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add isl_pw_aff_lt_set and isl_pw_aff_gt_set
[isl.git] / isl_map_simplify.c
blob7a24c5bb11f23f0b1f0f733c2636745bdc2a83f0
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_dim_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_dim_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_dim_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_dim_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_dim_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_dim_get_tuple_name(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_dim_drop(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_dim_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_dim_drop(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_dim_total(bmap->dim) + 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 int k;
380 int last_div;
381
382 total = isl_basic_map_total_dim(bmap);
383 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
384 bmap->n_div);
385 for (k = 0; k < bmap->n_eq; ++k) {
386 if (bmap->eq[k] == eq)
387 continue;
388 if (isl_int_is_zero(bmap->eq[k][1+pos]))
389 continue;
390 if (progress)
391 *progress = 1;
392 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
393 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
394 }
395
396 for (k = 0; k < bmap->n_ineq; ++k) {
397 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
398 continue;
399 if (progress)
400 *progress = 1;
401 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
402 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
403 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
404 }
405
406 for (k = 0; k < bmap->n_div; ++k) {
407 if (isl_int_is_zero(bmap->div[k][0]))
408 continue;
409 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
410 continue;
411 if (progress)
412 *progress = 1;
413 /* We need to be careful about circular definitions,
414 * so for now we just remove the definition of div k
415 * if the equality contains any divs.
416 * If keep_divs is set, then the divs have been ordered
417 * and we can keep the definition as long as the result
418 * is still ordered.
419 */
420 if (last_div == -1 || (keep_divs && last_div < k))
421 isl_seq_elim(bmap->div[k]+1, eq,
422 1+pos, 1+total, &bmap->div[k][0]);
423 else
424 isl_seq_clr(bmap->div[k], 1 + total);
425 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
426 }
427 }
428
429 /* Assumes divs have been ordered if keep_divs is set.
430 */
431 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
432 unsigned div, int keep_divs)
433 {
434 unsigned pos = isl_dim_total(bmap->dim) + div;
435
436 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
437
438 isl_basic_map_drop_div(bmap, div);
439 }
440
441 /* Check if elimination of div "div" using equality "eq" would not
442 * result in a div depending on a later div.
443 */
444 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
445 unsigned div)
446 {
447 int k;
448 int last_div;
449 unsigned pos = isl_dim_total(bmap->dim) + div;
450
451 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
452 bmap->n_div);
453 if (last_div < 0 || last_div <= div)
454 return 1;
455
456 for (k = 0; k <= last_div; ++k) {
457 if (isl_int_is_zero(bmap->div[k][0]))
458 return 1;
459 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
460 return 0;
461 }
462
463 return 1;
464 }
465
466 /* Elimininate divs based on equalities
467 */
468 static struct isl_basic_map *eliminate_divs_eq(
469 struct isl_basic_map *bmap, int *progress)
470 {
471 int d;
472 int i;
473 int modified = 0;
474 unsigned off;
475
476 bmap = isl_basic_map_order_divs(bmap);
477
478 if (!bmap)
479 return NULL;
480
481 off = 1 + isl_dim_total(bmap->dim);
482
483 for (d = bmap->n_div - 1; d >= 0 ; --d) {
484 for (i = 0; i < bmap->n_eq; ++i) {
485 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
486 !isl_int_is_negone(bmap->eq[i][off + d]))
487 continue;
488 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
489 continue;
490 modified = 1;
491 *progress = 1;
492 eliminate_div(bmap, bmap->eq[i], d, 1);
493 isl_basic_map_drop_equality(bmap, i);
494 break;
495 }
496 }
497 if (modified)
498 return eliminate_divs_eq(bmap, progress);
499 return bmap;
500 }
501
502 /* Elimininate divs based on inequalities
503 */
504 static struct isl_basic_map *eliminate_divs_ineq(
505 struct isl_basic_map *bmap, int *progress)
506 {
507 int d;
508 int i;
509 unsigned off;
510 struct isl_ctx *ctx;
511
512 if (!bmap)
513 return NULL;
514
515 ctx = bmap->ctx;
516 off = 1 + isl_dim_total(bmap->dim);
517
518 for (d = bmap->n_div - 1; d >= 0 ; --d) {
519 for (i = 0; i < bmap->n_eq; ++i)
520 if (!isl_int_is_zero(bmap->eq[i][off + d]))
521 break;
522 if (i < bmap->n_eq)
523 continue;
524 for (i = 0; i < bmap->n_ineq; ++i)
525 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
526 break;
527 if (i < bmap->n_ineq)
528 continue;
529 *progress = 1;
530 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
531 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
532 break;
533 bmap = isl_basic_map_drop_div(bmap, d);
534 if (!bmap)
535 break;
536 }
537 return bmap;
538 }
539
540 struct isl_basic_map *isl_basic_map_gauss(
541 struct isl_basic_map *bmap, int *progress)
542 {
543 int k;
544 int done;
545 int last_var;
546 unsigned total_var;
547 unsigned total;
548
549 bmap = isl_basic_map_order_divs(bmap);
550
551 if (!bmap)
552 return NULL;
553
554 total = isl_basic_map_total_dim(bmap);
555 total_var = total - bmap->n_div;
556
557 last_var = total - 1;
558 for (done = 0; done < bmap->n_eq; ++done) {
559 for (; last_var >= 0; --last_var) {
560 for (k = done; k < bmap->n_eq; ++k)
561 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
562 break;
563 if (k < bmap->n_eq)
564 break;
565 }
566 if (last_var < 0)
567 break;
568 if (k != done)
569 swap_equality(bmap, k, done);
570 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
571 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
572
573 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
574 progress);
575
576 if (last_var >= total_var &&
577 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
578 unsigned div = last_var - total_var;
579 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
580 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
581 isl_int_set(bmap->div[div][0],
582 bmap->eq[done][1+last_var]);
583 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
584 }
585 }
586 if (done == bmap->n_eq)
587 return bmap;
588 for (k = done; k < bmap->n_eq; ++k) {
589 if (isl_int_is_zero(bmap->eq[k][0]))
590 continue;
591 return isl_basic_map_set_to_empty(bmap);
592 }
593 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
594 return bmap;
595 }
596
597 struct isl_basic_set *isl_basic_set_gauss(
598 struct isl_basic_set *bset, int *progress)
599 {
600 return (struct isl_basic_set*)isl_basic_map_gauss(
601 (struct isl_basic_map *)bset, progress);
602 }
603
604
605 static unsigned int round_up(unsigned int v)
606 {
607 int old_v = v;
608
609 while (v) {
610 old_v = v;
611 v ^= v & -v;
612 }
613 return old_v << 1;
614 }
615
616 static int hash_index(isl_int ***index, unsigned int size, int bits,
617 struct isl_basic_map *bmap, int k)
618 {
619 int h;
620 unsigned total = isl_basic_map_total_dim(bmap);
621 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
622 for (h = hash; index[h]; h = (h+1) % size)
623 if (&bmap->ineq[k] != index[h] &&
624 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
625 break;
626 return h;
627 }
628
629 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
630 struct isl_basic_set *bset, int k)
631 {
632 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
633 }
634
635 /* If we can eliminate more than one div, then we need to make
636 * sure we do it from last div to first div, in order not to
637 * change the position of the other divs that still need to
638 * be removed.
