isl_map_simplify.c: extract out simplify and related code from isl_map.c

1 files changed, 2 insertions, 1315 deletions

diff --git a/isl_map.c b/isl_map.c
index 1677c753..69d4f6fa 100644
--- a/isl_map.c
+++ b/isl_map.c
@@ -3,7 +3,6 @@
 #include "isl_ctx.h"
 #include "isl_blk.h"
 #include "isl_dim.h"
-#include "isl_equalities.h"
 #include "isl_list.h"
 #include "isl_lp.h"
 #include "isl_seq.h"
@@ -735,7 +734,7 @@ error:
 	return NULL;
 }
 
-static struct isl_basic_set *set_add_constraints(struct isl_basic_set *bset1,
+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 *)
@@ -951,253 +950,6 @@ struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
 	return set;
 }
 
-static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
-{
-	isl_seq_cpy(c, c + n, rem);
-	isl_seq_clr(c + rem, n);
-}
-
-/* Drop n dimensions starting at first.
- *
- * In principle, this frees up some extra variables as the number
- * of columns remains constant, but we would have to extend
- * the div array too as the number of rows in this array is assumed
- * to be equal to extra.
- */
-struct isl_basic_set *isl_basic_set_drop_dims(
-		struct isl_basic_set *bset, unsigned first, unsigned n)
-{
-	int i;
-
-	if (!bset)
-		goto error;
-
-	isl_assert(bset->ctx, first + n <= bset->dim->n_out, 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->dim->nparam+first, n,
-				     (bset->dim->n_out-first-n)+bset->extra);
-
-	for (i = 0; i < bset->n_ineq; ++i)
-		constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
-				     (bset->dim->n_out-first-n)+bset->extra);
-
-	for (i = 0; i < bset->n_div; ++i)
-		constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
-				     (bset->dim->n_out-first-n)+bset->extra);
-
-	bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
-	if (!bset->dim)
-		goto error;
-
-	F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
-	bset = isl_basic_set_simplify(bset);
-	return isl_basic_set_finalize(bset);
-error:
-	isl_basic_set_free(bset);
-	return NULL;
-}
-
-static struct isl_set *isl_set_drop_dims(
-		struct isl_set *set, unsigned first, unsigned n)
-{
-	int i;
-
-	if (!set)
-		goto error;
-
-	isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
-
-	if (n == 0)
-		return set;
-	set = isl_set_cow(set);
-	if (!set)
-		goto error;
-	set->dim = isl_dim_drop_outputs(set->dim, first, n);
-	if (!set->dim)
-		goto error;
-
-	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
-		if (!set->p[i])
-			goto error;
-	}
-
-	F_CLR(set, ISL_SET_NORMALIZED);
-	return set;
-error:
-	isl_set_free(set);
-	return NULL;
-}
-
-/* Drop n input dimensions starting at first.
- *
- * In principle, this frees up some extra variables as the number
- * of columns remains constant, but we would have to extend
- * the div array too as the number of rows in this array is assumed
- * to be equal to extra.
- */
-struct isl_basic_map *isl_basic_map_drop_inputs(
-		struct isl_basic_map *bmap, unsigned first, unsigned n)
-{
-	int i;
-	unsigned nparam;
-	unsigned n_in;
-	unsigned n_out;
-
-	if (!bmap)
-		goto error;
-
-	nparam = isl_basic_map_n_param(bmap);
-	n_in = isl_basic_map_n_in(bmap);
-	n_out = isl_basic_map_n_out(bmap);
-	isl_assert(bmap->ctx, first + n <= n_in, goto error);
-
-	if (n == 0)
-		return bmap;
-
-	bmap = isl_basic_map_cow(bmap);
-	if (!bmap)
-		return NULL;
-
-	for (i = 0; i < bmap->n_eq; ++i)
-		constraint_drop_vars(bmap->eq[i]+1+nparam+first, n,
-				 (n_in-first-n)+n_out+bmap->extra);
-
-	for (i = 0; i < bmap->n_ineq; ++i)
-		constraint_drop_vars(bmap->ineq[i]+1+nparam+first, n,
-				 (n_in-first-n)+n_out+bmap->extra);
-
-	for (i = 0; i < bmap->n_div; ++i)
-		constraint_drop_vars(bmap->div[i]+1+1+nparam+first, n,
-				 (n_in-first-n)+n_out+bmap->extra);
-
-	bmap->dim = isl_dim_drop_inputs(bmap->dim, first, n);
-	if (!bmap->dim)
-		goto error;
-
-	F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	bmap = isl_basic_map_simplify(bmap);
-	return isl_basic_map_finalize(bmap);
-error:
-	isl_basic_map_free(bmap);
-	return NULL;
-}
-
-static struct isl_map *isl_map_drop_inputs(
-		struct isl_map *map, unsigned first, unsigned n)
-{
-	int i;
-
-	if (!map)
-		goto error;
-
-	isl_assert(map->ctx, first + n <= map->dim->n_in, goto error);
-
-	if (n == 0)
-		return map;
-	map = isl_map_cow(map);
-	if (!map)
-		goto error;
-	map->dim = isl_dim_drop_inputs(map->dim, first, n);
-	if (!map->dim)
-		goto error;
-
-	for (i = 0; i < map->n; ++i) {
-		map->p[i] = isl_basic_map_drop_inputs(map->p[i], first, n);
-		if (!map->p[i])
-			goto error;
-	}
-	F_CLR(map, ISL_MAP_NORMALIZED);
-
-	return map;
-error:
-	isl_map_free(map);
-	return NULL;
-}
-
-/*
- * We don't cow, as the div is assumed to be redundant.
