isl_basic_set_sample: break early if sample found in basic_set_range
[platform/upstream/isl.git] / isl_map.c
index d9d350a..f7efcb7 100644 (file)
--- a/isl_map.c
+++ b/isl_map.c
@@ -2,7 +2,7 @@
 #include <strings.h>
 #include "isl_ctx.h"
 #include "isl_blk.h"
-#include "isl_equalities.h"
+#include "isl_dim.h"
 #include "isl_list.h"
 #include "isl_lp.h"
 #include "isl_seq.h"
 #include "isl_sample.h"
 #include "isl_vec.h"
 
+/* Maps dst positions to src positions */
+struct isl_dim_map {
+       unsigned len;
+       int pos[1];
+};
+
+static struct isl_dim_map *isl_dim_map_alloc(struct isl_ctx *ctx, unsigned len)
+{
+       int i;
+       struct isl_dim_map *dim_map;
+       dim_map = isl_alloc(ctx, struct isl_dim_map,
+                               sizeof(struct isl_dim_map) + len * sizeof(int));
+       if (!dim_map)
+               return NULL;
+       dim_map->len = 1 + len;
+       dim_map->pos[0] = 0;
+       for (i = 0; i < len; ++i)
+               dim_map->pos[1 + i] = -1;
+       return dim_map;
+}
+
+static unsigned n(struct isl_dim *dim, enum isl_dim_type type)
+{
+       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;
+       }
+}
+
+static unsigned pos(struct isl_dim *dim, enum isl_dim_type type)
+{
+       switch (type) {
+       case isl_dim_param:     return 1;
+       case isl_dim_in:        return 1 + dim->nparam;
+       case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
+       }
+}
+
+static void isl_dim_map_dim(struct isl_dim_map *dim_map, struct isl_dim *dim,
+               enum isl_dim_type type, unsigned dst_pos)
+{
+       int i;
+       unsigned src_pos;
+
+       if (!dim_map || !dim)
+               return;
+       
+       src_pos = pos(dim, type);
+       for (i = 0; i < n(dim, type); ++i)
+               dim_map->pos[1 + dst_pos + i] = src_pos + i;
+}
+
+static void isl_dim_map_div(struct isl_dim_map *dim_map,
+               struct isl_basic_map *bmap, unsigned dst_pos)
+{
+       int i;
+       unsigned src_pos;
+
+       if (!dim_map || !bmap)
+               return;
+       
+       src_pos = 1 + isl_dim_total(bmap->dim);
+       for (i = 0; i < bmap->n_div; ++i)
+               dim_map->pos[1 + dst_pos + i] = src_pos + i;
+}
+
+static void isl_dim_map_dump(struct isl_dim_map *dim_map)
+{
+       int i;
+
+       for (i = 0; i < dim_map->len; ++i)
+               fprintf(stderr, "%d -> %d; ", i, dim_map->pos[i]);
+       fprintf(stderr, "\n");
+}
+
+unsigned isl_basic_map_dim(const struct isl_basic_map *bmap,
+                               enum isl_dim_type type)
+{
+       struct isl_dim *dim = bmap->dim;
+       switch (type) {
+       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);
+       }
+}
+
+unsigned isl_map_dim(const struct isl_map *map, enum isl_dim_type type)
+{
+       return n(map->dim, type);
+}
+
+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;
+       switch (type) {
+       case isl_dim_param:     return 1;
+       case isl_dim_in:        return 1 + dim->nparam;
+       case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
+       case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
+       }
+}
+
+static unsigned map_offset(struct isl_map *map, enum isl_dim_type type)
+{
+       return pos(map->dim, type);
+}
+
+unsigned isl_basic_set_dim(const struct isl_basic_set *bset,
+                               enum isl_dim_type type)
+{
+       return isl_basic_map_dim((const struct isl_basic_map*)bset, type);
+}
+
+unsigned isl_basic_set_n_dim(const struct isl_basic_set *bset)
+{
+       return bset->dim->n_out;
+}
+
+unsigned isl_basic_set_n_param(const struct isl_basic_set *bset)
+{
+       return bset->dim->nparam;
+}
+
+unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
+{
+       return isl_dim_total(bset->dim) + bset->n_div;
+}
+
+unsigned isl_set_n_dim(const struct isl_set *set)
+{
+       return set->dim->n_out;
+}
+
+unsigned isl_set_n_param(const struct isl_set *set)
+{
+       return set->dim->nparam;
+}
+
+unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
+{
+       return bmap->dim->n_in;
+}
+
+unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
+{
+       return bmap->dim->n_out;
+}
+
+unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
+{
+       return bmap->dim->nparam;
+}
+
+unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
+{
+       return bmap->n_div;
+}
+
+unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
+{
+       return isl_dim_total(bmap->dim) + bmap->n_div;
+}
+
+unsigned isl_map_n_in(const struct isl_map *map)
+{
+       return map->dim->n_in;
+}
+
+unsigned isl_map_n_out(const struct isl_map *map)
+{
+       return map->dim->n_out;
+}
+
+unsigned isl_map_n_param(const struct isl_map *map)
+{
+       return map->dim->nparam;
+}
+
+int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
+{
+       return map->dim->n_in == set->dim->n_out &&
+              map->dim->nparam == set->dim->nparam;
+}
+
+int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
+               struct isl_basic_set *bset)
+{
+       return bmap->dim->n_in == bset->dim->n_out &&
+              bmap->dim->nparam == bset->dim->nparam;
+}
+
+int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
+               struct isl_basic_set *bset)
+{
+       return bmap->dim->n_out == bset->dim->n_out &&
+              bmap->dim->nparam == bset->dim->nparam;
+}
+
+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_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 nparam, unsigned n_in, unsigned n_out, unsigned extra,
+               struct isl_basic_map *bmap, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
 {
        int i;
-       size_t row_size = 1 + nparam + n_in + n_out + extra;
+       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;
@@ -40,7 +260,7 @@ 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;
@@ -49,15 +269,15 @@ 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);
@@ -67,10 +287,7 @@ 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->nparam = nparam;
-       bmap->n_in = n_in;
-       bmap->n_out = n_out;
+       bmap->eq = bmap->ineq + n_ineq;
        bmap->extra = extra;
        bmap->n_eq = 0;
        bmap->n_ineq = 0;
@@ -78,6 +295,9 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
        bmap->sample = NULL;
 
        return bmap;
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
 }
 
 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
@@ -89,25 +309,55 @@ struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
        return (struct isl_basic_set *)bmap;
 }
 
+struct isl_basic_set *isl_basic_set_alloc_dim(struct isl_dim *dim,
+               unsigned extra, unsigned n_eq, unsigned n_ineq)
+{
+       struct isl_basic_map *bmap;
+       if (!dim)
+               return NULL;
+       isl_assert(dim->ctx, dim->n_in == 0, return NULL);
+       bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
+       return (struct isl_basic_set *)bmap;
+}
+
+struct isl_basic_map *isl_basic_map_alloc_dim(struct isl_dim *dim,
+               unsigned extra, unsigned n_eq, unsigned n_ineq)
+{
+       struct isl_basic_map *bmap;
+
+       if (!dim)
+               return NULL;
+       bmap = isl_alloc_type(dim->ctx, struct isl_basic_map);
+       if (!bmap)
+               goto error;
+       bmap->dim = dim;
+
+       return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
+error:
+       isl_dim_free(dim);
+       return NULL;
+}
+
 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
                unsigned nparam, unsigned in, unsigned out, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
 {
        struct isl_basic_map *bmap;
+       struct isl_dim *dim;
 
-       bmap = isl_alloc_type(ctx, struct isl_basic_map);
-       if (!bmap)
+       dim = isl_dim_alloc(ctx, nparam, in, out);
+       if (!dim)
                return NULL;
 
-       return basic_map_init(ctx, bmap,
-                              nparam, in, out, extra, n_eq, n_ineq);
+       bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
+       return bmap;
 }
 
 static void dup_constraints(
                struct isl_basic_map *dst, struct isl_basic_map *src)
 {
        int i;
-       unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
+       unsigned total = isl_basic_map_total_dim(src);
 
        for (i = 0; i < src->n_eq; ++i) {
                int j = isl_basic_map_alloc_equality(dst);
@@ -123,7 +373,7 @@ 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)
@@ -132,14 +382,13 @@ struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
 
        if (!bmap)
                return NULL;
-       dup = isl_basic_map_alloc(bmap->ctx, bmap->nparam,
-                       bmap->n_in, bmap->n_out,
+       dup = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
                        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;
 }
 
@@ -156,7 +405,7 @@ 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;
        }
@@ -177,7 +426,7 @@ 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;
        }
@@ -204,9 +453,10 @@ 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);
 }
 
@@ -215,25 +465,41 @@ 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++;
+               bmap->eq--;
+               return 0;
        }
+       isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
+                     bmap->extra - bmap->n_div);
        return bmap->n_eq++;
 }
 
@@ -251,6 +517,11 @@ 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;
@@ -278,13 +549,21 @@ 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);
+       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)
@@ -293,11 +572,14 @@ 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);
        return bmap->n_ineq++;
 }
 
@@ -331,7 +613,7 @@ 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;
@@ -347,9 +629,18 @@ int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
        if (!bmap)
                return -1;
        isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
+       isl_seq_clr(bmap->div[bmap->n_div] +
+                     1 + 1 + isl_basic_map_total_dim(bmap),
+                     bmap->extra - bmap->n_div);
+       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)
@@ -368,33 +659,39 @@ static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
                            struct isl_basic_map *src_map, isl_int *src,
                            unsigned in_off, unsigned out_off, unsigned div_off)
 {
+       unsigned src_nparam = isl_basic_map_n_param(src_map);
+       unsigned dst_nparam = isl_basic_map_n_param(dst_map);
+       unsigned src_in = isl_basic_map_n_in(src_map);
+       unsigned dst_in = isl_basic_map_n_in(dst_map);
+       unsigned src_out = isl_basic_map_n_out(src_map);
+       unsigned dst_out = isl_basic_map_n_out(dst_map);
        isl_int_set(dst[0], src[0]);
-       isl_seq_cpy(dst+1, src+1, isl_min(dst_map->nparam, src_map->nparam));
-       if (dst_map->nparam > src_map->nparam)
-               isl_seq_clr(dst+1+src_map->nparam,
-                               dst_map->nparam - src_map->nparam);
-       isl_seq_clr(dst+1+dst_map->nparam, in_off);
-       isl_seq_cpy(dst+1+dst_map->nparam+in_off,
-                   src+1+src_map->nparam,
-                   isl_min(dst_map->n_in-in_off, src_map->n_in));
-       if (dst_map->n_in-in_off > src_map->n_in)
-               isl_seq_clr(dst+1+dst_map->nparam+in_off+src_map->n_in,
-                               dst_map->n_in - in_off - src_map->n_in);
-       isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in, out_off);
-       isl_seq_cpy(dst+1+dst_map->nparam+dst_map->n_in+out_off,
-                   src+1+src_map->nparam+src_map->n_in,
-                   isl_min(dst_map->n_out-out_off, src_map->n_out));
-       if (dst_map->n_out-out_off > src_map->n_out)
-               isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+out_off+src_map->n_out,
-                               dst_map->n_out - out_off - src_map->n_out);
-       isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out, div_off);
-       isl_seq_cpy(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out+div_off,
-                   src+1+src_map->nparam+src_map->n_in+src_map->n_out,
-                   isl_min(dst_map->extra-div_off, src_map->extra));
-       if (dst_map->extra-div_off > src_map->extra)
-               isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out+
-                               div_off+src_map->extra,
-                               dst_map->extra - div_off - src_map->extra);
+       isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
+       if (dst_nparam > src_nparam)
+               isl_seq_clr(dst+1+src_nparam,
+                               dst_nparam - src_nparam);
+       isl_seq_clr(dst+1+dst_nparam, in_off);
+       isl_seq_cpy(dst+1+dst_nparam+in_off,
+                   src+1+src_nparam,
+                   isl_min(dst_in-in_off, src_in));
+       if (dst_in-in_off > src_in)
+               isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
+                               dst_in - in_off - src_in);
+       isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
+       isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
+                   src+1+src_nparam+src_in,
+                   isl_min(dst_out-out_off, src_out));
+       if (dst_out-out_off > src_out)
+               isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
+                               dst_out - out_off - src_out);
+       isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
+       isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
+                   src+1+src_nparam+src_in+src_out,
+                   isl_min(dst_map->extra-div_off, src_map->n_div));
+       if (dst_map->n_div-div_off > src_map->n_div)
+               isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
+                               div_off+src_map->n_div,
+                               dst_map->n_div - div_off - src_map->n_div);
 }
 
 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
@@ -450,7 +747,67 @@ error:
        return NULL;
 }
 
