gbsaObc1.cu

#define DIELECTRIC_OFFSET 0.009f
#define PROBE_RADIUS 0.14f
#define WARPS_PER_GROUP (FORCE_WORK_GROUP_SIZE/TILE_SIZE)

/**
 * Reduce the Born sums to compute the Born radii.
 */

extern "C" __global__ void reduceBornSum(float alpha, float beta, float gamma, const long long* __restrict__ bornSum,
            const float2* __restrict__ params, real* __restrict__ bornRadii, real* __restrict__ obcChain) {
    for (unsigned int index = blockIdx.x*blockDim.x+threadIdx.x; index < NUM_ATOMS; index += blockDim.x*gridDim.x) {
        // Get summed Born data

        real sum = RECIP(0x100000000)*bornSum[index];

        // Now calculate Born radius and OBC term.

        float offsetRadius = params[index].x;
        sum *= 0.5f*offsetRadius;
        real sum2 = sum*sum;
        real sum3 = sum*sum2;
        real tanhSum = tanh(alpha*sum - beta*sum2 + gamma*sum3);
        real nonOffsetRadius = offsetRadius + DIELECTRIC_OFFSET;
        real radius = RECIP(RECIP(offsetRadius) - tanhSum/nonOffsetRadius);
        real chain = offsetRadius*(alpha - 2.0f*beta*sum + 3.0f*gamma*sum2);
        chain = (1-tanhSum*tanhSum)*chain / nonOffsetRadius;
        bornRadii[index] = radius;
        obcChain[index] = chain;
    }
}

/**
 * Reduce the Born force.
 */

extern "C" __global__ void reduceBornForce(long long* __restrict__ bornForce, mixed* __restrict__ energyBuffer,
        const float2* __restrict__ params, const real* __restrict__ bornRadii, const real* __restrict__ obcChain) {
    mixed energy = 0;
    for (unsigned int index = blockIdx.x*blockDim.x+threadIdx.x; index < NUM_ATOMS; index += blockDim.x*gridDim.x) {
        // Get summed Born force

        real force = RECIP(0x100000000)*bornForce[index];

        // Now calculate the actual force

        float offsetRadius = params[index].x;
        real bornRadius = bornRadii[index];
        real r = offsetRadius+DIELECTRIC_OFFSET+PROBE_RADIUS;
        real ratio6 = POW((offsetRadius+DIELECTRIC_OFFSET)/bornRadius, 6);
        real saTerm = SURFACE_AREA_FACTOR*r*r*ratio6;
        force += saTerm/bornRadius;
        energy += saTerm;
        force *= bornRadius*bornRadius*obcChain[index];
        bornForce[index] = (long long) (force*0x100000000);
    }
    energyBuffer[blockIdx.x*blockDim.x+threadIdx.x] += energy/-6;
}

typedef struct {
    real x, y, z;
    real q;
    float radius, scaledRadius;
    real bornSum;
} AtomData1;

/**
 * Compute the Born sum.
 */
extern "C" __global__ void computeBornSum(unsigned long long* __restrict__ global_bornSum, const real4* __restrict__ posq, const float2* __restrict__ global_params,
#ifdef USE_CUTOFF
        const int* __restrict__ tiles, const unsigned int* __restrict__ interactionCount, real4 periodicBoxSize, real4 invPeriodicBoxSize,
        real4 periodicBoxVecX, real4 periodicBoxVecY, real4 periodicBoxVecZ, unsigned int maxTiles, const real4* __restrict__ blockCenter,
        const real4* __restrict__ blockSize, const unsigned int* __restrict__ interactingAtoms,
#else
        unsigned int numTiles,
#endif
        const ushort2* __restrict__ exclusionTiles) {
    const unsigned int totalWarps = (blockDim.x*gridDim.x)/TILE_SIZE;
    const unsigned int warp = (blockIdx.x*blockDim.x+threadIdx.x)/TILE_SIZE;
    const unsigned int tgx = threadIdx.x & (TILE_SIZE-1);
    const unsigned int tbx = threadIdx.x - tgx;
    __shared__ AtomData1 localData[FORCE_WORK_GROUP_SIZE];

    // First loop: process tiles that contain exclusions.
    
    const unsigned int firstExclusionTile = FIRST_EXCLUSION_TILE+warp*(LAST_EXCLUSION_TILE-FIRST_EXCLUSION_TILE)/totalWarps;
    const unsigned int lastExclusionTile = FIRST_EXCLUSION_TILE+(warp+1)*(LAST_EXCLUSION_TILE-FIRST_EXCLUSION_TILE)/totalWarps;
    for (int pos = firstExclusionTile; pos < lastExclusionTile; pos++) {
        const ushort2 tileIndices = exclusionTiles[pos];
        const unsigned int x = tileIndices.x;
        const unsigned int y = tileIndices.y;
        real bornSum = 0;
        unsigned int atom1 = x*TILE_SIZE + tgx;
        real4 posq1 = posq[atom1];
        float2 params1 = global_params[atom1];
        if (x == y) {
            // This tile is on the diagonal.

