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isl_morph_basic_set: preserve rationality of input
[isl.git] / isl_map_simplify.c
blob302c12343ba1ebf5f11757c60c265b2342e8b80d
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 <isl_map_private.h>
11 #include "isl_equalities.h"
12 #include <isl/map.h>
13 #include <isl/seq.h>
14 #include "isl_tab.h"
15 #include <isl_dim_private.h>
16 #include <isl_mat_private.h>
17
18 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
19 {
20 isl_int *t = bmap->eq[a];
21 bmap->eq[a] = bmap->eq[b];
22 bmap->eq[b] = t;
23 }
24
25 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
26 {
27 if (a != b) {
28 isl_int *t = bmap->ineq[a];
29 bmap->ineq[a] = bmap->ineq[b];
30 bmap->ineq[b] = t;
31 }
32 }
33
34 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
35 {
36 swap_inequality((struct isl_basic_map *)bset, a, b);
37 }
38
39 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
40 {
41 isl_seq_cpy(c, c + n, rem);
42 isl_seq_clr(c + rem, n);
43 }
44
45 /* Drop n dimensions starting at first.
46 *
47 * In principle, this frees up some extra variables as the number
48 * of columns remains constant, but we would have to extend
49 * the div array too as the number of rows in this array is assumed
50 * to be equal to extra.
51 */
52 struct isl_basic_set *isl_basic_set_drop_dims(
53 struct isl_basic_set *bset, unsigned first, unsigned n)
54 {
55 int i;
56
57 if (!bset)
58 goto error;
59
60 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
61
62 if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
63 return bset;
64
65 bset = isl_basic_set_cow(bset);
66 if (!bset)
67 return NULL;
68
69 for (i = 0; i < bset->n_eq; ++i)
70 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
71 (bset->dim->n_out-first-n)+bset->extra);
72
73 for (i = 0; i < bset->n_ineq; ++i)
74 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
75 (bset->dim->n_out-first-n)+bset->extra);
76
77 for (i = 0; i < bset->n_div; ++i)
78 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
79 (bset->dim->n_out-first-n)+bset->extra);
80
81 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
82 if (!bset->dim)
83 goto error;
84
85 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
86 bset = isl_basic_set_simplify(bset);
87 return isl_basic_set_finalize(bset);
88 error:
89 isl_basic_set_free(bset);
90 return NULL;
91 }
92
93 struct isl_set *isl_set_drop_dims(
94 struct isl_set *set, unsigned first, unsigned n)
95 {
96 int i;
97
98 if (!set)
99 goto error;
100
101 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
102
103 if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
104 return set;
105 set = isl_set_cow(set);
106 if (!set)
107 goto error;
108 set->dim = isl_dim_drop_outputs(set->dim, first, n);
109 if (!set->dim)
110 goto error;
111
112 for (i = 0; i < set->n; ++i) {
113 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
114 if (!set->p[i])
115 goto error;
116 }
117
118 ISL_F_CLR(set, ISL_SET_NORMALIZED);
119 return set;
120 error:
121 isl_set_free(set);
122 return NULL;
123 }
124
125 /* Move "n" divs starting at "first" to the end of the list of divs.
126 */
127 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
128 unsigned first, unsigned n)
129 {
130 isl_int **div;
131 int i;
132
133 if (first + n == bmap->n_div)
134 return bmap;
135
136 div = isl_alloc_array(bmap->ctx, isl_int *, n);
137 if (!div)
138 goto error;
139 for (i = 0; i < n; ++i)
140 div[i] = bmap->div[first + i];
141 for (i = 0; i < bmap->n_div - first - n; ++i)
142 bmap->div[first + i] = bmap->div[first + n + i];
143 for (i = 0; i < n; ++i)
144 bmap->div[bmap->n_div - n + i] = div[i];
145 free(div);
146 return bmap;
147 error:
148 isl_basic_map_free(bmap);
149 return NULL;
150 }
151
152 /* Drop "n" dimensions of type "type" starting at "first".
153 *
154 * In principle, this frees up some extra variables as the number
155 * of columns remains constant, but we would have to extend
156 * the div array too as the number of rows in this array is assumed
157 * to be equal to extra.
158 */
159 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
160 enum isl_dim_type type, unsigned first, unsigned n)
161 {
162 int i;
163 unsigned dim;
164 unsigned offset;
165 unsigned left;
166
167 if (!bmap)
168 goto error;
169
170 dim = isl_basic_map_dim(bmap, type);
171 isl_assert(bmap->ctx, first + n <= dim, goto error);
172
173 if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
174 return bmap;
175
176 bmap = isl_basic_map_cow(bmap);
177 if (!bmap)
178 return NULL;
179
180 offset = isl_basic_map_offset(bmap, type) + first;
181 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
182 for (i = 0; i < bmap->n_eq; ++i)
183 constraint_drop_vars(bmap->eq[i]+offset, n, left);
184
185 for (i = 0; i < bmap->n_ineq; ++i)
186 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
187
188 for (i = 0; i < bmap->n_div; ++i)
189 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
190
191 if (type == isl_dim_div) {
192 bmap = move_divs_last(bmap, first, n);
193 if (!bmap)
194 goto error;
195 isl_basic_map_free_div(bmap, n);
196 } else
197 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
198 if (!bmap->dim)
199 goto error;
200
201 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
202 bmap = isl_basic_map_simplify(bmap);
203 return isl_basic_map_finalize(bmap);
204 error:
205 isl_basic_map_free(bmap);
206 return NULL;
207 }
208
209 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
210 enum isl_dim_type type, unsigned first, unsigned n)
211 {
212 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
213 type, first, n);
214 }
215
216 struct isl_basic_map *isl_basic_map_drop_inputs(
217 struct isl_basic_map *bmap, unsigned first, unsigned n)
218 {
219 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
220 }
221
222 struct isl_map *isl_map_drop(struct isl_map *map,
223 enum isl_dim_type type, unsigned first, unsigned n)
224 {
225 int i;
226
227 if (!map)
228 goto error;
229
230 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
231
232 if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
233 return map;
234 map = isl_map_cow(map);
235 if (!map)
236 goto error;
237 map->dim = isl_dim_drop(map->dim, type, first, n);
238 if (!map->dim)
239 goto error;
240
241 for (i = 0; i < map->n; ++i) {
242 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
243 if (!map->p[i])
244 goto error;
245 }
246 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
247
248 return map;
249 error:
250 isl_map_free(map);
251 return NULL;
252 }
253
254 struct isl_set *isl_set_drop(struct isl_set *set,
255 enum isl_dim_type type, unsigned first, unsigned n)
256 {
257 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
258 }
259
260 struct isl_map *isl_map_drop_inputs(
261 struct isl_map *map, unsigned first, unsigned n)
262 {
263 return isl_map_drop(map, isl_dim_in, first, n);
264 }
265
266 /*
267 * We don't cow, as the div is assumed to be redundant.
268 */
269 static struct isl_basic_map *isl_basic_map_drop_div(
270 struct isl_basic_map *bmap, unsigned div)
271 {
272 int i;
273 unsigned pos;
274
275 if (!bmap)
276 goto error;
277
278 pos = 1 + isl_dim_total(bmap->dim) + div;
279
280 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
281
282 for (i = 0; i < bmap->n_eq; ++i)
283 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
284
285 for (i = 0; i < bmap->n_ineq; ++i) {
286 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
287 isl_basic_map_drop_inequality(bmap, i);
288 --i;
289 continue;
290 }
291 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
292 }
293
294 for (i = 0; i < bmap->n_div; ++i)
295 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
296
297 if (div != bmap->n_div - 1) {
298 int j;
299 isl_int *t = bmap->div[div];
300
301 for (j = div; j < bmap->n_div - 1; ++j)
302 bmap->div[j] = bmap->div[j+1];
303
304 bmap->div[bmap->n_div - 1] = t;
305 }
306 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
307 isl_basic_map_free_div(bmap, 1);
308
309 return bmap;
310 error:
311 isl_basic_map_free(bmap);
312 return NULL;
313 }
314
315 struct isl_basic_map *isl_basic_map_normalize_constraints(
316 struct isl_basic_map *bmap)
317 {
318 int i;
319 isl_int gcd;
320 unsigned total = isl_basic_map_total_dim(bmap);
321
322 if (!bmap)
323 return NULL;
324
325 isl_int_init(gcd);
326 for (i = bmap->n_eq - 1; i >= 0; --i) {
327 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
328 if (isl_int_is_zero(gcd)) {
329 if (!isl_int_is_zero(bmap->eq[i][0])) {
330 bmap = isl_basic_map_set_to_empty(bmap);
331 break;
332 }
333 isl_basic_map_drop_equality(bmap, i);
334 continue;
335 }
336 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
337 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
338 if (isl_int_is_one(gcd))
339 continue;
340 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
341 bmap = isl_basic_map_set_to_empty(bmap);
342 break;
343 }
344 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
345 }
346
347 for (i = bmap->n_ineq - 1; i >= 0; --i) {
348 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
349 if (isl_int_is_zero(gcd)) {
350 if (isl_int_is_neg(bmap->ineq[i][0])) {
351 bmap = isl_basic_map_set_to_empty(bmap);
352 break;
353 }
354 isl_basic_map_drop_inequality(bmap, i);
355 continue;
356 }
357 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
358 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
359 if (isl_int_is_one(gcd))
360 continue;
361 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
362 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
363 }
364 isl_int_clear(gcd);
365
366 return bmap;
367 }
368
369 struct isl_basic_set *isl_basic_set_normalize_constraints(
370 struct isl_basic_set *bset)
371 {
372 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
373 (struct isl_basic_map *)bset);
374 }
375
376 /* Assumes divs have been ordered if keep_divs is set.
