#include "isl_equalities.h"
#include "isl_map.h"
#include "isl_map_private.h"
+#include "isl_tab.h"
static void swap_equality(struct isl_basic_map *bmap, int a, int b)
{
if (!bset->dim)
goto error;
- F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
+ ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
bset = isl_basic_set_simplify(bset);
return isl_basic_set_finalize(bset);
error:
goto error;
}
- F_CLR(set, ISL_SET_NORMALIZED);
+ ISL_F_CLR(set, ISL_SET_NORMALIZED);
return set;
error:
isl_set_free(set);
return NULL;
}
-/* Drop n input dimensions starting at first.
+/* Move "n" divs starting at "first" to the end of the list of divs.
+ */
+static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
+ unsigned first, unsigned n)
+{
+ isl_int **div;
+ int i;
+
+ if (first + n == bmap->n_div)
+ return bmap;
+
+ div = isl_alloc_array(bmap->ctx, isl_int *, n);
+ if (!div)
+ goto error;
+ for (i = 0; i < n; ++i)
+ div[i] = bmap->div[first + i];
+ for (i = 0; i < bmap->n_div - first - n; ++i)
+ bmap->div[first + i] = bmap->div[first + n + i];
+ for (i = 0; i < n; ++i)
+ bmap->div[bmap->n_div - n + i] = div[i];
+ free(div);
+ return bmap;
+error:
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+/* Drop "n" dimensions of type "type" starting at "first".
*
* In principle, this frees up some extra variables as the number
* of columns remains constant, but we would have to extend
* the div array too as the number of rows in this array is assumed
* to be equal to extra.
*/
-struct isl_basic_map *isl_basic_map_drop_inputs(
- struct isl_basic_map *bmap, unsigned first, unsigned n)
+struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
+ enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
- unsigned nparam;
- unsigned n_in;
- unsigned n_out;
+ unsigned dim;
+ unsigned offset;
+ unsigned left;
if (!bmap)
goto error;
- nparam = isl_basic_map_n_param(bmap);
- n_in = isl_basic_map_n_in(bmap);
- n_out = isl_basic_map_n_out(bmap);
- isl_assert(bmap->ctx, first + n <= n_in, goto error);
+ dim = isl_basic_map_dim(bmap, type);
+ isl_assert(bmap->ctx, first + n <= dim, goto error);
if (n == 0)
return bmap;
if (!bmap)
return NULL;
+ offset = isl_basic_map_offset(bmap, type) + first;
+ left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
for (i = 0; i < bmap->n_eq; ++i)
- constraint_drop_vars(bmap->eq[i]+1+nparam+first, n,
- (n_in-first-n)+n_out+bmap->extra);
+ constraint_drop_vars(bmap->eq[i]+offset, n, left);
for (i = 0; i < bmap->n_ineq; ++i)
- constraint_drop_vars(bmap->ineq[i]+1+nparam+first, n,
- (n_in-first-n)+n_out+bmap->extra);
+ constraint_drop_vars(bmap->ineq[i]+offset, n, left);
for (i = 0; i < bmap->n_div; ++i)
- constraint_drop_vars(bmap->div[i]+1+1+nparam+first, n,
- (n_in-first-n)+n_out+bmap->extra);
+ constraint_drop_vars(bmap->div[i]+1+offset, n, left);
- bmap->dim = isl_dim_drop_inputs(bmap->dim, first, n);
+ if (type == isl_dim_div) {
+ bmap = move_divs_last(bmap, first, n);
+ if (!bmap)
+ goto error;
+ isl_basic_map_free_div(bmap, n);
+ } else
+ bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
if (!bmap->dim)
goto error;
- F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+ ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
bmap = isl_basic_map_simplify(bmap);
return isl_basic_map_finalize(bmap);
error:
return NULL;
}
-struct isl_map *isl_map_drop_inputs(
- struct isl_map *map, unsigned first, unsigned n)
+struct isl_basic_map *isl_basic_map_drop_inputs(
+ struct isl_basic_map *bmap, unsigned first, unsigned n)
+{
+ return isl_basic_map_drop(bmap, isl_dim_in, first, n);
+}
+
+struct isl_map *isl_map_drop(struct isl_map *map,
+ enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
if (!map)
goto error;
- isl_assert(map->ctx, first + n <= map->dim->n_in, goto error);
+ isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
if (n == 0)
return map;
map = isl_map_cow(map);
if (!map)
goto error;
- map->dim = isl_dim_drop_inputs(map->dim, first, n);
+ map->dim = isl_dim_drop(map->dim, type, first, n);
if (!map->dim)
goto error;
for (i = 0; i < map->n; ++i) {
- map->p[i] = isl_basic_map_drop_inputs(map->p[i], first, n);
+ map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
if (!map->p[i])
goto error;
}
- F_CLR(map, ISL_MAP_NORMALIZED);
+ ISL_F_CLR(map, ISL_MAP_NORMALIZED);
return map;
error:
return NULL;
}
+struct isl_map *isl_map_drop_inputs(
+ struct isl_map *map, unsigned first, unsigned n)
+{
+ return isl_map_drop(map, isl_dim_in, first, n);
+}
+
/*
* We don't cow, as the div is assumed to be redundant.
