?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
isl_tab.h: fix typo in comment
[isl.git] / isl_map_simplify.c
blob41aeb1e0294883aafc68032308cbb5d149979dd2
1 #include "isl_equalities.h"
2 #include "isl_map.h"
3 #include "isl_map_private.h"
4 #include "isl_tab.h"
5
6 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
7 {
8 isl_int *t = bmap->eq[a];
9 bmap->eq[a] = bmap->eq[b];
10 bmap->eq[b] = t;
11 }
12
13 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
14 {
15 if (a != b) {
16 isl_int *t = bmap->ineq[a];
17 bmap->ineq[a] = bmap->ineq[b];
18 bmap->ineq[b] = t;
19 }
20 }
21
22 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
23 {
24 swap_inequality((struct isl_basic_map *)bset, a, b);
25 }
26
27 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
28 {
29 isl_seq_cpy(c, c + n, rem);
30 isl_seq_clr(c + rem, n);
31 }
32
33 /* Drop n dimensions starting at first.
34 *
35 * In principle, this frees up some extra variables as the number
36 * of columns remains constant, but we would have to extend
37 * the div array too as the number of rows in this array is assumed
38 * to be equal to extra.
39 */
40 struct isl_basic_set *isl_basic_set_drop_dims(
41 struct isl_basic_set *bset, unsigned first, unsigned n)
42 {
43 int i;
44
45 if (!bset)
46 goto error;
47
48 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
49
50 if (n == 0)
51 return bset;
52
53 bset = isl_basic_set_cow(bset);
54 if (!bset)
55 return NULL;
56
57 for (i = 0; i < bset->n_eq; ++i)
58 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
59 (bset->dim->n_out-first-n)+bset->extra);
60
61 for (i = 0; i < bset->n_ineq; ++i)
62 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
63 (bset->dim->n_out-first-n)+bset->extra);
64
65 for (i = 0; i < bset->n_div; ++i)
66 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
67 (bset->dim->n_out-first-n)+bset->extra);
68
69 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
70 if (!bset->dim)
71 goto error;
72
73 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
74 bset = isl_basic_set_simplify(bset);
75 return isl_basic_set_finalize(bset);
76 error:
77 isl_basic_set_free(bset);
78 return NULL;
79 }
80
81 struct isl_set *isl_set_drop_dims(
82 struct isl_set *set, unsigned first, unsigned n)
83 {
84 int i;
85
86 if (!set)
87 goto error;
88
89 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
90
91 if (n == 0)
92 return set;
93 set = isl_set_cow(set);
94 if (!set)
95 goto error;
96 set->dim = isl_dim_drop_outputs(set->dim, first, n);
97 if (!set->dim)
98 goto error;
99
100 for (i = 0; i < set->n; ++i) {
101 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
102 if (!set->p[i])
103 goto error;
104 }
105
106 ISL_F_CLR(set, ISL_SET_NORMALIZED);
107 return set;
108 error:
109 isl_set_free(set);
110 return NULL;
111 }
112
113 /* Move "n" divs starting at "first" to the end of the list of divs.
114 */
115 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
116 unsigned first, unsigned n)
117 {
118 isl_int **div;
119 int i;
120
121 if (first + n == bmap->n_div)
122 return bmap;
123
124 div = isl_alloc_array(bmap->ctx, isl_int *, n);
125 if (!div)
126 goto error;
127 for (i = 0; i < n; ++i)
128 div[i] = bmap->div[first + i];
129 for (i = 0; i < bmap->n_div - first - n; ++i)
130 bmap->div[first + i] = bmap->div[first + n + i];
131 for (i = 0; i < n; ++i)
132 bmap->div[bmap->n_div - n + i] = div[i];
133 free(div);
134 return bmap;
135 error:
136 isl_basic_map_free(bmap);
137 return NULL;
138 }
139
140 /* Drop "n" dimensions of type "type" starting at "first".
141 *
142 * In principle, this frees up some extra variables as the number
143 * of columns remains constant, but we would have to extend
144 * the div array too as the number of rows in this array is assumed
145 * to be equal to extra.
146 */
147 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
148 enum isl_dim_type type, unsigned first, unsigned n)
149 {
150 int i;
151 unsigned dim;
152 unsigned offset;
153 unsigned left;
154
155 if (!bmap)
156 goto error;
157
158 dim = isl_basic_map_dim(bmap, type);
159 isl_assert(bmap->ctx, first + n <= dim, goto error);
160
161 if (n == 0)
162 return bmap;
163
164 bmap = isl_basic_map_cow(bmap);
165 if (!bmap)
166 return NULL;
167
168 offset = isl_basic_map_offset(bmap, type) + first;
169 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
170 for (i = 0; i < bmap->n_eq; ++i)
171 constraint_drop_vars(bmap->eq[i]+offset, n, left);
172
173 for (i = 0; i < bmap->n_ineq; ++i)
174 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
175
176 for (i = 0; i < bmap->n_div; ++i)
177 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
178
179 if (type == isl_dim_div) {
180 bmap = move_divs_last(bmap, first, n);
181 if (!bmap)
182 goto error;
183 isl_basic_map_free_div(bmap, n);
184 } else
185 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
186 if (!bmap->dim)
187 goto error;
188
189 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
190 bmap = isl_basic_map_simplify(bmap);
191 return isl_basic_map_finalize(bmap);
192 error:
193 isl_basic_map_free(bmap);
194 return NULL;
195 }
196
197 struct isl_basic_map *isl_basic_map_drop_inputs(
198 struct isl_basic_map *bmap, unsigned first, unsigned n)
199 {
200 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
201 }
202
203 struct isl_map *isl_map_drop(struct isl_map *map,
204 enum isl_dim_type type, unsigned first, unsigned n)
205 {
206 int i;
207
208 if (!map)
209 goto error;
210
211 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
212
213 if (n == 0)
214 return map;
215 map = isl_map_cow(map);
216 if (!map)
217 goto error;
218 map->dim = isl_dim_drop(map->dim, type, first, n);
219 if (!map->dim)
220 goto error;
221
222 for (i = 0; i < map->n; ++i) {
223 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
224 if (!map->p[i])
225 goto error;
226 }
227 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
228
229 return map;
230 error:
231 isl_map_free(map);
232 return NULL;
233 }
234
235 struct isl_map *isl_map_drop_inputs(
236 struct isl_map *map, unsigned first, unsigned n)
237 {
238 return isl_map_drop(map, isl_dim_in, first, n);
239 }
240
241 /*
242 * We don't cow, as the div is assumed to be redundant.
243 */
244 static struct isl_basic_map *isl_basic_map_drop_div(
245 struct isl_basic_map *bmap, unsigned div)
246 {
247 int i;
248 unsigned pos;
249
250 if (!bmap)
251 goto error;
252
253 pos = 1 + isl_dim_total(bmap->dim) + div;
254
255 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
256
257 for (i = 0; i < bmap->n_eq; ++i)
258 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
259
260 for (i = 0; i < bmap->n_ineq; ++i) {
261 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
262 isl_basic_map_drop_inequality(bmap, i);
263 --i;
264 continue;
265 }
266 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
267 }
268
269 for (i = 0; i < bmap->n_div; ++i)
270 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
271
272 if (div != bmap->n_div - 1) {
273 int j;
274 isl_int *t = bmap->div[div];
275
276 for (j = div; j < bmap->n_div - 1; ++j)
277 bmap->div[j] = bmap->div[j+1];
278
279 bmap->div[bmap->n_div - 1] = t;
280 }
281 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
282 isl_basic_map_free_div(bmap, 1);
283
284 return bmap;
285 error:
286 isl_basic_map_free(bmap);
287 return NULL;
288 }
289
290 struct isl_basic_map *isl_basic_map_normalize_constraints(
291 struct isl_basic_map *bmap)
292 {
293 int i;
294 isl_int gcd;
295 unsigned total = isl_basic_map_total_dim(bmap);
296
297 isl_int_init(gcd);
298 for (i = bmap->n_eq - 1; i >= 0; --i) {
299 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
300 if (isl_int_is_zero(gcd)) {
301 if (!isl_int_is_zero(bmap->eq[i][0])) {
302 bmap = isl_basic_map_set_to_empty(bmap);
303 break;
304 }
305 isl_basic_map_drop_equality(bmap, i);
306 continue;
307 }
308 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
309 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
310 if (isl_int_is_one(gcd))
311 continue;
312 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
313 bmap = isl_basic_map_set_to_empty(bmap);
314 break;
315 }
316 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
317 }
318
319 for (i = bmap->n_ineq - 1; i >= 0; --i) {
320 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
321 if (isl_int_is_zero(gcd)) {
322 if (isl_int_is_neg(bmap->ineq[i][0])) {
323 bmap = isl_basic_map_set_to_empty(bmap);
324 break;
325 }
326 isl_basic_map_drop_inequality(bmap, i);
327 continue;
328 }
329 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
330 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
331 if (isl_int_is_one(gcd))
332 continue;
333 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
334 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
335 }
336 isl_int_clear(gcd);
337
338 return bmap;
339 }
340
341 struct isl_basic_set *isl_basic_set_normalize_constraints(
342 struct isl_basic_set *bset)
343 {
344 (struct isl_basic_set *)isl_basic_map_normalize_constraints(
345 (struct isl_basic_map *)bset);
346 }
347
348 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
349 {
350 int i;
351 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
352 unsigned len;
353 len = 1 + isl_basic_map_total_dim(bmap);
354
355 for (i = 0; i < bmap->n_eq; ++i)
356 if (bmap->eq[i] != eq)
357 isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
358
359 for (i = 0; i < bmap->n_ineq; ++i)
360 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
361
362 /* We need to be careful about circular definitions,
363 * so for now we just remove the definitions of other divs that
364 * depend on this div and (possibly) recompute them later.
