▶ 第四章，逐步优化了一个三维卷积计算的过程
● 基准代码
1 #include <stdio.h> 2 #include <stdlib.h> 3 #include <string.h> 4 #include <math.h> 5 #include <time.h> 6 #include <sys/time.h> 7 #include <omp.h> 8 #include <assert.h> 9 #include <sys/mman.h> 10 11 #define REAL float 12 #define NX (64) 13 14 #ifndef M_PI 15 #define M_PI (3.1415926535897932384626) 16 #endif 17 18 // 初始化格点矩阵 19 void init(REAL *buff, const int nx, const int ny, const int nz, const REAL kx, const REAL ky, const REAL kz, 20 const REAL dx, const REAL dy, const REAL dz, const REAL kappa, const REAL time) 21 { 22 REAL ax = exp(-kappa * time*(kx*kx)), ay = exp(-kappa * time*(ky*ky)), az = exp(-kappa * time*(kz*kz)); 23 for (int jz = 0; jz < nz; jz++) 24 { 25 for (int jy = 0; jy < ny; jy++) 26 { 27 for (int jx = 0; jx < nx; jx++) 28 { 29 int j = (jz * ny + jy) * NX + jx; 30 REAL x = dx * ((REAL)(jx + 0.5)), y = dy * ((REAL)(jy + 0.5)), z = dz * ((REAL)(jz + 0.5)); 31 buff[j] = (REAL)0.125*(1.0 - ax * cos(kx * x))*(1.0 - ay * cos(ky * y))*(1.0 - az * cos(kz * z));; 32 } 33 } 34 } 35 } 36 37 // 计算卷积 38 void diffusion(REAL *f1, REAL *f2, int nx, int ny, int nz, 39 REAL ce, REAL cw, REAL cn, REAL cs, REAL ct, REAL cb, REAL cc, REAL dt, int count) 40 { 41 for (int i = 0; i < count; ++i) 42 { 43 for (int z = 0; z < nz; z++) 44 { 45 for (int y = 0; y < ny; y++) 46 { 47 for (int x = 0; x < nx; x++) 48 { 49 int c = (z * ny + y) * NX + x; 50 int w = (x == 0) ? c : c - 1; 51 int e = (x == NX - 1) ? c : c + 1; 52 int n = (y == 0) ? c : c - NX; 53 int s = (y == ny - 1) ? c : c + NX; 54 int b = (z == 0) ? c : c - NX * ny; 55 int t = (z == nz - 1) ? c : c + NX * ny; 56 f2[c] = cc * f1[c] + cw * f1[w] + ce * f1[e] + cs * f1[s] + cn * f1[n] + cb * f1[b] + ct * f1[t]; 57 } 58 } 59 } 60 REAL *t = f1; 61 f1 = f2; 62 f2 = t; 63 } 64 return; 65 } 66 67 static double cur_second(void) // 计时器，返回一个秒数 68 { 69 struct timeval tv; 70 gettimeofday(&tv, NULL); 71 return (double)tv.tv_sec + (double)tv.tv_usec / 1000000.0; 72 } 73 74 REAL accuracy(const REAL *b1, REAL *b2, const int len) //计算两个数组的差距 75 { 76 REAL err = 0.0; 77 for (int i = 0; i < len; i++) 78 err += (b1[i] - b2[i]) * (b1[i] - b2[i]); 79 return (REAL)sqrt(err / len); 80 } 81 82 void dump_result(REAL *f, int nx, int ny, int nz, char *out_path) // 将结果写到文件中 83 { 84 FILE *out = fopen(out_path, "w"); 85 assert(out); 86 fwrite(f, sizeof(REAL), nx * ny * nz, out); 87 fclose(out); 88 } 89 90 int main(int argc, char *argv[]) 91 { 92 int nx = NX, ny = NX, nz = NX; 93 REAL *f1 = (REAL *)malloc(sizeof(REAL) * NX * NX * NX); 94 REAL *f2 = (REAL *)malloc(sizeof(REAL) * NX * NX * NX); 95 REAL *f3 = (REAL *)malloc(sizeof(REAL) * NX * ny * nz); 96 assert(f1 != MAP_FAILED); 97 assert(f2 != MAP_FAILED); 98 assert(f3 != MAP_FAILED); 99 100 REAL dx, dy, dz, kx, ky, kz; 101 dx = dy = dz = 1.0 / nx; // 边长 1.0 102 kx = ky = kz = 2.0 * M_PI; 103 REAL kappa = 0.1; 104 REAL dt = 0.1 * dx * dx / kappa; 105 int count = 0.1 / dt; 106 107 init(f1, nx, ny, nz, kx, ky, kz, dx, dy, dz, kappa, 0.0); 108 109 REAL ce, cw, cn, cs, ct, cb, cc; 110 ce = cw = kappa * dt / (dx * dx); 111 cn = cs = kappa * dt / (dy * dy); 