639 */
640 static struct isl_basic_map *remove_duplicate_divs(
641 struct isl_basic_map *bmap, int *progress)
642 {
643 unsigned int size;
644 int *index;
645 int *elim_for;
646 int k, l, h;
647 int bits;
648 struct isl_blk eq;
649 unsigned total_var;
650 unsigned total;
651 struct isl_ctx *ctx;
652
653 if (!bmap || bmap->n_div <= 1)
654 return bmap;
655
656 total_var = isl_dim_total(bmap->dim);
657 total = total_var + bmap->n_div;
658
659 ctx = bmap->ctx;
660 for (k = bmap->n_div - 1; k >= 0; --k)
661 if (!isl_int_is_zero(bmap->div[k][0]))
662 break;
663 if (k <= 0)
664 return bmap;
665
666 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
667 size = round_up(4 * bmap->n_div / 3 - 1);
668 bits = ffs(size) - 1;
669 index = isl_calloc_array(ctx, int, size);
670 if (!index)
671 return bmap;
672 eq = isl_blk_alloc(ctx, 1+total);
673 if (isl_blk_is_error(eq))
674 goto out;
675
676 isl_seq_clr(eq.data, 1+total);
677 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
678 for (--k; k >= 0; --k) {
679 uint32_t hash;
680
681 if (isl_int_is_zero(bmap->div[k][0]))
682 continue;
683
684 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
685 for (h = hash; index[h]; h = (h+1) % size)
686 if (isl_seq_eq(bmap->div[k],
687 bmap->div[index[h]-1], 2+total))
688 break;
689 if (index[h]) {
690 *progress = 1;
691 l = index[h] - 1;
692 elim_for[l] = k + 1;
693 }
694 index[h] = k+1;
695 }
696 for (l = bmap->n_div - 1; l >= 0; --l) {
697 if (!elim_for[l])
698 continue;
699 k = elim_for[l] - 1;
700 isl_int_set_si(eq.data[1+total_var+k], -1);
701 isl_int_set_si(eq.data[1+total_var+l], 1);
702 eliminate_div(bmap, eq.data, l, 0);
703 isl_int_set_si(eq.data[1+total_var+k], 0);
704 isl_int_set_si(eq.data[1+total_var+l], 0);
705 }
706
707 isl_blk_free(ctx, eq);
708 out:
709 free(index);
710 free(elim_for);
711 return bmap;
712 }
713
714 static int n_pure_div_eq(struct isl_basic_map *bmap)
715 {
716 int i, j;
717 unsigned total;
718
719 total = isl_dim_total(bmap->dim);
720 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
721 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
722 --j;
723 if (j < 0)
724 break;
725 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
726 return 0;
727 }
728 return i;
729 }
730
731 /* Normalize divs that appear in equalities.
732 *
733 * In particular, we assume that bmap contains some equalities
734 * of the form
735 *
736 * a x = m * e_i
737 *
738 * and we want to replace the set of e_i by a minimal set and
739 * such that the new e_i have a canonical representation in terms
740 * of the vector x.
741 * If any of the equalities involves more than one divs, then
742 * we currently simply bail out.
743 *
744 * Let us first additionally assume that all equalities involve
745 * a div. The equalities then express modulo constraints on the
746 * remaining variables and we can use "parameter compression"
747 * to find a minimal set of constraints. The result is a transformation
748 *
749 * x = T(x') = x_0 + G x'
750 *
751 * with G a lower-triangular matrix with all elements below the diagonal
752 * non-negative and smaller than the diagonal element on the same row.
753 * We first normalize x_0 by making the same property hold in the affine
754 * T matrix.
755 * The rows i of G with a 1 on the diagonal do not impose any modulo
756 * constraint and simply express x_i = x'_i.
757 * For each of the remaining rows i, we introduce a div and a corresponding
758 * equality. In particular
759 *
760 * g_ii e_j = x_i - g_i(x')
761 *
762 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
763 * corresponding div (if g_kk != 1).
764 *
765 * If there are any equalities not involving any div, then we
766 * first apply a variable compression on the variables x:
767 *
768 * x = C x'' x'' = C_2 x
769 *
770 * and perform the above parameter compression on A C instead of on A.
771 * The resulting compression is then of the form
772 *
773 * x'' = T(x') = x_0 + G x'
774 *
775 * and in constructing the new divs and the corresponding equalities,
776 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
777 * by the corresponding row from C_2.
778 */
779 static struct isl_basic_map *normalize_divs(
780 struct isl_basic_map *bmap, int *progress)
781 {
782 int i, j, k;
783 int total;
784 int div_eq;
785 struct isl_mat *B;
786 struct isl_vec *d;
787 struct isl_mat *T = NULL;
788 struct isl_mat *C = NULL;
789 struct isl_mat *C2 = NULL;
790 isl_int v;
791 int *pos;
792 int dropped, needed;
793
794 if (!bmap)
795 return NULL;
796
797 if (bmap->n_div == 0)
798 return bmap;
799
800 if (bmap->n_eq == 0)
801 return bmap;
802
803 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
804 return bmap;
805
806 total = isl_dim_total(bmap->dim);
807 div_eq = n_pure_div_eq(bmap);
808 if (div_eq == 0)
809 return bmap;
810
811 if (div_eq < bmap->n_eq) {
812 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
813 bmap->n_eq - div_eq, 0, 1 + total);
814 C = isl_mat_variable_compression(B, &C2);
815 if (!C || !C2)
816 goto error;
817 if (C->n_col == 0) {
818 bmap = isl_basic_map_set_to_empty(bmap);
819 isl_mat_free(C);
820 isl_mat_free(C2);
821 goto done;
822 }
823 }
824
825 d = isl_vec_alloc(bmap->ctx, div_eq);
826 if (!d)
827 goto error;
828 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
829 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
830 --j;
831 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
832 }
833 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
834
835 if (C) {
836 B = isl_mat_product(B, C);
837 C = NULL;
838 }
839
840 T = isl_mat_parameter_compression(B, d);
841 if (!T)
842 goto error;
843 if (T->n_col == 0) {
844 bmap = isl_basic_map_set_to_empty(bmap);
845 isl_mat_free(C2);
846 isl_mat_free(T);
847 goto done;
848 }
849 isl_int_init(v);
850 for (i = 0; i < T->n_row - 1; ++i) {
851 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
852 if (isl_int_is_zero(v))
853 continue;
854 isl_mat_col_submul(T, 0, v, 1 + i);
855 }
856 isl_int_clear(v);
857 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
858 if (!pos)
859 goto error;
860 /* We have to be careful because dropping equalities may reorder them */
861 dropped = 0;
862 for (j = bmap->n_div - 1; j >= 0; --j) {
863 for (i = 0; i < bmap->n_eq; ++i)
864 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
865 break;
866 if (i < bmap->n_eq) {
867 bmap = isl_basic_map_drop_div(bmap, j);
868 isl_basic_map_drop_equality(bmap, i);
869 ++dropped;
870 }
871 }
872 pos[0] = 0;
873 needed = 0;
874 for (i = 1; i < T->n_row; ++i) {
875 if (isl_int_is_one(T->row[i][i]))
876 pos[i] = i;
877 else
878 needed++;
879 }
880 if (needed > dropped) {
881 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
882 needed, needed, 0);
883 if (!bmap)
884 goto error;
885 }
886 for (i = 1; i < T->n_row; ++i) {
887 if (isl_int_is_one(T->row[i][i]))
888 continue;
889 k = isl_basic_map_alloc_div(bmap);
890 pos[i] = 1 + total + k;
891 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
892 isl_int_set(bmap->div[k][0], T->row[i][i]);
893 if (C2)
894 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
895 else
896 isl_int_set_si(bmap->div[k][1 + i], 1);
897 for (j = 0; j < i; ++j) {
898 if (isl_int_is_zero(T->row[i][j]))
899 continue;
900 if (pos[j] < T->n_row && C2)
901 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
902 C2->row[pos[j]], 1 + total);
903 else
904 isl_int_neg(bmap->div[k][1 + pos[j]],
905 T->row[i][j]);
906 }
907 j = isl_basic_map_alloc_equality(bmap);
908 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
909 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
910 }
911 free(pos);
912 isl_mat_free(C2);
913 isl_mat_free(T);
914
915 if (progress)
916 *progress = 1;
917 done:
918 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
919
920 return bmap;
921 error:
922 isl_mat_free(C);
923 isl_mat_free(C2);
924 isl_mat_free(T);
925 return bmap;
926 }
927
928 static struct isl_basic_map *set_div_from_lower_bound(
929 struct isl_basic_map *bmap, int div, int ineq)
930 {
931 unsigned total = 1 + isl_dim_total(bmap->dim);
932
933 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
934 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
935 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
936 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
937 isl_int_set_si(bmap->div[div][1 + total + div], 0);
938
939 return bmap;
940 }
941
942 /* Check whether it is ok to define a div based on an inequality.