365 */
366 for (i = 0; i < bmap->n_div; ++i)
367 if (!isl_int_is_zero(bmap->div[i][0]) &&
368 !isl_int_is_zero(bmap->div[i][1 + pos]))
369 isl_seq_clr(bmap->div[i], 1 + len);
370
371 isl_basic_map_drop_div(bmap, div);
372 }
373
374 /* Elimininate divs based on equalities
375 */
376 static struct isl_basic_map *eliminate_divs_eq(
377 struct isl_basic_map *bmap, int *progress)
378 {
379 int d;
380 int i;
381 int modified = 0;
382 unsigned off;
383
384 if (!bmap)
385 return NULL;
386
387 off = 1 + isl_dim_total(bmap->dim);
388
389 for (d = bmap->n_div - 1; d >= 0 ; --d) {
390 for (i = 0; i < bmap->n_eq; ++i) {
391 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
392 !isl_int_is_negone(bmap->eq[i][off + d]))
393 continue;
394 modified = 1;
395 *progress = 1;
396 eliminate_div(bmap, bmap->eq[i], d);
397 isl_basic_map_drop_equality(bmap, i);
398 break;
399 }
400 }
401 if (modified)
402 return eliminate_divs_eq(bmap, progress);
403 return bmap;
404 }
405
406 /* Elimininate divs based on inequalities
407 */
408 static struct isl_basic_map *eliminate_divs_ineq(
409 struct isl_basic_map *bmap, int *progress)
410 {
411 int d;
412 int i;
413 unsigned off;
414 struct isl_ctx *ctx;
415
416 if (!bmap)
417 return NULL;
418
419 ctx = bmap->ctx;
420 off = 1 + isl_dim_total(bmap->dim);
421
422 for (d = bmap->n_div - 1; d >= 0 ; --d) {
423 for (i = 0; i < bmap->n_eq; ++i)
424 if (!isl_int_is_zero(bmap->eq[i][off + d]))
425 break;
426 if (i < bmap->n_eq)
427 continue;
428 for (i = 0; i < bmap->n_ineq; ++i)
429 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
430 break;
431 if (i < bmap->n_ineq)
432 continue;
433 *progress = 1;
434 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
435 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
436 break;
437 bmap = isl_basic_map_drop_div(bmap, d);
438 if (!bmap)
439 break;
440 }
441 return bmap;
442 }
443
444 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
445 unsigned pos, isl_int *eq, int *progress)
446 {
447 unsigned total;
448 int k;
449 int contains_divs;
450
451 total = isl_basic_map_total_dim(bmap);
452 contains_divs =
453 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
454 bmap->n_div) != -1;
455 for (k = 0; k < bmap->n_eq; ++k) {
456 if (bmap->eq[k] == eq)
457 continue;
458 if (isl_int_is_zero(bmap->eq[k][1+pos]))
459 continue;
460 if (progress)
461 *progress = 1;
462 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
463 }
464
465 for (k = 0; k < bmap->n_ineq; ++k) {
466 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
467 continue;
468 if (progress)
469 *progress = 1;
470 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
471 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
472 }
473
474 for (k = 0; k < bmap->n_div; ++k) {
475 if (isl_int_is_zero(bmap->div[k][0]))
476 continue;
477 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
478 continue;
479 if (progress)
480 *progress = 1;
481 /* We need to be careful about circular definitions,
482 * so for now we just remove the definition of div k
483 * if the equality contains any divs.
484 */
485 if (contains_divs)
486 isl_seq_clr(bmap->div[k], 1 + total);
487 else
488 isl_seq_elim(bmap->div[k]+1, eq,
489 1+pos, 1+total, &bmap->div[k][0]);
490 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
491 }
492 }
493
494 struct isl_basic_map *isl_basic_map_gauss(
495 struct isl_basic_map *bmap, int *progress)
496 {
497 int k;
498 int done;
499 int last_var;
500 unsigned total_var;
501 unsigned total;
502
503 if (!bmap)
504 return NULL;
505
506 total = isl_basic_map_total_dim(bmap);
507 total_var = total - bmap->n_div;
508
509 last_var = total - 1;
510 for (done = 0; done < bmap->n_eq; ++done) {
511 for (; last_var >= 0; --last_var) {
512 for (k = done; k < bmap->n_eq; ++k)
513 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
514 break;
515 if (k < bmap->n_eq)
516 break;
517 }
518 if (last_var < 0)
519 break;
520 if (k != done)
521 swap_equality(bmap, k, done);
522 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
523 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
524
525 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
526 progress);
527
528 if (last_var >= total_var &&
529 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
530 unsigned div = last_var - total_var;
531 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
532 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
533 isl_int_set(bmap->div[div][0],
534 bmap->eq[done][1+last_var]);
535 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
536 }
537 }
538 if (done == bmap->n_eq)
539 return bmap;
540 for (k = done; k < bmap->n_eq; ++k) {
541 if (isl_int_is_zero(bmap->eq[k][0]))
542 continue;
543 return isl_basic_map_set_to_empty(bmap);
544 }
545 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
546 return bmap;
547 }
548
549 struct isl_basic_set *isl_basic_set_gauss(
550 struct isl_basic_set *bset, int *progress)
551 {
552 return (struct isl_basic_set*)isl_basic_map_gauss(
553 (struct isl_basic_map *)bset, progress);
554 }
555
556
557 static unsigned int round_up(unsigned int v)
558 {
559 int old_v = v;
560
561 while (v) {
562 old_v = v;
563 v ^= v & -v;
564 }
565 return old_v << 1;
566 }
567
568 static int hash_index(isl_int ***index, unsigned int size, int bits,
569 struct isl_basic_map *bmap, int k)
570 {
571 int h;
572 unsigned total = isl_basic_map_total_dim(bmap);
573 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
574 for (h = hash; index[h]; h = (h+1) % size)
575 if (&bmap->ineq[k] != index[h] &&
576 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
577 break;
578 return h;
579 }
580
581 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
582 struct isl_basic_set *bset, int k)
583 {
584 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
585 }
586
587 /* If we can eliminate more than one div, then we need to make
588 * sure we do it from last div to first div, in order not to
589 * change the position of the other divs that still need to
590 * be removed.
591 */
592 static struct isl_basic_map *remove_duplicate_divs(
593 struct isl_basic_map *bmap, int *progress)
594 {
595 unsigned int size;
596 int *index;
597 int *elim_for;
598 int k, l, h;
599 int bits;
600 struct isl_blk eq;
601 unsigned total_var = isl_dim_total(bmap->dim);
602 unsigned total = total_var + bmap->n_div;
603 struct isl_ctx *ctx;
604
605 if (bmap->n_div <= 1)
606 return bmap;
607
608 ctx = bmap->ctx;
609 for (k = bmap->n_div - 1; k >= 0; --k)
610 if (!isl_int_is_zero(bmap->div[k][0]))
611 break;
612 if (k <= 0)
613 return bmap;
614
615 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
616 size = round_up(4 * bmap->n_div / 3 - 1);
617 bits = ffs(size) - 1;
618 index = isl_calloc_array(ctx, int, size);
619 if (!index)
620 return bmap;
621 eq = isl_blk_alloc(ctx, 1+total);
622 if (isl_blk_is_error(eq))
623 goto out;
624
625 isl_seq_clr(eq.data, 1+total);
626 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
627 for (--k; k >= 0; --k) {
628 uint32_t hash;
629
630 if (isl_int_is_zero(bmap->div[k][0]))
631 continue;
632
633 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
634 for (h = hash; index[h]; h = (h+1) % size)
635 if (isl_seq_eq(bmap->div[k],
636 bmap->div[index[h]-1], 2+total))
637 break;
638 if (index[h]) {
639 *progress = 1;
640 l = index[h] - 1;
641 elim_for[l] = k + 1;
642 }
643 index[h] = k+1;
644 }
645 for (l = bmap->n_div - 1; l >= 0; --l) {
646 if (!elim_for[l])
647 continue;
648 k = elim_for[l] - 1;
649 isl_int_set_si(eq.data[1+total_var+k], -1);
650 isl_int_set_si(eq.data[1+total_var+l], 1);
651 eliminate_div(bmap, eq.data, l);
652 isl_int_set_si(eq.data[1+total_var+k], 0);
653 isl_int_set_si(eq.data[1+total_var+l], 0);
654 }
655
656 isl_blk_free(ctx, eq);
657 out:
658 free(index);
659 free(elim_for);
660 return bmap;
661 }
662
663 static int n_pure_div_eq(struct isl_basic_map *bmap)
664 {
665 int i, j;
666 unsigned total;
667
668 total = isl_dim_total(bmap->dim);
669 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
670 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
671 --j;
672 if (j < 0)
673 break;
674 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
675 return 0;
676 }
677 return i;
678 }
679
680 /* Normalize divs that appear in equalities.
