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add isl_map_{lexmin,lexmax}_pw_multi_aff
[isl.git] / isl_aff.c
blobbfdc17fd134726c13cc955bfb609ce567003d7f0
1 /*
2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
4 * Copyright 2012 Ecole Normale Superieure
5 *
6 * Use of this software is governed by the GNU LGPLv2.1 license
7 *
8 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
9 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
10 * 91893 Orsay, France
11 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
12 */
13
14 #include <isl_ctx_private.h>
15 #define ISL_DIM_H
16 #include <isl_map_private.h>
17 #include <isl_union_map_private.h>
18 #include <isl_aff_private.h>
19 #include <isl_space_private.h>
20 #include <isl_local_space_private.h>
21 #include <isl_mat_private.h>
22 #include <isl_list_private.h>
23 #include <isl/constraint.h>
24 #include <isl/seq.h>
25 #include <isl/set.h>
26 #include <isl_config.h>
27
28 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
29 __isl_take isl_vec *v)
30 {
31 isl_aff *aff;
32
33 if (!ls || !v)
34 goto error;
35
36 aff = isl_calloc_type(v->ctx, struct isl_aff);
37 if (!aff)
38 goto error;
39
40 aff->ref = 1;
41 aff->ls = ls;
42 aff->v = v;
43
44 return aff;
45 error:
46 isl_local_space_free(ls);
47 isl_vec_free(v);
48 return NULL;
49 }
50
51 __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
52 {
53 isl_ctx *ctx;
54 isl_vec *v;
55 unsigned total;
56
57 if (!ls)
58 return NULL;
59
60 ctx = isl_local_space_get_ctx(ls);
61 if (!isl_local_space_divs_known(ls))
62 isl_die(ctx, isl_error_invalid, "local space has unknown divs",
63 goto error);
64 if (!isl_local_space_is_set(ls))
65 isl_die(ctx, isl_error_invalid,
66 "domain of affine expression should be a set",
67 goto error);
68
69 total = isl_local_space_dim(ls, isl_dim_all);
70 v = isl_vec_alloc(ctx, 1 + 1 + total);
71 return isl_aff_alloc_vec(ls, v);
72 error:
73 isl_local_space_free(ls);
74 return NULL;
75 }
76
77 __isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
78 {
79 isl_aff *aff;
80
81 aff = isl_aff_alloc(ls);
82 if (!aff)
83 return NULL;
84
85 isl_int_set_si(aff->v->el[0], 1);
86 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
87
88 return aff;
89 }
90
91 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
92 {
93 if (!aff)
94 return NULL;
95
96 aff->ref++;
97 return aff;
98 }
99
100 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
101 {
102 if (!aff)
103 return NULL;
104
105 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
106 isl_vec_copy(aff->v));
107 }
108
109 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
110 {
111 if (!aff)
112 return NULL;
113
114 if (aff->ref == 1)
115 return aff;
116 aff->ref--;
117 return isl_aff_dup(aff);
118 }
119
120 void *isl_aff_free(__isl_take isl_aff *aff)
121 {
122 if (!aff)
123 return NULL;
124
125 if (--aff->ref > 0)
126 return NULL;
127
128 isl_local_space_free(aff->ls);
129 isl_vec_free(aff->v);
130
131 free(aff);
132
133 return NULL;
134 }
135
136 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
137 {
138 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
139 }
140
141 /* Externally, an isl_aff has a map space, but internally, the
142 * ls field corresponds to the domain of that space.
143 */
144 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
145 {
146 if (!aff)
147 return 0;
148 if (type == isl_dim_out)
149 return 1;
150 if (type == isl_dim_in)
151 type = isl_dim_set;
152 return isl_local_space_dim(aff->ls, type);
153 }
154
155 __isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
156 {
157 return aff ? isl_local_space_get_space(aff->ls) : NULL;
158 }
159
160 __isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
161 {
162 isl_space *space;
163 if (!aff)
164 return NULL;
165 space = isl_local_space_get_space(aff->ls);
166 space = isl_space_from_domain(space);
167 space = isl_space_add_dims(space, isl_dim_out, 1);
168 return space;
169 }
170
171 __isl_give isl_local_space *isl_aff_get_domain_local_space(
172 __isl_keep isl_aff *aff)
173 {
174 return aff ? isl_local_space_copy(aff->ls) : NULL;
175 }
176
177 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
178 {
179 isl_local_space *ls;
180 if (!aff)
181 return NULL;
182 ls = isl_local_space_copy(aff->ls);
183 ls = isl_local_space_from_domain(ls);
184 ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
185 return ls;
186 }
187
188 /* Externally, an isl_aff has a map space, but internally, the
189 * ls field corresponds to the domain of that space.
190 */
191 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
192 enum isl_dim_type type, unsigned pos)
193 {
194 if (!aff)
195 return NULL;
196 if (type == isl_dim_out)
197 return NULL;
198 if (type == isl_dim_in)
199 type = isl_dim_set;
200 return isl_local_space_get_dim_name(aff->ls, type, pos);
201 }
202
203 __isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
204 __isl_take isl_space *dim)
205 {
206 aff = isl_aff_cow(aff);
207 if (!aff || !dim)
208 goto error;
209
210 aff->ls = isl_local_space_reset_space(aff->ls, dim);
211 if (!aff->ls)
212 return isl_aff_free(aff);
213
214 return aff;
215 error:
216 isl_aff_free(aff);
217 isl_space_free(dim);
218 return NULL;
219 }
220
221 /* Reset the space of "aff". This function is called from isl_pw_templ.c
222 * and doesn't know if the space of an element object is represented
223 * directly or through its domain. It therefore passes along both.
224 */
225 __isl_give isl_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
226 __isl_take isl_space *space, __isl_take isl_space *domain)
227 {
228 isl_space_free(space);
229 return isl_aff_reset_domain_space(aff, domain);
230 }
231
232 /* Reorder the coefficients of the affine expression based
233 * on the given reodering.
234 * The reordering r is assumed to have been extended with the local
235 * variables.
236 */
237 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
238 __isl_take isl_reordering *r, int n_div)
239 {
240 isl_vec *res;
241 int i;
242
243 if (!vec || !r)
244 goto error;
245
246 res = isl_vec_alloc(vec->ctx,
247 2 + isl_space_dim(r->dim, isl_dim_all) + n_div);
248 isl_seq_cpy(res->el, vec->el, 2);
249 isl_seq_clr(res->el + 2, res->size - 2);
250 for (i = 0; i < r->len; ++i)
251 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
252
253 isl_reordering_free(r);
254 isl_vec_free(vec);
255 return res;
256 error:
257 isl_vec_free(vec);
258 isl_reordering_free(r);
259 return NULL;
260 }
261
262 /* Reorder the dimensions of the domain of "aff" according
263 * to the given reordering.
264 */
265 __isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
266 __isl_take isl_reordering *r)
267 {
268 aff = isl_aff_cow(aff);
269 if (!aff)
270 goto error;
271
272 r = isl_reordering_extend(r, aff->ls->div->n_row);
273 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
274 aff->ls->div->n_row);
275 aff->ls = isl_local_space_realign(aff->ls, r);
276
277 if (!aff->v || !aff->ls)
278 return isl_aff_free(aff);
279
280 return aff;
281 error:
282 isl_aff_free(aff);
283 isl_reordering_free(r);
284 return NULL;
285 }
286
287 __isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
288 __isl_take isl_space *model)
289 {
290 if (!aff || !model)
291 goto error;
292
293 if (!isl_space_match(aff->ls->dim, isl_dim_param,
294 model, isl_dim_param)) {
295 isl_reordering *exp;
296
297 model = isl_space_drop_dims(model, isl_dim_in,
298 0, isl_space_dim(model, isl_dim_in));
299 model = isl_space_drop_dims(model, isl_dim_out,
300 0, isl_space_dim(model, isl_dim_out));
301 exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
302 exp = isl_reordering_extend_space(exp,
303 isl_aff_get_domain_space(aff));
304 aff = isl_aff_realign_domain(aff, exp);
305 }
306
307 isl_space_free(model);
308 return aff;
309 error:
310 isl_space_free(model);
311 isl_aff_free(aff);
312 return NULL;
313 }
314
315 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
316 {
317 if (!aff)
318 return -1;
319
320 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
321 }
322
323 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
324 {
325 int equal;
326
327 if (!aff1 || !aff2)
328 return -1;
329
330 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
331 if (equal < 0 || !equal)
332 return equal;
333
334 return isl_vec_is_equal(aff1->v, aff2->v);
335 }
336
337 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
338 {
339 if (!aff)
340 return -1;
341 isl_int_set(*v, aff->v->el[0]);
342 return 0;
343 }
344
345 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
346 {
347 if (!aff)
348 return -1;
349 isl_int_set(*v, aff->v->el[1]);
350 return 0;
351 }
352
353 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
354 enum isl_dim_type type, int pos, isl_int *v)
355 {
356 if (!aff)
357 return -1;
358
359 if (type == isl_dim_out)
360 isl_die(aff->v->ctx, isl_error_invalid,
361 "output/set dimension does not have a coefficient",
362 return -1);
363 if (type == isl_dim_in)
364 type = isl_dim_set;
365
366 if (pos >= isl_local_space_dim(aff->ls, type))
367 isl_die(aff->v->ctx, isl_error_invalid,
368 "position out of bounds", return -1);
369
370 pos += isl_local_space_offset(aff->ls, type);
371 isl_int_set(*v, aff->v->el[1 + pos]);
372
373 return 0;
374 }
375
376 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
377 {
378 aff = isl_aff_cow(aff);
379 if (!aff)
380 return NULL;
381
382 aff->v = isl_vec_cow(aff->v);
383 if (!aff->v)
384 return isl_aff_free(aff);
385
386 isl_int_set(aff->v->el[0], v);
387
388 return aff;
389 }
390
391 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
392 {
393 aff = isl_aff_cow(aff);
394 if (!aff)
395 return NULL;
396
397 aff->v = isl_vec_cow(aff->v);
398 if (!aff->v)
399 return isl_aff_free(aff);
400
401 isl_int_set(aff->v->el[1], v);
402
403 return aff;
404 }
405
406 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
407 {
408 if (isl_int_is_zero(v))
409 return 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 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
420
421 return aff;
422 }
423
424 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, 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_constant(aff, t);
431 isl_int_clear(t);
432
433 return aff;
434 }
435
436 /* Add "v" to the numerator of the constant term of "aff".
437 */
438 __isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v)
439 {
440 if (isl_int_is_zero(v))
441 return aff;
442
443 aff = isl_aff_cow(aff);
444 if (!aff)
445 return NULL;
446
447 aff->v = isl_vec_cow(aff->v);
448 if (!aff->v)
449 return isl_aff_free(aff);
450
451 isl_int_add(aff->v->el[1], aff->v->el[1], v);
452
453 return aff;
454 }
455
456 /* Add "v" to the numerator of the constant term of "aff".