943 * To avoid the introduction of circular definitions of divs, we
944 * do not allow such a definition if the resulting expression would refer to
945 * any other undefined divs or if any known div is defined in
946 * terms of the unknown div.
947 */
948 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
949 int div, int ineq)
950 {
951 int j;
952 unsigned total = 1 + isl_dim_total(bmap->dim);
953
954 /* Not defined in terms of unknown divs */
955 for (j = 0; j < bmap->n_div; ++j) {
956 if (div == j)
957 continue;
958 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
959 continue;
960 if (isl_int_is_zero(bmap->div[j][0]))
961 return 0;
962 }
963
964 /* No other div defined in terms of this one => avoid loops */
965 for (j = 0; j < bmap->n_div; ++j) {
966 if (div == j)
967 continue;
968 if (isl_int_is_zero(bmap->div[j][0]))
969 continue;
970 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
971 return 0;
972 }
973
974 return 1;
975 }
976
977 /* Given two constraints "k" and "l" that are opposite to each other,
978 * except for the constant term, check if we can use them
979 * to obtain an expression for one of the hitherto unknown divs.
980 * "sum" is the sum of the constant terms of the constraints.
981 * If this sum is strictly smaller than the coefficient of one
982 * of the divs, then this pair can be used define the div.
983 * To avoid the introduction of circular definitions of divs, we
984 * do not use the pair if the resulting expression would refer to
985 * any other undefined divs or if any known div is defined in
986 * terms of the unknown div.
987 */
988 static struct isl_basic_map *check_for_div_constraints(
989 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
990 {
991 int i;
992 unsigned total = 1 + isl_dim_total(bmap->dim);
993
994 for (i = 0; i < bmap->n_div; ++i) {
995 if (!isl_int_is_zero(bmap->div[i][0]))
996 continue;
997 if (isl_int_is_zero(bmap->ineq[k][total + i]))
998 continue;
999 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1000 continue;
1001 if (!ok_to_set_div_from_bound(bmap, i, k))
1002 break;
1003 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1004 bmap = set_div_from_lower_bound(bmap, i, k);
1005 else
1006 bmap = set_div_from_lower_bound(bmap, i, l);
1007 if (progress)
1008 *progress = 1;
1009 break;
1010 }
1011 return bmap;
1012 }
1013
1014 static struct isl_basic_map *remove_duplicate_constraints(
1015 struct isl_basic_map *bmap, int *progress, int detect_divs)
1016 {
1017 unsigned int size;
1018 isl_int ***index;
1019 int k, l, h;
1020 int bits;
1021 unsigned total = isl_basic_map_total_dim(bmap);
1022 isl_int sum;
1023 isl_ctx *ctx;
1024
1025 if (!bmap || bmap->n_ineq <= 1)
1026 return bmap;
1027
1028 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1029 bits = ffs(size) - 1;
1030 ctx = isl_basic_map_get_ctx(bmap);
1031 index = isl_calloc_array(ctx, isl_int **, size);
1032 if (!index)
1033 return bmap;
1034
1035 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1036 for (k = 1; k < bmap->n_ineq; ++k) {
1037 h = hash_index(index, size, bits, bmap, k);
1038 if (!index[h]) {
1039 index[h] = &bmap->ineq[k];
1040 continue;
1041 }
1042 if (progress)
1043 *progress = 1;
1044 l = index[h] - &bmap->ineq[0];
1045 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1046 swap_inequality(bmap, k, l);
1047 isl_basic_map_drop_inequality(bmap, k);
1048 --k;
1049 }
1050 isl_int_init(sum);
1051 for (k = 0; k < bmap->n_ineq-1; ++k) {
1052 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1053 h = hash_index(index, size, bits, bmap, k);
1054 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1055 if (!index[h])
1056 continue;
1057 l = index[h] - &bmap->ineq[0];
1058 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1059 if (isl_int_is_pos(sum)) {
1060 if (detect_divs)
1061 bmap = check_for_div_constraints(bmap, k, l,
1062 sum, progress);
1063 continue;
1064 }
1065 if (isl_int_is_zero(sum)) {
1066 /* We need to break out of the loop after these
1067 * changes since the contents of the hash
1068 * will no longer be valid.
1069 * Plus, we probably we want to regauss first.
1070 */
1071 if (progress)
1072 *progress = 1;
1073 isl_basic_map_drop_inequality(bmap, l);
1074 isl_basic_map_inequality_to_equality(bmap, k);
1075 } else
1076 bmap = isl_basic_map_set_to_empty(bmap);
1077 break;
1078 }
1079 isl_int_clear(sum);
1080
1081 free(index);
1082 return bmap;
1083 }
1084
1085
1086 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1087 {
1088 int progress = 1;
1089 if (!bmap)
1090 return NULL;
1091 while (progress) {
1092 progress = 0;
1093 bmap = isl_basic_map_normalize_constraints(bmap);
1094 bmap = remove_duplicate_divs(bmap, &progress);
1095 bmap = eliminate_divs_eq(bmap, &progress);
1096 bmap = eliminate_divs_ineq(bmap, &progress);
1097 bmap = isl_basic_map_gauss(bmap, &progress);
1098 /* requires equalities in normal form */
1099 bmap = normalize_divs(bmap, &progress);
1100 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1101 }
1102 return bmap;
1103 }
1104
1105 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1106 {
1107 return (struct isl_basic_set *)
1108 isl_basic_map_simplify((struct isl_basic_map *)bset);
1109 }
1110
1111
1112 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1113 isl_int *constraint, unsigned div)
1114 {
1115 unsigned pos;
1116
1117 if (!bmap)
1118 return -1;
1119
1120 pos = 1 + isl_dim_total(bmap->dim) + div;
1121
1122 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1123 int neg;
1124 isl_int_sub(bmap->div[div][1],
1125 bmap->div[div][1], bmap->div[div][0]);
1126 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1127 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1128 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1129 isl_int_add(bmap->div[div][1],
1130 bmap->div[div][1], bmap->div[div][0]);
1131 if (!neg)
1132 return 0;
1133 if (isl_seq_first_non_zero(constraint+pos+1,
1134 bmap->n_div-div-1) != -1)
1135 return 0;
1136 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1137 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1138 return 0;
1139 if (isl_seq_first_non_zero(constraint+pos+1,
1140 bmap->n_div-div-1) != -1)
1141 return 0;
1142 } else
1143 return 0;
1144
1145 return 1;
1146 }
1147
1148
1149 /* If the only constraints a div d=floor(f/m)
1150 * appears in are its two defining constraints
1151 *
1152 * f - m d >=0
1153 * -(f - (m - 1)) + m d >= 0
1154 *
1155 * then it can safely be removed.
1156 */
1157 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1158 {
1159 int i;
1160 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1161
1162 for (i = 0; i < bmap->n_eq; ++i)
1163 if (!isl_int_is_zero(bmap->eq[i][pos]))
1164 return 0;
1165
1166 for (i = 0; i < bmap->n_ineq; ++i) {
1167 if (isl_int_is_zero(bmap->ineq[i][pos]))
1168 continue;
1169 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1170 return 0;
1171 }
1172
1173 for (i = 0; i < bmap->n_div; ++i)
1174 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1175 return 0;
1176
1177 return 1;
1178 }
1179
1180 /*
1181 * Remove divs that don't occur in any of the constraints or other divs.
1182 * These can arise when dropping some of the variables in a quast
1183 * returned by piplib.
