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add isl_pw_aff_ne_set
[isl.git] / isl_aff.c
blob5faf8708ae4897366eb768470627b48a9359ce34
1 /*
2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Universiteit Leiden
4 *
5 * Use of this software is governed by the GNU LGPLv2.1 license
6 *
7 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
8 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
9 * 91893 Orsay, France
10 * and Leiden Institute of Advanced Computer Science,
11 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
12 */
13
14 #include <isl_map_private.h>
15 #include <isl_aff_private.h>
16 #include <isl_dim_private.h>
17 #include <isl_local_space_private.h>
18 #include <isl_mat_private.h>
19 #include <isl/constraint.h>
20 #include <isl/seq.h>
21 #include <isl/set.h>
22
23 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
24 __isl_take isl_vec *v)
25 {
26 isl_aff *aff;
27
28 if (!ls || !v)
29 goto error;
30
31 aff = isl_calloc_type(v->ctx, struct isl_aff);
32 if (!aff)
33 goto error;
34
35 aff->ref = 1;
36 aff->ls = ls;
37 aff->v = v;
38
39 return aff;
40 error:
41 isl_local_space_free(ls);
42 isl_vec_free(v);
43 return NULL;
44 }
45
46 __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
47 {
48 isl_ctx *ctx;
49 isl_vec *v;
50 unsigned total;
51
52 if (!ls)
53 return NULL;
54
55 ctx = isl_local_space_get_ctx(ls);
56 if (!isl_local_space_divs_known(ls))
57 isl_die(ctx, isl_error_invalid, "local space has unknown divs",
58 goto error);
59
60 total = isl_local_space_dim(ls, isl_dim_all);
61 v = isl_vec_alloc(ctx, 1 + 1 + total);
62 return isl_aff_alloc_vec(ls, v);
63 error:
64 isl_local_space_free(ls);
65 return NULL;
66 }
67
68 __isl_give isl_aff *isl_aff_zero(__isl_take isl_local_space *ls)
69 {
70 isl_aff *aff;
71
72 aff = isl_aff_alloc(ls);
73 if (!aff)
74 return NULL;
75
76 isl_int_set_si(aff->v->el[0], 1);
77 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
78
79 return aff;
80 }
81
82 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
83 {
84 if (!aff)
85 return NULL;
86
87 aff->ref++;
88 return aff;
89 }
90
91 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
92 {
93 if (!aff)
94 return NULL;
95
96 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
97 isl_vec_copy(aff->v));
98 }
99
100 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
101 {
102 if (!aff)
103 return NULL;
104
105 if (aff->ref == 1)
106 return aff;
107 aff->ref--;
108 return isl_aff_dup(aff);
109 }
110
111 void *isl_aff_free(__isl_take isl_aff *aff)
112 {
113 if (!aff)
114 return NULL;
115
116 if (--aff->ref > 0)
117 return NULL;
118
119 isl_local_space_free(aff->ls);
120 isl_vec_free(aff->v);
121
122 free(aff);
123
124 return NULL;
125 }
126
127 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
128 {
129 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
130 }
131
132 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
133 {
134 return aff ? isl_local_space_dim(aff->ls, type) : 0;
135 }
136
137 __isl_give isl_dim *isl_aff_get_dim(__isl_keep isl_aff *aff)
138 {
139 return aff ? isl_local_space_get_dim(aff->ls) : NULL;
140 }
141
142 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
143 {
144 return aff ? isl_local_space_copy(aff->ls) : NULL;
145 }
146
147 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
148 enum isl_dim_type type, unsigned pos)
149 {
150 return aff ? isl_local_space_get_dim_name(aff->ls, type, pos) : 0;
151 }
152
153 __isl_give isl_aff *isl_aff_reset_dim(__isl_take isl_aff *aff,
154 __isl_take isl_dim *dim)
155 {
156 aff = isl_aff_cow(aff);
157 if (!aff || !dim)
158 goto error;
159
160 aff->ls = isl_local_space_reset_dim(aff->ls, dim);
161 if (!aff->ls)
162 return isl_aff_free(aff);
163
164 return aff;
165 error:
166 isl_aff_free(aff);
167 isl_dim_free(dim);
168 return NULL;
169 }
170
171 /* Reorder the coefficients of the affine expression based
172 * on the given reodering.
173 * The reordering r is assumed to have been extended with the local
174 * variables.
