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add isl_union_pw_qpolynomial_to_polynomial
[isl.git] / isl_map_simplify.c
blob2d1179bac91a7b09902f064b8195ffe1c30e4fb5
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 #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)
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 bmap = check_for_div_constraints(bmap, k, l, sum,
1062 progress);
1063 continue;
1064 }
1065 if (isl_int_is_zero(sum)) {
1066 /* We need to break out of the loop after these
1067 * changes since the contents of the hash
1068 * will no longer be valid.
1069 * Plus, we probably we want to regauss first.
1070 */
1071 if (progress)
1072 *progress = 1;
1073 isl_basic_map_drop_inequality(bmap, l);
1074 isl_basic_map_inequality_to_equality(bmap, k);
1075 } else
1076 bmap = isl_basic_map_set_to_empty(bmap);
1077 break;
1078 }
1079 isl_int_clear(sum);
1080
1081 free(index);
1082 return bmap;
1083 }
1084
1085
1086 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1087 {
1088 int progress = 1;
1089 if (!bmap)
1090 return NULL;
1091 while (progress) {
1092 progress = 0;
1093 bmap = isl_basic_map_normalize_constraints(bmap);
1094 bmap = remove_duplicate_divs(bmap, &progress);
1095 bmap = eliminate_divs_eq(bmap, &progress);
1096 bmap = eliminate_divs_ineq(bmap, &progress);
1097 bmap = isl_basic_map_gauss(bmap, &progress);
1098 /* requires equalities in normal form */
1099 bmap = normalize_divs(bmap, &progress);
1100 bmap = remove_duplicate_constraints(bmap, &progress);
1101 }
1102 return bmap;
1103 }
1104
1105 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1106 {
1107 return (struct isl_basic_set *)
1108 isl_basic_map_simplify((struct isl_basic_map *)bset);
1109 }
1110
1111
1112 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1113 isl_int *constraint, unsigned div)
1114 {
1115 unsigned pos;
1116
1117 if (!bmap)
1118 return -1;
1119
1120 pos = 1 + isl_dim_total(bmap->dim) + div;
1121
1122 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1123 int neg;
1124 isl_int_sub(bmap->div[div][1],
1125 bmap->div[div][1], bmap->div[div][0]);
1126 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1127 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1128 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1129 isl_int_add(bmap->div[div][1],
1130 bmap->div[div][1], bmap->div[div][0]);
1131 if (!neg)
1132 return 0;
1133 if (isl_seq_first_non_zero(constraint+pos+1,
1134 bmap->n_div-div-1) != -1)
1135 return 0;
1136 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1137 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1138 return 0;
1139 if (isl_seq_first_non_zero(constraint+pos+1,
1140 bmap->n_div-div-1) != -1)
1141 return 0;
1142 } else
1143 return 0;
1144
1145 return 1;
1146 }
1147
1148
1149 /* If the only constraints a div d=floor(f/m)
1150 * appears in are its two defining constraints
1151 *
1152 * f - m d >=0
1153 * -(f - (m - 1)) + m d >= 0
1154 *
1155 * then it can safely be removed.
1156 */
1157 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1158 {
1159 int i;
1160 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1161
1162 for (i = 0; i < bmap->n_eq; ++i)
1163 if (!isl_int_is_zero(bmap->eq[i][pos]))
1164 return 0;
1165
1166 for (i = 0; i < bmap->n_ineq; ++i) {
1167 if (isl_int_is_zero(bmap->ineq[i][pos]))
1168 continue;
1169 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1170 return 0;
1171 }
1172
1173 for (i = 0; i < bmap->n_div; ++i)
1174 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1175 return 0;
1176
1177 return 1;
1178 }
1179
1180 /*
1181 * Remove divs that don't occur in any of the constraints or other divs.
1182 * These can arise when dropping some of the variables in a quast
1183 * returned by piplib.
1184 */
1185 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1186 {
1187 int i;
1188
1189 if (!bmap)
1190 return NULL;
1191
1192 for (i = bmap->n_div-1; i >= 0; --i) {
1193 if (!div_is_redundant(bmap, i))
1194 continue;
1195 bmap = isl_basic_map_drop_div(bmap, i);
1196 }
1197 return bmap;
1198 }
1199
1200 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1201 {
1202 bmap = remove_redundant_divs(bmap);
1203 if (!bmap)
1204 return NULL;
1205 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1206 return bmap;
1207 }
1208
1209 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1210 {
1211 return (struct isl_basic_set *)
1212 isl_basic_map_finalize((struct isl_basic_map *)bset);
1213 }
1214
1215 struct isl_set *isl_set_finalize(struct isl_set *set)
1216 {
1217 int i;
1218
1219 if (!set)
1220 return NULL;
1221 for (i = 0; i < set->n; ++i) {
1222 set->p[i] = isl_basic_set_finalize(set->p[i]);
1223 if (!set->p[i])
1224 goto error;
1225 }
1226 return set;
1227 error:
1228 isl_set_free(set);
1229 return NULL;
1230 }
1231
1232 struct isl_map *isl_map_finalize(struct isl_map *map)
1233 {
1234 int i;
1235
1236 if (!map)
1237 return NULL;
1238 for (i = 0; i < map->n; ++i) {
1239 map->p[i] = isl_basic_map_finalize(map->p[i]);
1240 if (!map->p[i])
1241 goto error;
1242 }
1243 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1244 return map;
1245 error:
1246 isl_map_free(map);
1247 return NULL;
1248 }
1249
1250
1251 /* Remove definition of any div that is defined in terms of the given variable.
1252 * The div itself is not removed. Functions such as
1253 * eliminate_divs_ineq depend on the other divs remaining in place.
