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isl_basic_map_simplify: normalize div expressions
[isl.git] / isl_map_simplify.c
blobfa80971a6905d7ea5a08137bce9dc87fda2e580b
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012 Ecole Normale Superieure
4 *
5 * Use of this software is governed by the GNU LGPLv2.1 license
6 *
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
10 */
11
12 #include <strings.h>
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include "isl_equalities.h"
16 #include <isl/map.h>
17 #include <isl/seq.h>
18 #include "isl_tab.h"
19 #include <isl_space_private.h>
20 #include <isl_mat_private.h>
21
22 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
23 {
24 isl_int *t = bmap->eq[a];
25 bmap->eq[a] = bmap->eq[b];
26 bmap->eq[b] = t;
27 }
28
29 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
30 {
31 if (a != b) {
32 isl_int *t = bmap->ineq[a];
33 bmap->ineq[a] = bmap->ineq[b];
34 bmap->ineq[b] = t;
35 }
36 }
37
38 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
39 {
40 isl_seq_cpy(c, c + n, rem);
41 isl_seq_clr(c + rem, n);
42 }
43
44 /* Drop n dimensions starting at first.
45 *
46 * In principle, this frees up some extra variables as the number
47 * of columns remains constant, but we would have to extend
48 * the div array too as the number of rows in this array is assumed
49 * to be equal to extra.
50 */
51 struct isl_basic_set *isl_basic_set_drop_dims(
52 struct isl_basic_set *bset, unsigned first, unsigned n)
53 {
54 int i;
55
56 if (!bset)
57 goto error;
58
59 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
60
61 if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
62 return bset;
63
64 bset = isl_basic_set_cow(bset);
65 if (!bset)
66 return NULL;
67
68 for (i = 0; i < bset->n_eq; ++i)
69 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
70 (bset->dim->n_out-first-n)+bset->extra);
71
72 for (i = 0; i < bset->n_ineq; ++i)
73 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
74 (bset->dim->n_out-first-n)+bset->extra);
75
76 for (i = 0; i < bset->n_div; ++i)
77 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
78 (bset->dim->n_out-first-n)+bset->extra);
79
80 bset->dim = isl_space_drop_outputs(bset->dim, first, n);
81 if (!bset->dim)
82 goto error;
83
84 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
85 bset = isl_basic_set_simplify(bset);
86 return isl_basic_set_finalize(bset);
87 error:
88 isl_basic_set_free(bset);
89 return NULL;
90 }
91
92 struct isl_set *isl_set_drop_dims(
93 struct isl_set *set, unsigned first, unsigned n)
94 {
95 int i;
96
97 if (!set)
98 goto error;
99
100 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
101
102 if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
103 return set;
104 set = isl_set_cow(set);
105 if (!set)
106 goto error;
107 set->dim = isl_space_drop_outputs(set->dim, first, n);
108 if (!set->dim)
109 goto error;
110
111 for (i = 0; i < set->n; ++i) {
112 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
113 if (!set->p[i])
114 goto error;
115 }
116
117 ISL_F_CLR(set, ISL_SET_NORMALIZED);
118 return set;
119 error:
120 isl_set_free(set);
121 return NULL;
122 }
123
124 /* Move "n" divs starting at "first" to the end of the list of divs.
125 */
126 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
127 unsigned first, unsigned n)
128 {
129 isl_int **div;
130 int i;
131
132 if (first + n == bmap->n_div)
133 return bmap;
134
135 div = isl_alloc_array(bmap->ctx, isl_int *, n);
136 if (!div)
137 goto error;
138 for (i = 0; i < n; ++i)
139 div[i] = bmap->div[first + i];
140 for (i = 0; i < bmap->n_div - first - n; ++i)
141 bmap->div[first + i] = bmap->div[first + n + i];
142 for (i = 0; i < n; ++i)
143 bmap->div[bmap->n_div - n + i] = div[i];
144 free(div);
145 return bmap;
146 error:
147 isl_basic_map_free(bmap);
148 return NULL;
149 }
150
151 /* Drop "n" dimensions of type "type" starting at "first".
152 *
153 * In principle, this frees up some extra variables as the number
154 * of columns remains constant, but we would have to extend
155 * the div array too as the number of rows in this array is assumed
156 * to be equal to extra.
157 */
158 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
159 enum isl_dim_type type, unsigned first, unsigned n)
160 {
161 int i;
162 unsigned dim;
163 unsigned offset;
164 unsigned left;
165
166 if (!bmap)
167 goto error;
168
169 dim = isl_basic_map_dim(bmap, type);
170 isl_assert(bmap->ctx, first + n <= dim, goto error);
171
172 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
173 return bmap;
174
175 bmap = isl_basic_map_cow(bmap);
176 if (!bmap)
177 return NULL;
178
179 offset = isl_basic_map_offset(bmap, type) + first;
180 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
181 for (i = 0; i < bmap->n_eq; ++i)
182 constraint_drop_vars(bmap->eq[i]+offset, n, left);
183
184 for (i = 0; i < bmap->n_ineq; ++i)
185 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
186
187 for (i = 0; i < bmap->n_div; ++i)
188 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
189
190 if (type == isl_dim_div) {
191 bmap = move_divs_last(bmap, first, n);
192 if (!bmap)
193 goto error;
194 isl_basic_map_free_div(bmap, n);
195 } else
196 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
197 if (!bmap->dim)
198 goto error;
199
200 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
201 bmap = isl_basic_map_simplify(bmap);
202 return isl_basic_map_finalize(bmap);
203 error:
204 isl_basic_map_free(bmap);
205 return NULL;
206 }
207
208 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
209 enum isl_dim_type type, unsigned first, unsigned n)
210 {
211 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
212 type, first, n);
213 }
214
215 struct isl_basic_map *isl_basic_map_drop_inputs(
216 struct isl_basic_map *bmap, unsigned first, unsigned n)
217 {
218 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
219 }
220
221 struct isl_map *isl_map_drop(struct isl_map *map,
222 enum isl_dim_type type, unsigned first, unsigned n)
223 {
224 int i;
225
226 if (!map)
227 goto error;
228
229 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
230
231 if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
232 return map;
233 map = isl_map_cow(map);
234 if (!map)
235 goto error;
236 map->dim = isl_space_drop_dims(map->dim, type, first, n);
237 if (!map->dim)
238 goto error;
239
240 for (i = 0; i < map->n; ++i) {
241 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
242 if (!map->p[i])
243 goto error;
244 }
245 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
246
247 return map;
248 error:
249 isl_map_free(map);
250 return NULL;
251 }
252
253 struct isl_set *isl_set_drop(struct isl_set *set,
254 enum isl_dim_type type, unsigned first, unsigned n)
255 {
256 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
257 }
258
259 struct isl_map *isl_map_drop_inputs(
260 struct isl_map *map, unsigned first, unsigned n)
261 {
262 return isl_map_drop(map, isl_dim_in, first, n);
263 }
264
265 /*
266 * We don't cow, as the div is assumed to be redundant.
267 */
268 static struct isl_basic_map *isl_basic_map_drop_div(
269 struct isl_basic_map *bmap, unsigned div)
270 {
271 int i;
272 unsigned pos;
273
274 if (!bmap)
275 goto error;
276
277 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
278
279 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
280
281 for (i = 0; i < bmap->n_eq; ++i)
282 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
283
284 for (i = 0; i < bmap->n_ineq; ++i) {
285 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
286 isl_basic_map_drop_inequality(bmap, i);
287 --i;
288 continue;
289 }
290 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
291 }
292
293 for (i = 0; i < bmap->n_div; ++i)
294 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
295
296 if (div != bmap->n_div - 1) {
297 int j;
298 isl_int *t = bmap->div[div];
299
300 for (j = div; j < bmap->n_div - 1; ++j)
301 bmap->div[j] = bmap->div[j+1];
302
303 bmap->div[bmap->n_div - 1] = t;
304 }
305 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
306 isl_basic_map_free_div(bmap, 1);
307
308 return bmap;
309 error:
310 isl_basic_map_free(bmap);
311 return NULL;
312 }
313
314 struct isl_basic_map *isl_basic_map_normalize_constraints(
315 struct isl_basic_map *bmap)
316 {
317 int i;
318 isl_int gcd;
319 unsigned total = isl_basic_map_total_dim(bmap);
320
321 if (!bmap)
322 return NULL;
323
324 isl_int_init(gcd);
325 for (i = bmap->n_eq - 1; i >= 0; --i) {
326 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
327 if (isl_int_is_zero(gcd)) {
328 if (!isl_int_is_zero(bmap->eq[i][0])) {
329 bmap = isl_basic_map_set_to_empty(bmap);
330 break;
331 }
332 isl_basic_map_drop_equality(bmap, i);
333 continue;
334 }
335 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
336 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
337 if (isl_int_is_one(gcd))
338 continue;
339 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
340 bmap = isl_basic_map_set_to_empty(bmap);
341 break;
342 }
343 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
344 }
345
346 for (i = bmap->n_ineq - 1; i >= 0; --i) {
347 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
348 if (isl_int_is_zero(gcd)) {
349 if (isl_int_is_neg(bmap->ineq[i][0])) {
350 bmap = isl_basic_map_set_to_empty(bmap);
351 break;
352 }
353 isl_basic_map_drop_inequality(bmap, i);
354 continue;
355 }
356 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
357 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
358 if (isl_int_is_one(gcd))
359 continue;
360 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
361 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
362 }
363 isl_int_clear(gcd);
364
365 return bmap;
366 }
367
368 struct isl_basic_set *isl_basic_set_normalize_constraints(
369 struct isl_basic_set *bset)
370 {
371 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
372 (struct isl_basic_map *)bset);
373 }
374
375 /* Remove any common factor in numerator and denominator of a div expression,
376 * not taking into account the constant term.
