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OpenCLKernels.cpp 440 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) 2008-2017 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/CustomCentroidBondForceImpl.h"
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#include "openmm/internal/CustomCompoundBondForceImpl.h"
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#include "openmm/internal/CustomHbondForceImpl.h"
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#include "openmm/internal/CustomManyParticleForceImpl.h"
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#include "openmm/internal/CustomNonbondedForceImpl.h"
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#include "openmm/internal/NonbondedForceImpl.h"
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#include "openmm/internal/OSRngSeed.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/CustomFunction.h"
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#include "lepton/ExpressionTreeNode.h"
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#include "lepton/Operation.h"
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#include "lepton/Parser.h"
#include "lepton/ParsedExpression.h"
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#include "ReferenceTabulatedFunction.h"
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#include "SimTKOpenMMRealType.h"
#include "SimTKOpenMMUtilities.h"
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#include <algorithm>
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#include <cmath>
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#include <set>
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using namespace OpenMM;
using namespace std;
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using namespace Lepton;
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static void setPosqCorrectionArg(OpenCLContext& cl, cl::Kernel& kernel, int index) {
    if (cl.getUseMixedPrecision())
        kernel.setArg<cl::Buffer>(index, cl.getPosqCorrection().getDeviceBuffer());
    else
        kernel.setArg<void*>(index, NULL);
}

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static void setPeriodicBoxSizeArg(OpenCLContext& cl, cl::Kernel& kernel, int index) {
    if (cl.getUseDoublePrecision())
        kernel.setArg<mm_double4>(index, cl.getPeriodicBoxSizeDouble());
    else
        kernel.setArg<mm_float4>(index, cl.getPeriodicBoxSize());
}

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static void setPeriodicBoxArgs(OpenCLContext& cl, cl::Kernel& kernel, int index) {
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    if (cl.getUseDoublePrecision()) {
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        kernel.setArg<mm_double4>(index++, cl.getPeriodicBoxSizeDouble());
        kernel.setArg<mm_double4>(index++, cl.getInvPeriodicBoxSizeDouble());
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        kernel.setArg<mm_double4>(index++, cl.getPeriodicBoxVecXDouble());
        kernel.setArg<mm_double4>(index++, cl.getPeriodicBoxVecYDouble());
        kernel.setArg<mm_double4>(index, cl.getPeriodicBoxVecZDouble());
    }
    else {
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        kernel.setArg<mm_float4>(index++, cl.getPeriodicBoxSize());
        kernel.setArg<mm_float4>(index++, cl.getInvPeriodicBoxSize());
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        kernel.setArg<mm_float4>(index++, cl.getPeriodicBoxVecX());
        kernel.setArg<mm_float4>(index++, cl.getPeriodicBoxVecY());
        kernel.setArg<mm_float4>(index, cl.getPeriodicBoxVecZ());
    }
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}

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

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static bool usesVariable(const Lepton::ExpressionTreeNode& node, const string& variable) {
    const Lepton::Operation& op = node.getOperation();
    if (op.getId() == Lepton::Operation::VARIABLE && op.getName() == variable)
        return true;
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    for (auto& child : node.getChildren())
        if (usesVariable(child, variable))
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            return true;
    return false;
}

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

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

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

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void OpenCLCalcForcesAndEnergyKernel::beginComputation(ContextImpl& context, bool includeForces, bool includeEnergy, int groups) {
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    cl.setForcesValid(true);
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    cl.clearAutoclearBuffers();
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    for (auto computation : cl.getPreComputations())
        computation->computeForceAndEnergy(includeForces, includeEnergy, groups);
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    OpenCLNonbondedUtilities& nb = cl.getNonbondedUtilities();
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    cl.setComputeForceCount(cl.getComputeForceCount()+1);
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    nb.prepareInteractions(groups);
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    map<string, double>& derivs = cl.getEnergyParamDerivWorkspace();
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    for (auto& param : context.getParameters())
        derivs[param.first] = 0;
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}

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double OpenCLCalcForcesAndEnergyKernel::finishComputation(ContextImpl& context, bool includeForces, bool includeEnergy, int groups, bool& valid) {
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    cl.getBondedUtilities().computeInteractions(groups);
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    cl.getNonbondedUtilities().computeInteractions(groups, includeForces, includeEnergy);
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    double sum = 0.0;
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    for (auto computation : cl.getPostComputations())
        sum += computation->computeForceAndEnergy(includeForces, includeEnergy, groups);
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    cl.reduceForces();
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    cl.getIntegrationUtilities().distributeForcesFromVirtualSites();
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    if (includeEnergy)
        sum += cl.reduceEnergy();
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    if (!cl.getForcesValid())
        valid = false;
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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;
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    for (auto ctx : contexts)
        ctx->setTime(time);
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}

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void OpenCLUpdateStateDataKernel::getPositions(ContextImpl& context, vector<Vec3>& positions) {
    int numParticles = context.getSystem().getNumParticles();
    positions.resize(numParticles);
    vector<mm_float4> posCorrection;
    if (cl.getUseDoublePrecision()) {
        mm_double4* posq = (mm_double4*) cl.getPinnedBuffer();
        cl.getPosq().download(posq);
    }
    else if (cl.getUseMixedPrecision()) {
        mm_float4* posq = (mm_float4*) cl.getPinnedBuffer();
        cl.getPosq().download(posq, false);
        posCorrection.resize(numParticles);
        cl.getPosqCorrection().download(posCorrection);
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    }
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    else {
        mm_float4* posq = (mm_float4*) cl.getPinnedBuffer();
        cl.getPosq().download(posq);
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    }
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    // Filling in the output array is done in parallel for speed.
    
    cl.getPlatformData().threads.execute([&] (ThreadPool& threads, int threadIndex) {
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        // Compute the position of each particle to return to the user.  This is done in parallel for speed.
        
        const vector<int>& order = cl.getAtomIndex();
        int numParticles = cl.getNumAtoms();
        Vec3 boxVectors[3];
        cl.getPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
        int numThreads = threads.getNumThreads();
        int start = threadIndex*numParticles/numThreads;
        int end = (threadIndex+1)*numParticles/numThreads;
        if (cl.getUseDoublePrecision()) {
            mm_double4* posq = (mm_double4*) cl.getPinnedBuffer();
            for (int i = start; i < end; ++i) {
                mm_double4 pos = posq[i];
                mm_int4 offset = cl.getPosCellOffsets()[i];
                positions[order[i]] = Vec3(pos.x, pos.y, pos.z)-boxVectors[0]*offset.x-boxVectors[1]*offset.y-boxVectors[2]*offset.z;
            }
        }
        else if (cl.getUseMixedPrecision()) {
            mm_float4* posq = (mm_float4*) cl.getPinnedBuffer();
            for (int i = start; i < end; ++i) {
                mm_float4 pos1 = posq[i];
                mm_float4 pos2 = posCorrection[i];
                mm_int4 offset = cl.getPosCellOffsets()[i];
                positions[order[i]] = Vec3((double)pos1.x+(double)pos2.x, (double)pos1.y+(double)pos2.y, (double)pos1.z+(double)pos2.z)-boxVectors[0]*offset.x-boxVectors[1]*offset.y-boxVectors[2]*offset.z;
            }
        }
        else {
            mm_float4* posq = (mm_float4*) cl.getPinnedBuffer();
            for (int i = start; i < end; ++i) {
                mm_float4 pos = posq[i];
                mm_int4 offset = cl.getPosCellOffsets()[i];
                positions[order[i]] = Vec3(pos.x, pos.y, pos.z)-boxVectors[0]*offset.x-boxVectors[1]*offset.y-boxVectors[2]*offset.z;
            }
        }
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    });
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    cl.getPlatformData().threads.waitForThreads();
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}

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void OpenCLUpdateStateDataKernel::setPositions(ContextImpl& context, const vector<Vec3>& positions) {
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    const vector<cl_int>& order = cl.getAtomIndex();
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    int numParticles = context.getSystem().getNumParticles();
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    if (cl.getUseDoublePrecision()) {
        mm_double4* posq = (mm_double4*) cl.getPinnedBuffer();
        cl.getPosq().download(posq);
        for (int i = 0; i < numParticles; ++i) {
            mm_double4& pos = posq[i];
            const Vec3& p = positions[order[i]];
            pos.x = p[0];
            pos.y = p[1];
            pos.z = p[2];
        }
        for (int i = numParticles; i < cl.getPaddedNumAtoms(); i++)
            posq[i] = mm_double4(0.0, 0.0, 0.0, 0.0);
        cl.getPosq().upload(posq);
    }
    else {
        mm_float4* posq = (mm_float4*) cl.getPinnedBuffer();
        cl.getPosq().download(posq);
        for (int i = 0; i < numParticles; ++i) {
            mm_float4& pos = posq[i];
            const Vec3& p = positions[order[i]];
            pos.x = (cl_float) p[0];
            pos.y = (cl_float) p[1];
            pos.z = (cl_float) p[2];
        }
        for (int i = numParticles; i < cl.getPaddedNumAtoms(); i++)
            posq[i] = mm_float4(0.0f, 0.0f, 0.0f, 0.0f);
        cl.getPosq().upload(posq);
    }
    if (cl.getUseMixedPrecision()) {
        mm_float4* posCorrection = (mm_float4*) cl.getPinnedBuffer();
        for (int i = 0; i < numParticles; ++i) {
            mm_float4& c = posCorrection[i];
            const Vec3& p = positions[order[i]];
            c.x = (cl_float) (p[0]-(cl_float)p[0]);
            c.y = (cl_float) (p[1]-(cl_float)p[1]);
            c.z = (cl_float) (p[2]-(cl_float)p[2]);
            c.w = 0;
        }
        for (int i = numParticles; i < cl.getPaddedNumAtoms(); i++)
            posCorrection[i] = mm_float4(0.0f, 0.0f, 0.0f, 0.0f);
        cl.getPosqCorrection().upload(posCorrection);
    }
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    for (auto& offset : cl.getPosCellOffsets())
        offset = mm_int4(0, 0, 0, 0);
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    cl.reorderAtoms();
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}

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void OpenCLUpdateStateDataKernel::getVelocities(ContextImpl& context, vector<Vec3>& velocities) {
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    const vector<cl_int>& order = cl.getAtomIndex();
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    int numParticles = context.getSystem().getNumParticles();
    velocities.resize(numParticles);
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    if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision()) {
        mm_double4* velm = (mm_double4*) cl.getPinnedBuffer();
        cl.getVelm().download(velm);
        for (int i = 0; i < numParticles; ++i) {
            mm_double4 vel = velm[i];
            mm_int4 offset = cl.getPosCellOffsets()[i];
            velocities[order[i]] = Vec3(vel.x, vel.y, vel.z);
        }
    }
    else {
        mm_float4* velm = (mm_float4*) cl.getPinnedBuffer();
        cl.getVelm().download(velm);
        for (int i = 0; i < numParticles; ++i) {
            mm_float4 vel = velm[i];
            mm_int4 offset = cl.getPosCellOffsets()[i];
            velocities[order[i]] = Vec3(vel.x, vel.y, vel.z);
        }
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    }
}

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void OpenCLUpdateStateDataKernel::setVelocities(ContextImpl& context, const vector<Vec3>& velocities) {
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    const vector<cl_int>& order = cl.getAtomIndex();
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    int numParticles = context.getSystem().getNumParticles();
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    if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision()) {
        mm_double4* velm = (mm_double4*) cl.getPinnedBuffer();
        cl.getVelm().download(velm);
        for (int i = 0; i < numParticles; ++i) {
            mm_double4& vel = velm[i];
            const Vec3& p = velocities[order[i]];
            vel.x = p[0];
            vel.y = p[1];
            vel.z = p[2];
        }
        for (int i = numParticles; i < cl.getPaddedNumAtoms(); i++)
            velm[i] = mm_double4(0.0, 0.0, 0.0, 0.0);
        cl.getVelm().upload(velm);
    }
    else {
        mm_float4* velm = (mm_float4*) cl.getPinnedBuffer();
        cl.getVelm().download(velm);
        for (int i = 0; i < numParticles; ++i) {
            mm_float4& vel = velm[i];
            const Vec3& p = velocities[order[i]];
            vel.x = p[0];
            vel.y = p[1];
            vel.z = p[2];
        }
        for (int i = numParticles; i < cl.getPaddedNumAtoms(); i++)
            velm[i] = mm_float4(0.0f, 0.0f, 0.0f, 0.0f);
        cl.getVelm().upload(velm);
    }
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}

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void OpenCLUpdateStateDataKernel::getForces(ContextImpl& context, vector<Vec3>& forces) {
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    const vector<cl_int>& order = cl.getAtomIndex();
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    int numParticles = context.getSystem().getNumParticles();
    forces.resize(numParticles);
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    if (cl.getUseDoublePrecision()) {
        mm_double4* force = (mm_double4*) cl.getPinnedBuffer();
        cl.getForce().download(force);
        for (int i = 0; i < numParticles; ++i) {
            mm_double4 f = force[i];
            forces[order[i]] = Vec3(f.x, f.y, f.z);
        }
    }
    else {
        mm_float4* force = (mm_float4*) cl.getPinnedBuffer();
        cl.getForce().download(force);
        for (int i = 0; i < numParticles; ++i) {
            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::getEnergyParameterDerivatives(ContextImpl& context, map<string, double>& derivs) {
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    const vector<string>& paramDerivNames = cl.getEnergyParamDerivNames();
    int numDerivs = paramDerivNames.size();
    if (numDerivs == 0)
        return;
    derivs = cl.getEnergyParamDerivWorkspace();
    OpenCLArray& derivArray = cl.getEnergyParamDerivBuffer();
    if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision()) {
        vector<double> derivBuffers;
        derivArray.download(derivBuffers);
        for (int i = numDerivs; i < derivArray.getSize(); i += numDerivs)
            for (int j = 0; j < numDerivs; j++)
                derivBuffers[j] += derivBuffers[i+j];
        for (int i = 0; i < numDerivs; i++)
            derivs[paramDerivNames[i]] += derivBuffers[i];
    }
    else {
        vector<float> derivBuffers;
        derivArray.download(derivBuffers);
        for (int i = numDerivs; i < derivArray.getSize(); i += numDerivs)
            for (int j = 0; j < numDerivs; j++)
                derivBuffers[j] += derivBuffers[i+j];
        for (int i = 0; i < numDerivs; i++)
            derivs[paramDerivNames[i]] += derivBuffers[i];
    }
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}

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void OpenCLUpdateStateDataKernel::getPeriodicBoxVectors(ContextImpl& context, Vec3& a, Vec3& b, Vec3& c) const {
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    cl.getPeriodicBoxVectors(a, b, c);
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}

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void OpenCLUpdateStateDataKernel::setPeriodicBoxVectors(ContextImpl& context, const Vec3& a, const Vec3& b, const Vec3& c) {
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    vector<OpenCLContext*>& contexts = cl.getPlatformData().contexts;
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    // If any particles have been wrapped to the first periodic box, we need to unwrap them
    // to avoid changing their positions.

    vector<Vec3> positions;
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    for (auto offset : cl.getPosCellOffsets()) {
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        if (offset.x != 0 || offset.y != 0 || offset.z != 0) {
            getPositions(context, positions);
            break;
        }
    }
    
    // Update the vectors.

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    for (auto ctx : contexts)
        ctx->setPeriodicBoxVectors(a, b, c);
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    if (positions.size() > 0)
        setPositions(context, positions);
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}

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void OpenCLUpdateStateDataKernel::createCheckpoint(ContextImpl& context, ostream& stream) {
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    int version = 2;
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    stream.write((char*) &version, sizeof(int));
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    int precision = (cl.getUseDoublePrecision() ? 2 : cl.getUseMixedPrecision() ? 1 : 0);
    stream.write((char*) &precision, sizeof(int));
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    double time = cl.getTime();
    stream.write((char*) &time, sizeof(double));
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    int stepCount = cl.getStepCount();
    stream.write((char*) &stepCount, sizeof(int));
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    int stepsSinceReorder = cl.getStepsSinceReorder();
    stream.write((char*) &stepsSinceReorder, sizeof(int));
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    char* buffer = (char*) cl.getPinnedBuffer();
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    cl.getPosq().download(buffer);
    stream.write(buffer, cl.getPosq().getSize()*cl.getPosq().getElementSize());
    if (cl.getUseMixedPrecision()) {
        cl.getPosqCorrection().download(buffer);
        stream.write(buffer, cl.getPosqCorrection().getSize()*cl.getPosqCorrection().getElementSize());
    }
    cl.getVelm().download(buffer);
    stream.write(buffer, cl.getVelm().getSize()*cl.getVelm().getElementSize());
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    stream.write((char*) &cl.getAtomIndex()[0], sizeof(cl_int)*cl.getAtomIndex().size());
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    stream.write((char*) &cl.getPosCellOffsets()[0], sizeof(mm_int4)*cl.getPosCellOffsets().size());
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    Vec3 boxVectors[3];
    cl.getPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
    stream.write((char*) boxVectors, 3*sizeof(Vec3));
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    cl.getIntegrationUtilities().createCheckpoint(stream);
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    SimTKOpenMMUtilities::createCheckpoint(stream);
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}

void OpenCLUpdateStateDataKernel::loadCheckpoint(ContextImpl& context, istream& stream) {
    int version;
    stream.read((char*) &version, sizeof(int));
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    if (version != 2)
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        throw OpenMMException("Checkpoint was created with a different version of OpenMM");
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    int precision;
    stream.read((char*) &precision, sizeof(int));
    int expectedPrecision = (cl.getUseDoublePrecision() ? 2 : cl.getUseMixedPrecision() ? 1 : 0);
    if (precision != expectedPrecision)
        throw OpenMMException("Checkpoint was created with a different numeric precision");
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    double time;
    stream.read((char*) &time, sizeof(double));
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    int stepCount, stepsSinceReorder;
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    stream.read((char*) &stepCount, sizeof(int));
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    stream.read((char*) &stepsSinceReorder, sizeof(int));
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    vector<OpenCLContext*>& contexts = cl.getPlatformData().contexts;
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    for (auto ctx : contexts) {
        ctx->setTime(time);
        ctx->setStepCount(stepCount);
        ctx->setStepsSinceReorder(stepsSinceReorder);
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    }
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    char* buffer = (char*) cl.getPinnedBuffer();
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    stream.read(buffer, cl.getPosq().getSize()*cl.getPosq().getElementSize());
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    cl.getPosq().upload(buffer);
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    if (cl.getUseMixedPrecision()) {
        stream.read(buffer, cl.getPosqCorrection().getSize()*cl.getPosqCorrection().getElementSize());
        cl.getPosqCorrection().upload(buffer);
    }
    stream.read(buffer, cl.getVelm().getSize()*cl.getVelm().getElementSize());
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    cl.getVelm().upload(buffer);
    stream.read((char*) &cl.getAtomIndex()[0], sizeof(cl_int)*cl.getAtomIndex().size());
    cl.getAtomIndexArray().upload(cl.getAtomIndex());
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    stream.read((char*) &cl.getPosCellOffsets()[0], sizeof(mm_int4)*cl.getPosCellOffsets().size());
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    Vec3 boxVectors[3];
    stream.read((char*) &boxVectors, 3*sizeof(Vec3));
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    for (auto ctx : contexts)
        ctx->setPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
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    cl.getIntegrationUtilities().loadCheckpoint(stream);
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    SimTKOpenMMUtilities::loadCheckpoint(stream);
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    for (auto listener : cl.getReorderListeners())
        listener->execute();
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}

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

void OpenCLApplyConstraintsKernel::apply(ContextImpl& context, double tol) {
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    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        map<string, string> defines;
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        defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
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        cl::Program program = cl.createProgram(OpenCLKernelSources::constraints, defines);
        applyDeltasKernel = cl::Kernel(program, "applyPositionDeltas");
        applyDeltasKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
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        setPosqCorrectionArg(cl, applyDeltasKernel, 1);
        applyDeltasKernel.setArg<cl::Buffer>(2, cl.getIntegrationUtilities().getPosDelta().getDeviceBuffer());
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    }
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    cl.clearBuffer(integration.getPosDelta());
    integration.applyConstraints(tol);
    cl.executeKernel(applyDeltasKernel, cl.getNumAtoms());
    integration.computeVirtualSites();
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}

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

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

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

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

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

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void OpenCLCalcHarmonicBondForceKernel::initialize(const System& system, const HarmonicBondForce& force) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumBonds()/numContexts;
    numBonds = endIndex-startIndex;
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    if (numBonds == 0)
        return;
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    vector<vector<int> > atoms(numBonds, vector<int>(2));
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    params = OpenCLArray::create<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;
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    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
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    replacements["COMPUTE_FORCE"] = OpenCLKernelSources::harmonicBondForce;
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    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float2");
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::bondForce, replacements), force.getForceGroup());
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    info = new ForceInfo(force);
    cl.addForce(info);
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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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void OpenCLCalcHarmonicBondForceKernel::copyParametersToContext(ContextImpl& context, const HarmonicBondForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumBonds()/numContexts;
    if (numBonds != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of bonds has changed");
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    if (numBonds == 0)
        return;
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    // Record the per-bond parameters.
    
    vector<mm_float2> paramVector(numBonds);
    for (int i = 0; i < numBonds; i++) {
        int atom1, atom2;
        double length, k;
        force.getBondParameters(startIndex+i, atom1, atom2, length, k);
        paramVector[i] = mm_float2((cl_float) length, (cl_float) k);
    }
    params->upload(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

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

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

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

    map<string, string> variables;
    variables["r"] = "r";
    for (int i = 0; i < force.getNumPerBondParameters(); i++) {
        const string& name = force.getPerBondParameterName(i);
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        variables[name] = "bondParams"+params->getParameterSuffix(i);
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    }
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    if (force.getNumGlobalParameters() > 0) {
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        globals = OpenCLArray::create<cl_float>(cl, force.getNumGlobalParameters(), "customBondGlobals", CL_MEM_READ_ONLY);
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        globals->upload(globalParamValues);
        string argName = cl.getBondedUtilities().addArgument(globals->getDeviceBuffer(), "float");
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
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            string value = argName+"["+cl.intToString(i)+"]";
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            variables[name] = value;
        }
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    }
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cl.getBondedUtilities().addEnergyParameterDerivative(paramName);
        Lepton::ParsedExpression derivExpression = energyExpression.differentiate(paramName).optimize();
        expressions[derivVariable+" += "] = derivExpression;
    }
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    stringstream compute;
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    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = "<<argName<<"[index];\n";
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    }
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    vector<const TabulatedFunction*> functions;
    vector<pair<string, string> > functionNames;
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    compute << cl.getExpressionUtilities().createExpressions(expressions, variables, functions, functionNames, "temp");
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    map<string, string> replacements;
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    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
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    replacements["COMPUTE_FORCE"] = compute.str();
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::bondForce, replacements), force.getForceGroup());
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}

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

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void OpenCLCalcCustomBondForceKernel::copyParametersToContext(ContextImpl& context, const CustomBondForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumBonds()/numContexts;
    if (numBonds != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of bonds has changed");
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    if (numBonds == 0)
        return;
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    // Record the per-bond parameters.
    
    vector<vector<cl_float> > paramVector(numBonds);
    vector<double> parameters;
    for (int i = 0; i < numBonds; i++) {
        int atom1, atom2;
        force.getBondParameters(startIndex+i, atom1, atom2, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

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

void OpenCLCalcHarmonicAngleForceKernel::initialize(const System& system, const HarmonicAngleForce& force) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumAngles()/numContexts;
    numAngles = endIndex-startIndex;
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    if (numAngles == 0)
        return;
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    vector<vector<int> > atoms(numAngles, vector<int>(3));
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    params = OpenCLArray::create<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;
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    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
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    replacements["COMPUTE_FORCE"] = OpenCLKernelSources::harmonicAngleForce;
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    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float2");
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::angleForce, replacements), force.getForceGroup());
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    info = new ForceInfo(force);
    cl.addForce(info);
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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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void OpenCLCalcHarmonicAngleForceKernel::copyParametersToContext(ContextImpl& context, const HarmonicAngleForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumAngles()/numContexts;
    if (numAngles != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of angles has changed");
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    if (numAngles == 0)
        return;
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    // Record the per-angle parameters.
    
    vector<mm_float2> paramVector(numAngles);
    for (int i = 0; i < numAngles; i++) {
        int atom1, atom2, atom3;
        double angle, k;
        force.getAngleParameters(startIndex+i, atom1, atom2, atom3, angle, k);
        paramVector[i] = mm_float2((cl_float) angle, (cl_float) k);
    }
    params->upload(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

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

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

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

    map<string, string> variables;
    variables["theta"] = "theta";
    for (int i = 0; i < force.getNumPerAngleParameters(); i++) {
        const string& name = force.getPerAngleParameterName(i);
        variables[name] = "angleParams"+params->getParameterSuffix(i);
    }
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    if (force.getNumGlobalParameters() > 0) {
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        globals = OpenCLArray::create<cl_float>(cl, force.getNumGlobalParameters(), "customAngleGlobals", CL_MEM_READ_ONLY);
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        globals->upload(globalParamValues);
        string argName = cl.getBondedUtilities().addArgument(globals->getDeviceBuffer(), "float");
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
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            string value = argName+"["+cl.intToString(i)+"]";
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            variables[name] = value;
        }
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    }
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cl.getBondedUtilities().addEnergyParameterDerivative(paramName);
        Lepton::ParsedExpression derivExpression = energyExpression.differentiate(paramName).optimize();
        expressions[derivVariable+" += "] = derivExpression;
    }
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    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" angleParams"<<(i+1)<<" = "<<argName<<"[index];\n";
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    }
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    vector<const TabulatedFunction*> functions;
    vector<pair<string, string> > functionNames;
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    compute << cl.getExpressionUtilities().createExpressions(expressions, variables, functions, functionNames, "temp");
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    map<string, string> replacements;
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    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
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    replacements["COMPUTE_FORCE"] = compute.str();
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::angleForce, replacements), force.getForceGroup());
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}

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

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void OpenCLCalcCustomAngleForceKernel::copyParametersToContext(ContextImpl& context, const CustomAngleForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumAngles()/numContexts;
    if (numAngles != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of angles has changed");
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    if (numAngles == 0)
        return;
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    // Record the per-angle parameters.
    
    vector<vector<cl_float> > paramVector(numAngles);
    vector<double> parameters;
    for (int i = 0; i < numAngles; i++) {
        int atom1, atom2, atom3;
        force.getAngleParameters(startIndex+i, atom1, atom2, atom3, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

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

void OpenCLCalcPeriodicTorsionForceKernel::initialize(const System& system, const PeriodicTorsionForce& force) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
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    if (numTorsions == 0)
        return;
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    vector<vector<int> > atoms(numTorsions, vector<int>(4));
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    params = OpenCLArray::create<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;
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    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
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    replacements["COMPUTE_FORCE"] = OpenCLKernelSources::periodicTorsionForce;
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    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float4");
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::torsionForce, replacements), force.getForceGroup());
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    info = new ForceInfo(force);
    cl.addForce(info);
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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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void OpenCLCalcPeriodicTorsionForceKernel::copyParametersToContext(ContextImpl& context, const PeriodicTorsionForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    if (numTorsions != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of torsions has changed");
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    if (numTorsions == 0)
        return;
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    // Record the per-torsion parameters.
    
    vector<mm_float4> paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        int atom1, atom2, atom3, atom4, periodicity;
        double phase, k;
        force.getTorsionParameters(startIndex+i, atom1, atom2, atom3, atom4, periodicity, phase, k);
        paramVector[i] = mm_float4((cl_float) k, (cl_float) phase, (cl_float) periodicity, 0.0f);
    }
    params->upload(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

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

void OpenCLCalcRBTorsionForceKernel::initialize(const System& system, const RBTorsionForce& force) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
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    if (numTorsions == 0)
        return;
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    vector<vector<int> > atoms(numTorsions, vector<int>(4));
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    params = OpenCLArray::create<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;
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    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
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    replacements["COMPUTE_FORCE"] = OpenCLKernelSources::rbTorsionForce;
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    replacements["PARAMS"] = cl.getBondedUtilities().addArgument(params->getDeviceBuffer(), "float8");
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::torsionForce, replacements), force.getForceGroup());
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    info = new ForceInfo(force);
    cl.addForce(info);
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}

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

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void OpenCLCalcRBTorsionForceKernel::copyParametersToContext(ContextImpl& context, const RBTorsionForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    if (numTorsions != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of torsions has changed");
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    if (numTorsions == 0)
        return;
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    // Record the per-torsion parameters.
    
    vector<mm_float8> paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        int atom1, atom2, atom3, atom4;
        double c0, c1, c2, c3, c4, c5;
        force.getTorsionParameters(startIndex+i, atom1, atom2, atom3, atom4, c0, c1, c2, c3, c4, c5);
        paramVector[i] = mm_float8((cl_float) c0, (cl_float) c1, (cl_float) c2, (cl_float) c3, (cl_float) c4, (cl_float) c5, 0.0f, 0.0f);
    }
    params->upload(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

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

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

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

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void OpenCLCalcCMAPTorsionForceKernel::copyParametersToContext(ContextImpl& context, const CMAPTorsionForce& force) {
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    int numMaps = force.getNumMaps();
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (mapPositions->getSize() != numMaps)
        throw OpenMMException("updateParametersInContext: The number of maps has changed");
    if (torsionMaps->getSize() != numTorsions)
        throw OpenMMException("updateParametersInContext: The number of CMAP torsions has changed");

    // Update the maps.

    vector<mm_float4> coeffVec;
    vector<double> energy;
    vector<vector<double> > c;
    int currentPosition = 0;
    for (int i = 0; i < numMaps; i++) {
        int size;
        force.getMapParameters(i, size, energy);
        if (size != mapPositionsVec[i].y)
            throw OpenMMException("updateParametersInContext: The size of a map has changed");
        CMAPTorsionForceImpl::calcMapDerivatives(size, energy, c);
        currentPosition += 4*size*size;
        for (int j = 0; j < size*size; j++) {
            coeffVec.push_back(mm_float4((float) c[j][0], (float) c[j][1], (float) c[j][2], (float) c[j][3]));
            coeffVec.push_back(mm_float4((float) c[j][4], (float) c[j][5], (float) c[j][6], (float) c[j][7]));
            coeffVec.push_back(mm_float4((float) c[j][8], (float) c[j][9], (float) c[j][10], (float) c[j][11]));
            coeffVec.push_back(mm_float4((float) c[j][12], (float) c[j][13], (float) c[j][14], (float) c[j][15]));
        }
    }
    coefficients->upload(coeffVec);

    // Update the indices.

    vector<int> torsionMapsVec(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        int index[8];
        force.getTorsionParameters(i, torsionMapsVec[i], index[0], index[1], index[2], index[3], index[4], index[5], index[6], index[7]);
    }
    torsionMaps->upload(torsionMapsVec);
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}

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

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

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

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

    map<string, string> variables;
    variables["theta"] = "theta";
    for (int i = 0; i < force.getNumPerTorsionParameters(); i++) {
        const string& name = force.getPerTorsionParameterName(i);
        variables[name] = "torsionParams"+params->getParameterSuffix(i);
    }
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    if (force.getNumGlobalParameters() > 0) {
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        globals = OpenCLArray::create<cl_float>(cl, force.getNumGlobalParameters(), "customTorsionGlobals", CL_MEM_READ_ONLY);
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        globals->upload(globalParamValues);
        string argName = cl.getBondedUtilities().addArgument(globals->getDeviceBuffer(), "float");
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
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            string value = argName+"["+cl.intToString(i)+"]";
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            variables[name] = value;
        }
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    }
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cl.getBondedUtilities().addEnergyParameterDerivative(paramName);
        Lepton::ParsedExpression derivExpression = energyExpression.differentiate(paramName).optimize();
        expressions[derivVariable+" += "] = derivExpression;
    }
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    stringstream compute;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" torsionParams"<<(i+1)<<" = "<<argName<<"[index];\n";
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    }
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    vector<const TabulatedFunction*> functions;
    vector<pair<string, string> > functionNames;
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    compute << cl.getExpressionUtilities().createExpressions(expressions, variables, functions, functionNames, "temp");
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    map<string, string> replacements;
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    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
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    replacements["COMPUTE_FORCE"] = compute.str();
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    cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::torsionForce, replacements), force.getForceGroup());
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}

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

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void OpenCLCalcCustomTorsionForceKernel::copyParametersToContext(ContextImpl& context, const CustomTorsionForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    if (numTorsions != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of torsions has changed");
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    if (numTorsions == 0)
        return;
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    // Record the per-torsion parameters.
    
    vector<vector<cl_float> > paramVector(numTorsions);
    vector<double> parameters;
    for (int i = 0; i < numTorsions; i++) {
        int atom1, atom2, atom3, atom4;
        force.getTorsionParameters(startIndex+i, atom1, atom2, atom3, atom4, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

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class OpenCLCalcNonbondedForceKernel::PmeIO : public CalcPmeReciprocalForceKernel::IO {
public:
    PmeIO(OpenCLContext& cl, cl::Kernel addForcesKernel) : cl(cl), addForcesKernel(addForcesKernel), forceTemp(NULL) {
        forceTemp = OpenCLArray::create<mm_float4>(cl, cl.getNumAtoms(), "PmeForce");
        addForcesKernel.setArg<cl::Buffer>(0, forceTemp->getDeviceBuffer());
    }
    ~PmeIO() {
        if (forceTemp != NULL)
            delete forceTemp;
    }
    float* getPosq() {
        cl.getPosq().download(posq);
        return (float*) &posq[0];
    }
    void setForce(float* force) {
        forceTemp->upload(force);
        addForcesKernel.setArg<cl::Buffer>(1, cl.getForce().getDeviceBuffer());
        cl.executeKernel(addForcesKernel, cl.getNumAtoms());
    }
private:
    OpenCLContext& cl;
    vector<mm_float4> posq;
    OpenCLArray* forceTemp;
    cl::Kernel addForcesKernel;
};

class OpenCLCalcNonbondedForceKernel::PmePreComputation : public OpenCLContext::ForcePreComputation {
public:
    PmePreComputation(OpenCLContext& cl, Kernel& pme, CalcPmeReciprocalForceKernel::IO& io) : cl(cl), pme(pme), io(io) {
    }
    void computeForceAndEnergy(bool includeForces, bool includeEnergy, int groups) {
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        Vec3 boxVectors[3] = {Vec3(cl.getPeriodicBoxSize().x, 0, 0), Vec3(0, cl.getPeriodicBoxSize().y, 0), Vec3(0, 0, cl.getPeriodicBoxSize().z)};
        pme.getAs<CalcPmeReciprocalForceKernel>().beginComputation(io, boxVectors, includeEnergy);
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    }
private:
    OpenCLContext& cl;
    Kernel pme;
    CalcPmeReciprocalForceKernel::IO& io;
};

class OpenCLCalcNonbondedForceKernel::PmePostComputation : public OpenCLContext::ForcePostComputation {
public:
    PmePostComputation(Kernel& pme, CalcPmeReciprocalForceKernel::IO& io) : pme(pme), io(io) {
    }
    double computeForceAndEnergy(bool includeForces, bool includeEnergy, int groups) {
        return pme.getAs<CalcPmeReciprocalForceKernel>().finishComputation(io);
    }
private:
    Kernel pme;
    CalcPmeReciprocalForceKernel::IO& io;
};

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class OpenCLCalcNonbondedForceKernel::SyncQueuePreComputation : public OpenCLContext::ForcePreComputation {
public:
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    SyncQueuePreComputation(OpenCLContext& cl, cl::CommandQueue queue, int forceGroup) : cl(cl), queue(queue), forceGroup(forceGroup) {
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    }
    void computeForceAndEnergy(bool includeForces, bool includeEnergy, int groups) {
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        if ((groups&(1<<forceGroup)) != 0) {
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            vector<cl::Event> events(1);
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            cl.getQueue().enqueueMarker(&events[0]);
            queue.enqueueWaitForEvents(events);
        }
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    }
private:
    OpenCLContext& cl;
    cl::CommandQueue queue;
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    int forceGroup;
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};

class OpenCLCalcNonbondedForceKernel::SyncQueuePostComputation : public OpenCLContext::ForcePostComputation {
public:
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    SyncQueuePostComputation(OpenCLContext& cl, cl::Event& event, OpenCLArray& pmeEnergyBuffer, int forceGroup) : cl(cl), event(event),
            pmeEnergyBuffer(pmeEnergyBuffer), forceGroup(forceGroup) {
    }
    void setKernel(cl::Kernel kernel) {
        addEnergyKernel = kernel;
        addEnergyKernel.setArg<cl::Buffer>(0, pmeEnergyBuffer.getDeviceBuffer());
        addEnergyKernel.setArg<cl::Buffer>(1, cl.getEnergyBuffer().getDeviceBuffer());
        addEnergyKernel.setArg<cl_int>(2, pmeEnergyBuffer.getSize());
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    }
    double computeForceAndEnergy(bool includeForces, bool includeEnergy, int groups) {
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        if ((groups&(1<<forceGroup)) != 0) {
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            vector<cl::Event> events(1);
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            events[0] = event;
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            event = cl::Event();
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            cl.getQueue().enqueueWaitForEvents(events);
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            if (includeEnergy)
                cl.executeKernel(addEnergyKernel, pmeEnergyBuffer.getSize());
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        }
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        return 0.0;
    }
private:
    OpenCLContext& cl;
    cl::Event& event;
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    cl::Kernel addEnergyKernel;
    OpenCLArray& pmeEnergyBuffer;
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    int forceGroup;
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};

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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;
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    if (pmeDispersionBsplineModuliX != NULL)
        delete pmeDispersionBsplineModuliX;
    if (pmeDispersionBsplineModuliY != NULL)
        delete pmeDispersionBsplineModuliY;
    if (pmeDispersionBsplineModuliZ != NULL)
        delete pmeDispersionBsplineModuliZ;
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    if (pmeBsplineTheta != NULL)
        delete pmeBsplineTheta;
    if (pmeAtomRange != NULL)
        delete pmeAtomRange;
    if (pmeAtomGridIndex != NULL)
        delete pmeAtomGridIndex;
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    if (pmeEnergyBuffer != NULL)
        delete pmeEnergyBuffer;
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    if (sort != NULL)
        delete sort;
    if (fft != NULL)
        delete fft;
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    if (dispersionFft != NULL)
        delete dispersionFft;
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    if (pmeio != NULL)
        delete pmeio;
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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();
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    sigmaEpsilon = OpenCLArray::create<mm_float2>(cl, cl.getPaddedNumAtoms(), "sigmaEpsilon");
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    vector<mm_float4> posqf(cl.getPaddedNumAtoms(), mm_float4(0,0,0,0));
    vector<mm_double4> posqd(cl.getPaddedNumAtoms(), mm_double4(0,0,0,0));
    vector<mm_float2> sigmaEpsilonVector(cl.getPaddedNumAtoms(), mm_float2(0,0));
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    vector<vector<int> > exclusionList(numParticles);
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    double sumSquaredCharges = 0.0;
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    double sumSquaredC6 = 0.0;
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    hasCoulomb = false;
    hasLJ = false;
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    for (int i = 0; i < numParticles; i++) {
        double charge, sigma, epsilon;
        force.getParticleParameters(i, charge, sigma, epsilon);
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        if (cl.getUseDoublePrecision())
            posqd[i] = mm_double4(0, 0, 0, charge);
        else
            posqf[i] = mm_float4(0, 0, 0, (float) charge);
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        double sig = 0.5*sigma;
        double eps = 2.0*sqrt(epsilon);
        sigmaEpsilonVector[i] = mm_float2((float) sig, (float) eps);
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        exclusionList[i].push_back(i);
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        sumSquaredCharges += charge*charge;
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        double C6 = 8.0*sig*sig*sig*eps;
        sumSquaredC6 += C6*C6;
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        if (charge != 0.0)
            hasCoulomb = true;
        if (epsilon != 0.0)
            hasLJ = true;
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    }
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    for (auto exclusion : exclusions) {
        exclusionList[exclusion.first].push_back(exclusion.second);
        exclusionList[exclusion.second].push_back(exclusion.first);
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    }
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    if (cl.getUseDoublePrecision())
        cl.getPosq().upload(posqd);
    else
        cl.getPosq().upload(posqf);
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    sigmaEpsilon->upload(sigmaEpsilonVector);
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    nonbondedMethod = CalcNonbondedForceKernel::NonbondedMethod(force.getNonbondedMethod());
    bool useCutoff = (nonbondedMethod != NoCutoff);
    bool usePeriodic = (nonbondedMethod != NoCutoff && nonbondedMethod != CutoffNonPeriodic);
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    doLJPME = (nonbondedMethod == LJPME);
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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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    defines["USE_LJ_SWITCH"] = (useCutoff && force.getUseSwitchingFunction() ? "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"] = cl.doubleToString(reactionFieldK);
        defines["REACTION_FIELD_C"] = cl.doubleToString(reactionFieldC);
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        // Compute the switching coefficients.
        
        if (force.getUseSwitchingFunction()) {
            defines["LJ_SWITCH_CUTOFF"] = cl.doubleToString(force.getSwitchingDistance());
            defines["LJ_SWITCH_C3"] = cl.doubleToString(10/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 3.0));
            defines["LJ_SWITCH_C4"] = cl.doubleToString(15/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 4.0));
            defines["LJ_SWITCH_C5"] = cl.doubleToString(6/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 5.0));
        }
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    }
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    if (force.getUseDispersionCorrection() && cl.getContextIndex() == 0 && !doLJPME)
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        dispersionCoefficient = NonbondedForceImpl::calcDispersionCorrection(system, force);
    else
        dispersionCoefficient = 0.0;
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    alpha = 0;
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    ewaldSelfEnergy = 0.0;
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    if (nonbondedMethod == Ewald) {
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        // Compute the Ewald parameters.

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

            // Create the reciprocal space kernels.

            map<string, string> replacements;
            replacements["NUM_ATOMS"] = cl.intToString(numParticles);
            replacements["KMAX_X"] = cl.intToString(kmaxx);
            replacements["KMAX_Y"] = cl.intToString(kmaxy);
            replacements["KMAX_Z"] = cl.intToString(kmaxz);
            replacements["EXP_COEFFICIENT"] = cl.doubleToString(-1.0/(4.0*alpha*alpha));
            cl::Program program = cl.createProgram(OpenCLKernelSources::ewald, replacements);
            ewaldSumsKernel = cl::Kernel(program, "calculateEwaldCosSinSums");
            ewaldForcesKernel = cl::Kernel(program, "calculateEwaldForces");
            int elementSize = (cl.getUseDoublePrecision() ? sizeof(mm_double2) : sizeof(mm_float2));
            cosSinSums = new OpenCLArray(cl, (2*kmaxx-1)*(2*kmaxy-1)*(2*kmaxz-1), elementSize, "cosSinSums");
        }
    }
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    else if (nonbondedMethod == PME || nonbondedMethod == LJPME) {
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        // Compute the PME parameters.

