/*

 * Copyright 2005-2007 Universiteit Leiden

 * Copyright 2008-2009 Katholieke Universiteit Leuven

 * Copyright 2010      INRIA Saclay

 * Copyright 2012      Universiteit Leiden

 * Copyright 2014      Ecole Normale Superieure

 *

 * Use of this software is governed by the MIT license

 *

 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,

 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,

 * B-3001 Leuven, Belgium

 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,

 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 

 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France

 */

#include <isl/set.h>

#include <isl/map.h>

#include <isl/union_set.h>

#include <isl/union_map.h>

#include <isl/flow.h>

#include <isl/schedule_node.h>

#include <isl_sort.h>

enum isl_restriction_type {

	isl_restriction_type_empty,

	isl_restriction_type_none,

	isl_restriction_type_input,

	isl_restriction_type_output

};

struct isl_restriction {

	enum isl_restriction_type type;

	isl_set *source;

	isl_set *sink;

};

/* Create a restriction of the given type.

 */

static __isl_give isl_restriction *isl_restriction_alloc(

	__isl_take isl_map *source_map, enum isl_restriction_type type)

{

	isl_ctx *ctx;

	isl_restriction *restr;

	if (!source_map)

		return NULL;

	ctx = isl_map_get_ctx(source_map);

	restr = isl_calloc_type(ctx, struct isl_restriction);

	if (!restr)

		goto error;

	restr->type = type;

	isl_map_free(source_map);

	return restr;

error:

	isl_map_free(source_map);

	return NULL;

}

/* Create a restriction that doesn't restrict anything.

 */

__isl_give isl_restriction *isl_restriction_none(__isl_take isl_map *source_map)

{

	return isl_restriction_alloc(source_map, isl_restriction_type_none);

}

/* Create a restriction that removes everything.

 */

__isl_give isl_restriction *isl_restriction_empty(

	__isl_take isl_map *source_map)

{

	return isl_restriction_alloc(source_map, isl_restriction_type_empty);

}

/* Create a restriction on the input of the maximization problem

 * based on the given source and sink restrictions.

 */

__isl_give isl_restriction *isl_restriction_input(

	__isl_take isl_set *source_restr, __isl_take isl_set *sink_restr)

{

	isl_ctx *ctx;

	isl_restriction *restr;

	if (!source_restr || !sink_restr)

		goto error;

	ctx = isl_set_get_ctx(source_restr);

	restr = isl_calloc_type(ctx, struct isl_restriction);

	if (!restr)

		goto error;

	restr->type = isl_restriction_type_input;

	restr->source = source_restr;

	restr->sink = sink_restr;

	return restr;

error:

	isl_set_free(source_restr);

	isl_set_free(sink_restr);

	return NULL;

}

/* Create a restriction on the output of the maximization problem

 * based on the given source restriction.

 */

__isl_give isl_restriction *isl_restriction_output(

	__isl_take isl_set *source_restr)

{

	isl_ctx *ctx;

	isl_restriction *restr;

	if (!source_restr)

		return NULL;

	ctx = isl_set_get_ctx(source_restr);

	restr = isl_calloc_type(ctx, struct isl_restriction);

	if (!restr)

		goto error;

	restr->type = isl_restriction_type_output;

	restr->source = source_restr;

	return restr;

error:

	isl_set_free(source_restr);

	return NULL;

}

__isl_null isl_restriction *isl_restriction_free(

	__isl_take isl_restriction *restr)

{

	if (!restr)

		return NULL;

	isl_set_free(restr->source);

	isl_set_free(restr->sink);

	free(restr);

	return NULL;

}

isl_ctx *isl_restriction_get_ctx(__isl_keep isl_restriction *restr)

{

	return restr ? isl_set_get_ctx(restr->source) : NULL;

}

/* A private structure to keep track of a mapping together with

 * a user-specified identifier and a boolean indicating whether

 * the map represents a must or may access/dependence.