457 */
458 __isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v)
459 {
460 isl_int t;
461
462 if (v == 0)
463 return aff;
464
465 isl_int_init(t);
466 isl_int_set_si(t, v);
467 aff = isl_aff_add_constant_num(aff, t);
468 isl_int_clear(t);
469
470 return aff;
471 }
472
473 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
474 {
475 aff = isl_aff_cow(aff);
476 if (!aff)
477 return NULL;
478
479 aff->v = isl_vec_cow(aff->v);
480 if (!aff->v)
481 return isl_aff_free(aff);
482
483 isl_int_set_si(aff->v->el[1], v);
484
485 return aff;
486 }
487
488 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
489 enum isl_dim_type type, int pos, isl_int v)
490 {
491 if (!aff)
492 return NULL;
493
494 if (type == isl_dim_out)
495 isl_die(aff->v->ctx, isl_error_invalid,
496 "output/set dimension does not have a coefficient",
497 return isl_aff_free(aff));
498 if (type == isl_dim_in)
499 type = isl_dim_set;
500
501 if (pos >= isl_local_space_dim(aff->ls, type))
502 isl_die(aff->v->ctx, isl_error_invalid,
503 "position out of bounds", return isl_aff_free(aff));
504
505 aff = isl_aff_cow(aff);
506 if (!aff)
507 return NULL;
508
509 aff->v = isl_vec_cow(aff->v);
510 if (!aff->v)
511 return isl_aff_free(aff);
512
513 pos += isl_local_space_offset(aff->ls, type);
514 isl_int_set(aff->v->el[1 + pos], v);
515
516 return aff;
517 }
518
519 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
520 enum isl_dim_type type, int pos, int v)
521 {
522 if (!aff)
523 return NULL;
524
525 if (type == isl_dim_out)
526 isl_die(aff->v->ctx, isl_error_invalid,
527 "output/set dimension does not have a coefficient",
528 return isl_aff_free(aff));
529 if (type == isl_dim_in)
530 type = isl_dim_set;
531
532 if (pos >= isl_local_space_dim(aff->ls, type))
533 isl_die(aff->v->ctx, isl_error_invalid,
534 "position out of bounds", return isl_aff_free(aff));
535
536 aff = isl_aff_cow(aff);
537 if (!aff)
538 return NULL;
539
540 aff->v = isl_vec_cow(aff->v);
541 if (!aff->v)
542 return isl_aff_free(aff);
543
544 pos += isl_local_space_offset(aff->ls, type);
545 isl_int_set_si(aff->v->el[1 + pos], v);
546
547 return aff;
548 }
549
550 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
551 enum isl_dim_type type, int pos, isl_int v)
552 {
553 if (!aff)
554 return NULL;
555
556 if (type == isl_dim_out)
557 isl_die(aff->v->ctx, isl_error_invalid,
558 "output/set dimension does not have a coefficient",
559 return isl_aff_free(aff));
560 if (type == isl_dim_in)
561 type = isl_dim_set;
562
563 if (pos >= isl_local_space_dim(aff->ls, type))
564 isl_die(aff->v->ctx, isl_error_invalid,
565 "position out of bounds", return isl_aff_free(aff));
566
567 aff = isl_aff_cow(aff);
568 if (!aff)
569 return NULL;
570
571 aff->v = isl_vec_cow(aff->v);
572 if (!aff->v)
573 return isl_aff_free(aff);
574
575 pos += isl_local_space_offset(aff->ls, type);
576 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
577
578 return aff;
579 }
580
581 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
582 enum isl_dim_type type, int pos, int v)
583 {
584 isl_int t;
585
586 isl_int_init(t);
587 isl_int_set_si(t, v);
588 aff = isl_aff_add_coefficient(aff, type, pos, t);
589 isl_int_clear(t);
590
591 return aff;
592 }
593
594 __isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
595 {
596 if (!aff)
597 return NULL;
598
599 return isl_local_space_get_div(aff->ls, pos);
600 }
601
602 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
603 {
604 aff = isl_aff_cow(aff);
605 if (!aff)
606 return NULL;
607 aff->v = isl_vec_cow(aff->v);
608 if (!aff->v)
609 return isl_aff_free(aff);
610
611 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
612
613 return aff;
614 }
615
616 /* Remove divs from the local space that do not appear in the affine
617 * expression.
618 * We currently only remove divs at the end.
619 * Some intermediate divs may also not appear directly in the affine
620 * expression, but we would also need to check that no other divs are
621 * defined in terms of them.
622 */
623 __isl_give isl_aff *isl_aff_remove_unused_divs( __isl_take isl_aff *aff)
624 {
625 int pos;
626 int off;
627 int n;
628
629 if (!aff)
630 return NULL;
631
632 n = isl_local_space_dim(aff->ls, isl_dim_div);
633 off = isl_local_space_offset(aff->ls, isl_dim_div);
634
635 pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
636 if (pos == n)
637 return aff;
638
639 aff = isl_aff_cow(aff);
640 if (!aff)
641 return NULL;
642
643 aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
644 aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
645 if (!aff->ls || !aff->v)
646 return isl_aff_free(aff);
647
648 return aff;
649 }
650
651 __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
652 {
653 if (!aff)
654 return NULL;
655 aff->v = isl_vec_normalize(aff->v);
656 if (!aff->v)
657 return isl_aff_free(aff);
658 aff = isl_aff_remove_unused_divs(aff);
659 return aff;
660 }
661
662 /* Given f, return floor(f).
663 * If f is an integer expression, then just return f.
664 * If f is a constant, then return the constant floor(f).
665 * Otherwise, if f = g/m, write g = q m + r,
666 * create a new div d = [r/m] and return the expression q + d.
667 * The coefficients in r are taken to lie between -m/2 and m/2.
668 */
669 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
670 {
671 int i;
672 int size;
673 isl_ctx *ctx;
674 isl_vec *div;
675
676 if (!aff)
677 return NULL;
678
679 if (isl_int_is_one(aff->v->el[0]))
680 return aff;
681
682 aff = isl_aff_cow(aff);
683 if (!aff)
684 return NULL;
685
686 aff->v = isl_vec_cow(aff->v);
687 if (!aff->v)
688 return isl_aff_free(aff);
689
690 if (isl_aff_is_cst(aff)) {
691 isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
692 isl_int_set_si(aff->v->el[0], 1);
693 return aff;
694 }
695
696 div = isl_vec_copy(aff->v);
697 div = isl_vec_cow(div);
698 if (!div)
699 return isl_aff_free(aff);
700
701 ctx = isl_aff_get_ctx(aff);
702 isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
703 for (i = 1; i < aff->v->size; ++i) {
704 isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
705 isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
706 if (isl_int_gt(div->el[i], aff->v->el[0])) {
707 isl_int_sub(div->el[i], div->el[i], div->el[0]);
708 isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
709 }
710 }
711
712 aff->ls = isl_local_space_add_div(aff->ls, div);
713 if (!aff->ls)
714 return isl_aff_free(aff);
715
716 size = aff->v->size;
717 aff->v = isl_vec_extend(aff->v, size + 1);
718 if (!aff->v)
719 return isl_aff_free(aff);
720 isl_int_set_si(aff->v->el[0], 1);
721 isl_int_set_si(aff->v->el[size], 1);
722
723 return aff;
724 }
725
726 /* Compute
727 *
728 * aff mod m = aff - m * floor(aff/m)
729 */
730 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
731 {
732 isl_aff *res;
733
734 res = isl_aff_copy(aff);
735 aff = isl_aff_scale_down(aff, m);
736 aff = isl_aff_floor(aff);
737 aff = isl_aff_scale(aff, m);
738 res = isl_aff_sub(res, aff);
739
740 return res;
741 }
742
743 /* Compute
744 *
745 * pwaff mod m = pwaff - m * floor(pwaff/m)
746 */
747 __isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
748 {
749 isl_pw_aff *res;
750
751 res = isl_pw_aff_copy(pwaff);
752 pwaff = isl_pw_aff_scale_down(pwaff, m);
753 pwaff = isl_pw_aff_floor(pwaff);
754 pwaff = isl_pw_aff_scale(pwaff, m);
755 res = isl_pw_aff_sub(res, pwaff);
756
757 return res;
758 }
759
760 /* Given f, return ceil(f).
761 * If f is an integer expression, then just return f.
762 * Otherwise, create a new div d = [-f] and return the expression -d.
763 */
764 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
765 {
766 if (!aff)
767 return NULL;
768
769 if (isl_int_is_one(aff->v->el[0]))
770 return aff;
771
772 aff = isl_aff_neg(aff);
773 aff = isl_aff_floor(aff);
774 aff = isl_aff_neg(aff);
775
776 return aff;
777 }
778
779 /* Apply the expansion computed by isl_merge_divs.
780 * The expansion itself is given by "exp" while the resulting
781 * list of divs is given by "div".
782 */
783 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
784 __isl_take isl_mat *div, int *exp)
785 {
786 int i, j;
787 int old_n_div;
788 int new_n_div;
789 int offset;
790
791 aff = isl_aff_cow(aff);
792 if (!aff || !div)
793 goto error;
794
795 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
796 new_n_div = isl_mat_rows(div);
797 if (new_n_div < old_n_div)
798 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
799 "not an expansion", goto error);
800
801 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
802 if (!aff->v)
803 goto error;
804
805 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
806 j = old_n_div - 1;
807 for (i = new_n_div - 1; i >= 0; --i) {
808 if (j >= 0 && exp[j] == i) {
809 if (i != j)
810 isl_int_swap(aff->v->el[offset + i],
811 aff->v->el[offset + j]);
812 j--;
813 } else
814 isl_int_set_si(aff->v->el[offset + i], 0);
815 }
816
817 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
818 if (!aff->ls)
819 goto error;
820 isl_mat_free(div);
821 return aff;
822 error:
823 isl_aff_free(aff);
824 isl_mat_free(div);
825 return NULL;
826 }
827
828 /* Add two affine expressions that live in the same local space.
829 */
830 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
831 __isl_take isl_aff *aff2)
832 {
833 isl_int gcd, f;
834
835 aff1 = isl_aff_cow(aff1);
836 if (!aff1 || !aff2)
837 goto error;
838
839 aff1->v = isl_vec_cow(aff1->v);
840 if (!aff1->v)
841 goto error;
842
843 isl_int_init(gcd);
844 isl_int_init(f);
845 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
846 isl_int_divexact(f, aff2->v->el[0], gcd);
847 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
848 isl_int_divexact(f, aff1->v->el[0], gcd);
849 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
850 isl_int_divexact(f, aff2->v->el[0], gcd);
851 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
852 isl_int_clear(f);
853 isl_int_clear(gcd);
854
855 isl_aff_free(aff2);
856 return aff1;
857 error:
858 isl_aff_free(aff1);
859 isl_aff_free(aff2);
860 return NULL;
861 }
862
863 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
864 __isl_take isl_aff *aff2)
865 {
866 isl_ctx *ctx;
867 int *exp1 = NULL;
868 int *exp2 = NULL;
869 isl_mat *div;
870
871 if (!aff1 || !aff2)
872 goto error;
873
874 ctx = isl_aff_get_ctx(aff1);
875 if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
876 isl_die(ctx, isl_error_invalid,
877 "spaces don't match", goto error);
878
879 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
880 return add_expanded(aff1, aff2);
881
882 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
883 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
884 if (!exp1 || !exp2)
885 goto error;
886
887 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
888 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
889 aff2 = isl_aff_expand_divs(aff2, div, exp2);
890 free(exp1);
891 free(exp2);
892
893 return add_expanded(aff1, aff2);
894 error:
895 free(exp1);
896 free(exp2);
897 isl_aff_free(aff1);
898 isl_aff_free(aff2);
899 return NULL;
900 }
901
902 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
903 __isl_take isl_aff *aff2)
904 {
905 return isl_aff_add(aff1, isl_aff_neg(aff2));
906 }
907
908 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
909 {
910 isl_int gcd;
911
912 if (isl_int_is_one(f))
913 return aff;
914
915 aff = isl_aff_cow(aff);
916 if (!aff)
917 return NULL;
918 aff->v = isl_vec_cow(aff->v);
919 if (!aff->v)
920 return isl_aff_free(aff);
921
922 isl_int_init(gcd);
923 isl_int_gcd(gcd, aff->v->el[0], f);
924 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
925 isl_int_divexact(gcd, f, gcd);
926 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
927 isl_int_clear(gcd);
928
929 return aff;
930 }
931
932 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
933 {
934 isl_int gcd;
935
936 if (isl_int_is_one(f))
937 return aff;
938
939 aff = isl_aff_cow(aff);
940 if (!aff)
941 return NULL;
942 aff->v = isl_vec_cow(aff->v);
943 if (!aff->v)
944 return isl_aff_free(aff);
945
946 isl_int_init(gcd);
947 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
948 isl_int_gcd(gcd, gcd, f);
949 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
950 isl_int_divexact(gcd, f, gcd);
951 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
952 isl_int_clear(gcd);
953
954 return aff;
955 }
956
957 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
958 {
959 isl_int v;
960
961 if (f == 1)
962 return aff;
963
964 isl_int_init(v);
965 isl_int_set_ui(v, f);
966 aff = isl_aff_scale_down(aff, v);
967 isl_int_clear(v);
968
969 return aff;
970 }
971
972 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
973 enum isl_dim_type type, unsigned pos, const char *s)
974 {
975 aff = isl_aff_cow(aff);
976 if (!aff)
977 return NULL;
978 if (type == isl_dim_out)
979 isl_die(aff->v->ctx, isl_error_invalid,
980 "cannot set name of output/set dimension",
981 return isl_aff_free(aff));
982 if (type == isl_dim_in)
983 type = isl_dim_set;
984 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
985 if (!aff->ls)
986 return isl_aff_free(aff);
987
988 return aff;
989 }
990
991 __isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
992 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
993 {
994 aff = isl_aff_cow(aff);
995 if (!aff)
996 return isl_id_free(id);
997 if (type == isl_dim_out)
998 isl_die(aff->v->ctx, isl_error_invalid,
999 "cannot set name of output/set dimension",
1000 goto error);
1001 if (type == isl_dim_in)
1002 type = isl_dim_set;
1003 aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
1004 if (!aff->ls)
1005 return isl_aff_free(aff);
1006
1007 return aff;
1008 error:
1009 isl_id_free(id);
1010 isl_aff_free(aff);
1011 return NULL;
1012 }
1013
1014 /* Exploit the equalities in "eq" to simplify the affine expression
1015 * and the expressions of the integer divisions in the local space.
