/*
* 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)
isl_assert(ctx, facet->n_eq == 0, goto error);
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)
goto error;
isl_int_set_si(lin->ineq[k][0], 0);
isl_seq_neg(lin->ineq[k] + 1, bset2->ineq[i] + 1, dim);
}
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return isl_basic_set_affine_hull(lin);
error:
isl_basic_set_free(lin);
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return NULL;
}
static struct isl_basic_set *uset_convex_hull(struct isl_set *set);
/* Given a set and a linear space "lin" of dimension n > 0,
* project the linear space from the set, compute the convex hull
* and then map the set back to the original space.
*
* Let
*
* M x = 0
*
* describe the linear space. We first compute the Hermite normal
* form H = M U of M = H Q, to obtain
*
* H Q x = 0
*
* The last n rows of H will be zero, so the last n variables of x' = Q x
* are the one we want to project out. We do this by transforming each
* basic set A x >= b to A U x' >= b and then removing the last n dimensions.
* After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
* we transform the hull back to the original space as A' Q_1 x >= b',
* with Q_1 all but the last n rows of Q.
*/
static struct isl_basic_set *modulo_lineality(struct isl_set *set,
struct isl_basic_set *lin)
{
unsigned total = isl_basic_set_total_dim(lin);
unsigned lin_dim;
struct isl_basic_set *hull;
struct isl_mat *M, *U, *Q;
if (!set || !lin)
goto error;
lin_dim = total - lin->n_eq;
M = isl_mat_sub_alloc6(set->ctx, lin->eq, 0, lin->n_eq, 1, total);
M = isl_mat_left_hermite(M, 0, &U, &Q);
if (!M)
goto error;
isl_mat_free(M);
isl_basic_set_free(lin);
Q = isl_mat_drop_rows(Q, Q->n_row - lin_dim, lin_dim);
U = isl_mat_lin_to_aff(U);
Q = isl_mat_lin_to_aff(Q);
set = isl_set_preimage(set, U);
set = isl_set_remove_dims(set, isl_dim_set, total - lin_dim, lin_dim);
hull = uset_convex_hull(set);
hull = isl_basic_set_preimage(hull, Q);
return hull;
error:
isl_basic_set_free(lin);
isl_set_free(set);
return NULL;
}
/* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
* set up an LP for solving
*
* \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
*
* \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
* The next \alpha{ij} correspond to the equalities and come in pairs.
* The final \alpha{ij} correspond to the inequalities.
*/
static struct isl_basic_set *valid_direction_lp(
struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
isl_space *dim;
struct isl_basic_set *lp;
unsigned d;
int n;
int i, j, k;
if (!bset1 || !bset2)
goto error;
d = 1 + isl_basic_set_total_dim(bset1);
n = 2 +
2 * bset1->n_eq + bset1->n_ineq + 2 * bset2->n_eq + bset2->n_ineq;
dim = isl_space_set_alloc(bset1->ctx, 0, n);
lp = isl_basic_set_alloc_space(dim, 0, d, n);
if (!lp)
goto error;
for (i = 0; i < n; ++i) {
k = isl_basic_set_alloc_inequality(lp);
if (k < 0)
goto error;
isl_seq_clr(lp->ineq[k] + 1, n);
isl_int_set_si(lp->ineq[k][0], -1);
isl_int_set_si(lp->ineq[k][1 + i], 1);
}
for (i = 0; i < d; ++i) {
k = isl_basic_set_alloc_equality(lp);
if (k < 0)
goto error;
n = 0;
isl_int_set_si(lp->eq[k][n], 0); n++;
/* positivity constraint 1 >= 0 */
isl_int_set_si(lp->eq[k][n], i == 0); n++;
for (j = 0; j < bset1->n_eq; ++j) {
isl_int_set(lp->eq[k][n], bset1->eq[j][i]); n++;
isl_int_neg(lp->eq[k][n], bset1->eq[j][i]); n++;
}
for (j = 0; j < bset1->n_ineq; ++j) {
isl_int_set(lp->eq[k][n], bset1->ineq[j][i]); n++;
}
/* positivity constraint 1 >= 0 */
isl_int_set_si(lp->eq[k][n], -(i == 0)); n++;
for (j = 0; j < bset2->n_eq; ++j) {
isl_int_neg(lp->eq[k][n], bset2->eq[j][i]); n++;
isl_int_set(lp->eq[k][n], bset2->eq[j][i]); n++;
}
for (j = 0; j < bset2->n_ineq; ++j) {
isl_int_neg(lp->eq[k][n], bset2->ineq[j][i]); n++;
}
}
lp = isl_basic_set_gauss(lp, NULL);
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return lp;
error:
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return NULL;
}
/* Compute a vector s in the homogeneous space such that <s, r> > 0
* for all rays in the homogeneous space of the two cones that correspond
* to the input polyhedra bset1 and bset2.
*
* We compute s as a vector that satisfies
*
* s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
*
* with h_{ij} the normals of the facets of polyhedron i
* (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
* strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
* We first set up an LP with as variables the \alpha{ij}.
* In this formulation, for each polyhedron i,
* the first constraint is the positivity constraint, followed by pairs
* of variables for the equalities, followed by variables for the inequalities.
* We then simply pick a feasible solution and compute s using (*).
*
* Note that we simply pick any valid direction and make no attempt
* to pick a "good" or even the "best" valid direction.
*/
static struct isl_vec *valid_direction(
struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
struct isl_basic_set *lp;
struct isl_tab *tab;
struct isl_vec *sample = NULL;
struct isl_vec *dir;
unsigned d;
int i;
int n;
if (!bset1 || !bset2)
goto error;
lp = valid_direction_lp(isl_basic_set_copy(bset1),
isl_basic_set_copy(bset2));
tab = isl_tab_from_basic_set(lp, 0);
sample = isl_tab_get_sample_value(tab);
isl_tab_free(tab);
isl_basic_set_free(lp);
if (!sample)
goto error;
d = isl_basic_set_total_dim(bset1);
dir = isl_vec_alloc(bset1->ctx, 1 + d);
if (!dir)
goto error;
isl_seq_clr(dir->block.data + 1, dir->size - 1);
n = 1;
/* positivity constraint 1 >= 0 */
isl_int_set(dir->block.data[0], sample->block.data[n]); n++;
for (i = 0; i < bset1->n_eq; ++i) {
isl_int_sub(sample->block.data[n],
sample->block.data[n], sample->block.data[n+1]);
isl_seq_combine(dir->block.data,
bset1->ctx->one, dir->block.data,
sample->block.data[n], bset1->eq[i], 1 + d);
n += 2;
}
for (i = 0; i < bset1->n_ineq; ++i)
isl_seq_combine(dir->block.data,
bset1->ctx->one, dir->block.data,
sample->block.data[n++], bset1->ineq[i], 1 + d);
isl_vec_free(sample);
isl_seq_normalize(bset1->ctx, dir->el, dir->size);
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return dir;
error:
isl_vec_free(sample);
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return NULL;
}
/* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
* compute b_i' + A_i' x' >= 0, with
*
* [ b_i A_i ] [ y' ] [ y' ]
* [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
*
* In particular, add the "positivity constraint" and then perform
* the mapping.
