void Matrix_Extend(Matrix *Mat, unsigned NbRows)
{
Value *p, **q;
int i,j;
q = (Value **)realloc(Mat->p, NbRows * sizeof(*q));
if(!q) {
errormsg1("Matrix_Extend", "outofmem", "out of memory space");
return;
}
Mat->p = q;
if (Mat->p_Init_size < NbRows * Mat->NbColumns) {
p = (Value *)realloc(Mat->p_Init, NbRows * Mat->NbColumns * sizeof(Value));
if(!p) {
errormsg1("Matrix_Extend", "outofmem", "out of memory space");
return;
}
Mat->p_Init = p;
Vector_Set(Mat->p_Init + Mat->NbRows*Mat->NbColumns, 0,
Mat->p_Init_size - Mat->NbRows*Mat->NbColumns);
for (i = Mat->p_Init_size; i < Mat->NbColumns*NbRows; ++i)
value_init(Mat->p_Init[i]);
Mat->p_Init_size = Mat->NbColumns*NbRows;
} else
Vector_Set(Mat->p_Init + Mat->NbRows*Mat->NbColumns, 0,
(NbRows - Mat->NbRows) * Mat->NbColumns);
for (i=0;i<NbRows;i++) {
Mat->p[i] = Mat->p_Init + (i * Mat->NbColumns);
}
Mat->NbRows = NbRows;
}
void Matrix_Read_Input(Matrix *Mat) {
Value *p;
int i,j,n;
char *c, s[1024],str[1024];
p = Mat->p_Init;
for (i=0;i<Mat->NbRows;i++) {
do {
c = fgets(s, 1024, stdin);
while(isspace(*c) && *c!='\n')
++c;
} while(c && (*c =='#' || *c== '\n'));
if (!c) {
errormsg1( "Matrix_Read", "baddim", "not enough rows" );
break;
}
for (j=0;j<Mat->NbColumns;j++) {
if(!c || *c=='\n' || *c=='#') {
errormsg1("Matrix_Read", "baddim", "not enough columns");
break;
}
if (sscanf(c,"%s%n",str,&n) == 0) {
errormsg1( "Matrix_Read", "baddim", "not enough columns" );
break;
}
value_read(*(p++),str);
c += n;
}
}
} /* Matrix_Read_Input */
/*
* Allocate space for matrix dimensioned by 'NbRows X NbColumns'.
*/
Matrix *Matrix_Alloc(unsigned NbRows,unsigned NbColumns) {
Matrix *Mat;
Value *p, **q;
int i,j;
Mat=(Matrix *)malloc(sizeof(Matrix));
if(!Mat) {
errormsg1("Matrix_Alloc", "outofmem", "out of memory space");
return 0;
}
Mat->NbRows=NbRows;
Mat->NbColumns=NbColumns;
if (NbRows==0 || NbColumns==0) {
Mat->p = (Value **)0;
Mat->p_Init= (Value *)0;
Mat->p_Init_size = 0;
} else {
q = (Value **)malloc(NbRows * sizeof(*q));
if(!q) {
free(Mat);
errormsg1("Matrix_Alloc", "outofmem", "out of memory space");
return 0;
}
p = value_alloc(NbRows * NbColumns, &Mat->p_Init_size);
if(!p) {
free(q);
free(Mat);
errormsg1("Matrix_Alloc", "outofmem", "out of memory space");
return 0;
}
Mat->p = q;
Mat->p_Init = p;
for (i=0;i<NbRows;i++) {
*q++ = p;
p += NbColumns;
}
}
p = NULL;
q = NULL;
return Mat;
} /* Matrix_Alloc */
/*
* Allocate memory space for Vector
*/
Vector *Vector_Alloc(unsigned length) {
int i;
Vector *vector;
vector = (Vector *)malloc(sizeof(Vector));
if (!vector) {
errormsg1("Vector_Alloc", "outofmem", "out of memory space");
return 0;
}
vector->Size=length;
vector->p=(Value *)malloc(length * sizeof(Value));
if (!vector->p) {
