add isl_basic_set_interval and isl_basic_set_product
[platform/upstream/isl.git] / isl_map.c
index 400826c..eaeccb0 100644 (file)
--- a/isl_map.c
+++ b/isl_map.c
@@ -2,6 +2,9 @@
 #include <strings.h>
 #include "isl_ctx.h"
 #include "isl_blk.h"
+#include "isl_equalities.h"
+#include "isl_list.h"
+#include "isl_lp.h"
 #include "isl_seq.h"
 #include "isl_set.h"
 #include "isl_map.h"
@@ -281,6 +284,7 @@ void isl_basic_map_inequality_to_equality(
        bmap->n_eq++;
        bmap->n_ineq--;
        bmap->ineq++;
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 }
 
 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
@@ -293,6 +297,7 @@ int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
                        return -1);
        F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
        F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        return bmap->n_ineq++;
 }
 
@@ -326,6 +331,7 @@ int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
                t = bmap->ineq[pos];
                bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
                bmap->ineq[bmap->n_ineq - 1] = t;
+               F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        }
        bmap->n_ineq--;
        return 0;
@@ -403,7 +409,12 @@ static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
                struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
 {
        int i;
-       unsigned div_off = bmap1->n_div;
+       unsigned div_off;
+
+       if (!bmap1 || !bmap2)
+               goto error;
+
+       div_off = bmap1->n_div;
 
        for (i = 0; i < bmap2->n_eq; ++i) {
                int i1 = isl_basic_map_alloc_equality(bmap1);
@@ -439,6 +450,14 @@ error:
        return NULL;
 }
 
+static struct isl_basic_set *set_add_constraints(struct isl_basic_set *bset1,
+               struct isl_basic_set *bset2, unsigned pos)
+{
+       return (struct isl_basic_set *)
+               add_constraints((struct isl_basic_map *)bset1,
+                               (struct isl_basic_map *)bset2, 0, pos);
+}
+
 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
                unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
@@ -580,6 +599,7 @@ struct isl_basic_set *isl_basic_set_swap_vars(
 
        isl_blk_free(bset->ctx, blk);
 
+       F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
        return bset;
 
 error:
@@ -601,6 +621,7 @@ struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
                        return NULL;
                }
        }
+       F_CLR(set, ISL_SET_NORMALIZED);
        return set;
 }
 
@@ -610,7 +631,7 @@ static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
        isl_seq_clr(c + rem, n);
 }
 
-struct isl_basic_set *isl_basic_set_drop_vars(
+struct isl_basic_set *isl_basic_set_drop_dims(
                struct isl_basic_set *bset, unsigned first, unsigned n)
 {
        int i;
@@ -642,13 +663,15 @@ struct isl_basic_set *isl_basic_set_drop_vars(
        bset->dim -= n;
        bset->extra += n;
 
+       F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
+       bset = isl_basic_set_simplify(bset);
        return isl_basic_set_finalize(bset);
 error:
        isl_basic_set_free(bset);
        return NULL;
 }
 
-struct isl_set *isl_set_drop_vars(
+static struct isl_set *isl_set_drop_dims(
                struct isl_set *set, unsigned first, unsigned n)
 {
        int i;
@@ -665,18 +688,89 @@ struct isl_set *isl_set_drop_vars(
                goto error;
 
        for (i = 0; i < set->n; ++i) {
-               set->p[i] = isl_basic_set_drop_vars(set->p[i], first, n);
+               set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
                if (!set->p[i])
                        goto error;
        }
        set->dim -= n;
 
+       F_CLR(set, ISL_SET_NORMALIZED);
        return set;
 error:
        isl_set_free(set);
        return NULL;
 }
 
+struct isl_basic_map *isl_basic_map_drop_inputs(
+               struct isl_basic_map *bmap, unsigned first, unsigned n)
+{
+       int i;
+
+       if (!bmap)
+               goto error;
+
+       isl_assert(bmap->ctx, first + n <= bmap->n_in, goto error);
+
+       if (n == 0)
+               return bmap;
+
+       bmap = isl_basic_map_cow(bmap);
+       if (!bmap)
+               return NULL;
+
+       for (i = 0; i < bmap->n_eq; ++i)
+               constraint_drop_vars(bmap->eq[i]+1+bmap->nparam+first, n,
+                                (bmap->n_in-first-n)+bmap->n_out+bmap->extra);
+
+       for (i = 0; i < bmap->n_ineq; ++i)
+               constraint_drop_vars(bmap->ineq[i]+1+bmap->nparam+first, n,
+                                (bmap->n_in-first-n)+bmap->n_out+bmap->extra);
+
+       for (i = 0; i < bmap->n_div; ++i)
+               constraint_drop_vars(bmap->div[i]+1+1+bmap->nparam+first, n,
+                                (bmap->n_in-first-n)+bmap->n_out+bmap->extra);
+
+       bmap->n_in -= n;
+       bmap->extra += n;
+
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+       bmap = isl_basic_map_simplify(bmap);
+       return isl_basic_map_finalize(bmap);
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+static struct isl_map *isl_map_drop_inputs(
+               struct isl_map *map, unsigned first, unsigned n)
+{
+       int i;
+
+       if (!map)
+               goto error;
+
+       isl_assert(map->ctx, first + n <= map->n_in, goto error);
+
+       if (n == 0)
+               return map;
+       map = isl_map_cow(map);
+       if (!map)
+               goto error;
+
+       for (i = 0; i < map->n; ++i) {
+               map->p[i] = isl_basic_map_drop_inputs(map->p[i], first, n);
+               if (!map->p[i])
+                       goto error;
+       }
+       map->n_in -= n;
+       F_CLR(map, ISL_MAP_NORMALIZED);
+
+       return map;
+error:
+       isl_map_free(map);
+       return NULL;
+}
+
 /*
  * We don't cow, as the div is assumed to be redundant.
  */
@@ -717,6 +811,7 @@ static struct isl_basic_map *isl_basic_map_drop_div(
 
                bmap->div[bmap->n_div - 1] = t;
        }
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        isl_basic_map_free_div(bmap, 1);
 
        return bmap;
@@ -791,9 +886,16 @@ static void swap_equality(struct isl_basic_map *bmap, int a, int b)
 
