isl_ast_graft.c: store_guard: coalesce guard after taking gist
[isl.git] / isl_transitive_closure.c
blob70d15b91ee3f4fa76c9f6a8711b5a1468e2902dd
1 /*
2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
11 #include <isl_ctx_private.h>
12 #include <isl_map_private.h>
13 #include <isl/map.h>
14 #include <isl/seq.h>
15 #include <isl_space_private.h>
16 #include <isl/lp.h>
17 #include <isl/union_map.h>
18 #include <isl_mat_private.h>
19 #include <isl_options_private.h>
20 #include <isl_tarjan.h>
22 int isl_map_is_transitively_closed(__isl_keep isl_map *map)
24 isl_map *map2;
25 int closed;
27 map2 = isl_map_apply_range(isl_map_copy(map), isl_map_copy(map));
28 closed = isl_map_is_subset(map2, map);
29 isl_map_free(map2);
31 return closed;
34 int isl_union_map_is_transitively_closed(__isl_keep isl_union_map *umap)
36 isl_union_map *umap2;
37 int closed;
39 umap2 = isl_union_map_apply_range(isl_union_map_copy(umap),
40 isl_union_map_copy(umap));
41 closed = isl_union_map_is_subset(umap2, umap);
42 isl_union_map_free(umap2);
44 return closed;
47 /* Given a map that represents a path with the length of the path
48 * encoded as the difference between the last output coordindate
49 * and the last input coordinate, set this length to either
50 * exactly "length" (if "exactly" is set) or at least "length"
51 * (if "exactly" is not set).
53 static __isl_give isl_map *set_path_length(__isl_take isl_map *map,
54 int exactly, int length)
56 isl_space *dim;
57 struct isl_basic_map *bmap;
58 unsigned d;
59 unsigned nparam;
60 int k;
61 isl_int *c;
63 if (!map)
64 return NULL;
66 dim = isl_map_get_space(map);
67 d = isl_space_dim(dim, isl_dim_in);
68 nparam = isl_space_dim(dim, isl_dim_param);
69 bmap = isl_basic_map_alloc_space(dim, 0, 1, 1);
70 if (exactly) {
71 k = isl_basic_map_alloc_equality(bmap);
72 c = bmap->eq[k];
73 } else {
74 k = isl_basic_map_alloc_inequality(bmap);
75 c = bmap->ineq[k];
77 if (k < 0)
78 goto error;
79 isl_seq_clr(c, 1 + isl_basic_map_total_dim(bmap));
80 isl_int_set_si(c[0], -length);
81 isl_int_set_si(c[1 + nparam + d - 1], -1);
82 isl_int_set_si(c[1 + nparam + d + d - 1], 1);
84 bmap = isl_basic_map_finalize(bmap);
85 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
87 return map;
88 error:
89 isl_basic_map_free(bmap);
90 isl_map_free(map);
91 return NULL;
94 /* Check whether the overapproximation of the power of "map" is exactly
95 * the power of "map". Let R be "map" and A_k the overapproximation.
96 * The approximation is exact if
98 * A_1 = R
99 * A_k = A_{k-1} \circ R k >= 2
101 * Since A_k is known to be an overapproximation, we only need to check
103 * A_1 \subset R
104 * A_k \subset A_{k-1} \circ R k >= 2
106 * In practice, "app" has an extra input and output coordinate
107 * to encode the length of the path. So, we first need to add
108 * this coordinate to "map" and set the length of the path to
109 * one.
111 static int check_power_exactness(__isl_take isl_map *map,
112 __isl_take isl_map *app)
114 int exact;
115 isl_map *app_1;
116 isl_map *app_2;
118 map = isl_map_add_dims(map, isl_dim_in, 1);
119 map = isl_map_add_dims(map, isl_dim_out, 1);
120 map = set_path_length(map, 1, 1);
122 app_1 = set_path_length(isl_map_copy(app), 1, 1);
124 exact = isl_map_is_subset(app_1, map);
125 isl_map_free(app_1);
127 if (!exact || exact < 0) {
128 isl_map_free(app);
129 isl_map_free(map);
130 return exact;
133 app_1 = set_path_length(isl_map_copy(app), 0, 1);
134 app_2 = set_path_length(app, 0, 2);
135 app_1 = isl_map_apply_range(map, app_1);
137 exact = isl_map_is_subset(app_2, app_1);
139 isl_map_free(app_1);
140 isl_map_free(app_2);
142 return exact;
145 /* Check whether the overapproximation of the power of "map" is exactly
146 * the power of "map", possibly after projecting out the power (if "project"
147 * is set).
149 * If "project" is set and if "steps" can only result in acyclic paths,
150 * then we check
152 * A = R \cup (A \circ R)
154 * where A is the overapproximation with the power projected out, i.e.,
155 * an overapproximation of the transitive closure.
156 * More specifically, since A is known to be an overapproximation, we check
158 * A \subset R \cup (A \circ R)
160 * Otherwise, we check if the power is exact.
162 * Note that "app" has an extra input and output coordinate to encode
163 * the length of the part. If we are only interested in the transitive
164 * closure, then we can simply project out these coordinates first.
166 static int check_exactness(__isl_take isl_map *map, __isl_take isl_map *app,
167 int project)
169 isl_map *test;
170 int exact;
171 unsigned d;
173 if (!project)
174 return check_power_exactness(map, app);
176 d = isl_map_dim(map, isl_dim_in);
177 app = set_path_length(app, 0, 1);
178 app = isl_map_project_out(app, isl_dim_in, d, 1);
179 app = isl_map_project_out(app, isl_dim_out, d, 1);
181 app = isl_map_reset_space(app, isl_map_get_space(map));
183 test = isl_map_apply_range(isl_map_copy(map), isl_map_copy(app));
184 test = isl_map_union(test, isl_map_copy(map));
186 exact = isl_map_is_subset(app, test);
188 isl_map_free(app);
189 isl_map_free(test);
191 isl_map_free(map);
193 return exact;
197 * The transitive closure implementation is based on the paper
198 * "Computing the Transitive Closure of a Union of Affine Integer
199 * Tuple Relations" by Anna Beletska, Denis Barthou, Wlodzimierz Bielecki and
200 * Albert Cohen.
203 /* Given a set of n offsets v_i (the rows of "steps"), construct a relation
204 * of the given dimension specification (Z^{n+1} -> Z^{n+1})
205 * that maps an element x to any element that can be reached
206 * by taking a non-negative number of steps along any of
207 * the extended offsets v'_i = [v_i 1].
208 * That is, construct
210 * { [x] -> [y] : exists k_i >= 0, y = x + \sum_i k_i v'_i }
212 * For any element in this relation, the number of steps taken
213 * is equal to the difference in the final coordinates.
215 static __isl_give isl_map *path_along_steps(__isl_take isl_space *dim,
216 __isl_keep isl_mat *steps)
218 int i, j, k;
219 struct isl_basic_map *path = NULL;
220 unsigned d;
221 unsigned n;
222 unsigned nparam;
224 if (!dim || !steps)
225 goto error;
227 d = isl_space_dim(dim, isl_dim_in);
228 n = steps->n_row;
229 nparam = isl_space_dim(dim, isl_dim_param);
231 path = isl_basic_map_alloc_space(isl_space_copy(dim), n, d, n);
233 for (i = 0; i < n; ++i) {
234 k = isl_basic_map_alloc_div(path);
235 if (k < 0)
236 goto error;
237 isl_assert(steps->ctx, i == k, goto error);
238 isl_int_set_si(path->div[k][0], 0);
241 for (i = 0; i < d; ++i) {
242 k = isl_basic_map_alloc_equality(path);
243 if (k < 0)
244 goto error;
245 isl_seq_clr(path->eq[k], 1 + isl_basic_map_total_dim(path));
246 isl_int_set_si(path->eq[k][1 + nparam + i], 1);
247 isl_int_set_si(path->eq[k][1 + nparam + d + i], -1);
248 if (i == d - 1)
249 for (j = 0; j < n; ++j)
250 isl_int_set_si(path->eq[k][1 + nparam + 2 * d + j], 1);
251 else
252 for (j = 0; j < n; ++j)
253 isl_int_set(path->eq[k][1 + nparam + 2 * d + j],
254 steps->row[j][i]);
257 for (i = 0; i < n; ++i) {
258 k = isl_basic_map_alloc_inequality(path);
259 if (k < 0)
260 goto error;
261 isl_seq_clr(path->ineq[k], 1 + isl_basic_map_total_dim(path));
262 isl_int_set_si(path->ineq[k][1 + nparam + 2 * d + i], 1);
265 isl_space_free(dim);
267 path = isl_basic_map_simplify(path);
268 path = isl_basic_map_finalize(path);
269 return isl_map_from_basic_map(path);
270 error:
271 isl_space_free(dim);
272 isl_basic_map_free(path);
273 return NULL;
276 #define IMPURE 0
277 #define PURE_PARAM 1
278 #define PURE_VAR 2
279 #define MIXED 3
281 /* Check whether the parametric constant term of constraint c is never
282 * positive in "bset".
284 static int parametric_constant_never_positive(__isl_keep isl_basic_set *bset,
285 isl_int *c, int *div_purity)
287 unsigned d;
288 unsigned n_div;
289 unsigned nparam;
290 int i;
291 int k;
292 int empty;
294 n_div = isl_basic_set_dim(bset, isl_dim_div);
295 d = isl_basic_set_dim(bset, isl_dim_set);
296 nparam = isl_basic_set_dim(bset, isl_dim_param);
298 bset = isl_basic_set_copy(bset);
299 bset = isl_basic_set_cow(bset);
300 bset = isl_basic_set_extend_constraints(bset, 0, 1);
301 k = isl_basic_set_alloc_inequality(bset);
302 if (k < 0)
303 goto error;
304 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
305 isl_seq_cpy(bset->ineq[k], c, 1 + nparam);
306 for (i = 0; i < n_div; ++i) {
307 if (div_purity[i] != PURE_PARAM)
308 continue;
309 isl_int_set(bset->ineq[k][1 + nparam + d + i],
310 c[1 + nparam + d + i]);
312 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
313 empty = isl_basic_set_is_empty(bset);
314 isl_basic_set_free(bset);
316 return empty;
317 error:
318 isl_basic_set_free(bset);
319 return -1;
322 /* Return PURE_PARAM if only the coefficients of the parameters are non-zero.
323 * Return PURE_VAR if only the coefficients of the set variables are non-zero.
324 * Return MIXED if only the coefficients of the parameters and the set
325 * variables are non-zero and if moreover the parametric constant
326 * can never attain positive values.
327 * Return IMPURE otherwise.
329 * If div_purity is NULL then we are dealing with a non-parametric set
330 * and so the constraint is obviously PURE_VAR.
332 static int purity(__isl_keep isl_basic_set *bset, isl_int *c, int *div_purity,
333 int eq)
335 unsigned d;
336 unsigned n_div;
337 unsigned nparam;
338 int empty;
339 int i;
340 int p = 0, v = 0;
342 if (!div_purity)
343 return PURE_VAR;
345 n_div = isl_basic_set_dim(bset, isl_dim_div);
346 d = isl_basic_set_dim(bset, isl_dim_set);
347 nparam = isl_basic_set_dim(bset, isl_dim_param);
349 for (i = 0; i < n_div; ++i) {
350 if (isl_int_is_zero(c[1 + nparam + d + i]))
351 continue;
352 switch (div_purity[i]) {
353 case PURE_PARAM: p = 1; break;
354 case PURE_VAR: v = 1; break;
355 default: return IMPURE;
358 if (!p && isl_seq_first_non_zero(c + 1, nparam) == -1)
359 return PURE_VAR;
360 if (!v && isl_seq_first_non_zero(c + 1 + nparam, d) == -1)
361 return PURE_PARAM;
363 empty = parametric_constant_never_positive(bset, c, div_purity);
364 if (eq && empty >= 0 && !empty) {
365 isl_seq_neg(c, c, 1 + nparam + d + n_div);
366 empty = parametric_constant_never_positive(bset, c, div_purity);
369 return empty < 0 ? -1 : empty ? MIXED : IMPURE;
372 /* Return an array of integers indicating the type of each div in bset.
373 * If the div is (recursively) defined in terms of only the parameters,
374 * then the type is PURE_PARAM.
375 * If the div is (recursively) defined in terms of only the set variables,
376 * then the type is PURE_VAR.
377 * Otherwise, the type is IMPURE.