errormsg1("Vector_Alloc", "outofmem", "out of memory space");
free(vector);
return 0;
}
for(i=0;i<length;i++)
value_init(vector->p[i]);
return vector;
} /* Vector_Alloc */
/*---------------------------------------------------------------------*/
static int exist_points(int pos,Polyhedron *Pol,Value *context) {
Value LB, UB, k,tmp;
value_init(LB); value_init(UB);
value_init(k); value_init(tmp);
value_set_si(LB,0);
value_set_si(UB,0);
/* Problem if UB or LB is INFINITY */
if (lower_upper_bounds(pos,Pol,context,&LB,&UB) !=0) {
errormsg1("exist_points", "infdom", "infinite domain");
value_clear(LB);
value_clear(UB);
value_clear(k);
value_clear(tmp);
return -1;
}
value_set_si(context[pos],0);
if(value_lt(UB,LB)) {
value_clear(LB);
value_clear(UB);
value_clear(k);
value_clear(tmp);
return 0;
}
if (!Pol->next) {
value_subtract(tmp,UB,LB);
value_increment(tmp,tmp);
value_clear(UB);
value_clear(LB);
value_clear(k);
return (value_pos_p(tmp));
}
for (value_assign(k,LB);value_le(k,UB);value_increment(k,k)) {
/* insert k in context */
value_assign(context[pos],k);
if (exist_points(pos+1,Pol->next,context) > 0 ) {
value_clear(LB); value_clear(UB);
value_clear(k); value_clear(tmp);
return 1;
}
}
/* Reset context */
value_set_si(context[pos],0);
value_clear(UB); value_clear(LB);
value_clear(k); value_clear(tmp);
return 0;
}
/*
* Read the contents of the matrix 'Mat' from standard input.
* A '#' in the first column is a comment line
*/
Matrix *Matrix_Read(void) {
Matrix *Mat;
unsigned NbRows, NbColumns;
char s[1024];
if (fgets(s, 1024, stdin) == NULL)
return NULL;
while ((*s=='#' || *s=='\n') ||
(sscanf(s, "%d %d", &NbRows, &NbColumns)<2)) {
if (fgets(s, 1024, stdin) == NULL)
return NULL;
}
Mat = Matrix_Alloc(NbRows,NbColumns);
if(!Mat) {
errormsg1("Matrix_Read", "outofmem", "out of memory space");
return(NULL);
}
Matrix_Read_Input(Mat);
return Mat;
} /* Matrix_Read */
/*
* Read the contents of a Vector
*/
Vector *Vector_Read() {
Vector *vector;
unsigned length;
int i;
char str[1024];
Value *p;
scanf("%d", &length);
vector = Vector_Alloc(length);
if (!vector) {
errormsg1("Vector_Read", "outofmem", "out of memory space");
return 0;
}
p = vector->p;
for (i=0;i<length;i++) {
scanf("%s",str);
value_read(*(p++),str);
}
return vector;
} /* Vector_Read */
void left_hermite(Matrix *A,Matrix **Hp,Matrix **Qp,Matrix **Up) {
Matrix *H, *HT, *Q, *U;
int i, j, nc, nr, rank;
Value tmp;
/* Computes left form: A = HQ , AU = H ,
T T T T T T
using right form A = Q H , U A = H */
nr = A->NbRows;
nc = A->NbColumns;
/* HT = A transpose */
HT = Matrix_Alloc(nc, nr);
if (!HT) {
errormsg1("DomLeftHermite", "outofmem", "out of memory space");
return;
}
value_init(tmp);
for (i=0; i<nr; i++)
for (j=0; j<nc; j++)