377 */
378 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
379 unsigned pos, isl_int *eq, int keep_divs, int *progress)
380 {
381 unsigned total;
382 int k;
383 int last_div;
384
385 total = isl_basic_map_total_dim(bmap);
386 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
387 bmap->n_div);
388 for (k = 0; k < bmap->n_eq; ++k) {
389 if (bmap->eq[k] == eq)
390 continue;
391 if (isl_int_is_zero(bmap->eq[k][1+pos]))
392 continue;
393 if (progress)
394 *progress = 1;
395 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
396 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
397 }
398
399 for (k = 0; k < bmap->n_ineq; ++k) {
400 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
401 continue;
402 if (progress)
403 *progress = 1;
404 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
405 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
406 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
407 }
408
409 for (k = 0; k < bmap->n_div; ++k) {
410 if (isl_int_is_zero(bmap->div[k][0]))
411 continue;
412 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
413 continue;
414 if (progress)
415 *progress = 1;
416 /* We need to be careful about circular definitions,
417 * so for now we just remove the definition of div k
418 * if the equality contains any divs.
419 * If keep_divs is set, then the divs have been ordered
420 * and we can keep the definition as long as the result
421 * is still ordered.
422 */
423 if (last_div == -1 || (keep_divs && last_div < k))
424 isl_seq_elim(bmap->div[k]+1, eq,
425 1+pos, 1+total, &bmap->div[k][0]);
426 else
427 isl_seq_clr(bmap->div[k], 1 + total);
428 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
429 }
430 }
431
432 /* Assumes divs have been ordered if keep_divs is set.
433 */
434 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
435 unsigned div, int keep_divs)
436 {
437 unsigned pos = isl_dim_total(bmap->dim) + div;
438
439 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
440
441 isl_basic_map_drop_div(bmap, div);
442 }
443
444 /* Check if elimination of div "div" using equality "eq" would not
445 * result in a div depending on a later div.
446 */
447 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
448 unsigned div)
449 {
450 int k;
451 int last_div;
452 unsigned pos = isl_dim_total(bmap->dim) + div;
453
454 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
455 bmap->n_div);
456 if (last_div < 0 || last_div <= div)
457 return 1;
458
459 for (k = 0; k <= last_div; ++k) {
460 if (isl_int_is_zero(bmap->div[k][0]))
461 return 1;
462 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
463 return 0;
464 }
465
466 return 1;
467 }
468
469 /* Elimininate divs based on equalities
470 */
471 static struct isl_basic_map *eliminate_divs_eq(
472 struct isl_basic_map *bmap, int *progress)
473 {
474 int d;
475 int i;
476 int modified = 0;
477 unsigned off;
478
479 bmap = isl_basic_map_order_divs(bmap);
480
481 if (!bmap)
482 return NULL;
483
484 off = 1 + isl_dim_total(bmap->dim);
485
486 for (d = bmap->n_div - 1; d >= 0 ; --d) {
487 for (i = 0; i < bmap->n_eq; ++i) {
488 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
489 !isl_int_is_negone(bmap->eq[i][off + d]))
490 continue;
491 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
492 continue;
493 modified = 1;
494 *progress = 1;
495 eliminate_div(bmap, bmap->eq[i], d, 1);
496 isl_basic_map_drop_equality(bmap, i);
497 break;
498 }
499 }
500 if (modified)
501 return eliminate_divs_eq(bmap, progress);
502 return bmap;
503 }
504
505 /* Elimininate divs based on inequalities
506 */
507 static struct isl_basic_map *eliminate_divs_ineq(
508 struct isl_basic_map *bmap, int *progress)
509 {
510 int d;
511 int i;
512 unsigned off;
513 struct isl_ctx *ctx;
514
515 if (!bmap)
516 return NULL;
517
518 ctx = bmap->ctx;
519 off = 1 + isl_dim_total(bmap->dim);
520
521 for (d = bmap->n_div - 1; d >= 0 ; --d) {
522 for (i = 0; i < bmap->n_eq; ++i)
523 if (!isl_int_is_zero(bmap->eq[i][off + d]))
524 break;
525 if (i < bmap->n_eq)
526 continue;
527 for (i = 0; i < bmap->n_ineq; ++i)
528 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
529 break;
530 if (i < bmap->n_ineq)
531 continue;
532 *progress = 1;
533 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
534 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
535 break;
536 bmap = isl_basic_map_drop_div(bmap, d);
537 if (!bmap)
538 break;
539 }
540 return bmap;
541 }
542
543 struct isl_basic_map *isl_basic_map_gauss(
544 struct isl_basic_map *bmap, int *progress)
545 {
546 int k;
547 int done;
548 int last_var;
549 unsigned total_var;
550 unsigned total;
551
552 bmap = isl_basic_map_order_divs(bmap);
553
554 if (!bmap)
555 return NULL;
556
557 total = isl_basic_map_total_dim(bmap);
558 total_var = total - bmap->n_div;
559
560 last_var = total - 1;
561 for (done = 0; done < bmap->n_eq; ++done) {
562 for (; last_var >= 0; --last_var) {
563 for (k = done; k < bmap->n_eq; ++k)
564 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
565 break;
566 if (k < bmap->n_eq)
567 break;
568 }
569 if (last_var < 0)
570 break;
571 if (k != done)
572 swap_equality(bmap, k, done);
573 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
574 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
575
576 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
577 progress);
578
579 if (last_var >= total_var &&
580 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
581 unsigned div = last_var - total_var;
582 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
583 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
584 isl_int_set(bmap->div[div][0],
585 bmap->eq[done][1+last_var]);
586 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
587 }
588 }
589 if (done == bmap->n_eq)
590 return bmap;
591 for (k = done; k < bmap->n_eq; ++k) {
592 if (isl_int_is_zero(bmap->eq[k][0]))
593 continue;
594 return isl_basic_map_set_to_empty(bmap);
595 }
596 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
597 return bmap;
598 }
599
600 struct isl_basic_set *isl_basic_set_gauss(
601 struct isl_basic_set *bset, int *progress)
602 {
603 return (struct isl_basic_set*)isl_basic_map_gauss(
604 (struct isl_basic_map *)bset, progress);
605 }
606
607
608 static unsigned int round_up(unsigned int v)
609 {
610 int old_v = v;
611
612 while (v) {
613 old_v = v;
614 v ^= v & -v;
615 }
616 return old_v << 1;
617 }
618
619 static int hash_index(isl_int ***index, unsigned int size, int bits,
620 struct isl_basic_map *bmap, int k)
621 {
622 int h;
623 unsigned total = isl_basic_map_total_dim(bmap);
624 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
625 for (h = hash; index[h]; h = (h+1) % size)
626 if (&bmap->ineq[k] != index[h] &&
627 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
628 break;
629 return h;
630 }
631
632 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
633 struct isl_basic_set *bset, int k)
634 {
635 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
636 }
637
638 /* If we can eliminate more than one div, then we need to make
639 * sure we do it from last div to first div, in order not to
640 * change the position of the other divs that still need to
641 * be removed.
