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isl_map_intersect_{range,domain}: stop allowing intersection with parameter set
[isl.git] / isl_aff.c
blob47797c964142f2eacfdedd376408970635af3186
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 MIT 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 /* Normalize the representation of "aff".
652 *
653 * This function should only be called of "new" isl_affs, i.e.,
654 * with only a single reference. We therefore do not need to
655 * worry about affecting other instances.
656 */
657 __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
658 {
659 if (!aff)
660 return NULL;
661 aff->v = isl_vec_normalize(aff->v);
662 if (!aff->v)
663 return isl_aff_free(aff);
664 aff = isl_aff_remove_unused_divs(aff);
665 return aff;
666 }
667
668 /* Given f, return floor(f).
669 * If f is an integer expression, then just return f.
670 * If f is a constant, then return the constant floor(f).
671 * Otherwise, if f = g/m, write g = q m + r,
672 * create a new div d = [r/m] and return the expression q + d.
673 * The coefficients in r are taken to lie between -m/2 and m/2.
674 */
675 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
676 {
677 int i;
678 int size;
679 isl_ctx *ctx;
680 isl_vec *div;
681
682 if (!aff)
683 return NULL;
684
685 if (isl_int_is_one(aff->v->el[0]))
686 return aff;
687
688 aff = isl_aff_cow(aff);
689 if (!aff)
690 return NULL;
691
692 aff->v = isl_vec_cow(aff->v);
693 if (!aff->v)
694 return isl_aff_free(aff);
695
696 if (isl_aff_is_cst(aff)) {
697 isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
698 isl_int_set_si(aff->v->el[0], 1);
699 return aff;
700 }
701
702 div = isl_vec_copy(aff->v);
703 div = isl_vec_cow(div);
704 if (!div)
705 return isl_aff_free(aff);
706
707 ctx = isl_aff_get_ctx(aff);
708 isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
709 for (i = 1; i < aff->v->size; ++i) {
710 isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
711 isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
712 if (isl_int_gt(div->el[i], aff->v->el[0])) {
713 isl_int_sub(div->el[i], div->el[i], div->el[0]);
714 isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
715 }
716 }
717
718 aff->ls = isl_local_space_add_div(aff->ls, div);
719 if (!aff->ls)
720 return isl_aff_free(aff);
721
722 size = aff->v->size;
723 aff->v = isl_vec_extend(aff->v, size + 1);
724 if (!aff->v)
725 return isl_aff_free(aff);
726 isl_int_set_si(aff->v->el[0], 1);
727 isl_int_set_si(aff->v->el[size], 1);
728
729 return aff;
730 }
731
732 /* Compute
733 *
734 * aff mod m = aff - m * floor(aff/m)
735 */
736 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
737 {
738 isl_aff *res;
739
740 res = isl_aff_copy(aff);
741 aff = isl_aff_scale_down(aff, m);
742 aff = isl_aff_floor(aff);
743 aff = isl_aff_scale(aff, m);
744 res = isl_aff_sub(res, aff);
745
746 return res;
747 }
748
749 /* Compute
750 *
751 * pwaff mod m = pwaff - m * floor(pwaff/m)
752 */
753 __isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
754 {
755 isl_pw_aff *res;
756
757 res = isl_pw_aff_copy(pwaff);
758 pwaff = isl_pw_aff_scale_down(pwaff, m);
759 pwaff = isl_pw_aff_floor(pwaff);
760 pwaff = isl_pw_aff_scale(pwaff, m);
761 res = isl_pw_aff_sub(res, pwaff);
762
763 return res;
764 }
765
766 /* Given f, return ceil(f).
767 * If f is an integer expression, then just return f.
768 * Otherwise, create a new div d = [-f] and return the expression -d.
769 */
770 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
771 {
772 if (!aff)
773 return NULL;
774
775 if (isl_int_is_one(aff->v->el[0]))
776 return aff;
777
778 aff = isl_aff_neg(aff);
779 aff = isl_aff_floor(aff);
780 aff = isl_aff_neg(aff);
781
782 return aff;
783 }
784
785 /* Apply the expansion computed by isl_merge_divs.
786 * The expansion itself is given by "exp" while the resulting
787 * list of divs is given by "div".
788 */
789 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
790 __isl_take isl_mat *div, int *exp)
791 {
792 int i, j;
793 int old_n_div;
794 int new_n_div;
795 int offset;
796
797 aff = isl_aff_cow(aff);
798 if (!aff || !div)
799 goto error;
800
801 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
802 new_n_div = isl_mat_rows(div);
803 if (new_n_div < old_n_div)
804 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
805 "not an expansion", goto error);
806
807 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
808 if (!aff->v)
809 goto error;
810
811 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
812 j = old_n_div - 1;
813 for (i = new_n_div - 1; i >= 0; --i) {
814 if (j >= 0 && exp[j] == i) {
815 if (i != j)
816 isl_int_swap(aff->v->el[offset + i],
817 aff->v->el[offset + j]);
818 j--;
819 } else
820 isl_int_set_si(aff->v->el[offset + i], 0);
821 }
822
823 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
824 if (!aff->ls)
825 goto error;
826 isl_mat_free(div);
827 return aff;
828 error:
829 isl_aff_free(aff);
830 isl_mat_free(div);
831 return NULL;
832 }
833
834 /* Add two affine expressions that live in the same local space.
