Xeon Phi 《协处理器高性能编程指南》随书代码整理 part 1

▶ 第三章，逐步优化了一个二维卷积计算的过程

● 基准代码

 #include <stdio.h>
 #include <stdlib.h>
 #include <string.h>
 #include <math.h>
 #include <time.h>
 #include <sys/time.h>
 #include <omp.h>
 #include <assert.h>
 #include <sys/mman.h>

 #define REAL    double
 #define WIDTH   1030
 #define HEIGHT  2048
 #define COUNT   1000
 #define PAD64   0
 #if PAD64                                                                   // 是否对齐到 64 Byte
     #define WIDTHP ((WIDTH * sizeof(REAL) + 63) / 64 * 64 / sizeof(REAL))
 #else
     #define WIDTHP WIDTH
 #endif

 void initbuf(REAL *fbuf, const int width, const int height)                 // 初始化矩阵
 {
     for (int y = ; y < height; y++)
     {
         REAL val = (y % ) ?  : 1.0;
         for (int x = ; x < width; x++)
             fbuf[y * WIDTHP + x] = val;
     }
     return;
 }

 // 重复计算模糊 count 次
 void stencil9pt(REAL *finp, REAL *foutp, const int width, const int height,
     const REAL ctr, const REAL next, const REAL diag, const int count)
 {
     REAL *fin = finp, *fout = foutp;
     for (int i = ; i < count; i++)
     {
         for (int y = ; y < height - ; y++)    // 不处理光环元素
         {
             int c =  + y * WIDTHP;         // ？为什么要加两次 1
             int n = c - WIDTHP, s = c + WIDTHP, w = c - , e = c + ;
             int nw = n - , ne = n + , sw = s - , se = s + ;
             for (int x = ; x < width - ; x++)
             {
                 fout[c] = diag * fin[nw] + diag * fin[ne] + diag * fin[sw] + diag * fin[se] +
                     next * fin[w] + next * fin[e] + next * fin[n] + next * fin[s] + ctr * fin[c];
                 c++; n++; s++; e++; w++; nw++; ne++; sw++; se++;
             }
         }
         REAL *ftmp = fin;
         fin = fout;
         fout = ftmp;
     }
     return;
 }

 static double dtime()
 {
     double tseconds = 0.0;
     struct timeval mytime;
     gettimeofday(&mytime, (struct timezone *) );
     tseconds = (double)(mytime.tv_sec + (double)mytime.tv_usec * 1.0e-6);
     return (tseconds);
 }

 int main(int argc, char *argv[])
 {
     REAL *fa = (REAL *)malloc(sizeof(REAL)*WIDTHP*HEIGHT), *fb = (REAL *)malloc(sizeof(REAL)*WIDTHP*HEIGHT);
     assert(fa != MAP_FAILED);
     assert(fb != MAP_FAILED);

     printf("Initializing..%d Threads, %d x %d, PAD=%d..\n\n", omp_get_num_threads(), WIDTH, HEIGHT, WIDTHP);
     initbuf(fa, WIDTHP, HEIGHT);
     initbuf(fb, WIDTHP, HEIGHT);

     printf("Running stencil kernel %d times\n", COUNT);
     const REAL stendiag = 0.00125, stennext = 0.00125, stenctr = 0.99;
     double time_b, time_e;
     time_b = dtime();
     stencil9pt(fa, fb, WIDTHP, HEIGHT, stenctr, stennext, stendiag, COUNT);
     time_e = dtime();
     printf("Elapsed time : %.3f (s)\n", time_e - time_b);
     printf("FLOPS: %.3f (MFlops)\n", (WIDTHP * HEIGHT) * 17.0 * COUNT / (time_e - time_b) * 1.0e-06);// 计算一个元素需要 17 次乘法或加法

     free(fa);
     free(fb);
     return ;
 }

■ 输出结果

Xeon:
Running stencil kernel  times
Elapsed time: 5.754 (s)
FLOPS       : 6232.567 (MFlops)

XeonPhi:
Running stencil kernel  times
Elapsed time: 102.042 (s)
FLOPS       : 351.428 (MFlops)

● 修改计算函数，忽略指针依赖关系

 void stencil9pt(REAL *finp, REAL *foutp, const int width, const int height,
     const REAL ctr, const REAL next, const REAL diag, const int count)
 {
     REAL *fin = finp, *fout = foutp;
     for (int i = ; i<count; i++)
     {
         for (int y = ; y < height - ; y++)
         {
             int c =  + y * WIDTHP;
             int n = c - WIDTHP, s = c + WIDTHP, w = c - , e = c + ;
             int nw = n - , ne = n + , sw = s - , se = s + ;
             #pragma ivdep                       // 忽略不明显的（指针）依赖关系
             for (int x = ; x < width - ; x++)
             {
                 fout[c] = diag * fin[nw] + diag * fin[ne] + diag * fin[sw] +diag * fin[se] +
                     next * fin[w] + next * fin[e] + next * fin[n] + next * fin[s] + ctr * fin[c];
                 c++; n++; s++; e++; w++; nw++; ne++; sw++; se++;
             }
         }
         REAL *ftmp = fin;
         fin = fout;
         fout = ftmp;
     }
     return;
 }

