nexmon – Blame information for rev 1

Subversion Repositories:
Rev:
Rev Author Line No. Line
1 office 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 GNU LGPLv2.1 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_qsort.h>
21  
22 enum 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  
29 struct isl_restriction {
30 enum isl_restriction_type type;
31  
32 isl_set *source;
33 isl_set *sink;
34 };
35  
36 /* Create a restriction that doesn't restrict anything.
37 */
38 __isl_give isl_restriction *isl_restriction_none(__isl_take isl_map *source_map)
39 {
40 isl_ctx *ctx;
41 isl_restriction *restr;
42  
43 if (!source_map)
44 return NULL;
45  
46 ctx = isl_map_get_ctx(source_map);
47 restr = isl_calloc_type(ctx, struct isl_restriction);
48 if (!restr)
49 goto error;
50  
51 restr->type = isl_restriction_type_none;
52  
53 isl_map_free(source_map);
54 return restr;
55 error:
56 isl_map_free(source_map);
57 return NULL;
58 }
59  
60 /* Create a restriction that removes everything.
61 */
62 __isl_give isl_restriction *isl_restriction_empty(
63 __isl_take isl_map *source_map)
64 {
65 isl_ctx *ctx;
66 isl_restriction *restr;
67  
68 if (!source_map)
69 return NULL;
70  
71 ctx = isl_map_get_ctx(source_map);
72 restr = isl_calloc_type(ctx, struct isl_restriction);
73 if (!restr)
74 goto error;
75  
76 restr->type = isl_restriction_type_empty;
77  
78 isl_map_free(source_map);
79 return restr;
80 error:
81 isl_map_free(source_map);
82 return NULL;
83 }
84  
85 /* Create a restriction on the input of the maximization problem
86 * based on the given source and sink restrictions.
87 */
88 __isl_give isl_restriction *isl_restriction_input(
89 __isl_take isl_set *source_restr, __isl_take isl_set *sink_restr)
90 {
91 isl_ctx *ctx;
92 isl_restriction *restr;
93  
94 if (!source_restr || !sink_restr)
95 goto error;
96  
97 ctx = isl_set_get_ctx(source_restr);
98 restr = isl_calloc_type(ctx, struct isl_restriction);
99 if (!restr)
100 goto error;
101  
102 restr->type = isl_restriction_type_input;
103 restr->source = source_restr;
104 restr->sink = sink_restr;
105  
106 return restr;
107 error:
108 isl_set_free(source_restr);
109 isl_set_free(sink_restr);
110 return NULL;
111 }
112  
113 /* Create a restriction on the output of the maximization problem
114 * based on the given source restriction.
115 */
116 __isl_give isl_restriction *isl_restriction_output(
117 __isl_take isl_set *source_restr)
118 {
119 isl_ctx *ctx;
120 isl_restriction *restr;
121  
122 if (!source_restr)
123 return NULL;
124  
125 ctx = isl_set_get_ctx(source_restr);
126 restr = isl_calloc_type(ctx, struct isl_restriction);
127 if (!restr)
128 goto error;
129  
130 restr->type = isl_restriction_type_output;
131 restr->source = source_restr;
132  
133 return restr;
134 error:
135 isl_set_free(source_restr);
136 return NULL;
137 }
138  
139 void *isl_restriction_free(__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  
150 isl_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 with
156 * a user-specified identifier and a boolean indicating whether
157 * the map represents a must or may access/dependence.
158 */
159 struct isl_labeled_map {
160 struct isl_map *map;
161 void *data;
162 int must;
163 };
164  
165 /* A structure containing the input for dependence analysis:
166 * - a sink
167 * - n_must + n_may (<= max_source) sources
168 * - a function for determining the relative order of sources and sink
169 * The must sources are placed before the may sources.
170 *
171 * domain_map is an auxiliary map that maps the sink access relation
172 * to the domain of this access relation.
173 *
174 * restrict_fn is a callback that (if not NULL) will be called
175 * right before any lexicographical maximization.
176 */
177 struct isl_access_info {
178 isl_map *domain_map;
179 struct isl_labeled_map sink;
180 isl_access_level_before level_before;
181  
182 isl_access_restrict restrict_fn;
183 void *restrict_user;
184  
185 int max_source;
186 int n_must;
187 int n_may;
188 struct isl_labeled_map source[1];
189 };
190  
191 /* A structure containing the output of dependence analysis:
192 * - n_source dependences
193 * - a wrapped subset of the sink for which definitely no source could be found
194 * - a wrapped subset of the sink for which possibly no source could be found
195 */
196 struct isl_flow {
197 isl_set *must_no_source;
198 isl_set *may_no_source;
199 int n_source;
200 struct isl_labeled_map *dep;
201 };
202  
203 /* Construct an isl_access_info structure and fill it up with
204 * the given data. The number of sources is set to 0.
205 */
206 __isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,
207 void *sink_user, isl_access_level_before fn, int max_source)
208 {
209 isl_ctx *ctx;
210 struct isl_access_info *acc;
211  
212 if (!sink)
213 return NULL;
214  
215 ctx = isl_map_get_ctx(sink);
216 isl_assert(ctx, max_source >= 0, goto error);
217  
218 acc = isl_calloc(ctx, struct isl_access_info,
219 sizeof(struct isl_access_info) +
220 (max_source - 1) * sizeof(struct isl_labeled_map));
221 if (!acc)
222 goto error;
223  
224 acc->sink.map = sink;
225 acc->sink.data = sink_user;
226 acc->level_before = fn;
227 acc->max_source = max_source;
228 acc->n_must = 0;
229 acc->n_may = 0;
230  
231 return acc;
232 error:
233 isl_map_free(sink);
234 return NULL;
235 }
236  
237 /* Free the given isl_access_info structure.
238 */
239 void isl_access_info_free(__isl_take isl_access_info *acc)
240 {
241 int i;
242  
243 if (!acc)
244 return;
245 isl_map_free(acc->domain_map);
246 isl_map_free(acc->sink.map);
247 for (i = 0; i < acc->n_must + acc->n_may; ++i)
248 isl_map_free(acc->source[i].map);
249 free(acc);
250 }
251  
252 isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)
253 {
254 return acc ? isl_map_get_ctx(acc->sink.map) : NULL;
255 }
256  
257 __isl_give isl_access_info *isl_access_info_set_restrict(
258 __isl_take isl_access_info *acc, isl_access_restrict fn, void *user)
259 {
260 if (!acc)
261 return NULL;
262 acc->restrict_fn = fn;
263 acc->restrict_user = user;
264 return acc;
265 }
266  
267 /* Add another source to an isl_access_info structure, making
268 * sure the "must" sources are placed before the "may" sources.
