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isl_map_read: extract out read_var_def
[isl.git] / isl_map_simplify.c
blob1c298c4c2199b730a4979907ebea4a62ccc3a44d
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include "isl_equalities.h"
11 #include "isl_map.h"
12 #include "isl_map_private.h"
13 #include "isl_seq.h"
14 #include "isl_tab.h"
15
16 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
17 {
18 isl_int *t = bmap->eq[a];
19 bmap->eq[a] = bmap->eq[b];
20 bmap->eq[b] = t;
21 }
22
23 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
24 {
25 if (a != b) {
26 isl_int *t = bmap->ineq[a];
27 bmap->ineq[a] = bmap->ineq[b];
28 bmap->ineq[b] = t;
29 }
30 }
31
32 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
33 {
34 swap_inequality((struct isl_basic_map *)bset, a, b);
35 }
36
37 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
38 {
39 isl_seq_cpy(c, c + n, rem);
40 isl_seq_clr(c + rem, n);
41 }
42
43 /* Drop n dimensions starting at first.
44 *
45 * In principle, this frees up some extra variables as the number
46 * of columns remains constant, but we would have to extend
47 * the div array too as the number of rows in this array is assumed
48 * to be equal to extra.
49 */
50 struct isl_basic_set *isl_basic_set_drop_dims(
51 struct isl_basic_set *bset, unsigned first, unsigned n)
52 {
53 int i;
54
55 if (!bset)
56 goto error;
57
58 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
59
60 if (n == 0)
61 return bset;
62
63 bset = isl_basic_set_cow(bset);
64 if (!bset)
65 return NULL;
66
67 for (i = 0; i < bset->n_eq; ++i)
68 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
69 (bset->dim->n_out-first-n)+bset->extra);
70
71 for (i = 0; i < bset->n_ineq; ++i)
72 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
73 (bset->dim->n_out-first-n)+bset->extra);
74
75 for (i = 0; i < bset->n_div; ++i)
76 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
77 (bset->dim->n_out-first-n)+bset->extra);
78
79 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
80 if (!bset->dim)
81 goto error;
82
83 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
84 bset = isl_basic_set_simplify(bset);
85 return isl_basic_set_finalize(bset);
86 error:
87 isl_basic_set_free(bset);
88 return NULL;
89 }
90
91 struct isl_set *isl_set_drop_dims(
92 struct isl_set *set, unsigned first, unsigned n)
93 {
94 int i;
95
96 if (!set)
97 goto error;
98
99 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
100
101 if (n == 0)
102 return set;
103 set = isl_set_cow(set);
104 if (!set)
105 goto error;
106 set->dim = isl_dim_drop_outputs(set->dim, first, n);
107 if (!set->dim)
108 goto error;
109
110 for (i = 0; i < set->n; ++i) {
111 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
112 if (!set->p[i])
113 goto error;
114 }
115
116 ISL_F_CLR(set, ISL_SET_NORMALIZED);
117 return set;
118 error:
119 isl_set_free(set);
120 return NULL;
121 }
122
123 /* Move "n" divs starting at "first" to the end of the list of divs.
124 */
125 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
126 unsigned first, unsigned n)
127 {
128 isl_int **div;
129 int i;
130
131 if (first + n == bmap->n_div)
132 return bmap;
133
134 div = isl_alloc_array(bmap->ctx, isl_int *, n);
135 if (!div)
136 goto error;
137 for (i = 0; i < n; ++i)
138 div[i] = bmap->div[first + i];
139 for (i = 0; i < bmap->n_div - first - n; ++i)
140 bmap->div[first + i] = bmap->div[first + n + i];
141 for (i = 0; i < n; ++i)
142 bmap->div[bmap->n_div - n + i] = div[i];
143 free(div);
144 return bmap;
145 error:
146 isl_basic_map_free(bmap);
147 return NULL;
148 }
149
150 /* Drop "n" dimensions of type "type" starting at "first".
151 *
152 * In principle, this frees up some extra variables as the number
153 * of columns remains constant, but we would have to extend
154 * the div array too as the number of rows in this array is assumed
155 * to be equal to extra.
156 */
157 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
158 enum isl_dim_type type, unsigned first, unsigned n)
159 {
160 int i;
161 unsigned dim;
162 unsigned offset;
163 unsigned left;
164
165 if (!bmap)
166 goto error;
167
168 dim = isl_basic_map_dim(bmap, type);
169 isl_assert(bmap->ctx, first + n <= dim, goto error);
170
171 if (n == 0)
172 return bmap;
173
174 bmap = isl_basic_map_cow(bmap);
175 if (!bmap)
176 return NULL;
177
178 offset = isl_basic_map_offset(bmap, type) + first;
179 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
180 for (i = 0; i < bmap->n_eq; ++i)
181 constraint_drop_vars(bmap->eq[i]+offset, n, left);
182
183 for (i = 0; i < bmap->n_ineq; ++i)
184 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
185
186 for (i = 0; i < bmap->n_div; ++i)
187 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
188
189 if (type == isl_dim_div) {
190 bmap = move_divs_last(bmap, first, n);
191 if (!bmap)
192 goto error;
193 isl_basic_map_free_div(bmap, n);
194 } else
195 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
196 if (!bmap->dim)
197 goto error;
198
199 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
200 bmap = isl_basic_map_simplify(bmap);
201 return isl_basic_map_finalize(bmap);
202 error:
203 isl_basic_map_free(bmap);
204 return NULL;
205 }
206
207 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
208 enum isl_dim_type type, unsigned first, unsigned n)
209 {
210 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
211 type, first, n);
212 }
213
214 struct isl_basic_map *isl_basic_map_drop_inputs(
215 struct isl_basic_map *bmap, unsigned first, unsigned n)
216 {
217 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
218 }
219
220 struct isl_map *isl_map_drop(struct isl_map *map,
221 enum isl_dim_type type, unsigned first, unsigned n)
222 {
223 int i;
224
225 if (!map)
226 goto error;
227
228 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
229
230 if (n == 0)
231 return map;
232 map = isl_map_cow(map);
233 if (!map)
234 goto error;
235 map->dim = isl_dim_drop(map->dim, type, first, n);
236 if (!map->dim)
237 goto error;
238
239 for (i = 0; i < map->n; ++i) {
240 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
241 if (!map->p[i])
242 goto error;
243 }
244 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
245
246 return map;
247 error:
248 isl_map_free(map);
249 return NULL;
250 }
251
252 struct isl_set *isl_set_drop(struct isl_set *set,
253 enum isl_dim_type type, unsigned first, unsigned n)
254 {
255 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
256 }
257
258 struct isl_map *isl_map_drop_inputs(
259 struct isl_map *map, unsigned first, unsigned n)
260 {
261 return isl_map_drop(map, isl_dim_in, first, n);
262 }
263
264 /*
265 * We don't cow, as the div is assumed to be redundant.
266 */
267 static struct isl_basic_map *isl_basic_map_drop_div(
268 struct isl_basic_map *bmap, unsigned div)
269 {
270 int i;
271 unsigned pos;
272
273 if (!bmap)
274 goto error;
275
276 pos = 1 + isl_dim_total(bmap->dim) + div;
277
278 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
279
280 for (i = 0; i < bmap->n_eq; ++i)
281 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
282
283 for (i = 0; i < bmap->n_ineq; ++i) {
284 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
285 isl_basic_map_drop_inequality(bmap, i);
286 --i;
287 continue;
288 }
289 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
290 }
291
292 for (i = 0; i < bmap->n_div; ++i)
293 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
294
295 if (div != bmap->n_div - 1) {
296 int j;
297 isl_int *t = bmap->div[div];
298
299 for (j = div; j < bmap->n_div - 1; ++j)
300 bmap->div[j] = bmap->div[j+1];
301
302 bmap->div[bmap->n_div - 1] = t;
303 }
304 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
305 isl_basic_map_free_div(bmap, 1);
306
307 return bmap;
308 error:
309 isl_basic_map_free(bmap);
310 return NULL;
311 }
312
313 struct isl_basic_map *isl_basic_map_normalize_constraints(
314 struct isl_basic_map *bmap)
315 {
316 int i;
317 isl_int gcd;
318 unsigned total = isl_basic_map_total_dim(bmap);
319
320 if (!bmap)
321 return NULL;
322
323 isl_int_init(gcd);
324 for (i = bmap->n_eq - 1; i >= 0; --i) {
325 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
326 if (isl_int_is_zero(gcd)) {
327 if (!isl_int_is_zero(bmap->eq[i][0])) {
328 bmap = isl_basic_map_set_to_empty(bmap);
329 break;
330 }
331 isl_basic_map_drop_equality(bmap, i);
332 continue;
333 }
334 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
335 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
336 if (isl_int_is_one(gcd))
337 continue;
338 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
339 bmap = isl_basic_map_set_to_empty(bmap);
340 break;
341 }
342 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
343 }
344
345 for (i = bmap->n_ineq - 1; i >= 0; --i) {
346 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
347 if (isl_int_is_zero(gcd)) {
348 if (isl_int_is_neg(bmap->ineq[i][0])) {
349 bmap = isl_basic_map_set_to_empty(bmap);
350 break;
351 }
352 isl_basic_map_drop_inequality(bmap, i);
353 continue;
354 }
355 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
356 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
357 if (isl_int_is_one(gcd))
358 continue;
359 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
360 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
361 }
362 isl_int_clear(gcd);
363
364 return bmap;
365 }
366
367 struct isl_basic_set *isl_basic_set_normalize_constraints(
368 struct isl_basic_set *bset)
369 {
370 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
371 (struct isl_basic_map *)bset);
372 }
373
374 /* Assumes divs have been ordered if keep_divs is set.
