bool incremental_closure_opt_dense(opt_oct_mat_t *oo, int dim, int v, bool is_int){
double *m = oo->mat;
int n = 2*dim;
int ii = 2*v + 1;
int j;
double *temp1, *temp2;
temp1 = (double *)calloc(2*dim, sizeof(double));
temp2 = (double *)calloc(2*dim, sizeof(double));
/******
incremental Floyd-Warshall : v in end-point position
******/
for(unsigned k = 0; k < n; k=k + 2){
int v1 = 2*v;
int v2 = 2*v + 1;
int v1v2 = v2 + (((v1 + 1)*(v1 + 1))/2);
int v2v1 = v1 + (((v2 + 1)*(v2 + 1))/2);
int kk = (k^1);
int br1 = k < v1 ? k : v1;
int br2 = kk < v1 ? kk : v1;
/*int v1v2 = v2 + (((v1 + 1)*(v1 + 1))/2);
int v2v1 = v1 + (((v2 + 1)*(v2 + 1))/2);
int v1k = k + (((v1 + 1)*(v1 + 1))/2);
int v2k = k + (((v2 + 1)*(v2 + 1))/2);
int kv1 = v1 + (((k + 1)*(k + 1))/2);
int kv2 = v2 + (((k + 1)*(k + 1))/2);*/
//m[n*2*v + (2*v + 1)] = min(m[n*2*v + (2*v + 1)], m[n*2*v + k] + m[n*k + 2*v + 1]);
//m[v1v2] = min(m[v1v2], m[v1k] + m[kv2]);
//m[n*(2*v + 1) + 2*v] = min(m[n*(2*v + 1) + 2*v], m[n*(2*v + 1) + k] + m[n*k + 2*v]);
//m[v2v1] = min(m[v2v1], m[v2k] + m[kv1]);
for(unsigned i = 2*v; i < 2*v + 2; i++){
//double ik = m[n*i + k];
int ind_ik, ind_ikk;
if(k <=i){
ind_ik = k + (((i + 1)*(i + 1))/2);
}
else{
ind_ik = (i^1) + ((((k^1) + 1)*((k^1) + 1))/2);
}
if(kk <=i){
ind_ikk = kk + (((i + 1)*(i + 1))/2);
}
else{
ind_ikk = (i^1) + ((((kk^1) + 1)*((kk^1) + 1))/2);
}
double ik = m[ind_ik];
double ikk = m[ind_ikk];
v_double_type vik = v_set1_double(m[ind_ik]);
v_double_type vikk = v_set1_double(m[ind_ikk]);
//double ki = m[n*k + i];
int ind_ki, ind_kki;
if ( k <= i){
ind_ki = (k^1) + ((((i^1) + 1)*((i^1) + 1))/2);
}
else{
ind_ki = i + (((k + 1)*(k + 1))/2);
}
if ( kk <= i){
ind_kki = (kk^1) + ((((i^1) + 1)*((i^1) + 1))/2);
}
else{
ind_kki = i + (((kk + 1)*(kk + 1))/2);
}
//int ind_ki = i + (((k + 1)*(k + 1))/2);
double ki = m[ind_ki];
double kki = m[ind_kki];
/*******
v in first end-point position.
This part is vectorized.