269 * This function may be called at most max_source times on a
270 * given isl_access_info structure, with max_source as specified
271 * in the call to isl_access_info_alloc that constructed the structure.
272 */
273 __isl_give isl_access_info *isl_access_info_add_source(
274 __isl_take isl_access_info *acc, __isl_take isl_map *source,
275 int must, void *source_user)
276 {
277 isl_ctx *ctx;
278  
279 if (!acc)
280 return NULL;
281 ctx = isl_map_get_ctx(acc->sink.map);
282 isl_assert(ctx, acc->n_must + acc->n_may < acc->max_source, goto error);
283  
284 if (must) {
285 if (acc->n_may)
286 acc->source[acc->n_must + acc->n_may] =
287 acc->source[acc->n_must];
288 acc->source[acc->n_must].map = source;
289 acc->source[acc->n_must].data = source_user;
290 acc->source[acc->n_must].must = 1;
291 acc->n_must++;
292 } else {
293 acc->source[acc->n_must + acc->n_may].map = source;
294 acc->source[acc->n_must + acc->n_may].data = source_user;
295 acc->source[acc->n_must + acc->n_may].must = 0;
296 acc->n_may++;
297 }
298  
299 return acc;
300 error:
301 isl_map_free(source);
302 isl_access_info_free(acc);
303 return NULL;
304 }
305  
306 /* Return -n, 0 or n (with n a positive value), depending on whether
307 * the source access identified by p1 should be sorted before, together
308 * or after that identified by p2.
309 *
310 * If p1 appears before p2, then it should be sorted first.
311 * For more generic initial schedules, it is possible that neither
312 * p1 nor p2 appears before the other, or at least not in any obvious way.
313 * We therefore also check if p2 appears before p1, in which case p2
314 * should be sorted first.
315 * If not, we try to order the two statements based on the description
316 * of the iteration domains. This results in an arbitrary, but fairly
317 * stable ordering.
318 */
319 static int access_sort_cmp(const void *p1, const void *p2, void *user)
320 {
321 isl_access_info *acc = user;
322 const struct isl_labeled_map *i1, *i2;
323 int level1, level2;
324 uint32_t h1, h2;
325 i1 = (const struct isl_labeled_map *) p1;
326 i2 = (const struct isl_labeled_map *) p2;
327  
328 level1 = acc->level_before(i1->data, i2->data);
329 if (level1 % 2)
330 return -1;
331  
332 level2 = acc->level_before(i2->data, i1->data);
333 if (level2 % 2)
334 return 1;
335  
336 h1 = isl_map_get_hash(i1->map);
337 h2 = isl_map_get_hash(i2->map);
338 return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;
339 }
340  
341 /* Sort the must source accesses in their textual order.
342 */
343 static __isl_give isl_access_info *isl_access_info_sort_sources(
344 __isl_take isl_access_info *acc)
345 {
346 if (!acc)
347 return NULL;
348 if (acc->n_must <= 1)
349 return acc;
350  
351 isl_quicksort(acc->source, acc->n_must, sizeof(struct isl_labeled_map),
352 access_sort_cmp, acc);
353  
354 return acc;
355 }
356  
357 /* Align the parameters of the two spaces if needed and then call
358 * isl_space_join.
359 */
360 static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,
361 __isl_take isl_space *right)
362 {
363 if (isl_space_match(left, isl_dim_param, right, isl_dim_param))
364 return isl_space_join(left, right);
365  
366 left = isl_space_align_params(left, isl_space_copy(right));
367 right = isl_space_align_params(right, isl_space_copy(left));
368 return isl_space_join(left, right);
369 }
370  
371 /* Initialize an empty isl_flow structure corresponding to a given
372 * isl_access_info structure.
373 * For each must access, two dependences are created (initialized
374 * to the empty relation), one for the resulting must dependences
375 * and one for the resulting may dependences. May accesses can
376 * only lead to may dependences, so only one dependence is created
377 * for each of them.
378 * This function is private as isl_flow structures are only supposed
379 * to be created by isl_access_info_compute_flow.
380 */
381 static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
382 {
383 int i;
384 struct isl_ctx *ctx;
385 struct isl_flow *dep;
386  
387 if (!acc)
388 return NULL;
389  
390 ctx = isl_map_get_ctx(acc->sink.map);
391 dep = isl_calloc_type(ctx, struct isl_flow);
392 if (!dep)
393 return NULL;
394  
395 dep->dep = isl_calloc_array(ctx, struct isl_labeled_map,
396 2 * acc->n_must + acc->n_may);
397 if (!dep->dep)
398 goto error;
399  
400 dep->n_source = 2 * acc->n_must + acc->n_may;
401 for (i = 0; i < acc->n_must; ++i) {
402 isl_space *dim;
403 dim = space_align_and_join(
404 isl_map_get_space(acc->source[i].map),
405 isl_space_reverse(isl_map_get_space(acc->sink.map)));
406 dep->dep[2 * i].map = isl_map_empty(dim);
407 dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);
408 dep->dep[2 * i].data = acc->source[i].data;
409 dep->dep[2 * i + 1].data = acc->source[i].data;
410 dep->dep[2 * i].must = 1;
411 dep->dep[2 * i + 1].must = 0;
412 if (!dep->dep[2 * i].map || !dep->dep[2 * i + 1].map)
413 goto error;
414 }
415 for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {
416 isl_space *dim;
417 dim = space_align_and_join(
418 isl_map_get_space(acc->source[i].map),
419 isl_space_reverse(isl_map_get_space(acc->sink.map)));
420 dep->dep[acc->n_must + i].map = isl_map_empty(dim);
421 dep->dep[acc->n_must + i].data = acc->source[i].data;
422 dep->dep[acc->n_must + i].must = 0;
423 if (!dep->dep[acc->n_must + i].map)
424 goto error;
425 }
426  
427 return dep;
428 error:
429 isl_flow_free(dep);
430 return NULL;
431 }
432  
433 /* Iterate over all sources and for each resulting flow dependence
434 * that is not empty, call the user specfied function.
435 * The second argument in this function call identifies the source,
436 * while the third argument correspond to the final argument of
437 * the isl_flow_foreach call.