            localData[threadIdx.x].x = posq1.x;
            localData[threadIdx.x].y = posq1.y;
            localData[threadIdx.x].z = posq1.z;
            localData[threadIdx.x].q = posq1.w;
            localData[threadIdx.x].radius = params1.x;
            localData[threadIdx.x].scaledRadius = params1.y;
            for (unsigned int j = 0; j < TILE_SIZE; j++) {
                real3 delta = make_real3(localData[tbx+j].x-posq1.x, localData[tbx+j].y-posq1.y, localData[tbx+j].z-posq1.z);
#ifdef USE_PERIODIC
                APPLY_PERIODIC_TO_DELTA(delta)
#endif
                real r2 = delta.x*delta.x + delta.y*delta.y + delta.z*delta.z;
#ifdef USE_CUTOFF
                if (atom1 < NUM_ATOMS && y*TILE_SIZE+j < NUM_ATOMS && r2 < CUTOFF_SQUARED) {
#else
                if (atom1 < NUM_ATOMS && y*TILE_SIZE+j < NUM_ATOMS) {
#endif
                    real invR = RSQRT(r2);
                    real r = r2*invR;
                    float2 params2 = make_float2(localData[tbx+j].radius, localData[tbx+j].scaledRadius);
                    real rScaledRadiusJ = r+params2.y;
                    if ((j != tgx) && (params1.x < rScaledRadiusJ)) {
                        real l_ij = RECIP(max(params1.x, fabs(r-params2.y)));
                        real u_ij = RECIP(rScaledRadiusJ);
                        real l_ij2 = l_ij*l_ij;
                        real u_ij2 = u_ij*u_ij;
                        real ratio = LOG(u_ij * RECIP(l_ij));
                        bornSum += l_ij - u_ij + (0.50f*invR*ratio) + 0.25f*(r*(u_ij2-l_ij2) +
                                            (params2.y*params2.y*invR)*(l_ij2-u_ij2));
                        bornSum += (params1.x < params2.y-r ? 2.0f*(RECIP(params1.x)-l_ij) : 0);
                    }
                }
            }
        }
        else {
            // This is an off-diagonal tile.

            unsigned int j = y*TILE_SIZE + tgx;
            real4 tempPosq = posq[j];
            localData[threadIdx.x].x = tempPosq.x;
            localData[threadIdx.x].y = tempPosq.y;
            localData[threadIdx.x].z = tempPosq.z;
            localData[threadIdx.x].q = tempPosq.w;
            float2 tempParams = global_params[j];
            localData[threadIdx.x].radius = tempParams.x;
            localData[threadIdx.x].scaledRadius = tempParams.y;
            localData[threadIdx.x].bornSum = 0.0f;

            // Compute the full set of interactions in this tile.

            unsigned int tj = tgx;
            for (j = 0; j < TILE_SIZE; j++) {
                real3 delta = make_real3(localData[tbx+tj].x-posq1.x, localData[tbx+tj].y-posq1.y, localData[tbx+tj].z-posq1.z);
#ifdef USE_PERIODIC
                APPLY_PERIODIC_TO_DELTA(delta)
#endif
                real r2 = delta.x*delta.x + delta.y*delta.y + delta.z*delta.z;
#ifdef USE_CUTOFF
                if (atom1 < NUM_ATOMS && y*TILE_SIZE+tj < NUM_ATOMS && r2 < CUTOFF_SQUARED) {
#else
                if (atom1 < NUM_ATOMS && y*TILE_SIZE+tj < NUM_ATOMS) {
#endif
                    real invR = RSQRT(r2);
                    real r = r2*invR;
                    float2 params2 = make_float2(localData[tbx+tj].radius, localData[tbx+tj].scaledRadius);
                    real rScaledRadiusJ = r+params2.y;
                    if (params1.x < rScaledRadiusJ) {
                        real l_ij = RECIP(max(params1.x, fabs(r-params2.y)));
                        real u_ij = RECIP(rScaledRadiusJ);
                        real l_ij2 = l_ij*l_ij;
                        real u_ij2 = u_ij*u_ij;
                        real ratio = LOG(u_ij * RECIP(l_ij));
                        bornSum += l_ij - u_ij + (0.50f*invR*ratio) + 0.25f*(r*(u_ij2-l_ij2) +
                                            (params2.y*params2.y*invR)*(l_ij2-u_ij2));
                        bornSum += (params1.x < params2.y-r ? 2.0f*(RECIP(params1.x)-l_ij) : 0);
                    }
                    real rScaledRadiusI = r+params1.y;
                    if (params2.x < rScaledRadiusI) {
                        real l_ij = RECIP(max(params2.x, fabs(r-params1.y)));
                        real u_ij = RECIP(rScaledRadiusI);
                        real l_ij2 = l_ij*l_ij;
                        real u_ij2 = u_ij*u_ij;
                        real ratio = LOG(u_ij * RECIP(l_ij));
                        real term = l_ij - u_ij + (0.50f*invR*ratio) + 0.25f*(r*(u_ij2-l_ij2) +
                                            (params1.y*params1.y*invR)*(l_ij2-u_ij2));
                        term += (params2.x < params1.y-r ? 2.0f*(RECIP(params2.x)-l_ij) : 0);
                        localData[tbx+tj].bornSum += term;
                    }
                }
                tj = (tj + 1) & (TILE_SIZE - 1);
            }
        }
        
        // Write results.
        
        unsigned int offset = x*TILE_SIZE + tgx;
        atomicAdd(&global_bornSum[offset], static_cast<unsigned long long>((long long) (bornSum*0x100000000)));
        if (x != y) {
            offset = y*TILE_SIZE + tgx;
            atomicAdd(&global_bornSum[offset], static_cast<unsigned long long>((long long) (localData[threadIdx.x].bornSum*0x100000000)));
        }
    }

    // Second loop: tiles without exclusions, either from the neighbor list (with cutoff) or just enumerating all
    // of them (no cutoff).