-static struct isl_basic_set *set_add_constraints(struct isl_basic_set *bset1,
+static void copy_constraint_dim_map(isl_int *dst, isl_int *src,
+                                       struct isl_dim_map *dim_map)
+{
+       int i;
+
+       for (i = 0; i < dim_map->len; ++i) {
+               if (dim_map->pos[i] < 0)
+                       isl_int_set_si(dst[i], 0);
+               else
+                       isl_int_set(dst[i], src[dim_map->pos[i]]);
+       }
+}
+
+static void copy_div_dim_map(isl_int *dst, isl_int *src,
+                                       struct isl_dim_map *dim_map)
+{
+       isl_int_set(dst[0], src[0]);
+       copy_constraint_dim_map(dst+1, src+1, dim_map);
+}
+
+static struct isl_basic_map *add_constraints_dim_map(struct isl_basic_map *dst,
+               struct isl_basic_map *src, struct isl_dim_map *dim_map)
+{
+       int i;
+
+       if (!src || !dst || !dim_map)
+               goto error;
+
+       for (i = 0; i < src->n_eq; ++i) {
+               int i1 = isl_basic_map_alloc_equality(dst);
+               if (i1 < 0)
+                       goto error;
+               copy_constraint_dim_map(dst->eq[i1], src->eq[i], dim_map);
+       }
+
+       for (i = 0; i < src->n_ineq; ++i) {
+               int i1 = isl_basic_map_alloc_inequality(dst);
+               if (i1 < 0)
+                       goto error;
+               copy_constraint_dim_map(dst->ineq[i1], src->ineq[i], dim_map);
+       }
+
+       for (i = 0; i < src->n_div; ++i) {
+               int i1 = isl_basic_map_alloc_div(dst);
+               if (i1 < 0)
+                       goto error;
+               copy_div_dim_map(dst->div[i1], src->div[i], dim_map);
+       }
+
+       free(dim_map);
+       isl_basic_map_free(src);
+
+       return dst;
+error:
+       free(dim_map);
+       isl_basic_map_free(src);
+       isl_basic_map_free(dst);
+       return NULL;
+}
+
+struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
                struct isl_basic_set *bset2, unsigned pos)
 {
        return (struct isl_basic_set *)
@@ -458,36 +815,38 @@ static struct isl_basic_set *set_add_constraints(struct isl_basic_set *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,
+struct isl_basic_map *isl_basic_map_extend_dim(struct isl_basic_map *base,
+               struct isl_dim *dim, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
 {
        struct isl_basic_map *ext;
        unsigned flags;
        int dims_ok;
 
-       base = isl_basic_map_cow(base);
+       if (!dim)
+               goto error;
+
        if (!base)
                goto error;
 
-       dims_ok = base && base->nparam == nparam &&
-                 base->n_in == n_in && base->n_out == n_out &&
+       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;
+       }
 
-       isl_assert(base->ctx, base->nparam <= nparam, goto error);
-       isl_assert(base->ctx, base->n_in <= n_in, goto error);
-       isl_assert(base->ctx, base->n_out <= n_out, goto error);
+       isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
+       isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
+       isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
        extra += base->extra;
        n_eq += base->n_eq;
        n_ineq += base->n_ineq;
 
-       ext = isl_basic_map_alloc(base->ctx, nparam, n_in, n_out,
-                                       extra, n_eq, n_ineq);
-       if (!base)
-               return ext;
+       ext = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
+       dim = NULL;
        if (!ext)
                goto error;
 
@@ -495,16 +854,52 @@ struct isl_basic_map *isl_basic_map_extend(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;
 
 error:
+       isl_dim_free(dim);
        isl_basic_map_free(base);
        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)
+{
+       if (!base)
+               return NULL;
+       return isl_basic_map_extend_dim(base, isl_dim_copy(base->dim),
+                                       0, n_eq, n_ineq);
+}
+
+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)
+{
+       struct isl_basic_map *bmap;
+       struct isl_dim *dim;
+
+       if (!base)
+               return NULL;
+       dim = isl_dim_alloc(base->ctx, nparam, n_in, n_out);
+       if (!dim)
+               return NULL;
+
+       bmap = isl_basic_map_extend_dim(base, dim, extra, n_eq, n_ineq);
+       return bmap;
+}
+
 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
                unsigned nparam, unsigned dim, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
@@ -514,6 +909,14 @@ struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
                                        nparam, 0, dim, extra, n_eq, n_ineq);
 }
 
+struct isl_basic_set *isl_basic_set_extend_constraints(
+               struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
+{
+       return (struct isl_basic_set *)
+               isl_basic_map_extend_constraints((struct isl_basic_map *)base,
+                                                   n_eq, n_ineq);
+}
+
 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
 {
        return (struct isl_basic_set *)
@@ -529,7 +932,7 @@ 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;
 }
 
@@ -568,38 +971,42 @@ struct isl_basic_set *isl_basic_set_swap_vars(
 {
        int i;
        struct isl_blk blk;
+       unsigned dim;
+       unsigned nparam;
 
        if (!bset)
                goto error;
 
-       isl_assert(bset->ctx, n <= bset->dim, goto error);
+       nparam = isl_basic_set_n_param(bset);
+       dim = isl_basic_set_n_dim(bset);
+       isl_assert(bset->ctx, n <= dim, goto error);
 
-       if (n == bset->dim)
+       if (n == dim)
                return bset;
 
        bset = isl_basic_set_cow(bset);
        if (!bset)
                return NULL;
 
-       blk = isl_blk_alloc(bset->ctx, bset->dim);
+       blk = isl_blk_alloc(bset->ctx, dim);
        if (isl_blk_is_error(blk))
                goto error;
 
        for (i = 0; i < bset->n_eq; ++i)
                swap_vars(blk,
-                         bset->eq[i]+1+bset->nparam, n, bset->dim - n);
+                         bset->eq[i]+1+nparam, n, dim - n);
 
        for (i = 0; i < bset->n_ineq; ++i)
                swap_vars(blk,
-                         bset->ineq[i]+1+bset->nparam, n, bset->dim - n);
+                         bset->ineq[i]+1+nparam, n, dim - n);
 
        for (i = 0; i < bset->n_div; ++i)
                swap_vars(blk,
-                         bset->div[i]+1+1+bset->nparam, n, bset->dim - n);
+                         bset->div[i]+1+1+nparam, n, dim - n);
 
        isl_blk_free(bset->ctx, blk);
 
-       F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
+       ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
        return bset;
 
 error:
@@ -621,287 +1028,45 @@ 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;
 }
 
-static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
+struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
 {
-       isl_seq_cpy(c, c + n, rem);
-       isl_seq_clr(c + rem, n);
+       int i = 0;
+       unsigned total;
+       if (!bmap)
+               goto error;
+       total = isl_basic_map_total_dim(bmap);
+       isl_basic_map_free_div(bmap, bmap->n_div);
+       isl_basic_map_free_inequality(bmap, bmap->n_ineq);
+       if (bmap->n_eq > 0)
+               isl_basic_map_free_equality(bmap, bmap->n_eq-1);
+       else {
+               isl_basic_map_alloc_equality(bmap);
+               if (i < 0)
+                       goto error;
+       }
+       isl_int_set_si(bmap->eq[i][0], 1);
+       isl_seq_clr(bmap->eq[i]+1, total);
+       ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
+       return isl_basic_map_finalize(bmap);
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_drop_dims(
-               struct isl_basic_set *bset, unsigned first, unsigned n)
+struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
 {
-       int i;
-
-       if (!bset)
-               goto error;
-
-       isl_assert(bset->ctx, first + n <= bset->dim, goto error);
-
-       if (n == 0)
-               return bset;
-
-       bset = isl_basic_set_cow(bset);
-       if (!bset)
-               return NULL;
-
-       for (i = 0; i < bset->n_eq; ++i)
-               constraint_drop_vars(bset->eq[i]+1+bset->nparam+first, n,
-                                    (bset->dim-first-n)+bset->extra);
-
-       for (i = 0; i < bset->n_ineq; ++i)
-               constraint_drop_vars(bset->ineq[i]+1+bset->nparam+first, n,
-                                    (bset->dim-first-n)+bset->extra);
-
-       for (i = 0; i < bset->n_div; ++i)
-               constraint_drop_vars(bset->div[i]+1+1+bset->nparam+first, n,
-                                    (bset->dim-first-n)+bset->extra);
-
-       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;
-}
-
-static struct isl_set *isl_set_drop_dims(
-               struct isl_set *set, unsigned first, unsigned n)
-{
-       int i;
-
-       if (!set)
-               goto error;
-
-       isl_assert(set->ctx, first + n <= set->dim, goto error);
-
-       if (n == 0)
-               return set;
-       set = isl_set_cow(set);
-       if (!set)
-               goto error;
-
-       for (i = 0; i < set->n; ++i) {
-               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.
- */
-static struct isl_basic_map *isl_basic_map_drop_div(
-               struct isl_basic_map *bmap, unsigned div)
-{
-       int i;
-       unsigned pos;
-
-       if (!bmap)
-               goto error;
-
-       pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
-
-       isl_assert(bmap->ctx, div < bmap->n_div, goto error);
-
-       for (i = 0; i < bmap->n_eq; ++i)
-               constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
-
-       for (i = 0; i < bmap->n_ineq; ++i) {
-               if (!isl_int_is_zero(bmap->ineq[i][pos])) {
-                       isl_basic_map_drop_inequality(bmap, i);
-                       --i;
-                       continue;
-               }
-               constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
-       }
-
-       for (i = 0; i < bmap->n_div; ++i)
-               constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
-
-       if (div != bmap->n_div - 1) {
-               int j;
-               isl_int *t = bmap->div[div];
-
-               for (j = div; j < bmap->n_div - 1; ++j)
-                       bmap->div[j] = bmap->div[j+1];
-
-               bmap->div[bmap->n_div - 1] = t;
-       }
-       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-       isl_basic_map_free_div(bmap, 1);
-
-       return bmap;
-error:
-       isl_basic_map_free(bmap);
-       return NULL;
-}
-
-static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
-{
-       int i;
-       unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
-       unsigned len;
-       len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-
-       for (i = 0; i < bmap->n_eq; ++i)
-               if (bmap->eq[i] != eq)
-                       isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
-
-       for (i = 0; i < bmap->n_ineq; ++i)
-               isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
-
-       /* We need to be careful about circular definitions,
-        * so for now we just remove the definitions of other divs that
-        * depend on this div and (possibly) recompute them later.
-        */
-       for (i = 0; i < bmap->n_div; ++i)
-               if (!isl_int_is_zero(bmap->div[i][0]) &&
-                   !isl_int_is_zero(bmap->div[i][1 + pos]))
-                       isl_seq_clr(bmap->div[i], 1 + len);
-
-       isl_basic_map_drop_div(bmap, div);
-}
-
-struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
-{
-       int i = 0;
-       unsigned total;
-       if (!bmap)
-               goto error;
-       total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
-       isl_basic_map_free_div(bmap, bmap->n_div);
-       isl_basic_map_free_inequality(bmap, bmap->n_ineq);
-       if (bmap->n_eq > 0)
-               isl_basic_map_free_equality(bmap, bmap->n_eq-1);
-       else {
-               isl_basic_map_alloc_equality(bmap);
-               if (i < 0)
-                       goto error;
-       }
-       isl_int_set_si(bmap->eq[i][0], 1);
-       isl_seq_clr(bmap->eq[i]+1, total);
-       F_SET(bmap, ISL_BASIC_MAP_EMPTY);
-       return isl_basic_map_finalize(bmap);
-error:
-       isl_basic_map_free(bmap);
-       return NULL;
-}
-
-struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
-{
-       return (struct isl_basic_set *)
-               isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
-}
-
-static void swap_equality(struct isl_basic_map *bmap, int a, int b)
-{
-       isl_int *t = bmap->eq[a];
-       bmap->eq[a] = bmap->eq[b];
-       bmap->eq[b] = t;
-}
-
-static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
-{
-       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);
-}
+       return (struct isl_basic_set *)
+               isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
+}
 
