X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_map.c;h=f7efcb734eb80b1a1f16a2dfe274e3a95ac8ac20;hb=53b68e6a8aa83abe708a094d552c6bdfcec3e29b;hp=54eb8ed3863798ade81c19508a181125b358f9a0;hpb=77db762d5bcd0266848d0a8def7c060335acf495;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_map.c b/isl_map.c
index 54eb8ed..f7efcb7 100644
--- 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_dim.h"
+#include "isl_list.h"
+#include "isl_lp.h"
 #include "isl_seq.h"
 #include "isl_set.h"
 #include "isl_map.h"
@@ -10,22 +13,242 @@
 #include "isl_sample.h"
 #include "isl_vec.h"
 
+/* Maps dst positions to src positions */
+struct isl_dim_map {
+	unsigned len;
+	int pos[1];
+};
+
+static struct isl_dim_map *isl_dim_map_alloc(struct isl_ctx *ctx, unsigned len)
+{
+	int i;
+	struct isl_dim_map *dim_map;
+	dim_map = isl_alloc(ctx, struct isl_dim_map,
+				sizeof(struct isl_dim_map) + len * sizeof(int));
+	if (!dim_map)
+		return NULL;
+	dim_map->len = 1 + len;
+	dim_map->pos[0] = 0;
+	for (i = 0; i < len; ++i)
+		dim_map->pos[1 + i] = -1;
+	return dim_map;
+}
+
+static unsigned n(struct isl_dim *dim, enum isl_dim_type type)
+{
+	switch (type) {
+	case isl_dim_param:	return dim->nparam;
+	case isl_dim_in:	return dim->n_in;
+	case isl_dim_out:	return dim->n_out;
+	}
+}
+
+static unsigned pos(struct isl_dim *dim, enum isl_dim_type type)
+{
+	switch (type) {
+	case isl_dim_param:	return 1;
+	case isl_dim_in:	return 1 + dim->nparam;
+	case isl_dim_out:	return 1 + dim->nparam + dim->n_in;
+	}
+}
+
+static void isl_dim_map_dim(struct isl_dim_map *dim_map, struct isl_dim *dim,
+		enum isl_dim_type type, unsigned dst_pos)
+{
+	int i;
+	unsigned src_pos;
+
+	if (!dim_map || !dim)
+		return;
+	
+	src_pos = pos(dim, type);
+	for (i = 0; i < n(dim, type); ++i)
+		dim_map->pos[1 + dst_pos + i] = src_pos + i;
+}
+
+static void isl_dim_map_div(struct isl_dim_map *dim_map,
+		struct isl_basic_map *bmap, unsigned dst_pos)
+{
+	int i;
+	unsigned src_pos;
+
+	if (!dim_map || !bmap)
+		return;
+	
+	src_pos = 1 + isl_dim_total(bmap->dim);
+	for (i = 0; i < bmap->n_div; ++i)
+		dim_map->pos[1 + dst_pos + i] = src_pos + i;
+}
+
+static void isl_dim_map_dump(struct isl_dim_map *dim_map)
+{
+	int i;
+
+	for (i = 0; i < dim_map->len; ++i)
+		fprintf(stderr, "%d -> %d; ", i, dim_map->pos[i]);
+	fprintf(stderr, "\n");
+}
+
+unsigned isl_basic_map_dim(const struct isl_basic_map *bmap,
+				enum isl_dim_type type)
+{
+	struct isl_dim *dim = bmap->dim;
+	switch (type) {
+	case isl_dim_param:
+	case isl_dim_in:
+	case isl_dim_out:	return isl_dim_size(bmap->dim, type);
+	case isl_dim_div:	return bmap->n_div;
+	case isl_dim_all:	return isl_basic_map_total_dim(bmap);
+	}
+}
+
+unsigned isl_map_dim(const struct isl_map *map, enum isl_dim_type type)
+{
+	return n(map->dim, type);
+}
+
+unsigned isl_set_dim(const struct isl_set *set, enum isl_dim_type type)
+{
+	return n(set->dim, type);
+}
+
+unsigned isl_basic_map_offset(struct isl_basic_map *bmap,
+					enum isl_dim_type type)
+{
+	struct isl_dim *dim = bmap->dim;
+	switch (type) {
+	case isl_dim_param:	return 1;
+	case isl_dim_in:	return 1 + dim->nparam;
+	case isl_dim_out:	return 1 + dim->nparam + dim->n_in;
+	case isl_dim_div:	return 1 + dim->nparam + dim->n_in + dim->n_out;
+	}
+}
+
+static unsigned map_offset(struct isl_map *map, enum isl_dim_type type)
+{
+	return pos(map->dim, type);
+}
+
+unsigned isl_basic_set_dim(const struct isl_basic_set *bset,
+				enum isl_dim_type type)
+{
+	return isl_basic_map_dim((const struct isl_basic_map*)bset, type);
+}
+
+unsigned isl_basic_set_n_dim(const struct isl_basic_set *bset)
+{
+	return bset->dim->n_out;
+}
+
+unsigned isl_basic_set_n_param(const struct isl_basic_set *bset)
+{
+	return bset->dim->nparam;
+}
+
+unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
+{
+	return isl_dim_total(bset->dim) + bset->n_div;
+}
+
+unsigned isl_set_n_dim(const struct isl_set *set)
+{
+	return set->dim->n_out;
+}
+
+unsigned isl_set_n_param(const struct isl_set *set)
+{
+	return set->dim->nparam;
+}
+
+unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
+{
+	return bmap->dim->n_in;
+}
+
+unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
+{
+	return bmap->dim->n_out;
+}
+
+unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
+{
+	return bmap->dim->nparam;
+}
+
+unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
+{
+	return bmap->n_div;
+}
+
+unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
+{
+	return isl_dim_total(bmap->dim) + bmap->n_div;
+}
+
+unsigned isl_map_n_in(const struct isl_map *map)
+{
+	return map->dim->n_in;
+}
+
+unsigned isl_map_n_out(const struct isl_map *map)
+{
+	return map->dim->n_out;
+}
+
+unsigned isl_map_n_param(const struct isl_map *map)
+{
+	return map->dim->nparam;
+}
+
+int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
+{
+	return map->dim->n_in == set->dim->n_out &&
+	       map->dim->nparam == set->dim->nparam;
+}
+
+int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
+		struct isl_basic_set *bset)
+{
+	return bmap->dim->n_in == bset->dim->n_out &&
+	       bmap->dim->nparam == bset->dim->nparam;
+}
+
+int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
+		struct isl_basic_set *bset)
+{
+	return bmap->dim->n_out == bset->dim->n_out &&
+	       bmap->dim->nparam == bset->dim->nparam;
+}
+
+struct isl_dim *isl_basic_set_get_dim(struct isl_basic_set *bset)
+{
+	if (!bset)
+		return NULL;
+	return isl_dim_copy(bset->dim);
+}
+
+struct isl_dim *isl_set_get_dim(struct isl_set *set)
+{
+	if (!set)
+		return NULL;
+	return isl_dim_copy(set->dim);
+}
+
 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
-		struct isl_basic_map *bmap,
-		unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
+		struct isl_basic_map *bmap, unsigned extra,
 		unsigned n_eq, unsigned n_ineq)
 {
 	int i;
-	size_t row_size = 1 + nparam + n_in + n_out + extra;
+	size_t row_size = 1 + isl_dim_total(bmap->dim) + extra;
 
-	bmap->block = isl_blk_alloc(ctx, (n_eq + n_ineq) * row_size);
+	bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
 	if (isl_blk_is_error(bmap->block)) {
 		free(bmap);
 		return NULL;
 	}
 
-	bmap->eq = isl_alloc_array(ctx, isl_int *, n_eq + n_ineq);
-	if (!bmap->eq) {
+	bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
+	if (!bmap->ineq) {
 		isl_blk_free(ctx, bmap->block);
 		free(bmap);
 		return NULL;
@@ -37,7 +260,7 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
 	} else {
 		bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
 		if (isl_blk_is_error(bmap->block2)) {
-			free(bmap->eq);
+			free(bmap->ineq);
 			isl_blk_free(ctx, bmap->block);
 			free(bmap);
 			return NULL;
@@ -46,15 +269,15 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
 		bmap->div = isl_alloc_array(ctx, isl_int *, extra);
 		if (!bmap->div) {
 			isl_blk_free(ctx, bmap->block2);
-			free(bmap->eq);
+			free(bmap->ineq);
 			isl_blk_free(ctx, bmap->block);
 			free(bmap);
 			return NULL;
 		}
 	}
 
-	for (i = 0; i < n_eq + n_ineq; ++i)
-		bmap->eq[i] = bmap->block.data + i * row_size;
+	for (i = 0; i < n_ineq + n_eq; ++i)
+		bmap->ineq[i] = bmap->block.data + i * row_size;
 
 	for (i = 0; i < extra; ++i)
 		bmap->div[i] = bmap->block2.data + i * (1 + row_size);
@@ -64,10 +287,7 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
 	bmap->ref = 1;
 	bmap->flags = 0;
 	bmap->c_size = n_eq + n_ineq;
-	bmap->ineq = bmap->eq + n_eq;
-	bmap->nparam = nparam;
-	bmap->n_in = n_in;
-	bmap->n_out = n_out;
+	bmap->eq = bmap->ineq + n_ineq;
 	bmap->extra = extra;
 	bmap->n_eq = 0;
 	bmap->n_ineq = 0;
@@ -75,6 +295,9 @@ static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
 	bmap->sample = NULL;
 
 	return bmap;
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
 }
 
 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
@@ -86,25 +309,55 @@ struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
 	return (struct isl_basic_set *)bmap;
 }
 
+struct isl_basic_set *isl_basic_set_alloc_dim(struct isl_dim *dim,
+		unsigned extra, unsigned n_eq, unsigned n_ineq)
+{
+	struct isl_basic_map *bmap;
+	if (!dim)
+		return NULL;
+	isl_assert(dim->ctx, dim->n_in == 0, return NULL);
+	bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
+	return (struct isl_basic_set *)bmap;
+}
+
+struct isl_basic_map *isl_basic_map_alloc_dim(struct isl_dim *dim,
+		unsigned extra, unsigned n_eq, unsigned n_ineq)
+{
+	struct isl_basic_map *bmap;
+
+	if (!dim)
+		return NULL;
+	bmap = isl_alloc_type(dim->ctx, struct isl_basic_map);
+	if (!bmap)
+		goto error;
+	bmap->dim = dim;
+
+	return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
+error:
+	isl_dim_free(dim);
+	return NULL;
+}
+
 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
 		unsigned nparam, unsigned in, unsigned out, unsigned extra,
 		unsigned n_eq, unsigned n_ineq)
 {
 	struct isl_basic_map *bmap;
+	struct isl_dim *dim;
 
-	bmap = isl_alloc_type(ctx, struct isl_basic_map);
-	if (!bmap)
+	dim = isl_dim_alloc(ctx, nparam, in, out);
+	if (!dim)
 		return NULL;
 
-	return basic_map_init(ctx, bmap,
-			       nparam, in, out, extra, n_eq, n_ineq);
+	bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
+	return bmap;
 }
 
 static void dup_constraints(
 		struct isl_basic_map *dst, struct isl_basic_map *src)
 {
 	int i;
-	unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
+	unsigned total = isl_basic_map_total_dim(src);
 
 	for (i = 0; i < src->n_eq; ++i) {
 		int j = isl_basic_map_alloc_equality(dst);
@@ -120,7 +373,7 @@ static void dup_constraints(
 		int j = isl_basic_map_alloc_div(dst);
 		isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
 	}
-	F_SET(dst, ISL_BASIC_SET_FINAL);
+	ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
 }
 
 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
@@ -129,14 +382,13 @@ struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
 
 	if (!bmap)
 		return NULL;
-	dup = isl_basic_map_alloc(bmap->ctx, bmap->nparam,
-			bmap->n_in, bmap->n_out,
+	dup = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
 			bmap->n_div, bmap->n_eq, bmap->n_ineq);
 	if (!dup)
 		return NULL;
-	dup->flags = bmap->flags;
 	dup_constraints(dup, bmap);
-	dup->sample = isl_vec_copy(bmap->ctx, bmap->sample);
+	dup->flags = bmap->flags;
+	dup->sample = isl_vec_copy(bmap->sample);
 	return dup;
 }
 
@@ -153,7 +405,7 @@ struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
 	if (!bset)
 		return NULL;
 
-	if (F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
+	if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
 		bset->ref++;
 		return bset;
 	}
@@ -174,7 +426,7 @@ struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
 	if (!bmap)
 		return NULL;
 
-	if (F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
+	if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
 		bmap->ref++;
 		return bmap;
 	}
@@ -201,9 +453,10 @@ void isl_basic_map_free(struct isl_basic_map *bmap)
 	isl_ctx_deref(bmap->ctx);
 	free(bmap->div);
 	isl_blk_free(bmap->ctx, bmap->block2);
-	free(bmap->eq);
+	free(bmap->ineq);
 	isl_blk_free(bmap->ctx, bmap->block);
-	isl_vec_free(bmap->ctx, bmap->sample);
+	isl_vec_free(bmap->sample);
+	isl_dim_free(bmap->dim);
 	free(bmap);
 }
 
@@ -212,25 +465,41 @@ void isl_basic_set_free(struct isl_basic_set *bset)
 	isl_basic_map_free((struct isl_basic_map *)bset);
 }
 
+static int room_for_con(struct isl_basic_map *bmap, unsigned n)
+{
+	return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
+}
+
 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
 {
 	struct isl_ctx *ctx;
 	if (!bmap)
 		return -1;
 	ctx = bmap->ctx;
-	isl_assert(ctx, bmap->n_eq + bmap->n_ineq < bmap->c_size, return -1);
-	isl_assert(ctx, bmap->eq + bmap->n_eq <= bmap->ineq, return -1);
-	if (bmap->eq + bmap->n_eq == bmap->ineq) {
+	isl_assert(ctx, room_for_con(bmap, 1), return -1);
+	isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
+			return -1);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
+	if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
 		isl_int *t;
 		int j = isl_basic_map_alloc_inequality(bmap);
 		if (j < 0)
 			return -1;
-		t = bmap->ineq[0];
-		bmap->ineq[0] = bmap->ineq[j];
-		bmap->ineq[j] = t;
+		t = bmap->ineq[j];
+		bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
+		bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
+		bmap->eq[-1] = t;
+		bmap->n_eq++;
 		bmap->n_ineq--;
-		bmap->ineq++;
+		bmap->eq--;
+		return 0;
 	}
+	isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
+		      bmap->extra - bmap->n_div);
 	return bmap->n_eq++;
 }
 
@@ -248,6 +517,11 @@ int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
 	return 0;
 }
 
+int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
+{
+	return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
+}
+
 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
 {
 	isl_int *t;
@@ -275,12 +549,21 @@ void isl_basic_map_inequality_to_equality(
 	isl_int *t;
 
 	t = bmap->ineq[pos];
-	bmap->ineq[pos] = bmap->ineq[0];
-	bmap->ineq[0] = bmap->eq[bmap->n_eq];
-	bmap->eq[bmap->n_eq] = t;
+	bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
+	bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
+	bmap->eq[-1] = t;
 	bmap->n_eq++;
 	bmap->n_ineq--;
-	bmap->ineq++;
+	bmap->eq--;
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
+}
+
+static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
+{
+	return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
 }
 
 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
@@ -289,10 +572,14 @@ int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
 	if (!bmap)
 		return -1;
 	ctx = bmap->ctx;
-	isl_assert(ctx, (bmap->ineq - bmap->eq) + bmap->n_ineq < bmap->c_size,
-			return -1);
-	F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
-	F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+	isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
+	isl_seq_clr(bmap->ineq[bmap->n_ineq] +
+		      1 + isl_basic_map_total_dim(bmap),
+		      bmap->extra - bmap->n_div);
 	return bmap->n_ineq++;
 }
 
@@ -326,6 +613,7 @@ int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
 		t = bmap->ineq[pos];
 		bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
 		bmap->ineq[bmap->n_ineq - 1] = t;
+		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 	}
 	bmap->n_ineq--;
 	return 0;
@@ -341,9 +629,18 @@ int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
 	if (!bmap)
 		return -1;
 	isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
+	isl_seq_clr(bmap->div[bmap->n_div] +
+		      1 + 1 + isl_basic_map_total_dim(bmap),
+		      bmap->extra - bmap->n_div);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 	return bmap->n_div++;
 }
 
+int isl_basic_set_alloc_div(struct isl_basic_set *bset)
+{
+	return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
+}
+
 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
 {
 	if (!bmap)
@@ -362,33 +659,39 @@ static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
 			    struct isl_basic_map *src_map, isl_int *src,
 			    unsigned in_off, unsigned out_off, unsigned div_off)
 {
+	unsigned src_nparam = isl_basic_map_n_param(src_map);
+	unsigned dst_nparam = isl_basic_map_n_param(dst_map);
+	unsigned src_in = isl_basic_map_n_in(src_map);
+	unsigned dst_in = isl_basic_map_n_in(dst_map);
+	unsigned src_out = isl_basic_map_n_out(src_map);
+	unsigned dst_out = isl_basic_map_n_out(dst_map);
 	isl_int_set(dst[0], src[0]);
-	isl_seq_cpy(dst+1, src+1, isl_min(dst_map->nparam, src_map->nparam));
-	if (dst_map->nparam > src_map->nparam)
-		isl_seq_clr(dst+1+src_map->nparam,
-				dst_map->nparam - src_map->nparam);
-	isl_seq_clr(dst+1+dst_map->nparam, in_off);
-	isl_seq_cpy(dst+1+dst_map->nparam+in_off,
-		    src+1+src_map->nparam,
-		    isl_min(dst_map->n_in-in_off, src_map->n_in));
-	if (dst_map->n_in-in_off > src_map->n_in)
-		isl_seq_clr(dst+1+dst_map->nparam+in_off+src_map->n_in,
-				dst_map->n_in - in_off - src_map->n_in);
-	isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in, out_off);
-	isl_seq_cpy(dst+1+dst_map->nparam+dst_map->n_in+out_off,
-		    src+1+src_map->nparam+src_map->n_in,
-		    isl_min(dst_map->n_out-out_off, src_map->n_out));
-	if (dst_map->n_out-out_off > src_map->n_out)
-		isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+out_off+src_map->n_out,
-				dst_map->n_out - out_off - src_map->n_out);
-	isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out, div_off);
-	isl_seq_cpy(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out+div_off,
-		    src+1+src_map->nparam+src_map->n_in+src_map->n_out,
-		    isl_min(dst_map->extra-div_off, src_map->extra));
-	if (dst_map->extra-div_off > src_map->extra)
-		isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out+
-				div_off+src_map->extra,
-				dst_map->extra - div_off - src_map->extra);
+	isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
+	if (dst_nparam > src_nparam)
+		isl_seq_clr(dst+1+src_nparam,
+				dst_nparam - src_nparam);
+	isl_seq_clr(dst+1+dst_nparam, in_off);
+	isl_seq_cpy(dst+1+dst_nparam+in_off,
+		    src+1+src_nparam,
+		    isl_min(dst_in-in_off, src_in));
+	if (dst_in-in_off > src_in)
+		isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
+				dst_in - in_off - src_in);
+	isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
+	isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
+		    src+1+src_nparam+src_in,
+		    isl_min(dst_out-out_off, src_out));
+	if (dst_out-out_off > src_out)
+		isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
+				dst_out - out_off - src_out);
+	isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
+	isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
+		    src+1+src_nparam+src_in+src_out,
+		    isl_min(dst_map->extra-div_off, src_map->n_div));
+	if (dst_map->n_div-div_off > src_map->n_div)
+		isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
+				div_off+src_map->n_div,
+				dst_map->n_div - div_off - src_map->n_div);
 }
 