value_assign(HT->p[j][i],A->p[i][j]);
/* U = I */
if (Up) {
*Up = U = Matrix_Alloc(nc,nc);
if (!U) {
errormsg1("DomLeftHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
Vector_Set(U->p_Init,0,nc*nc); /* zero's */
for (i=0;i<nc;i++) /* with diagonal of 1's */
value_set_si(U->p[i][i],1);
}
else U=(Matrix *)0;
/* Q = I */
if (Qp) {
*Qp = Q = Matrix_Alloc(nc, nc);
if (!Q) {
errormsg1("DomLeftHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
Vector_Set(Q->p_Init,0,nc*nc); /* zero's */
for (i=0;i<nc;i++) /* with diagonal of 1's */
value_set_si(Q->p[i][i],1);
}
else Q=(Matrix *)0;
rank = hermite(HT,U,Q);
/* H = HT transpose */
*Hp = H = Matrix_Alloc(nr,nc);
if (!H) {
errormsg1("DomLeftHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
for (i=0; i<nr; i++)
for (j=0;j<nc;j++)
value_assign(H->p[i][j],HT->p[j][i]);
Matrix_Free(HT);
/* Transpose U */
if (U) {
for (i=0; i<nc; i++) {
for (j=i+1; j<nc; j++) {
value_assign(tmp,U->p[i][j]);
value_assign(U->p[i][j],U->p[j][i] );
value_assign(U->p[j][i],tmp);
}
}
}
value_clear(tmp);
} /* left_hermite */
void right_hermite(Matrix *A,Matrix **Hp,Matrix **Up,Matrix **Qp) {
Matrix *H, *Q, *U;
int i, j, nr, nc, rank;
Value tmp;
/* Computes form: A = QH , UA = H */
nc = A->NbColumns;
nr = A->NbRows;
/* H = A */
*Hp = H = Matrix_Alloc(nr,nc);
if (!H) {
errormsg1("DomRightHermite", "outofmem", "out of memory space");
return;
}
/* Initialize all the 'Value' variables */
value_init(tmp);
Vector_Copy(A->p_Init,H->p_Init,nr*nc);
/* U = I */
if (Up) {
*Up = U = Matrix_Alloc(nr, nr);
if (!U) {
errormsg1("DomRightHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
Vector_Set(U->p_Init,0,nr*nr); /* zero's */
for(i=0;i<nr;i++) /* with diagonal of 1's */
value_set_si(U->p[i][i],1);
}
else
U = (Matrix *)0;
/* Q = I */
/* Actually I compute Q transpose... its easier */
if (Qp) {
*Qp = Q = Matrix_Alloc(nr,nr);
if (!Q) {
errormsg1("DomRightHermite", "outofmem", "out of memory space");
value_clear(tmp);
return;
}
Vector_Set(Q->p_Init,0,nr*nr); /* zero's */
for (i=0;i<nr;i++) /* with diagonal of 1's */
value_set_si(Q->p[i][i],1);
}
else
Q = (Matrix *)0;
rank = hermite(H,U,Q);
/* Q is returned transposed */
/* Transpose Q */
if (Q) {
for (i=0; i<nr; i++) {
for (j=i+1; j<nr; j++) {
value_assign(tmp,Q->p[i][j]);
value_assign(Q->p[i][j],Q->p[j][i] );
value_assign(Q->p[j][i],tmp);
}
}
}
value_clear(tmp);
return;
} /* right_hermite */
/*
* Basic hermite engine
*/
static int hermite(Matrix *H,Matrix *U,Matrix *Q) {
int nc, nr, i, j, k, rank, reduced, pivotrow;
Value pivot,x,aux;
Value *temp1, *temp2;
/* T -1 T */
/* Computes form: A = Q H and U A = H and U = Q */
if (!H) {
errormsg1("Domlib", "nullH", "hermite: ? Null H");
return -1;
}
nc = H->NbColumns;