 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
 {
-       isl_int *t = bmap->ineq[a];
-       bmap->ineq[a] = bmap->ineq[b];
-       bmap->ineq[b] = t;
+       if (a != b) {
+               isl_int *t = bmap->ineq[a];
+               bmap->ineq[a] = bmap->ineq[b];
+               bmap->ineq[b] = t;
+       }
+}
+
+static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
+{
+       swap_inequality((struct isl_basic_map *)bset, a, b);
 }
 
 static void swap_div(struct isl_basic_map *bmap, int a, int b)
@@ -812,7 +914,48 @@ static void swap_div(struct isl_basic_map *bmap, int a, int b)
 
        for (i = 0; i < bmap->n_div; ++i)
                isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+}
+
+static void eliminate_var_using_equality(struct isl_basic_map *bmap,
+       unsigned pos, isl_int *eq, int *progress)
+{
+       unsigned total;
+       int k;
+
+       total = bmap->nparam + bmap->n_in + bmap->n_out + 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 (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);
+               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;
+               isl_seq_elim(bmap->div[k]+1, eq,
+                               1+pos, 1+total, &bmap->div[k][0]);
+               F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+       }
 }
+       
 
 struct isl_basic_map *isl_basic_map_gauss(
        struct isl_basic_map *bmap, int *progress)
@@ -845,36 +988,8 @@ struct isl_basic_map *isl_basic_map_gauss(
                if (isl_int_is_neg(bmap->eq[done][1+last_var]))
                        isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 
-               for (k = 0; k < bmap->n_eq; ++k) {
-                       if (k == done)
-                               continue;
-                       if (isl_int_is_zero(bmap->eq[k][1+last_var]))
-                               continue;
-                       if (progress)
-                               *progress = 1;
-                       isl_seq_elim(bmap->eq[k], bmap->eq[done],
-                                       1+last_var, 1+total, NULL);
-               }
-
-               for (k = 0; k < bmap->n_ineq; ++k) {
-                       if (isl_int_is_zero(bmap->ineq[k][1+last_var]))
-                               continue;
-                       if (progress)
-                               *progress = 1;
-                       isl_seq_elim(bmap->ineq[k], bmap->eq[done],
-                                       1+last_var, 1+total, NULL);
-               }
-
-               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+last_var]))
-                               continue;
-                       if (progress)
-                               *progress = 1;
-                       isl_seq_elim(bmap->div[k]+1, bmap->eq[done],
-                                       1+last_var, 1+total, &bmap->div[k][0]);
-               }
+               eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
+                                               progress);
 
                if (last_var >= total_var &&
                    isl_int_is_zero(bmap->div[last_var - total_var][0])) {
@@ -883,6 +998,7 @@ struct isl_basic_map *isl_basic_map_gauss(
                        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);
                }
        }
        if (done == bmap->n_eq)
@@ -955,7 +1071,8 @@ static struct isl_basic_map *remove_duplicate_constraints(
                        index[h] = k+1;
                        continue;
                }
-               *progress = 1;
+               if (progress)
+                       *progress = 1;
                l = index[h] - 1;
                if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
                        swap_inequality(bmap, k, l);
@@ -991,6 +1108,149 @@ static struct isl_basic_map *remove_duplicate_constraints(
        return bmap;
 }
 
+static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
+{
+       int d, i;
+       unsigned total;
+
+       total = bmap->nparam + bmap->n_in + bmap->n_out;
+       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) {
+                       if (isl_int_is_zero(bmap->eq[i][1+d]))
+                               continue;
+                       elim[d] = i;
+                       break;
+               }
+       }
+}
+
+static int reduced_using_equalities(isl_int *c, struct isl_vec *v,
+       struct isl_basic_map *bmap, int *elim)
+{
+       int d, i;
+       int copied = 0;
+       unsigned total;
+
+       total = bmap->nparam + bmap->n_in + bmap->n_out;
+       for (d = total - 1; d >= 0; --d) {
+               if (isl_int_is_zero(c[1+d]))
+                       continue;
+               if (elim[d] == -1)
+                       continue;
+               if (!copied) {
+                       isl_seq_cpy(v->block.data, c, 1 + total);
+                       copied = 1;
+               }
+               isl_seq_elim(v->block.data, bmap->eq[elim[d]],
+                               1 + d, 1 + total, NULL);
+       }
+       return copied;
+}
+
+/* Quick check to see if two basic maps are disjoint.
+ * In particular, we reduce the equalities and inequalities of
+ * one basic map in the context of the equalities of the other
+ * basic map and check if we get a contradiction.
+ */
+int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
+       struct isl_basic_map *bmap2)
+{
+       struct isl_vec *v = NULL;
+       int *elim = NULL;
+       unsigned total;
+       int d, i;
+
+       if (!bmap1 || !bmap2)
+               return -1;
+       isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, return -1);
+       isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, return -1);
+       isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, return -1);
+       if (bmap1->n_div || bmap2->n_div)
+               return 0;
+       if (!bmap1->n_eq && !bmap2->n_eq)
+               return 0;
+
+       total = bmap1->nparam + bmap1->n_in + bmap1->n_out;
+       if (total == 0)
+               return 0;
+       v = isl_vec_alloc(bmap1->ctx, 1 + total);
+       if (!v)
+               goto error;
+       elim = isl_alloc_array(bmap1->ctx, int, total);
+       if (!elim)
+               goto error;
+       compute_elimination_index(bmap1, elim);
+       for (i = 0; i < bmap2->n_eq; ++i) {
+               int reduced;
+               reduced = reduced_using_equalities(bmap2->eq[i], v, bmap1, elim);
+               if (reduced && !isl_int_is_zero(v->block.data[0]) &&
+                   isl_seq_first_non_zero(v->block.data + 1, total) == -1)
+                       goto disjoint;
+       }
+       for (i = 0; i < bmap2->n_ineq; ++i) {
+               int reduced;
+               reduced = reduced_using_equalities(bmap2->ineq[i], v, bmap1, elim);
+               if (reduced && isl_int_is_neg(v->block.data[0]) &&
+                   isl_seq_first_non_zero(v->block.data + 1, total) == -1)
+                       goto disjoint;
+       }
+       compute_elimination_index(bmap2, elim);
+       for (i = 0; i < bmap1->n_ineq; ++i) {
+               int reduced;
+               reduced = reduced_using_equalities(bmap1->ineq[i], v, bmap2, elim);
+               if (reduced && isl_int_is_neg(v->block.data[0]) &&
+                   isl_seq_first_non_zero(v->block.data + 1, total) == -1)
+                       goto disjoint;
+       }
+       isl_vec_free(bmap1->ctx, v);
+       free(elim);
+       return 0;
+disjoint:
+       isl_vec_free(bmap1->ctx, v);
+       free(elim);
+       return 1;
+error:
+       isl_vec_free(bmap1->ctx, v);
+       free(elim);
+       return -1;
+}
+
+int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
+       struct isl_basic_set *bset2)
+{
+       return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
+                                             (struct isl_basic_map *)bset2);
+}
+
+int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
+{
+       int i, j;
+
+       if (!map1 || !map2)
+               return -1;
+
+       if (isl_map_fast_is_equal(map1, map2))
+               return 0;
+
+       for (i = 0; i < map1->n; ++i) {
+               for (j = 0; j < map2->n; ++j) {
+                       int d = isl_basic_map_fast_is_disjoint(map1->p[i],
+                                                              map2->p[j]);
+                       if (d != 1)
+                               return d;
+               }
+       }
+       return 1;
+}
+
+int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
+{
+       return isl_map_fast_is_disjoint((struct isl_map *)set1,
+                                       (struct isl_map *)set2);
+}
+
 static struct isl_basic_map *remove_duplicate_divs(
        struct isl_basic_map *bmap, int *progress)
 {
@@ -1154,7 +1414,6 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
        extra = bmap->extra - bmap->n_div;
 