835 */
836 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
837 __isl_take isl_aff *aff2)
838 {
839 isl_int gcd, f;
840
841 aff1 = isl_aff_cow(aff1);
842 if (!aff1 || !aff2)
843 goto error;
844
845 aff1->v = isl_vec_cow(aff1->v);
846 if (!aff1->v)
847 goto error;
848
849 isl_int_init(gcd);
850 isl_int_init(f);
851 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
852 isl_int_divexact(f, aff2->v->el[0], gcd);
853 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
854 isl_int_divexact(f, aff1->v->el[0], gcd);
855 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
856 isl_int_divexact(f, aff2->v->el[0], gcd);
857 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
858 isl_int_clear(f);
859 isl_int_clear(gcd);
860
861 isl_aff_free(aff2);
862 return aff1;
863 error:
864 isl_aff_free(aff1);
865 isl_aff_free(aff2);
866 return NULL;
867 }
868
869 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
870 __isl_take isl_aff *aff2)
871 {
872 isl_ctx *ctx;
873 int *exp1 = NULL;
874 int *exp2 = NULL;
875 isl_mat *div;
876
877 if (!aff1 || !aff2)
878 goto error;
879
880 ctx = isl_aff_get_ctx(aff1);
881 if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
882 isl_die(ctx, isl_error_invalid,
883 "spaces don't match", goto error);
884
885 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
886 return add_expanded(aff1, aff2);
887
888 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
889 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
890 if (!exp1 || !exp2)
891 goto error;
892
893 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
894 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
895 aff2 = isl_aff_expand_divs(aff2, div, exp2);
896 free(exp1);
897 free(exp2);
898
899 return add_expanded(aff1, aff2);
900 error:
901 free(exp1);
902 free(exp2);
903 isl_aff_free(aff1);
904 isl_aff_free(aff2);
905 return NULL;
906 }
907
908 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
909 __isl_take isl_aff *aff2)
910 {
911 return isl_aff_add(aff1, isl_aff_neg(aff2));
912 }
913
914 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
915 {
916 isl_int gcd;
917
918 if (isl_int_is_one(f))
919 return aff;
920
921 aff = isl_aff_cow(aff);
922 if (!aff)
923 return NULL;
924 aff->v = isl_vec_cow(aff->v);
925 if (!aff->v)
926 return isl_aff_free(aff);
927
928 isl_int_init(gcd);
929 isl_int_gcd(gcd, aff->v->el[0], f);
930 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
931 isl_int_divexact(gcd, f, gcd);
932 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
933 isl_int_clear(gcd);
934
935 return aff;
936 }
937
938 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
939 {
940 isl_int gcd;
941
942 if (isl_int_is_one(f))
943 return aff;
944
945 aff = isl_aff_cow(aff);
946 if (!aff)
947 return NULL;
948
949 if (isl_int_is_zero(f))
950 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
951 "cannot scale down by zero", return isl_aff_free(aff));
952
953 aff->v = isl_vec_cow(aff->v);
954 if (!aff->v)
955 return isl_aff_free(aff);
956
957 isl_int_init(gcd);
958 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
959 isl_int_gcd(gcd, gcd, f);
960 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
961 isl_int_divexact(gcd, f, gcd);
962 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
963 isl_int_clear(gcd);
964
965 return aff;
966 }
967
968 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
969 {
970 isl_int v;
971
972 if (f == 1)
973 return aff;
974
975 isl_int_init(v);
976 isl_int_set_ui(v, f);
977 aff = isl_aff_scale_down(aff, v);
978 isl_int_clear(v);
979
980 return aff;
981 }
982
983 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
984 enum isl_dim_type type, unsigned pos, const char *s)
985 {
986 aff = isl_aff_cow(aff);
987 if (!aff)
988 return NULL;
989 if (type == isl_dim_out)
990 isl_die(aff->v->ctx, isl_error_invalid,
991 "cannot set name of output/set dimension",
992 return isl_aff_free(aff));
993 if (type == isl_dim_in)
994 type = isl_dim_set;
995 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
996 if (!aff->ls)
997 return isl_aff_free(aff);
998
999 return aff;
1000 }
1001
1002 __isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
1003 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
1004 {
1005 aff = isl_aff_cow(aff);
1006 if (!aff)
1007 return isl_id_free(id);
1008 if (type == isl_dim_out)
1009 isl_die(aff->v->ctx, isl_error_invalid,
1010 "cannot set name of output/set dimension",
1011 goto error);
1012 if (type == isl_dim_in)
1013 type = isl_dim_set;
1014 aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
1015 if (!aff->ls)
1016 return isl_aff_free(aff);
1017
1018 return aff;
1019 error:
1020 isl_id_free(id);
1021 isl_aff_free(aff);
1022 return NULL;
1023 }
1024
1025 /* Exploit the equalities in "eq" to simplify the affine expression
1026 * and the expressions of the integer divisions in the local space.
1027 * The integer divisions in this local space are assumed to appear
1028 * as regular dimensions in "eq".
1029 */
1030 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
1031 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1032 {
1033 int i, j;
1034 unsigned total;
1035 unsigned n_div;
1036
1037 if (!eq)
1038 goto error;
1039 if (eq->n_eq == 0) {
1040 isl_basic_set_free(eq);
1041 return aff;
1042 }
1043
1044 aff = isl_aff_cow(aff);
1045 if (!aff)
1046 goto error;
1047
1048 aff->ls = isl_local_space_substitute_equalities(aff->ls,
1049 isl_basic_set_copy(eq));
1050 if (!aff->ls)
1051 goto error;
1052
1053 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
1054 n_div = eq->n_div;
1055 for (i = 0; i < eq->n_eq; ++i) {
1056 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
1057 if (j < 0 || j == 0 || j >= total)
1058 continue;
1059
1060 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
1061 &aff->v->el[0]);
1062 }
1063
1064 isl_basic_set_free(eq);
1065 aff = isl_aff_normalize(aff);
1066 return aff;
1067 error:
1068 isl_basic_set_free(eq);
1069 isl_aff_free(aff);
1070 return NULL;
1071 }
1072
1073 /* Exploit the equalities in "eq" to simplify the affine expression
1074 * and the expressions of the integer divisions in the local space.
