57
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Changes
→Kernel Version 2
Our initial idea was to use the neural network code for our assignment 2. But since the algorithm itself was not very accurate (2/10 correct predictions even after 10,000 training iterations), we decided to paralellize merge sort. Soon we realized that since its Big O classification was n log n, offloading computations to GPU would not be that effective. So, we settled with the cosine transform library, as described below.
====Cosine Tranformation (A Discrete Cosine Transform for Real Data)====
The Cosine_Transform is a simple C++ library which demonstrates properties of the Discrete cosine Transform for real data. The Discrete Cosine Transform or DCT is used to create jpeg (compressed images).
Where, u is the row index, v is the column index and n is the total number of elements in a row/column in the computational matrix.
This [https://www.youtube.com/watch?v=tW3Hc0Wrgl0 Link] can be used for better understanding of the above formula.----Here is the [https://people.sc.fsu.edu/~jburkardt/cpp_src/cosine_transform/cosine_transform.html source code] used.
=====Profiling=====The flat profile for the above execution serial code looks like:
{| class="wikitable mw-collapsible mw-collapsed"
=====Kernel Version 1=====
{| class="wikitable mw-collapsible mw-collapsed"
! Modified Code
=== Assignment 3 ===
For optimizing the code better, we thought of removing the iterative loop from the kernel by using threadIdx.y to control calculation of each element's cosine for that position in the supposed matrix. The problem in this was that each thread was in a racing condition to write to the same memory location, to sum up the cosine transformations for all elements of that row. We solved this by using the atomic function. Its prototype is as follows.
double atomicAdd(double* address, double value)
=====Kernel Version 2=====
{| class="wikitable mw-collapsible mw-collapsed"
! Kernel 2
|-
|
# include <cmath>
# include <cstdlib>
# include <iostream>
# include <iomanip>
# include <ctime>
# include <chrono>
# include <cstdlib>
# include <cmath>
#include <limits>
#include <cuda_runtime.h>
#include <cuda.h>
using namespace std;
using namespace std::chrono;
const double pi = 3.141592653589793;
const unsigned ntpb = 32;
void cosine_transform_test01 ( int size );
double *r8vec_uniform_01_new ( int n, int &seed ){
int i;
const int i4_huge = 2147483647;
int k;
double *r;
if ( seed == 0 ){
cerr << "\n";
cerr << "R8VEC_UNIFORM_01_NEW - Fatal error!\n";
cerr << " Input value of SEED = 0.\n";
exit ( 1 );
}
r = new double[n];
for ( i = 0; i < n; i++ ){
k = seed / 127773;
seed = 16807 * ( seed - k * 127773 ) - k * 2836;
if ( seed < 0 ){
seed = seed + i4_huge;
}
r[i] = ( double ) ( seed ) * 4.656612875E-10;
}
return r;
}
double *cosine_transform_data ( int n, double d[] ){
double angle;
double *c;
int i;
int j;
c = new double[n];
for ( i = 0; i < n; i++ ){
c[i] = 0.0;
for ( j = 0; j < n; j++ ){
angle = pi * ( double ) ( i * ( 2 * j + 1 ) ) / ( double ) ( 2 * n );
c[i] = c[i] + cos ( angle ) * d[j];
}
c[i] = c[i] * sqrt ( 2.0 / ( double ) ( n ) );
}
return c;
}
void reportTime(const char* msg, steady_clock::duration span) {
auto ms = duration_cast<milliseconds>(span);
std::cout << msg << " - took - " <<
ms.count() << " millisecs" << std::endl;
}
__global__ void cosTransformKernel(double *a, double *b, const int n){
double angle;
const double pi = 3.141592653589793;
int j = blockIdx.x * blockDim.x + threadIdx.x;
int i = blockIdx.y * blockDim.y + threadIdx.y;
if(i<n && j<n){
angle = pi * ( double ) ( i * ( 2 * j + 1 ) ) / ( double ) ( 2 * n );
double value = cos ( angle ) * a[j];
b[i] = atomicAdd(&b[i], value);
}
//square root of the whole cos transformed row term
if(j==n-1 && i<n){
b[i] *= sqrt ( 2.0 / ( double ) ( n ) );
}
}
int main (int argc, char* argv[] ){
if (argc != 2) {
std::cerr << argv[0] << ": invalid number of arguments\n";
std::cerr << "Usage: " << argv[0] << " size_of_vector\n";
return 1;
}
int n = std::atoi(argv[1]);
cosine_transform_test01 (n);
return 0;
}
void cosine_transform_test01 ( int size){
int n = size;
int seed;
double *r;
double *hs; //host side pointer to store the array returned from host side cosine_transform_data, for comparison purposes
double *s = new double[n];
//double *t;
double *d_a;
double *d_b;
//allocate memory on the device for the randomly generated array and for the array in which transform values will be stored
cudaMalloc((void**)&d_a,sizeof(double) * n);
cudaMalloc((void**)&d_b,sizeof(double) * n);
seed = 123456789;
r = r8vec_uniform_01_new ( n, seed );
//copy randomly generated values from host to device
for(int i=0; i<n; i++)
s[i]=0.0;
cudaMemcpy(d_a,r,sizeof(double)*n,cudaMemcpyHostToDevice);
cudaMemcpy(d_b,s,sizeof(double)*n,cudaMemcpyHostToDevice);
int nblks = (n + ntpb - 1) / ntpb;
dim3 grid(nblks,nblks,1);
dim3 block(ntpb,ntpb,1);
steady_clock::time_point ts, te;
ts = steady_clock::now();
cosTransformKernel<<<grid,block>>>(d_a,d_b,size);
cudaDeviceSynchronize();
te = steady_clock::now();
reportTime("Cosine Transform on device",te-ts);
cudaMemcpy(s,d_b,sizeof(double)*n,cudaMemcpyDeviceToHost);
ts = steady_clock::now();
hs = cosine_transform_data ( n, r );
te = steady_clock::now();
reportTime("Cosine Transform on host",te-ts);
cudaFree(d_a);
cudaFree(d_b);
delete [] r;
delete [] s;
delete [] hs;
//delete [] t;
return;
}
|}
Here is a comparison between the naive and optimized kernel
[[File:kernel2.jpg]]
Evidently, there is some performance boost for the new version. However, each call to atomicAdd by a thread locks the global memory until the old value is read and added to the passed value. This deters faster execution as might be expected.
