Merge pull request #52 from Nunigan/master

Multiplikation #1

1 files changed, 465 insertions, 0 deletions

diff --git a/buch/papers/multiplikation/code/MM.c b/buch/papers/multiplikation/code/MM.c
new file mode 100755
index 0000000..04c4dab
--- /dev/null
+++ b/buch/papers/multiplikation/code/MM.c
@@ -0,0 +1,465 @@
+#include <stdio.h>

+#include <stdint.h>

+#include <stdlib.h>

+#include <time.h>

+#include <omp.h>

+#include "c_matrix.h"

+#include <gsl/gsl_cblas.h>

+#include <string.h>

+

+void MM(int *A, int *B, int *C, int n);

+void openMP_MM(int *A, int *B, int *C, int n);

+void winograd(int *A, int *B, int *C, int n);

+int winograd_inner(int *a, int *b, int n);

+void run_algo(void (*algo)(), char alog_name[], int print);

+void run_algo_cblas(int print);

+void MM_dc(int *A, int *B, int *C, int n);

+void strassen(int *A, int *B, int *C, int n);

+void printMatrix(int *C, int n);

+void printMatrix_double(double *C, int n);

+void split(int *in, int *out, int n, int col, int row);

+void join(int *in, int *out, int n, int col, int row);

+void add(int *A, int *B, int *C, int n);

+void sub(int *A, int *B, int *C, int n);

+void multiply(int *A, int *B, int *C, int n);

+

+int main() {

+	// omp_set_dynamic(0);

+	// omp_set_num_threads(4);

+//	run_algo(openMP_MM, "openMP_MM",0);

+	run_algo(MM_dc, "MM_dc",0);

+	run_algo(strassen, "strassen",0);

+

+	run_algo(MM, "MM", 0);

+  // run_algo(winograd, "winograd", 0);

+  run_algo_cblas(0);

+

+	return 0;

+}

+

+void MM(int *A, int *B, int *C, int n) {

+	for (int i = 0; i < n; ++i) {

+		for (int j = 0; j < n; ++j) {

+			int sum = 0;

+			for (int k = 0; k < n; ++k) {

+				sum += (*((A + i * n) + k)) * (*((B + k * n) + j));

+			}

+			*((C + i * n) + j) = sum;

+		}

+	}

+}

+

+int winograd_inner(int *a, int *b, int n){

+	int ab = 0;

+	if(n%2==0)

+		{

+			int xi = 0;

+			int etha = 0;

+			for(int i = 0; i<n/2;++i)

+			{

+				xi += a[2*i]*a[2*i+1];

+				etha += b[2*i]*b[2*i+1];

+				ab += (a[2*i]+b[2*i+1])*(a[2*i+1]+b[2*i]);

+			}

+			ab = ab-etha-xi;

+		}

+		return ab;

+	}

+

+	void winograd(int *A, int *B, int *C, int n) {

+

+		int xi_array[n];

+		int etha_array[n];

+		int xi = 0;

+		int etha = 0;

+		int ab = 0;

+

+		for (int i = 0; i < n; ++i) {

+			xi = 0;

+			etha = 0;

+			for(int k = 0;k<n/2;++k)

+			{

+				xi += (*((A + i * n) + 2*k))*(*((A + i * n) + (2*k+1)));

+				etha += (*((B + 2*k * n) + i))*(*((B + (2*k+1) * n) + i));

+			}

+			xi_array[i] = xi;

+			etha_array[i] = etha;

+    }

+

+		for (int i = 0; i < n; ++i) {

+			for (int j = 0; j < n; ++j) {

+				ab = 0;

+				for(int k = 0;k<n/2;++k)

+				{

+			  	ab += ((*((A + i * n) + 2*k))+(*((B + (2*k+1) * n) + j)))*((*((A + i * n) + (2*k+1)))+(*((B + 2*k * n) + j)));

+				}

+				*((C + i * n) + j) =  ab-etha_array[j]-xi_array[i];

+				}

+			}

+

+

+

+

+		// for (int i = 0; i < n; ++i) {

+		// 	int *a = (int*) malloc(n * sizeof(int));

+		// 	for(int k = 0; k<n; ++k)

+		// 	{

+		// 		a[k] = (*((A + i * n) + k));

+		// 	}

+		//

+		// 	for (int j = 0; j < n; ++j) {

+		// 		int *b = (int*) malloc(n * sizeof(int));