 */

struct isl_labeled_map {

	struct isl_map	*map;

	void		*data;

	int		must;

};

/* A structure containing the input for dependence analysis:

 * - a sink

 * - n_must + n_may (<= max_source) sources

 * - a function for determining the relative order of sources and sink

 * The must sources are placed before the may sources.

 *

 * domain_map is an auxiliary map that maps the sink access relation

 * to the domain of this access relation.

 * This field is only needed when restrict_fn is set and

 * the field itself is set by isl_access_info_compute_flow.

 *

 * restrict_fn is a callback that (if not NULL) will be called

 * right before any lexicographical maximization.

 */

struct isl_access_info {

	isl_map				*domain_map;

	struct isl_labeled_map		sink;

	isl_access_level_before		level_before;

	isl_access_restrict		restrict_fn;

	void				*restrict_user;

	int		    		max_source;

	int		    		n_must;

	int		    		n_may;

	struct isl_labeled_map		source[1];

};

/* A structure containing the output of dependence analysis:

 * - n_source dependences

 * - a wrapped subset of the sink for which definitely no source could be found

 * - a wrapped subset of the sink for which possibly no source could be found

 */

struct isl_flow {

	isl_set			*must_no_source;

	isl_set			*may_no_source;

	int			n_source;

	struct isl_labeled_map	*dep;

};

/* Construct an isl_access_info structure and fill it up with

 * the given data.  The number of sources is set to 0.

 */

__isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,

	void *sink_user, isl_access_level_before fn, int max_source)

{

	isl_ctx *ctx;

	struct isl_access_info *acc;

	if (!sink)

		return NULL;

	ctx = isl_map_get_ctx(sink);

	isl_assert(ctx, max_source >= 0, goto error);

	acc = isl_calloc(ctx, struct isl_access_info,

			sizeof(struct isl_access_info) +

			(max_source - 1) * sizeof(struct isl_labeled_map));

	if (!acc)

		goto error;

	acc->sink.map = sink;

	acc->sink.data = sink_user;

	acc->level_before = fn;

	acc->max_source = max_source;

	acc->n_must = 0;

	acc->n_may = 0;

	return acc;

error:

	isl_map_free(sink);

	return NULL;

}

/* Free the given isl_access_info structure.

 */

__isl_null isl_access_info *isl_access_info_free(

	__isl_take isl_access_info *acc)

{

	int i;

	if (!acc)

		return NULL;

	isl_map_free(acc->domain_map);

	isl_map_free(acc->sink.map);

	for (i = 0; i < acc->n_must + acc->n_may; ++i)

		isl_map_free(acc->source[i].map);

	free(acc);

	return NULL;

}

isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)

{

	return acc ? isl_map_get_ctx(acc->sink.map) : NULL;

}

__isl_give isl_access_info *isl_access_info_set_restrict(

	__isl_take isl_access_info *acc, isl_access_restrict fn, void *user)

{

	if (!acc)

		return NULL;

	acc->restrict_fn = fn;

	acc->restrict_user = user;

	return acc;

}

/* Add another source to an isl_access_info structure, making

 * sure the "must" sources are placed before the "may" sources.

 * This function may be called at most max_source times on a

 * given isl_access_info structure, with max_source as specified

 * in the call to isl_access_info_alloc that constructed the structure.

 */

__isl_give isl_access_info *isl_access_info_add_source(

	__isl_take isl_access_info *acc, __isl_take isl_map *source,

	int must, void *source_user)

{

	isl_ctx *ctx;

	if (!acc)

		goto error;

	ctx = isl_map_get_ctx(acc->sink.map);

	isl_assert(ctx, acc->n_must + acc->n_may < acc->max_source, goto error);

	if (must) {

		if (acc->n_may)

			acc->source[acc->n_must + acc->n_may] =

				acc->source[acc->n_must];

		acc->source[acc->n_must].map = source;

		acc->source[acc->n_must].data = source_user;

		acc->source[acc->n_must].must = 1;

		acc->n_must++;

	} else {

		acc->source[acc->n_must + acc->n_may].map = source;

		acc->source[acc->n_must + acc->n_may].data = source_user;

		acc->source[acc->n_must + acc->n_may].must = 0;

		acc->n_may++;

	}

	return acc;

error:

	isl_map_free(source);

	isl_access_info_free(acc);

	return NULL;

}

/* Return -n, 0 or n (with n a positive value), depending on whether

 * the source access identified by p1 should be sorted before, together

 * or after that identified by p2.

