X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_map_simplify.c;h=7a24c5bb11f23f0b1f0f733c2636745bdc2a83f0;hb=0c59aae9f850bc3cea66e3fb6e70ad15d4b120ef;hp=57b13a3d26e94dbd48ed6167bb214ba5c8418ad8;hpb=1bc0f67b8b2c3a78752bbf2089710816ced3ae30;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_map_simplify.c b/isl_map_simplify.c
index 57b13a3..7a24c5b 100644
--- a/isl_map_simplify.c
+++ b/isl_map_simplify.c
@@ -1,8 +1,21 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ */
+
+#include <strings.h>
+#include <isl_ctx_private.h>
+#include <isl_map_private.h>
 #include "isl_equalities.h"
-#include "isl_map.h"
-#include "isl_map_private.h"
-#include "isl_seq.h"
+#include <isl/map.h>
+#include <isl/seq.h>
 #include "isl_tab.h"
+#include <isl_dim_private.h>
+#include <isl_mat_private.h>
 
 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
 {
@@ -20,11 +33,6 @@ static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
 	}
 }
 
-static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
-{
-	swap_inequality((struct isl_basic_map *)bset, a, b);
-}
-
 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
 {
 	isl_seq_cpy(c, c + n, rem);
@@ -48,7 +56,7 @@ struct isl_basic_set *isl_basic_set_drop_dims(
 
 	isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
 
-	if (n == 0)
+	if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
 		return bset;
 
 	bset = isl_basic_set_cow(bset);
@@ -89,7 +97,7 @@ struct isl_set *isl_set_drop_dims(
 
 	isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
 
-	if (n == 0)
+	if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
 		return set;
 	set = isl_set_cow(set);
 	if (!set)
@@ -159,7 +167,7 @@ struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 	dim = isl_basic_map_dim(bmap, type);
 	isl_assert(bmap->ctx, first + n <= dim, goto error);
 
-	if (n == 0)
+	if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
 		return bmap;
 
 	bmap = isl_basic_map_cow(bmap);
@@ -195,6 +203,13 @@ error:
 	return NULL;
 }
 
+__isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
+							type, first, n);
+}
+
 struct isl_basic_map *isl_basic_map_drop_inputs(
 		struct isl_basic_map *bmap, unsigned first, unsigned n)
 {
@@ -211,7 +226,7 @@ struct isl_map *isl_map_drop(struct isl_map *map,
 
 	isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 
-	if (n == 0)
+	if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
 		return map;
 	map = isl_map_cow(map);
 	if (!map)
@@ -233,6 +248,12 @@ error:
 	return NULL;
 }
 
+struct isl_set *isl_set_drop(struct isl_set *set,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
+}
+
 struct isl_map *isl_map_drop_inputs(
 		struct isl_map *map, unsigned first, unsigned n)
 {
@@ -295,6 +316,9 @@ struct isl_basic_map *isl_basic_map_normalize_constraints(
 	isl_int gcd;
 	unsigned total = isl_basic_map_total_dim(bmap);
 
+	if (!bmap)
+		return NULL;
+
 	isl_int_init(gcd);
 	for (i = bmap->n_eq - 1; i >= 0; --i) {
 		isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
@@ -342,36 +366,103 @@ struct isl_basic_map *isl_basic_map_normalize_constraints(
 struct isl_basic_set *isl_basic_set_normalize_constraints(
 	struct isl_basic_set *bset)
 {
-	(struct isl_basic_set *)isl_basic_map_normalize_constraints(
+	return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 		(struct isl_basic_map *)bset);
 }
 
-static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
+/* Assumes divs have been ordered if keep_divs is set.
+ */
+static void eliminate_var_using_equality(struct isl_basic_map *bmap,
+	unsigned pos, isl_int *eq, int keep_divs, int *progress)
 {
-	int i;
-	unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
-	unsigned len;
-	len = 1 + isl_basic_map_total_dim(bmap);
+	unsigned total;
+	int k;
+	int last_div;
 
-	for (i = 0; i < bmap->n_eq; ++i)
-		if (bmap->eq[i] != eq)
-			isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
+	total = isl_basic_map_total_dim(bmap);
+	last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
+						bmap->n_div);
+	for (k = 0; k < bmap->n_eq; ++k) {
+		if (bmap->eq[k] == eq)
+			continue;
+		if (isl_int_is_zero(bmap->eq[k][1+pos]))
+			continue;
+		if (progress)
+			*progress = 1;
+		isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
+		isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
+	}
 