377 * That is, look for any div of the form
378 *
379 * floor((a + m f(x))/(m d))
380 *
381 * and replace it by
382 *
383 * floor((floor(a/m) + f(x))/d)
384 *
385 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
386 * and can therefore not influence the result of the floor.
387 */
388 static __isl_give isl_basic_map *normalize_div_expressions(
389 __isl_take isl_basic_map *bmap)
390 {
391 int i;
392 isl_int gcd;
393 unsigned total = isl_basic_map_total_dim(bmap);
394
395 if (!bmap)
396 return NULL;
397 if (bmap->n_div == 0)
398 return bmap;
399
400 isl_int_init(gcd);
401 for (i = 0; i < bmap->n_div; ++i) {
402 if (isl_int_is_zero(bmap->div[i][0]))
403 continue;
404 isl_seq_gcd(bmap->div[i] + 2, total, &gcd);
405 isl_int_gcd(gcd, gcd, bmap->div[i][0]);
406 if (isl_int_is_one(gcd))
407 continue;
408 isl_int_fdiv_q(bmap->div[i][1], bmap->div[i][1], gcd);
409 isl_int_divexact(bmap->div[i][0], bmap->div[i][0], gcd);
410 isl_seq_scale_down(bmap->div[i] + 2, bmap->div[i] + 2, gcd,
411 total);
412 }
413 isl_int_clear(gcd);
414
415 return bmap;
416 }
417
418 /* Assumes divs have been ordered if keep_divs is set.
419 */
420 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
421 unsigned pos, isl_int *eq, int keep_divs, int *progress)
422 {
423 unsigned total;
424 unsigned space_total;
425 int k;
426 int last_div;
427
428 total = isl_basic_map_total_dim(bmap);
429 space_total = isl_space_dim(bmap->dim, isl_dim_all);
430 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
431 for (k = 0; k < bmap->n_eq; ++k) {
432 if (bmap->eq[k] == eq)
433 continue;
434 if (isl_int_is_zero(bmap->eq[k][1+pos]))
435 continue;
436 if (progress)
437 *progress = 1;
438 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
439 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
440 }
441
442 for (k = 0; k < bmap->n_ineq; ++k) {
443 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
444 continue;
445 if (progress)
446 *progress = 1;
447 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
448 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
449 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
450 }
451
452 for (k = 0; k < bmap->n_div; ++k) {
453 if (isl_int_is_zero(bmap->div[k][0]))
454 continue;
455 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
456 continue;
457 if (progress)
458 *progress = 1;
459 /* We need to be careful about circular definitions,
460 * so for now we just remove the definition of div k
461 * if the equality contains any divs.
462 * If keep_divs is set, then the divs have been ordered
463 * and we can keep the definition as long as the result
464 * is still ordered.
465 */
466 if (last_div == -1 || (keep_divs && last_div < k))
467 isl_seq_elim(bmap->div[k]+1, eq,
468 1+pos, 1+total, &bmap->div[k][0]);
469 else
470 isl_seq_clr(bmap->div[k], 1 + total);
471 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
472 }
473 }
474
475 /* Assumes divs have been ordered if keep_divs is set.
476 */
477 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
478 unsigned div, int keep_divs)
479 {
480 unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
481
482 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
483
484 isl_basic_map_drop_div(bmap, div);
485 }
486
487 /* Check if elimination of div "div" using equality "eq" would not
488 * result in a div depending on a later div.
489 */
490 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
491 unsigned div)
492 {
493 int k;
494 int last_div;
495 unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
496 unsigned pos = space_total + div;
497
498 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
499 if (last_div < 0 || last_div <= div)
500 return 1;
501
502 for (k = 0; k <= last_div; ++k) {
503 if (isl_int_is_zero(bmap->div[k][0]))
504 return 1;
505 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
506 return 0;
507 }
508
509 return 1;
510 }
511
512 /* Elimininate divs based on equalities
513 */
514 static struct isl_basic_map *eliminate_divs_eq(
515 struct isl_basic_map *bmap, int *progress)
516 {
517 int d;
518 int i;
519 int modified = 0;
520 unsigned off;
521
522 bmap = isl_basic_map_order_divs(bmap);
523
524 if (!bmap)
525 return NULL;
526
527 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
528
529 for (d = bmap->n_div - 1; d >= 0 ; --d) {
530 for (i = 0; i < bmap->n_eq; ++i) {
531 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
532 !isl_int_is_negone(bmap->eq[i][off + d]))
533 continue;
534 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
535 continue;
536 modified = 1;
537 *progress = 1;
538 eliminate_div(bmap, bmap->eq[i], d, 1);
539 isl_basic_map_drop_equality(bmap, i);
540 break;
541 }
542 }
543 if (modified)
544 return eliminate_divs_eq(bmap, progress);
545 return bmap;
546 }
547
548 /* Elimininate divs based on inequalities
549 */
550 static struct isl_basic_map *eliminate_divs_ineq(
551 struct isl_basic_map *bmap, int *progress)
552 {
553 int d;
554 int i;
555 unsigned off;
556 struct isl_ctx *ctx;
557
558 if (!bmap)
559 return NULL;
560
561 ctx = bmap->ctx;
562 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
563
564 for (d = bmap->n_div - 1; d >= 0 ; --d) {
565 for (i = 0; i < bmap->n_eq; ++i)
566 if (!isl_int_is_zero(bmap->eq[i][off + d]))
567 break;
568 if (i < bmap->n_eq)
569 continue;
570 for (i = 0; i < bmap->n_ineq; ++i)
571 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
572 break;
573 if (i < bmap->n_ineq)
574 continue;
575 *progress = 1;
576 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
577 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
578 break;
579 bmap = isl_basic_map_drop_div(bmap, d);
580 if (!bmap)
581 break;
582 }
583 return bmap;
584 }
585
586 struct isl_basic_map *isl_basic_map_gauss(
587 struct isl_basic_map *bmap, int *progress)
588 {
589 int k;
590 int done;
591 int last_var;
592 unsigned total_var;
593 unsigned total;
594
595 bmap = isl_basic_map_order_divs(bmap);
596
597 if (!bmap)
598 return NULL;
599
600 total = isl_basic_map_total_dim(bmap);
601 total_var = total - bmap->n_div;
602
603 last_var = total - 1;
604 for (done = 0; done < bmap->n_eq; ++done) {
605 for (; last_var >= 0; --last_var) {
606 for (k = done; k < bmap->n_eq; ++k)
607 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
608 break;
609 if (k < bmap->n_eq)
610 break;
611 }
612 if (last_var < 0)
613 break;
614 if (k != done)
615 swap_equality(bmap, k, done);
616 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
617 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
618
619 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
620 progress);
621
622 if (last_var >= total_var &&
623 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
624 unsigned div = last_var - total_var;
625 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
626 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
627 isl_int_set(bmap->div[div][0],
628 bmap->eq[done][1+last_var]);
629 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
630 }
631 }
632 if (done == bmap->n_eq)
633 return bmap;
634 for (k = done; k < bmap->n_eq; ++k) {
635 if (isl_int_is_zero(bmap->eq[k][0]))
636 continue;
637 return isl_basic_map_set_to_empty(bmap);
638 }
639 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
640 return bmap;
641 }
642
643 struct isl_basic_set *isl_basic_set_gauss(
644 struct isl_basic_set *bset, int *progress)
645 {
646 return (struct isl_basic_set*)isl_basic_map_gauss(
647 (struct isl_basic_map *)bset, progress);
648 }
649
650
651 static unsigned int round_up(unsigned int v)
652 {
653 int old_v = v;
654
655 while (v) {
656 old_v = v;
657 v ^= v & -v;
658 }
659 return old_v << 1;
660 }
661
662 static int hash_index(isl_int ***index, unsigned int size, int bits,
663 struct isl_basic_map *bmap, int k)
664 {
665 int h;
666 unsigned total = isl_basic_map_total_dim(bmap);
667 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
668 for (h = hash; index[h]; h = (h+1) % size)
669 if (&bmap->ineq[k] != index[h] &&
670 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
671 break;
672 return h;
673 }
674
675 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
676 struct isl_basic_set *bset, int k)
677 {
678 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
679 }
680
681 /* If we can eliminate more than one div, then we need to make
682 * sure we do it from last div to first div, in order not to
683 * change the position of the other divs that still need to
684 * be removed.
