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add isl_union_map_intersect_params
[isl.git] / isl_map_simplify.c
blobeafbb083171892a4a571492cbfa602bfb1177a98
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include <strings.h>
11 #include <isl_ctx_private.h>
12 #include <isl_map_private.h>
13 #include "isl_equalities.h"
14 #include <isl/map.h>
15 #include <isl/seq.h>
16 #include "isl_tab.h"
17 #include <isl_space_private.h>
18 #include <isl_mat_private.h>
19
20 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
21 {
22 isl_int *t = bmap->eq[a];
23 bmap->eq[a] = bmap->eq[b];
24 bmap->eq[b] = t;
25 }
26
27 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
28 {
29 if (a != b) {
30 isl_int *t = bmap->ineq[a];
31 bmap->ineq[a] = bmap->ineq[b];
32 bmap->ineq[b] = t;
33 }
34 }
35
36 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
37 {
38 isl_seq_cpy(c, c + n, rem);
39 isl_seq_clr(c + rem, n);
40 }
41
42 /* Drop n dimensions starting at first.
43 *
44 * In principle, this frees up some extra variables as the number
45 * of columns remains constant, but we would have to extend
46 * the div array too as the number of rows in this array is assumed
47 * to be equal to extra.
48 */
49 struct isl_basic_set *isl_basic_set_drop_dims(
50 struct isl_basic_set *bset, unsigned first, unsigned n)
51 {
52 int i;
53
54 if (!bset)
55 goto error;
56
57 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
58
59 if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
60 return bset;
61
62 bset = isl_basic_set_cow(bset);
63 if (!bset)
64 return NULL;
65
66 for (i = 0; i < bset->n_eq; ++i)
67 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
68 (bset->dim->n_out-first-n)+bset->extra);
69
70 for (i = 0; i < bset->n_ineq; ++i)
71 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
72 (bset->dim->n_out-first-n)+bset->extra);
73
74 for (i = 0; i < bset->n_div; ++i)
75 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
76 (bset->dim->n_out-first-n)+bset->extra);
77
78 bset->dim = isl_space_drop_outputs(bset->dim, first, n);
79 if (!bset->dim)
80 goto error;
81
82 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
83 bset = isl_basic_set_simplify(bset);
84 return isl_basic_set_finalize(bset);
85 error:
86 isl_basic_set_free(bset);
87 return NULL;
88 }
89
90 struct isl_set *isl_set_drop_dims(
91 struct isl_set *set, unsigned first, unsigned n)
92 {
93 int i;
94
95 if (!set)
96 goto error;
97
98 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
99
100 if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
101 return set;
102 set = isl_set_cow(set);
103 if (!set)
104 goto error;
105 set->dim = isl_space_drop_outputs(set->dim, first, n);
106 if (!set->dim)
107 goto error;
108
109 for (i = 0; i < set->n; ++i) {
110 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
111 if (!set->p[i])
112 goto error;
113 }
114
115 ISL_F_CLR(set, ISL_SET_NORMALIZED);
116 return set;
117 error:
118 isl_set_free(set);
119 return NULL;
120 }
121
122 /* Move "n" divs starting at "first" to the end of the list of divs.
123 */
124 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
125 unsigned first, unsigned n)
126 {
127 isl_int **div;
128 int i;
129
130 if (first + n == bmap->n_div)
131 return bmap;
132
133 div = isl_alloc_array(bmap->ctx, isl_int *, n);
134 if (!div)
135 goto error;
136 for (i = 0; i < n; ++i)
137 div[i] = bmap->div[first + i];
138 for (i = 0; i < bmap->n_div - first - n; ++i)
139 bmap->div[first + i] = bmap->div[first + n + i];
140 for (i = 0; i < n; ++i)
141 bmap->div[bmap->n_div - n + i] = div[i];
142 free(div);
143 return bmap;
144 error:
145 isl_basic_map_free(bmap);
146 return NULL;
147 }
148
149 /* Drop "n" dimensions of type "type" starting at "first".
150 *
151 * In principle, this frees up some extra variables as the number
152 * of columns remains constant, but we would have to extend
153 * the div array too as the number of rows in this array is assumed
154 * to be equal to extra.
155 */
156 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
157 enum isl_dim_type type, unsigned first, unsigned n)
158 {
159 int i;
160 unsigned dim;
161 unsigned offset;
162 unsigned left;
163
164 if (!bmap)
165 goto error;
166
167 dim = isl_basic_map_dim(bmap, type);
168 isl_assert(bmap->ctx, first + n <= dim, goto error);
169
170 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
171 return bmap;
172
173 bmap = isl_basic_map_cow(bmap);
174 if (!bmap)
175 return NULL;
176
177 offset = isl_basic_map_offset(bmap, type) + first;
178 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
179 for (i = 0; i < bmap->n_eq; ++i)
180 constraint_drop_vars(bmap->eq[i]+offset, n, left);
181
182 for (i = 0; i < bmap->n_ineq; ++i)
183 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
184
185 for (i = 0; i < bmap->n_div; ++i)
186 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
187
188 if (type == isl_dim_div) {
189 bmap = move_divs_last(bmap, first, n);
190 if (!bmap)
191 goto error;
192 isl_basic_map_free_div(bmap, n);
193 } else
194 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
195 if (!bmap->dim)
196 goto error;
197
198 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
199 bmap = isl_basic_map_simplify(bmap);
200 return isl_basic_map_finalize(bmap);
201 error:
202 isl_basic_map_free(bmap);
203 return NULL;
204 }
205
206 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
207 enum isl_dim_type type, unsigned first, unsigned n)
208 {
209 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
210 type, first, n);
211 }
212
213 struct isl_basic_map *isl_basic_map_drop_inputs(
214 struct isl_basic_map *bmap, unsigned first, unsigned n)
215 {
216 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
217 }
218
219 struct isl_map *isl_map_drop(struct isl_map *map,
220 enum isl_dim_type type, unsigned first, unsigned n)
221 {
222 int i;
223
224 if (!map)
225 goto error;
226
227 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
228
229 if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
230 return map;
231 map = isl_map_cow(map);
232 if (!map)
233 goto error;
234 map->dim = isl_space_drop_dims(map->dim, type, first, n);
235 if (!map->dim)
236 goto error;
237
238 for (i = 0; i < map->n; ++i) {
239 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
240 if (!map->p[i])
241 goto error;
242 }
243 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
244
245 return map;
246 error:
247 isl_map_free(map);
248 return NULL;
249 }
250
251 struct isl_set *isl_set_drop(struct isl_set *set,
252 enum isl_dim_type type, unsigned first, unsigned n)
253 {
254 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
255 }
256
257 struct isl_map *isl_map_drop_inputs(
258 struct isl_map *map, unsigned first, unsigned n)
259 {
260 return isl_map_drop(map, isl_dim_in, first, n);
261 }
262
263 /*
264 * We don't cow, as the div is assumed to be redundant.
265 */
266 static struct isl_basic_map *isl_basic_map_drop_div(
267 struct isl_basic_map *bmap, unsigned div)
268 {
269 int i;
270 unsigned pos;
271
272 if (!bmap)
273 goto error;
274
275 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
276
277 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
278
279 for (i = 0; i < bmap->n_eq; ++i)
280 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
281
282 for (i = 0; i < bmap->n_ineq; ++i) {
283 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
284 isl_basic_map_drop_inequality(bmap, i);
285 --i;
286 continue;
287 }
288 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
289 }
290
291 for (i = 0; i < bmap->n_div; ++i)
292 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
293
294 if (div != bmap->n_div - 1) {
295 int j;
296 isl_int *t = bmap->div[div];
297
298 for (j = div; j < bmap->n_div - 1; ++j)
299 bmap->div[j] = bmap->div[j+1];
300
301 bmap->div[bmap->n_div - 1] = t;
302 }
303 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
304 isl_basic_map_free_div(bmap, 1);
305
306 return bmap;
307 error:
308 isl_basic_map_free(bmap);
309 return NULL;
310 }
311
312 struct isl_basic_map *isl_basic_map_normalize_constraints(
313 struct isl_basic_map *bmap)
314 {
315 int i;
316 isl_int gcd;
317 unsigned total = isl_basic_map_total_dim(bmap);
318
319 if (!bmap)
320 return NULL;
321
322 isl_int_init(gcd);
323 for (i = bmap->n_eq - 1; i >= 0; --i) {
324 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
325 if (isl_int_is_zero(gcd)) {
326 if (!isl_int_is_zero(bmap->eq[i][0])) {
327 bmap = isl_basic_map_set_to_empty(bmap);
328 break;
329 }
330 isl_basic_map_drop_equality(bmap, i);
331 continue;
332 }
333 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
334 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
335 if (isl_int_is_one(gcd))
336 continue;
337 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
338 bmap = isl_basic_map_set_to_empty(bmap);
339 break;
340 }
341 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
342 }
343
344 for (i = bmap->n_ineq - 1; i >= 0; --i) {
345 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
346 if (isl_int_is_zero(gcd)) {
347 if (isl_int_is_neg(bmap->ineq[i][0])) {
348 bmap = isl_basic_map_set_to_empty(bmap);
349 break;
350 }
351 isl_basic_map_drop_inequality(bmap, i);
352 continue;
353 }
354 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
355 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
356 if (isl_int_is_one(gcd))
357 continue;
358 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
359 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
360 }
361 isl_int_clear(gcd);
362
363 return bmap;
364 }
365
366 struct isl_basic_set *isl_basic_set_normalize_constraints(
367 struct isl_basic_set *bset)
368 {
369 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
370 (struct isl_basic_map *)bset);
371 }
372
373 /* Assumes divs have been ordered if keep_divs is set.
