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finite_field_block.c
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finite_field_block.c
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#include <stdio.h>
#include <stdlib.h>
#include "covering_array.h"
#define MAX_q 23 // greatest prime power supported
#define MAX_degree 4
int Z_addition(int, int, int);
int Z_multiplication(int, int, int);
Design *finite_field_based_design(int value)
{
int i = 0;
int flag_primepower = 0;
int sprime;
int alpha, beta;
int new_value;
Design *bd;
if ((value < 1) ||(value > MAX_q)) {
fprintf(stderr, "exceed limit\n");
exit(1);
}
sprime = smallest_prime_power(value);
if (value == sprime)
flag_primepower = 1;
else
flag_primepower = 0;
bd = (Design *)malloc(sizeof(Design));
bd->no_pars = sprime + 1;
bd->size = sprime*sprime;
if ((bd->range = (int *)calloc(bd->no_pars, sizeof(int))) == NULL)
return NULL; // memory shortage
for(i = 0; i < bd->no_pars; i++)
bd->range[i] = value;
bd->value = (int *)calloc(bd->no_pars * bd->size, sizeof(int));
for (alpha = 0; alpha < sprime; alpha++) {
for (beta = 0; beta < sprime; beta++) {
for (i = 0; i < sprime; i++) {
new_value = Z_addition(Z_multiplication(alpha, i, sprime), beta, sprime);
if (new_value >= value)
new_value = -1;
set_value(bd, alpha * sprime + beta, i, new_value);
}
new_value = alpha;
if (new_value >= value)
new_value = -1;
set_value(bd, alpha * sprime + beta, sprime, new_value);
}
}
return bd;
}
int Z_multiplication(int x, int y, int q)
{
int i, tmp, result;
int prime, prime_power, factor = 0;
void Index2Coefficient();
if (q > MAX_q){
fprintf(stderr,"%d is too large.\n",q);
exit(-1);
}
prime = 1;
for(i=2; i<q; i++)
if((q % i) == 0) {
prime = 0;
break;
}
if(prime == 1) {
result = (x * y) % q;
return(result);
}
prime_power = 1;
for(i=2; i<q; i++)
if((q % i) == 0) {
factor = i;
break;
}
tmp = q / factor;
while(tmp != 1)
if((tmp % factor) == 0)
tmp = tmp/factor;
else {
prime_power = 0;
break;
}
if(prime_power == 0) {
fprintf(stderr,"%d is not a prime power.\n", q);
exit(-1);
}
if ((x==0)||(y==0))
return(0);
result = (((x-1) + (y-1)) % (q-1))+1;
return(result);
}
int Z_addition(int x, int y, int q)
{
int i, tmp, result;
int prime, prime_power, factor = 0;
int xc[MAX_degree];
int yc[MAX_degree];
int zc[MAX_degree];
void Index2Coefficient();
int Coefficient2Index();
if (q > MAX_q){
fprintf(stderr,"%d is too large.\n",q);
exit(-1);
}
prime = 1;
for(i=2; i<q; i++)
if((q % i) == 0) {
prime = 0;
break;
}
if(prime == 1) {
result = (x + y) % q;
return(result);
}
prime_power = 1;
for(i=2; i<q; i++)
if((q % i) == 0) {
factor = i;
break;
}
tmp = q / factor;
while(tmp != 1)
if((tmp % factor) == 0)
tmp = tmp/factor;
else {
prime_power = 0;
break;
}
if(prime_power == 0) {
fprintf(stderr,"%d is not a prime power.\n", q);
exit(-1);
}
Index2Coefficient(q, x-1, &xc[0], &xc[1], &xc[2], &xc[3]);
