OpenCLKernels.cpp 193 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/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/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 <cmath>
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#include <set>
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using namespace OpenMM;
using namespace std;

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

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void OpenCLCalcForcesAndEnergyKernel::beginComputation(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (cl.getNonbondedUtilities().getUseCutoff() && cl.getComputeForceCount()%100 == 0) {
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        cl.reorderAtoms();
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        cl.getNonbondedUtilities().updateNeighborListSize();
    }
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    cl.setComputeForceCount(cl.getComputeForceCount()+1);
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    cl.clearAutoclearBuffers();
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    cl.getNonbondedUtilities().prepareInteractions();
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}

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double OpenCLCalcForcesAndEnergyKernel::finishComputation(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    cl.getBondedUtilities().computeInteractions();
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    cl.getNonbondedUtilities().computeInteractions();
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    if (includeForces)
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        cl.reduceForces();
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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, std::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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    }
}

void OpenCLUpdateStateDataKernel::setPositions(ContextImpl& context, const std::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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}

void OpenCLUpdateStateDataKernel::getVelocities(ContextImpl& context, std::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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    }
}

void OpenCLUpdateStateDataKernel::setVelocities(ContextImpl& context, const std::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();
}

void OpenCLUpdateStateDataKernel::getForces(ContextImpl& context, std::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 OpenCLApplyConstraintsKernel::initialize(const System& system) {
}

void OpenCLApplyConstraintsKernel::apply(ContextImpl& context, double tol) {
    cl.getIntegrationUtilities().applyConstraints(tol);
}

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

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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");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::harmonicBondForce, replacements));
    cl.addForce(new OpenCLBondForceInfo(0, 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:
    OpenCLCustomBondForceInfo(int requiredBuffers, const CustomBondForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumBonds();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        int particle1, particle2;
        vector<double> parameters;
        force.getBondParameters(index, particle1, particle2, parameters);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2;
        vector<double> parameters1, parameters2;
        force.getBondParameters(group1, particle1, particle2, parameters1);
        force.getBondParameters(group2, particle1, particle2, parameters2);
        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
        return true;
    }
private:
    const CustomBondForce& force;
};

OpenCLCalcCustomBondForceKernel::~OpenCLCalcCustomBondForceKernel() {
    if (params != NULL)
        delete params;
    if (indices != NULL)
        delete indices;
    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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    params = new OpenCLParameterSet(cl, force.getNumPerBondParameters(), numBonds, "customBondParams");
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    indices = new OpenCLArray<mm_int4>(cl, numBonds, "customBondIndices");
    string extraArguments;
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customBondGlobals", false, CL_MEM_READ_ONLY);
        extraArguments += ", __constant float* globals";
    }
    vector<int> forceBufferCounter(system.getNumParticles(), 0);
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    vector<vector<cl_float> > paramVector(numBonds);
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    vector<mm_int4> indicesVector(numBonds);
    for (int i = 0; i < numBonds; i++) {
        int particle1, particle2;
        vector<double> parameters;
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        force.getBondParameters(startIndex+i, particle1, particle2, 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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        indicesVector[i] = mm_int4(particle1, particle2, forceBufferCounter[particle1]++, forceBufferCounter[particle2]++);
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    }
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    params->setParameterValues(paramVector);
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    indices->upload(indicesVector);
    int maxBuffers = 1;
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    for (int i = 0; i < (int) forceBufferCounter.size(); i++)
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        maxBuffers = max(maxBuffers, forceBufferCounter[i]);
    cl.addForce(new OpenCLCustomBondForceInfo(maxBuffers, force));

    // Record information for the expressions.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    if (globals != NULL)
        globals->upload(globalParamValues);
    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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    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
        string value = "globals["+intToString(i)+"]";
        variables[name] = value;
    }
    stringstream compute;
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    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        extraArguments += ", __global "+buffer.getType()+"* "+buffer.getName();
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = "<<buffer.getName()<<"[index];\n";
    }
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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();
    replacements["EXTRA_ARGUMENTS"] = extraArguments;
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    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customBondForce, replacements));
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    kernel = cl::Kernel(program, "computeCustomBondForces");
}

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double OpenCLCalcCustomBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numBonds == 0)
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        return 0.0;
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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);
    }
    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        kernel.setArg<cl_int>(0, cl.getPaddedNumAtoms());
        kernel.setArg<cl_int>(1, numBonds);
        kernel.setArg<cl::Buffer>(2, cl.getForceBuffers().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(3, cl.getEnergyBuffer().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(4, cl.getPosq().getDeviceBuffer());
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        kernel.setArg<cl::Buffer>(5, indices->getDeviceBuffer());
        int nextIndex = 6;
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        if (globals != NULL)
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            kernel.setArg<cl::Buffer>(nextIndex++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            kernel.setArg<cl::Memory>(nextIndex++, buffer.getMemory());
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        }
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    }
    cl.executeKernel(kernel, numBonds);
    return 0.0;
}

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

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

void OpenCLCalcHarmonicAngleForceKernel::initialize(const System& system, const HarmonicAngleForce& force) {
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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");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::harmonicAngleForce, replacements));
    cl.addForce(new OpenCLAngleForceInfo(0, 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:
    OpenCLCustomAngleForceInfo(int requiredBuffers, const CustomAngleForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumAngles();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        int particle1, particle2, particle3;
        vector<double> parameters;
        force.getAngleParameters(index, particle1, particle2, particle3, parameters);
        particles.resize(3);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3;
        vector<double> parameters1, parameters2;
        force.getAngleParameters(group1, particle1, particle2, particle3, parameters1);
        force.getAngleParameters(group2, particle1, particle2, particle3, parameters2);
        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
        return true;
    }
private:
    const CustomAngleForce& force;
};

