1/*
2 * Copyright 2005-2007 Universiteit Leiden
3 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Copyright 2010      INRIA Saclay
5 * Copyright 2012      Universiteit Leiden
6 *
7 * Use of this software is governed by the MIT license
8 *
9 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,
10 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
11 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,
12 * B-3001 Leuven, Belgium
13 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
14 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
15 */
16
17#include <isl/set.h>
18#include <isl/map.h>
19#include <isl/flow.h>
20#include <isl_sort.h>
21
22enum isl_restriction_type {
23	isl_restriction_type_empty,
24	isl_restriction_type_none,
25	isl_restriction_type_input,
26	isl_restriction_type_output
27};
28
29struct isl_restriction {
30	enum isl_restriction_type type;
31
32	isl_set *source;
33	isl_set *sink;
34};
35
36/* Create a restriction of the given type.
37 */
38static __isl_give isl_restriction *isl_restriction_alloc(
39	__isl_take isl_map *source_map, enum isl_restriction_type type)
40{
41	isl_ctx *ctx;
42	isl_restriction *restr;
43
44	if (!source_map)
45		return NULL;
46
47	ctx = isl_map_get_ctx(source_map);
48	restr = isl_calloc_type(ctx, struct isl_restriction);
49	if (!restr)
50		goto error;
51
52	restr->type = type;
53
54	isl_map_free(source_map);
55	return restr;
56error:
57	isl_map_free(source_map);
58	return NULL;
59}
60
61/* Create a restriction that doesn't restrict anything.
62 */
63__isl_give isl_restriction *isl_restriction_none(__isl_take isl_map *source_map)
64{
65	return isl_restriction_alloc(source_map, isl_restriction_type_none);
66}
67
68/* Create a restriction that removes everything.
69 */
70__isl_give isl_restriction *isl_restriction_empty(
71	__isl_take isl_map *source_map)
72{
73	return isl_restriction_alloc(source_map, isl_restriction_type_empty);
74}
75
76/* Create a restriction on the input of the maximization problem
77 * based on the given source and sink restrictions.
78 */
79__isl_give isl_restriction *isl_restriction_input(
80	__isl_take isl_set *source_restr, __isl_take isl_set *sink_restr)
81{
82	isl_ctx *ctx;
83	isl_restriction *restr;
84
85	if (!source_restr || !sink_restr)
86		goto error;
87
88	ctx = isl_set_get_ctx(source_restr);
89	restr = isl_calloc_type(ctx, struct isl_restriction);
90	if (!restr)
91		goto error;
92
93	restr->type = isl_restriction_type_input;
94	restr->source = source_restr;
95	restr->sink = sink_restr;
96
97	return restr;
98error:
99	isl_set_free(source_restr);
100	isl_set_free(sink_restr);
101	return NULL;
102}
103
104/* Create a restriction on the output of the maximization problem
105 * based on the given source restriction.
106 */
107__isl_give isl_restriction *isl_restriction_output(
108	__isl_take isl_set *source_restr)
109{
110	isl_ctx *ctx;
111	isl_restriction *restr;
112
113	if (!source_restr)
114		return NULL;
115
116	ctx = isl_set_get_ctx(source_restr);
117	restr = isl_calloc_type(ctx, struct isl_restriction);
118	if (!restr)
119		goto error;
120
121	restr->type = isl_restriction_type_output;
122	restr->source = source_restr;
123
124	return restr;
125error:
126	isl_set_free(source_restr);
127	return NULL;
128}
129
130void *isl_restriction_free(__isl_take isl_restriction *restr)
131{
132	if (!restr)
133		return NULL;
134
135	isl_set_free(restr->source);
136	isl_set_free(restr->sink);
137	free(restr);
138	return NULL;
139}
140
141isl_ctx *isl_restriction_get_ctx(__isl_keep isl_restriction *restr)
142{
143	return restr ? isl_set_get_ctx(restr->source) : NULL;
144}
145
146/* A private structure to keep track of a mapping together with
147 * a user-specified identifier and a boolean indicating whether
148 * the map represents a must or may access/dependence.
149 */
150struct isl_labeled_map {
151	struct isl_map	*map;
152	void		*data;
153	int		must;
154};
155
156/* A structure containing the input for dependence analysis:
157 * - a sink
158 * - n_must + n_may (<= max_source) sources
159 * - a function for determining the relative order of sources and sink
160 * The must sources are placed before the may sources.
161 *
162 * domain_map is an auxiliary map that maps the sink access relation
163 * to the domain of this access relation.
164 *
165 * restrict_fn is a callback that (if not NULL) will be called
166 * right before any lexicographical maximization.
167 */
168struct isl_access_info {
169	isl_map				*domain_map;
170	struct isl_labeled_map		sink;
171	isl_access_level_before		level_before;
172
173	isl_access_restrict		restrict_fn;
174	void				*restrict_user;
175
176	int		    		max_source;
177	int		    		n_must;
178	int		    		n_may;
179	struct isl_labeled_map		source[1];
180};
181
182/* A structure containing the output of dependence analysis:
183 * - n_source dependences
184 * - a wrapped subset of the sink for which definitely no source could be found
185 * - a wrapped subset of the sink for which possibly no source could be found
186 */
187struct isl_flow {
188	isl_set			*must_no_source;
189	isl_set			*may_no_source;
190	int			n_source;
191	struct isl_labeled_map	*dep;
192};
193
194/* Construct an isl_access_info structure and fill it up with
195 * the given data.  The number of sources is set to 0.
196 */
197__isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,
198	void *sink_user, isl_access_level_before fn, int max_source)
199{
200	isl_ctx *ctx;
201	struct isl_access_info *acc;
202
203	if (!sink)
204		return NULL;
205
206	ctx = isl_map_get_ctx(sink);
207	isl_assert(ctx, max_source >= 0, goto error);
208
209	acc = isl_calloc(ctx, struct isl_access_info,
210			sizeof(struct isl_access_info) +
211			(max_source - 1) * sizeof(struct isl_labeled_map));
212	if (!acc)
213		goto error;
214
215	acc->sink.map = sink;
216	acc->sink.data = sink_user;
217	acc->level_before = fn;
218	acc->max_source = max_source;
219	acc->n_must = 0;
220	acc->n_may = 0;
221
222	return acc;
223error:
224	isl_map_free(sink);
225	return NULL;
226}
227
228/* Free the given isl_access_info structure.