 static void swap_div(struct isl_basic_map *bmap, int a, int b)
 {
        int i;
-       unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
+       unsigned off = isl_dim_total(bmap->dim);
        isl_int *t = bmap->div[a];
        bmap->div[a] = bmap->div[b];
        bmap->div[b] = t;
@@ -914,596 +1079,7 @@ 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);
-}
-
-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)
-{
-       int k;
-       int done;
-       int last_var;
-       unsigned total_var;
-       unsigned total;
-
-       if (!bmap)
-               return NULL;
-
-       total_var = bmap->nparam + bmap->n_in + bmap->n_out;
-       total = total_var + bmap->n_div;
-
-       last_var = total - 1;
-       for (done = 0; done < bmap->n_eq; ++done) {
-               for (; last_var >= 0; --last_var) {
-                       for (k = done; k < bmap->n_eq; ++k)
-                               if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
-                                       break;
-                       if (k < bmap->n_eq)
-                               break;
-               }
-               if (last_var < 0)
-                       break;
-               if (k != done)
-                       swap_equality(bmap, k, done);
-               if (isl_int_is_neg(bmap->eq[done][1+last_var]))
-                       isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
-
-               eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
-                                               progress);
-
-               if (last_var >= total_var &&
-                   isl_int_is_zero(bmap->div[last_var - total_var][0])) {
-                       unsigned div = last_var - total_var;
-                       isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
-                       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)
-               return bmap;
-       for (k = done; k < bmap->n_eq; ++k) {
-               if (isl_int_is_zero(bmap->eq[k][0]))
-                       continue;
-               return isl_basic_map_set_to_empty(bmap);
-       }
-       isl_basic_map_free_equality(bmap, bmap->n_eq-done);
-       return bmap;
-}
-
-struct isl_basic_set *isl_basic_set_gauss(
-       struct isl_basic_set *bset, int *progress)
-{
-       return (struct isl_basic_set*)isl_basic_map_gauss(
-                       (struct isl_basic_map *)bset, progress);
-}
-
-static unsigned int round_up(unsigned int v)
-{
-       int old_v = v;
-
-       while (v) {
-               old_v = v;
-               v ^= v & -v;
-       }
-       return old_v << 1;
-}
-
-static int hash_index(isl_int ***index, unsigned int size, int bits,
-                       struct isl_basic_map *bmap, int k)
-{
-       int h;
-       unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-       u_int32_t hash = isl_seq_hash(bmap->ineq[k]+1, total, bits);
-       for (h = hash; index[h]; h = (h+1) % size)
-               if (&bmap->ineq[k] != index[h] &&
-                   isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
-                       break;
-       return h;
-}
-
-static int set_hash_index(isl_int ***index, unsigned int size, int bits,
-                         struct isl_basic_set *bset, int k)
-{
-       return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
-}
-
-static struct isl_basic_map *remove_duplicate_constraints(
-       struct isl_basic_map *bmap, int *progress)
-{
-       unsigned int size;
-       isl_int ***index;
-       int k, l, h;
-       int bits;
-       unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-       isl_int sum;
-
-       if (bmap->n_ineq <= 1)
-               return bmap;
-
-       size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
-       bits = ffs(size) - 1;
-       index = isl_alloc_array(ctx, isl_int **, size);
-       memset(index, 0, size * sizeof(isl_int **));
-       if (!index)
-               return bmap;
-
-       index[isl_seq_hash(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
-       for (k = 1; k < bmap->n_ineq; ++k) {
-               h = hash_index(index, size, bits, bmap, k);
-               if (!index[h]) {
-                       index[h] = &bmap->ineq[k];
-                       continue;
-               }
-               if (progress)
-                       *progress = 1;
-               l = index[h] - &bmap->ineq[0];
-               if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
-                       swap_inequality(bmap, k, l);
-               isl_basic_map_drop_inequality(bmap, k);
-               --k;
-       }
-       isl_int_init(sum);
-       for (k = 0; k < bmap->n_ineq-1; ++k) {
-               isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
-               h = hash_index(index, size, bits, bmap, k);
-               isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
-               if (!index[h])
-                       continue;
-               l = index[h] - &bmap->ineq[0];
-               isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
-               if (isl_int_is_pos(sum))
-                       continue;
-               if (isl_int_is_zero(sum)) {
-                       /* We need to break out of the loop after these
-                        * changes since the contents of the hash
-                        * will no longer be valid.
-                        * Plus, we probably we want to regauss first.
-                        */
-                       isl_basic_map_drop_inequality(bmap, l);
-                       isl_basic_map_inequality_to_equality(bmap, k);
-               } else
-                       bmap = isl_basic_map_set_to_empty(bmap);
-               break;
-       }
-       isl_int_clear(sum);
-
-       free(index);
-       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 void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
-{
-       return compute_elimination_index((struct isl_basic_map *)bset, elim);
-}
-
-static int reduced_using_equalities(isl_int *dst, isl_int *src,
-       struct isl_basic_map *bmap, int *elim)
-{
-       int d, i;
-       int 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(src[1+d]))
-                       continue;
-               if (elim[d] == -1)
-                       continue;
-               if (!copied) {
-                       isl_seq_cpy(dst, src, 1 + total);
-                       copied = 1;
-               }
-               isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
-       }
-       return copied;
-}
-
-static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
-       struct isl_basic_set *bset, int *elim)
-{
-       return reduced_using_equalities(dst, src,
-                                       (struct isl_basic_map *)bset, elim);
-}
-
-/* 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(v->block.data, bmap2->eq[i],
-                                                       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(v->block.data,
-                                               bmap2->ineq[i], 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(v->block.data,
-                                               bmap1->ineq[i], 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)
-{
-       unsigned int size;
-       int *index;
-       int k, l, h;
-       int bits;
-       struct isl_blk eq;
-       unsigned total_var = bmap->nparam + bmap->n_in + bmap->n_out;
-       unsigned total = total_var + bmap->n_div;
-       struct isl_ctx *ctx;
-
-       if (bmap->n_div <= 1)
-               return bmap;
-
-       ctx = bmap->ctx;
-       for (k = bmap->n_div - 1; k >= 0; --k)
-               if (!isl_int_is_zero(bmap->div[k][0]))
-                       break;
-       if (k <= 0)
-               return bmap;
-
-       size = round_up(4 * bmap->n_div / 3 - 1);
-       bits = ffs(size) - 1;
-       index = isl_alloc_array(ctx, int, size);
-       memset(index, 0, size * sizeof(int));
-       if (!index)
-               return bmap;
-       eq = isl_blk_alloc(ctx, 1+total);
-       if (isl_blk_is_error(eq))
-               goto out;
-
-       isl_seq_clr(eq.data, 1+total);
-       index[isl_seq_hash(bmap->div[k], 2+total, bits)] = k + 1;
-       for (--k; k >= 0; --k) {
-               u_int32_t hash;
-
-               if (isl_int_is_zero(bmap->div[k][0]))
-                       continue;
-
-               hash = isl_seq_hash(bmap->div[k], 2+total, bits);
-               for (h = hash; index[h]; h = (h+1) % size)
-                       if (isl_seq_eq(bmap->div[k],
-                                      bmap->div[index[h]-1], 2+total))
-                               break;
-               if (index[h]) {
-                       *progress = 1;
-                       l = index[h] - 1;
-                       isl_int_set_si(eq.data[1+total_var+k], -1);
-                       isl_int_set_si(eq.data[1+total_var+l], 1);
-                       eliminate_div(bmap, eq.data, l);
-                       isl_int_set_si(eq.data[1+total_var+k], 0);
-                       isl_int_set_si(eq.data[1+total_var+l], 0);
-               }
-               index[h] = k+1;
-       }
-
-       isl_blk_free(ctx, eq);
-out:
-       free(index);
-       return bmap;
-}
-
-/* Elimininate divs based on equalities
- */
-static struct isl_basic_map *eliminate_divs_eq(
-               struct isl_basic_map *bmap, int *progress)
-{
-       int d;
-       int i;
-       int modified = 0;
-       unsigned off;
-
-       if (!bmap)
-               return NULL;
-
-       off = 1 + bmap->nparam + bmap->n_in + bmap->n_out;
-
-       for (d = bmap->n_div - 1; d >= 0 ; --d) {
-               for (i = 0; i < bmap->n_eq; ++i) {
-                       if (!isl_int_is_one(bmap->eq[i][off + d]) &&
-                           !isl_int_is_negone(bmap->eq[i][off + d]))
-                               continue;
-                       modified = 1;
-                       *progress = 1;
-                       eliminate_div(bmap, bmap->eq[i], d);
-                       isl_basic_map_drop_equality(bmap, i);
-                       break;
-               }
-       }
-       if (modified)
-               return eliminate_divs_eq(bmap, progress);
-       return bmap;
-}
-
-static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
-{
-       int i;
-       isl_int gcd;
-       unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-
-       isl_int_init(gcd);
-       for (i = bmap->n_eq - 1; i >= 0; --i) {
-               isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
-               if (isl_int_is_zero(gcd)) {
-                       if (!isl_int_is_zero(bmap->eq[i][0])) {
-                               bmap = isl_basic_map_set_to_empty(bmap);
-                               break;
-                       }
-                       isl_basic_map_drop_equality(bmap, i);
-                       continue;
-               }
-               if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
-                       isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
-               if (isl_int_is_one(gcd))
-                       continue;
-               if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
-                       bmap = isl_basic_map_set_to_empty(bmap);
-                       break;
-               }
-               isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
-       }
-
-       for (i = bmap->n_ineq - 1; i >= 0; --i) {
-               isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
-               if (isl_int_is_zero(gcd)) {
-                       if (isl_int_is_neg(bmap->ineq[i][0])) {
-                               bmap = isl_basic_map_set_to_empty(bmap);
-                               break;
-                       }
-                       isl_basic_map_drop_inequality(bmap, i);
-                       continue;
-               }
-               if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
-                       isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
-               if (isl_int_is_one(gcd))
-                       continue;
-               isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
-               isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
-       }
-       isl_int_clear(gcd);
-
-       return bmap;
-}
-
-
-/* Eliminate the specified variables from the constraints using
- * Fourier-Motzkin.  The variables themselves are not removed.
- */
-struct isl_basic_map *isl_basic_map_eliminate_vars(
-       struct isl_basic_map *bmap, int pos, unsigned n)
-{
-       int d;
-       int i, j, k;
-       unsigned total;
-       unsigned extra;
-
-       if (!bmap)
-               return NULL;
-       total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-       extra = bmap->extra - bmap->n_div;
-
-       bmap = isl_basic_map_cow(bmap);
-       for (d = pos + n - 1; d >= pos; --d) {
-               int n_lower, n_upper;
-               if (!bmap)
-                       return NULL;
-               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;
-               }
-               if (i < bmap->n_eq)
-                       continue;
-               n_lower = 0;
-               n_upper = 0;
-               for (i = 0; i < bmap->n_ineq; ++i) {
-                       if (isl_int_is_pos(bmap->ineq[i][1+d]))
-                               n_lower++;
-                       else if (isl_int_is_neg(bmap->ineq[i][1+d]))
-                               n_upper++;
-               }
-               bmap = isl_basic_map_extend(bmap,
-                               bmap->nparam, bmap->n_in, bmap->n_out, 0,
-                               0, n_lower * n_upper);
-               for (i = bmap->n_ineq - 1; i >= 0; --i) {
-                       int last;
-                       if (isl_int_is_zero(bmap->ineq[i][1+d]))
-                               continue;
-                       last = -1;
-                       for (j = 0; j < i; ++j) {
-                               if (isl_int_is_zero(bmap->ineq[j][1+d]))
-                                       continue;
-                               last = j;
-                               if (isl_int_sgn(bmap->ineq[i][1+d]) ==
-                                   isl_int_sgn(bmap->ineq[j][1+d]))
-                                       continue;
-                               k = isl_basic_map_alloc_inequality(bmap);
-                               if (k < 0)
-                                       goto error;
-                               isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
-                                               1+total);
-                               isl_seq_clr(bmap->ineq[k]+1+total, extra);
-                               isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
-                                               1+d, 1+total, NULL);
-                       }
-                       isl_basic_map_drop_inequality(bmap, i);
-                       i = last + 1;
-               }
-               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);
-       return NULL;
-}
-
-struct isl_basic_set *isl_basic_set_eliminate_vars(
-       struct isl_basic_set *bset, unsigned pos, unsigned n)
-{
-       return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
-                       (struct isl_basic_map *)bset, pos, n);
+       ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 }
 
 /* Eliminate the specified n dimensions starting at first from the
@@ -1514,18 +1090,22 @@ struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
        unsigned first, unsigned n)
 {
        int i;
+       unsigned nparam;
 
+       if (!set)
+               return NULL;
        if (n == 0)
                return set;
 
        set = isl_set_cow(set);
        if (!set)
                return NULL;
-       isl_assert(set->ctx, first+n <= set->dim, goto error);
+       isl_assert(set->ctx, first+n <= isl_set_n_dim(set), goto error);
+       nparam = isl_set_n_param(set);
        
        for (i = 0; i < set->n; ++i) {
                set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
-                                                       set->nparam + first, n);
+                                                           nparam + first, n);
                if (!set->p[i])
                        goto error;
        }
@@ -1544,121 +1124,127 @@ struct isl_set *isl_set_remove_dims(struct isl_set *set,
        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)
+struct isl_basic_set *isl_basic_set_remove_divs(struct isl_basic_set *bset)
+{
+       bset = isl_basic_set_eliminate_vars(bset, isl_dim_total(bset->dim),
+                                               bset->n_div);
+       if (!bset)
+               return NULL;
+       bset->n_div = 0;
+       return bset;
+}
+
+struct isl_set *isl_set_remove_divs(struct isl_set *set)
 {
        int i;
 
-       if (n == 0)
-               return map;
+       if (!set)
+               return NULL;
+       if (set->n == 0)
+               return set;
 
-       map = isl_map_cow(map);
-       if (!map)
+       set = isl_set_cow(set);
+       if (!set)
                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])
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = isl_basic_set_remove_divs(set->p[i]);
+               if (!set->p[i])
                        goto error;
        }
-       map = isl_map_drop_inputs(map, first, n);
-       return map;
+       return set;
 error:
-       isl_map_free(map);
+       isl_set_free(set);
        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)
+struct isl_basic_map *isl_basic_map_remove(struct isl_basic_map *bmap,
+       enum isl_dim_type type, 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(
-               struct isl_basic_map *bmap, int *progress)
-{
-       int d;
-       int i;
-       unsigned off;
-       struct isl_ctx *ctx;
-
        if (!bmap)
                return NULL;
-
-       ctx = bmap->ctx;
-       off = 1 + bmap->nparam + bmap->n_in + bmap->n_out;
-
-       for (d = bmap->n_div - 1; d >= 0 ; --d) {
-               for (i = 0; i < bmap->n_eq; ++i)
-                       if (!isl_int_is_zero(bmap->eq[i][off + d]))
-                               break;
-               if (i < bmap->n_eq)
-                       continue;
-               for (i = 0; i < bmap->n_ineq; ++i)
-                       if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
-                               break;
-               if (i < bmap->n_ineq)
-                       continue;
-               *progress = 1;
-               bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
-               if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
-                       break;
-               bmap = isl_basic_map_drop_div(bmap, d);
-               if (!bmap)
-                       break;
-       }
+       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_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
+struct isl_map *isl_map_remove(struct isl_map *map,
+       enum isl_dim_type type, unsigned first, unsigned n)
 {
-       int progress = 1;
-       if (!bmap)
+       int i;
+       unsigned nparam;
+
+       if (n == 0)
+               return map;
+
+       map = isl_map_cow(map);
+       if (!map)
                return NULL;
-       while (progress) {
-               progress = 0;
-               bmap = normalize_constraints(bmap);
-               bmap = eliminate_divs_eq(bmap, &progress);
-               bmap = eliminate_divs_ineq(bmap, &progress);
-               bmap = isl_basic_map_gauss(bmap, &progress);
-               bmap = remove_duplicate_divs(bmap, &progress);
-               bmap = remove_duplicate_constraints(bmap, &progress);
+       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],
+                       isl_basic_map_offset(map->p[i], type) - 1 + first, n);
+               if (!map->p[i])
+                       goto error;
        }
-       return bmap;
+       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);
 }
 
-struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
+/* 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)
 {
-       return (struct isl_basic_set *)
-               isl_basic_map_simplify((struct isl_basic_map *)bset);
+       unsigned nparam = isl_basic_set_n_param(bset);
+       bset = isl_basic_set_eliminate_vars(bset, nparam + first, n);
+       bset = isl_basic_set_drop_dims(bset, first, n);
+       return bset;
 }
 
 static void dump_term(struct isl_basic_map *bmap,
                        isl_int c, int pos, FILE *out)
 {
-       unsigned in = bmap->n_in;
-       unsigned dim = bmap->n_in + bmap->n_out;
+       const char *name;
+       unsigned in = isl_basic_map_n_in(bmap);
+       unsigned dim = in + isl_basic_map_n_out(bmap);
+       unsigned nparam = isl_basic_map_n_param(bmap);
        if (!pos)
                isl_int_print(out, c, 0);
        else {
                if (!isl_int_is_one(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)
-                       fprintf(out, "i%d", pos - 1 - bmap->nparam);
-               else if (pos < 1 + bmap->nparam + dim)
-                       fprintf(out, "o%d", pos - 1 - bmap->nparam - in);
+               if (pos < 1 + nparam) {
+                       name = isl_dim_get_name(bmap->dim,
+                                               isl_dim_param, pos - 1);
+                       if (name)
+                               fprintf(out, "%s", name);
+                       else
+                               fprintf(out, "p%d", pos - 1);
+               } else if (pos < 1 + nparam + in)
+                       fprintf(out, "i%d", pos - 1 - nparam);
+               else if (pos < 1 + nparam + dim)
+                       fprintf(out, "o%d", pos - 1 - nparam - in);
                else
-                       fprintf(out, "e%d", pos - 1 - bmap->nparam - dim);
+                       fprintf(out, "e%d", pos - 1 - nparam - dim);
        }
 }
 
@@ -1667,7 +1253,7 @@ static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
 {
        int i;
        int first;
-       unsigned len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       unsigned len = 1 + isl_basic_map_total_dim(bmap);
        isl_int v;
 
        isl_int_init(v);
@@ -1699,10 +1285,11 @@ static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
        fprintf(out, "\n");
 
        for (i = bmap->n_div; i < bmap->extra; ++i) {
-               if (isl_int_is_zero(c[1+bmap->nparam+bmap->n_in+bmap->n_out+i]))
+               if (isl_int_is_zero(c[1+isl_dim_total(bmap->dim)+i]))
                        continue;
                fprintf(out, "%*s", indent, "");
                fprintf(out, "ERROR: unused div coefficient not zero\n");
+               abort();
        }
 }
 
@@ -1720,7 +1307,7 @@ static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
 {
        int j;
        int first = 1;
-       unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       unsigned total = isl_basic_map_total_dim(bmap);
 
        for (j = 0; j < 1 + total; ++j) {
                if (isl_int_is_zero(exp[j]))
@@ -1758,8 +1345,8 @@ void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
 
        fprintf(out, "%*s", indent, "");
        fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
-                       bset->ref, bset->nparam, bset->dim, bset->extra,
-                       bset->flags);
+                       bset->ref, bset->dim->nparam, bset->dim->n_out,
+                       bset->extra, bset->flags);
        dump((struct isl_basic_map *)bset, out, indent);
 }
 
@@ -1771,46 +1358,66 @@ void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
        }
 
        fprintf(out, "%*s", indent, "");
-       fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, flags: %x\n",
+       fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
+                       "flags: %x, n_name: %d\n",
                bmap->ref,
-               bmap->nparam, bmap->n_in, bmap->n_out, bmap->extra, bmap->flags);
+               bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
+               bmap->extra, bmap->flags, bmap->dim->n_name);
        dump(bmap, out, indent);
 }
 
 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
 {
-       unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       unsigned total;
        if (!bmap)
                return -1;
+       total = isl_basic_map_total_dim(bmap);
        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;
 }
 
-struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
-               unsigned nparam, unsigned dim, int n, unsigned flags)
+struct isl_set *isl_set_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
 {
        struct isl_set *set;
 
-       isl_assert(ctx, n >= 0, return NULL);
-       set = isl_alloc(ctx, struct isl_set,
+       if (!dim)
+               return NULL;
+       isl_assert(dim->ctx, dim->n_in == 0, return NULL);
+       isl_assert(dim->ctx, n >= 0, return NULL);
+       set = isl_alloc(dim->ctx, struct isl_set,
                        sizeof(struct isl_set) +
                        n * sizeof(struct isl_basic_set *));
        if (!set)
-               return NULL;
+               goto error;
 
-       set->ctx = ctx;
-       isl_ctx_ref(ctx);
+       set->ctx = dim->ctx;
+       isl_ctx_ref(set->ctx);
        set->ref = 1;
        set->size = n;
        set->n = 0;
-       set->nparam = nparam;
-       set->zero = 0;
        set->dim = dim;
        set->flags = flags;
        return set;
+error:
+       isl_dim_free(dim);
+       return NULL;
+}
+
+struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
+               unsigned nparam, unsigned dim, int n, unsigned flags)
+{
+       struct isl_set *set;
+       struct isl_dim *dims;
+
+       dims = isl_dim_alloc(ctx, nparam, 0, dim);
+       if (!dims)
+               return NULL;
+
+       set = isl_set_alloc_dim(dims, n, flags);
+       return set;
 }
 
 struct isl_set *isl_set_dup(struct isl_set *set)
@@ -1821,12 +1428,11 @@ struct isl_set *isl_set_dup(struct isl_set *set)
        if (!set)
                return NULL;
 
-       dup = isl_set_alloc(set->ctx, set->nparam, set->dim, set->n, set->flags);
+       dup = isl_set_alloc_dim(isl_dim_copy(set->dim), set->n, set->flags);
        if (!dup)
                return NULL;
        for (i = 0; i < set->n; ++i)
-               dup = isl_set_add(dup,
-                                 isl_basic_set_dup(set->p[i]));
+               dup = isl_set_add(dup, isl_basic_set_copy(set->p[i]));
        return dup;
 }
 
@@ -1837,7 +1443,7 @@ struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
        if (!bset)
                return NULL;
 
-       set = isl_set_alloc(bset->ctx, bset->nparam, bset->dim, 1, ISL_MAP_DISJOINT);
+       set = isl_set_alloc_dim(isl_dim_copy(bset->dim), 1, ISL_MAP_DISJOINT);
        if (!set) {
                isl_basic_set_free(bset);
                return NULL;
@@ -1852,8 +1458,7 @@ struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
        if (!bmap)
                return NULL;
 
-       map = isl_map_alloc(bmap->ctx, bmap->nparam, bmap->n_in, bmap->n_out, 1,
-                               ISL_MAP_DISJOINT);
+       map = isl_map_alloc_dim(isl_dim_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
        if (!map) {
                isl_basic_map_free(bmap);
                return NULL;
@@ -1865,8 +1470,7 @@ struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
 {
        if (!bset || !set)
                goto error;
-       isl_assert(set->ctx, set->nparam == bset->nparam, goto error);
-       isl_assert(set->ctx, set->dim == bset->dim, 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++;
@@ -1892,6 +1496,7 @@ void isl_set_free(struct isl_set *set)
        isl_ctx_deref(set->ctx);
        for (i = 0; i < set->n; ++i)
                isl_basic_set_free(set->p[i]);
+       isl_dim_free(set->dim);
        free(set);
 }
 
@@ -1906,7 +1511,8 @@ void isl_set_dump(struct isl_set *set, FILE *out, int indent)
 
        fprintf(out, "%*s", indent, "");
        fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
-                       set->ref, set->n, set->nparam, set->dim, set->flags);
+                       set->ref, set->n, set->dim->nparam, set->dim->n_out,
+                       set->flags);
        for (i = 0; i < set->n; ++i) {
                fprintf(out, "%*s", indent, "");
                fprintf(out, "basic set %d:\n", i);
@@ -1924,9 +1530,10 @@ void isl_map_dump(struct isl_map *map, FILE *out, int indent)
        }
 
        fprintf(out, "%*s", indent, "");
-       fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, flags: %x\n",
-                       map->ref, map->n, map->nparam, map->n_in, map->n_out,
-                       map->flags);
+       fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
+                    "flags: %x, n_name: %d\n",
+                       map->ref, map->n, map->dim->nparam, map->dim->n_in,
+                       map->dim->n_out, map->flags, map->dim->n_name);
        for (i = 0; i < map->n; ++i) {
                fprintf(out, "%*s", indent, "");
                fprintf(out, "basic map %d:\n", i);
@@ -1938,20 +1545,25 @@ struct isl_basic_map *isl_basic_map_intersect_domain(
                struct isl_basic_map *bmap, struct isl_basic_set *bset)
 {
        struct isl_basic_map *bmap_domain;
+       struct isl_dim *dim;
 
        if (!bmap || !bset)
                goto error;
 
-       isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
-       isl_assert(bset->ctx, bset->nparam == bmap->nparam, 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_extend(bmap,
-                       bset->nparam, bmap->n_in, bmap->n_out,
+       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)
                goto error;
-       bmap_domain = isl_basic_map_from_basic_set(bset,
-                                               bset->dim, 0);
+       dim = isl_dim_reverse(isl_dim_copy(bset->dim));
+       bmap_domain = isl_basic_map_from_basic_set(bset, dim);
        bmap = add_constraints(bmap, bmap_domain, 0, 0);
 
        bmap = isl_basic_map_simplify(bmap);
@@ -1970,16 +1582,19 @@ struct isl_basic_map *isl_basic_map_intersect_range(
        if (!bmap || !bset)
                goto error;
 
-       isl_assert(bset->ctx, bset->dim == bmap->n_out, goto error);
-       isl_assert(bset->ctx, bset->nparam == bmap->nparam, 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_extend(bmap,
-                       bset->nparam, bmap->n_in, bmap->n_out,
+       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)
                goto error;
-       bmap_range = isl_basic_map_from_basic_set(bset,
-                                               0, bset->dim);
+       bmap_range = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
        bmap = add_constraints(bmap, bmap_range, 0, 0);
 
        bmap = isl_basic_map_simplify(bmap);
@@ -1990,26 +1605,91 @@ 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(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
-       isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
-       isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
-
-       bmap1 = isl_basic_map_extend(bmap1,
-                       bmap1->nparam, bmap1->n_in, bmap1->n_out,
+       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;
@@ -2033,11 +1713,22 @@ 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);
 
-       result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
+       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);
        if (!result)
                goto error;
@@ -2072,6 +1763,7 @@ struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
 
 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
 {
+       struct isl_dim *dim;
        struct isl_basic_set *bset;
        unsigned in;
 
@@ -2080,10 +1772,11 @@ struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                return NULL;
-       in = bmap->n_in;
+       dim = isl_dim_reverse(isl_dim_copy(bmap->dim));
+       in = isl_basic_map_n_in(bmap);
        bset = isl_basic_set_from_basic_map(bmap);
        bset = isl_basic_set_swap_vars(bset, in);
-       return isl_basic_map_from_basic_set(bset, bset->dim-in, in);
+       return isl_basic_map_from_basic_set(bset, dim);
 }
 
 /* Turn final n dimensions into existentially quantified variables.
@@ -2099,14 +1792,14 @@ struct isl_basic_set *isl_basic_set_project_out(
        if (!bset)
                return NULL;
 
-       isl_assert(bset->ctx, n <= bset->dim, goto error);
+       isl_assert(bset->ctx, n <= isl_basic_set_n_dim(bset), goto error);
 
        if (n == 0)
                return bset;
 
        bset = isl_basic_set_cow(bset);
 
-       row_size = 1 + bset->nparam + bset->dim + bset->extra;
+       row_size = 1 + isl_dim_total(bset->dim) + bset->extra;
        old = bset->block2.data;
        bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
                                        (bset->extra + n) * (1 + row_size));
@@ -2126,7 +1819,10 @@ struct isl_basic_set *isl_basic_set_project_out(
        bset->div = new_div;
        bset->n_div += n;
        bset->extra += n;
-       bset->dim -= n;
+       bset->dim = isl_dim_drop_outputs(bset->dim,
+                                           isl_basic_set_n_dim(bset) - n, n);
+       if (!bset->dim)
+               goto error;
        bset = isl_basic_set_simplify(bset);
        return isl_basic_set_finalize(bset);
 error:
@@ -2134,35 +1830,62 @@ error:
        return NULL;
 }
 
+static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
+{
+       int i, j;
+
+       for (i = 0; i < n; ++i) {
+               j = isl_basic_map_alloc_div(bmap);
+               if (j < 0)
+                       goto error;
+               isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
+       }
+       return bmap;
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
 struct isl_basic_map *isl_basic_map_apply_range(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
-       struct isl_basic_set *bset;
-       unsigned n_in, n_out;
+       struct isl_dim *dim_result = NULL;
+       struct isl_basic_map *bmap;
+       unsigned n_in, n_out, n, nparam, total, pos;
+       struct isl_dim_map *dim_map1, *dim_map2;
 
        if (!bmap1 || !bmap2)
                goto error;
 
