nexmon – Rev 1
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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
*
* Use of this software is governed by the GNU LGPLv2.1 license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
*/
#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl/seq.h>
#include <isl/set.h>
#include <isl/lp.h>
#include <isl/map.h>
#include "isl_equalities.h"
#include "isl_sample.h"
#include "isl_tab.h"
#include <isl_mat_private.h>
struct isl_basic_map *isl_basic_map_implicit_equalities(
struct isl_basic_map *bmap)
{
struct isl_tab *tab;
if (!bmap)
return bmap;
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_IMPLICIT))
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;
bmap = isl_basic_map_update_from_tab(bmap, tab);
isl_tab_free(tab);
bmap = isl_basic_map_gauss(bmap, NULL);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
return bmap;
error:
isl_tab_free(tab);
isl_basic_map_free(bmap);
return NULL;
}
struct isl_basic_set *isl_basic_set_implicit_equalities(
struct isl_basic_set *bset)
{
return (struct isl_basic_set *)
isl_basic_map_implicit_equalities((struct isl_basic_map*)bset);
}
struct isl_map *isl_map_implicit_equalities(struct isl_map *map)
{
int i;
if (!map)
return map;
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_implicit_equalities(map->p[i]);
if (!map->p[i])
goto error;
}
return map;
error:
isl_map_free(map);
return NULL;
}
/* Make eq[row][col] of both bmaps equal so we can add the row
* add the column to the common matrix.
* Note that because of the echelon form, the columns of row row
* after column col are zero.
*/
static void set_common_multiple(
struct isl_basic_set *bset1, struct isl_basic_set *bset2,
unsigned row, unsigned col)
{
isl_int m, c;
if (isl_int_eq(bset1->eq[row][col], bset2->eq[row][col]))
return;
isl_int_init(c);
isl_int_init(m);
isl_int_lcm(m, bset1->eq[row][col], bset2->eq[row][col]);
isl_int_divexact(c, m, bset1->eq[row][col]);
isl_seq_scale(bset1->eq[row], bset1->eq[row], c, col+1);
isl_int_divexact(c, m, bset2->eq[row][col]);
isl_seq_scale(bset2->eq[row], bset2->eq[row], c, col+1);
isl_int_clear(c);
isl_int_clear(m);
}
/* Delete a given equality, moving all the following equalities one up.
*/
static void delete_row(struct isl_basic_set *bset, unsigned row)
{
isl_int *t;
int r;
t = bset->eq[row];
bset->n_eq--;
for (r = row; r < bset->n_eq; ++r)
bset->eq[r] = bset->eq[r+1];
bset->eq[bset->n_eq] = t;
}
/* Make first row entries in column col of bset1 identical to
* those of bset2, using the fact that entry bset1->eq[row][col]=a
* is non-zero. Initially, these elements of bset1 are all zero.
* For each row i < row, we set
* A[i] = a * A[i] + B[i][col] * A[row]
* B[i] = a * B[i]
* so that
* A[i][col] = B[i][col] = a * old(B[i][col])
*/
static void construct_column(
struct isl_basic_set *bset1, struct isl_basic_set *bset2,
unsigned row, unsigned col)
{
int r;
isl_int a;
isl_int b;
unsigned total;
isl_int_init(a);
isl_int_init(b);
total = 1 + isl_basic_set_n_dim(bset1);
for (r = 0; r < row; ++r) {
if (isl_int_is_zero(bset2->eq[r][col]))
continue;
isl_int_gcd(b, bset2->eq[r][col], bset1->eq[row][col]);
isl_int_divexact(a, bset1->eq[row][col], b);
isl_int_divexact(b, bset2->eq[r][col], b);
isl_seq_combine(bset1->eq[r], a, bset1->eq[r],
b, bset1->eq[row], total);
isl_seq_scale(bset2->eq[r], bset2->eq[r], a, total);
}
isl_int_clear(a);
isl_int_clear(b);
delete_row(bset1, row);
}
/* Make first row entries in column col of bset1 identical to
* those of bset2, using only these entries of the two matrices.
* Let t be the last row with different entries.