175 */
176 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
177 __isl_take isl_reordering *r, int n_div)
178 {
179 isl_vec *res;
180 int i;
181
182 if (!vec || !r)
183 goto error;
184
185 res = isl_vec_alloc(vec->ctx, 2 + isl_dim_total(r->dim) + n_div);
186 isl_seq_cpy(res->el, vec->el, 2);
187 isl_seq_clr(res->el + 2, res->size - 2);
188 for (i = 0; i < r->len; ++i)
189 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
190
191 isl_reordering_free(r);
192 isl_vec_free(vec);
193 return res;
194 error:
195 isl_vec_free(vec);
196 isl_reordering_free(r);
197 return NULL;
198 }
199
200 /* Reorder the dimensions of "aff" according to the given reordering.
201 */
202 __isl_give isl_aff *isl_aff_realign(__isl_take isl_aff *aff,
203 __isl_take isl_reordering *r)
204 {
205 aff = isl_aff_cow(aff);
206 if (!aff)
207 goto error;
208
209 r = isl_reordering_extend(r, aff->ls->div->n_row);
210 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
211 aff->ls->div->n_row);
212 aff->ls = isl_local_space_realign(aff->ls, r);
213
214 if (!aff->v || !aff->ls)
215 return isl_aff_free(aff);
216
217 return aff;
218 error:
219 isl_aff_free(aff);
220 isl_reordering_free(r);
221 return NULL;
222 }
223
224 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
225 {
226 if (!aff)
227 return -1;
228
229 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
230 }
231
232 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
233 {
234 int equal;
235
236 if (!aff1 || !aff2)
237 return -1;
238
239 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
240 if (equal < 0 || !equal)
241 return equal;
242
243 return isl_vec_is_equal(aff1->v, aff2->v);
244 }
245
246 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
247 {
248 if (!aff)
249 return -1;
250 isl_int_set(*v, aff->v->el[0]);
251 return 0;
252 }
253
254 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
255 {
256 if (!aff)
257 return -1;
258 isl_int_set(*v, aff->v->el[1]);
259 return 0;
260 }
261
262 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
263 enum isl_dim_type type, int pos, isl_int *v)
264 {
265 if (!aff)
266 return -1;
267
268 if (pos >= isl_local_space_dim(aff->ls, type))
269 isl_die(aff->v->ctx, isl_error_invalid,
270 "position out of bounds", return -1);
271
272 pos += isl_local_space_offset(aff->ls, type);
273 isl_int_set(*v, aff->v->el[1 + pos]);
274
275 return 0;
276 }
277
278 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
279 {
280 aff = isl_aff_cow(aff);
281 if (!aff)
282 return NULL;
283
284 aff->v = isl_vec_cow(aff->v);
285 if (!aff->v)
286 return isl_aff_free(aff);
287
288 isl_int_set(aff->v->el[0], v);
289
290 return aff;
291 }
292
293 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
294 {
295 aff = isl_aff_cow(aff);
296 if (!aff)
297 return NULL;
298
299 aff->v = isl_vec_cow(aff->v);
300 if (!aff->v)
301 return isl_aff_free(aff);
302
303 isl_int_set(aff->v->el[1], v);
304
305 return aff;
306 }
307
308 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
309 {
310 if (isl_int_is_zero(v))
311 return aff;
312
313 aff = isl_aff_cow(aff);
314 if (!aff)
315 return NULL;
316
317 aff->v = isl_vec_cow(aff->v);
318 if (!aff->v)
319 return isl_aff_free(aff);
320
321 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
322
323 return aff;
324 }
325
326 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
327 {
328 isl_int t;
329
330 isl_int_init(t);
331 isl_int_set_si(t, v);
332 aff = isl_aff_add_constant(aff, t);
333 isl_int_clear(t);
334
335 return aff;
336 }
337
338 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
339 {
340 aff = isl_aff_cow(aff);
341 if (!aff)
342 return NULL;
343
344 aff->v = isl_vec_cow(aff->v);
345 if (!aff->v)
346 return isl_aff_free(aff);
347
348 isl_int_set_si(aff->v->el[1], v);
349
350 return aff;
351 }
352
353 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
354 enum isl_dim_type type, int pos, isl_int v)
355 {
356 if (!aff)
357 return NULL;
358
359 if (pos >= isl_local_space_dim(aff->ls, type))
360 isl_die(aff->v->ctx, isl_error_invalid,
361 "position out of bounds", return isl_aff_free(aff));
362
363 aff = isl_aff_cow(aff);
364 if (!aff)
365 return NULL;
366
367 aff->v = isl_vec_cow(aff->v);
368 if (!aff->v)
369 return isl_aff_free(aff);
370
371 pos += isl_local_space_offset(aff->ls, type);
372 isl_int_set(aff->v->el[1 + pos], v);
373
374 return aff;
375 }
376
377 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
378 enum isl_dim_type type, int pos, int v)