379 static __isl_give int *get_div_purity(__isl_keep isl_basic_set *bset)
381 int i, j;
382 int *div_purity;
383 unsigned d;
384 unsigned n_div;
385 unsigned nparam;
387 if (!bset)
388 return NULL;
390 n_div = isl_basic_set_dim(bset, isl_dim_div);
391 d = isl_basic_set_dim(bset, isl_dim_set);
392 nparam = isl_basic_set_dim(bset, isl_dim_param);
394 div_purity = isl_alloc_array(bset->ctx, int, n_div);
395 if (!div_purity)
396 return NULL;
398 for (i = 0; i < bset->n_div; ++i) {
399 int p = 0, v = 0;
400 if (isl_int_is_zero(bset->div[i][0])) {
401 div_purity[i] = IMPURE;
402 continue;
404 if (isl_seq_first_non_zero(bset->div[i] + 2, nparam) != -1)
405 p = 1;
406 if (isl_seq_first_non_zero(bset->div[i] + 2 + nparam, d) != -1)
407 v = 1;
408 for (j = 0; j < i; ++j) {
409 if (isl_int_is_zero(bset->div[i][2 + nparam + d + j]))
410 continue;
411 switch (div_purity[j]) {
412 case PURE_PARAM: p = 1; break;
413 case PURE_VAR: v = 1; break;
414 default: p = v = 1; break;
417 div_purity[i] = v ? p ? IMPURE : PURE_VAR : PURE_PARAM;
420 return div_purity;
423 /* Given a path with the as yet unconstrained length at position "pos",
424 * check if setting the length to zero results in only the identity
425 * mapping.
427 static int empty_path_is_identity(__isl_keep isl_basic_map *path, unsigned pos)
429 isl_basic_map *test = NULL;
430 isl_basic_map *id = NULL;
431 int k;
432 int is_id;
434 test = isl_basic_map_copy(path);
435 test = isl_basic_map_extend_constraints(test, 1, 0);
436 k = isl_basic_map_alloc_equality(test);
437 if (k < 0)
438 goto error;
439 isl_seq_clr(test->eq[k], 1 + isl_basic_map_total_dim(test));
440 isl_int_set_si(test->eq[k][pos], 1);
441 id = isl_basic_map_identity(isl_basic_map_get_space(path));
442 is_id = isl_basic_map_is_equal(test, id);
443 isl_basic_map_free(test);
444 isl_basic_map_free(id);
445 return is_id;
446 error:
447 isl_basic_map_free(test);
448 return -1;
451 /* If any of the constraints is found to be impure then this function
452 * sets *impurity to 1.
454 static __isl_give isl_basic_map *add_delta_constraints(
455 __isl_take isl_basic_map *path,
456 __isl_keep isl_basic_set *delta, unsigned off, unsigned nparam,
457 unsigned d, int *div_purity, int eq, int *impurity)
459 int i, k;
460 int n = eq ? delta->n_eq : delta->n_ineq;
461 isl_int **delta_c = eq ? delta->eq : delta->ineq;
462 unsigned n_div;
464 n_div = isl_basic_set_dim(delta, isl_dim_div);
466 for (i = 0; i < n; ++i) {
467 isl_int *path_c;
468 int p = purity(delta, delta_c[i], div_purity, eq);
469 if (p < 0)
470 goto error;
471 if (p != PURE_VAR && p != PURE_PARAM && !*impurity)
472 *impurity = 1;
473 if (p == IMPURE)
474 continue;
475 if (eq && p != MIXED) {
476 k = isl_basic_map_alloc_equality(path);
477 path_c = path->eq[k];
478 } else {
479 k = isl_basic_map_alloc_inequality(path);
480 path_c = path->ineq[k];
482 if (k < 0)
483 goto error;
484 isl_seq_clr(path_c, 1 + isl_basic_map_total_dim(path));
485 if (p == PURE_VAR) {
486 isl_seq_cpy(path_c + off,
487 delta_c[i] + 1 + nparam, d);
488 isl_int_set(path_c[off + d], delta_c[i][0]);
489 } else if (p == PURE_PARAM) {
490 isl_seq_cpy(path_c, delta_c[i], 1 + nparam);
491 } else {
492 isl_seq_cpy(path_c + off,
493 delta_c[i] + 1 + nparam, d);
494 isl_seq_cpy(path_c, delta_c[i], 1 + nparam);
496 isl_seq_cpy(path_c + off - n_div,
497 delta_c[i] + 1 + nparam + d, n_div);
500 return path;
501 error:
502 isl_basic_map_free(path);
503 return NULL;
506 /* Given a set of offsets "delta", construct a relation of the
507 * given dimension specification (Z^{n+1} -> Z^{n+1}) that
508 * is an overapproximation of the relations that
509 * maps an element x to any element that can be reached
510 * by taking a non-negative number of steps along any of
511 * the elements in "delta".
512 * That is, construct an approximation of
514 * { [x] -> [y] : exists f \in \delta, k \in Z :
515 * y = x + k [f, 1] and k >= 0 }
517 * For any element in this relation, the number of steps taken
518 * is equal to the difference in the final coordinates.
520 * In particular, let delta be defined as
522 * \delta = [p] -> { [x] : A x + a >= 0 and B p + b >= 0 and
523 * C x + C'p + c >= 0 and
524 * D x + D'p + d >= 0 }
526 * where the constraints C x + C'p + c >= 0 are such that the parametric
527 * constant term of each constraint j, "C_j x + C'_j p + c_j",
528 * can never attain positive values, then the relation is constructed as
530 * { [x] -> [y] : exists [f, k] \in Z^{n+1} : y = x + f and
531 * A f + k a >= 0 and B p + b >= 0 and
532 * C f + C'p + c >= 0 and k >= 1 }
533 * union { [x] -> [x] }
535 * If the zero-length paths happen to correspond exactly to the identity
536 * mapping, then we return
538 * { [x] -> [y] : exists [f, k] \in Z^{n+1} : y = x + f and
539 * A f + k a >= 0 and B p + b >= 0 and
540 * C f + C'p + c >= 0 and k >= 0 }
542 * instead.
544 * Existentially quantified variables in \delta are handled by
545 * classifying them as independent of the parameters, purely
546 * parameter dependent and others. Constraints containing
547 * any of the other existentially quantified variables are removed.
548 * This is safe, but leads to an additional overapproximation.
550 * If there are any impure constraints, then we also eliminate
551 * the parameters from \delta, resulting in a set
553 * \delta' = { [x] : E x + e >= 0 }
555 * and add the constraints
557 * E f + k e >= 0
559 * to the constructed relation.
561 static __isl_give isl_map *path_along_delta(__isl_take isl_space *dim,
562 __isl_take isl_basic_set *delta)
564 isl_basic_map *path = NULL;
565 unsigned d;
566 unsigned n_div;
567 unsigned nparam;
568 unsigned off;
569 int i, k;
570 int is_id;
571 int *div_purity = NULL;
572 int impurity = 0;
574 if (!delta)
575 goto error;
576 n_div = isl_basic_set_dim(delta, isl_dim_div);
577 d = isl_basic_set_dim(delta, isl_dim_set);
578 nparam = isl_basic_set_dim(delta, isl_dim_param);
579 path = isl_basic_map_alloc_space(isl_space_copy(dim), n_div + d + 1,
580 d + 1 + delta->n_eq, delta->n_eq + delta->n_ineq + 1);
581 off = 1 + nparam + 2 * (d + 1) + n_div;
583 for (i = 0; i < n_div + d + 1; ++i) {
584 k = isl_basic_map_alloc_div(path);
585 if (k < 0)
586 goto error;
587 isl_int_set_si(path->div[k][0], 0);
590 for (i = 0; i < d + 1; ++i) {
591 k = isl_basic_map_alloc_equality(path);
592 if (k < 0)
593 goto error;
594 isl_seq_clr(path->eq[k], 1 + isl_basic_map_total_dim(path));
595 isl_int_set_si(path->eq[k][1 + nparam + i], 1);
596 isl_int_set_si(path->eq[k][1 + nparam + d + 1 + i], -1);
597 isl_int_set_si(path->eq[k][off + i], 1);
600 div_purity = get_div_purity(delta);
601 if (!div_purity)
602 goto error;
604 path = add_delta_constraints(path, delta, off, nparam, d,
605 div_purity, 1, &impurity);
606 path = add_delta_constraints(path, delta, off, nparam, d,
607 div_purity, 0, &impurity);
608 if (impurity) {
609 isl_space *dim = isl_basic_set_get_space(delta);
610 delta = isl_basic_set_project_out(delta,
611 isl_dim_param, 0, nparam);
612 delta = isl_basic_set_add_dims(delta, isl_dim_param, nparam);
613 delta = isl_basic_set_reset_space(delta, dim);
614 if (!delta)
615 goto error;
616 path = isl_basic_map_extend_constraints(path, delta->n_eq,
617 delta->n_ineq + 1);
618 path = add_delta_constraints(path, delta, off, nparam, d,
619 NULL, 1, &impurity);
620 path = add_delta_constraints(path, delta, off, nparam, d,
621 NULL, 0, &impurity);
622 path = isl_basic_map_gauss(path, NULL);
625 is_id = empty_path_is_identity(path, off + d);
626 if (is_id < 0)
627 goto error;
629 k = isl_basic_map_alloc_inequality(path);
630 if (k < 0)
631 goto error;
632 isl_seq_clr(path->ineq[k], 1 + isl_basic_map_total_dim(path));
633 if (!is_id)
634 isl_int_set_si(path->ineq[k][0], -1);
635 isl_int_set_si(path->ineq[k][off + d], 1);
637 free(div_purity);
638 isl_basic_set_free(delta);
639 path = isl_basic_map_finalize(path);
640 if (is_id) {
641 isl_space_free(dim);
642 return isl_map_from_basic_map(path);
644 return isl_basic_map_union(path, isl_basic_map_identity(dim));
645 error:
646 free(div_purity);
647 isl_space_free(dim);
648 isl_basic_set_free(delta);
649 isl_basic_map_free(path);
650 return NULL;
653 /* Given a dimension specification Z^{n+1} -> Z^{n+1} and a parameter "param",
654 * construct a map that equates the parameter to the difference
655 * in the final coordinates and imposes that this difference is positive.
656 * That is, construct
658 * { [x,x_s] -> [y,y_s] : k = y_s - x_s > 0 }
660 static __isl_give isl_map *equate_parameter_to_length(__isl_take isl_space *dim,
661 unsigned param)
663 struct isl_basic_map *bmap;
664 unsigned d;
665 unsigned nparam;
666 int k;
668 d = isl_space_dim(dim, isl_dim_in);
669 nparam = isl_space_dim(dim, isl_dim_param);
670 bmap = isl_basic_map_alloc_space(dim, 0, 1, 1);
671 k = isl_basic_map_alloc_equality(bmap);
672 if (k < 0)
673 goto error;
674 isl_seq_clr(bmap->eq[k], 1 + isl_basic_map_total_dim(bmap));
675 isl_int_set_si(bmap->eq[k][1 + param], -1);
676 isl_int_set_si(bmap->eq[k][1 + nparam + d - 1], -1);
677 isl_int_set_si(bmap->eq[k][1 + nparam + d + d - 1], 1);
679 k = isl_basic_map_alloc_inequality(bmap);
680 if (k < 0)
681 goto error;
682 isl_seq_clr(bmap->ineq[k], 1 + isl_basic_map_total_dim(bmap));
683 isl_int_set_si(bmap->ineq[k][1 + param], 1);
684 isl_int_set_si(bmap->ineq[k][0], -1);
686 bmap = isl_basic_map_finalize(bmap);
687 return isl_map_from_basic_map(bmap);
688 error:
689 isl_basic_map_free(bmap);
690 return NULL;
693 /* Check whether "path" is acyclic, where the last coordinates of domain
694 * and range of path encode the number of steps taken.
695 * That is, check whether
697 * { d | d = y - x and (x,y) in path }
699 * does not contain any element with positive last coordinate (positive length)
700 * and zero remaining coordinates (cycle).
