std::map<int, Matrix > get_coefficient(LinOp &lin){
std::map<int, Matrix > coeffs;
if (lin.type == VARIABLE){
std::map<int, Matrix> new_coeffs = get_variable_coeffs(lin);
typedef std::map<int, Matrix >::iterator it_type;
for(it_type it = new_coeffs.begin(); it != new_coeffs.end(); ++it){
if(coeffs.count(it->first) == 0)
coeffs[it->first] = it->second ;
else
coeffs[it->first] += it->second;
}
}
else if (lin.has_constant_type()){
/* ID will be CONSTANT_TYPE */
std::map<int, Matrix> new_coeffs = get_const_coeffs(lin);
typedef std::map<int, Matrix >::iterator it_type;
for(it_type it = new_coeffs.begin(); it != new_coeffs.end(); ++it){
if(coeffs.count(it->first) == 0)
coeffs[it->first] = it->second;
else
coeffs[it->first] += it->second;
}
}
else {
/* Multiply the arguments of the function coefficient in order */
std::vector<Matrix> coeff_mat = get_func_coeffs(lin);
for (unsigned i = 0; i < lin.args.size(); i++){
Matrix coeff = coeff_mat[i];
std::map<int, Matrix > rh_coeffs = get_coefficient(*lin.args[i]);
std::map<int, Matrix > new_coeffs;
mul_by_const(coeff, rh_coeffs, new_coeffs);
typedef std::map<int, Matrix>::iterator it_type;
for (it_type it = new_coeffs.begin(); it != new_coeffs.end(); ++it){
if(coeffs.count(it->first) == 0)
coeffs[it->first] = it->second;
else
coeffs[it->first] += it->second;
}
}
}
return coeffs;
}
void process_constraint(LinOp & lin, std::vector<double> &V,
std::vector<int> &I, std::vector<int> &J,
std::vector<double> &constant_vec, int &vert_offset,
std::map<int, int> &id_to_col, int & horiz_offset){
/* Get the coefficient for the current constraint */
std::map<int, Matrix > coeffs = get_coefficient(lin);
typedef std::map<int, Matrix >::iterator it_type;
for(it_type it = coeffs.begin(); it != coeffs.end(); ++it){
int id = it->first; // Horiz offset determined by the id
Matrix block = it->second;
if (id == CONSTANT_ID) { // Add to CONSTANT_VEC if linop is constant
extend_constant_vec(constant_vec, vert_offset, block);
}
else {
int offset = get_horiz_offset(id, id_to_col, horiz_offset, lin);
add_matrix_to_vectors(block, V, I, J, vert_offset, offset);
}
}
}
int main(){
CGAL::set_pretty_mode(std::cout);
typedef CGAL::Polynomial_type_generator<int,2>::Type Poly_2;
typedef CGAL::Polynomial_traits_d<Poly_2> PT_2;
//construction using shift
Poly_2 x = PT_2::Shift()(Poly_2(1),1,0); // = x^1
Poly_2 y = PT_2::Shift()(Poly_2(1),1,1); // = y^1
Poly_2 F // = (11*x^2 + 5*x)*y^4 + (7*x^2)*y^3
= 11 * CGAL::ipower(y,4) * CGAL::ipower(x,2)
+ 5 * CGAL::ipower(y,4) * CGAL::ipower(x,1)
+ 7 * CGAL::ipower(y,3) * CGAL::ipower(x,2);
std::cout << "The bivariate polynomial F: " << F <<"\n"<< std::endl;
PT_2::Get_coefficient get_coefficient;
std::cout << "Coefficient of y^0: "<< get_coefficient(F,0) << std::endl;
std::cout << "Coefficient of y^1: "<< get_coefficient(F,1) << std::endl;
std::cout << "Coefficient of y^2: "<< get_coefficient(F,2) << std::endl;
std::cout << "Coefficient of y^3: "<< get_coefficient(F,3) << std::endl;
std::cout << "Coefficient of y^4: "<< get_coefficient(F,4) << std::endl;
std::cout << "Coefficient of y^5: "<< get_coefficient(F,5) << std::endl;
std::cout << std::endl;
PT_2::Leading_coefficient lcoeff;
std::cout << "Leading coefficient with respect to y: "
<< lcoeff(F) // = 11*x^2 + 5*x
<< std::endl;
PT_2::Get_innermost_coefficient get_icoeff;
std::cout << "Innermost coefficient of monomial x^1y^4: "
<< get_icoeff(F,CGAL::Exponent_vector(1,4)) // = 5
<< std::endl;
PT_2::Innermost_leading_coefficient ilcoeff;