1254 */
1255 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1256 int pos)
1257 {
1258 int i;
1259
1260 for (i = 0; i < bmap->n_div; ++i) {
1261 if (isl_int_is_zero(bmap->div[i][0]))
1262 continue;
1263 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1264 continue;
1265 isl_int_set_si(bmap->div[i][0], 0);
1266 }
1267 return bmap;
1268 }
1269
1270 /* Eliminate the specified variables from the constraints using
1271 * Fourier-Motzkin. The variables themselves are not removed.
1272 */
1273 struct isl_basic_map *isl_basic_map_eliminate_vars(
1274 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1275 {
1276 int d;
1277 int i, j, k;
1278 unsigned total;
1279
1280 if (n == 0)
1281 return bmap;
1282 if (!bmap)
1283 return NULL;
1284 total = isl_basic_map_total_dim(bmap);
1285
1286 bmap = isl_basic_map_cow(bmap);
1287 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1288 bmap = remove_dependent_vars(bmap, d);
1289
1290 for (d = pos + n - 1;
1291 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1292 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1293 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1294 int n_lower, n_upper;
1295 if (!bmap)
1296 return NULL;
1297 for (i = 0; i < bmap->n_eq; ++i) {
1298 if (isl_int_is_zero(bmap->eq[i][1+d]))
1299 continue;
1300 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1301 isl_basic_map_drop_equality(bmap, i);
1302 break;
1303 }
1304 if (i < bmap->n_eq)
1305 continue;
1306 n_lower = 0;
1307 n_upper = 0;
1308 for (i = 0; i < bmap->n_ineq; ++i) {
1309 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1310 n_lower++;
1311 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1312 n_upper++;
1313 }
1314 bmap = isl_basic_map_extend_constraints(bmap,
1315 0, n_lower * n_upper);
1316 if (!bmap)
1317 goto error;
1318 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1319 int last;
1320 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1321 continue;
1322 last = -1;
1323 for (j = 0; j < i; ++j) {
1324 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1325 continue;
1326 last = j;
1327 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1328 isl_int_sgn(bmap->ineq[j][1+d]))
1329 continue;
1330 k = isl_basic_map_alloc_inequality(bmap);
1331 if (k < 0)
1332 goto error;
1333 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1334 1+total);
1335 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1336 1+d, 1+total, NULL);
1337 }
1338 isl_basic_map_drop_inequality(bmap, i);
1339 i = last + 1;
1340 }
1341 if (n_lower > 0 && n_upper > 0) {
1342 bmap = isl_basic_map_normalize_constraints(bmap);
1343 bmap = remove_duplicate_constraints(bmap, NULL);
1344 bmap = isl_basic_map_gauss(bmap, NULL);
1345 bmap = isl_basic_map_remove_redundancies(bmap);
1346 if (!bmap)
1347 goto error;
1348 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1349 break;
1350 }
1351 }
1352 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1353 return bmap;
1354 error:
1355 isl_basic_map_free(bmap);
1356 return NULL;
1357 }
1358
1359 struct isl_basic_set *isl_basic_set_eliminate_vars(
1360 struct isl_basic_set *bset, unsigned pos, unsigned n)
1361 {
1362 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1363 (struct isl_basic_map *)bset, pos, n);
1364 }
1365
1366 /* Don't assume equalities are in order, because align_divs
1367 * may have changed the order of the divs.
1368 */
1369 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1370 {
1371 int d, i;
1372 unsigned total;
1373
1374 total = isl_dim_total(bmap->dim);
1375 for (d = 0; d < total; ++d)
1376 elim[d] = -1;
1377 for (i = 0; i < bmap->n_eq; ++i) {
1378 for (d = total - 1; d >= 0; --d) {
1379 if (isl_int_is_zero(bmap->eq[i][1+d]))
1380 continue;
1381 elim[d] = i;
1382 break;
1383 }
1384 }
1385 }
1386
1387 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1388 {
1389 compute_elimination_index((struct isl_basic_map *)bset, elim);
1390 }
1391
1392 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1393 struct isl_basic_map *bmap, int *elim)
1394 {
1395 int d;
1396 int copied = 0;
1397 unsigned total;
1398
1399 total = isl_dim_total(bmap->dim);
1400 for (d = total - 1; d >= 0; --d) {
1401 if (isl_int_is_zero(src[1+d]))
1402 continue;
1403 if (elim[d] == -1)
1404 continue;
1405 if (!copied) {
1406 isl_seq_cpy(dst, src, 1 + total);
1407 copied = 1;
1408 }
1409 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1410 }
1411 return copied;
1412 }
1413
1414 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1415 struct isl_basic_set *bset, int *elim)
1416 {
1417 return reduced_using_equalities(dst, src,
1418 (struct isl_basic_map *)bset, elim);
1419 }
1420
1421 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1422 struct isl_basic_set *bset, struct isl_basic_set *context)
1423 {
1424 int i;
1425 int *elim;
1426
1427 if (!bset || !context)
1428 goto error;
1429
1430 if (context->n_eq == 0) {
1431 isl_basic_set_free(context);
1432 return bset;
1433 }
1434
1435 bset = isl_basic_set_cow(bset);
1436 if (!bset)
1437 goto error;
1438
1439 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1440 if (!elim)
1441 goto error;
1442 set_compute_elimination_index(context, elim);
1443 for (i = 0; i < bset->n_eq; ++i)
1444 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1445 context, elim);
1446 for (i = 0; i < bset->n_ineq; ++i)
1447 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1448 context, elim);
1449 isl_basic_set_free(context);
1450 free(elim);
1451 bset = isl_basic_set_simplify(bset);
1452 bset = isl_basic_set_finalize(bset);
1453 return bset;
1454 error:
1455 isl_basic_set_free(bset);
1456 isl_basic_set_free(context);
1457 return NULL;
1458 }
1459
1460 static struct isl_basic_set *remove_shifted_constraints(
1461 struct isl_basic_set *bset, struct isl_basic_set *context)
1462 {
1463 unsigned int size;
1464 isl_int ***index;
1465 int bits;
1466 int k, h, l;
1467
1468 if (!bset)
1469 return NULL;
1470
1471 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1472 bits = ffs(size) - 1;
1473 index = isl_calloc_array(ctx, isl_int **, size);
1474 if (!index)
1475 return bset;
1476
1477 for (k = 0; k < context->n_ineq; ++k) {
1478 h = set_hash_index(index, size, bits, context, k);
1479 index[h] = &context->ineq[k];
1480 }
1481 for (k = 0; k < bset->n_ineq; ++k) {
1482 h = set_hash_index(index, size, bits, bset, k);
1483 if (!index[h])
1484 continue;
1485 l = index[h] - &context->ineq[0];
1486 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1487 continue;
1488 bset = isl_basic_set_cow(bset);
1489 if (!bset)
1490 goto error;
1491 isl_basic_set_drop_inequality(bset, k);
1492 --k;
1493 }
1494 free(index);
1495 return bset;
1496 error:
1497 free(index);
1498 return bset;
1499 }
1500
1501 /* Tighten (decrease) the constant terms of the inequalities based
1502 * on the equalities, without removing any integer points.
