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Matrix_Multiplication.cpp
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Matrix_Multiplication.cpp
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/*
1.Blocked Matrix Multiplication
2.Simple Matrix Multiplciation: 6 types of loop permutation and its performance comparison
*/
#include<bits/stdc++.h>
using namespace std;
int **mult, **a, **b;
double **dmult, **da, **db;
int N;
int B = 8;
void block_mat_mul()
{
for(int jj = 0; jj < N; jj += B)
for(int kk = 0; kk < N; kk += B)
for(int i = 0; i < N; i++)
for(int j = jj; j < jj + B; j++)
for(int k = kk; k < kk + B; k++)
mult[i][j] += a[i][k]*b[k][j];
}
void mat_mul1()
{
for(int i = 0; i < N; ++i)
for(int j = 0; j < N; ++j)
for(int k = 0; k < N; ++k)
{
mult[i][j] += a[i][k] * b[k][j];
}
}
void mat_mul2()
{
for(int i = 0; i < N; ++i)
for(int j = 0; j < N; ++j)
for(int k = 0; k < N; ++k)
{
mult[j][i] += a[j][k] * b[k][i];
}
}
void mat_mul3()
{
for(int i = 0; i < N; ++i)
for(int j = 0; j < N; ++j)
for(int k = 0; k < N; ++k)
{
mult[k][j] += a[k][i] * b[i][j];
}
}
void mat_mul4()
{
for(int i = 0; i < N; ++i)
for(int j = 0; j < N; ++j)
for(int k = 0; k < N; ++k)
{
mult[k][i] += a[k][j] * b[j][i];
}
}
void mat_mul5()
{
for(int i = 0; i < N; ++i)
for(int j = 0; j < N; ++j)
for(int k = 0; k < N; ++k)
{
mult[i][k] += a[i][j] * b[j][k];
}
}
void mat_mul6()
{
for(int i = 0; i < N; ++i)
for(int j = 0; j < N; ++j)
for(int k = 0; k < N; ++k)
{
mult[j][k] += a[j][i] * b[i][k];
}
}
void double_mat_mul()
{
for(int i = 0; i < N; ++i)
for(int j = 0; j < N; ++j)
for(int k = 0; k < N; ++k)
{
dmult[i][j] += da[i][k] * db[k][j];
}
}
int main()
{
//------------------------------------------Blocked Matrix comparison
for(int i = 1<<8; i < 1<<12; i<<=1){
cout << "size is " << i << endl;
N = i;
mult = new int*[i];
a = new int*[i];
b = new int*[i];
for(int j = 0; j < i; j++) {
mult[j] = new int[i];
a[j] = new int[i];
b[j] = new int[i];
}
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
a[sz][col] = 10;
b[sz][col] = 10;
}
}
cout << "Simple Matrix Multiplication" << endl;
auto start = chrono::high_resolution_clock::now();
mat_mul1();
auto end = chrono::high_resolution_clock::now();
double total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << 2*pow(i,3)/total_time << endl;
for(int sz = 0; sz < i; sz++)
for(int col = 0; col < i; col++)
mult[sz][col] = 0;
cout << "Blocked Matrix Multiplication" << endl;
start = chrono::high_resolution_clock::now();
block_mat_mul();
end = chrono::high_resolution_clock::now();
total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << 2*pow(i,3)/total_time << endl;
}
//------------------------------------------1
cout << endl << endl;
for(int i = 1<<9; i < 1<<12;i<<=2){
N = i;
mult = new int*[i];
a = new int*[i];
b = new int*[i];
for(int j = 0; j < i; j++) {
mult[j] = new int[i];
a[j] = new int[i];
b[j] = new int[i];
}
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
a[sz][col] = 10;
b[sz][col] = 10;
}
}
auto start = chrono::high_resolution_clock::now();
mat_mul1();
auto end = chrono::high_resolution_clock::now();
double total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << "i j k: " << total_time << endl;
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
}
}
start = chrono::high_resolution_clock::now();
mat_mul2();
end = chrono::high_resolution_clock::now();
total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << "j i k: " << total_time << endl;
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
}
}
start = chrono::high_resolution_clock::now(); ;
mat_mul3();
end = chrono::high_resolution_clock::now();
total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << "k j i: " << total_time << endl;
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
}
}
start = chrono::high_resolution_clock::now();
mat_mul4();
end = chrono::high_resolution_clock::now();
total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << "k i j: " << total_time << endl;
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
}
}
start = chrono::high_resolution_clock::now();
mat_mul5();
end = chrono::high_resolution_clock::now();
total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << "i k j: " << total_time << endl;
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
}
}
start = chrono::high_resolution_clock::now();
mat_mul6();
end = chrono::high_resolution_clock::now();
total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << "j k i: " << total_time << endl;
cout << endl;
}
//------------------------------------------2
cout << endl << endl;
for(int i = 1<<8; i < 1<<12; i<<=1){
N = i;
mult = new int*[i];
a = new int*[i];
b = new int*[i];
for(int j = 0; j < i; j++) {
mult[j] = new int[i];
a[j] = new int[i];
b[j] = new int[i];
}
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
a[sz][col] = 10;
b[sz][col] = 10;
}
}
auto start = chrono::high_resolution_clock::now();
mat_mul1();
auto end = chrono::high_resolution_clock::now();
double total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << i << " " << total_time << " " << 2*pow(N,3)/total_time << endl;
}
//------------------------------------------3
cout << endl << endl;
for(int i = 1<<10; i < 1<<12; i<<=1){
cout << "size is " << i << endl;
cout << "Single Precision" << endl;
N = i;
mult = new int*[i];
a = new int*[i];
b = new int*[i];
for(int j = 0; j < i; j++) {
mult[j] = new int[i];
a[j] = new int[i];
b[j] = new int[i];
}
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
mult[sz][col] = 0;
a[sz][col] = 10;
b[sz][col] = 10;
}
}
auto start = chrono::high_resolution_clock::now();
mat_mul1();
auto end = chrono::high_resolution_clock::now();
double total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << fixed << setprecision(20) << total_time << " " << 2*pow(N,3)/total_time << endl;
N = i;
dmult = new double*[i];
da = new double*[i];
db = new double*[i];
for(int j = 0; j < i; j++) {
dmult[j] = new double[i];
da[j] = new double[i];
db[j] = new double[i];
}
for(int sz = 0; sz < i; sz++){
for(int col = 0; col < i; col++){
dmult[sz][col] = (double)0;
da[sz][col] = (double)10;
db[sz][col] = (double)10;
}
}
start = chrono::high_resolution_clock::now();
double_mat_mul();
end = chrono::high_resolution_clock::now();
total_time =
chrono::duration_cast<chrono::nanoseconds>(end - start).count();
total_time *= 1e-9;
cout << "Double Precision" << endl;
cout << fixed << setprecision(20) << total_time << " " << 2*pow(N,3)/total_time << endl;
}
return 0;
}