        bmap = isl_basic_map_cow(bmap);
-       bmap = isl_basic_map_gauss(bmap, NULL);
        for (d = pos + n - 1; d >= pos; --d) {
                int n_lower, n_upper;
                if (!bmap)
@@ -1162,6 +1421,7 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
                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);
                        isl_basic_map_drop_equality(bmap, i);
                        break;
                }
@@ -1204,11 +1464,16 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
                }
                if (n_lower > 0 && n_upper > 0) {
                        bmap = 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))
                                break;
                }
        }
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        return bmap;
 error:
        isl_basic_map_free(bmap);
@@ -1222,6 +1487,80 @@ struct isl_basic_set *isl_basic_set_eliminate_vars(
                        (struct isl_basic_map *)bset, pos, n);
 }
 
+/* Eliminate the specified n dimensions starting at first from the
+ * constraints using Fourier-Motzkin, The dimensions themselves
+ * are not removed.
+ */
+struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
+       unsigned first, unsigned n)
+{
+       int i;
+
+       if (n == 0)
+               return set;
+
+       set = isl_set_cow(set);
+       if (!set)
+               return NULL;
+       isl_assert(set->ctx, first+n <= set->dim, goto error);
+       
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
+                                                       set->nparam + first, n);
+               if (!set->p[i])
+                       goto error;
+       }
+       return set;
+error:
+       isl_set_free(set);
+       return NULL;
+}
+
+/* Project out n dimensions starting at first using Fourier-Motzkin */
+struct isl_set *isl_set_remove_dims(struct isl_set *set,
+       unsigned first, unsigned n)
+{
+       set = isl_set_eliminate_dims(set, first, n);
+       set = isl_set_drop_dims(set, first, n);
+       return set;
+}
+
+/* Project out n inputs starting at first using Fourier-Motzkin */
+struct isl_map *isl_map_remove_inputs(struct isl_map *map,
+       unsigned first, unsigned n)
+{
+       int i;
+
+       if (n == 0)
+               return map;
+
+       map = isl_map_cow(map);
+       if (!map)
+               return NULL;
+       isl_assert(map->ctx, first+n <= map->n_in, goto error);
+       
+       for (i = 0; i < map->n; ++i) {
+               map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
+                                                       map->nparam + first, n);
+               if (!map->p[i])
+                       goto error;
+       }
+       map = isl_map_drop_inputs(map, first, n);
+       return map;
+error:
+       isl_map_free(map);
+       return NULL;
+}
+
+/* Project out n dimensions starting at first using Fourier-Motzkin */
+struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
+       unsigned first, unsigned n)
+{
+       bset = isl_basic_set_eliminate_vars(bset, bset->nparam + first, n);
+       bset = isl_basic_set_drop_dims(bset, first, n);
+       return bset;
+}
+
 /* Elimininate divs based on inequalities
  */
 static struct isl_basic_map *eliminate_divs_ineq(
@@ -1289,10 +1628,10 @@ static void dump_term(struct isl_basic_map *bmap,
        unsigned in = bmap->n_in;
        unsigned dim = bmap->n_in + bmap->n_out;
        if (!pos)
-               isl_int_print(out, c);
+               isl_int_print(out, c, 0);
        else {
                if (!isl_int_is_one(c))
-                       isl_int_print(out, c);
+                       isl_int_print(out, c, 0);
                if (pos < 1 + bmap->nparam)
                        fprintf(out, "p%d", pos - 1);
                else if (pos < 1 + bmap->nparam + in)
@@ -1386,7 +1725,7 @@ static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
                fprintf(out, "e%d = [(", i);
                dump_affine(bmap, bmap->div[i]+1, out);
                fprintf(out, ")/");
-               isl_int_print(out, bmap->div[i][0]);
+               isl_int_print(out, bmap->div[i][0], 0);
                fprintf(out, "]\n");
        }
 }
@@ -1399,8 +1738,9 @@ void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
        }
 
        fprintf(out, "%*s", indent, "");
-       fprintf(out, "nparam: %d, dim: %d, extra: %d\n",
-                       bset->nparam, bset->dim, bset->extra);
+       fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
+                       bset->ref, bset->nparam, bset->dim, bset->extra,
+                       bset->flags);
        dump((struct isl_basic_map *)bset, out, indent);
 }
 