*/
bmap->div[bmap->n_div - 1] = t;
}
- F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+ ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
isl_basic_map_free_div(bmap, 1);
return bmap;
return NULL;
}
-static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
+struct isl_basic_map *isl_basic_map_normalize_constraints(
+ struct isl_basic_map *bmap)
{
int i;
isl_int gcd;
isl_basic_map_drop_equality(bmap, i);
continue;
}
- if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
if (isl_int_is_one(gcd))
continue;
isl_basic_map_drop_inequality(bmap, i);
continue;
}
- if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
if (isl_int_is_one(gcd))
continue;
return bmap;
}
+struct isl_basic_set *isl_basic_set_normalize_constraints(
+ struct isl_basic_set *bset)
+{
+ (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)
{
int i;
continue;
*progress = 1;
bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
- if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
break;
bmap = isl_basic_map_drop_div(bmap, d);
if (!bmap)
{
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 (progress)
*progress = 1;
isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
- F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+ ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
}
for (k = 0; k < bmap->n_div; ++k) {
continue;
if (progress)
*progress = 1;
- isl_seq_elim(bmap->div[k]+1, eq,
- 1+pos, 1+total, &bmap->div[k][0]);
- F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+ /* 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);
}
}
isl_int_set_si(bmap->div[div][1+1+last_var], 0);
isl_int_set(bmap->div[div][0],
bmap->eq[done][1+last_var]);
- F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+ ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
}
}
if (done == bmap->n_eq)
return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
}
+/* If we can eliminate more than one div, then we need to make
+ * sure we do it from last div to first div, in order not to
+ * change the position of the other divs that still need to
+ * be removed.
+ */
static struct isl_basic_map *remove_duplicate_divs(
struct isl_basic_map *bmap, int *progress)
{
unsigned int size;
int *index;
+ int *elim_for;
int k, l, h;
int bits;
struct isl_blk eq;
if (k <= 0)
return bmap;
+ elim_for = isl_calloc_array(ctx, int, bmap->n_div);
size = round_up(4 * bmap->n_div / 3 - 1);
bits = ffs(size) - 1;
index = isl_calloc_array(ctx, int, size);
if (index[h]) {
*progress = 1;
l = index[h] - 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);
- isl_int_set_si(eq.data[1+total_var+k], 0);
- isl_int_set_si(eq.data[1+total_var+l], 0);
+ elim_for[l] = k + 1;
}
index[h] = k+1;
}
+ for (l = bmap->n_div - 1; l >= 0; --l) {
+ if (!elim_for[l])
+ continue;
+ 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);
+ isl_int_set_si(eq.data[1+total_var+k], 0);
+ isl_int_set_si(eq.data[1+total_var+l], 0);
+ }
isl_blk_free(ctx, eq);
out:
free(index);
+ free(elim_for);
return bmap;
}
+static int n_pure_div_eq(struct isl_basic_map *bmap)
+{
+ int i, j;
+ unsigned total;
+
+ total = isl_dim_total(bmap->dim);
+ for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
+ while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
+ --j;
+ if (j < 0)
+ break;
+ if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
+ return 0;
+ }
+ return i;
+}
+
/* Normalize divs that appear in equalities.
