add isl_basic_set_interval and isl_basic_set_product
[platform/upstream/isl.git] / isl_map.c
index 38308ae..eaeccb0 100644 (file)
--- a/isl_map.c
+++ b/isl_map.c
@@ -2,6 +2,9 @@
 #include <strings.h>
 #include "isl_ctx.h"
 #include "isl_blk.h"
+#include "isl_equalities.h"
+#include "isl_list.h"
+#include "isl_lp.h"
 #include "isl_seq.h"
 #include "isl_set.h"
 #include "isl_map.h"
@@ -59,6 +62,8 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
        for (i = 0; i < extra; ++i)
                bmap->div[i] = bmap->block2.data + i * (1 + row_size);
 
+       bmap->ctx = ctx;
+       isl_ctx_ref(ctx);
        bmap->ref = 1;
        bmap->flags = 0;
        bmap->c_size = n_eq + n_ineq;
@@ -98,55 +103,55 @@ struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
                               nparam, in, out, extra, n_eq, n_ineq);
 }
 
-static void dup_constraints(struct isl_ctx *ctx,
+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;
 
        for (i = 0; i < src->n_eq; ++i) {
-               int j = isl_basic_map_alloc_equality(ctx, dst);
+               int j = isl_basic_map_alloc_equality(dst);
                isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
        }
 
        for (i = 0; i < src->n_ineq; ++i) {
-               int j = isl_basic_map_alloc_inequality(ctx, dst);
+               int j = isl_basic_map_alloc_inequality(dst);
                isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
        }
 
        for (i = 0; i < src->n_div; ++i) {
-               int j = isl_basic_map_alloc_div(ctx, dst);
+               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);
 }
 
-struct isl_basic_map *isl_basic_map_dup(struct isl_ctx *ctx,
-                                       struct isl_basic_map *bmap)
+struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
 {
        struct isl_basic_map *dup;
 
-       dup = isl_basic_map_alloc(ctx, bmap->nparam,
+       if (!bmap)
+               return NULL;
+       dup = isl_basic_map_alloc(bmap->ctx, bmap->nparam,
                        bmap->n_in, bmap->n_out,
                        bmap->n_div, bmap->n_eq, bmap->n_ineq);
        if (!dup)
                return NULL;
-       dup_constraints(ctx, dup, bmap);
-       dup->sample = isl_vec_copy(ctx, bmap->sample);
+       dup->flags = bmap->flags;
+       dup_constraints(dup, bmap);
+       dup->sample = isl_vec_copy(bmap->ctx, bmap->sample);
        return dup;
 }
 
-struct isl_basic_set *isl_basic_set_dup(struct isl_ctx *ctx,
-                                       struct isl_basic_set *bset)
+struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
 {
        struct isl_basic_map *dup;
 
-       dup = isl_basic_map_dup(ctx, (struct isl_basic_map *)bset);
+       dup = isl_basic_map_dup((struct isl_basic_map *)bset);
        return (struct isl_basic_set *)dup;
 }
 
-struct isl_basic_set *isl_basic_set_copy(struct isl_ctx *ctx,
-                                       struct isl_basic_set *bset)
+struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
 {
        if (!bset)
                return NULL;
@@ -155,10 +160,10 @@ struct isl_basic_set *isl_basic_set_copy(struct isl_ctx *ctx,
                bset->ref++;
                return bset;
        }
-       return isl_basic_set_dup(ctx, bset);
+       return isl_basic_set_dup(bset);
 }
 
-struct isl_set *isl_set_copy(struct isl_ctx *ctx, struct isl_set *set)
+struct isl_set *isl_set_copy(struct isl_set *set)
 {
        if (!set)
                return NULL;
@@ -167,8 +172,7 @@ struct isl_set *isl_set_copy(struct isl_ctx *ctx, struct isl_set *set)
        return set;
 }
 
-struct isl_basic_map *isl_basic_map_copy(struct isl_ctx *ctx,
-                                       struct isl_basic_map *bmap)
+struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
 {
        if (!bmap)
                return NULL;
@@ -177,10 +181,10 @@ struct isl_basic_map *isl_basic_map_copy(struct isl_ctx *ctx,
                bmap->ref++;
                return bmap;
        }
-       return isl_basic_map_dup(ctx, bmap);
+       return isl_basic_map_dup(bmap);
 }
 
-struct isl_map *isl_map_copy(struct isl_ctx *ctx, struct isl_map *map)
+struct isl_map *isl_map_copy(struct isl_map *map)
 {
        if (!map)
                return NULL;
@@ -189,7 +193,7 @@ struct isl_map *isl_map_copy(struct isl_ctx *ctx, struct isl_map *map)
        return map;
 }
 
-void isl_basic_map_free(struct isl_ctx *ctx, struct isl_basic_map *bmap)
+void isl_basic_map_free(struct isl_basic_map *bmap)
 {
        if (!bmap)
                return;
@@ -197,29 +201,31 @@ void isl_basic_map_free(struct isl_ctx *ctx, struct isl_basic_map *bmap)
        if (--bmap->ref > 0)
                return;
 
+       isl_ctx_deref(bmap->ctx);
        free(bmap->div);
-       isl_blk_free(ctx, bmap->block2);
+       isl_blk_free(bmap->ctx, bmap->block2);
        free(bmap->eq);
-       isl_blk_free(ctx, bmap->block);
-       isl_vec_free(ctx, bmap->sample);
+       isl_blk_free(bmap->ctx, bmap->block);
+       isl_vec_free(bmap->ctx, bmap->sample);
        free(bmap);
 }
 
-void isl_basic_set_free(struct isl_ctx *ctx, struct isl_basic_set *bset)
+void isl_basic_set_free(struct isl_basic_set *bset)
 {
-       isl_basic_map_free(ctx, (struct isl_basic_map *)bset);
+       isl_basic_map_free((struct isl_basic_map *)bset);
 }
 
-int isl_basic_map_alloc_equality(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+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_int *t;
-               int j = isl_basic_map_alloc_inequality(ctx, bmap);
+               int j = isl_basic_map_alloc_inequality(bmap);
                if (j < 0)
                        return -1;
                t = bmap->ineq[0];
@@ -231,25 +237,26 @@ int isl_basic_map_alloc_equality(struct isl_ctx *ctx,
        return bmap->n_eq++;
 }
 
-int isl_basic_set_alloc_equality(struct isl_ctx *ctx,
-               struct isl_basic_set *bset)
+int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
 {
-       return isl_basic_map_alloc_equality(ctx, (struct isl_basic_map *)bset);
+       return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
 }
 
-int isl_basic_map_free_equality(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned n)
+int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
 {
-       isl_assert(ctx, n <= bmap->n_eq, return -1);
+       if (!bmap)
+               return -1;
+       isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
        bmap->n_eq -= n;
        return 0;
 }
 
-int isl_basic_map_drop_equality(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned pos)
+int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
 {
        isl_int *t;
-       isl_assert(ctx, pos < bmap->n_eq, return -1);
+       if (!bmap)
+               return -1;
+       isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
 
        if (pos != bmap->n_eq - 1) {
                t = bmap->eq[pos];
@@ -260,7 +267,12 @@ int isl_basic_map_drop_equality(struct isl_ctx *ctx,
        return 0;
 }
 
-void isl_basic_map_inequality_to_equality(struct isl_ctx *ctx,
+int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
+{
+       return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
+}
+
+void isl_basic_map_inequality_to_equality(
                struct isl_basic_map *bmap, unsigned pos)
 {
        isl_int *t;
@@ -272,57 +284,77 @@ void isl_basic_map_inequality_to_equality(struct isl_ctx *ctx,
        bmap->n_eq++;
        bmap->n_ineq--;
        bmap->ineq++;
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 }
 
-int isl_basic_map_alloc_inequality(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
 {
+       struct isl_ctx *ctx;
+       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);
        return bmap->n_ineq++;
 }
 
-int isl_basic_set_alloc_inequality(struct isl_ctx *ctx,
-               struct isl_basic_set *bset)
+int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
 {
-       return isl_basic_map_alloc_inequality(ctx, (struct isl_basic_map *)bset);
+       return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
 }
 
-int isl_basic_map_free_inequality(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned n)
+int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
 {
-       isl_assert(ctx, n <= bmap->n_ineq, return -1);
+       if (!bmap)
+               return -1;
+       isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
        bmap->n_ineq -= n;
        return 0;
 }
 
-int isl_basic_map_drop_inequality(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned pos)
+int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
+{
+       return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
+}
+
+int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
 {
        isl_int *t;
-       isl_assert(ctx, pos < bmap->n_ineq, return -1);
+       if (!bmap)
+               return -1;
+       isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
 
        if (pos != bmap->n_ineq - 1) {
                t = bmap->ineq[pos];
                bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
                bmap->ineq[bmap->n_ineq - 1] = t;
+               F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        }
        bmap->n_ineq--;
        return 0;
 }
 
-int isl_basic_map_alloc_div(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
+{
+       return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
+}
+
+int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
 {
-       isl_assert(ctx, bmap->n_div < bmap->extra, return -1);
+       if (!bmap)
+               return -1;
+       isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
        return bmap->n_div++;
 }
 
-int isl_basic_map_free_div(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned n)
+int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
 {
-       isl_assert(ctx, n <= bmap->n_div, return -1);
+       if (!bmap)
+               return -1;
+       isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
        bmap->n_div -= n;
        return 0;
 }
@@ -373,15 +405,19 @@ static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
        copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
 }
 
-static struct isl_basic_map *add_constraints(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap1,
+static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
                struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
 {
        int i;
-       unsigned div_off = bmap1->n_div;
+       unsigned div_off;
+
+       if (!bmap1 || !bmap2)
+               goto error;
+
+       div_off = bmap1->n_div;
 
        for (i = 0; i < bmap2->n_eq; ++i) {
-               int i1 = isl_basic_map_alloc_equality(ctx, bmap1);
+               int i1 = isl_basic_map_alloc_equality(bmap1);
                if (i1 < 0)
                        goto error;
                copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
@@ -389,7 +425,7 @@ static struct isl_basic_map *add_constraints(struct isl_ctx *ctx,
        }
 
        for (i = 0; i < bmap2->n_ineq; ++i) {
-               int i1 = isl_basic_map_alloc_inequality(ctx, bmap1);
+               int i1 = isl_basic_map_alloc_inequality(bmap1);
                if (i1 < 0)
                        goto error;
                copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
@@ -397,32 +433,40 @@ static struct isl_basic_map *add_constraints(struct isl_ctx *ctx,
        }
 
        for (i = 0; i < bmap2->n_div; ++i) {
-               int i1 = isl_basic_map_alloc_div(ctx, bmap1);
+               int i1 = isl_basic_map_alloc_div(bmap1);
                if (i1 < 0)
                        goto error;
                copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
                         i_pos, o_pos, div_off);
        }
 
-       isl_basic_map_free(ctx, bmap2);
+       isl_basic_map_free(bmap2);
 
        return bmap1;
 
 error:
-       isl_basic_map_free(ctx, bmap1);
-       isl_basic_map_free(ctx, bmap2);
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
        return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_extend(struct isl_ctx *ctx,
-               struct isl_basic_map *base,
+static struct isl_basic_set *set_add_constraints(struct isl_basic_set *bset1,
+               struct isl_basic_set *bset2, unsigned pos)
+{
+       return (struct isl_basic_set *)
+               add_constraints((struct isl_basic_map *)bset1,
+                               (struct isl_basic_map *)bset2, 0, pos);
+}
+
+struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
                unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
 {
        struct isl_basic_map *ext;
+       unsigned flags;
        int dims_ok;
 
-       base = isl_basic_map_cow(ctx, base);
+       base = isl_basic_map_cow(base);
        if (!base)
                goto error;
 
@@ -433,63 +477,63 @@ struct isl_basic_map *isl_basic_map_extend(struct isl_ctx *ctx,
        if (dims_ok && n_eq == 0 && n_ineq == 0)
                return base;
 
-       if (base) {
-               isl_assert(ctx, base->nparam <= nparam, goto error);
-               isl_assert(ctx, base->n_in <= n_in, goto error);
-               isl_assert(ctx, base->n_out <= n_out, goto error);
-               extra += base->extra;
-               n_eq += base->n_eq;
-               n_ineq += base->n_ineq;
-       }
+       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);
+       extra += base->extra;
+       n_eq += base->n_eq;
+       n_ineq += base->n_ineq;
 
-       ext = isl_basic_map_alloc(ctx, nparam, n_in, n_out,
+       ext = isl_basic_map_alloc(base->ctx, nparam, n_in, n_out,
                                        extra, n_eq, n_ineq);
        if (!base)
                return ext;
        if (!ext)
                goto error;
 
-       ext = add_constraints(ctx, ext, base, 0, 0);
+       flags = base->flags;
+       ext = add_constraints(ext, base, 0, 0);
+       if (ext) {
+               ext->flags = flags;
+               F_CLR(ext, ISL_BASIC_SET_FINAL);
+       }
 
        return ext;
 
 error:
-       isl_basic_map_free(ctx, base);
+       isl_basic_map_free(base);
        return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_extend(struct isl_ctx *ctx,
-               struct isl_basic_set *base,
+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)
 {
        return (struct isl_basic_set *)
-               isl_basic_map_extend(ctx, (struct isl_basic_map *)base,
+               isl_basic_map_extend((struct isl_basic_map *)base,
                                        nparam, 0, dim, extra, n_eq, n_ineq);
 }
 
-struct isl_basic_set *isl_basic_set_cow(struct isl_ctx *ctx,
-               struct isl_basic_set *bset)
+struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
 {
        return (struct isl_basic_set *)
-               isl_basic_map_cow(ctx, (struct isl_basic_map *)bset);
+               isl_basic_map_cow((struct isl_basic_map *)bset);
 }
 
-struct isl_basic_map *isl_basic_map_cow(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
 {
        if (!bmap)
                return NULL;
 
        if (bmap->ref > 1) {
                bmap->ref--;
-               bmap = isl_basic_map_dup(ctx, bmap);
+               bmap = isl_basic_map_dup(bmap);
        }
        F_CLR(bmap, ISL_BASIC_SET_FINAL);
        return bmap;
 }
 
-static struct isl_set *isl_set_cow(struct isl_ctx *ctx, struct isl_set *set)
+struct isl_set *isl_set_cow(struct isl_set *set)
 {
        if (!set)
                return NULL;
@@ -497,10 +541,10 @@ static struct isl_set *isl_set_cow(struct isl_ctx *ctx, struct isl_set *set)
        if (set->ref == 1)
                return set;
        set->ref--;
-       return isl_set_dup(ctx, set);
+       return isl_set_dup(set);
 }
 
-struct isl_map *isl_map_cow(struct isl_ctx *ctx, struct isl_map *map)
+struct isl_map *isl_map_cow(struct isl_map *map)
 {
        if (!map)
                return NULL;
@@ -508,7 +552,7 @@ struct isl_map *isl_map_cow(struct isl_ctx *ctx, struct isl_map *map)
        if (map->ref == 1)
                return map;
        map->ref--;
-       return isl_map_dup(ctx, map);
+       return isl_map_dup(map);
 }
 
 static void swap_vars(struct isl_blk blk, isl_int *a,
@@ -519,7 +563,7 @@ static void swap_vars(struct isl_blk blk, isl_int *a,
        isl_seq_cpy(a, blk.data, b_len+a_len);
 }
 
-struct isl_basic_set *isl_basic_set_swap_vars(struct isl_ctx *ctx,
+struct isl_basic_set *isl_basic_set_swap_vars(
                struct isl_basic_set *bset, unsigned n)
 {
        int i;
@@ -528,16 +572,16 @@ struct isl_basic_set *isl_basic_set_swap_vars(struct isl_ctx *ctx,
        if (!bset)
                goto error;
 
-       isl_assert(ctx, n <= bset->dim, goto error);
+       isl_assert(bset->ctx, n <= bset->dim, goto error);
 
        if (n == bset->dim)
                return bset;
 
-       bset = isl_basic_set_cow(ctx, bset);
+       bset = isl_basic_set_cow(bset);
        if (!bset)
                return NULL;
 
-       blk = isl_blk_alloc(ctx, bset->dim);
+       blk = isl_blk_alloc(bset->ctx, bset->dim);
        if (isl_blk_is_error(blk))
                goto error;
 
@@ -553,30 +597,31 @@ struct isl_basic_set *isl_basic_set_swap_vars(struct isl_ctx *ctx,
                swap_vars(blk,
                          bset->div[i]+1+1+bset->nparam, n, bset->dim - n);
 
-       isl_blk_free(ctx, blk);
+       isl_blk_free(bset->ctx, blk);
 
+       F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
        return bset;
 
 error:
-       isl_basic_set_free(ctx, bset);
+       isl_basic_set_free(bset);
        return NULL;
 }
 