681 *
682 * In particular, we assume that bmap contains some equalities
683 * of the form
684 *
685 * a x = m * e_i
686 *
687 * and we want to replace the set of e_i by a minimal set and
688 * such that the new e_i have a canonical representation in terms
689 * of the vector x.
690 * If any of the equalities involves more than one divs, then
691 * we currently simply bail out.
692 *
693 * Let us first additionally assume that all equalities involve
694 * a div. The equalities then express modulo constraints on the
695 * remaining variables and we can use "parameter compression"
696 * to find a minimal set of constraints. The result is a transformation
697 *
698 * x = T(x') = x_0 + G x'
699 *
700 * with G a lower-triangular matrix with all elements below the diagonal
701 * non-negative and smaller than the diagonal element on the same row.
702 * We first normalize x_0 by making the same property hold in the affine
703 * T matrix.
704 * The rows i of G with a 1 on the diagonal do not impose any modulo
705 * constraint and simply express x_i = x'_i.
706 * For each of the remaining rows i, we introduce a div and a corresponding
707 * equality. In particular
708 *
709 * g_ii e_j = x_i - g_i(x')
710 *
711 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
712 * corresponding div (if g_kk != 1).
713 *
714 * If there are any equalities not involving any div, then we
715 * first apply a variable compression on the variables x:
716 *
717 * x = C x'' x'' = C_2 x
718 *
719 * and perform the above parameter compression on A C instead of on A.
720 * The resulting compression is then of the form
721 *
722 * x'' = T(x') = x_0 + G x'
723 *
724 * and in constructing the new divs and the corresponding equalities,
725 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
726 * by the corresponding row from C_2.
727 */
728 static struct isl_basic_map *normalize_divs(
729 struct isl_basic_map *bmap, int *progress)
730 {
731 int i, j, k;
732 int total;
733 int div_eq;
734 struct isl_mat *B;
735 struct isl_vec *d;
736 struct isl_mat *T = NULL;
737 struct isl_mat *C = NULL;
738 struct isl_mat *C2 = NULL;
739 isl_int v;
740 int *pos;
741 int dropped, needed;
742
743 if (!bmap)
744 return NULL;
745
746 if (bmap->n_div == 0)
747 return bmap;
748
749 if (bmap->n_eq == 0)
750 return bmap;
751
752 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
753 return bmap;
754
755 total = isl_dim_total(bmap->dim);
756 div_eq = n_pure_div_eq(bmap);
757 if (div_eq == 0)
758 return bmap;
759
760 if (div_eq < bmap->n_eq) {
761 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
762 bmap->n_eq - div_eq, 0, 1 + total);
763 C = isl_mat_variable_compression(B, &C2);
764 if (!C || !C2)
765 goto error;
766 if (C->n_col == 0) {
767 bmap = isl_basic_map_set_to_empty(bmap);
768 isl_mat_free(C);
769 isl_mat_free(C2);
770 goto done;
771 }
772 }
773
774 d = isl_vec_alloc(bmap->ctx, div_eq);
775 if (!d)
776 goto error;
777 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
778 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
779 --j;
780 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
781 }
782 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
783
784 if (C) {
785 B = isl_mat_product(B, C);
786 C = NULL;
787 }
788
789 T = isl_mat_parameter_compression(B, d);
790 if (!T)
791 goto error;
792 if (T->n_col == 0) {
793 bmap = isl_basic_map_set_to_empty(bmap);
794 isl_mat_free(C2);
795 isl_mat_free(T);
796 goto done;
797 }
798 isl_int_init(v);
799 for (i = 0; i < T->n_row - 1; ++i) {
800 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
801 if (isl_int_is_zero(v))
802 continue;
803 isl_mat_col_submul(T, 0, v, 1 + i);
804 }
805 isl_int_clear(v);
806 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
807 /* We have to be careful because dropping equalities may reorder them */
808 dropped = 0;
809 for (j = bmap->n_div - 1; j >= 0; --j) {
810 for (i = 0; i < bmap->n_eq; ++i)
811 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
812 break;
813 if (i < bmap->n_eq) {
814 bmap = isl_basic_map_drop_div(bmap, j);
815 isl_basic_map_drop_equality(bmap, i);
816 ++dropped;
817 }
818 }
819 pos[0] = 0;
820 needed = 0;
821 for (i = 1; i < T->n_row; ++i) {
822 if (isl_int_is_one(T->row[i][i]))
823 pos[i] = i;
824 else
825 needed++;
826 }
827 if (needed > dropped) {
828 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
829 needed, needed, 0);
830 if (!bmap)
831 goto error;
832 }
833 for (i = 1; i < T->n_row; ++i) {
834 if (isl_int_is_one(T->row[i][i]))
835 continue;
836 k = isl_basic_map_alloc_div(bmap);
837 pos[i] = 1 + total + k;
838 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
839 isl_int_set(bmap->div[k][0], T->row[i][i]);
840 if (C2)
841 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
842 else
843 isl_int_set_si(bmap->div[k][1 + i], 1);
844 for (j = 0; j < i; ++j) {
845 if (isl_int_is_zero(T->row[i][j]))
846 continue;
847 if (pos[j] < T->n_row && C2)
848 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
849 C2->row[pos[j]], 1 + total);
850 else
851 isl_int_neg(bmap->div[k][1 + pos[j]],
852 T->row[i][j]);
853 }
854 j = isl_basic_map_alloc_equality(bmap);
855 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
856 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
857 }
858 free(pos);
859 isl_mat_free(C2);
860 isl_mat_free(T);
861
862 if (progress)
863 *progress = 1;
864 done:
865 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
866
867 return bmap;
868 error:
869 isl_mat_free(C);
870 isl_mat_free(C2);
871 isl_mat_free(T);
872 return bmap;
873 }
874
875 static struct isl_basic_map *set_div_from_lower_bound(
876 struct isl_basic_map *bmap, int div, int ineq)
877 {
878 unsigned total = 1 + isl_dim_total(bmap->dim);
879
880 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
881 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
882 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
883 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
884 isl_int_set_si(bmap->div[div][1 + total + div], 0);
885
886 return bmap;
887 }
888
889 /* Check whether it is ok to define a div based on an inequality.
890 * To avoid the introduction of circular definitions of divs, we
891 * do not allow such a definition if the resulting expression would refer to
892 * any other undefined divs or if any known div is defined in
893 * terms of the unknown div.
894 */
895 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
896 int div, int ineq)
897 {
898 int j;
899 unsigned total = 1 + isl_dim_total(bmap->dim);
900
901 /* Not defined in terms of unknown divs */
902 for (j = 0; j < bmap->n_div; ++j) {
903 if (div == j)
904 continue;
905 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
906 continue;
907 if (isl_int_is_zero(bmap->div[j][0]))
908 return 0;
909 }
910
911 /* No other div defined in terms of this one => avoid loops */
912 for (j = 0; j < bmap->n_div; ++j) {
913 if (div == j)
914 continue;
915 if (isl_int_is_zero(bmap->div[j][0]))
916 continue;
917 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
918 return 0;
919 }
920
921 return 1;
922 }
923
924 /* Given two constraints "k" and "l" that are opposite to each other,
925 * except for the constant term, check if we can use them
926 * to obtain an expression for one of the hitherto unknown divs.
927 * "sum" is the sum of the constant terms of the constraints.
928 * If this sum is strictly smaller than the coefficient of one
929 * of the divs, then this pair can be used define the div.
