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add a rudimentary manual
[isl.git] / isl_map_simplify.c
blob9275c3b3b7c18139eb0d87e3fd23d98bc315a983
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 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
350 {
351 int i;
352 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
353 unsigned len;
354 len = 1 + isl_basic_map_total_dim(bmap);
355
356 for (i = 0; i < bmap->n_eq; ++i)
357 if (bmap->eq[i] != eq)
358 isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
359
360 for (i = 0; i < bmap->n_ineq; ++i)
361 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
362
363 /* We need to be careful about circular definitions,
364 * so for now we just remove the definitions of other divs that
365 * depend on this div and (possibly) recompute them later.
366 */
367 for (i = 0; i < bmap->n_div; ++i)
368 if (!isl_int_is_zero(bmap->div[i][0]) &&
369 !isl_int_is_zero(bmap->div[i][1 + pos]))
370 isl_seq_clr(bmap->div[i], 1 + len);
371
372 isl_basic_map_drop_div(bmap, div);
373 }
374
375 /* Elimininate divs based on equalities
376 */
377 static struct isl_basic_map *eliminate_divs_eq(
378 struct isl_basic_map *bmap, int *progress)
379 {
380 int d;
381 int i;
382 int modified = 0;
383 unsigned off;
384
385 if (!bmap)
386 return NULL;
387
388 off = 1 + isl_dim_total(bmap->dim);
389
390 for (d = bmap->n_div - 1; d >= 0 ; --d) {
391 for (i = 0; i < bmap->n_eq; ++i) {
392 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
393 !isl_int_is_negone(bmap->eq[i][off + d]))
394 continue;
395 modified = 1;
396 *progress = 1;
397 eliminate_div(bmap, bmap->eq[i], d);
398 isl_basic_map_drop_equality(bmap, i);
399 break;
400 }
401 }
402 if (modified)
403 return eliminate_divs_eq(bmap, progress);
404 return bmap;
405 }
406
407 /* Elimininate divs based on inequalities
408 */
409 static struct isl_basic_map *eliminate_divs_ineq(
410 struct isl_basic_map *bmap, int *progress)
411 {
412 int d;
413 int i;
414 unsigned off;
415 struct isl_ctx *ctx;
416
417 if (!bmap)
418 return NULL;
419
420 ctx = bmap->ctx;
421 off = 1 + isl_dim_total(bmap->dim);
422
423 for (d = bmap->n_div - 1; d >= 0 ; --d) {
424 for (i = 0; i < bmap->n_eq; ++i)
425 if (!isl_int_is_zero(bmap->eq[i][off + d]))
426 break;
427 if (i < bmap->n_eq)
428 continue;
429 for (i = 0; i < bmap->n_ineq; ++i)
430 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
431 break;
432 if (i < bmap->n_ineq)
433 continue;
434 *progress = 1;
435 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
436 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
437 break;
438 bmap = isl_basic_map_drop_div(bmap, d);
439 if (!bmap)
440 break;
441 }
442 return bmap;
443 }
444
445 /* Assumes divs have been ordered if keep_divs is set.
446 */
447 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
448 unsigned pos, isl_int *eq, int keep_divs, int *progress)
449 {
450 unsigned total;
451 int k;
452 int last_div;
453
454 total = isl_basic_map_total_dim(bmap);
455 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
456 bmap->n_div);
457 for (k = 0; k < bmap->n_eq; ++k) {
458 if (bmap->eq[k] == eq)
459 continue;
460 if (isl_int_is_zero(bmap->eq[k][1+pos]))
461 continue;
462 if (progress)
463 *progress = 1;
464 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
465 }
466
467 for (k = 0; k < bmap->n_ineq; ++k) {
468 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
469 continue;
470 if (progress)
471 *progress = 1;
472 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
473 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
474 }
475
476 for (k = 0; k < bmap->n_div; ++k) {
477 if (isl_int_is_zero(bmap->div[k][0]))
478 continue;
479 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
480 continue;
481 if (progress)
482 *progress = 1;
483 /* We need to be careful about circular definitions,
484 * so for now we just remove the definition of div k
485 * if the equality contains any divs.
486 * If keep_divs is set, then the divs have been ordered
487 * and we can keep the definition as long as the result
488 * is still ordered.
489 */
490 if (last_div == -1 || (keep_divs && last_div < k))
491 isl_seq_elim(bmap->div[k]+1, eq,
492 1+pos, 1+total, &bmap->div[k][0]);
493 else
494 isl_seq_clr(bmap->div[k], 1 + total);
495 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
496 }
497 }
498
499 struct isl_basic_map *isl_basic_map_gauss(
500 struct isl_basic_map *bmap, int *progress)
501 {
502 int k;
503 int done;
504 int last_var;
505 unsigned total_var;
506 unsigned total;
507
508 bmap = isl_basic_map_order_divs(bmap);
509
510 if (!bmap)
511 return NULL;
512
513 total = isl_basic_map_total_dim(bmap);
514 total_var = total - bmap->n_div;
515
516 last_var = total - 1;
517 for (done = 0; done < bmap->n_eq; ++done) {
518 for (; last_var >= 0; --last_var) {
519 for (k = done; k < bmap->n_eq; ++k)
520 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
521 break;
522 if (k < bmap->n_eq)
523 break;
524 }
525 if (last_var < 0)
526 break;
527 if (k != done)
528 swap_equality(bmap, k, done);
529 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
530 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
531
532 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
533 progress);
534
535 if (last_var >= total_var &&
536 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
537 unsigned div = last_var - total_var;
538 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
539 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
540 isl_int_set(bmap->div[div][0],
541 bmap->eq[done][1+last_var]);
542 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
543 }
544 }
545 if (done == bmap->n_eq)
546 return bmap;
547 for (k = done; k < bmap->n_eq; ++k) {
548 if (isl_int_is_zero(bmap->eq[k][0]))
549 continue;
550 return isl_basic_map_set_to_empty(bmap);
551 }
552 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
553 return bmap;
554 }
555
556 struct isl_basic_set *isl_basic_set_gauss(
557 struct isl_basic_set *bset, int *progress)
558 {
559 return (struct isl_basic_set*)isl_basic_map_gauss(
560 (struct isl_basic_map *)bset, progress);
561 }
562
563
564 static unsigned int round_up(unsigned int v)
565 {
566 int old_v = v;
567
568 while (v) {
569 old_v = v;
570 v ^= v & -v;
571 }
572 return old_v << 1;
573 }
574
575 static int hash_index(isl_int ***index, unsigned int size, int bits,
576 struct isl_basic_map *bmap, int k)
577 {
578 int h;
579 unsigned total = isl_basic_map_total_dim(bmap);
580 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
581 for (h = hash; index[h]; h = (h+1) % size)
582 if (&bmap->ineq[k] != index[h] &&
583 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
584 break;
585 return h;
586 }
587
588 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
589 struct isl_basic_set *bset, int k)
590 {
591 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
592 }
593
594 /* If we can eliminate more than one div, then we need to make
595 * sure we do it from last div to first div, in order not to
596 * change the position of the other divs that still need to
597 * be removed.
