nexmon – Rev 1
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/*
* Copyright 2010 INRIA Saclay
*
* Use of this software is governed by the GNU LGPLv2.1 license
*
* Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
* Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
* 91893 Orsay, France
*/
#include <isl_map_private.h>
#include <isl/set.h>
#include <isl/seq.h>
#include <isl_tab.h>
#include <isl_space_private.h>
#include <isl_morph.h>
#include <isl_vertices_private.h>
#include <isl_mat_private.h>
#define SELECTED 1
#define DESELECTED -1
#define UNSELECTED 0
static __isl_give isl_vertices *compute_chambers(__isl_take isl_basic_set *bset,
__isl_take isl_vertices *vertices);
__isl_give isl_vertices *isl_vertices_copy(__isl_keep isl_vertices *vertices)
{
if (!vertices)
return NULL;
vertices->ref++;
return vertices;
}
void isl_vertices_free(__isl_take isl_vertices *vertices)
{
int i;
if (!vertices)
return;
if (--vertices->ref > 0)
return;
for (i = 0; i < vertices->n_vertices; ++i) {
isl_basic_set_free(vertices->v[i].vertex);
isl_basic_set_free(vertices->v[i].dom);
}
free(vertices->v);
for (i = 0; i < vertices->n_chambers; ++i) {
free(vertices->c[i].vertices);
isl_basic_set_free(vertices->c[i].dom);
}
free(vertices->c);
isl_basic_set_free(vertices->bset);
free(vertices);
}
struct isl_vertex_list {
struct isl_vertex v;
struct isl_vertex_list *next;
};
static void free_vertex_list(struct isl_vertex_list *list)
{
struct isl_vertex_list *next;
for (; list; list = next) {
next = list->next;
isl_basic_set_free(list->v.vertex);
isl_basic_set_free(list->v.dom);
free(list);
}
}
static __isl_give isl_vertices *vertices_from_list(__isl_keep isl_basic_set *bset,
int n_vertices, struct isl_vertex_list *list)
{
int i;
struct isl_vertex_list *next;
isl_vertices *vertices;
vertices = isl_calloc_type(bset->ctx, isl_vertices);
if (!vertices)
goto error;
vertices->ref = 1;
vertices->bset = isl_basic_set_copy(bset);
vertices->v = isl_alloc_array(bset->ctx, struct isl_vertex, n_vertices);
if (!vertices->v)
goto error;
vertices->n_vertices = n_vertices;
for (i = 0; list; list = next, i++) {
next = list->next;
vertices->v[i] = list->v;
free(list);
}
return vertices;
error:
free(vertices);
free_vertex_list(list);
return NULL;
}
/* Prepend a vertex to the linked list "list" based on the equalities in "tab".
*/
static int add_vertex(struct isl_vertex_list **list,
__isl_keep isl_basic_set *bset, struct isl_tab *tab)
{
unsigned nvar;
unsigned nparam;
struct isl_vertex_list *v = NULL;
if (isl_tab_detect_implicit_equalities(tab) < 0)
return -1;
nvar = isl_basic_set_dim(bset, isl_dim_set);
nparam = isl_basic_set_dim(bset, isl_dim_param);
v = isl_calloc_type(tab->mat->ctx, struct isl_vertex_list);
if (!v)
goto error;
v->v.vertex = isl_basic_set_copy(bset);
v->v.vertex = isl_basic_set_cow(v->v.vertex);
v->v.vertex = isl_basic_set_update_from_tab(v->v.vertex, tab);
v->v.vertex = isl_basic_set_simplify(v->v.vertex);
v->v.vertex = isl_basic_set_finalize(v->v.vertex);
if (!v->v.vertex)
goto error;
isl_assert(bset->ctx, v->v.vertex->n_eq >= nvar, goto error);
v->v.dom = isl_basic_set_copy(v->v.vertex);
v->v.dom = isl_basic_set_project_out(v->v.dom, isl_dim_set, 0, nvar);
if (!v->v.dom)
goto error;
v->next = *list;
*list = v;
return 0;
error:
free_vertex_list(v);
return -1;
}
/* Compute the parametric vertices and the chamber decomposition
* of an empty parametric polytope.
*/
static __isl_give isl_vertices *vertices_empty(__isl_keep isl_basic_set *bset)
{
isl_vertices *vertices;
unsigned nparam;
if (!bset)
return NULL;
nparam = isl_basic_set_dim(bset, isl_dim_param);
vertices = isl_calloc_type(bset->ctx, isl_vertices);
if (!vertices)
return NULL;
vertices->bset = isl_basic_set_copy(bset);
vertices->ref = 1;
vertices->n_vertices = 0;
vertices->n_chambers = 0;
return vertices;
}
/* Compute the parametric vertices and the chamber decomposition
* of the parametric polytope defined using the same constraints
* as "bset" in the 0D case.
* There is exactly one 0D vertex and a single chamber containing
* the vertex.