#ifdef USE_CUTOFF
    unsigned int numTiles = interactionCount[0];
    if (numTiles > maxTiles)
        return; // There wasn't enough memory for the neighbor list.
    int pos = (int) (warp*(numTiles > maxTiles ? NUM_BLOCKS*((long long)NUM_BLOCKS+1)/2 : (long)numTiles)/totalWarps);
    int end = (int) ((warp+1)*(numTiles > maxTiles ? NUM_BLOCKS*((long long)NUM_BLOCKS+1)/2 : (long)numTiles)/totalWarps);
#else
    int pos = (int) (warp*(long long)numTiles/totalWarps);
    int end = (int) ((warp+1)*(long long)numTiles/totalWarps);
#endif
    int skipBase = 0;
    int currentSkipIndex = tbx;
    __shared__ int atomIndices[FORCE_WORK_GROUP_SIZE];
    __shared__ volatile int skipTiles[FORCE_WORK_GROUP_SIZE];
    skipTiles[threadIdx.x] = -1;

    while (pos < end) {
        real bornSum = 0;
        bool includeTile = true;

        // Extract the coordinates of this tile.
        
        int x, y;
        bool singlePeriodicCopy = false;
#ifdef USE_CUTOFF
            x = tiles[pos];
            real4 blockSizeX = blockSize[x];
            singlePeriodicCopy = (0.5f*periodicBoxSize.x-blockSizeX.x >= CUTOFF &&
                                  0.5f*periodicBoxSize.y-blockSizeX.y >= CUTOFF &&
                                  0.5f*periodicBoxSize.z-blockSizeX.z >= CUTOFF);
#else
        y = (int) floor(NUM_BLOCKS+0.5f-SQRT((NUM_BLOCKS+0.5f)*(NUM_BLOCKS+0.5f)-2*pos));
        x = (pos-y*NUM_BLOCKS+y*(y+1)/2);
        if (x < y || x >= NUM_BLOCKS) { // Occasionally happens due to roundoff error.
            y += (x < y ? -1 : 1);
            x = (pos-y*NUM_BLOCKS+y*(y+1)/2);
        }

        // Skip over tiles that have exclusions, since they were already processed.

        while (skipTiles[tbx+TILE_SIZE-1] < pos) {
            if (skipBase+tgx < NUM_TILES_WITH_EXCLUSIONS) {
                ushort2 tile = exclusionTiles[skipBase+tgx];
                skipTiles[threadIdx.x] = tile.x + tile.y*NUM_BLOCKS - tile.y*(tile.y+1)/2;
            }
            else
                skipTiles[threadIdx.x] = end;
            skipBase += TILE_SIZE;            
            currentSkipIndex = tbx;
        }
        while (skipTiles[currentSkipIndex] < pos)
            currentSkipIndex++;
        includeTile = (skipTiles[currentSkipIndex] != pos);
#endif
        if (includeTile) {
            unsigned int atom1 = x*TILE_SIZE + tgx;

            // Load atom data for this tile.

            real4 posq1 = posq[atom1];
            float2 params1 = global_params[atom1];
#ifdef USE_CUTOFF
            unsigned int j = (numTiles <= maxTiles ? interactingAtoms[pos*TILE_SIZE+tgx] : y*TILE_SIZE + tgx);
#else
            unsigned int j = y*TILE_SIZE + tgx;
#endif
            atomIndices[threadIdx.x] = j;
            if (j < PADDED_NUM_ATOMS) {
                real4 tempPosq = posq[j];
                localData[threadIdx.x].x = tempPosq.x;
                localData[threadIdx.x].y = tempPosq.y;
                localData[threadIdx.x].z = tempPosq.z;
                localData[threadIdx.x].q = tempPosq.w;
                float2 tempParams = global_params[j];
                localData[threadIdx.x].radius = tempParams.x;
                localData[threadIdx.x].scaledRadius = tempParams.y;
                localData[threadIdx.x].bornSum = 0.0f;
            }
#ifdef USE_PERIODIC
            if (singlePeriodicCopy) {
                // The box is small enough that we can just translate all the atoms into a single periodic
                // box, then skip having to apply periodic boundary conditions later.

