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isl_union_map: construct new isl_union_map on operations that change dimensions
[isl.git] / isl_map_simplify.c
blobe9727da578d48d08bce29b2207fc6d844d937d8f
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_equalities.h"
11 #include "isl_map.h"
12 #include "isl_map_private.h"
13 #include "isl_seq.h"
14 #include "isl_tab.h"
15 #include <isl_dim_private.h>
16
17 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
18 {
19 isl_int *t = bmap->eq[a];
20 bmap->eq[a] = bmap->eq[b];
21 bmap->eq[b] = t;
22 }
23
24 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
25 {
26 if (a != b) {
27 isl_int *t = bmap->ineq[a];
28 bmap->ineq[a] = bmap->ineq[b];
29 bmap->ineq[b] = t;
30 }
31 }
32
33 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
34 {
35 swap_inequality((struct isl_basic_map *)bset, a, b);
36 }
37
38 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
39 {
40 isl_seq_cpy(c, c + n, rem);
41 isl_seq_clr(c + rem, n);
42 }
43
44 /* Drop n dimensions starting at first.
45 *
46 * In principle, this frees up some extra variables as the number
47 * of columns remains constant, but we would have to extend
48 * the div array too as the number of rows in this array is assumed
49 * to be equal to extra.
50 */
51 struct isl_basic_set *isl_basic_set_drop_dims(
52 struct isl_basic_set *bset, unsigned first, unsigned n)
53 {
54 int i;
55
56 if (!bset)
57 goto error;
58
59 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
60
61 if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
62 return bset;
63
64 bset = isl_basic_set_cow(bset);
65 if (!bset)
66 return NULL;
67
68 for (i = 0; i < bset->n_eq; ++i)
69 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
70 (bset->dim->n_out-first-n)+bset->extra);
71
72 for (i = 0; i < bset->n_ineq; ++i)
73 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
74 (bset->dim->n_out-first-n)+bset->extra);
75
76 for (i = 0; i < bset->n_div; ++i)
77 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
78 (bset->dim->n_out-first-n)+bset->extra);
79
80 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
81 if (!bset->dim)
82 goto error;
83
84 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
85 bset = isl_basic_set_simplify(bset);
86 return isl_basic_set_finalize(bset);
87 error:
88 isl_basic_set_free(bset);
89 return NULL;
90 }
91
92 struct isl_set *isl_set_drop_dims(
93 struct isl_set *set, unsigned first, unsigned n)
94 {
95 int i;
96
97 if (!set)
98 goto error;
99
100 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
101
102 if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
103 return set;
104 set = isl_set_cow(set);
105 if (!set)
106 goto error;
107 set->dim = isl_dim_drop_outputs(set->dim, first, n);
108 if (!set->dim)
109 goto error;
110
111 for (i = 0; i < set->n; ++i) {
112 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
113 if (!set->p[i])
114 goto error;
115 }
116
117 ISL_F_CLR(set, ISL_SET_NORMALIZED);
118 return set;
119 error:
120 isl_set_free(set);
121 return NULL;
122 }
123
124 /* Move "n" divs starting at "first" to the end of the list of divs.
125 */
126 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
127 unsigned first, unsigned n)
128 {
129 isl_int **div;
130 int i;
131
132 if (first + n == bmap->n_div)
133 return bmap;
134
135 div = isl_alloc_array(bmap->ctx, isl_int *, n);
136 if (!div)
137 goto error;
138 for (i = 0; i < n; ++i)
139 div[i] = bmap->div[first + i];
140 for (i = 0; i < bmap->n_div - first - n; ++i)
141 bmap->div[first + i] = bmap->div[first + n + i];
142 for (i = 0; i < n; ++i)
143 bmap->div[bmap->n_div - n + i] = div[i];
144 free(div);
145 return bmap;
146 error:
147 isl_basic_map_free(bmap);
148 return NULL;
149 }
150
151 /* Drop "n" dimensions of type "type" starting at "first".
152 *
153 * In principle, this frees up some extra variables as the number
154 * of columns remains constant, but we would have to extend
155 * the div array too as the number of rows in this array is assumed
156 * to be equal to extra.
157 */
158 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
159 enum isl_dim_type type, unsigned first, unsigned n)
160 {
161 int i;
162 unsigned dim;
163 unsigned offset;
164 unsigned left;
165
166 if (!bmap)
167 goto error;
168
169 dim = isl_basic_map_dim(bmap, type);
170 isl_assert(bmap->ctx, first + n <= dim, goto error);
171
172 if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
173 return bmap;
174
175 bmap = isl_basic_map_cow(bmap);
176 if (!bmap)
177 return NULL;
178
179 offset = isl_basic_map_offset(bmap, type) + first;
180 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
181 for (i = 0; i < bmap->n_eq; ++i)
182 constraint_drop_vars(bmap->eq[i]+offset, n, left);
183
184 for (i = 0; i < bmap->n_ineq; ++i)
185 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
186
187 for (i = 0; i < bmap->n_div; ++i)
188 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
189
190 if (type == isl_dim_div) {
191 bmap = move_divs_last(bmap, first, n);
192 if (!bmap)
193 goto error;
194 isl_basic_map_free_div(bmap, n);
195 } else
196 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
197 if (!bmap->dim)
198 goto error;
199
200 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
201 bmap = isl_basic_map_simplify(bmap);
202 return isl_basic_map_finalize(bmap);
203 error:
204 isl_basic_map_free(bmap);
205 return NULL;
206 }
207
208 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
209 enum isl_dim_type type, unsigned first, unsigned n)
210 {
211 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
212 type, first, n);
213 }
214
215 struct isl_basic_map *isl_basic_map_drop_inputs(
216 struct isl_basic_map *bmap, unsigned first, unsigned n)
217 {
218 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
219 }
220
221 struct isl_map *isl_map_drop(struct isl_map *map,
222 enum isl_dim_type type, unsigned first, unsigned n)
223 {
224 int i;
225
226 if (!map)
227 goto error;
228
229 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
230
231 if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
232 return map;
233 map = isl_map_cow(map);
234 if (!map)
235 goto error;
236 map->dim = isl_dim_drop(map->dim, type, first, n);
237 if (!map->dim)
238 goto error;
239
240 for (i = 0; i < map->n; ++i) {
241 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
242 if (!map->p[i])
243 goto error;
244 }
245 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
246
247 return map;
248 error:
249 isl_map_free(map);
250 return NULL;
251 }
252
253 struct isl_set *isl_set_drop(struct isl_set *set,
254 enum isl_dim_type type, unsigned first, unsigned n)
255 {
256 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
257 }
258
259 struct isl_map *isl_map_drop_inputs(
260 struct isl_map *map, unsigned first, unsigned n)
261 {
262 return isl_map_drop(map, isl_dim_in, first, n);
263 }
264
265 /*
266 * We don't cow, as the div is assumed to be redundant.