685 */
686 static struct isl_basic_map *remove_duplicate_divs(
687 struct isl_basic_map *bmap, int *progress)
688 {
689 unsigned int size;
690 int *index;
691 int *elim_for;
692 int k, l, h;
693 int bits;
694 struct isl_blk eq;
695 unsigned total_var;
696 unsigned total;
697 struct isl_ctx *ctx;
698
699 if (!bmap || bmap->n_div <= 1)
700 return bmap;
701
702 total_var = isl_space_dim(bmap->dim, isl_dim_all);
703 total = total_var + bmap->n_div;
704
705 ctx = bmap->ctx;
706 for (k = bmap->n_div - 1; k >= 0; --k)
707 if (!isl_int_is_zero(bmap->div[k][0]))
708 break;
709 if (k <= 0)
710 return bmap;
711
712 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
713 size = round_up(4 * bmap->n_div / 3 - 1);
714 bits = ffs(size) - 1;
715 index = isl_calloc_array(ctx, int, size);
716 if (!index)
717 return bmap;
718 eq = isl_blk_alloc(ctx, 1+total);
719 if (isl_blk_is_error(eq))
720 goto out;
721
722 isl_seq_clr(eq.data, 1+total);
723 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
724 for (--k; k >= 0; --k) {
725 uint32_t hash;
726
727 if (isl_int_is_zero(bmap->div[k][0]))
728 continue;
729
730 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
731 for (h = hash; index[h]; h = (h+1) % size)
732 if (isl_seq_eq(bmap->div[k],
733 bmap->div[index[h]-1], 2+total))
734 break;
735 if (index[h]) {
736 *progress = 1;
737 l = index[h] - 1;
738 elim_for[l] = k + 1;
739 }
740 index[h] = k+1;
741 }
742 for (l = bmap->n_div - 1; l >= 0; --l) {
743 if (!elim_for[l])
744 continue;
745 k = elim_for[l] - 1;
746 isl_int_set_si(eq.data[1+total_var+k], -1);
747 isl_int_set_si(eq.data[1+total_var+l], 1);
748 eliminate_div(bmap, eq.data, l, 0);
749 isl_int_set_si(eq.data[1+total_var+k], 0);
750 isl_int_set_si(eq.data[1+total_var+l], 0);
751 }
752
753 isl_blk_free(ctx, eq);
754 out:
755 free(index);
756 free(elim_for);
757 return bmap;
758 }
759
760 static int n_pure_div_eq(struct isl_basic_map *bmap)
761 {
762 int i, j;
763 unsigned total;
764
765 total = isl_space_dim(bmap->dim, isl_dim_all);
766 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
767 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
768 --j;
769 if (j < 0)
770 break;
771 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
772 return 0;
773 }
774 return i;
775 }
776
777 /* Normalize divs that appear in equalities.
778 *
779 * In particular, we assume that bmap contains some equalities
780 * of the form
781 *
782 * a x = m * e_i
783 *
784 * and we want to replace the set of e_i by a minimal set and
785 * such that the new e_i have a canonical representation in terms
786 * of the vector x.
787 * If any of the equalities involves more than one divs, then
788 * we currently simply bail out.
789 *
790 * Let us first additionally assume that all equalities involve
791 * a div. The equalities then express modulo constraints on the
792 * remaining variables and we can use "parameter compression"
793 * to find a minimal set of constraints. The result is a transformation
794 *
795 * x = T(x') = x_0 + G x'
796 *
797 * with G a lower-triangular matrix with all elements below the diagonal
798 * non-negative and smaller than the diagonal element on the same row.
799 * We first normalize x_0 by making the same property hold in the affine
800 * T matrix.
801 * The rows i of G with a 1 on the diagonal do not impose any modulo
802 * constraint and simply express x_i = x'_i.
803 * For each of the remaining rows i, we introduce a div and a corresponding
804 * equality. In particular
805 *
806 * g_ii e_j = x_i - g_i(x')
807 *
808 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
809 * corresponding div (if g_kk != 1).
810 *
811 * If there are any equalities not involving any div, then we
812 * first apply a variable compression on the variables x:
813 *
814 * x = C x'' x'' = C_2 x
815 *
816 * and perform the above parameter compression on A C instead of on A.
817 * The resulting compression is then of the form
818 *
819 * x'' = T(x') = x_0 + G x'
820 *
821 * and in constructing the new divs and the corresponding equalities,
822 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
823 * by the corresponding row from C_2.
824 */
825 static struct isl_basic_map *normalize_divs(
826 struct isl_basic_map *bmap, int *progress)
827 {
828 int i, j, k;
829 int total;
830 int div_eq;
831 struct isl_mat *B;
832 struct isl_vec *d;
833 struct isl_mat *T = NULL;
834 struct isl_mat *C = NULL;
835 struct isl_mat *C2 = NULL;
836 isl_int v;
837 int *pos;
838 int dropped, needed;
839
840 if (!bmap)
841 return NULL;
842
843 if (bmap->n_div == 0)
844 return bmap;
845
846 if (bmap->n_eq == 0)
847 return bmap;
848
849 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
850 return bmap;
851
852 total = isl_space_dim(bmap->dim, isl_dim_all);
853 div_eq = n_pure_div_eq(bmap);
854 if (div_eq == 0)
855 return bmap;
856
857 if (div_eq < bmap->n_eq) {
858 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
859 bmap->n_eq - div_eq, 0, 1 + total);
860 C = isl_mat_variable_compression(B, &C2);
861 if (!C || !C2)
862 goto error;
863 if (C->n_col == 0) {
864 bmap = isl_basic_map_set_to_empty(bmap);
865 isl_mat_free(C);
866 isl_mat_free(C2);
867 goto done;
868 }
869 }
870
871 d = isl_vec_alloc(bmap->ctx, div_eq);
872 if (!d)
873 goto error;
874 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
875 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
876 --j;
877 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
878 }
879 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
880
881 if (C) {
882 B = isl_mat_product(B, C);
883 C = NULL;
884 }
885
886 T = isl_mat_parameter_compression(B, d);
887 if (!T)
888 goto error;
889 if (T->n_col == 0) {
890 bmap = isl_basic_map_set_to_empty(bmap);
891 isl_mat_free(C2);
892 isl_mat_free(T);
893 goto done;
894 }
895 isl_int_init(v);
896 for (i = 0; i < T->n_row - 1; ++i) {
897 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
898 if (isl_int_is_zero(v))
899 continue;
900 isl_mat_col_submul(T, 0, v, 1 + i);
901 }
902 isl_int_clear(v);
903 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
904 if (!pos)
905 goto error;
906 /* We have to be careful because dropping equalities may reorder them */
907 dropped = 0;
908 for (j = bmap->n_div - 1; j >= 0; --j) {
909 for (i = 0; i < bmap->n_eq; ++i)
910 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
911 break;
912 if (i < bmap->n_eq) {
913 bmap = isl_basic_map_drop_div(bmap, j);
914 isl_basic_map_drop_equality(bmap, i);
915 ++dropped;
916 }
917 }
918 pos[0] = 0;
919 needed = 0;
920 for (i = 1; i < T->n_row; ++i) {
921 if (isl_int_is_one(T->row[i][i]))
922 pos[i] = i;
923 else
924 needed++;
925 }
926 if (needed > dropped) {
927 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
928 needed, needed, 0);
929 if (!bmap)
930 goto error;
931 }
932 for (i = 1; i < T->n_row; ++i) {
933 if (isl_int_is_one(T->row[i][i]))
934 continue;
935 k = isl_basic_map_alloc_div(bmap);
936 pos[i] = 1 + total + k;
937 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
938 isl_int_set(bmap->div[k][0], T->row[i][i]);
939 if (C2)
940 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
941 else
942 isl_int_set_si(bmap->div[k][1 + i], 1);
943 for (j = 0; j < i; ++j) {
944 if (isl_int_is_zero(T->row[i][j]))
945 continue;
946 if (pos[j] < T->n_row && C2)
947 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
948 C2->row[pos[j]], 1 + total);
949 else
950 isl_int_neg(bmap->div[k][1 + pos[j]],
951 T->row[i][j]);
952 }
953 j = isl_basic_map_alloc_equality(bmap);
954 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
955 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
956 }
957 free(pos);
958 isl_mat_free(C2);
959 isl_mat_free(T);
960
961 if (progress)
962 *progress = 1;
963 done:
964 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
965
966 return bmap;
967 error:
968 isl_mat_free(C);
969 isl_mat_free(C2);
970 isl_mat_free(T);
971 return bmap;
972 }
973
974 static struct isl_basic_map *set_div_from_lower_bound(
975 struct isl_basic_map *bmap, int div, int ineq)
976 {
977 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
978
979 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
980 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
981 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
982 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
983 isl_int_set_si(bmap->div[div][1 + total + div], 0);
984
985 return bmap;
986 }
987
988 /* Check whether it is ok to define a div based on an inequality.
989 * To avoid the introduction of circular definitions of divs, we
990 * do not allow such a definition if the resulting expression would refer to
991 * any other undefined divs or if any known div is defined in
992 * terms of the unknown div.
993 */
994 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
995 int div, int ineq)
996 {
997 int j;
998 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
999
1000 /* Not defined in terms of unknown divs */
1001 for (j = 0; j < bmap->n_div; ++j) {
1002 if (div == j)
1003 continue;
1004 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
1005 continue;
1006 if (isl_int_is_zero(bmap->div[j][0]))
1007 return 0;
1008 }
1009
1010 /* No other div defined in terms of this one => avoid loops */
1011 for (j = 0; j < bmap->n_div; ++j) {
1012 if (div == j)
1013 continue;
1014 if (isl_int_is_zero(bmap->div[j][0]))
1015 continue;
1016 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
1017 return 0;
1018 }
1019
1020 return 1;
1021 }
1022
1023 /* Given two constraints "k" and "l" that are opposite to each other,
1024 * except for the constant term, check if we can use them
1025 * to obtain an expression for one of the hitherto unknown divs.
1026 * "sum" is the sum of the constant terms of the constraints.
1027 * If this sum is strictly smaller than the coefficient of one
1028 * of the divs, then this pair can be used define the div.
1029 * To avoid the introduction of circular definitions of divs, we
1030 * do not use the pair if the resulting expression would refer to
1031 * any other undefined divs or if any known div is defined in
1032 * terms of the unknown div.