*
* In particular, we assume that bmap contains some equalities
* x'' = T(x') = x_0 + G x'
*
* and in constructing the new divs and the corresponding equalities,
- * we have to replace each x'' by the corresponding row from C_2.
+ * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
+ * by the corresponding row from C_2.
*/
static struct isl_basic_map *normalize_divs(
struct isl_basic_map *bmap, int *progress)
struct isl_mat *C2 = NULL;
isl_int v;
int *pos;
+ int dropped, needed;
if (!bmap)
return NULL;
if (bmap->n_eq == 0)
return bmap;
- if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
return bmap;
total = isl_dim_total(bmap->dim);
- for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
- while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
- --j;
- if (j < 0)
- break;
- if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
- goto done;
- }
- div_eq = i;
+ div_eq = n_pure_div_eq(bmap);
if (div_eq == 0)
return bmap;
isl_int_clear(v);
pos = isl_alloc_array(bmap->ctx, int, T->n_row);
/* We have to be careful because dropping equalities may reorder them */
+ dropped = 0;
for (j = bmap->n_div - 1; j >= 0; --j) {
for (i = 0; i < bmap->n_eq; ++i)
if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
if (i < bmap->n_eq) {
bmap = isl_basic_map_drop_div(bmap, j);
isl_basic_map_drop_equality(bmap, i);
+ ++dropped;
}
}
pos[0] = 0;
+ needed = 0;
for (i = 1; i < T->n_row; ++i) {
- if (isl_int_is_one(T->row[i][i])) {
+ if (isl_int_is_one(T->row[i][i]))
pos[i] = i;
+ else
+ needed++;
+ }
+ if (needed > dropped) {
+ bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
+ needed, needed, 0);
+ if (!bmap)
+ goto error;
+ }
+ for (i = 1; i < T->n_row; ++i) {
+ if (isl_int_is_one(T->row[i][i]))
continue;
- }
k = isl_basic_map_alloc_div(bmap);
pos[i] = 1 + total + k;
isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
for (j = 0; j < i; ++j) {
if (isl_int_is_zero(T->row[i][j]))
continue;
- if (C2)
+ if (pos[j] < T->n_row && C2)
isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
C2->row[pos[j]], 1 + total);
else
isl_mat_free(bmap->ctx, C2);
isl_mat_free(bmap->ctx, T);
- *progress = 1;
+ if (progress)
+ *progress = 1;
done:
- F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
+ ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
return bmap;
error:
return bmap;
}
+static struct isl_basic_map *set_div_from_lower_bound(
+ struct isl_basic_map *bmap, int div, int ineq)
+{
+ unsigned total = 1 + isl_dim_total(bmap->dim);
+
+ isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
+ isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
+ isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
+ isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
+ isl_int_set_si(bmap->div[div][1 + total + div], 0);
+
+ return bmap;
+}
+
+/* Check whether it is ok to define a div based on an inequality.
+ * To avoid the introduction of circular definitions of divs, we
+ * do not allow such a definition if the resulting expression would refer to
+ * any other undefined divs or if any known div is defined in
+ * terms of the unknown div.
+ */
+static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
+ int div, int ineq)
+{
+ int j;
+ unsigned total = 1 + isl_dim_total(bmap->dim);
+
+ /* Not defined in terms of unknown divs */
+ for (j = 0; j < bmap->n_div; ++j) {
+ if (div == j)
+ continue;
+ if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
+ continue;
+ if (isl_int_is_zero(bmap->div[j][0]))
+ return 0;
+ }
+
+ /* No other div defined in terms of this one => avoid loops */
+ for (j = 0; j < bmap->n_div; ++j) {
+ if (div == j)
+ continue;
+ if (isl_int_is_zero(bmap->div[j][0]))
+ continue;
+ if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
+ return 0;
+ }
+
+ return 1;
+}
+
+/* Given two constraints "k" and "l" that are opposite to each other,
+ * except for the constant term, check if we can use them
+ * to obtain an expression for one of the hitherto unknown divs.
+ * "sum" is the sum of the constant terms of the constraints.
+ * If this sum is strictly smaller than the coefficient of one
+ * of the divs, then this pair can be used define the div.
+ * To avoid the introduction of circular definitions of divs, we
+ * do not use the pair if the resulting expression would refer to
+ * any other undefined divs or if any known div is defined in
+ * terms of the unknown div.