642 */
643 static struct isl_basic_map *remove_duplicate_divs(
644 struct isl_basic_map *bmap, int *progress)
645 {
646 unsigned int size;
647 int *index;
648 int *elim_for;
649 int k, l, h;
650 int bits;
651 struct isl_blk eq;
652 unsigned total_var;
653 unsigned total;
654 struct isl_ctx *ctx;
655
656 if (!bmap || bmap->n_div <= 1)
657 return bmap;
658
659 total_var = isl_dim_total(bmap->dim);
660 total = total_var + bmap->n_div;
661
662 ctx = bmap->ctx;
663 for (k = bmap->n_div - 1; k >= 0; --k)
664 if (!isl_int_is_zero(bmap->div[k][0]))
665 break;
666 if (k <= 0)
667 return bmap;
668
669 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
670 size = round_up(4 * bmap->n_div / 3 - 1);
671 bits = ffs(size) - 1;
672 index = isl_calloc_array(ctx, int, size);
673 if (!index)
674 return bmap;
675 eq = isl_blk_alloc(ctx, 1+total);
676 if (isl_blk_is_error(eq))
677 goto out;
678
679 isl_seq_clr(eq.data, 1+total);
680 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
681 for (--k; k >= 0; --k) {
682 uint32_t hash;
683
684 if (isl_int_is_zero(bmap->div[k][0]))
685 continue;
686
687 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
688 for (h = hash; index[h]; h = (h+1) % size)
689 if (isl_seq_eq(bmap->div[k],
690 bmap->div[index[h]-1], 2+total))
691 break;
692 if (index[h]) {
693 *progress = 1;
694 l = index[h] - 1;
695 elim_for[l] = k + 1;
696 }
697 index[h] = k+1;
698 }
699 for (l = bmap->n_div - 1; l >= 0; --l) {
700 if (!elim_for[l])
701 continue;
702 k = elim_for[l] - 1;
703 isl_int_set_si(eq.data[1+total_var+k], -1);
704 isl_int_set_si(eq.data[1+total_var+l], 1);
705 eliminate_div(bmap, eq.data, l, 0);
706 isl_int_set_si(eq.data[1+total_var+k], 0);
707 isl_int_set_si(eq.data[1+total_var+l], 0);
708 }
709
710 isl_blk_free(ctx, eq);
711 out:
712 free(index);
713 free(elim_for);
714 return bmap;
715 }
716
717 static int n_pure_div_eq(struct isl_basic_map *bmap)
718 {
719 int i, j;
720 unsigned total;
721
722 total = isl_dim_total(bmap->dim);
723 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
724 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
725 --j;
726 if (j < 0)
727 break;
728 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
729 return 0;
730 }
731 return i;
732 }
733
734 /* Normalize divs that appear in equalities.
735 *
736 * In particular, we assume that bmap contains some equalities
737 * of the form
738 *
739 * a x = m * e_i
740 *
741 * and we want to replace the set of e_i by a minimal set and
742 * such that the new e_i have a canonical representation in terms
743 * of the vector x.
744 * If any of the equalities involves more than one divs, then
745 * we currently simply bail out.
746 *
747 * Let us first additionally assume that all equalities involve
748 * a div. The equalities then express modulo constraints on the
749 * remaining variables and we can use "parameter compression"
750 * to find a minimal set of constraints. The result is a transformation
751 *
752 * x = T(x') = x_0 + G x'
753 *
754 * with G a lower-triangular matrix with all elements below the diagonal
755 * non-negative and smaller than the diagonal element on the same row.
756 * We first normalize x_0 by making the same property hold in the affine
757 * T matrix.
758 * The rows i of G with a 1 on the diagonal do not impose any modulo
759 * constraint and simply express x_i = x'_i.
760 * For each of the remaining rows i, we introduce a div and a corresponding
761 * equality. In particular
762 *
763 * g_ii e_j = x_i - g_i(x')
764 *
765 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
766 * corresponding div (if g_kk != 1).
767 *
768 * If there are any equalities not involving any div, then we
769 * first apply a variable compression on the variables x:
770 *
771 * x = C x'' x'' = C_2 x
772 *
773 * and perform the above parameter compression on A C instead of on A.
774 * The resulting compression is then of the form
775 *
776 * x'' = T(x') = x_0 + G x'
777 *
778 * and in constructing the new divs and the corresponding equalities,
779 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
780 * by the corresponding row from C_2.
781 */
782 static struct isl_basic_map *normalize_divs(
783 struct isl_basic_map *bmap, int *progress)
784 {
785 int i, j, k;
786 int total;
787 int div_eq;
788 struct isl_mat *B;
789 struct isl_vec *d;
790 struct isl_mat *T = NULL;
791 struct isl_mat *C = NULL;
792 struct isl_mat *C2 = NULL;
793 isl_int v;
794 int *pos;
795 int dropped, needed;
796
797 if (!bmap)
798 return NULL;
799
800 if (bmap->n_div == 0)
801 return bmap;
802
803 if (bmap->n_eq == 0)
804 return bmap;
805
806 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
807 return bmap;
808
809 total = isl_dim_total(bmap->dim);
810 div_eq = n_pure_div_eq(bmap);
811 if (div_eq == 0)
812 return bmap;
813
814 if (div_eq < bmap->n_eq) {
815 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
816 bmap->n_eq - div_eq, 0, 1 + total);
817 C = isl_mat_variable_compression(B, &C2);
818 if (!C || !C2)
819 goto error;
820 if (C->n_col == 0) {
821 bmap = isl_basic_map_set_to_empty(bmap);
822 isl_mat_free(C);
823 isl_mat_free(C2);
824 goto done;
825 }
826 }
827
828 d = isl_vec_alloc(bmap->ctx, div_eq);
829 if (!d)
830 goto error;
831 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
832 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
833 --j;
834 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
835 }
836 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
837
838 if (C) {
839 B = isl_mat_product(B, C);
840 C = NULL;
841 }
842
843 T = isl_mat_parameter_compression(B, d);
844 if (!T)
845 goto error;
846 if (T->n_col == 0) {
847 bmap = isl_basic_map_set_to_empty(bmap);
848 isl_mat_free(C2);
849 isl_mat_free(T);
850 goto done;
851 }
852 isl_int_init(v);
853 for (i = 0; i < T->n_row - 1; ++i) {
854 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
855 if (isl_int_is_zero(v))
856 continue;
857 isl_mat_col_submul(T, 0, v, 1 + i);
858 }
859 isl_int_clear(v);
860 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
861 if (!pos)
862 goto error;
863 /* We have to be careful because dropping equalities may reorder them */
864 dropped = 0;
865 for (j = bmap->n_div - 1; j >= 0; --j) {
866 for (i = 0; i < bmap->n_eq; ++i)
867 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
868 break;
869 if (i < bmap->n_eq) {
870 bmap = isl_basic_map_drop_div(bmap, j);
871 isl_basic_map_drop_equality(bmap, i);
872 ++dropped;
873 }
874 }
875 pos[0] = 0;
876 needed = 0;
877 for (i = 1; i < T->n_row; ++i) {
878 if (isl_int_is_one(T->row[i][i]))
879 pos[i] = i;
880 else
881 needed++;
882 }
883 if (needed > dropped) {
884 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
885 needed, needed, 0);
886 if (!bmap)
887 goto error;
888 }
889 for (i = 1; i < T->n_row; ++i) {
890 if (isl_int_is_one(T->row[i][i]))
891 continue;
892 k = isl_basic_map_alloc_div(bmap);
893 pos[i] = 1 + total + k;
894 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
895 isl_int_set(bmap->div[k][0], T->row[i][i]);
896 if (C2)
897 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
898 else
899 isl_int_set_si(bmap->div[k][1 + i], 1);
900 for (j = 0; j < i; ++j) {
901 if (isl_int_is_zero(T->row[i][j]))
902 continue;
903 if (pos[j] < T->n_row && C2)
904 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
905 C2->row[pos[j]], 1 + total);
906 else
907 isl_int_neg(bmap->div[k][1 + pos[j]],
908 T->row[i][j]);
909 }
910 j = isl_basic_map_alloc_equality(bmap);
911 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
912 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
913 }
914 free(pos);
915 isl_mat_free(C2);
916 isl_mat_free(T);
917
918 if (progress)
919 *progress = 1;
920 done:
921 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
922
923 return bmap;
924 error:
925 isl_mat_free(C);
926 isl_mat_free(C2);
927 isl_mat_free(T);
928 return bmap;
929 }
930
931 static struct isl_basic_map *set_div_from_lower_bound(
932 struct isl_basic_map *bmap, int div, int ineq)
933 {
934 unsigned total = 1 + isl_dim_total(bmap->dim);
935
936 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
937 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
938 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
939 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
940 isl_int_set_si(bmap->div[div][1 + total + div], 0);
941
942 return bmap;
943 }
944
945 /* Check whether it is ok to define a div based on an inequality.