                real4 blockCenterX = blockCenter[x];
                APPLY_PERIODIC_TO_POS_WITH_CENTER(posq1, blockCenterX)
                APPLY_PERIODIC_TO_POS_WITH_CENTER(localData[threadIdx.x], blockCenterX)
                unsigned int tj = tgx;
                for (j = 0; j < TILE_SIZE; j++) {
                    real3 delta = make_real3(localData[tbx+tj].x-posq1.x, localData[tbx+tj].y-posq1.y, localData[tbx+tj].z-posq1.z);
                    real r2 = delta.x*delta.x + delta.y*delta.y + delta.z*delta.z;
                    int atom2 = atomIndices[tbx+tj];
                    if (atom1 < NUM_ATOMS && atom2 < NUM_ATOMS && r2 < CUTOFF_SQUARED) {
                        real invR = RSQRT(r2);
                        real r = r2*invR;
                        float2 params2 = make_float2(localData[tbx+tj].radius, localData[tbx+tj].scaledRadius);
                        real rScaledRadiusJ = r+params2.y;
                        if (params1.x < rScaledRadiusJ) {
                            real l_ij = RECIP(max(params1.x, fabs(r-params2.y)));
                            real u_ij = RECIP(rScaledRadiusJ);
                            real l_ij2 = l_ij*l_ij;
                            real u_ij2 = u_ij*u_ij;
                            real ratio = LOG(u_ij * RECIP(l_ij));
                            bornSum += l_ij - u_ij + (0.50f*invR*ratio) + 0.25f*(r*(u_ij2-l_ij2) +
                                                (params2.y*params2.y*invR)*(l_ij2-u_ij2));
                            bornSum += (params1.x < params2.y-r ? 2.0f*(RECIP(params1.x)-l_ij) : 0);
                        }
                        real rScaledRadiusI = r+params1.y;
                        if (params2.x < rScaledRadiusI) {
                            real l_ij = RECIP(max(params2.x, fabs(r-params1.y)));
                            real u_ij = RECIP(rScaledRadiusI);
                            real l_ij2 = l_ij*l_ij;
                            real u_ij2 = u_ij*u_ij;
                            real ratio = LOG(u_ij * RECIP(l_ij));
                            real term = l_ij - u_ij + (0.50f*invR*ratio) + 0.25f*(r*(u_ij2-l_ij2) +
                                                (params1.y*params1.y*invR)*(l_ij2-u_ij2));
                            term += (params2.x < params1.y-r ? 2.0f*(RECIP(params2.x)-l_ij) : 0);
                            localData[tbx+tj].bornSum += term;
                        }
                    }
                    tj = (tj + 1) & (TILE_SIZE - 1);
                }
            }
            else
#endif
            {
                // We need to apply periodic boundary conditions separately for each interaction.

                unsigned int tj = tgx;
                for (j = 0; j < TILE_SIZE; j++) {
                    real3 delta = make_real3(localData[tbx+tj].x-posq1.x, localData[tbx+tj].y-posq1.y, localData[tbx+tj].z-posq1.z);
#ifdef USE_PERIODIC
                    APPLY_PERIODIC_TO_DELTA(delta)
#endif
                    real r2 = delta.x*delta.x + delta.y*delta.y + delta.z*delta.z;
                    int atom2 = atomIndices[tbx+tj];
#ifdef USE_CUTOFF
                    if (atom1 < NUM_ATOMS && atom2 < NUM_ATOMS && r2 < CUTOFF_SQUARED) {
#else
                    if (atom1 < NUM_ATOMS && atom2 < NUM_ATOMS) {
#endif
                        real invR = RSQRT(r2);
                        real r = r2*invR;
                        float2 params2 = make_float2(localData[tbx+tj].radius, localData[tbx+tj].scaledRadius);
                        real rScaledRadiusJ = r+params2.y;
                        if (params1.x < rScaledRadiusJ) {
                            real l_ij = RECIP(max(params1.x, fabs(r-params2.y)));
                            real u_ij = RECIP(rScaledRadiusJ);
                            real l_ij2 = l_ij*l_ij;
                            real u_ij2 = u_ij*u_ij;
                            real ratio = LOG(u_ij * RECIP(l_ij));
                            bornSum += l_ij - u_ij + (0.50f*invR*ratio) + 0.25f*(r*(u_ij2-l_ij2) +
                                                (params2.y*params2.y*invR)*(l_ij2-u_ij2));
                            bornSum += (params1.x < params2.y-r ? 2.0f*(RECIP(params1.x)-l_ij) : 0);
                        }
                        real rScaledRadiusI = r+params1.y;
                        if (params2.x < rScaledRadiusI) {
                            real l_ij = RECIP(max(params2.x, fabs(r-params1.y)));
                            real u_ij = RECIP(rScaledRadiusI);
                            real l_ij2 = l_ij*l_ij;
                            real u_ij2 = u_ij*u_ij;
                            real ratio = LOG(u_ij * RECIP(l_ij));
                            real term = l_ij - u_ij + (0.50f*invR*ratio) + 0.25f*(r*(u_ij2-l_ij2) +
                                                (params1.y*params1.y*invR)*(l_ij2-u_ij2));
                            term += (params2.x < params1.y-r ? 2.0f*(RECIP(params2.x)-l_ij) : 0);
                            localData[tbx+tj].bornSum += term;
                        }
                    }
                    tj = (tj + 1) & (TILE_SIZE - 1);
                }
            }
        
            // Write results.