@@ -1426,6 +1766,7 @@ int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
        isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
        isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
        isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        return 0;
 }
 
@@ -1434,6 +1775,7 @@ struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
 {
        struct isl_set *set;
 
+       isl_assert(ctx, n >= 0, return NULL);
        set = isl_alloc(ctx, struct isl_set,
                        sizeof(struct isl_set) +
                        n * sizeof(struct isl_basic_set *));
@@ -1544,7 +1886,8 @@ void isl_set_dump(struct isl_set *set, FILE *out, int indent)
        }
 
        fprintf(out, "%*s", indent, "");
-       fprintf(out, "ref: %d, n: %d\n", set->ref, set->n);
+       fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
+                       set->ref, set->n, set->nparam, set->dim, set->flags);
        for (i = 0; i < set->n; ++i) {
                fprintf(out, "%*s", indent, "");
                fprintf(out, "basic set %d:\n", i);
@@ -1701,6 +2044,13 @@ error:
        return NULL;
 }
 
+struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
+{
+       return (struct isl_set *)
+               isl_map_intersect((struct isl_map *)set1,
+                                 (struct isl_map *)set2);
+}
+
 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
 {
        struct isl_basic_set *bset;
@@ -2036,9 +2386,9 @@ struct isl_basic_map *isl_basic_map_overlying_set(
                return (struct isl_basic_map *)bset;
        }
        bset = isl_basic_set_cow(bset);
-       total = bset->dim + bset->extra;
        if (!bset)
                goto error;
+       total = bset->dim + bset->extra;
        bmap = (struct isl_basic_map *)bset;
        bmap->nparam = like->nparam;
        bmap->n_in = like->n_in;
@@ -2078,6 +2428,45 @@ error:
        return NULL;
 }
 
+struct isl_basic_set *isl_basic_set_from_underlying_set(
+       struct isl_basic_set *bset, struct isl_basic_set *like)
+{
+       return (struct isl_basic_set *)
+               isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
+}
+
+struct isl_set *isl_set_from_underlying_set(
+       struct isl_set *set, struct isl_basic_set *like)
+{
+       int i;
+
+       if (!set || !like)
+               goto error;
+       isl_assert(set->ctx, set->dim == like->nparam + like->dim + like->n_div,
+                   goto error);
+       if (like->nparam == 0 && like->n_div == 0) {
+               isl_basic_set_free(like);
+               return set;
+       }
+       set = isl_set_cow(set);
+       if (!set)
+               goto error;
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
+                                                     isl_basic_set_copy(like));
+               if (!set->p[i])
+                       goto error;
+       }
+       set->nparam = like->nparam;
+       set->dim = like->dim;
+       isl_basic_set_free(like);
+       return set;
+error:
+       isl_basic_set_free(like);
+       isl_set_free(set);
+       return NULL;
+}
+
 struct isl_set *isl_map_underlying_set(struct isl_map *map)
 {
        int i;
@@ -2105,6 +2494,11 @@ error:
        return NULL;
 }
 
+struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
+{
+       return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
+}
+
 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
 {
        struct isl_basic_set *domain;
@@ -2140,6 +2534,7 @@ struct isl_set *isl_map_range(struct isl_map *map)
                        goto error;
        }
        F_CLR(set, ISL_MAP_DISJOINT);
+       F_CLR(set, ISL_SET_NORMALIZED);
        return set;
 error:
        isl_map_free(map);
@@ -2173,24 +2568,48 @@ error:
        return NULL;
 }
 
-struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
-               unsigned nparam, unsigned in, unsigned out, int n,
-               unsigned flags)
+struct isl_set *isl_set_from_map(struct isl_map *map)
 {
-       struct isl_map *map;
+       int i;
+       struct isl_set *set = NULL;
 
-       map = isl_alloc(ctx, struct isl_map,
-                       sizeof(struct isl_map) +
-                       n * sizeof(struct isl_basic_map *));
        if (!map)
                return NULL;
-
-       map->ctx = ctx;
-       isl_ctx_ref(ctx);
-       map->ref = 1;
-       map->size = n;
-       map->n = 0;
-       map->nparam = nparam;
+       map = isl_map_cow(map);
+       if (!map)
+               return NULL;
+       map->n_out += map->n_in;
+       map->n_in = 0;
+       set = (struct isl_set *)map;
+       for (i = 0; i < map->n; ++i) {
+               set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
+               if (!set->p[i])
+                       goto error;
+       }
+       return set;
+error:
+       isl_map_free(map);
+       return NULL;
+}
+
+struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
+               unsigned nparam, unsigned in, unsigned out, int n,
+               unsigned flags)
+{
+       struct isl_map *map;
+
+       map = isl_alloc(ctx, struct isl_map,
+                       sizeof(struct isl_map) +
+                       n * sizeof(struct isl_basic_map *));
+       if (!map)
+               return NULL;
+
+       map->ctx = ctx;
+       isl_ctx_ref(ctx);
+       map->ref = 1;
+       map->size = n;
+       map->n = 0;
+       map->nparam = nparam;
        map->n_in = in;
        map->n_out = out;
        map->flags = flags;
@@ -2268,6 +2687,7 @@ struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
        isl_assert(map->ctx, map->n < map->size, goto error);
        map->p[map->n] = bmap;
        map->n++;
+       F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 error:
        if (map)
@@ -2320,6 +2740,13 @@ error:
        return NULL;
 }
 