********/
for(j = 0; j <br1/v_length; j++){
//double kj = m[n*k + j];
int ind_kj = j*v_length + (((k + 1)*(k + 1))/2);
v_double_type vkj = v_load_double(m+ind_kj);
int ind_kkj = j*v_length + (((kk + 1)*(kk + 1))/2);
v_double_type vkkj = v_load_double(m+ind_kkj);
//double jk = m[n*j + k];
//int ind_jk = k + (((j + 1)*(j + 1))/2);
//double jk = m[ind_jk];
//m[n*i + j] = min(m[n*i + j], ik + kj);
int ind_ij = j*v_length + (((i + 1)*(i + 1))/2);
v_double_type vij = v_load_double(m+ind_ij);
v_double_type op1 = v_add_double(vik,vkj);
v_double_type op2 = v_add_double(vikk,vkkj);
v_double_type op3 = v_min_double(op1, op2);
v_double_type res = v_min_double(vij,op3);
v_store_double(m+ind_ij,res);
//m[n*j + i] = min(m[n*j + i], jk + ki);
}
for(j = (br1/v_length)*v_length; j < br1; j++){
int ind_kj = j + (((k + 1)*(k + 1))/2);
double kj = m[ind_kj];
int ind_kkj = j + (((kk + 1)*(kk + 1))/2);
double kkj = m[ind_kkj];
int ind_ij = j + (((i + 1)*(i + 1))/2);
m[ind_ij] = min(m[ind_ij], ik + kj);
m[ind_ij] = min(m[ind_ij], ikk + kkj);
}
for(; j < v1; j++){
//double kj = m[n*k + j];
int ind_kj = (k^1) + ((((j^1) + 1)*((j^1) + 1))/2);
double kj = m[ind_kj];
int ind_kkj = (kk^1) + ((((j^1) + 1)*((j^1) + 1))/2);
double kkj = m[ind_kkj];
//double jk = m[n*j + k];
int ind_ij = j + (((i + 1)*(i + 1))/2);
//m[n*i + j] = min(m[n*i + j], ik + kj);
m[ind_ij] = min(m[ind_ij], ik + kj);
m[ind_ij] = min(m[ind_ij], ikk + kkj);
//m[n*j + i] = min(m[n*j + i], jk + ki);
}
/******
v in second end-point position.
This part is scalar.
*****/
for(j= v1+2; j < k; j++ ){
int ind_jk = (j^1) + ((((k^1) + 1)*((k^1) + 1))/2);
double jk = m[ind_jk];
int ind_jkk = (j^1) + ((((kk^1) + 1)*((kk^1) + 1))/2);
double jkk = m[ind_jkk];
int ind_ji = i + (((j + 1)*(j + 1))/2);
m[ind_ji] = min(m[ind_ji], jk + ki);
m[ind_ji] = min(m[ind_ji], jkk + kki);
}
for(; j < 2*dim; j++){
int ind_jk = k + (((j + 1)*(j + 1))/2);
double jk = m[ind_jk];
int ind_jkk = kk + (((j + 1)*(j + 1))/2);
double jkk = m[ind_jkk];
int ind_ji = i + (((j + 1)*(j + 1))/2);
m[ind_ji] = min(m[ind_ji], jk + ki);
m[ind_ji] = min(m[ind_ji], jkk + kki);
}
}
m[v1v2] = min(m[v1v2],m[opt_matpos2(v1,k)] + m[opt_matpos2(k,v2)]);
m[v1v2] = min(m[v1v2],m[opt_matpos2(v1,kk)] + m[opt_matpos2(kk,v2)]);
m[v2v1] = min(m[v2v1],m[opt_matpos2(v2,k)] + m[opt_matpos2(k,v1)]);
m[v2v1] = min(m[v2v1],m[opt_matpos2(v2,kk)] + m[opt_matpos2(kk,v1)]);
}
int v1 = (2*v);
int v2 = (2*v)^1;
int vi = (((v1 + 1)*(v1 + 1))/2);
int vvi = (((v2 + 1)*(v2 + 1))/2);
int pos1 = v2 + vi;
//int pos2 = opt_matpos2((2*k)^1, 2*k);
int pos2 = v1 + vvi;
int l = (v1 + 2);
int mod = l%v_length;
if(mod){
l = l + (v_length - mod);
}
//variable v in pivot position
for(int i = v1 + 2; i < n;i++){
int ind1 = v2 + (((i+1)*(i+1))/2);
int ind2 = v1 + (((i+1)*(i+1))/2);
m[ind1] = min(m[ind1], m[ind2] + m[pos1] );
temp2[i^1] = m[ind1];
}
for(int i = v1 + 2; i < n; i++){
int ind1 = v2 + (((i+1)*(i+1))/2);
int ind2 = v1 + (((i+1)*(i+1))/2);
m[ind2] = min(m[ind2], m[ind1] + m[pos2] );
temp1[i^1] = m[ind2];
}
for(int j = 0; j < v1; j++){
//int ind3 = opt_matpos2((2*k)^1,j);
int ind3 = j + vvi;
//int ind4 = opt_matpos2( 2*k,j);
int ind4 = j + vi;
//result[n*((2*k)^1) + j] = min(result[n*((2*k)^1) + j], result[n*((2*k)^1) + 2*k] + result[n*(2*k) + j]);
m[ind3] = min(m[ind3], m[pos2] + m[ind4]);
}
for(int j = 0; j < v1; j++){
//int ind3 = opt_matpos2((2*k)^1,j);
int ind3 = j + vvi;
//int ind4 = opt_matpos2(2*k,j);
int ind4 = j + vi;
//result[n*2*k + j] = min(result[n*2*k + j], result[n*2*k + ((2*k)^1)] + result[n*((2*k)^1) + j]);
m[ind4] = min(m[ind4], m[pos1] + m[ind3]);
}
//for(unsigned k = 2*v; k < 2*v + 2; k++){
/******
incremental Floyd-Warshall : v in pivot position.