+ */
+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;
+ unsigned total = 1 + 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->ineq[k][total + i]))
+ continue;
+ if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
+ continue;
+ if (!ok_to_set_div_from_bound(bmap, i, k))
+ break;
+ if (isl_int_is_pos(bmap->ineq[k][total + i]))
+ bmap = set_div_from_lower_bound(bmap, i, k);
+ else
+ bmap = set_div_from_lower_bound(bmap, i, l);
+ if (progress)
+ *progress = 1;
+ break;
+ }
+ return bmap;
+}
+
static struct isl_basic_map *remove_duplicate_constraints(
struct isl_basic_map *bmap, int *progress)
{
continue;
l = index[h] - &bmap->ineq[0];
isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
- if (isl_int_is_pos(sum))
+ if (isl_int_is_pos(sum)) {
+ bmap = check_for_div_constraints(bmap, k, l, sum,
+ progress);
continue;
+ }
if (isl_int_is_zero(sum)) {
/* We need to break out of the loop after these
* changes since the contents of the hash
return NULL;
while (progress) {
progress = 0;
- bmap = normalize_constraints(bmap);
+ bmap = isl_basic_map_normalize_constraints(bmap);
+ bmap = remove_duplicate_divs(bmap, &progress);
bmap = eliminate_divs_eq(bmap, &progress);
bmap = eliminate_divs_ineq(bmap, &progress);
bmap = isl_basic_map_gauss(bmap, &progress);
/* requires equalities in normal form */
bmap = normalize_divs(bmap, &progress);
- bmap = remove_duplicate_divs(bmap, &progress);
bmap = remove_duplicate_constraints(bmap, &progress);
}
return bmap;
bmap = remove_redundant_divs(bmap);
if (!bmap)
return NULL;
- F_SET(bmap, ISL_BASIC_SET_FINAL);
+ ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
return bmap;
}
if (!map->p[i])
goto error;
}
- F_CLR(map, ISL_MAP_NORMALIZED);
+ ISL_F_CLR(map, ISL_MAP_NORMALIZED);
return map;
error:
isl_map_free(map);
total = isl_basic_map_total_dim(bmap);
bmap = isl_basic_map_cow(bmap);
+ for (d = pos + n - 1; d >= 0 && d >= pos; --d)
+ bmap = remove_dependent_vars(bmap, d);
+
+ for (d = pos + n - 1;
+ d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
+ isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
int n_lower, n_upper;
- bmap = remove_dependent_vars(bmap, d);
if (!bmap)
return NULL;
- if (d >= total - bmap->n_div)
- isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
for (i = 0; i < bmap->n_eq; ++i) {
if (isl_int_is_zero(bmap->eq[i][1+d]))
continue;
i = last + 1;
}
if (n_lower > 0 && n_upper > 0) {
- bmap = normalize_constraints(bmap);
+ bmap = isl_basic_map_normalize_constraints(bmap);
bmap = remove_duplicate_constraints(bmap, NULL);
bmap = isl_basic_map_gauss(bmap, NULL);
bmap = isl_basic_map_convex_hull(bmap);
if (!bmap)
goto error;
- if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
break;
}
}
- F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+ ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
return bmap;
error:
isl_basic_map_free(bmap);
(struct isl_basic_map *)bset, pos, n);
}
+/* Don't assume equalities are in order, because align_divs
+ * may have changed the order of the divs.
+ */
static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
{
int d, i;
total = isl_dim_total(bmap->dim);
for (d = 0; d < total; ++d)
elim[d] = -1;
- for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
- for (; d >= 0; --d) {
+ for (i = 0; i < bmap->n_eq; ++i) {
+ for (d = total - 1; d >= 0; --d) {
if (isl_int_is_zero(bmap->eq[i][1+d]))
continue;
elim[d] = i;
return bset;
}
-static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
- struct isl_basic_set *context);
-
-static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
- struct isl_basic_set *context)
+/* Tighten (decrease) the constant terms of the inequalities based
+ * on the equalities, without removing any integer points.