+struct isl_set *isl_set_extend(struct isl_set *base,
+               unsigned nparam, unsigned dim)
+{
+       return (struct isl_set *)isl_map_extend((struct isl_map *)base,
+                                                       nparam, 0, dim);
+}
+
 static struct isl_basic_map *isl_basic_map_fix_var(struct isl_basic_map *bmap,
                unsigned var, int value)
 {
@@ -2383,6 +2810,7 @@ struct isl_map *isl_map_fix_input_si(struct isl_map *map,
                if (!map->p[i])
                        goto error;
        }
+       F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 error:
        isl_map_free(map);
@@ -2409,6 +2837,47 @@ error:
        return NULL;
 }
 
+struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
+       unsigned dim, isl_int value)
+{
+       int j;
+
+       bset = isl_basic_set_cow(bset);
+       bset = isl_basic_set_extend(bset, bset->nparam, bset->dim, 0, 0, 1);
+       j = isl_basic_set_alloc_inequality(bset);
+       if (j < 0)
+               goto error;
+       isl_seq_clr(bset->ineq[j], 1 + bset->nparam + bset->dim + bset->extra);
+       isl_int_set_si(bset->ineq[j][1 + bset->nparam + dim], 1);
+       isl_int_neg(bset->ineq[j][0], value);
+       bset = isl_basic_set_simplify(bset);
+       return isl_basic_set_finalize(bset);
+error:
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
+                                       isl_int value)
+{
+       int i;
+
+       set = isl_set_cow(set);
+       if (!set)
+               return NULL;
+
+       isl_assert(set->ctx, dim < set->dim, goto error);
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
+               if (!set->p[i])
+                       goto error;
+       }
+       return set;
+error:
+       isl_set_free(set);
+       return NULL;
+}
+
 struct isl_map *isl_map_reverse(struct isl_map *map)
 {
        int i;
@@ -2426,6 +2895,7 @@ struct isl_map *isl_map_reverse(struct isl_map *map)
                if (!map->p[i])
                        goto error;
        }
+       F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 error:
        isl_map_free(map);
@@ -2532,6 +3002,7 @@ struct isl_set *isl_map_domain(struct isl_map *map)
                        goto error;
        }
        F_CLR(set, ISL_MAP_DISJOINT);
+       F_CLR(set, ISL_SET_NORMALIZED);
        return set;
 error:
        isl_map_free(map);
@@ -2742,6 +3213,31 @@ error:
        return NULL;
 }
 
+/*
+ * returns range - domain
+ */
+struct isl_set *isl_map_deltas(struct isl_map *map)
+{
+       int i;
+       struct isl_set *result;
+
+       if (!map)
+               return NULL;
+
+       isl_assert(map->ctx, map->n_in == map->n_out, goto error);
+       result = isl_set_alloc(map->ctx, map->nparam, map->n_in, map->n, map->flags);
+       if (!result)
+               goto error;
+       for (i = 0; i < map->n; ++i)
+               result = isl_set_add(result,
+                         isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
+       isl_map_free(map);
+       return result;
+error:
+       isl_map_free(map);
+       return NULL;
+}
+
 /* If the only constraints a div d=floor(f/m)
  * appears in are its two defining constraints
  *
@@ -2856,6 +3352,7 @@ struct isl_map *isl_map_finalize(struct isl_map *map)
                if (!map->p[i])
                        goto error;
        }
+       F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 error:
        isl_map_free(map);
@@ -3084,6 +3581,14 @@ int isl_basic_map_is_empty(struct isl_basic_map *bmap)
        if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
                return 1;
 
+       if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
+               struct isl_basic_map *copy = isl_basic_map_copy(bmap);
+               copy = isl_basic_map_convex_hull(copy);
+               empty = F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
+               isl_basic_map_free(copy);
+               return empty;
+       }
+
        total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
        if (bmap->sample && bmap->sample->size == total) {
                int contains = basic_map_contains(bmap, bmap->sample);
@@ -3220,6 +3725,7 @@ struct isl_map *isl_map_align_divs(struct isl_map *map)
        for (i = 1; i < map->n; ++i)
                map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
 
+       F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 }
 
@@ -3416,8 +3922,10 @@ struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
                if (!F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
                        continue;
                isl_basic_map_free(map->p[i]);
-               if (i != map->n-1)
+               if (i != map->n-1) {
+                       F_CLR(map, ISL_MAP_NORMALIZED);
                        map->p[i] = map->p[map->n-1];
+               }
                map->n--;
        }
 