- */
-static struct isl_basic_map *isl_basic_map_drop_div(
-		struct isl_basic_map *bmap, unsigned div)
-{
-	int i;
-	unsigned pos;
-
-	if (!bmap)
-		goto error;
-
-	pos = 1 + isl_dim_total(bmap->dim) + div;
-
-	isl_assert(bmap->ctx, div < bmap->n_div, goto error);
-
-	for (i = 0; i < bmap->n_eq; ++i)
-		constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
-
-	for (i = 0; i < bmap->n_ineq; ++i) {
-		if (!isl_int_is_zero(bmap->ineq[i][pos])) {
-			isl_basic_map_drop_inequality(bmap, i);
-			--i;
-			continue;
-		}
-		constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
-	}
-
-	for (i = 0; i < bmap->n_div; ++i)
-		constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
-
-	if (div != bmap->n_div - 1) {
-		int j;
-		isl_int *t = bmap->div[div];
-
-		for (j = div; j < bmap->n_div - 1; ++j)
-			bmap->div[j] = bmap->div[j+1];
-
-		bmap->div[bmap->n_div - 1] = t;
-	}
-	F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	isl_basic_map_free_div(bmap, 1);
-
-	return bmap;
-error:
-	isl_basic_map_free(bmap);
-	return NULL;
-}
-
-static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
-{
-	int i;
-	unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
-	unsigned len;
-	len = 1 + isl_basic_map_total_dim(bmap);
-
-	for (i = 0; i < bmap->n_eq; ++i)
-		if (bmap->eq[i] != eq)
-			isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
-
-	for (i = 0; i < bmap->n_ineq; ++i)
-		isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
-
-	/* We need to be careful about circular definitions,
-	 * so for now we just remove the definitions of other divs that
-	 * depend on this div and (possibly) recompute them later.
-	 */
-	for (i = 0; i < bmap->n_div; ++i)
-		if (!isl_int_is_zero(bmap->div[i][0]) &&
-		    !isl_int_is_zero(bmap->div[i][1 + pos]))
-			isl_seq_clr(bmap->div[i], 1 + len);
-
-	isl_basic_map_drop_div(bmap, div);
-}
-
 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
 {
 	int i = 0;
@@ -1229,27 +981,6 @@ struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
 		isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
 }
 
-static void swap_equality(struct isl_basic_map *bmap, int a, int b)
-{
-	isl_int *t = bmap->eq[a];
-	bmap->eq[a] = bmap->eq[b];
-	bmap->eq[b] = t;
-}
-
-static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
-{
-	if (a != b) {
-		isl_int *t = bmap->ineq[a];
-		bmap->ineq[a] = bmap->ineq[b];
-		bmap->ineq[b] = t;
-	}
-}
-
-static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
-{
-	swap_inequality((struct isl_basic_map *)bset, a, b);
-}
-
 static void swap_div(struct isl_basic_map *bmap, int a, int b)
 {
 	int i;
@@ -1269,614 +1000,6 @@ static void swap_div(struct isl_basic_map *bmap, int a, int b)
 	F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 }
 
-static void eliminate_var_using_equality(struct isl_basic_map *bmap,
-	unsigned pos, isl_int *eq, int *progress)
-{
-	unsigned total;
-	int k;
-
-	total = isl_basic_map_total_dim(bmap);
-	for (k = 0; k < bmap->n_eq; ++k) {
-		if (bmap->eq[k] == eq)
-			continue;
-		if (isl_int_is_zero(bmap->eq[k][1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
-	}
-
-	for (k = 0; k < bmap->n_ineq; ++k) {
-		if (isl_int_is_zero(bmap->ineq[k][1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
-		F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	}
-
-	for (k = 0; k < bmap->n_div; ++k) {
-		if (isl_int_is_zero(bmap->div[k][0]))
-			continue;
-		if (isl_int_is_zero(bmap->div[k][1+1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		isl_seq_elim(bmap->div[k]+1, eq,
-				1+pos, 1+total, &bmap->div[k][0]);
-		F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	}
-}
-	
-
-struct isl_basic_map *isl_basic_map_gauss(
-	struct isl_basic_map *bmap, int *progress)
-{
