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privately export isl_basic_map_contains
[isl.git] / isl_map_simplify.c
blob41fee622131c7a40384338eb5e11039d656d6987
1 #include "isl_equalities.h"
2 #include "isl_map.h"
3 #include "isl_map_private.h"
4 #include "isl_seq.h"
5 #include "isl_tab.h"
6
7 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
8 {
9 isl_int *t = bmap->eq[a];
10 bmap->eq[a] = bmap->eq[b];
11 bmap->eq[b] = t;
12 }
13
14 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
15 {
16 if (a != b) {
17 isl_int *t = bmap->ineq[a];
18 bmap->ineq[a] = bmap->ineq[b];
19 bmap->ineq[b] = t;
20 }
21 }
22
23 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
24 {
25 swap_inequality((struct isl_basic_map *)bset, a, b);
26 }
27
28 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
29 {
30 isl_seq_cpy(c, c + n, rem);
31 isl_seq_clr(c + rem, n);
32 }
33
34 /* Drop n dimensions starting at first.
35 *
36 * In principle, this frees up some extra variables as the number
37 * of columns remains constant, but we would have to extend
38 * the div array too as the number of rows in this array is assumed
39 * to be equal to extra.
40 */
41 struct isl_basic_set *isl_basic_set_drop_dims(
42 struct isl_basic_set *bset, unsigned first, unsigned n)
43 {
44 int i;
45
46 if (!bset)
47 goto error;
48
49 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
50
51 if (n == 0)
52 return bset;
53
54 bset = isl_basic_set_cow(bset);
55 if (!bset)
56 return NULL;
57
58 for (i = 0; i < bset->n_eq; ++i)
59 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
60 (bset->dim->n_out-first-n)+bset->extra);
61
62 for (i = 0; i < bset->n_ineq; ++i)
63 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
64 (bset->dim->n_out-first-n)+bset->extra);
65
66 for (i = 0; i < bset->n_div; ++i)
67 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
68 (bset->dim->n_out-first-n)+bset->extra);
69
70 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
71 if (!bset->dim)
72 goto error;
73
74 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
75 bset = isl_basic_set_simplify(bset);
76 return isl_basic_set_finalize(bset);
77 error:
78 isl_basic_set_free(bset);
79 return NULL;
80 }
81
82 struct isl_set *isl_set_drop_dims(
83 struct isl_set *set, unsigned first, unsigned n)
84 {
85 int i;
86
87 if (!set)
88 goto error;
89
90 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
91
92 if (n == 0)
93 return set;
94 set = isl_set_cow(set);
95 if (!set)
96 goto error;
97 set->dim = isl_dim_drop_outputs(set->dim, first, n);
98 if (!set->dim)
99 goto error;
100
101 for (i = 0; i < set->n; ++i) {
102 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
103 if (!set->p[i])
104 goto error;
105 }
106
107 ISL_F_CLR(set, ISL_SET_NORMALIZED);
108 return set;
109 error:
110 isl_set_free(set);
111 return NULL;
112 }
113
114 /* Move "n" divs starting at "first" to the end of the list of divs.
115 */
116 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
117 unsigned first, unsigned n)
118 {
119 isl_int **div;
120 int i;
121
122 if (first + n == bmap->n_div)
123 return bmap;
124
125 div = isl_alloc_array(bmap->ctx, isl_int *, n);
126 if (!div)
127 goto error;
128 for (i = 0; i < n; ++i)
129 div[i] = bmap->div[first + i];
130 for (i = 0; i < bmap->n_div - first - n; ++i)
131 bmap->div[first + i] = bmap->div[first + n + i];
132 for (i = 0; i < n; ++i)
133 bmap->div[bmap->n_div - n + i] = div[i];
134 free(div);
135 return bmap;
136 error:
137 isl_basic_map_free(bmap);
138 return NULL;
139 }
140
141 /* Drop "n" dimensions of type "type" starting at "first".
142 *
143 * In principle, this frees up some extra variables as the number
144 * of columns remains constant, but we would have to extend
145 * the div array too as the number of rows in this array is assumed
146 * to be equal to extra.
147 */
148 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
149 enum isl_dim_type type, unsigned first, unsigned n)
150 {
151 int i;
152 unsigned dim;
153 unsigned offset;
154 unsigned left;
155
156 if (!bmap)
157 goto error;
158
159 dim = isl_basic_map_dim(bmap, type);
160 isl_assert(bmap->ctx, first + n <= dim, goto error);
161
162 if (n == 0)
163 return bmap;
164
165 bmap = isl_basic_map_cow(bmap);
166 if (!bmap)
167 return NULL;
168
169 offset = isl_basic_map_offset(bmap, type) + first;
170 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
171 for (i = 0; i < bmap->n_eq; ++i)
172 constraint_drop_vars(bmap->eq[i]+offset, n, left);
173
174 for (i = 0; i < bmap->n_ineq; ++i)
175 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
176
177 for (i = 0; i < bmap->n_div; ++i)
178 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
179
180 if (type == isl_dim_div) {
181 bmap = move_divs_last(bmap, first, n);
182 if (!bmap)
183 goto error;
184 isl_basic_map_free_div(bmap, n);
185 } else
186 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
187 if (!bmap->dim)
188 goto error;
189
190 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
191 bmap = isl_basic_map_simplify(bmap);
192 return isl_basic_map_finalize(bmap);
193 error:
194 isl_basic_map_free(bmap);
195 return NULL;
196 }
197
198 struct isl_basic_map *isl_basic_map_drop_inputs(
199 struct isl_basic_map *bmap, unsigned first, unsigned n)
200 {
201 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
202 }
203
204 struct isl_map *isl_map_drop(struct isl_map *map,
205 enum isl_dim_type type, unsigned first, unsigned n)
206 {
207 int i;
208
209 if (!map)
210 goto error;
211
212 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
213
214 if (n == 0)
215 return map;
216 map = isl_map_cow(map);
217 if (!map)
218 goto error;
219 map->dim = isl_dim_drop(map->dim, type, first, n);
220 if (!map->dim)
221 goto error;
222
223 for (i = 0; i < map->n; ++i) {
224 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
225 if (!map->p[i])
226 goto error;
227 }
228 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
229
230 return map;
231 error:
232 isl_map_free(map);
233 return NULL;
234 }
235
236 struct isl_map *isl_map_drop_inputs(
237 struct isl_map *map, unsigned first, unsigned n)
238 {
239 return isl_map_drop(map, isl_dim_in, first, n);
240 }
241
242 /*
243 * We don't cow, as the div is assumed to be redundant.
244 */
245 static struct isl_basic_map *isl_basic_map_drop_div(
246 struct isl_basic_map *bmap, unsigned div)
247 {
248 int i;
249 unsigned pos;
250
251 if (!bmap)
252 goto error;
253
254 pos = 1 + isl_dim_total(bmap->dim) + div;
255
256 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
257
258 for (i = 0; i < bmap->n_eq; ++i)
259 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
260
261 for (i = 0; i < bmap->n_ineq; ++i) {
262 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
263 isl_basic_map_drop_inequality(bmap, i);
264 --i;
265 continue;
266 }
267 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
268 }
269
270 for (i = 0; i < bmap->n_div; ++i)
271 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
272
273 if (div != bmap->n_div - 1) {
274 int j;
275 isl_int *t = bmap->div[div];
276
277 for (j = div; j < bmap->n_div - 1; ++j)
278 bmap->div[j] = bmap->div[j+1];
279
280 bmap->div[bmap->n_div - 1] = t;
281 }
282 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
283 isl_basic_map_free_div(bmap, 1);
284
285 return bmap;
286 error:
287 isl_basic_map_free(bmap);
288 return NULL;
289 }
290
291 struct isl_basic_map *isl_basic_map_normalize_constraints(
292 struct isl_basic_map *bmap)
293 {
294 int i;
295 isl_int gcd;
296 unsigned total = isl_basic_map_total_dim(bmap);
297
298 isl_int_init(gcd);
299 for (i = bmap->n_eq - 1; i >= 0; --i) {
300 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
301 if (isl_int_is_zero(gcd)) {
302 if (!isl_int_is_zero(bmap->eq[i][0])) {
303 bmap = isl_basic_map_set_to_empty(bmap);
304 break;
305 }
306 isl_basic_map_drop_equality(bmap, i);
307 continue;
308 }
309 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
310 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
311 if (isl_int_is_one(gcd))
312 continue;
313 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
314 bmap = isl_basic_map_set_to_empty(bmap);
315 break;
316 }
317 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
318 }
319
320 for (i = bmap->n_ineq - 1; i >= 0; --i) {
321 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
322 if (isl_int_is_zero(gcd)) {
323 if (isl_int_is_neg(bmap->ineq[i][0])) {
324 bmap = isl_basic_map_set_to_empty(bmap);
325 break;
326 }
327 isl_basic_map_drop_inequality(bmap, i);
328 continue;
329 }
330 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
331 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
332 if (isl_int_is_one(gcd))
333 continue;
334 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
335 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
336 }
337 isl_int_clear(gcd);
338
339 return bmap;
340 }
341
342 struct isl_basic_set *isl_basic_set_normalize_constraints(
343 struct isl_basic_set *bset)
344 {
345 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
346 (struct isl_basic_map *)bset);
347 }
348
349 /* Assumes divs have been ordered if keep_divs is set.