*/
static __isl_give isl_vertices *vertices_0D(__isl_keep isl_basic_set *bset)
{
isl_vertices *vertices;
unsigned nparam;
if (!bset)
return NULL;
nparam = isl_basic_set_dim(bset, isl_dim_param);
vertices = isl_calloc_type(bset->ctx, isl_vertices);
if (!vertices)
return NULL;
vertices->ref = 1;
vertices->bset = isl_basic_set_copy(bset);
vertices->v = isl_calloc_array(bset->ctx, struct isl_vertex, 1);
if (!vertices->v)
goto error;
vertices->n_vertices = 1;
vertices->v[0].vertex = isl_basic_set_copy(bset);
vertices->v[0].dom = isl_basic_set_params(isl_basic_set_copy(bset));
if (!vertices->v[0].vertex || !vertices->v[0].dom)
goto error;
vertices->c = isl_calloc_array(bset->ctx, struct isl_chamber, 1);
if (!vertices->c)
goto error;
vertices->n_chambers = 1;
vertices->c[0].n_vertices = 1;
vertices->c[0].vertices = isl_calloc_array(bset->ctx, int, 1);
if (!vertices->c[0].vertices)
goto error;
vertices->c[0].dom = isl_basic_set_copy(vertices->v[0].dom);
if (!vertices->c[0].dom)
goto error;
return vertices;
error:
isl_vertices_free(vertices);
return NULL;
}
static int isl_mat_rank(__isl_keep isl_mat *mat)
{
int row, col;
isl_mat *H;
H = isl_mat_left_hermite(isl_mat_copy(mat), 0, NULL, NULL);
if (!H)
return -1;
for (col = 0; col < H->n_col; ++col) {
for (row = 0; row < H->n_row; ++row)
if (!isl_int_is_zero(H->row[row][col]))
break;
if (row == H->n_row)
break;
}
isl_mat_free(H);
return col;
}
/* Is the row pointed to by "f" linearly independent of the "n" first
* rows in "facets"?
*/
static int is_independent(__isl_keep isl_mat *facets, int n, isl_int *f)
{
int rank;
if (isl_seq_first_non_zero(f, facets->n_col) < 0)
return 0;
isl_seq_cpy(facets->row[n], f, facets->n_col);
facets->n_row = n + 1;
rank = isl_mat_rank(facets);
if (rank < 0)
return -1;
return rank == n + 1;
}
/* Check whether we can select constraint "level", given the current selection
* reflected by facets in "tab", the rows of "facets" and the earlier
* "selected" elements of "selection".
*
* If the constraint is (strictly) redundant in the tableau, selecting it would
* result in an empty tableau, so it can't be selected.
* If the set variable part of the constraint is not linearly indepedent
* of the set variable parts of the already selected constraints,
* the constraint cannot be selected.
* If selecting the constraint results in an empty tableau, the constraint
* cannot be selected.
* Finally, if selecting the constraint results in some explicitly
* deselected constraints turning into equalities, then the corresponding
* vertices have already been generated, so the constraint cannot be selected.
*/
static int can_select(__isl_keep isl_basic_set *bset, int level,
struct isl_tab *tab, __isl_keep isl_mat *facets, int selected,
int *selection)
{
int i;
int indep;
unsigned ovar;
struct isl_tab_undo *snap;
if (isl_tab_is_redundant(tab, level))
return 0;
ovar = isl_space_offset(bset->dim, isl_dim_set);
indep = is_independent(facets, selected, bset->ineq[level] + 1 + ovar);
if (indep < 0)
return -1;
if (!indep)
return 0;
snap = isl_tab_snap(tab);
if (isl_tab_select_facet(tab, level) < 0)
return -1;
if (tab->empty) {
if (isl_tab_rollback(tab, snap) < 0)
return -1;
return 0;
}
for (i = 0; i < level; ++i) {
int sgn;
if (selection[i] != DESELECTED)
continue;
if (isl_tab_is_equality(tab, i))
sgn = 0;
else if (isl_tab_is_redundant(tab, i))
sgn = 1;
else
sgn = isl_tab_sign_of_max(tab, i);
if (sgn < -1)
return -1;
if (sgn <= 0) {
if (isl_tab_rollback(tab, snap) < 0)
return -1;
return 0;
}
}
return 1;
}
/* Compute the parametric vertices and the chamber decomposition
* of a parametric polytope that is not full-dimensional.
*
* Simply map the parametric polytope to a lower dimensional space
* and map the resulting vertices back.
*/
static __isl_give isl_vertices *lower_dim_vertices(
__isl_keep isl_basic_set *bset)
{
isl_morph *morph;
isl_vertices *vertices;
bset = isl_basic_set_copy(bset);
morph = isl_basic_set_full_compression(bset);
bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
vertices = isl_basic_set_compute_vertices(bset);
isl_basic_set_free(bset);
morph = isl_morph_inverse(morph);
vertices = isl_morph_vertices(morph, vertices);
return vertices;
}
/* Compute the parametric vertices and the chamber decomposition
* of the parametric polytope defined using the same constraints
* as "bset". "bset" is assumed to have no existentially quantified
* variables.
*
* The vertices themselves are computed in a fairly simplistic way.
* We simply run through all combinations of d constraints,
* with d the number of set variables, and check if those d constraints
* define a vertex. To avoid the generation of duplicate vertices,
* which we may happen if a vertex is defined by more that d constraints,
* we make sure we only generate the vertex for the d constraints with
* smallest index.
*
* We set up a tableau and keep track of which facets have been
* selected. The tableau is marked strict_redundant so that we can be
* sure that any constraint that is marked redundant (and that is not
* also marked zero) is not an equality.
* If a constraint is marked DESELECTED, it means the constraint was
* SELECTED before (in combination with the same selection of earlier
* constraints). If such a deselected constraint turns out to be an
* equality, then any vertex that may still be found with the current
* selection has already been generated when the constraint was selected.
