+/*
+ * 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_equalities.h"
#include "isl_map.h"
#include "isl_map_private.h"
+#include "isl_seq.h"
#include "isl_tab.h"
static void swap_equality(struct isl_basic_map *bmap, int a, int b)
return NULL;
}
+struct isl_set *isl_set_drop(struct isl_set *set,
+ enum isl_dim_type type, unsigned first, unsigned n)
+{
+ return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
+}
+
struct isl_map *isl_map_drop_inputs(
struct isl_map *map, unsigned first, unsigned n)
{
struct isl_basic_set *isl_basic_set_normalize_constraints(
struct isl_basic_set *bset)
{
- (struct isl_basic_set *)isl_basic_map_normalize_constraints(
+ return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
(struct isl_basic_map *)bset);
}
-static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
+/* Assumes divs have been ordered if keep_divs is set.
+ */
+static void eliminate_var_using_equality(struct isl_basic_map *bmap,
+ unsigned pos, isl_int *eq, int keep_divs, int *progress)
{
- int i;
- unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
- unsigned len;
- len = 1 + isl_basic_map_total_dim(bmap);
+ unsigned total;
+ int k;
+ int last_div;
- for (i = 0; i < bmap->n_eq; ++i)
- if (bmap->eq[i] != eq)
- isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
+ total = isl_basic_map_total_dim(bmap);
+ last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
+ bmap->n_div);
+ for (k = 0; k < bmap->n_eq; ++k) {
+ if (bmap->eq[k] == eq)
+ continue;
+ if (isl_int_is_zero(bmap->eq[k][1+pos]))
+ continue;
+ if (progress)
+ *progress = 1;
+ isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
+ }
- for (i = 0; i < bmap->n_ineq; ++i)
- isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
+ for (k = 0; k < bmap->n_ineq; ++k) {
+ if (isl_int_is_zero(bmap->ineq[k][1+pos]))
+ continue;
+ if (progress)
+ *progress = 1;
+ isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
+ ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+ }
- /* We need to be careful about circular definitions,
- * so for now we just remove the definitions of other divs that
- * depend on this div and (possibly) recompute them later.
- */
- for (i = 0; i < bmap->n_div; ++i)
- if (!isl_int_is_zero(bmap->div[i][0]) &&
- !isl_int_is_zero(bmap->div[i][1 + pos]))
- isl_seq_clr(bmap->div[i], 1 + len);
+ for (k = 0; k < bmap->n_div; ++k) {
+ if (isl_int_is_zero(bmap->div[k][0]))
+ continue;
+ if (isl_int_is_zero(bmap->div[k][1+1+pos]))
+ continue;
+ if (progress)
+ *progress = 1;
+ /* We need to be careful about circular definitions,
+ * so for now we just remove the definition of div k
+ * if the equality contains any divs.
+ * If keep_divs is set, then the divs have been ordered
+ * and we can keep the definition as long as the result
+ * is still ordered.
+ */
+ if (last_div == -1 || (keep_divs && last_div < k))
+ isl_seq_elim(bmap->div[k]+1, eq,
+ 1+pos, 1+total, &bmap->div[k][0]);
+ else
+ isl_seq_clr(bmap->div[k], 1 + total);
+ ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+ }
+}
+
+/* Assumes divs have been ordered if keep_divs is set.