112 ct = cb = kappa * dt / (dz * dz); 113 cc = 1.0 - (ce + cw + cn + cs + ct + cb); 114 115 printf("Running diffusion kernel %d times\n", count); 116 fflush(stdout); 117 struct timeval time_b, time_e; 118 gettimeofday(&time_b, NULL); 119 diffusion(f1, f2, nx, ny, nz, ce, cw, cn, cs, ct, cb, cc, dt, count); 120 gettimeofday(&time_e, NULL); 121 //dump_result((count % 2) ? f2 : f1, nx, ny, nz, "diffusion_result.dat"); 122 123 init(f3, nx, ny, nz, kx, ky, kz, dx, dy, dz, kappa, count * dt); // 对比基准结果 124 REAL err = accuracy((count % 2) ? f2 : f1, f3, nx*ny*nz); 125 double elapsed_time = (time_e.tv_sec - time_b.tv_sec) + (time_e.tv_usec - time_b.tv_usec) * 1.0e-6; 126 REAL mflops = (nx*ny*nz)*13.0*count / elapsed_time * 1.0e-06; 127 double thput = (nx * ny * nz) * sizeof(REAL) * 3.0 * count / elapsed_time * 1.0e-09; 128 129 printf("Elapsed time : %.3f (s)\nFLOPS : %.3f (MFlops)\n", elapsed_time, mflops); 130 printf("Throughput : %.3f (GB/s)\nAccuracy : %e\n", thput, err); 131 132 free(f1); 133 free(f2); 134 return 0; 135 }
■ 输出结果
Running diffusion kernel 1638 times Elapsed time : 177.015 (s) FLOPS : 252.276 (MFlops) Throughput : 0.233 (GB/s) Accuracy : 5.068947e-06
● 计算内核加入 OpenMP
1 void diffusion(REAL *restrict f1, REAL *restrict f2, int nx, int ny, int nz, 2 REAL ce, REAL cw, REAL cn, REAL cs, REAL ct, REAL cb, REAL cc, REAL dt, int count)// 加了 restrict 3 { 4 #pragma omp parallel // openMP 并行域 5 { 6 REAL *f1_t = f1, *f2_t = f2; // 使用局部的指针 7 for (int i = 0; i < count; ++i) 8 { 9 #pragma omp for collapse(2) // 展开外两层循环 10 for (int z = 0; z < nz; z++) 11 { 12 for (int y = 0; y < ny; y++) 13 { 14 for (int x = 0; x < nx; x++) 15 { 16 int c = (z * ny + y) * NX + x; 17 int w = (x == 0) ? c : c - 1; 18 int e = (x == NX - 1) ? c : c + 1; 19 int n = (y == 0) ? c : c - NX; 20 int s = (y == ny - 1) ? c : c + NX; 21 int b = (z == 0) ? c : c - NX * ny; 22 int t = (z == nz - 1) ? c : c + NX * ny; 23 f2_t[c] = cc * f1_t[c] + cw * f1_t[w] + ce * f1_t[e] + cs * f1_t[s] + cn * f1_t[n] + cb * f1_t[b] + ct * f1_t[t]; 24 } 25 } 26 } 27 REAL *t = f1_t; 28 f1_t = f2_t; 29 f2_t = t; 30 } 31 } 32 return; 33 }
■ 输出结果
Running diffusion kernel 1638 times Elapsed time : 2.936 (s) FLOPS : 15209.439 (MFlops) Throughput : 14.039 (GB/s) Accuracy : 4.789139e-06
● 保证向量化
1 void diffusion(REAL *restrict f1, REAL *restrict f2, int nx, int ny, int nz, 2 REAL ce, REAL cw, REAL cn, REAL cs, REAL ct, REAL cb, REAL cc, REAL dt, int count) 3 { 4 #pragma omp parallel 5 { 6 REAL *f1_t = f1, *f2_t = f2; 7 for (int i = 0; i < count; ++i) 8 { 9 #pragma omp for collapse(2) 10 for (int z = 0; z < nz; z++) 11 { 12 for (int y = 0; y < ny; y++) 13 { 14 #pragma simd // 保证向量化，不考虑 f1_t 和 f2_t 之间的独立子性 15 for (int x = 0; x < nx; x++) 16 { 17 int c = (z * ny + y) * NX + x; 18 int w = (x == 0) ? c : c - 1; 19 int e = (x == NX - 1) ? c : c + 1; 20 int n = (y == 0) ? c : c - NX; 21 int s = (y == ny - 1) ? c : c + NX; 22 int b = (z == 0) ? c : c - NX * ny; 23 int t = (z == nz - 1) ? c : c + NX * ny; 24 f2_t[c] = cc * f1_t[c] + cw * f1_t[w] + ce * f1_t[e] + cs * f1_t[s] + cn * f1_t[n] + cb * f1_t[b] + ct * f1_t[t]; 25 } 26 } 27 } 28 REAL *t = f1_t; 29 f1_t = f2_t; 30 f2_t = t; 31 } 32 } 33 return; 34 }