438 */
439 int isl_flow_foreach(__isl_keep isl_flow *deps,
440 int (*fn)(__isl_take isl_map *dep, int must, void *dep_user, void *user),
441 void *user)
442 {
443 int i;
444  
445 if (!deps)
446 return -1;
447  
448 for (i = 0; i < deps->n_source; ++i) {
449 if (isl_map_plain_is_empty(deps->dep[i].map))
450 continue;
451 if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,
452 deps->dep[i].data, user) < 0)
453 return -1;
454 }
455  
456 return 0;
457 }
458  
459 /* Return a copy of the subset of the sink for which no source could be found.
460 */
461 __isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
462 {
463 if (!deps)
464 return NULL;
465  
466 if (must)
467 return isl_set_unwrap(isl_set_copy(deps->must_no_source));
468 else
469 return isl_set_unwrap(isl_set_copy(deps->may_no_source));
470 }
471  
472 void isl_flow_free(__isl_take isl_flow *deps)
473 {
474 int i;
475  
476 if (!deps)
477 return;
478 isl_set_free(deps->must_no_source);
479 isl_set_free(deps->may_no_source);
480 if (deps->dep) {
481 for (i = 0; i < deps->n_source; ++i)
482 isl_map_free(deps->dep[i].map);
483 free(deps->dep);
484 }
485 free(deps);
486 }
487  
488 isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)
489 {
490 return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;
491 }
492  
493 /* Return a map that enforces that the domain iteration occurs after
494 * the range iteration at the given level.
495 * If level is odd, then the domain iteration should occur after
496 * the target iteration in their shared level/2 outermost loops.
497 * In this case we simply need to enforce that these outermost
498 * loop iterations are the same.
499 * If level is even, then the loop iterator of the domain should
500 * be greater than the loop iterator of the range at the last
501 * of the level/2 shared loops, i.e., loop level/2 - 1.
502 */
503 static __isl_give isl_map *after_at_level(__isl_take isl_space *dim, int level)
504 {
505 struct isl_basic_map *bmap;
506  
507 if (level % 2)
508 bmap = isl_basic_map_equal(dim, level/2);
509 else
510 bmap = isl_basic_map_more_at(dim, level/2 - 1);
511  
512 return isl_map_from_basic_map(bmap);
513 }
514  
515 /* Compute the partial lexicographic maximum of "dep" on domain "sink",
516 * but first check if the user has set acc->restrict_fn and if so
517 * update either the input or the output of the maximization problem
518 * with respect to the resulting restriction.
519 *
520 * Since the user expects a mapping from sink iterations to source iterations,
521 * whereas the domain of "dep" is a wrapped map, mapping sink iterations
522 * to accessed array elements, we first need to project out the accessed
523 * sink array elements by applying acc->domain_map.
524 * Similarly, the sink restriction specified by the user needs to be
525 * converted back to the wrapped map.
526 */
527 static __isl_give isl_map *restricted_partial_lexmax(
528 __isl_keep isl_access_info *acc, __isl_take isl_map *dep,
529 int source, __isl_take isl_set *sink, __isl_give isl_set **empty)
530 {
531 isl_map *source_map;
532 isl_restriction *restr;
533 isl_set *sink_domain;
534 isl_set *sink_restr;
535 isl_map *res;
536  
537 if (!acc->restrict_fn)
538 return isl_map_partial_lexmax(dep, sink, empty);
539  
540 source_map = isl_map_copy(dep);
541 source_map = isl_map_apply_domain(source_map,
542 isl_map_copy(acc->domain_map));
543 sink_domain = isl_set_copy(sink);
544 sink_domain = isl_set_apply(sink_domain, isl_map_copy(acc->domain_map));
545 restr = acc->restrict_fn(source_map, sink_domain,
546 acc->source[source].data, acc->restrict_user);
547 isl_set_free(sink_domain);
548 isl_map_free(source_map);
549  
550 if (!restr)
551 goto error;
552 if (restr->type == isl_restriction_type_input) {
553 dep = isl_map_intersect_range(dep, isl_set_copy(restr->source));
554 sink_restr = isl_set_copy(restr->sink);
555 sink_restr = isl_set_apply(sink_restr,
556 isl_map_reverse(isl_map_copy(acc->domain_map)));
557 sink = isl_set_intersect(sink, sink_restr);
558 } else if (restr->type == isl_restriction_type_empty) {
559 isl_space *space = isl_map_get_space(dep);
560 isl_map_free(dep);
561 dep = isl_map_empty(space);
562 }
563  
564 res = isl_map_partial_lexmax(dep, sink, empty);
565  
566 if (restr->type == isl_restriction_type_output)
567 res = isl_map_intersect_range(res, isl_set_copy(restr->source));
568  
569 isl_restriction_free(restr);
570 return res;
571 error:
572 isl_map_free(dep);
573 isl_set_free(sink);
574 *empty = NULL;
575 return NULL;
576 }
577  
578 /* Compute the last iteration of must source j that precedes the sink
579 * at the given level for sink iterations in set_C.
580 * The subset of set_C for which no such iteration can be found is returned
581 * in *empty.
582 */
583 static struct isl_map *last_source(struct isl_access_info *acc,
584 struct isl_set *set_C,
585 int j, int level, struct isl_set **empty)
586 {
587 struct isl_map *read_map;
588 struct isl_map *write_map;
589 struct isl_map *dep_map;
590 struct isl_map *after;
591 struct isl_map *result;
592  
593 read_map = isl_map_copy(acc->sink.map);
594 write_map = isl_map_copy(acc->source[j].map);
595 write_map = isl_map_reverse(write_map);
596 dep_map = isl_map_apply_range(read_map, write_map);
597 after = after_at_level(isl_map_get_space(dep_map), level);
598 dep_map = isl_map_intersect(dep_map, after);
599 result = restricted_partial_lexmax(acc, dep_map, j, set_C, empty);
600 result = isl_map_reverse(result);
601  
602 return result;
603 }
604  
605 /* For a given mapping between iterations of must source j and iterations
606 * of the sink, compute the last iteration of must source k preceding
607 * the sink at level before_level for any of the sink iterations,
608 * but following the corresponding iteration of must source j at level
609 * after_level.
