mergeSort.cu

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/*
 * Based on "Designing efficient sorting algorithms for manycore GPUs"
 * by Nadathur Satish, Mark Harris, and Michael Garland
 * http://mgarland.org/files/papers/gpusort-ipdps09.pdf
 *
 * Victor Podlozhnyuk 09/24/2009
 */

#include <assert.h>
#include <cooperative_groups.h>

namespace cg = cooperative_groups;

#include <helper_cuda.h>

#include "mergeSort_common.h"

////////////////////////////////////////////////////////////////////////////////
// Helper functions
////////////////////////////////////////////////////////////////////////////////
static inline __host__ __device__ uint iDivUp(uint a, uint b) { return ((a % b) == 0) ? (a / b) : (a / b + 1); }

static inline __host__ __device__ uint getSampleCount(uint dividend) { return iDivUp(dividend, SAMPLE_STRIDE); }

#define W (sizeof(uint) * 8)
static inline __device__ uint nextPowerOfTwo(uint x)
{
    /*
        --x;
        x |= x >> 1;
        x |= x >> 2;
        x |= x >> 4;
        x |= x >> 8;
        x |= x >> 16;
        return ++x;
    */
    return 1U << (W - __clz(x - 1));
}

template <uint sortDir> static inline __device__ uint binarySearchInclusive(uint val, uint *data, uint L, uint stride)
{
    if (L == 0) {
        return 0;
    }

    uint pos = 0;

    for (; stride > 0; stride >>= 1) {
        uint newPos = umin(pos + stride, L);

        if ((sortDir && (data[newPos - 1] <= val)) || (!sortDir && (data[newPos - 1] >= val))) {
            pos = newPos;
        }
    }

    return pos;
}

template <uint sortDir> static inline __device__ uint binarySearchExclusive(uint val, uint *data, uint L, uint stride)
{
    if (L == 0) {
        return 0;
    }

    uint pos = 0;

    for (; stride > 0; stride >>= 1) {
        uint newPos = umin(pos + stride, L);

        if ((sortDir && (data[newPos - 1] < val)) || (!sortDir && (data[newPos - 1] > val))) {
            pos = newPos;
        }
    }

    return pos;
}

////////////////////////////////////////////////////////////////////////////////
// Bottom-level merge sort (binary search-based)
////////////////////////////////////////////////////////////////////////////////
template <uint sortDir>
__global__ void mergeSortSharedKernel(uint *d_DstKey, uint *d_DstVal, uint *d_SrcKey, uint *d_SrcVal, uint arrayLength)
{
    // Handle to thread block group
    cg::thread_block cta = cg::this_thread_block();
    __shared__ uint  s_key[SHARED_SIZE_LIMIT];
    __shared__ uint  s_val[SHARED_SIZE_LIMIT];

    d_SrcKey += blockIdx.x * SHARED_SIZE_LIMIT + threadIdx.x;
    d_SrcVal += blockIdx.x * SHARED_SIZE_LIMIT + threadIdx.x;
    d_DstKey += blockIdx.x * SHARED_SIZE_LIMIT + threadIdx.x;
    d_DstVal += blockIdx.x * SHARED_SIZE_LIMIT + threadIdx.x;
    s_key[threadIdx.x + 0]                       = d_SrcKey[0];
    s_val[threadIdx.x + 0]                       = d_SrcVal[0];
    s_key[threadIdx.x + (SHARED_SIZE_LIMIT / 2)] = d_SrcKey[(SHARED_SIZE_LIMIT / 2)];
    s_val[threadIdx.x + (SHARED_SIZE_LIMIT / 2)] = d_SrcVal[(SHARED_SIZE_LIMIT / 2)];

    for (uint stride = 1; stride < arrayLength; stride <<= 1) {
        uint  lPos    = threadIdx.x & (stride - 1);
        uint *baseKey = s_key + 2 * (threadIdx.x - lPos);
        uint *baseVal = s_val + 2 * (threadIdx.x - lPos);

        cg::sync(cta);
        uint keyA = baseKey[lPos + 0];
        uint valA = baseVal[lPos + 0];
        uint keyB = baseKey[lPos + stride];
        uint valB = baseVal[lPos + stride];
        uint posA = binarySearchExclusive<sortDir>(keyA, baseKey + stride, stride, stride) + lPos;
        uint posB = binarySearchInclusive<sortDir>(keyB, baseKey + 0, stride, stride) + lPos;

        cg::sync(cta);
        baseKey[posA] = keyA;
        baseVal[posA] = valA;
        baseKey[posB] = keyB;
        baseVal[posB] = valB;
    }

