496
4497
4498
4499
4500
4501
4502
4503
4504
4505
4506
4507
4508
4509
4510
4511
4512
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());
4513
4514
    for (int i = 0; i < (int) cl.getPosCellOffsets().size(); i++)
        cl.getPosCellOffsets()[i] = mm_int4(0, 0, 0, 0);
4515
4516
4517
4518
4519
4520
}

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

4521
4522
4523
4524
4525
4526
4527
4528
4529
4530
4531
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.

4532
    OpenCLArray<mm_float4>& velm = cl.getVelm();
4533
    velm.download();
4534
    double energy = 0.0;
4535
    for (size_t i = 0; i < masses.size(); ++i) {
4536
4537
        mm_float4 v = velm[i];
        energy += masses[i]*(v.x*v.x+v.y*v.y+v.z*v.z);
4538
    }
4539
4540
    return 0.5*energy;
}
4541
4542
4543
4544
4545
4546
4547
4548
4549
4550
4551
4552
4553
4554
4555

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);
4556
    cl::Program program = cl.createProgram(OpenCLKernelSources::removeCM, defines);
4557
4558
4559
4560
4561
4562
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
    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());
}