@@ -3429,3 +3937,668 @@ struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
        return (struct isl_set *)
                isl_map_remove_empty_parts((struct isl_map *)set);
 }
+
+struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
+{
+       struct isl_basic_set *bset;
+       if (!set || set->n == 0)
+               return NULL;
+       bset = set->p[set->n-1];
+       isl_assert(set->ctx, F_ISSET(bset, ISL_BASIC_SET_FINAL), return NULL);
+       return isl_basic_set_copy(bset);
+}
+
+struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
+                                               struct isl_basic_set *bset)
+{
+       int i;
+
+       if (!set || !bset)
+               goto error;
+       for (i = set->n-1; i >= 0; --i) {
+               if (set->p[i] != bset)
+                       continue;
+               set = isl_set_cow(set);
+               if (!set)
+                       goto error;
+               isl_basic_set_free(set->p[i]);
+               if (i != set->n-1) {
+                       F_CLR(set, ISL_SET_NORMALIZED);
+                       set->p[i] = set->p[set->n-1];
+               }
+               set->n--;
+               return set;
+       }
+       isl_basic_set_free(bset);
+       return set;
+error:
+       isl_set_free(set);
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+/* Given two _disjoint_ basic sets bset1 and bset2, check whether
+ * for any common value of the parameters and dimensions preceding dim
+ * in both basic sets, the values of dimension pos in bset1 are
+ * smaller or larger then those in bset2.
+ *
+ * Returns
+ *      1 if bset1 follows bset2
+ *     -1 if bset1 precedes bset2
+ *      0 if bset1 and bset2 are incomparable
+ *     -2 if some error occurred.
+ */
+int isl_basic_set_compare_at(struct isl_basic_set *bset1,
+       struct isl_basic_set *bset2, int pos)
+{
+       struct isl_basic_map *bmap1 = NULL;
+       struct isl_basic_map *bmap2 = NULL;
+       struct isl_ctx *ctx;
+       struct isl_vec *obj;
+       unsigned total;
+       isl_int num, den;
+       enum isl_lp_result res;
+       int cmp;
+
+       if (!bset1 || !bset2)
+               return -2;
+
+       bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1),
+                                               pos, bset1->dim - pos);
+       bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2),
+                                               pos, bset2->dim - pos);
+       if (!bmap1 || !bmap2)
+               goto error;
+       bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
+                       bmap1->n_in, bmap1->n_out + bmap2->n_out,
+                       bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
+       if (!bmap1)
+               goto error;
+       total = bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
+       ctx = bmap1->ctx;
+       obj = isl_vec_alloc(ctx, total);
+       isl_seq_clr(obj->block.data, total);
+       isl_int_set_si(obj->block.data[bmap1->nparam+bmap1->n_in], 1);
+       isl_int_set_si(obj->block.data[bmap1->nparam+bmap1->n_in+
+                                       bmap1->n_out-bmap2->n_out], -1);
+       if (!obj)
+               goto error;
+       bmap1 = add_constraints(bmap1, bmap2, 0, bmap1->n_out - bmap2->n_out);
+       isl_int_init(num);
+       isl_int_init(den);
+       res = isl_solve_lp(bmap1, 0, obj->block.data, ctx->one, &num, &den);
+       if (res == isl_lp_empty)
+               cmp = 0;
+       else if (res == isl_lp_ok && isl_int_is_pos(num))
+               cmp = 1;
+       else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
+                 res == isl_lp_unbounded)
+               cmp = -1;
+       else
+               cmp = -2;
+       isl_int_clear(num);
+       isl_int_clear(den);
+       isl_basic_map_free(bmap1);
+       isl_vec_free(ctx, obj);
+       return cmp;
+error:
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
+       return -2;
+}
+
+static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
+       unsigned pos, isl_int *val)
+{
+       int i;
+       int d;
+       unsigned total;
+
+       if (!bmap)
+               return -1;
+       total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
+               for (; d+1 > pos; --d)
+                       if (!isl_int_is_zero(bmap->eq[i][1+d]))
+                               break;
+               if (d != pos)
+                       continue;
+               if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
+                       return 0;
+               if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
+                       return 0;
+               if (!isl_int_is_one(bmap->eq[i][1+d]))
+                       return 0;
+               if (val)
+                       isl_int_neg(*val, bmap->eq[i][0]);
+               return 1;
+       }
+       return 0;
+}
+
+static int isl_map_fast_has_fixed_var(struct isl_map *map,
+       unsigned pos, isl_int *val)
+{
+       int i;
+       isl_int v;
+       isl_int tmp;
+       int fixed;
+
+       if (!map)
+               return -1;
+       if (map->n == 0)
+               return 0;
+       if (map->n == 1)
+               return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val); 
+       isl_int_init(v);
+       isl_int_init(tmp);
+       fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v); 
+       for (i = 1; fixed == 1 && i < map->n; ++i) {
+               fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp); 
+               if (fixed == 1 && isl_int_ne(tmp, v))
+                       fixed = 0;
+       }
+       if (val)
+               isl_int_set(*val, v);
+       isl_int_clear(tmp);
+       isl_int_clear(v);
+       return fixed;
+}
+
+static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
+       isl_int *val)
+{
+       return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
+}
+
+/* Check if dimension dim has fixed value and if so and if val is not NULL,
+ * then return this fixed value in *val.
+ */
+int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
+{
+       return isl_set_fast_has_fixed_var(set, set->nparam + dim, val);
+}
+
+/* Check if input variable in has fixed value and if so and if val is not NULL,
+ * then return this fixed value in *val.
+ */
+int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
+{
+       return isl_map_fast_has_fixed_var(map, map->nparam + in, val);
+}
+
+/* Check if dimension dim has an (obvious) fixed lower bound and if so
+ * and if val is not NULL, then return this lower bound in *val.
+ */
+int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
+       unsigned dim, isl_int *val)
+{
+       int i, i_eq = -1, i_ineq = -1;
+       isl_int *c;
+       unsigned total;
+
+       if (!bset)
+               return -1;
+       total = bset->nparam + bset->dim + bset->n_div;
+       for (i = 0; i < bset->n_eq; ++i) {
+               if (isl_int_is_zero(bset->eq[i][1+bset->nparam+dim]))
+                       continue;
+               if (i_eq != -1)
+                       return 0;
+               i_eq = i;
+       }
+       for (i = 0; i < bset->n_ineq; ++i) {
+               if (!isl_int_is_pos(bset->ineq[i][1+bset->nparam+dim]))
+                       continue;
+               if (i_eq != -1 || i_ineq != -1)