■ 输出结果（Xeon Phi）

Running stencil kernel  times
Elapsed time: 24.052 (s)
FLOPS       : 1490.925 (MFlops)

● OpenMP

 void stencil9pt(REAL *finp, REAL *foutp, const int width, const int height,
     const REAL ctr, const REAL next, const REAL diag, const int count)
 {
     REAL *fin = finp, *fout = foutp;
     for (int i = ; i<count; i++)
     {
         int y, x;
 #pragma omp parallel for private(x)             // 一句 OpenMp，注意 x 线程私有
         for (y = ; y < height - ; y++)
         {
             int c =  + y * WIDTHP;
             int n = c - WIDTHP, s = c + WIDTHP, w = c - , e = c + ;
             int nw = n - , ne = n + , sw = s - , se = s + ;
 #pragma ivdep
             for (x = ; x < width - ; x++)
             {
                 fout[c] = diag * fin[nw] + diag * fin[ne] + diag * fin[sw] + diag * fin[se] +
                     next * fin[w] + next * fin[e] + next * fin[n] + next * fin[s] + ctr * fin[c];
                 c++; n++; s++; e++; w++; nw++; ne++; sw++; se++;
             }
         }
         REAL *ftmp = fin;
         fin = fout;
         fout = ftmp;
     }
     return;
 }

■ 输出结果（Xeon Phi）

Running stencil kernel  times
Elapsed time : 0.700 (s)
FLOPS        : 51201.595 (MFlops)

● 数组对齐

 // 打开 PAD64
 #define PAD64   1

 // 替换 malloc 和 free
     REAL *fa = (REAL *)malloc(sizeof(REAL)*WIDTHP*HEIGHT);
     REAL *fb = (REAL *)malloc(sizeof(REAL)*WIDTHP*HEIGHT);
     ...
     free(fa);
     free(fb);

 // 替换为
     REAL *fa = (REAL *)_mm_malloc(sizeof(REAL)*WIDTHP*HEIGHT, );
     REAL *fb = (REAL *)_mm_malloc(sizeof(REAL)*WIDTHP*HEIGHT, );
     ...
     _mm_free(fa);
     _mm_free(fb);

■ 输出结果（Xeon Phi）

Running stencil kernel  times
Elapsed time : 0.651 (s)
FLOPS        : 55155.399 (MFlops)

● 流存储

 void stencil9pt(REAL *finp, REAL *foutp, const int width, const int height,
     const REAL ctr, const REAL next, const REAL diag, const int count)
 {
     REAL *fin = finp, *fout = foutp;
     for (int i = ; i<count; i++)
     {
         int y, x;
 #pragma omp parallel for private(x)
         for (y = ; y < height - ; y++)
         {
             int c =  + y * WIDTHP;
             int n = c - WIDTHP, s = c + WIDTHP, w = c - , e = c + ;
             int nw = n - , ne = n + , sw = s - , se = s + ;
 #pragma ivdep
 #pragma vector nontemporal                      // 使用流存储指令（或使用编译选项 -opt-streaming-storesalways）
             for (x = ; x < width - ; x++)
             {
                 fout[c] = diag * fin[nw] + diag * fin[ne] + diag * fin[sw] + diag * fin[se] +
                     next * fin[w] + next * fin[e] + next * fin[n] + next * fin[s] + ctr * fin[c];
                 c++; n++; s++; e++; w++; nw++; ne++; sw++; se++;
             }
         }
         REAL *ftmp = fin;
         fin = fout;
         fout = ftmp;
     }
     return;
 }

■ 输出结果

Xeon:
Running stencil kernel  times
Elapsed time: 1.905 (s)
FLOPS       : 18824.053 (MFlops)

XeonPhi:
Running stencil kernel  times
Elapsed time: 0.639 (s)
FLOPS       : 56145.417 (MFlops)

● 2 MB 存储页（书中代码没有 munmap 的部分）。参考（https://www.aliyun.com/jiaocheng/208004.html），但是服务器上编译时找不到 MAP_ANONYMOUS | MAP_PRIVATE | MAP_HUGETLB 等定义，无法使用

 // 替换 _mm_malloc 和 _mm_free
     REAL *fa = (REAL *)_mm_malloc(sizeof(REAL)*WIDTHP*HEIGHT, );
     REAL *fb = (REAL *)_mm_malloc(sizeof(REAL)*WIDTHP*HEIGHT, );
     ...
     _mm_free(fa);
     _mm_free(fb);
 // 替换为
     REAL *fa = (REAL *)mmap(, WIDTHP*HEIGHT * sizeof(REAL), PROT_READ | PROT_WRITE, MAP_ANONYMOUS | MAP_PRIVATE | MAP_HUGETLB, -, );
     REAL *fb = (REAL *)mmap(, WIDTHP*HEIGHT * sizeof(REAL), PROT_READ | PROT_WRITE, MAP_ANONYMOUS | MAP_PRIVATE | MAP_HUGETLB, -, );
     ...
     munmap(fa, WIDTHP*HEIGHT * sizeof(REAL));
     munmap(fb, WIDTHP*HEIGHT * sizeof(REAL));