* A constraint is marked UNSELECTED when there is no way selecting
* the constraint could lead to a vertex (in combination with the current
* selection of earlier constraints).
*
* The set variable coefficients of the selected constraints are stored
* in the facets matrix.
*/
__isl_give isl_vertices *isl_basic_set_compute_vertices(
__isl_keep isl_basic_set *bset)
{
struct isl_tab *tab;
int level;
int init;
unsigned nvar;
int *selection = NULL;
int selected;
struct isl_tab_undo **snap = NULL;
isl_mat *facets = NULL;
struct isl_vertex_list *list = NULL;
int n_vertices = 0;
isl_vertices *vertices;
if (!bset)
return NULL;
if (isl_basic_set_plain_is_empty(bset))
return vertices_empty(bset);
if (bset->n_eq != 0)
return lower_dim_vertices(bset);
isl_assert(bset->ctx, isl_basic_set_dim(bset, isl_dim_div) == 0,
return NULL);
if (isl_basic_set_dim(bset, isl_dim_set) == 0)
return vertices_0D(bset);
nvar = isl_basic_set_dim(bset, isl_dim_set);
bset = isl_basic_set_copy(bset);
bset = isl_basic_set_set_rational(bset);
if (!bset)
return NULL;
tab = isl_tab_from_basic_set(bset, 0);
if (!tab)
goto error;
tab->strict_redundant = 1;
if (tab->empty) {
vertices = vertices_empty(bset);
isl_basic_set_free(bset);
isl_tab_free(tab);
return vertices;
}
selection = isl_alloc_array(bset->ctx, int, bset->n_ineq);
snap = isl_alloc_array(bset->ctx, struct isl_tab_undo *, bset->n_ineq);
facets = isl_mat_alloc(bset->ctx, nvar, nvar);
if (!selection || !snap || !facets)
goto error;
level = 0;
init = 1;
selected = 0;
while (level >= 0) {
if (level >= bset->n_ineq ||
(!init && selection[level] != SELECTED)) {
--level;
init = 0;
continue;
}
if (init) {
int ok;
snap[level] = isl_tab_snap(tab);
ok = can_select(bset, level, tab, facets, selected,
selection);
if (ok < 0)
goto error;
if (ok) {
selection[level] = SELECTED;
selected++;
} else
selection[level] = UNSELECTED;
} else {
selection[level] = DESELECTED;
selected--;
if (isl_tab_rollback(tab, snap[level]) < 0)
goto error;
}
if (selected == nvar) {
if (tab->n_dead == nvar) {
if (add_vertex(&list, bset, tab) < 0)
goto error;
n_vertices++;
}
init = 0;
continue;
}
++level;
init = 1;
}
isl_mat_free(facets);
free(selection);
free(snap);
isl_tab_free(tab);
vertices = vertices_from_list(bset, n_vertices, list);
vertices = compute_chambers(bset, vertices);
return vertices;
error:
isl_mat_free(facets);
free(selection);
free(snap);
isl_tab_free(tab);
isl_basic_set_free(bset);
return NULL;
}
struct isl_chamber_list {
struct isl_chamber c;
struct isl_chamber_list *next;
};
static void free_chamber_list(struct isl_chamber_list *list)
{
struct isl_chamber_list *next;
for (; list; list = next) {
next = list->next;
isl_basic_set_free(list->c.dom);
free(list->c.vertices);
free(list);
}
}
/* Check whether the basic set "bset" is a superset of the basic set described
* by "tab", i.e., check whether all constraints of "bset" are redundant.
*/
static int bset_covers_tab(__isl_keep isl_basic_set *bset, struct isl_tab *tab)
{
int i;
if (!bset || !tab)
return -1;
for (i = 0; i < bset->n_ineq; ++i) {
enum isl_ineq_type type = isl_tab_ineq_type(tab, bset->ineq[i]);
switch (type) {
case isl_ineq_error: return -1;
case isl_ineq_redundant: continue;
default: return 0;
}
}
return 1;
}
static __isl_give isl_vertices *vertices_add_chambers(
__isl_take isl_vertices *vertices, int n_chambers,
struct isl_chamber_list *list)
{
int i;
isl_ctx *ctx;
struct isl_chamber_list *next;
ctx = isl_vertices_get_ctx(vertices);
vertices->c = isl_alloc_array(ctx, struct isl_chamber, n_chambers);
if (!vertices->c)
goto error;
vertices->n_chambers = n_chambers;
for (i = 0; list; list = next, i++) {
next = list->next;
vertices->c[i] = list->c;
free(list);
}
return vertices;
error:
isl_vertices_free(vertices);
free_chamber_list(list);
return NULL;
}
/* Can "tab" be intersected with "bset" without resulting in
* a lower-dimensional set.