nr = H->NbRows;
temp1 = (Value *) malloc(nc * sizeof(Value));
temp2 = (Value *) malloc(nr * sizeof(Value));
if (!temp1 ||!temp2) {
errormsg1("Domlib", "outofmem", "out of memory space");
return -1;
}
/* Initialize all the 'Value' variables */
value_init(pivot); value_init(x);
value_init(aux);
for(i=0;i<nc;i++)
value_init(temp1[i]);
for(i=0;i<nr;i++)
value_init(temp2[i]);
#ifdef DEBUG
fprintf(stderr,"Start -----------\n");
Matrix_Print(stderr,0,H);
#endif
for (k=0, rank=0; k<nc && rank<nr; k=k+1) {
reduced = 1; /* go through loop the first time */
#ifdef DEBUG
fprintf(stderr, "Working on col %d. Rank=%d ----------\n", k+1, rank+1);
#endif
while (reduced) {
reduced=0;
/* 1. find pivot row */
value_absolute(pivot,H->p[rank][k]);
/* the kth-diagonal element */
pivotrow = rank;
/* find the row i>rank with smallest nonzero element in col k */
for (i=rank+1; i<nr; i++) {
value_absolute(x,H->p[i][k]);
if (value_notzero_p(x) &&
(value_lt(x,pivot) || value_zero_p(pivot))) {
value_assign(pivot,x);
pivotrow = i;
}
}
/* 2. Bring pivot to diagonal (exchange rows pivotrow and rank) */
if (pivotrow != rank) {
Vector_Exchange(H->p[pivotrow],H->p[rank],nc);
if (U)
Vector_Exchange(U->p[pivotrow],U->p[rank],nr);
if (Q)
Vector_Exchange(Q->p[pivotrow],Q->p[rank],nr);
#ifdef DEBUG
fprintf(stderr,"Exchange rows %d and %d -----------\n", rank+1, pivotrow+1);
Matrix_Print(stderr,0,H);
#endif
}
value_assign(pivot,H->p[rank][k]); /* actual ( no abs() ) pivot */
/* 3. Invert the row 'rank' if pivot is negative */
if (value_neg_p(pivot)) {
value_oppose(pivot,pivot); /* pivot = -pivot */
for (j=0; j<nc; j++)
value_oppose(H->p[rank][j],H->p[rank][j]);
/* H->p[rank][j] = -(H->p[rank][j]); */
if (U)
for (j=0; j<nr; j++)
value_oppose(U->p[rank][j],U->p[rank][j]);
/* U->p[rank][j] = -(U->p[rank][j]); */
if (Q)
for (j=0; j<nr; j++)
value_oppose(Q->p[rank][j],Q->p[rank][j]);
/* Q->p[rank][j] = -(Q->p[rank][j]); */
#ifdef DEBUG
fprintf(stderr,"Negate row %d -----------\n", rank+1);
Matrix_Print(stderr,0,H);
#endif
}
if (value_notzero_p(pivot)) {
/* 4. Reduce the column modulo the pivot */
/* This eventually zeros out everything below the */
/* diagonal and produces an upper triangular matrix */
for (i=rank+1;i<nr;i++) {
value_assign(x,H->p[i][k]);
if (value_notzero_p(x)) {
value_modulus(aux,x,pivot);
/* floor[integer division] (corrected for neg x) */
if (value_neg_p(x) && value_notzero_p(aux)) {
/* x=(x/pivot)-1; */
value_division(x,x,pivot);
value_decrement(x,x);
}
else
value_division(x,x,pivot);
for (j=0; j<nc; j++) {
value_multiply(aux,x,H->p[rank][j]);
value_subtract(H->p[i][j],H->p[i][j],aux);
}
/* U->p[i][j] -= (x * U->p[rank][j]); */
if (U)
for (j=0; j<nr; j++) {
value_multiply(aux,x,U->p[rank][j]);
