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isl_convex_hull.c
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isl_convex_hull.c
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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2014 INRIA Rocquencourt
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
* and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
* B.P. 105 - 78153 Le Chesnay, France
*/
#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl_lp_private.h>
#include <isl/map.h>
#include <isl_mat_private.h>
#include <isl_vec_private.h>
#include <isl/set.h>
#include <isl_seq.h>
#include <isl_options_private.h>
#include "isl_equalities.h"
#include "isl_tab.h"
#include <isl_sort.h>
static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set);
/* Return 1 if constraint c is redundant with respect to the constraints
* in bmap. If c is a lower [upper] bound in some variable and bmap
* does not have a lower [upper] bound in that variable, then c cannot
* be redundant and we do not need solve any lp.
*/
int isl_basic_map_constraint_is_redundant(struct isl_basic_map **bmap,
isl_int *c, isl_int *opt_n, isl_int *opt_d)
{
enum isl_lp_result res;
unsigned total;
int i, j;
if (!bmap)
return -1;
total = isl_basic_map_total_dim(*bmap);
for (i = 0; i < total; ++i) {
int sign;
if (isl_int_is_zero(c[1+i]))
continue;
sign = isl_int_sgn(c[1+i]);
for (j = 0; j < (*bmap)->n_ineq; ++j)
if (sign == isl_int_sgn((*bmap)->ineq[j][1+i]))
break;
if (j == (*bmap)->n_ineq)
break;
}
if (i < total)
return 0;
res = isl_basic_map_solve_lp(*bmap, 0, c, (*bmap)->ctx->one,
opt_n, opt_d, NULL);
if (res == isl_lp_unbounded)
return 0;
if (res == isl_lp_error)
return -1;
if (res == isl_lp_empty) {
*bmap = isl_basic_map_set_to_empty(*bmap);
return 0;
}
return !isl_int_is_neg(*opt_n);
}
int isl_basic_set_constraint_is_redundant(struct isl_basic_set **bset,
isl_int *c, isl_int *opt_n, isl_int *opt_d)
{
return isl_basic_map_constraint_is_redundant(
(struct isl_basic_map **)bset, c, opt_n, opt_d);
}
/* Remove redundant
* constraints. If the minimal value along the normal of a constraint
* is the same if the constraint is removed, then the constraint is redundant.
*
* Alternatively, we could have intersected the basic map with the
* corresponding equality and the checked if the dimension was that
* of a facet.
*/
__isl_give isl_basic_map *isl_basic_map_remove_redundancies(
__isl_take isl_basic_map *bmap)
{
struct isl_tab *tab;
if (!bmap)
return NULL;
bmap = isl_basic_map_gauss(bmap, NULL);
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
return bmap;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_REDUNDANT))
return bmap;
if (bmap->n_ineq <= 1)
return bmap;
tab = isl_tab_from_basic_map(bmap, 0);
if (isl_tab_detect_implicit_equalities(tab) < 0)
goto error;
if (isl_tab_detect_redundant(tab) < 0)
goto error;
bmap = isl_basic_map_update_from_tab(bmap, tab);
isl_tab_free(tab);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
return bmap;
error:
isl_tab_free(tab);
isl_basic_map_free(bmap);
return NULL;
}
__isl_give isl_basic_set *isl_basic_set_remove_redundancies(
__isl_take isl_basic_set *bset)
{
return (struct isl_basic_set *)
isl_basic_map_remove_redundancies((struct isl_basic_map *)bset);
}
/* Remove redundant constraints in each of the basic maps.
*/
__isl_give isl_map *isl_map_remove_redundancies(__isl_take isl_map *map)
{
return isl_map_inline_foreach_basic_map(map,
&isl_basic_map_remove_redundancies);
}
__isl_give isl_set *isl_set_remove_redundancies(__isl_take isl_set *set)
{
return isl_map_remove_redundancies(set);
}
/* Check if the set set is bound in the direction of the affine
* constraint c and if so, set the constant term such that the
* resulting constraint is a bounding constraint for the set.
