brintos / llvm-project-archived public Read only

1/*2 * Copyright 2005-2007 Universiteit Leiden3 * Copyright 2008-2009 Katholieke Universiteit Leuven4 * Copyright 2010      INRIA Saclay5 * Copyright 2012      Universiteit Leiden6 * Copyright 2014      Ecole Normale Superieure7 *8 * Use of this software is governed by the MIT license9 *10 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,11 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands12 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,13 * B-3001 Leuven, Belgium14 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,15 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 16 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France17 */18 19#include <isl/val.h>20#include <isl/space.h>21#include <isl/set.h>22#include <isl/map.h>23#include <isl/union_set.h>24#include <isl/union_map.h>25#include <isl/flow.h>26#include <isl/schedule_node.h>27#include <isl_sort.h>28#include <isl/stream.h>29 30enum isl_restriction_type {31	isl_restriction_type_empty,32	isl_restriction_type_none,33	isl_restriction_type_input,34	isl_restriction_type_output35};36 37struct isl_restriction {38	enum isl_restriction_type type;39 40	isl_set *source;41	isl_set *sink;42};43 44/* Create a restriction of the given type.45 */46static __isl_give isl_restriction *isl_restriction_alloc(47	__isl_take isl_map *source_map, enum isl_restriction_type type)48{49	isl_ctx *ctx;50	isl_restriction *restr;51 52	if (!source_map)53		return NULL;54 55	ctx = isl_map_get_ctx(source_map);56	restr = isl_calloc_type(ctx, struct isl_restriction);57	if (!restr)58		goto error;59 60	restr->type = type;61 62	isl_map_free(source_map);63	return restr;64error:65	isl_map_free(source_map);66	return NULL;67}68 69/* Create a restriction that doesn't restrict anything.70 */71__isl_give isl_restriction *isl_restriction_none(__isl_take isl_map *source_map)72{73	return isl_restriction_alloc(source_map, isl_restriction_type_none);74}75 76/* Create a restriction that removes everything.77 */78__isl_give isl_restriction *isl_restriction_empty(79	__isl_take isl_map *source_map)80{81	return isl_restriction_alloc(source_map, isl_restriction_type_empty);82}83 84/* Create a restriction on the input of the maximization problem85 * based on the given source and sink restrictions.86 */87__isl_give isl_restriction *isl_restriction_input(88	__isl_take isl_set *source_restr, __isl_take isl_set *sink_restr)89{90	isl_ctx *ctx;91	isl_restriction *restr;92 93	if (!source_restr || !sink_restr)94		goto error;95 96	ctx = isl_set_get_ctx(source_restr);97	restr = isl_calloc_type(ctx, struct isl_restriction);98	if (!restr)99		goto error;100 101	restr->type = isl_restriction_type_input;102	restr->source = source_restr;103	restr->sink = sink_restr;104 105	return restr;106error:107	isl_set_free(source_restr);108	isl_set_free(sink_restr);109	return NULL;110}111 112/* Create a restriction on the output of the maximization problem113 * based on the given source restriction.114 */115__isl_give isl_restriction *isl_restriction_output(116	__isl_take isl_set *source_restr)117{118	isl_ctx *ctx;119	isl_restriction *restr;120 121	if (!source_restr)122		return NULL;123 124	ctx = isl_set_get_ctx(source_restr);125	restr = isl_calloc_type(ctx, struct isl_restriction);126	if (!restr)127		goto error;128 129	restr->type = isl_restriction_type_output;130	restr->source = source_restr;131 132	return restr;133error:134	isl_set_free(source_restr);135	return NULL;136}137 138__isl_null isl_restriction *isl_restriction_free(139	__isl_take isl_restriction *restr)140{141	if (!restr)142		return NULL;143 144	isl_set_free(restr->source);145	isl_set_free(restr->sink);146	free(restr);147	return NULL;148}149 150isl_ctx *isl_restriction_get_ctx(__isl_keep isl_restriction *restr)151{152	return restr ? isl_set_get_ctx(restr->source) : NULL;153}154 155/* A private structure to keep track of a mapping together with156 * a user-specified identifier and a boolean indicating whether157 * the map represents a must or may access/dependence.158 */159struct isl_labeled_map {160	struct isl_map	*map;161	void		*data;162	int		must;163};164 165typedef isl_bool (*isl_access_coscheduled)(void *first, void *second);166 167/* A structure containing the input for dependence analysis:168 * - a sink169 * - n_must + n_may (<= max_source) sources170 * - a function for determining the relative order of sources and sink171 * - an optional function "coscheduled" for determining whether sources172 *   may be coscheduled.  If "coscheduled" is NULL, then the sources173 *   are assumed not to be coscheduled.174 * The must sources are placed before the may sources.175 *176 * domain_map is an auxiliary map that maps the sink access relation177 * to the domain of this access relation.178 * This field is only needed when restrict_fn is set and179 * the field itself is set by isl_access_info_compute_flow.180 *181 * restrict_fn is a callback that (if not NULL) will be called182 * right before any lexicographical maximization.183 */184struct isl_access_info {185	isl_map				*domain_map;186	struct isl_labeled_map		sink;187	isl_access_level_before		level_before;188	isl_access_coscheduled		coscheduled;189 190	isl_access_restrict		restrict_fn;191	void				*restrict_user;192 193	int		    		max_source;194	int		    		n_must;195	int		    		n_may;196	struct isl_labeled_map		source[1];197};198 199/* A structure containing the output of dependence analysis:200 * - n_source dependences201 * - a wrapped subset of the sink for which definitely no source could be found202 * - a wrapped subset of the sink for which possibly no source could be found203 */204struct isl_flow {205	isl_set			*must_no_source;206	isl_set			*may_no_source;207	int			n_source;208	struct isl_labeled_map	*dep;209};210 211/* Construct an isl_access_info structure and fill it up with212 * the given data.  The number of sources is set to 0.213 */214__isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,215	void *sink_user, isl_access_level_before fn, int max_source)216{217	isl_ctx *ctx;218	struct isl_access_info *acc;219 220	if (!sink)221		return NULL;222 223	ctx = isl_map_get_ctx(sink);224	isl_assert(ctx, max_source >= 0, goto error);225 226	acc = isl_calloc(ctx, struct isl_access_info,227			sizeof(struct isl_access_info) +228			(max_source - 1) * sizeof(struct isl_labeled_map));229	if (!acc)230		goto error;231 232	acc->sink.map = sink;233	acc->sink.data = sink_user;234	acc->level_before = fn;235	acc->max_source = max_source;236	acc->n_must = 0;237	acc->n_may = 0;238 239	return acc;240error:241	isl_map_free(sink);242	return NULL;243}244 245/* Free the given isl_access_info structure.246 */247__isl_null isl_access_info *isl_access_info_free(248	__isl_take isl_access_info *acc)249{250	int i;251 252	if (!acc)253		return NULL;254	isl_map_free(acc->domain_map);255	isl_map_free(acc->sink.map);256	for (i = 0; i < acc->n_must + acc->n_may; ++i)257		isl_map_free(acc->source[i].map);258	free(acc);259	return NULL;260}261 262isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)263{264	return acc ? isl_map_get_ctx(acc->sink.map) : NULL;265}266 267__isl_give isl_access_info *isl_access_info_set_restrict(268	__isl_take isl_access_info *acc, isl_access_restrict fn, void *user)269{270	if (!acc)271		return NULL;272	acc->restrict_fn = fn;273	acc->restrict_user = user;274	return acc;275}276 277/* Add another source to an isl_access_info structure, making278 * sure the "must" sources are placed before the "may" sources.279 * This function may be called at most max_source times on a280 * given isl_access_info structure, with max_source as specified281 * in the call to isl_access_info_alloc that constructed the structure.282 */283__isl_give isl_access_info *isl_access_info_add_source(284	__isl_take isl_access_info *acc, __isl_take isl_map *source,285	int must, void *source_user)286{287	isl_ctx *ctx;288 289	if (!acc)290		goto error;291	ctx = isl_map_get_ctx(acc->sink.map);292	isl_assert(ctx, acc->n_must + acc->n_may < acc->max_source, goto error);293	294	if (must) {295		if (acc->n_may)296			acc->source[acc->n_must + acc->n_may] =297				acc->source[acc->n_must];298		acc->source[acc->n_must].map = source;299		acc->source[acc->n_must].data = source_user;300		acc->source[acc->n_must].must = 1;301		acc->n_must++;302	} else {303		acc->source[acc->n_must + acc->n_may].map = source;304		acc->source[acc->n_must + acc->n_may].data = source_user;305		acc->source[acc->n_must + acc->n_may].must = 0;306		acc->n_may++;307	}308 309	return acc;310error:311	isl_map_free(source);312	isl_access_info_free(acc);313	return NULL;314}315 316/* A helper struct carrying the isl_access_info and an error condition.317 */318struct access_sort_info {319	isl_access_info *access_info;320	int error;321};322 323/* Return -n, 0 or n (with n a positive value), depending on whether324 * the source access identified by p1 should be sorted before, together325 * or after that identified by p2.326 *327 * If p1 appears before p2, then it should be sorted first.328 * For more generic initial schedules, it is possible that neither329 * p1 nor p2 appears before the other, or at least not in any obvious way.330 * We therefore also check if p2 appears before p1, in which case p2331 * should be sorted first.332 * If not, we try to order the two statements based on the description333 * of the iteration domains.  This results in an arbitrary, but fairly334 * stable ordering.335 *336 * In case of an error, sort_info.error is set to true and all elements are337 * reported to be equal.338 */339static int access_sort_cmp(const void *p1, const void *p2, void *user)340{341	struct access_sort_info *sort_info = user;342	isl_access_info *acc = sort_info->access_info;343 344	if (sort_info->error)345		return 0;346 347	const struct isl_labeled_map *i1, *i2;348	int level1, level2;349	uint32_t h1, h2;350	i1 = (const struct isl_labeled_map *) p1;351	i2 = (const struct isl_labeled_map *) p2;352 353	level1 = acc->level_before(i1->data, i2->data);354	if (level1 < 0)355		goto error;356	if (level1 % 2)357		return -1;358 359	level2 = acc->level_before(i2->data, i1->data);360	if (level2 < 0)361		goto error;362	if (level2 % 2)363		return 1;364 365	h1 = isl_map_get_hash(i1->map);366	h2 = isl_map_get_hash(i2->map);367	return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;368error:369	sort_info->error = 1;370	return 0;371}372 373/* Sort the must source accesses in their textual order.374 */375static __isl_give isl_access_info *isl_access_info_sort_sources(376	__isl_take isl_access_info *acc)377{378	struct access_sort_info sort_info;379 380	sort_info.access_info = acc;381	sort_info.error = 0;382 383	if (!acc)384		return NULL;385	if (acc->n_must <= 1)386		return acc;387 388	if (isl_sort(acc->source, acc->n_must, sizeof(struct isl_labeled_map),389		    access_sort_cmp, &sort_info) < 0)390		return isl_access_info_free(acc);391	if (sort_info.error)392		return isl_access_info_free(acc);393 394	return acc;395}396 397/* Align the parameters of the two spaces if needed and then call398 * isl_space_join.399 */400static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,401	__isl_take isl_space *right)402{403	isl_bool equal_params;404 405	equal_params = isl_space_has_equal_params(left, right);406	if (equal_params < 0)407		goto error;408	if (equal_params)409		return isl_space_join(left, right);410 411	left = isl_space_align_params(left, isl_space_copy(right));412	right = isl_space_align_params(right, isl_space_copy(left));413	return isl_space_join(left, right);414error:415	isl_space_free(left);416	isl_space_free(right);417	return NULL;418}419 420/* Initialize an empty isl_flow structure corresponding to a given421 * isl_access_info structure.422 * For each must access, two dependences are created (initialized423 * to the empty relation), one for the resulting must dependences424 * and one for the resulting may dependences.  