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        NonbondedForceImpl::calcPMEParameters(system, force, alpha, gridSizeX, gridSizeY, gridSizeZ, false);
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        gridSizeX = OpenCLFFT3D::findLegalDimension(gridSizeX);
        gridSizeY = OpenCLFFT3D::findLegalDimension(gridSizeY);
        gridSizeZ = OpenCLFFT3D::findLegalDimension(gridSizeZ);
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        if (doLJPME) {
            NonbondedForceImpl::calcPMEParameters(system, force, dispersionAlpha, dispersionGridSizeX,
                                                  dispersionGridSizeY, dispersionGridSizeZ, true);
            dispersionGridSizeX = OpenCLFFT3D::findLegalDimension(dispersionGridSizeX);
            dispersionGridSizeY = OpenCLFFT3D::findLegalDimension(dispersionGridSizeY);
            dispersionGridSizeZ = OpenCLFFT3D::findLegalDimension(dispersionGridSizeZ);
        }
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        defines["EWALD_ALPHA"] = cl.doubleToString(alpha);
        defines["TWO_OVER_SQRT_PI"] = cl.doubleToString(2.0/sqrt(M_PI));
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        defines["USE_EWALD"] = "1";
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        defines["DO_LJPME"] = doLJPME ? "1" : "0";
        if (doLJPME)
            defines["EWALD_DISPERSION_ALPHA"] = cl.doubleToString(dispersionAlpha);
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        if (cl.getContextIndex() == 0) {
            ewaldSelfEnergy = -ONE_4PI_EPS0*alpha*sumSquaredCharges/sqrt(M_PI);
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            if (doLJPME)
                ewaldSelfEnergy += pow(dispersionAlpha, 6)*sumSquaredC6/12.0;
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            pmeDefines["PME_ORDER"] = cl.intToString(PmeOrder);
            pmeDefines["NUM_ATOMS"] = cl.intToString(numParticles);
            pmeDefines["RECIP_EXP_FACTOR"] = cl.doubleToString(M_PI*M_PI/(alpha*alpha));
            pmeDefines["GRID_SIZE_X"] = cl.intToString(gridSizeX);
            pmeDefines["GRID_SIZE_Y"] = cl.intToString(gridSizeY);
            pmeDefines["GRID_SIZE_Z"] = cl.intToString(gridSizeZ);
            pmeDefines["EPSILON_FACTOR"] = cl.doubleToString(sqrt(ONE_4PI_EPS0));
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            pmeDefines["M_PI"] = cl.doubleToString(M_PI);
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            bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
            if (deviceIsCpu)
                pmeDefines["DEVICE_IS_CPU"] = "1";
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            if (cl.getPlatformData().useCpuPme && !doLJPME) {
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                // Create the CPU PME kernel.

                try {
                    cpuPme = getPlatform().createKernel(CalcPmeReciprocalForceKernel::Name(), *cl.getPlatformData().context);
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                    cpuPme.getAs<CalcPmeReciprocalForceKernel>().initialize(gridSizeX, gridSizeY, gridSizeZ, numParticles, alpha, false);
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                    cl::Program program = cl.createProgram(OpenCLKernelSources::pme, pmeDefines);
                    cl::Kernel addForcesKernel = cl::Kernel(program, "addForces");
                    pmeio = new PmeIO(cl, addForcesKernel);
                    cl.addPreComputation(new PmePreComputation(cl, cpuPme, *pmeio));
                    cl.addPostComputation(new PmePostComputation(cpuPme, *pmeio));
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                }
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                catch (OpenMMException& ex) {
                    // The CPU PME plugin isn't available.
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                }
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            }
            if (pmeio == NULL) {
                // Create required data structures.

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                if (doLJPME) {
                    double invRCut6 = pow(force.getCutoffDistance(), -6);
                    double dalphaR = dispersionAlpha * force.getCutoffDistance();
                    double dar2 = dalphaR*dalphaR;
                    double dar4 = dar2*dar2;
                    double multShift6 = -invRCut6*(1.0 - exp(-dar2) * (1.0 + dar2 + 0.5*dar4));
                    defines["INVCUT6"] = cl.doubleToString(invRCut6);
                    defines["MULTSHIFT6"] = cl.doubleToString(multShift6);
                }
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                int elementSize = (cl.getUseDoublePrecision() ? sizeof(double) : sizeof(float));
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                int gridElements = gridSizeX*gridSizeY*gridSizeZ;
                if (doLJPME)
                    gridElements = max(gridElements, dispersionGridSizeX*dispersionGridSizeY*dispersionGridSizeZ);
                pmeGrid = new OpenCLArray(cl, gridElements, 2*elementSize, "pmeGrid");
                pmeGrid2 = new OpenCLArray(cl, gridElements, 2*elementSize, "pmeGrid2");
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                if (cl.getSupports64BitGlobalAtomics())
                    cl.addAutoclearBuffer(*pmeGrid2);
                else
                    cl.addAutoclearBuffer(*pmeGrid);
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                pmeBsplineModuliX = new OpenCLArray(cl, gridSizeX, elementSize, "pmeBsplineModuliX");
                pmeBsplineModuliY = new OpenCLArray(cl, gridSizeY, elementSize, "pmeBsplineModuliY");
                pmeBsplineModuliZ = new OpenCLArray(cl, gridSizeZ, elementSize, "pmeBsplineModuliZ");
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                if (doLJPME) {
                    pmeDispersionBsplineModuliX = new OpenCLArray(cl, dispersionGridSizeX, elementSize, "pmeDispersionBsplineModuliX");
                    pmeDispersionBsplineModuliY = new OpenCLArray(cl, dispersionGridSizeY, elementSize, "pmeDispersionBsplineModuliY");
                    pmeDispersionBsplineModuliZ = new OpenCLArray(cl, dispersionGridSizeZ, elementSize, "pmeDispersionBsplineModuliZ");
                }
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                pmeBsplineTheta = new OpenCLArray(cl, PmeOrder*numParticles, 4*elementSize, "pmeBsplineTheta");
                pmeAtomRange = OpenCLArray::create<cl_int>(cl, gridSizeX*gridSizeY*gridSizeZ+1, "pmeAtomRange");
                pmeAtomGridIndex = OpenCLArray::create<mm_int2>(cl, numParticles, "pmeAtomGridIndex");
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                int energyElementSize = (cl.getUseDoublePrecision() || cl.getUseMixedPrecision() ? sizeof(double) : sizeof(float));
                pmeEnergyBuffer = new OpenCLArray(cl, cl.getNumThreadBlocks()*OpenCLContext::ThreadBlockSize, energyElementSize, "pmeEnergyBuffer");
                cl.clearBuffer(*pmeEnergyBuffer);
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                sort = new OpenCLSort(cl, new SortTrait(), cl.getNumAtoms());
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                fft = new OpenCLFFT3D(cl, gridSizeX, gridSizeY, gridSizeZ, true);
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                if (doLJPME)
                    dispersionFft = new OpenCLFFT3D(cl, dispersionGridSizeX, dispersionGridSizeY, dispersionGridSizeZ, true);
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                string vendor = cl.getDevice().getInfo<CL_DEVICE_VENDOR>();
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                bool isNvidia = (vendor.size() >= 6 && vendor.substr(0, 6) == "NVIDIA");
                if (isNvidia)
                    pmeDefines["USE_ALTERNATE_MEMORY_ACCESS_PATTERN"] = "1";
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                usePmeQueue = (!cl.getPlatformData().disablePmeStream && isNvidia);
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                if (usePmeQueue) {
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                    pmeDefines["USE_PME_STREAM"] = "1";
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                    pmeQueue = cl::CommandQueue(cl.getContext(), cl.getDevice());
                    int recipForceGroup = force.getReciprocalSpaceForceGroup();
                    if (recipForceGroup < 0)
                        recipForceGroup = force.getForceGroup();
                    cl.addPreComputation(new SyncQueuePreComputation(cl, pmeQueue, recipForceGroup));
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                    cl.addPostComputation(syncQueue = new SyncQueuePostComputation(cl, pmeSyncEvent, *pmeEnergyBuffer, recipForceGroup));
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                }
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                // Initialize the b-spline moduli.

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                for (int grid = 0; grid < 2; grid++) {
                    int xsize, ysize, zsize;
                    OpenCLArray *xmoduli, *ymoduli, *zmoduli;
                    if (grid == 0) {
                        xsize = gridSizeX;
                        ysize = gridSizeY;
                        zsize = gridSizeZ;
                        xmoduli = pmeBsplineModuliX;
                        ymoduli = pmeBsplineModuliY;
                        zmoduli = pmeBsplineModuliZ;
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                    }
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                    else {
                        if (!doLJPME)
                            continue;
                        xsize = dispersionGridSizeX;
                        ysize = dispersionGridSizeY;
                        zsize = dispersionGridSizeZ;
                        xmoduli = pmeDispersionBsplineModuliX;
                        ymoduli = pmeDispersionBsplineModuliY;
                        zmoduli = pmeDispersionBsplineModuliZ;
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                    }
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                    int maxSize = max(max(xsize, ysize), zsize);
                    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];
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                    }
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                    // 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 ? xsize : dim == 1 ? ysize : zsize);
                        vector<cl_double> 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);
                        }
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                        for (int i = 0; i < ndata; i++)
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                        {
                            if (moduli[i] < 1.0e-7)
                                moduli[i] = (moduli[i-1]+moduli[i+1])*0.5f;
                        }
                        if (cl.getUseDoublePrecision()) {
                            if (dim == 0)
                                xmoduli->upload(moduli);
                            else if (dim == 1)
                                ymoduli->upload(moduli);
                            else
                                zmoduli->upload(moduli);
                        }
                        else {
                            vector<float> modulif(ndata);
                            for (int i = 0; i < ndata; i++)
                                modulif[i] = (float) moduli[i];
                            if (dim == 0)
                                xmoduli->upload(modulif);
                            else if (dim == 1)
                                ymoduli->upload(modulif);
                            else
                                zmoduli->upload(modulif);
                        }
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                    }
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                }
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            }
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        }
    }
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    // Add the interaction to the default nonbonded kernel.
    
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    string source = cl.replaceStrings(OpenCLKernelSources::coulombLennardJones, defines);
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    cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source, force.getForceGroup());
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    if (hasLJ)
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        cl.getNonbondedUtilities().addParameter(OpenCLNonbondedUtilities::ParameterInfo("sigmaEpsilon", "float", 2, sizeof(cl_float2), sigmaEpsilon->getDeviceBuffer()));
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    // Initialize the exceptions.
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*exceptions.size()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*exceptions.size()/numContexts;
    int numExceptions = endIndex-startIndex;
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    if (numExceptions > 0) {
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        exceptionAtoms.resize(numExceptions);
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        vector<vector<int> > atoms(numExceptions, vector<int>(2));
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        exceptionParams = OpenCLArray::create<mm_float4>(cl, numExceptions, "exceptionParams");
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        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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            exceptionAtoms[i] = make_pair(atoms[i][0], atoms[i][1]);
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        }
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        exceptionParams->upload(exceptionParamsVector);
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        map<string, string> replacements;
        replacements["PARAMS"] = cl.getBondedUtilities().addArgument(exceptionParams->getDeviceBuffer(), "float4");
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        cl.getBondedUtilities().addInteraction(atoms, cl.replaceStrings(OpenCLKernelSources::nonbondedExceptions, replacements), force.getForceGroup());
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    }
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    info = new ForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force);
    cl.addForce(info);
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}

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double OpenCLCalcNonbondedForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy, bool includeDirect, bool includeReciprocal) {
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    bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
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    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        if (cosSinSums != NULL) {
            ewaldSumsKernel.setArg<cl::Buffer>(0, cl.getEnergyBuffer().getDeviceBuffer());
            ewaldSumsKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
            ewaldSumsKernel.setArg<cl::Buffer>(2, cosSinSums->getDeviceBuffer());
            ewaldForcesKernel.setArg<cl::Buffer>(0, cl.getForceBuffers().getDeviceBuffer());
            ewaldForcesKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
            ewaldForcesKernel.setArg<cl::Buffer>(2, cosSinSums->getDeviceBuffer());
        }
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        if (pmeGrid != NULL) {
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            // Create kernels for Coulomb PME.
            
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            cl::Program program = cl.createProgram(OpenCLKernelSources::pme, pmeDefines);
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            pmeUpdateBsplinesKernel = cl::Kernel(program, "updateBsplines");
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            pmeAtomRangeKernel = cl::Kernel(program, "findAtomRangeForGrid");
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            pmeZIndexKernel = cl::Kernel(program, "recordZIndex");
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            pmeSpreadChargeKernel = cl::Kernel(program, "gridSpreadCharge");
            pmeConvolutionKernel = cl::Kernel(program, "reciprocalConvolution");
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            pmeEvalEnergyKernel = cl::Kernel(program, "gridEvaluateEnergy");
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            pmeInterpolateForceKernel = cl::Kernel(program, "gridInterpolateForce");
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            int elementSize = (cl.getUseDoublePrecision() ? sizeof(mm_double4) : sizeof(mm_float4));
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            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*elementSize, NULL);
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            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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            pmeZIndexKernel.setArg<cl::Buffer>(0, pmeAtomGridIndex->getDeviceBuffer());
            pmeZIndexKernel.setArg<cl::Buffer>(1, 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());
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            if (cl.getSupports64BitGlobalAtomics())
                pmeSpreadChargeKernel.setArg<cl::Buffer>(3, pmeGrid2->getDeviceBuffer());
            else
                pmeSpreadChargeKernel.setArg<cl::Buffer>(3, pmeGrid->getDeviceBuffer());
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            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, pmeBsplineModuliX->getDeviceBuffer());
            pmeConvolutionKernel.setArg<cl::Buffer>(2, pmeBsplineModuliY->getDeviceBuffer());
            pmeConvolutionKernel.setArg<cl::Buffer>(3, pmeBsplineModuliZ->getDeviceBuffer());
            pmeEvalEnergyKernel.setArg<cl::Buffer>(0, pmeGrid2->getDeviceBuffer());
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            pmeEvalEnergyKernel.setArg<cl::Buffer>(1, usePmeQueue ? pmeEnergyBuffer->getDeviceBuffer() : cl.getEnergyBuffer().getDeviceBuffer());
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            pmeEvalEnergyKernel.setArg<cl::Buffer>(2, pmeBsplineModuliX->getDeviceBuffer());
            pmeEvalEnergyKernel.setArg<cl::Buffer>(3, pmeBsplineModuliY->getDeviceBuffer());
            pmeEvalEnergyKernel.setArg<cl::Buffer>(4, pmeBsplineModuliZ->getDeviceBuffer());
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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<cl::Buffer>(11, pmeAtomGridIndex->getDeviceBuffer());
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            if (cl.getSupports64BitGlobalAtomics()) {
                pmeFinishSpreadChargeKernel = cl::Kernel(program, "finishSpreadCharge");
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                pmeFinishSpreadChargeKernel.setArg<cl::Buffer>(0, pmeGrid2->getDeviceBuffer());
                pmeFinishSpreadChargeKernel.setArg<cl::Buffer>(1, pmeGrid->getDeviceBuffer());
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            }
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            if (usePmeQueue)
                syncQueue->setKernel(cl::Kernel(program, "addEnergy"));
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            if (doLJPME) {
                // Create kernels for LJ PME.

                pmeDefines["EWALD_ALPHA"] = cl.doubleToString(dispersionAlpha);
                pmeDefines["GRID_SIZE_X"] = cl.intToString(dispersionGridSizeX);
                pmeDefines["GRID_SIZE_Y"] = cl.intToString(dispersionGridSizeY);
                pmeDefines["GRID_SIZE_Z"] = cl.intToString(dispersionGridSizeZ);
                pmeDefines["EPSILON_FACTOR"] = "1";
                pmeDefines["RECIP_EXP_FACTOR"] = cl.doubleToString(M_PI*M_PI/(dispersionAlpha*dispersionAlpha));
                pmeDefines["USE_LJPME"] = "1";
                program = cl.createProgram(OpenCLKernelSources::pme, pmeDefines);
                pmeDispersionUpdateBsplinesKernel = cl::Kernel(program, "updateBsplines");
                pmeDispersionAtomRangeKernel = cl::Kernel(program, "findAtomRangeForGrid");
                pmeDispersionZIndexKernel = cl::Kernel(program, "recordZIndex");
                pmeDispersionSpreadChargeKernel = cl::Kernel(program, "gridSpreadCharge");
                pmeDispersionConvolutionKernel = cl::Kernel(program, "reciprocalConvolution");
                pmeDispersionEvalEnergyKernel = cl::Kernel(program, "gridEvaluateEnergy");
                pmeDispersionInterpolateForceKernel = cl::Kernel(program, "gridInterpolateForce");
                int elementSize = (cl.getUseDoublePrecision() ? sizeof(mm_double4) : sizeof(mm_float4));
                pmeDispersionUpdateBsplinesKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
                pmeDispersionUpdateBsplinesKernel.setArg<cl::Buffer>(1, pmeBsplineTheta->getDeviceBuffer());
                pmeDispersionUpdateBsplinesKernel.setArg(2, OpenCLContext::ThreadBlockSize*PmeOrder*elementSize, NULL);
                pmeDispersionUpdateBsplinesKernel.setArg<cl::Buffer>(3, pmeAtomGridIndex->getDeviceBuffer());
                pmeDispersionUpdateBsplinesKernel.setArg<cl::Buffer>(12, sigmaEpsilon->getDeviceBuffer());
                pmeDispersionAtomRangeKernel.setArg<cl::Buffer>(0, pmeAtomGridIndex->getDeviceBuffer());
                pmeDispersionAtomRangeKernel.setArg<cl::Buffer>(1, pmeAtomRange->getDeviceBuffer());
                pmeDispersionAtomRangeKernel.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
                pmeDispersionZIndexKernel.setArg<cl::Buffer>(0, pmeAtomGridIndex->getDeviceBuffer());
                pmeDispersionZIndexKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
                pmeDispersionSpreadChargeKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
                pmeDispersionSpreadChargeKernel.setArg<cl::Buffer>(1, pmeAtomGridIndex->getDeviceBuffer());
                pmeDispersionSpreadChargeKernel.setArg<cl::Buffer>(2, pmeAtomRange->getDeviceBuffer());
                if (cl.getSupports64BitGlobalAtomics())
                    pmeDispersionSpreadChargeKernel.setArg<cl::Buffer>(3, pmeGrid2->getDeviceBuffer());
                else
                    pmeDispersionSpreadChargeKernel.setArg<cl::Buffer>(3, pmeGrid->getDeviceBuffer());
                pmeDispersionSpreadChargeKernel.setArg<cl::Buffer>(4, pmeBsplineTheta->getDeviceBuffer());
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                if (deviceIsCpu || cl.getSupports64BitGlobalAtomics())
                    pmeDispersionSpreadChargeKernel.setArg<cl::Buffer>(13, sigmaEpsilon->getDeviceBuffer());
                else
                    pmeDispersionSpreadChargeKernel.setArg<cl::Buffer>(5, sigmaEpsilon->getDeviceBuffer());
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                pmeDispersionConvolutionKernel.setArg<cl::Buffer>(0, pmeGrid2->getDeviceBuffer());
                pmeDispersionConvolutionKernel.setArg<cl::Buffer>(1, pmeDispersionBsplineModuliX->getDeviceBuffer());
                pmeDispersionConvolutionKernel.setArg<cl::Buffer>(2, pmeDispersionBsplineModuliY->getDeviceBuffer());
                pmeDispersionConvolutionKernel.setArg<cl::Buffer>(3, pmeDispersionBsplineModuliZ->getDeviceBuffer());
                pmeDispersionEvalEnergyKernel.setArg<cl::Buffer>(0, pmeGrid2->getDeviceBuffer());
                pmeDispersionEvalEnergyKernel.setArg<cl::Buffer>(1, usePmeQueue ? pmeEnergyBuffer->getDeviceBuffer() : cl.getEnergyBuffer().getDeviceBuffer());
                pmeDispersionEvalEnergyKernel.setArg<cl::Buffer>(2, pmeDispersionBsplineModuliX->getDeviceBuffer());
                pmeDispersionEvalEnergyKernel.setArg<cl::Buffer>(3, pmeDispersionBsplineModuliY->getDeviceBuffer());
                pmeDispersionEvalEnergyKernel.setArg<cl::Buffer>(4, pmeDispersionBsplineModuliZ->getDeviceBuffer());
                pmeDispersionInterpolateForceKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
                pmeDispersionInterpolateForceKernel.setArg<cl::Buffer>(1, cl.getForceBuffers().getDeviceBuffer());
                pmeDispersionInterpolateForceKernel.setArg<cl::Buffer>(2, pmeGrid->getDeviceBuffer());
                pmeDispersionInterpolateForceKernel.setArg<cl::Buffer>(11, pmeAtomGridIndex->getDeviceBuffer());
                pmeDispersionInterpolateForceKernel.setArg<cl::Buffer>(12, sigmaEpsilon->getDeviceBuffer());
                if (cl.getSupports64BitGlobalAtomics()) {
                    pmeDispersionFinishSpreadChargeKernel = cl::Kernel(program, "finishSpreadCharge");
                    pmeDispersionFinishSpreadChargeKernel.setArg<cl::Buffer>(0, pmeGrid2->getDeviceBuffer());
                    pmeDispersionFinishSpreadChargeKernel.setArg<cl::Buffer>(1, pmeGrid->getDeviceBuffer());
                }
            }
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       }
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    }
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    if (cosSinSums != NULL && includeReciprocal) {
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        mm_double4 boxSize = cl.getPeriodicBoxSizeDouble();
        mm_double4 recipBoxSize = mm_double4(2*M_PI/boxSize.x, 2*M_PI/boxSize.y, 2*M_PI/boxSize.z, 0.0);
        double recipCoefficient = ONE_4PI_EPS0*4*M_PI/(boxSize.x*boxSize.y*boxSize.z);
        if (cl.getUseDoublePrecision()) {
            ewaldSumsKernel.setArg<mm_double4>(3, recipBoxSize);
            ewaldSumsKernel.setArg<cl_double>(4, recipCoefficient);
            ewaldForcesKernel.setArg<mm_double4>(3, recipBoxSize);
            ewaldForcesKernel.setArg<cl_double>(4, recipCoefficient);
        }
        else {
            ewaldSumsKernel.setArg<mm_float4>(3, mm_float4((float) recipBoxSize.x, (float) recipBoxSize.y, (float) recipBoxSize.z, 0));
            ewaldSumsKernel.setArg<cl_float>(4, (cl_float) recipCoefficient);
            ewaldForcesKernel.setArg<mm_float4>(3, mm_float4((float) recipBoxSize.x, (float) recipBoxSize.y, (float) recipBoxSize.z, 0));
            ewaldForcesKernel.setArg<cl_float>(4, (cl_float) recipCoefficient);
        }
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        cl.executeKernel(ewaldSumsKernel, cosSinSums->getSize());
        cl.executeKernel(ewaldForcesKernel, cl.getNumAtoms());
    }
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    if (pmeGrid != NULL && includeReciprocal) {
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        if (usePmeQueue && !includeEnergy)
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            cl.setQueue(pmeQueue);
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        // Invert the periodic box vectors.
        
        Vec3 boxVectors[3];
        cl.getPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
        double determinant = boxVectors[0][0]*boxVectors[1][1]*boxVectors[2][2];
        double scale = 1.0/determinant;
        mm_double4 recipBoxVectors[3];
        recipBoxVectors[0] = mm_double4(boxVectors[1][1]*boxVectors[2][2]*scale, 0, 0, 0);
        recipBoxVectors[1] = mm_double4(-boxVectors[1][0]*boxVectors[2][2]*scale, boxVectors[0][0]*boxVectors[2][2]*scale, 0, 0);
        recipBoxVectors[2] = mm_double4((boxVectors[1][0]*boxVectors[2][1]-boxVectors[1][1]*boxVectors[2][0])*scale, -boxVectors[0][0]*boxVectors[2][1]*scale, boxVectors[0][0]*boxVectors[1][1]*scale, 0);
        mm_float4 recipBoxVectorsFloat[3];
        for (int i = 0; i < 3; i++)
            recipBoxVectorsFloat[i] = mm_float4((float) recipBoxVectors[i].x, (float) recipBoxVectors[i].y, (float) recipBoxVectors[i].z, 0);
        
        // Execute the reciprocal space kernels.

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        setPeriodicBoxArgs(cl, pmeUpdateBsplinesKernel, 4);
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        if (cl.getUseDoublePrecision()) {
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            pmeUpdateBsplinesKernel.setArg<mm_double4>(9, recipBoxVectors[0]);
            pmeUpdateBsplinesKernel.setArg<mm_double4>(10, recipBoxVectors[1]);
            pmeUpdateBsplinesKernel.setArg<mm_double4>(11, recipBoxVectors[2]);
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        }
        else {
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            pmeUpdateBsplinesKernel.setArg<mm_float4>(9, recipBoxVectorsFloat[0]);
            pmeUpdateBsplinesKernel.setArg<mm_float4>(10, recipBoxVectorsFloat[1]);
            pmeUpdateBsplinesKernel.setArg<mm_float4>(11, recipBoxVectorsFloat[2]);
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        }
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        cl.executeKernel(pmeUpdateBsplinesKernel, cl.getNumAtoms());
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        if (deviceIsCpu && !cl.getSupports64BitGlobalAtomics()) {
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            setPeriodicBoxArgs(cl, pmeSpreadChargeKernel, 5);
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            if (cl.getUseDoublePrecision()) {
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                pmeSpreadChargeKernel.setArg<mm_double4>(10, recipBoxVectors[0]);
                pmeSpreadChargeKernel.setArg<mm_double4>(11, recipBoxVectors[1]);
                pmeSpreadChargeKernel.setArg<mm_double4>(12, recipBoxVectors[2]);
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            }
            else {
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                pmeSpreadChargeKernel.setArg<mm_float4>(10, recipBoxVectorsFloat[0]);
                pmeSpreadChargeKernel.setArg<mm_float4>(11, recipBoxVectorsFloat[1]);
                pmeSpreadChargeKernel.setArg<mm_float4>(12, recipBoxVectorsFloat[2]);
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            }
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            cl.executeKernel(pmeSpreadChargeKernel, 2*cl.getDevice().getInfo<CL_DEVICE_MAX_COMPUTE_UNITS>(), 1);
        }
        else {
            sort->sort(*pmeAtomGridIndex);
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            if (cl.getSupports64BitGlobalAtomics()) {
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                setPeriodicBoxArgs(cl, pmeSpreadChargeKernel, 5);
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                if (cl.getUseDoublePrecision()) {
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                    pmeSpreadChargeKernel.setArg<mm_double4>(10, recipBoxVectors[0]);
                    pmeSpreadChargeKernel.setArg<mm_double4>(11, recipBoxVectors[1]);
                    pmeSpreadChargeKernel.setArg<mm_double4>(12, recipBoxVectors[2]);
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                }
                else {
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                    pmeSpreadChargeKernel.setArg<mm_float4>(10, recipBoxVectorsFloat[0]);
                    pmeSpreadChargeKernel.setArg<mm_float4>(11, recipBoxVectorsFloat[1]);
                    pmeSpreadChargeKernel.setArg<mm_float4>(12, recipBoxVectorsFloat[2]);
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                }
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                cl.executeKernel(pmeSpreadChargeKernel, cl.getNumAtoms());
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                cl.executeKernel(pmeFinishSpreadChargeKernel, gridSizeX*gridSizeY*gridSizeZ);
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            }
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            else {
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                cl.executeKernel(pmeAtomRangeKernel, cl.getNumAtoms());
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                setPeriodicBoxSizeArg(cl, pmeZIndexKernel, 2);
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                if (cl.getUseDoublePrecision())
                    pmeZIndexKernel.setArg<mm_double4>(3, recipBoxVectors[2]);
                else
                    pmeZIndexKernel.setArg<mm_float4>(3, recipBoxVectorsFloat[2]);
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                cl.executeKernel(pmeZIndexKernel, cl.getNumAtoms());
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                cl.executeKernel(pmeSpreadChargeKernel, cl.getNumAtoms());
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            }
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        }
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        fft->execFFT(*pmeGrid, *pmeGrid2, true);
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        mm_double4 boxSize = cl.getPeriodicBoxSizeDouble();
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        if (cl.getUseDoublePrecision()) {
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            pmeConvolutionKernel.setArg<mm_double4>(4, recipBoxVectors[0]);
            pmeConvolutionKernel.setArg<mm_double4>(5, recipBoxVectors[1]);
            pmeConvolutionKernel.setArg<mm_double4>(6, recipBoxVectors[2]);
            pmeEvalEnergyKernel.setArg<mm_double4>(5, recipBoxVectors[0]);
            pmeEvalEnergyKernel.setArg<mm_double4>(6, recipBoxVectors[1]);
            pmeEvalEnergyKernel.setArg<mm_double4>(7, recipBoxVectors[2]);
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        }
        else {
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            pmeConvolutionKernel.setArg<mm_float4>(4, recipBoxVectorsFloat[0]);
            pmeConvolutionKernel.setArg<mm_float4>(5, recipBoxVectorsFloat[1]);
            pmeConvolutionKernel.setArg<mm_float4>(6, recipBoxVectorsFloat[2]);
            pmeEvalEnergyKernel.setArg<mm_float4>(5, recipBoxVectorsFloat[0]);
            pmeEvalEnergyKernel.setArg<mm_float4>(6, recipBoxVectorsFloat[1]);
            pmeEvalEnergyKernel.setArg<mm_float4>(7, recipBoxVectorsFloat[2]);
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        }
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        if (includeEnergy)
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            cl.executeKernel(pmeEvalEnergyKernel, gridSizeX*gridSizeY*gridSizeZ);
        cl.executeKernel(pmeConvolutionKernel, gridSizeX*gridSizeY*gridSizeZ);
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        fft->execFFT(*pmeGrid2, *pmeGrid, false);
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        setPeriodicBoxArgs(cl, pmeInterpolateForceKernel, 3);
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        if (cl.getUseDoublePrecision()) {
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            pmeInterpolateForceKernel.setArg<mm_double4>(8, recipBoxVectors[0]);
            pmeInterpolateForceKernel.setArg<mm_double4>(9, recipBoxVectors[1]);
            pmeInterpolateForceKernel.setArg<mm_double4>(10, recipBoxVectors[2]);
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        }
        else {
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            pmeInterpolateForceKernel.setArg<mm_float4>(8, recipBoxVectorsFloat[0]);
            pmeInterpolateForceKernel.setArg<mm_float4>(9, recipBoxVectorsFloat[1]);
            pmeInterpolateForceKernel.setArg<mm_float4>(10, recipBoxVectorsFloat[2]);
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        }
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        if (deviceIsCpu)
            cl.executeKernel(pmeInterpolateForceKernel, 2*cl.getDevice().getInfo<CL_DEVICE_MAX_COMPUTE_UNITS>(), 1);
        else
            cl.executeKernel(pmeInterpolateForceKernel, cl.getNumAtoms());
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        if (doLJPME) {
            setPeriodicBoxArgs(cl, pmeDispersionUpdateBsplinesKernel, 4);
            if (cl.getUseDoublePrecision()) {
                pmeDispersionUpdateBsplinesKernel.setArg<mm_double4>(9, recipBoxVectors[0]);
                pmeDispersionUpdateBsplinesKernel.setArg<mm_double4>(10, recipBoxVectors[1]);
                pmeDispersionUpdateBsplinesKernel.setArg<mm_double4>(11, recipBoxVectors[2]);
            }
            else {
                pmeDispersionUpdateBsplinesKernel.setArg<mm_float4>(9, recipBoxVectorsFloat[0]);
                pmeDispersionUpdateBsplinesKernel.setArg<mm_float4>(10, recipBoxVectorsFloat[1]);
                pmeDispersionUpdateBsplinesKernel.setArg<mm_float4>(11, recipBoxVectorsFloat[2]);
            }
            cl.executeKernel(pmeDispersionUpdateBsplinesKernel, cl.getNumAtoms());
            if (deviceIsCpu && !cl.getSupports64BitGlobalAtomics()) {
                cl.clearBuffer(*pmeGrid);
                setPeriodicBoxArgs(cl, pmeDispersionSpreadChargeKernel, 5);
                if (cl.getUseDoublePrecision()) {
                    pmeDispersionSpreadChargeKernel.setArg<mm_double4>(10, recipBoxVectors[0]);
                    pmeDispersionSpreadChargeKernel.setArg<mm_double4>(11, recipBoxVectors[1]);
                    pmeDispersionSpreadChargeKernel.setArg<mm_double4>(12, recipBoxVectors[2]);
                }
                else {
                    pmeDispersionSpreadChargeKernel.setArg<mm_float4>(10, recipBoxVectorsFloat[0]);
                    pmeDispersionSpreadChargeKernel.setArg<mm_float4>(11, recipBoxVectorsFloat[1]);
                    pmeDispersionSpreadChargeKernel.setArg<mm_float4>(12, recipBoxVectorsFloat[2]);
                }
                cl.executeKernel(pmeDispersionSpreadChargeKernel, 2*cl.getDevice().getInfo<CL_DEVICE_MAX_COMPUTE_UNITS>(), 1);
            }
            else {
                sort->sort(*pmeAtomGridIndex);
                if (cl.getSupports64BitGlobalAtomics()) {
                    cl.clearBuffer(*pmeGrid2);
                    setPeriodicBoxArgs(cl, pmeDispersionSpreadChargeKernel, 5);
                    if (cl.getUseDoublePrecision()) {
                        pmeDispersionSpreadChargeKernel.setArg<mm_double4>(10, recipBoxVectors[0]);
                        pmeDispersionSpreadChargeKernel.setArg<mm_double4>(11, recipBoxVectors[1]);
                        pmeDispersionSpreadChargeKernel.setArg<mm_double4>(12, recipBoxVectors[2]);
                    }
                    else {
                        pmeDispersionSpreadChargeKernel.setArg<mm_float4>(10, recipBoxVectorsFloat[0]);
                        pmeDispersionSpreadChargeKernel.setArg<mm_float4>(11, recipBoxVectorsFloat[1]);
                        pmeDispersionSpreadChargeKernel.setArg<mm_float4>(12, recipBoxVectorsFloat[2]);
                    }
                    cl.executeKernel(pmeDispersionSpreadChargeKernel, cl.getNumAtoms());
                    cl.executeKernel(pmeDispersionFinishSpreadChargeKernel, gridSizeX*gridSizeY*gridSizeZ);
                }
                else {
                    cl.clearBuffer(*pmeGrid);
                    cl.executeKernel(pmeDispersionAtomRangeKernel, cl.getNumAtoms());
                    setPeriodicBoxSizeArg(cl, pmeDispersionZIndexKernel, 2);
                    if (cl.getUseDoublePrecision())
                        pmeDispersionZIndexKernel.setArg<mm_double4>(3, recipBoxVectors[2]);
                    else
                        pmeDispersionZIndexKernel.setArg<mm_float4>(3, recipBoxVectorsFloat[2]);
                    cl.executeKernel(pmeDispersionZIndexKernel, cl.getNumAtoms());
                    cl.executeKernel(pmeDispersionSpreadChargeKernel, cl.getNumAtoms());
                }
            }
            dispersionFft->execFFT(*pmeGrid, *pmeGrid2, true);
            mm_double4 boxSize = cl.getPeriodicBoxSizeDouble();
            if (cl.getUseDoublePrecision()) {
                pmeDispersionConvolutionKernel.setArg<mm_double4>(4, recipBoxVectors[0]);
                pmeDispersionConvolutionKernel.setArg<mm_double4>(5, recipBoxVectors[1]);
                pmeDispersionConvolutionKernel.setArg<mm_double4>(6, recipBoxVectors[2]);
                pmeDispersionEvalEnergyKernel.setArg<mm_double4>(5, recipBoxVectors[0]);
                pmeDispersionEvalEnergyKernel.setArg<mm_double4>(6, recipBoxVectors[1]);
                pmeDispersionEvalEnergyKernel.setArg<mm_double4>(7, recipBoxVectors[2]);
            }
            else {
                pmeDispersionConvolutionKernel.setArg<mm_float4>(4, recipBoxVectorsFloat[0]);
                pmeDispersionConvolutionKernel.setArg<mm_float4>(5, recipBoxVectorsFloat[1]);
                pmeDispersionConvolutionKernel.setArg<mm_float4>(6, recipBoxVectorsFloat[2]);
                pmeDispersionEvalEnergyKernel.setArg<mm_float4>(5, recipBoxVectorsFloat[0]);
                pmeDispersionEvalEnergyKernel.setArg<mm_float4>(6, recipBoxVectorsFloat[1]);
                pmeDispersionEvalEnergyKernel.setArg<mm_float4>(7, recipBoxVectorsFloat[2]);
            }
            if (includeEnergy)
                cl.executeKernel(pmeDispersionEvalEnergyKernel, gridSizeX*gridSizeY*gridSizeZ);
            cl.executeKernel(pmeDispersionConvolutionKernel, gridSizeX*gridSizeY*gridSizeZ);
            fft->execFFT(*pmeGrid2, *pmeGrid, false);
            setPeriodicBoxArgs(cl, pmeDispersionInterpolateForceKernel, 3);
            if (cl.getUseDoublePrecision()) {
                pmeDispersionInterpolateForceKernel.setArg<mm_double4>(8, recipBoxVectors[0]);
                pmeDispersionInterpolateForceKernel.setArg<mm_double4>(9, recipBoxVectors[1]);
                pmeDispersionInterpolateForceKernel.setArg<mm_double4>(10, recipBoxVectors[2]);
            }
            else {
                pmeDispersionInterpolateForceKernel.setArg<mm_float4>(8, recipBoxVectorsFloat[0]);
                pmeDispersionInterpolateForceKernel.setArg<mm_float4>(9, recipBoxVectorsFloat[1]);
                pmeDispersionInterpolateForceKernel.setArg<mm_float4>(10, recipBoxVectorsFloat[2]);
            }
            if (deviceIsCpu)
                cl.executeKernel(pmeDispersionInterpolateForceKernel, 2*cl.getDevice().getInfo<CL_DEVICE_MAX_COMPUTE_UNITS>(), 1);
            else
                cl.executeKernel(pmeDispersionInterpolateForceKernel, cl.getNumAtoms());
        }
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        if (usePmeQueue) {
            pmeQueue.enqueueMarker(&pmeSyncEvent);
            cl.restoreDefaultQueue();
        }
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    }
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    double energy = (includeReciprocal ? ewaldSelfEnergy : 0.0);
    if (dispersionCoefficient != 0.0 && includeDirect) {
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        mm_double4 boxSize = cl.getPeriodicBoxSizeDouble();
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        energy += dispersionCoefficient/(boxSize.x*boxSize.y*boxSize.z);
    }
    return energy;
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}

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void OpenCLCalcNonbondedForceKernel::copyParametersToContext(ContextImpl& context, const NonbondedForce& force) {
    // Make sure the new parameters are acceptable.
    
    if (force.getNumParticles() != cl.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    if (!hasCoulomb || !hasLJ) {
        for (int i = 0; i < force.getNumParticles(); i++) {
            double charge, sigma, epsilon;
            force.getParticleParameters(i, charge, sigma, epsilon);
            if (!hasCoulomb && charge != 0.0)
                throw OpenMMException("updateParametersInContext: The nonbonded force kernel does not include Coulomb interactions, because all charges were originally 0");
            if (!hasLJ && epsilon != 0.0)
                throw OpenMMException("updateParametersInContext: The nonbonded force kernel does not include Lennard-Jones interactions, because all epsilons were originally 0");
        }
    }
    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);
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        if (exceptionAtoms.size() > exceptions.size() && make_pair(particle1, particle2) == exceptionAtoms[exceptions.size()])
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            exceptions.push_back(i);
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        else if (chargeProd != 0.0 || epsilon != 0.0)
            throw OpenMMException("updateParametersInContext: The set of non-excluded exceptions has changed");
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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;
    
    // Record the per-particle parameters.
    
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    vector<double> chargeVector(cl.getNumAtoms());
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    vector<mm_float2> sigmaEpsilonVector(cl.getPaddedNumAtoms(), mm_float2(0,0));
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    double sumSquaredCharges = 0.0;
    for (int i = 0; i < force.getNumParticles(); i++) {
        double charge, sigma, epsilon;
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        force.getParticleParameters(i, charge, sigma, epsilon);
        chargeVector[i] = charge;
        sigmaEpsilonVector[i] = mm_float2((float) (0.5*sigma), (float) (2.0*sqrt(epsilon)));
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        sumSquaredCharges += charge*charge;
    }
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    cl.setCharges(chargeVector);
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    sigmaEpsilon->upload(sigmaEpsilonVector);
    
    // Record the exceptions.
    
    if (numExceptions > 0) {
        vector<vector<int> > atoms(numExceptions, vector<int>(2));
        vector<mm_float4> exceptionParamsVector(numExceptions);
        for (int i = 0; i < numExceptions; i++) {
            double chargeProd, sigma, epsilon;
            force.getExceptionParameters(exceptions[startIndex+i], atoms[i][0], atoms[i][1], chargeProd, sigma, epsilon);
            exceptionParamsVector[i] = mm_float4((float) (ONE_4PI_EPS0*chargeProd), (float) sigma, (float) (4.0*epsilon), 0.0f);
        }
        exceptionParams->upload(exceptionParamsVector);
    }
    
    // Compute other values.
    