*/
static int uset_is_bound(struct isl_set *set, isl_int *c, unsigned len)
{
int first;
int j;
isl_int opt;
isl_int opt_denom;
isl_int_init(opt);
isl_int_init(opt_denom);
first = 1;
for (j = 0; j < set->n; ++j) {
enum isl_lp_result res;
if (ISL_F_ISSET(set->p[j], ISL_BASIC_SET_EMPTY))
continue;
res = isl_basic_set_solve_lp(set->p[j],
0, c, set->ctx->one, &opt, &opt_denom, NULL);
if (res == isl_lp_unbounded)
break;
if (res == isl_lp_error)
goto error;
if (res == isl_lp_empty) {
set->p[j] = isl_basic_set_set_to_empty(set->p[j]);
if (!set->p[j])
goto error;
continue;
}
if (first || isl_int_is_neg(opt)) {
if (!isl_int_is_one(opt_denom))
isl_seq_scale(c, c, opt_denom, len);
isl_int_sub(c[0], c[0], opt);
}
first = 0;
}
isl_int_clear(opt);
isl_int_clear(opt_denom);
return j >= set->n;
error:
isl_int_clear(opt);
isl_int_clear(opt_denom);
return -1;
}
__isl_give isl_basic_map *isl_basic_map_set_rational(
__isl_take isl_basic_set *bmap)
{
if (!bmap)
return NULL;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
return bmap;
bmap = isl_basic_map_cow(bmap);
if (!bmap)
return NULL;
ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
return isl_basic_map_finalize(bmap);
}
__isl_give isl_basic_set *isl_basic_set_set_rational(
__isl_take isl_basic_set *bset)
{
return isl_basic_map_set_rational(bset);
}
__isl_give isl_map *isl_map_set_rational(__isl_take isl_map *map)
{
int i;
map = isl_map_cow(map);
if (!map)
return NULL;
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_set_rational(map->p[i]);
if (!map->p[i])
goto error;
}
return map;
error:
isl_map_free(map);
return NULL;
}
__isl_give isl_set *isl_set_set_rational(__isl_take isl_set *set)
{
return isl_map_set_rational(set);
}
static struct isl_basic_set *isl_basic_set_add_equality(
struct isl_basic_set *bset, isl_int *c)
{
int i;
unsigned dim;
if (!bset)
return NULL;
if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
return bset;
isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
isl_assert(bset->ctx, bset->n_div == 0, goto error);
dim = isl_basic_set_n_dim(bset);
bset = isl_basic_set_cow(bset);
bset = isl_basic_set_extend(bset, 0, dim, 0, 1, 0);
i = isl_basic_set_alloc_equality(bset);
if (i < 0)
goto error;
isl_seq_cpy(bset->eq[i], c, 1 + dim);
return bset;
error:
isl_basic_set_free(bset);
return NULL;
}
static struct isl_set *isl_set_add_basic_set_equality(struct isl_set *set, isl_int *c)
{
int i;
set = isl_set_cow(set);
if (!set)
return NULL;
for (i = 0; i < set->n; ++i) {
set->p[i] = isl_basic_set_add_equality(set->p[i], c);
if (!set->p[i])
goto error;
}
return set;
error:
isl_set_free(set);
return NULL;
}
/* Given a union of basic sets, construct the constraints for wrapping
* a facet around one of its ridges.