OpenCLCalcCustomAngleForceKernel::~OpenCLCalcCustomAngleForceKernel() {
    if (params != NULL)
        delete params;
    if (indices != NULL)
        delete indices;
    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;
    params = new OpenCLParameterSet(cl, force.getNumPerAngleParameters(), numAngles, "customAngleParams");
    indices = new OpenCLArray<mm_int8>(cl, numAngles, "customAngleIndices");
    string extraArguments;
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customAngleGlobals", false, CL_MEM_READ_ONLY);
        extraArguments += ", __constant float* globals";
    }
    vector<int> forceBufferCounter(system.getNumParticles(), 0);
    vector<vector<cl_float> > paramVector(numAngles);
    vector<mm_int8> indicesVector(numAngles);
    for (int i = 0; i < numAngles; i++) {
        int particle1, particle2, particle3;
        vector<double> parameters;
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        force.getAngleParameters(startIndex+i, particle1, particle2, particle3, 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];
        indicesVector[i] = mm_int8(particle1, particle2, particle3, forceBufferCounter[particle1]++,
                forceBufferCounter[particle2]++, forceBufferCounter[particle3]++, 0, 0);
    }
    params->setParameterValues(paramVector);
    indices->upload(indicesVector);
    int maxBuffers = 1;
    for (int i = 0; i < (int) forceBufferCounter.size(); i++)
        maxBuffers = max(maxBuffers, forceBufferCounter[i]);
    cl.addForce(new OpenCLCustomAngleForceInfo(maxBuffers, force));

    // Record information for the expressions.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    if (globals != NULL)
        globals->upload(globalParamValues);
    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);
    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
        string value = "globals["+intToString(i)+"]";
        variables[name] = value;
    }
    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        extraArguments += ", __global "+buffer.getType()+"* "+buffer.getName();
        compute<<buffer.getType()<<" angleParams"<<(i+1)<<" = "<<buffer.getName()<<"[index];\n";
    }
    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
    replacements["EXTRA_ARGUMENTS"] = extraArguments;
    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customAngleForce, replacements));
    kernel = cl::Kernel(program, "computeCustomAngleForces");
}

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double OpenCLCalcCustomAngleForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numAngles == 0)
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        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;
        kernel.setArg<cl_int>(0, cl.getPaddedNumAtoms());
        kernel.setArg<cl_int>(1, numAngles);
        kernel.setArg<cl::Buffer>(2, cl.getForceBuffers().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(3, cl.getEnergyBuffer().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(4, cl.getPosq().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(5, indices->getDeviceBuffer());
        int nextIndex = 6;
        if (globals != NULL)
            kernel.setArg<cl::Buffer>(nextIndex++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            kernel.setArg<cl::Memory>(nextIndex++, buffer.getMemory());
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        }
    }
    cl.executeKernel(kernel, numAngles);
    return 0.0;
}

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class OpenCLPeriodicTorsionForceInfo : public OpenCLForceInfo {
public:
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    OpenCLPeriodicTorsionForceInfo(int requiredBuffers, const PeriodicTorsionForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        int particle1, particle2, particle3, particle4, periodicity;
        double phase, k;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, periodicity, phase, k);
        particles.resize(4);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
        particles[3] = particle4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3, particle4, periodicity1, periodicity2;
        double phase1, phase2, k1, k2;
        force.getTorsionParameters(group1, particle1, particle2, particle3, particle4, periodicity1, phase1, k1);
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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");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::periodicTorsionForce, replacements));
    cl.addForce(new OpenCLPeriodicTorsionForceInfo(0, 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(int requiredBuffers, const RBTorsionForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        int particle1, particle2, particle3, particle4;
        double c0, c1, c2, c3, c4, c5;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, c0, c1, c2, c3, c4, c5);
        particles.resize(4);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
        particles[3] = particle4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3, particle4;
        double c0a, c0b, c1a, c1b, c2a, c2b, c3a, c3b, c4a, c4b, c5a, c5b;
        force.getTorsionParameters(group1, particle1, particle2, particle3, particle4, c0a, c1a, c2a, c3a, c4a, c5a);
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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");
    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::rbTorsionForce, replacements));
    cl.addForce(new OpenCLRBTorsionForceInfo(0, 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:
    OpenCLCMAPTorsionForceInfo(int requiredBuffers, const CMAPTorsionForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        int map, a1, a2, a3, a4, b1, b2, b3, b4;
        force.getTorsionParameters(index, map, a1, a2, a3, a4, b1, b2, b3, b4);
        particles.resize(8);
        particles[0] = a1;
        particles[1] = a2;
        particles[2] = a3;
        particles[3] = a4;
        particles[4] = b1;
        particles[5] = b2;
        particles[6] = b3;
        particles[7] = b4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int map1, map2, a1, a2, a3, a4, b1, b2, b3, b4;
        force.getTorsionParameters(group1, map1, a1, a2, a3, a4, b1, b2, b3, b4);
        force.getTorsionParameters(group2, map2, a1, a2, a3, a4, b1, b2, b3, b4);
        return (map1 == map2);
    }
private:
    const CMAPTorsionForce& force;
};

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

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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        }
    }
    vector<int> forceBufferCounter(system.getNumParticles(), 0);
    vector<cl_int> torsionMapsVec(numTorsions);
    vector<mm_int16> torsionIndicesVec(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        mm_int16& ind = torsionIndicesVec[i];
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        force.getTorsionParameters(startIndex+i, torsionMapsVec[i], ind.s0, ind.s1, ind.s2, ind.s3, ind.s4, ind.s5, ind.s6, ind.s7);
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        ind.s8 = forceBufferCounter[ind.s0]++;
        ind.s9 = forceBufferCounter[ind.s1]++;
        ind.s10 = forceBufferCounter[ind.s2]++;
        ind.s11 = forceBufferCounter[ind.s3]++;
        ind.s12 = forceBufferCounter[ind.s4]++;
        ind.s13 = forceBufferCounter[ind.s5]++;
        ind.s14 = forceBufferCounter[ind.s6]++;
        ind.s15 = forceBufferCounter[ind.s7]++;
    }
    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");
    torsionIndices = new OpenCLArray<mm_int16>(cl, numTorsions, "cmapTorsionIndices");
    coefficients->upload(coeffVec);
    mapPositions->upload(mapPositionsVec);
    torsionMaps->upload(torsionMapsVec);
    torsionIndices->upload(torsionIndicesVec);
    int maxBuffers = 1;
    for (int i = 0; i < (int) forceBufferCounter.size(); i++)
        maxBuffers = max(maxBuffers, forceBufferCounter[i]);
    cl.addForce(new OpenCLCMAPTorsionForceInfo(maxBuffers, force));
    cl::Program program = cl.createProgram(OpenCLKernelSources::cmapTorsionForce);
    kernel = cl::Kernel(program, "computeCMAPTorsionForces");
}