702 static int is_acyclic(__isl_take isl_map *path)
704 int i;
705 int acyclic;
706 unsigned dim;
707 struct isl_set *delta;
709 delta = isl_map_deltas(path);
710 dim = isl_set_dim(delta, isl_dim_set);
711 for (i = 0; i < dim; ++i) {
712 if (i == dim -1)
713 delta = isl_set_lower_bound_si(delta, isl_dim_set, i, 1);
714 else
715 delta = isl_set_fix_si(delta, isl_dim_set, i, 0);
718 acyclic = isl_set_is_empty(delta);
719 isl_set_free(delta);
721 return acyclic;
724 /* Given a union of basic maps R = \cup_i R_i \subseteq D \times D
725 * and a dimension specification (Z^{n+1} -> Z^{n+1}),
726 * construct a map that is an overapproximation of the map
727 * that takes an element from the space D \times Z to another
728 * element from the same space, such that the first n coordinates of the
729 * difference between them is a sum of differences between images
730 * and pre-images in one of the R_i and such that the last coordinate
731 * is equal to the number of steps taken.
732 * That is, let
734 * \Delta_i = { y - x | (x, y) in R_i }
736 * then the constructed map is an overapproximation of
738 * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
739 * d = (\sum_i k_i \delta_i, \sum_i k_i) }
741 * The elements of the singleton \Delta_i's are collected as the
742 * rows of the steps matrix. For all these \Delta_i's together,
743 * a single path is constructed.
744 * For each of the other \Delta_i's, we compute an overapproximation
745 * of the paths along elements of \Delta_i.
746 * Since each of these paths performs an addition, composition is
747 * symmetric and we can simply compose all resulting paths in any order.
749 static __isl_give isl_map *construct_extended_path(__isl_take isl_space *dim,
750 __isl_keep isl_map *map, int *project)
752 struct isl_mat *steps = NULL;
753 struct isl_map *path = NULL;
754 unsigned d;
755 int i, j, n;
757 d = isl_map_dim(map, isl_dim_in);
759 path = isl_map_identity(isl_space_copy(dim));
761 steps = isl_mat_alloc(map->ctx, map->n, d);
762 if (!steps)
763 goto error;
765 n = 0;
766 for (i = 0; i < map->n; ++i) {
767 struct isl_basic_set *delta;
769 delta = isl_basic_map_deltas(isl_basic_map_copy(map->p[i]));
771 for (j = 0; j < d; ++j) {
772 int fixed;
774 fixed = isl_basic_set_plain_dim_is_fixed(delta, j,
775 &steps->row[n][j]);
776 if (fixed < 0) {
777 isl_basic_set_free(delta);
778 goto error;
780 if (!fixed)
781 break;
785 if (j < d) {
786 path = isl_map_apply_range(path,
787 path_along_delta(isl_space_copy(dim), delta));
788 path = isl_map_coalesce(path);
789 } else {
790 isl_basic_set_free(delta);
791 ++n;
795 if (n > 0) {
796 steps->n_row = n;
797 path = isl_map_apply_range(path,
798 path_along_steps(isl_space_copy(dim), steps));
801 if (project && *project) {
802 *project = is_acyclic(isl_map_copy(path));
803 if (*project < 0)
804 goto error;
807 isl_space_free(dim);
808 isl_mat_free(steps);
809 return path;
810 error:
811 isl_space_free(dim);
812 isl_mat_free(steps);
813 isl_map_free(path);
814 return NULL;
817 static int isl_set_overlaps(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
819 isl_set *i;
820 int no_overlap;
822 if (!isl_space_tuple_match(set1->dim, isl_dim_set, set2->dim, isl_dim_set))
823 return 0;
825 i = isl_set_intersect(isl_set_copy(set1), isl_set_copy(set2));
826 no_overlap = isl_set_is_empty(i);
827 isl_set_free(i);
829 return no_overlap < 0 ? -1 : !no_overlap;
832 /* Given a union of basic maps R = \cup_i R_i \subseteq D \times D
833 * and a dimension specification (Z^{n+1} -> Z^{n+1}),
834 * construct a map that is an overapproximation of the map
835 * that takes an element from the dom R \times Z to an
836 * element from ran R \times Z, such that the first n coordinates of the
837 * difference between them is a sum of differences between images
838 * and pre-images in one of the R_i and such that the last coordinate
839 * is equal to the number of steps taken.
840 * That is, let
842 * \Delta_i = { y - x | (x, y) in R_i }
844 * then the constructed map is an overapproximation of
846 * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
847 * d = (\sum_i k_i \delta_i, \sum_i k_i) and
848 * x in dom R and x + d in ran R and
849 * \sum_i k_i >= 1 }
851 static __isl_give isl_map *construct_component(__isl_take isl_space *dim,
852 __isl_keep isl_map *map, int *exact, int project)
854 struct isl_set *domain = NULL;
855 struct isl_set *range = NULL;
856 struct isl_map *app = NULL;
857 struct isl_map *path = NULL;
859 domain = isl_map_domain(isl_map_copy(map));
860 domain = isl_set_coalesce(domain);
861 range = isl_map_range(isl_map_copy(map));
862 range = isl_set_coalesce(range);
863 if (!isl_set_overlaps(domain, range)) {
864 isl_set_free(domain);
865 isl_set_free(range);
866 isl_space_free(dim);
868 map = isl_map_copy(map);
869 map = isl_map_add_dims(map, isl_dim_in, 1);
870 map = isl_map_add_dims(map, isl_dim_out, 1);
871 map = set_path_length(map, 1, 1);
872 return map;
874 app = isl_map_from_domain_and_range(domain, range);
875 app = isl_map_add_dims(app, isl_dim_in, 1);
876 app = isl_map_add_dims(app, isl_dim_out, 1);
878 path = construct_extended_path(isl_space_copy(dim), map,
879 exact && *exact ? &project : NULL);
880 app = isl_map_intersect(app, path);
882 if (exact && *exact &&
883 (*exact = check_exactness(isl_map_copy(map), isl_map_copy(app),
884 project)) < 0)
885 goto error;
887 isl_space_free(dim);
888 app = set_path_length(app, 0, 1);
889 return app;
890 error:
891 isl_space_free(dim);
892 isl_map_free(app);
893 return NULL;
896 /* Call construct_component and, if "project" is set, project out
897 * the final coordinates.
899 static __isl_give isl_map *construct_projected_component(
900 __isl_take isl_space *dim,
901 __isl_keep isl_map *map, int *exact, int project)
903 isl_map *app;
904 unsigned d;
906 if (!dim)
907 return NULL;
908 d = isl_space_dim(dim, isl_dim_in);
910 app = construct_component(dim, map, exact, project);
911 if (project) {
912 app = isl_map_project_out(app, isl_dim_in, d - 1, 1);
913 app = isl_map_project_out(app, isl_dim_out, d - 1, 1);
915 return app;
918 /* Compute an extended version, i.e., with path lengths, of
919 * an overapproximation of the transitive closure of "bmap"
920 * with path lengths greater than or equal to zero and with
921 * domain and range equal to "dom".
923 static __isl_give isl_map *q_closure(__isl_take isl_space *dim,
924 __isl_take isl_set *dom, __isl_keep isl_basic_map *bmap, int *exact)
926 int project = 1;
927 isl_map *path;
928 isl_map *map;
929 isl_map *app;
931 dom = isl_set_add_dims(dom, isl_dim_set, 1);
932 app = isl_map_from_domain_and_range(dom, isl_set_copy(dom));
933 map = isl_map_from_basic_map(isl_basic_map_copy(bmap));
934 path = construct_extended_path(dim, map, &project);
935 app = isl_map_intersect(app, path);
937 if ((*exact = check_exactness(map, isl_map_copy(app), project)) < 0)
938 goto error;
940 return app;
941 error:
942 isl_map_free(app);
943 return NULL;
946 /* Check whether qc has any elements of length at least one
947 * with domain and/or range outside of dom and ran.
949 static int has_spurious_elements(__isl_keep isl_map *qc,
950 __isl_keep isl_set *dom, __isl_keep isl_set *ran)
952 isl_set *s;
953 int subset;
954 unsigned d;
956 if (!qc || !dom || !ran)
957 return -1;
959 d = isl_map_dim(qc, isl_dim_in);
961 qc = isl_map_copy(qc);
962 qc = set_path_length(qc, 0, 1);
963 qc = isl_map_project_out(qc, isl_dim_in, d - 1, 1);
964 qc = isl_map_project_out(qc, isl_dim_out, d - 1, 1);
966 s = isl_map_domain(isl_map_copy(qc));
967 subset = isl_set_is_subset(s, dom);
968 isl_set_free(s);
969 if (subset < 0)
970 goto error;
971 if (!subset) {
972 isl_map_free(qc);
973 return 1;
976 s = isl_map_range(qc);
977 subset = isl_set_is_subset(s, ran);
978 isl_set_free(s);
980 return subset < 0 ? -1 : !subset;
981 error:
982 isl_map_free(qc);
983 return -1;
986 #define LEFT 2
987 #define RIGHT 1
989 /* For each basic map in "map", except i, check whether it combines
990 * with the transitive closure that is reflexive on C combines
991 * to the left and to the right.
993 * In particular, if
995 * dom map_j \subseteq C
997 * then right[j] is set to 1. Otherwise, if
999 * ran map_i \cap dom map_j = \emptyset
1001 * then right[j] is set to 0. Otherwise, composing to the right
1002 * is impossible.
1004 * Similar, for composing to the left, we have if
1006 * ran map_j \subseteq C
1008 * then left[j] is set to 1. Otherwise, if
1010 * dom map_i \cap ran map_j = \emptyset
1012 * then left[j] is set to 0. Otherwise, composing to the left
1013 * is impossible.
1015 * The return value is or'd with LEFT if composing to the left
1016 * is possible and with RIGHT if composing to the right is possible.
1018 static int composability(__isl_keep isl_set *C, int i,
1019 isl_set **dom, isl_set **ran, int *left, int *right,
1020 __isl_keep isl_map *map)
1022 int j;
1023 int ok;
1025 ok = LEFT | RIGHT;
1026 for (j = 0; j < map->n && ok; ++j) {
1027 int overlaps, subset;
1028 if (j == i)
1029 continue;
1031 if (ok & RIGHT) {
1032 if (!dom[j])
1033 dom[j] = isl_set_from_basic_set(
1034 isl_basic_map_domain(
1035 isl_basic_map_copy(map->p[j])));
1036 if (!dom[j])
1037 return -1;
1038 overlaps = isl_set_overlaps(ran[i], dom[j]);
1039 if (overlaps < 0)
1040 return -1;
1041 if (!overlaps)
1042 right[j] = 0;
1043 else {
1044 subset = isl_set_is_subset(dom[j], C);
1045 if (subset < 0)
1046 return -1;
1047 if (subset)
1048 right[j] = 1;
1049 else
1050 ok &= ~RIGHT;
1054 if (ok & LEFT) {
1055 if (!ran[j])
1056 ran[j] = isl_set_from_basic_set(
1057 isl_basic_map_range(
1058 isl_basic_map_copy(map->p[j])));
1059 if (!ran[j])
1060 return -1;
1061 overlaps = isl_set_overlaps(dom[i], ran[j]);
1062 if (overlaps < 0)
1063 return -1;
1064 if (!overlaps)
1065 left[j] = 0;
1066 else {
1067 subset = isl_set_is_subset(ran[j], C);
1068 if (subset < 0)
1069 return -1;
1070 if (subset)
1071 left[j] = 1;
1072 else
1073 ok &= ~LEFT;
1078 return ok;
1081 static __isl_give isl_map *anonymize(__isl_take isl_map *map)
1083 map = isl_map_reset(map, isl_dim_in);
1084 map = isl_map_reset(map, isl_dim_out);
1085 return map;
1088 /* Return a map that is a union of the basic maps in "map", except i,
1089 * composed to left and right with qc based on the entries of "left"
1090 * and "right".
1092 static __isl_give isl_map *compose(__isl_keep isl_map *map, int i,
1093 __isl_take isl_map *qc, int *left, int *right)
1095 int j;
1096 isl_map *comp;
1098 comp = isl_map_empty(isl_map_get_space(map));
1099 for (j = 0; j < map->n; ++j) {
1100 isl_map *map_j;
1102 if (j == i)
1103 continue;
1105 map_j = isl_map_from_basic_map(isl_basic_map_copy(map->p[j]));
1106 map_j = anonymize(map_j);
1107 if (left && left[j])
1108 map_j = isl_map_apply_range(map_j, isl_map_copy(qc));
1109 if (right && right[j])
1110 map_j = isl_map_apply_range(isl_map_copy(qc), map_j);
1111 comp = isl_map_union(comp, map_j);
1114 comp = isl_map_compute_divs(comp);
1115 comp = isl_map_coalesce(comp);
1117 isl_map_free(qc);
1119 return comp;
1122 /* Compute the transitive closure of "map" incrementally by
1123 * computing
1125 * map_i^+ \cup qc^+
1127 * or
1129 * map_i^+ \cup ((id \cup map_i^) \circ qc^+)
1131 * or
1133 * map_i^+ \cup (qc^+ \circ (id \cup map_i^))
1135 * depending on whether left or right are NULL.