■ 输出结果
Running diffusion kernel 1638 times Elapsed time : 0.865 (s) FLOPS : 51651.863 (MFlops) Throughput : 47.679 (GB/s) Accuracy : 4.427611e-06
● 手动剥离边界
1 void diffusion(REAL *restrict f1, REAL *restrict f2, int nx, int ny, int nz, 2 REAL ce, REAL cw, REAL cn, REAL cs, REAL ct, REAL cb, REAL cc, REAL dt, int count) 3 { 4 #pragma omp parallel 5 { 6 REAL *f1_t = f1, *f2_t = f2; 7 for (int i = 0; i < count; ++i) 8 { 9 #pragma omp for collapse(2) 10 for (int z = 0; z < nz; z++) 11 { 12 for (int y = 0; y < ny; y++) 13 { 14 int x = 0; // 每行首次 15 int c = (z * ny + y) * NX + x; // 注意 w 方向的下标是 c 16 int n = (y == 0) ? c : c - NX; 17 int s = (y == ny - 1) ? c : c + NX; 18 int b = (z == 0) ? c : c - NX * ny; 19 int t = (z == nz - 1) ? c : c + NX * ny; 20 f2_t[c] = cc * f1_t[c] + cw * f1_t[c] + ce * f1_t[c + 1] + cs * f1_t[s] + cn * f1_t[n] + cb * f1_t[b] + ct * f1_t[t]; 21 #pragma simd 22 for (x = 1; x < nx - 1; x++) // 中间部分，注意循环要按照 OpenMP 格式书写 23 { 24 c++; 25 n++; 26 s++; 27 b++; 28 t++; 29 f2_t[c] = cc * f1_t[c] + cw * f1_t[c - 1] + ce * f1_t[c + 1] + cs * f1_t[s] + cn * f1_t[n] + cb * f1_t[b] + ct * f1_t[t]; 30 } 31 c++; // 每行末次 32 n++; // 注意 e 方向的下标是 c 33 s++; 34 b++; 35 t++; 36 f2_t[c] = cc * f1_t[c] + cw * f1_t[c - 1] + ce * f1_t[c] + cs * f1_t[s] + cn * f1_t[n] + cb * f1_t[b] + ct * f1_t[t]; 37 } 38 } 39 REAL *t = f1_t; 40 f1_t = f2_t; 41 f2_t = t; 42 } 43 } 44 return; 45 }
■ 输出结果
Running diffusion kernel 1638 times Elapsed time : 0.565 (s) FLOPS : 79071.250 (MFlops) Throughput : 72.989 (GB/s) Accuracy : 4.577150e-06
● 数据切片
1 void diffusion(REAL *restrict f1, REAL *restrict f2, int nx, int ny, int nz, 2 REAL ce, REAL cw, REAL cn, REAL cs, REAL ct, REAL cb, REAL cc, REAL dt, int count) 3 { 4 #pragma omp parallel 5 { 6 REAL *f1_t = f1, *f2_t = f2; 7 for (int i = 0; i < count; ++i) 8 { 9 #define YBF 16 // 分块大小 10 #pragma omp for collapse(2) 11 for (int yy = 0; yy < ny; yy += YBF) // 在循环之外放入分块 12 { 13 for (int z = 0; z < nz; z++) 14 { 15 int yyy = (yy + YBF) >= ny ? ny : (yy + YBF); // 该分块的末端 16 for (int y = yy; y < yyy; y++) // y 限定在分块内循环 17 { 18 int x = 0; 19 int c = (z * ny + y) * NX + x; 20 int n = (y == 0) ? c : c - NX; 21 int s = (y == ny - 1) ? c : c + NX; 22 int b = (z == 0) ? c : c - NX * ny; 23 int t = (z == nz - 1) ? c : c + NX * ny; 24 f2_t[c] = cc * f1_t[c] + cw * f1_t[c] + ce * f1_t[c + 1] + cs * f1_t[s] + cn * f1_t[n] + cb * f1_t[b] + ct * f1_t[t]; 25 #pragma simd 26 for (x = 1; x < nx - 1; x++) 27 { 28 c++; 29 n++; 30 s++; 31 b++; 32 t++; 33 f2_t[c] = cc * f1_t[c] + cw * f1_t[c - 1] + ce * f1_t[c + 1] + cs * f1_t[s] + cn * f1_t[n] + cb * f1_t[b] + ct * f1_t[t]; 34 } 35 c++; 36 n++; 37 s++; 38 b++; 39 t++; 40 f2_t[c] = cc * f1_t[c] + cw * f1_t[c - 1] + ce * f1_t[c] + cs * f1_t[s] + cn * f1_t[n] + cb * f1_t[b] + ct * f1_t[t]; 41 } 42 } 43 } 44 REAL *t = f1_t; 45 f1_t = f2_t; 46 f2_t = t; 47 } 48 } 49 return; 50 }
■ 输出结果，没有明显优化
Running diffusion kernel 1638 times Elapsed time : 0.594 (s) FLOPS : 75224.680 (MFlops) Throughput : 69.438 (GB/s) Accuracy : 4.577150e-06