            atomicAdd(&global_bornSum[atom1], static_cast<unsigned long long>((long long) (bornSum*0x100000000)));
#ifdef USE_CUTOFF
            unsigned int atom2 = atomIndices[threadIdx.x];
#else
            unsigned int atom2 = y*TILE_SIZE + tgx;
#endif
            if (atom2 < PADDED_NUM_ATOMS)
                atomicAdd(&global_bornSum[atom2], static_cast<unsigned long long>((long long) (localData[threadIdx.x].bornSum*0x100000000)));
        }
        pos++;
    }
}

typedef struct {
    real x, y, z;
    real q;
    real fx, fy, fz, fw;
    real bornRadius;
} AtomData2;

/**
 * First part of computing the GBSA interaction.
 */

extern "C" __global__ void computeGBSAForce1(unsigned long long* __restrict__ forceBuffers, unsigned long long* __restrict__ global_bornForce,
        mixed* __restrict__ energyBuffer, const real4* __restrict__ posq, const real* __restrict__ global_bornRadii, bool needEnergy,
#ifdef USE_CUTOFF
        const int* __restrict__ tiles, const unsigned int* __restrict__ interactionCount, real4 periodicBoxSize, real4 invPeriodicBoxSize,
        real4 periodicBoxVecX, real4 periodicBoxVecY, real4 periodicBoxVecZ, unsigned int maxTiles, const real4* __restrict__ blockCenter,
        const real4* __restrict__ blockSize, const unsigned int* __restrict__ interactingAtoms,
#else
        unsigned int numTiles,
#endif
        const ushort2* __restrict__ exclusionTiles) {
    const unsigned int totalWarps = (blockDim.x*gridDim.x)/TILE_SIZE;
    const unsigned int warp = (blockIdx.x*blockDim.x+threadIdx.x)/TILE_SIZE;
    const unsigned int tgx = threadIdx.x & (TILE_SIZE-1);
    const unsigned int tbx = threadIdx.x - tgx;
    mixed energy = 0;
    __shared__ AtomData2 localData[FORCE_WORK_GROUP_SIZE];

    // First loop: process tiles that contain exclusions.
    
    const unsigned int firstExclusionTile = FIRST_EXCLUSION_TILE+warp*(LAST_EXCLUSION_TILE-FIRST_EXCLUSION_TILE)/totalWarps;
    const unsigned int lastExclusionTile = FIRST_EXCLUSION_TILE+(warp+1)*(LAST_EXCLUSION_TILE-FIRST_EXCLUSION_TILE)/totalWarps;
    for (int pos = firstExclusionTile; pos < lastExclusionTile; pos++) {
        const ushort2 tileIndices = exclusionTiles[pos];
        const unsigned int x = tileIndices.x;
        const unsigned int y = tileIndices.y;
        real4 force = make_real4(0);
        unsigned int atom1 = x*TILE_SIZE + tgx;
        real4 posq1 = posq[atom1];
        real bornRadius1 = global_bornRadii[atom1];
        if (x == y) {
            // This tile is on the diagonal.

            localData[threadIdx.x].x = posq1.x;
            localData[threadIdx.x].y = posq1.y;
            localData[threadIdx.x].z = posq1.z;
            localData[threadIdx.x].q = posq1.w;
            localData[threadIdx.x].bornRadius = bornRadius1;
            for (unsigned int j = 0; j < TILE_SIZE; j++) {
                if (atom1 < NUM_ATOMS && y*TILE_SIZE+j < NUM_ATOMS) {
                    real4 posq2 = make_real4(localData[tbx+j].x, localData[tbx+j].y, localData[tbx+j].z, localData[tbx+j].q);
                    real3 delta = make_real3(posq2.x-posq1.x, posq2.y-posq1.y, posq2.z-posq1.z);
#ifdef USE_PERIODIC
                    APPLY_PERIODIC_TO_DELTA(delta)
#endif
                    real r2 = delta.x*delta.x + delta.y*delta.y + delta.z*delta.z;
#ifdef USE_CUTOFF
                    if (r2 < CUTOFF_SQUARED) {
#endif
                        real invR = RSQRT(r2);
                        real r = r2*invR;
                        real bornRadius2 = localData[tbx+j].bornRadius;
                        real alpha2_ij = bornRadius1*bornRadius2;
                        real D_ij = r2*RECIP(4.0f*alpha2_ij);
                        real expTerm = EXP(-D_ij);
                        real denominator2 = r2 + alpha2_ij*expTerm;
                        real denominator = SQRT(denominator2);
                        real scaledChargeProduct = PREFACTOR*posq1.w*posq2.w;
                        real tempEnergy = scaledChargeProduct*RECIP(denominator);
                        real Gpol = tempEnergy*RECIP(denominator2);
                        real dGpol_dalpha2_ij = -0.5f*Gpol*expTerm*(1.0f+D_ij);
                        real dEdR = Gpol*(1.0f - 0.25f*expTerm);
                        force.w += dGpol_dalpha2_ij*bornRadius2;
#ifdef USE_CUTOFF
                        if (atom1 != y*TILE_SIZE+j)
                            tempEnergy -= scaledChargeProduct/CUTOFF;
#endif
                        if (needEnergy)
                            energy += 0.5f*tempEnergy;
                        delta *= dEdR;
                        force.x -= delta.x;
                        force.y -= delta.y;
                        force.z -= delta.z;
#ifdef USE_CUTOFF
                    }
#endif
                }
            }
        }
        else {
            // This is an off-diagonal tile.

