Hello I am trying to run a program that finds closest pair using brute force with caching techniques like the pdf here: Caching Performance Stanford
My original code is:
float compare_points_BF(int N,point *P){
int i,j;
float distance=0, min_dist=FLT_MAX;
point *p1, *p2;
unsigned long long calc = 0;
for (i=0;i<(N-1);i++){
for (j=i+1;j<N;j++){
if ((distance = (P[i].x - P[j].x) * (P[i].x - P[j].x) +
(P[i].y - P[j].y) * (P[i].y - P[j].y)) < min_dist){
min_dist = distance;
p1 = &P[i];
p2 = &P[j];
}
}
}
return sqrt(min_dist);
}
This program gives approximately these running times:
N 8192 16384 32768 65536 131072 262144 524288 1048576
seconds 0,070 0,280 1,130 5,540 18,080 72,838 295,660 1220,576
0,080 0,330 1,280 5,190 20,290 80,880 326,460 1318,631
The cache version of the above program is:
float compare_points_BF(register int N, register int B, point *P){
register int i, j, ib, jb, num_blocks = (N + (B-1)) / B;
register point *p1, *p2;
register float distance=0, min_dist=FLT_MAX, regx, regy;
//break array data in N/B blocks, ib is index for i cached block and jb is index for j strided cached block
//each i block is compared with the j block, (which j block is always after the i block)
for (i = 0; i < num_blocks; i++){
for (j = i; j < num_blocks; j++){
//reads the moving frame block to compare with the i cached block
for (jb = j * B; jb < ( ((j+1)*B) < N ? ((j+1)*B) : N); jb++){
//avoid float comparisons that occur when i block = j block
//Register Allocated
regx = P[jb].x;
regy = P[jb].y;
for (i == j ? (ib = jb + 1) : (ib = i * B); ib < ( ((i+1)*B) < N ? ((i+1)*B) : N); ib++){
//calculate distance of current points
if((distance = (P[ib].x - regx) * (P[ib].x - regx) +
(P[ib].y - regy) * (P[ib].y - regy)) < min_dist){
min_dist = distance;
p1 = &P[ib];
p2 = &P[jb];
}
}
}
}
}
return sqrt(min_dist);
}
and some results:
Block_size = 256 N = 8192 Run time: 0.090 sec
Block_size = 512 N = 8192 Run time: 0.090 sec
Block_size = 1024 N = 8192 Run time: 0.090 sec
Block_size = 2048 N = 8192 Run time: 0.100 sec
Block_size = 4096 N = 8192 Run time: 0.090 sec
Block_size = 8192 N = 8192 Run time: 0.090 sec
Block_size = 256 N = 16384 Run time: 0.357 sec
Block_size = 512 N = 16384 Run time: 0.353 sec
Block_size = 1024 N = 16384 Run time: 0.360 sec
Block_size = 2048 N = 16384 Run time: 0.360 sec
Block_size = 4096 N = 16384 Run time: 0.370 sec
Block_size = 8192 N = 16384 Run time: 0.350 sec
Block_size = 16384 N = 16384 Run time: 0.350 sec
Block_size = 128 N = 32768 Run time: 1.420 sec
Block_size = 256 N = 32768 Run time: 1.420 sec
Block_size = 512 N = 32768 Run time: 1.390 sec
Block_size = 1024 N = 32768 Run time: 1.410 sec
Block_size = 2048 N = 32768 Run time: 1.430 sec
Block_size = 4096 N = 32768 Run time: 1.430 sec
Block_size = 8192 N = 32768 Run time: 1.400 sec
Block_size = 16384 N = 32768 Run time: 1.380 sec
Block_size = 256 N = 65536 Run time: 5.760 sec
Block_size = 512 N = 65536 Run time: 5.790 sec
Block_size = 1024 N = 65536 Run time: 5.720 sec
Block_size = 2048 N = 65536 Run time: 5.720 sec
Block_size = 4096 N = 65536 Run time: 5.720 sec
Block_size = 8192 N = 65536 Run time: 5.530 sec
Block_size = 16384 N = 65536 Run time: 5.550 sec
Block_size = 256 N = 131072 Run time: 22.750 sec
Block_size = 512 N = 131072 Run time: 23.130 sec
Block_size = 1024 N = 131072 Run time: 22.810 sec
Block_size = 2048 N = 131072 Run time: 22.690 sec
Block_size = 4096 N = 131072 Run time: 22.710 sec
Block_size = 8192 N = 131072 Run time: 21.970 sec
Block_size = 16384 N = 131072 Run time: 22.010 sec
Block_size = 256 N = 262144 Run time: 90.220 sec
Block_size = 512 N = 262144 Run time: 92.140 sec
Block_size = 1024 N = 262144 Run time: 91.181 sec
Block_size = 2048 N = 262144 Run time: 90.681 sec
Block_size = 4096 N = 262144 Run time: 90.760 sec
Block_size = 8192 N = 262144 Run time: 87.660 sec
Block_size = 16384 N = 262144 Run time: 87.760 sec
Block_size = 256 N = 524288 Run time: 361.151 sec
Block_size = 512 N = 524288 Run time: 379.521 sec
Block_size = 1024 N = 524288 Run time: 379.801 sec
From what we can see the running time is slower than the non-cached code. Is this due to compiler optimization? Is the code bad or is it just because of the algorithm that does not perform well with tiling? I use VS 2010 compiled with 32bit executable. Thanks in advance!
This is an interesting case. The compiler did a poor job of loop invariant hoisting in the two inner loops. Namely, the two inner for-loop checks the following condition in each iteration:
(j+1)*B) < N ? ((j+1)*B) : N
and
(i+1)*B) < N ? ((i+1)*B) : N
The calculation and branching are both expensive; but they are actually loop invariant for the two inner for-loops. Once manually hoisting them out of the two inner for-loops, I was able to get the cache optimized version to perform better than the unoptimized version (10% when N==524288, 30% when N=1048576).
Here is the modified code (simple change really, look for u1, u2):
//break array data in N/B blocks, ib is index for i cached block and jb is index for j strided cached block
//each i block is compared with the j block, (which j block is always after the i block)
for (i = 0; i < num_blocks; i++){
for (j = i; j < num_blocks; j++){
int u1 = (((j+1)*B) < N ? ((j+1)*B) : N);
int u2 = (((i+1)*B) < N ? ((i+1)*B) : N);
//reads the moving frame block to compare with the i cached block
for (jb = j * B; jb < u1 ; jb++){
//avoid float comparisons that occur when i block = j block
//Register Allocated
regx = P[jb].x;
regy = P[jb].y;
for (i == j ? (ib = jb + 1) : (ib = i * B); ib < u2; ib++){
//calculate distance of current points
if((distance = (P[ib].x - regx) * (P[ib].x - regx) +
(P[ib].y - regy) * (P[ib].y - regy)) < min_dist){
min_dist = distance;
p1 = &P[ib];
p2 = &P[jb];
}
}
}
}
}