598 */
599 static struct isl_basic_map *remove_duplicate_divs(
600 struct isl_basic_map *bmap, int *progress)
601 {
602 unsigned int size;
603 int *index;
604 int *elim_for;
605 int k, l, h;
606 int bits;
607 struct isl_blk eq;
608 unsigned total_var = isl_dim_total(bmap->dim);
609 unsigned total = total_var + bmap->n_div;
610 struct isl_ctx *ctx;
611
612 if (bmap->n_div <= 1)
613 return bmap;
614
615 ctx = bmap->ctx;
616 for (k = bmap->n_div - 1; k >= 0; --k)
617 if (!isl_int_is_zero(bmap->div[k][0]))
618 break;
619 if (k <= 0)
620 return bmap;
621
622 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
623 size = round_up(4 * bmap->n_div / 3 - 1);
624 bits = ffs(size) - 1;
625 index = isl_calloc_array(ctx, int, size);
626 if (!index)
627 return bmap;
628 eq = isl_blk_alloc(ctx, 1+total);
629 if (isl_blk_is_error(eq))
630 goto out;
631
632 isl_seq_clr(eq.data, 1+total);
633 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
634 for (--k; k >= 0; --k) {
635 uint32_t hash;
636
637 if (isl_int_is_zero(bmap->div[k][0]))
638 continue;
639
640 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
641 for (h = hash; index[h]; h = (h+1) % size)
642 if (isl_seq_eq(bmap->div[k],
643 bmap->div[index[h]-1], 2+total))
644 break;
645 if (index[h]) {
646 *progress = 1;
647 l = index[h] - 1;
648 elim_for[l] = k + 1;
649 }
650 index[h] = k+1;
651 }
652 for (l = bmap->n_div - 1; l >= 0; --l) {
653 if (!elim_for[l])
654 continue;
655 k = elim_for[l] - 1;
656 isl_int_set_si(eq.data[1+total_var+k], -1);
657 isl_int_set_si(eq.data[1+total_var+l], 1);
658 eliminate_div(bmap, eq.data, l);
659 isl_int_set_si(eq.data[1+total_var+k], 0);
660 isl_int_set_si(eq.data[1+total_var+l], 0);
661 }
662
663 isl_blk_free(ctx, eq);
664 out:
665 free(index);
666 free(elim_for);
667 return bmap;
668 }
669
670 static int n_pure_div_eq(struct isl_basic_map *bmap)
671 {
672 int i, j;
673 unsigned total;
674
675 total = isl_dim_total(bmap->dim);
676 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
677 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
678 --j;
679 if (j < 0)
680 break;
681 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
682 return 0;
683 }
684 return i;
685 }
686
687 /* Normalize divs that appear in equalities.
688 *
689 * In particular, we assume that bmap contains some equalities
690 * of the form
691 *
692 * a x = m * e_i
693 *
694 * and we want to replace the set of e_i by a minimal set and
695 * such that the new e_i have a canonical representation in terms
696 * of the vector x.
697 * If any of the equalities involves more than one divs, then
698 * we currently simply bail out.
699 *
700 * Let us first additionally assume that all equalities involve
701 * a div. The equalities then express modulo constraints on the
702 * remaining variables and we can use "parameter compression"
703 * to find a minimal set of constraints. The result is a transformation
704 *
705 * x = T(x') = x_0 + G x'
706 *
707 * with G a lower-triangular matrix with all elements below the diagonal
708 * non-negative and smaller than the diagonal element on the same row.
709 * We first normalize x_0 by making the same property hold in the affine
710 * T matrix.
711 * The rows i of G with a 1 on the diagonal do not impose any modulo
712 * constraint and simply express x_i = x'_i.
713 * For each of the remaining rows i, we introduce a div and a corresponding
714 * equality. In particular
715 *
716 * g_ii e_j = x_i - g_i(x')
717 *
718 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
719 * corresponding div (if g_kk != 1).
720 *
721 * If there are any equalities not involving any div, then we
722 * first apply a variable compression on the variables x:
723 *
724 * x = C x'' x'' = C_2 x
725 *
726 * and perform the above parameter compression on A C instead of on A.
727 * The resulting compression is then of the form
728 *
729 * x'' = T(x') = x_0 + G x'
730 *
731 * and in constructing the new divs and the corresponding equalities,
732 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
733 * by the corresponding row from C_2.
734 */
735 static struct isl_basic_map *normalize_divs(
736 struct isl_basic_map *bmap, int *progress)
737 {
738 int i, j, k;
739 int total;
740 int div_eq;
741 struct isl_mat *B;
742 struct isl_vec *d;
743 struct isl_mat *T = NULL;
744 struct isl_mat *C = NULL;
745 struct isl_mat *C2 = NULL;
746 isl_int v;
747 int *pos;
748 int dropped, needed;
749
750 if (!bmap)
751 return NULL;
752
753 if (bmap->n_div == 0)
754 return bmap;
755
756 if (bmap->n_eq == 0)
757 return bmap;
758
759 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
760 return bmap;
761
762 total = isl_dim_total(bmap->dim);
763 div_eq = n_pure_div_eq(bmap);
764 if (div_eq == 0)
765 return bmap;
766
767 if (div_eq < bmap->n_eq) {
768 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
769 bmap->n_eq - div_eq, 0, 1 + total);
770 C = isl_mat_variable_compression(B, &C2);
771 if (!C || !C2)
772 goto error;
773 if (C->n_col == 0) {
774 bmap = isl_basic_map_set_to_empty(bmap);
775 isl_mat_free(C);
776 isl_mat_free(C2);
777 goto done;
778 }
779 }
780
781 d = isl_vec_alloc(bmap->ctx, div_eq);
782 if (!d)
783 goto error;
784 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
785 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
786 --j;
787 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
788 }
789 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
790
791 if (C) {
792 B = isl_mat_product(B, C);
793 C = NULL;
794 }
795
796 T = isl_mat_parameter_compression(B, d);
797 if (!T)
798 goto error;
799 if (T->n_col == 0) {
800 bmap = isl_basic_map_set_to_empty(bmap);
801 isl_mat_free(C2);
802 isl_mat_free(T);
803 goto done;
804 }
805 isl_int_init(v);
806 for (i = 0; i < T->n_row - 1; ++i) {
807 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
808 if (isl_int_is_zero(v))
809 continue;
810 isl_mat_col_submul(T, 0, v, 1 + i);
811 }
812 isl_int_clear(v);
813 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
814 /* We have to be careful because dropping equalities may reorder them */
815 dropped = 0;
816 for (j = bmap->n_div - 1; j >= 0; --j) {
817 for (i = 0; i < bmap->n_eq; ++i)
818 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
819 break;
820 if (i < bmap->n_eq) {
821 bmap = isl_basic_map_drop_div(bmap, j);
822 isl_basic_map_drop_equality(bmap, i);
823 ++dropped;
824 }
825 }
826 pos[0] = 0;
827 needed = 0;
828 for (i = 1; i < T->n_row; ++i) {
829 if (isl_int_is_one(T->row[i][i]))
830 pos[i] = i;
831 else
832 needed++;
833 }
834 if (needed > dropped) {
835 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
836 needed, needed, 0);
837 if (!bmap)
838 goto error;
839 }
840 for (i = 1; i < T->n_row; ++i) {
841 if (isl_int_is_one(T->row[i][i]))
842 continue;
843 k = isl_basic_map_alloc_div(bmap);
844 pos[i] = 1 + total + k;
845 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
846 isl_int_set(bmap->div[k][0], T->row[i][i]);
847 if (C2)
848 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
849 else
850 isl_int_set_si(bmap->div[k][1 + i], 1);
851 for (j = 0; j < i; ++j) {
852 if (isl_int_is_zero(T->row[i][j]))
853 continue;
854 if (pos[j] < T->n_row && C2)
855 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
856 C2->row[pos[j]], 1 + total);
857 else
858 isl_int_neg(bmap->div[k][1 + pos[j]],
859 T->row[i][j]);
860 }
861 j = isl_basic_map_alloc_equality(bmap);
862 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
863 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
864 }
865 free(pos);
866 isl_mat_free(C2);
867 isl_mat_free(T);
868
869 if (progress)
870 *progress = 1;
871 done:
872 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
873
874 return bmap;
875 error:
876 isl_mat_free(C);
877 isl_mat_free(C2);
878 isl_mat_free(T);
879 return bmap;
880 }
881
882 static struct isl_basic_map *set_div_from_lower_bound(
883 struct isl_basic_map *bmap, int div, int ineq)
884 {
885 unsigned total = 1 + isl_dim_total(bmap->dim);
886
887 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
888 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
889 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
890 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
891 isl_int_set_si(bmap->div[div][1 + total + div], 0);
892
893 return bmap;
894 }
895
896 /* Check whether it is ok to define a div based on an inequality.