std::cout << "Innermost leading coefficient with respect to y: "
<< ilcoeff(F) // = 11
<< std::endl;
}
//test raid6 algorithm
int main(int argc, char *argv[])
{
char disk_data[DISKNUM][BLOCKSIZE];
char read_data[DISKNUM-2][BLOCKSIZE];
int disk_id;
char temp_char;
int i, j;
int code_disk_id, parity_disk_id;
int data_disk_coeff;
int disk_failed_no = DISK_FAILED_NUM;
int disk_first_id = FIRST_FAIL_ID;
int disk_second_id = SECOND_FAIL_ID;
int disk_another_failed_id;
int g1, g2, g12;
char P_temp[BLOCKSIZE], Q_temp[BLOCKSIZE];
gen_tables(8);
printf("\nPrint gflog(x)\n");
for (i=0; i<256; i++){
printf("%d(%d) ",i,gflog[i]);
}
printf("\n");
printf("\nPrint gfilog(x)\n");
for (i=0; i<256; i++){
printf("%d(%d) ",i,gfilog[i]);
}
printf("\n");
for (i=0; i<DISKNUM; i++){
if (i < DISKNUM-2){
temp_char = TEST_DATA_BEGIN + i;
}
else{
temp_char = 0;
}
for (j=0; j<BLOCKSIZE; j++){
disk_data[i][j] = temp_char;
}
}
printf("\n****** PRINT DISK DATA ******\n");
for (i=0; i<DISKNUM; i++){
printf("Disk id: %d\n",i);
for (j=0; j<BLOCKSIZE; j++){
printf("%c(%d) ",disk_data[i][j],disk_data[i][j]);
}
printf("\n");
}
//write P and Q
code_disk_id = DISKNUM -1;
parity_disk_id = DISKNUM - 2;
for (i=0; i<DISKNUM; i++){
if ( (i != parity_disk_id) && (i != code_disk_id) ){
for (j=0; j<BLOCKSIZE; j++){
//calculate P
disk_data[parity_disk_id][j] =
disk_data[parity_disk_id][j] ^ disk_data[i][j];
//calculate the coefficient of the data block
data_disk_coeff = i;
if (i > code_disk_id){
(data_disk_coeff)--;
}
if (i > parity_disk_id){
(data_disk_coeff)--;
}
data_disk_coeff = DISKNUM - 3 - data_disk_coeff;
data_disk_coeff = get_coefficient(data_disk_coeff);
printf("\ndata disk coefficient = %d\n",data_disk_coeff);
//calculate Q
temp_char = disk_data[code_disk_id][j];
disk_data[code_disk_id][j] = temp_char ^
(char)gf_mul((unsigned char)disk_data[i][j],data_disk_coeff,FIELDSIZE);
printf(" newQ=%c(%d) \n",disk_data[code_disk_id][j],
(unsigned int)disk_data[code_disk_id][j]);
}
}
}
printf("\n****** PRINT DISK DATA ******\n");
for (i=0; i<DISKNUM; i++){
printf("Disk id: %d\n",i);
for (j=0; j<BLOCKSIZE; j++){
printf("%c(%d) ",disk_data[i][j],disk_data[i][j]);
}
printf("\n");
}
//read data
for (i=0; i<DISKNUM-2; i++){
for (j=0; j<BLOCKSIZE; j++){
read_data[i][j] = 0;
}
}
for (disk_id=0; disk_id<DISKNUM-2; disk_id++){
disk_another_failed_id = disk_second_id;
if (disk_id == disk_first_id){
disk_another_failed_id = disk_second_id;
}
else if (disk_id == disk_second_id){
disk_another_failed_id = disk_first_id;
}
printf("\nDisk ID: %d, another failed disk ID: %d\n",disk_id, disk_another_failed_id);
//case of the disk is not failed
if ( (disk_failed_no == 0) ||
((disk_id != disk_first_id) && (disk_id != disk_second_id)) ){
printf("NO DISK FAIL\n");
for (j=0; j<BLOCKSIZE; j++){
read_data[disk_id][j] = disk_data[disk_id][j];
}
}
//cases of single disk fail
else if ( (disk_failed_no == 1) ||
((disk_failed_no == 2) && (disk_another_failed_id == code_disk_id)) ){
printf("One disk fail, or 1 data plus Q disk fail\n");
for (i = 0; i < DISKNUM; i++){
if ( (i != disk_id) && (i != code_disk_id) ){
for (j=0; j<BLOCKSIZE; j++){
read_data[disk_id][j] =
read_data[disk_id][j] ^ disk_data[i][j];
}
}
}
}
else if (disk_failed_no == 2){
if (disk_another_failed_id == parity_disk_id){
printf("1 data plus P disk fail\n");
//calculate Q'
for (i=0; i<DISKNUM; i++){
if ( ((i != disk_first_id) && (i != disk_second_id))
&& (i != parity_disk_id) && (i != code_disk_id) ){
for (j=0; j < BLOCKSIZE; j++){