Index2Coefficient(q, y-1, &yc[0], &yc[1], &yc[2], &yc[3]);
for(i=0; i<MAX_degree; i++)
zc[i] = (xc[i]+yc[i]) % factor;
result = Coefficient2Index(q, zc[0], zc[1], zc[2], zc[3]);
result = result +1;
return(result);
}
void Index2Coefficient(int q, int x, int *c1, int *c2, int *c3, int *c4)
{
int order, i,j,k;
int ce[4][MAX_q][MAX_degree]; /* 4 = no_FILEDS */
int no_FILEDS;
enum FILED {
GF4, GF8, GF9, GF16
};
no_FILEDS = 4;
order = -1;
if (q == 4)
order = GF4;
if (q == 8)
order = GF8;
if (q == 9)
order = GF9;
if (q == 16)
order = GF16;
if (order < 0){
fprintf(stderr,"In Index2Coefficient: Error\n");
exit(-1);
}
if (x < 0) {
*c1 = *c2 = *c3 = *c4 = 0;
return;
}
for(i=0; i<no_FILEDS; i++)
for(j=0; j<MAX_q; j++)
for(k=0; k<MAX_degree; k++)
ce[i][j][k] = 0;
ce[GF4][0][0] = 0; ce[GF4][0][1] = 1;
ce[GF4][1][0] = 1; ce[GF4][1][1] = 0;
ce[GF4][2][0] = 1; ce[GF4][2][1] = 1;
ce[GF8][0][0] = 0; ce[GF8][0][1] = 0; ce[GF8][0][2] = 1;
ce[GF8][1][0] = 0; ce[GF8][1][1] = 1; ce[GF8][1][2] = 0;
ce[GF8][2][0] = 1; ce[GF8][2][1] = 0; ce[GF8][2][2] = 0;
ce[GF8][3][0] = 1; ce[GF8][3][1] = 0; ce[GF8][3][2] = 1;
ce[GF8][4][0] = 1; ce[GF8][4][1] = 1; ce[GF8][4][2] = 1;
ce[GF8][5][0] = 0; ce[GF8][5][1] = 1; ce[GF8][5][2] = 1;
ce[GF8][6][0] = 1; ce[GF8][6][1] = 1; ce[GF8][6][2] = 0;
ce[GF9][0][0] = 0; ce[GF9][0][1] = 1;
ce[GF9][1][0] = 1; ce[GF9][1][1] = 0;
ce[GF9][2][0] = 2; ce[GF9][2][1] = 1;
ce[GF9][3][0] = 2; ce[GF9][3][1] = 2;
ce[GF9][4][0] = 0; ce[GF9][4][1] = 2;
ce[GF9][5][0] = 2; ce[GF9][5][1] = 0;
ce[GF9][6][0] = 1; ce[GF9][6][1] = 2;
ce[GF9][7][0] = 1; ce[GF9][7][1] = 1;
ce[GF16][0][0] = 0; ce[GF16][0][1] = 0; ce[GF16][0][2] = 0; ce[GF16][0][3] = 1;
ce[GF16][1][0] = 0; ce[GF16][1][1] = 0; ce[GF16][1][2] = 1; ce[GF16][1][3] = 0;
ce[GF16][2][0] = 0; ce[GF16][2][1] = 1; ce[GF16][2][2] = 0; ce[GF16][2][3] = 0;
ce[GF16][3][0] = 1; ce[GF16][3][1] = 0; ce[GF16][3][2] = 0; ce[GF16][3][3] = 0;
ce[GF16][4][0] = 1; ce[GF16][4][1] = 0; ce[GF16][4][2] = 0; ce[GF16][4][3] = 1;
ce[GF16][5][0] = 1; ce[GF16][5][1] = 0; ce[GF16][5][2] = 1; ce[GF16][5][3] = 1;
ce[GF16][6][0] = 1; ce[GF16][6][1] = 1; ce[GF16][6][2] = 1; ce[GF16][6][3] = 1;
ce[GF16][7][0] = 0; ce[GF16][7][1] = 1; ce[GF16][7][2] = 1; ce[GF16][7][3] = 1;
ce[GF16][8][0] = 1; ce[GF16][8][1] = 1; ce[GF16][8][2] = 1; ce[GF16][8][3] = 0;
ce[GF16][9][0] = 0; ce[GF16][9][1] = 1; ce[GF16][9][2] = 0; ce[GF16][9][3] = 1;
ce[GF16][10][0] = 1; ce[GF16][10][1] = 0; ce[GF16][10][2] = 1; ce[GF16][10][3] = 0;
ce[GF16][11][0] = 1; ce[GF16][11][1] = 1; ce[GF16][11][2] = 0; ce[GF16][11][3] = 1;
ce[GF16][12][0] = 0; ce[GF16][12][1] = 0; ce[GF16][12][2] = 1; ce[GF16][12][3] = 1;
ce[GF16][13][0] = 0; ce[GF16][13][1] = 1; ce[GF16][13][2] = 1; ce[GF16][13][3] = 0;
ce[GF16][14][0] = 1; ce[GF16][14][1] = 1; ce[GF16][14][2] = 0; ce[GF16][14][3] = 0;
*c1 = ce[order][x][0];