374 */
375 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
376 unsigned pos, isl_int *eq, int keep_divs, int *progress)
377 {
378 unsigned total;
379 unsigned space_total;
380 int k;
381 int last_div;
382
383 total = isl_basic_map_total_dim(bmap);
384 space_total = isl_space_dim(bmap->dim, isl_dim_all);
385 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
386 for (k = 0; k < bmap->n_eq; ++k) {
387 if (bmap->eq[k] == eq)
388 continue;
389 if (isl_int_is_zero(bmap->eq[k][1+pos]))
390 continue;
391 if (progress)
392 *progress = 1;
393 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
394 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
395 }
396
397 for (k = 0; k < bmap->n_ineq; ++k) {
398 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
399 continue;
400 if (progress)
401 *progress = 1;
402 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
403 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
404 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
405 }
406
407 for (k = 0; k < bmap->n_div; ++k) {
408 if (isl_int_is_zero(bmap->div[k][0]))
409 continue;
410 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
411 continue;
412 if (progress)
413 *progress = 1;
414 /* We need to be careful about circular definitions,
415 * so for now we just remove the definition of div k
416 * if the equality contains any divs.
417 * If keep_divs is set, then the divs have been ordered
418 * and we can keep the definition as long as the result
419 * is still ordered.
420 */
421 if (last_div == -1 || (keep_divs && last_div < k))
422 isl_seq_elim(bmap->div[k]+1, eq,
423 1+pos, 1+total, &bmap->div[k][0]);
424 else
425 isl_seq_clr(bmap->div[k], 1 + total);
426 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
427 }
428 }
429
430 /* Assumes divs have been ordered if keep_divs is set.
431 */
432 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
433 unsigned div, int keep_divs)
434 {
435 unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
436
437 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
438
439 isl_basic_map_drop_div(bmap, div);
440 }
441
442 /* Check if elimination of div "div" using equality "eq" would not
443 * result in a div depending on a later div.
444 */
445 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
446 unsigned div)
447 {
448 int k;
449 int last_div;
450 unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
451 unsigned pos = space_total + div;
452
453 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
454 if (last_div < 0 || last_div <= div)
455 return 1;
456
457 for (k = 0; k <= last_div; ++k) {
458 if (isl_int_is_zero(bmap->div[k][0]))
459 return 1;
460 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
461 return 0;
462 }
463
464 return 1;
465 }
466
467 /* Elimininate divs based on equalities
468 */
469 static struct isl_basic_map *eliminate_divs_eq(
470 struct isl_basic_map *bmap, int *progress)
471 {
472 int d;
473 int i;
474 int modified = 0;
475 unsigned off;
476
477 bmap = isl_basic_map_order_divs(bmap);
478
479 if (!bmap)
480 return NULL;
481
482 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
483
484 for (d = bmap->n_div - 1; d >= 0 ; --d) {
485 for (i = 0; i < bmap->n_eq; ++i) {
486 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
487 !isl_int_is_negone(bmap->eq[i][off + d]))
488 continue;
489 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
490 continue;
491 modified = 1;
492 *progress = 1;
493 eliminate_div(bmap, bmap->eq[i], d, 1);
494 isl_basic_map_drop_equality(bmap, i);
495 break;
496 }
497 }
498 if (modified)
499 return eliminate_divs_eq(bmap, progress);
500 return bmap;
501 }
502
503 /* Elimininate divs based on inequalities
504 */
505 static struct isl_basic_map *eliminate_divs_ineq(
506 struct isl_basic_map *bmap, int *progress)
507 {
508 int d;
509 int i;
510 unsigned off;
511 struct isl_ctx *ctx;
512
513 if (!bmap)
514 return NULL;
515
516 ctx = bmap->ctx;
517 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
518
519 for (d = bmap->n_div - 1; d >= 0 ; --d) {
520 for (i = 0; i < bmap->n_eq; ++i)
521 if (!isl_int_is_zero(bmap->eq[i][off + d]))
522 break;
523 if (i < bmap->n_eq)
524 continue;
525 for (i = 0; i < bmap->n_ineq; ++i)
526 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
527 break;
528 if (i < bmap->n_ineq)
529 continue;
530 *progress = 1;
531 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
532 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
533 break;
534 bmap = isl_basic_map_drop_div(bmap, d);
535 if (!bmap)
536 break;
537 }
538 return bmap;
539 }
540
541 struct isl_basic_map *isl_basic_map_gauss(
542 struct isl_basic_map *bmap, int *progress)
543 {
544 int k;
545 int done;
546 int last_var;
547 unsigned total_var;
548 unsigned total;
549
550 bmap = isl_basic_map_order_divs(bmap);
551
552 if (!bmap)
553 return NULL;
554
555 total = isl_basic_map_total_dim(bmap);
556 total_var = total - bmap->n_div;
557
558 last_var = total - 1;
559 for (done = 0; done < bmap->n_eq; ++done) {
560 for (; last_var >= 0; --last_var) {
561 for (k = done; k < bmap->n_eq; ++k)
562 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
563 break;
564 if (k < bmap->n_eq)
565 break;
566 }
567 if (last_var < 0)
568 break;
569 if (k != done)
570 swap_equality(bmap, k, done);
571 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
572 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
573
574 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
575 progress);
576
577 if (last_var >= total_var &&
578 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
579 unsigned div = last_var - total_var;
580 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
581 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
582 isl_int_set(bmap->div[div][0],
583 bmap->eq[done][1+last_var]);
584 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
585 }
586 }
587 if (done == bmap->n_eq)
588 return bmap;
589 for (k = done; k < bmap->n_eq; ++k) {
590 if (isl_int_is_zero(bmap->eq[k][0]))
591 continue;
592 return isl_basic_map_set_to_empty(bmap);
593 }
594 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
595 return bmap;
596 }
597
598 struct isl_basic_set *isl_basic_set_gauss(
599 struct isl_basic_set *bset, int *progress)
600 {
601 return (struct isl_basic_set*)isl_basic_map_gauss(
602 (struct isl_basic_map *)bset, progress);
603 }
604
605
606 static unsigned int round_up(unsigned int v)
607 {
608 int old_v = v;
609
610 while (v) {
611 old_v = v;
612 v ^= v & -v;
613 }
614 return old_v << 1;
615 }
616
617 static int hash_index(isl_int ***index, unsigned int size, int bits,
618 struct isl_basic_map *bmap, int k)
619 {
620 int h;
621 unsigned total = isl_basic_map_total_dim(bmap);
622 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
623 for (h = hash; index[h]; h = (h+1) % size)
624 if (&bmap->ineq[k] != index[h] &&
625 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
626 break;
627 return h;
628 }
629
630 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
631 struct isl_basic_set *bset, int k)
632 {
633 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
634 }
635
636 /* If we can eliminate more than one div, then we need to make
637 * sure we do it from last div to first div, in order not to
638 * change the position of the other divs that still need to
639 * be removed.
640 */
641 static struct isl_basic_map *remove_duplicate_divs(
642 struct isl_basic_map *bmap, int *progress)
643 {
644 unsigned int size;
645 int *index;
646 int *elim_for;
647 int k, l, h;
648 int bits;
649 struct isl_blk eq;
650 unsigned total_var;
651 unsigned total;
652 struct isl_ctx *ctx;
653
654 if (!bmap || bmap->n_div <= 1)
655 return bmap;
656
657 total_var = isl_space_dim(bmap->dim, isl_dim_all);
658 total = total_var + bmap->n_div;
659
660 ctx = bmap->ctx;
661 for (k = bmap->n_div - 1; k >= 0; --k)
662 if (!isl_int_is_zero(bmap->div[k][0]))
663 break;
664 if (k <= 0)
665 return bmap;
666
667 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
668 size = round_up(4 * bmap->n_div / 3 - 1);
669 bits = ffs(size) - 1;
670 index = isl_calloc_array(ctx, int, size);
671 if (!index)
672 return bmap;
673 eq = isl_blk_alloc(ctx, 1+total);
674 if (isl_blk_is_error(eq))
675 goto out;
676
677 isl_seq_clr(eq.data, 1+total);
678 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
679 for (--k; k >= 0; --k) {
680 uint32_t hash;
681
682 if (isl_int_is_zero(bmap->div[k][0]))
683 continue;
684
685 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
686 for (h = hash; index[h]; h = (h+1) % size)
687 if (isl_seq_eq(bmap->div[k],
688 bmap->div[index[h]-1], 2+total))
689 break;
690 if (index[h]) {
691 *progress = 1;
692 l = index[h] - 1;
693 elim_for[l] = k + 1;
694 }
695 index[h] = k+1;
696 }
697 for (l = bmap->n_div - 1; l >= 0; --l) {
698 if (!elim_for[l])
699 continue;
700 k = elim_for[l] - 1;
701 isl_int_set_si(eq.data[1+total_var+k], -1);
702 isl_int_set_si(eq.data[1+total_var+l], 1);
703 eliminate_div(bmap, eq.data, l, 0);
704 isl_int_set_si(eq.data[1+total_var+k], 0);
705 isl_int_set_si(eq.data[1+total_var+l], 0);
706 }
707
708 isl_blk_free(ctx, eq);
709 out:
710 free(index);
711 free(elim_for);
712 return bmap;
713 }
714
715 static int n_pure_div_eq(struct isl_basic_map *bmap)
716 {
717 int i, j;
718 unsigned total;
719
720 total = isl_space_dim(bmap->dim, isl_dim_all);
721 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
722 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
723 --j;
724 if (j < 0)
725 break;
726 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
727 return 0;
728 }
729 return i;
730 }
731
732 /* Normalize divs that appear in equalities.