*/
static struct isl_basic_set *homogeneous_map(struct isl_basic_set *bset,
struct isl_mat *T)
{
int k;
if (!bset)
goto error;
bset = isl_basic_set_extend_constraints(bset, 0, 1);
k = isl_basic_set_alloc_inequality(bset);
if (k < 0)
goto error;
isl_seq_clr(bset->ineq[k] + 1, isl_basic_set_total_dim(bset));
isl_int_set_si(bset->ineq[k][0], 1);
bset = isl_basic_set_preimage(bset, T);
return bset;
error:
isl_mat_free(T);
isl_basic_set_free(bset);
return NULL;
}
/* Compute the convex hull of a pair of basic sets without any parameters or
* integer divisions, where the convex hull is known to be pointed,
* but the basic sets may be unbounded.
*
* We turn this problem into the computation of a convex hull of a pair
* _bounded_ polyhedra by "changing the direction of the homogeneous
* dimension". This idea is due to Matthias Koeppe.
*
* Consider the cones in homogeneous space that correspond to the
* input polyhedra. The rays of these cones are also rays of the
* polyhedra if the coordinate that corresponds to the homogeneous
* dimension is zero. That is, if the inner product of the rays
* with the homogeneous direction is zero.
* The cones in the homogeneous space can also be considered to
* correspond to other pairs of polyhedra by chosing a different
* homogeneous direction. To ensure that both of these polyhedra
* are bounded, we need to make sure that all rays of the cones
* correspond to vertices and not to rays.
* Let s be a direction such that <s, r> > 0 for all rays r of both cones.
* Then using s as a homogeneous direction, we obtain a pair of polytopes.
* The vector s is computed in valid_direction.
*
* Note that we need to consider _all_ rays of the cones and not just
* the rays that correspond to rays in the polyhedra. If we were to
* only consider those rays and turn them into vertices, then we
* may inadvertently turn some vertices into rays.
*
* The standard homogeneous direction is the unit vector in the 0th coordinate.
* We therefore transform the two polyhedra such that the selected
* direction is mapped onto this standard direction and then proceed
* with the normal computation.
* Let S be a non-singular square matrix with s as its first row,
* then we want to map the polyhedra to the space
*
* [ y' ] [ y ] [ y ] [ y' ]
* [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
*
* We take S to be the unimodular completion of s to limit the growth
* of the coefficients in the following computations.
*
* Let b_i + A_i x >= 0 be the constraints of polyhedron i.
* We first move to the homogeneous dimension
*
* b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
* y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
*
* Then we change directoin
*
* [ b_i A_i ] [ y' ] [ y' ]
* [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
*
* Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
* resulting in b' + A' x' >= 0, which we then convert back
*
* [ y ] [ y ]
* [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
*
* The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
*/
static struct isl_basic_set *convex_hull_pair_pointed(
struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
struct isl_ctx *ctx = NULL;
struct isl_vec *dir = NULL;
struct isl_mat *T = NULL;
struct isl_mat *T2 = NULL;
struct isl_basic_set *hull;
struct isl_set *set;
if (!bset1 || !bset2)
goto error;
ctx = bset1->ctx;
dir = valid_direction(isl_basic_set_copy(bset1),
isl_basic_set_copy(bset2));
if (!dir)
goto error;
T = isl_mat_alloc(bset1->ctx, dir->size, dir->size);
if (!T)
goto error;
isl_seq_cpy(T->row[0], dir->block.data, dir->size);
T = isl_mat_unimodular_complete(T, 1);
T2 = isl_mat_right_inverse(isl_mat_copy(T));
bset1 = homogeneous_map(bset1, isl_mat_copy(T2));
bset2 = homogeneous_map(bset2, T2);
set = isl_set_alloc_space(isl_basic_set_get_space(bset1), 2, 0);
set = isl_set_add_basic_set(set, bset1);
set = isl_set_add_basic_set(set, bset2);
hull = uset_convex_hull(set);
hull = isl_basic_set_preimage(hull, T);
isl_vec_free(dir);
return hull;
error:
isl_vec_free(dir);
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return NULL;
}
static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set);
static struct isl_basic_set *modulo_affine_hull(
struct isl_set *set, struct isl_basic_set *affine_hull);
/* Compute the convex hull of a pair of basic sets without any parameters or
* integer divisions.
*
* This function is called from uset_convex_hull_unbounded, which
* means that the complete convex hull is unbounded. Some pairs
* of basic sets may still be bounded, though.
* They may even lie inside a lower dimensional space, in which
* case they need to be handled inside their affine hull since
* the main algorithm assumes that the result is full-dimensional.
*
* If the convex hull of the two basic sets would have a non-trivial
* lineality space, we first project out this lineality space.
*/
static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
struct isl_basic_set *bset2)
{
isl_basic_set *lin, *aff;
int bounded1, bounded2;
if (bset1->ctx->opt->convex == ISL_CONVEX_HULL_FM)
return convex_hull_pair_elim(bset1, bset2);
aff = isl_set_affine_hull(isl_basic_set_union(isl_basic_set_copy(bset1),
isl_basic_set_copy(bset2)));
if (!aff)
goto error;
if (aff->n_eq != 0)
return modulo_affine_hull(isl_basic_set_union(bset1, bset2), aff);
isl_basic_set_free(aff);
bounded1 = isl_basic_set_is_bounded(bset1);
bounded2 = isl_basic_set_is_bounded(bset2);
if (bounded1 < 0 || bounded2 < 0)
goto error;
if (bounded1 && bounded2)
return uset_convex_hull_wrap(isl_basic_set_union(bset1, bset2));
if (bounded1 || bounded2)
return convex_hull_pair_pointed(bset1, bset2);
lin = induced_lineality_space(isl_basic_set_copy(bset1),
isl_basic_set_copy(bset2));
if (!lin)
goto error;
if (isl_basic_set_is_universe(lin)) {
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return lin;
}
if (lin->n_eq < isl_basic_set_total_dim(lin)) {
struct isl_set *set;
set = isl_set_alloc_space(isl_basic_set_get_space(bset1), 2, 0);
set = isl_set_add_basic_set(set, bset1);
set = isl_set_add_basic_set(set, bset2);
return modulo_lineality(set, lin);
}
isl_basic_set_free(lin);
return convex_hull_pair_pointed(bset1, bset2);
error:
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return NULL;
}
/* Compute the lineality space of a basic set.
* We currently do not allow the basic set to have any divs.
* We basically just drop the constants and turn every inequality
* into an equality.