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double OpenCLCalcCMAPTorsionForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numTorsions == 0)
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        return 0.0;
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    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        kernel.setArg<cl_int>(0, cl.getPaddedNumAtoms());
        kernel.setArg<cl_int>(1, numTorsions);
        kernel.setArg<cl::Buffer>(2, cl.getForceBuffers().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(3, cl.getEnergyBuffer().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(4, cl.getPosq().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(5, coefficients->getDeviceBuffer());
        kernel.setArg<cl::Buffer>(6, mapPositions->getDeviceBuffer());
        kernel.setArg<cl::Buffer>(7, torsionIndices->getDeviceBuffer());
        kernel.setArg<cl::Buffer>(8, torsionMaps->getDeviceBuffer());
    }
    cl.executeKernel(kernel, numTorsions);
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    return 0.0;
}

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class OpenCLCustomTorsionForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomTorsionForceInfo(int requiredBuffers, const CustomTorsionForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        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 (indices != NULL)
        delete indices;
    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;
    params = new OpenCLParameterSet(cl, force.getNumPerTorsionParameters(), numTorsions, "customTorsionParams");
    indices = new OpenCLArray<mm_int8>(cl, numTorsions, "customTorsionIndices");
    string extraArguments;
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customTorsionGlobals", false, CL_MEM_READ_ONLY);
        extraArguments += ", __constant float* globals";
    }
    vector<int> forceBufferCounter(system.getNumParticles(), 0);
    vector<vector<cl_float> > paramVector(numTorsions);
    vector<mm_int8> indicesVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        int particle1, particle2, particle3, particle4;
        vector<double> parameters;
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        force.getTorsionParameters(startIndex+i, particle1, particle2, particle3, particle4, 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];
        indicesVector[i] = mm_int8(particle1, particle2, particle3, particle4, forceBufferCounter[particle1]++,
                forceBufferCounter[particle2]++, forceBufferCounter[particle3]++, forceBufferCounter[particle4]++);
    }
    params->setParameterValues(paramVector);
    indices->upload(indicesVector);
    int maxBuffers = 1;
    for (int i = 0; i < (int) forceBufferCounter.size(); i++)
        maxBuffers = max(maxBuffers, forceBufferCounter[i]);
    cl.addForce(new OpenCLCustomTorsionForceInfo(maxBuffers, force));

    // Record information for the expressions.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    if (globals != NULL)
        globals->upload(globalParamValues);
    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);
    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
        string value = "globals["+intToString(i)+"]";
        variables[name] = value;
    }
    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        extraArguments += ", __global "+buffer.getType()+"* "+buffer.getName();
        compute<<buffer.getType()<<" torsionParams"<<(i+1)<<" = "<<buffer.getName()<<"[index];\n";
    }
    vector<pair<string, string> > functions;
    compute << OpenCLExpressionUtilities::createExpressions(expressions, variables, functions, "temp", "");
    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
    replacements["EXTRA_ARGUMENTS"] = extraArguments;
    replacements["M_PI"] = doubleToString(M_PI);
    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customTorsionForce, replacements));
    kernel = cl::Kernel(program, "computeCustomTorsionForces");
}

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double OpenCLCalcCustomTorsionForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numTorsions == 0)
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        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;
        kernel.setArg<cl_int>(0, cl.getPaddedNumAtoms());
        kernel.setArg<cl_int>(1, numTorsions);
        kernel.setArg<cl::Buffer>(2, cl.getForceBuffers().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(3, cl.getEnergyBuffer().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(4, cl.getPosq().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(5, indices->getDeviceBuffer());
        int nextIndex = 6;
        if (globals != NULL)
            kernel.setArg<cl::Buffer>(nextIndex++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            kernel.setArg<cl::Memory>(nextIndex++, buffer.getMemory());
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        }
    }
    cl.executeKernel(kernel, numTorsions);
    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();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        int particle1, particle2;
        double chargeProd, sigma, epsilon;
        force.getExceptionParameters(index, particle1, particle2, chargeProd, sigma, epsilon);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2;
        double chargeProd1, chargeProd2, sigma1, sigma2, epsilon1, epsilon2;
        force.getExceptionParameters(group1, particle1, particle2, chargeProd1, sigma1, epsilon1);
        force.getExceptionParameters(group2, particle1, particle2, chargeProd2, sigma2, epsilon2);
        return (chargeProd1 == chargeProd2 && sigma1 == sigma2 && epsilon1 == epsilon2);
    }
private:
    const NonbondedForce& force;
};

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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;
    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/std::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/std::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);
        pmeDefines["EPSILON_FACTOR"] = doubleToString(std::sqrt(ONE_4PI_EPS0));