-	for (i = 0; i < bmap->n_ineq; ++i)
-		isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
+	for (k = 0; k < bmap->n_ineq; ++k) {
+		if (isl_int_is_zero(bmap->ineq[k][1+pos]))
+			continue;
+		if (progress)
+			*progress = 1;
+		isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
+		isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
+		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	}
 
-	/* 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);
+	for (k = 0; k < bmap->n_div; ++k) {
+		if (isl_int_is_zero(bmap->div[k][0]))
+			continue;
+		if (isl_int_is_zero(bmap->div[k][1+1+pos]))
+			continue;
+		if (progress)
+			*progress = 1;
+		/* We need to be careful about circular definitions,
+		 * so for now we just remove the definition of div k
+		 * if the equality contains any divs.
+		 * If keep_divs is set, then the divs have been ordered
+		 * and we can keep the definition as long as the result
+		 * is still ordered.
+		 */
+		if (last_div == -1 || (keep_divs && last_div < k))
+			isl_seq_elim(bmap->div[k]+1, eq,
+					1+pos, 1+total, &bmap->div[k][0]);
+		else
+			isl_seq_clr(bmap->div[k], 1 + total);
+		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	}
+}
+
+/* Assumes divs have been ordered if keep_divs is set.
+ */
+static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
+	unsigned div, int keep_divs)
+{
+	unsigned pos = isl_dim_total(bmap->dim) + div;
+
+	eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 
 	isl_basic_map_drop_div(bmap, div);
 }
 
+/* Check if elimination of div "div" using equality "eq" would not
+ * result in a div depending on a later div.
+ */
+static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
+	unsigned div)
+{
+	int k;
+	int last_div;
+	unsigned pos = isl_dim_total(bmap->dim) + div;
+
+	last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
+						bmap->n_div);
+	if (last_div < 0 || last_div <= div)
+		return 1;
+
+	for (k = 0; k <= last_div; ++k) {
+		if (isl_int_is_zero(bmap->div[k][0]))
+			return 1;
+		if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
+			return 0;
+	}
+
+	return 1;
+}
+
 /* Elimininate divs based on equalities
  */
 static struct isl_basic_map *eliminate_divs_eq(
@@ -382,6 +473,8 @@ static struct isl_basic_map *eliminate_divs_eq(
 	int modified = 0;
 	unsigned off;
 
+	bmap = isl_basic_map_order_divs(bmap);
+
 	if (!bmap)
 		return NULL;
 
@@ -392,9 +485,11 @@ static struct isl_basic_map *eliminate_divs_eq(
 			if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 			    !isl_int_is_negone(bmap->eq[i][off + d]))
 				continue;
+			if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
+				continue;
 			modified = 1;
 			*progress = 1;
-			eliminate_div(bmap, bmap->eq[i], d);
+			eliminate_div(bmap, bmap->eq[i], d, 1);
 			isl_basic_map_drop_equality(bmap, i);
 			break;
 		}
@@ -433,7 +528,7 @@ static struct isl_basic_map *eliminate_divs_ineq(
 			continue;
 		*progress = 1;
 		bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
-		if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+		if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 			break;
 		bmap = isl_basic_map_drop_div(bmap, d);
 		if (!bmap)
@@ -442,60 +537,6 @@ static struct isl_basic_map *eliminate_divs_ineq(
 	return bmap;
 }
 
-/* Assumes divs have been ordered if keep_divs is set.
- */
-static void eliminate_var_using_equality(struct isl_basic_map *bmap,
-	unsigned pos, isl_int *eq, int keep_divs, int *progress)
-{
-	unsigned total;
-	int k;
-	int last_div;
-
-	total = isl_basic_map_total_dim(bmap);
-	last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
-						bmap->n_div);
-	for (k = 0; k < bmap->n_eq; ++k) {
-		if (bmap->eq[k] == eq)
-			continue;
-		if (isl_int_is_zero(bmap->eq[k][1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
-	}
-
-	for (k = 0; k < bmap->n_ineq; ++k) {
-		if (isl_int_is_zero(bmap->ineq[k][1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
-		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	}
-
-	for (k = 0; k < bmap->n_div; ++k) {
-		if (isl_int_is_zero(bmap->div[k][0]))
-			continue;
-		if (isl_int_is_zero(bmap->div[k][1+1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		/* We need to be careful about circular definitions,
-		 * so for now we just remove the definition of div k
-		 * if the equality contains any divs.
-		 * If keep_divs is set, then the divs have been ordered
-		 * and we can keep the definition as long as the result
-		 * is still ordered.
-		 */
-		if (last_div == -1 || (keep_divs && last_div < k))
-			isl_seq_elim(bmap->div[k]+1, eq,
-					1+pos, 1+total, &bmap->div[k][0]);
-		else
-			isl_seq_clr(bmap->div[k], 1 + total);
-		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	}
-}
-
 struct isl_basic_map *isl_basic_map_gauss(
 	struct isl_basic_map *bmap, int *progress)
 {
@@ -605,13 +646,16 @@ static struct isl_basic_map *remove_duplicate_divs(
 	int k, l, h;
 	int bits;
 	struct isl_blk eq;
-	unsigned total_var = isl_dim_total(bmap->dim);
-	unsigned total = total_var + bmap->n_div;
+	unsigned total_var;
+	unsigned total;
 	struct isl_ctx *ctx;
 
