isl_basic_map_compute_divs: use isl_basic_set_lexmin and move to isl_map.c
[platform/upstream/isl.git] / isl_map.c
index 99d247d..49291c6 100644 (file)
--- a/isl_map.c
+++ b/isl_map.c
@@ -3,6 +3,7 @@
 #include "isl_ctx.h"
 #include "isl_blk.h"
 #include "isl_dim.h"
+#include "isl_equalities.h"
 #include "isl_list.h"
 #include "isl_lp.h"
 #include "isl_seq.h"
@@ -40,6 +41,7 @@ static unsigned n(struct isl_dim *dim, enum isl_dim_type type)
        case isl_dim_param:     return dim->nparam;
        case isl_dim_in:        return dim->n_in;
        case isl_dim_out:       return dim->n_out;
+       case isl_dim_all:       return dim->nparam + dim->n_in + dim->n_out;
        }
 }
 
@@ -94,9 +96,9 @@ unsigned isl_basic_map_dim(const struct isl_basic_map *bmap,
 {
        struct isl_dim *dim = bmap->dim;
        switch (type) {
-       case isl_dim_param:     return dim->nparam;
-       case isl_dim_in:        return dim->n_in;
-       case isl_dim_out:       return dim->n_out;
+       case isl_dim_param:
+       case isl_dim_in:
+       case isl_dim_out:       return isl_dim_size(bmap->dim, type);
        case isl_dim_div:       return bmap->n_div;
        case isl_dim_all:       return isl_basic_map_total_dim(bmap);
        }
@@ -107,7 +109,12 @@ unsigned isl_map_dim(const struct isl_map *map, enum isl_dim_type type)
        return n(map->dim, type);
 }
 
-static unsigned basic_map_offset(struct isl_basic_map *bmap,
+unsigned isl_set_dim(const struct isl_set *set, enum isl_dim_type type)
+{
+       return n(set->dim, type);
+}
+
+unsigned isl_basic_map_offset(struct isl_basic_map *bmap,
                                        enum isl_dim_type type)
 {
        struct isl_dim *dim = bmap->dim;
@@ -215,6 +222,34 @@ int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
               bmap->dim->nparam == bset->dim->nparam;
 }
 
+struct isl_dim *isl_basic_map_get_dim(struct isl_basic_map *bmap)
+{
+       if (!bmap)
+               return NULL;
+       return isl_dim_copy(bmap->dim);
+}
+
+struct isl_dim *isl_basic_set_get_dim(struct isl_basic_set *bset)
+{
+       if (!bset)
+               return NULL;
+       return isl_dim_copy(bset->dim);
+}
+
+struct isl_dim *isl_map_get_dim(struct isl_map *map)
+{
+       if (!map)
+               return NULL;
+       return isl_dim_copy(map->dim);
+}
+
+struct isl_dim *isl_set_get_dim(struct isl_set *set)
+{
+       if (!set)
+               return NULL;
+       return isl_dim_copy(set->dim);
+}
+
 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
                struct isl_basic_map *bmap, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
@@ -222,14 +257,14 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
        int i;
        size_t row_size = 1 + isl_dim_total(bmap->dim) + extra;
 
-       bmap->block = isl_blk_alloc(ctx, (n_eq + n_ineq) * row_size);
+       bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
        if (isl_blk_is_error(bmap->block)) {
                free(bmap);
                return NULL;
        }
 
-       bmap->eq = isl_alloc_array(ctx, isl_int *, n_eq + n_ineq);
-       if (!bmap->eq) {
+       bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
+       if (!bmap->ineq) {
                isl_blk_free(ctx, bmap->block);
                free(bmap);
                return NULL;
@@ -241,7 +276,7 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
        } else {
                bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
                if (isl_blk_is_error(bmap->block2)) {
-                       free(bmap->eq);
+                       free(bmap->ineq);
                        isl_blk_free(ctx, bmap->block);
                        free(bmap);
                        return NULL;
@@ -250,15 +285,15 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
                bmap->div = isl_alloc_array(ctx, isl_int *, extra);
                if (!bmap->div) {
                        isl_blk_free(ctx, bmap->block2);
-                       free(bmap->eq);
+                       free(bmap->ineq);
                        isl_blk_free(ctx, bmap->block);
                        free(bmap);
                        return NULL;
                }
        }
 
-       for (i = 0; i < n_eq + n_ineq; ++i)
-               bmap->eq[i] = bmap->block.data + i * row_size;
+       for (i = 0; i < n_ineq + n_eq; ++i)
+               bmap->ineq[i] = bmap->block.data + i * row_size;
 
        for (i = 0; i < extra; ++i)
                bmap->div[i] = bmap->block2.data + i * (1 + row_size);
@@ -268,7 +303,7 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
        bmap->ref = 1;
        bmap->flags = 0;
        bmap->c_size = n_eq + n_ineq;
-       bmap->ineq = bmap->eq + n_eq;
+       bmap->eq = bmap->ineq + n_ineq;
        bmap->extra = extra;
        bmap->n_eq = 0;
        bmap->n_ineq = 0;
@@ -354,7 +389,7 @@ static void dup_constraints(
                int j = isl_basic_map_alloc_div(dst);
                isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
        }
-       F_SET(dst, ISL_BASIC_SET_FINAL);
+       ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
 }
 
 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
@@ -367,9 +402,9 @@ struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
                        bmap->n_div, bmap->n_eq, bmap->n_ineq);
        if (!dup)
                return NULL;
-       dup->flags = bmap->flags;
        dup_constraints(dup, bmap);
-       dup->sample = isl_vec_copy(bmap->ctx, bmap->sample);
+       dup->flags = bmap->flags;
+       dup->sample = isl_vec_copy(bmap->sample);
        return dup;
 }
 
@@ -386,7 +421,7 @@ struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
        if (!bset)
                return NULL;
 
-       if (F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
+       if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
                bset->ref++;
                return bset;
        }
@@ -407,7 +442,7 @@ struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
        if (!bmap)
                return NULL;
 
-       if (F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
+       if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
                bmap->ref++;
                return bmap;
        }
@@ -434,9 +469,9 @@ void isl_basic_map_free(struct isl_basic_map *bmap)
        isl_ctx_deref(bmap->ctx);
        free(bmap->div);
        isl_blk_free(bmap->ctx, bmap->block2);
-       free(bmap->eq);
+       free(bmap->ineq);
        isl_blk_free(bmap->ctx, bmap->block);
-       isl_vec_free(bmap->ctx, bmap->sample);
+       isl_vec_free(bmap->sample);
        isl_dim_free(bmap->dim);
        free(bmap);
 }
@@ -446,29 +481,41 @@ void isl_basic_set_free(struct isl_basic_set *bset)
        isl_basic_map_free((struct isl_basic_map *)bset);
 }
 
+static int room_for_con(struct isl_basic_map *bmap, unsigned n)
+{
+       return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
+}
+
 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
 {
        struct isl_ctx *ctx;
        if (!bmap)
                return -1;
        ctx = bmap->ctx;
-       isl_assert(ctx, bmap->n_eq + bmap->n_ineq < bmap->c_size, return -1);
-       isl_assert(ctx, bmap->eq + bmap->n_eq <= bmap->ineq, return -1);
-       if (bmap->eq + bmap->n_eq == bmap->ineq) {
+       isl_assert(ctx, room_for_con(bmap, 1), return -1);
+       isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
+                       return -1);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
+       if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
                isl_int *t;
                int j = isl_basic_map_alloc_inequality(bmap);
                if (j < 0)
                        return -1;
-               t = bmap->ineq[0];
-               bmap->ineq[0] = bmap->ineq[j];
-               bmap->ineq[j] = t;
+               t = bmap->ineq[j];
+               bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
+               bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
+               bmap->eq[-1] = t;
+               bmap->n_eq++;
                bmap->n_ineq--;
-               bmap->ineq++;
-       } else
-               isl_seq_clr(bmap->eq[bmap->n_eq] +
-                     1 + isl_basic_map_total_dim(bmap),
+               bmap->eq--;
+               return 0;
+       }
+       isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
                      bmap->extra - bmap->n_div);
-       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
        return bmap->n_eq++;
 }
 