* For each row i < t, we set
* A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t]
* B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t]
* so that
* A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col])
*/
static int transform_column(
struct isl_basic_set *bset1, struct isl_basic_set *bset2,
unsigned row, unsigned col)
{
int i, t;
isl_int a, b, g;
unsigned total;
for (t = row-1; t >= 0; --t)
if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col]))
break;
if (t < 0)
return 0;
total = 1 + isl_basic_set_n_dim(bset1);
isl_int_init(a);
isl_int_init(b);
isl_int_init(g);
isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col]);
for (i = 0; i < t; ++i) {
isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col]);
isl_int_gcd(g, a, b);
isl_int_divexact(a, a, g);
isl_int_divexact(g, b, g);
isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t],
total);
isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t],
total);
}
isl_int_clear(a);
isl_int_clear(b);
isl_int_clear(g);
delete_row(bset1, t);
delete_row(bset2, t);
return 1;
}
/* The implementation is based on Section 5.2 of Michael Karr,
* "Affine Relationships Among Variables of a Program",
* except that the echelon form we use starts from the last column
* and that we are dealing with integer coefficients.
*/
static struct isl_basic_set *affine_hull(
struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
unsigned total;
int col;
int row;
if (!bset1 || !bset2)
goto error;
total = 1 + isl_basic_set_n_dim(bset1);
row = 0;
for (col = total-1; col >= 0; --col) {
int is_zero1 = row >= bset1->n_eq ||
isl_int_is_zero(bset1->eq[row][col]);
int is_zero2 = row >= bset2->n_eq ||
isl_int_is_zero(bset2->eq[row][col]);
if (!is_zero1 && !is_zero2) {
set_common_multiple(bset1, bset2, row, col);
++row;
} else if (!is_zero1 && is_zero2) {
construct_column(bset1, bset2, row, col);
} else if (is_zero1 && !is_zero2) {
construct_column(bset2, bset1, row, col);
} else {
if (transform_column(bset1, bset2, row, col))
--row;
}
}
isl_assert(bset1->ctx, row == bset1->n_eq, goto error);
isl_basic_set_free(bset2);
bset1 = isl_basic_set_normalize_constraints(bset1);
return bset1;
error:
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return NULL;
}
/* Find an integer point in the set represented by "tab"
* that lies outside of the equality "eq" e(x) = 0.
* If "up" is true, look for a point satisfying e(x) - 1 >= 0.
* Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
* The point, if found, is returned.
* If no point can be found, a zero-length vector is returned.
*
* Before solving an ILP problem, we first check if simply
* adding the normal of the constraint to one of the known
* integer points in the basic set represented by "tab"
* yields another point inside the basic set.
*
* The caller of this function ensures that the tableau is bounded or
* that tab->basis and tab->n_unbounded have been set appropriately.
*/
static struct isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up)
{
struct isl_ctx *ctx;
struct isl_vec *sample = NULL;
struct isl_tab_undo *snap;
unsigned dim;
if (!tab)
return NULL;
ctx = tab->mat->ctx;
dim = tab->n_var;
sample = isl_vec_alloc(ctx, 1 + dim);
if (!sample)
return NULL;
isl_int_set_si(sample->el[0], 1);
isl_seq_combine(sample->el + 1,
ctx->one, tab->bmap->sample->el + 1,
up ? ctx->one : ctx->negone, eq + 1, dim);
if (isl_basic_map_contains(tab->bmap, sample))
return sample;
isl_vec_free(sample);
sample = NULL;
snap = isl_tab_snap(tab);
if (!up)
isl_seq_neg(eq, eq, 1 + dim);
isl_int_sub_ui(eq[0], eq[0], 1);
if (isl_tab_extend_cons(tab, 1) < 0)
goto error;
if (isl_tab_add_ineq(tab, eq) < 0)
goto error;
sample = isl_tab_sample(tab);
isl_int_add_ui(eq[0], eq[0], 1);
if (!up)
isl_seq_neg(eq, eq, 1 + dim);
if (sample && isl_tab_rollback(tab, snap) < 0)
goto error;
return sample;
error:
isl_vec_free(sample);
return NULL;
}
struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset)
{
int i;
bset = isl_basic_set_cow(bset);
if (!bset)
return NULL;
isl_assert(bset->ctx, bset->n_div == 0, goto error);
for (i = 0; i < bset->n_eq; ++i)
isl_int_set_si(bset->eq[i][0], 0);
for (i = 0; i < bset->n_ineq; ++i)
isl_int_set_si(bset->ineq[i][0], 0);
ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
return isl_basic_set_implicit_equalities(bset);
error:
isl_basic_set_free(bset);
return NULL;
}
__isl_give isl_set *isl_set_recession_cone(__isl_take isl_set *set)
{
int i;
if (!set)
return NULL;
if (set->n == 0)
return set;
set = isl_set_remove_divs(set);
set = isl_set_cow(set);
if (!set)
return NULL;
for (i = 0; i < set->n; ++i) {
set->p[i] = isl_basic_set_recession_cone(set->p[i]);
if (!set->p[i])
goto error;
}
return set;
error:
isl_set_free(set);
return NULL;
}
/* Move "sample" to a point that is one up (or down) from the original
* point in dimension "pos".