1075 */
1076 static __isl_give isl_aff *isl_aff_substitute_equalities(
1077 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1078 {
1079 int n_div;
1080
1081 if (!aff || !eq)
1082 goto error;
1083 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1084 if (n_div > 0)
1085 eq = isl_basic_set_add(eq, isl_dim_set, n_div);
1086 return isl_aff_substitute_equalities_lifted(aff, eq);
1087 error:
1088 isl_basic_set_free(eq);
1089 isl_aff_free(aff);
1090 return NULL;
1091 }
1092
1093 /* Look for equalities among the variables shared by context and aff
1094 * and the integer divisions of aff, if any.
1095 * The equalities are then used to eliminate coefficients and/or integer
1096 * divisions from aff.
1097 */
1098 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
1099 __isl_take isl_set *context)
1100 {
1101 isl_basic_set *hull;
1102 int n_div;
1103
1104 if (!aff)
1105 goto error;
1106 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1107 if (n_div > 0) {
1108 isl_basic_set *bset;
1109 isl_local_space *ls;
1110 context = isl_set_add_dims(context, isl_dim_set, n_div);
1111 ls = isl_aff_get_domain_local_space(aff);
1112 bset = isl_basic_set_from_local_space(ls);
1113 bset = isl_basic_set_lift(bset);
1114 bset = isl_basic_set_flatten(bset);
1115 context = isl_set_intersect(context,
1116 isl_set_from_basic_set(bset));
1117 }
1118
1119 hull = isl_set_affine_hull(context);
1120 return isl_aff_substitute_equalities_lifted(aff, hull);
1121 error:
1122 isl_aff_free(aff);
1123 isl_set_free(context);
1124 return NULL;
1125 }
1126
1127 __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
1128 __isl_take isl_set *context)
1129 {
1130 isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
1131 dom_context = isl_set_intersect_params(dom_context, context);
1132 return isl_aff_gist(aff, dom_context);
1133 }
1134
1135 /* Return a basic set containing those elements in the space
1136 * of aff where it is non-negative.
1137 */
1138 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
1139 {
1140 isl_constraint *ineq;
1141 isl_basic_set *bset;
1142
1143 ineq = isl_inequality_from_aff(aff);
1144
1145 bset = isl_basic_set_from_constraint(ineq);
1146 bset = isl_basic_set_simplify(bset);
1147 return bset;
1148 }
1149
1150 /* Return a basic set containing those elements in the domain space
1151 * of aff where it is negative.
1152 */
1153 __isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
1154 {
1155 aff = isl_aff_neg(aff);
1156 aff = isl_aff_add_constant_num_si(aff, -1);
1157 return isl_aff_nonneg_basic_set(aff);
1158 }
1159
1160 /* Return a basic set containing those elements in the space
1161 * of aff where it is zero.
1162 */
1163 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
1164 {
1165 isl_constraint *ineq;
1166 isl_basic_set *bset;
1167
1168 ineq = isl_equality_from_aff(aff);
1169
1170 bset = isl_basic_set_from_constraint(ineq);
1171 bset = isl_basic_set_simplify(bset);
1172 return bset;
1173 }
1174
1175 /* Return a basic set containing those elements in the shared space
1176 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1177 */
1178 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
1179 __isl_take isl_aff *aff2)
1180 {
1181 aff1 = isl_aff_sub(aff1, aff2);
1182
1183 return isl_aff_nonneg_basic_set(aff1);
1184 }
1185
1186 /* Return a basic set containing those elements in the shared space
1187 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1188 */
1189 __isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
1190 __isl_take isl_aff *aff2)
1191 {
1192 return isl_aff_ge_basic_set(aff2, aff1);
1193 }
1194
1195 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
1196 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
1197 {
1198 aff1 = isl_aff_add(aff1, aff2);
1199 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
1200 return aff1;
1201 }
1202
1203 int isl_aff_is_empty(__isl_keep isl_aff *aff)
1204 {
1205 if (!aff)
1206 return -1;
1207
1208 return 0;
1209 }
1210
1211 /* Check whether the given affine expression has non-zero coefficient
1212 * for any dimension in the given range or if any of these dimensions
1213 * appear with non-zero coefficients in any of the integer divisions
1214 * involved in the affine expression.
1215 */
1216 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
1217 enum isl_dim_type type, unsigned first, unsigned n)
1218 {
1219 int i;
1220 isl_ctx *ctx;
1221 int *active = NULL;
1222 int involves = 0;
1223
1224 if (!aff)
1225 return -1;
1226 if (n == 0)
1227 return 0;
1228
1229 ctx = isl_aff_get_ctx(aff);
1230 if (first + n > isl_aff_dim(aff, type))
1231 isl_die(ctx, isl_error_invalid,
1232 "range out of bounds", return -1);
1233
1234 active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
1235 if (!active)
1236 goto error;
1237
1238 first += isl_local_space_offset(aff->ls, type) - 1;
1239 for (i = 0; i < n; ++i)
1240 if (active[first + i]) {
1241 involves = 1;
1242 break;
1243 }
1244
1245 free(active);
1246
1247 return involves;
1248 error:
1249 free(active);
1250 return -1;
1251 }
1252
1253 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
1254 enum isl_dim_type type, unsigned first, unsigned n)
1255 {
1256 isl_ctx *ctx;
1257
1258 if (!aff)
1259 return NULL;
1260 if (type == isl_dim_out)
1261 isl_die(aff->v->ctx, isl_error_invalid,
1262 "cannot drop output/set dimension",
1263 return isl_aff_free(aff));
1264 if (type == isl_dim_in)
1265 type = isl_dim_set;
1266 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1267 return aff;
1268
1269 ctx = isl_aff_get_ctx(aff);
1270 if (first + n > isl_local_space_dim(aff->ls, type))
1271 isl_die(ctx, isl_error_invalid, "range out of bounds",
1272 return isl_aff_free(aff));
1273
1274 aff = isl_aff_cow(aff);
1275 if (!aff)
1276 return NULL;
1277
1278 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
1279 if (!aff->ls)
1280 return isl_aff_free(aff);
1281
1282 first += 1 + isl_local_space_offset(aff->ls, type);
1283 aff->v = isl_vec_drop_els(aff->v, first, n);
1284 if (!aff->v)
1285 return isl_aff_free(aff);
1286
1287 return aff;
1288 }
1289
1290 /* Project the domain of the affine expression onto its parameter space.