267 */
268 static struct isl_basic_map *isl_basic_map_drop_div(
269 struct isl_basic_map *bmap, unsigned div)
270 {
271 int i;
272 unsigned pos;
273
274 if (!bmap)
275 goto error;
276
277 pos = 1 + isl_dim_total(bmap->dim) + div;
278
279 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
280
281 for (i = 0; i < bmap->n_eq; ++i)
282 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
283
284 for (i = 0; i < bmap->n_ineq; ++i) {
285 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
286 isl_basic_map_drop_inequality(bmap, i);
287 --i;
288 continue;
289 }
290 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
291 }
292
293 for (i = 0; i < bmap->n_div; ++i)
294 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
295
296 if (div != bmap->n_div - 1) {
297 int j;
298 isl_int *t = bmap->div[div];
299
300 for (j = div; j < bmap->n_div - 1; ++j)
301 bmap->div[j] = bmap->div[j+1];
302
303 bmap->div[bmap->n_div - 1] = t;
304 }
305 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
306 isl_basic_map_free_div(bmap, 1);
307
308 return bmap;
309 error:
310 isl_basic_map_free(bmap);
311 return NULL;
312 }
313
314 struct isl_basic_map *isl_basic_map_normalize_constraints(
315 struct isl_basic_map *bmap)
316 {
317 int i;
318 isl_int gcd;
319 unsigned total = isl_basic_map_total_dim(bmap);
320
321 if (!bmap)
322 return NULL;
323
324 isl_int_init(gcd);
325 for (i = bmap->n_eq - 1; i >= 0; --i) {
326 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
327 if (isl_int_is_zero(gcd)) {
328 if (!isl_int_is_zero(bmap->eq[i][0])) {
329 bmap = isl_basic_map_set_to_empty(bmap);
330 break;
331 }
332 isl_basic_map_drop_equality(bmap, i);
333 continue;
334 }
335 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
336 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
337 if (isl_int_is_one(gcd))
338 continue;
339 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
340 bmap = isl_basic_map_set_to_empty(bmap);
341 break;
342 }
343 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
344 }
345
346 for (i = bmap->n_ineq - 1; i >= 0; --i) {
347 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
348 if (isl_int_is_zero(gcd)) {
349 if (isl_int_is_neg(bmap->ineq[i][0])) {
350 bmap = isl_basic_map_set_to_empty(bmap);
351 break;
352 }
353 isl_basic_map_drop_inequality(bmap, i);
354 continue;
355 }
356 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
357 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
358 if (isl_int_is_one(gcd))
359 continue;
360 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
361 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
362 }
363 isl_int_clear(gcd);
364
365 return bmap;
366 }
367
368 struct isl_basic_set *isl_basic_set_normalize_constraints(
369 struct isl_basic_set *bset)
370 {
371 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
372 (struct isl_basic_map *)bset);
373 }
374
375 /* Assumes divs have been ordered if keep_divs is set.
376 */
377 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
378 unsigned pos, isl_int *eq, int keep_divs, int *progress)
379 {
380 unsigned total;
381 int k;
382 int last_div;
383
384 total = isl_basic_map_total_dim(bmap);
385 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
386 bmap->n_div);
387 for (k = 0; k < bmap->n_eq; ++k) {
388 if (bmap->eq[k] == eq)
389 continue;
390 if (isl_int_is_zero(bmap->eq[k][1+pos]))
391 continue;
392 if (progress)
393 *progress = 1;
394 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
395 }
396
397 for (k = 0; k < bmap->n_ineq; ++k) {
398 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
399 continue;
400 if (progress)
401 *progress = 1;
402 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
403 ISL_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_alloc(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_alloc(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)
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
1024 if (!bmap || bmap->n_ineq <= 1)
1025 return bmap;
1026
1027 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1028 bits = ffs(size) - 1;
1029 index = isl_calloc_array(ctx, isl_int **, size);
1030 if (!index)
1031 return bmap;
1032
1033 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1034 for (k = 1; k < bmap->n_ineq; ++k) {
1035 h = hash_index(index, size, bits, bmap, k);
1036 if (!index[h]) {
1037 index[h] = &bmap->ineq[k];
1038 continue;
1039 }
1040 if (progress)
1041 *progress = 1;
1042 l = index[h] - &bmap->ineq[0];
1043 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1044 swap_inequality(bmap, k, l);
1045 isl_basic_map_drop_inequality(bmap, k);
1046 --k;
1047 }
1048 isl_int_init(sum);
1049 for (k = 0; k < bmap->n_ineq-1; ++k) {
1050 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1051 h = hash_index(index, size, bits, bmap, k);
1052 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1053 if (!index[h])
1054 continue;
1055 l = index[h] - &bmap->ineq[0];
1056 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1057 if (isl_int_is_pos(sum)) {
1058 bmap = check_for_div_constraints(bmap, k, l, sum,
1059 progress);
1060 continue;
1061 }
1062 if (isl_int_is_zero(sum)) {
1063 /* We need to break out of the loop after these
1064 * changes since the contents of the hash
1065 * will no longer be valid.
1066 * Plus, we probably we want to regauss first.
1067 */
1068 if (progress)
1069 *progress = 1;
1070 isl_basic_map_drop_inequality(bmap, l);
1071 isl_basic_map_inequality_to_equality(bmap, k);
1072 } else
1073 bmap = isl_basic_map_set_to_empty(bmap);
1074 break;
1075 }
1076 isl_int_clear(sum);
1077
1078 free(index);
1079 return bmap;
1080 }
1081
1082
1083 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1084 {
1085 int progress = 1;
1086 if (!bmap)
1087 return NULL;
1088 while (progress) {
1089 progress = 0;
1090 bmap = isl_basic_map_normalize_constraints(bmap);
1091 bmap = remove_duplicate_divs(bmap, &progress);
1092 bmap = eliminate_divs_eq(bmap, &progress);
1093 bmap = eliminate_divs_ineq(bmap, &progress);
1094 bmap = isl_basic_map_gauss(bmap, &progress);
1095 /* requires equalities in normal form */
1096 bmap = normalize_divs(bmap, &progress);
1097 bmap = remove_duplicate_constraints(bmap, &progress);
1098 }
1099 return bmap;
1100 }
1101
1102 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1103 {
1104 return (struct isl_basic_set *)
1105 isl_basic_map_simplify((struct isl_basic_map *)bset);
1106 }
1107
1108
1109 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1110 isl_int *constraint, unsigned div)
1111 {
1112 unsigned pos;
1113
1114 if (!bmap)
1115 return -1;
1116
1117 pos = 1 + isl_dim_total(bmap->dim) + div;
1118
1119 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1120 int neg;
1121 isl_int_sub(bmap->div[div][1],
1122 bmap->div[div][1], bmap->div[div][0]);
1123 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1124 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1125 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1126 isl_int_add(bmap->div[div][1],
1127 bmap->div[div][1], bmap->div[div][0]);
1128 if (!neg)
1129 return 0;
1130 if (isl_seq_first_non_zero(constraint+pos+1,
1131 bmap->n_div-div-1) != -1)
1132 return 0;
1133 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1134 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1135 return 0;
1136 if (isl_seq_first_non_zero(constraint+pos+1,
1137 bmap->n_div-div-1) != -1)
1138 return 0;
1139 } else
1140 return 0;
1141
1142 return 1;
1143 }
1144
1145
1146 /* If the only constraints a div d=floor(f/m)
1147 * appears in are its two defining constraints
1148 *
1149 * f - m d >=0
1150 * -(f - (m - 1)) + m d >= 0
1151 *
1152 * then it can safely be removed.
