/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010 INRIA Saclay
+ * Copyright 2012 Ecole Normale Superieure
*
* 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 Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
+ * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
*/
#include <isl_ctx_private.h>
isl_basic_map_affine_hull((struct isl_basic_map *)bset);
}
-struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
+/* Given a rational affine matrix "M", add stride constraints to "bmap"
+ * that ensure that
+ *
+ * M(x)
+ *
+ * is an integer vector. The variables x include all the variables
+ * of "bmap" except the unknown divs.
+ *
+ * If d is the common denominator of M, then we need to impose that
+ *
+ * d M(x) = 0 mod d
+ *
+ * or
+ *
+ * exists alpha : d M(x) = d alpha
+ *
+ * This function is similar to add_strides in isl_morph.c
+ */
+static __isl_give isl_basic_map *add_strides(__isl_take isl_basic_map *bmap,
+ __isl_keep isl_mat *M, int n_known)
+{
+ int i, div, k;
+ isl_int gcd;
+
+ if (isl_int_is_one(M->row[0][0]))
+ return bmap;
+
+ bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
+ M->n_row - 1, M->n_row - 1, 0);
+
+ isl_int_init(gcd);
+ for (i = 1; i < M->n_row; ++i) {
+ isl_seq_gcd(M->row[i], M->n_col, &gcd);
+ if (isl_int_is_divisible_by(gcd, M->row[0][0]))
+ continue;
+ div = isl_basic_map_alloc_div(bmap);
+ if (div < 0)
+ goto error;
+ isl_int_set_si(bmap->div[div][0], 0);
+ k = isl_basic_map_alloc_equality(bmap);
+ if (k < 0)
+ goto error;
+ isl_seq_cpy(bmap->eq[k], M->row[i], M->n_col);
+ isl_seq_clr(bmap->eq[k] + M->n_col, bmap->n_div - n_known);
+ isl_int_set(bmap->eq[k][M->n_col - n_known + div],
+ M->row[0][0]);
+ }
+ isl_int_clear(gcd);
+
+ return bmap;
+error:
+ isl_int_clear(gcd);
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+/* If there are any equalities that involve (multiple) unknown divs,
+ * then extract the stride information encoded by those equalities
+ * and make it explicitly available in "bmap".
+ *
+ * We first sort the divs so that the unknown divs appear last and
+ * then we count how many equalities involve these divs.
+ *
+ * Let these equalities be of the form
+ *
+ * A(x) + B y = 0
+ *
+ * where y represents the unknown divs and x the remaining variables.
+ * Let [H 0] be the Hermite Normal Form of B, i.e.,
+ *
+ * B = [H 0] Q
+ *
+ * Then x is a solution of the equalities iff
+ *
+ * H^-1 A(x) (= - [I 0] Q y)
+ *
+ * is an integer vector. Let d be the common denominator of H^-1.
+ * We impose
+ *
+ * d H^-1 A(x) = d alpha
+ *
+ * in add_strides, with alpha fresh existentially quantified variables.
