Merge branch 'master' of gitlab.ethz.ch:hpcse20/exercise

hw6/grade.py

+#!/usr/bin/env python
+# File       : grade.py
+# Description: Generate grading submission file
+# Copyright 2020 ETH Zurich. All Rights Reserved.
+
+'''
+Example:
+
+python grade.py -q1 7 -c1 "This is why I scored 7 points" -q2 20 -q3 15 -c3 "Second comment here" -c3 "More comments"
+'''
+
+#Modify this, according to a given homework
+exercise_conf = {
+    'Name' : 'Homework 6',
+    'Questions' : {
+        'Question 1': {'Total Points': 60},
+        'Question 2': {'Total Points': 40},
+        'Question 3': {'Total Points': 40},
+    }
+}
+
+
+
+
+'''
+==========================================
+Do not modify anything below this comment
+==========================================
+'''
+
+
+import argparse
+import datetime
+import sys
+
+def parse_args():
+    parser = argparse.ArgumentParser()
+
+    for i in range(1, len(exercise_conf['Questions'])+1, 1):
+        parser.add_argument('-q{:d}'.format(i),'--question{:d}'.format(i),
+                type=int, default=0,
+                help='Scored points for Question {:d}'.format(i))
+        parser.add_argument('-c{:d}'.format(i),'--comment{:d}'.format(i),
+                type=str, action='append', nargs='*',
+                help='Comments for Question {:d} (you can add multiple comments)'.format(i))
+
+    return vars(parser.parse_args())
+
+if __name__ == "__main__":
+    args = parse_args()
+
+    grade = lambda s,m: 2.0 + (6.0-2.0) * float(s)/m
+    summary = {}
+    score = 0
+    maxpoints = 0
+    header = '{name:s}: {date:s}\n'.format(
+        name = exercise_conf['Name'], date = str(datetime.datetime.now()))
+    width = len(header.rstrip())
+    summary[0] = [header]
+    for i in range(1, len(exercise_conf['Questions'])+1, 1):
+        content = []
+        qscore  = args['question{:d}'.format(i)]
+        qmax    = exercise_conf['Questions']['Question {:d}'.format(i)]['Total Points']
+        qscore  = max(0 , min(qscore, qmax))
+        content.append( 'Question {id:d}: {score:d}/{max:d}\n'.format(
+            id = i, score = qscore, max = qmax)
+            )
+        comments = args['comment{:d}'.format(i)]
+        if comments is not None:
+            for j,comment in enumerate([s for x in comments for s in x]):
+                content.append( ' -Comment {id:d}: {issue:s}\n'.format(
+                    id = j+1, issue = comment.strip())
+                    )
+        for line in content:
+            width = width if len(line.rstrip())<width else len(line.rstrip())
+        score += qscore
+        maxpoints += qmax
+        summary[i] = content
+    assert maxpoints > 0
+    with open('grade.txt', 'w') as out:
+        out.write(width*'*'+'\n')
+        for lines in summary.values():
+            for line in lines:
+                out.write(line)
+            out.write(width*'*'+'\n')
+        out.write('Grade: {:.2f}'.format(grade(score, maxpoints)))

hw6/solution/p1/.gitignore

+reduction_sum
+reduction_argmax

hw6/solution/p1/Makefile

+CUFLAGS=-O3 -std=c++14 --compiler-options "-Wall -Wextra -fopenmp"
+
+.PHONY: all clean
+
+all: reduction_sum reduction_argmax
+	@true
+
+clean:
+	rm -f reduction_sum reduction_argmax
+
+reduction_sum: reduction_sum.cu utils.h reduction_sum.h
+	nvcc $(CUFLAGS) $< -o $@
+
+reduction_argmax: reduction_argmax.cu utils.h reduction_argmax.h
+	nvcc $(CUFLAGS) $< -o $@