-struct isl_set *isl_set_swap_vars(struct isl_ctx *ctx,
-               struct isl_set *set, unsigned n)
+struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
 {
        int i;
-       set = isl_set_cow(ctx, set);
+       set = isl_set_cow(set);
        if (!set)
                return NULL;
 
        for (i = 0; i < set->n; ++i) {
-               set->p[i] = isl_basic_set_swap_vars(ctx, set->p[i], n);
+               set->p[i] = isl_basic_set_swap_vars(set->p[i], n);
                if (!set->p[i]) {
-                       isl_set_free(ctx, set);
+                       isl_set_free(set);
                        return NULL;
                }
        }
+       F_CLR(set, ISL_SET_NORMALIZED);
        return set;
 }
 
@@ -586,7 +631,7 @@ static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
        isl_seq_clr(c + rem, n);
 }
 
-struct isl_basic_set *isl_basic_set_drop_vars(struct isl_ctx *ctx,
+struct isl_basic_set *isl_basic_set_drop_dims(
                struct isl_basic_set *bset, unsigned first, unsigned n)
 {
        int i;
@@ -594,12 +639,12 @@ struct isl_basic_set *isl_basic_set_drop_vars(struct isl_ctx *ctx,
        if (!bset)
                goto error;
 
-       isl_assert(ctx, first + n <= bset->dim, goto error);
+       isl_assert(bset->ctx, first + n <= bset->dim, goto error);
 
        if (n == 0)
                return bset;
 
-       bset = isl_basic_set_cow(ctx, bset);
+       bset = isl_basic_set_cow(bset);
        if (!bset)
                return NULL;
 
@@ -618,16 +663,118 @@ struct isl_basic_set *isl_basic_set_drop_vars(struct isl_ctx *ctx,
        bset->dim -= n;
        bset->extra += n;
 
-       return isl_basic_set_finalize(ctx, bset);
+       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_basic_set_free(ctx, bset);
+       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_ctx *ctx,
+static struct isl_basic_map *isl_basic_map_drop_div(
                struct isl_basic_map *bmap, unsigned div)
 {
        int i;
@@ -638,14 +785,14 @@ static struct isl_basic_map *isl_basic_map_drop_div(struct isl_ctx *ctx,
 
        pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
 
-       isl_assert(ctx, div < bmap->n_div, goto error);
+       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(ctx, bmap, i);
+                       isl_basic_map_drop_inequality(bmap, i);
                        --i;
                        continue;
                }
@@ -664,16 +811,16 @@ static struct isl_basic_map *isl_basic_map_drop_div(struct isl_ctx *ctx,
 
                bmap->div[bmap->n_div - 1] = t;
        }
-       isl_basic_map_free_div(ctx, bmap, 1);
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+       isl_basic_map_free_div(bmap, 1);
 
        return bmap;
 error:
-       isl_basic_map_free(ctx, bmap);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
-static void eliminate_div(struct isl_ctx *ctx, struct isl_basic_map *bmap,
-                               isl_int *eq, unsigned div)
+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;
@@ -696,40 +843,38 @@ static void eliminate_div(struct isl_ctx *ctx, struct isl_basic_map *bmap,
                    !isl_int_is_zero(bmap->div[i][1 + pos]))
                        isl_seq_clr(bmap->div[i], 1 + len);
 
-       isl_basic_map_drop_div(ctx, bmap, div);
+       isl_basic_map_drop_div(bmap, div);
 }
 
-struct isl_basic_map *isl_basic_map_set_to_empty(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap)
+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(ctx, bmap, bmap->n_div);
-       isl_basic_map_free_inequality(ctx, bmap, bmap->n_ineq);
+       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(ctx, bmap, bmap->n_eq-1);
+               isl_basic_map_free_equality(bmap, bmap->n_eq-1);
        else {
-               isl_basic_map_alloc_equality(ctx, bmap);
+               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(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 error:
-       isl_basic_map_free(ctx, bmap);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_set_to_empty(
-               struct isl_ctx *ctx, struct isl_basic_set *bset)
+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(ctx, (struct isl_basic_map *)bset);
+               isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
 }
 
 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
@@ -741,9 +886,16 @@ static void swap_equality(struct isl_basic_map *bmap, int a, int b)
 
 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
 {
-       isl_int *t = bmap->ineq[a];
-       bmap->ineq[a] = bmap->ineq[b];
-       bmap->ineq[b] = t;
+       if (a != b) {
+               isl_int *t = bmap->ineq[a];
+               bmap->ineq[a] = bmap->ineq[b];
+               bmap->ineq[b] = t;
+       }
+}
+
+static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
+{
+       swap_inequality((struct isl_basic_map *)bset, a, b);
 }
 
 static void swap_div(struct isl_basic_map *bmap, int a, int b)
@@ -762,9 +914,50 @@ 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_ctx *ctx,
+struct isl_basic_map *isl_basic_map_gauss(
        struct isl_basic_map *bmap, int *progress)
 {
        int k;
@@ -795,36 +988,8 @@ struct isl_basic_map *isl_basic_map_gauss(struct isl_ctx *ctx,
                if (isl_int_is_neg(bmap->eq[done][1+last_var]))
                        isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 
-               for (k = 0; k < bmap->n_eq; ++k) {
-                       if (k == done)
-                               continue;
-                       if (isl_int_is_zero(bmap->eq[k][1+last_var]))
-                               continue;
-                       if (progress)
-                               *progress = 1;
-                       isl_seq_elim(bmap->eq[k], bmap->eq[done],
-                                       1+last_var, 1+total, NULL);
-               }
-
-               for (k = 0; k < bmap->n_ineq; ++k) {
-                       if (isl_int_is_zero(bmap->ineq[k][1+last_var]))
-                               continue;
-                       if (progress)
-                               *progress = 1;
-                       isl_seq_elim(bmap->ineq[k], bmap->eq[done],
-                                       1+last_var, 1+total, NULL);
-               }
-
-               for (k = 0; k < bmap->n_div; ++k) {
-                       if (isl_int_is_zero(bmap->div[k][0]))
-                               continue;
-                       if (isl_int_is_zero(bmap->div[k][1+1+last_var]))
-                               continue;
-                       if (progress)
-                               *progress = 1;
-                       isl_seq_elim(bmap->div[k]+1, bmap->eq[done],
-                                       1+last_var, 1+total, &bmap->div[k][0]);
-               }
+               eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
+                                               progress);
 
                if (last_var >= total_var &&
                    isl_int_is_zero(bmap->div[last_var - total_var][0])) {
@@ -833,6 +998,7 @@ struct isl_basic_map *isl_basic_map_gauss(struct isl_ctx *ctx,
                        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)
@@ -840,16 +1006,16 @@ struct isl_basic_map *isl_basic_map_gauss(struct isl_ctx *ctx,
        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(ctx, bmap);
+               return isl_basic_map_set_to_empty(bmap);
        }
-       isl_basic_map_free_equality(ctx, bmap, bmap->n_eq-done);
+       isl_basic_map_free_equality(bmap, bmap->n_eq-done);
        return bmap;
 }
 
-struct isl_basic_set *isl_basic_set_gauss(struct isl_ctx *ctx,
+struct isl_basic_set *isl_basic_set_gauss(
        struct isl_basic_set *bset, int *progress)
 {
-       return (struct isl_basic_set*)isl_basic_map_gauss(ctx,
+       return (struct isl_basic_set*)isl_basic_map_gauss(
                        (struct isl_basic_map *)bset, progress);
 }
 
@@ -879,7 +1045,6 @@ static int hash_index(int *index, unsigned int size, int bits,
 }
 
 static struct isl_basic_map *remove_duplicate_constraints(
-       struct isl_ctx *ctx,
        struct isl_basic_map *bmap, int *progress)
 {
        unsigned int size;
@@ -906,11 +1071,12 @@ static struct isl_basic_map *remove_duplicate_constraints(
                        index[h] = k+1;
                        continue;
                }
-               *progress = 1;
+               if (progress)
+                       *progress = 1;
                l = index[h] - 1;
                if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
                        swap_inequality(bmap, k, l);
-               isl_basic_map_drop_inequality(ctx, bmap, k);
+               isl_basic_map_drop_inequality(bmap, k);
                --k;
        }
        isl_int_init(sum);
@@ -930,10 +1096,10 @@ static struct isl_basic_map *remove_duplicate_constraints(
                         * will no longer be valid.
                         * Plus, we probably we want to regauss first.
                         */
-                       isl_basic_map_drop_inequality(ctx, bmap, l);
-                       isl_basic_map_inequality_to_equality(ctx, bmap, k);
+                       isl_basic_map_drop_inequality(bmap, l);
+                       isl_basic_map_inequality_to_equality(bmap, k);
                } else
-                       bmap = isl_basic_map_set_to_empty(ctx, bmap);
+                       bmap = isl_basic_map_set_to_empty(bmap);
                break;
        }
        isl_int_clear(sum);
@@ -942,7 +1108,150 @@ static struct isl_basic_map *remove_duplicate_constraints(
        return bmap;
 }
 
-static struct isl_basic_map *remove_duplicate_divs(struct isl_ctx *ctx,
+static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
+{
+       int d, i;
+       unsigned total;
+
+       total = bmap->nparam + bmap->n_in + bmap->n_out;
+       for (d = 0; d < total; ++d)
+               elim[d] = -1;
+       for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
+               for (; d >= 0; --d) {
+                       if (isl_int_is_zero(bmap->eq[i][1+d]))
+                               continue;
+                       elim[d] = i;
+                       break;
+               }
+       }
+}
+
+static int reduced_using_equalities(isl_int *c, struct isl_vec *v,
+       struct isl_basic_map *bmap, int *elim)
+{
+       int d, i;
+       int copied = 0;
+       unsigned total;
+
+       total = bmap->nparam + bmap->n_in + bmap->n_out;
+       for (d = total - 1; d >= 0; --d) {
+               if (isl_int_is_zero(c[1+d]))
+                       continue;
+               if (elim[d] == -1)
+                       continue;
+               if (!copied) {
+                       isl_seq_cpy(v->block.data, c, 1 + total);
+                       copied = 1;
+               }
+               isl_seq_elim(v->block.data, bmap->eq[elim[d]],
+                               1 + d, 1 + total, NULL);
+       }
+       return copied;
+}
+
+/* Quick check to see if two basic maps are disjoint.
+ * In particular, we reduce the equalities and inequalities of
+ * one basic map in the context of the equalities of the other
+ * basic map and check if we get a contradiction.
+ */
+int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
+       struct isl_basic_map *bmap2)
+{
+       struct isl_vec *v = NULL;
+       int *elim = NULL;
+       unsigned total;
+       int d, i;
+
+       if (!bmap1 || !bmap2)
+               return -1;
+       isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, return -1);
+       isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, return -1);
+       isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, return -1);
+       if (bmap1->n_div || bmap2->n_div)
+               return 0;
+       if (!bmap1->n_eq && !bmap2->n_eq)
+               return 0;
+
+       total = bmap1->nparam + bmap1->n_in + bmap1->n_out;
+       if (total == 0)
+               return 0;
+       v = isl_vec_alloc(bmap1->ctx, 1 + total);
+       if (!v)
+               goto error;
+       elim = isl_alloc_array(bmap1->ctx, int, total);
+       if (!elim)
+               goto error;
+       compute_elimination_index(bmap1, elim);
+       for (i = 0; i < bmap2->n_eq; ++i) {
+               int reduced;
+               reduced = reduced_using_equalities(bmap2->eq[i], v, bmap1, elim);
+               if (reduced && !isl_int_is_zero(v->block.data[0]) &&
+                   isl_seq_first_non_zero(v->block.data + 1, total) == -1)
+                       goto disjoint;
+       }
+       for (i = 0; i < bmap2->n_ineq; ++i) {
+               int reduced;
+               reduced = reduced_using_equalities(bmap2->ineq[i], v, bmap1, elim);
+               if (reduced && isl_int_is_neg(v->block.data[0]) &&
+                   isl_seq_first_non_zero(v->block.data + 1, total) == -1)
+                       goto disjoint;
+       }
+       compute_elimination_index(bmap2, elim);
+       for (i = 0; i < bmap1->n_ineq; ++i) {
+               int reduced;
+               reduced = reduced_using_equalities(bmap1->ineq[i], v, bmap2, elim);
+               if (reduced && isl_int_is_neg(v->block.data[0]) &&
+                   isl_seq_first_non_zero(v->block.data + 1, total) == -1)
+                       goto disjoint;
+       }
+       isl_vec_free(bmap1->ctx, v);
+       free(elim);
+       return 0;
+disjoint:
+       isl_vec_free(bmap1->ctx, v);
+       free(elim);
+       return 1;
+error:
+       isl_vec_free(bmap1->ctx, v);
+       free(elim);
+       return -1;
+}
+
+int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
+       struct isl_basic_set *bset2)
+{
+       return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
+                                             (struct isl_basic_map *)bset2);
+}
+
+int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
+{
+       int i, j;
+
+       if (!map1 || !map2)
+               return -1;
+
+       if (isl_map_fast_is_equal(map1, map2))
+               return 0;
+
+       for (i = 0; i < map1->n; ++i) {
+               for (j = 0; j < map2->n; ++j) {
+                       int d = isl_basic_map_fast_is_disjoint(map1->p[i],
+                                                              map2->p[j]);
+                       if (d != 1)
+                               return d;
+               }
+       }
+       return 1;
+}
+
+int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
+{
+       return isl_map_fast_is_disjoint((struct isl_map *)set1,
+                                       (struct isl_map *)set2);
+}
+
+static struct isl_basic_map *remove_duplicate_divs(
        struct isl_basic_map *bmap, int *progress)
 {
        unsigned int size;
@@ -952,10 +1261,12 @@ static struct isl_basic_map *remove_duplicate_divs(struct isl_ctx *ctx,
        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;
@@ -990,7 +1301,7 @@ static struct isl_basic_map *remove_duplicate_divs(struct isl_ctx *ctx,
                        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(ctx, bmap, eq.data, l);
+                       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);
                }
@@ -1003,9 +1314,10 @@ out:
        return bmap;
 }
 
-static struct isl_basic_map *eliminate_divs(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap,
-               int *progress)
+/* Elimininate divs based on equalities
+ */
+static struct isl_basic_map *eliminate_divs_eq(
+               struct isl_basic_map *bmap, int *progress)
 {
        int d;
        int i;
@@ -1024,17 +1336,17 @@ static struct isl_basic_map *eliminate_divs(
                                continue;
                        modified = 1;
                        *progress = 1;
-                       eliminate_div(ctx, bmap, bmap->eq[i], d);
-                       isl_basic_map_drop_equality(ctx, bmap, i);
+                       eliminate_div(bmap, bmap->eq[i], d);
+                       isl_basic_map_drop_equality(bmap, i);
+                       break;
                }
        }
        if (modified)
-               return eliminate_divs(ctx, bmap, progress);
+               return eliminate_divs_eq(bmap, progress);
        return bmap;
 }
 
-static struct isl_basic_map *normalize_constraints(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap)
+static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
 {
        int i;
        isl_int gcd;
@@ -1045,16 +1357,18 @@ static struct isl_basic_map *normalize_constraints(
                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(ctx, bmap);
+                               bmap = isl_basic_map_set_to_empty(bmap);
                                break;
                        }
-                       isl_basic_map_drop_equality(ctx, bmap, i);
+                       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(ctx, bmap);
+                       bmap = isl_basic_map_set_to_empty(bmap);
                        break;
                }
                isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
@@ -1064,12 +1378,14 @@ static struct isl_basic_map *normalize_constraints(
                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(ctx, bmap);
+                               bmap = isl_basic_map_set_to_empty(bmap);
                                break;
                        }
-                       isl_basic_map_drop_inequality(ctx, bmap, i);
+                       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);
@@ -1080,54 +1396,255 @@ static struct isl_basic_map *normalize_constraints(
        return bmap;
 }
 
-struct isl_basic_map *isl_basic_map_simplify(
-               struct isl_ctx *ctx, struct isl_basic_map *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 progress = 1;
+       int d;
+       int i, j, k;
+       unsigned total;
+       unsigned extra;
+
        if (!bmap)
                return NULL;
-       while (progress) {
-               progress = 0;
-               bmap = normalize_constraints(ctx, bmap);
-               bmap = eliminate_divs(ctx, bmap, &progress);
-               bmap = isl_basic_map_gauss(ctx, bmap, &progress);
-               bmap = remove_duplicate_divs(ctx, bmap, &progress);
-               bmap = remove_duplicate_constraints(ctx, bmap, &progress);
+       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_simplify(
-               struct isl_ctx *ctx, struct isl_basic_set *bset)
+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_simplify(ctx,
-                       (struct isl_basic_map *)bset);
+       return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
+                       (struct isl_basic_map *)bset, pos, n);
 }
 