1016 * The integer divisions in this local space are assumed to appear
1017 * as regular dimensions in "eq".
1018 */
1019 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
1020 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1021 {
1022 int i, j;
1023 unsigned total;
1024 unsigned n_div;
1025
1026 if (!eq)
1027 goto error;
1028 if (eq->n_eq == 0) {
1029 isl_basic_set_free(eq);
1030 return aff;
1031 }
1032
1033 aff = isl_aff_cow(aff);
1034 if (!aff)
1035 goto error;
1036
1037 aff->ls = isl_local_space_substitute_equalities(aff->ls,
1038 isl_basic_set_copy(eq));
1039 if (!aff->ls)
1040 goto error;
1041
1042 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
1043 n_div = eq->n_div;
1044 for (i = 0; i < eq->n_eq; ++i) {
1045 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
1046 if (j < 0 || j == 0 || j >= total)
1047 continue;
1048
1049 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
1050 &aff->v->el[0]);
1051 }
1052
1053 isl_basic_set_free(eq);
1054 aff = isl_aff_normalize(aff);
1055 return aff;
1056 error:
1057 isl_basic_set_free(eq);
1058 isl_aff_free(aff);
1059 return NULL;
1060 }
1061
1062 /* Exploit the equalities in "eq" to simplify the affine expression
1063 * and the expressions of the integer divisions in the local space.
1064 */
1065 static __isl_give isl_aff *isl_aff_substitute_equalities(
1066 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1067 {
1068 int n_div;
1069
1070 if (!aff || !eq)
1071 goto error;
1072 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1073 if (n_div > 0)
1074 eq = isl_basic_set_add(eq, isl_dim_set, n_div);
1075 return isl_aff_substitute_equalities_lifted(aff, eq);
1076 error:
1077 isl_basic_set_free(eq);
1078 isl_aff_free(aff);
1079 return NULL;
1080 }
1081
1082 /* Look for equalities among the variables shared by context and aff
1083 * and the integer divisions of aff, if any.
1084 * The equalities are then used to eliminate coefficients and/or integer
1085 * divisions from aff.
1086 */
1087 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
1088 __isl_take isl_set *context)
1089 {
1090 isl_basic_set *hull;
1091 int n_div;
1092
1093 if (!aff)
1094 goto error;
1095 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1096 if (n_div > 0) {
1097 isl_basic_set *bset;
1098 isl_local_space *ls;
1099 context = isl_set_add_dims(context, isl_dim_set, n_div);
1100 ls = isl_aff_get_domain_local_space(aff);
1101 bset = isl_basic_set_from_local_space(ls);
1102 bset = isl_basic_set_lift(bset);
1103 bset = isl_basic_set_flatten(bset);
1104 context = isl_set_intersect(context,
1105 isl_set_from_basic_set(bset));
1106 }
1107
1108 hull = isl_set_affine_hull(context);
1109 return isl_aff_substitute_equalities_lifted(aff, hull);
1110 error:
1111 isl_aff_free(aff);
1112 isl_set_free(context);
1113 return NULL;
1114 }
1115
1116 __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
1117 __isl_take isl_set *context)
1118 {
1119 isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
1120 dom_context = isl_set_intersect_params(dom_context, context);
1121 return isl_aff_gist(aff, dom_context);
1122 }
1123
1124 /* Return a basic set containing those elements in the space
1125 * of aff where it is non-negative.
1126 */
1127 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
1128 {
1129 isl_constraint *ineq;
1130 isl_basic_set *bset;
1131
1132 ineq = isl_inequality_from_aff(aff);
1133
1134 bset = isl_basic_set_from_constraint(ineq);
1135 bset = isl_basic_set_simplify(bset);
1136 return bset;
1137 }
1138
1139 /* Return a basic set containing those elements in the domain space
1140 * of aff where it is negative.
1141 */
1142 __isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
1143 {
1144 aff = isl_aff_neg(aff);
1145 aff = isl_aff_add_constant_num_si(aff, -1);
1146 return isl_aff_nonneg_basic_set(aff);
1147 }
1148
1149 /* Return a basic set containing those elements in the space
1150 * of aff where it is zero.
1151 */
1152 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
1153 {
1154 isl_constraint *ineq;
1155 isl_basic_set *bset;
1156
1157 ineq = isl_equality_from_aff(aff);
1158
1159 bset = isl_basic_set_from_constraint(ineq);
1160 bset = isl_basic_set_simplify(bset);
1161 return bset;
1162 }
1163
1164 /* Return a basic set containing those elements in the shared space
1165 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1166 */
1167 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
1168 __isl_take isl_aff *aff2)
1169 {
1170 aff1 = isl_aff_sub(aff1, aff2);
1171
1172 return isl_aff_nonneg_basic_set(aff1);
1173 }
1174
1175 /* Return a basic set containing those elements in the shared space
1176 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1177 */
1178 __isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
1179 __isl_take isl_aff *aff2)
1180 {
1181 return isl_aff_ge_basic_set(aff2, aff1);
1182 }
1183
1184 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
1185 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
1186 {
1187 aff1 = isl_aff_add(aff1, aff2);
1188 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
1189 return aff1;
1190 }
1191
1192 int isl_aff_is_empty(__isl_keep isl_aff *aff)
1193 {
1194 if (!aff)
1195 return -1;
1196
1197 return 0;
1198 }
1199
1200 /* Check whether the given affine expression has non-zero coefficient
1201 * for any dimension in the given range or if any of these dimensions
1202 * appear with non-zero coefficients in any of the integer divisions
1203 * involved in the affine expression.
1204 */
1205 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
1206 enum isl_dim_type type, unsigned first, unsigned n)
1207 {
1208 int i;
1209 isl_ctx *ctx;
1210 int *active = NULL;
1211 int involves = 0;
1212
1213 if (!aff)
1214 return -1;
1215 if (n == 0)
1216 return 0;
1217
1218 ctx = isl_aff_get_ctx(aff);
1219 if (first + n > isl_aff_dim(aff, type))
1220 isl_die(ctx, isl_error_invalid,
1221 "range out of bounds", return -1);
1222
1223 active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
1224 if (!active)
1225 goto error;
1226
1227 first += isl_local_space_offset(aff->ls, type) - 1;
1228 for (i = 0; i < n; ++i)
1229 if (active[first + i]) {
1230 involves = 1;
1231 break;
1232 }
1233
1234 free(active);
1235
1236 return involves;
1237 error:
1238 free(active);
1239 return -1;
1240 }
1241
1242 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
1243 enum isl_dim_type type, unsigned first, unsigned n)
1244 {
1245 isl_ctx *ctx;
1246
1247 if (!aff)
1248 return NULL;
1249 if (type == isl_dim_out)
1250 isl_die(aff->v->ctx, isl_error_invalid,
1251 "cannot drop output/set dimension",
1252 return isl_aff_free(aff));
1253 if (type == isl_dim_in)
1254 type = isl_dim_set;
1255 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1256 return aff;
1257
1258 ctx = isl_aff_get_ctx(aff);
1259 if (first + n > isl_local_space_dim(aff->ls, type))
1260 isl_die(ctx, isl_error_invalid, "range out of bounds",
1261 return isl_aff_free(aff));
1262
1263 aff = isl_aff_cow(aff);
1264 if (!aff)
1265 return NULL;
1266
1267 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
1268 if (!aff->ls)
1269 return isl_aff_free(aff);
1270
1271 first += 1 + isl_local_space_offset(aff->ls, type);
1272 aff->v = isl_vec_drop_els(aff->v, first, n);
1273 if (!aff->v)
1274 return isl_aff_free(aff);
1275
1276 return aff;
1277 }
1278
1279 /* Project the domain of the affine expression onto its parameter space.
1280 * The affine expression may not involve any of the domain dimensions.
1281 */
1282 __isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
1283 {
1284 isl_space *space;
1285 unsigned n;
1286 int involves;
1287
1288 n = isl_aff_dim(aff, isl_dim_in);
1289 involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
1290 if (involves < 0)
1291 return isl_aff_free(aff);
1292 if (involves)
1293 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1294 "affine expression involves some of the domain dimensions",
1295 return isl_aff_free(aff));
1296 aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
1297 space = isl_aff_get_domain_space(aff);
1298 space = isl_space_params(space);
1299 aff = isl_aff_reset_domain_space(aff, space);
1300 return aff;
1301 }
1302
1303 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
1304 enum isl_dim_type type, unsigned first, unsigned n)
1305 {
1306 isl_ctx *ctx;
1307
1308 if (!aff)
1309 return NULL;
1310 if (type == isl_dim_out)
1311 isl_die(aff->v->ctx, isl_error_invalid,
1312 "cannot insert output/set dimensions",
1313 return isl_aff_free(aff));
1314 if (type == isl_dim_in)
1315 type = isl_dim_set;
1316 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1317 return aff;
1318
1319 ctx = isl_aff_get_ctx(aff);
1320 if (first > isl_local_space_dim(aff->ls, type))
1321 isl_die(ctx, isl_error_invalid, "position out of bounds",
1322 return isl_aff_free(aff));
1323
1324 aff = isl_aff_cow(aff);
1325 if (!aff)
1326 return NULL;
1327
1328 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
1329 if (!aff->ls)
1330 return isl_aff_free(aff);
1331
1332 first += 1 + isl_local_space_offset(aff->ls, type);
1333 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
1334 if (!aff->v)
1335 return isl_aff_free(aff);
1336
1337 return aff;
1338 }
1339
1340 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
1341 enum isl_dim_type type, unsigned n)
1342 {
1343 unsigned pos;
1344
1345 pos = isl_aff_dim(aff, type);
1346
1347 return isl_aff_insert_dims(aff, type, pos, n);
1348 }
1349
1350 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
1351 enum isl_dim_type type, unsigned n)
1352 {
1353 unsigned pos;
1354
1355 pos = isl_pw_aff_dim(pwaff, type);
1356
1357 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
1358 }
1359
1360 __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
1361 {
1362 isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
1363 return isl_pw_aff_alloc(dom, aff);
1364 }
1365
1366 #undef PW
1367 #define PW isl_pw_aff
1368 #undef EL
1369 #define EL isl_aff
1370 #undef EL_IS_ZERO
1371 #define EL_IS_ZERO is_empty
1372 #undef ZERO
1373 #define ZERO empty
1374 #undef IS_ZERO
1375 #define IS_ZERO is_empty
1376 #undef FIELD
1377 #define FIELD aff
1378 #undef DEFAULT_IS_ZERO
1379 #define DEFAULT_IS_ZERO 0
1380
1381 #define NO_EVAL
1382 #define NO_OPT
1383 #define NO_MOVE_DIMS
1384 #define NO_LIFT
1385 #define NO_MORPH
1386
1387 #include <isl_pw_templ.c>
1388
1389 static __isl_give isl_set *align_params_pw_pw_set_and(
1390 __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
1391 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1392 __isl_take isl_pw_aff *pwaff2))
1393 {
1394 if (!pwaff1 || !pwaff2)
1395 goto error;
1396 if (isl_space_match(pwaff1->dim, isl_dim_param,
1397 pwaff2->dim, isl_dim_param))
1398 return fn(pwaff1, pwaff2);
1399 if (!isl_space_has_named_params(pwaff1->dim) ||
1400 !isl_space_has_named_params(pwaff2->dim))
1401 isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
1402 "unaligned unnamed parameters", goto error);
1403 pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
1404 pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
1405 return fn(pwaff1, pwaff2);
1406 error:
1407 isl_pw_aff_free(pwaff1);
1408 isl_pw_aff_free(pwaff2);
1409 return NULL;
1410 }
1411
1412 /* Compute a piecewise quasi-affine expression with a domain that
1413 * is the union of those of pwaff1 and pwaff2 and such that on each
1414 * cell, the quasi-affine expression is the better (according to cmp)
1415 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
1416 * is defined on a given cell, then the associated expression
1417 * is the defined one.