 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
@@ -403,7 +706,12 @@ static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
 		struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
 {
 	int i;
-	unsigned div_off = bmap1->n_div;
+	unsigned div_off;
+
+	if (!bmap1 || !bmap2)
+		goto error;
+
+	div_off = bmap1->n_div;
 
 	for (i = 0; i < bmap2->n_eq; ++i) {
 		int i1 = isl_basic_map_alloc_equality(bmap1);
@@ -439,36 +747,106 @@ error:
 	return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
-		unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
+static void copy_constraint_dim_map(isl_int *dst, isl_int *src,
+					struct isl_dim_map *dim_map)
+{
+	int i;
+
+	for (i = 0; i < dim_map->len; ++i) {
+		if (dim_map->pos[i] < 0)
+			isl_int_set_si(dst[i], 0);
+		else
+			isl_int_set(dst[i], src[dim_map->pos[i]]);
+	}
+}
+
+static void copy_div_dim_map(isl_int *dst, isl_int *src,
+					struct isl_dim_map *dim_map)
+{
+	isl_int_set(dst[0], src[0]);
+	copy_constraint_dim_map(dst+1, src+1, dim_map);
+}
+
+static struct isl_basic_map *add_constraints_dim_map(struct isl_basic_map *dst,
+		struct isl_basic_map *src, struct isl_dim_map *dim_map)
+{
+	int i;
+
+	if (!src || !dst || !dim_map)
+		goto error;
+
+	for (i = 0; i < src->n_eq; ++i) {
+		int i1 = isl_basic_map_alloc_equality(dst);
+		if (i1 < 0)
+			goto error;
+		copy_constraint_dim_map(dst->eq[i1], src->eq[i], dim_map);
+	}
+
+	for (i = 0; i < src->n_ineq; ++i) {
+		int i1 = isl_basic_map_alloc_inequality(dst);
+		if (i1 < 0)
+			goto error;
+		copy_constraint_dim_map(dst->ineq[i1], src->ineq[i], dim_map);
+	}
+
+	for (i = 0; i < src->n_div; ++i) {
+		int i1 = isl_basic_map_alloc_div(dst);
+		if (i1 < 0)
+			goto error;
+		copy_div_dim_map(dst->div[i1], src->div[i], dim_map);
+	}
+
+	free(dim_map);
+	isl_basic_map_free(src);
+
+	return dst;
+error:
+	free(dim_map);
+	isl_basic_map_free(src);
+	isl_basic_map_free(dst);
+	return NULL;
+}
+
+struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
+		struct isl_basic_set *bset2, unsigned pos)
+{
+	return (struct isl_basic_set *)
+		add_constraints((struct isl_basic_map *)bset1,
+				(struct isl_basic_map *)bset2, 0, pos);
+}
+
+struct isl_basic_map *isl_basic_map_extend_dim(struct isl_basic_map *base,
+		struct isl_dim *dim, unsigned extra,
 		unsigned n_eq, unsigned n_ineq)
 {
 	struct isl_basic_map *ext;
 	unsigned flags;
 	int dims_ok;
 
-	base = isl_basic_map_cow(base);
+	if (!dim)
+		goto error;
+
 	if (!base)
 		goto error;
 
-	dims_ok = base && base->nparam == nparam &&
-		  base->n_in == n_in && base->n_out == n_out &&
+	dims_ok = isl_dim_equal(base->dim, dim) &&
 		  base->extra >= base->n_div + extra;
 
-	if (dims_ok && n_eq == 0 && n_ineq == 0)
+	if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
+		       room_for_ineq(base, n_ineq)) {
+		isl_dim_free(dim);
 		return base;
+	}
 
-	isl_assert(base->ctx, base->nparam <= nparam, goto error);
-	isl_assert(base->ctx, base->n_in <= n_in, goto error);
-	isl_assert(base->ctx, base->n_out <= n_out, goto error);
+	isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
+	isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
+	isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
 	extra += base->extra;
 	n_eq += base->n_eq;
 	n_ineq += base->n_ineq;
 
-	ext = isl_basic_map_alloc(base->ctx, nparam, n_in, n_out,
-					extra, n_eq, n_ineq);
-	if (!base)
-		return ext;
+	ext = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
+	dim = NULL;
 	if (!ext)
 		goto error;
 
@@ -476,16 +854,52 @@ struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
 	ext = add_constraints(ext, base, 0, 0);
 	if (ext) {
 		ext->flags = flags;
-		F_CLR(ext, ISL_BASIC_SET_FINAL);
+		ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
 	}
 
 	return ext;
 
 error:
+	isl_dim_free(dim);
 	isl_basic_map_free(base);
 	return NULL;
 }
 
+struct isl_basic_set *isl_basic_set_extend_dim(struct isl_basic_set *base,
+		struct isl_dim *dim, unsigned extra,
+		unsigned n_eq, unsigned n_ineq)
+{
+	return (struct isl_basic_set *)
+		isl_basic_map_extend_dim((struct isl_basic_map *)base, dim,
+							extra, n_eq, n_ineq);
+}
+
+struct isl_basic_map *isl_basic_map_extend_constraints(
+		struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
+{
+	if (!base)
+		return NULL;
+	return isl_basic_map_extend_dim(base, isl_dim_copy(base->dim),
+					0, n_eq, n_ineq);
+}
+
+struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
+		unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
+		unsigned n_eq, unsigned n_ineq)
+{
+	struct isl_basic_map *bmap;
+	struct isl_dim *dim;
+
+	if (!base)
+		return NULL;
+	dim = isl_dim_alloc(base->ctx, nparam, n_in, n_out);
+	if (!dim)
+		return NULL;
+
+	bmap = isl_basic_map_extend_dim(base, dim, extra, n_eq, n_ineq);
+	return bmap;
+}
+
 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
 		unsigned nparam, unsigned dim, unsigned extra,
 		unsigned n_eq, unsigned n_ineq)
@@ -495,6 +909,14 @@ struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
 					nparam, 0, dim, extra, n_eq, n_ineq);
 }
 
+struct isl_basic_set *isl_basic_set_extend_constraints(
+		struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
+{
+	return (struct isl_basic_set *)
+		isl_basic_map_extend_constraints((struct isl_basic_map *)base,
+						    n_eq, n_ineq);
+}
+
 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
 {
 	return (struct isl_basic_set *)
@@ -510,7 +932,7 @@ struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
 		bmap->ref--;
 		bmap = isl_basic_map_dup(bmap);
 	}
-	F_CLR(bmap, ISL_BASIC_SET_FINAL);
+	ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
 	return bmap;
 }
 
@@ -549,37 +971,42 @@ struct isl_basic_set *isl_basic_set_swap_vars(
 {
 	int i;
 	struct isl_blk blk;
+	unsigned dim;
+	unsigned nparam;
 
 	if (!bset)
 		goto error;
 
-	isl_assert(bset->ctx, n <= bset->dim, goto error);
+	nparam = isl_basic_set_n_param(bset);
+	dim = isl_basic_set_n_dim(bset);
+	isl_assert(bset->ctx, n <= dim, goto error);
 
-	if (n == bset->dim)
+	if (n == dim)
 		return bset;
 
 	bset = isl_basic_set_cow(bset);
 	if (!bset)
 		return NULL;
 
-	blk = isl_blk_alloc(bset->ctx, bset->dim);
+	blk = isl_blk_alloc(bset->ctx, dim);
 	if (isl_blk_is_error(blk))
 		goto error;
 
 	for (i = 0; i < bset->n_eq; ++i)
 		swap_vars(blk,
-			  bset->eq[i]+1+bset->nparam, n, bset->dim - n);
+			  bset->eq[i]+1+nparam, n, dim - n);
 
 	for (i = 0; i < bset->n_ineq; ++i)
 		swap_vars(blk,
-			  bset->ineq[i]+1+bset->nparam, n, bset->dim - n);
+			  bset->ineq[i]+1+nparam, n, dim - n);
 
 	for (i = 0; i < bset->n_div; ++i)
 		swap_vars(blk,
-			  bset->div[i]+1+1+bset->nparam, n, bset->dim - n);
+			  bset->div[i]+1+1+nparam, n, dim - n);
 
 	isl_blk_free(bset->ctx, blk);
 
+	ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
 	return bset;
 
 error:
@@ -601,1024 +1028,542 @@ struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
 			return NULL;
 		}
 	}
+	ISL_F_CLR(set, ISL_SET_NORMALIZED);
 	return set;
 }
 
-static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
+struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
 {
-	isl_seq_cpy(c, c + n, rem);
-	isl_seq_clr(c + rem, n);
+	int i = 0;
+	unsigned total;
+	if (!bmap)
+		goto error;
+	total = isl_basic_map_total_dim(bmap);
+	isl_basic_map_free_div(bmap, bmap->n_div);
+	isl_basic_map_free_inequality(bmap, bmap->n_ineq);
+	if (bmap->n_eq > 0)
+		isl_basic_map_free_equality(bmap, bmap->n_eq-1);
+	else {
+		isl_basic_map_alloc_equality(bmap);
+		if (i < 0)
+			goto error;
+	}
+	isl_int_set_si(bmap->eq[i][0], 1);
+	isl_seq_clr(bmap->eq[i]+1, total);
+	ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
+	return isl_basic_map_finalize(bmap);
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_drop_dims(
-		struct isl_basic_set *bset, unsigned first, unsigned n)
+struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
 {
-	int i;
-
-	if (!bset)
-		goto error;
-
-	isl_assert(bset->ctx, first + n <= bset->dim, goto error);
-
-	if (n == 0)
-		return bset;
-
-	bset = isl_basic_set_cow(bset);
-	if (!bset)
-		return NULL;
-
-	for (i = 0; i < bset->n_eq; ++i)
-		constraint_drop_vars(bset->eq[i]+1+bset->nparam+first, n,
-				     (bset->dim-first-n)+bset->extra);
+	return (struct isl_basic_set *)
+		isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
+}
 
-	for (i = 0; i < bset->n_ineq; ++i)
-		constraint_drop_vars(bset->ineq[i]+1+bset->nparam+first, n,
-				     (bset->dim-first-n)+bset->extra);
+static void swap_div(struct isl_basic_map *bmap, int a, int b)
+{
+	int i;
+	unsigned off = isl_dim_total(bmap->dim);
+	isl_int *t = bmap->div[a];
+	bmap->div[a] = bmap->div[b];
+	bmap->div[b] = t;
 
-	for (i = 0; i < bset->n_div; ++i)
-		constraint_drop_vars(bset->div[i]+1+1+bset->nparam+first, n,
-				     (bset->dim-first-n)+bset->extra);
+	for (i = 0; i < bmap->n_eq; ++i)
+		isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
 
-	bset->dim -= n;
-	bset->extra += n;
+	for (i = 0; i < bmap->n_ineq; ++i)
+		isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
 
-	return isl_basic_set_finalize(bset);
-error:
-	isl_basic_set_free(bset);
-	return NULL;
+	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]);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 }
 
-static struct isl_set *isl_set_drop_dims(
-		struct isl_set *set, unsigned first, unsigned n)
+/* Eliminate the specified n dimensions starting at first from the
+ * constraints using Fourier-Motzkin, The dimensions themselves
+ * are not removed.
+ */
+struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
+	unsigned first, unsigned n)
 {
 	int i;
+	unsigned nparam;
 
 	if (!set)
-		goto error;
-
-	isl_assert(set->ctx, first + n <= set->dim, goto error);
-
+		return NULL;
 	if (n == 0)
 		return set;
+
 	set = isl_set_cow(set);
 	if (!set)
-		goto error;
-
+		return NULL;
+	isl_assert(set->ctx, first+n <= isl_set_n_dim(set), goto error);
+	nparam = isl_set_n_param(set);
+	
 	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
+		set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
+							    nparam + first, n);
 		if (!set->p[i])
 			goto error;
 	}
-	set->dim -= n;
-
 	return set;
 error:
 	isl_set_free(set);
 	return NULL;
 }
 
-/*
- * We don't cow, as the div is assumed to be redundant.
- */
-static struct isl_basic_map *isl_basic_map_drop_div(
-		struct isl_basic_map *bmap, unsigned div)
+/* 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)
 {
-	int i;
-	unsigned pos;
-
-	if (!bmap)
-		goto error;
-
-	pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
-
-	isl_assert(bmap->ctx, div < bmap->n_div, goto error);
-
-	for (i = 0; i < bmap->n_eq; ++i)
-		constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
-
-	for (i = 0; i < bmap->n_ineq; ++i) {
-		if (!isl_int_is_zero(bmap->ineq[i][pos])) {
-			isl_basic_map_drop_inequality(bmap, i);
-			--i;
-			continue;
-		}
-		constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
-	}
+	set = isl_set_eliminate_dims(set, first, n);
+	set = isl_set_drop_dims(set, first, n);
+	return set;
+}
 
-	for (i = 0; i < bmap->n_div; ++i)
-		constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
+struct isl_basic_set *isl_basic_set_remove_divs(struct isl_basic_set *bset)
+{
+	bset = isl_basic_set_eliminate_vars(bset, isl_dim_total(bset->dim),
+						bset->n_div);
+	if (!bset)
+		return NULL;
+	bset->n_div = 0;
+	return bset;
+}
 
-	if (div != bmap->n_div - 1) {
-		int j;
-		isl_int *t = bmap->div[div];
+struct isl_set *isl_set_remove_divs(struct isl_set *set)
+{
+	int i;
 
-		for (j = div; j < bmap->n_div - 1; ++j)
-			bmap->div[j] = bmap->div[j+1];
+	if (!set)
+		return NULL;
+	if (set->n == 0)
+		return set;
 
-		bmap->div[bmap->n_div - 1] = t;
+	set = isl_set_cow(set);
+	if (!set)
+		return NULL;
+	
+	for (i = 0; i < set->n; ++i) {
+		set->p[i] = isl_basic_set_remove_divs(set->p[i]);
+		if (!set->p[i])
+			goto error;
 	}
-	isl_basic_map_free_div(bmap, 1);
+	return set;
+error:
+	isl_set_free(set);
+	return NULL;
+}
 
+struct isl_basic_map *isl_basic_map_remove(struct isl_basic_map *bmap,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	if (!bmap)
+		return NULL;
+	isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
+			goto error);
+	if (n == 0)
+		return bmap;
+	bmap = isl_basic_map_eliminate_vars(bmap,
+			isl_basic_map_offset(bmap, type) - 1 + first, n);
+	bmap = isl_basic_map_drop(bmap, type, first, n);
 	return bmap;
 error:
 	isl_basic_map_free(bmap);
 	return NULL;
 }
 
-static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
+struct isl_map *isl_map_remove(struct isl_map *map,
+	enum isl_dim_type type, unsigned first, unsigned n)
 {
 	int i;
-	unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
-	unsigned len;
-	len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-
-	for (i = 0; i < bmap->n_eq; ++i)
-		if (bmap->eq[i] != eq)
-			isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
-
-	for (i = 0; i < bmap->n_ineq; ++i)
-		isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
-
-	/* We need to be careful about circular definitions,
-	 * so for now we just remove the definitions of other divs that
-	 * depend on this div and (possibly) recompute them later.
-	 */
-	for (i = 0; i < bmap->n_div; ++i)
-		if (!isl_int_is_zero(bmap->div[i][0]) &&
-		    !isl_int_is_zero(bmap->div[i][1 + pos]))
-			isl_seq_clr(bmap->div[i], 1 + len);
+	unsigned nparam;
 
-	isl_basic_map_drop_div(bmap, div);
-}
+	if (n == 0)
+		return map;
 
-struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
-{
-	int i = 0;
-	unsigned total;
-	if (!bmap)
-		goto error;
-	total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
-	isl_basic_map_free_div(bmap, bmap->n_div);
-	isl_basic_map_free_inequality(bmap, bmap->n_ineq);
-	if (bmap->n_eq > 0)
-		isl_basic_map_free_equality(bmap, bmap->n_eq-1);
-	else {
-		isl_basic_map_alloc_equality(bmap);
-		if (i < 0)
+	map = isl_map_cow(map);
+	if (!map)
+		return NULL;
+	isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
+	
+	for (i = 0; i < map->n; ++i) {
+		map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
+			isl_basic_map_offset(map->p[i], type) - 1 + first, n);
+		if (!map->p[i])
 			goto error;
 	}
-	isl_int_set_si(bmap->eq[i][0], 1);
-	isl_seq_clr(bmap->eq[i]+1, total);
-	F_SET(bmap, ISL_BASIC_MAP_EMPTY);
-	return isl_basic_map_finalize(bmap);
+	map = isl_map_drop(map, type, first, n);
+	return map;
 error:
-	isl_basic_map_free(bmap);
+	isl_map_free(map);
 	return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
+/* Project out n inputs starting at first using Fourier-Motzkin */
+struct isl_map *isl_map_remove_inputs(struct isl_map *map,
+	unsigned first, unsigned n)
 {
-	return (struct isl_basic_set *)
-		isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
+	return isl_map_remove(map, isl_dim_in, first, n);
 }
 
-static void swap_equality(struct isl_basic_map *bmap, int a, int b)
+/* 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)
 {
-	isl_int *t = bmap->eq[a];
-	bmap->eq[a] = bmap->eq[b];
-	bmap->eq[b] = t;
+	unsigned nparam = isl_basic_set_n_param(bset);
+	bset = isl_basic_set_eliminate_vars(bset, nparam + first, n);
+	bset = isl_basic_set_drop_dims(bset, first, n);
+	return bset;
 }
 
-static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
+static void dump_term(struct isl_basic_map *bmap,
+			isl_int c, int pos, FILE *out)
 {
-	isl_int *t = bmap->ineq[a];
-	bmap->ineq[a] = bmap->ineq[b];
-	bmap->ineq[b] = t;
+	const char *name;
+	unsigned in = isl_basic_map_n_in(bmap);
+	unsigned dim = in + isl_basic_map_n_out(bmap);
+	unsigned nparam = isl_basic_map_n_param(bmap);
+	if (!pos)
+		isl_int_print(out, c, 0);
+	else {
+		if (!isl_int_is_one(c))
+			isl_int_print(out, c, 0);
+		if (pos < 1 + nparam) {
+			name = isl_dim_get_name(bmap->dim,
+						isl_dim_param, pos - 1);
+			if (name)
+				fprintf(out, "%s", name);
+			else
+				fprintf(out, "p%d", pos - 1);
+		} else if (pos < 1 + nparam + in)
+			fprintf(out, "i%d", pos - 1 - nparam);
+		else if (pos < 1 + nparam + dim)
+			fprintf(out, "o%d", pos - 1 - nparam - in);
+		else
+			fprintf(out, "e%d", pos - 1 - nparam - dim);
+	}
 }
 
-static void swap_div(struct isl_basic_map *bmap, int a, int b)
+static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
+				int sign, FILE *out)
 {
 	int i;
-	unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
-	isl_int *t = bmap->div[a];
-	bmap->div[a] = bmap->div[b];
-	bmap->div[b] = t;
-
-	for (i = 0; i < bmap->n_eq; ++i)
-		isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
-
-	for (i = 0; i < bmap->n_ineq; ++i)
-		isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
+	int first;
+	unsigned len = 1 + isl_basic_map_total_dim(bmap);
+	isl_int v;
 
-	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]);
+	isl_int_init(v);
+	for (i = 0, first = 1; i < len; ++i) {
+		if (isl_int_sgn(c[i]) * sign <= 0)
+			continue;
+		if (!first)
+			fprintf(out, " + ");
+		first = 0;
+		isl_int_abs(v, c[i]);
+		dump_term(bmap, v, i, out);
+	}
+	isl_int_clear(v);
+	if (first)
+		fprintf(out, "0");
 }
 