930 * To avoid the introduction of circular definitions of divs, we
931 * do not use the pair if the resulting expression would refer to
932 * any other undefined divs or if any known div is defined in
933 * terms of the unknown div.
934 */
935 static struct isl_basic_map *check_for_div_constraints(
936 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
937 {
938 int i, j;
939 unsigned total = 1 + isl_dim_total(bmap->dim);
940
941 for (i = 0; i < bmap->n_div; ++i) {
942 if (!isl_int_is_zero(bmap->div[i][0]))
943 continue;
944 if (isl_int_is_zero(bmap->ineq[k][total + i]))
945 continue;
946 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
947 continue;
948 if (!ok_to_set_div_from_bound(bmap, i, k))
949 break;
950 if (isl_int_is_pos(bmap->ineq[k][total + i]))
951 bmap = set_div_from_lower_bound(bmap, i, k);
952 else
953 bmap = set_div_from_lower_bound(bmap, i, l);
954 if (progress)
955 *progress = 1;
956 break;
957 }
958 return bmap;
959 }
960
961 static struct isl_basic_map *remove_duplicate_constraints(
962 struct isl_basic_map *bmap, int *progress)
963 {
964 unsigned int size;
965 isl_int ***index;
966 int k, l, h;
967 int bits;
968 unsigned total = isl_basic_map_total_dim(bmap);
969 isl_int sum;
970
971 if (bmap->n_ineq <= 1)
972 return bmap;
973
974 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
975 bits = ffs(size) - 1;
976 index = isl_calloc_array(ctx, isl_int **, size);
977 if (!index)
978 return bmap;
979
980 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
981 for (k = 1; k < bmap->n_ineq; ++k) {
982 h = hash_index(index, size, bits, bmap, k);
983 if (!index[h]) {
984 index[h] = &bmap->ineq[k];
985 continue;
986 }
987 if (progress)
988 *progress = 1;
989 l = index[h] - &bmap->ineq[0];
990 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
991 swap_inequality(bmap, k, l);
992 isl_basic_map_drop_inequality(bmap, k);
993 --k;
994 }
995 isl_int_init(sum);
996 for (k = 0; k < bmap->n_ineq-1; ++k) {
997 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
998 h = hash_index(index, size, bits, bmap, k);
999 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1000 if (!index[h])
1001 continue;
1002 l = index[h] - &bmap->ineq[0];
1003 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1004 if (isl_int_is_pos(sum)) {
1005 bmap = check_for_div_constraints(bmap, k, l, sum,
1006 progress);
1007 continue;
1008 }
1009 if (isl_int_is_zero(sum)) {
1010 /* We need to break out of the loop after these
1011 * changes since the contents of the hash
1012 * will no longer be valid.
1013 * Plus, we probably we want to regauss first.
1014 */
1015 isl_basic_map_drop_inequality(bmap, l);
1016 isl_basic_map_inequality_to_equality(bmap, k);
1017 } else
1018 bmap = isl_basic_map_set_to_empty(bmap);
1019 break;
1020 }
1021 isl_int_clear(sum);
1022
1023 free(index);
1024 return bmap;
1025 }
1026
1027
1028 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1029 {
1030 int progress = 1;
1031 if (!bmap)
1032 return NULL;
1033 while (progress) {
1034 progress = 0;
1035 bmap = isl_basic_map_normalize_constraints(bmap);
1036 bmap = remove_duplicate_divs(bmap, &progress);
1037 bmap = eliminate_divs_eq(bmap, &progress);
1038 bmap = eliminate_divs_ineq(bmap, &progress);
1039 bmap = isl_basic_map_gauss(bmap, &progress);
1040 /* requires equalities in normal form */
1041 bmap = normalize_divs(bmap, &progress);
1042 bmap = remove_duplicate_constraints(bmap, &progress);
1043 }
1044 return bmap;
1045 }
1046
1047 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1048 {
1049 return (struct isl_basic_set *)
1050 isl_basic_map_simplify((struct isl_basic_map *)bset);
1051 }
1052
1053
1054 /* If the only constraints a div d=floor(f/m)
1055 * appears in are its two defining constraints
1056 *
1057 * f - m d >=0
1058 * -(f - (m - 1)) + m d >= 0
1059 *
1060 * then it can safely be removed.
1061 */
1062 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1063 {
1064 int i;
1065 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1066
1067 for (i = 0; i < bmap->n_eq; ++i)
1068 if (!isl_int_is_zero(bmap->eq[i][pos]))
1069 return 0;
1070
1071 for (i = 0; i < bmap->n_ineq; ++i) {
1072 if (isl_int_is_zero(bmap->ineq[i][pos]))
1073 continue;
1074 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1075 int neg;
1076 isl_int_sub(bmap->div[div][1],
1077 bmap->div[div][1], bmap->div[div][0]);
1078 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1079 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1080 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1081 isl_int_add(bmap->div[div][1],
1082 bmap->div[div][1], bmap->div[div][0]);
1083 if (!neg)
1084 return 0;
1085 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1086 bmap->n_div-div-1) != -1)
1087 return 0;
1088 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1089 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1090 return 0;
1091 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1092 bmap->n_div-div-1) != -1)
1093 return 0;
1094 } else
1095 return 0;
1096 }
1097
1098 for (i = 0; i < bmap->n_div; ++i)
1099 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1100 return 0;
1101
1102 return 1;
1103 }
1104
1105 /*
1106 * Remove divs that don't occur in any of the constraints or other divs.
1107 * These can arise when dropping some of the variables in a quast
1108 * returned by piplib.
1109 */
1110 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1111 {
1112 int i;
1113
1114 if (!bmap)
1115 return NULL;
1116
1117 for (i = bmap->n_div-1; i >= 0; --i) {
1118 if (!div_is_redundant(bmap, i))
1119 continue;
1120 bmap = isl_basic_map_drop_div(bmap, i);
1121 }
1122 return bmap;
1123 }
1124
1125 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1126 {
1127 bmap = remove_redundant_divs(bmap);
1128 if (!bmap)
1129 return NULL;
1130 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1131 return bmap;
1132 }
1133
1134 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1135 {
1136 return (struct isl_basic_set *)
1137 isl_basic_map_finalize((struct isl_basic_map *)bset);
1138 }
1139
1140 struct isl_set *isl_set_finalize(struct isl_set *set)
1141 {
1142 int i;
1143
1144 if (!set)
1145 return NULL;
1146 for (i = 0; i < set->n; ++i) {
1147 set->p[i] = isl_basic_set_finalize(set->p[i]);
1148 if (!set->p[i])
1149 goto error;
1150 }
1151 return set;
1152 error:
1153 isl_set_free(set);
1154 return NULL;
1155 }
1156
1157 struct isl_map *isl_map_finalize(struct isl_map *map)
1158 {
1159 int i;
1160
1161 if (!map)
1162 return NULL;
1163 for (i = 0; i < map->n; ++i) {
1164 map->p[i] = isl_basic_map_finalize(map->p[i]);
1165 if (!map->p[i])
1166 goto error;
1167 }
1168 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1169 return map;
1170 error:
1171 isl_map_free(map);
1172 return NULL;
1173 }
1174
1175
1176 /* Remove definition of any div that is defined in terms of the given variable.
1177 * The div itself is not removed. Functions such as
1178 * eliminate_divs_ineq depend on the other divs remaining in place.
1179 */
1180 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1181 int pos)
1182 {
1183 int i;
1184 unsigned dim = isl_dim_total(bmap->dim);
1185
1186 for (i = 0; i < bmap->n_div; ++i) {
1187 if (isl_int_is_zero(bmap->div[i][0]))
1188 continue;
1189 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1190 continue;
1191 isl_int_set_si(bmap->div[i][0], 0);
1192 }
1193 return bmap;
1194 }
1195
1196 /* Eliminate the specified variables from the constraints using
1197 * Fourier-Motzkin. The variables themselves are not removed.