* In particular, if each of n the d-dimensional basic sets i in "set"
* contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0
* and is defined by the constraints
* [ 1 ]
* A_i [ x ] >= 0
*
* then the resulting set is of dimension n*(1+d) and has as constraints
*
* [ a_i ]
* A_i [ x_i ] >= 0
*
* a_i >= 0
*
* \sum_i x_{i,1} = 1
*/
static struct isl_basic_set *wrap_constraints(struct isl_set *set)
{
struct isl_basic_set *lp;
unsigned n_eq;
unsigned n_ineq;
int i, j, k;
unsigned dim, lp_dim;
if (!set)
return NULL;
dim = 1 + isl_set_n_dim(set);
n_eq = 1;
n_ineq = set->n;
for (i = 0; i < set->n; ++i) {
n_eq += set->p[i]->n_eq;
n_ineq += set->p[i]->n_ineq;
}
lp = isl_basic_set_alloc(set->ctx, 0, dim * set->n, 0, n_eq, n_ineq);
lp = isl_basic_set_set_rational(lp);
if (!lp)
return NULL;
lp_dim = isl_basic_set_n_dim(lp);
k = isl_basic_set_alloc_equality(lp);
isl_int_set_si(lp->eq[k][0], -1);
for (i = 0; i < set->n; ++i) {
isl_int_set_si(lp->eq[k][1+dim*i], 0);
isl_int_set_si(lp->eq[k][1+dim*i+1], 1);
isl_seq_clr(lp->eq[k]+1+dim*i+2, dim-2);
}
for (i = 0; i < set->n; ++i) {
k = isl_basic_set_alloc_inequality(lp);
isl_seq_clr(lp->ineq[k], 1+lp_dim);
isl_int_set_si(lp->ineq[k][1+dim*i], 1);
for (j = 0; j < set->p[i]->n_eq; ++j) {
k = isl_basic_set_alloc_equality(lp);
isl_seq_clr(lp->eq[k], 1+dim*i);
isl_seq_cpy(lp->eq[k]+1+dim*i, set->p[i]->eq[j], dim);
isl_seq_clr(lp->eq[k]+1+dim*(i+1), dim*(set->n-i-1));
}
for (j = 0; j < set->p[i]->n_ineq; ++j) {
k = isl_basic_set_alloc_inequality(lp);
isl_seq_clr(lp->ineq[k], 1+dim*i);
isl_seq_cpy(lp->ineq[k]+1+dim*i, set->p[i]->ineq[j], dim);
isl_seq_clr(lp->ineq[k]+1+dim*(i+1), dim*(set->n-i-1));
}
}
return lp;
}
/* Given a facet "facet" of the convex hull of "set" and a facet "ridge"
* of that facet, compute the other facet of the convex hull that contains
* the ridge.
*
* We first transform the set such that the facet constraint becomes
*
* x_1 >= 0
*
* I.e., the facet lies in
*
* x_1 = 0
*
* and on that facet, the constraint that defines the ridge is
*
* x_2 >= 0
*
* (This transformation is not strictly needed, all that is needed is
* that the ridge contains the origin.)
*
* Since the ridge contains the origin, the cone of the convex hull
* will be of the form
*
* x_1 >= 0
* x_2 >= a x_1
*
* with this second constraint defining the new facet.
* The constant a is obtained by settting x_1 in the cone of the
* convex hull to 1 and minimizing x_2.
* Now, each element in the cone of the convex hull is the sum
* of elements in the cones of the basic sets.
* If a_i is the dilation factor of basic set i, then the problem
* we need to solve is
*
* min \sum_i x_{i,2}
* st
* \sum_i x_{i,1} = 1
* a_i >= 0
* [ a_i ]
* A [ x_i ] >= 0
*
* with
* [ 1 ]
* A_i [ x_i ] >= 0
*
* the constraints of each (transformed) basic set.
* If a = n/d, then the constraint defining the new facet (in the transformed
* space) is
*
* -n x_1 + d x_2 >= 0
*
* In the original space, we need to take the same combination of the
* corresponding constraints "facet" and "ridge".
*
* If a = -infty = "-1/0", then we just return the original facet constraint.
* This means that the facet is unbounded, but has a bounded intersection
* with the union of sets.
