I’m trying to optimize an algorithm (Lattice Boltzmann) for parallel computing using C++ AMP. And looking for some suggestions to optimize the memory layout, just found out that removing one parameter from the structure into another vector (the blocked vector) gave and increase of about 10%.
Anyone got any tips that can further improve this, or something i should take into consideration?
Below is the most time consuming function that is executed for each timestep, and the structure used for the layout.
struct grid_cell {
// int blocked; // Define if blocked
float n; // North
float ne; // North-East
float e; // East
float se; // South-East
float s;
float sw;
float w;
float nw;
float c; // Center
};
int collision(const struct st_parameters param, vector<struct grid_cell> &node, vector<struct grid_cell> &tmp_node, vector<int> &obstacle) {
int x,y;
int i = 0;
float c_sq = 1.0f/3.0f; // Square of speed of sound
float w0 = 4.0f/9.0f; // Weighting factors
float w1 = 1.0f/9.0f;
float w2 = 1.0f/36.0f;
int chunk = param.ny/20;
float total_density = 0;
float u_x,u_y; // Avrage velocities in x and y direction
float u[9]; // Directional velocities
float d_equ[9]; // Equalibrium densities
float u_sq; // Squared velocity
float local_density; // Sum of densities in a particular node
for(y=0;y<param.ny;y++) {
for(x=0;x<param.nx;x++) {
i = y*param.nx + x; // Node index
// Dont consider blocked cells
if (obstacle[i] == 0) {
// Calculate local density
local_density = 0.0;
local_density += tmp_node[i].n;
local_density += tmp_node[i].e;
local_density += tmp_node[i].s;
local_density += tmp_node[i].w;
local_density += tmp_node[i].ne;
local_density += tmp_node[i].se;
local_density += tmp_node[i].sw;
local_density += tmp_node[i].nw;
local_density += tmp_node[i].c;
// Calculate x velocity component
u_x = (tmp_node[i].e + tmp_node[i].ne + tmp_node[i].se -
(tmp_node[i].w + tmp_node[i].nw + tmp_node[i].sw))
/ local_density;
// Calculate y velocity component
u_y = (tmp_node[i].n + tmp_node[i].ne + tmp_node[i].nw -
(tmp_node[i].s + tmp_node[i].sw + tmp_node[i].se))
/ local_density;
// Velocity squared
u_sq = u_x*u_x +u_y*u_y;
// Directional velocity components;
u[1] = u_x; // East
u[2] = u_y; // North
u[3] = -u_x; // West
u[4] = - u_y; // South
u[5] = u_x + u_y; // North-East
u[6] = -u_x + u_y; // North-West
u[7] = -u_x - u_y; // South-West
u[8] = u_x - u_y; // South-East
// Equalibrium densities
// Zero velocity density: weight w0
d_equ[0] = w0 * local_density * (1.0f - u_sq / (2.0f * c_sq));
// Axis speeds: weight w1
d_equ[1] = w1 * local_density * (1.0f + u[1] / c_sq
+ (u[1] * u[1]) / (2.0f * c_sq * c_sq)
- u_sq / (2.0f * c_sq));
d_equ[2] = w1 * local_density * (1.0f + u[2] / c_sq
+ (u[2] * u[2]) / (2.0f * c_sq * c_sq)
- u_sq / (2.0f * c_sq));
d_equ[3] = w1 * local_density * (1.0f + u[3] / c_sq
+ (u[3] * u[3]) / (2.0f * c_sq * c_sq)
- u_sq / (2.0f * c_sq));
d_equ[4] = w1 * local_density * (1.0f + u[4] / c_sq
+ (u[4] * u[4]) / (2.0f * c_sq * c_sq)
- u_sq / (2.0f * c_sq));
// Diagonal speeds: weight w2
d_equ[5] = w2 * local_density * (1.0f + u[5] / c_sq
+ (u[5] * u[5]) / (2.0f * c_sq * c_sq)
- u_sq / (2.0f * c_sq));
d_equ[6] = w2 * local_density * (1.0f + u[6] / c_sq
+ (u[6] * u[6]) / (2.0f * c_sq * c_sq)
- u_sq / (2.0f * c_sq));
d_equ[7] = w2 * local_density * (1.0f + u[7] / c_sq
+ (u[7] * u[7]) / (2.0f * c_sq * c_sq)
- u_sq / (2.0f * c_sq));
d_equ[8] = w2 * local_density * (1.0f + u[8] / c_sq
+ (u[8] * u[8]) / (2.0f * c_sq * c_sq)
- u_sq / (2.0f * c_sq));
// Relaxation step
node[i].c = (tmp_node[i].c + param.omega * (d_equ[0] - tmp_node[i].c));
node[i].e = (tmp_node[i].e + param.omega * (d_equ[1] - tmp_node[i].e));
node[i].n = (tmp_node[i].n + param.omega * (d_equ[2] - tmp_node[i].n));
node[i].w = (tmp_node[i].w + param.omega * (d_equ[3] - tmp_node[i].w));
node[i].s = (tmp_node[i].s + param.omega * (d_equ[4] - tmp_node[i].s));
node[i].ne = (tmp_node[i].ne + param.omega * (d_equ[5] - tmp_node[i].ne));
node[i].nw = (tmp_node[i].nw + param.omega * (d_equ[6] - tmp_node[i].nw));
node[i].sw = (tmp_node[i].sw + param.omega * (d_equ[7] - tmp_node[i].sw));
node[i].se = (tmp_node[i].se + param.omega * (d_equ[8] - tmp_node[i].se));
}
}
}
return 1;
}
Current GPUs are notoriously depending about memory layout. Without more details about your application here are some things I would suggest you explore:
Unit-stride access is very important so GPUs prefer “structs of arrays” to “arrays of structures”. As you did moving field “blocked” into vector “obstacle”, it should be advantageous to convert all of the fields of “grid_cell” into separate vectors. This should show benefit on CPU as well for loops that don’t access all of the fields.
If “obstacle” is very sparse (which I guess is unlikely) then moving it to its own vector is particularly value. GPUs like CPUs will load more than one word from the memory system either in cache lines or some other form and you waste bandwidth when you don’t need some of the data. For many system memory bandwidth is the bottleneck resource so any way to reduce bandwidth helps.
This is more speculative, but now that you are writing all of the output vector, it is possible the memory subsystem is avoiding reading values in “node” that will simply be overwritten
On some systems, the on-chip memory is split into banks and having an odd number of fields within your structure may help remove bank conflicts.
Some systems will also “vectorize” loads and stores so again removing “blocked” from the structure might enable more vectorization. The shift to struct-of-arrays mitigates this worry.
Thanks for your interest in C++ AMP.
David Callahan
http://blogs.msdn.com/b/nativeconcurrency/ C++ AMP Team Blog