CudaKernels.cpp 423 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) 2008-2018 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 "CudaKernels.h"
#include "CudaForceInfo.h"
#include "openmm/LangevinIntegrator.h"
#include "openmm/Context.h"
#include "openmm/internal/AndersenThermostatImpl.h"
#include "openmm/internal/CMAPTorsionForceImpl.h"
#include "openmm/internal/ContextImpl.h"
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#include "openmm/internal/CustomCentroidBondForceImpl.h"
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#include "openmm/internal/CustomCompoundBondForceImpl.h"
#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 "CudaBondedUtilities.h"
#include "CudaExpressionUtilities.h"
#include "CudaIntegrationUtilities.h"
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#include "CudaNonbondedUtilities.h"
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#include "CudaKernelSources.h"
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#include "lepton/CustomFunction.h"
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#include "lepton/ExpressionTreeNode.h"
#include "lepton/Operation.h"
#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 "jama_eig.h"
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#include <algorithm>
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#include <cmath>
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#include <iterator>
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#include <set>

using namespace OpenMM;
using namespace std;
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using namespace Lepton;
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#define CHECK_RESULT(result, prefix) \
    if (result != CUDA_SUCCESS) { \
        std::stringstream m; \
        m<<prefix<<": "<<CudaContext::getErrorString(result)<<" ("<<result<<")"<<" at "<<__FILE__<<":"<<__LINE__; \
        throw OpenMMException(m.str());\
    }

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

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);
}

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

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

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

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

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

double CudaUpdateStateDataKernel::getTime(const ContextImpl& context) const {
    return cu.getTime();
}

void CudaUpdateStateDataKernel::setTime(ContextImpl& context, double time) {
    vector<CudaContext*>& contexts = cu.getPlatformData().contexts;
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    for (auto ctx : contexts)
        ctx->setTime(time);
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}

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void CudaUpdateStateDataKernel::getPositions(ContextImpl& context, vector<Vec3>& positions) {
    cu.setAsCurrent();
    int numParticles = context.getSystem().getNumParticles();
    positions.resize(numParticles);
    vector<float4> posCorrection;
    if (cu.getUseDoublePrecision()) {
        double4* posq = (double4*) cu.getPinnedBuffer();
        cu.getPosq().download(posq);
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    }
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    else if (cu.getUseMixedPrecision()) {
        float4* posq = (float4*) cu.getPinnedBuffer();
        cu.getPosq().download(posq, false);
        posCorrection.resize(numParticles);
        cu.getPosqCorrection().download(posCorrection);
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    }
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    else {
        float4* posq = (float4*) cu.getPinnedBuffer();
        cu.getPosq().download(posq);
    }
    
    // Filling in the output array is done in parallel for speed.
    
    cu.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 = cu.getAtomIndex();
        int numParticles = cu.getNumAtoms();
        Vec3 boxVectors[3];
        cu.getPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
        int numThreads = threads.getNumThreads();
        int start = threadIndex*numParticles/numThreads;
        int end = (threadIndex+1)*numParticles/numThreads;
        if (cu.getUseDoublePrecision()) {
            double4* posq = (double4*) cu.getPinnedBuffer();
            for (int i = start; i < end; ++i) {
                double4 pos = posq[i];
                int4 offset = cu.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 (cu.getUseMixedPrecision()) {
            float4* posq = (float4*) cu.getPinnedBuffer();
            for (int i = start; i < end; ++i) {
                float4 pos1 = posq[i];
                float4 pos2 = posCorrection[i];
                int4 offset = cu.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 {
            float4* posq = (float4*) cu.getPinnedBuffer();
            for (int i = start; i < end; ++i) {
                float4 pos = posq[i];
                int4 offset = cu.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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    cu.getPlatformData().threads.waitForThreads();
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}

void CudaUpdateStateDataKernel::setPositions(ContextImpl& context, const vector<Vec3>& positions) {
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    cu.setAsCurrent();
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    const vector<int>& order = cu.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
    if (cu.getUseDoublePrecision()) {
        double4* posq = (double4*) cu.getPinnedBuffer();
        cu.getPosq().download(posq);
        for (int i = 0; i < numParticles; ++i) {
            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 < cu.getPaddedNumAtoms(); i++)
            posq[i] = make_double4(0.0, 0.0, 0.0, 0.0);
        cu.getPosq().upload(posq);
    }
    else {
        float4* posq = (float4*) cu.getPinnedBuffer();
        cu.getPosq().download(posq);
        for (int i = 0; i < numParticles; ++i) {
            float4& pos = posq[i];
            const Vec3& p = positions[order[i]];
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            pos.x = (float) p[0];
            pos.y = (float) p[1];
            pos.z = (float) p[2];
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        }
        for (int i = numParticles; i < cu.getPaddedNumAtoms(); i++)
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            posq[i] = make_float4(0.0f, 0.0f, 0.0f, 0.0f);
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        cu.getPosq().upload(posq);
    }
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    if (cu.getUseMixedPrecision()) {
        float4* posCorrection = (float4*) cu.getPinnedBuffer();
        for (int i = 0; i < numParticles; ++i) {
            float4& c = posCorrection[i];
            const Vec3& p = positions[order[i]];
            c.x = (float) (p[0]-(float)p[0]);
            c.y = (float) (p[1]-(float)p[1]);
            c.z = (float) (p[2]-(float)p[2]);
            c.w = 0;
        }
        for (int i = numParticles; i < cu.getPaddedNumAtoms(); i++)
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            posCorrection[i] = make_float4(0.0f, 0.0f, 0.0f, 0.0f);
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        cu.getPosqCorrection().upload(posCorrection);
    }
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    for (auto& offset : cu.getPosCellOffsets())
        offset = make_int4(0, 0, 0, 0);
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    cu.reorderAtoms();
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}

void CudaUpdateStateDataKernel::getVelocities(ContextImpl& context, vector<Vec3>& velocities) {
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    cu.setAsCurrent();
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    const vector<int>& order = cu.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
    velocities.resize(numParticles);
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    if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision()) {
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        double4* velm = (double4*) cu.getPinnedBuffer();
        cu.getVelm().download(velm);
        for (int i = 0; i < numParticles; ++i) {
            double4 vel = velm[i];
            int4 offset = cu.getPosCellOffsets()[i];
            velocities[order[i]] = Vec3(vel.x, vel.y, vel.z);
        }
    }
    else {
        float4* velm = (float4*) cu.getPinnedBuffer();
        cu.getVelm().download(velm);
        for (int i = 0; i < numParticles; ++i) {
            float4 vel = velm[i];
            int4 offset = cu.getPosCellOffsets()[i];
            velocities[order[i]] = Vec3(vel.x, vel.y, vel.z);
        }
    }
}

void CudaUpdateStateDataKernel::setVelocities(ContextImpl& context, const vector<Vec3>& velocities) {
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    cu.setAsCurrent();
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    const vector<int>& order = cu.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
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    if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision()) {
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        double4* velm = (double4*) cu.getPinnedBuffer();
        cu.getVelm().download(velm);
        for (int i = 0; i < numParticles; ++i) {
            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 < cu.getPaddedNumAtoms(); i++)
            velm[i] = make_double4(0.0, 0.0, 0.0, 0.0);
        cu.getVelm().upload(velm);
    }
    else {
        float4* velm = (float4*) cu.getPinnedBuffer();
        cu.getVelm().download(velm);
        for (int i = 0; i < numParticles; ++i) {
            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 < cu.getPaddedNumAtoms(); i++)
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            velm[i] = make_float4(0.0f, 0.0f, 0.0f, 0.0f);
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        cu.getVelm().upload(velm);
    }
}

void CudaUpdateStateDataKernel::getForces(ContextImpl& context, vector<Vec3>& forces) {
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    cu.setAsCurrent();
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    long long* force = (long long*) cu.getPinnedBuffer();
    cu.getForce().download(force);
    const vector<int>& order = cu.getAtomIndex();
    int numParticles = context.getSystem().getNumParticles();
    int paddedNumParticles = cu.getPaddedNumAtoms();
    forces.resize(numParticles);
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    double scale = 1.0/(double) 0x100000000LL;
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    for (int i = 0; i < numParticles; ++i)
        forces[order[i]] = Vec3(scale*force[i], scale*force[i+paddedNumParticles], scale*force[i+paddedNumParticles*2]);
}

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void CudaUpdateStateDataKernel::getEnergyParameterDerivatives(ContextImpl& context, map<string, double>& derivs) {
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    const vector<string>& paramDerivNames = cu.getEnergyParamDerivNames();
    int numDerivs = paramDerivNames.size();
    if (numDerivs == 0)
        return;
    derivs = cu.getEnergyParamDerivWorkspace();
    CudaArray& derivArray = cu.getEnergyParamDerivBuffer();
    if (cu.getUseDoublePrecision() || cu.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 CudaUpdateStateDataKernel::getPeriodicBoxVectors(ContextImpl& context, Vec3& a, Vec3& b, Vec3& c) const {
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    cu.getPeriodicBoxVectors(a, b, c);
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}

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void CudaUpdateStateDataKernel::setPeriodicBoxVectors(ContextImpl& context, const Vec3& a, const Vec3& b, const Vec3& c) {
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    vector<CudaContext*>& contexts = cu.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 : cu.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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}

void CudaUpdateStateDataKernel::createCheckpoint(ContextImpl& context, ostream& stream) {
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    cu.setAsCurrent();
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    int version = 2;
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    stream.write((char*) &version, sizeof(int));
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    int precision = (cu.getUseDoublePrecision() ? 2 : cu.getUseMixedPrecision() ? 1 : 0);
    stream.write((char*) &precision, sizeof(int));
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    double time = cu.getTime();
    stream.write((char*) &time, sizeof(double));
    int stepCount = cu.getStepCount();
    stream.write((char*) &stepCount, sizeof(int));
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    int stepsSinceReorder = cu.getStepsSinceReorder();
    stream.write((char*) &stepsSinceReorder, sizeof(int));
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    char* buffer = (char*) cu.getPinnedBuffer();
    cu.getPosq().download(buffer);
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    stream.write(buffer, cu.getPosq().getSize()*cu.getPosq().getElementSize());
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    if (cu.getUseMixedPrecision()) {
        cu.getPosqCorrection().download(buffer);
        stream.write(buffer, cu.getPosqCorrection().getSize()*cu.getPosqCorrection().getElementSize());
    }
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    cu.getVelm().download(buffer);
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    stream.write(buffer, cu.getVelm().getSize()*cu.getVelm().getElementSize());
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    stream.write((char*) &cu.getAtomIndex()[0], sizeof(int)*cu.getAtomIndex().size());
    stream.write((char*) &cu.getPosCellOffsets()[0], sizeof(int4)*cu.getPosCellOffsets().size());
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    Vec3 boxVectors[3];
    cu.getPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
    stream.write((char*) boxVectors, 3*sizeof(Vec3));
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    cu.getIntegrationUtilities().createCheckpoint(stream);
    SimTKOpenMMUtilities::createCheckpoint(stream);
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}

void CudaUpdateStateDataKernel::loadCheckpoint(ContextImpl& context, istream& stream) {
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    cu.setAsCurrent();
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    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 = (cu.getUseDoublePrecision() ? 2 : cu.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<CudaContext*>& contexts = cu.getPlatformData().contexts;
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    for (auto ctx : contexts) {
        ctx->setTime(time);
        ctx->setStepCount(stepCount);
        ctx->setStepsSinceReorder(stepsSinceReorder);
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    }
    char* buffer = (char*) cu.getPinnedBuffer();
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    stream.read(buffer, cu.getPosq().getSize()*cu.getPosq().getElementSize());
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    cu.getPosq().upload(buffer);
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    if (cu.getUseMixedPrecision()) {
        stream.read(buffer, cu.getPosqCorrection().getSize()*cu.getPosqCorrection().getElementSize());
        cu.getPosqCorrection().upload(buffer);
    }
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    stream.read(buffer, cu.getVelm().getSize()*cu.getVelm().getElementSize());
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    cu.getVelm().upload(buffer);
    stream.read((char*) &cu.getAtomIndex()[0], sizeof(int)*cu.getAtomIndex().size());
    cu.getAtomIndexArray().upload(cu.getAtomIndex());
    stream.read((char*) &cu.getPosCellOffsets()[0], sizeof(int4)*cu.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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    cu.getIntegrationUtilities().loadCheckpoint(stream);
    SimTKOpenMMUtilities::loadCheckpoint(stream);
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    for (auto listener : cu.getReorderListeners())
        listener->execute();
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}

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

void CudaApplyConstraintsKernel::apply(ContextImpl& context, double tol) {
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    cu.setAsCurrent();
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    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        map<string, string> defines;
        CUmodule module = cu.createModule(CudaKernelSources::constraints, defines);
        applyDeltasKernel = cu.getKernel(module, "applyPositionDeltas");
    }
    CudaIntegrationUtilities& integration = cu.getIntegrationUtilities();
    cu.clearBuffer(integration.getPosDelta());
    integration.applyConstraints(tol);
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    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
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    int numAtoms = cu.getNumAtoms();
    void* args[] = {&numAtoms, &cu.getPosq().getDevicePointer(), &posCorrection, &cu.getIntegrationUtilities().getPosDelta().getDevicePointer()};
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    cu.executeKernel(applyDeltasKernel, args, cu.getNumAtoms());
    integration.computeVirtualSites();
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}

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

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

void CudaVirtualSitesKernel::computePositions(ContextImpl& context) {
    cu.getIntegrationUtilities().computeVirtualSites();
}

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

void CudaCalcHarmonicBondForceKernel::initialize(const System& system, const HarmonicBondForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumBonds()/numContexts;
    numBonds = endIndex-startIndex;
    if (numBonds == 0)
        return;
    vector<vector<int> > atoms(numBonds, vector<int>(2));
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    params.initialize<float2>(cu, numBonds, "bondParams");
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    vector<float2> paramVector(numBonds);
    for (int i = 0; i < numBonds; i++) {
        double length, k;
        force.getBondParameters(startIndex+i, atoms[i][0], atoms[i][1], length, k);
        paramVector[i] = make_float2((float) length, (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"] = CudaKernelSources::harmonicBondForce;
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    replacements["PARAMS"] = cu.getBondedUtilities().addArgument(params.getDevicePointer(), "float2");
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    cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::bondForce, replacements), force.getForceGroup());
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    info = new ForceInfo(force);
    cu.addForce(info);
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}

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

void CudaCalcHarmonicBondForceKernel::copyParametersToContext(ContextImpl& context, const HarmonicBondForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cu.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<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] = make_float2((float) length, (float) k);
    }
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    params.upload(paramVector);
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    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

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

CudaCalcCustomBondForceKernel::~CudaCalcCustomBondForceKernel() {
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    cu.setAsCurrent();
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    if (params != NULL)
        delete params;
}

void CudaCalcCustomBondForceKernel::initialize(const System& system, const CustomBondForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumBonds()/numContexts;
    numBonds = endIndex-startIndex;
    if (numBonds == 0)
        return;
    vector<vector<int> > atoms(numBonds, vector<int>(2));
    params = new CudaParameterSet(cu, force.getNumPerBondParameters(), numBonds, "customBondParams");
    vector<vector<float> > paramVector(numBonds);
    for (int i = 0; i < numBonds; i++) {
        vector<double> parameters;
        force.getBondParameters(startIndex+i, atoms[i][0], atoms[i][1], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
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    info = new ForceInfo(force);
    cu.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] = (float) force.getGlobalParameterDefaultValue(i);
    }
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction()).optimize();
    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("r").optimize();
    map<string, Lepton::ParsedExpression> expressions;
    expressions["energy += "] = energyExpression;
    expressions["float dEdR = "] = forceExpression;

    // Create the kernels.

    map<string, string> variables;
    variables["r"] = "r";
    for (int i = 0; i < force.getNumPerBondParameters(); i++) {
        const string& name = force.getPerBondParameterName(i);
        variables[name] = "bondParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
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        globals.initialize<float>(cu, force.getNumGlobalParameters(), "customBondGlobals");
        globals.upload(globalParamValues);
        string argName = cu.getBondedUtilities().addArgument(globals.getDevicePointer(), "float");
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        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+cu.intToString(i)+"]";
            variables[name] = value;
        }
    }
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cu.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++) {
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        CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cu.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
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    vector<const TabulatedFunction*> functions;
    vector<pair<string, string> > functionNames;
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    compute << cu.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();
    cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::bondForce, replacements), force.getForceGroup());
}

double CudaCalcCustomBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (globals.isInitialized()) {
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        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)
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            globals.upload(globalParamValues);
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    }
    return 0.0;
}

void CudaCalcCustomBondForceKernel::copyParametersToContext(ContextImpl& context, const CustomBondForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cu.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<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] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}
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class CudaCalcHarmonicAngleForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const HarmonicAngleForce& force) : force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumAngles();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3;
        double angle, k;
        force.getAngleParameters(index, particle1, particle2, particle3, angle, k);
        particles.resize(3);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3;
        double angle1, angle2, k1, k2;
        force.getAngleParameters(group1, particle1, particle2, particle3, angle1, k1);
        force.getAngleParameters(group2, particle1, particle2, particle3, angle2, k2);
        return (angle1 == angle2 && k1 == k2);
    }
private:
    const HarmonicAngleForce& force;
};

void CudaCalcHarmonicAngleForceKernel::initialize(const System& system, const HarmonicAngleForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumAngles()/numContexts;
    numAngles = endIndex-startIndex;
    if (numAngles == 0)
        return;
    vector<vector<int> > atoms(numAngles, vector<int>(3));
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    params.initialize<float2>(cu, numAngles, "angleParams");
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    vector<float2> paramVector(numAngles);
    for (int i = 0; i < numAngles; i++) {
        double angle, k;
        force.getAngleParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], angle, k);
        paramVector[i] = make_float2((float) angle, (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"] = CudaKernelSources::harmonicAngleForce;
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    replacements["PARAMS"] = cu.getBondedUtilities().addArgument(params.getDevicePointer(), "float2");
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    cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::angleForce, replacements), force.getForceGroup());
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    info = new ForceInfo(force);
    cu.addForce(info);
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}

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

void CudaCalcHarmonicAngleForceKernel::copyParametersToContext(ContextImpl& context, const HarmonicAngleForce& force) {
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cu.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<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] = make_float2((float) angle, (float) k);
    }
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    params.upload(paramVector);
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    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

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class CudaCalcCustomAngleForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const CustomAngleForce& force) : force(force) {
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    }
    int getNumParticleGroups() {
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        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;
};

CudaCalcCustomAngleForceKernel::~CudaCalcCustomAngleForceKernel() {
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    cu.setAsCurrent();
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    if (params != NULL)
        delete params;
}

void CudaCalcCustomAngleForceKernel::initialize(const System& system, const CustomAngleForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumAngles()/numContexts;
    numAngles = endIndex-startIndex;
    if (numAngles == 0)
        return;
    vector<vector<int> > atoms(numAngles, vector<int>(3));
    params = new CudaParameterSet(cu, force.getNumPerAngleParameters(), numAngles, "customAngleParams");
    vector<vector<float> > paramVector(numAngles);
    for (int i = 0; i < numAngles; i++) {
        vector<double> parameters;
        force.getAngleParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
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    info = new ForceInfo(force);
    cu.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] = (float) force.getGlobalParameterDefaultValue(i);
    }
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction()).optimize();
    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("theta").optimize();
    map<string, Lepton::ParsedExpression> expressions;
    expressions["energy += "] = energyExpression;
    expressions["float dEdAngle = "] = forceExpression;

    // Create the kernels.

    map<string, string> variables;
    variables["theta"] = "theta";
    for (int i = 0; i < force.getNumPerAngleParameters(); i++) {
        const string& name = force.getPerAngleParameterName(i);
        variables[name] = "angleParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
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        globals.initialize<float>(cu, force.getNumGlobalParameters(), "customAngleGlobals");
        globals.upload(globalParamValues);
        string argName = cu.getBondedUtilities().addArgument(globals.getDevicePointer(), "float");
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        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+cu.intToString(i)+"]";
            variables[name] = value;
        }
    }
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cu.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++) {
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        CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cu.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" angleParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
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    vector<const TabulatedFunction*> functions;
    vector<pair<string, string> > functionNames;
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    compute << cu.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();
    cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::angleForce, replacements), force.getForceGroup());
}

double CudaCalcCustomAngleForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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        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)
923
            globals.upload(globalParamValues);
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    }
    return 0.0;
}

void CudaCalcCustomAngleForceKernel::copyParametersToContext(ContextImpl& context, const CustomAngleForce& force) {
929
    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumAngles()/numContexts;
    int endIndex = (cu.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<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] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

956
class CudaCalcPeriodicTorsionForceKernel::ForceInfo : public CudaForceInfo {
957
public:
958
    ForceInfo(const PeriodicTorsionForce& force) : force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3, particle4, periodicity;
        double phase, k;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, periodicity, phase, k);
        particles.resize(4);
        particles[0] = particle1;
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        particles[1] = particle2;
        particles[2] = particle3;
        particles[3] = particle4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3, particle4, periodicity1, periodicity2;
        double phase1, phase2, k1, k2;
        force.getTorsionParameters(group1, particle1, particle2, particle3, particle4, periodicity1, phase1, k1);
        force.getTorsionParameters(group2, particle1, particle2, particle3, particle4, periodicity2, phase2, k2);
        return (periodicity1 == periodicity2 && phase1 == phase2 && k1 == k2);
    }
private:
    const PeriodicTorsionForce& force;
};

void CudaCalcPeriodicTorsionForceKernel::initialize(const System& system, const PeriodicTorsionForce& force) {
985
    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (numTorsions == 0)
        return;
    vector<vector<int> > atoms(numTorsions, vector<int>(4));
993
    params.initialize<float4>(cu, numTorsions, "periodicTorsionParams");
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    vector<float4> paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        int periodicity;
        double phase, k;
        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], periodicity, phase, k);
        paramVector[i] = make_float4((float) k, (float) phase, (float) periodicity, 0.0f);
    }
1001
    params.upload(paramVector);
1002
    map<string, string> replacements;
1003
    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
1004
    replacements["COMPUTE_FORCE"] = CudaKernelSources::periodicTorsionForce;
1005
    replacements["PARAMS"] = cu.getBondedUtilities().addArgument(params.getDevicePointer(), "float4");
1006
    cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::torsionForce, replacements), force.getForceGroup());
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    info = new ForceInfo(force);
    cu.addForce(info);
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}

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

void CudaCalcPeriodicTorsionForceKernel::copyParametersToContext(ContextImpl& context, const PeriodicTorsionForce& force) {
1016
    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    if (numTorsions != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of torsions has changed");
1022
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    if (numTorsions == 0)
        return;
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    // Record the per-torsion parameters.
    
    vector<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] = make_float4((float) k, (float) phase, (float) periodicity, 0.0f);
    }
1034
    params.upload(paramVector);
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    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

1041
class CudaCalcRBTorsionForceKernel::ForceInfo : public CudaForceInfo {
1042
public:
1043
    ForceInfo(const RBTorsionForce& force) : force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3, particle4;
        double c0, c1, c2, c3, c4, c5;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, c0, c1, c2, c3, c4, c5);
        particles.resize(4);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
        particles[3] = particle4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3, particle4;
        double c0a, c0b, c1a, c1b, c2a, c2b, c3a, c3b, c4a, c4b, c5a, c5b;
        force.getTorsionParameters(group1, particle1, particle2, particle3, particle4, c0a, c1a, c2a, c3a, c4a, c5a);
        force.getTorsionParameters(group2, particle1, particle2, particle3, particle4, c0b, c1b, c2b, c3b, c4b, c5b);
        return (c0a == c0b && c1a == c1b && c2a == c2b && c3a == c3b && c4a == c4b && c5a == c5b);
    }
private:
    const RBTorsionForce& force;
};

void CudaCalcRBTorsionForceKernel::initialize(const System& system, const RBTorsionForce& force) {
1070
    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (numTorsions == 0)
        return;
    vector<vector<int> > atoms(numTorsions, vector<int>(4));
1078
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    params1.initialize<float4>(cu, numTorsions, "rbTorsionParams1");
    params2.initialize<float2>(cu, numTorsions, "rbTorsionParams2");
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    vector<float4> paramVector1(numTorsions);
    vector<float2> paramVector2(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        double c0, c1, c2, c3, c4, c5;
        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], c0, c1, c2, c3, c4, c5);
        paramVector1[i] = make_float4((float) c0, (float) c1, (float) c2, (float) c3);
        paramVector2[i] = make_float2((float) c4, (float) c5);

    }
1089
1090
    params1.upload(paramVector1);
    params2.upload(paramVector2);
1091
    map<string, string> replacements;
1092
    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
1093
    replacements["COMPUTE_FORCE"] = CudaKernelSources::rbTorsionForce;
1094
1095
    replacements["PARAMS1"] = cu.getBondedUtilities().addArgument(params1.getDevicePointer(), "float4");
    replacements["PARAMS2"] = cu.getBondedUtilities().addArgument(params2.getDevicePointer(), "float2");
1096
    cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::torsionForce, replacements), force.getForceGroup());
1097
1098
    info = new ForceInfo(force);
    cu.addForce(info);
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1105
}

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

void CudaCalcRBTorsionForceKernel::copyParametersToContext(ContextImpl& context, const RBTorsionForce& force) {
1106
    cu.setAsCurrent();
1107
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1111
    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    if (numTorsions != endIndex-startIndex)
        throw OpenMMException("updateParametersInContext: The number of torsions has changed");
1112
1113
    if (numTorsions == 0)
        return;
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1125
    
    // Record the per-torsion parameters.
    
    vector<float4> paramVector1(numTorsions);
    vector<float2> paramVector2(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);
        paramVector1[i] = make_float4((float) c0, (float) c1, (float) c2, (float) c3);
        paramVector2[i] = make_float2((float) c4, (float) c5);
    }
1126
1127
    params1.upload(paramVector1);
    params2.upload(paramVector2);
1128
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1131
1132
1133
    
    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

1134
class CudaCalcCMAPTorsionForceKernel::ForceInfo : public CudaForceInfo {
1135
public:
1136
    ForceInfo(const CMAPTorsionForce& force) : force(force) {
1137
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1140
1141
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1164
    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int map, a1, a2, a3, a4, b1, b2, b3, b4;
        force.getTorsionParameters(index, map, a1, a2, a3, a4, b1, b2, b3, b4);
        particles.resize(8);
        particles[0] = a1;
        particles[1] = a2;
        particles[2] = a3;
        particles[3] = a4;
        particles[4] = b1;
        particles[5] = b2;
        particles[6] = b3;
        particles[7] = b4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int map1, map2, a1, a2, a3, a4, b1, b2, b3, b4;
        force.getTorsionParameters(group1, map1, a1, a2, a3, a4, b1, b2, b3, b4);
        force.getTorsionParameters(group2, map2, a1, a2, a3, a4, b1, b2, b3, b4);
        return (map1 == map2);
    }
private:
    const CMAPTorsionForce& force;
};

void CudaCalcCMAPTorsionForceKernel::initialize(const System& system, const CMAPTorsionForce& force) {
1165
    cu.setAsCurrent();
1166
1167
1168
1169
1170
1171
1172
1173
    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (numTorsions == 0)
        return;
    int numMaps = force.getNumMaps();
    vector<float4> coeffVec;
1174
    mapPositionsVec.resize(numMaps);
1175
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1194
    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] = make_int2(currentPosition, size);
        currentPosition += 4*size*size;
        for (int j = 0; j < size*size; j++) {
            coeffVec.push_back(make_float4((float) c[j][0], (float) c[j][1], (float) c[j][2], (float) c[j][3]));
            coeffVec.push_back(make_float4((float) c[j][4], (float) c[j][5], (float) c[j][6], (float) c[j][7]));
            coeffVec.push_back(make_float4((float) c[j][8], (float) c[j][9], (float) c[j][10], (float) c[j][11]));
            coeffVec.push_back(make_float4((float) c[j][12], (float) c[j][13], (float) c[j][14], (float) c[j][15]));
        }
    }
    vector<vector<int> > atoms(numTorsions, vector<int>(8));
    vector<int> torsionMapsVec(numTorsions);
    for (int i = 0; i < numTorsions; i++)
        force.getTorsionParameters(startIndex+i, torsionMapsVec[i], atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], atoms[i][4], atoms[i][5], atoms[i][6], atoms[i][7]);
1195
1196
1197
1198
1199
1200
    coefficients.initialize<float4>(cu, coeffVec.size(), "cmapTorsionCoefficients");
    mapPositions.initialize<int2>(cu, numMaps, "cmapTorsionMapPositions");
    torsionMaps.initialize<int>(cu, numTorsions, "cmapTorsionMaps");
    coefficients.upload(coeffVec);
    mapPositions.upload(mapPositionsVec);
    torsionMaps.upload(torsionMapsVec);
1201
    map<string, string> replacements;
1202
    replacements["APPLY_PERIODIC"] = (force.usesPeriodicBoundaryConditions() ? "1" : "0");
1203
1204
1205
    replacements["COEFF"] = cu.getBondedUtilities().addArgument(coefficients.getDevicePointer(), "float4");
    replacements["MAP_POS"] = cu.getBondedUtilities().addArgument(mapPositions.getDevicePointer(), "int2");
    replacements["MAPS"] = cu.getBondedUtilities().addArgument(torsionMaps.getDevicePointer(), "int");
1206
    cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::cmapTorsionForce, replacements), force.getForceGroup());
1207
1208
    info = new ForceInfo(force);
    cu.addForce(info);
1209
1210
1211
1212
1213
1214
}

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

1215
void CudaCalcCMAPTorsionForceKernel::copyParametersToContext(ContextImpl& context, const CMAPTorsionForce& force) {
1216
1217
1218
1219
1220
    int numMaps = force.getNumMaps();
    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
1221
    if (mapPositions.getSize() != numMaps)
1222
        throw OpenMMException("updateParametersInContext: The number of maps has changed");
1223
    if (torsionMaps.getSize() != numTorsions)
1224
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1230
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1233
1234
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1245
        throw OpenMMException("updateParametersInContext: The number of CMAP torsions has changed");

    // Update the maps.

    vector<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(make_float4((float) c[j][0], (float) c[j][1], (float) c[j][2], (float) c[j][3]));
            coeffVec.push_back(make_float4((float) c[j][4], (float) c[j][5], (float) c[j][6], (float) c[j][7]));
            coeffVec.push_back(make_float4((float) c[j][8], (float) c[j][9], (float) c[j][10], (float) c[j][11]));
            coeffVec.push_back(make_float4((float) c[j][12], (float) c[j][13], (float) c[j][14], (float) c[j][15]));
        }
    }
1246
    coefficients.upload(coeffVec);
1247
1248
1249
1250
1251
1252
1253
1254

    // 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]);
    }
1255
    torsionMaps.upload(torsionMapsVec);
1256
1257
}

1258
class CudaCalcCustomTorsionForceKernel::ForceInfo : public CudaForceInfo {
1259
public:
1260
    ForceInfo(const CustomTorsionForce& force) : force(force) {
1261
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    }
    int getNumParticleGroups() {
        return force.getNumTorsions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2, particle3, particle4;
        vector<double> parameters;
        force.getTorsionParameters(index, particle1, particle2, particle3, particle4, parameters);
        particles.resize(4);
        particles[0] = particle1;
        particles[1] = particle2;
        particles[2] = particle3;
        particles[3] = particle4;
    }
    bool areGroupsIdentical(int group1, int group2) {
        int particle1, particle2, particle3, particle4;
        vector<double> parameters1, parameters2;
        force.getTorsionParameters(group1, particle1, particle2, particle3, particle4, parameters1);
        force.getTorsionParameters(group2, particle1, particle2, particle3, particle4, parameters2);
        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
        return true;
    }
private:
    const CustomTorsionForce& force;
};

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

void CudaCalcCustomTorsionForceKernel::initialize(const System& system, const CustomTorsionForce& force) {
1295
    cu.setAsCurrent();
1296
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumTorsions()/numContexts;
    numTorsions = endIndex-startIndex;
    if (numTorsions == 0)
        return;
    vector<vector<int> > atoms(numTorsions, vector<int>(4));
    params = new CudaParameterSet(cu, force.getNumPerTorsionParameters(), numTorsions, "customTorsionParams");
    vector<vector<float> > paramVector(numTorsions);
    for (int i = 0; i < numTorsions; i++) {
        vector<double> parameters;
        force.getTorsionParameters(startIndex+i, atoms[i][0], atoms[i][1], atoms[i][2], atoms[i][3], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
1313
1314
    info = new ForceInfo(force);
    cu.addForce(info);
1315
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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] = (float) force.getGlobalParameterDefaultValue(i);
    }
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction()).optimize();
    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("theta").optimize();
    map<string, Lepton::ParsedExpression> expressions;
    expressions["energy += "] = energyExpression;
    expressions["float dEdAngle = "] = forceExpression;

    // Create the kernels.

    map<string, string> variables;
    variables["theta"] = "theta";
    for (int i = 0; i < force.getNumPerTorsionParameters(); i++) {
        const string& name = force.getPerTorsionParameterName(i);
        variables[name] = "torsionParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
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        globals.initialize<float>(cu, force.getNumGlobalParameters(), "customTorsionGlobals");
        globals.upload(globalParamValues);
        string argName = cu.getBondedUtilities().addArgument(globals.getDevicePointer(), "float");
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        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+cu.intToString(i)+"]";
            variables[name] = value;
        }
    }
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cu.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++) {
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        CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cu.getBondedUtilities().addArgument(buffer.getMemory(), buffer.getType());
        compute<<buffer.getType()<<" torsionParams"<<(i+1)<<" = "<<argName<<"[index];\n";
    }
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    vector<const TabulatedFunction*> functions;
    vector<pair<string, string> > functionNames;
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    compute << cu.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();
    cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::torsionForce, replacements), force.getForceGroup());
}

double CudaCalcCustomTorsionForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (globals.isInitialized()) {
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        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)
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            globals.upload(globalParamValues);
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    }
    return 0.0;
}

void CudaCalcCustomTorsionForceKernel::copyParametersToContext(ContextImpl& context, const CustomTorsionForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumTorsions()/numContexts;
    int endIndex = (cu.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<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] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

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

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class CudaCalcNonbondedForceKernel::PmeIO : public CalcPmeReciprocalForceKernel::IO {
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    PmeIO(CudaContext& cu, CUfunction addForcesKernel) : cu(cu), addForcesKernel(addForcesKernel) {
        forceTemp.initialize<float4>(cu, cu.getNumAtoms(), "PmeForce");
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    }
    float* getPosq() {
        cu.setAsCurrent();
        cu.getPosq().download(posq);
        return (float*) &posq[0];
    }
    void setForce(float* force) {
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        forceTemp.upload(force);
        void* args[] = {&forceTemp.getDevicePointer(), &cu.getForce().getDevicePointer()};
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        cu.executeKernel(addForcesKernel, args, cu.getNumAtoms());
    }
private:
    CudaContext& cu;
    vector<float4> posq;
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    CudaArray forceTemp;
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    CUfunction addForcesKernel;
};