-struct isl_basic_map *isl_basic_map_gauss(
-	struct isl_basic_map *bmap, int *progress)
+static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
+				const char *op, FILE *out, int indent)
 {
-	int k;
-	int done;
-	int last_var;
-	unsigned total_var;
-	unsigned total;
-
-	if (!bmap)
-		return NULL;
-
-	total_var = bmap->nparam + bmap->n_in + bmap->n_out;
-	total = total_var + bmap->n_div;
-
-	last_var = total - 1;
-	for (done = 0; done < bmap->n_eq; ++done) {
-		for (; last_var >= 0; --last_var) {
-			for (k = done; k < bmap->n_eq; ++k)
-				if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
-					break;
-			if (k < bmap->n_eq)
-				break;
-		}
-		if (last_var < 0)
-			break;
-		if (k != done)
-			swap_equality(bmap, k, done);
-		if (isl_int_is_neg(bmap->eq[done][1+last_var]))
-			isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
+	int i;
 
-		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);
-		}
+	fprintf(out, "%*s", indent, "");
 
-		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);
-		}
+	dump_constraint_sign(bmap, c, 1, out);
+	fprintf(out, " %s ", op);
+	dump_constraint_sign(bmap, c, -1, out);
 
-		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]);
-		}
+	fprintf(out, "\n");
 
-		if (last_var >= total_var &&
-		    isl_int_is_zero(bmap->div[last_var - total_var][0])) {
-			unsigned div = last_var - total_var;
-			isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
-			isl_int_set_si(bmap->div[div][1+1+last_var], 0);
-			isl_int_set(bmap->div[div][0],
-				    bmap->eq[done][1+last_var]);
-		}
-	}
-	if (done == bmap->n_eq)
-		return bmap;
-	for (k = done; k < bmap->n_eq; ++k) {
-		if (isl_int_is_zero(bmap->eq[k][0]))
+	for (i = bmap->n_div; i < bmap->extra; ++i) {
+		if (isl_int_is_zero(c[1+isl_dim_total(bmap->dim)+i]))
 			continue;
-		return isl_basic_map_set_to_empty(bmap);
+		fprintf(out, "%*s", indent, "");
+		fprintf(out, "ERROR: unused div coefficient not zero\n");
+		abort();
 	}
-	isl_basic_map_free_equality(bmap, bmap->n_eq-done);
-	return bmap;
 }
 
-struct isl_basic_set *isl_basic_set_gauss(
-	struct isl_basic_set *bset, int *progress)
+static void dump_constraints(struct isl_basic_map *bmap,
+				isl_int **c, unsigned n,
+				const char *op, FILE *out, int indent)
 {
-	return (struct isl_basic_set*)isl_basic_map_gauss(
-			(struct isl_basic_map *)bset, progress);
+	int i;
+
+	for (i = 0; i < n; ++i)
+		dump_constraint(bmap, c[i], op, out, indent);
 }
 
-static unsigned int round_up(unsigned int v)
+static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
 {
-	int old_v = v;
+	int j;
+	int first = 1;
+	unsigned total = isl_basic_map_total_dim(bmap);
 
-	while (v) {
-		old_v = v;
-		v ^= v & -v;
+	for (j = 0; j < 1 + total; ++j) {
+		if (isl_int_is_zero(exp[j]))
+			continue;
+		if (!first && isl_int_is_pos(exp[j]))
+			fprintf(out, "+");
+		dump_term(bmap, exp[j], j, out);
+		first = 0;
 	}
-	return old_v << 1;
-}
-
-static int hash_index(int *index, unsigned int size, int bits,
-			struct isl_basic_map *bmap, int k)
-{
-	int h;
-	unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-	u_int32_t hash = isl_seq_hash(bmap->ineq[k]+1, total, bits);
-	for (h = hash; index[h]; h = (h+1) % size)
-		if (k != index[h]-1 &&
-		    isl_seq_eq(bmap->ineq[k]+1,
-			       bmap->ineq[index[h]-1]+1, total))
-			break;
-	return h;
 }
 
-static struct isl_basic_map *remove_duplicate_constraints(
-	struct isl_basic_map *bmap, int *progress)
+static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
 {
-	unsigned int size;
-	int *index;
-	int k, l, h;
-	int bits;
-	unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-	isl_int sum;
-
-	if (bmap->n_ineq <= 1)
-		return bmap;
+	int i;
 
-	size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
-	bits = ffs(size) - 1;
-	index = isl_alloc_array(ctx, int, size);
-	memset(index, 0, size * sizeof(int));
-	if (!index)
-		return bmap;
+	dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
+	dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
 
-	index[isl_seq_hash(bmap->ineq[0]+1, total, bits)] = 1;
-	for (k = 1; k < bmap->n_ineq; ++k) {
-		h = hash_index(index, size, bits, bmap, k);
-		if (!index[h]) {
-			index[h] = k+1;
-			continue;
-		}
-		*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(bmap, k);
-		--k;
-	}
-	isl_int_init(sum);
-	for (k = 0; k < bmap->n_ineq-1; ++k) {
-		isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
-		h = hash_index(index, size, bits, bmap, k);
-		isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
-		if (!index[h])
-			continue;
-		l = index[h] - 1;
-		isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
-		if (isl_int_is_pos(sum))
-			continue;
-		if (isl_int_is_zero(sum)) {
-			/* We need to break out of the loop after these
-			 * changes since the contents of the hash
-			 * will no longer be valid.
-			 * Plus, we probably we want to regauss first.
-			 */
-			isl_basic_map_drop_inequality(bmap, l);
-			isl_basic_map_inequality_to_equality(bmap, k);
-		} else
-			bmap = isl_basic_map_set_to_empty(bmap);
-		break;
-	}
-	isl_int_clear(sum);
-
-	free(index);
-	return bmap;
+	for (i = 0; i < bmap->n_div; ++i) {
+		fprintf(out, "%*s", indent, "");
+		fprintf(out, "e%d = [(", i);
+		dump_affine(bmap, bmap->div[i]+1, out);
+		fprintf(out, ")/");
+		isl_int_print(out, bmap->div[i][0], 0);
+		fprintf(out, "]\n");
+	}
 }
 
-static struct isl_basic_map *remove_duplicate_divs(
-	struct isl_basic_map *bmap, int *progress)
+void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
 {
-	unsigned int size;
-	int *index;
-	int k, l, h;
-	int bits;
-	struct isl_blk eq;
-	unsigned total_var = bmap->nparam + bmap->n_in + bmap->n_out;
-	unsigned total = total_var + bmap->n_div;
-	struct isl_ctx *ctx;
+	if (!bset) {
+		fprintf(out, "null basic set\n");
+		return;
+	}
 
-	if (bmap->n_div <= 1)
-		return bmap;
-
-	ctx = bmap->ctx;
-	for (k = bmap->n_div - 1; k >= 0; --k)
-		if (!isl_int_is_zero(bmap->div[k][0]))
-			break;
-	if (k <= 0)
-		return bmap;
-
-	size = round_up(4 * bmap->n_div / 3 - 1);
-	bits = ffs(size) - 1;
-	index = isl_alloc_array(ctx, int, size);
-	memset(index, 0, size * sizeof(int));
-	if (!index)
-		return bmap;
-	eq = isl_blk_alloc(ctx, 1+total);
-	if (isl_blk_is_error(eq))
-		goto out;
-
-	isl_seq_clr(eq.data, 1+total);
-	index[isl_seq_hash(bmap->div[k], 2+total, bits)] = k + 1;
-	for (--k; k >= 0; --k) {
-		u_int32_t hash;
-
-		if (isl_int_is_zero(bmap->div[k][0]))
-			continue;
-
-		hash = isl_seq_hash(bmap->div[k], 2+total, bits);
-		for (h = hash; index[h]; h = (h+1) % size)
-			if (isl_seq_eq(bmap->div[k],
-				       bmap->div[index[h]-1], 2+total))
-				break;
-		if (index[h]) {
-			*progress = 1;
-			l = index[h] - 1;
-			isl_int_set_si(eq.data[1+total_var+k], -1);
-			isl_int_set_si(eq.data[1+total_var+l], 1);
-			eliminate_div(bmap, eq.data, l);
-			isl_int_set_si(eq.data[1+total_var+k], 0);
-			isl_int_set_si(eq.data[1+total_var+l], 0);
-		}
-		index[h] = k+1;
-	}
-
-	isl_blk_free(ctx, eq);
-out:
-	free(index);
-	return bmap;
+	fprintf(out, "%*s", indent, "");
+	fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
+			bset->ref, bset->dim->nparam, bset->dim->n_out,
+			bset->extra, bset->flags);
+	dump((struct isl_basic_map *)bset, out, indent);
 }
 
-/* Elimininate divs based on equalities
- */
-static struct isl_basic_map *eliminate_divs_eq(
-		struct isl_basic_map *bmap, int *progress)
+void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
 {
-	int d;
-	int i;
-	int modified = 0;
-	unsigned off;
-
-	if (!bmap)
-		return NULL;
-
-	off = 1 + bmap->nparam + bmap->n_in + bmap->n_out;
-
-	for (d = bmap->n_div - 1; d >= 0 ; --d) {
-		for (i = 0; i < bmap->n_eq; ++i) {
-			if (!isl_int_is_one(bmap->eq[i][off + d]) &&
-			    !isl_int_is_negone(bmap->eq[i][off + d]))
-				continue;
-			modified = 1;
-			*progress = 1;
-			eliminate_div(bmap, bmap->eq[i], d);
-			isl_basic_map_drop_equality(bmap, i);
-			break;
-		}
+	if (!bmap) {
+		fprintf(out, "null basic map\n");
+		return;
 	}
-	if (modified)
-		return eliminate_divs_eq(bmap, progress);
-	return bmap;
+
+	fprintf(out, "%*s", indent, "");
+	fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
+			"flags: %x, n_name: %d\n",
+		bmap->ref,
+		bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
+		bmap->extra, bmap->flags, bmap->dim->n_name);
+	dump(bmap, out, indent);
 }
 
-static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
+int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
 {
-	int i;
-	isl_int gcd;
-	unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-
-	isl_int_init(gcd);
-	for (i = bmap->n_eq - 1; i >= 0; --i) {
-		isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
-		if (isl_int_is_zero(gcd)) {
-			if (!isl_int_is_zero(bmap->eq[i][0])) {
-				bmap = isl_basic_map_set_to_empty(bmap);
-				break;
-			}
-			isl_basic_map_drop_equality(bmap, i);
-			continue;
-		}
-		if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
-			isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
-		if (isl_int_is_one(gcd))
-			continue;
-		if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
-			bmap = isl_basic_map_set_to_empty(bmap);
-			break;
-		}
-		isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
-	}
-
-	for (i = bmap->n_ineq - 1; i >= 0; --i) {
-		isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
-		if (isl_int_is_zero(gcd)) {
-			if (isl_int_is_neg(bmap->ineq[i][0])) {
-				bmap = isl_basic_map_set_to_empty(bmap);
-				break;
-			}
-			isl_basic_map_drop_inequality(bmap, i);
-			continue;
-		}
-		if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
-			isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
-		if (isl_int_is_one(gcd))
-			continue;
-		isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
-		isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
-	}
-	isl_int_clear(gcd);
-
-	return bmap;
+	unsigned total;
+	if (!bmap)
+		return -1;
+	total = isl_basic_map_total_dim(bmap);
+	isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
+	isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
+	isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
+	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	return 0;
 }
 
-
-/* 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)
+struct isl_set *isl_set_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
 {
-	int d;
-	int i, j, k;
-	unsigned total;
-	unsigned extra;
+	struct isl_set *set;
 
-	if (!bmap)
+	if (!dim)
 		return NULL;
-	total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-	extra = bmap->extra - bmap->n_div;
+	isl_assert(dim->ctx, dim->n_in == 0, return NULL);
+	isl_assert(dim->ctx, n >= 0, return NULL);
+	set = isl_alloc(dim->ctx, struct isl_set,
+			sizeof(struct isl_set) +
+			n * sizeof(struct isl_basic_set *));
+	if (!set)
+		goto error;
 
-	bmap = isl_basic_map_cow(bmap);
-	bmap = isl_basic_map_gauss(bmap, NULL);
-	for (d = pos + n - 1; d >= pos; --d) {
-		int n_lower, n_upper;
-		if (!bmap)
-			return NULL;
-		for (i = 0; i < bmap->n_eq; ++i) {
-			if (isl_int_is_zero(bmap->eq[i][1+d]))
-				continue;
-			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 = isl_basic_map_gauss(bmap, NULL);
-			if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
-				break;
-		}
-	}
-	return bmap;
+	set->ctx = dim->ctx;
+	isl_ctx_ref(set->ctx);
+	set->ref = 1;
+	set->size = n;
+	set->n = 0;
+	set->dim = dim;
+	set->flags = flags;
+	return set;
 error:
-	isl_basic_map_free(bmap);
+	isl_dim_free(dim);
 	return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_eliminate_vars(
-	struct isl_basic_set *bset, unsigned pos, unsigned n)
+struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
+		unsigned nparam, unsigned dim, int n, unsigned flags)
 {
-	return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
-			(struct isl_basic_map *)bset, pos, n);
+	struct isl_set *set;
+	struct isl_dim *dims;
+
+	dims = isl_dim_alloc(ctx, nparam, 0, dim);
+	if (!dims)
+		return NULL;
+
+	set = isl_set_alloc_dim(dims, n, flags);
+	return set;
 }
 
-/* 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)
+struct isl_set *isl_set_dup(struct isl_set *set)
 {
 	int i;
+	struct isl_set *dup;
 
-	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;
-	}
-	set = isl_set_drop_dims(set, first, n);
-	return set;
-error:
-	isl_set_free(set);
-	return NULL;
+
+	dup = isl_set_alloc_dim(isl_dim_copy(set->dim), set->n, set->flags);
+	if (!dup)
+		return NULL;
+	for (i = 0; i < set->n; ++i)
+		dup = isl_set_add(dup, isl_basic_set_copy(set->p[i]));
+	return dup;
 }
 
-/* Elimininate divs based on inequalities
- */
-static struct isl_basic_map *eliminate_divs_ineq(
-		struct isl_basic_map *bmap, int *progress)
+struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
 {
-	int d;
-	int i;
-	unsigned off;
-	struct isl_ctx *ctx;
+	struct isl_set *set;
 
-	if (!bmap)
+	if (!bset)
 		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;
+	set = isl_set_alloc_dim(isl_dim_copy(bset->dim), 1, ISL_MAP_DISJOINT);
+	if (!set) {
+		isl_basic_set_free(bset);
+		return NULL;
 	}
-	return bmap;
+	return isl_set_add(set, bset);
 }
 
-struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
+struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
 {
-	int progress = 1;
+	struct isl_map *map;
+
 	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);
+
+	map = isl_map_alloc_dim(isl_dim_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
+	if (!map) {
+		isl_basic_map_free(bmap);
+		return NULL;
 	}
-	return bmap;
+	return isl_map_add(map, bmap);
 }
 
-struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
+struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
 {
-	return (struct isl_basic_set *)
-		isl_basic_map_simplify((struct isl_basic_map *)bset);
+	if (!bset || !set)
+		goto error;
+	isl_assert(set->ctx, isl_dim_equal(set->dim, bset->dim), goto error);
+	isl_assert(set->ctx, set->n < set->size, goto error);
+	set->p[set->n] = bset;
+	set->n++;
+	return set;
+error:
+	if (set)
+		isl_set_free(set);
+	if (bset)
+		isl_basic_set_free(bset);
+	return NULL;
 }
 
-static void dump_term(struct isl_basic_map *bmap,
-			isl_int c, int pos, FILE *out)
+void isl_set_free(struct isl_set *set)
 {
-	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;
+
+	if (!set)
+		return;
+
+	if (--set->ref > 0)
+		return;
+
+	isl_ctx_deref(set->ctx);
+	for (i = 0; i < set->n; ++i)
+		isl_basic_set_free(set->p[i]);
+	isl_dim_free(set->dim);
+	free(set);
 }
 
-static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
-				int sign, FILE *out)
+void isl_set_dump(struct isl_set *set, FILE *out, int indent)
 {
 	int i;
-	int first;
-	unsigned len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-	isl_int v;
 
-	isl_int_init(v);
-	for (i = 0, first = 1; i < len; ++i) {
-		if (isl_int_sgn(c[i]) * sign <= 0)
-			continue;
-		if (!first)
-			fprintf(out, " + ");
-		first = 0;
-		isl_int_abs(v, c[i]);
-		dump_term(bmap, v, i, out);
+	if (!set) {
+		fprintf(out, "null set\n");
+		return;
+	}
+
+	fprintf(out, "%*s", indent, "");
+	fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
+			set->ref, set->n, set->dim->nparam, set->dim->n_out,
+			set->flags);
+	for (i = 0; i < set->n; ++i) {
+		fprintf(out, "%*s", indent, "");
+		fprintf(out, "basic set %d:\n", i);
+		isl_basic_set_dump(set->p[i], out, indent+4);
 	}
-	isl_int_clear(v);
-	if (first)
-		fprintf(out, "0");
 }
 
-static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
-				const char *op, FILE *out, int indent)
+void isl_map_dump(struct isl_map *map, FILE *out, int indent)
 {
 	int i;
 
-	fprintf(out, "%*s", indent, "");
-
-	dump_constraint_sign(bmap, c, 1, out);
-	fprintf(out, " %s ", op);
-	dump_constraint_sign(bmap, c, -1, out);
-
-	fprintf(out, "\n");
+	if (!map) {
+		fprintf(out, "null map\n");
+		return;
+	}
 
-	for (i = bmap->n_div; i < bmap->extra; ++i) {
-		if (isl_int_is_zero(c[1+bmap->nparam+bmap->n_in+bmap->n_out+i]))
-			continue;
+	fprintf(out, "%*s", indent, "");
+	fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
+		     "flags: %x, n_name: %d\n",
+			map->ref, map->n, map->dim->nparam, map->dim->n_in,
+			map->dim->n_out, map->flags, map->dim->n_name);
+	for (i = 0; i < map->n; ++i) {
 		fprintf(out, "%*s", indent, "");
-		fprintf(out, "ERROR: unused div coefficient not zero\n");
+		fprintf(out, "basic map %d:\n", i);
+		isl_basic_map_dump(map->p[i], out, indent+4);
 	}
 }
 
-static void dump_constraints(struct isl_basic_map *bmap,
-				isl_int **c, unsigned n,
-				const char *op, FILE *out, int indent)
+struct isl_basic_map *isl_basic_map_intersect_domain(
+		struct isl_basic_map *bmap, struct isl_basic_set *bset)
 {
-	int i;
+	struct isl_basic_map *bmap_domain;
+	struct isl_dim *dim;
 
-	for (i = 0; i < n; ++i)
-		dump_constraint(bmap, c[i], op, out, indent);
-}
+	if (!bmap || !bset)
+		goto error;
 