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    if (nonbondedMethod == Ewald || nonbondedMethod == PME)
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        ewaldSelfEnergy = (cl.getContextIndex() == 0 ? -ONE_4PI_EPS0*alpha*sumSquaredCharges/sqrt(M_PI) : 0.0);
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    if (force.getUseDispersionCorrection() && cl.getContextIndex() == 0 && (nonbondedMethod == CutoffPeriodic || nonbondedMethod == Ewald || nonbondedMethod == PME))
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        dispersionCoefficient = NonbondedForceImpl::calcDispersionCorrection(context.getSystem(), force);
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    cl.invalidateMolecules(info);
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}

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void OpenCLCalcNonbondedForceKernel::getPMEParameters(double& alpha, int& nx, int& ny, int& nz) const {
    if (nonbondedMethod != PME)
        throw OpenMMException("getPMEParametersInContext: This Context is not using PME");
    if (cl.getPlatformData().useCpuPme)
        cpuPme.getAs<CalcPmeReciprocalForceKernel>().getPMEParameters(alpha, nx, ny, nz);
    else {
        alpha = this->alpha;
        nx = gridSizeX;
        ny = gridSizeY;
        nz = gridSizeZ;
    }
}

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void OpenCLCalcNonbondedForceKernel::getLJPMEParameters(double& alpha, int& nx, int& ny, int& nz) const {
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    if (nonbondedMethod != LJPME)
        throw OpenMMException("getPMEParametersInContext: This Context is not using PME");
    if (cl.getPlatformData().useCpuPme)
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        //cpuPme.getAs<CalcPmeReciprocalForceKernel>().getLJPMEParameters(alpha, nx, ny, nz);
        throw OpenMMException("getPMEParametersInContext: CPUPME has not been implemented for LJPME yet.");
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    else {
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        alpha = this->dispersionAlpha;
        nx = dispersionGridSizeX;
        ny = dispersionGridSizeY;
        nz = dispersionGridSizeZ;
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    }
}

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class OpenCLCalcCustomNonbondedForceKernel::ForceInfo : public OpenCLForceInfo {
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public:
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    ForceInfo(int requiredBuffers, const CustomNonbondedForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
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        if (force.getNumInteractionGroups() > 0) {
            groupsForParticle.resize(force.getNumParticles());
            for (int i = 0; i < force.getNumInteractionGroups(); i++) {
                set<int> set1, set2;
                force.getInteractionGroupParameters(i, set1, set2);
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                for (int p : set1)
                    groupsForParticle[p].insert(2*i);
                for (int p : set2)
                    groupsForParticle[p].insert(2*i+1);
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            }
        }
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    }
    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;
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        if (groupsForParticle.size() > 0 && groupsForParticle[particle1] != groupsForParticle[particle2])
            return false;
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        return true;
    }
    int getNumParticleGroups() {
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        return force.getNumExclusions();
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    }
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    void getParticlesInGroup(int index, vector<int>& particles) {
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        int particle1, particle2;
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        force.getExclusionParticles(index, particle1, particle2);
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        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        return true;
    }
private:
    const CustomNonbondedForce& force;
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    vector<set<int> > groupsForParticle;
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};

OpenCLCalcCustomNonbondedForceKernel::~OpenCLCalcCustomNonbondedForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
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    if (interactionGroupData != NULL)
        delete interactionGroupData;
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    for (auto function : tabulatedFunctions)
        delete function;
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    if (forceCopy != NULL)
        delete forceCopy;
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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)
        ;
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    string prefix = (force.getNumInteractionGroups() == 0 ? "custom"+cl.intToString(forceIndex)+"_" : "");
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    // 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 = OpenCLArray::create<cl_float>(cl, force.getNumGlobalParameters(), "customNonbondedGlobals", 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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    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
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    vector<const TabulatedFunction*> functionList;
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    vector<string> tableTypes;
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    for (int i = 0; i < force.getNumFunctions(); i++) {
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        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
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        string arrayName = prefix+"table"+cl.intToString(i);
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        functionDefinitions.push_back(make_pair(name, arrayName));
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        functions[name] = cl.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
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        int width;
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        vector<float> f = cl.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        tabulatedFunctions.push_back(OpenCLArray::create<float>(cl, f.size(), "TabulatedFunction"));
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        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
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        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(arrayName, "float", width, width*sizeof(float), tabulatedFunctions[tabulatedFunctions.size()-1]->getDeviceBuffer()));
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        if (width == 1)
            tableTypes.push_back("float");
        else
            tableTypes.push_back("float"+cl.intToString(width));
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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;
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    forceExpressions["real customEnergy = "] = energyExpression;
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    forceExpressions["tempForce -= "] = forceExpression;
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    // Create the kernels.

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    vector<pair<ExpressionTreeNode, string> > variables;
    ExpressionTreeNode rnode(new Operation::Variable("r"));
    variables.push_back(make_pair(rnode, "r"));
    variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
    variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
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    for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
        const string& name = force.getPerParticleParameterName(i);
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        variables.push_back(makeVariable(name+"1", prefix+"params"+params->getParameterSuffix(i, "1")));
        variables.push_back(makeVariable(name+"2", prefix+"params"+params->getParameterSuffix(i, "2")));
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    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
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        string value = "globals["+cl.intToString(i)+"]";
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        variables.push_back(makeVariable(name, prefix+value));
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    }
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cl.getNonbondedUtilities().addEnergyParameterDerivative(paramName);
        Lepton::ParsedExpression derivExpression = energyExpression.differentiate(paramName).optimize();
        forceExpressions[derivVariable+" += interactionScale*switchValue*"] = derivExpression;
    }
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    stringstream compute;
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    compute << cl.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, prefix+"temp");
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    map<string, string> replacements;
    replacements["COMPUTE_FORCE"] = compute.str();
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    replacements["USE_SWITCH"] = (useCutoff && force.getUseSwitchingFunction() ? "1" : "0");
    if (force.getUseSwitchingFunction()) {
        // Compute the switching coefficients.
        
        replacements["SWITCH_CUTOFF"] = cl.doubleToString(force.getSwitchingDistance());
        replacements["SWITCH_C3"] = cl.doubleToString(10/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 3.0));
        replacements["SWITCH_C4"] = cl.doubleToString(15/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 4.0));
        replacements["SWITCH_C5"] = cl.doubleToString(6/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 5.0));
    }
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    string source = cl.replaceStrings(OpenCLKernelSources::customNonbonded, replacements);
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    if (force.getNumInteractionGroups() > 0)
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        initInteractionGroups(force, source, tableTypes);
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    else {
        cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source, force.getForceGroup());
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            cl.getNonbondedUtilities().addParameter(OpenCLNonbondedUtilities::ParameterInfo(prefix+"params"+cl.intToString(i+1), buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
        }
        if (globals != NULL) {
            globals->upload(globalParamValues);
            cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(prefix+"globals", "float", 1, sizeof(cl_float), globals->getDeviceBuffer()));
        }
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    }
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    info = new ForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force);
    cl.addForce(info);
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    // Record information for the long range correction.
    
    if (force.getNonbondedMethod() == CustomNonbondedForce::CutoffPeriodic && force.getUseLongRangeCorrection() && cl.getContextIndex() == 0) {
        forceCopy = new CustomNonbondedForce(force);
        hasInitializedLongRangeCorrection = false;
    }
    else {
        longRangeCoefficient = 0.0;
        hasInitializedLongRangeCorrection = true;
    }
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}

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void OpenCLCalcCustomNonbondedForceKernel::initInteractionGroups(const CustomNonbondedForce& force, const string& interactionSource, const vector<string>& tableTypes) {
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    // Process groups to form tiles.
    
    vector<vector<int> > atomLists;
    vector<pair<int, int> > tiles;
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    map<pair<int, int>, int> duplicateInteractions;
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    for (int group = 0; group < force.getNumInteractionGroups(); group++) {
        // Get the list of atoms in this group and sort them.
        
        set<int> set1, set2;
        force.getInteractionGroupParameters(group, set1, set2);
        vector<int> atoms1, atoms2;
        atoms1.insert(atoms1.begin(), set1.begin(), set1.end());
        atoms2.insert(atoms2.begin(), set2.begin(), set2.end());
        sort(atoms1.begin(), atoms1.end());
        sort(atoms2.begin(), atoms2.end());
        
        // Find how many tiles we will create for this group.
        
        int tileWidth = min(min(32, (int) atoms1.size()), (int) atoms2.size());
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        if (tileWidth == 0)
            continue;
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        int numBlocks1 = (atoms1.size()+tileWidth-1)/tileWidth;
        int numBlocks2 = (atoms2.size()+tileWidth-1)/tileWidth;
        
        // Add the tiles.
        
        for (int i = 0; i < numBlocks1; i++)
            for (int j = 0; j < numBlocks2; j++)
                tiles.push_back(make_pair(atomLists.size()+i, atomLists.size()+numBlocks1+j));
        
        // Add the atom lists.
        
        for (int i = 0; i < numBlocks1; i++) {
            vector<int> atoms;
            int first = i*tileWidth;
            int last = min((i+1)*tileWidth, (int) atoms1.size());
            for (int j = first; j < last; j++)
                atoms.push_back(atoms1[j]);
            atomLists.push_back(atoms);
        }
        for (int i = 0; i < numBlocks2; i++) {
            vector<int> atoms;
            int first = i*tileWidth;
            int last = min((i+1)*tileWidth, (int) atoms2.size());
            for (int j = first; j < last; j++)
                atoms.push_back(atoms2[j]);
            atomLists.push_back(atoms);
        }
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        // If this group contains duplicate interactions, record that we need to skip them once.
        
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        for (int a1 : atoms1) {
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            if (set2.find(a1) == set2.end())
                continue;
            for (int j = 0; j < (int) atoms2.size() && atoms2[j] < a1; j++) {
                int a2 = atoms2[j];
                if (set1.find(a2) != set1.end()) {
                    pair<int, int> key = make_pair(a2, a1);
                    if (duplicateInteractions.find(key) == duplicateInteractions.end())
                        duplicateInteractions[key] = 0;
                    duplicateInteractions[key]++;
                }
            }
        }
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    }
    
    // Build a lookup table for quickly identifying excluded interactions.
    
    set<pair<int, int> > exclusions;
    for (int i = 0; i < force.getNumExclusions(); i++) {
        int p1, p2;
        force.getExclusionParticles(i, p1, p2);
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        exclusions.insert(make_pair(min(p1, p2), max(p1, p2)));
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    }
    
    // Build the exclusion flags for each tile.  While we're at it, filter out tiles
    // where all interactions are excluded, and sort the tiles by size.

    vector<vector<int> > exclusionFlags(tiles.size());
    vector<pair<int, int> > tileOrder;
    for (int tile = 0; tile < tiles.size(); tile++) {
        if (atomLists[tiles[tile].first].size() < atomLists[tiles[tile].second].size()) {
            // For efficiency, we want the first axis to be the larger one.
            
            int swap = tiles[tile].first;
            tiles[tile].first = tiles[tile].second;
            tiles[tile].second = swap;
        }
        vector<int>& atoms1 = atomLists[tiles[tile].first];
        vector<int>& atoms2 = atomLists[tiles[tile].second];
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        vector<int> flags(atoms1.size(), (int) (1LL<<atoms2.size())-1);
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        int numExcluded = 0;
        for (int i = 0; i < (int) atoms1.size(); i++)
            for (int j = 0; j < (int) atoms2.size(); j++) {
                int a1 = atoms1[i];
                int a2 = atoms2[j];
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                bool isExcluded = false;
                pair<int, int> key = make_pair(min(a1, a2), max(a1, a2));
                if (a1 == a2 || exclusions.find(key) != exclusions.end())
                    isExcluded = true; // This is an excluded interaction.
                else if (duplicateInteractions.find(key) != duplicateInteractions.end() && duplicateInteractions[key] > 0) {
                    // Both atoms are in both sets, so skip duplicate interactions.
                    
                    isExcluded = true;
                    duplicateInteractions[key]--;
                }
                if (isExcluded) {
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                    flags[i] &= -1-(1<<j);
                    numExcluded++;
                }
            }
        if (numExcluded == atoms1.size()*atoms2.size())
            continue; // All interactions are excluded.
        tileOrder.push_back(make_pair((int) -atoms2.size(), tile));
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        exclusionFlags[tile] = flags;
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    }
    sort(tileOrder.begin(), tileOrder.end());
    
    // Merge tiles to get as close as possible to 32 along the first axis of each one.
    
    vector<int> tileSetStart;
    tileSetStart.push_back(0);
    int tileSetSize = 0;
    for (int i = 0; i < tileOrder.size(); i++) {
        int tile = tileOrder[i].second;
        int size = atomLists[tiles[tile].first].size();
        if (tileSetSize+size > 32) {
            tileSetStart.push_back(i);
            tileSetSize = 0;
        }
        tileSetSize += size;
    }
    tileSetStart.push_back(tileOrder.size());
    
    // Build the data structures.
    
    int numTileSets = tileSetStart.size()-1;
    vector<mm_int4> groupData;
    for (int tileSet = 0; tileSet < numTileSets; tileSet++) {
        int indexInTileSet = 0;
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        int minSize = 0;
        if (cl.getSIMDWidth() < 32) {
            // We need to include a barrier inside the inner loop, so ensure that all
            // threads will loop the same number of times.
            
            for (int i = tileSetStart[tileSet]; i < tileSetStart[tileSet+1]; i++)
                minSize = max(minSize, (int) atomLists[tiles[tileOrder[i].second].first].size());
        }
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        for (int i = tileSetStart[tileSet]; i < tileSetStart[tileSet+1]; i++) {
            int tile = tileOrder[i].second;
            vector<int>& atoms1 = atomLists[tiles[tile].first];
            vector<int>& atoms2 = atomLists[tiles[tile].second];
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            int range = indexInTileSet + ((indexInTileSet+max(minSize, (int) atoms1.size()))<<16);
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            int allFlags = (1<<atoms2.size())-1;
            for (int j = 0; j < (int) atoms1.size(); j++) {
                int a1 = atoms1[j];
                int a2 = (j < atoms2.size() ? atoms2[j] : 0);
                int flags = (exclusionFlags[tile].size() > 0 ? exclusionFlags[tile][j] : allFlags);
                groupData.push_back(mm_int4(a1, a2, range, flags<<indexInTileSet));
            }
            indexInTileSet += atoms1.size();
        }
        for (; indexInTileSet < 32; indexInTileSet++)
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            groupData.push_back(mm_int4(0, 0, minSize<<16, 0));
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    }
    interactionGroupData = OpenCLArray::create<mm_int4>(cl, groupData.size(), "interactionGroupData");
    interactionGroupData->upload(groupData);
    
    // Create the kernel.
    
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    hasParamDerivs = (force.getNumEnergyParameterDerivatives() > 0);
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    map<string, string> replacements;
    replacements["COMPUTE_INTERACTION"] = interactionSource;
    const string suffixes[] = {"x", "y", "z", "w"};
    stringstream localData;
    int localDataSize = 0;
    vector<OpenCLNonbondedUtilities::ParameterInfo>& buffers = params->getBuffers(); 
    for (int i = 0; i < (int) buffers.size(); i++) {
        if (buffers[i].getNumComponents() == 1)
            localData<<buffers[i].getComponentType()<<" params"<<(i+1)<<";\n";
        else {
            for (int j = 0; j < buffers[i].getNumComponents(); ++j)
                localData<<buffers[i].getComponentType()<<" params"<<(i+1)<<"_"<<suffixes[j]<<";\n";
        }
        localDataSize += buffers[i].getSize();
    }
    replacements["ATOM_PARAMETER_DATA"] = localData.str();
    stringstream args;
    for (int i = 0; i < (int) buffers.size(); i++)
        args<<", __global const "<<buffers[i].getType()<<"* restrict global_params"<<(i+1);
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    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        args << ", __global const " << tableTypes[i]<< "* restrict table" << i;
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    if (globals != NULL)
        args<<", __global const float* restrict globals";
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    if (hasParamDerivs)
        args << ", __global mixed* restrict energyParamDerivs";
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    replacements["PARAMETER_ARGUMENTS"] = args.str();
    stringstream load1;
    for (int i = 0; i < (int) buffers.size(); i++)
        load1<<buffers[i].getType()<<" params"<<(i+1)<<"1 = global_params"<<(i+1)<<"[atom1];\n";
    replacements["LOAD_ATOM1_PARAMETERS"] = load1.str();
    stringstream loadLocal2;
    for (int i = 0; i < (int) buffers.size(); i++) {
        if (buffers[i].getNumComponents() == 1)
            loadLocal2<<"localData[get_local_id(0)].params"<<(i+1)<<" = global_params"<<(i+1)<<"[atom2];\n";
        else {
            loadLocal2<<buffers[i].getType()<<" temp_params"<<(i+1)<<" = global_params"<<(i+1)<<"[atom2];\n";
            for (int j = 0; j < buffers[i].getNumComponents(); ++j)
                loadLocal2<<"localData[get_local_id(0)].params"<<(i+1)<<"_"<<suffixes[j]<<" = temp_params"<<(i+1)<<"."<<suffixes[j]<<";\n";
        }
    }
    replacements["LOAD_LOCAL_PARAMETERS"] = loadLocal2.str();
    stringstream load2;
    for (int i = 0; i < (int) buffers.size(); i++) {
        if (buffers[i].getNumComponents() == 1)
            load2<<buffers[i].getType()<<" params"<<(i+1)<<"2 = localData[localIndex].params"<<(i+1)<<";\n";
        else {
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            load2<<buffers[i].getType()<<" params"<<(i+1)<<"2 = ("<<buffers[i].getType()<<") (";
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            for (int j = 0; j < buffers[i].getNumComponents(); ++j) {
                if (j > 0)
                    load2<<", ";
                load2<<"localData[localIndex].params"<<(i+1)<<"_"<<suffixes[j];
            }
            load2<<");\n";
        }
    }
    replacements["LOAD_ATOM2_PARAMETERS"] = load2.str();
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    stringstream initDerivs, saveDerivs;
    const vector<string>& allParamDerivNames = cl.getEnergyParamDerivNames();
    int numDerivs = allParamDerivNames.size();
    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cl.getNonbondedUtilities().addEnergyParameterDerivative(paramName);
        initDerivs<<"mixed "<<derivVariable<<" = 0;\n";
        for (int index = 0; index < numDerivs; index++)
            if (allParamDerivNames[index] == paramName)
                saveDerivs<<"energyParamDerivs[get_global_id(0)*"<<numDerivs<<"+"<<index<<"] += "<<derivVariable<<";\n";
    }
    replacements["INIT_DERIVATIVES"] = initDerivs.str();
    replacements["SAVE_DERIVATIVES"] = saveDerivs.str();
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    map<string, string> defines;
    if (force.getNonbondedMethod() != CustomNonbondedForce::NoCutoff)
        defines["USE_CUTOFF"] = "1";
    if (force.getNonbondedMethod() == CustomNonbondedForce::CutoffPeriodic)
        defines["USE_PERIODIC"] = "1";
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    defines["LOCAL_MEMORY_SIZE"] = cl.intToString(max(32, cl.getNonbondedUtilities().getForceThreadBlockSize()));
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    double cutoff = force.getCutoffDistance();
    defines["CUTOFF_SQUARED"] = cl.doubleToString(cutoff*cutoff);
    defines["PADDED_NUM_ATOMS"] = cl.intToString(cl.getPaddedNumAtoms());
    defines["TILE_SIZE"] = "32";
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*numTileSets/numContexts;
    int endIndex = (cl.getContextIndex()+1)*numTileSets/numContexts;
    defines["FIRST_TILE"] = cl.intToString(startIndex);
    defines["LAST_TILE"] = cl.intToString(endIndex);
    if ((localDataSize/4)%2 == 0 && !cl.getUseDoublePrecision())
        defines["PARAMETER_SIZE_IS_EVEN"] = "1";
    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customNonbondedGroups, replacements), defines);
    interactionGroupKernel = cl::Kernel(program, "computeInteractionGroups");
    numGroupThreadBlocks = cl.getNonbondedUtilities().getNumForceThreadBlocks();
}

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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;
        }
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        if (changed) {
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            globals->upload(globalParamValues);
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            if (forceCopy != NULL) {
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                CustomNonbondedForceImpl::calcLongRangeCorrection(*forceCopy, context.getOwner(), longRangeCoefficient, longRangeCoefficientDerivs);
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                hasInitializedLongRangeCorrection = true;
            }
        }
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    }
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    if (!hasInitializedLongRangeCorrection) {
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        CustomNonbondedForceImpl::calcLongRangeCorrection(*forceCopy, context.getOwner(), longRangeCoefficient, longRangeCoefficientDerivs);
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        hasInitializedLongRangeCorrection = true;
    }
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    if (interactionGroupData != NULL) {
        if (!hasInitializedKernel) {
            hasInitializedKernel = true;
            int index = 0;
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            bool useLong = cl.getSupports64BitGlobalAtomics();
            interactionGroupKernel.setArg<cl::Buffer>(index++, (useLong ? cl.getLongForceBuffer() : cl.getForceBuffers()).getDeviceBuffer());
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            interactionGroupKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
            interactionGroupKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
            interactionGroupKernel.setArg<cl::Buffer>(index++, interactionGroupData->getDeviceBuffer());
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            index += 5;
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            for (auto& buffer : params->getBuffers())
                interactionGroupKernel.setArg<cl::Memory>(index++, buffer.getMemory());
            for (auto function : tabulatedFunctions)
                interactionGroupKernel.setArg<cl::Memory>(index++, function->getDeviceBuffer());
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            if (globals != NULL)
                interactionGroupKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
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            if (hasParamDerivs)
                interactionGroupKernel.setArg<cl::Memory>(index++, cl.getEnergyParamDerivBuffer().getDeviceBuffer());
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        }
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        setPeriodicBoxArgs(cl, interactionGroupKernel, 4);
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        int forceThreadBlockSize = max(32, cl.getNonbondedUtilities().getForceThreadBlockSize());
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        cl.executeKernel(interactionGroupKernel, numGroupThreadBlocks*forceThreadBlockSize, forceThreadBlockSize);
    }
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    mm_double4 boxSize = cl.getPeriodicBoxSizeDouble();
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    double volume = boxSize.x*boxSize.y*boxSize.z;
    map<string, double>& derivs = cl.getEnergyParamDerivWorkspace();
    for (int i = 0; i < longRangeCoefficientDerivs.size(); i++)
        derivs[forceCopy->getEnergyParameterDerivativeName(i)] += longRangeCoefficientDerivs[i]/volume;
    return longRangeCoefficient/volume;
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}
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void OpenCLCalcCustomNonbondedForceKernel::copyParametersToContext(ContextImpl& context, const CustomNonbondedForce& force) {
    int numParticles = force.getNumParticles();
    if (numParticles != cl.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    
    // Record the per-particle parameters.
    
    vector<vector<cl_float> > paramVector(numParticles);
    vector<double> parameters;
    for (int i = 0; i < numParticles; i++) {
        force.getParticleParameters(i, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
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    // If necessary, recompute the long range correction.
    
    if (forceCopy != NULL) {
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        CustomNonbondedForceImpl::calcLongRangeCorrection(force, context.getOwner(), longRangeCoefficient, longRangeCoefficientDerivs);
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        hasInitializedLongRangeCorrection = true;
        *forceCopy = force;
    }
    
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    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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class OpenCLCalcGBSAOBCForceKernel::ForceInfo : public OpenCLForceInfo {
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public:
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    ForceInfo(int requiredBuffers, const GBSAOBCForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
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    }
    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 = OpenCLArray::create<mm_float2>(cl, cl.getPaddedNumAtoms(), "gbsaObcParams");
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    int elementSize = (cl.getUseDoublePrecision() ? sizeof(cl_double) : sizeof(cl_float));
    bornRadii = new OpenCLArray(cl, cl.getPaddedNumAtoms(), elementSize, "bornRadii");
    obcChain = new OpenCLArray(cl, cl.getPaddedNumAtoms(), elementSize, "obcChain");
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    if (cl.getSupports64BitGlobalAtomics()) {
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        longBornSum = OpenCLArray::create<cl_long>(cl, cl.getPaddedNumAtoms(), "longBornSum");
        longBornForce = OpenCLArray::create<cl_long>(cl, cl.getPaddedNumAtoms(), "longBornForce");
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        bornForce = new OpenCLArray(cl, cl.getPaddedNumAtoms(), elementSize, "bornForce");
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        cl.addAutoclearBuffer(*longBornSum);
        cl.addAutoclearBuffer(*longBornForce);
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    }
    else {
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        bornSum = new OpenCLArray(cl, cl.getPaddedNumAtoms()*nb.getNumForceBuffers(), elementSize, "bornSum");
        bornForce = new OpenCLArray(cl, cl.getPaddedNumAtoms()*nb.getNumForceBuffers(), elementSize, "bornForce");
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        cl.addAutoclearBuffer(*bornSum);
        cl.addAutoclearBuffer(*bornForce);
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    }
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    vector<mm_float4> posqf(cl.getPaddedNumAtoms());
    vector<mm_double4> posqd(cl.getPaddedNumAtoms());
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    vector<mm_float2> paramsVector(cl.getPaddedNumAtoms(), mm_float2(1,1));
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    const double dielectricOffset = 0.009;
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    for (int i = 0; i < force.getNumParticles(); i++) {
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        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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        if (cl.getUseDoublePrecision())
            posqd[i] = mm_double4(0, 0, 0, charge);
        else
            posqf[i] = mm_float4(0, 0, 0, (float) charge);
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    }
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    if (cl.getUseDoublePrecision())
        cl.getPosq().upload(posqd);
    else
        cl.getPosq().upload(posqf);
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    params->upload(paramsVector);
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    prefactor = -ONE_4PI_EPS0*((1.0/force.getSoluteDielectric())-(1.0/force.getSolventDielectric()));
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    surfaceAreaFactor = -6.0*4*M_PI*force.getSurfaceAreaEnergy();
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    bool useCutoff = (force.getNonbondedMethod() != GBSAOBCForce::NoCutoff);
    bool usePeriodic = (force.getNonbondedMethod() != GBSAOBCForce::NoCutoff && force.getNonbondedMethod() != GBSAOBCForce::CutoffNonPeriodic);
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    cutoff = force.getCutoffDistance();
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    string source = OpenCLKernelSources::gbsaObc2;
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    nb.addInteraction(useCutoff, usePeriodic, false, cutoff, vector<vector<int> >(), source, force.getForceGroup());
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    nb.addParameter(OpenCLNonbondedUtilities::ParameterInfo("obcParams", "float", 2, sizeof(cl_float2), params->getDeviceBuffer()));;
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    nb.addParameter(OpenCLNonbondedUtilities::ParameterInfo("bornForce", "real", 1, elementSize, bornForce->getDeviceBuffer()));;
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    info = new ForceInfo(nb.getNumForceBuffers(), force);
    cl.addForce(info);
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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.getUseCutoff())
            defines["USE_CUTOFF"] = "1";
        if (nb.getUsePeriodic())
            defines["USE_PERIODIC"] = "1";
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        defines["CUTOFF_SQUARED"] = cl.doubleToString(cutoff*cutoff);
        defines["CUTOFF"] = cl.doubleToString(cutoff);
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        defines["PREFACTOR"] = cl.doubleToString(prefactor);
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        defines["SURFACE_AREA_FACTOR"] = cl.doubleToString(surfaceAreaFactor);
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        defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = cl.intToString(cl.getPaddedNumAtoms());
        defines["NUM_BLOCKS"] = cl.intToString(cl.getNumAtomBlocks());
        defines["FORCE_WORK_GROUP_SIZE"] = cl.intToString(nb.getForceThreadBlockSize());
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        defines["TILE_SIZE"] = cl.intToString(OpenCLContext::TileSize);
        int numExclusionTiles = nb.getExclusionTiles().getSize();
        defines["NUM_TILES_WITH_EXCLUSIONS"] = cl.intToString(numExclusionTiles);
        int numContexts = cl.getPlatformData().contexts.size();
        int startExclusionIndex = cl.getContextIndex()*numExclusionTiles/numContexts;
        int endExclusionIndex = (cl.getContextIndex()+1)*numExclusionTiles/numContexts;
        defines["FIRST_EXCLUSION_TILE"] = cl.intToString(startExclusionIndex);
        defines["LAST_EXCLUSION_TILE"] = cl.intToString(endExclusionIndex);
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        string platformVendor = cl::Platform(cl.getDevice().getInfo<CL_DEVICE_PLATFORM>()).getInfo<CL_PLATFORM_VENDOR>();
        if (platformVendor == "Apple")
            defines["USE_APPLE_WORKAROUND"] = "1";
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        string file;
        if (deviceIsCpu)
            file = OpenCLKernelSources::gbsaObc_cpu;
        else
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            file = OpenCLKernelSources::gbsaObc;
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        cl::Program program = cl.createProgram(file, defines);
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        bool useLong = cl.getSupports64BitGlobalAtomics();
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        int index = 0;
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        computeBornSumKernel = cl::Kernel(program, "computeBornSum");
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        computeBornSumKernel.setArg<cl::Buffer>(index++, (useLong ? longBornSum->getDeviceBuffer() : bornSum->getDeviceBuffer()));
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        computeBornSumKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        computeBornSumKernel.setArg<cl::Buffer>(index++, params->getDeviceBuffer());
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        if (nb.getUseCutoff()) {
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            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractingTiles().getDeviceBuffer());
            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractionCount().getDeviceBuffer());
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            index += 5; // The periodic box size arguments are set when the kernel is executed.
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            computeBornSumKernel.setArg<cl_uint>(index++, maxTiles);
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            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getBlockCenters().getDeviceBuffer());
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            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getBlockBoundingBoxes().getDeviceBuffer());
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            computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getInteractingAtoms().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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        computeBornSumKernel.setArg<cl::Buffer>(index++, nb.getExclusionTiles().getDeviceBuffer());
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        force1Kernel = cl::Kernel(program, "computeGBSAForce1");
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        index = 0;
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        force1Kernel.setArg<cl::Buffer>(index++, (useLong ? cl.getLongForceBuffer().getDeviceBuffer() : cl.getForceBuffers().getDeviceBuffer()));
        force1Kernel.setArg<cl::Buffer>(index++, (useLong ? longBornForce->getDeviceBuffer() : bornForce->getDeviceBuffer()));
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        force1Kernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        force1Kernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        force1Kernel.setArg<cl::Buffer>(index++, bornRadii->getDeviceBuffer());
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        index++; // Whether to include energy.
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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 += 5; // The periodic box size arguments are set when the kernel is executed.
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            force1Kernel.setArg<cl_uint>(index++, maxTiles);
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            force1Kernel.setArg<cl::Buffer>(index++, nb.getBlockCenters().getDeviceBuffer());
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            force1Kernel.setArg<cl::Buffer>(index++, nb.getBlockBoundingBoxes().getDeviceBuffer());
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            force1Kernel.setArg<cl::Buffer>(index++, nb.getInteractingAtoms().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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        force1Kernel.setArg<cl::Buffer>(index++, nb.getExclusionTiles().getDeviceBuffer());
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        program = cl.createProgram(OpenCLKernelSources::gbsaObcReductions, defines);
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        reduceBornSumKernel = cl::Kernel(program, "reduceBornSum");
        reduceBornSumKernel.setArg<cl_int>(0, cl.getPaddedNumAtoms());
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        reduceBornSumKernel.setArg<cl_int>(1, nb.getNumForceBuffers());
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        reduceBornSumKernel.setArg<cl_float>(2, 1.0f);
        reduceBornSumKernel.setArg<cl_float>(3, 0.8f);
        reduceBornSumKernel.setArg<cl_float>(4, 4.85f);
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        reduceBornSumKernel.setArg<cl::Buffer>(5, (useLong ? longBornSum->getDeviceBuffer() : bornSum->getDeviceBuffer()));
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        reduceBornSumKernel.setArg<cl::Buffer>(6, params->getDeviceBuffer());
        reduceBornSumKernel.setArg<cl::Buffer>(7, bornRadii->getDeviceBuffer());
        reduceBornSumKernel.setArg<cl::Buffer>(8, obcChain->getDeviceBuffer());
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        reduceBornForceKernel = cl::Kernel(program, "reduceBornForce");
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        index = 0;
        reduceBornForceKernel.setArg<cl_int>(index++, cl.getPaddedNumAtoms());
        reduceBornForceKernel.setArg<cl_int>(index++, nb.getNumForceBuffers());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, bornForce->getDeviceBuffer());
        if (useLong)
            reduceBornForceKernel.setArg<cl::Buffer>(index++, longBornForce->getDeviceBuffer());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, params->getDeviceBuffer());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, bornRadii->getDeviceBuffer());
        reduceBornForceKernel.setArg<cl::Buffer>(index++, obcChain->getDeviceBuffer());
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    }
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    force1Kernel.setArg<cl_int>(5, includeEnergy);
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    if (nb.getUseCutoff()) {
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        setPeriodicBoxArgs(cl, computeBornSumKernel, 5);
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        setPeriodicBoxArgs(cl, force1Kernel, 8);
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        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
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            computeBornSumKernel.setArg<cl::Buffer>(3, nb.getInteractingTiles().getDeviceBuffer());
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            computeBornSumKernel.setArg<cl_uint>(10, maxTiles);
            computeBornSumKernel.setArg<cl::Buffer>(13, nb.getInteractingAtoms().getDeviceBuffer());
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            force1Kernel.setArg<cl::Buffer>(6, nb.getInteractingTiles().getDeviceBuffer());
            force1Kernel.setArg<cl_uint>(13, maxTiles);
            force1Kernel.setArg<cl::Buffer>(16, nb.getInteractingAtoms().getDeviceBuffer());
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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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void OpenCLCalcGBSAOBCForceKernel::copyParametersToContext(ContextImpl& context, const GBSAOBCForce& force) {
    // Make sure the new parameters are acceptable.
    
    int numParticles = force.getNumParticles();
    if (numParticles != cl.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    
    // Record the per-particle parameters.
    
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    vector<double> chargeVector(cl.getNumAtoms());
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    vector<mm_float2> paramsVector(cl.getPaddedNumAtoms(), mm_float2(1,1));
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    const double dielectricOffset = 0.009;
    for (int i = 0; i < numParticles; i++) {
        double charge, radius, scalingFactor;
        force.getParticleParameters(i, charge, radius, scalingFactor);
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        chargeVector[i] = charge;
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        radius -= dielectricOffset;
        paramsVector[i] = mm_float2((float) radius, (float) (scalingFactor*radius));
    }
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    cl.setCharges(chargeVector);
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    params->upload(paramsVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

OpenCLCalcCustomGBForceKernel::~OpenCLCalcCustomGBForceKernel() {
    if (params != NULL)
        delete params;
    if (computedValues != NULL)
        delete computedValues;
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    if (energyDerivs != NULL)
        delete energyDerivs;
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    if (energyDerivChain != NULL)
        delete energyDerivChain;
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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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    for (auto function : tabulatedFunctions)
        delete function;
    for (auto d : dValue0dParam)
        delete d;
    for (auto d : dValuedParam)
        delete d;
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}

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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    cutoff = force.getCutoffDistance();
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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)
        ;
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    string prefix = "custom"+cl.intToString(forceIndex)+"_";
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    // Record parameters and exclusions.

    int numParticles = force.getNumParticles();
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    int paddedNumParticles = cl.getPaddedNumAtoms();
    int numParams = force.getNumPerParticleParameters();
    params = new OpenCLParameterSet(cl, force.getNumPerParticleParameters(), paddedNumParticles, "customGBParameters", true);
    computedValues = new OpenCLParameterSet(cl, force.getNumComputedValues(), paddedNumParticles, "customGBComputedValues", true, cl.getUseDoublePrecision());
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    if (force.getNumGlobalParameters() > 0)
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        globals = OpenCLArray::create<cl_float>(cl, force.getNumGlobalParameters(), "customGBGlobals", CL_MEM_READ_ONLY);
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    vector<vector<cl_float> > paramVector(paddedNumParticles, vector<cl_float>(numParams, 0));
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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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        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.

    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
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    vector<const TabulatedFunction*> functionList;
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    stringstream tableArgs;
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    for (int i = 0; i < force.getNumTabulatedFunctions(); i++) {
        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
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        string arrayName = prefix+"table"+cl.intToString(i);
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        functionDefinitions.push_back(make_pair(name, arrayName));
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        functions[name] = cl.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
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        int width;
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        vector<float> f = cl.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        tabulatedFunctions.push_back(OpenCLArray::create<float>(cl, f.size(), "TabulatedFunction"));
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        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
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        cl.getNonbondedUtilities().addArgument(OpenCLNonbondedUtilities::ParameterInfo(arrayName, "float", width, width*sizeof(float), tabulatedFunctions[tabulatedFunctions.size()-1]->getDeviceBuffer()));
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        tableArgs << ", __global const float";
        if (width > 1)
            tableArgs << width;
        tableArgs << "* restrict " << arrayName;
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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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    vector<vector<Lepton::ParsedExpression> > valueParamDerivExpressions(force.getNumComputedValues());
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    needParameterGradient = false;
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    for (int i = 0; i < force.getNumComputedValues(); i++) {
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        Lepton::ParsedExpression ex = Lepton::Parser::parse(computedValueExpressions[i], functions).optimize();
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        if (i > 0) {
            valueGradientExpressions[i].push_back(ex.differentiate("x").optimize());
            valueGradientExpressions[i].push_back(ex.differentiate("y").optimize());
            valueGradientExpressions[i].push_back(ex.differentiate("z").optimize());
            if (!isZeroExpression(valueGradientExpressions[i][0]) || !isZeroExpression(valueGradientExpressions[i][1]) || !isZeroExpression(valueGradientExpressions[i][2]))
                needParameterGradient = true;
             for (int j = 0; j < i; j++)
                valueDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]).optimize());
        }
        for (int j = 0; j < force.getNumEnergyParameterDerivatives(); j++)
            valueParamDerivExpressions[i].push_back(ex.differentiate(force.getEnergyParameterDerivativeName(j)).optimize());
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    }
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    vector<vector<Lepton::ParsedExpression> > energyDerivExpressions(force.getNumEnergyTerms());
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    vector<vector<Lepton::ParsedExpression> > energyParamDerivExpressions(force.getNumEnergyTerms());
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    vector<bool> needChainForValue(force.getNumComputedValues(), false);
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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++) {
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            if (type == CustomGBForce::SingleParticle) {
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                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]).optimize());
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                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
            }
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            else {
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]+"1").optimize());
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                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
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                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]+"2").optimize());
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                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
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            }
        }
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        for (int j = 0; j < force.getNumEnergyParameterDerivatives(); j++)
            energyParamDerivExpressions[i].push_back(ex.differentiate(force.getEnergyParameterDerivativeName(j)).optimize());
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    }
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    bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
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    bool useLong = cl.getSupports64BitGlobalAtomics();
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    if (useLong) {
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        longEnergyDerivs = OpenCLArray::create<cl_long>(cl, force.getNumComputedValues()*cl.getPaddedNumAtoms(), "customGBLongEnergyDerivatives");
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        energyDerivs = new OpenCLParameterSet(cl, force.getNumComputedValues(), cl.getPaddedNumAtoms(), "customGBEnergyDerivatives", true);
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    }
    else
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        energyDerivs = new OpenCLParameterSet(cl, force.getNumComputedValues(), cl.getPaddedNumAtoms()*cl.getNonbondedUtilities().getNumForceBuffers(), "customGBEnergyDerivatives", true);
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    energyDerivChain = new OpenCLParameterSet(cl, force.getNumComputedValues(), cl.getPaddedNumAtoms(), "customGBEnergyDerivativeChain", true);
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    int elementSize = (cl.getUseDoublePrecision() ? sizeof(cl_double) : sizeof(cl_float));
    needEnergyParamDerivs = (force.getNumEnergyParameterDerivatives() > 0);
    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
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        dValuedParam.push_back(new OpenCLParameterSet(cl, force.getNumComputedValues(), cl.getPaddedNumAtoms(), "dValuedParam", true, cl.getUseDoublePrecision()));
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        if (useLong)
            dValue0dParam.push_back(OpenCLArray::create<cl_long>(cl, cl.getPaddedNumAtoms(), "dValue0dParam"));
        else
            dValue0dParam.push_back(new OpenCLArray(cl, cl.getPaddedNumAtoms()*cl.getNonbondedUtilities().getNumForceBuffers(), elementSize, "dValue0dParam"));
        cl.addAutoclearBuffer(*dValue0dParam.back());
        string name = force.getEnergyParameterDerivativeName(i);
        cl.addEnergyParameterDerivative(name);
    }
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    // Create the kernels.

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

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        vector<pair<ExpressionTreeNode, string> > variables;
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        map<string, string> rename;
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        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
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        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
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            variables.push_back(makeVariable(name+"1", "params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", "params"+params->getParameterSuffix(i, "2")));
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            rename[name+"1"] = name+"2";
            rename[name+"2"] = name+"1";
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        }
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
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            string value = "globals["+cl.intToString(i)+"]";
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            variables.push_back(makeVariable(name, value));
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        }
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        map<string, Lepton::ParsedExpression> n2ValueExpressions;
        stringstream n2ValueSource;
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        Lepton::ParsedExpression ex = Lepton::Parser::parse(computedValueExpressions[0], functions).optimize();
        n2ValueExpressions["tempValue1 = "] = ex;
        n2ValueExpressions["tempValue2 = "] = ex.renameVariables(rename);
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        for (int i = 0; i < valueParamDerivExpressions[0].size(); i++) {
            string variableBase = "temp_dValue0dParam"+cl.intToString(i+1);
            if (!isZeroExpression(valueParamDerivExpressions[0][i])) {
                n2ValueExpressions[variableBase+"_1 = "] = valueParamDerivExpressions[0][i];
                n2ValueExpressions[variableBase+"_2 = "] = valueParamDerivExpressions[0][i].renameVariables(rename);
            }
        }
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        n2ValueSource << cl.getExpressionUtilities().createExpressions(n2ValueExpressions, variables, functionList, functionDefinitions, "temp");
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        map<string, string> replacements;
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        string n2ValueStr = n2ValueSource.str();
        replacements["COMPUTE_VALUE"] = n2ValueStr;
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        stringstream extraArgs, loadLocal1, loadLocal2, load1, load2, tempDerivs1, tempDerivs2, storeDeriv1, storeDeriv2;
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        if (force.getNumGlobalParameters() > 0)
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            extraArgs << ", __global const float* globals";
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        pairValueUsesParam.resize(params->getBuffers().size(), false);
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            string paramName = "params"+cl.intToString(i+1);
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            if (n2ValueStr.find(paramName+"1") != n2ValueStr.npos || n2ValueStr.find(paramName+"2") != n2ValueStr.npos) {
                extraArgs << ", __global const " << buffer.getType() << "* restrict global_" << paramName << ", __local " << buffer.getType() << "* restrict local_" << paramName;
                loadLocal1 << "local_" << paramName << "[localAtomIndex] = " << paramName << "1;\n";
                loadLocal2 << "local_" << paramName << "[localAtomIndex] = global_" << paramName << "[j];\n";
                load1 << buffer.getType() << " " << paramName << "1 = global_" << paramName << "[atom1];\n";
                load2 << buffer.getType() << " " << paramName << "2 = local_" << paramName << "[atom2];\n";
                pairValueUsesParam[i] = true;
            }
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        }
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        for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
            string derivName = "dValue0dParam"+cl.intToString(i+1);
            if (useLong)
                extraArgs << ", __global long* restrict global_" << derivName;
            else
                extraArgs << ", __global real* restrict global_" << derivName;
            extraArgs << ", __local real* restrict local_" << derivName;
            loadLocal2 << "local_" << derivName << "[localAtomIndex] = 0;\n";
            load1 << "real " << derivName << " = 0;\n";
            if (!isZeroExpression(valueParamDerivExpressions[0][i])) {
                load2 << "real temp_" << derivName << "_1 = 0;\n";
                load2 << "real temp_" << derivName << "_2 = 0;\n";
                tempDerivs1 << derivName << " += temp_" << derivName << "_1;\n";
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                if (deviceIsCpu)
                    tempDerivs2 << "local_" << derivName << "[j] += temp_" << derivName << "_2;\n";
                else
                    tempDerivs2 << "local_" << derivName << "[tbx+tj] += temp_" << derivName << "_2;\n";
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                if (useLong) {
                    storeDeriv1 << "atom_add(&global_" << derivName << "[offset1], (long) (" << derivName << "*0x100000000));\n";
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                    if (deviceIsCpu)
                        storeDeriv2 << "atom_add(&global_" << derivName << "[offset2], (long) (local_" << derivName << "[tgx]*0x100000000));\n";
                    else
                        storeDeriv2 << "atom_add(&global_" << derivName << "[offset2], (long) (local_" << derivName << "[get_local_id(0)]*0x100000000));\n";
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                }
                else {
                    storeDeriv1 << "global_" << derivName << "[offset1] += " << derivName << ";\n";
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                    if (deviceIsCpu)
                        storeDeriv2 << "global_" << derivName << "[offset2] += local_" << derivName << "[tgx];\n";
                    else
                        storeDeriv2 << "global_" << derivName << "[offset2] += local_" << derivName << "[get_local_id(0)];\n";
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                }
            }
        }
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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();
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        replacements["ADD_TEMP_DERIVS1"] = tempDerivs1.str();
        replacements["ADD_TEMP_DERIVS2"] = tempDerivs2.str();
        replacements["STORE_PARAM_DERIVS1"] = storeDeriv1.str();
        replacements["STORE_PARAM_DERIVS2"] = storeDeriv2.str();
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        if (useCutoff)
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            pairValueDefines["USE_CUTOFF"] = "1";
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        if (usePeriodic)
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            pairValueDefines["USE_PERIODIC"] = "1";
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        if (useExclusionsForValue)
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            pairValueDefines["USE_EXCLUSIONS"] = "1";
        pairValueDefines["FORCE_WORK_GROUP_SIZE"] = cl.intToString(cl.getNonbondedUtilities().getForceThreadBlockSize());
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        pairValueDefines["CUTOFF_SQUARED"] = cl.doubleToString(cutoff*cutoff);
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        pairValueDefines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
        pairValueDefines["PADDED_NUM_ATOMS"] = cl.intToString(cl.getPaddedNumAtoms());
        pairValueDefines["NUM_BLOCKS"] = cl.intToString(cl.getNumAtomBlocks());
        pairValueDefines["TILE_SIZE"] = cl.intToString(OpenCLContext::TileSize);
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        string file;
        if (deviceIsCpu)
            file = OpenCLKernelSources::customGBValueN2_cpu;
        else
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            file = OpenCLKernelSources::customGBValueN2;
        pairValueSrc = cl.replaceStrings(file, replacements);
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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.