375 */
376 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
377 unsigned pos, isl_int *eq, int keep_divs, int *progress)
378 {
379 unsigned total;
380 int k;
381 int last_div;
382
383 total = isl_basic_map_total_dim(bmap);
384 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
385 bmap->n_div);
386 for (k = 0; k < bmap->n_eq; ++k) {
387 if (bmap->eq[k] == eq)
388 continue;
389 if (isl_int_is_zero(bmap->eq[k][1+pos]))
390 continue;
391 if (progress)
392 *progress = 1;
393 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
394 }
395
396 for (k = 0; k < bmap->n_ineq; ++k) {
397 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
398 continue;
399 if (progress)
400 *progress = 1;
401 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
402 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
403 }
404
405 for (k = 0; k < bmap->n_div; ++k) {
406 if (isl_int_is_zero(bmap->div[k][0]))
407 continue;
408 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
409 continue;
410 if (progress)
411 *progress = 1;
412 /* We need to be careful about circular definitions,
413 * so for now we just remove the definition of div k
414 * if the equality contains any divs.
415 * If keep_divs is set, then the divs have been ordered
416 * and we can keep the definition as long as the result
417 * is still ordered.
418 */
419 if (last_div == -1 || (keep_divs && last_div < k))
420 isl_seq_elim(bmap->div[k]+1, eq,
421 1+pos, 1+total, &bmap->div[k][0]);
422 else
423 isl_seq_clr(bmap->div[k], 1 + total);
424 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
425 }
426 }
427
428 /* Assumes divs have been ordered if keep_divs is set.
429 */
430 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
431 unsigned div, int keep_divs)
432 {
433 unsigned pos = isl_dim_total(bmap->dim) + div;
434
435 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
436
437 isl_basic_map_drop_div(bmap, div);
438 }
439
440 /* Check if elimination of div "div" using equality "eq" would not
441 * result in a div depending on a later div.
442 */
443 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
444 unsigned div)
445 {
446 int k;
447 int last_div;
448 unsigned pos = isl_dim_total(bmap->dim) + div;
449
450 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
451 bmap->n_div);
452 if (last_div < 0 || last_div <= div)
453 return 1;
454
455 for (k = 0; k <= last_div; ++k) {
456 if (isl_int_is_zero(bmap->div[k][0]))
457 return 1;
458 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
459 return 0;
460 }
461
462 return 1;
463 }
464
465 /* Elimininate divs based on equalities
466 */
467 static struct isl_basic_map *eliminate_divs_eq(
468 struct isl_basic_map *bmap, int *progress)
469 {
470 int d;
471 int i;
472 int modified = 0;
473 unsigned off;
474
475 bmap = isl_basic_map_order_divs(bmap);
476
477 if (!bmap)
478 return NULL;
479
480 off = 1 + isl_dim_total(bmap->dim);
481
482 for (d = bmap->n_div - 1; d >= 0 ; --d) {
483 for (i = 0; i < bmap->n_eq; ++i) {
484 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
485 !isl_int_is_negone(bmap->eq[i][off + d]))
486 continue;
487 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
488 continue;
489 modified = 1;
490 *progress = 1;
491 eliminate_div(bmap, bmap->eq[i], d, 1);
492 isl_basic_map_drop_equality(bmap, i);
493 break;
494 }
495 }
496 if (modified)
497 return eliminate_divs_eq(bmap, progress);
498 return bmap;
499 }
500
501 /* Elimininate divs based on inequalities
502 */
503 static struct isl_basic_map *eliminate_divs_ineq(
504 struct isl_basic_map *bmap, int *progress)
505 {
506 int d;
507 int i;
508 unsigned off;
509 struct isl_ctx *ctx;
510
511 if (!bmap)
512 return NULL;
513
514 ctx = bmap->ctx;
515 off = 1 + isl_dim_total(bmap->dim);
516
517 for (d = bmap->n_div - 1; d >= 0 ; --d) {
518 for (i = 0; i < bmap->n_eq; ++i)
519 if (!isl_int_is_zero(bmap->eq[i][off + d]))
520 break;
521 if (i < bmap->n_eq)
522 continue;
523 for (i = 0; i < bmap->n_ineq; ++i)
524 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
525 break;
526 if (i < bmap->n_ineq)
527 continue;
528 *progress = 1;
529 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
530 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
531 break;
532 bmap = isl_basic_map_drop_div(bmap, d);
533 if (!bmap)
534 break;
535 }
536 return bmap;
537 }
538
539 struct isl_basic_map *isl_basic_map_gauss(
540 struct isl_basic_map *bmap, int *progress)
541 {
542 int k;
543 int done;
544 int last_var;
545 unsigned total_var;
546 unsigned total;
547
548 bmap = isl_basic_map_order_divs(bmap);
549
550 if (!bmap)
551 return NULL;
552
553 total = isl_basic_map_total_dim(bmap);
554 total_var = total - bmap->n_div;
555
556 last_var = total - 1;
557 for (done = 0; done < bmap->n_eq; ++done) {
558 for (; last_var >= 0; --last_var) {
559 for (k = done; k < bmap->n_eq; ++k)
560 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
561 break;
562 if (k < bmap->n_eq)
563 break;
564 }
565 if (last_var < 0)
566 break;
567 if (k != done)
568 swap_equality(bmap, k, done);
569 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
570 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
571
572 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
573 progress);
574
575 if (last_var >= total_var &&
576 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
577 unsigned div = last_var - total_var;
578 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
579 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
580 isl_int_set(bmap->div[div][0],
581 bmap->eq[done][1+last_var]);
582 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
583 }
584 }
585 if (done == bmap->n_eq)
586 return bmap;
587 for (k = done; k < bmap->n_eq; ++k) {
588 if (isl_int_is_zero(bmap->eq[k][0]))
589 continue;
590 return isl_basic_map_set_to_empty(bmap);
591 }
592 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
593 return bmap;
594 }
595
596 struct isl_basic_set *isl_basic_set_gauss(
597 struct isl_basic_set *bset, int *progress)
598 {
599 return (struct isl_basic_set*)isl_basic_map_gauss(
600 (struct isl_basic_map *)bset, progress);
601 }
602
603
604 static unsigned int round_up(unsigned int v)
605 {
606 int old_v = v;
607
608 while (v) {
609 old_v = v;
610 v ^= v & -v;
611 }
612 return old_v << 1;
613 }
614
615 static int hash_index(isl_int ***index, unsigned int size, int bits,
616 struct isl_basic_map *bmap, int k)
617 {
618 int h;
619 unsigned total = isl_basic_map_total_dim(bmap);
620 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
621 for (h = hash; index[h]; h = (h+1) % size)
622 if (&bmap->ineq[k] != index[h] &&
623 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
624 break;
625 return h;
626 }
627
628 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
629 struct isl_basic_set *bset, int k)
630 {
631 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
632 }
633
634 /* If we can eliminate more than one div, then we need to make
635 * sure we do it from last div to first div, in order not to
636 * change the position of the other divs that still need to
637 * be removed.
638 */
639 static struct isl_basic_map *remove_duplicate_divs(
640 struct isl_basic_map *bmap, int *progress)
641 {
642 unsigned int size;
643 int *index;
644 int *elim_for;
645 int k, l, h;
646 int bits;
647 struct isl_blk eq;
648 unsigned total_var;
649 unsigned total;
650 struct isl_ctx *ctx;
651
652 if (!bmap || bmap->n_div <= 1)
653 return bmap;
654
655 total_var = isl_dim_total(bmap->dim);
656 total = total_var + bmap->n_div;
657
658 ctx = bmap->ctx;
659 for (k = bmap->n_div - 1; k >= 0; --k)
660 if (!isl_int_is_zero(bmap->div[k][0]))
661 break;
662 if (k <= 0)
663 return bmap;
664
665 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
666 size = round_up(4 * bmap->n_div / 3 - 1);
667 bits = ffs(size) - 1;
668 index = isl_calloc_array(ctx, int, size);
669 if (!index)
670 return bmap;
671 eq = isl_blk_alloc(ctx, 1+total);
672 if (isl_blk_is_error(eq))
673 goto out;
674
675 isl_seq_clr(eq.data, 1+total);
676 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
677 for (--k; k >= 0; --k) {
678 uint32_t hash;
679
680 if (isl_int_is_zero(bmap->div[k][0]))
681 continue;
682
683 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
684 for (h = hash; index[h]; h = (h+1) % size)
685 if (isl_seq_eq(bmap->div[k],
686 bmap->div[index[h]-1], 2+total))
687 break;
688 if (index[h]) {
689 *progress = 1;
690 l = index[h] - 1;
691 elim_for[l] = k + 1;
692 }
693 index[h] = k+1;
694 }
695 for (l = bmap->n_div - 1; l >= 0; --l) {
696 if (!elim_for[l])
697 continue;
698 k = elim_for[l] - 1;
699 isl_int_set_si(eq.data[1+total_var+k], -1);
700 isl_int_set_si(eq.data[1+total_var+l], 1);
701 eliminate_div(bmap, eq.data, l, 0);
702 isl_int_set_si(eq.data[1+total_var+k], 0);
703 isl_int_set_si(eq.data[1+total_var+l], 0);
704 }
705
706 isl_blk_free(ctx, eq);
707 out:
708 free(index);
709 free(elim_for);
710 return bmap;
711 }
712
713 static int n_pure_div_eq(struct isl_basic_map *bmap)
714 {
715 int i, j;
716 unsigned total;
717
718 total = isl_dim_total(bmap->dim);
719 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
720 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
721 --j;
722 if (j < 0)
723 break;
724 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
725 return 0;
726 }
727 return i;
728 }
729
730 /* Normalize divs that appear in equalities.