+ * For example, if there is an equality
+ *
+ * i = 3 * j
+ *
+ * and an inequality
+ *
+ * i >= 1
+ *
+ * then we want to replace the inequality by
+ *
+ * i >= 3
+ *
+ * We do this by computing a variable compression and translating
+ * the constraints to the compressed space.
+ * If any constraint has coefficients (except the contant term)
+ * with a common factor "f", then we can replace the constant term "c"
+ * by
+ *
+ * f * floor(c/f)
+ *
+ * That is, we add
+ *
+ * f * floor(c/f) - c = -fract(c/f)
+ *
+ * and we can add the same value to the original constraint.
+ *
+ * In the example, the compressed space only contains "j",
+ * and the inequality translates to
+ *
+ * 3 * j - 1 >= 0
+ *
+ * We add -fract(-1/3) = -2 to the original constraint to obtain
+ *
+ * i - 3 >= 0
+ */
+static struct isl_basic_set *normalize_constraints_in_compressed_space(
+ struct isl_basic_set *bset)
{
- struct isl_mat *T;
- struct isl_mat *T2;
- struct isl_ctx *ctx = context->ctx;
- struct isl_basic_set *reduced_context;
- reduced_context = isl_basic_set_remove_equalities(
- isl_basic_set_copy(context), &T, &T2);
- if (!reduced_context)
- goto error;
- bset = isl_basic_set_preimage(ctx, bset, T);
- bset = uset_gist(bset, reduced_context);
- bset = isl_basic_set_preimage(ctx, bset, T2);
- bset = isl_basic_set_reduce_using_equalities(bset, context);
- return bset;
-error:
- isl_basic_set_free(context);
- isl_basic_set_free(bset);
- return NULL;
-}
+ int i;
+ unsigned total;
+ struct isl_mat *B, *C;
+ isl_int gcd;
-static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
- struct isl_basic_set *context)
-{
- struct isl_mat *T;
- struct isl_mat *T2;
- struct isl_ctx *ctx = context->ctx;
- struct isl_basic_set *affine_hull = NULL;
+ if (!bset)
+ return NULL;
- affine_hull = isl_basic_set_copy(bset);
- affine_hull = isl_basic_set_cow(affine_hull);
- if (!affine_hull)
- goto error;
- isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
+ if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
+ return bset;
+
+ if (!bset->n_ineq)
+ return bset;
- bset = isl_basic_set_remove_equalities(bset, &T, &T2);
+ bset = isl_basic_set_cow(bset);
if (!bset)
- goto error;
- context = isl_basic_set_preimage(ctx, context, T);
- bset = uset_gist(bset, context);
- bset = isl_basic_set_preimage(ctx, bset, T2);
- bset = isl_basic_set_intersect(bset, affine_hull);
+ return NULL;
+
+ 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);
+ if (!C)
+ return bset;
+ if (C->n_col == 0) {
+ isl_mat_free(bset->ctx, 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);
+ if (!C)
+ return bset;
+
+ isl_int_init(gcd);
+ for (i = 0; i < bset->n_ineq; ++i) {
+ isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
+ if (isl_int_is_one(gcd))
+ continue;
+ isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
+ isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
+ }
+ isl_int_clear(gcd);
+
+ isl_mat_free(bset->ctx, C);
+
return bset;
-error:
- isl_basic_set_free(affine_hull);
- isl_basic_set_free(context);
- isl_basic_set_free(bset);
- return NULL;
}
/* Remove all information from bset that is redundant in the context
* of those in context are removed. Then the inequalities that are
* redundant in the context of the equalities and inequalities of
* context are removed.
+ *
+ * We first simplify the constraints of "bset" in the context of the
+ * equalities of "context".
+ * Then we simplify the inequalities of the context in the context
+ * of the equalities of bset and remove the inequalities from "bset"
+ * that are obviously redundant with respect to some inequality in "context".
+ *
+ * If there are any inequalities left, we construct a tableau for
+ * the context and then add the inequalities of "bset".
+ * Before adding these equalities, we freeze all constraints such that
+ * they won't be considered redundant in terms of the constraints of "bset".
+ * Then we detect all equalities and redundant constraints (among the
+ * constraints that weren't frozen) and update bset according to the results.
+ * We have to be careful here because we don't want any of the context
+ * constraints to remain and because we haven't added the equalities of "bset"
+ * to the tableau so we temporarily have to pretend that there were no
+ * equalities.