1291 * The affine expression may not involve any of the domain dimensions.
1292 */
1293 __isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
1294 {
1295 isl_space *space;
1296 unsigned n;
1297 int involves;
1298
1299 n = isl_aff_dim(aff, isl_dim_in);
1300 involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
1301 if (involves < 0)
1302 return isl_aff_free(aff);
1303 if (involves)
1304 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1305 "affine expression involves some of the domain dimensions",
1306 return isl_aff_free(aff));
1307 aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
1308 space = isl_aff_get_domain_space(aff);
1309 space = isl_space_params(space);
1310 aff = isl_aff_reset_domain_space(aff, space);
1311 return aff;
1312 }
1313
1314 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
1315 enum isl_dim_type type, unsigned first, unsigned n)
1316 {
1317 isl_ctx *ctx;
1318
1319 if (!aff)
1320 return NULL;
1321 if (type == isl_dim_out)
1322 isl_die(aff->v->ctx, isl_error_invalid,
1323 "cannot insert output/set dimensions",
1324 return isl_aff_free(aff));
1325 if (type == isl_dim_in)
1326 type = isl_dim_set;
1327 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1328 return aff;
1329
1330 ctx = isl_aff_get_ctx(aff);
1331 if (first > isl_local_space_dim(aff->ls, type))
1332 isl_die(ctx, isl_error_invalid, "position out of bounds",
1333 return isl_aff_free(aff));
1334
1335 aff = isl_aff_cow(aff);
1336 if (!aff)
1337 return NULL;
1338
1339 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
1340 if (!aff->ls)
1341 return isl_aff_free(aff);
1342
1343 first += 1 + isl_local_space_offset(aff->ls, type);
1344 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
1345 if (!aff->v)
1346 return isl_aff_free(aff);
1347
1348 return aff;
1349 }
1350
1351 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
1352 enum isl_dim_type type, unsigned n)
1353 {
1354 unsigned pos;
1355
1356 pos = isl_aff_dim(aff, type);
1357
1358 return isl_aff_insert_dims(aff, type, pos, n);
1359 }
1360
1361 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
1362 enum isl_dim_type type, unsigned n)
1363 {
1364 unsigned pos;
1365
1366 pos = isl_pw_aff_dim(pwaff, type);
1367
1368 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
1369 }
1370
1371 __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
1372 {
1373 isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
1374 return isl_pw_aff_alloc(dom, aff);
1375 }
1376
1377 #undef PW
1378 #define PW isl_pw_aff
1379 #undef EL
1380 #define EL isl_aff
1381 #undef EL_IS_ZERO
1382 #define EL_IS_ZERO is_empty
1383 #undef ZERO
1384 #define ZERO empty
1385 #undef IS_ZERO
1386 #define IS_ZERO is_empty
1387 #undef FIELD
1388 #define FIELD aff
1389 #undef DEFAULT_IS_ZERO
1390 #define DEFAULT_IS_ZERO 0
1391
1392 #define NO_EVAL
1393 #define NO_OPT
1394 #define NO_MOVE_DIMS
1395 #define NO_LIFT
1396 #define NO_MORPH
1397
1398 #include <isl_pw_templ.c>
1399
1400 static __isl_give isl_set *align_params_pw_pw_set_and(
1401 __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
1402 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1403 __isl_take isl_pw_aff *pwaff2))
1404 {
1405 if (!pwaff1 || !pwaff2)
1406 goto error;
1407 if (isl_space_match(pwaff1->dim, isl_dim_param,
1408 pwaff2->dim, isl_dim_param))
1409 return fn(pwaff1, pwaff2);
1410 if (!isl_space_has_named_params(pwaff1->dim) ||
1411 !isl_space_has_named_params(pwaff2->dim))
1412 isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
1413 "unaligned unnamed parameters", goto error);
1414 pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
1415 pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
1416 return fn(pwaff1, pwaff2);
1417 error:
1418 isl_pw_aff_free(pwaff1);
1419 isl_pw_aff_free(pwaff2);
1420 return NULL;
1421 }
1422
1423 /* Compute a piecewise quasi-affine expression with a domain that
1424 * is the union of those of pwaff1 and pwaff2 and such that on each
1425 * cell, the quasi-affine expression is the better (according to cmp)
1426 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
1427 * is defined on a given cell, then the associated expression
1428 * is the defined one.