-static void dump_term(struct isl_basic_map *bmap,
-                       isl_int c, int pos, FILE *out)
+/* Eliminate the specified n dimensions starting at first from the
+ * constraints using Fourier-Motzkin, The dimensions themselves
+ * are not removed.
+ */
+struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
+       unsigned first, unsigned n)
 {
-       unsigned in = bmap->n_in;
-       unsigned dim = bmap->n_in + bmap->n_out;
-       if (!pos)
-               isl_int_print(out, c);
-       else {
-               if (!isl_int_is_one(c))
-                       isl_int_print(out, c);
-               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);
-               else
-                       fprintf(out, "e%d", pos - 1 - bmap->nparam - dim);
-       }
-}
+       int i;
 
-static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
-                               int sign, FILE *out)
+       if (n == 0)
+               return set;
+
+       set = isl_set_cow(set);
+       if (!set)
+               return NULL;
+       isl_assert(set->ctx, first+n <= set->dim, goto error);
+       
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
+                                                       set->nparam + first, n);
+               if (!set->p[i])
+                       goto error;
+       }
+       return set;
+error:
+       isl_set_free(set);
+       return NULL;
+}
+
+/* Project out n dimensions starting at first using Fourier-Motzkin */
+struct isl_set *isl_set_remove_dims(struct isl_set *set,
+       unsigned first, unsigned n)
+{
+       set = isl_set_eliminate_dims(set, first, n);
+       set = isl_set_drop_dims(set, first, n);
+       return set;
+}
+
+/* Project out n inputs starting at first using Fourier-Motzkin */
+struct isl_map *isl_map_remove_inputs(struct isl_map *map,
+       unsigned first, unsigned n)
+{
+       int i;
+
+       if (n == 0)
+               return map;
+
+       map = isl_map_cow(map);
+       if (!map)
+               return NULL;
+       isl_assert(map->ctx, first+n <= map->n_in, goto error);
+       
+       for (i = 0; i < map->n; ++i) {
+               map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
+                                                       map->nparam + first, n);
+               if (!map->p[i])
+                       goto error;
+       }
+       map = isl_map_drop_inputs(map, first, n);
+       return map;
+error:
+       isl_map_free(map);
+       return NULL;
+}
+
+/* Project out n dimensions starting at first using Fourier-Motzkin */
+struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
+       unsigned first, unsigned n)
+{
+       bset = isl_basic_set_eliminate_vars(bset, bset->nparam + first, n);
+       bset = isl_basic_set_drop_dims(bset, first, n);
+       return bset;
+}
+
+/* Elimininate divs based on inequalities
+ */
+static struct isl_basic_map *eliminate_divs_ineq(
+               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;
+       }
+       return bmap;
+}
+
+struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
+{
+       int progress = 1;
+       if (!bmap)
+               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);
+       }
+       return bmap;
+}
+
+struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
+{
+       return (struct isl_basic_set *)
+               isl_basic_map_simplify((struct isl_basic_map *)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;
+       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);
+               else
+                       fprintf(out, "e%d", pos - 1 - bmap->nparam - dim);
+       }
+}
+
+static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
+                               int sign, FILE *out)
 {
        int i;
        int first;
@@ -1208,13 +1725,12 @@ static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
                fprintf(out, "e%d = [(", i);
                dump_affine(bmap, bmap->div[i]+1, out);
                fprintf(out, ")/");
-               isl_int_print(out, bmap->div[i][0]);
+               isl_int_print(out, bmap->div[i][0], 0);
                fprintf(out, "]\n");
        }
 }
 
-void isl_basic_set_dump(struct isl_ctx *ctx, struct isl_basic_set *bset,
-                               FILE *out, int indent)
+void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
 {
        if (!bset) {
                fprintf(out, "null basic set\n");
@@ -1222,13 +1738,13 @@ void isl_basic_set_dump(struct isl_ctx *ctx, struct isl_basic_set *bset,
        }
 
        fprintf(out, "%*s", indent, "");
-       fprintf(out, "nparam: %d, dim: %d, extra: %d\n",
-                       bset->nparam, bset->dim, bset->extra);
+       fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
+                       bset->ref, bset->nparam, bset->dim, bset->extra,
+                       bset->flags);
        dump((struct isl_basic_map *)bset, out, indent);
 }
 
-void isl_basic_map_dump(struct isl_ctx *ctx, struct isl_basic_map *bmap,
-                               FILE *out, int indent)
+void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
 {
        if (!bmap) {
                fprintf(out, "null basic map\n");
@@ -1236,19 +1752,21 @@ void isl_basic_map_dump(struct isl_ctx *ctx, struct isl_basic_map *bmap,
        }
 
        fprintf(out, "%*s", indent, "");
-       fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d\n",
+       fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, flags: %x\n",
                bmap->ref,
-               bmap->nparam, bmap->n_in, bmap->n_out, bmap->extra);
+               bmap->nparam, bmap->n_in, bmap->n_out, bmap->extra, bmap->flags);
        dump(bmap, out, indent);
 }
 
-int isl_inequality_negate(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap, unsigned pos)
+int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
 {
        unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-       isl_assert(ctx, pos < bmap->n_ineq, return -1);
+       if (!bmap)
+               return -1;
+       isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
        isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
        isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
+       F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        return 0;
 }
 
@@ -1257,12 +1775,15 @@ struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
 {
        struct isl_set *set;
 
+       isl_assert(ctx, n >= 0, return NULL);
        set = isl_alloc(ctx, struct isl_set,
                        sizeof(struct isl_set) +
                        n * sizeof(struct isl_basic_set *));
        if (!set)
                return NULL;
 
+       set->ctx = ctx;
+       isl_ctx_ref(ctx);
        set->ref = 1;
        set->size = n;
        set->n = 0;
@@ -1273,67 +1794,73 @@ struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
        return set;
 }
 
-struct isl_set *isl_set_dup(struct isl_ctx *ctx, struct isl_set *set)
+struct isl_set *isl_set_dup(struct isl_set *set)
 {
        int i;
        struct isl_set *dup;
 
-       dup = isl_set_alloc(ctx, set->nparam, set->dim, set->n, set->flags);
+       if (!set)
+               return NULL;
+
+       dup = isl_set_alloc(set->ctx, set->nparam, set->dim, set->n, set->flags);
        if (!dup)
                return NULL;
        for (i = 0; i < set->n; ++i)
-               dup = isl_set_add(ctx, dup,
-                                 isl_basic_set_dup(ctx, set->p[i]));
+               dup = isl_set_add(dup,
+                                 isl_basic_set_dup(set->p[i]));
        return dup;
 }
 
-struct isl_set *isl_set_from_basic_set(struct isl_ctx *ctx,
-                               struct isl_basic_set *bset)
+struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
 {
        struct isl_set *set;
 
-       set = isl_set_alloc(ctx, bset->nparam, bset->dim, 1, ISL_MAP_DISJOINT);
+       if (!bset)
+               return NULL;
+
+       set = isl_set_alloc(bset->ctx, bset->nparam, bset->dim, 1, ISL_MAP_DISJOINT);
        if (!set) {
-               isl_basic_set_free(ctx, bset);
+               isl_basic_set_free(bset);
                return NULL;
        }
-       return isl_set_add(ctx, set, bset);
+       return isl_set_add(set, bset);
 }
 
-struct isl_map *isl_map_from_basic_map(struct isl_ctx *ctx,
-                               struct isl_basic_map *bmap)
+struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
 {
        struct isl_map *map;
 
-       map = isl_map_alloc(ctx, bmap->nparam, bmap->n_in, bmap->n_out, 1,
+       if (!bmap)
+               return NULL;
+
+       map = isl_map_alloc(bmap->ctx, bmap->nparam, bmap->n_in, bmap->n_out, 1,
                                ISL_MAP_DISJOINT);
        if (!map) {
-               isl_basic_map_free(ctx, bmap);
+               isl_basic_map_free(bmap);
                return NULL;
        }
-       return isl_map_add(ctx, map, bmap);
+       return isl_map_add(map, bmap);
 }
 
-struct isl_set *isl_set_add(struct isl_ctx *ctx, struct isl_set *set,
-                               struct isl_basic_set *bset)
+struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
 {
        if (!bset || !set)
                goto error;
-       isl_assert(ctx, set->nparam == bset->nparam, goto error);
-       isl_assert(ctx, set->dim == bset->dim, goto error);
-       isl_assert(ctx, set->n < set->size, 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, set->n < set->size, goto error);
        set->p[set->n] = bset;
        set->n++;
        return set;
 error:
        if (set)
-               isl_set_free(ctx, set);
+               isl_set_free(set);
        if (bset)
-               isl_basic_set_free(ctx, bset);
+               isl_basic_set_free(bset);
        return NULL;
 }
 
-void isl_set_free(struct isl_ctx *ctx, struct isl_set *set)
+void isl_set_free(struct isl_set *set)
 {
        int i;
 
@@ -1343,13 +1870,13 @@ void isl_set_free(struct isl_ctx *ctx, struct isl_set *set)
        if (--set->ref > 0)
                return;
 
+       isl_ctx_deref(set->ctx);
        for (i = 0; i < set->n; ++i)
-               isl_basic_set_free(ctx, set->p[i]);
+               isl_basic_set_free(set->p[i]);
        free(set);
 }
 
-void isl_set_dump(struct isl_ctx *ctx, struct isl_set *set, FILE *out,
-                 int indent)
+void isl_set_dump(struct isl_set *set, FILE *out, int indent)
 {
        int i;
 
@@ -1359,16 +1886,16 @@ void isl_set_dump(struct isl_ctx *ctx, struct isl_set *set, FILE *out,
        }
 
        fprintf(out, "%*s", indent, "");
-       fprintf(out, "ref: %d, n: %d\n", set->ref, set->n);
+       fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
+                       set->ref, set->n, set->nparam, set->dim, set->flags);
        for (i = 0; i < set->n; ++i) {
                fprintf(out, "%*s", indent, "");
                fprintf(out, "basic set %d:\n", i);
-               isl_basic_set_dump(ctx, set->p[i], out, indent+4);
+               isl_basic_set_dump(set->p[i], out, indent+4);
        }
 }
 
-void isl_map_dump(struct isl_ctx *ctx, struct isl_map *map, FILE *out,
-                 int indent)
+void isl_map_dump(struct isl_map *map, FILE *out, int indent)
 {
        int i;
 
@@ -1378,111 +1905,107 @@ void isl_map_dump(struct isl_ctx *ctx, struct isl_map *map, FILE *out,
        }
 
        fprintf(out, "%*s", indent, "");
-       fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d\n",
-                       map->ref, map->n, map->nparam, map->n_in, map->n_out);
+       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);
        for (i = 0; i < map->n; ++i) {
                fprintf(out, "%*s", indent, "");
                fprintf(out, "basic map %d:\n", i);
-               isl_basic_map_dump(ctx, map->p[i], out, indent+4);
+               isl_basic_map_dump(map->p[i], out, indent+4);
        }
 }
 
 struct isl_basic_map *isl_basic_map_intersect_domain(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap,
-               struct isl_basic_set *bset)
+               struct isl_basic_map *bmap, struct isl_basic_set *bset)
 {
        struct isl_basic_map *bmap_domain;
 
        if (!bmap || !bset)
                goto error;
 
-       isl_assert(ctx, bset->dim == bmap->n_in, goto error);
-       isl_assert(ctx, bset->nparam == bmap->nparam, goto error);
+       isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
+       isl_assert(bset->ctx, bset->nparam == bmap->nparam, goto error);
 
-       bmap = isl_basic_map_extend(ctx, bmap,
+       bmap = isl_basic_map_extend(bmap,
                        bset->nparam, bmap->n_in, bmap->n_out,
                        bset->n_div, bset->n_eq, bset->n_ineq);
        if (!bmap)
                goto error;
-       bmap_domain = isl_basic_map_from_basic_set(ctx, bset,
+       bmap_domain = isl_basic_map_from_basic_set(bset,
                                                bset->dim, 0);
-       bmap = add_constraints(ctx, bmap, bmap_domain, 0, 0);
+       bmap = add_constraints(bmap, bmap_domain, 0, 0);
 
-       bmap = isl_basic_map_simplify(ctx, bmap);
-       return isl_basic_map_finalize(ctx, bmap);
+       bmap = isl_basic_map_simplify(bmap);
+       return isl_basic_map_finalize(bmap);
 error:
-       isl_basic_map_free(ctx, bmap);
-       isl_basic_set_free(ctx, bset);
+       isl_basic_map_free(bmap);
+       isl_basic_set_free(bset);
        return NULL;
 }
 
 struct isl_basic_map *isl_basic_map_intersect_range(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap,
-               struct isl_basic_set *bset)
+               struct isl_basic_map *bmap, struct isl_basic_set *bset)
 {
        struct isl_basic_map *bmap_range;
 
        if (!bmap || !bset)
                goto error;
 
-       isl_assert(ctx, bset->dim == bmap->n_out, goto error);
-       isl_assert(ctx, bset->nparam == bmap->nparam, goto error);
+       isl_assert(bset->ctx, bset->dim == bmap->n_out, goto error);
+       isl_assert(bset->ctx, bset->nparam == bmap->nparam, goto error);
 
-       bmap = isl_basic_map_extend(ctx, bmap,
+       bmap = isl_basic_map_extend(bmap,
                        bset->nparam, bmap->n_in, bmap->n_out,
                        bset->n_div, bset->n_eq, bset->n_ineq);
        if (!bmap)
                goto error;
-       bmap_range = isl_basic_map_from_basic_set(ctx, bset,
+       bmap_range = isl_basic_map_from_basic_set(bset,
                                                0, bset->dim);
-       bmap = add_constraints(ctx, bmap, bmap_range, 0, 0);
+       bmap = add_constraints(bmap, bmap_range, 0, 0);
 
-       bmap = isl_basic_map_simplify(ctx, bmap);
-       return isl_basic_map_finalize(ctx, bmap);
+       bmap = isl_basic_map_simplify(bmap);
+       return isl_basic_map_finalize(bmap);
 error:
-       isl_basic_map_free(ctx, bmap);
-       isl_basic_set_free(ctx, bset);
+       isl_basic_map_free(bmap);
+       isl_basic_set_free(bset);
        return NULL;
 }
 
 struct isl_basic_map *isl_basic_map_intersect(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap1,
-               struct isl_basic_map *bmap2)
+               struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
        if (!bmap1 || !bmap2)
                goto error;
 
-       isl_assert(ctx, bmap1->nparam == bmap2->nparam, goto error);
-       isl_assert(ctx, bmap1->n_in == bmap2->n_in, goto error);
-       isl_assert(ctx, bmap1->n_out == bmap2->n_out, 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(ctx, bmap1,
+       bmap1 = isl_basic_map_extend(bmap1,
                        bmap1->nparam, bmap1->n_in, bmap1->n_out,
                        bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
        if (!bmap1)
                goto error;
-       bmap1 = add_constraints(ctx, bmap1, bmap2, 0, 0);
+       bmap1 = add_constraints(bmap1, bmap2, 0, 0);
 
-       bmap1 = isl_basic_map_simplify(ctx, bmap1);
-       return isl_basic_map_finalize(ctx, bmap1);
+       bmap1 = isl_basic_map_simplify(bmap1);
+       return isl_basic_map_finalize(bmap1);
 error:
-       isl_basic_map_free(ctx, bmap1);
-       isl_basic_map_free(ctx, bmap2);
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
        return NULL;
 }
 
 struct isl_basic_set *isl_basic_set_intersect(
-               struct isl_ctx *ctx, struct isl_basic_set *bset1,
-               struct isl_basic_set *bset2)
+               struct isl_basic_set *bset1, struct isl_basic_set *bset2)
 {
        return (struct isl_basic_set *)
-               isl_basic_map_intersect(ctx,
+               isl_basic_map_intersect(
                        (struct isl_basic_map *)bset1,
                        (struct isl_basic_map *)bset2);
 }
 
-struct isl_map *isl_map_intersect(struct isl_ctx *ctx, struct isl_map *map1,
-               struct isl_map *map2)
+struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
 {
        unsigned flags = 0;
        struct isl_map *result;
@@ -1495,54 +2018,59 @@ struct isl_map *isl_map_intersect(struct isl_ctx *ctx, struct isl_map *map1,
            F_ISSET(map2, ISL_MAP_DISJOINT))
                FL_SET(flags, ISL_MAP_DISJOINT);
 