1184 */
1185 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1186 {
1187 int i;
1188
1189 if (!bmap)
1190 return NULL;
1191
1192 for (i = bmap->n_div-1; i >= 0; --i) {
1193 if (!div_is_redundant(bmap, i))
1194 continue;
1195 bmap = isl_basic_map_drop_div(bmap, i);
1196 }
1197 return bmap;
1198 }
1199
1200 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1201 {
1202 bmap = remove_redundant_divs(bmap);
1203 if (!bmap)
1204 return NULL;
1205 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1206 return bmap;
1207 }
1208
1209 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1210 {
1211 return (struct isl_basic_set *)
1212 isl_basic_map_finalize((struct isl_basic_map *)bset);
1213 }
1214
1215 struct isl_set *isl_set_finalize(struct isl_set *set)
1216 {
1217 int i;
1218
1219 if (!set)
1220 return NULL;
1221 for (i = 0; i < set->n; ++i) {
1222 set->p[i] = isl_basic_set_finalize(set->p[i]);
1223 if (!set->p[i])
1224 goto error;
1225 }
1226 return set;
1227 error:
1228 isl_set_free(set);
1229 return NULL;
1230 }
1231
1232 struct isl_map *isl_map_finalize(struct isl_map *map)
1233 {
1234 int i;
1235
1236 if (!map)
1237 return NULL;
1238 for (i = 0; i < map->n; ++i) {
1239 map->p[i] = isl_basic_map_finalize(map->p[i]);
1240 if (!map->p[i])
1241 goto error;
1242 }
1243 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1244 return map;
1245 error:
1246 isl_map_free(map);
1247 return NULL;
1248 }
1249
1250
1251 /* Remove definition of any div that is defined in terms of the given variable.
1252 * The div itself is not removed. Functions such as
1253 * eliminate_divs_ineq depend on the other divs remaining in place.
1254 */
1255 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1256 int pos)
1257 {
1258 int i;
1259
1260 for (i = 0; i < bmap->n_div; ++i) {
1261 if (isl_int_is_zero(bmap->div[i][0]))
1262 continue;
1263 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1264 continue;
1265 isl_int_set_si(bmap->div[i][0], 0);
1266 }
1267 return bmap;
1268 }
1269
1270 /* Eliminate the specified variables from the constraints using
1271 * Fourier-Motzkin. The variables themselves are not removed.
1272 */
1273 struct isl_basic_map *isl_basic_map_eliminate_vars(
1274 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1275 {
1276 int d;
1277 int i, j, k;
1278 unsigned total;
1279
1280 if (n == 0)
1281 return bmap;
1282 if (!bmap)
1283 return NULL;
1284 total = isl_basic_map_total_dim(bmap);
1285
1286 bmap = isl_basic_map_cow(bmap);
1287 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1288 bmap = remove_dependent_vars(bmap, d);
1289
1290 for (d = pos + n - 1;
1291 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1292 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1293 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1294 int n_lower, n_upper;
1295 if (!bmap)
1296 return NULL;
1297 for (i = 0; i < bmap->n_eq; ++i) {
1298 if (isl_int_is_zero(bmap->eq[i][1+d]))
1299 continue;
1300 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1301 isl_basic_map_drop_equality(bmap, i);
1302 break;
1303 }
1304 if (i < bmap->n_eq)
1305 continue;
1306 n_lower = 0;
1307 n_upper = 0;
1308 for (i = 0; i < bmap->n_ineq; ++i) {
1309 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1310 n_lower++;
1311 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1312 n_upper++;
1313 }
1314 bmap = isl_basic_map_extend_constraints(bmap,
1315 0, n_lower * n_upper);
1316 if (!bmap)
1317 goto error;
1318 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1319 int last;
1320 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1321 continue;
1322 last = -1;
1323 for (j = 0; j < i; ++j) {
1324 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1325 continue;
1326 last = j;
1327 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1328 isl_int_sgn(bmap->ineq[j][1+d]))
1329 continue;
1330 k = isl_basic_map_alloc_inequality(bmap);
1331 if (k < 0)
1332 goto error;
1333 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1334 1+total);
1335 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1336 1+d, 1+total, NULL);
1337 }
1338 isl_basic_map_drop_inequality(bmap, i);
1339 i = last + 1;
1340 }
1341 if (n_lower > 0 && n_upper > 0) {
1342 bmap = isl_basic_map_normalize_constraints(bmap);
1343 bmap = remove_duplicate_constraints(bmap, NULL, 0);
1344 bmap = isl_basic_map_gauss(bmap, NULL);
1345 bmap = isl_basic_map_remove_redundancies(bmap);
1346 if (!bmap)
1347 goto error;
1348 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1349 break;
1350 }
1351 }
1352 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1353 return bmap;
1354 error:
1355 isl_basic_map_free(bmap);
1356 return NULL;
1357 }
1358
1359 struct isl_basic_set *isl_basic_set_eliminate_vars(
1360 struct isl_basic_set *bset, unsigned pos, unsigned n)
1361 {
1362 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1363 (struct isl_basic_map *)bset, pos, n);
1364 }
1365
1366 /* Don't assume equalities are in order, because align_divs
1367 * may have changed the order of the divs.
1368 */
1369 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1370 {
1371 int d, i;
1372 unsigned total;
1373
1374 total = isl_dim_total(bmap->dim);
1375 for (d = 0; d < total; ++d)
1376 elim[d] = -1;
1377 for (i = 0; i < bmap->n_eq; ++i) {
1378 for (d = total - 1; d >= 0; --d) {
1379 if (isl_int_is_zero(bmap->eq[i][1+d]))
1380 continue;
1381 elim[d] = i;
1382 break;
1383 }
1384 }
1385 }
1386
1387 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1388 {
1389 compute_elimination_index((struct isl_basic_map *)bset, elim);
1390 }
1391
1392 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1393 struct isl_basic_map *bmap, int *elim)
1394 {
1395 int d;
1396 int copied = 0;
1397 unsigned total;
1398
1399 total = isl_dim_total(bmap->dim);
1400 for (d = total - 1; d >= 0; --d) {
1401 if (isl_int_is_zero(src[1+d]))
1402 continue;
1403 if (elim[d] == -1)
1404 continue;
1405 if (!copied) {
1406 isl_seq_cpy(dst, src, 1 + total);
1407 copied = 1;
1408 }
1409 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1410 }
1411 return copied;
1412 }
1413
1414 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1415 struct isl_basic_set *bset, int *elim)
1416 {
1417 return reduced_using_equalities(dst, src,
1418 (struct isl_basic_map *)bset, elim);
1419 }
1420
1421 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1422 struct isl_basic_set *bset, struct isl_basic_set *context)
1423 {
1424 int i;
1425 int *elim;
1426
1427 if (!bset || !context)
1428 goto error;
1429
1430 if (context->n_eq == 0) {
1431 isl_basic_set_free(context);
1432 return bset;
1433 }
1434
1435 bset = isl_basic_set_cow(bset);
1436 if (!bset)
1437 goto error;
1438
1439 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1440 if (!elim)
1441 goto error;
1442 set_compute_elimination_index(context, elim);
1443 for (i = 0; i < bset->n_eq; ++i)
1444 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1445 context, elim);
1446 for (i = 0; i < bset->n_ineq; ++i)
1447 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1448 context, elim);
1449 isl_basic_set_free(context);
1450 free(elim);
1451 bset = isl_basic_set_simplify(bset);
1452 bset = isl_basic_set_finalize(bset);
1453 return bset;
1454 error:
1455 isl_basic_set_free(bset);
1456 isl_basic_set_free(context);
1457 return NULL;
1458 }
1459
1460 static struct isl_basic_set *remove_shifted_constraints(
1461 struct isl_basic_set *bset, struct isl_basic_set *context)
1462 {
1463 unsigned int size;
1464 isl_int ***index;
1465 int bits;
1466 int k, h, l;
1467 isl_ctx *ctx;
1468
1469 if (!bset)
1470 return NULL;
1471
1472 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1473 bits = ffs(size) - 1;
1474 ctx = isl_basic_set_get_ctx(bset);
1475 index = isl_calloc_array(ctx, isl_int **, size);
1476 if (!index)
1477 return bset;
1478
1479 for (k = 0; k < context->n_ineq; ++k) {
1480 h = set_hash_index(index, size, bits, context, k);
1481 index[h] = &context->ineq[k];
1482 }
1483 for (k = 0; k < bset->n_ineq; ++k) {
1484 h = set_hash_index(index, size, bits, bset, k);
1485 if (!index[h])
1486 continue;
1487 l = index[h] - &context->ineq[0];
1488 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1489 continue;
1490 bset = isl_basic_set_cow(bset);
1491 if (!bset)
1492 goto error;
1493 isl_basic_set_drop_inequality(bset, k);
1494 --k;
1495 }
1496 free(index);
1497 return bset;
1498 error:
1499 free(index);
1500 return bset;
1501 }
1502
1503 /* Remove all information from bset that is redundant in the context
1504 * of context. Both bset and context are assumed to be full-dimensional.