 *

 * If p1 appears before p2, then it should be sorted first.

 * For more generic initial schedules, it is possible that neither

 * p1 nor p2 appears before the other, or at least not in any obvious way.

 * We therefore also check if p2 appears before p1, in which case p2

 * should be sorted first.

 * If not, we try to order the two statements based on the description

 * of the iteration domains.  This results in an arbitrary, but fairly

 * stable ordering.

 */

static int access_sort_cmp(const void *p1, const void *p2, void *user)

{

	isl_access_info *acc = user;

	const struct isl_labeled_map *i1, *i2;

	int level1, level2;

	uint32_t h1, h2;

	i1 = (const struct isl_labeled_map *) p1;

	i2 = (const struct isl_labeled_map *) p2;

	level1 = acc->level_before(i1->data, i2->data);

	if (level1 % 2)

		return -1;

	level2 = acc->level_before(i2->data, i1->data);

	if (level2 % 2)

		return 1;

	h1 = isl_map_get_hash(i1->map);

	h2 = isl_map_get_hash(i2->map);

	return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;

}

/* Sort the must source accesses in their textual order.

 */

static __isl_give isl_access_info *isl_access_info_sort_sources(

	__isl_take isl_access_info *acc)

{

	if (!acc)

		return NULL;

	if (acc->n_must <= 1)

		return acc;

	if (isl_sort(acc->source, acc->n_must, sizeof(struct isl_labeled_map),

		    access_sort_cmp, acc) < 0)

		return isl_access_info_free(acc);

	return acc;

}

/* Align the parameters of the two spaces if needed and then call

 * isl_space_join.

 */

static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,

	__isl_take isl_space *right)

{

	if (isl_space_match(left, isl_dim_param, right, isl_dim_param))

		return isl_space_join(left, right);

	left = isl_space_align_params(left, isl_space_copy(right));

	right = isl_space_align_params(right, isl_space_copy(left));

	return isl_space_join(left, right);

}

/* Initialize an empty isl_flow structure corresponding to a given

 * isl_access_info structure.

 * For each must access, two dependences are created (initialized

 * to the empty relation), one for the resulting must dependences

 * and one for the resulting may dependences.  May accesses can

 * only lead to may dependences, so only one dependence is created

 * for each of them.

 * This function is private as isl_flow structures are only supposed

 * to be created by isl_access_info_compute_flow.

 */

static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)

{

	int i, n;

	struct isl_ctx *ctx;

	struct isl_flow *dep;

	if (!acc)

		return NULL;

	ctx = isl_map_get_ctx(acc->sink.map);

	dep = isl_calloc_type(ctx, struct isl_flow);

	if (!dep)

		return NULL;

	n = 2 * acc->n_must + acc->n_may;

	dep->dep = isl_calloc_array(ctx, struct isl_labeled_map, n);

	if (n && !dep->dep)

		goto error;

	dep->n_source = n;

	for (i = 0; i < acc->n_must; ++i) {

		isl_space *dim;

		dim = space_align_and_join(

			isl_map_get_space(acc->source[i].map),

			isl_space_reverse(isl_map_get_space(acc->sink.map)));

		dep->dep[2 * i].map = isl_map_empty(dim);

		dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);

		dep->dep[2 * i].data = acc->source[i].data;

		dep->dep[2 * i + 1].data = acc->source[i].data;

		dep->dep[2 * i].must = 1;

		dep->dep[2 * i + 1].must = 0;

		if (!dep->dep[2 * i].map || !dep->dep[2 * i + 1].map)

			goto error;