*/
struct isl_basic_set *isl_basic_set_lineality_space(struct isl_basic_set *bset)
{
int i, k;
struct isl_basic_set *lin = NULL;
unsigned dim;
if (!bset)
goto error;
isl_assert(bset->ctx, bset->n_div == 0, goto error);
dim = isl_basic_set_total_dim(bset);
lin = isl_basic_set_alloc_space(isl_basic_set_get_space(bset), 0, dim, 0);
if (!lin)
goto error;
for (i = 0; i < bset->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, bset->eq[i] + 1, dim);
}
lin = isl_basic_set_gauss(lin, NULL);
if (!lin)
goto error;
for (i = 0; i < bset->n_ineq && lin->n_eq < dim; ++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, bset->ineq[i] + 1, dim);
lin = isl_basic_set_gauss(lin, NULL);
if (!lin)
goto error;
}
isl_basic_set_free(bset);
return lin;
error:
isl_basic_set_free(lin);
isl_basic_set_free(bset);
return NULL;
}
/* Compute the (linear) hull of the lineality spaces of the basic sets in the
* "underlying" set "set".
*/
static struct isl_basic_set *uset_combined_lineality_space(struct isl_set *set)
{
int i;
struct isl_set *lin = NULL;
if (!set)
return NULL;
if (set->n == 0) {
isl_space *dim = isl_set_get_space(set);
isl_set_free(set);
return isl_basic_set_empty(dim);
}
lin = isl_set_alloc_space(isl_set_get_space(set), set->n, 0);
for (i = 0; i < set->n; ++i)
lin = isl_set_add_basic_set(lin,
isl_basic_set_lineality_space(isl_basic_set_copy(set->p[i])));
isl_set_free(set);
return isl_set_affine_hull(lin);
}
/* Compute the convex hull of a set without any parameters or
* integer divisions.
* In each step, we combined two basic sets until only one
* basic set is left.
* The input basic sets are assumed not to have a non-trivial
* lineality space. If any of the intermediate results has
* a non-trivial lineality space, it is projected out.
*/
static struct isl_basic_set *uset_convex_hull_unbounded(struct isl_set *set)
{
struct isl_basic_set *convex_hull = NULL;
convex_hull = isl_set_copy_basic_set(set);
set = isl_set_drop_basic_set(set, convex_hull);
if (!set)
goto error;
while (set->n > 0) {
struct isl_basic_set *t;
t = isl_set_copy_basic_set(set);
if (!t)
goto error;
set = isl_set_drop_basic_set(set, t);
if (!set)
goto error;
convex_hull = convex_hull_pair(convex_hull, t);
if (set->n == 0)
break;
t = isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull));
if (!t)
goto error;
if (isl_basic_set_is_universe(t)) {
isl_basic_set_free(convex_hull);
convex_hull = t;
break;
}
if (t->n_eq < isl_basic_set_total_dim(t)) {
set = isl_set_add_basic_set(set, convex_hull);
return modulo_lineality(set, t);
}
isl_basic_set_free(t);
}
isl_set_free(set);
return convex_hull;
error:
isl_set_free(set);
isl_basic_set_free(convex_hull);
return NULL;
}
/* Compute an initial hull for wrapping containing a single initial
* facet.
* This function assumes that the given set is bounded.
*/
static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
struct isl_set *set)
{
struct isl_mat *bounds = NULL;
unsigned dim;
int k;
if (!hull)
goto error;
bounds = initial_facet_constraint(set);
if (!bounds)
goto error;
k = isl_basic_set_alloc_inequality(hull);
if (k < 0)
goto error;
dim = isl_set_n_dim(set);
isl_assert(set->ctx, 1 + dim == bounds->n_col, goto error);
isl_seq_cpy(hull->ineq[k], bounds->row[0], bounds->n_col);
isl_mat_free(bounds);
return hull;
error:
isl_basic_set_free(hull);
isl_mat_free(bounds);
return NULL;
}
struct max_constraint {
struct isl_mat *c;
int count;
int ineq;
};
static int max_constraint_equal(const void *entry, const void *val)
{
struct max_constraint *a = (struct max_constraint *)entry;
isl_int *b = (isl_int *)val;
return isl_seq_eq(a->c->row[0] + 1, b, a->c->n_col - 1);
}
static void update_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
isl_int *con, unsigned len, int n, int ineq)
{
struct isl_hash_table_entry *entry;
struct max_constraint *c;
uint32_t c_hash;
c_hash = isl_seq_get_hash(con + 1, len);
entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
con + 1, 0);
if (!entry)
return;
c = entry->data;
if (c->count < n) {
isl_hash_table_remove(ctx, table, entry);
return;
}
c->count++;
if (isl_int_gt(c->c->row[0][0], con[0]))
return;
if (isl_int_eq(c->c->row[0][0], con[0])) {
if (ineq)
c->ineq = ineq;
return;
}
c->c = isl_mat_cow(c->c);
isl_int_set(c->c->row[0][0], con[0]);
c->ineq = ineq;
}
/* Check whether the constraint hash table "table" constains the constraint
* "con".
*/
static int has_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
isl_int *con, unsigned len, int n)
{
struct isl_hash_table_entry *entry;
struct max_constraint *c;
uint32_t c_hash;
c_hash = isl_seq_get_hash(con + 1, len);
entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
con + 1, 0);
if (!entry)
return 0;
c = entry->data;
if (c->count < n)
return 0;
return isl_int_eq(c->c->row[0][0], con[0]);
}
/* Check for inequality constraints of a basic set without equalities
* such that the same or more stringent copies of the constraint appear
* in all of the basic sets. Such constraints are necessarily facet
* constraints of the convex hull.
*
* If the resulting basic set is by chance identical to one of
* the basic sets in "set", then we know that this basic set contains
* all other basic sets and is therefore the convex hull of set.
* In this case we set *is_hull to 1.