1505 *
1506 * We first * remove the inequalities from "bset"
1507 * that are obviously redundant with respect to some inequality in "context".
1508 *
1509 * If there are any inequalities left, we construct a tableau for
1510 * the context and then add the inequalities of "bset".
1511 * Before adding these inequalities, we freeze all constraints such that
1512 * they won't be considered redundant in terms of the constraints of "bset".
1513 * Then we detect all redundant constraints (among the
1514 * constraints that weren't frozen), first by checking for redundancy in the
1515 * the tableau and then by checking if replacing a constraint by its negation
1516 * would lead to an empty set. This last step is fairly expensive
1517 * and could be optimized by more reuse of the tableau.
1518 * Finally, we update bset according to the results.
1519 */
1520 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1521 __isl_take isl_basic_set *context)
1522 {
1523 int i, k;
1524 isl_basic_set *combined = NULL;
1525 struct isl_tab *tab = NULL;
1526 unsigned context_ineq;
1527 unsigned total;
1528
1529 if (!bset || !context)
1530 goto error;
1531
1532 if (isl_basic_set_is_universe(bset)) {
1533 isl_basic_set_free(context);
1534 return bset;
1535 }
1536
1537 if (isl_basic_set_is_universe(context)) {
1538 isl_basic_set_free(context);
1539 return bset;
1540 }
1541
1542 bset = remove_shifted_constraints(bset, context);
1543 if (!bset)
1544 goto error;
1545 if (bset->n_ineq == 0)
1546 goto done;
1547
1548 context_ineq = context->n_ineq;
1549 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1550 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1551 tab = isl_tab_from_basic_set(combined);
1552 for (i = 0; i < context_ineq; ++i)
1553 if (isl_tab_freeze_constraint(tab, i) < 0)
1554 goto error;
1555 tab = isl_tab_extend(tab, bset->n_ineq);
1556 for (i = 0; i < bset->n_ineq; ++i)
1557 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1558 goto error;
1559 bset = isl_basic_set_add_constraints(combined, bset, 0);
1560 combined = NULL;
1561 if (!bset)
1562 goto error;
1563 if (isl_tab_detect_redundant(tab) < 0)
1564 goto error;
1565 total = isl_basic_set_total_dim(bset);
1566 for (i = context_ineq; i < bset->n_ineq; ++i) {
1567 int is_empty;
1568 if (tab->con[i].is_redundant)
1569 continue;
1570 tab->con[i].is_redundant = 1;
1571 combined = isl_basic_set_dup(bset);
1572 combined = isl_basic_set_update_from_tab(combined, tab);
1573 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1574 k = isl_basic_set_alloc_inequality(combined);
1575 if (k < 0)
1576 goto error;
1577 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1578 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1579 is_empty = isl_basic_set_is_empty(combined);
1580 if (is_empty < 0)
1581 goto error;
1582 isl_basic_set_free(combined);
1583 combined = NULL;
1584 if (!is_empty)
1585 tab->con[i].is_redundant = 0;
1586 }
1587 for (i = 0; i < context_ineq; ++i)
1588 tab->con[i].is_redundant = 1;
1589 bset = isl_basic_set_update_from_tab(bset, tab);
1590 if (bset) {
1591 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1592 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1593 }
1594
1595 isl_tab_free(tab);
1596 done:
1597 bset = isl_basic_set_simplify(bset);
1598 bset = isl_basic_set_finalize(bset);
1599 isl_basic_set_free(context);
1600 return bset;
1601 error:
1602 isl_tab_free(tab);
1603 isl_basic_set_free(combined);
1604 isl_basic_set_free(context);
1605 isl_basic_set_free(bset);
1606 return NULL;
1607 }
1608
1609 /* Remove all information from bset that is redundant in the context
1610 * of context. In particular, equalities that are linear combinations
1611 * of those in context are removed. Then the inequalities that are
1612 * redundant in the context of the equalities and inequalities of
1613 * context are removed.
1614 *
1615 * We first compute the integer affine hull of the intersection,
1616 * compute the gist inside this affine hull and then add back
1617 * those equalities that are not implied by the context.
1618 *
1619 * If two constraints are mutually redundant, then uset_gist_full
1620 * will remove the second of those constraints. We therefore first
1621 * sort the constraints so that constraints not involving existentially
1622 * quantified variables are given precedence over those that do.
1623 * We have to perform this sorting before the variable compression,
1624 * because that may effect the order of the variables.
1625 */
1626 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1627 __isl_take isl_basic_set *context)
1628 {
1629 isl_mat *eq;
1630 isl_mat *T, *T2;
1631 isl_basic_set *aff;
1632 isl_basic_set *aff_context;
1633 unsigned total;
1634
1635 if (!bset || !context)
1636 goto error;
1637
1638 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1639 if (isl_basic_set_plain_is_empty(bset)) {
1640 isl_basic_set_free(context);
1641 return bset;
1642 }
1643 bset = isl_basic_set_sort_constraints(bset);
1644 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1645 if (!aff)
1646 goto error;
1647 if (isl_basic_set_plain_is_empty(aff)) {
1648 isl_basic_set_free(aff);
1649 isl_basic_set_free(context);
1650 return bset;
1651 }
1652 if (aff->n_eq == 0) {
1653 isl_basic_set_free(aff);
1654 return uset_gist_full(bset, context);
1655 }
1656 total = isl_basic_set_total_dim(bset);
1657 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1658 eq = isl_mat_cow(eq);
1659 T = isl_mat_variable_compression(eq, &T2);
1660 if (T && T->n_col == 0) {
1661 isl_mat_free(T);
1662 isl_mat_free(T2);
1663 isl_basic_set_free(context);
1664 isl_basic_set_free(aff);
1665 return isl_basic_set_set_to_empty(bset);
1666 }
1667
1668 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1669
1670 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1671 context = isl_basic_set_preimage(context, T);
1672
1673 bset = uset_gist_full(bset, context);
1674 bset = isl_basic_set_preimage(bset, T2);
1675 bset = isl_basic_set_intersect(bset, aff);
1676 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1677
1678 if (bset) {
1679 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1680 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1681 }
1682
1683 return bset;
1684 error:
1685 isl_basic_set_free(bset);
1686 isl_basic_set_free(context);
1687 return NULL;
1688 }
1689
1690 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1691 * We simply add the equalities in context to bmap and then do a regular
1692 * div normalizations. Better results can be obtained by normalizing
1693 * only the divs in bmap than do not also appear in context.
1694 * We need to be careful to reduce the divs using the equalities
1695 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1696 * spurious constraints.