hw6/solution/p1/reduction_argmax.cu

+#include "utils.h"
+#include <cassert>
+#include <limits>
+
+struct Pair {
+    double max;
+    int idx;
+};
+
+/*
+__device__ Pair shfl_xor_sync(Pair value, unsigned delta) {
+    return Pair{
+        __shfl_xor_sync(0xFFFFFFFF, value.max, delta),
+        __shfl_xor_sync(0xFFFFFFFF, value.idx, delta),
+    };
+}
+
+__device__ Pair argMaxOp(Pair a, Pair b) {
+    return a.max > b.max ? a : b;
+}
+
+__device__ Pair argMaxWarp(double a) {
+    Pair t{a, (int)threadIdx.x & 31};
+    t = argMaxOp(t, shfl_xor_sync(t, 1));
+    t = argMaxOp(t, shfl_xor_sync(t, 2));
+    t = argMaxOp(t, shfl_xor_sync(t, 4));
+    t = argMaxOp(t, shfl_xor_sync(t, 8));
+    t = argMaxOp(t, shfl_xor_sync(t, 16));
+    return t;
+}
+*/
+
+/// Find the maximum value `a` among all warps and return {max value, index of
+/// the max}. The result must be correct on at least the 0th thread of each warp.
+__device__ Pair argMaxWarp(double a) {
+    double t = a;  // max;
+    t = max(t, __shfl_xor_sync(0xFFFFFFFF, t, 1));
+    t = max(t, __shfl_xor_sync(0xFFFFFFFF, t, 2));
+    t = max(t, __shfl_xor_sync(0xFFFFFFFF, t, 4));
+    t = max(t, __shfl_xor_sync(0xFFFFFFFF, t, 8));
+    t = max(t, __shfl_xor_sync(0xFFFFFFFF, t, 16));
+    unsigned ballot = __ballot_sync(0xFFFFFFFF, a == t);
+    int idx = __ffs(ballot) - 1;
+    return {t, idx};
+}
+
+
+
+/// Second stage of argMaxBlock.
+/// Returns {max value of a.value, thread index 0..1023 with the max value}.
+__device__ Pair argMaxWarp(Pair a) {
+    Pair partial = argMaxWarp(a.max);
+    double maxBlock = partial.max;
+    int idxBlock = __shfl_sync(0xFFFFFFFF, a.idx, partial.idx);
+    return {maxBlock, idxBlock};
+}
+
+/// Returns the argmax of all values `a` within a block,
+/// with the correct answer returned at least by the 0th thread of a block.
+__device__ Pair argMaxBlock(double a) {
+    __shared__ Pair partials[32];
+    int warpIdx = threadIdx.x / warpSize;
+    Pair partial = argMaxWarp(a);
+    if (threadIdx.x % warpSize == 0) {
+        partials[warpIdx].max = partial.max;
+        partials[warpIdx].idx = partial.idx + threadIdx.x;
+    }
+    __syncthreads();
+    if (warpIdx == 0)
+        return argMaxWarp(partials[threadIdx.x]);
+    return Pair{0, 0};
+}
+
+/// Returns the argmax of all values `a` within a block,