-	int k;
-	int done;
-	int last_var;
-	unsigned total_var;
-	unsigned total;
-
-	if (!bmap)
-		return NULL;
-
-	total = isl_basic_map_total_dim(bmap);
-	total_var = total - bmap->n_div;
-
-	last_var = total - 1;
-	for (done = 0; done < bmap->n_eq; ++done) {
-		for (; last_var >= 0; --last_var) {
-			for (k = done; k < bmap->n_eq; ++k)
-				if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
-					break;
-			if (k < bmap->n_eq)
-				break;
-		}
-		if (last_var < 0)
-			break;
-		if (k != done)
-			swap_equality(bmap, k, done);
-		if (isl_int_is_neg(bmap->eq[done][1+last_var]))
-			isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
-
-		eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
-						progress);
-
-		if (last_var >= total_var &&
-		    isl_int_is_zero(bmap->div[last_var - total_var][0])) {
-			unsigned div = last_var - total_var;
-			isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
-			isl_int_set_si(bmap->div[div][1+1+last_var], 0);
-			isl_int_set(bmap->div[div][0],
-				    bmap->eq[done][1+last_var]);
-			F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-		}
-	}
-	if (done == bmap->n_eq)
-		return bmap;
-	for (k = done; k < bmap->n_eq; ++k) {
-		if (isl_int_is_zero(bmap->eq[k][0]))
-			continue;
-		return isl_basic_map_set_to_empty(bmap);
-	}
-	isl_basic_map_free_equality(bmap, bmap->n_eq-done);
-	return bmap;
-}
-
-struct isl_basic_set *isl_basic_set_gauss(
-	struct isl_basic_set *bset, int *progress)
-{
-	return (struct isl_basic_set*)isl_basic_map_gauss(
-			(struct isl_basic_map *)bset, progress);
-}
-
-static unsigned int round_up(unsigned int v)
-{
-	int old_v = v;
-
-	while (v) {
-		old_v = v;
-		v ^= v & -v;
-	}
-	return old_v << 1;
-}
-
-static int hash_index(isl_int ***index, unsigned int size, int bits,
-			struct isl_basic_map *bmap, int k)
-{
-	int h;
-	unsigned total = isl_basic_map_total_dim(bmap);
-	uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
-	for (h = hash; index[h]; h = (h+1) % size)
-		if (&bmap->ineq[k] != index[h] &&
-		    isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
-			break;
-	return h;
-}
-
-static int set_hash_index(isl_int ***index, unsigned int size, int bits,
-			  struct isl_basic_set *bset, int k)
-{
-	return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
-}
-
-static struct isl_basic_map *remove_duplicate_constraints(
-	struct isl_basic_map *bmap, int *progress)
-{
-	unsigned int size;
-	isl_int ***index;
-	int k, l, h;
-	int bits;
-	unsigned total = isl_basic_map_total_dim(bmap);
-	isl_int sum;
-
-	if (bmap->n_ineq <= 1)
-		return bmap;
-
-	size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
-	bits = ffs(size) - 1;
-	index = isl_calloc_array(ctx, isl_int **, size);
-	if (!index)
-		return bmap;
-
-	index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
-	for (k = 1; k < bmap->n_ineq; ++k) {
-		h = hash_index(index, size, bits, bmap, k);
-		if (!index[h]) {
-			index[h] = &bmap->ineq[k];
-			continue;
-		}
-		if (progress)
-			*progress = 1;
-		l = index[h] - &bmap->ineq[0];
-		if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
-			swap_inequality(bmap, k, l);
-		isl_basic_map_drop_inequality(bmap, k);
-		--k;
-	}
-	isl_int_init(sum);
-	for (k = 0; k < bmap->n_ineq-1; ++k) {
-		isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
-		h = hash_index(index, size, bits, bmap, k);
-		isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
-		if (!index[h])
-			continue;
-		l = index[h] - &bmap->ineq[0];
-		isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
-		if (isl_int_is_pos(sum))
-			continue;
-		if (isl_int_is_zero(sum)) {
-			/* We need to break out of the loop after these
-			 * changes since the contents of the hash
-			 * will no longer be valid.