897 * To avoid the introduction of circular definitions of divs, we
898 * do not allow such a definition if the resulting expression would refer to
899 * any other undefined divs or if any known div is defined in
900 * terms of the unknown div.
901 */
902 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
903 int div, int ineq)
904 {
905 int j;
906 unsigned total = 1 + isl_dim_total(bmap->dim);
907
908 /* Not defined in terms of unknown divs */
909 for (j = 0; j < bmap->n_div; ++j) {
910 if (div == j)
911 continue;
912 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
913 continue;
914 if (isl_int_is_zero(bmap->div[j][0]))
915 return 0;
916 }
917
918 /* No other div defined in terms of this one => avoid loops */
919 for (j = 0; j < bmap->n_div; ++j) {
920 if (div == j)
921 continue;
922 if (isl_int_is_zero(bmap->div[j][0]))
923 continue;
924 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
925 return 0;
926 }
927
928 return 1;
929 }
930
931 /* Given two constraints "k" and "l" that are opposite to each other,
932 * except for the constant term, check if we can use them
933 * to obtain an expression for one of the hitherto unknown divs.
934 * "sum" is the sum of the constant terms of the constraints.
935 * If this sum is strictly smaller than the coefficient of one
936 * of the divs, then this pair can be used define the div.
937 * To avoid the introduction of circular definitions of divs, we
938 * do not use the pair if the resulting expression would refer to
939 * any other undefined divs or if any known div is defined in
940 * terms of the unknown div.
941 */
942 static struct isl_basic_map *check_for_div_constraints(
943 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
944 {
945 int i;
946 unsigned total = 1 + isl_dim_total(bmap->dim);
947
948 for (i = 0; i < bmap->n_div; ++i) {
949 if (!isl_int_is_zero(bmap->div[i][0]))
950 continue;
951 if (isl_int_is_zero(bmap->ineq[k][total + i]))
952 continue;
953 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
954 continue;
955 if (!ok_to_set_div_from_bound(bmap, i, k))
956 break;
957 if (isl_int_is_pos(bmap->ineq[k][total + i]))
958 bmap = set_div_from_lower_bound(bmap, i, k);
959 else
960 bmap = set_div_from_lower_bound(bmap, i, l);
961 if (progress)
962 *progress = 1;
963 break;
964 }
965 return bmap;
966 }
967
968 static struct isl_basic_map *remove_duplicate_constraints(
969 struct isl_basic_map *bmap, int *progress)
970 {
971 unsigned int size;
972 isl_int ***index;
973 int k, l, h;
974 int bits;
975 unsigned total = isl_basic_map_total_dim(bmap);
976 isl_int sum;
977
978 if (bmap->n_ineq <= 1)
979 return bmap;
980
981 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
982 bits = ffs(size) - 1;
983 index = isl_calloc_array(ctx, isl_int **, size);
984 if (!index)
985 return bmap;
986
987 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
988 for (k = 1; k < bmap->n_ineq; ++k) {
989 h = hash_index(index, size, bits, bmap, k);
990 if (!index[h]) {
991 index[h] = &bmap->ineq[k];
992 continue;
993 }
994 if (progress)
995 *progress = 1;
996 l = index[h] - &bmap->ineq[0];
997 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
998 swap_inequality(bmap, k, l);
999 isl_basic_map_drop_inequality(bmap, k);
1000 --k;
1001 }
1002 isl_int_init(sum);
1003 for (k = 0; k < bmap->n_ineq-1; ++k) {
1004 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1005 h = hash_index(index, size, bits, bmap, k);
1006 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1007 if (!index[h])
1008 continue;
1009 l = index[h] - &bmap->ineq[0];
1010 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1011 if (isl_int_is_pos(sum)) {
1012 bmap = check_for_div_constraints(bmap, k, l, sum,
1013 progress);
1014 continue;
1015 }
1016 if (isl_int_is_zero(sum)) {
1017 /* We need to break out of the loop after these
1018 * changes since the contents of the hash
1019 * will no longer be valid.
1020 * Plus, we probably we want to regauss first.
1021 */
1022 isl_basic_map_drop_inequality(bmap, l);
1023 isl_basic_map_inequality_to_equality(bmap, k);
1024 } else
1025 bmap = isl_basic_map_set_to_empty(bmap);
1026 break;
1027 }
1028 isl_int_clear(sum);
1029
1030 free(index);
1031 return bmap;
1032 }
1033
1034
1035 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1036 {
1037 int progress = 1;
1038 if (!bmap)
1039 return NULL;
1040 while (progress) {
1041 progress = 0;
1042 bmap = isl_basic_map_normalize_constraints(bmap);
1043 bmap = remove_duplicate_divs(bmap, &progress);
1044 bmap = eliminate_divs_eq(bmap, &progress);
1045 bmap = eliminate_divs_ineq(bmap, &progress);
1046 bmap = isl_basic_map_gauss(bmap, &progress);
1047 /* requires equalities in normal form */
1048 bmap = normalize_divs(bmap, &progress);
1049 bmap = remove_duplicate_constraints(bmap, &progress);
1050 }
1051 return bmap;
1052 }
1053
1054 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1055 {
1056 return (struct isl_basic_set *)
1057 isl_basic_map_simplify((struct isl_basic_map *)bset);
1058 }
1059
1060
1061 /* If the only constraints a div d=floor(f/m)
1062 * appears in are its two defining constraints
1063 *
1064 * f - m d >=0
1065 * -(f - (m - 1)) + m d >= 0
1066 *
1067 * then it can safely be removed.
1068 */
1069 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1070 {
1071 int i;
1072 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1073
1074 for (i = 0; i < bmap->n_eq; ++i)
1075 if (!isl_int_is_zero(bmap->eq[i][pos]))
1076 return 0;
1077
1078 for (i = 0; i < bmap->n_ineq; ++i) {
1079 if (isl_int_is_zero(bmap->ineq[i][pos]))
1080 continue;
1081 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1082 int neg;
1083 isl_int_sub(bmap->div[div][1],
1084 bmap->div[div][1], bmap->div[div][0]);
1085 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1086 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1087 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1088 isl_int_add(bmap->div[div][1],
1089 bmap->div[div][1], bmap->div[div][0]);
1090 if (!neg)
1091 return 0;
1092 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1093 bmap->n_div-div-1) != -1)
1094 return 0;
1095 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1096 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1097 return 0;
1098 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1099 bmap->n_div-div-1) != -1)
1100 return 0;
1101 } else
1102 return 0;
1103 }
1104
1105 for (i = 0; i < bmap->n_div; ++i)
1106 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1107 return 0;
1108
1109 return 1;
1110 }
1111
1112 /*
1113 * Remove divs that don't occur in any of the constraints or other divs.
1114 * These can arise when dropping some of the variables in a quast
1115 * returned by piplib.