1153 */
1154 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1155 {
1156 int i;
1157 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1158
1159 for (i = 0; i < bmap->n_eq; ++i)
1160 if (!isl_int_is_zero(bmap->eq[i][pos]))
1161 return 0;
1162
1163 for (i = 0; i < bmap->n_ineq; ++i) {
1164 if (isl_int_is_zero(bmap->ineq[i][pos]))
1165 continue;
1166 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1167 return 0;
1168 }
1169
1170 for (i = 0; i < bmap->n_div; ++i)
1171 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1172 return 0;
1173
1174 return 1;
1175 }
1176
1177 /*
1178 * Remove divs that don't occur in any of the constraints or other divs.
1179 * These can arise when dropping some of the variables in a quast
1180 * returned by piplib.
1181 */
1182 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1183 {
1184 int i;
1185
1186 if (!bmap)
1187 return NULL;
1188
1189 for (i = bmap->n_div-1; i >= 0; --i) {
1190 if (!div_is_redundant(bmap, i))
1191 continue;
1192 bmap = isl_basic_map_drop_div(bmap, i);
1193 }
1194 return bmap;
1195 }
1196
1197 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1198 {
1199 bmap = remove_redundant_divs(bmap);
1200 if (!bmap)
1201 return NULL;
1202 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1203 return bmap;
1204 }
1205
1206 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1207 {
1208 return (struct isl_basic_set *)
1209 isl_basic_map_finalize((struct isl_basic_map *)bset);
1210 }
1211
1212 struct isl_set *isl_set_finalize(struct isl_set *set)
1213 {
1214 int i;
1215
1216 if (!set)
1217 return NULL;
1218 for (i = 0; i < set->n; ++i) {
1219 set->p[i] = isl_basic_set_finalize(set->p[i]);
1220 if (!set->p[i])
1221 goto error;
1222 }
1223 return set;
1224 error:
1225 isl_set_free(set);
1226 return NULL;
1227 }
1228
1229 struct isl_map *isl_map_finalize(struct isl_map *map)
1230 {
1231 int i;
1232
1233 if (!map)
1234 return NULL;
1235 for (i = 0; i < map->n; ++i) {
1236 map->p[i] = isl_basic_map_finalize(map->p[i]);
1237 if (!map->p[i])
1238 goto error;
1239 }
1240 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1241 return map;
1242 error:
1243 isl_map_free(map);
1244 return NULL;
1245 }
1246
1247
1248 /* Remove definition of any div that is defined in terms of the given variable.
1249 * The div itself is not removed. Functions such as
1250 * eliminate_divs_ineq depend on the other divs remaining in place.
1251 */
1252 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1253 int pos)
1254 {
1255 int i;
1256
1257 for (i = 0; i < bmap->n_div; ++i) {
1258 if (isl_int_is_zero(bmap->div[i][0]))
1259 continue;
1260 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1261 continue;
1262 isl_int_set_si(bmap->div[i][0], 0);
1263 }
1264 return bmap;
1265 }
1266
1267 /* Eliminate the specified variables from the constraints using
1268 * Fourier-Motzkin. The variables themselves are not removed.
1269 */
1270 struct isl_basic_map *isl_basic_map_eliminate_vars(
1271 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1272 {
1273 int d;
1274 int i, j, k;
1275 unsigned total;
1276
1277 if (n == 0)
1278 return bmap;
1279 if (!bmap)
1280 return NULL;
1281 total = isl_basic_map_total_dim(bmap);
1282
1283 bmap = isl_basic_map_cow(bmap);
1284 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1285 bmap = remove_dependent_vars(bmap, d);
1286
1287 for (d = pos + n - 1;
1288 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1289 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1290 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1291 int n_lower, n_upper;
1292 if (!bmap)
1293 return NULL;
1294 for (i = 0; i < bmap->n_eq; ++i) {
1295 if (isl_int_is_zero(bmap->eq[i][1+d]))
1296 continue;
1297 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1298 isl_basic_map_drop_equality(bmap, i);
1299 break;
1300 }
1301 if (i < bmap->n_eq)
1302 continue;
1303 n_lower = 0;
1304 n_upper = 0;
1305 for (i = 0; i < bmap->n_ineq; ++i) {
1306 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1307 n_lower++;
1308 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1309 n_upper++;
1310 }
1311 bmap = isl_basic_map_extend_constraints(bmap,
1312 0, n_lower * n_upper);
1313 if (!bmap)
1314 goto error;
1315 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1316 int last;
1317 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1318 continue;
1319 last = -1;
1320 for (j = 0; j < i; ++j) {
1321 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1322 continue;
1323 last = j;
1324 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1325 isl_int_sgn(bmap->ineq[j][1+d]))
1326 continue;
1327 k = isl_basic_map_alloc_inequality(bmap);
1328 if (k < 0)
1329 goto error;
1330 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1331 1+total);
1332 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1333 1+d, 1+total, NULL);
1334 }
1335 isl_basic_map_drop_inequality(bmap, i);
1336 i = last + 1;
1337 }
1338 if (n_lower > 0 && n_upper > 0) {
1339 bmap = isl_basic_map_normalize_constraints(bmap);
1340 bmap = remove_duplicate_constraints(bmap, NULL);
1341 bmap = isl_basic_map_gauss(bmap, NULL);
1342 bmap = isl_basic_map_remove_redundancies(bmap);
1343 if (!bmap)
1344 goto error;
1345 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1346 break;
1347 }
1348 }
1349 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1350 return bmap;
1351 error:
1352 isl_basic_map_free(bmap);
1353 return NULL;
1354 }
1355
1356 struct isl_basic_set *isl_basic_set_eliminate_vars(
1357 struct isl_basic_set *bset, unsigned pos, unsigned n)
1358 {
1359 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1360 (struct isl_basic_map *)bset, pos, n);
1361 }
1362
1363 /* Don't assume equalities are in order, because align_divs
1364 * may have changed the order of the divs.