379 {
380 if (!aff)
381 return NULL;
382
383 if (pos >= isl_local_space_dim(aff->ls, type))
384 isl_die(aff->v->ctx, isl_error_invalid,
385 "position out of bounds", return isl_aff_free(aff));
386
387 aff = isl_aff_cow(aff);
388 if (!aff)
389 return NULL;
390
391 aff->v = isl_vec_cow(aff->v);
392 if (!aff->v)
393 return isl_aff_free(aff);
394
395 pos += isl_local_space_offset(aff->ls, type);
396 isl_int_set_si(aff->v->el[1 + pos], v);
397
398 return aff;
399 }
400
401 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
402 enum isl_dim_type type, int pos, isl_int v)
403 {
404 if (!aff)
405 return NULL;
406
407 if (pos >= isl_local_space_dim(aff->ls, type))
408 isl_die(aff->v->ctx, isl_error_invalid,
409 "position out of bounds", return isl_aff_free(aff));
410
411 aff = isl_aff_cow(aff);
412 if (!aff)
413 return NULL;
414
415 aff->v = isl_vec_cow(aff->v);
416 if (!aff->v)
417 return isl_aff_free(aff);
418
419 pos += isl_local_space_offset(aff->ls, type);
420 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
421
422 return aff;
423 }
424
425 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
426 enum isl_dim_type type, int pos, int v)
427 {
428 isl_int t;
429
430 isl_int_init(t);
431 isl_int_set_si(t, v);
432 aff = isl_aff_add_coefficient(aff, type, pos, t);
433 isl_int_clear(t);
434
435 return aff;
436 }
437
438 __isl_give isl_div *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
439 {
440 if (!aff)
441 return NULL;
442
443 return isl_local_space_get_div(aff->ls, pos);
444 }
445
446 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
447 {
448 aff = isl_aff_cow(aff);
449 if (!aff)
450 return NULL;
451 aff->v = isl_vec_cow(aff->v);
452 if (!aff->v)
453 return isl_aff_free(aff);
454
455 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
456
457 return aff;
458 }
459
460 /* Given f, return floor(f).
461 * If f is an integer expression, then just return f.
462 * Otherwise, create a new div d = [f] and return the expression d.
463 */
464 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
465 {
466 int size;
467 isl_ctx *ctx;
468
469 if (!aff)
470 return NULL;
471
472 if (isl_int_is_one(aff->v->el[0]))
473 return aff;
474
475 aff = isl_aff_cow(aff);
476 if (!aff)
477 return NULL;
478
479 aff->ls = isl_local_space_add_div(aff->ls, isl_vec_copy(aff->v));
480 if (!aff->ls)
481 return isl_aff_free(aff);
482
483 ctx = isl_aff_get_ctx(aff);
484 size = aff->v->size;
485 isl_vec_free(aff->v);
486 aff->v = isl_vec_alloc(ctx, size + 1);
487 aff->v = isl_vec_clr(aff->v);
488 if (!aff->v)
489 return isl_aff_free(aff);
490 isl_int_set_si(aff->v->el[0], 1);
491 isl_int_set_si(aff->v->el[size], 1);
492
493 return aff;
494 }
495
496 /* Given f, return ceil(f).
497 * If f is an integer expression, then just return f.
498 * Otherwise, create a new div d = [-f] and return the expression -d.
499 */
500 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
501 {
502 if (!aff)
503 return NULL;
504
505 if (isl_int_is_one(aff->v->el[0]))
506 return aff;
507
508 aff = isl_aff_neg(aff);
509 aff = isl_aff_floor(aff);
510 aff = isl_aff_neg(aff);
511
512 return aff;
513 }
514
515 /* Apply the expansion computed by isl_merge_divs.
516 * The expansion itself is given by "exp" while the resulting
517 * list of divs is given by "div".
518 */
519 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
520 __isl_take isl_mat *div, int *exp)
521 {
522 int i, j;
523 int old_n_div;
524 int new_n_div;
525 int offset;
526
527 aff = isl_aff_cow(aff);
528 if (!aff || !div)
529 goto error;
530
531 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
532 new_n_div = isl_mat_rows(div);
533 if (new_n_div < old_n_div)
534 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
535 "not an expansion", goto error);
536
537 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
538 if (!aff->v)
539 goto error;
540
541 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
542 j = old_n_div - 1;
543 for (i = new_n_div - 1; i >= 0; --i) {
544 if (j >= 0 && exp[j] == i) {
545 if (i != j)
546 isl_int_swap(aff->v->el[offset + i],
547 aff->v->el[offset + j]);
548 j--;
549 } else
550 isl_int_set_si(aff->v->el[offset + i], 0);
551 }
552
553 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
554 if (!aff->ls)
555 goto error;
556 isl_mat_free(div);
557 return aff;
558 error:
559 isl_aff_free(aff);
560 isl_mat_free(div);
561 return NULL;
562 }
563
564 /* Add two affine expressions that live in the same local space.