*/
static void adjacent_point(__isl_keep isl_vec *sample, int pos, int up)
{
if (up)
isl_int_add_ui(sample->el[1 + pos], sample->el[1 + pos], 1);
else
isl_int_sub_ui(sample->el[1 + pos], sample->el[1 + pos], 1);
}
/* Check if any points that are adjacent to "sample" also belong to "bset".
* If so, add them to "hull" and return the updated hull.
*
* Before checking whether and adjacent point belongs to "bset", we first
* check whether it already belongs to "hull" as this test is typically
* much cheaper.
*/
static __isl_give isl_basic_set *add_adjacent_points(
__isl_take isl_basic_set *hull, __isl_take isl_vec *sample,
__isl_keep isl_basic_set *bset)
{
int i, up;
int dim;
if (!sample)
goto error;
dim = isl_basic_set_dim(hull, isl_dim_set);
for (i = 0; i < dim; ++i) {
for (up = 0; up <= 1; ++up) {
int contains;
isl_basic_set *point;
adjacent_point(sample, i, up);
contains = isl_basic_set_contains(hull, sample);
if (contains < 0)
goto error;
if (contains) {
adjacent_point(sample, i, !up);
continue;
}
contains = isl_basic_set_contains(bset, sample);
if (contains < 0)
goto error;
if (contains) {
point = isl_basic_set_from_vec(
isl_vec_copy(sample));
hull = affine_hull(hull, point);
}
adjacent_point(sample, i, !up);
if (contains)
break;
}
}
isl_vec_free(sample);
return hull;
error:
isl_vec_free(sample);
isl_basic_set_free(hull);
return NULL;
}
/* Extend an initial (under-)approximation of the affine hull of basic
* set represented by the tableau "tab"
* by looking for points that do not satisfy one of the equalities
* in the current approximation and adding them to that approximation
* until no such points can be found any more.
*
* The caller of this function ensures that "tab" is bounded or
* that tab->basis and tab->n_unbounded have been set appropriately.
*
* "bset" may be either NULL or the basic set represented by "tab".
* If "bset" is not NULL, we check for any point we find if any
* of its adjacent points also belong to "bset".
*/
static __isl_give isl_basic_set *extend_affine_hull(struct isl_tab *tab,
__isl_take isl_basic_set *hull, __isl_keep isl_basic_set *bset)
{
int i, j;
unsigned dim;
if (!tab || !hull)
goto error;
dim = tab->n_var;
if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0)
goto error;
for (i = 0; i < dim; ++i) {
struct isl_vec *sample;
struct isl_basic_set *point;
for (j = 0; j < hull->n_eq; ++j) {
sample = outside_point(tab, hull->eq[j], 1);
if (!sample)
goto error;
if (sample->size > 0)
break;
isl_vec_free(sample);
sample = outside_point(tab, hull->eq[j], 0);
if (!sample)
goto error;
if (sample->size > 0)
break;
isl_vec_free(sample);
if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
goto error;
}
if (j == hull->n_eq)
break;
if (tab->samples)
tab = isl_tab_add_sample(tab, isl_vec_copy(sample));
if (!tab)
goto error;
if (bset)
hull = add_adjacent_points(hull, isl_vec_copy(sample),
bset);
point = isl_basic_set_from_vec(sample);
hull = affine_hull(hull, point);
if (!hull)
return NULL;
}
return hull;
error:
isl_basic_set_free(hull);
return NULL;
}
/* Drop all constraints in bset that involve any of the dimensions
* first to first+n-1.