*/
static int can_intersect(struct isl_tab *tab, __isl_keep isl_basic_set *bset)
{
int i;
struct isl_tab_undo *snap;
if (isl_tab_extend_cons(tab, bset->n_ineq) < 0)
return -1;
snap = isl_tab_snap(tab);
for (i = 0; i < bset->n_ineq; ++i) {
if (isl_tab_ineq_type(tab, bset->ineq[i]) == isl_ineq_redundant)
continue;
if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
return -1;
}
if (isl_tab_detect_implicit_equalities(tab) < 0)
return -1;
if (tab->n_dead) {
if (isl_tab_rollback(tab, snap) < 0)
return -1;
return 0;
}
return 1;
}
static int add_chamber(struct isl_chamber_list **list,
__isl_keep isl_vertices *vertices, struct isl_tab *tab, int *selection)
{
int n_frozen;
int i, j;
int n_vertices = 0;
struct isl_tab_undo *snap;
struct isl_chamber_list *c = NULL;
for (i = 0; i < vertices->n_vertices; ++i)
if (selection[i])
n_vertices++;
snap = isl_tab_snap(tab);
for (i = 0; i < tab->n_con && tab->con[i].frozen; ++i)
tab->con[i].frozen = 0;
n_frozen = i;
if (isl_tab_detect_redundant(tab) < 0)
return -1;
c = isl_calloc_type(tab->mat->ctx, struct isl_chamber_list);
if (!c)
goto error;
c->c.vertices = isl_alloc_array(tab->mat->ctx, int, n_vertices);
if (!c->c.vertices)
goto error;
c->c.dom = isl_basic_set_from_basic_map(isl_basic_map_copy(tab->bmap));
c->c.dom = isl_basic_set_set_rational(c->c.dom);
c->c.dom = isl_basic_set_cow(c->c.dom);
c->c.dom = isl_basic_set_update_from_tab(c->c.dom, tab);
c->c.dom = isl_basic_set_simplify(c->c.dom);
c->c.dom = isl_basic_set_finalize(c->c.dom);
if (!c->c.dom)
goto error;
c->c.n_vertices = n_vertices;
for (i = 0, j = 0; i < vertices->n_vertices; ++i)
if (selection[i]) {
c->c.vertices[j] = i;
j++;
}
c->next = *list;
*list = c;
for (i = 0; i < n_frozen; ++i)
tab->con[i].frozen = 1;
if (isl_tab_rollback(tab, snap) < 0)
return -1;
return 0;
error:
free_chamber_list(c);
return -1;
}
struct isl_facet_todo {
struct isl_tab *tab; /* A tableau representation of the facet */
isl_basic_set *bset; /* A normalized basic set representation */
isl_vec *constraint; /* Constraint pointing to the other side */
struct isl_facet_todo *next;
};
static void free_todo(struct isl_facet_todo *todo)
{
while (todo) {
struct isl_facet_todo *next = todo->next;
isl_tab_free(todo->tab);
isl_basic_set_free(todo->bset);
isl_vec_free(todo->constraint);
free(todo);
todo = next;
}
}
static struct isl_facet_todo *create_todo(struct isl_tab *tab, int con)
{
int i;
int n_frozen;
struct isl_tab_undo *snap;
struct isl_facet_todo *todo;
snap = isl_tab_snap(tab);
for (i = 0; i < tab->n_con && tab->con[i].frozen; ++i)
tab->con[i].frozen = 0;
n_frozen = i;
if (isl_tab_detect_redundant(tab) < 0)
return NULL;
todo = isl_calloc_type(tab->mat->ctx, struct isl_facet_todo);
if (!todo)
return NULL;
todo->constraint = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
if (!todo->constraint)
goto error;
isl_seq_neg(todo->constraint->el, tab->bmap->ineq[con], 1 + tab->n_var);
todo->bset = isl_basic_set_from_basic_map(isl_basic_map_copy(tab->bmap));
todo->bset = isl_basic_set_set_rational(todo->bset);
todo->bset = isl_basic_set_cow(todo->bset);
todo->bset = isl_basic_set_update_from_tab(todo->bset, tab);
todo->bset = isl_basic_set_simplify(todo->bset);
todo->bset = isl_basic_set_sort_constraints(todo->bset);
if (!todo->bset)
goto error;
ISL_F_SET(todo->bset, ISL_BASIC_SET_NORMALIZED);
todo->tab = isl_tab_dup(tab);
if (!todo->tab)
goto error;
for (i = 0; i < n_frozen; ++i)
tab->con[i].frozen = 1;
if (isl_tab_rollback(tab, snap) < 0)
goto error;
return todo;
error:
free_todo(todo);
return NULL;
}
/* Create todo items for all interior facets of the chamber represented
* by "tab" and collect them in "next".
*/
static int init_todo(struct isl_facet_todo **next, struct isl_tab *tab)
{
int i;
struct isl_tab_undo *snap;
struct isl_facet_todo *todo;
snap = isl_tab_snap(tab);
for (i = 0; i < tab->n_con; ++i) {
if (tab->con[i].frozen)
continue;
if (tab->con[i].is_redundant)
continue;
if (isl_tab_select_facet(tab, i) < 0)
return -1;
todo = create_todo(tab, i);
if (!todo)
return -1;
todo->next = *next;
*next = todo;
if (isl_tab_rollback(tab, snap) < 0)
return -1;
}
return 0;
}
/* Does the linked list contain a todo item that is the opposite of "todo".
* If so, return 1 and remove the opposite todo item.
*/
static int has_opposite(struct isl_facet_todo *todo,
struct isl_facet_todo **list)
{
for (; *list; list = &(*list)->next) {
int eq;
eq = isl_basic_set_plain_is_equal(todo->bset, (*list)->bset);
if (eq < 0)
return -1;
if (!eq)
continue;
todo = *list;
*list = todo->next;
todo->next = NULL;
free_todo(todo);
return 1;
}
return 0;
}
/* Create todo items for all interior facets of the chamber represented
* by "tab" and collect them in first->next, taking care to cancel
* opposite todo items.