	}

	for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {

		isl_space *dim;

		dim = space_align_and_join(

			isl_map_get_space(acc->source[i].map),

			isl_space_reverse(isl_map_get_space(acc->sink.map)));

		dep->dep[acc->n_must + i].map = isl_map_empty(dim);

		dep->dep[acc->n_must + i].data = acc->source[i].data;

		dep->dep[acc->n_must + i].must = 0;

		if (!dep->dep[acc->n_must + i].map)

			goto error;

	}

	return dep;

error:

	isl_flow_free(dep);

	return NULL;

}

/* Iterate over all sources and for each resulting flow dependence

 * that is not empty, call the user specfied function.

 * The second argument in this function call identifies the source,

 * while the third argument correspond to the final argument of

 * the isl_flow_foreach call.

 */

isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,

	isl_stat (*fn)(__isl_take isl_map *dep, int must, void *dep_user,

		void *user),

	void *user)

{

	int i;

	if (!deps)

		return isl_stat_error;

	for (i = 0; i < deps->n_source; ++i) {

		if (isl_map_plain_is_empty(deps->dep[i].map))

			continue;

		if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,

				deps->dep[i].data, user) < 0)

			return isl_stat_error;

	}

	return isl_stat_ok;

}

/* Return a copy of the subset of the sink for which no source could be found.

 */

__isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)

{

	if (!deps)

		return NULL;

	if (must)

		return isl_set_unwrap(isl_set_copy(deps->must_no_source));

	else

		return isl_set_unwrap(isl_set_copy(deps->may_no_source));

}

void isl_flow_free(__isl_take isl_flow *deps)

{

	int i;

	if (!deps)

		return;

	isl_set_free(deps->must_no_source);

	isl_set_free(deps->may_no_source);

	if (deps->dep) {

		for (i = 0; i < deps->n_source; ++i)

			isl_map_free(deps->dep[i].map);

		free(deps->dep);

	}

	free(deps);

}

isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)

{

	return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;

}

/* Return a map that enforces that the domain iteration occurs after

 * the range iteration at the given level.

 * If level is odd, then the domain iteration should occur after

 * the target iteration in their shared level/2 outermost loops.

 * In this case we simply need to enforce that these outermost

 * loop iterations are the same.

 * If level is even, then the loop iterator of the domain should

 * be greater than the loop iterator of the range at the last

 * of the level/2 shared loops, i.e., loop level/2 - 1.

 */

static __isl_give isl_map *after_at_level(__isl_take isl_space *dim, int level)

{

	struct isl_basic_map *bmap;

	if (level % 2)

		bmap = isl_basic_map_equal(dim, level/2);

	else

		bmap = isl_basic_map_more_at(dim, level/2 - 1);

	return isl_map_from_basic_map(bmap);

}

/* Compute the partial lexicographic maximum of "dep" on domain "sink",

 * but first check if the user has set acc->restrict_fn and if so

 * update either the input or the output of the maximization problem

 * with respect to the resulting restriction.

 *

 * Since the user expects a mapping from sink iterations to source iterations,

 * whereas the domain of "dep" is a wrapped map, mapping sink iterations

 * to accessed array elements, we first need to project out the accessed

 * sink array elements by applying acc->domain_map.

 * Similarly, the sink restriction specified by the user needs to be

 * converted back to the wrapped map.

 */

static __isl_give isl_map *restricted_partial_lexmax(

	__isl_keep isl_access_info *acc, __isl_take isl_map *dep,

	int source, __isl_take isl_set *sink, __isl_give isl_set **empty)