733 *
734 * In particular, we assume that bmap contains some equalities
735 * of the form
736 *
737 * a x = m * e_i
738 *
739 * and we want to replace the set of e_i by a minimal set and
740 * such that the new e_i have a canonical representation in terms
741 * of the vector x.
742 * If any of the equalities involves more than one divs, then
743 * we currently simply bail out.
744 *
745 * Let us first additionally assume that all equalities involve
746 * a div. The equalities then express modulo constraints on the
747 * remaining variables and we can use "parameter compression"
748 * to find a minimal set of constraints. The result is a transformation
749 *
750 * x = T(x') = x_0 + G x'
751 *
752 * with G a lower-triangular matrix with all elements below the diagonal
753 * non-negative and smaller than the diagonal element on the same row.
754 * We first normalize x_0 by making the same property hold in the affine
755 * T matrix.
756 * The rows i of G with a 1 on the diagonal do not impose any modulo
757 * constraint and simply express x_i = x'_i.
758 * For each of the remaining rows i, we introduce a div and a corresponding
759 * equality. In particular
760 *
761 * g_ii e_j = x_i - g_i(x')
762 *
763 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
764 * corresponding div (if g_kk != 1).
765 *
766 * If there are any equalities not involving any div, then we
767 * first apply a variable compression on the variables x:
768 *
769 * x = C x'' x'' = C_2 x
770 *
771 * and perform the above parameter compression on A C instead of on A.
772 * The resulting compression is then of the form
773 *
774 * x'' = T(x') = x_0 + G x'
775 *
776 * and in constructing the new divs and the corresponding equalities,
777 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
778 * by the corresponding row from C_2.
779 */
780 static struct isl_basic_map *normalize_divs(
781 struct isl_basic_map *bmap, int *progress)
782 {
783 int i, j, k;
784 int total;
785 int div_eq;
786 struct isl_mat *B;
787 struct isl_vec *d;
788 struct isl_mat *T = NULL;
789 struct isl_mat *C = NULL;
790 struct isl_mat *C2 = NULL;
791 isl_int v;
792 int *pos;
793 int dropped, needed;
794
795 if (!bmap)
796 return NULL;
797
798 if (bmap->n_div == 0)
799 return bmap;
800
801 if (bmap->n_eq == 0)
802 return bmap;
803
804 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
805 return bmap;
806
807 total = isl_space_dim(bmap->dim, isl_dim_all);
808 div_eq = n_pure_div_eq(bmap);
809 if (div_eq == 0)
810 return bmap;
811
812 if (div_eq < bmap->n_eq) {
813 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
814 bmap->n_eq - div_eq, 0, 1 + total);
815 C = isl_mat_variable_compression(B, &C2);
816 if (!C || !C2)
817 goto error;
818 if (C->n_col == 0) {
819 bmap = isl_basic_map_set_to_empty(bmap);
820 isl_mat_free(C);
821 isl_mat_free(C2);
822 goto done;
823 }
824 }
825
826 d = isl_vec_alloc(bmap->ctx, div_eq);
827 if (!d)
828 goto error;
829 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
830 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
831 --j;
832 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
833 }
834 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
835
836 if (C) {
837 B = isl_mat_product(B, C);
838 C = NULL;
839 }
840
841 T = isl_mat_parameter_compression(B, d);
842 if (!T)
843 goto error;
844 if (T->n_col == 0) {
845 bmap = isl_basic_map_set_to_empty(bmap);
846 isl_mat_free(C2);
847 isl_mat_free(T);
848 goto done;
849 }
850 isl_int_init(v);
851 for (i = 0; i < T->n_row - 1; ++i) {
852 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
853 if (isl_int_is_zero(v))
854 continue;
855 isl_mat_col_submul(T, 0, v, 1 + i);
856 }
857 isl_int_clear(v);
858 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
859 if (!pos)
860 goto error;
861 /* We have to be careful because dropping equalities may reorder them */
862 dropped = 0;
863 for (j = bmap->n_div - 1; j >= 0; --j) {
864 for (i = 0; i < bmap->n_eq; ++i)
865 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
866 break;
867 if (i < bmap->n_eq) {
868 bmap = isl_basic_map_drop_div(bmap, j);
869 isl_basic_map_drop_equality(bmap, i);
870 ++dropped;
871 }
872 }
873 pos[0] = 0;
874 needed = 0;
875 for (i = 1; i < T->n_row; ++i) {
876 if (isl_int_is_one(T->row[i][i]))
877 pos[i] = i;
878 else
879 needed++;
880 }
881 if (needed > dropped) {
882 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
883 needed, needed, 0);
884 if (!bmap)
885 goto error;
886 }
887 for (i = 1; i < T->n_row; ++i) {
888 if (isl_int_is_one(T->row[i][i]))
889 continue;
890 k = isl_basic_map_alloc_div(bmap);
891 pos[i] = 1 + total + k;
892 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
893 isl_int_set(bmap->div[k][0], T->row[i][i]);
894 if (C2)
895 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
896 else
897 isl_int_set_si(bmap->div[k][1 + i], 1);
898 for (j = 0; j < i; ++j) {
899 if (isl_int_is_zero(T->row[i][j]))
900 continue;
901 if (pos[j] < T->n_row && C2)
902 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
903 C2->row[pos[j]], 1 + total);
904 else
905 isl_int_neg(bmap->div[k][1 + pos[j]],
906 T->row[i][j]);
907 }
908 j = isl_basic_map_alloc_equality(bmap);
909 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
910 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
911 }
912 free(pos);
913 isl_mat_free(C2);
914 isl_mat_free(T);
915
916 if (progress)
917 *progress = 1;
918 done:
919 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
920
921 return bmap;
922 error:
923 isl_mat_free(C);
924 isl_mat_free(C2);
925 isl_mat_free(T);
926 return bmap;
927 }
928
929 static struct isl_basic_map *set_div_from_lower_bound(
930 struct isl_basic_map *bmap, int div, int ineq)
931 {
932 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
933
934 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
935 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
936 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
937 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
938 isl_int_set_si(bmap->div[div][1 + total + div], 0);
939
940 return bmap;
941 }
942
943 /* Check whether it is ok to define a div based on an inequality.
944 * To avoid the introduction of circular definitions of divs, we
945 * do not allow such a definition if the resulting expression would refer to
946 * any other undefined divs or if any known div is defined in
947 * terms of the unknown div.
948 */
949 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
950 int div, int ineq)
951 {
952 int j;
953 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
954
955 /* Not defined in terms of unknown divs */
956 for (j = 0; j < bmap->n_div; ++j) {
957 if (div == j)
958 continue;
959 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
960 continue;
961 if (isl_int_is_zero(bmap->div[j][0]))
962 return 0;
963 }
964
965 /* No other div defined in terms of this one => avoid loops */
966 for (j = 0; j < bmap->n_div; ++j) {
967 if (div == j)
968 continue;
969 if (isl_int_is_zero(bmap->div[j][0]))
970 continue;
971 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
972 return 0;
973 }
974
975 return 1;
976 }
977
978 /* Given two constraints "k" and "l" that are opposite to each other,
979 * except for the constant term, check if we can use them
980 * to obtain an expression for one of the hitherto unknown divs.
981 * "sum" is the sum of the constant terms of the constraints.
982 * If this sum is strictly smaller than the coefficient of one
983 * of the divs, then this pair can be used define the div.
984 * To avoid the introduction of circular definitions of divs, we
985 * do not use the pair if the resulting expression would refer to
986 * any other undefined divs or if any known div is defined in
987 * terms of the unknown div.