1503 * For example, if there is an equality
1504 *
1505 * i = 3 * j
1506 *
1507 * and an inequality
1508 *
1509 * i >= 1
1510 *
1511 * then we want to replace the inequality by
1512 *
1513 * i >= 3
1514 *
1515 * We do this by computing a variable compression and translating
1516 * the constraints to the compressed space.
1517 * If any constraint has coefficients (except the contant term)
1518 * with a common factor "f", then we can replace the constant term "c"
1519 * by
1520 *
1521 * f * floor(c/f)
1522 *
1523 * That is, we add
1524 *
1525 * f * floor(c/f) - c = -fract(c/f)
1526 *
1527 * and we can add the same value to the original constraint.
1528 *
1529 * In the example, the compressed space only contains "j",
1530 * and the inequality translates to
1531 *
1532 * 3 * j - 1 >= 0
1533 *
1534 * We add -fract(-1/3) = -2 to the original constraint to obtain
1535 *
1536 * i - 3 >= 0
1537 */
1538 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1539 struct isl_basic_set *bset)
1540 {
1541 int i;
1542 unsigned total;
1543 struct isl_mat *B, *C;
1544 isl_int gcd;
1545
1546 if (!bset)
1547 return NULL;
1548
1549 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1550 return bset;
1551
1552 if (!bset->n_ineq)
1553 return bset;
1554
1555 bset = isl_basic_set_cow(bset);
1556 if (!bset)
1557 return NULL;
1558
1559 total = isl_basic_set_total_dim(bset);
1560 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1561 C = isl_mat_variable_compression(B, NULL);
1562 if (!C)
1563 return bset;
1564 if (C->n_col == 0) {
1565 isl_mat_free(C);
1566 return isl_basic_set_set_to_empty(bset);
1567 }
1568 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1569 0, bset->n_ineq, 0, 1 + total);
1570 C = isl_mat_product(B, C);
1571 if (!C)
1572 return bset;
1573
1574 isl_int_init(gcd);
1575 for (i = 0; i < bset->n_ineq; ++i) {
1576 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1577 if (isl_int_is_one(gcd))
1578 continue;
1579 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1580 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1581 }
1582 isl_int_clear(gcd);
1583
1584 isl_mat_free(C);
1585
1586 return bset;
1587 }
1588
1589 /* Remove all information from bset that is redundant in the context
1590 * of context. Both bset and context are assumed to be full-dimensional.
1591 *
1592 * We first * remove the inequalities from "bset"
1593 * that are obviously redundant with respect to some inequality in "context".
1594 *
1595 * If there are any inequalities left, we construct a tableau for
1596 * the context and then add the inequalities of "bset".
1597 * Before adding these inequalities, we freeze all constraints such that
1598 * they won't be considered redundant in terms of the constraints of "bset".
1599 * Then we detect all redundant constraints (among the
1600 * constraints that weren't frozen), first by checking for redundancy in the
1601 * the tableau and then by checking if replacing a constraint by its negation
1602 * would lead to an empty set. This last step is fairly expensive
1603 * and could be optimized by more reuse of the tableau.
1604 * Finally, we update bset according to the results.