946 * To avoid the introduction of circular definitions of divs, we
947 * do not allow such a definition if the resulting expression would refer to
948 * any other undefined divs or if any known div is defined in
949 * terms of the unknown div.
950 */
951 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
952 int div, int ineq)
953 {
954 int j;
955 unsigned total = 1 + isl_dim_total(bmap->dim);
956
957 /* Not defined in terms of unknown divs */
958 for (j = 0; j < bmap->n_div; ++j) {
959 if (div == j)
960 continue;
961 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
962 continue;
963 if (isl_int_is_zero(bmap->div[j][0]))
964 return 0;
965 }
966
967 /* No other div defined in terms of this one => avoid loops */
968 for (j = 0; j < bmap->n_div; ++j) {
969 if (div == j)
970 continue;
971 if (isl_int_is_zero(bmap->div[j][0]))
972 continue;
973 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
974 return 0;
975 }
976
977 return 1;
978 }
979
980 /* Given two constraints "k" and "l" that are opposite to each other,
981 * except for the constant term, check if we can use them
982 * to obtain an expression for one of the hitherto unknown divs.
983 * "sum" is the sum of the constant terms of the constraints.
984 * If this sum is strictly smaller than the coefficient of one
985 * of the divs, then this pair can be used define the div.
986 * To avoid the introduction of circular definitions of divs, we
987 * do not use the pair if the resulting expression would refer to
988 * any other undefined divs or if any known div is defined in
989 * terms of the unknown div.
990 */
991 static struct isl_basic_map *check_for_div_constraints(
992 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
993 {
994 int i;
995 unsigned total = 1 + isl_dim_total(bmap->dim);
996
997 for (i = 0; i < bmap->n_div; ++i) {
998 if (!isl_int_is_zero(bmap->div[i][0]))
999 continue;
1000 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1001 continue;
1002 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1003 continue;
1004 if (!ok_to_set_div_from_bound(bmap, i, k))
1005 break;
1006 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1007 bmap = set_div_from_lower_bound(bmap, i, k);
1008 else
1009 bmap = set_div_from_lower_bound(bmap, i, l);
1010 if (progress)
1011 *progress = 1;
1012 break;
1013 }
1014 return bmap;
1015 }
1016
1017 static struct isl_basic_map *remove_duplicate_constraints(
1018 struct isl_basic_map *bmap, int *progress, int detect_divs)
1019 {
1020 unsigned int size;
1021 isl_int ***index;
1022 int k, l, h;
1023 int bits;
1024 unsigned total = isl_basic_map_total_dim(bmap);
1025 isl_int sum;
1026
1027 if (!bmap || bmap->n_ineq <= 1)
1028 return bmap;
1029
1030 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1031 bits = ffs(size) - 1;
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_dim_total(bmap->dim) + 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_dim_total(bmap->dim) + 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
1281 if (n == 0)
1282 return bmap;
1283 if (!bmap)
1284 return NULL;
1285 total = isl_basic_map_total_dim(bmap);
1286
1287 bmap = isl_basic_map_cow(bmap);
1288 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1289 bmap = remove_dependent_vars(bmap, d);
1290
1291 for (d = pos + n - 1;
1292 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1293 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1294 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1295 int n_lower, n_upper;
1296 if (!bmap)
1297 return NULL;
1298 for (i = 0; i < bmap->n_eq; ++i) {
1299 if (isl_int_is_zero(bmap->eq[i][1+d]))
1300 continue;
1301 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1302 isl_basic_map_drop_equality(bmap, i);
1303 break;
1304 }
1305 if (i < bmap->n_eq)
1306 continue;
1307 n_lower = 0;
1308 n_upper = 0;
1309 for (i = 0; i < bmap->n_ineq; ++i) {
1310 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1311 n_lower++;
1312 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1313 n_upper++;
1314 }
1315 bmap = isl_basic_map_extend_constraints(bmap,
1316 0, n_lower * n_upper);
1317 if (!bmap)
1318 goto error;
1319 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1320 int last;
1321 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1322 continue;
1323 last = -1;
1324 for (j = 0; j < i; ++j) {
1325 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1326 continue;
1327 last = j;
1328 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1329 isl_int_sgn(bmap->ineq[j][1+d]))
1330 continue;
1331 k = isl_basic_map_alloc_inequality(bmap);
1332 if (k < 0)
1333 goto error;
1334 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1335 1+total);
1336 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1337 1+d, 1+total, NULL);
1338 }
1339 isl_basic_map_drop_inequality(bmap, i);
1340 i = last + 1;
1341 }
1342 if (n_lower > 0 && n_upper > 0) {
1343 bmap = isl_basic_map_normalize_constraints(bmap);
1344 bmap = remove_duplicate_constraints(bmap, NULL, 0);
1345 bmap = isl_basic_map_gauss(bmap, NULL);
1346 bmap = isl_basic_map_remove_redundancies(bmap);
1347 if (!bmap)
1348 goto error;
1349 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1350 break;
1351 }
1352 }
1353 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1354 return bmap;
1355 error:
1356 isl_basic_map_free(bmap);
1357 return NULL;
1358 }
1359
1360 struct isl_basic_set *isl_basic_set_eliminate_vars(
1361 struct isl_basic_set *bset, unsigned pos, unsigned n)
1362 {
1363 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1364 (struct isl_basic_map *)bset, pos, n);
1365 }
1366
1367 /* Don't assume equalities are in order, because align_divs
1368 * may have changed the order of the divs.
1369 */
1370 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1371 {
1372 int d, i;
1373 unsigned total;
1374
1375 total = isl_dim_total(bmap->dim);
1376 for (d = 0; d < total; ++d)
1377 elim[d] = -1;
1378 for (i = 0; i < bmap->n_eq; ++i) {
1379 for (d = total - 1; d >= 0; --d) {
1380 if (isl_int_is_zero(bmap->eq[i][1+d]))
1381 continue;
1382 elim[d] = i;
1383 break;
1384 }
1385 }
1386 }
1387
1388 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1389 {
1390 compute_elimination_index((struct isl_basic_map *)bset, elim);
1391 }
1392
1393 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1394 struct isl_basic_map *bmap, int *elim)
1395 {
1396 int d;
1397 int copied = 0;
1398 unsigned total;
1399
1400 total = isl_dim_total(bmap->dim);
1401 for (d = total - 1; d >= 0; --d) {
1402 if (isl_int_is_zero(src[1+d]))
1403 continue;
1404 if (elim[d] == -1)
1405 continue;
1406 if (!copied) {
1407 isl_seq_cpy(dst, src, 1 + total);
1408 copied = 1;
1409 }
1410 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1411 }
1412 return copied;
1413 }
1414
1415 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1416 struct isl_basic_set *bset, int *elim)
1417 {
1418 return reduced_using_equalities(dst, src,
1419 (struct isl_basic_map *)bset, elim);
1420 }
1421
1422 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1423 struct isl_basic_set *bset, struct isl_basic_set *context)
1424 {
1425 int i;
1426 int *elim;
1427
1428 if (!bset || !context)
1429 goto error;
1430
1431 if (context->n_eq == 0) {
1432 isl_basic_set_free(context);
1433 return bset;
1434 }
1435
1436 bset = isl_basic_set_cow(bset);
1437 if (!bset)
1438 goto error;
1439
1440 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1441 if (!elim)
1442 goto error;
1443 set_compute_elimination_index(context, elim);
1444 for (i = 0; i < bset->n_eq; ++i)
1445 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1446 context, elim);
1447 for (i = 0; i < bset->n_ineq; ++i)
1448 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1449 context, elim);
1450 isl_basic_set_free(context);
1451 free(elim);
1452 bset = isl_basic_set_simplify(bset);
1453 bset = isl_basic_set_finalize(bset);
1454 return bset;
1455 error:
1456 isl_basic_set_free(bset);
1457 isl_basic_set_free(context);
1458 return NULL;
1459 }
1460
1461 static struct isl_basic_set *remove_shifted_constraints(
1462 struct isl_basic_set *bset, struct isl_basic_set *context)
1463 {
1464 unsigned int size;
1465 isl_int ***index;
1466 int bits;
1467 int k, h, l;
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 index = isl_calloc_array(ctx, isl_int **, size);
1475 if (!index)
1476 return bset;
1477
1478 for (k = 0; k < context->n_ineq; ++k) {
1479 h = set_hash_index(index, size, bits, context, k);
1480 index[h] = &context->ineq[k];
1481 }
1482 for (k = 0; k < bset->n_ineq; ++k) {
1483 h = set_hash_index(index, size, bits, bset, k);
1484 if (!index[h])
1485 continue;
1486 l = index[h] - &context->ineq[0];
1487 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1488 continue;
1489 bset = isl_basic_set_cow(bset);
1490 if (!bset)
1491 goto error;
1492 isl_basic_set_drop_inequality(bset, k);
1493 --k;
1494 }
1495 free(index);
1496 return bset;
1497 error:
1498 free(index);
1499 return bset;
1500 }
1501
1502 /* Tighten (decrease) the constant terms of the inequalities based
1503 * on the equalities, without removing any integer points.