-       result = isl_map_alloc(ctx, map1->nparam, map1->n_in, map1->n_out,
+       result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
                                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_intersect(ctx,
-                                   isl_basic_map_copy(ctx, map1->p[i]),
-                                   isl_basic_map_copy(ctx, map2->p[j]));
-                       if (isl_basic_map_is_empty(ctx, part))
-                               isl_basic_map_free(ctx, part);
+                       part = isl_basic_map_intersect(
+                                   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(ctx, result, part);
+                               result = isl_map_add(result, part);
                        if (!result)
                                goto error;
                }
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map1);
+       isl_map_free(map2);
        return result;
 error:
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map1);
+       isl_map_free(map2);
        return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_reverse(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
+{
+       return (struct isl_set *)
+               isl_map_intersect((struct isl_map *)set1,
+                                 (struct isl_map *)set2);
+}
+
+struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
 {
        struct isl_basic_set *bset;
        unsigned in;
 
        if (!bmap)
                return NULL;
-       bmap = isl_basic_map_cow(ctx, bmap);
+       bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                return NULL;
        in = bmap->n_in;
-       bset = isl_basic_set_from_basic_map(ctx, bmap);
-       bset = isl_basic_set_swap_vars(ctx, bset, in);
-       return isl_basic_map_from_basic_set(ctx, bset, bset->dim-in, in);
+       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);
 }
 
 /* Turn final n dimensions into existentially quantified variables.
  */
 struct isl_basic_set *isl_basic_set_project_out(
-               struct isl_ctx *ctx, struct isl_basic_set *bset,
-               unsigned n, unsigned flags)
+               struct isl_basic_set *bset, unsigned n, unsigned flags)
 {
        int i;
        size_t row_size;
@@ -1552,16 +2080,16 @@ struct isl_basic_set *isl_basic_set_project_out(
        if (!bset)
                return NULL;
 
-       isl_assert(ctx, n <= bset->dim, goto error);
+       isl_assert(bset->ctx, n <= bset->dim, goto error);
 
        if (n == 0)
                return bset;
 
-       bset = isl_basic_set_cow(ctx, bset);
+       bset = isl_basic_set_cow(bset);
 
        row_size = 1 + bset->nparam + bset->dim + bset->extra;
        old = bset->block2.data;
-       bset->block2 = isl_blk_extend(ctx, bset->block2,
+       bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
                                        (bset->extra + n) * (1 + row_size));
        if (!bset->block2.data)
                goto error;
@@ -1580,16 +2108,15 @@ struct isl_basic_set *isl_basic_set_project_out(
        bset->n_div += n;
        bset->extra += n;
        bset->dim -= n;
-       bset = isl_basic_set_simplify(ctx, bset);
-       return isl_basic_set_finalize(ctx, bset);
+       bset = isl_basic_set_simplify(bset);
+       return isl_basic_set_finalize(bset);
 error:
-       isl_basic_set_free(ctx, bset);
+       isl_basic_set_free(bset);
        return NULL;
 }
 
 struct isl_basic_map *isl_basic_map_apply_range(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap1,
-               struct isl_basic_map *bmap2)
+               struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
        struct isl_basic_set *bset;
        unsigned n_in, n_out;
@@ -1597,35 +2124,50 @@ struct isl_basic_map *isl_basic_map_apply_range(
        if (!bmap1 || !bmap2)
                goto error;
 
-       isl_assert(ctx, bmap1->n_out == bmap2->n_in, goto error);
-       isl_assert(ctx, bmap1->nparam == bmap2->nparam, 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(ctx, bmap2);
+       bmap2 = isl_basic_map_reverse(bmap2);
        if (!bmap2)
                goto error;
-       bmap1 = isl_basic_map_extend(ctx, bmap1, bmap1->nparam,
+       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(ctx, bmap1, bmap2, bmap1->n_in - bmap2->n_in, 0);
-       bmap1 = isl_basic_map_simplify(ctx, bmap1);
-       bset = isl_basic_set_from_basic_map(ctx, bmap1);
-       bset = isl_basic_set_project_out(ctx, bset,
+       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(ctx, bset, n_in, n_out);
+       return isl_basic_map_from_basic_set(bset, n_in, n_out);
+error:
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
+       return NULL;
+}
+
+struct isl_basic_set *isl_basic_set_apply(
+               struct isl_basic_set *bset, struct isl_basic_map *bmap)
+{
+       if (!bset || !bmap)
+               goto error;
+
+       isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
+
+       return (struct isl_basic_set *)
+               isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
 error:
-       isl_basic_map_free(ctx, bmap1);
-       isl_basic_map_free(ctx, bmap2);
+       isl_basic_set_free(bset);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
 struct isl_basic_map *isl_basic_map_apply_domain(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap1,
-               struct isl_basic_map *bmap2)
+               struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
        if (!bmap1 || !bmap2)
                goto error;
@@ -1633,12 +2175,12 @@ struct isl_basic_map *isl_basic_map_apply_domain(
        isl_assert(ctx, bmap1->n_in == bmap2->n_in, goto error);
        isl_assert(ctx, bmap1->nparam == bmap2->nparam, goto error);
 
-       bmap1 = isl_basic_map_reverse(ctx, bmap1);
-       bmap1 = isl_basic_map_apply_range(ctx, bmap1, bmap2);
-       return isl_basic_map_reverse(ctx, bmap1);
+       bmap1 = isl_basic_map_reverse(bmap1);
+       bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
+       return isl_basic_map_reverse(bmap1);
 error:
-       isl_basic_map_free(ctx, bmap1);
-       isl_basic_map_free(ctx, bmap2);
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
        return NULL;
 }
 
@@ -1646,16 +2188,16 @@ static struct isl_basic_map *var_equal(struct isl_ctx *ctx,
                struct isl_basic_map *bmap, unsigned pos)
 {
        int i;
-       i = isl_basic_map_alloc_equality(ctx, bmap);
+       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);
-       return isl_basic_map_finalize(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 error:
-       isl_basic_map_free(ctx, bmap);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
@@ -1663,7 +2205,7 @@ static struct isl_basic_map *var_more(struct isl_ctx *ctx,
                struct isl_basic_map *bmap, unsigned pos)
 {
        int i;
-       i = isl_basic_map_alloc_inequality(ctx, bmap);
+       i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
                goto error;
        isl_seq_clr(bmap->ineq[i],
@@ -1671,9 +2213,9 @@ static struct isl_basic_map *var_more(struct isl_ctx *ctx,
        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);
-       return isl_basic_map_finalize(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 error:
-       isl_basic_map_free(ctx, bmap);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
@@ -1681,7 +2223,7 @@ static struct isl_basic_map *var_less(struct isl_ctx *ctx,
                struct isl_basic_map *bmap, unsigned pos)
 {
        int i;
-       i = isl_basic_map_alloc_inequality(ctx, bmap);
+       i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
                goto error;
        isl_seq_clr(bmap->ineq[i],
@@ -1689,9 +2231,9 @@ static struct isl_basic_map *var_less(struct isl_ctx *ctx,
        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);
-       return isl_basic_map_finalize(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 error:
-       isl_basic_map_free(ctx, bmap);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
@@ -1705,7 +2247,7 @@ struct isl_basic_map *isl_basic_map_equal(struct isl_ctx *ctx,
                return NULL;
        for (i = 0; i < n_equal && bmap; ++i)
                bmap = var_equal(ctx, bmap, i);
-       return isl_basic_map_finalize(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 }
 
 struct isl_basic_map *isl_basic_map_less_at(struct isl_ctx *ctx,
@@ -1720,7 +2262,7 @@ struct isl_basic_map *isl_basic_map_less_at(struct isl_ctx *ctx,
                bmap = var_equal(ctx, bmap, i);
        if (bmap)
                bmap = var_less(ctx, bmap, pos);
-       return isl_basic_map_finalize(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 }
 
 struct isl_basic_map *isl_basic_map_more_at(struct isl_ctx *ctx,
@@ -1735,16 +2277,15 @@ struct isl_basic_map *isl_basic_map_more_at(struct isl_ctx *ctx,
                bmap = var_equal(ctx, bmap, i);
        if (bmap)
                bmap = var_more(ctx, bmap, pos);
-       return isl_basic_map_finalize(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 }
 
 struct isl_basic_map *isl_basic_map_from_basic_set(
-               struct isl_ctx *ctx, struct isl_basic_set *bset,
-               unsigned n_in, unsigned n_out)
+               struct isl_basic_set *bset, unsigned n_in, unsigned n_out)
 {
        struct isl_basic_map *bmap;
 
-       bset = isl_basic_set_cow(ctx, bset);
+       bset = isl_basic_set_cow(bset);
        if (!bset)
                return NULL;
 
@@ -1752,96 +2293,255 @@ struct isl_basic_map *isl_basic_map_from_basic_set(
        bmap = (struct isl_basic_map *) bset;
        bmap->n_in = n_in;
        bmap->n_out = n_out;
-       return isl_basic_map_finalize(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 error:
-       isl_basic_set_free(ctx, bset);
+       isl_basic_set_free(bset);
        return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_from_basic_map(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap)
+struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
 {
        if (!bmap)
                goto error;
        if (bmap->n_in == 0)
                return (struct isl_basic_set *)bmap;
-       bmap = isl_basic_map_cow(ctx, bmap);
+       bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                goto error;
        bmap->n_out += bmap->n_in;
        bmap->n_in = 0;
-       bmap = isl_basic_map_finalize(ctx, bmap);
+       bmap = isl_basic_map_finalize(bmap);
        return (struct isl_basic_set *)bmap;
 error:
        return NULL;
 }
 
-static struct isl_basic_set *isl_basic_map_underlying_set(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap)
+/* For a div d = floor(f/m), add the constraints
+ *
+ *             f - m d >= 0
+ *             -(f-(n-1)) + m d >= 0
+ *
+ * Note that the second constraint is the negation of
+ *
+ *             f - m d >= n
+ */
+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;
+
+       i = isl_basic_map_alloc_inequality(bmap);
+       if (i < 0)
+               return -1;
+       isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
+       isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
+
+       j = isl_basic_map_alloc_inequality(bmap);
+       if (j < 0)
+               return -1;
+       isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
+       isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
+       isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
+       return j;
+}
+
+struct isl_basic_set *isl_basic_map_underlying_set(
+               struct isl_basic_map *bmap)
 {
        if (!bmap)
                goto error;
        if (bmap->nparam == 0 && bmap->n_in == 0 && bmap->n_div == 0)
                return (struct isl_basic_set *)bmap;
-       bmap = isl_basic_map_cow(ctx, 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->extra -= bmap->n_div;
        bmap->n_div = 0;
-       bmap = isl_basic_map_finalize(ctx, bmap);
+       bmap = isl_basic_map_finalize(bmap);
        return (struct isl_basic_set *)bmap;
 error:
        return NULL;
 }
 
-struct isl_basic_set *isl_basic_map_domain(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+struct isl_basic_map *isl_basic_map_overlying_set(
+       struct isl_basic_set *bset, struct isl_basic_map *like)
+{
+       struct isl_basic_map *bmap;
+       struct isl_ctx *ctx;
+       unsigned total;
+       int i, k;
+
+       if (!bset || !like)
+               goto error;
+       ctx = bset->ctx;
+       isl_assert(ctx, bset->dim ==
+                       like->nparam + like->n_in + like->n_out + like->n_div,
+                       goto error);
+       if (like->nparam == 0 && like->n_in == 0 && 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;
+       bmap = (struct isl_basic_map *)bset;
+       bmap->nparam = like->nparam;
+       bmap->n_in = like->n_in;
+       bmap->n_out = like->n_out;
+       bmap->extra += like->n_div;
+       if (bmap->extra) {
+               unsigned ltotal;
+               ltotal = total - bmap->extra + like->extra;
+               if (ltotal > total)
+                       ltotal = total;
+               bmap->block2 = isl_blk_extend(ctx, bmap->block2,
+                                       bmap->extra * (1 + 1 + total));
+               if (isl_blk_is_error(bmap->block2))
+                       goto error;
+               bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
+                                               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 < 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)
+                               goto error;
+               }
+       }
+       isl_basic_map_free(like);
+       bmap = isl_basic_map_finalize(bmap);
+       return bmap;
+error:
+       isl_basic_map_free(like);
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+struct isl_basic_set *isl_basic_set_from_underlying_set(
+       struct isl_basic_set *bset, struct isl_basic_set *like)
+{
+       return (struct isl_basic_set *)
+               isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
+}
+
+struct isl_set *isl_set_from_underlying_set(
+       struct isl_set *set, struct isl_basic_set *like)
+{
+       int i;
+
+       if (!set || !like)
+               goto error;
+       isl_assert(set->ctx, set->dim == like->nparam + like->dim + like->n_div,
+                   goto error);
+       if (like->nparam == 0 && like->n_div == 0) {
+               isl_basic_set_free(like);
+               return set;
+       }
+       set = isl_set_cow(set);
+       if (!set)
+               goto error;
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
+                                                     isl_basic_set_copy(like));
+               if (!set->p[i])
+                       goto error;
+       }
+       set->nparam = like->nparam;
+       set->dim = like->dim;
+       isl_basic_set_free(like);
+       return set;
+error:
+       isl_basic_set_free(like);
+       isl_set_free(set);
+       return NULL;
+}
+
+struct isl_set *isl_map_underlying_set(struct isl_map *map)
+{
+       int i;
+
+       map = isl_map_align_divs(map);
+       map = isl_map_cow(map);
+       if (!map)
+               return NULL;
+
+       for (i = 0; i < map->n; ++i) {
+               map->p[i] = (struct isl_basic_map *)
+                               isl_basic_map_underlying_set(map->p[i]);
+               if (!map->p[i])
+                       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;
+       return (struct isl_set *)map;
+error:
+       isl_map_free(map);
+       return NULL;
+}
+
+struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
+{
+       return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
+}
+
+struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
 {
        struct isl_basic_set *domain;
        unsigned n_out;
        if (!bmap)
                return NULL;
        n_out = bmap->n_out;
-       domain = isl_basic_set_from_basic_map(ctx, bmap);
-       return isl_basic_set_project_out(ctx, domain, n_out, 0);
+       domain = isl_basic_set_from_basic_map(bmap);
+       return isl_basic_set_project_out(domain, n_out, 0);
 }
 
-struct isl_basic_set *isl_basic_map_range(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
 {
-       return isl_basic_map_domain(ctx,
-                       isl_basic_map_reverse(ctx, bmap));
+       return isl_basic_map_domain(isl_basic_map_reverse(bmap));
 }
 
-struct isl_set *isl_map_range(struct isl_ctx *ctx, struct isl_map *map)
+struct isl_set *isl_map_range(struct isl_map *map)
 {
        int i;
        struct isl_set *set;
 
        if (!map)
                goto error;
-       map = isl_map_cow(ctx, map);
+       map = isl_map_cow(map);
        if (!map)
                goto error;
 
        set = (struct isl_set *) map;
        set->zero = 0;
        for (i = 0; i < map->n; ++i) {
-               set->p[i] = isl_basic_map_range(ctx, map->p[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);
        return set;
 error:
-       isl_map_free(ctx, map);
+       isl_map_free(map);
        return NULL;
 }
 
-struct isl_map *isl_map_from_set(
-               struct isl_ctx *ctx, struct isl_set *set,
+struct isl_map *isl_map_from_set(struct isl_set *set,
                unsigned n_in, unsigned n_out)
 {
        int i;
@@ -1849,13 +2549,13 @@ struct isl_map *isl_map_from_set(
 
        if (!set)
                return NULL;
-       isl_assert(ctx, set->dim == n_in + n_out, goto error);
-       set = isl_set_cow(ctx, set);
+       isl_assert(set->ctx, set->dim == n_in + n_out, goto error);
+       set = isl_set_cow(set);
        if (!set)
                return NULL;
        map = (struct isl_map *)set;
        for (i = 0; i < set->n; ++i) {
-               map->p[i] = isl_basic_map_from_basic_set(ctx,
+               map->p[i] = isl_basic_map_from_basic_set(
                                set->p[i], n_in, n_out);
                if (!map->p[i])
                        goto error;
@@ -1864,7 +2564,31 @@ struct isl_map *isl_map_from_set(
        map->n_out = n_out;
        return map;
 error:
-       isl_set_free(ctx, set);
+       isl_set_free(set);
+       return NULL;
+}
+
+struct isl_set *isl_set_from_map(struct isl_map *map)
+{
+       int i;
+       struct isl_set *set = NULL;
+
+       if (!map)
+               return NULL;
+       map = isl_map_cow(map);
+       if (!map)
+               return NULL;
+       map->n_out += map->n_in;
+       map->n_in = 0;
+       set = (struct isl_set *)map;
+       for (i = 0; i < map->n; ++i) {
+               set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
+               if (!set->p[i])
+                       goto error;
+       }
+       return set;
+error:
+       isl_map_free(map);
        return NULL;
 }
 