value_subtract(U->p[i][j],U->p[i][j],aux);
}
/* Q->p[rank][j] += (x * Q->p[i][j]); */
if (Q)
for(j=0;j<nr;j++) {
value_addmul(Q->p[rank][j], x, Q->p[i][j]);
}
reduced = 1;
#ifdef DEBUG
fprintf(stderr,
"row %d = row %d - %d row %d -----------\n", i+1, i+1, x, rank+1);
Matrix_Print(stderr,0,H);
#endif
} /* if (x) */
} /* for (i) */
} /* if (pivot != 0) */
} /* while (reduced) */
/* Last finish up this column */
/* 5. Make pivot column positive (above pivot row) */
/* x should be zero for i>k */
if (value_notzero_p(pivot)) {
for (i=0; i<rank; i++) {
value_assign(x,H->p[i][k]);
if (value_notzero_p(x)) {
value_modulus(aux,x,pivot);
/* floor[integer division] (corrected for neg x) */
if (value_neg_p(x) && value_notzero_p(aux)) {
value_division(x,x,pivot);
value_decrement(x,x);
/* x=(x/pivot)-1; */
}
else
value_division(x,x,pivot);
/* H->p[i][j] -= x * H->p[rank][j]; */
for (j=0; j<nc; j++) {
value_multiply(aux,x,H->p[rank][j]);
value_subtract(H->p[i][j],H->p[i][j],aux);
}
/* U->p[i][j] -= x * U->p[rank][j]; */
if (U)
for (j=0; j<nr; j++) {
value_multiply(aux,x,U->p[rank][j]);
value_subtract(U->p[i][j],U->p[i][j],aux);
}
/* Q->p[rank][j] += x * Q->p[i][j]; */
if (Q)
for (j=0; j<nr; j++) {
value_addmul(Q->p[rank][j], x, Q->p[i][j]);
}
#ifdef DEBUG
fprintf(stderr,
"row %d = row %d - %d row %d -----------\n", i+1, i+1, x, rank+1);
Matrix_Print(stderr,0,H);
#endif
} /* if (x) */
} /* for (i) */
rank++;
} /* if (pivot!=0) */
} /* for (k) */
/* Clear all the 'Value' variables */
value_clear(pivot); value_clear(x);
value_clear(aux);
for(i=0;i<nc;i++)
value_clear(temp1[i]);
for(i=0;i<nr;i++)
value_clear(temp2[i]);
free(temp2);
free(temp1);
return rank;
} /* Hermite */
/* GaussSimplify --
Given Mat1, a matrix of equalities, performs Gaussian elimination.
Find a minimum basis, Returns the rank.
Mat1 is context, Mat2 is reduced in context of Mat1
*/
int GaussSimplify(Matrix *Mat1,Matrix *Mat2) {
int NbRows = Mat1->NbRows;
int NbCols = Mat1->NbColumns;
int *column_index;
int i, j, k, n, t, pivot, Rank;
Value gcd, tmp, *cp;
column_index=(int *)malloc(NbCols * sizeof(int));
if (!column_index) {
errormsg1("GaussSimplify", "outofmem", "out of memory space\n");
Pol_status = 1;
return 0;
}
/* Initialize all the 'Value' variables */
value_init(gcd); value_init(tmp);
Rank=0;
for (j=0; j<NbCols; j++) { /* for each column starting at */
for (i=Rank; i<NbRows; i++) /* diagonal, look down to find */
if (value_notzero_p(Mat1->p[i][j])) /* the first non-zero entry */
break;
if (i!=NbRows) { /* was one found ? */
if (i!=Rank) /* was it found below the diagonal?*/
Vector_Exchange(Mat1->p[Rank],Mat1->p[i],NbCols);
/* Normalize the pivot row */
Vector_Gcd(Mat1->p[Rank],NbCols,&gcd);