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

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

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class CudaCalcNonbondedForceKernel::SyncStreamPreComputation : public CudaContext::ForcePreComputation {
public:
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    SyncStreamPreComputation(CudaContext& cu, CUstream stream, CUevent event, int forceGroup) : cu(cu), stream(stream), event(event), 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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            cuEventRecord(event, cu.getCurrentStream());
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            cuStreamWaitEvent(stream, event, 0);
        }
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    }
private:
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    CudaContext& cu;
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    CUstream stream;
    CUevent event;
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    int forceGroup;
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};

class CudaCalcNonbondedForceKernel::SyncStreamPostComputation : public CudaContext::ForcePostComputation {
public:
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    SyncStreamPostComputation(CudaContext& cu, CUevent event, CUfunction addEnergyKernel, CudaArray& pmeEnergyBuffer, int forceGroup) : cu(cu), event(event),
            addEnergyKernel(addEnergyKernel), pmeEnergyBuffer(pmeEnergyBuffer), forceGroup(forceGroup) {
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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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            cuStreamWaitEvent(cu.getCurrentStream(), event, 0);
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            if (includeEnergy) {
                int bufferSize = pmeEnergyBuffer.getSize();
                void* args[] = {&pmeEnergyBuffer.getDevicePointer(), &cu.getEnergyBuffer().getDevicePointer(), &bufferSize};
                cu.executeKernel(addEnergyKernel, args, bufferSize);
            }
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        }
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        return 0.0;
    }
private:
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    CudaContext& cu;
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    CUevent event;
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    CUfunction addEnergyKernel;
    CudaArray& pmeEnergyBuffer;
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    int forceGroup;
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};

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CudaCalcNonbondedForceKernel::~CudaCalcNonbondedForceKernel() {
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    cu.setAsCurrent();
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    if (sort != NULL)
        delete sort;
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    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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    if (hasInitializedFFT) {
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        if (useCudaFFT) {
            cufftDestroy(fftForward);
            cufftDestroy(fftBackward);
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            if (doLJPME) {
                cufftDestroy(dispersionFftForward);
                cufftDestroy(dispersionFftBackward);                
            }
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        }
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        if (usePmeStream) {
            cuStreamDestroy(pmeStream);
            cuEventDestroy(pmeSyncEvent);
        }
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    }
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}

void CudaCalcNonbondedForceKernel::initialize(const System& system, const NonbondedForce& force) {
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    cu.setAsCurrent();
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    int forceIndex;
    for (forceIndex = 0; forceIndex < system.getNumForces() && &system.getForce(forceIndex) != &force; ++forceIndex)
        ;
    string prefix = "nonbonded"+cu.intToString(forceIndex)+"_";
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    // 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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    vector<float4> baseParticleParamVec(cu.getPaddedNumAtoms(), make_float4(0, 0, 0, 0));
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    vector<vector<int> > exclusionList(numParticles);
    hasCoulomb = false;
    hasLJ = false;
    for (int i = 0; i < numParticles; i++) {
        double charge, sigma, epsilon;
        force.getParticleParameters(i, charge, sigma, epsilon);
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        baseParticleParamVec[i] = make_float4(charge, sigma, epsilon, 0);
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        exclusionList[i].push_back(i);
        if (charge != 0.0)
            hasCoulomb = true;
        if (epsilon != 0.0)
            hasLJ = true;
    }
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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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    nonbondedMethod = CalcNonbondedForceKernel::NonbondedMethod(force.getNonbondedMethod());
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    bool useCutoff = (nonbondedMethod != NoCutoff);
    bool usePeriodic = (nonbondedMethod != NoCutoff && nonbondedMethod != CutoffNonPeriodic);
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    doLJPME = (nonbondedMethod == LJPME && hasLJ);
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    if (hasCoulomb)
        usePosqCharges = cu.requestPosqCharges();
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    map<string, string> defines;
    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) {
        // Compute the reaction field constants.

        double reactionFieldK = pow(force.getCutoffDistance(), -3.0)*(force.getReactionFieldDielectric()-1.0)/(2.0*force.getReactionFieldDielectric()+1.0);
        double reactionFieldC = (1.0 / force.getCutoffDistance())*(3.0*force.getReactionFieldDielectric())/(2.0*force.getReactionFieldDielectric()+1.0);
        defines["REACTION_FIELD_K"] = cu.doubleToString(reactionFieldK);
        defines["REACTION_FIELD_C"] = cu.doubleToString(reactionFieldC);
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        // Compute the switching coefficients.
        
        if (force.getUseSwitchingFunction()) {
            defines["LJ_SWITCH_CUTOFF"] = cu.doubleToString(force.getSwitchingDistance());
            defines["LJ_SWITCH_C3"] = cu.doubleToString(10/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 3.0));
            defines["LJ_SWITCH_C4"] = cu.doubleToString(15/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 4.0));
            defines["LJ_SWITCH_C5"] = cu.doubleToString(6/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 5.0));
        }
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    }
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    if (force.getUseDispersionCorrection() && cu.getContextIndex() == 0 && !doLJPME)
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        dispersionCoefficient = NonbondedForceImpl::calcDispersionCorrection(system, force);
    else
        dispersionCoefficient = 0.0;
    alpha = 0;
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    ewaldSelfEnergy = 0.0;
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    map<string, string> paramsDefines;
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    hasOffsets = (force.getNumParticleParameterOffsets() > 0 || force.getNumExceptionParameterOffsets() > 0);
    if (hasOffsets)
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        paramsDefines["HAS_OFFSETS"] = "1";
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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);
        defines["EWALD_ALPHA"] = cu.doubleToString(alpha);
        defines["TWO_OVER_SQRT_PI"] = cu.doubleToString(2.0/sqrt(M_PI));
        defines["USE_EWALD"] = "1";
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        if (cu.getContextIndex() == 0) {
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            paramsDefines["INCLUDE_EWALD"] = "1";
            paramsDefines["EWALD_SELF_ENERGY_SCALE"] = cu.doubleToString(ONE_4PI_EPS0*alpha/sqrt(M_PI));
            for (int i = 0; i < numParticles; i++)
                ewaldSelfEnergy += baseParticleParamVec[i].x*baseParticleParamVec[i].x*ONE_4PI_EPS0*alpha/sqrt(M_PI);
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            // Create the reciprocal space kernels.

            map<string, string> replacements;
            replacements["NUM_ATOMS"] = cu.intToString(numParticles);
            replacements["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
            replacements["KMAX_X"] = cu.intToString(kmaxx);
            replacements["KMAX_Y"] = cu.intToString(kmaxy);
            replacements["KMAX_Z"] = cu.intToString(kmaxz);
            replacements["EXP_COEFFICIENT"] = cu.doubleToString(-1.0/(4.0*alpha*alpha));
            replacements["ONE_4PI_EPS0"] = cu.doubleToString(ONE_4PI_EPS0);
            replacements["M_PI"] = cu.doubleToString(M_PI);
            CUmodule module = cu.createModule(CudaKernelSources::vectorOps+CudaKernelSources::ewald, replacements);
            ewaldSumsKernel = cu.getKernel(module, "calculateEwaldCosSinSums");
            ewaldForcesKernel = cu.getKernel(module, "calculateEwaldForces");
            int elementSize = (cu.getUseDoublePrecision() ? sizeof(double2) : sizeof(float2));
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            cosSinSums.initialize(cu, (2*kmaxx-1)*(2*kmaxy-1)*(2*kmaxz-1), elementSize, "cosSinSums");
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        }
    }
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    else if (((nonbondedMethod == PME || nonbondedMethod == LJPME) && hasCoulomb) || doLJPME) {
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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 = CudaFFT3D::findLegalDimension(gridSizeX);
        gridSizeY = CudaFFT3D::findLegalDimension(gridSizeY);
        gridSizeZ = CudaFFT3D::findLegalDimension(gridSizeZ);
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        if (doLJPME) {
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            NonbondedForceImpl::calcPMEParameters(system, force, dispersionAlpha, dispersionGridSizeX,
                                                  dispersionGridSizeY, dispersionGridSizeZ, true);
            dispersionGridSizeX = CudaFFT3D::findLegalDimension(dispersionGridSizeX);
            dispersionGridSizeY = CudaFFT3D::findLegalDimension(dispersionGridSizeY);
            dispersionGridSizeZ = CudaFFT3D::findLegalDimension(dispersionGridSizeZ);
        }
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        defines["EWALD_ALPHA"] = cu.doubleToString(alpha);
        defines["TWO_OVER_SQRT_PI"] = cu.doubleToString(2.0/sqrt(M_PI));
        defines["USE_EWALD"] = "1";
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        defines["DO_LJPME"] = doLJPME ? "1" : "0";
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        if (doLJPME)
            defines["EWALD_DISPERSION_ALPHA"] = cu.doubleToString(dispersionAlpha);
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        if (cu.getContextIndex() == 0) {
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            paramsDefines["INCLUDE_EWALD"] = "1";
            paramsDefines["EWALD_SELF_ENERGY_SCALE"] = cu.doubleToString(ONE_4PI_EPS0*alpha/sqrt(M_PI));
            for (int i = 0; i < numParticles; i++)
                ewaldSelfEnergy -= baseParticleParamVec[i].x*baseParticleParamVec[i].x*ONE_4PI_EPS0*alpha/sqrt(M_PI);
            if (doLJPME) {
                paramsDefines["INCLUDE_LJPME"] = "1";
                paramsDefines["LJPME_SELF_ENERGY_SCALE"] = cu.doubleToString(pow(dispersionAlpha, 6)/3.0);
                for (int i = 0; i < numParticles; i++)
                    ewaldSelfEnergy += baseParticleParamVec[i].z*pow(baseParticleParamVec[i].y*dispersionAlpha, 6)/3.0;
            }
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            char deviceName[100];
            cuDeviceGetName(deviceName, 100, cu.getDevice());
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            usePmeStream = (!cu.getPlatformData().disablePmeStream && string(deviceName) != "GeForce GTX 980"); // Using a separate stream is slower on GTX 980
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            map<string, string> pmeDefines;
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            pmeDefines["PME_ORDER"] = cu.intToString(PmeOrder);
            pmeDefines["NUM_ATOMS"] = cu.intToString(numParticles);
            pmeDefines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
            pmeDefines["RECIP_EXP_FACTOR"] = cu.doubleToString(M_PI*M_PI/(alpha*alpha));
            pmeDefines["GRID_SIZE_X"] = cu.intToString(gridSizeX);
            pmeDefines["GRID_SIZE_Y"] = cu.intToString(gridSizeY);
            pmeDefines["GRID_SIZE_Z"] = cu.intToString(gridSizeZ);
            pmeDefines["EPSILON_FACTOR"] = cu.doubleToString(sqrt(ONE_4PI_EPS0));
            pmeDefines["M_PI"] = cu.doubleToString(M_PI);
            if (cu.getUseDoublePrecision())
                pmeDefines["USE_DOUBLE_PRECISION"] = "1";
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            if (usePmeStream)
                pmeDefines["USE_PME_STREAM"] = "1";
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            if (cu.getPlatformData().deterministicForces)
                pmeDefines["USE_DETERMINISTIC_FORCES"] = "1";
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            map<string, string> replacements;
            replacements["CHARGE"] = (usePosqCharges ? "pos.w" : "charges[atom]");
            CUmodule module = cu.createModule(CudaKernelSources::vectorOps+cu.replaceStrings(CudaKernelSources::pme, replacements), pmeDefines);
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            if (cu.getPlatformData().useCpuPme && !doLJPME && usePosqCharges) {
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                // Create the CPU PME kernel.

                try {
                    cpuPme = getPlatform().createKernel(CalcPmeReciprocalForceKernel::Name(), *cu.getPlatformData().context);
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                    cpuPme.getAs<CalcPmeReciprocalForceKernel>().initialize(gridSizeX, gridSizeY, gridSizeZ, numParticles, alpha, cu.getPlatformData().deterministicForces);
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                    CUfunction addForcesKernel = cu.getKernel(module, "addForces");
                    pmeio = new PmeIO(cu, addForcesKernel);
                    cu.addPreComputation(new PmePreComputation(cu, cpuPme, *pmeio));
                    cu.addPostComputation(new PmePostComputation(cpuPme, *pmeio));
                }
                catch (OpenMMException& ex) {
                    // The CPU PME plugin isn't available.
                }
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            }
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            if (pmeio == NULL) {
                pmeGridIndexKernel = cu.getKernel(module, "findAtomGridIndex");
                pmeSpreadChargeKernel = cu.getKernel(module, "gridSpreadCharge");
                pmeConvolutionKernel = cu.getKernel(module, "reciprocalConvolution");
                pmeInterpolateForceKernel = cu.getKernel(module, "gridInterpolateForce");
                pmeEvalEnergyKernel = cu.getKernel(module, "gridEvaluateEnergy");
                pmeFinishSpreadChargeKernel = cu.getKernel(module, "finishSpreadCharge");
                cuFuncSetCacheConfig(pmeSpreadChargeKernel, CU_FUNC_CACHE_PREFER_L1);
                cuFuncSetCacheConfig(pmeInterpolateForceKernel, CU_FUNC_CACHE_PREFER_L1);
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                if (doLJPME) {
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                    pmeDefines["EWALD_ALPHA"] = cu.doubleToString(dispersionAlpha);
                    pmeDefines["GRID_SIZE_X"] = cu.intToString(dispersionGridSizeX);
                    pmeDefines["GRID_SIZE_Y"] = cu.intToString(dispersionGridSizeY);
                    pmeDefines["GRID_SIZE_Z"] = cu.intToString(dispersionGridSizeZ);
                    pmeDefines["EPSILON_FACTOR"] = "1";
                    pmeDefines["RECIP_EXP_FACTOR"] = cu.doubleToString(M_PI*M_PI/(dispersionAlpha*dispersionAlpha));
                    pmeDefines["USE_LJPME"] = "1";
                    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"] = cu.doubleToString(invRCut6);
                    defines["MULTSHIFT6"] = cu.doubleToString(multShift6);
                    module = cu.createModule(CudaKernelSources::vectorOps+CudaKernelSources::pme, pmeDefines);
                    pmeDispersionFinishSpreadChargeKernel = cu.getKernel(module, "finishSpreadCharge");
                    pmeDispersionGridIndexKernel = cu.getKernel(module, "findAtomGridIndex");
                    pmeDispersionSpreadChargeKernel = cu.getKernel(module, "gridSpreadCharge");
                    pmeDispersionConvolutionKernel = cu.getKernel(module, "reciprocalConvolution");
                    pmeEvalDispersionEnergyKernel = cu.getKernel(module, "gridEvaluateEnergy");
                    pmeInterpolateDispersionForceKernel = cu.getKernel(module, "gridInterpolateForce");
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                    cuFuncSetCacheConfig(pmeDispersionSpreadChargeKernel, CU_FUNC_CACHE_PREFER_L1);
                }
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                // Create required data structures.

                int elementSize = (cu.getUseDoublePrecision() ? sizeof(double) : sizeof(float));
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                int gridElements = gridSizeX*gridSizeY*gridSizeZ;
                if (doLJPME)
                    gridElements = max(gridElements, dispersionGridSizeX*dispersionGridSizeY*dispersionGridSizeZ);
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                directPmeGrid.initialize(cu, gridElements, cu.getComputeCapability() >= 2.0 ? 2*elementSize : 2*sizeof(long long), "originalPmeGrid");
                reciprocalPmeGrid.initialize(cu, gridElements, 2*elementSize, "reciprocalPmeGrid");
                cu.addAutoclearBuffer(directPmeGrid);
                pmeBsplineModuliX.initialize(cu, gridSizeX, elementSize, "pmeBsplineModuliX");
                pmeBsplineModuliY.initialize(cu, gridSizeY, elementSize, "pmeBsplineModuliY");
                pmeBsplineModuliZ.initialize(cu, gridSizeZ, elementSize, "pmeBsplineModuliZ");
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                if (doLJPME) {
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                    pmeDispersionBsplineModuliX.initialize(cu, dispersionGridSizeX, elementSize, "pmeDispersionBsplineModuliX");
                    pmeDispersionBsplineModuliY.initialize(cu, dispersionGridSizeY, elementSize, "pmeDispersionBsplineModuliY");
                    pmeDispersionBsplineModuliZ.initialize(cu, dispersionGridSizeZ, elementSize, "pmeDispersionBsplineModuliZ");
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                }
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                pmeAtomRange.initialize<int>(cu, gridSizeX*gridSizeY*gridSizeZ+1, "pmeAtomRange");
                pmeAtomGridIndex.initialize<int2>(cu, numParticles, "pmeAtomGridIndex");
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                int energyElementSize = (cu.getUseDoublePrecision() || cu.getUseMixedPrecision() ? sizeof(double) : sizeof(float));
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                pmeEnergyBuffer.initialize(cu, cu.getNumThreadBlocks()*CudaContext::ThreadBlockSize, energyElementSize, "pmeEnergyBuffer");
                cu.clearBuffer(pmeEnergyBuffer);
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                sort = new CudaSort(cu, new SortTrait(), cu.getNumAtoms());
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                int cufftVersion;
                cufftGetVersion(&cufftVersion);
                useCudaFFT = (cufftVersion >= 7050); // There was a critical bug in version 7.0
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                if (useCudaFFT) {
                    cufftResult result = cufftPlan3d(&fftForward, gridSizeX, gridSizeY, gridSizeZ, cu.getUseDoublePrecision() ? CUFFT_D2Z : CUFFT_R2C);
                    if (result != CUFFT_SUCCESS)
                        throw OpenMMException("Error initializing FFT: "+cu.intToString(result));
                    result = cufftPlan3d(&fftBackward, gridSizeX, gridSizeY, gridSizeZ, cu.getUseDoublePrecision() ? CUFFT_Z2D : CUFFT_C2R);
                    if (result != CUFFT_SUCCESS)
                        throw OpenMMException("Error initializing FFT: "+cu.intToString(result));
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                    if (doLJPME) {
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                        result = cufftPlan3d(&dispersionFftForward, dispersionGridSizeX, dispersionGridSizeY, 
                                                dispersionGridSizeZ, cu.getUseDoublePrecision() ? CUFFT_D2Z : CUFFT_R2C);
                        if (result != CUFFT_SUCCESS)
                            throw OpenMMException("Error initializing disperison FFT: "+cu.intToString(result));
                        result = cufftPlan3d(&dispersionFftBackward, dispersionGridSizeX, dispersionGridSizeY,
                                             dispersionGridSizeZ, cu.getUseDoublePrecision() ? CUFFT_Z2D : CUFFT_C2R);
                        if (result != CUFFT_SUCCESS)
                            throw OpenMMException("Error initializing disperison FFT: "+cu.intToString(result));
                    }
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                }
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                else {
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                    fft = new CudaFFT3D(cu, gridSizeX, gridSizeY, gridSizeZ, true);
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                    if (doLJPME)
                        dispersionFft = new CudaFFT3D(cu, dispersionGridSizeX, dispersionGridSizeY, dispersionGridSizeZ, true);
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                }

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                // Prepare for doing PME on its own stream.
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                if (usePmeStream) {
                    cuStreamCreate(&pmeStream, CU_STREAM_NON_BLOCKING);
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                    if (useCudaFFT) {
                        cufftSetStream(fftForward, pmeStream);
                        cufftSetStream(fftBackward, pmeStream);
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                        cufftSetStream(dispersionFftForward, pmeStream);
                        cufftSetStream(dispersionFftBackward, pmeStream);
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                    }
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                    CHECK_RESULT(cuEventCreate(&pmeSyncEvent, CU_EVENT_DISABLE_TIMING), "Error creating event for NonbondedForce");
                    int recipForceGroup = force.getReciprocalSpaceForceGroup();
                    if (recipForceGroup < 0)
                        recipForceGroup = force.getForceGroup();
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                    cu.addPreComputation(new SyncStreamPreComputation(cu, pmeStream, pmeSyncEvent, recipForceGroup));
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                    cu.addPostComputation(new SyncStreamPostComputation(cu, pmeSyncEvent, cu.getKernel(module, "addEnergy"), pmeEnergyBuffer, recipForceGroup));
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                }
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                hasInitializedFFT = true;
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                // Initialize the b-spline moduli.

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                for (int grid = 0; grid < 2; grid++) {
                    int xsize, ysize, zsize;
                    CudaArray *xmoduli, *ymoduli, *zmoduli;
                    if (grid == 0) {
                        xsize = gridSizeX;
                        ysize = gridSizeY;
                        zsize = gridSizeZ;
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                        xmoduli = &pmeBsplineModuliX;
                        ymoduli = &pmeBsplineModuliY;
                        zmoduli = &pmeBsplineModuliZ;
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                    }
                    else {
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                        if (!doLJPME)
                            continue;
                        xsize = dispersionGridSizeX;
                        ysize = dispersionGridSizeY;
                        zsize = dispersionGridSizeZ;
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                        xmoduli = &pmeDispersionBsplineModuliX;
                        ymoduli = &pmeDispersionBsplineModuliY;
                        zmoduli = &pmeDispersionBsplineModuliZ;
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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];
                    }

                    // 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<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] = 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])*0.5;
                        if (cu.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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    // Add the interaction to the default nonbonded kernel.
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    string source = cu.replaceStrings(CudaKernelSources::coulombLennardJones, defines);
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    charges.initialize(cu, cu.getPaddedNumAtoms(), cu.getUseDoublePrecision() ? sizeof(double) : sizeof(float), "charges");
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    baseParticleParams.initialize<float4>(cu, cu.getPaddedNumAtoms(), "baseParticleParams");
    baseParticleParams.upload(baseParticleParamVec);
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    map<string, string> replacements;
    if (usePosqCharges) {
        replacements["CHARGE1"] = "posq1.w";
        replacements["CHARGE2"] = "posq2.w";
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        paramsDefines["USE_POSQ_CHARGES"] = "1";
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    }
    else {
        replacements["CHARGE1"] = prefix+"charge1";
        replacements["CHARGE2"] = prefix+"charge2";
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    }
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    if (hasCoulomb)
        cu.getNonbondedUtilities().addParameter(CudaNonbondedUtilities::ParameterInfo(prefix+"charge", "real", 1, charges.getElementSize(), charges.getDevicePointer()));
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    sigmaEpsilon.initialize<float2>(cu, cu.getPaddedNumAtoms(), "sigmaEpsilon");
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    if (hasLJ) {
        replacements["SIGMA_EPSILON1"] = prefix+"sigmaEpsilon1";
        replacements["SIGMA_EPSILON2"] = prefix+"sigmaEpsilon2";
        cu.getNonbondedUtilities().addParameter(CudaNonbondedUtilities::ParameterInfo(prefix+"sigmaEpsilon", "float", 2, sizeof(float2), sigmaEpsilon.getDevicePointer()));
    }
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    source = cu.replaceStrings(source, replacements);
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    cu.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source, force.getForceGroup(), true);
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    // Initialize the exceptions.

    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*exceptions.size()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*exceptions.size()/numContexts;
    int numExceptions = endIndex-startIndex;
    if (numExceptions > 0) {
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        paramsDefines["HAS_EXCEPTIONS"] = "1";
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        exceptionAtoms.resize(numExceptions);
        vector<vector<int> > atoms(numExceptions, vector<int>(2));
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        exceptionParams.initialize<float4>(cu, numExceptions, "exceptionParams");
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        baseExceptionParams.initialize<float4>(cu, numExceptions, "baseExceptionParams");
        vector<float4> baseExceptionParamsVec(numExceptions);
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        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);
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            baseExceptionParamsVec[i] = make_float4(chargeProd, sigma, epsilon, 0);
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            exceptionAtoms[i] = make_pair(atoms[i][0], atoms[i][1]);
        }
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        baseExceptionParams.upload(baseExceptionParamsVec);
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        map<string, string> replacements;
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        replacements["PARAMS"] = cu.getBondedUtilities().addArgument(exceptionParams.getDevicePointer(), "float4");
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        cu.getBondedUtilities().addInteraction(atoms, cu.replaceStrings(CudaKernelSources::nonbondedExceptions, replacements), force.getForceGroup());
    }
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    // Initialize parameter offsets.

    vector<vector<float4> > particleOffsetVec(force.getNumParticles());
    vector<vector<float4> > exceptionOffsetVec(force.getNumExceptions());
    for (int i = 0; i < force.getNumParticleParameterOffsets(); i++) {
        string param;
        int particle;
        double charge, sigma, epsilon;
        force.getParticleParameterOffset(i, param, particle, charge, sigma, epsilon);
        auto paramPos = find(paramNames.begin(), paramNames.end(), param);
        int paramIndex;
        if (paramPos == paramNames.end()) {
            paramIndex = paramNames.size();
            paramNames.push_back(param);
        }
        else
            paramIndex = paramPos-paramNames.begin();
        particleOffsetVec[particle].push_back(make_float4(charge, sigma, epsilon, paramIndex));
    }
    for (int i = 0; i < force.getNumExceptionParameterOffsets(); i++) {
        string param;
        int exception;
        double charge, sigma, epsilon;
        force.getExceptionParameterOffset(i, param, exception, charge, sigma, epsilon);
        auto paramPos = find(paramNames.begin(), paramNames.end(), param);
        int paramIndex;
        if (paramPos == paramNames.end()) {
            paramIndex = paramNames.size();
            paramNames.push_back(param);
        }
        else
            paramIndex = paramPos-paramNames.begin();
        exceptionOffsetVec[exception].push_back(make_float4(charge, sigma, epsilon, paramIndex));
    }
    paramValues.resize(paramNames.size(), 0.0);
    particleParamOffsets.initialize<float4>(cu, max(force.getNumParticleParameterOffsets(), 1), "particleParamOffsets");
    exceptionParamOffsets.initialize<float4>(cu, max(force.getNumExceptionParameterOffsets(), 1), "exceptionParamOffsets");
    particleOffsetIndices.initialize<int>(cu, force.getNumParticles()+1, "particleOffsetIndices");
    exceptionOffsetIndices.initialize<int>(cu, force.getNumExceptions()+1, "exceptionOffsetIndices");
    vector<int> particleOffsetIndicesVec, exceptionOffsetIndicesVec;
    vector<float4> p, e;
    for (int i = 0; i < particleOffsetVec.size(); i++) {
        particleOffsetIndicesVec.push_back(p.size());
        for (int j = 0; j < particleOffsetVec[i].size(); j++)
            p.push_back(particleOffsetVec[i][j]);
    }
    particleOffsetIndicesVec.push_back(p.size());
    for (int i = 0; i < exceptionOffsetVec.size(); i++) {
        exceptionOffsetIndicesVec.push_back(e.size());
        for (int j = 0; j < exceptionOffsetVec[i].size(); j++)
            e.push_back(exceptionOffsetVec[i][j]);
    }
    exceptionOffsetIndicesVec.push_back(e.size());
    if (force.getNumParticleParameterOffsets() > 0) {
        particleParamOffsets.upload(p);
        particleOffsetIndices.upload(particleOffsetIndicesVec);
    }
    if (force.getNumExceptionParameterOffsets() > 0) {
        exceptionParamOffsets.upload(e);
        exceptionOffsetIndices.upload(exceptionOffsetIndicesVec);
    }
    globalParams.initialize(cu, max((int) paramValues.size(), 1), cu.getUseDoublePrecision() ? sizeof(double) : sizeof(float), "globalParams");
    recomputeParams = true;
    
    // Initialize the kernel for updating parameters.
    
    CUmodule module = cu.createModule(CudaKernelSources::nonbondedParameters, paramsDefines);
    computeParamsKernel = cu.getKernel(module, "computeParameters");
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    info = new ForceInfo(force);
    cu.addForce(info);
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}

double CudaCalcNonbondedForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy, bool includeDirect, bool includeReciprocal) {
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    // Update particle and exception parameters.

    bool paramChanged = false;
    for (int i = 0; i < paramNames.size(); i++) {
        double value = context.getParameter(paramNames[i]);
        if (value != paramValues[i]) {
            paramValues[i] = value;;
            paramChanged = true;
        }
    }
    if (paramChanged) {
        recomputeParams = true;
        if (cu.getUseDoublePrecision())
            globalParams.upload(paramValues);
        else {
            vector<float> v(paramValues.size());
            for (int i = 0; i < v.size(); i++)
                v[i] = paramValues[i];
            globalParams.upload(v);
        }
    }
    double energy = (includeReciprocal ? ewaldSelfEnergy : 0.0);
    if (recomputeParams || hasOffsets) {
        bool computeSelfEnergy = (includeEnergy && includeReciprocal);
        int numAtoms = cu.getPaddedNumAtoms();
        vector<void*> paramsArgs = {&cu.getEnergyBuffer().getDevicePointer(), &computeSelfEnergy, &globalParams.getDevicePointer(), &numAtoms,
                &baseParticleParams.getDevicePointer(), &cu.getPosq().getDevicePointer(), &charges.getDevicePointer(), &sigmaEpsilon.getDevicePointer(),
                &particleParamOffsets.getDevicePointer(), &particleOffsetIndices.getDevicePointer()};
        if (exceptionParams.isInitialized()) {
            int numExceptions = exceptionParams.getSize();
            paramsArgs.push_back(&numExceptions);
            paramsArgs.push_back(&baseExceptionParams.getDevicePointer());
            paramsArgs.push_back(&exceptionParams.getDevicePointer());
            paramsArgs.push_back(&exceptionParamOffsets.getDevicePointer());
            paramsArgs.push_back(&exceptionOffsetIndices.getDevicePointer());
        }
        cu.executeKernel(computeParamsKernel, &paramsArgs[0], cu.getPaddedNumAtoms());
        if (usePmeStream) {
            cuEventRecord(pmeSyncEvent, cu.getCurrentStream());
            cuStreamWaitEvent(pmeStream, pmeSyncEvent, 0);
        }
        energy = 0.0; // The Ewald self energy was computed in the kernel.
        recomputeParams = false;
    }
    
    // Do reciprocal space calculations.
    
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    if (cosSinSums.isInitialized() && includeReciprocal) {
        void* sumsArgs[] = {&cu.getEnergyBuffer().getDevicePointer(), &cu.getPosq().getDevicePointer(), &cosSinSums.getDevicePointer(), cu.getPeriodicBoxSizePointer()};
        cu.executeKernel(ewaldSumsKernel, sumsArgs, cosSinSums.getSize());
        void* forcesArgs[] = {&cu.getForce().getDevicePointer(), &cu.getPosq().getDevicePointer(), &cosSinSums.getDevicePointer(), cu.getPeriodicBoxSizePointer()};
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        cu.executeKernel(ewaldForcesKernel, forcesArgs, cu.getNumAtoms());
    }
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    if (directPmeGrid.isInitialized() && includeReciprocal) {
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        if (usePmeStream)
            cu.setCurrentStream(pmeStream);
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        // Invert the periodic box vectors.
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        Vec3 boxVectors[3];
        cu.getPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
        double determinant = boxVectors[0][0]*boxVectors[1][1]*boxVectors[2][2];
        double scale = 1.0/determinant;
        double3 recipBoxVectors[3];
        recipBoxVectors[0] = make_double3(boxVectors[1][1]*boxVectors[2][2]*scale, 0, 0);
        recipBoxVectors[1] = make_double3(-boxVectors[1][0]*boxVectors[2][2]*scale, boxVectors[0][0]*boxVectors[2][2]*scale, 0);
        recipBoxVectors[2] = make_double3((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);
        float3 recipBoxVectorsFloat[3];
        void* recipBoxVectorPointer[3];
        if (cu.getUseDoublePrecision()) {
            recipBoxVectorPointer[0] = &recipBoxVectors[0];
            recipBoxVectorPointer[1] = &recipBoxVectors[1];
            recipBoxVectorPointer[2] = &recipBoxVectors[2];
        }
        else {
            recipBoxVectorsFloat[0] = make_float3((float) recipBoxVectors[0].x, 0, 0);
            recipBoxVectorsFloat[1] = make_float3((float) recipBoxVectors[1].x, (float) recipBoxVectors[1].y, 0);
            recipBoxVectorsFloat[2] = make_float3((float) recipBoxVectors[2].x, (float) recipBoxVectors[2].y, (float) recipBoxVectors[2].z);
            recipBoxVectorPointer[0] = &recipBoxVectorsFloat[0];
            recipBoxVectorPointer[1] = &recipBoxVectorsFloat[1];
            recipBoxVectorPointer[2] = &recipBoxVectorsFloat[2];
        }
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        // Execute the reciprocal space kernels.