988 */
989 static struct isl_basic_map *check_for_div_constraints(
990 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
991 {
992 int i;
993 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
994
995 for (i = 0; i < bmap->n_div; ++i) {
996 if (!isl_int_is_zero(bmap->div[i][0]))
997 continue;
998 if (isl_int_is_zero(bmap->ineq[k][total + i]))
999 continue;
1000 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1001 continue;
1002 if (!ok_to_set_div_from_bound(bmap, i, k))
1003 break;
1004 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1005 bmap = set_div_from_lower_bound(bmap, i, k);
1006 else
1007 bmap = set_div_from_lower_bound(bmap, i, l);
1008 if (progress)
1009 *progress = 1;
1010 break;
1011 }
1012 return bmap;
1013 }
1014
1015 static struct isl_basic_map *remove_duplicate_constraints(
1016 struct isl_basic_map *bmap, int *progress, int detect_divs)
1017 {
1018 unsigned int size;
1019 isl_int ***index;
1020 int k, l, h;
1021 int bits;
1022 unsigned total = isl_basic_map_total_dim(bmap);
1023 isl_int sum;
1024 isl_ctx *ctx;
1025
1026 if (!bmap || bmap->n_ineq <= 1)
1027 return bmap;
1028
1029 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1030 bits = ffs(size) - 1;
1031 ctx = isl_basic_map_get_ctx(bmap);
1032 index = isl_calloc_array(ctx, isl_int **, size);
1033 if (!index)
1034 return bmap;
1035
1036 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1037 for (k = 1; k < bmap->n_ineq; ++k) {
1038 h = hash_index(index, size, bits, bmap, k);
1039 if (!index[h]) {
1040 index[h] = &bmap->ineq[k];
1041 continue;
1042 }
1043 if (progress)
1044 *progress = 1;
1045 l = index[h] - &bmap->ineq[0];
1046 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1047 swap_inequality(bmap, k, l);
1048 isl_basic_map_drop_inequality(bmap, k);
1049 --k;
1050 }
1051 isl_int_init(sum);
1052 for (k = 0; k < bmap->n_ineq-1; ++k) {
1053 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1054 h = hash_index(index, size, bits, bmap, k);
1055 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1056 if (!index[h])
1057 continue;
1058 l = index[h] - &bmap->ineq[0];
1059 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1060 if (isl_int_is_pos(sum)) {
1061 if (detect_divs)
1062 bmap = check_for_div_constraints(bmap, k, l,
1063 sum, progress);
1064 continue;
1065 }
1066 if (isl_int_is_zero(sum)) {
1067 /* We need to break out of the loop after these
1068 * changes since the contents of the hash
1069 * will no longer be valid.
1070 * Plus, we probably we want to regauss first.
1071 */
1072 if (progress)
1073 *progress = 1;
1074 isl_basic_map_drop_inequality(bmap, l);
1075 isl_basic_map_inequality_to_equality(bmap, k);
1076 } else
1077 bmap = isl_basic_map_set_to_empty(bmap);
1078 break;
1079 }
1080 isl_int_clear(sum);
1081
1082 free(index);
1083 return bmap;
1084 }
1085
1086
1087 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1088 {
1089 int progress = 1;
1090 if (!bmap)
1091 return NULL;
1092 while (progress) {
1093 progress = 0;
1094 bmap = isl_basic_map_normalize_constraints(bmap);
1095 bmap = remove_duplicate_divs(bmap, &progress);
1096 bmap = eliminate_divs_eq(bmap, &progress);
1097 bmap = eliminate_divs_ineq(bmap, &progress);
1098 bmap = isl_basic_map_gauss(bmap, &progress);
1099 /* requires equalities in normal form */
1100 bmap = normalize_divs(bmap, &progress);
1101 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1102 }
1103 return bmap;
1104 }
1105
1106 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1107 {
1108 return (struct isl_basic_set *)
1109 isl_basic_map_simplify((struct isl_basic_map *)bset);
1110 }
1111
1112
1113 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1114 isl_int *constraint, unsigned div)
1115 {
1116 unsigned pos;
1117
1118 if (!bmap)
1119 return -1;
1120
1121 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1122
1123 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1124 int neg;
1125 isl_int_sub(bmap->div[div][1],
1126 bmap->div[div][1], bmap->div[div][0]);
1127 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1128 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1129 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1130 isl_int_add(bmap->div[div][1],
1131 bmap->div[div][1], bmap->div[div][0]);
1132 if (!neg)
1133 return 0;
1134 if (isl_seq_first_non_zero(constraint+pos+1,
1135 bmap->n_div-div-1) != -1)
1136 return 0;
1137 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1138 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1139 return 0;
1140 if (isl_seq_first_non_zero(constraint+pos+1,
1141 bmap->n_div-div-1) != -1)
1142 return 0;
1143 } else
1144 return 0;
1145
1146 return 1;
1147 }
1148
1149
1150 /* If the only constraints a div d=floor(f/m)
1151 * appears in are its two defining constraints
1152 *
1153 * f - m d >=0
1154 * -(f - (m - 1)) + m d >= 0
1155 *
1156 * then it can safely be removed.
1157 */
1158 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1159 {
1160 int i;
1161 unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1162
1163 for (i = 0; i < bmap->n_eq; ++i)
1164 if (!isl_int_is_zero(bmap->eq[i][pos]))
1165 return 0;
1166
1167 for (i = 0; i < bmap->n_ineq; ++i) {
1168 if (isl_int_is_zero(bmap->ineq[i][pos]))
1169 continue;
1170 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1171 return 0;
1172 }
1173
1174 for (i = 0; i < bmap->n_div; ++i)
1175 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1176 return 0;
1177
1178 return 1;
1179 }
1180
1181 /*
1182 * Remove divs that don't occur in any of the constraints or other divs.
1183 * These can arise when dropping some of the variables in a quast
1184 * returned by piplib.
1185 */
1186 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1187 {
1188 int i;
1189
1190 if (!bmap)
1191 return NULL;
1192
1193 for (i = bmap->n_div-1; i >= 0; --i) {
1194 if (!div_is_redundant(bmap, i))
1195 continue;
1196 bmap = isl_basic_map_drop_div(bmap, i);
1197 }
1198 return bmap;
1199 }
1200
1201 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1202 {
1203 bmap = remove_redundant_divs(bmap);
1204 if (!bmap)
1205 return NULL;
1206 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1207 return bmap;
1208 }
1209
1210 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1211 {
1212 return (struct isl_basic_set *)
1213 isl_basic_map_finalize((struct isl_basic_map *)bset);
1214 }
1215
1216 struct isl_set *isl_set_finalize(struct isl_set *set)
1217 {
1218 int i;
1219
1220 if (!set)
1221 return NULL;
1222 for (i = 0; i < set->n; ++i) {
1223 set->p[i] = isl_basic_set_finalize(set->p[i]);
1224 if (!set->p[i])
1225 goto error;
1226 }
1227 return set;
1228 error:
1229 isl_set_free(set);
1230 return NULL;
1231 }
1232
1233 struct isl_map *isl_map_finalize(struct isl_map *map)
1234 {
1235 int i;
1236
1237 if (!map)
1238 return NULL;
1239 for (i = 0; i < map->n; ++i) {
1240 map->p[i] = isl_basic_map_finalize(map->p[i]);
1241 if (!map->p[i])
1242 goto error;
1243 }
1244 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1245 return map;
1246 error:
1247 isl_map_free(map);
1248 return NULL;
1249 }
1250
1251
1252 /* Remove definition of any div that is defined in terms of the given variable.
1253 * The div itself is not removed. Functions such as
1254 * eliminate_divs_ineq depend on the other divs remaining in place.
1255 */
1256 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1257 int pos)
1258 {
1259 int i;
1260
1261 for (i = 0; i < bmap->n_div; ++i) {
1262 if (isl_int_is_zero(bmap->div[i][0]))
1263 continue;
1264 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1265 continue;
1266 isl_int_set_si(bmap->div[i][0], 0);
1267 }
1268 return bmap;
1269 }
1270
1271 /* Eliminate the specified variables from the constraints using
1272 * Fourier-Motzkin. The variables themselves are not removed.
1273 */
1274 struct isl_basic_map *isl_basic_map_eliminate_vars(
1275 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1276 {
1277 int d;
1278 int i, j, k;
1279 unsigned total;
1280 int need_gauss = 0;
1281
1282 if (n == 0)
1283 return bmap;
1284 if (!bmap)
1285 return NULL;
1286 total = isl_basic_map_total_dim(bmap);
1287
1288 bmap = isl_basic_map_cow(bmap);
1289 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1290 bmap = remove_dependent_vars(bmap, d);
1291
1292 for (d = pos + n - 1;
1293 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1294 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1295 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1296 int n_lower, n_upper;
1297 if (!bmap)
1298 return NULL;
1299 for (i = 0; i < bmap->n_eq; ++i) {
1300 if (isl_int_is_zero(bmap->eq[i][1+d]))
1301 continue;
1302 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1303 isl_basic_map_drop_equality(bmap, i);
1304 need_gauss = 1;
1305 break;
1306 }
1307 if (i < bmap->n_eq)
1308 continue;
1309 n_lower = 0;
1310 n_upper = 0;
1311 for (i = 0; i < bmap->n_ineq; ++i) {
1312 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1313 n_lower++;
1314 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1315 n_upper++;
1316 }
1317 bmap = isl_basic_map_extend_constraints(bmap,
1318 0, n_lower * n_upper);
1319 if (!bmap)
1320 goto error;
1321 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1322 int last;
1323 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1324 continue;
1325 last = -1;
1326 for (j = 0; j < i; ++j) {
1327 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1328 continue;
1329 last = j;
1330 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1331 isl_int_sgn(bmap->ineq[j][1+d]))
1332 continue;
1333 k = isl_basic_map_alloc_inequality(bmap);
1334 if (k < 0)
1335 goto error;
1336 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1337 1+total);
1338 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1339 1+d, 1+total, NULL);
1340 }
1341 isl_basic_map_drop_inequality(bmap, i);
1342 i = last + 1;
1343 }
1344 if (n_lower > 0 && n_upper > 0) {
1345 bmap = isl_basic_map_normalize_constraints(bmap);
1346 bmap = remove_duplicate_constraints(bmap, NULL, 0);
1347 bmap = isl_basic_map_gauss(bmap, NULL);
1348 bmap = isl_basic_map_remove_redundancies(bmap);
1349 need_gauss = 0;
1350 if (!bmap)
1351 goto error;
1352 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1353 break;
1354 }
1355 }
1356 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1357 if (need_gauss)
1358 bmap = isl_basic_map_gauss(bmap, NULL);
1359 return bmap;
1360 error:
1361 isl_basic_map_free(bmap);
1362 return NULL;
1363 }
1364
1365 struct isl_basic_set *isl_basic_set_eliminate_vars(
1366 struct isl_basic_set *bset, unsigned pos, unsigned n)
1367 {
1368 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1369 (struct isl_basic_map *)bset, pos, n);
1370 }
1371
1372 /* Eliminate the specified n dimensions starting at first from the
1373 * constraints using Fourier-Motzkin. The dimensions themselves
1374 * are not removed.