1033 */
1034 static struct isl_basic_map *check_for_div_constraints(
1035 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
1036 {
1037 int i;
1038 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1039
1040 for (i = 0; i < bmap->n_div; ++i) {
1041 if (!isl_int_is_zero(bmap->div[i][0]))
1042 continue;
1043 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1044 continue;
1045 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1046 continue;
1047 if (!ok_to_set_div_from_bound(bmap, i, k))
1048 break;
1049 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1050 bmap = set_div_from_lower_bound(bmap, i, k);
1051 else
1052 bmap = set_div_from_lower_bound(bmap, i, l);
1053 if (progress)
1054 *progress = 1;
1055 break;
1056 }
1057 return bmap;
1058 }
1059
1060 static struct isl_basic_map *remove_duplicate_constraints(
1061 struct isl_basic_map *bmap, int *progress, int detect_divs)
1062 {
1063 unsigned int size;
1064 isl_int ***index;
1065 int k, l, h;
1066 int bits;
1067 unsigned total = isl_basic_map_total_dim(bmap);
1068 isl_int sum;
1069 isl_ctx *ctx;
1070
1071 if (!bmap || bmap->n_ineq <= 1)
1072 return bmap;
1073
1074 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1075 bits = ffs(size) - 1;
1076 ctx = isl_basic_map_get_ctx(bmap);
1077 index = isl_calloc_array(ctx, isl_int **, size);
1078 if (!index)
1079 return bmap;
1080
1081 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1082 for (k = 1; k < bmap->n_ineq; ++k) {
1083 h = hash_index(index, size, bits, bmap, k);
1084 if (!index[h]) {
1085 index[h] = &bmap->ineq[k];
1086 continue;
1087 }
1088 if (progress)
1089 *progress = 1;
1090 l = index[h] - &bmap->ineq[0];
1091 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1092 swap_inequality(bmap, k, l);
1093 isl_basic_map_drop_inequality(bmap, k);
1094 --k;
1095 }
1096 isl_int_init(sum);
1097 for (k = 0; k < bmap->n_ineq-1; ++k) {
1098 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1099 h = hash_index(index, size, bits, bmap, k);
1100 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1101 if (!index[h])
1102 continue;
1103 l = index[h] - &bmap->ineq[0];
1104 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1105 if (isl_int_is_pos(sum)) {
1106 if (detect_divs)
1107 bmap = check_for_div_constraints(bmap, k, l,
1108 sum, progress);
1109 continue;
1110 }
1111 if (isl_int_is_zero(sum)) {
1112 /* We need to break out of the loop after these
1113 * changes since the contents of the hash
1114 * will no longer be valid.
1115 * Plus, we probably we want to regauss first.
1116 */
1117 if (progress)
1118 *progress = 1;
1119 isl_basic_map_drop_inequality(bmap, l);
1120 isl_basic_map_inequality_to_equality(bmap, k);
1121 } else
1122 bmap = isl_basic_map_set_to_empty(bmap);
1123 break;
1124 }
1125 isl_int_clear(sum);
1126
1127 free(index);
1128 return bmap;
1129 }
1130
1131
1132 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1133 {
1134 int progress = 1;
1135 if (!bmap)
1136 return NULL;
1137 while (progress) {
1138 progress = 0;
1139 bmap = isl_basic_map_normalize_constraints(bmap);
1140 bmap = normalize_div_expressions(bmap);
1141 bmap = remove_duplicate_divs(bmap, &progress);
1142 bmap = eliminate_divs_eq(bmap, &progress);
1143 bmap = eliminate_divs_ineq(bmap, &progress);
1144 bmap = isl_basic_map_gauss(bmap, &progress);
1145 /* requires equalities in normal form */
1146 bmap = normalize_divs(bmap, &progress);
1147 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1148 }
1149 return bmap;
1150 }
1151
1152 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1153 {
1154 return (struct isl_basic_set *)
1155 isl_basic_map_simplify((struct isl_basic_map *)bset);
1156 }
1157
1158
1159 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1160 isl_int *constraint, unsigned div)
1161 {
1162 unsigned pos;
1163
1164 if (!bmap)
1165 return -1;
1166
1167 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1168
1169 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1170 int neg;
1171 isl_int_sub(bmap->div[div][1],
1172 bmap->div[div][1], bmap->div[div][0]);
1173 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1174 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1175 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1176 isl_int_add(bmap->div[div][1],
1177 bmap->div[div][1], bmap->div[div][0]);
1178 if (!neg)
1179 return 0;
1180 if (isl_seq_first_non_zero(constraint+pos+1,
1181 bmap->n_div-div-1) != -1)
1182 return 0;
1183 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1184 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1185 return 0;
1186 if (isl_seq_first_non_zero(constraint+pos+1,
1187 bmap->n_div-div-1) != -1)
1188 return 0;
1189 } else
1190 return 0;
1191
1192 return 1;
1193 }
1194
1195 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1196 isl_int *constraint, unsigned div)
1197 {
1198 return isl_basic_map_is_div_constraint(bset, constraint, div);
1199 }
1200
1201
1202 /* If the only constraints a div d=floor(f/m)
1203 * appears in are its two defining constraints
1204 *
1205 * f - m d >=0
1206 * -(f - (m - 1)) + m d >= 0
1207 *
1208 * then it can safely be removed.
1209 */
1210 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1211 {
1212 int i;
1213 unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1214
1215 for (i = 0; i < bmap->n_eq; ++i)
1216 if (!isl_int_is_zero(bmap->eq[i][pos]))
1217 return 0;
1218
1219 for (i = 0; i < bmap->n_ineq; ++i) {
1220 if (isl_int_is_zero(bmap->ineq[i][pos]))
1221 continue;
1222 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1223 return 0;
1224 }
1225
1226 for (i = 0; i < bmap->n_div; ++i)
1227 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1228 return 0;
1229
1230 return 1;
1231 }
1232
1233 /*
1234 * Remove divs that don't occur in any of the constraints or other divs.
1235 * These can arise when dropping some of the variables in a quast
1236 * returned by piplib.
1237 */
1238 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1239 {
1240 int i;
1241
1242 if (!bmap)
1243 return NULL;
1244
1245 for (i = bmap->n_div-1; i >= 0; --i) {
1246 if (!div_is_redundant(bmap, i))
1247 continue;
1248 bmap = isl_basic_map_drop_div(bmap, i);
1249 }
1250 return bmap;
1251 }
1252
1253 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1254 {
1255 bmap = remove_redundant_divs(bmap);
1256 if (!bmap)
1257 return NULL;
1258 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1259 return bmap;
1260 }
1261
1262 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1263 {
1264 return (struct isl_basic_set *)
1265 isl_basic_map_finalize((struct isl_basic_map *)bset);
1266 }
1267
1268 struct isl_set *isl_set_finalize(struct isl_set *set)
1269 {
1270 int i;
1271
1272 if (!set)
1273 return NULL;
1274 for (i = 0; i < set->n; ++i) {
1275 set->p[i] = isl_basic_set_finalize(set->p[i]);
1276 if (!set->p[i])
1277 goto error;
1278 }
1279 return set;
1280 error:
1281 isl_set_free(set);
1282 return NULL;
1283 }
1284
1285 struct isl_map *isl_map_finalize(struct isl_map *map)
1286 {
1287 int i;
1288
1289 if (!map)
1290 return NULL;
1291 for (i = 0; i < map->n; ++i) {
1292 map->p[i] = isl_basic_map_finalize(map->p[i]);
1293 if (!map->p[i])
1294 goto error;
1295 }
1296 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1297 return map;
1298 error:
1299 isl_map_free(map);
1300 return NULL;
1301 }
1302
1303
1304 /* Remove definition of any div that is defined in terms of the given variable.
1305 * The div itself is not removed. Functions such as
1306 * eliminate_divs_ineq depend on the other divs remaining in place.
1307 */
1308 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1309 int pos)
1310 {
1311 int i;
1312
1313 for (i = 0; i < bmap->n_div; ++i) {
1314 if (isl_int_is_zero(bmap->div[i][0]))
1315 continue;
1316 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1317 continue;
1318 isl_int_set_si(bmap->div[i][0], 0);
1319 }
1320 return bmap;
1321 }
1322
1323 /* Eliminate the specified variables from the constraints using
1324 * Fourier-Motzkin. The variables themselves are not removed.
1325 */
1326 struct isl_basic_map *isl_basic_map_eliminate_vars(
1327 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1328 {
1329 int d;
1330 int i, j, k;
1331 unsigned total;
1332 int need_gauss = 0;
1333
1334 if (n == 0)
1335 return bmap;
1336 if (!bmap)
1337 return NULL;
1338 total = isl_basic_map_total_dim(bmap);
1339
1340 bmap = isl_basic_map_cow(bmap);
1341 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1342 bmap = remove_dependent_vars(bmap, d);
1343
1344 for (d = pos + n - 1;
1345 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1346 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1347 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1348 int n_lower, n_upper;
1349 if (!bmap)
1350 return NULL;
1351 for (i = 0; i < bmap->n_eq; ++i) {
1352 if (isl_int_is_zero(bmap->eq[i][1+d]))
1353 continue;
1354 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1355 isl_basic_map_drop_equality(bmap, i);
1356 need_gauss = 1;
1357 break;
1358 }
1359 if (i < bmap->n_eq)
1360 continue;
1361 n_lower = 0;
1362 n_upper = 0;
1363 for (i = 0; i < bmap->n_ineq; ++i) {
1364 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1365 n_lower++;
1366 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1367 n_upper++;
1368 }
1369 bmap = isl_basic_map_extend_constraints(bmap,
1370 0, n_lower * n_upper);
1371 if (!bmap)
1372 goto error;
1373 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1374 int last;
1375 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1376 continue;
1377 last = -1;
1378 for (j = 0; j < i; ++j) {
1379 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1380 continue;
1381 last = j;
1382 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1383 isl_int_sgn(bmap->ineq[j][1+d]))
1384 continue;
1385 k = isl_basic_map_alloc_inequality(bmap);
1386 if (k < 0)
1387 goto error;
1388 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1389 1+total);
1390 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1391 1+d, 1+total, NULL);
1392 }
1393 isl_basic_map_drop_inequality(bmap, i);
1394 i = last + 1;
1395 }
1396 if (n_lower > 0 && n_upper > 0) {
1397 bmap = isl_basic_map_normalize_constraints(bmap);
1398 bmap = remove_duplicate_constraints(bmap, NULL, 0);
1399 bmap = isl_basic_map_gauss(bmap, NULL);
1400 bmap = isl_basic_map_remove_redundancies(bmap);
1401 need_gauss = 0;
1402 if (!bmap)
1403 goto error;
1404 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1405 break;
1406 }
1407 }
1408 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1409 if (need_gauss)
1410 bmap = isl_basic_map_gauss(bmap, NULL);
1411 return bmap;
1412 error:
1413 isl_basic_map_free(bmap);
1414 return NULL;
1415 }
1416
1417 struct isl_basic_set *isl_basic_set_eliminate_vars(
1418 struct isl_basic_set *bset, unsigned pos, unsigned n)
1419 {
1420 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1421 (struct isl_basic_map *)bset, pos, n);
1422 }
1423
1424 /* Eliminate the specified n dimensions starting at first from the
1425 * constraints, without removing the dimensions from the space.