-			 * Plus, we probably we want to regauss first.
-			 */
-			isl_basic_map_drop_inequality(bmap, l);
-			isl_basic_map_inequality_to_equality(bmap, k);
-		} else
-			bmap = isl_basic_map_set_to_empty(bmap);
-		break;
-	}
-	isl_int_clear(sum);
-
-	free(index);
-	return bmap;
-}
-
-static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
-{
-	int d, i;
-	unsigned total;
-
-	total = isl_dim_total(bmap->dim);
-	for (d = 0; d < total; ++d)
-		elim[d] = -1;
-	for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
-		for (; d >= 0; --d) {
-			if (isl_int_is_zero(bmap->eq[i][1+d]))
-				continue;
-			elim[d] = i;
-			break;
-		}
-	}
-}
-
-static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
-{
-	return compute_elimination_index((struct isl_basic_map *)bset, elim);
-}
-
-static int reduced_using_equalities(isl_int *dst, isl_int *src,
-	struct isl_basic_map *bmap, int *elim)
-{
-	int d, i;
-	int copied = 0;
-	unsigned total;
-
-	total = isl_dim_total(bmap->dim);
-	for (d = total - 1; d >= 0; --d) {
-		if (isl_int_is_zero(src[1+d]))
-			continue;
-		if (elim[d] == -1)
-			continue;
-		if (!copied) {
-			isl_seq_cpy(dst, src, 1 + total);
-			copied = 1;
-		}
-		isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
-	}
-	return copied;
-}
-
-static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
-	struct isl_basic_set *bset, int *elim)
-{
-	return reduced_using_equalities(dst, src,
-					(struct isl_basic_map *)bset, elim);
-}
-
-/* Quick check to see if two basic maps are disjoint.
- * In particular, we reduce the equalities and inequalities of
- * one basic map in the context of the equalities of the other
- * basic map and check if we get a contradiction.
- */
-int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
-	struct isl_basic_map *bmap2)
-{
-	struct isl_vec *v = NULL;
-	int *elim = NULL;
-	unsigned total;
-	int d, i;
-
-	if (!bmap1 || !bmap2)
-		return -1;
-	isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
-			return -1);
-	if (bmap1->n_div || bmap2->n_div)
-		return 0;
-	if (!bmap1->n_eq && !bmap2->n_eq)
-		return 0;
-
-	total = isl_dim_total(bmap1->dim);
-	if (total == 0)
-		return 0;
-	v = isl_vec_alloc(bmap1->ctx, 1 + total);
-	if (!v)
-		goto error;
-	elim = isl_alloc_array(bmap1->ctx, int, total);
-	if (!elim)
-		goto error;
-	compute_elimination_index(bmap1, elim);
-	for (i = 0; i < bmap2->n_eq; ++i) {
-		int reduced;
-		reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
-							bmap1, elim);
-		if (reduced && !isl_int_is_zero(v->block.data[0]) &&
-		    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
-			goto disjoint;
-	}
-	for (i = 0; i < bmap2->n_ineq; ++i) {
-		int reduced;
-		reduced = reduced_using_equalities(v->block.data,
-						bmap2->ineq[i], bmap1, elim);
-		if (reduced && isl_int_is_neg(v->block.data[0]) &&
-		    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
-			goto disjoint;
-	}
-	compute_elimination_index(bmap2, elim);
-	for (i = 0; i < bmap1->n_ineq; ++i) {
-		int reduced;
-		reduced = reduced_using_equalities(v->block.data,
-						bmap1->ineq[i], bmap2, elim);
-		if (reduced && isl_int_is_neg(v->block.data[0]) &&
-		    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
-			goto disjoint;
-	}
-	isl_vec_free(bmap1->ctx, v);
-	free(elim);
-	return 0;
-disjoint:
-	isl_vec_free(bmap1->ctx, v);
-	free(elim);
-	return 1;
-error:
-	isl_vec_free(bmap1->ctx, v);
-	free(elim);
-	return -1;
-}
-