350 */
351 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
352 unsigned pos, isl_int *eq, int keep_divs, int *progress)
353 {
354 unsigned total;
355 int k;
356 int last_div;
357
358 total = isl_basic_map_total_dim(bmap);
359 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
360 bmap->n_div);
361 for (k = 0; k < bmap->n_eq; ++k) {
362 if (bmap->eq[k] == eq)
363 continue;
364 if (isl_int_is_zero(bmap->eq[k][1+pos]))
365 continue;
366 if (progress)
367 *progress = 1;
368 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
369 }
370
371 for (k = 0; k < bmap->n_ineq; ++k) {
372 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
373 continue;
374 if (progress)
375 *progress = 1;
376 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
377 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
378 }
379
380 for (k = 0; k < bmap->n_div; ++k) {
381 if (isl_int_is_zero(bmap->div[k][0]))
382 continue;
383 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
384 continue;
385 if (progress)
386 *progress = 1;
387 /* We need to be careful about circular definitions,
388 * so for now we just remove the definition of div k
389 * if the equality contains any divs.
390 * If keep_divs is set, then the divs have been ordered
391 * and we can keep the definition as long as the result
392 * is still ordered.
393 */
394 if (last_div == -1 || (keep_divs && last_div < k))
395 isl_seq_elim(bmap->div[k]+1, eq,
396 1+pos, 1+total, &bmap->div[k][0]);
397 else
398 isl_seq_clr(bmap->div[k], 1 + total);
399 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
400 }
401 }
402
403 /* Assumes divs have been ordered if keep_divs is set.
404 */
405 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
406 unsigned div, int keep_divs)
407 {
408 unsigned pos = isl_dim_total(bmap->dim) + div;
409
410 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
411
412 isl_basic_map_drop_div(bmap, div);
413 }
414
415 /* Elimininate divs based on equalities
416 */
417 static struct isl_basic_map *eliminate_divs_eq(
418 struct isl_basic_map *bmap, int *progress)
419 {
420 int d;
421 int i;
422 int modified = 0;
423 unsigned off;
424
425 bmap = isl_basic_map_order_divs(bmap);
426
427 if (!bmap)
428 return NULL;
429
430 off = 1 + isl_dim_total(bmap->dim);
431
432 for (d = bmap->n_div - 1; d >= 0 ; --d) {
433 for (i = 0; i < bmap->n_eq; ++i) {
434 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
435 !isl_int_is_negone(bmap->eq[i][off + d]))
436 continue;
437 modified = 1;
438 *progress = 1;
439 eliminate_div(bmap, bmap->eq[i], d, 1);
440 isl_basic_map_drop_equality(bmap, i);
441 break;
442 }
443 }
444 if (modified)
445 return eliminate_divs_eq(bmap, progress);
446 return bmap;
447 }
448
449 /* Elimininate divs based on inequalities
450 */
451 static struct isl_basic_map *eliminate_divs_ineq(
452 struct isl_basic_map *bmap, int *progress)
453 {
454 int d;
455 int i;
456 unsigned off;
457 struct isl_ctx *ctx;
458
459 if (!bmap)
460 return NULL;
461
462 ctx = bmap->ctx;
463 off = 1 + isl_dim_total(bmap->dim);
464
465 for (d = bmap->n_div - 1; d >= 0 ; --d) {
466 for (i = 0; i < bmap->n_eq; ++i)
467 if (!isl_int_is_zero(bmap->eq[i][off + d]))
468 break;
469 if (i < bmap->n_eq)
470 continue;
471 for (i = 0; i < bmap->n_ineq; ++i)
472 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
473 break;
474 if (i < bmap->n_ineq)
475 continue;
476 *progress = 1;
477 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
478 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
479 break;
480 bmap = isl_basic_map_drop_div(bmap, d);
481 if (!bmap)
482 break;
483 }
484 return bmap;
485 }
486
487 struct isl_basic_map *isl_basic_map_gauss(
488 struct isl_basic_map *bmap, int *progress)
489 {
490 int k;
491 int done;
492 int last_var;
493 unsigned total_var;
494 unsigned total;
495
496 bmap = isl_basic_map_order_divs(bmap);
497
498 if (!bmap)
499 return NULL;
500
501 total = isl_basic_map_total_dim(bmap);
502 total_var = total - bmap->n_div;
503
504 last_var = total - 1;
505 for (done = 0; done < bmap->n_eq; ++done) {
506 for (; last_var >= 0; --last_var) {
507 for (k = done; k < bmap->n_eq; ++k)
508 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
509 break;
510 if (k < bmap->n_eq)
511 break;
512 }
513 if (last_var < 0)
514 break;
515 if (k != done)
516 swap_equality(bmap, k, done);
517 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
518 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
519
520 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
521 progress);
522
523 if (last_var >= total_var &&
524 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
525 unsigned div = last_var - total_var;
526 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
527 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
528 isl_int_set(bmap->div[div][0],
529 bmap->eq[done][1+last_var]);
530 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
531 }
532 }
533 if (done == bmap->n_eq)
534 return bmap;
535 for (k = done; k < bmap->n_eq; ++k) {
536 if (isl_int_is_zero(bmap->eq[k][0]))
537 continue;
538 return isl_basic_map_set_to_empty(bmap);
539 }
540 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
541 return bmap;
542 }
543
544 struct isl_basic_set *isl_basic_set_gauss(
545 struct isl_basic_set *bset, int *progress)
546 {
547 return (struct isl_basic_set*)isl_basic_map_gauss(
548 (struct isl_basic_map *)bset, progress);
549 }
550
551
552 static unsigned int round_up(unsigned int v)
553 {
554 int old_v = v;
555
556 while (v) {
557 old_v = v;
558 v ^= v & -v;
559 }
560 return old_v << 1;
561 }
562
563 static int hash_index(isl_int ***index, unsigned int size, int bits,
564 struct isl_basic_map *bmap, int k)
565 {
566 int h;
567 unsigned total = isl_basic_map_total_dim(bmap);
568 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
569 for (h = hash; index[h]; h = (h+1) % size)
570 if (&bmap->ineq[k] != index[h] &&
571 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
572 break;
573 return h;
574 }
575
576 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
577 struct isl_basic_set *bset, int k)
578 {
579 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
580 }
581
582 /* If we can eliminate more than one div, then we need to make
583 * sure we do it from last div to first div, in order not to
584 * change the position of the other divs that still need to
585 * be removed.
586 */
587 static struct isl_basic_map *remove_duplicate_divs(
588 struct isl_basic_map *bmap, int *progress)
589 {
590 unsigned int size;
591 int *index;
592 int *elim_for;
593 int k, l, h;
594 int bits;
595 struct isl_blk eq;
596 unsigned total_var = isl_dim_total(bmap->dim);
597 unsigned total = total_var + bmap->n_div;
598 struct isl_ctx *ctx;
599
600 if (bmap->n_div <= 1)
601 return bmap;
602
603 ctx = bmap->ctx;
604 for (k = bmap->n_div - 1; k >= 0; --k)
605 if (!isl_int_is_zero(bmap->div[k][0]))
606 break;
607 if (k <= 0)
608 return bmap;
609
610 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
611 size = round_up(4 * bmap->n_div / 3 - 1);
612 bits = ffs(size) - 1;
613 index = isl_calloc_array(ctx, int, size);
614 if (!index)
615 return bmap;
616 eq = isl_blk_alloc(ctx, 1+total);
617 if (isl_blk_is_error(eq))
618 goto out;
619
620 isl_seq_clr(eq.data, 1+total);
621 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
622 for (--k; k >= 0; --k) {
623 uint32_t hash;
624
625 if (isl_int_is_zero(bmap->div[k][0]))
626 continue;
627
628 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
629 for (h = hash; index[h]; h = (h+1) % size)
630 if (isl_seq_eq(bmap->div[k],
631 bmap->div[index[h]-1], 2+total))
632 break;
633 if (index[h]) {
634 *progress = 1;
635 l = index[h] - 1;
636 elim_for[l] = k + 1;
637 }
638 index[h] = k+1;
639 }
640 for (l = bmap->n_div - 1; l >= 0; --l) {
641 if (!elim_for[l])
642 continue;
643 k = elim_for[l] - 1;
644 isl_int_set_si(eq.data[1+total_var+k], -1);
645 isl_int_set_si(eq.data[1+total_var+l], 1);
646 eliminate_div(bmap, eq.data, l, 0);
647 isl_int_set_si(eq.data[1+total_var+k], 0);
648 isl_int_set_si(eq.data[1+total_var+l], 0);
649 }
650
651 isl_blk_free(ctx, eq);
652 out:
653 free(index);
654 free(elim_for);
655 return bmap;
656 }
657
658 static int n_pure_div_eq(struct isl_basic_map *bmap)
659 {
660 int i, j;
661 unsigned total;
662
663 total = isl_dim_total(bmap->dim);
664 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
665 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
666 --j;
667 if (j < 0)
668 break;
669 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
670 return 0;
671 }
672 return i;
673 }
674
675 /* Normalize divs that appear in equalities.