*/
isl_int *isl_set_wrap_facet(__isl_keep isl_set *set,
isl_int *facet, isl_int *ridge)
{
int i;
isl_ctx *ctx;
struct isl_mat *T = NULL;
struct isl_basic_set *lp = NULL;
struct isl_vec *obj;
enum isl_lp_result res;
isl_int num, den;
unsigned dim;
if (!set)
return NULL;
ctx = set->ctx;
set = isl_set_copy(set);
set = isl_set_set_rational(set);
dim = 1 + isl_set_n_dim(set);
T = isl_mat_alloc(ctx, 3, dim);
if (!T)
goto error;
isl_int_set_si(T->row[0][0], 1);
isl_seq_clr(T->row[0]+1, dim - 1);
isl_seq_cpy(T->row[1], facet, dim);
isl_seq_cpy(T->row[2], ridge, dim);
T = isl_mat_right_inverse(T);
set = isl_set_preimage(set, T);
T = NULL;
if (!set)
goto error;
lp = wrap_constraints(set);
obj = isl_vec_alloc(ctx, 1 + dim*set->n);
if (!obj)
goto error;
isl_int_set_si(obj->block.data[0], 0);
for (i = 0; i < set->n; ++i) {
isl_seq_clr(obj->block.data + 1 + dim*i, 2);
isl_int_set_si(obj->block.data[1 + dim*i+2], 1);
isl_seq_clr(obj->block.data + 1 + dim*i+3, dim-3);
}
isl_int_init(num);
isl_int_init(den);
res = isl_basic_set_solve_lp(lp, 0,
obj->block.data, ctx->one, &num, &den, NULL);
if (res == isl_lp_ok) {
isl_int_neg(num, num);
isl_seq_combine(facet, num, facet, den, ridge, dim);
isl_seq_normalize(ctx, facet, dim);
}
isl_int_clear(num);
isl_int_clear(den);
isl_vec_free(obj);
isl_basic_set_free(lp);
isl_set_free(set);
if (res == isl_lp_error)
return NULL;
isl_assert(ctx, res == isl_lp_ok || res == isl_lp_unbounded,
return NULL);
return facet;
error:
isl_basic_set_free(lp);
isl_mat_free(T);
isl_set_free(set);
return NULL;
}
/* Compute the constraint of a facet of "set".
*
* We first compute the intersection with a bounding constraint
* that is orthogonal to one of the coordinate axes.
* If the affine hull of this intersection has only one equality,
* we have found a facet.
* Otherwise, we wrap the current bounding constraint around
* one of the equalities of the face (one that is not equal to
* the current bounding constraint).
* This process continues until we have found a facet.
* The dimension of the intersection increases by at least
* one on each iteration, so termination is guaranteed.
*/
static __isl_give isl_mat *initial_facet_constraint(__isl_keep isl_set *set)
{
struct isl_set *slice = NULL;
struct isl_basic_set *face = NULL;
int i;
unsigned dim = isl_set_n_dim(set);
int is_bound;
isl_mat *bounds = NULL;
isl_assert(set->ctx, set->n > 0, goto error);
bounds = isl_mat_alloc(set->ctx, 1, 1 + dim);
if (!bounds)
return NULL;
isl_seq_clr(bounds->row[0], dim);
isl_int_set_si(bounds->row[0][1 + dim - 1], 1);
is_bound = uset_is_bound(set, bounds->row[0], 1 + dim);
if (is_bound < 0)
goto error;
isl_assert(set->ctx, is_bound, goto error);
isl_seq_normalize(set->ctx, bounds->row[0], 1 + dim);
bounds->n_row = 1;
for (;;) {
slice = isl_set_copy(set);
slice = isl_set_add_basic_set_equality(slice, bounds->row[0]);
face = isl_set_affine_hull(slice);
if (!face)
goto error;
if (face->n_eq == 1) {
isl_basic_set_free(face);
break;
}
for (i = 0; i < face->n_eq; ++i)
if (!isl_seq_eq(bounds->row[0], face->eq[i], 1 + dim) &&
!isl_seq_is_neg(bounds->row[0],
face->eq[i], 1 + dim))
break;
isl_assert(set->ctx, i < face->n_eq, goto error);
if (!isl_set_wrap_facet(set, bounds->row[0], face->eq[i]))
goto error;
isl_seq_normalize(set->ctx, bounds->row[0], bounds->n_col);
isl_basic_set_free(face);
}
return bounds;
error:
isl_basic_set_free(face);
isl_mat_free(bounds);
return NULL;
}
/* Given the bounding constraint "c" of a facet of the convex hull of "set",
* compute a hyperplane description of the facet, i.e., compute the facets
* of the facet.