1365 */
1366 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1367 {
1368 int d, i;
1369 unsigned total;
1370
1371 total = isl_dim_total(bmap->dim);
1372 for (d = 0; d < total; ++d)
1373 elim[d] = -1;
1374 for (i = 0; i < bmap->n_eq; ++i) {
1375 for (d = total - 1; d >= 0; --d) {
1376 if (isl_int_is_zero(bmap->eq[i][1+d]))
1377 continue;
1378 elim[d] = i;
1379 break;
1380 }
1381 }
1382 }
1383
1384 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1385 {
1386 compute_elimination_index((struct isl_basic_map *)bset, elim);
1387 }
1388
1389 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1390 struct isl_basic_map *bmap, int *elim)
1391 {
1392 int d;
1393 int copied = 0;
1394 unsigned total;
1395
1396 total = isl_dim_total(bmap->dim);
1397 for (d = total - 1; d >= 0; --d) {
1398 if (isl_int_is_zero(src[1+d]))
1399 continue;
1400 if (elim[d] == -1)
1401 continue;
1402 if (!copied) {
1403 isl_seq_cpy(dst, src, 1 + total);
1404 copied = 1;
1405 }
1406 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1407 }
1408 return copied;
1409 }
1410
1411 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1412 struct isl_basic_set *bset, int *elim)
1413 {
1414 return reduced_using_equalities(dst, src,
1415 (struct isl_basic_map *)bset, elim);
1416 }
1417
1418 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1419 struct isl_basic_set *bset, struct isl_basic_set *context)
1420 {
1421 int i;
1422 int *elim;
1423
1424 if (!bset || !context)
1425 goto error;
1426
1427 if (context->n_eq == 0) {
1428 isl_basic_set_free(context);
1429 return bset;
1430 }
1431
1432 bset = isl_basic_set_cow(bset);
1433 if (!bset)
1434 goto error;
1435
1436 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1437 if (!elim)
1438 goto error;
1439 set_compute_elimination_index(context, elim);
1440 for (i = 0; i < bset->n_eq; ++i)
1441 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1442 context, elim);
1443 for (i = 0; i < bset->n_ineq; ++i)
1444 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1445 context, elim);
1446 isl_basic_set_free(context);
1447 free(elim);
1448 bset = isl_basic_set_simplify(bset);
1449 bset = isl_basic_set_finalize(bset);
1450 return bset;
1451 error:
1452 isl_basic_set_free(bset);
1453 isl_basic_set_free(context);
1454 return NULL;
1455 }
1456
1457 static struct isl_basic_set *remove_shifted_constraints(
1458 struct isl_basic_set *bset, struct isl_basic_set *context)
1459 {
1460 unsigned int size;
1461 isl_int ***index;
1462 int bits;
1463 int k, h, l;
1464
1465 if (!bset)
1466 return NULL;
1467
1468 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1469 bits = ffs(size) - 1;
1470 index = isl_calloc_array(ctx, isl_int **, size);
1471 if (!index)
1472 return bset;
1473
1474 for (k = 0; k < context->n_ineq; ++k) {
1475 h = set_hash_index(index, size, bits, context, k);
1476 index[h] = &context->ineq[k];
1477 }
1478 for (k = 0; k < bset->n_ineq; ++k) {
1479 h = set_hash_index(index, size, bits, bset, k);
1480 if (!index[h])
1481 continue;
1482 l = index[h] - &context->ineq[0];
1483 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1484 continue;
1485 bset = isl_basic_set_cow(bset);
1486 if (!bset)
1487 goto error;
1488 isl_basic_set_drop_inequality(bset, k);
1489 --k;
1490 }
1491 free(index);
1492 return bset;
1493 error:
1494 free(index);
1495 return bset;
1496 }
1497
1498 /* Tighten (decrease) the constant terms of the inequalities based
1499 * on the equalities, without removing any integer points.
1500 * For example, if there is an equality
1501 *
1502 * i = 3 * j
1503 *
1504 * and an inequality
1505 *
1506 * i >= 1
1507 *
1508 * then we want to replace the inequality by
1509 *
1510 * i >= 3
1511 *
1512 * We do this by computing a variable compression and translating
1513 * the constraints to the compressed space.
1514 * If any constraint has coefficients (except the contant term)
1515 * with a common factor "f", then we can replace the constant term "c"
1516 * by
1517 *
1518 * f * floor(c/f)
1519 *
1520 * That is, we add
1521 *
1522 * f * floor(c/f) - c = -fract(c/f)
1523 *
1524 * and we can add the same value to the original constraint.
1525 *
1526 * In the example, the compressed space only contains "j",
1527 * and the inequality translates to
1528 *
1529 * 3 * j - 1 >= 0
1530 *
1531 * We add -fract(-1/3) = -2 to the original constraint to obtain
1532 *
1533 * i - 3 >= 0
1534 */
1535 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1536 struct isl_basic_set *bset)
1537 {
1538 int i;
1539 unsigned total;
1540 struct isl_mat *B, *C;
1541 isl_int gcd;
1542
1543 if (!bset)
1544 return NULL;
1545
1546 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1547 return bset;
1548
1549 if (!bset->n_ineq)
1550 return bset;
1551
1552 bset = isl_basic_set_cow(bset);
1553 if (!bset)
1554 return NULL;
1555
1556 total = isl_basic_set_total_dim(bset);
1557 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1558 C = isl_mat_variable_compression(B, NULL);
1559 if (!C)
1560 return bset;
1561 if (C->n_col == 0) {
1562 isl_mat_free(C);
1563 return isl_basic_set_set_to_empty(bset);
1564 }
1565 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1566 0, bset->n_ineq, 0, 1 + total);
1567 C = isl_mat_product(B, C);
1568 if (!C)
1569 return bset;
1570
1571 isl_int_init(gcd);
1572 for (i = 0; i < bset->n_ineq; ++i) {
1573 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1574 if (isl_int_is_one(gcd))
1575 continue;
1576 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1577 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1578 }
1579 isl_int_clear(gcd);
1580
1581 isl_mat_free(C);
1582
1583 return bset;
1584 }
1585
1586 /* Remove all information from bset that is redundant in the context
1587 * of context. Both bset and context are assumed to be full-dimensional.
1588 *
1589 * We first * remove the inequalities from "bset"
1590 * that are obviously redundant with respect to some inequality in "context".
1591 *
1592 * If there are any inequalities left, we construct a tableau for
1593 * the context and then add the inequalities of "bset".
1594 * Before adding these inequalities, we freeze all constraints such that
1595 * they won't be considered redundant in terms of the constraints of "bset".
1596 * Then we detect all redundant constraints (among the
1597 * constraints that weren't frozen), first by checking for redundancy in the
1598 * the tableau and then by checking if replacing a constraint by its negation
1599 * would lead to an empty set. This last step is fairly expensive
1600 * and could be optimized by more reuse of the tableau.
1601 * Finally, we update bset according to the results.