676 *
677 * In particular, we assume that bmap contains some equalities
678 * of the form
679 *
680 * a x = m * e_i
681 *
682 * and we want to replace the set of e_i by a minimal set and
683 * such that the new e_i have a canonical representation in terms
684 * of the vector x.
685 * If any of the equalities involves more than one divs, then
686 * we currently simply bail out.
687 *
688 * Let us first additionally assume that all equalities involve
689 * a div. The equalities then express modulo constraints on the
690 * remaining variables and we can use "parameter compression"
691 * to find a minimal set of constraints. The result is a transformation
692 *
693 * x = T(x') = x_0 + G x'
694 *
695 * with G a lower-triangular matrix with all elements below the diagonal
696 * non-negative and smaller than the diagonal element on the same row.
697 * We first normalize x_0 by making the same property hold in the affine
698 * T matrix.
699 * The rows i of G with a 1 on the diagonal do not impose any modulo
700 * constraint and simply express x_i = x'_i.
701 * For each of the remaining rows i, we introduce a div and a corresponding
702 * equality. In particular
703 *
704 * g_ii e_j = x_i - g_i(x')
705 *
706 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
707 * corresponding div (if g_kk != 1).
708 *
709 * If there are any equalities not involving any div, then we
710 * first apply a variable compression on the variables x:
711 *
712 * x = C x'' x'' = C_2 x
713 *
714 * and perform the above parameter compression on A C instead of on A.
715 * The resulting compression is then of the form
716 *
717 * x'' = T(x') = x_0 + G x'
718 *
719 * and in constructing the new divs and the corresponding equalities,
720 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
721 * by the corresponding row from C_2.
722 */
723 static struct isl_basic_map *normalize_divs(
724 struct isl_basic_map *bmap, int *progress)
725 {
726 int i, j, k;
727 int total;
728 int div_eq;
729 struct isl_mat *B;
730 struct isl_vec *d;
731 struct isl_mat *T = NULL;
732 struct isl_mat *C = NULL;
733 struct isl_mat *C2 = NULL;
734 isl_int v;
735 int *pos;
736 int dropped, needed;
737
738 if (!bmap)
739 return NULL;
740
741 if (bmap->n_div == 0)
742 return bmap;
743
744 if (bmap->n_eq == 0)
745 return bmap;
746
747 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
748 return bmap;
749
750 total = isl_dim_total(bmap->dim);
751 div_eq = n_pure_div_eq(bmap);
752 if (div_eq == 0)
753 return bmap;
754
755 if (div_eq < bmap->n_eq) {
756 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
757 bmap->n_eq - div_eq, 0, 1 + total);
758 C = isl_mat_variable_compression(B, &C2);
759 if (!C || !C2)
760 goto error;
761 if (C->n_col == 0) {
762 bmap = isl_basic_map_set_to_empty(bmap);
763 isl_mat_free(C);
764 isl_mat_free(C2);
765 goto done;
766 }
767 }
768
769 d = isl_vec_alloc(bmap->ctx, div_eq);
770 if (!d)
771 goto error;
772 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
773 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
774 --j;
775 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
776 }
777 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
778
779 if (C) {
780 B = isl_mat_product(B, C);
781 C = NULL;
782 }
783
784 T = isl_mat_parameter_compression(B, d);
785 if (!T)
786 goto error;
787 if (T->n_col == 0) {
788 bmap = isl_basic_map_set_to_empty(bmap);
789 isl_mat_free(C2);
790 isl_mat_free(T);
791 goto done;
792 }
793 isl_int_init(v);
794 for (i = 0; i < T->n_row - 1; ++i) {
795 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
796 if (isl_int_is_zero(v))
797 continue;
798 isl_mat_col_submul(T, 0, v, 1 + i);
799 }
800 isl_int_clear(v);
801 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
802 /* We have to be careful because dropping equalities may reorder them */
803 dropped = 0;
804 for (j = bmap->n_div - 1; j >= 0; --j) {
805 for (i = 0; i < bmap->n_eq; ++i)
806 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
807 break;
808 if (i < bmap->n_eq) {
809 bmap = isl_basic_map_drop_div(bmap, j);
810 isl_basic_map_drop_equality(bmap, i);
811 ++dropped;
812 }
813 }
814 pos[0] = 0;
815 needed = 0;
816 for (i = 1; i < T->n_row; ++i) {
817 if (isl_int_is_one(T->row[i][i]))
818 pos[i] = i;
819 else
820 needed++;
821 }
822 if (needed > dropped) {
823 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
824 needed, needed, 0);
825 if (!bmap)
826 goto error;
827 }
828 for (i = 1; i < T->n_row; ++i) {
829 if (isl_int_is_one(T->row[i][i]))
830 continue;
831 k = isl_basic_map_alloc_div(bmap);
832 pos[i] = 1 + total + k;
833 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
834 isl_int_set(bmap->div[k][0], T->row[i][i]);
835 if (C2)
836 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
837 else
838 isl_int_set_si(bmap->div[k][1 + i], 1);
839 for (j = 0; j < i; ++j) {
840 if (isl_int_is_zero(T->row[i][j]))
841 continue;
842 if (pos[j] < T->n_row && C2)
843 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
844 C2->row[pos[j]], 1 + total);
845 else
846 isl_int_neg(bmap->div[k][1 + pos[j]],
847 T->row[i][j]);
848 }
849 j = isl_basic_map_alloc_equality(bmap);
850 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
851 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
852 }
853 free(pos);
854 isl_mat_free(C2);
855 isl_mat_free(T);
856
857 if (progress)
858 *progress = 1;
859 done:
860 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
861
862 return bmap;
863 error:
864 isl_mat_free(C);
865 isl_mat_free(C2);
866 isl_mat_free(T);
867 return bmap;
868 }
869
870 static struct isl_basic_map *set_div_from_lower_bound(
871 struct isl_basic_map *bmap, int div, int ineq)
872 {
873 unsigned total = 1 + isl_dim_total(bmap->dim);
874
875 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
876 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
877 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
878 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
879 isl_int_set_si(bmap->div[div][1 + total + div], 0);
880
881 return bmap;
882 }
883
884 /* Check whether it is ok to define a div based on an inequality.
885 * To avoid the introduction of circular definitions of divs, we
886 * do not allow such a definition if the resulting expression would refer to
887 * any other undefined divs or if any known div is defined in
888 * terms of the unknown div.
889 */
890 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
891 int div, int ineq)
892 {
893 int j;
894 unsigned total = 1 + isl_dim_total(bmap->dim);
895
896 /* Not defined in terms of unknown divs */
897 for (j = 0; j < bmap->n_div; ++j) {
898 if (div == j)
899 continue;
900 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
901 continue;
902 if (isl_int_is_zero(bmap->div[j][0]))
903 return 0;
904 }
905
906 /* No other div defined in terms of this one => avoid loops */
907 for (j = 0; j < bmap->n_div; ++j) {
908 if (div == j)
909 continue;
910 if (isl_int_is_zero(bmap->div[j][0]))
911 continue;
912 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
913 return 0;
914 }
915
916 return 1;
917 }
918
919 /* Given two constraints "k" and "l" that are opposite to each other,
920 * except for the constant term, check if we can use them
921 * to obtain an expression for one of the hitherto unknown divs.
922 * "sum" is the sum of the constant terms of the constraints.
923 * If this sum is strictly smaller than the coefficient of one
924 * of the divs, then this pair can be used define the div.
925 * To avoid the introduction of circular definitions of divs, we
926 * do not use the pair if the resulting expression would refer to
927 * any other undefined divs or if any known div is defined in
928 * terms of the unknown div.