*/
static struct isl_basic_set *common_constraints(struct isl_basic_set *hull,
struct isl_set *set, int *is_hull)
{
int i, j, s, n;
int min_constraints;
int best;
struct max_constraint *constraints = NULL;
struct isl_hash_table *table = NULL;
unsigned total;
*is_hull = 0;
for (i = 0; i < set->n; ++i)
if (set->p[i]->n_eq == 0)
break;
if (i >= set->n)
return hull;
min_constraints = set->p[i]->n_ineq;
best = i;
for (i = best + 1; i < set->n; ++i) {
if (set->p[i]->n_eq != 0)
continue;
if (set->p[i]->n_ineq >= min_constraints)
continue;
min_constraints = set->p[i]->n_ineq;
best = i;
}
constraints = isl_calloc_array(hull->ctx, struct max_constraint,
min_constraints);
if (!constraints)
return hull;
table = isl_alloc_type(hull->ctx, struct isl_hash_table);
if (isl_hash_table_init(hull->ctx, table, min_constraints))
goto error;
total = isl_space_dim(set->dim, isl_dim_all);
for (i = 0; i < set->p[best]->n_ineq; ++i) {
constraints[i].c = isl_mat_sub_alloc6(hull->ctx,
set->p[best]->ineq + i, 0, 1, 0, 1 + total);
if (!constraints[i].c)
goto error;
constraints[i].ineq = 1;
}
for (i = 0; i < min_constraints; ++i) {
struct isl_hash_table_entry *entry;
uint32_t c_hash;
c_hash = isl_seq_get_hash(constraints[i].c->row[0] + 1, total);
entry = isl_hash_table_find(hull->ctx, table, c_hash,
max_constraint_equal, constraints[i].c->row[0] + 1, 1);
if (!entry)
goto error;
isl_assert(hull->ctx, !entry->data, goto error);
entry->data = &constraints[i];
}
n = 0;
for (s = 0; s < set->n; ++s) {
if (s == best)
continue;
for (i = 0; i < set->p[s]->n_eq; ++i) {
isl_int *eq = set->p[s]->eq[i];
for (j = 0; j < 2; ++j) {
isl_seq_neg(eq, eq, 1 + total);
update_constraint(hull->ctx, table,
eq, total, n, 0);
}
}
for (i = 0; i < set->p[s]->n_ineq; ++i) {
isl_int *ineq = set->p[s]->ineq[i];
update_constraint(hull->ctx, table, ineq, total, n,
set->p[s]->n_eq == 0);
}
++n;
}
for (i = 0; i < min_constraints; ++i) {
if (constraints[i].count < n)
continue;
if (!constraints[i].ineq)
continue;
j = isl_basic_set_alloc_inequality(hull);
if (j < 0)
goto error;
isl_seq_cpy(hull->ineq[j], constraints[i].c->row[0], 1 + total);
}
for (s = 0; s < set->n; ++s) {
if (set->p[s]->n_eq)
continue;
if (set->p[s]->n_ineq != hull->n_ineq)
continue;
for (i = 0; i < set->p[s]->n_ineq; ++i) {
isl_int *ineq = set->p[s]->ineq[i];
if (!has_constraint(hull->ctx, table, ineq, total, n))
break;
}
if (i == set->p[s]->n_ineq)
*is_hull = 1;
}
isl_hash_table_clear(table);
for (i = 0; i < min_constraints; ++i)
isl_mat_free(constraints[i].c);
free(constraints);
free(table);
return hull;
error:
isl_hash_table_clear(table);
free(table);
if (constraints)
for (i = 0; i < min_constraints; ++i)
isl_mat_free(constraints[i].c);
free(constraints);
return hull;
}
/* Create a template for the convex hull of "set" and fill it up
* obvious facet constraints, if any. If the result happens to
* be the convex hull of "set" then *is_hull is set to 1.
*/
static struct isl_basic_set *proto_hull(struct isl_set *set, int *is_hull)
{
struct isl_basic_set *hull;
unsigned n_ineq;
int i;
n_ineq = 1;
for (i = 0; i < set->n; ++i) {
n_ineq += set->p[i]->n_eq;
n_ineq += set->p[i]->n_ineq;
}
hull = isl_basic_set_alloc_space(isl_space_copy(set->dim), 0, 0, n_ineq);
hull = isl_basic_set_set_rational(hull);
if (!hull)
return NULL;
return common_constraints(hull, set, is_hull);
}
static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set)
{
struct isl_basic_set *hull;
int is_hull;
hull = proto_hull(set, &is_hull);
if (hull && !is_hull) {
if (hull->n_ineq == 0)
hull = initial_hull(hull, set);
hull = extend(hull, set);
}
isl_set_free(set);
return hull;
}
/* Compute the convex hull of a set without any parameters or
* integer divisions. Depending on whether the set is bounded,
* we pass control to the wrapping based convex hull or
* the Fourier-Motzkin elimination based convex hull.
* We also handle a few special cases before checking the boundedness.
*/
static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
{
struct isl_basic_set *convex_hull = NULL;
struct isl_basic_set *lin;
if (isl_set_n_dim(set) == 0)
return convex_hull_0d(set);
set = isl_set_coalesce(set);
set = isl_set_set_rational(set);
if (!set)
goto error;
if (!set)
return NULL;
if (set->n == 1) {
convex_hull = isl_basic_set_copy(set->p[0]);
isl_set_free(set);
return convex_hull;
}
if (isl_set_n_dim(set) == 1)
return convex_hull_1d(set);
if (isl_set_is_bounded(set) &&
set->ctx->opt->convex == ISL_CONVEX_HULL_WRAP)
return uset_convex_hull_wrap(set);
lin = uset_combined_lineality_space(isl_set_copy(set));
if (!lin)
goto error;
if (isl_basic_set_is_universe(lin)) {
isl_set_free(set);
return lin;
}
if (lin->n_eq < isl_basic_set_total_dim(lin))
return modulo_lineality(set, lin);
isl_basic_set_free(lin);
return uset_convex_hull_unbounded(set);
error:
isl_set_free(set);
isl_basic_set_free(convex_hull);
return NULL;
}
/* This is the core procedure, where "set" is a "pure" set, i.e.,
* without parameters or divs and where the convex hull of set is
* known to be full-dimensional.
*/
static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
{
struct isl_basic_set *convex_hull = NULL;
if (!set)
goto error;
if (isl_set_n_dim(set) == 0) {
convex_hull = isl_basic_set_universe(isl_space_copy(set->dim));
isl_set_free(set);
convex_hull = isl_basic_set_set_rational(convex_hull);
return convex_hull;
}
set = isl_set_set_rational(set);
set = isl_set_coalesce(set);
if (!set)
goto error;
if (set->n == 1) {
convex_hull = isl_basic_set_copy(set->p[0]);
isl_set_free(set);
convex_hull = isl_basic_map_remove_redundancies(convex_hull);
return convex_hull;
}
if (isl_set_n_dim(set) == 1)
return convex_hull_1d(set);
return uset_convex_hull_wrap(set);
error:
isl_set_free(set);
return NULL;
}
/* Compute the convex hull of set "set" with affine hull "affine_hull",
* We first remove the equalities (transforming the set), compute the
* convex hull of the transformed set and then add the equalities back
* (after performing the inverse transformation.
*/
static struct isl_basic_set *modulo_affine_hull(
struct isl_set *set, struct isl_basic_set *affine_hull)
{
struct isl_mat *T;
struct isl_mat *T2;
struct isl_basic_set *dummy;
struct isl_basic_set *convex_hull;
dummy = isl_basic_set_remove_equalities(
isl_basic_set_copy(affine_hull), &T, &T2);
if (!dummy)
goto error;
isl_basic_set_free(dummy);
set = isl_set_preimage(set, T);
convex_hull = uset_convex_hull(set);
convex_hull = isl_basic_set_preimage(convex_hull, T2);
convex_hull = isl_basic_set_intersect(convex_hull, affine_hull);
return convex_hull;
error:
isl_basic_set_free(affine_hull);
isl_set_free(set);
return NULL;
}
/* Compute the convex hull of a map.