+ */
+static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
+ unsigned div, int keep_divs)
+{
+ unsigned pos = isl_dim_total(bmap->dim) + div;
+
+ eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
isl_basic_map_drop_div(bmap, div);
}
int modified = 0;
unsigned off;
+ bmap = isl_basic_map_order_divs(bmap);
+
if (!bmap)
return NULL;
continue;
modified = 1;
*progress = 1;
- eliminate_div(bmap, bmap->eq[i], d);
+ eliminate_div(bmap, bmap->eq[i], d, 1);
isl_basic_map_drop_equality(bmap, i);
break;
}
return bmap;
}
-static void eliminate_var_using_equality(struct isl_basic_map *bmap,
- unsigned pos, isl_int *eq, int *progress)
-{
- unsigned total;
- int k;
- int contains_divs;
-
- total = isl_basic_map_total_dim(bmap);
- contains_divs =
- isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
- bmap->n_div) != -1;
- for (k = 0; k < bmap->n_eq; ++k) {
- if (bmap->eq[k] == eq)
- continue;
- if (isl_int_is_zero(bmap->eq[k][1+pos]))
- continue;
- if (progress)
- *progress = 1;
- isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
- }
-
- for (k = 0; k < bmap->n_ineq; ++k) {
- if (isl_int_is_zero(bmap->ineq[k][1+pos]))
- continue;
- if (progress)
- *progress = 1;
- isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
- ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
- }
-
- for (k = 0; k < bmap->n_div; ++k) {
- if (isl_int_is_zero(bmap->div[k][0]))
- continue;
- if (isl_int_is_zero(bmap->div[k][1+1+pos]))
- continue;
- if (progress)
- *progress = 1;
- /* We need to be careful about circular definitions,
- * so for now we just remove the definition of div k
- * if the equality contains any divs.
- */
- if (contains_divs)
- isl_seq_clr(bmap->div[k], 1 + total);
- else
- isl_seq_elim(bmap->div[k]+1, eq,
- 1+pos, 1+total, &bmap->div[k][0]);
- ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
- }
-}
-
struct isl_basic_map *isl_basic_map_gauss(
struct isl_basic_map *bmap, int *progress)
{
unsigned total_var;
unsigned total;
+ bmap = isl_basic_map_order_divs(bmap);
+
if (!bmap)
return NULL;
if (isl_int_is_neg(bmap->eq[done][1+last_var]))
isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
- eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
+ eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
progress);
if (last_var >= total_var &&
k = elim_for[l] - 1;
isl_int_set_si(eq.data[1+total_var+k], -1);
isl_int_set_si(eq.data[1+total_var+l], 1);
- eliminate_div(bmap, eq.data, l);
+ eliminate_div(bmap, eq.data, l, 0);
isl_int_set_si(eq.data[1+total_var+k], 0);
isl_int_set_si(eq.data[1+total_var+l], 0);
}
if (div_eq < bmap->n_eq) {
B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
bmap->n_eq - div_eq, 0, 1 + total);
- C = isl_mat_variable_compression(bmap->ctx, B, &C2);
+ C = isl_mat_variable_compression(B, &C2);
if (!C || !C2)
goto error;
if (C->n_col == 0) {
bmap = isl_basic_map_set_to_empty(bmap);
- isl_mat_free(bmap->ctx, C);
- isl_mat_free(bmap->ctx, C2);
+ isl_mat_free(C);
+ isl_mat_free(C2);
goto done;
}
}
B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
if (C) {
- B = isl_mat_product(bmap->ctx, B, C);
+ B = isl_mat_product(B, C);
C = NULL;
}
- T = isl_mat_parameter_compression(bmap->ctx, B, d);
+ T = isl_mat_parameter_compression(B, d);
if (!T)
goto error;
if (T->n_col == 0) {
bmap = isl_basic_map_set_to_empty(bmap);
- isl_mat_free(bmap->ctx, C2);
- isl_mat_free(bmap->ctx, T);
+ isl_mat_free(C2);
+ isl_mat_free(T);
goto done;
}
isl_int_init(v);
isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
}
free(pos);
- isl_mat_free(bmap->ctx, C2);
- isl_mat_free(bmap->ctx, T);
+ isl_mat_free(C2);
+ isl_mat_free(T);
if (progress)
*progress = 1;
return bmap;
error:
- isl_mat_free(bmap->ctx, C);
- isl_mat_free(bmap->ctx, C2);
- isl_mat_free(bmap->ctx, T);
+ isl_mat_free(C);
+ isl_mat_free(C2);
+ isl_mat_free(T);
return bmap;
}
static struct isl_basic_map *check_for_div_constraints(
struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
{
- int i, j;
+ int i;
unsigned total = 1 + isl_dim_total(bmap->dim);
for (i = 0; i < bmap->n_div; ++i) {
* will no longer be valid.