-	if (bmap->n_div <= 1)
+	if (!bmap || bmap->n_div <= 1)
 		return bmap;
 
+	total_var = isl_dim_total(bmap->dim);
+	total = total_var + bmap->n_div;
+
 	ctx = bmap->ctx;
 	for (k = bmap->n_div - 1; k >= 0; --k)
 		if (!isl_int_is_zero(bmap->div[k][0]))
@@ -655,7 +699,7 @@ static struct isl_basic_map *remove_duplicate_divs(
 		k = elim_for[l] - 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);
+		eliminate_div(bmap, eq.data, l, 0);
 		isl_int_set_si(eq.data[1+total_var+k], 0);
 		isl_int_set_si(eq.data[1+total_var+l], 0);
 	}
@@ -765,7 +809,7 @@ static struct isl_basic_map *normalize_divs(
 		return bmap;
 
 	if (div_eq < bmap->n_eq) {
-		B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
+		B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
 					bmap->n_eq - div_eq, 0, 1 + total);
 		C = isl_mat_variable_compression(B, &C2);
 		if (!C || !C2)
@@ -786,7 +830,7 @@ static struct isl_basic_map *normalize_divs(
 			--j;
 		isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 	}
-	B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
+	B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 
 	if (C) {
 		B = isl_mat_product(B, C);
@@ -811,6 +855,8 @@ static struct isl_basic_map *normalize_divs(
 	}
 	isl_int_clear(v);
 	pos = isl_alloc_array(bmap->ctx, int, T->n_row);
+	if (!pos)
+		goto error;
 	/* We have to be careful because dropping equalities may reorder them */
 	dropped = 0;
 	for (j = bmap->n_div - 1; j >= 0; --j) {
@@ -942,7 +988,7 @@ static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
 static struct isl_basic_map *check_for_div_constraints(
 	struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
 {
-	int i, j;
+	int i;
 	unsigned total = 1 + isl_dim_total(bmap->dim);
 
 	for (i = 0; i < bmap->n_div; ++i) {
@@ -966,7 +1012,7 @@ static struct isl_basic_map *check_for_div_constraints(
 }
 
 static struct isl_basic_map *remove_duplicate_constraints(
-	struct isl_basic_map *bmap, int *progress)
+	struct isl_basic_map *bmap, int *progress, int detect_divs)
 {
 	unsigned int size;
 	isl_int ***index;
@@ -974,12 +1020,14 @@ static struct isl_basic_map *remove_duplicate_constraints(
 	int bits;
 	unsigned total = isl_basic_map_total_dim(bmap);
 	isl_int sum;
+	isl_ctx *ctx;
 
-	if (bmap->n_ineq <= 1)
+	if (!bmap || bmap->n_ineq <= 1)
 		return bmap;
 
 	size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 	bits = ffs(size) - 1;
+	ctx = isl_basic_map_get_ctx(bmap);
 	index = isl_calloc_array(ctx, isl_int **, size);
 	if (!index)
 		return bmap;
@@ -1009,8 +1057,9 @@ static struct isl_basic_map *remove_duplicate_constraints(
 		l = index[h] - &bmap->ineq[0];
 		isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 		if (isl_int_is_pos(sum)) {
-			bmap = check_for_div_constraints(bmap, k, l, sum,
-							 progress);
+			if (detect_divs)
+				bmap = check_for_div_constraints(bmap, k, l,
+								 sum, progress);
 			continue;
 		}
 		if (isl_int_is_zero(sum)) {
@@ -1019,6 +1068,8 @@ static struct isl_basic_map *remove_duplicate_constraints(
 			 * will no longer be valid.
 			 * Plus, we probably we want to regauss first.
 			 */
+			if (progress)
+				*progress = 1;
 			isl_basic_map_drop_inequality(bmap, l);
 			isl_basic_map_inequality_to_equality(bmap, k);
 		} else
@@ -1046,7 +1097,7 @@ struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 		bmap = isl_basic_map_gauss(bmap, &progress);
 		/* requires equalities in normal form */
 		bmap = normalize_divs(bmap, &progress);
-		bmap = remove_duplicate_constraints(bmap, &progress);
+		bmap = remove_duplicate_constraints(bmap, &progress, 1);
 	}
 	return bmap;
 }
@@ -1058,6 +1109,43 @@ struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 }
 