229 */
230void *isl_access_info_free(__isl_take isl_access_info *acc)
231{
232	int i;
233
234	if (!acc)
235		return NULL;
236	isl_map_free(acc->domain_map);
237	isl_map_free(acc->sink.map);
238	for (i = 0; i < acc->n_must + acc->n_may; ++i)
239		isl_map_free(acc->source[i].map);
240	free(acc);
241	return NULL;
242}
243
244isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)
245{
246	return acc ? isl_map_get_ctx(acc->sink.map) : NULL;
247}
248
249__isl_give isl_access_info *isl_access_info_set_restrict(
250	__isl_take isl_access_info *acc, isl_access_restrict fn, void *user)
251{
252	if (!acc)
253		return NULL;
254	acc->restrict_fn = fn;
255	acc->restrict_user = user;
256	return acc;
257}
258
259/* Add another source to an isl_access_info structure, making
260 * sure the "must" sources are placed before the "may" sources.
261 * This function may be called at most max_source times on a
262 * given isl_access_info structure, with max_source as specified
263 * in the call to isl_access_info_alloc that constructed the structure.
264 */
265__isl_give isl_access_info *isl_access_info_add_source(
266	__isl_take isl_access_info *acc, __isl_take isl_map *source,
267	int must, void *source_user)
268{
269	isl_ctx *ctx;
270
271	if (!acc)
272		goto error;
273	ctx = isl_map_get_ctx(acc->sink.map);
274	isl_assert(ctx, acc->n_must + acc->n_may < acc->max_source, goto error);
275
276	if (must) {
277		if (acc->n_may)
278			acc->source[acc->n_must + acc->n_may] =
279				acc->source[acc->n_must];
280		acc->source[acc->n_must].map = source;
281		acc->source[acc->n_must].data = source_user;
282		acc->source[acc->n_must].must = 1;
283		acc->n_must++;
284	} else {
285		acc->source[acc->n_must + acc->n_may].map = source;
286		acc->source[acc->n_must + acc->n_may].data = source_user;
287		acc->source[acc->n_must + acc->n_may].must = 0;
288		acc->n_may++;
289	}
290
291	return acc;
292error:
293	isl_map_free(source);
294	isl_access_info_free(acc);
295	return NULL;
296}
297
298/* Return -n, 0 or n (with n a positive value), depending on whether
299 * the source access identified by p1 should be sorted before, together
300 * or after that identified by p2.
301 *
302 * If p1 appears before p2, then it should be sorted first.
303 * For more generic initial schedules, it is possible that neither
304 * p1 nor p2 appears before the other, or at least not in any obvious way.
305 * We therefore also check if p2 appears before p1, in which case p2
306 * should be sorted first.
307 * If not, we try to order the two statements based on the description
308 * of the iteration domains.  This results in an arbitrary, but fairly
309 * stable ordering.
310 */
311static int access_sort_cmp(const void *p1, const void *p2, void *user)
312{
313	isl_access_info *acc = user;
314	const struct isl_labeled_map *i1, *i2;
315	int level1, level2;
316	uint32_t h1, h2;
317	i1 = (const struct isl_labeled_map *) p1;
318	i2 = (const struct isl_labeled_map *) p2;
319
320	level1 = acc->level_before(i1->data, i2->data);
321	if (level1 % 2)
322		return -1;
323
324	level2 = acc->level_before(i2->data, i1->data);
325	if (level2 % 2)
326		return 1;
327
328	h1 = isl_map_get_hash(i1->map);
329	h2 = isl_map_get_hash(i2->map);
330	return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;
331}
332
333/* Sort the must source accesses in their textual order.
334 */
335static __isl_give isl_access_info *isl_access_info_sort_sources(
336	__isl_take isl_access_info *acc)
337{
338	if (!acc)
339		return NULL;
340	if (acc->n_must <= 1)
341		return acc;
342
343	if (isl_sort(acc->source, acc->n_must, sizeof(struct isl_labeled_map),
344		    access_sort_cmp, acc) < 0)
345		return isl_access_info_free(acc);
346
347	return acc;
348}
349
350/* Align the parameters of the two spaces if needed and then call
351 * isl_space_join.
352 */
353static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,
354	__isl_take isl_space *right)
355{
356	if (isl_space_match(left, isl_dim_param, right, isl_dim_param))
357		return isl_space_join(left, right);
358
359	left = isl_space_align_params(left, isl_space_copy(right));
360	right = isl_space_align_params(right, isl_space_copy(left));
361	return isl_space_join(left, right);
362}
363
364/* Initialize an empty isl_flow structure corresponding to a given
365 * isl_access_info structure.
366 * For each must access, two dependences are created (initialized
367 * to the empty relation), one for the resulting must dependences
368 * and one for the resulting may dependences.  May accesses can
369 * only lead to may dependences, so only one dependence is created
370 * for each of them.
371 * This function is private as isl_flow structures are only supposed
372 * to be created by isl_access_info_compute_flow.
373 */
374static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
375{
376	int i, n;
377	struct isl_ctx *ctx;
378	struct isl_flow *dep;
379
380	if (!acc)
381		return NULL;
382
383	ctx = isl_map_get_ctx(acc->sink.map);
384	dep = isl_calloc_type(ctx, struct isl_flow);
385	if (!dep)
386		return NULL;
387
388	n = 2 * acc->n_must + acc->n_may;
389	dep->dep = isl_calloc_array(ctx, struct isl_labeled_map, n);
390	if (n && !dep->dep)
391		goto error;
392
393	dep->n_source = n;
394	for (i = 0; i < acc->n_must; ++i) {
395		isl_space *dim;
396		dim = space_align_and_join(
397			isl_map_get_space(acc->source[i].map),
398			isl_space_reverse(isl_map_get_space(acc->sink.map)));
399		dep->dep[2 * i].map = isl_map_empty(dim);
400		dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);
401		dep->dep[2 * i].data = acc->source[i].data;
402		dep->dep[2 * i + 1].data = acc->source[i].data;
403		dep->dep[2 * i].must = 1;
404		dep->dep[2 * i + 1].must = 0;
405		if (!dep->dep[2 * i].map || !dep->dep[2 * i + 1].map)
406			goto error;
407	}
408	for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {
409		isl_space *dim;
410		dim = space_align_and_join(
411			isl_map_get_space(acc->source[i].map),
412			isl_space_reverse(isl_map_get_space(acc->sink.map)));
413		dep->dep[acc->n_must + i].map = isl_map_empty(dim);
414		dep->dep[acc->n_must + i].data = acc->source[i].data;
415		dep->dep[acc->n_must + i].must = 0;
416		if (!dep->dep[acc->n_must + i].map)
417			goto error;
418	}
419
420	return dep;
421error:
422	isl_flow_free(dep);
423	return NULL;
424}
425
426/* Iterate over all sources and for each resulting flow dependence
427 * that is not empty, call the user specfied function.