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        if (hasCoulomb) {
            void* gridIndexArgs[] = {&cu.getPosq().getDevicePointer(), &pmeAtomGridIndex.getDevicePointer(), cu.getPeriodicBoxSizePointer(),
                    cu.getInvPeriodicBoxSizePointer(), cu.getPeriodicBoxVecXPointer(), cu.getPeriodicBoxVecYPointer(), cu.getPeriodicBoxVecZPointer(),
                    recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2]};
            cu.executeKernel(pmeGridIndexKernel, gridIndexArgs, cu.getNumAtoms());
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            sort->sort(pmeAtomGridIndex);
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            void* spreadArgs[] = {&cu.getPosq().getDevicePointer(), &directPmeGrid.getDevicePointer(), cu.getPeriodicBoxSizePointer(),
                    cu.getInvPeriodicBoxSizePointer(), cu.getPeriodicBoxVecXPointer(), cu.getPeriodicBoxVecYPointer(), cu.getPeriodicBoxVecZPointer(),
                    recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2], &pmeAtomGridIndex.getDevicePointer(),
                    &charges.getDevicePointer()};
            cu.executeKernel(pmeSpreadChargeKernel, spreadArgs, cu.getNumAtoms(), 128);
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            if (cu.getUseDoublePrecision() || cu.getComputeCapability() < 2.0 || cu.getPlatformData().deterministicForces) {
                void* finishSpreadArgs[] = {&directPmeGrid.getDevicePointer()};
                cu.executeKernel(pmeFinishSpreadChargeKernel, finishSpreadArgs, gridSizeX*gridSizeY*gridSizeZ, 256);
            }
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            if (useCudaFFT) {
                if (cu.getUseDoublePrecision())
                    cufftExecD2Z(fftForward, (double*) directPmeGrid.getDevicePointer(), (double2*) reciprocalPmeGrid.getDevicePointer());
                else
                    cufftExecR2C(fftForward, (float*) directPmeGrid.getDevicePointer(), (float2*) reciprocalPmeGrid.getDevicePointer());
            }
            else {
                fft->execFFT(directPmeGrid, reciprocalPmeGrid, true);
            }
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            if (includeEnergy) {
                void* computeEnergyArgs[] = {&reciprocalPmeGrid.getDevicePointer(), usePmeStream ? &pmeEnergyBuffer.getDevicePointer() : &cu.getEnergyBuffer().getDevicePointer(),
                        &pmeBsplineModuliX.getDevicePointer(), &pmeBsplineModuliY.getDevicePointer(), &pmeBsplineModuliZ.getDevicePointer(),
                        cu.getPeriodicBoxSizePointer(), recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2]};
                cu.executeKernel(pmeEvalEnergyKernel, computeEnergyArgs, gridSizeX*gridSizeY*gridSizeZ);
            }

            void* convolutionArgs[] = {&reciprocalPmeGrid.getDevicePointer(), &cu.getEnergyBuffer().getDevicePointer(),
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                    &pmeBsplineModuliX.getDevicePointer(), &pmeBsplineModuliY.getDevicePointer(), &pmeBsplineModuliZ.getDevicePointer(),
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                    cu.getPeriodicBoxSizePointer(), recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2]};
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            cu.executeKernel(pmeConvolutionKernel, convolutionArgs, gridSizeX*gridSizeY*gridSizeZ, 256);
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            if (useCudaFFT) {
                if (cu.getUseDoublePrecision())
                    cufftExecZ2D(fftBackward, (double2*) reciprocalPmeGrid.getDevicePointer(), (double*) directPmeGrid.getDevicePointer());
                else
                    cufftExecC2R(fftBackward, (float2*) reciprocalPmeGrid.getDevicePointer(), (float*)  directPmeGrid.getDevicePointer());
            }
            else {
                fft->execFFT(reciprocalPmeGrid, directPmeGrid, false);
            }
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            void* interpolateArgs[] = {&cu.getPosq().getDevicePointer(), &cu.getForce().getDevicePointer(), &directPmeGrid.getDevicePointer(), cu.getPeriodicBoxSizePointer(),
                    cu.getInvPeriodicBoxSizePointer(), cu.getPeriodicBoxVecXPointer(), cu.getPeriodicBoxVecYPointer(), cu.getPeriodicBoxVecZPointer(),
                    recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2], &pmeAtomGridIndex.getDevicePointer(),
                    &charges.getDevicePointer()};
            cu.executeKernel(pmeInterpolateForceKernel, interpolateArgs, cu.getNumAtoms(), 128);
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        }
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        // As written, we check only the Electrostatic grid pointer to get here.  We could separate them out, but for
        // now we assume that LJPME can only be used if electrostatic PME is also active.
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        if (doLJPME && hasLJ) {
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            void* gridIndexArgs[] = {&cu.getPosq().getDevicePointer(), &pmeAtomGridIndex.getDevicePointer(), cu.getPeriodicBoxSizePointer(),
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                    cu.getInvPeriodicBoxSizePointer(), cu.getPeriodicBoxVecXPointer(), cu.getPeriodicBoxVecYPointer(), cu.getPeriodicBoxVecZPointer(),
                    recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2]};
            cu.executeKernel(pmeDispersionGridIndexKernel, gridIndexArgs, cu.getNumAtoms());

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            sort->sort(pmeAtomGridIndex);
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            cu.clearBuffer(directPmeGrid);
            void* spreadArgs[] = {&cu.getPosq().getDevicePointer(), &directPmeGrid.getDevicePointer(), cu.getPeriodicBoxSizePointer(),
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                    cu.getInvPeriodicBoxSizePointer(), cu.getPeriodicBoxVecXPointer(), cu.getPeriodicBoxVecYPointer(), cu.getPeriodicBoxVecZPointer(),
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                    recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2], &pmeAtomGridIndex.getDevicePointer(),
                    &sigmaEpsilon.getDevicePointer()};
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            cu.executeKernel(pmeDispersionSpreadChargeKernel, spreadArgs, cu.getNumAtoms(), 128);

            if (cu.getUseDoublePrecision() || cu.getComputeCapability() < 2.0 || cu.getPlatformData().deterministicForces) {
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                void* finishSpreadArgs[] = {&directPmeGrid.getDevicePointer()};
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                cu.executeKernel(pmeDispersionFinishSpreadChargeKernel, finishSpreadArgs, dispersionGridSizeX*dispersionGridSizeY*dispersionGridSizeZ, 256);
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            }

            if (useCudaFFT) {
                if (cu.getUseDoublePrecision())
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                    cufftExecD2Z(dispersionFftForward, (double*) directPmeGrid.getDevicePointer(), (double2*) reciprocalPmeGrid.getDevicePointer());
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                else
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                    cufftExecR2C(dispersionFftForward, (float*) directPmeGrid.getDevicePointer(), (float2*) reciprocalPmeGrid.getDevicePointer());
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            }
            else {
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                dispersionFft->execFFT(directPmeGrid, reciprocalPmeGrid, true);
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            }

            if (includeEnergy) {
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                void* computeEnergyArgs[] = {&reciprocalPmeGrid.getDevicePointer(), usePmeStream ? &pmeEnergyBuffer.getDevicePointer() : &cu.getEnergyBuffer().getDevicePointer(),
                        &pmeDispersionBsplineModuliX.getDevicePointer(), &pmeDispersionBsplineModuliY.getDevicePointer(), &pmeDispersionBsplineModuliZ.getDevicePointer(),
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                        cu.getPeriodicBoxSizePointer(), recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2]};
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                cu.executeKernel(pmeEvalDispersionEnergyKernel, computeEnergyArgs, dispersionGridSizeX*dispersionGridSizeY*dispersionGridSizeZ);
            }

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            void* convolutionArgs[] = {&reciprocalPmeGrid.getDevicePointer(), &cu.getEnergyBuffer().getDevicePointer(),
                    &pmeDispersionBsplineModuliX.getDevicePointer(), &pmeDispersionBsplineModuliY.getDevicePointer(), &pmeDispersionBsplineModuliZ.getDevicePointer(),
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                    cu.getPeriodicBoxSizePointer(), recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2]};
            cu.executeKernel(pmeDispersionConvolutionKernel, convolutionArgs, dispersionGridSizeX*dispersionGridSizeY*dispersionGridSizeZ, 256);

            if (useCudaFFT) {
                if (cu.getUseDoublePrecision())
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                    cufftExecZ2D(dispersionFftBackward, (double2*) reciprocalPmeGrid.getDevicePointer(), (double*) directPmeGrid.getDevicePointer());
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                else
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                    cufftExecC2R(dispersionFftBackward, (float2*) reciprocalPmeGrid.getDevicePointer(), (float*)  directPmeGrid.getDevicePointer());
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            }
            else {
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                dispersionFft->execFFT(reciprocalPmeGrid, directPmeGrid, false);
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            }

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            void* interpolateArgs[] = {&cu.getPosq().getDevicePointer(), &cu.getForce().getDevicePointer(), &directPmeGrid.getDevicePointer(), cu.getPeriodicBoxSizePointer(),
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                    cu.getInvPeriodicBoxSizePointer(), cu.getPeriodicBoxVecXPointer(), cu.getPeriodicBoxVecYPointer(), cu.getPeriodicBoxVecZPointer(),
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                    recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2], &pmeAtomGridIndex.getDevicePointer(),
                    &sigmaEpsilon.getDevicePointer()};
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            cu.executeKernel(pmeInterpolateDispersionForceKernel, interpolateArgs, cu.getNumAtoms(), 128);
        }
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        if (usePmeStream) {
            cuEventRecord(pmeSyncEvent, pmeStream);
            cu.restoreDefaultStream();
        }
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    }
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    if (dispersionCoefficient != 0.0 && includeDirect) {
        double4 boxSize = cu.getPeriodicBoxSize();
        energy += dispersionCoefficient/(boxSize.x*boxSize.y*boxSize.z);
    }
    return energy;
}

void CudaCalcNonbondedForceKernel::copyParametersToContext(ContextImpl& context, const NonbondedForce& force) {
    // Make sure the new parameters are acceptable.
    
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    cu.setAsCurrent();
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    if (force.getNumParticles() != cu.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);
        if (exceptionAtoms.size() > exceptions.size() && make_pair(particle1, particle2) == exceptionAtoms[exceptions.size()])
            exceptions.push_back(i);
        else if (chargeProd != 0.0 || epsilon != 0.0)
            throw OpenMMException("updateParametersInContext: The set of non-excluded exceptions has changed");
    }
    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*exceptions.size()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*exceptions.size()/numContexts;
    int numExceptions = endIndex-startIndex;
    
    // Record the per-particle parameters.
    
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    vector<float4> baseParticleParamVec(cu.getPaddedNumAtoms(), make_float4(0, 0, 0, 0));
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    const vector<int>& order = cu.getAtomIndex();
    for (int i = 0; i < force.getNumParticles(); i++) {
        double charge, sigma, epsilon;
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        force.getParticleParameters(i, charge, sigma, epsilon);
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        baseParticleParamVec[i] = make_float4(charge, sigma, epsilon, 0);
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    }
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    baseParticleParams.upload(baseParticleParamVec);
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    // Record the exceptions.
    
    if (numExceptions > 0) {
        vector<vector<int> > atoms(numExceptions, vector<int>(2));
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        vector<float4> baseExceptionParamsVec(numExceptions);
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        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);
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            baseExceptionParamsVec[i] = make_float4(chargeProd, sigma, epsilon, 0);
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        }
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        baseExceptionParams.upload(baseExceptionParamsVec);
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    }
    
    // Compute other values.
    
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    ewaldSelfEnergy = 0.0;
    if (nonbondedMethod == Ewald || nonbondedMethod == PME || nonbondedMethod == LJPME) {
        for (int i = 0; i < force.getNumParticles(); i++) {
            ewaldSelfEnergy -= baseParticleParamVec[i].x*baseParticleParamVec[i].x*ONE_4PI_EPS0*alpha/sqrt(M_PI);
            if (doLJPME)
                ewaldSelfEnergy += baseParticleParamVec[i].z*pow(baseParticleParamVec[i].y*dispersionAlpha, 6)/3.0;
        }
    }
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    if (force.getUseDispersionCorrection() && cu.getContextIndex() == 0 && (nonbondedMethod == CutoffPeriodic || nonbondedMethod == Ewald || nonbondedMethod == PME))
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        dispersionCoefficient = NonbondedForceImpl::calcDispersionCorrection(context.getSystem(), force);
    cu.invalidateMolecules();
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    recomputeParams = true;
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}

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

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class CudaCalcCustomNonbondedForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const CustomNonbondedForce& force) : 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);
        for (int i = 0; i < (int) params1.size(); i++)
            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() {
        return force.getNumExclusions();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        int particle1, particle2;
        force.getExclusionParticles(index, particle1, particle2);
        particles.resize(2);
        particles[0] = particle1;
        particles[1] = particle2;
    }
    bool areGroupsIdentical(int group1, int group2) {
        return true;
    }
private:
    const CustomNonbondedForce& force;
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    vector<set<int> > groupsForParticle;
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};

CudaCalcCustomNonbondedForceKernel::~CudaCalcCustomNonbondedForceKernel() {
    cu.setAsCurrent();
    if (params != NULL)
        delete params;
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    if (forceCopy != NULL)
        delete forceCopy;
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}

void CudaCalcCustomNonbondedForceKernel::initialize(const System& system, const CustomNonbondedForce& force) {
    cu.setAsCurrent();
    int forceIndex;
    for (forceIndex = 0; forceIndex < system.getNumForces() && &system.getForce(forceIndex) != &force; ++forceIndex)
        ;
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    string prefix = (force.getNumInteractionGroups() == 0 ? "custom"+cu.intToString(forceIndex)+"_" : "");
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    // Record parameters and exclusions.

    int numParticles = force.getNumParticles();
    params = new CudaParameterSet(cu, force.getNumPerParticleParameters(), numParticles, "customNonbondedParameters");
    if (force.getNumGlobalParameters() > 0)
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        globals.initialize<float>(cu, force.getNumGlobalParameters(), "customNonbondedGlobals");
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    vector<vector<float> > paramVector(numParticles);
    vector<vector<int> > exclusionList(numParticles);
    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
        force.getParticleParameters(i, parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (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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    vector<string> tableTypes;
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    tabulatedFunctions.resize(force.getNumTabulatedFunctions());
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    for (int i = 0; i < force.getNumTabulatedFunctions(); i++) {
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        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
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        string arrayName = prefix+"table"+cu.intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
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        functions[name] = cu.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
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        int width;
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        vector<float> f = cu.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        tabulatedFunctions[i].initialize<float>(cu, f.size(), "TabulatedFunction");
        tabulatedFunctions[i].upload(f);
        cu.getNonbondedUtilities().addArgument(CudaNonbondedUtilities::ParameterInfo(arrayName, "float", width, width*sizeof(float), tabulatedFunctions[i].getDevicePointer()));
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        if (width == 1)
            tableTypes.push_back("float");
        else
            tableTypes.push_back("float"+cu.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] = (float) force.getGlobalParameterDefaultValue(i);
    }
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    if (globals.isInitialized())
        globals.upload(globalParamValues);
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    bool useCutoff = (force.getNonbondedMethod() != CustomNonbondedForce::NoCutoff);
    bool usePeriodic = (force.getNonbondedMethod() != CustomNonbondedForce::NoCutoff && force.getNonbondedMethod() != CustomNonbondedForce::CutoffNonPeriodic);
    Lepton::ParsedExpression energyExpression = Lepton::Parser::parse(force.getEnergyFunction(), functions).optimize();
    Lepton::ParsedExpression forceExpression = energyExpression.differentiate("r").optimize();
    map<string, Lepton::ParsedExpression> forceExpressions;
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    forceExpressions["real customEnergy = "] = energyExpression;
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    forceExpressions["tempForce -= "] = forceExpression;

    // Create the kernels.

    vector<pair<ExpressionTreeNode, string> > variables;
    ExpressionTreeNode rnode(new Operation::Variable("r"));
    variables.push_back(make_pair(rnode, "r"));
    variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
    variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
    for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
        const string& name = force.getPerParticleParameterName(i);
        variables.push_back(makeVariable(name+"1", prefix+"params"+params->getParameterSuffix(i, "1")));
        variables.push_back(makeVariable(name+"2", prefix+"params"+params->getParameterSuffix(i, "2")));
    }
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        const string& name = force.getGlobalParameterName(i);
        string value = "globals["+cu.intToString(i)+"]";
        variables.push_back(makeVariable(name, prefix+value));
    }
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    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cu.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 << cu.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"] = cu.doubleToString(force.getSwitchingDistance());
        replacements["SWITCH_C3"] = cu.doubleToString(10/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 3.0));
        replacements["SWITCH_C4"] = cu.doubleToString(15/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 4.0));
        replacements["SWITCH_C5"] = cu.doubleToString(6/pow(force.getSwitchingDistance()-force.getCutoffDistance(), 5.0));
    }
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    string source = cu.replaceStrings(CudaKernelSources::customNonbonded, replacements);
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    if (force.getNumInteractionGroups() > 0)
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        initInteractionGroups(force, source, tableTypes);
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    else {
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        cu.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source, force.getForceGroup(), true);
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            cu.getNonbondedUtilities().addParameter(CudaNonbondedUtilities::ParameterInfo(prefix+"params"+cu.intToString(i+1), buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
        }
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        if (globals.isInitialized()) {
            globals.upload(globalParamValues);
            cu.getNonbondedUtilities().addArgument(CudaNonbondedUtilities::ParameterInfo(prefix+"globals", "float", 1, sizeof(float), globals.getDevicePointer()));
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        }
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    }
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    info = new ForceInfo(force);
    cu.addForce(info);
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    // Record information for the long range correction.
    
    if (force.getNonbondedMethod() == CustomNonbondedForce::CutoffPeriodic && force.getUseLongRangeCorrection() && cu.getContextIndex() == 0) {
        forceCopy = new CustomNonbondedForce(force);
        hasInitializedLongRangeCorrection = false;
    }
    else {
        longRangeCoefficient = 0.0;
        hasInitializedLongRangeCorrection = true;
    }
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}

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void CudaCalcCustomNonbondedForceKernel::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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    vector<int> tileGroup;
    vector<vector<int> > duplicateAtomsForGroup;
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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());
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        duplicateAtomsForGroup.push_back(vector<int>());
        set_intersection(set1.begin(), set1.end(), set2.begin(), set2.end(),
                inserter(duplicateAtomsForGroup[group], duplicateAtomsForGroup[group].begin()));
        sort(duplicateAtomsForGroup[group].begin(), duplicateAtomsForGroup[group].end());
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        // Find how many tiles we will create for this group.
        
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        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.
        
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        int firstTile = tiles.size();
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        for (int i = 0; i < numBlocks1; i++)
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            for (int j = 0; j < numBlocks2; j++) {
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                tiles.push_back(make_pair(atomLists.size()+i, atomLists.size()+numBlocks1+j));
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                tileGroup.push_back(group);
            }
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        // 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);
        }
    }
    
    // Build a lookup table for quickly identifying excluded interactions.
    
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    vector<set<int> > exclusions(force.getNumParticles());
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    for (int i = 0; i < force.getNumExclusions(); i++) {
        int p1, p2;
        force.getExclusionParticles(i, p1, p2);
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        exclusions[p1].insert(p2);
        exclusions[p2].insert(p1);
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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++) {
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        bool swapped = false;
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        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;
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            swapped = true;
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        }
        vector<int>& atoms1 = atomLists[tiles[tile].first];
        vector<int>& atoms2 = atomLists[tiles[tile].second];
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        vector<int>& duplicateAtoms = duplicateAtomsForGroup[tileGroup[tile]];
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        vector<int>& flags = exclusionFlags[tile];
        flags.resize(atoms1.size(), (int) (1LL<<atoms2.size())-1);
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        int numExcluded = 0;
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        for (int i = 0; i < (int) atoms1.size(); i++) {
            int a1 = atoms1[i];
            bool a1IsDuplicate = binary_search(duplicateAtoms.begin(), duplicateAtoms.end(), a1);
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            for (int j = 0; j < (int) atoms2.size(); j++) {
                int a2 = atoms2[j];
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                bool isExcluded = false;
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                if (a1 == a2 || exclusions[a1].find(a2) != exclusions[a1].end())
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                    isExcluded = true; // This is an excluded interaction.
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                else if ((a1 > a2) == swapped && a1IsDuplicate && binary_search(duplicateAtoms.begin(), duplicateAtoms.end(), a2))
                    isExcluded = true; // Both atoms are in both sets, so skip duplicate interactions.
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                if (isExcluded) {
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                    flags[i] &= -1-(1<<j);
                    numExcluded++;
                }
            }
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        }
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        if (numExcluded == atoms1.size()*atoms2.size())
            continue; // All interactions are excluded.
        tileOrder.push_back(make_pair((int) -atoms2.size(), tile));
    }
    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<int4> groupData;
    for (int tileSet = 0; tileSet < numTileSets; tileSet++) {
        int indexInTileSet = 0;
        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];
            int range = indexInTileSet + ((indexInTileSet+atoms1.size())<<16);
            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(make_int4(a1, a2, range, flags<<indexInTileSet));
            }
            indexInTileSet += atoms1.size();
        }
        for (; indexInTileSet < 32; indexInTileSet++)
            groupData.push_back(make_int4(0, 0, 0, 0));
    }
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    interactionGroupData.initialize<int4>(cu, groupData.size(), "interactionGroupData");
    interactionGroupData.upload(groupData);
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    numGroupTiles.initialize<int>(cu, 1, "numGroupTiles");

    // Allocate space for a neighbor list, if necessary.

    if (force.getNonbondedMethod() != CustomNonbondedForce::NoCutoff && groupData.size() > cu.getNumThreadBlocks()) {
        filteredGroupData.initialize<int4>(cu, groupData.size(), "filteredGroupData");
        interactionGroupData.copyTo(filteredGroupData);
        int numTiles = groupData.size()/32;
        numGroupTiles.upload(&numTiles);
    }
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    // 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<CudaNonbondedUtilities::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<<", const "<<buffers[i].getType()<<"* __restrict__ global_params"<<(i+1);
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    for (int i = 0; i < (int) tabulatedFunctions.size(); i++)
        args << ", const " << tableTypes[i]<< "* __restrict__ table" << i;
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    if (globals.isInitialized())
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        args<<", const float* __restrict__ globals";
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    if (hasParamDerivs)
        args << ", 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[threadIdx.x].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[threadIdx.x].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 {
            load2<<buffers[i].getType()<<" params"<<(i+1)<<"2 = make_"<<buffers[i].getType()<<"(";
            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 = cu.getEnergyParamDerivNames();
    int numDerivs = allParamDerivNames.size();
    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
        string paramName = force.getEnergyParameterDerivativeName(i);
        string derivVariable = cu.getNonbondedUtilities().addEnergyParameterDerivative(paramName);
        initDerivs<<"mixed "<<derivVariable<<" = 0;\n";
        for (int index = 0; index < numDerivs; index++)
            if (allParamDerivNames[index] == paramName)
                saveDerivs<<"energyParamDerivs[(blockIdx.x*blockDim.x+threadIdx.x)*"<<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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    int localMemorySize = max(32, cu.getNonbondedUtilities().getForceThreadBlockSize());
    defines["LOCAL_MEMORY_SIZE"] = cu.intToString(localMemorySize);
    defines["WARPS_IN_BLOCK"] = cu.intToString(localMemorySize/32);
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    double cutoff = force.getCutoffDistance();
    defines["CUTOFF_SQUARED"] = cu.doubleToString(cutoff*cutoff);
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    double paddedCutoff = cu.getNonbondedUtilities().padCutoff(cutoff);
    defines["PADDED_CUTOFF_SQUARED"] = cu.doubleToString(paddedCutoff*paddedCutoff);
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    defines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
    defines["TILE_SIZE"] = "32";
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    defines["NUM_TILES"] = cu.intToString(numTileSets);
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*numTileSets/numContexts;
    int endIndex = (cu.getContextIndex()+1)*numTileSets/numContexts;
    defines["FIRST_TILE"] = cu.intToString(startIndex);
    defines["LAST_TILE"] = cu.intToString(endIndex);
    if ((localDataSize/4)%2 == 0 && !cu.getUseDoublePrecision())
        defines["PARAMETER_SIZE_IS_EVEN"] = "1";
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    CUmodule module = cu.createModule(CudaKernelSources::vectorOps+cu.replaceStrings(CudaKernelSources::customNonbondedGroups, replacements), defines);
    interactionGroupKernel = cu.getKernel(module, "computeInteractionGroups");
    prepareNeighborListKernel = cu.getKernel(module, "prepareToBuildNeighborList");
    buildNeighborListKernel = cu.getKernel(module, "buildNeighborList");
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    numGroupThreadBlocks = cu.getNonbondedUtilities().getNumForceThreadBlocks();
}

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double CudaCalcCustomNonbondedForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    useNeighborList = (filteredGroupData.isInitialized() && cu.getNonbondedUtilities().getUseCutoff());
    if (useNeighborList && cu.getContextIndex() > 0) {
        // When using a neighbor list, run the whole calculation on a single device.
        return 0.0;
    }
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    if (globals.isInitialized()) {
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        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;
        }
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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.isInitialized()) {
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        if (!hasInitializedKernel) {
            hasInitializedKernel = true;
            interactionGroupArgs.push_back(&cu.getForce().getDevicePointer());
            interactionGroupArgs.push_back(&cu.getEnergyBuffer().getDevicePointer());
            interactionGroupArgs.push_back(&cu.getPosq().getDevicePointer());
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            interactionGroupArgs.push_back(&(useNeighborList ? filteredGroupData : interactionGroupData).getDevicePointer());
            interactionGroupArgs.push_back(&numGroupTiles.getDevicePointer());
            interactionGroupArgs.push_back(&useNeighborList);
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            interactionGroupArgs.push_back(cu.getPeriodicBoxSizePointer());
            interactionGroupArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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            interactionGroupArgs.push_back(cu.getPeriodicBoxVecXPointer());
            interactionGroupArgs.push_back(cu.getPeriodicBoxVecYPointer());
            interactionGroupArgs.push_back(cu.getPeriodicBoxVecZPointer());
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            for (auto& buffer : params->getBuffers())
                interactionGroupArgs.push_back(&buffer.getMemory());
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            for (auto& function : tabulatedFunctions)
                interactionGroupArgs.push_back(&function.getDevicePointer());
            if (globals.isInitialized())
                interactionGroupArgs.push_back(&globals.getDevicePointer());
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            if (hasParamDerivs)
                interactionGroupArgs.push_back(&cu.getEnergyParamDerivBuffer().getDevicePointer());
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            if (useNeighborList) {
                // Initialize kernels for building the interaction group neighbor list.

                prepareNeighborListArgs.push_back(&cu.getNonbondedUtilities().getRebuildNeighborList().getDevicePointer());
                prepareNeighborListArgs.push_back(&numGroupTiles.getDevicePointer());
                buildNeighborListArgs.push_back(&cu.getNonbondedUtilities().getRebuildNeighborList().getDevicePointer());
                buildNeighborListArgs.push_back(&numGroupTiles.getDevicePointer());
                buildNeighborListArgs.push_back(&cu.getPosq().getDevicePointer());
                buildNeighborListArgs.push_back(&interactionGroupData.getDevicePointer());
                buildNeighborListArgs.push_back(&filteredGroupData.getDevicePointer());
                buildNeighborListArgs.push_back(cu.getPeriodicBoxSizePointer());
                buildNeighborListArgs.push_back(cu.getInvPeriodicBoxSizePointer());
                buildNeighborListArgs.push_back(cu.getPeriodicBoxVecXPointer());
                buildNeighborListArgs.push_back(cu.getPeriodicBoxVecYPointer());
                buildNeighborListArgs.push_back(cu.getPeriodicBoxVecZPointer());
            }
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        }
        int forceThreadBlockSize = cu.getNonbondedUtilities().getForceThreadBlockSize();
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        if (useNeighborList) {
            // Rebuild the neighbor list, if necessary.

            cu.executeKernel(prepareNeighborListKernel, &prepareNeighborListArgs[0], 1, 1);
            cu.executeKernel(buildNeighborListKernel, &buildNeighborListArgs[0], numGroupThreadBlocks*forceThreadBlockSize, forceThreadBlockSize);
        }
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        cu.executeKernel(interactionGroupKernel, &interactionGroupArgs[0], numGroupThreadBlocks*forceThreadBlockSize, forceThreadBlockSize);
    }
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    double4 boxSize = cu.getPeriodicBoxSize();
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    double volume = boxSize.x*boxSize.y*boxSize.z;
    map<string, double>& derivs = cu.getEnergyParamDerivWorkspace();
    for (int i = 0; i < longRangeCoefficientDerivs.size(); i++)
        derivs[forceCopy->getEnergyParameterDerivativeName(i)] += longRangeCoefficientDerivs[i]/volume;
    return longRangeCoefficient/volume;
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}

void CudaCalcCustomNonbondedForceKernel::copyParametersToContext(ContextImpl& context, const CustomNonbondedForce& force) {
    cu.setAsCurrent();
    int numParticles = force.getNumParticles();
    if (numParticles != cu.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    
    // Record the per-particle parameters.
    
    vector<vector<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] = (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.
    
    cu.invalidateMolecules();
}

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class CudaCalcGBSAOBCForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const GBSAOBCForce& force) : 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;
};

void CudaCalcGBSAOBCForceKernel::initialize(const System& system, const GBSAOBCForce& force) {
    cu.setAsCurrent();
    if (cu.getPlatformData().contexts.size() > 1)
        throw OpenMMException("GBSAOBCForce does not support using multiple CUDA devices");
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    int forceIndex;
    for (forceIndex = 0; forceIndex < system.getNumForces() && &system.getForce(forceIndex) != &force; ++forceIndex)
        ;
    string prefix = "obc"+cu.intToString(forceIndex)+"_";
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    CudaNonbondedUtilities& nb = cu.getNonbondedUtilities();
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    params.initialize<float2>(cu, cu.getPaddedNumAtoms(), "gbsaObcParams");
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    int elementSize = (cu.getUseDoublePrecision() ? sizeof(double) : sizeof(float));
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    charges.initialize(cu, cu.getPaddedNumAtoms(), elementSize, "gbsaObcCharges");
    bornRadii.initialize(cu, cu.getPaddedNumAtoms(), elementSize, "bornRadii");
    obcChain.initialize(cu, cu.getPaddedNumAtoms(), elementSize, "obcChain");
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    bornSum.initialize<long long>(cu, cu.getPaddedNumAtoms(), "bornSum");
    bornForce.initialize<long long>(cu, cu.getPaddedNumAtoms(), "bornForce");
    cu.addAutoclearBuffer(bornSum);
    cu.addAutoclearBuffer(bornForce);
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    CudaArray& posq = cu.getPosq();
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    vector<double> chargeVec(cu.getPaddedNumAtoms());
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    vector<float2> paramsVector(cu.getPaddedNumAtoms(), make_float2(1, 1));
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    const double dielectricOffset = 0.009;
    for (int i = 0; i < force.getNumParticles(); i++) {
        double charge, radius, scalingFactor;
        force.getParticleParameters(i, charge, radius, scalingFactor);
        radius -= dielectricOffset;
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        chargeVec[i] = charge;
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        paramsVector[i] = make_float2((float) radius, (float) (scalingFactor*radius));
    }
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    if (cu.getUseDoublePrecision())
        charges.upload(chargeVec);
    else {
        vector<float> c(charges.getSize());
        for (int i = 0; i < c.size(); i++)
            c[i] = (float) chargeVec[i];
        charges.upload(c);
    }
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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 = CudaKernelSources::gbsaObc2;
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    map<string, string> replacements;
    replacements["CHARGE1"] = prefix+"charge1";
    replacements["CHARGE2"] = prefix+"charge2";
    replacements["OBC_PARAMS1"] = prefix+"obcParams1";
    replacements["OBC_PARAMS2"] = prefix+"obcParams2";
    replacements["BORN_FORCE1"] = prefix+"bornForce1";
    replacements["BORN_FORCE2"] = prefix+"bornForce2";
    source = cu.replaceStrings(source, replacements);
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    nb.addInteraction(useCutoff, usePeriodic, false, cutoff, vector<vector<int> >(), source, force.getForceGroup());
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    nb.addParameter(CudaNonbondedUtilities::ParameterInfo(prefix+"charge", "float", 1, sizeof(float), charges.getDevicePointer()));;
    nb.addParameter(CudaNonbondedUtilities::ParameterInfo(prefix+"obcParams", "float", 2, sizeof(float2), params.getDevicePointer()));
    nb.addParameter(CudaNonbondedUtilities::ParameterInfo(prefix+"bornForce", "long long", 1, sizeof(long long), bornForce.getDevicePointer()));
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    info = new ForceInfo(force);
    cu.addForce(info);
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}

double CudaCalcGBSAOBCForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    CudaNonbondedUtilities& nb = cu.getNonbondedUtilities();
    if (!hasCreatedKernels) {
        // These Kernels cannot be created in initialize(), because the CudaNonbondedUtilities has not been initialized yet then.

        hasCreatedKernels = true;
        maxTiles = (nb.getUseCutoff() ? nb.getInteractingTiles().getSize() : cu.getNumAtomBlocks()*(cu.getNumAtomBlocks()+1)/2);
        map<string, string> defines;
        if (nb.getUseCutoff())
            defines["USE_CUTOFF"] = "1";
        if (nb.getUsePeriodic())
            defines["USE_PERIODIC"] = "1";
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        if (cu.getComputeCapability() >= 3.0 && !cu.getUseDoublePrecision())
            defines["ENABLE_SHUFFLE"] = "1";
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        defines["CUTOFF_SQUARED"] = cu.doubleToString(cutoff*cutoff);
        defines["CUTOFF"] = cu.doubleToString(cutoff);
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        defines["PREFACTOR"] = cu.doubleToString(prefactor);
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        defines["SURFACE_AREA_FACTOR"] = cu.doubleToString(surfaceAreaFactor);
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        defines["NUM_ATOMS"] = cu.intToString(cu.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
        defines["NUM_BLOCKS"] = cu.intToString(cu.getNumAtomBlocks());
        defines["FORCE_WORK_GROUP_SIZE"] = cu.intToString(nb.getForceThreadBlockSize());
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        defines["TILE_SIZE"] = cu.intToString(CudaContext::TileSize);
        int numExclusionTiles = nb.getExclusionTiles().getSize();
        defines["NUM_TILES_WITH_EXCLUSIONS"] = cu.intToString(numExclusionTiles);
        int numContexts = cu.getPlatformData().contexts.size();
        int startExclusionIndex = cu.getContextIndex()*numExclusionTiles/numContexts;
        int endExclusionIndex = (cu.getContextIndex()+1)*numExclusionTiles/numContexts;
        defines["FIRST_EXCLUSION_TILE"] = cu.intToString(startExclusionIndex);
        defines["LAST_EXCLUSION_TILE"] = cu.intToString(endExclusionIndex);
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        map<string, string> replacements;
        CUmodule module = cu.createModule(CudaKernelSources::vectorOps+cu.replaceStrings(CudaKernelSources::gbsaObc1, replacements), defines);
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        computeBornSumKernel = cu.getKernel(module, "computeBornSum");
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        computeSumArgs.push_back(&bornSum.getDevicePointer());
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        computeSumArgs.push_back(&cu.getPosq().getDevicePointer());
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        computeSumArgs.push_back(&charges.getDevicePointer());
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        computeSumArgs.push_back(&params.getDevicePointer());
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        if (nb.getUseCutoff()) {
            computeSumArgs.push_back(&nb.getInteractingTiles().getDevicePointer());
            computeSumArgs.push_back(&nb.getInteractionCount().getDevicePointer());
            computeSumArgs.push_back(cu.getPeriodicBoxSizePointer());
            computeSumArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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            computeSumArgs.push_back(cu.getPeriodicBoxVecXPointer());
            computeSumArgs.push_back(cu.getPeriodicBoxVecYPointer());
            computeSumArgs.push_back(cu.getPeriodicBoxVecZPointer());
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            computeSumArgs.push_back(&maxTiles);
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            computeSumArgs.push_back(&nb.getBlockCenters().getDevicePointer());
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            computeSumArgs.push_back(&nb.getBlockBoundingBoxes().getDevicePointer());
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            computeSumArgs.push_back(&nb.getInteractingAtoms().getDevicePointer());
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        }
        else
            computeSumArgs.push_back(&maxTiles);
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        computeSumArgs.push_back(&nb.getExclusionTiles().getDevicePointer());
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        force1Kernel = cu.getKernel(module, "computeGBSAForce1");
        force1Args.push_back(&cu.getForce().getDevicePointer());
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        force1Args.push_back(&bornForce.getDevicePointer());
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        force1Args.push_back(&cu.getEnergyBuffer().getDevicePointer());
        force1Args.push_back(&cu.getPosq().getDevicePointer());
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        force1Args.push_back(&charges.getDevicePointer());
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        force1Args.push_back(&bornRadii.getDevicePointer());
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        force1Args.push_back(NULL);
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        if (nb.getUseCutoff()) {
            force1Args.push_back(&nb.getInteractingTiles().getDevicePointer());
            force1Args.push_back(&nb.getInteractionCount().getDevicePointer());
            force1Args.push_back(cu.getPeriodicBoxSizePointer());
            force1Args.push_back(cu.getInvPeriodicBoxSizePointer());
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            force1Args.push_back(cu.getPeriodicBoxVecXPointer());
            force1Args.push_back(cu.getPeriodicBoxVecYPointer());
            force1Args.push_back(cu.getPeriodicBoxVecZPointer());
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            force1Args.push_back(&maxTiles);
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            force1Args.push_back(&nb.getBlockCenters().getDevicePointer());
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            force1Args.push_back(&nb.getBlockBoundingBoxes().getDevicePointer());
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            force1Args.push_back(&nb.getInteractingAtoms().getDevicePointer());
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        }
        else
            force1Args.push_back(&maxTiles);
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        force1Args.push_back(&nb.getExclusionTiles().getDevicePointer());
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        reduceBornSumKernel = cu.getKernel(module, "reduceBornSum");
        reduceBornForceKernel = cu.getKernel(module, "reduceBornForce");
    }
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    force1Args[6] = &includeEnergy;
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    if (nb.getUseCutoff()) {
        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
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            computeSumArgs[4] = &nb.getInteractingTiles().getDevicePointer();
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            force1Args[7] = &nb.getInteractingTiles().getDevicePointer();
            computeSumArgs[14] = &nb.getInteractingAtoms().getDevicePointer();
            force1Args[17] = &nb.getInteractingAtoms().getDevicePointer();
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        }
    }
    cu.executeKernel(computeBornSumKernel, &computeSumArgs[0], nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
    float alpha = 1.0f, beta = 0.8f, gamma = 4.85f;
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    void* reduceSumArgs[] = {&alpha, &beta, &gamma, &bornSum.getDevicePointer(), &params.getDevicePointer(),
            &bornRadii.getDevicePointer(), &obcChain.getDevicePointer()};
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    cu.executeKernel(reduceBornSumKernel, reduceSumArgs, cu.getPaddedNumAtoms());
    cu.executeKernel(force1Kernel, &force1Args[0], nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
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    void* reduceForceArgs[] = {&bornForce.getDevicePointer(), &cu.getEnergyBuffer().getDevicePointer(), &params.getDevicePointer(),
            &bornRadii.getDevicePointer(), &obcChain.getDevicePointer()};
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    cu.executeKernel(reduceBornForceKernel, &reduceForceArgs[0], cu.getPaddedNumAtoms());
    return 0.0;
}

void CudaCalcGBSAOBCForceKernel::copyParametersToContext(ContextImpl& context, const GBSAOBCForce& force) {
    // Make sure the new parameters are acceptable.
    
    cu.setAsCurrent();
    int numParticles = force.getNumParticles();
    if (numParticles != cu.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    
    // Record the per-particle parameters.
    