* Plus, we probably we want to regauss first.
*/
+ if (progress)
+ *progress = 1;
isl_basic_map_drop_inequality(bmap, l);
isl_basic_map_inequality_to_equality(bmap, k);
} else
}
-/* Remove any div that is defined in terms of the given variable.
+/* Remove definition of any div that is defined in terms of the given variable.
+ * The div itself is not removed. Functions such as
+ * eliminate_divs_ineq depend on the other divs remaining in place.
*/
static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
int pos)
{
int i;
- unsigned dim = isl_dim_total(bmap->dim);
for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0]))
continue;
if (isl_int_is_zero(bmap->div[i][1+1+pos]))
continue;
- bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
- if (!bmap)
- return NULL;
+ isl_int_set_si(bmap->div[i][0], 0);
}
return bmap;
}
for (i = 0; i < bmap->n_eq; ++i) {
if (isl_int_is_zero(bmap->eq[i][1+d]))
continue;
- eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
+ eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
isl_basic_map_drop_equality(bmap, i);
break;
}
static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
{
- return compute_elimination_index((struct isl_basic_map *)bset, elim);
+ compute_elimination_index((struct isl_basic_map *)bset, elim);
}
static int reduced_using_equalities(isl_int *dst, isl_int *src,
struct isl_basic_map *bmap, int *elim)
{
- int d, i;
+ int d;
int copied = 0;
unsigned total;
total = isl_basic_set_total_dim(bset);
B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
- C = isl_mat_variable_compression(bset->ctx, B, NULL);
+ C = isl_mat_variable_compression(B, NULL);
if (!C)
return bset;
if (C->n_col == 0) {
- isl_mat_free(bset->ctx, C);
+ isl_mat_free(C);
return isl_basic_set_set_to_empty(bset);
}
B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
0, bset->n_ineq, 0, 1 + total);
- C = isl_mat_product(bset->ctx, B, C);
+ C = isl_mat_product(B, C);
if (!C)
return bset;
}
isl_int_clear(gcd);
- isl_mat_free(bset->ctx, C);
+ isl_mat_free(C);
return bset;
}
bset = remove_shifted_constraints(bset, context);
if (!bset->n_ineq)
goto done;
- isl_basic_set_free_equality(context, context->n_eq);
context_ineq = context->n_ineq;
combined = isl_basic_set_cow(isl_basic_set_copy(context));
+ if (isl_basic_set_free_equality(combined, context->n_eq) < 0)
+ goto error;
combined = isl_basic_set_extend_constraints(combined,
bset->n_eq, bset->n_ineq);
tab = isl_tab_from_basic_set(combined);
if (!tab)
goto error;
for (i = 0; i < context_ineq; ++i)
- tab->con[i].frozen = 1;
- tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
+ if (isl_tab_freeze_constraint(tab, i) < 0)
+ goto error;
+ tab = isl_tab_extend(tab, bset->n_ineq);
if (!tab)
goto error;
for (i = 0; i < bset->n_ineq; ++i)
- tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
+ if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
+ goto error;
bset = isl_basic_set_add_constraints(combined, bset, 0);
- tab = isl_tab_detect_equalities(bset->ctx, tab);
- tab = isl_tab_detect_redundant(bset->ctx, tab);
- if (!tab)
+ tab = isl_tab_detect_implicit_equalities(tab);
+ if (isl_tab_detect_redundant(tab) < 0) {
+ isl_tab_free(tab);
goto error2;
+ }
for (i = 0; i < context_ineq; ++i) {
tab->con[i].is_zero = 0;
tab->con[i].is_redundant = 1;
}
bset = isl_basic_set_update_from_tab(bset, tab);
- isl_tab_free(bset->ctx, tab);
+ isl_tab_free(tab);
ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
done:
struct isl_vec *v = NULL;
int *elim = NULL;
unsigned total;
- int d, i;
+ int i;
if (!bmap1 || !bmap2)
return -1;
isl_seq_first_non_zero(v->block.data + 1, total) == -1)
goto disjoint;
}
- isl_vec_free(bmap1->ctx, v);
+ isl_vec_free(v);
free(elim);
return 0;
disjoint:
- isl_vec_free(bmap1->ctx, v);
+ isl_vec_free(v);
free(elim);
return 1;
error:
- isl_vec_free(bmap1->ctx, v);
+ isl_vec_free(v);
free(elim);
return -1;
}
(struct isl_map *)set2);
}
+/* Check if we can combine a given div with lower bound l and upper
+ * bound u with some other div and if so return that other div.