1137 static __isl_give isl_map *compute_incremental(
1138 __isl_take isl_space *dim, __isl_keep isl_map *map,
1139 int i, __isl_take isl_map *qc, int *left, int *right, int *exact)
1141 isl_map *map_i;
1142 isl_map *tc;
1143 isl_map *rtc = NULL;
1145 if (!map)
1146 goto error;
1147 isl_assert(map->ctx, left || right, goto error);
1149 map_i = isl_map_from_basic_map(isl_basic_map_copy(map->p[i]));
1150 tc = construct_projected_component(isl_space_copy(dim), map_i,
1151 exact, 1);
1152 isl_map_free(map_i);
1154 if (*exact)
1155 qc = isl_map_transitive_closure(qc, exact);
1157 if (!*exact) {
1158 isl_space_free(dim);
1159 isl_map_free(tc);
1160 isl_map_free(qc);
1161 return isl_map_universe(isl_map_get_space(map));
1164 if (!left || !right)
1165 rtc = isl_map_union(isl_map_copy(tc),
1166 isl_map_identity(isl_map_get_space(tc)));
1167 if (!right)
1168 qc = isl_map_apply_range(rtc, qc);
1169 if (!left)
1170 qc = isl_map_apply_range(qc, rtc);
1171 qc = isl_map_union(tc, qc);
1173 isl_space_free(dim);
1175 return qc;
1176 error:
1177 isl_space_free(dim);
1178 isl_map_free(qc);
1179 return NULL;
1182 /* Given a map "map", try to find a basic map such that
1183 * map^+ can be computed as
1185 * map^+ = map_i^+ \cup
1186 * \bigcup_j ((map_i^+ \cup Id_C)^+ \circ map_j \circ (map_i^+ \cup Id_C))^+
1188 * with C the simple hull of the domain and range of the input map.
1189 * map_i^ \cup Id_C is computed by allowing the path lengths to be zero
1190 * and by intersecting domain and range with C.
1191 * Of course, we need to check that this is actually equal to map_i^ \cup Id_C.
1192 * Also, we only use the incremental computation if all the transitive
1193 * closures are exact and if the number of basic maps in the union,
1194 * after computing the integer divisions, is smaller than the number
1195 * of basic maps in the input map.
1197 static int incemental_on_entire_domain(__isl_keep isl_space *dim,
1198 __isl_keep isl_map *map,
1199 isl_set **dom, isl_set **ran, int *left, int *right,
1200 __isl_give isl_map **res)
1202 int i;
1203 isl_set *C;
1204 unsigned d;
1206 *res = NULL;
1208 C = isl_set_union(isl_map_domain(isl_map_copy(map)),
1209 isl_map_range(isl_map_copy(map)));
1210 C = isl_set_from_basic_set(isl_set_simple_hull(C));
1211 if (!C)
1212 return -1;
1213 if (C->n != 1) {
1214 isl_set_free(C);
1215 return 0;
1218 d = isl_map_dim(map, isl_dim_in);
1220 for (i = 0; i < map->n; ++i) {
1221 isl_map *qc;
1222 int exact_i, spurious;
1223 int j;
1224 dom[i] = isl_set_from_basic_set(isl_basic_map_domain(
1225 isl_basic_map_copy(map->p[i])));
1226 ran[i] = isl_set_from_basic_set(isl_basic_map_range(
1227 isl_basic_map_copy(map->p[i])));
1228 qc = q_closure(isl_space_copy(dim), isl_set_copy(C),
1229 map->p[i], &exact_i);
1230 if (!qc)
1231 goto error;
1232 if (!exact_i) {
1233 isl_map_free(qc);
1234 continue;
1236 spurious = has_spurious_elements(qc, dom[i], ran[i]);
1237 if (spurious) {
1238 isl_map_free(qc);
1239 if (spurious < 0)
1240 goto error;
1241 continue;
1243 qc = isl_map_project_out(qc, isl_dim_in, d, 1);
1244 qc = isl_map_project_out(qc, isl_dim_out, d, 1);
1245 qc = isl_map_compute_divs(qc);
1246 for (j = 0; j < map->n; ++j)
1247 left[j] = right[j] = 1;
1248 qc = compose(map, i, qc, left, right);
1249 if (!qc)
1250 goto error;
1251 if (qc->n >= map->n) {
1252 isl_map_free(qc);
1253 continue;
1255 *res = compute_incremental(isl_space_copy(dim), map, i, qc,
1256 left, right, &exact_i);
1257 if (!*res)
1258 goto error;
1259 if (exact_i)
1260 break;
1261 isl_map_free(*res);
1262 *res = NULL;
1265 isl_set_free(C);
1267 return *res != NULL;
1268 error:
1269 isl_set_free(C);
1270 return -1;
1273 /* Try and compute the transitive closure of "map" as
1275 * map^+ = map_i^+ \cup
1276 * \bigcup_j ((map_i^+ \cup Id_C)^+ \circ map_j \circ (map_i^+ \cup Id_C))^+
1278 * with C either the simple hull of the domain and range of the entire
1279 * map or the simple hull of domain and range of map_i.
1281 static __isl_give isl_map *incremental_closure(__isl_take isl_space *dim,
1282 __isl_keep isl_map *map, int *exact, int project)
1284 int i;
1285 isl_set **dom = NULL;
1286 isl_set **ran = NULL;
1287 int *left = NULL;
1288 int *right = NULL;
1289 isl_set *C;
1290 unsigned d;
1291 isl_map *res = NULL;
1293 if (!project)
1294 return construct_projected_component(dim, map, exact, project);
1296 if (!map)
1297 goto error;
1298 if (map->n <= 1)
1299 return construct_projected_component(dim, map, exact, project);
1301 d = isl_map_dim(map, isl_dim_in);
1303 dom = isl_calloc_array(map->ctx, isl_set *, map->n);
1304 ran = isl_calloc_array(map->ctx, isl_set *, map->n);
1305 left = isl_calloc_array(map->ctx, int, map->n);
1306 right = isl_calloc_array(map->ctx, int, map->n);
1307 if (!ran || !dom || !left || !right)
1308 goto error;
1310 if (incemental_on_entire_domain(dim, map, dom, ran, left, right, &res) < 0)
1311 goto error;
1313 for (i = 0; !res && i < map->n; ++i) {
1314 isl_map *qc;
1315 int exact_i, spurious, comp;
1316 if (!dom[i])
1317 dom[i] = isl_set_from_basic_set(
1318 isl_basic_map_domain(
1319 isl_basic_map_copy(map->p[i])));
1320 if (!dom[i])
1321 goto error;
1322 if (!ran[i])
1323 ran[i] = isl_set_from_basic_set(
1324 isl_basic_map_range(
1325 isl_basic_map_copy(map->p[i])));
1326 if (!ran[i])
1327 goto error;
1328 C = isl_set_union(isl_set_copy(dom[i]),
1329 isl_set_copy(ran[i]));
1330 C = isl_set_from_basic_set(isl_set_simple_hull(C));
1331 if (!C)
1332 goto error;
1333 if (C->n != 1) {
1334 isl_set_free(C);
1335 continue;
1337 comp = composability(C, i, dom, ran, left, right, map);
1338 if (!comp || comp < 0) {
1339 isl_set_free(C);
1340 if (comp < 0)
1341 goto error;
1342 continue;
1344 qc = q_closure(isl_space_copy(dim), C, map->p[i], &exact_i);
1345 if (!qc)
1346 goto error;
1347 if (!exact_i) {
1348 isl_map_free(qc);
1349 continue;
1351 spurious = has_spurious_elements(qc, dom[i], ran[i]);
1352 if (spurious) {
1353 isl_map_free(qc);
1354 if (spurious < 0)
1355 goto error;
1356 continue;
1358 qc = isl_map_project_out(qc, isl_dim_in, d, 1);
1359 qc = isl_map_project_out(qc, isl_dim_out, d, 1);
1360 qc = isl_map_compute_divs(qc);
1361 qc = compose(map, i, qc, (comp & LEFT) ? left : NULL,
1362 (comp & RIGHT) ? right : NULL);
1363 if (!qc)
1364 goto error;
1365 if (qc->n >= map->n) {
1366 isl_map_free(qc);
1367 continue;
1369 res = compute_incremental(isl_space_copy(dim), map, i, qc,
1370 (comp & LEFT) ? left : NULL,
1371 (comp & RIGHT) ? right : NULL, &exact_i);
1372 if (!res)
1373 goto error;
1374 if (exact_i)
1375 break;
1376 isl_map_free(res);
1377 res = NULL;
1380 for (i = 0; i < map->n; ++i) {
1381 isl_set_free(dom[i]);
1382 isl_set_free(ran[i]);
1384 free(dom);
1385 free(ran);
1386 free(left);
1387 free(right);
1389 if (res) {
1390 isl_space_free(dim);
1391 return res;
1394 return construct_projected_component(dim, map, exact, project);
1395 error:
1396 if (dom)
1397 for (i = 0; i < map->n; ++i)
1398 isl_set_free(dom[i]);
1399 free(dom);
1400 if (ran)
1401 for (i = 0; i < map->n; ++i)
1402 isl_set_free(ran[i]);
1403 free(ran);
1404 free(left);
1405 free(right);
1406 isl_space_free(dim);
1407 return NULL;
1410 /* Given an array of sets "set", add "dom" at position "pos"
1411 * and search for elements at earlier positions that overlap with "dom".
1412 * If any can be found, then merge all of them, together with "dom", into
1413 * a single set and assign the union to the first in the array,
1414 * which becomes the new group leader for all groups involved in the merge.
1415 * During the search, we only consider group leaders, i.e., those with
1416 * group[i] = i, as the other sets have already been combined
1417 * with one of the group leaders.
1419 static int merge(isl_set **set, int *group, __isl_take isl_set *dom, int pos)
1421 int i;
1423 group[pos] = pos;
1424 set[pos] = isl_set_copy(dom);
1426 for (i = pos - 1; i >= 0; --i) {
1427 int o;
1429 if (group[i] != i)
1430 continue;
1432 o = isl_set_overlaps(set[i], dom);
1433 if (o < 0)
1434 goto error;
1435 if (!o)
1436 continue;
1438 set[i] = isl_set_union(set[i], set[group[pos]]);
1439 set[group[pos]] = NULL;
1440 if (!set[i])
1441 goto error;
1442 group[group[pos]] = i;
1443 group[pos] = i;
1446 isl_set_free(dom);
1447 return 0;
1448 error:
1449 isl_set_free(dom);
1450 return -1;
1453 /* Replace each entry in the n by n grid of maps by the cross product
1454 * with the relation { [i] -> [i + 1] }.
1456 static int add_length(__isl_keep isl_map *map, isl_map ***grid, int n)
1458 int i, j, k;
1459 isl_space *dim;
1460 isl_basic_map *bstep;
1461 isl_map *step;
1462 unsigned nparam;
1464 if (!map)
1465 return -1;
1467 dim = isl_map_get_space(map);
1468 nparam = isl_space_dim(dim, isl_dim_param);
1469 dim = isl_space_drop_dims(dim, isl_dim_in, 0, isl_space_dim(dim, isl_dim_in));
1470 dim = isl_space_drop_dims(dim, isl_dim_out, 0, isl_space_dim(dim, isl_dim_out));
1471 dim = isl_space_add_dims(dim, isl_dim_in, 1);
1472 dim = isl_space_add_dims(dim, isl_dim_out, 1);
1473 bstep = isl_basic_map_alloc_space(dim, 0, 1, 0);
1474 k = isl_basic_map_alloc_equality(bstep);
1475 if (k < 0) {
1476 isl_basic_map_free(bstep);
1477 return -1;
1479 isl_seq_clr(bstep->eq[k], 1 + isl_basic_map_total_dim(bstep));
1480 isl_int_set_si(bstep->eq[k][0], 1);
1481 isl_int_set_si(bstep->eq[k][1 + nparam], 1);
1482 isl_int_set_si(bstep->eq[k][1 + nparam + 1], -1);
1483 bstep = isl_basic_map_finalize(bstep);
1484 step = isl_map_from_basic_map(bstep);
1486 for (i = 0; i < n; ++i)
1487 for (j = 0; j < n; ++j)
1488 grid[i][j] = isl_map_product(grid[i][j],
1489 isl_map_copy(step));
1491 isl_map_free(step);
1493 return 0;
1496 /* The core of the Floyd-Warshall algorithm.