1602 */
1603 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1604 __isl_take isl_basic_set *context)
1605 {
1606 int i, k;
1607 isl_basic_set *combined = NULL;
1608 struct isl_tab *tab = NULL;
1609 unsigned context_ineq;
1610 unsigned total;
1611
1612 if (!bset || !context)
1613 goto error;
1614
1615 if (isl_basic_set_is_universe(bset)) {
1616 isl_basic_set_free(context);
1617 return bset;
1618 }
1619
1620 if (isl_basic_set_is_universe(context)) {
1621 isl_basic_set_free(context);
1622 return bset;
1623 }
1624
1625 bset = remove_shifted_constraints(bset, context);
1626 if (!bset)
1627 goto error;
1628 if (bset->n_ineq == 0)
1629 goto done;
1630
1631 context_ineq = context->n_ineq;
1632 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1633 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1634 tab = isl_tab_from_basic_set(combined);
1635 for (i = 0; i < context_ineq; ++i)
1636 if (isl_tab_freeze_constraint(tab, i) < 0)
1637 goto error;
1638 tab = isl_tab_extend(tab, bset->n_ineq);
1639 for (i = 0; i < bset->n_ineq; ++i)
1640 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1641 goto error;
1642 bset = isl_basic_set_add_constraints(combined, bset, 0);
1643 combined = NULL;
1644 if (!bset)
1645 goto error;
1646 if (isl_tab_detect_redundant(tab) < 0)
1647 goto error;
1648 total = isl_basic_set_total_dim(bset);
1649 for (i = context_ineq; i < bset->n_ineq; ++i) {
1650 int is_empty;
1651 if (tab->con[i].is_redundant)
1652 continue;
1653 tab->con[i].is_redundant = 1;
1654 combined = isl_basic_set_dup(bset);
1655 combined = isl_basic_set_update_from_tab(combined, tab);
1656 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1657 k = isl_basic_set_alloc_inequality(combined);
1658 if (k < 0)
1659 goto error;
1660 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1661 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1662 is_empty = isl_basic_set_is_empty(combined);
1663 if (is_empty < 0)
1664 goto error;
1665 isl_basic_set_free(combined);
1666 combined = NULL;
1667 if (!is_empty)
1668 tab->con[i].is_redundant = 0;
1669 }
1670 for (i = 0; i < context_ineq; ++i)
1671 tab->con[i].is_redundant = 1;
1672 bset = isl_basic_set_update_from_tab(bset, tab);
1673 if (bset) {
1674 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1675 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1676 }
1677
1678 isl_tab_free(tab);
1679 done:
1680 bset = isl_basic_set_simplify(bset);
1681 bset = isl_basic_set_finalize(bset);
1682 isl_basic_set_free(context);
1683 return bset;
1684 error:
1685 isl_tab_free(tab);
1686 isl_basic_set_free(combined);
1687 isl_basic_set_free(context);
1688 isl_basic_set_free(bset);
1689 return NULL;
1690 }
1691
1692 /* Remove all information from bset that is redundant in the context
1693 * of context. In particular, equalities that are linear combinations
1694 * of those in context are removed. Then the inequalities that are
1695 * redundant in the context of the equalities and inequalities of
1696 * context are removed.
1697 *
1698 * We first compute the integer affine hull of the intersection,
1699 * compute the gist inside this affine hull and then add back
1700 * those equalities that are not implied by the context.
1701 */
1702 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1703 __isl_take isl_basic_set *context)
1704 {
1705 isl_mat *eq;
1706 isl_mat *T, *T2;
1707 isl_basic_set *aff;
1708 isl_basic_set *aff_context;
1709 unsigned total;
1710
1711 if (!bset || !context)
1712 goto error;
1713
1714 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1715 if (isl_basic_set_fast_is_empty(bset)) {
1716 isl_basic_set_free(context);
1717 return bset;
1718 }
1719 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1720 if (!aff)
1721 goto error;
1722 if (isl_basic_set_fast_is_empty(aff)) {
1723 isl_basic_set_free(aff);
1724 isl_basic_set_free(context);
1725 return bset;
1726 }
1727 if (aff->n_eq == 0) {
1728 isl_basic_set_free(aff);
1729 return uset_gist_full(bset, context);
1730 }
1731 total = isl_basic_set_total_dim(bset);
1732 eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1733 eq = isl_mat_cow(eq);
1734 T = isl_mat_variable_compression(eq, &T2);
1735 if (T && T->n_col == 0) {
1736 isl_mat_free(T);
1737 isl_mat_free(T2);
1738 isl_basic_set_free(context);
1739 isl_basic_set_free(aff);
1740 return isl_basic_set_set_to_empty(bset);
1741 }
1742
1743 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1744
1745 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1746 context = isl_basic_set_preimage(context, T);
1747
1748 bset = uset_gist_full(bset, context);
1749 bset = isl_basic_set_preimage(bset, T2);
1750 bset = isl_basic_set_intersect(bset, aff);
1751 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1752
1753 if (bset) {
1754 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1755 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1756 }
1757
1758 return bset;
1759 error:
1760 isl_basic_set_free(bset);
1761 isl_basic_set_free(context);
1762 return NULL;
1763 }
1764
1765 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1766 * We simply add the equalities in context to bmap and then do a regular
1767 * div normalizations. Better results can be obtained by normalizing
1768 * only the divs in bmap than do not also appear in context.
1769 * We need to be careful to reduce the divs using the equalities
1770 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1771 * spurious constraints.
1772 */
1773 static struct isl_basic_map *normalize_divs_in_context(
1774 struct isl_basic_map *bmap, struct isl_basic_map *context)
1775 {
1776 int i;
1777 unsigned total_context;
1778 int div_eq;
1779
1780 div_eq = n_pure_div_eq(bmap);
1781 if (div_eq == 0)
1782 return bmap;
1783
1784 if (context->n_div > 0)
1785 bmap = isl_basic_map_align_divs(bmap, context);
1786
1787 total_context = isl_basic_map_total_dim(context);
1788 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1789 for (i = 0; i < context->n_eq; ++i) {
1790 int k;
1791 k = isl_basic_map_alloc_equality(bmap);
1792 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1793 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1794 isl_basic_map_total_dim(bmap) - total_context);
1795 }
1796 bmap = isl_basic_map_gauss(bmap, NULL);
1797 bmap = normalize_divs(bmap, NULL);
1798 bmap = isl_basic_map_gauss(bmap, NULL);
1799 return bmap;
1800 }
1801
1802 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1803 struct isl_basic_map *context)
1804 {
1805 struct isl_basic_set *bset;
1806
1807 if (!bmap || !context)
1808 goto error;
1809
1810 if (isl_basic_map_is_universe(context)) {
1811 isl_basic_map_free(context);
1812 return bmap;
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_is_universe(context)) {
1860 isl_basic_map_free(context);
1861 return map;
1862 }
1863 if (isl_basic_map_fast_is_empty(context)) {
1864 struct isl_dim *dim = isl_dim_copy(map->dim);
1865 isl_basic_map_free(context);
1866 isl_map_free(map);
1867 return isl_map_universe(dim);
1868 }
1869
1870 context = isl_basic_map_remove_redundancies(context);
1871 map = isl_map_cow(map);
1872 if (!map || !context)
1873 goto error;;
1874 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1875 map = isl_map_compute_divs(map);
1876 for (i = 0; i < map->n; ++i)
1877 context = isl_basic_map_align_divs(context, map->p[i]);
1878 for (i = 0; i < map->n; ++i) {
1879 map->p[i] = isl_basic_map_gist(map->p[i],
1880 isl_basic_map_copy(context));
1881 if (!map->p[i])
1882 goto error;
1883 }
1884 isl_basic_map_free(context);
1885 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1886 return map;
1887 error:
1888 isl_map_free(map);
1889 isl_basic_map_free(context);
1890 return NULL;
1891 }
1892
1893 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1894 __isl_take isl_map *context)
1895 {
1896 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1897 }
1898
1899 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1900 struct isl_basic_set *context)
1901 {
1902 return (struct isl_basic_set *)isl_basic_map_gist(
1903 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1904 }
1905
1906 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1907 __isl_take isl_basic_set *context)
1908 {
1909 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1910 (struct isl_basic_map *)context);
1911 }
1912
1913 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1914 __isl_take isl_set *context)
1915 {
1916 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1917 (struct isl_map *)context);
1918 }
1919
1920 /* Quick check to see if two basic maps are disjoint.