+/// with the correct answer returned only by the 0th thread of a block.
+__device__ Pair argMaxBlock(Pair a) {
+    __shared__ Pair partials[32];
+    int warpIdx = threadIdx.x / warpSize;
+    Pair partial = argMaxWarp(a);
+    if (threadIdx.x % warpSize == 0)
+        partials[warpIdx] = partial;
+    __syncthreads();
+    if (warpIdx == 0)
+        return argMaxWarp(partials[threadIdx.x]);
+    return Pair{-1, -1};
+}
+
+__global__ void argMax1MKernel1(const double *a, Pair *tmp, int N) {
+    int idx = blockIdx.x * blockDim.x + threadIdx.x;
+    double value = idx < N ? a[idx] : 0.0;
+    Pair result = argMaxBlock(value);
+    if (threadIdx.x == 0) {
+        tmp[blockIdx.x].max = result.max;
+        tmp[blockIdx.x].idx = result.idx + blockIdx.x * blockDim.x;
+    }
+}
+__global__ void argMax1MKernel2(const Pair *tmp, Pair *b, int numBlocks) {
+    int idx = threadIdx.x;
+    Pair partial = idx < numBlocks ? tmp[idx] : Pair{-1e100, -1};  // -infty should be here.
+    Pair result = argMaxBlock(partial);
+    if (threadIdx.x == 0)
+        *b = result;
+}
+
+void argMax1M(const double *aDev, Pair *bDev, int N) {
+    assert(N <= 1024 * 1024);
+    int blocks = (N + 1023) / 1024;
+    Pair *tmpDev;
+    CUDA_CHECK(cudaMalloc(&tmpDev, blocks * sizeof(double)));
+
+    argMax1MKernel1<<<blocks, 1024>>>(aDev, tmpDev, N);
+    argMax1MKernel2<<<1, 1024>>>(tmpDev, bDev, blocks);
+
+    CUDA_CHECK(cudaFree(tmpDev));
+}
+
+#include "reduction_argmax.h"
+
+int main() {
+    testSmallArgMax(argMaxWarpTestKernel, argMaxWarpCheck, 32, 3);
+    testSmallArgMax(argMaxWarpTestKernel, argMaxWarpCheck, 32, 32);
+    testSmallArgMax(argMaxWarpTestKernel, argMaxWarpCheck, 32, 320);
+    testSmallArgMax(argMaxWarpTestKernel, argMaxWarpCheck, 32, 1023123);
+    printf("argMaxWarp OK.\n");
+
+    testSmallArgMax(argMaxBlockTestKernel, argMaxBlockCheck, 1024, 32);
+    testSmallArgMax(argMaxBlockTestKernel, argMaxBlockCheck, 1024, 1024);
+    testSmallArgMax(argMaxBlockTestKernel, argMaxBlockCheck, 1024, 12341);
+    testSmallArgMax(argMaxBlockTestKernel, argMaxBlockCheck, 1024, 1012311);
+    printf("argMaxBlock OK.\n");
+
+    testLargeArgMax("argMax1M", argMax1M, 32);
+    testLargeArgMax("argMax1M", argMax1M, 1024);
+    testLargeArgMax("argMax1M", argMax1M, 12341);
+    testLargeArgMax("argMax1M", argMax1M, 1012311);
+    printf("argMax1M OK.\n");
+}
+