    cg::sync(cta);
    d_DstKey[0]                       = s_key[threadIdx.x + 0];
    d_DstVal[0]                       = s_val[threadIdx.x + 0];
    d_DstKey[(SHARED_SIZE_LIMIT / 2)] = s_key[threadIdx.x + (SHARED_SIZE_LIMIT / 2)];
    d_DstVal[(SHARED_SIZE_LIMIT / 2)] = s_val[threadIdx.x + (SHARED_SIZE_LIMIT / 2)];
}

static void mergeSortShared(uint *d_DstKey,
                            uint *d_DstVal,
                            uint *d_SrcKey,
                            uint *d_SrcVal,
                            uint  batchSize,
                            uint  arrayLength,
                            uint  sortDir)
{
    if (arrayLength < 2) {
        return;
    }

    assert(SHARED_SIZE_LIMIT % arrayLength == 0);
    assert(((batchSize * arrayLength) % SHARED_SIZE_LIMIT) == 0);
    uint blockCount  = batchSize * arrayLength / SHARED_SIZE_LIMIT;
    uint threadCount = SHARED_SIZE_LIMIT / 2;

    if (sortDir) {
        mergeSortSharedKernel<1U><<<blockCount, threadCount>>>(d_DstKey, d_DstVal, d_SrcKey, d_SrcVal, arrayLength);
        getLastCudaError("mergeSortShared<1><<<>>> failed\n");
    }
    else {
        mergeSortSharedKernel<0U><<<blockCount, threadCount>>>(d_DstKey, d_DstVal, d_SrcKey, d_SrcVal, arrayLength);
        getLastCudaError("mergeSortShared<0><<<>>> failed\n");
    }
}

////////////////////////////////////////////////////////////////////////////////
// Merge step 1: generate sample ranks
////////////////////////////////////////////////////////////////////////////////
template <uint sortDir>
__global__ void
generateSampleRanksKernel(uint *d_RanksA, uint *d_RanksB, uint *d_SrcKey, uint stride, uint N, uint threadCount)
{
    uint pos = blockIdx.x * blockDim.x + threadIdx.x;

    if (pos >= threadCount) {
        return;
    }

    const uint i           = pos & ((stride / SAMPLE_STRIDE) - 1);
    const uint segmentBase = (pos - i) * (2 * SAMPLE_STRIDE);
    d_SrcKey += segmentBase;
    d_RanksA += segmentBase / SAMPLE_STRIDE;
    d_RanksB += segmentBase / SAMPLE_STRIDE;

    const uint segmentElementsA = stride;
    const uint segmentElementsB = umin(stride, N - segmentBase - stride);
    const uint segmentSamplesA  = getSampleCount(segmentElementsA);
    const uint segmentSamplesB  = getSampleCount(segmentElementsB);

    if (i < segmentSamplesA) {
        d_RanksA[i] = i * SAMPLE_STRIDE;
        d_RanksB[i] = binarySearchExclusive<sortDir>(
            d_SrcKey[i * SAMPLE_STRIDE], d_SrcKey + stride, segmentElementsB, nextPowerOfTwo(segmentElementsB));
    }

    if (i < segmentSamplesB) {
        d_RanksB[(stride / SAMPLE_STRIDE) + i] = i * SAMPLE_STRIDE;
        d_RanksA[(stride / SAMPLE_STRIDE) + i] = binarySearchInclusive<sortDir>(
            d_SrcKey[stride + i * SAMPLE_STRIDE], d_SrcKey + 0, segmentElementsA, nextPowerOfTwo(segmentElementsA));
    }
}

static void generateSampleRanks(uint *d_RanksA, uint *d_RanksB, uint *d_SrcKey, uint stride, uint N, uint sortDir)
{
    uint lastSegmentElements = N % (2 * stride);
    uint threadCount = (lastSegmentElements > stride) ? (N + 2 * stride - lastSegmentElements) / (2 * SAMPLE_STRIDE)
                                                      : (N - lastSegmentElements) / (2 * SAMPLE_STRIDE);

    if (sortDir) {
        generateSampleRanksKernel<1U>
            <<<iDivUp(threadCount, 256), 256>>>(d_RanksA, d_RanksB, d_SrcKey, stride, N, threadCount);
        getLastCudaError("generateSampleRanksKernel<1U><<<>>> failed\n");
    }
    else {
        generateSampleRanksKernel<0U>
            <<<iDivUp(threadCount, 256), 256>>>(d_RanksA, d_RanksB, d_SrcKey, stride, N, threadCount);
        getLastCudaError("generateSampleRanksKernel<0U><<<>>> failed\n");
    }
}