/* If (gcd >= 2) */
value_set_si(tmp,2);
if (value_ge(gcd,tmp)) {
cp = Mat1->p[Rank];
for (k=0; k<NbCols; k++,cp++)
value_division(*cp,*cp,gcd);
}
if (value_neg_p(Mat1->p[Rank][j])) {
cp = Mat1->p[Rank];
for (k=0; k<NbCols; k++,cp++)
value_oppose(*cp,*cp);
}
/* End of normalize */
pivot=i;
for (i=0;i<NbRows;i++) /* Zero out the rest of the column */
if (i!=Rank) {
if (value_notzero_p(Mat1->p[i][j])) {
Value a, a1, a2, a1abs, a2abs;
value_init(a); value_init(a1); value_init(a2);
value_init(a1abs); value_init(a2abs);
value_assign(a1,Mat1->p[i][j]);
value_absolute(a1abs,a1);
value_assign(a2,Mat1->p[Rank][j]);
value_absolute(a2abs,a2);
value_gcd(a, a1abs, a2abs);
value_divexact(a1, a1, a);
value_divexact(a2, a2, a);
value_oppose(a1,a1);
Vector_Combine(Mat1->p[i],Mat1->p[Rank],Mat1->p[i],a2,
a1,NbCols);
Vector_Normalize(Mat1->p[i],NbCols);
value_clear(a); value_clear(a1); value_clear(a2);
value_clear(a1abs); value_clear(a2abs);
}
}
column_index[Rank]=j;
Rank++;
}
} /* end of Gauss elimination */
if (Mat2) { /* Mat2 is a transformation matrix (i,j->f(i,j))....
can't scale it because can't scale both sides of -> */
/* normalizes an affine transformation */
/* priority of forms */
/* 1. i' -> i (identity) */
/* 2. i' -> i + constant (uniform) */
/* 3. i' -> constant (broadcast) */
/* 4. i' -> j (permutation) */
/* 5. i' -> j + constant ( ) */
/* 6. i' -> i + j + constant (non-uniform) */
for (k=0; k<Rank; k++) {
j = column_index[k];
for (i=0; i<(Mat2->NbRows-1);i++) { /* all but the last row 0...0 1 */
if ((i!=j) && value_notzero_p(Mat2->p[i][j])) {
/* Remove dependency of i' on j */
Value a, a1, a1abs, a2, a2abs;
value_init(a); value_init(a1); value_init(a2);
value_init(a1abs); value_init(a2abs);
value_assign(a1,Mat2->p[i][j]);
value_absolute(a1abs,a1);
value_assign(a2,Mat1->p[k][j]);
value_absolute(a2abs,a2);
value_gcd(a, a1abs, a2abs);
value_divexact(a1, a1, a);
value_divexact(a2, a2, a);
value_oppose(a1,a1);
if (value_one_p(a2)) {
Vector_Combine(Mat2->p[i],Mat1->p[k],Mat2->p[i],a2,
a1,NbCols);
/* Vector_Normalize(Mat2->p[i],NbCols); -- can't do T */
} /* otherwise, can't do it without mult lhs prod (2i,3j->...) */
value_clear(a); value_clear(a1); value_clear(a2);
value_clear(a1abs); value_clear(a2abs);
}
else if ((i==j) && value_zero_p(Mat2->p[i][j])) {
/* 'i' does not depend on j */
for (n=j+1; n < (NbCols-1); n++) {
if (value_notzero_p(Mat2->p[i][n])) { /* i' depends on some n */
value_set_si(tmp,1);
Vector_Combine(Mat2->p[i],Mat1->p[k],Mat2->p[i],tmp,
tmp,NbCols);
break;
} /* if 'i' depends on just a constant, then leave it alone.*/
}
}
}
}
/* Check last row of transformation Mat2 */
for (j=0; j<(NbCols-1); j++)
if (value_notzero_p(Mat2->p[Mat2->NbRows-1][j])) {