1605 */
1606 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1607 __isl_take isl_basic_set *context)
1608 {
1609 int i, k;
1610 isl_basic_set *combined = NULL;
1611 struct isl_tab *tab = NULL;
1612 unsigned context_ineq;
1613 unsigned total;
1614
1615 if (!bset || !context)
1616 goto error;
1617
1618 if (isl_basic_set_is_universe(bset)) {
1619 isl_basic_set_free(context);
1620 return bset;
1621 }
1622
1623 if (isl_basic_set_is_universe(context)) {
1624 isl_basic_set_free(context);
1625 return bset;
1626 }
1627
1628 bset = remove_shifted_constraints(bset, context);
1629 if (!bset)
1630 goto error;
1631 if (bset->n_ineq == 0)
1632 goto done;
1633
1634 context_ineq = context->n_ineq;
1635 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1636 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1637 tab = isl_tab_from_basic_set(combined);
1638 for (i = 0; i < context_ineq; ++i)
1639 if (isl_tab_freeze_constraint(tab, i) < 0)
1640 goto error;
1641 tab = isl_tab_extend(tab, bset->n_ineq);
1642 for (i = 0; i < bset->n_ineq; ++i)
1643 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1644 goto error;
1645 bset = isl_basic_set_add_constraints(combined, bset, 0);
1646 combined = NULL;
1647 if (!bset)
1648 goto error;
1649 if (isl_tab_detect_redundant(tab) < 0)
1650 goto error;
1651 total = isl_basic_set_total_dim(bset);
1652 for (i = context_ineq; i < bset->n_ineq; ++i) {
1653 int is_empty;
1654 if (tab->con[i].is_redundant)
1655 continue;
1656 tab->con[i].is_redundant = 1;
1657 combined = isl_basic_set_dup(bset);
1658 combined = isl_basic_set_update_from_tab(combined, tab);
1659 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1660 k = isl_basic_set_alloc_inequality(combined);
1661 if (k < 0)
1662 goto error;
1663 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1664 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1665 is_empty = isl_basic_set_is_empty(combined);
1666 if (is_empty < 0)
1667 goto error;
1668 isl_basic_set_free(combined);
1669 combined = NULL;
1670 if (!is_empty)
1671 tab->con[i].is_redundant = 0;
1672 }
1673 for (i = 0; i < context_ineq; ++i)
1674 tab->con[i].is_redundant = 1;
1675 bset = isl_basic_set_update_from_tab(bset, tab);
1676 if (bset) {
1677 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1678 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1679 }
1680
1681 isl_tab_free(tab);
1682 done:
1683 bset = isl_basic_set_simplify(bset);
1684 bset = isl_basic_set_finalize(bset);
1685 isl_basic_set_free(context);
1686 return bset;
1687 error:
1688 isl_tab_free(tab);
1689 isl_basic_set_free(combined);
1690 isl_basic_set_free(context);
1691 isl_basic_set_free(bset);
1692 return NULL;
1693 }
1694
1695 /* Remove all information from bset that is redundant in the context
1696 * of context. In particular, equalities that are linear combinations
1697 * of those in context are removed. Then the inequalities that are
1698 * redundant in the context of the equalities and inequalities of
1699 * context are removed.
1700 *
1701 * We first compute the integer affine hull of the intersection,
1702 * compute the gist inside this affine hull and then add back
1703 * those equalities that are not implied by the context.
1704 */
1705 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1706 __isl_take isl_basic_set *context)
1707 {
1708 isl_mat *eq;
1709 isl_mat *T, *T2;
1710 isl_basic_set *aff;
1711 isl_basic_set *aff_context;
1712 unsigned total;
1713
1714 if (!bset || !context)
1715 goto error;
1716
1717 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1718 if (isl_basic_set_fast_is_empty(bset)) {
1719 isl_basic_set_free(context);
1720 return bset;
1721 }
1722 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1723 if (!aff)
1724 goto error;
1725 if (isl_basic_set_fast_is_empty(aff)) {
1726 isl_basic_set_free(aff);
1727 isl_basic_set_free(context);
1728 return bset;
1729 }
1730 if (aff->n_eq == 0) {
1731 isl_basic_set_free(aff);
1732 return uset_gist_full(bset, context);
1733 }
1734 total = isl_basic_set_total_dim(bset);
1735 eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1736 eq = isl_mat_cow(eq);
1737 T = isl_mat_variable_compression(eq, &T2);
1738 if (T && T->n_col == 0) {
1739 isl_mat_free(T);
1740 isl_mat_free(T2);
1741 isl_basic_set_free(context);
1742 isl_basic_set_free(aff);
1743 return isl_basic_set_set_to_empty(bset);
1744 }
1745
1746 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1747
1748 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1749 context = isl_basic_set_preimage(context, T);
1750
1751 bset = uset_gist_full(bset, context);
1752 bset = isl_basic_set_preimage(bset, T2);
1753 bset = isl_basic_set_intersect(bset, aff);
1754 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1755
1756 if (bset) {
1757 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1758 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1759 }
1760
1761 return bset;
1762 error:
1763 isl_basic_set_free(bset);
1764 isl_basic_set_free(context);
1765 return NULL;
1766 }
1767
1768 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1769 * We simply add the equalities in context to bmap and then do a regular
1770 * div normalizations. Better results can be obtained by normalizing
1771 * only the divs in bmap than do not also appear in context.
1772 * We need to be careful to reduce the divs using the equalities
1773 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1774 * spurious constraints.
1775 */
1776 static struct isl_basic_map *normalize_divs_in_context(
1777 struct isl_basic_map *bmap, struct isl_basic_map *context)
1778 {
1779 int i;
1780 unsigned total_context;
1781 int div_eq;
1782
1783 div_eq = n_pure_div_eq(bmap);
1784 if (div_eq == 0)
1785 return bmap;
1786
1787 if (context->n_div > 0)
1788 bmap = isl_basic_map_align_divs(bmap, context);
1789
1790 total_context = isl_basic_map_total_dim(context);
1791 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1792 for (i = 0; i < context->n_eq; ++i) {
1793 int k;
1794 k = isl_basic_map_alloc_equality(bmap);
1795 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1796 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1797 isl_basic_map_total_dim(bmap) - total_context);
1798 }
1799 bmap = isl_basic_map_gauss(bmap, NULL);
1800 bmap = normalize_divs(bmap, NULL);
1801 bmap = isl_basic_map_gauss(bmap, NULL);
1802 return bmap;
1803 }
1804
1805 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1806 struct isl_basic_map *context)
1807 {
1808 struct isl_basic_set *bset;
1809
1810 if (!bmap || !context)
1811 goto error;
1812
1813 if (isl_basic_map_is_universe(bmap)) {
1814 isl_basic_map_free(context);
1815 return bmap;
1816 }
1817 if (isl_basic_map_fast_is_empty(context)) {
1818 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1819 isl_basic_map_free(context);
1820 isl_basic_map_free(bmap);
1821 return isl_basic_map_universe(dim);
1822 }
1823 if (isl_basic_map_fast_is_empty(bmap)) {
1824 isl_basic_map_free(context);
1825 return bmap;
1826 }
1827
1828 bmap = isl_basic_map_remove_redundancies(bmap);
1829 context = isl_basic_map_remove_redundancies(context);
1830
1831 if (context->n_eq)
1832 bmap = normalize_divs_in_context(bmap, context);
1833
1834 context = isl_basic_map_align_divs(context, bmap);
1835 bmap = isl_basic_map_align_divs(bmap, context);
1836
1837 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1838 isl_basic_map_underlying_set(context));
1839
1840 return isl_basic_map_overlying_set(bset, bmap);
1841 error:
1842 isl_basic_map_free(bmap);
1843 isl_basic_map_free(context);
1844 return NULL;
1845 }
1846
1847 /*
1848 * Assumes context has no implicit divs.