1504 * For example, if there is an equality
1505 *
1506 * i = 3 * j
1507 *
1508 * and an inequality
1509 *
1510 * i >= 1
1511 *
1512 * then we want to replace the inequality by
1513 *
1514 * i >= 3
1515 *
1516 * We do this by computing a variable compression and translating
1517 * the constraints to the compressed space.
1518 * If any constraint has coefficients (except the contant term)
1519 * with a common factor "f", then we can replace the constant term "c"
1520 * by
1521 *
1522 * f * floor(c/f)
1523 *
1524 * That is, we add
1525 *
1526 * f * floor(c/f) - c = -fract(c/f)
1527 *
1528 * and we can add the same value to the original constraint.
1529 *
1530 * In the example, the compressed space only contains "j",
1531 * and the inequality translates to
1532 *
1533 * 3 * j - 1 >= 0
1534 *
1535 * We add -fract(-1/3) = -2 to the original constraint to obtain
1536 *
1537 * i - 3 >= 0
1538 */
1539 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1540 struct isl_basic_set *bset)
1541 {
1542 int i;
1543 unsigned total;
1544 struct isl_mat *B, *C;
1545 isl_int gcd;
1546
1547 if (!bset)
1548 return NULL;
1549
1550 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1551 return bset;
1552
1553 if (!bset->n_ineq)
1554 return bset;
1555
1556 bset = isl_basic_set_cow(bset);
1557 if (!bset)
1558 return NULL;
1559
1560 total = isl_basic_set_total_dim(bset);
1561 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1562 C = isl_mat_variable_compression(B, NULL);
1563 if (!C)
1564 return bset;
1565 if (C->n_col == 0) {
1566 isl_mat_free(C);
1567 return isl_basic_set_set_to_empty(bset);
1568 }
1569 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1570 0, bset->n_ineq, 0, 1 + total);
1571 C = isl_mat_product(B, C);
1572 if (!C)
1573 return bset;
1574
1575 isl_int_init(gcd);
1576 for (i = 0; i < bset->n_ineq; ++i) {
1577 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1578 if (isl_int_is_one(gcd))
1579 continue;
1580 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1581 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1582 }
1583 isl_int_clear(gcd);
1584
1585 isl_mat_free(C);
1586
1587 return bset;
1588 }
1589
1590 /* Remove all information from bset that is redundant in the context
1591 * of context. Both bset and context are assumed to be full-dimensional.
1592 *
1593 * We first * remove the inequalities from "bset"
1594 * that are obviously redundant with respect to some inequality in "context".
1595 *
1596 * If there are any inequalities left, we construct a tableau for
1597 * the context and then add the inequalities of "bset".
1598 * Before adding these inequalities, we freeze all constraints such that
1599 * they won't be considered redundant in terms of the constraints of "bset".
1600 * Then we detect all redundant constraints (among the
1601 * constraints that weren't frozen), first by checking for redundancy in the
1602 * the tableau and then by checking if replacing a constraint by its negation
1603 * would lead to an empty set. This last step is fairly expensive
1604 * and could be optimized by more reuse of the tableau.
1605 * Finally, we update bset according to the results.
1606 */
1607 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1608 __isl_take isl_basic_set *context)
1609 {
1610 int i, k;
1611 isl_basic_set *combined = NULL;
1612 struct isl_tab *tab = NULL;
1613 unsigned context_ineq;
1614 unsigned total;
1615
1616 if (!bset || !context)
1617 goto error;
1618
1619 if (isl_basic_set_is_universe(bset)) {
1620 isl_basic_set_free(context);
1621 return bset;
1622 }
1623
1624 if (isl_basic_set_is_universe(context)) {
1625 isl_basic_set_free(context);
1626 return bset;
1627 }
1628
1629 bset = remove_shifted_constraints(bset, context);
1630 if (!bset)
1631 goto error;
1632 if (bset->n_ineq == 0)
1633 goto done;
1634
1635 context_ineq = context->n_ineq;
1636 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1637 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1638 tab = isl_tab_from_basic_set(combined);
1639 for (i = 0; i < context_ineq; ++i)
1640 if (isl_tab_freeze_constraint(tab, i) < 0)
1641 goto error;
1642 tab = isl_tab_extend(tab, bset->n_ineq);
1643 for (i = 0; i < bset->n_ineq; ++i)
1644 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1645 goto error;
1646 bset = isl_basic_set_add_constraints(combined, bset, 0);
1647 combined = NULL;
1648 if (!bset)
1649 goto error;
1650 if (isl_tab_detect_redundant(tab) < 0)
1651 goto error;
1652 total = isl_basic_set_total_dim(bset);
1653 for (i = context_ineq; i < bset->n_ineq; ++i) {
1654 int is_empty;
1655 if (tab->con[i].is_redundant)
1656 continue;
1657 tab->con[i].is_redundant = 1;
1658 combined = isl_basic_set_dup(bset);
1659 combined = isl_basic_set_update_from_tab(combined, tab);
1660 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1661 k = isl_basic_set_alloc_inequality(combined);
1662 if (k < 0)
1663 goto error;
1664 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1665 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1666 is_empty = isl_basic_set_is_empty(combined);
1667 if (is_empty < 0)
1668 goto error;
1669 isl_basic_set_free(combined);
1670 combined = NULL;
1671 if (!is_empty)
1672 tab->con[i].is_redundant = 0;
1673 }
1674 for (i = 0; i < context_ineq; ++i)
1675 tab->con[i].is_redundant = 1;
1676 bset = isl_basic_set_update_from_tab(bset, tab);
1677 if (bset) {
1678 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1679 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1680 }
1681
1682 isl_tab_free(tab);
1683 done:
1684 bset = isl_basic_set_simplify(bset);
1685 bset = isl_basic_set_finalize(bset);
1686 isl_basic_set_free(context);
1687 return bset;
1688 error:
1689 isl_tab_free(tab);
1690 isl_basic_set_free(combined);
1691 isl_basic_set_free(context);
1692 isl_basic_set_free(bset);
1693 return NULL;
1694 }
1695
1696 /* Remove all information from bset that is redundant in the context
1697 * of context. In particular, equalities that are linear combinations
1698 * of those in context are removed. Then the inequalities that are
1699 * redundant in the context of the equalities and inequalities of
1700 * context are removed.
1701 *
1702 * We first compute the integer affine hull of the intersection,
1703 * compute the gist inside this affine hull and then add back
1704 * those equalities that are not implied by the context.