929 */
930 static struct isl_basic_map *check_for_div_constraints(
931 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
932 {
933 int i;
934 unsigned total = 1 + isl_dim_total(bmap->dim);
935
936 for (i = 0; i < bmap->n_div; ++i) {
937 if (!isl_int_is_zero(bmap->div[i][0]))
938 continue;
939 if (isl_int_is_zero(bmap->ineq[k][total + i]))
940 continue;
941 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
942 continue;
943 if (!ok_to_set_div_from_bound(bmap, i, k))
944 break;
945 if (isl_int_is_pos(bmap->ineq[k][total + i]))
946 bmap = set_div_from_lower_bound(bmap, i, k);
947 else
948 bmap = set_div_from_lower_bound(bmap, i, l);
949 if (progress)
950 *progress = 1;
951 break;
952 }
953 return bmap;
954 }
955
956 static struct isl_basic_map *remove_duplicate_constraints(
957 struct isl_basic_map *bmap, int *progress)
958 {
959 unsigned int size;
960 isl_int ***index;
961 int k, l, h;
962 int bits;
963 unsigned total = isl_basic_map_total_dim(bmap);
964 isl_int sum;
965
966 if (bmap->n_ineq <= 1)
967 return bmap;
968
969 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
970 bits = ffs(size) - 1;
971 index = isl_calloc_array(ctx, isl_int **, size);
972 if (!index)
973 return bmap;
974
975 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
976 for (k = 1; k < bmap->n_ineq; ++k) {
977 h = hash_index(index, size, bits, bmap, k);
978 if (!index[h]) {
979 index[h] = &bmap->ineq[k];
980 continue;
981 }
982 if (progress)
983 *progress = 1;
984 l = index[h] - &bmap->ineq[0];
985 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
986 swap_inequality(bmap, k, l);
987 isl_basic_map_drop_inequality(bmap, k);
988 --k;
989 }
990 isl_int_init(sum);
991 for (k = 0; k < bmap->n_ineq-1; ++k) {
992 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
993 h = hash_index(index, size, bits, bmap, k);
994 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
995 if (!index[h])
996 continue;
997 l = index[h] - &bmap->ineq[0];
998 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
999 if (isl_int_is_pos(sum)) {
1000 bmap = check_for_div_constraints(bmap, k, l, sum,
1001 progress);
1002 continue;
1003 }
1004 if (isl_int_is_zero(sum)) {
1005 /* We need to break out of the loop after these
1006 * changes since the contents of the hash
1007 * will no longer be valid.
1008 * Plus, we probably we want to regauss first.
1009 */
1010 if (progress)
1011 *progress = 1;
1012 isl_basic_map_drop_inequality(bmap, l);
1013 isl_basic_map_inequality_to_equality(bmap, k);
1014 } else
1015 bmap = isl_basic_map_set_to_empty(bmap);
1016 break;
1017 }
1018 isl_int_clear(sum);
1019
1020 free(index);
1021 return bmap;
1022 }
1023
1024
1025 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1026 {
1027 int progress = 1;
1028 if (!bmap)
1029 return NULL;
1030 while (progress) {
1031 progress = 0;
1032 bmap = isl_basic_map_normalize_constraints(bmap);
1033 bmap = remove_duplicate_divs(bmap, &progress);
1034 bmap = eliminate_divs_eq(bmap, &progress);
1035 bmap = eliminate_divs_ineq(bmap, &progress);
1036 bmap = isl_basic_map_gauss(bmap, &progress);
1037 /* requires equalities in normal form */
1038 bmap = normalize_divs(bmap, &progress);
1039 bmap = remove_duplicate_constraints(bmap, &progress);
1040 }
1041 return bmap;
1042 }
1043
1044 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1045 {
1046 return (struct isl_basic_set *)
1047 isl_basic_map_simplify((struct isl_basic_map *)bset);
1048 }
1049
1050
1051 /* If the only constraints a div d=floor(f/m)
1052 * appears in are its two defining constraints
1053 *
1054 * f - m d >=0
1055 * -(f - (m - 1)) + m d >= 0
1056 *
1057 * then it can safely be removed.
1058 */
1059 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1060 {
1061 int i;
1062 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1063
1064 for (i = 0; i < bmap->n_eq; ++i)
1065 if (!isl_int_is_zero(bmap->eq[i][pos]))
1066 return 0;
1067
1068 for (i = 0; i < bmap->n_ineq; ++i) {
1069 if (isl_int_is_zero(bmap->ineq[i][pos]))
1070 continue;
1071 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1072 int neg;
1073 isl_int_sub(bmap->div[div][1],
1074 bmap->div[div][1], bmap->div[div][0]);
1075 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1076 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1077 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1078 isl_int_add(bmap->div[div][1],
1079 bmap->div[div][1], bmap->div[div][0]);
1080 if (!neg)
1081 return 0;
1082 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1083 bmap->n_div-div-1) != -1)
1084 return 0;
1085 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1086 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1087 return 0;
1088 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1089 bmap->n_div-div-1) != -1)
1090 return 0;
1091 } else
1092 return 0;
1093 }
1094
1095 for (i = 0; i < bmap->n_div; ++i)
1096 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1097 return 0;
1098
1099 return 1;
1100 }
1101
1102 /*
1103 * Remove divs that don't occur in any of the constraints or other divs.
1104 * These can arise when dropping some of the variables in a quast
1105 * returned by piplib.
1106 */
1107 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1108 {
1109 int i;
1110
1111 if (!bmap)
1112 return NULL;
1113
1114 for (i = bmap->n_div-1; i >= 0; --i) {
1115 if (!div_is_redundant(bmap, i))
1116 continue;
1117 bmap = isl_basic_map_drop_div(bmap, i);
1118 }
1119 return bmap;
1120 }
1121
1122 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1123 {
1124 bmap = remove_redundant_divs(bmap);
1125 if (!bmap)
1126 return NULL;
1127 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1128 return bmap;
1129 }
1130
1131 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1132 {
1133 return (struct isl_basic_set *)
1134 isl_basic_map_finalize((struct isl_basic_map *)bset);
1135 }
1136
1137 struct isl_set *isl_set_finalize(struct isl_set *set)
1138 {
1139 int i;
1140
1141 if (!set)
1142 return NULL;
1143 for (i = 0; i < set->n; ++i) {
1144 set->p[i] = isl_basic_set_finalize(set->p[i]);
1145 if (!set->p[i])
1146 goto error;
1147 }
1148 return set;
1149 error:
1150 isl_set_free(set);
1151 return NULL;
1152 }
1153
1154 struct isl_map *isl_map_finalize(struct isl_map *map)
1155 {
1156 int i;
1157
1158 if (!map)
1159 return NULL;
1160 for (i = 0; i < map->n; ++i) {
1161 map->p[i] = isl_basic_map_finalize(map->p[i]);
1162 if (!map->p[i])
1163 goto error;
1164 }
1165 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1166 return map;
1167 error:
1168 isl_map_free(map);
1169 return NULL;
1170 }
1171
1172
1173 /* Remove definition of any div that is defined in terms of the given variable.
1174 * The div itself is not removed. Functions such as
1175 * eliminate_divs_ineq depend on the other divs remaining in place.
1176 */
1177 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1178 int pos)
1179 {
1180 int i;
1181
1182 for (i = 0; i < bmap->n_div; ++i) {
1183 if (isl_int_is_zero(bmap->div[i][0]))
1184 continue;
1185 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1186 continue;
1187 isl_int_set_si(bmap->div[i][0], 0);
1188 }
1189 return bmap;
1190 }
1191
1192 /* Eliminate the specified variables from the constraints using
1193 * Fourier-Motzkin. The variables themselves are not removed.
1194 */
1195 struct isl_basic_map *isl_basic_map_eliminate_vars(
1196 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1197 {
1198 int d;
1199 int i, j, k;
1200 unsigned total;
1201
1202 if (n == 0)
1203 return bmap;
1204 if (!bmap)
1205 return NULL;
1206 total = isl_basic_map_total_dim(bmap);
1207
1208 bmap = isl_basic_map_cow(bmap);
1209 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1210 bmap = remove_dependent_vars(bmap, d);
1211
1212 for (d = pos + n - 1;
1213 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1214 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1215 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1216 int n_lower, n_upper;
1217 if (!bmap)
1218 return NULL;
1219 for (i = 0; i < bmap->n_eq; ++i) {
1220 if (isl_int_is_zero(bmap->eq[i][1+d]))
1221 continue;
1222 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1223 isl_basic_map_drop_equality(bmap, i);
1224 break;
1225 }
1226 if (i < bmap->n_eq)
1227 continue;
1228 n_lower = 0;
1229 n_upper = 0;
1230 for (i = 0; i < bmap->n_ineq; ++i) {
1231 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1232 n_lower++;
1233 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1234 n_upper++;
1235 }
1236 bmap = isl_basic_map_extend_constraints(bmap,
1237 0, n_lower * n_upper);
1238 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1239 int last;
1240 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1241 continue;
1242 last = -1;
1243 for (j = 0; j < i; ++j) {
1244 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1245 continue;
1246 last = j;
1247 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1248 isl_int_sgn(bmap->ineq[j][1+d]))
1249 continue;
1250 k = isl_basic_map_alloc_inequality(bmap);
1251 if (k < 0)
1252 goto error;
1253 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1254 1+total);
1255 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1256 1+d, 1+total, NULL);
1257 }
1258 isl_basic_map_drop_inequality(bmap, i);
1259 i = last + 1;
1260 }
1261 if (n_lower > 0 && n_upper > 0) {
1262 bmap = isl_basic_map_normalize_constraints(bmap);
1263 bmap = remove_duplicate_constraints(bmap, NULL);
1264 bmap = isl_basic_map_gauss(bmap, NULL);
1265 bmap = isl_basic_map_convex_hull(bmap);
1266 if (!bmap)
1267 goto error;
1268 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1269 break;
1270 }
1271 }
1272 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1273 return bmap;
1274 error:
1275 isl_basic_map_free(bmap);
1276 return NULL;
1277 }
1278
1279 struct isl_basic_set *isl_basic_set_eliminate_vars(
1280 struct isl_basic_set *bset, unsigned pos, unsigned n)
1281 {
1282 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1283 (struct isl_basic_map *)bset, pos, n);
1284 }
1285
1286 /* Don't assume equalities are in order, because align_divs
1287 * may have changed the order of the divs.