1849 */
1850 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1851 __isl_take isl_basic_map *context)
1852 {
1853 int i;
1854
1855 if (!map || !context)
1856 goto error;;
1857
1858 if (isl_basic_map_fast_is_empty(context)) {
1859 struct isl_dim *dim = isl_dim_copy(map->dim);
1860 isl_basic_map_free(context);
1861 isl_map_free(map);
1862 return isl_map_universe(dim);
1863 }
1864
1865 context = isl_basic_map_remove_redundancies(context);
1866 map = isl_map_cow(map);
1867 if (!map || !context)
1868 goto error;;
1869 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1870 map = isl_map_compute_divs(map);
1871 for (i = 0; i < map->n; ++i)
1872 context = isl_basic_map_align_divs(context, map->p[i]);
1873 for (i = map->n - 1; i >= 0; --i) {
1874 map->p[i] = isl_basic_map_gist(map->p[i],
1875 isl_basic_map_copy(context));
1876 if (!map->p[i])
1877 goto error;
1878 if (isl_basic_map_fast_is_empty(map->p[i])) {
1879 isl_basic_map_free(map->p[i]);
1880 if (i != map->n - 1)
1881 map->p[i] = map->p[map->n - 1];
1882 map->n--;
1883 }
1884 }
1885 isl_basic_map_free(context);
1886 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1887 return map;
1888 error:
1889 isl_map_free(map);
1890 isl_basic_map_free(context);
1891 return NULL;
1892 }
1893
1894 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1895 __isl_take isl_map *context)
1896 {
1897 context = isl_map_compute_divs(context);
1898 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1899 }
1900
1901 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1902 struct isl_basic_set *context)
1903 {
1904 return (struct isl_basic_set *)isl_basic_map_gist(
1905 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1906 }
1907
1908 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1909 __isl_take isl_basic_set *context)
1910 {
1911 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1912 (struct isl_basic_map *)context);
1913 }
1914
1915 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1916 __isl_take isl_set *context)
1917 {
1918 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1919 (struct isl_map *)context);
1920 }
1921
1922 /* Quick check to see if two basic maps are disjoint.
1923 * In particular, we reduce the equalities and inequalities of
1924 * one basic map in the context of the equalities of the other
1925 * basic map and check if we get a contradiction.
1926 */
1927 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1928 struct isl_basic_map *bmap2)
1929 {
1930 struct isl_vec *v = NULL;
1931 int *elim = NULL;
1932 unsigned total;
1933 int i;
1934
1935 if (!bmap1 || !bmap2)
1936 return -1;
1937 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1938 return -1);
1939 if (bmap1->n_div || bmap2->n_div)
1940 return 0;
1941 if (!bmap1->n_eq && !bmap2->n_eq)
1942 return 0;
1943
1944 total = isl_dim_total(bmap1->dim);
1945 if (total == 0)
1946 return 0;
1947 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1948 if (!v)
1949 goto error;
1950 elim = isl_alloc_array(bmap1->ctx, int, total);
1951 if (!elim)
1952 goto error;
1953 compute_elimination_index(bmap1, elim);
1954 for (i = 0; i < bmap2->n_eq; ++i) {
1955 int reduced;
1956 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1957 bmap1, elim);
1958 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1959 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1960 goto disjoint;
1961 }
1962 for (i = 0; i < bmap2->n_ineq; ++i) {
1963 int reduced;
1964 reduced = reduced_using_equalities(v->block.data,
1965 bmap2->ineq[i], bmap1, elim);
1966 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1967 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1968 goto disjoint;
1969 }
1970 compute_elimination_index(bmap2, elim);
1971 for (i = 0; i < bmap1->n_ineq; ++i) {
1972 int reduced;
1973 reduced = reduced_using_equalities(v->block.data,
1974 bmap1->ineq[i], bmap2, elim);
1975 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1976 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1977 goto disjoint;
1978 }
1979 isl_vec_free(v);
1980 free(elim);
1981 return 0;
1982 disjoint:
1983 isl_vec_free(v);
1984 free(elim);
1985 return 1;
1986 error:
1987 isl_vec_free(v);
1988 free(elim);
1989 return -1;
1990 }
1991
1992 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1993 struct isl_basic_set *bset2)
1994 {
1995 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1996 (struct isl_basic_map *)bset2);
1997 }
1998
1999 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
2000 {
2001 int i, j;
2002
2003 if (!map1 || !map2)
2004 return -1;
2005
2006 if (isl_map_fast_is_equal(map1, map2))
2007 return 0;
2008
2009 for (i = 0; i < map1->n; ++i) {
2010 for (j = 0; j < map2->n; ++j) {
2011 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
2012 map2->p[j]);
2013 if (d != 1)
2014 return d;
2015 }
2016 }
2017 return 1;
2018 }
2019
2020 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2021 {
2022 return isl_map_fast_is_disjoint((struct isl_map *)set1,
2023 (struct isl_map *)set2);
2024 }
2025
2026 /* Check if we can combine a given div with lower bound l and upper
2027 * bound u with some other div and if so return that other div.