1375 */
1376 __isl_give isl_basic_map *isl_basic_map_eliminate(
1377 __isl_take isl_basic_map *bmap,
1378 enum isl_dim_type type, unsigned first, unsigned n)
1379 {
1380 if (!bmap)
1381 return NULL;
1382 if (n == 0)
1383 return bmap;
1384
1385 if (first + n > isl_basic_map_dim(bmap, type))
1386 isl_die(bmap->ctx, isl_error_invalid,
1387 "index out of bounds", goto error);
1388
1389 first += isl_basic_map_offset(bmap, type) - 1;
1390 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1391 return isl_basic_map_finalize(bmap);
1392 error:
1393 isl_basic_map_free(bmap);
1394 return NULL;
1395 }
1396
1397 /* Don't assume equalities are in order, because align_divs
1398 * may have changed the order of the divs.
1399 */
1400 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1401 {
1402 int d, i;
1403 unsigned total;
1404
1405 total = isl_space_dim(bmap->dim, isl_dim_all);
1406 for (d = 0; d < total; ++d)
1407 elim[d] = -1;
1408 for (i = 0; i < bmap->n_eq; ++i) {
1409 for (d = total - 1; d >= 0; --d) {
1410 if (isl_int_is_zero(bmap->eq[i][1+d]))
1411 continue;
1412 elim[d] = i;
1413 break;
1414 }
1415 }
1416 }
1417
1418 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1419 {
1420 compute_elimination_index((struct isl_basic_map *)bset, elim);
1421 }
1422
1423 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1424 struct isl_basic_map *bmap, int *elim)
1425 {
1426 int d;
1427 int copied = 0;
1428 unsigned total;
1429
1430 total = isl_space_dim(bmap->dim, isl_dim_all);
1431 for (d = total - 1; d >= 0; --d) {
1432 if (isl_int_is_zero(src[1+d]))
1433 continue;
1434 if (elim[d] == -1)
1435 continue;
1436 if (!copied) {
1437 isl_seq_cpy(dst, src, 1 + total);
1438 copied = 1;
1439 }
1440 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1441 }
1442 return copied;
1443 }
1444
1445 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1446 struct isl_basic_set *bset, int *elim)
1447 {
1448 return reduced_using_equalities(dst, src,
1449 (struct isl_basic_map *)bset, elim);
1450 }
1451
1452 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1453 struct isl_basic_set *bset, struct isl_basic_set *context)
1454 {
1455 int i;
1456 int *elim;
1457
1458 if (!bset || !context)
1459 goto error;
1460
1461 if (context->n_eq == 0) {
1462 isl_basic_set_free(context);
1463 return bset;
1464 }
1465
1466 bset = isl_basic_set_cow(bset);
1467 if (!bset)
1468 goto error;
1469
1470 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1471 if (!elim)
1472 goto error;
1473 set_compute_elimination_index(context, elim);
1474 for (i = 0; i < bset->n_eq; ++i)
1475 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1476 context, elim);
1477 for (i = 0; i < bset->n_ineq; ++i)
1478 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1479 context, elim);
1480 isl_basic_set_free(context);
1481 free(elim);
1482 bset = isl_basic_set_simplify(bset);
1483 bset = isl_basic_set_finalize(bset);
1484 return bset;
1485 error:
1486 isl_basic_set_free(bset);
1487 isl_basic_set_free(context);
1488 return NULL;
1489 }
1490
1491 static struct isl_basic_set *remove_shifted_constraints(
1492 struct isl_basic_set *bset, struct isl_basic_set *context)
1493 {
1494 unsigned int size;
1495 isl_int ***index;
1496 int bits;
1497 int k, h, l;
1498 isl_ctx *ctx;
1499
1500 if (!bset)
1501 return NULL;
1502
1503 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1504 bits = ffs(size) - 1;
1505 ctx = isl_basic_set_get_ctx(bset);
1506 index = isl_calloc_array(ctx, isl_int **, size);
1507 if (!index)
1508 return bset;
1509
1510 for (k = 0; k < context->n_ineq; ++k) {
1511 h = set_hash_index(index, size, bits, context, k);
1512 index[h] = &context->ineq[k];
1513 }
1514 for (k = 0; k < bset->n_ineq; ++k) {
1515 h = set_hash_index(index, size, bits, bset, k);
1516 if (!index[h])
1517 continue;
1518 l = index[h] - &context->ineq[0];
1519 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1520 continue;
1521 bset = isl_basic_set_cow(bset);
1522 if (!bset)
1523 goto error;
1524 isl_basic_set_drop_inequality(bset, k);
1525 --k;
1526 }
1527 free(index);
1528 return bset;
1529 error:
1530 free(index);
1531 return bset;
1532 }
1533
1534 /* Remove all information from bset that is redundant in the context
1535 * of context. Both bset and context are assumed to be full-dimensional.
1536 *
1537 * We first * remove the inequalities from "bset"
1538 * that are obviously redundant with respect to some inequality in "context".
1539 *
1540 * If there are any inequalities left, we construct a tableau for
1541 * the context and then add the inequalities of "bset".
1542 * Before adding these inequalities, we freeze all constraints such that
1543 * they won't be considered redundant in terms of the constraints of "bset".
1544 * Then we detect all redundant constraints (among the
1545 * constraints that weren't frozen), first by checking for redundancy in the
1546 * the tableau and then by checking if replacing a constraint by its negation
1547 * would lead to an empty set. This last step is fairly expensive
1548 * and could be optimized by more reuse of the tableau.
1549 * Finally, we update bset according to the results.
1550 */
1551 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1552 __isl_take isl_basic_set *context)
1553 {
1554 int i, k;
1555 isl_basic_set *combined = NULL;
1556 struct isl_tab *tab = NULL;
1557 unsigned context_ineq;
1558 unsigned total;
1559
1560 if (!bset || !context)
1561 goto error;
1562
1563 if (isl_basic_set_is_universe(bset)) {
1564 isl_basic_set_free(context);
1565 return bset;
1566 }
1567
1568 if (isl_basic_set_is_universe(context)) {
1569 isl_basic_set_free(context);
1570 return bset;
1571 }
1572
1573 bset = remove_shifted_constraints(bset, context);
1574 if (!bset)
1575 goto error;
1576 if (bset->n_ineq == 0)
1577 goto done;
1578
1579 context_ineq = context->n_ineq;
1580 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1581 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1582 tab = isl_tab_from_basic_set(combined);
1583 for (i = 0; i < context_ineq; ++i)
1584 if (isl_tab_freeze_constraint(tab, i) < 0)
1585 goto error;
1586 tab = isl_tab_extend(tab, bset->n_ineq);
1587 for (i = 0; i < bset->n_ineq; ++i)
1588 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1589 goto error;
1590 bset = isl_basic_set_add_constraints(combined, bset, 0);
1591 combined = NULL;
1592 if (!bset)
1593 goto error;
1594 if (isl_tab_detect_redundant(tab) < 0)
1595 goto error;
1596 total = isl_basic_set_total_dim(bset);
1597 for (i = context_ineq; i < bset->n_ineq; ++i) {
1598 int is_empty;
1599 if (tab->con[i].is_redundant)
1600 continue;
1601 tab->con[i].is_redundant = 1;
1602 combined = isl_basic_set_dup(bset);
1603 combined = isl_basic_set_update_from_tab(combined, tab);
1604 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1605 k = isl_basic_set_alloc_inequality(combined);
1606 if (k < 0)
1607 goto error;
1608 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1609 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1610 is_empty = isl_basic_set_is_empty(combined);
1611 if (is_empty < 0)
1612 goto error;
1613 isl_basic_set_free(combined);
1614 combined = NULL;
1615 if (!is_empty)
1616 tab->con[i].is_redundant = 0;
1617 }
1618 for (i = 0; i < context_ineq; ++i)
1619 tab->con[i].is_redundant = 1;
1620 bset = isl_basic_set_update_from_tab(bset, tab);
1621 if (bset) {
1622 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1623 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1624 }
1625
1626 isl_tab_free(tab);
1627 done:
1628 bset = isl_basic_set_simplify(bset);
1629 bset = isl_basic_set_finalize(bset);
1630 isl_basic_set_free(context);
1631 return bset;
1632 error:
1633 isl_tab_free(tab);
1634 isl_basic_set_free(combined);
1635 isl_basic_set_free(context);
1636 isl_basic_set_free(bset);
1637 return NULL;
1638 }
1639
1640 /* Remove all information from bset that is redundant in the context
1641 * of context. In particular, equalities that are linear combinations
1642 * of those in context are removed. Then the inequalities that are
1643 * redundant in the context of the equalities and inequalities of
1644 * context are removed.