hw6/solution/p1/reduction_argmax.h

+#include <algorithm>
+#include <cstdio>
+#include <numeric>
+#include <random>
+
+constexpr int kWarpSize = 32;
+
+// Kernel for testing `argMaxWarp`. Do not edit.
+__global__ void argMaxWarpTestKernel(const double *a, Pair *b, int N) {
+    int idx = blockIdx.x * blockDim.x + threadIdx.x;
+    // All threads of a warp must call `argMaxWarp`!
+    Pair argMax = argMaxWarp(idx < N ? a[idx] : 0.0);
+    if (threadIdx.x % warpSize == 0 && idx / warpSize < (N + warpSize - 1) / warpSize)
+        b[idx / warpSize] = argMax;
+}
+
+/// Check results of `argMaxWarp`. Do not edit.
+void argMaxWarpCheck(int N, int K, const double *aHost, const Pair *bHost) {
+    for (int k = 0; k < K; ++k) {
+        int expectedIdx = std::max_element(aHost + k * kWarpSize, aHost + std::min((k + 1) * kWarpSize, N))
+                          - (aHost + k * kWarpSize);
+        Pair expected{aHost[k * kWarpSize + expectedIdx], expectedIdx};
+        Pair received = bHost[k];
+        if (expected.idx != received.idx || expected.max != received.max) {
+            printf("argMaxWarp incorrect result:  k=%d  expected=%d %f  received=%d %f\n",
+                   k, expected.idx, expected.max, received.idx, received.max);
+            exit(1);
+        }
+    }
+}
+
+// Do not edit.
+__global__ void argMaxBlockTestKernel(const double *a, Pair *b, int N) {
+    int idx = blockIdx.x * blockDim.x + threadIdx.x;
+    Pair out = argMaxBlock(idx < N ? a[idx] : 0.0);
+    if (threadIdx.x == 0)
+        b[blockIdx.x] = out;
+}
+
+
+// Do not edit.
+void argMaxBlockCheck(int N, int K, const double *aHost, const Pair *bHost) {
+    for (int k = 0; k < K; ++k) {
+        int expectedIdx = std::max_element(aHost + k * 1024, aHost + std::min((k + 1) * 1024, N))
+                        - (aHost + k * 1024);
+        Pair expected{aHost[k * 1024 + expectedIdx], expectedIdx};
+        Pair received = bHost[k];
+        if (expected.idx != received.idx || expected.max != received.max) {
+            printf("argMaxBlock incorrect result:  k=%d  expected=%d %f  received=%d %f\n",
+                   k, expected.idx, expected.max, received.idx, received.max);
+            exit(1);
+        }
+    }
+}
+
+
+/// Test small argmax reductions (warp-level and block-level).
+template <typename Kernel, typename CheckFunc>