+                       return 0;
+               i_ineq = i;
+       }
+       if (i_eq == -1 && i_ineq == -1)
+               return 0;
+       c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
+       /* The coefficient should always be one due to normalization. */
+       if (!isl_int_is_one(c[1+bset->nparam+dim]))
+               return 0;
+       if (isl_seq_first_non_zero(c+1, bset->nparam+dim) != -1)
+               return 0;
+       if (isl_seq_first_non_zero(c+1+bset->nparam+dim+1,
+                                       total - bset->nparam - dim - 1) != -1)
+               return 0;
+       if (val)
+               isl_int_neg(*val, c[0]);
+       return 1;
+}
+
+int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
+       unsigned dim, isl_int *val)
+{
+       int i;
+       isl_int v;
+       isl_int tmp;
+       int fixed;
+
+       if (!set)
+               return -1;
+       if (set->n == 0)
+               return 0;
+       if (set->n == 1)
+               return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
+                                                               dim, val);
+       isl_int_init(v);
+       isl_int_init(tmp);
+       fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
+                                                               dim, &v);
+       for (i = 1; fixed == 1 && i < set->n; ++i) {
+               fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
+                                                               dim, &tmp);
+               if (fixed == 1 && isl_int_ne(tmp, v))
+                       fixed = 0;
+       }
+       if (val)
+               isl_int_set(*val, v);
+       isl_int_clear(tmp);
+       isl_int_clear(v);
+       return fixed;
+}
+
+/* Remove all information from bset that is redundant in the context
+ * of context.  In particular, equalities that are linear combinations
+ * of those in context are remobed.  Then the inequalities that are
+ * redundant in the context of the equalities and inequalities of
+ * context are removed.
+ */
+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;
+       enum isl_lp_result res = isl_lp_ok;
+
+       if (!bset || !context)
+               goto error;
+
+       if (context->n_eq > 0) {
+               struct isl_mat *T;
+               struct isl_mat *T2;
+               struct isl_ctx *ctx = context->ctx;
+               context = isl_basic_set_remove_equalities(context, &T, &T2);
+               if (!context)
+                       goto error;
+               bset = isl_basic_set_preimage(ctx, bset, T);
+               bset = uset_gist(bset, context);
+               bset = isl_basic_set_preimage(ctx, bset, T2);
+               return bset;
+       }
+       combined = isl_basic_set_extend(isl_basic_set_copy(bset),
+                       0, bset->dim, 0, context->n_eq, context->n_ineq);
+       context = set_add_constraints(combined, context, 0);
+       if (!context)
+               goto error;
+       ctx = context->ctx;
+       isl_int_init(opt);
+       for (i = bset->n_ineq-1; i >= 0; --i) {
+               set_swap_inequality(context, i, context->n_ineq-1);
+               context->n_ineq--;
+               res = isl_solve_lp((struct isl_basic_map *)context, 0,
+                       context->ineq[context->n_ineq]+1, ctx->one, &opt, NULL);
+               context->n_ineq++;
+               set_swap_inequality(context, i, context->n_ineq-1);
+               if (res == isl_lp_unbounded)
+                       continue;
+               if (res == isl_lp_error)
+                       break;
+               if (res == isl_lp_empty) {
+                       bset = isl_basic_set_set_to_empty(bset);
+                       break;
+               }
+               isl_int_add(opt, opt, context->ineq[i][0]);
+               if (!isl_int_is_neg(opt)) {
+                       isl_basic_set_drop_inequality(context, i);
+                       isl_basic_set_drop_inequality(bset, i);
+               }
+       }
+       isl_int_clear(opt);
+       if (res == isl_lp_error)
+               goto error;
+       isl_basic_set_free(context);
+       return bset;
+error:
+       isl_basic_set_free(context);
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
+       struct isl_basic_map *context)
+{
+       struct isl_basic_set *bset;
+
+       if (!bmap || !context)
+               goto error;
+
+       context = isl_basic_map_align_divs(context, bmap);
+       bmap = isl_basic_map_align_divs(bmap, context);
+
+       bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
+                        isl_basic_map_underlying_set(context));
+
+       return isl_basic_map_overlying_set(bset, bmap);
+error:
+       isl_basic_map_free(bmap);
+       isl_basic_map_free(context);
+       return NULL;
+}
+
+struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
+{
+       int i;
+
+       map = isl_map_cow(map);
+       if (!map || !context)
+               return NULL;
+       isl_assert(map->ctx, map->nparam == context->nparam, goto error);
+       isl_assert(map->ctx, map->n_in == context->n_in, goto error);
+       isl_assert(map->ctx, map->n_out == context->n_out, goto error);
+       for (i = 0; i < map->n; ++i)
+               context = isl_basic_map_align_divs(context, map->p[i]);
+       for (i = 0; i < map->n; ++i) {
+               map->p[i] = isl_basic_map_gist(map->p[i],
+                                               isl_basic_map_copy(context));
+               if (!map->p[i])
+                       goto error;
+       }
+       isl_basic_map_free(context);
+       F_CLR(map, ISL_MAP_NORMALIZED);
+       return map;
+error:
+       isl_map_free(map);
+       isl_basic_map_free(context);
+       return NULL;
+}
+
+struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
+{
+       return (struct isl_set *)isl_map_gist((struct isl_map *)set,
+                                       (struct isl_basic_map *)context);
+}
+
+struct constraint {
+       unsigned        size;
+       isl_int         *c;
+};
+
+static int qsort_constraint_cmp(const void *p1, const void *p2)
+{
+       const struct constraint *c1 = (const struct constraint *)p1;
+       const struct constraint *c2 = (const struct constraint *)p2;
+       unsigned size = isl_min(c1->size, c2->size);
+       return isl_seq_cmp(c1->c, c2->c, size);
+}
+
+static struct isl_basic_map *isl_basic_map_sort_constraints(
+       struct isl_basic_map *bmap)
+{
+       int i;
+       struct constraint *c;
+       unsigned total;
+
+       if (!bmap)
+               return NULL;
+       total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
+       if (!c)
+               goto error;
+       for (i = 0; i < bmap->n_ineq; ++i) {
+               c[i].size = total;
+               c[i].c = bmap->ineq[i];
+       }
+       qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
+       for (i = 0; i < bmap->n_ineq; ++i)
+               bmap->ineq[i] = c[i].c;
+       free(c);
+       return bmap;
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
+{
+       if (!bmap)
+               return NULL;
+       if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
+               return bmap;
+       bmap = isl_basic_map_convex_hull(bmap);
+       bmap = isl_basic_map_sort_constraints(bmap);