*/
static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
struct isl_basic_set *context)
{
int i;
- isl_int opt;
- struct isl_basic_set *combined;
- struct isl_ctx *ctx;
+ struct isl_tab *tab;
+ unsigned context_ineq;
+ struct isl_basic_set *combined = NULL;
- if (!bset || !context)
+ if (!context || !bset)
goto error;
if (context->n_eq > 0)
- return uset_gist_context_eq(bset, context);
+ bset = isl_basic_set_reduce_using_equalities(bset,
+ isl_basic_set_copy(context));
+ if (!bset)
+ goto error;
+ if (isl_basic_set_fast_is_empty(bset))
+ goto done;
+ if (!bset->n_ineq)
+ goto done;
+
+ if (bset->n_eq > 0) {
+ struct isl_basic_set *affine_hull;
+ affine_hull = isl_basic_set_copy(bset);
+ affine_hull = isl_basic_set_cow(affine_hull);
+ if (!affine_hull)
+ goto error;
+ isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
+ context = isl_basic_set_intersect(context, affine_hull);
+ context = isl_basic_set_gauss(context, NULL);
+ context = normalize_constraints_in_compressed_space(context);
+ }
+ if (!context)
+ goto error;
+ if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
+ isl_basic_set_free(bset);
+ return context;
+ }
if (!context->n_ineq)
goto done;
- if (bset->n_eq > 0)
- return uset_gist_set_eq(bset, context);
bset = remove_shifted_constraints(bset, context);
- combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
- context->n_eq, context->n_ineq);
- context = isl_basic_set_add_constraints(combined, context, 0);
- if (!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));
+ combined = isl_basic_set_extend_constraints(combined,
+ bset->n_eq, bset->n_ineq);
+ tab = isl_tab_from_basic_set(combined);
+ if (!tab)
goto error;
- ctx = context->ctx;
- isl_int_init(opt);
- for (i = bset->n_ineq-1; i >= 0; --i) {
- int redundant;
- set_swap_inequality(context, i, context->n_ineq-1);
- context->n_ineq--;
- redundant = isl_basic_set_constraint_is_redundant(&context,
- context->ineq[context->n_ineq], &opt, NULL);
- if (redundant == -1) {
- isl_int_clear(opt);
- goto error;
- }
- if (F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
- bset = isl_basic_set_set_to_empty(bset);
- break;
- }
- context->n_ineq++;
- set_swap_inequality(context, i, context->n_ineq-1);
- if (redundant) {
- isl_basic_set_drop_inequality(context, i);
- isl_basic_set_drop_inequality(bset, i);
- }
+ for (i = 0; i < context_ineq; ++i)
+ tab->con[i].frozen = 1;
+ tab = isl_tab_extend(bset->ctx, 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]);
+ 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)
+ goto error2;
+ for (i = 0; i < context_ineq; ++i) {
+ tab->con[i].is_zero = 0;
+ tab->con[i].is_redundant = 1;
}
- isl_int_clear(opt);
+ bset = isl_basic_set_update_from_tab(bset, tab);
+ isl_tab_free(bset->ctx, tab);
+ ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
+ ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
done:
+ bset = isl_basic_set_simplify(bset);
+ bset = isl_basic_set_finalize(bset);
isl_basic_set_free(context);
return bset;
error:
- isl_basic_set_free(context);
+ isl_basic_set_free(combined);
+error2:
isl_basic_set_free(bset);
+ isl_basic_set_free(context);
return NULL;
}
+/* Normalize the divs in "bmap" in the context of the equalities in "context".
+ * We simply add the equalities in context to bmap and then do a regular
+ * div normalizations. Better results can be obtained by normalizing
+ * only the divs in bmap than do not also appear in context.
+ * We need to be careful to reduce the divs using the equalities
+ * so that later calls to isl_basic_map_overlying_set wouldn't introduce
+ * spurious constraints.