-       isl_assert(bmap->ctx, bmap1->n_out == bmap2->n_in, goto error);
-       isl_assert(bmap->ctx, bmap1->nparam == bmap2->nparam, goto error);
-
-       n_in = bmap1->n_in;
-       n_out = bmap2->n_out;
-
-       bmap2 = isl_basic_map_reverse(bmap2);
-       if (!bmap2)
-               goto error;
-       bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
-                       bmap1->n_in + bmap2->n_in, bmap1->n_out,
-                       bmap2->extra, bmap2->n_eq, bmap2->n_ineq);
-       if (!bmap1)
-               goto error;
-       bmap1 = add_constraints(bmap1, bmap2, bmap1->n_in - bmap2->n_in, 0);
-       bmap1 = isl_basic_map_simplify(bmap1);
-       bset = isl_basic_set_from_basic_map(bmap1);
-       bset = isl_basic_set_project_out(bset,
-                                               bset->dim - (n_in + n_out), 0);
-       return isl_basic_map_from_basic_set(bset, n_in, n_out);
+       dim_result = isl_dim_join(isl_dim_copy(bmap1->dim),
+                                 isl_dim_copy(bmap2->dim));
+
+       n_in = isl_basic_map_n_in(bmap1);
+       n_out = isl_basic_map_n_out(bmap2);
+       n = isl_basic_map_n_out(bmap1);
+       nparam = isl_basic_map_n_param(bmap1);
+
+       total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
+       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_out, pos += n_in);
+       isl_dim_map_div(dim_map1, bmap1, pos += n_out);
+       isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
+       isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
+       isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
+
+       bmap = isl_basic_map_alloc_dim(dim_result,
+                       bmap1->n_div + bmap2->n_div + n,
+                       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 = add_divs(bmap, n);
+       bmap = isl_basic_map_simplify(bmap);
+       return isl_basic_map_finalize(bmap);
 error:
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
@@ -2175,7 +1898,8 @@ struct isl_basic_set *isl_basic_set_apply(
        if (!bset || !bmap)
                goto error;
 
-       isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
+       isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
+                   goto error);
 
        return (struct isl_basic_set *)
                isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
@@ -2191,8 +1915,11 @@ struct isl_basic_map *isl_basic_map_apply_domain(
        if (!bmap1 || !bmap2)
                goto error;
 
-       isl_assert(ctx, bmap1->n_in == bmap2->n_in, goto error);
-       isl_assert(ctx, bmap1->nparam == bmap2->nparam, goto error);
+       isl_assert(ctx,
+           isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
+       isl_assert(ctx,
+           isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
+           goto error);
 
        bmap1 = isl_basic_map_reverse(bmap1);
        bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
@@ -2203,118 +1930,263 @@ error:
        return NULL;
 }
 
-static struct isl_basic_map *var_equal(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned pos)
+/* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
+ * A \cap B -> f(A) + f(B)
+ */
+struct isl_basic_map *isl_basic_map_sum(
+               struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+{
+       unsigned n_in, n_out, nparam, total, pos;
+       struct isl_basic_map *bmap = NULL;
+       struct isl_dim_map *dim_map1, *dim_map2;
+       int i;
+
+       if (!bmap1 || !bmap2)
+               goto error;
+
+       isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
+               goto error);
+
+       nparam = isl_basic_map_n_param(bmap1);
+       n_in = isl_basic_map_n_in(bmap1);
+       n_out = isl_basic_map_n_out(bmap1);
+
+       total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
+       dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
+       dim_map2 = isl_dim_map_alloc(bmap2->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);
+       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);
+       isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
+       isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
+       isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
+       isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
+
+       bmap = isl_basic_map_alloc_dim(isl_dim_copy(bmap1->dim),
+                       bmap1->n_div + bmap2->n_div + 2 * n_out,
+                       bmap1->n_eq + bmap2->n_eq + n_out,
+                       bmap1->n_ineq + bmap2->n_ineq);
+       for (i = 0; i < n_out; ++i) {
+               int j = isl_basic_map_alloc_equality(bmap);
+               if (j < 0)
+                       goto error;
+               isl_seq_clr(bmap->eq[j], 1+total);
+               isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
+               isl_int_set_si(bmap->eq[j][1+pos+i], 1);
+               isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
+       }
+       bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
+       bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
+       bmap = add_divs(bmap, 2 * n_out);
+
+       bmap = isl_basic_map_simplify(bmap);
+       return isl_basic_map_finalize(bmap);
+error:
+       isl_basic_map_free(bmap);
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
+       return NULL;
+}
+
+/* Given a basic map A -> f(A), construct A -> -f(A).
+ */
+struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
+{
+       int i, j;
+       unsigned off, n;
+
+       bmap = isl_basic_map_cow(bmap);
+       if (!bmap)
+               return NULL;
+
+       n = isl_basic_map_dim(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]);
+       for (i = 0; i < bmap->n_ineq; ++i)
+               for (j = 0; j < n; ++j)
+                       isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
+       for (i = 0; i < bmap->n_div; ++i)
+               for (j = 0; j < n; ++j)
+                       isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
+       return isl_basic_map_finalize(bmap);
+}
+
+/* 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;
+       unsigned n_in;
+
        i = isl_basic_map_alloc_equality(bmap);
        if (i < 0)
                goto error;
-       isl_seq_clr(bmap->eq[i],
-                   1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
-       isl_int_set_si(bmap->eq[i][1+bmap->nparam+pos], -1);
-       isl_int_set_si(bmap->eq[i][1+bmap->nparam+bmap->n_in+pos], 1);
+       nparam = isl_basic_map_n_param(bmap);
+       n_in = isl_basic_map_n_in(bmap);
+       isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
+       isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
+       isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
        return isl_basic_map_finalize(bmap);
 error:
        isl_basic_map_free(bmap);
        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;
+       unsigned n_in;
+
        i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
                goto error;
-       isl_seq_clr(bmap->ineq[i],
-                   1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
+       nparam = isl_basic_map_n_param(bmap);
+       n_in = isl_basic_map_n_in(bmap);
+       isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->ineq[i][0], -1);
-       isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], -1);
-       isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], 1);
+       isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
+       isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
        return isl_basic_map_finalize(bmap);
 error:
        isl_basic_map_free(bmap);
        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;
+       unsigned n_in;
+
        i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
                goto error;
-       isl_seq_clr(bmap->ineq[i],
-                   1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
+       nparam = isl_basic_map_n_param(bmap);
+       n_in = isl_basic_map_n_in(bmap);
+       isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->ineq[i][0], -1);
-       isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], 1);
-       isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], -1);
+       isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
+       isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
        return isl_basic_map_finalize(bmap);
 error:
        isl_basic_map_free(bmap);
        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);
 }
 
 struct isl_basic_map *isl_basic_map_from_basic_set(
-               struct isl_basic_set *bset, unsigned n_in, unsigned n_out)
+               struct isl_basic_set *bset, struct isl_dim *dim)
 {
        struct isl_basic_map *bmap;
 
        bset = isl_basic_set_cow(bset);
-       if (!bset)
-               return NULL;
+       if (!bset || !dim)
+               goto error;
 
-       isl_assert(ctx, bset->dim == n_in + n_out, goto error);
+       isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
+       isl_dim_free(bset->dim);
        bmap = (struct isl_basic_map *) bset;
-       bmap->n_in = n_in;
-       bmap->n_out = n_out;
+       bmap->dim = dim;
        return isl_basic_map_finalize(bmap);
 error:
        isl_basic_set_free(bset);
+       isl_dim_free(dim);
        return NULL;
 }
 
@@ -2322,16 +2194,20 @@ struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
 {
        if (!bmap)
                goto error;
-       if (bmap->n_in == 0)
+       if (bmap->dim->n_in == 0)
                return (struct isl_basic_set *)bmap;
        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                goto error;
-       bmap->n_out += bmap->n_in;
-       bmap->n_in = 0;
+       bmap->dim = isl_dim_cow(bmap->dim);
+       if (!bmap->dim)
+               goto error;
+       bmap->dim->n_out += bmap->dim->n_in;
+       bmap->dim->n_in = 0;
        bmap = isl_basic_map_finalize(bmap);
        return (struct isl_basic_set *)bmap;
 error:
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
@@ -2347,8 +2223,8 @@ error:
 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
 {
        int i, j;
-       unsigned div_pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
-       unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
+       unsigned total = isl_basic_map_total_dim(bmap);
+       unsigned div_pos = 1 + total - bmap->n_div + div;
 
        i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
@@ -2370,14 +2246,14 @@ struct isl_basic_set *isl_basic_map_underlying_set(
 {
        if (!bmap)
                goto error;
-       if (bmap->nparam == 0 && bmap->n_in == 0 && bmap->n_div == 0)
+       if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
                return (struct isl_basic_set *)bmap;
        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                goto error;
-       bmap->n_out += bmap->nparam + bmap->n_in + bmap->n_div;
-       bmap->nparam = 0;
-       bmap->n_in = 0;
+       bmap->dim = isl_dim_underlying(bmap->dim, bmap->n_div);
+       if (!bmap->dim)
+               goto error;
        bmap->extra -= bmap->n_div;
        bmap->n_div = 0;
        bmap = isl_basic_map_finalize(bmap);
@@ -2392,26 +2268,29 @@ struct isl_basic_map *isl_basic_map_overlying_set(
        struct isl_basic_map *bmap;
        struct isl_ctx *ctx;
        unsigned total;
-       int i, k;
+       int i;
 
        if (!bset || !like)
                goto error;
        ctx = bset->ctx;
-       isl_assert(ctx, bset->dim ==
-                       like->nparam + like->n_in + like->n_out + like->n_div,
+       isl_assert(ctx, bset->n_div == 0, goto error);
+       isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
+       isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
                        goto error);
-       if (like->nparam == 0 && like->n_in == 0 && like->n_div == 0) {
+       if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
                isl_basic_map_free(like);
                return (struct isl_basic_map *)bset;
        }
        bset = isl_basic_set_cow(bset);
        if (!bset)
                goto error;
-       total = bset->dim + bset->extra;
+       total = bset->dim->n_out + bset->extra;
        bmap = (struct isl_basic_map *)bset;
-       bmap->nparam = like->nparam;
-       bmap->n_in = like->n_in;
-       bmap->n_out = like->n_out;
+       isl_dim_free(bmap->dim);
+       bmap->dim = isl_dim_copy(like->dim);
+       if (!bmap->dim)
+               goto error;
+       bmap->n_div = like->n_div;
        bmap->extra += like->n_div;
        if (bmap->extra) {
                unsigned ltotal;
@@ -2426,19 +2305,23 @@ struct isl_basic_map *isl_basic_map_overlying_set(
                                                bmap->extra);
                if (!bmap->div)
                        goto error;
-               bmap = isl_basic_map_extend(bmap, bmap->nparam,
-                       bmap->n_in, bmap->n_out, 0, 0, 2 * like->n_div);
+               for (i = 0; i < bmap->extra; ++i)
+                       bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
                for (i = 0; i < like->n_div; ++i) {
-                       k = isl_basic_map_alloc_div(bmap);
-                       if (k < 0)
-                               goto error;
-                       isl_seq_cpy(bmap->div[k], like->div[i], 1 + 1 + ltotal);
-                       isl_seq_clr(bmap->div[k]+1+1+ltotal, total - ltotal);
-                       if (add_div_constraints(bmap, k) < 0)
+                       isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
+                       isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
+               }
+               bmap = isl_basic_map_extend_constraints(bmap, 
+                                                       0, 2 * like->n_div);
+               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);
        bmap = isl_basic_map_finalize(bmap);
        return bmap;
 error:
@@ -2461,9 +2344,9 @@ struct isl_set *isl_set_from_underlying_set(
 
        if (!set || !like)
                goto error;
-       isl_assert(set->ctx, set->dim == like->nparam + like->dim + like->n_div,
+       isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
                    goto error);
-       if (like->nparam == 0 && like->n_div == 0) {
+       if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
                isl_basic_set_free(like);
                return set;
        }
@@ -2476,8 +2359,10 @@ struct isl_set *isl_set_from_underlying_set(
                if (!set->p[i])
                        goto error;
        }
-       set->nparam = like->nparam;
-       set->dim = like->dim;
+       isl_dim_free(set->dim);
+       set->dim = isl_dim_copy(like->dim);
+       if (!set->dim)
+               goto error;
        isl_basic_set_free(like);
        return set;
 error:
@@ -2490,11 +2375,16 @@ struct isl_set *isl_map_underlying_set(struct isl_map *map)
 {
        int i;
 
-       map = isl_map_align_divs(map);
        map = isl_map_cow(map);
        if (!map)
                return NULL;
+       map->dim = isl_dim_cow(map->dim);
+       if (!map->dim)
+               goto error;
 
+       for (i = 1; i < map->n; ++i)
+               isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
+                               goto error);
        for (i = 0; i < map->n; ++i) {
                map->p[i] = (struct isl_basic_map *)
                                isl_basic_map_underlying_set(map->p[i]);
@@ -2502,11 +2392,13 @@ struct isl_set *isl_map_underlying_set(struct isl_map *map)
                        goto error;
        }
        if (map->n == 0)
-               map->n_out += map->nparam + map->n_in;
-       else
-               map->n_out = map->p[0]->n_out;
-       map->nparam = 0;
-       map->n_in = 0;
+               map->dim = isl_dim_underlying(map->dim, 0);
+       else {
+               isl_dim_free(map->dim);
+               map->dim = isl_dim_copy(map->p[0]->dim);
+       }
+       if (!map->dim)
+               goto error;
        return (struct isl_set *)map;
 error:
        isl_map_free(map);
@@ -2524,7 +2416,7 @@ struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
        unsigned n_out;
        if (!bmap)
                return NULL;
-       n_out = bmap->n_out;
+       n_out = isl_basic_map_n_out(bmap);
        domain = isl_basic_set_from_basic_map(bmap);
        return isl_basic_set_project_out(domain, n_out, 0);
 }
@@ -2546,47 +2438,54 @@ struct isl_set *isl_map_range(struct isl_map *map)
                goto error;
 
        set = (struct isl_set *) map;
-       set->zero = 0;
+       if (set->dim->n_in != 0) {
+               set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
+               if (!set->dim)
+                       goto error;
+       }
        for (i = 0; i < map->n; ++i) {
                set->p[i] = isl_basic_map_range(map->p[i]);
                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);
        return NULL;
 }
 