        // 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");
        pmeAtomRange = new OpenCLArray<cl_int>(cl, gridSizeX*gridSizeY*gridSizeZ+1, "pmeAtomRange");
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        pmeAtomGridIndex = new OpenCLArray<mm_int2>(cl, numParticles, "pmeAtomGridIndex");
        sort = new OpenCLSort<mm_int2>(cl, cl.getNumAtoms(), "int2", "value.y");
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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);
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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");
        cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::nonbondedExceptions, replacements));
    }
    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) {
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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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            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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            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) {
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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) {
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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 = ewaldSelfEnergy;
    if (dispersionCoefficient != 0.0) {
        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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    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        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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    map<string, string> variables;
    variables["r"] = "r";
    for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
        const string& name = force.getPerParticleParameterName(i);
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        variables[name+"1"] = prefix+"params"+params->getParameterSuffix(i, "1");
        variables[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[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);
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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);
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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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        if (cl.getSIMDWidth() == 32)
            defines["WARPS_PER_GROUP"] = OpenCLExpressionUtilities::intToString(cl.getNonbondedUtilities().getForceThreadBlockSize()/OpenCLContext::TileSize);
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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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        computeBornSumKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*13*sizeof(cl_float), NULL);
        computeBornSumKernel.setArg(index++, (deviceIsCpu ? 1 : nb.getForceThreadBlockSize())*sizeof(cl_float), NULL);
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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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        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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        force1Kernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*13*sizeof(cl_float), NULL);
        force1Kernel.setArg(index++, (deviceIsCpu ? 1 : nb.getForceThreadBlockSize())*sizeof(mm_float4), NULL);
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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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        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>(7, cl.getPeriodicBoxSize());
        computeBornSumKernel.setArg<mm_float4>(8, cl.getInvPeriodicBoxSize());
        force1Kernel.setArg<mm_float4>(9, cl.getPeriodicBoxSize());
        force1Kernel.setArg<mm_float4>(10, cl.getInvPeriodicBoxSize());
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        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
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            computeBornSumKernel.setArg<cl_uint>(10, maxTiles);
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            force1Kernel.setArg<cl_uint>(11, maxTiles);
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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();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        int particle1, particle2;
        force.getExclusionParticles(index, particle1, particle2);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        return true;
    }
private:
    const CustomGBForce& force;
};

OpenCLCalcCustomGBForceKernel::~OpenCLCalcCustomGBForceKernel() {
    if (params != NULL)
        delete params;
    if (computedValues != NULL)
        delete computedValues;
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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 float4* " << 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 << ", __constant 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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        map<string, string> variables;
        map<string, string> rename;
        variables["r"] = "r";
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        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
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            variables[name+"1"] = "params"+params->getParameterSuffix(i, "1");
            variables[name+"2"] = "params"+params->getParameterSuffix(i, "2");
            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[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)
            extraArgs << ", __constant float* globals";
        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 " << buffer.getType() << "* global_" << paramName << ", __local " << buffer.getType() << "* 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)
            extraArgs << ", __constant float* globals";
        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);
            extraArgs << ", __global " << buffer.getType() << "* " << 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() << "* global_" << valueName;
            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();
            reductionSource << OpenCLExpressionUtilities::createExpressions(valueExpressions, variables, functionDefinitions, "value"+intToString(i)+"_temp", "functionParams");
        }
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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.