This is vectorized.
******/
for(unsigned i = 0; i < v1; i++){
int i2 = (i|1);
int br = i2;
int j;
int ind_ik, ind_ikk;
//ind_ik = (i^1) + ((((k^1) + 1)*((k^1) + 1))/2);
ind_ik = (i^1) + vvi;
//ind_ikk = (i^1) + ((((kk^1) + 1)*((kk^1) + 1))/2);
ind_ikk = (i^1) + vi;
//double ik = m[n*i + k];
v_double_type ik = v_set1_double(m[ind_ik]);
v_double_type ikk = v_set1_double(m[ind_ikk]);
double ikd = m[ind_ik];
double ikkd = m[ind_ikk];
for(j = 0; j < br/v_length; j++){
//int ind_kj = j + (((k + 1)*(k + 1))/2);
int ind_kj = j*v_length + vi;
//double kj = m[n*k + j];
//double kj = m[ind_kj];
v_double_type kj = v_load_double(m + ind_kj);
//int ind_kkj = j + (((kk + 1)*(kk + 1))/2);
int ind_kkj = j*v_length + vvi;
//double kkj = m[ind_kkj];
v_double_type kkj = v_load_double(m + ind_kkj);
int ind_ij = j*v_length + (((i + 1)*(i + 1))/2);
//m[n*i + j] = min(m[n*i + j], ik + kj);
v_double_type ij = v_load_double(m + ind_ij);
v_double_type op1 = v_add_double(ik,kj);
v_double_type op2 = v_add_double(ikk,kkj);
v_double_type op3 = v_min_double(op1,op2);
v_double_type res = v_min_double(ij,op3);
//m[ind_ij] = min(m[ind_ij], ik + kj);
//m[ind_ij] = min(m[ind_ij], ikk + kkj);
v_store_double(m + ind_ij,res);
}
for(j = (br/v_length)*v_length; j <= br; j++){
//int ind_kj = j + (((k + 1)*(k + 1))/2);
int ind_kj = j + vi;
//double kj = m[n*k + j];
double kj = m[ind_kj];
//int ind_kkj = j + (((kk + 1)*(kk + 1))/2);
int ind_kkj = j + vvi;
double kkj = m[ind_kkj];
int ind_ij = j + (((i + 1)*(i + 1))/2);
//m[n*i + j] = min(m[n*i + j], ik + kj);
m[ind_ij] = min(m[ind_ij], ikd + kj);
m[ind_ij] = min(m[ind_ij], ikkd + kkj);
}
}
for(unsigned i = 2*v + 2; i < n; i++){
int i2 = (i|1);
int br = v1;
int j;
int ind_ik, ind_ikk;
ind_ik = v1 + (((i + 1)*(i + 1))/2);
ind_ikk = v2 + (((i + 1)*(i + 1))/2);
//double ik = m[n*i + k];
v_double_type ik = v_set1_double(m[ind_ik]);
v_double_type ikk = v_set1_double(m[ind_ikk]);
double ikd = m[ind_ik];
double ikkd = m[ind_ikk];
int b = min(l,i2);
for(j = 0; j < br/v_length; j++){
//int ind_kj = j + (((k + 1)*(k + 1))/2);
int ind_kj = j*v_length + vi;
//double kj = m[n*k + j];
//double kj = m[ind_kj];
v_double_type kj = v_load_double(m + ind_kj);
//int ind_kkj = j + (((kk + 1)*(kk + 1))/2);
int ind_kkj = j*v_length + vvi;
//double kkj = m[ind_kkj];
v_double_type kkj = v_load_double(m + ind_kkj);
int ind_ij = j*v_length + (((i + 1)*(i + 1))/2);
//m[n*i + j] = min(m[n*i + j], ik + kj);
v_double_type ij = v_load_double(m + ind_ij);
v_double_type op1 = v_add_double(ik,kj);