+		// 		for(int k = 0; k<n; ++k)

+		// 		{

+		// 			b[k] =(*((B + k * n) + j));

+		// 		}

+		// 		*((C + i * n) + j) = winograd_inner(a,b,n);

+		// 		}

+		// 	}

+		}

+

+

+void openMP_MM(int *A, int *B, int *C, int n) {

+

+		#pragma omp parallel for

+		for (int i = 0; i < n; ++i) {

+			for (int j = 0; j < n; ++j) {

+				int sum = 0;

+				for (int k = 0; k < n; ++k) {

+					sum += (*((A + i * n) + k)) * (*((B + k * n) + j));

+				}

+				*((C + i * n) + j) = sum;

+			}

+		}

+}

+

+void MM_dc(int *A, int *B, int *C, int n) {

+	if (n <= 2) {

+		MM((int*) A, (int*) B, (int*) C, n);

+	} else {

+		int *A11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *A12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *A21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *A22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *B11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *B12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *B21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *B22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+

+		split((int*) A, (int*) A11, n / 2, 0, 0);

+		split((int*) A, (int*) A12, n / 2, 0, n / 2);

+		split((int*) A, (int*) A21, n / 2, n / 2, 0);

+		split((int*) A, (int*) A22, n / 2, n / 2, n / 2);

+		split((int*) B, (int*) B11, n / 2, 0, 0);

+		split((int*) B, (int*) B12, n / 2, 0, n / 2);

+		split((int*) B, (int*) B21, n / 2, n / 2, 0);

+		split((int*) B, (int*) B22, n / 2, n / 2, n / 2);

+

+		int *tmp1 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *tmp2 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *tmp3 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *tmp4 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *tmp5 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *tmp6 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *tmp7 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *tmp8 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+

+		MM_dc((int*) A11, (int*) B11, (int*) tmp1, n / 2);

+		MM_dc((int*) A12, (int*) B21, (int*) tmp2, n / 2);

+		MM_dc((int*) A11, (int*) B12, (int*) tmp3, n / 2);

+		MM_dc((int*) A12, (int*) B22, (int*) tmp4, n / 2);

+		MM_dc((int*) A21, (int*) B11, (int*) tmp5, n / 2);

+		MM_dc((int*) A22, (int*) B21, (int*) tmp6, n / 2);

+		MM_dc((int*) A21, (int*) B12, (int*) tmp7, n / 2);

+		MM_dc((int*) A22, (int*) B22, (int*) tmp8, n / 2);

+

+		free(A11);

+		free(A12);

+		free(A21);

+		free(A22);

+		free(B11);

+		free(B12);

+		free(B21);

+		free(B22);

+

+		int *C11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *C12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *C21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *C22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+

+		add((int*) tmp1, (int*) tmp2, (int*) C11, n / 2);

+		add((int*) tmp3, (int*) tmp4, (int*) C12, n / 2);

+		add((int*) tmp5, (int*) tmp6, (int*) C21, n / 2);

+		add((int*) tmp7, (int*) tmp8, (int*) C22, n / 2);

+

+		free(tmp1);

+		free(tmp2);

+		free(tmp3);

+		free(tmp4);

+		free(tmp5);

+		free(tmp6);

+		free(tmp7);

+		free(tmp8);

+

+		join((int*) C11, (int*) C, n / 2, 0, 0);

+		join((int*) C12, (int*) C, n / 2, 0, n / 2);

+		join((int*) C21, (int*) C, n / 2, n / 2, 0);

+		join((int*) C22, (int*) C, n / 2, n / 2, n / 2);

+

+		free(C11);

+		free(C12);

+		free(C21);

+		free(C22);

+

+	}

+}

+

+void strassen(int *A, int *B, int *C, int n) {

+	if (n <= 2) {

+

+		int P, Q, R, S, T, U, V;

+		P = ((*((A + 0 * n) + 0)) + (*((A + 1 * n) + 1)))

+				* ((*((B + 0 * n) + 0)) + (*((B + 1 * n) + 1)));

+		Q = ((*((A + 1 * n) + 0)) + (*((A + 1 * n) + 1)))

+				* ((*((B + 0 * n) + 0)));

+		R = ((*((A + 0 * n) + 0)))

+				* ((*((B + 0 * n) + 1)) - (*((B + 1 * n) + 1)));

+		S = ((*((A + 1 * n) + 1)))