        map<string, string> variables;
        variables["r"] = "r";
        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
            variables[name+"1"] = "params"+params->getParameterSuffix(i, "1");
            variables[name+"2"] = "params"+params->getParameterSuffix(i, "2");
        }
        for (int i = 0; i < force.getNumComputedValues(); i++) {
            variables[computedValueNames[i]+"1"] = "values"+computedValues->getParameterSuffix(i, "1");
            variables[computedValueNames[i]+"2"] = "values"+computedValues->getParameterSuffix(i, "2");
        }
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables[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)
            extraArgs << ", __constant float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* global_" << paramName << ", __local " << buffer.getType() << "* 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);
            extraArgs << ", __global " << buffer.getType() << "* global_" << valueName << ", __local " << buffer.getType() << "* 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) {
            extraArgs << ", __global long* derivBuffers";
            for (int i = 0; i < force.getNumComputedValues(); i++) {
                string index = intToString(i+1);
                extraArgs << ", __local float* local_deriv" << index;
                clearLocal << "local_deriv" << index << "[localAtomIndex] = 0.0f;\n";
                declare1 << "float deriv" << index << "_1 = 0.0f;\n";
                load2 << "float deriv" << index << "_2 = 0.0f;\n";
                recordDeriv << "local_deriv" << index << "[atom2] += deriv" << index << "_2;\n";
                storeDerivs1 << "STORE_DERIVATIVE_1(" << index << ")\n";
                storeDerivs2 << "STORE_DERIVATIVE_2(" << index << ")\n";
                declareTemps << "__local float tempDerivBuffer" << index << "[64];\n";
                setTemps << "tempDerivBuffer" << index << "[get_local_id(0)] = deriv" << index << "_1;\n";
            }
        }
        else {
            for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
                string index = intToString(i+1);
                extraArgs << ", __global " << buffer.getType() << "* derivBuffers" << index << ", __local " << buffer.getType() << "* local_deriv" << index;
                clearLocal << "local_deriv" << index << "[localAtomIndex] = 0.0f;\n";
                declare1 << buffer.getType() << " deriv" << index << "_1 = 0.0f;\n";
                load2 << buffer.getType() << " deriv" << index << "_2 = 0.0f;\n";
                recordDeriv << "local_deriv" << index << "[atom2] += deriv" << index << "_2;\n";
                storeDerivs1 << "STORE_DERIVATIVE_1(" << index << ")\n";
                storeDerivs2 << "STORE_DERIVATIVE_2(" << index << ")\n";
                declareTemps << "__local " << buffer.getType() << " tempDerivBuffer" << index << "[64];\n";
                setTemps << "tempDerivBuffer" << index << "[get_local_id(0)] = deriv" << index << "_1;\n";
            }
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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)
            extraArgs << ", __constant float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* " << paramName;
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* " << 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);
            extraArgs << ", __global " << buffer.getType() << "* derivBuffers" << index;
            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
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        if (useLong) {
            extraArgs << ", __global long* derivBuffersIn";
            for (int i = 0; i < energyDerivs->getNumParameters(); ++i)
                reduce << "derivBuffers" << energyDerivs->getParameterSuffix(i, "[index]") <<
                        " = (1.0f/0xFFFFFFFF)*derivBuffersIn[index+PADDED_NUM_ATOMS*" << intToString(i) << "];\n";
        }
        else {
            for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++)
                reduce << "REDUCE_VALUE(derivBuffers" << intToString(i+1) << ", " << energyDerivs->getBuffers()[i].getType() << ")\n";
        }
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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)
            extraArgs << ", __constant float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* " << paramName;
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* " << valueName;
        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            string index = intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* derivBuffers" << index;
            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
        map<string, string> variables;
        variables["x"] = "pos.x";
        variables["y"] = "pos.y";
        variables["z"] = "pos.z";
        for (int i = 0; i < force.getNumPerParticleParameters(); i++)
            variables[force.getPerParticleParameterName(i)] = "params"+params->getParameterSuffix(i, "[index]");
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables[force.getGlobalParameterName(i)] = "globals["+intToString(i)+"]";
        for (int i = 0; i < force.getNumComputedValues(); i++)
            variables[computedValueNames[i]] = "values"+computedValues->getParameterSuffix(i, "[index]");
        for (int i = 1; i < force.getNumComputedValues(); i++) {
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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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        map<string, string> globalVariables;
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+intToString(i)+"]";
            globalVariables[name] = prefix+value;
        }
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        map<string, string> variables = globalVariables;
        map<string, string> rename;
        variables["r"] = "r";
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        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
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            variables[name+"1"] = prefix+"params"+params->getParameterSuffix(i, "1");
            variables[name+"2"] = prefix+"params"+params->getParameterSuffix(i, "2");
            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["x1"] = "posq1.x";
        variables["y1"] = "posq1.y";
        variables["z1"] = "posq1.z";
        variables["x2"] = "posq2.x";
        variables["y2"] = "posq2.y";
        variables["z2"] = "posq2.z";
        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[name+"1"] = prefix+"params"+params->getParameterSuffix(i, "1");
            variables[name+"2"] = prefix+"params"+params->getParameterSuffix(i, "2");
            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[name+"1"] = prefix+"values"+computedValues->getParameterSuffix(i, "1");
            variables[name+"2"] = prefix+"values"+computedValues->getParameterSuffix(i, "2");
            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);
        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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    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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    if (useLong)
        cl.addAutoclearBuffer(longEnergyDerivs->getDeviceBuffer(), 2*longEnergyDerivs->getSize());
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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++, 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);
        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++, 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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        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_uint>(12, maxTiles);
            pairEnergyKernel.setArg<cl_uint>(13, maxTiles);
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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:
    OpenCLCustomExternalForceInfo(const CustomExternalForce& force, int numParticles) : OpenCLForceInfo(1), force(force), indices(numParticles, -1) {
        vector<double> params;
        for (int i = 0; i < force.getNumParticles(); i++) {
            int particle;
            force.getParticleParameters(i, particle, params);
            indices[particle] = i;
        }
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        particle1 = indices[particle1];
        particle2 = indices[particle2];
        if (particle1 == -1 && particle2 == -1)
            return true;
        if (particle1 == -1 || particle2 == -1)
            return false;
        int temp;
        vector<double> params1;
        vector<double> params2;
        force.getParticleParameters(particle1, temp, params1);
        force.getParticleParameters(particle2, temp, params2);
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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 (indices != NULL)
        delete indices;
    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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    params = new OpenCLParameterSet(cl, force.getNumPerParticleParameters(), numParticles, "customExternalParams");
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    indices = new OpenCLArray<cl_int>(cl, numParticles, "customExternalIndices");
    string extraArguments;
    if (force.getNumGlobalParameters() > 0) {
        globals = new OpenCLArray<cl_float>(cl, force.getNumGlobalParameters(), "customExternalGlobals", false, CL_MEM_READ_ONLY);
        extraArguments += ", __constant float* globals";
    }
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    vector<vector<cl_float> > paramVector(numParticles);
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    vector<cl_int> indicesVector(numParticles);
    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
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        force.getParticleParameters(startIndex+i, indicesVector[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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    }
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    params->setParameterValues(paramVector);
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    indices->upload(indicesVector);
    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);
    }
    if (globals != NULL)
        globals->upload(globalParamValues);
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction()).optimize();
    Lepton::ParsedExpression forceExpressionX = energyExpression.differentiate("x").optimize();
    Lepton::ParsedExpression forceExpressionY = energyExpression.differentiate("y").optimize();
    Lepton::ParsedExpression forceExpressionZ = energyExpression.differentiate("z").optimize();
    map<string, Lepton::ParsedExpression> expressions;
    expressions["energy += "] = energyExpression;
    expressions["float dEdX = "] = forceExpressionX;
    expressions["float dEdY = "] = forceExpressionY;
    expressions["float dEdZ = "] = forceExpressionZ;

    // Create the kernels.

    map<string, string> variables;
    variables["x"] = "pos.x";
    variables["y"] = "pos.y";
    variables["z"] = "pos.z";
    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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    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
        string value = "globals["+intToString(i)+"]";
        variables[name] = value;
    }
    stringstream compute;
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    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        extraArguments += ", __global "+buffer.getType()+"* "+buffer.getName();
        compute<<buffer.getType()<<" particleParams"<<(i+1)<<" = "<<buffer.getName()<<"[index];\n";
    }
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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();
    replacements["EXTRA_ARGUMENTS"] = extraArguments;
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    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customExternalForce, replacements));
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    kernel = cl::Kernel(program, "computeCustomExternalForces");
}

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double OpenCLCalcCustomExternalForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numParticles == 0)
        return 0.0;
2721
2722
    if (globals != NULL) {
        bool changed = false;
2723
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
            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;
        kernel.setArg<cl_int>(0, numParticles);
        kernel.setArg<cl::Buffer>(1, cl.getForceBuffers().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(2, cl.getEnergyBuffer().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(3, cl.getPosq().getDeviceBuffer());
2738
2739
        kernel.setArg<cl::Buffer>(4, indices->getDeviceBuffer());
        int nextIndex = 5;
2740
        if (globals != NULL)
2741
2742
2743
            kernel.setArg<cl::Buffer>(nextIndex++, globals->getDeviceBuffer());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
2744
            kernel.setArg<cl::Memory>(nextIndex++, buffer.getMemory());
2745
        }
2746
2747
2748
    }
    cl.executeKernel(kernel, numParticles);
    return 0.0;
2749
}
2750