+ * Otherwise return -1.
+ *
+ * We first check that
+ * - the bounds are opposites of each other (except for the constant
+ * term)
+ * - the bounds do not reference any other div
+ * - no div is defined in terms of this div
+ *
+ * Let m be the size of the range allowed on the div by the bounds.
+ * That is, the bounds are of the form
+ *
+ * e <= a <= e + m - 1
+ *
+ * with e some expression in the other variables.
+ * We look for another div b such that no third div is defined in terms
+ * of this second div b and such that in any constraint that contains
+ * a (except for the given lower and upper bound), also contains b
+ * with a coefficient that is m times that of b.
+ * That is, all constraints (execpt for the lower and upper bound)
+ * are of the form
+ *
+ * e + f (a + m b) >= 0
+ *
+ * If so, we return b so that "a + m b" can be replaced by
+ * a single div "c = a + m b".
+ */
+static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
+ unsigned div, unsigned l, unsigned u)
+{
+ int i, j;
+ unsigned dim;
+ int coalesce = -1;
+
+ if (bmap->n_div <= 1)
+ return -1;
+ dim = isl_dim_total(bmap->dim);
+ if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
+ return -1;
+ if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
+ bmap->n_div - div - 1) != -1)
+ return -1;
+ if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
+ dim + bmap->n_div))
+ return -1;
+
+ for (i = 0; i < bmap->n_div; ++i) {
+ if (isl_int_is_zero(bmap->div[i][0]))
+ continue;
+ if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
+ return -1;
+ }
+
+ isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
+ if (isl_int_is_neg(bmap->ineq[l][0])) {
+ isl_int_sub(bmap->ineq[l][0],
+ bmap->ineq[l][0], bmap->ineq[u][0]);
+ bmap = isl_basic_map_copy(bmap);
+ bmap = isl_basic_map_set_to_empty(bmap);
+ isl_basic_map_free(bmap);
+ return -1;
+ }
+ isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
+ for (i = 0; i < bmap->n_div; ++i) {
+ if (i == div)
+ continue;
+ if (!pairs[i])
+ continue;
+ for (j = 0; j < bmap->n_div; ++j) {
+ if (isl_int_is_zero(bmap->div[j][0]))
+ continue;
+ if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
+ break;
+ }
+ if (j < bmap->n_div)
+ continue;
+ for (j = 0; j < bmap->n_ineq; ++j) {
+ int valid;
+ if (j == l || j == u)
+ continue;
+ if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
+ continue;
+ if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
+ break;
+ isl_int_mul(bmap->ineq[j][1 + dim + div],
+ bmap->ineq[j][1 + dim + div],
+ bmap->ineq[l][0]);
+ valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
+ bmap->ineq[j][1 + dim + i]);
+ isl_int_divexact(bmap->ineq[j][1 + dim + div],
+ bmap->ineq[j][1 + dim + div],
+ bmap->ineq[l][0]);
+ if (!valid)
+ break;
+ }
+ if (j < bmap->n_ineq)
+ continue;
+ coalesce = i;
+ break;
+ }
+ isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
+ isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
+ return coalesce;
+}
+
+/* Given a lower and an upper bound on div i, construct an inequality
+ * that when nonnegative ensures that this pair of bounds always allows
+ * for an integer value of the given div.
+ * The lower bound is inequality l, while the upper bound is inequality u.
+ * The constructed inequality is stored in ineq.
+ * g, fl, fu are temporary scalars.