731 *
732 * In particular, we assume that bmap contains some equalities
733 * of the form
734 *
735 * a x = m * e_i
736 *
737 * and we want to replace the set of e_i by a minimal set and
738 * such that the new e_i have a canonical representation in terms
739 * of the vector x.
740 * If any of the equalities involves more than one divs, then
741 * we currently simply bail out.
742 *
743 * Let us first additionally assume that all equalities involve
744 * a div. The equalities then express modulo constraints on the
745 * remaining variables and we can use "parameter compression"
746 * to find a minimal set of constraints. The result is a transformation
747 *
748 * x = T(x') = x_0 + G x'
749 *
750 * with G a lower-triangular matrix with all elements below the diagonal
751 * non-negative and smaller than the diagonal element on the same row.
752 * We first normalize x_0 by making the same property hold in the affine
753 * T matrix.
754 * The rows i of G with a 1 on the diagonal do not impose any modulo
755 * constraint and simply express x_i = x'_i.
756 * For each of the remaining rows i, we introduce a div and a corresponding
757 * equality. In particular
758 *
759 * g_ii e_j = x_i - g_i(x')
760 *
761 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
762 * corresponding div (if g_kk != 1).
763 *
764 * If there are any equalities not involving any div, then we
765 * first apply a variable compression on the variables x:
766 *
767 * x = C x'' x'' = C_2 x
768 *
769 * and perform the above parameter compression on A C instead of on A.
770 * The resulting compression is then of the form
771 *
772 * x'' = T(x') = x_0 + G x'
773 *
774 * and in constructing the new divs and the corresponding equalities,
775 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
776 * by the corresponding row from C_2.
777 */
778 static struct isl_basic_map *normalize_divs(
779 struct isl_basic_map *bmap, int *progress)
780 {
781 int i, j, k;
782 int total;
783 int div_eq;
784 struct isl_mat *B;
785 struct isl_vec *d;
786 struct isl_mat *T = NULL;
787 struct isl_mat *C = NULL;
788 struct isl_mat *C2 = NULL;
789 isl_int v;
790 int *pos;
791 int dropped, needed;
792
793 if (!bmap)
794 return NULL;
795
796 if (bmap->n_div == 0)
797 return bmap;
798
799 if (bmap->n_eq == 0)
800 return bmap;
801
802 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
803 return bmap;
804
805 total = isl_dim_total(bmap->dim);
806 div_eq = n_pure_div_eq(bmap);
807 if (div_eq == 0)
808 return bmap;
809
810 if (div_eq < bmap->n_eq) {
811 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
812 bmap->n_eq - div_eq, 0, 1 + total);
813 C = isl_mat_variable_compression(B, &C2);
814 if (!C || !C2)
815 goto error;
816 if (C->n_col == 0) {
817 bmap = isl_basic_map_set_to_empty(bmap);
818 isl_mat_free(C);
819 isl_mat_free(C2);
820 goto done;
821 }
822 }
823
824 d = isl_vec_alloc(bmap->ctx, div_eq);
825 if (!d)
826 goto error;
827 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
828 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
829 --j;
830 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
831 }
832 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
833
834 if (C) {
835 B = isl_mat_product(B, C);
836 C = NULL;
837 }
838
839 T = isl_mat_parameter_compression(B, d);
840 if (!T)
841 goto error;
842 if (T->n_col == 0) {
843 bmap = isl_basic_map_set_to_empty(bmap);
844 isl_mat_free(C2);
845 isl_mat_free(T);
846 goto done;
847 }
848 isl_int_init(v);
849 for (i = 0; i < T->n_row - 1; ++i) {
850 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
851 if (isl_int_is_zero(v))
852 continue;
853 isl_mat_col_submul(T, 0, v, 1 + i);
854 }
855 isl_int_clear(v);
856 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
857 if (!pos)
858 goto error;
859 /* We have to be careful because dropping equalities may reorder them */
860 dropped = 0;
861 for (j = bmap->n_div - 1; j >= 0; --j) {
862 for (i = 0; i < bmap->n_eq; ++i)
863 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
864 break;
865 if (i < bmap->n_eq) {
866 bmap = isl_basic_map_drop_div(bmap, j);
867 isl_basic_map_drop_equality(bmap, i);
868 ++dropped;
869 }
870 }
871 pos[0] = 0;
872 needed = 0;
873 for (i = 1; i < T->n_row; ++i) {
874 if (isl_int_is_one(T->row[i][i]))
875 pos[i] = i;
876 else
877 needed++;
878 }
879 if (needed > dropped) {
880 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
881 needed, needed, 0);
882 if (!bmap)
883 goto error;
884 }
885 for (i = 1; i < T->n_row; ++i) {
886 if (isl_int_is_one(T->row[i][i]))
887 continue;
888 k = isl_basic_map_alloc_div(bmap);
889 pos[i] = 1 + total + k;
890 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
891 isl_int_set(bmap->div[k][0], T->row[i][i]);
892 if (C2)
893 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
894 else
895 isl_int_set_si(bmap->div[k][1 + i], 1);
896 for (j = 0; j < i; ++j) {
897 if (isl_int_is_zero(T->row[i][j]))
898 continue;
899 if (pos[j] < T->n_row && C2)
900 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
901 C2->row[pos[j]], 1 + total);
902 else
903 isl_int_neg(bmap->div[k][1 + pos[j]],
904 T->row[i][j]);
905 }
906 j = isl_basic_map_alloc_equality(bmap);
907 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
908 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
909 }
910 free(pos);
911 isl_mat_free(C2);
912 isl_mat_free(T);
913
914 if (progress)
915 *progress = 1;
916 done:
917 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
918
919 return bmap;
920 error:
921 isl_mat_free(C);
922 isl_mat_free(C2);
923 isl_mat_free(T);
924 return bmap;
925 }
926
927 static struct isl_basic_map *set_div_from_lower_bound(
928 struct isl_basic_map *bmap, int div, int ineq)
929 {
930 unsigned total = 1 + isl_dim_total(bmap->dim);
931
932 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
933 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
934 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
935 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
936 isl_int_set_si(bmap->div[div][1 + total + div], 0);
937
938 return bmap;
939 }
940
941 /* Check whether it is ok to define a div based on an inequality.
942 * To avoid the introduction of circular definitions of divs, we
943 * do not allow such a definition if the resulting expression would refer to
944 * any other undefined divs or if any known div is defined in
945 * terms of the unknown div.
946 */
947 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
948 int div, int ineq)
949 {
950 int j;
951 unsigned total = 1 + isl_dim_total(bmap->dim);
952
953 /* Not defined in terms of unknown divs */
954 for (j = 0; j < bmap->n_div; ++j) {
955 if (div == j)
956 continue;
957 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
958 continue;
959 if (isl_int_is_zero(bmap->div[j][0]))
960 return 0;
961 }
962
963 /* No other div defined in terms of this one => avoid loops */
964 for (j = 0; j < bmap->n_div; ++j) {
965 if (div == j)
966 continue;
967 if (isl_int_is_zero(bmap->div[j][0]))
968 continue;
969 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
970 return 0;
971 }
972
973 return 1;
974 }
975
976 /* Given two constraints "k" and "l" that are opposite to each other,
977 * except for the constant term, check if we can use them
978 * to obtain an expression for one of the hitherto unknown divs.
979 * "sum" is the sum of the constant terms of the constraints.
980 * If this sum is strictly smaller than the coefficient of one
981 * of the divs, then this pair can be used define the div.
982 * To avoid the introduction of circular definitions of divs, we
983 * do not use the pair if the resulting expression would refer to
984 * any other undefined divs or if any known div is defined in
985 * terms of the unknown div.
