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add isl_mat_diag
[isl.git] / isl_aff.c
blob941dcb6e05e171651c0e7dea22c8929e7bdc33d2
1 /*
2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
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 */
11
12 #include <isl_map_private.h>
13 #include <isl_aff_private.h>
14 #include <isl_dim_private.h>
15 #include <isl_local_space_private.h>
16 #include <isl_mat_private.h>
17 #include <isl/constraint.h>
18 #include <isl/seq.h>
19 #include <isl/set.h>
20
21 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
22 __isl_take isl_vec *v)
23 {
24 isl_aff *aff;
25
26 if (!ls || !v)
27 goto error;
28
29 aff = isl_calloc_type(v->ctx, struct isl_aff);
30 if (!aff)
31 goto error;
32
33 aff->ref = 1;
34 aff->ls = ls;
35 aff->v = v;
36
37 return aff;
38 error:
39 isl_local_space_free(ls);
40 isl_vec_free(v);
41 return NULL;
42 }
43
44 __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
45 {
46 isl_ctx *ctx;
47 isl_vec *v;
48 unsigned total;
49
50 if (!ls)
51 return NULL;
52
53 ctx = isl_local_space_get_ctx(ls);
54 if (!isl_local_space_divs_known(ls))
55 isl_die(ctx, isl_error_invalid, "local space has unknown divs",
56 goto error);
57
58 total = isl_local_space_dim(ls, isl_dim_all);
59 v = isl_vec_alloc(ctx, 1 + 1 + total);
60 return isl_aff_alloc_vec(ls, v);
61 error:
62 isl_local_space_free(ls);
63 return NULL;
64 }
65
66 __isl_give isl_aff *isl_aff_zero(__isl_take isl_local_space *ls)
67 {
68 isl_aff *aff;
69
70 aff = isl_aff_alloc(ls);
71 if (!aff)
72 return NULL;
73
74 isl_int_set_si(aff->v->el[0], 1);
75 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
76
77 return aff;
78 }
79
80 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
81 {
82 if (!aff)
83 return NULL;
84
85 aff->ref++;
86 return aff;
87 }
88
89 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
90 {
91 if (!aff)
92 return NULL;
93
94 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
95 isl_vec_copy(aff->v));
96 }
97
98 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
99 {
100 if (!aff)
101 return NULL;
102
103 if (aff->ref == 1)
104 return aff;
105 aff->ref--;
106 return isl_aff_dup(aff);
107 }
108
109 void *isl_aff_free(__isl_take isl_aff *aff)
110 {
111 if (!aff)
112 return NULL;
113
114 if (--aff->ref > 0)
115 return NULL;
116
117 isl_local_space_free(aff->ls);
118 isl_vec_free(aff->v);
119
120 free(aff);
121
122 return NULL;
123 }
124
125 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
126 {
127 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
128 }
129
130 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
131 {
132 return aff ? isl_local_space_dim(aff->ls, type) : 0;
133 }
134
135 __isl_give isl_dim *isl_aff_get_dim(__isl_keep isl_aff *aff)
136 {
137 return aff ? isl_local_space_get_dim(aff->ls) : NULL;
138 }
139
140 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
141 {
142 return aff ? isl_local_space_copy(aff->ls) : NULL;
143 }
144
145 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
146 enum isl_dim_type type, unsigned pos)
147 {
148 return aff ? isl_local_space_get_dim_name(aff->ls, type, pos) : 0;
149 }
150
151 __isl_give isl_aff *isl_aff_reset_dim(__isl_take isl_aff *aff,
152 __isl_take isl_dim *dim)
153 {
154 aff = isl_aff_cow(aff);
155 if (!aff || !dim)
156 goto error;
157
158 aff->ls = isl_local_space_reset_dim(aff->ls, dim);
159 if (!aff->ls)
160 return isl_aff_free(aff);
161
162 return aff;
163 error:
164 isl_aff_free(aff);
165 isl_dim_free(dim);
166 return NULL;
167 }
168
169 /* Reorder the coefficients of the affine expression based
170 * on the given reodering.
171 * The reordering r is assumed to have been extended with the local
172 * variables.
173 */
174 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
175 __isl_take isl_reordering *r, int n_div)
176 {
177 isl_vec *res;
178 int i;
179
180 if (!vec || !r)
181 goto error;
182
183 res = isl_vec_alloc(vec->ctx, 2 + isl_dim_total(r->dim) + n_div);
184 isl_seq_cpy(res->el, vec->el, 2);
185 isl_seq_clr(res->el + 2, res->size - 2);
186 for (i = 0; i < r->len; ++i)
187 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
188
189 isl_reordering_free(r);
190 isl_vec_free(vec);
191 return res;
192 error:
193 isl_vec_free(vec);
194 isl_reordering_free(r);
195 return NULL;
196 }
197
198 /* Reorder the dimensions of "aff" according to the given reordering.