*/
static int update_todo(struct isl_facet_todo *first, struct isl_tab *tab)
{
int i;
struct isl_tab_undo *snap;
struct isl_facet_todo *todo;
snap = isl_tab_snap(tab);
for (i = 0; i < tab->n_con; ++i) {
int drop;
if (tab->con[i].frozen)
continue;
if (tab->con[i].is_redundant)
continue;
if (isl_tab_select_facet(tab, i) < 0)
return -1;
todo = create_todo(tab, i);
if (!todo)
return -1;
drop = has_opposite(todo, &first->next);
if (drop < 0)
return -1;
if (drop)
free_todo(todo);
else {
todo->next = first->next;
first->next = todo;
}
if (isl_tab_rollback(tab, snap) < 0)
return -1;
}
return 0;
}
/* Compute the chamber decomposition of the parametric polytope respresented
* by "bset" given the parametric vertices and their activity domains.
*
* We are only interested in full-dimensional chambers.
* Each of these chambers is the intersection of the activity domains of
* one or more vertices and the union of all chambers is equal to the
* projection of the entire parametric polytope onto the parameter space.
*
* We first create an initial chamber by intersecting as many activity
* domains as possible without ending up with an empty or lower-dimensional
* set. As a minor optimization, we only consider those activity domains
* that contain some arbitrary point.
*
* For each of interior facets of the chamber, we construct a todo item,
* containing the facet and a constraint containing the other side of the facet,
* for constructing the chamber on the other side.
* While their are any todo items left, we pick a todo item and
* create the required chamber by intersecting all activity domains
* that contain the facet and have a full-dimensional intersection with
* the other side of the facet. For each of the interior facets, we
* again create todo items, taking care to cancel opposite todo items.
*/
static __isl_give isl_vertices *compute_chambers(__isl_take isl_basic_set *bset,
__isl_take isl_vertices *vertices)
{
int i;
isl_ctx *ctx;
isl_vec *sample = NULL;
struct isl_tab *tab = NULL;
struct isl_tab_undo *snap;
int *selection = NULL;
int n_chambers = 0;
struct isl_chamber_list *list = NULL;
struct isl_facet_todo *todo = NULL;
if (!bset || !vertices)
goto error;
ctx = isl_vertices_get_ctx(vertices);
selection = isl_alloc_array(ctx, int, vertices->n_vertices);
if (!selection)
goto error;
bset = isl_basic_set_params(bset);
tab = isl_tab_from_basic_set(bset, 1);
for (i = 0; i < bset->n_ineq; ++i)
if (isl_tab_freeze_constraint(tab, i) < 0)
goto error;
isl_basic_set_free(bset);
snap = isl_tab_snap(tab);
sample = isl_tab_get_sample_value(tab);
for (i = 0; i < vertices->n_vertices; ++i) {
selection[i] = isl_basic_set_contains(vertices->v[i].dom, sample);
if (selection[i] < 0)
goto error;
if (!selection[i])
continue;
selection[i] = can_intersect(tab, vertices->v[i].dom);
if (selection[i] < 0)
goto error;
}
if (isl_tab_detect_redundant(tab) < 0)
goto error;
if (add_chamber(&list, vertices, tab, selection) < 0)
goto error;
n_chambers++;
if (init_todo(&todo, tab) < 0)
goto error;
while (todo) {
struct isl_facet_todo *next;
if (isl_tab_rollback(tab, snap) < 0)
goto error;
if (isl_tab_add_ineq(tab, todo->constraint->el) < 0)
goto error;
if (isl_tab_freeze_constraint(tab, tab->n_con - 1) < 0)
goto error;
for (i = 0; i < vertices->n_vertices; ++i) {
selection[i] = bset_covers_tab(vertices->v[i].dom,
todo->tab);
if (selection[i] < 0)
goto error;
if (!selection[i])
continue;
selection[i] = can_intersect(tab, vertices->v[i].dom);
if (selection[i] < 0)
goto error;
}
if (isl_tab_detect_redundant(tab) < 0)
goto error;
if (add_chamber(&list, vertices, tab, selection) < 0)
goto error;
n_chambers++;
if (update_todo(todo, tab) < 0)
goto error;
next = todo->next;
todo->next = NULL;
free_todo(todo);
todo = next;
}
isl_vec_free(sample);
isl_tab_free(tab);
free(selection);
vertices = vertices_add_chambers(vertices, n_chambers, list);
for (i = 0; vertices && i < vertices->n_vertices; ++i) {
isl_basic_set_free(vertices->v[i].dom);
vertices->v[i].dom = NULL;
}
return vertices;
error:
free_chamber_list(list);
free_todo(todo);
isl_vec_free(sample);
isl_tab_free(tab);
free(selection);