-int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
-	struct isl_basic_set *bset2)
-{
-	return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
-					      (struct isl_basic_map *)bset2);
-}
-
-int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
-{
-	int i, j;
-
-	if (!map1 || !map2)
-		return -1;
-
-	if (isl_map_fast_is_equal(map1, map2))
-		return 0;
-
-	for (i = 0; i < map1->n; ++i) {
-		for (j = 0; j < map2->n; ++j) {
-			int d = isl_basic_map_fast_is_disjoint(map1->p[i],
-							       map2->p[j]);
-			if (d != 1)
-				return d;
-		}
-	}
-	return 1;
-}
-
-int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
-{
-	return isl_map_fast_is_disjoint((struct isl_map *)set1,
-					(struct isl_map *)set2);
-}
-
-static struct isl_basic_map *remove_duplicate_divs(
-	struct isl_basic_map *bmap, int *progress)
-{
-	unsigned int size;
-	int *index;
-	int k, l, h;
-	int bits;
-	struct isl_blk eq;
-	unsigned total_var = isl_dim_total(bmap->dim);
-	unsigned total = total_var + bmap->n_div;
-	struct isl_ctx *ctx;
-
-	if (bmap->n_div <= 1)
-		return bmap;
-
-	ctx = bmap->ctx;
-	for (k = bmap->n_div - 1; k >= 0; --k)
-		if (!isl_int_is_zero(bmap->div[k][0]))
-			break;
-	if (k <= 0)
-		return bmap;
-
-	size = round_up(4 * bmap->n_div / 3 - 1);
-	bits = ffs(size) - 1;
-	index = isl_calloc_array(ctx, int, size);
-	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_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
-	for (--k; k >= 0; --k) {
-		uint32_t hash;
-
-		if (isl_int_is_zero(bmap->div[k][0]))
-			continue;
-
-		hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
-		for (h = hash; index[h]; h = (h+1) % size)
-			if (isl_seq_eq(bmap->div[k],
-				       bmap->div[index[h]-1], 2+total))
-				break;
-		if (index[h]) {
-			*progress = 1;
-			l = index[h] - 1;
-			isl_int_set_si(eq.data[1+total_var+k], -1);
-			isl_int_set_si(eq.data[1+total_var+l], 1);
-			eliminate_div(bmap, eq.data, l);
-			isl_int_set_si(eq.data[1+total_var+k], 0);
-			isl_int_set_si(eq.data[1+total_var+l], 0);
-		}
-		index[h] = k+1;
-	}
-
-	isl_blk_free(ctx, eq);
-out:
-	free(index);
-	return bmap;
-}
-
-/* Elimininate divs based on equalities
- */
-static struct isl_basic_map *eliminate_divs_eq(
-		struct isl_basic_map *bmap, int *progress)
-{
-	int d;
-	int i;
-	int modified = 0;
-	unsigned off;
-
-	if (!bmap)
-		return NULL;
-
-	off = 1 + isl_dim_total(bmap->dim);
-
-	for (d = bmap->n_div - 1; d >= 0 ; --d) {
-		for (i = 0; i < bmap->n_eq; ++i) {
-			if (!isl_int_is_one(bmap->eq[i][off + d]) &&
-			    !isl_int_is_negone(bmap->eq[i][off + d]))
-				continue;
-			modified = 1;
-			*progress = 1;
-			eliminate_div(bmap, bmap->eq[i], d);
-			isl_basic_map_drop_equality(bmap, i);
-			break;
-		}
-	}
-	if (modified)
-		return eliminate_divs_eq(bmap, progress);
-	return bmap;
-}
-
-static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
-{
-	int i;
-	isl_int gcd;
-	unsigned total = isl_basic_map_total_dim(bmap);
-
-	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;
-}
-
-
-/* Remove any div that is defined in terms of the given variable.
- */
-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]))
-			continue;
-		if (isl_int_is_zero(bmap->div[i][1+1+pos]))
-			continue;
-		bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
-		if (!bmap)
-			return NULL;
-	}
-	return bmap;
-}
-
-
-/* Eliminate the specified variables from the constraints using
- * Fourier-Motzkin.  The variables themselves are not removed.