*
* The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
* specifically, the wrapping of facets to obtain new facets.
*/
struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
{
struct isl_basic_set *bset;
struct isl_basic_map *model = NULL;
struct isl_basic_set *affine_hull = NULL;
struct isl_basic_map *convex_hull = NULL;
struct isl_set *set = NULL;
struct isl_ctx *ctx;
map = isl_map_detect_equalities(map);
map = isl_map_align_divs(map);
if (!map)
goto error;
ctx = map->ctx;
if (map->n == 0) {
convex_hull = isl_basic_map_empty_like_map(map);
isl_map_free(map);
return convex_hull;
}
model = isl_basic_map_copy(map->p[0]);
set = isl_map_underlying_set(map);
if (!set)
goto error;
affine_hull = isl_set_affine_hull(isl_set_copy(set));
if (!affine_hull)
goto error;
if (affine_hull->n_eq != 0)
bset = modulo_affine_hull(set, affine_hull);
else {
isl_basic_set_free(affine_hull);
bset = uset_convex_hull(set);
}
convex_hull = isl_basic_map_overlying_set(bset, model);
if (!convex_hull)
return NULL;
ISL_F_SET(convex_hull, ISL_BASIC_MAP_NO_IMPLICIT);
ISL_F_SET(convex_hull, ISL_BASIC_MAP_ALL_EQUALITIES);
ISL_F_CLR(convex_hull, ISL_BASIC_MAP_RATIONAL);
return convex_hull;
error:
isl_set_free(set);
isl_basic_map_free(model);
return NULL;
}
struct isl_basic_set *isl_set_convex_hull(struct isl_set *set)
{
return (struct isl_basic_set *)
isl_map_convex_hull((struct isl_map *)set);
}
__isl_give isl_basic_map *isl_map_polyhedral_hull(__isl_take isl_map *map)
{
isl_basic_map *hull;
hull = isl_map_convex_hull(map);
return isl_basic_map_remove_divs(hull);
}
__isl_give isl_basic_set *isl_set_polyhedral_hull(__isl_take isl_set *set)
{
return (isl_basic_set *)isl_map_polyhedral_hull((isl_map *)set);
}
struct sh_data_entry {
struct isl_hash_table *table;
struct isl_tab *tab;
};
/* Holds the data needed during the simple hull computation.
* In particular,
* n the number of basic sets in the original set
* hull_table a hash table of already computed constraints
* in the simple hull
* p for each basic set,
* table a hash table of the constraints
* tab the tableau corresponding to the basic set
*/
struct sh_data {
struct isl_ctx *ctx;
unsigned n;
struct isl_hash_table *hull_table;
struct sh_data_entry p[1];
};
static void sh_data_free(struct sh_data *data)
{
int i;
if (!data)
return;
isl_hash_table_free(data->ctx, data->hull_table);
for (i = 0; i < data->n; ++i) {
isl_hash_table_free(data->ctx, data->p[i].table);
isl_tab_free(data->p[i].tab);
}
free(data);
}
struct ineq_cmp_data {
unsigned len;
isl_int *p;
};
static int has_ineq(const void *entry, const void *val)
{
isl_int *row = (isl_int *)entry;
struct ineq_cmp_data *v = (struct ineq_cmp_data *)val;
return isl_seq_eq(row + 1, v->p + 1, v->len) ||
isl_seq_is_neg(row + 1, v->p + 1, v->len);
}
static int hash_ineq(struct isl_ctx *ctx, struct isl_hash_table *table,
isl_int *ineq, unsigned len)
{
uint32_t c_hash;
struct ineq_cmp_data v;
struct isl_hash_table_entry *entry;
v.len = len;
v.p = ineq;
c_hash = isl_seq_get_hash(ineq + 1, len);
entry = isl_hash_table_find(ctx, table, c_hash, has_ineq, &v, 1);
if (!entry)
return - 1;
entry->data = ineq;
return 0;
}
/* Fill hash table "table" with the constraints of "bset".
* Equalities are added as two inequalities.
* The value in the hash table is a pointer to the (in)equality of "bset".
*/
static int hash_basic_set(struct isl_hash_table *table,
struct isl_basic_set *bset)
{
int i, j;
unsigned dim = isl_basic_set_total_dim(bset);
for (i = 0; i < bset->n_eq; ++i) {
for (j = 0; j < 2; ++j) {
isl_seq_neg(bset->eq[i], bset->eq[i], 1 + dim);
if (hash_ineq(bset->ctx, table, bset->eq[i], dim) < 0)
return -1;
}
}
for (i = 0; i < bset->n_ineq; ++i) {
if (hash_ineq(bset->ctx, table, bset->ineq[i], dim) < 0)
return -1;
}
return 0;
}
static struct sh_data *sh_data_alloc(struct isl_set *set, unsigned n_ineq)
{
struct sh_data *data;
int i;
data = isl_calloc(set->ctx, struct sh_data,
sizeof(struct sh_data) +
(set->n - 1) * sizeof(struct sh_data_entry));
if (!data)
return NULL;
data->ctx = set->ctx;
data->n = set->n;
data->hull_table = isl_hash_table_alloc(set->ctx, n_ineq);
if (!data->hull_table)
goto error;
for (i = 0; i < set->n; ++i) {
data->p[i].table = isl_hash_table_alloc(set->ctx,
2 * set->p[i]->n_eq + set->p[i]->n_ineq);
if (!data->p[i].table)
goto error;
if (hash_basic_set(data->p[i].table, set->p[i]) < 0)
goto error;
}
return data;
error:
sh_data_free(data);
return NULL;
}
/* Check if inequality "ineq" is a bound for basic set "j" or if
* it can be relaxed (by increasing the constant term) to become
* a bound for that basic set. In the latter case, the constant
* term is updated.
* Relaxation of the constant term is only allowed if "shift" is set.
*
* Return 1 if "ineq" is a bound
* 0 if "ineq" may attain arbitrarily small values on basic set "j"
* -1 if some error occurred
*/
static int is_bound(struct sh_data *data, struct isl_set *set, int j,
isl_int *ineq, int shift)
{
enum isl_lp_result res;
isl_int opt;
if (!data->p[j].tab) {
data->p[j].tab = isl_tab_from_basic_set(set->p[j], 0);
if (!data->p[j].tab)
return -1;
}
isl_int_init(opt);
res = isl_tab_min(data->p[j].tab, ineq, data->ctx->one,
&opt, NULL, 0);
if (res == isl_lp_ok && isl_int_is_neg(opt)) {
if (shift)
isl_int_sub(ineq[0], ineq[0], opt);
else
res = isl_lp_unbounded;
}
isl_int_clear(opt);
return (res == isl_lp_ok || res == isl_lp_empty) ? 1 :
res == isl_lp_unbounded ? 0 : -1;
}
/* Check if inequality "ineq" from basic set "i" is or can be relaxed to
* become a bound on the whole set. If so, add the (relaxed) inequality
* to "hull". Relaxation is only allowed if "shift" is set.
