java - 为什么这种并行矩阵加法效率如此低下？

Question

我对多线程非常陌生，并且没有太多使用内部类的经验。

任务是以并行方式添加两个包含 double 值的矩阵。

我的想法是递归地执行此操作，将大矩阵拆分为较小的矩阵，并在矩阵达到一定大小限制时执行加法，然后融合它们。

并行化代码的运行速度比序列化代码慢 40-80 倍。

我怀疑我在这里做错了什么。也许是因为我创建了很多新矩阵，或者因为我遍历了它们很多次。

这是代码:

package concurrency;

import java.util.Random;
import java.util.concurrent.ForkJoinPool;
import java.util.concurrent.RecursiveTask;

public class ParallelMatrixAddition {
public static void main(String[] args) {

    Random rand = new Random();

    final int SIZE = 1000;
    double[][] one = new double[SIZE][SIZE];
    double[][] two = new double[SIZE][SIZE];
    double[][] serialSums = new double[SIZE][SIZE];
    double[][] parallelSums = new double[SIZE][SIZE];

    for (int i = 0; i < one.length; i++) {
        for (int j = 0; j < one.length; j++) {
            one[i][j] = rand.nextDouble();
            two[i][j] = rand.nextDouble();
        }
    }

    long serialStartTime = System.currentTimeMillis();

    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            serialSums[i][j] = one[i][j] + two[i][j];
        }
    }

    long serialEndTime = System.currentTimeMillis();

    System.out.println("Serial runtime is: " + (serialEndTime - serialStartTime) + " milliseconds");

    long startTime = System.currentTimeMillis();

    parallelSums = parallelAddMatrix(one, two);

    long endTime = System.currentTimeMillis();

    System.out.println("Parallel execution took " + (endTime - startTime) + " milliseconds.");

}

public static double[][] parallelAddMatrix(double[][] a, double[][] b) {
    RecursiveTask<double[][]> task = new SumMatricesTask(a, b);
    ForkJoinPool pool = new ForkJoinPool();
    double[][] result = new double[a.length][a.length];
    result = pool.invoke(task);
    return result;
}

@SuppressWarnings("serial")
private static class SumMatricesTask extends RecursiveTask<double[][]> {
    private final static int THRESHOLD = 200;

    private double[][] sumz;
    private double[][] one;
    private double[][] two;

    public SumMatricesTask(double[][] one, double[][] two) {
        this.one = one;
        this.two = two;
        this.sumz = new double[one.length][one.length];
    }

    @Override
    public double[][] compute() {
        if (this.one.length < THRESHOLD) {
            // Compute a sum here.
            // Add the sums of the matrices and store the result in the
            // matrix we will return later.

            double[][] aStuff = new double[this.one.length][this.one.length];

            for (int i = 0; i < one.length; i++) {
                for (int j = 0; j < one.length; j++) {
                    aStuff[i][j] = this.one[i][j] + this.two[i][j];
                }
            }

            return aStuff;

        } else {

            // Split a matrix into four smaller submatrices.
            // Create four forks, then four joins.

            int currentSize = this.one.length;

            int newSize = currentSize / 2;

            double[][] topLeftA = new double[newSize][newSize];
            double[][] topLeftB = new double[newSize][newSize];
            double[][] topLeftSums = new double[newSize][newSize];

            double[][] topRightA = new double[newSize][newSize];
            double[][] topRightB = new double[newSize][newSize];
            double[][] topRightSums = new double[newSize][newSize];

            double[][] bottomLeftA = new double[newSize][newSize];
            double[][] bottomLeftB = new double[newSize][newSize];
            double[][] bottomLeftSums = new double[newSize][newSize];

            double[][] bottomRightA = new double[newSize][newSize];
            double[][] bottomRightB = new double[newSize][newSize];
            double[][] bottomRightSums = new double[newSize][newSize];

            // Populate topLeftA and topLeftB
            for (int i = 0; i < newSize; i++) {
                for (int j = 0; j < newSize; j++) {
                    topLeftA[i][j] = this.one[i][j];
                    topLeftB[i][j] = this.two[i][j];
                }
            }

            // Populate bottomLeftA and bottomLeftB

            for (int i = 0; i < newSize; i++) {
                for (int j = 0; j < newSize; j++) {
                    bottomLeftA[i][j] = this.one[i + newSize][j];
                    bottomLeftB[i][j] = this.two[i + newSize][j];
                }
            }

            // Populate topRightA and topRightB

            for (int i = 0; i < newSize; i++) {
                for (int j = 0; j < newSize; j++) {
                    topRightA[i][j] = this.one[i][j + newSize];
                    topRightB[i][j] = this.two[i][j + newSize];
                }
            }

            // Populate bottomRightA and bottomRightB

            for (int i = 0; i < newSize; i++) {
                for (int j = 0; j < newSize; j++) {
                    bottomRightA[i][j] = this.one[i + newSize][j + newSize];
                    bottomRightB[i][j] = this.two[i + newSize][j + newSize];
                }
            }

            SumMatricesTask topLeft = new SumMatricesTask(topLeftA, topLeftB);
            SumMatricesTask topRight = new SumMatricesTask(topRightA, topRightB);
            SumMatricesTask bottomLeft = new SumMatricesTask(bottomLeftA, bottomLeftB);
            SumMatricesTask bottomRight = new SumMatricesTask(bottomRightA, bottomRightB);

            topLeft.fork();
            topRight.fork();
            bottomLeft.fork();
            bottomRight.fork();

            topLeftSums = topLeft.join();
            topRightSums = topRight.join();
            bottomLeftSums = bottomLeft.join();
            bottomRightSums = bottomRight.join();

            // Fuse the four matrices into one and return it.

            for (int i = 0; i < newSize; i++) {
                for (int j = 0; j < newSize; j++) {
                    this.sumz[i][j] = topLeftSums[i][j];
                }
            }

            for (int i = newSize; i < newSize * 2; i++) {
                for (int j = 0; j < newSize; j++) {
                    this.sumz[i][j] = bottomLeftSums[i - newSize][j];
                }
            }

            for (int i = 0; i < newSize; i++) {
                for (int j = newSize; j < newSize * 2; j++) {
                    this.sumz[i][j] = topRightSums[i][j - newSize];
                }
            }

            for (int i = newSize; i < newSize * 2; i++) {
                for (int j = newSize; j < newSize * 2; j++) {
                    this.sumz[i][j] = bottomRightSums[i - newSize][j - newSize];
                }
            }

            return this.sumz;
        }
    }
}

}

感谢您的帮助。

Answer 1

即使对于 double，创建对象也比执行 + 慢很多倍。

这意味着创建一个对象对于添加来说并不是一个好的权衡。更糟糕的是，使用更多内存意味着您的 CPU 缓存无法高效工作，在最坏的情况下，在 L1/L2 cpu 缓存中工作的内容现在位于 L3 缓存中，该缓存是共享的且不可扩展，甚至更糟您最终会使用主内存。

我建议你重写这个，以便

• 您没有创建任何对象。
• 您认为跨缓存行工作比分解它更有效。即按行而不是按列分解工作。
• 在 Java 中处理一维数组可能会更高效，因此请考虑如何使用仅显示为 2D martix 的一维数组来实现此目的。