610 */
611 static struct isl_map *last_later_source(struct isl_access_info *acc,
612 struct isl_map *old_map,
613 int j, int before_level,
614 int k, int after_level,
615 struct isl_set **empty)
616 {
617 isl_space *dim;
618 struct isl_set *set_C;
619 struct isl_map *read_map;
620 struct isl_map *write_map;
621 struct isl_map *dep_map;
622 struct isl_map *after_write;
623 struct isl_map *before_read;
624 struct isl_map *result;
625  
626 set_C = isl_map_range(isl_map_copy(old_map));
627 read_map = isl_map_copy(acc->sink.map);
628 write_map = isl_map_copy(acc->source[k].map);
629  
630 write_map = isl_map_reverse(write_map);
631 dep_map = isl_map_apply_range(read_map, write_map);
632 dim = space_align_and_join(isl_map_get_space(acc->source[k].map),
633 isl_space_reverse(isl_map_get_space(acc->source[j].map)));
634 after_write = after_at_level(dim, after_level);
635 after_write = isl_map_apply_range(after_write, old_map);
636 after_write = isl_map_reverse(after_write);
637 dep_map = isl_map_intersect(dep_map, after_write);
638 before_read = after_at_level(isl_map_get_space(dep_map), before_level);
639 dep_map = isl_map_intersect(dep_map, before_read);
640 result = restricted_partial_lexmax(acc, dep_map, k, set_C, empty);
641 result = isl_map_reverse(result);
642  
643 return result;
644 }
645  
646 /* Given a shared_level between two accesses, return 1 if the
647 * the first can precede the second at the requested target_level.
648 * If the target level is odd, i.e., refers to a statement level
649 * dimension, then first needs to precede second at the requested
650 * level, i.e., shared_level must be equal to target_level.
651 * If the target level is odd, then the two loops should share
652 * at least the requested number of outer loops.
653 */
654 static int can_precede_at_level(int shared_level, int target_level)
655 {
656 if (shared_level < target_level)
657 return 0;
658 if ((target_level % 2) && shared_level > target_level)
659 return 0;
660 return 1;
661 }
662  
663 /* Given a possible flow dependence temp_rel[j] between source j and the sink
664 * at level sink_level, remove those elements for which
665 * there is an iteration of another source k < j that is closer to the sink.
666 * The flow dependences temp_rel[k] are updated with the improved sources.
667 * Any improved source needs to precede the sink at the same level
668 * and needs to follow source j at the same or a deeper level.
669 * The lower this level, the later the execution date of source k.
670 * We therefore consider lower levels first.
671 *
672 * If temp_rel[j] is empty, then there can be no improvement and
673 * we return immediately.
674 */
675 static int intermediate_sources(__isl_keep isl_access_info *acc,
676 struct isl_map **temp_rel, int j, int sink_level)
677 {
678 int k, level;
679 int depth = 2 * isl_map_dim(acc->source[j].map, isl_dim_in) + 1;
680  
681 if (isl_map_plain_is_empty(temp_rel[j]))
682 return 0;
683  
684 for (k = j - 1; k >= 0; --k) {
685 int plevel, plevel2;
686 plevel = acc->level_before(acc->source[k].data, acc->sink.data);
687 if (!can_precede_at_level(plevel, sink_level))
688 continue;
689  
690 plevel2 = acc->level_before(acc->source[j].data,
691 acc->source[k].data);
692  
693 for (level = sink_level; level <= depth; ++level) {
694 struct isl_map *T;
695 struct isl_set *trest;
696 struct isl_map *copy;
697  
698 if (!can_precede_at_level(plevel2, level))
699 continue;
700  
701 copy = isl_map_copy(temp_rel[j]);
702 T = last_later_source(acc, copy, j, sink_level, k,
703 level, &trest);
704 if (isl_map_plain_is_empty(T)) {
705 isl_set_free(trest);
706 isl_map_free(T);
707 continue;
708 }
709 temp_rel[j] = isl_map_intersect_range(temp_rel[j], trest);
710 temp_rel[k] = isl_map_union_disjoint(temp_rel[k], T);
711 }
712 }
713  
714 return 0;
715 }
716  
717 /* Compute all iterations of may source j that precedes the sink at the given
718 * level for sink iterations in set_C.
719 */
720 static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,
721 __isl_take isl_set *set_C, int j, int level)
722 {
723 isl_map *read_map;
724 isl_map *write_map;
725 isl_map *dep_map;
726 isl_map *after;
727  
728 read_map = isl_map_copy(acc->sink.map);
729 read_map = isl_map_intersect_domain(read_map, set_C);
730 write_map = isl_map_copy(acc->source[acc->n_must + j].map);
731 write_map = isl_map_reverse(write_map);
732 dep_map = isl_map_apply_range(read_map, write_map);
733 after = after_at_level(isl_map_get_space(dep_map), level);
734 dep_map = isl_map_intersect(dep_map, after);
735  
736 return isl_map_reverse(dep_map);
737 }
738  
739 /* For a given mapping between iterations of must source k and iterations
740 * of the sink, compute the all iteration of may source j preceding
741 * the sink at level before_level for any of the sink iterations,
742 * but following the corresponding iteration of must source k at level
743 * after_level.
744 */
745 static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,
746 __isl_keep isl_map *old_map,
747 int j, int before_level, int k, int after_level)
748 {
749 isl_space *dim;
750 isl_set *set_C;
751 isl_map *read_map;
752 isl_map *write_map;
753 isl_map *dep_map;
754 isl_map *after_write;
755 isl_map *before_read;
756  
757 set_C = isl_map_range(isl_map_copy(old_map));
758 read_map = isl_map_copy(acc->sink.map);
759 read_map = isl_map_intersect_domain(read_map, set_C);
760 write_map = isl_map_copy(acc->source[acc->n_must + j].map);
761  
762 write_map = isl_map_reverse(write_map);
763 dep_map = isl_map_apply_range(read_map, write_map);
764 dim = isl_space_join(isl_map_get_space(acc->source[acc->n_must + j].map),
765 isl_space_reverse(isl_map_get_space(acc->source[k].map)));
766 after_write = after_at_level(dim, after_level);
767 after_write = isl_map_apply_range(after_write, old_map);
768 after_write = isl_map_reverse(after_write);
769 dep_map = isl_map_intersect(dep_map, after_write);
770 before_read = after_at_level(isl_map_get_space(dep_map), before_level);
771 dep_map = isl_map_intersect(dep_map, before_read);
772 return isl_map_reverse(dep_map);
773 }
774  
775 /* Given the must and may dependence relations for the must accesses
776 * for level sink_level, check if there are any accesses of may access j
777 * that occur in between and return their union.
778 * If some of these accesses are intermediate with respect to
779 * (previously thought to be) must dependences, then these
780 * must dependences are turned into may dependences.