@@ -486,6 +533,11 @@ int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
        return 0;
 }
 
+int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
+{
+       return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
+}
+
 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
 {
        isl_int *t;
@@ -513,14 +565,21 @@ void isl_basic_map_inequality_to_equality(
        isl_int *t;
 
        t = bmap->ineq[pos];
-       bmap->ineq[pos] = bmap->ineq[0];
-       bmap->ineq[0] = bmap->eq[bmap->n_eq];
-       bmap->eq[bmap->n_eq] = t;
+       bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
+       bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
+       bmap->eq[-1] = t;
        bmap->n_eq++;
        bmap->n_ineq--;
-       bmap->ineq++;
-       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
+       bmap->eq--;
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
+}
+
+static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
+{
+       return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
 }
 
 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
@@ -529,11 +588,11 @@ int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
        if (!bmap)
                return -1;
        ctx = bmap->ctx;
-       isl_assert(ctx, (bmap->ineq - bmap->eq) + bmap->n_ineq < bmap->c_size,
-                       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);
+       isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
        isl_seq_clr(bmap->ineq[bmap->n_ineq] +
                      1 + isl_basic_map_total_dim(bmap),
                      bmap->extra - bmap->n_div);
@@ -570,7 +629,7 @@ 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);
+               ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        }
        bmap->n_ineq--;
        return 0;
@@ -589,10 +648,15 @@ int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
        isl_seq_clr(bmap->div[bmap->n_div] +
                      1 + 1 + isl_basic_map_total_dim(bmap),
                      bmap->extra - bmap->n_div);
-       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
        return bmap->n_div++;
 }
 
+int isl_basic_set_alloc_div(struct isl_basic_set *bset)
+{
+       return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
+}
+
 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
 {
        if (!bmap)
@@ -602,6 +666,11 @@ int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
        return 0;
 }
 
+int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
+{
+       return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
+}
+
 /* Copy constraint from src to dst, putting the vars of src at offset
  * dim_off in dst and the divs of src at offset div_off in dst.
  * If both sets are actually map, then dim_off applies to the input
@@ -778,14 +847,14 @@ struct isl_basic_map *isl_basic_map_extend_dim(struct isl_basic_map *base,
        if (!dim)
                goto error;
 
-       base = isl_basic_map_cow(base);
        if (!base)
                goto error;
 
        dims_ok = isl_dim_equal(base->dim, dim) &&
                  base->extra >= base->n_div + extra;
 
-       if (dims_ok && n_eq == 0 && n_ineq == 0) {
+       if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
+                      room_for_ineq(base, n_ineq)) {
                isl_dim_free(dim);
                return base;
        }
@@ -806,7 +875,7 @@ struct isl_basic_map *isl_basic_map_extend_dim(struct isl_basic_map *base,
        ext = add_constraints(ext, base, 0, 0);
        if (ext) {
                ext->flags = flags;
-               F_CLR(ext, ISL_BASIC_SET_FINAL);
+               ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
        }
 
        return ext;
@@ -817,6 +886,15 @@ error:
        return NULL;
 }
 
+struct isl_basic_set *isl_basic_set_extend_dim(struct isl_basic_set *base,
+               struct isl_dim *dim, unsigned extra,
+               unsigned n_eq, unsigned n_ineq)
+{
+       return (struct isl_basic_set *)
+               isl_basic_map_extend_dim((struct isl_basic_map *)base, dim,
+                                                       extra, n_eq, n_ineq);
+}
+
 struct isl_basic_map *isl_basic_map_extend_constraints(
                struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
 {
@@ -875,7 +953,7 @@ struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
                bmap->ref--;
                bmap = isl_basic_map_dup(bmap);
        }
-       F_CLR(bmap, ISL_BASIC_SET_FINAL);
+       ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
        return bmap;
 }
 
@@ -949,7 +1027,7 @@ struct isl_basic_set *isl_basic_set_swap_vars(
 
        isl_blk_free(bset->ctx, blk);
 
-       F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
+       ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
        return bset;
 
 error:
@@ -971,7 +1049,7 @@ struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
                        return NULL;
                }
        }
-       F_CLR(set, ISL_SET_NORMALIZED);
+       ISL_F_CLR(set, ISL_SET_NORMALIZED);
        return set;
 }
 
@@ -993,7 +1071,7 @@ struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
        }
        isl_int_set_si(bmap->eq[i][0], 1);
        isl_seq_clr(bmap->eq[i]+1, total);
-       F_SET(bmap, ISL_BASIC_MAP_EMPTY);
+       ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
        return isl_basic_map_finalize(bmap);
 error:
        isl_basic_map_free(bmap);
@@ -1006,7 +1084,7 @@ struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
                isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
 }
 
-static void swap_div(struct isl_basic_map *bmap, int a, int b)
+void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
 {
        int i;
        unsigned off = isl_dim_total(bmap->dim);
@@ -1022,7 +1100,7 @@ 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);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 }
 
 /* Eliminate the specified n dimensions starting at first from the
@@ -1101,9 +1179,26 @@ error:
        return NULL;
 }
 
-/* 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)
+struct isl_basic_map *isl_basic_map_remove(struct isl_basic_map *bmap,
+       enum isl_dim_type type, unsigned first, unsigned n)
+{
+       if (!bmap)
+               return NULL;
+       isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
+                       goto error);
+       if (n == 0)
+               return bmap;
+       bmap = isl_basic_map_eliminate_vars(bmap,
+                       isl_basic_map_offset(bmap, type) - 1 + first, n);
+       bmap = isl_basic_map_drop(bmap, type, first, n);
+       return bmap;
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+struct isl_map *isl_map_remove(struct isl_map *map,
+       enum isl_dim_type type, unsigned first, unsigned n)
 {
        int i;
        unsigned nparam;
@@ -1114,22 +1209,28 @@ struct isl_map *isl_map_remove_inputs(struct isl_map *map,
        map = isl_map_cow(map);
        if (!map)
                return NULL;
-       nparam = isl_map_n_param(map);
-       isl_assert(map->ctx, first+n <= isl_map_n_in(map), goto error);
+       isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
        
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
-                                                           nparam + first, n);
+                       isl_basic_map_offset(map->p[i], type) - 1 + first, n);
                if (!map->p[i])
                        goto error;
        }
-       map = isl_map_drop_inputs(map, first, n);
+       map = isl_map_drop(map, type, first, n);
        return map;
 error:
        isl_map_free(map);
        return NULL;
 }
 
+/* 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)
+{
+       return isl_map_remove(map, isl_dim_in, first, n);
+}
+
 /* 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)
@@ -1295,7 +1396,7 @@ 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);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        return 0;
 }
 
@@ -1340,6 +1441,42 @@ struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
        return set;
 }
 