-static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
-{
-	int j;
-	int first = 1;
-	unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-
-	for (j = 0; j < 1 + total; ++j) {
-		if (isl_int_is_zero(exp[j]))
-			continue;
-		if (!first && isl_int_is_pos(exp[j]))
-			fprintf(out, "+");
-		dump_term(bmap, exp[j], j, out);
-		first = 0;
-	}
-}
-
-static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
-{
-	int i;
-
-	dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
-	dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
-
-	for (i = 0; i < bmap->n_div; ++i) {
-		fprintf(out, "%*s", indent, "");
-		fprintf(out, "e%d = [(", i);
-		dump_affine(bmap, bmap->div[i]+1, out);
-		fprintf(out, ")/");
-		isl_int_print(out, bmap->div[i][0]);
-		fprintf(out, "]\n");
-	}
-}
-
-void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
-{
-	if (!bset) {
-		fprintf(out, "null basic set\n");
-		return;
-	}
-
-	fprintf(out, "%*s", indent, "");
-	fprintf(out, "nparam: %d, dim: %d, extra: %d\n",
-			bset->nparam, bset->dim, bset->extra);
-	dump((struct isl_basic_map *)bset, out, indent);
-}
-
-void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
-{
-	if (!bmap) {
-		fprintf(out, "null basic map\n");
-		return;
-	}
-
-	fprintf(out, "%*s", indent, "");
-	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->flags);
-	dump(bmap, out, indent);
-}
-
-int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
-{
-	unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-	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);
-	return 0;
-}
-
-struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
-		unsigned nparam, unsigned dim, int n, unsigned flags)
-{
-	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;
-	set->nparam = nparam;
-	set->zero = 0;
-	set->dim = dim;
-	set->flags = flags;
-	return set;
-}
-
-struct isl_set *isl_set_dup(struct isl_set *set)
-{
-	int i;
-	struct isl_set *dup;
-
-	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(dup,
-				  isl_basic_set_dup(set->p[i]));
-	return dup;
-}
-
-struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
-{
-	struct isl_set *set;
-
-	if (!bset)
-		return NULL;
-
-	set = isl_set_alloc(bset->ctx, bset->nparam, bset->dim, 1, ISL_MAP_DISJOINT);
-	if (!set) {
-		isl_basic_set_free(bset);
-		return NULL;
-	}
-	return isl_set_add(set, bset);
-}
-
-struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
-{
-	struct isl_map *map;
-
-	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(bmap);
-		return NULL;
-	}
-	return isl_map_add(map, bmap);
-}
-
-struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
-{
-	if (!bset || !set)
-		goto error;
-	isl_assert(set->ctx, 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(set);
-	if (bset)
-		isl_basic_set_free(bset);
-	return NULL;
-}
-
-void isl_set_free(struct isl_set *set)
-{
-	int i;
-
-	if (!set)
-		return;
-
-	if (--set->ref > 0)
-		return;
-
-	isl_ctx_deref(set->ctx);
-	for (i = 0; i < set->n; ++i)
-		isl_basic_set_free(set->p[i]);
-	free(set);
-}
-
-void isl_set_dump(struct isl_set *set, FILE *out, int indent)
-{
-	int i;
-
-	if (!set) {
-		fprintf(out, "null set\n");
-		return;
-	}
-
-	fprintf(out, "%*s", indent, "");
-	fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
-			set->ref, set->n, set->nparam, set->dim, set->flags);
-	for (i = 0; i < set->n; ++i) {
-		fprintf(out, "%*s", indent, "");
-		fprintf(out, "basic set %d:\n", i);
-		isl_basic_set_dump(set->p[i], out, indent+4);
-	}
-}
-
-void isl_map_dump(struct isl_map *map, FILE *out, int indent)
-{
-	int i;
-
-	if (!map) {
-		fprintf(out, "null map\n");
-		return;
-	}
-
-	fprintf(out, "%*s", indent, "");
-	fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, flags: %x\n",
-			map->ref, map->n, map->nparam, map->n_in, map->n_out,
-			map->flags);
-	for (i = 0; i < map->n; ++i) {
-		fprintf(out, "%*s", indent, "");
-		fprintf(out, "basic map %d:\n", i);
-		isl_basic_map_dump(map->p[i], out, indent+4);
-	}
-}
-
-struct isl_basic_map *isl_basic_map_intersect_domain(
-		struct isl_basic_map *bmap, struct isl_basic_set *bset)
-{
-	struct isl_basic_map *bmap_domain;
+	isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
+					bset->dim, isl_dim_param), goto error);
 
-	if (!bmap || !bset)
-		goto error;
+	if (isl_dim_size(bset->dim, isl_dim_set) != 0)
+		isl_assert(bset->ctx,
+		    isl_basic_map_compatible_domain(bmap, bset), goto error);
 
-	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(bmap,
-			bset->nparam, bmap->n_in, bmap->n_out,
+	bmap = isl_basic_map_cow(bmap);
+	bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 			bset->n_div, bset->n_eq, bset->n_ineq);
 	if (!bmap)
 		goto error;
-	bmap_domain = isl_basic_map_from_basic_set(bset,
-						bset->dim, 0);
+	dim = isl_dim_reverse(isl_dim_copy(bset->dim));
+	bmap_domain = isl_basic_map_from_basic_set(bset, dim);
 	bmap = add_constraints(bmap, bmap_domain, 0, 0);
 
 	bmap = isl_basic_map_simplify(bmap);
@@ -1637,16 +1582,19 @@ struct isl_basic_map *isl_basic_map_intersect_range(
 	if (!bmap || !bset)
 		goto error;
 
-	isl_assert(bset->ctx, bset->dim == bmap->n_out, goto error);
-	isl_assert(bset->ctx, bset->nparam == bmap->nparam, goto error);
+	isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
+					bset->dim, isl_dim_param), goto error);
 
-	bmap = isl_basic_map_extend(bmap,
-			bset->nparam, bmap->n_in, bmap->n_out,
+	if (isl_dim_size(bset->dim, isl_dim_set) != 0)
+		isl_assert(bset->ctx,
+		    isl_basic_map_compatible_range(bmap, bset), goto error);
+
+	bmap = isl_basic_map_cow(bmap);
+	bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 			bset->n_div, bset->n_eq, bset->n_ineq);
 	if (!bmap)
 		goto error;
-	bmap_range = isl_basic_map_from_basic_set(bset,
-						0, bset->dim);
+	bmap_range = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
 	bmap = add_constraints(bmap, bmap_range, 0, 0);
 
 	bmap = isl_basic_map_simplify(bmap);
@@ -1657,26 +1605,91 @@ error:
 	return NULL;
 }
 
+static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
+{
+	int i;
+	unsigned total;
+	isl_int s;
+
+	total = 1 + isl_basic_map_total_dim(bmap);
+	if (total != vec->size)
+		return -1;
+
+	isl_int_init(s);
+
+	for (i = 0; i < bmap->n_eq; ++i) {
+		isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
+		if (!isl_int_is_zero(s)) {
+			isl_int_clear(s);
+			return 0;
+		}
+	}
+
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
+		if (isl_int_is_neg(s)) {
+			isl_int_clear(s);
+			return 0;
+		}
+	}
+
+	isl_int_clear(s);
+
+	return 1;
+}
+
+int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
+{
+	return basic_map_contains((struct isl_basic_map *)bset, vec);
+}
+
 struct isl_basic_map *isl_basic_map_intersect(
 		struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
+	struct isl_vec *sample = NULL;
+
 	if (!bmap1 || !bmap2)
 		goto error;
 
-	isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
-	isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
-	isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
-
-	bmap1 = isl_basic_map_extend(bmap1,
-			bmap1->nparam, bmap1->n_in, bmap1->n_out,
+	isl_assert(bmap1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
+				     bmap2->dim, isl_dim_param), goto error);
+	if (isl_dim_total(bmap1->dim) ==
+				isl_dim_size(bmap1->dim, isl_dim_param) &&
+	    isl_dim_total(bmap2->dim) !=
+				isl_dim_size(bmap2->dim, isl_dim_param))
+		return isl_basic_map_intersect(bmap2, bmap1);
+
+	if (isl_dim_total(bmap2->dim) !=
+					isl_dim_size(bmap2->dim, isl_dim_param))
+		isl_assert(bmap1->ctx,
+			    isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
+
+	if (bmap1->sample &&
+	    basic_map_contains(bmap1, bmap1->sample) > 0 &&
+	    basic_map_contains(bmap2, bmap1->sample) > 0)
+		sample = isl_vec_copy(bmap1->sample);
+	else if (bmap2->sample &&
+	    basic_map_contains(bmap1, bmap2->sample) > 0 &&
+	    basic_map_contains(bmap2, bmap2->sample) > 0)
+		sample = isl_vec_copy(bmap2->sample);
+
+	bmap1 = isl_basic_map_cow(bmap1);
+	bmap1 = isl_basic_map_extend_dim(bmap1, isl_dim_copy(bmap1->dim),
 			bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
 	if (!bmap1)
 		goto error;
 	bmap1 = add_constraints(bmap1, bmap2, 0, 0);
 
+	if (sample) {
+		isl_vec_free(bmap1->sample);
+		bmap1->sample = sample;
+	}
+
 	bmap1 = isl_basic_map_simplify(bmap1);
 	return isl_basic_map_finalize(bmap1);
 error:
+	if (sample)
+		isl_vec_free(sample);
 	isl_basic_map_free(bmap1);
 	isl_basic_map_free(bmap2);
 	return NULL;
@@ -1700,11 +1713,22 @@ struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
 	if (!map1 || !map2)
 		goto error;
 
-	if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
-	    F_ISSET(map2, ISL_MAP_DISJOINT))
-		FL_SET(flags, ISL_MAP_DISJOINT);
+	isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
+					 map2->dim, isl_dim_param), goto error);
+	if (isl_dim_total(map1->dim) ==
+				isl_dim_size(map1->dim, isl_dim_param) &&
+	    isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
+		return isl_map_intersect(map2, map1);
 
-	result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
+	if (isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
+		isl_assert(map1->ctx,
+			    isl_dim_equal(map1->dim, map2->dim), goto error);
+
+	if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
+	    ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
+		ISL_FL_SET(flags, ISL_MAP_DISJOINT);
+
+	result = isl_map_alloc_dim(isl_dim_copy(map1->dim),
 				map1->n * map2->n, flags);
 	if (!result)
 		goto error;
@@ -1739,6 +1763,7 @@ struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
 
 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
 {
+	struct isl_dim *dim;
 	struct isl_basic_set *bset;
 	unsigned in;
 
@@ -1747,10 +1772,11 @@ struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
 	bmap = isl_basic_map_cow(bmap);
 	if (!bmap)
 		return NULL;
-	in = bmap->n_in;
+	dim = isl_dim_reverse(isl_dim_copy(bmap->dim));
+	in = isl_basic_map_n_in(bmap);
 	bset = isl_basic_set_from_basic_map(bmap);
 	bset = isl_basic_set_swap_vars(bset, in);
-	return isl_basic_map_from_basic_set(bset, bset->dim-in, in);
+	return isl_basic_map_from_basic_set(bset, dim);
 }
 
 /* Turn final n dimensions into existentially quantified variables.
@@ -1766,14 +1792,14 @@ struct isl_basic_set *isl_basic_set_project_out(
 	if (!bset)
 		return NULL;
 
-	isl_assert(bset->ctx, n <= bset->dim, goto error);
+	isl_assert(bset->ctx, n <= isl_basic_set_n_dim(bset), goto error);
 
 	if (n == 0)
 		return bset;
 
 	bset = isl_basic_set_cow(bset);
 
-	row_size = 1 + bset->nparam + bset->dim + bset->extra;
+	row_size = 1 + isl_dim_total(bset->dim) + bset->extra;
 	old = bset->block2.data;
 	bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
 					(bset->extra + n) * (1 + row_size));
@@ -1793,7 +1819,10 @@ struct isl_basic_set *isl_basic_set_project_out(
 	bset->div = new_div;
 	bset->n_div += n;
 	bset->extra += n;
-	bset->dim -= n;
+	bset->dim = isl_dim_drop_outputs(bset->dim,
+					    isl_basic_set_n_dim(bset) - n, n);
+	if (!bset->dim)
+		goto error;
 	bset = isl_basic_set_simplify(bset);
 	return isl_basic_set_finalize(bset);
 error:
@@ -1801,35 +1830,62 @@ error:
 	return NULL;
 }
 
+static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
+{
+	int i, j;
+
+	for (i = 0; i < n; ++i) {
+		j = isl_basic_map_alloc_div(bmap);
+		if (j < 0)
+			goto error;
+		isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
+	}
+	return bmap;
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
 struct isl_basic_map *isl_basic_map_apply_range(
 		struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
 {
-	struct isl_basic_set *bset;
-	unsigned n_in, n_out;
+	struct isl_dim *dim_result = NULL;
+	struct isl_basic_map *bmap;
+	unsigned n_in, n_out, n, nparam, total, pos;
+	struct isl_dim_map *dim_map1, *dim_map2;
 
 	if (!bmap1 || !bmap2)
 		goto error;
 
-	isl_assert(bmap->ctx, bmap1->n_out == bmap2->n_in, goto error);
-	isl_assert(bmap->ctx, bmap1->nparam == bmap2->nparam, goto error);
-
-	n_in = bmap1->n_in;
-	n_out = bmap2->n_out;
-
-	bmap2 = isl_basic_map_reverse(bmap2);
-	if (!bmap2)
-		goto error;
-	bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
-			bmap1->n_in + bmap2->n_in, bmap1->n_out,
-			bmap2->extra, bmap2->n_eq, bmap2->n_ineq);
-	if (!bmap1)
-		goto error;
-	bmap1 = add_constraints(bmap1, bmap2, bmap1->n_in - bmap2->n_in, 0);
-	bmap1 = isl_basic_map_simplify(bmap1);
-	bset = isl_basic_set_from_basic_map(bmap1);
-	bset = isl_basic_set_project_out(bset,
-						bset->dim - (n_in + n_out), 0);
-	return isl_basic_map_from_basic_set(bset, n_in, n_out);
+	dim_result = isl_dim_join(isl_dim_copy(bmap1->dim),
+				  isl_dim_copy(bmap2->dim));
+
+	n_in = isl_basic_map_n_in(bmap1);
+	n_out = isl_basic_map_n_out(bmap2);
+	n = isl_basic_map_n_out(bmap1);
+	nparam = isl_basic_map_n_param(bmap1);
+
+	total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
+	dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
+	dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
+	isl_dim_map_div(dim_map1, bmap1, pos += n_out);
+	isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
+
+	bmap = isl_basic_map_alloc_dim(dim_result,
+			bmap1->n_div + bmap2->n_div + n,
+			bmap1->n_eq + bmap2->n_eq,
+			bmap1->n_ineq + bmap2->n_ineq);
+	bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
+	bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
+	bmap = add_divs(bmap, n);
+	bmap = isl_basic_map_simplify(bmap);
+	return isl_basic_map_finalize(bmap);
 error:
 	isl_basic_map_free(bmap1);
 	isl_basic_map_free(bmap2);
@@ -1842,7 +1898,8 @@ struct isl_basic_set *isl_basic_set_apply(
 	if (!bset || !bmap)
 		goto error;
 
-	isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
+	isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
+		    goto error);
 
 	return (struct isl_basic_set *)
 		isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
@@ -1858,8 +1915,11 @@ struct isl_basic_map *isl_basic_map_apply_domain(
 	if (!bmap1 || !bmap2)
 		goto error;
 
-	isl_assert(ctx, bmap1->n_in == bmap2->n_in, goto error);
-	isl_assert(ctx, bmap1->nparam == bmap2->nparam, goto error);
+	isl_assert(ctx,
+	    isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
+	isl_assert(ctx,
+	    isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
+	    goto error);
 
 	bmap1 = isl_basic_map_reverse(bmap1);
 	bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
@@ -1870,118 +1930,263 @@ error:
 	return NULL;
 }
 
-static struct isl_basic_map *var_equal(struct isl_ctx *ctx,
-		struct isl_basic_map *bmap, unsigned pos)
+/* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
+ * A \cap B -> f(A) + f(B)
+ */
+struct isl_basic_map *isl_basic_map_sum(
+		struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+{
+	unsigned n_in, n_out, nparam, total, pos;
+	struct isl_basic_map *bmap = NULL;
+	struct isl_dim_map *dim_map1, *dim_map2;
+	int i;
+
+	if (!bmap1 || !bmap2)
+		goto error;
+
+	isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
+		goto error);
+
+	nparam = isl_basic_map_n_param(bmap1);
+	n_in = isl_basic_map_n_in(bmap1);
+	n_out = isl_basic_map_n_out(bmap1);
+
+	total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
+	dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
+	dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
+	isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
+	isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
+
+	bmap = isl_basic_map_alloc_dim(isl_dim_copy(bmap1->dim),
+			bmap1->n_div + bmap2->n_div + 2 * n_out,
+			bmap1->n_eq + bmap2->n_eq + n_out,
+			bmap1->n_ineq + bmap2->n_ineq);
+	for (i = 0; i < n_out; ++i) {
+		int j = isl_basic_map_alloc_equality(bmap);
+		if (j < 0)
+			goto error;
+		isl_seq_clr(bmap->eq[j], 1+total);
+		isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
+		isl_int_set_si(bmap->eq[j][1+pos+i], 1);
+		isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
+	}
+	bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
+	bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
+	bmap = add_divs(bmap, 2 * n_out);
+
+	bmap = isl_basic_map_simplify(bmap);
+	return isl_basic_map_finalize(bmap);
+error:
+	isl_basic_map_free(bmap);
+	isl_basic_map_free(bmap1);
+	isl_basic_map_free(bmap2);
+	return NULL;
+}
+
+/* Given a basic map A -> f(A), construct A -> -f(A).
+ */
+struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
+{
+	int i, j;
+	unsigned off, n;
+
+	bmap = isl_basic_map_cow(bmap);
+	if (!bmap)
+		return NULL;
+
+	n = isl_basic_map_dim(bmap, isl_dim_out);
+	off = isl_basic_map_offset(bmap, isl_dim_out);
+	for (i = 0; i < bmap->n_eq; ++i)
+		for (j = 0; j < n; ++j)
+			isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
+	for (i = 0; i < bmap->n_ineq; ++i)
+		for (j = 0; j < n; ++j)
+			isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
+	for (i = 0; i < bmap->n_div; ++i)
+		for (j = 0; j < n; ++j)
+			isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
+	return isl_basic_map_finalize(bmap);
+}
+
+/* Given a basic map A -> f(A) and an integer d, construct a basic map
+ * A -> floor(f(A)/d).
+ */
+struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
+		isl_int d)
+{
+	unsigned n_in, n_out, nparam, total, pos;
+	struct isl_basic_map *result = NULL;
+	struct isl_dim_map *dim_map;
+	int i;
+
+	if (!bmap)
+		return NULL;
+
+	nparam = isl_basic_map_n_param(bmap);
+	n_in = isl_basic_map_n_in(bmap);
+	n_out = isl_basic_map_n_out(bmap);
+
+	total = nparam + n_in + n_out + bmap->n_div + n_out;
+	dim_map = isl_dim_map_alloc(bmap->ctx, total);
+	isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
+	isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
+	isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
+	isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
+
+	result = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
+			bmap->n_div + n_out,
+			bmap->n_eq, bmap->n_ineq + 2 * n_out);
+	result = add_constraints_dim_map(result, bmap, dim_map);
+	result = add_divs(result, n_out);
+	for (i = 0; i < n_out; ++i) {
+		int j;
+		j = isl_basic_map_alloc_inequality(result);
+		if (j < 0)
+			goto error;
+		isl_seq_clr(result->ineq[j], 1+total);
+		isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
+		isl_int_set_si(result->ineq[j][1+pos+i], 1);
+		j = isl_basic_map_alloc_inequality(result);
+		if (j < 0)
+			goto error;
+		isl_seq_clr(result->ineq[j], 1+total);
+		isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
+		isl_int_set_si(result->ineq[j][1+pos+i], -1);
+		isl_int_sub_ui(result->ineq[j][0], d, 1);
+	}
+
+	result = isl_basic_map_simplify(result);
+	return isl_basic_map_finalize(result);
+error:
+	isl_basic_map_free(result);
+	return NULL;
+}
+
+static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
 {
 	int i;
+	unsigned nparam;
+	unsigned n_in;
+
 	i = isl_basic_map_alloc_equality(bmap);
 	if (i < 0)
 		goto error;
-	isl_seq_clr(bmap->eq[i],
-		    1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
-	isl_int_set_si(bmap->eq[i][1+bmap->nparam+pos], -1);
-	isl_int_set_si(bmap->eq[i][1+bmap->nparam+bmap->n_in+pos], 1);
+	nparam = isl_basic_map_n_param(bmap);
+	n_in = isl_basic_map_n_in(bmap);
+	isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
+	isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
+	isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
 	return isl_basic_map_finalize(bmap);
 error:
 	isl_basic_map_free(bmap);
 	return NULL;
 }
 