1697 */
1698 static struct isl_basic_map *normalize_divs_in_context(
1699 struct isl_basic_map *bmap, struct isl_basic_map *context)
1700 {
1701 int i;
1702 unsigned total_context;
1703 int div_eq;
1704
1705 div_eq = n_pure_div_eq(bmap);
1706 if (div_eq == 0)
1707 return bmap;
1708
1709 if (context->n_div > 0)
1710 bmap = isl_basic_map_align_divs(bmap, context);
1711
1712 total_context = isl_basic_map_total_dim(context);
1713 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1714 for (i = 0; i < context->n_eq; ++i) {
1715 int k;
1716 k = isl_basic_map_alloc_equality(bmap);
1717 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1718 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1719 isl_basic_map_total_dim(bmap) - total_context);
1720 }
1721 bmap = isl_basic_map_gauss(bmap, NULL);
1722 bmap = normalize_divs(bmap, NULL);
1723 bmap = isl_basic_map_gauss(bmap, NULL);
1724 return bmap;
1725 }
1726
1727 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1728 struct isl_basic_map *context)
1729 {
1730 struct isl_basic_set *bset;
1731
1732 if (!bmap || !context)
1733 goto error;
1734
1735 if (isl_basic_map_is_universe(bmap)) {
1736 isl_basic_map_free(context);
1737 return bmap;
1738 }
1739 if (isl_basic_map_plain_is_empty(context)) {
1740 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1741 isl_basic_map_free(context);
1742 isl_basic_map_free(bmap);
1743 return isl_basic_map_universe(dim);
1744 }
1745 if (isl_basic_map_plain_is_empty(bmap)) {
1746 isl_basic_map_free(context);
1747 return bmap;
1748 }
1749
1750 bmap = isl_basic_map_remove_redundancies(bmap);
1751 context = isl_basic_map_remove_redundancies(context);
1752
1753 if (context->n_eq)
1754 bmap = normalize_divs_in_context(bmap, context);
1755
1756 context = isl_basic_map_align_divs(context, bmap);
1757 bmap = isl_basic_map_align_divs(bmap, context);
1758
1759 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1760 isl_basic_map_underlying_set(context));
1761
1762 return isl_basic_map_overlying_set(bset, bmap);
1763 error:
1764 isl_basic_map_free(bmap);
1765 isl_basic_map_free(context);
1766 return NULL;
1767 }
1768
1769 /*
1770 * Assumes context has no implicit divs.
1771 */
1772 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1773 __isl_take isl_basic_map *context)
1774 {
1775 int i;
1776
1777 if (!map || !context)
1778 goto error;;
1779
1780 if (isl_basic_map_plain_is_empty(context)) {
1781 struct isl_dim *dim = isl_dim_copy(map->dim);
1782 isl_basic_map_free(context);
1783 isl_map_free(map);
1784 return isl_map_universe(dim);
1785 }
1786
1787 context = isl_basic_map_remove_redundancies(context);
1788 map = isl_map_cow(map);
1789 if (!map || !context)
1790 goto error;;
1791 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1792 map = isl_map_compute_divs(map);
1793 for (i = 0; i < map->n; ++i)
1794 context = isl_basic_map_align_divs(context, map->p[i]);
1795 for (i = map->n - 1; i >= 0; --i) {
1796 map->p[i] = isl_basic_map_gist(map->p[i],
1797 isl_basic_map_copy(context));
1798 if (!map->p[i])
1799 goto error;
1800 if (isl_basic_map_plain_is_empty(map->p[i])) {
1801 isl_basic_map_free(map->p[i]);
1802 if (i != map->n - 1)
1803 map->p[i] = map->p[map->n - 1];
1804 map->n--;
1805 }
1806 }
1807 isl_basic_map_free(context);
1808 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1809 return map;
1810 error:
1811 isl_map_free(map);
1812 isl_basic_map_free(context);
1813 return NULL;
1814 }
1815
1816 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1817 __isl_take isl_map *context)
1818 {
1819 context = isl_map_compute_divs(context);
1820 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1821 }
1822
1823 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1824 struct isl_basic_set *context)
1825 {
1826 return (struct isl_basic_set *)isl_basic_map_gist(
1827 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1828 }
1829
1830 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1831 __isl_take isl_basic_set *context)
1832 {
1833 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1834 (struct isl_basic_map *)context);
1835 }
1836
1837 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1838 __isl_take isl_set *context)
1839 {
1840 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1841 (struct isl_map *)context);
1842 }
1843
1844 /* Quick check to see if two basic maps are disjoint.
1845 * In particular, we reduce the equalities and inequalities of
1846 * one basic map in the context of the equalities of the other
1847 * basic map and check if we get a contradiction.
1848 */
1849 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1850 __isl_keep isl_basic_map *bmap2)
1851 {
1852 struct isl_vec *v = NULL;
1853 int *elim = NULL;
1854 unsigned total;
1855 int i;
1856
1857 if (!bmap1 || !bmap2)
1858 return -1;
1859 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1860 return -1);
1861 if (bmap1->n_div || bmap2->n_div)
1862 return 0;
1863 if (!bmap1->n_eq && !bmap2->n_eq)
1864 return 0;
1865
1866 total = isl_dim_total(bmap1->dim);
1867 if (total == 0)
1868 return 0;
1869 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1870 if (!v)
1871 goto error;
1872 elim = isl_alloc_array(bmap1->ctx, int, total);
1873 if (!elim)
1874 goto error;
1875 compute_elimination_index(bmap1, elim);
1876 for (i = 0; i < bmap2->n_eq; ++i) {
1877 int reduced;
1878 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1879 bmap1, elim);
1880 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1881 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1882 goto disjoint;
1883 }
1884 for (i = 0; i < bmap2->n_ineq; ++i) {
1885 int reduced;
1886 reduced = reduced_using_equalities(v->block.data,
1887 bmap2->ineq[i], bmap1, elim);
1888 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1889 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1890 goto disjoint;
1891 }
1892 compute_elimination_index(bmap2, elim);
1893 for (i = 0; i < bmap1->n_ineq; ++i) {
1894 int reduced;
1895 reduced = reduced_using_equalities(v->block.data,
1896 bmap1->ineq[i], bmap2, elim);
1897 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1898 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1899 goto disjoint;
1900 }
1901 isl_vec_free(v);
1902 free(elim);
1903 return 0;
1904 disjoint:
1905 isl_vec_free(v);
1906 free(elim);
1907 return 1;
1908 error:
1909 isl_vec_free(v);
1910 free(elim);
1911 return -1;
1912 }
1913
1914 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1915 __isl_keep isl_basic_set *bset2)
1916 {
1917 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
1918 (struct isl_basic_map *)bset2);
1919 }
1920
1921 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
1922 __isl_keep isl_map *map2)
1923 {
1924 int i, j;
1925
1926 if (!map1 || !map2)
1927 return -1;
1928
1929 if (isl_map_plain_is_equal(map1, map2))
1930 return 0;
1931
1932 for (i = 0; i < map1->n; ++i) {
1933 for (j = 0; j < map2->n; ++j) {
1934 int d = isl_basic_map_plain_is_disjoint(map1->p[i],
1935 map2->p[j]);
1936 if (d != 1)
1937 return d;
1938 }
1939 }
1940 return 1;
1941 }
1942
1943 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1944 __isl_keep isl_set *set2)
1945 {
1946 return isl_map_plain_is_disjoint((struct isl_map *)set1,
1947 (struct isl_map *)set2);
1948 }
1949
1950 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
1951 {
1952 return isl_set_plain_is_disjoint(set1, set2);
1953 }
1954
1955 /* Check if we can combine a given div with lower bound l and upper
1956 * bound u with some other div and if so return that other div.
1957 * Otherwise return -1.
1958 *
1959 * We first check that
1960 * - the bounds are opposites of each other (except for the constant
1961 * term)
1962 * - the bounds do not reference any other div
1963 * - no div is defined in terms of this div
1964 *
1965 * Let m be the size of the range allowed on the div by the bounds.
1966 * That is, the bounds are of the form
1967 *
1968 * e <= a <= e + m - 1
1969 *
1970 * with e some expression in the other variables.
1971 * We look for another div b such that no third div is defined in terms
1972 * of this second div b and such that in any constraint that contains
1973 * a (except for the given lower and upper bound), also contains b
1974 * with a coefficient that is m times that of b.