*c2 = ce[order][x][1];
*c3 = ce[order][x][2];
*c4 = ce[order][x][3];
return;
}
int Coefficient2Index(int q, int c1, int c2, int c3, int c4)
{
int order, i,j,k;
int ce[4][MAX_q][MAX_degree]; /* 4 = no_FILEDS */
int no_FILEDS;
enum FILED {
GF4, GF8, GF9, GF16
};
no_FILEDS = 4;
order = -1;
if (q == 4)
order = GF4;
if (q == 8)
order = GF8;
if (q == 9)
order = GF9;
if (q == 16)
order = GF16;
if (order < 0){
fprintf(stderr,"In Coefficient2Index: Error\n");
exit(-1);
}
if((c1==0)&&(c2==0)&&(c3==0)&&(c4==0))
return(-1);
for(i=0; i<no_FILEDS; i++)
for(j=0; j<MAX_q; j++)
for(k=0; k<MAX_degree; k++)
ce[i][j][k] = 0;
ce[GF4][0][0] = 0; ce[GF4][0][1] = 1;
ce[GF4][1][0] = 1; ce[GF4][1][1] = 0;
ce[GF4][2][0] = 1; ce[GF4][2][1] = 1;
ce[GF8][0][0] = 0; ce[GF8][0][1] = 0; ce[GF8][0][2] = 1;
ce[GF8][1][0] = 0; ce[GF8][1][1] = 1; ce[GF8][1][2] = 0;
ce[GF8][2][0] = 1; ce[GF8][2][1] = 0; ce[GF8][2][2] = 0;
ce[GF8][3][0] = 1; ce[GF8][3][1] = 0; ce[GF8][3][2] = 1;
ce[GF8][4][0] = 1; ce[GF8][4][1] = 1; ce[GF8][4][2] = 1;
ce[GF8][5][0] = 0; ce[GF8][5][1] = 1; ce[GF8][5][2] = 1;
ce[GF8][6][0] = 1; ce[GF8][6][1] = 1; ce[GF8][6][2] = 0;
ce[GF9][0][0] = 0; ce[GF9][0][1] = 1;
ce[GF9][1][0] = 1; ce[GF9][1][1] = 0;
ce[GF9][2][0] = 2; ce[GF9][2][1] = 1;
ce[GF9][3][0] = 2; ce[GF9][3][1] = 2;
ce[GF9][4][0] = 0; ce[GF9][4][1] = 2;
ce[GF9][5][0] = 2; ce[GF9][5][1] = 0;
ce[GF9][6][0] = 1; ce[GF9][6][1] = 2;
ce[GF9][7][0] = 1; ce[GF9][7][1] = 1;
ce[GF16][0][0] = 0; ce[GF16][0][1] = 0; ce[GF16][0][2] = 0; ce[GF16][0][3] = 1;
ce[GF16][1][0] = 0; ce[GF16][1][1] = 0; ce[GF16][1][2] = 1; ce[GF16][1][3] = 0;
ce[GF16][2][0] = 0; ce[GF16][2][1] = 1; ce[GF16][2][2] = 0; ce[GF16][2][3] = 0;
ce[GF16][3][0] = 1; ce[GF16][3][1] = 0; ce[GF16][3][2] = 0; ce[GF16][3][3] = 0;
ce[GF16][4][0] = 1; ce[GF16][4][1] = 0; ce[GF16][4][2] = 0; ce[GF16][4][3] = 1;
ce[GF16][5][0] = 1; ce[GF16][5][1] = 0; ce[GF16][5][2] = 1; ce[GF16][5][3] = 1;
ce[GF16][6][0] = 1; ce[GF16][6][1] = 1; ce[GF16][6][2] = 1; ce[GF16][6][3] = 1;
ce[GF16][7][0] = 0; ce[GF16][7][1] = 1; ce[GF16][7][2] = 1; ce[GF16][7][3] = 1;
ce[GF16][8][0] = 1; ce[GF16][8][1] = 1; ce[GF16][8][2] = 1; ce[GF16][8][3] = 0;
ce[GF16][9][0] = 0; ce[GF16][9][1] = 1; ce[GF16][9][2] = 0; ce[GF16][9][3] = 1;
ce[GF16][10][0] = 1; ce[GF16][10][1] = 0; ce[GF16][10][2] = 1; ce[GF16][10][3] = 0;
ce[GF16][11][0] = 1; ce[GF16][11][1] = 1; ce[GF16][11][2] = 0; ce[GF16][11][3] = 1;
ce[GF16][12][0] = 0; ce[GF16][12][1] = 0; ce[GF16][12][2] = 1; ce[GF16][12][3] = 1;
ce[GF16][13][0] = 0; ce[GF16][13][1] = 1; ce[GF16][13][2] = 1; ce[GF16][13][3] = 0;
ce[GF16][14][0] = 1; ce[GF16][14][1] = 1; ce[GF16][14][2] = 0; ce[GF16][14][3] = 0;
for(i=0;i<MAX_q;i++)
if((ce[order][i][0]==c1)&&(ce[order][i][1]==c2)&&
(ce[order][i][2]==c3)&&(ce[order][i][3]==c4))
return(i);
fprintf(stderr,"In Coefficient2Index: Error\n");
exit(-1);
}