+ */
+static __isl_give isl_basic_map *isl_basic_map_make_strides_explicit(
+ __isl_take isl_basic_map *bmap)
+{
+ int known;
+ int n_known;
+ int n, n_col;
+ int total;
+ isl_ctx *ctx;
+ isl_mat *A, *B, *M;
+
+ known = isl_basic_map_divs_known(bmap);
+ if (known < 0)
+ return isl_basic_map_free(bmap);
+ if (known)
+ return bmap;
+ bmap = isl_basic_map_sort_divs(bmap);
+ bmap = isl_basic_map_gauss(bmap, NULL);
+ if (!bmap)
+ return NULL;
+
+ for (n_known = 0; n_known < bmap->n_div; ++n_known)
+ if (isl_int_is_zero(bmap->div[n_known][0]))
+ break;
+ ctx = isl_basic_map_get_ctx(bmap);
+ total = isl_space_dim(bmap->dim, isl_dim_all);
+ for (n = 0; n < bmap->n_eq; ++n)
+ if (isl_seq_first_non_zero(bmap->eq[n] + 1 + total + n_known,
+ bmap->n_div - n_known) == -1)
+ break;
+ if (n == 0)
+ return bmap;
+ B = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 0, 1 + total + n_known);
+ n_col = bmap->n_div - n_known;
+ A = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 1 + total + n_known, n_col);
+ A = isl_mat_left_hermite(A, 0, NULL, NULL);
+ A = isl_mat_drop_cols(A, n, n_col - n);
+ A = isl_mat_lin_to_aff(A);
+ A = isl_mat_right_inverse(A);
+ B = isl_mat_insert_zero_rows(B, 0, 1);
+ B = isl_mat_set_element_si(B, 0, 0, 1);
+ M = isl_mat_product(A, B);
+ if (!M)
+ return isl_basic_map_free(bmap);
+ bmap = add_strides(bmap, M, n_known);
+ bmap = isl_basic_map_gauss(bmap, NULL);
+ isl_mat_free(M);
+
+ return bmap;
+}
+
+/* Compute the affine hull of each basic map in "map" separately
+ * and make all stride information explicit so that we can remove
+ * all unknown divs without losing this information.
+ * The result is also guaranteed to be gaussed.
+ *
+ * In simple cases where a div is determined by an equality,
+ * calling isl_basic_map_gauss is enough to make the stride information
+ * explicit, as it will derive an explicit representation for the div
+ * from the equality. If, however, the stride information
+ * is encoded through multiple unknown divs then we need to make
+ * some extra effort in isl_basic_map_make_strides_explicit.
+ */
+static __isl_give isl_map *isl_map_local_affine_hull(__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_affine_hull(map->p[i]);
+ map->p[i] = isl_basic_map_gauss(map->p[i], NULL);
+ map->p[i] = isl_basic_map_make_strides_explicit(map->p[i]);
+ if (!map->p[i])
+ return isl_map_free(map);
+ }
+
+ return map;
+}
+
+static __isl_give isl_set *isl_set_local_affine_hull(__isl_take isl_set *set)
+{
+ return isl_map_local_affine_hull(set);
+}
+
+/* Compute the affine hull of "map".
+ *
+ * We first compute the affine hull of each basic map separately.
+ * Then we align the divs and recompute the affine hulls of the basic
+ * maps since some of them may now have extra divs.
+ * In order to avoid performing parametric integer programming to
+ * compute explicit expressions for the divs, possible leading to
+ * an explosion in the number of basic maps, we first drop all unknown
+ * divs before aligning the divs. Note that isl_map_local_affine_hull tries
+ * to make sure that all stride information is explicitly available
+ * in terms of known divs. This involves calling isl_basic_set_gauss,
+ * which is also needed because affine_hull assumes its input has been gaussed,
+ * while isl_map_affine_hull may be called on input that has not been gaussed,
+ * in particular from initial_facet_constraint.
+ * Similarly, align_divs may reorder some divs so that we need to
+ * gauss the result again.
+ * Finally, we combine the individual affine hulls into a single
+ * affine hull.
+ */
+__isl_give isl_basic_map *isl_map_affine_hull(__isl_take isl_map *map)
+{
struct isl_basic_map *model = NULL;
struct isl_basic_map *hull = NULL;
struct isl_set *set;
+ isl_basic_set *bset;
map = isl_map_detect_equalities(map);
+ map = isl_map_local_affine_hull(map);
+ map = isl_map_remove_empty_parts(map);
+ map = isl_map_remove_unknown_divs(map);
map = isl_map_align_divs(map);
if (!map)
model = isl_basic_map_copy(map->p[0]);
set = isl_map_underlying_set(map);
set = isl_set_cow(set);
+ set = isl_set_local_affine_hull(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);
- }
+ while (set->n > 1)
+ set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
+
+ 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);
projects / platform / upstream / isl.git / blobdiff