1429 */
1430 static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1431 __isl_take isl_pw_aff *pwaff2,
1432 __isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
1433 __isl_take isl_aff *aff2))
1434 {
1435 int i, j, n;
1436 isl_pw_aff *res;
1437 isl_ctx *ctx;
1438 isl_set *set;
1439
1440 if (!pwaff1 || !pwaff2)
1441 goto error;
1442
1443 ctx = isl_space_get_ctx(pwaff1->dim);
1444 if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
1445 isl_die(ctx, isl_error_invalid,
1446 "arguments should live in same space", goto error);
1447
1448 if (isl_pw_aff_is_empty(pwaff1)) {
1449 isl_pw_aff_free(pwaff1);
1450 return pwaff2;
1451 }
1452
1453 if (isl_pw_aff_is_empty(pwaff2)) {
1454 isl_pw_aff_free(pwaff2);
1455 return pwaff1;
1456 }
1457
1458 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
1459 res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
1460
1461 for (i = 0; i < pwaff1->n; ++i) {
1462 set = isl_set_copy(pwaff1->p[i].set);
1463 for (j = 0; j < pwaff2->n; ++j) {
1464 struct isl_set *common;
1465 isl_set *better;
1466
1467 common = isl_set_intersect(
1468 isl_set_copy(pwaff1->p[i].set),
1469 isl_set_copy(pwaff2->p[j].set));
1470 better = isl_set_from_basic_set(cmp(
1471 isl_aff_copy(pwaff2->p[j].aff),
1472 isl_aff_copy(pwaff1->p[i].aff)));
1473 better = isl_set_intersect(common, better);
1474 if (isl_set_plain_is_empty(better)) {
1475 isl_set_free(better);
1476 continue;
1477 }
1478 set = isl_set_subtract(set, isl_set_copy(better));
1479
1480 res = isl_pw_aff_add_piece(res, better,
1481 isl_aff_copy(pwaff2->p[j].aff));
1482 }
1483 res = isl_pw_aff_add_piece(res, set,
1484 isl_aff_copy(pwaff1->p[i].aff));
1485 }
1486
1487 for (j = 0; j < pwaff2->n; ++j) {
1488 set = isl_set_copy(pwaff2->p[j].set);
1489 for (i = 0; i < pwaff1->n; ++i)
1490 set = isl_set_subtract(set,
1491 isl_set_copy(pwaff1->p[i].set));
1492 res = isl_pw_aff_add_piece(res, set,
1493 isl_aff_copy(pwaff2->p[j].aff));
1494 }
1495
1496 isl_pw_aff_free(pwaff1);
1497 isl_pw_aff_free(pwaff2);
1498
1499 return res;
1500 error:
1501 isl_pw_aff_free(pwaff1);
1502 isl_pw_aff_free(pwaff2);
1503 return NULL;
1504 }
1505
1506 /* Compute a piecewise quasi-affine expression with a domain that
1507 * is the union of those of pwaff1 and pwaff2 and such that on each
1508 * cell, the quasi-affine expression is the maximum of those of pwaff1
1509 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1510 * cell, then the associated expression is the defined one.
1511 */
1512 static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1513 __isl_take isl_pw_aff *pwaff2)
1514 {
1515 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
1516 }
1517
1518 __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1519 __isl_take isl_pw_aff *pwaff2)
1520 {
1521 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1522 &pw_aff_union_max);
1523 }
1524
1525 /* Compute a piecewise quasi-affine expression with a domain that
1526 * is the union of those of pwaff1 and pwaff2 and such that on each
1527 * cell, the quasi-affine expression is the minimum of those of pwaff1
1528 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1529 * cell, then the associated expression is the defined one.
1530 */
1531 static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1532 __isl_take isl_pw_aff *pwaff2)
1533 {
1534 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
1535 }
1536
1537 __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1538 __isl_take isl_pw_aff *pwaff2)
1539 {
1540 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1541 &pw_aff_union_min);
1542 }
1543
1544 __isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1545 __isl_take isl_pw_aff *pwaff2, int max)
1546 {
1547 if (max)
1548 return isl_pw_aff_union_max(pwaff1, pwaff2);
1549 else
1550 return isl_pw_aff_union_min(pwaff1, pwaff2);
1551 }
1552
1553 /* Construct a map with as domain the domain of pwaff and
1554 * one-dimensional range corresponding to the affine expressions.
1555 */
1556 static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1557 {
1558 int i;
1559 isl_space *dim;
1560 isl_map *map;
1561
1562 if (!pwaff)
1563 return NULL;
1564
1565 dim = isl_pw_aff_get_space(pwaff);
1566 map = isl_map_empty(dim);
1567
1568 for (i = 0; i < pwaff->n; ++i) {
1569 isl_basic_map *bmap;
1570 isl_map *map_i;
1571
1572 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
1573 map_i = isl_map_from_basic_map(bmap);
1574 map_i = isl_map_intersect_domain(map_i,
1575 isl_set_copy(pwaff->p[i].set));
1576 map = isl_map_union_disjoint(map, map_i);
1577 }
1578
1579 isl_pw_aff_free(pwaff);
1580
1581 return map;
1582 }
1583
1584 /* Construct a map with as domain the domain of pwaff and
1585 * one-dimensional range corresponding to the affine expressions.
1586 */
1587 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1588 {
1589 if (!pwaff)
1590 return NULL;
1591 if (isl_space_is_set(pwaff->dim))
1592 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1593 "space of input is not a map",
1594 return isl_pw_aff_free(pwaff));
1595 return map_from_pw_aff(pwaff);
1596 }
1597
1598 /* Construct a one-dimensional set with as parameter domain
1599 * the domain of pwaff and the single set dimension
1600 * corresponding to the affine expressions.
1601 */
1602 __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1603 {
1604 if (!pwaff)
1605 return NULL;
1606 if (!isl_space_is_set(pwaff->dim))
1607 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1608 "space of input is not a set",
1609 return isl_pw_aff_free(pwaff));
1610 return map_from_pw_aff(pwaff);
1611 }
1612
1613 /* Return a set containing those elements in the domain
1614 * of pwaff where it is non-negative.