//calculate the coefficient of the data block
data_disk_coeff = i;
if (i > code_disk_id){
(data_disk_coeff)--;
}
if (i > parity_disk_id){
(data_disk_coeff)--;
}
data_disk_coeff = DISKNUM - 3 - data_disk_coeff;
data_disk_coeff = get_coefficient(data_disk_coeff);
printf("\ndata disk coefficient = %d\n",data_disk_coeff);
temp_char = read_data[disk_id][j];
read_data[disk_id][j] = read_data[disk_id][j] ^
(char)gf_mul((unsigned char)disk_data[i][j],data_disk_coeff,FIELDSIZE);
}
}
for (j=0; j<BLOCKSIZE; j++){
printf("Q'=%c(%d) ",read_data[disk_id][j],read_data[disk_id][j]);
}
}
//calculate Q xor Q'
for (j=0; j < BLOCKSIZE; j++){
read_data[disk_id][j] = read_data[disk_id][j] ^ disk_data[code_disk_id][j];
}
for (j=0; j<BLOCKSIZE; j++){
printf("Q'+Q=%c(%d) ",read_data[disk_id][j],read_data[disk_id][j]);
}
//calculate the coefficient of the data block
data_disk_coeff = disk_id;
if (disk_id > code_disk_id){
(data_disk_coeff)--;
}
if (disk_id > parity_disk_id){
(data_disk_coeff)--;
}
data_disk_coeff = DISKNUM - 3 - data_disk_coeff;
data_disk_coeff = get_coefficient(data_disk_coeff);
printf("\ndata disk coefficient = %d\n",data_disk_coeff);
//decode the origianl data block
for (j=0; j < BLOCKSIZE; j++){
temp_char = read_data[disk_id][j];
read_data[disk_id][j] = (char)gf_div((unsigned char)temp_char,data_disk_coeff,FIELDSIZE);
}
}
else{
//case of two data disk fail
printf("2 data disk fail\n");
//calculate g1
g1 = disk_id;
if (g1 > code_disk_id){
(g1)--;
}
if (g1 > parity_disk_id){
(g1)--;
}
g1 = DISKNUM - 3 - g1;
g1 = get_coefficient(g1);
printf("g1=%d \n",g1);
//calculate g2
g2 = disk_another_failed_id;
if (g2 > code_disk_id){
(g2)--;
}
if (g2 > parity_disk_id){
(g2)--;
}
g2 = DISKNUM - 3 - g2;
g2 = get_coefficient(g2);
printf("g2=%d \n",g2);
//calculate g12
g12 = g1 ^ g2;
//calculate P'
for (j=0; j<BLOCKSIZE; j++){
P_temp[j] = 0;
}
for (i=0; i<DISKNUM; i++){
if ( (i != disk_first_id) && (i != disk_second_id) &&
(i != parity_disk_id) && (i != code_disk_id) )
{
for (j=0; j<BLOCKSIZE; j++){
P_temp[j] = P_temp[j] ^ disk_data[i][j];
}
}
}
for (j=0; j<BLOCKSIZE; j++){
P_temp[j] = P_temp[j] ^ disk_data[parity_disk_id][j];
//P_temp = P' xor P
}
//calculate Q'
for (j=0; j<BLOCKSIZE; j++){
Q_temp[j] = 0;
}
for (i=0; i<DISKNUM; i++){
if ( ((i != disk_first_id) && (i != disk_second_id))
&& (i != parity_disk_id) && (i != code_disk_id) ){
//calculate the coefficient of the data block
data_disk_coeff = i;
if (i > code_disk_id){
(data_disk_coeff)--;
}
if (i > parity_disk_id){
(data_disk_coeff)--;
}
data_disk_coeff = DISKNUM - 3 - data_disk_coeff;
data_disk_coeff = get_coefficient(data_disk_coeff);
printf("\ndata disk coefficient = %d\n",data_disk_coeff);
for (j=0; j < BLOCKSIZE; j++){
temp_char = Q_temp[j];
Q_temp[j] = temp_char ^
(char)gf_mul((unsigned char)disk_data[i][j],data_disk_coeff,FIELDSIZE);
}
}
for (j=0; j<BLOCKSIZE; j++){
printf("Q'=%c(%d) ",Q_temp[j],Q_temp[j]);
}
}
//calculate D
for (j=0; j<BLOCKSIZE; j++){
temp_char = (char)(gf_mul(g2,(unsigned char)P_temp[j],FIELDSIZE)
^ Q_temp[j] ^ disk_data[code_disk_id][j]);
read_data[disk_id][j] = (char)gf_div((unsigned char)temp_char, g12, FIELDSIZE);
}
}
}
}
//print data read
printf("\n****** PRINT READ DATA ******\n");
for (i=0; i<DISKNUM-2; i++){
printf("Read disk id: %d\n",i);
for (j=0; j<BLOCKSIZE; j++){
printf("%c(%d) ",read_data[i][j],read_data[i][j]);
}
printf("\n");
}
return 0;
}
/**
* Just an alias for get_coefficient() method.
*/
inline double get_coef(int i, int j)
{
return get_coefficient(i, j);
}