565 */
566 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
567 __isl_take isl_aff *aff2)
568 {
569 isl_int gcd, f;
570
571 aff1 = isl_aff_cow(aff1);
572 if (!aff1 || !aff2)
573 goto error;
574
575 aff1->v = isl_vec_cow(aff1->v);
576 if (!aff1->v)
577 goto error;
578
579 isl_int_init(gcd);
580 isl_int_init(f);
581 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
582 isl_int_divexact(f, aff2->v->el[0], gcd);
583 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
584 isl_int_divexact(f, aff1->v->el[0], gcd);
585 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
586 isl_int_divexact(f, aff2->v->el[0], gcd);
587 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
588 isl_int_clear(f);
589 isl_int_clear(gcd);
590
591 isl_aff_free(aff2);
592 return aff1;
593 error:
594 isl_aff_free(aff1);
595 isl_aff_free(aff2);
596 return NULL;
597 }
598
599 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
600 __isl_take isl_aff *aff2)
601 {
602 isl_ctx *ctx;
603 int *exp1 = NULL;
604 int *exp2 = NULL;
605 isl_mat *div;
606
607 if (!aff1 || !aff2)
608 goto error;
609
610 ctx = isl_aff_get_ctx(aff1);
611 if (!isl_dim_equal(aff1->ls->dim, aff2->ls->dim))
612 isl_die(ctx, isl_error_invalid,
613 "spaces don't match", goto error);
614
615 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
616 return add_expanded(aff1, aff2);
617
618 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
619 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
620 if (!exp1 || !exp2)
621 goto error;
622
623 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
624 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
625 aff2 = isl_aff_expand_divs(aff2, div, exp2);
626 free(exp1);
627 free(exp2);
628
629 return add_expanded(aff1, aff2);
630 error:
631 free(exp1);
632 free(exp2);
633 isl_aff_free(aff1);
634 isl_aff_free(aff2);
635 return NULL;
636 }
637
638 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
639 __isl_take isl_aff *aff2)
640 {
641 return isl_aff_add(aff1, isl_aff_neg(aff2));
642 }
643
644 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
645 {
646 isl_int gcd;
647
648 if (isl_int_is_one(f))
649 return aff;
650
651 aff = isl_aff_cow(aff);
652 if (!aff)
653 return NULL;
654 aff->v = isl_vec_cow(aff->v);
655 if (!aff->v)
656 return isl_aff_free(aff);
657
658 isl_int_init(gcd);
659 isl_int_gcd(gcd, aff->v->el[0], f);
660 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
661 isl_int_divexact(gcd, f, gcd);
662 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
663 isl_int_clear(gcd);
664
665 return aff;
666 }
667
668 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
669 {
670 isl_int gcd;
671
672 if (isl_int_is_one(f))
673 return aff;
674
675 aff = isl_aff_cow(aff);
676 if (!aff)
677 return NULL;
678 aff->v = isl_vec_cow(aff->v);
679 if (!aff->v)
680 return isl_aff_free(aff);
681
682 isl_int_init(gcd);
683 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
684 isl_int_gcd(gcd, gcd, f);
685 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
686 isl_int_divexact(gcd, f, gcd);
687 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
688 isl_int_clear(gcd);
689
690 return aff;
691 }
692
693 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
694 {
695 isl_int v;
696
697 if (f == 1)
698 return aff;
699
700 isl_int_init(v);
701 isl_int_set_ui(v, f);
702 aff = isl_aff_scale_down(aff, v);
703 isl_int_clear(v);
704
705 return aff;
706 }
707
708 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
709 enum isl_dim_type type, unsigned pos, const char *s)
710 {
711 aff = isl_aff_cow(aff);
712 if (!aff)
713 return NULL;
714 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
715 if (!aff->ls)
716 return isl_aff_free(aff);
717
718 return aff;
719 }
720
721 /* Exploit the equalities in "eq" to simplify the affine expression
722 * and the expressions of the integer divisions in the local space.
723 * The integer divisions in this local space are assumed to appear
724 * as regular dimensions in "eq".