*
* We first check if "hull" already contains a translate of the inequality.
* If so, we are done.
* Then, we check if any of the previous basic sets contains a translate
* of the inequality. If so, then we have already considered this
* inequality and we are done.
* Otherwise, for each basic set other than "i", we check if the inequality
* is a bound on the basic set.
* For previous basic sets, we know that they do not contain a translate
* of the inequality, so we directly call is_bound.
* For following basic sets, we first check if a translate of the
* inequality appears in its description and if so directly update
* the inequality accordingly.
*/
static struct isl_basic_set *add_bound(struct isl_basic_set *hull,
struct sh_data *data, struct isl_set *set, int i, isl_int *ineq,
int shift)
{
uint32_t c_hash;
struct ineq_cmp_data v;
struct isl_hash_table_entry *entry;
int j, k;
if (!hull)
return NULL;
v.len = isl_basic_set_total_dim(hull);
v.p = ineq;
c_hash = isl_seq_get_hash(ineq + 1, v.len);
entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
has_ineq, &v, 0);
if (entry)
return hull;
for (j = 0; j < i; ++j) {
entry = isl_hash_table_find(hull->ctx, data->p[j].table,
c_hash, has_ineq, &v, 0);
if (entry)
break;
}
if (j < i)
return hull;
k = isl_basic_set_alloc_inequality(hull);
if (k < 0)
goto error;
isl_seq_cpy(hull->ineq[k], ineq, 1 + v.len);
for (j = 0; j < i; ++j) {
int bound;
bound = is_bound(data, set, j, hull->ineq[k], shift);
if (bound < 0)
goto error;
if (!bound)
break;
}
if (j < i) {
isl_basic_set_free_inequality(hull, 1);
return hull;
}
for (j = i + 1; j < set->n; ++j) {
int bound, neg;
isl_int *ineq_j;
entry = isl_hash_table_find(hull->ctx, data->p[j].table,
c_hash, has_ineq, &v, 0);
if (entry) {
ineq_j = entry->data;
neg = isl_seq_is_neg(ineq_j + 1,
hull->ineq[k] + 1, v.len);
if (neg)
isl_int_neg(ineq_j[0], ineq_j[0]);
if (isl_int_gt(ineq_j[0], hull->ineq[k][0]))
isl_int_set(hull->ineq[k][0], ineq_j[0]);
if (neg)
isl_int_neg(ineq_j[0], ineq_j[0]);
continue;
}
bound = is_bound(data, set, j, hull->ineq[k], shift);
if (bound < 0)
goto error;
if (!bound)
break;
}
if (j < set->n) {
isl_basic_set_free_inequality(hull, 1);
return hull;
}
entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
has_ineq, &v, 1);
if (!entry)
goto error;
entry->data = hull->ineq[k];
return hull;
error:
isl_basic_set_free(hull);
return NULL;
}
/* Check if any inequality from basic set "i" is or can be relaxed to
* become a bound on the whole set. If so, add the (relaxed) inequality
* to "hull". Relaxation is only allowed if "shift" is set.
*/
static struct isl_basic_set *add_bounds(struct isl_basic_set *bset,
struct sh_data *data, struct isl_set *set, int i, int shift)
{
int j, k;
unsigned dim = isl_basic_set_total_dim(bset);
for (j = 0; j < set->p[i]->n_eq; ++j) {
for (k = 0; k < 2; ++k) {
isl_seq_neg(set->p[i]->eq[j], set->p[i]->eq[j], 1+dim);
bset = add_bound(bset, data, set, i, set->p[i]->eq[j],
shift);
}
}
for (j = 0; j < set->p[i]->n_ineq; ++j)
bset = add_bound(bset, data, set, i, set->p[i]->ineq[j], shift);
return bset;
}
/* Compute a superset of the convex hull of set that is described
* by only (translates of) the constraints in the constituents of set.
* Translation is only allowed if "shift" is set.
*/
static __isl_give isl_basic_set *uset_simple_hull(__isl_take isl_set *set,
int shift)
{
struct sh_data *data = NULL;
struct isl_basic_set *hull = NULL;
unsigned n_ineq;
int i;
if (!set)
return NULL;
n_ineq = 0;
for (i = 0; i < set->n; ++i) {
if (!set->p[i])
goto error;
n_ineq += 2 * set->p[i]->n_eq + set->p[i]->n_ineq;
}
hull = isl_basic_set_alloc_space(isl_space_copy(set->dim), 0, 0, n_ineq);
if (!hull)
goto error;
data = sh_data_alloc(set, n_ineq);
if (!data)
goto error;
for (i = 0; i < set->n; ++i)
hull = add_bounds(hull, data, set, i, shift);
sh_data_free(data);
isl_set_free(set);
return hull;
error:
sh_data_free(data);
isl_basic_set_free(hull);
isl_set_free(set);
return NULL;
}
/* Compute a superset of the convex hull of map that is described
* by only (translates of) the constraints in the constituents of map.
* Translation is only allowed if "shift" is set.
*/
static __isl_give isl_basic_map *map_simple_hull(__isl_take isl_map *map,
int shift)
{
struct isl_set *set = NULL;
struct isl_basic_map *model = NULL;
struct isl_basic_map *hull;
struct isl_basic_map *affine_hull;
struct isl_basic_set *bset = NULL;
if (!map)
return NULL;
if (map->n == 0) {
hull = isl_basic_map_empty_like_map(map);
isl_map_free(map);
return hull;
}
if (map->n == 1) {
hull = isl_basic_map_copy(map->p[0]);
isl_map_free(map);
return hull;
}
map = isl_map_detect_equalities(map);
affine_hull = isl_map_affine_hull(isl_map_copy(map));
map = isl_map_align_divs(map);
model = map ? isl_basic_map_copy(map->p[0]) : NULL;
set = isl_map_underlying_set(map);
bset = uset_simple_hull(set, shift);
hull = isl_basic_map_overlying_set(bset, model);
hull = isl_basic_map_intersect(hull, affine_hull);
hull = isl_basic_map_remove_redundancies(hull);
if (!hull)
return NULL;
ISL_F_SET(hull, ISL_BASIC_MAP_NO_IMPLICIT);
ISL_F_SET(hull, ISL_BASIC_MAP_ALL_EQUALITIES);
hull = isl_basic_map_finalize(hull);
return hull;
}
/* Compute a superset of the convex hull of map that is described
* by only translates of the constraints in the constituents of map.
*/
__isl_give isl_basic_map *isl_map_simple_hull(__isl_take isl_map *map)
{
return map_simple_hull(map, 1);
}
struct isl_basic_set *isl_set_simple_hull(struct isl_set *set)
{
return (struct isl_basic_set *)
isl_map_simple_hull((struct isl_map *)set);
}
/* Compute a superset of the convex hull of map that is described
* by only the constraints in the constituents of map.