+/* Make sure "map" has room for at least "n" more basic maps.
+ */
+struct isl_map *isl_map_grow(struct isl_map *map, int n)
+{
+       int i;
+       struct isl_map *grown = NULL;
+
+       if (!map)
+               return NULL;
+       isl_assert(map->ctx, n >= 0, goto error);
+       if (map->n + n <= map->size)
+               return map;
+       grown = isl_map_alloc_dim(isl_map_get_dim(map), map->n + n, map->flags);
+       if (!grown)
+               goto error;
+       for (i = 0; i < map->n; ++i) {
+               grown->p[i] = isl_basic_map_copy(map->p[i]);
+               if (!grown->p[i])
+                       goto error;
+               grown->n++;
+       }
+       isl_map_free(map);
+       return grown;
+error:
+       isl_map_free(grown);
+       isl_map_free(map);
+       return NULL;
+}
+
+/* Make sure "set" has room for at least "n" more basic sets.
+ */
+struct isl_set *isl_set_grow(struct isl_set *set, int n)
+{
+       return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
+}
+
 struct isl_set *isl_set_dup(struct isl_set *set)
 {
        int i;
@@ -1388,19 +1525,8 @@ struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
 
 struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
 {
-       if (!bset || !set)
-               goto error;
-       isl_assert(set->ctx, isl_dim_equal(set->dim, bset->dim), goto error);
-       isl_assert(set->ctx, set->n < set->size, goto error);
-       set->p[set->n] = bset;
-       set->n++;
-       return set;
-error:
-       if (set)
-               isl_set_free(set);
-       if (bset)
-               isl_basic_set_free(bset);
-       return NULL;
+       return (struct isl_set *)isl_map_add((struct isl_map *)set,
+                                               (struct isl_basic_map *)bset);
 }
 
 void isl_set_free(struct isl_set *set)
@@ -1470,9 +1596,14 @@ struct isl_basic_map *isl_basic_map_intersect_domain(
        if (!bmap || !bset)
                goto error;
 
-       isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
-                   goto error);
+       isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
+                                       bset->dim, isl_dim_param), goto error);
+
+       if (isl_dim_size(bset->dim, isl_dim_set) != 0)
+               isl_assert(bset->ctx,
+                   isl_basic_map_compatible_domain(bmap, bset), goto error);
 
+       bmap = isl_basic_map_cow(bmap);
        bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
                        bset->n_div, bset->n_eq, bset->n_ineq);
        if (!bmap)
@@ -1497,9 +1628,14 @@ struct isl_basic_map *isl_basic_map_intersect_range(
        if (!bmap || !bset)
                goto error;
 
-       isl_assert(bset->ctx, isl_basic_map_compatible_range(bmap, bset),
-                  goto error);
+       isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
+                                       bset->dim, isl_dim_param), goto error);
+
+       if (isl_dim_size(bset->dim, isl_dim_set) != 0)
+               isl_assert(bset->ctx,
+                   isl_basic_map_compatible_range(bmap, bset), goto error);
 
+       bmap = isl_basic_map_cow(bmap);
        bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
                        bset->n_div, bset->n_eq, bset->n_ineq);
        if (!bmap)
@@ -1515,23 +1651,91 @@ error:
        return NULL;
 }
 
+static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
+{
+       int i;
+       unsigned total;
+       isl_int s;
+
+       total = 1 + isl_basic_map_total_dim(bmap);
+       if (total != vec->size)
+               return -1;
+
+       isl_int_init(s);
+
+       for (i = 0; i < bmap->n_eq; ++i) {
+               isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
+               if (!isl_int_is_zero(s)) {
+                       isl_int_clear(s);
+                       return 0;
+               }
+       }
+
+       for (i = 0; i < bmap->n_ineq; ++i) {
+               isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
+               if (isl_int_is_neg(s)) {
+                       isl_int_clear(s);
+                       return 0;
+               }
+       }
+
+       isl_int_clear(s);
+
+       return 1;
+}
+
+int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
+{
+       return basic_map_contains((struct isl_basic_map *)bset, vec);
+}
+
 struct isl_basic_map *isl_basic_map_intersect(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
+       struct isl_vec *sample = NULL;
+
        if (!bmap1 || !bmap2)
                goto error;
 
-       isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
-
+       isl_assert(bmap1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
+                                    bmap2->dim, isl_dim_param), goto error);
+       if (isl_dim_total(bmap1->dim) ==
+                               isl_dim_size(bmap1->dim, isl_dim_param) &&
+           isl_dim_total(bmap2->dim) !=
+                               isl_dim_size(bmap2->dim, isl_dim_param))
+               return isl_basic_map_intersect(bmap2, bmap1);
+
+       if (isl_dim_total(bmap2->dim) !=
+                                       isl_dim_size(bmap2->dim, isl_dim_param))
+               isl_assert(bmap1->ctx,
+                           isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
+
+       if (bmap1->sample &&
+           basic_map_contains(bmap1, bmap1->sample) > 0 &&
+           basic_map_contains(bmap2, bmap1->sample) > 0)
+               sample = isl_vec_copy(bmap1->sample);
+       else if (bmap2->sample &&
+           basic_map_contains(bmap1, bmap2->sample) > 0 &&
+           basic_map_contains(bmap2, bmap2->sample) > 0)
+               sample = isl_vec_copy(bmap2->sample);
+
+       bmap1 = isl_basic_map_cow(bmap1);
        bmap1 = isl_basic_map_extend_dim(bmap1, isl_dim_copy(bmap1->dim),
                        bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
        if (!bmap1)
                goto error;
        bmap1 = add_constraints(bmap1, bmap2, 0, 0);
 
+       if (sample) {
+               isl_vec_free(bmap1->sample);
+               bmap1->sample = sample;
+       }
+
        bmap1 = isl_basic_map_simplify(bmap1);
        return isl_basic_map_finalize(bmap1);
 error:
+       if (sample)
+               isl_vec_free(sample);
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return NULL;
@@ -1555,9 +1759,20 @@ struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
        if (!map1 || !map2)
                goto error;
 
-       if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
-           F_ISSET(map2, ISL_MAP_DISJOINT))
-               FL_SET(flags, ISL_MAP_DISJOINT);
+       isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
+                                        map2->dim, isl_dim_param), goto error);
+       if (isl_dim_total(map1->dim) ==
+                               isl_dim_size(map1->dim, isl_dim_param) &&
+           isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
+               return isl_map_intersect(map2, map1);
+
+       if (isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
+               isl_assert(map1->ctx,
+                           isl_dim_equal(map1->dim, map2->dim), goto error);
+
+       if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
+           ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
+               ISL_FL_SET(flags, ISL_MAP_DISJOINT);
 
        result = isl_map_alloc_dim(isl_dim_copy(map1->dim),
                                map1->n * map2->n, flags);
@@ -1661,7 +1876,7 @@ error:
        return NULL;
 }
 
-struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
+static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
 {
        int i, j;
 
@@ -1832,7 +2047,7 @@ struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
                return NULL;
 
        n = isl_basic_map_dim(bmap, isl_dim_out);
-       off = basic_map_offset(bmap, isl_dim_out);
+       off = isl_basic_map_offset(bmap, isl_dim_out);
        for (i = 0; i < bmap->n_eq; ++i)
                for (j = 0; j < n; ++j)
                        isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
@@ -1845,8 +2060,61 @@ struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
        return isl_basic_map_finalize(bmap);
 }
 