2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
class OpenCLCustomHbondForceInfo : public OpenCLForceInfo {
public:
    OpenCLCustomHbondForceInfo(int requiredBuffers, const CustomHbondForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        return true;
    }
    int getNumParticleGroups() {
        return force.getNumDonors()+force.getNumAcceptors()+force.getNumExclusions();
    }
    void getParticlesInGroup(int index, std::vector<int>& particles) {
        int p1, p2, p3;
        vector<double> parameters;
        if (index < force.getNumDonors()) {
            force.getDonorParameters(index, p1, p2, p3, parameters);
2766
2767
2768
2769
2770
2771
            particles.clear();
            particles.push_back(p1);
            if (p2 > -1)
                particles.push_back(p2);
            if (p3 > -1)
                particles.push_back(p3);
2772
2773
2774
2775
2776
            return;
        }
        index -= force.getNumDonors();
        if (index < force.getNumAcceptors()) {
            force.getAcceptorParameters(index, p1, p2, p3, parameters);
2777
2778
2779
2780
2781
2782
            particles.clear();
            particles.push_back(p1);
            if (p2 > -1)
                particles.push_back(p2);
            if (p3 > -1)
                particles.push_back(p3);
2783
2784
2785
2786
2787
            return;
        }
        index -= force.getNumAcceptors();
        int donor, acceptor;
        force.getExclusionParticles(index, donor, acceptor);
2788
        particles.clear();
2789
        force.getDonorParameters(donor, p1, p2, p3, parameters);
2790
2791
2792
2793
2794
        particles.push_back(p1);
        if (p2 > -1)
            particles.push_back(p2);
        if (p3 > -1)
            particles.push_back(p3);
2795
        force.getAcceptorParameters(acceptor, p1, p2, p3, parameters);
2796
2797
2798
2799
2800
        particles.push_back(p1);
        if (p2 > -1)
            particles.push_back(p2);
        if (p3 > -1)
            particles.push_back(p3);
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
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2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
    }
    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;
2842
2843
2844
2845
    if (donorExclusions != NULL)
        delete donorExclusions;
    if (acceptorExclusions != NULL)
        delete acceptorExclusions;
2846
2847
2848
2849
2850
2851
    if (tabulatedFunctionParams != NULL)
        delete tabulatedFunctionParams;
    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        delete tabulatedFunctions[i];
}

2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
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";
}
2864

2865
void OpenCLCalcCustomHbondForceKernel::initialize(const System& system, const CustomHbondForce& force) {
2866
2867
    // Record the lists of donors and acceptors, and the parameters for each one.

2868
2869
2870
2871
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumDonors()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumDonors()/numContexts;
    numDonors = endIndex-startIndex;
2872
    numAcceptors = force.getNumAcceptors();
2873
2874
    if (numDonors == 0 || numAcceptors == 0)
        return;
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
    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;
2886
        force.getDonorParameters(startIndex+i, donorVector[i].x, donorVector[i].y, donorVector[i].z, parameters);
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
        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);

2905
    // Select an output buffer index for each donor and acceptor.
2906
2907
2908
2909
2910

    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);
2911
    vector<int> donorBufferCounter(numParticles, 0);
2912
    for (int i = 0; i < numDonors; i++)
2913
2914
2915
        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);
2916
    vector<int> acceptorBufferCounter(numParticles, 0);
2917
    for (int i = 0; i < numAcceptors; i++)
2918
2919
2920
        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);
2921
2922
    donorBufferIndices->upload(donorBufferVector);
    acceptorBufferIndices->upload(acceptorBufferVector);
2923
2924
2925
2926
2927
2928
    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));
2929
2930
2931

    // Record exclusions.

2932
2933
    vector<mm_int4> donorExclusionVector(numDonors, mm_int4(-1, -1, -1, -1));
    vector<mm_int4> acceptorExclusionVector(numAcceptors, mm_int4(-1, -1, -1, -1));
2934
2935
2936
    for (int i = 0; i < force.getNumExclusions(); i++) {
        int donor, acceptor;
        force.getExclusionParticles(i, donor, acceptor);
2937
2938
2939
        if (donor < startIndex || donor >= endIndex)
            continue;
        donor -= startIndex;
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
        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");
2960
    }
2961
2962
2963
2964
    donorExclusions = new OpenCLArray<mm_int4>(cl, numDonors, "customHbondDonorExclusions");
    acceptorExclusions = new OpenCLArray<mm_int4>(cl, numDonors, "customHbondAcceptorExclusions");
    donorExclusions->upload(donorExclusionVector);
    acceptorExclusions->upload(acceptorExclusionVector);
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976

    // 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;
2977
        force.getFunctionParameters(i, name, values, min, max);
2978
        string arrayName = "table"+intToString(i);
2979
2980
        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = &fp;
2981
        tabulatedFunctionParamsVec[i] = mm_float4((float) min, (float) max, (float) ((values.size()-1)/(max-min)), (float) values.size()-2);
2982
        vector<mm_float4> f = OpenCLExpressionUtilities::computeFunctionCoefficients(values, min, max);
2983
2984
2985
2986
2987
2988
2989
        tabulatedFunctions.push_back(new OpenCLArray<mm_float4>(cl, values.size()-1, "TabulatedFunction"));
        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
        tableArgs << ", __global float4* " << arrayName;
    }
    if (force.getNumFunctions() > 0) {
        tabulatedFunctionParams = new OpenCLArray<mm_float4>(cl, tabulatedFunctionParamsVec.size(), "tabulatedFunctionParameters", false, CL_MEM_READ_ONLY);
        tabulatedFunctionParams->upload(tabulatedFunctionParamsVec);
2990
        tableArgs << ", __global float4* functionParams";
2991
2992
    }

2993
    // Record information about parameters.
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015

    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)+"]";
    }
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090

    // 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.