1705 */
1706 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1707 __isl_take isl_basic_set *context)
1708 {
1709 isl_mat *eq;
1710 isl_mat *T, *T2;
1711 isl_basic_set *aff;
1712 isl_basic_set *aff_context;
1713 unsigned total;
1714
1715 if (!bset || !context)
1716 goto error;
1717
1718 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1719 if (isl_basic_set_fast_is_empty(bset)) {
1720 isl_basic_set_free(context);
1721 return bset;
1722 }
1723 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1724 if (!aff)
1725 goto error;
1726 if (isl_basic_set_fast_is_empty(aff)) {
1727 isl_basic_set_free(aff);
1728 isl_basic_set_free(context);
1729 return bset;
1730 }
1731 if (aff->n_eq == 0) {
1732 isl_basic_set_free(aff);
1733 return uset_gist_full(bset, context);
1734 }
1735 total = isl_basic_set_total_dim(bset);
1736 eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1737 eq = isl_mat_cow(eq);
1738 T = isl_mat_variable_compression(eq, &T2);
1739 if (T && T->n_col == 0) {
1740 isl_mat_free(T);
1741 isl_mat_free(T2);
1742 isl_basic_set_free(context);
1743 isl_basic_set_free(aff);
1744 return isl_basic_set_set_to_empty(bset);
1745 }
1746
1747 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1748
1749 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1750 context = isl_basic_set_preimage(context, T);
1751
1752 bset = uset_gist_full(bset, context);
1753 bset = isl_basic_set_preimage(bset, T2);
1754 bset = isl_basic_set_intersect(bset, aff);
1755 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1756
1757 if (bset) {
1758 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1759 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1760 }
1761
1762 return bset;
1763 error:
1764 isl_basic_set_free(bset);
1765 isl_basic_set_free(context);
1766 return NULL;
1767 }
1768
1769 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1770 * We simply add the equalities in context to bmap and then do a regular
1771 * div normalizations. Better results can be obtained by normalizing
1772 * only the divs in bmap than do not also appear in context.
1773 * We need to be careful to reduce the divs using the equalities
1774 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1775 * spurious constraints.
1776 */
1777 static struct isl_basic_map *normalize_divs_in_context(
1778 struct isl_basic_map *bmap, struct isl_basic_map *context)
1779 {
1780 int i;
1781 unsigned total_context;
1782 int div_eq;
1783
1784 div_eq = n_pure_div_eq(bmap);
1785 if (div_eq == 0)
1786 return bmap;
1787
1788 if (context->n_div > 0)
1789 bmap = isl_basic_map_align_divs(bmap, context);
1790
1791 total_context = isl_basic_map_total_dim(context);
1792 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1793 for (i = 0; i < context->n_eq; ++i) {
1794 int k;
1795 k = isl_basic_map_alloc_equality(bmap);
1796 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1797 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1798 isl_basic_map_total_dim(bmap) - total_context);
1799 }
1800 bmap = isl_basic_map_gauss(bmap, NULL);
1801 bmap = normalize_divs(bmap, NULL);
1802 bmap = isl_basic_map_gauss(bmap, NULL);
1803 return bmap;
1804 }
1805
1806 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1807 struct isl_basic_map *context)
1808 {
1809 struct isl_basic_set *bset;
1810
1811 if (!bmap || !context)
1812 goto error;
1813
1814 if (isl_basic_map_is_universe(bmap)) {
1815 isl_basic_map_free(context);
1816 return bmap;
1817 }
1818 if (isl_basic_map_fast_is_empty(context)) {
1819 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1820 isl_basic_map_free(context);
1821 isl_basic_map_free(bmap);
1822 return isl_basic_map_universe(dim);
1823 }
1824 if (isl_basic_map_fast_is_empty(bmap)) {
1825 isl_basic_map_free(context);
1826 return bmap;
1827 }
1828
1829 bmap = isl_basic_map_remove_redundancies(bmap);
1830 context = isl_basic_map_remove_redundancies(context);
1831
1832 if (context->n_eq)
1833 bmap = normalize_divs_in_context(bmap, context);
1834
1835 context = isl_basic_map_align_divs(context, bmap);
1836 bmap = isl_basic_map_align_divs(bmap, context);
1837
1838 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1839 isl_basic_map_underlying_set(context));
1840
1841 return isl_basic_map_overlying_set(bset, bmap);
1842 error:
1843 isl_basic_map_free(bmap);
1844 isl_basic_map_free(context);
1845 return NULL;
1846 }
1847
1848 /*
1849 * Assumes context has no implicit divs.
1850 */
1851 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1852 __isl_take isl_basic_map *context)
1853 {
1854 int i;
1855
1856 if (!map || !context)
1857 goto error;;
1858
1859 if (isl_basic_map_fast_is_empty(context)) {
1860 struct isl_dim *dim = isl_dim_copy(map->dim);
1861 isl_basic_map_free(context);
1862 isl_map_free(map);
1863 return isl_map_universe(dim);
1864 }
1865
1866 context = isl_basic_map_remove_redundancies(context);
1867 map = isl_map_cow(map);
1868 if (!map || !context)
1869 goto error;;
1870 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1871 map = isl_map_compute_divs(map);
1872 for (i = 0; i < map->n; ++i)
1873 context = isl_basic_map_align_divs(context, map->p[i]);
1874 for (i = map->n - 1; i >= 0; --i) {
1875 map->p[i] = isl_basic_map_gist(map->p[i],
1876 isl_basic_map_copy(context));
1877 if (!map->p[i])
1878 goto error;
1879 if (isl_basic_map_fast_is_empty(map->p[i])) {
1880 isl_basic_map_free(map->p[i]);
1881 if (i != map->n - 1)
1882 map->p[i] = map->p[map->n - 1];
1883 map->n--;
1884 }
1885 }
1886 isl_basic_map_free(context);
1887 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1888 return map;
1889 error:
1890 isl_map_free(map);
1891 isl_basic_map_free(context);
1892 return NULL;
1893 }
1894
1895 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1896 __isl_take isl_map *context)
1897 {
1898 context = isl_map_compute_divs(context);
1899 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1900 }
1901
1902 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1903 struct isl_basic_set *context)
1904 {
1905 return (struct isl_basic_set *)isl_basic_map_gist(
1906 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1907 }
1908
1909 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1910 __isl_take isl_basic_set *context)
1911 {
1912 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1913 (struct isl_basic_map *)context);
1914 }
1915
1916 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1917 __isl_take isl_set *context)
1918 {
1919 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1920 (struct isl_map *)context);
1921 }
1922
1923 /* Quick check to see if two basic maps are disjoint.
1924 * In particular, we reduce the equalities and inequalities of
1925 * one basic map in the context of the equalities of the other
1926 * basic map and check if we get a contradiction.
1927 */
1928 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1929 struct isl_basic_map *bmap2)
1930 {
1931 struct isl_vec *v = NULL;
1932 int *elim = NULL;
1933 unsigned total;
1934 int i;
1935
1936 if (!bmap1 || !bmap2)
1937 return -1;
1938 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1939 return -1);
1940 if (bmap1->n_div || bmap2->n_div)
1941 return 0;
1942 if (!bmap1->n_eq && !bmap2->n_eq)
1943 return 0;
1944
1945 total = isl_dim_total(bmap1->dim);
1946 if (total == 0)
1947 return 0;
1948 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1949 if (!v)
1950 goto error;
1951 elim = isl_alloc_array(bmap1->ctx, int, total);
1952 if (!elim)
1953 goto error;
1954 compute_elimination_index(bmap1, elim);
1955 for (i = 0; i < bmap2->n_eq; ++i) {
1956 int reduced;
1957 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1958 bmap1, elim);
1959 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1960 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1961 goto disjoint;
1962 }
1963 for (i = 0; i < bmap2->n_ineq; ++i) {
1964 int reduced;
1965 reduced = reduced_using_equalities(v->block.data,
1966 bmap2->ineq[i], bmap1, elim);
1967 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1968 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1969 goto disjoint;
1970 }
1971 compute_elimination_index(bmap2, elim);
1972 for (i = 0; i < bmap1->n_ineq; ++i) {
1973 int reduced;
1974 reduced = reduced_using_equalities(v->block.data,
1975 bmap1->ineq[i], bmap2, elim);
1976 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1977 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1978 goto disjoint;
1979 }
1980 isl_vec_free(v);
1981 free(elim);
1982 return 0;
1983 disjoint:
1984 isl_vec_free(v);
1985 free(elim);
1986 return 1;
1987 error:
1988 isl_vec_free(v);
1989 free(elim);
1990 return -1;
1991 }
1992
1993 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1994 struct isl_basic_set *bset2)
1995 {
1996 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1997 (struct isl_basic_map *)bset2);
1998 }
1999
2000 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
2001 {
2002 int i, j;
2003
2004 if (!map1 || !map2)
2005 return -1;
2006
2007 if (isl_map_fast_is_equal(map1, map2))
2008 return 0;
2009
2010 for (i = 0; i < map1->n; ++i) {
2011 for (j = 0; j < map2->n; ++j) {
2012 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
2013 map2->p[j]);
2014 if (d != 1)
2015 return d;
2016 }
2017 }
2018 return 1;
2019 }
2020
2021 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2022 {
2023 return isl_map_fast_is_disjoint((struct isl_map *)set1,
2024 (struct isl_map *)set2);
2025 }
2026
2027 /* Check if we can combine a given div with lower bound l and upper
2028 * bound u with some other div and if so return that other div.
