使用多个线程时性能几乎没有提高

我正在实现求解线性系统的多线程Jordan Gauss方法，我发现在两个线程上运行只比在单线程上运行少15%的时间，而不是理想的50%。所以我写了一个简单的程序来复制这个。在这里，我创建了一个矩阵2000x2000，并为每个线程提供2000/THREADS_NUM行，以便用它们进行一些计算。

#include <stdlib.h>
#include <stdio.h>
#include <pthread.h>
#include <time.h>
#ifndef THREADS_NUM
#define THREADS_NUM 1
#endif
#define MATRIX_SIZE 2000

typedef struct {
    double *a;
    int row_length;
    int rows_number;
} TWorkerParams;
void *worker_thread(void *params_v)
{
    TWorkerParams *params = (TWorkerParams *)params_v;
    int row_length = params->row_length;
    int i, j, k;
    int rows_number = params->rows_number;
    double *a = params->a;
    for(i = 0; i < row_length; ++i) // row_length is always the same
    {
        for(j = 0; j < rows_number; ++j) // rows_number is inverse proportional
                                         // to the number of threads
        {
            for(k = i; k < row_length; ++k) // row_length is always the same
            {
                a[j*row_length + k] -= 2.;
            }
        }
    }
    return NULL;
}

int main(int argc, char *argv[])
{
    // The matrix is of size NxN
    double *a =
        (double *)malloc(MATRIX_SIZE * MATRIX_SIZE * sizeof(double));
    TWorkerParams *params =
        (TWorkerParams *)malloc(THREADS_NUM * sizeof(TWorkerParams));
    pthread_t *workers = (pthread_t *)malloc(THREADS_NUM * sizeof(pthread_t));
    struct timespec start_time, end_time;
    int rows_per_worker = MATRIX_SIZE / THREADS_NUM;
    int i;
    if(!a || !params || !workers)
    {
        fprintf(stderr, "Error allocating memoryn");
        return 1;
    }
    for(i = 0; i < MATRIX_SIZE*MATRIX_SIZE; ++i)
        a[i] = 4. * i; // just an example matrix
    // Initializtion of matrix is done, now initialize threads' params
    for(i = 0; i < THREADS_NUM; ++i)
    {
        params[i].a = a + i * rows_per_worker * MATRIX_SIZE;
        params[i].row_length = MATRIX_SIZE;
        params[i].rows_number = rows_per_worker;
    }
    // Get start time
    clock_gettime(CLOCK_MONOTONIC, &start_time);
    // Create threads
    for(i = 0; i < THREADS_NUM; ++i)
    {
        if(pthread_create(workers + i, NULL, worker_thread, params + i))
        {
            fprintf(stderr, "Error creating threadn");
            return 1;
        }
    }
    // Join threads
    for(i = 0; i < THREADS_NUM; ++i)
    {
        if(pthread_join(workers[i], NULL))
        {
            fprintf(stderr, "Error creating threadn");
            return 1;
        }
    }
    clock_gettime(CLOCK_MONOTONIC, &end_time);
    printf("Duration: %lf msec.n", (end_time.tv_sec - start_time.tv_sec)*1e3 +
            (end_time.tv_nsec - start_time.tv_nsec)*1e-6);
    return 0;
}

以下是我如何编译它：

gcc threads_test.c -o threads_test1 -lrt -pthread -DTHREADS_NUM=1 -Wall -Werror -Ofast
gcc threads_test.c -o threads_test2 -lrt -pthread -DTHREADS_NUM=2 -Wall -Werror -Ofast

现在，当我运行时，我得到：

./threads_test1
Duration: 3695.359552 msec.
./threads_test2
Duration: 3211.236612 msec.

这意味着两线程程序的运行速度比单线程快13%，即使线程之间并没有同步，并且它们不共享任何内存。我找到了这个答案：https://stackoverflow.com/a/14812411/5647501并认为处理器缓存可能存在一些问题，所以我添加了填充，但结果仍然保持不变。我更改了我的代码如下：

typedef struct {
    double *a;
    int row_length;
    int rows_number;
    volatile char padding[64 - 2*sizeof(int)-sizeof(double)];
} TWorkerParams;
#define VAR_SIZE (sizeof(int)*5 + sizeof(double)*2)
#define MEM_SIZE ((VAR_SIZE / 64 + 1) * 64  )
void *worker_thread(void *params_v)
{
    TWorkerParams *params = (TWorkerParams *)params_v;
    volatile char memory[MEM_SIZE];
    int *row_length  =      (int *)(memory + 0);
    int *i           =      (int *)(memory + sizeof(int)*1);
    int *j           =      (int *)(memory + sizeof(int)*2);
    int *k           =      (int *)(memory + sizeof(int)*3);
    int *rows_number =      (int *)(memory + sizeof(int)*4);
    double **a        = (double **)(memory + sizeof(int)*5);
    *row_length = params->row_length;
    *rows_number = params->rows_number;
    *a = params->a;
    for(*i = 0; *i < *row_length; ++*i) // row_length is always the same
    {
        for(*j = 0; *j < *rows_number; ++*j) // rows_number is inverse proportional
                                         // to the number of threads
        {
            for(*k = 0; *k < *row_length; ++*k) // row_length is always the same
            {
                (*a + *j * *row_length)[*k] -= 2. * *k;
            }
        }
    }
    return NULL;
}

所以我的问题是：为什么在这里使用两个线程时，我的加速率只有15%，而不是50%？如有任何帮助或建议，我们将不胜感激。我运行的是64位Ubuntu Linux，内核3.19.0-39-generic，CPU Intel Core i5 4200M（两个带多线程的物理内核），但我也在另外两台机器上进行了测试，结果相同。

编辑：如果我用a[0] -= 2.;替换a[j*row_length + k] -= 2.;，我会得到预期的加速：

./threads_test1
Duration: 1823.689481 msec.
./threads_test2
Duration: 949.745232 msec.

第2版：现在，当我用a[k] -= 2.;替换它时，我得到了以下内容：

./threads_test1
Duration: 1039.666979 msec.
./threads_test2
Duration: 1323.460080 msec.

这个我根本拿不到。