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        stringstream reductionSource, extraArgs, deriv0;
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        if (force.getNumGlobalParameters() > 0)
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            extraArgs << ", __global const float* globals";
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            string paramName = "params"+cl.intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << paramName;
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        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
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            string valueName = "values"+cl.intToString(i+1);
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            extraArgs << ", __global " << buffer.getType() << "* restrict global_" << valueName;
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            reductionSource << buffer.getType() << " local_" << valueName << ";\n";
        }
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        for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
            string variableName = "dValuedParam_0_"+cl.intToString(i);
            if (useLong) {
                extraArgs << ", __global const long* restrict dValue0dParam" << i;
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                deriv0 << "real " << variableName << " = (1.0f/0x100000000)*dValue0dParam" << i << "[index];\n";
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            }
            else {
                extraArgs << ", __global const real* restrict dValue0dParam" << i;
                deriv0 << "real " << variableName << " = dValue0dParam" << i << "[index];\n";
                deriv0 << "for (int i = index+bufferSize; i < totalSize; i += bufferSize)\n";
                deriv0 << "    " << variableName << " += dValue0dParam" << i << "[i];\n";
            }
            for (int j = 0; j < dValuedParam[i]->getBuffers().size(); j++)
                extraArgs << ", __global real* restrict global_dValuedParam_" << j << "_" << i;
            deriv0 << "global_dValuedParam_0_" << i << "[index] = dValuedParam_0_" << i << ";\n";
        }
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        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++)
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            variables[force.getGlobalParameterName(i)] = "globals["+cl.intToString(i)+"]";
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        for (int i = 1; i < force.getNumComputedValues(); i++) {
            variables[computedValueNames[i-1]] = "local_values"+computedValues->getParameterSuffix(i-1);
            map<string, Lepton::ParsedExpression> valueExpressions;
            valueExpressions["local_values"+computedValues->getParameterSuffix(i)+" = "] = Lepton::Parser::parse(computedValueExpressions[i], functions).optimize();
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            reductionSource << cl.getExpressionUtilities().createExpressions(valueExpressions, variables, functionList, functionDefinitions, "value"+cl.intToString(i)+"_temp");
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        }
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        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
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            string valueName = "values"+cl.intToString(i+1);
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            reductionSource << "global_" << valueName << "[index] = local_" << valueName << ";\n";
        }
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        if (needEnergyParamDerivs) {
            map<string, Lepton::ParsedExpression> derivExpressions;
            for (int i = 1; i < force.getNumComputedValues(); i++) {
                for (int j = 0; j < valueParamDerivExpressions[i].size(); j++)
                    derivExpressions["real dValuedParam_"+cl.intToString(i)+"_"+cl.intToString(j)+" = "] = valueParamDerivExpressions[i][j];
                for (int j = 0; j < i; j++)
                    derivExpressions["real dVdV_"+cl.intToString(i)+"_"+cl.intToString(j)+" = "] = valueDerivExpressions[i][j];
            }
            reductionSource << cl.getExpressionUtilities().createExpressions(derivExpressions, variables, functionList, functionDefinitions, "derivChain_temp");
            for (int i = 1; i < force.getNumComputedValues(); i++) {
                for (int j = 0; j < i; j++)
                    for (int k = 0; k < valueParamDerivExpressions[i].size(); k++)
                        reductionSource << "dValuedParam_" << i << "_" << k << " += dVdV_" << i << "_" << j << "*dValuedParam_" << j <<"_" << k << ";\n";
                for (int j = 0; j < valueParamDerivExpressions[i].size(); j++)
                    reductionSource << "global_dValuedParam_" << i << "_" << j << "[index] = dValuedParam_" << i << "_" << j << ";\n";
            }
        }
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        map<string, string> replacements;
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        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
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        replacements["REDUCE_PARAM0_DERIV"] = deriv0.str();
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        replacements["COMPUTE_VALUES"] = reductionSource.str();
        map<string, string> defines;
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        defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
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        cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customGBValuePerParticle, replacements), defines);
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        perParticleValueKernel = cl::Kernel(program, "computePerParticleValues");
    }
    {
        // Create the N2 energy kernel.

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        vector<pair<ExpressionTreeNode, string> > variables;
        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
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        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
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            variables.push_back(makeVariable(name+"1", "params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", "params"+params->getParameterSuffix(i, "2")));
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        }
        for (int i = 0; i < force.getNumComputedValues(); i++) {
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            variables.push_back(makeVariable(computedValueNames[i]+"1", "values"+computedValues->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(computedValueNames[i]+"2", "values"+computedValues->getParameterSuffix(i, "2")));
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        }
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
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            variables.push_back(makeVariable(force.getGlobalParameterName(i), "globals["+cl.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++) {
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                    if (needChainForValue[j]) {
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                        string index = cl.intToString(j+1);
                        n2EnergyExpressions["/*"+cl.intToString(i+1)+"*/ deriv"+index+"_1 += "] = energyDerivExpressions[i][2*j];
                        n2EnergyExpressions["/*"+cl.intToString(i+1)+"*/ deriv"+index+"_2 += "] = energyDerivExpressions[i][2*j+1];
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                    }
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                }
            }
            else {
                for (int j = 0; j < force.getNumComputedValues(); j++) {
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                    if (needChainForValue[j]) {
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                        n2EnergyExpressions["/*"+cl.intToString(i+1)+"*/ deriv"+energyDerivs->getParameterSuffix(j, "_1")+" += "] = energyDerivExpressions[i][2*j];
                        n2EnergyExpressions["/*"+cl.intToString(i+1)+"*/ deriv"+energyDerivs->getParameterSuffix(j, "_2")+" += "] = energyDerivExpressions[i][2*j+1];
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                    }
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                }
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            }
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            for (int j = 0; j < force.getNumEnergyParameterDerivatives(); j++)
                n2EnergyExpressions["energyParamDeriv"+cl.intToString(j)+" += interactionScale*"] = energyParamDerivExpressions[i][j];
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            if (exclude)
                n2EnergySource << "if (!isExcluded) {\n";
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            n2EnergySource << cl.getExpressionUtilities().createExpressions(n2EnergyExpressions, variables, functionList, functionDefinitions, "temp");
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            if (exclude)
                n2EnergySource << "}\n";
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        }
        map<string, string> replacements;
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        string n2EnergyStr = n2EnergySource.str();
        replacements["COMPUTE_INTERACTION"] = n2EnergyStr;
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        stringstream extraArgs, loadLocal1, loadLocal2, clearLocal, load1, load2, declare1, recordDeriv, storeDerivs1, storeDerivs2, declareTemps, setTemps, initParamDerivs, saveParamDerivs;
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        if (force.getNumGlobalParameters() > 0)
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            extraArgs << ", __global const float* globals";
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        pairEnergyUsesParam.resize(params->getBuffers().size(), false);
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            string paramName = "params"+cl.intToString(i+1);
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            if (n2EnergyStr.find(paramName+"1") != n2EnergyStr.npos || n2EnergyStr.find(paramName+"2") != n2EnergyStr.npos) {
                extraArgs << ", __global const " << buffer.getType() << "* restrict global_" << paramName << ", __local " << buffer.getType() << "* restrict local_" << paramName;
                loadLocal1 << "local_" << paramName << "[localAtomIndex] = " << paramName << "1;\n";
                loadLocal2 << "local_" << paramName << "[localAtomIndex] = global_" << paramName << "[j];\n";
                load1 << buffer.getType() << " " << paramName << "1 = global_" << paramName << "[atom1];\n";
                load2 << buffer.getType() << " " << paramName << "2 = local_" << paramName << "[atom2];\n";
                pairEnergyUsesParam[i] = true;
            }
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        }
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        pairEnergyUsesValue.resize(computedValues->getBuffers().size(), false);
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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"+cl.intToString(i+1);
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            if (n2EnergyStr.find(valueName+"1") != n2EnergyStr.npos || n2EnergyStr.find(valueName+"2") != n2EnergyStr.npos) {
                extraArgs << ", __global const " << buffer.getType() << "* restrict global_" << valueName << ", __local " << buffer.getType() << "* restrict local_" << valueName;
                loadLocal1 << "local_" << valueName << "[localAtomIndex] = " << valueName << "1;\n";
                loadLocal2 << "local_" << valueName << "[localAtomIndex] = global_" << valueName << "[j];\n";
                load1 << buffer.getType() << " " << valueName << "1 = global_" << valueName << "[atom1];\n";
                load2 << buffer.getType() << " " << valueName << "2 = local_" << valueName << "[atom2];\n";
                pairEnergyUsesValue[i] = true;
            }
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        }
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        if (useLong) {
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            extraArgs << ", __global long* restrict derivBuffers";
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            for (int i = 0; i < force.getNumComputedValues(); i++) {
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                string index = cl.intToString(i+1);
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                extraArgs << ", __local real* restrict local_deriv" << index;
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                clearLocal << "local_deriv" << index << "[localAtomIndex] = 0.0f;\n";
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                declare1 << "real deriv" << index << "_1 = 0;\n";
                load2 << "real deriv" << index << "_2 = 0;\n";
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                recordDeriv << "local_deriv" << index << "[atom2] += deriv" << index << "_2;\n";
                storeDerivs1 << "STORE_DERIVATIVE_1(" << index << ")\n";
                storeDerivs2 << "STORE_DERIVATIVE_2(" << index << ")\n";
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                declareTemps << "__local real tempDerivBuffer" << index << "[64];\n";
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                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];
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                string index = cl.intToString(i+1);
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                extraArgs << ", __global " << buffer.getType() << "* restrict derivBuffers" << index << ", __local " << buffer.getType() << "* restrict local_deriv" << index;
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                clearLocal << "local_deriv" << index << "[localAtomIndex] = 0.0f;\n";
                declare1 << buffer.getType() << " deriv" << index << "_1 = 0.0f;\n";
                load2 << buffer.getType() << " deriv" << index << "_2 = 0.0f;\n";
                recordDeriv << "local_deriv" << index << "[atom2] += deriv" << index << "_2;\n";
                storeDerivs1 << "STORE_DERIVATIVE_1(" << index << ")\n";
                storeDerivs2 << "STORE_DERIVATIVE_2(" << index << ")\n";
                declareTemps << "__local " << buffer.getType() << " tempDerivBuffer" << index << "[64];\n";
                setTemps << "tempDerivBuffer" << index << "[get_local_id(0)] = deriv" << index << "_1;\n";
            }
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        }
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        if (needEnergyParamDerivs) {
            extraArgs << ", __global mixed* restrict energyParamDerivs";
            const vector<string>& allParamDerivNames = cl.getEnergyParamDerivNames();
            int numDerivs = allParamDerivNames.size();
            for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
                initParamDerivs << "mixed energyParamDeriv" << i << " = 0;\n";
                for (int index = 0; index < numDerivs; index++)
                    if (allParamDerivNames[index] == force.getEnergyParameterDerivativeName(i))
                        saveParamDerivs << "energyParamDerivs[get_global_id(0)*" << numDerivs << "+" << index << "] += energyParamDeriv" << i << ";\n";
            }
        }
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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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        replacements["INIT_PARAM_DERIVS"] = initParamDerivs.str();
        replacements["SAVE_PARAM_DERIVS"] = saveParamDerivs.str();
3747
        if (useCutoff)
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            pairEnergyDefines["USE_CUTOFF"] = "1";
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        if (usePeriodic)
3750
            pairEnergyDefines["USE_PERIODIC"] = "1";
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        if (anyExclusions)
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            pairEnergyDefines["USE_EXCLUSIONS"] = "1";
        pairEnergyDefines["FORCE_WORK_GROUP_SIZE"] = cl.intToString(cl.getNonbondedUtilities().getForceThreadBlockSize());
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        pairEnergyDefines["CUTOFF_SQUARED"] = cl.doubleToString(cutoff*cutoff);
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        pairEnergyDefines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
        pairEnergyDefines["PADDED_NUM_ATOMS"] = cl.intToString(cl.getPaddedNumAtoms());
        pairEnergyDefines["NUM_BLOCKS"] = cl.intToString(cl.getNumAtomBlocks());
        pairEnergyDefines["TILE_SIZE"] = cl.intToString(OpenCLContext::TileSize);
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        string file;
        if (deviceIsCpu)
            file = OpenCLKernelSources::customGBEnergyN2_cpu;
        else
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            file = OpenCLKernelSources::customGBEnergyN2;
        pairEnergySrc = cl.replaceStrings(file, replacements);
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    }
    {
        // Create the kernel to reduce the derivatives and calculate per-particle energy terms.

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        stringstream compute, extraArgs, reduce, initParamDerivs, saveParamDerivs;
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        if (force.getNumGlobalParameters() > 0)
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            extraArgs << ", __global const float* globals";
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            string paramName = "params"+cl.intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << paramName;
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        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
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            string valueName = "values"+cl.intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << valueName;
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        }
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        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
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            string index = cl.intToString(i+1);
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            extraArgs << ", __global " << buffer.getType() << "* restrict derivBuffers" << index;
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            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
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        for (int i = 0; i < (int) energyDerivChain->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivChain->getBuffers()[i];
            string index = cl.intToString(i+1);
            extraArgs << ", __global " << buffer.getType() << "* restrict derivChain" << index;
        }
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        if (useLong) {
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            extraArgs << ", __global const long* restrict derivBuffersIn";
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            for (int i = 0; i < energyDerivs->getNumParameters(); ++i)
                reduce << "derivBuffers" << energyDerivs->getParameterSuffix(i, "[index]") <<
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                        " = (1.0f/0x100000000)*derivBuffersIn[index+PADDED_NUM_ATOMS*" << cl.intToString(i) << "];\n";
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        }
        else {
            for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++)
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                reduce << "REDUCE_VALUE(derivBuffers" << cl.intToString(i+1) << ", " << energyDerivs->getBuffers()[i].getType() << ")\n";
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        }
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        if (needEnergyParamDerivs) {
            extraArgs << ", __global mixed* restrict energyParamDerivs";
            const vector<string>& allParamDerivNames = cl.getEnergyParamDerivNames();
            int numDerivs = allParamDerivNames.size();
            for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
                initParamDerivs << "mixed energyParamDeriv" << i << " = 0;\n";
                for (int index = 0; index < numDerivs; index++)
                    if (allParamDerivNames[index] == force.getEnergyParameterDerivativeName(i))
                        saveParamDerivs << "energyParamDerivs[get_global_id(0)*" << numDerivs << "+" << index << "] += energyParamDeriv" << i << ";\n";
            }
        }
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        // Compute the various expressions.
        
3817
        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++)
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            variables[force.getGlobalParameterName(i)] = "globals["+cl.intToString(i)+"]";
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        for (int i = 0; i < force.getNumComputedValues(); i++)
            variables[computedValueNames[i]] = "values"+computedValues->getParameterSuffix(i, "[index]");
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        map<string, Lepton::ParsedExpression> expressions;
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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();
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            expressions["/*"+cl.intToString(i+1)+"*/ energy += "] = parsed;
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            for (int j = 0; j < force.getNumComputedValues(); j++)
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                expressions["/*"+cl.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))
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                expressions["/*"+cl.intToString(i+1)+"*/ force.x -= "] = gradx;
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            if (!isZeroExpression(grady))
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                expressions["/*"+cl.intToString(i+1)+"*/ force.y -= "] = grady;
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            if (!isZeroExpression(gradz))
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                expressions["/*"+cl.intToString(i+1)+"*/ force.z -= "] = gradz;
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            for (int j = 0; j < force.getNumEnergyParameterDerivatives(); j++)
                expressions["/*"+cl.intToString(i+1)+"*/ energyParamDeriv"+cl.intToString(j)+" += "] = energyParamDerivExpressions[i][j];
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        }
        for (int i = 1; i < force.getNumComputedValues(); i++)
            for (int j = 0; j < i; j++)
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                expressions["real dV"+cl.intToString(i)+"dV"+cl.intToString(j)+" = "] = valueDerivExpressions[i][j];
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        compute << cl.getExpressionUtilities().createExpressions(expressions, variables, functionList, functionDefinitions, "temp");
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        // Record values.
        
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        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            string index = cl.intToString(i+1);
            compute << "derivBuffers" << index << "[index] = deriv" << index << ";\n";
        }
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        compute << "forceBuffers[index] = forceBuffers[index]+force;\n";
        for (int i = 1; i < force.getNumComputedValues(); i++) {
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            compute << "real totalDeriv"<<i<<" = dV"<<i<<"dV0";
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            for (int j = 1; j < i; j++)
                compute << " + totalDeriv"<<j<<"*dV"<<i<<"dV"<<j;
            compute << ";\n";
            compute << "deriv"<<(i+1)<<" *= totalDeriv"<<i<<";\n";
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        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
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            string index = cl.intToString(i+1);
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            compute << "derivChain" << index << "[index] = deriv" << index << ";\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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        replacements["INIT_PARAM_DERIVS"] = initParamDerivs.str();
        replacements["SAVE_PARAM_DERIVS"] = saveParamDerivs.str();
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        map<string, string> defines;
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        defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = cl.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 || needEnergyParamDerivs) {
        // Create the kernel to compute chain rule terms for computed values that depend explicitly on particle coordinates, and for
        // derivatives with respect to global parameters.
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        stringstream compute, extraArgs, initParamDerivs, saveParamDerivs;
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        if (force.getNumGlobalParameters() > 0)
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            extraArgs << ", __global const float* globals";
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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            string paramName = "params"+cl.intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << paramName;
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        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
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            string valueName = "values"+cl.intToString(i+1);
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            extraArgs << ", __global const " << buffer.getType() << "* restrict " << valueName;
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        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
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            string index = cl.intToString(i+1);
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            extraArgs << ", __global " << buffer.getType() << "* restrict derivBuffers" << index;
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            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
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        if (needEnergyParamDerivs) {
            extraArgs << ", __global mixed* restrict energyParamDerivs";
            const vector<string>& allParamDerivNames = cl.getEnergyParamDerivNames();
            int numDerivs = allParamDerivNames.size();
            for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
                for (int j = 0; j < dValuedParam[i]->getBuffers().size(); j++)
                    extraArgs << ", __global real* restrict dValuedParam_" << j << "_" << i;
                initParamDerivs << "mixed energyParamDeriv" << i << " = 0;\n";
                for (int index = 0; index < numDerivs; index++)
                    if (allParamDerivNames[index] == force.getEnergyParameterDerivativeName(i))
                        saveParamDerivs << "energyParamDerivs[get_global_id(0)*" << numDerivs << "+" << index << "] += energyParamDeriv" << i << ";\n";
            }
        }
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        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++)
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            variables[force.getGlobalParameterName(i)] = "globals["+cl.intToString(i)+"]";
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        for (int i = 0; i < force.getNumComputedValues(); i++)
            variables[computedValueNames[i]] = "values"+computedValues->getParameterSuffix(i, "[index]");
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        if (needParameterGradient) {
            for (int i = 1; i < force.getNumComputedValues(); i++) {
                string is = cl.intToString(i);
                compute << "real4 dV"<<is<<"dR = (real4) 0;\n";
                for (int j = 1; j < i; j++) {
                    if (!isZeroExpression(valueDerivExpressions[i][j])) {
                        map<string, Lepton::ParsedExpression> derivExpressions;
                        string js = cl.intToString(j);
                        derivExpressions["real dV"+is+"dV"+js+" = "] = valueDerivExpressions[i][j];
                        compute << cl.getExpressionUtilities().createExpressions(derivExpressions, variables, functionList, functionDefinitions, "temp_"+is+"_"+js);
                        compute << "dV"<<is<<"dR += dV"<<is<<"dV"<<js<<"*dV"<<js<<"dR;\n";
                    }
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                }
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                map<string, Lepton::ParsedExpression> gradientExpressions;
                if (!isZeroExpression(valueGradientExpressions[i][0]))
                    gradientExpressions["dV"+is+"dR.x += "] = valueGradientExpressions[i][0];
                if (!isZeroExpression(valueGradientExpressions[i][1]))
                    gradientExpressions["dV"+is+"dR.y += "] = valueGradientExpressions[i][1];
                if (!isZeroExpression(valueGradientExpressions[i][2]))
                    gradientExpressions["dV"+is+"dR.z += "] = valueGradientExpressions[i][2];
                compute << cl.getExpressionUtilities().createExpressions(gradientExpressions, variables, functionList, functionDefinitions, "temp");
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            }
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            for (int i = 1; i < force.getNumComputedValues(); i++)
                compute << "force -= deriv"<<energyDerivs->getParameterSuffix(i)<<"*dV"<<i<<"dR;\n";
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        }
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        if (needEnergyParamDerivs)
            for (int i = 0; i < force.getNumComputedValues(); i++)
                for (int j = 0; j < dValuedParam.size(); j++)
                    compute << "energyParamDeriv"<<j<<" += deriv"<<energyDerivs->getParameterSuffix(i)<<"*dValuedParam_"<<i<<"_"<<j<<"[index];\n";
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        map<string, string> replacements;
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
        replacements["COMPUTE_FORCES"] = compute.str();
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        replacements["INIT_PARAM_DERIVS"] = initParamDerivs.str();
        replacements["SAVE_PARAM_DERIVS"] = saveParamDerivs.str();
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        map<string, string> defines;
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        defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
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        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 rule terms as part of the default nonbonded kernel.
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        vector<pair<ExpressionTreeNode, string> > globalVariables;
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        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
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            string value = "globals["+cl.intToString(i)+"]";
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            globalVariables.push_back(makeVariable(name, prefix+value));
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        }
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        vector<pair<ExpressionTreeNode, string> > variables = globalVariables;
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        map<string, string> rename;
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        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
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        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
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            variables.push_back(makeVariable(name+"1", prefix+"params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", prefix+"params"+params->getParameterSuffix(i, "2")));
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            rename[name+"1"] = name+"2";
            rename[name+"2"] = name+"1";
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        }
        map<string, Lepton::ParsedExpression> derivExpressions;
        stringstream chainSource;
        Lepton::ParsedExpression dVdR = Lepton::Parser::parse(computedValueExpressions[0], functions).differentiate("r").optimize();
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        derivExpressions["real dV0dR1 = "] = dVdR;
        derivExpressions["real dV0dR2 = "] = dVdR.renameVariables(rename);
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        chainSource << cl.getExpressionUtilities().createExpressions(derivExpressions, variables, functionList, functionDefinitions, prefix+"temp0_");
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        if (needChainForValue[0]) {
            if (useExclusionsForValue)
                chainSource << "if (!isExcluded) {\n";
            chainSource << "tempForce -= dV0dR1*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(0, "1") << ";\n";
            chainSource << "tempForce -= dV0dR2*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(0, "2") << ";\n";
            if (useExclusionsForValue)
                chainSource << "}\n";
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        }
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        for (int i = 1; i < force.getNumComputedValues(); i++) {
            if (needChainForValue[i]) {
                chainSource << "tempForce -= dV0dR1*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(i, "1") << ";\n";
                chainSource << "tempForce -= dV0dR2*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(i, "2") << ";\n";
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            }
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        }
        map<string, string> replacements;
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        string chainStr = chainSource.str();
        replacements["COMPUTE_FORCE"] = chainStr;
4015
        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];
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            string paramName = prefix+"params"+cl.intToString(i+1);
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            if (chainStr.find(paramName+"1") != chainStr.npos || chainStr.find(paramName+"2") != chainStr.npos)
                parameters.push_back(OpenCLNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
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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 paramName = prefix+"values"+cl.intToString(i+1);
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            if (chainStr.find(paramName+"1") != chainStr.npos || chainStr.find(paramName+"2") != chainStr.npos)
                parameters.push_back(OpenCLNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
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        }
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        for (int i = 0; i < (int) energyDerivChain->getBuffers().size(); i++) {
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            if (needChainForValue[i]) { 
4032
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = energyDerivChain->getBuffers()[i];
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                string paramName = prefix+"dEdV"+cl.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, cutoff, exclusionList, source, force.getForceGroup());
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        for (auto param : parameters)
            cl.getNonbondedUtilities().addParameter(param);
        for (auto arg : arguments)
            cl.getNonbondedUtilities().addArgument(arg);
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    }
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    info = new ForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force);
    cl.addForce(info);
4049
    if (useLong)
4050
        cl.addAutoclearBuffer(*longEnergyDerivs);
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    else {
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        for (auto& buffer : energyDerivs->getBuffers())
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            cl.addAutoclearBuffer(buffer.getMemory(), buffer.getSize()*energyDerivs->getNumObjects());
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    }
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}

4057
double OpenCLCalcCustomGBForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
4058
    bool deviceIsCpu = (cl.getDevice().getInfo<CL_DEVICE_TYPE>() == CL_DEVICE_TYPE_CPU);
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    OpenCLNonbondedUtilities& nb = cl.getNonbondedUtilities();
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    int elementSize = (cl.getUseDoublePrecision() ? sizeof(cl_double) : sizeof(cl_float));
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    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
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        // These two kernels can't be compiled in initialize(), because the nonbonded utilities object
        // has not yet been initialized then.

        {
            int numExclusionTiles = nb.getExclusionTiles().getSize();
            pairValueDefines["NUM_TILES_WITH_EXCLUSIONS"] = cl.intToString(numExclusionTiles);
            int numContexts = cl.getPlatformData().contexts.size();
            int startExclusionIndex = cl.getContextIndex()*numExclusionTiles/numContexts;
            int endExclusionIndex = (cl.getContextIndex()+1)*numExclusionTiles/numContexts;
            pairValueDefines["FIRST_EXCLUSION_TILE"] = cl.intToString(startExclusionIndex);
            pairValueDefines["LAST_EXCLUSION_TILE"] = cl.intToString(endExclusionIndex);
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            pairValueDefines["CUTOFF"] = cl.doubleToString(cutoff);
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            cl::Program program = cl.createProgram(pairValueSrc, pairValueDefines);
            pairValueKernel = cl::Kernel(program, "computeN2Value");
            pairValueSrc = "";
            pairValueDefines.clear();
        }
        {
            int numExclusionTiles = nb.getExclusionTiles().getSize();
            pairEnergyDefines["NUM_TILES_WITH_EXCLUSIONS"] = cl.intToString(numExclusionTiles);
            int numContexts = cl.getPlatformData().contexts.size();
            int startExclusionIndex = cl.getContextIndex()*numExclusionTiles/numContexts;
            int endExclusionIndex = (cl.getContextIndex()+1)*numExclusionTiles/numContexts;
            pairEnergyDefines["FIRST_EXCLUSION_TILE"] = cl.intToString(startExclusionIndex);
            pairEnergyDefines["LAST_EXCLUSION_TILE"] = cl.intToString(endExclusionIndex);
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            pairEnergyDefines["CUTOFF"] = cl.doubleToString(cutoff);
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            cl::Program program = cl.createProgram(pairEnergySrc, pairEnergyDefines);
            pairEnergyKernel = cl::Kernel(program, "computeN2Energy");
            pairEnergySrc = "";
            pairEnergyDefines.clear();
        }

        // Set arguments for kernels.
        
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        maxTiles = (nb.getUseCutoff() ? nb.getInteractingTiles().getSize() : 0);
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        bool useLong = cl.getSupports64BitGlobalAtomics();
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        if (useLong) {
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            longValueBuffers = OpenCLArray::create<cl_long>(cl, cl.getPaddedNumAtoms(), "customGBLongValueBuffers");
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            cl.addAutoclearBuffer(*longValueBuffers);
            cl.clearBuffer(*longValueBuffers);
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        }
        else {
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            valueBuffers = new OpenCLArray(cl, cl.getPaddedNumAtoms()*nb.getNumForceBuffers(), elementSize, "customGBValueBuffers");
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            cl.addAutoclearBuffer(*valueBuffers);
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            cl.clearBuffer(*valueBuffers);
        }
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        int index = 0;
        pairValueKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*4*elementSize, NULL);
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        pairValueKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusions().getDeviceBuffer());
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        pairValueKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionTiles().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())*elementSize, 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 += 5; // 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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            pairValueKernel.setArg<cl::Buffer>(index++, nb.getBlockCenters().getDeviceBuffer());
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            pairValueKernel.setArg<cl::Buffer>(index++, nb.getBlockBoundingBoxes().getDeviceBuffer());
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            pairValueKernel.setArg<cl::Buffer>(index++, nb.getInteractingAtoms().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++) {
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            if (pairValueUsesParam[i]) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
                pairValueKernel.setArg<cl::Memory>(index++, buffer.getMemory());
                pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
            }
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        }
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        for (auto d : dValue0dParam) {
            pairValueKernel.setArg<cl::Buffer>(index++, d->getDeviceBuffer());
            pairValueKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*d->getElementSize(), NULL);
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        }
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        for (auto function : tabulatedFunctions)
            pairValueKernel.setArg<cl::Buffer>(index++, function->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 (auto& buffer : params->getBuffers())
            perParticleValueKernel.setArg<cl::Memory>(index++, buffer.getMemory());
        for (auto& buffer : computedValues->getBuffers())
            perParticleValueKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        for (int i = 0; i < dValuedParam.size(); i++) {
            perParticleValueKernel.setArg<cl::Memory>(index++, dValue0dParam[i]->getDeviceBuffer());
            for (int j = 0; j < dValuedParam[i]->getBuffers().size(); j++)
                perParticleValueKernel.setArg<cl::Memory>(index++, dValuedParam[i]->getBuffers()[j].getMemory());
        }
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        for (auto function : tabulatedFunctions)
            perParticleValueKernel.setArg<cl::Buffer>(index++, function->getDeviceBuffer());
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        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())*4*elementSize, 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())*4*elementSize, NULL);
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        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusions().getDeviceBuffer());
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        pairEnergyKernel.setArg<cl::Buffer>(index++, cl.getNonbondedUtilities().getExclusionTiles().getDeviceBuffer());
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        index++; // Whether to include energy.
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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 += 5; // 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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            pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getBlockCenters().getDeviceBuffer());
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            pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getBlockBoundingBoxes().getDeviceBuffer());
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            pairEnergyKernel.setArg<cl::Buffer>(index++, nb.getInteractingAtoms().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++) {
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            if (pairEnergyUsesParam[i]) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
                pairEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
                pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
            }
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        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
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            if (pairEnergyUsesValue[i]) {
                const OpenCLNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
                pairEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
                pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*buffer.getSize(), NULL);
            }
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        }
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        if (useLong) {
            pairEnergyKernel.setArg<cl::Memory>(index++, longEnergyDerivs->getDeviceBuffer());
            for (int i = 0; i < numComputedValues; ++i)
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                pairEnergyKernel.setArg(index++, (deviceIsCpu ? OpenCLContext::TileSize : nb.getForceThreadBlockSize())*elementSize, NULL);
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        }
        else {
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            for (auto& buffer : energyDerivs->getBuffers()) {
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                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 (needEnergyParamDerivs)
            pairEnergyKernel.setArg<cl::Memory>(index++, cl.getEnergyParamDerivBuffer().getDeviceBuffer());
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        for (auto function : tabulatedFunctions)
            pairEnergyKernel.setArg<cl::Buffer>(index++, function->getDeviceBuffer());
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        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());
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        for (auto& buffer : params->getBuffers())
            perParticleEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
        for (auto& buffer : computedValues->getBuffers())
            perParticleEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
        for (auto& buffer : energyDerivs->getBuffers())
            perParticleEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
        for (auto& buffer : energyDerivChain->getBuffers())
            perParticleEnergyKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        if (useLong)
            perParticleEnergyKernel.setArg<cl::Memory>(index++, longEnergyDerivs->getDeviceBuffer());
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        if (needEnergyParamDerivs)
            perParticleEnergyKernel.setArg<cl::Memory>(index++, cl.getEnergyParamDerivBuffer().getDeviceBuffer());
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        for (auto function : tabulatedFunctions)
            perParticleEnergyKernel.setArg<cl::Buffer>(index++, function->getDeviceBuffer());
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        if (needParameterGradient || needEnergyParamDerivs) {
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            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());
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            for (auto& buffer : params->getBuffers())
                gradientChainRuleKernel.setArg<cl::Memory>(index++, buffer.getMemory());
            for (auto& buffer : computedValues->getBuffers())
                gradientChainRuleKernel.setArg<cl::Memory>(index++, buffer.getMemory());
            for (auto& buffer : energyDerivs->getBuffers())
                gradientChainRuleKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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            if (needEnergyParamDerivs) {
                gradientChainRuleKernel.setArg<cl::Buffer>(index++, cl.getEnergyParamDerivBuffer().getDeviceBuffer());
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                for (auto d : dValuedParam)
                    for (auto& buffer : d->getBuffers())
                        gradientChainRuleKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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            }
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        }
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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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    pairEnergyKernel.setArg<cl_int>(7, includeEnergy);
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    if (nb.getUseCutoff()) {
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        setPeriodicBoxArgs(cl, pairValueKernel, 8);
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        setPeriodicBoxArgs(cl, pairEnergyKernel, 10);
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        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
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            pairValueKernel.setArg<cl::Buffer>(6, nb.getInteractingTiles().getDeviceBuffer());
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            pairValueKernel.setArg<cl_uint>(13, maxTiles);
            pairValueKernel.setArg<cl::Buffer>(16, nb.getInteractingAtoms().getDeviceBuffer());
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            pairEnergyKernel.setArg<cl::Buffer>(8, nb.getInteractingTiles().getDeviceBuffer());
            pairEnergyKernel.setArg<cl_uint>(15, maxTiles);
            pairEnergyKernel.setArg<cl::Buffer>(18, nb.getInteractingAtoms().getDeviceBuffer());
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        }
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    }
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    cl.executeKernel(pairValueKernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
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    cl.executeKernel(perParticleValueKernel, cl.getPaddedNumAtoms());
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    cl.executeKernel(pairEnergyKernel, nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
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    cl.executeKernel(perParticleEnergyKernel, cl.getPaddedNumAtoms());
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    if (needParameterGradient || needEnergyParamDerivs)
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        cl.executeKernel(gradientChainRuleKernel, cl.getPaddedNumAtoms());
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    return 0.0;
}

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void OpenCLCalcCustomGBForceKernel::copyParametersToContext(ContextImpl& context, const CustomGBForce& force) {
    int numParticles = force.getNumParticles();
    if (numParticles != cl.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    
    // Record the per-particle parameters.
    
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    vector<vector<cl_float> > paramVector(cl.getPaddedNumAtoms(), vector<cl_float>(force.getNumPerParticleParameters(), 0));
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    vector<double> parameters;
    for (int i = 0; i < numParticles; i++) {
        force.getParticleParameters(i, parameters);
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

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

void OpenCLCalcCustomExternalForceKernel::initialize(const System& system, const CustomExternalForce& force) {
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    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumParticles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumParticles()/numContexts;
    numParticles = endIndex-startIndex;
    if (numParticles == 0)
        return;
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    vector<vector<int> > atoms(numParticles, vector<int>(1));
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    params = new OpenCLParameterSet(cl, force.getNumPerParticleParameters(), numParticles, "customExternalParams");
    vector<vector<cl_float> > paramVector(numParticles);
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    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
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        force.getParticleParameters(startIndex+i, atoms[i][0], parameters);
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        paramVector[i].resize(parameters.size());
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        for (int j = 0; j < (int) parameters.size(); j++)
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            paramVector[i][j] = (cl_float) parameters[j];
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    }
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    params->setParameterValues(paramVector);
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    info = new ForceInfo(force, system.getNumParticles());
    cl.addForce(info);
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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);
    }
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    map<string, Lepton::CustomFunction*> customFunctions;
    customFunctions["periodicdistance"] = cl.getExpressionUtilities().getPeriodicDistancePlaceholder();
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction(), customFunctions).optimize();
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    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;
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    expressions["real dEdX = "] = forceExpressionX;
    expressions["real dEdY = "] = forceExpressionY;
    expressions["real dEdZ = "] = forceExpressionZ;
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    // Create the kernels.

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

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double OpenCLCalcCustomExternalForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (globals != NULL) {
        bool changed = false;
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        for (int i = 0; i < (int) globalParamNames.size(); i++) {
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            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    return 0.0;
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}
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void OpenCLCalcCustomExternalForceKernel::copyParametersToContext(ContextImpl& context, const CustomExternalForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumParticles()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumParticles()/numContexts;
    if (numParticles != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
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    if (numParticles == 0)
        return;
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    // Record the per-particle parameters.
    
    vector<vector<cl_float> > paramVector(numParticles);
    vector<double> parameters;
    for (int i = 0; i < numParticles; i++) {
        int particle;
        force.getParticleParameters(startIndex+i, particle, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

OpenCLCalcCustomHbondForceKernel::~OpenCLCalcCustomHbondForceKernel() {
    if (donorParams != NULL)
        delete donorParams;
    if (acceptorParams != NULL)
        delete acceptorParams;
    if (donors != NULL)
        delete donors;
    if (acceptors != NULL)
        delete acceptors;
    if (donorBufferIndices != NULL)
        delete donorBufferIndices;
    if (acceptorBufferIndices != NULL)
        delete acceptorBufferIndices;
    if (globals != NULL)
        delete globals;
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    if (donorExclusions != NULL)
        delete donorExclusions;
    if (acceptorExclusions != NULL)
        delete acceptorExclusions;
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    for (auto function : tabulatedFunctions)
        delete function;
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}

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

static void applyDonorAndAcceptorForces(stringstream& applyToDonor, stringstream& applyToAcceptor, int atom, const string& value) {
    string forceNames[] = {"f1", "f2", "f3"};
    if (atom < 3)
        applyToAcceptor << forceNames[atom]<<".xyz += "<<value<<";\n";
    else
        applyToDonor << forceNames[atom-3]<<".xyz += "<<value<<";\n";
}
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void OpenCLCalcCustomHbondForceKernel::initialize(const System& system, const CustomHbondForce& force) {
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    // Record the lists of donors and acceptors, and the parameters for each one.

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

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    // Select an output buffer index for each donor and acceptor.
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    donorBufferIndices = OpenCLArray::create<mm_int4>(cl, numDonors, "customHbondDonorBuffers");
    acceptorBufferIndices = OpenCLArray::create<mm_int4>(cl, numAcceptors, "customHbondAcceptorBuffers");
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    vector<mm_int4> donorBufferVector(numDonors);
    vector<mm_int4> acceptorBufferVector(numAcceptors);
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    vector<int> donorBufferCounter(numParticles, 0);
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    for (int i = 0; i < numDonors; i++)
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        donorBufferVector[i] = mm_int4(donorVector[i].x > -1 ? donorBufferCounter[donorVector[i].x]++ : 0,
                                       donorVector[i].y > -1 ? donorBufferCounter[donorVector[i].y]++ : 0,
                                       donorVector[i].z > -1 ? donorBufferCounter[donorVector[i].z]++ : 0, 0);
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    vector<int> acceptorBufferCounter(numParticles, 0);
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    for (int i = 0; i < numAcceptors; i++)
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        acceptorBufferVector[i] = mm_int4(acceptorVector[i].x > -1 ? acceptorBufferCounter[acceptorVector[i].x]++ : 0,
                                       acceptorVector[i].y > -1 ? acceptorBufferCounter[acceptorVector[i].y]++ : 0,
                                       acceptorVector[i].z > -1 ? acceptorBufferCounter[acceptorVector[i].z]++ : 0, 0);
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    donorBufferIndices->upload(donorBufferVector);
    acceptorBufferIndices->upload(acceptorBufferVector);
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    int maxBuffers = 1;
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    for (int i : donorBufferCounter)
        maxBuffers = max(maxBuffers, i);
    for (int i : acceptorBufferCounter)
        maxBuffers = max(maxBuffers, i);
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    info = new ForceInfo(maxBuffers, force);
    cl.addForce(info);
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    // Record exclusions.