errormsg1("GaussSimplify", "corrtrans", "Corrupted transformation\n");
break;
}
if (value_notone_p(Mat2->p[Mat2->NbRows-1][NbCols-1])) {
errormsg1("GaussSimplify", "corrtrans", "Corrupted transformation\n");
}
}
value_clear(gcd); value_clear(tmp);
free(column_index);
return Rank;
} /* GaussSimplify */
/* INDEX = 1 .... Dimension */
int PolyhedronLTQ (Polyhedron *Pol1,Polyhedron *Pol2,int INDEX, int PDIM, int NbMaxConstrs) {
int res, dim, i, j, k;
Polyhedron *Q1, *Q2, *Q3, *Q4, *Q;
Matrix *Mat;
if (Pol1->next || Pol2->next) {
errormsg1("PolyhedronLTQ", "compoly", "Can only compare polyhedra");
return 0;
}
if (Pol1->Dimension != Pol2->Dimension) {
errormsg1("PolyhedronLTQ","diffdim","Polyhedra are not same dimension");
return 0;
}
dim = Pol1->Dimension+2;
POL_ENSURE_FACETS(Pol1);
POL_ENSURE_VERTICES(Pol1);
POL_ENSURE_FACETS(Pol2);
POL_ENSURE_VERTICES(Pol2);
#ifdef DEBUG
fprintf(stdout, "P1\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Pol1);
fprintf(stdout, "P2\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Pol2);
#endif
/* Create the Line to add */
k = Pol1->Dimension-INDEX+1-PDIM;
Mat = Matrix_Alloc(k,dim);
Vector_Set(Mat->p_Init,0,dim*k);
for(j=0,i=INDEX;j<k;i++,j++)
value_set_si(Mat->p[j][i],1);
Q1 = AddRays(Mat->p[0],k,Pol1,NbMaxConstrs);
Q2 = AddRays(Mat->p[0],k,Pol2,NbMaxConstrs);
#ifdef DEBUG
fprintf(stdout, "Q1\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q1);
fprintf(stdout, "Q2\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q2);
#endif
Matrix_Free(Mat);
Q = DomainIntersection(Q1,Q2,NbMaxConstrs);
#ifdef DEBUG
fprintf(stdout, "Q\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q);
#endif
Domain_Free(Q1);
Domain_Free(Q2);
if (emptyQ(Q)) res = 0; /* not comparable */
else {
Q1 = DomainIntersection(Pol1,Q,NbMaxConstrs);
Q2 = DomainIntersection(Pol2,Q,NbMaxConstrs);
#ifdef DEBUG
fprintf(stdout, "Q1\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q1);
fprintf(stdout, "Q2\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q2);
#endif
k = Q1->NbConstraints + Q2->NbConstraints;
Mat = Matrix_Alloc(k, dim);
Vector_Set(Mat->p_Init,0,k*dim);
/* First compute surrounding polyhedron */
j=0;
for (i=0; i<Q1->NbConstraints; i++) {
if ((value_one_p(Q1->Constraint[i][0])) && (value_pos_p(Q1->Constraint[i][INDEX]))) {
/* keep Q1's lower bounds */
for (k=0; k<dim; k++)
value_assign(Mat->p[j][k],Q1->Constraint[i][k]);
j++;
}
}
for (i=0; i<Q2->NbConstraints; i++) {
if ((value_one_p(Q2->Constraint[i][0])) && (value_neg_p(Q2->Constraint[i][INDEX]))) {
/* and keep Q2's upper bounds */
for (k=0; k<dim; k++)
value_assign(Mat->p[j][k],Q2->Constraint[i][k]);
j++;
}
}
Q4 = AddConstraints(Mat->p[0], j, Q, NbMaxConstrs);
Matrix_Free(Mat);
#ifdef debug
