-#include "isl_ctx.h"
-#include "isl_seq.h"
-#include "isl_set.h"
-#include "isl_lp.h"
-#include "isl_map.h"
-#include "isl_map_private.h"
-
-struct isl_basic_map *isl_basic_map_affine_hull(struct isl_ctx *ctx,
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * 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
+ */
+
+#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)
{
- int i;
- isl_int opt;
+ struct isl_tab *tab;
- bmap = isl_basic_map_cow(ctx, bmap);
if (!bmap)
- return NULL;
+ return bmap;
- isl_int_init(opt);
- for (i = 0; i < bmap->n_ineq; ++i) {
- enum isl_lp_result res;
- res = isl_solve_lp(bmap, 1, bmap->ineq[i]+1, ctx->one, &opt);
- if (res == isl_lp_unbounded)
- continue;
- if (res == isl_lp_error)
- goto error;
- if (res == isl_lp_empty) {
- bmap = isl_basic_map_set_to_empty(ctx, bmap);
- break;
- }
- isl_int_add(opt, opt, bmap->ineq[i][0]);
- if (isl_int_is_zero(opt)) {
- isl_basic_map_inequality_to_equality(ctx, bmap, i);
- --i;
- }
- }
- isl_basic_map_free_inequality(ctx, bmap, bmap->n_ineq);
- isl_int_clear(opt);
- return isl_basic_map_finalize(ctx, 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_int_clear(opt);
- isl_basic_map_free(ctx, bmap);
+ isl_tab_free(tab);
+ isl_basic_map_free(bmap);
return NULL;
}
-struct isl_basic_set *isl_basic_set_affine_hull(struct isl_ctx *ctx,
+struct isl_basic_set *isl_basic_set_implicit_equalities(
struct isl_basic_set *bset)
{
return (struct isl_basic_set *)
- isl_basic_map_affine_hull(ctx, (struct isl_basic_map *)bset);
+ 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
* after column col are zero.
*/
static void set_common_multiple(
- struct isl_basic_map *bmap1, struct isl_basic_map *bmap2,
+ struct isl_basic_set *bset1, struct isl_basic_set *bset2,
unsigned row, unsigned col)
{
isl_int m, c;
- if (isl_int_eq(bmap1->eq[row][col], bmap2->eq[row][col]))
+ 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, bmap1->eq[row][col], bmap2->eq[row][col]);
- isl_int_divexact(c, m, bmap1->eq[row][col]);
- isl_seq_scale(bmap1->eq[row], bmap1->eq[row], c, col+1);
- isl_int_divexact(c, m, bmap2->eq[row][col]);
- isl_seq_scale(bmap2->eq[row], bmap2->eq[row], c, col+1);
+ 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_map *bmap, unsigned row)
+static void delete_row(struct isl_basic_set *bset, unsigned row)
{
isl_int *t;
int r;
- t = bmap->eq[row];
- bmap->n_eq--;
- for (r = row; r < bmap->n_eq; ++r)
- bmap->eq[r] = bmap->eq[r+1];
- bmap->eq[bmap->n_eq] = t;
+ 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 bmap1 identical to
- * those of bmap2, using the fact that entry bmap1->eq[row][col]=a
- * is non-zero. Initially, these elements of bmap1 are all zero.
+/* 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]
* A[i][col] = B[i][col] = a * old(B[i][col])
*/
static void construct_column(
- struct isl_basic_map *bmap1, struct isl_basic_map *bmap2,
+ struct isl_basic_set *bset1, struct isl_basic_set *bset2,
unsigned row, unsigned col)
{
int r;
isl_int_init(a);
isl_int_init(b);
- total = 1 + bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
+ total = 1 + isl_basic_set_n_dim(bset1);
for (r = 0; r < row; ++r) {
- if (isl_int_is_zero(bmap2->eq[r][col]))
+ if (isl_int_is_zero(bset2->eq[r][col]))
continue;
- isl_int_gcd(b, bmap2->eq[r][col], bmap1->eq[row][col]);
- isl_int_divexact(a, bmap1->eq[row][col], b);
- isl_int_divexact(b, bmap2->eq[r][col], b);
- isl_seq_combine(bmap1->eq[r], a, bmap1->eq[r],
- b, bmap1->eq[row], total);
- isl_seq_scale(bmap2->eq[r], bmap2->eq[r], a, total);
+ 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(bmap1, row);
+ delete_row(bset1, row);
}
-/* Make first row entries in column col of bmap1 identical to
- * those of bmap2, using only these entries of the two matrices.