1198 */
1199 struct isl_basic_map *isl_basic_map_eliminate_vars(
1200 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1201 {
1202 int d;
1203 int i, j, k;
1204 unsigned total;
1205
1206 if (n == 0)
1207 return bmap;
1208 if (!bmap)
1209 return NULL;
1210 total = isl_basic_map_total_dim(bmap);
1211
1212 bmap = isl_basic_map_cow(bmap);
1213 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1214 bmap = remove_dependent_vars(bmap, d);
1215
1216 for (d = pos + n - 1;
1217 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1218 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1219 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1220 int n_lower, n_upper;
1221 if (!bmap)
1222 return NULL;
1223 for (i = 0; i < bmap->n_eq; ++i) {
1224 if (isl_int_is_zero(bmap->eq[i][1+d]))
1225 continue;
1226 eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1227 isl_basic_map_drop_equality(bmap, i);
1228 break;
1229 }
1230 if (i < bmap->n_eq)
1231 continue;
1232 n_lower = 0;
1233 n_upper = 0;
1234 for (i = 0; i < bmap->n_ineq; ++i) {
1235 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1236 n_lower++;
1237 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1238 n_upper++;
1239 }
1240 bmap = isl_basic_map_extend_constraints(bmap,
1241 0, n_lower * n_upper);
1242 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1243 int last;
1244 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1245 continue;
1246 last = -1;
1247 for (j = 0; j < i; ++j) {
1248 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1249 continue;
1250 last = j;
1251 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1252 isl_int_sgn(bmap->ineq[j][1+d]))
1253 continue;
1254 k = isl_basic_map_alloc_inequality(bmap);
1255 if (k < 0)
1256 goto error;
1257 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1258 1+total);
1259 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1260 1+d, 1+total, NULL);
1261 }
1262 isl_basic_map_drop_inequality(bmap, i);
1263 i = last + 1;
1264 }
1265 if (n_lower > 0 && n_upper > 0) {
1266 bmap = isl_basic_map_normalize_constraints(bmap);
1267 bmap = remove_duplicate_constraints(bmap, NULL);
1268 bmap = isl_basic_map_gauss(bmap, NULL);
1269 bmap = isl_basic_map_convex_hull(bmap);
1270 if (!bmap)
1271 goto error;
1272 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1273 break;
1274 }
1275 }
1276 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1277 return bmap;
1278 error:
1279 isl_basic_map_free(bmap);
1280 return NULL;
1281 }
1282
1283 struct isl_basic_set *isl_basic_set_eliminate_vars(
1284 struct isl_basic_set *bset, unsigned pos, unsigned n)
1285 {
1286 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1287 (struct isl_basic_map *)bset, pos, n);
1288 }
1289
1290 /* Don't assume equalities are in order, because align_divs
1291 * may have changed the order of the divs.
1292 */
1293 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1294 {
1295 int d, i;
1296 unsigned total;
1297
1298 total = isl_dim_total(bmap->dim);
1299 for (d = 0; d < total; ++d)
1300 elim[d] = -1;
1301 for (i = 0; i < bmap->n_eq; ++i) {
1302 for (d = total - 1; d >= 0; --d) {
1303 if (isl_int_is_zero(bmap->eq[i][1+d]))
1304 continue;
1305 elim[d] = i;
1306 break;
1307 }
1308 }
1309 }
1310
1311 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1312 {
1313 return compute_elimination_index((struct isl_basic_map *)bset, elim);
1314 }
1315
1316 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1317 struct isl_basic_map *bmap, int *elim)
1318 {
1319 int d, i;
1320 int copied = 0;
1321 unsigned total;
1322
1323 total = isl_dim_total(bmap->dim);
1324 for (d = total - 1; d >= 0; --d) {
1325 if (isl_int_is_zero(src[1+d]))
1326 continue;
1327 if (elim[d] == -1)
1328 continue;
1329 if (!copied) {
1330 isl_seq_cpy(dst, src, 1 + total);
1331 copied = 1;
1332 }
1333 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1334 }
1335 return copied;
1336 }
1337
1338 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1339 struct isl_basic_set *bset, int *elim)
1340 {
1341 return reduced_using_equalities(dst, src,
1342 (struct isl_basic_map *)bset, elim);
1343 }
1344
1345 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1346 struct isl_basic_set *bset, struct isl_basic_set *context)
1347 {
1348 int i;
1349 int *elim;
1350
1351 if (!bset || !context)
1352 goto error;
1353
1354 bset = isl_basic_set_cow(bset);
1355 if (!bset)
1356 goto error;
1357
1358 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1359 if (!elim)
1360 goto error;
1361 set_compute_elimination_index(context, elim);
1362 for (i = 0; i < bset->n_eq; ++i)
1363 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1364 context, elim);
1365 for (i = 0; i < bset->n_ineq; ++i)
1366 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1367 context, elim);
1368 isl_basic_set_free(context);
1369 free(elim);
1370 bset = isl_basic_set_simplify(bset);
1371 bset = isl_basic_set_finalize(bset);
1372 return bset;
1373 error:
1374 isl_basic_set_free(bset);
1375 isl_basic_set_free(context);
1376 return NULL;
1377 }
1378
1379 static struct isl_basic_set *remove_shifted_constraints(
1380 struct isl_basic_set *bset, struct isl_basic_set *context)
1381 {
1382 unsigned int size;
1383 isl_int ***index;
1384 int bits;
1385 int k, h, l;
1386
1387 if (!bset)
1388 return NULL;
1389
1390 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1391 bits = ffs(size) - 1;
1392 index = isl_calloc_array(ctx, isl_int **, size);
1393 if (!index)
1394 return bset;
1395
1396 for (k = 0; k < context->n_ineq; ++k) {
1397 h = set_hash_index(index, size, bits, context, k);
1398 index[h] = &context->ineq[k];
1399 }
1400 for (k = 0; k < bset->n_ineq; ++k) {
1401 h = set_hash_index(index, size, bits, bset, k);
1402 if (!index[h])
1403 continue;
1404 l = index[h] - &context->ineq[0];
1405 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1406 continue;
1407 bset = isl_basic_set_cow(bset);
1408 if (!bset)
1409 goto error;
1410 isl_basic_set_drop_inequality(bset, k);
1411 --k;
1412 }
1413 free(index);
1414 return bset;
1415 error:
1416 free(index);
1417 return bset;
1418 }
1419
1420 /* Tighten (decrease) the constant terms of the inequalities based
1421 * on the equalities, without removing any integer points.
1422 * For example, if there is an equality
1423 *
1424 * i = 3 * j
1425 *
1426 * and an inequality
1427 *
1428 * i >= 1
1429 *
1430 * then we want to replace the inequality by
1431 *
1432 * i >= 3
1433 *
1434 * We do this by computing a variable compression and translating
1435 * the constraints to the compressed space.
1436 * If any constraint has coefficients (except the contant term)
1437 * with a common factor "f", then we can replace the constant term "c"
1438 * by
1439 *
1440 * f * floor(c/f)
1441 *
1442 * That is, we add
1443 *
1444 * f * floor(c/f) - c = -fract(c/f)
1445 *
1446 * and we can add the same value to the original constraint.
1447 *
1448 * In the example, the compressed space only contains "j",
1449 * and the inequality translates to
1450 *
1451 * 3 * j - 1 >= 0
1452 *
1453 * We add -fract(-1/3) = -2 to the original constraint to obtain
1454 *
1455 * i - 3 >= 0
1456 */
1457 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1458 struct isl_basic_set *bset)
1459 {
1460 int i;
1461 unsigned total;
1462 struct isl_mat *B, *C;
1463 isl_int gcd;
1464
1465 if (!bset)
1466 return NULL;
1467
1468 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1469 return bset;
1470
1471 if (!bset->n_ineq)
1472 return bset;
1473
1474 bset = isl_basic_set_cow(bset);
1475 if (!bset)
1476 return NULL;
1477
1478 total = isl_basic_set_total_dim(bset);
1479 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1480 C = isl_mat_variable_compression(B, NULL);
1481 if (!C)
1482 return bset;
1483 if (C->n_col == 0) {
1484 isl_mat_free(C);
1485 return isl_basic_set_set_to_empty(bset);
1486 }
1487 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1488 0, bset->n_ineq, 0, 1 + total);
1489 C = isl_mat_product(B, C);
1490 if (!C)
1491 return bset;
1492
1493 isl_int_init(gcd);
1494 for (i = 0; i < bset->n_ineq; ++i) {
1495 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1496 if (isl_int_is_one(gcd))
1497 continue;
1498 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1499 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1500 }
1501 isl_int_clear(gcd);
1502
1503 isl_mat_free(C);
1504
1505 return bset;
1506 }
1507
1508 /* Remove all information from bset that is redundant in the context
1509 * of context. In particular, equalities that are linear combinations
1510 * of those in context are removed. Then the inequalities that are
1511 * redundant in the context of the equalities and inequalities of
1512 * context are removed.
1513 *
1514 * We first simplify the constraints of "bset" in the context of the
1515 * equalities of "context".
1516 * Then we simplify the inequalities of the context in the context
1517 * of the equalities of bset and remove the inequalities from "bset"
1518 * that are obviously redundant with respect to some inequality in "context".
1519 *
1520 * If there are any inequalities left, we construct a tableau for
1521 * the context and then add the inequalities of "bset".
1522 * Before adding these equalities, we freeze all constraints such that
1523 * they won't be considered redundant in terms of the constraints of "bset".
1524 * Then we detect all equalities and redundant constraints (among the
1525 * constraints that weren't frozen) and update bset according to the results.