-struct isl_map *isl_map_from_set(struct isl_set *set,
-               unsigned n_in, unsigned n_out)
+struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
 {
        int i;
        struct isl_map *map = NULL;
 
-       if (!set)
-               return NULL;
-       isl_assert(set->ctx, set->dim == n_in + n_out, goto error);
        set = isl_set_cow(set);
-       if (!set)
-               return NULL;
+       if (!set || !dim)
+               goto error;
+       isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
        map = (struct isl_map *)set;
        for (i = 0; i < set->n; ++i) {
                map->p[i] = isl_basic_map_from_basic_set(
-                               set->p[i], n_in, n_out);
+                               set->p[i], isl_dim_copy(dim));
                if (!map->p[i])
                        goto error;
        }
-       map->n_in = n_in;
-       map->n_out = n_out;
+       isl_dim_free(map->dim);
+       map->dim = dim;
        return map;
 error:
+       isl_dim_free(dim);
        isl_set_free(set);
        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;
@@ -2597,8 +2496,11 @@ struct isl_set *isl_set_from_map(struct isl_map *map)
        map = isl_map_cow(map);
        if (!map)
                return NULL;
-       map->n_out += map->n_in;
-       map->n_in = 0;
+       map->dim = isl_dim_cow(map->dim);
+       if (!map->dim)
+               goto error;
+       map->dim->n_out += map->dim->n_in;
+       map->dim->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]);
@@ -2611,74 +2513,164 @@ 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_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
 {
        struct isl_map *map;
 
-       map = isl_alloc(ctx, struct isl_map,
+       if (!dim)
+               return NULL;
+       isl_assert(dim->ctx, n >= 0, return NULL);
+       map = isl_alloc(dim->ctx, struct isl_map,
                        sizeof(struct isl_map) +
                        n * sizeof(struct isl_basic_map *));
        if (!map)
+               goto error;
+
+       map->ctx = dim->ctx;
+       isl_ctx_ref(map->ctx);
+       map->ref = 1;
+       map->size = n;
+       map->n = 0;
+       map->dim = dim;
+       map->flags = flags;
+       return map;
+error:
+       isl_dim_free(dim);
+       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;
+       struct isl_dim *dims;
+
+       dims = isl_dim_alloc(ctx, nparam, in, out);
+       if (!dims)
                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;
-       return map;
+       map = isl_map_alloc_dim(dims, n, flags);
+       return map;
+}
+
+struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
+               unsigned nparam, unsigned in, unsigned out)
+{
+       struct isl_basic_map *bmap;
+       bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
+       bmap = isl_basic_map_set_to_empty(bmap);
+       return bmap;
+}
+
+struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
+{
+       struct isl_basic_set *bset;
+       bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
+       bset = isl_basic_set_set_to_empty(bset);
+       return bset;
+}
+
+struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
+{
+       struct isl_basic_map *bmap;
+       if (!model)
+               return NULL;
+       bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
+       bmap = isl_basic_map_set_to_empty(bmap);
+       return bmap;
 }
 
-struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
-               unsigned nparam, unsigned in, unsigned out)
+struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
 {
        struct isl_basic_map *bmap;
-       bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
+       if (!model)
+               return NULL;
+       bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
        bmap = isl_basic_map_set_to_empty(bmap);
        return bmap;
 }
 
-struct isl_basic_set *isl_basic_set_empty(struct isl_ctx *ctx,
-               unsigned nparam, unsigned dim)
+struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
 {
        struct isl_basic_set *bset;
-       bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 1, 0);
+       if (!model)
+               return NULL;
+       bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
        bset = isl_basic_set_set_to_empty(bset);
        return bset;
 }
 
-struct isl_basic_map *isl_basic_map_universe(struct isl_ctx *ctx,
-               unsigned nparam, unsigned in, unsigned out)
+struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
 {
        struct isl_basic_map *bmap;
-       bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 0, 0);
+       bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
        return bmap;
 }
 
-struct isl_basic_set *isl_basic_set_universe(struct isl_ctx *ctx,
-               unsigned nparam, unsigned dim)
+struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
 {
        struct isl_basic_set *bset;
-       bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 0, 0);
+       bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
        return bset;
 }
 
-struct isl_map *isl_map_empty(struct isl_ctx *ctx,
-               unsigned nparam, unsigned in, unsigned out)
+struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
 {
-       return isl_map_alloc(ctx, nparam, in, out, 0, ISL_MAP_DISJOINT);
+       if (!model)
+               return NULL;
+       return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
 }
 
-struct isl_set *isl_set_empty(struct isl_ctx *ctx,
-               unsigned nparam, unsigned dim)
+struct isl_map *isl_map_empty(struct isl_dim *dim)
+{
+       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)
+{
+       if (!model)
+               return NULL;
+       return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
+}
+
+struct isl_set *isl_set_empty(struct isl_dim *dim)
+{
+       return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
+}
+
+struct isl_set *isl_set_empty_like(struct isl_set *model)
+{
+       if (!model)
+               return NULL;
+       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)
 {
-       return isl_set_alloc(ctx, nparam, dim, 0, ISL_MAP_DISJOINT);
+       struct isl_set *set;
+       if (!dim)
+               return NULL;
+       set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
+       set = isl_set_add(set, isl_basic_set_universe(dim));
+       return set;
 }
 
 struct isl_map *isl_map_dup(struct isl_map *map)
@@ -2688,11 +2680,9 @@ struct isl_map *isl_map_dup(struct isl_map *map)
 
        if (!map)
                return NULL;
-       dup = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out, map->n,
-                               map->flags);
+       dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
        for (i = 0; i < map->n; ++i)
-               dup = isl_map_add(dup,
-                                 isl_basic_map_dup(map->p[i]));
+               dup = isl_map_add(dup, isl_basic_map_copy(map->p[i]));
        return dup;
 }
 
@@ -2700,13 +2690,11 @@ struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
 {
        if (!bmap || !map)
                goto error;
-       isl_assert(map->ctx, map->nparam == bmap->nparam, goto error);
-       isl_assert(map->ctx, map->n_in == bmap->n_in, goto error);
-       isl_assert(map->ctx, map->n_out == bmap->n_out, goto error);
+       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)
@@ -2729,6 +2717,7 @@ void isl_map_free(struct isl_map *map)
        isl_ctx_deref(map->ctx);
        for (i = 0; i < map->n; ++i)
                isl_basic_map_free(map->p[i]);
+       isl_dim_free(map->dim);
        free(map);
 }
 
@@ -2741,15 +2730,12 @@ struct isl_map *isl_map_extend(struct isl_map *base,
        if (!base)
                return NULL;
 
-       isl_assert(base->ctx, base->nparam <= nparam, goto error);
-       isl_assert(base->ctx, base->n_in <= n_in, goto error);
-       isl_assert(base->ctx, base->n_out <= n_out, goto error);
-       base->nparam = nparam;
-       base->n_in = n_in;
-       base->n_out = n_out;
+       base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
+       if (!base->dim)
+               goto error;
        for (i = 0; i < base->n; ++i) {
-               base->p[i] = isl_basic_map_extend(base->p[i],
-                               nparam, n_in, n_out, 0, 0, 0);
+               base->p[i] = isl_basic_map_extend_dim(base->p[i],
+                               isl_dim_copy(base->dim), 0, 0, 0);
                if (!base->p[i])
                        goto error;
        }
@@ -2766,20 +2752,18 @@ struct isl_set *isl_set_extend(struct isl_set *base,
                                                        nparam, 0, dim);
 }
 
-static struct isl_basic_map *isl_basic_map_fix_var(struct isl_basic_map *bmap,
-               unsigned var, int value)
+static struct isl_basic_map *isl_basic_map_fix_pos(struct isl_basic_map *bmap,
+               unsigned pos, int value)
 {
        int j;
 
        bmap = isl_basic_map_cow(bmap);
-       bmap = isl_basic_map_extend(bmap,
-                       bmap->nparam, bmap->n_in, bmap->n_out, 0, 1, 0);
+       bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
        j = isl_basic_map_alloc_equality(bmap);
        if (j < 0)
                goto error;
-       isl_seq_clr(bmap->eq[j],
-                   1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
-       isl_int_set_si(bmap->eq[j][1 + var], -1);
+       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);
        return isl_basic_map_finalize(bmap);
@@ -2788,34 +2772,43 @@ error:
        return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
-               unsigned input, int value)
+struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
+               enum isl_dim_type type, unsigned pos, int value)
 {
        if (!bmap)
                return NULL;
-       isl_assert(bmap->ctx, input < bmap->n_in, goto error);
-       return isl_basic_map_fix_var(bmap, bmap->nparam + input, value);
+       isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
+       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)
+{
+       return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
+}
+
 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
                unsigned dim, int value)
 {
-       if (!bset)
-               return NULL;
-       isl_assert(bset->ctx, dim < bset->dim, goto error);
        return (struct isl_basic_set *)
-               isl_basic_map_fix_var((struct isl_basic_map *)bset,
-                                               bset->nparam + dim, value);
-error:
-       isl_basic_set_free(bset);
-       return NULL;
+               isl_basic_map_fix_si((struct isl_basic_map *)bset,
+                                       isl_dim_set, dim, value);
 }
 
-struct isl_map *isl_map_fix_input_si(struct isl_map *map,
-               unsigned input, int value)
+struct isl_map *isl_map_fix_si(struct isl_map *map,
+               enum isl_dim_type type, unsigned pos, int value)
 {
        int i;
 
@@ -2823,51 +2816,44 @@ struct isl_map *isl_map_fix_input_si(struct isl_map *map,
        if (!map)
                return NULL;
 
-       isl_assert(ctx, input < map->n_in, goto error);
+       isl_assert(ctx, pos < isl_map_dim(map, type), goto error);
        for (i = 0; i < map->n; ++i) {
-               map->p[i] = isl_basic_map_fix_input_si(map->p[i], input, value);
+               map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
                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_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
+struct isl_map *isl_map_fix_input_si(struct isl_map *map,
+               unsigned input, int value)
 {
-       int i;
-
-       set = isl_set_cow(set);
-       if (!set)
-               return NULL;
+       return isl_map_fix_si(map, isl_dim_in, input, value);
+}
 
-       isl_assert(set->ctx, dim < set->dim, goto error);
-       for (i = 0; i < set->n; ++i) {
-               set->p[i] = isl_basic_set_fix_dim_si(set->p[i], dim, value);
-               if (!set->p[i])
-                       goto error;
-       }
-       return set;
-error:
-       isl_set_free(set);
-       return NULL;
+struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
+{
+       return (struct isl_set *)
+               isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
 }
 
 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
        unsigned dim, isl_int value)
 {
        int j;
+       unsigned nparam;
 
        bset = isl_basic_set_cow(bset);
-       bset = isl_basic_set_extend(bset, bset->nparam, bset->dim, 0, 0, 1);
+       bset = isl_basic_set_extend_constraints(bset, 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_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
+       isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
        isl_int_neg(bset->ineq[j][0], value);
        bset = isl_basic_set_simplify(bset);
        return isl_basic_set_finalize(bset);
@@ -2885,7 +2871,7 @@ struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
        if (!set)
                return NULL;
 
-       isl_assert(set->ctx, dim < set->dim, goto error);
+       isl_assert(set->ctx, dim < isl_set_n_dim(set), 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])
@@ -2906,15 +2892,15 @@ struct isl_map *isl_map_reverse(struct isl_map *map)
        if (!map)
                return NULL;
 
-       t = map->n_in;
-       map->n_in = map->n_out;
-       map->n_out = t;
+       map->dim = isl_dim_reverse(map->dim);
+       if (!map->dim)
+               goto error;
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_reverse(map->p[i]);
                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);
@@ -2940,13 +2926,15 @@ struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
        struct isl_basic_map *bmap = NULL;
        struct isl_basic_set *dom = NULL;
        struct isl_map *min;
+       struct isl_dim *param_dim;
 
        if (!bset)
                goto error;
-       bmap = isl_basic_map_from_basic_set(bset, 0, bset->dim);
+       bmap = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
        if (!bmap)
                goto error;
-       dom = isl_basic_set_alloc(bmap->ctx, bmap->nparam, 0, 0, 0, 0);
+       param_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
+       dom = isl_basic_set_universe(param_dim);
        if (!dom)
                goto error;
        min = isl_basic_map_lexmin(bmap, dom, NULL);
@@ -2956,13 +2944,40 @@ error:
        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;
-       if (bmap->n_div == 0)
+       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);
-       return isl_pip_basic_map_compute_divs(bmap);
+       struct isl_map *map = isl_pip_basic_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)
@@ -2978,7 +2993,7 @@ struct isl_map *isl_map_compute_divs(struct isl_map *map)
        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))
+               if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
                        res = isl_map_union_disjoint(res, r2);
                else
                        res = isl_map_union(res, r2);
@@ -3013,15 +3028,16 @@ struct isl_set *isl_map_domain(struct isl_map *map)
                return NULL;
 
        set = (struct isl_set *)map;
-       set->dim = map->n_in;
-       set->zero = 0;
+       set->dim = isl_dim_domain(set->dim);
+       if (!set->dim)
+               goto error;
        for (i = 0; i < map->n; ++i) {
                set->p[i] = isl_basic_map_domain(map->p[i]);
                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);
@@ -3047,15 +3063,13 @@ struct isl_map *isl_map_union_disjoint(
                return map1;
        }
 
-       isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
-       isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
-       isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
+       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(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
+       map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
                                map1->n + map2->n, flags);
        if (!map)
                goto error;
@@ -3087,7 +3101,7 @@ 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;
 }
 