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

    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
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    vector<const TabulatedFunction*> functionList;
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    stringstream tableArgs;
    for (int i = 0; i < force.getNumFunctions(); i++) {
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        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
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        string arrayName = "table"+cl.intToString(i);
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        functionDefinitions.push_back(make_pair(name, arrayName));
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        functions[name] = cl.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
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        int width;
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        vector<float> f = cl.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        tabulatedFunctions.push_back(OpenCLArray::create<float>(cl, f.size(), "TabulatedFunction"));
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        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
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        tableArgs << ", __global const float";
        if (width > 1)
            tableArgs << width;
        tableArgs << "* restrict " << arrayName;
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    }

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    // Record information about parameters.
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    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (cl_float) force.getGlobalParameterDefaultValue(i);
    }
    if (globals != NULL)
        globals->upload(globalParamValues);
    map<string, string> variables;
    for (int i = 0; i < force.getNumPerDonorParameters(); i++) {
        const string& name = force.getPerDonorParameterName(i);
        variables[name] = "donorParams"+donorParams->getParameterSuffix(i);
    }
    for (int i = 0; i < force.getNumPerAcceptorParameters(); i++) {
        const string& name = force.getPerAcceptorParameterName(i);
        variables[name] = "acceptorParams"+acceptorParams->getParameterSuffix(i);
    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
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        variables[name] = "globals["+cl.intToString(i)+"]";
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    }
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    // Now to generate the kernel.  First, it needs to calculate all distances, angles,
    // and dihedrals the expression depends on.

    map<string, vector<int> > distances;
    map<string, vector<int> > angles;
    map<string, vector<int> > dihedrals;
    Lepton::ParsedExpression energyExpression = CustomHbondForceImpl::prepareExpression(force, functions, distances, angles, dihedrals);
    map<string, Lepton::ParsedExpression> forceExpressions;
    set<string> computedDeltas;
    computedDeltas.insert("D1A1");
    string atomNames[] = {"A1", "A2", "A3", "D1", "D2", "D3"};
    string atomNamesLower[] = {"a1", "a2", "a3", "d1", "d2", "d3"};
    stringstream computeDonor, computeAcceptor, extraArgs;
    int index = 0;
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    for (auto& distance : distances) {
        const vector<int>& atoms = distance.second;
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        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
        if (computedDeltas.count(deltaName) == 0) {
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            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 delta"+deltaName+" = delta("+atomNamesLower[atoms[0]]+", "+atomNamesLower[atoms[1]]+", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n");
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            computedDeltas.insert(deltaName);
        }
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real r_"+deltaName+" = SQRT(delta"+deltaName+".w);\n");
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        variables[distance.first] = "r_"+deltaName;
        forceExpressions["real dEdDistance"+cl.intToString(index)+" = "] = energyExpression.differentiate(distance.first).optimize();
        index++;
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    }
    index = 0;
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    for (auto& angle : angles) {
        const vector<int>& atoms = angle.second;
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        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) {
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            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 delta"+deltaName1+" = delta("+atomNamesLower[atoms[1]]+", "+atomNamesLower[atoms[0]]+", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n");
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            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
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            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 delta"+deltaName2+" = delta("+atomNamesLower[atoms[1]]+", "+atomNamesLower[atoms[2]]+", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n");
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            computedDeltas.insert(deltaName2);
        }
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real "+angleName+" = computeAngle(delta"+deltaName1+", delta"+deltaName2+");\n");
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        variables[angle.first] = angleName;
        forceExpressions["real dEdAngle"+cl.intToString(index)+" = "] = energyExpression.differentiate(angle.first).optimize();
        index++;
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    }
    index = 0;
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    for (auto& dihedral : dihedrals) {
        const vector<int>& atoms = dihedral.second;
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        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) {
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            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 delta"+deltaName1+" = delta("+atomNamesLower[atoms[0]]+", "+atomNamesLower[atoms[1]]+", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n");
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            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
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            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 delta"+deltaName2+" = delta("+atomNamesLower[atoms[2]]+", "+atomNamesLower[atoms[1]]+", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n");
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            computedDeltas.insert(deltaName2);
        }
        if (computedDeltas.count(deltaName3) == 0) {
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            addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 delta"+deltaName3+" = delta("+atomNamesLower[atoms[2]]+", "+atomNamesLower[atoms[3]]+", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n");
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            computedDeltas.insert(deltaName3);
        }
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 "+crossName1+" = computeCross(delta"+deltaName1+", delta"+deltaName2+");\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 "+crossName2+" = computeCross(delta"+deltaName2+", delta"+deltaName3+");\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real "+dihedralName+" = computeAngle("+crossName1+", "+crossName2+");\n");
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, dihedralName+" *= (delta"+deltaName1+".x*"+crossName2+".x + delta"+deltaName1+".y*"+crossName2+".y + delta"+deltaName1+".z*"+crossName2+".z < 0 ? -1 : 1);\n");
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        variables[dihedral.first] = dihedralName;
        forceExpressions["real dEdDihedral"+cl.intToString(index)+" = "] = energyExpression.differentiate(dihedral.first).optimize();
        index++;
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    }

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

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

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    computeAcceptor << cl.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, "temp");
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    forceExpressions["energy += "] = energyExpression;
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    computeDonor << cl.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, "temp");
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    // Finally, apply forces to atoms.

    index = 0;
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    for (auto& distance : distances) {
        const vector<int>& atoms = distance.second;
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        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
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        string value = "(dEdDistance"+cl.intToString(index)+"/r_"+deltaName+")*delta"+deltaName+".xyz";
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        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[0], "-"+value);
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[1], value);
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        index++;
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    }
    index = 0;
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    for (auto& angle : angles) {
        const vector<int>& atoms = angle.second;
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        string deltaName1 = atomNames[atoms[1]]+atomNames[atoms[0]];
        string deltaName2 = atomNames[atoms[1]]+atomNames[atoms[2]];
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "{\n");
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 crossProd = cross(delta"+deltaName2+", delta"+deltaName1+");\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real lengthCross = max(length(crossProd), (real) 1e-6f);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 deltaCross0 = -cross(delta"+deltaName1+", crossProd)*dEdAngle"+cl.intToString(index)+"/(delta"+deltaName1+".w*lengthCross);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 deltaCross2 = cross(delta"+deltaName2+", crossProd)*dEdAngle"+cl.intToString(index)+"/(delta"+deltaName2+".w*lengthCross);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 deltaCross1 = -(deltaCross0+deltaCross2);\n");
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        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");
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        index++;
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    }
    index = 0;
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    for (auto& dihedral : dihedrals) {
        const vector<int>& atoms = dihedral.second;
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        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");
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real r = SQRT(delta"+deltaName2+".w);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 ff;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.x = (-dEdDihedral"+cl.intToString(index)+"*r)/"+crossName1+".w;\n");
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        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");
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.w = (dEdDihedral"+cl.intToString(index)+"*r)/"+crossName2+".w;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 internalF0 = ff.x*"+crossName1+";\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 internalF3 = ff.w*"+crossName2+";\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 s = ff.y*internalF0 - ff.z*internalF3;\n");
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        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");
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        index++;
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    }

    // Generate the kernels.

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

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double OpenCLCalcCustomHbondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numDonors == 0 || numAcceptors == 0)
        return 0.0;
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    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            cl_float value = (cl_float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        int index = 0;
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        donorKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        donorKernel.setArg<cl::Buffer>(index++, donorExclusions->getDeviceBuffer());
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        donorKernel.setArg<cl::Buffer>(index++, donors->getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, acceptors->getDeviceBuffer());
        donorKernel.setArg<cl::Buffer>(index++, donorBufferIndices->getDeviceBuffer());
        donorKernel.setArg(index++, 3*OpenCLContext::ThreadBlockSize*sizeof(mm_float4), NULL);
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        index += 5; // Periodic box size arguments are set when the kernel is executed.
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        if (globals != NULL)
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            donorKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
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        for (auto& buffer : donorParams->getBuffers())
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            donorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        for (auto& buffer : acceptorParams->getBuffers())
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            donorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        for (auto function : tabulatedFunctions)
            donorKernel.setArg<cl::Buffer>(index++, function->getDeviceBuffer());
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        index = 0;
        acceptorKernel.setArg<cl::Buffer>(index++, cl.getForceBuffers().getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        acceptorKernel.setArg<cl::Buffer>(index++, acceptorExclusions->getDeviceBuffer());
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        acceptorKernel.setArg<cl::Buffer>(index++, donors->getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, acceptors->getDeviceBuffer());
        acceptorKernel.setArg<cl::Buffer>(index++, acceptorBufferIndices->getDeviceBuffer());
        acceptorKernel.setArg(index++, 3*OpenCLContext::ThreadBlockSize*sizeof(mm_float4), NULL);
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        index += 5; // Periodic box size arguments are set when the kernel is executed.
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        if (globals != NULL)
            acceptorKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
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        for (auto& buffer : donorParams->getBuffers())
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            acceptorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        for (auto& buffer : acceptorParams->getBuffers())
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            acceptorKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        for (auto function : tabulatedFunctions)
            acceptorKernel.setArg<cl::Buffer>(index++, function->getDeviceBuffer());
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    }
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    setPeriodicBoxArgs(cl, donorKernel, 8);
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    cl.executeKernel(donorKernel, max(numDonors, numAcceptors));
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    setPeriodicBoxArgs(cl, acceptorKernel, 8);
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    cl.executeKernel(acceptorKernel, max(numDonors, numAcceptors));
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    return 0.0;
}

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void OpenCLCalcCustomHbondForceKernel::copyParametersToContext(ContextImpl& context, const CustomHbondForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumDonors()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumDonors()/numContexts;
    if (numDonors != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of donors has changed");
    if (numAcceptors != force.getNumAcceptors())
        throw OpenMMException("updateParametersInContext: The number of acceptors has changed");
    
    // Record the per-donor parameters.
    
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    if (numDonors > 0) {
        vector<vector<cl_float> > donorParamVector(numDonors);
        vector<double> parameters;
        for (int i = 0; i < numDonors; i++) {
            int d1, d2, d3;
            force.getDonorParameters(startIndex+i, d1, d2, d3, parameters);
            donorParamVector[i].resize(parameters.size());
            for (int j = 0; j < (int) parameters.size(); j++)
                donorParamVector[i][j] = (cl_float) parameters[j];
        }
        donorParams->setParameterValues(donorParamVector);
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    }
    
    // Record the per-acceptor parameters.
    
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    if (numAcceptors > 0) {
        vector<vector<cl_float> > acceptorParamVector(numAcceptors);
        vector<double> parameters;
        for (int i = 0; i < numAcceptors; i++) {
            int a1, a2, a3;
            force.getAcceptorParameters(i, a1, a2, a3, parameters);
            acceptorParamVector[i].resize(parameters.size());
            for (int j = 0; j < (int) parameters.size(); j++)
                acceptorParamVector[i][j] = (cl_float) parameters[j];
        }
        acceptorParams->setParameterValues(acceptorParamVector);
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    }
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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class OpenCLCalcCustomCentroidBondForceKernel::ForceInfo : public OpenCLForceInfo {
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public:
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    ForceInfo(const CustomCentroidBondForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumBonds();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        vector<double> parameters;
        vector<int> groups;
        force.getBondParameters(index, groups, parameters);
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        for (int group : groups) {
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            vector<int> groupParticles;
            vector<double> weights;
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            force.getGroupParameters(group, groupParticles, weights);
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            particles.insert(particles.end(), groupParticles.begin(), groupParticles.end());
        }
    }
    bool areGroupsIdentical(int group1, int group2) {
        vector<int> groups1, groups2;
        vector<double> parameters1, parameters2;
        force.getBondParameters(group1, groups1, parameters1);
        force.getBondParameters(group2, groups2, parameters2);
        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
        for (int i = 0; i < groups1.size(); i++) {
            vector<int> groupParticles;
            vector<double> weights1, weights2;
            force.getGroupParameters(groups1[i], groupParticles, weights1);
            force.getGroupParameters(groups2[i], groupParticles, weights2);
            if (weights1.size() != weights2.size())
                return false;
            for (int j = 0; j < weights1.size(); j++)
                if (weights1[j] != weights2[j])
                    return false;
        }
        return true;
    }
private:
    const CustomCentroidBondForce& force;
};

OpenCLCalcCustomCentroidBondForceKernel::~OpenCLCalcCustomCentroidBondForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
    if (groupParticles != NULL)
        delete groupParticles;
    if (groupWeights != NULL)
        delete groupWeights;
    if (groupOffsets != NULL)
        delete groupOffsets;
    if (groupForces != NULL)
        delete groupForces;
    if (bondGroups != NULL)
        delete bondGroups;
    if (centerPositions != NULL)
        delete centerPositions;
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    for (auto function : tabulatedFunctions)
        delete function;
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}

void OpenCLCalcCustomCentroidBondForceKernel::initialize(const System& system, const CustomCentroidBondForce& force) {
    numBonds = force.getNumBonds();
    if (numBonds == 0)
        return;
    if (!cl.getSupports64BitGlobalAtomics())
        throw OpenMMException("CustomCentroidBondForce requires a device that supports 64 bit atomic operations");
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    info = new ForceInfo(force);
    cl.addForce(info);
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    // Record the groups.
    
    numGroups = force.getNumGroups();
    vector<cl_int> groupParticleVec;
    vector<cl_float> groupWeightVecFloat;
    vector<cl_double> groupWeightVecDouble;
    vector<cl_int> groupOffsetVec;
    groupOffsetVec.push_back(0);
    for (int i = 0; i < numGroups; i++) {
        vector<int> particles;
        vector<double> weights;
        force.getGroupParameters(i, particles, weights);
        groupParticleVec.insert(groupParticleVec.end(), particles.begin(), particles.end());
        groupOffsetVec.push_back(groupParticleVec.size());
    }
    vector<vector<double> > normalizedWeights;
    CustomCentroidBondForceImpl::computeNormalizedWeights(force, system, normalizedWeights);
    if (cl.getUseDoublePrecision()) {
        for (int i = 0; i < numGroups; i++)
            groupWeightVecDouble.insert(groupWeightVecDouble.end(), normalizedWeights[i].begin(), normalizedWeights[i].end());
    }
    else {
        for (int i = 0; i < numGroups; i++)
            for (int j = 0; j < normalizedWeights[i].size(); j++)
                groupWeightVecFloat.push_back((float) normalizedWeights[i][j]);
    }
    groupParticles = OpenCLArray::create<int>(cl, groupParticleVec.size(), "groupParticles");
    groupParticles->upload(groupParticleVec);
    if (cl.getUseDoublePrecision()) {
        groupWeights = OpenCLArray::create<double>(cl, groupParticleVec.size(), "groupWeights");
        groupWeights->upload(groupWeightVecDouble);
        centerPositions = OpenCLArray::create<mm_double4>(cl, numGroups, "centerPositions");
    }
    else {
        groupWeights = OpenCLArray::create<float>(cl, groupParticleVec.size(), "groupWeights");
        groupWeights->upload(groupWeightVecFloat);
        centerPositions = OpenCLArray::create<mm_float4>(cl, numGroups, "centerPositions");
    }
    groupOffsets = OpenCLArray::create<int>(cl, groupOffsetVec.size(), "groupOffsets");
    groupOffsets->upload(groupOffsetVec);
    groupForces = OpenCLArray::create<long long>(cl, numGroups*3, "groupForces");
    cl.addAutoclearBuffer(*groupForces);
    
    // Record the bonds.
    
    int groupsPerBond = force.getNumGroupsPerBond();
    vector<cl_int> bondGroupVec(numBonds*groupsPerBond);
    params = new OpenCLParameterSet(cl, force.getNumPerBondParameters(), numBonds, "customCentroidBondParams");
    vector<vector<float> > paramVector(numBonds);
    for (int i = 0; i < numBonds; i++) {
        vector<int> groups;
        vector<double> parameters;
        force.getBondParameters(i, groups, parameters);
        for (int j = 0; j < groups.size(); j++)
            bondGroupVec[i+j*numBonds] = groups[j];
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    bondGroups = OpenCLArray::create<int>(cl, bondGroupVec.size(), "bondGroups");
    bondGroups->upload(bondGroupVec);

    // Record the tabulated functions.

    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
    vector<const TabulatedFunction*> functionList;
    stringstream extraArgs;
    for (int i = 0; i < force.getNumTabulatedFunctions(); i++) {
        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
        string arrayName = "table"+cl.intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = cl.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
        int width;
        vector<float> f = cl.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
        tabulatedFunctions.push_back(OpenCLArray::create<float>(cl, f.size(), "TabulatedFunction"));
        tabulatedFunctions.back()->upload(f);
        extraArgs << ", __global const float";
        if (width > 1)
            extraArgs << width;
        extraArgs << "* restrict " << arrayName;
    }
    
    // Record information about parameters.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (float) force.getGlobalParameterDefaultValue(i);
    }
    map<string, string> variables;
    for (int i = 0; i < groupsPerBond; i++) {
        string index = cl.intToString(i+1);
        variables["x"+index] = "pos"+index+".x";
        variables["y"+index] = "pos"+index+".y";
        variables["z"+index] = "pos"+index+".z";
    }
    for (int i = 0; i < force.getNumPerBondParameters(); i++) {
        const string& name = force.getPerBondParameterName(i);
        variables[name] = "bondParams"+params->getParameterSuffix(i);
    }
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    needEnergyParamDerivs = (force.getNumEnergyParameterDerivatives() > 0);
    if (needEnergyParamDerivs)
        extraArgs << ", __global mixed* restrict energyParamDerivs";
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    if (force.getNumGlobalParameters() > 0) {
        globals = OpenCLArray::create<float>(cl, force.getNumGlobalParameters(), "customCentroidBondGlobals");
        globals->upload(globalParamValues);
        extraArgs << ", __global const float* restrict globals";
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+cl.intToString(i)+"]";
            variables[name] = value;
        }
    }

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

    map<string, vector<int> > distances;
    map<string, vector<int> > angles;
    map<string, vector<int> > dihedrals;
    Lepton::ParsedExpression energyExpression = CustomCentroidBondForceImpl::prepareExpression(force, functions, distances, angles, dihedrals);
    map<string, Lepton::ParsedExpression> forceExpressions;
    set<string> computedDeltas;
    vector<string> atomNames, posNames;
    for (int i = 0; i < groupsPerBond; i++) {
        string index = cl.intToString(i+1);
        atomNames.push_back("P"+index);
        posNames.push_back("pos"+index);
    }
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    stringstream compute, initParamDerivs, saveParamDerivs;
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    for (int i = 0; i < groupsPerBond; i++) {
        compute<<"int group"<<(i+1)<<" = bondGroups[index+"<<(i*numBonds)<<"];\n";
        compute<<"real4 pos"<<(i+1)<<" = centerPositions[group"<<(i+1)<<"];\n";
    }
    int index = 0;
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    for (auto& distance : distances) {
        const vector<int>& groups = distance.second;
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        string deltaName = atomNames[groups[0]]+atomNames[groups[1]];
        if (computedDeltas.count(deltaName) == 0) {
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            compute<<"real4 delta"<<deltaName<<" = delta("<<posNames[groups[0]]<<", "<<posNames[groups[1]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName);
        }
        compute<<"real r_"<<deltaName<<" = sqrt(delta"<<deltaName<<".w);\n";
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        variables[distance.first] = "r_"+deltaName;
        forceExpressions["real dEdDistance"+cl.intToString(index)+" = "] = energyExpression.differentiate(distance.first).optimize();
        index++;
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    }
    index = 0;
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    for (auto& angle : angles) {
        const vector<int>& groups = angle.second;
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        string deltaName1 = atomNames[groups[1]]+atomNames[groups[0]];
        string deltaName2 = atomNames[groups[1]]+atomNames[groups[2]];
        string angleName = "angle_"+atomNames[groups[0]]+atomNames[groups[1]]+atomNames[groups[2]];
        if (computedDeltas.count(deltaName1) == 0) {
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            compute<<"real4 delta"<<deltaName1<<" = delta("<<posNames[groups[1]]<<", "<<posNames[groups[0]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
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            compute<<"real4 delta"<<deltaName2<<" = delta("<<posNames[groups[1]]<<", "<<posNames[groups[2]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName2);
        }
        compute<<"real "<<angleName<<" = computeAngle(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
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        variables[angle.first] = angleName;
        forceExpressions["real dEdAngle"+cl.intToString(index)+" = "] = energyExpression.differentiate(angle.first).optimize();
        index++;
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    }
    index = 0;
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    for (auto& dihedral : dihedrals) {
        const vector<int>& groups = dihedral.second;
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        string deltaName1 = atomNames[groups[0]]+atomNames[groups[1]];
        string deltaName2 = atomNames[groups[2]]+atomNames[groups[1]];
        string deltaName3 = atomNames[groups[2]]+atomNames[groups[3]];
        string crossName1 = "cross_"+deltaName1+"_"+deltaName2;
        string crossName2 = "cross_"+deltaName2+"_"+deltaName3;
        string dihedralName = "dihedral_"+atomNames[groups[0]]+atomNames[groups[1]]+atomNames[groups[2]]+atomNames[groups[3]];
        if (computedDeltas.count(deltaName1) == 0) {
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            compute<<"real4 delta"<<deltaName1<<" = delta("<<posNames[groups[0]]<<", "<<posNames[groups[1]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
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            compute<<"real4 delta"<<deltaName2<<" = delta("<<posNames[groups[2]]<<", "<<posNames[groups[1]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName2);
        }
        if (computedDeltas.count(deltaName3) == 0) {
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            compute<<"real4 delta"<<deltaName3<<" = delta("<<posNames[groups[2]]<<", "<<posNames[groups[3]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName3);
        }
        compute<<"real4 "<<crossName1<<" = computeCross(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
        compute<<"real4 "<<crossName2<<" = computeCross(delta"<<deltaName2<<", delta"<<deltaName3<<");\n";
        compute<<"real "<<dihedralName<<" = computeAngle("<<crossName1<<", "<<crossName2<<");\n";
        compute<<dihedralName<<" *= (delta"<<deltaName1<<".x*"<<crossName2<<".x + delta"<<deltaName1<<".y*"<<crossName2<<".y + delta"<<deltaName1<<".z*"<<crossName2<<".z < 0 ? -1 : 1);\n";
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        variables[dihedral.first] = dihedralName;
        forceExpressions["real dEdDihedral"+cl.intToString(index)+" = "] = energyExpression.differentiate(dihedral.first).optimize();
        index++;
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    }

    // Now evaluate the expressions.

    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        extraArgs<<", __global const "<<buffer.getType()<<"* restrict globalParams"<<i;
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = globalParams"<<i<<"[index];\n";
    }
    forceExpressions["energy += "] = energyExpression;
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    if (needEnergyParamDerivs) {
        for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
            string paramName = force.getEnergyParameterDerivativeName(i);
            cl.addEnergyParameterDerivative(paramName);
            Lepton::ParsedExpression derivExpression = energyExpression.differentiate(paramName).optimize();
            forceExpressions[string("energyParamDeriv")+cl.intToString(i)+" += "] = derivExpression;
            initParamDerivs << "mixed energyParamDeriv" << i << " = 0;\n";
        }
        const vector<string>& allParamDerivNames = cl.getEnergyParamDerivNames();
        int numDerivs = allParamDerivNames.size();
        for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++)
            for (int index = 0; index < numDerivs; index++)
                if (allParamDerivNames[index] == force.getEnergyParameterDerivativeName(i))
                    saveParamDerivs << "energyParamDerivs[get_global_id(0)*" << numDerivs << "+" << index << "] += energyParamDeriv" << i << ";\n";
    }
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    compute << cl.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, "temp");

    // Finally, apply forces to groups.

    vector<string> forceNames;
    for (int i = 0; i < groupsPerBond; i++) {
        string istr = cl.intToString(i+1);
        string forceName = "force"+istr;
        forceNames.push_back(forceName);
        compute<<"real3 "<<forceName<<" = (real3) 0;\n";
        compute<<"{\n";
        Lepton::ParsedExpression forceExpressionX = energyExpression.differentiate("x"+istr).optimize();
        Lepton::ParsedExpression forceExpressionY = energyExpression.differentiate("y"+istr).optimize();
        Lepton::ParsedExpression forceExpressionZ = energyExpression.differentiate("z"+istr).optimize();
        map<string, Lepton::ParsedExpression> expressions;
        if (!isZeroExpression(forceExpressionX))
            expressions[forceName+".x -= "] = forceExpressionX;
        if (!isZeroExpression(forceExpressionY))
            expressions[forceName+".y -= "] = forceExpressionY;
        if (!isZeroExpression(forceExpressionZ))
            expressions[forceName+".z -= "] = forceExpressionZ;
        if (expressions.size() > 0)
            compute<<cl.getExpressionUtilities().createExpressions(expressions, variables, functionList, functionDefinitions, "coordtemp");
        compute<<"}\n";
    }
    index = 0;
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    for (auto& distance : distances) {
        const vector<int>& groups = distance.second;
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        string deltaName = atomNames[groups[0]]+atomNames[groups[1]];
        string value = "(dEdDistance"+cl.intToString(index)+"/r_"+deltaName+")*delta"+deltaName+".xyz";
        compute<<forceNames[groups[0]]<<" += "<<"-"<<value<<";\n";
        compute<<forceNames[groups[1]]<<" += "<<value<<";\n";
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        index++;
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    }
    index = 0;
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    for (auto& angle : angles) {
        const vector<int>& groups = angle.second;
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        string deltaName1 = atomNames[groups[1]]+atomNames[groups[0]];
        string deltaName2 = atomNames[groups[1]]+atomNames[groups[2]];
        compute<<"{\n";
        compute<<"real4 crossProd = cross(delta"<<deltaName2<<", delta"<<deltaName1<<");\n";
        compute<<"real lengthCross = max(length(crossProd), (real) 1e-6f);\n";
        compute<<"real4 deltaCross0 = -cross(delta"<<deltaName1<<", crossProd)*dEdAngle"<<cl.intToString(index)<<"/(delta"<<deltaName1<<".w*lengthCross);\n";
        compute<<"real4 deltaCross2 = cross(delta"<<deltaName2<<", crossProd)*dEdAngle"<<cl.intToString(index)<<"/(delta"<<deltaName2<<".w*lengthCross);\n";
        compute<<"real4 deltaCross1 = -(deltaCross0+deltaCross2);\n";
        compute<<forceNames[groups[0]]<<".xyz += deltaCross0.xyz;\n";
        compute<<forceNames[groups[1]]<<".xyz += deltaCross1.xyz;\n";
        compute<<forceNames[groups[2]]<<".xyz += deltaCross2.xyz;\n";
        compute<<"}\n";
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        index++;
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    }
    index = 0;
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    for (auto& dihedral : dihedrals) {
        const vector<int>& groups = dihedral.second;
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        string deltaName1 = atomNames[groups[0]]+atomNames[groups[1]];
        string deltaName2 = atomNames[groups[2]]+atomNames[groups[1]];
        string deltaName3 = atomNames[groups[2]]+atomNames[groups[3]];
        string crossName1 = "cross_"+deltaName1+"_"+deltaName2;
        string crossName2 = "cross_"+deltaName2+"_"+deltaName3;
        compute<<"{\n";
        compute<<"real r = sqrt(delta"<<deltaName2<<".w);\n";
        compute<<"real4 ff;\n";
        compute<<"ff.x = (-dEdDihedral"<<cl.intToString(index)<<"*r)/"<<crossName1<<".w;\n";
        compute<<"ff.y = (delta"<<deltaName1<<".x*delta"<<deltaName2<<".x + delta"<<deltaName1<<".y*delta"<<deltaName2<<".y + delta"<<deltaName1<<".z*delta"<<deltaName2<<".z)/delta"<<deltaName2<<".w;\n";
        compute<<"ff.z = (delta"<<deltaName3<<".x*delta"<<deltaName2<<".x + delta"<<deltaName3<<".y*delta"<<deltaName2<<".y + delta"<<deltaName3<<".z*delta"<<deltaName2<<".z)/delta"<<deltaName2<<".w;\n";
        compute<<"ff.w = (dEdDihedral"<<cl.intToString(index)<<"*r)/"<<crossName2<<".w;\n";
        compute<<"real4 internalF0 = ff.x*"<<crossName1<<";\n";
        compute<<"real4 internalF3 = ff.w*"<<crossName2<<";\n";
        compute<<"real4 s = ff.y*internalF0 - ff.z*internalF3;\n";
        compute<<forceNames[groups[0]]<<".xyz += internalF0.xyz;\n";
        compute<<forceNames[groups[1]]<<".xyz += s.xyz-internalF0.xyz;\n";
        compute<<forceNames[groups[2]]<<".xyz += -s.xyz-internalF3.xyz;\n";
        compute<<forceNames[groups[3]]<<".xyz += internalF3.xyz;\n";
        compute<<"}\n";
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        index++;
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    }
    
    // Save the forces to global memory.
    
    for (int i = 0; i < groupsPerBond; i++) {
        compute<<"atom_add(&groupForce[group"<<(i+1)<<"], (long) (force"<<(i+1)<<".x*0x100000000));\n";
        compute<<"atom_add(&groupForce[group"<<(i+1)<<"+NUM_GROUPS], (long) (force"<<(i+1)<<".y*0x100000000));\n";
        compute<<"atom_add(&groupForce[group"<<(i+1)<<"+NUM_GROUPS*2], (long) (force"<<(i+1)<<".z*0x100000000));\n";
    }
    map<string, string> replacements;
    replacements["M_PI"] = cl.doubleToString(M_PI);
    replacements["NUM_GROUPS"] = cl.intToString(numGroups);
    replacements["NUM_BONDS"] = cl.intToString(numBonds);
    replacements["PADDED_NUM_ATOMS"] = cl.intToString(cl.getPaddedNumAtoms());
    replacements["EXTRA_ARGS"] = extraArgs.str();
    replacements["COMPUTE_FORCE"] = compute.str();
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    replacements["INIT_PARAM_DERIVS"] = initParamDerivs.str();
    replacements["SAVE_PARAM_DERIVS"] = saveParamDerivs.str();
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    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customCentroidBond, replacements));
    index = 0;
    computeCentersKernel = cl::Kernel(program, "computeGroupCenters");
    computeCentersKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
    computeCentersKernel.setArg<cl::Buffer>(index++, groupParticles->getDeviceBuffer());
    computeCentersKernel.setArg<cl::Buffer>(index++, groupWeights->getDeviceBuffer());
    computeCentersKernel.setArg<cl::Buffer>(index++, groupOffsets->getDeviceBuffer());
    computeCentersKernel.setArg<cl::Buffer>(index++, centerPositions->getDeviceBuffer());
    index = 0;
    groupForcesKernel = cl::Kernel(program, "computeGroupForces");
    groupForcesKernel.setArg<cl::Buffer>(index++, groupForces->getDeviceBuffer());
    index++; // Energy buffer hasn't been created yet
    groupForcesKernel.setArg<cl::Buffer>(index++, centerPositions->getDeviceBuffer());
    groupForcesKernel.setArg<cl::Buffer>(index++, bondGroups->getDeviceBuffer());
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    index += 5; // Periodic box information
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    if (needEnergyParamDerivs)
        index++; // Deriv buffer hasn't been created yet.
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    for (auto function : tabulatedFunctions)
        groupForcesKernel.setArg<cl::Buffer>(index++, function->getDeviceBuffer());
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    if (globals != NULL)
        groupForcesKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
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    for (auto& buffer : params->getBuffers())
        groupForcesKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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    index = 0;
    applyForcesKernel = cl::Kernel(program, "applyForcesToAtoms");
    applyForcesKernel.setArg<cl::Buffer>(index++, groupParticles->getDeviceBuffer());
    applyForcesKernel.setArg<cl::Buffer>(index++, groupWeights->getDeviceBuffer());
    applyForcesKernel.setArg<cl::Buffer>(index++, groupOffsets->getDeviceBuffer());
    applyForcesKernel.setArg<cl::Buffer>(index++, groupForces->getDeviceBuffer());
}

double OpenCLCalcCustomCentroidBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numBonds == 0)
        return 0.0;
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    if (globals != NULL) {
        bool changed = false;
        for (int i = 0; i < (int) globalParamNames.size(); i++) {
            float value = (float) context.getParameter(globalParamNames[i]);
            if (value != globalParamValues[i])
                changed = true;
            globalParamValues[i] = value;
        }
        if (changed)
            globals->upload(globalParamValues);
    }
    cl.executeKernel(computeCentersKernel, OpenCLContext::TileSize*numGroups);
    groupForcesKernel.setArg<cl::Buffer>(1, cl.getEnergyBuffer().getDeviceBuffer());
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    setPeriodicBoxArgs(cl, groupForcesKernel, 4);
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    if (needEnergyParamDerivs)
        groupForcesKernel.setArg<cl::Memory>(9, cl.getEnergyParamDerivBuffer().getDeviceBuffer());
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    cl.executeKernel(groupForcesKernel, numBonds);
    applyForcesKernel.setArg<cl::Buffer>(4, cl.getLongForceBuffer().getDeviceBuffer());
    cl.executeKernel(applyForcesKernel, OpenCLContext::TileSize*numGroups);
    return 0.0;
}

void OpenCLCalcCustomCentroidBondForceKernel::copyParametersToContext(ContextImpl& context, const CustomCentroidBondForce& force) {
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    if (numBonds != force.getNumBonds())
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        throw OpenMMException("updateParametersInContext: The number of bonds has changed");
    if (numBonds == 0)
        return;
    
    // Record the per-bond parameters.
    
    vector<vector<float> > paramVector(numBonds);
    vector<int> particles;
    vector<double> parameters;
    for (int i = 0; i < numBonds; i++) {
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        force.getBondParameters(i, particles, parameters);
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        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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

OpenCLCalcCustomCompoundBondForceKernel::~OpenCLCalcCustomCompoundBondForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
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    for (auto function : tabulatedFunctions)
        delete function;
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}

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

    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
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    vector<const TabulatedFunction*> functionList;
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    stringstream tableArgs;
    for (int i = 0; i < force.getNumFunctions(); i++) {
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        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
        functions[name] = cl.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
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        int width;
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        vector<float> f = cl.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        OpenCLArray* array = OpenCLArray::create<float>(cl, f.size(), "TabulatedFunction");
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        tabulatedFunctions.push_back(array);
        array->upload(f);
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        string arrayName = cl.getBondedUtilities().addArgument(array->getDeviceBuffer(), width == 1 ? "float" : "float"+cl.intToString(width));
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        functionDefinitions.push_back(make_pair(name, arrayName));
    }
    
    // Record information about parameters.

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

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

    map<string, vector<int> > distances;
    map<string, vector<int> > angles;
    map<string, vector<int> > dihedrals;
    Lepton::ParsedExpression energyExpression = CustomCompoundBondForceImpl::prepareExpression(force, functions, distances, angles, dihedrals);
    map<string, Lepton::ParsedExpression> forceExpressions;
    set<string> computedDeltas;
    vector<string> atomNames, posNames;
    for (int i = 0; i < particlesPerBond; i++) {
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        string index = cl.intToString(i+1);
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        atomNames.push_back("P"+index);
        posNames.push_back("pos"+index);
    }
    stringstream compute;
    int index = 0;
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    for (auto& distance : distances) {
        const vector<int>& atoms = distance.second;
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        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
        if (computedDeltas.count(deltaName) == 0) {
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            compute<<"real4 delta"<<deltaName<<" = ccb_delta("<<posNames[atoms[0]]<<", "<<posNames[atoms[1]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName);
        }
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        compute<<"real r_"<<deltaName<<" = sqrt(delta"<<deltaName<<".w);\n";
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        variables[distance.first] = "r_"+deltaName;
        forceExpressions["real dEdDistance"+cl.intToString(index)+" = "] = energyExpression.differentiate(distance.first).optimize();
        index++;
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    }
    index = 0;
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    for (auto& angle : angles) {
        const vector<int>& atoms = angle.second;
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        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) {
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            compute<<"real4 delta"<<deltaName1<<" = ccb_delta("<<posNames[atoms[1]]<<", "<<posNames[atoms[0]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
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            compute<<"real4 delta"<<deltaName2<<" = ccb_delta("<<posNames[atoms[1]]<<", "<<posNames[atoms[2]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName2);
        }
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        compute<<"real "<<angleName<<" = ccb_computeAngle(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
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        variables[angle.first] = angleName;
        forceExpressions["real dEdAngle"+cl.intToString(index)+" = "] = energyExpression.differentiate(angle.first).optimize();
        index++;
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    }
    index = 0;
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    for (auto& dihedral : dihedrals) {
        const vector<int>& atoms = dihedral.second;
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        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) {
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            compute<<"real4 delta"<<deltaName1<<" = ccb_delta("<<posNames[atoms[0]]<<", "<<posNames[atoms[1]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
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            compute<<"real4 delta"<<deltaName2<<" = ccb_delta("<<posNames[atoms[2]]<<", "<<posNames[atoms[1]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName2);
        }
        if (computedDeltas.count(deltaName3) == 0) {
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            compute<<"real4 delta"<<deltaName3<<" = ccb_delta("<<posNames[atoms[2]]<<", "<<posNames[atoms[3]]<<", "<<force.usesPeriodicBoundaryConditions()<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName3);
        }
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        compute<<"real4 "<<crossName1<<" = ccb_computeCross(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
        compute<<"real4 "<<crossName2<<" = ccb_computeCross(delta"<<deltaName2<<", delta"<<deltaName3<<");\n";
        compute<<"real "<<dihedralName<<" = ccb_computeAngle("<<crossName1<<", "<<crossName2<<");\n";
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        compute<<dihedralName<<" *= (delta"<<deltaName1<<".x*"<<crossName2<<".x + delta"<<deltaName1<<".y*"<<crossName2<<".y + delta"<<deltaName1<<".z*"<<crossName2<<".z < 0 ? -1 : 1);\n";
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        variables[dihedral.first] = dihedralName;
        forceExpressions["real dEdDihedral"+cl.intToString(index)+" = "] = energyExpression.differentiate(dihedral.first).optimize();
        index++;
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    }

    // Now evaluate the expressions.

    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        const OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        string argName = cl.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
    forceExpressions["energy += "] = energyExpression;
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cl.getBondedUtilities().addEnergyParameterDerivative(paramName);
        Lepton::ParsedExpression derivExpression = energyExpression.differentiate(paramName).optimize();
        forceExpressions[derivVariable+" += "] = derivExpression;
    }
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    compute << cl.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, "temp");
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    // Finally, apply forces to atoms.

    vector<string> forceNames;
    for (int i = 0; i < particlesPerBond; i++) {
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        string istr = cl.intToString(i+1);
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        string forceName = "force"+istr;
        forceNames.push_back(forceName);
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        compute<<"real4 "<<forceName<<" = (real4) 0;\n";
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        compute<<"{\n";
        Lepton::ParsedExpression forceExpressionX = energyExpression.differentiate("x"+istr).optimize();
        Lepton::ParsedExpression forceExpressionY = energyExpression.differentiate("y"+istr).optimize();
        Lepton::ParsedExpression forceExpressionZ = energyExpression.differentiate("z"+istr).optimize();
        map<string, Lepton::ParsedExpression> expressions;
        if (!isZeroExpression(forceExpressionX))
            expressions[forceName+".x -= "] = forceExpressionX;
        if (!isZeroExpression(forceExpressionY))
            expressions[forceName+".y -= "] = forceExpressionY;
        if (!isZeroExpression(forceExpressionZ))
            expressions[forceName+".z -= "] = forceExpressionZ;
        if (expressions.size() > 0)
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            compute<<cl.getExpressionUtilities().createExpressions(expressions, variables, functionList, functionDefinitions, "coordtemp");
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        compute<<"}\n";
    }
    index = 0;
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    for (auto& distance : distances) {
        const vector<int>& atoms = distance.second;
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        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
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        string value = "(dEdDistance"+cl.intToString(index)+"/r_"+deltaName+")*delta"+deltaName+".xyz";
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        compute<<forceNames[atoms[0]]<<".xyz += "<<"-"<<value<<";\n";
        compute<<forceNames[atoms[1]]<<".xyz += "<<value<<";\n";
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        index++;
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    }
    index = 0;
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    for (auto& angle : angles) {
        const vector<int>& atoms = angle.second;
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        string deltaName1 = atomNames[atoms[1]]+atomNames[atoms[0]];
        string deltaName2 = atomNames[atoms[1]]+atomNames[atoms[2]];
        compute<<"{\n";
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        compute<<"real4 crossProd = cross(delta"<<deltaName2<<", delta"<<deltaName1<<");\n";
        compute<<"real lengthCross = max(length(crossProd), (real) 1e-6f);\n";
        compute<<"real4 deltaCross0 = -cross(delta"<<deltaName1<<", crossProd)*dEdAngle"<<cl.intToString(index)<<"/(delta"<<deltaName1<<".w*lengthCross);\n";
        compute<<"real4 deltaCross2 = cross(delta"<<deltaName2<<", crossProd)*dEdAngle"<<cl.intToString(index)<<"/(delta"<<deltaName2<<".w*lengthCross);\n";
        compute<<"real4 deltaCross1 = -(deltaCross0+deltaCross2);\n";
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        compute<<forceNames[atoms[0]]<<".xyz += deltaCross0.xyz;\n";
        compute<<forceNames[atoms[1]]<<".xyz += deltaCross1.xyz;\n";
        compute<<forceNames[atoms[2]]<<".xyz += deltaCross2.xyz;\n";
        compute<<"}\n";
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        index++;
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    }
    index = 0;
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    for (auto& dihedral : dihedrals) {
        const vector<int>& atoms = dihedral.second;
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        string deltaName1 = atomNames[atoms[0]]+atomNames[atoms[1]];
        string deltaName2 = atomNames[atoms[2]]+atomNames[atoms[1]];
        string deltaName3 = atomNames[atoms[2]]+atomNames[atoms[3]];
        string crossName1 = "cross_"+deltaName1+"_"+deltaName2;
        string crossName2 = "cross_"+deltaName2+"_"+deltaName3;
        compute<<"{\n";
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        compute<<"real r = SQRT(delta"<<deltaName2<<".w);\n";
        compute<<"real4 ff;\n";
        compute<<"ff.x = (-dEdDihedral"<<cl.intToString(index)<<"*r)/"<<crossName1<<".w;\n";
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        compute<<"ff.y = (delta"<<deltaName1<<".x*delta"<<deltaName2<<".x + delta"<<deltaName1<<".y*delta"<<deltaName2<<".y + delta"<<deltaName1<<".z*delta"<<deltaName2<<".z)/delta"<<deltaName2<<".w;\n";
        compute<<"ff.z = (delta"<<deltaName3<<".x*delta"<<deltaName2<<".x + delta"<<deltaName3<<".y*delta"<<deltaName2<<".y + delta"<<deltaName3<<".z*delta"<<deltaName2<<".z)/delta"<<deltaName2<<".w;\n";
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        compute<<"ff.w = (dEdDihedral"<<cl.intToString(index)<<"*r)/"<<crossName2<<".w;\n";
        compute<<"real4 internalF0 = ff.x*"<<crossName1<<";\n";
        compute<<"real4 internalF3 = ff.w*"<<crossName2<<";\n";
        compute<<"real4 s = ff.y*internalF0 - ff.z*internalF3;\n";
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        compute<<forceNames[atoms[0]]<<".xyz += internalF0.xyz;\n";
        compute<<forceNames[atoms[1]]<<".xyz += s.xyz-internalF0.xyz;\n";
        compute<<forceNames[atoms[2]]<<".xyz += -s.xyz-internalF3.xyz;\n";
        compute<<forceNames[atoms[3]]<<".xyz += internalF3.xyz;\n";
        compute<<"}\n";
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        index++;
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    }
    cl.getBondedUtilities().addInteraction(atoms, compute.str(), force.getForceGroup());
    map<string, string> replacements;
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    replacements["M_PI"] = cl.doubleToString(M_PI);
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    cl.getBondedUtilities().addPrefixCode(cl.replaceStrings(OpenCLKernelSources::customCompoundBond, replacements));;
}

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

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void OpenCLCalcCustomCompoundBondForceKernel::copyParametersToContext(ContextImpl& context, const CustomCompoundBondForce& force) {
    int numContexts = cl.getPlatformData().contexts.size();
    int startIndex = cl.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cl.getContextIndex()+1)*force.getNumBonds()/numContexts;
    if (numBonds != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of bonds has changed");
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    if (numBonds == 0)
        return;
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    // Record the per-bond parameters.
    
    vector<vector<cl_float> > paramVector(numBonds);
    vector<int> particles;
    vector<double> parameters;
    for (int i = 0; i < numBonds; i++) {
        force.getBondParameters(startIndex+i, particles, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (cl_float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
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    cl.invalidateMolecules(info);
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}

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class OpenCLCalcCustomManyParticleForceKernel::ForceInfo : public OpenCLForceInfo {
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public:
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    ForceInfo(const CustomManyParticleForce& force) : OpenCLForceInfo(0), force(force) {
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    }
    bool areParticlesIdentical(int particle1, int particle2) {
        vector<double> params1, params2;
        int type1, type2;
        force.getParticleParameters(particle1, params1, type1);
        force.getParticleParameters(particle2, params2, type2);
        if (type1 != type2)
            return false;
        for (int i = 0; i < (int) params1.size(); i++)
            if (params1[i] != params2[i])
                return false;
        return true;
    }
    int getNumParticleGroups() {
        return force.getNumExclusions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2;
        force.getExclusionParticles(index, particle1, particle2);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        return true;
    }
private:
    const CustomManyParticleForce& force;
};

OpenCLCalcCustomManyParticleForceKernel::~OpenCLCalcCustomManyParticleForceKernel() {
    if (params != NULL)
        delete params;
    if (globals != NULL)
        delete globals;
    if (orderIndex != NULL)
        delete orderIndex;
    if (particleOrder != NULL)
        delete particleOrder;
    if (particleTypes != NULL)
        delete particleTypes;
    if (exclusions != NULL)
        delete exclusions;
    if (exclusionStartIndex != NULL)
        delete exclusionStartIndex;
    if (blockCenter != NULL)
        delete blockCenter;
    if (blockBoundingBox != NULL)
        delete blockBoundingBox;
    if (neighborPairs != NULL)
        delete neighborPairs;
    if (numNeighborPairs != NULL)
        delete numNeighborPairs;
    if (neighborStartIndex != NULL)
        delete neighborStartIndex;
    if (neighbors != NULL)
        delete neighbors;
    if (numNeighborsForAtom != NULL)
        delete numNeighborsForAtom;
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    for (auto function : tabulatedFunctions)
        delete function;
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}

void OpenCLCalcCustomManyParticleForceKernel::initialize(const System& system, const CustomManyParticleForce& force) {
    if (!cl.getSupports64BitGlobalAtomics())
        throw OpenMMException("CustomManyParticleForce requires a device that supports 64 bit atomic operations");
    int numParticles = force.getNumParticles();
    int particlesPerSet = force.getNumParticlesPerSet();
    bool centralParticleMode = (force.getPermutationMode() == CustomManyParticleForce::UniqueCentralParticle);
    nonbondedMethod = CalcCustomManyParticleForceKernel::NonbondedMethod(force.getNonbondedMethod());
    forceWorkgroupSize = 128;
    findNeighborsWorkgroupSize = (cl.getSIMDWidth() >= 32 ? 128 : 32);
    
    // Record parameter values.
    
    params = new OpenCLParameterSet(cl, force.getNumPerParticleParameters(), numParticles, "customManyParticleParameters");
    vector<vector<float> > paramVector(numParticles);
    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
        int type;
        force.getParticleParameters(i, parameters, type);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
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    info = new ForceInfo(force);
    cl.addForce(info);
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    // Record the tabulated functions.