@@ -1880,6 +2604,8 @@ struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
        if (!map)
                return NULL;
 
+       map->ctx = ctx;
+       isl_ctx_ref(ctx);
        map->ref = 1;
        map->size = n;
        map->n = 0;
@@ -1895,10 +2621,35 @@ struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
 {
        struct isl_basic_map *bmap;
        bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
-       bmap = isl_basic_map_set_to_empty(ctx, bmap);
+       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 *bset;
+       bset = isl_basic_set_alloc(ctx, nparam, 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 *bmap;
+       bmap = isl_basic_map_alloc(ctx, nparam, in, out, 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 *bset;
+       bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 0, 0);
+       return bset;
+}
+
 struct isl_map *isl_map_empty(struct isl_ctx *ctx,
                unsigned nparam, unsigned in, unsigned out)
 {
@@ -1911,40 +2662,42 @@ struct isl_set *isl_set_empty(struct isl_ctx *ctx,
        return isl_set_alloc(ctx, nparam, dim, 0, ISL_MAP_DISJOINT);
 }
 
-struct isl_map *isl_map_dup(struct isl_ctx *ctx, struct isl_map *map)
+struct isl_map *isl_map_dup(struct isl_map *map)
 {
        int i;
        struct isl_map *dup;
 
-       dup = isl_map_alloc(ctx, map->nparam, map->n_in, map->n_out, map->n,
+       if (!map)
+               return NULL;
+       dup = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out, map->n,
                                map->flags);
        for (i = 0; i < map->n; ++i)
-               dup = isl_map_add(ctx, dup,
-                                 isl_basic_map_dup(ctx, map->p[i]));
+               dup = isl_map_add(dup,
+                                 isl_basic_map_dup(map->p[i]));
        return dup;
 }
 
-struct isl_map *isl_map_add(struct isl_ctx *ctx, struct isl_map *map,
-                               struct isl_basic_map *bmap)
+struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
 {
        if (!bmap || !map)
                goto error;
-       isl_assert(ctx, map->nparam == bmap->nparam, goto error);
-       isl_assert(ctx, map->n_in == bmap->n_in, goto error);
-       isl_assert(ctx, map->n_out == bmap->n_out, goto error);
-       isl_assert(ctx, map->n < map->size, 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, map->n < map->size, goto error);
        map->p[map->n] = bmap;
        map->n++;
+       F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 error:
        if (map)
-               isl_map_free(ctx, map);
+               isl_map_free(map);
        if (bmap)
-               isl_basic_map_free(ctx, bmap);
+               isl_basic_map_free(bmap);
        return NULL;
 }
 
-void isl_map_free(struct isl_ctx *ctx, struct isl_map *map)
+void isl_map_free(struct isl_map *map)
 {
        int i;
 
@@ -1954,93 +2707,183 @@ void isl_map_free(struct isl_ctx *ctx, struct isl_map *map)
        if (--map->ref > 0)
                return;
 
+       isl_ctx_deref(map->ctx);
        for (i = 0; i < map->n; ++i)
-               isl_basic_map_free(ctx, map->p[i]);
+               isl_basic_map_free(map->p[i]);
        free(map);
 }
 
-struct isl_map *isl_map_extend(struct isl_ctx *ctx, struct isl_map *base,
+struct isl_map *isl_map_extend(struct isl_map *base,
                unsigned nparam, unsigned n_in, unsigned n_out)
 {
        int i;
 
-       base = isl_map_cow(ctx, base);
+       base = isl_map_cow(base);
        if (!base)
                return NULL;
 
-       isl_assert(ctx, base->nparam <= nparam, goto error);
-       isl_assert(ctx, base->n_in <= n_in, goto error);
-       isl_assert(ctx, base->n_out <= n_out, goto error);
+       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;
        for (i = 0; i < base->n; ++i) {
-               base->p[i] = isl_basic_map_extend(ctx, base->p[i],
+               base->p[i] = isl_basic_map_extend(base->p[i],
                                nparam, n_in, n_out, 0, 0, 0);
                if (!base->p[i])
                        goto error;
        }
        return base;
 error:
-       isl_map_free(ctx, base);
+       isl_map_free(base);
        return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap,
-               unsigned input, int value)
+struct isl_set *isl_set_extend(struct isl_set *base,
+               unsigned nparam, unsigned dim)
 {
-       int j;
+       return (struct isl_set *)isl_map_extend((struct isl_map *)base,
+                                                       nparam, 0, dim);
+}
 
-       bmap = isl_basic_map_cow(ctx, bmap);
-       if (!bmap)
-               return NULL;
-       isl_assert(ctx, input < bmap->n_in, goto error);
+static struct isl_basic_map *isl_basic_map_fix_var(struct isl_basic_map *bmap,
+               unsigned var, int value)
+{
+       int j;
 
-       bmap = isl_basic_map_extend(ctx, bmap,
+       bmap = isl_basic_map_cow(bmap);
+       bmap = isl_basic_map_extend(bmap,
                        bmap->nparam, bmap->n_in, bmap->n_out, 0, 1, 0);
-       j = isl_basic_map_alloc_equality(ctx, bmap);
+       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+bmap->nparam+input], -1);
+       isl_int_set_si(bmap->eq[j][1 + var], -1);
        isl_int_set_si(bmap->eq[j][0], value);
-       bmap = isl_basic_map_simplify(ctx, bmap);
-       return isl_basic_map_finalize(ctx, bmap);
+       bmap = isl_basic_map_simplify(bmap);
+       return isl_basic_map_finalize(bmap);
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
+               unsigned input, 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);
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+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_map_free(ctx, bmap);
+       isl_basic_set_free(bset);
        return NULL;
 }
 
-struct isl_map *isl_map_fix_input_si(struct isl_ctx *ctx, struct isl_map *map,
+struct isl_map *isl_map_fix_input_si(struct isl_map *map,
                unsigned input, int value)
 {
        int i;
 
-       map = isl_map_cow(ctx, map);
+       map = isl_map_cow(map);
        if (!map)
                return NULL;
 
        isl_assert(ctx, input < map->n_in, goto error);
        for (i = 0; i < map->n; ++i) {
-               map->p[i] = isl_basic_map_fix_input_si(ctx, map->p[i],
-                                                               input, value);
+               map->p[i] = isl_basic_map_fix_input_si(map->p[i], input, value);
                if (!map->p[i])
                        goto error;
        }
+       F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 error:
-       isl_map_free(ctx, map);
+       isl_map_free(map);
+       return NULL;
+}
+
+struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
+{
+       int i;
+
+       set = isl_set_cow(set);
+       if (!set)
+               return NULL;
+
+       isl_assert(set->ctx, dim < set->dim, goto error);
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = isl_basic_set_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_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
+       unsigned dim, isl_int value)
+{
+       int j;
+
+       bset = isl_basic_set_cow(bset);
+       bset = isl_basic_set_extend(bset, bset->nparam, bset->dim, 0, 0, 1);
+       j = isl_basic_set_alloc_inequality(bset);
+       if (j < 0)
+               goto error;
+       isl_seq_clr(bset->ineq[j], 1 + bset->nparam + bset->dim + bset->extra);
+       isl_int_set_si(bset->ineq[j][1 + bset->nparam + dim], 1);
+       isl_int_neg(bset->ineq[j][0], value);
+       bset = isl_basic_set_simplify(bset);
+       return isl_basic_set_finalize(bset);
+error:
+       isl_basic_set_free(bset);
        return NULL;
 }
 
-struct isl_map *isl_map_reverse(struct isl_ctx *ctx, struct isl_map *map)
+struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
+                                       isl_int value)
+{
+       int i;
+
+       set = isl_set_cow(set);
+       if (!set)
+               return NULL;
+
+       isl_assert(set->ctx, dim < set->dim, goto error);
+       for (i = 0; i < set->n; ++i) {
+               set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
+               if (!set->p[i])
+                       goto error;
+       }
+       return set;
+error:
+       isl_set_free(set);
+       return NULL;
+}
+
+struct isl_map *isl_map_reverse(struct isl_map *map)
 {
        int i;
        unsigned t;
 
-       map = isl_map_cow(ctx, map);
+       map = isl_map_cow(map);
        if (!map)
                return NULL;
 
@@ -2048,32 +2891,32 @@ struct isl_map *isl_map_reverse(struct isl_ctx *ctx, struct isl_map *map)
        map->n_in = map->n_out;
        map->n_out = t;
        for (i = 0; i < map->n; ++i) {
-               map->p[i] = isl_basic_map_reverse(ctx, map->p[i]);
+               map->p[i] = isl_basic_map_reverse(map->p[i]);
                if (!map->p[i])
                        goto error;
        }
+       F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
 error:
-       isl_map_free(ctx, map);
+       isl_map_free(map);
        return NULL;
 }
 
-struct isl_map *isl_basic_map_lexmax(struct isl_ctx *ctx,
+struct isl_map *isl_basic_map_lexmax(
                struct isl_basic_map *bmap, struct isl_basic_set *dom,
                struct isl_set **empty)
 {
-       return isl_pip_basic_map_lexmax(ctx, bmap, dom, empty);
+       return isl_pip_basic_map_lexmax(bmap, dom, empty);
 }
 
-struct isl_map *isl_basic_map_lexmin(struct isl_ctx *ctx,
+struct isl_map *isl_basic_map_lexmin(
                struct isl_basic_map *bmap, struct isl_basic_set *dom,
                struct isl_set **empty)
 {
-       return isl_pip_basic_map_lexmin(ctx, bmap, dom, empty);
+       return isl_pip_basic_map_lexmin(bmap, dom, empty);
 }
 
-struct isl_set *isl_basic_set_lexmin(struct isl_ctx *ctx,
-               struct isl_basic_set *bset)
+struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
 {
        struct isl_basic_map *bmap = NULL;
        struct isl_basic_set *dom = NULL;
@@ -2081,30 +2924,29 @@ struct isl_set *isl_basic_set_lexmin(struct isl_ctx *ctx,
 
        if (!bset)
                goto error;
-       bmap = isl_basic_map_from_basic_set(ctx, bset, 0, bset->dim);
+       bmap = isl_basic_map_from_basic_set(bset, 0, bset->dim);
        if (!bmap)
                goto error;
-       dom = isl_basic_set_alloc(ctx, bmap->nparam, 0, 0, 0, 0);
+       dom = isl_basic_set_alloc(bmap->ctx, bmap->nparam, 0, 0, 0, 0);
        if (!dom)
                goto error;
-       min = isl_basic_map_lexmin(ctx, bmap, dom, NULL);
-       return isl_map_range(ctx, min);
+       min = isl_basic_map_lexmin(bmap, dom, NULL);
+       return isl_map_range(min);
 error:
-       isl_basic_map_free(ctx, bmap);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
-struct isl_map *isl_basic_map_compute_divs(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
 {
        if (!bmap)
                return NULL;
        if (bmap->n_div == 0)
-               return isl_map_from_basic_map(ctx, bmap);
-       return isl_pip_basic_map_compute_divs(ctx, bmap);
+               return isl_map_from_basic_map(bmap);
+       return isl_pip_basic_map_compute_divs(bmap);
 }
 
-struct isl_map *isl_map_compute_divs(struct isl_ctx *ctx, struct isl_map *map)
+struct isl_map *isl_map_compute_divs(struct isl_map *map)
 {
        int i;
        struct isl_map *res;
@@ -2113,31 +2955,33 @@ struct isl_map *isl_map_compute_divs(struct isl_ctx *ctx, struct isl_map *map)
                return NULL;
        if (map->n == 0)
                return map;
-       res = isl_basic_map_compute_divs(ctx,
-               isl_basic_map_copy(ctx, map->p[0]));
+       res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
        for (i = 1 ; i < map->n; ++i) {
                struct isl_map *r2;
-               r2 = isl_basic_map_compute_divs(ctx,
-                       isl_basic_map_copy(ctx, map->p[i]));
+               r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
                if (F_ISSET(map, ISL_MAP_DISJOINT))
-                       res = isl_map_union_disjoint(ctx, res, r2);
+                       res = isl_map_union_disjoint(res, r2);
                else
-                       res = isl_map_union(ctx, res, r2);
+                       res = isl_map_union(res, r2);
        }
-       isl_map_free(ctx, map);
+       isl_map_free(map);
 
        return res;
 }
 
-struct isl_set *isl_basic_set_compute_divs(struct isl_ctx *ctx,
-               struct isl_basic_set *bset)
+struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
 {
        return (struct isl_set *)
-               isl_basic_map_compute_divs(ctx,
-                       (struct isl_basic_map *)bset);
+               isl_basic_map_compute_divs((struct isl_basic_map *)bset);
 }
 
-struct isl_set *isl_map_domain(struct isl_ctx *ctx, struct isl_map *map)
+struct isl_set *isl_set_compute_divs(struct isl_set *set)
+{
+       return (struct isl_set *)
+               isl_map_compute_divs((struct isl_map *)set);
+}
+
+struct isl_set *isl_map_domain(struct isl_map *map)
 {
        int i;
        struct isl_set *set;
@@ -2145,7 +2989,7 @@ struct isl_set *isl_map_domain(struct isl_ctx *ctx, struct isl_map *map)
        if (!map)
                goto error;
 
-       map = isl_map_cow(ctx, map);
+       map = isl_map_cow(map);
        if (!map)
                return NULL;
 
@@ -2153,18 +2997,19 @@ struct isl_set *isl_map_domain(struct isl_ctx *ctx, struct isl_map *map)
        set->dim = map->n_in;
        set->zero = 0;
        for (i = 0; i < map->n; ++i) {
-               set->p[i] = isl_basic_map_domain(ctx, map->p[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);
        return set;
 error:
-       isl_map_free(ctx, map);
+       isl_map_free(map);
        return NULL;
 }
 
-struct isl_map *isl_map_union_disjoint(struct isl_ctx *ctx,
+struct isl_map *isl_map_union_disjoint(
                        struct isl_map *map1, struct isl_map *map2)
 {
        int i;
@@ -2175,52 +3020,51 @@ struct isl_map *isl_map_union_disjoint(struct isl_ctx *ctx,
                goto error;
 
        if (map1->n == 0) {
-               isl_map_free(ctx, map1);
+               isl_map_free(map1);
                return map2;
        }
        if (map2->n == 0) {
-               isl_map_free(ctx, map2);
+               isl_map_free(map2);
                return map1;
        }
 
-       isl_assert(ctx, map1->nparam == map2->nparam, goto error);
-       isl_assert(ctx, map1->n_in == map2->n_in, goto error);
-       isl_assert(ctx, map1->n_out == map2->n_out, 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);
 
        if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
            F_ISSET(map2, ISL_MAP_DISJOINT))
                FL_SET(flags, ISL_MAP_DISJOINT);
 
-       map = isl_map_alloc(ctx, map1->nparam, map1->n_in, map1->n_out,
+       map = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
                                map1->n + map2->n, flags);
        if (!map)
                goto error;
        for (i = 0; i < map1->n; ++i) {
-               map = isl_map_add(ctx, map,
-                                 isl_basic_map_copy(ctx, map1->p[i]));
+               map = isl_map_add(map,
+                                 isl_basic_map_copy(map1->p[i]));
                if (!map)
                        goto error;
        }
        for (i = 0; i < map2->n; ++i) {
-               map = isl_map_add(ctx, map,
-                                 isl_basic_map_copy(ctx, map2->p[i]));
+               map = isl_map_add(map,
+                                 isl_basic_map_copy(map2->p[i]));
                if (!map)
                        goto error;
        }
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map1);
+       isl_map_free(map2);
        return map;
 error:
-       isl_map_free(ctx, map);
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map);
+       isl_map_free(map1);
+       isl_map_free(map2);
        return NULL;
 }
 
-struct isl_map *isl_map_union(struct isl_ctx *ctx,
-                       struct isl_map *map1, struct isl_map *map2)
+struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
 {
-       map1 = isl_map_union_disjoint(ctx, map1, map2);
+       map1 = isl_map_union_disjoint(map1, map2);
        if (!map1)
                return NULL;
        if (map1->n > 1)
@@ -2228,25 +3072,22 @@ struct isl_map *isl_map_union(struct isl_ctx *ctx,
        return map1;
 }
 
-struct isl_set *isl_set_union_disjoint(struct isl_ctx *ctx,
+struct isl_set *isl_set_union_disjoint(
                        struct isl_set *set1, struct isl_set *set2)
 {
        return (struct isl_set *)
-               isl_map_union_disjoint(ctx,
+               isl_map_union_disjoint(
                        (struct isl_map *)set1, (struct isl_map *)set2);
 }
 