1921 * In particular, we reduce the equalities and inequalities of
1922 * one basic map in the context of the equalities of the other
1923 * basic map and check if we get a contradiction.
1924 */
1925 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1926 struct isl_basic_map *bmap2)
1927 {
1928 struct isl_vec *v = NULL;
1929 int *elim = NULL;
1930 unsigned total;
1931 int i;
1932
1933 if (!bmap1 || !bmap2)
1934 return -1;
1935 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1936 return -1);
1937 if (bmap1->n_div || bmap2->n_div)
1938 return 0;
1939 if (!bmap1->n_eq && !bmap2->n_eq)
1940 return 0;
1941
1942 total = isl_dim_total(bmap1->dim);
1943 if (total == 0)
1944 return 0;
1945 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1946 if (!v)
1947 goto error;
1948 elim = isl_alloc_array(bmap1->ctx, int, total);
1949 if (!elim)
1950 goto error;
1951 compute_elimination_index(bmap1, elim);
1952 for (i = 0; i < bmap2->n_eq; ++i) {
1953 int reduced;
1954 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1955 bmap1, elim);
1956 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1957 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1958 goto disjoint;
1959 }
1960 for (i = 0; i < bmap2->n_ineq; ++i) {
1961 int reduced;
1962 reduced = reduced_using_equalities(v->block.data,
1963 bmap2->ineq[i], bmap1, elim);
1964 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1965 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1966 goto disjoint;
1967 }
1968 compute_elimination_index(bmap2, elim);
1969 for (i = 0; i < bmap1->n_ineq; ++i) {
1970 int reduced;
1971 reduced = reduced_using_equalities(v->block.data,
1972 bmap1->ineq[i], bmap2, elim);
1973 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1974 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1975 goto disjoint;
1976 }
1977 isl_vec_free(v);
1978 free(elim);
1979 return 0;
1980 disjoint:
1981 isl_vec_free(v);
1982 free(elim);
1983 return 1;
1984 error:
1985 isl_vec_free(v);
1986 free(elim);
1987 return -1;
1988 }
1989
1990 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1991 struct isl_basic_set *bset2)
1992 {
1993 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1994 (struct isl_basic_map *)bset2);
1995 }
1996
1997 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1998 {
1999 int i, j;
2000
2001 if (!map1 || !map2)
2002 return -1;
2003
2004 if (isl_map_fast_is_equal(map1, map2))
2005 return 0;
2006
2007 for (i = 0; i < map1->n; ++i) {
2008 for (j = 0; j < map2->n; ++j) {
2009 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
2010 map2->p[j]);
2011 if (d != 1)
2012 return d;
2013 }
2014 }
2015 return 1;
2016 }
2017
2018 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2019 {
2020 return isl_map_fast_is_disjoint((struct isl_map *)set1,
2021 (struct isl_map *)set2);
2022 }
2023
2024 /* Check if we can combine a given div with lower bound l and upper
2025 * bound u with some other div and if so return that other div.
2026 * Otherwise return -1.
2027 *
2028 * We first check that
2029 * - the bounds are opposites of each other (except for the constant
2030 * term)
2031 * - the bounds do not reference any other div
2032 * - no div is defined in terms of this div
2033 *
2034 * Let m be the size of the range allowed on the div by the bounds.
2035 * That is, the bounds are of the form
2036 *
2037 * e <= a <= e + m - 1
2038 *
2039 * with e some expression in the other variables.
2040 * We look for another div b such that no third div is defined in terms
2041 * of this second div b and such that in any constraint that contains
2042 * a (except for the given lower and upper bound), also contains b
2043 * with a coefficient that is m times that of b.
2044 * That is, all constraints (execpt for the lower and upper bound)
2045 * are of the form
2046 *
2047 * e + f (a + m b) >= 0
2048 *
2049 * If so, we return b so that "a + m b" can be replaced by
2050 * a single div "c = a + m b".
2051 */
2052 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2053 unsigned div, unsigned l, unsigned u)
2054 {
2055 int i, j;
2056 unsigned dim;
2057 int coalesce = -1;
2058
2059 if (bmap->n_div <= 1)
2060 return -1;
2061 dim = isl_dim_total(bmap->dim);
2062 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2063 return -1;
2064 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2065 bmap->n_div - div - 1) != -1)
2066 return -1;
2067 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2068 dim + bmap->n_div))
2069 return -1;
2070
2071 for (i = 0; i < bmap->n_div; ++i) {
2072 if (isl_int_is_zero(bmap->div[i][0]))
2073 continue;
2074 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2075 return -1;
2076 }
2077
2078 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2079 if (isl_int_is_neg(bmap->ineq[l][0])) {
2080 isl_int_sub(bmap->ineq[l][0],
2081 bmap->ineq[l][0], bmap->ineq[u][0]);
2082 bmap = isl_basic_map_copy(bmap);
2083 bmap = isl_basic_map_set_to_empty(bmap);
2084 isl_basic_map_free(bmap);
2085 return -1;
2086 }
2087 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2088 for (i = 0; i < bmap->n_div; ++i) {
2089 if (i == div)
2090 continue;
2091 if (!pairs[i])
2092 continue;
2093 for (j = 0; j < bmap->n_div; ++j) {
2094 if (isl_int_is_zero(bmap->div[j][0]))
2095 continue;
2096 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2097 break;
2098 }
2099 if (j < bmap->n_div)
2100 continue;
2101 for (j = 0; j < bmap->n_ineq; ++j) {
2102 int valid;
2103 if (j == l || j == u)
2104 continue;
2105 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2106 continue;
2107 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2108 break;
2109 isl_int_mul(bmap->ineq[j][1 + dim + div],
2110 bmap->ineq[j][1 + dim + div],
2111 bmap->ineq[l][0]);
2112 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2113 bmap->ineq[j][1 + dim + i]);
2114 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2115 bmap->ineq[j][1 + dim + div],
2116 bmap->ineq[l][0]);
2117 if (!valid)
2118 break;
2119 }
2120 if (j < bmap->n_ineq)
2121 continue;
2122 coalesce = i;
2123 break;
2124 }
2125 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2126 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2127 return coalesce;
2128 }
2129
2130 /* Given a lower and an upper bound on div i, construct an inequality
2131 * that when nonnegative ensures that this pair of bounds always allows
2132 * for an integer value of the given div.