    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
    vector<const TabulatedFunction*> functionList;
    stringstream tableArgs;
    for (int i = 0; i < force.getNumTabulatedFunctions(); i++) {
        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
        string arrayName = "table"+cl.intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = cl.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
        int width;
        vector<float> f = cl.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
        tabulatedFunctions.push_back(OpenCLArray::create<float>(cl, f.size(), "TabulatedFunction"));
        tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
        tableArgs << ", __global const float";
        if (width > 1)
            tableArgs << width;
        tableArgs << "* restrict " << arrayName;
    }
    
    // Record information about parameters.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (float) force.getGlobalParameterDefaultValue(i);
    }
    vector<pair<ExpressionTreeNode, string> > variables;
    for (int i = 0; i < particlesPerSet; i++) {
        string index = cl.intToString(i+1);
        variables.push_back(makeVariable("x"+index, "pos"+index+".x"));
        variables.push_back(makeVariable("y"+index, "pos"+index+".y"));
        variables.push_back(makeVariable("z"+index, "pos"+index+".z"));
    }
    for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
        const string& name = force.getPerParticleParameterName(i);
        for (int j = 0; j < particlesPerSet; j++) {
            string index = cl.intToString(j+1);
            variables.push_back(makeVariable(name+index, "params"+params->getParameterSuffix(i, index)));
        }
    }
    if (force.getNumGlobalParameters() > 0) {
        globals = OpenCLArray::create<cl_float>(cl, force.getNumGlobalParameters(), "customManyParticleGlobals", CL_MEM_READ_ONLY);
        globals->upload(globalParamValues);
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+cl.intToString(i)+"]";
            variables.push_back(makeVariable(name, value));
        }
    }
    
    // Build data structures for type filters.
    
    vector<int> particleTypesVec;
    vector<int> orderIndexVec;
    vector<std::vector<int> > particleOrderVec;
    int numTypes;
    CustomManyParticleForceImpl::buildFilterArrays(force, numTypes, particleTypesVec, orderIndexVec, particleOrderVec);
    bool hasTypeFilters = (particleOrderVec.size() > 1);
    if (hasTypeFilters) {
        particleTypes = OpenCLArray::create<int>(cl, particleTypesVec.size(), "customManyParticleTypes");
        orderIndex = OpenCLArray::create<int>(cl, orderIndexVec.size(), "customManyParticleOrderIndex");
        particleOrder = OpenCLArray::create<int>(cl, particleOrderVec.size()*particlesPerSet, "customManyParticleOrder");
        particleTypes->upload(particleTypesVec);
        orderIndex->upload(orderIndexVec);
        vector<int> flattenedOrder(particleOrder->getSize());
        for (int i = 0; i < (int) particleOrderVec.size(); i++)
            for (int j = 0; j < particlesPerSet; j++)
                flattenedOrder[i*particlesPerSet+j] = particleOrderVec[i][j];
        particleOrder->upload(flattenedOrder);
    }
    
    // Build data structures for exclusions.
    
    if (force.getNumExclusions() > 0) {
        vector<vector<int> > particleExclusions(numParticles);
        for (int i = 0; i < force.getNumExclusions(); i++) {
            int p1, p2;
            force.getExclusionParticles(i, p1, p2);
            particleExclusions[p1].push_back(p2);
            particleExclusions[p2].push_back(p1);
        }
        vector<int> exclusionsVec;
        vector<int> exclusionStartIndexVec(numParticles+1);
        exclusionStartIndexVec[0] = 0;
        for (int i = 0; i < numParticles; i++) {
            sort(particleExclusions[i].begin(), particleExclusions[i].end());
            exclusionsVec.insert(exclusionsVec.end(), particleExclusions[i].begin(), particleExclusions[i].end());
            exclusionStartIndexVec[i+1] = exclusionsVec.size();
        }
        exclusions = OpenCLArray::create<int>(cl, exclusionsVec.size(), "customManyParticleExclusions");
        exclusionStartIndex = OpenCLArray::create<int>(cl, exclusionStartIndexVec.size(), "customManyParticleExclusionStart");
        exclusions->upload(exclusionsVec);
        exclusionStartIndex->upload(exclusionStartIndexVec);
    }
    
    // Build data structures for the neighbor list.
    
    if (nonbondedMethod != NoCutoff) {
        int numAtomBlocks = cl.getNumAtomBlocks();
        int elementSize = (cl.getUseDoublePrecision() ? sizeof(double) : sizeof(float));
        blockCenter = new OpenCLArray(cl, numAtomBlocks, 4*elementSize, "blockCenter");
        blockBoundingBox = new OpenCLArray(cl, numAtomBlocks, 4*elementSize, "blockBoundingBox");
        numNeighborPairs = OpenCLArray::create<int>(cl, 1, "customManyParticleNumNeighborPairs");
        neighborStartIndex = OpenCLArray::create<int>(cl, numParticles+1, "customManyParticleNeighborStartIndex");
        numNeighborsForAtom = OpenCLArray::create<int>(cl, numParticles, "customManyParticleNumNeighborsForAtom");

        // Select a size for the array that holds the neighbor list.  We have to make a fairly
        // arbitrary guess, but if this turns out to be too small we'll increase it later.

        maxNeighborPairs = 150*numParticles;
        neighborPairs = OpenCLArray::create<mm_int2>(cl, maxNeighborPairs, "customManyParticleNeighborPairs");
        neighbors = OpenCLArray::create<int>(cl, maxNeighborPairs, "customManyParticleNeighbors");
    }

    // 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 = CustomManyParticleForceImpl::prepareExpression(force, functions, distances, angles, dihedrals);
    map<string, Lepton::ParsedExpression> forceExpressions;
    set<string> computedDeltas;
    vector<string> atomNames, posNames;
    for (int i = 0; i < particlesPerSet; i++) {
        string index = cl.intToString(i+1);
        atomNames.push_back("P"+index);
        posNames.push_back("pos"+index);
    }
    stringstream compute;
    int index = 0;
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    for (auto& distance : distances) {
        const vector<int>& atoms = distance.second;
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        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
        if (computedDeltas.count(deltaName) == 0) {
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            compute<<"real4 delta"<<deltaName<<" = delta("<<posNames[atoms[0]]<<", "<<posNames[atoms[1]]<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName);
        }
        compute<<"real r_"<<deltaName<<" = sqrt(delta"<<deltaName<<".w);\n";
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        variables.push_back(makeVariable(distance.first, "r_"+deltaName));
        forceExpressions["real dEdDistance"+cl.intToString(index)+" = "] = energyExpression.differentiate(distance.first).optimize();
        index++;
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    }
    index = 0;
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    for (auto& angle : angles) {
        const vector<int>& atoms = angle.second;
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        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) {
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            compute<<"real4 delta"<<deltaName1<<" = delta("<<posNames[atoms[1]]<<", "<<posNames[atoms[0]]<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
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            compute<<"real4 delta"<<deltaName2<<" = delta("<<posNames[atoms[1]]<<", "<<posNames[atoms[2]]<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName2);
        }
        compute<<"real "<<angleName<<" = computeAngle(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
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        variables.push_back(makeVariable(angle.first, angleName));
        forceExpressions["real dEdAngle"+cl.intToString(index)+" = "] = energyExpression.differentiate(angle.first).optimize();
        index++;
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    }
    index = 0;
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    for (auto& dihedral : dihedrals) {
        const vector<int>& atoms = dihedral.second;
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        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) {
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            compute<<"real4 delta"<<deltaName1<<" = delta("<<posNames[atoms[0]]<<", "<<posNames[atoms[1]]<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName1);
        }
        if (computedDeltas.count(deltaName2) == 0) {
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            compute<<"real4 delta"<<deltaName2<<" = delta("<<posNames[atoms[2]]<<", "<<posNames[atoms[1]]<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName2);
        }
        if (computedDeltas.count(deltaName3) == 0) {
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            compute<<"real4 delta"<<deltaName3<<" = delta("<<posNames[atoms[2]]<<", "<<posNames[atoms[3]]<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ);\n";
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            computedDeltas.insert(deltaName3);
        }
        compute<<"real4 "<<crossName1<<" = computeCross(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
        compute<<"real4 "<<crossName2<<" = computeCross(delta"<<deltaName2<<", delta"<<deltaName3<<");\n";
        compute<<"real "<<dihedralName<<" = computeAngle("<<crossName1<<", "<<crossName2<<");\n";
        compute<<dihedralName<<" *= (delta"<<deltaName1<<".x*"<<crossName2<<".x + delta"<<deltaName1<<".y*"<<crossName2<<".y + delta"<<deltaName1<<".z*"<<crossName2<<".z < 0 ? -1 : 1);\n";
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        variables.push_back(makeVariable(dihedral.first, dihedralName));
        forceExpressions["real dEdDihedral"+cl.intToString(index)+" = "] = energyExpression.differentiate(dihedral.first).optimize();
        index++;
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    }

    // Now evaluate the expressions.

    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        compute<<buffer.getType()<<" params"<<(i+1)<<" = global_params"<<(i+1)<<"[index];\n";
    }
    forceExpressions["energy += "] = energyExpression;
    compute << cl.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, "temp");

    // Apply forces to atoms.

    vector<string> forceNames;
    for (int i = 0; i < particlesPerSet; i++) {
        string istr = cl.intToString(i+1);
        string forceName = "force"+istr;
        forceNames.push_back(forceName);
        compute<<"real4 "<<forceName<<" = (real4) 0;\n";
        compute<<"{\n";
        Lepton::ParsedExpression forceExpressionX = energyExpression.differentiate("x"+istr).optimize();
        Lepton::ParsedExpression forceExpressionY = energyExpression.differentiate("y"+istr).optimize();
        Lepton::ParsedExpression forceExpressionZ = energyExpression.differentiate("z"+istr).optimize();
        map<string, Lepton::ParsedExpression> expressions;
        if (!isZeroExpression(forceExpressionX))
            expressions[forceName+".x -= "] = forceExpressionX;
        if (!isZeroExpression(forceExpressionY))
            expressions[forceName+".y -= "] = forceExpressionY;
        if (!isZeroExpression(forceExpressionZ))
            expressions[forceName+".z -= "] = forceExpressionZ;
        if (expressions.size() > 0)
            compute<<cl.getExpressionUtilities().createExpressions(expressions, variables, functionList, functionDefinitions, "coordtemp");
        compute<<"}\n";
    }
    index = 0;
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    for (auto& distance : distances) {
        const vector<int>& atoms = distance.second;
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        string deltaName = atomNames[atoms[0]]+atomNames[atoms[1]];
        string value = "(dEdDistance"+cl.intToString(index)+"/r_"+deltaName+")*delta"+deltaName+".xyz";
        compute<<forceNames[atoms[0]]<<".xyz += "<<"-"<<value<<";\n";
        compute<<forceNames[atoms[1]]<<".xyz += "<<value<<";\n";
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        index++;
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    }
    index = 0;
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    for (auto& angle : angles) {
        const vector<int>& atoms = angle.second;
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        string deltaName1 = atomNames[atoms[1]]+atomNames[atoms[0]];
        string deltaName2 = atomNames[atoms[1]]+atomNames[atoms[2]];
        compute<<"{\n";
        compute<<"real4 crossProd = cross(delta"<<deltaName2<<", delta"<<deltaName1<<");\n";
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        compute<<"real lengthCross = max(SQRT(dot(crossProd, crossProd)), (real) 1e-6f);\n";
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        compute<<"real4 deltaCross0 = -cross(delta"<<deltaName1<<", crossProd)*dEdAngle"<<cl.intToString(index)<<"/(delta"<<deltaName1<<".w*lengthCross);\n";
        compute<<"real4 deltaCross2 = cross(delta"<<deltaName2<<", crossProd)*dEdAngle"<<cl.intToString(index)<<"/(delta"<<deltaName2<<".w*lengthCross);\n";
        compute<<"real4 deltaCross1 = -(deltaCross0+deltaCross2);\n";
        compute<<forceNames[atoms[0]]<<".xyz += deltaCross0.xyz;\n";
        compute<<forceNames[atoms[1]]<<".xyz += deltaCross1.xyz;\n";
        compute<<forceNames[atoms[2]]<<".xyz += deltaCross2.xyz;\n";
        compute<<"}\n";
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        index++;
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    }
    index = 0;
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    for (auto& dihedral : dihedrals) {
        const vector<int>& atoms = dihedral.second;
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        string deltaName1 = atomNames[atoms[0]]+atomNames[atoms[1]];
        string deltaName2 = atomNames[atoms[2]]+atomNames[atoms[1]];
        string deltaName3 = atomNames[atoms[2]]+atomNames[atoms[3]];
        string crossName1 = "cross_"+deltaName1+"_"+deltaName2;
        string crossName2 = "cross_"+deltaName2+"_"+deltaName3;
        compute<<"{\n";
        compute<<"real r = sqrt(delta"<<deltaName2<<".w);\n";
        compute<<"real4 ff;\n";
        compute<<"ff.x = (-dEdDihedral"<<cl.intToString(index)<<"*r)/"<<crossName1<<".w;\n";
        compute<<"ff.y = (delta"<<deltaName1<<".x*delta"<<deltaName2<<".x + delta"<<deltaName1<<".y*delta"<<deltaName2<<".y + delta"<<deltaName1<<".z*delta"<<deltaName2<<".z)/delta"<<deltaName2<<".w;\n";
        compute<<"ff.z = (delta"<<deltaName3<<".x*delta"<<deltaName2<<".x + delta"<<deltaName3<<".y*delta"<<deltaName2<<".y + delta"<<deltaName3<<".z*delta"<<deltaName2<<".z)/delta"<<deltaName2<<".w;\n";
        compute<<"ff.w = (dEdDihedral"<<cl.intToString(index)<<"*r)/"<<crossName2<<".w;\n";
        compute<<"real4 internalF0 = ff.x*"<<crossName1<<";\n";
        compute<<"real4 internalF3 = ff.w*"<<crossName2<<";\n";
        compute<<"real4 s = ff.y*internalF0 - ff.z*internalF3;\n";
        compute<<forceNames[atoms[0]]<<".xyz += internalF0.xyz;\n";
        compute<<forceNames[atoms[1]]<<".xyz += s.xyz-internalF0.xyz;\n";
        compute<<forceNames[atoms[2]]<<".xyz += -s.xyz-internalF3.xyz;\n";
        compute<<forceNames[atoms[3]]<<".xyz += internalF3.xyz;\n";
        compute<<"}\n";
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        index++;
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    }
    
    // Store forces to global memory.
    
    for (int i = 0; i < particlesPerSet; i++)
        compute<<"storeForce(atom"<<(i+1)<<", "<<forceNames[i]<<", forceBuffers);\n";
    
    // Create other replacements that depend on the number of particles per set.
    
    stringstream numCombinations, atomsForCombination, isValidCombination, permute, loadData, verifyCutoff, verifyExclusions;
    if (hasTypeFilters) {
        permute<<"int particleSet[] = {";
        for (int i = 0; i < particlesPerSet; i++) {
            permute<<"p"<<(i+1);
            if (i < particlesPerSet-1)
                permute<<", ";
        }
        permute<<"};\n";
    }
    for (int i = 0; i < particlesPerSet; i++) {
        if (hasTypeFilters)
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            permute<<"int atom"<<(i+1)<<" = particleSet[particleOrder["<<particlesPerSet<<"*order+"<<i<<"]];\n";
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        else
            permute<<"int atom"<<(i+1)<<" = p"<<(i+1)<<";\n";
        loadData<<"real4 pos"<<(i+1)<<" = posq[atom"<<(i+1)<<"];\n";
        for (int j = 0; j < (int) params->getBuffers().size(); j++)
            loadData<<params->getBuffers()[j].getType()<<" params"<<(j+1)<<(i+1)<<" = global_params"<<(j+1)<<"[atom"<<(i+1)<<"];\n";
    }
    if (centralParticleMode) {
        for (int i = 1; i < particlesPerSet; i++) {
            if (i > 1)
                isValidCombination<<" && p"<<(i+1)<<">p"<<i<<" && ";
            isValidCombination<<"p"<<(i+1)<<"!=p1";
        }
    }
    else {
        for (int i = 2; i < particlesPerSet; i++) {
            if (i > 2)
                isValidCombination<<" && ";
            isValidCombination<<"a"<<(i+1)<<">a"<<i;
        }
    }
    atomsForCombination<<"int tempIndex = index;\n";
    for (int i = 1; i < particlesPerSet; i++) {
        if (i > 1)
            numCombinations<<"*";
        numCombinations<<"numNeighbors";
        if (centralParticleMode)
            atomsForCombination<<"int a"<<(i+1)<<" = tempIndex%numNeighbors;\n";
        else
            atomsForCombination<<"int a"<<(i+1)<<" = 1+tempIndex%numNeighbors;\n";
        if (i < particlesPerSet-1)
            atomsForCombination<<"tempIndex /= numNeighbors;\n";
    }
    if (particlesPerSet > 2) {
        if (centralParticleMode)
            atomsForCombination<<"a2 = (a3%2 == 0 ? a2 : numNeighbors-a2-1);\n";
        else
            atomsForCombination<<"a2 = (a3%2 == 0 ? a2 : numNeighbors-a2+1);\n";
    }
    for (int i = 1; i < particlesPerSet; i++) {
        if (nonbondedMethod == NoCutoff) {
            if (centralParticleMode)
                atomsForCombination<<"int p"<<(i+1)<<" = a"<<(i+1)<<";\n";
            else
                atomsForCombination<<"int p"<<(i+1)<<" = p1+a"<<(i+1)<<";\n";
        }
        else {
            if (centralParticleMode)
                atomsForCombination<<"int p"<<(i+1)<<" = neighbors[firstNeighbor+a"<<(i+1)<<"];\n";
            else
                atomsForCombination<<"int p"<<(i+1)<<" = neighbors[firstNeighbor-1+a"<<(i+1)<<"];\n";
        }
    }
    if (nonbondedMethod != NoCutoff) {
        for (int i = 1; i < particlesPerSet; i++)
            verifyCutoff<<"real4 pos"<<(i+1)<<" = posq[p"<<(i+1)<<"];\n";
        if (!centralParticleMode) {
            for (int i = 1; i < particlesPerSet; i++) {
                for (int j = i+1; j < particlesPerSet; j++)
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                    verifyCutoff<<"includeInteraction &= (delta(pos"<<(i+1)<<", pos"<<(j+1)<<", periodicBoxSize, invPeriodicBoxSize, periodicBoxVecX, periodicBoxVecY, periodicBoxVecZ).w < CUTOFF_SQUARED);\n";
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            }
        }
    }
    if (force.getNumExclusions() > 0) {
        int startCheckFrom = (nonbondedMethod == NoCutoff ? 0 : 1);
        for (int i = startCheckFrom; i < particlesPerSet; i++)
            for (int j = i+1; j < particlesPerSet; j++)
                verifyExclusions<<"includeInteraction &= !isInteractionExcluded(p"<<(i+1)<<", p"<<(j+1)<<", exclusions, exclusionStartIndex);\n";
    }
    string computeTypeIndex = "particleTypes[p"+cl.intToString(particlesPerSet)+"]";
    for (int i = particlesPerSet-2; i >= 0; i--)
        computeTypeIndex = "particleTypes[p"+cl.intToString(i+1)+"]+"+cl.intToString(numTypes)+"*("+computeTypeIndex+")";
    
    // Create replacements for extra arguments.
    
    stringstream extraArgs;
    if (force.getNumGlobalParameters() > 0)
        extraArgs << ", __global const float* globals";
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        OpenCLNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        extraArgs<<", __global const "<<buffer.getType()<<"* restrict global_params"<<(i+1);
    }

    // Create the kernels.

    map<string, string> replacements;
    replacements["COMPUTE_INTERACTION"] = compute.str();
    replacements["NUM_CANDIDATE_COMBINATIONS"] = numCombinations.str();
    replacements["FIND_ATOMS_FOR_COMBINATION_INDEX"] = atomsForCombination.str();
    replacements["IS_VALID_COMBINATION"] = isValidCombination.str();
    replacements["VERIFY_CUTOFF"] = verifyCutoff.str();
    replacements["VERIFY_EXCLUSIONS"] = verifyExclusions.str();
    replacements["PERMUTE_ATOMS"] = permute.str();
    replacements["LOAD_PARTICLE_DATA"] = loadData.str();
    replacements["COMPUTE_TYPE_INDEX"] = computeTypeIndex;
    replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
    map<string, string> defines;
    if (nonbondedMethod != NoCutoff)
        defines["USE_CUTOFF"] = "1";
    if (nonbondedMethod == CutoffPeriodic)
        defines["USE_PERIODIC"] = "1";
    if (centralParticleMode)
        defines["USE_CENTRAL_PARTICLE"] = "1";
    if (hasTypeFilters)
        defines["USE_FILTERS"] = "1";
    if (force.getNumExclusions() > 0)
        defines["USE_EXCLUSIONS"] = "1";
    defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
    defines["PADDED_NUM_ATOMS"] = cl.intToString(cl.getPaddedNumAtoms());
    defines["M_PI"] = cl.doubleToString(M_PI);
    defines["CUTOFF_SQUARED"] = cl.doubleToString(force.getCutoffDistance()*force.getCutoffDistance());
    defines["TILE_SIZE"] = cl.intToString(OpenCLContext::TileSize);
    defines["NUM_BLOCKS"] = cl.intToString(cl.getNumAtomBlocks());
    defines["FIND_NEIGHBORS_WORKGROUP_SIZE"] = cl.intToString(findNeighborsWorkgroupSize);
    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customManyParticle, replacements), defines);
    forceKernel = cl::Kernel(program, "computeInteraction");
    blockBoundsKernel = cl::Kernel(program, "findBlockBounds");
    neighborsKernel = cl::Kernel(program, "findNeighbors");
    startIndicesKernel = cl::Kernel(program, "computeNeighborStartIndices");
    copyPairsKernel = cl::Kernel(program, "copyPairsToNeighborList");
}

double OpenCLCalcCustomManyParticleForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        
        // Set arguments for the force kernel.
        
        int index = 0;
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        forceKernel.setArg<cl::Buffer>(index++, cl.getLongForceBuffer().getDeviceBuffer());
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        forceKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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        setPeriodicBoxArgs(cl, forceKernel, index);
        index += 5;
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        if (nonbondedMethod != NoCutoff) {
            forceKernel.setArg<cl::Buffer>(index++, neighbors->getDeviceBuffer());
            forceKernel.setArg<cl::Buffer>(index++, neighborStartIndex->getDeviceBuffer());
        }
        if (particleTypes != NULL) {
            forceKernel.setArg<cl::Buffer>(index++, particleTypes->getDeviceBuffer());
            forceKernel.setArg<cl::Buffer>(index++, orderIndex->getDeviceBuffer());
            forceKernel.setArg<cl::Buffer>(index++, particleOrder->getDeviceBuffer());
        }
        if (exclusions != NULL) {
            forceKernel.setArg<cl::Buffer>(index++, exclusions->getDeviceBuffer());
            forceKernel.setArg<cl::Buffer>(index++, exclusionStartIndex->getDeviceBuffer());
        }
        if (globals != NULL)
            forceKernel.setArg<cl::Buffer>(index++, globals->getDeviceBuffer());
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        for (auto& buffer : params->getBuffers())
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            forceKernel.setArg<cl::Memory>(index++, buffer.getMemory());
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        for (auto function : tabulatedFunctions)
            forceKernel.setArg<cl::Buffer>(index++, function->getDeviceBuffer());
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        if (nonbondedMethod != NoCutoff) {
            // Set arguments for the block bounds kernel.

            index = 0;
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            setPeriodicBoxArgs(cl, blockBoundsKernel, index);
            index += 5;
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            blockBoundsKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
            blockBoundsKernel.setArg<cl::Buffer>(index++, blockCenter->getDeviceBuffer());
            blockBoundsKernel.setArg<cl::Buffer>(index++, blockBoundingBox->getDeviceBuffer());
            blockBoundsKernel.setArg<cl::Buffer>(index++, numNeighborPairs->getDeviceBuffer());

            // Set arguments for the neighbor list kernel.

            index = 0;
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            setPeriodicBoxArgs(cl, neighborsKernel, index);
            index += 5;
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            neighborsKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
            neighborsKernel.setArg<cl::Buffer>(index++, blockCenter->getDeviceBuffer());
            neighborsKernel.setArg<cl::Buffer>(index++, blockBoundingBox->getDeviceBuffer());
            neighborsKernel.setArg<cl::Buffer>(index++, neighborPairs->getDeviceBuffer());
            neighborsKernel.setArg<cl::Buffer>(index++, numNeighborPairs->getDeviceBuffer());
            neighborsKernel.setArg<cl::Buffer>(index++, numNeighborsForAtom->getDeviceBuffer());
            index++;
            if (exclusions != NULL) {
                neighborsKernel.setArg<cl::Buffer>(index++, exclusions->getDeviceBuffer());
                neighborsKernel.setArg<cl::Buffer>(index++, exclusionStartIndex->getDeviceBuffer());
            }
            
            // Set arguments for the kernel to find neighbor list start indices.
            
            index = 0;
            startIndicesKernel.setArg<cl::Buffer>(index++, numNeighborsForAtom->getDeviceBuffer());
            startIndicesKernel.setArg<cl::Buffer>(index++, neighborStartIndex->getDeviceBuffer());
            startIndicesKernel.setArg<cl::Buffer>(index++, numNeighborPairs->getDeviceBuffer());

            // Set arguments for the kernel to assemble the final neighbor list.
            
            index = 0;
            copyPairsKernel.setArg<cl::Buffer>(index++, neighborPairs->getDeviceBuffer());
            copyPairsKernel.setArg<cl::Buffer>(index++, neighbors->getDeviceBuffer());
            copyPairsKernel.setArg<cl::Buffer>(index++, numNeighborPairs->getDeviceBuffer());
            index++;
            copyPairsKernel.setArg<cl::Buffer>(index++, numNeighborsForAtom->getDeviceBuffer());
            copyPairsKernel.setArg<cl::Buffer>(index++, neighborStartIndex->getDeviceBuffer());
       }
    }
    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);
    }
    while (true) {
        int* numPairs = (int*) cl.getPinnedBuffer();
        cl::Event event;
        if (nonbondedMethod != NoCutoff) {
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            neighborsKernel.setArg<int>(11, maxNeighborPairs);
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            startIndicesKernel.setArg<int>(3, maxNeighborPairs);
            copyPairsKernel.setArg<int>(3, maxNeighborPairs);
            cl.executeKernel(blockBoundsKernel, cl.getNumAtomBlocks());
            cl.executeKernel(neighborsKernel, cl.getNumAtoms(), findNeighborsWorkgroupSize);

            // We need to make sure there was enough memory for the neighbor list.  Download the
            // information asynchronously so kernels can be running at the same time.

            numNeighborPairs->download(numPairs, false);
            cl.getQueue().enqueueMarker(&event);
            cl.executeKernel(startIndicesKernel, 256, 256);
            cl.executeKernel(copyPairsKernel, maxNeighborPairs);
        }
6413
6414
        int maxThreads = min(cl.getNumAtoms()*forceWorkgroupSize, cl.getEnergyBuffer().getSize());
        cl.executeKernel(forceKernel, maxThreads, forceWorkgroupSize);
6415
6416
6417
6418
6419
6420
6421
6422
6423
6424
6425
6426
6427
6428
        if (nonbondedMethod != NoCutoff) {
            // Make sure there was enough memory for the neighbor list.

            event.wait();
            if (*numPairs > maxNeighborPairs) {
                // Resize the arrays and run the calculation again.

                delete neighborPairs;
                neighborPairs = NULL;
                delete neighbors;
                neighbors = NULL;
                maxNeighborPairs = (int) (1.1*(*numPairs));
                neighborPairs = OpenCLArray::create<mm_int2>(cl, maxNeighborPairs, "customManyParticleNeighborPairs");
                neighbors = OpenCLArray::create<int>(cl, maxNeighborPairs, "customManyParticleNeighbors");
6429
6430
                forceKernel.setArg<cl::Buffer>(8, neighbors->getDeviceBuffer());
                neighborsKernel.setArg<cl::Buffer>(8, neighborPairs->getDeviceBuffer());
6431
6432
                copyPairsKernel.setArg<cl::Buffer>(0, neighborPairs->getDeviceBuffer());
                copyPairsKernel.setArg<cl::Buffer>(1, neighbors->getDeviceBuffer());
6433
6434
6435
6436
6437
6438
6439
6440
6441
6442
6443
6444
6445
6446
6447
6448
6449
6450
6451
6452
6453
6454
6455
6456
6457
6458
6459
6460
                continue;
            }
        }
        break;
    }
    return 0.0;
}

void OpenCLCalcCustomManyParticleForceKernel::copyParametersToContext(ContextImpl& context, const CustomManyParticleForce& force) {
    int numParticles = force.getNumParticles();
    if (numParticles != cl.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    
    // Record the per-particle parameters.
    
    vector<vector<float> > paramVector(numParticles);
    vector<double> parameters;
    int type;
    for (int i = 0; i < numParticles; i++) {
        force.getParticleParameters(i, parameters, type);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
6461
    cl.invalidateMolecules(info);
6462
6463
}

6464
class OpenCLCalcGayBerneForceKernel::ForceInfo : public OpenCLForceInfo {
6465
public:
6466
    ForceInfo(int requiredBuffers, const GayBerneForce& force) : OpenCLForceInfo(requiredBuffers), force(force) {
6467
6468
6469
6470
6471
6472
6473
6474
6475
6476
6477
6478
6479
6480
6481
6482
6483
6484
6485
6486
6487
6488
6489
6490
6491
6492
6493
6494
6495
6496
6497
6498
6499
6500
6501
6502
6503
6504
6505
6506
6507
6508
6509
6510
6511
6512
6513
6514
6515
6516
6517
6518
6519
6520
6521
6522
6523
6524
6525
6526
6527
6528
6529
6530
6531
6532
6533
6534
6535
6536
6537
6538
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6540
6541
6542
6543
6544
6545
6546
6547
6548
6549
6550
6551
6552
6553
6554
6555
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        int xparticle1, yparticle1;
        double sigma1, epsilon1, sx1, sy1, sz1, ex1, ey1, ez1;
        int xparticle2, yparticle2;
        double sigma2, epsilon2, sx2, sy2, sz2, ex2, ey2, ez2;
        force.getParticleParameters(particle1, sigma1, epsilon1, xparticle1, yparticle1, sx1, sy1, sz1, ex1, ey1, ez1);
        force.getParticleParameters(particle2, sigma2, epsilon2, xparticle2, yparticle2, sx2, sy2, sz2, ex2, ey2, ez2);
        return (sigma1 == sigma2 && epsilon1 == epsilon2 && sx1 == sx2 && sy1 == sy2 && sz1 == sz2 && ex1 == ex2 && ey1 == ey2 && ez1 == ez2);
    }
    int getNumParticleGroups() {
        return force.getNumExceptions()+force.getNumParticles();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        if (index < force.getNumExceptions()) {
            int particle1, particle2;
            double sigma, epsilon;
            force.getExceptionParameters(index, particle1, particle2, sigma, epsilon);
            particles.resize(2);
            particles[0] = particle1;
            particles[1] = particle2;
        }
        else {
            int particle = index-force.getNumExceptions();
            int xparticle, yparticle;
            double sigma, epsilon, sx, sy, sz, ex, ey, ez;
            force.getParticleParameters(particle, sigma, epsilon, xparticle, yparticle, sx, sy, sz, ex, ey, ez);
            particles.clear();
            particles.push_back(particle);
            if (xparticle > -1)
                particles.push_back(xparticle);
            if (yparticle > -1)
                particles.push_back(yparticle);
        }
    }
    bool areGroupsIdentical(int group1, int group2) {
        if (group1 < force.getNumExceptions() && group2 < force.getNumExceptions()) {
            int particle1, particle2;
            double sigma1, sigma2, epsilon1, epsilon2;
            force.getExceptionParameters(group1, particle1, particle2, sigma1, epsilon1);
            force.getExceptionParameters(group2, particle1, particle2, sigma2, epsilon2);
            return (sigma1 == sigma2 && epsilon1 == epsilon2);
        }
        return true;
    }
private:
    const GayBerneForce& force;
};

class OpenCLCalcGayBerneForceKernel::ReorderListener : public OpenCLContext::ReorderListener {
public:
    ReorderListener(OpenCLCalcGayBerneForceKernel& owner) : owner(owner) {
    }
    void execute() {
        owner.sortAtoms();
    }
private:
    OpenCLCalcGayBerneForceKernel& owner;
};

OpenCLCalcGayBerneForceKernel::~OpenCLCalcGayBerneForceKernel() {
    if (sortedParticles != NULL)
        delete sortedParticles;
    if (axisParticleIndices != NULL)
        delete axisParticleIndices;
    if (sigParams != NULL)
        delete sigParams;
    if (epsParams != NULL)
        delete epsParams;
    if (scale != NULL)
        delete scale;
    if (exceptionParticles != NULL)
        delete exceptionParticles;
    if (exceptionParams != NULL)
        delete exceptionParams;
    if (aMatrix != NULL)
        delete aMatrix;
    if (bMatrix != NULL)
        delete bMatrix;
    if (gMatrix != NULL)
        delete gMatrix;
    if (exclusions != NULL)
        delete exclusions;
    if (exclusionStartIndex != NULL)
        delete exclusionStartIndex;
    if (blockCenter != NULL)
        delete blockCenter;
    if (blockBoundingBox != NULL)
        delete blockBoundingBox;
6556
6557
6558
6559
6560
6561
    if (neighbors != NULL)
        delete neighbors;
    if (neighborIndex != NULL)
        delete neighborIndex;
    if (neighborBlockCount != NULL)
        delete neighborBlockCount;
6562
6563
6564
6565
6566
6567
6568
    if (sortedPos != NULL)
        delete sortedPos;
    if (torque != NULL)
        delete torque;
}

void OpenCLCalcGayBerneForceKernel::initialize(const System& system, const GayBerneForce& force) {
6569
6570
    if (!cl.getSupports64BitGlobalAtomics())
        throw OpenMMException("GayBerneForce requires a device that supports 64 bit atomic operations");
6571
6572
6573
6574
6575
6576
6577
6578
6579
6580
6581
6582
6583
6584
6585
6586
6587
6588
6589
6590
6591
6592
6593
6594
6595

    // Initialize interactions.

    int numParticles = force.getNumParticles();
    sigParams = OpenCLArray::create<mm_float4>(cl, cl.getPaddedNumAtoms(), "sigParams");
    epsParams = OpenCLArray::create<mm_float2>(cl, cl.getPaddedNumAtoms(), "epsParams");
    scale = OpenCLArray::create<mm_float4>(cl, cl.getPaddedNumAtoms(), "scale");
    axisParticleIndices = OpenCLArray::create<mm_int2>(cl, cl.getPaddedNumAtoms(), "axisParticleIndices");
    sortedParticles = OpenCLArray::create<cl_int>(cl, cl.getPaddedNumAtoms(), "sortedParticles");
    aMatrix = OpenCLArray::create<cl_float>(cl, 9*cl.getPaddedNumAtoms(), "aMatrix");
    bMatrix = OpenCLArray::create<cl_float>(cl, 9*cl.getPaddedNumAtoms(), "bMatrix");
    gMatrix = OpenCLArray::create<cl_float>(cl, 9*cl.getPaddedNumAtoms(), "gMatrix");
    vector<mm_float4> sigParamsVector(cl.getPaddedNumAtoms(), mm_float4(0, 0, 0, 0));
    vector<mm_float2> epsParamsVector(cl.getPaddedNumAtoms(), mm_float2(0, 0));
    vector<mm_float4> scaleVector(cl.getPaddedNumAtoms(), mm_float4(0, 0, 0, 0));
    vector<mm_int2> axisParticleVector(cl.getPaddedNumAtoms(), mm_int2(0, 0));
    isRealParticle.resize(cl.getPaddedNumAtoms());
    for (int i = 0; i < numParticles; i++) {
        int xparticle, yparticle;
        double sigma, epsilon, sx, sy, sz, ex, ey, ez;
        force.getParticleParameters(i, sigma, epsilon, xparticle, yparticle, sx, sy, sz, ex, ey, ez);
        axisParticleVector[i] = mm_int2(xparticle, yparticle);
        sigParamsVector[i] = mm_float4((float) (0.5*sigma), (float) (0.25*sx*sx), (float) (0.25*sy*sy), (float) (0.25*sz*sz));
        epsParamsVector[i] = mm_float2((float) sqrt(epsilon), (float) (0.125*(sx*sy + sz*sz)*sqrt(sx*sy)));
        scaleVector[i] = mm_float4((float) (1/sqrt(ex)), (float) (1/sqrt(ey)), (float) (1/sqrt(ez)), 0);
6596
        isRealParticle[i] = (epsilon != 0.0);
6597
6598
6599
6600
6601
6602
    }
    sigParams->upload(sigParamsVector);
    epsParams->upload(epsParamsVector);
    scale->upload(scaleVector);
    axisParticleIndices->upload(axisParticleVector);
    
6603
6604
6605
6606
6607
6608
6609
6610
6611
6612
6613
6614
6615
6616
6617
6618
6619
6620
6621
6622
6623
6624
6625
6626
6627
6628
6629
6630
    // Record exceptions and exclusions.

    vector<mm_float2> exceptionParamsVec;
    for (int i = 0; i < force.getNumExceptions(); i++) {
        int particle1, particle2;
        double sigma, epsilon;
        force.getExceptionParameters(i, particle1, particle2, sigma, epsilon);
        if (epsilon != 0.0) {
            exceptionParamsVec.push_back(mm_float2((float) sigma, (float) epsilon));
            exceptionAtoms.push_back(make_pair(particle1, particle2));
            isRealParticle[particle1] = true;
            isRealParticle[particle2] = true;
        }
        if (isRealParticle[particle1] && isRealParticle[particle2])
            excludedPairs.push_back(pair<int, int>(particle1, particle2));
    }
    numRealParticles = 0;
    for (int i = 0; i < isRealParticle.size(); i++)
        if (isRealParticle[i])
            numRealParticles++;
    int numExceptions = exceptionParamsVec.size();
    exclusions = OpenCLArray::create<cl_int>(cl, max(1, (int) excludedPairs.size()), "exclusions");
    exclusionStartIndex = OpenCLArray::create<cl_int>(cl, numRealParticles+1, "exclusionStartIndex");
    exceptionParticles = OpenCLArray::create<mm_int4>(cl, max(1, numExceptions), "exceptionParticles");
    exceptionParams = OpenCLArray::create<mm_float2>(cl, max(1, numExceptions), "exceptionParams");
    if (numExceptions > 0)
        exceptionParams->upload(exceptionParamsVec);
    
6631
6632
6633
6634
6635
6636
6637
    // Create data structures used for the neighbor list.