- */
-struct isl_basic_map *isl_basic_map_eliminate_vars(
-	struct isl_basic_map *bmap, unsigned pos, unsigned n)
-{
-	int d;
-	int i, j, k;
-	unsigned total;
-
-	if (n == 0)
-		return bmap;
-	if (!bmap)
-		return NULL;
-	total = isl_basic_map_total_dim(bmap);
-
-	bmap = isl_basic_map_cow(bmap);
-	for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
-		int n_lower, n_upper;
-		bmap = remove_dependent_vars(bmap, d);
-		if (!bmap)
-			return NULL;
-		if (d >= total - bmap->n_div)
-			isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
-		for (i = 0; i < bmap->n_eq; ++i) {
-			if (isl_int_is_zero(bmap->eq[i][1+d]))
-				continue;
-			eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
-			isl_basic_map_drop_equality(bmap, i);
-			break;
-		}
-		if (i < bmap->n_eq)
-			continue;
-		n_lower = 0;
-		n_upper = 0;
-		for (i = 0; i < bmap->n_ineq; ++i) {
-			if (isl_int_is_pos(bmap->ineq[i][1+d]))
-				n_lower++;
-			else if (isl_int_is_neg(bmap->ineq[i][1+d]))
-				n_upper++;
-		}
-		bmap = isl_basic_map_extend_constraints(bmap,
-				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_elim(bmap->ineq[k], bmap->ineq[j],
-						1+d, 1+total, NULL);
-			}
-			isl_basic_map_drop_inequality(bmap, i);
-			i = last + 1;
-		}
-		if (n_lower > 0 && n_upper > 0) {
-			bmap = normalize_constraints(bmap);
-			bmap = remove_duplicate_constraints(bmap, NULL);
-			bmap = isl_basic_map_gauss(bmap, NULL);
-			bmap = isl_basic_map_convex_hull(bmap);
-			if (!bmap)
-				goto error;
-			if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
-				break;
-		}
-	}
-	F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	return bmap;
-error:
-	isl_basic_map_free(bmap);
-	return NULL;
-}
-
-struct isl_basic_set *isl_basic_set_eliminate_vars(
-	struct isl_basic_set *bset, unsigned pos, unsigned n)
-{
-	return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
-			(struct isl_basic_map *)bset, pos, n);
-}
-
 /* Eliminate the specified n dimensions starting at first from the
  * constraints using Fourier-Motzkin, The dimensions themselves
  * are not removed.
@@ -1992,67 +1115,6 @@ struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
 	return bset;
 }
 
-/* Elimininate divs based on inequalities
- */
-static struct isl_basic_map *eliminate_divs_ineq(
-		struct isl_basic_map *bmap, int *progress)
-{
-	int d;
-	int i;
-	unsigned off;
-	struct isl_ctx *ctx;
-
-	if (!bmap)
-		return NULL;
-
-	ctx = bmap->ctx;
-	off = 1 + isl_dim_total(bmap->dim);
-
-	for (d = bmap->n_div - 1; d >= 0 ; --d) {
-		for (i = 0; i < bmap->n_eq; ++i)
-			if (!isl_int_is_zero(bmap->eq[i][off + d]))
-				break;
-		if (i < bmap->n_eq)
-			continue;
-		for (i = 0; i < bmap->n_ineq; ++i)
-			if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
-				break;
-		if (i < bmap->n_ineq)
-			continue;
-		*progress = 1;
-		bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
-		if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
-			break;
-		bmap = isl_basic_map_drop_div(bmap, d);
-		if (!bmap)
-			break;
-	}
-	return bmap;
-}
-
-struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
-{
-	int progress = 1;
-	if (!bmap)
-		return NULL;
-	while (progress) {
-		progress = 0;
-		bmap = normalize_constraints(bmap);
-		bmap = eliminate_divs_eq(bmap, &progress);
-		bmap = eliminate_divs_ineq(bmap, &progress);
-		bmap = isl_basic_map_gauss(bmap, &progress);
-		bmap = remove_duplicate_divs(bmap, &progress);
-		bmap = remove_duplicate_constraints(bmap, &progress);
-	}
-	return bmap;
-}
-
-struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
-{
-	return (struct isl_basic_set *)
-		isl_basic_map_simplify((struct isl_basic_map *)bset);
-}
-
 static void dump_term(struct isl_basic_map *bmap,
 			isl_int c, int pos, FILE *out)
 {
@@ -3848,127 +2910,6 @@ error:
 	return NULL;
 }
 
-/* If the only constraints a div d=floor(f/m)
- * appears in are its two defining constraints
- *
- *	f - m d >=0
- *	-(f - (m - 1)) + m d >= 0
- *
- * then it can safely be removed.
- */
-static int div_is_redundant(struct isl_basic_map *bmap, int div)
-{
-	int i;
-	unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
-
-	for (i = 0; i < bmap->n_eq; ++i)
-		if (!isl_int_is_zero(bmap->eq[i][pos]))
-			return 0;
-
-	for (i = 0; i < bmap->n_ineq; ++i) {
-		if (isl_int_is_zero(bmap->ineq[i][pos]))
-			continue;
-		if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
-			int neg;
-			isl_int_sub(bmap->div[div][1],
-					bmap->div[div][1], bmap->div[div][0]);
-			isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
-			neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
-			isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
-			isl_int_add(bmap->div[div][1],
-					bmap->div[div][1], bmap->div[div][0]);
-			if (!neg)
-				return 0;
-			if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
-						    bmap->n_div-div-1) != -1)
-				return 0;
-		} else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
-			if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
-				return 0;
-			if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
-						    bmap->n_div-div-1) != -1)
-				return 0;
-		} else
-			return 0;
-	}
-
-	for (i = 0; i < bmap->n_div; ++i)
-		if (!isl_int_is_zero(bmap->div[i][1+pos]))
-			return 0;
-
-	return 1;
-}
-
-/*
- * Remove divs that don't occur in any of the constraints or other divs.