-static struct isl_basic_map *var_more(struct isl_ctx *ctx,
-		struct isl_basic_map *bmap, unsigned pos)
+static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
 {
 	int i;
+	unsigned nparam;
+	unsigned n_in;
+
 	i = isl_basic_map_alloc_inequality(bmap);
 	if (i < 0)
 		goto error;
-	isl_seq_clr(bmap->ineq[i],
-		    1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
+	nparam = isl_basic_map_n_param(bmap);
+	n_in = isl_basic_map_n_in(bmap);
+	isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
 	isl_int_set_si(bmap->ineq[i][0], -1);
-	isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], -1);
-	isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], 1);
+	isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
+	isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
 	return isl_basic_map_finalize(bmap);
 error:
 	isl_basic_map_free(bmap);
 	return NULL;
 }
 
-static struct isl_basic_map *var_less(struct isl_ctx *ctx,
-		struct isl_basic_map *bmap, unsigned pos)
+static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
 {
 	int i;
+	unsigned nparam;
+	unsigned n_in;
+
 	i = isl_basic_map_alloc_inequality(bmap);
 	if (i < 0)
 		goto error;
-	isl_seq_clr(bmap->ineq[i],
-		    1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
+	nparam = isl_basic_map_n_param(bmap);
+	n_in = isl_basic_map_n_in(bmap);
+	isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
 	isl_int_set_si(bmap->ineq[i][0], -1);
-	isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], 1);
-	isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], -1);
+	isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
+	isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
 	return isl_basic_map_finalize(bmap);
 error:
 	isl_basic_map_free(bmap);
 	return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_equal(struct isl_ctx *ctx,
-		unsigned nparam, unsigned in, unsigned out, unsigned n_equal)
+struct isl_basic_map *isl_basic_map_equal(struct isl_dim *dim, unsigned n_equal)
 {
 	int i;
 	struct isl_basic_map *bmap;
-	bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, n_equal, 0);
+	bmap = isl_basic_map_alloc_dim(dim, 0, n_equal, 0);
 	if (!bmap)
 		return NULL;
 	for (i = 0; i < n_equal && bmap; ++i)
-		bmap = var_equal(ctx, bmap, i);
+		bmap = var_equal(bmap, i);
 	return isl_basic_map_finalize(bmap);
 }
 
-struct isl_basic_map *isl_basic_map_less_at(struct isl_ctx *ctx,
-		unsigned nparam, unsigned in, unsigned out, unsigned pos)
+struct isl_basic_map *isl_basic_map_less_at(struct isl_dim *dim, unsigned pos)
 {
 	int i;
 	struct isl_basic_map *bmap;
-	bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
+	bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
 	if (!bmap)
 		return NULL;
 	for (i = 0; i < pos && bmap; ++i)
-		bmap = var_equal(ctx, bmap, i);
+		bmap = var_equal(bmap, i);
 	if (bmap)
-		bmap = var_less(ctx, bmap, pos);
+		bmap = var_less(bmap, pos);
 	return isl_basic_map_finalize(bmap);
 }
 
-struct isl_basic_map *isl_basic_map_more_at(struct isl_ctx *ctx,
-		unsigned nparam, unsigned in, unsigned out, unsigned pos)
+struct isl_basic_map *isl_basic_map_more_at(struct isl_dim *dim, unsigned pos)
 {
 	int i;
 	struct isl_basic_map *bmap;
-	bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
+	bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
 	if (!bmap)
 		return NULL;
 	for (i = 0; i < pos && bmap; ++i)
-		bmap = var_equal(ctx, bmap, i);
+		bmap = var_equal(bmap, i);
 	if (bmap)
-		bmap = var_more(ctx, bmap, pos);
+		bmap = var_more(bmap, pos);
 	return isl_basic_map_finalize(bmap);
 }
 
 struct isl_basic_map *isl_basic_map_from_basic_set(
-		struct isl_basic_set *bset, unsigned n_in, unsigned n_out)
+		struct isl_basic_set *bset, struct isl_dim *dim)
 {
 	struct isl_basic_map *bmap;
 
 	bset = isl_basic_set_cow(bset);
-	if (!bset)
-		return NULL;
+	if (!bset || !dim)
+		goto error;
 
-	isl_assert(ctx, bset->dim == n_in + n_out, goto error);
+	isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
+	isl_dim_free(bset->dim);
 	bmap = (struct isl_basic_map *) bset;
-	bmap->n_in = n_in;
-	bmap->n_out = n_out;
+	bmap->dim = dim;
 	return isl_basic_map_finalize(bmap);
 error:
 	isl_basic_set_free(bset);
+	isl_dim_free(dim);
 	return NULL;
 }
 
@@ -1989,16 +2194,20 @@ struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
 {
 	if (!bmap)
 		goto error;
-	if (bmap->n_in == 0)
+	if (bmap->dim->n_in == 0)
 		return (struct isl_basic_set *)bmap;
 	bmap = isl_basic_map_cow(bmap);
 	if (!bmap)
 		goto error;
-	bmap->n_out += bmap->n_in;
-	bmap->n_in = 0;
+	bmap->dim = isl_dim_cow(bmap->dim);
+	if (!bmap->dim)
+		goto error;
+	bmap->dim->n_out += bmap->dim->n_in;
+	bmap->dim->n_in = 0;
 	bmap = isl_basic_map_finalize(bmap);
 	return (struct isl_basic_set *)bmap;
 error:
+	isl_basic_map_free(bmap);
 	return NULL;
 }
 
@@ -2014,8 +2223,8 @@ error:
 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
 {
 	int i, j;
-	unsigned div_pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
-	unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
+	unsigned total = isl_basic_map_total_dim(bmap);
+	unsigned div_pos = 1 + total - bmap->n_div + div;
 
 	i = isl_basic_map_alloc_inequality(bmap);
 	if (i < 0)
@@ -2037,14 +2246,14 @@ struct isl_basic_set *isl_basic_map_underlying_set(
 {
 	if (!bmap)
 		goto error;
-	if (bmap->nparam == 0 && bmap->n_in == 0 && bmap->n_div == 0)
+	if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
 		return (struct isl_basic_set *)bmap;
 	bmap = isl_basic_map_cow(bmap);
 	if (!bmap)
 		goto error;
-	bmap->n_out += bmap->nparam + bmap->n_in + bmap->n_div;
-	bmap->nparam = 0;
-	bmap->n_in = 0;
+	bmap->dim = isl_dim_underlying(bmap->dim, bmap->n_div);
+	if (!bmap->dim)
+		goto error;
 	bmap->extra -= bmap->n_div;
 	bmap->n_div = 0;
 	bmap = isl_basic_map_finalize(bmap);
@@ -2059,26 +2268,29 @@ struct isl_basic_map *isl_basic_map_overlying_set(
 	struct isl_basic_map *bmap;
 	struct isl_ctx *ctx;
 	unsigned total;
-	int i, k;
+	int i;
 
 	if (!bset || !like)
 		goto error;
 	ctx = bset->ctx;
-	isl_assert(ctx, bset->dim ==
-			like->nparam + like->n_in + like->n_out + like->n_div,
+	isl_assert(ctx, bset->n_div == 0, goto error);
+	isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
+	isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
 			goto error);
-	if (like->nparam == 0 && like->n_in == 0 && like->n_div == 0) {
+	if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
 		isl_basic_map_free(like);
 		return (struct isl_basic_map *)bset;
 	}
 	bset = isl_basic_set_cow(bset);
 	if (!bset)
 		goto error;
-	total = bset->dim + bset->extra;
+	total = bset->dim->n_out + bset->extra;
 	bmap = (struct isl_basic_map *)bset;
-	bmap->nparam = like->nparam;
-	bmap->n_in = like->n_in;
-	bmap->n_out = like->n_out;
+	isl_dim_free(bmap->dim);
+	bmap->dim = isl_dim_copy(like->dim);
+	if (!bmap->dim)
+		goto error;
+	bmap->n_div = like->n_div;
 	bmap->extra += like->n_div;
 	if (bmap->extra) {
 		unsigned ltotal;
@@ -2093,19 +2305,23 @@ struct isl_basic_map *isl_basic_map_overlying_set(
 						bmap->extra);
 		if (!bmap->div)
 			goto error;
-		bmap = isl_basic_map_extend(bmap, bmap->nparam,
-			bmap->n_in, bmap->n_out, 0, 0, 2 * like->n_div);
+		for (i = 0; i < bmap->extra; ++i)
+			bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
 		for (i = 0; i < like->n_div; ++i) {
-			k = isl_basic_map_alloc_div(bmap);
-			if (k < 0)
-				goto error;
-			isl_seq_cpy(bmap->div[k], like->div[i], 1 + 1 + ltotal);
-			isl_seq_clr(bmap->div[k]+1+1+ltotal, total - ltotal);
-			if (add_div_constraints(bmap, k) < 0)
+			isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
+			isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
+		}
+		bmap = isl_basic_map_extend_constraints(bmap, 
+							0, 2 * like->n_div);
+		for (i = 0; i < like->n_div; ++i) {
+			if (isl_int_is_zero(bmap->div[i][0]))
+				continue;
+			if (add_div_constraints(bmap, i) < 0)
 				goto error;
 		}
 	}
 	isl_basic_map_free(like);
+	bmap = isl_basic_map_simplify(bmap);
 	bmap = isl_basic_map_finalize(bmap);
 	return bmap;
 error:
@@ -2128,9 +2344,9 @@ struct isl_set *isl_set_from_underlying_set(
 
 	if (!set || !like)
 		goto error;
-	isl_assert(set->ctx, set->dim == like->nparam + like->dim + like->n_div,
+	isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
 		    goto error);
-	if (like->nparam == 0 && like->n_div == 0) {
+	if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
 		isl_basic_set_free(like);
 		return set;
 	}
@@ -2143,8 +2359,10 @@ struct isl_set *isl_set_from_underlying_set(
 		if (!set->p[i])
 			goto error;
 	}
-	set->nparam = like->nparam;
-	set->dim = like->dim;
+	isl_dim_free(set->dim);
+	set->dim = isl_dim_copy(like->dim);
+	if (!set->dim)
+		goto error;
 	isl_basic_set_free(like);
 	return set;
 error:
@@ -2157,11 +2375,16 @@ struct isl_set *isl_map_underlying_set(struct isl_map *map)
 {
 	int i;
 
-	map = isl_map_align_divs(map);
 	map = isl_map_cow(map);
 	if (!map)
 		return NULL;
+	map->dim = isl_dim_cow(map->dim);
+	if (!map->dim)
+		goto error;
 
+	for (i = 1; i < map->n; ++i)
+		isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
+				goto error);
 	for (i = 0; i < map->n; ++i) {
 		map->p[i] = (struct isl_basic_map *)
 				isl_basic_map_underlying_set(map->p[i]);
@@ -2169,11 +2392,13 @@ struct isl_set *isl_map_underlying_set(struct isl_map *map)
 			goto error;
 	}
 	if (map->n == 0)
-		map->n_out += map->nparam + map->n_in;
-	else
-		map->n_out = map->p[0]->n_out;
-	map->nparam = 0;
-	map->n_in = 0;
+		map->dim = isl_dim_underlying(map->dim, 0);
+	else {
+		isl_dim_free(map->dim);
+		map->dim = isl_dim_copy(map->p[0]->dim);
+	}
+	if (!map->dim)
+		goto error;
 	return (struct isl_set *)map;
 error:
 	isl_map_free(map);
@@ -2191,7 +2416,7 @@ struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
 	unsigned n_out;
 	if (!bmap)
 		return NULL;
-	n_out = bmap->n_out;
+	n_out = isl_basic_map_n_out(bmap);
 	domain = isl_basic_set_from_basic_map(bmap);
 	return isl_basic_set_project_out(domain, n_out, 0);
 }
@@ -2213,46 +2438,54 @@ struct isl_set *isl_map_range(struct isl_map *map)
 		goto error;
 
 	set = (struct isl_set *) map;
-	set->zero = 0;
+	if (set->dim->n_in != 0) {
+		set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
+		if (!set->dim)
+			goto error;
+	}
 	for (i = 0; i < map->n; ++i) {
 		set->p[i] = isl_basic_map_range(map->p[i]);
 		if (!set->p[i])
 			goto error;
 	}
-	F_CLR(set, ISL_MAP_DISJOINT);
+	ISL_F_CLR(set, ISL_MAP_DISJOINT);
+	ISL_F_CLR(set, ISL_SET_NORMALIZED);
 	return set;
 error:
 	isl_map_free(map);
 	return NULL;
 }
 
-struct isl_map *isl_map_from_set(struct isl_set *set,
-		unsigned n_in, unsigned n_out)
+struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
 {
 	int i;
 	struct isl_map *map = NULL;
 
-	if (!set)
-		return NULL;
-	isl_assert(set->ctx, set->dim == n_in + n_out, goto error);
 	set = isl_set_cow(set);
-	if (!set)
-		return NULL;
+	if (!set || !dim)
+		goto error;
+	isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
 	map = (struct isl_map *)set;
 	for (i = 0; i < set->n; ++i) {
 		map->p[i] = isl_basic_map_from_basic_set(
-				set->p[i], n_in, n_out);
+				set->p[i], isl_dim_copy(dim));
 		if (!map->p[i])
 			goto error;
 	}
-	map->n_in = n_in;
-	map->n_out = n_out;
+	isl_dim_free(map->dim);
+	map->dim = dim;
 	return map;
 error:
+	isl_dim_free(dim);
 	isl_set_free(set);
 	return NULL;
 }
 
+struct isl_map *isl_map_from_range(struct isl_set *set)
+{
+	return (struct isl_map *)set;
+}
+
 struct isl_set *isl_set_from_map(struct isl_map *map)
 {
 	int i;
@@ -2263,8 +2496,11 @@ struct isl_set *isl_set_from_map(struct isl_map *map)
 	map = isl_map_cow(map);
 	if (!map)
 		return NULL;
-	map->n_out += map->n_in;
-	map->n_in = 0;
+	map->dim = isl_dim_cow(map->dim);
+	if (!map->dim)
+		goto error;
+	map->dim->n_out += map->dim->n_in;
+	map->dim->n_in = 0;
 	set = (struct isl_set *)map;
 	for (i = 0; i < map->n; ++i) {
 		set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
@@ -2277,28 +2513,45 @@ error:
 	return NULL;
 }
 
-struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
-		unsigned nparam, unsigned in, unsigned out, int n,
-		unsigned flags)
+struct isl_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
 {
 	struct isl_map *map;
 
-	map = isl_alloc(ctx, struct isl_map,
+	if (!dim)
+		return NULL;
+	isl_assert(dim->ctx, n >= 0, return NULL);
+	map = isl_alloc(dim->ctx, struct isl_map,
 			sizeof(struct isl_map) +
 			n * sizeof(struct isl_basic_map *));
 	if (!map)
-		return NULL;
+		goto error;
 
-	map->ctx = ctx;
-	isl_ctx_ref(ctx);
+	map->ctx = dim->ctx;
+	isl_ctx_ref(map->ctx);
 	map->ref = 1;
 	map->size = n;
 	map->n = 0;
-	map->nparam = nparam;
-	map->n_in = in;
-	map->n_out = out;
+	map->dim = dim;
 	map->flags = flags;
 	return map;
+error:
+	isl_dim_free(dim);
+	return NULL;
+}
+
+struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
+		unsigned nparam, unsigned in, unsigned out, int n,
+		unsigned flags)
+{
+	struct isl_map *map;
+	struct isl_dim *dims;
+
+	dims = isl_dim_alloc(ctx, nparam, in, out);
+	if (!dims)
+		return NULL;
+
+	map = isl_map_alloc_dim(dims, n, flags);
+	return map;
 }
 
 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
@@ -2310,41 +2563,114 @@ struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
 	return bmap;
 }
 
-struct isl_basic_set *isl_basic_set_empty(struct isl_ctx *ctx,
-		unsigned nparam, unsigned dim)
+struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
 {
 	struct isl_basic_set *bset;
-	bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 1, 0);
+	bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
 	bset = isl_basic_set_set_to_empty(bset);
 	return bset;
 }
 
-struct isl_basic_map *isl_basic_map_universe(struct isl_ctx *ctx,
-		unsigned nparam, unsigned in, unsigned out)
+struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
+{
+	struct isl_basic_map *bmap;
+	if (!model)
+		return NULL;
+	bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
+	bmap = isl_basic_map_set_to_empty(bmap);
+	return bmap;
+}
+
+struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
 {
 	struct isl_basic_map *bmap;
-	bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 0, 0);
+	if (!model)
+		return NULL;
+	bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
+	bmap = isl_basic_map_set_to_empty(bmap);
 	return bmap;
 }
 
-struct isl_basic_set *isl_basic_set_universe(struct isl_ctx *ctx,
-		unsigned nparam, unsigned dim)
+struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
 {
 	struct isl_basic_set *bset;
-	bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 0, 0);
+	if (!model)
+		return NULL;
+	bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
+	bset = isl_basic_set_set_to_empty(bset);
 	return bset;
 }
 
-struct isl_map *isl_map_empty(struct isl_ctx *ctx,
-		unsigned nparam, unsigned in, unsigned out)
+struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
 {
-	return isl_map_alloc(ctx, nparam, in, out, 0, ISL_MAP_DISJOINT);
+	struct isl_basic_map *bmap;
+	bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
+	return bmap;
 }
 
-struct isl_set *isl_set_empty(struct isl_ctx *ctx,
-		unsigned nparam, unsigned dim)
+struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
+{
+	struct isl_basic_set *bset;
+	bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
+	return bset;
+}
+
+struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
+{
+	if (!model)
+		return NULL;
+	return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
+}
+
+struct isl_map *isl_map_empty(struct isl_dim *dim)
+{
+	return isl_map_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
+}
+
+struct isl_map *isl_map_empty_like(struct isl_map *model)
+{
+	if (!model)
+		return NULL;
+	return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
+}
+
+struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
+{
+	if (!model)
+		return NULL;
+	return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
+}
+
+struct isl_set *isl_set_empty(struct isl_dim *dim)
+{
+	return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
+}
+
+struct isl_set *isl_set_empty_like(struct isl_set *model)
+{
+	if (!model)
+		return NULL;
+	return isl_set_empty(isl_dim_copy(model->dim));
+}
+
+struct isl_map *isl_map_universe(struct isl_dim *dim)
+{
+	struct isl_map *map;
+	if (!dim)
+		return NULL;
+	map = isl_map_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
+	map = isl_map_add(map, isl_basic_map_universe(dim));
+	return map;
+}
+
+struct isl_set *isl_set_universe(struct isl_dim *dim)
 {
-	return isl_set_alloc(ctx, nparam, dim, 0, ISL_MAP_DISJOINT);
+	struct isl_set *set;
+	if (!dim)
+		return NULL;
+	set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
+	set = isl_set_add(set, isl_basic_set_universe(dim));
+	return set;
 }
 
 struct isl_map *isl_map_dup(struct isl_map *map)
@@ -2354,11 +2680,9 @@ struct isl_map *isl_map_dup(struct isl_map *map)
 
 	if (!map)
 		return NULL;
-	dup = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out, map->n,
-				map->flags);
+	dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
 	for (i = 0; i < map->n; ++i)
-		dup = isl_map_add(dup,
-				  isl_basic_map_dup(map->p[i]));
+		dup = isl_map_add(dup, isl_basic_map_copy(map->p[i]));
 	return dup;
 }
 