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    vector<double> chargeVector(cu.getPaddedNumAtoms(), 0.0);
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    vector<float2> paramsVector(cu.getPaddedNumAtoms());
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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] = make_float2((float) radius, (float) (scalingFactor*radius));
    }
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    for (int i = numParticles; i < cu.getPaddedNumAtoms(); i++)
        paramsVector[i] = make_float2(1, 1);
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    if (cu.getUseDoublePrecision())
        charges.upload(chargeVector);
    else {
        vector<float> c(charges.getSize());
        for (int i = 0; i < c.size(); i++)
            c[i] = (float) chargeVector[i];
        charges.upload(c);
    }
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    params.upload(paramsVector);
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    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

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

CudaCalcCustomGBForceKernel::~CudaCalcCustomGBForceKernel() {
    cu.setAsCurrent();
    if (params != NULL)
        delete params;
    if (computedValues != NULL)
        delete computedValues;
    if (energyDerivs != NULL)
        delete energyDerivs;
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    if (energyDerivChain != NULL)
        delete energyDerivChain;
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    for (auto d : dValuedParam)
        delete d;
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}

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

    // Record parameters and exclusions.

    int numParticles = force.getNumParticles();
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    int paddedNumParticles = cu.getPaddedNumAtoms();
    int numParams = force.getNumPerParticleParameters();
    params = new CudaParameterSet(cu, force.getNumPerParticleParameters(), paddedNumParticles, "customGBParameters", true);
    computedValues = new CudaParameterSet(cu, force.getNumComputedValues(), paddedNumParticles, "customGBComputedValues", true, cu.getUseDoublePrecision());
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    if (force.getNumGlobalParameters() > 0)
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        globals.initialize<float>(cu, force.getNumGlobalParameters(), "customGBGlobals");
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    vector<vector<float> > paramVector(paddedNumParticles, vector<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);
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (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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    tabulatedFunctions.resize(force.getNumTabulatedFunctions());
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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"+cu.intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
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        functions[name] = cu.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
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        int width;
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        vector<float> f = cu.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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3271
3272
        tabulatedFunctions[i].initialize<float>(cu, f.size(), "TabulatedFunction");
        tabulatedFunctions[i].upload(f);
        cu.getNonbondedUtilities().addArgument(CudaNonbondedUtilities::ParameterInfo(arrayName, "float", width, width*sizeof(float), tabulatedFunctions[i].getDevicePointer()));
3273
3274
3275
3276
        tableArgs << ", const float";
        if (width > 1)
            tableArgs << width;
        tableArgs << "* __restrict__ " << arrayName;
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
    }

    // Record the global parameters.

    globalParamNames.resize(force.getNumGlobalParameters());
    globalParamValues.resize(force.getNumGlobalParameters());
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        globalParamNames[i] = force.getGlobalParameterName(i);
        globalParamValues[i] = (float) force.getGlobalParameterDefaultValue(i);
    }
3287
3288
    if (globals.isInitialized())
        globals.upload(globalParamValues);
3289
3290
3291
3292
3293

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

    vector<vector<Lepton::ParsedExpression> > valueGradientExpressions(force.getNumComputedValues());
    vector<vector<Lepton::ParsedExpression> > valueDerivExpressions(force.getNumComputedValues());
3294
    vector<vector<Lepton::ParsedExpression> > valueParamDerivExpressions(force.getNumComputedValues());
3295
    needParameterGradient = false;
3296
    for (int i = 0; i < force.getNumComputedValues(); i++) {
3297
        Lepton::ParsedExpression ex = Lepton::Parser::parse(computedValueExpressions[i], functions).optimize();
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
        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());
3309
3310
    }
    vector<vector<Lepton::ParsedExpression> > energyDerivExpressions(force.getNumEnergyTerms());
3311
    vector<vector<Lepton::ParsedExpression> > energyParamDerivExpressions(force.getNumEnergyTerms());
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
    vector<bool> needChainForValue(force.getNumComputedValues(), false);
    for (int i = 0; i < force.getNumEnergyTerms(); i++) {
        string expression;
        CustomGBForce::ComputationType type;
        force.getEnergyTermParameters(i, expression, type);
        Lepton::ParsedExpression ex = Lepton::Parser::parse(expression, functions).optimize();
        for (int j = 0; j < force.getNumComputedValues(); j++) {
            if (type == CustomGBForce::SingleParticle) {
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]).optimize());
                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
            }
            else {
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]+"1").optimize());
                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
                energyDerivExpressions[i].push_back(ex.differentiate(computedValueNames[j]+"2").optimize());
                if (!isZeroExpression(energyDerivExpressions[i].back()))
                    needChainForValue[j] = true;
            }
        }
3333
3334
        for (int j = 0; j < force.getNumEnergyParameterDerivatives(); j++)
            energyParamDerivExpressions[i].push_back(ex.differentiate(force.getEnergyParameterDerivativeName(j)).optimize());
3335
    }
3336
    longEnergyDerivs.initialize<long long>(cu, force.getNumComputedValues()*cu.getPaddedNumAtoms(), "customGBLongEnergyDerivatives");
3337
    energyDerivs = new CudaParameterSet(cu, force.getNumComputedValues(), cu.getPaddedNumAtoms(), "customGBEnergyDerivatives", true);
3338
    energyDerivChain = new CudaParameterSet(cu, force.getNumComputedValues(), cu.getPaddedNumAtoms(), "customGBEnergyDerivativeChain", true);
3339
3340
    int elementSize = (cu.getUseDoublePrecision() ? sizeof(double) : sizeof(float));
    needEnergyParamDerivs = (force.getNumEnergyParameterDerivatives() > 0);
3341
    dValue0dParam.resize(force.getNumEnergyParameterDerivatives());
3342
    for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
3343
        dValuedParam.push_back(new CudaParameterSet(cu, force.getNumComputedValues(), cu.getPaddedNumAtoms(), "dValuedParam", true, cu.getUseDoublePrecision()));
3344
3345
        dValue0dParam[i].initialize<long long>(cu, cu.getPaddedNumAtoms(), "dValue0dParam");
        cu.addAutoclearBuffer(dValue0dParam[i]);
3346
3347
3348
        string name = force.getEnergyParameterDerivativeName(i);
        cu.addEnergyParameterDerivative(name);
    }
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
 
    // Create the kernels.

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

        vector<pair<ExpressionTreeNode, string> > variables;
        map<string, string> rename;
        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
            variables.push_back(makeVariable(name+"1", "params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", "params"+params->getParameterSuffix(i, "2")));
            rename[name+"1"] = name+"2";
            rename[name+"2"] = name+"1";
        }
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+cu.intToString(i)+"]";
            variables.push_back(makeVariable(name, value));
        }
        map<string, Lepton::ParsedExpression> n2ValueExpressions;
        stringstream n2ValueSource;
        Lepton::ParsedExpression ex = Lepton::Parser::parse(computedValueExpressions[0], functions).optimize();
        n2ValueExpressions["tempValue1 = "] = ex;
        n2ValueExpressions["tempValue2 = "] = ex.renameVariables(rename);
3380
3381
3382
3383
3384
3385
3386
        for (int i = 0; i < valueParamDerivExpressions[0].size(); i++) {
            string variableBase = "temp_dValue0dParam"+cu.intToString(i+1);
            if (!isZeroExpression(valueParamDerivExpressions[0][i])) {
                n2ValueExpressions[variableBase+"_1 = "] = valueParamDerivExpressions[0][i];
                n2ValueExpressions[variableBase+"_2 = "] = valueParamDerivExpressions[0][i].renameVariables(rename);
            }
        }
3387
        n2ValueSource << cu.getExpressionUtilities().createExpressions(n2ValueExpressions, variables, functionList, functionDefinitions, "temp");
3388
3389
3390
        map<string, string> replacements;
        string n2ValueStr = n2ValueSource.str();
        replacements["COMPUTE_VALUE"] = n2ValueStr;
3391
        stringstream extraArgs, atomParams, loadLocal1, loadLocal2, load1, load2, tempDerivs1, tempDerivs2, storeDeriv1, storeDeriv2;
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", const float* globals";
        pairValueUsesParam.resize(params->getBuffers().size(), false);
        int atomParamSize = 6;
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+cu.intToString(i+1);
            if (n2ValueStr.find(paramName+"1") != n2ValueStr.npos || n2ValueStr.find(paramName+"2") != n2ValueStr.npos) {
                extraArgs << ", const " << buffer.getType() << "* __restrict__ global_" << paramName;
                atomParams << buffer.getType() << " " << paramName << ";\n";
                loadLocal1 << "localData[localAtomIndex]." << paramName << " = " << paramName << "1;\n";
                loadLocal2 << "localData[localAtomIndex]." << paramName << " = global_" << paramName << "[j];\n";
                load1 << buffer.getType() << " " << paramName << "1 = global_" << paramName << "[atom1];\n";
                load2 << buffer.getType() << " " << paramName << "2 = localData[atom2]." << paramName << ";\n";
                pairValueUsesParam[i] = true;
                atomParamSize += buffer.getNumComponents();
            }
        }
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
        for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
            string derivName = "dValue0dParam"+cu.intToString(i+1);
            extraArgs << ", unsigned long long* __restrict__ global_" << derivName;
            atomParams << "real " << derivName << ";\n";
            loadLocal2 << "localData[localAtomIndex]." << derivName << " = 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";
                tempDerivs2 << "localData[tbx+tj]." << derivName << " += temp_" << derivName << "_2;\n";
                storeDeriv1 << "atomicAdd(&global_" << derivName << "[offset1], static_cast<unsigned long long>((long long) (" << derivName << "*0x100000000)));\n";
                storeDeriv2 << "atomicAdd(&global_" << derivName << "[offset2], static_cast<unsigned long long>((long long) (localData[threadIdx.x]." << derivName << "*0x100000000)));\n";
            }
        }
3425
3426
3427
3428
3429
3430
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
        replacements["ATOM_PARAMETER_DATA"] = atomParams.str();
        replacements["LOAD_LOCAL_PARAMETERS_FROM_1"] = loadLocal1.str();
        replacements["LOAD_LOCAL_PARAMETERS_FROM_GLOBAL"] = loadLocal2.str();
        replacements["LOAD_ATOM1_PARAMETERS"] = load1.str();
        replacements["LOAD_ATOM2_PARAMETERS"] = load2.str();
3431
3432
3433
3434
        replacements["ADD_TEMP_DERIVS1"] = tempDerivs1.str();
        replacements["ADD_TEMP_DERIVS2"] = tempDerivs2.str();
        replacements["STORE_PARAM_DERIVS1"] = storeDeriv1.str();
        replacements["STORE_PARAM_DERIVS2"] = storeDeriv2.str();
3435
        if (useCutoff)
3436
            pairValueDefines["USE_CUTOFF"] = "1";
3437
        if (usePeriodic)
3438
            pairValueDefines["USE_PERIODIC"] = "1";
3439
        if (useExclusionsForValue)
3440
            pairValueDefines["USE_EXCLUSIONS"] = "1";
3441
        if (atomParamSize%2 == 0 && !cu.getUseDoublePrecision())
3442
3443
3444
            pairValueDefines["NEED_PADDING"] = "1";
        pairValueDefines["WARPS_PER_GROUP"] = cu.intToString(cu.getNonbondedUtilities().getForceThreadBlockSize()/CudaContext::TileSize);
        pairValueDefines["THREAD_BLOCK_SIZE"] = cu.intToString(cu.getNonbondedUtilities().getForceThreadBlockSize());
3445
        pairValueDefines["CUTOFF_SQUARED"] = cu.doubleToString(cutoff*cutoff);
3446
3447
3448
3449
3450
        pairValueDefines["NUM_ATOMS"] = cu.intToString(cu.getNumAtoms());
        pairValueDefines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
        pairValueDefines["NUM_BLOCKS"] = cu.intToString(cu.getNumAtomBlocks());
        pairValueDefines["TILE_SIZE"] = cu.intToString(CudaContext::TileSize);
        pairValueSrc = cu.replaceStrings(CudaKernelSources::customGBValueN2, replacements);
3451
3452
3453
3454
3455
3456
        if (useExclusionsForValue)
            cu.getNonbondedUtilities().requestExclusions(exclusionList);
    }
    {
        // Create the kernel to reduce the N2 value and calculate other values.

3457
        stringstream reductionSource, extraArgs, deriv0;
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", const float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+cu.intToString(i+1);
            extraArgs << ", const " << buffer.getType() << "* __restrict__ " << paramName;
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+cu.intToString(i+1);
            extraArgs << ", " << buffer.getType() << "* __restrict__ global_" << valueName;
            reductionSource << buffer.getType() << " local_" << valueName << ";\n";
        }
3471
3472
3473
3474
3475
3476
3477
3478
        for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
            string variableName = "dValuedParam_0_"+cu.intToString(i);
            extraArgs << ", const long long* __restrict__ dValue0dParam" << i;
            deriv0 << "real " << variableName << " = (1.0f/0x100000000)*dValue0dParam" << i << "[index];\n";
            for (int j = 0; j < dValuedParam[i]->getBuffers().size(); j++)
                extraArgs << ", real* __restrict__ global_dValuedParam_" << j << "_" << i;
            deriv0 << "global_dValuedParam_0_" << i << "[index] = dValuedParam_0_" << i << ";\n";
        }
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
        reductionSource << "local_values" << computedValues->getParameterSuffix(0) << " = sum;\n";
        map<string, string> variables;
        variables["x"] = "pos.x";
        variables["y"] = "pos.y";
        variables["z"] = "pos.z";
        for (int i = 0; i < force.getNumPerParticleParameters(); i++)
            variables[force.getPerParticleParameterName(i)] = "params"+params->getParameterSuffix(i, "[index]");
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables[force.getGlobalParameterName(i)] = "globals["+cu.intToString(i)+"]";
        for (int i = 1; i < force.getNumComputedValues(); i++) {
            variables[computedValueNames[i-1]] = "local_values"+computedValues->getParameterSuffix(i-1);
            map<string, Lepton::ParsedExpression> valueExpressions;
            valueExpressions["local_values"+computedValues->getParameterSuffix(i)+" = "] = Lepton::Parser::parse(computedValueExpressions[i], functions).optimize();
3492
            reductionSource << cu.getExpressionUtilities().createExpressions(valueExpressions, variables, functionList, functionDefinitions, "value"+cu.intToString(i)+"_temp");
3493
3494
3495
3496
3497
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            string valueName = "values"+cu.intToString(i+1);
            reductionSource << "global_" << valueName << "[index] = local_" << valueName << ";\n";
        }
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
        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_"+cu.intToString(i)+"_"+cu.intToString(j)+" = "] = valueParamDerivExpressions[i][j];
                for (int j = 0; j < i; j++)
                    derivExpressions["real dVdV_"+cu.intToString(i)+"_"+cu.intToString(j)+" = "] = valueDerivExpressions[i][j];
            }
            reductionSource << cu.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";
            }
        }
3515
3516
        map<string, string> replacements;
        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
3517
        replacements["REDUCE_PARAM0_DERIV"] = deriv0.str();
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
        replacements["COMPUTE_VALUES"] = reductionSource.str();
        map<string, string> defines;
        defines["NUM_ATOMS"] = cu.intToString(cu.getNumAtoms());
        CUmodule module = cu.createModule(cu.replaceStrings(CudaKernelSources::customGBValuePerParticle, replacements), defines);
        perParticleValueKernel = cu.getKernel(module, "computePerParticleValues");
    }
    {
        // Create the N2 energy kernel.

        vector<pair<ExpressionTreeNode, string> > variables;
        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
            variables.push_back(makeVariable(name+"1", "params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", "params"+params->getParameterSuffix(i, "2")));
        }
        for (int i = 0; i < force.getNumComputedValues(); i++) {
            variables.push_back(makeVariable(computedValueNames[i]+"1", "values"+computedValues->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(computedValueNames[i]+"2", "values"+computedValues->getParameterSuffix(i, "2")));
        }
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables.push_back(makeVariable(force.getGlobalParameterName(i), "globals["+cu.intToString(i)+"]"));
        stringstream n2EnergySource;
        bool anyExclusions = (force.getNumExclusions() > 0);
        for (int i = 0; i < force.getNumEnergyTerms(); i++) {
            string expression;
            CustomGBForce::ComputationType type;
            force.getEnergyTermParameters(i, expression, type);
            if (type == CustomGBForce::SingleParticle)
                continue;
            bool exclude = (anyExclusions && type == CustomGBForce::ParticlePair);
            map<string, Lepton::ParsedExpression> n2EnergyExpressions;
            n2EnergyExpressions["tempEnergy += "] = Lepton::Parser::parse(expression, functions).optimize();
            n2EnergyExpressions["dEdR += "] = Lepton::Parser::parse(expression, functions).differentiate("r").optimize();
            for (int j = 0; j < force.getNumComputedValues(); j++) {
                if (needChainForValue[j]) {
                    string index = cu.intToString(j+1);
                    n2EnergyExpressions["/*"+cu.intToString(i+1)+"*/ deriv"+index+"_1 += "] = energyDerivExpressions[i][2*j];
                    n2EnergyExpressions["/*"+cu.intToString(i+1)+"*/ deriv"+index+"_2 += "] = energyDerivExpressions[i][2*j+1];
                }
            }
3562
3563
            for (int j = 0; j < force.getNumEnergyParameterDerivatives(); j++)
                n2EnergyExpressions["energyParamDeriv"+cu.intToString(j)+" += interactionScale*"] = energyParamDerivExpressions[i][j];
3564
3565
            if (exclude)
                n2EnergySource << "if (!isExcluded) {\n";
3566
            n2EnergySource << cu.getExpressionUtilities().createExpressions(n2EnergyExpressions, variables, functionList, functionDefinitions, "temp");
3567
3568
3569
3570
3571
3572
            if (exclude)
                n2EnergySource << "}\n";
        }
        map<string, string> replacements;
        string n2EnergyStr = n2EnergySource.str();
        replacements["COMPUTE_INTERACTION"] = n2EnergyStr;
3573
        stringstream extraArgs, atomParams, loadLocal1, loadLocal2, clearLocal, load1, load2, declare1, recordDeriv, storeDerivs1, storeDerivs2, initParamDerivs, saveParamDerivs;
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", const float* globals";
        pairEnergyUsesParam.resize(params->getBuffers().size(), false);
        int atomParamSize = 7;
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+cu.intToString(i+1);
            if (n2EnergyStr.find(paramName+"1") != n2EnergyStr.npos || n2EnergyStr.find(paramName+"2") != n2EnergyStr.npos) {
                extraArgs << ", const " << buffer.getType() << "* __restrict__ global_" << paramName;
                atomParams << buffer.getType() << " " << paramName << ";\n";
                loadLocal1 << "localData[localAtomIndex]." << paramName << " = " << paramName << "1;\n";
                loadLocal2 << "localData[localAtomIndex]." << paramName << " = global_" << paramName << "[j];\n";
                load1 << buffer.getType() << " " << paramName << "1 = global_" << paramName << "[atom1];\n";
                load2 << buffer.getType() << " " << paramName << "2 = localData[atom2]." << paramName << ";\n";
                pairEnergyUsesParam[i] = true;
                atomParamSize += buffer.getNumComponents();
            }
        }
        pairEnergyUsesValue.resize(computedValues->getBuffers().size(), false);
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+cu.intToString(i+1);
            if (n2EnergyStr.find(valueName+"1") != n2EnergyStr.npos || n2EnergyStr.find(valueName+"2") != n2EnergyStr.npos) {
                extraArgs << ", const " << buffer.getType() << "* __restrict__ global_" << valueName;
                atomParams << buffer.getType() << " " << valueName << ";\n";
                loadLocal1 << "localData[localAtomIndex]." << valueName << " = " << valueName << "1;\n";
                loadLocal2 << "localData[localAtomIndex]." << valueName << " = global_" << valueName << "[j];\n";
                load1 << buffer.getType() << " " << valueName << "1 = global_" << valueName << "[atom1];\n";
                load2 << buffer.getType() << " " << valueName << "2 = localData[atom2]." << valueName << ";\n";
                pairEnergyUsesValue[i] = true;
                atomParamSize += buffer.getNumComponents();
            }
        }
        extraArgs << ", unsigned long long* __restrict__ derivBuffers";
        for (int i = 0; i < force.getNumComputedValues(); i++) {
            string index = cu.intToString(i+1);
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            atomParams << "real deriv" << index << ";\n";
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            clearLocal << "localData[localAtomIndex].deriv" << index << " = 0;\n";
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            declare1 << "real deriv" << index << "_1 = 0;\n";
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            load2 << "real deriv" << index << "_2 = 0;\n";
            recordDeriv << "localData[atom2].deriv" << index << " += deriv" << index << "_2;\n";
            storeDerivs1 << "STORE_DERIVATIVE_1(" << index << ")\n";
            storeDerivs2 << "STORE_DERIVATIVE_2(" << index << ")\n";
            atomParamSize++;
        }
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        if (needEnergyParamDerivs) {
            extraArgs << ", mixed* __restrict__ energyParamDerivs";
            const vector<string>& allParamDerivNames = cu.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[(blockIdx.x*blockDim.x+threadIdx.x)*" << numDerivs << "+" << index << "] += energyParamDeriv" << i << ";\n";
            }
        }
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        replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
        replacements["ATOM_PARAMETER_DATA"] = atomParams.str();
        replacements["LOAD_LOCAL_PARAMETERS_FROM_1"] = loadLocal1.str();
        replacements["LOAD_LOCAL_PARAMETERS_FROM_GLOBAL"] = loadLocal2.str();
        replacements["CLEAR_LOCAL_DERIVATIVES"] = clearLocal.str();
        replacements["LOAD_ATOM1_PARAMETERS"] = load1.str();
        replacements["LOAD_ATOM2_PARAMETERS"] = load2.str();
        replacements["DECLARE_ATOM1_DERIVATIVES"] = declare1.str();
        replacements["RECORD_DERIVATIVE_2"] = recordDeriv.str();
        replacements["STORE_DERIVATIVES_1"] = storeDerivs1.str();
        replacements["STORE_DERIVATIVES_2"] = storeDerivs2.str();
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        replacements["INIT_PARAM_DERIVS"] = initParamDerivs.str();
        replacements["SAVE_PARAM_DERIVS"] = saveParamDerivs.str();
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        if (useCutoff)
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            pairEnergyDefines["USE_CUTOFF"] = "1";
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        if (usePeriodic)
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            pairEnergyDefines["USE_PERIODIC"] = "1";
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        if (anyExclusions)
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            pairEnergyDefines["USE_EXCLUSIONS"] = "1";
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        if (atomParamSize%2 != 0 && !cu.getUseDoublePrecision())
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            pairEnergyDefines["NEED_PADDING"] = "1";
        pairEnergyDefines["THREAD_BLOCK_SIZE"] = cu.intToString(cu.getNonbondedUtilities().getForceThreadBlockSize());
        pairEnergyDefines["WARPS_PER_GROUP"] = cu.intToString(cu.getNonbondedUtilities().getForceThreadBlockSize()/CudaContext::TileSize);
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        pairEnergyDefines["CUTOFF_SQUARED"] = cu.doubleToString(cutoff*cutoff);
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        pairEnergyDefines["NUM_ATOMS"] = cu.intToString(cu.getNumAtoms());
        pairEnergyDefines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
        pairEnergyDefines["NUM_BLOCKS"] = cu.intToString(cu.getNumAtomBlocks());
        pairEnergyDefines["TILE_SIZE"] = cu.intToString(CudaContext::TileSize);
        pairEnergySrc = cu.replaceStrings(CudaKernelSources::customGBEnergyN2, 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, load, initParamDerivs, saveParamDerivs;
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        if (force.getNumGlobalParameters() > 0)
            extraArgs << ", const float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+cu.intToString(i+1);
            extraArgs << ", const " << buffer.getType() << "* __restrict__ " << paramName;
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+cu.intToString(i+1);
            extraArgs << ", const " << buffer.getType() << "* __restrict__ " << valueName;
        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            string index = cu.intToString(i+1);
            extraArgs << ", " << buffer.getType() << "* __restrict__ derivBuffers" << index;
            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
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        for (int i = 0; i < (int) energyDerivChain->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = energyDerivChain->getBuffers()[i];
            string index = cu.intToString(i+1);
            extraArgs << ", " << buffer.getType() << "* __restrict__ derivChain" << index;
        }
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        extraArgs << ", const long long* __restrict__ derivBuffersIn";
        for (int i = 0; i < energyDerivs->getNumParameters(); ++i)
            load << "derivBuffers" << energyDerivs->getParameterSuffix(i, "[index]") <<
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                    " = RECIP(0x100000000)*derivBuffersIn[index+PADDED_NUM_ATOMS*" << cu.intToString(i) << "];\n";
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        if (needEnergyParamDerivs) {
            extraArgs << ", mixed* __restrict__ energyParamDerivs";
            const vector<string>& allParamDerivNames = cu.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[(blockIdx.x*blockDim.x+threadIdx.x)*" << numDerivs << "+" << index << "] += energyParamDeriv" << i << ";\n";
            }
        }
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        // Compute the various expressions.
        
        map<string, string> variables;
        variables["x"] = "pos.x";
        variables["y"] = "pos.y";
        variables["z"] = "pos.z";
        for (int i = 0; i < force.getNumPerParticleParameters(); i++)
            variables[force.getPerParticleParameterName(i)] = "params"+params->getParameterSuffix(i, "[index]");
        for (int i = 0; i < force.getNumGlobalParameters(); i++)
            variables[force.getGlobalParameterName(i)] = "globals["+cu.intToString(i)+"]";
        for (int i = 0; i < force.getNumComputedValues(); i++)
            variables[computedValueNames[i]] = "values"+computedValues->getParameterSuffix(i, "[index]");
        map<string, Lepton::ParsedExpression> expressions;
        for (int i = 0; i < force.getNumEnergyTerms(); i++) {
            string expression;
            CustomGBForce::ComputationType type;
            force.getEnergyTermParameters(i, expression, type);
            if (type != CustomGBForce::SingleParticle)
                continue;
            Lepton::ParsedExpression parsed = Lepton::Parser::parse(expression, functions).optimize();
            expressions["/*"+cu.intToString(i+1)+"*/ energy += "] = parsed;
            for (int j = 0; j < force.getNumComputedValues(); j++)
                expressions["/*"+cu.intToString(i+1)+"*/ deriv"+energyDerivs->getParameterSuffix(j)+" += "] = energyDerivExpressions[i][j];
            Lepton::ParsedExpression gradx = parsed.differentiate("x").optimize();
            Lepton::ParsedExpression grady = parsed.differentiate("y").optimize();
            Lepton::ParsedExpression gradz = parsed.differentiate("z").optimize();
            if (!isZeroExpression(gradx))
                expressions["/*"+cu.intToString(i+1)+"*/ force.x -= "] = gradx;
            if (!isZeroExpression(grady))
                expressions["/*"+cu.intToString(i+1)+"*/ force.y -= "] = grady;
            if (!isZeroExpression(gradz))
                expressions["/*"+cu.intToString(i+1)+"*/ force.z -= "] = gradz;
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            for (int j = 0; j < force.getNumEnergyParameterDerivatives(); j++)
                expressions["/*"+cu.intToString(i+1)+"*/ energyParamDeriv"+cu.intToString(j)+" += "] = energyParamDerivExpressions[i][j];
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        }
        for (int i = 1; i < force.getNumComputedValues(); i++)
            for (int j = 0; j < i; j++)
                expressions["real dV"+cu.intToString(i)+"dV"+cu.intToString(j)+" = "] = valueDerivExpressions[i][j];
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        compute << cu.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 = cu.intToString(i+1);
            compute << "derivBuffers" << index << "[index] = deriv" << index << ";\n";
        }
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        compute << "forceBuffers[index] += (long long) (force.x*0x100000000);\n";
        compute << "forceBuffers[index+PADDED_NUM_ATOMS] += (long long) (force.y*0x100000000);\n";
        compute << "forceBuffers[index+PADDED_NUM_ATOMS*2] += (long long) (force.z*0x100000000);\n";
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        for (int i = 1; i < force.getNumComputedValues(); i++) {
            compute << "real totalDeriv"<<i<<" = dV"<<i<<"dV0";
            for (int j = 1; j < i; j++)
                compute << " + totalDeriv"<<j<<"*dV"<<i<<"dV"<<j;
            compute << ";\n";
            compute << "deriv"<<(i+1)<<" *= totalDeriv"<<i<<";\n";
        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            string index = cu.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();
        replacements["LOAD_DERIVATIVES"] = load.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;
        defines["NUM_ATOMS"] = cu.intToString(cu.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
        CUmodule module = cu.createModule(cu.replaceStrings(CudaKernelSources::customGBEnergyPerParticle, replacements), defines);
        perParticleEnergyKernel = cu.getKernel(module, "computePerParticleEnergy");
    }
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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)
            extraArgs << ", const float* globals";
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = "params"+cu.intToString(i+1);
            extraArgs << ", const " << buffer.getType() << "* __restrict__ " << paramName;
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string valueName = "values"+cu.intToString(i+1);
            extraArgs << ", const " << buffer.getType() << "* __restrict__ " << valueName;
        }
        for (int i = 0; i < (int) energyDerivs->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = energyDerivs->getBuffers()[i];
            string index = cu.intToString(i+1);
            extraArgs << ", " << buffer.getType() << "* __restrict__ derivBuffers" << index;
            compute << buffer.getType() << " deriv" << index << " = derivBuffers" << index << "[index];\n";
        }
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        if (needEnergyParamDerivs) {
            extraArgs << ", mixed* __restrict__ energyParamDerivs";
            const vector<string>& allParamDerivNames = cu.getEnergyParamDerivNames();
            int numDerivs = allParamDerivNames.size();
            for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
                for (int j = 0; j < dValuedParam[i]->getBuffers().size(); j++)
                    extraArgs << ", 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[(blockIdx.x*blockDim.x+threadIdx.x)*" << 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++)
            variables[force.getGlobalParameterName(i)] = "globals["+cu.intToString(i)+"]";
        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 = cu.intToString(i);
                compute << "real3 dV"<<is<<"dR = make_real3(0);\n";
                for (int j = 1; j < i; j++) {
                    if (!isZeroExpression(valueDerivExpressions[i][j])) {
                        map<string, Lepton::ParsedExpression> derivExpressions;
                        string js = cu.intToString(j);
                        derivExpressions["real dV"+is+"dV"+js+" = "] = valueDerivExpressions[i][j];
                        compute << cu.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 << cu.getExpressionUtilities().createExpressions(gradientExpressions, variables, functionList, functionDefinitions, "temp");
            }
            for (int i = 1; i < force.getNumComputedValues(); i++) {
                string is = cu.intToString(i);
                compute << "force -= deriv"<<energyDerivs->getParameterSuffix(i)<<"*dV"<<is<<"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;
        defines["NUM_ATOMS"] = cu.intToString(cu.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
        CUmodule module = cu.createModule(CudaKernelSources::vectorOps+cu.replaceStrings(CudaKernelSources::customGBGradientChainRule, replacements), defines);
        gradientChainRuleKernel = cu.getKernel(module, "computeGradientChainRuleTerms");
    }
    {
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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;
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+cu.intToString(i)+"]";
            globalVariables.push_back(makeVariable(name, prefix+value));
        }
        vector<pair<ExpressionTreeNode, string> > variables = globalVariables;
        map<string, string> rename;
        ExpressionTreeNode rnode(new Operation::Variable("r"));
        variables.push_back(make_pair(rnode, "r"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Square(), rnode), "r2"));
        variables.push_back(make_pair(ExpressionTreeNode(new Operation::Reciprocal(), rnode), "invR"));
        for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
            const string& name = force.getPerParticleParameterName(i);
            variables.push_back(makeVariable(name+"1", prefix+"params"+params->getParameterSuffix(i, "1")));
            variables.push_back(makeVariable(name+"2", prefix+"params"+params->getParameterSuffix(i, "2")));
            rename[name+"1"] = name+"2";
            rename[name+"2"] = name+"1";
        }
        map<string, Lepton::ParsedExpression> derivExpressions;
        stringstream chainSource;
        Lepton::ParsedExpression dVdR = Lepton::Parser::parse(computedValueExpressions[0], functions).differentiate("r").optimize();
        derivExpressions["real dV0dR1 = "] = dVdR;
        derivExpressions["real dV0dR2 = "] = dVdR.renameVariables(rename);
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        chainSource << cu.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";
        }
        for (int i = 1; i < force.getNumComputedValues(); i++) {
            if (needChainForValue[i]) {
                chainSource << "tempForce -= dV0dR1*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(i, "1") << ";\n";
                chainSource << "tempForce -= dV0dR2*" << prefix << "dEdV" << energyDerivs->getParameterSuffix(i, "2") << ";\n";
            }
        }
        map<string, string> replacements;
        string chainStr = chainSource.str();
        replacements["COMPUTE_FORCE"] = chainStr;
        string source = cu.replaceStrings(CudaKernelSources::customGBChainRule, replacements);
        vector<CudaNonbondedUtilities::ParameterInfo> parameters;
        vector<CudaNonbondedUtilities::ParameterInfo> arguments;
        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
            string paramName = prefix+"params"+cu.intToString(i+1);
            if (chainStr.find(paramName+"1") != chainStr.npos || chainStr.find(paramName+"2") != chainStr.npos)
                parameters.push_back(CudaNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            CudaNonbondedUtilities::ParameterInfo& buffer = computedValues->getBuffers()[i];
            string paramName = prefix+"values"+cu.intToString(i+1);
            if (chainStr.find(paramName+"1") != chainStr.npos || chainStr.find(paramName+"2") != chainStr.npos)
                parameters.push_back(CudaNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
        }
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        for (int i = 0; i < (int) energyDerivChain->getBuffers().size(); i++) {
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            if (needChainForValue[i]) { 
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                CudaNonbondedUtilities::ParameterInfo& buffer = energyDerivChain->getBuffers()[i];
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                string paramName = prefix+"dEdV"+cu.intToString(i+1);
                parameters.push_back(CudaNonbondedUtilities::ParameterInfo(paramName, buffer.getComponentType(), buffer.getNumComponents(), buffer.getSize(), buffer.getMemory()));
            }
        }
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        if (globals.isInitialized()) {
            globals.upload(globalParamValues);
            arguments.push_back(CudaNonbondedUtilities::ParameterInfo(prefix+"globals", "float", 1, sizeof(float), globals.getDevicePointer()));
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        }
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        cu.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, force.getNumExclusions() > 0, cutoff, exclusionList, source, force.getForceGroup());
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        for (auto param : parameters)
            cu.getNonbondedUtilities().addParameter(param);
        for (auto arg : arguments)
            cu.getNonbondedUtilities().addArgument(arg);
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    }
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    info = new ForceInfo(force);
    cu.addForce(info);
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    cu.addAutoclearBuffer(longEnergyDerivs);
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}

double CudaCalcCustomGBForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    CudaNonbondedUtilities& nb = cu.getNonbondedUtilities();
    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 = cu.getNonbondedUtilities().getExclusionTiles().getSize();
            pairValueDefines["NUM_TILES_WITH_EXCLUSIONS"] = cu.intToString(numExclusionTiles);
            int numContexts = cu.getPlatformData().contexts.size();
            int startExclusionIndex = cu.getContextIndex()*numExclusionTiles/numContexts;
            int endExclusionIndex = (cu.getContextIndex()+1)*numExclusionTiles/numContexts;
            pairValueDefines["FIRST_EXCLUSION_TILE"] = cu.intToString(startExclusionIndex);
            pairValueDefines["LAST_EXCLUSION_TILE"] = cu.intToString(endExclusionIndex);
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            pairValueDefines["CUTOFF"] = cu.doubleToString(cutoff);
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            CUmodule module = cu.createModule(CudaKernelSources::vectorOps+pairValueSrc, pairValueDefines);
            pairValueKernel = cu.getKernel(module, "computeN2Value");
            pairValueSrc = "";
            pairValueDefines.clear();
        }
        {
            int numExclusionTiles = cu.getNonbondedUtilities().getExclusionTiles().getSize();
            pairEnergyDefines["NUM_TILES_WITH_EXCLUSIONS"] = cu.intToString(numExclusionTiles);
            int numContexts = cu.getPlatformData().contexts.size();
            int startExclusionIndex = cu.getContextIndex()*numExclusionTiles/numContexts;
            int endExclusionIndex = (cu.getContextIndex()+1)*numExclusionTiles/numContexts;
            pairEnergyDefines["FIRST_EXCLUSION_TILE"] = cu.intToString(startExclusionIndex);
            pairEnergyDefines["LAST_EXCLUSION_TILE"] = cu.intToString(endExclusionIndex);
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            pairEnergyDefines["CUTOFF"] = cu.doubleToString(cutoff);
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            CUmodule module = cu.createModule(CudaKernelSources::vectorOps+pairEnergySrc, pairEnergyDefines);
            pairEnergyKernel = cu.getKernel(module, "computeN2Energy");
            pairEnergySrc = "";
            pairEnergyDefines.clear();
        }

        // Set arguments for kernels.
        