    int numAtomBlocks = (numRealParticles+31)/32;
    int elementSize = (cl.getUseDoublePrecision() ? sizeof(cl_double) : sizeof(cl_float));
    blockCenter = new OpenCLArray(cl, numAtomBlocks, 4*elementSize, "blockCenter");
    blockBoundingBox = new OpenCLArray(cl, numAtomBlocks, 4*elementSize, "blockBoundingBox");
    sortedPos = new OpenCLArray(cl, numRealParticles, 4*elementSize, "sortedPos");
6638
6639
    maxNeighborBlocks = numRealParticles*2;
    neighbors = OpenCLArray::create<cl_int>(cl, maxNeighborBlocks*32, "neighbors");
6640
    neighborIndex = OpenCLArray::create<cl_int>(cl, maxNeighborBlocks, "neighborIndex");
6641
    neighborBlockCount = OpenCLArray::create<cl_int>(cl, 1, "neighborBlockCount");
6642

6643
    // Create array for accumulating torques.
6644
    
6645
    torque = OpenCLArray::create<cl_long>(cl, 3*cl.getPaddedNumAtoms(), "torque");
6646
6647
6648
6649
6650
6651
6652
6653
6654
    cl.addAutoclearBuffer(*torque);

    // Create the kernels.
    
    nonbondedMethod = force.getNonbondedMethod();
    bool useCutoff = (nonbondedMethod != GayBerneForce::NoCutoff);
    bool usePeriodic = (nonbondedMethod == GayBerneForce::CutoffPeriodic);
    map<string, string> defines;
    defines["USE_SWITCH"] = (useCutoff && force.getUseSwitchingFunction() ? "1" : "0");
6655
6656
    double cutoff = force.getCutoffDistance();
    defines["CUTOFF_SQUARED"] = cl.doubleToString(cutoff*cutoff);
6657
    if (useCutoff) {
6658
6659
6660
6661
        defines["USE_CUTOFF"] = 1;
        if (usePeriodic)
            defines["USE_PERIODIC"] = "1";
        
6662
6663
6664
6665
        // Compute the switching coefficients.
        
        if (force.getUseSwitchingFunction()) {
            defines["SWITCH_CUTOFF"] = cl.doubleToString(force.getSwitchingDistance());
6666
6667
6668
            defines["SWITCH_C3"] = cl.doubleToString(10/pow(force.getSwitchingDistance()-cutoff, 3.0));
            defines["SWITCH_C4"] = cl.doubleToString(15/pow(force.getSwitchingDistance()-cutoff, 4.0));
            defines["SWITCH_C5"] = cl.doubleToString(6/pow(force.getSwitchingDistance()-cutoff, 5.0));
6669
6670
        }
    }
6671
    defines["PADDED_NUM_ATOMS"] = cl.intToString(cl.getPaddedNumAtoms());
6672
6673
6674
6675
6676
    cl::Program program = cl.createProgram(OpenCLKernelSources::gayBerne, defines);
    framesKernel = cl::Kernel(program, "computeEllipsoidFrames");
    blockBoundsKernel = cl::Kernel(program, "findBlockBounds");
    neighborsKernel = cl::Kernel(program, "findNeighbors");
    forceKernel = cl::Kernel(program, "computeForce");
6677
    torqueKernel = cl::Kernel(program, "applyTorques");
6678
6679
    info = new ForceInfo(cl.getNonbondedUtilities().getNumForceBuffers(), force);
    cl.addForce(info);
6680
6681
6682
6683
6684
6685
6686
6687
6688
6689
6690
6691
6692
6693
6694
6695
6696
6697
6698
6699
6700
6701
    cl.addReorderListener(new ReorderListener(*this));
}

double OpenCLCalcGayBerneForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        sortAtoms();
        framesKernel.setArg<cl_int>(0, numRealParticles);
        framesKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
        framesKernel.setArg<cl::Buffer>(2, axisParticleIndices->getDeviceBuffer());
        framesKernel.setArg<cl::Buffer>(3, sigParams->getDeviceBuffer());
        framesKernel.setArg<cl::Buffer>(4, scale->getDeviceBuffer());
        framesKernel.setArg<cl::Buffer>(5, aMatrix->getDeviceBuffer());
        framesKernel.setArg<cl::Buffer>(6, bMatrix->getDeviceBuffer());
        framesKernel.setArg<cl::Buffer>(7, gMatrix->getDeviceBuffer());
        framesKernel.setArg<cl::Buffer>(8, sortedParticles->getDeviceBuffer());
        blockBoundsKernel.setArg<cl_int>(0, numRealParticles);
        blockBoundsKernel.setArg<cl::Buffer>(6, sortedParticles->getDeviceBuffer());
        blockBoundsKernel.setArg<cl::Buffer>(7, cl.getPosq().getDeviceBuffer());
        blockBoundsKernel.setArg<cl::Buffer>(8, sortedPos->getDeviceBuffer());
        blockBoundsKernel.setArg<cl::Buffer>(9, blockCenter->getDeviceBuffer());
        blockBoundsKernel.setArg<cl::Buffer>(10, blockBoundingBox->getDeviceBuffer());
6702
6703
6704
6705
6706
6707
6708
6709
6710
        blockBoundsKernel.setArg<cl::Buffer>(11, neighborBlockCount->getDeviceBuffer());
        neighborsKernel.setArg<cl_int>(0, numRealParticles);
        neighborsKernel.setArg<cl_int>(1, maxNeighborBlocks);
        neighborsKernel.setArg<cl::Buffer>(7, sortedPos->getDeviceBuffer());
        neighborsKernel.setArg<cl::Buffer>(8, blockCenter->getDeviceBuffer());
        neighborsKernel.setArg<cl::Buffer>(9, blockBoundingBox->getDeviceBuffer());
        neighborsKernel.setArg<cl::Buffer>(10, neighbors->getDeviceBuffer());
        neighborsKernel.setArg<cl::Buffer>(11, neighborIndex->getDeviceBuffer());
        neighborsKernel.setArg<cl::Buffer>(12, neighborBlockCount->getDeviceBuffer());
6711
6712
        neighborsKernel.setArg<cl::Buffer>(13, exclusions->getDeviceBuffer());
        neighborsKernel.setArg<cl::Buffer>(14, exclusionStartIndex->getDeviceBuffer());
6713
        int index = 0;
6714
        forceKernel.setArg<cl::Buffer>(index++, cl.getLongForceBuffer().getDeviceBuffer());
6715
6716
        forceKernel.setArg<cl::Buffer>(index++, torque->getDeviceBuffer());
        forceKernel.setArg<cl_int>(index++, numRealParticles);
6717
        forceKernel.setArg<cl_int>(index++, exceptionAtoms.size());
6718
6719
6720
6721
6722
6723
6724
6725
6726
6727
        forceKernel.setArg<cl::Buffer>(index++, cl.getEnergyBuffer().getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, sortedPos->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, sigParams->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, epsParams->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, sortedParticles->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, aMatrix->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, bMatrix->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, gMatrix->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, exclusions->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, exclusionStartIndex->getDeviceBuffer());
6728
6729
        forceKernel.setArg<cl::Buffer>(index++, exceptionParticles->getDeviceBuffer());
        forceKernel.setArg<cl::Buffer>(index++, exceptionParams->getDeviceBuffer());
6730
6731
6732
6733
6734
6735
        if (nonbondedMethod != GayBerneForce::NoCutoff) {
            forceKernel.setArg<cl_int>(index++, maxNeighborBlocks);
            forceKernel.setArg<cl::Buffer>(index++, neighbors->getDeviceBuffer());
            forceKernel.setArg<cl::Buffer>(index++, neighborIndex->getDeviceBuffer());
            forceKernel.setArg<cl::Buffer>(index++, neighborBlockCount->getDeviceBuffer());
        }
6736
        index = 0;
6737
        torqueKernel.setArg<cl::Buffer>(index++, cl.getLongForceBuffer().getDeviceBuffer());
6738
6739
6740
6741
6742
6743
6744
        torqueKernel.setArg<cl::Buffer>(index++, torque->getDeviceBuffer());
        torqueKernel.setArg<cl_int>(index++, numRealParticles);
        torqueKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        torqueKernel.setArg<cl::Buffer>(index++, axisParticleIndices->getDeviceBuffer());
        torqueKernel.setArg<cl::Buffer>(index++, sortedParticles->getDeviceBuffer());
    }
    cl.executeKernel(framesKernel, numRealParticles);
6745
6746
    setPeriodicBoxArgs(cl, blockBoundsKernel, 1);
    cl.executeKernel(blockBoundsKernel, (numRealParticles+31)/32);
6747
6748
6749
6750
6751
6752
6753
6754
6755
6756
6757
6758
6759
6760
6761
6762
6763
6764
6765
6766
6767
6768
6769
6770
    if (nonbondedMethod == GayBerneForce::NoCutoff) {
        cl.executeKernel(forceKernel, cl.getNonbondedUtilities().getNumForceThreadBlocks()*cl.getNonbondedUtilities().getForceThreadBlockSize());
    }
    else {
        while (true) {
            setPeriodicBoxArgs(cl, neighborsKernel, 2);
            cl.executeKernel(neighborsKernel, numRealParticles);
            cl_int* count = (cl_int*) cl.getPinnedBuffer();
            cl::Event event;
            cl.getQueue().enqueueReadBuffer(neighborBlockCount->getDeviceBuffer(), CL_FALSE, 0, neighborBlockCount->getSize()*neighborBlockCount->getElementSize(), count, NULL, &event);
            setPeriodicBoxArgs(cl, forceKernel, 20);
            cl.executeKernel(forceKernel, cl.getNonbondedUtilities().getNumForceThreadBlocks()*cl.getNonbondedUtilities().getForceThreadBlockSize());
            event.wait();
            if (*count <= maxNeighborBlocks)
                break;
            
            // There wasn't enough room for the neighbor list, so we need to recreate it.

            delete neighbors;
            neighbors = NULL;
            delete neighborIndex;
            neighborIndex = NULL;
            maxNeighborBlocks = (int) ceil((*count)*1.1);
            neighbors = OpenCLArray::create<cl_int>(cl, maxNeighborBlocks*32, "neighbors");
6771
            neighborIndex = OpenCLArray::create<cl_int>(cl, maxNeighborBlocks, "neighborIndex");
6772
6773
6774
6775
6776
            neighborsKernel.setArg<cl::Buffer>(10, neighbors->getDeviceBuffer());
            neighborsKernel.setArg<cl::Buffer>(11, neighborIndex->getDeviceBuffer());
            forceKernel.setArg<cl::Buffer>(17, neighbors->getDeviceBuffer());
            forceKernel.setArg<cl::Buffer>(18, neighborIndex->getDeviceBuffer());
        }
6777
    }
6778
    cl.executeKernel(torqueKernel, numRealParticles);
6779
6780
6781
6782
6783
6784
6785
6786
6787
6788
6789
6790
6791
6792
6793
6794
6795
6796
    return 0.0;
}

void OpenCLCalcGayBerneForceKernel::copyParametersToContext(ContextImpl& context, const GayBerneForce& force) {
    // Make sure the new parameters are acceptable.
    
    if (force.getNumParticles() != cl.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    vector<int> exceptions;
    for (int i = 0; i < force.getNumExceptions(); i++) {
        int particle1, particle2;
        double sigma, epsilon;
        force.getExceptionParameters(i, particle1, particle2, sigma, epsilon);
        if (exceptionAtoms.size() > exceptions.size() && make_pair(particle1, particle2) == exceptionAtoms[exceptions.size()])
            exceptions.push_back(i);
        else if (epsilon != 0.0)
            throw OpenMMException("updateParametersInContext: The set of non-excluded exceptions has changed");
    }
6797
    int numExceptions = exceptionAtoms.size();
6798
6799
6800
6801
6802
6803
6804
6805
6806
6807
    
    // Record the per-particle parameters.
    
    vector<mm_float4> sigParamsVector(cl.getPaddedNumAtoms(), mm_float4(0, 0, 0, 0));
    vector<mm_float2> epsParamsVector(cl.getPaddedNumAtoms(), mm_float2(0, 0));
    vector<mm_float4> scaleVector(cl.getPaddedNumAtoms(), mm_float4(0, 0, 0, 0));
    for (int i = 0; i < force.getNumParticles(); i++) {
        int xparticle, yparticle;
        double sigma, epsilon, sx, sy, sz, ex, ey, ez;
        force.getParticleParameters(i, sigma, epsilon, xparticle, yparticle, sx, sy, sz, ex, ey, ez);
6808
        sigParamsVector[i] = mm_float4((float) (0.5*sigma), (float) (0.25*sx*sx), (float) (0.25*sy*sy), (float) (0.25*sz*sz));
6809
6810
        epsParamsVector[i] = mm_float2((float) sqrt(epsilon), (float) (0.125*(sx*sy + sz*sz)*sqrt(sx*sy)));
        scaleVector[i] = mm_float4((float) (1/sqrt(ex)), (float) (1/sqrt(ey)), (float) (1/sqrt(ez)), 0);
6811
6812
        if (epsilon != 0.0 && !isRealParticle[i])
            throw OpenMMException("updateParametersInContext: The set of ignored particles (ones with epsilon=0) has changed");
6813
6814
6815
6816
6817
6818
6819
6820
    }
    sigParams->upload(sigParamsVector);
    epsParams->upload(epsParamsVector);
    scale->upload(scaleVector);
    
    // Record the exceptions.
    
    if (numExceptions > 0) {
6821
        vector<mm_float2> exceptionParamsVec(numExceptions);
6822
        for (int i = 0; i < numExceptions; i++) {
6823
            int atom1, atom2;
6824
            double sigma, epsilon;
6825
6826
            force.getExceptionParameters(exceptions[i], atom1, atom2, sigma, epsilon);
            exceptionParamsVec[i] = mm_float2((float) sigma, (float) epsilon);
6827
        }
6828
        exceptionParams->upload(exceptionParamsVec);
6829
    }
6830
    cl.invalidateMolecules(info);
6831
6832
6833
6834
6835
6836
6837
6838
6839
6840
    sortAtoms();
}

void OpenCLCalcGayBerneForceKernel::sortAtoms() {
    // Sort the list of atoms by type to avoid thread divergence.  This is executed every time
    // the atoms are reordered.
    
    int nextIndex = 0;
    vector<cl_int> particles(cl.getPaddedNumAtoms(), 0);
    const vector<int>& order = cl.getAtomIndex();
6841
    vector<int> inverseOrder(order.size(), -1);
6842
6843
    for (int i = 0; i < cl.getNumAtoms(); i++) {
        int atom = order[i];
6844
6845
        if (isRealParticle[atom]) {
            inverseOrder[atom] = nextIndex;
6846
            particles[nextIndex++] = atom;
6847
        }
6848
6849
6850
    }
    sortedParticles->upload(particles);
    
6851
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6853
6854
6855
6856
6857
6858
6859
6860
    // Update the list of exception particles.
    
    int numExceptions = exceptionAtoms.size();
    if (numExceptions > 0) {
        vector<mm_int4> exceptionParticlesVec(numExceptions);
        for (int i = 0; i < numExceptions; i++)
            exceptionParticlesVec[i] = mm_int4(exceptionAtoms[i].first, exceptionAtoms[i].second, inverseOrder[exceptionAtoms[i].first], inverseOrder[exceptionAtoms[i].second]);
        exceptionParticles->upload(exceptionParticlesVec);
    }
    
6861
6862
6863
6864
    // Rebuild the list of exclusions.
    
    vector<vector<int> > excludedAtoms(numRealParticles);
    for (int i = 0; i < excludedPairs.size(); i++) {
6865
6866
        int first = inverseOrder[min(excludedPairs[i].first, excludedPairs[i].second)];
        int second = inverseOrder[max(excludedPairs[i].first, excludedPairs[i].second)];
6867
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6875
6876
6877
6878
6879
6880
6881
        excludedAtoms[first].push_back(second);
    }
    int index = 0;
    vector<int> exclusionVec(exclusions->getSize());
    vector<int> startIndexVec(exclusionStartIndex->getSize());
    for (int i = 0; i < numRealParticles; i++) {
        startIndexVec[i] = index;
        for (int j = 0; j < excludedAtoms[i].size(); j++)
            exclusionVec[index++] = excludedAtoms[i][j];
    }
    startIndexVec[numRealParticles] = index;
    exclusions->upload(exclusionVec);
    exclusionStartIndex->upload(startIndexVec);
}

6882
6883
6884
6885
6886
class OpenCLCalcCustomCVForceKernel::ReorderListener : public OpenCLContext::ReorderListener {
public:
    ReorderListener(OpenCLContext& cl, OpenCLArray& invAtomOrder) : cl(cl), invAtomOrder(invAtomOrder) {
    }
    void execute() {
6887
        vector<cl_int> invOrder(cl.getPaddedNumAtoms());
6888
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6901
6902
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6906
        const vector<int>& order = cl.getAtomIndex();
        for (int i = 0; i < order.size(); i++)
            invOrder[order[i]] = i;
        invAtomOrder.upload(invOrder);
    }
private:
    OpenCLContext& cl;
    OpenCLArray& invAtomOrder;
};

OpenCLCalcCustomCVForceKernel::~OpenCLCalcCustomCVForceKernel() {
    for (auto force : cvForces)
        delete force;
    if (invAtomOrder != NULL)
        delete invAtomOrder;
    if (innerInvAtomOrder != NULL)
        delete innerInvAtomOrder;
}

6907
void OpenCLCalcCustomCVForceKernel::initialize(const System& system, const CustomCVForce& force, ContextImpl& innerContext) {
6908
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6911
6912
6913
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6920
6921
6922
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6928
6929
6930
6931
    int numCVs = force.getNumCollectiveVariables();
    cl.addForce(new OpenCLForceInfo(1));
    for (int i = 0; i < force.getNumGlobalParameters(); i++)
        globalParameterNames.push_back(force.getGlobalParameterName(i));
    
    // Create custom functions for the tabulated functions.

    map<string, Lepton::CustomFunction*> functions;
    for (int i = 0; i < (int) force.getNumTabulatedFunctions(); i++)
        functions[force.getTabulatedFunctionName(i)] = createReferenceTabulatedFunction(force.getTabulatedFunction(i));

    // Create the expressions.

    Lepton::ParsedExpression energyExpr = Lepton::Parser::parse(force.getEnergyFunction(), functions);
    energyExpression = energyExpr.createProgram();
    for (int i = 0; i < numCVs; i++) {
        string name = force.getCollectiveVariableName(i);
        variableNames.push_back(name);
        variableDerivExpressions.push_back(energyExpr.differentiate(name).optimize().createProgram());
    }
    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string name = force.getEnergyParameterDerivativeName(i);
        paramDerivNames.push_back(name);
        paramDerivExpressions.push_back(energyExpr.differentiate(name).optimize().createProgram());
6932
        cl.addEnergyParameterDerivative(name);
6933
6934
6935
6936
6937
6938
    }

    // Delete the custom functions.

    for (auto& function : functions)
        delete function.second;
6939
6940
6941
6942
6943
6944
        
    // Copy parameter derivatives from the inner context.

    OpenCLContext& cl2 = *reinterpret_cast<OpenCLPlatform::PlatformData*>(innerContext.getPlatformData())->contexts[0];
    for (auto& param : cl2.getEnergyParamDerivNames())
        cl.addEnergyParameterDerivative(param);
6945
6946
6947
6948
6949
    
    // Create arrays for storing information.
    
    int elementSize = (cl.getUseDoublePrecision() || cl.getUseMixedPrecision() ? sizeof(double) : sizeof(float));
    for (int i = 0; i < numCVs; i++)
6950
6951
6952
        cvForces.push_back(new OpenCLArray(cl, cl.getNumAtoms(), 4*elementSize, "cvForce"));
    invAtomOrder = OpenCLArray::create<cl_int>(cl, cl.getPaddedNumAtoms(), "invAtomOrder");
    innerInvAtomOrder = OpenCLArray::create<cl_int>(cl, cl.getPaddedNumAtoms(), "innerInvAtomOrder");
6953
6954
6955
6956
6957
6958
6959
6960
6961
6962
6963
6964
6965
6966
6967
6968
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6977
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6980
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6983
6984
6985
6986
6987
6988
6989
6990
6991
6992
6993
6994
6995
6996
6997
6998
    
    // Create the kernels.
    
    stringstream args, add;
    for (int i = 0; i < numCVs; i++) {
        args << ", __global real4* restrict force" << i << ", real dEdV" << i;
        add << "f += force" << i << "[i]*dEdV" << i << ";\n";
    }
    map<string, string> replacements;
    replacements["PARAMETER_ARGUMENTS"] = args.str();
    replacements["ADD_FORCES"] = add.str();
    cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customCVForce, replacements));
    copyStateKernel = cl::Kernel(program, "copyState");
    copyForcesKernel = cl::Kernel(program, "copyForces");
    addForcesKernel = cl::Kernel(program, "addForces");
}

double OpenCLCalcCustomCVForceKernel::execute(ContextImpl& context, ContextImpl& innerContext, bool includeForces, bool includeEnergy) {
    copyState(context, innerContext);
    int numCVs = variableNames.size();
    int numAtoms = cl.getNumAtoms();
    OpenCLContext& cl2 = *reinterpret_cast<OpenCLPlatform::PlatformData*>(innerContext.getPlatformData())->contexts[0];
    vector<double> cvValues;
    vector<map<string, double> > cvDerivs(numCVs);
    for (int i = 0; i < numCVs; i++) {
        cvValues.push_back(innerContext.calcForcesAndEnergy(true, true, 1<<i));
        copyForcesKernel.setArg<cl::Buffer>(0, cvForces[i]->getDeviceBuffer());
        cl.executeKernel(copyForcesKernel, numAtoms);
        innerContext.getEnergyParameterDerivatives(cvDerivs[i]);
    }
    
    // Compute the energy and forces.
    
    map<string, double> variables;
    for (auto& name : globalParameterNames)
        variables[name] = context.getParameter(name);
    for (int i = 0; i < numCVs; i++)
        variables[variableNames[i]] = cvValues[i];
    double energy = energyExpression.evaluate(variables);
    for (int i = 0; i < numCVs; i++) {
        double dEdV = variableDerivExpressions[i].evaluate(variables);
        if (cl.getUseDoublePrecision())
            addForcesKernel.setArg<cl_double>(2*i+3, dEdV);
        else
            addForcesKernel.setArg<cl_float>(2*i+3, dEdV);
    }
6999
    cl.executeKernel(addForcesKernel, numAtoms);
7000
7001
7002
7003
7004
7005
7006
7007
7008
7009
7010
7011
7012
7013
7014
7015
    
    // Compute the energy parameter derivatives.
    
    map<string, double>& energyParamDerivs = cl.getEnergyParamDerivWorkspace();
    for (int i = 0; i < paramDerivExpressions.size(); i++)
        energyParamDerivs[paramDerivNames[i]] += paramDerivExpressions[i].evaluate(variables);
    for (int i = 0; i < numCVs; i++) {
        double dEdV = variableDerivExpressions[i].evaluate(variables);
        for (auto& deriv : cvDerivs[i])
            energyParamDerivs[deriv.first] += dEdV*deriv.second;
    }
    return energy;
}

void OpenCLCalcCustomCVForceKernel::copyState(ContextImpl& context, ContextImpl& innerContext) {
    int numAtoms = cl.getNumAtoms();
7016
    OpenCLContext& cl2 = *reinterpret_cast<OpenCLPlatform::PlatformData*>(innerContext.getPlatformData())->contexts[0];
7017
7018
7019
7020
7021
7022
7023
7024
7025
7026
7027
7028
7029
7030
7031
7032
7033
7034
7035
7036
7037
7038
7039
7040
7041
7042
7043
7044
7045
7046
7047
7048
7049
7050
7051
7052
7053
7054
7055
7056
7057
7058
7059
7060
7061
7062
7063
7064
7065
7066
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        
        // Initialize the listeners.
        
        ReorderListener* listener1 = new ReorderListener(cl, *invAtomOrder);
        ReorderListener* listener2 = new ReorderListener(cl2, *innerInvAtomOrder);
        cl.addReorderListener(listener1);
        cl2.addReorderListener(listener2);
        listener1->execute();
        listener2->execute();
        
        // Initialize the kernels.
        
        copyStateKernel.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
        copyStateKernel.setArg<cl::Buffer>(2, cl.getVelm().getDeviceBuffer());
        copyStateKernel.setArg<cl::Buffer>(3, cl.getAtomIndexArray().getDeviceBuffer());
        copyStateKernel.setArg<cl::Buffer>(4, cl2.getPosq().getDeviceBuffer());
        copyStateKernel.setArg<cl::Buffer>(6, cl2.getVelm().getDeviceBuffer());
        copyStateKernel.setArg<cl::Buffer>(7, innerInvAtomOrder->getDeviceBuffer());
        copyStateKernel.setArg<cl_int>(8, numAtoms);
        if (cl.getUseMixedPrecision()) {
            copyStateKernel.setArg<cl::Buffer>(1, cl.getPosqCorrection().getDeviceBuffer());
            copyStateKernel.setArg<cl::Buffer>(5, cl2.getPosqCorrection().getDeviceBuffer());
        }
        else {
            copyStateKernel.setArg<void*>(1, NULL);
            copyStateKernel.setArg<void*>(5, NULL);
        }

        copyForcesKernel.setArg<cl::Buffer>(1, invAtomOrder->getDeviceBuffer());
        copyForcesKernel.setArg<cl::Buffer>(2, cl2.getForce().getDeviceBuffer());
        copyForcesKernel.setArg<cl::Buffer>(3, cl2.getAtomIndexArray().getDeviceBuffer());
        copyForcesKernel.setArg<cl_int>(4, numAtoms);

        addForcesKernel.setArg<cl::Buffer>(0, cl.getForce().getDeviceBuffer());
        addForcesKernel.setArg<cl_int>(1, numAtoms);
        for (int i = 0; i < cvForces.size(); i++)
            addForcesKernel.setArg<cl::Buffer>(2*i+2, cvForces[i]->getDeviceBuffer());
    }
    cl.executeKernel(copyStateKernel, numAtoms);
    Vec3 a, b, c;
    context.getPeriodicBoxVectors(a, b, c);
    innerContext.setPeriodicBoxVectors(a, b, c);
    innerContext.setTime(context.getTime());
    map<string, double> innerParameters = innerContext.getParameters();
    for (auto& param : innerParameters)
        innerContext.setParameter(param.first, context.getParameter(param.first));
}

7067
7068
7069
7070
OpenCLIntegrateVerletStepKernel::~OpenCLIntegrateVerletStepKernel() {
}

void OpenCLIntegrateVerletStepKernel::initialize(const System& system, const VerletIntegrator& integrator) {
7071
    cl.getPlatformData().initializeContexts(system);
7072
    cl::Program program = cl.createProgram(OpenCLKernelSources::verlet, "");
7073
7074
    kernel1 = cl::Kernel(program, "integrateVerletPart1");
    kernel2 = cl::Kernel(program, "integrateVerletPart2");
7075
7076
7077
}

void OpenCLIntegrateVerletStepKernel::execute(ContextImpl& context, const VerletIntegrator& integrator) {
7078
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
7079
7080
    int numAtoms = cl.getNumAtoms();
    double dt = integrator.getStepSize();
7081
7082
7083
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        kernel1.setArg<cl_int>(0, numAtoms);
7084
        kernel1.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
7085
        kernel1.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
7086
7087
7088
7089
        setPosqCorrectionArg(cl, kernel1, 3);
        kernel1.setArg<cl::Buffer>(4, cl.getVelm().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, cl.getForce().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(6, integration.getPosDelta().getDeviceBuffer());
7090
        kernel2.setArg<cl_int>(0, numAtoms);
7091
        kernel2.setArg<cl::Buffer>(1, cl.getIntegrationUtilities().getStepSize().getDeviceBuffer());
7092
        kernel2.setArg<cl::Buffer>(2, cl.getPosq().getDeviceBuffer());
7093
7094
7095
        setPosqCorrectionArg(cl, kernel2, 3);
        kernel2.setArg<cl::Buffer>(4, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(5, integration.getPosDelta().getDeviceBuffer());
7096
    }
7097
    cl.getIntegrationUtilities().setNextStepSize(dt);
7098
7099
7100
7101
7102
7103
7104

    // Call the first integration kernel.

    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

7105
    integration.applyConstraints(integrator.getConstraintTolerance());
7106
7107
7108
7109

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
7110
    integration.computeVirtualSites();
7111
7112
7113
7114
7115

    // Update the time and step count.

    cl.setTime(cl.getTime()+dt);
    cl.setStepCount(cl.getStepCount()+1);
7116
    cl.reorderAtoms();
7117
7118
7119
7120
7121
7122
    
    // Reduce UI lag.
    
#ifdef WIN32
    cl.getQueue().flush();
#endif
7123
7124
}

7125
7126
7127
7128
double OpenCLIntegrateVerletStepKernel::computeKineticEnergy(ContextImpl& context, const VerletIntegrator& integrator) {
    return cl.getIntegrationUtilities().computeKineticEnergy(0.5*integrator.getStepSize());
}

7129
7130
7131
7132
7133
7134
OpenCLIntegrateLangevinStepKernel::~OpenCLIntegrateLangevinStepKernel() {
    if (params != NULL)
        delete params;
}

void OpenCLIntegrateLangevinStepKernel::initialize(const System& system, const LangevinIntegrator& integrator) {
7135
    cl.getPlatformData().initializeContexts(system);
7136
7137
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
7138
7139
    defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
    defines["PADDED_NUM_ATOMS"] = cl.intToString(cl.getPaddedNumAtoms());
7140
    cl::Program program = cl.createProgram(OpenCLKernelSources::langevin, defines, "");
7141
7142
    kernel1 = cl::Kernel(program, "integrateLangevinPart1");
    kernel2 = cl::Kernel(program, "integrateLangevinPart2");
7143
    params = new OpenCLArray(cl, 3, cl.getUseDoublePrecision() || cl.getUseMixedPrecision() ? sizeof(cl_double) : sizeof(cl_float), "langevinParams");
7144
7145
7146
7147
    prevStepSize = -1.0;
}

void OpenCLIntegrateLangevinStepKernel::execute(ContextImpl& context, const LangevinIntegrator& integrator) {
7148
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
7149
    int numAtoms = cl.getNumAtoms();
7150
7151
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
7152
7153
7154
7155
        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());
7156
7157
7158
        kernel1.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
        kernel1.setArg<cl::Buffer>(5, integration.getRandom().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(0, cl.getPosq().getDeviceBuffer());
7159
7160
7161
7162
        setPosqCorrectionArg(cl, kernel2, 1);
        kernel2.setArg<cl::Buffer>(2, integration.getPosDelta().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(3, cl.getVelm().getDeviceBuffer());
        kernel2.setArg<cl::Buffer>(4, integration.getStepSize().getDeviceBuffer());
7163
    }
7164
7165
7166
    double temperature = integrator.getTemperature();
    double friction = integrator.getFriction();
    double stepSize = integrator.getStepSize();
7167
    cl.getIntegrationUtilities().setNextStepSize(stepSize);
7168
7169
7170
7171
    if (temperature != prevTemp || friction != prevFriction || stepSize != prevStepSize) {
        // Calculate the integration parameters.

        double kT = BOLTZ*temperature;
7172
7173
7174
        double vscale = exp(-stepSize*friction);
        double fscale = (friction == 0 ? stepSize : (1-vscale)/friction);
        double noisescale = sqrt(kT*(1-vscale*vscale));
7175
7176
7177
7178
7179
7180
7181
7182
7183
7184
7185
7186
7187
7188
        if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision()) {
            vector<cl_double> p(params->getSize());
            p[0] = vscale;
            p[1] = fscale;
            p[2] = noisescale;
            params->upload(p);
        }
        else {
            vector<cl_float> p(params->getSize());
            p[0] = (cl_float) vscale;
            p[1] = (cl_float) fscale;
            p[2] = (cl_float) noisescale;
            params->upload(p);
        }
7189
7190
7191
7192
7193
7194
7195
        prevTemp = temperature;
        prevFriction = friction;
        prevStepSize = stepSize;
    }

    // Call the first integration kernel.

7196
    kernel1.setArg<cl_uint>(6, integration.prepareRandomNumbers(cl.getPaddedNumAtoms()));
7197
7198
7199
7200
    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

7201
    integration.applyConstraints(integrator.getConstraintTolerance());
7202
7203
7204
7205

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
7206
    integration.computeVirtualSites();
7207
7208
7209
7210
7211

    // Update the time and step count.

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
7212
    cl.reorderAtoms();
7213
7214
7215
7216
7217
7218
    
    // Reduce UI lag.
    
#ifdef WIN32
    cl.getQueue().flush();
#endif
7219
}
7220

7221
7222
7223
7224
double OpenCLIntegrateLangevinStepKernel::computeKineticEnergy(ContextImpl& context, const LangevinIntegrator& integrator) {
    return cl.getIntegrationUtilities().computeKineticEnergy(0.5*integrator.getStepSize());
}

7225
7226
7227
7228
OpenCLIntegrateBrownianStepKernel::~OpenCLIntegrateBrownianStepKernel() {
}

void OpenCLIntegrateBrownianStepKernel::initialize(const System& system, const BrownianIntegrator& integrator) {
7229
    cl.getPlatformData().initializeContexts(system);
7230
7231
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
7232
    defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
7233
    cl::Program program = cl.createProgram(OpenCLKernelSources::brownian, defines, "");
7234
7235
7236
7237
7238
7239
7240
7241
7242
7243
7244
7245
    kernel1 = cl::Kernel(program, "integrateBrownianPart1");
    kernel2 = cl::Kernel(program, "integrateBrownianPart2");
    prevStepSize = -1.0;
}

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

    // Call the first integration kernel.

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

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

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

    cl.setTime(cl.getTime()+stepSize);
    cl.setStepCount(cl.getStepCount()+1);
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    cl.reorderAtoms();
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    // Reduce UI lag.
    
#ifdef WIN32
    cl.getQueue().flush();
#endif
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}
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double OpenCLIntegrateBrownianStepKernel::computeKineticEnergy(ContextImpl& context, const BrownianIntegrator& integrator) {
    return cl.getIntegrationUtilities().computeKineticEnergy(0);
}

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OpenCLIntegrateVariableVerletStepKernel::~OpenCLIntegrateVariableVerletStepKernel() {
}

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

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

    // Select the step size to use.

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    double maxStepSize = maxTime-cl.getTime();
    float maxStepSizeFloat = (float) maxStepSize;
    if (useDouble) {
        selectSizeKernel.setArg<cl_double>(1, maxStepSize);
        selectSizeKernel.setArg<cl_double>(2, integrator.getErrorTolerance());
    }
    else {
        selectSizeKernel.setArg<cl_float>(1, maxStepSizeFloat);
        selectSizeKernel.setArg<cl_float>(2, (cl_float) integrator.getErrorTolerance());
    }
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    cl.executeKernel(selectSizeKernel, blockSize, blockSize);

    // Call the first integration kernel.

    cl.executeKernel(kernel1, numAtoms);

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
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    integration.computeVirtualSites();
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    // Reduce UI lag.
    
#ifdef WIN32
    cl.getQueue().flush();
#endif
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    // Update the time and step count.

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    double dt = cl.getIntegrationUtilities().getLastStepSize();
    double time = cl.getTime()+dt;
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    if (useDouble) {
        if (dt == maxStepSize)
            time = maxTime; // Avoid round-off error
    }
    else {
        if (dt == maxStepSizeFloat)
            time = maxTime; // Avoid round-off error
    }
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    cl.setTime(time);
    cl.setStepCount(cl.getStepCount()+1);
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    cl.reorderAtoms();
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    return dt;
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}

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double OpenCLIntegrateVariableVerletStepKernel::computeKineticEnergy(ContextImpl& context, const VariableVerletIntegrator& integrator) {
    return cl.getIntegrationUtilities().computeKineticEnergy(0.5*integrator.getStepSize());
}

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

void OpenCLIntegrateVariableLangevinStepKernel::initialize(const System& system, const VariableLangevinIntegrator& integrator) {
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    cl.getPlatformData().initializeContexts(system);
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    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
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    defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
    defines["PADDED_NUM_ATOMS"] = cl.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, 3, cl.getUseDoublePrecision() || cl.getUseMixedPrecision() ? sizeof(cl_double) : sizeof(cl_float), "langevinParams");
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    blockSize = min(256, system.getNumParticles());
    blockSize = max(blockSize, params->getSize());
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    blockSize = min(blockSize, (int) selectSizeKernel.getWorkGroupInfo<CL_KERNEL_WORK_GROUP_SIZE>(cl.getDevice()));
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}

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

    // Select the step size to use.

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    double maxStepSize = maxTime-cl.getTime();
    float maxStepSizeFloat = (float) maxStepSize;
    if (useDouble) {
        selectSizeKernel.setArg<cl_double>(0, maxStepSize);
        selectSizeKernel.setArg<cl_double>(1, integrator.getErrorTolerance());
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        selectSizeKernel.setArg<cl_double>(2, integrator.getFriction());
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        selectSizeKernel.setArg<cl_double>(3, BOLTZ*integrator.getTemperature());
    }
    else {
        selectSizeKernel.setArg<cl_float>(0, maxStepSizeFloat);
        selectSizeKernel.setArg<cl_float>(1, (cl_float) integrator.getErrorTolerance());
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        selectSizeKernel.setArg<cl_float>(2, (cl_float) integrator.getFriction());
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        selectSizeKernel.setArg<cl_float>(3, (cl_float) (BOLTZ*integrator.getTemperature()));
    }
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    cl.executeKernel(selectSizeKernel, blockSize, blockSize);

    // Call the first integration kernel.

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

    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

    cl.executeKernel(kernel2, numAtoms);
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    integration.computeVirtualSites();
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    // Reduce UI lag.
    
#ifdef WIN32
    cl.getQueue().flush();
#endif
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    // Update the time and step count.