May accesses can425 * only lead to may dependences, so only one dependence is created426 * for each of them.427 * This function is private as isl_flow structures are only supposed428 * to be created by isl_access_info_compute_flow.429 */430static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)431{432	int i, n;433	struct isl_ctx *ctx;434	struct isl_flow *dep;435 436	if (!acc)437		return NULL;438 439	ctx = isl_map_get_ctx(acc->sink.map);440	dep = isl_calloc_type(ctx, struct isl_flow);441	if (!dep)442		return NULL;443 444	n = 2 * acc->n_must + acc->n_may;445	dep->dep = isl_calloc_array(ctx, struct isl_labeled_map, n);446	if (n && !dep->dep)447		goto error;448 449	dep->n_source = n;450	for (i = 0; i < acc->n_must; ++i) {451		isl_space *space;452		space = space_align_and_join(453			isl_map_get_space(acc->source[i].map),454			isl_space_reverse(isl_map_get_space(acc->sink.map)));455		dep->dep[2 * i].map = isl_map_empty(space);456		dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);457		dep->dep[2 * i].data = acc->source[i].data;458		dep->dep[2 * i + 1].data = acc->source[i].data;459		dep->dep[2 * i].must = 1;460		dep->dep[2 * i + 1].must = 0;461		if (!dep->dep[2 * i].map || !dep->dep[2 * i + 1].map)462			goto error;463	}464	for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {465		isl_space *space;466		space = space_align_and_join(467			isl_map_get_space(acc->source[i].map),468			isl_space_reverse(isl_map_get_space(acc->sink.map)));469		dep->dep[acc->n_must + i].map = isl_map_empty(space);470		dep->dep[acc->n_must + i].data = acc->source[i].data;471		dep->dep[acc->n_must + i].must = 0;472		if (!dep->dep[acc->n_must + i].map)473			goto error;474	}475 476	return dep;477error:478	isl_flow_free(dep);479	return NULL;480}481 482/* Iterate over all sources and for each resulting flow dependence483 * that is not empty, call the user specfied function.484 * The second argument in this function call identifies the source,485 * while the third argument correspond to the final argument of486 * the isl_flow_foreach call.487 */488isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,489	isl_stat (*fn)(__isl_take isl_map *dep, int must, void *dep_user,490		void *user),491	void *user)492{493	int i;494 495	if (!deps)496		return isl_stat_error;497 498	for (i = 0; i < deps->n_source; ++i) {499		if (isl_map_plain_is_empty(deps->dep[i].map))500			continue;501		if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,502				deps->dep[i].data, user) < 0)503			return isl_stat_error;504	}505 506	return isl_stat_ok;507}508 509/* Return a copy of the subset of the sink for which no source could be found.510 */511__isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)512{513	if (!deps)514		return NULL;515	516	if (must)517		return isl_set_unwrap(isl_set_copy(deps->must_no_source));518	else519		return isl_set_unwrap(isl_set_copy(deps->may_no_source));520}521 522__isl_null isl_flow *isl_flow_free(__isl_take isl_flow *deps)523{524	int i;525 526	if (!deps)527		return NULL;528	isl_set_free(deps->must_no_source);529	isl_set_free(deps->may_no_source);530	if (deps->dep) {531		for (i = 0; i < deps->n_source; ++i)532			isl_map_free(deps->dep[i].map);533		free(deps->dep);534	}535	free(deps);536 537	return NULL;538}539 540isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)541{542	return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;543}544 545/* Return a map that enforces that the domain iteration occurs after546 * the range iteration at the given level.547 * If level is odd, then the domain iteration should occur after548 * the target iteration in their shared level/2 outermost loops.549 * In this case we simply need to enforce that these outermost550 * loop iterations are the same.551 * If level is even, then the loop iterator of the domain should552 * be greater than the loop iterator of the range at the last553 * of the level/2 shared loops, i.e., loop level/2 - 1.554 */555static __isl_give isl_map *after_at_level(__isl_take isl_space *space,556	int level)557{558	struct isl_basic_map *bmap;559 560	if (level % 2)561		bmap = isl_basic_map_equal(space, level/2);562	else563		bmap = isl_basic_map_more_at(space, level/2 - 1);564 565	return isl_map_from_basic_map(bmap);566}567 568/* Compute the partial lexicographic maximum of "dep" on domain "sink",569 * but first check if the user has set acc->restrict_fn and if so570 * update either the input or the output of the maximization problem571 * with respect to the resulting restriction.572 *573 * Since the user expects a mapping from sink iterations to source iterations,574 * whereas the domain of "dep" is a wrapped map, mapping sink iterations575 * to accessed array elements, we first need to project out the accessed576 * sink array elements by applying acc->domain_map.577 * Similarly, the sink restriction specified by the user needs to be578 * converted back to the wrapped map.579 */580static __isl_give isl_map *restricted_partial_lexmax(581	__isl_keep isl_access_info *acc, __isl_take isl_map *dep,582	int source, __isl_take isl_set *sink, __isl_give isl_set **empty)583{584	isl_map *source_map;585	isl_restriction *restr;586	isl_set *sink_domain;587	isl_set *sink_restr;588	isl_map *res;589 590	if (!acc->restrict_fn)591		return isl_map_partial_lexmax(dep, sink, empty);592 593	source_map = isl_map_copy(dep);594	source_map = isl_map_apply_domain(source_map,595					    isl_map_copy(acc->domain_map));596	sink_domain = isl_set_copy(sink);597	sink_domain = isl_set_apply(sink_domain, isl_map_copy(acc->domain_map));598	restr = acc->restrict_fn(source_map, sink_domain,599				acc->source[source].data, acc->restrict_user);600	isl_set_free(sink_domain);601	isl_map_free(source_map);602 603	if (!restr)604		goto error;605	if (restr->type == isl_restriction_type_input) {606		dep = isl_map_intersect_range(dep, isl_set_copy(restr->source));607		sink_restr = isl_set_copy(restr->sink);608		sink_restr = isl_set_apply(sink_restr,609				isl_map_reverse(isl_map_copy(acc->domain_map)));610		sink = isl_set_intersect(sink, sink_restr);611	} else if (restr->type == isl_restriction_type_empty) {612		isl_space *space = isl_map_get_space(dep);613		isl_map_free(dep);614		dep = isl_map_empty(space);615	}616 617	res = isl_map_partial_lexmax(dep, sink, empty);618 619	if (restr->type == isl_restriction_type_output)620		res = isl_map_intersect_range(res, isl_set_copy(restr->source));621 622	isl_restriction_free(restr);623	return res;624error:625	isl_map_free(dep);626	isl_set_free(sink);627	*empty = NULL;628	return NULL;629}630 631/* Compute the last iteration of must source j that precedes the sink632 * at the given level for sink iterations in set_C.633 * The subset of set_C for which no such iteration can be found is returned634 * in *empty.635 */636static struct isl_map *last_source(struct isl_access_info *acc, 637				    struct isl_set *set_C,638				    int j, int level, struct isl_set **empty)639{640	struct isl_map *read_map;641	struct isl_map *write_map;642	struct isl_map *dep_map;643	struct isl_map *after;644	struct isl_map *result;645 646	read_map = isl_map_copy(acc->sink.map);647	write_map = isl_map_copy(acc->source[j].map);648	write_map = isl_map_reverse(write_map);649	dep_map = isl_map_apply_range(read_map, write_map);650	after = after_at_level(isl_map_get_space(dep_map), level);651	dep_map = isl_map_intersect(dep_map, after);652	result = restricted_partial_lexmax(acc, dep_map, j, set_C, empty);653	result = isl_map_reverse(result);654 655	return result;656}657 658/* For a given mapping between iterations of must source j and iterations659 * of the sink, compute the last iteration of must source k preceding660 * the sink at level before_level for any of the sink iterations,661 * but following the corresponding iteration of must source j at level662 * after_level.663 */664static struct isl_map *last_later_source(struct isl_access_info *acc,665					 struct isl_map *old_map,666					 int j, int before_level,667					 int k, int after_level,668					 struct isl_set **empty)669{670	isl_space *space;671	struct isl_set *set_C;672	struct isl_map *read_map;673	struct isl_map *write_map;674	struct isl_map *dep_map;675	struct isl_map *after_write;676	struct isl_map *before_read;677	struct isl_map *result;678 679	set_C = isl_map_range(isl_map_copy(old_map));680	read_map = isl_map_copy(acc->sink.map);681	write_map = isl_map_copy(acc->source[k].map);682 683	write_map = isl_map_reverse(write_map);684	dep_map = isl_map_apply_range(read_map, write_map);685	space = space_align_and_join(isl_map_get_space(acc->source[k].map),686		    isl_space_reverse(isl_map_get_space(acc->source[j].map)));687	after_write = after_at_level(space, after_level);688	after_write = isl_map_apply_range(after_write, old_map);689	after_write = isl_map_reverse(after_write);690	dep_map = isl_map_intersect(dep_map, after_write);691	before_read = after_at_level(isl_map_get_space(dep_map), before_level);692	dep_map = isl_map_intersect(dep_map, before_read);693	result = restricted_partial_lexmax(acc, dep_map, k, set_C, empty);694	result = isl_map_reverse(result);695 696	return result;697}698 699/* Given a shared_level between two accesses, return 1 if the700 * the first can precede the second at the requested target_level.701 * If the target level is odd, i.e., refers to a statement level702 * dimension, then first needs to precede second at the requested703 * level, i.e., shared_level must be equal to target_level.704 * If the target level is odd, then the two loops should share705 * at least the requested number of outer loops.706 */707static int can_precede_at_level(int shared_level, int target_level)708{709	if (shared_level < target_level)710		return 0;711	if ((target_level % 2) && shared_level > target_level)712		return 0;713	return 1;714}715 716/* Given a possible flow dependence temp_rel[j] between source j and the sink717 * at level sink_level, remove those elements for which718 * there is an iteration of another source k < j that is closer to the sink.719 * The flow dependences temp_rel[k] are updated with the improved sources.720 * Any improved source needs to precede the sink at the same level721 * and needs to follow source j at the same or a deeper level.722 * The lower this level, the later the execution date of source k.723 * We therefore consider lower levels first.724 *725 * If temp_rel[j] is empty, then there can be no improvement and726 * we return immediately.727 *728 * This function returns isl_stat_ok in case it was executed successfully and729 * isl_stat_error in case of errors during the execution of this function.730 */731static isl_stat intermediate_sources(__isl_keep isl_access_info *acc,732	struct isl_map **temp_rel, int j, int sink_level)733{734	int k, level;735	isl_size n_in = isl_map_dim(acc->source[j].map, isl_dim_in);736	int depth = 2 * n_in + 1;737 738	if (n_in < 0)739		return isl_stat_error;740	if (isl_map_plain_is_empty(temp_rel[j]))741		return isl_stat_ok;742 743	for (k = j - 1; k >= 0; --k) {744		int plevel, plevel2;745		plevel = acc->level_before(acc->source[k].data, acc->sink.data);746		if (plevel < 0)747			return isl_stat_error;748		if (!can_precede_at_level(plevel, sink_level))749			continue;750 751		plevel2 = acc->level_before(acc->source[j].data,752						acc->source[k].data);753		if (plevel2 < 0)754			return isl_stat_error;755 756		for (level = sink_level; level <= depth; ++level) {757			struct isl_map *T;758			struct isl_set *trest;759			struct isl_map *copy;760 761			if (!can_precede_at_level(plevel2, level))762				continue;763 764			copy = isl_map_copy(temp_rel[j]);765			T = last_later_source(acc, copy, j, sink_level, k,766					      level, &trest);767			if (isl_map_plain_is_empty(T)) {768				isl_set_free(trest);769				isl_map_free(T);770				continue;771			}772			temp_rel[j] = isl_map_intersect_range(temp_rel[j], trest);773			temp_rel[k] = isl_map_union_disjoint(temp_rel[k], T);774		}775	}776 777	return isl_stat_ok;778}779 780/* Compute all iterations of may source j that precedes the sink at the given781 * level for sink iterations in set_C.782 */783static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,784				    __isl_take isl_set *set_C, int j, int level)785{786	isl_map *read_map;787	isl_map *write_map;788	isl_map *dep_map;789	isl_map *after;790 791	read_map = isl_map_copy(acc->sink.map);792	read_map = isl_map_intersect_domain(read_map, set_C);793	write_map = isl_map_copy(acc->source[acc->n_must + j].map);794	write_map = isl_map_reverse(write_map);795	dep_map = isl_map_apply_range(read_map, write_map);796	after = after_at_level(isl_map_get_space(dep_map), level);797	dep_map = isl_map_intersect(dep_map, after);798 799	return isl_map_reverse(dep_map);800}801 802/* For a given mapping between iterations of must source k and iterations803 * of the sink, compute all iterations of may source j preceding804 * the sink at level before_level for any of the sink iterations,805 * but following the corresponding iteration of must source k at level806 * after_level.807 */808static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,809	__isl_take isl_map *old_map,810	int j, int before_level, int k, int after_level)811{812	isl_space *space;813	isl_set *set_C;814	isl_map *read_map;815	isl_map *write_map;816	isl_map *dep_map;817	isl_map *after_write;818	isl_map *before_read;819 820	set_C = isl_map_range(isl_map_copy(old_map));821	read_map = isl_map_copy(acc->sink.map);822	read_map = isl_map_intersect_domain(read_map, set_C);823	write_map = isl_map_copy(acc->source[acc->n_must + j].map);824 825	write_map = isl_map_reverse(write_map);826	dep_map = isl_map_apply_range(read_map, write_map);827	space = isl_space_join(isl_map_get_space(828		    acc->source[acc->n_must + j].map),829		    isl_space_reverse(isl_map_get_space(acc->source[k].map)));830	after_write = after_at_level(space, after_level);831	after_write = isl_map_apply_range(after_write, old_map);832	after_write = isl_map_reverse(after_write);833	dep_map = isl_map_intersect(dep_map, after_write);834	before_read = after_at_level(isl_map_get_space(dep_map), before_level);835	dep_map = isl_map_intersect(dep_map, before_read);836	return isl_map_reverse(dep_map);837}838 839/* Given the must and may dependence relations for the must accesses840 * for level sink_level, check if there are any accesses of may access j841 * that occur in between and return their union.842 * If some of these accesses are intermediate with respect to843 * (previously thought to be) must dependences, then these844 * must dependences are turned into may dependences.845 */846static __isl_give isl_map *all_intermediate_sources(847	__isl_keep isl_access_info *acc, __isl_take isl_map *map,848	struct isl_map **must_rel, struct isl_map **may_rel,849	int j, int sink_level)850{851	int k, level;852	isl_size n_in = isl_map_dim(acc->source[acc->n_must + j].map,853				    isl_dim_in);854	