+void testSmallArgMax(Kernel kernel, CheckFunc checkFunc, int div, int N) {
+    int K = (N + div - 1) / div;
+    double *aHost;
+    Pair *bHost;
+    double *aDev;
+    Pair *bDev;
+
+    CUDA_CHECK(cudaMallocHost(&aHost, N * sizeof(double)));
+    CUDA_CHECK(cudaMallocHost(&bHost, K * sizeof(Pair)));
+    CUDA_CHECK(cudaMalloc(&aDev, N * sizeof(double)));
+    CUDA_CHECK(cudaMalloc(&bDev, K * sizeof(Pair)));
+
+    for (int i = 0; i < N; ++i) {
+        // aHost[i] = (long long)i * i % 12345;
+        aHost[i] = 10 * i;
+    }
+    std::mt19937 gen;
+    std::shuffle(aHost, aHost + N, gen);
+    CUDA_CHECK(cudaMemcpy(aDev, aHost, N * sizeof(double), cudaMemcpyHostToDevice));
+
+    const int threads = 1024;
+    const int blocks = (N + threads - 1) / threads;
+    kernel<<<blocks, threads>>>(aDev, bDev, N);
+    CUDA_CHECK(cudaMemcpy(bHost, bDev, K * sizeof(Pair), cudaMemcpyDeviceToHost));
+
+    checkFunc(N, K, aHost, bHost);
+
+    CUDA_CHECK(cudaFree(bDev));
+    CUDA_CHECK(cudaFree(aDev));
+    CUDA_CHECK(cudaFreeHost(bHost));
+    CUDA_CHECK(cudaFreeHost(aHost));
+}
+
+/// Test large reductions (up to 1024^3 and larger).
+template <typename Func>
+void testLargeArgMax(const char *name, Func func, int N) {
+    double *aHost;
+    double *aDev;
+    Pair *bDev;
+
+    CUDA_CHECK(cudaMallocHost(&aHost, N * sizeof(double)));
+    CUDA_CHECK(cudaMalloc(&aDev, N * sizeof(double)));
+    CUDA_CHECK(cudaMalloc(&bDev, 1 * sizeof(Pair)));
+
+    for (int i = 0; i < N; ++i) {
+        // aHost[i] = (N + 13241LL * i * i) % 432141;
+        aHost[i] = 10 * i;
+    }
+    std::mt19937 gen;
+    std::shuffle(aHost, aHost + N, gen);
+    CUDA_CHECK(cudaMemcpy(aDev, aHost, N * sizeof(double), cudaMemcpyHostToDevice));
+
+    func(aDev, bDev, N);
+
+    int expectedIdx = std::max_element(aHost, aHost + N) - aHost;
+    Pair expected{aHost[expectedIdx], expectedIdx};
+    Pair received;
+    CUDA_CHECK(cudaMemcpy(&received, bDev, 1 * sizeof(Pair), cudaMemcpyDeviceToHost));
+    if (expected.idx != received.idx || expected.max != received.max) {
+        printf("large %s incorrect result:  N=%d  expected=%d %f  received=%d %f\n",
+               name, N, expected.idx, expected.max, received.idx, received.max);
+        exit(1);
+    }
+
+    CUDA_CHECK(cudaFree(bDev));
+    CUDA_CHECK(cudaFree(aDev));
+    CUDA_CHECK(cudaFreeHost(aHost));
+}