+       F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
+       return bmap;
+}
+
+static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
+       const struct isl_basic_map *bmap2)
+{
+       int i, cmp;
+       unsigned total;
+
+       if (bmap1 == bmap2)
+               return 0;
+       if (bmap1->nparam != bmap2->nparam)
+               return bmap1->nparam - bmap2->nparam;
+       if (bmap1->n_in != bmap2->n_in)
+               return bmap1->n_in - bmap2->n_in;
+       if (bmap1->n_out != bmap2->n_out)
+               return bmap1->n_out - bmap2->n_out;
+       if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
+           F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
+               return 0;
+       if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
+               return 1;
+       if (F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
+               return -1;
+       if (bmap1->n_eq != bmap2->n_eq)
+               return bmap1->n_eq - bmap2->n_eq;
+       if (bmap1->n_ineq != bmap2->n_ineq)
+               return bmap1->n_ineq - bmap2->n_ineq;
+       if (bmap1->n_div != bmap2->n_div)
+               return bmap1->n_div - bmap2->n_div;
+       total = bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
+       for (i = 0; i < bmap1->n_eq; ++i) {
+               cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
+               if (cmp)
+                       return cmp;
+       }
+       for (i = 0; i < bmap1->n_ineq; ++i) {
+               cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
+               if (cmp)
+                       return cmp;
+       }
+       for (i = 0; i < bmap1->n_div; ++i) {
+               cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
+               if (cmp)
+                       return cmp;
+       }
+       return 0;
+}
+
+static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
+       struct isl_basic_map *bmap2)
+{
+       return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
+}
+
+static int qsort_bmap_cmp(const void *p1, const void *p2)
+{
+       const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
+       const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
+
+       return isl_basic_map_fast_cmp(bmap1, bmap2);
+}
+
+/* We normalize in place, but if anything goes wrong we need
+ * to return NULL, so we need to make sure we don't change the
+ * meaning of any possible other copies of map.
+ */
+struct isl_map *isl_map_normalize(struct isl_map *map)
+{
+       int i, j;
+       struct isl_basic_map *bmap;
+
+       if (!map)
+               return NULL;
+       if (F_ISSET(map, ISL_MAP_NORMALIZED))
+               return map;
+       for (i = 0; i < map->n; ++i) {
+               bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
+               if (!bmap)
+                       goto error;
+               isl_basic_map_free(map->p[i]);
+               map->p[i] = bmap;
+       }
+       qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
+       F_SET(map, ISL_MAP_NORMALIZED);
+       map = isl_map_remove_empty_parts(map);
+       if (!map)
+               return NULL;
+       for (i = map->n - 1; i >= 1; --i) {
+               if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
+                       continue;
+               isl_basic_map_free(map->p[i-1]);
+               for (j = i; j < map->n; ++j)
+                       map->p[j-1] = map->p[j];
+               map->n--;
+       }
+       return map;
+error:
+       isl_map_free(map);
+       return NULL;
+
+}
+
+struct isl_set *isl_set_normalize(struct isl_set *set)
+{
+       return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
+}
+
+int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
+{
+       int i;
+       int equal;
+
+       if (!map1 || !map2)
+               return -1;
+
+       if (map1 == map2)
+               return 1;
+       if (map1->nparam != map2->nparam)
+               return 0;
+       if (map1->n_in != map2->n_in)
+               return 0;
+       if (map1->n_out != map2->n_out)
+               return 0;
+
+       map1 = isl_map_copy(map1);
+       map2 = isl_map_copy(map2);
+       map1 = isl_map_normalize(map1);
+       map2 = isl_map_normalize(map2);
+       if (!map1 || !map2)
+               goto error;
+       equal = map1->n == map2->n;
+       for (i = 0; equal && i < map1->n; ++i) {
+               equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
+               if (equal < 0)
+                       goto error;
+       }
+       isl_map_free(map1);
+       isl_map_free(map2);
+       return equal;
+error:
+       isl_map_free(map1);
+       isl_map_free(map2);
+       return -1;
+}
+
+int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
+{
+       return isl_map_fast_is_equal((struct isl_map *)set1,
+                                               (struct isl_map *)set2);
+}
+
+/* Return an interval that ranges from min to max (inclusive)
+ */
+struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
+       isl_int min, isl_int max)
+{
+       int k;
+       struct isl_basic_set *bset = NULL;
+
+       bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
+       if (!bset)
+               goto error;
+
+       k = isl_basic_set_alloc_inequality(bset);
+       if (k < 0)
+               goto error;
+       isl_int_set_si(bset->ineq[k][1], 1);
+       isl_int_neg(bset->ineq[k][0], min);
+
+       k = isl_basic_set_alloc_inequality(bset);
+       if (k < 0)
+               goto error;
+       isl_int_set_si(bset->ineq[k][1], -1);
+       isl_int_set(bset->ineq[k][0], max);
+
+       return bset;
+error:
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+/* Return the Cartesian product of the basic sets in list (in the given order).
+ */
+struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
+{
+       int i;
+       unsigned dim;
+       unsigned nparam;
+       unsigned extra;
+       unsigned n_eq;
+       unsigned n_ineq;
+       struct isl_basic_set *product = NULL;
+
+       if (!list)
+               goto error;
+       isl_assert(list->ctx, list->n > 0, goto error);
+       isl_assert(list->ctx, list->p[0], goto error);
+       nparam = list->p[0]->nparam;
+       dim = list->p[0]->dim;
+       extra = list->p[0]->n_div;
+       n_eq = list->p[0]->n_eq;
+       n_ineq = list->p[0]->n_ineq;
+       for (i = 1; i < list->n; ++i) {
+               isl_assert(list->ctx, list->p[i], goto error);
+               isl_assert(list->ctx, nparam == list->p[i]->nparam, goto error);
+               dim += list->p[i]->dim;
+               extra += list->p[i]->n_div;
+               n_eq += list->p[i]->n_eq;
+               n_ineq += list->p[i]->n_ineq;
+       }
+       product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
+                                       n_eq, n_ineq);
+       if (!product)
+               goto error;
+       dim = 0;
+       for (i = 0; i < list->n; ++i) {
+               set_add_constraints(product,
+                                       isl_basic_set_copy(list->p[i]), dim);
+               dim += list->p[i]->dim;
+       }
+       isl_basic_set_list_free(list);
+       return product;
+error:
+       isl_basic_set_free(product);
+       isl_basic_set_list_free(list);
+       return NULL;
+}