1288 */
1289 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1290 {
1291 int d, i;
1292 unsigned total;
1293
1294 total = isl_dim_total(bmap->dim);
1295 for (d = 0; d < total; ++d)
1296 elim[d] = -1;
1297 for (i = 0; i < bmap->n_eq; ++i) {
1298 for (d = total - 1; d >= 0; --d) {
1299 if (isl_int_is_zero(bmap->eq[i][1+d]))
1300 continue;
1301 elim[d] = i;
1302 break;
1303 }
1304 }
1305 }
1306
1307 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1308 {
1309 compute_elimination_index((struct isl_basic_map *)bset, elim);
1310 }
1311
1312 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1313 struct isl_basic_map *bmap, int *elim)
1314 {
1315 int d;
1316 int copied = 0;
1317 unsigned total;
1318
1319 total = isl_dim_total(bmap->dim);
1320 for (d = total - 1; d >= 0; --d) {
1321 if (isl_int_is_zero(src[1+d]))
1322 continue;
1323 if (elim[d] == -1)
1324 continue;
1325 if (!copied) {
1326 isl_seq_cpy(dst, src, 1 + total);
1327 copied = 1;
1328 }
1329 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1330 }
1331 return copied;
1332 }
1333
1334 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1335 struct isl_basic_set *bset, int *elim)
1336 {
1337 return reduced_using_equalities(dst, src,
1338 (struct isl_basic_map *)bset, elim);
1339 }
1340
1341 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1342 struct isl_basic_set *bset, struct isl_basic_set *context)
1343 {
1344 int i;
1345 int *elim;
1346
1347 if (!bset || !context)
1348 goto error;
1349
1350 bset = isl_basic_set_cow(bset);
1351 if (!bset)
1352 goto error;
1353
1354 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1355 if (!elim)
1356 goto error;
1357 set_compute_elimination_index(context, elim);
1358 for (i = 0; i < bset->n_eq; ++i)
1359 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1360 context, elim);
1361 for (i = 0; i < bset->n_ineq; ++i)
1362 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1363 context, elim);
1364 isl_basic_set_free(context);
1365 free(elim);
1366 bset = isl_basic_set_simplify(bset);
1367 bset = isl_basic_set_finalize(bset);
1368 return bset;
1369 error:
1370 isl_basic_set_free(bset);
1371 isl_basic_set_free(context);
1372 return NULL;
1373 }
1374
1375 static struct isl_basic_set *remove_shifted_constraints(
1376 struct isl_basic_set *bset, struct isl_basic_set *context)
1377 {
1378 unsigned int size;
1379 isl_int ***index;
1380 int bits;
1381 int k, h, l;
1382
1383 if (!bset)
1384 return NULL;
1385
1386 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1387 bits = ffs(size) - 1;
1388 index = isl_calloc_array(ctx, isl_int **, size);
1389 if (!index)
1390 return bset;
1391
1392 for (k = 0; k < context->n_ineq; ++k) {
1393 h = set_hash_index(index, size, bits, context, k);
1394 index[h] = &context->ineq[k];
1395 }
1396 for (k = 0; k < bset->n_ineq; ++k) {
1397 h = set_hash_index(index, size, bits, bset, k);
1398 if (!index[h])
1399 continue;
1400 l = index[h] - &context->ineq[0];
1401 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1402 continue;
1403 bset = isl_basic_set_cow(bset);
1404 if (!bset)
1405 goto error;
1406 isl_basic_set_drop_inequality(bset, k);
1407 --k;
1408 }
1409 free(index);
1410 return bset;
1411 error:
1412 free(index);
1413 return bset;
1414 }
1415
1416 /* Tighten (decrease) the constant terms of the inequalities based
1417 * on the equalities, without removing any integer points.
1418 * For example, if there is an equality
1419 *
1420 * i = 3 * j
1421 *
1422 * and an inequality
1423 *
1424 * i >= 1
1425 *
1426 * then we want to replace the inequality by
1427 *
1428 * i >= 3
1429 *
1430 * We do this by computing a variable compression and translating
1431 * the constraints to the compressed space.
1432 * If any constraint has coefficients (except the contant term)
1433 * with a common factor "f", then we can replace the constant term "c"
1434 * by
1435 *
1436 * f * floor(c/f)
1437 *
1438 * That is, we add
1439 *
1440 * f * floor(c/f) - c = -fract(c/f)
1441 *
1442 * and we can add the same value to the original constraint.
1443 *
1444 * In the example, the compressed space only contains "j",
1445 * and the inequality translates to
1446 *
1447 * 3 * j - 1 >= 0
1448 *
1449 * We add -fract(-1/3) = -2 to the original constraint to obtain
1450 *
1451 * i - 3 >= 0
1452 */
1453 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1454 struct isl_basic_set *bset)
1455 {
1456 int i;
1457 unsigned total;
1458 struct isl_mat *B, *C;
1459 isl_int gcd;
1460
1461 if (!bset)
1462 return NULL;
1463
1464 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1465 return bset;
1466
1467 if (!bset->n_ineq)
1468 return bset;
1469
1470 bset = isl_basic_set_cow(bset);
1471 if (!bset)
1472 return NULL;
1473
1474 total = isl_basic_set_total_dim(bset);
1475 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1476 C = isl_mat_variable_compression(B, NULL);
1477 if (!C)
1478 return bset;
1479 if (C->n_col == 0) {
1480 isl_mat_free(C);
1481 return isl_basic_set_set_to_empty(bset);
1482 }
1483 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1484 0, bset->n_ineq, 0, 1 + total);
1485 C = isl_mat_product(B, C);
1486 if (!C)
1487 return bset;
1488
1489 isl_int_init(gcd);
1490 for (i = 0; i < bset->n_ineq; ++i) {
1491 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1492 if (isl_int_is_one(gcd))
1493 continue;
1494 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1495 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1496 }
1497 isl_int_clear(gcd);
1498
1499 isl_mat_free(C);
1500
1501 return bset;
1502 }
1503
1504 /* Remove all information from bset that is redundant in the context
1505 * of context. In particular, equalities that are linear combinations
1506 * of those in context are removed. Then the inequalities that are
1507 * redundant in the context of the equalities and inequalities of
1508 * context are removed.
1509 *
1510 * We first simplify the constraints of "bset" in the context of the
1511 * equalities of "context".
1512 * Then we simplify the inequalities of the context in the context
1513 * of the equalities of bset and remove the inequalities from "bset"
1514 * that are obviously redundant with respect to some inequality in "context".
1515 *
1516 * If there are any inequalities left, we construct a tableau for
1517 * the context and then add the inequalities of "bset".
1518 * Before adding these equalities, we freeze all constraints such that
1519 * they won't be considered redundant in terms of the constraints of "bset".
1520 * Then we detect all equalities and redundant constraints (among the
1521 * constraints that weren't frozen) and update bset according to the results.
1522 * We have to be careful here because we don't want any of the context
1523 * constraints to remain and because we haven't added the equalities of "bset"
1524 * to the tableau so we temporarily have to pretend that there were no
1525 * equalities.