2133 * The lower bound is inequality l, while the upper bound is inequality u.
2134 * The constructed inequality is stored in ineq.
2135 * g, fl, fu are temporary scalars.
2136 *
2137 * Let the upper bound be
2138 *
2139 * -n_u a + e_u >= 0
2140 *
2141 * and the lower bound
2142 *
2143 * n_l a + e_l >= 0
2144 *
2145 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2146 * We have
2147 *
2148 * - f_u e_l <= f_u f_l g a <= f_l e_u
2149 *
2150 * Since all variables are integer valued, this is equivalent to
2151 *
2152 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2153 *
2154 * If this interval is at least f_u f_l g, then it contains at least
2155 * one integer value for a.
2156 * That is, the test constraint is
2157 *
2158 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2159 */
2160 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2161 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2162 {
2163 unsigned dim;
2164 dim = isl_dim_total(bmap->dim);
2165
2166 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2167 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2168 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2169 isl_int_neg(fu, fu);
2170 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2171 1 + dim + bmap->n_div);
2172 isl_int_add(ineq[0], ineq[0], fl);
2173 isl_int_add(ineq[0], ineq[0], fu);
2174 isl_int_sub_ui(ineq[0], ineq[0], 1);
2175 isl_int_mul(g, g, fl);
2176 isl_int_mul(g, g, fu);
2177 isl_int_sub(ineq[0], ineq[0], g);
2178 }
2179
2180 /* Remove more kinds of divs that are not strictly needed.
2181 * In particular, if all pairs of lower and upper bounds on a div
2182 * are such that they allow at least one integer value of the div,
2183 * the we can eliminate the div using Fourier-Motzkin without
2184 * introducing any spurious solutions.
2185 */
2186 static struct isl_basic_map *drop_more_redundant_divs(
2187 struct isl_basic_map *bmap, int *pairs, int n)
2188 {
2189 struct isl_tab *tab = NULL;
2190 struct isl_vec *vec = NULL;
2191 unsigned dim;
2192 int remove = -1;
2193 isl_int g, fl, fu;
2194
2195 isl_int_init(g);
2196 isl_int_init(fl);
2197 isl_int_init(fu);
2198
2199 if (!bmap)
2200 goto error;
2201
2202 dim = isl_dim_total(bmap->dim);
2203 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2204 if (!vec)
2205 goto error;
2206
2207 tab = isl_tab_from_basic_map(bmap);
2208
2209 while (n > 0) {
2210 int i, l, u;
2211 int best = -1;
2212 enum isl_lp_result res;
2213
2214 for (i = 0; i < bmap->n_div; ++i) {
2215 if (!pairs[i])
2216 continue;
2217 if (best >= 0 && pairs[best] <= pairs[i])
2218 continue;
2219 best = i;
2220 }
2221
2222 i = best;
2223 for (l = 0; l < bmap->n_ineq; ++l) {
2224 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2225 continue;
2226 for (u = 0; u < bmap->n_ineq; ++u) {
2227 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2228 continue;
2229 construct_test_ineq(bmap, i, l, u,
2230 vec->el, g, fl, fu);
2231 res = isl_tab_min(tab, vec->el,
2232 bmap->ctx->one, &g, NULL, 0);
2233 if (res == isl_lp_error)
2234 goto error;
2235 if (res == isl_lp_empty) {
2236 bmap = isl_basic_map_set_to_empty(bmap);
2237 break;
2238 }
2239 if (res != isl_lp_ok || isl_int_is_neg(g))
2240 break;
2241 }
2242 if (u < bmap->n_ineq)
2243 break;
2244 }
2245 if (l == bmap->n_ineq) {
2246 remove = i;
2247 break;
2248 }
2249 pairs[i] = 0;
2250 --n;
2251 }
2252
2253 isl_tab_free(tab);
2254 isl_vec_free(vec);
2255
2256 isl_int_clear(g);
2257 isl_int_clear(fl);
2258 isl_int_clear(fu);
2259
2260 free(pairs);
2261
2262 if (remove < 0)
2263 return bmap;
2264
2265 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2266 return isl_basic_map_drop_redundant_divs(bmap);
2267 error:
2268 free(pairs);
2269 isl_basic_map_free(bmap);
2270 isl_tab_free(tab);
2271 isl_vec_free(vec);
2272 isl_int_clear(g);
2273 isl_int_clear(fl);
2274 isl_int_clear(fu);
2275 return NULL;
2276 }
2277
2278 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2279 * and the upper bound u, div1 always occurs together with div2 in the form
2280 * (div1 + m div2), where m is the constant range on the variable div1
2281 * allowed by l and u, replace the pair div1 and div2 by a single
2282 * div that is equal to div1 + m div2.
2283 *
2284 * The new div will appear in the location that contains div2.
2285 * We need to modify all constraints that contain
2286 * div2 = (div - div1) / m
2287 * (If a constraint does not contain div2, it will also not contain div1.)
2288 * If the constraint also contains div1, then we know they appear
2289 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2290 * i.e., the coefficient of div is f.
2291 *
2292 * Otherwise, we first need to introduce div1 into the constraint.
2293 * Let the l be
2294 *
2295 * div1 + f >=0
2296 *
2297 * and u
2298 *
2299 * -div1 + f' >= 0
2300 *
2301 * A lower bound on div2
2302 *
2303 * n div2 + t >= 0
2304 *
2305 * can be replaced by
2306 *
2307 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2308 *
2309 * with g = gcd(m,n).
2310 * An upper bound
2311 *
2312 * -n div2 + t >= 0
2313 *
2314 * can be replaced by
2315 *
2316 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2317 *
2318 * These constraint are those that we would obtain from eliminating
2319 * div1 using Fourier-Motzkin.
2320 *
2321 * After all constraints have been modified, we drop the lower and upper
2322 * bound and then drop div1.