1645 *
1646 * We first compute the integer affine hull of the intersection,
1647 * compute the gist inside this affine hull and then add back
1648 * those equalities that are not implied by the context.
1649 *
1650 * If two constraints are mutually redundant, then uset_gist_full
1651 * will remove the second of those constraints. We therefore first
1652 * sort the constraints so that constraints not involving existentially
1653 * quantified variables are given precedence over those that do.
1654 * We have to perform this sorting before the variable compression,
1655 * because that may effect the order of the variables.
1656 */
1657 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1658 __isl_take isl_basic_set *context)
1659 {
1660 isl_mat *eq;
1661 isl_mat *T, *T2;
1662 isl_basic_set *aff;
1663 isl_basic_set *aff_context;
1664 unsigned total;
1665
1666 if (!bset || !context)
1667 goto error;
1668
1669 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1670 if (isl_basic_set_plain_is_empty(bset)) {
1671 isl_basic_set_free(context);
1672 return bset;
1673 }
1674 bset = isl_basic_set_sort_constraints(bset);
1675 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1676 if (!aff)
1677 goto error;
1678 if (isl_basic_set_plain_is_empty(aff)) {
1679 isl_basic_set_free(aff);
1680 isl_basic_set_free(context);
1681 return bset;
1682 }
1683 if (aff->n_eq == 0) {
1684 isl_basic_set_free(aff);
1685 return uset_gist_full(bset, context);
1686 }
1687 total = isl_basic_set_total_dim(bset);
1688 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1689 eq = isl_mat_cow(eq);
1690 T = isl_mat_variable_compression(eq, &T2);
1691 if (T && T->n_col == 0) {
1692 isl_mat_free(T);
1693 isl_mat_free(T2);
1694 isl_basic_set_free(context);
1695 isl_basic_set_free(aff);
1696 return isl_basic_set_set_to_empty(bset);
1697 }
1698
1699 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1700
1701 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1702 context = isl_basic_set_preimage(context, T);
1703
1704 bset = uset_gist_full(bset, context);
1705 bset = isl_basic_set_preimage(bset, T2);
1706 bset = isl_basic_set_intersect(bset, aff);
1707 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1708
1709 if (bset) {
1710 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1711 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1712 }
1713
1714 return bset;
1715 error:
1716 isl_basic_set_free(bset);
1717 isl_basic_set_free(context);
1718 return NULL;
1719 }
1720
1721 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1722 * We simply add the equalities in context to bmap and then do a regular
1723 * div normalizations. Better results can be obtained by normalizing
1724 * only the divs in bmap than do not also appear in context.
1725 * We need to be careful to reduce the divs using the equalities
1726 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1727 * spurious constraints.
1728 */
1729 static struct isl_basic_map *normalize_divs_in_context(
1730 struct isl_basic_map *bmap, struct isl_basic_map *context)
1731 {
1732 int i;
1733 unsigned total_context;
1734 int div_eq;
1735
1736 div_eq = n_pure_div_eq(bmap);
1737 if (div_eq == 0)
1738 return bmap;
1739
1740 if (context->n_div > 0)
1741 bmap = isl_basic_map_align_divs(bmap, context);
1742
1743 total_context = isl_basic_map_total_dim(context);
1744 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1745 for (i = 0; i < context->n_eq; ++i) {
1746 int k;
1747 k = isl_basic_map_alloc_equality(bmap);
1748 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1749 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1750 isl_basic_map_total_dim(bmap) - total_context);
1751 }
1752 bmap = isl_basic_map_gauss(bmap, NULL);
1753 bmap = normalize_divs(bmap, NULL);
1754 bmap = isl_basic_map_gauss(bmap, NULL);
1755 return bmap;
1756 }
1757
1758 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1759 struct isl_basic_map *context)
1760 {
1761 struct isl_basic_set *bset;
1762
1763 if (!bmap || !context)
1764 goto error;
1765
1766 if (isl_basic_map_is_universe(bmap)) {
1767 isl_basic_map_free(context);
1768 return bmap;
1769 }
1770 if (isl_basic_map_plain_is_empty(context)) {
1771 isl_space *dim = isl_space_copy(bmap->dim);
1772 isl_basic_map_free(context);
1773 isl_basic_map_free(bmap);
1774 return isl_basic_map_universe(dim);
1775 }
1776 if (isl_basic_map_plain_is_empty(bmap)) {
1777 isl_basic_map_free(context);
1778 return bmap;
1779 }
1780
1781 bmap = isl_basic_map_remove_redundancies(bmap);
1782 context = isl_basic_map_remove_redundancies(context);
1783
1784 if (context->n_eq)
1785 bmap = normalize_divs_in_context(bmap, context);
1786
1787 context = isl_basic_map_align_divs(context, bmap);
1788 bmap = isl_basic_map_align_divs(bmap, context);
1789
1790 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1791 isl_basic_map_underlying_set(context));
1792
1793 return isl_basic_map_overlying_set(bset, bmap);
1794 error:
1795 isl_basic_map_free(bmap);
1796 isl_basic_map_free(context);
1797 return NULL;
1798 }
1799
1800 /*
1801 * Assumes context has no implicit divs.
1802 */
1803 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1804 __isl_take isl_basic_map *context)
1805 {
1806 int i;
1807
1808 if (!map || !context)
1809 goto error;;
1810
1811 if (isl_basic_map_plain_is_empty(context)) {
1812 isl_space *dim = isl_space_copy(map->dim);
1813 isl_basic_map_free(context);
1814 isl_map_free(map);
1815 return isl_map_universe(dim);
1816 }
1817
1818 context = isl_basic_map_remove_redundancies(context);
1819 map = isl_map_cow(map);
1820 if (!map || !context)
1821 goto error;;
1822 isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1823 map = isl_map_compute_divs(map);
1824 for (i = 0; i < map->n; ++i)
1825 context = isl_basic_map_align_divs(context, map->p[i]);
1826 for (i = map->n - 1; i >= 0; --i) {
1827 map->p[i] = isl_basic_map_gist(map->p[i],
1828 isl_basic_map_copy(context));
1829 if (!map->p[i])
1830 goto error;
1831 if (isl_basic_map_plain_is_empty(map->p[i])) {
1832 isl_basic_map_free(map->p[i]);
1833 if (i != map->n - 1)
1834 map->p[i] = map->p[map->n - 1];
1835 map->n--;
1836 }
1837 }
1838 isl_basic_map_free(context);
1839 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1840 return map;
1841 error:
1842 isl_map_free(map);
1843 isl_basic_map_free(context);
1844 return NULL;
1845 }
1846
1847 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1848 __isl_take isl_map *context)
1849 {
1850 context = isl_map_compute_divs(context);
1851 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1852 }
1853
1854 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1855 __isl_take isl_map *context)
1856 {
1857 return isl_map_align_params_map_map_and(map, context, &map_gist);
1858 }
1859
1860 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1861 struct isl_basic_set *context)
1862 {
1863 return (struct isl_basic_set *)isl_basic_map_gist(
1864 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1865 }
1866
1867 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1868 __isl_take isl_basic_set *context)
1869 {
1870 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1871 (struct isl_basic_map *)context);
1872 }
1873
1874 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1875 __isl_take isl_set *context)
1876 {
1877 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1878 (struct isl_map *)context);
1879 }
1880
1881 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
1882 __isl_take isl_set *context)
1883 {
1884 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1885 map_context = isl_map_intersect_params(map_context, context);
1886 return isl_map_gist(map, map_context);
1887 }
1888
1889 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
1890 __isl_take isl_set *context)
1891 {
1892 return isl_map_gist_params(set, context);
1893 }
1894
1895 /* Quick check to see if two basic maps are disjoint.
1896 * In particular, we reduce the equalities and inequalities of
1897 * one basic map in the context of the equalities of the other
1898 * basic map and check if we get a contradiction.