986 */
987 static struct isl_basic_map *check_for_div_constraints(
988 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
989 {
990 int i;
991 unsigned total = 1 + isl_dim_total(bmap->dim);
992
993 for (i = 0; i < bmap->n_div; ++i) {
994 if (!isl_int_is_zero(bmap->div[i][0]))
995 continue;
996 if (isl_int_is_zero(bmap->ineq[k][total + i]))
997 continue;
998 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
999 continue;
1000 if (!ok_to_set_div_from_bound(bmap, i, k))
1001 break;
1002 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1003 bmap = set_div_from_lower_bound(bmap, i, k);
1004 else
1005 bmap = set_div_from_lower_bound(bmap, i, l);
1006 if (progress)
1007 *progress = 1;
1008 break;
1009 }
1010 return bmap;
1011 }
1012
1013 static struct isl_basic_map *remove_duplicate_constraints(
1014 struct isl_basic_map *bmap, int *progress)
1015 {
1016 unsigned int size;
1017 isl_int ***index;
1018 int k, l, h;
1019 int bits;
1020 unsigned total = isl_basic_map_total_dim(bmap);
1021 isl_int sum;
1022
1023 if (!bmap || bmap->n_ineq <= 1)
1024 return bmap;
1025
1026 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1027 bits = ffs(size) - 1;
1028 index = isl_calloc_array(ctx, isl_int **, size);
1029 if (!index)
1030 return bmap;
1031
1032 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1033 for (k = 1; k < bmap->n_ineq; ++k) {
1034 h = hash_index(index, size, bits, bmap, k);
1035 if (!index[h]) {
1036 index[h] = &bmap->ineq[k];
1037 continue;
1038 }
1039 if (progress)
1040 *progress = 1;
1041 l = index[h] - &bmap->ineq[0];
1042 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1043 swap_inequality(bmap, k, l);
1044 isl_basic_map_drop_inequality(bmap, k);
1045 --k;
1046 }
1047 isl_int_init(sum);
1048 for (k = 0; k < bmap->n_ineq-1; ++k) {
1049 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1050 h = hash_index(index, size, bits, bmap, k);
1051 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1052 if (!index[h])
1053 continue;
1054 l = index[h] - &bmap->ineq[0];
1055 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1056 if (isl_int_is_pos(sum)) {
1057 bmap = check_for_div_constraints(bmap, k, l, sum,
1058 progress);
1059 continue;
1060 }
1061 if (isl_int_is_zero(sum)) {
1062 /* We need to break out of the loop after these
1063 * changes since the contents of the hash
1064 * will no longer be valid.
1065 * Plus, we probably we want to regauss first.
1066 */
1067 if (progress)
1068 *progress = 1;
1069 isl_basic_map_drop_inequality(bmap, l);
1070 isl_basic_map_inequality_to_equality(bmap, k);
1071 } else
1072 bmap = isl_basic_map_set_to_empty(bmap);
1073 break;
1074 }
1075 isl_int_clear(sum);
1076
1077 free(index);
1078 return bmap;
1079 }
1080
1081
1082 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1083 {
1084 int progress = 1;
1085 if (!bmap)
1086 return NULL;
1087 while (progress) {
1088 progress = 0;
1089 bmap = isl_basic_map_normalize_constraints(bmap);
1090 bmap = remove_duplicate_divs(bmap, &progress);
1091 bmap = eliminate_divs_eq(bmap, &progress);
1092 bmap = eliminate_divs_ineq(bmap, &progress);
1093 bmap = isl_basic_map_gauss(bmap, &progress);
1094 /* requires equalities in normal form */
1095 bmap = normalize_divs(bmap, &progress);
1096 bmap = remove_duplicate_constraints(bmap, &progress);
1097 }
1098 return bmap;
1099 }
1100
1101 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1102 {
1103 return (struct isl_basic_set *)
1104 isl_basic_map_simplify((struct isl_basic_map *)bset);
1105 }
1106
1107
1108 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1109 isl_int *constraint, unsigned div)
1110 {
1111 unsigned pos;
1112
1113 if (!bmap)
1114 return -1;
1115
1116 pos = 1 + isl_dim_total(bmap->dim) + div;
1117
1118 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1119 int neg;
1120 isl_int_sub(bmap->div[div][1],
1121 bmap->div[div][1], bmap->div[div][0]);
1122 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1123 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1124 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1125 isl_int_add(bmap->div[div][1],
1126 bmap->div[div][1], bmap->div[div][0]);
1127 if (!neg)
1128 return 0;
1129 if (isl_seq_first_non_zero(constraint+pos+1,
1130 bmap->n_div-div-1) != -1)
1131 return 0;
1132 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1133 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1134 return 0;
1135 if (isl_seq_first_non_zero(constraint+pos+1,
1136 bmap->n_div-div-1) != -1)
1137 return 0;
1138 } else
1139 return 0;
1140
1141 return 1;
1142 }
1143
1144
1145 /* If the only constraints a div d=floor(f/m)
1146 * appears in are its two defining constraints
1147 *
1148 * f - m d >=0
1149 * -(f - (m - 1)) + m d >= 0
1150 *
1151 * then it can safely be removed.
1152 */
1153 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1154 {
1155 int i;
1156 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1157
1158 for (i = 0; i < bmap->n_eq; ++i)
1159 if (!isl_int_is_zero(bmap->eq[i][pos]))
1160 return 0;
1161
1162 for (i = 0; i < bmap->n_ineq; ++i) {
1163 if (isl_int_is_zero(bmap->ineq[i][pos]))
1164 continue;
1165 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1166 return 0;
1167 }
1168
1169 for (i = 0; i < bmap->n_div; ++i)
1170 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1171 return 0;
1172
1173 return 1;
1174 }
1175
1176 /*
1177 * Remove divs that don't occur in any of the constraints or other divs.
1178 * These can arise when dropping some of the variables in a quast
1179 * returned by piplib.
1180 */
1181 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1182 {
1183 int i;
1184
1185 if (!bmap)
1186 return NULL;
1187
1188 for (i = bmap->n_div-1; i >= 0; --i) {
1189 if (!div_is_redundant(bmap, i))
1190 continue;
1191 bmap = isl_basic_map_drop_div(bmap, i);
1192 }
1193 return bmap;
1194 }
1195
1196 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1197 {
1198 bmap = remove_redundant_divs(bmap);
1199 if (!bmap)
1200 return NULL;
1201 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1202 return bmap;
1203 }
1204
1205 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1206 {
1207 return (struct isl_basic_set *)
1208 isl_basic_map_finalize((struct isl_basic_map *)bset);
1209 }
1210
1211 struct isl_set *isl_set_finalize(struct isl_set *set)
1212 {
1213 int i;
1214
1215 if (!set)
1216 return NULL;
1217 for (i = 0; i < set->n; ++i) {
1218 set->p[i] = isl_basic_set_finalize(set->p[i]);
1219 if (!set->p[i])
1220 goto error;
1221 }
1222 return set;
1223 error:
1224 isl_set_free(set);
1225 return NULL;
1226 }
1227
1228 struct isl_map *isl_map_finalize(struct isl_map *map)
1229 {
1230 int i;
1231
1232 if (!map)
1233 return NULL;
1234 for (i = 0; i < map->n; ++i) {
1235 map->p[i] = isl_basic_map_finalize(map->p[i]);
1236 if (!map->p[i])
1237 goto error;
1238 }
1239 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1240 return map;
1241 error:
1242 isl_map_free(map);
1243 return NULL;
1244 }
1245
1246
1247 /* Remove definition of any div that is defined in terms of the given variable.
1248 * The div itself is not removed. Functions such as
1249 * eliminate_divs_ineq depend on the other divs remaining in place.
1250 */
1251 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1252 int pos)
1253 {
1254 int i;
1255
1256 for (i = 0; i < bmap->n_div; ++i) {
1257 if (isl_int_is_zero(bmap->div[i][0]))
1258 continue;
1259 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1260 continue;
1261 isl_int_set_si(bmap->div[i][0], 0);
1262 }
1263 return bmap;
1264 }
1265
1266 /* Eliminate the specified variables from the constraints using
1267 * Fourier-Motzkin. The variables themselves are not removed.
1268 */
1269 struct isl_basic_map *isl_basic_map_eliminate_vars(
1270 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1271 {
1272 int d;
1273 int i, j, k;
1274 unsigned total;
1275
1276 if (n == 0)
1277 return bmap;
1278 if (!bmap)
1279 return NULL;
1280 total = isl_basic_map_total_dim(bmap);
1281
1282 bmap = isl_basic_map_cow(bmap);
1283 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1284 bmap = remove_dependent_vars(bmap, d);
1285
1286 for (d = pos + n - 1;
1287 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1288 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1289 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1290 int n_lower, n_upper;
1291 if (!bmap)
1292 return NULL;
1293 for (i = 0; i < bmap->n_eq; ++i) {
1294 if (isl_int_is_zero(bmap->eq[i][1+d]))
1295 continue;
1296 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1297 isl_basic_map_drop_equality(bmap, i);
1298 break;
1299 }
1300 if (i < bmap->n_eq)
1301 continue;
1302 n_lower = 0;
1303 n_upper = 0;
1304 for (i = 0; i < bmap->n_ineq; ++i) {
1305 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1306 n_lower++;
1307 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1308 n_upper++;
1309 }
1310 bmap = isl_basic_map_extend_constraints(bmap,
1311 0, n_lower * n_upper);
1312 if (!bmap)
1313 goto error;
1314 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1315 int last;
1316 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1317 continue;
1318 last = -1;
1319 for (j = 0; j < i; ++j) {
1320 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1321 continue;
1322 last = j;
1323 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1324 isl_int_sgn(bmap->ineq[j][1+d]))
1325 continue;
1326 k = isl_basic_map_alloc_inequality(bmap);
1327 if (k < 0)
1328 goto error;
1329 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1330 1+total);
1331 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1332 1+d, 1+total, NULL);
1333 }
1334 isl_basic_map_drop_inequality(bmap, i);
1335 i = last + 1;
1336 }
1337 if (n_lower > 0 && n_upper > 0) {
1338 bmap = isl_basic_map_normalize_constraints(bmap);
1339 bmap = remove_duplicate_constraints(bmap, NULL);
1340 bmap = isl_basic_map_gauss(bmap, NULL);
1341 bmap = isl_basic_map_remove_redundancies(bmap);
1342 if (!bmap)
1343 goto error;
1344 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1345 break;
1346 }
1347 }
1348 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1349 return bmap;
1350 error:
1351 isl_basic_map_free(bmap);
1352 return NULL;
1353 }
1354
1355 struct isl_basic_set *isl_basic_set_eliminate_vars(
1356 struct isl_basic_set *bset, unsigned pos, unsigned n)
1357 {
1358 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1359 (struct isl_basic_map *)bset, pos, n);
1360 }
1361
1362 /* Don't assume equalities are in order, because align_divs
1363 * may have changed the order of the divs.