-static struct isl_basic_map *var_equal(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned pos)
+/* Given a basic map A -> f(A) and an integer d, construct a basic map
+ * A -> floor(f(A)/d).
+ */
+struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
+               isl_int d)
+{
+       unsigned n_in, n_out, nparam, total, pos;
+       struct isl_basic_map *result = NULL;
+       struct isl_dim_map *dim_map;
+       int i;
+
+       if (!bmap)
+               return NULL;
+
+       nparam = isl_basic_map_n_param(bmap);
+       n_in = isl_basic_map_n_in(bmap);
+       n_out = isl_basic_map_n_out(bmap);
+
+       total = nparam + n_in + n_out + bmap->n_div + n_out;
+       dim_map = isl_dim_map_alloc(bmap->ctx, total);
+       isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
+       isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
+       isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
+       isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
+
+       result = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
+                       bmap->n_div + n_out,
+                       bmap->n_eq, bmap->n_ineq + 2 * n_out);
+       result = add_constraints_dim_map(result, bmap, dim_map);
+       result = add_divs(result, n_out);
+       for (i = 0; i < n_out; ++i) {
+               int j;
+               j = isl_basic_map_alloc_inequality(result);
+               if (j < 0)
+                       goto error;
+               isl_seq_clr(result->ineq[j], 1+total);
+               isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
+               isl_int_set_si(result->ineq[j][1+pos+i], 1);
+               j = isl_basic_map_alloc_inequality(result);
+               if (j < 0)
+                       goto error;
+               isl_seq_clr(result->ineq[j], 1+total);
+               isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
+               isl_int_set_si(result->ineq[j][1+pos+i], -1);
+               isl_int_sub_ui(result->ineq[j][0], d, 1);
+       }
+
+       result = isl_basic_map_simplify(result);
+       return isl_basic_map_finalize(result);
+error:
+       isl_basic_map_free(result);
+       return NULL;
+}
+
+static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
 {
        int i;
        unsigned nparam;
@@ -1866,8 +2134,7 @@ error:
        return NULL;
 }
 
-static struct isl_basic_map *var_more(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned pos)
+static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
 {
        int i;
        unsigned nparam;
@@ -1888,8 +2155,7 @@ error:
        return NULL;
 }
 
-static struct isl_basic_map *var_less(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned pos)
+static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
 {
        int i;
        unsigned nparam;
@@ -1910,46 +2176,43 @@ error:
        return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_equal(struct isl_ctx *ctx,
-               unsigned nparam, unsigned in, unsigned out, unsigned n_equal)
+struct isl_basic_map *isl_basic_map_equal(struct isl_dim *dim, unsigned n_equal)
 {
        int i;
        struct isl_basic_map *bmap;
-       bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, n_equal, 0);
+       bmap = isl_basic_map_alloc_dim(dim, 0, n_equal, 0);
        if (!bmap)
                return NULL;
        for (i = 0; i < n_equal && bmap; ++i)
-               bmap = var_equal(ctx, bmap, i);
+               bmap = var_equal(bmap, i);
        return isl_basic_map_finalize(bmap);
 }
 
-struct isl_basic_map *isl_basic_map_less_at(struct isl_ctx *ctx,
-               unsigned nparam, unsigned in, unsigned out, unsigned pos)
+struct isl_basic_map *isl_basic_map_less_at(struct isl_dim *dim, unsigned pos)
 {
        int i;
        struct isl_basic_map *bmap;
-       bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
+       bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
        if (!bmap)
                return NULL;
        for (i = 0; i < pos && bmap; ++i)
-               bmap = var_equal(ctx, bmap, i);
+               bmap = var_equal(bmap, i);
        if (bmap)
-               bmap = var_less(ctx, bmap, pos);
+               bmap = var_less(bmap, pos);
        return isl_basic_map_finalize(bmap);
 }
 
-struct isl_basic_map *isl_basic_map_more_at(struct isl_ctx *ctx,
-               unsigned nparam, unsigned in, unsigned out, unsigned pos)
+struct isl_basic_map *isl_basic_map_more_at(struct isl_dim *dim, unsigned pos)
 {
        int i;
        struct isl_basic_map *bmap;
-       bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
+       bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
        if (!bmap)
                return NULL;
        for (i = 0; i < pos && bmap; ++i)
-               bmap = var_equal(ctx, bmap, i);
+               bmap = var_equal(bmap, i);
        if (bmap)
-               bmap = var_more(ctx, bmap, pos);
+               bmap = var_more(bmap, pos);
        return isl_basic_map_finalize(bmap);
 }
 
@@ -2096,9 +2359,12 @@ struct isl_basic_map *isl_basic_map_overlying_set(
                }
                bmap = isl_basic_map_extend_constraints(bmap, 
                                                        0, 2 * like->n_div);
-               for (i = 0; i < like->n_div; ++i)
+               for (i = 0; i < like->n_div; ++i) {
+                       if (isl_int_is_zero(bmap->div[i][0]))
+                               continue;
                        if (add_div_constraints(bmap, i) < 0)
                                goto error;
+               }
        }
        isl_basic_map_free(like);
        bmap = isl_basic_map_simplify(bmap);
@@ -2228,8 +2494,8 @@ struct isl_set *isl_map_range(struct isl_map *map)
                if (!set->p[i])
                        goto error;
        }
-       F_CLR(set, ISL_MAP_DISJOINT);
-       F_CLR(set, ISL_SET_NORMALIZED);
+       ISL_F_CLR(set, ISL_MAP_DISJOINT);
+       ISL_F_CLR(set, ISL_SET_NORMALIZED);
        return set;
 error:
        isl_map_free(map);
@@ -2261,6 +2527,11 @@ error:
        return NULL;
 }
 
+struct isl_map *isl_map_from_range(struct isl_set *set)
+{
+       return (struct isl_map *)set;
+}
+
 struct isl_set *isl_set_from_map(struct isl_map *map)
 {
        int i;
@@ -2397,10 +2668,16 @@ struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
        return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
 }
 
-struct isl_map *isl_map_empty(struct isl_ctx *ctx,
-               unsigned nparam, unsigned in, unsigned out)
+struct isl_map *isl_map_empty(struct isl_dim *dim)
 {
-       return isl_map_alloc(ctx, nparam, in, out, 0, ISL_MAP_DISJOINT);
+       return isl_map_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
+}
+
+struct isl_map *isl_map_empty_like(struct isl_map *model)
+{
+       if (!model)
+               return NULL;
+       return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
 }
 
 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
@@ -2422,6 +2699,16 @@ struct isl_set *isl_set_empty_like(struct isl_set *model)
        return isl_set_empty(isl_dim_copy(model->dim));
 }
 
+struct isl_map *isl_map_universe(struct isl_dim *dim)
+{
+       struct isl_map *map;
+       if (!dim)
+               return NULL;
+       map = isl_map_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
+       map = isl_map_add(map, isl_basic_map_universe(dim));
+       return map;
+}
+
 struct isl_set *isl_set_universe(struct isl_dim *dim)
 {
        struct isl_set *set;
@@ -2449,11 +2736,15 @@ struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
 {
        if (!bmap || !map)
                goto error;
+       if (isl_basic_map_fast_is_empty(bmap)) {
+               isl_basic_map_free(bmap);
+               return map;
+       }
        isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
        isl_assert(map->ctx, map->n < map->size, goto error);
        map->p[map->n] = bmap;
        map->n++;
-       F_CLR(map, ISL_MAP_NORMALIZED);
+       ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 error:
        if (map)
@@ -2521,7 +2812,7 @@ static struct isl_basic_map *isl_basic_map_fix_pos(struct isl_basic_map *bmap,
        j = isl_basic_map_alloc_equality(bmap);
        if (j < 0)
                goto error;
-       isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
+       isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->eq[j][pos], -1);
        isl_int_set_si(bmap->eq[j][0], value);
        bmap = isl_basic_map_simplify(bmap);
@@ -2537,13 +2828,21 @@ struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
        if (!bmap)
                return NULL;
        isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
-       return isl_basic_map_fix_pos(bmap, basic_map_offset(bmap, type) + pos,
+       return isl_basic_map_fix_pos(bmap, isl_basic_map_offset(bmap, type) + pos,
                                        value);
 error:
        isl_basic_map_free(bmap);
        return NULL;
 }
 
+struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
+               enum isl_dim_type type, unsigned pos, int value)
+{
+       return (struct isl_basic_set *)
+               isl_basic_map_fix_si((struct isl_basic_map *)bset,
+                                       type, pos, value);
+}
+
 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
                unsigned input, int value)
 {
@@ -2573,7 +2872,7 @@ struct isl_map *isl_map_fix_si(struct isl_map *map,
                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);
@@ -2651,25 +2950,50 @@ struct isl_map *isl_map_reverse(struct isl_map *map)
                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);
        return NULL;
 }
 
-struct isl_map *isl_basic_map_lexmax(
+static struct isl_map *isl_basic_map_partial_lexopt(
+               struct isl_basic_map *bmap, struct isl_basic_set *dom,
+               struct isl_set **empty, int max)
+{
+       return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
+}
+
+struct isl_map *isl_basic_map_partial_lexmax(
                struct isl_basic_map *bmap, struct isl_basic_set *dom,
                struct isl_set **empty)
 {
-       return isl_pip_basic_map_lexmax(bmap, dom, empty);
+       return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
 }
 
-struct isl_map *isl_basic_map_lexmin(
+struct isl_map *isl_basic_map_partial_lexmin(
                struct isl_basic_map *bmap, struct isl_basic_set *dom,
                struct isl_set **empty)
 {
-       return isl_pip_basic_map_lexmin(bmap, dom, empty);
+       return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
+}
+
+struct isl_set *isl_basic_set_partial_lexmin(
+               struct isl_basic_set *bset, struct isl_basic_set *dom,
+               struct isl_set **empty)
+{
+       return (struct isl_set *)
+               isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
+                       dom, empty);
+}
+
+struct isl_set *isl_basic_set_partial_lexmax(
+               struct isl_basic_set *bset, struct isl_basic_set *dom,
+               struct isl_set **empty)
+{
+       return (struct isl_set *)
+               isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
+                       dom, empty);
 }
 
 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
@@ -2688,52 +3012,324 @@ struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
        dom = isl_basic_set_universe(param_dim);
        if (!dom)
                goto error;
-       min = isl_basic_map_lexmin(bmap, dom, NULL);
+       min = isl_basic_map_partial_lexmin(bmap, dom, NULL);
        return isl_map_range(min);
 error:
        isl_basic_map_free(bmap);
        return NULL;
 }
 
-struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
+static struct isl_map *isl_map_reset_dim(struct isl_map *map,
+       struct isl_dim *dim)
 {
        int i;
-       unsigned off;
 
-       if (!bmap)
-               return NULL;
-       off = isl_dim_total(bmap->dim);
-       for (i = 0; i < bmap->n_div; ++i) {
-               if (isl_int_is_zero(bmap->div[i][0]))
-                       return isl_pip_basic_map_compute_divs(bmap);
-               isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
-                               goto error);
+       if (!map || !dim)
+               goto error;
+
+       for (i = 0; i < map->n; ++i) {
+               isl_dim_free(map->p[i]->dim);
+               map->p[i]->dim = isl_dim_copy(dim);
        }
-       return isl_map_from_basic_map(bmap);
+       isl_dim_free(map->dim);
+       map->dim = dim;
+
+       return map;
 error:
-       isl_basic_map_free(bmap);
+       isl_map_free(map);
+       isl_dim_free(dim);
        return NULL;
 }
 
-struct isl_map *isl_map_compute_divs(struct isl_map *map)
+static struct isl_set *isl_set_reset_dim(struct isl_set *set,
+       struct isl_dim *dim)
 {
-       int i;
-       struct isl_map *res;
+       return (struct isl_set *) isl_map_reset_dim((struct isl_map *)set, dim);
+}
 