1418 */
1419 static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1420 __isl_take isl_pw_aff *pwaff2,
1421 __isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
1422 __isl_take isl_aff *aff2))
1423 {
1424 int i, j, n;
1425 isl_pw_aff *res;
1426 isl_ctx *ctx;
1427 isl_set *set;
1428
1429 if (!pwaff1 || !pwaff2)
1430 goto error;
1431
1432 ctx = isl_space_get_ctx(pwaff1->dim);
1433 if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
1434 isl_die(ctx, isl_error_invalid,
1435 "arguments should live in same space", goto error);
1436
1437 if (isl_pw_aff_is_empty(pwaff1)) {
1438 isl_pw_aff_free(pwaff1);
1439 return pwaff2;
1440 }
1441
1442 if (isl_pw_aff_is_empty(pwaff2)) {
1443 isl_pw_aff_free(pwaff2);
1444 return pwaff1;
1445 }
1446
1447 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
1448 res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
1449
1450 for (i = 0; i < pwaff1->n; ++i) {
1451 set = isl_set_copy(pwaff1->p[i].set);
1452 for (j = 0; j < pwaff2->n; ++j) {
1453 struct isl_set *common;
1454 isl_set *better;
1455
1456 common = isl_set_intersect(
1457 isl_set_copy(pwaff1->p[i].set),
1458 isl_set_copy(pwaff2->p[j].set));
1459 better = isl_set_from_basic_set(cmp(
1460 isl_aff_copy(pwaff2->p[j].aff),
1461 isl_aff_copy(pwaff1->p[i].aff)));
1462 better = isl_set_intersect(common, better);
1463 if (isl_set_plain_is_empty(better)) {
1464 isl_set_free(better);
1465 continue;
1466 }
1467 set = isl_set_subtract(set, isl_set_copy(better));
1468
1469 res = isl_pw_aff_add_piece(res, better,
1470 isl_aff_copy(pwaff2->p[j].aff));
1471 }
1472 res = isl_pw_aff_add_piece(res, set,
1473 isl_aff_copy(pwaff1->p[i].aff));
1474 }
1475
1476 for (j = 0; j < pwaff2->n; ++j) {
1477 set = isl_set_copy(pwaff2->p[j].set);
1478 for (i = 0; i < pwaff1->n; ++i)
1479 set = isl_set_subtract(set,
1480 isl_set_copy(pwaff1->p[i].set));
1481 res = isl_pw_aff_add_piece(res, set,
1482 isl_aff_copy(pwaff2->p[j].aff));
1483 }
1484
1485 isl_pw_aff_free(pwaff1);
1486 isl_pw_aff_free(pwaff2);
1487
1488 return res;
1489 error:
1490 isl_pw_aff_free(pwaff1);
1491 isl_pw_aff_free(pwaff2);
1492 return NULL;
1493 }
1494
1495 /* Compute a piecewise quasi-affine expression with a domain that
1496 * is the union of those of pwaff1 and pwaff2 and such that on each
1497 * cell, the quasi-affine expression is the maximum of those of pwaff1
1498 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1499 * cell, then the associated expression is the defined one.
1500 */
1501 static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1502 __isl_take isl_pw_aff *pwaff2)
1503 {
1504 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
1505 }
1506
1507 __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1508 __isl_take isl_pw_aff *pwaff2)
1509 {
1510 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1511 &pw_aff_union_max);
1512 }
1513
1514 /* Compute a piecewise quasi-affine expression with a domain that
1515 * is the union of those of pwaff1 and pwaff2 and such that on each
1516 * cell, the quasi-affine expression is the minimum of those of pwaff1
1517 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1518 * cell, then the associated expression is the defined one.
1519 */
1520 static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1521 __isl_take isl_pw_aff *pwaff2)
1522 {
1523 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
1524 }
1525
1526 __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1527 __isl_take isl_pw_aff *pwaff2)
1528 {
1529 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1530 &pw_aff_union_min);
1531 }
1532
1533 __isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1534 __isl_take isl_pw_aff *pwaff2, int max)
1535 {
1536 if (max)
1537 return isl_pw_aff_union_max(pwaff1, pwaff2);
1538 else
1539 return isl_pw_aff_union_min(pwaff1, pwaff2);
1540 }
1541
1542 /* Construct a map with as domain the domain of pwaff and
1543 * one-dimensional range corresponding to the affine expressions.
1544 */
1545 static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1546 {
1547 int i;
1548 isl_space *dim;
1549 isl_map *map;
1550
1551 if (!pwaff)
1552 return NULL;
1553
1554 dim = isl_pw_aff_get_space(pwaff);
1555 map = isl_map_empty(dim);
1556
1557 for (i = 0; i < pwaff->n; ++i) {
1558 isl_basic_map *bmap;
1559 isl_map *map_i;
1560
1561 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
1562 map_i = isl_map_from_basic_map(bmap);
1563 map_i = isl_map_intersect_domain(map_i,
1564 isl_set_copy(pwaff->p[i].set));
1565 map = isl_map_union_disjoint(map, map_i);
1566 }
1567
1568 isl_pw_aff_free(pwaff);
1569
1570 return map;
1571 }
1572
1573 /* Construct a map with as domain the domain of pwaff and
1574 * one-dimensional range corresponding to the affine expressions.
1575 */
1576 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1577 {
1578 if (!pwaff)
1579 return NULL;
1580 if (isl_space_is_set(pwaff->dim))
1581 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1582 "space of input is not a map",
1583 return isl_pw_aff_free(pwaff));
1584 return map_from_pw_aff(pwaff);
1585 }
1586
1587 /* Construct a one-dimensional set with as parameter domain
1588 * the domain of pwaff and the single set dimension
1589 * corresponding to the affine expressions.
1590 */
1591 __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1592 {
1593 if (!pwaff)
1594 return NULL;
1595 if (!isl_space_is_set(pwaff->dim))
1596 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1597 "space of input is not a set",
1598 return isl_pw_aff_free(pwaff));
1599 return map_from_pw_aff(pwaff);
1600 }
1601
1602 /* Return a set containing those elements in the domain
1603 * of pwaff where it is non-negative.
1604 */
1605 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
1606 {
1607 int i;
1608 isl_set *set;
1609
1610 if (!pwaff)
1611 return NULL;
1612
1613 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1614
1615 for (i = 0; i < pwaff->n; ++i) {
1616 isl_basic_set *bset;
1617 isl_set *set_i;
1618
1619 bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff));
1620 set_i = isl_set_from_basic_set(bset);
1621 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1622 set = isl_set_union_disjoint(set, set_i);
1623 }
1624
1625 isl_pw_aff_free(pwaff);
1626
1627 return set;
1628 }
1629
1630 /* Return a set containing those elements in the domain
1631 * of pwaff where it is zero (if complement is 0) or not zero
1632 * (if complement is 1).
1633 */
1634 static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
1635 int complement)
1636 {
1637 int i;
1638 isl_set *set;
1639
1640 if (!pwaff)
1641 return NULL;
1642
1643 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1644
1645 for (i = 0; i < pwaff->n; ++i) {
1646 isl_basic_set *bset;
1647 isl_set *set_i, *zero;
1648
1649 bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
1650 zero = isl_set_from_basic_set(bset);
1651 set_i = isl_set_copy(pwaff->p[i].set);
1652 if (complement)
1653 set_i = isl_set_subtract(set_i, zero);
1654 else
1655 set_i = isl_set_intersect(set_i, zero);
1656 set = isl_set_union_disjoint(set, set_i);
1657 }
1658
1659 isl_pw_aff_free(pwaff);
1660
1661 return set;
1662 }
1663
1664 /* Return a set containing those elements in the domain
1665 * of pwaff where it is zero.
1666 */
1667 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
1668 {
1669 return pw_aff_zero_set(pwaff, 0);
1670 }
1671
1672 /* Return a set containing those elements in the domain
1673 * of pwaff where it is not zero.
1674 */
1675 __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
1676 {
1677 return pw_aff_zero_set(pwaff, 1);
1678 }
1679
1680 /* Return a set containing those elements in the shared domain
1681 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1682 *
1683 * We compute the difference on the shared domain and then construct
1684 * the set of values where this difference is non-negative.
1685 * If strict is set, we first subtract 1 from the difference.
1686 * If equal is set, we only return the elements where pwaff1 and pwaff2
1687 * are equal.
1688 */
1689 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
1690 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
1691 {
1692 isl_set *set1, *set2;
1693
1694 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
1695 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
1696 set1 = isl_set_intersect(set1, set2);
1697 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
1698 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
1699 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
1700
1701 if (strict) {
1702 isl_space *dim = isl_set_get_space(set1);
1703 isl_aff *aff;
1704 aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
1705 aff = isl_aff_add_constant_si(aff, -1);
1706 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
1707 } else
1708 isl_set_free(set1);
1709
1710 if (equal)
1711 return isl_pw_aff_zero_set(pwaff1);
1712 return isl_pw_aff_nonneg_set(pwaff1);
1713 }
1714
1715 /* Return a set containing those elements in the shared domain
1716 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1717 */
1718 static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1719 __isl_take isl_pw_aff *pwaff2)
1720 {
1721 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
1722 }
1723
1724 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1725 __isl_take isl_pw_aff *pwaff2)
1726 {
1727 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
1728 }
1729
1730 /* Return a set containing those elements in the shared domain
1731 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
1732 */
1733 static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1734 __isl_take isl_pw_aff *pwaff2)
1735 {
1736 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
1737 }
1738
1739 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1740 __isl_take isl_pw_aff *pwaff2)
1741 {
1742 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
1743 }
1744
1745 /* Return a set containing those elements in the shared domain
1746 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
1747 */
1748 static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1749 __isl_take isl_pw_aff *pwaff2)
1750 {
1751 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
1752 }
1753
1754 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1755 __isl_take isl_pw_aff *pwaff2)
1756 {
1757 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
1758 }
1759
1760 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
1761 __isl_take isl_pw_aff *pwaff2)
1762 {
1763 return isl_pw_aff_ge_set(pwaff2, pwaff1);
1764 }
1765
1766 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
1767 __isl_take isl_pw_aff *pwaff2)
1768 {
1769 return isl_pw_aff_gt_set(pwaff2, pwaff1);
1770 }
1771
1772 /* Return a set containing those elements in the shared domain
1773 * of the elements of list1 and list2 where each element in list1
1774 * has the relation specified by "fn" with each element in list2.
1775 */
1776 static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
1777 __isl_take isl_pw_aff_list *list2,
1778 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1779 __isl_take isl_pw_aff *pwaff2))
1780 {
1781 int i, j;
1782 isl_ctx *ctx;
1783 isl_set *set;
1784
1785 if (!list1 || !list2)
1786 goto error;
1787
1788 ctx = isl_pw_aff_list_get_ctx(list1);
1789 if (list1->n < 1 || list2->n < 1)
1790 isl_die(ctx, isl_error_invalid,
1791 "list should contain at least one element", goto error);
1792
1793 set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
1794 for (i = 0; i < list1->n; ++i)
1795 for (j = 0; j < list2->n; ++j) {
1796 isl_set *set_ij;
1797
1798 set_ij = fn(isl_pw_aff_copy(list1->p[i]),
1799 isl_pw_aff_copy(list2->p[j]));
1800 set = isl_set_intersect(set, set_ij);
1801 }
1802
1803 isl_pw_aff_list_free(list1);
1804 isl_pw_aff_list_free(list2);
1805 return set;
1806 error:
1807 isl_pw_aff_list_free(list1);
1808 isl_pw_aff_list_free(list2);
1809 return NULL;
1810 }
1811
1812 /* Return a set containing those elements in the shared domain
1813 * of the elements of list1 and list2 where each element in list1
1814 * is equal to each element in list2.
1815 */
1816 __isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
1817 __isl_take isl_pw_aff_list *list2)
1818 {
1819 return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
1820 }
1821
1822 __isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
1823 __isl_take isl_pw_aff_list *list2)
1824 {
1825 return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
1826 }
1827
1828 /* Return a set containing those elements in the shared domain
1829 * of the elements of list1 and list2 where each element in list1
1830 * is less than or equal to each element in list2.