1526 * We have to be careful here because we don't want any of the context
1527 * constraints to remain and because we haven't added the equalities of "bset"
1528 * to the tableau so we temporarily have to pretend that there were no
1529 * equalities.
1530 */
1531 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1532 struct isl_basic_set *context)
1533 {
1534 int i;
1535 struct isl_tab *tab;
1536 unsigned context_ineq;
1537 struct isl_basic_set *combined = NULL;
1538
1539 if (!context || !bset)
1540 goto error;
1541
1542 if (context->n_eq > 0)
1543 bset = isl_basic_set_reduce_using_equalities(bset,
1544 isl_basic_set_copy(context));
1545 if (!bset)
1546 goto error;
1547 if (isl_basic_set_fast_is_empty(bset))
1548 goto done;
1549 if (!bset->n_ineq)
1550 goto done;
1551
1552 if (bset->n_eq > 0) {
1553 struct isl_basic_set *affine_hull;
1554 affine_hull = isl_basic_set_copy(bset);
1555 affine_hull = isl_basic_set_cow(affine_hull);
1556 if (!affine_hull)
1557 goto error;
1558 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1559 context = isl_basic_set_intersect(context, affine_hull);
1560 context = isl_basic_set_gauss(context, NULL);
1561 context = normalize_constraints_in_compressed_space(context);
1562 }
1563 if (!context)
1564 goto error;
1565 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1566 isl_basic_set_free(bset);
1567 return context;
1568 }
1569 if (!context->n_ineq)
1570 goto done;
1571 bset = remove_shifted_constraints(bset, context);
1572 if (!bset->n_ineq)
1573 goto done;
1574 isl_basic_set_free_equality(context, context->n_eq);
1575 context_ineq = context->n_ineq;
1576 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1577 combined = isl_basic_set_extend_constraints(combined,
1578 bset->n_eq, bset->n_ineq);
1579 tab = isl_tab_from_basic_set(combined);
1580 if (!tab)
1581 goto error;
1582 for (i = 0; i < context_ineq; ++i)
1583 tab->con[i].frozen = 1;
1584 tab = isl_tab_extend(tab, bset->n_ineq);
1585 if (!tab)
1586 goto error;
1587 for (i = 0; i < bset->n_ineq; ++i)
1588 tab = isl_tab_add_ineq(tab, bset->ineq[i]);
1589 bset = isl_basic_set_add_constraints(combined, bset, 0);
1590 tab = isl_tab_detect_equalities(tab);
1591 tab = isl_tab_detect_redundant(tab);
1592 if (!tab)
1593 goto error2;
1594 for (i = 0; i < context_ineq; ++i) {
1595 tab->con[i].is_zero = 0;
1596 tab->con[i].is_redundant = 1;
1597 }
1598 bset = isl_basic_set_update_from_tab(bset, tab);
1599 isl_tab_free(tab);
1600 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1601 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1602 done:
1603 bset = isl_basic_set_simplify(bset);
1604 bset = isl_basic_set_finalize(bset);
1605 isl_basic_set_free(context);
1606 return bset;
1607 error:
1608 isl_basic_set_free(combined);
1609 error2:
1610 isl_basic_set_free(bset);
1611 isl_basic_set_free(context);
1612 return NULL;
1613 }
1614
1615 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1616 * We simply add the equalities in context to bmap and then do a regular
1617 * div normalizations. Better results can be obtained by normalizing
1618 * only the divs in bmap than do not also appear in context.
1619 * We need to be careful to reduce the divs using the equalities
1620 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1621 * spurious constraints.
1622 */
1623 static struct isl_basic_map *normalize_divs_in_context(
1624 struct isl_basic_map *bmap, struct isl_basic_map *context)
1625 {
1626 int i;
1627 unsigned total_context;
1628 int div_eq;
1629
1630 div_eq = n_pure_div_eq(bmap);
1631 if (div_eq == 0)
1632 return bmap;
1633
1634 if (context->n_div > 0)
1635 bmap = isl_basic_map_align_divs(bmap, context);
1636
1637 total_context = isl_basic_map_total_dim(context);
1638 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1639 for (i = 0; i < context->n_eq; ++i) {
1640 int k;
1641 k = isl_basic_map_alloc_equality(bmap);
1642 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1643 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1644 isl_basic_map_total_dim(bmap) - total_context);
1645 }
1646 bmap = isl_basic_map_gauss(bmap, NULL);
1647 bmap = normalize_divs(bmap, NULL);
1648 bmap = isl_basic_map_gauss(bmap, NULL);
1649 return bmap;
1650 }
1651
1652 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1653 struct isl_basic_map *context)
1654 {
1655 struct isl_basic_set *bset;
1656
1657 if (!bmap || !context)
1658 goto error;
1659
1660 if (isl_basic_map_is_universe(context)) {
1661 isl_basic_map_free(context);
1662 return bmap;
1663 }
1664 if (isl_basic_map_is_universe(bmap)) {
1665 isl_basic_map_free(context);
1666 return bmap;
1667 }
1668 if (isl_basic_map_fast_is_empty(context)) {
1669 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1670 isl_basic_map_free(context);
1671 isl_basic_map_free(bmap);
1672 return isl_basic_map_universe(dim);
1673 }
1674 if (isl_basic_map_fast_is_empty(bmap)) {
1675 isl_basic_map_free(context);
1676 return bmap;
1677 }
1678
1679 bmap = isl_basic_map_convex_hull(bmap);
1680 context = isl_basic_map_convex_hull(context);
1681
1682 if (context->n_eq)
1683 bmap = normalize_divs_in_context(bmap, context);
1684
1685 context = isl_basic_map_align_divs(context, bmap);
1686 bmap = isl_basic_map_align_divs(bmap, context);
1687
1688 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1689 isl_basic_map_underlying_set(context));
1690
1691 return isl_basic_map_overlying_set(bset, bmap);
1692 error:
1693 isl_basic_map_free(bmap);
1694 isl_basic_map_free(context);
1695 return NULL;
1696 }
1697
1698 /*
1699 * Assumes context has no implicit divs.
1700 */
1701 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1702 {
1703 int i;
1704
1705 if (!map || !context)
1706 goto error;;
1707
1708 if (isl_basic_map_is_universe(context)) {
1709 isl_basic_map_free(context);
1710 return map;
1711 }
1712 if (isl_basic_map_fast_is_empty(context)) {
1713 struct isl_dim *dim = isl_dim_copy(map->dim);
1714 isl_basic_map_free(context);
1715 isl_map_free(map);
1716 return isl_map_universe(dim);
1717 }
1718
1719 context = isl_basic_map_convex_hull(context);
1720 map = isl_map_cow(map);
1721 if (!map || !context)
1722 goto error;;
1723 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1724 map = isl_map_compute_divs(map);
1725 for (i = 0; i < map->n; ++i)
1726 context = isl_basic_map_align_divs(context, map->p[i]);
1727 for (i = 0; i < map->n; ++i) {
1728 map->p[i] = isl_basic_map_gist(map->p[i],
1729 isl_basic_map_copy(context));
1730 if (!map->p[i])
1731 goto error;
1732 }
1733 isl_basic_map_free(context);
1734 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1735 return map;
1736 error:
1737 isl_map_free(map);
1738 isl_basic_map_free(context);
1739 return NULL;
1740 }
1741
1742 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1743 struct isl_basic_set *context)
1744 {
1745 return (struct isl_basic_set *)isl_basic_map_gist(
1746 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1747 }
1748
1749 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1750 {
1751 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1752 (struct isl_basic_map *)context);
1753 }
1754
1755 /* Quick check to see if two basic maps are disjoint.
1756 * In particular, we reduce the equalities and inequalities of
1757 * one basic map in the context of the equalities of the other
1758 * basic map and check if we get a contradiction.