v_double_type op2 = v_add_double(ikk,kkj);
v_double_type op3 = v_min_double(op1,op2);
v_double_type res = v_min_double(ij,op3);
//m[ind_ij] = min(m[ind_ij], ik + kj);
//m[ind_ij] = min(m[ind_ij], ikk + kkj);
v_store_double(m + ind_ij,res);
}
for(j = (br/v_length)*v_length; j <= br; j++){
//int ind_kj = j + (((k + 1)*(k + 1))/2);
int ind_kj = j + vi;
//double kj = m[n*k + j];
double kj = m[ind_kj];
//int ind_kkj = j + (((kk + 1)*(kk + 1))/2);
int ind_kkj = j + vvi;
double kkj = m[ind_kkj];
int ind_ij = j + (((i + 1)*(i + 1))/2);
//m[n*i + j] = min(m[n*i + j], ik + kj);
m[ind_ij] = min(m[ind_ij], ikd + kj);
m[ind_ij] = min(m[ind_ij], ikkd + kkj);
}
for(j = v1 + 2; j <= b; j++){
//double kj = m[n*k + j];
double kj = temp2[j];
//int ind_kkj = (kk^1) + ((((j^1) + 1)*((j^1) + 1))/2);
//int ind_kkj = temp1[j];
double kkj = temp1[j];
//m[n*i + j] = min(m[n*i + j], ik + kj);
int ind_ij = j + (((i + 1)*(i + 1))/2);
m[ind_ij] = min(m[ind_ij], ikd + kj);
m[ind_ij] = min(m[ind_ij], ikkd + kkj);
}
if(b < i2){
for(j = b/v_length; j < i2/v_length; j++){
v_double_type kj = v_load_double(temp2 + j*v_length);
v_double_type kkj = v_load_double(temp1 + j*v_length);
int ind_ij = j*v_length + (((i + 1)*(i + 1))/2);
v_double_type ij = v_load_double(m + ind_ij);
v_double_type op1 = v_add_double(ik,kj);
v_double_type op2 = v_add_double(ikk,kkj);
v_double_type op3 = v_min_double(op1,op2);
v_double_type res = v_min_double(ij,op3);
v_store_double(m + ind_ij,res);
}
for(j = (i2/v_length)*v_length; j <=i2; j++){
//int ind_kj = (k^1) + ((((j^1) + 1)*((j^1) + 1))/2);
//int ind_kj = v2 + ((((j^1) + 1)*((j^1) + 1))/2);
//double kj = m[n*k + j];
double kj = temp2[j];
//int ind_kkj = (kk^1) + ((((j^1) + 1)*((j^1) + 1))/2);
//int ind_kkj = v1 + ((((j^1) + 1)*((j^1) + 1))/2);
double kkj = temp1[j];
//m[n*i + j] = min(m[n*i + j], ik + kj);
int ind_ij = j + (((i + 1)*(i + 1))/2);
m[ind_ij] = min(m[ind_ij], ikd + kj);
m[ind_ij] = min(m[ind_ij], ikkd + kkj);
}
}
}
oo->nni = 2*dim*(dim+1);
bool res;
if(is_int){
res = strengthning_int_dense(oo, temp1, n);
}
else{
res = strengthning_dense(oo, temp1, n);
}
return res;
}
opt_oct_t* opt_oct_add_epsilon(ap_manager_t* man, opt_oct_t* o, ap_scalar_t* epsilon)
{
opt_oct_internal_t* pr = opt_oct_init_from_manager(man,AP_FUNID_WIDENING,2);
opt_oct_t* r = opt_oct_alloc_internal(pr,o->dim,o->intdim);
opt_oct_mat_t * oo;
oo = o->m ? o->m : o->closed;
if (oo) {
double *m = oo->mat;
size_t i;
/* compute max of finite bounds */
pr->tmp[0] = 0;
int size = 2*(o->dim)*(o->dim+1);