hw6/solution/p1/reduction_sum.cu

+#include "utils.h"
+#include <cassert>
+#include <algorithm>
+
+/// Returns the sum of all values `a` within a warp,
+/// with the correct answer returned only by the 0th thread of a warp.
+__device__ double sumWarp(double a) {
+    a += __shfl_down_sync(0xFFFFFFFF, a, 1);
+    a += __shfl_down_sync(0xFFFFFFFF, a, 2);
+    a += __shfl_down_sync(0xFFFFFFFF, a, 4);
+    a += __shfl_down_sync(0xFFFFFFFF, a, 8);
+    a += __shfl_down_sync(0xFFFFFFFF, a, 16);
+    return a;
+}
+
+/// Returns the sum of all values `a` within a warp,
+/// with the correct answer returned by all threads of a warp.
+__device__ double sumWarpAll(double a) {
+    a += __shfl_xor_sync(0xFFFFFFFF, a, 1);
+    a += __shfl_xor_sync(0xFFFFFFFF, a, 2);
+    a += __shfl_xor_sync(0xFFFFFFFF, a, 4);
+    a += __shfl_xor_sync(0xFFFFFFFF, a, 8);
+    a += __shfl_xor_sync(0xFFFFFFFF, a, 16);
+    return a;
+}
+
+
+/// Returns the sum of all values `a` within a block,
+/// with the correct answer returned only by the 0th thread of a block.
+__device__ double sumBlock(double a) {
+    __shared__ double warpSums[32];
+    int warpIdx = threadIdx.x / warpSize;
+    double warpSum = sumWarp(a);
+    if (threadIdx.x % warpSize == 0)
+        warpSums[warpIdx] = warpSum;
+    __syncthreads();
+    double blockSum = 0;
+    if (warpIdx == 0)
+        blockSum = sumWarp(warpSums[threadIdx.x]);
+    return blockSum;
+}
+
+__global__ void sum1MKernel(const double *a, double *b, int N) {
+    int idx = blockIdx.x * blockDim.x + threadIdx.x;
+    double value = idx < N ? a[idx] : 0.0;
+    double sum = sumBlock(value);
+    if (threadIdx.x == 0)
+        b[blockIdx.x] = sum;
+}
+
+/// Compute the sum of all values aDev[0]..aDev[N-1] for N <= 1024^2 and store the result to bDev[0].
+void sum1M(const double *aDev, double *bDev, int N) {
+    assert(N <= 1024 * 1024);
+    int blocks = (N + 1023) / 1024;
+    double *tmpDev;
+    CUDA_CHECK(cudaMalloc(&tmpDev, blocks * sizeof(double)));
+
+    sum1MKernel<<<blocks, 1024>>>(aDev, tmpDev, N);
+    sum1MKernel<<<1, 1024>>>(tmpDev, bDev, blocks);
+
+    CUDA_CHECK(cudaFree(tmpDev));
+}
+
+
+__global__ void sumVeryLargeKernel(const double *a, double *b, int N) {
+    double value = 0.0;
+    for (int idx = blockIdx.x * blockDim.x + threadIdx.x; idx < N; idx += blockDim.x * gridDim.x)
+        value += a[idx];
+
+    double sum = sumBlock(value);
+    if (threadIdx.x == 0)
+        b[blockIdx.x] = sum;
+}
+
+// Implementation of (1e) (note: it was not required to implement it).
+void sumVeryLarge(const double *aDev, double *bDev, int N) {
+    int blocks = std::min(1024, (N + 1023) / 1024);
+    double *tmpDev;
+    CUDA_CHECK(cudaMalloc(&tmpDev, blocks * sizeof(double)));
+
+    sumVeryLargeKernel<<<blocks, 1024>>>(aDev, tmpDev, N);
+    sumVeryLargeKernel<<<1, 1024>>>(aDev, bDev, N);
+
+    CUDA_CHECK(cudaFree(tmpDev));
+}
+
+
+#include "reduction_sum.h"
+
+
+int main() {
+    testSmallSum(sumWarpTestKernel, sumWarpCheck, 32, 3);
+    testSmallSum(sumWarpTestKernel, sumWarpCheck, 32, 32);
+    testSmallSum(sumWarpTestKernel, sumWarpCheck, 32, 320);
+    testSmallSum(sumWarpTestKernel, sumWarpCheck, 32, 1023123);
+    printf("sumWarp OK.\n");
+
+    testSmallSum(sumWarpAllTestKernel, sumWarpAllCheck, 1, 3);
+    testSmallSum(sumWarpAllTestKernel, sumWarpAllCheck, 1, 32);
+    testSmallSum(sumWarpAllTestKernel, sumWarpAllCheck, 1, 320);
+    testSmallSum(sumWarpAllTestKernel, sumWarpAllCheck, 1, 1023123);
+    printf("sumWarpAll OK.\n");
+
+    testSmallSum(sumBlockTestKernel, sumBlockCheck, 1024, 32);
+    testSmallSum(sumBlockTestKernel, sumBlockCheck, 1024, 1024);
+    testSmallSum(sumBlockTestKernel, sumBlockCheck, 1024, 12341);
+    testSmallSum(sumBlockTestKernel, sumBlockCheck, 1024, 1012311);
+    printf("sumBlock OK.\n");
+
+    testLargeSum("sum1M", sum1M, 32);
+    testLargeSum("sum1M", sum1M, 1024);
+    testLargeSum("sum1M", sum1M, 12341);
+    testLargeSum("sum1M", sum1M, 1012311);
+    printf("sum1M OK.\n");
+
+    testLargeSum("sumVeryLarge", sumVeryLarge, 32);
+    testLargeSum("sumVeryLarge", sumVeryLarge, 1024);
+    testLargeSum("sumVeryLarge", sumVeryLarge, 12341);
+    testLargeSum("sumVeryLarge", sumVeryLarge, 1012311);
+    testLargeSum("sumVeryLarge", sumVeryLarge, 1001002003);
+    printf("sumVeryLarge OK.\n");
+}