 
+int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
+	isl_int *constraint, unsigned div)
+{
+	unsigned pos;
+
+	if (!bmap)
+		return -1;
+
+	pos = 1 + isl_dim_total(bmap->dim) + div;
+
+	if (isl_int_eq(constraint[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(constraint, 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(constraint+pos+1,
+					    bmap->n_div-div-1) != -1)
+			return 0;
+	} else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
+		if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
+			return 0;
+		if (isl_seq_first_non_zero(constraint+pos+1,
+					    bmap->n_div-div-1) != -1)
+			return 0;
+	} else
+		return 0;
+
+	return 1;
+}
+
+
 /* If the only constraints a div d=floor(f/m)
  * appears in are its two defining constraints
  *
@@ -1078,27 +1166,7 @@ static int div_is_redundant(struct isl_basic_map *bmap, int div)
 	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
+		if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
 			return 0;
 	}
 
@@ -1188,7 +1256,6 @@ static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
 									int pos)
 {
 	int i;
-	unsigned dim = isl_dim_total(bmap->dim);
 
 	for (i = 0; i < bmap->n_div; ++i) {
 		if (isl_int_is_zero(bmap->div[i][0]))
@@ -1246,6 +1313,8 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 		}
 		bmap = isl_basic_map_extend_constraints(bmap,
 				0, n_lower * n_upper);
+		if (!bmap)
+			goto error;
 		for (i = bmap->n_ineq - 1; i >= 0; --i) {
 			int last;
 			if (isl_int_is_zero(bmap->ineq[i][1+d]))
@@ -1271,9 +1340,9 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 		}
 		if (n_lower > 0 && n_upper > 0) {
 			bmap = isl_basic_map_normalize_constraints(bmap);
-			bmap = remove_duplicate_constraints(bmap, NULL);
+			bmap = remove_duplicate_constraints(bmap, NULL, 0);
 			bmap = isl_basic_map_gauss(bmap, NULL);
-			bmap = isl_basic_map_convex_hull(bmap);
+			bmap = isl_basic_map_remove_redundancies(bmap);
 			if (!bmap)
 				goto error;
 			if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
@@ -1323,7 +1392,7 @@ static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
 static int reduced_using_equalities(isl_int *dst, isl_int *src,
 	struct isl_basic_map *bmap, int *elim)
 {
-	int d, i;
+	int d;
 	int copied = 0;
 	unsigned total;
 
@@ -1358,11 +1427,16 @@ static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
 	if (!bset || !context)
 		goto error;
 
+	if (context->n_eq == 0) {
+		isl_basic_set_free(context);
+		return bset;
+	}
+
 	bset = isl_basic_set_cow(bset);
 	if (!bset)
 		goto error;
 
-	elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
+	elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
 	if (!elim)
 		goto error;
 	set_compute_elimination_index(context, elim);
@@ -1390,12 +1464,14 @@ static struct isl_basic_set *remove_shifted_constraints(
 	isl_int ***index;
 	int bits;
 	int k, h, l;
+	isl_ctx *ctx;
 
 	if (!bset)
 		return NULL;
 
 	size = round_up(4 * (context->n_ineq+1) / 3 - 1);
 	bits = ffs(size) - 1;
+	ctx = isl_basic_set_get_ctx(bset);
 	index = isl_calloc_array(ctx, isl_int **, size);
 	if (!index)
 		return bset;
@@ -1424,92 +1500,110 @@ error:
 	return bset;
 }
 