            unsigned int j = y*TILE_SIZE + tgx;
            real4 tempPosq = posq[j];
            localData[threadIdx.x].x = tempPosq.x;
            localData[threadIdx.x].y = tempPosq.y;
            localData[threadIdx.x].z = tempPosq.z;
            localData[threadIdx.x].q = tempPosq.w;
            localData[threadIdx.x].bornRadius = global_bornRadii[j];
            localData[threadIdx.x].fx = 0.0f;
            localData[threadIdx.x].fy = 0.0f;
            localData[threadIdx.x].fz = 0.0f;
            localData[threadIdx.x].fw = 0.0f;
            unsigned int tj = tgx;
            for (j = 0; j < TILE_SIZE; j++) {
                if (atom1 < NUM_ATOMS && y*TILE_SIZE+tj < NUM_ATOMS) {
                    real4 posq2 = make_real4(localData[tbx+tj].x, localData[tbx+tj].y, localData[tbx+tj].z, localData[tbx+tj].q);
                    real3 delta = make_real3(posq2.x-posq1.x, posq2.y-posq1.y, posq2.z-posq1.z);
#ifdef USE_PERIODIC
                    APPLY_PERIODIC_TO_DELTA(delta)
#endif
                    real r2 = delta.x*delta.x + delta.y*delta.y + delta.z*delta.z;
#ifdef USE_CUTOFF
                    if (r2 < CUTOFF_SQUARED) {
#endif
                        real invR = RSQRT(r2);
                        real r = r2*invR;
                        real bornRadius2 = localData[tbx+tj].bornRadius;
                        real alpha2_ij = bornRadius1*bornRadius2;
                        real D_ij = r2*RECIP(4.0f*alpha2_ij);
                        real expTerm = EXP(-D_ij);
                        real denominator2 = r2 + alpha2_ij*expTerm;
                        real denominator = SQRT(denominator2);
                        real scaledChargeProduct = PREFACTOR*posq1.w*posq2.w;
                        real tempEnergy = scaledChargeProduct*RECIP(denominator);
                        real Gpol = tempEnergy*RECIP(denominator2);
                        real dGpol_dalpha2_ij = -0.5f*Gpol*expTerm*(1.0f+D_ij);
                        real dEdR = Gpol*(1.0f - 0.25f*expTerm);
                        force.w += dGpol_dalpha2_ij*bornRadius2;
#ifdef USE_CUTOFF
                        tempEnergy -= scaledChargeProduct/CUTOFF;
#endif
                        if (needEnergy)
                            energy += tempEnergy;
                        delta *= dEdR;
                        force.x -= delta.x;
                        force.y -= delta.y;
                        force.z -= delta.z;
                        localData[tbx+tj].fx += delta.x;
                        localData[tbx+tj].fy += delta.y;
                        localData[tbx+tj].fz += delta.z;
                        localData[tbx+tj].fw += dGpol_dalpha2_ij*bornRadius1;
#ifdef USE_CUTOFF
                    }
#endif
                }
                tj = (tj + 1) & (TILE_SIZE - 1);
            }
        }
        
        // Write results.
        
        unsigned int offset = x*TILE_SIZE + tgx;
        atomicAdd(&forceBuffers[offset], static_cast<unsigned long long>((long long) (force.x*0x100000000)));
        atomicAdd(&forceBuffers[offset+PADDED_NUM_ATOMS], static_cast<unsigned long long>((long long) (force.y*0x100000000)));
        atomicAdd(&forceBuffers[offset+2*PADDED_NUM_ATOMS], static_cast<unsigned long long>((long long) (force.z*0x100000000)));
        atomicAdd(&global_bornForce[offset], static_cast<unsigned long long>((long long) (force.w*0x100000000)));
        if (x != y) {
            offset = y*TILE_SIZE + tgx;
            atomicAdd(&forceBuffers[offset], static_cast<unsigned long long>((long long) (localData[threadIdx.x].fx*0x100000000)));
            atomicAdd(&forceBuffers[offset+PADDED_NUM_ATOMS], static_cast<unsigned long long>((long long) (localData[threadIdx.x].fy*0x100000000)));
            atomicAdd(&forceBuffers[offset+2*PADDED_NUM_ATOMS], static_cast<unsigned long long>((long long) (localData[threadIdx.x].fz*0x100000000)));
            atomicAdd(&global_bornForce[offset], static_cast<unsigned long long>((long long) (localData[threadIdx.x].fw*0x100000000)));
        }
    }

    // Second loop: tiles without exclusions, either from the neighbor list (with cutoff) or just enumerating all
    // of them (no cutoff).