781 */
782 static __isl_give isl_map *all_intermediate_sources(
783 __isl_keep isl_access_info *acc, __isl_take isl_map *map,
784 struct isl_map **must_rel, struct isl_map **may_rel,
785 int j, int sink_level)
786 {
787 int k, level;
788 int depth = 2 * isl_map_dim(acc->source[acc->n_must + j].map,
789 isl_dim_in) + 1;
790  
791 for (k = 0; k < acc->n_must; ++k) {
792 int plevel;
793  
794 if (isl_map_plain_is_empty(may_rel[k]) &&
795 isl_map_plain_is_empty(must_rel[k]))
796 continue;
797  
798 plevel = acc->level_before(acc->source[k].data,
799 acc->source[acc->n_must + j].data);
800  
801 for (level = sink_level; level <= depth; ++level) {
802 isl_map *T;
803 isl_map *copy;
804 isl_set *ran;
805  
806 if (!can_precede_at_level(plevel, level))
807 continue;
808  
809 copy = isl_map_copy(may_rel[k]);
810 T = all_later_sources(acc, copy, j, sink_level, k, level);
811 map = isl_map_union(map, T);
812  
813 copy = isl_map_copy(must_rel[k]);
814 T = all_later_sources(acc, copy, j, sink_level, k, level);
815 ran = isl_map_range(isl_map_copy(T));
816 map = isl_map_union(map, T);
817 may_rel[k] = isl_map_union_disjoint(may_rel[k],
818 isl_map_intersect_range(isl_map_copy(must_rel[k]),
819 isl_set_copy(ran)));
820 T = isl_map_from_domain_and_range(
821 isl_set_universe(
822 isl_space_domain(isl_map_get_space(must_rel[k]))),
823 ran);
824 must_rel[k] = isl_map_subtract(must_rel[k], T);
825 }
826 }
827  
828 return map;
829 }
830  
831 /* Compute dependences for the case where all accesses are "may"
832 * accesses, which boils down to computing memory based dependences.
833 * The generic algorithm would also work in this case, but it would
834 * be overkill to use it.
835 */
836 static __isl_give isl_flow *compute_mem_based_dependences(
837 __isl_keep isl_access_info *acc)
838 {
839 int i;
840 isl_set *mustdo;
841 isl_set *maydo;
842 isl_flow *res;
843  
844 res = isl_flow_alloc(acc);
845 if (!res)
846 return NULL;
847  
848 mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
849 maydo = isl_set_copy(mustdo);
850  
851 for (i = 0; i < acc->n_may; ++i) {
852 int plevel;
853 int is_before;
854 isl_space *dim;
855 isl_map *before;
856 isl_map *dep;
857  
858 plevel = acc->level_before(acc->source[i].data, acc->sink.data);
859 is_before = plevel & 1;
860 plevel >>= 1;
861  
862 dim = isl_map_get_space(res->dep[i].map);
863 if (is_before)
864 before = isl_map_lex_le_first(dim, plevel);
865 else
866 before = isl_map_lex_lt_first(dim, plevel);
867 dep = isl_map_apply_range(isl_map_copy(acc->source[i].map),
868 isl_map_reverse(isl_map_copy(acc->sink.map)));
869 dep = isl_map_intersect(dep, before);
870 mustdo = isl_set_subtract(mustdo,
871 isl_map_range(isl_map_copy(dep)));
872 res->dep[i].map = isl_map_union(res->dep[i].map, dep);
873 }
874  
875 res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));
876 res->must_no_source = mustdo;
877  
878 return res;
879 }
880  
881 /* Compute dependences for the case where there is at least one
882 * "must" access.
883 *
884 * The core algorithm considers all levels in which a source may precede
885 * the sink, where a level may either be a statement level or a loop level.
886 * The outermost statement level is 1, the first loop level is 2, etc...
887 * The algorithm basically does the following:
888 * for all levels l of the read access from innermost to outermost
889 * for all sources w that may precede the sink access at that level
890 * compute the last iteration of the source that precedes the sink access
891 * at that level
892 * add result to possible last accesses at level l of source w
893 * for all sources w2 that we haven't considered yet at this level that may
894 * also precede the sink access
895 * for all levels l2 of w from l to innermost
896 * for all possible last accesses dep of w at l
897 * compute last iteration of w2 between the source and sink
898 * of dep
899 * add result to possible last accesses at level l of write w2
900 * and replace possible last accesses dep by the remainder
901 *
902 *
903 * The above algorithm is applied to the must access. During the course
904 * of the algorithm, we keep track of sink iterations that still
905 * need to be considered. These iterations are split into those that
906 * haven't been matched to any source access (mustdo) and those that have only
907 * been matched to may accesses (maydo).
908 * At the end of each level, we also consider the may accesses.
909 * In particular, we consider may accesses that precede the remaining
910 * sink iterations, moving elements from mustdo to maydo when appropriate,
911 * and may accesses that occur between a must source and a sink of any
912 * dependences found at the current level, turning must dependences into
913 * may dependences when appropriate.