hw6/solution/p1/reduction_sum.h

+#pragma once
+
+#include "utils.h"
+#include <algorithm>
+#include <numeric>
+
+constexpr int kWarpSize = 32;
+
+
+/// Kernel for testing `sumWarp`. Do not edit.
+__global__ void sumWarpTestKernel(const double *a, double *b, int N) {
+    int idx = blockIdx.x * blockDim.x + threadIdx.x;
+    // All threads of a warp must call `sumWarp`!
+    double sum = sumWarp(idx < N ? a[idx] : 0.0);
+    if (threadIdx.x % warpSize == 0 && idx / warpSize < (N + warpSize - 1) / warpSize)
+        b[idx / warpSize] = sum;
+}
+
+/// Check results of `sumWarp`. Do not edit.
+inline void sumWarpCheck(int N, int K, const double *aHost, const double *bHost) {
+    for (int k = 0; k < K; ++k) {
+        double expected = std::accumulate(aHost + k * kWarpSize, aHost + std::min((k + 1) * kWarpSize, N), 0.0);
+        double received = bHost[k];
+        if (expected != received) {
+            printf("sumWarp incorrect result:  k=%d  expected=%f  received=%f\n", k, expected, received);
+            exit(1);
+        }
+    }
+}
+
+/// Kernel for testing `sumWarpAll`. Do not edit.
+__global__ void sumWarpAllTestKernel(const double *a, double *b, int N) {
+    int idx = blockIdx.x * blockDim.x + threadIdx.x;
+    // All threads of a warp must call `sumWarpAll`!
+    double sum = sumWarpAll(idx < N ? a[idx] : 0.0);
+    if (idx < N)
+        b[idx] = sum;
+}
+
+/// Check result of `sumWarpAll`. Do not edit.
+inline void sumWarpAllCheck(int N, int K, const double *aHost, const double *bHost) {
+    for (int k = 0; k < K; k += kWarpSize) {
+        double expected = std::accumulate(aHost + k, aHost + std::min(k + kWarpSize, N), 0.0);
+        for (int j = k; j < std::min(k + kWarpSize, N); ++j) {
+            double received = bHost[j];
+            if (expected != received) {
+                printf("sumWarpAll incorrect result:  k=%d j=%d  expected=%f  received=%f\n", k, j, expected, received);
+                exit(1);
+            }
+        }
+    }
+}
+
+// Do not edit.
+__global__ void sumBlockTestKernel(const double *a, double *b, int N) {
+    int idx = blockIdx.x * blockDim.x + threadIdx.x;
+    double sum = sumBlock(idx < N ? a[idx] : 0.0);
+    if (threadIdx.x == 0)
+        b[blockIdx.x] = sum;
+}
+
+// Do not edit.
+inline void sumBlockCheck(int N, int K, const double *aHost, const double *bHost) {
+    for (int k = 0; k < K; ++k) {
+        double expected = std::accumulate(aHost + k * 1024, aHost + std::min((k + 1) * 1024, N), 0.0);
+        double received = bHost[k];
+        if (expected != received) {
+            printf("sumBlock incorrect result:  k=%d  expected=%f  received=%f\n", k, expected, received);
+            exit(1);
+        }
+    }
+}
+
+
+
+/// Test small reductions (warp-level and block-level).
+template <typename Kernel, typename CheckFunc>
+void testSmallSum(Kernel kernel, CheckFunc checkFunc, int div, int N) {
+    int K = (N + div - 1) / div;
+    double *aHost;
+    double *bHost;
+    double *aDev;
+    double *bDev;
+
+    CUDA_CHECK(cudaMallocHost(&aHost, N * sizeof(double)));
+    CUDA_CHECK(cudaMallocHost(&bHost, K * sizeof(double)));
+    CUDA_CHECK(cudaMalloc(&aDev, N * sizeof(double)));
+    CUDA_CHECK(cudaMalloc(&bDev, K * sizeof(double)));
+
+    for (int i = 0; i < N; ++i)
+        aHost[i] = i;
+    CUDA_CHECK(cudaMemcpy(aDev, aHost, N * sizeof(double), cudaMemcpyHostToDevice));
+
+    const int threads = 1024;
+    const int blocks = (N + threads - 1) / threads;
+    kernel<<<blocks, threads>>>(aDev, bDev, N);
+    CUDA_CHECK(cudaMemcpy(bHost, bDev, K * sizeof(double), cudaMemcpyDeviceToHost));
+
+    checkFunc(N, K, aHost, bHost);
+
+    CUDA_CHECK(cudaFree(bDev));
+    CUDA_CHECK(cudaFree(aDev));
+    CUDA_CHECK(cudaFreeHost(bHost));
+    CUDA_CHECK(cudaFreeHost(aHost));
+}
+
+/// Test large reductions (up to 1024^3 and larger).
+template <typename Func>
+void testLargeSum(const char *name, Func func, int N) {
+    double *aHost;
+    double *aDev;
+    double *bDev;