+				* ((*((B + 1 * n) + 0)) - (*((B + 0 * n) + 0)));

+		T = ((*((A + 0 * n) + 0)) + (*((A + 0 * n) + 1)))

+				* ((*((B + 1 * n) + 1)));

+		U = ((*((A + 1 * n) + 0)) - (*((A + 0 * n) + 0)))

+				* ((*((B + 0 * n) + 0)) + (*((B + 0 * n) + 1)));

+		V = ((*((A + 0 * n) + 1)) - (*((A + 1 * n) + 1)))

+				* ((*((B + 1 * n) + 0)) + (*((B + 1 * n) + 1)));

+		(*((C + 0 * n) + 0)) = P + S - T + V;

+		(*((C + 0 * n) + 1)) = R + T;

+		(*((C + 1 * n) + 0)) = Q + S;

+		(*((C + 1 * n) + 1)) = P + R - Q + U;

+

+	} else {

+		int *A11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *A12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *A21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *A22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *B11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *B12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *B21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *B22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+

+		split((int*) A, (int*) A11, n / 2, 0, 0);

+		split((int*) A, (int*) A12, n / 2, 0, n / 2);

+		split((int*) A, (int*) A21, n / 2, n / 2, 0);

+		split((int*) A, (int*) A22, n / 2, n / 2, n / 2);

+		split((int*) B, (int*) B11, n / 2, 0, 0);

+		split((int*) B, (int*) B12, n / 2, 0, n / 2);

+		split((int*) B, (int*) B21, n / 2, n / 2, 0);

+		split((int*) B, (int*) B22, n / 2, n / 2, n / 2);

+

+		int *P = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *Q = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *R = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *S = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *T = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *U = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *V = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+

+		int *addA = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *addB = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+

+    add((int*) A11, (int*) A22, (int*) addA, n / 2);

+		add((int*) B11, (int*) B22, (int*) addB, n / 2);

+		strassen((int*) addA, (int*) addB, (int*) P, n / 2);

+

+		add((int*) A21, (int*) A22, (int*) addA, n / 2);

+		strassen((int*) addA, (int*) B11, (int*) Q, n / 2);

+

+		sub((int*) B12, (int*) B22, (int*) addB, n / 2);

+		strassen((int*) A11, (int*) addB, (int*) R, n / 2);

+

+		sub((int*) B21, (int*) B11, (int*) addB, n / 2);

+		strassen((int*) A22, (int*) addB, (int*) S, n / 2);

+

+		add((int*) A11, (int*) A12, (int*) addA, n / 2);

+		strassen((int*) addA, (int*) B22, (int*) T, n / 2);

+

+		sub((int*) A21, (int*) A11, (int*) addA, n / 2);

+		add((int*) B11, (int*) B12, (int*) addB, n / 2);

+		strassen((int*) addA, (int*) addB, (int*) U, n / 2);

+

+		sub((int*) A12, (int*) A22, (int*) addA, n / 2);

+		add((int*) B21, (int*) B22, (int*) addB, n / 2);

+		strassen((int*) addA, (int*) addB, (int*) V, n / 2);

+

+		free(A11);

+		free(A12);

+		free(A21);

+		free(A22);

+		free(B11);

+		free(B12);

+		free(B21);

+		free(B22);

+		free(addA);

+		free(addB);

+

+		int *C11 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *C12 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *C21 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *C22 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+

+		int *resAdd1 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+		int *resAdd2 = (int*) malloc(n / 2 * n / 2 * sizeof(int));

+

+		add((int*) R, (int*) T, (int*) C12, n / 2);

+		add((int*) Q, (int*) S, (int*) C21, n / 2);

+

+		add((int*) P, (int*) S, (int*) resAdd1, n / 2);

+		add((int*) resAdd1, (int*) V, (int*) resAdd2, n / 2);

+		sub((int*) resAdd2, (int*) T, (int*) C11, n / 2);

+

+		add((int*) P, (int*) R, (int*) resAdd1, n / 2);

+		add((int*) resAdd1, (int*) U, (int*) resAdd2, n / 2);

+		sub((int*) resAdd2, (int*) Q, (int*) C22, n / 2);

+

+		free(P);

+		free(Q);

+		free(R);

+		free(S);

+		free(T);

+		free(U);

+		free(V);

+		free(resAdd1);

+		free(resAdd2);