#ifdef USE_CUTOFF
    unsigned int numTiles = interactionCount[0];
    if (numTiles > maxTiles)
        return; // There wasn't enough memory for the neighbor list.
    int pos = (int) (warp*(numTiles > maxTiles ? NUM_BLOCKS*((long long)NUM_BLOCKS+1)/2 : (long)numTiles)/totalWarps);
    int end = (int) ((warp+1)*(numTiles > maxTiles ? NUM_BLOCKS*((long long)NUM_BLOCKS+1)/2 : (long)numTiles)/totalWarps);
#else
    int pos = (int) (warp*(long long)numTiles/totalWarps);
    int end = (int) ((warp+1)*(long long)numTiles/totalWarps);
#endif
    int skipBase = 0;
    int currentSkipIndex = tbx;
    __shared__ int atomIndices[FORCE_WORK_GROUP_SIZE];
    __shared__ volatile int skipTiles[FORCE_WORK_GROUP_SIZE];
    skipTiles[threadIdx.x] = -1;

    while (pos < end) {
        real4 force = make_real4(0);
        bool includeTile = true;

        // Extract the coordinates of this tile.
        
        int x, y;
        bool singlePeriodicCopy = false;
#ifdef USE_CUTOFF
        x = tiles[pos];
        real4 blockSizeX = blockSize[x];
        singlePeriodicCopy = (0.5f*periodicBoxSize.x-blockSizeX.x >= CUTOFF &&
                              0.5f*periodicBoxSize.y-blockSizeX.y >= CUTOFF &&
                              0.5f*periodicBoxSize.z-blockSizeX.z >= CUTOFF);
#else
        y = (int) floor(NUM_BLOCKS+0.5f-SQRT((NUM_BLOCKS+0.5f)*(NUM_BLOCKS+0.5f)-2*pos));
        x = (pos-y*NUM_BLOCKS+y*(y+1)/2);
        if (x < y || x >= NUM_BLOCKS) { // Occasionally happens due to roundoff error.
            y += (x < y ? -1 : 1);
            x = (pos-y*NUM_BLOCKS+y*(y+1)/2);
        }

        // Skip over tiles that have exclusions, since they were already processed.

        while (skipTiles[tbx+TILE_SIZE-1] < pos) {
            if (skipBase+tgx < NUM_TILES_WITH_EXCLUSIONS) {
                ushort2 tile = exclusionTiles[skipBase+tgx];
                skipTiles[threadIdx.x] = tile.x + tile.y*NUM_BLOCKS - tile.y*(tile.y+1)/2;
            }
            else
                skipTiles[threadIdx.x] = end;
            skipBase += TILE_SIZE;            
            currentSkipIndex = tbx;
        }
        while (skipTiles[currentSkipIndex] < pos)
            currentSkipIndex++;
        includeTile = (skipTiles[currentSkipIndex] != pos);
#endif
        if (includeTile) {
            unsigned int atom1 = x*TILE_SIZE + tgx;

            // Load atom data for this tile.
            
            real4 posq1 = posq[atom1];
            real bornRadius1 = global_bornRadii[atom1];
#ifdef USE_CUTOFF
            unsigned int j = (numTiles <= maxTiles ? interactingAtoms[pos*TILE_SIZE+tgx] : y*TILE_SIZE + tgx);
#else
            unsigned int j = y*TILE_SIZE + tgx;
#endif
            atomIndices[threadIdx.x] = j;
            if (j < PADDED_NUM_ATOMS) {
                real4 tempPosq = posq[j];
                localData[threadIdx.x].x = tempPosq.x;
                localData[threadIdx.x].y = tempPosq.y;
                localData[threadIdx.x].z = tempPosq.z;
                localData[threadIdx.x].q = tempPosq.w;
                localData[threadIdx.x].bornRadius = global_bornRadii[j];
                localData[threadIdx.x].fx = 0.0f;
                localData[threadIdx.x].fy = 0.0f;
                localData[threadIdx.x].fz = 0.0f;
                localData[threadIdx.x].fw = 0.0f;
            }
#ifdef USE_PERIODIC
            if (singlePeriodicCopy) {
                // The box is small enough that we can just translate all the atoms into a single periodic
                // box, then skip having to apply periodic boundary conditions later.

                real4 blockCenterX = blockCenter[x];
                APPLY_PERIODIC_TO_POS_WITH_CENTER(posq1, blockCenterX)
                APPLY_PERIODIC_TO_POS_WITH_CENTER(localData[threadIdx.x], blockCenterX)
                unsigned int tj = tgx;
                for (j = 0; j < TILE_SIZE; j++) {
                    int atom2 = atomIndices[tbx+tj];
                    if (atom1 < NUM_ATOMS && atom2 < NUM_ATOMS) {
                        real4 posq2 = make_real4(localData[tbx+tj].x, localData[tbx+tj].y, localData[tbx+tj].z, localData[tbx+tj].q);
                        real3 delta = make_real3(posq2.x-posq1.x, posq2.y-posq1.y, posq2.z-posq1.z);
                        real r2 = delta.x*delta.x + delta.y*delta.y + delta.z*delta.z;
                        if (r2 < CUTOFF_SQUARED) {
                            real invR = RSQRT(r2);
                            real r = r2*invR;
                            real bornRadius2 = localData[tbx+tj].bornRadius;
                            real alpha2_ij = bornRadius1*bornRadius2;
                            real D_ij = r2*RECIP(4.0f*alpha2_ij);
                            real expTerm = EXP(-D_ij);
                            real denominator2 = r2 + alpha2_ij*expTerm;
                            real denominator = SQRT(denominator2);
                            real scaledChargeProduct = PREFACTOR*posq1.w*posq2.w;
                            real tempEnergy = scaledChargeProduct*RECIP(denominator);
                            real Gpol = tempEnergy*RECIP(denominator2);
                            real dGpol_dalpha2_ij = -0.5f*Gpol*expTerm*(1.0f+D_ij);
                            real dEdR = Gpol*(1.0f - 0.25f*expTerm);
                            force.w += dGpol_dalpha2_ij*bornRadius2;
#ifdef USE_CUTOFF
                            tempEnergy -= scaledChargeProduct/CUTOFF;
#endif
                            if (needEnergy)
                                energy += tempEnergy;
                            delta *= dEdR;
                            force.x -= delta.x;
                            force.y -= delta.y;
                            force.z -= delta.z;
                            localData[tbx+tj].fx += delta.x;
                            localData[tbx+tj].fy += delta.y;
                            localData[tbx+tj].fz += delta.z;
                            localData[tbx+tj].fw += dGpol_dalpha2_ij*bornRadius1;
                        }
                    }
                    tj = (tj + 1) & (TILE_SIZE - 1);
                }
            }
            else
#endif
            {
                // We need to apply periodic boundary conditions separately for each interaction.