1426 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1427 * Otherwise, they are projected out and the original space is restored.
1428 */
1429 __isl_give isl_basic_map *isl_basic_map_eliminate(
1430 __isl_take isl_basic_map *bmap,
1431 enum isl_dim_type type, unsigned first, unsigned n)
1432 {
1433 isl_space *space;
1434
1435 if (!bmap)
1436 return NULL;
1437 if (n == 0)
1438 return bmap;
1439
1440 if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
1441 isl_die(bmap->ctx, isl_error_invalid,
1442 "index out of bounds", goto error);
1443
1444 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
1445 first += isl_basic_map_offset(bmap, type) - 1;
1446 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1447 return isl_basic_map_finalize(bmap);
1448 }
1449
1450 space = isl_basic_map_get_space(bmap);
1451 bmap = isl_basic_map_project_out(bmap, type, first, n);
1452 bmap = isl_basic_map_insert(bmap, type, first, n);
1453 bmap = isl_basic_map_reset_space(bmap, space);
1454 return bmap;
1455 error:
1456 isl_basic_map_free(bmap);
1457 return NULL;
1458 }
1459
1460 /* Don't assume equalities are in order, because align_divs
1461 * may have changed the order of the divs.
1462 */
1463 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1464 {
1465 int d, i;
1466 unsigned total;
1467
1468 total = isl_space_dim(bmap->dim, isl_dim_all);
1469 for (d = 0; d < total; ++d)
1470 elim[d] = -1;
1471 for (i = 0; i < bmap->n_eq; ++i) {
1472 for (d = total - 1; d >= 0; --d) {
1473 if (isl_int_is_zero(bmap->eq[i][1+d]))
1474 continue;
1475 elim[d] = i;
1476 break;
1477 }
1478 }
1479 }
1480
1481 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1482 {
1483 compute_elimination_index((struct isl_basic_map *)bset, elim);
1484 }
1485
1486 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1487 struct isl_basic_map *bmap, int *elim)
1488 {
1489 int d;
1490 int copied = 0;
1491 unsigned total;
1492
1493 total = isl_space_dim(bmap->dim, isl_dim_all);
1494 for (d = total - 1; d >= 0; --d) {
1495 if (isl_int_is_zero(src[1+d]))
1496 continue;
1497 if (elim[d] == -1)
1498 continue;
1499 if (!copied) {
1500 isl_seq_cpy(dst, src, 1 + total);
1501 copied = 1;
1502 }
1503 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1504 }
1505 return copied;
1506 }
1507
1508 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1509 struct isl_basic_set *bset, int *elim)
1510 {
1511 return reduced_using_equalities(dst, src,
1512 (struct isl_basic_map *)bset, elim);
1513 }
1514
1515 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1516 struct isl_basic_set *bset, struct isl_basic_set *context)
1517 {
1518 int i;
1519 int *elim;
1520
1521 if (!bset || !context)
1522 goto error;
1523
1524 if (context->n_eq == 0) {
1525 isl_basic_set_free(context);
1526 return bset;
1527 }
1528
1529 bset = isl_basic_set_cow(bset);
1530 if (!bset)
1531 goto error;
1532
1533 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1534 if (!elim)
1535 goto error;
1536 set_compute_elimination_index(context, elim);
1537 for (i = 0; i < bset->n_eq; ++i)
1538 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1539 context, elim);
1540 for (i = 0; i < bset->n_ineq; ++i)
1541 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1542 context, elim);
1543 isl_basic_set_free(context);
1544 free(elim);
1545 bset = isl_basic_set_simplify(bset);
1546 bset = isl_basic_set_finalize(bset);
1547 return bset;
1548 error:
1549 isl_basic_set_free(bset);
1550 isl_basic_set_free(context);
1551 return NULL;
1552 }
1553
1554 static struct isl_basic_set *remove_shifted_constraints(
1555 struct isl_basic_set *bset, struct isl_basic_set *context)
1556 {
1557 unsigned int size;
1558 isl_int ***index;
1559 int bits;
1560 int k, h, l;
1561 isl_ctx *ctx;
1562
1563 if (!bset)
1564 return NULL;
1565
1566 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1567 bits = ffs(size) - 1;
1568 ctx = isl_basic_set_get_ctx(bset);
1569 index = isl_calloc_array(ctx, isl_int **, size);
1570 if (!index)
1571 return bset;
1572
1573 for (k = 0; k < context->n_ineq; ++k) {
1574 h = set_hash_index(index, size, bits, context, k);
1575 index[h] = &context->ineq[k];
1576 }
1577 for (k = 0; k < bset->n_ineq; ++k) {
1578 h = set_hash_index(index, size, bits, bset, k);
1579 if (!index[h])
1580 continue;
1581 l = index[h] - &context->ineq[0];
1582 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1583 continue;
1584 bset = isl_basic_set_cow(bset);
1585 if (!bset)
1586 goto error;
1587 isl_basic_set_drop_inequality(bset, k);
1588 --k;
1589 }
1590 free(index);
1591 return bset;
1592 error:
1593 free(index);
1594 return bset;
1595 }
1596
1597 /* Remove all information from bset that is redundant in the context
1598 * of context. Both bset and context are assumed to be full-dimensional.
1599 *
1600 * We first * remove the inequalities from "bset"
1601 * that are obviously redundant with respect to some inequality in "context".
1602 *
1603 * If there are any inequalities left, we construct a tableau for
1604 * the context and then add the inequalities of "bset".
1605 * Before adding these inequalities, we freeze all constraints such that
1606 * they won't be considered redundant in terms of the constraints of "bset".
1607 * Then we detect all redundant constraints (among the
1608 * constraints that weren't frozen), first by checking for redundancy in the
1609 * the tableau and then by checking if replacing a constraint by its negation
1610 * would lead to an empty set. This last step is fairly expensive
1611 * and could be optimized by more reuse of the tableau.
1612 * Finally, we update bset according to the results.
1613 */
1614 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1615 __isl_take isl_basic_set *context)
1616 {
1617 int i, k;
1618 isl_basic_set *combined = NULL;
1619 struct isl_tab *tab = NULL;
1620 unsigned context_ineq;
1621 unsigned total;
1622
1623 if (!bset || !context)
1624 goto error;
1625
1626 if (isl_basic_set_is_universe(bset)) {
1627 isl_basic_set_free(context);
1628 return bset;
1629 }
1630
1631 if (isl_basic_set_is_universe(context)) {
1632 isl_basic_set_free(context);
1633 return bset;
1634 }
1635
1636 bset = remove_shifted_constraints(bset, context);
1637 if (!bset)
1638 goto error;
1639 if (bset->n_ineq == 0)
1640 goto done;
1641
1642 context_ineq = context->n_ineq;
1643 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1644 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1645 tab = isl_tab_from_basic_set(combined, 0);
1646 for (i = 0; i < context_ineq; ++i)
1647 if (isl_tab_freeze_constraint(tab, i) < 0)
1648 goto error;
1649 tab = isl_tab_extend(tab, bset->n_ineq);
1650 for (i = 0; i < bset->n_ineq; ++i)
1651 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1652 goto error;
1653 bset = isl_basic_set_add_constraints(combined, bset, 0);
1654 combined = NULL;
1655 if (!bset)
1656 goto error;
1657 if (isl_tab_detect_redundant(tab) < 0)
1658 goto error;
1659 total = isl_basic_set_total_dim(bset);
1660 for (i = context_ineq; i < bset->n_ineq; ++i) {
1661 int is_empty;
1662 if (tab->con[i].is_redundant)
1663 continue;
1664 tab->con[i].is_redundant = 1;
1665 combined = isl_basic_set_dup(bset);
1666 combined = isl_basic_set_update_from_tab(combined, tab);
1667 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1668 k = isl_basic_set_alloc_inequality(combined);
1669 if (k < 0)
1670 goto error;
1671 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1672 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1673 is_empty = isl_basic_set_is_empty(combined);
1674 if (is_empty < 0)
1675 goto error;
1676 isl_basic_set_free(combined);
1677 combined = NULL;
1678 if (!is_empty)
1679 tab->con[i].is_redundant = 0;
1680 }
1681 for (i = 0; i < context_ineq; ++i)
1682 tab->con[i].is_redundant = 1;
1683 bset = isl_basic_set_update_from_tab(bset, tab);
1684 if (bset) {
1685 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1686 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1687 }
1688
1689 isl_tab_free(tab);
1690 done:
1691 bset = isl_basic_set_simplify(bset);
1692 bset = isl_basic_set_finalize(bset);
1693 isl_basic_set_free(context);
1694 return bset;
1695 error:
1696 isl_tab_free(tab);
1697 isl_basic_set_free(combined);
1698 isl_basic_set_free(context);
1699 isl_basic_set_free(bset);
1700 return NULL;
1701 }
1702
1703 /* Remove all information from bset that is redundant in the context
1704 * of context. In particular, equalities that are linear combinations
1705 * of those in context are removed. Then the inequalities that are
1706 * redundant in the context of the equalities and inequalities of
1707 * context are removed.