1364 */
1365 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1366 {
1367 int d, i;
1368 unsigned total;
1369
1370 total = isl_dim_total(bmap->dim);
1371 for (d = 0; d < total; ++d)
1372 elim[d] = -1;
1373 for (i = 0; i < bmap->n_eq; ++i) {
1374 for (d = total - 1; d >= 0; --d) {
1375 if (isl_int_is_zero(bmap->eq[i][1+d]))
1376 continue;
1377 elim[d] = i;
1378 break;
1379 }
1380 }
1381 }
1382
1383 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1384 {
1385 compute_elimination_index((struct isl_basic_map *)bset, elim);
1386 }
1387
1388 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1389 struct isl_basic_map *bmap, int *elim)
1390 {
1391 int d;
1392 int copied = 0;
1393 unsigned total;
1394
1395 total = isl_dim_total(bmap->dim);
1396 for (d = total - 1; d >= 0; --d) {
1397 if (isl_int_is_zero(src[1+d]))
1398 continue;
1399 if (elim[d] == -1)
1400 continue;
1401 if (!copied) {
1402 isl_seq_cpy(dst, src, 1 + total);
1403 copied = 1;
1404 }
1405 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1406 }
1407 return copied;
1408 }
1409
1410 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1411 struct isl_basic_set *bset, int *elim)
1412 {
1413 return reduced_using_equalities(dst, src,
1414 (struct isl_basic_map *)bset, elim);
1415 }
1416
1417 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1418 struct isl_basic_set *bset, struct isl_basic_set *context)
1419 {
1420 int i;
1421 int *elim;
1422
1423 if (!bset || !context)
1424 goto error;
1425
1426 if (context->n_eq == 0) {
1427 isl_basic_set_free(context);
1428 return bset;
1429 }
1430
1431 bset = isl_basic_set_cow(bset);
1432 if (!bset)
1433 goto error;
1434
1435 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1436 if (!elim)
1437 goto error;
1438 set_compute_elimination_index(context, elim);
1439 for (i = 0; i < bset->n_eq; ++i)
1440 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1441 context, elim);
1442 for (i = 0; i < bset->n_ineq; ++i)
1443 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1444 context, elim);
1445 isl_basic_set_free(context);
1446 free(elim);
1447 bset = isl_basic_set_simplify(bset);
1448 bset = isl_basic_set_finalize(bset);
1449 return bset;
1450 error:
1451 isl_basic_set_free(bset);
1452 isl_basic_set_free(context);
1453 return NULL;
1454 }
1455
1456 static struct isl_basic_set *remove_shifted_constraints(
1457 struct isl_basic_set *bset, struct isl_basic_set *context)
1458 {
1459 unsigned int size;
1460 isl_int ***index;
1461 int bits;
1462 int k, h, l;
1463
1464 if (!bset)
1465 return NULL;
1466
1467 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1468 bits = ffs(size) - 1;
1469 index = isl_calloc_array(ctx, isl_int **, size);
1470 if (!index)
1471 return bset;
1472
1473 for (k = 0; k < context->n_ineq; ++k) {
1474 h = set_hash_index(index, size, bits, context, k);
1475 index[h] = &context->ineq[k];
1476 }
1477 for (k = 0; k < bset->n_ineq; ++k) {
1478 h = set_hash_index(index, size, bits, bset, k);
1479 if (!index[h])
1480 continue;
1481 l = index[h] - &context->ineq[0];
1482 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1483 continue;
1484 bset = isl_basic_set_cow(bset);
1485 if (!bset)
1486 goto error;
1487 isl_basic_set_drop_inequality(bset, k);
1488 --k;
1489 }
1490 free(index);
1491 return bset;
1492 error:
1493 free(index);
1494 return bset;
1495 }
1496
1497 /* Tighten (decrease) the constant terms of the inequalities based
1498 * on the equalities, without removing any integer points.
1499 * For example, if there is an equality
1500 *
1501 * i = 3 * j
1502 *
1503 * and an inequality
1504 *
1505 * i >= 1
1506 *
1507 * then we want to replace the inequality by
1508 *
1509 * i >= 3
1510 *
1511 * We do this by computing a variable compression and translating
1512 * the constraints to the compressed space.
1513 * If any constraint has coefficients (except the contant term)
1514 * with a common factor "f", then we can replace the constant term "c"
1515 * by
1516 *
1517 * f * floor(c/f)
1518 *
1519 * That is, we add
1520 *
1521 * f * floor(c/f) - c = -fract(c/f)
1522 *
1523 * and we can add the same value to the original constraint.
1524 *
1525 * In the example, the compressed space only contains "j",
1526 * and the inequality translates to
1527 *
1528 * 3 * j - 1 >= 0
1529 *
1530 * We add -fract(-1/3) = -2 to the original constraint to obtain
1531 *
1532 * i - 3 >= 0
1533 */
1534 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1535 struct isl_basic_set *bset)
1536 {
1537 int i;
1538 unsigned total;
1539 struct isl_mat *B, *C;
1540 isl_int gcd;
1541
1542 if (!bset)
1543 return NULL;
1544
1545 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1546 return bset;
1547
1548 if (!bset->n_ineq)
1549 return bset;
1550
1551 bset = isl_basic_set_cow(bset);
1552 if (!bset)
1553 return NULL;
1554
1555 total = isl_basic_set_total_dim(bset);
1556 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1557 C = isl_mat_variable_compression(B, NULL);
1558 if (!C)
1559 return bset;
1560 if (C->n_col == 0) {
1561 isl_mat_free(C);
1562 return isl_basic_set_set_to_empty(bset);
1563 }
1564 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1565 0, bset->n_ineq, 0, 1 + total);
1566 C = isl_mat_product(B, C);
1567 if (!C)
1568 return bset;
1569
1570 isl_int_init(gcd);
1571 for (i = 0; i < bset->n_ineq; ++i) {
1572 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1573 if (isl_int_is_one(gcd))
1574 continue;
1575 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1576 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1577 }
1578 isl_int_clear(gcd);
1579
1580 isl_mat_free(C);
1581
1582 return bset;
1583 }
1584
1585 /* Remove all information from bset that is redundant in the context
1586 * of context. Both bset and context are assumed to be full-dimensional.
1587 *
1588 * We first * remove the inequalities from "bset"
1589 * that are obviously redundant with respect to some inequality in "context".
1590 *
1591 * If there are any inequalities left, we construct a tableau for
1592 * the context and then add the inequalities of "bset".
1593 * Before adding these inequalities, we freeze all constraints such that
1594 * they won't be considered redundant in terms of the constraints of "bset".
1595 * Then we detect all redundant constraints (among the
1596 * constraints that weren't frozen), first by checking for redundancy in the
1597 * the tableau and then by checking if replacing a constraint by its negation
1598 * would lead to an empty set. This last step is fairly expensive
1599 * and could be optimized by more reuse of the tableau.
1600 * Finally, we update bset according to the results.