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        maxTiles = (nb.getUseCutoff() ? nb.getInteractingTiles().getSize() : cu.getNumAtomBlocks()*(cu.getNumAtomBlocks()+1)/2);
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        valueBuffers.initialize<long long>(cu, cu.getPaddedNumAtoms(), "customGBValueBuffers");
        cu.addAutoclearBuffer(valueBuffers);
        cu.clearBuffer(valueBuffers.getDevicePointer(), sizeof(long long)*valueBuffers.getSize());
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        pairValueArgs.push_back(&cu.getPosq().getDevicePointer());
        pairValueArgs.push_back(&cu.getNonbondedUtilities().getExclusions().getDevicePointer());
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        pairValueArgs.push_back(&cu.getNonbondedUtilities().getExclusionTiles().getDevicePointer());
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        pairValueArgs.push_back(&valueBuffers.getDevicePointer());
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        if (nb.getUseCutoff()) {
            pairValueArgs.push_back(&nb.getInteractingTiles().getDevicePointer());
            pairValueArgs.push_back(&nb.getInteractionCount().getDevicePointer());
            pairValueArgs.push_back(cu.getPeriodicBoxSizePointer());
            pairValueArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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            pairValueArgs.push_back(cu.getPeriodicBoxVecXPointer());
            pairValueArgs.push_back(cu.getPeriodicBoxVecYPointer());
            pairValueArgs.push_back(cu.getPeriodicBoxVecZPointer());
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            pairValueArgs.push_back(&maxTiles);
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            pairValueArgs.push_back(&nb.getBlockCenters().getDevicePointer());
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            pairValueArgs.push_back(&nb.getBlockBoundingBoxes().getDevicePointer());
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            pairValueArgs.push_back(&nb.getInteractingAtoms().getDevicePointer());
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        }
        else
            pairValueArgs.push_back(&maxTiles);
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        if (globals.isInitialized())
            pairValueArgs.push_back(&globals.getDevicePointer());
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            if (pairValueUsesParam[i])
                pairValueArgs.push_back(&params->getBuffers()[i].getMemory());
        }
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        for (auto& d : dValue0dParam)
            pairValueArgs.push_back(&d.getDevicePointer());
        for (auto& function : tabulatedFunctions)
            pairValueArgs.push_back(&function.getDevicePointer());
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        perParticleValueArgs.push_back(&cu.getPosq().getDevicePointer());
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        perParticleValueArgs.push_back(&valueBuffers.getDevicePointer());
        if (globals.isInitialized())
            perParticleValueArgs.push_back(&globals.getDevicePointer());
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        for (auto& buffer : params->getBuffers())
            perParticleValueArgs.push_back(&buffer.getMemory());
        for (auto& buffer : computedValues->getBuffers())
            perParticleValueArgs.push_back(&buffer.getMemory());
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        for (int i = 0; i < dValuedParam.size(); i++) {
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            perParticleValueArgs.push_back(&dValue0dParam[i].getDevicePointer());
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            for (int j = 0; j < dValuedParam[i]->getBuffers().size(); j++)
                perParticleValueArgs.push_back(&dValuedParam[i]->getBuffers()[j].getMemory());
        }
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        for (auto& function : tabulatedFunctions)
            perParticleValueArgs.push_back(&function.getDevicePointer());
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        pairEnergyArgs.push_back(&cu.getForce().getDevicePointer());
        pairEnergyArgs.push_back(&cu.getEnergyBuffer().getDevicePointer());
        pairEnergyArgs.push_back(&cu.getPosq().getDevicePointer());
        pairEnergyArgs.push_back(&cu.getNonbondedUtilities().getExclusions().getDevicePointer());
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        pairEnergyArgs.push_back(&cu.getNonbondedUtilities().getExclusionTiles().getDevicePointer());
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        pairEnergyArgs.push_back(NULL);
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        if (nb.getUseCutoff()) {
            pairEnergyArgs.push_back(&nb.getInteractingTiles().getDevicePointer());
            pairEnergyArgs.push_back(&nb.getInteractionCount().getDevicePointer());
            pairEnergyArgs.push_back(cu.getPeriodicBoxSizePointer());
            pairEnergyArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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            pairEnergyArgs.push_back(cu.getPeriodicBoxVecXPointer());
            pairEnergyArgs.push_back(cu.getPeriodicBoxVecYPointer());
            pairEnergyArgs.push_back(cu.getPeriodicBoxVecZPointer());
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            pairEnergyArgs.push_back(&maxTiles);
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            pairEnergyArgs.push_back(&nb.getBlockCenters().getDevicePointer());
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            pairEnergyArgs.push_back(&nb.getBlockBoundingBoxes().getDevicePointer());
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            pairEnergyArgs.push_back(&nb.getInteractingAtoms().getDevicePointer());
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        }
        else
            pairEnergyArgs.push_back(&maxTiles);
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        if (globals.isInitialized())
            pairEnergyArgs.push_back(&globals.getDevicePointer());
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        for (int i = 0; i < (int) params->getBuffers().size(); i++) {
            if (pairEnergyUsesParam[i])
                pairEnergyArgs.push_back(&params->getBuffers()[i].getMemory());
        }
        for (int i = 0; i < (int) computedValues->getBuffers().size(); i++) {
            if (pairEnergyUsesValue[i])
                pairEnergyArgs.push_back(&computedValues->getBuffers()[i].getMemory());
        }
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        pairEnergyArgs.push_back(&longEnergyDerivs.getDevicePointer());
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        if (needEnergyParamDerivs)
            pairEnergyArgs.push_back(&cu.getEnergyParamDerivBuffer().getDevicePointer());
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        for (auto& function : tabulatedFunctions)
            pairEnergyArgs.push_back(&function.getDevicePointer());
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        perParticleEnergyArgs.push_back(&cu.getForce().getDevicePointer());
        perParticleEnergyArgs.push_back(&cu.getEnergyBuffer().getDevicePointer());
        perParticleEnergyArgs.push_back(&cu.getPosq().getDevicePointer());
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        if (globals.isInitialized())
            perParticleEnergyArgs.push_back(&globals.getDevicePointer());
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        for (auto& buffer : params->getBuffers())
            perParticleEnergyArgs.push_back(&buffer.getMemory());
        for (auto& buffer : computedValues->getBuffers())
            perParticleEnergyArgs.push_back(&buffer.getMemory());
        for (auto& buffer : energyDerivs->getBuffers())
            perParticleEnergyArgs.push_back(&buffer.getMemory());
        for (auto& buffer : energyDerivChain->getBuffers())
            perParticleEnergyArgs.push_back(&buffer.getMemory());
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        perParticleEnergyArgs.push_back(&longEnergyDerivs.getDevicePointer());
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        if (needEnergyParamDerivs)
            perParticleEnergyArgs.push_back(&cu.getEnergyParamDerivBuffer().getDevicePointer());
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        for (auto& function : tabulatedFunctions)
            perParticleEnergyArgs.push_back(&function.getDevicePointer());
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        if (needParameterGradient || needEnergyParamDerivs) {
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            gradientChainRuleArgs.push_back(&cu.getForce().getDevicePointer());
            gradientChainRuleArgs.push_back(&cu.getPosq().getDevicePointer());
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            if (globals.isInitialized())
                gradientChainRuleArgs.push_back(&globals.getDevicePointer());
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            for (auto& buffer : params->getBuffers())
                gradientChainRuleArgs.push_back(&buffer.getMemory());
            for (auto& buffer : computedValues->getBuffers())
                gradientChainRuleArgs.push_back(&buffer.getMemory());
            for (auto& buffer : energyDerivs->getBuffers())
                gradientChainRuleArgs.push_back(&buffer.getMemory());
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            if (needEnergyParamDerivs) {
                gradientChainRuleArgs.push_back(&cu.getEnergyParamDerivBuffer().getDevicePointer());
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                for (auto d : dValuedParam)
                    for (auto& buffer : d->getBuffers())
                        gradientChainRuleArgs.push_back(&buffer.getMemory());
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            }
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        }
    }
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    if (globals.isInitialized()) {
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        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)
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            globals.upload(globalParamValues);
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    }
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    pairEnergyArgs[5] = &includeEnergy;
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    if (nb.getUseCutoff()) {
        if (maxTiles < nb.getInteractingTiles().getSize()) {
            maxTiles = nb.getInteractingTiles().getSize();
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            pairValueArgs[4] = &nb.getInteractingTiles().getDevicePointer();
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            pairEnergyArgs[6] = &nb.getInteractingTiles().getDevicePointer();
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            pairValueArgs[14] = &nb.getInteractingAtoms().getDevicePointer();
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            pairEnergyArgs[16] = &nb.getInteractingAtoms().getDevicePointer();
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        }
    }
    cu.executeKernel(pairValueKernel, &pairValueArgs[0], nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
    cu.executeKernel(perParticleValueKernel, &perParticleValueArgs[0], cu.getPaddedNumAtoms());
    cu.executeKernel(pairEnergyKernel, &pairEnergyArgs[0], nb.getNumForceThreadBlocks()*nb.getForceThreadBlockSize(), nb.getForceThreadBlockSize());
    cu.executeKernel(perParticleEnergyKernel, &perParticleEnergyArgs[0], cu.getPaddedNumAtoms());
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    if (needParameterGradient || needEnergyParamDerivs)
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        cu.executeKernel(gradientChainRuleKernel, &gradientChainRuleArgs[0], cu.getPaddedNumAtoms());
    return 0.0;
}

void CudaCalcCustomGBForceKernel::copyParametersToContext(ContextImpl& context, const CustomGBForce& force) {
    cu.setAsCurrent();
    int numParticles = force.getNumParticles();
    if (numParticles != cu.getNumAtoms())
        throw OpenMMException("updateParametersInContext: The number of particles has changed");
    
    // Record the per-particle parameters.
    
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    vector<vector<float> > paramVector(cu.getPaddedNumAtoms(), vector<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] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}
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class CudaCalcCustomExternalForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const CustomExternalForce& force, int numParticles) : 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);
        for (int i = 0; i < (int) params1.size(); i++)
            if (params1[i] != params2[i])
                return false;
        return true;
    }
private:
    const CustomExternalForce& force;
    vector<int> indices;
};

CudaCalcCustomExternalForceKernel::~CudaCalcCustomExternalForceKernel() {
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    cu.setAsCurrent();
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    if (params != NULL)
        delete params;
}

void CudaCalcCustomExternalForceKernel::initialize(const System& system, const CustomExternalForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumParticles()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumParticles()/numContexts;
    numParticles = endIndex-startIndex;
    if (numParticles == 0)
        return;
    vector<vector<int> > atoms(numParticles, vector<int>(1));
    params = new CudaParameterSet(cu, force.getNumPerParticleParameters(), numParticles, "customExternalParams");
    vector<vector<float> > paramVector(numParticles);
    for (int i = 0; i < numParticles; i++) {
        vector<double> parameters;
        force.getParticleParameters(startIndex+i, atoms[i][0], parameters);
        paramVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            paramVector[i][j] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
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    info = new ForceInfo(force, system.getNumParticles());
    cu.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] = (float) force.getGlobalParameterDefaultValue(i);
    }
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    map<string, Lepton::CustomFunction*> customFunctions;
    customFunctions["periodicdistance"] = cu.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;
    expressions["float dEdX = "] = forceExpressionX;
    expressions["float dEdY = "] = forceExpressionY;
    expressions["float dEdZ = "] = forceExpressionZ;

    // Create the kernels.

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

double CudaCalcCustomExternalForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (globals.isInitialized()) {
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        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)
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            globals.upload(globalParamValues);
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    }
    return 0.0;
}

void CudaCalcCustomExternalForceKernel::copyParametersToContext(ContextImpl& context, const CustomExternalForce& force) {
    cu.setAsCurrent();
    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumParticles()/numContexts;
    int endIndex = (cu.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<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] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

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

CudaCalcCustomHbondForceKernel::~CudaCalcCustomHbondForceKernel() {
    cu.setAsCurrent();
    if (donorParams != NULL)
        delete donorParams;
    if (acceptorParams != NULL)
        delete acceptorParams;
}

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]<<" += trim("<<value<<");\n";
    else
        applyToDonor << forceNames[atom-3]<<" += trim("<<value<<");\n";
}

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

    cu.setAsCurrent();
    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumDonors()/numContexts;
    int endIndex = (cu.getContextIndex()+1)*force.getNumDonors()/numContexts;
    numDonors = endIndex-startIndex;
    numAcceptors = force.getNumAcceptors();
    if (numDonors == 0 || numAcceptors == 0)
        return;
    int numParticles = system.getNumParticles();
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    donors.initialize<int4>(cu, numDonors, "customHbondDonors");
    acceptors.initialize<int4>(cu, numAcceptors, "customHbondAcceptors");
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    donorParams = new CudaParameterSet(cu, force.getNumPerDonorParameters(), numDonors, "customHbondDonorParameters");
    acceptorParams = new CudaParameterSet(cu, force.getNumPerAcceptorParameters(), numAcceptors, "customHbondAcceptorParameters");
    if (force.getNumGlobalParameters() > 0)
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        globals.initialize<float>(cu, force.getNumGlobalParameters(), "customHbondGlobals");
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    vector<vector<float> > donorParamVector(numDonors);
    vector<int4> donorVector(numDonors);
    for (int i = 0; i < numDonors; i++) {
        vector<double> parameters;
        force.getDonorParameters(startIndex+i, donorVector[i].x, donorVector[i].y, donorVector[i].z, parameters);
        donorParamVector[i].resize(parameters.size());
        for (int j = 0; j < (int) parameters.size(); j++)
            donorParamVector[i][j] = (float) parameters[j];
    }
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    donors.upload(donorVector);
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    donorParams->setParameterValues(donorParamVector);
    vector<vector<float> > acceptorParamVector(numAcceptors);
    vector<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] = (float) parameters[j];
    }
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    acceptors.upload(acceptorVector);
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    acceptorParams->setParameterValues(acceptorParamVector);
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    info = new ForceInfo(force);
    cu.addForce(info);
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    // Record exclusions.

    vector<int4> donorExclusionVector(numDonors, make_int4(-1, -1, -1, -1));
    vector<int4> acceptorExclusionVector(numAcceptors, make_int4(-1, -1, -1, -1));
    for (int i = 0; i < force.getNumExclusions(); i++) {
        int donor, acceptor;
        force.getExclusionParticles(i, donor, acceptor);
        if (donor < startIndex || donor >= endIndex)
            continue;
        donor -= startIndex;
        if (donorExclusionVector[donor].x == -1)
            donorExclusionVector[donor].x = acceptor;
        else if (donorExclusionVector[donor].y == -1)
            donorExclusionVector[donor].y = acceptor;
        else if (donorExclusionVector[donor].z == -1)
            donorExclusionVector[donor].z = acceptor;
        else if (donorExclusionVector[donor].w == -1)
            donorExclusionVector[donor].w = acceptor;
        else
            throw OpenMMException("CustomHbondForce: CudaPlatform 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: CudaPlatform does not support more than four exclusions per acceptor");
    }
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    donorExclusions.initialize<int4>(cu, numDonors, "customHbondDonorExclusions");
    acceptorExclusions.initialize<int4>(cu, numAcceptors, "customHbondAcceptorExclusions");
    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;
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    tabulatedFunctions.resize(force.getNumTabulatedFunctions());
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    for (int i = 0; i < force.getNumTabulatedFunctions(); i++) {
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        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
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        string arrayName = "table"+cu.intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
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        functions[name] = cu.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
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        int width;
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        vector<float> f = cu.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        tabulatedFunctions[i].initialize<float>(cu, f.size(), "TabulatedFunction");
        tabulatedFunctions[i].upload(f);
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        tableArgs << ", const float";
        if (width > 1)
            tableArgs << width;
        tableArgs << "* __restrict__ " << arrayName;
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    }

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

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

    map<string, vector<int> > distances;
    map<string, vector<int> > angles;
    map<string, vector<int> > dihedrals;
    Lepton::ParsedExpression energyExpression = CustomHbondForceImpl::prepareExpression(force, functions, distances, angles, dihedrals);
    map<string, Lepton::ParsedExpression> forceExpressions;
    set<string> computedDeltas;
    computedDeltas.insert("D1A1");
    string atomNames[] = {"A1", "A2", "A3", "D1", "D2", "D3"};
    string atomNamesLower[] = {"a1", "a2", "a3", "d1", "d2", "d3"};
    stringstream computeDonor, computeAcceptor, extraArgs;
    int index = 0;
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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);
        }
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real r_"+deltaName+" = SQRT(delta"+deltaName+".w);\n");
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        variables[distance.first] = "r_"+deltaName;
        forceExpressions["real dEdDistance"+cu.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);
        }
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real "+angleName+" = computeAngle(delta"+deltaName1+", delta"+deltaName2+");\n");
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        variables[angle.first] = angleName;
        forceExpressions["real dEdAngle"+cu.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);
        }
        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");
        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"+cu.intToString(index)+" = "] = energyExpression.differentiate(dihedral.first).optimize();
        index++;
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    }
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    // Next it needs to load parameters from global memory.
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    if (force.getNumGlobalParameters() > 0)
        extraArgs << ", const float* __restrict__ globals";
    for (int i = 0; i < (int) donorParams->getBuffers().size(); i++) {
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        CudaNonbondedUtilities::ParameterInfo& buffer = donorParams->getBuffers()[i];
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        extraArgs << ", const "+buffer.getType()+"* __restrict__ donor"+buffer.getName();
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, buffer.getType()+" donorParams"+cu.intToString(i+1)+" = donor"+buffer.getName()+"[donorIndex];\n");
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    }
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    for (int i = 0; i < (int) acceptorParams->getBuffers().size(); i++) {
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        CudaNonbondedUtilities::ParameterInfo& buffer = acceptorParams->getBuffers()[i];
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        extraArgs << ", const "+buffer.getType()+"* __restrict__ acceptor"+buffer.getName();
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        addDonorAndAcceptorCode(computeDonor, computeAcceptor, buffer.getType()+" acceptorParams"+cu.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 << cu.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, "temp");
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    forceExpressions["energy += "] = energyExpression;
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    computeDonor << cu.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]];
        string value = "(dEdDistance"+cu.intToString(index)+"/r_"+deltaName+")*delta"+deltaName;
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[0], "-"+value);
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[1], value);
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        index++;
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    }
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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");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real3 crossProd = cross(delta"+deltaName2+", delta"+deltaName1+");\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real lengthCross = max(SQRT(dot(crossProd,crossProd)), 1e-6f);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real3 deltaCross0 = -cross(trim(delta"+deltaName1+"), crossProd)*dEdAngle"+cu.intToString(index)+"/(delta"+deltaName1+".w*lengthCross);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real3 deltaCross2 = cross(trim(delta"+deltaName2+"), crossProd)*dEdAngle"+cu.intToString(index)+"/(delta"+deltaName2+".w*lengthCross);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real3 deltaCross1 = -(deltaCross0+deltaCross2);\n");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[0], "deltaCross0");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[1], "deltaCross1");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[2], "deltaCross2");
        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");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real r = SQRT(delta"+deltaName2+".w);\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "real4 ff;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.x = (-dEdDihedral"+cu.intToString(index)+"*r)/"+crossName1+".w;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.y = (delta"+deltaName1+".x*delta"+deltaName2+".x + delta"+deltaName1+".y*delta"+deltaName2+".y + delta"+deltaName1+".z*delta"+deltaName2+".z)/delta"+deltaName2+".w;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.z = (delta"+deltaName3+".x*delta"+deltaName2+".x + delta"+deltaName3+".y*delta"+deltaName2+".y + delta"+deltaName3+".z*delta"+deltaName2+".z)/delta"+deltaName2+".w;\n");
        addDonorAndAcceptorCode(computeDonor, computeAcceptor, "ff.w = (dEdDihedral"+cu.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");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[0], "internalF0");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[1], "s-internalF0");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[2], "-s-internalF3");
        applyDonorAndAcceptorForces(computeDonor, computeAcceptor, atoms[3], "internalF3");
        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();
    replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
    map<string, string> defines;
    defines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
    defines["NUM_DONORS"] = cu.intToString(numDonors);
    defines["NUM_ACCEPTORS"] = cu.intToString(numAcceptors);
    defines["M_PI"] = cu.doubleToString(M_PI);
    if (force.getNonbondedMethod() != CustomHbondForce::NoCutoff) {
        defines["USE_CUTOFF"] = "1";
        defines["CUTOFF_SQUARED"] = cu.doubleToString(force.getCutoffDistance()*force.getCutoffDistance());
    }
    if (force.getNonbondedMethod() != CustomHbondForce::NoCutoff && force.getNonbondedMethod() != CustomHbondForce::CutoffNonPeriodic)
        defines["USE_PERIODIC"] = "1";
    if (force.getNumExclusions() > 0)
        defines["USE_EXCLUSIONS"] = "1";
    CUmodule module = cu.createModule(cu.replaceStrings(CudaKernelSources::vectorOps+CudaKernelSources::customHbondForce, replacements), defines);
    donorKernel = cu.getKernel(module, "computeDonorForces");
    acceptorKernel = cu.getKernel(module, "computeAcceptorForces");
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}

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double CudaCalcCustomHbondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (numDonors == 0 || numAcceptors == 0)
        return 0.0;
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    if (globals.isInitialized()) {
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        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)
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            globals.upload(globalParamValues);
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    }
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    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
        int index = 0;
        donorArgs.push_back(&cu.getForce().getDevicePointer());
        donorArgs.push_back(&cu.getEnergyBuffer().getDevicePointer());
        donorArgs.push_back(&cu.getPosq().getDevicePointer());
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        donorArgs.push_back(&donorExclusions.getDevicePointer());
        donorArgs.push_back(&donors.getDevicePointer());
        donorArgs.push_back(&acceptors.getDevicePointer());
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        donorArgs.push_back(cu.getPeriodicBoxSizePointer());
        donorArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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        donorArgs.push_back(cu.getPeriodicBoxVecXPointer());
        donorArgs.push_back(cu.getPeriodicBoxVecYPointer());
        donorArgs.push_back(cu.getPeriodicBoxVecZPointer());
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        if (globals.isInitialized())
            donorArgs.push_back(&globals.getDevicePointer());
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        for (auto& buffer : donorParams->getBuffers())
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            donorArgs.push_back(&buffer.getMemory());
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        for (auto& buffer : acceptorParams->getBuffers())
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            donorArgs.push_back(&buffer.getMemory());
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        for (auto& function : tabulatedFunctions)
            donorArgs.push_back(&function.getDevicePointer());
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        index = 0;
        acceptorArgs.push_back(&cu.getForce().getDevicePointer());
        acceptorArgs.push_back(&cu.getEnergyBuffer().getDevicePointer());
        acceptorArgs.push_back(&cu.getPosq().getDevicePointer());
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        acceptorArgs.push_back(&acceptorExclusions.getDevicePointer());
        acceptorArgs.push_back(&donors.getDevicePointer());
        acceptorArgs.push_back(&acceptors.getDevicePointer());
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        acceptorArgs.push_back(cu.getPeriodicBoxSizePointer());
        acceptorArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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        acceptorArgs.push_back(cu.getPeriodicBoxVecXPointer());
        acceptorArgs.push_back(cu.getPeriodicBoxVecYPointer());
        acceptorArgs.push_back(cu.getPeriodicBoxVecZPointer());
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        if (globals.isInitialized())
            acceptorArgs.push_back(&globals.getDevicePointer());
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        for (auto& buffer : donorParams->getBuffers())
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            acceptorArgs.push_back(&buffer.getMemory());
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        for (auto& buffer : acceptorParams->getBuffers())
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            acceptorArgs.push_back(&buffer.getMemory());
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        for (auto& function : tabulatedFunctions)
            acceptorArgs.push_back(&function.getDevicePointer());
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    }
    int sharedMemorySize = 3*CudaContext::ThreadBlockSize*sizeof(float4);
    cu.executeKernel(donorKernel, &donorArgs[0], max(numDonors, numAcceptors), CudaContext::ThreadBlockSize, sharedMemorySize);
    cu.executeKernel(acceptorKernel, &acceptorArgs[0], max(numDonors, numAcceptors), CudaContext::ThreadBlockSize, sharedMemorySize);
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    return 0.0;
}

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void CudaCalcCustomHbondForceKernel::copyParametersToContext(ContextImpl& context, const CustomHbondForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
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    int startIndex = cu.getContextIndex()*force.getNumDonors()/numContexts;
    int endIndex = (cu.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");
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    // Record the per-donor parameters.
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    if (numDonors > 0) {
        vector<vector<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] = (float) parameters[j];
        }
        donorParams->setParameterValues(donorParamVector);
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    }
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    // Record the per-acceptor parameters.
    
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    if (numAcceptors > 0) {
        vector<vector<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] = (float) parameters[j];
        }
        acceptorParams->setParameterValues(acceptorParamVector);
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    }
    
    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}
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class CudaCalcCustomCentroidBondForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const CustomCentroidBondForce& force) : force(force) {
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    }
    int getNumParticleGroups() {
        return force.getNumBonds();
    }
    void getParticlesInGroup(int index, vector<int>& particles) {
        vector<double> parameters;
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        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());
        }
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    }
    bool areGroupsIdentical(int group1, int group2) {
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        vector<int> groups1, groups2;
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        vector<double> parameters1, parameters2;
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        force.getBondParameters(group1, groups1, parameters1);
        force.getBondParameters(group2, groups2, parameters2);
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        for (int i = 0; i < (int) parameters1.size(); i++)
            if (parameters1[i] != parameters2[i])
                return false;
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        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;
        }
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        return true;
    }
private:
    const CustomCentroidBondForce& force;
};

CudaCalcCustomCentroidBondForceKernel::~CudaCalcCustomCentroidBondForceKernel() {
    cu.setAsCurrent();
    if (params != NULL)
        delete params;
}

void CudaCalcCustomCentroidBondForceKernel::initialize(const System& system, const CustomCentroidBondForce& force) {
    cu.setAsCurrent();
    numBonds = force.getNumBonds();
    if (numBonds == 0)
        return;
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    info = new ForceInfo(force);
    cu.addForce(info);
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    // Record the groups.
    
    numGroups = force.getNumGroups();
    vector<int> groupParticleVec;
    vector<float> groupWeightVecFloat;
    vector<double> groupWeightVecDouble;
    vector<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 (cu.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]);
    }
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    groupParticles.initialize<int>(cu, groupParticleVec.size(), "groupParticles");
    groupParticles.upload(groupParticleVec);
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    if (cu.getUseDoublePrecision()) {
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        groupWeights.initialize<double>(cu, groupParticleVec.size(), "groupWeights");
        groupWeights.upload(groupWeightVecDouble);
        centerPositions.initialize<double4>(cu, numGroups, "centerPositions");
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    }
    else {
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        groupWeights.initialize<float>(cu, groupParticleVec.size(), "groupWeights");
        groupWeights.upload(groupWeightVecFloat);
        centerPositions.initialize<float4>(cu, numGroups, "centerPositions");
    }
    groupOffsets.initialize<int>(cu, groupOffsetVec.size(), "groupOffsets");
    groupOffsets.upload(groupOffsetVec);
    groupForces.initialize<long long>(cu, numGroups*3, "groupForces");
    cu.addAutoclearBuffer(groupForces);
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    // Record the bonds.
    
    int groupsPerBond = force.getNumGroupsPerBond();
    vector<int> bondGroupVec(numBonds*groupsPerBond);
    params = new CudaParameterSet(cu, 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);
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    bondGroups.initialize<int>(cu, bondGroupVec.size(), "bondGroups");
    bondGroups.upload(bondGroupVec);
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    // Record the arguments to the force kernel.
    