*
* We compute an affine transformation that transforms the constraint
*
* [ 1 ]
* c [ x ] = 0
*
* to the constraint
*
* z_1 = 0
*
* by computing the right inverse U of a matrix that starts with the rows
*
* [ 1 0 ]
* [ c ]
*
* Then
* [ 1 ] [ 1 ]
* [ x ] = U [ z ]
* and
* [ 1 ] [ 1 ]
* [ z ] = Q [ x ]
*
* with Q = U^{-1}
* Since z_1 is zero, we can drop this variable as well as the corresponding
* column of U to obtain
*
* [ 1 ] [ 1 ]
* [ x ] = U' [ z' ]
* and
* [ 1 ] [ 1 ]
* [ z' ] = Q' [ x ]
*
* with Q' equal to Q, but without the corresponding row.
* After computing the facets of the facet in the z' space,
* we convert them back to the x space through Q.
*/
static struct isl_basic_set *compute_facet(struct isl_set *set, isl_int *c)
{
struct isl_mat *m, *U, *Q;
struct isl_basic_set *facet = NULL;
struct isl_ctx *ctx;
unsigned dim;
ctx = set->ctx;
set = isl_set_copy(set);
dim = isl_set_n_dim(set);
m = isl_mat_alloc(set->ctx, 2, 1 + dim);
if (!m)
goto error;
isl_int_set_si(m->row[0][0], 1);
isl_seq_clr(m->row[0]+1, dim);
isl_seq_cpy(m->row[1], c, 1+dim);
U = isl_mat_right_inverse(m);
Q = isl_mat_right_inverse(isl_mat_copy(U));
U = isl_mat_drop_cols(U, 1, 1);
Q = isl_mat_drop_rows(Q, 1, 1);
set = isl_set_preimage(set, U);
facet = uset_convex_hull_wrap_bounded(set);
facet = isl_basic_set_preimage(facet, Q);
if (facet && facet->n_eq != 0)
isl_die(ctx, isl_error_internal, "unexpected equality",
return isl_basic_set_free(facet));
return facet;
error:
isl_basic_set_free(facet);
isl_set_free(set);
return NULL;
}
/* Given an initial facet constraint, compute the remaining facets.
* We do this by running through all facets found so far and computing
* the adjacent facets through wrapping, adding those facets that we
* hadn't already found before.
*
* For each facet we have found so far, we first compute its facets
* in the resulting convex hull. That is, we compute the ridges
* of the resulting convex hull contained in the facet.
* We also compute the corresponding facet in the current approximation
* of the convex hull. There is no need to wrap around the ridges
* in this facet since that would result in a facet that is already
* present in the current approximation.
*
* This function can still be significantly optimized by checking which of
* the facets of the basic sets are also facets of the convex hull and
* using all the facets so far to help in constructing the facets of the
* facets
* and/or
* using the technique in section "3.1 Ridge Generation" of
* "Extended Convex Hull" by Fukuda et al.
*/
static struct isl_basic_set *extend(struct isl_basic_set *hull,
struct isl_set *set)
{
int i, j, f;
int k;
struct isl_basic_set *facet = NULL;
struct isl_basic_set *hull_facet = NULL;
unsigned dim;
if (!hull)
return NULL;
isl_assert(set->ctx, set->n > 0, goto error);
dim = isl_set_n_dim(set);
for (i = 0; i < hull->n_ineq; ++i) {
facet = compute_facet(set, hull->ineq[i]);
facet = isl_basic_set_add_equality(facet, hull->ineq[i]);
facet = isl_basic_set_gauss(facet, NULL);
facet = isl_basic_set_normalize_constraints(facet);
hull_facet = isl_basic_set_copy(hull);
hull_facet = isl_basic_set_add_equality(hull_facet, hull->ineq[i]);
hull_facet = isl_basic_set_gauss(hull_facet, NULL);
hull_facet = isl_basic_set_normalize_constraints(hull_facet);
if (!facet || !hull_facet)
goto error;
hull = isl_basic_set_cow(hull);
hull = isl_basic_set_extend_space(hull,
isl_space_copy(hull->dim), 0, 0, facet->n_ineq);
if (!hull)
goto error;
for (j = 0; j < facet->n_ineq; ++j) {
for (f = 0; f < hull_facet->n_ineq; ++f)
if (isl_seq_eq(facet->ineq[j],
hull_facet->ineq[f], 1 + dim))
break;
if (f < hull_facet->n_ineq)
continue;
k = isl_basic_set_alloc_inequality(hull);
if (k < 0)
goto error;
isl_seq_cpy(hull->ineq[k], hull->ineq[i], 1+dim);
if (!isl_set_wrap_facet(set, hull->ineq[k], facet->ineq[j]))
goto error;
}
isl_basic_set_free(hull_facet);
isl_basic_set_free(facet);
}
hull = isl_basic_set_simplify(hull);
hull = isl_basic_set_finalize(hull);
return hull;
error:
isl_basic_set_free(hull_facet);
isl_basic_set_free(facet);
isl_basic_set_free(hull);
return NULL;
}
/* Special case for computing the convex hull of a one dimensional set.