1831 */
1832 __isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
1833 __isl_take isl_pw_aff_list *list2)
1834 {
1835 return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
1836 }
1837
1838 __isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
1839 __isl_take isl_pw_aff_list *list2)
1840 {
1841 return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
1842 }
1843
1844 __isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
1845 __isl_take isl_pw_aff_list *list2)
1846 {
1847 return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
1848 }
1849
1850 __isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
1851 __isl_take isl_pw_aff_list *list2)
1852 {
1853 return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
1854 }
1855
1856
1857 /* Return a set containing those elements in the shared domain
1858 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
1859 */
1860 static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1861 __isl_take isl_pw_aff *pwaff2)
1862 {
1863 isl_set *set_lt, *set_gt;
1864
1865 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
1866 isl_pw_aff_copy(pwaff2));
1867 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
1868 return isl_set_union_disjoint(set_lt, set_gt);
1869 }
1870
1871 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1872 __isl_take isl_pw_aff *pwaff2)
1873 {
1874 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
1875 }
1876
1877 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
1878 isl_int v)
1879 {
1880 int i;
1881
1882 if (isl_int_is_one(v))
1883 return pwaff;
1884 if (!isl_int_is_pos(v))
1885 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1886 "factor needs to be positive",
1887 return isl_pw_aff_free(pwaff));
1888 pwaff = isl_pw_aff_cow(pwaff);
1889 if (!pwaff)
1890 return NULL;
1891 if (pwaff->n == 0)
1892 return pwaff;
1893
1894 for (i = 0; i < pwaff->n; ++i) {
1895 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
1896 if (!pwaff->p[i].aff)
1897 return isl_pw_aff_free(pwaff);
1898 }
1899
1900 return pwaff;
1901 }
1902
1903 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
1904 {
1905 int i;
1906
1907 pwaff = isl_pw_aff_cow(pwaff);
1908 if (!pwaff)
1909 return NULL;
1910 if (pwaff->n == 0)
1911 return pwaff;
1912
1913 for (i = 0; i < pwaff->n; ++i) {
1914 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
1915 if (!pwaff->p[i].aff)
1916 return isl_pw_aff_free(pwaff);
1917 }
1918
1919 return pwaff;
1920 }
1921
1922 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
1923 {
1924 int i;
1925
1926 pwaff = isl_pw_aff_cow(pwaff);
1927 if (!pwaff)
1928 return NULL;
1929 if (pwaff->n == 0)
1930 return pwaff;
1931
1932 for (i = 0; i < pwaff->n; ++i) {
1933 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
1934 if (!pwaff->p[i].aff)
1935 return isl_pw_aff_free(pwaff);
1936 }
1937
1938 return pwaff;
1939 }
1940
1941 /* Assuming that "cond1" and "cond2" are disjoint,
1942 * return an affine expression that is equal to pwaff1 on cond1
1943 * and to pwaff2 on cond2.
1944 */
1945 static __isl_give isl_pw_aff *isl_pw_aff_select(
1946 __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
1947 __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
1948 {
1949 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
1950 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
1951
1952 return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
1953 }
1954
1955 /* Return an affine expression that is equal to pwaff_true for elements
1956 * where "cond" is non-zero and to pwaff_false for elements where "cond"
1957 * is zero.
1958 * That is, return cond ? pwaff_true : pwaff_false;
1959 */
1960 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
1961 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
1962 {
1963 isl_set *cond_true, *cond_false;
1964
1965 cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
1966 cond_false = isl_pw_aff_zero_set(cond);
1967 return isl_pw_aff_select(cond_true, pwaff_true,
1968 cond_false, pwaff_false);
1969 }
1970
1971 int isl_aff_is_cst(__isl_keep isl_aff *aff)
1972 {
1973 if (!aff)
1974 return -1;
1975
1976 return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
1977 }
1978
1979 /* Check whether pwaff is a piecewise constant.
1980 */
1981 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
1982 {
1983 int i;
1984
1985 if (!pwaff)
1986 return -1;
1987
1988 for (i = 0; i < pwaff->n; ++i) {
1989 int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
1990 if (is_cst < 0 || !is_cst)
1991 return is_cst;
1992 }
1993
1994 return 1;
1995 }
1996
1997 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
1998 __isl_take isl_aff *aff2)
1999 {
2000 if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
2001 return isl_aff_mul(aff2, aff1);
2002
2003 if (!isl_aff_is_cst(aff2))
2004 isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
2005 "at least one affine expression should be constant",
2006 goto error);
2007
2008 aff1 = isl_aff_cow(aff1);
2009 if (!aff1 || !aff2)
2010 goto error;
2011
2012 aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
2013 aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
2014
2015 isl_aff_free(aff2);
2016 return aff1;
2017 error:
2018 isl_aff_free(aff1);
2019 isl_aff_free(aff2);
2020 return NULL;
2021 }
2022
2023 static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2024 __isl_take isl_pw_aff *pwaff2)
2025 {
2026 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
2027 }
2028
2029 __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2030 __isl_take isl_pw_aff *pwaff2)
2031 {
2032 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
2033 }
2034
2035 __isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
2036 __isl_take isl_pw_aff *pwaff2)
2037 {
2038 return isl_pw_aff_union_add_(pwaff1, pwaff2);
2039 }
2040
2041 static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2042 __isl_take isl_pw_aff *pwaff2)
2043 {
2044 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
2045 }
2046
2047 __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2048 __isl_take isl_pw_aff *pwaff2)
2049 {
2050 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
2051 }
2052
2053 static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2054 __isl_take isl_pw_aff *pwaff2)
2055 {
2056 isl_set *le;
2057 isl_set *dom;
2058
2059 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2060 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2061 le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
2062 isl_pw_aff_copy(pwaff2));
2063 dom = isl_set_subtract(dom, isl_set_copy(le));
2064 return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
2065 }
2066
2067 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2068 __isl_take isl_pw_aff *pwaff2)
2069 {
2070 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
2071 }
2072
2073 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2074 __isl_take isl_pw_aff *pwaff2)
2075 {
2076 isl_set *ge;
2077 isl_set *dom;
2078
2079 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2080 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2081 ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
2082 isl_pw_aff_copy(pwaff2));
2083 dom = isl_set_subtract(dom, isl_set_copy(ge));
2084 return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
2085 }
2086
2087 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2088 __isl_take isl_pw_aff *pwaff2)
2089 {
2090 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
2091 }
2092
2093 static __isl_give isl_pw_aff *pw_aff_list_reduce(
2094 __isl_take isl_pw_aff_list *list,
2095 __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
2096 __isl_take isl_pw_aff *pwaff2))
2097 {
2098 int i;
2099 isl_ctx *ctx;
2100 isl_pw_aff *res;
2101
2102 if (!list)
2103 return NULL;
2104
2105 ctx = isl_pw_aff_list_get_ctx(list);
2106 if (list->n < 1)
2107 isl_die(ctx, isl_error_invalid,
2108 "list should contain at least one element",
2109 return isl_pw_aff_list_free(list));
2110
2111 res = isl_pw_aff_copy(list->p[0]);
2112 for (i = 1; i < list->n; ++i)
2113 res = fn(res, isl_pw_aff_copy(list->p[i]));
2114
2115 isl_pw_aff_list_free(list);
2116 return res;
2117 }
2118
2119 /* Return an isl_pw_aff that maps each element in the intersection of the
2120 * domains of the elements of list to the minimal corresponding affine
2121 * expression.
2122 */
2123 __isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
2124 {
2125 return pw_aff_list_reduce(list, &isl_pw_aff_min);
2126 }
2127
2128 /* Return an isl_pw_aff that maps each element in the intersection of the
2129 * domains of the elements of list to the maximal corresponding affine
2130 * expression.
2131 */
2132 __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
2133 {
2134 return pw_aff_list_reduce(list, &isl_pw_aff_max);
2135 }
2136
2137 #undef BASE
2138 #define BASE aff
2139
2140 #include <isl_multi_templ.c>
2141
2142 /* Construct an isl_multi_aff in the given space with value zero in
2143 * each of the output dimensions.
2144 */
2145 __isl_give isl_multi_aff *isl_multi_aff_zero(__isl_take isl_space *space)
2146 {
2147 int n;
2148 isl_multi_aff *ma;
2149
2150 if (!space)
2151 return NULL;
2152
2153 n = isl_space_dim(space , isl_dim_out);
2154 ma = isl_multi_aff_alloc(isl_space_copy(space));
2155
2156 if (!n)
2157 isl_space_free(space);
2158 else {
2159 int i;
2160 isl_local_space *ls;
2161 isl_aff *aff;
2162
2163 space = isl_space_domain(space);
2164 ls = isl_local_space_from_space(space);
2165 aff = isl_aff_zero_on_domain(ls);
2166
2167 for (i = 0; i < n; ++i)
2168 ma = isl_multi_aff_set_aff(ma, i, isl_aff_copy(aff));
2169
2170 isl_aff_free(aff);
2171 }
2172
2173 return ma;
2174 }
2175
2176 /* Create an isl_multi_aff in the given space that maps each
2177 * input dimension to the corresponding output dimension.
2178 */
2179 __isl_give isl_multi_aff *isl_multi_aff_identity(__isl_take isl_space *space)
2180 {
2181 int n;
2182 isl_multi_aff *ma;
2183
2184 if (!space)
2185 return NULL;
2186
2187 if (isl_space_is_set(space))
2188 isl_die(isl_space_get_ctx(space), isl_error_invalid,
2189 "expecting map space", goto error);
2190
2191 n = isl_space_dim(space, isl_dim_out);
2192 if (n != isl_space_dim(space, isl_dim_in))
2193 isl_die(isl_space_get_ctx(space), isl_error_invalid,
2194 "number of input and output dimensions needs to be "
2195 "the same", goto error);
2196
2197 ma = isl_multi_aff_alloc(isl_space_copy(space));
2198
2199 if (!n)
2200 isl_space_free(space);
2201 else {
2202 int i;
2203 isl_local_space *ls;
2204 isl_aff *aff;
2205
2206 space = isl_space_domain(space);
2207 ls = isl_local_space_from_space(space);
2208 aff = isl_aff_zero_on_domain(ls);
2209
2210 for (i = 0; i < n; ++i) {
2211 isl_aff *aff_i;
2212 aff_i = isl_aff_copy(aff);
2213 aff_i = isl_aff_add_coefficient_si(aff_i,
2214 isl_dim_in, i, 1);
2215 ma = isl_multi_aff_set_aff(ma, i, aff_i);
2216 }
2217
2218 isl_aff_free(aff);
2219 }
2220
2221 return ma;
2222 error:
2223 isl_space_free(space);
2224 return NULL;
2225 }
2226
2227 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
2228 * domain.
2229 */
2230 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
2231 __isl_take isl_multi_aff *ma)
2232 {
2233 isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
2234 return isl_pw_multi_aff_alloc(dom, ma);
2235 }
2236
2237 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
2238 __isl_take isl_multi_aff *maff2)
2239 {
2240 int i;
2241 isl_ctx *ctx;
2242
2243 maff1 = isl_multi_aff_cow(maff1);
2244 if (!maff1 || !maff2)
2245 goto error;
2246
2247 ctx = isl_multi_aff_get_ctx(maff1);
2248 if (!isl_space_is_equal(maff1->space, maff2->space))
2249 isl_die(ctx, isl_error_invalid,
2250 "spaces don't match", goto error);
2251
2252 for (i = 0; i < maff1->n; ++i) {
2253 maff1->p[i] = isl_aff_add(maff1->p[i],
2254 isl_aff_copy(maff2->p[i]));
2255 if (!maff1->p[i])
2256 goto error;
2257 }
2258
2259 isl_multi_aff_free(maff2);
2260 return maff1;
2261 error:
2262 isl_multi_aff_free(maff1);
2263 isl_multi_aff_free(maff2);
2264 return NULL;
2265 }
2266
2267 /* Given two multi-affine expressions A -> B and C -> D,
2268 * construct a multi-affine expression [A -> C] -> [B -> D].
2269 */
2270 __isl_give isl_multi_aff *isl_multi_aff_product(
2271 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
2272 {
2273 int i;
2274 isl_aff *aff;
2275 isl_space *space;
2276 isl_multi_aff *res;
2277 int in1, in2, out1, out2;
2278
2279 in1 = isl_multi_aff_dim(ma1, isl_dim_in);
2280 in2 = isl_multi_aff_dim(ma2, isl_dim_in);
2281 out1 = isl_multi_aff_dim(ma1, isl_dim_out);
2282 out2 = isl_multi_aff_dim(ma2, isl_dim_out);
2283 space = isl_space_product(isl_multi_aff_get_space(ma1),
2284 isl_multi_aff_get_space(ma2));
2285 res = isl_multi_aff_alloc(isl_space_copy(space));
2286 space = isl_space_domain(space);
2287
2288 for (i = 0; i < out1; ++i) {
2289 aff = isl_multi_aff_get_aff(ma1, i);
2290 aff = isl_aff_insert_dims(aff, isl_dim_in, in1, in2);
2291 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
2292 res = isl_multi_aff_set_aff(res, i, aff);
2293 }
2294
2295 for (i = 0; i < out2; ++i) {
2296 aff = isl_multi_aff_get_aff(ma2, i);
2297 aff = isl_aff_insert_dims(aff, isl_dim_in, 0, in1);
2298 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
2299 res = isl_multi_aff_set_aff(res, out1 + i, aff);
2300 }
2301
2302 isl_space_free(space);
2303 isl_multi_aff_free(ma1);
2304 isl_multi_aff_free(ma2);
2305 return res;
2306 }
2307
2308 /* Exploit the equalities in "eq" to simplify the affine expressions.