-       if (!map)
-               return NULL;
-       if (map->n == 0)
-               return map;
-       res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
-       for (i = 1 ; i < map->n; ++i) {
-               struct isl_map *r2;
-               r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
-               if (F_ISSET(map, ISL_MAP_DISJOINT))
-                       res = isl_map_union_disjoint(res, r2);
-               else
-                       res = isl_map_union(res, r2);
-       }
-       isl_map_free(map);
+/* Apply a preimage specified by "mat" on the parameters of "bset".
+ * bset is assumed to have only parameters and divs.
+ */
+static struct isl_basic_set *basic_set_parameter_preimage(
+       struct isl_basic_set *bset, struct isl_mat *mat)
+{
+       unsigned nparam;
+
+       if (!bset || !mat)
+               goto error;
+
+       bset->dim = isl_dim_cow(bset->dim);
+       if (!bset->dim)
+               goto error;
+
+       nparam = isl_basic_set_dim(bset, isl_dim_param);
+
+       isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
+
+       bset->dim->nparam = 0;
+       bset->dim->n_out = nparam;
+       bset = isl_basic_set_preimage(bset, mat);
+       if (bset) {
+               bset->dim->nparam = bset->dim->n_out;
+               bset->dim->n_out = 0;
+       }
+       return bset;
+error:
+       isl_mat_free(mat);
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+/* Apply a preimage specified by "mat" on the parameters of "set".
+ * set is assumed to have only parameters and divs.
+ */
+static struct isl_set *set_parameter_preimage(
+       struct isl_set *set, struct isl_mat *mat)
+{
+       struct isl_dim *dim = NULL;
+       unsigned nparam;
+
+       if (!set || !mat)
+               goto error;
+
+       dim = isl_dim_copy(set->dim);
+       dim = isl_dim_cow(dim);
+       if (!dim)
+               goto error;
+
+       nparam = isl_set_dim(set, isl_dim_param);
+
+       isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
+
+       dim->nparam = 0;
+       dim->n_out = nparam;
+       isl_set_reset_dim(set, dim);
+       set = isl_set_preimage(set, mat);
+       if (!set)
+               goto error2;
+       dim = isl_dim_copy(set->dim);
+       dim = isl_dim_cow(dim);
+       if (!dim)
+               goto error2;
+       dim->nparam = dim->n_out;
+       dim->n_out = 0;
+       isl_set_reset_dim(set, dim);
+       return set;
+error:
+       isl_dim_free(dim);
+       isl_mat_free(mat);
+error2:
+       isl_set_free(set);
+       return NULL;
+}
+
+/* Intersect the basic set "bset" with the affine space specified by the
+ * equalities in "eq".
+ */
+static struct isl_basic_set *basic_set_append_equalities(
+       struct isl_basic_set *bset, struct isl_mat *eq)
+{
+       int i, k;
+       unsigned len;
+
+       if (!bset || !eq)
+               goto error;
+
+       bset = isl_basic_set_extend_dim(bset, isl_dim_copy(bset->dim), 0,
+                                       eq->n_row, 0);
+       if (!bset)
+               goto error;
+
+       len = 1 + isl_dim_total(bset->dim) + bset->extra;
+       for (i = 0; i < eq->n_row; ++i) {
+               k = isl_basic_set_alloc_equality(bset);
+               if (k < 0)
+                       goto error;
+               isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
+               isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
+       }
+       isl_mat_free(eq);
+
+       return bset;
+error:
+       isl_mat_free(eq);
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+/* Intersect the set "set" with the affine space specified by the
+ * equalities in "eq".
+ */
+static struct isl_set *set_append_equalities(struct isl_set *set,
+       struct isl_mat *eq)
+{
+       int i;
+
+       if (!set || !eq)
+               goto error;
+
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = basic_set_append_equalities(set->p[i],
+                                       isl_mat_copy(eq));
+               if (!set->p[i])
+                       goto error;
+       }
+       isl_mat_free(eq);
+       return set;
+error:
+       isl_mat_free(eq);
+       isl_set_free(set);
+       return NULL;
+}
+
+/* Project the given basic set onto its parameter domain, possibly introducing
+ * new, explicit, existential variables in the constraints.
+ * The input has parameters and (possibly implicit) existential variables.
+ * The output has the same parameters, but only
+ * explicit existentially quantified variables.
+ *
+ * The actual projection is performed by pip, but pip doesn't seem
+ * to like equalities very much, so we first remove the equalities
+ * among the parameters by performing a variable compression on
+ * the parameters.  Afterward, an inverse transformation is performed
+ * and the equalities among the parameters are inserted back in.
+ */
+static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
+{
+       int i, j;
+       struct isl_mat *eq;
+       struct isl_mat *T, *T2;
+       struct isl_set *set;
+       unsigned nparam, n_div;
+
+       bset = isl_basic_set_cow(bset);
+       if (!bset)
+               return NULL;
+
+       if (bset->n_eq == 0)
+               return isl_basic_set_lexmin(bset);
+
+       isl_basic_set_gauss(bset, NULL);
+
+       nparam = isl_basic_set_dim(bset, isl_dim_param);
+       n_div = isl_basic_set_dim(bset, isl_dim_div);
+
+       for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
+               if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
+                       ++i;
+       }
+       if (i == bset->n_eq)
+               return isl_basic_set_lexmin(bset);
+
+       eq = isl_mat_sub_alloc(bset->ctx, bset->eq, i, bset->n_eq - i,
+               0, 1 + nparam);
+       eq = isl_mat_cow(eq);
+       T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
+       bset = basic_set_parameter_preimage(bset, T);
+
+       set = isl_basic_set_lexmin(bset);
+       set = set_parameter_preimage(set, T2);
+       set = set_append_equalities(set, eq);
+       return set;
+}
+
+/* Compute an explicit representation for all the existentially
+ * quantified variables.
+ * The input and output dimensions are first turned into parameters.
+ * compute_divs then returns a map with the same parameters and
+ * no input or output dimensions and the dimension specification
+ * is reset to that of the input.
+ */
+static struct isl_map *compute_divs(struct isl_basic_map *bmap)
+{
+       struct isl_basic_set *bset;
+       struct isl_set *set;
+       struct isl_map *map;
+       struct isl_dim *dim, *orig_dim = NULL;
+       unsigned         nparam;
+       unsigned         n_in;
+       unsigned         n_out;
+
+       bmap = isl_basic_map_cow(bmap);
+       if (!bmap)
+               return NULL;
+
+       nparam = isl_basic_map_dim(bmap, isl_dim_param);
+       n_in = isl_basic_map_dim(bmap, isl_dim_in);
+       n_out = isl_basic_map_dim(bmap, isl_dim_out);
+       dim = isl_dim_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
+       if (!dim)
+               goto error;
+
+       orig_dim = bmap->dim;
+       bmap->dim = dim;
+       bset = (struct isl_basic_set *)bmap;
+
+       set = parameter_compute_divs(bset);
+       map = (struct isl_map *)set;
+       map = isl_map_reset_dim(map, orig_dim);
+
+       return map;
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+/* If bmap contains any unknown divs, then compute explicit
+ * expressions for them.  However, this computation may be
+ * quite expensive, so first try to remove divs that aren't
+ * strictly needed.
+ */
+struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
+{
+       int i;
+       unsigned off;
+
+       if (!bmap)
+               return NULL;
+       off = isl_dim_total(bmap->dim);
+       for (i = 0; i < bmap->n_div; ++i) {
+               if (isl_int_is_zero(bmap->div[i][0]))
+                       break;
+               isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
+                               goto error);
+       }
+       if (i == bmap->n_div)
+               return isl_map_from_basic_map(bmap);
+       bmap = isl_basic_map_drop_redundant_divs(bmap);
+       if (!bmap)
+               goto error;
+       for (i = 0; i < bmap->n_div; ++i)
+               if (isl_int_is_zero(bmap->div[i][0]))
+                       break;
+       if (i == bmap->n_div)
+               return isl_map_from_basic_map(bmap);
+       struct isl_map *map = compute_divs(bmap);
+       return map;
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+struct isl_map *isl_map_compute_divs(struct isl_map *map)
+{
+       int i;
+       struct isl_map *res;
+
+       if (!map)
+               return NULL;
+       if (map->n == 0)
+               return map;
+       res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
+       for (i = 1 ; i < map->n; ++i) {
+               struct isl_map *r2;
+               r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
+               if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
+                       res = isl_map_union_disjoint(res, r2);
+               else
+                       res = isl_map_union(res, r2);
+       }
+       isl_map_free(map);
 
        return res;
 }
@@ -2771,8 +3367,8 @@ struct isl_set *isl_map_domain(struct isl_map *map)
                if (!set->p[i])
                        goto error;
        }
-       F_CLR(set, ISL_MAP_DISJOINT);
-       F_CLR(set, ISL_SET_NORMALIZED);
+       ISL_F_CLR(set, ISL_MAP_DISJOINT);
+       ISL_F_CLR(set, ISL_SET_NORMALIZED);
        return set;
 error:
        isl_map_free(map);
@@ -2800,9 +3396,9 @@ struct isl_map *isl_map_union_disjoint(
 
        isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
 
-       if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
-           F_ISSET(map2, ISL_MAP_DISJOINT))
-               FL_SET(flags, ISL_MAP_DISJOINT);
+       if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
+           ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
+               ISL_FL_SET(flags, ISL_MAP_DISJOINT);
 
        map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
                                map1->n + map2->n, flags);
@@ -2836,7 +3432,7 @@ struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
        if (!map1)
                return NULL;
        if (map1->n > 1)
-               F_CLR(map1, ISL_MAP_DISJOINT);
+               ISL_F_CLR(map1, ISL_MAP_DISJOINT);
        return map1;
 }
 
@@ -2864,9 +3460,9 @@ struct isl_map *isl_map_intersect_range(
        if (!map || !set)
                goto error;
 
-       if (F_ISSET(map, ISL_MAP_DISJOINT) &&
-           F_ISSET(set, ISL_MAP_DISJOINT))
-               FL_SET(flags, ISL_MAP_DISJOINT);
+       if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
+           ISL_F_ISSET(set, ISL_MAP_DISJOINT))
+               ISL_FL_SET(flags, ISL_MAP_DISJOINT);
 
        result = isl_map_alloc_dim(isl_dim_copy(map->dim),
                                        map->n * set->n, flags);
@@ -2942,7 +3538,7 @@ struct isl_map *isl_map_apply_range(
        isl_map_free(map1);
        isl_map_free(map2);
        if (result && result->n <= 1)
-               F_SET(result, ISL_MAP_DISJOINT);
+               ISL_F_SET(result, ISL_MAP_DISJOINT);
        return result;
 error:
        isl_map_free(map1);
@@ -2966,6 +3562,7 @@ struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
        nparam = isl_basic_map_n_param(bmap);
        isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
        bset = isl_basic_set_from_basic_map(bmap);
+       bset = isl_basic_set_cow(bset);
        bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
        bset = isl_basic_set_swap_vars(bset, 2*dim);
        for (i = 0; i < dim; ++i) {
@@ -3080,6 +3677,36 @@ struct isl_map *isl_map_identity_like(struct isl_basic_map *model)
        return map_identity(isl_dim_copy(model->dim));
 }
 