914 *
915 */
916 static __isl_give isl_flow *compute_val_based_dependences(
917 __isl_keep isl_access_info *acc)
918 {
919 isl_ctx *ctx;
920 isl_flow *res;
921 isl_set *mustdo = NULL;
922 isl_set *maydo = NULL;
923 int level, j;
924 int depth;
925 isl_map **must_rel = NULL;
926 isl_map **may_rel = NULL;
927  
928 if (!acc)
929 return NULL;
930  
931 res = isl_flow_alloc(acc);
932 if (!res)
933 goto error;
934 ctx = isl_map_get_ctx(acc->sink.map);
935  
936 depth = 2 * isl_map_dim(acc->sink.map, isl_dim_in) + 1;
937 mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
938 maydo = isl_set_empty_like(mustdo);
939 if (!mustdo || !maydo)
940 goto error;
941 if (isl_set_plain_is_empty(mustdo))
942 goto done;
943  
944 must_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
945 may_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
946 if (!must_rel || !may_rel)
947 goto error;
948  
949 for (level = depth; level >= 1; --level) {
950 for (j = acc->n_must-1; j >=0; --j) {
951 must_rel[j] = isl_map_empty_like(res->dep[j].map);
952 may_rel[j] = isl_map_copy(must_rel[j]);
953 }
954  
955 for (j = acc->n_must - 1; j >= 0; --j) {
956 struct isl_map *T;
957 struct isl_set *rest;
958 int plevel;
959  
960 plevel = acc->level_before(acc->source[j].data,
961 acc->sink.data);
962 if (!can_precede_at_level(plevel, level))
963 continue;
964  
965 T = last_source(acc, mustdo, j, level, &rest);
966 must_rel[j] = isl_map_union_disjoint(must_rel[j], T);
967 mustdo = rest;
968  
969 intermediate_sources(acc, must_rel, j, level);
970  
971 T = last_source(acc, maydo, j, level, &rest);
972 may_rel[j] = isl_map_union_disjoint(may_rel[j], T);
973 maydo = rest;
974  
975 intermediate_sources(acc, may_rel, j, level);
976  
977 if (isl_set_plain_is_empty(mustdo) &&
978 isl_set_plain_is_empty(maydo))
979 break;
980 }
981 for (j = j - 1; j >= 0; --j) {
982 int plevel;
983  
984 plevel = acc->level_before(acc->source[j].data,
985 acc->sink.data);
986 if (!can_precede_at_level(plevel, level))
987 continue;
988  
989 intermediate_sources(acc, must_rel, j, level);
990 intermediate_sources(acc, may_rel, j, level);
991 }
992  
993 for (j = 0; j < acc->n_may; ++j) {
994 int plevel;
995 isl_map *T;
996 isl_set *ran;
997  
998 plevel = acc->level_before(acc->source[acc->n_must + j].data,
999 acc->sink.data);
1000 if (!can_precede_at_level(plevel, level))
1001 continue;
1002  
1003 T = all_sources(acc, isl_set_copy(maydo), j, level);
1004 res->dep[2 * acc->n_must + j].map =
1005 isl_map_union(res->dep[2 * acc->n_must + j].map, T);
1006 T = all_sources(acc, isl_set_copy(mustdo), j, level);
1007 ran = isl_map_range(isl_map_copy(T));
1008 res->dep[2 * acc->n_must + j].map =
1009 isl_map_union(res->dep[2 * acc->n_must + j].map, T);
1010 mustdo = isl_set_subtract(mustdo, isl_set_copy(ran));
1011 maydo = isl_set_union_disjoint(maydo, ran);
1012  
1013 T = res->dep[2 * acc->n_must + j].map;
1014 T = all_intermediate_sources(acc, T, must_rel, may_rel,
1015 j, level);
1016 res->dep[2 * acc->n_must + j].map = T;
1017 }
1018  
1019 for (j = acc->n_must - 1; j >= 0; --j) {
1020 res->dep[2 * j].map =
1021 isl_map_union_disjoint(res->dep[2 * j].map,
1022 must_rel[j]);
1023 res->dep[2 * j + 1].map =
1024 isl_map_union_disjoint(res->dep[2 * j + 1].map,
1025 may_rel[j]);
1026 }
1027  
1028 if (isl_set_plain_is_empty(mustdo) &&
1029 isl_set_plain_is_empty(maydo))
1030 break;
1031 }
1032  
1033 free(must_rel);
1034 free(may_rel);
1035 done:
1036 res->must_no_source = mustdo;
1037 res->may_no_source = maydo;
1038 return res;
1039 error:
1040 isl_flow_free(res);
1041 isl_set_free(mustdo);
1042 isl_set_free(maydo);
1043 free(must_rel);
1044 free(may_rel);
1045 return NULL;
1046 }
1047  
1048 /* Given a "sink" access, a list of n "source" accesses,
1049 * compute for each iteration of the sink access
1050 * and for each element accessed by that iteration,
1051 * the source access in the list that last accessed the
1052 * element accessed by the sink access before this sink access.
1053 * Each access is given as a map from the loop iterators
1054 * to the array indices.
1055 * The result is a list of n relations between source and sink
1056 * iterations and a subset of the domain of the sink access,
1057 * corresponding to those iterations that access an element
1058 * not previously accessed.
1059 *
1060 * To deal with multi-valued sink access relations, the sink iteration
1061 * domain is first extended with dimensions that correspond to the data
1062 * space. After the computation is finished, these extra dimensions are
1063 * projected out again.
1064 */
1065 __isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)
1066 {
1067 int j;
1068 struct isl_flow *res = NULL;
1069  
1070 if (!acc)
1071 return NULL;
1072  
1073 acc->domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));
1074 acc->sink.map = isl_map_range_map(acc->sink.map);
1075 if (!acc->sink.map)
1076 goto error;
1077  
1078 if (acc->n_must == 0)
1079 res = compute_mem_based_dependences(acc);
1080 else {
1081 acc = isl_access_info_sort_sources(acc);
1082 res = compute_val_based_dependences(acc);
1083 }
1084 if (!res)
1085 goto error;
1086  
1087 for (j = 0; j < res->n_source; ++j) {
1088 res->dep[j].map = isl_map_apply_range(res->dep[j].map,
1089 isl_map_copy(acc->domain_map));
1090 if (!res->dep[j].map)
1091 goto error;
1092 }
1093 if (!res->must_no_source || !res->may_no_source)
1094 goto error;
1095  
1096 isl_access_info_free(acc);
1097 return res;
1098 error:
1099 isl_access_info_free(acc);
1100 isl_flow_free(res);
1101 return NULL;
1102 }
1103  
1104  
1105 /* Keep track of some information about a schedule for a given
1106 * access. In particular, keep track of which dimensions
1107 * have a constant value and of the actual constant values.
1108 */
1109 struct isl_sched_info {
1110 int *is_cst;
1111 isl_vec *cst;
1112 };
1113  
1114 static void sched_info_free(__isl_take struct isl_sched_info *info)
1115 {
1116 if (!info)
1117 return;
1118 isl_vec_free(info->cst);
1119 free(info->is_cst);
1120 free(info);
1121 }
1122  
1123 /* Extract information on the constant dimensions of the schedule
1124 * for a given access. The "map" is of the form
1125 *
1126 * [S -> D] -> A
1127 *
1128 * with S the schedule domain, D the iteration domain and A the data domain.