428 * The second argument in this function call identifies the source,
429 * while the third argument correspond to the final argument of
430 * the isl_flow_foreach call.
431 */
432int isl_flow_foreach(__isl_keep isl_flow *deps,
433	int (*fn)(__isl_take isl_map *dep, int must, void *dep_user, void *user),
434	void *user)
435{
436	int i;
437
438	if (!deps)
439		return -1;
440
441	for (i = 0; i < deps->n_source; ++i) {
442		if (isl_map_plain_is_empty(deps->dep[i].map))
443			continue;
444		if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,
445				deps->dep[i].data, user) < 0)
446			return -1;
447	}
448
449	return 0;
450}
451
452/* Return a copy of the subset of the sink for which no source could be found.
453 */
454__isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
455{
456	if (!deps)
457		return NULL;
458
459	if (must)
460		return isl_set_unwrap(isl_set_copy(deps->must_no_source));
461	else
462		return isl_set_unwrap(isl_set_copy(deps->may_no_source));
463}
464
465void isl_flow_free(__isl_take isl_flow *deps)
466{
467	int i;
468
469	if (!deps)
470		return;
471	isl_set_free(deps->must_no_source);
472	isl_set_free(deps->may_no_source);
473	if (deps->dep) {
474		for (i = 0; i < deps->n_source; ++i)
475			isl_map_free(deps->dep[i].map);
476		free(deps->dep);
477	}
478	free(deps);
479}
480
481isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)
482{
483	return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;
484}
485
486/* Return a map that enforces that the domain iteration occurs after
487 * the range iteration at the given level.
488 * If level is odd, then the domain iteration should occur after
489 * the target iteration in their shared level/2 outermost loops.
490 * In this case we simply need to enforce that these outermost
491 * loop iterations are the same.
492 * If level is even, then the loop iterator of the domain should
493 * be greater than the loop iterator of the range at the last
494 * of the level/2 shared loops, i.e., loop level/2 - 1.
495 */
496static __isl_give isl_map *after_at_level(__isl_take isl_space *dim, int level)
497{
498	struct isl_basic_map *bmap;
499
500	if (level % 2)
501		bmap = isl_basic_map_equal(dim, level/2);
502	else
503		bmap = isl_basic_map_more_at(dim, level/2 - 1);
504
505	return isl_map_from_basic_map(bmap);
506}
507
508/* Compute the partial lexicographic maximum of "dep" on domain "sink",
509 * but first check if the user has set acc->restrict_fn and if so
510 * update either the input or the output of the maximization problem
511 * with respect to the resulting restriction.
512 *
513 * Since the user expects a mapping from sink iterations to source iterations,
514 * whereas the domain of "dep" is a wrapped map, mapping sink iterations
515 * to accessed array elements, we first need to project out the accessed
516 * sink array elements by applying acc->domain_map.
517 * Similarly, the sink restriction specified by the user needs to be
518 * converted back to the wrapped map.
519 */
520static __isl_give isl_map *restricted_partial_lexmax(
521	__isl_keep isl_access_info *acc, __isl_take isl_map *dep,
522	int source, __isl_take isl_set *sink, __isl_give isl_set **empty)
523{
524	isl_map *source_map;
525	isl_restriction *restr;
526	isl_set *sink_domain;
527	isl_set *sink_restr;
528	isl_map *res;
529
530	if (!acc->restrict_fn)
531		return isl_map_partial_lexmax(dep, sink, empty);
532
533	source_map = isl_map_copy(dep);
534	source_map = isl_map_apply_domain(source_map,
535					    isl_map_copy(acc->domain_map));
536	sink_domain = isl_set_copy(sink);
537	sink_domain = isl_set_apply(sink_domain, isl_map_copy(acc->domain_map));
538	restr = acc->restrict_fn(source_map, sink_domain,
539				acc->source[source].data, acc->restrict_user);
540	isl_set_free(sink_domain);
541	isl_map_free(source_map);
542
543	if (!restr)
544		goto error;
545	if (restr->type == isl_restriction_type_input) {
546		dep = isl_map_intersect_range(dep, isl_set_copy(restr->source));
547		sink_restr = isl_set_copy(restr->sink);
548		sink_restr = isl_set_apply(sink_restr,
549				isl_map_reverse(isl_map_copy(acc->domain_map)));
550		sink = isl_set_intersect(sink, sink_restr);
551	} else if (restr->type == isl_restriction_type_empty) {
552		isl_space *space = isl_map_get_space(dep);
553		isl_map_free(dep);
554		dep = isl_map_empty(space);
555	}
556
557	res = isl_map_partial_lexmax(dep, sink, empty);
558
559	if (restr->type == isl_restriction_type_output)
560		res = isl_map_intersect_range(res, isl_set_copy(restr->source));
561
562	isl_restriction_free(restr);
563	return res;
564error:
565	isl_map_free(dep);
566	isl_set_free(sink);
567	*empty = NULL;
568	return NULL;
569}
570
571/* Compute the last iteration of must source j that precedes the sink
572 * at the given level for sink iterations in set_C.
573 * The subset of set_C for which no such iteration can be found is returned
574 * in *empty.
575 */
576static struct isl_map *last_source(struct isl_access_info *acc,
577				    struct isl_set *set_C,
578				    int j, int level, struct isl_set **empty)
579{
580	struct isl_map *read_map;
581	struct isl_map *write_map;
582	struct isl_map *dep_map;
583	struct isl_map *after;
584	struct isl_map *result;
585
586	read_map = isl_map_copy(acc->sink.map);
587	write_map = isl_map_copy(acc->source[j].map);
588	write_map = isl_map_reverse(write_map);
589	dep_map = isl_map_apply_range(read_map, write_map);
590	after = after_at_level(isl_map_get_space(dep_map), level);
591	dep_map = isl_map_intersect(dep_map, after);
592	result = restricted_partial_lexmax(acc, dep_map, j, set_C, empty);
593	result = isl_map_reverse(result);
594
595	return result;
596}
597
598/* For a given mapping between iterations of must source j and iterations
599 * of the sink, compute the last iteration of must source k preceding
600 * the sink at level before_level for any of the sink iterations,
601 * but following the corresponding iteration of must source j at level
602 * after_level.