+/* Construct a basic set with all set dimensions having only non-negative
+ * values.
+ */
+struct isl_basic_set *isl_basic_set_positive_orthant(struct isl_dim *dims)
+{
+       int i;
+       unsigned nparam;
+       unsigned dim;
+       struct isl_basic_set *bset;
+
+       if (!dims)
+               return NULL;
+       nparam = dims->nparam;
+       dim = dims->n_out;
+       bset = isl_basic_set_alloc_dim(dims, 0, 0, dim);
+       if (!bset)
+               return NULL;
+       for (i = 0; i < dim; ++i) {
+               int k = isl_basic_set_alloc_inequality(bset);
+               if (k < 0)
+                       goto error;
+               isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
+               isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
+       }
+       return bset;
+error:
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
 {
        return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
@@ -3150,6 +3777,11 @@ int isl_map_is_empty(struct isl_map *map)
        return 1;
 }
 
+int isl_map_fast_is_empty(struct isl_map *map)
+{
+       return map->n == 0;
+}
+
 int isl_set_is_empty(struct isl_set *set)
 {
        return isl_map_is_empty((struct isl_map *)set);
@@ -3209,44 +3841,18 @@ int isl_basic_map_is_strict_subset(
        return !is_subset;
 }
 
-static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
+int isl_basic_map_is_universe(struct isl_basic_map *bmap)
 {
-       int i;
-       unsigned total;
-       isl_int s;
-
-       total = 1 + isl_basic_map_total_dim(bmap);
-       if (total != vec->size)
+       if (!bmap)
                return -1;
-
-       isl_int_init(s);
-
-       for (i = 0; i < bmap->n_eq; ++i) {
-               isl_seq_inner_product(vec->block.data, bmap->eq[i], total, &s);
-               if (!isl_int_is_zero(s)) {
-                       isl_int_clear(s);
-                       return 0;
-               }
-       }
-
-       for (i = 0; i < bmap->n_ineq; ++i) {
-               isl_seq_inner_product(vec->block.data, bmap->ineq[i], total, &s);
-               if (isl_int_is_neg(s)) {
-                       isl_int_clear(s);
-                       return 0;
-               }
-       }
-
-       isl_int_clear(s);
-
-       return 1;
+       return bmap->n_eq == 0 && bmap->n_ineq == 0;
 }
 
-int isl_basic_map_is_universe(struct isl_basic_map *bmap)
+int isl_basic_set_is_universe(struct isl_basic_set *bset)
 {
-       if (!bmap)
+       if (!bset)
                return -1;
-       return bmap->n_eq == 0 && bmap->n_ineq == 0;
+       return bset->n_eq == 0 && bset->n_ineq == 0;
 }
 
 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
@@ -3259,13 +3865,13 @@ int isl_basic_map_is_empty(struct isl_basic_map *bmap)
        if (!bmap)
                return -1;
 
-       if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+       if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
                return 1;
 
-       if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
+       if (ISL_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);
+               empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
                isl_basic_map_free(copy);
                return empty;
        }
@@ -3278,6 +3884,8 @@ int isl_basic_map_is_empty(struct isl_basic_map *bmap)
                if (contains)
                        return 0;
        }
+       isl_vec_free(bmap->sample);
+       bmap->sample = NULL;
        bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
        if (!bset)
                return -1;
@@ -3285,13 +3893,28 @@ int isl_basic_map_is_empty(struct isl_basic_map *bmap)
        if (!sample)
                return -1;
        empty = sample->size == 0;
-       if (bmap->sample)
-               isl_vec_free(bmap->ctx, bmap->sample);
+       isl_vec_free(bmap->sample);
        bmap->sample = sample;
+       if (empty)
+               ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
 
        return empty;
 }
 
+int isl_basic_map_fast_is_empty(struct isl_basic_map *bmap)
+{
+       if (!bmap)
+               return -1;
+       return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
+}
+
+int isl_basic_set_fast_is_empty(struct isl_basic_set *bset)
+{
+       if (!bset)
+               return -1;
+       return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
+}
+
 int isl_basic_set_is_empty(struct isl_basic_set *bset)
 {
        return isl_basic_map_is_empty((struct isl_basic_map *)bset);
@@ -3338,7 +3961,7 @@ static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
                                                            bmap->n_div-i);
                if (pos == -1)
                        continue;
-               swap_div(bmap, i, pos);
+               isl_basic_map_swap_div(bmap, i, i + pos);
                --i;
        }
        return bmap;
@@ -3382,6 +4005,7 @@ struct isl_basic_map *isl_basic_map_align_divs(
                isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
 
        src = order_divs(src);
+       dst = isl_basic_map_cow(dst);
        dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
                        src->n_div, 0, 2 * src->n_div);
        if (!dst)
@@ -3398,7 +4022,7 @@ struct isl_basic_map *isl_basic_map_align_divs(
                                goto error;
                }
                if (j != i)
-                       swap_div(dst, i, j);
+                       isl_basic_map_swap_div(dst, i, j);
        }
        return dst;
 error:
@@ -3427,10 +4051,15 @@ 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);
+       ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 }
 
+struct isl_set *isl_set_align_divs(struct isl_set *set)
+{
+       return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
+}
+
 static struct isl_map *add_cut_constraint(struct isl_map *dst,
                struct isl_basic_map *src, isl_int *c,
                unsigned len, int oppose)
@@ -3484,8 +4113,8 @@ static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
        if (!map)
                goto error;
 
-       if (F_ISSET(map, ISL_MAP_DISJOINT))
-               FL_SET(flags, ISL_MAP_DISJOINT);
+       if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
+               ISL_FL_SET(flags, ISL_MAP_DISJOINT);
 
        max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
        rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
@@ -3615,11 +4244,11 @@ struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
                return NULL;
 
        for (i = map->n-1; i >= 0; --i) {
-               if (!F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
+               if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
                        continue;
                isl_basic_map_free(map->p[i]);
                if (i != map->n-1) {
-                       F_CLR(map, ISL_MAP_NORMALIZED);
+                       ISL_F_CLR(map, ISL_MAP_NORMALIZED);
                        map->p[i] = map->p[map->n-1];
                }
                map->n--;
@@ -3634,45 +4263,57 @@ struct isl_set *isl_set_remove_empty_parts(struct isl_set *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_map *isl_map_copy_basic_map(struct isl_map *map)
 {
-       struct isl_basic_set *bset;
-       if (!set || set->n == 0)
+       struct isl_basic_map *bmap;
+       if (!map || map->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);
+       bmap = map->p[map->n-1];
+       isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
+       return isl_basic_map_copy(bmap);
 }
 
-struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
-                                               struct isl_basic_set *bset)
+struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
+{
+       (struct isl_basic_set *)isl_map_copy_basic_map((struct isl_map *)set);
+}
+
+struct isl_map *isl_map_drop_basic_map(struct isl_map *map,
+                                               struct isl_basic_map *bmap)
 {
        int i;
 