*/
__isl_give isl_basic_set *isl_basic_set_drop_constraints_involving(
__isl_take isl_basic_set *bset, unsigned first, unsigned n)
{
int i;
if (n == 0)
return bset;
bset = isl_basic_set_cow(bset);
if (!bset)
return NULL;
for (i = bset->n_eq - 1; i >= 0; --i) {
if (isl_seq_first_non_zero(bset->eq[i] + 1 + first, n) == -1)
continue;
isl_basic_set_drop_equality(bset, i);
}
for (i = bset->n_ineq - 1; i >= 0; --i) {
if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
continue;
isl_basic_set_drop_inequality(bset, i);
}
return bset;
}
/* Construct an initial underapproximatino of the hull of "bset"
* from "sample" and any of its adjacent points that also belong to "bset".
*/
static __isl_give isl_basic_set *initialize_hull(__isl_keep isl_basic_set *bset,
__isl_take isl_vec *sample)
{
isl_basic_set *hull;
hull = isl_basic_set_from_vec(isl_vec_copy(sample));
hull = add_adjacent_points(hull, sample, bset);
return hull;
}
/* Look for all equalities satisfied by the integer points in bset,
* which is assumed to be bounded.
*
* The equalities are obtained by successively looking for
* a point that is affinely independent of the points found so far.
* In particular, for each equality satisfied by the points so far,
* we check if there is any point on a hyperplane parallel to the
* corresponding hyperplane shifted by at least one (in either direction).
*/
static struct isl_basic_set *uset_affine_hull_bounded(struct isl_basic_set *bset)
{
struct isl_vec *sample = NULL;
struct isl_basic_set *hull;
struct isl_tab *tab = NULL;
unsigned dim;
if (isl_basic_set_plain_is_empty(bset))
return bset;
dim = isl_basic_set_n_dim(bset);
if (bset->sample && bset->sample->size == 1 + dim) {
int contains = isl_basic_set_contains(bset, bset->sample);
if (contains < 0)
goto error;
if (contains) {
if (dim == 0)
return bset;
sample = isl_vec_copy(bset->sample);
} else {
isl_vec_free(bset->sample);
bset->sample = NULL;
}
}
tab = isl_tab_from_basic_set(bset, 1);
if (!tab)
goto error;
if (tab->empty) {
isl_tab_free(tab);
isl_vec_free(sample);
return isl_basic_set_set_to_empty(bset);
}
if (!sample) {
struct isl_tab_undo *snap;
snap = isl_tab_snap(tab);
sample = isl_tab_sample(tab);
if (isl_tab_rollback(tab, snap) < 0)
goto error;
isl_vec_free(tab->bmap->sample);
tab->bmap->sample = isl_vec_copy(sample);
}
if (!sample)
goto error;
if (sample->size == 0) {
isl_tab_free(tab);
isl_vec_free(sample);
return isl_basic_set_set_to_empty(bset);
}
hull = initialize_hull(bset, sample);
hull = extend_affine_hull(tab, hull, bset);
isl_basic_set_free(bset);
isl_tab_free(tab);
return hull;
error:
isl_vec_free(sample);
isl_tab_free(tab);
isl_basic_set_free(bset);
return NULL;
}
/* Given an unbounded tableau and an integer point satisfying the tableau,
* construct an initial affine hull containing the recession cone
* shifted to the given point.
*
* The unbounded directions are taken from the last rows of the basis,
* which is assumed to have been initialized appropriately.
