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/*
This file is part of PolyLib.
PolyLib is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
PolyLib is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with PolyLib. If not, see <http://www.gnu.org/licenses/>.
*/
/**
* Tools to compute the ranking function of an iteration J: the number of
* integer points in P that are lexicographically inferior to J
* B. Meister
* 6/2005
* LSIIT-ICPS, UMR 7005 CNRS Universite Louis Pasteur
* HiPEAC Network
*/
#include <polylib/polylib.h>
#include <polylib/ranking.h>
/**
* Returns a list of polytopes needed to compute
* the number of points in P that are lexicographically
* smaller than a given point in D.
* Only the first dim dimensions are taken into account
* for computing the lexsmaller relation.
* The remaining variables are assumed to be extra
* existential/control variables.
* When P == D, this is the conventional ranking function.
* P and D are assumed to have the same parameter domain C.
*
* The first polyhedron in the list returned is the
* updated context: a combination of D and C or an extended C.
*
* The order of the variables in the remaining polyhedra is
* - first dim variables of P
* - existential variables of P
* - existential variables of D
* - first dim variables of D
* - the parameters
*/
Polyhedron *LexSmaller(Polyhedron *P, Polyhedron *D, unsigned dim,
Polyhedron *C, unsigned MAXRAYS)
{
unsigned i, j, k, r;
unsigned nb_parms = C->Dimension;
unsigned nb_vars = dim;
unsigned P_extra = P->Dimension - nb_vars - nb_parms;
unsigned D_extra = D->Dimension - nb_vars - nb_parms;
unsigned nb_new_parms;
unsigned ncons;
Matrix * cur_element, * C_times_J, * Klon;
Polyhedron * P1, *C1;
Polyhedron * lexico_lesser_union = NULL;
POL_ENSURE_INEQUALITIES(C);
POL_ENSURE_INEQUALITIES(D);
POL_ENSURE_INEQUALITIES(P);
assert(P->Dimension >= C->Dimension + dim);
assert(D->Dimension >= C->Dimension + dim);
nb_new_parms = nb_vars;
/* the number of variables must be positive */
if (nb_vars<=0) {
printf("\nRanking > No variables, returning NULL.\n");
return NULL;
}
/*
* if D has extra variables, then we can't squeeze the contraints
* of D in the new context, so we simply add them to each element.
*/
if (D_extra)
cur_element = Matrix_Alloc(P->NbConstraints+D->NbConstraints+nb_new_parms,
P->Dimension+D_extra+nb_new_parms+2);
else
cur_element = Matrix_Alloc(P->NbConstraints+nb_new_parms,
P->Dimension+D_extra+nb_new_parms+2);
/* 0- Put P in the first rows of cur_element */
for (i=0; i < P->NbConstraints; i++) {
Vector_Copy(P->Constraint[i], cur_element->p[i], nb_vars+P_extra+1);
Vector_Copy(P->Constraint[i]+1+nb_vars+P_extra,
cur_element->p[i]+1+nb_vars+P_extra+D_extra+nb_new_parms,
nb_parms+1);
}
ncons = P->NbConstraints;
if (D_extra) {
for (i=0; i < D->NbConstraints; i++) {
r = P->NbConstraints + i;
Vector_Copy(D->Constraint[i], cur_element->p[r], 1);
Vector_Copy(D->Constraint[i]+1,
cur_element->p[r]+1+nb_vars+P_extra+D_extra, nb_new_parms);
Vector_Copy(D->Constraint[i]+1+nb_new_parms,
cur_element->p[r]+1+nb_vars+P_extra, D_extra);
Vector_Copy(D->Constraint[i]+1+nb_new_parms+D_extra,
cur_element->p[r]+1+nb_vars+P_extra+D_extra+nb_new_parms,
nb_parms+1);
}
ncons += D->NbConstraints;
}
/* 1- compute the Ehrhart polynomial of each disjoint polyhedron defining the
lexicographic order */
for (k=0, r = ncons; k < nb_vars; k++, r++) {
/* a- build the corresponding matrix
* the nb of rows of cur_element is fake, so that we do not have to
* re-allocate it. */
cur_element->NbRows = r+1;
/* convert the previous (strict) inequality into an equality */
if (k>=1) {
value_set_si(cur_element->p[r-1][0], 0);
value_set_si(cur_element->p[r-1][cur_element->NbColumns-1], 0);
}
/* build the k-th inequality from P */
value_set_si(cur_element->p[r][0], 1);
value_set_si(cur_element->p[r][k+1], -1);
value_set_si(cur_element->p[r][nb_vars+P_extra+D_extra+k+1], 1);
/* we want a strict inequality */
value_set_si(cur_element->p[r][cur_element->NbColumns-1], -1);
#ifdef ERDEBUG
show_matrix(cur_element);
#endif
/* b- add it to the current union
as Constraints2Polyhedron modifies its input, we must clone cur_element */
Klon = Matrix_Copy(cur_element);
P1 = Constraints2Polyhedron(Klon, MAXRAYS);
Matrix_Free(Klon);
P1->next = lexico_lesser_union;
lexico_lesser_union = P1;
}
/* 2- as we introduce n parameters, we must introduce them into the context
* as well.