1129 */
1130 static __isl_give struct isl_sched_info *sched_info_alloc(
1131 __isl_keep isl_map *map)
1132 {
1133 isl_ctx *ctx;
1134 isl_space *dim;
1135 struct isl_sched_info *info;
1136 int i, n;
1137 isl_int v;
1138  
1139 if (!map)
1140 return NULL;
1141  
1142 dim = isl_space_unwrap(isl_space_domain(isl_map_get_space(map)));
1143 if (!dim)
1144 return NULL;
1145 n = isl_space_dim(dim, isl_dim_in);
1146 isl_space_free(dim);
1147  
1148 ctx = isl_map_get_ctx(map);
1149 info = isl_alloc_type(ctx, struct isl_sched_info);
1150 if (!info)
1151 return NULL;
1152 info->is_cst = isl_alloc_array(ctx, int, n);
1153 info->cst = isl_vec_alloc(ctx, n);
1154 if (!info->is_cst || !info->cst)
1155 goto error;
1156  
1157 isl_int_init(v);
1158 for (i = 0; i < n; ++i) {
1159 info->is_cst[i] = isl_map_plain_is_fixed(map, isl_dim_in, i,
1160 &v);
1161 info->cst = isl_vec_set_element(info->cst, i, v);
1162 }
1163 isl_int_clear(v);
1164  
1165 return info;
1166 error:
1167 sched_info_free(info);
1168 return NULL;
1169 }
1170  
1171 struct isl_compute_flow_data {
1172 isl_union_map *must_source;
1173 isl_union_map *may_source;
1174 isl_union_map *must_dep;
1175 isl_union_map *may_dep;
1176 isl_union_map *must_no_source;
1177 isl_union_map *may_no_source;
1178  
1179 int count;
1180 int must;
1181 isl_space *dim;
1182 struct isl_sched_info *sink_info;
1183 struct isl_sched_info **source_info;
1184 isl_access_info *accesses;
1185 };
1186  
1187 static int count_matching_array(__isl_take isl_map *map, void *user)
1188 {
1189 int eq;
1190 isl_space *dim;
1191 struct isl_compute_flow_data *data;
1192  
1193 data = (struct isl_compute_flow_data *)user;
1194  
1195 dim = isl_space_range(isl_map_get_space(map));
1196  
1197 eq = isl_space_is_equal(dim, data->dim);
1198  
1199 isl_space_free(dim);
1200 isl_map_free(map);
1201  
1202 if (eq < 0)
1203 return -1;
1204 if (eq)
1205 data->count++;
1206  
1207 return 0;
1208 }
1209  
1210 static int collect_matching_array(__isl_take isl_map *map, void *user)
1211 {
1212 int eq;
1213 isl_space *dim;
1214 struct isl_sched_info *info;
1215 struct isl_compute_flow_data *data;
1216  
1217 data = (struct isl_compute_flow_data *)user;
1218  
1219 dim = isl_space_range(isl_map_get_space(map));
1220  
1221 eq = isl_space_is_equal(dim, data->dim);
1222  
1223 isl_space_free(dim);
1224  
1225 if (eq < 0)
1226 goto error;
1227 if (!eq) {
1228 isl_map_free(map);
1229 return 0;
1230 }
1231  
1232 info = sched_info_alloc(map);
1233 data->source_info[data->count] = info;
1234  
1235 data->accesses = isl_access_info_add_source(data->accesses,
1236 map, data->must, info);
1237  
1238 data->count++;
1239  
1240 return 0;
1241 error:
1242 isl_map_free(map);
1243 return -1;
1244 }
1245  
1246 /* Determine the shared nesting level and the "textual order" of
1247 * the given accesses.
1248 *
1249 * We first determine the minimal schedule dimension for both accesses.
1250 *
1251 * If among those dimensions, we can find one where both have a fixed
1252 * value and if moreover those values are different, then the previous
1253 * dimension is the last shared nesting level and the textual order
1254 * is determined based on the order of the fixed values.
1255 * If no such fixed values can be found, then we set the shared
1256 * nesting level to the minimal schedule dimension, with no textual ordering.
1257 */
1258 static int before(void *first, void *second)
1259 {
1260 struct isl_sched_info *info1 = first;
1261 struct isl_sched_info *info2 = second;
1262 int n1, n2;
1263 int i;
1264 isl_int v1, v2;
1265  
1266 n1 = isl_vec_size(info1->cst);
1267 n2 = isl_vec_size(info2->cst);
1268  
1269 if (n2 < n1)
1270 n1 = n2;
1271  
1272 isl_int_init(v1);
1273 isl_int_init(v2);
1274 for (i = 0; i < n1; ++i) {
1275 int r;
1276  
1277 if (!info1->is_cst[i])
1278 continue;
1279 if (!info2->is_cst[i])
1280 continue;
1281 isl_vec_get_element(info1->cst, i, &v1);
1282 isl_vec_get_element(info2->cst, i, &v2);
1283 if (isl_int_eq(v1, v2))
1284 continue;
1285  
1286 r = 2 * i + isl_int_lt(v1, v2);
1287  
1288 isl_int_clear(v1);
1289 isl_int_clear(v2);
1290 return r;
1291 }
1292 isl_int_clear(v1);
1293 isl_int_clear(v2);
1294  
1295 return 2 * n1;
1296 }
1297  
1298 /* Given a sink access, look for all the source accesses that access
1299 * the same array and perform dataflow analysis on them using
1300 * isl_access_info_compute_flow.