1899 */
1900 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1901 __isl_keep isl_basic_map *bmap2)
1902 {
1903 struct isl_vec *v = NULL;
1904 int *elim = NULL;
1905 unsigned total;
1906 int i;
1907
1908 if (!bmap1 || !bmap2)
1909 return -1;
1910 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
1911 return -1);
1912 if (bmap1->n_div || bmap2->n_div)
1913 return 0;
1914 if (!bmap1->n_eq && !bmap2->n_eq)
1915 return 0;
1916
1917 total = isl_space_dim(bmap1->dim, isl_dim_all);
1918 if (total == 0)
1919 return 0;
1920 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1921 if (!v)
1922 goto error;
1923 elim = isl_alloc_array(bmap1->ctx, int, total);
1924 if (!elim)
1925 goto error;
1926 compute_elimination_index(bmap1, elim);
1927 for (i = 0; i < bmap2->n_eq; ++i) {
1928 int reduced;
1929 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1930 bmap1, elim);
1931 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1932 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1933 goto disjoint;
1934 }
1935 for (i = 0; i < bmap2->n_ineq; ++i) {
1936 int reduced;
1937 reduced = reduced_using_equalities(v->block.data,
1938 bmap2->ineq[i], bmap1, elim);
1939 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1940 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1941 goto disjoint;
1942 }
1943 compute_elimination_index(bmap2, elim);
1944 for (i = 0; i < bmap1->n_ineq; ++i) {
1945 int reduced;
1946 reduced = reduced_using_equalities(v->block.data,
1947 bmap1->ineq[i], bmap2, elim);
1948 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1949 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1950 goto disjoint;
1951 }
1952 isl_vec_free(v);
1953 free(elim);
1954 return 0;
1955 disjoint:
1956 isl_vec_free(v);
1957 free(elim);
1958 return 1;
1959 error:
1960 isl_vec_free(v);
1961 free(elim);
1962 return -1;
1963 }
1964
1965 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1966 __isl_keep isl_basic_set *bset2)
1967 {
1968 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
1969 (struct isl_basic_map *)bset2);
1970 }
1971
1972 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
1973 __isl_keep isl_map *map2)
1974 {
1975 int i, j;
1976
1977 if (!map1 || !map2)
1978 return -1;
1979
1980 if (isl_map_plain_is_equal(map1, map2))
1981 return 0;
1982
1983 for (i = 0; i < map1->n; ++i) {
1984 for (j = 0; j < map2->n; ++j) {
1985 int d = isl_basic_map_plain_is_disjoint(map1->p[i],
1986 map2->p[j]);
1987 if (d != 1)
1988 return d;
1989 }
1990 }
1991 return 1;
1992 }
1993
1994 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1995 __isl_keep isl_set *set2)
1996 {
1997 return isl_map_plain_is_disjoint((struct isl_map *)set1,
1998 (struct isl_map *)set2);
1999 }
2000
2001 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2002 {
2003 return isl_set_plain_is_disjoint(set1, set2);
2004 }
2005
2006 /* Check if we can combine a given div with lower bound l and upper
2007 * bound u with some other div and if so return that other div.
2008 * Otherwise return -1.
2009 *
2010 * We first check that
2011 * - the bounds are opposites of each other (except for the constant
2012 * term)
2013 * - the bounds do not reference any other div
2014 * - no div is defined in terms of this div
2015 *
2016 * Let m be the size of the range allowed on the div by the bounds.
2017 * That is, the bounds are of the form
2018 *
2019 * e <= a <= e + m - 1
2020 *
2021 * with e some expression in the other variables.
2022 * We look for another div b such that no third div is defined in terms
2023 * of this second div b and such that in any constraint that contains
2024 * a (except for the given lower and upper bound), also contains b
2025 * with a coefficient that is m times that of b.
2026 * That is, all constraints (execpt for the lower and upper bound)
2027 * are of the form
2028 *
2029 * e + f (a + m b) >= 0
2030 *
2031 * If so, we return b so that "a + m b" can be replaced by
2032 * a single div "c = a + m b".
2033 */
2034 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2035 unsigned div, unsigned l, unsigned u)
2036 {
2037 int i, j;
2038 unsigned dim;
2039 int coalesce = -1;
2040
2041 if (bmap->n_div <= 1)
2042 return -1;
2043 dim = isl_space_dim(bmap->dim, isl_dim_all);
2044 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2045 return -1;
2046 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2047 bmap->n_div - div - 1) != -1)
2048 return -1;
2049 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2050 dim + bmap->n_div))
2051 return -1;
2052
2053 for (i = 0; i < bmap->n_div; ++i) {
2054 if (isl_int_is_zero(bmap->div[i][0]))
2055 continue;
2056 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2057 return -1;
2058 }
2059
2060 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2061 if (isl_int_is_neg(bmap->ineq[l][0])) {
2062 isl_int_sub(bmap->ineq[l][0],
2063 bmap->ineq[l][0], bmap->ineq[u][0]);
2064 bmap = isl_basic_map_copy(bmap);
2065 bmap = isl_basic_map_set_to_empty(bmap);
2066 isl_basic_map_free(bmap);
2067 return -1;
2068 }
2069 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2070 for (i = 0; i < bmap->n_div; ++i) {
2071 if (i == div)
2072 continue;
2073 if (!pairs[i])
2074 continue;
2075 for (j = 0; j < bmap->n_div; ++j) {
2076 if (isl_int_is_zero(bmap->div[j][0]))
2077 continue;
2078 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2079 break;
2080 }
2081 if (j < bmap->n_div)
2082 continue;
2083 for (j = 0; j < bmap->n_ineq; ++j) {
2084 int valid;
2085 if (j == l || j == u)
2086 continue;
2087 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2088 continue;
2089 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2090 break;
2091 isl_int_mul(bmap->ineq[j][1 + dim + div],
2092 bmap->ineq[j][1 + dim + div],
2093 bmap->ineq[l][0]);
2094 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2095 bmap->ineq[j][1 + dim + i]);
2096 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2097 bmap->ineq[j][1 + dim + div],
2098 bmap->ineq[l][0]);
2099 if (!valid)
2100 break;
2101 }
2102 if (j < bmap->n_ineq)
2103 continue;
2104 coalesce = i;
2105 break;
2106 }
2107 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2108 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2109 return coalesce;
2110 }
2111
2112 /* Given a lower and an upper bound on div i, construct an inequality
2113 * that when nonnegative ensures that this pair of bounds always allows
2114 * for an integer value of the given div.
2115 * The lower bound is inequality l, while the upper bound is inequality u.
2116 * The constructed inequality is stored in ineq.
2117 * g, fl, fu are temporary scalars.
2118 *
2119 * Let the upper bound be
2120 *
2121 * -n_u a + e_u >= 0
2122 *
2123 * and the lower bound
2124 *
2125 * n_l a + e_l >= 0
2126 *
2127 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2128 * We have
2129 *
2130 * - f_u e_l <= f_u f_l g a <= f_l e_u
2131 *
2132 * Since all variables are integer valued, this is equivalent to
2133 *
2134 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2135 *
2136 * If this interval is at least f_u f_l g, then it contains at least
2137 * one integer value for a.
2138 * That is, the test constraint is
2139 *
2140 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2141 */
2142 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2143 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2144 {
2145 unsigned dim;
2146 dim = isl_space_dim(bmap->dim, isl_dim_all);
2147
2148 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2149 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2150 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2151 isl_int_neg(fu, fu);
2152 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2153 1 + dim + bmap->n_div);
2154 isl_int_add(ineq[0], ineq[0], fl);
2155 isl_int_add(ineq[0], ineq[0], fu);
2156 isl_int_sub_ui(ineq[0], ineq[0], 1);
2157 isl_int_mul(g, g, fl);
2158 isl_int_mul(g, g, fu);
2159 isl_int_sub(ineq[0], ineq[0], g);
2160 }
2161
2162 /* Remove more kinds of divs that are not strictly needed.
2163 * In particular, if all pairs of lower and upper bounds on a div
2164 * are such that they allow at least one integer value of the div,
2165 * the we can eliminate the div using Fourier-Motzkin without
2166 * introducing any spurious solutions.
2167 */
2168 static struct isl_basic_map *drop_more_redundant_divs(
2169 struct isl_basic_map *bmap, int *pairs, int n)
2170 {
2171 struct isl_tab *tab = NULL;
2172 struct isl_vec *vec = NULL;
2173 unsigned dim;
2174 int remove = -1;
2175 isl_int g, fl, fu;
2176
2177 isl_int_init(g);
2178 isl_int_init(fl);
2179 isl_int_init(fu);
2180
2181 if (!bmap)
2182 goto error;
2183
2184 dim = isl_space_dim(bmap->dim, isl_dim_all);
2185 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2186 if (!vec)
2187 goto error;
2188
2189 tab = isl_tab_from_basic_map(bmap);
2190
2191 while (n > 0) {
2192 int i, l, u;
2193 int best = -1;
2194 enum isl_lp_result res;
2195
2196 for (i = 0; i < bmap->n_div; ++i) {
2197 if (!pairs[i])
2198 continue;
2199 if (best >= 0 && pairs[best] <= pairs[i])
2200 continue;
2201 best = i;
2202 }
2203
2204 i = best;
2205 for (l = 0; l < bmap->n_ineq; ++l) {
2206 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2207 continue;
2208 for (u = 0; u < bmap->n_ineq; ++u) {
2209 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2210 continue;
2211 construct_test_ineq(bmap, i, l, u,
2212 vec->el, g, fl, fu);
2213 res = isl_tab_min(tab, vec->el,
2214 bmap->ctx->one, &g, NULL, 0);
2215 if (res == isl_lp_error)
2216 goto error;
2217 if (res == isl_lp_empty) {
2218 bmap = isl_basic_map_set_to_empty(bmap);
2219 break;
2220 }
2221 if (res != isl_lp_ok || isl_int_is_neg(g))
2222 break;
2223 }
2224 if (u < bmap->n_ineq)
2225 break;
2226 }
2227 if (l == bmap->n_ineq) {
2228 remove = i;
2229 break;
2230 }
2231 pairs[i] = 0;
2232 --n;
2233 }
2234
2235 isl_tab_free(tab);
2236 isl_vec_free(vec);
2237
2238 isl_int_clear(g);
2239 isl_int_clear(fl);
2240 isl_int_clear(fu);
2241
2242 free(pairs);
2243
2244 if (remove < 0)
2245 return bmap;
2246
2247 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2248 return isl_basic_map_drop_redundant_divs(bmap);
2249 error:
2250 free(pairs);
2251 isl_basic_map_free(bmap);
2252 isl_tab_free(tab);
2253 isl_vec_free(vec);
2254 isl_int_clear(g);
2255 isl_int_clear(fl);
2256 isl_int_clear(fu);
2257 return NULL;
2258 }
2259
2260 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2261 * and the upper bound u, div1 always occurs together with div2 in the form
2262 * (div1 + m div2), where m is the constant range on the variable div1
2263 * allowed by l and u, replace the pair div1 and div2 by a single
2264 * div that is equal to div1 + m div2.