2309 */
2310 static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
2311 __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
2312 {
2313 int i;
2314
2315 maff = isl_multi_aff_cow(maff);
2316 if (!maff || !eq)
2317 goto error;
2318
2319 for (i = 0; i < maff->n; ++i) {
2320 maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
2321 isl_basic_set_copy(eq));
2322 if (!maff->p[i])
2323 goto error;
2324 }
2325
2326 isl_basic_set_free(eq);
2327 return maff;
2328 error:
2329 isl_basic_set_free(eq);
2330 isl_multi_aff_free(maff);
2331 return NULL;
2332 }
2333
2334 __isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
2335 isl_int f)
2336 {
2337 int i;
2338
2339 maff = isl_multi_aff_cow(maff);
2340 if (!maff)
2341 return NULL;
2342
2343 for (i = 0; i < maff->n; ++i) {
2344 maff->p[i] = isl_aff_scale(maff->p[i], f);
2345 if (!maff->p[i])
2346 return isl_multi_aff_free(maff);
2347 }
2348
2349 return maff;
2350 }
2351
2352 __isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
2353 __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
2354 {
2355 maff1 = isl_multi_aff_add(maff1, maff2);
2356 maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
2357 return maff1;
2358 }
2359
2360 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
2361 {
2362 if (!maff)
2363 return -1;
2364
2365 return 0;
2366 }
2367
2368 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
2369 __isl_keep isl_multi_aff *maff2)
2370 {
2371 int i;
2372 int equal;
2373
2374 if (!maff1 || !maff2)
2375 return -1;
2376 if (maff1->n != maff2->n)
2377 return 0;
2378 equal = isl_space_is_equal(maff1->space, maff2->space);
2379 if (equal < 0 || !equal)
2380 return equal;
2381
2382 for (i = 0; i < maff1->n; ++i) {
2383 equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
2384 if (equal < 0 || !equal)
2385 return equal;
2386 }
2387
2388 return 1;
2389 }
2390
2391 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
2392 __isl_take isl_multi_aff *maff,
2393 enum isl_dim_type type, unsigned pos, const char *s)
2394 {
2395 int i;
2396
2397 maff = isl_multi_aff_cow(maff);
2398 if (!maff)
2399 return NULL;
2400
2401 maff->space = isl_space_set_dim_name(maff->space, type, pos, s);
2402 if (!maff->space)
2403 return isl_multi_aff_free(maff);
2404
2405 if (type == isl_dim_out)
2406 return maff;
2407 for (i = 0; i < maff->n; ++i) {
2408 maff->p[i] = isl_aff_set_dim_name(maff->p[i], type, pos, s);
2409 if (!maff->p[i])
2410 return isl_multi_aff_free(maff);
2411 }
2412
2413 return maff;
2414 }
2415
2416 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff,
2417 enum isl_dim_type type, unsigned first, unsigned n)
2418 {
2419 int i;
2420
2421 maff = isl_multi_aff_cow(maff);
2422 if (!maff)
2423 return NULL;
2424
2425 maff->space = isl_space_drop_dims(maff->space, type, first, n);
2426 if (!maff->space)
2427 return isl_multi_aff_free(maff);
2428
2429 if (type == isl_dim_out) {
2430 for (i = 0; i < n; ++i)
2431 isl_aff_free(maff->p[first + i]);
2432 for (i = first; i + n < maff->n; ++i)
2433 maff->p[i] = maff->p[i + n];
2434 maff->n -= n;
2435 return maff;
2436 }
2437
2438 for (i = 0; i < maff->n; ++i) {
2439 maff->p[i] = isl_aff_drop_dims(maff->p[i], type, first, n);
2440 if (!maff->p[i])
2441 return isl_multi_aff_free(maff);
2442 }
2443
2444 return maff;
2445 }
2446
2447 /* Return the set of domain elements where "ma1" is lexicographically
2448 * smaller than or equal to "ma2".
2449 */
2450 __isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
2451 __isl_take isl_multi_aff *ma2)
2452 {
2453 return isl_multi_aff_lex_ge_set(ma2, ma1);
2454 }
2455
2456 /* Return the set of domain elements where "ma1" is lexicographically
2457 * greater than or equal to "ma2".
2458 */
2459 __isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
2460 __isl_take isl_multi_aff *ma2)
2461 {
2462 isl_space *space;
2463 isl_map *map1, *map2;
2464 isl_map *map, *ge;
2465
2466 map1 = isl_map_from_multi_aff(ma1);
2467 map2 = isl_map_from_multi_aff(ma2);
2468 map = isl_map_range_product(map1, map2);
2469 space = isl_space_range(isl_map_get_space(map));
2470 space = isl_space_domain(isl_space_unwrap(space));
2471 ge = isl_map_lex_ge(space);
2472 map = isl_map_intersect_range(map, isl_map_wrap(ge));
2473
2474 return isl_map_domain(map);
2475 }
2476
2477 #undef PW
2478 #define PW isl_pw_multi_aff
2479 #undef EL
2480 #define EL isl_multi_aff
2481 #undef EL_IS_ZERO
2482 #define EL_IS_ZERO is_empty
2483 #undef ZERO
2484 #define ZERO empty
2485 #undef IS_ZERO
2486 #define IS_ZERO is_empty
2487 #undef FIELD
2488 #define FIELD maff
2489 #undef DEFAULT_IS_ZERO
2490 #define DEFAULT_IS_ZERO 0
2491
2492 #define NO_NEG
2493 #define NO_EVAL
2494 #define NO_OPT
2495 #define NO_INVOLVES_DIMS
2496 #define NO_MOVE_DIMS
2497 #define NO_INSERT_DIMS
2498 #define NO_LIFT
2499 #define NO_MORPH
2500
2501 #include <isl_pw_templ.c>
2502
2503 #undef UNION
2504 #define UNION isl_union_pw_multi_aff
2505 #undef PART
2506 #define PART isl_pw_multi_aff
2507 #undef PARTS
2508 #define PARTS pw_multi_aff
2509 #define ALIGN_DOMAIN
2510
2511 #define NO_EVAL
2512
2513 #include <isl_union_templ.c>
2514
2515 /* Given a function "cmp" that returns the set of elements where
2516 * "ma1" is "better" than "ma2", return the intersection of this
2517 * set with "dom1" and "dom2".
2518 */
2519 static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1,
2520 __isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1,
2521 __isl_keep isl_multi_aff *ma2,
2522 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
2523 __isl_take isl_multi_aff *ma2))
2524 {
2525 isl_set *common;
2526 isl_set *better;
2527 int is_empty;
2528
2529 common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2));
2530 is_empty = isl_set_plain_is_empty(common);
2531 if (is_empty >= 0 && is_empty)
2532 return common;
2533 if (is_empty < 0)
2534 return isl_set_free(common);
2535 better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2));
2536 better = isl_set_intersect(common, better);
2537
2538 return better;
2539 }
2540
2541 /* Given a function "cmp" that returns the set of elements where
2542 * "ma1" is "better" than "ma2", return a piecewise multi affine
2543 * expression defined on the union of the definition domains
2544 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
2545 * "pma2" on each cell. If only one of the two input functions
2546 * is defined on a given cell, then it is considered the best.
2547 */
2548 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt(
2549 __isl_take isl_pw_multi_aff *pma1,
2550 __isl_take isl_pw_multi_aff *pma2,
2551 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
2552 __isl_take isl_multi_aff *ma2))
2553 {
2554 int i, j, n;
2555 isl_pw_multi_aff *res = NULL;
2556 isl_ctx *ctx;
2557 isl_set *set = NULL;
2558
2559 if (!pma1 || !pma2)
2560 goto error;
2561
2562 ctx = isl_space_get_ctx(pma1->dim);
2563 if (!isl_space_is_equal(pma1->dim, pma2->dim))
2564 isl_die(ctx, isl_error_invalid,
2565 "arguments should live in the same space", goto error);
2566
2567 if (isl_pw_multi_aff_is_empty(pma1)) {
2568 isl_pw_multi_aff_free(pma1);
2569 return pma2;
2570 }
2571
2572 if (isl_pw_multi_aff_is_empty(pma2)) {
2573 isl_pw_multi_aff_free(pma2);
2574 return pma1;
2575 }
2576
2577 n = 2 * (pma1->n + 1) * (pma2->n + 1);
2578 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n);
2579
2580 for (i = 0; i < pma1->n; ++i) {
2581 set = isl_set_copy(pma1->p[i].set);
2582 for (j = 0; j < pma2->n; ++j) {
2583 isl_set *better;
2584 int is_empty;
2585
2586 better = shared_and_better(pma2->p[j].set,
2587 pma1->p[i].set, pma2->p[j].maff,
2588 pma1->p[i].maff, cmp);
2589 is_empty = isl_set_plain_is_empty(better);
2590 if (is_empty < 0 || is_empty) {
2591 isl_set_free(better);
2592 if (is_empty < 0)
2593 goto error;
2594 continue;
2595 }
2596 set = isl_set_subtract(set, isl_set_copy(better));
2597
2598 res = isl_pw_multi_aff_add_piece(res, better,
2599 isl_multi_aff_copy(pma2->p[j].maff));
2600 }
2601 res = isl_pw_multi_aff_add_piece(res, set,
2602 isl_multi_aff_copy(pma1->p[i].maff));
2603 }
2604
2605 for (j = 0; j < pma2->n; ++j) {
2606 set = isl_set_copy(pma2->p[j].set);
2607 for (i = 0; i < pma1->n; ++i)
2608 set = isl_set_subtract(set,
2609 isl_set_copy(pma1->p[i].set));
2610 res = isl_pw_multi_aff_add_piece(res, set,
2611 isl_multi_aff_copy(pma2->p[j].maff));
2612 }
2613
2614 isl_pw_multi_aff_free(pma1);
2615 isl_pw_multi_aff_free(pma2);
2616
2617 return res;
2618 error:
2619 isl_pw_multi_aff_free(pma1);
2620 isl_pw_multi_aff_free(pma2);
2621 isl_set_free(set);
2622 return isl_pw_multi_aff_free(res);
2623 }
2624
2625 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
2626 __isl_take isl_pw_multi_aff *pma1,
2627 __isl_take isl_pw_multi_aff *pma2)
2628 {
2629 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_ge_set);
2630 }
2631
2632 /* Given two piecewise multi affine expressions, return a piecewise
2633 * multi-affine expression defined on the union of the definition domains
2634 * of the inputs that is equal to the lexicographic maximum of the two
2635 * inputs on each cell. If only one of the two inputs is defined on
2636 * a given cell, then it is considered to be the maximum.
2637 */
2638 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
2639 __isl_take isl_pw_multi_aff *pma1,
2640 __isl_take isl_pw_multi_aff *pma2)
2641 {
2642 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2643 &pw_multi_aff_union_lexmax);
2644 }
2645
2646 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
2647 __isl_take isl_pw_multi_aff *pma1,
2648 __isl_take isl_pw_multi_aff *pma2)
2649 {
2650 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_set);
2651 }
2652
2653 /* Given two piecewise multi affine expressions, return a piecewise
2654 * multi-affine expression defined on the union of the definition domains
2655 * of the inputs that is equal to the lexicographic minimum of the two
2656 * inputs on each cell. If only one of the two inputs is defined on
2657 * a given cell, then it is considered to be the minimum.
2658 */
2659 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
2660 __isl_take isl_pw_multi_aff *pma1,
2661 __isl_take isl_pw_multi_aff *pma2)
2662 {
2663 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2664 &pw_multi_aff_union_lexmin);
2665 }
2666
2667 static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
2668 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2669 {
2670 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
2671 &isl_multi_aff_add);
2672 }
2673
2674 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
2675 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2676 {
2677 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2678 &pw_multi_aff_add);
2679 }
2680
2681 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
2682 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2683 {
2684 return isl_pw_multi_aff_union_add_(pma1, pma2);
2685 }
2686
2687 /* Given two piecewise multi-affine expressions A -> B and C -> D,
2688 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
2689 */
2690 static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
2691 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2692 {
2693 int i, j, n;
2694 isl_space *space;
2695 isl_pw_multi_aff *res;
2696
2697 if (!pma1 || !pma2)
2698 goto error;
2699
2700 n = pma1->n * pma2->n;
2701 space = isl_space_product(isl_space_copy(pma1->dim),
2702 isl_space_copy(pma2->dim));
2703 res = isl_pw_multi_aff_alloc_size(space, n);
2704
2705 for (i = 0; i < pma1->n; ++i) {
2706 for (j = 0; j < pma2->n; ++j) {
2707 isl_set *domain;
2708 isl_multi_aff *ma;
2709
2710 domain = isl_set_product(isl_set_copy(pma1->p[i].set),
2711 isl_set_copy(pma2->p[j].set));
2712 ma = isl_multi_aff_product(
2713 isl_multi_aff_copy(pma1->p[i].maff),
2714 isl_multi_aff_copy(pma2->p[i].maff));
2715 res = isl_pw_multi_aff_add_piece(res, domain, ma);
2716 }
2717 }
2718
2719 isl_pw_multi_aff_free(pma1);
2720 isl_pw_multi_aff_free(pma2);
2721 return res;
2722 error:
2723 isl_pw_multi_aff_free(pma1);
2724 isl_pw_multi_aff_free(pma2);
2725 return NULL;
2726 }
2727
2728 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
2729 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2730 {
2731 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2732 &pw_multi_aff_product);
2733 }
2734
2735 /* Construct a map mapping the domain of the piecewise multi-affine expression
2736 * to its range, with each dimension in the range equated to the
2737 * corresponding affine expression on its cell.