* We simply collect the lower and upper bounds of each basic set
* and the biggest of those.
*/
static struct isl_basic_set *convex_hull_1d(struct isl_set *set)
{
struct isl_mat *c = NULL;
isl_int *lower = NULL;
isl_int *upper = NULL;
int i, j, k;
isl_int a, b;
struct isl_basic_set *hull;
for (i = 0; i < set->n; ++i) {
set->p[i] = isl_basic_set_simplify(set->p[i]);
if (!set->p[i])
goto error;
}
set = isl_set_remove_empty_parts(set);
if (!set)
goto error;
isl_assert(set->ctx, set->n > 0, goto error);
c = isl_mat_alloc(set->ctx, 2, 2);
if (!c)
goto error;
if (set->p[0]->n_eq > 0) {
isl_assert(set->ctx, set->p[0]->n_eq == 1, goto error);
lower = c->row[0];
upper = c->row[1];
if (isl_int_is_pos(set->p[0]->eq[0][1])) {
isl_seq_cpy(lower, set->p[0]->eq[0], 2);
isl_seq_neg(upper, set->p[0]->eq[0], 2);
} else {
isl_seq_neg(lower, set->p[0]->eq[0], 2);
isl_seq_cpy(upper, set->p[0]->eq[0], 2);
}
} else {
for (j = 0; j < set->p[0]->n_ineq; ++j) {
if (isl_int_is_pos(set->p[0]->ineq[j][1])) {
lower = c->row[0];
isl_seq_cpy(lower, set->p[0]->ineq[j], 2);
} else {
upper = c->row[1];
isl_seq_cpy(upper, set->p[0]->ineq[j], 2);
}
}
}
isl_int_init(a);
isl_int_init(b);
for (i = 0; i < set->n; ++i) {
struct isl_basic_set *bset = set->p[i];
int has_lower = 0;
int has_upper = 0;
for (j = 0; j < bset->n_eq; ++j) {
has_lower = 1;
has_upper = 1;
if (lower) {
isl_int_mul(a, lower[0], bset->eq[j][1]);
isl_int_mul(b, lower[1], bset->eq[j][0]);
if (isl_int_lt(a, b) && isl_int_is_pos(bset->eq[j][1]))
isl_seq_cpy(lower, bset->eq[j], 2);
if (isl_int_gt(a, b) && isl_int_is_neg(bset->eq[j][1]))
isl_seq_neg(lower, bset->eq[j], 2);
}
if (upper) {
isl_int_mul(a, upper[0], bset->eq[j][1]);
isl_int_mul(b, upper[1], bset->eq[j][0]);
if (isl_int_lt(a, b) && isl_int_is_pos(bset->eq[j][1]))
isl_seq_neg(upper, bset->eq[j], 2);
if (isl_int_gt(a, b) && isl_int_is_neg(bset->eq[j][1]))
isl_seq_cpy(upper, bset->eq[j], 2);
}
}
for (j = 0; j < bset->n_ineq; ++j) {
if (isl_int_is_pos(bset->ineq[j][1]))
has_lower = 1;
if (isl_int_is_neg(bset->ineq[j][1]))
has_upper = 1;
if (lower && isl_int_is_pos(bset->ineq[j][1])) {
isl_int_mul(a, lower[0], bset->ineq[j][1]);
isl_int_mul(b, lower[1], bset->ineq[j][0]);
if (isl_int_lt(a, b))
isl_seq_cpy(lower, bset->ineq[j], 2);
}
if (upper && isl_int_is_neg(bset->ineq[j][1])) {
isl_int_mul(a, upper[0], bset->ineq[j][1]);
isl_int_mul(b, upper[1], bset->ineq[j][0]);
if (isl_int_gt(a, b))
isl_seq_cpy(upper, bset->ineq[j], 2);
}
}
if (!has_lower)
lower = NULL;
if (!has_upper)
upper = NULL;
}
isl_int_clear(a);
isl_int_clear(b);
hull = isl_basic_set_alloc(set->ctx, 0, 1, 0, 0, 2);
hull = isl_basic_set_set_rational(hull);
if (!hull)
goto error;
if (lower) {
k = isl_basic_set_alloc_inequality(hull);
isl_seq_cpy(hull->ineq[k], lower, 2);
}
if (upper) {
k = isl_basic_set_alloc_inequality(hull);