1497 * Updates the given n x x matrix of relations in place.
1499 * The algorithm iterates over all vertices. In each step, the whole
1500 * matrix is updated to include all paths that go to the current vertex,
1501 * possibly stay there a while (including passing through earlier vertices)
1502 * and then come back. At the start of each iteration, the diagonal
1503 * element corresponding to the current vertex is replaced by its
1504 * transitive closure to account for all indirect paths that stay
1505 * in the current vertex.
1507 static void floyd_warshall_iterate(isl_map ***grid, int n, int *exact)
1509 int r, p, q;
1511 for (r = 0; r < n; ++r) {
1512 int r_exact;
1513 grid[r][r] = isl_map_transitive_closure(grid[r][r],
1514 (exact && *exact) ? &r_exact : NULL);
1515 if (exact && *exact && !r_exact)
1516 *exact = 0;
1518 for (p = 0; p < n; ++p)
1519 for (q = 0; q < n; ++q) {
1520 isl_map *loop;
1521 if (p == r && q == r)
1522 continue;
1523 loop = isl_map_apply_range(
1524 isl_map_copy(grid[p][r]),
1525 isl_map_copy(grid[r][q]));
1526 grid[p][q] = isl_map_union(grid[p][q], loop);
1527 loop = isl_map_apply_range(
1528 isl_map_copy(grid[p][r]),
1529 isl_map_apply_range(
1530 isl_map_copy(grid[r][r]),
1531 isl_map_copy(grid[r][q])));
1532 grid[p][q] = isl_map_union(grid[p][q], loop);
1533 grid[p][q] = isl_map_coalesce(grid[p][q]);
1538 /* Given a partition of the domains and ranges of the basic maps in "map",
1539 * apply the Floyd-Warshall algorithm with the elements in the partition
1540 * as vertices.
1542 * In particular, there are "n" elements in the partition and "group" is
1543 * an array of length 2 * map->n with entries in [0,n-1].
1545 * We first construct a matrix of relations based on the partition information,
1546 * apply Floyd-Warshall on this matrix of relations and then take the
1547 * union of all entries in the matrix as the final result.
1549 * If we are actually computing the power instead of the transitive closure,
1550 * i.e., when "project" is not set, then the result should have the
1551 * path lengths encoded as the difference between an extra pair of
1552 * coordinates. We therefore apply the nested transitive closures
1553 * to relations that include these lengths. In particular, we replace
1554 * the input relation by the cross product with the unit length relation
1555 * { [i] -> [i + 1] }.
1557 static __isl_give isl_map *floyd_warshall_with_groups(__isl_take isl_space *dim,
1558 __isl_keep isl_map *map, int *exact, int project, int *group, int n)
1560 int i, j, k;
1561 isl_map ***grid = NULL;
1562 isl_map *app;
1564 if (!map)
1565 goto error;
1567 if (n == 1) {
1568 free(group);
1569 return incremental_closure(dim, map, exact, project);
1572 grid = isl_calloc_array(map->ctx, isl_map **, n);
1573 if (!grid)
1574 goto error;
1575 for (i = 0; i < n; ++i) {
1576 grid[i] = isl_calloc_array(map->ctx, isl_map *, n);
1577 if (!grid[i])
1578 goto error;
1579 for (j = 0; j < n; ++j)
1580 grid[i][j] = isl_map_empty(isl_map_get_space(map));
1583 for (k = 0; k < map->n; ++k) {
1584 i = group[2 * k];
1585 j = group[2 * k + 1];
1586 grid[i][j] = isl_map_union(grid[i][j],
1587 isl_map_from_basic_map(
1588 isl_basic_map_copy(map->p[k])));
1591 if (!project && add_length(map, grid, n) < 0)
1592 goto error;
1594 floyd_warshall_iterate(grid, n, exact);
1596 app = isl_map_empty(isl_map_get_space(map));
1598 for (i = 0; i < n; ++i) {
1599 for (j = 0; j < n; ++j)
1600 app = isl_map_union(app, grid[i][j]);
1601 free(grid[i]);
1603 free(grid);
1605 free(group);
1606 isl_space_free(dim);
1608 return app;
1609 error:
1610 if (grid)
1611 for (i = 0; i < n; ++i) {
1612 if (!grid[i])
1613 continue;
1614 for (j = 0; j < n; ++j)
1615 isl_map_free(grid[i][j]);
1616 free(grid[i]);
1618 free(grid);
1619 free(group);
1620 isl_space_free(dim);
1621 return NULL;
1624 /* Partition the domains and ranges of the n basic relations in list
1625 * into disjoint cells.
1627 * To find the partition, we simply consider all of the domains
1628 * and ranges in turn and combine those that overlap.
1629 * "set" contains the partition elements and "group" indicates
1630 * to which partition element a given domain or range belongs.
1631 * The domain of basic map i corresponds to element 2 * i in these arrays,
1632 * while the domain corresponds to element 2 * i + 1.
1633 * During the construction group[k] is either equal to k,
1634 * in which case set[k] contains the union of all the domains and
1635 * ranges in the corresponding group, or is equal to some l < k,
1636 * with l another domain or range in the same group.
1638 static int *setup_groups(isl_ctx *ctx, __isl_keep isl_basic_map **list, int n,
1639 isl_set ***set, int *n_group)
1641 int i;
1642 int *group = NULL;
1643 int g;
1645 *set = isl_calloc_array(ctx, isl_set *, 2 * n);
1646 group = isl_alloc_array(ctx, int, 2 * n);
1648 if (!*set || !group)
1649 goto error;
1651 for (i = 0; i < n; ++i) {
1652 isl_set *dom;
1653 dom = isl_set_from_basic_set(isl_basic_map_domain(
1654 isl_basic_map_copy(list[i])));
1655 if (merge(*set, group, dom, 2 * i) < 0)
1656 goto error;
1657 dom = isl_set_from_basic_set(isl_basic_map_range(
1658 isl_basic_map_copy(list[i])));
1659 if (merge(*set, group, dom, 2 * i + 1) < 0)
1660 goto error;
1663 g = 0;
1664 for (i = 0; i < 2 * n; ++i)
1665 if (group[i] == i) {
1666 if (g != i) {
1667 (*set)[g] = (*set)[i];
1668 (*set)[i] = NULL;
1670 group[i] = g++;
1671 } else
1672 group[i] = group[group[i]];
1674 *n_group = g;
1676 return group;
1677 error:
1678 if (*set) {
1679 for (i = 0; i < 2 * n; ++i)
1680 isl_set_free((*set)[i]);
1681 free(*set);
1682 *set = NULL;
1684 free(group);
1685 return NULL;
1688 /* Check if the domains and ranges of the basic maps in "map" can
1689 * be partitioned, and if so, apply Floyd-Warshall on the elements
1690 * of the partition. Note that we also apply this algorithm
1691 * if we want to compute the power, i.e., when "project" is not set.
1692 * However, the results are unlikely to be exact since the recursive
1693 * calls inside the Floyd-Warshall algorithm typically result in
1694 * non-linear path lengths quite quickly.
1696 static __isl_give isl_map *floyd_warshall(__isl_take isl_space *dim,
1697 __isl_keep isl_map *map, int *exact, int project)
1699 int i;
1700 isl_set **set = NULL;
1701 int *group = NULL;
1702 int n;
1704 if (!map)
1705 goto error;
1706 if (map->n <= 1)
1707 return incremental_closure(dim, map, exact, project);
1709 group = setup_groups(map->ctx, map->p, map->n, &set, &n);
1710 if (!group)
1711 goto error;
1713 for (i = 0; i < 2 * map->n; ++i)
1714 isl_set_free(set[i]);
1716 free(set);
1718 return floyd_warshall_with_groups(dim, map, exact, project, group, n);
1719 error:
1720 isl_space_free(dim);
1721 return NULL;
1724 /* Structure for representing the nodes of the graph of which
1725 * strongly connected components are being computed.
1727 * list contains the actual nodes
1728 * check_closed is set if we may have used the fact that
1729 * a pair of basic maps can be interchanged
1731 struct isl_tc_follows_data {
1732 isl_basic_map **list;
1733 int check_closed;
1736 /* Check whether in the computation of the transitive closure
1737 * "list[i]" (R_1) should follow (or be part of the same component as)
1738 * "list[j]" (R_2).
1740 * That is check whether
1742 * R_1 \circ R_2
1744 * is a subset of
1746 * R_2 \circ R_1
1748 * If so, then there is no reason for R_1 to immediately follow R_2
1749 * in any path.
1751 * *check_closed is set if the subset relation holds while
1752 * R_1 \circ R_2 is not empty.
1754 static int basic_map_follows(int i, int j, void *user)
1756 struct isl_tc_follows_data *data = user;
1757 struct isl_map *map12 = NULL;
1758 struct isl_map *map21 = NULL;
1759 int subset;
1761 if (!isl_space_tuple_match(data->list[i]->dim, isl_dim_in,
1762 data->list[j]->dim, isl_dim_out))
1763 return 0;
1765 map21 = isl_map_from_basic_map(
1766 isl_basic_map_apply_range(
1767 isl_basic_map_copy(data->list[j]),
1768 isl_basic_map_copy(data->list[i])));
1769 subset = isl_map_is_empty(map21);
1770 if (subset < 0)
1771 goto error;
1772 if (subset) {
1773 isl_map_free(map21);
1774 return 0;
1777 if (!isl_space_tuple_match(data->list[i]->dim, isl_dim_in,
1778 data->list[i]->dim, isl_dim_out) ||
1779 !isl_space_tuple_match(data->list[j]->dim, isl_dim_in,
1780 data->list[j]->dim, isl_dim_out)) {
1781 isl_map_free(map21);
1782 return 1;
1785 map12 = isl_map_from_basic_map(
1786 isl_basic_map_apply_range(
1787 isl_basic_map_copy(data->list[i]),
1788 isl_basic_map_copy(data->list[j])));
1790 subset = isl_map_is_subset(map21, map12);
1792 isl_map_free(map12);
1793 isl_map_free(map21);
1795 if (subset)
1796 data->check_closed = 1;
1798 return subset < 0 ? -1 : !subset;
1799 error:
1800 isl_map_free(map21);
1801 return -1;
1804 /* Given a union of basic maps R = \cup_i R_i \subseteq D \times D
1805 * and a dimension specification (Z^{n+1} -> Z^{n+1}),
1806 * construct a map that is an overapproximation of the map
1807 * that takes an element from the dom R \times Z to an
1808 * element from ran R \times Z, such that the first n coordinates of the
1809 * difference between them is a sum of differences between images
1810 * and pre-images in one of the R_i and such that the last coordinate
1811 * is equal to the number of steps taken.
1812 * If "project" is set, then these final coordinates are not included,
1813 * i.e., a relation of type Z^n -> Z^n is returned.
1814 * That is, let
1816 * \Delta_i = { y - x | (x, y) in R_i }
1818 * then the constructed map is an overapproximation of
1820 * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
1821 * d = (\sum_i k_i \delta_i, \sum_i k_i) and
1822 * x in dom R and x + d in ran R }
1824 * or
1826 * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
1827 * d = (\sum_i k_i \delta_i) and
1828 * x in dom R and x + d in ran R }
1830 * if "project" is set.
1832 * We first split the map into strongly connected components, perform
1833 * the above on each component and then join the results in the correct
1834 * order, at each join also taking in the union of both arguments
1835 * to allow for paths that do not go through one of the two arguments.