1116 */
1117 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1118 {
1119 int i;
1120
1121 if (!bmap)
1122 return NULL;
1123
1124 for (i = bmap->n_div-1; i >= 0; --i) {
1125 if (!div_is_redundant(bmap, i))
1126 continue;
1127 bmap = isl_basic_map_drop_div(bmap, i);
1128 }
1129 return bmap;
1130 }
1131
1132 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1133 {
1134 bmap = remove_redundant_divs(bmap);
1135 if (!bmap)
1136 return NULL;
1137 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1138 return bmap;
1139 }
1140
1141 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1142 {
1143 return (struct isl_basic_set *)
1144 isl_basic_map_finalize((struct isl_basic_map *)bset);
1145 }
1146
1147 struct isl_set *isl_set_finalize(struct isl_set *set)
1148 {
1149 int i;
1150
1151 if (!set)
1152 return NULL;
1153 for (i = 0; i < set->n; ++i) {
1154 set->p[i] = isl_basic_set_finalize(set->p[i]);
1155 if (!set->p[i])
1156 goto error;
1157 }
1158 return set;
1159 error:
1160 isl_set_free(set);
1161 return NULL;
1162 }
1163
1164 struct isl_map *isl_map_finalize(struct isl_map *map)
1165 {
1166 int i;
1167
1168 if (!map)
1169 return NULL;
1170 for (i = 0; i < map->n; ++i) {
1171 map->p[i] = isl_basic_map_finalize(map->p[i]);
1172 if (!map->p[i])
1173 goto error;
1174 }
1175 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1176 return map;
1177 error:
1178 isl_map_free(map);
1179 return NULL;
1180 }
1181
1182
1183 /* Remove definition of any div that is defined in terms of the given variable.
1184 * The div itself is not removed. Functions such as
1185 * eliminate_divs_ineq depend on the other divs remaining in place.
1186 */
1187 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1188 int pos)
1189 {
1190 int i;
1191
1192 for (i = 0; i < bmap->n_div; ++i) {
1193 if (isl_int_is_zero(bmap->div[i][0]))
1194 continue;
1195 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1196 continue;
1197 isl_int_set_si(bmap->div[i][0], 0);
1198 }
1199 return bmap;
1200 }
1201
1202 /* Eliminate the specified variables from the constraints using
1203 * Fourier-Motzkin. The variables themselves are not removed.
1204 */
1205 struct isl_basic_map *isl_basic_map_eliminate_vars(
1206 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1207 {
1208 int d;
1209 int i, j, k;
1210 unsigned total;
1211
1212 if (n == 0)
1213 return bmap;
1214 if (!bmap)
1215 return NULL;
1216 total = isl_basic_map_total_dim(bmap);
1217
1218 bmap = isl_basic_map_cow(bmap);
1219 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1220 bmap = remove_dependent_vars(bmap, d);
1221
1222 for (d = pos + n - 1;
1223 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1224 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1225 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1226 int n_lower, n_upper;
1227 if (!bmap)
1228 return NULL;
1229 for (i = 0; i < bmap->n_eq; ++i) {
1230 if (isl_int_is_zero(bmap->eq[i][1+d]))
1231 continue;
1232 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1233 isl_basic_map_drop_equality(bmap, i);
1234 break;
1235 }
1236 if (i < bmap->n_eq)
1237 continue;
1238 n_lower = 0;
1239 n_upper = 0;
1240 for (i = 0; i < bmap->n_ineq; ++i) {
1241 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1242 n_lower++;
1243 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1244 n_upper++;
1245 }
1246 bmap = isl_basic_map_extend_constraints(bmap,
1247 0, n_lower * n_upper);
1248 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1249 int last;
1250 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1251 continue;
1252 last = -1;
1253 for (j = 0; j < i; ++j) {
1254 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1255 continue;
1256 last = j;
1257 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1258 isl_int_sgn(bmap->ineq[j][1+d]))
1259 continue;
1260 k = isl_basic_map_alloc_inequality(bmap);
1261 if (k < 0)
1262 goto error;
1263 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1264 1+total);
1265 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1266 1+d, 1+total, NULL);
1267 }
1268 isl_basic_map_drop_inequality(bmap, i);
1269 i = last + 1;
1270 }
1271 if (n_lower > 0 && n_upper > 0) {
1272 bmap = isl_basic_map_normalize_constraints(bmap);
1273 bmap = remove_duplicate_constraints(bmap, NULL);
1274 bmap = isl_basic_map_gauss(bmap, NULL);
1275 bmap = isl_basic_map_convex_hull(bmap);
1276 if (!bmap)
1277 goto error;
1278 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1279 break;
1280 }
1281 }
1282 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1283 return bmap;
1284 error:
1285 isl_basic_map_free(bmap);
1286 return NULL;
1287 }
1288
1289 struct isl_basic_set *isl_basic_set_eliminate_vars(
1290 struct isl_basic_set *bset, unsigned pos, unsigned n)
1291 {
1292 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1293 (struct isl_basic_map *)bset, pos, n);
1294 }
1295
1296 /* Don't assume equalities are in order, because align_divs
1297 * may have changed the order of the divs.
1298 */
1299 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1300 {
1301 int d, i;
1302 unsigned total;
1303
1304 total = isl_dim_total(bmap->dim);
1305 for (d = 0; d < total; ++d)
1306 elim[d] = -1;
1307 for (i = 0; i < bmap->n_eq; ++i) {
1308 for (d = total - 1; d >= 0; --d) {
1309 if (isl_int_is_zero(bmap->eq[i][1+d]))
1310 continue;
1311 elim[d] = i;
1312 break;
1313 }
1314 }
1315 }
1316
1317 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1318 {
1319 compute_elimination_index((struct isl_basic_map *)bset, elim);
1320 }
1321
1322 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1323 struct isl_basic_map *bmap, int *elim)
1324 {
1325 int d;
1326 int copied = 0;
1327 unsigned total;
1328
1329 total = isl_dim_total(bmap->dim);
1330 for (d = total - 1; d >= 0; --d) {
1331 if (isl_int_is_zero(src[1+d]))
1332 continue;
1333 if (elim[d] == -1)
1334 continue;
1335 if (!copied) {
1336 isl_seq_cpy(dst, src, 1 + total);
1337 copied = 1;
1338 }
1339 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1340 }
1341 return copied;
1342 }
1343
1344 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1345 struct isl_basic_set *bset, int *elim)
1346 {
1347 return reduced_using_equalities(dst, src,
1348 (struct isl_basic_map *)bset, elim);
1349 }
1350
1351 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1352 struct isl_basic_set *bset, struct isl_basic_set *context)
1353 {
1354 int i;
1355 int *elim;
1356
1357 if (!bset || !context)
1358 goto error;
1359
1360 bset = isl_basic_set_cow(bset);
1361 if (!bset)
1362 goto error;
1363
1364 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1365 if (!elim)
1366 goto error;
1367 set_compute_elimination_index(context, elim);
1368 for (i = 0; i < bset->n_eq; ++i)
1369 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1370 context, elim);
1371 for (i = 0; i < bset->n_ineq; ++i)
1372 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1373 context, elim);
1374 isl_basic_set_free(context);
1375 free(elim);
1376 bset = isl_basic_set_simplify(bset);
1377 bset = isl_basic_set_finalize(bset);
1378 return bset;
1379 error:
1380 isl_basic_set_free(bset);
1381 isl_basic_set_free(context);
1382 return NULL;
1383 }
1384
1385 static struct isl_basic_set *remove_shifted_constraints(
1386 struct isl_basic_set *bset, struct isl_basic_set *context)
1387 {
1388 unsigned int size;
1389 isl_int ***index;
1390 int bits;
1391 int k, h, l;
1392
1393 if (!bset)
1394 return NULL;
1395
1396 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1397 bits = ffs(size) - 1;
1398 index = isl_calloc_array(ctx, isl_int **, size);
1399 if (!index)
1400 return bset;
1401
1402 for (k = 0; k < context->n_ineq; ++k) {
1403 h = set_hash_index(index, size, bits, context, k);
1404 index[h] = &context->ineq[k];
1405 }
1406 for (k = 0; k < bset->n_ineq; ++k) {
1407 h = set_hash_index(index, size, bits, bset, k);
1408 if (!index[h])
1409 continue;
1410 l = index[h] - &context->ineq[0];
1411 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1412 continue;
1413 bset = isl_basic_set_cow(bset);
1414 if (!bset)
1415 goto error;
1416 isl_basic_set_drop_inequality(bset, k);
1417 --k;
1418 }
1419 free(index);
1420 return bset;
1421 error:
1422 free(index);
1423 return bset;
1424 }
1425
1426 /* Tighten (decrease) the constant terms of the inequalities based
1427 * on the equalities, without removing any integer points.