1615 */
1616 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
1617 {
1618 int i;
1619 isl_set *set;
1620
1621 if (!pwaff)
1622 return NULL;
1623
1624 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1625
1626 for (i = 0; i < pwaff->n; ++i) {
1627 isl_basic_set *bset;
1628 isl_set *set_i;
1629
1630 bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff));
1631 set_i = isl_set_from_basic_set(bset);
1632 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1633 set = isl_set_union_disjoint(set, set_i);
1634 }
1635
1636 isl_pw_aff_free(pwaff);
1637
1638 return set;
1639 }
1640
1641 /* Return a set containing those elements in the domain
1642 * of pwaff where it is zero (if complement is 0) or not zero
1643 * (if complement is 1).
1644 */
1645 static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
1646 int complement)
1647 {
1648 int i;
1649 isl_set *set;
1650
1651 if (!pwaff)
1652 return NULL;
1653
1654 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1655
1656 for (i = 0; i < pwaff->n; ++i) {
1657 isl_basic_set *bset;
1658 isl_set *set_i, *zero;
1659
1660 bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
1661 zero = isl_set_from_basic_set(bset);
1662 set_i = isl_set_copy(pwaff->p[i].set);
1663 if (complement)
1664 set_i = isl_set_subtract(set_i, zero);
1665 else
1666 set_i = isl_set_intersect(set_i, zero);
1667 set = isl_set_union_disjoint(set, set_i);
1668 }
1669
1670 isl_pw_aff_free(pwaff);
1671
1672 return set;
1673 }
1674
1675 /* Return a set containing those elements in the domain
1676 * of pwaff where it is zero.
1677 */
1678 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
1679 {
1680 return pw_aff_zero_set(pwaff, 0);
1681 }
1682
1683 /* Return a set containing those elements in the domain
1684 * of pwaff where it is not zero.
1685 */
1686 __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
1687 {
1688 return pw_aff_zero_set(pwaff, 1);
1689 }
1690
1691 /* Return a set containing those elements in the shared domain
1692 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1693 *
1694 * We compute the difference on the shared domain and then construct
1695 * the set of values where this difference is non-negative.
1696 * If strict is set, we first subtract 1 from the difference.
1697 * If equal is set, we only return the elements where pwaff1 and pwaff2
1698 * are equal.
1699 */
1700 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
1701 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
1702 {
1703 isl_set *set1, *set2;
1704
1705 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
1706 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
1707 set1 = isl_set_intersect(set1, set2);
1708 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
1709 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
1710 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
1711
1712 if (strict) {
1713 isl_space *dim = isl_set_get_space(set1);
1714 isl_aff *aff;
1715 aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
1716 aff = isl_aff_add_constant_si(aff, -1);
1717 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
1718 } else
1719 isl_set_free(set1);
1720
1721 if (equal)
1722 return isl_pw_aff_zero_set(pwaff1);
1723 return isl_pw_aff_nonneg_set(pwaff1);
1724 }
1725
1726 /* Return a set containing those elements in the shared domain
1727 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1728 */
1729 static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1730 __isl_take isl_pw_aff *pwaff2)
1731 {
1732 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
1733 }
1734
1735 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1736 __isl_take isl_pw_aff *pwaff2)
1737 {
1738 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
1739 }
1740
1741 /* Return a set containing those elements in the shared domain
1742 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
1743 */
1744 static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1745 __isl_take isl_pw_aff *pwaff2)
1746 {
1747 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
1748 }
1749
1750 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1751 __isl_take isl_pw_aff *pwaff2)
1752 {
1753 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
1754 }
1755
1756 /* Return a set containing those elements in the shared domain
1757 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
1758 */
1759 static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1760 __isl_take isl_pw_aff *pwaff2)
1761 {
1762 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
1763 }
1764
1765 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1766 __isl_take isl_pw_aff *pwaff2)
1767 {
1768 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
1769 }
1770
1771 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
1772 __isl_take isl_pw_aff *pwaff2)
1773 {
1774 return isl_pw_aff_ge_set(pwaff2, pwaff1);
1775 }
1776
1777 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
1778 __isl_take isl_pw_aff *pwaff2)
1779 {
1780 return isl_pw_aff_gt_set(pwaff2, pwaff1);
1781 }
1782
1783 /* Return a set containing those elements in the shared domain
1784 * of the elements of list1 and list2 where each element in list1
1785 * has the relation specified by "fn" with each element in list2.
1786 */
1787 static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
1788 __isl_take isl_pw_aff_list *list2,
1789 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1790 __isl_take isl_pw_aff *pwaff2))
1791 {
1792 int i, j;
1793 isl_ctx *ctx;
1794 isl_set *set;
1795
1796 if (!list1 || !list2)
1797 goto error;
1798
1799 ctx = isl_pw_aff_list_get_ctx(list1);
1800 if (list1->n < 1 || list2->n < 1)
1801 isl_die(ctx, isl_error_invalid,
1802 "list should contain at least one element", goto error);
1803
1804 set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
1805 for (i = 0; i < list1->n; ++i)
1806 for (j = 0; j < list2->n; ++j) {
1807 isl_set *set_ij;
1808
1809 set_ij = fn(isl_pw_aff_copy(list1->p[i]),
1810 isl_pw_aff_copy(list2->p[j]));
1811 set = isl_set_intersect(set, set_ij);
1812 }
1813
1814 isl_pw_aff_list_free(list1);
1815 isl_pw_aff_list_free(list2);
1816 return set;
1817 error:
1818 isl_pw_aff_list_free(list1);
1819 isl_pw_aff_list_free(list2);
1820 return NULL;
1821 }
1822
1823 /* Return a set containing those elements in the shared domain
1824 * of the elements of list1 and list2 where each element in list1
1825 * is equal to each element in list2.
1826 */
1827 __isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
1828 __isl_take isl_pw_aff_list *list2)
1829 {
1830 return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
1831 }
1832
1833 __isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
1834 __isl_take isl_pw_aff_list *list2)
1835 {
1836 return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
1837 }
1838
1839 /* Return a set containing those elements in the shared domain
1840 * of the elements of list1 and list2 where each element in list1
1841 * is less than or equal to each element in list2.