1975 * That is, all constraints (execpt for the lower and upper bound)
1976 * are of the form
1977 *
1978 * e + f (a + m b) >= 0
1979 *
1980 * If so, we return b so that "a + m b" can be replaced by
1981 * a single div "c = a + m b".
1982 */
1983 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1984 unsigned div, unsigned l, unsigned u)
1985 {
1986 int i, j;
1987 unsigned dim;
1988 int coalesce = -1;
1989
1990 if (bmap->n_div <= 1)
1991 return -1;
1992 dim = isl_dim_total(bmap->dim);
1993 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1994 return -1;
1995 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1996 bmap->n_div - div - 1) != -1)
1997 return -1;
1998 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1999 dim + bmap->n_div))
2000 return -1;
2001
2002 for (i = 0; i < bmap->n_div; ++i) {
2003 if (isl_int_is_zero(bmap->div[i][0]))
2004 continue;
2005 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2006 return -1;
2007 }
2008
2009 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2010 if (isl_int_is_neg(bmap->ineq[l][0])) {
2011 isl_int_sub(bmap->ineq[l][0],
2012 bmap->ineq[l][0], bmap->ineq[u][0]);
2013 bmap = isl_basic_map_copy(bmap);
2014 bmap = isl_basic_map_set_to_empty(bmap);
2015 isl_basic_map_free(bmap);
2016 return -1;
2017 }
2018 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2019 for (i = 0; i < bmap->n_div; ++i) {
2020 if (i == div)
2021 continue;
2022 if (!pairs[i])
2023 continue;
2024 for (j = 0; j < bmap->n_div; ++j) {
2025 if (isl_int_is_zero(bmap->div[j][0]))
2026 continue;
2027 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2028 break;
2029 }
2030 if (j < bmap->n_div)
2031 continue;
2032 for (j = 0; j < bmap->n_ineq; ++j) {
2033 int valid;
2034 if (j == l || j == u)
2035 continue;
2036 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2037 continue;
2038 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2039 break;
2040 isl_int_mul(bmap->ineq[j][1 + dim + div],
2041 bmap->ineq[j][1 + dim + div],
2042 bmap->ineq[l][0]);
2043 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2044 bmap->ineq[j][1 + dim + i]);
2045 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2046 bmap->ineq[j][1 + dim + div],
2047 bmap->ineq[l][0]);
2048 if (!valid)
2049 break;
2050 }
2051 if (j < bmap->n_ineq)
2052 continue;
2053 coalesce = i;
2054 break;
2055 }
2056 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2057 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2058 return coalesce;
2059 }
2060
2061 /* Given a lower and an upper bound on div i, construct an inequality
2062 * that when nonnegative ensures that this pair of bounds always allows
2063 * for an integer value of the given div.
2064 * The lower bound is inequality l, while the upper bound is inequality u.
2065 * The constructed inequality is stored in ineq.
2066 * g, fl, fu are temporary scalars.
2067 *
2068 * Let the upper bound be
2069 *
2070 * -n_u a + e_u >= 0
2071 *
2072 * and the lower bound
2073 *
2074 * n_l a + e_l >= 0
2075 *
2076 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2077 * We have
2078 *
2079 * - f_u e_l <= f_u f_l g a <= f_l e_u
2080 *
2081 * Since all variables are integer valued, this is equivalent to
2082 *
2083 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2084 *
2085 * If this interval is at least f_u f_l g, then it contains at least
2086 * one integer value for a.
2087 * That is, the test constraint is
2088 *
2089 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2090 */
2091 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2092 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2093 {
2094 unsigned dim;
2095 dim = isl_dim_total(bmap->dim);
2096
2097 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2098 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2099 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2100 isl_int_neg(fu, fu);
2101 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2102 1 + dim + bmap->n_div);
2103 isl_int_add(ineq[0], ineq[0], fl);
2104 isl_int_add(ineq[0], ineq[0], fu);
2105 isl_int_sub_ui(ineq[0], ineq[0], 1);
2106 isl_int_mul(g, g, fl);
2107 isl_int_mul(g, g, fu);
2108 isl_int_sub(ineq[0], ineq[0], g);
2109 }
2110
2111 /* Remove more kinds of divs that are not strictly needed.
2112 * In particular, if all pairs of lower and upper bounds on a div
2113 * are such that they allow at least one integer value of the div,
2114 * the we can eliminate the div using Fourier-Motzkin without
2115 * introducing any spurious solutions.
2116 */
2117 static struct isl_basic_map *drop_more_redundant_divs(
2118 struct isl_basic_map *bmap, int *pairs, int n)
2119 {
2120 struct isl_tab *tab = NULL;
2121 struct isl_vec *vec = NULL;
2122 unsigned dim;
2123 int remove = -1;
2124 isl_int g, fl, fu;
2125
2126 isl_int_init(g);
2127 isl_int_init(fl);
2128 isl_int_init(fu);
2129
2130 if (!bmap)
2131 goto error;
2132
2133 dim = isl_dim_total(bmap->dim);
2134 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2135 if (!vec)
2136 goto error;
2137
2138 tab = isl_tab_from_basic_map(bmap);
2139
2140 while (n > 0) {
2141 int i, l, u;
2142 int best = -1;
2143 enum isl_lp_result res;
2144
2145 for (i = 0; i < bmap->n_div; ++i) {
2146 if (!pairs[i])
2147 continue;
2148 if (best >= 0 && pairs[best] <= pairs[i])
2149 continue;
2150 best = i;
2151 }
2152
2153 i = best;
2154 for (l = 0; l < bmap->n_ineq; ++l) {
2155 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2156 continue;
2157 for (u = 0; u < bmap->n_ineq; ++u) {
2158 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2159 continue;
2160 construct_test_ineq(bmap, i, l, u,
2161 vec->el, g, fl, fu);
2162 res = isl_tab_min(tab, vec->el,
2163 bmap->ctx->one, &g, NULL, 0);
2164 if (res == isl_lp_error)
2165 goto error;
2166 if (res == isl_lp_empty) {
2167 bmap = isl_basic_map_set_to_empty(bmap);
2168 break;
2169 }
2170 if (res != isl_lp_ok || isl_int_is_neg(g))
2171 break;
2172 }
2173 if (u < bmap->n_ineq)
2174 break;
2175 }
2176 if (l == bmap->n_ineq) {
2177 remove = i;
2178 break;
2179 }
2180 pairs[i] = 0;
2181 --n;
2182 }
2183
2184 isl_tab_free(tab);
2185 isl_vec_free(vec);
2186
2187 isl_int_clear(g);
2188 isl_int_clear(fl);
2189 isl_int_clear(fu);
2190
2191 free(pairs);
2192
2193 if (remove < 0)
2194 return bmap;
2195
2196 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2197 return isl_basic_map_drop_redundant_divs(bmap);
2198 error:
2199 free(pairs);
2200 isl_basic_map_free(bmap);
2201 isl_tab_free(tab);
2202 isl_vec_free(vec);
2203 isl_int_clear(g);
2204 isl_int_clear(fl);
2205 isl_int_clear(fu);
2206 return NULL;
2207 }
2208
2209 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2210 * and the upper bound u, div1 always occurs together with div2 in the form
2211 * (div1 + m div2), where m is the constant range on the variable div1
2212 * allowed by l and u, replace the pair div1 and div2 by a single
2213 * div that is equal to div1 + m div2.
2214 *
2215 * The new div will appear in the location that contains div2.
2216 * We need to modify all constraints that contain
2217 * div2 = (div - div1) / m
2218 * (If a constraint does not contain div2, it will also not contain div1.)
2219 * If the constraint also contains div1, then we know they appear
2220 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2221 * i.e., the coefficient of div is f.
2222 *
2223 * Otherwise, we first need to introduce div1 into the constraint.
2224 * Let the l be
2225 *
2226 * div1 + f >=0
2227 *
2228 * and u
2229 *
2230 * -div1 + f' >= 0
2231 *
2232 * A lower bound on div2
2233 *
2234 * n div2 + t >= 0
2235 *
2236 * can be replaced by
2237 *
2238 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2239 *
2240 * with g = gcd(m,n).