2029 * Otherwise return -1.
2030 *
2031 * We first check that
2032 * - the bounds are opposites of each other (except for the constant
2033 * term)
2034 * - the bounds do not reference any other div
2035 * - no div is defined in terms of this div
2036 *
2037 * Let m be the size of the range allowed on the div by the bounds.
2038 * That is, the bounds are of the form
2039 *
2040 * e <= a <= e + m - 1
2041 *
2042 * with e some expression in the other variables.
2043 * We look for another div b such that no third div is defined in terms
2044 * of this second div b and such that in any constraint that contains
2045 * a (except for the given lower and upper bound), also contains b
2046 * with a coefficient that is m times that of b.
2047 * That is, all constraints (execpt for the lower and upper bound)
2048 * are of the form
2049 *
2050 * e + f (a + m b) >= 0
2051 *
2052 * If so, we return b so that "a + m b" can be replaced by
2053 * a single div "c = a + m b".
2054 */
2055 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2056 unsigned div, unsigned l, unsigned u)
2057 {
2058 int i, j;
2059 unsigned dim;
2060 int coalesce = -1;
2061
2062 if (bmap->n_div <= 1)
2063 return -1;
2064 dim = isl_dim_total(bmap->dim);
2065 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2066 return -1;
2067 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2068 bmap->n_div - div - 1) != -1)
2069 return -1;
2070 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2071 dim + bmap->n_div))
2072 return -1;
2073
2074 for (i = 0; i < bmap->n_div; ++i) {
2075 if (isl_int_is_zero(bmap->div[i][0]))
2076 continue;
2077 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2078 return -1;
2079 }
2080
2081 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2082 if (isl_int_is_neg(bmap->ineq[l][0])) {
2083 isl_int_sub(bmap->ineq[l][0],
2084 bmap->ineq[l][0], bmap->ineq[u][0]);
2085 bmap = isl_basic_map_copy(bmap);
2086 bmap = isl_basic_map_set_to_empty(bmap);
2087 isl_basic_map_free(bmap);
2088 return -1;
2089 }
2090 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2091 for (i = 0; i < bmap->n_div; ++i) {
2092 if (i == div)
2093 continue;
2094 if (!pairs[i])
2095 continue;
2096 for (j = 0; j < bmap->n_div; ++j) {
2097 if (isl_int_is_zero(bmap->div[j][0]))
2098 continue;
2099 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2100 break;
2101 }
2102 if (j < bmap->n_div)
2103 continue;
2104 for (j = 0; j < bmap->n_ineq; ++j) {
2105 int valid;
2106 if (j == l || j == u)
2107 continue;
2108 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2109 continue;
2110 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2111 break;
2112 isl_int_mul(bmap->ineq[j][1 + dim + div],
2113 bmap->ineq[j][1 + dim + div],
2114 bmap->ineq[l][0]);
2115 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2116 bmap->ineq[j][1 + dim + i]);
2117 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2118 bmap->ineq[j][1 + dim + div],
2119 bmap->ineq[l][0]);
2120 if (!valid)
2121 break;
2122 }
2123 if (j < bmap->n_ineq)
2124 continue;
2125 coalesce = i;
2126 break;
2127 }
2128 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2129 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2130 return coalesce;
2131 }
2132
2133 /* Given a lower and an upper bound on div i, construct an inequality
2134 * that when nonnegative ensures that this pair of bounds always allows
2135 * for an integer value of the given div.
2136 * The lower bound is inequality l, while the upper bound is inequality u.
2137 * The constructed inequality is stored in ineq.
2138 * g, fl, fu are temporary scalars.
2139 *
2140 * Let the upper bound be
2141 *
2142 * -n_u a + e_u >= 0
2143 *
2144 * and the lower bound
2145 *
2146 * n_l a + e_l >= 0
2147 *
2148 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2149 * We have
2150 *
2151 * - f_u e_l <= f_u f_l g a <= f_l e_u
2152 *
2153 * Since all variables are integer valued, this is equivalent to
2154 *
2155 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2156 *
2157 * If this interval is at least f_u f_l g, then it contains at least
2158 * one integer value for a.
2159 * That is, the test constraint is
2160 *
2161 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2162 */
2163 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2164 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2165 {
2166 unsigned dim;
2167 dim = isl_dim_total(bmap->dim);
2168
2169 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2170 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2171 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2172 isl_int_neg(fu, fu);
2173 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2174 1 + dim + bmap->n_div);
2175 isl_int_add(ineq[0], ineq[0], fl);
2176 isl_int_add(ineq[0], ineq[0], fu);
2177 isl_int_sub_ui(ineq[0], ineq[0], 1);
2178 isl_int_mul(g, g, fl);
2179 isl_int_mul(g, g, fu);
2180 isl_int_sub(ineq[0], ineq[0], g);
2181 }
2182
2183 /* Remove more kinds of divs that are not strictly needed.
2184 * In particular, if all pairs of lower and upper bounds on a div
2185 * are such that they allow at least one integer value of the div,
2186 * the we can eliminate the div using Fourier-Motzkin without
2187 * introducing any spurious solutions.
2188 */
2189 static struct isl_basic_map *drop_more_redundant_divs(
2190 struct isl_basic_map *bmap, int *pairs, int n)
2191 {
2192 struct isl_tab *tab = NULL;
2193 struct isl_vec *vec = NULL;
2194 unsigned dim;
2195 int remove = -1;
2196 isl_int g, fl, fu;
2197
2198 isl_int_init(g);
2199 isl_int_init(fl);
2200 isl_int_init(fu);
2201
2202 if (!bmap)
2203 goto error;
2204
2205 dim = isl_dim_total(bmap->dim);
2206 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2207 if (!vec)
2208 goto error;
2209
2210 tab = isl_tab_from_basic_map(bmap);
2211
2212 while (n > 0) {
2213 int i, l, u;
2214 int best = -1;
2215 enum isl_lp_result res;
2216
2217 for (i = 0; i < bmap->n_div; ++i) {
2218 if (!pairs[i])
2219 continue;
2220 if (best >= 0 && pairs[best] <= pairs[i])
2221 continue;
2222 best = i;
2223 }
2224
2225 i = best;
2226 for (l = 0; l < bmap->n_ineq; ++l) {
2227 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2228 continue;
2229 for (u = 0; u < bmap->n_ineq; ++u) {
2230 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2231 continue;
2232 construct_test_ineq(bmap, i, l, u,
2233 vec->el, g, fl, fu);
2234 res = isl_tab_min(tab, vec->el,
2235 bmap->ctx->one, &g, NULL, 0);
2236 if (res == isl_lp_error)
2237 goto error;
2238 if (res == isl_lp_empty) {
2239 bmap = isl_basic_map_set_to_empty(bmap);
2240 break;
2241 }
2242 if (res != isl_lp_ok || isl_int_is_neg(g))
2243 break;
2244 }
2245 if (u < bmap->n_ineq)
2246 break;
2247 }
2248 if (l == bmap->n_ineq) {
2249 remove = i;
2250 break;
2251 }
2252 pairs[i] = 0;
2253 --n;
2254 }
2255
2256 isl_tab_free(tab);
2257 isl_vec_free(vec);
2258
2259 isl_int_clear(g);
2260 isl_int_clear(fl);
2261 isl_int_clear(fu);
2262
2263 free(pairs);
2264
2265 if (remove < 0)
2266 return bmap;
2267
2268 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2269 return isl_basic_map_drop_redundant_divs(bmap);
2270 error:
2271 free(pairs);
2272 isl_basic_map_free(bmap);
2273 isl_tab_free(tab);
2274 isl_vec_free(vec);
2275 isl_int_clear(g);
2276 isl_int_clear(fl);
2277 isl_int_clear(fu);
2278 return NULL;
2279 }
2280
2281 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2282 * and the upper bound u, div1 always occurs together with div2 in the form
2283 * (div1 + m div2), where m is the constant range on the variable div1
2284 * allowed by l and u, replace the pair div1 and div2 by a single
2285 * div that is equal to div1 + m div2.
2286 *
2287 * The new div will appear in the location that contains div2.
2288 * We need to modify all constraints that contain
2289 * div2 = (div - div1) / m
2290 * (If a constraint does not contain div2, it will also not contain div1.)