1842 */
1843 __isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
1844 __isl_take isl_pw_aff_list *list2)
1845 {
1846 return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
1847 }
1848
1849 __isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
1850 __isl_take isl_pw_aff_list *list2)
1851 {
1852 return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
1853 }
1854
1855 __isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
1856 __isl_take isl_pw_aff_list *list2)
1857 {
1858 return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
1859 }
1860
1861 __isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
1862 __isl_take isl_pw_aff_list *list2)
1863 {
1864 return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
1865 }
1866
1867
1868 /* Return a set containing those elements in the shared domain
1869 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
1870 */
1871 static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1872 __isl_take isl_pw_aff *pwaff2)
1873 {
1874 isl_set *set_lt, *set_gt;
1875
1876 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
1877 isl_pw_aff_copy(pwaff2));
1878 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
1879 return isl_set_union_disjoint(set_lt, set_gt);
1880 }
1881
1882 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1883 __isl_take isl_pw_aff *pwaff2)
1884 {
1885 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
1886 }
1887
1888 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
1889 isl_int v)
1890 {
1891 int i;
1892
1893 if (isl_int_is_one(v))
1894 return pwaff;
1895 if (!isl_int_is_pos(v))
1896 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1897 "factor needs to be positive",
1898 return isl_pw_aff_free(pwaff));
1899 pwaff = isl_pw_aff_cow(pwaff);
1900 if (!pwaff)
1901 return NULL;
1902 if (pwaff->n == 0)
1903 return pwaff;
1904
1905 for (i = 0; i < pwaff->n; ++i) {
1906 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
1907 if (!pwaff->p[i].aff)
1908 return isl_pw_aff_free(pwaff);
1909 }
1910
1911 return pwaff;
1912 }
1913
1914 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
1915 {
1916 int i;
1917
1918 pwaff = isl_pw_aff_cow(pwaff);
1919 if (!pwaff)
1920 return NULL;
1921 if (pwaff->n == 0)
1922 return pwaff;
1923
1924 for (i = 0; i < pwaff->n; ++i) {
1925 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
1926 if (!pwaff->p[i].aff)
1927 return isl_pw_aff_free(pwaff);
1928 }
1929
1930 return pwaff;
1931 }
1932
1933 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
1934 {
1935 int i;
1936
1937 pwaff = isl_pw_aff_cow(pwaff);
1938 if (!pwaff)
1939 return NULL;
1940 if (pwaff->n == 0)
1941 return pwaff;
1942
1943 for (i = 0; i < pwaff->n; ++i) {
1944 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
1945 if (!pwaff->p[i].aff)
1946 return isl_pw_aff_free(pwaff);
1947 }
1948
1949 return pwaff;
1950 }
1951
1952 /* Assuming that "cond1" and "cond2" are disjoint,
1953 * return an affine expression that is equal to pwaff1 on cond1
1954 * and to pwaff2 on cond2.
1955 */
1956 static __isl_give isl_pw_aff *isl_pw_aff_select(
1957 __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
1958 __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
1959 {
1960 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
1961 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
1962
1963 return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
1964 }
1965
1966 /* Return an affine expression that is equal to pwaff_true for elements
1967 * where "cond" is non-zero and to pwaff_false for elements where "cond"
1968 * is zero.
1969 * That is, return cond ? pwaff_true : pwaff_false;
1970 */
1971 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
1972 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
1973 {
1974 isl_set *cond_true, *cond_false;
1975
1976 cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
1977 cond_false = isl_pw_aff_zero_set(cond);
1978 return isl_pw_aff_select(cond_true, pwaff_true,
1979 cond_false, pwaff_false);
1980 }
1981
1982 int isl_aff_is_cst(__isl_keep isl_aff *aff)
1983 {
1984 if (!aff)
1985 return -1;
1986
1987 return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
1988 }
1989
1990 /* Check whether pwaff is a piecewise constant.
1991 */
1992 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
1993 {
1994 int i;
1995
1996 if (!pwaff)
1997 return -1;
1998
1999 for (i = 0; i < pwaff->n; ++i) {
2000 int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
2001 if (is_cst < 0 || !is_cst)
2002 return is_cst;
2003 }
2004
2005 return 1;
2006 }
2007
2008 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2009 __isl_take isl_aff *aff2)
2010 {
2011 if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
2012 return isl_aff_mul(aff2, aff1);
2013
2014 if (!isl_aff_is_cst(aff2))
2015 isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
2016 "at least one affine expression should be constant",
2017 goto error);
2018
2019 aff1 = isl_aff_cow(aff1);
2020 if (!aff1 || !aff2)
2021 goto error;
2022
2023 aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
2024 aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
2025
2026 isl_aff_free(aff2);
2027 return aff1;
2028 error:
2029 isl_aff_free(aff1);
2030 isl_aff_free(aff2);
2031 return NULL;
2032 }
2033
2034 static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2035 __isl_take isl_pw_aff *pwaff2)
2036 {
2037 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
2038 }
2039
2040 __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2041 __isl_take isl_pw_aff *pwaff2)
2042 {
2043 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
2044 }
2045
2046 __isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
2047 __isl_take isl_pw_aff *pwaff2)
2048 {
2049 return isl_pw_aff_union_add_(pwaff1, pwaff2);
2050 }
2051
2052 static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2053 __isl_take isl_pw_aff *pwaff2)