1526 */
1527 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1528 struct isl_basic_set *context)
1529 {
1530 int i;
1531 struct isl_tab *tab;
1532 unsigned context_ineq;
1533 struct isl_basic_set *combined = NULL;
1534
1535 if (!context || !bset)
1536 goto error;
1537
1538 if (context->n_eq > 0)
1539 bset = isl_basic_set_reduce_using_equalities(bset,
1540 isl_basic_set_copy(context));
1541 if (!bset)
1542 goto error;
1543 if (isl_basic_set_fast_is_empty(bset))
1544 goto done;
1545 if (!bset->n_ineq)
1546 goto done;
1547
1548 if (bset->n_eq > 0) {
1549 struct isl_basic_set *affine_hull;
1550 affine_hull = isl_basic_set_copy(bset);
1551 affine_hull = isl_basic_set_cow(affine_hull);
1552 if (!affine_hull)
1553 goto error;
1554 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1555 context = isl_basic_set_intersect(context, affine_hull);
1556 context = isl_basic_set_gauss(context, NULL);
1557 context = normalize_constraints_in_compressed_space(context);
1558 }
1559 if (!context)
1560 goto error;
1561 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1562 isl_basic_set_free(bset);
1563 return context;
1564 }
1565 if (!context->n_ineq)
1566 goto done;
1567 bset = remove_shifted_constraints(bset, context);
1568 if (!bset->n_ineq)
1569 goto done;
1570 isl_basic_set_free_equality(context, context->n_eq);
1571 context_ineq = context->n_ineq;
1572 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1573 combined = isl_basic_set_extend_constraints(combined,
1574 bset->n_eq, bset->n_ineq);
1575 tab = isl_tab_from_basic_set(combined);
1576 if (!tab)
1577 goto error;
1578 for (i = 0; i < context_ineq; ++i)
1579 if (isl_tab_freeze_constraint(tab, i) < 0)
1580 goto error;
1581 tab = isl_tab_extend(tab, bset->n_ineq);
1582 if (!tab)
1583 goto error;
1584 for (i = 0; i < bset->n_ineq; ++i)
1585 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1586 goto error;
1587 bset = isl_basic_set_add_constraints(combined, bset, 0);
1588 tab = isl_tab_detect_implicit_equalities(tab);
1589 if (isl_tab_detect_redundant(tab) < 0) {
1590 isl_tab_free(tab);
1591 goto error2;
1592 }
1593 for (i = 0; i < context_ineq; ++i) {
1594 tab->con[i].is_zero = 0;
1595 tab->con[i].is_redundant = 1;
1596 }
1597 bset = isl_basic_set_update_from_tab(bset, tab);
1598 isl_tab_free(tab);
1599 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1600 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1601 done:
1602 bset = isl_basic_set_simplify(bset);
1603 bset = isl_basic_set_finalize(bset);
1604 isl_basic_set_free(context);
1605 return bset;
1606 error:
1607 isl_basic_set_free(combined);
1608 error2:
1609 isl_basic_set_free(bset);
1610 isl_basic_set_free(context);
1611 return NULL;
1612 }
1613
1614 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1615 * We simply add the equalities in context to bmap and then do a regular
1616 * div normalizations. Better results can be obtained by normalizing
1617 * only the divs in bmap than do not also appear in context.
1618 * We need to be careful to reduce the divs using the equalities
1619 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1620 * spurious constraints.
1621 */
1622 static struct isl_basic_map *normalize_divs_in_context(
1623 struct isl_basic_map *bmap, struct isl_basic_map *context)
1624 {
1625 int i;
1626 unsigned total_context;
1627 int div_eq;
1628
1629 div_eq = n_pure_div_eq(bmap);
1630 if (div_eq == 0)
1631 return bmap;
1632
1633 if (context->n_div > 0)
1634 bmap = isl_basic_map_align_divs(bmap, context);
1635
1636 total_context = isl_basic_map_total_dim(context);
1637 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1638 for (i = 0; i < context->n_eq; ++i) {
1639 int k;
1640 k = isl_basic_map_alloc_equality(bmap);
1641 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1642 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1643 isl_basic_map_total_dim(bmap) - total_context);
1644 }
1645 bmap = isl_basic_map_gauss(bmap, NULL);
1646 bmap = normalize_divs(bmap, NULL);
1647 bmap = isl_basic_map_gauss(bmap, NULL);
1648 return bmap;
1649 }
1650
1651 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1652 struct isl_basic_map *context)
1653 {
1654 struct isl_basic_set *bset;
1655
1656 if (!bmap || !context)
1657 goto error;
1658
1659 if (isl_basic_map_is_universe(context)) {
1660 isl_basic_map_free(context);
1661 return bmap;
1662 }
1663 if (isl_basic_map_is_universe(bmap)) {
1664 isl_basic_map_free(context);
1665 return bmap;
1666 }
1667 if (isl_basic_map_fast_is_empty(context)) {
1668 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1669 isl_basic_map_free(context);
1670 isl_basic_map_free(bmap);
1671 return isl_basic_map_universe(dim);
1672 }
1673 if (isl_basic_map_fast_is_empty(bmap)) {
1674 isl_basic_map_free(context);
1675 return bmap;
1676 }
1677
1678 bmap = isl_basic_map_convex_hull(bmap);
1679 context = isl_basic_map_convex_hull(context);
1680
1681 if (context->n_eq)
1682 bmap = normalize_divs_in_context(bmap, context);
1683
1684 context = isl_basic_map_align_divs(context, bmap);
1685 bmap = isl_basic_map_align_divs(bmap, context);
1686
1687 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1688 isl_basic_map_underlying_set(context));
1689
1690 return isl_basic_map_overlying_set(bset, bmap);
1691 error:
1692 isl_basic_map_free(bmap);
1693 isl_basic_map_free(context);
1694 return NULL;
1695 }
1696
1697 /*
1698 * Assumes context has no implicit divs.
1699 */
1700 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1701 {
1702 int i;
1703
1704 if (!map || !context)
1705 goto error;;
1706
1707 if (isl_basic_map_is_universe(context)) {
1708 isl_basic_map_free(context);
1709 return map;
1710 }
1711 if (isl_basic_map_fast_is_empty(context)) {
1712 struct isl_dim *dim = isl_dim_copy(map->dim);
1713 isl_basic_map_free(context);
1714 isl_map_free(map);
1715 return isl_map_universe(dim);
1716 }
1717
1718 context = isl_basic_map_convex_hull(context);
1719 map = isl_map_cow(map);
1720 if (!map || !context)
1721 goto error;;
1722 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1723 map = isl_map_compute_divs(map);
1724 for (i = 0; i < map->n; ++i)
1725 context = isl_basic_map_align_divs(context, map->p[i]);
1726 for (i = 0; i < map->n; ++i) {
1727 map->p[i] = isl_basic_map_gist(map->p[i],
1728 isl_basic_map_copy(context));
1729 if (!map->p[i])
1730 goto error;
1731 }
1732 isl_basic_map_free(context);
1733 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1734 return map;
1735 error:
1736 isl_map_free(map);
1737 isl_basic_map_free(context);
1738 return NULL;
1739 }
1740
1741 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1742 struct isl_basic_set *context)
1743 {
1744 return (struct isl_basic_set *)isl_basic_map_gist(
1745 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1746 }
1747
1748 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1749 {
1750 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1751 (struct isl_basic_map *)context);
1752 }
1753
1754 /* Quick check to see if two basic maps are disjoint.
1755 * In particular, we reduce the equalities and inequalities of
1756 * one basic map in the context of the equalities of the other
1757 * basic map and check if we get a contradiction.
1758 */
1759 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1760 struct isl_basic_map *bmap2)
1761 {
1762 struct isl_vec *v = NULL;
1763 int *elim = NULL;
1764 unsigned total;
1765 int i;
1766
1767 if (!bmap1 || !bmap2)
1768 return -1;
1769 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1770 return -1);
1771 if (bmap1->n_div || bmap2->n_div)
1772 return 0;
1773 if (!bmap1->n_eq && !bmap2->n_eq)
1774 return 0;
1775
1776 total = isl_dim_total(bmap1->dim);
1777 if (total == 0)
1778 return 0;
1779 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1780 if (!v)
1781 goto error;
1782 elim = isl_alloc_array(bmap1->ctx, int, total);
1783 if (!elim)
1784 goto error;
1785 compute_elimination_index(bmap1, elim);
1786 for (i = 0; i < bmap2->n_eq; ++i) {
1787 int reduced;
1788 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1789 bmap1, elim);
1790 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1791 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1792 goto disjoint;
1793 }
1794 for (i = 0; i < bmap2->n_ineq; ++i) {
1795 int reduced;
1796 reduced = reduced_using_equalities(v->block.data,
1797 bmap2->ineq[i], bmap1, elim);
1798 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1799 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1800 goto disjoint;
1801 }
1802 compute_elimination_index(bmap2, elim);
1803 for (i = 0; i < bmap1->n_ineq; ++i) {
1804 int reduced;
1805 reduced = reduced_using_equalities(v->block.data,
1806 bmap1->ineq[i], bmap2, elim);
1807 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1808 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1809 goto disjoint;
1810 }
1811 isl_vec_free(v);
1812 free(elim);
1813 return 0;
1814 disjoint:
1815 isl_vec_free(v);
1816 free(elim);
1817 return 1;
1818 error:
1819 isl_vec_free(v);
1820 free(elim);
1821 return -1;
1822 }
1823
1824 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1825 struct isl_basic_set *bset2)
1826 {
1827 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1828 (struct isl_basic_map *)bset2);
1829 }
1830
1831 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1832 {
1833 int i, j;
1834
1835 if (!map1 || !map2)
1836 return -1;
1837
1838 if (isl_map_fast_is_equal(map1, map2))
1839 return 0;
1840
1841 for (i = 0; i < map1->n; ++i) {
1842 for (j = 0; j < map2->n; ++j) {
1843 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1844 map2->p[j]);
1845 if (d != 1)
1846 return d;
1847 }
1848 }
1849 return 1;
1850 }
1851
1852 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1853 {
1854 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1855 (struct isl_map *)set2);
1856 }
1857
1858 /* Check if we can combine a given div with lower bound l and upper
1859 * bound u with some other div and if so return that other div.