1759 */
1760 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1761 struct isl_basic_map *bmap2)
1762 {
1763 struct isl_vec *v = NULL;
1764 int *elim = NULL;
1765 unsigned total;
1766 int d, i;
1767
1768 if (!bmap1 || !bmap2)
1769 return -1;
1770 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1771 return -1);
1772 if (bmap1->n_div || bmap2->n_div)
1773 return 0;
1774 if (!bmap1->n_eq && !bmap2->n_eq)
1775 return 0;
1776
1777 total = isl_dim_total(bmap1->dim);
1778 if (total == 0)
1779 return 0;
1780 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1781 if (!v)
1782 goto error;
1783 elim = isl_alloc_array(bmap1->ctx, int, total);
1784 if (!elim)
1785 goto error;
1786 compute_elimination_index(bmap1, elim);
1787 for (i = 0; i < bmap2->n_eq; ++i) {
1788 int reduced;
1789 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1790 bmap1, elim);
1791 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1792 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1793 goto disjoint;
1794 }
1795 for (i = 0; i < bmap2->n_ineq; ++i) {
1796 int reduced;
1797 reduced = reduced_using_equalities(v->block.data,
1798 bmap2->ineq[i], bmap1, elim);
1799 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1800 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1801 goto disjoint;
1802 }
1803 compute_elimination_index(bmap2, elim);
1804 for (i = 0; i < bmap1->n_ineq; ++i) {
1805 int reduced;
1806 reduced = reduced_using_equalities(v->block.data,
1807 bmap1->ineq[i], bmap2, elim);
1808 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1809 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1810 goto disjoint;
1811 }
1812 isl_vec_free(v);
1813 free(elim);
1814 return 0;
1815 disjoint:
1816 isl_vec_free(v);
1817 free(elim);
1818 return 1;
1819 error:
1820 isl_vec_free(v);
1821 free(elim);
1822 return -1;
1823 }
1824
1825 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1826 struct isl_basic_set *bset2)
1827 {
1828 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1829 (struct isl_basic_map *)bset2);
1830 }
1831
1832 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1833 {
1834 int i, j;
1835
1836 if (!map1 || !map2)
1837 return -1;
1838
1839 if (isl_map_fast_is_equal(map1, map2))
1840 return 0;
1841
1842 for (i = 0; i < map1->n; ++i) {
1843 for (j = 0; j < map2->n; ++j) {
1844 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1845 map2->p[j]);
1846 if (d != 1)
1847 return d;
1848 }
1849 }
1850 return 1;
1851 }
1852
1853 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1854 {
1855 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1856 (struct isl_map *)set2);
1857 }
1858
1859 /* Check if we can combine a given div with lower bound l and upper
1860 * bound u with some other div and if so return that other div.
1861 * Otherwise return -1.
1862 *
1863 * We first check that
1864 * - the bounds are opposites of each other (expect for the constant
1865 * term
1866 * - the bounds do not reference any other div
1867 * - no div is defined in terms of this div
1868 *
1869 * Let m be the size of the range allowed on the div by the bounds.
1870 * That is, the bounds are of the form
1871 *
1872 * e <= a <= e + m - 1
1873 *
1874 * with e some expression in the other variables.
1875 * We look for another div b such that no third div is defined in terms
1876 * of this second div b and such that in any constraint that contains
1877 * a (except for the given lower and upper bound), also contains b
1878 * with a coefficient that is m times that of b.
1879 * That is, all constraints (execpt for the lower and upper bound)
1880 * are of the form
1881 *
1882 * e + f (a + m b) >= 0
1883 *
1884 * If so, we return b so that "a + m b" can be replaced by
1885 * a single div "c = a + m b".
1886 */
1887 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1888 unsigned div, unsigned l, unsigned u)
1889 {
1890 int i, j;
1891 unsigned dim;
1892 int coalesce = -1;
1893
1894 if (bmap->n_div <= 1)
1895 return -1;
1896 dim = isl_dim_total(bmap->dim);
1897 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1898 return -1;
1899 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1900 bmap->n_div - div - 1) != -1)
1901 return -1;
1902 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1903 dim + bmap->n_div))
1904 return -1;
1905
1906 for (i = 0; i < bmap->n_div; ++i) {
1907 if (isl_int_is_zero(bmap->div[i][0]))
1908 continue;
1909 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
1910 return -1;
1911 }
1912
1913 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1914 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1915 for (i = 0; i < bmap->n_div; ++i) {
1916 if (i == div)
1917 continue;
1918 if (!pairs[i])
1919 continue;
1920 for (j = 0; j < bmap->n_div; ++j) {
1921 if (isl_int_is_zero(bmap->div[j][0]))
1922 continue;
1923 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
1924 break;
1925 }
1926 if (j < bmap->n_div)
1927 continue;
1928 for (j = 0; j < bmap->n_ineq; ++j) {
1929 int valid;
1930 if (j == l || j == u)
1931 continue;
1932 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
1933 continue;
1934 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
1935 break;
1936 isl_int_mul(bmap->ineq[j][1 + dim + div],
1937 bmap->ineq[j][1 + dim + div],
1938 bmap->ineq[l][0]);
1939 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
1940 bmap->ineq[j][1 + dim + i]);
1941 isl_int_divexact(bmap->ineq[j][1 + dim + div],
1942 bmap->ineq[j][1 + dim + div],
1943 bmap->ineq[l][0]);
1944 if (!valid)
1945 break;
1946 }
1947 if (j < bmap->n_ineq)
1948 continue;
1949 coalesce = i;
1950 break;
1951 }
1952 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1953 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1954 return coalesce;
1955 }
1956
1957 /* Given a lower and an upper bound on div i, construct an inequality
1958 * that when nonnegative ensures that this pair of bounds always allows
1959 * for an integer value of the given div.
1960 * The lower bound is inequality l, while the upper bound is inequality u.
1961 * The constructed inequality is stored in ineq.
1962 * g, fl, fu are temporary scalars.
1963 *
1964 * Let the upper bound be
1965 *
1966 * -n_u a + e_u >= 0
1967 *
1968 * and the lower bound
1969 *
1970 * n_l a + e_l >= 0
1971 *
1972 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1973 * We have
1974 *
1975 * - f_u e_l <= f_u f_l g a <= f_l e_u
1976 *
1977 * Since all variables are integer valued, this is equivalent to
1978 *
1979 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1980 *
1981 * If this interval is at least f_u f_l g, then it contains at least
1982 * one integer value for a.
1983 * That is, the test constraint is
1984 *
1985 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
1986 */
1987 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
1988 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
1989 {
1990 unsigned dim;
1991 dim = isl_dim_total(bmap->dim);
1992
1993 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
1994 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
1995 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
1996 isl_int_neg(fu, fu);
1997 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
1998 1 + dim + bmap->n_div);
1999 isl_int_add(ineq[0], ineq[0], fl);
2000 isl_int_add(ineq[0], ineq[0], fu);
2001 isl_int_sub_ui(ineq[0], ineq[0], 1);
2002 isl_int_mul(g, g, fl);
2003 isl_int_mul(g, g, fu);
2004 isl_int_sub(ineq[0], ineq[0], g);
2005 }
2006
2007 /* Remove more kinds of divs that are not strictly needed.
2008 * In particular, if all pairs of lower and upper bounds on a div
2009 * are such that they allow at least one integer value of the div,
2010 * the we can eliminate the div using Fourier-Motzkin without
2011 * introducing any spurious solutions.
2012 */
2013 static struct isl_basic_map *drop_more_redundant_divs(
2014 struct isl_basic_map *bmap, int *pairs, int n)
2015 {
2016 struct isl_tab *tab = NULL;
2017 struct isl_vec *vec = NULL;
2018 unsigned dim;
2019 int remove = -1;
2020 isl_int g, fl, fu;
2021
2022 isl_int_init(g);
2023 isl_int_init(fl);
2024 isl_int_init(fu);
2025
2026 if (!bmap)
2027 goto error;
2028
2029 dim = isl_dim_total(bmap->dim);
2030 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2031 if (!vec)
2032 goto error;
2033
2034 tab = isl_tab_from_basic_map(bmap);
2035
2036 while (n > 0) {
2037 int i, l, u;
2038 int best = -1;
2039 enum isl_lp_result res;
2040
2041 for (i = 0; i < bmap->n_div; ++i) {
2042 if (!pairs[i])
2043 continue;
2044 if (best >= 0 && pairs[best] <= pairs[i])
2045 continue;
2046 best = i;
2047 }
2048
2049 i = best;
2050 for (l = 0; l < bmap->n_ineq; ++l) {
2051 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2052 continue;
2053 for (u = 0; u < bmap->n_ineq; ++u) {
2054 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2055 continue;
2056 construct_test_ineq(bmap, i, l, u,
2057 vec->el, g, fl, fu);
2058 res = isl_tab_min(tab, vec->el,
2059 bmap->ctx->one, &g, NULL, 0);
2060 if (res == isl_lp_error)
2061 goto error;
2062 if (res == isl_lp_empty) {
2063 bmap = isl_basic_map_set_to_empty(bmap);
2064 break;
2065 }
2066 if (res != isl_lp_ok || isl_int_is_neg(g))
2067 break;
2068 }
2069 if (u < bmap->n_ineq)
2070 break;
2071 }
2072 if (l == bmap->n_ineq) {
2073 remove = i;
2074 break;
2075 }
2076 pairs[i] = 0;
2077 --n;
2078 }
2079
2080 isl_tab_free(tab);
2081 isl_vec_free(vec);
2082
2083 isl_int_clear(g);
2084 isl_int_clear(fl);
2085 isl_int_clear(fu);
2086
2087 free(pairs);
2088
2089 if (remove < 0)
2090 return bmap;
2091
2092 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2093 return isl_basic_map_drop_redundant_divs(bmap);
2094 error:
2095 free(pairs);
2096 isl_basic_map_free(bmap);
2097 isl_tab_free(tab);
2098 isl_vec_free(vec);
2099 isl_int_clear(g);
2100 isl_int_clear(fl);
2101 isl_int_clear(fu);
2102 return NULL;
2103 }
2104
2105 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2106 * and the upper bound u, div1 always occurs together with div2 in the form
2107 * (div1 + m div2), where m is the constant range on the variable div1
2108 * allowed by l and u, replace the pair div1 and div2 by a single
2109 * div that is equal to div1 + m div2.