199 */
200 __isl_give isl_aff *isl_aff_realign(__isl_take isl_aff *aff,
201 __isl_take isl_reordering *r)
202 {
203 aff = isl_aff_cow(aff);
204 if (!aff)
205 goto error;
206
207 r = isl_reordering_extend(r, aff->ls->div->n_row);
208 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
209 aff->ls->div->n_row);
210 aff->ls = isl_local_space_realign(aff->ls, r);
211
212 if (!aff->v || !aff->ls)
213 return isl_aff_free(aff);
214
215 return aff;
216 error:
217 isl_aff_free(aff);
218 isl_reordering_free(r);
219 return NULL;
220 }
221
222 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
223 {
224 if (!aff)
225 return -1;
226
227 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
228 }
229
230 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
231 {
232 int equal;
233
234 if (!aff1 || !aff2)
235 return -1;
236
237 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
238 if (equal < 0 || !equal)
239 return equal;
240
241 return isl_vec_is_equal(aff1->v, aff2->v);
242 }
243
244 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
245 {
246 if (!aff)
247 return -1;
248 isl_int_set(*v, aff->v->el[0]);
249 return 0;
250 }
251
252 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
253 {
254 if (!aff)
255 return -1;
256 isl_int_set(*v, aff->v->el[1]);
257 return 0;
258 }
259
260 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
261 enum isl_dim_type type, int pos, isl_int *v)
262 {
263 if (!aff)
264 return -1;
265
266 if (pos >= isl_local_space_dim(aff->ls, type))
267 isl_die(aff->v->ctx, isl_error_invalid,
268 "position out of bounds", return -1);
269
270 pos += isl_local_space_offset(aff->ls, type);
271 isl_int_set(*v, aff->v->el[1 + pos]);
272
273 return 0;
274 }
275
276 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
277 {
278 aff = isl_aff_cow(aff);
279 if (!aff)
280 return NULL;
281
282 aff->v = isl_vec_cow(aff->v);
283 if (!aff->v)
284 return isl_aff_free(aff);
285
286 isl_int_set(aff->v->el[0], v);
287
288 return aff;
289 }
290
291 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
292 {
293 aff = isl_aff_cow(aff);
294 if (!aff)
295 return NULL;
296
297 aff->v = isl_vec_cow(aff->v);
298 if (!aff->v)
299 return isl_aff_free(aff);
300
301 isl_int_set(aff->v->el[1], v);
302
303 return aff;
304 }
305
306 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
307 {
308 if (isl_int_is_zero(v))
309 return aff;
310
311 aff = isl_aff_cow(aff);
312 if (!aff)
313 return NULL;
314
315 aff->v = isl_vec_cow(aff->v);
316 if (!aff->v)
317 return isl_aff_free(aff);
318
319 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
320
321 return aff;
322 }
323
324 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
325 {
326 isl_int t;
327
328 isl_int_init(t);
329 isl_int_set_si(t, v);
330 aff = isl_aff_add_constant(aff, t);
331 isl_int_clear(t);
332
333 return aff;
334 }
335
336 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
337 {
338 aff = isl_aff_cow(aff);
339 if (!aff)
340 return NULL;
341
342 aff->v = isl_vec_cow(aff->v);
343 if (!aff->v)
344 return isl_aff_free(aff);
345
346 isl_int_set_si(aff->v->el[1], v);
347
348 return aff;
349 }
350
351 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
352 enum isl_dim_type type, int pos, isl_int v)
353 {
354 if (!aff)
355 return NULL;
356
357 if (pos >= isl_local_space_dim(aff->ls, type))
358 isl_die(aff->v->ctx, isl_error_invalid,
359 "position out of bounds", return isl_aff_free(aff));
360
361 aff = isl_aff_cow(aff);
362 if (!aff)
363 return NULL;
364
365 aff->v = isl_vec_cow(aff->v);
366 if (!aff->v)
367 return isl_aff_free(aff);
368
369 pos += isl_local_space_offset(aff->ls, type);
370 isl_int_set(aff->v->el[1 + pos], v);
371
372 return aff;
373 }
374
375 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
376 enum isl_dim_type type, int pos, int v)
377 {
378 if (!aff)
379 return NULL;
380
381 if (pos >= isl_local_space_dim(aff->ls, type))
382 isl_die(aff->v->ctx, isl_error_invalid,
383 "position out of bounds", return isl_aff_free(aff));
384
385 aff = isl_aff_cow(aff);
386 if (!aff)
387 return NULL;
388
389 aff->v = isl_vec_cow(aff->v);
390 if (!aff->v)
391 return isl_aff_free(aff);