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    groupForcesArgs.push_back(&groupForces.getDevicePointer());
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    groupForcesArgs.push_back(NULL); // Energy buffer hasn't been created yet
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    groupForcesArgs.push_back(&centerPositions.getDevicePointer());
    groupForcesArgs.push_back(&bondGroups.getDevicePointer());
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    groupForcesArgs.push_back(cu.getPeriodicBoxSizePointer());
    groupForcesArgs.push_back(cu.getInvPeriodicBoxSizePointer());
    groupForcesArgs.push_back(cu.getPeriodicBoxVecXPointer());
    groupForcesArgs.push_back(cu.getPeriodicBoxVecYPointer());
    groupForcesArgs.push_back(cu.getPeriodicBoxVecZPointer());
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    needEnergyParamDerivs = (force.getNumEnergyParameterDerivatives() > 0);
    if (needEnergyParamDerivs)
        groupForcesArgs.push_back(NULL); // Derivatives buffer hasn't been created yet
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    // Record the tabulated functions.

    map<string, Lepton::CustomFunction*> functions;
    vector<pair<string, string> > functionDefinitions;
    vector<const TabulatedFunction*> functionList;
    stringstream extraArgs;
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    tabulatedFunctions.resize(force.getNumTabulatedFunctions());
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    for (int i = 0; i < force.getNumTabulatedFunctions(); i++) {
        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
        string arrayName = "table"+cu.intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
        functions[name] = cu.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
        int width;
        vector<float> f = cu.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        tabulatedFunctions[i].initialize<float>(cu, f.size(), "TabulatedFunction");
        tabulatedFunctions[i].upload(f);
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        extraArgs << ", const float";
        if (width > 1)
            extraArgs << width;
        extraArgs << "* __restrict__ " << arrayName;
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        groupForcesArgs.push_back(&tabulatedFunctions[i].getDevicePointer());
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    }
    
    // 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 = cu.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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    if (needEnergyParamDerivs)
        extraArgs << ", mixed* __restrict__ energyParamDerivs";
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    if (force.getNumGlobalParameters() > 0) {
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        globals.initialize<float>(cu, force.getNumGlobalParameters(), "customCentroidBondGlobals");
        globals.upload(globalParamValues);
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        extraArgs << ", const float* __restrict__ globals";
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+cu.intToString(i)+"]";
            variables[name] = value;
        }
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        groupForcesArgs.push_back(&globals.getDevicePointer());
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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 = 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 = cu.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"+cu.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"+cu.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"+cu.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++) {
        CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        extraArgs<<", const "<<buffer.getType()<<"* __restrict__ globalParams"<<i;
        compute<<buffer.getType()<<" bondParams"<<(i+1)<<" = globalParams"<<i<<"[index];\n";
        groupForcesArgs.push_back(&buffer.getMemory());
    }
    forceExpressions["energy += "] = energyExpression;
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    if (needEnergyParamDerivs) {
        for (int i = 0; i < force.getNumEnergyParameterDerivatives(); i++) {
            string paramName = force.getEnergyParameterDerivativeName(i);
            cu.addEnergyParameterDerivative(paramName);
            Lepton::ParsedExpression derivExpression = energyExpression.differentiate(paramName).optimize();
            forceExpressions[string("energyParamDeriv")+cu.intToString(i)+" += "] = derivExpression;
            initParamDerivs << "mixed energyParamDeriv" << i << " = 0;\n";
        }
        const vector<string>& allParamDerivNames = cu.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[(blockIdx.x*blockDim.x+threadIdx.x)*" << numDerivs << "+" << index << "] += energyParamDeriv" << i << ";\n";
    }
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    compute << cu.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, "temp");

    // Finally, apply forces to groups.

    vector<string> forceNames;
    for (int i = 0; i < groupsPerBond; i++) {
        string istr = cu.intToString(i+1);
        string forceName = "force"+istr;
        forceNames.push_back(forceName);
        compute<<"real3 "<<forceName<<" = make_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<<cu.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"+cu.intToString(index)+"/r_"+deltaName+")*trim(delta"+deltaName+")";
        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<<"real3 crossProd = cross(delta"<<deltaName2<<", delta"<<deltaName1<<");\n";
        compute<<"real lengthCross = max(SQRT(dot(crossProd, crossProd)), 1e-6f);\n";
        compute<<"real3 deltaCross0 = -cross(trim(delta"<<deltaName1<<"), crossProd)*dEdAngle"<<cu.intToString(index)<<"/(delta"<<deltaName1<<".w*lengthCross);\n";
        compute<<"real3 deltaCross2 = cross(trim(delta"<<deltaName2<<"), crossProd)*dEdAngle"<<cu.intToString(index)<<"/(delta"<<deltaName2<<".w*lengthCross);\n";
        compute<<"real3 deltaCross1 = -(deltaCross0+deltaCross2);\n";
        compute<<forceNames[groups[0]]<<" += deltaCross0;\n";
        compute<<forceNames[groups[1]]<<" += deltaCross1;\n";
        compute<<forceNames[groups[2]]<<" += deltaCross2;\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"<<cu.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"<<cu.intToString(index)<<"*r)/"<<crossName2<<".w;\n";
        compute<<"real3 internalF0 = ff.x*trim("<<crossName1<<");\n";
        compute<<"real3 internalF3 = ff.w*trim("<<crossName2<<");\n";
        compute<<"real3 s = ff.y*internalF0 - ff.z*internalF3;\n";
        compute<<forceNames[groups[0]]<<" += internalF0;\n";
        compute<<forceNames[groups[1]]<<" += s-internalF0;\n";
        compute<<forceNames[groups[2]]<<" += -s-internalF3;\n";
        compute<<forceNames[groups[3]]<<" += internalF3;\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<<"atomicAdd(&groupForce[group"<<(i+1)<<"], static_cast<unsigned long long>((long long) (force"<<(i+1)<<".x*0x100000000)));\n";
        compute<<"atomicAdd(&groupForce[group"<<(i+1)<<"+NUM_GROUPS], static_cast<unsigned long long>((long long) (force"<<(i+1)<<".y*0x100000000)));\n";
        compute<<"atomicAdd(&groupForce[group"<<(i+1)<<"+NUM_GROUPS*2], static_cast<unsigned long long>((long long) (force"<<(i+1)<<".z*0x100000000)));\n";
        compute<<"__threadfence_block();\n";
    }
    map<string, string> replacements;
    replacements["M_PI"] = cu.doubleToString(M_PI);
    replacements["NUM_GROUPS"] = cu.intToString(numGroups);
    replacements["NUM_BONDS"] = cu.intToString(numBonds);
    replacements["PADDED_NUM_ATOMS"] = cu.intToString(cu.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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    CUmodule module = cu.createModule(CudaKernelSources::vectorOps+cu.replaceStrings(CudaKernelSources::customCentroidBond, replacements));
    computeCentersKernel = cu.getKernel(module, "computeGroupCenters");
    groupForcesKernel = cu.getKernel(module, "computeGroupForces");
    applyForcesKernel = cu.getKernel(module, "applyForcesToAtoms");
}

double CudaCalcCustomCentroidBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (numBonds == 0)
        return 0.0;
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    if (globals.isInitialized()) {
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        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)
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            globals.upload(globalParamValues);
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    }
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    void* computeCentersArgs[] = {&cu.getPosq().getDevicePointer(), &groupParticles.getDevicePointer(), &groupWeights.getDevicePointer(),
            &groupOffsets.getDevicePointer(), &centerPositions.getDevicePointer()};
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    cu.executeKernel(computeCentersKernel, computeCentersArgs, CudaContext::TileSize*numGroups);
    groupForcesArgs[1] = &cu.getEnergyBuffer().getDevicePointer();
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    if (needEnergyParamDerivs)
        groupForcesArgs[9] = &cu.getEnergyParamDerivBuffer().getDevicePointer();
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    cu.executeKernel(groupForcesKernel, &groupForcesArgs[0], numBonds);
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    void* applyForcesArgs[] = {&groupParticles.getDevicePointer(), &groupWeights.getDevicePointer(), &groupOffsets.getDevicePointer(),
            &groupForces.getDevicePointer(), &cu.getForce().getDevicePointer()};
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    cu.executeKernel(applyForcesKernel, applyForcesArgs, CudaContext::TileSize*numGroups);
    return 0.0;
}

void CudaCalcCustomCentroidBondForceKernel::copyParametersToContext(ContextImpl& context, const CustomCentroidBondForce& force) {
    cu.setAsCurrent();
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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.
    
    cu.invalidateMolecules();
}

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class CudaCalcCustomCompoundBondForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const CustomCompoundBondForce& force) : 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;
};

CudaCalcCustomCompoundBondForceKernel::~CudaCalcCustomCompoundBondForceKernel() {
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    cu.setAsCurrent();
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    if (params != NULL)
        delete params;
}

void CudaCalcCustomCompoundBondForceKernel::initialize(const System& system, const CustomCompoundBondForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cu.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 CudaParameterSet(cu, force.getNumPerBondParameters(), numBonds, "customCompoundBondParams");
    vector<vector<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] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
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    info = new ForceInfo(force);
    cu.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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    tabulatedFunctions.resize(force.getNumTabulatedFunctions());
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    for (int i = 0; i < force.getNumTabulatedFunctions(); i++) {
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        functionList.push_back(&force.getTabulatedFunction(i));
        string name = force.getTabulatedFunctionName(i);
        functions[name] = cu.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
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        int width;
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        vector<float> f = cu.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        tabulatedFunctions[i].initialize<float>(cu, f.size(), "TabulatedFunction");
        tabulatedFunctions[i].upload(f);
        string arrayName = cu.getBondedUtilities().addArgument(tabulatedFunctions[i].getDevicePointer(), width == 1 ? "float" : "float"+cu.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] = (float) force.getGlobalParameterDefaultValue(i);
    }
    map<string, string> variables;
    for (int i = 0; i < particlesPerBond; i++) {
        string index = cu.intToString(i+1);
        variables["x"+index] = "pos"+index+".x";
        variables["y"+index] = "pos"+index+".y";
        variables["z"+index] = "pos"+index+".z";
    }
    for (int i = 0; i < force.getNumPerBondParameters(); i++) {
        const string& name = force.getPerBondParameterName(i);
        variables[name] = "bondParams"+params->getParameterSuffix(i);
    }
    if (force.getNumGlobalParameters() > 0) {
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        globals.initialize<float>(cu, force.getNumGlobalParameters(), "customCompoundBondGlobals");
        globals.upload(globalParamValues);
        string argName = cu.getBondedUtilities().addArgument(globals.getDevicePointer(), "float");
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        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = argName+"["+cu.intToString(i)+"]";
            variables[name] = value;
        }
    }

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

    map<string, vector<int> > distances;
    map<string, vector<int> > angles;
    map<string, vector<int> > dihedrals;
    Lepton::ParsedExpression energyExpression = CustomCompoundBondForceImpl::prepareExpression(force, functions, distances, angles, dihedrals);
    map<string, Lepton::ParsedExpression> forceExpressions;
    set<string> computedDeltas;
    vector<string> atomNames, posNames;
    for (int i = 0; i < particlesPerBond; i++) {
        string index = cu.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<<" = ccb_delta("<<posNames[atoms[0]]<<", "<<posNames[atoms[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"+cu.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);
        }
        compute<<"real "<<angleName<<" = ccb_computeAngle(delta"<<deltaName1<<", delta"<<deltaName2<<");\n";
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        variables[angle.first] = angleName;
        forceExpressions["real dEdAngle"+cu.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);
        }
        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";
        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"+cu.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++) {
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        CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        string argName = cu.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 = cu.getBondedUtilities().addEnergyParameterDerivative(paramName);
        Lepton::ParsedExpression derivExpression = energyExpression.differentiate(paramName).optimize();
        forceExpressions[derivVariable+" += "] = derivExpression;
    }
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    compute << cu.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++) {
        string istr = cu.intToString(i+1);
        string forceName = "force"+istr;
        forceNames.push_back(forceName);
        compute<<"real3 "<<forceName<<" = make_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)
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            compute<<cu.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]];
        string value = "(dEdDistance"+cu.intToString(index)+"/r_"+deltaName+")*ccb_trim(delta"+deltaName+")";
        compute<<forceNames[atoms[0]]<<" += "<<"-"<<value<<";\n";
        compute<<forceNames[atoms[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>& 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<<"real3 crossProd = cross(delta"<<deltaName2<<", delta"<<deltaName1<<");\n";
        compute<<"real lengthCross = max(SQRT(dot(crossProd, crossProd)), 1e-6f);\n";
        compute<<"real3 deltaCross0 = -cross(ccb_trim(delta"<<deltaName1<<"), crossProd)*dEdAngle"<<cu.intToString(index)<<"/(delta"<<deltaName1<<".w*lengthCross);\n";
        compute<<"real3 deltaCross2 = cross(ccb_trim(delta"<<deltaName2<<"), crossProd)*dEdAngle"<<cu.intToString(index)<<"/(delta"<<deltaName2<<".w*lengthCross);\n";
        compute<<"real3 deltaCross1 = -(deltaCross0+deltaCross2);\n";
        compute<<forceNames[atoms[0]]<<" += deltaCross0;\n";
        compute<<forceNames[atoms[1]]<<" += deltaCross1;\n";
        compute<<forceNames[atoms[2]]<<" += deltaCross2;\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"<<cu.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"<<cu.intToString(index)<<"*r)/"<<crossName2<<".w;\n";
        compute<<"real3 internalF0 = ff.x*ccb_trim("<<crossName1<<");\n";
        compute<<"real3 internalF3 = ff.w*ccb_trim("<<crossName2<<");\n";
        compute<<"real3 s = ff.y*internalF0 - ff.z*internalF3;\n";
        compute<<forceNames[atoms[0]]<<" += internalF0;\n";
        compute<<forceNames[atoms[1]]<<" += s-internalF0;\n";
        compute<<forceNames[atoms[2]]<<" += -s-internalF3;\n";
        compute<<forceNames[atoms[3]]<<" += internalF3;\n";
        compute<<"}\n";
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        index++;
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    }
    cu.getBondedUtilities().addInteraction(atoms, compute.str(), force.getForceGroup());
    map<string, string> replacements;
    replacements["M_PI"] = cu.doubleToString(M_PI);
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    cu.getBondedUtilities().addPrefixCode(cu.replaceStrings(CudaKernelSources::customCompoundBond, replacements));
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}

double CudaCalcCustomCompoundBondForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
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    if (globals.isInitialized()) {
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        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)
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            globals.upload(globalParamValues);
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    }
    return 0.0;
}

void CudaCalcCustomCompoundBondForceKernel::copyParametersToContext(ContextImpl& context, const CustomCompoundBondForce& force) {
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    cu.setAsCurrent();
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    int numContexts = cu.getPlatformData().contexts.size();
    int startIndex = cu.getContextIndex()*force.getNumBonds()/numContexts;
    int endIndex = (cu.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<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] = (float) parameters[j];
    }
    params->setParameterValues(paramVector);
    
    // Mark that the current reordering may be invalid.
    
    cu.invalidateMolecules();
}

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class CudaCalcCustomManyParticleForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const CustomManyParticleForce& force) : 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() {
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        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;
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    }
    bool areGroupsIdentical(int group1, int group2) {
        return true;
    }
private:
    const CustomManyParticleForce& force;
};

CudaCalcCustomManyParticleForceKernel::~CudaCalcCustomManyParticleForceKernel() {
    cu.setAsCurrent();
    if (params != NULL)
        delete params;
}

void CudaCalcCustomManyParticleForceKernel::initialize(const System& system, const CustomManyParticleForce& force) {
    cu.setAsCurrent();
    int numParticles = force.getNumParticles();
    int particlesPerSet = force.getNumParticlesPerSet();
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    bool centralParticleMode = (force.getPermutationMode() == CustomManyParticleForce::UniqueCentralParticle);
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    nonbondedMethod = CalcCustomManyParticleForceKernel::NonbondedMethod(force.getNonbondedMethod());
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    forceWorkgroupSize = 128;
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    findNeighborsWorkgroupSize = 128;
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    // Record parameter values.
    
    params = new CudaParameterSet(cu, 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);
    cu.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;
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    tabulatedFunctions.resize(force.getNumTabulatedFunctions());
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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 = "table"+cu.intToString(i);
        functionDefinitions.push_back(make_pair(name, arrayName));
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        functions[name] = cu.getExpressionUtilities().getFunctionPlaceholder(force.getTabulatedFunction(i));
        int width;
        vector<float> f = cu.getExpressionUtilities().computeFunctionCoefficients(force.getTabulatedFunction(i), width);
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        tabulatedFunctions[i].initialize<float>(cu, f.size(), "TabulatedFunction");
        tabulatedFunctions[i].upload(f);
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        tableArgs << ", const float";
        if (width > 1)
            tableArgs << width;
        tableArgs << "* __restrict__ " << arrayName;
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    }
    
    // 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);
    }
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    vector<pair<ExpressionTreeNode, string> > variables;
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    for (int i = 0; i < particlesPerSet; i++) {
        string index = cu.intToString(i+1);
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        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"));
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    }
    for (int i = 0; i < force.getNumPerParticleParameters(); i++) {
        const string& name = force.getPerParticleParameterName(i);
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        for (int j = 0; j < particlesPerSet; j++) {
            string index = cu.intToString(j+1);
            variables.push_back(makeVariable(name+index, "params"+params->getParameterSuffix(i, index)));
        }
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    }
    if (force.getNumGlobalParameters() > 0) {
        for (int i = 0; i < force.getNumGlobalParameters(); i++) {
            const string& name = force.getGlobalParameterName(i);
            string value = "globals["+cu.intToString(i)+"]";
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            variables.push_back(makeVariable(name, value));
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        }
    }
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    // 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) {
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        particleTypes.initialize<int>(cu, particleTypesVec.size(), "customManyParticleTypes");
        orderIndex.initialize<int>(cu, orderIndexVec.size(), "customManyParticleOrderIndex");
        particleOrder.initialize<int>(cu, particleOrderVec.size()*particlesPerSet, "customManyParticleOrder");
        particleTypes.upload(particleTypesVec);
        orderIndex.upload(orderIndexVec);
        vector<int> flattenedOrder(particleOrder.getSize());
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        for (int i = 0; i < (int) particleOrderVec.size(); i++)
            for (int j = 0; j < particlesPerSet; j++)
                flattenedOrder[i*particlesPerSet+j] = particleOrderVec[i][j];
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        particleOrder.upload(flattenedOrder);
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    }
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    // 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();
        }
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        exclusions.initialize<int>(cu, exclusionsVec.size(), "customManyParticleExclusions");
        exclusionStartIndex.initialize<int>(cu, exclusionStartIndexVec.size(), "customManyParticleExclusionStart");
        exclusions.upload(exclusionsVec);
        exclusionStartIndex.upload(exclusionStartIndexVec);
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    }
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    // Build data structures for the neighbor list.
    
    if (nonbondedMethod != NoCutoff) {
        int numAtomBlocks = cu.getNumAtomBlocks();
        int elementSize = (cu.getUseDoublePrecision() ? sizeof(double) : sizeof(float));
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        blockCenter.initialize(cu, numAtomBlocks, 4*elementSize, "blockCenter");
        blockBoundingBox.initialize(cu, numAtomBlocks, 4*elementSize, "blockBoundingBox");
        numNeighborPairs.initialize<int>(cu, 1, "customManyParticleNumNeighborPairs");
        neighborStartIndex.initialize<int>(cu, numParticles+1, "customManyParticleNeighborStartIndex");
        numNeighborsForAtom.initialize<int>(cu, numParticles, "customManyParticleNumNeighborsForAtom");
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        CHECK_RESULT(cuEventCreate(&event, CU_EVENT_DISABLE_TIMING), "Error creating event for CustomManyParticleForce");

        // 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;
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        neighborPairs.initialize<int2>(cu, maxNeighborPairs, "customManyParticleNeighborPairs");
        neighbors.initialize<int>(cu, maxNeighborPairs, "customManyParticleNeighbors");
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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 = 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 = cu.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"+cu.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"+cu.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"+cu.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++) {
        CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
        compute<<buffer.getType()<<" params"<<(i+1)<<" = global_params"<<(i+1)<<"[index];\n";
    }
    forceExpressions["energy += "] = energyExpression;
    compute << cu.getExpressionUtilities().createExpressions(forceExpressions, variables, functionList, functionDefinitions, "temp");

    // Apply forces to atoms.

    vector<string> forceNames;
    for (int i = 0; i < particlesPerSet; i++) {
        string istr = cu.intToString(i+1);
        string forceName = "force"+istr;
        forceNames.push_back(forceName);
        compute<<"real3 "<<forceName<<" = make_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<<cu.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"+cu.intToString(index)+"/r_"+deltaName+")*trim(delta"+deltaName+")";
        compute<<forceNames[atoms[0]]<<" += "<<"-"<<value<<";\n";
        compute<<forceNames[atoms[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>& 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<<"real3 crossProd = cross(delta"<<deltaName2<<", delta"<<deltaName1<<");\n";
        compute<<"real lengthCross = max(SQRT(dot(crossProd, crossProd)), 1e-6f);\n";
        compute<<"real3 deltaCross0 = -cross(trim(delta"<<deltaName1<<"), crossProd)*dEdAngle"<<cu.intToString(index)<<"/(delta"<<deltaName1<<".w*lengthCross);\n";
        compute<<"real3 deltaCross2 = cross(trim(delta"<<deltaName2<<"), crossProd)*dEdAngle"<<cu.intToString(index)<<"/(delta"<<deltaName2<<".w*lengthCross);\n";
        compute<<"real3 deltaCross1 = -(deltaCross0+deltaCross2);\n";
        compute<<forceNames[atoms[0]]<<" += deltaCross0;\n";
        compute<<forceNames[atoms[1]]<<" += deltaCross1;\n";
        compute<<forceNames[atoms[2]]<<" += deltaCross2;\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"<<cu.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"<<cu.intToString(index)<<"*r)/"<<crossName2<<".w;\n";
        compute<<"real3 internalF0 = ff.x*trim("<<crossName1<<");\n";
        compute<<"real3 internalF3 = ff.w*trim("<<crossName2<<");\n";
        compute<<"real3 s = ff.y*internalF0 - ff.z*internalF3;\n";
        compute<<forceNames[atoms[0]]<<" += internalF0;\n";
        compute<<forceNames[atoms[1]]<<" += s-internalF0;\n";
        compute<<forceNames[atoms[2]]<<" += -s-internalF3;\n";
        compute<<forceNames[atoms[3]]<<" += internalF3;\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.
    
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    stringstream numCombinations, atomsForCombination, isValidCombination, permute, loadData, verifyCutoff, verifyExclusions;
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    if (hasTypeFilters) {
        permute<<"int particleSet[] = {";
        for (int i = 0; i < particlesPerSet; i++) {
            permute<<"p"<<(i+1);
            if (i < particlesPerSet-1)
                permute<<", ";
        }
        permute<<"};\n";
    }
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    for (int i = 0; i < particlesPerSet; i++) {
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        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";
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        loadData<<"real3 pos"<<(i+1)<<" = trim(posq[atom"<<(i+1)<<"]);\n";
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        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";
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    }
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    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;
        }
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    }
    atomsForCombination<<"int tempIndex = index;\n";
    for (int i = 1; i < particlesPerSet; i++) {
        if (i > 1)
            numCombinations<<"*";
        numCombinations<<"numNeighbors";
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        if (centralParticleMode)
            atomsForCombination<<"int a"<<(i+1)<<" = tempIndex%numNeighbors;\n";
        else
            atomsForCombination<<"int a"<<(i+1)<<" = 1+tempIndex%numNeighbors;\n";
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        if (i < particlesPerSet-1)
            atomsForCombination<<"tempIndex /= numNeighbors;\n";
    }
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    if (particlesPerSet > 2) {
        if (centralParticleMode)
            atomsForCombination<<"a2 = (a3%2 == 0 ? a2 : numNeighbors-a2-1);\n";
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        else
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            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";
        }
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    }
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    if (nonbondedMethod != NoCutoff) {
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        for (int i = 1; i < particlesPerSet; i++)
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            verifyCutoff<<"real3 pos"<<(i+1)<<" = trim(posq[p"<<(i+1)<<"]);\n";
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        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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            }
        }
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    }
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    if (force.getNumExclusions() > 0) {
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        int startCheckFrom = (nonbondedMethod == NoCutoff ? 0 : 1);
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        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";
    }
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    string computeTypeIndex = "particleTypes[p"+cu.intToString(particlesPerSet)+"]";
    for (int i = particlesPerSet-2; i >= 0; i--)
        computeTypeIndex = "particleTypes[p"+cu.intToString(i+1)+"]+"+cu.intToString(numTypes)+"*("+computeTypeIndex+")";
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    // Create replacements for extra arguments.
    
    stringstream extraArgs;
    for (int i = 0; i < (int) params->getBuffers().size(); i++) {
        CudaNonbondedUtilities::ParameterInfo& buffer = params->getBuffers()[i];
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        extraArgs<<", const "<<buffer.getType()<<"* __restrict__ global_params"<<(i+1);
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    }

    // 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();
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    replacements["VERIFY_CUTOFF"] = verifyCutoff.str();
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    replacements["VERIFY_EXCLUSIONS"] = verifyExclusions.str();
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    replacements["PERMUTE_ATOMS"] = permute.str();
    replacements["LOAD_PARTICLE_DATA"] = loadData.str();
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    replacements["COMPUTE_TYPE_INDEX"] = computeTypeIndex;
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    replacements["PARAMETER_ARGUMENTS"] = extraArgs.str()+tableArgs.str();
    map<string, string> defines;
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    if (nonbondedMethod != NoCutoff)
        defines["USE_CUTOFF"] = "1";
    if (nonbondedMethod == CutoffPeriodic)
        defines["USE_PERIODIC"] = "1";
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    if (centralParticleMode)
        defines["USE_CENTRAL_PARTICLE"] = "1";
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    if (hasTypeFilters)
        defines["USE_FILTERS"] = "1";
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    if (force.getNumExclusions() > 0)
        defines["USE_EXCLUSIONS"] = "1";
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    defines["NUM_ATOMS"] = cu.intToString(cu.getNumAtoms());
    defines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
    defines["M_PI"] = cu.doubleToString(M_PI);
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    defines["CUTOFF_SQUARED"] = cu.doubleToString(force.getCutoffDistance()*force.getCutoffDistance());
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    defines["TILE_SIZE"] = cu.intToString(CudaContext::TileSize);
    defines["NUM_BLOCKS"] = cu.intToString(cu.getNumAtomBlocks());
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    defines["NUM_GLOBALS"] = cu.intToString(max(1, force.getNumGlobalParameters()));
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    defines["FIND_NEIGHBORS_WORKGROUP_SIZE"] = cu.intToString(findNeighborsWorkgroupSize);
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    CUmodule module = cu.createModule(cu.replaceStrings(CudaKernelSources::vectorOps+CudaKernelSources::customManyParticle, replacements), defines);
    forceKernel = cu.getKernel(module, "computeInteraction");
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    blockBoundsKernel = cu.getKernel(module, "findBlockBounds");
    neighborsKernel = cu.getKernel(module, "findNeighbors");
    startIndicesKernel = cu.getKernel(module, "computeNeighborStartIndices");
    copyPairsKernel = cu.getKernel(module, "copyPairsToNeighborList");
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    cuFuncSetCacheConfig(forceKernel, CU_FUNC_CACHE_PREFER_L1);
    cuFuncSetCacheConfig(neighborsKernel, CU_FUNC_CACHE_PREFER_L1);
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    size_t bytes;
    CHECK_RESULT(cuModuleGetGlobal(&globalsPtr, &bytes, module, "globals"), "Error getting address for constant memory")
    cuMemcpyHtoD(globalsPtr, &globalParamValues[0], globalParamValues.size()*sizeof(float));
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}

double CudaCalcCustomManyParticleForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (!hasInitializedKernel) {
        hasInitializedKernel = true;
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        // Set arguments for the force kernel.
        
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        forceArgs.push_back(&cu.getForce().getDevicePointer());
        forceArgs.push_back(&cu.getEnergyBuffer().getDevicePointer());
        forceArgs.push_back(&cu.getPosq().getDevicePointer());
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        forceArgs.push_back(cu.getPeriodicBoxSizePointer());
        forceArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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        forceArgs.push_back(cu.getPeriodicBoxVecXPointer());
        forceArgs.push_back(cu.getPeriodicBoxVecYPointer());
        forceArgs.push_back(cu.getPeriodicBoxVecZPointer());
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        if (nonbondedMethod != NoCutoff) {
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            forceArgs.push_back(&neighbors.getDevicePointer());
            forceArgs.push_back(&neighborStartIndex.getDevicePointer());
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        }
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        if (particleTypes.isInitialized()) {
            forceArgs.push_back(&particleTypes.getDevicePointer());
            forceArgs.push_back(&orderIndex.getDevicePointer());
            forceArgs.push_back(&particleOrder.getDevicePointer());
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        }
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        if (exclusions.isInitialized()) {
            forceArgs.push_back(&exclusions.getDevicePointer());
            forceArgs.push_back(&exclusionStartIndex.getDevicePointer());
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        }
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        for (auto& buffer : params->getBuffers())
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            forceArgs.push_back(&buffer.getMemory());
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        for (auto& function : tabulatedFunctions)
            forceArgs.push_back(&function.getDevicePointer());
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        if (nonbondedMethod != NoCutoff) {
            // Set arguments for the block bounds kernel.

            blockBoundsArgs.push_back(cu.getPeriodicBoxSizePointer());
            blockBoundsArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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            blockBoundsArgs.push_back(cu.getPeriodicBoxVecXPointer());
            blockBoundsArgs.push_back(cu.getPeriodicBoxVecYPointer());
            blockBoundsArgs.push_back(cu.getPeriodicBoxVecZPointer());
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            blockBoundsArgs.push_back(&cu.getPosq().getDevicePointer());
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            blockBoundsArgs.push_back(&blockCenter.getDevicePointer());
            blockBoundsArgs.push_back(&blockBoundingBox.getDevicePointer());
            blockBoundsArgs.push_back(&numNeighborPairs.getDevicePointer());
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            // Set arguments for the neighbor list kernel.

            neighborsArgs.push_back(cu.getPeriodicBoxSizePointer());
            neighborsArgs.push_back(cu.getInvPeriodicBoxSizePointer());
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            neighborsArgs.push_back(cu.getPeriodicBoxVecXPointer());
            neighborsArgs.push_back(cu.getPeriodicBoxVecYPointer());
            neighborsArgs.push_back(cu.getPeriodicBoxVecZPointer());
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            neighborsArgs.push_back(&cu.getPosq().getDevicePointer());
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            neighborsArgs.push_back(&blockCenter.getDevicePointer());
            neighborsArgs.push_back(&blockBoundingBox.getDevicePointer());
            neighborsArgs.push_back(&neighborPairs.getDevicePointer());
            neighborsArgs.push_back(&numNeighborPairs.getDevicePointer());
            neighborsArgs.push_back(&numNeighborsForAtom.getDevicePointer());
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            neighborsArgs.push_back(&maxNeighborPairs);
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            if (exclusions.isInitialized()) {
                neighborsArgs.push_back(&exclusions.getDevicePointer());
                neighborsArgs.push_back(&exclusionStartIndex.getDevicePointer());
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            }
            
            // Set arguments for the kernel to find neighbor list start indices.
            
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            startIndicesArgs.push_back(&numNeighborsForAtom.getDevicePointer());
            startIndicesArgs.push_back(&neighborStartIndex.getDevicePointer());
            startIndicesArgs.push_back(&numNeighborPairs.getDevicePointer());
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            startIndicesArgs.push_back(&maxNeighborPairs);
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            // Set arguments for the kernel to assemble the final neighbor list.
            
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            copyPairsArgs.push_back(&neighborPairs.getDevicePointer());
            copyPairsArgs.push_back(&neighbors.getDevicePointer());
            copyPairsArgs.push_back(&numNeighborPairs.getDevicePointer());
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            copyPairsArgs.push_back(&maxNeighborPairs);
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            copyPairsArgs.push_back(&numNeighborsForAtom.getDevicePointer());
            copyPairsArgs.push_back(&neighborStartIndex.getDevicePointer());
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       }
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    }
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    if (globalParamValues.size() > 0) {
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        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)
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            cuMemcpyHtoD(globalsPtr, &globalParamValues[0], globalParamValues.size()*sizeof(float));
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    }
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    while (true) {
        int* numPairs = (int*) cu.getPinnedBuffer();
        if (nonbondedMethod != NoCutoff) {
            cu.executeKernel(blockBoundsKernel, &blockBoundsArgs[0], cu.getNumAtomBlocks());
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            cu.executeKernel(neighborsKernel, &neighborsArgs[0], cu.getNumAtoms(), findNeighborsWorkgroupSize);
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            // 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.

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            numNeighborPairs.download(numPairs, false);
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            CHECK_RESULT(cuEventRecord(event, 0), "Error recording event for CustomManyParticleForce");
            cu.executeKernel(startIndicesKernel, &startIndicesArgs[0], 256, 256, 256*sizeof(int));
            cu.executeKernel(copyPairsKernel, &copyPairsArgs[0], maxNeighborPairs);
        }
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        int maxThreads = min(cu.getNumAtoms()*forceWorkgroupSize, cu.getEnergyBuffer().getSize());
        cu.executeKernel(forceKernel, &forceArgs[0], maxThreads, forceWorkgroupSize);
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        if (nonbondedMethod != NoCutoff) {
            // Make sure there was enough memory for the neighbor list.

            CHECK_RESULT(cuEventSynchronize(event), "Error synchronizing on event for CustomManyParticleForce");
            if (*numPairs > maxNeighborPairs) {
                // Resize the arrays and run the calculation again.

                maxNeighborPairs = (int) (1.1*(*numPairs));
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                neighborPairs.resize(maxNeighborPairs);
                neighbors.resize(maxNeighborPairs);
                forceArgs[5] = &neighbors.getDevicePointer();
                neighborsArgs[5] = &neighborPairs.getDevicePointer();
                copyPairsArgs[0] = &neighborPairs.getDevicePointer();
                copyPairsArgs[1] = &neighbors.getDevicePointer();
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                continue;
            }
        }
        break;
    }
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    return 0.0;
}

void CudaCalcCustomManyParticleForceKernel::copyParametersToContext(ContextImpl& context, const CustomManyParticleForce& force) {
    cu.setAsCurrent();
    int numParticles = force.getNumParticles();
    if (numParticles != cu.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.
    
    cu.invalidateMolecules();
}

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class CudaCalcGayBerneForceKernel::ForceInfo : public CudaForceInfo {
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public:
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    ForceInfo(const GayBerneForce& force) : force(force) {
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    }
    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 CudaCalcGayBerneForceKernel::ReorderListener : public CudaContext::ReorderListener {
public:
    ReorderListener(CudaCalcGayBerneForceKernel& owner) : owner(owner) {
    }
    void execute() {
        owner.sortAtoms();
    }
private:
    CudaCalcGayBerneForceKernel& owner;
};

void CudaCalcGayBerneForceKernel::initialize(const System& system, const GayBerneForce& force) {
    // Initialize interactions.

    int numParticles = force.getNumParticles();
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    sigParams.initialize<float4>(cu, cu.getPaddedNumAtoms(), "sigParams");
    epsParams.initialize<float2>(cu, cu.getPaddedNumAtoms(), "epsParams");
    scale.initialize<float4>(cu, cu.getPaddedNumAtoms(), "scale");
    axisParticleIndices.initialize<int2>(cu, cu.getPaddedNumAtoms(), "axisParticleIndices");
    sortedParticles.initialize<int>(cu, cu.getPaddedNumAtoms(), "sortedParticles");
    aMatrix.initialize<float>(cu, 9*cu.getPaddedNumAtoms(), "aMatrix");
    bMatrix.initialize<float>(cu, 9*cu.getPaddedNumAtoms(), "bMatrix");
    gMatrix.initialize<float>(cu, 9*cu.getPaddedNumAtoms(), "gMatrix");
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    vector<float4> sigParamsVector(cu.getPaddedNumAtoms(), make_float4(0, 0, 0, 0));
    vector<float2> epsParamsVector(cu.getPaddedNumAtoms(), make_float2(0, 0));
    vector<float4> scaleVector(cu.getPaddedNumAtoms(), make_float4(0, 0, 0, 0));
    vector<int2> axisParticleVector(cu.getPaddedNumAtoms(), make_int2(0, 0));
    isRealParticle.resize(cu.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] = make_int2(xparticle, yparticle);
        sigParamsVector[i] = make_float4((float) (0.5*sigma), (float) (0.25*sx*sx), (float) (0.25*sy*sy), (float) (0.25*sz*sz));
        epsParamsVector[i] = make_float2((float) sqrt(epsilon), (float) (0.125*(sx*sy + sz*sz)*sqrt(sx*sy)));
        scaleVector[i] = make_float4((float) (1/sqrt(ex)), (float) (1/sqrt(ey)), (float) (1/sqrt(ez)), 0);
        isRealParticle[i] = (epsilon != 0.0);
    }
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    sigParams.upload(sigParamsVector);
    epsParams.upload(epsParamsVector);
    scale.upload(scaleVector);
    axisParticleIndices.upload(axisParticleVector);
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    // Record exceptions and exclusions.

    vector<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(make_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++;
    numExceptions = exceptionParamsVec.size();
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    exclusions.initialize<int>(cu, max(1, (int) excludedPairs.size()), "exclusions");
    exclusionStartIndex.initialize<int>(cu, numRealParticles+1, "exclusionStartIndex");
    exceptionParticles.initialize<int4>(cu, max(1, numExceptions), "exceptionParticles");
    exceptionParams.initialize<float2>(cu, max(1, numExceptions), "exceptionParams");
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    if (numExceptions > 0)
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        exceptionParams.upload(exceptionParamsVec);
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    // Create data structures used for the neighbor list.

    int numAtomBlocks = (numRealParticles+31)/32;
    int elementSize = (cu.getUseDoublePrecision() ? sizeof(double) : sizeof(float));
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    blockCenter.initialize(cu, numAtomBlocks, 4*elementSize, "blockCenter");
    blockBoundingBox.initialize(cu, numAtomBlocks, 4*elementSize, "blockBoundingBox");
    sortedPos.initialize(cu, numRealParticles, 4*elementSize, "sortedPos");
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    maxNeighborBlocks = numRealParticles*2;
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    neighbors.initialize<int>(cu, maxNeighborBlocks*32, "neighbors");
    neighborIndex.initialize<int>(cu, maxNeighborBlocks, "neighborIndex");
    neighborBlockCount.initialize<int>(cu, 1, "neighborBlockCount");
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    if (force.getNonbondedMethod() != GayBerneForce::NoCutoff)
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        CHECK_RESULT(cuEventCreate(&event, CU_EVENT_DISABLE_TIMING), "Error creating event for CustomManyParticleForce");

    // Create array for accumulating torques.
    