1601 */
1602 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1603 __isl_take isl_basic_set *context)
1604 {
1605 int i, k;
1606 isl_basic_set *combined = NULL;
1607 struct isl_tab *tab = NULL;
1608 unsigned context_ineq;
1609 unsigned total;
1610
1611 if (!bset || !context)
1612 goto error;
1613
1614 if (isl_basic_set_is_universe(bset)) {
1615 isl_basic_set_free(context);
1616 return bset;
1617 }
1618
1619 if (isl_basic_set_is_universe(context)) {
1620 isl_basic_set_free(context);
1621 return bset;
1622 }
1623
1624 bset = remove_shifted_constraints(bset, context);
1625 if (!bset)
1626 goto error;
1627 if (bset->n_ineq == 0)
1628 goto done;
1629
1630 context_ineq = context->n_ineq;
1631 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1632 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1633 tab = isl_tab_from_basic_set(combined);
1634 for (i = 0; i < context_ineq; ++i)
1635 if (isl_tab_freeze_constraint(tab, i) < 0)
1636 goto error;
1637 tab = isl_tab_extend(tab, bset->n_ineq);
1638 for (i = 0; i < bset->n_ineq; ++i)
1639 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1640 goto error;
1641 bset = isl_basic_set_add_constraints(combined, bset, 0);
1642 combined = NULL;
1643 if (!bset)
1644 goto error;
1645 if (isl_tab_detect_redundant(tab) < 0)
1646 goto error;
1647 total = isl_basic_set_total_dim(bset);
1648 for (i = context_ineq; i < bset->n_ineq; ++i) {
1649 int is_empty;
1650 if (tab->con[i].is_redundant)
1651 continue;
1652 tab->con[i].is_redundant = 1;
1653 combined = isl_basic_set_dup(bset);
1654 combined = isl_basic_set_update_from_tab(combined, tab);
1655 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1656 k = isl_basic_set_alloc_inequality(combined);
1657 if (k < 0)
1658 goto error;
1659 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1660 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1661 is_empty = isl_basic_set_is_empty(combined);
1662 if (is_empty < 0)
1663 goto error;
1664 isl_basic_set_free(combined);
1665 combined = NULL;
1666 if (!is_empty)
1667 tab->con[i].is_redundant = 0;
1668 }
1669 for (i = 0; i < context_ineq; ++i)
1670 tab->con[i].is_redundant = 1;
1671 bset = isl_basic_set_update_from_tab(bset, tab);
1672 if (bset) {
1673 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1674 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1675 }
1676
1677 isl_tab_free(tab);
1678 done:
1679 bset = isl_basic_set_simplify(bset);
1680 bset = isl_basic_set_finalize(bset);
1681 isl_basic_set_free(context);
1682 return bset;
1683 error:
1684 isl_tab_free(tab);
1685 isl_basic_set_free(combined);
1686 isl_basic_set_free(context);
1687 isl_basic_set_free(bset);
1688 return NULL;
1689 }
1690
1691 /* Remove all information from bset that is redundant in the context
1692 * of context. In particular, equalities that are linear combinations
1693 * of those in context are removed. Then the inequalities that are
1694 * redundant in the context of the equalities and inequalities of
1695 * context are removed.
1696 *
1697 * We first compute the integer affine hull of the intersection,
1698 * compute the gist inside this affine hull and then add back
1699 * those equalities that are not implied by the context.
1700 */
1701 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1702 __isl_take isl_basic_set *context)
1703 {
1704 isl_mat *eq;
1705 isl_mat *T, *T2;
1706 isl_basic_set *aff;
1707 isl_basic_set *aff_context;
1708 unsigned total;
1709
1710 if (!bset || !context)
1711 goto error;
1712
1713 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1714 if (isl_basic_set_fast_is_empty(bset)) {
1715 isl_basic_set_free(context);
1716 return bset;
1717 }
1718 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1719 if (!aff)
1720 goto error;
1721 if (isl_basic_set_fast_is_empty(aff)) {
1722 isl_basic_set_free(aff);
1723 isl_basic_set_free(context);
1724 return bset;
1725 }
1726 if (aff->n_eq == 0) {
1727 isl_basic_set_free(aff);
1728 return uset_gist_full(bset, context);
1729 }
1730 total = isl_basic_set_total_dim(bset);
1731 eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1732 eq = isl_mat_cow(eq);
1733 T = isl_mat_variable_compression(eq, &T2);
1734 if (T && T->n_col == 0) {
1735 isl_mat_free(T);
1736 isl_mat_free(T2);
1737 isl_basic_set_free(context);
1738 isl_basic_set_free(aff);
1739 return isl_basic_set_set_to_empty(bset);
1740 }
1741
1742 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1743
1744 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1745 context = isl_basic_set_preimage(context, T);
1746
1747 bset = uset_gist_full(bset, context);
1748 bset = isl_basic_set_preimage(bset, T2);
1749 bset = isl_basic_set_intersect(bset, aff);
1750 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1751
1752 if (bset) {
1753 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1754 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1755 }
1756
1757 return bset;
1758 error:
1759 isl_basic_set_free(bset);
1760 isl_basic_set_free(context);
1761 return NULL;
1762 }
1763
1764 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1765 * We simply add the equalities in context to bmap and then do a regular
1766 * div normalizations. Better results can be obtained by normalizing
1767 * only the divs in bmap than do not also appear in context.
1768 * We need to be careful to reduce the divs using the equalities
1769 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1770 * spurious constraints.
1771 */
1772 static struct isl_basic_map *normalize_divs_in_context(
1773 struct isl_basic_map *bmap, struct isl_basic_map *context)
1774 {
1775 int i;
1776 unsigned total_context;
1777 int div_eq;
1778
1779 div_eq = n_pure_div_eq(bmap);
1780 if (div_eq == 0)
1781 return bmap;
1782
1783 if (context->n_div > 0)
1784 bmap = isl_basic_map_align_divs(bmap, context);
1785
1786 total_context = isl_basic_map_total_dim(context);
1787 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1788 for (i = 0; i < context->n_eq; ++i) {
1789 int k;
1790 k = isl_basic_map_alloc_equality(bmap);
1791 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1792 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1793 isl_basic_map_total_dim(bmap) - total_context);
1794 }
1795 bmap = isl_basic_map_gauss(bmap, NULL);
1796 bmap = normalize_divs(bmap, NULL);
1797 bmap = isl_basic_map_gauss(bmap, NULL);
1798 return bmap;
1799 }
1800
1801 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1802 struct isl_basic_map *context)
1803 {
1804 struct isl_basic_set *bset;
1805
1806 if (!bmap || !context)
1807 goto error;
1808
1809 if (isl_basic_map_is_universe(context)) {
1810 isl_basic_map_free(context);
1811 return bmap;
1812 }
1813 if (isl_basic_map_is_universe(bmap)) {
1814 isl_basic_map_free(context);
1815 return bmap;
1816 }
1817 if (isl_basic_map_fast_is_empty(context)) {
1818 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1819 isl_basic_map_free(context);
1820 isl_basic_map_free(bmap);
1821 return isl_basic_map_universe(dim);
1822 }
1823 if (isl_basic_map_fast_is_empty(bmap)) {
1824 isl_basic_map_free(context);
1825 return bmap;
1826 }
1827
1828 bmap = isl_basic_map_remove_redundancies(bmap);
1829 context = isl_basic_map_remove_redundancies(context);
1830
1831 if (context->n_eq)
1832 bmap = normalize_divs_in_context(bmap, context);
1833
1834 context = isl_basic_map_align_divs(context, bmap);
1835 bmap = isl_basic_map_align_divs(bmap, context);
1836
1837 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1838 isl_basic_map_underlying_set(context));
1839
1840 return isl_basic_map_overlying_set(bset, bmap);
1841 error:
1842 isl_basic_map_free(bmap);
1843 isl_basic_map_free(context);
1844 return NULL;
1845 }
1846
1847 /*
1848 * Assumes context has no implicit divs.
1849 */
1850 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1851 __isl_take isl_basic_map *context)
1852 {
1853 int i;
1854
1855 if (!map || !context)
1856 goto error;;
1857
1858 if (isl_basic_map_is_universe(context)) {
1859 isl_basic_map_free(context);
1860 return map;
1861 }
1862 if (isl_basic_map_fast_is_empty(context)) {
1863 struct isl_dim *dim = isl_dim_copy(map->dim);
1864 isl_basic_map_free(context);
1865 isl_map_free(map);
1866 return isl_map_universe(dim);
1867 }
1868
1869 context = isl_basic_map_remove_redundancies(context);
1870 map = isl_map_cow(map);
1871 if (!map || !context)
1872 goto error;;
1873 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1874 map = isl_map_compute_divs(map);
1875 for (i = 0; i < map->n; ++i)
1876 context = isl_basic_map_align_divs(context, map->p[i]);
1877 for (i = 0; i < map->n; ++i) {
1878 map->p[i] = isl_basic_map_gist(map->p[i],
1879 isl_basic_map_copy(context));
1880 if (!map->p[i])
1881 goto error;
1882 }
1883 isl_basic_map_free(context);
1884 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1885 return map;
1886 error:
1887 isl_map_free(map);
1888 isl_basic_map_free(context);
1889 return NULL;
1890 }
1891
1892 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1893 __isl_take isl_map *context)
1894 {
1895 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1896 }
1897
1898 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1899 struct isl_basic_set *context)
1900 {
1901 return (struct isl_basic_set *)isl_basic_map_gist(
1902 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1903 }
1904
1905 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1906 __isl_take isl_basic_set *context)
1907 {
1908 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1909 (struct isl_basic_map *)context);
1910 }
1911
1912 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1913 __isl_take isl_set *context)
1914 {
1915 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1916 (struct isl_map *)context);
1917 }
1918
1919 /* Quick check to see if two basic maps are disjoint.
1920 * In particular, we reduce the equalities and inequalities of
1921 * one basic map in the context of the equalities of the other
1922 * basic map and check if we get a contradiction.