392
393 pos += isl_local_space_offset(aff->ls, type);
394 isl_int_set_si(aff->v->el[1 + pos], v);
395
396 return aff;
397 }
398
399 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
400 enum isl_dim_type type, int pos, isl_int v)
401 {
402 if (!aff)
403 return NULL;
404
405 if (pos >= isl_local_space_dim(aff->ls, type))
406 isl_die(aff->v->ctx, isl_error_invalid,
407 "position out of bounds", return isl_aff_free(aff));
408
409 aff = isl_aff_cow(aff);
410 if (!aff)
411 return NULL;
412
413 aff->v = isl_vec_cow(aff->v);
414 if (!aff->v)
415 return isl_aff_free(aff);
416
417 pos += isl_local_space_offset(aff->ls, type);
418 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
419
420 return aff;
421 }
422
423 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
424 enum isl_dim_type type, int pos, int v)
425 {
426 isl_int t;
427
428 isl_int_init(t);
429 isl_int_set_si(t, v);
430 aff = isl_aff_add_coefficient(aff, type, pos, t);
431 isl_int_clear(t);
432
433 return aff;
434 }
435
436 __isl_give isl_div *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
437 {
438 if (!aff)
439 return NULL;
440
441 return isl_local_space_get_div(aff->ls, pos);
442 }
443
444 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
445 {
446 aff = isl_aff_cow(aff);
447 if (!aff)
448 return NULL;
449 aff->v = isl_vec_cow(aff->v);
450 if (!aff->v)
451 return isl_aff_free(aff);
452
453 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
454
455 return aff;
456 }
457
458 /* Given f, return floor(f).
459 * If f is an integer expression, then just return f.
460 * Otherwise, create a new div d = [f] and return the expression d.
461 */
462 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
463 {
464 int size;
465 isl_ctx *ctx;
466
467 if (!aff)
468 return NULL;
469
470 if (isl_int_is_one(aff->v->el[0]))
471 return aff;
472
473 aff = isl_aff_cow(aff);
474 if (!aff)
475 return NULL;
476
477 aff->ls = isl_local_space_add_div(aff->ls, isl_vec_copy(aff->v));
478 if (!aff->ls)
479 return isl_aff_free(aff);
480
481 ctx = isl_aff_get_ctx(aff);
482 size = aff->v->size;
483 isl_vec_free(aff->v);
484 aff->v = isl_vec_alloc(ctx, size + 1);
485 aff->v = isl_vec_clr(aff->v);
486 if (!aff->v)
487 return isl_aff_free(aff);
488 isl_int_set_si(aff->v->el[0], 1);
489 isl_int_set_si(aff->v->el[size], 1);
490
491 return aff;
492 }
493
494 /* Given f, return ceil(f).
495 * If f is an integer expression, then just return f.
496 * Otherwise, create a new div d = [-f] and return the expression -d.
497 */
498 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
499 {
500 if (!aff)
501 return NULL;
502
503 if (isl_int_is_one(aff->v->el[0]))
504 return aff;
505
506 aff = isl_aff_neg(aff);
507 aff = isl_aff_floor(aff);
508 aff = isl_aff_neg(aff);
509
510 return aff;
511 }
512
513 /* Apply the expansion computed by isl_merge_divs.
514 * The expansion itself is given by "exp" while the resulting
515 * list of divs is given by "div".
516 */
517 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
518 __isl_take isl_mat *div, int *exp)
519 {
520 int i, j;
521 int old_n_div;
522 int new_n_div;
523 int offset;
524
525 aff = isl_aff_cow(aff);
526 if (!aff || !div)
527 goto error;
528
529 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
530 new_n_div = isl_mat_rows(div);
531 if (new_n_div < old_n_div)
532 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
533 "not an expansion", goto error);
534
535 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
536 if (!aff->v)
537 goto error;
538
539 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
540 j = old_n_div - 1;
541 for (i = new_n_div - 1; i >= 0; --i) {
542 if (j >= 0 && exp[j] == i) {
543 if (i != j)
544 isl_int_swap(aff->v->el[offset + i],
545 aff->v->el[offset + j]);
546 j--;
547 } else
548 isl_int_set_si(aff->v->el[offset + i], 0);
549 }
550
551 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
552 if (!aff->ls)
553 goto error;
554 isl_mat_free(div);
555 return aff;
556 error:
557 isl_aff_free(aff);
558 isl_mat_free(div);
559 return NULL;
560 }
561
562 /* Add two affine expressions that live in the same local space.