2738 */
2739 __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
2740 {
2741 int i;
2742 isl_map *map;
2743
2744 if (!pma)
2745 return NULL;
2746
2747 map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
2748
2749 for (i = 0; i < pma->n; ++i) {
2750 isl_multi_aff *maff;
2751 isl_basic_map *bmap;
2752 isl_map *map_i;
2753
2754 maff = isl_multi_aff_copy(pma->p[i].maff);
2755 bmap = isl_basic_map_from_multi_aff(maff);
2756 map_i = isl_map_from_basic_map(bmap);
2757 map_i = isl_map_intersect_domain(map_i,
2758 isl_set_copy(pma->p[i].set));
2759 map = isl_map_union_disjoint(map, map_i);
2760 }
2761
2762 isl_pw_multi_aff_free(pma);
2763 return map;
2764 }
2765
2766 __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
2767 {
2768 if (!isl_space_is_set(pma->dim))
2769 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
2770 "isl_pw_multi_aff cannot be converted into an isl_set",
2771 return isl_pw_multi_aff_free(pma));
2772
2773 return isl_map_from_pw_multi_aff(pma);
2774 }
2775
2776 /* Given a basic map with a single output dimension that is defined
2777 * in terms of the parameters and input dimensions using an equality,
2778 * extract an isl_aff that expresses the output dimension in terms
2779 * of the parameters and input dimensions.
2780 *
2781 * Since some applications expect the result of isl_pw_multi_aff_from_map
2782 * to only contain integer affine expressions, we compute the floor
2783 * of the expression before returning.
2784 *
2785 * This function shares some similarities with
2786 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
2787 */
2788 static __isl_give isl_aff *extract_isl_aff_from_basic_map(
2789 __isl_take isl_basic_map *bmap)
2790 {
2791 int i;
2792 unsigned offset;
2793 unsigned total;
2794 isl_local_space *ls;
2795 isl_aff *aff;
2796
2797 if (!bmap)
2798 return NULL;
2799 if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
2800 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
2801 "basic map should have a single output dimension",
2802 goto error);
2803 offset = isl_basic_map_offset(bmap, isl_dim_out);
2804 total = isl_basic_map_total_dim(bmap);
2805 for (i = 0; i < bmap->n_eq; ++i) {
2806 if (isl_int_is_zero(bmap->eq[i][offset]))
2807 continue;
2808 if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
2809 1 + total - (offset + 1)) != -1)
2810 continue;
2811 break;
2812 }
2813 if (i >= bmap->n_eq)
2814 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
2815 "unable to find suitable equality", goto error);
2816 ls = isl_basic_map_get_local_space(bmap);
2817 aff = isl_aff_alloc(isl_local_space_domain(ls));
2818 if (!aff)
2819 goto error;
2820 if (isl_int_is_neg(bmap->eq[i][offset]))
2821 isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
2822 else
2823 isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
2824 isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
2825 isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
2826 isl_basic_map_free(bmap);
2827
2828 aff = isl_aff_remove_unused_divs(aff);
2829 aff = isl_aff_floor(aff);
2830 return aff;
2831 error:
2832 isl_basic_map_free(bmap);
2833 return NULL;
2834 }
2835
2836 /* Given a basic map where each output dimension is defined
2837 * in terms of the parameters and input dimensions using an equality,
2838 * extract an isl_multi_aff that expresses the output dimensions in terms
2839 * of the parameters and input dimensions.
2840 */
2841 static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
2842 __isl_take isl_basic_map *bmap)
2843 {
2844 int i;
2845 unsigned n_out;
2846 isl_multi_aff *ma;
2847
2848 if (!bmap)
2849 return NULL;
2850
2851 ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
2852 n_out = isl_basic_map_dim(bmap, isl_dim_out);
2853
2854 for (i = 0; i < n_out; ++i) {
2855 isl_basic_map *bmap_i;
2856 isl_aff *aff;
2857
2858 bmap_i = isl_basic_map_copy(bmap);
2859 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
2860 i + 1, n_out - (1 + i));
2861 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
2862 aff = extract_isl_aff_from_basic_map(bmap_i);
2863 ma = isl_multi_aff_set_aff(ma, i, aff);
2864 }
2865
2866 isl_basic_map_free(bmap);
2867
2868 return ma;
2869 }
2870
2871 /* Create an isl_pw_multi_aff that is equivalent to
2872 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
2873 * The given basic map is such that each output dimension is defined
2874 * in terms of the parameters and input dimensions using an equality.
2875 */
2876 static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
2877 __isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
2878 {
2879 isl_multi_aff *ma;
2880
2881 ma = extract_isl_multi_aff_from_basic_map(bmap);
2882 return isl_pw_multi_aff_alloc(domain, ma);
2883 }
2884
2885 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
2886 * This obivously only works if the input "map" is single-valued.
2887 * If so, we compute the lexicographic minimum of the image in the form
2888 * of an isl_pw_multi_aff. Since the image is unique, it is equal
2889 * to its lexicographic minimum.
2890 * If the input is not single-valued, we produce an error.
2891 *
2892 * As a special case, we first check if all output dimensions are uniquely
2893 * defined in terms of the parameters and input dimensions over the entire
2894 * domain. If so, we extract the desired isl_pw_multi_aff directly
2895 * from the affine hull of "map" and its domain.
2896 */
2897 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
2898 {
2899 int i;
2900 int sv;
2901 isl_pw_multi_aff *pma;
2902 isl_basic_map *hull;
2903
2904 if (!map)
2905 return NULL;
2906
2907 hull = isl_map_affine_hull(isl_map_copy(map));
2908 sv = isl_basic_map_plain_is_single_valued(hull);
2909 if (sv >= 0 && sv)
2910 return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
2911 isl_basic_map_free(hull);
2912 if (sv < 0)
2913 goto error;
2914
2915 sv = isl_map_is_single_valued(map);
2916 if (sv < 0)
2917 goto error;
2918 if (!sv)
2919 isl_die(isl_map_get_ctx(map), isl_error_invalid,
2920 "map is not single-valued", goto error);
2921 map = isl_map_make_disjoint(map);
2922 if (!map)
2923 return NULL;
2924
2925 pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
2926
2927 for (i = 0; i < map->n; ++i) {
2928 isl_pw_multi_aff *pma_i;
2929 isl_basic_map *bmap;
2930 bmap = isl_basic_map_copy(map->p[i]);
2931 pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
2932 pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
2933 }
2934
2935 isl_map_free(map);
2936 return pma;
2937 error:
2938 isl_map_free(map);
2939 return NULL;
2940 }
2941
2942 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
2943 {
2944 return isl_pw_multi_aff_from_map(set);
2945 }
2946
2947 /* Return the piecewise affine expression "set ? 1 : 0".
2948 */
2949 __isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
2950 {
2951 isl_pw_aff *pa;
2952 isl_space *space = isl_set_get_space(set);
2953 isl_local_space *ls = isl_local_space_from_space(space);
2954 isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
2955 isl_aff *one = isl_aff_zero_on_domain(ls);
2956
2957 one = isl_aff_add_constant_si(one, 1);
2958 pa = isl_pw_aff_alloc(isl_set_copy(set), one);
2959 set = isl_set_complement(set);
2960 pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
2961
2962 return pa;
2963 }
2964
2965 /* Plug in "subs" for dimension "type", "pos" of "aff".
2966 *
2967 * Let i be the dimension to replace and let "subs" be of the form
2968 *
2969 * f/d
2970 *
2971 * and "aff" of the form
2972 *
2973 * (a i + g)/m
2974 *
2975 * The result is
2976 *
2977 * floor((a f + d g')/(m d))
2978 *
2979 * where g' is the result of plugging in "subs" in each of the integer
2980 * divisions in g.
2981 */
2982 __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
2983 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
2984 {
2985 isl_ctx *ctx;
2986 isl_int v;
2987
2988 aff = isl_aff_cow(aff);
2989 if (!aff || !subs)
2990 return isl_aff_free(aff);
2991
2992 ctx = isl_aff_get_ctx(aff);
2993 if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
2994 isl_die(ctx, isl_error_invalid,
2995 "spaces don't match", return isl_aff_free(aff));
2996 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
2997 isl_die(ctx, isl_error_unsupported,
2998 "cannot handle divs yet", return isl_aff_free(aff));
2999
3000 aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
3001 if (!aff->ls)
3002 return isl_aff_free(aff);
3003
3004 aff->v = isl_vec_cow(aff->v);
3005 if (!aff->v)
3006 return isl_aff_free(aff);
3007
3008 pos += isl_local_space_offset(aff->ls, type);
3009
3010 isl_int_init(v);
3011 isl_int_set(v, aff->v->el[1 + pos]);
3012 isl_int_set_si(aff->v->el[1 + pos], 0);
3013 isl_seq_combine(aff->v->el + 1, subs->v->el[0], aff->v->el + 1,
3014 v, subs->v->el + 1, subs->v->size - 1);
3015 isl_int_mul(aff->v->el[0], aff->v->el[0], subs->v->el[0]);
3016 isl_int_clear(v);
3017
3018 return aff;
3019 }
3020
3021 /* Plug in "subs" for dimension "type", "pos" in each of the affine
3022 * expressions in "maff".
3023 */
3024 __isl_give isl_multi_aff *isl_multi_aff_substitute(
3025 __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
3026 __isl_keep isl_aff *subs)
3027 {
3028 int i;
3029
3030 maff = isl_multi_aff_cow(maff);
3031 if (!maff || !subs)
3032 return isl_multi_aff_free(maff);
3033
3034 if (type == isl_dim_in)
3035 type = isl_dim_set;
3036
3037 for (i = 0; i < maff->n; ++i) {
3038 maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
3039 if (!maff->p[i])
3040 return isl_multi_aff_free(maff);
3041 }
3042
3043 return maff;
3044 }
3045
3046 /* Plug in "subs" for dimension "type", "pos" of "pma".
3047 *
3048 * pma is of the form
3049 *
3050 * A_i(v) -> M_i(v)
3051 *
3052 * while subs is of the form
3053 *
3054 * v' = B_j(v) -> S_j
3055 *
3056 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
3057 * has a contribution in the result, in particular
3058 *
3059 * C_ij(S_j) -> M_i(S_j)
3060 *
3061 * Note that plugging in S_j in C_ij may also result in an empty set
3062 * and this contribution should simply be discarded.
3063 */
3064 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
3065 __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
3066 __isl_keep isl_pw_aff *subs)
3067 {
3068 int i, j, n;
3069 isl_pw_multi_aff *res;
3070
3071 if (!pma || !subs)
3072 return isl_pw_multi_aff_free(pma);
3073
3074 n = pma->n * subs->n;
3075 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
3076
3077 for (i = 0; i < pma->n; ++i) {
3078 for (j = 0; j < subs->n; ++j) {
3079 isl_set *common;
3080 isl_multi_aff *res_ij;
3081 common = isl_set_intersect(
3082 isl_set_copy(pma->p[i].set),
3083 isl_set_copy(subs->p[j].set));
3084 common = isl_set_substitute(common,
3085 type, pos, subs->p[j].aff);
3086 if (isl_set_plain_is_empty(common)) {
3087 isl_set_free(common);
3088 continue;
3089 }
3090
3091 res_ij = isl_multi_aff_substitute(
3092 isl_multi_aff_copy(pma->p[i].maff),
3093 type, pos, subs->p[j].aff);
3094
3095 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
3096 }
3097 }
3098
3099 isl_pw_multi_aff_free(pma);
3100 return res;
3101 }
3102
3103 /* Extend the local space of "dst" to include the divs
3104 * in the local space of "src".