603 */
604static struct isl_map *last_later_source(struct isl_access_info *acc,
605					 struct isl_map *old_map,
606					 int j, int before_level,
607					 int k, int after_level,
608					 struct isl_set **empty)
609{
610	isl_space *dim;
611	struct isl_set *set_C;
612	struct isl_map *read_map;
613	struct isl_map *write_map;
614	struct isl_map *dep_map;
615	struct isl_map *after_write;
616	struct isl_map *before_read;
617	struct isl_map *result;
618
619	set_C = isl_map_range(isl_map_copy(old_map));
620	read_map = isl_map_copy(acc->sink.map);
621	write_map = isl_map_copy(acc->source[k].map);
622
623	write_map = isl_map_reverse(write_map);
624	dep_map = isl_map_apply_range(read_map, write_map);
625	dim = space_align_and_join(isl_map_get_space(acc->source[k].map),
626		    isl_space_reverse(isl_map_get_space(acc->source[j].map)));
627	after_write = after_at_level(dim, after_level);
628	after_write = isl_map_apply_range(after_write, old_map);
629	after_write = isl_map_reverse(after_write);
630	dep_map = isl_map_intersect(dep_map, after_write);
631	before_read = after_at_level(isl_map_get_space(dep_map), before_level);
632	dep_map = isl_map_intersect(dep_map, before_read);
633	result = restricted_partial_lexmax(acc, dep_map, k, set_C, empty);
634	result = isl_map_reverse(result);
635
636	return result;
637}
638
639/* Given a shared_level between two accesses, return 1 if the
640 * the first can precede the second at the requested target_level.
641 * If the target level is odd, i.e., refers to a statement level
642 * dimension, then first needs to precede second at the requested
643 * level, i.e., shared_level must be equal to target_level.
644 * If the target level is odd, then the two loops should share
645 * at least the requested number of outer loops.
646 */
647static int can_precede_at_level(int shared_level, int target_level)
648{
649	if (shared_level < target_level)
650		return 0;
651	if ((target_level % 2) && shared_level > target_level)
652		return 0;
653	return 1;
654}
655
656/* Given a possible flow dependence temp_rel[j] between source j and the sink
657 * at level sink_level, remove those elements for which
658 * there is an iteration of another source k < j that is closer to the sink.
659 * The flow dependences temp_rel[k] are updated with the improved sources.
660 * Any improved source needs to precede the sink at the same level
661 * and needs to follow source j at the same or a deeper level.
662 * The lower this level, the later the execution date of source k.
663 * We therefore consider lower levels first.
664 *
665 * If temp_rel[j] is empty, then there can be no improvement and
666 * we return immediately.
667 */
668static int intermediate_sources(__isl_keep isl_access_info *acc,
669	struct isl_map **temp_rel, int j, int sink_level)
670{
671	int k, level;
672	int depth = 2 * isl_map_dim(acc->source[j].map, isl_dim_in) + 1;
673
674	if (isl_map_plain_is_empty(temp_rel[j]))
675		return 0;
676
677	for (k = j - 1; k >= 0; --k) {
678		int plevel, plevel2;
679		plevel = acc->level_before(acc->source[k].data, acc->sink.data);
680		if (!can_precede_at_level(plevel, sink_level))
681			continue;
682
683		plevel2 = acc->level_before(acc->source[j].data,
684						acc->source[k].data);
685
686		for (level = sink_level; level <= depth; ++level) {
687			struct isl_map *T;
688			struct isl_set *trest;
689			struct isl_map *copy;
690
691			if (!can_precede_at_level(plevel2, level))
692				continue;
693
694			copy = isl_map_copy(temp_rel[j]);
695			T = last_later_source(acc, copy, j, sink_level, k,
696					      level, &trest);
697			if (isl_map_plain_is_empty(T)) {
698				isl_set_free(trest);
699				isl_map_free(T);
700				continue;
701			}
702			temp_rel[j] = isl_map_intersect_range(temp_rel[j], trest);
703			temp_rel[k] = isl_map_union_disjoint(temp_rel[k], T);
704		}
705	}
706
707	return 0;
708}
709
710/* Compute all iterations of may source j that precedes the sink at the given
711 * level for sink iterations in set_C.
712 */
713static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,
714				    __isl_take isl_set *set_C, int j, int level)
715{
716	isl_map *read_map;
717	isl_map *write_map;
718	isl_map *dep_map;
719	isl_map *after;
720
721	read_map = isl_map_copy(acc->sink.map);
722	read_map = isl_map_intersect_domain(read_map, set_C);
723	write_map = isl_map_copy(acc->source[acc->n_must + j].map);
724	write_map = isl_map_reverse(write_map);
725	dep_map = isl_map_apply_range(read_map, write_map);
726	after = after_at_level(isl_map_get_space(dep_map), level);
727	dep_map = isl_map_intersect(dep_map, after);
728
729	return isl_map_reverse(dep_map);
730}
731
732/* For a given mapping between iterations of must source k and iterations
733 * of the sink, compute the all iteration of may source j preceding
734 * the sink at level before_level for any of the sink iterations,
735 * but following the corresponding iteration of must source k at level
736 * after_level.
737 */
738static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,
739	__isl_keep isl_map *old_map,
740	int j, int before_level, int k, int after_level)
741{
742	isl_space *dim;
743	isl_set *set_C;
744	isl_map *read_map;
745	isl_map *write_map;
746	isl_map *dep_map;
747	isl_map *after_write;
748	isl_map *before_read;
749
750	set_C = isl_map_range(isl_map_copy(old_map));
751	read_map = isl_map_copy(acc->sink.map);
752	read_map = isl_map_intersect_domain(read_map, set_C);
753	write_map = isl_map_copy(acc->source[acc->n_must + j].map);
754
755	write_map = isl_map_reverse(write_map);
756	dep_map = isl_map_apply_range(read_map, write_map);
757	dim = isl_space_join(isl_map_get_space(acc->source[acc->n_must + j].map),
758		    isl_space_reverse(isl_map_get_space(acc->source[k].map)));
759	after_write = after_at_level(dim, after_level);
760	after_write = isl_map_apply_range(after_write, old_map);
761	after_write = isl_map_reverse(after_write);
762	dep_map = isl_map_intersect(dep_map, after_write);
763	before_read = after_at_level(isl_map_get_space(dep_map), before_level);
764	dep_map = isl_map_intersect(dep_map, before_read);
765	return isl_map_reverse(dep_map);
766}
767
768/* Given the must and may dependence relations for the must accesses
769 * for level sink_level, check if there are any accesses of may access j
770 * that occur in between and return their union.