563 */
564 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
565 __isl_take isl_aff *aff2)
566 {
567 isl_int gcd, f;
568
569 aff1 = isl_aff_cow(aff1);
570 if (!aff1 || !aff2)
571 goto error;
572
573 aff1->v = isl_vec_cow(aff1->v);
574 if (!aff1->v)
575 goto error;
576
577 isl_int_init(gcd);
578 isl_int_init(f);
579 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
580 isl_int_divexact(f, aff2->v->el[0], gcd);
581 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
582 isl_int_divexact(f, aff1->v->el[0], gcd);
583 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
584 isl_int_divexact(f, aff2->v->el[0], gcd);
585 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
586 isl_int_clear(f);
587 isl_int_clear(gcd);
588
589 isl_aff_free(aff2);
590 return aff1;
591 error:
592 isl_aff_free(aff1);
593 isl_aff_free(aff2);
594 return NULL;
595 }
596
597 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
598 __isl_take isl_aff *aff2)
599 {
600 isl_ctx *ctx;
601 int *exp1 = NULL;
602 int *exp2 = NULL;
603 isl_mat *div;
604
605 if (!aff1 || !aff2)
606 goto error;
607
608 ctx = isl_aff_get_ctx(aff1);
609 if (!isl_dim_equal(aff1->ls->dim, aff2->ls->dim))
610 isl_die(ctx, isl_error_invalid,
611 "spaces don't match", goto error);
612
613 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
614 return add_expanded(aff1, aff2);
615
616 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
617 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
618 if (!exp1 || !exp2)
619 goto error;
620
621 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
622 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
623 aff2 = isl_aff_expand_divs(aff2, div, exp2);
624 free(exp1);
625 free(exp2);
626
627 return add_expanded(aff1, aff2);
628 error:
629 free(exp1);
630 free(exp2);
631 isl_aff_free(aff1);
632 isl_aff_free(aff2);
633 return NULL;
634 }
635
636 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
637 __isl_take isl_aff *aff2)
638 {
639 return isl_aff_add(aff1, isl_aff_neg(aff2));
640 }
641
642 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
643 {
644 isl_int gcd;
645
646 if (isl_int_is_one(f))
647 return aff;
648
649 aff = isl_aff_cow(aff);
650 if (!aff)
651 return NULL;
652 aff->v = isl_vec_cow(aff->v);
653 if (!aff->v)
654 return isl_aff_free(aff);
655
656 isl_int_init(gcd);
657 isl_int_gcd(gcd, aff->v->el[0], f);
658 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
659 isl_int_divexact(gcd, f, gcd);
660 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
661 isl_int_clear(gcd);
662
663 return aff;
664 }
665
666 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
667 {
668 isl_int gcd;
669
670 if (isl_int_is_one(f))
671 return aff;
672
673 aff = isl_aff_cow(aff);
674 if (!aff)
675 return NULL;
676 aff->v = isl_vec_cow(aff->v);
677 if (!aff->v)
678 return isl_aff_free(aff);
679
680 isl_int_init(gcd);
681 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
682 isl_int_gcd(gcd, gcd, f);
683 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
684 isl_int_divexact(gcd, f, gcd);
685 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
686 isl_int_clear(gcd);
687
688 return aff;
689 }
690
691 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
692 {
693 isl_int v;
694
695 if (f == 1)
696 return aff;
697
698 isl_int_init(v);
699 isl_int_set_ui(v, f);
700 aff = isl_aff_scale_down(aff, v);
701 isl_int_clear(v);
702
703 return aff;
704 }
705
706 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
707 enum isl_dim_type type, unsigned pos, const char *s)
708 {
709 aff = isl_aff_cow(aff);
710 if (!aff)
711 return NULL;
712 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
713 if (!aff->ls)
714 return isl_aff_free(aff);
715
716 return aff;
717 }
718
719 /* Exploit the equalities in "eq" to simplify the affine expression
720 * and the expressions of the integer divisions in the local space.
721 * The integer divisions in this local space are assumed to appear
722 * as regular dimensions in "eq".