3091
    if (force.getNumGlobalParameters() > 0)
3092
        extraArgs << ", __global float* globals";
3093
3094
3095
    for (int i = 0; i < (int) donorParams->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = donorParams->getBuffers()[i];
        extraArgs << ", __global "+buffer.getType()+"* donor"+buffer.getName();
3096
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, buffer.getType()+" donorParams"+intToString(i+1)+" = donor"+buffer.getName()+"[index];\n");
3097
3098
3099
3100
    }
    for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
        extraArgs << ", __global "+buffer.getType()+"* acceptor"+buffer.getName();
3101
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, buffer.getType()+" acceptorParams"+intToString(i+1)+" = acceptor"+buffer.getName()+"[index];\n");
3102
    }
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162

    // 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.

3163
    map<string, string> replacements;
3164
3165
    replacements["COMPUTE_DONOR_FORCE"] = computeDonor.str();
    replacements["COMPUTE_ACCEPTOR_FORCE"] = computeAcceptor.str();
3166
3167
3168
    replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
    map<string, string> defines;
    defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
3169
3170
    defines["NUM_DONORS"] = intToString(numDonors);
    defines["NUM_ACCEPTORS"] = intToString(numAcceptors);
3171
    defines["M_PI"] = doubleToString(M_PI);
3172
3173
3174
3175
3176
3177
    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";
3178
3179
    if (force.getNumExclusions() > 0)
        defines["USE_EXCLUSIONS"] = "1";
3180
    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customHbondForce, replacements), defines);
3181
3182
    donorKernel = cl::Kernel(program, "computeDonorForces");
    acceptorKernel = cl::Kernel(program, "computeAcceptorForces");
3183
3184
}

3185
double OpenCLCalcCustomHbondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
3186
3187
    if (numDonors == 0 || numAcceptors == 0)
        return 0.0;
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
    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;
3202
3203
3204
        donorKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
3205
        donorKernel.setArg<cl::Buffer>(index++, donorExclusions->getDeviceBuffer());
3206
3207
3208
3209
        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);
3210
        index += 2; // Periodic box size arguments are set when the kernel is executed.
3211
        if (globals != NULL)
3212
            donorKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
3213
3214
        for (int i = 0; i < (int) donorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = donorParams->getBuffers()[i];
3215
            donorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
3216
3217
3218
        }
        for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
3219
            donorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
        }
        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());
3230
        acceptorKernel.setArg<cl::Buffer>(index++, acceptorExclusions->getDeviceBuffer());
3231
3232
3233
3234
        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);
3235
        index += 2; // Periodic box size arguments are set when the kernel is executed.
3236
3237
3238
3239
        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];
3240
            acceptorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
3241
3242
3243
        }
        for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
3244
            acceptorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
3245
3246
3247
3248
3249
        }
        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());
3250
3251
        }
    }
3252
3253
    donorKernel.setArg<mm_float4>(8, cl.getPeriodicBoxSize());
    donorKernel.setArg<mm_float4>(9, cl.getInvPeriodicBoxSize());
3254
    cl.executeKernel(donorKernel, std::max(numDonors, numAcceptors));
3255
3256
    acceptorKernel.setArg<mm_float4>(8, cl.getPeriodicBoxSize());
    acceptorKernel.setArg<mm_float4>(9, cl.getInvPeriodicBoxSize());
3257
    cl.executeKernel(acceptorKernel, std::max(numDonors, numAcceptors));
3258
3259
3260
    return 0.0;
}

3261
3262
3263
3264
OpenCLIntegrateVerletStepKernel::~OpenCLIntegrateVerletStepKernel() {
}

void OpenCLIntegrateVerletStepKernel::initialize(const System& system, const VerletIntegrator& integrator) {
3265
    cl.getPlatformData().initializeContexts(system);
3266
    cl::Program program = cl.createProgram(OpenCLKernelSources::verlet, "");
3267
3268
    kernel1 = cl::Kernel(program, "integrateVerletPart1");
    kernel2 = cl::Kernel(program, "integrateVerletPart2");
3269
    prevStepSize = -1.0;
3270
3271
3272
}

void OpenCLIntegrateVerletStepKernel::execute(ContextImpl& context, const VerletIntegrator& integrator) {
3273
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
3274
3275
    int numAtoms = cl.getNumAtoms();
    double dt = integrator.getStepSize();
3276
3277
3278
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl_int>(0, numAtoms);
3279
        kernel1.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
3280
3281
3282
3283
3284
        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);
3285
        kernel2.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
3286
3287
3288
3289
        kernel2.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(4, integration.getPosDelta().getDeviceBuffer());
    }
3290
3291
    if (dt != prevStepSize) {
        vector<mm_float2> stepSizeVec(1);
3292
        stepSizeVec[0] = mm_float2((cl_float) dt, (cl_float) dt);
3293
        cl.getIntegrationUtilities().getStepSize().upload(stepSizeVec);
3294
3295
        prevStepSize = dt;
    }
3296
3297
3298
3299
3300
3301
3302

    // Call the first integration kernel.

    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

3303
    integration.applyConstraints(integrator.getConstraintTolerance());
3304
3305
3306
3307
3308
3309
3310
3311
3312

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);

    // Update the time and step count.

    cl.setTime(cl.getTime()+dt);
    cl.setStepCount(cl.getStepCount()+1);
3313
3314
}

3315
3316
3317
3318
3319
3320
OpenCLIntegrateLangevinStepKernel::~OpenCLIntegrateLangevinStepKernel() {
    if (params != NULL)
        delete params;
}

void OpenCLIntegrateLangevinStepKernel::initialize(const System& system, const LangevinIntegrator& integrator) {
3321
    cl.getPlatformData().initializeContexts(system);
3322
3323
3324
3325
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
    defines["PADDED_NUM_ATOMS"] = intToString(cl.getPaddedNumAtoms());
3326
    cl::Program program = cl.createProgram(OpenCLKernelSources::langevin, defines, "");
3327
3328
    kernel1 = cl::Kernel(program, "integrateLangevinPart1");
    kernel2 = cl::Kernel(program, "integrateLangevinPart2");
3329
    params = new OpenCLArray<cl_float>(cl, 3, "langevinParams");
3330
3331
3332
3333
    prevStepSize = -1.0;
}