- * These can arise when dropping some of the variables in a quast
- * returned by piplib.
- */
-static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
-{
-	int i;
-
-	if (!bmap)
-		return NULL;
-
-	for (i = bmap->n_div-1; i >= 0; --i) {
-		if (!div_is_redundant(bmap, i))
-			continue;
-		bmap = isl_basic_map_drop_div(bmap, i);
-	}
-	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;
-}
-
-struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
-{
-	return (struct isl_basic_set *)
-		isl_basic_map_finalize((struct isl_basic_map *)bset);
-}
-
-struct isl_set *isl_set_finalize(struct isl_set *set)
-{
-	int i;
-
-	if (!set)
-		return NULL;
-	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_finalize(set->p[i]);
-		if (!set->p[i])
-			goto error;
-	}
-	return set;
-error:
-	isl_set_free(set);
-	return NULL;
-}
-
-struct isl_map *isl_map_finalize(struct isl_map *map)
-{
-	int i;
-
-	if (!map)
-		return NULL;
-	for (i = 0; i < map->n; ++i) {
-		map->p[i] = isl_basic_map_finalize(map->p[i]);
-		if (!map->p[i])
-			goto error;
-	}
-	F_CLR(map, ISL_MAP_NORMALIZED);
-	return map;
-error:
-	isl_map_free(map);
-	return NULL;
-}
-
 static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
 {
 	struct isl_basic_map *bmap;
@@ -4859,260 +3800,6 @@ int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
 	return fixed;
 }
 
-static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
-	struct isl_basic_set *bset, struct isl_basic_set *context)
-{
-	int i;
-	int *elim;
-
-	if (!bset || !context)
-		goto error;
-
-	bset = isl_basic_set_cow(bset);
-	if (!bset)
-		goto error;
-
-	elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
-	if (!elim)
-		goto error;
-	set_compute_elimination_index(context, elim);
-	for (i = 0; i < bset->n_eq; ++i)
-		set_reduced_using_equalities(bset->eq[i], bset->eq[i],
-							context, elim);
-	for (i = 0; i < bset->n_ineq; ++i)
-		set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
-							context, elim);
-	isl_basic_set_free(context);
-	free(elim);
-	bset = isl_basic_set_simplify(bset);
-	bset = isl_basic_set_finalize(bset);
-	return bset;
-error:
-	isl_basic_set_free(bset);
-	isl_basic_set_free(context);
-	return NULL;
-}
-
-static struct isl_basic_set *remove_shifted_constraints(
-	struct isl_basic_set *bset, struct isl_basic_set *context)
-{
-	unsigned int size;
-	isl_int ***index;
-	int bits;
-	int k, h, l;
-
-	if (!bset)
-		return NULL;
-
-	size = round_up(4 * (context->n_ineq+1) / 3 - 1);
-	bits = ffs(size) - 1;
-	index = isl_calloc_array(ctx, isl_int **, size);
-	if (!index)
-		return bset;
-
-	for (k = 0; k < context->n_ineq; ++k) {
-		h = set_hash_index(index, size, bits, context, k);
-		index[h] = &context->ineq[k];
-	}
-	for (k = 0; k < bset->n_ineq; ++k) {
-		h = set_hash_index(index, size, bits, bset, k);
-		if (!index[h])
-			continue;
-		l = index[h] - &context->ineq[0];
-		if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
-			continue;
-		bset = isl_basic_set_cow(bset);
-		if (!bset)
-			goto error;
-		isl_basic_set_drop_inequality(bset, k);
-		--k;
-	}
-	free(index);
-	return bset;
-error:
-	free(index);
-	return bset;
-}
-
-static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
-	struct isl_basic_set *context);
-
-static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
-	struct isl_basic_set *context)
-{
-	struct isl_mat *T;
-	struct isl_mat *T2;
-	struct isl_ctx *ctx = context->ctx;
-	struct isl_basic_set *reduced_context;
-	reduced_context = isl_basic_set_remove_equalities(
-				isl_basic_set_copy(context), &T, &T2);
-	if (!reduced_context)
-		goto error;
-	bset = isl_basic_set_preimage(ctx, bset, T);
-	bset = uset_gist(bset, reduced_context);
-	bset = isl_basic_set_preimage(ctx, bset, T2);
-	bset = isl_basic_set_reduce_using_equalities(bset, context);
-	return bset;
-error:
-	isl_basic_set_free(context);
-	isl_basic_set_free(bset);
-	return NULL;
-}
-
-static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
-	struct isl_basic_set *context)
-{
-	struct isl_mat *T;
-	struct isl_mat *T2;
-	struct isl_ctx *ctx = context->ctx;
-	struct isl_basic_set *affine_hull = NULL;
-
-	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);
-
-	bset = isl_basic_set_remove_equalities(bset, &T, &T2);
-	if (!bset)
-		goto error;
-	context = isl_basic_set_preimage(ctx, context, T);
-	bset = uset_gist(bset, context);
-	bset = isl_basic_set_preimage(ctx, bset, T2);
-	bset = isl_basic_set_intersect(bset, affine_hull);
-	return bset;
-error:
-	isl_basic_set_free(affine_hull);
-	isl_basic_set_free(context);
-	isl_basic_set_free(bset);
-	return NULL;
-}
-
-/* Remove all information from bset that is redundant in the context
- * of context.  In particular, equalities that are linear combinations
- * of those in context are removed.  Then the inequalities that are
- * redundant in the context of the equalities and inequalities of
- * context are removed.