1860 * Otherwise return -1.
1861 *
1862 * We first check that
1863 * - the bounds are opposites of each other (except for the constant
1864 * term)
1865 * - the bounds do not reference any other div
1866 * - no div is defined in terms of this div
1867 *
1868 * Let m be the size of the range allowed on the div by the bounds.
1869 * That is, the bounds are of the form
1870 *
1871 * e <= a <= e + m - 1
1872 *
1873 * with e some expression in the other variables.
1874 * We look for another div b such that no third div is defined in terms
1875 * of this second div b and such that in any constraint that contains
1876 * a (except for the given lower and upper bound), also contains b
1877 * with a coefficient that is m times that of b.
1878 * That is, all constraints (execpt for the lower and upper bound)
1879 * are of the form
1880 *
1881 * e + f (a + m b) >= 0
1882 *
1883 * If so, we return b so that "a + m b" can be replaced by
1884 * a single div "c = a + m b".
1885 */
1886 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1887 unsigned div, unsigned l, unsigned u)
1888 {
1889 int i, j;
1890 unsigned dim;
1891 int coalesce = -1;
1892
1893 if (bmap->n_div <= 1)
1894 return -1;
1895 dim = isl_dim_total(bmap->dim);
1896 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1897 return -1;
1898 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1899 bmap->n_div - div - 1) != -1)
1900 return -1;
1901 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1902 dim + bmap->n_div))
1903 return -1;
1904
1905 for (i = 0; i < bmap->n_div; ++i) {
1906 if (isl_int_is_zero(bmap->div[i][0]))
1907 continue;
1908 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
1909 return -1;
1910 }
1911
1912 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1913 if (isl_int_is_neg(bmap->ineq[l][0])) {
1914 isl_int_sub(bmap->ineq[l][0],
1915 bmap->ineq[l][0], bmap->ineq[u][0]);
1916 bmap = isl_basic_map_copy(bmap);
1917 bmap = isl_basic_map_set_to_empty(bmap);
1918 isl_basic_map_free(bmap);
1919 return -1;
1920 }
1921 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1922 for (i = 0; i < bmap->n_div; ++i) {
1923 if (i == div)
1924 continue;
1925 if (!pairs[i])
1926 continue;
1927 for (j = 0; j < bmap->n_div; ++j) {
1928 if (isl_int_is_zero(bmap->div[j][0]))
1929 continue;
1930 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
1931 break;
1932 }
1933 if (j < bmap->n_div)
1934 continue;
1935 for (j = 0; j < bmap->n_ineq; ++j) {
1936 int valid;
1937 if (j == l || j == u)
1938 continue;
1939 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
1940 continue;
1941 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
1942 break;
1943 isl_int_mul(bmap->ineq[j][1 + dim + div],
1944 bmap->ineq[j][1 + dim + div],
1945 bmap->ineq[l][0]);
1946 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
1947 bmap->ineq[j][1 + dim + i]);
1948 isl_int_divexact(bmap->ineq[j][1 + dim + div],
1949 bmap->ineq[j][1 + dim + div],
1950 bmap->ineq[l][0]);
1951 if (!valid)
1952 break;
1953 }
1954 if (j < bmap->n_ineq)
1955 continue;
1956 coalesce = i;
1957 break;
1958 }
1959 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1960 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1961 return coalesce;
1962 }
1963
1964 /* Given a lower and an upper bound on div i, construct an inequality
1965 * that when nonnegative ensures that this pair of bounds always allows
1966 * for an integer value of the given div.
1967 * The lower bound is inequality l, while the upper bound is inequality u.
1968 * The constructed inequality is stored in ineq.
1969 * g, fl, fu are temporary scalars.
1970 *
1971 * Let the upper bound be
1972 *
1973 * -n_u a + e_u >= 0
1974 *
1975 * and the lower bound
1976 *
1977 * n_l a + e_l >= 0
1978 *
1979 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1980 * We have
1981 *
1982 * - f_u e_l <= f_u f_l g a <= f_l e_u
1983 *
1984 * Since all variables are integer valued, this is equivalent to
1985 *
1986 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1987 *
1988 * If this interval is at least f_u f_l g, then it contains at least
1989 * one integer value for a.
1990 * That is, the test constraint is
1991 *
1992 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
1993 */
1994 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
1995 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
1996 {
1997 unsigned dim;
1998 dim = isl_dim_total(bmap->dim);
1999
2000 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2001 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2002 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2003 isl_int_neg(fu, fu);
2004 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2005 1 + dim + bmap->n_div);
2006 isl_int_add(ineq[0], ineq[0], fl);
2007 isl_int_add(ineq[0], ineq[0], fu);
2008 isl_int_sub_ui(ineq[0], ineq[0], 1);
2009 isl_int_mul(g, g, fl);
2010 isl_int_mul(g, g, fu);
2011 isl_int_sub(ineq[0], ineq[0], g);
2012 }
2013
2014 /* Remove more kinds of divs that are not strictly needed.
2015 * In particular, if all pairs of lower and upper bounds on a div
2016 * are such that they allow at least one integer value of the div,
2017 * the we can eliminate the div using Fourier-Motzkin without
2018 * introducing any spurious solutions.
2019 */
2020 static struct isl_basic_map *drop_more_redundant_divs(
2021 struct isl_basic_map *bmap, int *pairs, int n)
2022 {
2023 struct isl_tab *tab = NULL;
2024 struct isl_vec *vec = NULL;
2025 unsigned dim;
2026 int remove = -1;
2027 isl_int g, fl, fu;
2028
2029 isl_int_init(g);
2030 isl_int_init(fl);
2031 isl_int_init(fu);
2032
2033 if (!bmap)
2034 goto error;
2035
2036 dim = isl_dim_total(bmap->dim);
2037 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2038 if (!vec)
2039 goto error;
2040
2041 tab = isl_tab_from_basic_map(bmap);
2042
2043 while (n > 0) {
2044 int i, l, u;
2045 int best = -1;
2046 enum isl_lp_result res;
2047
2048 for (i = 0; i < bmap->n_div; ++i) {
2049 if (!pairs[i])
2050 continue;
2051 if (best >= 0 && pairs[best] <= pairs[i])
2052 continue;
2053 best = i;
2054 }
2055
2056 i = best;
2057 for (l = 0; l < bmap->n_ineq; ++l) {
2058 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2059 continue;
2060 for (u = 0; u < bmap->n_ineq; ++u) {
2061 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2062 continue;
2063 construct_test_ineq(bmap, i, l, u,
2064 vec->el, g, fl, fu);
2065 res = isl_tab_min(tab, vec->el,
2066 bmap->ctx->one, &g, NULL, 0);
2067 if (res == isl_lp_error)
2068 goto error;
2069 if (res == isl_lp_empty) {
2070 bmap = isl_basic_map_set_to_empty(bmap);
2071 break;
2072 }
2073 if (res != isl_lp_ok || isl_int_is_neg(g))
2074 break;
2075 }
2076 if (u < bmap->n_ineq)
2077 break;
2078 }
2079 if (l == bmap->n_ineq) {
2080 remove = i;
2081 break;
2082 }
2083 pairs[i] = 0;
2084 --n;
2085 }
2086
2087 isl_tab_free(tab);
2088 isl_vec_free(vec);
2089
2090 isl_int_clear(g);
2091 isl_int_clear(fl);
2092 isl_int_clear(fu);
2093
2094 free(pairs);
2095
2096 if (remove < 0)
2097 return bmap;
2098
2099 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2100 return isl_basic_map_drop_redundant_divs(bmap);
2101 error:
2102 free(pairs);
2103 isl_basic_map_free(bmap);
2104 isl_tab_free(tab);
2105 isl_vec_free(vec);
2106 isl_int_clear(g);
2107 isl_int_clear(fl);
2108 isl_int_clear(fu);
2109 return NULL;
2110 }
2111
2112 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2113 * and the upper bound u, div1 always occurs together with div2 in the form
2114 * (div1 + m div2), where m is the constant range on the variable div1
2115 * allowed by l and u, replace the pair div1 and div2 by a single
2116 * div that is equal to div1 + m div2.