isl_seq_cpy(hull->ineq[k], upper, 2);
}
hull = isl_basic_set_finalize(hull);
isl_set_free(set);
isl_mat_free(c);
return hull;
error:
isl_set_free(set);
isl_mat_free(c);
return NULL;
}
static struct isl_basic_set *convex_hull_0d(struct isl_set *set)
{
struct isl_basic_set *convex_hull;
if (!set)
return NULL;
if (isl_set_is_empty(set))
convex_hull = isl_basic_set_empty(isl_space_copy(set->dim));
else
convex_hull = isl_basic_set_universe(isl_space_copy(set->dim));
isl_set_free(set);
return convex_hull;
}
/* Compute the convex hull of a pair of basic sets without any parameters or
* integer divisions using Fourier-Motzkin elimination.
* The convex hull is the set of all points that can be written as
* the sum of points from both basic sets (in homogeneous coordinates).
* We set up the constraints in a space with dimensions for each of
* the three sets and then project out the dimensions corresponding
* to the two original basic sets, retaining only those corresponding
* to the convex hull.
*/
static struct isl_basic_set *convex_hull_pair_elim(struct isl_basic_set *bset1,
struct isl_basic_set *bset2)
{
int i, j, k;
struct isl_basic_set *bset[2];
struct isl_basic_set *hull = NULL;
unsigned dim;
if (!bset1 || !bset2)
goto error;
dim = isl_basic_set_n_dim(bset1);
hull = isl_basic_set_alloc(bset1->ctx, 0, 2 + 3 * dim, 0,
1 + dim + bset1->n_eq + bset2->n_eq,
2 + bset1->n_ineq + bset2->n_ineq);
bset[0] = bset1;
bset[1] = bset2;
for (i = 0; i < 2; ++i) {
for (j = 0; j < bset[i]->n_eq; ++j) {
k = isl_basic_set_alloc_equality(hull);
if (k < 0)
goto error;
isl_seq_clr(hull->eq[k], (i+1) * (1+dim));
isl_seq_clr(hull->eq[k]+(i+2)*(1+dim), (1-i)*(1+dim));
isl_seq_cpy(hull->eq[k]+(i+1)*(1+dim), bset[i]->eq[j],
1+dim);
}
for (j = 0; j < bset[i]->n_ineq; ++j) {
k = isl_basic_set_alloc_inequality(hull);
if (k < 0)
goto error;
isl_seq_clr(hull->ineq[k], (i+1) * (1+dim));
isl_seq_clr(hull->ineq[k]+(i+2)*(1+dim), (1-i)*(1+dim));
isl_seq_cpy(hull->ineq[k]+(i+1)*(1+dim),
bset[i]->ineq[j], 1+dim);
}
k = isl_basic_set_alloc_inequality(hull);
if (k < 0)
goto error;
isl_seq_clr(hull->ineq[k], 1+2+3*dim);
isl_int_set_si(hull->ineq[k][(i+1)*(1+dim)], 1);
}
for (j = 0; j < 1+dim; ++j) {
k = isl_basic_set_alloc_equality(hull);
if (k < 0)
goto error;
isl_seq_clr(hull->eq[k], 1+2+3*dim);
isl_int_set_si(hull->eq[k][j], -1);
isl_int_set_si(hull->eq[k][1+dim+j], 1);
isl_int_set_si(hull->eq[k][2*(1+dim)+j], 1);
}
hull = isl_basic_set_set_rational(hull);
hull = isl_basic_set_remove_dims(hull, isl_dim_set, dim, 2*(1+dim));
hull = isl_basic_set_remove_redundancies(hull);
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return hull;
error:
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
isl_basic_set_free(hull);
return NULL;
}
/* Is the set bounded for each value of the parameters?