723 */
724 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
725 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
726 {
727 int i, j;
728 unsigned total;
729 unsigned n_div;
730
731 if (!eq)
732 goto error;
733 if (eq->n_eq == 0) {
734 isl_basic_set_free(eq);
735 return aff;
736 }
737
738 aff = isl_aff_cow(aff);
739 if (!aff)
740 goto error;
741
742 aff->ls = isl_local_space_substitute_equalities(aff->ls,
743 isl_basic_set_copy(eq));
744 if (!aff->ls)
745 goto error;
746
747 total = 1 + isl_dim_total(eq->dim);
748 n_div = eq->n_div;
749 for (i = 0; i < eq->n_eq; ++i) {
750 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
751 if (j < 0 || j == 0 || j >= total)
752 continue;
753
754 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
755 &aff->v->el[0]);
756 }
757
758 isl_basic_set_free(eq);
759 return aff;
760 error:
761 isl_basic_set_free(eq);
762 isl_aff_free(aff);
763 return NULL;
764 }
765
766 /* Exploit the equalities in "eq" to simplify the affine expression
767 * and the expressions of the integer divisions in the local space.
768 */
769 static __isl_give isl_aff *isl_aff_substitute_equalities(
770 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
771 {
772 int n_div;
773
774 if (!aff || !eq)
775 goto error;
776 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
777 if (n_div > 0)
778 eq = isl_basic_set_add(eq, isl_dim_set, n_div);
779 return isl_aff_substitute_equalities_lifted(aff, eq);
780 error:
781 isl_basic_set_free(eq);
782 isl_aff_free(aff);
783 return NULL;
784 }
785
786 /* Look for equalities among the variables shared by context and aff
787 * and the integer divisions of aff, if any.
788 * The equalities are then used to eliminate coefficients and/or integer
789 * divisions from aff.
790 */
791 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
792 __isl_take isl_set *context)
793 {
794 isl_basic_set *hull;
795 int n_div;
796
797 if (!aff)
798 goto error;
799 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
800 if (n_div > 0) {
801 isl_basic_set *bset;
802 context = isl_set_add_dims(context, isl_dim_set, n_div);
803 bset = isl_basic_set_from_local_space(
804 isl_aff_get_local_space(aff));
805 bset = isl_basic_set_lift(bset);
806 bset = isl_basic_set_flatten(bset);
807 context = isl_set_intersect(context,
808 isl_set_from_basic_set(bset));
809 }
810
811 hull = isl_set_affine_hull(context);
812 return isl_aff_substitute_equalities_lifted(aff, hull);
813 error:
814 isl_aff_free(aff);
815 isl_set_free(context);
816 return NULL;
817 }
818
819 /* Return a basic set containing those elements in the space
820 * of aff where it is non-negative.
821 */
822 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
823 {
824 isl_constraint *ineq;
825
826 ineq = isl_inequality_from_aff(aff);
827
828 return isl_basic_set_from_constraint(ineq);
829 }
830
831 /* Return a basic set containing those elements in the space
832 * of aff where it is zero.
833 */
834 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
835 {
836 isl_constraint *ineq;
837
838 ineq = isl_equality_from_aff(aff);
839
840 return isl_basic_set_from_constraint(ineq);
841 }
842
843 /* Return a basic set containing those elements in the shared space
844 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
845 */
846 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
847 __isl_take isl_aff *aff2)
848 {
849 aff1 = isl_aff_sub(aff1, aff2);
850
851 return isl_aff_nonneg_basic_set(aff1);
852 }
853
854 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
855 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
856 {
857 aff1 = isl_aff_add(aff1, aff2);
858 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
859 return aff1;
860 }
861
862 int isl_aff_is_empty(__isl_keep isl_aff *aff)
863 {
864 if (!aff)
865 return -1;
866
867 return 0;
868 }
869
870 /* Set active[i] to 1 if the dimension at position i is involved
871 * in the affine expression.
872 */
873 static int set_active(__isl_keep isl_aff *aff, int *active)
874 {
875 int i, j;
876 unsigned total;
877 unsigned offset;
878
879 if (!aff || !active)
880 return -1;
881
882 total = aff->v->size - 2;
883 for (i = 0; i < total; ++i)
884 active[i] = !isl_int_is_zero(aff->v->el[2 + i]);
885
886 offset = isl_local_space_offset(aff->ls, isl_dim_div) - 1;
887 for (i = aff->ls->div->n_row - 1; i >= 0; --i) {
888 if (!active[offset + i])
889 continue;
890 for (j = 0; j < total; ++j)
891 active[j] |=
892 !isl_int_is_zero(aff->ls->div->row[i][2 + j]);
893 }
894
895 return 0;
896 }
897
898 /* Check whether the given affine expression has non-zero coefficient
899 * for any dimension in the given range or if any of these dimensions
900 * appear with non-zero coefficients in any of the integer divisions
901 * involved in the affine expression.