fprintf(stderr, "Q4 surrounding polyhedron\n");
Polyhderon_Print(stderr,P_VALUE_FMT, Q4);
#endif
/* if surrounding polyhedron is empty, D1>D2 */
if (emptyQ(Q4)) {
res = 1;
#ifdef debug
fprintf(stderr, "Surrounding polyhedron is empty\n");
#endif
goto LTQdone2;
}
/* Test if Q1 < Q2 */
/* Build a constraint array for >= Q1 and <= Q2 */
Mat = Matrix_Alloc(2,dim);
Vector_Set(Mat->p_Init,0,2*dim);
/* Choose a contraint from Q1 */
for (i=0; i<Q1->NbConstraints; i++) {
if (value_zero_p(Q1->Constraint[i][0])) {
/* Equality */
if (value_zero_p(Q1->Constraint[i][INDEX])) {
/* Ignore side constraint (they are in Q) */
continue;
}
else if (value_neg_p(Q1->Constraint[i][INDEX])) {
/* copy -constraint to Mat */
value_set_si(Mat->p[0][0],1);
for (k=1; k<dim; k++)
value_oppose(Mat->p[0][k],Q1->Constraint[i][k]);
}
else {
/* Copy constraint to Mat */
value_set_si(Mat->p[0][0],1);
for (k=1; k<dim; k++)
value_assign(Mat->p[0][k],Q1->Constraint[i][k]);
}
}
else if(value_neg_p(Q1->Constraint[i][INDEX])) {
/* Upper bound -- make a lower bound from it */
value_set_si(Mat->p[0][0],1);
for (k=1; k<dim; k++)
value_oppose(Mat->p[0][k],Q1->Constraint[i][k]);
}
else {
/* Lower or side bound -- ignore it */
continue;
}
/* Choose a constraint from Q2 */
for (j=0; j<Q2->NbConstraints; j++) {
if (value_zero_p(Q2->Constraint[j][0])) { /* equality */
if (value_zero_p(Q2->Constraint[j][INDEX])) {
/* Ignore side constraint (they are in Q) */
continue;
}
else if (value_pos_p(Q2->Constraint[j][INDEX])) {
/* Copy -constraint to Mat */
value_set_si(Mat->p[1][0],1);
for (k=1; k<dim; k++)
value_oppose(Mat->p[1][k],Q2->Constraint[j][k]);
}
else {
/* Copy constraint to Mat */
value_set_si(Mat->p[1][0],1);
for (k=1; k<dim; k++)
value_assign(Mat->p[1][k],Q2->Constraint[j][k]);
};
}
else if (value_pos_p(Q2->Constraint[j][INDEX])) {
/* Lower bound -- make an upper bound from it */
value_set_si(Mat->p[1][0],1);
for(k=1;k<dim;k++)
value_oppose(Mat->p[1][k],Q2->Constraint[j][k]);
}
else {
/* Upper or side bound -- ignore it */
continue;
};
#ifdef DEBUG
fprintf(stdout, "i=%d j=%d M=\n", i+1, j+1);
Matrix_Print(stdout,P_VALUE_FMT,Mat);
#endif
/* Add Mat to Q and see if anything is made */
Q3 = AddConstraints(Mat->p[0],2,Q,NbMaxConstrs);
#ifdef DEBUG
fprintf(stdout, "Q3\n");
Polyhedron_Print(stdout,P_VALUE_FMT,Q3);
#endif
if (!emptyQ(Q3)) {
Domain_Free(Q3);
#ifdef DEBUG
fprintf(stdout, "not empty\n");
#endif
res = -1;
goto LTQdone;
}
#ifdef DEBUG
fprintf(stdout,"empty\n");
#endif
Domain_Free(Q3);
} /* end for j */
} /* end for i */
res = 1;
LTQdone:
Matrix_Free(Mat);
LTQdone2:
Domain_Free(Q4);
Domain_Free(Q1);
Domain_Free(Q2);
}
Domain_Free(Q);
#ifdef DEBUG
fprintf(stdout, "res = %d\n", res);
#endif
return res;
} /* PolyhedronLTQ */