1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173 | #include "apsp.h"
const int MAXN = 1 << 5;
const int EXTEND = 6;
const int DIV = 2; // Registers per thread uses will be more than 64 if I set DIV = 3.
namespace {
__shared__ int foo[MAXN * EXTEND][MAXN];
__shared__ int bar[MAXN][MAXN * EXTEND];
__global__ void step1(int n, int p, int* graph) {
int x = p * MAXN + threadIdx.y;
int y = p * MAXN + threadIdx.x;
if (x < n && y < n) {
foo[threadIdx.y][threadIdx.x] = graph[x * n + y];
}
__syncthreads();
int m = min(n, (p + 1) * MAXN) - p * MAXN;
int result;
if (x < n && y < n) {
result = graph[x * n + y];
}
for (int k = 0; k < m; ++k) {
if (x < n && y < n) {
result = min(result, foo[threadIdx.y][k] + foo[k][threadIdx.x]);
foo[threadIdx.y][threadIdx.x] = result;
}
__syncthreads();
}
if (x < n && y < n) {
graph[x * n + y] = result;
}
}
/**
* The following naive implementation of step-2 only runs around 7ms at n = 10000,
* and its performance went worse after I eliminated all bank conflicts.
* Therefore I'm not going to change it.
*/
/**
* tag:
* 0: reset foo
* 1: reset bar
*/
__device__ void rewrite(int n, int begin_x, int step_x, int begin_y, int step_y, int* graph, int tag) {
for (int i = 0; i < step_x; ++i) {
for (int j = 0; j < step_y; ++j) {
int cur_x = threadIdx.y * step_x + i;
int cur_y = threadIdx.x * step_y + j;
int x = begin_x + cur_x;
int y = begin_y + cur_y;
if (x < n && y < n) {
if (tag == 0) {
foo[cur_x][cur_y] = graph[x * n + y];
} else {
bar[cur_x][cur_y] = graph[x * n + y];
}
}
}
}
}
__global__ void step2(int n, int p, int* graph) {
int begin_x = blockIdx.y == 0 ? p * MAXN : blockIdx.x * MAXN * EXTEND;
int begin_y = blockIdx.y == 1 ? p * MAXN : blockIdx.x * MAXN * EXTEND;
int step_x = blockIdx.y == 0 ? 1 : EXTEND;
int step_y = blockIdx.y == 1 ? 1 : EXTEND;
rewrite(n, begin_x, step_x, p * MAXN, 1, graph, 0);
rewrite(n, p * MAXN, 1, begin_y, step_y, graph, 1);
__syncthreads();
for (int i = 0; i < step_x; ++i) {
for (int j = 0; j < step_y; ++j) {
int cur_x = threadIdx.y * step_x + i;
int cur_y = threadIdx.x * step_y + j;
int x = begin_x + cur_x;
int y = begin_y + cur_y;
if (x < n && y < n) {
int result = graph[x * n + y];
int m = min(n, (p + 1) * MAXN) - p * MAXN;
for (int k = 0; k < m; ++k) {
result = min(result, foo[cur_x][k] + bar[k][cur_y]);
}
graph[x * n + y] = result;
}
}
}
}
/**
* Step-3 is what I should optimize mainly.
*/
__global__ void step3(int n, int p, int* graph) {
int begin_x = blockIdx.y * MAXN * EXTEND;
int begin_y = blockIdx.x * MAXN * EXTEND;
for (int i = 0; i < EXTEND; ++i) {
int cur_x = i * MAXN + threadIdx.y;
int cur_y = threadIdx.x;
int x = begin_x + cur_x;
int y = p * MAXN + cur_y;
if (x < n && y < n) {
foo[cur_x][cur_y] = graph[x * n + y];
}
}
for (int i = 0; i < EXTEND; ++i) {
int cur_x = threadIdx.y;
int cur_y = i * MAXN + threadIdx.x;
int x = p * MAXN + cur_x;
int y = begin_y + cur_y;
if (x < n && y < n) {
bar[cur_x][cur_y] = graph[x * n + y];
}
}
__syncthreads();
for (int cur = 0; cur < (EXTEND / DIV); ++cur) {
int result[DIV][EXTEND];
for (int i = 0; i < DIV; ++i) {
for (int j = 0; j < EXTEND; ++j) {
int x = begin_x + (cur * DIV + i) * MAXN + threadIdx.y;
int y = begin_y + j * MAXN + threadIdx.x;
if (x < n && y < n) {
result[i][j] = graph[x * n + y];
}
}
}
int m = min(n, (p + 1) * MAXN) - p * MAXN;
#pragma unroll(16)
for (int k = 0; k < m; ++k) {
for (int i = 0; i < DIV; ++i) {
for (int j = 0; j < EXTEND; ++j) {
int cur_x = (cur * DIV + i) * MAXN + threadIdx.y;
int cur_y = j * MAXN + threadIdx.x;
result[i][j] = min(result[i][j], foo[cur_x][k] + bar[k][cur_y]);
}
}
}
for (int i = 0; i < DIV; ++i) {
for (int j = 0; j < EXTEND; ++j) {
int x = begin_x + (cur * DIV + i) * MAXN + threadIdx.y;
int y = begin_y + j * MAXN + threadIdx.x;
if (x < n && y < n) {
graph[x * n + y] = result[i][j];
}
}
}
}
}
}
void apsp(int n, /* device */ int* graph) {
int block_n = (n - 1) / (MAXN * EXTEND) + 1;
for (int p = 0; p * MAXN < n; ++p) {
dim3 threads(MAXN, MAXN);
// Step 1
step1<<<1, threads>>>(n, p, graph);
cudaDeviceSynchronize();
// Step 2
dim3 blocks_2(block_n, 2);
step2<<<block_n, threads>>>(n, p, graph);
cudaDeviceSynchronize();
// Step 3
dim3 blocks_3(block_n, block_n);
step3<<<blocks_3, threads>>>(n, p, graph);
cudaDeviceSynchronize();
}
}
|