1428 * For example, if there is an equality
1429 *
1430 * i = 3 * j
1431 *
1432 * and an inequality
1433 *
1434 * i >= 1
1435 *
1436 * then we want to replace the inequality by
1437 *
1438 * i >= 3
1439 *
1440 * We do this by computing a variable compression and translating
1441 * the constraints to the compressed space.
1442 * If any constraint has coefficients (except the contant term)
1443 * with a common factor "f", then we can replace the constant term "c"
1444 * by
1445 *
1446 * f * floor(c/f)
1447 *
1448 * That is, we add
1449 *
1450 * f * floor(c/f) - c = -fract(c/f)
1451 *
1452 * and we can add the same value to the original constraint.
1453 *
1454 * In the example, the compressed space only contains "j",
1455 * and the inequality translates to
1456 *
1457 * 3 * j - 1 >= 0
1458 *
1459 * We add -fract(-1/3) = -2 to the original constraint to obtain
1460 *
1461 * i - 3 >= 0
1462 */
1463 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1464 struct isl_basic_set *bset)
1465 {
1466 int i;
1467 unsigned total;
1468 struct isl_mat *B, *C;
1469 isl_int gcd;
1470
1471 if (!bset)
1472 return NULL;
1473
1474 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1475 return bset;
1476
1477 if (!bset->n_ineq)
1478 return bset;
1479
1480 bset = isl_basic_set_cow(bset);
1481 if (!bset)
1482 return NULL;
1483
1484 total = isl_basic_set_total_dim(bset);
1485 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1486 C = isl_mat_variable_compression(B, NULL);
1487 if (!C)
1488 return bset;
1489 if (C->n_col == 0) {
1490 isl_mat_free(C);
1491 return isl_basic_set_set_to_empty(bset);
1492 }
1493 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1494 0, bset->n_ineq, 0, 1 + total);
1495 C = isl_mat_product(B, C);
1496 if (!C)
1497 return bset;
1498
1499 isl_int_init(gcd);
1500 for (i = 0; i < bset->n_ineq; ++i) {
1501 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1502 if (isl_int_is_one(gcd))
1503 continue;
1504 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1505 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1506 }
1507 isl_int_clear(gcd);
1508
1509 isl_mat_free(C);
1510
1511 return bset;
1512 }
1513
1514 /* Remove all information from bset that is redundant in the context
1515 * of context. In particular, equalities that are linear combinations
1516 * of those in context are removed. Then the inequalities that are
1517 * redundant in the context of the equalities and inequalities of
1518 * context are removed.
1519 *
1520 * We first simplify the constraints of "bset" in the context of the
1521 * equalities of "context".
1522 * Then we simplify the inequalities of the context in the context
1523 * of the equalities of bset and remove the inequalities from "bset"
1524 * that are obviously redundant with respect to some inequality in "context".
1525 *
1526 * If there are any inequalities left, we construct a tableau for
1527 * the context and then add the inequalities of "bset".
1528 * Before adding these equalities, we freeze all constraints such that
1529 * they won't be considered redundant in terms of the constraints of "bset".
1530 * Then we detect all equalities and redundant constraints (among the
1531 * constraints that weren't frozen) and update bset according to the results.
1532 * We have to be careful here because we don't want any of the context
1533 * constraints to remain and because we haven't added the equalities of "bset"
1534 * to the tableau so we temporarily have to pretend that there were no
1535 * equalities.
1536 */
1537 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1538 struct isl_basic_set *context)
1539 {
1540 int i;
1541 struct isl_tab *tab;
1542 unsigned context_ineq;
1543 struct isl_basic_set *combined = NULL;
1544
1545 if (!context || !bset)
1546 goto error;
1547
1548 if (context->n_eq > 0)
1549 bset = isl_basic_set_reduce_using_equalities(bset,
1550 isl_basic_set_copy(context));
1551 if (!bset)
1552 goto error;
1553 if (isl_basic_set_fast_is_empty(bset))
1554 goto done;
1555 if (!bset->n_ineq)
1556 goto done;
1557
1558 if (bset->n_eq > 0) {
1559 struct isl_basic_set *affine_hull;
1560 affine_hull = isl_basic_set_copy(bset);
1561 affine_hull = isl_basic_set_cow(affine_hull);
1562 if (!affine_hull)
1563 goto error;
1564 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1565 context = isl_basic_set_intersect(context, affine_hull);
1566 context = isl_basic_set_gauss(context, NULL);
1567 context = normalize_constraints_in_compressed_space(context);
1568 }
1569 if (!context)
1570 goto error;
1571 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1572 isl_basic_set_free(bset);
1573 return context;
1574 }
1575 if (!context->n_ineq)
1576 goto done;
1577 bset = remove_shifted_constraints(bset, context);
1578 if (!bset->n_ineq)
1579 goto done;
1580 isl_basic_set_free_equality(context, context->n_eq);
1581 context_ineq = context->n_ineq;
1582 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1583 combined = isl_basic_set_extend_constraints(combined,
1584 bset->n_eq, bset->n_ineq);
1585 tab = isl_tab_from_basic_set(combined);
1586 if (!tab)
1587 goto error;
1588 for (i = 0; i < context_ineq; ++i)
1589 tab->con[i].frozen = 1;
1590 tab = isl_tab_extend(tab, bset->n_ineq);
1591 if (!tab)
1592 goto error;
1593 for (i = 0; i < bset->n_ineq; ++i)
1594 tab = isl_tab_add_ineq(tab, bset->ineq[i]);
1595 bset = isl_basic_set_add_constraints(combined, bset, 0);
1596 tab = isl_tab_detect_equalities(tab);
1597 tab = isl_tab_detect_redundant(tab);
1598 if (!tab)
1599 goto error2;
1600 for (i = 0; i < context_ineq; ++i) {
1601 tab->con[i].is_zero = 0;
1602 tab->con[i].is_redundant = 1;
1603 }
1604 bset = isl_basic_set_update_from_tab(bset, tab);
1605 isl_tab_free(tab);
1606 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1607 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1608 done:
1609 bset = isl_basic_set_simplify(bset);
1610 bset = isl_basic_set_finalize(bset);
1611 isl_basic_set_free(context);
1612 return bset;
1613 error:
1614 isl_basic_set_free(combined);
1615 error2:
1616 isl_basic_set_free(bset);
1617 isl_basic_set_free(context);
1618 return NULL;
1619 }
1620
1621 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1622 * We simply add the equalities in context to bmap and then do a regular
1623 * div normalizations. Better results can be obtained by normalizing
1624 * only the divs in bmap than do not also appear in context.
1625 * We need to be careful to reduce the divs using the equalities
1626 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1627 * spurious constraints.