{

	isl_map *source_map;

	isl_restriction *restr;

	isl_set *sink_domain;

	isl_set *sink_restr;

	isl_map *res;

	if (!acc->restrict_fn)

		return isl_map_partial_lexmax(dep, sink, empty);

	source_map = isl_map_copy(dep);

	source_map = isl_map_apply_domain(source_map,

					    isl_map_copy(acc->domain_map));

	sink_domain = isl_set_copy(sink);

	sink_domain = isl_set_apply(sink_domain, isl_map_copy(acc->domain_map));

	restr = acc->restrict_fn(source_map, sink_domain,

				acc->source[source].data, acc->restrict_user);

	isl_set_free(sink_domain);

	isl_map_free(source_map);

	if (!restr)

		goto error;

	if (restr->type == isl_restriction_type_input) {

		dep = isl_map_intersect_range(dep, isl_set_copy(restr->source));

		sink_restr = isl_set_copy(restr->sink);

		sink_restr = isl_set_apply(sink_restr,

				isl_map_reverse(isl_map_copy(acc->domain_map)));

		sink = isl_set_intersect(sink, sink_restr);

	} else if (restr->type == isl_restriction_type_empty) {

		isl_space *space = isl_map_get_space(dep);

		isl_map_free(dep);

		dep = isl_map_empty(space);

	}

	res = isl_map_partial_lexmax(dep, sink, empty);

	if (restr->type == isl_restriction_type_output)

		res = isl_map_intersect_range(res, isl_set_copy(restr->source));

	isl_restriction_free(restr);

	return res;

error:

	isl_map_free(dep);

	isl_set_free(sink);

	*empty = NULL;

	return NULL;

}

/* Compute the last iteration of must source j that precedes the sink

 * at the given level for sink iterations in set_C.

 * The subset of set_C for which no such iteration can be found is returned

 * in *empty.

 */

static struct isl_map *last_source(struct isl_access_info *acc, 

				    struct isl_set *set_C,

				    int j, int level, struct isl_set **empty)

{

	struct isl_map *read_map;

	struct isl_map *write_map;

	struct isl_map *dep_map;

	struct isl_map *after;

	struct isl_map *result;

	read_map = isl_map_copy(acc->sink.map);

	write_map = isl_map_copy(acc->source[j].map);

	write_map = isl_map_reverse(write_map);

	dep_map = isl_map_apply_range(read_map, write_map);

	after = after_at_level(isl_map_get_space(dep_map), level);

	dep_map = isl_map_intersect(dep_map, after);

	result = restricted_partial_lexmax(acc, dep_map, j, set_C, empty);

	result = isl_map_reverse(result);

	return result;

}

/* For a given mapping between iterations of must source j and iterations

 * of the sink, compute the last iteration of must source k preceding

 * the sink at level before_level for any of the sink iterations,

 * but following the corresponding iteration of must source j at level

 * after_level.

 */

static struct isl_map *last_later_source(struct isl_access_info *acc,

					 struct isl_map *old_map,

					 int j, int before_level,

					 int k, int after_level,

					 struct isl_set **empty)

{

	isl_space *dim;

	struct isl_set *set_C;

	struct isl_map *read_map;

	struct isl_map *write_map;

	struct isl_map *dep_map;

	struct isl_map *after_write;

	struct isl_map *before_read;

	struct isl_map *result;

	set_C = isl_map_range(isl_map_copy(old_map));

	read_map = isl_map_copy(acc->sink.map);

	write_map = isl_map_copy(acc->source[k].map);

	write_map = isl_map_reverse(write_map);

	dep_map = isl_map_apply_range(read_map, write_map);

	dim = space_align_and_join(isl_map_get_space(acc->source[k].map),

		    isl_space_reverse(isl_map_get_space(acc->source[j].map)));

	after_write = after_at_level(dim, after_level);

	after_write = isl_map_apply_range(after_write, old_map);

	after_write = isl_map_reverse(after_write);

	dep_map = isl_map_intersect(dep_map, after_write);

	before_read = after_at_level(isl_map_get_space(dep_map), before_level);

	dep_map = isl_map_intersect(dep_map, before_read);

	result = restricted_partial_lexmax(acc, dep_map, k, set_C, empty);

	result = isl_map_reverse(result);

	return result;

}

/* Given a shared_level between two accesses, return 1 if the

 * the first can precede the second at the requested target_level.

 * If the target level is odd, i.e., refers to a statement level

 * dimension, then first needs to precede second at the requested

 * level, i.e., shared_level must be equal to target_level.