+ */
+static struct isl_basic_map *normalize_divs_in_context(
+ struct isl_basic_map *bmap, struct isl_basic_map *context)
+{
+ int i;
+ unsigned total_context;
+ int div_eq;
+
+ div_eq = n_pure_div_eq(bmap);
+ if (div_eq == 0)
+ return bmap;
+
+ if (context->n_div > 0)
+ bmap = isl_basic_map_align_divs(bmap, context);
+
+ total_context = isl_basic_map_total_dim(context);
+ bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
+ for (i = 0; i < context->n_eq; ++i) {
+ int k;
+ k = isl_basic_map_alloc_equality(bmap);
+ isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
+ isl_seq_clr(bmap->eq[k] + 1 + total_context,
+ isl_basic_map_total_dim(bmap) - total_context);
+ }
+ bmap = isl_basic_map_gauss(bmap, NULL);
+ bmap = normalize_divs(bmap, NULL);
+ bmap = isl_basic_map_gauss(bmap, NULL);
+ return bmap;
+}
+
struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
struct isl_basic_map *context)
{
if (!bmap || !context)
goto error;
+ if (isl_basic_map_is_universe(context)) {
+ isl_basic_map_free(context);
+ return bmap;
+ }
+ if (isl_basic_map_is_universe(bmap)) {
+ isl_basic_map_free(context);
+ return bmap;
+ }
+ if (isl_basic_map_fast_is_empty(context)) {
+ struct isl_dim *dim = isl_dim_copy(bmap->dim);
+ isl_basic_map_free(context);
+ isl_basic_map_free(bmap);
+ return isl_basic_map_universe(dim);
+ }
+ if (isl_basic_map_fast_is_empty(bmap)) {
+ isl_basic_map_free(context);
+ return bmap;
+ }
+
+ bmap = isl_basic_map_convex_hull(bmap);
+ context = isl_basic_map_convex_hull(context);
+
+ if (context->n_eq)
+ bmap = normalize_divs_in_context(bmap, context);
+
context = isl_basic_map_align_divs(context, bmap);
bmap = isl_basic_map_align_divs(bmap, context);
{
int i;
+ if (!map || !context)
+ goto error;;
+
+ if (isl_basic_map_is_universe(context)) {
+ isl_basic_map_free(context);
+ return map;
+ }
+ if (isl_basic_map_fast_is_empty(context)) {
+ struct isl_dim *dim = isl_dim_copy(map->dim);
+ isl_basic_map_free(context);
+ isl_map_free(map);
+ return isl_map_universe(dim);
+ }
+
+ context = isl_basic_map_convex_hull(context);
map = isl_map_cow(map);
if (!map || !context)
- return NULL;
+ goto error;;
isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
map = isl_map_compute_divs(map);
for (i = 0; i < map->n; ++i)
goto error;
}
isl_basic_map_free(context);
- F_CLR(map, ISL_MAP_NORMALIZED);
+ ISL_F_CLR(map, ISL_MAP_NORMALIZED);
return map;
error:
isl_map_free(map);
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;
}
return isl_map_fast_is_disjoint((struct isl_map *)set1,
(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 (expect 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]);
+ 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_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->el, g, fl, fu);
+ res = isl_tab_min(ctx, tab, vec->el,
+ 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(ctx, 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);
+ if (ctx) {
+ isl_tab_free(ctx, 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);
+ }
+ }
+ }
+
+ 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.
+ * Also, if a div occurs only occurs in two constraints and if moreover
+ * those two constraints are opposite to each other, except for the constant
+ * term and if the sum of the constant terms is such that for any value
+ * of the other values, there is always at least one integer value of the
+ * 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;
+
+ if (!isl_int_is_zero(bmap->div[i][0]))
+ continue;
+ 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])) {
+ last_pos = j;
+ ++pos;
+ }
+ if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
+ last_neg = j;
+ ++neg;
+ }
+ }
+ 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 (pairs[i] != 1)
+ continue;
+ if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
+ bmap->ineq[last_neg] + 1,
+ off + bmap->n_div))
+ continue;
+
+ isl_int_add(bmap->ineq[last_pos][0],
+ bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
+ isl_int_add_ui(bmap->ineq[last_pos][0],
+ bmap->ineq[last_pos][0], 1);
+ redundant = isl_int_ge(bmap->ineq[last_pos][0],
+ bmap->ineq[last_pos][1+off+i]);
+ isl_int_sub_ui(bmap->ineq[last_pos][0],
+ 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 (!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);
+ } else {
+ 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;
+}