1708 *
1709 * We first compute the integer affine hull of the intersection,
1710 * compute the gist inside this affine hull and then add back
1711 * those equalities that are not implied by the context.
1712 *
1713 * If two constraints are mutually redundant, then uset_gist_full
1714 * will remove the second of those constraints. We therefore first
1715 * sort the constraints so that constraints not involving existentially
1716 * quantified variables are given precedence over those that do.
1717 * We have to perform this sorting before the variable compression,
1718 * because that may effect the order of the variables.
1719 */
1720 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1721 __isl_take isl_basic_set *context)
1722 {
1723 isl_mat *eq;
1724 isl_mat *T, *T2;
1725 isl_basic_set *aff;
1726 isl_basic_set *aff_context;
1727 unsigned total;
1728
1729 if (!bset || !context)
1730 goto error;
1731
1732 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1733 if (isl_basic_set_plain_is_empty(bset)) {
1734 isl_basic_set_free(context);
1735 return bset;
1736 }
1737 bset = isl_basic_set_sort_constraints(bset);
1738 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1739 if (!aff)
1740 goto error;
1741 if (isl_basic_set_plain_is_empty(aff)) {
1742 isl_basic_set_free(aff);
1743 isl_basic_set_free(context);
1744 return bset;
1745 }
1746 if (aff->n_eq == 0) {
1747 isl_basic_set_free(aff);
1748 return uset_gist_full(bset, context);
1749 }
1750 total = isl_basic_set_total_dim(bset);
1751 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1752 eq = isl_mat_cow(eq);
1753 T = isl_mat_variable_compression(eq, &T2);
1754 if (T && T->n_col == 0) {
1755 isl_mat_free(T);
1756 isl_mat_free(T2);
1757 isl_basic_set_free(context);
1758 isl_basic_set_free(aff);
1759 return isl_basic_set_set_to_empty(bset);
1760 }
1761
1762 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1763
1764 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1765 context = isl_basic_set_preimage(context, T);
1766
1767 bset = uset_gist_full(bset, context);
1768 bset = isl_basic_set_preimage(bset, T2);
1769 bset = isl_basic_set_intersect(bset, aff);
1770 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1771
1772 if (bset) {
1773 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1774 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1775 }
1776
1777 return bset;
1778 error:
1779 isl_basic_set_free(bset);
1780 isl_basic_set_free(context);
1781 return NULL;
1782 }
1783
1784 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1785 * We simply add the equalities in context to bmap and then do a regular
1786 * div normalizations. Better results can be obtained by normalizing
1787 * only the divs in bmap than do not also appear in context.
1788 * We need to be careful to reduce the divs using the equalities
1789 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1790 * spurious constraints.
1791 */
1792 static struct isl_basic_map *normalize_divs_in_context(
1793 struct isl_basic_map *bmap, struct isl_basic_map *context)
1794 {
1795 int i;
1796 unsigned total_context;
1797 int div_eq;
1798
1799 div_eq = n_pure_div_eq(bmap);
1800 if (div_eq == 0)
1801 return bmap;
1802
1803 if (context->n_div > 0)
1804 bmap = isl_basic_map_align_divs(bmap, context);
1805
1806 total_context = isl_basic_map_total_dim(context);
1807 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1808 for (i = 0; i < context->n_eq; ++i) {
1809 int k;
1810 k = isl_basic_map_alloc_equality(bmap);
1811 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1812 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1813 isl_basic_map_total_dim(bmap) - total_context);
1814 }
1815 bmap = isl_basic_map_gauss(bmap, NULL);
1816 bmap = normalize_divs(bmap, NULL);
1817 bmap = isl_basic_map_gauss(bmap, NULL);
1818 return bmap;
1819 }
1820
1821 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1822 struct isl_basic_map *context)
1823 {
1824 struct isl_basic_set *bset;
1825
1826 if (!bmap || !context)
1827 goto error;
1828
1829 if (isl_basic_map_is_universe(bmap)) {
1830 isl_basic_map_free(context);
1831 return bmap;
1832 }
1833 if (isl_basic_map_plain_is_empty(context)) {
1834 isl_basic_map_free(bmap);
1835 return context;
1836 }
1837 if (isl_basic_map_plain_is_empty(bmap)) {
1838 isl_basic_map_free(context);
1839 return bmap;
1840 }
1841
1842 bmap = isl_basic_map_remove_redundancies(bmap);
1843 context = isl_basic_map_remove_redundancies(context);
1844
1845 if (context->n_eq)
1846 bmap = normalize_divs_in_context(bmap, context);
1847
1848 context = isl_basic_map_align_divs(context, bmap);
1849 bmap = isl_basic_map_align_divs(bmap, context);
1850
1851 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1852 isl_basic_map_underlying_set(context));
1853
1854 return isl_basic_map_overlying_set(bset, bmap);
1855 error:
1856 isl_basic_map_free(bmap);
1857 isl_basic_map_free(context);
1858 return NULL;
1859 }
1860
1861 /*
1862 * Assumes context has no implicit divs.
1863 */
1864 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1865 __isl_take isl_basic_map *context)
1866 {
1867 int i;
1868
1869 if (!map || !context)
1870 goto error;;
1871
1872 if (isl_basic_map_plain_is_empty(context)) {
1873 isl_map_free(map);
1874 return isl_map_from_basic_map(context);
1875 }
1876
1877 context = isl_basic_map_remove_redundancies(context);
1878 map = isl_map_cow(map);
1879 if (!map || !context)
1880 goto error;;
1881 isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1882 map = isl_map_compute_divs(map);
1883 for (i = 0; i < map->n; ++i)
1884 context = isl_basic_map_align_divs(context, map->p[i]);
1885 for (i = map->n - 1; i >= 0; --i) {
1886 map->p[i] = isl_basic_map_gist(map->p[i],
1887 isl_basic_map_copy(context));
1888 if (!map->p[i])
1889 goto error;
1890 if (isl_basic_map_plain_is_empty(map->p[i])) {
1891 isl_basic_map_free(map->p[i]);
1892 if (i != map->n - 1)
1893 map->p[i] = map->p[map->n - 1];
1894 map->n--;
1895 }
1896 }
1897 isl_basic_map_free(context);
1898 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1899 return map;
1900 error:
1901 isl_map_free(map);
1902 isl_basic_map_free(context);
1903 return NULL;
1904 }
1905
1906 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1907 __isl_take isl_map *context)
1908 {
1909 context = isl_map_compute_divs(context);
1910 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1911 }
1912
1913 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1914 __isl_take isl_map *context)
1915 {
1916 return isl_map_align_params_map_map_and(map, context, &map_gist);
1917 }
1918
1919 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1920 struct isl_basic_set *context)
1921 {
1922 return (struct isl_basic_set *)isl_basic_map_gist(
1923 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1924 }
1925
1926 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1927 __isl_take isl_basic_set *context)
1928 {
1929 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1930 (struct isl_basic_map *)context);
1931 }
1932
1933 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
1934 __isl_take isl_basic_set *context)
1935 {
1936 isl_space *space = isl_set_get_space(set);
1937 isl_basic_set *dom_context = isl_basic_set_universe(space);
1938 dom_context = isl_basic_set_intersect_params(dom_context, context);
1939 return isl_set_gist_basic_set(set, dom_context);
1940 }
1941
1942 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1943 __isl_take isl_set *context)
1944 {
1945 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1946 (struct isl_map *)context);
1947 }
1948
1949 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
1950 __isl_take isl_set *context)
1951 {
1952 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1953 map_context = isl_map_intersect_domain(map_context, context);
1954 return isl_map_gist(map, map_context);
1955 }
1956
1957 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
1958 __isl_take isl_set *context)
1959 {
1960 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1961 map_context = isl_map_intersect_range(map_context, context);
1962 return isl_map_gist(map, map_context);
1963 }
1964
1965 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
1966 __isl_take isl_set *context)
1967 {
1968 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1969 map_context = isl_map_intersect_params(map_context, context);
1970 return isl_map_gist(map, map_context);
1971 }
1972
1973 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
1974 __isl_take isl_set *context)
1975 {
1976 return isl_map_gist_params(set, context);
1977 }
1978
1979 /* Quick check to see if two basic maps are disjoint.
1980 * In particular, we reduce the equalities and inequalities of
1981 * one basic map in the context of the equalities of the other
1982 * basic map and check if we get a contradiction.