if (!tab)
isl_basic_set_free(bset);
isl_vertices_free(vertices);
return NULL;
}
isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex)
{
return vertex ? isl_vertices_get_ctx(vertex->vertices) : NULL;
}
int isl_vertex_get_id(__isl_keep isl_vertex *vertex)
{
return vertex ? vertex->id : -1;
}
__isl_give isl_basic_set *isl_vertex_get_domain(__isl_keep isl_vertex *vertex)
{
struct isl_vertex *v;
if (!vertex)
return NULL;
v = &vertex->vertices->v[vertex->id];
if (!v->dom) {
unsigned nvar;
nvar = isl_basic_set_dim(v->vertex, isl_dim_set);
v->dom = isl_basic_set_copy(v->vertex);
v->dom = isl_basic_set_project_out(v->dom, isl_dim_set, 0, nvar);
}
return isl_basic_set_copy(v->dom);
}
__isl_give isl_basic_set *isl_vertex_get_expr(__isl_keep isl_vertex *vertex)
{
struct isl_vertex *v;
if (!vertex)
return NULL;
v = &vertex->vertices->v[vertex->id];
return isl_basic_set_copy(v->vertex);
}
static __isl_give isl_vertex *isl_vertex_alloc(__isl_take isl_vertices *vertices,
int id)
{
isl_ctx *ctx;
isl_vertex *vertex;
if (!vertices)
return NULL;
ctx = isl_vertices_get_ctx(vertices);
vertex = isl_alloc_type(ctx, isl_vertex);
if (!vertex)
goto error;
vertex->vertices = vertices;
vertex->id = id;
return vertex;
error:
isl_vertices_free(vertices);
return NULL;
}
void isl_vertex_free(__isl_take isl_vertex *vertex)
{
if (!vertex)
return;
isl_vertices_free(vertex->vertices);
free(vertex);
}
__isl_give isl_basic_set *isl_basic_set_set_integral(__isl_take isl_basic_set *bset)
{
if (!bset)
return NULL;
if (!ISL_F_ISSET(bset, ISL_BASIC_MAP_RATIONAL))
return bset;
bset = isl_basic_set_cow(bset);
if (!bset)
return NULL;
ISL_F_CLR(bset, ISL_BASIC_MAP_RATIONAL);
return isl_basic_set_finalize(bset);
}
isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell)
{
return cell ? cell->dom->ctx : NULL;
}
__isl_give isl_basic_set *isl_cell_get_domain(__isl_keep isl_cell *cell)
{
return cell ? isl_basic_set_copy(cell->dom) : NULL;
}
static __isl_give isl_cell *isl_cell_alloc(__isl_take isl_vertices *vertices,
__isl_take isl_basic_set *dom, int id)
{
int i;
isl_cell *cell = NULL;
if (!vertices || !dom)
goto error;
cell = isl_calloc_type(dom->ctx, isl_cell);
if (!cell)
goto error;
cell->n_vertices = vertices->c[id].n_vertices;
cell->ids = isl_alloc_array(dom->ctx, int, cell->n_vertices);
if (!cell->ids)
goto error;
for (i = 0; i < cell->n_vertices; ++i)
cell->ids[i] = vertices->c[id].vertices[i];
cell->vertices = vertices;
cell->dom = dom;
return cell;
error:
isl_cell_free(cell);
isl_vertices_free(vertices);
isl_basic_set_free(dom);
return NULL;
}
void isl_cell_free(__isl_take isl_cell *cell)
{
if (!cell)
return;
isl_vertices_free(cell->vertices);
free(cell->ids);
isl_basic_set_free(cell->dom);
free(cell);
}
/* Create a tableau of the cone obtained by first homogenizing the given
* polytope and then making all inequalities strict by setting the
* constant term to -1.
*/
static struct isl_tab *tab_for_shifted_cone(__isl_keep isl_basic_set *bset)
{
int i;
isl_vec *c = NULL;
struct isl_tab *tab;
if (!bset)
return NULL;
tab = isl_tab_alloc(bset->ctx, bset->n_ineq + 1,
1 + isl_basic_set_total_dim(bset), 0);
if (!tab)
return NULL;
tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
if (ISL_F_ISSET(bset, ISL_BASIC_MAP_EMPTY)) {
if (isl_tab_mark_empty(tab) < 0)
goto error;
return tab;
}
c = isl_vec_alloc(bset->ctx, 1 + 1 + isl_basic_set_total_dim(bset));
if (!c)
goto error;
isl_int_set_si(c->el[0], 0);
for (i = 0; i < bset->n_eq; ++i) {
isl_seq_cpy(c->el + 1, bset->eq[i], c->size - 1);
if (isl_tab_add_eq(tab, c->el) < 0)
goto error;
}
isl_int_set_si(c->el[0], -1);
for (i = 0; i < bset->n_ineq; ++i) {
isl_seq_cpy(c->el + 1, bset->ineq[i], c->size - 1);
if (isl_tab_add_ineq(tab, c->el) < 0)
goto error;
if (tab->empty) {
isl_vec_free(c);
return tab;
}
}
isl_seq_clr(c->el + 1, c->size - 1);
isl_int_set_si(c->el[1], 1);
if (isl_tab_add_ineq(tab, c->el) < 0)
goto error;
isl_vec_free(c);
return tab;
error:
isl_vec_free(c);
isl_tab_free(tab);
return NULL;
}
/* Compute an interior point of "bset" by selecting an interior
* point in homogeneous space and projecting the point back down.