2028 * Otherwise return -1.
2029 *
2030 * We first check that
2031 * - the bounds are opposites of each other (except for the constant
2032 * term)
2033 * - the bounds do not reference any other div
2034 * - no div is defined in terms of this div
2035 *
2036 * Let m be the size of the range allowed on the div by the bounds.
2037 * That is, the bounds are of the form
2038 *
2039 * e <= a <= e + m - 1
2040 *
2041 * with e some expression in the other variables.
2042 * We look for another div b such that no third div is defined in terms
2043 * of this second div b and such that in any constraint that contains
2044 * a (except for the given lower and upper bound), also contains b
2045 * with a coefficient that is m times that of b.
2046 * That is, all constraints (execpt for the lower and upper bound)
2047 * are of the form
2048 *
2049 * e + f (a + m b) >= 0
2050 *
2051 * If so, we return b so that "a + m b" can be replaced by
2052 * a single div "c = a + m b".
2053 */
2054 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2055 unsigned div, unsigned l, unsigned u)
2056 {
2057 int i, j;
2058 unsigned dim;
2059 int coalesce = -1;
2060
2061 if (bmap->n_div <= 1)
2062 return -1;
2063 dim = isl_dim_total(bmap->dim);
2064 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2065 return -1;
2066 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2067 bmap->n_div - div - 1) != -1)
2068 return -1;
2069 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2070 dim + bmap->n_div))
2071 return -1;
2072
2073 for (i = 0; i < bmap->n_div; ++i) {
2074 if (isl_int_is_zero(bmap->div[i][0]))
2075 continue;
2076 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2077 return -1;
2078 }
2079
2080 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2081 if (isl_int_is_neg(bmap->ineq[l][0])) {
2082 isl_int_sub(bmap->ineq[l][0],
2083 bmap->ineq[l][0], bmap->ineq[u][0]);
2084 bmap = isl_basic_map_copy(bmap);
2085 bmap = isl_basic_map_set_to_empty(bmap);
2086 isl_basic_map_free(bmap);
2087 return -1;
2088 }
2089 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2090 for (i = 0; i < bmap->n_div; ++i) {
2091 if (i == div)
2092 continue;
2093 if (!pairs[i])
2094 continue;
2095 for (j = 0; j < bmap->n_div; ++j) {
2096 if (isl_int_is_zero(bmap->div[j][0]))
2097 continue;
2098 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2099 break;
2100 }
2101 if (j < bmap->n_div)
2102 continue;
2103 for (j = 0; j < bmap->n_ineq; ++j) {
2104 int valid;
2105 if (j == l || j == u)
2106 continue;
2107 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2108 continue;
2109 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2110 break;
2111 isl_int_mul(bmap->ineq[j][1 + dim + div],
2112 bmap->ineq[j][1 + dim + div],
2113 bmap->ineq[l][0]);
2114 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2115 bmap->ineq[j][1 + dim + i]);
2116 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2117 bmap->ineq[j][1 + dim + div],
2118 bmap->ineq[l][0]);
2119 if (!valid)
2120 break;
2121 }
2122 if (j < bmap->n_ineq)
2123 continue;
2124 coalesce = i;
2125 break;
2126 }
2127 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2128 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2129 return coalesce;
2130 }
2131
2132 /* Given a lower and an upper bound on div i, construct an inequality
2133 * that when nonnegative ensures that this pair of bounds always allows
2134 * for an integer value of the given div.
2135 * The lower bound is inequality l, while the upper bound is inequality u.
2136 * The constructed inequality is stored in ineq.
2137 * g, fl, fu are temporary scalars.
2138 *
2139 * Let the upper bound be
2140 *
2141 * -n_u a + e_u >= 0
2142 *
2143 * and the lower bound
2144 *
2145 * n_l a + e_l >= 0
2146 *
2147 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2148 * We have
2149 *
2150 * - f_u e_l <= f_u f_l g a <= f_l e_u
2151 *
2152 * Since all variables are integer valued, this is equivalent to
2153 *
2154 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2155 *
2156 * If this interval is at least f_u f_l g, then it contains at least
2157 * one integer value for a.
2158 * That is, the test constraint is
2159 *
2160 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2161 */
2162 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2163 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2164 {
2165 unsigned dim;
2166 dim = isl_dim_total(bmap->dim);
2167
2168 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2169 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2170 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2171 isl_int_neg(fu, fu);
2172 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2173 1 + dim + bmap->n_div);
2174 isl_int_add(ineq[0], ineq[0], fl);
2175 isl_int_add(ineq[0], ineq[0], fu);
2176 isl_int_sub_ui(ineq[0], ineq[0], 1);
2177 isl_int_mul(g, g, fl);
2178 isl_int_mul(g, g, fu);
2179 isl_int_sub(ineq[0], ineq[0], g);
2180 }
2181
2182 /* Remove more kinds of divs that are not strictly needed.
2183 * In particular, if all pairs of lower and upper bounds on a div
2184 * are such that they allow at least one integer value of the div,
2185 * the we can eliminate the div using Fourier-Motzkin without
2186 * introducing any spurious solutions.