725 */
726 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
727 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
728 {
729 int i, j;
730 unsigned total;
731 unsigned n_div;
732
733 if (!eq)
734 goto error;
735 if (eq->n_eq == 0) {
736 isl_basic_set_free(eq);
737 return aff;
738 }
739
740 aff = isl_aff_cow(aff);
741 if (!aff)
742 goto error;
743
744 aff->ls = isl_local_space_substitute_equalities(aff->ls,
745 isl_basic_set_copy(eq));
746 if (!aff->ls)
747 goto error;
748
749 total = 1 + isl_dim_total(eq->dim);
750 n_div = eq->n_div;
751 for (i = 0; i < eq->n_eq; ++i) {
752 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
753 if (j < 0 || j == 0 || j >= total)
754 continue;
755
756 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
757 &aff->v->el[0]);
758 }
759
760 isl_basic_set_free(eq);
761 return aff;
762 error:
763 isl_basic_set_free(eq);
764 isl_aff_free(aff);
765 return NULL;
766 }
767
768 /* Exploit the equalities in "eq" to simplify the affine expression
769 * and the expressions of the integer divisions in the local space.
770 */
771 static __isl_give isl_aff *isl_aff_substitute_equalities(
772 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
773 {
774 int n_div;
775
776 if (!aff || !eq)
777 goto error;
778 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
779 if (n_div > 0)
780 eq = isl_basic_set_add(eq, isl_dim_set, n_div);
781 return isl_aff_substitute_equalities_lifted(aff, eq);
782 error:
783 isl_basic_set_free(eq);
784 isl_aff_free(aff);
785 return NULL;
786 }
787
788 /* Look for equalities among the variables shared by context and aff
789 * and the integer divisions of aff, if any.
790 * The equalities are then used to eliminate coefficients and/or integer
791 * divisions from aff.
792 */
793 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
794 __isl_take isl_set *context)
795 {
796 isl_basic_set *hull;
797 int n_div;
798
799 if (!aff)
800 goto error;
801 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
802 if (n_div > 0) {
803 isl_basic_set *bset;
804 context = isl_set_add_dims(context, isl_dim_set, n_div);
805 bset = isl_basic_set_from_local_space(
806 isl_aff_get_local_space(aff));
807 bset = isl_basic_set_lift(bset);
808 bset = isl_basic_set_flatten(bset);
809 context = isl_set_intersect(context,
810 isl_set_from_basic_set(bset));
811 }
812
813 hull = isl_set_affine_hull(context);
814 return isl_aff_substitute_equalities_lifted(aff, hull);
815 error:
816 isl_aff_free(aff);
817 isl_set_free(context);
818 return NULL;
819 }
820
821 /* Return a basic set containing those elements in the space
822 * of aff where it is non-negative.
823 */
824 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
825 {
826 isl_constraint *ineq;
827
828 ineq = isl_inequality_from_aff(aff);
829
830 return isl_basic_set_from_constraint(ineq);
831 }
832
833 /* Return a basic set containing those elements in the space
834 * of aff where it is zero.
835 */
836 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
837 {
838 isl_constraint *ineq;
839
840 ineq = isl_equality_from_aff(aff);
841
842 return isl_basic_set_from_constraint(ineq);
843 }
844
845 /* Return a basic set containing those elements in the shared space
846 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
847 */
848 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
849 __isl_take isl_aff *aff2)
850 {
851 aff1 = isl_aff_sub(aff1, aff2);
852
853 return isl_aff_nonneg_basic_set(aff1);
854 }
855
856 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
857 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
858 {
859 aff1 = isl_aff_add(aff1, aff2);
860 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
861 return aff1;
862 }
863
864 int isl_aff_is_empty(__isl_keep isl_aff *aff)
865 {
866 if (!aff)
867 return -1;
868
869 return 0;
870 }
871
872 /* Set active[i] to 1 if the dimension at position i is involved
873 * in the affine expression.
874 */
875 static int set_active(__isl_keep isl_aff *aff, int *active)
876 {
877 int i, j;
878 unsigned total;
879 unsigned offset;
880
881 if (!aff || !active)
882 return -1;
883
884 total = aff->v->size - 2;
885 for (i = 0; i < total; ++i)
886 active[i] = !isl_int_is_zero(aff->v->el[2 + i]);
887
888 offset = isl_local_space_offset(aff->ls, isl_dim_div) - 1;
889 for (i = aff->ls->div->n_row - 1; i >= 0; --i) {
890 if (!active[offset + i])
891 continue;
892 for (j = 0; j < total; ++j)
893 active[j] |=
894 !isl_int_is_zero(aff->ls->div->row[i][2 + j]);
895 }
896
897 return 0;
898 }
899
900 /* Check whether the given affine expression has non-zero coefficient
901 * for any dimension in the given range or if any of these dimensions
902 * appear with non-zero coefficients in any of the integer divisions
903 * involved in the affine expression.