+

+		join((int*) C11, (int*) C, n / 2, 0, 0);

+		join((int*) C12, (int*) C, n / 2, 0, n / 2);

+		join((int*) C21, (int*) C, n / 2, n / 2, 0);

+		join((int*) C22, (int*) C, n / 2, n / 2, n / 2);

+

+		free(C11);

+		free(C12);

+		free(C21);

+		free(C22);

+	}

+}

+

+void add(int *A, int *B, int *C, int n) {

+	for (int i = 0; i < n; i++) {

+		for (int j = 0; j < n; j++) {

+			*((C + i * n) + j) = *((A + i * n) + j) + *((B + i * n) + j);

+		}

+	}

+}

+

+void sub(int *A, int *B, int *C, int n) {

+	for (int i = 0; i < n; i++) {

+		for (int j = 0; j < n; j++) {

+			*((C + i * n) + j) = *((A + i * n) + j) - *((B + i * n) + j);

+		}

+	}

+}

+

+void multiply(int *A, int *B, int *C, int n) {

+	int mul;

+

+	for (int i = 0; i < n; ++i) {

+		for (int j = 0; j < n; ++j) {

+			mul = (*((A + i * n) + j)) * (*((B + i * n) + j));

+			*((C + i * n) + j) = mul;

+		}

+	}

+}

+

+void split(int *in, int *out, int n, int col, int row) {

+	for (int i1 = 0, i2 = col; i1 < n; i1++, i2++)

+		for (int j1 = 0, j2 = row; j1 < n; j1++, j2++) {

+			*((out + i1 * n) + j1) = *((in + i2 * n * 2) + j2);

+

+		}

+}

+

+void join(int *in, int *out, int n, int col, int row) {

+	for (int i1 = 0, i2 = col; i1 < n; i1++, i2++)

+		for (int j1 = 0, j2 = row; j1 < n; j1++, j2++)

+			*((out + i2 * n * 2) + j2) = *((in + i1 * n) + j1);

+}

+

+void printMatrix(int *C, int n) {

+	for (int i = 0; i < n; ++i) {

+		for (int j = 0; j < n; ++j) {

+			printf("%d ", *((C + i * n) + j));

+		}

+		printf("\n");

+	}

+}

+

+void printMatrix_double(double *C, int n) {

+	for (int i = 0; i < n; ++i) {

+		for (int j = 0; j < n; ++j) {

+			printf("%.0f ", *((C + i * n) + j));

+		}

+		printf("\n");

+	}

+}

+

+void run_algo(void (*algo)(), char alog_name[], int print)

+{

+	FILE *fptr;

+

+	char fileName[40] =  "meas/";

+	strcat(fileName, alog_name);

+	strcat(fileName, ".txt");

+	fptr = fopen(fileName, "w");

+

+

+	for(int i=0; i<n_arrays; ++i)

+	{

+		for(int j = 0; j<1; ++j)

+		{

+	    int *C = (int*) malloc(n[i] * n[i] * sizeof(int));

+    	double dtime = omp_get_wtime();

+      algo(Ap[i], Bp[i], (int*) C, n[i]);

+	    dtime = omp_get_wtime() - dtime;

+			// printf("The %s program took %f seconds to execute \n", alog_name, dtime);

+			fprintf(fptr, "%f,%d\n", dtime, n[i]);

+

+			if(print==1)

+			{

+				printMatrix((int*)C, n[i]);

+			}

+			free(C);

+  }

+	}

+	fclose(fptr);

+

+}

+

+void run_algo_cblas(int print)

+{

+

+	FILE *fptr;

+

+	fptr = fopen("meas/blas.txt", "w");

+	for(int i=0; i<n_arrays; ++i)

+	{

+		for(int j = 0; j<1; ++j)

+		{

+			double *dC = (double*) malloc(n[i] * n[i] * sizeof(double));

+			double dtime = omp_get_wtime();

+			cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n[i], n[i], n[i], 1.0, dAp[i], n[i],

+			dBp[i], n[i], 0.0, dC, n[i]);

+			dtime = omp_get_wtime() - dtime;

+			// printf("The cblas program took %f seconds to execute \n", dtime);

+			fprintf(fptr, "%f,%d\n",dtime, n[i]);

+

+			if(print==1)

+			{

+				printMatrix_double( (double*)dC, n[i]);

+			}

+

+			free(dC);

+		}

+	}

+	fclose(fptr);

+

+}