-struct isl_set *isl_set_union(struct isl_ctx *ctx,
-                       struct isl_set *set1, struct isl_set *set2)
+struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
 {
        return (struct isl_set *)
-               isl_map_union(ctx,
-                       (struct isl_map *)set1, (struct isl_map *)set2);
+               isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
 }
 
 struct isl_map *isl_map_intersect_range(
-               struct isl_ctx *ctx, struct isl_map *map,
-               struct isl_set *set)
+               struct isl_map *map, struct isl_set *set)
 {
        unsigned flags = 0;
        struct isl_map *result;
@@ -2259,54 +3100,51 @@ struct isl_map *isl_map_intersect_range(
            F_ISSET(set, ISL_MAP_DISJOINT))
                FL_SET(flags, ISL_MAP_DISJOINT);
 
-       result = isl_map_alloc(ctx, map->nparam, map->n_in, map->n_out,
+       result = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
                                map->n * set->n, flags);
        if (!result)
                goto error;
        for (i = 0; i < map->n; ++i)
                for (j = 0; j < set->n; ++j) {
-                       result = isl_map_add(ctx, result,
-                           isl_basic_map_intersect_range(ctx,
-                               isl_basic_map_copy(ctx, map->p[i]),
-                               isl_basic_set_copy(ctx, set->p[j])));
+                       result = isl_map_add(result,
+                           isl_basic_map_intersect_range(
+                               isl_basic_map_copy(map->p[i]),
+                               isl_basic_set_copy(set->p[j])));
                        if (!result)
                                goto error;
                }
-       isl_map_free(ctx, map);
-       isl_set_free(ctx, set);
+       isl_map_free(map);
+       isl_set_free(set);
        return result;
 error:
-       isl_map_free(ctx, map);
-       isl_set_free(ctx, set);
+       isl_map_free(map);
+       isl_set_free(set);
        return NULL;
 }
 
 struct isl_map *isl_map_intersect_domain(
-               struct isl_ctx *ctx, struct isl_map *map,
-               struct isl_set *set)
+               struct isl_map *map, struct isl_set *set)
 {
-       return isl_map_reverse(ctx,
-               isl_map_intersect_range(ctx, isl_map_reverse(ctx, map), set));
+       return isl_map_reverse(
+               isl_map_intersect_range(isl_map_reverse(map), set));
 }
 
 struct isl_map *isl_map_apply_domain(
-               struct isl_ctx *ctx, struct isl_map *map1,
-               struct isl_map *map2)
+               struct isl_map *map1, struct isl_map *map2)
 {
        if (!map1 || !map2)
                goto error;
-       map1 = isl_map_reverse(ctx, map1);
-       map1 = isl_map_apply_range(ctx, map1, map2);
-       return isl_map_reverse(ctx, map1);
+       map1 = isl_map_reverse(map1);
+       map1 = isl_map_apply_range(map1, map2);
+       return isl_map_reverse(map1);
 error:
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map1);
+       isl_map_free(map2);
        return NULL;
 }
 
 struct isl_map *isl_map_apply_range(
-               struct isl_ctx *ctx, struct isl_map *map1,
-               struct isl_map *map2)
+               struct isl_map *map1, struct isl_map *map2)
 {
        struct isl_map *result;
        int i, j;
@@ -2314,36 +3152,37 @@ struct isl_map *isl_map_apply_range(
        if (!map1 || !map2)
                goto error;
 
-       isl_assert(ctx, map1->nparam == map2->nparam, goto error);
-       isl_assert(ctx, map1->n_out == map2->n_in, goto error);
+       isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
+       isl_assert(map1->ctx, map1->n_out == map2->n_in, goto error);
 
-       result = isl_map_alloc(ctx, map1->nparam, map1->n_in, map2->n_out,
+       result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map2->n_out,
                                map1->n * map2->n, 0);
        if (!result)
                goto error;
        for (i = 0; i < map1->n; ++i)
                for (j = 0; j < map2->n; ++j) {
-                       result = isl_map_add(ctx, result,
-                           isl_basic_map_apply_range(ctx,
-                               isl_basic_map_copy(ctx, map1->p[i]),
-                               isl_basic_map_copy(ctx, map2->p[j])));
+                       result = isl_map_add(result,
+                           isl_basic_map_apply_range(
+                               isl_basic_map_copy(map1->p[i]),
+                               isl_basic_map_copy(map2->p[j])));
                        if (!result)
                                goto error;
                }
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map1);
+       isl_map_free(map2);
+       if (result && result->n <= 1)
+               F_SET(result, ISL_MAP_DISJOINT);
        return result;
 error:
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map1);
+       isl_map_free(map2);
        return NULL;
 }
 
 /*
  * returns range - domain
  */
-struct isl_basic_set *isl_basic_map_deltas(struct isl_ctx *ctx,
-                               struct isl_basic_map *bmap)
+struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
 {
        struct isl_basic_set *bset;
        unsigned dim;
@@ -2351,14 +3190,14 @@ struct isl_basic_set *isl_basic_map_deltas(struct isl_ctx *ctx,
 
        if (!bmap)
                goto error;
-       isl_assert(ctx, bmap->n_in == bmap->n_out, goto error);
+       isl_assert(bmap->ctx, bmap->n_in == bmap->n_out, goto error);
        dim = bmap->n_in;
-       bset = isl_basic_set_from_basic_map(ctx, bmap);
-       bset = isl_basic_set_extend(ctx, bset, bset->nparam, 3*dim, 0,
+       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_swap_vars(ctx, bset, 2*dim);
+       bset = isl_basic_set_swap_vars(bset, 2*dim);
        for (i = 0; i < dim; ++i) {
-               int j = isl_basic_map_alloc_equality(ctx,
+               int j = isl_basic_map_alloc_equality(
                                            (struct isl_basic_map *)bset);
                if (j < 0)
                        goto error;
@@ -2368,9 +3207,34 @@ struct isl_basic_set *isl_basic_map_deltas(struct isl_ctx *ctx,
                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);
        }
-       return isl_basic_set_project_out(ctx, bset, 2*dim, 0);
+       return isl_basic_set_project_out(bset, 2*dim, 0);
 error:
-       isl_basic_map_free(ctx, bmap);
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+/*
+ * returns range - domain
+ */
+struct isl_set *isl_map_deltas(struct isl_map *map)
+{
+       int i;
+       struct isl_set *result;
+
+       if (!map)
+               return NULL;
+
+       isl_assert(map->ctx, map->n_in == map->n_out, goto error);
+       result = isl_set_alloc(map->ctx, map->nparam, map->n_in, map->n, map->flags);
+       if (!result)
+               goto error;
+       for (i = 0; i < map->n; ++i)
+               result = isl_set_add(result,
+                         isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
+       isl_map_free(map);
+       return result;
+error:
+       isl_map_free(map);
        return NULL;
 }
 
@@ -2382,8 +3246,7 @@ error:
  *
  * then it can safely be removed.
  */
-static int div_is_redundant(struct isl_ctx *ctx, struct isl_basic_map *bmap,
-                               int div)
+static int div_is_redundant(struct isl_basic_map *bmap, int div)
 {
        int i;
        unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
@@ -2431,68 +3294,68 @@ static int div_is_redundant(struct isl_ctx *ctx, struct isl_basic_map *bmap,
  * 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_ctx *ctx,
-               struct isl_basic_map *bmap)
+static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
 {
        int i;
 
+       if (!bmap)
+               return NULL;
+
        for (i = bmap->n_div-1; i >= 0; --i) {
-               if (!div_is_redundant(ctx, bmap, i))
+               if (!div_is_redundant(bmap, i))
                        continue;
-               bmap = isl_basic_map_drop_div(ctx, bmap, i);
+               bmap = isl_basic_map_drop_div(bmap, i);
        }
        return bmap;
 }
 
-struct isl_basic_map *isl_basic_map_finalize(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
 {
-       bmap = remove_redundant_divs(ctx, bmap);
+       bmap = remove_redundant_divs(bmap);
        if (!bmap)
                return NULL;
        F_SET(bmap, ISL_BASIC_SET_FINAL);
        return bmap;
 }
 
-struct isl_basic_set *isl_basic_set_finalize(struct isl_ctx *ctx,
-               struct isl_basic_set *bset)
+struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
 {
        return (struct isl_basic_set *)
-               isl_basic_map_finalize(ctx,
-                       (struct isl_basic_map *)bset);
+               isl_basic_map_finalize((struct isl_basic_map *)bset);
 }
 
-struct isl_set *isl_set_finalize(struct isl_ctx *ctx, struct isl_set *set)
+struct isl_set *isl_set_finalize(struct isl_set *set)
 {
        int i;
 
        if (!set)
                return NULL;
        for (i = 0; i < set->n; ++i) {
-               set->p[i] = isl_basic_set_finalize(ctx, set->p[i]);
+               set->p[i] = isl_basic_set_finalize(set->p[i]);
                if (!set->p[i])
                        goto error;
        }
        return set;
 error:
-       isl_set_free(ctx, set);
+       isl_set_free(set);
        return NULL;
 }
 
-struct isl_map *isl_map_finalize(struct isl_ctx *ctx, struct isl_map *map)
+struct isl_map *isl_map_finalize(struct isl_map *map)
 {
        int i;
 
        if (!map)
                return NULL;
        for (i = 0; i < map->n; ++i) {
-               map->p[i] = isl_basic_map_finalize(ctx, map->p[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(ctx, map);
+       isl_map_free(map);
        return NULL;
 }
 
@@ -2507,7 +3370,7 @@ struct isl_basic_map *isl_basic_map_identity(struct isl_ctx *ctx,
                goto error;
 
        for (i = 0; i < dim; ++i) {
-               int j = isl_basic_map_alloc_equality(ctx, bmap);
+               int j = isl_basic_map_alloc_equality(bmap);
                if (j < 0)
                        goto error;
                isl_seq_clr(bmap->eq[j],
@@ -2515,9 +3378,9 @@ struct isl_basic_map *isl_basic_map_identity(struct isl_ctx *ctx,
                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(ctx, bmap);
+       return isl_basic_map_finalize(bmap);
 error:
-       isl_basic_map_free(ctx, bmap);
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
@@ -2528,31 +3391,27 @@ struct isl_map *isl_map_identity(struct isl_ctx *ctx,
                                                ISL_MAP_DISJOINT);
        if (!map)
                goto error;
-       map = isl_map_add(ctx, map,
+       map = isl_map_add(map,
                isl_basic_map_identity(ctx, nparam, dim));
        return map;
 error:
-       isl_map_free(ctx, map);
+       isl_map_free(map);
        return NULL;
 }
 
-int isl_set_is_equal(struct isl_ctx *ctx,
-               struct isl_set *set1, struct isl_set *set2)
+int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
 {
-       return isl_map_is_equal(ctx,
-                       (struct isl_map *)set1, (struct isl_map *)set2);
+       return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
 }
 
-int isl_set_is_subset(struct isl_ctx *ctx,
-               struct isl_set *set1, struct isl_set *set2)
+int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
 {
-       return isl_map_is_subset(ctx,
+       return isl_map_is_subset(
                        (struct isl_map *)set1, (struct isl_map *)set2);
 }
 
-int isl_basic_map_is_subset(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap1,
-               struct isl_basic_map *bmap2)
+int isl_basic_map_is_subset(
+               struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
        int is_subset;
        struct isl_map *map1;
@@ -2561,20 +3420,39 @@ int isl_basic_map_is_subset(struct isl_ctx *ctx,
        if (!bmap1 || !bmap2)
                return -1;
 
-       map1 = isl_map_from_basic_map(ctx,
-                       isl_basic_map_copy(ctx, bmap1));
-       map2 = isl_map_from_basic_map(ctx,
-                       isl_basic_map_copy(ctx, bmap2));
+       map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
+       map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
 
-       is_subset = isl_map_is_subset(ctx, map1, map2);
+       is_subset = isl_map_is_subset(map1, map2);
 
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map1);
+       isl_map_free(map2);
 
        return is_subset;
 }
 
-int isl_map_is_empty(struct isl_ctx *ctx, struct isl_map *map)
+int isl_basic_map_is_equal(
+               struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+{
+       int is_subset;
+
+       if (!bmap1 || !bmap2)
+               return -1;
+       is_subset = isl_basic_map_is_subset(bmap1, bmap2);
+       if (is_subset != 1)
+               return is_subset;
+       is_subset = isl_basic_map_is_subset(bmap2, bmap1);
+       return is_subset;
+}
+
+int isl_basic_set_is_equal(
+               struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+       return isl_basic_map_is_equal(
+               (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
+}
+
+int isl_map_is_empty(struct isl_map *map)
 {
        int i;
        int is_empty;
@@ -2582,7 +3460,7 @@ int isl_map_is_empty(struct isl_ctx *ctx, struct isl_map *map)
        if (!map)
                return -1;
        for (i = 0; i < map->n; ++i) {
-               is_empty = isl_basic_map_is_empty(ctx, map->p[i]);
+               is_empty = isl_basic_map_is_empty(map->p[i]);
                if (is_empty < 0)
                        return -1;
                if (!is_empty)
@@ -2591,13 +3469,12 @@ int isl_map_is_empty(struct isl_ctx *ctx, struct isl_map *map)
        return 1;
 }
 
-int isl_set_is_empty(struct isl_ctx *ctx, struct isl_set *set)
+int isl_set_is_empty(struct isl_set *set)
 {
-       return isl_map_is_empty(ctx, (struct isl_map *)set);
+       return isl_map_is_empty((struct isl_map *)set);
 }
 
-int isl_map_is_subset(struct isl_ctx *ctx, struct isl_map *map1,
-               struct isl_map *map2)
+int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
 {
        int i;
        int is_subset = 0;
@@ -2606,56 +3483,52 @@ int isl_map_is_subset(struct isl_ctx *ctx, struct isl_map *map1,
        if (!map1 || !map2)
                return -1;
 
-       if (isl_map_is_empty(ctx, map1))
+       if (isl_map_is_empty(map1))
                return 1;
 
-       if (isl_map_is_empty(ctx, map2))
+       if (isl_map_is_empty(map2))
                return 0;
 
-       diff = isl_map_subtract(ctx, isl_map_copy(ctx, map1),
-                                    isl_map_copy(ctx, map2));
+       diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
        if (!diff)
                return -1;
 
-       is_subset = isl_map_is_empty(ctx, diff);
-       isl_map_free(ctx, diff);
+       is_subset = isl_map_is_empty(diff);
+       isl_map_free(diff);
 
        return is_subset;
 }
 
-int isl_map_is_equal(struct isl_ctx *ctx,
-               struct isl_map *map1, struct isl_map *map2)
+int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
 {
        int is_subset;
 
        if (!map1 || !map2)
                return -1;
-       is_subset = isl_map_is_subset(ctx, map1, map2);
+       is_subset = isl_map_is_subset(map1, map2);
        if (is_subset != 1)
                return is_subset;
-       is_subset = isl_map_is_subset(ctx, map2, map1);
+       is_subset = isl_map_is_subset(map2, map1);
        return is_subset;
 }
 
-int isl_basic_map_is_strict_subset(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap1,
-               struct isl_basic_map *bmap2)
+int isl_basic_map_is_strict_subset(
+               struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
        int is_subset;
 
        if (!bmap1 || !bmap2)
                return -1;
-       is_subset = isl_basic_map_is_subset(ctx, bmap1, bmap2);
+       is_subset = isl_basic_map_is_subset(bmap1, bmap2);
        if (is_subset != 1)
                return is_subset;
-       is_subset = isl_basic_map_is_subset(ctx, bmap2, bmap1);
+       is_subset = isl_basic_map_is_subset(bmap2, bmap1);
        if (is_subset == -1)
                return is_subset;
        return !is_subset;
 }
 
-static int basic_map_contains(struct isl_ctx *ctx, struct isl_basic_map *bmap,
-                                        struct isl_vec *vec)
+static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
 {
        int i;
        unsigned total;
@@ -2688,8 +3561,14 @@ static int basic_map_contains(struct isl_ctx *ctx, struct isl_basic_map *bmap,
        return 1;
 }
 
-int isl_basic_map_is_empty(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+int isl_basic_map_is_universe(struct isl_basic_map *bmap)
+{
+       if (!bmap)
+               return -1;
+       return bmap->n_eq == 0 && bmap->n_ineq == 0;
+}
+
+int isl_basic_map_is_empty(struct isl_basic_map *bmap)
 {
        struct isl_basic_set *bset = NULL;
        struct isl_vec *sample = NULL;
@@ -2702,66 +3581,70 @@ int isl_basic_map_is_empty(struct isl_ctx *ctx,
        if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
                return 1;
 