 * If the target level is odd, then the two loops should share

 * at least the requested number of outer loops.

 */

static int can_precede_at_level(int shared_level, int target_level)

{

	if (shared_level < target_level)

		return 0;

	if ((target_level % 2) && shared_level > target_level)

		return 0;

	return 1;

}

/* Given a possible flow dependence temp_rel[j] between source j and the sink

 * at level sink_level, remove those elements for which

 * there is an iteration of another source k < j that is closer to the sink.

 * The flow dependences temp_rel[k] are updated with the improved sources.

 * Any improved source needs to precede the sink at the same level

 * and needs to follow source j at the same or a deeper level.

 * The lower this level, the later the execution date of source k.

 * We therefore consider lower levels first.

 *

 * If temp_rel[j] is empty, then there can be no improvement and

 * we return immediately.

 */

static int intermediate_sources(__isl_keep isl_access_info *acc,

	struct isl_map **temp_rel, int j, int sink_level)

{

	int k, level;

	int depth = 2 * isl_map_dim(acc->source[j].map, isl_dim_in) + 1;

	if (isl_map_plain_is_empty(temp_rel[j]))

		return 0;

	for (k = j - 1; k >= 0; --k) {

		int plevel, plevel2;

		plevel = acc->level_before(acc->source[k].data, acc->sink.data);

		if (!can_precede_at_level(plevel, sink_level))

			continue;

		plevel2 = acc->level_before(acc->source[j].data,

						acc->source[k].data);

		for (level = sink_level; level <= depth; ++level) {

			struct isl_map *T;

			struct isl_set *trest;

			struct isl_map *copy;

			if (!can_precede_at_level(plevel2, level))

				continue;

			copy = isl_map_copy(temp_rel[j]);

			T = last_later_source(acc, copy, j, sink_level, k,

					      level, &trest);

			if (isl_map_plain_is_empty(T)) {

				isl_set_free(trest);

				isl_map_free(T);

				continue;

			}

			temp_rel[j] = isl_map_intersect_range(temp_rel[j], trest);

			temp_rel[k] = isl_map_union_disjoint(temp_rel[k], T);

		}

	}

	return 0;

}

/* Compute all iterations of may source j that precedes the sink at the given

 * level for sink iterations in set_C.

 */

static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,

				    __isl_take isl_set *set_C, int j, int level)

{

	isl_map *read_map;

	isl_map *write_map;

	isl_map *dep_map;

	isl_map *after;

	read_map = isl_map_copy(acc->sink.map);

	read_map = isl_map_intersect_domain(read_map, set_C);

	write_map = isl_map_copy(acc->source[acc->n_must + j].map);

	write_map = isl_map_reverse(write_map);

	dep_map = isl_map_apply_range(read_map, write_map);

	after = after_at_level(isl_map_get_space(dep_map), level);

	dep_map = isl_map_intersect(dep_map, after);

	return isl_map_reverse(dep_map);

}

/* For a given mapping between iterations of must source k and iterations

 * of the sink, compute the all iteration of may source j preceding

 * the sink at level before_level for any of the sink iterations,

 * but following the corresponding iteration of must source k at level

 * after_level.

 */

static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,

	__isl_take isl_map *old_map,

	int j, int before_level, int k, int after_level)

{

	isl_space *dim;

	isl_set *set_C;

	isl_map *read_map;

	isl_map *write_map;

	isl_map *dep_map;

	isl_map *after_write;

	isl_map *before_read;

	set_C = isl_map_range(isl_map_copy(old_map));

	read_map = isl_map_copy(acc->sink.map);

	read_map = isl_map_intersect_domain(read_map, set_C);

	write_map = isl_map_copy(acc->source[acc->n_must + j].map);

	write_map = isl_map_reverse(write_map);

	dep_map = isl_map_apply_range(read_map, write_map);

	dim = isl_space_join(isl_map_get_space(acc->source[acc->n_must + j].map),

		    isl_space_reverse(isl_map_get_space(acc->source[k].map)));

	after_write = after_at_level(dim, after_level);

	after_write = isl_map_apply_range(after_write, old_map);

	after_write = isl_map_reverse(after_write);

	dep_map = isl_map_intersect(dep_map, after_write);

	before_read = after_at_level(isl_map_get_space(dep_map), before_level);

	dep_map = isl_map_intersect(dep_map, before_read);

	return isl_map_reverse(dep_map);