////////////////////////////////////////////////////////////////////////////////
// Merge step 2: generate sample ranks and indices
////////////////////////////////////////////////////////////////////////////////
__global__ void mergeRanksAndIndicesKernel(uint *d_Limits, uint *d_Ranks, uint stride, uint N, uint threadCount)
{
    uint pos = blockIdx.x * blockDim.x + threadIdx.x;

    if (pos >= threadCount) {
        return;
    }

    const uint i           = pos & ((stride / SAMPLE_STRIDE) - 1);
    const uint segmentBase = (pos - i) * (2 * SAMPLE_STRIDE);
    d_Ranks += (pos - i) * 2;
    d_Limits += (pos - i) * 2;

    const uint segmentElementsA = stride;
    const uint segmentElementsB = umin(stride, N - segmentBase - stride);
    const uint segmentSamplesA  = getSampleCount(segmentElementsA);
    const uint segmentSamplesB  = getSampleCount(segmentElementsB);

    if (i < segmentSamplesA) {
        uint dstPos = binarySearchExclusive<1U>(
                          d_Ranks[i], d_Ranks + segmentSamplesA, segmentSamplesB, nextPowerOfTwo(segmentSamplesB))
                    + i;
        d_Limits[dstPos] = d_Ranks[i];
    }

    if (i < segmentSamplesB) {
        uint dstPos = binarySearchInclusive<1U>(
                          d_Ranks[segmentSamplesA + i], d_Ranks, segmentSamplesA, nextPowerOfTwo(segmentSamplesA))
                    + i;
        d_Limits[dstPos] = d_Ranks[segmentSamplesA + i];
    }
}

static void mergeRanksAndIndices(uint *d_LimitsA, uint *d_LimitsB, uint *d_RanksA, uint *d_RanksB, uint stride, uint N)
{
    uint lastSegmentElements = N % (2 * stride);
    uint threadCount = (lastSegmentElements > stride) ? (N + 2 * stride - lastSegmentElements) / (2 * SAMPLE_STRIDE)
                                                      : (N - lastSegmentElements) / (2 * SAMPLE_STRIDE);

    mergeRanksAndIndicesKernel<<<iDivUp(threadCount, 256), 256>>>(d_LimitsA, d_RanksA, stride, N, threadCount);
    getLastCudaError("mergeRanksAndIndicesKernel(A)<<<>>> failed\n");

    mergeRanksAndIndicesKernel<<<iDivUp(threadCount, 256), 256>>>(d_LimitsB, d_RanksB, stride, N, threadCount);
    getLastCudaError("mergeRanksAndIndicesKernel(B)<<<>>> failed\n");
}

////////////////////////////////////////////////////////////////////////////////
// Merge step 3: merge elementary intervals
////////////////////////////////////////////////////////////////////////////////
template <uint sortDir>
inline __device__ void merge(uint            *dstKey,
                             uint            *dstVal,
                             uint            *srcAKey,
                             uint            *srcAVal,
                             uint            *srcBKey,
                             uint            *srcBVal,
                             uint             lenA,
                             uint             nPowTwoLenA,
                             uint             lenB,
                             uint             nPowTwoLenB,
                             cg::thread_block cta)
{
    uint keyA, valA, keyB, valB, dstPosA, dstPosB;

    if (threadIdx.x < lenA) {
        keyA    = srcAKey[threadIdx.x];
        valA    = srcAVal[threadIdx.x];
        dstPosA = binarySearchExclusive<sortDir>(keyA, srcBKey, lenB, nPowTwoLenB) + threadIdx.x;
    }

    if (threadIdx.x < lenB) {
        keyB    = srcBKey[threadIdx.x];
        valB    = srcBVal[threadIdx.x];
        dstPosB = binarySearchInclusive<sortDir>(keyB, srcAKey, lenA, nPowTwoLenA) + threadIdx.x;
    }

    cg::sync(cta);

    if (threadIdx.x < lenA) {
        dstKey[dstPosA] = keyA;
        dstVal[dstPosA] = valA;
    }

    if (threadIdx.x < lenB) {
        dstKey[dstPosB] = keyB;
        dstVal[dstPosB] = valB;
    }
}