void OpenCLIntegrateLangevinStepKernel::execute(ContextImpl& context, const LangevinIntegrator& integrator) {
3334
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
3335
    int numAtoms = cl.getNumAtoms();
3336
3337
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
3338
3339
3340
3341
        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());
3342
3343
3344
        kernel1.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
3345
        kernel2.setArg<cl::Buffer>(1, integration.getPosDelta().getDeviceBuffer());
3346
3347
        kernel2.setArg<cl::Buffer>(2, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, integration.getStepSize().getDeviceBuffer());
3348
    }
3349
3350
3351
3352
3353
3354
3355
3356
    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;
3357
3358
3359
        double vscale = std::exp(-stepSize/tau);
        double fscale = (1-vscale)*tau;
        double noisescale = std::sqrt(2*kT/tau)*std::sqrt(0.5*(1-vscale*vscale)*tau);
3360
        vector<cl_float> p(params->getSize());
3361
3362
3363
        p[0] = (cl_float) vscale;
        p[1] = (cl_float) fscale;
        p[2] = (cl_float) noisescale;
3364
        params->upload(p);
3365
        integration.getStepSize()[0].y = (cl_float) stepSize;
3366
        integration.getStepSize().upload();
3367
3368
3369
3370
3371
3372
3373
        prevTemp = temperature;
        prevFriction = friction;
        prevStepSize = stepSize;
    }

    // Call the first integration kernel.

3374
    kernel1.setArg<cl_uint>(6, integration.prepareRandomNumbers(cl.getPaddedNumAtoms()));
3375
3376
3377
3378
    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

3379
    integration.applyConstraints(integrator.getConstraintTolerance());
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);

    // Update the time and step count.

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
}
3390
3391
3392
3393
3394

OpenCLIntegrateBrownianStepKernel::~OpenCLIntegrateBrownianStepKernel() {
}

void OpenCLIntegrateBrownianStepKernel::initialize(const System& system, const BrownianIntegrator& integrator) {
3395
    cl.getPlatformData().initializeContexts(system);
3396
3397
3398
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
3399
    cl::Program program = cl.createProgram(OpenCLKernelSources::brownian, defines, "");
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
    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());
3412
3413
        kernel1.setArg<cl::Buffer>(4, cl.getVelm().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
        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.

3433
    kernel1.setArg<cl_uint>(6, integration.prepareRandomNumbers(cl.getPaddedNumAtoms()));
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);

    // Update the time and step count.

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
}
3449
3450
3451
3452
3453

OpenCLIntegrateVariableVerletStepKernel::~OpenCLIntegrateVariableVerletStepKernel() {
}

void OpenCLIntegrateVariableVerletStepKernel::initialize(const System& system, const VariableVerletIntegrator& integrator) {
3454
    cl.getPlatformData().initializeContexts(system);
3455
    cl::Program program = cl.createProgram(OpenCLKernelSources::verlet, "");
3456
3457
3458
3459
3460
3461
3462
    kernel1 = cl::Kernel(program, "integrateVerletPart1");
    kernel2 = cl::Kernel(program, "integrateVerletPart2");
    selectSizeKernel = cl::Kernel(program, "selectVerletStepSize");
    blockSize = std::min(std::min(256, system.getNumParticles()), (int) cl.getDevice().getInfo<CL_DEVICE_MAX_WORK_GROUP_SIZE>());
}

void OpenCLIntegrateVariableVerletStepKernel::execute(ContextImpl& context, const VariableVerletIntegrator& integrator, double maxTime) {
3463
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
3464
3465
3466
3467
    int numAtoms = cl.getNumAtoms();
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl_int>(0, numAtoms);
3468
        kernel1.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
3469
3470
3471
3472
3473
        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);
3474
        kernel2.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
3475
3476
3477
3478
        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);
3479
        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);
3489
    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);

    // 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);
}

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

void OpenCLIntegrateVariableLangevinStepKernel::initialize(const System& system, const VariableLangevinIntegrator& integrator) {
3521
    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 = std::min(256, system.getNumParticles());
    blockSize = std::max(blockSize, params->getSize());
    blockSize = std::min(blockSize, (int) cl.getDevice().getInfo<CL_DEVICE_MAX_WORK_GROUP_SIZE>());
}

void OpenCLIntegrateVariableLangevinStepKernel::execute(ContextImpl& context, const VariableLangevinIntegrator& integrator, double maxTime) {
3537
    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);

    // 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);
}

3592
OpenCLApplyAndersenThermostatKernel::~OpenCLApplyAndersenThermostatKernel() {
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    if (atomGroups != NULL)
        delete atomGroups;
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}

void OpenCLApplyAndersenThermostatKernel::initialize(const System& system, const AndersenThermostat& thermostat) {
    randomSeed = thermostat.getRandomNumberSeed();
    map<string, string> defines;
    defines["NUM_ATOMS"] = intToString(cl.getNumAtoms());
3601
    cl::Program program = cl.createProgram(OpenCLKernelSources::andersenThermostat, defines);
3602
    kernel = cl::Kernel(program, "applyAndersenThermostat");
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    // 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);
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}

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());
3623
        kernel.setArg<cl::Buffer>(6, atomGroups->getDeviceBuffer());
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    }
    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());
}

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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());
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3681
    for (int i = 0; i < (int) cl.getPosCellOffsets().size(); i++)
        cl.getPosCellOffsets()[i] = mm_int4(0, 0, 0, 0);
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3687
}

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

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3698
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.

3699
    OpenCLArray<mm_float4>& velm = cl.getVelm();
3700
    velm.download();
3701
    double energy = 0.0;
3702
    for (size_t i = 0; i < masses.size(); ++i) {
3703
3704
        mm_float4 v = velm[i];
        energy += masses[i]*(v.x*v.x+v.y*v.y+v.z*v.z);
3705
    }
3706
3707
    return 0.5*energy;
}
3708
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3711
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3713
3714
3715
3716
3717
3718
3719
3720
3721
3722

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);
3723
    cl::Program program = cl.createProgram(OpenCLKernelSources::removeCM, defines);
3724
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3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
    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());
}