}

/* Given the must and may dependence relations for the must accesses

 * for level sink_level, check if there are any accesses of may access j

 * that occur in between and return their union.

 * If some of these accesses are intermediate with respect to

 * (previously thought to be) must dependences, then these

 * must dependences are turned into may dependences.

 */

static __isl_give isl_map *all_intermediate_sources(

	__isl_keep isl_access_info *acc, __isl_take isl_map *map,

	struct isl_map **must_rel, struct isl_map **may_rel,

	int j, int sink_level)

{

	int k, level;

	int depth = 2 * isl_map_dim(acc->source[acc->n_must + j].map,

					isl_dim_in) + 1;

	for (k = 0; k < acc->n_must; ++k) {

		int plevel;

		if (isl_map_plain_is_empty(may_rel[k]) &&

		    isl_map_plain_is_empty(must_rel[k]))

			continue;

		plevel = acc->level_before(acc->source[k].data,

					acc->source[acc->n_must + j].data);

		for (level = sink_level; level <= depth; ++level) {

			isl_map *T;

			isl_map *copy;

			isl_set *ran;

			if (!can_precede_at_level(plevel, level))

				continue;

			copy = isl_map_copy(may_rel[k]);

			T = all_later_sources(acc, copy, j, sink_level, k, level);

			map = isl_map_union(map, T);

			copy = isl_map_copy(must_rel[k]);

			T = all_later_sources(acc, copy, j, sink_level, k, level);

			ran = isl_map_range(isl_map_copy(T));

			map = isl_map_union(map, T);

			may_rel[k] = isl_map_union_disjoint(may_rel[k],

			    isl_map_intersect_range(isl_map_copy(must_rel[k]),

						    isl_set_copy(ran)));

			T = isl_map_from_domain_and_range(

			    isl_set_universe(

				isl_space_domain(isl_map_get_space(must_rel[k]))),

			    ran);

			must_rel[k] = isl_map_subtract(must_rel[k], T);

		}

	}

	return map;

}

/* Compute dependences for the case where all accesses are "may"

 * accesses, which boils down to computing memory based dependences.

 * The generic algorithm would also work in this case, but it would

 * be overkill to use it.

 */

static __isl_give isl_flow *compute_mem_based_dependences(

	__isl_keep isl_access_info *acc)

{

	int i;

	isl_set *mustdo;

	isl_set *maydo;

	isl_flow *res;

	res = isl_flow_alloc(acc);

	if (!res)

		return NULL;

	mustdo = isl_map_domain(isl_map_copy(acc->sink.map));

	maydo = isl_set_copy(mustdo);

	for (i = 0; i < acc->n_may; ++i) {

		int plevel;

		int is_before;

		isl_space *dim;

		isl_map *before;

		isl_map *dep;

		plevel = acc->level_before(acc->source[i].data, acc->sink.data);

		is_before = plevel & 1;

		plevel >>= 1;

		dim = isl_map_get_space(res->dep[i].map);

		if (is_before)

			before = isl_map_lex_le_first(dim, plevel);

		else

			before = isl_map_lex_lt_first(dim, plevel);

		dep = isl_map_apply_range(isl_map_copy(acc->source[i].map),

			isl_map_reverse(isl_map_copy(acc->sink.map)));

		dep = isl_map_intersect(dep, before);

		mustdo = isl_set_subtract(mustdo,

					    isl_map_range(isl_map_copy(dep)));

		res->dep[i].map = isl_map_union(res->dep[i].map, dep);

	}

	res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));

	res->must_no_source = mustdo;