                unsigned int tj = tgx;
                for (j = 0; j < TILE_SIZE; j++) {
                    int atom2 = atomIndices[tbx+tj];
                    if (atom1 < NUM_ATOMS && atom2 < NUM_ATOMS) {
                        real4 posq2 = make_real4(localData[tbx+tj].x, localData[tbx+tj].y, localData[tbx+tj].z, localData[tbx+tj].q);
                        real3 delta = make_real3(posq2.x-posq1.x, posq2.y-posq1.y, posq2.z-posq1.z);
#ifdef USE_PERIODIC
                        APPLY_PERIODIC_TO_DELTA(delta)
#endif
                        real r2 = delta.x*delta.x + delta.y*delta.y + delta.z*delta.z;
#ifdef USE_CUTOFF
                        if (r2 < CUTOFF_SQUARED) {
#endif
                            real invR = RSQRT(r2);
                            real r = r2*invR;
                            real bornRadius2 = localData[tbx+tj].bornRadius;
                            real alpha2_ij = bornRadius1*bornRadius2;
                            real D_ij = r2*RECIP(4.0f*alpha2_ij);
                            real expTerm = EXP(-D_ij);
                            real denominator2 = r2 + alpha2_ij*expTerm;
                            real denominator = SQRT(denominator2);
                            real scaledChargeProduct = PREFACTOR*posq1.w*posq2.w;
                            real tempEnergy = scaledChargeProduct*RECIP(denominator);
                            real Gpol = tempEnergy*RECIP(denominator2);
                            real dGpol_dalpha2_ij = -0.5f*Gpol*expTerm*(1.0f+D_ij);
                            real dEdR = Gpol*(1.0f - 0.25f*expTerm);
                            force.w += dGpol_dalpha2_ij*bornRadius2;
#ifdef USE_CUTOFF
                            tempEnergy -= scaledChargeProduct/CUTOFF;
#endif
                            if (needEnergy)
                                energy += tempEnergy;
                            delta *= dEdR;
                            force.x -= delta.x;
                            force.y -= delta.y;
                            force.z -= delta.z;
                            localData[tbx+tj].fx += delta.x;
                            localData[tbx+tj].fy += delta.y;
                            localData[tbx+tj].fz += delta.z;
                            localData[tbx+tj].fw += dGpol_dalpha2_ij*bornRadius1;
#ifdef USE_CUTOFF
                        }
#endif
                    }
                    tj = (tj + 1) & (TILE_SIZE - 1);
                }
            }

            // Write results.

            atomicAdd(&forceBuffers[atom1], static_cast<unsigned long long>((long long) (force.x*0x100000000)));
            atomicAdd(&forceBuffers[atom1+PADDED_NUM_ATOMS], static_cast<unsigned long long>((long long) (force.y*0x100000000)));
            atomicAdd(&forceBuffers[atom1+2*PADDED_NUM_ATOMS], static_cast<unsigned long long>((long long) (force.z*0x100000000)));
            atomicAdd(&global_bornForce[atom1], static_cast<unsigned long long>((long long) (force.w*0x100000000)));
#ifdef USE_CUTOFF
            unsigned int atom2 = atomIndices[threadIdx.x];
#else
            unsigned int atom2 = y*TILE_SIZE + tgx;
#endif
            if (atom2 < PADDED_NUM_ATOMS) {
                atomicAdd(&forceBuffers[atom2], static_cast<unsigned long long>((long long) (localData[threadIdx.x].fx*0x100000000)));
                atomicAdd(&forceBuffers[atom2+PADDED_NUM_ATOMS], static_cast<unsigned long long>((long long) (localData[threadIdx.x].fy*0x100000000)));
                atomicAdd(&forceBuffers[atom2+2*PADDED_NUM_ATOMS], static_cast<unsigned long long>((long long) (localData[threadIdx.x].fz*0x100000000)));
                atomicAdd(&global_bornForce[atom2], static_cast<unsigned long long>((long long) (localData[threadIdx.x].fw*0x100000000)));
            }
        }
        pos++;
    }
    energyBuffer[blockIdx.x*blockDim.x+threadIdx.x] += energy;
}