*/
__isl_give isl_basic_map *isl_map_unshifted_simple_hull(
__isl_take isl_map *map)
{
return map_simple_hull(map, 0);
}
__isl_give isl_basic_set *isl_set_unshifted_simple_hull(
__isl_take isl_set *set)
{
return isl_map_unshifted_simple_hull(set);
}
/* Check if "ineq" is a bound on "set" and, if so, add it to "hull".
*
* For each basic set in "set", we first check if the basic set
* contains a translate of "ineq". If this translate is more relaxed,
* then we assume that "ineq" is not a bound on this basic set.
* Otherwise, we know that it is a bound.
* If the basic set does not contain a translate of "ineq", then
* we call is_bound to perform the test.
*/
static __isl_give isl_basic_set *add_bound_from_constraint(
__isl_take isl_basic_set *hull, struct sh_data *data,
__isl_keep isl_set *set, isl_int *ineq)
{
int i, k;
isl_ctx *ctx;
uint32_t c_hash;
struct ineq_cmp_data v;
if (!hull || !set)
return isl_basic_set_free(hull);
v.len = isl_basic_set_total_dim(hull);
v.p = ineq;
c_hash = isl_seq_get_hash(ineq + 1, v.len);
ctx = isl_basic_set_get_ctx(hull);
for (i = 0; i < set->n; ++i) {
int bound;
struct isl_hash_table_entry *entry;
entry = isl_hash_table_find(ctx, data->p[i].table,
c_hash, &has_ineq, &v, 0);
if (entry) {
isl_int *ineq_i = entry->data;
int neg, more_relaxed;
neg = isl_seq_is_neg(ineq_i + 1, ineq + 1, v.len);
if (neg)
isl_int_neg(ineq_i[0], ineq_i[0]);
more_relaxed = isl_int_gt(ineq_i[0], ineq[0]);
if (neg)
isl_int_neg(ineq_i[0], ineq_i[0]);
if (more_relaxed)
break;
else
continue;
}
bound = is_bound(data, set, i, ineq, 0);
if (bound < 0)
return isl_basic_set_free(hull);
if (!bound)
break;
}
if (i < set->n)
return hull;
k = isl_basic_set_alloc_inequality(hull);
if (k < 0)
return isl_basic_set_free(hull);
isl_seq_cpy(hull->ineq[k], ineq, 1 + v.len);
return hull;
}
/* Compute a superset of the convex hull of "set" that is described
* by only some of the "n_ineq" constraints in the list "ineq", where "set"
* has no parameters or integer divisions.
*
* The inequalities in "ineq" are assumed to have been sorted such
* that constraints with the same linear part appear together and
* that among constraints with the same linear part, those with
* smaller constant term appear first.
*
* We reuse the same data structure that is used by uset_simple_hull,
* but we do not need the hull table since we will not consider the
* same constraint more than once. We therefore allocate it with zero size.
*
* We run through the constraints and try to add them one by one,
* skipping identical constraints. If we have added a constraint and
* the next constraint is a more relaxed translate, then we skip this
* next constraint as well.
*/
static __isl_give isl_basic_set *uset_unshifted_simple_hull_from_constraints(
__isl_take isl_set *set, int n_ineq, isl_int **ineq)
{
int i;
int last_added = 0;
struct sh_data *data = NULL;
isl_basic_set *hull = NULL;
unsigned dim;
hull = isl_basic_set_alloc_space(isl_set_get_space(set), 0, 0, n_ineq);
if (!hull)
goto error;
data = sh_data_alloc(set, 0);
if (!data)
goto error;
dim = isl_set_dim(set, isl_dim_set);
for (i = 0; i < n_ineq; ++i) {
int hull_n_ineq = hull->n_ineq;
int parallel;
parallel = i > 0 && isl_seq_eq(ineq[i - 1] + 1, ineq[i] + 1,
dim);
if (parallel &&
(last_added || isl_int_eq(ineq[i - 1][0], ineq[i][0])))
continue;
hull = add_bound_from_constraint(hull, data, set, ineq[i]);
if (!hull)
goto error;
last_added = hull->n_ineq > hull_n_ineq;
}
sh_data_free(data);
isl_set_free(set);
return hull;
error:
sh_data_free(data);
isl_set_free(set);
isl_basic_set_free(hull);
return NULL;
}
/* Collect pointers to all the inequalities in the elements of "list"
* in "ineq". For equalities, store both a pointer to the equality and
* a pointer to its opposite, which is first copied to "mat".
* "ineq" and "mat" are assumed to have been preallocated to the right size
* (the number of inequalities + 2 times the number of equalites and
* the number of equalities, respectively).
*/
static __isl_give isl_mat *collect_inequalities(__isl_take isl_mat *mat,
__isl_keep isl_basic_set_list *list, isl_int **ineq)
{
int i, j, n, n_eq, n_ineq;
if (!mat)
return NULL;
n_eq = 0;
n_ineq = 0;
n = isl_basic_set_list_n_basic_set(list);
for (i = 0; i < n; ++i) {
isl_basic_set *bset;
bset = isl_basic_set_list_get_basic_set(list, i);
if (!bset)
return isl_mat_free(mat);
for (j = 0; j < bset->n_eq; ++j) {
ineq[n_ineq++] = mat->row[n_eq];
ineq[n_ineq++] = bset->eq[j];
isl_seq_neg(mat->row[n_eq++], bset->eq[j], mat->n_col);
}
for (j = 0; j < bset->n_ineq; ++j)
ineq[n_ineq++] = bset->ineq[j];
isl_basic_set_free(bset);
}
return mat;
}
/* Comparison routine for use as an isl_sort callback.
*
* Constraints with the same linear part are sorted together and
* among constraints with the same linear part, those with smaller
* constant term are sorted first.
*/
static int cmp_ineq(const void *a, const void *b, void *arg)
{
unsigned dim = *(unsigned *) arg;
isl_int * const *ineq1 = a;
isl_int * const *ineq2 = b;
int cmp;
cmp = isl_seq_cmp((*ineq1) + 1, (*ineq2) + 1, dim);
if (cmp != 0)
return cmp;
return isl_int_cmp((*ineq1)[0], (*ineq2)[0]);
}
/* Compute a superset of the convex hull of "set" that is described
* by only constraints in the elements of "list", where "set" has
* no parameters or integer divisions.
*
* We collect all the constraints in those elements and then
* sort the constraints such that constraints with the same linear part
* are sorted together and that those with smaller constant term are
* sorted first.