3105 */
3106 __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
3107 __isl_keep isl_aff *src)
3108 {
3109 isl_ctx *ctx;
3110 int *exp1 = NULL;
3111 int *exp2 = NULL;
3112 isl_mat *div;
3113
3114 if (!src || !dst)
3115 return isl_aff_free(dst);
3116
3117 ctx = isl_aff_get_ctx(src);
3118 if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
3119 isl_die(ctx, isl_error_invalid,
3120 "spaces don't match", goto error);
3121
3122 if (src->ls->div->n_row == 0)
3123 return dst;
3124
3125 exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
3126 exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
3127 if (!exp1 || !exp2)
3128 goto error;
3129
3130 div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
3131 dst = isl_aff_expand_divs(dst, div, exp2);
3132 free(exp1);
3133 free(exp2);
3134
3135 return dst;
3136 error:
3137 free(exp1);
3138 free(exp2);
3139 return isl_aff_free(dst);
3140 }
3141
3142 /* Adjust the local spaces of the affine expressions in "maff"
3143 * such that they all have the save divs.
3144 */
3145 __isl_give isl_multi_aff *isl_multi_aff_align_divs(
3146 __isl_take isl_multi_aff *maff)
3147 {
3148 int i;
3149
3150 if (!maff)
3151 return NULL;
3152 if (maff->n == 0)
3153 return maff;
3154 maff = isl_multi_aff_cow(maff);
3155 if (!maff)
3156 return NULL;
3157
3158 for (i = 1; i < maff->n; ++i)
3159 maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
3160 for (i = 1; i < maff->n; ++i) {
3161 maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
3162 if (!maff->p[i])
3163 return isl_multi_aff_free(maff);
3164 }
3165
3166 return maff;
3167 }
3168
3169 __isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
3170 {
3171 aff = isl_aff_cow(aff);
3172 if (!aff)
3173 return NULL;
3174
3175 aff->ls = isl_local_space_lift(aff->ls);
3176 if (!aff->ls)
3177 return isl_aff_free(aff);
3178
3179 return aff;
3180 }
3181
3182 /* Lift "maff" to a space with extra dimensions such that the result
3183 * has no more existentially quantified variables.
3184 * If "ls" is not NULL, then *ls is assigned the local space that lies
3185 * at the basis of the lifting applied to "maff".
3186 */
3187 __isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
3188 __isl_give isl_local_space **ls)
3189 {
3190 int i;
3191 isl_space *space;
3192 unsigned n_div;
3193
3194 if (ls)
3195 *ls = NULL;
3196
3197 if (!maff)
3198 return NULL;
3199
3200 if (maff->n == 0) {
3201 if (ls) {
3202 isl_space *space = isl_multi_aff_get_domain_space(maff);
3203 *ls = isl_local_space_from_space(space);
3204 if (!*ls)
3205 return isl_multi_aff_free(maff);
3206 }
3207 return maff;
3208 }
3209
3210 maff = isl_multi_aff_cow(maff);
3211 maff = isl_multi_aff_align_divs(maff);
3212 if (!maff)
3213 return NULL;
3214
3215 n_div = isl_aff_dim(maff->p[0], isl_dim_div);
3216 space = isl_multi_aff_get_space(maff);
3217 space = isl_space_lift(isl_space_domain(space), n_div);
3218 space = isl_space_extend_domain_with_range(space,
3219 isl_multi_aff_get_space(maff));
3220 if (!space)
3221 return isl_multi_aff_free(maff);
3222 isl_space_free(maff->space);
3223 maff->space = space;
3224
3225 if (ls) {
3226 *ls = isl_aff_get_domain_local_space(maff->p[0]);
3227 if (!*ls)
3228 return isl_multi_aff_free(maff);
3229 }
3230
3231 for (i = 0; i < maff->n; ++i) {
3232 maff->p[i] = isl_aff_lift(maff->p[i]);
3233 if (!maff->p[i])
3234 goto error;
3235 }
3236
3237 return maff;
3238 error:
3239 if (ls)
3240 isl_local_space_free(*ls);
3241 return isl_multi_aff_free(maff);
3242 }
3243
3244
3245 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
3246 */
3247 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3248 __isl_keep isl_pw_multi_aff *pma, int pos)
3249 {
3250 int i;
3251 int n_out;
3252 isl_space *space;
3253 isl_pw_aff *pa;
3254
3255 if (!pma)
3256 return NULL;
3257
3258 n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
3259 if (pos < 0 || pos >= n_out)
3260 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3261 "index out of bounds", return NULL);
3262
3263 space = isl_pw_multi_aff_get_space(pma);
3264 space = isl_space_drop_dims(space, isl_dim_out,
3265 pos + 1, n_out - pos - 1);
3266 space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
3267
3268 pa = isl_pw_aff_alloc_size(space, pma->n);
3269 for (i = 0; i < pma->n; ++i) {
3270 isl_aff *aff;
3271 aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
3272 pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
3273 }
3274
3275 return pa;
3276 }
3277
3278 /* Return an isl_pw_multi_aff with the given "set" as domain and
3279 * an unnamed zero-dimensional range.
3280 */
3281 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3282 __isl_take isl_set *set)
3283 {
3284 isl_multi_aff *ma;
3285 isl_space *space;
3286
3287 space = isl_set_get_space(set);
3288 space = isl_space_from_domain(space);
3289 ma = isl_multi_aff_zero(space);
3290 return isl_pw_multi_aff_alloc(set, ma);
3291 }
3292
3293 /* Add an isl_pw_multi_aff with the given "set" as domain and
3294 * an unnamed zero-dimensional range to *user.
3295 */
3296 static int add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user)
3297 {
3298 isl_union_pw_multi_aff **upma = user;
3299 isl_pw_multi_aff *pma;
3300
3301 pma = isl_pw_multi_aff_from_domain(set);
3302 *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
3303
3304 return 0;
3305 }
3306
3307 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
3308 * an unnamed zero-dimensional range.
3309 */
3310 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain(
3311 __isl_take isl_union_set *uset)
3312 {
3313 isl_space *space;
3314 isl_union_pw_multi_aff *upma;
3315
3316 if (!uset)
3317 return NULL;
3318
3319 space = isl_union_set_get_space(uset);
3320 upma = isl_union_pw_multi_aff_empty(space);
3321
3322 if (isl_union_set_foreach_set(uset,
3323 &add_pw_multi_aff_from_domain, &upma) < 0)
3324 goto error;
3325
3326 isl_union_set_free(uset);
3327 return upma;
3328 error:
3329 isl_union_set_free(uset);
3330 isl_union_pw_multi_aff_free(upma);
3331 return NULL;
3332 }
3333
3334 /* Convert "pma" to an isl_map and add it to *umap.
3335 */
3336 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
3337 {
3338 isl_union_map **umap = user;
3339 isl_map *map;
3340
3341 map = isl_map_from_pw_multi_aff(pma);
3342 *umap = isl_union_map_add_map(*umap, map);
3343
3344 return 0;
3345 }
3346
3347 /* Construct a union map mapping the domain of the union
3348 * piecewise multi-affine expression to its range, with each dimension
3349 * in the range equated to the corresponding affine expression on its cell.
3350 */
3351 __isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff(
3352 __isl_take isl_union_pw_multi_aff *upma)
3353 {
3354 isl_space *space;
3355 isl_union_map *umap;
3356
3357 if (!upma)
3358 return NULL;
3359
3360 space = isl_union_pw_multi_aff_get_space(upma);
3361 umap = isl_union_map_empty(space);
3362
3363 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
3364 &map_from_pw_multi_aff, &umap) < 0)
3365 goto error;
3366
3367 isl_union_pw_multi_aff_free(upma);
3368 return umap;
3369 error:
3370 isl_union_pw_multi_aff_free(upma);
3371 isl_union_map_free(umap);
3372 return NULL;
3373 }
3374
3375 /* Local data for bin_entry and the callback "fn".
3376 */
3377 struct isl_union_pw_multi_aff_bin_data {
3378 isl_union_pw_multi_aff *upma2;
3379 isl_union_pw_multi_aff *res;
3380 isl_pw_multi_aff *pma;
3381 int (*fn)(void **entry, void *user);
3382 };
3383
3384 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
3385 * and call data->fn for each isl_pw_multi_aff in data->upma2.
3386 */
3387 static int bin_entry(void **entry, void *user)
3388 {
3389 struct isl_union_pw_multi_aff_bin_data *data = user;
3390 isl_pw_multi_aff *pma = *entry;
3391
3392 data->pma = pma;
3393 if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
3394 data->fn, data) < 0)
3395 return -1;
3396
3397 return 0;
3398 }
3399
3400 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
3401 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
3402 * passed as user field) and the isl_pw_multi_aff from upma2 is available
3403 * as *entry. The callback should adjust data->res if desired.
3404 */
3405 static __isl_give isl_union_pw_multi_aff *bin_op(
3406 __isl_take isl_union_pw_multi_aff *upma1,
3407 __isl_take isl_union_pw_multi_aff *upma2,
3408 int (*fn)(void **entry, void *user))
3409 {
3410 isl_space *space;
3411 struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
3412
3413 space = isl_union_pw_multi_aff_get_space(upma2);
3414 upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
3415 space = isl_union_pw_multi_aff_get_space(upma1);
3416 upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
3417
3418 if (!upma1 || !upma2)
3419 goto error;
3420
3421 data.upma2 = upma2;
3422 data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
3423 upma1->table.n);
3424 if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
3425 &bin_entry, &data) < 0)
3426 goto error;
3427
3428 isl_union_pw_multi_aff_free(upma1);
3429 isl_union_pw_multi_aff_free(upma2);
3430 return data.res;
3431 error:
3432 isl_union_pw_multi_aff_free(upma1);
3433 isl_union_pw_multi_aff_free(upma2);
3434 isl_union_pw_multi_aff_free(data.res);
3435 return NULL;
3436 }
3437
3438 /* Given two isl_multi_affs A -> B and C -> D,
3439 * construct an isl_multi_aff (A * C) -> (B, D).
3440 */
3441 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3442 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
3443 {
3444 int i, n1, n2;
3445 isl_aff *aff;
3446 isl_space *space;
3447 isl_multi_aff *res;
3448
3449 if (!ma1 || !ma2)
3450 goto error;
3451
3452 space = isl_space_range_product(isl_multi_aff_get_space(ma1),
3453 isl_multi_aff_get_space(ma2));
3454 space = isl_space_flatten_range(space);
3455 res = isl_multi_aff_alloc(space);
3456
3457 n1 = isl_multi_aff_dim(ma1, isl_dim_out);
3458 n2 = isl_multi_aff_dim(ma2, isl_dim_out);
3459
3460 for (i = 0; i < n1; ++i) {
3461 aff = isl_multi_aff_get_aff(ma1, i);
3462 res = isl_multi_aff_set_aff(res, i, aff);
3463 }
3464
3465 for (i = 0; i < n2; ++i) {
3466 aff = isl_multi_aff_get_aff(ma2, i);
3467 res = isl_multi_aff_set_aff(res, n1 + i, aff);
3468 }
3469
3470 isl_multi_aff_free(ma1);
3471 isl_multi_aff_free(ma2);
3472 return res;
3473 error:
3474 isl_multi_aff_free(ma1);
3475 isl_multi_aff_free(ma2);
3476 return NULL;
3477 }
3478
3479 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
3480 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3481 */
3482 static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
3483 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3484 {
3485 isl_space *space;
3486
3487 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
3488 isl_pw_multi_aff_get_space(pma2));
3489 space = isl_space_flatten_range(space);
3490 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
3491 &isl_multi_aff_flat_range_product);
3492 }
3493
3494 /* Given two isl_pw_multi_affs A -> B and C -> D,
3495 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3496 */
3497 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
3498 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3499 {
3500 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3501 &pw_multi_aff_flat_range_product);
3502 }
3503
3504 /* If data->pma and *entry have the same domain space, then compute
3505 * their flat range product and the result to data->res.
3506 */
3507 static int flat_range_product_entry(void **entry, void *user)
3508 {
3509 struct isl_union_pw_multi_aff_bin_data *data = user;
3510 isl_pw_multi_aff *pma2 = *entry;
3511
3512 if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
3513 pma2->dim, isl_dim_in))
3514 return 0;
3515
3516 pma2 = isl_pw_multi_aff_flat_range_product(
3517 isl_pw_multi_aff_copy(data->pma),
3518 isl_pw_multi_aff_copy(pma2));
3519
3520 data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
3521
3522 return 0;
3523 }
3524
3525 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
3526 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
3527 */
3528 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
3529 __isl_take isl_union_pw_multi_aff *upma1,
3530 __isl_take isl_union_pw_multi_aff *upma2)
3531 {
3532 return bin_op(upma1, upma2, &flat_range_product_entry);
3533 }
Integer set library