2187 */
2188 static struct isl_basic_map *drop_more_redundant_divs(
2189 struct isl_basic_map *bmap, int *pairs, int n)
2190 {
2191 struct isl_tab *tab = NULL;
2192 struct isl_vec *vec = NULL;
2193 unsigned dim;
2194 int remove = -1;
2195 isl_int g, fl, fu;
2196
2197 isl_int_init(g);
2198 isl_int_init(fl);
2199 isl_int_init(fu);
2200
2201 if (!bmap)
2202 goto error;
2203
2204 dim = isl_dim_total(bmap->dim);
2205 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2206 if (!vec)
2207 goto error;
2208
2209 tab = isl_tab_from_basic_map(bmap);
2210
2211 while (n > 0) {
2212 int i, l, u;
2213 int best = -1;
2214 enum isl_lp_result res;
2215
2216 for (i = 0; i < bmap->n_div; ++i) {
2217 if (!pairs[i])
2218 continue;
2219 if (best >= 0 && pairs[best] <= pairs[i])
2220 continue;
2221 best = i;
2222 }
2223
2224 i = best;
2225 for (l = 0; l < bmap->n_ineq; ++l) {
2226 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2227 continue;
2228 for (u = 0; u < bmap->n_ineq; ++u) {
2229 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2230 continue;
2231 construct_test_ineq(bmap, i, l, u,
2232 vec->el, g, fl, fu);
2233 res = isl_tab_min(tab, vec->el,
2234 bmap->ctx->one, &g, NULL, 0);
2235 if (res == isl_lp_error)
2236 goto error;
2237 if (res == isl_lp_empty) {
2238 bmap = isl_basic_map_set_to_empty(bmap);
2239 break;
2240 }
2241 if (res != isl_lp_ok || isl_int_is_neg(g))
2242 break;
2243 }
2244 if (u < bmap->n_ineq)
2245 break;
2246 }
2247 if (l == bmap->n_ineq) {
2248 remove = i;
2249 break;
2250 }
2251 pairs[i] = 0;
2252 --n;
2253 }
2254
2255 isl_tab_free(tab);
2256 isl_vec_free(vec);
2257
2258 isl_int_clear(g);
2259 isl_int_clear(fl);
2260 isl_int_clear(fu);
2261
2262 free(pairs);
2263
2264 if (remove < 0)
2265 return bmap;
2266
2267 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2268 return isl_basic_map_drop_redundant_divs(bmap);
2269 error:
2270 free(pairs);
2271 isl_basic_map_free(bmap);
2272 isl_tab_free(tab);
2273 isl_vec_free(vec);
2274 isl_int_clear(g);
2275 isl_int_clear(fl);
2276 isl_int_clear(fu);
2277 return NULL;
2278 }
2279
2280 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2281 * and the upper bound u, div1 always occurs together with div2 in the form
2282 * (div1 + m div2), where m is the constant range on the variable div1
2283 * allowed by l and u, replace the pair div1 and div2 by a single
2284 * div that is equal to div1 + m div2.
2285 *
2286 * The new div will appear in the location that contains div2.
2287 * We need to modify all constraints that contain
2288 * div2 = (div - div1) / m
2289 * (If a constraint does not contain div2, it will also not contain div1.)
2290 * If the constraint also contains div1, then we know they appear
2291 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2292 * i.e., the coefficient of div is f.
2293 *
2294 * Otherwise, we first need to introduce div1 into the constraint.
2295 * Let the l be
2296 *
2297 * div1 + f >=0
2298 *
2299 * and u
2300 *
2301 * -div1 + f' >= 0
2302 *
2303 * A lower bound on div2
2304 *
2305 * n div2 + t >= 0
2306 *
2307 * can be replaced by
2308 *
2309 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2310 *
2311 * with g = gcd(m,n).
2312 * An upper bound
2313 *
2314 * -n div2 + t >= 0
2315 *
2316 * can be replaced by
2317 *
2318 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2319 *
2320 * These constraint are those that we would obtain from eliminating
2321 * div1 using Fourier-Motzkin.
2322 *
2323 * After all constraints have been modified, we drop the lower and upper
2324 * bound and then drop div1.
2325 */
2326 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2327 unsigned div1, unsigned div2, unsigned l, unsigned u)
2328 {
2329 isl_int a;
2330 isl_int b;
2331 isl_int m;
2332 unsigned dim, total;
2333 int i;
2334
2335 dim = isl_dim_total(bmap->dim);
2336 total = 1 + dim + bmap->n_div;
2337
2338 isl_int_init(a);
2339 isl_int_init(b);
2340 isl_int_init(m);
2341 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2342 isl_int_add_ui(m, m, 1);
2343
2344 for (i = 0; i < bmap->n_ineq; ++i) {
2345 if (i == l || i == u)
2346 continue;
2347 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2348 continue;
2349 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2350 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2351 isl_int_divexact(a, m, b);
2352 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2353 if (isl_int_is_pos(b)) {
2354 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2355 b, bmap->ineq[l], total);
2356 } else {
2357 isl_int_neg(b, b);
2358 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2359 b, bmap->ineq[u], total);
2360 }
2361 }
2362 isl_int_set(bmap->ineq[i][1 + dim + div2],
2363 bmap->ineq[i][1 + dim + div1]);
2364 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2365 }
2366
2367 isl_int_clear(a);
2368 isl_int_clear(b);
2369 isl_int_clear(m);
2370 if (l > u) {
2371 isl_basic_map_drop_inequality(bmap, l);
2372 isl_basic_map_drop_inequality(bmap, u);
2373 } else {
2374 isl_basic_map_drop_inequality(bmap, u);
2375 isl_basic_map_drop_inequality(bmap, l);
2376 }
2377 bmap = isl_basic_map_drop_div(bmap, div1);
2378 return bmap;
2379 }
2380
2381 /* First check if we can coalesce any pair of divs and
2382 * then continue with dropping more redundant divs.