904 */
905 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
906 enum isl_dim_type type, unsigned first, unsigned n)
907 {
908 int i;
909 isl_ctx *ctx;
910 int *active = NULL;
911 int involves = 0;
912
913 if (!aff)
914 return -1;
915 if (n == 0)
916 return 0;
917
918 ctx = isl_aff_get_ctx(aff);
919 if (first + n > isl_aff_dim(aff, type))
920 isl_die(ctx, isl_error_invalid,
921 "range out of bounds", return -1);
922
923 active = isl_calloc_array(ctx, int,
924 isl_local_space_dim(aff->ls, isl_dim_all));
925 if (set_active(aff, active) < 0)
926 goto error;
927
928 first += isl_local_space_offset(aff->ls, type) - 1;
929 for (i = 0; i < n; ++i)
930 if (active[first + i]) {
931 involves = 1;
932 break;
933 }
934
935 free(active);
936
937 return involves;
938 error:
939 free(active);
940 return -1;
941 }
942
943 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
944 enum isl_dim_type type, unsigned first, unsigned n)
945 {
946 isl_ctx *ctx;
947
948 if (!aff)
949 return NULL;
950 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
951 return aff;
952
953 ctx = isl_aff_get_ctx(aff);
954 if (first + n > isl_aff_dim(aff, type))
955 isl_die(ctx, isl_error_invalid, "range out of bounds",
956 return isl_aff_free(aff));
957
958 aff = isl_aff_cow(aff);
959 if (!aff)
960 return NULL;
961
962 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
963 if (!aff->ls)
964 return isl_aff_free(aff);
965
966 first += 1 + isl_local_space_offset(aff->ls, type);
967 aff->v = isl_vec_drop_els(aff->v, first, n);
968 if (!aff->v)
969 return isl_aff_free(aff);
970
971 return aff;
972 }
973
974 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
975 enum isl_dim_type type, unsigned first, unsigned n)
976 {
977 isl_ctx *ctx;
978
979 if (!aff)
980 return NULL;
981 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
982 return aff;
983
984 ctx = isl_aff_get_ctx(aff);
985 if (first > isl_aff_dim(aff, type))
986 isl_die(ctx, isl_error_invalid, "position out of bounds",
987 return isl_aff_free(aff));
988
989 aff = isl_aff_cow(aff);
990 if (!aff)
991 return NULL;
992
993 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
994 if (!aff->ls)
995 return isl_aff_free(aff);
996
997 first += 1 + isl_local_space_offset(aff->ls, type);
998 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
999 if (!aff->v)
1000 return isl_aff_free(aff);
1001
1002 return aff;
1003 }
1004
1005 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
1006 enum isl_dim_type type, unsigned n)
1007 {
1008 unsigned pos;
1009
1010 pos = isl_aff_dim(aff, type);
1011
1012 return isl_aff_insert_dims(aff, type, pos, n);
1013 }
1014
1015 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
1016 enum isl_dim_type type, unsigned n)
1017 {
1018 unsigned pos;
1019
1020 pos = isl_pw_aff_dim(pwaff, type);
1021
1022 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
1023 }
1024
1025 #undef PW
1026 #define PW isl_pw_aff
1027 #undef EL
1028 #define EL isl_aff
1029 #undef EL_IS_ZERO
1030 #define EL_IS_ZERO is_empty
1031 #undef ZERO
1032 #define ZERO empty
1033 #undef IS_ZERO
1034 #define IS_ZERO is_empty
1035 #undef FIELD
1036 #define FIELD aff
1037
1038 #define NO_EVAL
1039 #define NO_OPT
1040 #define NO_MOVE_DIMS
1041 #define NO_LIFT
1042 #define NO_MORPH
1043
1044 #include <isl_pw_templ.c>
1045
1046 /* Compute a piecewise quasi-affine expression with a domain that
1047 * is the union of those of pwaff1 and pwaff2 and such that on each
1048 * cell, the quasi-affine expression is the maximum of those of pwaff1
1049 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1050 * cell, then the associated expression is the defined one.