2241 * An upper bound
2242 *
2243 * -n div2 + t >= 0
2244 *
2245 * can be replaced by
2246 *
2247 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2248 *
2249 * These constraint are those that we would obtain from eliminating
2250 * div1 using Fourier-Motzkin.
2251 *
2252 * After all constraints have been modified, we drop the lower and upper
2253 * bound and then drop div1.
2254 */
2255 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2256 unsigned div1, unsigned div2, unsigned l, unsigned u)
2257 {
2258 isl_int a;
2259 isl_int b;
2260 isl_int m;
2261 unsigned dim, total;
2262 int i;
2263
2264 dim = isl_dim_total(bmap->dim);
2265 total = 1 + dim + bmap->n_div;
2266
2267 isl_int_init(a);
2268 isl_int_init(b);
2269 isl_int_init(m);
2270 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2271 isl_int_add_ui(m, m, 1);
2272
2273 for (i = 0; i < bmap->n_ineq; ++i) {
2274 if (i == l || i == u)
2275 continue;
2276 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2277 continue;
2278 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2279 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2280 isl_int_divexact(a, m, b);
2281 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2282 if (isl_int_is_pos(b)) {
2283 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2284 b, bmap->ineq[l], total);
2285 } else {
2286 isl_int_neg(b, b);
2287 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2288 b, bmap->ineq[u], total);
2289 }
2290 }
2291 isl_int_set(bmap->ineq[i][1 + dim + div2],
2292 bmap->ineq[i][1 + dim + div1]);
2293 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2294 }
2295
2296 isl_int_clear(a);
2297 isl_int_clear(b);
2298 isl_int_clear(m);
2299 if (l > u) {
2300 isl_basic_map_drop_inequality(bmap, l);
2301 isl_basic_map_drop_inequality(bmap, u);
2302 } else {
2303 isl_basic_map_drop_inequality(bmap, u);
2304 isl_basic_map_drop_inequality(bmap, l);
2305 }
2306 bmap = isl_basic_map_drop_div(bmap, div1);
2307 return bmap;
2308 }
2309
2310 /* First check if we can coalesce any pair of divs and
2311 * then continue with dropping more redundant divs.
2312 *
2313 * We loop over all pairs of lower and upper bounds on a div
2314 * with coefficient 1 and -1, respectively, check if there
2315 * is any other div "c" with which we can coalesce the div
2316 * and if so, perform the coalescing.
2317 */
2318 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2319 struct isl_basic_map *bmap, int *pairs, int n)
2320 {
2321 int i, l, u;
2322 unsigned dim;
2323
2324 dim = isl_dim_total(bmap->dim);
2325
2326 for (i = 0; i < bmap->n_div; ++i) {
2327 if (!pairs[i])
2328 continue;
2329 for (l = 0; l < bmap->n_ineq; ++l) {
2330 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2331 continue;
2332 for (u = 0; u < bmap->n_ineq; ++u) {
2333 int c;
2334
2335 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2336 continue;
2337 c = div_find_coalesce(bmap, pairs, i, l, u);
2338 if (c < 0)
2339 continue;
2340 free(pairs);
2341 bmap = coalesce_divs(bmap, i, c, l, u);
2342 return isl_basic_map_drop_redundant_divs(bmap);
2343 }
2344 }
2345 }
2346
2347 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2348 return bmap;
2349
2350 return drop_more_redundant_divs(bmap, pairs, n);
2351 }
2352
2353 /* Remove divs that are not strictly needed.
2354 * In particular, if a div only occurs positively (or negatively)
2355 * in constraints, then it can simply be dropped.
2356 * Also, if a div occurs only occurs in two constraints and if moreover
2357 * those two constraints are opposite to each other, except for the constant
2358 * term and if the sum of the constant terms is such that for any value
2359 * of the other values, there is always at least one integer value of the
2360 * div, i.e., if one plus this sum is greater than or equal to
2361 * the (absolute value) of the coefficent of the div in the constraints,
2362 * then we can also simply drop the div.
2363 *
2364 * If any divs are left after these simple checks then we move on
2365 * to more complicated cases in drop_more_redundant_divs.
2366 */
2367 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2368 struct isl_basic_map *bmap)
2369 {
2370 int i, j;
2371 unsigned off;
2372 int *pairs = NULL;
2373 int n = 0;
2374
2375 if (!bmap)
2376 goto error;
2377
2378 off = isl_dim_total(bmap->dim);
2379 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2380 if (!pairs)
2381 goto error;
2382
2383 for (i = 0; i < bmap->n_div; ++i) {
2384 int pos, neg;
2385 int last_pos, last_neg;
2386 int redundant;
2387 int defined;
2388
2389 defined = !isl_int_is_zero(bmap->div[i][0]);
2390 for (j = 0; j < bmap->n_eq; ++j)
2391 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2392 break;
2393 if (j < bmap->n_eq)
2394 continue;
2395 ++n;
2396 pos = neg = 0;
2397 for (j = 0; j < bmap->n_ineq; ++j) {
2398 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2399 last_pos = j;
2400 ++pos;
2401 }
2402 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2403 last_neg = j;
2404 ++neg;
2405 }
2406 }
2407 pairs[i] = pos * neg;
2408 if (pairs[i] == 0) {
2409 for (j = bmap->n_ineq - 1; j >= 0; --j)
2410 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2411 isl_basic_map_drop_inequality(bmap, j);
2412 bmap = isl_basic_map_drop_div(bmap, i);
2413 free(pairs);
2414 return isl_basic_map_drop_redundant_divs(bmap);
2415 }
2416 if (pairs[i] != 1)
2417 continue;
2418 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2419 bmap->ineq[last_neg] + 1,
2420 off + bmap->n_div))
2421 continue;
2422
2423 isl_int_add(bmap->ineq[last_pos][0],
2424 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2425 isl_int_add_ui(bmap->ineq[last_pos][0],
2426 bmap->ineq[last_pos][0], 1);
2427 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2428 bmap->ineq[last_pos][1+off+i]);
2429 isl_int_sub_ui(bmap->ineq[last_pos][0],
2430 bmap->ineq[last_pos][0], 1);
2431 isl_int_sub(bmap->ineq[last_pos][0],
2432 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2433 if (!redundant) {
2434 if (defined ||
2435 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2436 pairs[i] = 0;
2437 --n;
2438 continue;
2439 }
2440 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2441 bmap = isl_basic_map_simplify(bmap);
2442 free(pairs);
2443 return isl_basic_map_drop_redundant_divs(bmap);
2444 }
2445 if (last_pos > last_neg) {
2446 isl_basic_map_drop_inequality(bmap, last_pos);
2447 isl_basic_map_drop_inequality(bmap, last_neg);
2448 } else {
2449 isl_basic_map_drop_inequality(bmap, last_neg);
2450 isl_basic_map_drop_inequality(bmap, last_pos);
2451 }
2452 bmap = isl_basic_map_drop_div(bmap, i);
2453 free(pairs);
2454 return isl_basic_map_drop_redundant_divs(bmap);
2455 }
2456
2457 if (n > 0)
2458 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2459
2460 free(pairs);
2461 return bmap;
2462 error:
2463 free(pairs);
2464 isl_basic_map_free(bmap);
2465 return NULL;
2466 }
2467
2468 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2469 struct isl_basic_set *bset)
2470 {
2471 return (struct isl_basic_set *)
2472 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2473 }
2474
2475 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2476 {
2477 int i;
2478
2479 if (!map)
2480 return NULL;
2481 for (i = 0; i < map->n; ++i) {
2482 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2483 if (!map->p[i])
2484 goto error;
2485 }
2486 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2487 return map;
2488 error:
2489 isl_map_free(map);
2490 return NULL;
2491 }
2492
2493 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2494 {
2495 return (struct isl_set *)
2496 isl_map_drop_redundant_divs((struct isl_map *)set);
2497 }
Integer set library