1923 */
1924 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1925 struct isl_basic_map *bmap2)
1926 {
1927 struct isl_vec *v = NULL;
1928 int *elim = NULL;
1929 unsigned total;
1930 int i;
1931
1932 if (!bmap1 || !bmap2)
1933 return -1;
1934 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1935 return -1);
1936 if (bmap1->n_div || bmap2->n_div)
1937 return 0;
1938 if (!bmap1->n_eq && !bmap2->n_eq)
1939 return 0;
1940
1941 total = isl_dim_total(bmap1->dim);
1942 if (total == 0)
1943 return 0;
1944 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1945 if (!v)
1946 goto error;
1947 elim = isl_alloc_array(bmap1->ctx, int, total);
1948 if (!elim)
1949 goto error;
1950 compute_elimination_index(bmap1, elim);
1951 for (i = 0; i < bmap2->n_eq; ++i) {
1952 int reduced;
1953 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1954 bmap1, elim);
1955 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1956 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1957 goto disjoint;
1958 }
1959 for (i = 0; i < bmap2->n_ineq; ++i) {
1960 int reduced;
1961 reduced = reduced_using_equalities(v->block.data,
1962 bmap2->ineq[i], bmap1, elim);
1963 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1964 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1965 goto disjoint;
1966 }
1967 compute_elimination_index(bmap2, elim);
1968 for (i = 0; i < bmap1->n_ineq; ++i) {
1969 int reduced;
1970 reduced = reduced_using_equalities(v->block.data,
1971 bmap1->ineq[i], bmap2, elim);
1972 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1973 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1974 goto disjoint;
1975 }
1976 isl_vec_free(v);
1977 free(elim);
1978 return 0;
1979 disjoint:
1980 isl_vec_free(v);
1981 free(elim);
1982 return 1;
1983 error:
1984 isl_vec_free(v);
1985 free(elim);
1986 return -1;
1987 }
1988
1989 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1990 struct isl_basic_set *bset2)
1991 {
1992 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1993 (struct isl_basic_map *)bset2);
1994 }
1995
1996 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1997 {
1998 int i, j;
1999
2000 if (!map1 || !map2)
2001 return -1;
2002
2003 if (isl_map_fast_is_equal(map1, map2))
2004 return 0;
2005
2006 for (i = 0; i < map1->n; ++i) {
2007 for (j = 0; j < map2->n; ++j) {
2008 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
2009 map2->p[j]);
2010 if (d != 1)
2011 return d;
2012 }
2013 }
2014 return 1;
2015 }
2016
2017 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2018 {
2019 return isl_map_fast_is_disjoint((struct isl_map *)set1,
2020 (struct isl_map *)set2);
2021 }
2022
2023 /* Check if we can combine a given div with lower bound l and upper
2024 * bound u with some other div and if so return that other div.
2025 * Otherwise return -1.
2026 *
2027 * We first check that
2028 * - the bounds are opposites of each other (except for the constant
2029 * term)
2030 * - the bounds do not reference any other div
2031 * - no div is defined in terms of this div
2032 *
2033 * Let m be the size of the range allowed on the div by the bounds.
2034 * That is, the bounds are of the form
2035 *
2036 * e <= a <= e + m - 1
2037 *
2038 * with e some expression in the other variables.
2039 * We look for another div b such that no third div is defined in terms
2040 * of this second div b and such that in any constraint that contains
2041 * a (except for the given lower and upper bound), also contains b
2042 * with a coefficient that is m times that of b.
2043 * That is, all constraints (execpt for the lower and upper bound)
2044 * are of the form
2045 *
2046 * e + f (a + m b) >= 0
2047 *
2048 * If so, we return b so that "a + m b" can be replaced by
2049 * a single div "c = a + m b".
2050 */
2051 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2052 unsigned div, unsigned l, unsigned u)
2053 {
2054 int i, j;
2055 unsigned dim;
2056 int coalesce = -1;
2057
2058 if (bmap->n_div <= 1)
2059 return -1;
2060 dim = isl_dim_total(bmap->dim);
2061 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2062 return -1;
2063 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2064 bmap->n_div - div - 1) != -1)
2065 return -1;
2066 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2067 dim + bmap->n_div))
2068 return -1;
2069
2070 for (i = 0; i < bmap->n_div; ++i) {
2071 if (isl_int_is_zero(bmap->div[i][0]))
2072 continue;
2073 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2074 return -1;
2075 }
2076
2077 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2078 if (isl_int_is_neg(bmap->ineq[l][0])) {
2079 isl_int_sub(bmap->ineq[l][0],
2080 bmap->ineq[l][0], bmap->ineq[u][0]);
2081 bmap = isl_basic_map_copy(bmap);
2082 bmap = isl_basic_map_set_to_empty(bmap);
2083 isl_basic_map_free(bmap);
2084 return -1;
2085 }
2086 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2087 for (i = 0; i < bmap->n_div; ++i) {
2088 if (i == div)
2089 continue;
2090 if (!pairs[i])
2091 continue;
2092 for (j = 0; j < bmap->n_div; ++j) {
2093 if (isl_int_is_zero(bmap->div[j][0]))
2094 continue;
2095 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2096 break;
2097 }
2098 if (j < bmap->n_div)
2099 continue;
2100 for (j = 0; j < bmap->n_ineq; ++j) {
2101 int valid;
2102 if (j == l || j == u)
2103 continue;
2104 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2105 continue;
2106 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2107 break;
2108 isl_int_mul(bmap->ineq[j][1 + dim + div],
2109 bmap->ineq[j][1 + dim + div],
2110 bmap->ineq[l][0]);
2111 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2112 bmap->ineq[j][1 + dim + i]);
2113 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2114 bmap->ineq[j][1 + dim + div],
2115 bmap->ineq[l][0]);
2116 if (!valid)
2117 break;
2118 }
2119 if (j < bmap->n_ineq)
2120 continue;
2121 coalesce = i;
2122 break;
2123 }
2124 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2125 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2126 return coalesce;
2127 }
2128
2129 /* Given a lower and an upper bound on div i, construct an inequality
2130 * that when nonnegative ensures that this pair of bounds always allows
2131 * for an integer value of the given div.
2132 * The lower bound is inequality l, while the upper bound is inequality u.
2133 * The constructed inequality is stored in ineq.
2134 * g, fl, fu are temporary scalars.
2135 *
2136 * Let the upper bound be
2137 *
2138 * -n_u a + e_u >= 0
2139 *
2140 * and the lower bound
2141 *
2142 * n_l a + e_l >= 0
2143 *
2144 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2145 * We have
2146 *
2147 * - f_u e_l <= f_u f_l g a <= f_l e_u
2148 *
2149 * Since all variables are integer valued, this is equivalent to
2150 *
2151 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2152 *
2153 * If this interval is at least f_u f_l g, then it contains at least
2154 * one integer value for a.
2155 * That is, the test constraint is
2156 *
2157 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2158 */
2159 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2160 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2161 {
2162 unsigned dim;
2163 dim = isl_dim_total(bmap->dim);
2164
2165 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2166 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2167 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2168 isl_int_neg(fu, fu);
2169 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2170 1 + dim + bmap->n_div);
2171 isl_int_add(ineq[0], ineq[0], fl);
2172 isl_int_add(ineq[0], ineq[0], fu);
2173 isl_int_sub_ui(ineq[0], ineq[0], 1);
2174 isl_int_mul(g, g, fl);
2175 isl_int_mul(g, g, fu);
2176 isl_int_sub(ineq[0], ineq[0], g);
2177 }
2178
2179 /* Remove more kinds of divs that are not strictly needed.
2180 * In particular, if all pairs of lower and upper bounds on a div
2181 * are such that they allow at least one integer value of the div,
2182 * the we can eliminate the div using Fourier-Motzkin without
2183 * introducing any spurious solutions.
2184 */
2185 static struct isl_basic_map *drop_more_redundant_divs(
2186 struct isl_basic_map *bmap, int *pairs, int n)
2187 {
2188 struct isl_tab *tab = NULL;
2189 struct isl_vec *vec = NULL;
2190 unsigned dim;
2191 int remove = -1;
2192 isl_int g, fl, fu;
2193
2194 isl_int_init(g);
2195 isl_int_init(fl);
2196 isl_int_init(fu);
2197
2198 if (!bmap)
2199 goto error;
2200
2201 dim = isl_dim_total(bmap->dim);
2202 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2203 if (!vec)
2204 goto error;
2205
2206 tab = isl_tab_from_basic_map(bmap);
2207
2208 while (n > 0) {
2209 int i, l, u;
2210 int best = -1;
2211 enum isl_lp_result res;
2212
2213 for (i = 0; i < bmap->n_div; ++i) {
2214 if (!pairs[i])
2215 continue;
2216 if (best >= 0 && pairs[best] <= pairs[i])
2217 continue;
2218 best = i;
2219 }
2220
2221 i = best;
2222 for (l = 0; l < bmap->n_ineq; ++l) {
2223 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2224 continue;
2225 for (u = 0; u < bmap->n_ineq; ++u) {
2226 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2227 continue;
2228 construct_test_ineq(bmap, i, l, u,
2229 vec->el, g, fl, fu);
2230 res = isl_tab_min(tab, vec->el,
2231 bmap->ctx->one, &g, NULL, 0);
2232 if (res == isl_lp_error)
2233 goto error;
2234 if (res == isl_lp_empty) {
2235 bmap = isl_basic_map_set_to_empty(bmap);
2236 break;
2237 }
2238 if (res != isl_lp_ok || isl_int_is_neg(g))
2239 break;
2240 }
2241 if (u < bmap->n_ineq)
2242 break;
2243 }
2244 if (l == bmap->n_ineq) {
2245 remove = i;
2246 break;
2247 }
2248 pairs[i] = 0;
2249 --n;
2250 }
2251
2252 isl_tab_free(tab);
2253 isl_vec_free(vec);
2254
2255 isl_int_clear(g);
2256 isl_int_clear(fl);
2257 isl_int_clear(fu);
2258
2259 free(pairs);
2260
2261 if (remove < 0)
2262 return bmap;
2263
2264 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2265 return isl_basic_map_drop_redundant_divs(bmap);
2266 error:
2267 free(pairs);
2268 isl_basic_map_free(bmap);
2269 isl_tab_free(tab);
2270 isl_vec_free(vec);
2271 isl_int_clear(g);
2272 isl_int_clear(fl);
2273 isl_int_clear(fu);
2274 return NULL;
2275 }
2276
2277 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2278 * and the upper bound u, div1 always occurs together with div2 in the form
2279 * (div1 + m div2), where m is the constant range on the variable div1
2280 * allowed by l and u, replace the pair div1 and div2 by a single
2281 * div that is equal to div1 + m div2.