+/* 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]
* 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_map *bmap1, struct isl_basic_map *bmap2,
+ struct isl_basic_set *bset1, struct isl_basic_set *bset2,
unsigned row, unsigned col)
{
int i, t;
unsigned total;
for (t = row-1; t >= 0; --t)
- if (isl_int_ne(bmap1->eq[t][col], bmap2->eq[t][col]))
+ if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col]))
break;
if (t < 0)
return 0;
- total = 1 + bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
+ total = 1 + isl_basic_set_n_dim(bset1);
isl_int_init(a);
isl_int_init(b);
isl_int_init(g);
- isl_int_sub(b, bmap1->eq[t][col], bmap2->eq[t][col]);
+ isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col]);
for (i = 0; i < t; ++i) {
- isl_int_sub(a, bmap2->eq[i][col], bmap1->eq[i][col]);
+ 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(bmap1->eq[i], g, bmap1->eq[i], a, bmap1->eq[t],
+ isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t],
total);
- isl_seq_combine(bmap2->eq[i], g, bmap2->eq[i], a, bmap2->eq[t],
+ 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(bmap1, t);
- delete_row(bmap2, t);
+ delete_row(bset1, t);
+ delete_row(bset2, t);
return 1;
}
* except that the echelon form we use starts from the last column
* and that we are dealing with integer coefficients.
*/
-static struct isl_basic_map *affine_hull(struct isl_ctx *ctx,
- struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+static struct isl_basic_set *affine_hull(
+ struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
unsigned total;
int col;
int row;
- total = 1 + bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
+ 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 >= bmap1->n_eq ||
- isl_int_is_zero(bmap1->eq[row][col]);
- int is_zero2 = row >= bmap2->n_eq ||
- isl_int_is_zero(bmap2->eq[row][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(bmap1, bmap2, row, col);
+ set_common_multiple(bset1, bset2, row, col);
++row;
} else if (!is_zero1 && is_zero2) {
- construct_column(bmap1, bmap2, row, col);
+ construct_column(bset1, bset2, row, col);
} else if (is_zero1 && !is_zero2) {
- construct_column(bmap2, bmap1, row, col);
+ construct_column(bset2, bset1, row, col);
} else {
- if (transform_column(bmap1, bmap2, row, col))
+ if (transform_column(bset1, bset2, row, col))
--row;
}
}
- isl_basic_map_free(ctx, bmap2);
- return bmap1;
+ 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_map *isl_map_affine_hull(struct isl_ctx *ctx,
- struct isl_map *map)
+struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset)
{
int i;
- struct isl_basic_map *bmap;
- map = isl_map_compute_divs(ctx, map);
- map = isl_map_cow(ctx, map);
- if (!map)
+ bset = isl_basic_set_cow(bset);
+ if (!bset)
return NULL;
+ isl_assert(bset->ctx, bset->n_div == 0, goto error);
- if (map->n == 0) {
- bmap = isl_basic_map_empty(ctx,
- map->nparam, map->n_in, map->n_out);
- isl_map_free(ctx, map);
+ 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 bmap that involve any of the dimensions
+ * first to first+n-1.
+ */
+static __isl_give isl_basic_map *isl_basic_map_drop_constraints_involving(
+ __isl_take isl_basic_map *bmap, unsigned first, unsigned n)
+{
+ int i;
+
+ if (n == 0)
return bmap;
+
+ bmap = isl_basic_map_cow(bmap);
+
+ if (!bmap)
+ return NULL;
+
+ for (i = bmap->n_eq - 1; i >= 0; --i) {
+ if (isl_seq_first_non_zero(bmap->eq[i] + 1 + first, n) == -1)
+ continue;
+ isl_basic_map_drop_equality(bmap, i);
+ }
+
+ for (i = bmap->n_ineq - 1; i >= 0; --i) {
+ if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + first, n) == -1)
+ continue;
+ isl_basic_map_drop_inequality(bmap, i);
+ }
+
+ return bmap;
+}
+
+/* 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)
+{
+ return isl_basic_map_drop_constraints_involving(bset, first, n);
+}
+
+/* Drop all constraints in bmap that do not involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_basic_map *isl_basic_map_drop_constraints_not_involving_dims(
+ __isl_take isl_basic_map *bmap,
+ enum isl_dim_type type, unsigned first, unsigned n)
+{
+ int i;
+ unsigned dim;
+
+ if (n == 0)
+ return isl_basic_map_set_to_empty(bmap);
+ bmap = isl_basic_map_cow(bmap);
+ if (!bmap)
+ return NULL;
+
+ dim = isl_basic_map_dim(bmap, type);
+ if (first + n > dim || first + n < first)
+ isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
+ "index out of bounds", return isl_basic_map_free(bmap));