902 */
903 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
904 enum isl_dim_type type, unsigned first, unsigned n)
905 {
906 int i;
907 isl_ctx *ctx;
908 int *active = NULL;
909 int involves = 0;
910
911 if (!aff)
912 return -1;
913 if (n == 0)
914 return 0;
915
916 ctx = isl_aff_get_ctx(aff);
917 if (first + n > isl_aff_dim(aff, type))
918 isl_die(ctx, isl_error_invalid,
919 "range out of bounds", return -1);
920
921 active = isl_calloc_array(ctx, int,
922 isl_local_space_dim(aff->ls, isl_dim_all));
923 if (set_active(aff, active) < 0)
924 goto error;
925
926 first += isl_local_space_offset(aff->ls, type) - 1;
927 for (i = 0; i < n; ++i)
928 if (active[first + i]) {
929 involves = 1;
930 break;
931 }
932
933 free(active);
934
935 return involves;
936 error:
937 free(active);
938 return -1;
939 }
940
941 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
942 enum isl_dim_type type, unsigned first, unsigned n)
943 {
944 isl_ctx *ctx;
945
946 if (!aff)
947 return NULL;
948 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
949 return aff;
950
951 ctx = isl_aff_get_ctx(aff);
952 if (first + n > isl_aff_dim(aff, type))
953 isl_die(ctx, isl_error_invalid, "range out of bounds",
954 return isl_aff_free(aff));
955
956 aff = isl_aff_cow(aff);
957 if (!aff)
958 return NULL;
959
960 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
961 if (!aff->ls)
962 return isl_aff_free(aff);
963
964 first += 1 + isl_local_space_offset(aff->ls, type);
965 aff->v = isl_vec_drop_els(aff->v, first, n);
966 if (!aff->v)
967 return isl_aff_free(aff);
968
969 return aff;
970 }
971
972 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
973 enum isl_dim_type type, unsigned first, unsigned n)
974 {
975 isl_ctx *ctx;
976
977 if (!aff)
978 return NULL;
979 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
980 return aff;
981
982 ctx = isl_aff_get_ctx(aff);
983 if (first > isl_aff_dim(aff, type))
984 isl_die(ctx, isl_error_invalid, "position out of bounds",
985 return isl_aff_free(aff));
986
987 aff = isl_aff_cow(aff);
988 if (!aff)
989 return NULL;
990
991 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
992 if (!aff->ls)
993 return isl_aff_free(aff);
994
995 first += 1 + isl_local_space_offset(aff->ls, type);
996 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
997 if (!aff->v)
998 return isl_aff_free(aff);
999
1000 return aff;
1001 }
1002
1003 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
1004 enum isl_dim_type type, unsigned n)
1005 {
1006 unsigned pos;
1007
1008 pos = isl_aff_dim(aff, type);
1009
1010 return isl_aff_insert_dims(aff, type, pos, n);
1011 }
1012
1013 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
1014 enum isl_dim_type type, unsigned n)
1015 {
1016 unsigned pos;
1017
1018 pos = isl_pw_aff_dim(pwaff, type);
1019
1020 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
1021 }
1022
1023 #undef PW
1024 #define PW isl_pw_aff
1025 #undef EL
1026 #define EL isl_aff
1027 #undef EL_IS_ZERO
1028 #define EL_IS_ZERO is_empty
1029 #undef ZERO
1030 #define ZERO empty
1031 #undef IS_ZERO
1032 #define IS_ZERO is_empty
1033 #undef FIELD
1034 #define FIELD aff
1035
1036 #define NO_EVAL
1037 #define NO_OPT
1038 #define NO_MOVE_DIMS
1039 #define NO_LIFT
1040 #define NO_MORPH
1041
1042 #include <isl_pw_templ.c>
1043
1044 /* Compute a piecewise quasi-affine expression with a domain that
1045 * is the union of those of pwaff1 and pwaff2 and such that on each
1046 * cell, the quasi-affine expression is the maximum of those of pwaff1
1047 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1048 * cell, then the associated expression is the defined one.
