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→Kernel Version 2
=== Assignment 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 TRANSFORMATION (A Discrete ==Cosine Transform for Real Data) Tranformation====
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).
The formula used here is:
| (√1/n) , if u=0; 0≤v≤n-1
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 respectively.
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.
1 2 3 4 granularity: each sample hit covers 2 byte(s) for 0.68% of 1.47 seconds 5 6 index % time self children called name 7 <spontaneous> 8 [1] 100.0 0.00 1.47 main [1] 9 0.00 1.47 1/1 cosine_transform_test01(int) [3] 10 ----------------------------------------------- 11 1.47 0.00 1/1 cosine_transform_test01(int) [3] 12 [2] 100.0 1.47 0.00 1 cosine_transform_data(int, double*) [2] 13 ----------------------------------------------- 14 0.00 1.47 1/1 main [1] 15 [3] 100.0 0.00 1.47 1 cosine_transform_test01(int) [3] 16 1.47 0.00 1/1 cosine_transform_data(int, double*) [2] 17 0.00 0.00 1/1 r8vec_uniform_01_new(int, int&) [14] 18 0.00 0.00 1/1 reportTime(char const*, std::chrono::duration<long, std::ratio<1l, 1000000000l> >) [13] 19 0.00 0.00 1/1 std::common_type<std::chrono::duration<long, std::ratio<1l, 1000000000l> >, std::chrono::duration<long, std::ratio<1l, 1000000000l> > >::type std::chrono::operator-<std::chrono::_V2::s teady_clock, std::chrono::duration<long, std::ratio<1l, 1000000000l> >, std::chrono::duration<long, std::ratio<1l, 1000000000l> > >(std::chrono::time_point<std::chrono::_V2::steady_clock, std::chrono::duration<long, std::ratio<1l, 10 00000000l> > > const&, std::chrono::time_point<std::chrono::_V2::steady_clock, std::chrono::duration<long, std::ratio<1l, 1000000000l> > > const&) [21] 20 ----------------------------------------------- 21 0.00 0.00 1/3 std::chrono::duration<long, std::ratio<1l, 1000l> > std::chrono::__duration_cast_impl<std::chrono::duration<long, std::ratio<1l, 1000l> >, std::ratio<1l, 1000000l>, long, true, false>: :__cast<long, std::ratio<1l, 1000000000l> >(std::chrono::duration<long, std::ratio<1l, 1000000000l> > const&) [18] 22 0.00 0.00 2/3 std::common_type<std::chrono::duration<long, std::ratio<1l, 1000000000l> >, std::chrono::duration<long, std::ratio<1l, 1000000000l> > >::type std::chrono::operator-<long, std::ratio<1l , 1000000000l>, long, std::ratio<1l, 1000000000l> >(std::chrono::duration<long, std::ratio<1l, 1000000000l> > const&, std::chrono::duration<long, std::ratio<1l, 1000000000l> > const&) [22] 23 [10] 0.0 0.00 0.00 3 std::chrono::duration<long, std::ratio<1l, 1000000000l> >::count() const [10] 24 ----------------------------------------------- 25 0.00 0.00 2/2 std::common_type<std::chrono::duration<long, std::ratio<1l, 1000000000l> >, std::chrono::duration<long, std::ratio<1l, 1000000000l> > >::type std::chrono::operator-<std::chrono::_V2::s teady_clock, std::chrono::duration<long, std::ratio<1l, 1000000000l> >, std::chrono::duration<long, std::ratio<1l, 1000000000l> > >(std::chrono::time_point<std::chrono::_V2::steady_clock, std::chrono::duration<long, std::ratio<1l, 10 00000000l> > > const&, std::chrono::time_point<std::chrono::_V2::steady_clock, std::chrono::duration<long, std::ratio<1l, 1000000000l> > > const&) [21] 26 [11] 0.0 0.00 0.00 2 std::chrono::time_point<std::chrono::_V2::steady_clock, std::chrono::duration<long, std::ratio<1l, 1000000000l> > >::time_since_epoch() const [11] 27 ----------------------------------------------- 28 0.00 0.00 1/1 __libc_csu_init [28] 29 [12] 0.0 0.00 0.00 1 _GLOBAL__sub_I__Z20r8vec_uniform_01_newiRi [12] 30 0.00 0.00 1/1 __static_initialization_and_destruction_0(int, int) [15] 31 ----------------------------------------------- 32 0.00 0.00 1/1 cosine_transform_test01(int) [3] 33 [13] 0.0 0.00 0.00 1 reportTime(char const*, std::chrono::duration<long, std::ratio<1l, 1000000000l> >) [13] 34 0.00 0.00 1/1 std::enable_if<std::chrono::__is_duration<std::chrono::duration<long, std::ratio<1l, 1000l> > >::value, std::chrono::duration<long, std::ratio<1l, 1000l> > >::type