2291 * If the constraint also contains div1, then we know they appear
2292 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2293 * i.e., the coefficient of div is f.
2294 *
2295 * Otherwise, we first need to introduce div1 into the constraint.
2296 * Let the l be
2297 *
2298 * div1 + f >=0
2299 *
2300 * and u
2301 *
2302 * -div1 + f' >= 0
2303 *
2304 * A lower bound on div2
2305 *
2306 * n div2 + t >= 0
2307 *
2308 * can be replaced by
2309 *
2310 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2311 *
2312 * with g = gcd(m,n).
2313 * An upper bound
2314 *
2315 * -n div2 + t >= 0
2316 *
2317 * can be replaced by
2318 *
2319 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2320 *
2321 * These constraint are those that we would obtain from eliminating
2322 * div1 using Fourier-Motzkin.
2323 *
2324 * After all constraints have been modified, we drop the lower and upper
2325 * bound and then drop div1.
2326 */
2327 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2328 unsigned div1, unsigned div2, unsigned l, unsigned u)
2329 {
2330 isl_int a;
2331 isl_int b;
2332 isl_int m;
2333 unsigned dim, total;
2334 int i;
2335
2336 dim = isl_dim_total(bmap->dim);
2337 total = 1 + dim + bmap->n_div;
2338
2339 isl_int_init(a);
2340 isl_int_init(b);
2341 isl_int_init(m);
2342 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2343 isl_int_add_ui(m, m, 1);
2344
2345 for (i = 0; i < bmap->n_ineq; ++i) {
2346 if (i == l || i == u)
2347 continue;
2348 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2349 continue;
2350 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2351 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2352 isl_int_divexact(a, m, b);
2353 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2354 if (isl_int_is_pos(b)) {
2355 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2356 b, bmap->ineq[l], total);
2357 } else {
2358 isl_int_neg(b, b);
2359 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2360 b, bmap->ineq[u], total);
2361 }
2362 }
2363 isl_int_set(bmap->ineq[i][1 + dim + div2],
2364 bmap->ineq[i][1 + dim + div1]);
2365 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2366 }
2367
2368 isl_int_clear(a);
2369 isl_int_clear(b);
2370 isl_int_clear(m);
2371 if (l > u) {
2372 isl_basic_map_drop_inequality(bmap, l);
2373 isl_basic_map_drop_inequality(bmap, u);
2374 } else {
2375 isl_basic_map_drop_inequality(bmap, u);
2376 isl_basic_map_drop_inequality(bmap, l);
2377 }
2378 bmap = isl_basic_map_drop_div(bmap, div1);
2379 return bmap;
2380 }
2381
2382 /* First check if we can coalesce any pair of divs and
2383 * then continue with dropping more redundant divs.
2384 *
2385 * We loop over all pairs of lower and upper bounds on a div
2386 * with coefficient 1 and -1, respectively, check if there
2387 * is any other div "c" with which we can coalesce the div
2388 * and if so, perform the coalescing.
2389 */
2390 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2391 struct isl_basic_map *bmap, int *pairs, int n)
2392 {
2393 int i, l, u;
2394 unsigned dim;
2395
2396 dim = isl_dim_total(bmap->dim);
2397
2398 for (i = 0; i < bmap->n_div; ++i) {
2399 if (!pairs[i])
2400 continue;
2401 for (l = 0; l < bmap->n_ineq; ++l) {
2402 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2403 continue;
2404 for (u = 0; u < bmap->n_ineq; ++u) {
2405 int c;
2406
2407 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2408 continue;
2409 c = div_find_coalesce(bmap, pairs, i, l, u);
2410 if (c < 0)
2411 continue;
2412 free(pairs);
2413 bmap = coalesce_divs(bmap, i, c, l, u);
2414 return isl_basic_map_drop_redundant_divs(bmap);
2415 }
2416 }
2417 }
2418
2419 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2420 return bmap;
2421
2422 return drop_more_redundant_divs(bmap, pairs, n);
2423 }
2424
2425 /* Remove divs that are not strictly needed.
2426 * In particular, if a div only occurs positively (or negatively)
2427 * in constraints, then it can simply be dropped.
2428 * Also, if a div occurs only occurs in two constraints and if moreover
2429 * those two constraints are opposite to each other, except for the constant
2430 * term and if the sum of the constant terms is such that for any value
2431 * of the other values, there is always at least one integer value of the
2432 * div, i.e., if one plus this sum is greater than or equal to
2433 * the (absolute value) of the coefficent of the div in the constraints,
2434 * then we can also simply drop the div.
2435 *
2436 * If any divs are left after these simple checks then we move on
2437 * to more complicated cases in drop_more_redundant_divs.
2438 */
2439 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2440 struct isl_basic_map *bmap)
2441 {
2442 int i, j;
2443 unsigned off;
2444 int *pairs = NULL;
2445 int n = 0;
2446
2447 if (!bmap)
2448 goto error;
2449
2450 off = isl_dim_total(bmap->dim);
2451 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2452 if (!pairs)
2453 goto error;
2454
2455 for (i = 0; i < bmap->n_div; ++i) {
2456 int pos, neg;
2457 int last_pos, last_neg;
2458 int redundant;
2459 int defined;
2460
2461 defined = !isl_int_is_zero(bmap->div[i][0]);
2462 for (j = 0; j < bmap->n_eq; ++j)
2463 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2464 break;
2465 if (j < bmap->n_eq)
2466 continue;
2467 ++n;
2468 pos = neg = 0;
2469 for (j = 0; j < bmap->n_ineq; ++j) {
2470 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2471 last_pos = j;
2472 ++pos;
2473 }
2474 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2475 last_neg = j;
2476 ++neg;
2477 }
2478 }
2479 pairs[i] = pos * neg;
2480 if (pairs[i] == 0) {
2481 for (j = bmap->n_ineq - 1; j >= 0; --j)
2482 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2483 isl_basic_map_drop_inequality(bmap, j);
2484 bmap = isl_basic_map_drop_div(bmap, i);
2485 free(pairs);
2486 return isl_basic_map_drop_redundant_divs(bmap);
2487 }
2488 if (pairs[i] != 1)
2489 continue;
2490 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2491 bmap->ineq[last_neg] + 1,
2492 off + bmap->n_div))
2493 continue;
2494
2495 isl_int_add(bmap->ineq[last_pos][0],
2496 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2497 isl_int_add_ui(bmap->ineq[last_pos][0],
2498 bmap->ineq[last_pos][0], 1);
2499 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2500 bmap->ineq[last_pos][1+off+i]);
2501 isl_int_sub_ui(bmap->ineq[last_pos][0],
2502 bmap->ineq[last_pos][0], 1);
2503 isl_int_sub(bmap->ineq[last_pos][0],
2504 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2505 if (!redundant) {
2506 if (defined ||
2507 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2508 pairs[i] = 0;
2509 --n;
2510 continue;
2511 }
2512 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2513 bmap = isl_basic_map_simplify(bmap);
2514 free(pairs);
2515 return isl_basic_map_drop_redundant_divs(bmap);
2516 }
2517 if (last_pos > last_neg) {
2518 isl_basic_map_drop_inequality(bmap, last_pos);
2519 isl_basic_map_drop_inequality(bmap, last_neg);
2520 } else {
2521 isl_basic_map_drop_inequality(bmap, last_neg);
2522 isl_basic_map_drop_inequality(bmap, last_pos);
2523 }
2524 bmap = isl_basic_map_drop_div(bmap, i);
2525 free(pairs);
2526 return isl_basic_map_drop_redundant_divs(bmap);
2527 }
2528
2529 if (n > 0)
2530 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2531
2532 free(pairs);
2533 return bmap;
2534 error:
2535 free(pairs);
2536 isl_basic_map_free(bmap);
2537 return NULL;
2538 }
2539
2540 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2541 struct isl_basic_set *bset)
2542 {
2543 return (struct isl_basic_set *)
2544 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2545 }
2546
2547 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2548 {
2549 int i;
2550
2551 if (!map)
2552 return NULL;
2553 for (i = 0; i < map->n; ++i) {
2554 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2555 if (!map->p[i])
2556 goto error;
2557 }
2558 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2559 return map;
2560 error:
2561 isl_map_free(map);
2562 return NULL;
2563 }
2564
2565 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2566 {
2567 return (struct isl_set *)
2568 isl_map_drop_redundant_divs((struct isl_map *)set);
2569 }
Integer set library