- */
-static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
-	struct isl_basic_set *context)
-{
-	int i;
-	isl_int opt;
-	struct isl_basic_set *combined;
-	struct isl_ctx *ctx;
-
-	if (!bset || !context)
-		goto error;
-
-	if (context->n_eq > 0)
-		return uset_gist_context_eq(bset, context);
-	if (!context->n_ineq)
-		goto done;
-	if (bset->n_eq > 0)
-		return uset_gist_set_eq(bset, context);
-	bset = remove_shifted_constraints(bset, context);
-	combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
-			context->n_eq, context->n_ineq);
-	context = set_add_constraints(combined, context, 0);
-	if (!context)
-		goto error;
-	ctx = context->ctx;
-	isl_int_init(opt);
-	for (i = bset->n_ineq-1; i >= 0; --i) {
-		int redundant;
-		set_swap_inequality(context, i, context->n_ineq-1);
-		context->n_ineq--;
-		redundant = isl_basic_set_constraint_is_redundant(&context,
-				context->ineq[context->n_ineq], &opt, NULL);
-		if (redundant == -1) {
-			isl_int_clear(opt);
-			goto error;
-		}
-		if (F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
-			bset = isl_basic_set_set_to_empty(bset);
-			break;
-		}
-		context->n_ineq++;
-		set_swap_inequality(context, i, context->n_ineq-1);
-		if (redundant) {
-			isl_basic_set_drop_inequality(context, i);
-			isl_basic_set_drop_inequality(bset, i);
-		}
-	}
-	isl_int_clear(opt);
-done:
-	isl_basic_set_free(context);
-	return bset;
-error:
-	isl_basic_set_free(context);
-	isl_basic_set_free(bset);
-	return NULL;
-}
-
-struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
-	struct isl_basic_map *context)
-{
-	struct isl_basic_set *bset;
-
-	if (!bmap || !context)
-		goto error;
-
-	context = isl_basic_map_align_divs(context, bmap);
-	bmap = isl_basic_map_align_divs(bmap, context);
-
-	bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
-			 isl_basic_map_underlying_set(context));
-
-	return isl_basic_map_overlying_set(bset, bmap);
-error:
-	isl_basic_map_free(bmap);
-	isl_basic_map_free(context);
-	return NULL;
-}
-
-/*
- * Assumes context has no implicit divs.
- */
-struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
-{
-	int i;
-
-	map = isl_map_cow(map);
-	if (!map || !context)
-		return NULL;
-	isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
-	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) {
-		map->p[i] = isl_basic_map_gist(map->p[i],
-						isl_basic_map_copy(context));
-		if (!map->p[i])
-			goto error;
-	}
-	isl_basic_map_free(context);
-	F_CLR(map, ISL_MAP_NORMALIZED);
-	return map;
-error:
-	isl_map_free(map);
-	isl_basic_map_free(context);
-	return NULL;
-}
-
-struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
-						struct isl_basic_set *context)
-{
-	return (struct isl_basic_set *)isl_basic_map_gist(
-		(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)
-{
-	return (struct isl_set *)isl_map_gist((struct isl_map *)set,
-					(struct isl_basic_map *)context);
-}
-
 struct constraint {
 	unsigned	size;
 	isl_int		*c;
@@ -5382,7 +4069,7 @@ struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
 		goto error;
 	dim = 0;
 	for (i = 0; i < list->n; ++i) {
-		set_add_constraints(product,
+		isl_basic_set_add_constraints(product,
 					isl_basic_set_copy(list->p[i]), dim);
 		dim += isl_basic_set_n_dim(list->p[i]);
 	}