2265 *
2266 * The new div will appear in the location that contains div2.
2267 * We need to modify all constraints that contain
2268 * div2 = (div - div1) / m
2269 * (If a constraint does not contain div2, it will also not contain div1.)
2270 * If the constraint also contains div1, then we know they appear
2271 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2272 * i.e., the coefficient of div is f.
2273 *
2274 * Otherwise, we first need to introduce div1 into the constraint.
2275 * Let the l be
2276 *
2277 * div1 + f >=0
2278 *
2279 * and u
2280 *
2281 * -div1 + f' >= 0
2282 *
2283 * A lower bound on div2
2284 *
2285 * n div2 + t >= 0
2286 *
2287 * can be replaced by
2288 *
2289 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2290 *
2291 * with g = gcd(m,n).
2292 * An upper bound
2293 *
2294 * -n div2 + t >= 0
2295 *
2296 * can be replaced by
2297 *
2298 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2299 *
2300 * These constraint are those that we would obtain from eliminating
2301 * div1 using Fourier-Motzkin.
2302 *
2303 * After all constraints have been modified, we drop the lower and upper
2304 * bound and then drop div1.
2305 */
2306 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2307 unsigned div1, unsigned div2, unsigned l, unsigned u)
2308 {
2309 isl_int a;
2310 isl_int b;
2311 isl_int m;
2312 unsigned dim, total;
2313 int i;
2314
2315 dim = isl_space_dim(bmap->dim, isl_dim_all);
2316 total = 1 + dim + bmap->n_div;
2317
2318 isl_int_init(a);
2319 isl_int_init(b);
2320 isl_int_init(m);
2321 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2322 isl_int_add_ui(m, m, 1);
2323
2324 for (i = 0; i < bmap->n_ineq; ++i) {
2325 if (i == l || i == u)
2326 continue;
2327 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2328 continue;
2329 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2330 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2331 isl_int_divexact(a, m, b);
2332 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2333 if (isl_int_is_pos(b)) {
2334 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2335 b, bmap->ineq[l], total);
2336 } else {
2337 isl_int_neg(b, b);
2338 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2339 b, bmap->ineq[u], total);
2340 }
2341 }
2342 isl_int_set(bmap->ineq[i][1 + dim + div2],
2343 bmap->ineq[i][1 + dim + div1]);
2344 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2345 }
2346
2347 isl_int_clear(a);
2348 isl_int_clear(b);
2349 isl_int_clear(m);
2350 if (l > u) {
2351 isl_basic_map_drop_inequality(bmap, l);
2352 isl_basic_map_drop_inequality(bmap, u);
2353 } else {
2354 isl_basic_map_drop_inequality(bmap, u);
2355 isl_basic_map_drop_inequality(bmap, l);
2356 }
2357 bmap = isl_basic_map_drop_div(bmap, div1);
2358 return bmap;
2359 }
2360
2361 /* First check if we can coalesce any pair of divs and
2362 * then continue with dropping more redundant divs.
2363 *
2364 * We loop over all pairs of lower and upper bounds on a div
2365 * with coefficient 1 and -1, respectively, check if there
2366 * is any other div "c" with which we can coalesce the div
2367 * and if so, perform the coalescing.
2368 */
2369 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2370 struct isl_basic_map *bmap, int *pairs, int n)
2371 {
2372 int i, l, u;
2373 unsigned dim;
2374
2375 dim = isl_space_dim(bmap->dim, isl_dim_all);
2376
2377 for (i = 0; i < bmap->n_div; ++i) {
2378 if (!pairs[i])
2379 continue;
2380 for (l = 0; l < bmap->n_ineq; ++l) {
2381 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2382 continue;
2383 for (u = 0; u < bmap->n_ineq; ++u) {
2384 int c;
2385
2386 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2387 continue;
2388 c = div_find_coalesce(bmap, pairs, i, l, u);
2389 if (c < 0)
2390 continue;
2391 free(pairs);
2392 bmap = coalesce_divs(bmap, i, c, l, u);
2393 return isl_basic_map_drop_redundant_divs(bmap);
2394 }
2395 }
2396 }
2397
2398 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2399 return bmap;
2400
2401 return drop_more_redundant_divs(bmap, pairs, n);
2402 }
2403
2404 /* Remove divs that are not strictly needed.
2405 * In particular, if a div only occurs positively (or negatively)
2406 * in constraints, then it can simply be dropped.
2407 * Also, if a div occurs only occurs in two constraints and if moreover
2408 * those two constraints are opposite to each other, except for the constant
2409 * term and if the sum of the constant terms is such that for any value
2410 * of the other values, there is always at least one integer value of the
2411 * div, i.e., if one plus this sum is greater than or equal to
2412 * the (absolute value) of the coefficent of the div in the constraints,
2413 * then we can also simply drop the div.
2414 *
2415 * If any divs are left after these simple checks then we move on
2416 * to more complicated cases in drop_more_redundant_divs.
2417 */
2418 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2419 struct isl_basic_map *bmap)
2420 {
2421 int i, j;
2422 unsigned off;
2423 int *pairs = NULL;
2424 int n = 0;
2425
2426 if (!bmap)
2427 goto error;
2428
2429 off = isl_space_dim(bmap->dim, isl_dim_all);
2430 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2431 if (!pairs)
2432 goto error;
2433
2434 for (i = 0; i < bmap->n_div; ++i) {
2435 int pos, neg;
2436 int last_pos, last_neg;
2437 int redundant;
2438 int defined;
2439
2440 defined = !isl_int_is_zero(bmap->div[i][0]);
2441 for (j = 0; j < bmap->n_eq; ++j)
2442 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2443 break;
2444 if (j < bmap->n_eq)
2445 continue;
2446 ++n;
2447 pos = neg = 0;
2448 for (j = 0; j < bmap->n_ineq; ++j) {
2449 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2450 last_pos = j;
2451 ++pos;
2452 }
2453 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2454 last_neg = j;
2455 ++neg;
2456 }
2457 }
2458 pairs[i] = pos * neg;
2459 if (pairs[i] == 0) {
2460 for (j = bmap->n_ineq - 1; j >= 0; --j)
2461 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2462 isl_basic_map_drop_inequality(bmap, j);
2463 bmap = isl_basic_map_drop_div(bmap, i);
2464 free(pairs);
2465 return isl_basic_map_drop_redundant_divs(bmap);
2466 }
2467 if (pairs[i] != 1)
2468 continue;
2469 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2470 bmap->ineq[last_neg] + 1,
2471 off + bmap->n_div))
2472 continue;
2473
2474 isl_int_add(bmap->ineq[last_pos][0],
2475 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2476 isl_int_add_ui(bmap->ineq[last_pos][0],
2477 bmap->ineq[last_pos][0], 1);
2478 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2479 bmap->ineq[last_pos][1+off+i]);
2480 isl_int_sub_ui(bmap->ineq[last_pos][0],
2481 bmap->ineq[last_pos][0], 1);
2482 isl_int_sub(bmap->ineq[last_pos][0],
2483 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2484 if (!redundant) {
2485 if (defined ||
2486 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2487 pairs[i] = 0;
2488 --n;
2489 continue;
2490 }
2491 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2492 bmap = isl_basic_map_simplify(bmap);
2493 free(pairs);
2494 return isl_basic_map_drop_redundant_divs(bmap);
2495 }
2496 if (last_pos > last_neg) {
2497 isl_basic_map_drop_inequality(bmap, last_pos);
2498 isl_basic_map_drop_inequality(bmap, last_neg);
2499 } else {
2500 isl_basic_map_drop_inequality(bmap, last_neg);
2501 isl_basic_map_drop_inequality(bmap, last_pos);
2502 }
2503 bmap = isl_basic_map_drop_div(bmap, i);
2504 free(pairs);
2505 return isl_basic_map_drop_redundant_divs(bmap);
2506 }
2507
2508 if (n > 0)
2509 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2510
2511 free(pairs);
2512 return bmap;
2513 error:
2514 free(pairs);
2515 isl_basic_map_free(bmap);
2516 return NULL;
2517 }
2518
2519 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2520 struct isl_basic_set *bset)
2521 {
2522 return (struct isl_basic_set *)
2523 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2524 }
2525
2526 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2527 {
2528 int i;
2529
2530 if (!map)
2531 return NULL;
2532 for (i = 0; i < map->n; ++i) {
2533 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2534 if (!map->p[i])
2535 goto error;
2536 }
2537 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2538 return map;
2539 error:
2540 isl_map_free(map);
2541 return NULL;
2542 }
2543
2544 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2545 {
2546 return (struct isl_set *)
2547 isl_map_drop_redundant_divs((struct isl_map *)set);
2548 }
Integer set library