* The added constraints are P.M.(J N 1 )^T >=0 */
if (D_extra)
C_times_J = Matrix_Alloc(C->NbConstraints, nb_new_parms+nb_parms+2);
else
C_times_J = Matrix_Alloc(C->NbConstraints + D->NbConstraints, D->Dimension+2);
/* copy the initial context while adding the new parameters */
for (i = 0; i < C->NbConstraints; i++) {
value_assign(C_times_J->p[i][0], C->Constraint[i][0]);
Vector_Copy(C->Constraint[i]+1, C_times_J->p[i]+1+nb_new_parms, nb_parms+1);
}
/* copy constraints from evaluation domain */
if (!D_extra)
for (i = 0; i < D->NbConstraints; i++)
Vector_Copy(D->Constraint[i], C_times_J->p[C->NbConstraints+i],
D->Dimension+2);
#ifdef ERDEBUG
show_matrix(C_times_J);
#endif
C1 = Constraints2Polyhedron(C_times_J, POL_NO_DUAL);
/* 4- clean up */
Matrix_Free(cur_element);
Matrix_Free(C_times_J);
C1->next = P1;
return C1;
} /* LexSmaller */
/**
* Returns the number of points in P that are lexicographically
* smaller than a given point in D.
* Only the first dim dimensions are taken into account
* for computing the lexsmaller relation.
* The remaining variables are assumed to be extra
* existential/control variables.
* When P == D, this is the conventional ranking function.
* P and D are assumed to have the same parameter domain C.
* The variables in the Enumeration correspond to the first dim variables
* in D followed by the parameters of D (the variables of C).
*/
Enumeration *Polyhedron_LexSmallerEnumerate(Polyhedron *P, Polyhedron *D,
unsigned dim,
Polyhedron *C, unsigned MAXRAYS)
{
Enumeration * ranking;
Polyhedron *RC, *RD;
RC = LexSmaller(P, D, dim, C, MAXRAYS);
RD = RC->next;
RC->next = NULL;
/* Compute the ranking, which is the sum of the Ehrhart polynomials of the n
disjoint polyhedra we just put in P1. */
/* OPT : our polyhdera are (already) disjoint, so Domain_Enumerate does
probably too much work uselessly */
ranking = Domain_Enumerate(RD, RC, MAXRAYS, NULL);
Domain_Free(RD);
Polyhedron_Free(RC);
return ranking;
}
/*
* Returns a function that assigns a unique number to each point in the
* polytope P ranging from zero to (number of points in P)-1.
* The order of the numbers corresponds to the lexicographical order.
*
* C is the parameter context of the polytope
*/
Enumeration *Polyhedron_Ranking(Polyhedron *P, Polyhedron *C, unsigned MAXRAYS)
{
return Polyhedron_LexSmallerEnumerate(P, P, P->Dimension-C->Dimension,
C, MAXRAYS);
}
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