771 * If some of these accesses are intermediate with respect to
772 * (previously thought to be) must dependences, then these
773 * must dependences are turned into may dependences.
774 */
775static __isl_give isl_map *all_intermediate_sources(
776	__isl_keep isl_access_info *acc, __isl_take isl_map *map,
777	struct isl_map **must_rel, struct isl_map **may_rel,
778	int j, int sink_level)
779{
780	int k, level;
781	int depth = 2 * isl_map_dim(acc->source[acc->n_must + j].map,
782					isl_dim_in) + 1;
783
784	for (k = 0; k < acc->n_must; ++k) {
785		int plevel;
786
787		if (isl_map_plain_is_empty(may_rel[k]) &&
788		    isl_map_plain_is_empty(must_rel[k]))
789			continue;
790
791		plevel = acc->level_before(acc->source[k].data,
792					acc->source[acc->n_must + j].data);
793
794		for (level = sink_level; level <= depth; ++level) {
795			isl_map *T;
796			isl_map *copy;
797			isl_set *ran;
798
799			if (!can_precede_at_level(plevel, level))
800				continue;
801
802			copy = isl_map_copy(may_rel[k]);
803			T = all_later_sources(acc, copy, j, sink_level, k, level);
804			map = isl_map_union(map, T);
805
806			copy = isl_map_copy(must_rel[k]);
807			T = all_later_sources(acc, copy, j, sink_level, k, level);
808			ran = isl_map_range(isl_map_copy(T));
809			map = isl_map_union(map, T);
810			may_rel[k] = isl_map_union_disjoint(may_rel[k],
811			    isl_map_intersect_range(isl_map_copy(must_rel[k]),
812						    isl_set_copy(ran)));
813			T = isl_map_from_domain_and_range(
814			    isl_set_universe(
815				isl_space_domain(isl_map_get_space(must_rel[k]))),
816			    ran);
817			must_rel[k] = isl_map_subtract(must_rel[k], T);
818		}
819	}
820
821	return map;
822}
823
824/* Compute dependences for the case where all accesses are "may"
825 * accesses, which boils down to computing memory based dependences.
826 * The generic algorithm would also work in this case, but it would
827 * be overkill to use it.
828 */
829static __isl_give isl_flow *compute_mem_based_dependences(
830	__isl_keep isl_access_info *acc)
831{
832	int i;
833	isl_set *mustdo;
834	isl_set *maydo;
835	isl_flow *res;
836
837	res = isl_flow_alloc(acc);
838	if (!res)
839		return NULL;
840
841	mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
842	maydo = isl_set_copy(mustdo);
843
844	for (i = 0; i < acc->n_may; ++i) {
845		int plevel;
846		int is_before;
847		isl_space *dim;
848		isl_map *before;
849		isl_map *dep;
850
851		plevel = acc->level_before(acc->source[i].data, acc->sink.data);
852		is_before = plevel & 1;
853		plevel >>= 1;
854
855		dim = isl_map_get_space(res->dep[i].map);
856		if (is_before)
857			before = isl_map_lex_le_first(dim, plevel);
858		else
859			before = isl_map_lex_lt_first(dim, plevel);
860		dep = isl_map_apply_range(isl_map_copy(acc->source[i].map),
861			isl_map_reverse(isl_map_copy(acc->sink.map)));
862		dep = isl_map_intersect(dep, before);
863		mustdo = isl_set_subtract(mustdo,
864					    isl_map_range(isl_map_copy(dep)));
865		res->dep[i].map = isl_map_union(res->dep[i].map, dep);
866	}
867
868	res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));
869	res->must_no_source = mustdo;
870
871	return res;
872}
873
874/* Compute dependences for the case where there is at least one
875 * "must" access.
876 *
877 * The core algorithm considers all levels in which a source may precede
878 * the sink, where a level may either be a statement level or a loop level.
879 * The outermost statement level is 1, the first loop level is 2, etc...
880 * The algorithm basically does the following:
881 * for all levels l of the read access from innermost to outermost
882 *	for all sources w that may precede the sink access at that level
883 *	    compute the last iteration of the source that precedes the sink access
884 *					    at that level
885 *	    add result to possible last accesses at level l of source w
886 *	    for all sources w2 that we haven't considered yet at this level that may
887 *					    also precede the sink access
888 *		for all levels l2 of w from l to innermost
889 *		    for all possible last accesses dep of w at l
890 *			compute last iteration of w2 between the source and sink
891 *								of dep
892 *			add result to possible last accesses at level l of write w2
893 *			and replace possible last accesses dep by the remainder
894 *
895 *
896 * The above algorithm is applied to the must access.  During the course
897 * of the algorithm, we keep track of sink iterations that still
898 * need to be considered.  These iterations are split into those that
899 * haven't been matched to any source access (mustdo) and those that have only
900 * been matched to may accesses (maydo).
901 * At the end of each level, we also consider the may accesses.
902 * In particular, we consider may accesses that precede the remaining
903 * sink iterations, moving elements from mustdo to maydo when appropriate,
904 * and may accesses that occur between a must source and a sink of any
905 * dependences found at the current level, turning must dependences into
906 * may dependences when appropriate.