-/* Tighten (decrease) the constant terms of the inequalities based
- * on the equalities, without removing any integer points.
- * For example, if there is an equality
- *
- *		i = 3 * j
- *
- * and an inequality
- *
- *		i >= 1
- *
- * then we want to replace the inequality by
- *
- *		i >= 3
- *
- * We do this by computing a variable compression and translating
- * the constraints to the compressed space.
- * If any constraint has coefficients (except the contant term)
- * with a common factor "f", then we can replace the constant term "c"
- * by
- *
- *		f * floor(c/f)
- *
- * That is, we add
- *
- *		f * floor(c/f) - c = -fract(c/f)
- *
- * and we can add the same value to the original constraint.
- *
- * In the example, the compressed space only contains "j",
- * and the inequality translates to
- *
- *		3 * j - 1 >= 0
+/* Remove all information from bset that is redundant in the context
+ * of context.  Both bset and context are assumed to be full-dimensional.
  *
- * We add -fract(-1/3) = -2 to the original constraint to obtain
+ * We first * remove the inequalities from "bset"
+ * that are obviously redundant with respect to some inequality in "context".
  *
- *		i - 3 >= 0
+ * If there are any inequalities left, we construct a tableau for
+ * the context and then add the inequalities of "bset".
+ * Before adding these inequalities, we freeze all constraints such that
+ * they won't be considered redundant in terms of the constraints of "bset".
+ * Then we detect all redundant constraints (among the
+ * constraints that weren't frozen), first by checking for redundancy in the
+ * the tableau and then by checking if replacing a constraint by its negation
+ * would lead to an empty set.  This last step is fairly expensive
+ * and could be optimized by more reuse of the tableau.
+ * Finally, we update bset according to the results.
  */
-static struct isl_basic_set *normalize_constraints_in_compressed_space(
-	struct isl_basic_set *bset)
+static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
+	__isl_take isl_basic_set *context)
 {
-	int i;
+	int i, k;
+	isl_basic_set *combined = NULL;
+	struct isl_tab *tab = NULL;
+	unsigned context_ineq;
 	unsigned total;
-	struct isl_mat *B, *C;
-	isl_int gcd;
 
-	if (!bset)
-		return NULL;
+	if (!bset || !context)
+		goto error;
 
-	if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
+	if (isl_basic_set_is_universe(bset)) {
+		isl_basic_set_free(context);
 		return bset;
+	}
 
-	if (!bset->n_ineq)
+	if (isl_basic_set_is_universe(context)) {
+		isl_basic_set_free(context);
 		return bset;
+	}
 
-	bset = isl_basic_set_cow(bset);
+	bset = remove_shifted_constraints(bset, context);
 	if (!bset)
-		return NULL;
+		goto error;
+	if (bset->n_ineq == 0)
+		goto done;
 
+	context_ineq = context->n_ineq;
+	combined = isl_basic_set_cow(isl_basic_set_copy(context));
+	combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
+	tab = isl_tab_from_basic_set(combined);
+	for (i = 0; i < context_ineq; ++i)
+		if (isl_tab_freeze_constraint(tab, i) < 0)
+			goto error;
+	tab = isl_tab_extend(tab, bset->n_ineq);
+	for (i = 0; i < bset->n_ineq; ++i)
+		if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
+			goto error;
+	bset = isl_basic_set_add_constraints(combined, bset, 0);
+	combined = NULL;
+	if (!bset)
+		goto error;
+	if (isl_tab_detect_redundant(tab) < 0)
+		goto error;
 	total = isl_basic_set_total_dim(bset);
-	B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
-	C = isl_mat_variable_compression(B, NULL);
-	if (!C)
-		return bset;
-	if (C->n_col == 0) {
-		isl_mat_free(C);
-		return isl_basic_set_set_to_empty(bset);
-	}
-	B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
-						0, bset->n_ineq, 0, 1 + total);
-	C = isl_mat_product(B, C);
-	if (!C)
-		return bset;
-
-	isl_int_init(gcd);
-	for (i = 0; i < bset->n_ineq; ++i) {
-		isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
-		if (isl_int_is_one(gcd))
+	for (i = context_ineq; i < bset->n_ineq; ++i) {
+		int is_empty;
+		if (tab->con[i].is_redundant)
 			continue;
-		isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
-		isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
+		tab->con[i].is_redundant = 1;
+		combined = isl_basic_set_dup(bset);
+		combined = isl_basic_set_update_from_tab(combined, tab);
+		combined = isl_basic_set_extend_constraints(combined, 0, 1);
+		k = isl_basic_set_alloc_inequality(combined);
+		if (k < 0)
+			goto error;
+		isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
+		isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
+		is_empty = isl_basic_set_is_empty(combined);
+		if (is_empty < 0)
+			goto error;
+		isl_basic_set_free(combined);
+		combined = NULL;
+		if (!is_empty)
+			tab->con[i].is_redundant = 0;
+	}
+	for (i = 0; i < context_ineq; ++i)
+		tab->con[i].is_redundant = 1;
+	bset = isl_basic_set_update_from_tab(bset, tab);
+	if (bset) {
+		ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
+		ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
 	}
-	isl_int_clear(gcd);
-
-	isl_mat_free(C);
 