*/
static __isl_give isl_basic_set *uset_unshifted_simple_hull_from_basic_set_list(
__isl_take isl_set *set, __isl_take isl_basic_set_list *list)
{
int i, n, n_eq, n_ineq;
unsigned dim;
isl_ctx *ctx;
isl_mat *mat = NULL;
isl_int **ineq = NULL;
isl_basic_set *hull;
if (!set)
goto error;
ctx = isl_set_get_ctx(set);
n_eq = 0;
n_ineq = 0;
n = isl_basic_set_list_n_basic_set(list);
for (i = 0; i < n; ++i) {
isl_basic_set *bset;
bset = isl_basic_set_list_get_basic_set(list, i);
if (!bset)
goto error;
n_eq += bset->n_eq;
n_ineq += 2 * bset->n_eq + bset->n_ineq;
isl_basic_set_free(bset);
}
ineq = isl_alloc_array(ctx, isl_int *, n_ineq);
if (n_ineq > 0 && !ineq)
goto error;
dim = isl_set_dim(set, isl_dim_set);
mat = isl_mat_alloc(ctx, n_eq, 1 + dim);
mat = collect_inequalities(mat, list, ineq);
if (!mat)
goto error;
if (isl_sort(ineq, n_ineq, sizeof(ineq[0]), &cmp_ineq, &dim) < 0)
goto error;
hull = uset_unshifted_simple_hull_from_constraints(set, n_ineq, ineq);
isl_mat_free(mat);
free(ineq);
isl_basic_set_list_free(list);
return hull;
error:
isl_mat_free(mat);
free(ineq);
isl_set_free(set);
isl_basic_set_list_free(list);
return NULL;
}
/* Compute a superset of the convex hull of "set" that is described
* by only constraints in the elements of "list".
*
* If the list is empty, then we can only describe the universe set.
* If the input set is empty, then all constraints are valid, so
* we return the intersection of the elements in "list".
*
* Otherwise, we align all divs and temporarily treat them
* as regular variables, computing the unshifted simple hull in
* uset_unshifted_simple_hull_from_basic_set_list.
*/
static __isl_give isl_basic_set *set_unshifted_simple_hull_from_basic_set_list(
__isl_take isl_set *set, __isl_take isl_basic_set_list *list)
{
isl_basic_set *model;
isl_basic_set *hull;
if (!set || !list)
goto error;
if (isl_basic_set_list_n_basic_set(list) == 0) {
isl_space *space;
space = isl_set_get_space(set);
isl_set_free(set);
isl_basic_set_list_free(list);
return isl_basic_set_universe(space);
}
if (isl_set_plain_is_empty(set)) {
isl_set_free(set);
return isl_basic_set_list_intersect(list);
}
set = isl_set_align_divs_to_basic_set_list(set, list);
if (!set)
goto error;
list = isl_basic_set_list_align_divs_to_basic_set(list, set->p[0]);
model = isl_basic_set_list_get_basic_set(list, 0);
set = isl_set_to_underlying_set(set);
list = isl_basic_set_list_underlying_set(list);
hull = uset_unshifted_simple_hull_from_basic_set_list(set, list);
hull = isl_basic_map_overlying_set(hull, model);
return hull;
error:
isl_set_free(set);
isl_basic_set_list_free(list);
return NULL;
}
/* Return a sequence of the basic sets that make up the sets in "list".
*/
static __isl_give isl_basic_set_list *collect_basic_sets(
__isl_take isl_set_list *list)
{
int i, n;
isl_ctx *ctx;
isl_basic_set_list *bset_list;
if (!list)
return NULL;
n = isl_set_list_n_set(list);
ctx = isl_set_list_get_ctx(list);
bset_list = isl_basic_set_list_alloc(ctx, 0);
for (i = 0; i < n; ++i) {
isl_set *set;
isl_basic_set_list *list_i;
set = isl_set_list_get_set(list, i);
set = isl_set_compute_divs(set);
list_i = isl_set_get_basic_set_list(set);
isl_set_free(set);
bset_list = isl_basic_set_list_concat(bset_list, list_i);
}
isl_set_list_free(list);
return bset_list;
}
/* Compute a superset of the convex hull of "set" that is described
* by only constraints in the elements of "list".
*
* If "set" is the universe, then the convex hull (and therefore
* any superset of the convexhull) is the universe as well.
*
* Otherwise, we collect all the basic sets in the set list and
* continue with set_unshifted_simple_hull_from_basic_set_list.
*/
__isl_give isl_basic_set *isl_set_unshifted_simple_hull_from_set_list(
__isl_take isl_set *set, __isl_take isl_set_list *list)
{
isl_basic_set_list *bset_list;
int is_universe;
is_universe = isl_set_plain_is_universe(set);
if (is_universe < 0)
set = isl_set_free(set);
if (is_universe < 0 || is_universe) {
isl_set_list_free(list);
return isl_set_unshifted_simple_hull(set);
}
bset_list = collect_basic_sets(list);
return set_unshifted_simple_hull_from_basic_set_list(set, bset_list);
}
/* Given a set "set", return parametric bounds on the dimension "dim".
*/
static struct isl_basic_set *set_bounds(struct isl_set *set, int dim)
{
unsigned set_dim = isl_set_dim(set, isl_dim_set);
set = isl_set_copy(set);
set = isl_set_eliminate_dims(set, dim + 1, set_dim - (dim + 1));
set = isl_set_eliminate_dims(set, 0, dim);
return isl_set_convex_hull(set);
}
/* Computes a "simple hull" and then check if each dimension in the
* resulting hull is bounded by a symbolic constant. If not, the
* hull is intersected with the corresponding bounds on the whole set.
*/
struct isl_basic_set *isl_set_bounded_simple_hull(struct isl_set *set)
{
int i, j;
struct isl_basic_set *hull;
unsigned nparam, left;
int removed_divs = 0;
hull = isl_set_simple_hull(isl_set_copy(set));
if (!hull)
goto error;
nparam = isl_basic_set_dim(hull, isl_dim_param);
for (i = 0; i < isl_basic_set_dim(hull, isl_dim_set); ++i) {
int lower = 0, upper = 0;
struct isl_basic_set *bounds;
left = isl_basic_set_total_dim(hull) - nparam - i - 1;
for (j = 0; j < hull->n_eq; ++j) {
if (isl_int_is_zero(hull->eq[j][1 + nparam + i]))
continue;
if (isl_seq_first_non_zero(hull->eq[j]+1+nparam+i+1,
left) == -1)
break;
}
if (j < hull->n_eq)
continue;
for (j = 0; j < hull->n_ineq; ++j) {
if (isl_int_is_zero(hull->ineq[j][1 + nparam + i]))
continue;
if (isl_seq_first_non_zero(hull->ineq[j]+1+nparam+i+1,
left) != -1 ||
isl_seq_first_non_zero(hull->ineq[j]+1+nparam,
i) != -1)
continue;
if (isl_int_is_pos(hull->ineq[j][1 + nparam + i]))
lower = 1;
else
upper = 1;
if (lower && upper)
break;
}
if (lower && upper)
continue;
if (!removed_divs) {
set = isl_set_remove_divs(set);
if (!set)
goto error;
removed_divs = 1;
}
bounds = set_bounds(set, i);
hull = isl_basic_set_intersect(hull, bounds);
if (!hull)
goto error;
}
isl_set_free(set);
return hull;
error:
isl_set_free(set);
return NULL;
}