1983 */
1984 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1985 __isl_keep isl_basic_map *bmap2)
1986 {
1987 struct isl_vec *v = NULL;
1988 int *elim = NULL;
1989 unsigned total;
1990 int i;
1991
1992 if (!bmap1 || !bmap2)
1993 return -1;
1994 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
1995 return -1);
1996 if (bmap1->n_div || bmap2->n_div)
1997 return 0;
1998 if (!bmap1->n_eq && !bmap2->n_eq)
1999 return 0;
2000
2001 total = isl_space_dim(bmap1->dim, isl_dim_all);
2002 if (total == 0)
2003 return 0;
2004 v = isl_vec_alloc(bmap1->ctx, 1 + total);
2005 if (!v)
2006 goto error;
2007 elim = isl_alloc_array(bmap1->ctx, int, total);
2008 if (!elim)
2009 goto error;
2010 compute_elimination_index(bmap1, elim);
2011 for (i = 0; i < bmap2->n_eq; ++i) {
2012 int reduced;
2013 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
2014 bmap1, elim);
2015 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
2016 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2017 goto disjoint;
2018 }
2019 for (i = 0; i < bmap2->n_ineq; ++i) {
2020 int reduced;
2021 reduced = reduced_using_equalities(v->block.data,
2022 bmap2->ineq[i], bmap1, elim);
2023 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2024 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2025 goto disjoint;
2026 }
2027 compute_elimination_index(bmap2, elim);
2028 for (i = 0; i < bmap1->n_ineq; ++i) {
2029 int reduced;
2030 reduced = reduced_using_equalities(v->block.data,
2031 bmap1->ineq[i], bmap2, elim);
2032 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2033 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2034 goto disjoint;
2035 }
2036 isl_vec_free(v);
2037 free(elim);
2038 return 0;
2039 disjoint:
2040 isl_vec_free(v);
2041 free(elim);
2042 return 1;
2043 error:
2044 isl_vec_free(v);
2045 free(elim);
2046 return -1;
2047 }
2048
2049 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
2050 __isl_keep isl_basic_set *bset2)
2051 {
2052 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2053 (struct isl_basic_map *)bset2);
2054 }
2055
2056 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2057 __isl_keep isl_map *map2)
2058 {
2059 int i, j;
2060
2061 if (!map1 || !map2)
2062 return -1;
2063
2064 if (isl_map_plain_is_equal(map1, map2))
2065 return 0;
2066
2067 for (i = 0; i < map1->n; ++i) {
2068 for (j = 0; j < map2->n; ++j) {
2069 int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2070 map2->p[j]);
2071 if (d != 1)
2072 return d;
2073 }
2074 }
2075 return 1;
2076 }
2077
2078 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2079 __isl_keep isl_set *set2)
2080 {
2081 return isl_map_plain_is_disjoint((struct isl_map *)set1,
2082 (struct isl_map *)set2);
2083 }
2084
2085 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2086 {
2087 return isl_set_plain_is_disjoint(set1, set2);
2088 }
2089
2090 /* Check if we can combine a given div with lower bound l and upper
2091 * bound u with some other div and if so return that other div.
2092 * Otherwise return -1.
2093 *
2094 * We first check that
2095 * - the bounds are opposites of each other (except for the constant
2096 * term)
2097 * - the bounds do not reference any other div
2098 * - no div is defined in terms of this div
2099 *
2100 * Let m be the size of the range allowed on the div by the bounds.
2101 * That is, the bounds are of the form
2102 *
2103 * e <= a <= e + m - 1
2104 *
2105 * with e some expression in the other variables.
2106 * We look for another div b such that no third div is defined in terms
2107 * of this second div b and such that in any constraint that contains
2108 * a (except for the given lower and upper bound), also contains b
2109 * with a coefficient that is m times that of b.
2110 * That is, all constraints (execpt for the lower and upper bound)
2111 * are of the form
2112 *
2113 * e + f (a + m b) >= 0
2114 *
2115 * If so, we return b so that "a + m b" can be replaced by
2116 * a single div "c = a + m b".
2117 */
2118 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2119 unsigned div, unsigned l, unsigned u)
2120 {
2121 int i, j;
2122 unsigned dim;
2123 int coalesce = -1;
2124
2125 if (bmap->n_div <= 1)
2126 return -1;
2127 dim = isl_space_dim(bmap->dim, isl_dim_all);
2128 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2129 return -1;
2130 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2131 bmap->n_div - div - 1) != -1)
2132 return -1;
2133 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2134 dim + bmap->n_div))
2135 return -1;
2136
2137 for (i = 0; i < bmap->n_div; ++i) {
2138 if (isl_int_is_zero(bmap->div[i][0]))
2139 continue;
2140 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2141 return -1;
2142 }
2143
2144 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2145 if (isl_int_is_neg(bmap->ineq[l][0])) {
2146 isl_int_sub(bmap->ineq[l][0],
2147 bmap->ineq[l][0], bmap->ineq[u][0]);
2148 bmap = isl_basic_map_copy(bmap);
2149 bmap = isl_basic_map_set_to_empty(bmap);
2150 isl_basic_map_free(bmap);
2151 return -1;
2152 }
2153 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2154 for (i = 0; i < bmap->n_div; ++i) {
2155 if (i == div)
2156 continue;
2157 if (!pairs[i])
2158 continue;
2159 for (j = 0; j < bmap->n_div; ++j) {
2160 if (isl_int_is_zero(bmap->div[j][0]))
2161 continue;
2162 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2163 break;
2164 }
2165 if (j < bmap->n_div)
2166 continue;
2167 for (j = 0; j < bmap->n_ineq; ++j) {
2168 int valid;
2169 if (j == l || j == u)
2170 continue;
2171 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2172 continue;
2173 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2174 break;
2175 isl_int_mul(bmap->ineq[j][1 + dim + div],
2176 bmap->ineq[j][1 + dim + div],
2177 bmap->ineq[l][0]);
2178 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2179 bmap->ineq[j][1 + dim + i]);
2180 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2181 bmap->ineq[j][1 + dim + div],
2182 bmap->ineq[l][0]);
2183 if (!valid)
2184 break;
2185 }
2186 if (j < bmap->n_ineq)
2187 continue;
2188 coalesce = i;
2189 break;
2190 }
2191 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2192 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2193 return coalesce;
2194 }
2195
2196 /* Given a lower and an upper bound on div i, construct an inequality
2197 * that when nonnegative ensures that this pair of bounds always allows
2198 * for an integer value of the given div.
2199 * The lower bound is inequality l, while the upper bound is inequality u.
2200 * The constructed inequality is stored in ineq.
2201 * g, fl, fu are temporary scalars.
2202 *
2203 * Let the upper bound be
2204 *
2205 * -n_u a + e_u >= 0
2206 *
2207 * and the lower bound
2208 *
2209 * n_l a + e_l >= 0
2210 *
2211 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2212 * We have
2213 *
2214 * - f_u e_l <= f_u f_l g a <= f_l e_u
2215 *
2216 * Since all variables are integer valued, this is equivalent to
2217 *
2218 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2219 *
2220 * If this interval is at least f_u f_l g, then it contains at least
2221 * one integer value for a.
2222 * That is, the test constraint is
2223 *
2224 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2225 */
2226 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2227 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2228 {
2229 unsigned dim;
2230 dim = isl_space_dim(bmap->dim, isl_dim_all);
2231
2232 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2233 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2234 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2235 isl_int_neg(fu, fu);
2236 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2237 1 + dim + bmap->n_div);
2238 isl_int_add(ineq[0], ineq[0], fl);
2239 isl_int_add(ineq[0], ineq[0], fu);
2240 isl_int_sub_ui(ineq[0], ineq[0], 1);
2241 isl_int_mul(g, g, fl);
2242 isl_int_mul(g, g, fu);
2243 isl_int_sub(ineq[0], ineq[0], g);
2244 }
2245
2246 /* Remove more kinds of divs that are not strictly needed.
2247 * In particular, if all pairs of lower and upper bounds on a div
2248 * are such that they allow at least one integer value of the div,
2249 * the we can eliminate the div using Fourier-Motzkin without
2250 * introducing any spurious solutions.
2251 */
2252 static struct isl_basic_map *drop_more_redundant_divs(
2253 struct isl_basic_map *bmap, int *pairs, int n)
2254 {
2255 struct isl_tab *tab = NULL;
2256 struct isl_vec *vec = NULL;
2257 unsigned dim;
2258 int remove = -1;
2259 isl_int g, fl, fu;
2260
2261 isl_int_init(g);
2262 isl_int_init(fl);
2263 isl_int_init(fu);
2264
2265 if (!bmap)
2266 goto error;
2267
2268 dim = isl_space_dim(bmap->dim, isl_dim_all);
2269 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2270 if (!vec)
2271 goto error;
2272
2273 tab = isl_tab_from_basic_map(bmap, 0);
2274
2275 while (n > 0) {
2276 int i, l, u;
2277 int best = -1;
2278 enum isl_lp_result res;
2279
2280 for (i = 0; i < bmap->n_div; ++i) {
2281 if (!pairs[i])
2282 continue;
2283 if (best >= 0 && pairs[best] <= pairs[i])
2284 continue;
2285 best = i;
2286 }
2287
2288 i = best;
2289 for (l = 0; l < bmap->n_ineq; ++l) {
2290 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2291 continue;
2292 for (u = 0; u < bmap->n_ineq; ++u) {
2293 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2294 continue;
2295 construct_test_ineq(bmap, i, l, u,
2296 vec->el, g, fl, fu);
2297 res = isl_tab_min(tab, vec->el,
2298 bmap->ctx->one, &g, NULL, 0);
2299 if (res == isl_lp_error)
2300 goto error;
2301 if (res == isl_lp_empty) {
2302 bmap = isl_basic_map_set_to_empty(bmap);
2303 break;
2304 }
2305 if (res != isl_lp_ok || isl_int_is_neg(g))
2306 break;
2307 }
2308 if (u < bmap->n_ineq)
2309 break;
2310 }
2311 if (l == bmap->n_ineq) {
2312 remove = i;
2313 break;
2314 }
2315 pairs[i] = 0;
2316 --n;
2317 }
2318
2319 isl_tab_free(tab);
2320 isl_vec_free(vec);
2321
2322 isl_int_clear(g);
2323 isl_int_clear(fl);
2324 isl_int_clear(fu);
2325
2326 free(pairs);
2327
2328 if (remove < 0)
2329 return bmap;
2330
2331 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2332 return isl_basic_map_drop_redundant_divs(bmap);
2333 error:
2334 free(pairs);
2335 isl_basic_map_free(bmap);
2336 isl_tab_free(tab);
2337 isl_vec_free(vec);
2338 isl_int_clear(g);
2339 isl_int_clear(fl);
2340 isl_int_clear(fu);
2341 return NULL;
2342 }
2343
2344 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2345 * and the upper bound u, div1 always occurs together with div2 in the form
2346 * (div1 + m div2), where m is the constant range on the variable div1
2347 * allowed by l and u, replace the pair div1 and div2 by a single
2348 * div that is equal to div1 + m div2.