*/
int isl_basic_set_is_bounded(__isl_keep isl_basic_set *bset)
{
struct isl_tab *tab;
int bounded;
if (!bset)
return -1;
if (isl_basic_set_plain_is_empty(bset))
return 1;
tab = isl_tab_from_recession_cone(bset, 1);
bounded = isl_tab_cone_is_bounded(tab);
isl_tab_free(tab);
return bounded;
}
/* Is the image bounded for each value of the parameters and
* the domain variables?
*/
int isl_basic_map_image_is_bounded(__isl_keep isl_basic_map *bmap)
{
unsigned nparam = isl_basic_map_dim(bmap, isl_dim_param);
unsigned n_in = isl_basic_map_dim(bmap, isl_dim_in);
int bounded;
bmap = isl_basic_map_copy(bmap);
bmap = isl_basic_map_cow(bmap);
bmap = isl_basic_map_move_dims(bmap, isl_dim_param, nparam,
isl_dim_in, 0, n_in);
bounded = isl_basic_set_is_bounded((isl_basic_set *)bmap);
isl_basic_map_free(bmap);
return bounded;
}
/* Is the set bounded for each value of the parameters?
*/
int isl_set_is_bounded(__isl_keep isl_set *set)
{
int i;
if (!set)
return -1;
for (i = 0; i < set->n; ++i) {
int bounded = isl_basic_set_is_bounded(set->p[i]);
if (!bounded || bounded < 0)
return bounded;
}
return 1;
}
/* Compute the lineality space of the convex hull of bset1 and bset2.
*
* We first compute the intersection of the recession cone of bset1
* with the negative of the recession cone of bset2 and then compute
* the linear hull of the resulting cone.
*/
static struct isl_basic_set *induced_lineality_space(
struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
int i, k;
struct isl_basic_set *lin = NULL;
unsigned dim;
if (!bset1 || !bset2)
goto error;
dim = isl_basic_set_total_dim(bset1);
lin = isl_basic_set_alloc_space(isl_basic_set_get_space(bset1), 0,
bset1->n_eq + bset2->n_eq,
bset1->n_ineq + bset2->n_ineq);
lin = isl_basic_set_set_rational(lin);
if (!lin)
goto error;
for (i = 0; i < bset1->n_eq; ++i) {
k = isl_basic_set_alloc_equality(lin);
if (k < 0)
goto error;
isl_int_set_si(lin->eq[k][0], 0);
isl_seq_cpy(lin->eq[k] + 1, bset1->eq[i] + 1, dim);
}
for (i = 0; i < bset1->n_ineq; ++i) {
k = isl_basic_set_alloc_inequality(lin);
if (k < 0)
goto error;
isl_int_set_si(lin->ineq[k][0], 0);
isl_seq_cpy(lin->ineq[k] + 1, bset1->ineq[i] + 1, dim);
}
for (i = 0; i < bset2->n_eq; ++i) {
k = isl_basic_set_alloc_equality(lin);
if (k < 0)
goto error;
isl_int_set_si(lin->eq[k][0], 0);
isl_seq_neg(lin->eq[k] + 1, bset2->eq[i] + 1, dim);
}
for (i = 0; i < bset2->n_ineq; ++i) {
k = isl_basic_set_alloc_inequality(lin);
if (k < 0)