1837 static __isl_give isl_map *construct_power_components(__isl_take isl_space *dim,
1838 __isl_keep isl_map *map, int *exact, int project)
1840 int i, n, c;
1841 struct isl_map *path = NULL;
1842 struct isl_tc_follows_data data;
1843 struct isl_tarjan_graph *g = NULL;
1844 int *orig_exact;
1845 int local_exact;
1847 if (!map)
1848 goto error;
1849 if (map->n <= 1)
1850 return floyd_warshall(dim, map, exact, project);
1852 data.list = map->p;
1853 data.check_closed = 0;
1854 g = isl_tarjan_graph_init(map->ctx, map->n, &basic_map_follows, &data);
1855 if (!g)
1856 goto error;
1858 orig_exact = exact;
1859 if (data.check_closed && !exact)
1860 exact = &local_exact;
1862 c = 0;
1863 i = 0;
1864 n = map->n;
1865 if (project)
1866 path = isl_map_empty(isl_map_get_space(map));
1867 else
1868 path = isl_map_empty(isl_space_copy(dim));
1869 path = anonymize(path);
1870 while (n) {
1871 struct isl_map *comp;
1872 isl_map *path_comp, *path_comb;
1873 comp = isl_map_alloc_space(isl_map_get_space(map), n, 0);
1874 while (g->order[i] != -1) {
1875 comp = isl_map_add_basic_map(comp,
1876 isl_basic_map_copy(map->p[g->order[i]]));
1877 --n;
1878 ++i;
1880 path_comp = floyd_warshall(isl_space_copy(dim),
1881 comp, exact, project);
1882 path_comp = anonymize(path_comp);
1883 path_comb = isl_map_apply_range(isl_map_copy(path),
1884 isl_map_copy(path_comp));
1885 path = isl_map_union(path, path_comp);
1886 path = isl_map_union(path, path_comb);
1887 isl_map_free(comp);
1888 ++i;
1889 ++c;
1892 if (c > 1 && data.check_closed && !*exact) {
1893 int closed;
1895 closed = isl_map_is_transitively_closed(path);
1896 if (closed < 0)
1897 goto error;
1898 if (!closed) {
1899 isl_tarjan_graph_free(g);
1900 isl_map_free(path);
1901 return floyd_warshall(dim, map, orig_exact, project);
1905 isl_tarjan_graph_free(g);
1906 isl_space_free(dim);
1908 return path;
1909 error:
1910 isl_tarjan_graph_free(g);
1911 isl_space_free(dim);
1912 isl_map_free(path);
1913 return NULL;
1916 /* Given a union of basic maps R = \cup_i R_i \subseteq D \times D,
1917 * construct a map that is an overapproximation of the map
1918 * that takes an element from the space D to another
1919 * element from the same space, such that the difference between
1920 * them is a strictly positive sum of differences between images
1921 * and pre-images in one of the R_i.
1922 * The number of differences in the sum is equated to parameter "param".
1923 * That is, let
1925 * \Delta_i = { y - x | (x, y) in R_i }
1927 * then the constructed map is an overapproximation of
1929 * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
1930 * d = \sum_i k_i \delta_i and k = \sum_i k_i > 0 }
1931 * or
1933 * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
1934 * d = \sum_i k_i \delta_i and \sum_i k_i > 0 }
1936 * if "project" is set.
1938 * If "project" is not set, then
1939 * we construct an extended mapping with an extra coordinate
1940 * that indicates the number of steps taken. In particular,
1941 * the difference in the last coordinate is equal to the number
1942 * of steps taken to move from a domain element to the corresponding
1943 * image element(s).
1945 static __isl_give isl_map *construct_power(__isl_keep isl_map *map,
1946 int *exact, int project)
1948 struct isl_map *app = NULL;
1949 isl_space *dim = NULL;
1950 unsigned d;
1952 if (!map)
1953 return NULL;
1955 dim = isl_map_get_space(map);
1957 d = isl_space_dim(dim, isl_dim_in);
1958 dim = isl_space_add_dims(dim, isl_dim_in, 1);
1959 dim = isl_space_add_dims(dim, isl_dim_out, 1);
1961 app = construct_power_components(isl_space_copy(dim), map,
1962 exact, project);
1964 isl_space_free(dim);
1966 return app;
1969 /* Compute the positive powers of "map", or an overapproximation.
1970 * If the result is exact, then *exact is set to 1.
1972 * If project is set, then we are actually interested in the transitive
1973 * closure, so we can use a more relaxed exactness check.
1974 * The lengths of the paths are also projected out instead of being
1975 * encoded as the difference between an extra pair of final coordinates.
1977 static __isl_give isl_map *map_power(__isl_take isl_map *map,
1978 int *exact, int project)
1980 struct isl_map *app = NULL;
1982 if (exact)
1983 *exact = 1;
1985 if (!map)
1986 return NULL;
1988 isl_assert(map->ctx,
1989 isl_map_dim(map, isl_dim_in) == isl_map_dim(map, isl_dim_out),
1990 goto error);
1992 app = construct_power(map, exact, project);
1994 isl_map_free(map);
1995 return app;
1996 error:
1997 isl_map_free(map);
1998 isl_map_free(app);
1999 return NULL;
2002 /* Compute the positive powers of "map", or an overapproximation.
2003 * The result maps the exponent to a nested copy of the corresponding power.
2004 * If the result is exact, then *exact is set to 1.
2005 * map_power constructs an extended relation with the path lengths
2006 * encoded as the difference between the final coordinates.
2007 * In the final step, this difference is equated to an extra parameter
2008 * and made positive. The extra coordinates are subsequently projected out
2009 * and the parameter is turned into the domain of the result.
2011 __isl_give isl_map *isl_map_power(__isl_take isl_map *map, int *exact)
2013 isl_space *target_dim;
2014 isl_space *dim;
2015 isl_map *diff;
2016 unsigned d;
2017 unsigned param;
2019 if (!map)
2020 return NULL;
2022 d = isl_map_dim(map, isl_dim_in);
2023 param = isl_map_dim(map, isl_dim_param);
2025 map = isl_map_compute_divs(map);
2026 map = isl_map_coalesce(map);
2028 if (isl_map_plain_is_empty(map)) {
2029 map = isl_map_from_range(isl_map_wrap(map));
2030 map = isl_map_add_dims(map, isl_dim_in, 1);
2031 map = isl_map_set_dim_name(map, isl_dim_in, 0, "k");
2032 return map;
2035 target_dim = isl_map_get_space(map);
2036 target_dim = isl_space_from_range(isl_space_wrap(target_dim));
2037 target_dim = isl_space_add_dims(target_dim, isl_dim_in, 1);
2038 target_dim = isl_space_set_dim_name(target_dim, isl_dim_in, 0, "k");
2040 map = map_power(map, exact, 0);
2042 map = isl_map_add_dims(map, isl_dim_param, 1);
2043 dim = isl_map_get_space(map);
2044 diff = equate_parameter_to_length(dim, param);
2045 map = isl_map_intersect(map, diff);
2046 map = isl_map_project_out(map, isl_dim_in, d, 1);
2047 map = isl_map_project_out(map, isl_dim_out, d, 1);
2048 map = isl_map_from_range(isl_map_wrap(map));
2049 map = isl_map_move_dims(map, isl_dim_in, 0, isl_dim_param, param, 1);
2051 map = isl_map_reset_space(map, target_dim);
2053 return map;
2056 /* Compute a relation that maps each element in the range of the input
2057 * relation to the lengths of all paths composed of edges in the input
2058 * relation that end up in the given range element.
2059 * The result may be an overapproximation, in which case *exact is set to 0.
2060 * The resulting relation is very similar to the power relation.
2061 * The difference are that the domain has been projected out, the
2062 * range has become the domain and the exponent is the range instead
2063 * of a parameter.
2065 __isl_give isl_map *isl_map_reaching_path_lengths(__isl_take isl_map *map,
2066 int *exact)
2068 isl_space *dim;
2069 isl_map *diff;
2070 unsigned d;
2071 unsigned param;
2073 if (!map)
2074 return NULL;
2076 d = isl_map_dim(map, isl_dim_in);
2077 param = isl_map_dim(map, isl_dim_param);
2079 map = isl_map_compute_divs(map);
2080 map = isl_map_coalesce(map);
2082 if (isl_map_plain_is_empty(map)) {
2083 if (exact)
2084 *exact = 1;
2085 map = isl_map_project_out(map, isl_dim_out, 0, d);
2086 map = isl_map_add_dims(map, isl_dim_out, 1);
2087 return map;
2090 map = map_power(map, exact, 0);
2092 map = isl_map_add_dims(map, isl_dim_param, 1);
2093 dim = isl_map_get_space(map);
2094 diff = equate_parameter_to_length(dim, param);
2095 map = isl_map_intersect(map, diff);
2096 map = isl_map_project_out(map, isl_dim_in, 0, d + 1);
2097 map = isl_map_project_out(map, isl_dim_out, d, 1);
2098 map = isl_map_reverse(map);
2099 map = isl_map_move_dims(map, isl_dim_out, 0, isl_dim_param, param, 1);
2101 return map;
2104 /* Check whether equality i of bset is a pure stride constraint
2105 * on a single dimensions, i.e., of the form
2107 * v = k e
2109 * with k a constant and e an existentially quantified variable.
2111 static int is_eq_stride(__isl_keep isl_basic_set *bset, int i)
2113 unsigned nparam;
2114 unsigned d;
2115 unsigned n_div;
2116 int pos1;
2117 int pos2;
2119 if (!bset)
2120 return -1;
2122 if (!isl_int_is_zero(bset->eq[i][0]))
2123 return 0;
2125 nparam = isl_basic_set_dim(bset, isl_dim_param);
2126 d = isl_basic_set_dim(bset, isl_dim_set);
2127 n_div = isl_basic_set_dim(bset, isl_dim_div);
2129 if (isl_seq_first_non_zero(bset->eq[i] + 1, nparam) != -1)
2130 return 0;
2131 pos1 = isl_seq_first_non_zero(bset->eq[i] + 1 + nparam, d);
2132 if (pos1 == -1)
2133 return 0;
2134 if (isl_seq_first_non_zero(bset->eq[i] + 1 + nparam + pos1 + 1,
2135 d - pos1 - 1) != -1)
2136 return 0;
2138 pos2 = isl_seq_first_non_zero(bset->eq[i] + 1 + nparam + d, n_div);
2139 if (pos2 == -1)
2140 return 0;
2141 if (isl_seq_first_non_zero(bset->eq[i] + 1 + nparam + d + pos2 + 1,
2142 n_div - pos2 - 1) != -1)
2143 return 0;
2144 if (!isl_int_is_one(bset->eq[i][1 + nparam + pos1]) &&
2145 !isl_int_is_negone(bset->eq[i][1 + nparam + pos1]))
2146 return 0;
2148 return 1;
2151 /* Given a map, compute the smallest superset of this map that is of the form
2153 * { i -> j : L <= j - i <= U and exists a_p: j_p - i_p = M_p a_p }
2155 * (where p ranges over the (non-parametric) dimensions),
2156 * compute the transitive closure of this map, i.e.,
2158 * { i -> j : exists k > 0:
2159 * k L <= j - i <= k U and exists a: j_p - i_p = M_p a_p }
2161 * and intersect domain and range of this transitive closure with
2162 * the given domain and range.
2164 * If with_id is set, then try to include as much of the identity mapping
2165 * as possible, by computing
2167 * { i -> j : exists k >= 0:
2168 * k L <= j - i <= k U and exists a: j_p - i_p = M_p a_p }
2170 * instead (i.e., allow k = 0).
2172 * In practice, we compute the difference set
2174 * delta = { j - i | i -> j in map },
2176 * look for stride constraint on the individual dimensions and compute
2177 * (constant) lower and upper bounds for each individual dimension,
2178 * adding a constraint for each bound not equal to infinity.