1628 */
1629 static struct isl_basic_map *normalize_divs_in_context(
1630 struct isl_basic_map *bmap, struct isl_basic_map *context)
1631 {
1632 int i;
1633 unsigned total_context;
1634 int div_eq;
1635
1636 div_eq = n_pure_div_eq(bmap);
1637 if (div_eq == 0)
1638 return bmap;
1639
1640 if (context->n_div > 0)
1641 bmap = isl_basic_map_align_divs(bmap, context);
1642
1643 total_context = isl_basic_map_total_dim(context);
1644 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1645 for (i = 0; i < context->n_eq; ++i) {
1646 int k;
1647 k = isl_basic_map_alloc_equality(bmap);
1648 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1649 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1650 isl_basic_map_total_dim(bmap) - total_context);
1651 }
1652 bmap = isl_basic_map_gauss(bmap, NULL);
1653 bmap = normalize_divs(bmap, NULL);
1654 bmap = isl_basic_map_gauss(bmap, NULL);
1655 return bmap;
1656 }
1657
1658 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1659 struct isl_basic_map *context)
1660 {
1661 struct isl_basic_set *bset;
1662
1663 if (!bmap || !context)
1664 goto error;
1665
1666 if (isl_basic_map_is_universe(context)) {
1667 isl_basic_map_free(context);
1668 return bmap;
1669 }
1670 if (isl_basic_map_is_universe(bmap)) {
1671 isl_basic_map_free(context);
1672 return bmap;
1673 }
1674 if (isl_basic_map_fast_is_empty(context)) {
1675 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1676 isl_basic_map_free(context);
1677 isl_basic_map_free(bmap);
1678 return isl_basic_map_universe(dim);
1679 }
1680 if (isl_basic_map_fast_is_empty(bmap)) {
1681 isl_basic_map_free(context);
1682 return bmap;
1683 }
1684
1685 bmap = isl_basic_map_convex_hull(bmap);
1686 context = isl_basic_map_convex_hull(context);
1687
1688 if (context->n_eq)
1689 bmap = normalize_divs_in_context(bmap, context);
1690
1691 context = isl_basic_map_align_divs(context, bmap);
1692 bmap = isl_basic_map_align_divs(bmap, context);
1693
1694 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1695 isl_basic_map_underlying_set(context));
1696
1697 return isl_basic_map_overlying_set(bset, bmap);
1698 error:
1699 isl_basic_map_free(bmap);
1700 isl_basic_map_free(context);
1701 return NULL;
1702 }
1703
1704 /*
1705 * Assumes context has no implicit divs.
1706 */
1707 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1708 {
1709 int i;
1710
1711 if (!map || !context)
1712 goto error;;
1713
1714 if (isl_basic_map_is_universe(context)) {
1715 isl_basic_map_free(context);
1716 return map;
1717 }
1718 if (isl_basic_map_fast_is_empty(context)) {
1719 struct isl_dim *dim = isl_dim_copy(map->dim);
1720 isl_basic_map_free(context);
1721 isl_map_free(map);
1722 return isl_map_universe(dim);
1723 }
1724
1725 context = isl_basic_map_convex_hull(context);
1726 map = isl_map_cow(map);
1727 if (!map || !context)
1728 goto error;;
1729 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1730 map = isl_map_compute_divs(map);
1731 for (i = 0; i < map->n; ++i)
1732 context = isl_basic_map_align_divs(context, map->p[i]);
1733 for (i = 0; i < map->n; ++i) {
1734 map->p[i] = isl_basic_map_gist(map->p[i],
1735 isl_basic_map_copy(context));
1736 if (!map->p[i])
1737 goto error;
1738 }
1739 isl_basic_map_free(context);
1740 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1741 return map;
1742 error:
1743 isl_map_free(map);
1744 isl_basic_map_free(context);
1745 return NULL;
1746 }
1747
1748 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1749 struct isl_basic_set *context)
1750 {
1751 return (struct isl_basic_set *)isl_basic_map_gist(
1752 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1753 }
1754
1755 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1756 {
1757 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1758 (struct isl_basic_map *)context);
1759 }
1760
1761 /* Quick check to see if two basic maps are disjoint.
1762 * In particular, we reduce the equalities and inequalities of
1763 * one basic map in the context of the equalities of the other
1764 * basic map and check if we get a contradiction.
1765 */
1766 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1767 struct isl_basic_map *bmap2)
1768 {
1769 struct isl_vec *v = NULL;
1770 int *elim = NULL;
1771 unsigned total;
1772 int i;
1773
1774 if (!bmap1 || !bmap2)
1775 return -1;
1776 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1777 return -1);
1778 if (bmap1->n_div || bmap2->n_div)
1779 return 0;
1780 if (!bmap1->n_eq && !bmap2->n_eq)
1781 return 0;
1782
1783 total = isl_dim_total(bmap1->dim);
1784 if (total == 0)
1785 return 0;
1786 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1787 if (!v)
1788 goto error;
1789 elim = isl_alloc_array(bmap1->ctx, int, total);
1790 if (!elim)
1791 goto error;
1792 compute_elimination_index(bmap1, elim);
1793 for (i = 0; i < bmap2->n_eq; ++i) {
1794 int reduced;
1795 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1796 bmap1, elim);
1797 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1798 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1799 goto disjoint;
1800 }
1801 for (i = 0; i < bmap2->n_ineq; ++i) {
1802 int reduced;
1803 reduced = reduced_using_equalities(v->block.data,
1804 bmap2->ineq[i], bmap1, elim);
1805 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1806 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1807 goto disjoint;
1808 }
1809 compute_elimination_index(bmap2, elim);
1810 for (i = 0; i < bmap1->n_ineq; ++i) {
1811 int reduced;
1812 reduced = reduced_using_equalities(v->block.data,
1813 bmap1->ineq[i], bmap2, elim);
1814 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1815 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1816 goto disjoint;
1817 }
1818 isl_vec_free(v);
1819 free(elim);
1820 return 0;
1821 disjoint:
1822 isl_vec_free(v);
1823 free(elim);
1824 return 1;
1825 error:
1826 isl_vec_free(v);
1827 free(elim);
1828 return -1;
1829 }
1830
1831 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1832 struct isl_basic_set *bset2)
1833 {
1834 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1835 (struct isl_basic_map *)bset2);
1836 }
1837
1838 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1839 {
1840 int i, j;
1841
1842 if (!map1 || !map2)
1843 return -1;
1844
1845 if (isl_map_fast_is_equal(map1, map2))
1846 return 0;
1847
1848 for (i = 0; i < map1->n; ++i) {
1849 for (j = 0; j < map2->n; ++j) {
1850 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1851 map2->p[j]);
1852 if (d != 1)
1853 return d;
1854 }
1855 }
1856 return 1;
1857 }
1858
1859 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1860 {
1861 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1862 (struct isl_map *)set2);
1863 }
1864
1865 /* Check if we can combine a given div with lower bound l and upper
1866 * bound u with some other div and if so return that other div.
1867 * Otherwise return -1.
1868 *
1869 * We first check that
1870 * - the bounds are opposites of each other (except for the constant
1871 * term)
1872 * - the bounds do not reference any other div
1873 * - no div is defined in terms of this div
1874 *
1875 * Let m be the size of the range allowed on the div by the bounds.
1876 * That is, the bounds are of the form
1877 *
1878 * e <= a <= e + m - 1
1879 *
1880 * with e some expression in the other variables.
1881 * We look for another div b such that no third div is defined in terms
1882 * of this second div b and such that in any constraint that contains
1883 * a (except for the given lower and upper bound), also contains b
1884 * with a coefficient that is m times that of b.
1885 * That is, all constraints (execpt for the lower and upper bound)
1886 * are of the form
1887 *
1888 * e + f (a + m b) >= 0
1889 *
1890 * If so, we return b so that "a + m b" can be replaced by
1891 * a single div "c = a + m b".