*/
static __isl_give isl_basic_set *initial_hull(struct isl_tab *tab,
__isl_take isl_vec *vec)
{
int i;
int k;
struct isl_basic_set *bset = NULL;
struct isl_ctx *ctx;
unsigned dim;
if (!vec || !tab)
return NULL;
ctx = vec->ctx;
isl_assert(ctx, vec->size != 0, goto error);
bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
if (!bset)
goto error;
dim = isl_basic_set_n_dim(bset) - tab->n_unbounded;
for (i = 0; i < dim; ++i) {
k = isl_basic_set_alloc_equality(bset);
if (k < 0)
goto error;
isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1,
vec->size - 1);
isl_seq_inner_product(bset->eq[k] + 1, vec->el +1,
vec->size - 1, &bset->eq[k][0]);
isl_int_neg(bset->eq[k][0], bset->eq[k][0]);
}
bset->sample = vec;
bset = isl_basic_set_gauss(bset, NULL);
return bset;
error:
isl_basic_set_free(bset);
isl_vec_free(vec);
return NULL;
}
/* Given a tableau of a set and a tableau of the corresponding
* recession cone, detect and add all equalities to the tableau.
* If the tableau is bounded, then we can simply keep the
* tableau in its state after the return from extend_affine_hull.
* However, if the tableau is unbounded, then
* isl_tab_set_initial_basis_with_cone will add some additional
* constraints to the tableau that have to be removed again.
* In this case, we therefore rollback to the state before
* any constraints were added and then add the equalities back in.
*/
struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
struct isl_tab *tab_cone)
{
int j;
struct isl_vec *sample;
struct isl_basic_set *hull;
struct isl_tab_undo *snap;
if (!tab || !tab_cone)
goto error;
snap = isl_tab_snap(tab);
isl_mat_free(tab->basis);
tab->basis = NULL;
isl_assert(tab->mat->ctx, tab->bmap, goto error);
isl_assert(tab->mat->ctx, tab->samples, goto error);
isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error);
if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0)
goto error;
sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
if (!sample)
goto error;
isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size);
isl_vec_free(tab->bmap->sample);
tab->bmap->sample = isl_vec_copy(sample);
if (tab->n_unbounded == 0)
hull = isl_basic_set_from_vec(isl_vec_copy(sample));
else
hull = initial_hull(tab, isl_vec_copy(sample));
for (j = tab->n_outside + 1; j < tab->n_sample; ++j) {
isl_seq_cpy(sample->el, tab->samples->row[j], sample->size);
hull = affine_hull(hull,
isl_basic_set_from_vec(isl_vec_copy(sample)));
}
isl_vec_free(sample);
hull = extend_affine_hull(tab, hull, NULL);
if (!hull)
goto error;
if (tab->n_unbounded == 0) {
isl_basic_set_free(hull);
return tab;
}
if (isl_tab_rollback(tab, snap) < 0)
goto error;
if (hull->n_eq > tab->n_zero) {
for (j = 0; j < hull->n_eq; ++j) {
isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var);
if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
goto error;
}
}
isl_basic_set_free(hull);
return tab;
error:
isl_tab_free(tab);
return NULL;
}
/* Compute the affine hull of "bset", where "cone" is the recession cone
* of "bset".
*
* We first compute a unimodular transformation that puts the unbounded
* directions in the last dimensions. In particular, we take a transformation
* that maps all equalities to equalities (in HNF) on the first dimensions.
* Let x be the original dimensions and y the transformed, with y_1 bounded
* and y_2 unbounded.
*
* [ y_1 ] [ y_1 ] [ Q_1 ]
* x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x
*
* Let's call the input basic set S. We compute S' = preimage(S, U)
* and drop the final dimensions including any constraints involving them.
* This results in set S''.
* Then we compute the affine hull A'' of S''.
* Let F y_1 >= g be the constraint system of A''. In the transformed
* space the y_2 are unbounded, so we can add them back without any constraints,
* resulting in
*
* [ y_1 ]
* [ F 0 ] [ y_2 ] >= g
* or
* [ Q_1 ]
* [ F 0 ] [ Q_2 ] x >= g
* or
* F Q_1 x >= g
*
* The affine hull in the original space is then obtained as
* A = preimage(A'', Q_1).