2349 *
2350 * The new div will appear in the location that contains div2.
2351 * We need to modify all constraints that contain
2352 * div2 = (div - div1) / m
2353 * (If a constraint does not contain div2, it will also not contain div1.)
2354 * If the constraint also contains div1, then we know they appear
2355 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2356 * i.e., the coefficient of div is f.
2357 *
2358 * Otherwise, we first need to introduce div1 into the constraint.
2359 * Let the l be
2360 *
2361 * div1 + f >=0
2362 *
2363 * and u
2364 *
2365 * -div1 + f' >= 0
2366 *
2367 * A lower bound on div2
2368 *
2369 * n div2 + t >= 0
2370 *
2371 * can be replaced by
2372 *
2373 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2374 *
2375 * with g = gcd(m,n).
2376 * An upper bound
2377 *
2378 * -n div2 + t >= 0
2379 *
2380 * can be replaced by
2381 *
2382 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2383 *
2384 * These constraint are those that we would obtain from eliminating
2385 * div1 using Fourier-Motzkin.
2386 *
2387 * After all constraints have been modified, we drop the lower and upper
2388 * bound and then drop div1.
2389 */
2390 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2391 unsigned div1, unsigned div2, unsigned l, unsigned u)
2392 {
2393 isl_int a;
2394 isl_int b;
2395 isl_int m;
2396 unsigned dim, total;
2397 int i;
2398
2399 dim = isl_space_dim(bmap->dim, isl_dim_all);
2400 total = 1 + dim + bmap->n_div;
2401
2402 isl_int_init(a);
2403 isl_int_init(b);
2404 isl_int_init(m);
2405 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2406 isl_int_add_ui(m, m, 1);
2407
2408 for (i = 0; i < bmap->n_ineq; ++i) {
2409 if (i == l || i == u)
2410 continue;
2411 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2412 continue;
2413 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2414 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2415 isl_int_divexact(a, m, b);
2416 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2417 if (isl_int_is_pos(b)) {
2418 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2419 b, bmap->ineq[l], total);
2420 } else {
2421 isl_int_neg(b, b);
2422 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2423 b, bmap->ineq[u], total);
2424 }
2425 }
2426 isl_int_set(bmap->ineq[i][1 + dim + div2],
2427 bmap->ineq[i][1 + dim + div1]);
2428 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2429 }
2430
2431 isl_int_clear(a);
2432 isl_int_clear(b);
2433 isl_int_clear(m);
2434 if (l > u) {
2435 isl_basic_map_drop_inequality(bmap, l);
2436 isl_basic_map_drop_inequality(bmap, u);
2437 } else {
2438 isl_basic_map_drop_inequality(bmap, u);
2439 isl_basic_map_drop_inequality(bmap, l);
2440 }
2441 bmap = isl_basic_map_drop_div(bmap, div1);
2442 return bmap;
2443 }
2444
2445 /* First check if we can coalesce any pair of divs and
2446 * then continue with dropping more redundant divs.
2447 *
2448 * We loop over all pairs of lower and upper bounds on a div
2449 * with coefficient 1 and -1, respectively, check if there
2450 * is any other div "c" with which we can coalesce the div
2451 * and if so, perform the coalescing.
2452 */
2453 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2454 struct isl_basic_map *bmap, int *pairs, int n)
2455 {
2456 int i, l, u;
2457 unsigned dim;
2458
2459 dim = isl_space_dim(bmap->dim, isl_dim_all);
2460
2461 for (i = 0; i < bmap->n_div; ++i) {
2462 if (!pairs[i])
2463 continue;
2464 for (l = 0; l < bmap->n_ineq; ++l) {
2465 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2466 continue;
2467 for (u = 0; u < bmap->n_ineq; ++u) {
2468 int c;
2469
2470 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2471 continue;
2472 c = div_find_coalesce(bmap, pairs, i, l, u);
2473 if (c < 0)
2474 continue;
2475 free(pairs);
2476 bmap = coalesce_divs(bmap, i, c, l, u);
2477 return isl_basic_map_drop_redundant_divs(bmap);
2478 }
2479 }
2480 }
2481
2482 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2483 return bmap;
2484
2485 return drop_more_redundant_divs(bmap, pairs, n);
2486 }
2487
2488 /* Remove divs that are not strictly needed.
2489 * In particular, if a div only occurs positively (or negatively)
2490 * in constraints, then it can simply be dropped.
2491 * Also, if a div occurs only occurs in two constraints and if moreover
2492 * those two constraints are opposite to each other, except for the constant
2493 * term and if the sum of the constant terms is such that for any value
2494 * of the other values, there is always at least one integer value of the
2495 * div, i.e., if one plus this sum is greater than or equal to
2496 * the (absolute value) of the coefficent of the div in the constraints,
2497 * then we can also simply drop the div.
2498 *
2499 * If any divs are left after these simple checks then we move on
2500 * to more complicated cases in drop_more_redundant_divs.
2501 */
2502 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2503 struct isl_basic_map *bmap)
2504 {
2505 int i, j;
2506 unsigned off;
2507 int *pairs = NULL;
2508 int n = 0;
2509
2510 if (!bmap)
2511 goto error;
2512
2513 off = isl_space_dim(bmap->dim, isl_dim_all);
2514 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2515 if (!pairs)
2516 goto error;
2517
2518 for (i = 0; i < bmap->n_div; ++i) {
2519 int pos, neg;
2520 int last_pos, last_neg;
2521 int redundant;
2522 int defined;
2523
2524 defined = !isl_int_is_zero(bmap->div[i][0]);
2525 for (j = 0; j < bmap->n_eq; ++j)
2526 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2527 break;
2528 if (j < bmap->n_eq)
2529 continue;
2530 ++n;
2531 pos = neg = 0;
2532 for (j = 0; j < bmap->n_ineq; ++j) {
2533 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2534 last_pos = j;
2535 ++pos;
2536 }
2537 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2538 last_neg = j;
2539 ++neg;
2540 }
2541 }
2542 pairs[i] = pos * neg;
2543 if (pairs[i] == 0) {
2544 for (j = bmap->n_ineq - 1; j >= 0; --j)
2545 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2546 isl_basic_map_drop_inequality(bmap, j);
2547 bmap = isl_basic_map_drop_div(bmap, i);
2548 free(pairs);
2549 return isl_basic_map_drop_redundant_divs(bmap);
2550 }
2551 if (pairs[i] != 1)
2552 continue;
2553 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2554 bmap->ineq[last_neg] + 1,
2555 off + bmap->n_div))
2556 continue;
2557
2558 isl_int_add(bmap->ineq[last_pos][0],
2559 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2560 isl_int_add_ui(bmap->ineq[last_pos][0],
2561 bmap->ineq[last_pos][0], 1);
2562 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2563 bmap->ineq[last_pos][1+off+i]);
2564 isl_int_sub_ui(bmap->ineq[last_pos][0],
2565 bmap->ineq[last_pos][0], 1);
2566 isl_int_sub(bmap->ineq[last_pos][0],
2567 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2568 if (!redundant) {
2569 if (defined ||
2570 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2571 pairs[i] = 0;
2572 --n;
2573 continue;
2574 }
2575 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2576 bmap = isl_basic_map_simplify(bmap);
2577 free(pairs);
2578 return isl_basic_map_drop_redundant_divs(bmap);
2579 }
2580 if (last_pos > last_neg) {
2581 isl_basic_map_drop_inequality(bmap, last_pos);
2582 isl_basic_map_drop_inequality(bmap, last_neg);
2583 } else {
2584 isl_basic_map_drop_inequality(bmap, last_neg);
2585 isl_basic_map_drop_inequality(bmap, last_pos);
2586 }
2587 bmap = isl_basic_map_drop_div(bmap, i);
2588 free(pairs);
2589 return isl_basic_map_drop_redundant_divs(bmap);
2590 }
2591
2592 if (n > 0)
2593 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2594
2595 free(pairs);
2596 return bmap;
2597 error:
2598 free(pairs);
2599 isl_basic_map_free(bmap);
2600 return NULL;
2601 }
2602
2603 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2604 struct isl_basic_set *bset)
2605 {
2606 return (struct isl_basic_set *)
2607 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2608 }
2609
2610 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2611 {
2612 int i;
2613
2614 if (!map)
2615 return NULL;
2616 for (i = 0; i < map->n; ++i) {
2617 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2618 if (!map->p[i])
2619 goto error;
2620 }
2621 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2622 return map;
2623 error:
2624 isl_map_free(map);
2625 return NULL;
2626 }
2627
2628 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2629 {
2630 return (struct isl_set *)
2631 isl_map_drop_redundant_divs((struct isl_map *)set);
2632 }
Integer set library