1892 */
1893 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1894 unsigned div, unsigned l, unsigned u)
1895 {
1896 int i, j;
1897 unsigned dim;
1898 int coalesce = -1;
1899
1900 if (bmap->n_div <= 1)
1901 return -1;
1902 dim = isl_dim_total(bmap->dim);
1903 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1904 return -1;
1905 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1906 bmap->n_div - div - 1) != -1)
1907 return -1;
1908 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1909 dim + bmap->n_div))
1910 return -1;
1911
1912 for (i = 0; i < bmap->n_div; ++i) {
1913 if (isl_int_is_zero(bmap->div[i][0]))
1914 continue;
1915 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
1916 return -1;
1917 }
1918
1919 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1920 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1921 for (i = 0; i < bmap->n_div; ++i) {
1922 if (i == div)
1923 continue;
1924 if (!pairs[i])
1925 continue;
1926 for (j = 0; j < bmap->n_div; ++j) {
1927 if (isl_int_is_zero(bmap->div[j][0]))
1928 continue;
1929 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
1930 break;
1931 }
1932 if (j < bmap->n_div)
1933 continue;
1934 for (j = 0; j < bmap->n_ineq; ++j) {
1935 int valid;
1936 if (j == l || j == u)
1937 continue;
1938 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
1939 continue;
1940 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
1941 break;
1942 isl_int_mul(bmap->ineq[j][1 + dim + div],
1943 bmap->ineq[j][1 + dim + div],
1944 bmap->ineq[l][0]);
1945 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
1946 bmap->ineq[j][1 + dim + i]);
1947 isl_int_divexact(bmap->ineq[j][1 + dim + div],
1948 bmap->ineq[j][1 + dim + div],
1949 bmap->ineq[l][0]);
1950 if (!valid)
1951 break;
1952 }
1953 if (j < bmap->n_ineq)
1954 continue;
1955 coalesce = i;
1956 break;
1957 }
1958 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1959 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1960 return coalesce;
1961 }
1962
1963 /* Given a lower and an upper bound on div i, construct an inequality
1964 * that when nonnegative ensures that this pair of bounds always allows
1965 * for an integer value of the given div.
1966 * The lower bound is inequality l, while the upper bound is inequality u.
1967 * The constructed inequality is stored in ineq.
1968 * g, fl, fu are temporary scalars.
1969 *
1970 * Let the upper bound be
1971 *
1972 * -n_u a + e_u >= 0
1973 *
1974 * and the lower bound
1975 *
1976 * n_l a + e_l >= 0
1977 *
1978 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1979 * We have
1980 *
1981 * - f_u e_l <= f_u f_l g a <= f_l e_u
1982 *
1983 * Since all variables are integer valued, this is equivalent to
1984 *
1985 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1986 *
1987 * If this interval is at least f_u f_l g, then it contains at least
1988 * one integer value for a.
1989 * That is, the test constraint is
1990 *
1991 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
1992 */
1993 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
1994 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
1995 {
1996 unsigned dim;
1997 dim = isl_dim_total(bmap->dim);
1998
1999 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2000 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2001 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2002 isl_int_neg(fu, fu);
2003 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2004 1 + dim + bmap->n_div);
2005 isl_int_add(ineq[0], ineq[0], fl);
2006 isl_int_add(ineq[0], ineq[0], fu);
2007 isl_int_sub_ui(ineq[0], ineq[0], 1);
2008 isl_int_mul(g, g, fl);
2009 isl_int_mul(g, g, fu);
2010 isl_int_sub(ineq[0], ineq[0], g);
2011 }
2012
2013 /* Remove more kinds of divs that are not strictly needed.
2014 * In particular, if all pairs of lower and upper bounds on a div
2015 * are such that they allow at least one integer value of the div,
2016 * the we can eliminate the div using Fourier-Motzkin without
2017 * introducing any spurious solutions.
2018 */
2019 static struct isl_basic_map *drop_more_redundant_divs(
2020 struct isl_basic_map *bmap, int *pairs, int n)
2021 {
2022 struct isl_tab *tab = NULL;
2023 struct isl_vec *vec = NULL;
2024 unsigned dim;
2025 int remove = -1;
2026 isl_int g, fl, fu;
2027
2028 isl_int_init(g);
2029 isl_int_init(fl);
2030 isl_int_init(fu);
2031
2032 if (!bmap)
2033 goto error;
2034
2035 dim = isl_dim_total(bmap->dim);
2036 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2037 if (!vec)
2038 goto error;
2039
2040 tab = isl_tab_from_basic_map(bmap);
2041
2042 while (n > 0) {
2043 int i, l, u;
2044 int best = -1;
2045 enum isl_lp_result res;
2046
2047 for (i = 0; i < bmap->n_div; ++i) {
2048 if (!pairs[i])
2049 continue;
2050 if (best >= 0 && pairs[best] <= pairs[i])
2051 continue;
2052 best = i;
2053 }
2054
2055 i = best;
2056 for (l = 0; l < bmap->n_ineq; ++l) {
2057 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2058 continue;
2059 for (u = 0; u < bmap->n_ineq; ++u) {
2060 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2061 continue;
2062 construct_test_ineq(bmap, i, l, u,
2063 vec->el, g, fl, fu);
2064 res = isl_tab_min(tab, vec->el,
2065 bmap->ctx->one, &g, NULL, 0);
2066 if (res == isl_lp_error)
2067 goto error;
2068 if (res == isl_lp_empty) {
2069 bmap = isl_basic_map_set_to_empty(bmap);
2070 break;
2071 }
2072 if (res != isl_lp_ok || isl_int_is_neg(g))
2073 break;
2074 }
2075 if (u < bmap->n_ineq)
2076 break;
2077 }
2078 if (l == bmap->n_ineq) {
2079 remove = i;
2080 break;
2081 }
2082 pairs[i] = 0;
2083 --n;
2084 }
2085
2086 isl_tab_free(tab);
2087 isl_vec_free(vec);
2088
2089 isl_int_clear(g);
2090 isl_int_clear(fl);
2091 isl_int_clear(fu);
2092
2093 free(pairs);
2094
2095 if (remove < 0)
2096 return bmap;
2097
2098 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2099 return isl_basic_map_drop_redundant_divs(bmap);
2100 error:
2101 free(pairs);
2102 isl_basic_map_free(bmap);
2103 isl_tab_free(tab);
2104 isl_vec_free(vec);
2105 isl_int_clear(g);
2106 isl_int_clear(fl);
2107 isl_int_clear(fu);
2108 return NULL;
2109 }
2110
2111 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2112 * and the upper bound u, div1 always occurs together with div2 in the form
2113 * (div1 + m div2), where m is the constant range on the variable div1
2114 * allowed by l and u, replace the pair div1 and div2 by a single
2115 * div that is equal to div1 + m div2.
2116 *
2117 * The new div will appear in the location that contains div2.
2118 * We need to modify all constraints that contain
2119 * div2 = (div - div1) / m
2120 * (If a constraint does not contain div2, it will also not contain div1.)
2121 * If the constraint also contains div1, then we know they appear
2122 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2123 * i.e., the coefficient of div is f.
2124 *
2125 * Otherwise, we first need to introduce div1 into the constraint.
2126 * Let the l be
2127 *
2128 * div1 + f >=0
2129 *
2130 * and u
2131 *
2132 * -div1 + f' >= 0
2133 *
2134 * A lower bound on div2
2135 *
2136 * n div2 + t >= 0
2137 *
2138 * can be replaced by
2139 *
2140 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2141 *
2142 * with g = gcd(m,n).
2143 * An upper bound
2144 *
2145 * -n div2 + t >= 0
2146 *
2147 * can be replaced by
2148 *
2149 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2150 *
2151 * These constraint are those that we would obtain from eliminating
2152 * div1 using Fourier-Motzkin.