+ *
+ * Let the upper bound be
+ *
+ * -n_u a + e_u >= 0
+ *
+ * and the lower bound
+ *
+ * n_l a + e_l >= 0
+ *
+ * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
+ * We have
+ *
+ * - f_u e_l <= f_u f_l g a <= f_l e_u
+ *
+ * Since all variables are integer valued, this is equivalent to
+ *
+ * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
+ *
+ * If this interval is at least f_u f_l g, then it contains at least
+ * one integer value for a.
+ * That is, the test constraint is
+ *
+ * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
+ */
+static void construct_test_ineq(struct isl_basic_map *bmap, int i,
+ int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
+{
+ unsigned dim;
+ dim = isl_dim_total(bmap->dim);
+
+ isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
+ isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
+ isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
+ isl_int_neg(fu, fu);
+ isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
+ 1 + dim + bmap->n_div);
+ isl_int_add(ineq[0], ineq[0], fl);
+ isl_int_add(ineq[0], ineq[0], fu);
+ isl_int_sub_ui(ineq[0], ineq[0], 1);
+ isl_int_mul(g, g, fl);
+ isl_int_mul(g, g, fu);
+ isl_int_sub(ineq[0], ineq[0], g);
+}
+
+/* Remove more kinds of divs that are not strictly needed.
+ * In particular, if all pairs of lower and upper bounds on a div
+ * are such that they allow at least one integer value of the div,
+ * the we can eliminate the div using Fourier-Motzkin without
+ * introducing any spurious solutions.
+ */
+static struct isl_basic_map *drop_more_redundant_divs(
+ struct isl_basic_map *bmap, int *pairs, int n)
+{
+ struct isl_tab *tab = NULL;
+ struct isl_vec *vec = NULL;
+ unsigned dim;
+ int remove = -1;
+ isl_int g, fl, fu;
+
+ isl_int_init(g);
+ isl_int_init(fl);
+ isl_int_init(fu);
+
+ if (!bmap)
+ goto error;
+
+ dim = isl_dim_total(bmap->dim);
+ vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
+ if (!vec)
+ goto error;
+
+ tab = isl_tab_from_basic_map(bmap);
+
+ while (n > 0) {
+ int i, l, u;
+ int best = -1;
+ enum isl_lp_result res;
+
+ for (i = 0; i < bmap->n_div; ++i) {
+ if (!pairs[i])
+ continue;
+ if (best >= 0 && pairs[best] <= pairs[i])
+ continue;
+ best = i;
+ }
+
+ i = best;
+ for (l = 0; l < bmap->n_ineq; ++l) {
+ if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
+ continue;
+ for (u = 0; u < bmap->n_ineq; ++u) {
+ if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
+ continue;
+ construct_test_ineq(bmap, i, l, u,
+ vec->el, g, fl, fu);
+ res = isl_tab_min(tab, vec->el,
+ bmap->ctx->one, &g, NULL, 0);
+ if (res == isl_lp_error)
+ goto error;
+ if (res == isl_lp_empty) {
+ bmap = isl_basic_map_set_to_empty(bmap);
+ break;
+ }
+ if (res != isl_lp_ok || isl_int_is_neg(g))
+ break;
+ }
+ if (u < bmap->n_ineq)
+ break;
+ }
+ if (l == bmap->n_ineq) {
+ remove = i;
+ break;
+ }
+ pairs[i] = 0;
+ --n;
+ }
+
+ isl_tab_free(tab);
+ isl_vec_free(vec);
+
+ isl_int_clear(g);
+ isl_int_clear(fl);
+ isl_int_clear(fu);
+
+ free(pairs);
+
+ if (remove < 0)
+ return bmap;
+
+ bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
+ return isl_basic_map_drop_redundant_divs(bmap);
+error:
+ free(pairs);
+ isl_basic_map_free(bmap);
+ isl_tab_free(tab);
+ isl_vec_free(vec);
+ isl_int_clear(g);
+ isl_int_clear(fl);
+ isl_int_clear(fu);
+ return NULL;
+}
+
+/* Given a pair of divs div1 and div2 such that, expect for the lower bound l
+ * and the upper bound u, div1 always occurs together with div2 in the form
+ * (div1 + m div2), where m is the constant range on the variable div1
+ * allowed by l and u, replace the pair div1 and div2 by a single
+ * div that is equal to div1 + m div2.