+	isl_tab_free(tab);
+done:
+	bset = isl_basic_set_simplify(bset);
+	bset = isl_basic_set_finalize(bset);
+	isl_basic_set_free(context);
 	return bset;
+error:
+	isl_tab_free(tab);
+	isl_basic_set_free(combined);
+	isl_basic_set_free(context);
+	isl_basic_set_free(bset);
+	return NULL;
 }
 
 /* Remove all information from bset that is redundant in the context
@@ -1518,102 +1612,76 @@ static struct isl_basic_set *normalize_constraints_in_compressed_space(
  * redundant in the context of the equalities and inequalities of
  * context are removed.
  *
- * We first simplify the constraints of "bset" in the context of the
- * equalities of "context".
- * Then we simplify the inequalities of the context in the context
- * of the equalities of bset and remove the inequalities from "bset"
- * that are obviously redundant with respect to some inequality in "context".
+ * We first compute the integer affine hull of the intersection,
+ * compute the gist inside this affine hull and then add back
+ * those equalities that are not implied by the context.
  *
- * If there are any inequalities left, we construct a tableau for
- * the context and then add the inequalities of "bset".
- * Before adding these equalities, we freeze all constraints such that
- * they won't be considered redundant in terms of the constraints of "bset".
- * Then we detect all equalities and redundant constraints (among the
- * constraints that weren't frozen) and update bset according to the results.
- * We have to be careful here because we don't want any of the context
- * constraints to remain and because we haven't added the equalities of "bset"
- * to the tableau so we temporarily have to pretend that there were no
- * equalities.
+ * If two constraints are mutually redundant, then uset_gist_full
+ * will remove the second of those constraints.  We therefore first
+ * sort the constraints so that constraints not involving existentially
+ * quantified variables are given precedence over those that do.
+ * We have to perform this sorting before the variable compression,
+ * because that may effect the order of the variables.
  */
-static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
-	struct isl_basic_set *context)
+static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
+	__isl_take isl_basic_set *context)
 {
-	int i;
-	struct isl_tab *tab;
-	unsigned context_ineq;
-	struct isl_basic_set *combined = NULL;
-
-	if (!context || !bset)
-		goto error;
+	isl_mat *eq;
+	isl_mat *T, *T2;
+	isl_basic_set *aff;
+	isl_basic_set *aff_context;
+	unsigned total;
 
-	if (context->n_eq > 0)
-		bset = isl_basic_set_reduce_using_equalities(bset,
-					isl_basic_set_copy(context));
-	if (!bset)
+	if (!bset || !context)
 		goto error;
-	if (isl_basic_set_fast_is_empty(bset))
-		goto done;
-	if (!bset->n_ineq)
-		goto done;
 