int depth = 2 * n_in + 1;855 856	if (n_in < 0)857		return isl_map_free(map);858	for (k = 0; k < acc->n_must; ++k) {859		int plevel;860 861		if (isl_map_plain_is_empty(may_rel[k]) &&862		    isl_map_plain_is_empty(must_rel[k]))863			continue;864 865		plevel = acc->level_before(acc->source[k].data,866					acc->source[acc->n_must + j].data);867		if (plevel < 0)868			return isl_map_free(map);869 870		for (level = sink_level; level <= depth; ++level) {871			isl_map *T;872			isl_map *copy;873			isl_set *ran;874 875			if (!can_precede_at_level(plevel, level))876				continue;877 878			copy = isl_map_copy(may_rel[k]);879			T = all_later_sources(acc, copy, j, sink_level, k, level);880			map = isl_map_union(map, T);881 882			copy = isl_map_copy(must_rel[k]);883			T = all_later_sources(acc, copy, j, sink_level, k, level);884			ran = isl_map_range(isl_map_copy(T));885			map = isl_map_union(map, T);886			may_rel[k] = isl_map_union_disjoint(may_rel[k],887			    isl_map_intersect_range(isl_map_copy(must_rel[k]),888						    isl_set_copy(ran)));889			T = isl_map_from_domain_and_range(890			    isl_set_universe(891				isl_space_domain(isl_map_get_space(must_rel[k]))),892			    ran);893			must_rel[k] = isl_map_subtract(must_rel[k], T);894		}895	}896 897	return map;898}899 900/* Given a dependence relation "old_map" between a must-source and the sink,901 * return a subset of the dependences, augmented with instances902 * of the source at position "pos" in "acc" that are coscheduled903 * with the must-source and that access the same element.904 * That is, if the input lives in a space T -> K, then the output905 * lives in the space [T -> S] -> K, with S the space of source "pos", and906 * the domain factor of the domain product is a subset of the input.907 * The sources are considered to be coscheduled if they have the same values908 * for the initial "depth" coordinates.909 *910 * First construct a dependence relation S -> K and a mapping911 * between coscheduled sources T -> S.912 * The second is combined with the original dependence relation T -> K913 * to form a relation in T -> [S -> K], which is subsequently914 * uncurried to [T -> S] -> K.915 * This result is then intersected with the dependence relation S -> K916 * to form the output.917 *918 * In case a negative depth is given, NULL is returned to indicate an error.919 */920static __isl_give isl_map *coscheduled_source(__isl_keep isl_access_info *acc,921	__isl_keep isl_map *old_map, int pos, int depth)922{923	isl_space *space;924	isl_set *set_C;925	isl_map *read_map;926	isl_map *write_map;927	isl_map *dep_map;928	isl_map *equal;929	isl_map *map;930 931	if (depth < 0)932		return NULL;933 934	set_C = isl_map_range(isl_map_copy(old_map));935	read_map = isl_map_copy(acc->sink.map);936	read_map = isl_map_intersect_domain(read_map, set_C);937	write_map = isl_map_copy(acc->source[pos].map);938	dep_map = isl_map_domain_product(write_map, read_map);939	dep_map = isl_set_unwrap(isl_map_domain(dep_map));940	space = isl_space_join(isl_map_get_space(old_map),941				isl_space_reverse(isl_map_get_space(dep_map)));942	equal = isl_map_from_basic_map(isl_basic_map_equal(space, depth));943	map = isl_map_range_product(equal, isl_map_copy(old_map));944	map = isl_map_uncurry(map);945	map = isl_map_intersect_domain_factor_range(map, dep_map);946 947	return map;948}949 950/* After the dependences derived from a must-source have been computed951 * at a certain level, check if any of the sources of the must-dependences952 * may be coscheduled with other sources.953 * If they are any such sources, then there is no way of determining954 * which of the sources actually comes last and the must-dependences955 * need to be turned into may-dependences, while dependences from956 * the other sources need to be added to the may-dependences as well.957 * "acc" describes the sources and a callback for checking whether958 * two sources may be coscheduled.  If acc->coscheduled is NULL then959 * the sources are assumed not to be coscheduled.960 * "must_rel" and "may_rel" describe the must and may-dependence relations961 * computed at the current level for the must-sources.  Some of the dependences962 * may be moved from "must_rel" to "may_rel".963 * "flow" contains all dependences computed so far (apart from those964 * in "must_rel" and "may_rel") and may be updated with additional965 * dependences derived from may-sources.966 *967 * In particular, consider all the must-sources with a non-empty968 * dependence relation in "must_rel".  They are considered in reverse969 * order because that is the order in which they are considered in the caller.970 * If any of the must-sources are coscheduled, then the last one971 * is the one that will have a corresponding dependence relation.972 * For each must-source i, consider both all the previous must-sources973 * and all the may-sources.  If any of those may be coscheduled with974 * must-source i, then compute the coscheduled instances that access975 * the same memory elements.  The result is a relation [T -> S] -> K.976 * The projection onto T -> K is a subset of the must-dependence relation977 * that needs to be turned into may-dependences.978 * The projection onto S -> K needs to be added to the may-dependences979 * of source S.980 * Since a given must-source instance may be coscheduled with several981 * other source instances, the dependences that need to be turned982 * into may-dependences are first collected and only actually removed983 * from the must-dependences after all other sources have been considered.984 */985static __isl_give isl_flow *handle_coscheduled(__isl_keep isl_access_info *acc,986	__isl_keep isl_map **must_rel, __isl_keep isl_map **may_rel,987	__isl_take isl_flow *flow)988{989	int i, j;990 991	if (!acc->coscheduled)992		return flow;993	for (i = acc->n_must - 1; i >= 0; --i) {994		isl_map *move;995 996		if (isl_map_plain_is_empty(must_rel[i]))997			continue;998		move = isl_map_empty(isl_map_get_space(must_rel[i]));999		for (j = i - 1; j >= 0; --j) {1000			int depth;1001			isl_bool coscheduled;1002			isl_map *map, *factor;1003 1004			coscheduled = acc->coscheduled(acc->source[i].data,1005							acc->source[j].data);1006			if (coscheduled < 0) {1007				isl_map_free(move);1008				return isl_flow_free(flow);1009			}1010			if (!coscheduled)1011				continue;1012			depth = acc->level_before(acc->source[i].data,1013						acc->source[j].data) / 2;1014			map = coscheduled_source(acc, must_rel[i], j, depth);1015			factor = isl_map_domain_factor_range(isl_map_copy(map));1016			may_rel[j] = isl_map_union(may_rel[j], factor);1017			map = isl_map_domain_factor_domain(map);1018			move = isl_map_union(move, map);1019		}1020		for (j = 0; j < acc->n_may; ++j) {1021			int depth, pos;1022			isl_bool coscheduled;1023			isl_map *map, *factor;1024 1025			pos = acc->n_must + j;1026			coscheduled = acc->coscheduled(acc->source[i].data,1027							acc->source[pos].data);1028			if (coscheduled < 0) {1029				isl_map_free(move);1030				return isl_flow_free(flow);1031			}1032			if (!coscheduled)1033				continue;1034			depth = acc->level_before(acc->source[i].data,1035						acc->source[pos].data) / 2;1036			map = coscheduled_source(acc, must_rel[i], pos, depth);1037			factor = isl_map_domain_factor_range(isl_map_copy(map));1038			pos = 2 * acc->n_must + j;1039			flow->dep[pos].map = isl_map_union(flow->dep[pos].map,1040							    factor);1041			map = isl_map_domain_factor_domain(map);1042			move = isl_map_union(move, map);1043		}1044		must_rel[i] = isl_map_subtract(must_rel[i], isl_map_copy(move));1045		may_rel[i] = isl_map_union(may_rel[i], move);1046	}1047 1048	return flow;1049}1050 1051/* Compute dependences for the case where all accesses are "may"1052 * accesses, which boils down to computing memory based dependences.1053 * The generic algorithm would also work in this case, but it would1054 * be overkill to use it.1055 */1056static __isl_give isl_flow *compute_mem_based_dependences(1057	__isl_keep isl_access_info *acc)1058{1059	int i;1060	isl_set *mustdo;1061	isl_set *maydo;1062	isl_flow *res;1063 1064	res = isl_flow_alloc(acc);1065	if (!res)1066		return NULL;1067 1068	mustdo = isl_map_domain(isl_map_copy(acc->sink.map));1069	maydo = isl_set_copy(mustdo);1070 1071	for (i = 0; i < acc->n_may; ++i) {1072		int plevel;1073		int is_before;1074		isl_space *space;1075		isl_map *before;1076		isl_map *dep;1077 1078		plevel = acc->level_before(acc->source[i].data, acc->sink.data);1079		if (plevel < 0)1080			goto error;1081 1082		is_before = plevel & 1;1083		plevel >>= 1;1084 1085		space = isl_map_get_space(res->dep[i].map);1086		if (is_before)1087			before = isl_map_lex_le_first(space, plevel);1088		else1089			before = isl_map_lex_lt_first(space, plevel);1090		dep = isl_map_apply_range(isl_map_copy(acc->source[i].map),1091			isl_map_reverse(isl_map_copy(acc->sink.map)));1092		dep = isl_map_intersect(dep, before);1093		mustdo = isl_set_subtract(mustdo,1094					    isl_map_range(isl_map_copy(dep)));1095		res->dep[i].map = isl_map_union(res->dep[i].map, dep);1096	}1097 1098	res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));1099	res->must_no_source = mustdo;1100 1101	return res;1102error:1103	isl_set_free(mustdo);1104	isl_set_free(maydo);1105	isl_flow_free(res);1106	return NULL;1107}1108 1109/* Compute dependences for the case where there is at least one1110 * "must" access.1111 *1112 * The core algorithm considers all levels in which a source may precede1113 * the sink, where a level may either be a statement level or a loop level.1114 * The outermost statement level is 1, the first loop level is 2, etc...1115 * The algorithm basically does the following:1116 * for all levels l of the read access from innermost to outermost1117 *	for all sources w that may precede the sink access at that level1118 *	    compute the last iteration of the source that precedes the sink access1119 *					    at that level1120 *	    add result to possible last accesses at level l of source w1121 *	    for all sources w2 that we haven't considered yet at this level that may1122 *					    also precede the sink access1123 *		for all levels l2 of w from l to innermost1124 *		    for all possible last accesses dep of w at l1125 *			compute last iteration of w2 between the source and sink1126 *								of dep1127 *			add result to possible last accesses at level l of write w21128 *			and replace possible last accesses dep by the remainder1129 *1130 *1131 * The above algorithm is applied to the must access.  During the course1132 * of the algorithm, we keep track of sink iterations that still1133 * need to be considered.  These iterations are split into those that1134 * haven't been matched to any source access (mustdo) and those that have only1135 * been matched to may accesses (maydo).1136 * At the end of each level, must-sources and may-sources that are coscheduled1137 * with the sources of the must-dependences at that level are considered.1138 * If any coscheduled instances are found, then corresponding may-dependences1139 * are added and the original must-dependences are turned into may-dependences.1140 * Afterwards, the may accesses that occur after must-dependence sources1141 * are considered.1142 * In particular, we consider may accesses that precede the remaining1143 * sink iterations, moving elements from mustdo to maydo when appropriate,1144 * and may accesses that occur between a must source and a sink of any 1145 * dependences found at the current level, turning must dependences into1146 * may dependences when appropriate.1147 * 1148 */1149static __isl_give isl_flow *compute_val_based_dependences(1150	__isl_keep isl_access_info *acc)1151{1152	isl_ctx *ctx;1153	isl_flow *res;1154	isl_set *mustdo = NULL;1155	isl_set *maydo = NULL;1156	int level, j;1157	isl_size n_in;1158	int depth;1159	isl_map **must_rel = NULL;1160	isl_map **may_rel = NULL;1161 1162	if (!acc)1163		return NULL;1164 1165	res = isl_flow_alloc(acc);1166	if (!res)1167		goto error;1168	ctx = isl_map_get_ctx(acc->sink.map);1169 1170	n_in = isl_map_dim(acc->sink.map, isl_dim_in);1171	if (n_in < 0)1172		goto error;1173	depth = 2 * n_in + 1;1174	mustdo = isl_map_domain(isl_map_copy(acc->sink.map));1175	maydo = isl_set_empty(isl_set_get_space(mustdo));1176	if (!mustdo || !maydo)1177		goto error;1178	if (isl_set_plain_is_empty(mustdo))1179		goto done;1180 1181	must_rel = isl_calloc_array(ctx, struct isl_map *, acc->n_must);1182	may_rel = isl_calloc_array(ctx, struct isl_map *, acc->n_must);1183	if (!must_rel || !may_rel)1184		goto error;1185 1186	for (level = depth; level >= 1; --level) {1187		for (j = acc->n_must-1; j >=0; --j) {1188			isl_space *space;1189			space = isl_map_get_space(res->dep[2 * j].map);1190			must_rel[j] = isl_map_empty(space);1191			may_rel[j] = isl_map_copy(must_rel[j]);1192		}1193 1194		for (j = acc->n_must - 1; j >= 0; --j) {1195			struct isl_map *T;1196			struct isl_set *rest;1197			int plevel;1198 1199			plevel = acc->level_before(acc->source[j].data,1200						     acc->sink.data);1201			if (plevel < 0)1202				goto error;1203			if (!can_precede_at_level(plevel, level))1204				continue;1205 1206			T = last_source(acc, mustdo, j, level, &rest);1207			must_rel[j] = isl_map_union_disjoint(must_rel[j], T);1208			mustdo = rest;1209 1210			if (intermediate_sources(acc, must_rel, j, level) < 0)1211				goto error;1212 1213			T = last_source(acc, maydo, j, level, &rest);1214			may_rel[j] = isl_map_union_disjoint(may_rel[j], T);1215			maydo = rest;1216 1217			if (intermediate_sources(acc, may_rel, j, level) < 0)1218				goto error;1219 1220			if (isl_set_plain_is_empty(mustdo) &&1221			    isl_set_plain_is_empty(maydo))1222				break;1223		}1224		for (j = j - 1; j >= 0; --j) {1225			int plevel;1226 1227			plevel = acc->level_before(acc->source[j].data,1228						     acc->sink.data);1229			if (plevel < 0)1230				goto error;1231			if (!can_precede_at_level(plevel, level))1232				continue;1233 1234			if (intermediate_sources(acc, must_rel, j, level) < 0)1235				goto error;1236			if (intermediate_sources(acc, may_rel, j, level) < 0)1237				goto error;1238		}1239 1240		res = handle_coscheduled(acc, must_rel, may_rel, res);1241		if (!res)1242			goto error;1243 1244		for (j = 0; j < acc->n_may; ++j) {1245			int plevel;1246			isl_map *T;1247			isl_set *ran;1248 1249			plevel = acc->level_before(acc->source[acc->n_must + j].data,1250						     acc->sink.data);1251			if (plevel < 0)1252				goto error;1253			if (!can_precede_at_level(plevel, level))1254				continue;1255 1256			T = all_sources(acc, isl_set_copy(maydo), j, level);1257			res->dep[2 * acc->n_must + j].map =1258			    isl_map_union(res->dep[2 * acc->n_must + j].map, T);1259			T = all_sources(acc, isl_set_copy(mustdo), j, level);1260			ran = isl_map_range(isl_map_copy(T));1261			res->dep[2 * acc->n_must + j].map =1262			    isl_map_union(res->dep[2 * acc->n_must + j].map, T);1263			mustdo = isl_set_subtract(mustdo, isl_set_copy(ran));1264			maydo = isl_set_union_disjoint(maydo, ran);1265 1266			T = res->dep[2 * acc->n_must + j].map;1267			T = all_intermediate_sources(acc, T, must_rel, may_rel,1268							j, level);1269			res->dep[2 * acc->n_must + j].map = T;1270		}1271 1272		for (j = acc->n_must - 1; j >= 0; --j) {1273			res->dep[2 * j].map =1274				isl_map_union_disjoint(res->dep[2 * j].map,1275							     must_rel[j]);1276			res->dep[2 * j + 1].map =1277				isl_map_union_disjoint(res->dep[2 * j + 1].map,1278							     may_rel[j]);1279		}1280 1281		if (isl_set_plain_is_empty(mustdo) &&1282		    isl_set_plain_is_empty(maydo))1283			break;1284	}1285 1286	free(must_rel);1287	free(may_rel);1288done:1289	res->must_no_source = mustdo;1290	res->may_no_source = maydo;1291	return res;1292error:1293	if (must_rel)1294		for (j = 0; j < acc->n_must; ++j)1295			isl_map_free(must_rel[j]);1296	if (may_rel)1297		for (j = 0; j < acc->n_must; ++j)1298			isl_map_free(may_rel[j]);1299	isl_flow_free(res);1300	isl_set_free(mustdo);1301	isl_set_free(maydo);1302	free(must_rel);1303	free(may_rel);1304	return NULL;1305}1306 1307/* Given a "sink" access, a list of n "source" accesses,1308 * compute for each iteration of the sink access1309 * and for each element accessed by that iteration,1310 * the source access in the list that last accessed the1311 * element accessed by the sink access before this sink access.1312 * Each access is given as a map from the loop iterators1313 * to the array indices.1314 * The result is a list of n relations between source and sink1315 * iterations and a subset of the domain of the sink access,1316 * corresponding to those iterations that access an element1317 * not previously accessed.1318 *1319 * To deal with multi-valued sink access relations, the sink iteration1320 * domain is first extended with dimensions that correspond to the data1321 * space.  However, these extra dimensions are not projected out again.1322 * It is up to the caller to decide whether these dimensions should be kept.1323 */1324static __isl_give isl_flow *access_info_compute_flow_core(1325	__isl_take isl_access_info *acc)1326{1327	struct isl_flow *res = NULL;1328 1329	if (!acc)1330		return NULL;1331 1332	acc->sink.map = isl_map_range_map(acc->sink.map);1333	if (!acc->sink.map)1334		goto error;1335 1336	if (acc->n_must == 0)1337		res = compute_mem_based_dependences(acc);1338	else {1339		acc = isl_access_info_sort_sources(acc);1340		res = compute_val_based_dependences(acc);1341	}1342	acc = isl_access_info_free(acc);1343	if (!res)1344		return NULL;1345	if (!res->must_no_source || !res->may_no_source)1346		goto error;1347	return res;1348error:1349	isl_access_info_free(acc);1350	isl_flow_free(res);1351	return NULL;1352}1353 1354/* Given a "sink" access, a list of n "source" accesses,1355 * compute for each iteration of the sink access1356 * and for each element accessed by that iteration,1357 * the source access in the list that last accessed the1358 * element accessed by the sink access before this sink access.1359 * Each access is given as a map from the loop iterators1360 * to the array indices.1361 * The result is a list of n relations between source and sink1362 * iterations and a subset of the domain of the sink access,1363 * corresponding to those iterations that access an element1364 * not previously accessed.1365 *1366 * To deal with multi-valued sink access relations,1367 * access_info_compute_flow_core extends the sink iteration domain1368 * with dimensions that correspond to the data space.  These extra dimensions1369 * are projected out from the result of access_info_compute_flow_core.1370 */1371__isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)1372{1373	int j;1374	struct isl_flow *res;1375 1376	if (!acc)1377		return NULL;1378 1379	acc->domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));1380	res = access_info_compute_flow_core(acc);1381	if (!res)1382		return NULL;1383 1384	for (j = 0; j < res->n_source; ++j) {1385		res->dep[j].map = isl_map_range_factor_domain(res->dep[j].map);1386		if (!res->dep[j].map)1387			goto error;1388	}1389 1390	return res;1391error:1392	isl_flow_free(res);1393	return NULL;1394}1395 1396 1397/* Keep track of some information about a schedule for a given1398 * access.  In particular, keep track of which dimensions1399 * have a constant value and of the actual constant values.1400 */1401struct isl_sched_info {1402	int *is_cst;1403	isl_vec *cst;1404};1405 1406static void sched_info_free(__isl_take struct isl_sched_info *info)1407{1408	if (!info)1409		return;1410	isl_vec_free(info->cst);1411	free(info->is_cst);1412	free(info);1413}1414 1415/* Extract information on the constant dimensions of the schedule1416 * for a given access.  The "map" is of the form1417 *1418 *	[S -> D] -> A1419 *1420 * with S the schedule domain, D the iteration domain and A the data domain.1421 */1422static __isl_give struct isl_sched_info *sched_info_alloc(1423	__isl_keep isl_map *map)1424{1425	isl_ctx *ctx;1426	isl_space *space;1427	struct isl_sched_info *info;1428	int i;1429	isl_size n;1430 1431	if (!map)1432		return NULL;1433 1434	space = isl_space_unwrap(isl_space_domain(isl_map_get_space(map)));1435	if (!space)1436		return NULL;1437	n = isl_space_dim(space, isl_dim_in);1438	isl_space_free(space);1439	if (n < 0)1440		return NULL;1441 1442	ctx = isl_map_get_ctx(map);1443	info = isl_alloc_type(ctx, struct isl_sched_info);1444	if (!info)1445		return NULL;1446	info->is_cst = isl_alloc_array(ctx, int, n);1447	info->cst = isl_vec_alloc(ctx, n);1448	if (n && (!info->is_cst || !info->cst))1449		goto error;1450 1451	for (i = 0; i < n; ++i) {1452		isl_val *v;1453 1454		v = isl_map_plain_get_val_if_fixed(map, isl_dim_in, i);1455		if (!v)1456			goto error;1457		info->is_cst[i] = !isl_val_is_nan(v);1458		if (info->is_cst[i])1459			info->cst = isl_vec_set_element_val(info->cst, i, v);1460		else1461			isl_val_free(v);1462	}1463 1464	return info;1465error:1466	sched_info_free(info);1467	return NULL;1468}1469 1470/* The different types of access relations that isl_union_access_info1471 * keeps track of.1472 1473 * "isl_access_sink" represents the sink accesses.1474 * "isl_access_must_source" represents the definite source accesses.1475 * "isl_access_may_source" represents the possible source accesses.1476 * "isl_access_kill" represents the kills.1477 *1478 * isl_access_sink is sometimes treated differently and1479 * should therefore appear first.1480 */1481enum isl_access_type {1482	isl_access_sink,1483	isl_access_must_source,1484	isl_access_may_source,1485	isl_access_kill,1486	isl_access_end1487};1488 1489/* This structure represents the input for a dependence analysis computation.1490 *1491 * "access" contains the access relations.1492 *1493 * "schedule" or "schedule_map" represents the execution order.1494 * Exactly one of these fields should be NULL.  The other field1495 * determines the execution order.1496 *1497 * The domains of these four maps refer to the same iteration spaces(s).1498 * The ranges of the first three maps also refer to the same data space(s).1499 *1500 * After a call to isl_union_access_info_introduce_schedule,1501 * the "schedule_map" field no longer contains useful information.1502 */1503struct isl_union_access_info {1504	isl_union_map *access[isl_access_end];1505 1506	isl_schedule *schedule;1507	isl_union_map *schedule_map;1508};1509 1510/* Free "access" and return NULL.1511 */1512__isl_null isl_union_access_info *isl_union_access_info_free(1513	__isl_take isl_union_access_info *access)1514{1515	enum isl_access_type i;1516 1517	if (!access)1518		return NULL;1519 1520	for (i = isl_access_sink; i < isl_access_end; ++i)1521		isl_union_map_free(access->access[i]);1522	isl_schedule_free(access->schedule);1523	isl_union_map_free(access->schedule_map);1524	free(access);1525 1526	return NULL;1527}1528 1529/* Return the isl_ctx to which "access" belongs.1530 */1531isl_ctx *isl_union_access_info_get_ctx(__isl_keep isl_union_access_info *access)1532{1533	if (!access)1534		return NULL;1535	return isl_union_map_get_ctx(access->access[isl_access_sink]);1536}1537 1538/* Construct an empty (invalid) isl_union_access_info object.1539 * The caller is responsible for setting the sink access relation and1540 * initializing all the other fields, e.g., by calling1541 * isl_union_access_info_init.1542 */1543static __isl_give isl_union_access_info *isl_union_access_info_alloc(1544	isl_ctx *ctx)1545{1546	return isl_calloc_type(ctx, isl_union_access_info);1547}1548 1549/* Initialize all the fields of "info", except the sink access relation,1550 * which is assumed to have been set by the caller.1551 *1552 * By default, we use the schedule field of the isl_union_access_info,1553 * but this may be overridden by a call1554 * to isl_union_access_info_set_schedule_map.1555 */1556static __isl_give isl_union_access_info *isl_union_access_info_init(1557	__isl_take isl_union_access_info *info)1558{1559	isl_space *space;1560	isl_union_map *empty;1561	enum isl_access_type i;1562 1563	if (!info)1564		return NULL;1565	if (!info->access[isl_access_sink])1566		return isl_union_access_info_free(info);1567 1568	space = isl_union_map_get_space(info->access[isl_access_sink]);1569	empty = isl_union_map_empty(isl_space_copy(space));1570	for (i = isl_access_sink + 1; i < isl_access_end; ++i)1571		if (!info->access[i])1572			info->access[i] = isl_union_map_copy(empty);1573	isl_union_map_free(empty);1574	if (!info->schedule && !info->schedule_map)1575		info->schedule = isl_schedule_empty(isl_space_copy(space));1576	isl_space_free(space);1577 1578	for (i = isl_access_sink + 1; i < isl_access_end; ++i)1579		if (!info->access[i])1580			return isl_union_access_info_free(info);1581	if (!info->schedule && !info->schedule_map)1582		return isl_union_access_info_free(info);1583 1584	return info;1585}1586 1587/* Create a new isl_union_access_info with the given sink accesses and1588 * and no other accesses or schedule information.1589 */1590__isl_give isl_union_access_info *isl_union_access_info_from_sink(1591	__isl_take isl_union_map *sink)1592{1593	isl_ctx *ctx;1594	isl_union_access_info *access;1595 1596	if (!sink)1597		return NULL;1598	ctx = isl_union_map_get_ctx(sink);1599	access = isl_union_access_info_alloc(ctx);1600	if (!access)1601		goto error;1602	access->access[isl_access_sink] = sink;1603	return isl_union_access_info_init(access);1604error:1605	isl_union_map_free(sink);1606	return NULL;1607}1608 1609/* Replace the access relation of type "type" of "info" by "access".1610 */1611static __isl_give isl_union_access_info *isl_union_access_info_set(1612	__isl_take isl_union_access_info *info,1613	enum isl_access_type type, __isl_take isl_union_map *access)1614{1615	if (!info || !access)1616		goto error;1617 1618	isl_union_map_free(info->access[type]);1619	info->access[type] = access;1620 1621	return info;1622error:1623	isl_union_access_info_free(info);1624	isl_union_map_free(access);1625	return NULL;1626}1627 1628/* Replace the definite source accesses of "access" by "must_source".1629 */1630__isl_give isl_union_access_info *isl_union_access_info_set_must_source(1631	__isl_take isl_union_access_info *access,1632	__isl_take isl_union_map *must_source)1633{1634	return isl_union_access_info_set(access, isl_access_must_source,1635					must_source);1636}1637 1638/* Replace the possible source accesses of "access" by "may_source".1639 */1640__isl_give isl_union_access_info *isl_union_access_info_set_may_source(1641	__isl_take isl_union_access_info *access,1642	__isl_take isl_union_map *may_source)1643{1644	return isl_union_access_info_set(access, isl_access_may_source,1645					may_source);1646}1647 1648/* Replace the kills of "info" by "kill".1649 */1650__isl_give isl_union_access_info *isl_union_access_info_set_kill(1651	__isl_take isl_union_access_info *info, __isl_take isl_union_map *kill)1652{1653	return isl_union_access_info_set(info, isl_access_kill, kill);1654}1655 1656/* Return the access relation of type "type" of "info".1657 */1658static __isl_give isl_union_map *isl_union_access_info_get(1659	__isl_keep isl_union_access_info *info, enum isl_access_type type)1660{1661	if (!info)1662		return NULL;1663	return isl_union_map_copy(info->access[type]);1664}1665 1666/* Return the definite source accesses of "info".1667 */1668__isl_give isl_union_map *isl_union_access_info_get_must_source(1669	__isl_keep isl_union_access_info *info)1670{1671	return isl_union_access_info_get(info, isl_access_must_source);1672}1673 1674/* Return the possible source accesses of "info".1675 */1676__isl_give isl_union_map *isl_union_access_info_get_may_source(1677	__isl_keep isl_union_access_info *info)1678{1679	return isl_union_access_info_get(info, isl_access_may_source);1680}1681 1682/* Return the kills of "info".1683 */1684__isl_give isl_union_map *isl_union_access_info_get_kill(1685	__isl_keep isl_union_access_info *info)1686{1687	return isl_union_access_info_get(info, isl_access_kill);1688}1689 1690/* Does "info" specify any kills?1691 */1692static isl_bool isl_union_access_has_kill(1693	__isl_keep isl_union_access_info *info)1694{1695	isl_bool empty;1696 1697	if (!info)1698		return isl_bool_error;1699	empty = isl_union_map_is_empty(info->access[isl_access_kill]);1700	return isl_bool_not(empty);1701}1702 1703/* Replace the schedule of "access" by "schedule".1704 * Also free the schedule_map in case it was set last.1705 */1706__isl_give isl_union_access_info *isl_union_access_info_set_schedule(1707	__isl_take isl_union_access_info *access,1708	__isl_take isl_schedule *schedule)1709{1710	if (!access || !schedule)1711		goto error;1712 1713	access->schedule_map = isl_union_map_free(access->schedule_map);1714	isl_schedule_free(access->schedule);1715	access->schedule = schedule;1716 1717	return access;1718error:1719	isl_union_access_info_free(access);1720	isl_schedule_free(schedule);1721	return NULL;1722}1723 1724/* Replace the schedule map of "access" by "schedule_map".1725 * Also free the schedule in case it was set last.1726 */1727__isl_give isl_union_access_info *isl_union_access_info_set_schedule_map(1728	__isl_take isl_union_access_info *access,1729	__isl_take isl_union_map *schedule_map)1730{1731	if (!access || !schedule_map)1732		goto error;1733 1734	isl_union_map_free(access->schedule_map);1735	access->schedule = isl_schedule_free(access->schedule);1736	access->schedule_map = schedule_map;1737 1738	return access;1739error:1740	isl_union_access_info_free(access);1741	isl_union_map_free(schedule_map);1742	return NULL;1743}1744 1745__isl_give isl_union_access_info *isl_union_access_info_copy(1746	__isl_keep isl_union_access_info *access)1747{1748	isl_union_access_info *copy;1749	enum isl_access_type i;1750 1751	if (!access)1752		return NULL;1753	copy = isl_union_access_info_from_sink(1754		    isl_union_map_copy(access->access[isl_access_sink]));1755	for (i = isl_access_sink + 1; i < isl_access_end; ++i)1756		copy = isl_union_access_info_set(copy, i,1757					isl_union_map_copy(access->access[i]));1758	if (access->schedule)1759		copy = isl_union_access_info_set_schedule(copy,1760				isl_schedule_copy(access->schedule));1761	else1762		copy = isl_union_access_info_set_schedule_map(copy,1763				isl_union_map_copy(access->schedule_map));1764 1765	return copy;1766}1767 1768#undef BASE1769#define BASE union_map1770#include "print_yaml_field_templ.c"1771 1772/* An enumeration of the various keys that may appear in a YAML mapping1773 * of an isl_union_access_info object.1774 * The keys for the access relation types are assumed to have the same values1775 * as the access relation types in isl_access_type.1776 */1777enum isl_ai_key {1778	isl_ai_key_error = -1,1779	isl_ai_key_sink = isl_access_sink,1780	isl_ai_key_must_source = isl_access_must_source,1781	isl_ai_key_may_source = isl_access_may_source,1782	isl_ai_key_kill = isl_access_kill,1783	isl_ai_key_schedule_map,1784	isl_ai_key_schedule,1785	isl_ai_key_end1786};1787 1788/* Textual representations of the YAML keys for an isl_union_access_info1789 * object.1790 */1791static char *key_str[] = {1792	[isl_ai_key_sink] = "sink",1793	[isl_ai_key_must_source] = "must_source",1794	[isl_ai_key_may_source] = "may_source",1795	[isl_ai_key_kill] = "kill",1796	[isl_ai_key_schedule_map] = "schedule_map",1797	[isl_ai_key_schedule] = "schedule",1798};1799 1800/* Print a key-value pair corresponding to the access relation of type "type"1801 * of a YAML mapping of "info" to "p".1802 *1803 * The sink access relation is always printed, but any other access relation1804 * is only printed if it is non-empty.1805 */1806static __isl_give isl_printer *print_access_field(__isl_take isl_printer *p,1807	__isl_keep isl_union_access_info *info, enum isl_access_type type)1808{1809	if (type != isl_access_sink) {1810		isl_bool empty;1811 1812		empty = isl_union_map_is_empty(info->access[type]);1813		if (empty < 0)1814			return isl_printer_free(p);1815		if (empty)1816			return p;1817	}1818	return print_yaml_field_union_map(p, key_str[type], info->access[type]);1819}1820 1821/* Print the information contained in "access" to "p".1822 * The information is printed as a YAML document.1823 */1824__isl_give isl_printer *isl_printer_print_union_access_info(1825	__isl_take isl_printer *p, __isl_keep isl_union_access_info *access)1826{1827	enum isl_access_type i;1828 1829	if (!access)1830		return isl_printer_free(p);1831 1832	p = isl_printer_yaml_start_mapping(p);1833	for (i = isl_access_sink; i < isl_access_end; ++i)1834		p = print_access_field(p, access, i);1835	if (access->schedule) {1836		p = isl_printer_print_str(p, key_str[isl_ai_key_schedule]);1837		p = isl_printer_yaml_next(p);1838		p = isl_printer_print_schedule(p, access->schedule);1839		p = isl_printer_yaml_next(p);1840	} else {1841		p = print_yaml_field_union_map(p,1842			key_str[isl_ai_key_schedule_map], access->schedule_map);1843	}1844	p = isl_printer_yaml_end_mapping(p);1845 1846	return p;1847}1848 1849/* Return a string representation of the information in "access".1850 * The information is printed in flow format.1851 */1852__isl_give char *isl_union_access_info_to_str(1853	__isl_keep isl_union_access_info *access)1854{1855	isl_printer *p;1856	char *s;1857 1858	if (!access)1859		return NULL;1860 1861	p = isl_printer_to_str(isl_union_access_info_get_ctx(access));1862	p = isl_printer_set_yaml_style(p, ISL_YAML_STYLE_FLOW);1863	p = isl_printer_print_union_access_info(p, access);1864	s = isl_printer_get_str(p);1865	isl_printer_free(p);1866 1867	return s;1868}1869 1870#undef KEY1871#define KEY enum isl_ai_key1872#undef KEY_ERROR1873#define KEY_ERROR isl_ai_key_error1874#undef KEY_END1875#define KEY_END isl_ai_key_end1876#undef KEY_STR1877#define KEY_STR key_str1878#undef KEY_EXTRACT1879#define KEY_EXTRACT extract_key1880#undef KEY_GET1881#define KEY_GET get_key1882#include "extract_key.c"1883 1884#undef BASE1885#define BASE union_map1886#include "read_in_string_templ.c"1887 1888/* Read an isl_union_access_info object from "s".1889 *1890 * Start off with an empty (invalid) isl_union_access_info object and1891 * then fill up the fields based on the input.1892 * The input needs to contain at least a description of the sink1893 * access relation as well as some form of schedule.1894 * The other access relations are set to empty relations1895 * by isl_union_access_info_init if they are not specified in the input.1896 */1897__isl_give isl_union_access_info *isl_stream_read_union_access_info(1898	isl_stream *s)1899{1900	isl_ctx *ctx;1901	isl_union_access_info *info;1902	isl_bool more;1903	int sink_set = 0;1904	int schedule_set = 0;1905 1906	if (isl_stream_yaml_read_start_mapping(s) < 0)1907		return NULL;1908 1909	ctx = isl_stream_get_ctx(s);1910	info = isl_union_access_info_alloc(ctx);1911	while ((more = isl_stream_yaml_next(s)) == isl_bool_true) {1912		enum isl_ai_key key;1913		enum isl_access_type type;1914		isl_union_map *access, *schedule_map;1915		isl_schedule *schedule;1916 1917		key = get_key(s);1918		if (isl_stream_yaml_next(s) < 0)1919			return isl_union_access_info_free(info);1920		switch (key) {1921		case isl_ai_key_end:1922		case isl_ai_key_error:1923			return isl_union_access_info_free(info);1924		case isl_ai_key_sink:1925			sink_set = 1;1926		case isl_ai_key_must_source:1927		case isl_ai_key_may_source:1928		case isl_ai_key_kill:1929			type = (enum isl_access_type) key;1930			access = read_union_map(s);1931			info = isl_union_access_info_set(info, type, access);1932			if (!info)1933				return NULL;1934			break;1935		case isl_ai_key_schedule_map:1936			schedule_set = 1;1937			schedule_map = read_union_map(s);1938			info = isl_union_access_info_set_schedule_map(info,1939								schedule_map);1940			if (!info)1941				return NULL;1942			break;1943		case isl_ai_key_schedule:1944			schedule_set = 1;1945			schedule = isl_stream_read_schedule(s);1946			info = isl_union_access_info_set_schedule(info,1947								schedule);1948			if (!info)1949				return NULL;1950			break;1951		}1952	}1953	if (more < 0)1954		return isl_union_access_info_free(info);1955 1956	if (isl_stream_yaml_read_end_mapping(s) < 0)1957		return isl_union_access_info_free(info);1958 1959	if (!sink_set) {1960		isl_stream_error(s, NULL, "no sink specified");1961		return isl_union_access_info_free(info);1962	}1963 1964	if (!schedule_set) {1965		isl_stream_error(s, NULL, "no schedule specified");1966		return isl_union_access_info_free(info);1967	}1968 1969	return isl_union_access_info_init(info);1970}1971 1972/* Read an isl_union_access_info object from the file "input".1973 */1974__isl_give isl_union_access_info *isl_union_access_info_read_from_file(1975	isl_ctx *ctx, FILE *input)1976{1977	isl_stream *s;1978	isl_union_access_info *access;1979 1980	s = isl_stream_new_file(ctx, input);1981	if (!s)1982		return NULL;1983	access = isl_stream_read_union_access_info(s);1984	isl_stream_free(s);1985 1986	return access;1987}1988 1989/* Update the fields of "access" such that they all have the same parameters,1990 * keeping in mind that the schedule_map field may be NULL and ignoring1991 * the schedule field.1992 */1993static __isl_give isl_union_access_info *isl_union_access_info_align_params(1994	__isl_take isl_union_access_info *access)1995{1996	isl_space *space;1997	enum isl_access_type i;1998 1999	if (!access)2000		return NULL;2001 2002	space = isl_union_map_get_space(access->access[isl_access_sink]);2003	for (i = isl_access_sink + 1; i < isl_access_end; ++i)2004		space = isl_space_align_params(space,2005				isl_union_map_get_space(access->access[i]));2006	if (access->schedule_map)2007		space = isl_space_align_params(space,2008				isl_union_map_get_space(access->schedule_map));2009	for (i = isl_access_sink; i < isl_access_end; ++i)2010		access->access[i] =2011			isl_union_map_align_params(access->access[i],2012							isl_space_copy(space));2013	if (!access->schedule_map) {2014		isl_space_free(space);2015	} else {2016		access->schedule_map =2017		    isl_union_map_align_params(access->schedule_map, space);2018		if (!access->schedule_map)2019			return isl_union_access_info_free(access);2020	}2021 2022	for (i = isl_access_sink; i < isl_access_end; ++i)2023		if (!access->access[i])2024			return isl_union_access_info_free(access);2025 2026	return access;2027}2028 2029/* Prepend the schedule dimensions to the iteration domains.2030 *2031 * That is, if the schedule is of the form2032 *2033 *	D -> S2034 *2035 * while the access relations are of the form2036 *2037 *	D -> A2038 *2039 * then the updated access relations are of the form2040 *2041 *	[S -> D] -> A2042 *2043 * The schedule map is also replaced by the map2044 *2045 *	[S -> D] -> D2046 *2047 * that is used during the internal computation.2048 * Neither the original schedule map nor this updated schedule map2049 * are used after the call to this function.2050 */2051static __isl_give isl_union_access_info *2052isl_union_access_info_introduce_schedule(2053	__isl_take isl_union_access_info *access)2054{2055	isl_union_map *sm;2056	enum isl_access_type i;2057 2058	if (!access)2059		return NULL;2060 2061	sm = isl_union_map_reverse(access->schedule_map);2062	sm = isl_union_map_range_map(sm);2063	for (i = isl_access_sink; i < isl_access_end; ++i)2064		access->access[i] =2065			isl_union_map_apply_range(isl_union_map_copy(sm),2066						access->access[i]);2067	access->schedule_map = sm;2068 2069	for (i = isl_access_sink; i < isl_access_end; ++i)2070		if (!access->access[i])2071			return isl_union_access_info_free(access);2072	if (!access->schedule_map)2073		return isl_union_access_info_free(access);2074 2075	return access;2076}2077 2078/* This structure represents the result of a dependence analysis computation.2079 *2080 * "must_dep" represents the full definite dependences2081 * "may_dep" represents the full non-definite dependences.2082 * Both are of the form2083 *2084 *	[Source] -> [[Sink -> Data]]2085 *2086 * (after the schedule dimensions have been projected out).2087 * "must_no_source" represents the subset of the sink accesses for which2088 * definitely no source was found.2089 * "may_no_source" represents the subset of the sink accesses for which2090 * possibly, but not definitely, no source was found.2091 */2092struct isl_union_flow {2093	isl_union_map *must_dep;2094	