907 *
908 */
909static __isl_give isl_flow *compute_val_based_dependences(
910	__isl_keep isl_access_info *acc)
911{
912	isl_ctx *ctx;
913	isl_flow *res;
914	isl_set *mustdo = NULL;
915	isl_set *maydo = NULL;
916	int level, j;
917	int depth;
918	isl_map **must_rel = NULL;
919	isl_map **may_rel = NULL;
920
921	if (!acc)
922		return NULL;
923
924	res = isl_flow_alloc(acc);
925	if (!res)
926		goto error;
927	ctx = isl_map_get_ctx(acc->sink.map);
928
929	depth = 2 * isl_map_dim(acc->sink.map, isl_dim_in) + 1;
930	mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
931	maydo = isl_set_empty_like(mustdo);
932	if (!mustdo || !maydo)
933		goto error;
934	if (isl_set_plain_is_empty(mustdo))
935		goto done;
936
937	must_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
938	may_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
939	if (!must_rel || !may_rel)
940		goto error;
941
942	for (level = depth; level >= 1; --level) {
943		for (j = acc->n_must-1; j >=0; --j) {
944			must_rel[j] = isl_map_empty_like(res->dep[j].map);
945			may_rel[j] = isl_map_copy(must_rel[j]);
946		}
947
948		for (j = acc->n_must - 1; j >= 0; --j) {
949			struct isl_map *T;
950			struct isl_set *rest;
951			int plevel;
952
953			plevel = acc->level_before(acc->source[j].data,
954						     acc->sink.data);
955			if (!can_precede_at_level(plevel, level))
956				continue;
957
958			T = last_source(acc, mustdo, j, level, &rest);
959			must_rel[j] = isl_map_union_disjoint(must_rel[j], T);
960			mustdo = rest;
961
962			intermediate_sources(acc, must_rel, j, level);
963
964			T = last_source(acc, maydo, j, level, &rest);
965			may_rel[j] = isl_map_union_disjoint(may_rel[j], T);
966			maydo = rest;
967
968			intermediate_sources(acc, may_rel, j, level);
969
970			if (isl_set_plain_is_empty(mustdo) &&
971			    isl_set_plain_is_empty(maydo))
972				break;
973		}
974		for (j = j - 1; j >= 0; --j) {
975			int plevel;
976
977			plevel = acc->level_before(acc->source[j].data,
978						     acc->sink.data);
979			if (!can_precede_at_level(plevel, level))
980				continue;
981
982			intermediate_sources(acc, must_rel, j, level);
983			intermediate_sources(acc, may_rel, j, level);
984		}
985
986		for (j = 0; j < acc->n_may; ++j) {
987			int plevel;
988			isl_map *T;
989			isl_set *ran;
990
991			plevel = acc->level_before(acc->source[acc->n_must + j].data,
992						     acc->sink.data);
993			if (!can_precede_at_level(plevel, level))
994				continue;
995
996			T = all_sources(acc, isl_set_copy(maydo), j, level);
997			res->dep[2 * acc->n_must + j].map =
998			    isl_map_union(res->dep[2 * acc->n_must + j].map, T);
999			T = all_sources(acc, isl_set_copy(mustdo), j, level);
1000			ran = isl_map_range(isl_map_copy(T));
1001			res->dep[2 * acc->n_must + j].map =
1002			    isl_map_union(res->dep[2 * acc->n_must + j].map, T);
1003			mustdo = isl_set_subtract(mustdo, isl_set_copy(ran));
1004			maydo = isl_set_union_disjoint(maydo, ran);
1005
1006			T = res->dep[2 * acc->n_must + j].map;
1007			T = all_intermediate_sources(acc, T, must_rel, may_rel,
1008							j, level);
1009			res->dep[2 * acc->n_must + j].map = T;
1010		}
1011
1012		for (j = acc->n_must - 1; j >= 0; --j) {
1013			res->dep[2 * j].map =
1014				isl_map_union_disjoint(res->dep[2 * j].map,
1015							     must_rel[j]);
1016			res->dep[2 * j + 1].map =
1017				isl_map_union_disjoint(res->dep[2 * j + 1].map,
1018							     may_rel[j]);
1019		}
1020
1021		if (isl_set_plain_is_empty(mustdo) &&
1022		    isl_set_plain_is_empty(maydo))
1023			break;
1024	}
1025
1026	free(must_rel);
1027	free(may_rel);
1028done:
1029	res->must_no_source = mustdo;
1030	res->may_no_source = maydo;
1031	return res;
1032error:
1033	isl_flow_free(res);
1034	isl_set_free(mustdo);
1035	isl_set_free(maydo);
1036	free(must_rel);
1037	free(may_rel);
1038	return NULL;
1039}
1040
1041/* Given a "sink" access, a list of n "source" accesses,
1042 * compute for each iteration of the sink access
1043 * and for each element accessed by that iteration,
1044 * the source access in the list that last accessed the
1045 * element accessed by the sink access before this sink access.
1046 * Each access is given as a map from the loop iterators
1047 * to the array indices.
1048 * The result is a list of n relations between source and sink
1049 * iterations and a subset of the domain of the sink access,
1050 * corresponding to those iterations that access an element
1051 * not previously accessed.
1052 *
1053 * To deal with multi-valued sink access relations, the sink iteration
1054 * domain is first extended with dimensions that correspond to the data
1055 * space.  After the computation is finished, these extra dimensions are
1056 * projected out again.
1057 */
1058__isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)
1059{
1060	int j;
1061	struct isl_flow *res = NULL;
1062
1063	if (!acc)
1064		return NULL;
1065
1066	acc->domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));
1067	acc->sink.map = isl_map_range_map(acc->sink.map);
1068	if (!acc->sink.map)
1069		goto error;
1070
1071	if (acc->n_must == 0)
1072		res = compute_mem_based_dependences(acc);
1073	else {
1074		acc = isl_access_info_sort_sources(acc);
1075		res = compute_val_based_dependences(acc);
1076	}
1077	if (!res)
1078		goto error;
1079
1080	for (j = 0; j < res->n_source; ++j) {
1081		res->dep[j].map = isl_map_apply_range(res->dep[j].map,
1082					isl_map_copy(acc->domain_map));
1083		if (!res->dep[j].map)
1084			goto error;
1085	}
1086	if (!res->must_no_source || !res->may_no_source)
1087		goto error;
1088
1089	isl_access_info_free(acc);
1090	return res;
1091error:
1092	isl_access_info_free(acc);
1093	isl_flow_free(res);
1094	return NULL;
1095}
1096
1097
1098/* Keep track of some information about a schedule for a given
1099 * access.  In particular, keep track of which dimensions
1100 * have a constant value and of the actual constant values.
1101 */
1102struct isl_sched_info {
1103	int *is_cst;
1104	isl_vec *cst;
1105};
1106
1107static void sched_info_free(__isl_take struct isl_sched_info *info)
1108{
1109	if (!info)
1110		return;
1111	isl_vec_free(info->cst);
1112	free(info->is_cst);
1113	free(info);
1114}
1115
1116/* Extract information on the constant dimensions of the schedule
1117 * for a given access.  The "map" is of the form
1118 *
1119 *	[S -> D] -> A
1120 *
1121 * with S the schedule domain, D the iteration domain and A the data domain.