*/
static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
struct isl_basic_set *cone)
{
unsigned total;
unsigned cone_dim;
struct isl_basic_set *hull;
struct isl_mat *M, *U, *Q;
if (!bset || !cone)
goto error;
total = isl_basic_set_total_dim(cone);
cone_dim = total - cone->n_eq;
M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
M = isl_mat_left_hermite(M, 0, &U, &Q);
if (!M)
goto error;
isl_mat_free(M);
U = isl_mat_lin_to_aff(U);
bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim,
cone_dim);
bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
Q = isl_mat_lin_to_aff(Q);
Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
if (bset && bset->sample && bset->sample->size == 1 + total)
bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
hull = uset_affine_hull_bounded(bset);
if (!hull)
isl_mat_free(U);
else {
struct isl_vec *sample = isl_vec_copy(hull->sample);
U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim);
if (sample && sample->size > 0)
sample = isl_mat_vec_product(U, sample);
else
isl_mat_free(U);
hull = isl_basic_set_preimage(hull, Q);
if (hull) {
isl_vec_free(hull->sample);
hull->sample = sample;
} else
isl_vec_free(sample);
}
isl_basic_set_free(cone);
return hull;
error:
isl_basic_set_free(bset);
isl_basic_set_free(cone);
return NULL;
}
/* Look for all equalities satisfied by the integer points in bset,
* which is assumed not to have any explicit equalities.
*
* The equalities are obtained by successively looking for
* a point that is affinely independent of the points found so far.
* In particular, for each equality satisfied by the points so far,
* we check if there is any point on a hyperplane parallel to the
* corresponding hyperplane shifted by at least one (in either direction).
*
* Before looking for any outside points, we first compute the recession
* cone. The directions of this recession cone will always be part
* of the affine hull, so there is no need for looking for any points
* in these directions.
* In particular, if the recession cone is full-dimensional, then
* the affine hull is simply the whole universe.
*/
static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset)
{
struct isl_basic_set *cone;
if (isl_basic_set_plain_is_empty(bset))
return bset;
cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
if (!cone)
goto error;
if (cone->n_eq == 0) {
struct isl_basic_set *hull;
isl_basic_set_free(cone);
hull = isl_basic_set_universe_like(bset);
isl_basic_set_free(bset);
return hull;
}
if (cone->n_eq < isl_basic_set_total_dim(cone))
return affine_hull_with_cone(bset, cone);
isl_basic_set_free(cone);
return uset_affine_hull_bounded(bset);
error:
isl_basic_set_free(bset);
return NULL;
}
/* Look for all equalities satisfied by the integer points in bmap
* that are independent of the equalities already explicitly available
* in bmap.
*
* We first remove all equalities already explicitly available,
* then look for additional equalities in the reduced space
* and then transform the result to the original space.
* The original equalities are _not_ added to this set. This is
* the responsibility of the calling function.
* The resulting basic set has all meaning about the dimensions removed.
* In particular, dimensions that correspond to existential variables
* in bmap and that are found to be fixed are not removed.
*/
static struct isl_basic_set *equalities_in_underlying_set(
struct isl_basic_map *bmap)
{
struct isl_mat *T1 = NULL;
struct isl_mat *T2 = NULL;
struct isl_basic_set *bset = NULL;
struct isl_basic_set *hull = NULL;
bset = isl_basic_map_underlying_set(bmap);
if (!bset)
return NULL;
if (bset->n_eq)
bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
if (!bset)
goto error;
hull = uset_affine_hull(bset);
if (!T2)
return hull;
if (!hull) {
isl_mat_free(T1);
isl_mat_free(T2);
} else {
struct isl_vec *sample = isl_vec_copy(hull->sample);
if (sample && sample->size > 0)
sample = isl_mat_vec_product(T1, sample);
else
isl_mat_free(T1);
hull = isl_basic_set_preimage(hull, T2);
if (hull) {
isl_vec_free(hull->sample);
hull->sample = sample;
} else
isl_vec_free(sample);
}
return hull;
error:
isl_mat_free(T2);
isl_basic_set_free(bset);
isl_basic_set_free(hull);
return NULL;
}
/* Detect and make explicit all equalities satisfied by the (integer)
* points in bmap.