isl_union_map *may_dep;2095	isl_union_map *must_no_source;2096	isl_union_map *may_no_source;2097};2098 2099/* Return the isl_ctx to which "flow" belongs.2100 */2101isl_ctx *isl_union_flow_get_ctx(__isl_keep isl_union_flow *flow)2102{2103	return flow ? isl_union_map_get_ctx(flow->must_dep) : NULL;2104}2105 2106/* Free "flow" and return NULL.2107 */2108__isl_null isl_union_flow *isl_union_flow_free(__isl_take isl_union_flow *flow)2109{2110	if (!flow)2111		return NULL;2112	isl_union_map_free(flow->must_dep);2113	isl_union_map_free(flow->may_dep);2114	isl_union_map_free(flow->must_no_source);2115	isl_union_map_free(flow->may_no_source);2116	free(flow);2117	return NULL;2118}2119 2120void isl_union_flow_dump(__isl_keep isl_union_flow *flow)2121{2122	if (!flow)2123		return;2124 2125	fprintf(stderr, "must dependences: ");2126	isl_union_map_dump(flow->must_dep);2127	fprintf(stderr, "may dependences: ");2128	isl_union_map_dump(flow->may_dep);2129	fprintf(stderr, "must no source: ");2130	isl_union_map_dump(flow->must_no_source);2131	fprintf(stderr, "may no source: ");2132	isl_union_map_dump(flow->may_no_source);2133}2134 2135/* Return the full definite dependences in "flow", with accessed elements.2136 */2137__isl_give isl_union_map *isl_union_flow_get_full_must_dependence(2138	__isl_keep isl_union_flow *flow)2139{2140	if (!flow)2141		return NULL;2142	return isl_union_map_copy(flow->must_dep);2143}2144 2145/* Return the full possible dependences in "flow", including the definite2146 * dependences, with accessed elements.2147 */2148__isl_give isl_union_map *isl_union_flow_get_full_may_dependence(2149	__isl_keep isl_union_flow *flow)2150{2151	if (!flow)2152		return NULL;2153	return isl_union_map_union(isl_union_map_copy(flow->must_dep),2154				    isl_union_map_copy(flow->may_dep));2155}2156 2157/* Return the definite dependences in "flow", without the accessed elements.2158 */2159__isl_give isl_union_map *isl_union_flow_get_must_dependence(2160	__isl_keep isl_union_flow *flow)2161{2162	isl_union_map *dep;2163 2164	if (!flow)2165		return NULL;2166	dep = isl_union_map_copy(flow->must_dep);2167	return isl_union_map_range_factor_domain(dep);2168}2169 2170/* Return the possible dependences in "flow", including the definite2171 * dependences, without the accessed elements.2172 */2173__isl_give isl_union_map *isl_union_flow_get_may_dependence(2174	__isl_keep isl_union_flow *flow)2175{2176	isl_union_map *dep;2177 2178	if (!flow)2179		return NULL;2180	dep = isl_union_map_union(isl_union_map_copy(flow->must_dep),2181				    isl_union_map_copy(flow->may_dep));2182	return isl_union_map_range_factor_domain(dep);2183}2184 2185/* Return the non-definite dependences in "flow".2186 */2187static __isl_give isl_union_map *isl_union_flow_get_non_must_dependence(2188	__isl_keep isl_union_flow *flow)2189{2190	if (!flow)2191		return NULL;2192	return isl_union_map_copy(flow->may_dep);2193}2194 2195/* Return the subset of the sink accesses for which definitely2196 * no source was found.2197 */2198__isl_give isl_union_map *isl_union_flow_get_must_no_source(2199	__isl_keep isl_union_flow *flow)2200{2201	if (!flow)2202		return NULL;2203	return isl_union_map_copy(flow->must_no_source);2204}2205 2206/* Return the subset of the sink accesses for which possibly2207 * no source was found, including those for which definitely2208 * no source was found.2209 */2210__isl_give isl_union_map *isl_union_flow_get_may_no_source(2211	__isl_keep isl_union_flow *flow)2212{2213	if (!flow)2214		return NULL;2215	return isl_union_map_union(isl_union_map_copy(flow->must_no_source),2216				    isl_union_map_copy(flow->may_no_source));2217}2218 2219/* Return the subset of the sink accesses for which possibly, but not2220 * definitely, no source was found.2221 */2222static __isl_give isl_union_map *isl_union_flow_get_non_must_no_source(2223	__isl_keep isl_union_flow *flow)2224{2225	if (!flow)2226		return NULL;2227	return isl_union_map_copy(flow->may_no_source);2228}2229 2230/* Create a new isl_union_flow object, initialized with empty2231 * dependence relations and sink subsets.2232 */2233static __isl_give isl_union_flow *isl_union_flow_alloc(2234	__isl_take isl_space *space)2235{2236	isl_ctx *ctx;2237	isl_union_map *empty;2238	isl_union_flow *flow;2239 2240	if (!space)2241		return NULL;2242	ctx = isl_space_get_ctx(space);2243	flow = isl_alloc_type(ctx, isl_union_flow);2244	if (!flow)2245		goto error;2246 2247	empty = isl_union_map_empty(space);2248	flow->must_dep = isl_union_map_copy(empty);2249	flow->may_dep = isl_union_map_copy(empty);2250	flow->must_no_source = isl_union_map_copy(empty);2251	flow->may_no_source = empty;2252 2253	if (!flow->must_dep || !flow->may_dep ||2254	    !flow->must_no_source || !flow->may_no_source)2255		return isl_union_flow_free(flow);2256 2257	return flow;2258error:2259	isl_space_free(space);2260	return NULL;2261}2262 2263/* Copy this isl_union_flow object.2264 */2265__isl_give isl_union_flow *isl_union_flow_copy(__isl_keep isl_union_flow *flow)2266{2267	isl_union_flow *copy;2268 2269	if (!flow)2270		return NULL;2271 2272	copy = isl_union_flow_alloc(isl_union_map_get_space(flow->must_dep));2273 2274	if (!copy)2275		return NULL;2276 2277	copy->must_dep = isl_union_map_union(copy->must_dep,2278		isl_union_map_copy(flow->must_dep));2279	copy->may_dep = isl_union_map_union(copy->may_dep,2280		isl_union_map_copy(flow->may_dep));2281	copy->must_no_source = isl_union_map_union(copy->must_no_source,2282		isl_union_map_copy(flow->must_no_source));2283	copy->may_no_source = isl_union_map_union(copy->may_no_source,2284		isl_union_map_copy(flow->may_no_source));2285 2286	if (!copy->must_dep || !copy->may_dep ||2287	    !copy->must_no_source || !copy->may_no_source)2288		return isl_union_flow_free(copy);2289 2290	return copy;2291}2292 2293/* Drop the schedule dimensions from the iteration domains in "flow".2294 * In particular, the schedule dimensions have been prepended2295 * to the iteration domains prior to the dependence analysis by2296 * replacing the iteration domain D, by the wrapped map [S -> D].2297 * Replace these wrapped maps by the original D.2298 *2299 * In particular, the dependences computed by access_info_compute_flow_core2300 * are of the form2301 *2302 *	[S -> D] -> [[S' -> D'] -> A]2303 *2304 * The schedule dimensions are projected out by first currying the range,2305 * resulting in2306 *2307 *	[S -> D] -> [S' -> [D' -> A]]2308 *2309 * and then computing the factor range2310 *2311 *	D -> [D' -> A]2312 */2313static __isl_give isl_union_flow *isl_union_flow_drop_schedule(2314	__isl_take isl_union_flow *flow)2315{2316	if (!flow)2317		return NULL;2318 2319	flow->must_dep = isl_union_map_range_curry(flow->must_dep);2320	flow->must_dep = isl_union_map_factor_range(flow->must_dep);2321	flow->may_dep = isl_union_map_range_curry(flow->may_dep);2322	flow->may_dep = isl_union_map_factor_range(flow->may_dep);2323	flow->must_no_source =2324		isl_union_map_domain_factor_range(flow->must_no_source);2325	flow->may_no_source =2326		isl_union_map_domain_factor_range(flow->may_no_source);2327 2328	if (!flow->must_dep || !flow->may_dep ||2329	    !flow->must_no_source || !flow->may_no_source)2330		return isl_union_flow_free(flow);2331 2332	return flow;2333}2334 2335struct isl_compute_flow_data {2336	isl_union_map *must_source;2337	isl_union_map *may_source;2338	isl_union_flow *flow;2339 2340	int count;2341	int must;2342	isl_space *dim;2343	struct isl_sched_info *sink_info;2344	struct isl_sched_info **source_info;2345	isl_access_info *accesses;2346};2347 2348static isl_stat count_matching_array(__isl_take isl_map *map, void *user)2349{2350	int eq;2351	isl_space *space;2352	struct isl_compute_flow_data *data;2353 2354	data = (struct isl_compute_flow_data *)user;2355 2356	space = isl_space_range(isl_map_get_space(map));2357 2358	eq = isl_space_is_equal(space, data->dim);2359 2360	isl_space_free(space);2361	isl_map_free(map);2362 2363	if (eq < 0)2364		return isl_stat_error;2365	if (eq)2366		data->count++;2367 2368	return isl_stat_ok;2369}2370 2371static isl_stat collect_matching_array(__isl_take isl_map *map, void *user)2372{2373	int eq;2374	isl_space *space;2375	struct isl_sched_info *info;2376	struct isl_compute_flow_data *data;2377 2378	data = (struct isl_compute_flow_data *)user;2379 2380	space = isl_space_range(isl_map_get_space(map));2381 2382	eq = isl_space_is_equal(space, data->dim);2383 2384	isl_space_free(space);2385 2386	if (eq < 0)2387		goto error;2388	if (!eq) {2389		isl_map_free(map);2390		return isl_stat_ok;2391	}2392 2393	info = sched_info_alloc(map);2394	data->source_info[data->count] = info;2395 2396	data->accesses = isl_access_info_add_source(data->accesses,2397						    map, data->must, info);2398 2399	data->count++;2400 2401	return isl_stat_ok;2402error:2403	isl_map_free(map);2404	return isl_stat_error;2405}2406 2407/* Determine the shared nesting level and the "textual order" of2408 * the given accesses.2409 *2410 * We first determine the minimal schedule dimension for both accesses.2411 *2412 * If among those dimensions, we can find one where both have a fixed2413 * value and if moreover those values are different, then the previous2414 * dimension is the last shared nesting level and the textual order2415 * is determined based on the order of the fixed values.2416 * If no such fixed values can be found, then we set the shared2417 * nesting level to the minimal schedule dimension, with no textual ordering.2418 */2419static int before(void *first, void *second)2420{2421	struct isl_sched_info *info1 = first;2422	struct isl_sched_info *info2 = second;2423	isl_size n1, n2;2424	int i;2425 2426	n1 = isl_vec_size(info1->cst);2427	n2 = isl_vec_size(info2->cst);2428	if (n1 < 0 || n2 < 0)2429		return -1;2430 2431	if (n2 < n1)2432		n1 = n2;2433 2434	for (i = 0; i < n1; ++i) {2435		int r;2436		int cmp;2437 2438		if (!info1->is_cst[i])2439			continue;2440		if (!info2->is_cst[i])2441			continue;2442		cmp = isl_vec_cmp_element(info1->cst, info2->cst, i);2443		if (cmp == 0)2444			continue;2445 2446		r = 2 * i + (cmp < 0);2447 2448		return r;2449	}2450 2451	return 2 * n1;2452}2453 2454/* Check if the given two accesses may be coscheduled.2455 * If so, return isl_bool_true.  Otherwise return isl_bool_false.2456 *2457 * Two accesses may only be coscheduled if the fixed schedule2458 * coordinates have the same values.2459 */2460static isl_bool coscheduled(void *first, void *second)2461{2462	struct isl_sched_info *info1 = first;2463	struct isl_sched_info *info2 = second;2464	isl_size n1, n2;2465	int i;2466 2467	n1 = isl_vec_size(info1->cst);2468	n2 = isl_vec_size(info2->cst);2469	if (n1 < 0 || n2 < 0)2470		return isl_bool_error;2471 2472	if (n2 < n1)2473		n1 = n2;2474 2475	for (i = 0; i < n1; ++i) {2476		int cmp;2477 2478		if (!info1->is_cst[i])2479			continue;2480		if (!info2->is_cst[i])2481			continue;2482		cmp = isl_vec_cmp_element(info1->cst, info2->cst, i);2483		if (cmp != 0)2484			return isl_bool_false;2485	}2486 2487	return isl_bool_true;2488}2489 2490/* Given a sink access, look for all the source accesses that access2491 * the same array and perform dataflow analysis on them using2492 * isl_access_info_compute_flow_core.2493 */2494static isl_stat compute_flow(__isl_take isl_map *map, void *user)2495{2496	int i;2497	isl_ctx *ctx;2498	struct isl_compute_flow_data *data;2499	isl_flow *flow;2500	isl_union_flow *df;2501 2502	data = (struct isl_compute_flow_data *)user;2503	df = data->flow;2504 2505	ctx = isl_map_get_ctx(map);2506 2507	data->accesses = NULL;2508	data->sink_info = NULL;2509	data->source_info = NULL;2510	data->count = 0;2511	data->dim = isl_space_range(isl_map_get_space(map));2512 2513	if (isl_union_map_foreach_map(data->must_source,2514					&count_matching_array, data) < 0)2515		goto error;2516	if (isl_union_map_foreach_map(data->may_source,2517					&count_matching_array, data) < 0)2518		goto error;2519 2520	data->sink_info = sched_info_alloc(map);2521	data->source_info = isl_calloc_array(ctx, struct isl_sched_info *,2522					     data->count);2523 2524	data->accesses = isl_access_info_alloc(isl_map_copy(map),2525				data->sink_info, &before, data->count);2526	if (!data->sink_info || (data->count && !data->source_info) ||2527	    !data->accesses)2528		goto error;2529	data->accesses->coscheduled = &coscheduled;2530	data->count = 0;2531	data->must = 1;2532	if (isl_union_map_foreach_map(data->must_source,2533					&collect_matching_array, data) < 0)2534		goto error;2535	data->must = 0;2536	if (isl_union_map_foreach_map(data->may_source,2537					&collect_matching_array, data) < 0)2538		goto error;2539 2540	flow = access_info_compute_flow_core(data->accesses);2541	data->accesses = NULL;2542 2543	if (!flow)2544		goto error;2545 2546	df->must_no_source = isl_union_map_union(df->must_no_source,2547		    isl_union_map_from_map(isl_flow_get_no_source(flow, 1)));2548	df->may_no_source = isl_union_map_union(df->may_no_source,2549		    isl_union_map_from_map(isl_flow_get_no_source(flow, 0)));2550 2551	for (i = 0; i < flow->n_source; ++i) {2552		isl_union_map *dep;2553		dep = isl_union_map_from_map(isl_map_copy(flow->dep[i].map));2554		if (flow->dep[i].must)2555			df->must_dep = isl_union_map_union(df->must_dep, dep);2556		else2557			df->may_dep = isl_union_map_union(df->may_dep, dep);2558	}2559 2560	isl_flow_free(flow);2561 2562	sched_info_free(data->sink_info);2563	if (data->source_info) {2564		for (i = 0; i < data->count; ++i)2565			sched_info_free(data->source_info[i]);2566		free(data->source_info);2567	}2568	isl_space_free(data->dim);2569	isl_map_free(map);2570 2571	return isl_stat_ok;2572error:2573	isl_access_info_free(data->accesses);2574	sched_info_free(data->sink_info);2575	if (data->source_info) {2576		for (i = 0; i < data->count; ++i)2577			sched_info_free(data->source_info[i]);2578		free(data->source_info);2579	}2580	isl_space_free(data->dim);2581	isl_map_free(map);2582 2583	return isl_stat_error;2584}2585 2586/* Add the kills of "info" to the must-sources.2587 */2588static __isl_give isl_union_access_info *2589isl_union_access_info_add_kill_to_must_source(2590	__isl_take isl_union_access_info *info)2591{2592	isl_union_map *must, *kill;2593 2594	must = isl_union_access_info_get_must_source(info);2595	kill = isl_union_access_info_get_kill(info);2596	must = isl_union_map_union(must, kill);2597	return isl_union_access_info_set_must_source(info, must);2598}2599 2600/* Drop dependences from "flow" that purely originate from kills.2601 * That is, only keep those dependences that originate from2602 * the original must-sources "must" and/or the original may-sources "may".2603 * In particular, "must" contains the must-sources from before2604 * the kills were added and "may" contains the may-source from before2605 * the kills were removed.2606 *2607 * The dependences are of the form2608 *2609 *	Source -> [Sink -> Data]2610 *2611 * Only those dependences are kept where the Source -> Data part2612 * is a subset of the original may-sources or must-sources.2613 * Of those, only the must-dependences that intersect with the must-sources2614 * remain must-dependences.2615 * If there is some overlap between the may-sources and the must-sources,2616 * then the may-dependences and must-dependences may also overlap.2617 * This should be fine since the may-dependences are only kept2618 * disjoint from the must-dependences for the isl_union_map_compute_flow2619 * interface.  This interface does not support kills, so it will2620 * not end up calling this function.2621 */2622static __isl_give isl_union_flow *isl_union_flow_drop_kill_source(2623	__isl_take isl_union_flow *flow, __isl_take isl_union_map *must,2624	__isl_take isl_union_map *may)2625{2626	isl_union_map *move;2627 2628	if (!flow)2629		goto error;2630	move = isl_union_map_copy(flow->must_dep);2631	move = isl_union_map_intersect_range_factor_range(move,2632				isl_union_map_copy(may));2633	may = isl_union_map_union(may, isl_union_map_copy(must));2634	flow->may_dep = isl_union_map_intersect_range_factor_range(2635				flow->may_dep, may);2636	flow->must_dep = isl_union_map_intersect_range_factor_range(2637				flow->must_dep, must);2638	flow->may_dep = isl_union_map_union(flow->may_dep, move);2639	if (!flow->must_dep || !flow->may_dep)2640		return isl_union_flow_free(flow);2641 2642	return flow;2643error:2644	isl_union_map_free(must);2645	isl_union_map_free(may);2646	return NULL;2647}2648 2649/* Remove the must accesses from the may accesses.2650 *2651 * A must access always trumps a may access, so there is no need2652 * for a must access to also be considered as a may access.  Doing so2653 * would only cost extra computations only to find out that2654 * the duplicated may access does not make any difference.2655 */2656static __isl_give isl_union_access_info *isl_union_access_info_normalize(2657	__isl_take isl_union_access_info *access)2658{2659	if (!access)2660		return NULL;2661	access->access[isl_access_may_source] =2662		isl_union_map_subtract(access->access[isl_access_may_source],2663		    isl_union_map_copy(access->access[isl_access_must_source]));2664	if (!access->access[isl_access_may_source])2665		return isl_union_access_info_free(access);2666 2667	return access;2668}2669 2670/* Given a description of the "sink" accesses, the "source" accesses and2671 * a schedule, compute for each instance of a sink access2672 * and for each element accessed by that instance,2673 * the possible or definite source accesses that last accessed the2674 * element accessed by the sink access before this sink access2675 * in the sense that there is no intermediate definite source access.2676 *2677 * The must_no_source and may_no_source elements of the result2678 * are subsets of access->sink.  The elements must_dep and may_dep2679 * map domain elements of access->{may,must)_source to2680 * domain elements of access->sink.2681 *2682 * This function is used when only the schedule map representation2683 * is available.2684 *2685 * We first prepend the schedule dimensions to the domain2686 * of the accesses so that we can easily compare their relative order.2687 * Then we consider each sink access individually in compute_flow.2688 */2689static __isl_give isl_union_flow *compute_flow_union_map(2690	__isl_take isl_union_access_info *access)2691{2692	struct isl_compute_flow_data data;2693	isl_union_map *sink;2694 2695	access = isl_union_access_info_align_params(access);2696	access = isl_union_access_info_introduce_schedule(access);2697	if (!access)2698		return NULL;2699 2700	data.must_source = access->access[isl_access_must_source];2701	data.may_source = access->access[isl_access_may_source];2702 2703	sink = access->access[isl_access_sink];2704	data.flow = isl_union_flow_alloc(isl_union_map_get_space(sink));2705 2706	if (isl_union_map_foreach_map(sink, &compute_flow, &data) < 0)2707		goto error;2708 2709	data.flow = isl_union_flow_drop_schedule(data.flow);2710 2711	isl_union_access_info_free(access);2712	return data.flow;2713error:2714	isl_union_access_info_free(access);2715	isl_union_flow_free(data.flow);2716	return NULL;2717}2718 2719/* A schedule access relation.2720 *2721 * The access relation "access" is of the form [S -> D] -> A,2722 * where S corresponds to the prefix schedule at "node".2723 * "must" is only relevant for source accesses and indicates2724 * whether the access is a must source or a may source.2725 */2726struct isl_scheduled_access {2727	isl_map *access;2728	int must;2729	isl_schedule_node *node;2730};2731 2732/* Data structure for keeping track of individual scheduled sink and source2733 * accesses when computing dependence analysis based on a schedule tree.2734 *2735 * "n_sink" is the number of used entries in "sink"2736 * "n_source" is the number of used entries in "source"2737 *2738 * "set_sink", "must" and "node" are only used inside collect_sink_source,2739 * to keep track of the current node and2740 * of what extract_sink_source needs to do.2741 */2742struct isl_compute_flow_schedule_data {2743	isl_union_access_info *access;2744 2745	int n_sink;2746	int n_source;2747 2748	struct isl_scheduled_access *sink;2749	struct isl_scheduled_access *source;2750 2751	int set_sink;2752	int must;2753	isl_schedule_node *node;2754};2755 2756/* Align the parameters of all sinks with all sources.2757 *2758 * If there are no sinks or no sources, then no alignment is needed.2759 */2760static void isl_compute_flow_schedule_data_align_params(2761	struct isl_compute_flow_schedule_data *data)2762{2763	int i;2764	isl_space *space;2765 2766	if (data->n_sink == 0 || data->n_source == 0)2767		return;2768 2769	space = isl_map_get_space(data->sink[0].access);2770 2771	for (i = 1; i < data->n_sink; ++i)2772		space = isl_space_align_params(space,2773				isl_map_get_space(data->sink[i].access));2774	for (i = 0; i < data->n_source; ++i)2775		space = isl_space_align_params(space,2776				isl_map_get_space(data->source[i].access));2777 2778	for (i = 0; i < data->n_sink; ++i)2779		data->sink[i].access =2780			isl_map_align_params(data->sink[i].access,2781							isl_space_copy(space));2782	for (i = 0; i < data->n_source; ++i)2783		data->source[i].access =2784			isl_map_align_params(data->source[i].access,2785							isl_space_copy(space));2786 2787	isl_space_free(space);2788}2789 2790/* Free all the memory referenced from "data".2791 * Do not free "data" itself as it may be allocated on the stack.2792 */2793static void isl_compute_flow_schedule_data_clear(2794	struct isl_compute_flow_schedule_data *data)2795{2796	int i;2797 2798	if (!data->sink)2799		return;2800 2801	for (i = 0; i < data->n_sink; ++i) {2802		isl_map_free(data->sink[i].access);2803		isl_schedule_node_free(data->sink[i].node);2804	}2805 2806	for (i = 0; i < data->n_source; ++i) {2807		isl_map_free(data->source[i].access);2808		isl_schedule_node_free(data->source[i].node);2809	}2810 2811	free(data->sink);2812}2813 2814/* isl_schedule_foreach_schedule_node_top_down callback for counting2815 * (an upper bound on) the number of sinks and sources.2816 *2817 * Sinks and sources are only extracted at leaves of the tree,2818 * so we skip the node if it is not a leaf.2819 * Otherwise we increment data->n_sink and data->n_source with2820 * the number of spaces in the sink and source access domains2821 * that reach this node.2822 */2823static isl_bool count_sink_source(__isl_keep isl_schedule_node *node,2824	void *user)2825{2826	struct isl_compute_flow_schedule_data *data = user;2827	isl_union_set *domain;2828	isl_union_map *umap;2829	isl_bool r = isl_bool_false;2830	isl_size n;2831 2832	if (isl_schedule_node_get_type(node) != isl_schedule_node_leaf)2833		return isl_bool_true;2834 2835	domain = isl_schedule_node_get_universe_domain(node);2836 2837	umap = isl_union_map_copy(data->access->access[isl_access_sink]);2838	umap = isl_union_map_intersect_domain(umap, isl_union_set_copy(domain));2839	data->n_sink += n = isl_union_map_n_map(umap);2840	isl_union_map_free(umap);2841	if (n < 0)2842		r = isl_bool_error;2843 2844	umap = isl_union_map_copy(data->access->access[isl_access_must_source]);2845	umap = isl_union_map_intersect_domain(umap, isl_union_set_copy(domain));2846	data->n_source += n = isl_union_map_n_map(umap);2847	isl_union_map_free(umap);2848	if (n < 0)2849		r = isl_bool_error;2850 2851	umap = isl_union_map_copy(data->access->access[isl_access_may_source]);2852	umap = isl_union_map_intersect_domain(umap, isl_union_set_copy(domain));2853	data->n_source += n = isl_union_map_n_map(umap);2854	isl_union_map_free(umap);2855	if (n < 0)2856		r = isl_bool_error;2857 2858	isl_union_set_free(domain);2859 2860	return r;2861}2862 2863/* Add a single scheduled sink or source (depending on data->set_sink)2864 * with scheduled access relation "map", must property data->must and2865 * schedule node data->node to the list of sinks or sources.2866 */2867static isl_stat extract_sink_source(__isl_take isl_map *map, void *user)2868{2869	struct isl_compute_flow_schedule_data *data = user;2870	struct isl_scheduled_access *access;2871 2872	if (data->set_sink)2873		access = data->sink + data->n_sink++;2874	else2875		access = data->source + data->n_source++;2876 2877	access->access = map;2878	access->must = data->must;2879	access->node = isl_schedule_node_copy(data->node);2880 2881	return isl_stat_ok;2882}2883 2884/* isl_schedule_foreach_schedule_node_top_down callback for collecting2885 * individual scheduled source and sink accesses (taking into account2886 * the domain of the schedule).2887 *2888 * We only collect accesses at the leaves of the schedule tree.2889 * We prepend the schedule dimensions at the leaf to the iteration2890 * domains of the source and sink accesses and then extract2891 * the individual accesses (per space).2892 *2893 * In particular, if the prefix schedule at the node is of the form2894 *2895 *	D -> S2896 *2897 * while the access relations are of the form2898 *2899 *	D -> A2900 *2901 * then the updated access relations are of the form2902 *2903 *	[S -> D] -> A2904 *2905 * Note that S consists of a single space such that introducing S2906 * in the access relations does not increase the number of spaces.2907 */2908static isl_bool collect_sink_source(__isl_keep isl_schedule_node *node,2909	void *user)2910{2911	struct isl_compute_flow_schedule_data *data = user;2912	isl_union_map *prefix;2913	isl_union_map *umap;2914	isl_bool r = isl_bool_false;2915 2916	if (isl_schedule_node_get_type(node) != isl_schedule_node_leaf)2917		return isl_bool_true;2918 2919	data->node = node;2920 2921	prefix = isl_schedule_node_get_prefix_schedule_relation(node);2922	prefix = isl_union_map_reverse(prefix);2923	prefix = isl_union_map_range_map(prefix);2924 2925	data->set_sink = 1;2926	umap = isl_union_map_copy(data->access->access[isl_access_sink]);2927	umap = isl_union_map_apply_range(isl_union_map_copy(prefix), umap);2928	if (isl_union_map_foreach_map(umap, &extract_sink_source, data) < 0)2929		r = isl_bool_error;2930	isl_union_map_free(umap);2931 2932	data->set_sink = 0;2933	data->must = 1;2934	umap = isl_union_map_copy(data->access->access[isl_access_must_source]);2935	umap = isl_union_map_apply_range(isl_union_map_copy(prefix), umap);2936	if (isl_union_map_foreach_map(umap, &extract_sink_source, data) < 0)2937		r = isl_bool_error;2938	isl_union_map_free(umap);2939 2940	data->set_sink = 0;2941	data->must = 0;2942	umap = isl_union_map_copy(data->access->access[isl_access_may_source]);2943	umap = isl_union_map_apply_range(isl_union_map_copy(prefix), umap);2944	if (isl_union_map_foreach_map(umap, &extract_sink_source, data) < 0)2945		r = isl_bool_error;2946	isl_union_map_free(umap);2947 2948	isl_union_map_free(prefix);2949 2950	return r;2951}2952 2953/* isl_access_info_compute_flow callback for determining whether2954 * the shared nesting level and the ordering within that level2955 * for two scheduled accesses for use in compute_single_flow.2956 *2957 * The tokens passed to this function refer to the leaves2958 * in the schedule tree where the accesses take place.2959 *2960 * If n is the shared number of loops, then we need to return2961 * "2 * n + 1" if "first" precedes "second" inside the innermost2962 * shared loop and "2 * n" otherwise.2963 *2964 * The innermost shared ancestor may be the leaves themselves2965 * if the accesses take place in the same leaf.  