@@ -3115,12 +3129,12 @@ 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(map->ctx, map->nparam, map->n_in, map->n_out,
-                               map->n * set->n, flags);
+       result = isl_map_alloc_dim(isl_dim_copy(map->dim),
+                                       map->n * set->n, flags);
        if (!result)
                goto error;
        for (i = 0; i < map->n; ++i)
@@ -3165,17 +3179,20 @@ error:
 struct isl_map *isl_map_apply_range(
                struct isl_map *map1, struct isl_map *map2)
 {
+       struct isl_dim *dim_result;
        struct isl_map *result;
        int i, j;
+       unsigned nparam;
+       unsigned n_in;
+       unsigned n_out;
 
        if (!map1 || !map2)
                goto error;
 
-       isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
-       isl_assert(map1->ctx, map1->n_out == map2->n_in, goto error);
+       dim_result = isl_dim_join(isl_dim_copy(map1->dim),
+                                 isl_dim_copy(map2->dim));
 
-       result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map2->n_out,
-                               map1->n * map2->n, 0);
+       result = isl_map_alloc_dim(dim_result, map1->n * map2->n, 0);
        if (!result)
                goto error;
        for (i = 0; i < map1->n; ++i)
@@ -3190,7 +3207,7 @@ 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);
@@ -3205,26 +3222,27 @@ struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
 {
        struct isl_basic_set *bset;
        unsigned dim;
+       unsigned nparam;
        int i;
 
        if (!bmap)
                goto error;
-       isl_assert(bmap->ctx, bmap->n_in == bmap->n_out, goto error);
-       dim = bmap->n_in;
+       dim = isl_basic_map_n_in(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_extend(bset, bset->nparam, 3*dim, 0,
-                                       dim, 0);
+       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) {
                int j = isl_basic_map_alloc_equality(
                                            (struct isl_basic_map *)bset);
                if (j < 0)
                        goto error;
-               isl_seq_clr(bset->eq[j],
-                           1 + bset->nparam + bset->dim + bset->extra);
-               isl_int_set_si(bset->eq[j][1+bset->nparam+i], 1);
-               isl_int_set_si(bset->eq[j][1+bset->nparam+dim+i], 1);
-               isl_int_set_si(bset->eq[j][1+bset->nparam+2*dim+i], -1);
+               isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
+               isl_int_set_si(bset->eq[j][1+nparam+i], 1);
+               isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
+               isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
        }
        return isl_basic_set_project_out(bset, 2*dim, 0);
 error:
@@ -3243,8 +3261,9 @@ struct isl_set *isl_map_deltas(struct isl_map *map)
        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);
+       isl_assert(map->ctx, isl_map_n_in(map) == isl_map_n_out(map), goto error);
+       result = isl_set_alloc(map->ctx, isl_map_n_param(map),
+                                       isl_map_n_in(map), map->n, map->flags);
        if (!result)
                goto error;
        for (i = 0; i < map->n; ++i)
@@ -3257,165 +3276,74 @@ error:
        return NULL;
 }
 
-/* If the only constraints a div d=floor(f/m)
- * appears in are its two defining constraints
- *
- *     f - m d >=0
- *     -(f - (m - 1)) + m d >= 0
- *
- * then it can safely be removed.
- */
-static int div_is_redundant(struct isl_basic_map *bmap, int div)
+static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
 {
+       struct isl_basic_map *bmap;
+       unsigned nparam;
+       unsigned dim;
        int i;
-       unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
-
-       for (i = 0; i < bmap->n_eq; ++i)
-               if (!isl_int_is_zero(bmap->eq[i][pos]))
-                       return 0;
-
-       for (i = 0; i < bmap->n_ineq; ++i) {
-               if (isl_int_is_zero(bmap->ineq[i][pos]))
-                       continue;
-               if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
-                       int neg;
-                       isl_int_sub(bmap->div[div][1],
-                                       bmap->div[div][1], bmap->div[div][0]);
-                       isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
-                       neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
-                       isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
-                       isl_int_add(bmap->div[div][1],
-                                       bmap->div[div][1], bmap->div[div][0]);
-                       if (!neg)
-                               return 0;
-                       if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
-                                                   bmap->n_div-div-1) != -1)
-                               return 0;
-               } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
-                       if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
-                               return 0;
-                       if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
-                                                   bmap->n_div-div-1) != -1)
-                               return 0;
-               } else
-                       return 0;
-       }
-
-       for (i = 0; i < bmap->n_div; ++i)
-               if (!isl_int_is_zero(bmap->div[i][1+pos]))
-                       return 0;
-
-       return 1;
-}
 
-/*
- * Remove divs that don't occur in any of the constraints or other divs.
- * These can arise when dropping some of the variables in a quast
- * returned by piplib.
- */
-static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
-{
-       int i;
+       if (!dims)
+               return NULL;
 
+       nparam = dims->nparam;
+       dim = dims->n_out;
+       bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
        if (!bmap)
-               return NULL;
+               goto error;
 
-       for (i = bmap->n_div-1; i >= 0; --i) {
-               if (!div_is_redundant(bmap, i))
-                       continue;
-               bmap = isl_basic_map_drop_div(bmap, i);
+       for (i = 0; i < dim; ++i) {
+               int 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_int_set_si(bmap->eq[j][1+nparam+i], 1);
+               isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
        }
-       return bmap;
+       return isl_basic_map_finalize(bmap);
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
+struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
 {
-       bmap = remove_redundant_divs(bmap);
-       if (!bmap)
+       struct isl_dim *dim = isl_dim_map(set_dim);
+       if (!dim)
                return NULL;
-       F_SET(bmap, ISL_BASIC_SET_FINAL);
-       return bmap;
-}
-
-struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
-{
-       return (struct isl_basic_set *)
-               isl_basic_map_finalize((struct isl_basic_map *)bset);
+       return basic_map_identity(dim);
 }
 
-struct isl_set *isl_set_finalize(struct isl_set *set)
+struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
 {
-       int i;
-
-       if (!set)
+       if (!model || !model->dim)
                return NULL;
-       for (i = 0; i < set->n; ++i) {
-               set->p[i] = isl_basic_set_finalize(set->p[i]);
-               if (!set->p[i])
-                       goto error;
-       }
-       return set;
-error:
-       isl_set_free(set);
-       return NULL;
+       isl_assert(model->ctx,
+                       model->dim->n_in == model->dim->n_out, return NULL);
+       return basic_map_identity(isl_dim_copy(model->dim));
 }
 
-struct isl_map *isl_map_finalize(struct isl_map *map)
+static struct isl_map *map_identity(struct isl_dim *dim)
 {
-       int i;
-
-       if (!map)
-               return NULL;
-       for (i = 0; i < map->n; ++i) {
-               map->p[i] = isl_basic_map_finalize(map->p[i]);
-               if (!map->p[i])
-                       goto error;
-       }
-       F_CLR(map, ISL_MAP_NORMALIZED);
-       return map;
-error:
-       isl_map_free(map);
-       return NULL;
+       struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
+       return isl_map_add(map, basic_map_identity(isl_dim_copy(dim)));
 }
 
-struct isl_basic_map *isl_basic_map_identity(struct isl_ctx *ctx,
-               unsigned nparam, unsigned dim)
+struct isl_map *isl_map_identity(struct isl_dim *set_dim)
 {
-       struct isl_basic_map *bmap;
-       int i;
-
-       bmap = isl_basic_map_alloc(ctx, nparam, dim, dim, 0, dim, 0);
-       if (!bmap)
-               goto error;
-
-       for (i = 0; i < dim; ++i) {
-               int j = isl_basic_map_alloc_equality(bmap);
-               if (j < 0)
-                       goto error;
-               isl_seq_clr(bmap->eq[j],
-                   1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
-               isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
-               isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
-       }
-       return isl_basic_map_finalize(bmap);
-error:
-       isl_basic_map_free(bmap);
-       return NULL;
+       struct isl_dim *dim = isl_dim_map(set_dim);
+       if (!dim)
+               return NULL;
+       return map_identity(dim);
 }
 
-struct isl_map *isl_map_identity(struct isl_ctx *ctx,
-               unsigned nparam, unsigned dim)
+struct isl_map *isl_map_identity_like(struct isl_basic_map *model)
 {
-       struct isl_map *map = isl_map_alloc(ctx, nparam, dim, dim, 1,
-                                               ISL_MAP_DISJOINT);
-       if (!map)
-               goto error;
-       map = isl_map_add(map,
-               isl_basic_map_identity(ctx, nparam, dim));
-       return map;
-error:
-       isl_map_free(map);
-       return NULL;
+       if (!model || !model->dim)
+               return NULL;
+       isl_assert(model->ctx,
+                       model->dim->n_in == model->dim->n_out, return NULL);
+       return map_identity(isl_dim_copy(model->dim));
 }
 
 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
@@ -3488,6 +3416,11 @@ 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);
@@ -3547,44 +3480,18 @@ 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 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-       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)
@@ -3597,18 +3504,18 @@ 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;
        }
 
-       total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       total = 1 + isl_basic_map_total_dim(bmap);
        if (bmap->sample && bmap->sample->size == total) {
                int contains = basic_map_contains(bmap, bmap->sample);
                if (contains < 0)
@@ -3616,18 +3523,40 @@ 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;
-       sample = isl_basic_set_sample(bset);
-       if (!sample)
+       sample = isl_basic_set_sample(bset);
+       if (!sample)
+               return -1;
+       empty = sample->size == 0;
+       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;
-       empty = sample->size == 0;
-       if (bmap->sample)
-               isl_vec_free(bmap->ctx, bmap->sample);
-       bmap->sample = sample;
+       return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
+}
 
-       return empty;
+int isl_basic_set_is_empty(struct isl_basic_set *bset)
+{
+       return isl_basic_map_is_empty((struct isl_basic_map *)bset);
 }
 
 struct isl_map *isl_basic_map_union(
@@ -3637,12 +3566,9 @@ struct isl_map *isl_basic_map_union(
        if (!bmap1 || !bmap2)
                return NULL;
 
-       isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
-       isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
-       isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
+       isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
 
-       map = isl_map_alloc(bmap1->ctx, bmap1->nparam,
-                               bmap1->n_in, bmap1->n_out, 2, 0);
+       map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
        if (!map)
                goto error;
        map = isl_map_add(map, bmap1);
@@ -3666,7 +3592,7 @@ struct isl_set *isl_basic_set_union(
 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
 {
        int i;
-       unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
+       unsigned off = isl_dim_total(bmap->dim);
 
        for (i = 0; i < bmap->n_div; ++i) {
                int pos;
@@ -3674,23 +3600,30 @@ 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);
+               swap_div(bmap, i, i + pos);
                --i;
        }
        return bmap;
 }
 
+/* Look for a div in dst that corresponds to the div "div" in src.
+ * The divs before "div" in src and dst are assumed to be the same.
+ * 
+ * Returns -1 if no corresponding div was found and the position
+ * of the corresponding div in dst otherwise.
+ */
 static int find_div(struct isl_basic_map *dst,
                        struct isl_basic_map *src, unsigned div)
 {
        int i;
 
-       unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
+       unsigned total = isl_dim_total(src->dim);
 
-       for (i = 0; i < dst->n_div; ++i)
-               if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total) &&
-                   isl_seq_first_non_zero(dst->div[i]+1+1+total,
-                                               dst->n_div - src->n_div) == -1)
+       isl_assert(dst->ctx, div <= dst->n_div, return -1);
+       for (i = div; i < dst->n_div; ++i)
+               if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
+                   isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
+                                               dst->n_div - div) == -1)
                        return i;
        return -1;
 }
@@ -3699,7 +3632,7 @@ struct isl_basic_map *isl_basic_map_align_divs(
                struct isl_basic_map *dst, struct isl_basic_map *src)
 {
        int i;
-       unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
+       unsigned total = isl_dim_total(src->dim);
 
        if (!dst || !src)
                goto error;
@@ -3707,9 +3640,13 @@ struct isl_basic_map *isl_basic_map_align_divs(
        if (src->n_div == 0)
                return dst;
 
+       for (i = 0; i < src->n_div; ++i)
+               isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
+
        src = order_divs(src);
-       dst = isl_basic_map_extend(dst, dst->nparam, dst->n_in,
-                       dst->n_out, src->n_div, 0, 2 * src->n_div);
+       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)
                return NULL;
        for (i = 0; i < src->n_div; ++i) {
@@ -3718,9 +3655,8 @@ struct isl_basic_map *isl_basic_map_align_divs(
                        j = isl_basic_map_alloc_div(dst);
                        if (j < 0)
                                goto error;
-                       isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
-                       isl_seq_clr(dst->div[j]+1+1+total,
-                                                   dst->extra - src->n_div);
+                       isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
+                       isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
                        if (add_div_constraints(dst, j) < 0)
                                goto error;
                }
@@ -3754,10 +3690,15 @@ 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)
@@ -3771,8 +3712,7 @@ static struct isl_map *add_cut_constraint(struct isl_map *dst,
        copy = isl_basic_map_cow(copy);
        if (!copy)
                goto error;
-       copy = isl_basic_map_extend(copy,
-               copy->nparam, copy->n_in, copy->n_out, 0, 0, 1);
+       copy = isl_basic_map_extend_constraints(copy, 0, 1);
        k = isl_basic_map_alloc_inequality(copy);
        if (k < 0)
                goto error;
@@ -3780,7 +3720,7 @@ static struct isl_map *add_cut_constraint(struct isl_map *dst,
                isl_seq_neg(copy->ineq[k], c, len);
        else
                isl_seq_cpy(copy->ineq[k], c, len);
-       total = 1 + copy->nparam + copy->n_in + copy->n_out + copy->extra;
+       total = 1 + isl_basic_map_total_dim(copy);
        isl_seq_clr(copy->ineq[k]+len, total - len);
        isl_inequality_negate(copy, k);
        copy = isl_basic_map_simplify(copy);
@@ -3805,19 +3745,18 @@ static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
        unsigned flags = 0;
        struct isl_map *rest = NULL;
        unsigned max;
-       unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       unsigned total = isl_basic_map_total_dim(bmap);
 
        assert(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(map->ctx, map->nparam, map->n_in, map->n_out,
-                               max, flags);
+       rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
        if (!rest)
                goto error;
 