1122 */
1123static __isl_give struct isl_sched_info *sched_info_alloc(
1124	__isl_keep isl_map *map)
1125{
1126	isl_ctx *ctx;
1127	isl_space *dim;
1128	struct isl_sched_info *info;
1129	int i, n;
1130
1131	if (!map)
1132		return NULL;
1133
1134	dim = isl_space_unwrap(isl_space_domain(isl_map_get_space(map)));
1135	if (!dim)
1136		return NULL;
1137	n = isl_space_dim(dim, isl_dim_in);
1138	isl_space_free(dim);
1139
1140	ctx = isl_map_get_ctx(map);
1141	info = isl_alloc_type(ctx, struct isl_sched_info);
1142	if (!info)
1143		return NULL;
1144	info->is_cst = isl_alloc_array(ctx, int, n);
1145	info->cst = isl_vec_alloc(ctx, n);
1146	if (n && (!info->is_cst || !info->cst))
1147		goto error;
1148
1149	for (i = 0; i < n; ++i) {
1150		isl_val *v;
1151
1152		v = isl_map_plain_get_val_if_fixed(map, isl_dim_in, i);
1153		if (!v)
1154			goto error;
1155		info->is_cst[i] = !isl_val_is_nan(v);
1156		if (info->is_cst[i])
1157			info->cst = isl_vec_set_element_val(info->cst, i, v);
1158		else
1159			isl_val_free(v);
1160	}
1161
1162	return info;
1163error:
1164	sched_info_free(info);
1165	return NULL;
1166}
1167
1168struct isl_compute_flow_data {
1169	isl_union_map *must_source;
1170	isl_union_map *may_source;
1171	isl_union_map *must_dep;
1172	isl_union_map *may_dep;
1173	isl_union_map *must_no_source;
1174	isl_union_map *may_no_source;
1175
1176	int count;
1177	int must;
1178	isl_space *dim;
1179	struct isl_sched_info *sink_info;
1180	struct isl_sched_info **source_info;
1181	isl_access_info *accesses;
1182};
1183
1184static int count_matching_array(__isl_take isl_map *map, void *user)
1185{
1186	int eq;
1187	isl_space *dim;
1188	struct isl_compute_flow_data *data;
1189
1190	data = (struct isl_compute_flow_data *)user;
1191
1192	dim = isl_space_range(isl_map_get_space(map));
1193
1194	eq = isl_space_is_equal(dim, data->dim);
1195
1196	isl_space_free(dim);
1197	isl_map_free(map);
1198
1199	if (eq < 0)
1200		return -1;
1201	if (eq)
1202		data->count++;
1203
1204	return 0;
1205}
1206
1207static int collect_matching_array(__isl_take isl_map *map, void *user)
1208{
1209	int eq;
1210	isl_space *dim;
1211	struct isl_sched_info *info;
1212	struct isl_compute_flow_data *data;
1213
1214	data = (struct isl_compute_flow_data *)user;
1215
1216	dim = isl_space_range(isl_map_get_space(map));
1217
1218	eq = isl_space_is_equal(dim, data->dim);
1219
1220	isl_space_free(dim);
1221
1222	if (eq < 0)
1223		goto error;
1224	if (!eq) {
1225		isl_map_free(map);
1226		return 0;
1227	}
1228
1229	info = sched_info_alloc(map);
1230	data->source_info[data->count] = info;
1231
1232	data->accesses = isl_access_info_add_source(data->accesses,
1233						    map, data->must, info);
1234
1235	data->count++;
1236
1237	return 0;
1238error:
1239	isl_map_free(map);
1240	return -1;
1241}
1242
1243/* Determine the shared nesting level and the "textual order" of
1244 * the given accesses.
1245 *
1246 * We first determine the minimal schedule dimension for both accesses.
1247 *
1248 * If among those dimensions, we can find one where both have a fixed
1249 * value and if moreover those values are different, then the previous
1250 * dimension is the last shared nesting level and the textual order
1251 * is determined based on the order of the fixed values.
1252 * If no such fixed values can be found, then we set the shared
1253 * nesting level to the minimal schedule dimension, with no textual ordering.
1254 */
1255static int before(void *first, void *second)
1256{
1257	struct isl_sched_info *info1 = first;
1258	struct isl_sched_info *info2 = second;
1259	int n1, n2;
1260	int i;
1261
1262	n1 = isl_vec_size(info1->cst);
1263	n2 = isl_vec_size(info2->cst);
1264
1265	if (n2 < n1)
1266		n1 = n2;
1267
1268	for (i = 0; i < n1; ++i) {
1269		int r;
1270		int cmp;
1271
1272		if (!info1->is_cst[i])
1273			continue;
1274		if (!info2->is_cst[i])
1275			continue;
1276		cmp = isl_vec_cmp_element(info1->cst, info2->cst, i);
1277		if (cmp == 0)
1278			continue;
1279
1280		r = 2 * i + (cmp < 0);
1281
1282		return r;
1283	}
1284
1285	return 2 * n1;
1286}
1287
1288/* Given a sink access, look for all the source accesses that access
1289 * the same array and perform dataflow analysis on them using
1290 * isl_access_info_compute_flow.
1291 */
1292static int compute_flow(__isl_take isl_map *map, void *user)
1293{
1294	int i;
1295	isl_ctx *ctx;
1296	struct isl_compute_flow_data *data;
1297	isl_flow *flow;
1298
1299	data = (struct isl_compute_flow_data *)user;
1300
1301	ctx = isl_map_get_ctx(map);
1302
1303	data->accesses = NULL;
1304	data->sink_info = NULL;
1305	data->source_info = NULL;
1306	data->count = 0;
1307	data->dim = isl_space_range(isl_map_get_space(map));
1308
1309	if (isl_union_map_foreach_map(data->must_source,
1310					&count_matching_array, data) < 0)
1311		goto error;
1312	if (isl_union_map_foreach_map(data->may_source,
1313					&count_matching_array, data) < 0)
1314		goto error;
1315
1316	data->sink_info = sched_info_alloc(map);
1317	data->source_info = isl_calloc_array(ctx, struct isl_sched_info *,
1318					     data->count);
1319
1320	data->accesses = isl_access_info_alloc(isl_map_copy(map),
1321				data->sink_info, &before, data->count);
1322	if (!data->sink_info || (data->count && !data->source_info) ||
1323	    !data->accesses)
1324		goto error;
1325	data->count = 0;
1326	data->must = 1;
1327	if (isl_union_map_foreach_map(data->must_source,
1328					&collect_matching_array, data) < 0)
1329		goto error;
1330	data->must = 0;
1331	if (isl_union_map_foreach_map(data->may_source,
1332					&collect_matching_array, data) < 0)
1333		goto error;
1334
1335	flow = isl_access_info_compute_flow(data->accesses);
1336	data->accesses = NULL;
1337
1338	if (!flow)
1339		goto error;
1340
1341	data->must_no_source = isl_union_map_union(data->must_no_source,
1342		    isl_union_map_from_map(isl_flow_get_no_source(flow, 1)));
1343	data->may_no_source = isl_union_map_union(data->may_no_source,
1344		    isl_union_map_from_map(isl_flow_get_no_source(flow, 0)));
1345
1346	for (i = 0; i < flow->n_source; ++i) {
1347		isl_union_map *dep;
1348		dep = isl_union_map_from_map(isl_map_copy(flow->dep[i].map));
1349		if (flow->dep[i].must)
1350			data->must_dep = isl_union_map_union(data->must_dep, dep);
1351		else
1352			data->may_dep = isl_union_map_union(data->may_dep, dep);
1353	}
1354
1355	isl_flow_free(flow);
1356
1357	sched_info_free(data->sink_info);
1358	if (data->source_info) {
1359		for (i = 0; i < data->count; ++i)
1360			sched_info_free(data->source_info[i]);
1361		free(data->source_info);
1362	}
1363	isl_space_free(data->dim);
1364	isl_map_free(map);
1365
1366	return 0;
1367error:
1368	isl_access_info_free(data->accesses);
1369	sched_info_free(data->sink_info);
1370	if (data->source_info) {
1371		for (i = 0; i < data->count; ++i)
1372			sched_info_free(data->source_info[i]);
1373		free(data->source_info);
1374	}
1375	isl_space_free(data->dim);
1376	isl_map_free(map);
1377
1378	return -1;
1379}
1380
1381/* Given a collection of "sink" and "source" accesses,
1382 * compute for each iteration of a sink access
1383 * and for each element accessed by that iteration,
1384 * the source access in the list that last accessed the
1385 * element accessed by the sink access before this sink access.