Otherwise,2966 * it is either a set node or a sequence node.  Only in the case2967 * of a sequence node do we consider one access to precede the other.2968 */2969static int before_node(void *first, void *second)2970{2971	isl_schedule_node *node1 = first;2972	isl_schedule_node *node2 = second;2973	isl_schedule_node *shared;2974	isl_size depth;2975	int before = 0;2976 2977	shared = isl_schedule_node_get_shared_ancestor(node1, node2);2978	depth = isl_schedule_node_get_schedule_depth(shared);2979	if (depth < 0) {2980		isl_schedule_node_free(shared);2981		return -1;2982	}2983 2984	if (isl_schedule_node_get_type(shared) == isl_schedule_node_sequence) {2985		isl_size pos1, pos2;2986 2987		pos1 = isl_schedule_node_get_ancestor_child_position(node1,2988								    shared);2989		pos2 = isl_schedule_node_get_ancestor_child_position(node2,2990								    shared);2991		if (pos1 < 0 || pos2 < 0) {2992			isl_schedule_node_free(shared);2993			return -1;2994		}2995		before = pos1 < pos2;2996	}2997 2998	isl_schedule_node_free(shared);2999 3000	return 2 * depth + before;3001}3002 3003/* Check if the given two accesses may be coscheduled.3004 * If so, return isl_bool_true.  Otherwise return isl_bool_false.3005 *3006 * Two accesses may only be coscheduled if they appear in the same leaf.3007 */3008static isl_bool coscheduled_node(void *first, void *second)3009{3010	isl_schedule_node *node1 = first;3011	isl_schedule_node *node2 = second;3012 3013	return isl_bool_ok(node1 == node2);3014}3015 3016/* Add the scheduled sources from "data" that access3017 * the same data space as "sink" to "access".3018 */3019static __isl_give isl_access_info *add_matching_sources(3020	__isl_take isl_access_info *access, struct isl_scheduled_access *sink,3021	struct isl_compute_flow_schedule_data *data)3022{3023	int i;3024	isl_space *space;3025 3026	space = isl_space_range(isl_map_get_space(sink->access));3027	for (i = 0; i < data->n_source; ++i) {3028		struct isl_scheduled_access *source;3029		isl_space *source_space;3030		int eq;3031 3032		source = &data->source[i];3033		source_space = isl_map_get_space(source->access);3034		source_space = isl_space_range(source_space);3035		eq = isl_space_is_equal(space, source_space);3036		isl_space_free(source_space);3037 3038		if (!eq)3039			continue;3040		if (eq < 0)3041			goto error;3042 3043		access = isl_access_info_add_source(access,3044		    isl_map_copy(source->access), source->must, source->node);3045	}3046 3047	isl_space_free(space);3048	return access;3049error:3050	isl_space_free(space);3051	isl_access_info_free(access);3052	return NULL;3053}3054 3055/* Given a scheduled sink access relation "sink", compute the corresponding3056 * dependences on the sources in "data" and add the computed dependences3057 * to "uf".3058 *3059 * The dependences computed by access_info_compute_flow_core are of the form3060 *3061 *	[S -> I] -> [[S' -> I'] -> A]3062 *3063 * The schedule dimensions are projected out by first currying the range,3064 * resulting in3065 *3066 *	[S -> I] -> [S' -> [I' -> A]]3067 *3068 * and then computing the factor range3069 *3070 *	I -> [I' -> A]3071 */3072static __isl_give isl_union_flow *compute_single_flow(3073	__isl_take isl_union_flow *uf, struct isl_scheduled_access *sink,3074	struct isl_compute_flow_schedule_data *data)3075{3076	int i;3077	isl_access_info *access;3078	isl_flow *flow;3079	isl_map *map;3080 3081	if (!uf)3082		return NULL;3083 3084	access = isl_access_info_alloc(isl_map_copy(sink->access), sink->node,3085					&before_node, data->n_source);3086	if (access)3087		access->coscheduled = &coscheduled_node;3088	access = add_matching_sources(access, sink, data);3089 3090	flow = access_info_compute_flow_core(access);3091	if (!flow)3092		return isl_union_flow_free(uf);3093 3094	map = isl_map_domain_factor_range(isl_flow_get_no_source(flow, 1));3095	uf->must_no_source = isl_union_map_union(uf->must_no_source,3096						isl_union_map_from_map(map));3097	map = isl_map_domain_factor_range(isl_flow_get_no_source(flow, 0));3098	uf->may_no_source = isl_union_map_union(uf->may_no_source,3099						isl_union_map_from_map(map));3100 3101	for (i = 0; i < flow->n_source; ++i) {3102		isl_union_map *dep;3103 3104		map = isl_map_range_curry(isl_map_copy(flow->dep[i].map));3105		map = isl_map_factor_range(map);3106		dep = isl_union_map_from_map(map);3107		if (flow->dep[i].must)3108			uf->must_dep = isl_union_map_union(uf->must_dep, dep);3109		else3110			uf->may_dep = isl_union_map_union(uf->may_dep, dep);3111	}3112 3113	isl_flow_free(flow);3114 3115	return uf;3116}3117 3118/* Given a description of the "sink" accesses, the "source" accesses and3119 * a schedule, compute for each instance of a sink access3120 * and for each element accessed by that instance,3121 * the possible or definite source accesses that last accessed the3122 * element accessed by the sink access before this sink access3123 * in the sense that there is no intermediate definite source access.3124 * Only consider dependences between statement instances that belong3125 * to the domain of the schedule.3126 *3127 * The must_no_source and may_no_source elements of the result3128 * are subsets of access->sink.  The elements must_dep and may_dep3129 * map domain elements of access->{may,must)_source to3130 * domain elements of access->sink.3131 *3132 * This function is used when a schedule tree representation3133 * is available.3134 *3135 * We extract the individual scheduled source and sink access relations3136 * (taking into account the domain of the schedule) and3137 * then compute dependences for each scheduled sink individually.3138 */3139static __isl_give isl_union_flow *compute_flow_schedule(3140	__isl_take isl_union_access_info *access)3141{3142	struct isl_compute_flow_schedule_data data = { access };3143	int i, n;3144	isl_ctx *ctx;3145	isl_space *space;3146	isl_union_flow *flow;3147 3148	ctx = isl_union_access_info_get_ctx(access);3149 3150	data.n_sink = 0;3151	data.n_source = 0;3152	if (isl_schedule_foreach_schedule_node_top_down(access->schedule,3153						&count_sink_source, &data) < 0)3154		goto error;3155 3156	n = data.n_sink + data.n_source;3157	data.sink = isl_calloc_array(ctx, struct isl_scheduled_access, n);3158	if (n && !data.sink)3159		goto error;3160	data.source = data.sink + data.n_sink;3161 3162	data.n_sink = 0;3163	data.n_source = 0;3164	if (isl_schedule_foreach_schedule_node_top_down(access->schedule,3165					    &collect_sink_source, &data) < 0)3166		goto error;3167 3168	space = isl_union_map_get_space(access->access[isl_access_sink]);3169	flow = isl_union_flow_alloc(space);3170 3171	isl_compute_flow_schedule_data_align_params(&data);3172 3173	for (i = 0; i < data.n_sink; ++i)3174		flow = compute_single_flow(flow, &data.sink[i], &data);3175 3176	isl_compute_flow_schedule_data_clear(&data);3177 3178	isl_union_access_info_free(access);3179	return flow;3180error:3181	isl_union_access_info_free(access);3182	isl_compute_flow_schedule_data_clear(&data);3183	return NULL;3184}3185 3186/* Given a description of the "sink" accesses, the "source" accesses and3187 * a schedule, compute for each instance of a sink access3188 * and for each element accessed by that instance,3189 * the possible or definite source accesses that last accessed the3190 * element accessed by the sink access before this sink access3191 * in the sense that there is no intermediate definite source access.3192 *3193 * The must_no_source and may_no_source elements of the result3194 * are subsets of access->sink.  The elements must_dep and may_dep3195 * map domain elements of access->{may,must)_source to3196 * domain elements of access->sink.3197 *3198 * If any kills have been specified, then they are treated as3199 * must-sources internally.  Any dependence that purely derives3200 * from an original kill is removed from the output.3201 *3202 * We check whether the schedule is available as a schedule tree3203 * or a schedule map and call the corresponding function to perform3204 * the analysis.3205 */3206__isl_give isl_union_flow *isl_union_access_info_compute_flow(3207	__isl_take isl_union_access_info *access)3208{3209	isl_bool has_kill;3210	isl_union_map *must = NULL, *may = NULL;3211	isl_union_flow *flow;3212 3213	has_kill = isl_union_access_has_kill(access);3214	if (has_kill < 0)3215		goto error;3216	if (has_kill) {3217		must = isl_union_access_info_get_must_source(access);3218		may = isl_union_access_info_get_may_source(access);3219	}3220	access = isl_union_access_info_add_kill_to_must_source(access);3221	access = isl_union_access_info_normalize(access);3222	if (!access)3223		goto error;3224	if (access->schedule)3225		flow = compute_flow_schedule(access);3226	else3227		flow = compute_flow_union_map(access);3228	if (has_kill)3229		flow = isl_union_flow_drop_kill_source(flow, must, may);3230	return flow;3231error:3232	isl_union_access_info_free(access);3233	isl_union_map_free(must);3234	isl_union_map_free(may);3235	return NULL;3236}3237 3238/* Print the information contained in "flow" to "p".3239 * The information is printed as a YAML document.3240 */3241__isl_give isl_printer *isl_printer_print_union_flow(3242	__isl_take isl_printer *p, __isl_keep isl_union_flow *flow)3243{3244	isl_union_map *umap;3245 3246	if (!flow)3247		return isl_printer_free(p);3248 3249	p = isl_printer_yaml_start_mapping(p);3250	umap = isl_union_flow_get_full_must_dependence(flow);3251	p = print_yaml_field_union_map(p, "must_dependence", umap);3252	isl_union_map_free(umap);3253	umap = isl_union_flow_get_full_may_dependence(flow);3254	p = print_yaml_field_union_map(p, "may_dependence", umap);3255	isl_union_map_free(umap);3256	p = print_yaml_field_union_map(p, "must_no_source",3257					flow->must_no_source);3258	umap = isl_union_flow_get_may_no_source(flow);3259	p = print_yaml_field_union_map(p, "may_no_source", umap);3260	isl_union_map_free(umap);3261	p = isl_printer_yaml_end_mapping(p);3262 3263	return p;3264}3265 3266/* Return a string representation of the information in "flow".3267 * The information is printed in flow format.3268 */3269__isl_give char *isl_union_flow_to_str(__isl_keep isl_union_flow *flow)3270{3271	isl_printer *p;3272	char *s;3273 3274	if (!flow)3275		return NULL;3276 3277	p = isl_printer_to_str(isl_union_flow_get_ctx(flow));3278	p = isl_printer_set_yaml_style(p, ISL_YAML_STYLE_FLOW);3279	p = isl_printer_print_union_flow(p, flow);3280	s = isl_printer_get_str(p);3281	isl_printer_free(p);3282 3283	return s;3284}3285 3286/* Given a collection of "sink" and "source" accesses,3287 * compute for each iteration of a sink access3288 * and for each element accessed by that iteration,3289 * the source access in the list that last accessed the3290 * element accessed by the sink access before this sink access.3291 * Each access is given as a map from the loop iterators3292 * to the array indices.3293 * The result is a relations between source and sink3294 * iterations and a subset of the domain of the sink accesses,3295 * corresponding to those iterations that access an element3296 * not previously accessed.3297 *3298 * We collect the inputs in an isl_union_access_info object,3299 * call isl_union_access_info_compute_flow and extract3300 * the outputs from the result.3301 */3302int isl_union_map_compute_flow(__isl_take isl_union_map *sink,3303	__isl_take isl_union_map *must_source,3304	__isl_take isl_union_map *may_source,3305	__isl_take isl_union_map *schedule,3306	__isl_give isl_union_map **must_dep, __isl_give isl_union_map **may_dep,3307	__isl_give isl_union_map **must_no_source,3308	__isl_give isl_union_map **may_no_source)3309{3310	isl_union_access_info *access;3311	isl_union_flow *flow;3312 3313	access = isl_union_access_info_from_sink(sink);3314	access = isl_union_access_info_set_must_source(access, must_source);3315	access = isl_union_access_info_set_may_source(access, may_source);3316	access = isl_union_access_info_set_schedule_map(access, schedule);3317	flow = isl_union_access_info_compute_flow(access);3318 3319	if (must_dep)3320		*must_dep = isl_union_flow_get_must_dependence(flow);3321	if (may_dep)3322		*may_dep = isl_union_flow_get_non_must_dependence(flow);3323	if (must_no_source)3324		*must_no_source = isl_union_flow_get_must_no_source(flow);3325	if (may_no_source)3326		*may_no_source = isl_union_flow_get_non_must_no_source(flow);3327 3328	isl_union_flow_free(flow);3329 3330	if ((must_dep && !*must_dep) || (may_dep && !*may_dep) ||3331	    (must_no_source && !*must_no_source) ||3332	    (may_no_source && !*may_no_source))3333		goto error;3334 3335	return 0;3336error:3337	if (must_dep)3338		*must_dep = isl_union_map_free(*must_dep);3339	if (may_dep)3340		*may_dep = isl_union_map_free(*may_dep);3341	if (must_no_source)3342		*must_no_source = isl_union_map_free(*must_no_source);3343	if (may_no_source)3344		*may_no_source = isl_union_map_free(*may_no_source);3345	return -1;3346}3347