2383 *
2384 * We loop over all pairs of lower and upper bounds on a div
2385 * with coefficient 1 and -1, respectively, check if there
2386 * is any other div "c" with which we can coalesce the div
2387 * and if so, perform the coalescing.
2388 */
2389 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2390 struct isl_basic_map *bmap, int *pairs, int n)
2391 {
2392 int i, l, u;
2393 unsigned dim;
2394
2395 dim = isl_dim_total(bmap->dim);
2396
2397 for (i = 0; i < bmap->n_div; ++i) {
2398 if (!pairs[i])
2399 continue;
2400 for (l = 0; l < bmap->n_ineq; ++l) {
2401 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2402 continue;
2403 for (u = 0; u < bmap->n_ineq; ++u) {
2404 int c;
2405
2406 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2407 continue;
2408 c = div_find_coalesce(bmap, pairs, i, l, u);
2409 if (c < 0)
2410 continue;
2411 free(pairs);
2412 bmap = coalesce_divs(bmap, i, c, l, u);
2413 return isl_basic_map_drop_redundant_divs(bmap);
2414 }
2415 }
2416 }
2417
2418 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2419 return bmap;
2420
2421 return drop_more_redundant_divs(bmap, pairs, n);
2422 }
2423
2424 /* Remove divs that are not strictly needed.
2425 * In particular, if a div only occurs positively (or negatively)
2426 * in constraints, then it can simply be dropped.
2427 * Also, if a div occurs only occurs in two constraints and if moreover
2428 * those two constraints are opposite to each other, except for the constant
2429 * term and if the sum of the constant terms is such that for any value
2430 * of the other values, there is always at least one integer value of the
2431 * div, i.e., if one plus this sum is greater than or equal to
2432 * the (absolute value) of the coefficent of the div in the constraints,
2433 * then we can also simply drop the div.
2434 *
2435 * If any divs are left after these simple checks then we move on
2436 * to more complicated cases in drop_more_redundant_divs.
2437 */
2438 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2439 struct isl_basic_map *bmap)
2440 {
2441 int i, j;
2442 unsigned off;
2443 int *pairs = NULL;
2444 int n = 0;
2445
2446 if (!bmap)
2447 goto error;
2448
2449 off = isl_dim_total(bmap->dim);
2450 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2451 if (!pairs)
2452 goto error;
2453
2454 for (i = 0; i < bmap->n_div; ++i) {
2455 int pos, neg;
2456 int last_pos, last_neg;
2457 int redundant;
2458 int defined;
2459
2460 defined = !isl_int_is_zero(bmap->div[i][0]);
2461 for (j = 0; j < bmap->n_eq; ++j)
2462 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2463 break;
2464 if (j < bmap->n_eq)
2465 continue;
2466 ++n;
2467 pos = neg = 0;
2468 for (j = 0; j < bmap->n_ineq; ++j) {
2469 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2470 last_pos = j;
2471 ++pos;
2472 }
2473 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2474 last_neg = j;
2475 ++neg;
2476 }
2477 }
2478 pairs[i] = pos * neg;
2479 if (pairs[i] == 0) {
2480 for (j = bmap->n_ineq - 1; j >= 0; --j)
2481 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2482 isl_basic_map_drop_inequality(bmap, j);
2483 bmap = isl_basic_map_drop_div(bmap, i);
2484 free(pairs);
2485 return isl_basic_map_drop_redundant_divs(bmap);
2486 }
2487 if (pairs[i] != 1)
2488 continue;
2489 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2490 bmap->ineq[last_neg] + 1,
2491 off + bmap->n_div))
2492 continue;
2493
2494 isl_int_add(bmap->ineq[last_pos][0],
2495 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2496 isl_int_add_ui(bmap->ineq[last_pos][0],
2497 bmap->ineq[last_pos][0], 1);
2498 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2499 bmap->ineq[last_pos][1+off+i]);
2500 isl_int_sub_ui(bmap->ineq[last_pos][0],
2501 bmap->ineq[last_pos][0], 1);
2502 isl_int_sub(bmap->ineq[last_pos][0],
2503 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2504 if (!redundant) {
2505 if (defined ||
2506 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2507 pairs[i] = 0;
2508 --n;
2509 continue;
2510 }
2511 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2512 bmap = isl_basic_map_simplify(bmap);
2513 free(pairs);
2514 return isl_basic_map_drop_redundant_divs(bmap);
2515 }
2516 if (last_pos > last_neg) {
2517 isl_basic_map_drop_inequality(bmap, last_pos);
2518 isl_basic_map_drop_inequality(bmap, last_neg);
2519 } else {
2520 isl_basic_map_drop_inequality(bmap, last_neg);
2521 isl_basic_map_drop_inequality(bmap, last_pos);
2522 }
2523 bmap = isl_basic_map_drop_div(bmap, i);
2524 free(pairs);
2525 return isl_basic_map_drop_redundant_divs(bmap);
2526 }
2527
2528 if (n > 0)
2529 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2530
2531 free(pairs);
2532 return bmap;
2533 error:
2534 free(pairs);
2535 isl_basic_map_free(bmap);
2536 return NULL;
2537 }
2538
2539 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2540 struct isl_basic_set *bset)
2541 {
2542 return (struct isl_basic_set *)
2543 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2544 }
2545
2546 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2547 {
2548 int i;
2549
2550 if (!map)
2551 return NULL;
2552 for (i = 0; i < map->n; ++i) {
2553 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2554 if (!map->p[i])
2555 goto error;
2556 }
2557 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2558 return map;
2559 error:
2560 isl_map_free(map);
2561 return NULL;
2562 }
2563
2564 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2565 {
2566 return (struct isl_set *)
2567 isl_map_drop_redundant_divs((struct isl_map *)set);
2568 }
Integer set library