-       if (!set || !bset)
+       if (!map || !bmap)
                goto error;
-       for (i = set->n-1; i >= 0; --i) {
-               if (set->p[i] != bset)
+       for (i = map->n-1; i >= 0; --i) {
+               if (map->p[i] != bmap)
                        continue;
-               set = isl_set_cow(set);
-               if (!set)
+               map = isl_map_cow(map);
+               if (!map)
                        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];
+               isl_basic_map_free(map->p[i]);
+               if (i != map->n-1) {
+                       ISL_F_CLR(map, ISL_SET_NORMALIZED);
+                       map->p[i] = map->p[map->n-1];
                }
-               set->n--;
-               return set;
+               map->n--;
+               return map;
        }
-       isl_basic_set_free(bset);
-       return set;
+       isl_basic_map_free(bmap);
+       return map;
 error:
-       isl_set_free(set);
-       isl_basic_set_free(bset);
+       isl_map_free(map);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
+struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
+                                               struct isl_basic_set *bset)
+{
+       (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
+                                               (struct isl_basic_map *)bset);
+}
+
 /* 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
@@ -3711,6 +4352,7 @@ int isl_basic_set_compare_at(struct isl_basic_set *bset1,
        bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
        if (!bmap1 || !bmap2)
                goto error;
+       bmap1 = isl_basic_map_cow(bmap1);
        bmap1 = isl_basic_map_extend(bmap1, nparam,
                        pos, (dim1 - pos) + (dim2 - pos),
                        bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
@@ -3719,10 +4361,10 @@ int isl_basic_set_compare_at(struct isl_basic_set *bset1,
                goto error;
        total = isl_basic_map_total_dim(bmap1);
        ctx = bmap1->ctx;
-       obj = isl_vec_alloc(ctx, total);
-       isl_seq_clr(obj->block.data, total);
-       isl_int_set_si(obj->block.data[nparam+pos], 1);
-       isl_int_set_si(obj->block.data[nparam+pos+(dim1-pos)], -1);
+       obj = isl_vec_alloc(ctx, 1 + total);
+       isl_seq_clr(obj->block.data, 1 + total);
+       isl_int_set_si(obj->block.data[1+nparam+pos], 1);
+       isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
        if (!obj)
                goto error;
        isl_int_init(num);
@@ -3740,7 +4382,7 @@ int isl_basic_set_compare_at(struct isl_basic_set *bset1,
        isl_int_clear(num);
        isl_int_clear(den);
        isl_basic_map_free(bmap1);
-       isl_vec_free(ctx, obj);
+       isl_vec_free(obj);
        return cmp;
 error:
        isl_basic_map_free(bmap1);
@@ -3806,12 +4448,38 @@ static int isl_map_fast_has_fixed_var(struct isl_map *map,
        return fixed;
 }
 
+static int isl_basic_set_fast_has_fixed_var(struct isl_basic_set *bset,
+       unsigned pos, isl_int *val)
+{
+       return isl_basic_map_fast_has_fixed_var((struct isl_basic_map *)bset,
+                                               pos, val);
+}
+
 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);
 }
 
+int isl_basic_map_fast_is_fixed(struct isl_basic_map *bmap,
+       enum isl_dim_type type, unsigned pos, isl_int *val)
+{
+       if (pos >= isl_basic_map_dim(bmap, type))
+               return -1;
+       return isl_basic_map_fast_has_fixed_var(bmap,
+               isl_basic_map_offset(bmap, type) - 1 + 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_basic_set_fast_dim_is_fixed(struct isl_basic_set *bset, unsigned dim,
+       isl_int *val)
+{
+       return isl_basic_set_fast_has_fixed_var(bset,
+                                       isl_basic_set_n_param(bset) + dim, val);
+}
+
 /* Check if dimension dim has fixed value and if so and if val is not NULL,
  * then return this fixed value in *val.
  */
@@ -3949,11 +4617,11 @@ 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))
+       if (ISL_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);
+       ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
        return bmap;
 }
 
@@ -3977,12 +4645,12 @@ static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
                return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
        if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
                return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
-       if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
-           F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
+       if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
+           ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
                return 0;
-       if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
+       if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
                return 1;
-       if (F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
+       if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
                return -1;
        if (bmap1->n_eq != bmap2->n_eq)
                return bmap1->n_eq - bmap2->n_eq;
@@ -4034,7 +4702,7 @@ struct isl_map *isl_map_normalize(struct isl_map *map)
 
        if (!map)
                return NULL;
-       if (F_ISSET(map, ISL_MAP_NORMALIZED))
+       if (ISL_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]));
@@ -4044,7 +4712,7 @@ struct isl_map *isl_map_normalize(struct isl_map *map)
                map->p[i] = bmap;
        }
        qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
-       F_SET(map, ISL_MAP_NORMALIZED);
+       ISL_F_SET(map, ISL_MAP_NORMALIZED);
        map = isl_map_remove_empty_parts(map);
        if (!map)
                return NULL;
@@ -4186,6 +4854,107 @@ error:
        return NULL;
 }
 
+struct isl_basic_map *isl_basic_map_product(
+               struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+{
+       struct isl_dim *dim_result = NULL;
+       struct isl_basic_map *bmap;
+       unsigned in1, in2, out1, out2, nparam, total, pos;
+       struct isl_dim_map *dim_map1, *dim_map2;
+
+       if (!bmap1 || !bmap2)
+               goto error;
+
+       isl_assert(map1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
+                                    bmap2->dim, isl_dim_param), goto error);
+       dim_result = isl_dim_product(isl_dim_copy(bmap1->dim),
+                                                  isl_dim_copy(bmap2->dim));
+
+       in1 = isl_basic_map_n_in(bmap1);
+       in2 = isl_basic_map_n_in(bmap2);
+       out1 = isl_basic_map_n_out(bmap1);
+       out2 = isl_basic_map_n_out(bmap2);
+       nparam = isl_basic_map_n_param(bmap1);
+
+       total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
+       dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
+       dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
+       isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
+       isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
+       isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
+       isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
+       isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
+       isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
+       isl_dim_map_div(dim_map1, bmap1, pos += out2);
+       isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
+
+       bmap = isl_basic_map_alloc_dim(dim_result,
+                       bmap1->n_div + bmap2->n_div,
+                       bmap1->n_eq + bmap2->n_eq,
+                       bmap1->n_ineq + bmap2->n_ineq);
+       bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
+       bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
+       bmap = isl_basic_map_simplify(bmap);
+       return isl_basic_map_finalize(bmap);
+error:
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
+       return NULL;
+}
+
+/* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
+ */
+struct isl_map *isl_map_product(struct isl_map *map1, struct isl_map *map2)
+{
+       unsigned flags = 0;
+       struct isl_map *result;
+       int i, j;
+
+       if (!map1 || !map2)
+               goto error;
+
+       isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
+                                        map2->dim, isl_dim_param), goto error);
+
+       if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
+           ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
+               ISL_FL_SET(flags, ISL_MAP_DISJOINT);
+
+       result = isl_map_alloc_dim(isl_dim_product(isl_dim_copy(map1->dim),
+                                                  isl_dim_copy(map2->dim)),
+                               map1->n * map2->n, flags);
+       if (!result)
+               goto error;
+       for (i = 0; i < map1->n; ++i)
+               for (j = 0; j < map2->n; ++j) {
+                       struct isl_basic_map *part;
+                       part = isl_basic_map_product(
+                                   isl_basic_map_copy(map1->p[i]),
+                                   isl_basic_map_copy(map2->p[j]));
+                       if (isl_basic_map_is_empty(part))
+                               isl_basic_map_free(part);
+                       else
+                               result = isl_map_add(result, part);
+                       if (!result)
+                               goto error;
+               }
+       isl_map_free(map1);
+       isl_map_free(map2);
+       return result;
+error:
+       isl_map_free(map1);
+       isl_map_free(map2);
+       return NULL;
+}
+
+/* Given two set A and B, construct its Cartesian product A x B.
+ */
+struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
+{
+       return (struct isl_set *)isl_map_product((struct isl_map *)set1,
+                                                (struct isl_map *)set2);
+}
+
 uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
 {
        int i;