1386 * Each access is given as a map from the loop iterators
1387 * to the array indices.
1388 * The result is a relations between source and sink
1389 * iterations and a subset of the domain of the sink accesses,
1390 * corresponding to those iterations that access an element
1391 * not previously accessed.
1392 *
1393 * We first prepend the schedule dimensions to the domain
1394 * of the accesses so that we can easily compare their relative order.
1395 * Then we consider each sink access individually in compute_flow.
1396 */
1397int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
1398	__isl_take isl_union_map *must_source,
1399	__isl_take isl_union_map *may_source,
1400	__isl_take isl_union_map *schedule,
1401	__isl_give isl_union_map **must_dep, __isl_give isl_union_map **may_dep,
1402	__isl_give isl_union_map **must_no_source,
1403	__isl_give isl_union_map **may_no_source)
1404{
1405	isl_space *dim;
1406	isl_union_map *range_map = NULL;
1407	struct isl_compute_flow_data data;
1408
1409	sink = isl_union_map_align_params(sink,
1410					    isl_union_map_get_space(must_source));
1411	sink = isl_union_map_align_params(sink,
1412					    isl_union_map_get_space(may_source));
1413	sink = isl_union_map_align_params(sink,
1414					    isl_union_map_get_space(schedule));
1415	dim = isl_union_map_get_space(sink);
1416	must_source = isl_union_map_align_params(must_source, isl_space_copy(dim));
1417	may_source = isl_union_map_align_params(may_source, isl_space_copy(dim));
1418	schedule = isl_union_map_align_params(schedule, isl_space_copy(dim));
1419
1420	schedule = isl_union_map_reverse(schedule);
1421	range_map = isl_union_map_range_map(schedule);
1422	schedule = isl_union_map_reverse(isl_union_map_copy(range_map));
1423	sink = isl_union_map_apply_domain(sink, isl_union_map_copy(schedule));
1424	must_source = isl_union_map_apply_domain(must_source,
1425						isl_union_map_copy(schedule));
1426	may_source = isl_union_map_apply_domain(may_source, schedule);
1427
1428	data.must_source = must_source;
1429	data.may_source = may_source;
1430	data.must_dep = must_dep ?
1431		isl_union_map_empty(isl_space_copy(dim)) : NULL;
1432	data.may_dep = may_dep ? isl_union_map_empty(isl_space_copy(dim)) : NULL;
1433	data.must_no_source = must_no_source ?
1434		isl_union_map_empty(isl_space_copy(dim)) : NULL;
1435	data.may_no_source = may_no_source ?
1436		isl_union_map_empty(isl_space_copy(dim)) : NULL;
1437
1438	isl_space_free(dim);
1439
1440	if (isl_union_map_foreach_map(sink, &compute_flow, &data) < 0)
1441		goto error;
1442
1443	isl_union_map_free(sink);
1444	isl_union_map_free(must_source);
1445	isl_union_map_free(may_source);
1446
1447	if (must_dep) {
1448		data.must_dep = isl_union_map_apply_domain(data.must_dep,
1449					isl_union_map_copy(range_map));
1450		data.must_dep = isl_union_map_apply_range(data.must_dep,
1451					isl_union_map_copy(range_map));
1452		*must_dep = data.must_dep;
1453	}
1454	if (may_dep) {
1455		data.may_dep = isl_union_map_apply_domain(data.may_dep,
1456					isl_union_map_copy(range_map));
1457		data.may_dep = isl_union_map_apply_range(data.may_dep,
1458					isl_union_map_copy(range_map));
1459		*may_dep = data.may_dep;
1460	}
1461	if (must_no_source) {
1462		data.must_no_source = isl_union_map_apply_domain(
1463			data.must_no_source, isl_union_map_copy(range_map));
1464		*must_no_source = data.must_no_source;
1465	}
1466	if (may_no_source) {
1467		data.may_no_source = isl_union_map_apply_domain(
1468			data.may_no_source, isl_union_map_copy(range_map));
1469		*may_no_source = data.may_no_source;
1470	}
1471
1472	isl_union_map_free(range_map);
1473
1474	return 0;
1475error:
1476	isl_union_map_free(range_map);
1477	isl_union_map_free(sink);
1478	isl_union_map_free(must_source);
1479	isl_union_map_free(may_source);
1480	isl_union_map_free(data.must_dep);
1481	isl_union_map_free(data.may_dep);
1482	isl_union_map_free(data.must_no_source);
1483	isl_union_map_free(data.may_no_source);
1484
1485	if (must_dep)
1486		*must_dep = NULL;
1487	if (may_dep)
1488		*may_dep = NULL;
1489	if (must_no_source)
1490		*must_no_source = NULL;
1491	if (may_no_source)
1492		*may_no_source = NULL;
1493	return -1;
1494}
1495