template <uint sortDir>
__global__ void mergeElementaryIntervalsKernel(uint *d_DstKey,
                                               uint *d_DstVal,
                                               uint *d_SrcKey,
                                               uint *d_SrcVal,
                                               uint *d_LimitsA,
                                               uint *d_LimitsB,
                                               uint  stride,
                                               uint  N)
{
    // Handle to thread block group
    cg::thread_block cta = cg::this_thread_block();
    __shared__ uint  s_key[2 * SAMPLE_STRIDE];
    __shared__ uint  s_val[2 * SAMPLE_STRIDE];

    const uint intervalI   = blockIdx.x & ((2 * stride) / SAMPLE_STRIDE - 1);
    const uint segmentBase = (blockIdx.x - intervalI) * SAMPLE_STRIDE;
    d_SrcKey += segmentBase;
    d_SrcVal += segmentBase;
    d_DstKey += segmentBase;
    d_DstVal += segmentBase;

    // Set up threadblock-wide parameters
    __shared__ uint startSrcA, startSrcB, lenSrcA, lenSrcB, startDstA, startDstB;

    if (threadIdx.x == 0) {
        uint segmentElementsA = stride;
        uint segmentElementsB = umin(stride, N - segmentBase - stride);
        uint segmentSamplesA  = getSampleCount(segmentElementsA);
        uint segmentSamplesB  = getSampleCount(segmentElementsB);
        uint segmentSamples   = segmentSamplesA + segmentSamplesB;

        startSrcA    = d_LimitsA[blockIdx.x];
        startSrcB    = d_LimitsB[blockIdx.x];
        uint endSrcA = (intervalI + 1 < segmentSamples) ? d_LimitsA[blockIdx.x + 1] : segmentElementsA;
        uint endSrcB = (intervalI + 1 < segmentSamples) ? d_LimitsB[blockIdx.x + 1] : segmentElementsB;
        lenSrcA      = endSrcA - startSrcA;
        lenSrcB      = endSrcB - startSrcB;
        startDstA    = startSrcA + startSrcB;
        startDstB    = startDstA + lenSrcA;
    }

    // Load main input data
    cg::sync(cta);

    if (threadIdx.x < lenSrcA) {
        s_key[threadIdx.x + 0] = d_SrcKey[0 + startSrcA + threadIdx.x];
        s_val[threadIdx.x + 0] = d_SrcVal[0 + startSrcA + threadIdx.x];
    }

    if (threadIdx.x < lenSrcB) {
        s_key[threadIdx.x + SAMPLE_STRIDE] = d_SrcKey[stride + startSrcB + threadIdx.x];
        s_val[threadIdx.x + SAMPLE_STRIDE] = d_SrcVal[stride + startSrcB + threadIdx.x];
    }

    // Merge data in shared memory
    cg::sync(cta);
    merge<sortDir>(s_key,
                   s_val,
                   s_key + 0,
                   s_val + 0,
                   s_key + SAMPLE_STRIDE,
                   s_val + SAMPLE_STRIDE,
                   lenSrcA,
                   SAMPLE_STRIDE,
                   lenSrcB,
                   SAMPLE_STRIDE,
                   cta);

    // Store merged data
    cg::sync(cta);

    if (threadIdx.x < lenSrcA) {
        d_DstKey[startDstA + threadIdx.x] = s_key[threadIdx.x];
        d_DstVal[startDstA + threadIdx.x] = s_val[threadIdx.x];
    }

    if (threadIdx.x < lenSrcB) {
        d_DstKey[startDstB + threadIdx.x] = s_key[lenSrcA + threadIdx.x];
        d_DstVal[startDstB + threadIdx.x] = s_val[lenSrcA + threadIdx.x];
    }
}

static void mergeElementaryIntervals(uint *d_DstKey,
                                     uint *d_DstVal,
                                     uint *d_SrcKey,
                                     uint *d_SrcVal,
                                     uint *d_LimitsA,
                                     uint *d_LimitsB,
                                     uint  stride,
                                     uint  N,
                                     uint  sortDir)
{
    uint lastSegmentElements = N % (2 * stride);
    uint mergePairs = (lastSegmentElements > stride) ? getSampleCount(N) : (N - lastSegmentElements) / SAMPLE_STRIDE;

    if (sortDir) {
        mergeElementaryIntervalsKernel<1U>
            <<<mergePairs, SAMPLE_STRIDE>>>(d_DstKey, d_DstVal, d_SrcKey, d_SrcVal, d_LimitsA, d_LimitsB, stride, N);
        getLastCudaError("mergeElementaryIntervalsKernel<1> failed\n");
    }
    else {
        mergeElementaryIntervalsKernel<0U>
            <<<mergePairs, SAMPLE_STRIDE>>>(d_DstKey, d_DstVal, d_SrcKey, d_SrcVal, d_LimitsA, d_LimitsB, stride, N);
        getLastCudaError("mergeElementaryIntervalsKernel<0> failed\n");
    }
}