2323 */
2324 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2325 unsigned div1, unsigned div2, unsigned l, unsigned u)
2326 {
2327 isl_int a;
2328 isl_int b;
2329 isl_int m;
2330 unsigned dim, total;
2331 int i;
2332
2333 dim = isl_dim_total(bmap->dim);
2334 total = 1 + dim + bmap->n_div;
2335
2336 isl_int_init(a);
2337 isl_int_init(b);
2338 isl_int_init(m);
2339 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2340 isl_int_add_ui(m, m, 1);
2341
2342 for (i = 0; i < bmap->n_ineq; ++i) {
2343 if (i == l || i == u)
2344 continue;
2345 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2346 continue;
2347 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2348 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2349 isl_int_divexact(a, m, b);
2350 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2351 if (isl_int_is_pos(b)) {
2352 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2353 b, bmap->ineq[l], total);
2354 } else {
2355 isl_int_neg(b, b);
2356 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2357 b, bmap->ineq[u], total);
2358 }
2359 }
2360 isl_int_set(bmap->ineq[i][1 + dim + div2],
2361 bmap->ineq[i][1 + dim + div1]);
2362 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2363 }
2364
2365 isl_int_clear(a);
2366 isl_int_clear(b);
2367 isl_int_clear(m);
2368 if (l > u) {
2369 isl_basic_map_drop_inequality(bmap, l);
2370 isl_basic_map_drop_inequality(bmap, u);
2371 } else {
2372 isl_basic_map_drop_inequality(bmap, u);
2373 isl_basic_map_drop_inequality(bmap, l);
2374 }
2375 bmap = isl_basic_map_drop_div(bmap, div1);
2376 return bmap;
2377 }
2378
2379 /* First check if we can coalesce any pair of divs and
2380 * then continue with dropping more redundant divs.
2381 *
2382 * We loop over all pairs of lower and upper bounds on a div
2383 * with coefficient 1 and -1, respectively, check if there
2384 * is any other div "c" with which we can coalesce the div
2385 * and if so, perform the coalescing.
2386 */
2387 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2388 struct isl_basic_map *bmap, int *pairs, int n)
2389 {
2390 int i, l, u;
2391 unsigned dim;
2392
2393 dim = isl_dim_total(bmap->dim);
2394
2395 for (i = 0; i < bmap->n_div; ++i) {
2396 if (!pairs[i])
2397 continue;
2398 for (l = 0; l < bmap->n_ineq; ++l) {
2399 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2400 continue;
2401 for (u = 0; u < bmap->n_ineq; ++u) {
2402 int c;
2403
2404 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2405 continue;
2406 c = div_find_coalesce(bmap, pairs, i, l, u);
2407 if (c < 0)
2408 continue;
2409 free(pairs);
2410 bmap = coalesce_divs(bmap, i, c, l, u);
2411 return isl_basic_map_drop_redundant_divs(bmap);
2412 }
2413 }
2414 }
2415
2416 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2417 return bmap;
2418
2419 return drop_more_redundant_divs(bmap, pairs, n);
2420 }
2421
2422 /* Remove divs that are not strictly needed.
2423 * In particular, if a div only occurs positively (or negatively)
2424 * in constraints, then it can simply be dropped.
2425 * Also, if a div occurs only occurs in two constraints and if moreover
2426 * those two constraints are opposite to each other, except for the constant
2427 * term and if the sum of the constant terms is such that for any value
2428 * of the other values, there is always at least one integer value of the
2429 * div, i.e., if one plus this sum is greater than or equal to
2430 * the (absolute value) of the coefficent of the div in the constraints,
2431 * then we can also simply drop the div.
2432 *
2433 * If any divs are left after these simple checks then we move on
2434 * to more complicated cases in drop_more_redundant_divs.
2435 */
2436 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2437 struct isl_basic_map *bmap)
2438 {
2439 int i, j;
2440 unsigned off;
2441 int *pairs = NULL;
2442 int n = 0;
2443
2444 if (!bmap)
2445 goto error;
2446
2447 off = isl_dim_total(bmap->dim);
2448 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2449 if (!pairs)
2450 goto error;
2451
2452 for (i = 0; i < bmap->n_div; ++i) {
2453 int pos, neg;
2454 int last_pos, last_neg;
2455 int redundant;
2456 int defined;
2457
2458 defined = !isl_int_is_zero(bmap->div[i][0]);
2459 for (j = 0; j < bmap->n_eq; ++j)
2460 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2461 break;
2462 if (j < bmap->n_eq)
2463 continue;
2464 ++n;
2465 pos = neg = 0;
2466 for (j = 0; j < bmap->n_ineq; ++j) {
2467 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2468 last_pos = j;
2469 ++pos;
2470 }
2471 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2472 last_neg = j;
2473 ++neg;
2474 }
2475 }
2476 pairs[i] = pos * neg;
2477 if (pairs[i] == 0) {
2478 for (j = bmap->n_ineq - 1; j >= 0; --j)
2479 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2480 isl_basic_map_drop_inequality(bmap, j);
2481 bmap = isl_basic_map_drop_div(bmap, i);
2482 free(pairs);
2483 return isl_basic_map_drop_redundant_divs(bmap);
2484 }
2485 if (pairs[i] != 1)
2486 continue;
2487 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2488 bmap->ineq[last_neg] + 1,
2489 off + bmap->n_div))
2490 continue;
2491
2492 isl_int_add(bmap->ineq[last_pos][0],
2493 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2494 isl_int_add_ui(bmap->ineq[last_pos][0],
2495 bmap->ineq[last_pos][0], 1);
2496 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2497 bmap->ineq[last_pos][1+off+i]);
2498 isl_int_sub_ui(bmap->ineq[last_pos][0],
2499 bmap->ineq[last_pos][0], 1);
2500 isl_int_sub(bmap->ineq[last_pos][0],
2501 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2502 if (!redundant) {
2503 if (defined ||
2504 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2505 pairs[i] = 0;
2506 --n;
2507 continue;
2508 }
2509 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2510 bmap = isl_basic_map_simplify(bmap);
2511 free(pairs);
2512 return isl_basic_map_drop_redundant_divs(bmap);
2513 }
2514 if (last_pos > last_neg) {
2515 isl_basic_map_drop_inequality(bmap, last_pos);
2516 isl_basic_map_drop_inequality(bmap, last_neg);
2517 } else {
2518 isl_basic_map_drop_inequality(bmap, last_neg);
2519 isl_basic_map_drop_inequality(bmap, last_pos);
2520 }
2521 bmap = isl_basic_map_drop_div(bmap, i);
2522 free(pairs);
2523 return isl_basic_map_drop_redundant_divs(bmap);
2524 }
2525
2526 if (n > 0)
2527 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2528
2529 free(pairs);
2530 return bmap;
2531 error:
2532 free(pairs);
2533 isl_basic_map_free(bmap);
2534 return NULL;
2535 }
2536
2537 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2538 struct isl_basic_set *bset)
2539 {
2540 return (struct isl_basic_set *)
2541 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2542 }
2543
2544 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2545 {
2546 int i;
2547
2548 if (!map)
2549 return NULL;
2550 for (i = 0; i < map->n; ++i) {
2551 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2552 if (!map->p[i])
2553 goto error;
2554 }
2555 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2556 return map;
2557 error:
2558 isl_map_free(map);
2559 return NULL;
2560 }
2561
2562 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2563 {
2564 return (struct isl_set *)
2565 isl_map_drop_redundant_divs((struct isl_map *)set);
2566 }
Integer set library