*/
static __isl_give isl_vec *isl_basic_set_interior_point(
__isl_keep isl_basic_set *bset)
{
isl_vec *vec;
struct isl_tab *tab;
tab = tab_for_shifted_cone(bset);
vec = isl_tab_get_sample_value(tab);
isl_tab_free(tab);
if (!vec)
return NULL;
isl_seq_cpy(vec->el, vec->el + 1, vec->size - 1);
vec->size--;
return vec;
}
/* Call "fn" on all chambers of the parametric polytope with the shared
* facets of neighboring chambers only appearing in one of the chambers.
*
* We pick an interior point from one of the chambers and then make
* all constraints that do not satisfy this point strict.
*/
int isl_vertices_foreach_disjoint_cell(__isl_keep isl_vertices *vertices,
int (*fn)(__isl_take isl_cell *cell, void *user), void *user)
{
int i, j;
isl_vec *vec;
isl_int v;
isl_cell *cell;
if (!vertices)
return -1;
if (vertices->n_chambers == 0)
return 0;
if (vertices->n_chambers == 1) {
isl_basic_set *dom = isl_basic_set_copy(vertices->c[0].dom);
dom = isl_basic_set_set_integral(dom);
cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, 0);
if (!cell)
return -1;
return fn(cell, user);
}
vec = isl_basic_set_interior_point(vertices->c[0].dom);
if (!vec)
return -1;
isl_int_init(v);
for (i = 0; i < vertices->n_chambers; ++i) {
int r;
isl_basic_set *dom = isl_basic_set_copy(vertices->c[i].dom);
dom = isl_basic_set_cow(dom);
if (!dom)
goto error;
for (j = 0; i && j < dom->n_ineq; ++j) {
isl_seq_inner_product(vec->el, dom->ineq[j], vec->size,
&v);
if (!isl_int_is_neg(v))
continue;
isl_int_sub_ui(dom->ineq[j][0], dom->ineq[j][0], 1);
}
dom = isl_basic_set_set_integral(dom);
cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, i);
if (!cell)
goto error;
r = fn(cell, user);
if (r < 0)
goto error;
}
isl_int_clear(v);
isl_vec_free(vec);
return 0;
error:
isl_int_clear(v);
isl_vec_free(vec);
return -1;
}
int isl_vertices_foreach_cell(__isl_keep isl_vertices *vertices,
int (*fn)(__isl_take isl_cell *cell, void *user), void *user)
{
int i;
isl_cell *cell;
if (!vertices)
return -1;
if (vertices->n_chambers == 0)
return 0;
for (i = 0; i < vertices->n_chambers; ++i) {
int r;
isl_basic_set *dom = isl_basic_set_copy(vertices->c[i].dom);
cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, i);
if (!cell)
return -1;
r = fn(cell, user);
if (r < 0)
return -1;
}
return 0;
}
int isl_vertices_foreach_vertex(__isl_keep isl_vertices *vertices,
int (*fn)(__isl_take isl_vertex *vertex, void *user), void *user)
{
int i;
isl_vertex *vertex;
if (!vertices)
return -1;
if (vertices->n_vertices == 0)
return 0;
for (i = 0; i < vertices->n_vertices; ++i) {
int r;
vertex = isl_vertex_alloc(isl_vertices_copy(vertices), i);
if (!vertex)
return -1;
r = fn(vertex, user);
if (r < 0)
return -1;
}
return 0;
}
int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
int (*fn)(__isl_take isl_vertex *vertex, void *user), void *user)
{
int i;
isl_vertex *vertex;
if (!cell)
return -1;
if (cell->n_vertices == 0)
return 0;
for (i = 0; i < cell->n_vertices; ++i) {
int r;
vertex = isl_vertex_alloc(isl_vertices_copy(cell->vertices),
cell->ids[i]);
if (!vertex)
return -1;
r = fn(vertex, user);
if (r < 0)
return -1;
}
return 0;
}
isl_ctx *isl_vertices_get_ctx(__isl_keep isl_vertices *vertices)
{
return vertices ? vertices->bset->ctx : NULL;
}
int isl_vertices_get_n_vertices(__isl_keep isl_vertices *vertices)
{
return vertices ? vertices->n_vertices : -1;
}
__isl_give isl_vertices *isl_morph_vertices(__isl_take isl_morph *morph,
__isl_take isl_vertices *vertices)
{
int i;
isl_morph *param_morph = NULL;
if (!morph || !vertices)
goto error;
isl_assert(vertices->bset->ctx, vertices->ref == 1, goto error);
param_morph = isl_morph_copy(morph);
param_morph = isl_morph_dom_params(param_morph);
param_morph = isl_morph_ran_params(param_morph);
for (i = 0; i < vertices->n_vertices; ++i) {
vertices->v[i].dom = isl_morph_basic_set(
isl_morph_copy(param_morph), vertices->v[i].dom);
vertices->v[i].vertex = isl_morph_basic_set(
isl_morph_copy(morph), vertices->v[i].vertex);
if (!vertices->v[i].vertex)
goto error;
}
for (i = 0; i < vertices->n_chambers; ++i) {
vertices->c[i].dom = isl_morph_basic_set(
isl_morph_copy(param_morph), vertices->c[i].dom);
if (!vertices->c[i].dom)
goto error;
}
isl_morph_free(param_morph);
isl_morph_free(morph);
return vertices;
error:
isl_morph_free(param_morph);
isl_morph_free(morph);
isl_vertices_free(vertices);
return NULL;
}
/* Construct a simplex isl_cell spanned by the vertices with indices in
* "simplex_ids" and "other_ids" and call "fn" on this isl_cell.