+
+ first += isl_basic_map_offset(bmap, type) - 1;
+
+ for (i = bmap->n_eq - 1; i >= 0; --i) {
+ if (isl_seq_first_non_zero(bmap->eq[i] + 1 + first, n) != -1)
+ continue;
+ isl_basic_map_drop_equality(bmap, i);
}
- for (i = 1; i < map->n; ++i)
- map->p[0] = isl_basic_map_align_divs(ctx, map->p[0], map->p[i]);
- for (i = 1; i < map->n; ++i)
- map->p[i] = isl_basic_map_align_divs(ctx, map->p[i], map->p[0]);
+ for (i = bmap->n_ineq - 1; i >= 0; --i) {
+ if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + first, n) != -1)
+ continue;
+ isl_basic_map_drop_inequality(bmap, i);
+ }
+
+ return bmap;
+}
+
+/* Drop all constraints in bset that do not involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_basic_set *isl_basic_set_drop_constraints_not_involving_dims(
+ __isl_take isl_basic_set *bset,
+ enum isl_dim_type type, unsigned first, unsigned n)
+{
+ return isl_basic_map_drop_constraints_not_involving_dims(bset,
+ type, first, n);
+}
+
+/* Drop all constraints in bmap that involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_basic_map *isl_basic_map_drop_constraints_involving_dims(
+ __isl_take isl_basic_map *bmap,
+ enum isl_dim_type type, unsigned first, unsigned n)
+{
+ unsigned dim;
+
+ if (!bmap)
+ return NULL;
+ if (n == 0)
+ return bmap;
+
+ dim = isl_basic_map_dim(bmap, type);
+ if (first + n > dim || first + n < first)
+ isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
+ "index out of bounds", return isl_basic_map_free(bmap));
+
+ bmap = isl_basic_map_remove_divs_involving_dims(bmap, type, first, n);
+ first += isl_basic_map_offset(bmap, type) - 1;
+ return isl_basic_map_drop_constraints_involving(bmap, first, n);
+}
+
+/* Drop all constraints in bset that involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_basic_set *isl_basic_set_drop_constraints_involving_dims(
+ __isl_take isl_basic_set *bset,
+ enum isl_dim_type type, unsigned first, unsigned n)
+{
+ return isl_basic_map_drop_constraints_involving_dims(bset,
+ type, first, n);
+}
+
+/* Drop all constraints in map that involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_map *isl_map_drop_constraints_involving_dims(
+ __isl_take isl_map *map,
+ enum isl_dim_type type, unsigned first, unsigned n)
+{
+ int i;
+ unsigned dim;
+
+ if (!map)
+ return NULL;
+ if (n == 0)
+ return map;
+
+ dim = isl_map_dim(map, type);
+ if (first + n > dim || first + n < first)
+ isl_die(isl_map_get_ctx(map), isl_error_invalid,
+ "index out of bounds", return isl_map_free(map));
+
+ map = isl_map_cow(map);
+ if (!map)
+ return NULL;
for (i = 0; i < map->n; ++i) {
- map->p[i] = isl_basic_map_cow(ctx, map->p[i]);
- map->p[i] = isl_basic_map_affine_hull(ctx, map->p[i]);
- map->p[i] = isl_basic_map_gauss(ctx, map->p[i], NULL);
+ map->p[i] = isl_basic_map_drop_constraints_involving_dims(
+ map->p[i], type, first, n);
if (!map->p[i])
+ return isl_map_free(map);
+ }
+
+ return map;
+}
+
+/* Drop all constraints in set that involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_set *isl_set_drop_constraints_involving_dims(
+ __isl_take isl_set *set,
+ enum isl_dim_type type, unsigned first, unsigned n)
+{
+ return isl_map_drop_constraints_involving_dims(set, type, first, n);
+}
+
+/* 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);
}
- while (map->n > 1) {
- map->p[0] = affine_hull(ctx, map->p[0], map->p[--map->n]);
- if (!map->p[0])
+
+ 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 = NULL;
+ 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_basic_set_free(hull);
+ 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(Q);
+ 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(T1);
+ 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);
}
- bmap = isl_basic_map_copy(ctx, map->p[0]);
- isl_map_free(ctx, map);
- bmap = isl_basic_map_finalize(ctx, bmap);
- return isl_basic_map_simplify(ctx, bmap);
+ isl_set_free(set);
+ hull = isl_basic_map_simplify(hull);
+ return isl_basic_map_finalize(hull);
error:
- isl_map_free(ctx, map);
+ isl_basic_map_free(model);
+ isl_set_free(set);
return NULL;
}
-struct isl_basic_set *isl_set_affine_hull(struct isl_ctx *ctx,
- struct isl_set *set)
+struct isl_basic_set *isl_set_affine_hull(struct isl_set *set)
{
return (struct isl_basic_set *)
- isl_map_affine_hull(ctx, (struct isl_map *)set);
+ isl_map_affine_hull((struct isl_map *)set);
}
projects / platform / upstream / isl.git / blobdiff