2110 *
2111 * The new div will appear in the location that contains div2.
2112 * We need to modify all constraints that contain
2113 * div2 = (div - div1) / m
2114 * (If a constraint does not contain div2, it will also not contain div1.)
2115 * If the constraint also contains div1, then we know they appear
2116 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2117 * i.e., the coefficient of div is f.
2118 *
2119 * Otherwise, we first need to introduce div1 into the constraint.
2120 * Let the l be
2121 *
2122 * div1 + f >=0
2123 *
2124 * and u
2125 *
2126 * -div1 + f' >= 0
2127 *
2128 * A lower bound on div2
2129 *
2130 * n div2 + t >= 0
2131 *
2132 * can be replaced by
2133 *
2134 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2135 *
2136 * with g = gcd(m,n).
2137 * An upper bound
2138 *
2139 * -n div2 + t >= 0
2140 *
2141 * can be replaced by
2142 *
2143 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2144 *
2145 * These constraint are those that we would obtain from eliminating
2146 * div1 using Fourier-Motzkin.
2147 *
2148 * After all constraints have been modified, we drop the lower and upper
2149 * bound and then drop div1.
2150 */
2151 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2152 unsigned div1, unsigned div2, unsigned l, unsigned u)
2153 {
2154 isl_int a;
2155 isl_int b;
2156 isl_int m;
2157 unsigned dim, total;
2158 int i;
2159
2160 dim = isl_dim_total(bmap->dim);
2161 total = 1 + dim + bmap->n_div;
2162
2163 isl_int_init(a);
2164 isl_int_init(b);
2165 isl_int_init(m);
2166 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2167 isl_int_add_ui(m, m, 1);
2168
2169 for (i = 0; i < bmap->n_ineq; ++i) {
2170 if (i == l || i == u)
2171 continue;
2172 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2173 continue;
2174 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2175 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2176 isl_int_divexact(a, m, b);
2177 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2178 if (isl_int_is_pos(b)) {
2179 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2180 b, bmap->ineq[l], total);
2181 } else {
2182 isl_int_neg(b, b);
2183 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2184 b, bmap->ineq[u], total);
2185 }
2186 }
2187 isl_int_set(bmap->ineq[i][1 + dim + div2],
2188 bmap->ineq[i][1 + dim + div1]);
2189 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2190 }
2191
2192 isl_int_clear(a);
2193 isl_int_clear(b);
2194 isl_int_clear(m);
2195 if (l > u) {
2196 isl_basic_map_drop_inequality(bmap, l);
2197 isl_basic_map_drop_inequality(bmap, u);
2198 } else {
2199 isl_basic_map_drop_inequality(bmap, u);
2200 isl_basic_map_drop_inequality(bmap, l);
2201 }
2202 bmap = isl_basic_map_drop_div(bmap, div1);
2203 return bmap;
2204 }
2205
2206 /* First check if we can coalesce any pair of divs and
2207 * then continue with dropping more redundant divs.
2208 *
2209 * We loop over all pairs of lower and upper bounds on a div
2210 * with coefficient 1 and -1, respectively, check if there
2211 * is any other div "c" with which we can coalesce the div
2212 * and if so, perform the coalescing.
2213 */
2214 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2215 struct isl_basic_map *bmap, int *pairs, int n)
2216 {
2217 int i, l, u;
2218 unsigned dim;
2219
2220 dim = isl_dim_total(bmap->dim);
2221
2222 for (i = 0; i < bmap->n_div; ++i) {
2223 if (!pairs[i])
2224 continue;
2225 for (l = 0; l < bmap->n_ineq; ++l) {
2226 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2227 continue;
2228 for (u = 0; u < bmap->n_ineq; ++u) {
2229 int c;
2230
2231 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2232 continue;
2233 c = div_find_coalesce(bmap, pairs, i, l, u);
2234 if (c < 0)
2235 continue;
2236 free(pairs);
2237 bmap = coalesce_divs(bmap, i, c, l, u);
2238 return isl_basic_map_drop_redundant_divs(bmap);
2239 }
2240 }
2241 }
2242
2243 return drop_more_redundant_divs(bmap, pairs, n);
2244 }
2245
2246 /* Remove divs that are not strictly needed.
2247 * In particular, if a div only occurs positively (or negatively)
2248 * in constraints, then it can simply be dropped.
2249 * Also, if a div occurs only occurs in two constraints and if moreover
2250 * those two constraints are opposite to each other, except for the constant
2251 * term and if the sum of the constant terms is such that for any value
2252 * of the other values, there is always at least one integer value of the
2253 * div, i.e., if one plus this sum is greater than or equal to
2254 * the (absolute value) of the coefficent of the div in the constraints,
2255 * then we can also simply drop the div.
2256 *
2257 * If any divs are left after these simple checks then we move on
2258 * to more complicated cases in drop_more_redundant_divs.
2259 */
2260 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2261 struct isl_basic_map *bmap)
2262 {
2263 int i, j;
2264 unsigned off;
2265 int *pairs = NULL;
2266 int n = 0;
2267
2268 if (!bmap)
2269 goto error;
2270
2271 off = isl_dim_total(bmap->dim);
2272 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2273 if (!pairs)
2274 goto error;
2275
2276 for (i = 0; i < bmap->n_div; ++i) {
2277 int pos, neg;
2278 int last_pos, last_neg;
2279 int redundant;
2280
2281 if (!isl_int_is_zero(bmap->div[i][0]))
2282 continue;
2283 for (j = 0; j < bmap->n_eq; ++j)
2284 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2285 break;
2286 if (j < bmap->n_eq)
2287 continue;
2288 ++n;
2289 pos = neg = 0;
2290 for (j = 0; j < bmap->n_ineq; ++j) {
2291 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2292 last_pos = j;
2293 ++pos;
2294 }
2295 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2296 last_neg = j;
2297 ++neg;
2298 }
2299 }
2300 pairs[i] = pos * neg;
2301 if (pairs[i] == 0) {
2302 for (j = bmap->n_ineq - 1; j >= 0; --j)
2303 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2304 isl_basic_map_drop_inequality(bmap, j);
2305 bmap = isl_basic_map_drop_div(bmap, i);
2306 free(pairs);
2307 return isl_basic_map_drop_redundant_divs(bmap);
2308 }
2309 if (pairs[i] != 1)
2310 continue;
2311 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2312 bmap->ineq[last_neg] + 1,
2313 off + bmap->n_div))
2314 continue;
2315
2316 isl_int_add(bmap->ineq[last_pos][0],
2317 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2318 isl_int_add_ui(bmap->ineq[last_pos][0],
2319 bmap->ineq[last_pos][0], 1);
2320 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2321 bmap->ineq[last_pos][1+off+i]);
2322 isl_int_sub_ui(bmap->ineq[last_pos][0],
2323 bmap->ineq[last_pos][0], 1);
2324 isl_int_sub(bmap->ineq[last_pos][0],
2325 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2326 if (!redundant) {
2327 if (!ok_to_set_div_from_bound(bmap, i, last_pos)) {
2328 pairs[i] = 0;
2329 --n;
2330 continue;
2331 }
2332 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2333 bmap = isl_basic_map_simplify(bmap);
2334 free(pairs);
2335 return isl_basic_map_drop_redundant_divs(bmap);
2336 }
2337 if (last_pos > last_neg) {
2338 isl_basic_map_drop_inequality(bmap, last_pos);
2339 isl_basic_map_drop_inequality(bmap, last_neg);
2340 } else {
2341 isl_basic_map_drop_inequality(bmap, last_neg);
2342 isl_basic_map_drop_inequality(bmap, last_pos);
2343 }
2344 bmap = isl_basic_map_drop_div(bmap, i);
2345 free(pairs);
2346 return isl_basic_map_drop_redundant_divs(bmap);
2347 }
2348
2349 if (n > 0)
2350 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2351
2352 free(pairs);
2353 return bmap;
2354 error:
2355 free(pairs);
2356 isl_basic_map_free(bmap);
2357 return NULL;
2358 }
Integer set library