+ *
+ * The new div will appear in the location that contains div2.
+ * We need to modify all constraints that contain
+ * div2 = (div - div1) / m
+ * (If a constraint does not contain div2, it will also not contain div1.)
+ * If the constraint also contains div1, then we know they appear
+ * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
+ * i.e., the coefficient of div is f.
+ *
+ * Otherwise, we first need to introduce div1 into the constraint.
+ * Let the l be
+ *
+ * div1 + f >=0
+ *
+ * and u
+ *
+ * -div1 + f' >= 0
+ *
+ * A lower bound on div2
+ *
+ * n div2 + t >= 0
+ *
+ * can be replaced by
+ *
+ * (n * (m div 2 + div1) + m t + n f)/g >= 0
+ *
+ * with g = gcd(m,n).
+ * An upper bound
+ *
+ * -n div2 + t >= 0
+ *
+ * can be replaced by
+ *
+ * (-n * (m div2 + div1) + m t + n f')/g >= 0
+ *
+ * These constraint are those that we would obtain from eliminating
+ * div1 using Fourier-Motzkin.
+ *
+ * After all constraints have been modified, we drop the lower and upper
+ * bound and then drop div1.
+ */
+static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
+ unsigned div1, unsigned div2, unsigned l, unsigned u)
+{
+ isl_int a;
+ isl_int b;
+ isl_int m;
+ unsigned dim, total;
+ int i;
+
+ dim = isl_dim_total(bmap->dim);
+ total = 1 + dim + bmap->n_div;
+
+ isl_int_init(a);
+ isl_int_init(b);
+ isl_int_init(m);
+ isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
+ isl_int_add_ui(m, m, 1);
+
+ for (i = 0; i < bmap->n_ineq; ++i) {
+ if (i == l || i == u)
+ continue;
+ if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
+ continue;
+ if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
+ isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
+ isl_int_divexact(a, m, b);
+ isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
+ if (isl_int_is_pos(b)) {
+ isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
+ b, bmap->ineq[l], total);
+ } else {
+ isl_int_neg(b, b);
+ isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
+ b, bmap->ineq[u], total);
+ }
+ }
+ isl_int_set(bmap->ineq[i][1 + dim + div2],
+ bmap->ineq[i][1 + dim + div1]);
+ isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
+ }
+
+ isl_int_clear(a);
+ isl_int_clear(b);
+ isl_int_clear(m);
+ if (l > u) {
+ isl_basic_map_drop_inequality(bmap, l);
+ isl_basic_map_drop_inequality(bmap, u);
+ } else {
+ isl_basic_map_drop_inequality(bmap, u);
+ isl_basic_map_drop_inequality(bmap, l);
+ }
+ bmap = isl_basic_map_drop_div(bmap, div1);
+ return bmap;
+}
+
+/* First check if we can coalesce any pair of divs and
+ * then continue with dropping more redundant divs.
+ *
+ * We loop over all pairs of lower and upper bounds on a div
+ * with coefficient 1 and -1, respectively, check if there
+ * is any other div "c" with which we can coalesce the div
+ * and if so, perform the coalescing.
+ */
+static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
+ struct isl_basic_map *bmap, int *pairs, int n)
+{
+ int i, l, u;
+ unsigned dim;
+
+ dim = isl_dim_total(bmap->dim);
+
+ for (i = 0; i < bmap->n_div; ++i) {
+ if (!pairs[i])
+ continue;
+ for (l = 0; l < bmap->n_ineq; ++l) {
+ if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
+ continue;
+ for (u = 0; u < bmap->n_ineq; ++u) {
+ int c;
+
+ if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
+ continue;
+ c = div_find_coalesce(bmap, pairs, i, l, u);
+ if (c < 0)
+ continue;
+ free(pairs);
+ bmap = coalesce_divs(bmap, i, c, l, u);
+ return isl_basic_map_drop_redundant_divs(bmap);
+ }
+ }
+ }
+
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+ return bmap;
+
+ return drop_more_redundant_divs(bmap, pairs, n);
+}
+
/* Remove divs that are not strictly needed.