@@ -2366,12 +2690,11 @@ struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
 {
 	if (!bmap || !map)
 		goto error;
-	isl_assert(map->ctx, map->nparam == bmap->nparam, goto error);
-	isl_assert(map->ctx, map->n_in == bmap->n_in, goto error);
-	isl_assert(map->ctx, map->n_out == bmap->n_out, goto error);
+	isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
 	isl_assert(map->ctx, map->n < map->size, goto error);
 	map->p[map->n] = bmap;
 	map->n++;
+	ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 	return map;
 error:
 	if (map)
@@ -2394,6 +2717,7 @@ void isl_map_free(struct isl_map *map)
 	isl_ctx_deref(map->ctx);
 	for (i = 0; i < map->n; ++i)
 		isl_basic_map_free(map->p[i]);
+	isl_dim_free(map->dim);
 	free(map);
 }
 
@@ -2406,15 +2730,12 @@ struct isl_map *isl_map_extend(struct isl_map *base,
 	if (!base)
 		return NULL;
 
-	isl_assert(base->ctx, base->nparam <= nparam, goto error);
-	isl_assert(base->ctx, base->n_in <= n_in, goto error);
-	isl_assert(base->ctx, base->n_out <= n_out, goto error);
-	base->nparam = nparam;
-	base->n_in = n_in;
-	base->n_out = n_out;
+	base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
+	if (!base->dim)
+		goto error;
 	for (i = 0; i < base->n; ++i) {
-		base->p[i] = isl_basic_map_extend(base->p[i],
-				nparam, n_in, n_out, 0, 0, 0);
+		base->p[i] = isl_basic_map_extend_dim(base->p[i],
+				isl_dim_copy(base->dim), 0, 0, 0);
 		if (!base->p[i])
 			goto error;
 	}
@@ -2431,20 +2752,18 @@ struct isl_set *isl_set_extend(struct isl_set *base,
 							nparam, 0, dim);
 }
 
-static struct isl_basic_map *isl_basic_map_fix_var(struct isl_basic_map *bmap,
-		unsigned var, int value)
+static struct isl_basic_map *isl_basic_map_fix_pos(struct isl_basic_map *bmap,
+		unsigned pos, int value)
 {
 	int j;
 
 	bmap = isl_basic_map_cow(bmap);
-	bmap = isl_basic_map_extend(bmap,
-			bmap->nparam, bmap->n_in, bmap->n_out, 0, 1, 0);
+	bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
 	j = isl_basic_map_alloc_equality(bmap);
 	if (j < 0)
 		goto error;
-	isl_seq_clr(bmap->eq[j],
-		    1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
-	isl_int_set_si(bmap->eq[j][1 + var], -1);
+	isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
+	isl_int_set_si(bmap->eq[j][pos], -1);
 	isl_int_set_si(bmap->eq[j][0], value);
 	bmap = isl_basic_map_simplify(bmap);
 	return isl_basic_map_finalize(bmap);
@@ -2453,34 +2772,43 @@ error:
 	return NULL;
 }
 
-struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
-		unsigned input, int value)
+struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
+		enum isl_dim_type type, unsigned pos, int value)
 {
 	if (!bmap)
 		return NULL;
-	isl_assert(bmap->ctx, input < bmap->n_in, goto error);
-	return isl_basic_map_fix_var(bmap, bmap->nparam + input, value);
+	isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
+	return isl_basic_map_fix_pos(bmap, isl_basic_map_offset(bmap, type) + pos,
+					value);
 error:
 	isl_basic_map_free(bmap);
 	return NULL;
 }
 
+struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
+		enum isl_dim_type type, unsigned pos, int value)
+{
+	return (struct isl_basic_set *)
+		isl_basic_map_fix_si((struct isl_basic_map *)bset,
+					type, pos, value);
+}
+
+struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
+		unsigned input, int value)
+{
+	return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
+}
+
 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
 		unsigned dim, int value)
 {
-	if (!bset)
-		return NULL;
-	isl_assert(bset->ctx, dim < bset->dim, goto error);
 	return (struct isl_basic_set *)
-		isl_basic_map_fix_var((struct isl_basic_map *)bset,
-						bset->nparam + dim, value);
-error:
-	isl_basic_set_free(bset);
-	return NULL;
+		isl_basic_map_fix_si((struct isl_basic_map *)bset,
+					isl_dim_set, dim, value);
 }
 
-struct isl_map *isl_map_fix_input_si(struct isl_map *map,
-		unsigned input, int value)
+struct isl_map *isl_map_fix_si(struct isl_map *map,
+		enum isl_dim_type type, unsigned pos, int value)
 {
 	int i;
 
@@ -2488,29 +2816,64 @@ struct isl_map *isl_map_fix_input_si(struct isl_map *map,
 	if (!map)
 		return NULL;
 
-	isl_assert(ctx, input < map->n_in, goto error);
+	isl_assert(ctx, pos < isl_map_dim(map, type), goto error);
 	for (i = 0; i < map->n; ++i) {
-		map->p[i] = isl_basic_map_fix_input_si(map->p[i], input, value);
+		map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
 		if (!map->p[i])
 			goto error;
 	}
+	ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 	return map;
 error:
 	isl_map_free(map);
 	return NULL;
 }
 
+struct isl_map *isl_map_fix_input_si(struct isl_map *map,
+		unsigned input, int value)
+{
+	return isl_map_fix_si(map, isl_dim_in, input, value);
+}
+
 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
 {
+	return (struct isl_set *)
+		isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
+}
+
+struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
+	unsigned dim, isl_int value)
+{
+	int j;
+	unsigned nparam;
+
+	bset = isl_basic_set_cow(bset);
+	bset = isl_basic_set_extend_constraints(bset, 0, 1);
+	j = isl_basic_set_alloc_inequality(bset);
+	if (j < 0)
+		goto error;
+	isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
+	isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
+	isl_int_neg(bset->ineq[j][0], value);
+	bset = isl_basic_set_simplify(bset);
+	return isl_basic_set_finalize(bset);
+error:
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
+					isl_int value)
+{
 	int i;
 
 	set = isl_set_cow(set);
 	if (!set)
 		return NULL;
 
-	isl_assert(set->ctx, dim < set->dim, goto error);
+	isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
 	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_fix_dim_si(set->p[i], dim, value);
+		set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
 		if (!set->p[i])
 			goto error;
 	}
@@ -2529,14 +2892,15 @@ struct isl_map *isl_map_reverse(struct isl_map *map)
 	if (!map)
 		return NULL;
 
-	t = map->n_in;
-	map->n_in = map->n_out;
-	map->n_out = t;
+	map->dim = isl_dim_reverse(map->dim);
+	if (!map->dim)
+		goto error;
 	for (i = 0; i < map->n; ++i) {
 		map->p[i] = isl_basic_map_reverse(map->p[i]);
 		if (!map->p[i])
 			goto error;
 	}
+	ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 	return map;
 error:
 	isl_map_free(map);
@@ -2562,13 +2926,15 @@ struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
 	struct isl_basic_map *bmap = NULL;
 	struct isl_basic_set *dom = NULL;
 	struct isl_map *min;
+	struct isl_dim *param_dim;
 
 	if (!bset)
 		goto error;
-	bmap = isl_basic_map_from_basic_set(bset, 0, bset->dim);
+	bmap = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
 	if (!bmap)
 		goto error;
-	dom = isl_basic_set_alloc(bmap->ctx, bmap->nparam, 0, 0, 0, 0);
+	param_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
+	dom = isl_basic_set_universe(param_dim);
 	if (!dom)
 		goto error;
 	min = isl_basic_map_lexmin(bmap, dom, NULL);
@@ -2578,13 +2944,40 @@ error:
 	return NULL;
 }
 
+/* If bmap contains any unknown divs, then compute explicit
+ * expressions for them.  However, this computation may be
+ * quite expensive, so first try to remove divs that aren't
+ * strictly needed.
+ */
 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
 {
+	int i;
+	unsigned off;
+
 	if (!bmap)
 		return NULL;
-	if (bmap->n_div == 0)
+	off = isl_dim_total(bmap->dim);
+	for (i = 0; i < bmap->n_div; ++i) {
+		if (isl_int_is_zero(bmap->div[i][0]))
+			break;
+		isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
+				goto error);
+	}
+	if (i == bmap->n_div)
+		return isl_map_from_basic_map(bmap);
+	bmap = isl_basic_map_drop_redundant_divs(bmap);
+	if (!bmap)
+		goto error;
+	for (i = 0; i < bmap->n_div; ++i)
+		if (isl_int_is_zero(bmap->div[i][0]))
+			break;
+	if (i == bmap->n_div)
 		return isl_map_from_basic_map(bmap);
-	return isl_pip_basic_map_compute_divs(bmap);
+	struct isl_map *map = isl_pip_basic_map_compute_divs(bmap);
+	return map;
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
 }
 
 struct isl_map *isl_map_compute_divs(struct isl_map *map)
@@ -2600,7 +2993,7 @@ struct isl_map *isl_map_compute_divs(struct isl_map *map)
 	for (i = 1 ; i < map->n; ++i) {
 		struct isl_map *r2;
 		r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
-		if (F_ISSET(map, ISL_MAP_DISJOINT))
+		if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
 			res = isl_map_union_disjoint(res, r2);
 		else
 			res = isl_map_union(res, r2);
@@ -2635,14 +3028,16 @@ struct isl_set *isl_map_domain(struct isl_map *map)
 		return NULL;
 
 	set = (struct isl_set *)map;
-	set->dim = map->n_in;
-	set->zero = 0;
+	set->dim = isl_dim_domain(set->dim);
+	if (!set->dim)
+		goto error;
 	for (i = 0; i < map->n; ++i) {
 		set->p[i] = isl_basic_map_domain(map->p[i]);
 		if (!set->p[i])
 			goto error;
 	}
-	F_CLR(set, ISL_MAP_DISJOINT);
+	ISL_F_CLR(set, ISL_MAP_DISJOINT);
+	ISL_F_CLR(set, ISL_SET_NORMALIZED);
 	return set;
 error:
 	isl_map_free(map);
@@ -2668,15 +3063,13 @@ struct isl_map *isl_map_union_disjoint(
 		return map1;
 	}
 
-	isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
-	isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
-	isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
+	isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
 
-	if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
-	    F_ISSET(map2, ISL_MAP_DISJOINT))
-		FL_SET(flags, ISL_MAP_DISJOINT);
+	if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
+	    ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
+		ISL_FL_SET(flags, ISL_MAP_DISJOINT);
 
-	map = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
+	map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
 				map1->n + map2->n, flags);
 	if (!map)
 		goto error;
@@ -2708,7 +3101,7 @@ struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
 	if (!map1)
 		return NULL;
 	if (map1->n > 1)
-		F_CLR(map1, ISL_MAP_DISJOINT);
+		ISL_F_CLR(map1, ISL_MAP_DISJOINT);
 	return map1;
 }
 
@@ -2726,817 +3119,1560 @@ struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
 		isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
 }
 
-struct isl_map *isl_map_intersect_range(
-		struct isl_map *map, struct isl_set *set)
-{
-	unsigned flags = 0;
-	struct isl_map *result;
-	int i, j;
+struct isl_map *isl_map_intersect_range(
+		struct isl_map *map, struct isl_set *set)
+{
+	unsigned flags = 0;
+	struct isl_map *result;
+	int i, j;
+
+	if (!map || !set)
+		goto error;
+
+	if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
+	    ISL_F_ISSET(set, ISL_MAP_DISJOINT))
+		ISL_FL_SET(flags, ISL_MAP_DISJOINT);
+
+	result = isl_map_alloc_dim(isl_dim_copy(map->dim),
+					map->n * set->n, flags);
+	if (!result)
+		goto error;
+	for (i = 0; i < map->n; ++i)
+		for (j = 0; j < set->n; ++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(map);
+	isl_set_free(set);
+	return result;
+error:
+	isl_map_free(map);
+	isl_set_free(set);
+	return NULL;
+}
+
+struct isl_map *isl_map_intersect_domain(
+		struct isl_map *map, struct isl_set *set)
+{
+	return isl_map_reverse(
+		isl_map_intersect_range(isl_map_reverse(map), set));
+}
+
+struct isl_map *isl_map_apply_domain(
+		struct isl_map *map1, struct isl_map *map2)
+{
+	if (!map1 || !map2)
+		goto error;
+	map1 = isl_map_reverse(map1);
+	map1 = isl_map_apply_range(map1, map2);
+	return isl_map_reverse(map1);
+error:
+	isl_map_free(map1);
+	isl_map_free(map2);
+	return NULL;
+}
+
+struct isl_map *isl_map_apply_range(
+		struct isl_map *map1, struct isl_map *map2)
+{
+	struct isl_dim *dim_result;
+	struct isl_map *result;
+	int i, j;
+	unsigned nparam;
+	unsigned n_in;
+	unsigned n_out;
+
+	if (!map1 || !map2)
+		goto error;
+
+	dim_result = isl_dim_join(isl_dim_copy(map1->dim),
+				  isl_dim_copy(map2->dim));
+
+	result = isl_map_alloc_dim(dim_result, 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(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(map1);
+	isl_map_free(map2);
+	if (result && result->n <= 1)
+		ISL_F_SET(result, ISL_MAP_DISJOINT);
+	return result;
+error:
+	isl_map_free(map1);
+	isl_map_free(map2);
+	return NULL;
+}
+
+/*
+ * returns range - domain
+ */
+struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
+{
+	struct isl_basic_set *bset;
+	unsigned dim;
+	unsigned nparam;
+	int i;
+
+	if (!bmap)
+		goto error;
+	dim = isl_basic_map_n_in(bmap);
+	nparam = isl_basic_map_n_param(bmap);
+	isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
+	bset = isl_basic_set_from_basic_map(bmap);
+	bset = isl_basic_set_cow(bset);
+	bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
+	bset = isl_basic_set_swap_vars(bset, 2*dim);
+	for (i = 0; i < dim; ++i) {
+		int j = isl_basic_map_alloc_equality(
+					    (struct isl_basic_map *)bset);
+		if (j < 0)
+			goto error;
+		isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
+		isl_int_set_si(bset->eq[j][1+nparam+i], 1);
+		isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
+		isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
+	}
+	return isl_basic_set_project_out(bset, 2*dim, 0);
+error:
+	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, isl_map_n_in(map) == isl_map_n_out(map), goto error);
+	result = isl_set_alloc(map->ctx, isl_map_n_param(map),
+					isl_map_n_in(map), map->n, map->flags);
+	if (!result)
+		goto error;
+	for (i = 0; i < map->n; ++i)
+		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;
+}
+
+static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
+{
+	struct isl_basic_map *bmap;
+	unsigned nparam;
+	unsigned dim;
+	int i;
+
+	if (!dims)
+		return NULL;
+
+	nparam = dims->nparam;
+	dim = dims->n_out;
+	bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
+	if (!bmap)
+		goto error;
+
+	for (i = 0; i < dim; ++i) {
+		int j = isl_basic_map_alloc_equality(bmap);
+		if (j < 0)
+			goto error;
+		isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
+		isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
+		isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
+	}
+	return isl_basic_map_finalize(bmap);
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
+{
+	struct isl_dim *dim = isl_dim_map(set_dim);
+	if (!dim)
+		return NULL;
+	return basic_map_identity(dim);
+}
+
+struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
+{
+	if (!model || !model->dim)
+		return NULL;
+	isl_assert(model->ctx,
+			model->dim->n_in == model->dim->n_out, return NULL);
+	return basic_map_identity(isl_dim_copy(model->dim));
+}
+
+static struct isl_map *map_identity(struct isl_dim *dim)
+{
+	struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
+	return isl_map_add(map, basic_map_identity(isl_dim_copy(dim)));
+}
+
+struct isl_map *isl_map_identity(struct isl_dim *set_dim)
+{
+	struct isl_dim *dim = isl_dim_map(set_dim);
+	if (!dim)
+		return NULL;
+	return map_identity(dim);
+}
+
+struct isl_map *isl_map_identity_like(struct isl_basic_map *model)
+{
+	if (!model || !model->dim)
+		return NULL;
+	isl_assert(model->ctx,
+			model->dim->n_in == model->dim->n_out, return NULL);
+	return map_identity(isl_dim_copy(model->dim));
+}
+
+int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
+{
+	return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
+}
+
+int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
+{
+	return isl_map_is_subset(
+			(struct isl_map *)set1, (struct isl_map *)set2);
+}
+
+int isl_basic_map_is_subset(
+		struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+{
+	int is_subset;
+	struct isl_map *map1;
+	struct isl_map *map2;
+
+	if (!bmap1 || !bmap2)
+		return -1;
+
+	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(map1, map2);
+
+	isl_map_free(map1);
+	isl_map_free(map2);
+
+	return is_subset;
+}
+
+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;
+
+	if (!map)
+		return -1;
+	for (i = 0; i < map->n; ++i) {
+		is_empty = isl_basic_map_is_empty(map->p[i]);
+		if (is_empty < 0)
+			return -1;
+		if (!is_empty)
+			return 0;
+	}
+	return 1;
+}
+
+int isl_map_fast_is_empty(struct isl_map *map)
+{
+	return map->n == 0;
+}
+
+int isl_set_is_empty(struct isl_set *set)
+{
+	return isl_map_is_empty((struct isl_map *)set);
+}
+
+int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
+{
+	int i;
+	int is_subset = 0;
+	struct isl_map *diff;
+
+	if (!map1 || !map2)
+		return -1;
+
+	if (isl_map_is_empty(map1))
+		return 1;
+
+	if (isl_map_is_empty(map2))
+		return 0;
+
+	diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
+	if (!diff)
+		return -1;
+
+	is_subset = isl_map_is_empty(diff);
+	isl_map_free(diff);
+
+	return is_subset;
+}
+
+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(map1, map2);
+	if (is_subset != 1)
+		return is_subset;
+	is_subset = isl_map_is_subset(map2, map1);
+	return is_subset;
+}
+
+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(bmap1, bmap2);
+	if (is_subset != 1)
+		return is_subset;
+	is_subset = isl_basic_map_is_subset(bmap2, bmap1);
+	if (is_subset == -1)
+		return is_subset;
+	return !is_subset;
+}
+
+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_set_is_universe(struct isl_basic_set *bset)
+{
+	if (!bset)
+		return -1;
+	return bset->n_eq == 0 && bset->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;
+	int empty;
+	unsigned total;
+
+	if (!bmap)
+		return -1;
+
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+		return 1;
+
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
+		struct isl_basic_map *copy = isl_basic_map_copy(bmap);
+		copy = isl_basic_map_convex_hull(copy);
+		empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
+		isl_basic_map_free(copy);
+		return empty;
+	}
+
+	total = 1 + isl_basic_map_total_dim(bmap);
+	if (bmap->sample && bmap->sample->size == total) {
+		int contains = basic_map_contains(bmap, bmap->sample);
+		if (contains < 0)
+			return -1;
+		if (contains)
+			return 0;
+	}
+	isl_vec_free(bmap->sample);
+	bmap->sample = NULL;
+	bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
+	if (!bset)
+		return -1;
+	sample = isl_basic_set_sample(bset);
+	if (!sample)
+		return -1;
+	empty = sample->size == 0;
+	isl_vec_free(bmap->sample);
+	bmap->sample = sample;
+	if (empty)
+		ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
+
+	return empty;
+}
+
+int isl_basic_map_fast_is_empty(struct isl_basic_map *bmap)
+{
+	if (!bmap)
+		return -1;
+	return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
+}
+
+int isl_basic_set_fast_is_empty(struct isl_basic_set *bset)
+{
+	if (!bset)
+		return -1;
+	return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
+}
+
+int isl_basic_set_is_empty(struct isl_basic_set *bset)
+{
+	return isl_basic_map_is_empty((struct isl_basic_map *)bset);
+}
+
+struct isl_map *isl_basic_map_union(
+	struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+{
+	struct isl_map *map;
+	if (!bmap1 || !bmap2)
+		return NULL;
+
+	isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
+
+	map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
+	if (!map)
+		goto error;
+	map = isl_map_add(map, bmap1);
+	map = isl_map_add(map, bmap2);
+	return map;
+error:
+	isl_basic_map_free(bmap1);
+	isl_basic_map_free(bmap2);
+	return NULL;
+}
+
+struct isl_set *isl_basic_set_union(
+		struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+	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_basic_map *bmap)
+{
+	int i;
+	unsigned off = isl_dim_total(bmap->dim);
+
+	for (i = 0; i < bmap->n_div; ++i) {
+		int pos;
+		pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
+							    bmap->n_div-i);
+		if (pos == -1)
+			continue;
+		swap_div(bmap, i, i + pos);
+		--i;
+	}
+	return bmap;
+}
+
+/* Look for a div in dst that corresponds to the div "div" in src.
+ * The divs before "div" in src and dst are assumed to be the same.
+ * 
+ * Returns -1 if no corresponding div was found and the position
+ * of the corresponding div in dst otherwise.
+ */
+static int find_div(struct isl_basic_map *dst,
+			struct isl_basic_map *src, unsigned div)
+{
+	int i;
+
+	unsigned total = isl_dim_total(src->dim);
+
+	isl_assert(dst->ctx, div <= dst->n_div, return -1);
+	for (i = div; i < dst->n_div; ++i)
+		if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
+		    isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
+						dst->n_div - div) == -1)
+			return i;
+	return -1;
+}
+
+struct isl_basic_map *isl_basic_map_align_divs(
+		struct isl_basic_map *dst, struct isl_basic_map *src)
+{
+	int i;
+	unsigned total = isl_dim_total(src->dim);
+
+	if (!dst || !src)
+		goto error;
+
+	if (src->n_div == 0)
+		return dst;
+
+	for (i = 0; i < src->n_div; ++i)
+		isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
+
+	src = order_divs(src);
+	dst = isl_basic_map_cow(dst);
+	dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
+			src->n_div, 0, 2 * src->n_div);
+	if (!dst)
+		return NULL;
+	for (i = 0; i < src->n_div; ++i) {
+		int j = find_div(dst, src, i);
+		if (j < 0) {
+			j = isl_basic_map_alloc_div(dst);
+			if (j < 0)
+				goto error;
+			isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
+			isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
+			if (add_div_constraints(dst, j) < 0)
+				goto error;
+		}
+		if (j != i)
+			swap_div(dst, i, j);
+	}
+	return dst;
+error:
+	isl_basic_map_free(dst);
+	return NULL;
+}
+
+struct isl_basic_set *isl_basic_set_align_divs(
+		struct isl_basic_set *dst, struct isl_basic_set *src)
+{
+	return (struct isl_basic_set *)isl_basic_map_align_divs(
+		(struct isl_basic_map *)dst, (struct isl_basic_map *)src);
+}
+
+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]);
+
+	ISL_F_CLR(map, ISL_MAP_NORMALIZED);
+	return map;
+}
+
+struct isl_set *isl_set_align_divs(struct isl_set *set)
+{
+	return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
+}
+
+static struct isl_map *add_cut_constraint(struct isl_map *dst,
+		struct isl_basic_map *src, isl_int *c,
+		unsigned len, int oppose)
+{
+	struct isl_basic_map *copy = NULL;
+	int is_empty;
+	int k;
+	unsigned total;
+
+	copy = isl_basic_map_copy(src);
+	copy = isl_basic_map_cow(copy);
+	if (!copy)
+		goto error;
+	copy = isl_basic_map_extend_constraints(copy, 0, 1);
+	k = isl_basic_map_alloc_inequality(copy);
+	if (k < 0)
+		goto error;
+	if (oppose)
+		isl_seq_neg(copy->ineq[k], c, len);
+	else
+		isl_seq_cpy(copy->ineq[k], c, len);
+	total = 1 + isl_basic_map_total_dim(copy);
+	isl_seq_clr(copy->ineq[k]+len, total - len);
+	isl_inequality_negate(copy, k);
+	copy = isl_basic_map_simplify(copy);
+	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(dst, copy);
+	else
+		isl_basic_map_free(copy);
+	return dst;
+error:
+	isl_basic_map_free(copy);
+	isl_map_free(dst);
+	return NULL;
+}
+
+static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
+{
+	int i, j, k;
+	unsigned flags = 0;
+	struct isl_map *rest = NULL;
+	unsigned max;
+	unsigned total = isl_basic_map_total_dim(bmap);
+
+	assert(bmap);
+
+	if (!map)
+		goto error;
+
+	if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
+		ISL_FL_SET(flags, ISL_MAP_DISJOINT);
+
+	max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
+	rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
+	if (!rest)
+		goto error;
+
+	for (i = 0; i < map->n; ++i) {
+		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(map->p[j]);
+
+	for (i = 0; i < bmap->n_eq; ++i) {
+		for (j = 0; j < map->n; ++j) {
+			rest = add_cut_constraint(rest,
+				map->p[j], bmap->eq[i], 1+total, 0);
+			if (!rest)
+				goto error;
+
+			rest = add_cut_constraint(rest,
+				map->p[j], bmap->eq[i], 1+total, 1);
+			if (!rest)
+				goto error;
 