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    torque.initialize<long long>(cu, 3*cu.getPaddedNumAtoms(), "torque");
    cu.addAutoclearBuffer(torque);
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    // 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");
    double cutoff = force.getCutoffDistance();
    defines["CUTOFF_SQUARED"] = cu.doubleToString(cutoff*cutoff);
    if (useCutoff) {
        defines["USE_CUTOFF"] = 1;
        if (usePeriodic)
            defines["USE_PERIODIC"] = "1";
        
        // Compute the switching coefficients.
        
        if (force.getUseSwitchingFunction()) {
            defines["SWITCH_CUTOFF"] = cu.doubleToString(force.getSwitchingDistance());
            defines["SWITCH_C3"] = cu.doubleToString(10/pow(force.getSwitchingDistance()-cutoff, 3.0));
            defines["SWITCH_C4"] = cu.doubleToString(15/pow(force.getSwitchingDistance()-cutoff, 4.0));
            defines["SWITCH_C5"] = cu.doubleToString(6/pow(force.getSwitchingDistance()-cutoff, 5.0));
        }
    }
    defines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
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    CUmodule module = cu.createModule(CudaKernelSources::vectorOps+CudaKernelSources::gayBerne, defines);
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    framesKernel = cu.getKernel(module, "computeEllipsoidFrames");
    blockBoundsKernel = cu.getKernel(module, "findBlockBounds");
    neighborsKernel = cu.getKernel(module, "findNeighbors");
    forceKernel = cu.getKernel(module, "computeForce");
    torqueKernel = cu.getKernel(module, "applyTorques");
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    info = new ForceInfo(force);
    cu.addForce(info);
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    cu.addReorderListener(new ReorderListener(*this));
}

double CudaCalcGayBerneForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        sortAtoms();
        framesArgs.push_back(&numRealParticles);
        framesArgs.push_back(&cu.getPosq().getDevicePointer());
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        framesArgs.push_back(&axisParticleIndices.getDevicePointer());
        framesArgs.push_back(&sigParams.getDevicePointer());
        framesArgs.push_back(&scale.getDevicePointer());
        framesArgs.push_back(&aMatrix.getDevicePointer());
        framesArgs.push_back(&bMatrix.getDevicePointer());
        framesArgs.push_back(&gMatrix.getDevicePointer());
        framesArgs.push_back(&sortedParticles.getDevicePointer());
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        blockBoundsArgs.push_back(&numRealParticles);
        blockBoundsArgs.push_back(cu.getPeriodicBoxSizePointer());
        blockBoundsArgs.push_back(cu.getInvPeriodicBoxSizePointer());
        blockBoundsArgs.push_back(cu.getPeriodicBoxVecXPointer());
        blockBoundsArgs.push_back(cu.getPeriodicBoxVecYPointer());
        blockBoundsArgs.push_back(cu.getPeriodicBoxVecZPointer());
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        blockBoundsArgs.push_back(&sortedParticles.getDevicePointer());
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        blockBoundsArgs.push_back(&cu.getPosq().getDevicePointer());
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        blockBoundsArgs.push_back(&sortedPos.getDevicePointer());
        blockBoundsArgs.push_back(&blockCenter.getDevicePointer());
        blockBoundsArgs.push_back(&blockBoundingBox.getDevicePointer());
        blockBoundsArgs.push_back(&neighborBlockCount.getDevicePointer());
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        neighborsArgs.push_back(&numRealParticles);
        neighborsArgs.push_back(&maxNeighborBlocks);
        neighborsArgs.push_back(cu.getPeriodicBoxSizePointer());
        neighborsArgs.push_back(cu.getInvPeriodicBoxSizePointer());
        neighborsArgs.push_back(cu.getPeriodicBoxVecXPointer());
        neighborsArgs.push_back(cu.getPeriodicBoxVecYPointer());
        neighborsArgs.push_back(cu.getPeriodicBoxVecZPointer());
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        neighborsArgs.push_back(&sortedPos.getDevicePointer());
        neighborsArgs.push_back(&blockCenter.getDevicePointer());
        neighborsArgs.push_back(&blockBoundingBox.getDevicePointer());
        neighborsArgs.push_back(&neighbors.getDevicePointer());
        neighborsArgs.push_back(&neighborIndex.getDevicePointer());
        neighborsArgs.push_back(&neighborBlockCount.getDevicePointer());
        neighborsArgs.push_back(&exclusions.getDevicePointer());
        neighborsArgs.push_back(&exclusionStartIndex.getDevicePointer());
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        forceArgs.push_back(&cu.getForce().getDevicePointer());
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        forceArgs.push_back(&torque.getDevicePointer());
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        forceArgs.push_back(&numRealParticles);
        forceArgs.push_back(&numExceptions);
        forceArgs.push_back(&cu.getEnergyBuffer().getDevicePointer());
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        forceArgs.push_back(&sortedPos.getDevicePointer());
        forceArgs.push_back(&sigParams.getDevicePointer());
        forceArgs.push_back(&epsParams.getDevicePointer());
        forceArgs.push_back(&sortedParticles.getDevicePointer());
        forceArgs.push_back(&aMatrix.getDevicePointer());
        forceArgs.push_back(&bMatrix.getDevicePointer());
        forceArgs.push_back(&gMatrix.getDevicePointer());
        forceArgs.push_back(&exclusions.getDevicePointer());
        forceArgs.push_back(&exclusionStartIndex.getDevicePointer());
        forceArgs.push_back(&exceptionParticles.getDevicePointer());
        forceArgs.push_back(&exceptionParams.getDevicePointer());
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        if (nonbondedMethod != GayBerneForce::NoCutoff) {
            forceArgs.push_back(&maxNeighborBlocks);
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            forceArgs.push_back(&neighbors.getDevicePointer());
            forceArgs.push_back(&neighborIndex.getDevicePointer());
            forceArgs.push_back(&neighborBlockCount.getDevicePointer());
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            forceArgs.push_back(cu.getPeriodicBoxSizePointer());
            forceArgs.push_back(cu.getInvPeriodicBoxSizePointer());
            forceArgs.push_back(cu.getPeriodicBoxVecXPointer());
            forceArgs.push_back(cu.getPeriodicBoxVecYPointer());
            forceArgs.push_back(cu.getPeriodicBoxVecZPointer());
        }
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        torqueArgs.push_back(&cu.getForce().getDevicePointer());
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        torqueArgs.push_back(&torque.getDevicePointer());
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        torqueArgs.push_back(&numRealParticles);
        torqueArgs.push_back(&cu.getPosq().getDevicePointer());
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        torqueArgs.push_back(&axisParticleIndices.getDevicePointer());
        torqueArgs.push_back(&sortedParticles.getDevicePointer());
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    }
    cu.executeKernel(framesKernel, &framesArgs[0], numRealParticles);
    cu.executeKernel(blockBoundsKernel, &blockBoundsArgs[0], (numRealParticles+31)/32);
    if (nonbondedMethod == GayBerneForce::NoCutoff) {
        cu.executeKernel(forceKernel, &forceArgs[0], cu.getNonbondedUtilities().getNumForceThreadBlocks()*cu.getNonbondedUtilities().getForceThreadBlockSize());
    }
    else {
        while (true) {
            cu.executeKernel(neighborsKernel, &neighborsArgs[0], numRealParticles);
            int* count = (int*) cu.getPinnedBuffer();
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            neighborBlockCount.download(count, false);
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            CHECK_RESULT(cuEventRecord(event, 0), "Error recording event for GayBerneForce");
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            cu.executeKernel(forceKernel, &forceArgs[0], cu.getNonbondedUtilities().getNumForceThreadBlocks()*cu.getNonbondedUtilities().getForceThreadBlockSize());
            CHECK_RESULT(cuEventSynchronize(event), "Error synchronizing on event for GayBerneForce");
            if (*count <= maxNeighborBlocks)
                break;
            
            // There wasn't enough room for the neighbor list, so we need to recreate it.

            maxNeighborBlocks = (int) ceil((*count)*1.1);
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            neighbors.resize(maxNeighborBlocks*32);
            neighborIndex.resize(maxNeighborBlocks);
            neighborsArgs[10] = &neighbors.getDevicePointer();
            neighborsArgs[11] = &neighborIndex.getDevicePointer();
            forceArgs[17] = &neighbors.getDevicePointer();
            forceArgs[18] = &neighborIndex.getDevicePointer();
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        }
    }
    cu.executeKernel(torqueKernel, &torqueArgs[0], numRealParticles);
    return 0.0;
}

void CudaCalcGayBerneForceKernel::copyParametersToContext(ContextImpl& context, const GayBerneForce& force) {
    // Make sure the new parameters are acceptable.
    
    if (force.getNumParticles() != cu.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");
    }
    int numExceptions = exceptionAtoms.size();
    
    // Record the per-particle parameters.
    
    vector<float4> sigParamsVector(cu.getPaddedNumAtoms(), make_float4(0, 0, 0, 0));
    vector<float2> epsParamsVector(cu.getPaddedNumAtoms(), make_float2(0, 0));
    vector<float4> scaleVector(cu.getPaddedNumAtoms(), make_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);
        sigParamsVector[i] = make_float4((float) (0.5*sigma), (float) (0.25*sx*sx), (float) (0.25*sy*sy), (float) (0.25*sz*sz));
        epsParamsVector[i] = make_float2((float) sqrt(epsilon), (float) (0.125*(sx*sy + sz*sz)*sqrt(sx*sy)));
        scaleVector[i] = make_float4((float) (1/sqrt(ex)), (float) (1/sqrt(ey)), (float) (1/sqrt(ez)), 0);
        if (epsilon != 0.0 && !isRealParticle[i])
            throw OpenMMException("updateParametersInContext: The set of ignored particles (ones with epsilon=0) has changed");
    }
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    sigParams.upload(sigParamsVector);
    epsParams.upload(epsParamsVector);
    scale.upload(scaleVector);
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    // Record the exceptions.
    
    if (numExceptions > 0) {
        vector<float2> exceptionParamsVec(numExceptions);
        for (int i = 0; i < numExceptions; i++) {
            int atom1, atom2;
            double sigma, epsilon;
            force.getExceptionParameters(exceptions[i], atom1, atom2, sigma, epsilon);
            exceptionParamsVec[i] = make_float2((float) sigma, (float) epsilon);
        }
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        exceptionParams.upload(exceptionParamsVec);
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    }
    cu.invalidateMolecules();
    sortAtoms();
}

void CudaCalcGayBerneForceKernel::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<int> particles(cu.getPaddedNumAtoms(), 0);
    const vector<int>& order = cu.getAtomIndex();
    vector<int> inverseOrder(order.size(), -1);
    for (int i = 0; i < cu.getNumAtoms(); i++) {
        int atom = order[i];
        if (isRealParticle[atom]) {
            inverseOrder[atom] = nextIndex;
            particles[nextIndex++] = atom;
        }
    }
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    sortedParticles.upload(particles);
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    // Update the list of exception particles.
    
    int numExceptions = exceptionAtoms.size();
    if (numExceptions > 0) {
        vector<int4> exceptionParticlesVec(numExceptions);
        for (int i = 0; i < numExceptions; i++)
            exceptionParticlesVec[i] = make_int4(exceptionAtoms[i].first, exceptionAtoms[i].second, inverseOrder[exceptionAtoms[i].first], inverseOrder[exceptionAtoms[i].second]);
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        exceptionParticles.upload(exceptionParticlesVec);
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    }
    
    // Rebuild the list of exclusions.
    
    vector<vector<int> > excludedAtoms(numRealParticles);
    for (int i = 0; i < excludedPairs.size(); i++) {
        int first = inverseOrder[min(excludedPairs[i].first, excludedPairs[i].second)];
        int second = inverseOrder[max(excludedPairs[i].first, excludedPairs[i].second)];
        excludedAtoms[first].push_back(second);
    }
    int index = 0;
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    vector<int> exclusionVec(exclusions.getSize());
    vector<int> startIndexVec(exclusionStartIndex.getSize());
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    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;
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    exclusions.upload(exclusionVec);
    exclusionStartIndex.upload(startIndexVec);
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}

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class CudaCalcCustomCVForceKernel::ReorderListener : public CudaContext::ReorderListener {
public:
    ReorderListener(CudaContext& cu, CudaArray& invAtomOrder) : cu(cu), invAtomOrder(invAtomOrder) {
    }
    void execute() {
        vector<int> invOrder(cu.getPaddedNumAtoms());
        const vector<int>& order = cu.getAtomIndex();
        for (int i = 0; i < order.size(); i++)
            invOrder[order[i]] = i;
        invAtomOrder.upload(invOrder);
    }
private:
    CudaContext& cu;
    CudaArray& invAtomOrder;
};

void CudaCalcCustomCVForceKernel::initialize(const System& system, const CustomCVForce& force, ContextImpl& innerContext) {
    int numCVs = force.getNumCollectiveVariables();
    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());
        cu.addEnergyParameterDerivative(name);
    }

    // Delete the custom functions.

    for (auto& function : functions)
        delete function.second;
        
    // Copy parameter derivatives from the inner context.

    CudaContext& cu2 = *reinterpret_cast<CudaPlatform::PlatformData*>(innerContext.getPlatformData())->contexts[0];
    for (auto& param : cu2.getEnergyParamDerivNames())
        cu.addEnergyParameterDerivative(param);
    
    // Create arrays for storing information.
    
    int elementSize = (cu.getUseDoublePrecision() || cu.getUseMixedPrecision() ? sizeof(double) : sizeof(float));
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    cvForces.resize(numCVs);
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    for (int i = 0; i < numCVs; i++)
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        cvForces[i].initialize<long long>(cu, 3*cu.getPaddedNumAtoms(), "cvForce");
    invAtomOrder.initialize<int>(cu, cu.getPaddedNumAtoms(), "invAtomOrder");
    innerInvAtomOrder.initialize<int>(cu, cu.getPaddedNumAtoms(), "innerInvAtomOrder");
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    // Create the kernels.
    
    stringstream args, add;
    for (int i = 0; i < numCVs; i++) {
        args << ", long long* __restrict__ force" << i << ", real dEdV" << i;
        add << "forces[i] += (long long) (force" << i << "[i]*dEdV" << i << ");\n";
    }
    map<string, string> replacements;
    replacements["PARAMETER_ARGUMENTS"] = args.str();
    replacements["ADD_FORCES"] = add.str();
    CUmodule module = cu.createModule(cu.replaceStrings(CudaKernelSources::vectorOps+CudaKernelSources::customCVForce, replacements));
    copyStateKernel = cu.getKernel(module, "copyState");
    copyForcesKernel = cu.getKernel(module, "copyForces");
    addForcesKernel = cu.getKernel(module, "addForces");
}

double CudaCalcCustomCVForceKernel::execute(ContextImpl& context, ContextImpl& innerContext, bool includeForces, bool includeEnergy) {
    copyState(context, innerContext);
    int numCVs = variableNames.size();
    int numAtoms = cu.getNumAtoms();
    int paddedNumAtoms = cu.getPaddedNumAtoms();
    CudaContext& cu2 = *reinterpret_cast<CudaPlatform::PlatformData*>(innerContext.getPlatformData())->contexts[0];
    vector<double> cvValues;
    vector<map<string, double> > cvDerivs(numCVs);
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    void* copyForcesArgs[] = {NULL, &invAtomOrder.getDevicePointer(), &cu2.getForce().getDevicePointer(), &cu2.getAtomIndexArray().getDevicePointer(), &numAtoms, &paddedNumAtoms};
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    for (int i = 0; i < numCVs; i++) {
        cvValues.push_back(innerContext.calcForcesAndEnergy(true, true, 1<<i));
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        copyForcesArgs[0] = &cvForces[i].getDevicePointer();
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        cu.executeKernel(copyForcesKernel, copyForcesArgs, 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);
    int bufferSize = cu.getForce().getSize();
    vector<void*> addForcesArgs;
    addForcesArgs.push_back(&cu.getForce().getDevicePointer());
    addForcesArgs.push_back(&bufferSize);
    vector<double> dEdV(numCVs);
    vector<float> dEdVFloat(numCVs);
    for (int i = 0; i < numCVs; i++) {
        dEdV[i] = variableDerivExpressions[i].evaluate(variables);
        dEdVFloat[i] = (float) dEdV[i];
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        addForcesArgs.push_back(&cvForces[i].getDevicePointer());
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        if (cu.getUseDoublePrecision())
            addForcesArgs.push_back(&dEdV[i]);
        else
            addForcesArgs.push_back(&dEdVFloat[i]);
    }
    cu.executeKernel(addForcesKernel, &addForcesArgs[0], numAtoms);
    
    // Compute the energy parameter derivatives.
    
    map<string, double>& energyParamDerivs = cu.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 CudaCalcCustomCVForceKernel::copyState(ContextImpl& context, ContextImpl& innerContext) {
    int numAtoms = cu.getNumAtoms();
    CudaContext& cu2 = *reinterpret_cast<CudaPlatform::PlatformData*>(innerContext.getPlatformData())->contexts[0];
    if (!hasInitializedListeners) {
        hasInitializedListeners = true;
        
        // Initialize the listeners.
        
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        ReorderListener* listener1 = new ReorderListener(cu, invAtomOrder);
        ReorderListener* listener2 = new ReorderListener(cu2, innerInvAtomOrder);
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        cu.addReorderListener(listener1);
        cu2.addReorderListener(listener2);
        listener1->execute();
        listener2->execute();
    }
    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
    CUdeviceptr posCorrection2 = (cu2.getUseMixedPrecision() ? cu2.getPosqCorrection().getDevicePointer() : 0);
    void* copyStateArgs[] = {&cu.getPosq().getDevicePointer(), &posCorrection, &cu.getVelm().getDevicePointer(), &cu.getAtomIndexArray().getDevicePointer(),
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        &cu2.getPosq().getDevicePointer(), &posCorrection2,& cu2.getVelm().getDevicePointer(), &innerInvAtomOrder.getDevicePointer(), &numAtoms};
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    cu.executeKernel(copyStateKernel, copyStateArgs, 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));
}

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class CudaCalcRMSDForceKernel::ForceInfo : public CudaForceInfo {
public:
    ForceInfo(const RMSDForce& force) : force(force) {
        updateParticles();
    }
    void updateParticles() {
        particles.clear();
        for (int i : force.getParticles())
            particles.insert(i);
    }
    bool areParticlesIdentical(int particle1, int particle2) {
        bool include1 = (particles.find(particle1) != particles.end());
        bool include2 = (particles.find(particle2) != particles.end());
        return (include1 == include2);
    }
private:
    const RMSDForce& force;
    set<int> particles;
};

void CudaCalcRMSDForceKernel::initialize(const System& system, const RMSDForce& force) {
    // Create data structures.
    
    bool useDouble = cu.getUseDoublePrecision();
    int elementSize = (useDouble ? sizeof(double) : sizeof(float));
    int numParticles = force.getParticles().size();
    if (numParticles == 0)
        numParticles = system.getNumParticles();
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    referencePos.initialize(cu, system.getNumParticles(), 4*elementSize, "referencePos");
    particles.initialize<int>(cu, numParticles, "particles");
    buffer.initialize(cu, 13, elementSize, "buffer");
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    recordParameters(force);
    info = new ForceInfo(force);
    cu.addForce(info);
    
    // Create the kernels.

    CUmodule module = cu.createModule(CudaKernelSources::vectorOps+CudaKernelSources::rmsd);
    kernel1 = cu.getKernel(module, "computeRMSDPart1");
    kernel2 = cu.getKernel(module, "computeRMSDForces");
}

void CudaCalcRMSDForceKernel::recordParameters(const RMSDForce& force) {
    // Record the parameters and center the reference positions.
    
    vector<int> particleVec = force.getParticles();
    if (particleVec.size() == 0)
        for (int i = 0; i < cu.getNumAtoms(); i++)
            particleVec.push_back(i);
    vector<Vec3> centeredPositions = force.getReferencePositions();
    Vec3 center;
    for (int i : particleVec)
        center += centeredPositions[i];
    center /= particleVec.size();
    for (Vec3& p : centeredPositions)
        p -= center;

    // Upload them to the device.

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    particles.upload(particleVec);
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    if (cu.getUseDoublePrecision()) {
        vector<double4> pos;
        for (Vec3 p : centeredPositions)
            pos.push_back(make_double4(p[0], p[1], p[2], 0));
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        referencePos.upload(pos);
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    }
    else {
        vector<float4> pos;
        for (Vec3 p : centeredPositions)
            pos.push_back(make_float4(p[0], p[1], p[2], 0));
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        referencePos.upload(pos);
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    }

    // Record the sum of the norms of the reference positions.

    sumNormRef = 0.0;
    for (int i : particleVec) {
        Vec3 p = centeredPositions[i];
        sumNormRef += p.dot(p);
    }
}

double CudaCalcRMSDForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy) {
    if (cu.getUseDoublePrecision())
        return executeImpl<double>(context);
    return executeImpl<float>(context);
}

template <class REAL>
double CudaCalcRMSDForceKernel::executeImpl(ContextImpl& context) {
    // Execute the first kernel.

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    int numParticles = particles.getSize();
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    int blockSize = 256;
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    void* args1[] = {&numParticles, &cu.getPosq().getDevicePointer(), &referencePos.getDevicePointer(),
            &particles.getDevicePointer(), &buffer.getDevicePointer()};
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    cu.executeKernel(kernel1, args1, blockSize, blockSize, blockSize*sizeof(REAL));
    
    // Download the results, build the F matrix, and find the maximum eigenvalue
    // and eigenvector.

    vector<REAL> b;
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    buffer.download(b);
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    Array2D<double> F(4, 4);
    F[0][0] =  b[0*3+0] + b[1*3+1] + b[2*3+2];
    F[1][0] =  b[1*3+2] - b[2*3+1];
    F[2][0] =  b[2*3+0] - b[0*3+2];
    F[3][0] =  b[0*3+1] - b[1*3+0];
    F[0][1] =  b[1*3+2] - b[2*3+1];
    F[1][1] =  b[0*3+0] - b[1*3+1] - b[2*3+2];
    F[2][1] =  b[0*3+1] + b[1*3+0];
    F[3][1] =  b[0*3+2] + b[2*3+0];
    F[0][2] =  b[2*3+0] - b[0*3+2];
    F[1][2] =  b[0*3+1] + b[1*3+0];
    F[2][2] = -b[0*3+0] + b[1*3+1] - b[2*3+2];
    F[3][2] =  b[1*3+2] + b[2*3+1];
    F[0][3] =  b[0*3+1] - b[1*3+0];
    F[1][3] =  b[0*3+2] + b[2*3+0];
    F[2][3] =  b[1*3+2] + b[2*3+1];
    F[3][3] = -b[0*3+0] - b[1*3+1] + b[2*3+2];
    JAMA::Eigenvalue<double> eigen(F);
    Array1D<double> values;
    eigen.getRealEigenvalues(values);
    Array2D<double> vectors;
    eigen.getV(vectors);

    // Compute the RMSD.

    double msd = (sumNormRef+b[9]-2*values[3])/numParticles;
    if (msd < 1e-20) {
        // The particles are perfectly aligned, so all the forces should be zero.
        // Numerical error can lead to NaNs, so just return 0 now.
        return 0.0;
    }
    double rmsd = sqrt(msd);
    b[9] = rmsd;

    // Compute the rotation matrix.

    double q[] = {vectors[0][3], vectors[1][3], vectors[2][3], vectors[3][3]};
    double q00 = q[0]*q[0], q01 = q[0]*q[1], q02 = q[0]*q[2], q03 = q[0]*q[3];
    double q11 = q[1]*q[1], q12 = q[1]*q[2], q13 = q[1]*q[3];
    double q22 = q[2]*q[2], q23 = q[2]*q[3];
    double q33 = q[3]*q[3];
    b[0] = q00+q11-q22-q33;
    b[1] = 2*(q12-q03);
    b[2] = 2*(q13+q02);
    b[3] = 2*(q12+q03);
    b[4] = q00-q11+q22-q33;
    b[5] = 2*(q23-q01);
    b[6] = 2*(q13-q02);
    b[7] = 2*(q23+q01);
    b[8] = q00-q11-q22+q33;

    // Upload it to the device and invoke the kernel to apply forces.
    
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    buffer.upload(b);
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    int paddedNumAtoms = cu.getPaddedNumAtoms();
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    void* args2[] = {&numParticles, &paddedNumAtoms, &cu.getPosq().getDevicePointer(), &referencePos.getDevicePointer(),
            &particles.getDevicePointer(), &buffer.getDevicePointer(), &cu.getForce().getDevicePointer()};
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    cu.executeKernel(kernel2, args2, numParticles);
    return rmsd;
}

void CudaCalcRMSDForceKernel::copyParametersToContext(ContextImpl& context, const RMSDForce& force) {
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    if (referencePos.getSize() != force.getReferencePositions().size())
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        throw OpenMMException("updateParametersInContext: The number of reference positions has changed");
    int numParticles = force.getParticles().size();
    if (numParticles == 0)
        numParticles = context.getSystem().getNumParticles();
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    if (numParticles != particles.getSize())
        particles.resize(numParticles);
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    recordParameters(force);
    
    // Mark that the current reordering may be invalid.
    
    info->updateParticles();
    cu.invalidateMolecules(info);
}

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void CudaIntegrateVerletStepKernel::initialize(const System& system, const VerletIntegrator& integrator) {
    cu.getPlatformData().initializeContexts(system);
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    cu.setAsCurrent();
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    map<string, string> defines;
    CUmodule module = cu.createModule(CudaKernelSources::verlet, defines, "");
    kernel1 = cu.getKernel(module, "integrateVerletPart1");
    kernel2 = cu.getKernel(module, "integrateVerletPart2");
}

void CudaIntegrateVerletStepKernel::execute(ContextImpl& context, const VerletIntegrator& integrator) {
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    cu.setAsCurrent();
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    CudaIntegrationUtilities& integration = cu.getIntegrationUtilities();
    int numAtoms = cu.getNumAtoms();
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    int paddedNumAtoms = cu.getPaddedNumAtoms();
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    double dt = integrator.getStepSize();
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    cu.getIntegrationUtilities().setNextStepSize(dt);
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    // Call the first integration kernel.

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    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
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    void* args1[] = {&numAtoms, &paddedNumAtoms, &cu.getIntegrationUtilities().getStepSize().getDevicePointer(), &cu.getPosq().getDevicePointer(), &posCorrection,
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            &cu.getVelm().getDevicePointer(), &cu.getForce().getDevicePointer(), &integration.getPosDelta().getDevicePointer()};
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    cu.executeKernel(kernel1, args1, numAtoms, 128);
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    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

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    void* args2[] = {&numAtoms, &cu.getIntegrationUtilities().getStepSize().getDevicePointer(), &cu.getPosq().getDevicePointer(), &posCorrection,
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            &cu.getVelm().getDevicePointer(), &integration.getPosDelta().getDevicePointer()};
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    cu.executeKernel(kernel2, args2, numAtoms, 128);
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    integration.computeVirtualSites();

    // Update the time and step count.

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

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double CudaIntegrateVerletStepKernel::computeKineticEnergy(ContextImpl& context, const VerletIntegrator& integrator) {
    return cu.getIntegrationUtilities().computeKineticEnergy(0.5*integrator.getStepSize());
}

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void CudaIntegrateLangevinStepKernel::initialize(const System& system, const LangevinIntegrator& integrator) {
    cu.getPlatformData().initializeContexts(system);
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    cu.setAsCurrent();
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    cu.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    CUmodule module = cu.createModule(CudaKernelSources::langevin, defines, "");
    kernel1 = cu.getKernel(module, "integrateLangevinPart1");
    kernel2 = cu.getKernel(module, "integrateLangevinPart2");
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    params.initialize(cu, 3, cu.getUseDoublePrecision() || cu.getUseMixedPrecision() ? sizeof(double) : sizeof(float), "langevinParams");
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    prevStepSize = -1.0;
}

void CudaIntegrateLangevinStepKernel::execute(ContextImpl& context, const LangevinIntegrator& integrator) {
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    cu.setAsCurrent();
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    CudaIntegrationUtilities& integration = cu.getIntegrationUtilities();
    int numAtoms = cu.getNumAtoms();
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    int paddedNumAtoms = cu.getPaddedNumAtoms();
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    double temperature = integrator.getTemperature();
    double friction = integrator.getFriction();
    double stepSize = integrator.getStepSize();
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    cu.getIntegrationUtilities().setNextStepSize(stepSize);
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    if (temperature != prevTemp || friction != prevFriction || stepSize != prevStepSize) {
        // Calculate the integration parameters.

        double kT = BOLTZ*temperature;
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        double vscale = exp(-stepSize*friction);
        double fscale = (friction == 0 ? stepSize : (1-vscale)/friction);
        double noisescale = sqrt(kT*(1-vscale*vscale));
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        if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision()) {
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            vector<double> p(params.getSize());
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            p[0] = vscale;
            p[1] = fscale;
            p[2] = noisescale;
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            params.upload(p);
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        }
        else {
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            vector<float> p(params.getSize());
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            p[0] = (float) vscale;
            p[1] = (float) fscale;
            p[2] = (float) noisescale;
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            params.upload(p);
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        }
        prevTemp = temperature;
        prevFriction = friction;
        prevStepSize = stepSize;
    }

    // Call the first integration kernel.

    int randomIndex = integration.prepareRandomNumbers(cu.getPaddedNumAtoms());
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    void* args1[] = {&numAtoms, &paddedNumAtoms, &cu.getVelm().getDevicePointer(), &cu.getForce().getDevicePointer(), &integration.getPosDelta().getDevicePointer(),
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            &params.getDevicePointer(), &integration.getStepSize().getDevicePointer(), &integration.getRandom().getDevicePointer(), &randomIndex};
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    cu.executeKernel(kernel1, args1, numAtoms, 128);
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    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

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    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
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    void* args2[] = {&numAtoms, &cu.getPosq().getDevicePointer(), &posCorrection, &integration.getPosDelta().getDevicePointer(),
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            &cu.getVelm().getDevicePointer(), &integration.getStepSize().getDevicePointer()};
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    cu.executeKernel(kernel2, args2, numAtoms, 128);
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    integration.computeVirtualSites();

    // Update the time and step count.

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

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double CudaIntegrateLangevinStepKernel::computeKineticEnergy(ContextImpl& context, const LangevinIntegrator& integrator) {
    return cu.getIntegrationUtilities().computeKineticEnergy(0.5*integrator.getStepSize());
}

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void CudaIntegrateBrownianStepKernel::initialize(const System& system, const BrownianIntegrator& integrator) {
    cu.getPlatformData().initializeContexts(system);
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    cu.setAsCurrent();
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    cu.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    CUmodule module = cu.createModule(CudaKernelSources::brownian, defines, "");
    kernel1 = cu.getKernel(module, "integrateBrownianPart1");
    kernel2 = cu.getKernel(module, "integrateBrownianPart2");
    prevStepSize = -1.0;
}

void CudaIntegrateBrownianStepKernel::execute(ContextImpl& context, const BrownianIntegrator& integrator) {
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    cu.setAsCurrent();
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    CudaIntegrationUtilities& integration = cu.getIntegrationUtilities();
    int numAtoms = cu.getNumAtoms();
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    int paddedNumAtoms = cu.getPaddedNumAtoms();
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    double temperature = integrator.getTemperature();
    double friction = integrator.getFriction();
    double stepSize = integrator.getStepSize();
    double tau = (friction == 0.0 ? 0.0 : 1.0/friction);
    double tauDt = tau*stepSize;
    double noise = sqrt(2.0f*BOLTZ*temperature*stepSize*tau);
    float stepSizeFloat = (float) stepSize;
    float tauDtFloat = (float) tauDt;
    float noiseFloat = (float) noise;
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    bool useDouble = cu.getUseDoublePrecision() || cu.getUseMixedPrecision();
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    // Call the first integration kernel.

    int randomIndex = integration.prepareRandomNumbers(cu.getPaddedNumAtoms());
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    void* args1[] = {&numAtoms, &paddedNumAtoms, useDouble ? (void*) &tauDt : (void*) &tauDtFloat,
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            useDouble ? (void*) &noise : (void*) &noiseFloat,
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            &cu.getForce().getDevicePointer(), &integration.getPosDelta().getDevicePointer(),
            &cu.getVelm().getDevicePointer(), &integration.getRandom().getDevicePointer(), &randomIndex};
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    cu.executeKernel(kernel1, args1, numAtoms, 128);
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    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

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    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
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    void* args2[] = {&numAtoms, useDouble ? (void*) &stepSize : (void*) &stepSizeFloat,
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            &cu.getPosq().getDevicePointer(), &posCorrection, &cu.getVelm().getDevicePointer(), &integration.getPosDelta().getDevicePointer()};
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    cu.executeKernel(kernel2, args2, numAtoms, 128);
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    integration.computeVirtualSites();

    // Update the time and step count.

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

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double CudaIntegrateBrownianStepKernel::computeKineticEnergy(ContextImpl& context, const BrownianIntegrator& integrator) {
    return cu.getIntegrationUtilities().computeKineticEnergy(0);
}

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void CudaIntegrateVariableVerletStepKernel::initialize(const System& system, const VariableVerletIntegrator& integrator) {
    cu.getPlatformData().initializeContexts(system);
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    cu.setAsCurrent();
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    map<string, string> defines;
    CUmodule module = cu.createModule(CudaKernelSources::verlet, defines, "");
    kernel1 = cu.getKernel(module, "integrateVerletPart1");
    kernel2 = cu.getKernel(module, "integrateVerletPart2");
    selectSizeKernel = cu.getKernel(module, "selectVerletStepSize");
    blockSize = min(256, system.getNumParticles());
}

double CudaIntegrateVariableVerletStepKernel::execute(ContextImpl& context, const VariableVerletIntegrator& integrator, double maxTime) {
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    cu.setAsCurrent();
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    CudaIntegrationUtilities& integration = cu.getIntegrationUtilities();
    int numAtoms = cu.getNumAtoms();
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    int paddedNumAtoms = cu.getPaddedNumAtoms();
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    // Select the step size to use.

    double maxStepSize = maxTime-cu.getTime();
    float maxStepSizeFloat = (float) maxStepSize;
    double tol = integrator.getErrorTolerance();
    float tolFloat = (float) tol;
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    bool useDouble = cu.getUseDoublePrecision() || cu.getUseMixedPrecision();
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    void* argsSelect[] = {&numAtoms, &paddedNumAtoms, useDouble ? (void*) &maxStepSize : (void*) &maxStepSizeFloat,
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            useDouble ? (void*) &tol : (void*) &tolFloat,
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            &cu.getIntegrationUtilities().getStepSize().getDevicePointer(),
            &cu.getVelm().getDevicePointer(), &cu.getForce().getDevicePointer()};
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    int sharedSize = blockSize*(useDouble ? sizeof(double) : sizeof(float));
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    cu.executeKernel(selectSizeKernel, argsSelect, blockSize, blockSize, sharedSize);

    // Call the first integration kernel.

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    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
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    void* args1[] = {&numAtoms, &paddedNumAtoms, &cu.getIntegrationUtilities().getStepSize().getDevicePointer(), &cu.getPosq().getDevicePointer(), &posCorrection,
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            &cu.getVelm().getDevicePointer(), &cu.getForce().getDevicePointer(), &integration.getPosDelta().getDevicePointer()};
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    cu.executeKernel(kernel1, args1, numAtoms, 128);
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    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

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    void* args2[] = {&numAtoms, &cu.getIntegrationUtilities().getStepSize().getDevicePointer(), &cu.getPosq().getDevicePointer(), &posCorrection,
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            &cu.getVelm().getDevicePointer(), &integration.getPosDelta().getDevicePointer()};
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    cu.executeKernel(kernel2, args2, numAtoms, 128);
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    integration.computeVirtualSites();

    // Update the time and step count.