2153 *
2154 * After all constraints have been modified, we drop the lower and upper
2155 * bound and then drop div1.
2156 */
2157 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2158 unsigned div1, unsigned div2, unsigned l, unsigned u)
2159 {
2160 isl_int a;
2161 isl_int b;
2162 isl_int m;
2163 unsigned dim, total;
2164 int i;
2165
2166 dim = isl_dim_total(bmap->dim);
2167 total = 1 + dim + bmap->n_div;
2168
2169 isl_int_init(a);
2170 isl_int_init(b);
2171 isl_int_init(m);
2172 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2173 isl_int_add_ui(m, m, 1);
2174
2175 for (i = 0; i < bmap->n_ineq; ++i) {
2176 if (i == l || i == u)
2177 continue;
2178 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2179 continue;
2180 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2181 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2182 isl_int_divexact(a, m, b);
2183 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2184 if (isl_int_is_pos(b)) {
2185 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2186 b, bmap->ineq[l], total);
2187 } else {
2188 isl_int_neg(b, b);
2189 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2190 b, bmap->ineq[u], total);
2191 }
2192 }
2193 isl_int_set(bmap->ineq[i][1 + dim + div2],
2194 bmap->ineq[i][1 + dim + div1]);
2195 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2196 }
2197
2198 isl_int_clear(a);
2199 isl_int_clear(b);
2200 isl_int_clear(m);
2201 if (l > u) {
2202 isl_basic_map_drop_inequality(bmap, l);
2203 isl_basic_map_drop_inequality(bmap, u);
2204 } else {
2205 isl_basic_map_drop_inequality(bmap, u);
2206 isl_basic_map_drop_inequality(bmap, l);
2207 }
2208 bmap = isl_basic_map_drop_div(bmap, div1);
2209 return bmap;
2210 }
2211
2212 /* First check if we can coalesce any pair of divs and
2213 * then continue with dropping more redundant divs.
2214 *
2215 * We loop over all pairs of lower and upper bounds on a div
2216 * with coefficient 1 and -1, respectively, check if there
2217 * is any other div "c" with which we can coalesce the div
2218 * and if so, perform the coalescing.
2219 */
2220 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2221 struct isl_basic_map *bmap, int *pairs, int n)
2222 {
2223 int i, l, u;
2224 unsigned dim;
2225
2226 dim = isl_dim_total(bmap->dim);
2227
2228 for (i = 0; i < bmap->n_div; ++i) {
2229 if (!pairs[i])
2230 continue;
2231 for (l = 0; l < bmap->n_ineq; ++l) {
2232 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2233 continue;
2234 for (u = 0; u < bmap->n_ineq; ++u) {
2235 int c;
2236
2237 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2238 continue;
2239 c = div_find_coalesce(bmap, pairs, i, l, u);
2240 if (c < 0)
2241 continue;
2242 free(pairs);
2243 bmap = coalesce_divs(bmap, i, c, l, u);
2244 return isl_basic_map_drop_redundant_divs(bmap);
2245 }
2246 }
2247 }
2248
2249 return drop_more_redundant_divs(bmap, pairs, n);
2250 }
2251
2252 /* Remove divs that are not strictly needed.
2253 * In particular, if a div only occurs positively (or negatively)
2254 * in constraints, then it can simply be dropped.
2255 * Also, if a div occurs only occurs in two constraints and if moreover
2256 * those two constraints are opposite to each other, except for the constant
2257 * term and if the sum of the constant terms is such that for any value
2258 * of the other values, there is always at least one integer value of the
2259 * div, i.e., if one plus this sum is greater than or equal to
2260 * the (absolute value) of the coefficent of the div in the constraints,
2261 * then we can also simply drop the div.
2262 *
2263 * If any divs are left after these simple checks then we move on
2264 * to more complicated cases in drop_more_redundant_divs.
2265 */
2266 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2267 struct isl_basic_map *bmap)
2268 {
2269 int i, j;
2270 unsigned off;
2271 int *pairs = NULL;
2272 int n = 0;
2273
2274 if (!bmap)
2275 goto error;
2276
2277 off = isl_dim_total(bmap->dim);
2278 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2279 if (!pairs)
2280 goto error;
2281
2282 for (i = 0; i < bmap->n_div; ++i) {
2283 int pos, neg;
2284 int last_pos, last_neg;
2285 int redundant;
2286 int defined;
2287
2288 defined = !isl_int_is_zero(bmap->div[i][0]);
2289 for (j = 0; j < bmap->n_eq; ++j)
2290 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2291 break;
2292 if (j < bmap->n_eq)
2293 continue;
2294 ++n;
2295 pos = neg = 0;
2296 for (j = 0; j < bmap->n_ineq; ++j) {
2297 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2298 last_pos = j;
2299 ++pos;
2300 }
2301 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2302 last_neg = j;
2303 ++neg;
2304 }
2305 }
2306 pairs[i] = pos * neg;
2307 if (pairs[i] == 0) {
2308 for (j = bmap->n_ineq - 1; j >= 0; --j)
2309 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2310 isl_basic_map_drop_inequality(bmap, j);
2311 bmap = isl_basic_map_drop_div(bmap, i);
2312 free(pairs);
2313 return isl_basic_map_drop_redundant_divs(bmap);
2314 }
2315 if (pairs[i] != 1)
2316 continue;
2317 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2318 bmap->ineq[last_neg] + 1,
2319 off + bmap->n_div))
2320 continue;
2321
2322 isl_int_add(bmap->ineq[last_pos][0],
2323 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2324 isl_int_add_ui(bmap->ineq[last_pos][0],
2325 bmap->ineq[last_pos][0], 1);
2326 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2327 bmap->ineq[last_pos][1+off+i]);
2328 isl_int_sub_ui(bmap->ineq[last_pos][0],
2329 bmap->ineq[last_pos][0], 1);
2330 isl_int_sub(bmap->ineq[last_pos][0],
2331 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2332 if (!redundant) {
2333 if (defined ||
2334 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2335 pairs[i] = 0;
2336 --n;
2337 continue;
2338 }
2339 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2340 bmap = isl_basic_map_simplify(bmap);
2341 free(pairs);
2342 return isl_basic_map_drop_redundant_divs(bmap);
2343 }
2344 if (last_pos > last_neg) {
2345 isl_basic_map_drop_inequality(bmap, last_pos);
2346 isl_basic_map_drop_inequality(bmap, last_neg);
2347 } else {
2348 isl_basic_map_drop_inequality(bmap, last_neg);
2349 isl_basic_map_drop_inequality(bmap, last_pos);
2350 }
2351 bmap = isl_basic_map_drop_div(bmap, i);
2352 free(pairs);
2353 return isl_basic_map_drop_redundant_divs(bmap);
2354 }
2355
2356 if (n > 0)
2357 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2358
2359 free(pairs);
2360 return bmap;
2361 error:
2362 free(pairs);
2363 isl_basic_map_free(bmap);
2364 return NULL;
2365 }
2366
2367 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2368 struct isl_basic_set *bset)
2369 {
2370 return (struct isl_basic_set *)
2371 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2372 }
2373
2374 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2375 {
2376 int i;
2377
2378 if (!map)
2379 return NULL;
2380 for (i = 0; i < map->n; ++i) {
2381 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2382 if (!map->p[i])
2383 goto error;
2384 }
2385 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2386 return map;
2387 error:
2388 isl_map_free(map);
2389 return NULL;
2390 }
2391
2392 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2393 {
2394 return (struct isl_set *)
2395 isl_map_drop_redundant_divs((struct isl_map *)set);
2396 }
Integer set library