-	if (!map || !set)
-		goto error;
+			map->p[j] = isl_basic_map_extend_constraints(map->p[j],
+				1, 0);
+			if (!map->p[j])
+				goto error;
+			k = isl_basic_map_alloc_equality(map->p[j]);
+			if (k < 0)
+				goto error;
+			isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
+			isl_seq_clr(map->p[j]->eq[k]+1+total,
+					map->p[j]->n_div - bmap->n_div);
+		}
+	}
 
-	if (F_ISSET(map, ISL_MAP_DISJOINT) &&
-	    F_ISSET(set, ISL_MAP_DISJOINT))
-		FL_SET(flags, ISL_MAP_DISJOINT);
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		for (j = 0; j < map->n; ++j) {
+			rest = add_cut_constraint(rest,
+				map->p[j], bmap->ineq[i], 1+total, 0);
+			if (!rest)
+				goto error;
 
-	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(result,
-			    isl_basic_map_intersect_range(
-				isl_basic_map_copy(map->p[i]),
-				isl_basic_set_copy(set->p[j])));
-			if (!result)
+			map->p[j] = isl_basic_map_extend_constraints(map->p[j],
+				0, 1);
+			if (!map->p[j])
 				goto error;
+			k = isl_basic_map_alloc_inequality(map->p[j]);
+			if (k < 0)
+				goto error;
+			isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
+			isl_seq_clr(map->p[j]->ineq[k]+1+total,
+					map->p[j]->n_div - bmap->n_div);
 		}
+	}
+
 	isl_map_free(map);
-	isl_set_free(set);
-	return result;
+	return rest;
 error:
 	isl_map_free(map);
-	isl_set_free(set);
+	isl_map_free(rest);
 	return NULL;
 }
 
-struct isl_map *isl_map_intersect_domain(
-		struct isl_map *map, struct isl_set *set)
-{
-	return isl_map_reverse(
-		isl_map_intersect_range(isl_map_reverse(map), set));
-}
-
-struct isl_map *isl_map_apply_domain(
-		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;
-	map1 = isl_map_reverse(map1);
-	map1 = isl_map_apply_range(map1, map2);
-	return isl_map_reverse(map1);
-error:
-	isl_map_free(map1);
-	isl_map_free(map2);
-	return NULL;
-}
 
-struct isl_map *isl_map_apply_range(
-		struct isl_map *map1, struct isl_map *map2)
-{
-	struct isl_map *result;
-	int i, j;
+	isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
+
+	if (isl_map_is_empty(map2)) {
+		isl_map_free(map2);
+		return map1;
+	}
 
+	map1 = isl_map_compute_divs(map1);
+	map2 = isl_map_compute_divs(map2);
 	if (!map1 || !map2)
 		goto error;
 
-	isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
-	isl_assert(map1->ctx, map1->n_out == map2->n_in, goto error);
+	for (i = 0; map1 && i < map2->n; ++i)
+		map1 = subtract(map1, map2->p[i]);
 
-	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(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(map1);
 	isl_map_free(map2);
-	if (result && result->n <= 1)
-		F_SET(result, ISL_MAP_DISJOINT);
-	return result;
+	return map1;
 error:
 	isl_map_free(map1);
 	isl_map_free(map2);
 	return NULL;
 }
 
-/*
- * returns range - domain
- */
-struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
+struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
 {
-	struct isl_basic_set *bset;
-	unsigned dim;
-	int i;
+	return (struct isl_set *)
+		isl_map_subtract(
+			(struct isl_map *)set1, (struct isl_map *)set2);
+}
 
-	if (!bmap)
+struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
+{
+	if (!set || !map)
 		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(bmap);
-	bset = isl_basic_set_extend(bset, bset->nparam, 3*dim, 0,
-					dim, 0);
-	bset = isl_basic_set_swap_vars(bset, 2*dim);
-	for (i = 0; i < dim; ++i) {
-		int j = isl_basic_map_alloc_equality(
-					    (struct isl_basic_map *)bset);
-		if (j < 0)
-			goto error;
-		isl_seq_clr(bset->eq[j],
-			    1 + bset->nparam + bset->dim + bset->extra);
-		isl_int_set_si(bset->eq[j][1+bset->nparam+i], 1);
-		isl_int_set_si(bset->eq[j][1+bset->nparam+dim+i], 1);
-		isl_int_set_si(bset->eq[j][1+bset->nparam+2*dim+i], -1);
-	}
-	return isl_basic_set_project_out(bset, 2*dim, 0);
+	isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
+	map = isl_map_intersect_domain(map, set);
+	set = isl_map_range(map);
+	return set;
 error:
-	isl_basic_map_free(bmap);
+	isl_set_free(set);
+	isl_map_free(map);
 	return NULL;
 }
 
-/* If the only constraints a div d=floor(f/m)
- * appears in are its two defining constraints
- *
- *	f - m d >=0
- *	-(f - (m - 1)) + m d >= 0
- *
- * then it can safely be removed.
- */
-static int div_is_redundant(struct isl_basic_map *bmap, int div)
-{
-	int i;
-	unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
-
-	for (i = 0; i < bmap->n_eq; ++i)
-		if (!isl_int_is_zero(bmap->eq[i][pos]))
-			return 0;
-
-	for (i = 0; i < bmap->n_ineq; ++i) {
-		if (isl_int_is_zero(bmap->ineq[i][pos]))
-			continue;
-		if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
-			int neg;
-			isl_int_sub(bmap->div[div][1],
-					bmap->div[div][1], bmap->div[div][0]);
-			isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
-			neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
-			isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
-			isl_int_add(bmap->div[div][1],
-					bmap->div[div][1], bmap->div[div][0]);
-			if (!neg)
-				return 0;
-			if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
-						    bmap->n_div-div-1) != -1)
-				return 0;
-		} else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
-			if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
-				return 0;
-			if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
-						    bmap->n_div-div-1) != -1)
-				return 0;
-		} else
-			return 0;
-	}
-
-	for (i = 0; i < bmap->n_div; ++i)
-		if (!isl_int_is_zero(bmap->div[i][1+pos]))
-			return 0;
-
-	return 1;
-}
-
-/*
- * Remove divs that don't occur in any of the constraints or other divs.
- * These can arise when dropping some of the variables in a quast
- * returned by piplib.
+/* There is no need to cow as removing empty parts doesn't change
+ * the meaning of the set.
  */
-static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
+struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
 {
 	int i;
 
-	if (!bmap)
+	if (!map)
 		return NULL;
 
-	for (i = bmap->n_div-1; i >= 0; --i) {
-		if (!div_is_redundant(bmap, i))
+	for (i = map->n-1; i >= 0; --i) {
+		if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
 			continue;
-		bmap = isl_basic_map_drop_div(bmap, i);
+		isl_basic_map_free(map->p[i]);
+		if (i != map->n-1) {
+			ISL_F_CLR(map, ISL_MAP_NORMALIZED);
+			map->p[i] = map->p[map->n-1];
+		}
+		map->n--;
 	}
-	return bmap;
-}
 
-struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
-{
-	bmap = remove_redundant_divs(bmap);
-	if (!bmap)
-		return NULL;
-	F_SET(bmap, ISL_BASIC_SET_FINAL);
-	return bmap;
+	return map;
 }
 
-struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
+struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
 {
-	return (struct isl_basic_set *)
-		isl_basic_map_finalize((struct isl_basic_map *)bset);
+	return (struct isl_set *)
+		isl_map_remove_empty_parts((struct isl_map *)set);
 }
 
-struct isl_set *isl_set_finalize(struct isl_set *set)
+struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
 {
-	int i;
-
-	if (!set)
+	struct isl_basic_map *bmap;
+	if (!map || map->n == 0)
 		return NULL;
-	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_finalize(set->p[i]);
-		if (!set->p[i])
-			goto error;
-	}
-	return set;
-error:
-	isl_set_free(set);
-	return NULL;
+	bmap = map->p[map->n-1];
+	isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
+	return isl_basic_map_copy(bmap);
 }
 
-struct isl_map *isl_map_finalize(struct isl_map *map)
+struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
 {
-	int i;
-
-	if (!map)
-		return NULL;
-	for (i = 0; i < map->n; ++i) {
-		map->p[i] = isl_basic_map_finalize(map->p[i]);
-		if (!map->p[i])
-			goto error;
-	}
-	return map;
-error:
-	isl_map_free(map);
-	return NULL;
+	(struct isl_basic_set *)isl_map_copy_basic_map((struct isl_map *)set);
 }
 
-struct isl_basic_map *isl_basic_map_identity(struct isl_ctx *ctx,
-		unsigned nparam, unsigned dim)
+struct isl_map *isl_map_drop_basic_map(struct isl_map *map,
+						struct isl_basic_map *bmap)
 {
-	struct isl_basic_map *bmap;
 	int i;
 
-	bmap = isl_basic_map_alloc(ctx, nparam, dim, dim, 0, dim, 0);
-	if (!bmap)
+	if (!map || !bmap)
 		goto error;
-
-	for (i = 0; i < dim; ++i) {
-		int j = isl_basic_map_alloc_equality(bmap);
-		if (j < 0)
+	for (i = map->n-1; i >= 0; --i) {
+		if (map->p[i] != bmap)
+			continue;
+		map = isl_map_cow(map);
+		if (!map)
 			goto error;
-		isl_seq_clr(bmap->eq[j],
-		    1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
-		isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
-		isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
+		isl_basic_map_free(map->p[i]);
+		if (i != map->n-1) {
+			ISL_F_CLR(map, ISL_SET_NORMALIZED);
+			map->p[i] = map->p[map->n-1];
+		}
+		map->n--;
+		return map;
 	}
-	return isl_basic_map_finalize(bmap);
-error:
 	isl_basic_map_free(bmap);
-	return NULL;
-}
-
-struct isl_map *isl_map_identity(struct isl_ctx *ctx,
-		unsigned nparam, unsigned dim)
-{
-	struct isl_map *map = isl_map_alloc(ctx, nparam, dim, dim, 1,
-						ISL_MAP_DISJOINT);
-	if (!map)
-		goto error;
-	map = isl_map_add(map,
-		isl_basic_map_identity(ctx, nparam, dim));
 	return map;
 error:
 	isl_map_free(map);
-	return NULL;
-}
-
-int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
-{
-	return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
-}
-
-int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
-{
-	return isl_map_is_subset(
-			(struct isl_map *)set1, (struct isl_map *)set2);
-}
-
-int isl_basic_map_is_subset(
-		struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
-{
-	int is_subset;
-	struct isl_map *map1;
-	struct isl_map *map2;
-
-	if (!bmap1 || !bmap2)
-		return -1;
-
-	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(map1, map2);
-
-	isl_map_free(map1);
-	isl_map_free(map2);
-
-	return is_subset;
+	isl_basic_map_free(bmap);
+	return NULL;
 }
 
-int isl_basic_map_is_equal(
-		struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
+						struct isl_basic_set *bset)
 {
-	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;
+	(struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
+						(struct isl_basic_map *)bset);
 }
 
-int isl_basic_set_is_equal(
-		struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+/* 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 than 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)
 {
-	return isl_basic_map_is_equal(
-		(struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
+	struct isl_dim *dims;
+	struct isl_basic_map *bmap1 = NULL;
+	struct isl_basic_map *bmap2 = NULL;
+	struct isl_ctx *ctx;
+	struct isl_vec *obj;
+	unsigned total;
+	unsigned nparam;
+	unsigned dim1, dim2;
+	isl_int num, den;
+	enum isl_lp_result res;
+	int cmp;
+
+	if (!bset1 || !bset2)
+		return -2;
+
+	nparam = isl_basic_set_n_param(bset1);
+	dim1 = isl_basic_set_n_dim(bset1);
+	dim2 = isl_basic_set_n_dim(bset2);
+	dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
+	bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
+	dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
+	bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
+	if (!bmap1 || !bmap2)
+		goto error;
+	bmap1 = isl_basic_map_cow(bmap1);
+	bmap1 = isl_basic_map_extend(bmap1, nparam,
+			pos, (dim1 - pos) + (dim2 - pos),
+			bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
+	bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
+	if (!bmap1)
+		goto error;
+	total = isl_basic_map_total_dim(bmap1);
+	ctx = bmap1->ctx;
+	obj = isl_vec_alloc(ctx, 1 + total);
+	isl_seq_clr(obj->block.data, 1 + total);
+	isl_int_set_si(obj->block.data[1+nparam+pos], 1);
+	isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
+	if (!obj)
+		goto error;
+	isl_int_init(num);
+	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(obj);
+	return cmp;
+error:
+	isl_basic_map_free(bmap1);
+	isl_basic_map_free(bmap2);
+	return -2;
 }
 
-int isl_map_is_empty(struct isl_map *map)
+static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
+	unsigned pos, isl_int *val)
 {
 	int i;
-	int is_empty;
+	int d;
+	unsigned total;
 
-	if (!map)
+	if (!bmap)
 		return -1;
-	for (i = 0; i < map->n; ++i) {
-		is_empty = isl_basic_map_is_empty(map->p[i]);
-		if (is_empty < 0)
-			return -1;
-		if (!is_empty)
+	total = isl_basic_map_total_dim(bmap);
+	for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
+		for (; d+1 > pos; --d)
+			if (!isl_int_is_zero(bmap->eq[i][1+d]))
+				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 1;
-}
-
-int isl_set_is_empty(struct isl_set *set)
-{
-	return isl_map_is_empty((struct isl_map *)set);
+	return 0;
 }
 
-int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
+static int isl_map_fast_has_fixed_var(struct isl_map *map,
+	unsigned pos, isl_int *val)
 {
 	int i;
-	int is_subset = 0;
-	struct isl_map *diff;
+	isl_int v;
+	isl_int tmp;
+	int fixed;
 