+       if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
+               struct isl_basic_map *copy = isl_basic_map_copy(bmap);
+               copy = isl_basic_map_convex_hull(copy);
+               empty = F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
+               isl_basic_map_free(copy);
+               return empty;
+       }
+
        total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
        if (bmap->sample && bmap->sample->size == total) {
-               int contains = basic_map_contains(ctx, bmap, bmap->sample);
+               int contains = basic_map_contains(bmap, bmap->sample);
                if (contains < 0)
                        return -1;
                if (contains)
                        return 0;
        }
-       bset = isl_basic_map_underlying_set(ctx,
-                       isl_basic_map_copy(ctx, bmap));
+       bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
        if (!bset)
                return -1;
-       sample = isl_basic_set_sample(ctx, bset);
+       sample = isl_basic_set_sample(bset);
        if (!sample)
                return -1;
        empty = sample->size == 0;
        if (bmap->sample)
-               isl_vec_free(ctx, bmap->sample);
+               isl_vec_free(bmap->ctx, bmap->sample);
        bmap->sample = sample;
 
        return empty;
 }
 
 struct isl_map *isl_basic_map_union(
-               struct isl_ctx *ctx, struct isl_basic_map *bmap1,
-               struct isl_basic_map *bmap2)
+       struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
        struct isl_map *map;
        if (!bmap1 || !bmap2)
                return NULL;
 
-       isl_assert(ctx, bmap1->nparam == bmap2->nparam, goto error);
-       isl_assert(ctx, bmap1->n_in == bmap2->n_in, goto error);
-       isl_assert(ctx, bmap1->n_out == bmap2->n_out, 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);
 
-       map = isl_map_alloc(ctx, bmap1->nparam,
+       map = isl_map_alloc(bmap1->ctx, bmap1->nparam,
                                bmap1->n_in, bmap1->n_out, 2, 0);
        if (!map)
                goto error;
-       map = isl_map_add(ctx, map, bmap1);
-       map = isl_map_add(ctx, map, bmap2);
+       map = isl_map_add(map, bmap1);
+       map = isl_map_add(map, bmap2);
        return map;
 error:
-       isl_basic_map_free(ctx, bmap1);
-       isl_basic_map_free(ctx, bmap2);
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
        return NULL;
 }
 
 struct isl_set *isl_basic_set_union(
-               struct isl_ctx *ctx, struct isl_basic_set *bset1,
-               struct isl_basic_set *bset2)
+               struct isl_basic_set *bset1, struct isl_basic_set *bset2)
 {
-       return (struct isl_set *)isl_basic_map_union(ctx,
+       return (struct isl_set *)isl_basic_map_union(
                                            (struct isl_basic_map *)bset1,
                                            (struct isl_basic_map *)bset2);
 }
 
 /* Order divs such that any div only depends on previous divs */
-static struct isl_basic_map *order_divs(struct isl_ctx *ctx,
-               struct isl_basic_map *bmap)
+static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
 {
        int i;
        unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
@@ -2793,38 +3676,7 @@ static int find_div(struct isl_basic_map *dst,
        return -1;
 }
 
-/* For a div d = floor(f/m), add the constraints
- *
- *             f - m d >= 0
- *             -(f-(n-1)) + m d >= 0
- *
- * Note that the second constraint is the negation of
- *
- *             f - m d >= n
- */
-static int add_div_constraints(struct isl_ctx *ctx,
-               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;
-
-       i = isl_basic_map_alloc_inequality(ctx, bmap);
-       if (i < 0)
-               return -1;
-       isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
-       isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
-
-       j = isl_basic_map_alloc_inequality(ctx, bmap);
-       if (j < 0)
-               return -1;
-       isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
-       isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
-       isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
-       return j;
-}
-
-struct isl_basic_map *isl_basic_map_align_divs(struct isl_ctx *ctx,
+struct isl_basic_map *isl_basic_map_align_divs(
                struct isl_basic_map *dst, struct isl_basic_map *src)
 {
        int i;
@@ -2833,21 +3685,21 @@ struct isl_basic_map *isl_basic_map_align_divs(struct isl_ctx *ctx,
        if (src->n_div == 0)
                return dst;
 
-       src = order_divs(ctx, src);
-       dst = isl_basic_map_extend(ctx, dst, dst->nparam, dst->n_in,
+       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);
        if (!dst)
                return NULL;
        for (i = 0; i < src->n_div; ++i) {
                int j = find_div(dst, src, i);
                if (j < 0) {
-                       j = isl_basic_map_alloc_div(ctx, dst);
+                       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);
-                       if (add_div_constraints(ctx, dst, j) < 0)
+                       if (add_div_constraints(dst, j) < 0)
                                goto error;
                }
                if (j != i)
@@ -2855,12 +3707,29 @@ struct isl_basic_map *isl_basic_map_align_divs(struct isl_ctx *ctx,
        }
        return dst;
 error:
-       isl_basic_map_free(ctx, dst);
+       isl_basic_map_free(dst);
        return NULL;
 }
 
-static struct isl_map *add_cut_constraint(struct isl_ctx *ctx,
-               struct isl_map *dst,
+struct isl_map *isl_map_align_divs(struct isl_map *map)
+{
+       int i;
+
+       map = isl_map_compute_divs(map);
+       map = isl_map_cow(map);
+       if (!map)
+               return NULL;
+
+       for (i = 1; i < map->n; ++i)
+               map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
+       for (i = 1; i < map->n; ++i)
+               map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
+
+       F_CLR(map, ISL_MAP_NORMALIZED);
+       return map;
+}
+
+static struct isl_map *add_cut_constraint(struct isl_map *dst,
                struct isl_basic_map *src, isl_int *c,
                unsigned len, int oppose)
 {
@@ -2869,13 +3738,13 @@ static struct isl_map *add_cut_constraint(struct isl_ctx *ctx,
        int k;
        unsigned total;
 
-       copy = isl_basic_map_copy(ctx, src);
-       copy = isl_basic_map_cow(ctx, copy);
+       copy = isl_basic_map_copy(src);
+       copy = isl_basic_map_cow(copy);
        if (!copy)
                goto error;
-       copy = isl_basic_map_extend(ctx, copy,
+       copy = isl_basic_map_extend(copy,
                copy->nparam, copy->n_in, copy->n_out, 0, 0, 1);
-       k = isl_basic_map_alloc_inequality(ctx, copy);
+       k = isl_basic_map_alloc_inequality(copy);
        if (k < 0)
                goto error;
        if (oppose)
@@ -2884,25 +3753,24 @@ static struct isl_map *add_cut_constraint(struct isl_ctx *ctx,
                isl_seq_cpy(copy->ineq[k], c, len);
        total = 1 + copy->nparam + copy->n_in + copy->n_out + copy->extra;
        isl_seq_clr(copy->ineq[k]+len, total - len);
-       isl_inequality_negate(ctx, copy, k);
-       copy = isl_basic_map_simplify(ctx, copy);
-       copy = isl_basic_map_finalize(ctx, copy);
-       is_empty = isl_basic_map_is_empty(ctx, copy);
+       isl_inequality_negate(copy, k);
+       copy = isl_basic_map_simplify(copy);
+       copy = isl_basic_map_finalize(copy);
+       is_empty = isl_basic_map_is_empty(copy);
        if (is_empty < 0)
                goto error;
        if (!is_empty)
-               dst = isl_map_add(ctx, dst, copy);
+               dst = isl_map_add(dst, copy);
        else
-               isl_basic_map_free(ctx, copy);
+               isl_basic_map_free(copy);
        return dst;
 error:
-       isl_basic_map_free(ctx, copy);
-       isl_map_free(ctx, dst);
+       isl_basic_map_free(copy);
+       isl_map_free(dst);
        return NULL;
 }
 
-static struct isl_map *subtract(struct isl_ctx *ctx, struct isl_map *map,
-               struct isl_basic_map *bmap)
+static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
 {
        int i, j, k;
        unsigned flags = 0;
@@ -2919,38 +3787,38 @@ static struct isl_map *subtract(struct isl_ctx *ctx, struct isl_map *map,
                FL_SET(flags, ISL_MAP_DISJOINT);
 
        max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
-       rest = isl_map_alloc(ctx, map->nparam, map->n_in, map->n_out,
+       rest = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
                                max, flags);
        if (!rest)
                goto error;
 
        for (i = 0; i < map->n; ++i) {
-               map->p[i] = isl_basic_map_align_divs(ctx, map->p[i], bmap);
+               map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
                if (!map->p[i])
                        goto error;
        }
 
        for (j = 0; j < map->n; ++j)
-               map->p[j] = isl_basic_map_cow(ctx, map->p[j]);
+               map->p[j] = isl_basic_map_cow(map->p[j]);
 
        for (i = 0; i < bmap->n_eq; ++i) {
                for (j = 0; j < map->n; ++j) {
-                       rest = add_cut_constraint(ctx, rest,
+                       rest = add_cut_constraint(rest,
                                map->p[j], bmap->eq[i], 1+total, 0);
                        if (!rest)
                                goto error;
 
-                       rest = add_cut_constraint(ctx, rest,
+                       rest = add_cut_constraint(rest,
                                map->p[j], bmap->eq[i], 1+total, 1);
                        if (!rest)
                                goto error;
 
-                       map->p[j] = isl_basic_map_extend(ctx, map->p[j],
+                       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);
                        if (!map->p[j])
                                goto error;
-                       k = isl_basic_map_alloc_equality(ctx, map->p[j]);
+                       k = isl_basic_map_alloc_equality(map->p[j]);
                        if (k < 0)
                                goto error;
                        isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
@@ -2961,17 +3829,17 @@ static struct isl_map *subtract(struct isl_ctx *ctx, struct isl_map *map,
 
        for (i = 0; i < bmap->n_ineq; ++i) {
                for (j = 0; j < map->n; ++j) {
-                       rest = add_cut_constraint(ctx, rest,
+                       rest = add_cut_constraint(rest,
                                map->p[j], bmap->ineq[i], 1+total, 0);
                        if (!rest)
                                goto error;
 
-                       map->p[j] = isl_basic_map_extend(ctx, map->p[j],
+                       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);
                        if (!map->p[j])
                                goto error;
-                       k = isl_basic_map_alloc_inequality(ctx, map->p[j]);
+                       k = isl_basic_map_alloc_inequality(map->p[j]);
                        if (k < 0)
                                goto error;
                        isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
@@ -2980,72 +3848,70 @@ static struct isl_map *subtract(struct isl_ctx *ctx, struct isl_map *map,
                }
        }
 
-       isl_map_free(ctx, map);
+       isl_map_free(map);
        return rest;
 error:
-       isl_map_free(ctx, map);
-       isl_map_free(ctx, rest);
+       isl_map_free(map);
+       isl_map_free(rest);
        return NULL;
 }
 
-struct isl_map *isl_map_subtract(struct isl_ctx *ctx, struct isl_map *map1,
-               struct isl_map *map2)
+struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
 {
        int i;
        if (!map1 || !map2)
                goto error;
 
-       isl_assert(ctx, map1->nparam == map2->nparam, goto error);
-       isl_assert(ctx, map1->n_in == map2->n_in, goto error);
-       isl_assert(ctx, map1->n_out == map2->n_out, 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);
 
-       if (isl_map_is_empty(ctx, map2)) {
-               isl_map_free(ctx, map2);
+       if (isl_map_is_empty(map2)) {
+               isl_map_free(map2);
                return map1;
        }
 
-       map1 = isl_map_compute_divs(ctx, map1);
-       map2 = isl_map_compute_divs(ctx, map2);
+       map1 = isl_map_compute_divs(map1);
+       map2 = isl_map_compute_divs(map2);
        if (!map1 || !map2)
                goto error;
 
        for (i = 0; map1 && i < map2->n; ++i)
-               map1 = subtract(ctx, map1, map2->p[i]);
+               map1 = subtract(map1, map2->p[i]);
 
-       isl_map_free(ctx, map2);
+       isl_map_free(map2);
        return map1;
 error:
-       isl_map_free(ctx, map1);
-       isl_map_free(ctx, map2);
+       isl_map_free(map1);
+       isl_map_free(map2);
        return NULL;
 }
 
-struct isl_set *isl_set_subtract(struct isl_ctx *ctx, struct isl_set *set1,
-               struct isl_set *set2)
+struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
 {
        return (struct isl_set *)
-               isl_map_subtract(ctx,
+               isl_map_subtract(
                        (struct isl_map *)set1, (struct isl_map *)set2);
 }
 
-struct isl_set *isl_set_apply(struct isl_ctx *ctx, struct isl_set *set,
-               struct isl_map *map)
+struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
 {
-       isl_assert(ctx, set->dim == map->n_in, goto error);
-       map = isl_map_intersect_domain(ctx, map, set);
-       set = isl_map_range(ctx, map);
+       if (!set || !map)
+               goto error;
+       isl_assert(set->ctx, set->dim == map->n_in, goto error);
+       map = isl_map_intersect_domain(map, set);
+       set = isl_map_range(map);
        return set;
 error:
-       isl_set_free(ctx, set);
-       isl_map_free(ctx, map);
+       isl_set_free(set);
+       isl_map_free(map);
        return NULL;
 }
 
 /* There is no need to cow as removing empty parts doesn't change
  * the meaning of the set.
  */
-struct isl_map *isl_map_remove_empty_parts(struct isl_ctx *ctx,
-       struct isl_map *map)
+struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
 {
        int i;
 
@@ -3055,18 +3921,684 @@ struct isl_map *isl_map_remove_empty_parts(struct isl_ctx *ctx,
        for (i = map->n-1; i >= 0; --i) {
                if (!F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
                        continue;
-               isl_basic_map_free(ctx, map->p[i]);
-               if (i != map->n-1)
+               isl_basic_map_free(map->p[i]);
+               if (i != map->n-1) {
+                       F_CLR(map, ISL_MAP_NORMALIZED);
                        map->p[i] = map->p[map->n-1];
+               }
                map->n--;
        }
 