*/
struct isl_basic_map *isl_basic_map_detect_equalities(
struct isl_basic_map *bmap)
{
int i, j;
struct isl_basic_set *hull = NULL;
if (!bmap)
return NULL;
if (bmap->n_ineq == 0)
return bmap;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
return bmap;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES))
return bmap;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
return isl_basic_map_implicit_equalities(bmap);
hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
if (!hull)
goto error;
if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) {
isl_basic_set_free(hull);
return isl_basic_map_set_to_empty(bmap);
}
bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), 0,
hull->n_eq, 0);
for (i = 0; i < hull->n_eq; ++i) {
j = isl_basic_map_alloc_equality(bmap);
if (j < 0)
goto error;
isl_seq_cpy(bmap->eq[j], hull->eq[i],
1 + isl_basic_set_total_dim(hull));
}
isl_vec_free(bmap->sample);
bmap->sample = isl_vec_copy(hull->sample);
isl_basic_set_free(hull);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES);
bmap = isl_basic_map_simplify(bmap);
return isl_basic_map_finalize(bmap);
error:
isl_basic_set_free(hull);
isl_basic_map_free(bmap);
return NULL;
}
__isl_give isl_basic_set *isl_basic_set_detect_equalities(
__isl_take isl_basic_set *bset)
{
return (isl_basic_set *)
isl_basic_map_detect_equalities((isl_basic_map *)bset);
}
__isl_give isl_map *isl_map_inline_foreach_basic_map(__isl_take isl_map *map,
__isl_give isl_basic_map *(*fn)(__isl_take isl_basic_map *bmap))
{
struct isl_basic_map *bmap;
int i;
if (!map)
return NULL;
for (i = 0; i < map->n; ++i) {
bmap = isl_basic_map_copy(map->p[i]);
bmap = fn(bmap);
if (!bmap)
goto error;
isl_basic_map_free(map->p[i]);
map->p[i] = bmap;
}
return map;
error:
isl_map_free(map);
return NULL;
}
__isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map)
{
return isl_map_inline_foreach_basic_map(map,
&isl_basic_map_detect_equalities);
}
__isl_give isl_set *isl_set_detect_equalities(__isl_take isl_set *set)
{
return (isl_set *)isl_map_detect_equalities((isl_map *)set);
}
/* After computing the rational affine hull (by detecting the implicit
* equalities), we compute the additional equalities satisfied by
* the integer points (if any) and add the original equalities back in.
*/
struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap)
{
bmap = isl_basic_map_detect_equalities(bmap);
bmap = isl_basic_map_cow(bmap);
if (bmap)
isl_basic_map_free_inequality(bmap, bmap->n_ineq);
bmap = isl_basic_map_finalize(bmap);
return bmap;
}
struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
{
return (struct isl_basic_set *)
isl_basic_map_affine_hull((struct isl_basic_map *)bset);
}
struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
{
int i;
struct isl_basic_map *model = NULL;
struct isl_basic_map *hull = NULL;
struct isl_set *set;
map = isl_map_detect_equalities(map);
map = isl_map_align_divs(map);
if (!map)
return NULL;
if (map->n == 0) {
hull = isl_basic_map_empty_like_map(map);
isl_map_free(map);
return hull;
}
model = isl_basic_map_copy(map->p[0]);
set = isl_map_underlying_set(map);
set = isl_set_cow(set);
if (!set)
goto error;
for (i = 0; i < set->n; ++i) {
set->p[i] = isl_basic_set_cow(set->p[i]);
set->p[i] = isl_basic_set_affine_hull(set->p[i]);
set->p[i] = isl_basic_set_gauss(set->p[i], NULL);
if (!set->p[i])
goto error;
}
set = isl_set_remove_empty_parts(set);
if (set->n == 0) {
hull = isl_basic_map_empty_like(model);
isl_basic_map_free(model);
} else {
struct isl_basic_set *bset;
while (set->n > 1) {
set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
if (!set->p[0])
goto error;
}
bset = isl_basic_set_copy(set->p[0]);
hull = isl_basic_map_overlying_set(bset, model);
}
isl_set_free(set);
hull = isl_basic_map_simplify(hull);
return isl_basic_map_finalize(hull);
error:
isl_basic_map_free(model);
isl_set_free(set);
return NULL;
}
struct isl_basic_set *isl_set_affine_hull(struct isl_set *set)
{
return (struct isl_basic_set *)
isl_map_affine_hull((struct isl_map *)set);
}