1301 */
1302 static int compute_flow(__isl_take isl_map *map, void *user)
1303 {
1304 int i;
1305 isl_ctx *ctx;
1306 struct isl_compute_flow_data *data;
1307 isl_flow *flow;
1308  
1309 data = (struct isl_compute_flow_data *)user;
1310  
1311 ctx = isl_map_get_ctx(map);
1312  
1313 data->accesses = NULL;
1314 data->sink_info = NULL;
1315 data->source_info = NULL;
1316 data->count = 0;
1317 data->dim = isl_space_range(isl_map_get_space(map));
1318  
1319 if (isl_union_map_foreach_map(data->must_source,
1320 &count_matching_array, data) < 0)
1321 goto error;
1322 if (isl_union_map_foreach_map(data->may_source,
1323 &count_matching_array, data) < 0)
1324 goto error;
1325  
1326 data->sink_info = sched_info_alloc(map);
1327 data->source_info = isl_calloc_array(ctx, struct isl_sched_info *,
1328 data->count);
1329  
1330 data->accesses = isl_access_info_alloc(isl_map_copy(map),
1331 data->sink_info, &before, data->count);
1332 if (!data->sink_info || !data->source_info || !data->accesses)
1333 goto error;
1334 data->count = 0;
1335 data->must = 1;
1336 if (isl_union_map_foreach_map(data->must_source,
1337 &collect_matching_array, data) < 0)
1338 goto error;
1339 data->must = 0;
1340 if (isl_union_map_foreach_map(data->may_source,
1341 &collect_matching_array, data) < 0)
1342 goto error;
1343  
1344 flow = isl_access_info_compute_flow(data->accesses);
1345 data->accesses = NULL;
1346  
1347 if (!flow)
1348 goto error;
1349  
1350 data->must_no_source = isl_union_map_union(data->must_no_source,
1351 isl_union_map_from_map(isl_flow_get_no_source(flow, 1)));
1352 data->may_no_source = isl_union_map_union(data->may_no_source,
1353 isl_union_map_from_map(isl_flow_get_no_source(flow, 0)));
1354  
1355 for (i = 0; i < flow->n_source; ++i) {
1356 isl_union_map *dep;
1357 dep = isl_union_map_from_map(isl_map_copy(flow->dep[i].map));
1358 if (flow->dep[i].must)
1359 data->must_dep = isl_union_map_union(data->must_dep, dep);
1360 else
1361 data->may_dep = isl_union_map_union(data->may_dep, dep);
1362 }
1363  
1364 isl_flow_free(flow);
1365  
1366 sched_info_free(data->sink_info);
1367 if (data->source_info) {
1368 for (i = 0; i < data->count; ++i)
1369 sched_info_free(data->source_info[i]);
1370 free(data->source_info);
1371 }
1372 isl_space_free(data->dim);
1373 isl_map_free(map);
1374  
1375 return 0;
1376 error:
1377 isl_access_info_free(data->accesses);
1378 sched_info_free(data->sink_info);
1379 if (data->source_info) {
1380 for (i = 0; i < data->count; ++i)
1381 sched_info_free(data->source_info[i]);
1382 free(data->source_info);
1383 }
1384 isl_space_free(data->dim);
1385 isl_map_free(map);
1386  
1387 return -1;
1388 }
1389  
1390 /* Given a collection of "sink" and "source" accesses,
1391 * compute for each iteration of a sink access
1392 * and for each element accessed by that iteration,
1393 * the source access in the list that last accessed the
1394 * element accessed by the sink access before this sink access.
1395 * Each access is given as a map from the loop iterators
1396 * to the array indices.
1397 * The result is a relations between source and sink
1398 * iterations and a subset of the domain of the sink accesses,
1399 * corresponding to those iterations that access an element
1400 * not previously accessed.
1401 *
1402 * We first prepend the schedule dimensions to the domain
1403 * of the accesses so that we can easily compare their relative order.
1404 * Then we consider each sink access individually in compute_flow.
1405 */
1406 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
1407 __isl_take isl_union_map *must_source,
1408 __isl_take isl_union_map *may_source,
1409 __isl_take isl_union_map *schedule,
1410 __isl_give isl_union_map **must_dep, __isl_give isl_union_map **may_dep,
1411 __isl_give isl_union_map **must_no_source,
1412 __isl_give isl_union_map **may_no_source)
1413 {
1414 isl_space *dim;
1415 isl_union_map *range_map = NULL;
1416 struct isl_compute_flow_data data;
1417  
1418 sink = isl_union_map_align_params(sink,
1419 isl_union_map_get_space(must_source));
1420 sink = isl_union_map_align_params(sink,
1421 isl_union_map_get_space(may_source));
1422 sink = isl_union_map_align_params(sink,
1423 isl_union_map_get_space(schedule));
1424 dim = isl_union_map_get_space(sink);
1425 must_source = isl_union_map_align_params(must_source, isl_space_copy(dim));
1426 may_source = isl_union_map_align_params(may_source, isl_space_copy(dim));
1427 schedule = isl_union_map_align_params(schedule, isl_space_copy(dim));
1428  
1429 schedule = isl_union_map_reverse(schedule);
1430 range_map = isl_union_map_range_map(schedule);
1431 schedule = isl_union_map_reverse(isl_union_map_copy(range_map));
1432 sink = isl_union_map_apply_domain(sink, isl_union_map_copy(schedule));
1433 must_source = isl_union_map_apply_domain(must_source,
1434 isl_union_map_copy(schedule));
1435 may_source = isl_union_map_apply_domain(may_source, schedule);
1436  
1437 data.must_source = must_source;
1438 data.may_source = may_source;
1439 data.must_dep = must_dep ?
1440 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1441 data.may_dep = may_dep ? isl_union_map_empty(isl_space_copy(dim)) : NULL;
1442 data.must_no_source = must_no_source ?
1443 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1444 data.may_no_source = may_no_source ?
1445 isl_union_map_empty(isl_space_copy(dim)) : NULL;
1446  
1447 isl_space_free(dim);
1448  
1449 if (isl_union_map_foreach_map(sink, &compute_flow, &data) < 0)
1450 goto error;
1451  
1452 isl_union_map_free(sink);
1453 isl_union_map_free(must_source);
1454 isl_union_map_free(may_source);
1455  
1456 if (must_dep) {
1457 data.must_dep = isl_union_map_apply_domain(data.must_dep,
1458 isl_union_map_copy(range_map));
1459 data.must_dep = isl_union_map_apply_range(data.must_dep,
1460 isl_union_map_copy(range_map));
1461 *must_dep = data.must_dep;
1462 }
1463 if (may_dep) {
1464 data.may_dep = isl_union_map_apply_domain(data.may_dep,
1465 isl_union_map_copy(range_map));
1466 data.may_dep = isl_union_map_apply_range(data.may_dep,
1467 isl_union_map_copy(range_map));
1468 *may_dep = data.may_dep;
1469 }
1470 if (must_no_source) {
1471 data.must_no_source = isl_union_map_apply_domain(
1472 data.must_no_source, isl_union_map_copy(range_map));
1473 *must_no_source = data.must_no_source;
1474 }
1475 if (may_no_source) {
1476 data.may_no_source = isl_union_map_apply_domain(
1477 data.may_no_source, isl_union_map_copy(range_map));
1478 *may_no_source = data.may_no_source;
1479 }
1480  
1481 isl_union_map_free(range_map);
1482  
1483 return 0;
1484 error:
1485 isl_union_map_free(range_map);
1486 isl_union_map_free(sink);
1487 isl_union_map_free(must_source);
1488 isl_union_map_free(may_source);
1489 isl_union_map_free(data.must_dep);
1490 isl_union_map_free(data.may_dep);
1491 isl_union_map_free(data.must_no_source);
1492 isl_union_map_free(data.may_no_source);
1493  
1494 if (must_dep)
1495 *must_dep = NULL;
1496 if (may_dep)
1497 *may_dep = NULL;
1498 if (must_no_source)
1499 *must_no_source = NULL;
1500 if (may_no_source)
1501 *may_no_source = NULL;
1502 return -1;
1503 }