        return map;
 }
 
-struct isl_set *isl_set_remove_empty_parts(struct isl_ctx *ctx,
-       struct isl_set *set)
+struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
 {
        return (struct isl_set *)
-               isl_map_remove_empty_parts(ctx, (struct isl_map *)set);
+               isl_map_remove_empty_parts((struct isl_map *)set);
+}
+
+struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
+{
+       struct isl_basic_set *bset;
+       if (!set || set->n == 0)
+               return NULL;
+       bset = set->p[set->n-1];
+       isl_assert(set->ctx, F_ISSET(bset, ISL_BASIC_SET_FINAL), return NULL);
+       return isl_basic_set_copy(bset);
+}
+
+struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
+                                               struct isl_basic_set *bset)
+{
+       int i;
+
+       if (!set || !bset)
+               goto error;
+       for (i = set->n-1; i >= 0; --i) {
+               if (set->p[i] != bset)
+                       continue;
+               set = isl_set_cow(set);
+               if (!set)
+                       goto error;
+               isl_basic_set_free(set->p[i]);
+               if (i != set->n-1) {
+                       F_CLR(set, ISL_SET_NORMALIZED);
+                       set->p[i] = set->p[set->n-1];
+               }
+               set->n--;
+               return set;
+       }
+       isl_basic_set_free(bset);
+       return set;
+error:
+       isl_set_free(set);
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+/* Given two _disjoint_ basic sets bset1 and bset2, check whether
+ * for any common value of the parameters and dimensions preceding dim
+ * in both basic sets, the values of dimension pos in bset1 are
+ * smaller or larger then those in bset2.
+ *
+ * Returns
+ *      1 if bset1 follows bset2
+ *     -1 if bset1 precedes bset2
+ *      0 if bset1 and bset2 are incomparable
+ *     -2 if some error occurred.
+ */
+int isl_basic_set_compare_at(struct isl_basic_set *bset1,
+       struct isl_basic_set *bset2, int pos)
+{
+       struct isl_basic_map *bmap1 = NULL;
+       struct isl_basic_map *bmap2 = NULL;
+       struct isl_ctx *ctx;
+       struct isl_vec *obj;
+       unsigned total;
+       isl_int num, den;
+       enum isl_lp_result res;
+       int cmp;
+
+       if (!bset1 || !bset2)
+               return -2;
+
+       bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1),
+                                               pos, bset1->dim - pos);
+       bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2),
+                                               pos, bset2->dim - pos);
+       if (!bmap1 || !bmap2)
+               goto error;
+       bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
+                       bmap1->n_in, bmap1->n_out + bmap2->n_out,
+                       bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
+       if (!bmap1)
+               goto error;
+       total = bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
+       ctx = bmap1->ctx;
+       obj = isl_vec_alloc(ctx, total);
+       isl_seq_clr(obj->block.data, total);
+       isl_int_set_si(obj->block.data[bmap1->nparam+bmap1->n_in], 1);
+       isl_int_set_si(obj->block.data[bmap1->nparam+bmap1->n_in+
+                                       bmap1->n_out-bmap2->n_out], -1);
+       if (!obj)
+               goto error;
+       bmap1 = add_constraints(bmap1, bmap2, 0, bmap1->n_out - bmap2->n_out);
+       isl_int_init(num);
+       isl_int_init(den);
+       res = isl_solve_lp(bmap1, 0, obj->block.data, ctx->one, &num, &den);
+       if (res == isl_lp_empty)
+               cmp = 0;
+       else if (res == isl_lp_ok && isl_int_is_pos(num))
+               cmp = 1;
+       else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
+                 res == isl_lp_unbounded)
+               cmp = -1;
+       else
+               cmp = -2;
+       isl_int_clear(num);
+       isl_int_clear(den);
+       isl_basic_map_free(bmap1);
+       isl_vec_free(ctx, obj);
+       return cmp;
+error:
+       isl_basic_map_free(bmap1);
+       isl_basic_map_free(bmap2);
+       return -2;
+}
+
+static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
+       unsigned pos, isl_int *val)
+{
+       int i;
+       int d;
+       unsigned total;
+
+       if (!bmap)
+               return -1;
+       total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
+               for (; d+1 > pos; --d)
+                       if (!isl_int_is_zero(bmap->eq[i][1+d]))
+                               break;
+               if (d != pos)
+                       continue;
+               if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
+                       return 0;
+               if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
+                       return 0;
+               if (!isl_int_is_one(bmap->eq[i][1+d]))
+                       return 0;
+               if (val)
+                       isl_int_neg(*val, bmap->eq[i][0]);
+               return 1;
+       }
+       return 0;
+}
+
+static int isl_map_fast_has_fixed_var(struct isl_map *map,
+       unsigned pos, isl_int *val)
+{
+       int i;
+       isl_int v;
+       isl_int tmp;
+       int fixed;
+
+       if (!map)
+               return -1;
+       if (map->n == 0)
+               return 0;
+       if (map->n == 1)
+               return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val); 
+       isl_int_init(v);
+       isl_int_init(tmp);
+       fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v); 
+       for (i = 1; fixed == 1 && i < map->n; ++i) {
+               fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp); 
+               if (fixed == 1 && isl_int_ne(tmp, v))
+                       fixed = 0;
+       }
+       if (val)
+               isl_int_set(*val, v);
+       isl_int_clear(tmp);
+       isl_int_clear(v);
+       return fixed;
+}
+
+static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
+       isl_int *val)
+{
+       return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
+}
+
+/* Check if dimension dim has fixed value and if so and if val is not NULL,
+ * then return this fixed value in *val.
+ */
+int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
+{
+       return isl_set_fast_has_fixed_var(set, set->nparam + dim, val);
+}
+
+/* Check if input variable in has fixed value and if so and if val is not NULL,
+ * then return this fixed value in *val.
+ */
+int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
+{
+       return isl_map_fast_has_fixed_var(map, map->nparam + in, val);
+}
+
+/* Check if dimension dim has an (obvious) fixed lower bound and if so
+ * and if val is not NULL, then return this lower bound in *val.
+ */
+int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
+       unsigned dim, isl_int *val)
+{
+       int i, i_eq = -1, i_ineq = -1;
+       isl_int *c;
+       unsigned total;
+
+       if (!bset)
+               return -1;
+       total = bset->nparam + bset->dim + bset->n_div;
+       for (i = 0; i < bset->n_eq; ++i) {
+               if (isl_int_is_zero(bset->eq[i][1+bset->nparam+dim]))
+                       continue;
+               if (i_eq != -1)
+                       return 0;
+               i_eq = i;
+       }
+       for (i = 0; i < bset->n_ineq; ++i) {
+               if (!isl_int_is_pos(bset->ineq[i][1+bset->nparam+dim]))
+                       continue;
+               if (i_eq != -1 || i_ineq != -1)
+                       return 0;
+               i_ineq = i;
+       }
+       if (i_eq == -1 && i_ineq == -1)
+               return 0;
+       c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
+       /* The coefficient should always be one due to normalization. */
+       if (!isl_int_is_one(c[1+bset->nparam+dim]))
+               return 0;
+       if (isl_seq_first_non_zero(c+1, bset->nparam+dim) != -1)
+               return 0;
+       if (isl_seq_first_non_zero(c+1+bset->nparam+dim+1,
+                                       total - bset->nparam - dim - 1) != -1)
+               return 0;
+       if (val)
+               isl_int_neg(*val, c[0]);
+       return 1;
+}
+
+int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
+       unsigned dim, isl_int *val)
+{
+       int i;
+       isl_int v;
+       isl_int tmp;
+       int fixed;
+
+       if (!set)
+               return -1;
+       if (set->n == 0)
+               return 0;
+       if (set->n == 1)
+               return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
+                                                               dim, val);
+       isl_int_init(v);
+       isl_int_init(tmp);
+       fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
+                                                               dim, &v);
+       for (i = 1; fixed == 1 && i < set->n; ++i) {
+               fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
+                                                               dim, &tmp);
+               if (fixed == 1 && isl_int_ne(tmp, v))
+                       fixed = 0;
+       }
+       if (val)
+               isl_int_set(*val, v);
+       isl_int_clear(tmp);
+       isl_int_clear(v);
+       return fixed;
+}
+
+/* Remove all information from bset that is redundant in the context
+ * of context.  In particular, equalities that are linear combinations
+ * of those in context are remobed.  Then the inequalities that are
+ * redundant in the context of the equalities and inequalities of
+ * context are removed.
+ */
+static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
+       struct isl_basic_set *context)
+{
+       int i;
+       isl_int opt;
+       struct isl_basic_set *combined;
+       struct isl_ctx *ctx;
+       enum isl_lp_result res = isl_lp_ok;
+
+       if (!bset || !context)
+               goto error;
+
+       if (context->n_eq > 0) {
+               struct isl_mat *T;
+               struct isl_mat *T2;
+               struct isl_ctx *ctx = context->ctx;
+               context = isl_basic_set_remove_equalities(context, &T, &T2);
+               if (!context)
+                       goto error;
+               bset = isl_basic_set_preimage(ctx, bset, T);
+               bset = uset_gist(bset, context);
+               bset = isl_basic_set_preimage(ctx, bset, T2);
+               return bset;
+       }
+       combined = isl_basic_set_extend(isl_basic_set_copy(bset),
+                       0, bset->dim, 0, context->n_eq, context->n_ineq);
+       context = set_add_constraints(combined, context, 0);
+       if (!context)
+               goto error;
+       ctx = context->ctx;
+       isl_int_init(opt);
+       for (i = bset->n_ineq-1; i >= 0; --i) {
+               set_swap_inequality(context, i, context->n_ineq-1);
+               context->n_ineq--;
+               res = isl_solve_lp((struct isl_basic_map *)context, 0,
+                       context->ineq[context->n_ineq]+1, ctx->one, &opt, NULL);
+               context->n_ineq++;
+               set_swap_inequality(context, i, context->n_ineq-1);
+               if (res == isl_lp_unbounded)
+                       continue;
+               if (res == isl_lp_error)
+                       break;
+               if (res == isl_lp_empty) {
+                       bset = isl_basic_set_set_to_empty(bset);
+                       break;
+               }
+               isl_int_add(opt, opt, context->ineq[i][0]);
+               if (!isl_int_is_neg(opt)) {
+                       isl_basic_set_drop_inequality(context, i);
+                       isl_basic_set_drop_inequality(bset, i);
+               }
+       }
+       isl_int_clear(opt);
+       if (res == isl_lp_error)
+               goto error;
+       isl_basic_set_free(context);
+       return bset;
+error:
+       isl_basic_set_free(context);
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
+       struct isl_basic_map *context)
+{
+       struct isl_basic_set *bset;
+
+       if (!bmap || !context)
+               goto error;
+
+       context = isl_basic_map_align_divs(context, bmap);
+       bmap = isl_basic_map_align_divs(bmap, context);
+
+       bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
+                        isl_basic_map_underlying_set(context));
+
+       return isl_basic_map_overlying_set(bset, bmap);
+error:
+       isl_basic_map_free(bmap);
+       isl_basic_map_free(context);
+       return NULL;
+}
+
+struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
+{
+       int i;
+
+       map = isl_map_cow(map);
+       if (!map || !context)
+               return NULL;
+       isl_assert(map->ctx, map->nparam == context->nparam, goto error);
+       isl_assert(map->ctx, map->n_in == context->n_in, goto error);
+       isl_assert(map->ctx, map->n_out == context->n_out, goto error);
+       for (i = 0; i < map->n; ++i)
+               context = isl_basic_map_align_divs(context, map->p[i]);
+       for (i = 0; i < map->n; ++i) {
+               map->p[i] = isl_basic_map_gist(map->p[i],
+                                               isl_basic_map_copy(context));
+               if (!map->p[i])
+                       goto error;
+       }
+       isl_basic_map_free(context);
+       F_CLR(map, ISL_MAP_NORMALIZED);
+       return map;
+error:
+       isl_map_free(map);
+       isl_basic_map_free(context);
+       return NULL;
+}
+
+struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
+{
+       return (struct isl_set *)isl_map_gist((struct isl_map *)set,
+                                       (struct isl_basic_map *)context);
+}
+
+struct constraint {
+       unsigned        size;
+       isl_int         *c;
+};
+
+static int qsort_constraint_cmp(const void *p1, const void *p2)
+{
+       const struct constraint *c1 = (const struct constraint *)p1;
+       const struct constraint *c2 = (const struct constraint *)p2;
+       unsigned size = isl_min(c1->size, c2->size);
+       return isl_seq_cmp(c1->c, c2->c, size);
+}
+
+static struct isl_basic_map *isl_basic_map_sort_constraints(
+       struct isl_basic_map *bmap)
+{
+       int i;
+       struct constraint *c;
+       unsigned total;
+
+       if (!bmap)
+               return NULL;
+       total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
+       c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
+       if (!c)
+               goto error;
+       for (i = 0; i < bmap->n_ineq; ++i) {
+               c[i].size = total;
+               c[i].c = bmap->ineq[i];
+       }
+       qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
+       for (i = 0; i < bmap->n_ineq; ++i)
+               bmap->ineq[i] = c[i].c;
+       free(c);
+       return bmap;
+error:
+       isl_basic_map_free(bmap);
+       return NULL;
+}
+
+struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
+{
+       if (!bmap)
+               return NULL;
+       if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
+               return bmap;
+       bmap = isl_basic_map_convex_hull(bmap);
+       bmap = isl_basic_map_sort_constraints(bmap);
+       F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
+       return bmap;
+}
+
+static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
+       const struct isl_basic_map *bmap2)
+{
+       int i, cmp;
+       unsigned total;
+
+       if (bmap1 == bmap2)
+               return 0;
+       if (bmap1->nparam != bmap2->nparam)
+               return bmap1->nparam - bmap2->nparam;
+       if (bmap1->n_in != bmap2->n_in)
+               return bmap1->n_in - bmap2->n_in;
+       if (bmap1->n_out != bmap2->n_out)
+               return bmap1->n_out - bmap2->n_out;
+       if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
+           F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
+               return 0;
+       if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
+               return 1;
+       if (F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
+               return -1;
+       if (bmap1->n_eq != bmap2->n_eq)
+               return bmap1->n_eq - bmap2->n_eq;
+       if (bmap1->n_ineq != bmap2->n_ineq)
+               return bmap1->n_ineq - bmap2->n_ineq;
+       if (bmap1->n_div != bmap2->n_div)
+               return bmap1->n_div - bmap2->n_div;
+       total = bmap1->nparam + bmap1->n_in + bmap1->n_out + bmap1->n_div;
+       for (i = 0; i < bmap1->n_eq; ++i) {
+               cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
+               if (cmp)
+                       return cmp;
+       }
+       for (i = 0; i < bmap1->n_ineq; ++i) {
+               cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
+               if (cmp)
+                       return cmp;
+       }
+       for (i = 0; i < bmap1->n_div; ++i) {
+               cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
+               if (cmp)
+                       return cmp;
+       }
+       return 0;
+}
+
+static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
+       struct isl_basic_map *bmap2)
+{
+       return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
+}
+
+static int qsort_bmap_cmp(const void *p1, const void *p2)
+{
+       const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
+       const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
+
+       return isl_basic_map_fast_cmp(bmap1, bmap2);
+}
+
+/* We normalize in place, but if anything goes wrong we need
+ * to return NULL, so we need to make sure we don't change the
+ * meaning of any possible other copies of map.
+ */
+struct isl_map *isl_map_normalize(struct isl_map *map)
+{
+       int i, j;
+       struct isl_basic_map *bmap;
+
+       if (!map)
+               return NULL;
+       if (F_ISSET(map, ISL_MAP_NORMALIZED))
+               return map;
+       for (i = 0; i < map->n; ++i) {
+               bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
+               if (!bmap)
+                       goto error;
+               isl_basic_map_free(map->p[i]);
+               map->p[i] = bmap;
+       }
+       qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
+       F_SET(map, ISL_MAP_NORMALIZED);
+       map = isl_map_remove_empty_parts(map);
+       if (!map)
+               return NULL;
+       for (i = map->n - 1; i >= 1; --i) {
+               if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
+                       continue;
+               isl_basic_map_free(map->p[i-1]);
+               for (j = i; j < map->n; ++j)
+                       map->p[j-1] = map->p[j];
+               map->n--;
+       }
+       return map;
+error:
+       isl_map_free(map);
+       return NULL;
+
+}
+
+struct isl_set *isl_set_normalize(struct isl_set *set)
+{
+       return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
+}
+
+int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
+{
+       int i;
+       int equal;
+
+       if (!map1 || !map2)
+               return -1;
+
+       if (map1 == map2)
+               return 1;
+       if (map1->nparam != map2->nparam)
+               return 0;
+       if (map1->n_in != map2->n_in)
+               return 0;
+       if (map1->n_out != map2->n_out)
+               return 0;
+
+       map1 = isl_map_copy(map1);
+       map2 = isl_map_copy(map2);
+       map1 = isl_map_normalize(map1);
+       map2 = isl_map_normalize(map2);
+       if (!map1 || !map2)
+               goto error;
+       equal = map1->n == map2->n;
+       for (i = 0; equal && i < map1->n; ++i) {
+               equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
+               if (equal < 0)
+                       goto error;
+       }
+       isl_map_free(map1);
+       isl_map_free(map2);
+       return equal;
+error:
+       isl_map_free(map1);
+       isl_map_free(map2);
+       return -1;
+}
+
+int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
+{
+       return isl_map_fast_is_equal((struct isl_map *)set1,
+                                               (struct isl_map *)set2);
+}
+
+/* Return an interval that ranges from min to max (inclusive)
+ */
+struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
+       isl_int min, isl_int max)
+{
+       int k;
+       struct isl_basic_set *bset = NULL;
+
+       bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
+       if (!bset)
+               goto error;
+
+       k = isl_basic_set_alloc_inequality(bset);
+       if (k < 0)
+               goto error;
+       isl_int_set_si(bset->ineq[k][1], 1);
+       isl_int_neg(bset->ineq[k][0], min);
+
+       k = isl_basic_set_alloc_inequality(bset);
+       if (k < 0)
+               goto error;
+       isl_int_set_si(bset->ineq[k][1], -1);
+       isl_int_set(bset->ineq[k][0], max);
+
+       return bset;
+error:
+       isl_basic_set_free(bset);
+       return NULL;
+}
+
+/* Return the Cartesian product of the basic sets in list (in the given order).
+ */
+struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
+{
+       int i;
+       unsigned dim;
+       unsigned nparam;
+       unsigned extra;
+       unsigned n_eq;
+       unsigned n_ineq;
+       struct isl_basic_set *product = NULL;
+
+       if (!list)
+               goto error;
+       isl_assert(list->ctx, list->n > 0, goto error);
+       isl_assert(list->ctx, list->p[0], goto error);
+       nparam = list->p[0]->nparam;
+       dim = list->p[0]->dim;
+       extra = list->p[0]->n_div;
+       n_eq = list->p[0]->n_eq;
+       n_ineq = list->p[0]->n_ineq;
+       for (i = 1; i < list->n; ++i) {
+               isl_assert(list->ctx, list->p[i], goto error);
+               isl_assert(list->ctx, nparam == list->p[i]->nparam, goto error);
+               dim += list->p[i]->dim;
+               extra += list->p[i]->n_div;
+               n_eq += list->p[i]->n_eq;
+               n_ineq += list->p[i]->n_ineq;
+       }
+       product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
+                                       n_eq, n_ineq);
+       if (!product)
+               goto error;
+       dim = 0;
+       for (i = 0; i < list->n; ++i) {
+               set_add_constraints(product,
+                                       isl_basic_set_copy(list->p[i]), dim);
+               dim += list->p[i]->dim;
+       }
+       isl_basic_set_list_free(list);
+       return product;
+error:
+       isl_basic_set_free(product);
+       isl_basic_set_list_free(list);
+       return NULL;
 }