1051 */
1052 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
1053 __isl_take isl_pw_aff *pwaff2)
1054 {
1055 int i, j, n;
1056 isl_pw_aff *res;
1057 isl_ctx *ctx;
1058 isl_set *set;
1059
1060 if (!pwaff1 || !pwaff2)
1061 goto error;
1062
1063 ctx = isl_dim_get_ctx(pwaff1->dim);
1064 if (!isl_dim_equal(pwaff1->dim, pwaff2->dim))
1065 isl_die(ctx, isl_error_invalid,
1066 "arguments should live in same space", goto error);
1067
1068 if (isl_pw_aff_is_empty(pwaff1)) {
1069 isl_pw_aff_free(pwaff1);
1070 return pwaff2;
1071 }
1072
1073 if (isl_pw_aff_is_empty(pwaff2)) {
1074 isl_pw_aff_free(pwaff2);
1075 return pwaff1;
1076 }
1077
1078 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
1079 res = isl_pw_aff_alloc_(isl_dim_copy(pwaff1->dim), n);
1080
1081 for (i = 0; i < pwaff1->n; ++i) {
1082 set = isl_set_copy(pwaff1->p[i].set);
1083 for (j = 0; j < pwaff2->n; ++j) {
1084 struct isl_set *common;
1085 isl_set *ge;
1086
1087 common = isl_set_intersect(
1088 isl_set_copy(pwaff1->p[i].set),
1089 isl_set_copy(pwaff2->p[j].set));
1090 ge = isl_set_from_basic_set(isl_aff_ge_basic_set(
1091 isl_aff_copy(pwaff2->p[j].aff),
1092 isl_aff_copy(pwaff1->p[i].aff)));
1093 ge = isl_set_intersect(common, ge);
1094 if (isl_set_plain_is_empty(ge)) {
1095 isl_set_free(ge);
1096 continue;
1097 }
1098 set = isl_set_subtract(set, isl_set_copy(ge));
1099
1100 res = isl_pw_aff_add_piece(res, ge,
1101 isl_aff_copy(pwaff2->p[j].aff));
1102 }
1103 res = isl_pw_aff_add_piece(res, set,
1104 isl_aff_copy(pwaff1->p[i].aff));
1105 }
1106
1107 for (j = 0; j < pwaff2->n; ++j) {
1108 set = isl_set_copy(pwaff2->p[j].set);
1109 for (i = 0; i < pwaff1->n; ++i)
1110 set = isl_set_subtract(set,
1111 isl_set_copy(pwaff1->p[i].set));
1112 res = isl_pw_aff_add_piece(res, set,
1113 isl_aff_copy(pwaff2->p[j].aff));
1114 }
1115
1116 isl_pw_aff_free(pwaff1);
1117 isl_pw_aff_free(pwaff2);
1118
1119 return res;
1120 error:
1121 isl_pw_aff_free(pwaff1);
1122 isl_pw_aff_free(pwaff2);
1123 return NULL;
1124 }
1125
1126 /* Construct a map with as domain the domain of pwaff and
1127 * one-dimensional range corresponding to the affine expressions.
1128 */
1129 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1130 {
1131 int i;
1132 isl_dim *dim;
1133 isl_map *map;
1134
1135 if (!pwaff)
1136 return NULL;
1137
1138 dim = isl_pw_aff_get_dim(pwaff);
1139 dim = isl_dim_from_domain(dim);
1140 dim = isl_dim_add(dim, isl_dim_out, 1);
1141 map = isl_map_empty(dim);
1142
1143 for (i = 0; i < pwaff->n; ++i) {
1144 isl_basic_map *bmap;
1145 isl_map *map_i;
1146
1147 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
1148 map_i = isl_map_from_basic_map(bmap);
1149 map_i = isl_map_intersect_domain(map_i,
1150 isl_set_copy(pwaff->p[i].set));
1151 map = isl_map_union_disjoint(map, map_i);
1152 }
1153
1154 isl_pw_aff_free(pwaff);
1155
1156 return map;
1157 }
1158
1159 /* Return a set containing those elements in the domain
1160 * of pwaff where it is non-negative.
1161 */
1162 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
1163 {
1164 int i;
1165 isl_set *set;
1166
1167 if (!pwaff)
1168 return NULL;
1169
1170 set = isl_set_empty(isl_pw_aff_get_dim(pwaff));
1171
1172 for (i = 0; i < pwaff->n; ++i) {
1173 isl_basic_set *bset;
1174 isl_set *set_i;
1175
1176 bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff));
1177 set_i = isl_set_from_basic_set(bset);
1178 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1179 set = isl_set_union_disjoint(set, set_i);
1180 }
1181
1182 isl_pw_aff_free(pwaff);
1183
1184 return set;
1185 }
1186
1187 /* Return a set containing those elements in the domain
1188 * of pwaff where it is zero.
1189 */
1190 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
1191 {
1192 int i;
1193 isl_set *set;
1194
1195 if (!pwaff)
1196 return NULL;
1197
1198 set = isl_set_empty(isl_pw_aff_get_dim(pwaff));
1199
1200 for (i = 0; i < pwaff->n; ++i) {
1201 isl_basic_set *bset;
1202 isl_set *set_i;
1203
1204 bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
1205 set_i = isl_set_from_basic_set(bset);
1206 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1207 set = isl_set_union_disjoint(set, set_i);
1208 }
1209
1210 isl_pw_aff_free(pwaff);
1211
1212 return set;
1213 }
1214
1215 /* Return a set containing those elements in the shared domain
1216 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1217 *
1218 * We compute the difference on the shared domain and then construct
1219 * the set of values where this difference is non-negative.