std::chrono::duratio n_cast<std::chrono::duration<long, std::ratio<1l, 1000l> >, long, std::ratio<1l, 1000000000l> >(std::chrono::duration<long, std::ratio<1l, 1000000000l> > const&) [17] 35 0.00 0.00 1/1 std::chrono::duration<long, std::ratio<1l, 1000l> >::count() const [16] 36 ----------------------------------------------- 37 0.00 0.00 1/1 cosine_transform_test01(int) [File3] 38 [14] 0.0 0.00 0.00 1 r8vec_uniform_01_new(int, int&) [14] 39 ----------------------------------------------- 40 0.00 0.00 1/1 _GLOBAL__sub_I__Z20r8vec_uniform_01_newiRi [12] 41 [15] 0.0 0.00 0.00 1 __static_initialization_and_destruction_0(int, int) [15] 42 ----------------------------------------------- 43 0.00 0.00 1/1 reportTime(char const*, std::chrono::duration<long, std::ratio<1l, 1000000000l> >) [13] 44 [16] 0.0 0.00 0.00 1 std::chrono::duration<long, std::ratio<1l, 1000l> >:host:count() const [16] 45 ----------------------------------------------- 46 0.00 0.00 1/1 reportTime(char const*, std::chrono::duration<long, std::ratio<1l, 1000000000l> >) [13] 47 [17] 0.0 0.00 0.jpg00 1 std::enable_if<std::chrono::__is_duration<std::chrono::duration<long, std::ratio<1l, 1000l> > >::value, std::chrono::duration<long, std::ratio<1l, 1000l> > >::type std::chrono::duration_ca st<std::chrono::duration<long, std::ratio<1l, 1000l> >, long, std::ratio<1l, 1000000000l> >(std::chrono::duration<long, std::ratio<1l, 1000000000l> > const&) [17] 48 0.00 0.00 1/1 std::chrono::duration<long, std::ratio<1l, 1000l> > std::chrono::__duration_cast_impl<std::chrono::duration<long, std::ratio<1l, 1000l> >, std::ratio<1l, 1000000l>, long, true, false>: :__cast<long, std::ratio<1l, 1000000000l> >(std::chrono::duration<long, std::ratio<1l, 1000000000l> > const&) [18] 49 ----------------------------------------------- 50 0.00 0.00 1/1 std::enable_if<std::chrono::__is_duration<std::chrono::duration<long, std::ratio<1l, 1000l> > >::value, std::chrono::duration<long, std::ratio<1l, 1000l> > >::type std::chrono::duratio n_cast<std::chrono::duration<long, std::ratio<1l, 1000l> >, long, std::ratio<1l, 1000000000l> >(std::chrono::duration<long, std::ratio<1l, 1000000000l> > const&) [17] 51 [18] 0.0 0.00 0.00 1 std::chrono::duration<long, std::ratio<1l, 1000l> > std::chrono::__duration_cast_impl<std::chrono::duration<long, std::ratio<1l, 1000l> >, std::ratio<1l, 1000000l>, long, true, false>::__c ast<long, std::ratio<1l, 1000000000l> >(std::chrono::duration<long, std::ratio<1l, 1000000000l> > const&) [18]To increase the efficiency of the program we transformed the '''cosine_transform_data''' function into a kernel name '''cosTransformKernel''' which offload the compute intense calculation of the program to the GPU 52 0.00 0.00 1/3 std::chrono::duration<long, std::ratio<1l, 1000000000l> >::count() const [10] |}
As is evident, the algorithm is O(n2) currently. Using thread indices on the GPU to replace the for loops could potentially improve performance.
To increase the efficiency of the program we transformed the '''cosine_transform_data''' function into a kernel named '''cosTransformKernel''' which offloads the compute intense calculation of the program to the GPU.
=====Kernel Version 1=====
{| class="wikitable mw-collapsible mw-collapsed"
! Modified Code
|
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";
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;
}
}
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];
}
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, int n){
double angle;
const double pi = 3.141592653589793;
}
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";
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 *d_a;
delete [] hs;
}
|}
The graph for the execution time difference between the device and the host looks like:
{| class="wikitable mw-collapsible mw-collapsed"
! Flat ProfileKernel 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;
}
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;
}
cudaFree(d_a);
cudaFree(d_b);
delete [] r;
delete [] s;
delete [] hs;
//delete [] t;
return;
}
[[File:kernel2.jpg]]