1049 */
1050 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
1051 __isl_take isl_pw_aff *pwaff2)
1052 {
1053 int i, j, n;
1054 isl_pw_aff *res;
1055 isl_ctx *ctx;
1056 isl_set *set;
1057
1058 if (!pwaff1 || !pwaff2)
1059 goto error;
1060
1061 ctx = isl_dim_get_ctx(pwaff1->dim);
1062 if (!isl_dim_equal(pwaff1->dim, pwaff2->dim))
1063 isl_die(ctx, isl_error_invalid,
1064 "arguments should live in same space", goto error);
1065
1066 if (isl_pw_aff_is_empty(pwaff1)) {
1067 isl_pw_aff_free(pwaff1);
1068 return pwaff2;
1069 }
1070
1071 if (isl_pw_aff_is_empty(pwaff2)) {
1072 isl_pw_aff_free(pwaff2);
1073 return pwaff1;
1074 }
1075
1076 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
1077 res = isl_pw_aff_alloc_(isl_dim_copy(pwaff1->dim), n);
1078
1079 for (i = 0; i < pwaff1->n; ++i) {
1080 set = isl_set_copy(pwaff1->p[i].set);
1081 for (j = 0; j < pwaff2->n; ++j) {
1082 struct isl_set *common;
1083 isl_set *ge;
1084
1085 common = isl_set_intersect(
1086 isl_set_copy(pwaff1->p[i].set),
1087 isl_set_copy(pwaff2->p[j].set));
1088 ge = isl_set_from_basic_set(isl_aff_ge_basic_set(
1089 isl_aff_copy(pwaff2->p[j].aff),
1090 isl_aff_copy(pwaff1->p[i].aff)));
1091 ge = isl_set_intersect(common, ge);
1092 if (isl_set_plain_is_empty(ge)) {
1093 isl_set_free(ge);
1094 continue;
1095 }
1096 set = isl_set_subtract(set, isl_set_copy(ge));
1097
1098 res = isl_pw_aff_add_piece(res, ge,
1099 isl_aff_copy(pwaff2->p[j].aff));
1100 }
1101 res = isl_pw_aff_add_piece(res, set,
1102 isl_aff_copy(pwaff1->p[i].aff));
1103 }
1104
1105 for (j = 0; j < pwaff2->n; ++j) {
1106 set = isl_set_copy(pwaff2->p[j].set);
1107 for (i = 0; i < pwaff1->n; ++i)
1108 set = isl_set_subtract(set,
1109 isl_set_copy(pwaff1->p[i].set));
1110 res = isl_pw_aff_add_piece(res, set,
1111 isl_aff_copy(pwaff2->p[j].aff));
1112 }
1113
1114 isl_pw_aff_free(pwaff1);
1115 isl_pw_aff_free(pwaff2);
1116
1117 return res;
1118 error:
1119 isl_pw_aff_free(pwaff1);
1120 isl_pw_aff_free(pwaff2);
1121 return NULL;
1122 }
1123
1124 /* Construct a map with as domain the domain of pwaff and
1125 * one-dimensional range corresponding to the affine expressions.
1126 */
1127 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1128 {
1129 int i;
1130 isl_dim *dim;
1131 isl_map *map;
1132
1133 if (!pwaff)
1134 return NULL;
1135
1136 dim = isl_pw_aff_get_dim(pwaff);
1137 dim = isl_dim_from_domain(dim);
1138 dim = isl_dim_add(dim, isl_dim_out, 1);
1139 map = isl_map_empty(dim);
1140
1141 for (i = 0; i < pwaff->n; ++i) {
1142 isl_basic_map *bmap;
1143 isl_map *map_i;
1144
1145 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
1146 map_i = isl_map_from_basic_map(bmap);
1147 map_i = isl_map_intersect_domain(map_i,
1148 isl_set_copy(pwaff->p[i].set));
1149 map = isl_map_union_disjoint(map, map_i);
1150 }
1151
1152 isl_pw_aff_free(pwaff);
1153
1154 return map;
1155 }
1156
1157 /* Return a set containing those elements in the domain
1158 * of pwaff where it is non-negative.
1159 */
1160 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
1161 {
1162 int i;
1163 isl_set *set;
1164
1165 if (!pwaff)
1166 return NULL;
1167
1168 set = isl_set_empty(isl_pw_aff_get_dim(pwaff));
1169
1170 for (i = 0; i < pwaff->n; ++i) {
1171 isl_basic_set *bset;
1172 isl_set *set_i;
1173
1174 bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff));
1175 set_i = isl_set_from_basic_set(bset);
1176 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1177 set = isl_set_union_disjoint(set, set_i);
1178 }
1179
1180 isl_pw_aff_free(pwaff);
1181
1182 return set;
1183 }
1184
1185 /* Return a set containing those elements in the domain
1186 * of pwaff where it is zero.
1187 */
1188 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
1189 {
1190 int i;
1191 isl_set *set;
1192
1193 if (!pwaff)
1194 return NULL;
1195
1196 set = isl_set_empty(isl_pw_aff_get_dim(pwaff));
1197
1198 for (i = 0; i < pwaff->n; ++i) {
1199 isl_basic_set *bset;
1200 isl_set *set_i;
1201
1202 bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
1203 set_i = isl_set_from_basic_set(bset);
1204 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1205 set = isl_set_union_disjoint(set, set_i);
1206 }
1207
1208 isl_pw_aff_free(pwaff);
1209
1210 return set;
1211 }
1212
1213 /* Return a set containing those elements in the shared domain
1214 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1215 *
1216 * We compute the difference on the shared domain and then construct
1217 * the set of values where this difference is non-negative.