-	if (!map1 || !map2)
+	if (!map)
 		return -1;
-
-	if (isl_map_is_empty(map1))
-		return 1;
-
-	if (isl_map_is_empty(map2))
+	if (map->n == 0)
 		return 0;
-
-	diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
-	if (!diff)
-		return -1;
-
-	is_subset = isl_map_is_empty(diff);
-	isl_map_free(diff);
-
-	return is_subset;
+	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;
 }
 
-int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
+static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
+	isl_int *val)
 {
-	int is_subset;
+	return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
+}
 
-	if (!map1 || !map2)
+int isl_basic_map_fast_is_fixed(struct isl_basic_map *bmap,
+	enum isl_dim_type type, unsigned pos, isl_int *val)
+{
+	if (pos >= isl_basic_map_dim(bmap, type))
 		return -1;
-	is_subset = isl_map_is_subset(map1, map2);
-	if (is_subset != 1)
-		return is_subset;
-	is_subset = isl_map_is_subset(map2, map1);
-	return is_subset;
+	return isl_basic_map_fast_has_fixed_var(bmap,
+		isl_basic_map_offset(bmap, type) - 1 + pos, val);
 }
 
-int isl_basic_map_is_strict_subset(
-		struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+/* 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)
 {
-	int is_subset;
+	return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
+}
 
-	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);
-	if (is_subset == -1)
-		return is_subset;
-	return !is_subset;
+/* 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, isl_map_n_param(map) + in, val);
 }
 
-static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
+/* 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;
+	int i, i_eq = -1, i_ineq = -1;
+	isl_int *c;
 	unsigned total;
-	isl_int s;
+	unsigned nparam;
 
-	total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-	if (total != vec->size)
+	if (!bset)
 		return -1;
-
-	isl_int_init(s);
-
-	for (i = 0; i < bmap->n_eq; ++i) {
-		isl_seq_inner_product(vec->block.data, bmap->eq[i], total, &s);
-		if (!isl_int_is_zero(s)) {
-			isl_int_clear(s);
+	total = isl_basic_set_total_dim(bset);
+	nparam = isl_basic_set_n_param(bset);
+	for (i = 0; i < bset->n_eq; ++i) {
+		if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
+			continue;
+		if (i_eq != -1)
 			return 0;
-		}
+		i_eq = i;
 	}
-
-	for (i = 0; i < bmap->n_ineq; ++i) {
-		isl_seq_inner_product(vec->block.data, bmap->ineq[i], total, &s);
-		if (isl_int_is_neg(s)) {
-			isl_int_clear(s);
+	for (i = 0; i < bset->n_ineq; ++i) {
+		if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
+			continue;
+		if (i_eq != -1 || i_ineq != -1)
 			return 0;
-		}
+		i_ineq = i;
 	}
-
-	isl_int_clear(s);
-
+	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+nparam+dim]))
+		return 0;
+	if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
+		return 0;
+	if (isl_seq_first_non_zero(c+1+nparam+dim+1,
+					total - nparam - dim - 1) != -1)
+		return 0;
+	if (val)
+		isl_int_neg(*val, c[0]);
 	return 1;
 }
 
-int isl_basic_map_is_universe(struct isl_basic_map *bmap)
+int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
+	unsigned dim, isl_int *val)
 {
-	if (!bmap)
+	int i;
+	isl_int v;
+	isl_int tmp;
+	int fixed;
+
+	if (!set)
 		return -1;
-	return bmap->n_eq == 0 && bmap->n_ineq == 0;
+	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;
 }
 
-int isl_basic_map_is_empty(struct isl_basic_map *bmap)
+struct constraint {
+	unsigned	size;
+	isl_int		*c;
+};
+
+static int qsort_constraint_cmp(const void *p1, const void *p2)
 {
-	struct isl_basic_set *bset = NULL;
-	struct isl_vec *sample = NULL;
-	int empty;
+	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 -1;
-
-	if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
-		return 1;
-
-	total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-	if (bmap->sample && bmap->sample->size == total) {
-		int contains = basic_map_contains(bmap, bmap->sample);
-		if (contains < 0)
-			return -1;
-		if (contains)
-			return 0;
+		return NULL;
+	total = isl_basic_map_total_dim(bmap);
+	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];
 	}
-	bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
-	if (!bset)
-		return -1;
-	sample = isl_basic_set_sample(bset);
-	if (!sample)
-		return -1;
-	empty = sample->size == 0;
-	if (bmap->sample)
-		isl_vec_free(bmap->ctx, bmap->sample);
-	bmap->sample = sample;
-
-	return empty;
+	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_map *isl_basic_map_union(
-	struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
 {
-	struct isl_map *map;
-	if (!bmap1 || !bmap2)
+	if (!bmap)
 		return NULL;
-
-	isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
-	isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
-	isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
-
-	map = isl_map_alloc(bmap1->ctx, bmap1->nparam,
-				bmap1->n_in, bmap1->n_out, 2, 0);
-	if (!map)
-		goto error;
-	map = isl_map_add(map, bmap1);
-	map = isl_map_add(map, bmap2);
-	return map;
-error:
-	isl_basic_map_free(bmap1);
-	isl_basic_map_free(bmap2);
-	return NULL;
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
+		return bmap;
+	bmap = isl_basic_map_convex_hull(bmap);
+	bmap = isl_basic_map_sort_constraints(bmap);
+	ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
+	return bmap;
 }
 
-struct isl_set *isl_basic_set_union(
-		struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
 {
-	return (struct isl_set *)isl_basic_map_union(
-					    (struct isl_basic_map *)bset1,
-					    (struct isl_basic_map *)bset2);
+	return (struct isl_basic_set *)isl_basic_map_normalize(
+						(struct isl_basic_map *)bset);
 }
 
-/* Order divs such that any div only depends on previous divs */
-static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
+static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
+	const struct isl_basic_map *bmap2)
 {
-	int i;
-	unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
+	int i, cmp;
+	unsigned total;
 
-	for (i = 0; i < bmap->n_div; ++i) {
-		int pos;
-		pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
-							    bmap->n_div-i);
-		if (pos == -1)
-			continue;
-		swap_div(bmap, i, pos);
-		--i;
+	if (bmap1 == bmap2)
+		return 0;
+	if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
+		return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
+	if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
+		return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
+	if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
+		return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
+	if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
+	    ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
+		return 0;
+	if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
+		return 1;
+	if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
+		return -1;
+	if (bmap1->n_eq != bmap2->n_eq)
+		return bmap1->n_eq - bmap2->n_eq;
+	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 = isl_basic_map_total_dim(bmap1);
+	for (i = 0; i < bmap1->n_eq; ++i) {
+		cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
+		if (cmp)
+			return cmp;
 	}
-	return bmap;
+	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 find_div(struct isl_basic_map *dst,
-			struct isl_basic_map *src, unsigned div)
+static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
+	struct isl_basic_map *bmap2)
 {
-	int i;
+	return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
+}
 
-	unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
+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;
 
-	for (i = 0; i < dst->n_div; ++i)
-		if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total) &&
-		    isl_seq_first_non_zero(dst->div[i]+1+1+total,
-						dst->n_div - src->n_div) == -1)
-			return i;
-	return -1;
+	return isl_basic_map_fast_cmp(bmap1, bmap2);
 }
 
-struct isl_basic_map *isl_basic_map_align_divs(
-		struct isl_basic_map *dst, struct isl_basic_map *src)
+/* 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;
-	unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
-
-	if (src->n_div == 0)
-		return dst;
+	int i, j;
+	struct isl_basic_map *bmap;
 
-	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)
+	if (!map)
 		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(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(dst, j) < 0)
-				goto error;
-		}
-		if (j != i)
-			swap_div(dst, i, j);
+	if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
+		return map;
+	for (i = 0; i < map->n; ++i) {
+		bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
+		if (!bmap)
+			goto error;
+		isl_basic_map_free(map->p[i]);
+		map->p[i] = bmap;
 	}
-	return dst;
+	qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
+	ISL_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_basic_map_free(dst);
+	isl_map_free(map);
 	return NULL;
+
 }
 
-struct isl_map *isl_map_align_divs(struct isl_map *map)
+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;
 
-	map = isl_map_compute_divs(map);
-	map = isl_map_cow(map);
-	if (!map)
-		return NULL;
+	if (!map1 || !map2)
+		return -1;
 
-	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]);
+	if (map1 == map2)
+		return 1;
+	if (!isl_dim_equal(map1->dim, map2->dim))
+		return 0;
 
-	return map;
+	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;
 }
 
-static struct isl_map *add_cut_constraint(struct isl_map *dst,
-		struct isl_basic_map *src, isl_int *c,
-		unsigned len, int oppose)
+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)
 {
-	struct isl_basic_map *copy = NULL;
-	int is_empty;
 	int k;
-	unsigned total;
+	struct isl_basic_set *bset = NULL;
 
-	copy = isl_basic_map_copy(src);
-	copy = isl_basic_map_cow(copy);
-	if (!copy)
+	bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
+	if (!bset)
 		goto error;
-	copy = isl_basic_map_extend(copy,
-		copy->nparam, copy->n_in, copy->n_out, 0, 0, 1);
-	k = isl_basic_map_alloc_inequality(copy);
+
+	k = isl_basic_set_alloc_inequality(bset);
 	if (k < 0)
 		goto error;
-	if (oppose)
-		isl_seq_neg(copy->ineq[k], c, len);
-	else
-		isl_seq_cpy(copy->ineq[k], c, len);
-	total = 1 + copy->nparam + copy->n_in + copy->n_out + copy->extra;
-	isl_seq_clr(copy->ineq[k]+len, total - len);
-	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)
+	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;
-	if (!is_empty)
-		dst = isl_map_add(dst, copy);
-	else
-		isl_basic_map_free(copy);
-	return dst;
+	isl_int_set_si(bset->ineq[k][1], -1);
+	isl_int_set(bset->ineq[k][0], max);
+
+	return bset;
 error:
-	isl_basic_map_free(copy);
-	isl_map_free(dst);
+	isl_basic_set_free(bset);
 	return NULL;
 }
 
-static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
+/* 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, j, k;
-	unsigned flags = 0;
-	struct isl_map *rest = NULL;
-	unsigned max;
-	unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
-
-	assert(bmap);
-
-	if (!map)
-		goto error;
-
-	if (F_ISSET(map, ISL_MAP_DISJOINT))
-		FL_SET(flags, ISL_MAP_DISJOINT);
+	int i;
+	unsigned dim;
+	unsigned nparam;
+	unsigned extra;
+	unsigned n_eq;
+	unsigned n_ineq;
+	struct isl_basic_set *product = NULL;
 
-	max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
-	rest = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
-				max, flags);
-	if (!rest)
+	if (!list)
 		goto error;
-
-	for (i = 0; i < map->n; ++i) {
-		map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
-		if (!map->p[i])
-			goto error;
+	isl_assert(list->ctx, list->n > 0, goto error);
+	isl_assert(list->ctx, list->p[0], goto error);
+	nparam = isl_basic_set_n_param(list->p[0]);
+	dim = isl_basic_set_n_dim(list->p[0]);
+	extra = list->p[0]->n_div;
+	n_eq = list->p[0]->n_eq;
+	n_ineq = list->p[0]->n_ineq;
+	for (i = 1; i < list->n; ++i) {
+		isl_assert(list->ctx, list->p[i], goto error);
+		isl_assert(list->ctx,
+		    nparam == isl_basic_set_n_param(list->p[i]), goto error);
+		dim += isl_basic_set_n_dim(list->p[i]);
+		extra += list->p[i]->n_div;
+		n_eq += list->p[i]->n_eq;
+		n_ineq += list->p[i]->n_ineq;
 	}
-
-	for (j = 0; j < map->n; ++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(rest,
-				map->p[j], bmap->eq[i], 1+total, 0);
-			if (!rest)
-				goto error;
-
-			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(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(map->p[j]);
-			if (k < 0)
-				goto error;
-			isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
-			isl_seq_clr(map->p[j]->eq[k]+1+total,
-					map->p[j]->extra - bmap->n_div);
-		}
+	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) {
+		isl_basic_set_add_constraints(product,
+					isl_basic_set_copy(list->p[i]), dim);
+		dim += isl_basic_set_n_dim(list->p[i]);
 	}
+	isl_basic_set_list_free(list);
+	return product;
+error:
+	isl_basic_set_free(product);
+	isl_basic_set_list_free(list);
+	return NULL;
+}
 
-	for (i = 0; i < bmap->n_ineq; ++i) {
-		for (j = 0; j < map->n; ++j) {
-			rest = add_cut_constraint(rest,
-				map->p[j], bmap->ineq[i], 1+total, 0);
-			if (!rest)
-				goto error;
+struct isl_basic_map *isl_basic_map_product(
+		struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
+{
+	struct isl_dim *dim_result = NULL;
+	struct isl_basic_map *bmap;
+	unsigned in1, in2, out1, out2, nparam, total, pos;
+	struct isl_dim_map *dim_map1, *dim_map2;
 
-			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(map->p[j]);
-			if (k < 0)
-				goto error;
-			isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
-			isl_seq_clr(map->p[j]->ineq[k]+1+total,
-					map->p[j]->extra - bmap->n_div);
-		}
-	}
+	if (!bmap1 || !bmap2)
+		goto error;
 
-	isl_map_free(map);
-	return rest;
+	isl_assert(map1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
+				     bmap2->dim, isl_dim_param), goto error);
+	dim_result = isl_dim_product(isl_dim_copy(bmap1->dim),
+						   isl_dim_copy(bmap2->dim));
+
+	in1 = isl_basic_map_n_in(bmap1);
+	in2 = isl_basic_map_n_in(bmap2);
+	out1 = isl_basic_map_n_out(bmap1);
+	out2 = isl_basic_map_n_out(bmap2);
+	nparam = isl_basic_map_n_param(bmap1);
+
+	total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
+	dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
+	dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
+	isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
+	isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
+	isl_dim_map_div(dim_map1, bmap1, pos += out2);
+	isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
+
+	bmap = isl_basic_map_alloc_dim(dim_result,
+			bmap1->n_div + bmap2->n_div,
+			bmap1->n_eq + bmap2->n_eq,
+			bmap1->n_ineq + bmap2->n_ineq);
+	bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
+	bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
+	bmap = isl_basic_map_simplify(bmap);
+	return isl_basic_map_finalize(bmap);
 error:
-	isl_map_free(map);
-	isl_map_free(rest);
+	isl_basic_map_free(bmap1);
+	isl_basic_map_free(bmap2);
 	return NULL;
 }
 
-struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
+/* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
+ */
+struct isl_map *isl_map_product(struct isl_map *map1, struct isl_map *map2)
 {
-	int i;
+	unsigned flags = 0;
+	struct isl_map *result;
+	int i, j;
+
 	if (!map1 || !map2)
 		goto error;
 
-	isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
-	isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
-	isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
+	isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
+					 map2->dim, isl_dim_param), goto error);
 
-	if (isl_map_is_empty(map2)) {
-		isl_map_free(map2);
-		return map1;
-	}
+	if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
+	    ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
+		ISL_FL_SET(flags, ISL_MAP_DISJOINT);
 
-	map1 = isl_map_compute_divs(map1);
-	map2 = isl_map_compute_divs(map2);
-	if (!map1 || !map2)
+	result = isl_map_alloc_dim(isl_dim_product(isl_dim_copy(map1->dim),
+						   isl_dim_copy(map2->dim)),
+				map1->n * map2->n, flags);
+	if (!result)
 		goto error;
-
-	for (i = 0; map1 && i < map2->n; ++i)
-		map1 = subtract(map1, map2->p[i]);
-
+	for (i = 0; i < map1->n; ++i)
+		for (j = 0; j < map2->n; ++j) {
+			struct isl_basic_map *part;
+			part = isl_basic_map_product(
+				    isl_basic_map_copy(map1->p[i]),
+				    isl_basic_map_copy(map2->p[j]));
+			if (isl_basic_map_is_empty(part))
+				isl_basic_map_free(part);
+			else
+				result = isl_map_add(result, part);
+			if (!result)
+				goto error;
+		}
+	isl_map_free(map1);
 	isl_map_free(map2);
-	return map1;
+	return result;
 error:
 	isl_map_free(map1);
 	isl_map_free(map2);
 	return NULL;
 }
 
-struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
+/* Given two set A and B, construct its Cartesian product A x B.
+ */
+struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
 {
-	return (struct isl_set *)
-		isl_map_subtract(
-			(struct isl_map *)set1, (struct isl_map *)set2);
+	return (struct isl_set *)isl_map_product((struct isl_map *)set1,
+						 (struct isl_map *)set2);
 }
 
-struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
+uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
 {
-	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(set);
-	isl_map_free(map);
-	return NULL;
+	int i;
+	uint32_t hash;
+	unsigned total;
+
+	if (!bset)
+		return 0;
+	bset = isl_basic_set_copy(bset);
+	bset = isl_basic_set_normalize(bset);
+	if (!bset)
+		return 0;
+	total = isl_basic_set_total_dim(bset);
+	isl_hash_byte(hash, bset->n_eq & 0xFF);
+	for (i = 0; i < bset->n_eq; ++i) {
+		uint32_t c_hash;
+		c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
+		isl_hash_hash(hash, c_hash);
+	}
+	isl_hash_byte(hash, bset->n_ineq & 0xFF);
+	for (i = 0; i < bset->n_ineq; ++i) {
+		uint32_t c_hash;
+		c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
+		isl_hash_hash(hash, c_hash);
+	}
+	isl_hash_byte(hash, bset->n_div & 0xFF);
+	for (i = 0; i < bset->n_div; ++i) {
+		uint32_t c_hash;
+		if (isl_int_is_zero(bset->div[i][0]))
+			continue;
+		isl_hash_byte(hash, i & 0xFF);
+		c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
+		isl_hash_hash(hash, c_hash);
+	}
+	isl_basic_set_free(bset);
+	return hash;
 }
 
-/* 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_map *map)
+uint32_t isl_set_get_hash(struct isl_set *set)
 {
 	int i;
+	uint32_t hash;
 
-	if (!map)
-		return NULL;
+	if (!set)
+		return 0;
+	set = isl_set_copy(set);
+	set = isl_set_normalize(set);
+	if (!set)
+		return 0;
 
-	for (i = map->n-1; i >= 0; --i) {
-		if (!F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
-			continue;
-		isl_basic_map_free(map->p[i]);
-		if (i != map->n-1)
-			map->p[i] = map->p[map->n-1];
-		map->n--;
+	hash = isl_hash_init();
+	for (i = 0; i < set->n; ++i) {
+		uint32_t bset_hash;
+		bset_hash = isl_basic_set_get_hash(set->p[i]);
+		isl_hash_hash(hash, bset_hash);
 	}
+		
+	isl_set_free(set);
 
-	return map;
+	return hash;
 }
 
-struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
+/* Check if the value for dimension dim is completely determined
+ * by the values of the other parameters and variables.
+ * That is, check if dimension dim is involved in an equality.
+ */
+int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
 {
-	return (struct isl_set *)
-		isl_map_remove_empty_parts((struct isl_map *)set);
+	int i;
+	unsigned nparam;
+
+	if (!bset)
+		return -1;
+	nparam = isl_basic_set_n_param(bset);
+	for (i = 0; i < bset->n_eq; ++i)
+		if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
+			return 1;
+	return 0;
+}
+
+/* Check if the value for dimension dim is completely determined
+ * by the values of the other parameters and variables.
+ * That is, check if dimension dim is involved in an equality
+ * for each of the subsets.
+ */
+int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
+{
+	int i;
+
+	if (!set)
+		return -1;
+	for (i = 0; i < set->n; ++i) {
+		int unique;
+		unique = isl_basic_set_dim_is_unique(set->p[i], dim);
+		if (unique != 1)
+			return unique;
+	}
+	return 1;
 }