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

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

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void CudaIntegrateVariableLangevinStepKernel::initialize(const System& system, const VariableLangevinIntegrator& integrator) {
    cu.getPlatformData().initializeContexts(system);
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    cu.setAsCurrent();
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    cu.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    map<string, string> defines;
    CUmodule module = cu.createModule(CudaKernelSources::langevin, defines, "");
    kernel1 = cu.getKernel(module, "integrateLangevinPart1");
    kernel2 = cu.getKernel(module, "integrateLangevinPart2");
    selectSizeKernel = cu.getKernel(module, "selectLangevinStepSize");
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    params.initialize(cu, 3, cu.getUseDoublePrecision() || cu.getUseMixedPrecision() ? sizeof(double) : sizeof(float), "langevinParams");
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    blockSize = min(256, system.getNumParticles());
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    blockSize = max(blockSize, params.getSize());
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}

double CudaIntegrateVariableLangevinStepKernel::execute(ContextImpl& context, const VariableLangevinIntegrator& integrator, double maxTime) {
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    cu.setAsCurrent();
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    CudaIntegrationUtilities& integration = cu.getIntegrationUtilities();
    int numAtoms = cu.getNumAtoms();
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    int paddedNumAtoms = cu.getPaddedNumAtoms();
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    // Select the step size to use.

    double maxStepSize = maxTime-cu.getTime();
    float maxStepSizeFloat = (float) maxStepSize;
    double tol = integrator.getErrorTolerance();
    float tolFloat = (float) tol;
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    double friction = integrator.getFriction();
    float frictionFloat = (float) friction;
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    double kT = BOLTZ*integrator.getTemperature();
    float kTFloat = (float) kT;
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    bool useDouble = cu.getUseDoublePrecision() || cu.getUseMixedPrecision();
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    void* argsSelect[] = {&numAtoms, &paddedNumAtoms, useDouble ? (void*) &maxStepSize : (void*) &maxStepSizeFloat,
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            useDouble ? (void*) &tol : (void*) &tolFloat,
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            useDouble ? (void*) &friction : (void*) &frictionFloat,
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            useDouble ? (void*) &kT : (void*) &kTFloat,
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            &cu.getIntegrationUtilities().getStepSize().getDevicePointer(),
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            &cu.getVelm().getDevicePointer(), &cu.getForce().getDevicePointer(), &params.getDevicePointer()};
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    int sharedSize = 2*blockSize*(useDouble ? sizeof(double) : sizeof(float));
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    cu.executeKernel(selectSizeKernel, argsSelect, blockSize, blockSize, sharedSize);

    // Call the first integration kernel.

    int randomIndex = integration.prepareRandomNumbers(cu.getPaddedNumAtoms());
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    void* args1[] = {&numAtoms, &paddedNumAtoms, &cu.getVelm().getDevicePointer(), &cu.getForce().getDevicePointer(), &integration.getPosDelta().getDevicePointer(),
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            &params.getDevicePointer(), &integration.getStepSize().getDevicePointer(), &integration.getRandom().getDevicePointer(), &randomIndex};
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    cu.executeKernel(kernel1, args1, numAtoms, 128);
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    // Apply constraints.

    integration.applyConstraints(integrator.getConstraintTolerance());

    // Call the second integration kernel.

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    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
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    void* args2[] = {&numAtoms, &cu.getPosq().getDevicePointer(), &posCorrection, &integration.getPosDelta().getDevicePointer(),
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            &cu.getVelm().getDevicePointer(), &integration.getStepSize().getDevicePointer()};
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    cu.executeKernel(kernel2, args2, numAtoms, 128);
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    integration.computeVirtualSites();

    // Update the time and step count.

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

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

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class CudaIntegrateCustomStepKernel::ReorderListener : public CudaContext::ReorderListener {
public:
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    ReorderListener(CudaContext& cu, vector<CudaArray>& perDofValues, vector<vector<float4> >& localPerDofValuesFloat, vector<vector<double4> >& localPerDofValuesDouble, vector<bool>& deviceValuesAreCurrent) :
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            cu(cu), perDofValues(perDofValues), localPerDofValuesFloat(localPerDofValuesFloat), localPerDofValuesDouble(localPerDofValuesDouble), deviceValuesAreCurrent(deviceValuesAreCurrent) {
        int numAtoms = cu.getNumAtoms();
        lastAtomOrder.resize(numAtoms);
        for (int i = 0; i < numAtoms; i++)
            lastAtomOrder[i] = cu.getAtomIndex()[i];
    }
    void execute() {
        // Reorder the per-DOF variables to reflect the new atom order.

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        if (perDofValues.size() == 0)
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            return;
        int numAtoms = cu.getNumAtoms();
        const vector<int>& order = cu.getAtomIndex();
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        for (int index = 0; index < perDofValues.size(); index++) {
            if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision()) {
                if (deviceValuesAreCurrent[index])
                    perDofValues[index].download(localPerDofValuesDouble[index]);
                vector<double4> swap(numAtoms);
                for (int i = 0; i < numAtoms; i++)
                    swap[lastAtomOrder[i]] = localPerDofValuesDouble[index][i];
                for (int i = 0; i < numAtoms; i++)
                    localPerDofValuesDouble[index][i] = swap[order[i]];
                perDofValues[index].upload(localPerDofValuesDouble[index]);
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            }
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            else {
                if (deviceValuesAreCurrent[index])
                    perDofValues[index].download(localPerDofValuesFloat[index]);
                vector<float4> swap(numAtoms);
                for (int i = 0; i < numAtoms; i++)
                    swap[lastAtomOrder[i]] = localPerDofValuesFloat[index][i];
                for (int i = 0; i < numAtoms; i++)
                    localPerDofValuesFloat[index][i] = swap[order[i]];
                perDofValues[index].upload(localPerDofValuesFloat[index]);
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            }
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            deviceValuesAreCurrent[index] = true;
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        }
        for (int i = 0; i < numAtoms; i++)
            lastAtomOrder[i] = order[i];
    }
private:
    CudaContext& cu;
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    vector<CudaArray>& perDofValues;
    vector<vector<float4> >& localPerDofValuesFloat;
    vector<vector<double4> >& localPerDofValuesDouble;
    vector<bool>& deviceValuesAreCurrent;
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    vector<int> lastAtomOrder;
};

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class CudaIntegrateCustomStepKernel::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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void CudaIntegrateCustomStepKernel::initialize(const System& system, const CustomIntegrator& integrator) {
    cu.getPlatformData().initializeContexts(system);
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    cu.setAsCurrent();
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    cu.getIntegrationUtilities().initRandomNumberGenerator(integrator.getRandomNumberSeed());
    numGlobalVariables = integrator.getNumGlobalVariables();
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    int elementSize = (cu.getUseDoublePrecision() || cu.getUseMixedPrecision() ? sizeof(double) : sizeof(float));
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    sumBuffer.initialize(cu, system.getNumParticles(), elementSize, "sumBuffer");
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    summedValue.initialize(cu, 1, elementSize, "summedValue");
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    perDofValues.resize(integrator.getNumPerDofVariables());
    localPerDofValuesFloat.resize(perDofValues.size());
    localPerDofValuesDouble.resize(perDofValues.size());
    for (int i = 0; i < perDofValues.size(); i++)
        perDofValues[i].initialize(cu, system.getNumParticles(), 4*elementSize, "perDofVariables");
    localValuesAreCurrent.resize(integrator.getNumPerDofVariables(), false);
    deviceValuesAreCurrent.resize(integrator.getNumPerDofVariables(), false);
    cu.addReorderListener(new ReorderListener(cu, perDofValues, localPerDofValuesFloat, localPerDofValuesDouble, deviceValuesAreCurrent));
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    SimTKOpenMMUtilities::setRandomNumberSeed(integrator.getRandomNumberSeed());
}

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string CudaIntegrateCustomStepKernel::createPerDofComputation(const string& variable, const Lepton::ParsedExpression& expr, CustomIntegrator& integrator,
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        const string& forceName, const string& energyName, vector<const TabulatedFunction*>& functions, vector<pair<string, string> >& functionNames) {
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    map<string, Lepton::ParsedExpression> expressions;
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    expressions["double3 tempResult = "] = expr;
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    map<string, string> variables;
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    variables["x"] = "trimTo3(position)";
    variables["v"] = "trimTo3(velocity)";
    variables[forceName] = "trimTo3(f)";
    variables["gaussian"] = "trimTo3(gaussian)";
    variables["uniform"] = "trimTo3(uniform)";
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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)] = "make_double3(globals["+cu.intToString(globalVariableIndex[i])+"])";
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    for (int i = 0; i < integrator.getNumPerDofVariables(); i++)
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        variables[integrator.getPerDofVariableName(i)] = "perDof"+cu.intToString(i);
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    for (int i = 0; i < (int) parameterNames.size(); i++)
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        variables[parameterNames[i]] = "make_double3(globals["+cu.intToString(parameterVariableIndex[i])+"])";
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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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    string result = cu.getExpressionUtilities().createExpressions(expressions, variableNodes, functions, functionNames, "temp", "double3");
    if (variable == "x")
        result += "position.x = tempResult.x; position.y = tempResult.y; position.z = tempResult.z;\n";
    else if (variable == "v")
        result += "velocity.x = tempResult.x; velocity.y = tempResult.y; velocity.z = tempResult.z;\n";
    else if (variable == "")
        result += "sum[index] = tempResult.x+tempResult.y+tempResult.z;\n";
    else {
        for (int i = 0; i < integrator.getNumPerDofVariables(); i++)
            if (variable == integrator.getPerDofVariableName(i)) {
                string varName = "perDof"+cu.intToString(i);
                result += varName+".x = tempResult.x; "+varName+".y = tempResult.y; "+varName+".z = tempResult.z;\n";
            }
    }
    return result;
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}

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void CudaIntegrateCustomStepKernel::prepareForComputation(ContextImpl& context, CustomIntegrator& integrator, bool& forcesAreValid) {
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    cu.setAsCurrent();
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    CudaIntegrationUtilities& integration = cu.getIntegrationUtilities();
    int numAtoms = cu.getNumAtoms();
    int numSteps = integrator.getNumComputations();
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    bool useDouble = cu.getUseDoublePrecision() || cu.getUseMixedPrecision();
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    string perDofType = (useDouble ? "double4" : "float4");
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    if (!hasInitializedKernels) {
        hasInitializedKernels = true;
        
        // 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());
        kernelArgs.resize(integrator.getNumComputations());
        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);
        modifiesParameters = false;
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        sumWorkGroupSize = 512;
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        map<string, string> defines;
        defines["NUM_ATOMS"] = cu.intToString(cu.getNumAtoms());
        defines["PADDED_NUM_ATOMS"] = cu.intToString(cu.getPaddedNumAtoms());
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        defines["WORK_GROUP_SIZE"] = cu.intToString(sumWorkGroupSize);
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        defines["SUM_BUFFER_SIZE"] = "0";
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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;
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        tabulatedFunctions.resize(integrator.getNumTabulatedFunctions());
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        for (int i = 0; i < integrator.getNumTabulatedFunctions(); i++) {
            functionList.push_back(&integrator.getTabulatedFunction(i));
            string name = integrator.getTabulatedFunctionName(i);
            string arrayName = "table"+cu.intToString(i);
            functionNames.push_back(make_pair(name, arrayName));
            functions[name] = createReferenceTabulatedFunction(integrator.getTabulatedFunction(i));
            int width;
            vector<float> f = cu.getExpressionUtilities().computeFunctionCoefficients(integrator.getTabulatedFunction(i), width);
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            tabulatedFunctions[i].initialize<float>(cu, f.size(), "TabulatedFunction");
            tabulatedFunctions[i].upload(f);
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            if (width == 1)
                tableTypes.push_back("float");
            else
                tableTypes.push_back("float"+cu.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;
        vector<string> energyGroupName;
        for (int i = 0; i < 32; i++) {
            stringstream fname;
            fname << "f" << i;
            forceGroupName.push_back(fname.str());
            stringstream ename;
            ename << "energy" << i;
            energyGroupName.push_back(ename.str());
        }
        vector<string> forceName(numSteps, "f");
        vector<string> energyName(numSteps, "energy");
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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];
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            if (forceGroupFlags[step] != -2 && savedForces.find(forceGroupFlags[step]) == savedForces.end()) {
                savedForces[forceGroupFlags[step]] = CudaArray();
                savedForces[forceGroupFlags[step]].initialize(cu, cu.getForce().getSize(), cu.getForce().getElementSize(), "savedForces");
            }
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        }
        
        // Allocate space for storing global values, both on the host and the device.
        
        globalValuesFloat.resize(expressionSet.getNumVariables());
        globalValuesDouble.resize(expressionSet.getNumVariables());
        int elementSize = (cu.getUseDoublePrecision() || cu.getUseMixedPrecision() ? sizeof(double) : sizeof(float));
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        globalValues.initialize(cu, expressionSet.getNumVariables(), elementSize, "globalValues");
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        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);
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        perDofEnergyParamDerivs.initialize(cu, 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;
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                        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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            }
        }
        
        // 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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        }
        
        // 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--) 
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            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++) {
            if ((stepType[step] == CustomIntegrator::ComputePerDof || stepType[step] == CustomIntegrator::ComputeSum) && !merged[step]) {
                // Compute a per-DOF value.
                
                stringstream compute;
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                for (int i = 0; i < perDofValues.size(); i++)
                    compute << "double3 perDof"<<cu.intToString(i)<<" = trimTo3(convertToDouble4(perDofValues"<<cu.intToString(i)<<"[index]));\n";
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                int numGaussian = 0, numUniform = 0;
                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 << "double4 gaussian = convertToDouble4(gaussianValues[gaussianIndex+index]);\n";
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                    if (numUniform > 0)
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                        compute << "double4 uniform = convertToDouble4(uniformValues[uniformIndex+index]);\n";
                    compute << createPerDofComputation(stepType[j] == CustomIntegrator::ComputePerDof ? variable[j] : "", expression[j][0], integrator, forceName[j], energyName[j], functionList, functionNames);
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                    if (variable[j] == "x") {
                        if (storePosAsDelta[j])
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                            compute << "posDelta[index] = convertFromDouble4(position-convertToDouble4(loadPos(posq, posqCorrection, index)));\n";
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                        else
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                            compute << "storePos(posq, posqCorrection, index, convertFromDouble4(position));\n";
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                    }
                    else if (variable[j] == "v")
                        compute << "velm[index] = convertFromDouble4(velocity);\n";
                    else {
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                        for (int i = 0; i < perDofValues.size(); i++)
                            compute << "perDofValues"<<cu.intToString(i)<<"[index] = make_"<<perDofType<<"(perDof"<<cu.intToString(i)<<".x, perDof"<<cu.intToString(i)<<".y, perDof"<<cu.intToString(i)<<".z, 0);\n";
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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";
                }
                map<string, string> replacements;
                replacements["COMPUTE_STEP"] = compute.str();
                stringstream args;
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                for (int i = 0; i < perDofValues.size(); i++) {
                    string valueName = "perDofValues"+cu.intToString(i);
                    args << ", " << perDofType << "* __restrict__ " << valueName;
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                }
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                for (int i = 0; i < (int) tableTypes.size(); i++)
                    args << ", const " << tableTypes[i]<< "* __restrict__ table" << i;
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                replacements["PARAMETER_ARGUMENTS"] = args.str();
                if (loadPosAsDelta[step])
                    defines["LOAD_POS_AS_DELTA"] = "1";
                else if (defines.find("LOAD_POS_AS_DELTA") != defines.end())
                    defines.erase("LOAD_POS_AS_DELTA");
                CUmodule module = cu.createModule(cu.replaceStrings(CudaKernelSources::vectorOps+CudaKernelSources::customIntegratorPerDof, replacements), defines);
                CUfunction kernel = cu.getKernel(module, "computePerDof");
                kernels[step].push_back(kernel);
                requiredGaussian[step] = numGaussian;
                requiredUniform[step] = numUniform;
                vector<void*> args1;
                args1.push_back(&cu.getPosq().getDevicePointer());
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                args1.push_back(NULL);
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                args1.push_back(&integration.getPosDelta().getDevicePointer());
                args1.push_back(&cu.getVelm().getDevicePointer());
                args1.push_back(&cu.getForce().getDevicePointer());
                args1.push_back(&integration.getStepSize().getDevicePointer());
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                args1.push_back(&globalValues.getDevicePointer());
                args1.push_back(&sumBuffer.getDevicePointer());
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                args1.push_back(NULL);
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                args1.push_back(NULL);
                args1.push_back(NULL);
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                if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision())
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                    args1.push_back(&energy);
                else
                    args1.push_back(&energyFloat);
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                args1.push_back(&perDofEnergyParamDerivs.getDevicePointer());
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                for (auto& array : perDofValues)
                    args1.push_back(&array.getDevicePointer());
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                for (auto& array : tabulatedFunctions)
                    args1.push_back(&array.getDevicePointer());
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                kernelArgs[step].push_back(args1);
                if (stepType[step] == CustomIntegrator::ComputeSum) {
                    // Create a second kernel for this step that sums the values.

                    vector<void*> args2;
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                    args2.push_back(&sumBuffer.getDevicePointer());
                    args2.push_back(&summedValue.getDevicePointer());
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                    defines["SUM_BUFFER_SIZE"] = cu.intToString(numAtoms);
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                    module = cu.createModule(CudaKernelSources::customIntegrator, defines);
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                    kernel = cu.getKernel(module, useDouble ? "computeDoubleSum" : "computeFloatSum");
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                    kernels[step].push_back(kernel);
                    kernelArgs[step].push_back(args2);
                }
            }
            else if (stepType[step] == CustomIntegrator::ConstrainPositions) {
                // Apply position constraints.

                CUmodule module = cu.createModule(CudaKernelSources::customIntegrator, defines);
                CUfunction kernel = cu.getKernel(module, "applyPositionDeltas");
                kernels[step].push_back(kernel);
                vector<void*> args;
                args.push_back(&cu.getPosq().getDevicePointer());
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                args.push_back(NULL);
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                args.push_back(&integration.getPosDelta().getDevicePointer());
                kernelArgs[step].push_back(args);
            }
        }
        
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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.initialize<float4>(cu, maxUniformRandoms, "uniformRandoms");
        randomSeed.initialize<int4>(cu, cu.getNumThreadBlocks()*CudaContext::ThreadBlockSize, "randomSeed");
        vector<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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        }
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        randomSeed.upload(seed);
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        CUmodule randomProgram = cu.createModule(CudaKernelSources::customIntegrator, defines);
        randomKernel = cu.getKernel(randomProgram, "generateRandomNumbers");
        
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        // Create the kernel for computing kinetic energy.

        stringstream computeKE;
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        for (int i = 0; i < perDofValues.size(); i++)
            computeKE << "double3 perDof"<<cu.intToString(i)<<" = trimTo3(convertToDouble4(perDofValues"<<cu.intToString(i)<<"[index]));\n";
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        Lepton::ParsedExpression keExpression = Lepton::Parser::parse(integrator.getKineticEnergyExpression()).optimize();
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        computeKE << createPerDofComputation("", keExpression, integrator, "f", "", functionList, functionNames);
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        map<string, string> replacements;
        replacements["COMPUTE_STEP"] = computeKE.str();
        stringstream args;
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        for (int i = 0; i < perDofValues.size(); i++) {
            string valueName = "perDofValues"+cu.intToString(i);
            args << ", " << perDofType << "* __restrict__ " << valueName;
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        }
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        for (int i = 0; i < (int) tableTypes.size(); i++)
            args << ", const " << tableTypes[i]<< "* __restrict__ table" << i;
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        replacements["PARAMETER_ARGUMENTS"] = args.str();
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        defines["SUM_BUFFER_SIZE"] = cu.intToString(numAtoms);
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        if (defines.find("LOAD_POS_AS_DELTA") != defines.end())
            defines.erase("LOAD_POS_AS_DELTA");
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        CUmodule module = cu.createModule(cu.replaceStrings(CudaKernelSources::vectorOps+CudaKernelSources::customIntegratorPerDof, replacements), defines);
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        kineticEnergyKernel = cu.getKernel(module, "computePerDof");
        kineticEnergyArgs.push_back(&cu.getPosq().getDevicePointer());
        kineticEnergyArgs.push_back(NULL);
        kineticEnergyArgs.push_back(&integration.getPosDelta().getDevicePointer());
        kineticEnergyArgs.push_back(&cu.getVelm().getDevicePointer());
        kineticEnergyArgs.push_back(&cu.getForce().getDevicePointer());
        kineticEnergyArgs.push_back(&integration.getStepSize().getDevicePointer());
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        kineticEnergyArgs.push_back(&globalValues.getDevicePointer());
        kineticEnergyArgs.push_back(&sumBuffer.getDevicePointer());
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        kineticEnergyArgs.push_back(NULL);
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        kineticEnergyArgs.push_back(NULL);
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        kineticEnergyArgs.push_back(&uniformRandoms.getDevicePointer());
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        if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision())
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            kineticEnergyArgs.push_back(&energy);
        else
            kineticEnergyArgs.push_back(&energyFloat);
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        kineticEnergyArgs.push_back(&perDofEnergyParamDerivs.getDevicePointer());
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        for (auto& array : perDofValues)
            kineticEnergyArgs.push_back(&array.getDevicePointer());
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        for (auto& array : tabulatedFunctions)
            kineticEnergyArgs.push_back(&array.getDevicePointer());
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        keNeedsForce = usesVariable(keExpression, "f");

        // Create a second kernel to sum the values.

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        defines["SUM_BUFFER_SIZE"] = cu.intToString(numAtoms);
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        module = cu.createModule(CudaKernelSources::customIntegrator, defines);
        sumKineticEnergyKernel = cu.getKernel(module, useDouble ? "computeDoubleSum" : "computeFloatSum");
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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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    for (int i = 0; i < perDofValues.size(); i++) {
        if (!deviceValuesAreCurrent[i]) {
            if (useDouble)
                perDofValues[i].upload(localPerDofValuesDouble[i]);
            else
                perDofValues[i].upload(localPerDofValuesFloat[i]);
            deviceValuesAreCurrent[i] = true;
        }
        localValuesAreCurrent[i] = false;
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    }
    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 CudaIntegrateCustomStepKernel::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 CudaIntegrateCustomStepKernel::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);
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        variableNodes.push_back(make_pair(node, "make_double3(energyParamDerivs["+cu.intToString(index)+"])"));
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        needsEnergyParamDerivs = true;
    }
    else {
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        for (auto& child : node.getChildren())
            findExpressionsForDerivs(child, variableNodes);
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    }
}

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void CudaIntegrateCustomStepKernel::execute(ContextImpl& context, CustomIntegrator& integrator, bool& forcesAreValid) {
    prepareForComputation(context, integrator, forcesAreValid);
    CudaIntegrationUtilities& integration = cu.getIntegrationUtilities();
    int numAtoms = cu.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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    int maxUniformRandoms = uniformRandoms.getSize();
    void* randomArgs[] = {&maxUniformRandoms, &uniformRandoms.getDevicePointer(), &randomSeed.getDevicePointer()};
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    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
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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.

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                    cu.getForce().copyTo(savedForces[lastForceGroups]);
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                    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(cu.getForce());
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                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 (cu.getUseDoublePrecision() || cu.getUseMixedPrecision()) {
                            for (int i = 0; i < perDofEnergyParamDerivNames.size(); i++)
                                localPerDofEnergyParamDerivsDouble[i] = energyParamDerivs[perDofEnergyParamDerivNames[i]];
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                            perDofEnergyParamDerivs.upload(localPerDofEnergyParamDerivsDouble);
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                        }
                        else {
                            for (int i = 0; i < perDofEnergyParamDerivNames.size(); i++)
                                localPerDofEnergyParamDerivsFloat[i] = (float) energyParamDerivs[perDofEnergyParamDerivNames[i]];
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                            perDofEnergyParamDerivs.upload(localPerDofEnergyParamDerivsFloat);
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                        }
                    }
                }
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            }
            forcesAreValid = true;
        }
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        if (needsEnergy[step]) {
            energy = savedEnergy[forceGroups];
            energyFloat = (float) energy;
        }
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        if (needsGlobals[step] && !deviceGlobalsAreCurrent) {
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            // Upload the global values to the device.
            
            if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision())
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                globalValues.upload(globalValuesDouble);
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            else {
                for (int j = 0; j < (int) globalValuesDouble.size(); j++)
                    globalValuesFloat[j] = (float) globalValuesDouble[j];
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                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]) {
            int randomIndex = integration.prepareRandomNumbers(requiredGaussian[step]);
            kernelArgs[step][0][1] = &posCorrection;
            kernelArgs[step][0][8] = &integration.getRandom().getDevicePointer();
            kernelArgs[step][0][9] = &randomIndex;
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            kernelArgs[step][0][10] = &uniformRandoms.getDevicePointer();
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            if (requiredUniform[step] > 0)
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                cu.executeKernel(randomKernel, &randomArgs[0], numAtoms);
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            cu.executeKernel(kernels[step][0], &kernelArgs[step][0][0], numAtoms, 128);
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        }
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        else if (stepType[step] == CustomIntegrator::ComputeGlobal) {
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            expressionSet.setVariable(uniformVariableIndex, SimTKOpenMMUtilities::getUniformlyDistributedRandomNumber());
            expressionSet.setVariable(gaussianVariableIndex, SimTKOpenMMUtilities::getNormallyDistributedRandomNumber());
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            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) {
            int randomIndex = integration.prepareRandomNumbers(requiredGaussian[step]);
            kernelArgs[step][0][1] = &posCorrection;
            kernelArgs[step][0][8] = &integration.getRandom().getDevicePointer();
            kernelArgs[step][0][9] = &randomIndex;
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            kernelArgs[step][0][10] = &uniformRandoms.getDevicePointer();
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            if (requiredUniform[step] > 0)
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                cu.executeKernel(randomKernel, &randomArgs[0], numAtoms);
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            cu.clearBuffer(sumBuffer);
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            cu.executeKernel(kernels[step][0], &kernelArgs[step][0][0], numAtoms, 128);
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            cu.executeKernel(kernels[step][1], &kernelArgs[step][1][0], sumWorkGroupSize, sumWorkGroupSize);
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            if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision()) {
                double value;
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                summedValue.download(&value);
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                recordGlobalValue(value, stepTarget[step], integrator);
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            }
            else {
                float value;
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                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) {
                cu.getIntegrationUtilities().applyConstraints(integrator.getConstraintTolerance());
                kernelArgs[step][0][1] = &posCorrection;
                cu.executeKernel(kernels[step][0], &kernelArgs[step][0][0], numAtoms);
            }
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            cu.getIntegrationUtilities().computeVirtualSites();
        }
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        else if (stepType[step] == CustomIntegrator::ConstrainVelocities) {
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            cu.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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    }
    recordChangedParameters(context);

    // Update the time and step count.

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    cu.setTime(cu.getTime()+integrator.getStepSize());
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    cu.setStepCount(cu.getStepCount()+1);
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    cu.reorderAtoms();
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    if (cu.getAtomsWereReordered()) {
        forcesAreValid = false;
        validSavedForces.clear();
    }
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}

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bool CudaIntegrateCustomStepKernel::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 CudaIntegrateCustomStepKernel::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);
        energyFloat = (float) energy;
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        forcesAreValid = true;
    }
    CUdeviceptr posCorrection = (cu.getUseMixedPrecision() ? cu.getPosqCorrection().getDevicePointer() : 0);
    int randomIndex = 0;
    kineticEnergyArgs[1] = &posCorrection;
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    kineticEnergyArgs[8] = &cu.getIntegrationUtilities().getRandom().getDevicePointer();
    kineticEnergyArgs[9] = &randomIndex;
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    cu.clearBuffer(sumBuffer);
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    cu.executeKernel(kineticEnergyKernel, &kineticEnergyArgs[0], cu.getNumAtoms());
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    void* args[] = {&sumBuffer.getDevicePointer(), &summedValue.getDevicePointer()};
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    cu.executeKernel(sumKineticEnergyKernel, args, sumWorkGroupSize, sumWorkGroupSize);
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    if (cu.getUseDoublePrecision() || cu.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 CudaIntegrateCustomStepKernel::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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            cu.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 CudaIntegrateCustomStepKernel::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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    }
}

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

void CudaIntegrateCustomStepKernel::getPerDofVariable(ContextImpl& context, int variable, vector<Vec3>& values) const {
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    values.resize(perDofValues[variable].getSize());
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    const vector<int>& order = cu.getAtomIndex();
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    if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision()) {
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        if (!localValuesAreCurrent[variable]) {
            perDofValues[variable].download(localPerDofValuesDouble[variable]);
            localValuesAreCurrent[variable] = true;
        }
        for (int i = 0; i < (int) values.size(); i++) {
            values[order[i]][0] = localPerDofValuesDouble[variable][i].x;
            values[order[i]][1] = localPerDofValuesDouble[variable][i].y;
            values[order[i]][2] = localPerDofValuesDouble[variable][i].z;
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        }
    }
    else {
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        if (!localValuesAreCurrent[variable]) {
            perDofValues[variable].download(localPerDofValuesFloat[variable]);
            localValuesAreCurrent[variable] = true;
        }
        for (int i = 0; i < (int) values.size(); i++) {
            values[order[i]][0] = localPerDofValuesFloat[variable][i].x;
            values[order[i]][1] = localPerDofValuesFloat[variable][i].y;
            values[order[i]][2] = localPerDofValuesFloat[variable][i].z;
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        }
    }
}

void CudaIntegrateCustomStepKernel::setPerDofVariable(ContextImpl& context, int variable, const vector<Vec3>& values) {
    const vector<int>& order = cu.getAtomIndex();
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    localValuesAreCurrent[variable] = true;
    deviceValuesAreCurrent[variable] = false;
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    if (cu.getUseDoublePrecision() || cu.getUseMixedPrecision()) {
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        localPerDofValuesDouble[variable].resize(values.size());
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        for (int i = 0; i < (int) values.size(); i++)
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            localPerDofValuesDouble[variable][i] = make_double4(values[order[i]][0], values[order[i]][1], values[order[i]][2], 0);
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    }
    else {
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        localPerDofValuesFloat[variable].resize(values.size());
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        for (int i = 0; i < (int) values.size(); i++)
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            localPerDofValuesFloat[variable][i] = make_float4(values[order[i]][0], values[order[i]][1], values[order[i]][2], 0);
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    }
}
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void CudaApplyAndersenThermostatKernel::initialize(const System& system, const AndersenThermostat& thermostat) {
    cu.setAsCurrent();
    randomSeed = thermostat.getRandomNumberSeed();
    map<string, string> defines;
    CUmodule module = cu.createModule(CudaKernelSources::andersenThermostat, defines);
    kernel = cu.getKernel(module, "applyAndersenThermostat");
    cu.getIntegrationUtilities().initRandomNumberGenerator(randomSeed);

    // Create the arrays with the group definitions.

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

void CudaApplyAndersenThermostatKernel::execute(ContextImpl& context) {
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    cu.setAsCurrent();
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    float frequency = (float) context.getParameter(AndersenThermostat::CollisionFrequency());
    float kT = (float) (BOLTZ*context.getParameter(AndersenThermostat::Temperature()));
    int randomIndex = cu.getIntegrationUtilities().prepareRandomNumbers(cu.getPaddedNumAtoms());
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    int numAtoms = cu.getNumAtoms();
    void* args[] = {&numAtoms, &frequency, &kT, &cu.getVelm().getDevicePointer(), &cu.getIntegrationUtilities().getStepSize().getDevicePointer(),
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            &cu.getIntegrationUtilities().getRandom().getDevicePointer(), &randomIndex, &atomGroups.getDevicePointer()};
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    cu.executeKernel(kernel, args, cu.getNumAtoms());
}

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void CudaApplyMonteCarloBarostatKernel::initialize(const System& system, const Force& thermostat) {
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    cu.setAsCurrent();
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    savedPositions.initialize(cu, cu.getPaddedNumAtoms(), cu.getUseDoublePrecision() ? sizeof(double4) : sizeof(float4), "savedPositions");
    savedForces.initialize<long long>(cu, cu.getPaddedNumAtoms()*3, "savedForces");
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    CUmodule module = cu.createModule(CudaKernelSources::monteCarloBarostat);
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    kernel = cu.getKernel(module, "scalePositions");
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}

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

        // Create the arrays with the molecule definitions.

        vector<vector<int> > molecules = context.getMolecules();
        numMolecules = molecules.size();
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        moleculeAtoms.initialize<int>(cu, cu.getNumAtoms(), "moleculeAtoms");
        moleculeStartIndex.initialize<int>(cu, numMolecules+1, "moleculeStartIndex");
        vector<int> atoms(moleculeAtoms.getSize());
        vector<int> startIndex(moleculeStartIndex.getSize());
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        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;
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        moleculeAtoms.upload(atoms);
        moleculeStartIndex.upload(startIndex);
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        // Initialize the kernel arguments.
        
    }
    int bytesToCopy = cu.getPosq().getSize()*(cu.getUseDoublePrecision() ? sizeof(double4) : sizeof(float4));
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    CUresult result = cuMemcpyDtoD(savedPositions.getDevicePointer(), cu.getPosq().getDevicePointer(), bytesToCopy);
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    if (result != CUDA_SUCCESS) {
        std::stringstream m;
        m<<"Error saving positions for MC barostat: "<<cu.getErrorString(result)<<" ("<<result<<")";
        throw OpenMMException(m.str());
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    }
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    result = cuMemcpyDtoD(savedForces.getDevicePointer(), cu.getForce().getDevicePointer(), savedForces.getSize()*savedForces.getElementSize());
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    if (result != CUDA_SUCCESS) {
        std::stringstream m;
        m<<"Error saving forces for MC barostat: "<<cu.getErrorString(result)<<" ("<<result<<")";
        throw OpenMMException(m.str());
    }
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    float scalefX = (float) scaleX;
    float scalefY = (float) scaleY;
    float scalefZ = (float) scaleZ;
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    void* args[] = {&scalefX, &scalefY, &scalefZ, &numMolecules, cu.getPeriodicBoxSizePointer(), cu.getInvPeriodicBoxSizePointer(),
                    cu.getPeriodicBoxVecXPointer(), cu.getPeriodicBoxVecYPointer(), cu.getPeriodicBoxVecZPointer(),
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		    &cu.getPosq().getDevicePointer(), &moleculeAtoms.getDevicePointer(), &moleculeStartIndex.getDevicePointer()};
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    cu.executeKernel(kernel, args, cu.getNumAtoms());
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    for (auto& offset : cu.getPosCellOffsets())
        offset = make_int4(0, 0, 0, 0);
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    lastAtomOrder = cu.getAtomIndex();
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}

void CudaApplyMonteCarloBarostatKernel::restoreCoordinates(ContextImpl& context) {
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    cu.setAsCurrent();
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    int bytesToCopy = cu.getPosq().getSize()*(cu.getUseDoublePrecision() ? sizeof(double4) : sizeof(float4));
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    CUresult result = cuMemcpyDtoD(cu.getPosq().getDevicePointer(), savedPositions.getDevicePointer(), bytesToCopy);
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    if (result != CUDA_SUCCESS) {
        std::stringstream m;
        m<<"Error restoring positions for MC barostat: "<<cu.getErrorString(result)<<" ("<<result<<")";
        throw OpenMMException(m.str());
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    }
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    result = cuMemcpyDtoD(cu.getForce().getDevicePointer(), savedForces.getDevicePointer(), savedForces.getSize()*savedForces.getElementSize());
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    if (result != CUDA_SUCCESS) {
        std::stringstream m;
        m<<"Error restoring forces for MC barostat: "<<cu.getErrorString(result)<<" ("<<result<<")";
        throw OpenMMException(m.str());
    }
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}
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void CudaRemoveCMMotionKernel::initialize(const System& system, const CMMotionRemover& force) {
    cu.setAsCurrent();
    frequency = force.getFrequency();
    int numAtoms = cu.getNumAtoms();
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    cmMomentum.initialize<float4>(cu, (numAtoms+CudaContext::ThreadBlockSize-1)/CudaContext::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"] = cu.doubleToString(totalMass == 0 ? 0.0 : 1.0/totalMass);
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    CUmodule module = cu.createModule(CudaKernelSources::removeCM, defines);
    kernel1 = cu.getKernel(module, "calcCenterOfMassMomentum");
    kernel2 = cu.getKernel(module, "removeCenterOfMassMomentum");
}

void CudaRemoveCMMotionKernel::execute(ContextImpl& context) {
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    cu.setAsCurrent();
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    int numAtoms = cu.getNumAtoms();
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    void* args[] = {&numAtoms, &cu.getVelm().getDevicePointer(), &cmMomentum.getDevicePointer()};
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    cu.executeKernel(kernel1, args, cu.getNumAtoms(), cu.ThreadBlockSize, cu.ThreadBlockSize*sizeof(float4));
    cu.executeKernel(kernel2, args, cu.getNumAtoms(), cu.ThreadBlockSize, cu.ThreadBlockSize*sizeof(float4));
}