@@ -3842,9 +3781,8 @@ static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
                        if (!rest)
                                goto error;
 
-                       map->p[j] = isl_basic_map_extend(map->p[j],
-                               map->p[j]->nparam, map->p[j]->n_in,
-                               map->p[j]->n_out, 0, 1, 0);
+                       map->p[j] = isl_basic_map_extend_constraints(map->p[j],
+                               1, 0);
                        if (!map->p[j])
                                goto error;
                        k = isl_basic_map_alloc_equality(map->p[j]);
@@ -3852,7 +3790,7 @@ static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
                                goto error;
                        isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
                        isl_seq_clr(map->p[j]->eq[k]+1+total,
-                                       map->p[j]->extra - bmap->n_div);
+                                       map->p[j]->n_div - bmap->n_div);
                }
        }
 
@@ -3863,9 +3801,8 @@ static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
                        if (!rest)
                                goto error;
 
-                       map->p[j] = isl_basic_map_extend(map->p[j],
-                               map->p[j]->nparam, map->p[j]->n_in,
-                               map->p[j]->n_out, 0, 0, 1);
+                       map->p[j] = isl_basic_map_extend_constraints(map->p[j],
+                               0, 1);
                        if (!map->p[j])
                                goto error;
                        k = isl_basic_map_alloc_inequality(map->p[j]);
@@ -3873,7 +3810,7 @@ static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
                                goto error;
                        isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
                        isl_seq_clr(map->p[j]->ineq[k]+1+total,
-                                       map->p[j]->extra - bmap->n_div);
+                                       map->p[j]->n_div - bmap->n_div);
                }
        }
 
@@ -3891,9 +3828,7 @@ struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
        if (!map1 || !map2)
                goto error;
 
-       isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
-       isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
-       isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
+       isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
 
        if (isl_map_is_empty(map2)) {
                isl_map_free(map2);
@@ -3927,7 +3862,7 @@ struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
 {
        if (!set || !map)
                goto error;
-       isl_assert(set->ctx, set->dim == map->n_in, goto error);
+       isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
        map = isl_map_intersect_domain(map, set);
        set = isl_map_range(map);
        return set;
@@ -3948,11 +3883,11 @@ 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--;
@@ -3967,49 +3902,61 @@ 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
- * smaller or larger then those in bset2.
+ * smaller or larger than those in bset2.
  *
  * Returns
  *      1 if bset1 follows bset2
@@ -4020,11 +3967,14 @@ error:
 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
        struct isl_basic_set *bset2, int pos)
 {
+       struct isl_dim *dims;
        struct isl_basic_map *bmap1 = NULL;
        struct isl_basic_map *bmap2 = NULL;
        struct isl_ctx *ctx;
        struct isl_vec *obj;
        unsigned total;
+       unsigned nparam;
+       unsigned dim1, dim2;
        isl_int num, den;
        enum isl_lp_result res;
        int cmp;
@@ -4032,27 +3982,30 @@ int isl_basic_set_compare_at(struct isl_basic_set *bset1,
        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);
+       nparam = isl_basic_set_n_param(bset1);
+       dim1 = isl_basic_set_n_dim(bset1);
+       dim2 = isl_basic_set_n_dim(bset2);
+       dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
+       bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
+       dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
+       bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
        if (!bmap1 || !bmap2)
                goto error;
-       bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
-                       bmap1->n_in, bmap1->n_out + bmap2->n_out,
+       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);
+       bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
        if (!bmap1)
                goto error;
-       total = bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
+       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[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);
+       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;
-       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);
@@ -4068,7 +4021,7 @@ 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);
@@ -4085,7 +4038,7 @@ static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
 
        if (!bmap)
                return -1;
-       total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       total = isl_basic_map_total_dim(bmap);
        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]))
@@ -4140,12 +4093,21 @@ static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
        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_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);
+       return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
 }
 
 /* Check if input variable in has fixed value and if so and if val is not NULL,
@@ -4153,7 +4115,7 @@ int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *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);
+       return isl_map_fast_has_fixed_var(map, isl_map_n_param(map) + in, val);
 }
 
 /* Check if dimension dim has an (obvious) fixed lower bound and if so
@@ -4165,19 +4127,21 @@ int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
        int i, i_eq = -1, i_ineq = -1;
        isl_int *c;
        unsigned total;
+       unsigned nparam;
 
        if (!bset)
                return -1;
-       total = bset->nparam + bset->dim + bset->n_div;
+       total = isl_basic_set_total_dim(bset);
+       nparam = isl_basic_set_n_param(bset);
        for (i = 0; i < bset->n_eq; ++i) {
-               if (isl_int_is_zero(bset->eq[i][1+bset->nparam+dim]))
+               if (isl_int_is_zero(bset->eq[i][1+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]))
+               if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
                        continue;
                if (i_eq != -1 || i_ineq != -1)
                        return 0;
@@ -4187,12 +4151,12 @@ int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
                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]))
+       if (!isl_int_is_one(c[1+nparam+dim]))
                return 0;
-       if (isl_seq_first_non_zero(c+1, bset->nparam+dim) != -1)
+       if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
                return 0;
-       if (isl_seq_first_non_zero(c+1+bset->nparam+dim+1,
-                                       total - bset->nparam - dim - 1) != -1)
+       if (isl_seq_first_non_zero(c+1+nparam+dim+1,
+                                       total - nparam - dim - 1) != -1)
                return 0;
        if (val)
                isl_int_neg(*val, c[0]);
@@ -4231,212 +4195,6 @@ int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
        return fixed;
 }
 
-static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
-       struct isl_basic_set *bset, struct isl_basic_set *context)
-{
-       int i;
-       int *elim;
-
-       if (!bset || !context)
-               goto error;
-
-       bset = isl_basic_set_cow(bset);
-       if (!bset)
-               goto error;
-
-       elim = isl_alloc_array(ctx, int, bset->dim);
-       if (!elim)
-               goto error;
-       set_compute_elimination_index(context, elim);
-       for (i = 0; i < bset->n_eq; ++i)
-               set_reduced_using_equalities(bset->eq[i], bset->eq[i],
-                                                       context, elim);
-       for (i = 0; i < bset->n_ineq; ++i)
-               set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
-                                                       context, elim);
-       isl_basic_set_free(context);
-       free(elim);
-       bset = isl_basic_set_simplify(bset);
-       bset = isl_basic_set_finalize(bset);
-       return bset;
-error:
-       isl_basic_set_free(bset);
-       isl_basic_set_free(context);
-       return NULL;
-}
-
-static struct isl_basic_set *remove_shifted_constraints(
-       struct isl_basic_set *bset, struct isl_basic_set *context)
-{
-       unsigned int size;
-       isl_int ***index;
-       int bits;
-       int k, h, l;
-
-       if (!bset)
-               return NULL;
-
-       size = round_up(4 * (context->n_ineq+1) / 3 - 1);
-       bits = ffs(size) - 1;
-       index = isl_alloc_array(ctx, isl_int **, size);
-       memset(index, 0, size * sizeof(isl_int **));
-       if (!index)
-               return bset;
-
-       for (k = 0; k < context->n_ineq; ++k) {
-               h = set_hash_index(index, size, bits, context, k);
-               index[h] = &context->ineq[k];
-       }
-       for (k = 0; k < bset->n_ineq; ++k) {
-               h = set_hash_index(index, size, bits, bset, k);
-               if (!index[h])
-                       continue;
-               l = index[h] - &context->ineq[0];
-               if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
-                       continue;
-               bset = isl_basic_set_cow(bset);
-               if (!bset)
-                       goto error;
-               isl_basic_set_drop_inequality(bset, k);
-               --k;
-       }
-       free(index);
-       return bset;
-error:
-       free(index);
-       return bset;
-}
-
-/* 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;
-               struct isl_basic_set *reduced_context;
-               reduced_context = isl_basic_set_remove_equalities(
-                                       isl_basic_set_copy(context), &T, &T2);
-               if (!reduced_context)
-                       goto error;
-               bset = isl_basic_set_preimage(ctx, bset, T);
-               bset = uset_gist(bset, reduced_context);
-               bset = isl_basic_set_preimage(ctx, bset, T2);
-               bset = isl_basic_set_reduce_using_equalities(bset, context);
-               return bset;
-       }
-       if (!context->n_ineq)
-               goto done;
-       bset = remove_shifted_constraints(bset, context);
-       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;
-done:
-       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;
@@ -4459,7 +4217,7 @@ static struct isl_basic_map *isl_basic_map_sort_constraints(
 
        if (!bmap)
                return NULL;
-       total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       total = isl_basic_map_total_dim(bmap);
        c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
        if (!c)
                goto error;
@@ -4481,14 +4239,20 @@ 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;
 }
 
+struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
+{
+       return (struct isl_basic_set *)isl_basic_map_normalize(
+                                               (struct isl_basic_map *)bset);
+}
+
 static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
        const struct isl_basic_map *bmap2)
 {
@@ -4497,18 +4261,18 @@ static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
 
        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))
+       if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
+               return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
+       if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
+               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 (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;
@@ -4516,7 +4280,7 @@ static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
                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;
+       total = isl_basic_map_total_dim(bmap1);
        for (i = 0; i < bmap1->n_eq; ++i) {
                cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
                if (cmp)
@@ -4560,7 +4324,7 @@ 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]));
@@ -4570,7 +4334,7 @@ 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;
@@ -4604,11 +4368,7 @@ int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
 
        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)
+       if (!isl_dim_equal(map1->dim, map2->dim))
                return 0;
 
        map1 = isl_map_copy(map1);
@@ -4684,15 +4444,16 @@ struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *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;
+       nparam = isl_basic_set_n_param(list->p[0]);
+       dim = isl_basic_set_n_dim(list->p[0]);
        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;
+               isl_assert(list->ctx,
+                   nparam == isl_basic_set_n_param(list->p[i]), goto error);
+               dim += isl_basic_set_n_dim(list->p[i]);
                extra += list->p[i]->n_div;
                n_eq += list->p[i]->n_eq;
                n_ineq += list->p[i]->n_ineq;
@@ -4703,9 +4464,9 @@ struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
                goto error;
        dim = 0;
        for (i = 0; i < list->n; ++i) {
-               set_add_constraints(product,
+               isl_basic_set_add_constraints(product,
                                        isl_basic_set_copy(list->p[i]), dim);
-               dim += list->p[i]->dim;
+               dim += isl_basic_set_n_dim(list->p[i]);
        }
        isl_basic_set_list_free(list);
        return product;
@@ -4714,3 +4475,204 @@ error:
        isl_basic_set_list_free(list);
        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;
+       uint32_t hash;
+       unsigned total;
+
+       if (!bset)
+               return 0;
+       bset = isl_basic_set_copy(bset);
+       bset = isl_basic_set_normalize(bset);
+       if (!bset)
+               return 0;
+       total = isl_basic_set_total_dim(bset);
+       isl_hash_byte(hash, bset->n_eq & 0xFF);
+       for (i = 0; i < bset->n_eq; ++i) {
+               uint32_t c_hash;
+               c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
+               isl_hash_hash(hash, c_hash);
+       }
+       isl_hash_byte(hash, bset->n_ineq & 0xFF);
+       for (i = 0; i < bset->n_ineq; ++i) {
+               uint32_t c_hash;
+               c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
+               isl_hash_hash(hash, c_hash);
+       }
+       isl_hash_byte(hash, bset->n_div & 0xFF);
+       for (i = 0; i < bset->n_div; ++i) {
+               uint32_t c_hash;
+               if (isl_int_is_zero(bset->div[i][0]))
+                       continue;
+               isl_hash_byte(hash, i & 0xFF);
+               c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
+               isl_hash_hash(hash, c_hash);
+       }
+       isl_basic_set_free(bset);
+       return hash;
+}
+
+uint32_t isl_set_get_hash(struct isl_set *set)
+{
+       int i;
+       uint32_t hash;
+
+       if (!set)
+               return 0;
+       set = isl_set_copy(set);
+       set = isl_set_normalize(set);
+       if (!set)
+               return 0;
+
+       hash = isl_hash_init();
+       for (i = 0; i < set->n; ++i) {
+               uint32_t bset_hash;
+               bset_hash = isl_basic_set_get_hash(set->p[i]);
+               isl_hash_hash(hash, bset_hash);
+       }
+               
+       isl_set_free(set);
+
+       return hash;
+}
+
+/* Check if the value for dimension dim is completely determined
+ * by the values of the other parameters and variables.
+ * That is, check if dimension dim is involved in an equality.
+ */
+int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
+{
+       int i;
+       unsigned nparam;
+
+       if (!bset)
+               return -1;
+       nparam = isl_basic_set_n_param(bset);
+       for (i = 0; i < bset->n_eq; ++i)
+               if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
+                       return 1;
+       return 0;
+}
+
+/* Check if the value for dimension dim is completely determined
+ * by the values of the other parameters and variables.
+ * That is, check if dimension dim is involved in an equality
+ * for each of the subsets.
+ */
+int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
+{
+       int i;
+
+       if (!set)
+               return -1;
+       for (i = 0; i < set->n; ++i) {
+               int unique;
+               unique = isl_basic_set_dim_is_unique(set->p[i], dim);
+               if (unique != 1)
+                       return unique;
+       }
+       return 1;
+}