2180 static __isl_give isl_map *box_closure_on_domain(__isl_take isl_map *map,
2181 __isl_take isl_set *dom, __isl_take isl_set *ran, int with_id)
2183 int i;
2184 int k;
2185 unsigned d;
2186 unsigned nparam;
2187 unsigned total;
2188 isl_space *dim;
2189 isl_set *delta;
2190 isl_map *app = NULL;
2191 isl_basic_set *aff = NULL;
2192 isl_basic_map *bmap = NULL;
2193 isl_vec *obj = NULL;
2194 isl_int opt;
2196 isl_int_init(opt);
2198 delta = isl_map_deltas(isl_map_copy(map));
2200 aff = isl_set_affine_hull(isl_set_copy(delta));
2201 if (!aff)
2202 goto error;
2203 dim = isl_map_get_space(map);
2204 d = isl_space_dim(dim, isl_dim_in);
2205 nparam = isl_space_dim(dim, isl_dim_param);
2206 total = isl_space_dim(dim, isl_dim_all);
2207 bmap = isl_basic_map_alloc_space(dim,
2208 aff->n_div + 1, aff->n_div, 2 * d + 1);
2209 for (i = 0; i < aff->n_div + 1; ++i) {
2210 k = isl_basic_map_alloc_div(bmap);
2211 if (k < 0)
2212 goto error;
2213 isl_int_set_si(bmap->div[k][0], 0);
2215 for (i = 0; i < aff->n_eq; ++i) {
2216 if (!is_eq_stride(aff, i))
2217 continue;
2218 k = isl_basic_map_alloc_equality(bmap);
2219 if (k < 0)
2220 goto error;
2221 isl_seq_clr(bmap->eq[k], 1 + nparam);
2222 isl_seq_cpy(bmap->eq[k] + 1 + nparam + d,
2223 aff->eq[i] + 1 + nparam, d);
2224 isl_seq_neg(bmap->eq[k] + 1 + nparam,
2225 aff->eq[i] + 1 + nparam, d);
2226 isl_seq_cpy(bmap->eq[k] + 1 + nparam + 2 * d,
2227 aff->eq[i] + 1 + nparam + d, aff->n_div);
2228 isl_int_set_si(bmap->eq[k][1 + total + aff->n_div], 0);
2230 obj = isl_vec_alloc(map->ctx, 1 + nparam + d);
2231 if (!obj)
2232 goto error;
2233 isl_seq_clr(obj->el, 1 + nparam + d);
2234 for (i = 0; i < d; ++ i) {
2235 enum isl_lp_result res;
2237 isl_int_set_si(obj->el[1 + nparam + i], 1);
2239 res = isl_set_solve_lp(delta, 0, obj->el, map->ctx->one, &opt,
2240 NULL, NULL);
2241 if (res == isl_lp_error)
2242 goto error;
2243 if (res == isl_lp_ok) {
2244 k = isl_basic_map_alloc_inequality(bmap);
2245 if (k < 0)
2246 goto error;
2247 isl_seq_clr(bmap->ineq[k],
2248 1 + nparam + 2 * d + bmap->n_div);
2249 isl_int_set_si(bmap->ineq[k][1 + nparam + i], -1);
2250 isl_int_set_si(bmap->ineq[k][1 + nparam + d + i], 1);
2251 isl_int_neg(bmap->ineq[k][1 + nparam + 2 * d + aff->n_div], opt);
2254 res = isl_set_solve_lp(delta, 1, obj->el, map->ctx->one, &opt,
2255 NULL, NULL);
2256 if (res == isl_lp_error)
2257 goto error;
2258 if (res == isl_lp_ok) {
2259 k = isl_basic_map_alloc_inequality(bmap);
2260 if (k < 0)
2261 goto error;
2262 isl_seq_clr(bmap->ineq[k],
2263 1 + nparam + 2 * d + bmap->n_div);
2264 isl_int_set_si(bmap->ineq[k][1 + nparam + i], 1);
2265 isl_int_set_si(bmap->ineq[k][1 + nparam + d + i], -1);
2266 isl_int_set(bmap->ineq[k][1 + nparam + 2 * d + aff->n_div], opt);
2269 isl_int_set_si(obj->el[1 + nparam + i], 0);
2271 k = isl_basic_map_alloc_inequality(bmap);
2272 if (k < 0)
2273 goto error;
2274 isl_seq_clr(bmap->ineq[k],
2275 1 + nparam + 2 * d + bmap->n_div);
2276 if (!with_id)
2277 isl_int_set_si(bmap->ineq[k][0], -1);
2278 isl_int_set_si(bmap->ineq[k][1 + nparam + 2 * d + aff->n_div], 1);
2280 app = isl_map_from_domain_and_range(dom, ran);
2282 isl_vec_free(obj);
2283 isl_basic_set_free(aff);
2284 isl_map_free(map);
2285 bmap = isl_basic_map_finalize(bmap);
2286 isl_set_free(delta);
2287 isl_int_clear(opt);
2289 map = isl_map_from_basic_map(bmap);
2290 map = isl_map_intersect(map, app);
2292 return map;
2293 error:
2294 isl_vec_free(obj);
2295 isl_basic_map_free(bmap);
2296 isl_basic_set_free(aff);
2297 isl_set_free(dom);
2298 isl_set_free(ran);
2299 isl_map_free(map);
2300 isl_set_free(delta);
2301 isl_int_clear(opt);
2302 return NULL;
2305 /* Given a map, compute the smallest superset of this map that is of the form
2307 * { i -> j : L <= j - i <= U and exists a_p: j_p - i_p = M_p a_p }
2309 * (where p ranges over the (non-parametric) dimensions),
2310 * compute the transitive closure of this map, i.e.,
2312 * { i -> j : exists k > 0:
2313 * k L <= j - i <= k U and exists a: j_p - i_p = M_p a_p }
2315 * and intersect domain and range of this transitive closure with
2316 * domain and range of the original map.
2318 static __isl_give isl_map *box_closure(__isl_take isl_map *map)
2320 isl_set *domain;
2321 isl_set *range;
2323 domain = isl_map_domain(isl_map_copy(map));
2324 domain = isl_set_coalesce(domain);
2325 range = isl_map_range(isl_map_copy(map));
2326 range = isl_set_coalesce(range);
2328 return box_closure_on_domain(map, domain, range, 0);
2331 /* Given a map, compute the smallest superset of this map that is of the form
2333 * { i -> j : L <= j - i <= U and exists a_p: j_p - i_p = M_p a_p }
2335 * (where p ranges over the (non-parametric) dimensions),
2336 * compute the transitive and partially reflexive closure of this map, i.e.,
2338 * { i -> j : exists k >= 0:
2339 * k L <= j - i <= k U and exists a: j_p - i_p = M_p a_p }
2341 * and intersect domain and range of this transitive closure with
2342 * the given domain.
2344 static __isl_give isl_map *box_closure_with_identity(__isl_take isl_map *map,
2345 __isl_take isl_set *dom)
2347 return box_closure_on_domain(map, dom, isl_set_copy(dom), 1);
2350 /* Check whether app is the transitive closure of map.
2351 * In particular, check that app is acyclic and, if so,
2352 * check that
2354 * app \subset (map \cup (map \circ app))
2356 static int check_exactness_omega(__isl_keep isl_map *map,
2357 __isl_keep isl_map *app)
2359 isl_set *delta;
2360 int i;
2361 int is_empty, is_exact;
2362 unsigned d;
2363 isl_map *test;
2365 delta = isl_map_deltas(isl_map_copy(app));
2366 d = isl_set_dim(delta, isl_dim_set);
2367 for (i = 0; i < d; ++i)
2368 delta = isl_set_fix_si(delta, isl_dim_set, i, 0);
2369 is_empty = isl_set_is_empty(delta);
2370 isl_set_free(delta);
2371 if (is_empty < 0)
2372 return -1;
2373 if (!is_empty)
2374 return 0;
2376 test = isl_map_apply_range(isl_map_copy(app), isl_map_copy(map));
2377 test = isl_map_union(test, isl_map_copy(map));
2378 is_exact = isl_map_is_subset(app, test);
2379 isl_map_free(test);
2381 return is_exact;
2384 /* Check if basic map M_i can be combined with all the other
2385 * basic maps such that
2387 * (\cup_j M_j)^+
2389 * can be computed as
2391 * M_i \cup (\cup_{j \ne i} M_i^* \circ M_j \circ M_i^*)^+
2393 * In particular, check if we can compute a compact representation
2394 * of
2396 * M_i^* \circ M_j \circ M_i^*
2398 * for each j != i.
2399 * Let M_i^? be an extension of M_i^+ that allows paths
2400 * of length zero, i.e., the result of box_closure(., 1).
2401 * The criterion, as proposed by Kelly et al., is that
2402 * id = M_i^? - M_i^+ can be represented as a basic map
2403 * and that
2405 * id \circ M_j \circ id = M_j
2407 * for each j != i.
2409 * If this function returns 1, then tc and qc are set to
2410 * M_i^+ and M_i^?, respectively.
2412 static int can_be_split_off(__isl_keep isl_map *map, int i,
2413 __isl_give isl_map **tc, __isl_give isl_map **qc)
2415 isl_map *map_i, *id = NULL;
2416 int j = -1;
2417 isl_set *C;
2419 *tc = NULL;
2420 *qc = NULL;
2422 C = isl_set_union(isl_map_domain(isl_map_copy(map)),
2423 isl_map_range(isl_map_copy(map)));
2424 C = isl_set_from_basic_set(isl_set_simple_hull(C));
2425 if (!C)
2426 goto error;
2428 map_i = isl_map_from_basic_map(isl_basic_map_copy(map->p[i]));
2429 *tc = box_closure(isl_map_copy(map_i));
2430 *qc = box_closure_with_identity(map_i, C);
2431 id = isl_map_subtract(isl_map_copy(*qc), isl_map_copy(*tc));
2433 if (!id || !*qc)
2434 goto error;
2435 if (id->n != 1 || (*qc)->n != 1)
2436 goto done;
2438 for (j = 0; j < map->n; ++j) {
2439 isl_map *map_j, *test;
2440 int is_ok;
2442 if (i == j)
2443 continue;
2444 map_j = isl_map_from_basic_map(
2445 isl_basic_map_copy(map->p[j]));
2446 test = isl_map_apply_range(isl_map_copy(id),
2447 isl_map_copy(map_j));
2448 test = isl_map_apply_range(test, isl_map_copy(id));
2449 is_ok = isl_map_is_equal(test, map_j);
2450 isl_map_free(map_j);
2451 isl_map_free(test);
2452 if (is_ok < 0)
2453 goto error;
2454 if (!is_ok)
2455 break;
2458 done:
2459 isl_map_free(id);
2460 if (j == map->n)
2461 return 1;
2463 isl_map_free(*qc);
2464 isl_map_free(*tc);
2465 *qc = NULL;
2466 *tc = NULL;
2468 return 0;
2469 error:
2470 isl_map_free(id);
2471 isl_map_free(*qc);
2472 isl_map_free(*tc);
2473 *qc = NULL;
2474 *tc = NULL;
2475 return -1;
2478 static __isl_give isl_map *box_closure_with_check(__isl_take isl_map *map,
2479 int *exact)
2481 isl_map *app;
2483 app = box_closure(isl_map_copy(map));
2484 if (exact)
2485 *exact = check_exactness_omega(map, app);
2487 isl_map_free(map);
2488 return app;
2491 /* Compute an overapproximation of the transitive closure of "map"
2492 * using a variation of the algorithm from
2493 * "Transitive Closure of Infinite Graphs and its Applications"
2494 * by Kelly et al.
2496 * We first check whether we can can split of any basic map M_i and
2497 * compute
2499 * (\cup_j M_j)^+
2501 * as
2503 * M_i \cup (\cup_{j \ne i} M_i^* \circ M_j \circ M_i^*)^+
2505 * using a recursive call on the remaining map.
2507 * If not, we simply call box_closure on the whole map.
2509 static __isl_give isl_map *transitive_closure_omega(__isl_take isl_map *map,
2510 int *exact)
2512 int i, j;
2513 int exact_i;
2514 isl_map *app;
2516 if (!map)
2517 return NULL;
2518 if (map->n == 1)
2519 return box_closure_with_check(map, exact);
2521 for (i = 0; i < map->n; ++i) {
2522 int ok;
2523 isl_map *qc, *tc;
2524 ok = can_be_split_off(map, i, &tc, &qc);
2525 if (ok < 0)
2526 goto error;
2527 if (!ok)
2528 continue;
2530 app = isl_map_alloc_space(isl_map_get_space(map), map->n - 1, 0);
2532 for (j = 0; j < map->n; ++j) {
2533 if (j == i)
2534 continue;
2535 app = isl_map_add_basic_map(app,
2536 isl_basic_map_copy(map->p[j]));
2539 app = isl_map_apply_range(isl_map_copy(qc), app);
2540 app = isl_map_apply_range(app, qc);
2542 app = isl_map_union(tc, transitive_closure_omega(app, NULL));
2543 exact_i = check_exactness_omega(map, app);
2544 if (exact_i == 1) {
2545 if (exact)
2546 *exact = exact_i;
2547 isl_map_free(map);
2548 return app;
2550 isl_map_free(app);
2551 if (exact_i < 0)
2552 goto error;
2555 return box_closure_with_check(map, exact);
2556 error:
2557 isl_map_free(map);
2558 return NULL;
2561 /* Compute the transitive closure of "map", or an overapproximation.
2562 * If the result is exact, then *exact is set to 1.
2563 * Simply use map_power to compute the powers of map, but tell
2564 * it to project out the lengths of the paths instead of equating
2565 * the length to a parameter.