1218 * If strict is set, we first subtract 1 from the difference.
1219 * If equal is set, we only return the elements where pwaff1 and pwaff2
1220 * are equal.
1221 */
1222 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
1223 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
1224 {
1225 isl_set *set1, *set2;
1226
1227 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
1228 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
1229 set1 = isl_set_intersect(set1, set2);
1230 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
1231 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
1232 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
1233
1234 if (strict) {
1235 isl_dim *dim = isl_set_get_dim(set1);
1236 isl_aff *aff;
1237 aff = isl_aff_zero(isl_local_space_from_dim(dim));
1238 aff = isl_aff_add_constant_si(aff, -1);
1239 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
1240 } else
1241 isl_set_free(set1);
1242
1243 if (equal)
1244 return isl_pw_aff_zero_set(pwaff1);
1245 return isl_pw_aff_nonneg_set(pwaff1);
1246 }
1247
1248 /* Return a set containing those elements in the shared domain
1249 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1250 */
1251 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1252 __isl_take isl_pw_aff *pwaff2)
1253 {
1254 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
1255 }
1256
1257 /* Return a set containing those elements in the shared domain
1258 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
1259 */
1260 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1261 __isl_take isl_pw_aff *pwaff2)
1262 {
1263 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
1264 }
1265
1266 /* Return a set containing those elements in the shared domain
1267 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
1268 */
1269 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1270 __isl_take isl_pw_aff *pwaff2)
1271 {
1272 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
1273 }
1274
1275 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
1276 __isl_take isl_pw_aff *pwaff2)
1277 {
1278 return isl_pw_aff_ge_set(pwaff2, pwaff1);
1279 }
1280
1281 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
1282 __isl_take isl_pw_aff *pwaff2)
1283 {
1284 return isl_pw_aff_gt_set(pwaff2, pwaff1);
1285 }
1286
1287 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
1288 isl_int v)
1289 {
1290 int i;
1291
1292 if (isl_int_is_one(v))
1293 return pwaff;
1294 if (!isl_int_is_pos(v))
1295 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1296 "factor needs to be positive",
1297 return isl_pw_aff_free(pwaff));
1298 pwaff = isl_pw_aff_cow(pwaff);
1299 if (!pwaff)
1300 return NULL;
1301 if (pwaff->n == 0)
1302 return pwaff;
1303
1304 for (i = 0; i < pwaff->n; ++i) {
1305 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
1306 if (!pwaff->p[i].aff)
1307 return isl_pw_aff_free(pwaff);
1308 }
1309
1310 return pwaff;
1311 }
1312
1313 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
1314 {
1315 int i;
1316
1317 pwaff = isl_pw_aff_cow(pwaff);
1318 if (!pwaff)
1319 return NULL;
1320 if (pwaff->n == 0)
1321 return pwaff;
1322
1323 for (i = 0; i < pwaff->n; ++i) {
1324 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
1325 if (!pwaff->p[i].aff)
1326 return isl_pw_aff_free(pwaff);
1327 }
1328
1329 return pwaff;
1330 }
1331
1332 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
1333 {
1334 int i;
1335
1336 pwaff = isl_pw_aff_cow(pwaff);
1337 if (!pwaff)
1338 return NULL;
1339 if (pwaff->n == 0)
1340 return pwaff;
1341
1342 for (i = 0; i < pwaff->n; ++i) {
1343 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
1344 if (!pwaff->p[i].aff)
1345 return isl_pw_aff_free(pwaff);
1346 }
1347
1348 return pwaff;
1349 }
1350
1351 /* Return an affine expression that is equal to pwaff_true for elements
1352 * in "cond" and to pwaff_false for elements not in "cond".
1353 * That is, return cond ? pwaff_true : pwaff_false;
1354 */
1355 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_set *cond,
1356 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
1357 {
1358 isl_set *comp;
1359
1360 comp = isl_set_complement(isl_set_copy(cond));
1361 pwaff_true = isl_pw_aff_intersect_domain(pwaff_true, cond);
1362 pwaff_false = isl_pw_aff_intersect_domain(pwaff_false, comp);
1363
1364 return isl_pw_aff_add_disjoint(pwaff_true, pwaff_false);
1365 }
Integer set library