2117 *
2118 * The new div will appear in the location that contains div2.
2119 * We need to modify all constraints that contain
2120 * div2 = (div - div1) / m
2121 * (If a constraint does not contain div2, it will also not contain div1.)
2122 * If the constraint also contains div1, then we know they appear
2123 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2124 * i.e., the coefficient of div is f.
2125 *
2126 * Otherwise, we first need to introduce div1 into the constraint.
2127 * Let the l be
2128 *
2129 * div1 + f >=0
2130 *
2131 * and u
2132 *
2133 * -div1 + f' >= 0
2134 *
2135 * A lower bound on div2
2136 *
2137 * n div2 + t >= 0
2138 *
2139 * can be replaced by
2140 *
2141 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2142 *
2143 * with g = gcd(m,n).
2144 * An upper bound
2145 *
2146 * -n div2 + t >= 0
2147 *
2148 * can be replaced by
2149 *
2150 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2151 *
2152 * These constraint are those that we would obtain from eliminating
2153 * div1 using Fourier-Motzkin.
2154 *
2155 * After all constraints have been modified, we drop the lower and upper
2156 * bound and then drop div1.
2157 */
2158 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2159 unsigned div1, unsigned div2, unsigned l, unsigned u)
2160 {
2161 isl_int a;
2162 isl_int b;
2163 isl_int m;
2164 unsigned dim, total;
2165 int i;
2166
2167 dim = isl_dim_total(bmap->dim);
2168 total = 1 + dim + bmap->n_div;
2169
2170 isl_int_init(a);
2171 isl_int_init(b);
2172 isl_int_init(m);
2173 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2174 isl_int_add_ui(m, m, 1);
2175
2176 for (i = 0; i < bmap->n_ineq; ++i) {
2177 if (i == l || i == u)
2178 continue;
2179 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2180 continue;
2181 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2182 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2183 isl_int_divexact(a, m, b);
2184 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2185 if (isl_int_is_pos(b)) {
2186 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2187 b, bmap->ineq[l], total);
2188 } else {
2189 isl_int_neg(b, b);
2190 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2191 b, bmap->ineq[u], total);
2192 }
2193 }
2194 isl_int_set(bmap->ineq[i][1 + dim + div2],
2195 bmap->ineq[i][1 + dim + div1]);
2196 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2197 }
2198
2199 isl_int_clear(a);
2200 isl_int_clear(b);
2201 isl_int_clear(m);
2202 if (l > u) {
2203 isl_basic_map_drop_inequality(bmap, l);
2204 isl_basic_map_drop_inequality(bmap, u);
2205 } else {
2206 isl_basic_map_drop_inequality(bmap, u);
2207 isl_basic_map_drop_inequality(bmap, l);
2208 }
2209 bmap = isl_basic_map_drop_div(bmap, div1);
2210 return bmap;
2211 }
2212
2213 /* First check if we can coalesce any pair of divs and
2214 * then continue with dropping more redundant divs.
2215 *
2216 * We loop over all pairs of lower and upper bounds on a div
2217 * with coefficient 1 and -1, respectively, check if there
2218 * is any other div "c" with which we can coalesce the div
2219 * and if so, perform the coalescing.
2220 */
2221 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2222 struct isl_basic_map *bmap, int *pairs, int n)
2223 {
2224 int i, l, u;
2225 unsigned dim;
2226
2227 dim = isl_dim_total(bmap->dim);
2228
2229 for (i = 0; i < bmap->n_div; ++i) {
2230 if (!pairs[i])
2231 continue;
2232 for (l = 0; l < bmap->n_ineq; ++l) {
2233 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2234 continue;
2235 for (u = 0; u < bmap->n_ineq; ++u) {
2236 int c;
2237
2238 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2239 continue;
2240 c = div_find_coalesce(bmap, pairs, i, l, u);
2241 if (c < 0)
2242 continue;
2243 free(pairs);
2244 bmap = coalesce_divs(bmap, i, c, l, u);
2245 return isl_basic_map_drop_redundant_divs(bmap);
2246 }
2247 }
2248 }
2249
2250 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2251 return bmap;
2252
2253 return drop_more_redundant_divs(bmap, pairs, n);
2254 }
2255
2256 /* Remove divs that are not strictly needed.
2257 * In particular, if a div only occurs positively (or negatively)
2258 * in constraints, then it can simply be dropped.
2259 * Also, if a div occurs only occurs in two constraints and if moreover
2260 * those two constraints are opposite to each other, except for the constant
2261 * term and if the sum of the constant terms is such that for any value
2262 * of the other values, there is always at least one integer value of the
2263 * div, i.e., if one plus this sum is greater than or equal to
2264 * the (absolute value) of the coefficent of the div in the constraints,
2265 * then we can also simply drop the div.
2266 *
2267 * If any divs are left after these simple checks then we move on
2268 * to more complicated cases in drop_more_redundant_divs.
2269 */
2270 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2271 struct isl_basic_map *bmap)
2272 {
2273 int i, j;
2274 unsigned off;
2275 int *pairs = NULL;
2276 int n = 0;
2277
2278 if (!bmap)
2279 goto error;
2280
2281 off = isl_dim_total(bmap->dim);
2282 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2283 if (!pairs)
2284 goto error;
2285
2286 for (i = 0; i < bmap->n_div; ++i) {
2287 int pos, neg;
2288 int last_pos, last_neg;
2289 int redundant;
2290 int defined;
2291
2292 defined = !isl_int_is_zero(bmap->div[i][0]);
2293 for (j = 0; j < bmap->n_eq; ++j)
2294 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2295 break;
2296 if (j < bmap->n_eq)
2297 continue;
2298 ++n;
2299 pos = neg = 0;
2300 for (j = 0; j < bmap->n_ineq; ++j) {
2301 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2302 last_pos = j;
2303 ++pos;
2304 }
2305 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2306 last_neg = j;
2307 ++neg;
2308 }
2309 }
2310 pairs[i] = pos * neg;
2311 if (pairs[i] == 0) {
2312 for (j = bmap->n_ineq - 1; j >= 0; --j)
2313 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2314 isl_basic_map_drop_inequality(bmap, j);
2315 bmap = isl_basic_map_drop_div(bmap, i);
2316 free(pairs);
2317 return isl_basic_map_drop_redundant_divs(bmap);
2318 }
2319 if (pairs[i] != 1)
2320 continue;
2321 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2322 bmap->ineq[last_neg] + 1,
2323 off + bmap->n_div))
2324 continue;
2325
2326 isl_int_add(bmap->ineq[last_pos][0],
2327 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2328 isl_int_add_ui(bmap->ineq[last_pos][0],
2329 bmap->ineq[last_pos][0], 1);
2330 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2331 bmap->ineq[last_pos][1+off+i]);
2332 isl_int_sub_ui(bmap->ineq[last_pos][0],
2333 bmap->ineq[last_pos][0], 1);
2334 isl_int_sub(bmap->ineq[last_pos][0],
2335 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2336 if (!redundant) {
2337 if (defined ||
2338 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2339 pairs[i] = 0;
2340 --n;
2341 continue;
2342 }
2343 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2344 bmap = isl_basic_map_simplify(bmap);
2345 free(pairs);
2346 return isl_basic_map_drop_redundant_divs(bmap);
2347 }
2348 if (last_pos > last_neg) {
2349 isl_basic_map_drop_inequality(bmap, last_pos);
2350 isl_basic_map_drop_inequality(bmap, last_neg);
2351 } else {
2352 isl_basic_map_drop_inequality(bmap, last_neg);
2353 isl_basic_map_drop_inequality(bmap, last_pos);
2354 }
2355 bmap = isl_basic_map_drop_div(bmap, i);
2356 free(pairs);
2357 return isl_basic_map_drop_redundant_divs(bmap);
2358 }
2359
2360 if (n > 0)
2361 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2362
2363 free(pairs);
2364 return bmap;
2365 error:
2366 free(pairs);
2367 isl_basic_map_free(bmap);
2368 return NULL;
2369 }
2370
2371 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2372 struct isl_basic_set *bset)
2373 {
2374 return (struct isl_basic_set *)
2375 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2376 }
2377
2378 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2379 {
2380 int i;
2381
2382 if (!map)
2383 return NULL;
2384 for (i = 0; i < map->n; ++i) {
2385 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2386 if (!map->p[i])
2387 goto error;
2388 }
2389 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2390 return map;
2391 error:
2392 isl_map_free(map);
2393 return NULL;
2394 }
2395
2396 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2397 {
2398 return (struct isl_set *)
2399 isl_map_drop_redundant_divs((struct isl_map *)set);
2400 }
Integer set library