-	if (bset->n_eq > 0) {
-		struct isl_basic_set *affine_hull;
-		affine_hull = isl_basic_set_copy(bset);
-		affine_hull = isl_basic_set_cow(affine_hull);
-		if (!affine_hull)
-			goto error;
-		isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
-		context = isl_basic_set_intersect(context, affine_hull);
-		context = isl_basic_set_gauss(context, NULL);
-		context = normalize_constraints_in_compressed_space(context);
+	bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
+	if (isl_basic_set_plain_is_empty(bset)) {
+		isl_basic_set_free(context);
+		return bset;
 	}
-	if (!context)
+	bset = isl_basic_set_sort_constraints(bset);
+	aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
+	if (!aff)
 		goto error;
-	if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
-		isl_basic_set_free(bset);
-		return context;
+	if (isl_basic_set_plain_is_empty(aff)) {
+		isl_basic_set_free(aff);
+		isl_basic_set_free(context);
+		return bset;
 	}
-	if (!context->n_ineq)
-		goto done;
-	bset = remove_shifted_constraints(bset, context);
-	if (!bset->n_ineq)
-		goto done;
-	isl_basic_set_free_equality(context, context->n_eq);
-	context_ineq = context->n_ineq;
-	combined = isl_basic_set_cow(isl_basic_set_copy(context));
-	combined = isl_basic_set_extend_constraints(combined,
-						    bset->n_eq, bset->n_ineq);
-	tab = isl_tab_from_basic_set(combined);
-	if (!tab)
-		goto error;
-	for (i = 0; i < context_ineq; ++i)
-		tab->con[i].frozen = 1;
-	tab = isl_tab_extend(tab, bset->n_ineq);
-	if (!tab)
-		goto error;
-	for (i = 0; i < bset->n_ineq; ++i)
-		tab = isl_tab_add_ineq(tab, bset->ineq[i]);
-	bset = isl_basic_set_add_constraints(combined, bset, 0);
-	tab = isl_tab_detect_equalities(tab);
-	tab = isl_tab_detect_redundant(tab);
-	if (!tab)
-		goto error2;
-	for (i = 0; i < context_ineq; ++i) {
-		tab->con[i].is_zero = 0;
-		tab->con[i].is_redundant = 1;
+	if (aff->n_eq == 0) {
+		isl_basic_set_free(aff);
+		return uset_gist_full(bset, context);
 	}
-	bset = isl_basic_set_update_from_tab(bset, tab);
-	isl_tab_free(tab);
-	ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
-	ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
-done:
-	bset = isl_basic_set_simplify(bset);
-	bset = isl_basic_set_finalize(bset);
-	isl_basic_set_free(context);
+	total = isl_basic_set_total_dim(bset);
+	eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
+	eq = isl_mat_cow(eq);
+	T = isl_mat_variable_compression(eq, &T2);
+	if (T && T->n_col == 0) {
+		isl_mat_free(T);
+		isl_mat_free(T2);
+		isl_basic_set_free(context);
+		isl_basic_set_free(aff);
+		return isl_basic_set_set_to_empty(bset);
+	}
+
+	aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
+
+	bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
+	context = isl_basic_set_preimage(context, T);
+
+	bset = uset_gist_full(bset, context);
+	bset = isl_basic_set_preimage(bset, T2);
+	bset = isl_basic_set_intersect(bset, aff);
+	bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
+
+	if (bset) {
+		ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
+		ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
+	}
+
 	return bset;
 error:
-	isl_basic_set_free(combined);
-error2:
 	isl_basic_set_free(bset);
 	isl_basic_set_free(context);
 	return NULL;
@@ -1664,27 +1732,23 @@ struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
 	if (!bmap || !context)
 		goto error;
 
-	if (isl_basic_map_is_universe(context)) {
-		isl_basic_map_free(context);
-		return bmap;
-	}
 	if (isl_basic_map_is_universe(bmap)) {
 		isl_basic_map_free(context);
 		return bmap;
 	}
-	if (isl_basic_map_fast_is_empty(context)) {
+	if (isl_basic_map_plain_is_empty(context)) {
 		struct isl_dim *dim = isl_dim_copy(bmap->dim);
 		isl_basic_map_free(context);
 		isl_basic_map_free(bmap);
 		return isl_basic_map_universe(dim);
 	}
-	if (isl_basic_map_fast_is_empty(bmap)) {
+	if (isl_basic_map_plain_is_empty(bmap)) {
 		isl_basic_map_free(context);
 		return bmap;
 	}
 
-	bmap = isl_basic_map_convex_hull(bmap);
-	context = isl_basic_map_convex_hull(context);
+	bmap = isl_basic_map_remove_redundancies(bmap);
+	context = isl_basic_map_remove_redundancies(context);
 
 	if (context->n_eq)
 		bmap = normalize_divs_in_context(bmap, context);
@@ -1705,25 +1769,22 @@ error:
 /*
  * Assumes context has no implicit divs.
  */
-struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
+__isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
+	__isl_take isl_basic_map *context)
 {
 	int i;
 
 	if (!map || !context)
 		goto error;;
 
-	if (isl_basic_map_is_universe(context)) {
-		isl_basic_map_free(context);
-		return map;
-	}
-	if (isl_basic_map_fast_is_empty(context)) {
+	if (isl_basic_map_plain_is_empty(context)) {
 		struct isl_dim *dim = isl_dim_copy(map->dim);
 		isl_basic_map_free(context);
 		isl_map_free(map);
 		return isl_map_universe(dim);
 	}
 