*/
static int call_on_simplex(__isl_keep isl_cell *cell,
int *simplex_ids, int n_simplex, int *other_ids, int n_other,
int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
{
int i;
isl_ctx *ctx;
struct isl_cell *simplex;
ctx = isl_cell_get_ctx(cell);
simplex = isl_calloc_type(ctx, struct isl_cell);
if (!simplex)
return -1;
simplex->vertices = isl_vertices_copy(cell->vertices);
if (!simplex->vertices)
goto error;
simplex->dom = isl_basic_set_copy(cell->dom);
if (!simplex->dom)
goto error;
simplex->n_vertices = n_simplex + n_other;
simplex->ids = isl_alloc_array(ctx, int, simplex->n_vertices);
if (!simplex->ids)
goto error;
for (i = 0; i < n_simplex; ++i)
simplex->ids[i] = simplex_ids[i];
for (i = 0; i < n_other; ++i)
simplex->ids[n_simplex + i] = other_ids[i];
return fn(simplex, user);
error:
isl_cell_free(simplex);
return -1;
}
/* Check whether the parametric vertex described by "vertex"
* lies on the facet corresponding to constraint "facet" of "bset".
* The isl_vec "v" is a temporary vector than can be used by this function.
*
* We eliminate the variables from the facet constraint using the
* equalities defining the vertex and check if the result is identical
* to zero.
*
* It would probably be better to keep track of the constraints defining
* a vertex during the vertex construction so that we could simply look
* it up here.
*/
static int vertex_on_facet(__isl_keep isl_basic_set *vertex,
__isl_keep isl_basic_set *bset, int facet, __isl_keep isl_vec *v)
{
int i;
isl_int m;
isl_seq_cpy(v->el, bset->ineq[facet], v->size);
isl_int_init(m);
for (i = 0; i < vertex->n_eq; ++i) {
int k = isl_seq_last_non_zero(vertex->eq[i], v->size);
isl_seq_elim(v->el, vertex->eq[i], k, v->size, &m);
}
isl_int_clear(m);
return isl_seq_first_non_zero(v->el, v->size) == -1;
}
/* Triangulate the polytope spanned by the vertices with ids
* in "simplex_ids" and "other_ids" and call "fn" on each of
* the resulting simplices.
* If the input polytope is already a simplex, we simply call "fn".
* Otherwise, we pick a point from "other_ids" and add it to "simplex_ids".
* Then we consider each facet of "bset" that does not contain the point
* we just picked, but does contain some of the other points in "other_ids"
* and call ourselves recursively on the polytope spanned by the new
* "simplex_ids" and those points in "other_ids" that lie on the facet.
*/
static int triangulate(__isl_keep isl_cell *cell, __isl_keep isl_vec *v,
int *simplex_ids, int n_simplex, int *other_ids, int n_other,
int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
{
int i, j, k;
int d, nparam;
int *ids;
isl_ctx *ctx;
isl_basic_set *vertex;
isl_basic_set *bset;
ctx = isl_cell_get_ctx(cell);
d = isl_basic_set_dim(cell->vertices->bset, isl_dim_set);
nparam = isl_basic_set_dim(cell->vertices->bset, isl_dim_param);
if (n_simplex + n_other == d + 1)
return call_on_simplex(cell, simplex_ids, n_simplex,
other_ids, n_other, fn, user);
simplex_ids[n_simplex] = other_ids[0];
vertex = cell->vertices->v[other_ids[0]].vertex;
bset = cell->vertices->bset;
ids = isl_alloc_array(ctx, int, n_other - 1);
for (i = 0; i < bset->n_ineq; ++i) {
if (isl_seq_first_non_zero(bset->ineq[i] + 1 + nparam, d) == -1)
continue;
if (vertex_on_facet(vertex, bset, i, v))
continue;
for (j = 1, k = 0; j < n_other; ++j) {
isl_basic_set *ov;
ov = cell->vertices->v[other_ids[j]].vertex;
if (vertex_on_facet(ov, bset, i, v))
ids[k++] = other_ids[j];
}
if (k == 0)
continue;
if (triangulate(cell, v, simplex_ids, n_simplex + 1,
ids, k, fn, user) < 0)
goto error;
}
free(ids);
return 0;
error:
free(ids);
return -1;
}
/* Triangulate the given cell and call "fn" on each of the resulting
* simplices.
*/
int isl_cell_foreach_simplex(__isl_take isl_cell *cell,
int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
{
int d, total;
int r;
isl_ctx *ctx;
isl_vec *v = NULL;
int *simplex_ids = NULL;
if (!cell)
return -1;
d = isl_basic_set_dim(cell->vertices->bset, isl_dim_set);
total = isl_basic_set_total_dim(cell->vertices->bset);
if (cell->n_vertices == d + 1)
return fn(cell, user);
ctx = isl_cell_get_ctx(cell);
simplex_ids = isl_alloc_array(ctx, int, d + 1);
if (!simplex_ids)
goto error;
v = isl_vec_alloc(ctx, 1 + total);
if (!v)
goto error;
r = triangulate(cell, v, simplex_ids, 0,
cell->ids, cell->n_vertices, fn, user);
isl_vec_free(v);
free(simplex_ids);
isl_cell_free(cell);
return r;
error:
free(simplex_ids);
isl_vec_free(v);
isl_cell_free(cell);
return -1;
}