2567 __isl_give isl_map *isl_map_transitive_closure(__isl_take isl_map *map,
2568 int *exact)
2570 isl_space *target_dim;
2571 int closed;
2573 if (!map)
2574 goto error;
2576 if (map->ctx->opt->closure == ISL_CLOSURE_BOX)
2577 return transitive_closure_omega(map, exact);
2579 map = isl_map_compute_divs(map);
2580 map = isl_map_coalesce(map);
2581 closed = isl_map_is_transitively_closed(map);
2582 if (closed < 0)
2583 goto error;
2584 if (closed) {
2585 if (exact)
2586 *exact = 1;
2587 return map;
2590 target_dim = isl_map_get_space(map);
2591 map = map_power(map, exact, 1);
2592 map = isl_map_reset_space(map, target_dim);
2594 return map;
2595 error:
2596 isl_map_free(map);
2597 return NULL;
2600 static int inc_count(__isl_take isl_map *map, void *user)
2602 int *n = user;
2604 *n += map->n;
2606 isl_map_free(map);
2608 return 0;
2611 static int collect_basic_map(__isl_take isl_map *map, void *user)
2613 int i;
2614 isl_basic_map ***next = user;
2616 for (i = 0; i < map->n; ++i) {
2617 **next = isl_basic_map_copy(map->p[i]);
2618 if (!**next)
2619 goto error;
2620 (*next)++;
2623 isl_map_free(map);
2624 return 0;
2625 error:
2626 isl_map_free(map);
2627 return -1;
2630 /* Perform Floyd-Warshall on the given list of basic relations.
2631 * The basic relations may live in different dimensions,
2632 * but basic relations that get assigned to the diagonal of the
2633 * grid have domains and ranges of the same dimension and so
2634 * the standard algorithm can be used because the nested transitive
2635 * closures are only applied to diagonal elements and because all
2636 * compositions are peformed on relations with compatible domains and ranges.
2638 static __isl_give isl_union_map *union_floyd_warshall_on_list(isl_ctx *ctx,
2639 __isl_keep isl_basic_map **list, int n, int *exact)
2641 int i, j, k;
2642 int n_group;
2643 int *group = NULL;
2644 isl_set **set = NULL;
2645 isl_map ***grid = NULL;
2646 isl_union_map *app;
2648 group = setup_groups(ctx, list, n, &set, &n_group);
2649 if (!group)
2650 goto error;
2652 grid = isl_calloc_array(ctx, isl_map **, n_group);
2653 if (!grid)
2654 goto error;
2655 for (i = 0; i < n_group; ++i) {
2656 grid[i] = isl_calloc_array(ctx, isl_map *, n_group);
2657 if (!grid[i])
2658 goto error;
2659 for (j = 0; j < n_group; ++j) {
2660 isl_space *dim1, *dim2, *dim;
2661 dim1 = isl_space_reverse(isl_set_get_space(set[i]));
2662 dim2 = isl_set_get_space(set[j]);
2663 dim = isl_space_join(dim1, dim2);
2664 grid[i][j] = isl_map_empty(dim);
2668 for (k = 0; k < n; ++k) {
2669 i = group[2 * k];
2670 j = group[2 * k + 1];
2671 grid[i][j] = isl_map_union(grid[i][j],
2672 isl_map_from_basic_map(
2673 isl_basic_map_copy(list[k])));
2676 floyd_warshall_iterate(grid, n_group, exact);
2678 app = isl_union_map_empty(isl_map_get_space(grid[0][0]));
2680 for (i = 0; i < n_group; ++i) {
2681 for (j = 0; j < n_group; ++j)
2682 app = isl_union_map_add_map(app, grid[i][j]);
2683 free(grid[i]);
2685 free(grid);
2687 for (i = 0; i < 2 * n; ++i)
2688 isl_set_free(set[i]);
2689 free(set);
2691 free(group);
2692 return app;
2693 error:
2694 if (grid)
2695 for (i = 0; i < n_group; ++i) {
2696 if (!grid[i])
2697 continue;
2698 for (j = 0; j < n_group; ++j)
2699 isl_map_free(grid[i][j]);
2700 free(grid[i]);
2702 free(grid);
2703 if (set) {
2704 for (i = 0; i < 2 * n; ++i)
2705 isl_set_free(set[i]);
2706 free(set);
2708 free(group);
2709 return NULL;
2712 /* Perform Floyd-Warshall on the given union relation.
2713 * The implementation is very similar to that for non-unions.
2714 * The main difference is that it is applied unconditionally.
2715 * We first extract a list of basic maps from the union map
2716 * and then perform the algorithm on this list.
2718 static __isl_give isl_union_map *union_floyd_warshall(
2719 __isl_take isl_union_map *umap, int *exact)
2721 int i, n;
2722 isl_ctx *ctx;
2723 isl_basic_map **list = NULL;
2724 isl_basic_map **next;
2725 isl_union_map *res;
2727 n = 0;
2728 if (isl_union_map_foreach_map(umap, inc_count, &n) < 0)
2729 goto error;
2731 ctx = isl_union_map_get_ctx(umap);
2732 list = isl_calloc_array(ctx, isl_basic_map *, n);
2733 if (!list)
2734 goto error;
2736 next = list;
2737 if (isl_union_map_foreach_map(umap, collect_basic_map, &next) < 0)
2738 goto error;
2740 res = union_floyd_warshall_on_list(ctx, list, n, exact);
2742 if (list) {
2743 for (i = 0; i < n; ++i)
2744 isl_basic_map_free(list[i]);
2745 free(list);
2748 isl_union_map_free(umap);
2749 return res;
2750 error:
2751 if (list) {
2752 for (i = 0; i < n; ++i)
2753 isl_basic_map_free(list[i]);
2754 free(list);
2756 isl_union_map_free(umap);
2757 return NULL;
2760 /* Decompose the give union relation into strongly connected components.
2761 * The implementation is essentially the same as that of
2762 * construct_power_components with the major difference that all
2763 * operations are performed on union maps.
2765 static __isl_give isl_union_map *union_components(
2766 __isl_take isl_union_map *umap, int *exact)
2768 int i;
2769 int n;
2770 isl_ctx *ctx;
2771 isl_basic_map **list = NULL;
2772 isl_basic_map **next;
2773 isl_union_map *path = NULL;
2774 struct isl_tc_follows_data data;
2775 struct isl_tarjan_graph *g = NULL;
2776 int c, l;
2777 int recheck = 0;
2779 n = 0;
2780 if (isl_union_map_foreach_map(umap, inc_count, &n) < 0)
2781 goto error;
2783 if (n <= 1)
2784 return union_floyd_warshall(umap, exact);
2786 ctx = isl_union_map_get_ctx(umap);
2787 list = isl_calloc_array(ctx, isl_basic_map *, n);
2788 if (!list)
2789 goto error;
2791 next = list;
2792 if (isl_union_map_foreach_map(umap, collect_basic_map, &next) < 0)
2793 goto error;
2795 data.list = list;
2796 data.check_closed = 0;
2797 g = isl_tarjan_graph_init(ctx, n, &basic_map_follows, &data);
2798 if (!g)
2799 goto error;
2801 c = 0;
2802 i = 0;
2803 l = n;
2804 path = isl_union_map_empty(isl_union_map_get_space(umap));
2805 while (l) {
2806 isl_union_map *comp;
2807 isl_union_map *path_comp, *path_comb;
2808 comp = isl_union_map_empty(isl_union_map_get_space(umap));
2809 while (g->order[i] != -1) {
2810 comp = isl_union_map_add_map(comp,
2811 isl_map_from_basic_map(
2812 isl_basic_map_copy(list[g->order[i]])));
2813 --l;
2814 ++i;
2816 path_comp = union_floyd_warshall(comp, exact);
2817 path_comb = isl_union_map_apply_range(isl_union_map_copy(path),
2818 isl_union_map_copy(path_comp));
2819 path = isl_union_map_union(path, path_comp);
2820 path = isl_union_map_union(path, path_comb);
2821 ++i;
2822 ++c;
2825 if (c > 1 && data.check_closed && !*exact) {
2826 int closed;
2828 closed = isl_union_map_is_transitively_closed(path);
2829 if (closed < 0)
2830 goto error;
2831 recheck = !closed;
2834 isl_tarjan_graph_free(g);
2836 for (i = 0; i < n; ++i)
2837 isl_basic_map_free(list[i]);
2838 free(list);
2840 if (recheck) {
2841 isl_union_map_free(path);
2842 return union_floyd_warshall(umap, exact);
2845 isl_union_map_free(umap);
2847 return path;
2848 error:
2849 isl_tarjan_graph_free(g);
2850 if (list) {
2851 for (i = 0; i < n; ++i)
2852 isl_basic_map_free(list[i]);
2853 free(list);
2855 isl_union_map_free(umap);
2856 isl_union_map_free(path);
2857 return NULL;
2860 /* Compute the transitive closure of "umap", or an overapproximation.
2861 * If the result is exact, then *exact is set to 1.
2863 __isl_give isl_union_map *isl_union_map_transitive_closure(
2864 __isl_take isl_union_map *umap, int *exact)
2866 int closed;
2868 if (!umap)
2869 return NULL;
2871 if (exact)
2872 *exact = 1;
2874 umap = isl_union_map_compute_divs(umap);
2875 umap = isl_union_map_coalesce(umap);
2876 closed = isl_union_map_is_transitively_closed(umap);
2877 if (closed < 0)
2878 goto error;
2879 if (closed)
2880 return umap;
2881 umap = union_components(umap, exact);
2882 return umap;
2883 error:
2884 isl_union_map_free(umap);
2885 return NULL;
2888 struct isl_union_power {
2889 isl_union_map *pow;
2890 int *exact;
2893 static int power(__isl_take isl_map *map, void *user)
2895 struct isl_union_power *up = user;
2897 map = isl_map_power(map, up->exact);
2898 up->pow = isl_union_map_from_map(map);
2900 return -1;
2903 /* Construct a map [x] -> [x+1], with parameters prescribed by "dim".
2905 static __isl_give isl_union_map *increment(__isl_take isl_space *dim)
2907 int k;
2908 isl_basic_map *bmap;
2910 dim = isl_space_add_dims(dim, isl_dim_in, 1);
2911 dim = isl_space_add_dims(dim, isl_dim_out, 1);
2912 bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
2913 k = isl_basic_map_alloc_equality(bmap);
2914 if (k < 0)
2915 goto error;
2916 isl_seq_clr(bmap->eq[k], isl_basic_map_total_dim(bmap));
2917 isl_int_set_si(bmap->eq[k][0], 1);
2918 isl_int_set_si(bmap->eq[k][isl_basic_map_offset(bmap, isl_dim_in)], 1);
2919 isl_int_set_si(bmap->eq[k][isl_basic_map_offset(bmap, isl_dim_out)], -1);
2920 return isl_union_map_from_map(isl_map_from_basic_map(bmap));
2921 error:
2922 isl_basic_map_free(bmap);
2923 return NULL;
2926 /* Construct a map [[x]->[y]] -> [y-x], with parameters prescribed by "dim".
2928 static __isl_give isl_union_map *deltas_map(__isl_take isl_space *dim)
2930 isl_basic_map *bmap;
2932 dim = isl_space_add_dims(dim, isl_dim_in, 1);
2933 dim = isl_space_add_dims(dim, isl_dim_out, 1);
2934 bmap = isl_basic_map_universe(dim);
2935 bmap = isl_basic_map_deltas_map(bmap);
2937 return isl_union_map_from_map(isl_map_from_basic_map(bmap));
2940 /* Compute the positive powers of "map", or an overapproximation.
2941 * The result maps the exponent to a nested copy of the corresponding power.
2942 * If the result is exact, then *exact is set to 1.
2944 __isl_give isl_union_map *isl_union_map_power(__isl_take isl_union_map *umap,
2945 int *exact)
2947 int n;
2948 isl_union_map *inc;
2949 isl_union_map *dm;
2951 if (!umap)
2952 return NULL;
2953 n = isl_union_map_n_map(umap);
2954 if (n == 0)
2955 return umap;
2956 if (n == 1) {
2957 struct isl_union_power up = { NULL, exact };
2958 isl_union_map_foreach_map(umap, &power, &up);
2959 isl_union_map_free(umap);
2960 return up.pow;
2962 inc = increment(isl_union_map_get_space(umap));
2963 umap = isl_union_map_product(inc, umap);
2964 umap = isl_union_map_transitive_closure(umap, exact);
2965 umap = isl_union_map_zip(umap);
2966 dm = deltas_map(isl_union_map_get_space(umap));
2967 umap = isl_union_map_apply_domain(umap, dm);
2969 return umap;
2972 #undef TYPE
2973 #define TYPE isl_map
2974 #include "isl_power_templ.c"
2976 #undef TYPE
2977 #define TYPE isl_union_map
2978 #include "isl_power_templ.c"