1220 * If strict is set, we first subtract 1 from the difference.
1221 * If equal is set, we only return the elements where pwaff1 and pwaff2
1222 * are equal.
1223 */
1224 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
1225 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
1226 {
1227 isl_set *set1, *set2;
1228
1229 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
1230 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
1231 set1 = isl_set_intersect(set1, set2);
1232 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
1233 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
1234 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
1235
1236 if (strict) {
1237 isl_dim *dim = isl_set_get_dim(set1);
1238 isl_aff *aff;
1239 aff = isl_aff_zero(isl_local_space_from_dim(dim));
1240 aff = isl_aff_add_constant_si(aff, -1);
1241 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
1242 } else
1243 isl_set_free(set1);
1244
1245 if (equal)
1246 return isl_pw_aff_zero_set(pwaff1);
1247 return isl_pw_aff_nonneg_set(pwaff1);
1248 }
1249
1250 /* Return a set containing those elements in the shared domain
1251 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1252 */
1253 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1254 __isl_take isl_pw_aff *pwaff2)
1255 {
1256 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
1257 }
1258
1259 /* Return a set containing those elements in the shared domain
1260 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
1261 */
1262 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1263 __isl_take isl_pw_aff *pwaff2)
1264 {
1265 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
1266 }
1267
1268 /* Return a set containing those elements in the shared domain
1269 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
1270 */
1271 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1272 __isl_take isl_pw_aff *pwaff2)
1273 {
1274 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
1275 }
1276
1277 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
1278 __isl_take isl_pw_aff *pwaff2)
1279 {
1280 return isl_pw_aff_ge_set(pwaff2, pwaff1);
1281 }
1282
1283 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
1284 __isl_take isl_pw_aff *pwaff2)
1285 {
1286 return isl_pw_aff_gt_set(pwaff2, pwaff1);
1287 }
1288
1289 /* Return a set containing those elements in the shared domain
1290 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
1291 */
1292 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1293 __isl_take isl_pw_aff *pwaff2)
1294 {
1295 isl_set *set_lt, *set_gt;
1296
1297 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
1298 isl_pw_aff_copy(pwaff2));
1299 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
1300 return isl_set_union_disjoint(set_lt, set_gt);
1301 }
1302
1303 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
1304 isl_int v)
1305 {
1306 int i;
1307
1308 if (isl_int_is_one(v))
1309 return pwaff;
1310 if (!isl_int_is_pos(v))
1311 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1312 "factor needs to be positive",
1313 return isl_pw_aff_free(pwaff));
1314 pwaff = isl_pw_aff_cow(pwaff);
1315 if (!pwaff)
1316 return NULL;
1317 if (pwaff->n == 0)
1318 return pwaff;
1319
1320 for (i = 0; i < pwaff->n; ++i) {
1321 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
1322 if (!pwaff->p[i].aff)
1323 return isl_pw_aff_free(pwaff);
1324 }
1325
1326 return pwaff;
1327 }
1328
1329 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
1330 {
1331 int i;
1332
1333 pwaff = isl_pw_aff_cow(pwaff);
1334 if (!pwaff)
1335 return NULL;
1336 if (pwaff->n == 0)
1337 return pwaff;
1338
1339 for (i = 0; i < pwaff->n; ++i) {
1340 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
1341 if (!pwaff->p[i].aff)
1342 return isl_pw_aff_free(pwaff);
1343 }
1344
1345 return pwaff;
1346 }
1347
1348 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
1349 {
1350 int i;
1351
1352 pwaff = isl_pw_aff_cow(pwaff);
1353 if (!pwaff)
1354 return NULL;
1355 if (pwaff->n == 0)
1356 return pwaff;
1357
1358 for (i = 0; i < pwaff->n; ++i) {
1359 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
1360 if (!pwaff->p[i].aff)
1361 return isl_pw_aff_free(pwaff);
1362 }
1363
1364 return pwaff;
1365 }
1366
1367 /* Return an affine expression that is equal to pwaff_true for elements
1368 * in "cond" and to pwaff_false for elements not in "cond".
1369 * That is, return cond ? pwaff_true : pwaff_false;
1370 */
1371 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_set *cond,
1372 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
1373 {
1374 isl_set *comp;
1375
1376 comp = isl_set_complement(isl_set_copy(cond));
1377 pwaff_true = isl_pw_aff_intersect_domain(pwaff_true, cond);
1378 pwaff_false = isl_pw_aff_intersect_domain(pwaff_false, comp);
1379
1380 return isl_pw_aff_add_disjoint(pwaff_true, pwaff_false);
1381 }
Integer set library