extern "C" void bitonicSortShared(uint *d_DstKey,
                                  uint *d_DstVal,
                                  uint *d_SrcKey,
                                  uint *d_SrcVal,
                                  uint  batchSize,
                                  uint  arrayLength,
                                  uint  sortDir);

extern "C" void bitonicMergeElementaryIntervals(uint *d_DstKey,
                                                uint *d_DstVal,
                                                uint *d_SrcKey,
                                                uint *d_SrcVal,
                                                uint *d_LimitsA,
                                                uint *d_LimitsB,
                                                uint  stride,
                                                uint  N,
                                                uint  sortDir);

static uint      *d_RanksA, *d_RanksB, *d_LimitsA, *d_LimitsB;
static const uint MAX_SAMPLE_COUNT = 32768;

extern "C" void initMergeSort(void)
{
    checkCudaErrors(cudaMalloc((void **)&d_RanksA, MAX_SAMPLE_COUNT * sizeof(uint)));
    checkCudaErrors(cudaMalloc((void **)&d_RanksB, MAX_SAMPLE_COUNT * sizeof(uint)));
    checkCudaErrors(cudaMalloc((void **)&d_LimitsA, MAX_SAMPLE_COUNT * sizeof(uint)));
    checkCudaErrors(cudaMalloc((void **)&d_LimitsB, MAX_SAMPLE_COUNT * sizeof(uint)));
}

extern "C" void closeMergeSort(void)
{
    checkCudaErrors(cudaFree(d_RanksA));
    checkCudaErrors(cudaFree(d_RanksB));
    checkCudaErrors(cudaFree(d_LimitsB));
    checkCudaErrors(cudaFree(d_LimitsA));
}

extern "C" void mergeSort(uint *d_DstKey,
                          uint *d_DstVal,
                          uint *d_BufKey,
                          uint *d_BufVal,
                          uint *d_SrcKey,
                          uint *d_SrcVal,
                          uint  N,
                          uint  sortDir)
{
    uint stageCount = 0;

    for (uint stride = SHARED_SIZE_LIMIT; stride < N; stride <<= 1, stageCount++)
        ;

    uint *ikey, *ival, *okey, *oval;

    if (stageCount & 1) {
        ikey = d_BufKey;
        ival = d_BufVal;
        okey = d_DstKey;
        oval = d_DstVal;
    }
    else {
        ikey = d_DstKey;
        ival = d_DstVal;
        okey = d_BufKey;
        oval = d_BufVal;
    }

    assert(N <= (SAMPLE_STRIDE * MAX_SAMPLE_COUNT));
    assert(N % SHARED_SIZE_LIMIT == 0);
    mergeSortShared(ikey, ival, d_SrcKey, d_SrcVal, N / SHARED_SIZE_LIMIT, SHARED_SIZE_LIMIT, sortDir);

    for (uint stride = SHARED_SIZE_LIMIT; stride < N; stride <<= 1) {
        uint lastSegmentElements = N % (2 * stride);

        // Find sample ranks and prepare for limiters merge
        generateSampleRanks(d_RanksA, d_RanksB, ikey, stride, N, sortDir);

        // Merge ranks and indices
        mergeRanksAndIndices(d_LimitsA, d_LimitsB, d_RanksA, d_RanksB, stride, N);

        // Merge elementary intervals
        mergeElementaryIntervals(okey, oval, ikey, ival, d_LimitsA, d_LimitsB, stride, N, sortDir);

        if (lastSegmentElements <= stride) {
            // Last merge segment consists of a single array which just needs to be
            // passed through
            checkCudaErrors(cudaMemcpy(okey + (N - lastSegmentElements),
                                       ikey + (N - lastSegmentElements),
                                       lastSegmentElements * sizeof(uint),
                                       cudaMemcpyDeviceToDevice));
            checkCudaErrors(cudaMemcpy(oval + (N - lastSegmentElements),
                                       ival + (N - lastSegmentElements),
                                       lastSegmentElements * sizeof(uint),
                                       cudaMemcpyDeviceToDevice));
        }

        uint *t;
        t    = ikey;
        ikey = okey;
        okey = t;
        t    = ival;
        ival = oval;
        oval = t;
    }
}