2282 *
2283 * The new div will appear in the location that contains div2.
2284 * We need to modify all constraints that contain
2285 * div2 = (div - div1) / m
2286 * (If a constraint does not contain div2, it will also not contain div1.)
2287 * If the constraint also contains div1, then we know they appear
2288 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2289 * i.e., the coefficient of div is f.
2290 *
2291 * Otherwise, we first need to introduce div1 into the constraint.
2292 * Let the l be
2293 *
2294 * div1 + f >=0
2295 *
2296 * and u
2297 *
2298 * -div1 + f' >= 0
2299 *
2300 * A lower bound on div2
2301 *
2302 * n div2 + t >= 0
2303 *
2304 * can be replaced by
2305 *
2306 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2307 *
2308 * with g = gcd(m,n).
2309 * An upper bound
2310 *
2311 * -n div2 + t >= 0
2312 *
2313 * can be replaced by
2314 *
2315 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2316 *
2317 * These constraint are those that we would obtain from eliminating
2318 * div1 using Fourier-Motzkin.
2319 *
2320 * After all constraints have been modified, we drop the lower and upper
2321 * bound and then drop div1.
2322 */
2323 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2324 unsigned div1, unsigned div2, unsigned l, unsigned u)
2325 {
2326 isl_int a;
2327 isl_int b;
2328 isl_int m;
2329 unsigned dim, total;
2330 int i;
2331
2332 dim = isl_dim_total(bmap->dim);
2333 total = 1 + dim + bmap->n_div;
2334
2335 isl_int_init(a);
2336 isl_int_init(b);
2337 isl_int_init(m);
2338 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2339 isl_int_add_ui(m, m, 1);
2340
2341 for (i = 0; i < bmap->n_ineq; ++i) {
2342 if (i == l || i == u)
2343 continue;
2344 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2345 continue;
2346 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2347 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2348 isl_int_divexact(a, m, b);
2349 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2350 if (isl_int_is_pos(b)) {
2351 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2352 b, bmap->ineq[l], total);
2353 } else {
2354 isl_int_neg(b, b);
2355 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2356 b, bmap->ineq[u], total);
2357 }
2358 }
2359 isl_int_set(bmap->ineq[i][1 + dim + div2],
2360 bmap->ineq[i][1 + dim + div1]);
2361 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2362 }
2363
2364 isl_int_clear(a);
2365 isl_int_clear(b);
2366 isl_int_clear(m);
2367 if (l > u) {
2368 isl_basic_map_drop_inequality(bmap, l);
2369 isl_basic_map_drop_inequality(bmap, u);
2370 } else {
2371 isl_basic_map_drop_inequality(bmap, u);
2372 isl_basic_map_drop_inequality(bmap, l);
2373 }
2374 bmap = isl_basic_map_drop_div(bmap, div1);
2375 return bmap;
2376 }
2377
2378 /* First check if we can coalesce any pair of divs and
2379 * then continue with dropping more redundant divs.
2380 *
2381 * We loop over all pairs of lower and upper bounds on a div
2382 * with coefficient 1 and -1, respectively, check if there
2383 * is any other div "c" with which we can coalesce the div
2384 * and if so, perform the coalescing.
2385 */
2386 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2387 struct isl_basic_map *bmap, int *pairs, int n)
2388 {
2389 int i, l, u;
2390 unsigned dim;
2391
2392 dim = isl_dim_total(bmap->dim);
2393
2394 for (i = 0; i < bmap->n_div; ++i) {
2395 if (!pairs[i])
2396 continue;
2397 for (l = 0; l < bmap->n_ineq; ++l) {
2398 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2399 continue;
2400 for (u = 0; u < bmap->n_ineq; ++u) {
2401 int c;
2402
2403 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2404 continue;
2405 c = div_find_coalesce(bmap, pairs, i, l, u);
2406 if (c < 0)
2407 continue;
2408 free(pairs);
2409 bmap = coalesce_divs(bmap, i, c, l, u);
2410 return isl_basic_map_drop_redundant_divs(bmap);
2411 }
2412 }
2413 }
2414
2415 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2416 return bmap;
2417
2418 return drop_more_redundant_divs(bmap, pairs, n);
2419 }
2420
2421 /* Remove divs that are not strictly needed.
2422 * In particular, if a div only occurs positively (or negatively)
2423 * in constraints, then it can simply be dropped.
2424 * Also, if a div occurs only occurs in two constraints and if moreover
2425 * those two constraints are opposite to each other, except for the constant
2426 * term and if the sum of the constant terms is such that for any value
2427 * of the other values, there is always at least one integer value of the
2428 * div, i.e., if one plus this sum is greater than or equal to
2429 * the (absolute value) of the coefficent of the div in the constraints,
2430 * then we can also simply drop the div.
2431 *
2432 * If any divs are left after these simple checks then we move on
2433 * to more complicated cases in drop_more_redundant_divs.
2434 */
2435 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2436 struct isl_basic_map *bmap)
2437 {
2438 int i, j;
2439 unsigned off;
2440 int *pairs = NULL;
2441 int n = 0;
2442
2443 if (!bmap)
2444 goto error;
2445
2446 off = isl_dim_total(bmap->dim);
2447 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2448 if (!pairs)
2449 goto error;
2450
2451 for (i = 0; i < bmap->n_div; ++i) {
2452 int pos, neg;
2453 int last_pos, last_neg;
2454 int redundant;
2455 int defined;
2456
2457 defined = !isl_int_is_zero(bmap->div[i][0]);
2458 for (j = 0; j < bmap->n_eq; ++j)
2459 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2460 break;
2461 if (j < bmap->n_eq)
2462 continue;
2463 ++n;
2464 pos = neg = 0;
2465 for (j = 0; j < bmap->n_ineq; ++j) {
2466 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2467 last_pos = j;
2468 ++pos;
2469 }
2470 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2471 last_neg = j;
2472 ++neg;
2473 }
2474 }
2475 pairs[i] = pos * neg;
2476 if (pairs[i] == 0) {
2477 for (j = bmap->n_ineq - 1; j >= 0; --j)
2478 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2479 isl_basic_map_drop_inequality(bmap, j);
2480 bmap = isl_basic_map_drop_div(bmap, i);
2481 free(pairs);
2482 return isl_basic_map_drop_redundant_divs(bmap);
2483 }
2484 if (pairs[i] != 1)
2485 continue;
2486 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2487 bmap->ineq[last_neg] + 1,
2488 off + bmap->n_div))
2489 continue;
2490
2491 isl_int_add(bmap->ineq[last_pos][0],
2492 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2493 isl_int_add_ui(bmap->ineq[last_pos][0],
2494 bmap->ineq[last_pos][0], 1);
2495 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2496 bmap->ineq[last_pos][1+off+i]);
2497 isl_int_sub_ui(bmap->ineq[last_pos][0],
2498 bmap->ineq[last_pos][0], 1);
2499 isl_int_sub(bmap->ineq[last_pos][0],
2500 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2501 if (!redundant) {
2502 if (defined ||
2503 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2504 pairs[i] = 0;
2505 --n;
2506 continue;
2507 }
2508 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2509 bmap = isl_basic_map_simplify(bmap);
2510 free(pairs);
2511 return isl_basic_map_drop_redundant_divs(bmap);
2512 }
2513 if (last_pos > last_neg) {
2514 isl_basic_map_drop_inequality(bmap, last_pos);
2515 isl_basic_map_drop_inequality(bmap, last_neg);
2516 } else {
2517 isl_basic_map_drop_inequality(bmap, last_neg);
2518 isl_basic_map_drop_inequality(bmap, last_pos);
2519 }
2520 bmap = isl_basic_map_drop_div(bmap, i);
2521 free(pairs);
2522 return isl_basic_map_drop_redundant_divs(bmap);
2523 }
2524
2525 if (n > 0)
2526 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2527
2528 free(pairs);
2529 return bmap;
2530 error:
2531 free(pairs);
2532 isl_basic_map_free(bmap);
2533 return NULL;
2534 }
2535
2536 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2537 struct isl_basic_set *bset)
2538 {
2539 return (struct isl_basic_set *)
2540 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2541 }
2542
2543 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2544 {
2545 int i;
2546
2547 if (!map)
2548 return NULL;
2549 for (i = 0; i < map->n; ++i) {
2550 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2551 if (!map->p[i])
2552 goto error;
2553 }
2554 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2555 return map;
2556 error:
2557 isl_map_free(map);
2558 return NULL;
2559 }
2560
2561 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2562 {
2563 return (struct isl_set *)
2564 isl_map_drop_redundant_divs((struct isl_map *)set);
2565 }
Integer set library