* In particular, if a div only occurs positively (or negatively)
* in constraints, then it can simply be dropped.
* div, i.e., if one plus this sum is greater than or equal to
* the (absolute value) of the coefficent of the div in the constraints,
* then we can also simply drop the div.
+ *
+ * If any divs are left after these simple checks then we move on
+ * to more complicated cases in drop_more_redundant_divs.
*/
struct isl_basic_map *isl_basic_map_drop_redundant_divs(
struct isl_basic_map *bmap)
{
int i, j;
unsigned off;
+ int *pairs = NULL;
+ int n = 0;
if (!bmap)
goto error;
off = isl_dim_total(bmap->dim);
+ pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
+ if (!pairs)
+ goto error;
for (i = 0; i < bmap->n_div; ++i) {
int pos, neg;
int last_pos, last_neg;
int redundant;
+ int defined;
- if (!isl_int_is_zero(bmap->div[i][0]))
- continue;
+ defined = !isl_int_is_zero(bmap->div[i][0]);
for (j = 0; j < bmap->n_eq; ++j)
if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
break;
if (j < bmap->n_eq)
continue;
+ ++n;
pos = neg = 0;
for (j = 0; j < bmap->n_ineq; ++j) {
if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
++neg;
}
}
- if (pos * neg == 0) {
+ pairs[i] = pos * neg;
+ if (pairs[i] == 0) {
for (j = bmap->n_ineq - 1; j >= 0; --j)
if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
isl_basic_map_drop_inequality(bmap, j);
bmap = isl_basic_map_drop_div(bmap, i);
+ free(pairs);
return isl_basic_map_drop_redundant_divs(bmap);
}
- if (pos * neg != 1)
+ if (pairs[i] != 1)
continue;
if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
bmap->ineq[last_neg] + 1,
bmap->ineq[last_pos][0], 1);
isl_int_sub(bmap->ineq[last_pos][0],
bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
- if (!redundant)
- continue;
+ if (!redundant) {
+ if (defined ||
+ !ok_to_set_div_from_bound(bmap, i, last_pos)) {
+ pairs[i] = 0;
+ --n;
+ continue;
+ }
+ bmap = set_div_from_lower_bound(bmap, i, last_pos);
+ bmap = isl_basic_map_simplify(bmap);
+ free(pairs);
+ return isl_basic_map_drop_redundant_divs(bmap);
+ }
if (last_pos > last_neg) {
isl_basic_map_drop_inequality(bmap, last_pos);
isl_basic_map_drop_inequality(bmap, last_neg);
isl_basic_map_drop_inequality(bmap, last_pos);
}
bmap = isl_basic_map_drop_div(bmap, i);
+ free(pairs);
return isl_basic_map_drop_redundant_divs(bmap);
}
+ if (n > 0)
+ return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
+
+ free(pairs);
return bmap;
error:
+ free(pairs);
isl_basic_map_free(bmap);
return NULL;
}
+
+struct isl_basic_set *isl_basic_set_drop_redundant_divs(
+ struct isl_basic_set *bset)
+{
+ return (struct isl_basic_set *)
+ isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
+}
+
+struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
+{
+ int i;
+
+ if (!map)
+ return NULL;
+ for (i = 0; i < map->n; ++i) {
+ map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
+ if (!map->p[i])
+ goto error;
+ }
+ ISL_F_CLR(map, ISL_MAP_NORMALIZED);
+ return map;
+error:
+ isl_map_free(map);
+ return NULL;
+}
+
+struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
+{
+ return (struct isl_set *)
+ isl_map_drop_redundant_divs((struct isl_map *)set);
+}
projects / platform / upstream / isl.git / blobdiff