-	context = isl_basic_map_convex_hull(context);
+	context = isl_basic_map_remove_redundancies(context);
 	map = isl_map_cow(map);
 	if (!map || !context)
 		goto error;;
@@ -1731,11 +1792,17 @@ struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
 	map = isl_map_compute_divs(map);
 	for (i = 0; i < map->n; ++i)
 		context = isl_basic_map_align_divs(context, map->p[i]);
-	for (i = 0; i < map->n; ++i) {
+	for (i = map->n - 1; i >= 0; --i) {
 		map->p[i] = isl_basic_map_gist(map->p[i],
 						isl_basic_map_copy(context));
 		if (!map->p[i])
 			goto error;
+		if (isl_basic_map_plain_is_empty(map->p[i])) {
+			isl_basic_map_free(map->p[i]);
+			if (i != map->n - 1)
+				map->p[i] = map->p[map->n - 1];
+			map->n--;
+		}
 	}
 	isl_basic_map_free(context);
 	ISL_F_CLR(map, ISL_MAP_NORMALIZED);
@@ -1746,6 +1813,13 @@ error:
 	return NULL;
 }
 
+__isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
+	__isl_take isl_map *context)
+{
+	context = isl_map_compute_divs(context);
+	return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
+}
+
 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
 						struct isl_basic_set *context)
 {
@@ -1753,24 +1827,32 @@ struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
 		(struct isl_basic_map *)bset, (struct isl_basic_map *)context);
 }
 
-struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
+__isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
+	__isl_take isl_basic_set *context)
 {
-	return (struct isl_set *)isl_map_gist((struct isl_map *)set,
+	return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
 					(struct isl_basic_map *)context);
 }
 
+__isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
+	__isl_take isl_set *context)
+{
+	return (struct isl_set *)isl_map_gist((struct isl_map *)set,
+					(struct isl_map *)context);
+}
+
 /* Quick check to see if two basic maps are disjoint.
  * In particular, we reduce the equalities and inequalities of
  * one basic map in the context of the equalities of the other
  * basic map and check if we get a contradiction.
  */
-int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
-	struct isl_basic_map *bmap2)
+int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
+	__isl_keep isl_basic_map *bmap2)
 {
 	struct isl_vec *v = NULL;
 	int *elim = NULL;
 	unsigned total;
-	int d, i;
+	int i;
 
 	if (!bmap1 || !bmap2)
 		return -1;
@@ -1829,26 +1911,27 @@ error:
 	return -1;
 }
 
-int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
-	struct isl_basic_set *bset2)
+int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
+	__isl_keep isl_basic_set *bset2)
 {
-	return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
+	return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
 					      (struct isl_basic_map *)bset2);
 }
 
-int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
+int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
+	__isl_keep isl_map *map2)
 {
 	int i, j;
 
 	if (!map1 || !map2)
 		return -1;
 
-	if (isl_map_fast_is_equal(map1, map2))
+	if (isl_map_plain_is_equal(map1, map2))
 		return 0;
 
 	for (i = 0; i < map1->n; ++i) {
 		for (j = 0; j < map2->n; ++j) {
-			int d = isl_basic_map_fast_is_disjoint(map1->p[i],
+			int d = isl_basic_map_plain_is_disjoint(map1->p[i],
 							       map2->p[j]);
 			if (d != 1)
 				return d;
@@ -1857,12 +1940,18 @@ int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
 	return 1;
 }
 
-int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
+int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
+	__isl_keep isl_set *set2)
 {
-	return isl_map_fast_is_disjoint((struct isl_map *)set1,
+	return isl_map_plain_is_disjoint((struct isl_map *)set1,
 					(struct isl_map *)set2);
 }
 
+int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
+{
+	return isl_set_plain_is_disjoint(set1, set2);
+}
+
 /* Check if we can combine a given div with lower bound l and upper
  * bound u with some other div and if so return that other div.
  * Otherwise return -1.
@@ -1918,6 +2007,14 @@ static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
 	}
 
 	isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
+	if (isl_int_is_neg(bmap->ineq[l][0])) {
+		isl_int_sub(bmap->ineq[l][0],
+			    bmap->ineq[l][0], bmap->ineq[u][0]);
+		bmap = isl_basic_map_copy(bmap);
+		bmap = isl_basic_map_set_to_empty(bmap);
+		isl_basic_map_free(bmap);
+		return -1;
+	}
 	isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
 	for (i = 0; i < bmap->n_div; ++i) {
 		if (i == div)
@@ -2096,7 +2193,7 @@ static struct isl_basic_map *drop_more_redundant_divs(
 	if (remove < 0)
 		return bmap;
 
-	bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
+	bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
 	return isl_basic_map_drop_redundant_divs(bmap);
 error:
 	free(pairs);
@@ -2247,6 +2344,9 @@ static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
 		}
 	}
 
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+		return bmap;
+
 	return drop_more_redundant_divs(bmap, pairs, n);
 }