(struct isl_map *)set2);
}
+/* 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_ctx *ctx = NULL;
+ 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;
+
+ ctx = bmap->ctx;
+
+ dim = isl_dim_total(bmap->dim);
+ vec = isl_vec_alloc(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->block.data, g, fl, fu);
+ res = isl_tab_min(ctx, tab, vec->block.data,
+ ctx->one, &g, NULL);
+ 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(ctx, tab);
+ isl_vec_free(ctx, 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);
+ if (ctx) {
+ isl_tab_free(ctx, tab);
+ isl_vec_free(ctx, vec);
+ }
+ isl_int_clear(g);
+ isl_int_clear(fl);
+ isl_int_clear(fu);
+ return NULL;
+}
+
/* 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;
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)
+ if (!redundant) {
+ pairs[i] = 0;
+ --n;
continue;
+ }
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 drop_more_redundant_divs(bmap, pairs, n);
+
+ free(pairs);
return bmap;
error:
+ free(pairs);
isl_basic_map_free(bmap);
return NULL;
}
projects / platform / upstream / isl.git / commitdiff