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    double dt = cl.getIntegrationUtilities().getLastStepSize();
    double time = cl.getTime()+dt;
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    if (useDouble) {
        if (dt == maxStepSize)
            time = maxTime; // Avoid round-off error
    }
    else {
        if (dt == maxStepSizeFloat)
            time = maxTime; // Avoid round-off error
    }
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    cl.setTime(time);
    cl.setStepCount(cl.getStepCount()+1);
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    cl.reorderAtoms();
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    return dt;
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}

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double OpenCLIntegrateVariableLangevinStepKernel::computeKineticEnergy(ContextImpl& context, const VariableLangevinIntegrator& integrator) {
    return cl.getIntegrationUtilities().computeKineticEnergy(0.5*integrator.getStepSize());
}

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

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        if (perDofValues.getNumParameters() == 0)
            return;
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        int numAtoms = cl.getNumAtoms();
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        const vector<int>& order = cl.getAtomIndex();
        if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision()) {
            if (deviceValuesAreCurrent)
                perDofValues.getParameterValues(localPerDofValuesDouble);
            vector<vector<cl_double> > swap(3*numAtoms);
            for (int i = 0; i < numAtoms; i++) {
                swap[3*lastAtomOrder[i]] = localPerDofValuesDouble[3*i];
                swap[3*lastAtomOrder[i]+1] = localPerDofValuesDouble[3*i+1];
                swap[3*lastAtomOrder[i]+2] = localPerDofValuesDouble[3*i+2];
            }
            for (int i = 0; i < numAtoms; i++) {
                localPerDofValuesDouble[3*i] = swap[3*order[i]];
                localPerDofValuesDouble[3*i+1] = swap[3*order[i]+1];
                localPerDofValuesDouble[3*i+2] = swap[3*order[i]+2];
            }
            perDofValues.setParameterValues(localPerDofValuesDouble);
        }
        else {
            if (deviceValuesAreCurrent)
                perDofValues.getParameterValues(localPerDofValuesFloat);
            vector<vector<cl_float> > swap(3*numAtoms);
            for (int i = 0; i < numAtoms; i++) {
                swap[3*lastAtomOrder[i]] = localPerDofValuesFloat[3*i];
                swap[3*lastAtomOrder[i]+1] = localPerDofValuesFloat[3*i+1];
                swap[3*lastAtomOrder[i]+2] = localPerDofValuesFloat[3*i+2];
            }
            for (int i = 0; i < numAtoms; i++) {
                localPerDofValuesFloat[3*i] = swap[3*order[i]];
                localPerDofValuesFloat[3*i+1] = swap[3*order[i]+1];
                localPerDofValuesFloat[3*i+2] = swap[3*order[i]+2];
            }
            perDofValues.setParameterValues(localPerDofValuesFloat);
        }
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        for (int i = 0; i < numAtoms; i++)
            lastAtomOrder[i] = order[i];
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        deviceValuesAreCurrent = true;
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    }
private:
    OpenCLContext& cl;
    OpenCLParameterSet& perDofValues;
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    vector<vector<cl_float> >& localPerDofValuesFloat;
    vector<vector<cl_double> >& localPerDofValuesDouble;
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    bool& deviceValuesAreCurrent;
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    vector<int> lastAtomOrder;
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};

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class OpenCLIntegrateCustomStepKernel::DerivFunction : public CustomFunction {
public:
    DerivFunction(map<string, double>& energyParamDerivs, const string& param) : energyParamDerivs(energyParamDerivs), param(param) {
    }
    int getNumArguments() const {
        return 0;
    }
    double evaluate(const double* arguments) const {
        return energyParamDerivs[param];
    }
    double evaluateDerivative(const double* arguments, const int* derivOrder) const {
        return 0;
    }
    CustomFunction* clone() const {
        return new DerivFunction(energyParamDerivs, param);
    }
private:
    map<string, double>& energyParamDerivs;
    string param;
};

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OpenCLIntegrateCustomStepKernel::~OpenCLIntegrateCustomStepKernel() {
    if (globalValues != NULL)
        delete globalValues;
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    if (sumBuffer != NULL)
        delete sumBuffer;
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    if (summedValue != NULL)
        delete summedValue;
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    if (uniformRandoms != NULL)
        delete uniformRandoms;
    if (randomSeed != NULL)
        delete randomSeed;
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    if (perDofEnergyParamDerivs != NULL)
        delete perDofEnergyParamDerivs;
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    if (perDofValues != NULL)
        delete perDofValues;
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    for (auto function : tabulatedFunctions)
        delete function;
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    for (auto& f : savedForces)
        delete f.second;
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}

void OpenCLIntegrateCustomStepKernel::initialize(const System& system, const CustomIntegrator& integrator) {
    cl.getPlatformData().initializeContexts(system);
    cl.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    numGlobalVariables = integrator.getNumGlobalVariables();
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    int elementSize = (cl.getUseDoublePrecision() || cl.getUseMixedPrecision() ? sizeof(double) : sizeof(float));
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    sumBuffer = new OpenCLArray(cl, ((3*system.getNumParticles()+3)/4)*4, elementSize, "sumBuffer");
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    summedValue = new OpenCLArray(cl, 1, elementSize, "summedValue");
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    perDofValues = new OpenCLParameterSet(cl, integrator.getNumPerDofVariables(), 3*system.getNumParticles(), "perDofVariables", false, cl.getUseDoublePrecision() || cl.getUseMixedPrecision());
    cl.addReorderListener(new ReorderListener(cl, *perDofValues, localPerDofValuesFloat, localPerDofValuesDouble, deviceValuesAreCurrent));
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    SimTKOpenMMUtilities::setRandomNumberSeed(integrator.getRandomNumberSeed());
}

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

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void OpenCLIntegrateCustomStepKernel::prepareForComputation(ContextImpl& context, CustomIntegrator& integrator, bool& forcesAreValid) {
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    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    int numAtoms = cl.getNumAtoms();
    int numSteps = integrator.getNumComputations();
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    bool useDouble = cl.getUseDoublePrecision() || cl.getUseMixedPrecision();
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    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
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        // Initialize various data structures.
        
        const map<string, double>& params = context.getParameters();
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        for (auto& param : params)
            parameterNames.push_back(param.first);
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        kernels.resize(integrator.getNumComputations());
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        requiredGaussian.resize(integrator.getNumComputations(), 0);
        requiredUniform.resize(integrator.getNumComputations(), 0);
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        needsGlobals.resize(numSteps, false);
        globalExpressions.resize(numSteps);
        stepType.resize(numSteps);
        stepTarget.resize(numSteps);
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        merged.resize(numSteps, false);
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        modifiesParameters = false;
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        sumWorkGroupSize = cl.getDevice().getInfo<CL_DEVICE_MAX_WORK_GROUP_SIZE>();
        if (sumWorkGroupSize > 512)
            sumWorkGroupSize = 512;
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        map<string, string> defines;
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        defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
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        defines["WORK_GROUP_SIZE"] = cl.intToString(sumWorkGroupSize);
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        // Record the tabulated functions.

        map<string, Lepton::CustomFunction*> functions;
        vector<pair<string, string> > functionNames;
        vector<const TabulatedFunction*> functionList;
        vector<string> tableTypes;
        for (int i = 0; i < integrator.getNumTabulatedFunctions(); i++) {
            functionList.push_back(&integrator.getTabulatedFunction(i));
            string name = integrator.getTabulatedFunctionName(i);
            string arrayName = "table"+cl.intToString(i);
            functionNames.push_back(make_pair(name, arrayName));
            functions[name] = createReferenceTabulatedFunction(integrator.getTabulatedFunction(i));
            int width;
            vector<float> f = cl.getExpressionUtilities().computeFunctionCoefficients(integrator.getTabulatedFunction(i), width);
            tabulatedFunctions.push_back(OpenCLArray::create<float>(cl, f.size(), "TabulatedFunction"));
            tabulatedFunctions[tabulatedFunctions.size()-1]->upload(f);
            if (width == 1)
                tableTypes.push_back("float");
            else
                tableTypes.push_back("float"+cl.intToString(width));
        }

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        // Record information about all the computation steps.

        vector<string> variable(numSteps);
        vector<int> forceGroup;
        vector<vector<Lepton::ParsedExpression> > expression;
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        CustomIntegratorUtilities::analyzeComputations(context, integrator, expression, comparisons, blockEnd, invalidatesForces, needsForces, needsEnergy, computeBothForceAndEnergy, forceGroup, functions);
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        for (int step = 0; step < numSteps; step++) {
            string expr;
            integrator.getComputationStep(step, stepType[step], variable[step], expr);
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            if (stepType[step] == CustomIntegrator::WhileBlockStart)
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                blockEnd[blockEnd[step]] = step; // Record where to branch back to.
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            if (stepType[step] == CustomIntegrator::ComputeGlobal || stepType[step] == CustomIntegrator::IfBlockStart || stepType[step] == CustomIntegrator::WhileBlockStart)
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                for (auto& expr : expression[step])
                    globalExpressions[step].push_back(ParsedExpression(replaceDerivFunctions(expr.getRootNode(), context)).createCompiledExpression());
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        }
        for (int step = 0; step < numSteps; step++) {
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            for (auto& expr : globalExpressions[step])
                expressionSet.registerExpression(expr);
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        }
        
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        // Record the indices for variables in the CompiledExpressionSet.
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        gaussianVariableIndex = expressionSet.getVariableIndex("gaussian");
        uniformVariableIndex = expressionSet.getVariableIndex("uniform");
        dtVariableIndex = expressionSet.getVariableIndex("dt");
        for (int i = 0; i < integrator.getNumGlobalVariables(); i++)
            globalVariableIndex.push_back(expressionSet.getVariableIndex(integrator.getGlobalVariableName(i)));
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        for (auto& name : parameterNames)
            parameterVariableIndex.push_back(expressionSet.getVariableIndex(name));
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        // Record the variable names and flags for the force and energy in each step.

        forceGroupFlags.resize(numSteps, -1);
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        vector<string> forceGroupName;
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        vector<string> energyGroupName;
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        for (int i = 0; i < 32; i++) {
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            stringstream fname;
            fname << "f" << i;
            forceGroupName.push_back(fname.str());
            stringstream ename;
            ename << "energy" << i;
            energyGroupName.push_back(ename.str());
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        }
        vector<string> forceName(numSteps, "f");
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        vector<string> energyName(numSteps, "energy");
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        stepEnergyVariableIndex.resize(numSteps, expressionSet.getVariableIndex("energy"));
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        for (int step = 0; step < numSteps; step++) {
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            if (needsForces[step] && forceGroup[step] > -1)
                forceName[step] = forceGroupName[forceGroup[step]];
            if (needsEnergy[step] && forceGroup[step] > -1) {
                energyName[step] = energyGroupName[forceGroup[step]];
                stepEnergyVariableIndex[step] = expressionSet.getVariableIndex(energyName[step]);
            }
            if (forceGroup[step] > -1)
                forceGroupFlags[step] = 1<<forceGroup[step];
            if (forceGroupFlags[step] == -2 && step > 0)
                forceGroupFlags[step] = forceGroupFlags[step-1];
            if (forceGroupFlags[step] != -2 && savedForces.find(forceGroupFlags[step]) == savedForces.end())
                savedForces[forceGroupFlags[step]] = new OpenCLArray(cl, cl.getForce().getSize(), cl.getForce().getElementSize(), "savedForces");
        }
        
        // Allocate space for storing global values, both on the host and the device.
        
        globalValuesFloat.resize(expressionSet.getNumVariables());
        globalValuesDouble.resize(expressionSet.getNumVariables());
        int elementSize = (cl.getUseDoublePrecision() || cl.getUseMixedPrecision() ? sizeof(double) : sizeof(float));
        globalValues = new OpenCLArray(cl, expressionSet.getNumVariables(), elementSize, "globalValues");
        for (int i = 0; i < integrator.getNumGlobalVariables(); i++) {
            globalValuesDouble[globalVariableIndex[i]] = initialGlobalVariables[i];
            expressionSet.setVariable(globalVariableIndex[i], initialGlobalVariables[i]);
        }
        for (int i = 0; i < (int) parameterVariableIndex.size(); i++) {
            double value = context.getParameter(parameterNames[i]);
            globalValuesDouble[parameterVariableIndex[i]] = value;
            expressionSet.setVariable(parameterVariableIndex[i], value);
        }
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        int numContextParams = context.getParameters().size();
        localPerDofEnergyParamDerivsFloat.resize(numContextParams);
        localPerDofEnergyParamDerivsDouble.resize(numContextParams);
        perDofEnergyParamDerivs = new OpenCLArray(cl, max(1, numContextParams), elementSize, "perDofEnergyParamDerivs");
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        // Record information about the targets of steps that will be stored in global variables.
        
        for (int step = 0; step < numSteps; step++) {
            if (stepType[step] == CustomIntegrator::ComputeGlobal || stepType[step] == CustomIntegrator::ComputeSum) {
                if (variable[step] == "dt")
                    stepTarget[step].type = DT;
                for (int i = 0; i < integrator.getNumGlobalVariables(); i++)
                    if (variable[step] == integrator.getGlobalVariableName(i))
                        stepTarget[step].type = VARIABLE;
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                for (auto& name : parameterNames)
                    if (variable[step] == name) {
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                        stepTarget[step].type = PARAMETER;
                        modifiesParameters = true;
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                    }
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                stepTarget[step].variableIndex = expressionSet.getVariableIndex(variable[step]);
            }
        }

        // Identify which per-DOF steps are going to require global variables or context parameters.

        for (int step = 0; step < numSteps; step++) {
            if (stepType[step] == CustomIntegrator::ComputePerDof || stepType[step] == CustomIntegrator::ComputeSum) {
                for (int i = 0; i < integrator.getNumGlobalVariables(); i++)
                    if (usesVariable(expression[step][0], integrator.getGlobalVariableName(i)))
                        needsGlobals[step] = true;
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                for (auto& name : parameterNames)
                    if (usesVariable(expression[step][0], name))
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                        needsGlobals[step] = true;
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            }
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        }
        
        // Determine how each step will represent the position (as just a value, or a value plus a delta).
        
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        hasAnyConstraints = (context.getSystem().getNumConstraints() > 0);
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        vector<bool> storePosAsDelta(numSteps, false);
        vector<bool> loadPosAsDelta(numSteps, false);
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        if (hasAnyConstraints) {
            bool beforeConstrain = false;
            for (int step = numSteps-1; step >= 0; step--) {
                if (stepType[step] == CustomIntegrator::ConstrainPositions)
                    beforeConstrain = true;
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                else if (stepType[step] == CustomIntegrator::ComputePerDof && variable[step] == "x" && beforeConstrain) {
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                    storePosAsDelta[step] = true;
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                    beforeConstrain = false;
                }
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            }
            bool storedAsDelta = false;
            for (int step = 0; step < numSteps; step++) {
                loadPosAsDelta[step] = storedAsDelta;
                if (storePosAsDelta[step] == true)
                    storedAsDelta = true;
                if (stepType[step] == CustomIntegrator::ConstrainPositions)
                    storedAsDelta = false;
            }
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        }
        
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        // Identify steps that can be merged into a single kernel.
        
        for (int step = 1; step < numSteps; step++) {
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            if (invalidatesForces[step-1] || forceGroupFlags[step] != forceGroupFlags[step-1])
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                continue;
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            if (stepType[step-1] == CustomIntegrator::ComputePerDof && stepType[step] == CustomIntegrator::ComputePerDof)
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                merged[step] = true;
        }
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        for (int step = numSteps-1; step > 0; step--)
            if (merged[step]) {
                needsForces[step-1] = (needsForces[step] || needsForces[step-1]);
                needsEnergy[step-1] = (needsEnergy[step] || needsEnergy[step-1]);
                needsGlobals[step-1] = (needsGlobals[step] || needsGlobals[step-1]);
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                computeBothForceAndEnergy[step-1] = (computeBothForceAndEnergy[step] || computeBothForceAndEnergy[step-1]);
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            }
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        // Loop over all steps and create the kernels for them.
        
        for (int step = 0; step < numSteps; step++) {
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            if ((stepType[step] == CustomIntegrator::ComputePerDof || stepType[step] == CustomIntegrator::ComputeSum) && !merged[step]) {
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                // Compute a per-DOF value.
                
                stringstream compute;
                for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++) {
                    const OpenCLNonbondedUtilities::ParameterInfo& buffer = perDofValues->getBuffers()[i];
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                    compute << buffer.getType()<<" perDofx"<<cl.intToString(i+1)<<" = perDofValues"<<cl.intToString(i+1)<<"[3*index];\n";
                    compute << buffer.getType()<<" perDofy"<<cl.intToString(i+1)<<" = perDofValues"<<cl.intToString(i+1)<<"[3*index+1];\n";
                    compute << buffer.getType()<<" perDofz"<<cl.intToString(i+1)<<" = perDofValues"<<cl.intToString(i+1)<<"[3*index+2];\n";
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                }
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                int numGaussian = 0, numUniform = 0;
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                for (int j = step; j < numSteps && (j == step || merged[j]); j++) {
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                    numGaussian += numAtoms*usesVariable(expression[j][0], "gaussian");
                    numUniform += numAtoms*usesVariable(expression[j][0], "uniform");
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                    compute << "{\n";
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                    if (numGaussian > 0)
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                        compute << "float4 gaussian = gaussianValues[gaussianIndex+index];\n";
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                    if (numUniform > 0)
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                        compute << "float4 uniform = uniformValues[uniformIndex+index];\n";
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                    for (int i = 0; i < 3; i++)
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                        compute << createPerDofComputation(stepType[j] == CustomIntegrator::ComputePerDof ? variable[j] : "", expression[j][0], i, integrator, forceName[j], energyName[j], functionList, functionNames);
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                    if (variable[j] == "x") {
                        if (storePosAsDelta[j]) {
                            if (cl.getSupportsDoublePrecision())
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                                compute << "posDelta[index] = convert_mixed4(convert_double4(position)-convert_double4(loadPos(posq, posqCorrection, index)));\n";
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                            else
                                compute << "posDelta[index] = position-posq[index];\n";
                        }
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                        else
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                            compute << "storePos(posq, posqCorrection, index, position);\n";
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                    }
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                    else if (variable[j] == "v")
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                        compute << "velm[index] = convert_mixed4(velocity);\n";
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                    else {
                        for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++) {
                            const OpenCLNonbondedUtilities::ParameterInfo& buffer = perDofValues->getBuffers()[i];
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                            compute << "perDofValues"<<cl.intToString(i+1)<<"[3*index] = perDofx"<<cl.intToString(i+1)<<";\n";
                            compute << "perDofValues"<<cl.intToString(i+1)<<"[3*index+1] = perDofy"<<cl.intToString(i+1)<<";\n";
                            compute << "perDofValues"<<cl.intToString(i+1)<<"[3*index+2] = perDofz"<<cl.intToString(i+1)<<";\n";
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                        }
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                    }
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                    if (numGaussian > 0)
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                        compute << "gaussianIndex += NUM_ATOMS;\n";
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                    if (numUniform > 0)
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                        compute << "uniformIndex += NUM_ATOMS;\n";
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                    compute << "}\n";
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                }
                map<string, string> replacements;
                replacements["COMPUTE_STEP"] = compute.str();
                stringstream args;
                for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++) {
                    const OpenCLNonbondedUtilities::ParameterInfo& buffer = perDofValues->getBuffers()[i];
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                    string valueName = "perDofValues"+cl.intToString(i+1);
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                    args << ", __global " << buffer.getType() << "* restrict " << valueName;
                }
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                for (int i = 0; i < (int) tableTypes.size(); i++)
                    args << ", __global const " << tableTypes[i]<< "* restrict table" << i;
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                replacements["PARAMETER_ARGUMENTS"] = args.str();
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                if (loadPosAsDelta[step])
                    defines["LOAD_POS_AS_DELTA"] = "1";
                else if (defines.find("LOAD_POS_AS_DELTA") != defines.end())
                    defines.erase("LOAD_POS_AS_DELTA");
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                cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customIntegratorPerDof, replacements), defines);
                cl::Kernel kernel = cl::Kernel(program, "computePerDof");
                kernels[step].push_back(kernel);
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                requiredGaussian[step] = numGaussian;
                requiredUniform[step] = numUniform;
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                int index = 0;
                kernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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                setPosqCorrectionArg(cl, kernel, index++);
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                kernel.setArg<cl::Buffer>(index++, integration.getPosDelta().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, cl.getVelm().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, cl.getForce().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, integration.getStepSize().getDeviceBuffer());
                kernel.setArg<cl::Buffer>(index++, globalValues->getDeviceBuffer());
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                kernel.setArg<cl::Buffer>(index++, sumBuffer->getDeviceBuffer());
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                index += 4;
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                kernel.setArg<cl::Buffer>(index++, perDofEnergyParamDerivs->getDeviceBuffer());
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                for (auto& buffer : perDofValues->getBuffers())
                    kernel.setArg<cl::Memory>(index++, buffer.getMemory());
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                for (auto array : tabulatedFunctions)
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                    kernel.setArg<cl::Buffer>(index++, array->getDeviceBuffer());
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                if (stepType[step] == CustomIntegrator::ComputeSum) {
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                    // Create a second kernel for this step that sums the values.

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                    program = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
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                    kernel = cl::Kernel(program, useDouble ? "computeDoubleSum" : "computeFloatSum");
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                    kernels[step].push_back(kernel);
                    index = 0;
                    kernel.setArg<cl::Buffer>(index++, sumBuffer->getDeviceBuffer());
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                    kernel.setArg<cl::Buffer>(index++, summedValue->getDeviceBuffer());
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                    kernel.setArg<cl_int>(index++, 3*numAtoms);
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                }
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            }
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            else if (stepType[step] == CustomIntegrator::ConstrainPositions) {
                // Apply position constraints.

                cl::Program program = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
                cl::Kernel kernel = cl::Kernel(program, "applyPositionDeltas");
                kernels[step].push_back(kernel);
                int index = 0;
                kernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
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                setPosqCorrectionArg(cl, kernel, index++);
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                kernel.setArg<cl::Buffer>(index++, integration.getPosDelta().getDeviceBuffer());
            }
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        }
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        // Initialize the random number generator.
        
        int maxUniformRandoms = 1;
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        for (int required : requiredUniform)
            maxUniformRandoms = max(maxUniformRandoms, required);
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        uniformRandoms = OpenCLArray::create<mm_float4>(cl, maxUniformRandoms, "uniformRandoms");
        randomSeed = OpenCLArray::create<mm_int4>(cl, cl.getNumThreadBlocks()*OpenCLContext::ThreadBlockSize, "randomSeed");
        vector<mm_int4> seed(randomSeed->getSize());
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        int rseed = integrator.getRandomNumberSeed();
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        // A random seed of 0 means use a unique one
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        if (rseed == 0)
            rseed = osrngseed();
        unsigned int r = (unsigned int) (rseed+1);
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        for (auto& s : seed) {
            s.x = r = (1664525*r + 1013904223) & 0xFFFFFFFF;
            s.y = r = (1664525*r + 1013904223) & 0xFFFFFFFF;
            s.z = r = (1664525*r + 1013904223) & 0xFFFFFFFF;
            s.w = r = (1664525*r + 1013904223) & 0xFFFFFFFF;
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        }
        randomSeed->upload(seed);
        cl::Program randomProgram = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
        randomKernel = cl::Kernel(randomProgram, "generateRandomNumbers");
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        randomKernel.setArg<cl_int>(0, maxUniformRandoms);
        randomKernel.setArg<cl::Buffer>(1, uniformRandoms->getDeviceBuffer());
        randomKernel.setArg<cl::Buffer>(2, randomSeed->getDeviceBuffer());
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        // Create the kernel for computing kinetic energy.

        stringstream computeKE;
        for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = perDofValues->getBuffers()[i];
            computeKE << buffer.getType()<<" perDofx"<<cl.intToString(i+1)<<" = perDofValues"<<cl.intToString(i+1)<<"[3*index];\n";
            computeKE << buffer.getType()<<" perDofy"<<cl.intToString(i+1)<<" = perDofValues"<<cl.intToString(i+1)<<"[3*index+1];\n";
            computeKE << buffer.getType()<<" perDofz"<<cl.intToString(i+1)<<" = perDofValues"<<cl.intToString(i+1)<<"[3*index+2];\n";
        }
        Lepton::ParsedExpression keExpression = Lepton::Parser::parse(integrator.getKineticEnergyExpression()).optimize();
        for (int i = 0; i < 3; i++)
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            computeKE << createPerDofComputation("", keExpression, i, integrator, "f", "", functionList, functionNames);
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        map<string, string> replacements;
        replacements["COMPUTE_STEP"] = computeKE.str();
        stringstream args;
        for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++) {
            const OpenCLNonbondedUtilities::ParameterInfo& buffer = perDofValues->getBuffers()[i];
            string valueName = "perDofValues"+cl.intToString(i+1);
            args << ", __global " << buffer.getType() << "* restrict " << valueName;
        }
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        for (int i = 0; i < (int) tableTypes.size(); i++)
            args << ", __global const " << tableTypes[i]<< "* restrict table" << i;
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        replacements["PARAMETER_ARGUMENTS"] = args.str();
        if (defines.find("LOAD_POS_AS_DELTA") != defines.end())
            defines.erase("LOAD_POS_AS_DELTA");
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        cl::Program program = cl.createProgram(cl.replaceStrings(OpenCLKernelSources::customIntegratorPerDof, replacements), defines);
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        kineticEnergyKernel = cl::Kernel(program, "computePerDof");
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        int index = 0;
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        kineticEnergyKernel.setArg<cl::Buffer>(index++, cl.getPosq().getDeviceBuffer());
        setPosqCorrectionArg(cl, kineticEnergyKernel, index++);
        kineticEnergyKernel.setArg<cl::Buffer>(index++, integration.getPosDelta().getDeviceBuffer());
        kineticEnergyKernel.setArg<cl::Buffer>(index++, cl.getVelm().getDeviceBuffer());
        kineticEnergyKernel.setArg<cl::Buffer>(index++, cl.getForce().getDeviceBuffer());
        kineticEnergyKernel.setArg<cl::Buffer>(index++, integration.getStepSize().getDeviceBuffer());
        kineticEnergyKernel.setArg<cl::Buffer>(index++, globalValues->getDeviceBuffer());
        kineticEnergyKernel.setArg<cl::Buffer>(index++, sumBuffer->getDeviceBuffer());
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        index += 2;
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        kineticEnergyKernel.setArg<cl::Buffer>(index++, uniformRandoms->getDeviceBuffer());
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        if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision())
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            kineticEnergyKernel.setArg<cl_double>(index++, 0.0);
        else
            kineticEnergyKernel.setArg<cl_float>(index++, 0.0f);
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        kineticEnergyKernel.setArg<cl::Buffer>(index++, perDofEnergyParamDerivs->getDeviceBuffer());
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        for (int i = 0; i < (int) perDofValues->getBuffers().size(); i++)
            kineticEnergyKernel.setArg<cl::Memory>(index++, perDofValues->getBuffers()[i].getMemory());
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        for (auto array : tabulatedFunctions)
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            kineticEnergyKernel.setArg<cl::Buffer>(index++, array->getDeviceBuffer());
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        keNeedsForce = usesVariable(keExpression, "f");

        // Create a second kernel to sum the values.

        program = cl.createProgram(OpenCLKernelSources::customIntegrator, defines);
        sumKineticEnergyKernel = cl::Kernel(program, useDouble ? "computeDoubleSum" : "computeFloatSum");
        index = 0;
        sumKineticEnergyKernel.setArg<cl::Buffer>(index++, sumBuffer->getDeviceBuffer());
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        sumKineticEnergyKernel.setArg<cl::Buffer>(index++, summedValue->getDeviceBuffer());
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        sumKineticEnergyKernel.setArg<cl_int>(index++, 3*numAtoms);
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        // Delete the custom functions.

        for (auto& function : functions)
            delete function.second;
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    }
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    // Make sure all values (variables, parameters, etc.) are up to date.
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    if (!deviceValuesAreCurrent) {
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        if (useDouble)
            perDofValues->setParameterValues(localPerDofValuesDouble);
        else
            perDofValues->setParameterValues(localPerDofValuesFloat);
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        deviceValuesAreCurrent = true;
    }
    localValuesAreCurrent = false;
    double stepSize = integrator.getStepSize();
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    recordGlobalValue(stepSize, GlobalTarget(DT, dtVariableIndex), integrator);
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    for (int i = 0; i < (int) parameterNames.size(); i++) {
        double value = context.getParameter(parameterNames[i]);
        if (value != globalValuesDouble[parameterVariableIndex[i]]) {
            globalValuesDouble[parameterVariableIndex[i]] = value;
            deviceGlobalsAreCurrent = false;
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        }
    }
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}
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ExpressionTreeNode OpenCLIntegrateCustomStepKernel::replaceDerivFunctions(const ExpressionTreeNode& node, ContextImpl& context) {
    // This is called recursively to identify calls to the deriv() function inside global expressions,
    // and replace them with a custom function that returns the correct value.
    
    const Operation& op = node.getOperation();
    if (op.getId() == Operation::CUSTOM && op.getName() == "deriv") {
        string param = node.getChildren()[1].getOperation().getName();
        if (context.getParameters().find(param) == context.getParameters().end())
            throw OpenMMException("The second argument to deriv() must be a context parameter");
        needsEnergyParamDerivs = true;
        return ExpressionTreeNode(new Operation::Custom("deriv", new DerivFunction(energyParamDerivs, param)));
    }
    else {
        vector<ExpressionTreeNode> children;
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        for (auto& child : node.getChildren())
            children.push_back(replaceDerivFunctions(child, context));
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        return ExpressionTreeNode(op.clone(), children);
    }
}

void OpenCLIntegrateCustomStepKernel::findExpressionsForDerivs(const ExpressionTreeNode& node, vector<pair<ExpressionTreeNode, string> >& variableNodes) {
    // This is called recursively to identify calls to the deriv() function inside per-DOF expressions,
    // and record the code to replace them with.
    
    const Operation& op = node.getOperation();
    if (op.getId() == Operation::CUSTOM && op.getName() == "deriv") {
        string param = node.getChildren()[1].getOperation().getName();
        int index;
        for (index = 0; index < perDofEnergyParamDerivNames.size() && param != perDofEnergyParamDerivNames[index]; index++)
            ;
        if (index == perDofEnergyParamDerivNames.size())
            perDofEnergyParamDerivNames.push_back(param);
        variableNodes.push_back(make_pair(node, "energyParamDerivs["+cl.intToString(index)+"]"));
        needsEnergyParamDerivs = true;
    }
    else {
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        for (auto& child : node.getChildren())
            findExpressionsForDerivs(child, variableNodes);
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    }
}

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void OpenCLIntegrateCustomStepKernel::execute(ContextImpl& context, CustomIntegrator& integrator, bool& forcesAreValid) {
    prepareForComputation(context, integrator, forcesAreValid);
    OpenCLIntegrationUtilities& integration = cl.getIntegrationUtilities();
    int numAtoms = cl.getNumAtoms();
    int numSteps = integrator.getNumComputations();
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    if (!forcesAreValid)
        savedEnergy.clear();
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    // Loop over computation steps in the integrator and execute them.

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    for (int step = 0; step < numSteps; ) {
        int nextStep = step+1;
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        int forceGroups = forceGroupFlags[step];
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        int lastForceGroups = context.getLastForceGroups();
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        bool haveForces = (!needsForces[step] || (forcesAreValid && lastForceGroups == forceGroups));
        bool haveEnergy = (!needsEnergy[step] || savedEnergy.find(forceGroups) != savedEnergy.end());
        if (!haveForces || !haveEnergy) {
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            if (forcesAreValid) {
                if (savedForces.find(lastForceGroups) != savedForces.end() && validSavedForces.find(lastForceGroups) == validSavedForces.end()) {
                    // The forces are still valid.  We just need a different force group right now.  Save the old
                    // forces in case we need them again.

                    cl.getForce().copyTo(*savedForces[lastForceGroups]);
                    validSavedForces.insert(lastForceGroups);
                }
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            }
            else
                validSavedForces.clear();
            
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            // Recompute forces and/or energy.  Figure out what is actually needed
            // between now and the next time they get invalidated again.
            
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            bool computeForce = (needsForces[step] || computeBothForceAndEnergy[step]);
            bool computeEnergy = (needsEnergy[step] || computeBothForceAndEnergy[step]);
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            if (!computeEnergy && validSavedForces.find(forceGroups) != validSavedForces.end()) {
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                // We can just restore the forces we saved earlier.
                
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                savedForces[forceGroups]->copyTo(cl.getForce());
                context.getLastForceGroups() = forceGroups;
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            }
            else {
                recordChangedParameters(context);
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                energy = context.calcForcesAndEnergy(computeForce, computeEnergy, forceGroups);
                savedEnergy[forceGroups] = energy;
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                if (needsEnergyParamDerivs) {
                    context.getEnergyParameterDerivatives(energyParamDerivs);
                    if (perDofEnergyParamDerivNames.size() > 0) {
                        if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision()) {
                            for (int i = 0; i < perDofEnergyParamDerivNames.size(); i++)
                                localPerDofEnergyParamDerivsDouble[i] = energyParamDerivs[perDofEnergyParamDerivNames[i]];
                            perDofEnergyParamDerivs->upload(localPerDofEnergyParamDerivsDouble);
                        }
                        else {
                            for (int i = 0; i < perDofEnergyParamDerivNames.size(); i++)
                                localPerDofEnergyParamDerivsFloat[i] = (float) energyParamDerivs[perDofEnergyParamDerivNames[i]];
                            perDofEnergyParamDerivs->upload(localPerDofEnergyParamDerivsFloat);
                        }
                    }
                }
                forcesAreValid = true;
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            }
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        }
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        if (needsEnergy[step])
            energy = savedEnergy[forceGroups];
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        if (needsGlobals[step] && !deviceGlobalsAreCurrent) {
            // Upload the global values to the device.
            
            if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision())
                globalValues->upload(globalValuesDouble);
            else {
                for (int j = 0; j < (int) globalValuesDouble.size(); j++)
                    globalValuesFloat[j] = (float) globalValuesDouble[j];
                globalValues->upload(globalValuesFloat);
            }
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        }
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        bool stepInvalidatesForces = invalidatesForces[step];
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        if (stepType[step] == CustomIntegrator::ComputePerDof && !merged[step]) {
            kernels[step][0].setArg<cl_uint>(9, integration.prepareRandomNumbers(requiredGaussian[step]));
            kernels[step][0].setArg<cl::Buffer>(8, integration.getRandom().getDeviceBuffer());
            kernels[step][0].setArg<cl::Buffer>(10, uniformRandoms->getDeviceBuffer());
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            if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision())
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                kernels[step][0].setArg<cl_double>(11, energy);
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            else
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                kernels[step][0].setArg<cl_float>(11, (cl_float) energy);
            if (requiredUniform[step] > 0)
                cl.executeKernel(randomKernel, numAtoms);
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            cl.executeKernel(kernels[step][0], numAtoms, 128);
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        }
        else if (stepType[step] == CustomIntegrator::ComputeGlobal) {
            expressionSet.setVariable(uniformVariableIndex, SimTKOpenMMUtilities::getUniformlyDistributedRandomNumber());
            expressionSet.setVariable(gaussianVariableIndex, SimTKOpenMMUtilities::getNormallyDistributedRandomNumber());
            expressionSet.setVariable(stepEnergyVariableIndex[step], energy);
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            recordGlobalValue(globalExpressions[step][0].evaluate(), stepTarget[step], integrator);
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        }
        else if (stepType[step] == CustomIntegrator::ComputeSum) {
            kernels[step][0].setArg<cl_uint>(9, integration.prepareRandomNumbers(requiredGaussian[step]));
            kernels[step][0].setArg<cl::Buffer>(8, integration.getRandom().getDeviceBuffer());
            kernels[step][0].setArg<cl::Buffer>(10, uniformRandoms->getDeviceBuffer());
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            if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision())
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                kernels[step][0].setArg<cl_double>(11, energy);
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            else
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                kernels[step][0].setArg<cl_float>(11, (cl_float) energy);
            if (requiredUniform[step] > 0)
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                cl.executeKernel(randomKernel, numAtoms);
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            cl.clearBuffer(*sumBuffer);
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            cl.executeKernel(kernels[step][0], numAtoms, 128);
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            cl.executeKernel(kernels[step][1], sumWorkGroupSize, sumWorkGroupSize);
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            if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision()) {
                double value;
                summedValue->download(&value);
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                recordGlobalValue(value, stepTarget[step], integrator);
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            }
            else {
                float value;
                summedValue->download(&value);
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                recordGlobalValue(value, stepTarget[step], integrator);
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            }
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        }
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        else if (stepType[step] == CustomIntegrator::UpdateContextState) {
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            recordChangedParameters(context);
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            stepInvalidatesForces = context.updateContextState();
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        }
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        else if (stepType[step] == CustomIntegrator::ConstrainPositions) {
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            if (hasAnyConstraints) {
                cl.getIntegrationUtilities().applyConstraints(integrator.getConstraintTolerance());
                cl.executeKernel(kernels[step][0], numAtoms);
            }
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            cl.getIntegrationUtilities().computeVirtualSites();
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        }
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        else if (stepType[step] == CustomIntegrator::ConstrainVelocities) {
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            cl.getIntegrationUtilities().applyVelocityConstraints(integrator.getConstraintTolerance());
        }
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        else if (stepType[step] == CustomIntegrator::IfBlockStart) {
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            if (!evaluateCondition(step))
                nextStep = blockEnd[step]+1;
        }
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        else if (stepType[step] == CustomIntegrator::WhileBlockStart) {
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            if (!evaluateCondition(step))
                nextStep = blockEnd[step]+1;
        }
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        else if (stepType[step] == CustomIntegrator::BlockEnd) {
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            if (blockEnd[step] != -1)
                nextStep = blockEnd[step]; // Return to the start of a while block.
        }
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        if (stepInvalidatesForces) {
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            forcesAreValid = false;
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            savedEnergy.clear();
        }
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        step = nextStep;
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    }
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    recordChangedParameters(context);
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    // Update the time and step count.

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    cl.setTime(cl.getTime()+integrator.getStepSize());
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    cl.setStepCount(cl.getStepCount()+1);
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    cl.reorderAtoms();
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    if (cl.getAtomsWereReordered()) {
        forcesAreValid = false;
        validSavedForces.clear();
    }
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    // Reduce UI lag.
    
#ifdef WIN32
    cl.getQueue().flush();
#endif
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}

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bool OpenCLIntegrateCustomStepKernel::evaluateCondition(int step) {
    expressionSet.setVariable(uniformVariableIndex, SimTKOpenMMUtilities::getUniformlyDistributedRandomNumber());
    expressionSet.setVariable(gaussianVariableIndex, SimTKOpenMMUtilities::getNormallyDistributedRandomNumber());
    expressionSet.setVariable(stepEnergyVariableIndex[step], energy);
    double lhs = globalExpressions[step][0].evaluate();
    double rhs = globalExpressions[step][1].evaluate();
    switch (comparisons[step]) {
        case CustomIntegratorUtilities::EQUAL:
            return (lhs == rhs);
        case CustomIntegratorUtilities::LESS_THAN:
            return (lhs < rhs);
        case CustomIntegratorUtilities::GREATER_THAN:
            return (lhs > rhs);
        case CustomIntegratorUtilities::NOT_EQUAL:
            return (lhs != rhs);
        case CustomIntegratorUtilities::LESS_THAN_OR_EQUAL:
            return (lhs <= rhs);
        case CustomIntegratorUtilities::GREATER_THAN_OR_EQUAL:
            return (lhs >= rhs);
    }
    throw OpenMMException("Invalid comparison operator");
}

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double OpenCLIntegrateCustomStepKernel::computeKineticEnergy(ContextImpl& context, CustomIntegrator& integrator, bool& forcesAreValid) {
    prepareForComputation(context, integrator, forcesAreValid);
    if (keNeedsForce && !forcesAreValid) {
        // Compute the force.  We want to then mark that forces are valid, which means also computing
        // potential energy if any steps will expect it to be valid too.
        
        bool willNeedEnergy = false;
        for (int i = 0; i < integrator.getNumComputations(); i++)
            willNeedEnergy |= needsEnergy[i];
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        energy = context.calcForcesAndEnergy(true, willNeedEnergy, -1);
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        forcesAreValid = true;
    }
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    cl.clearBuffer(*sumBuffer);
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    kineticEnergyKernel.setArg<cl::Buffer>(8, cl.getIntegrationUtilities().getRandom().getDeviceBuffer());
    kineticEnergyKernel.setArg<cl_uint>(9, 0);
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    cl.executeKernel(kineticEnergyKernel, cl.getNumAtoms());
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    cl.executeKernel(sumKineticEnergyKernel, sumWorkGroupSize, sumWorkGroupSize);
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    if (cl.getUseDoublePrecision() || cl.getUseMixedPrecision()) {
        double ke;
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        summedValue->download(&ke);
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        return ke;
    }
    else {
        float ke;
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        summedValue->download(&ke);
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        return ke;
    }
}

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void OpenCLIntegrateCustomStepKernel::recordGlobalValue(double value, GlobalTarget target, CustomIntegrator& integrator) {
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    switch (target.type) {
        case DT:
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            if (value != globalValuesDouble[dtVariableIndex])
                deviceGlobalsAreCurrent = false;
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            expressionSet.setVariable(dtVariableIndex, value);
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            globalValuesDouble[dtVariableIndex] = value;
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            cl.getIntegrationUtilities().setNextStepSize(value);
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            integrator.setStepSize(value);
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            break;
        case VARIABLE:
        case PARAMETER:
            expressionSet.setVariable(target.variableIndex, value);
            globalValuesDouble[target.variableIndex] = value;
            deviceGlobalsAreCurrent = false;
            break;
    }
}

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void OpenCLIntegrateCustomStepKernel::recordChangedParameters(ContextImpl& context) {
    if (!modifiesParameters)
        return;
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    for (int i = 0; i < (int) parameterNames.size(); i++) {
        double value = context.getParameter(parameterNames[i]);
        if (value != globalValuesDouble[parameterVariableIndex[i]])
            context.setParameter(parameterNames[i], globalValuesDouble[parameterVariableIndex[i]]);
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    }
}

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void OpenCLIntegrateCustomStepKernel::getGlobalVariables(ContextImpl& context, vector<double>& values) const {
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    if (globalValues == NULL) {
        // The data structures haven't been created yet, so just return the list of values that was given earlier.
        
        values = initialGlobalVariables;
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        return;
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    }
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    values.resize(numGlobalVariables);
    for (int i = 0; i < numGlobalVariables; i++)
        values[i] = globalValuesDouble[globalVariableIndex[i]];
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}

void OpenCLIntegrateCustomStepKernel::setGlobalVariables(ContextImpl& context, const vector<double>& values) {
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    if (numGlobalVariables == 0)
        return;
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    if (globalValues == NULL) {
        // The data structures haven't been created yet, so just store the list of values.
        
        initialGlobalVariables = values;
        return;
    }
    for (int i = 0; i < numGlobalVariables; i++) {
        globalValuesDouble[globalVariableIndex[i]] = values[i];
        expressionSet.setVariable(globalVariableIndex[i], values[i]);
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    }
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    deviceGlobalsAreCurrent = false;
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}

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

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

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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;
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    defines["NUM_ATOMS"] = cl.intToString(cl.getNumAtoms());
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    cl::Program program = cl.createProgram(OpenCLKernelSources::andersenThermostat, defines);
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    kernel = cl::Kernel(program, "applyAndersenThermostat");
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    cl.getIntegrationUtilities().initRandomNumberGenerator(randomSeed);
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    // Create the arrays with the group definitions.

    vector<vector<int> > groups = AndersenThermostatImpl::calcParticleGroups(system);
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    atomGroups = OpenCLArray::create<int>(cl, cl.getNumAtoms(), "atomGroups");
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    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;
        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());
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        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;
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    if (savedForces != NULL)
        delete savedForces;
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    if (moleculeAtoms != NULL)
        delete moleculeAtoms;
    if (moleculeStartIndex != NULL)
        delete moleculeStartIndex;
}

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void OpenCLApplyMonteCarloBarostatKernel::initialize(const System& system, const Force& thermostat) {
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    savedPositions = new OpenCLArray(cl, cl.getPaddedNumAtoms(), cl.getUseDoublePrecision() ? sizeof(mm_double4) : sizeof(mm_float4), "savedPositions");
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    savedForces = new OpenCLArray(cl, cl.getPaddedNumAtoms(), cl.getUseDoublePrecision() ? sizeof(mm_double4) : sizeof(mm_float4), "savedForces");
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    cl::Program program = cl.createProgram(OpenCLKernelSources::monteCarloBarostat);
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    kernel = cl::Kernel(program, "scalePositions");
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}

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

        // Create the arrays with the molecule definitions.

        vector<vector<int> > molecules = context.getMolecules();
        numMolecules = molecules.size();
        moleculeAtoms = OpenCLArray::create<int>(cl, cl.getNumAtoms(), "moleculeAtoms");
        moleculeStartIndex = OpenCLArray::create<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;
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            for (int molecule : molecules[i])
                atoms[index++] = molecule;
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        }
        startIndex[numMolecules] = index;
        moleculeAtoms->upload(atoms);
        moleculeStartIndex->upload(startIndex);

        // Initialize the kernel arguments.
        
        kernel.setArg<cl_int>(3, numMolecules);
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        kernel.setArg<cl::Buffer>(9, cl.getPosq().getDeviceBuffer());
        kernel.setArg<cl::Buffer>(10, moleculeAtoms->getDeviceBuffer());
        kernel.setArg<cl::Buffer>(11, moleculeStartIndex->getDeviceBuffer());
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    }
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    int bytesToCopy = cl.getPosq().getSize()*(cl.getUseDoublePrecision() ? sizeof(mm_double4) : sizeof(mm_float4));
    cl.getQueue().enqueueCopyBuffer(cl.getPosq().getDeviceBuffer(), savedPositions->getDeviceBuffer(), 0, 0, bytesToCopy);
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    cl.getQueue().enqueueCopyBuffer(cl.getForce().getDeviceBuffer(), savedForces->getDeviceBuffer(), 0, 0, bytesToCopy);
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    kernel.setArg<cl_float>(0, (cl_float) scaleX);
    kernel.setArg<cl_float>(1, (cl_float) scaleY);
    kernel.setArg<cl_float>(2, (cl_float) scaleZ);
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    setPeriodicBoxArgs(cl, kernel, 4);
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    cl.executeKernel(kernel, cl.getNumAtoms());
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    for (auto& offset : cl.getPosCellOffsets())
        offset = mm_int4(0, 0, 0, 0);
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    lastAtomOrder = cl.getAtomIndex();
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}

void OpenCLApplyMonteCarloBarostatKernel::restoreCoordinates(ContextImpl& context) {
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    int bytesToCopy = cl.getPosq().getSize()*(cl.getUseDoublePrecision() ? sizeof(mm_double4) : sizeof(mm_float4));
    cl.getQueue().enqueueCopyBuffer(savedPositions->getDeviceBuffer(), cl.getPosq().getDeviceBuffer(), 0, 0, bytesToCopy);
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    cl.getQueue().enqueueCopyBuffer(savedForces->getDeviceBuffer(), cl.getForce().getDeviceBuffer(), 0, 0, bytesToCopy);
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}

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

void OpenCLRemoveCMMotionKernel::initialize(const System& system, const CMMotionRemover& force) {
    frequency = force.getFrequency();
    int numAtoms = cl.getNumAtoms();
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    cmMomentum = OpenCLArray::create<mm_float4>(cl, (numAtoms+OpenCLContext::ThreadBlockSize-1)/OpenCLContext::ThreadBlockSize, "cmMomentum");
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    double totalMass = 0.0;
    for (int i = 0; i < numAtoms; i++)
        totalMass += system.getParticleMass(i);
    map<string, string> defines;
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    defines["INVERSE_TOTAL_MASS"] = cl.doubleToString(totalMass == 0 ? 0.0 : 1.0/totalMass);
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    cl::Program program = cl.createProgram(OpenCLKernelSources::removeCM, defines);
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    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());
}