r->m = opt_hmat_alloc(size);
free_array_comp_list(r->m->acl);
double *mm = r->m->mat;
if(!oo->is_dense){
r->m->is_dense = false;
r->m->ti = false;
r->m->acl = copy_array_comp_list(oo->acl);
comp_list_t * cl = oo->acl->head;
while(cl != NULL){
unsigned short int * ca = to_sorted_array(cl,o->dim);
unsigned short int comp_size = cl->size;
for(int i = 0; i < 2*comp_size; i++){
unsigned short int i1 = (i%2==0)? 2*ca[i/2] : 2*ca[i/2]+1;
for(int j = 0; j < 2*comp_size; j++){
unsigned short int j1 = (j%2==0) ? 2*ca[j/2] : 2*ca[j/2] + 1;
if(j1 > (i1|1)){
break;
}
int ind = j1 + (((i1 + 1)*(i1 + 1))/2);
if(m[ind]==INFINITY){
continue;
}
if(m[ind] >= 0){
pr->tmp[0] = max(pr->tmp[0],m[ind]);
}
else{
pr->tmp[1] = -1*m[ind];
pr->tmp[0] = max(pr->tmp[0],pr->tmp[1]);
}
}
}
cl =cl->next;
free(ca);
}
/* multiply by epsilon */
opt_bound_of_scalar(pr,&pr->tmp[1],epsilon,false,false);
pr->tmp[0] = pr->tmp[0]*pr->tmp[1];
/* enlarge bounds */
cl = oo->acl->head;
while(cl != NULL){
unsigned short int * ca = to_sorted_array(cl,o->dim);
unsigned short int comp_size = cl->size;
for(int i = 0; i < 2*comp_size; i++){
unsigned short int i1 = (i%2==0)? 2*ca[i/2] : 2*ca[i/2]+1;
for(int j = 0; j < 2*comp_size; j++){
unsigned short int j1 = (j%2==0) ? 2*ca[j/2] : 2*ca[j/2] + 1;
if(j1 > (i1|1)){
break;
}
int ind = j1 + (((i1 + 1)*(i1 + 1))/2);
mm[ind] = m[ind] + pr->tmp[0];
}
}
cl =cl->next;
free(ca);
}
/*for(int i = 0; i < o->dim; i++){
//if(find(oo->acl,i)==NULL){
int i1 = 2*i;
int i2 = i1+1;
int ind1 = i1 + (((i1+1)*(i1+1))/2);
mm[ind1] = pr->tmp[0];
int ind2 = i2 + (((i2+1)*(i2+1))/2);
mm[ind2] = pr->tmp[0];
comp_list_t * cl1 = create_comp_list();
insert_comp(cl1,i);
insert_comp_list(oo->acl,cl1);
//}
}*/
}
else{
r->m->is_dense = true;
r->m->ti = true;
for (i=0;i<size;i++) {
if (m[i]==INFINITY){
continue;
}
if (m[i]>=0){
pr->tmp[0] = max(pr->tmp[0],m[i]);
}
else {
pr->tmp[1] = -1*m[i];
pr->tmp[0] = max(pr->tmp[0],pr->tmp[1]);
}
}
/* multiply by epsilon */
opt_bound_of_scalar(pr,&pr->tmp[1],epsilon,false,false);
pr->tmp[0] = pr->tmp[0]*pr->tmp[1];
/* enlarge bounds */
#if defined(VECTOR)
v_double_type val = v_set1_double(pr->tmp[0]);
for(i = 0; i < size/v_length; i++){
v_double_type op1 = v_load_double(m + i*v_length);
v_double_type op2 = v_add_double(val,op1);
v_store_double(mm + i*v_length,op2);
}
#else
for (i=0;i<(size/v_length)*v_length;i++){
mm[i] = m[i] + pr->tmp[0];
}
#endif
for(i = (size/v_length)*v_length;i < size; i++){
mm[i] = m[i] + pr->tmp[0];
}
}
r->m->nni = oo->nni;
}
return r;
}