2054 {
2055 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
2056 }
2057
2058 __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2059 __isl_take isl_pw_aff *pwaff2)
2060 {
2061 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
2062 }
2063
2064 static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2065 __isl_take isl_pw_aff *pwaff2)
2066 {
2067 isl_set *le;
2068 isl_set *dom;
2069
2070 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2071 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2072 le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
2073 isl_pw_aff_copy(pwaff2));
2074 dom = isl_set_subtract(dom, isl_set_copy(le));
2075 return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
2076 }
2077
2078 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2079 __isl_take isl_pw_aff *pwaff2)
2080 {
2081 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
2082 }
2083
2084 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2085 __isl_take isl_pw_aff *pwaff2)
2086 {
2087 isl_set *ge;
2088 isl_set *dom;
2089
2090 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2091 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2092 ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
2093 isl_pw_aff_copy(pwaff2));
2094 dom = isl_set_subtract(dom, isl_set_copy(ge));
2095 return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
2096 }
2097
2098 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2099 __isl_take isl_pw_aff *pwaff2)
2100 {
2101 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
2102 }
2103
2104 static __isl_give isl_pw_aff *pw_aff_list_reduce(
2105 __isl_take isl_pw_aff_list *list,
2106 __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
2107 __isl_take isl_pw_aff *pwaff2))
2108 {
2109 int i;
2110 isl_ctx *ctx;
2111 isl_pw_aff *res;
2112
2113 if (!list)
2114 return NULL;
2115
2116 ctx = isl_pw_aff_list_get_ctx(list);
2117 if (list->n < 1)
2118 isl_die(ctx, isl_error_invalid,
2119 "list should contain at least one element",
2120 return isl_pw_aff_list_free(list));
2121
2122 res = isl_pw_aff_copy(list->p[0]);
2123 for (i = 1; i < list->n; ++i)
2124 res = fn(res, isl_pw_aff_copy(list->p[i]));
2125
2126 isl_pw_aff_list_free(list);
2127 return res;
2128 }
2129
2130 /* Return an isl_pw_aff that maps each element in the intersection of the
2131 * domains of the elements of list to the minimal corresponding affine
2132 * expression.
2133 */
2134 __isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
2135 {
2136 return pw_aff_list_reduce(list, &isl_pw_aff_min);
2137 }
2138
2139 /* Return an isl_pw_aff that maps each element in the intersection of the
2140 * domains of the elements of list to the maximal corresponding affine
2141 * expression.
2142 */
2143 __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
2144 {
2145 return pw_aff_list_reduce(list, &isl_pw_aff_max);
2146 }
2147
2148 #undef BASE
2149 #define BASE aff
2150
2151 #include <isl_multi_templ.c>
2152
2153 /* Construct an isl_multi_aff in the given space with value zero in
2154 * each of the output dimensions.
2155 */
2156 __isl_give isl_multi_aff *isl_multi_aff_zero(__isl_take isl_space *space)
2157 {
2158 int n;
2159 isl_multi_aff *ma;
2160
2161 if (!space)
2162 return NULL;
2163
2164 n = isl_space_dim(space , isl_dim_out);
2165 ma = isl_multi_aff_alloc(isl_space_copy(space));
2166
2167 if (!n)
2168 isl_space_free(space);
2169 else {
2170 int i;
2171 isl_local_space *ls;
2172 isl_aff *aff;
2173
2174 space = isl_space_domain(space);
2175 ls = isl_local_space_from_space(space);
2176 aff = isl_aff_zero_on_domain(ls);
2177
2178 for (i = 0; i < n; ++i)
2179 ma = isl_multi_aff_set_aff(ma, i, isl_aff_copy(aff));
2180
2181 isl_aff_free(aff);
2182 }
2183
2184 return ma;
2185 }
2186
2187 /* Create an isl_multi_aff in the given space that maps each
2188 * input dimension to the corresponding output dimension.
2189 */
2190 __isl_give isl_multi_aff *isl_multi_aff_identity(__isl_take isl_space *space)
2191 {
2192 int n;
2193 isl_multi_aff *ma;
2194
2195 if (!space)
2196 return NULL;
2197
2198 if (isl_space_is_set(space))
2199 isl_die(isl_space_get_ctx(space), isl_error_invalid,
2200 "expecting map space", goto error);
2201
2202 n = isl_space_dim(space, isl_dim_out);
2203 if (n != isl_space_dim(space, isl_dim_in))
2204 isl_die(isl_space_get_ctx(space), isl_error_invalid,
2205 "number of input and output dimensions needs to be "
2206 "the same", goto error);
2207
2208 ma = isl_multi_aff_alloc(isl_space_copy(space));
2209
2210 if (!n)
2211 isl_space_free(space);
2212 else {
2213 int i;
2214 isl_local_space *ls;
2215 isl_aff *aff;
2216
2217 space = isl_space_domain(space);
2218 ls = isl_local_space_from_space(space);
2219 aff = isl_aff_zero_on_domain(ls);
2220
2221 for (i = 0; i < n; ++i) {
2222 isl_aff *aff_i;
2223 aff_i = isl_aff_copy(aff);
2224 aff_i = isl_aff_add_coefficient_si(aff_i,
2225 isl_dim_in, i, 1);
2226 ma = isl_multi_aff_set_aff(ma, i, aff_i);
2227 }
2228
2229 isl_aff_free(aff);
2230 }
2231
2232 return ma;
2233 error:
2234 isl_space_free(space);
2235 return NULL;
2236 }
2237
2238 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
2239 * domain.
2240 */
2241 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
2242 __isl_take isl_multi_aff *ma)
2243 {
2244 isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
2245 return isl_pw_multi_aff_alloc(dom, ma);
2246 }
2247
2248 /* Create a piecewise multi-affine expression in the given space that maps each
2249 * input dimension to the corresponding output dimension.
2250 */
2251 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2252 __isl_take isl_space *space)
2253 {
2254 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space));
2255 }
2256
2257 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
2258 __isl_take isl_multi_aff *maff2)
2259 {
2260 int i;
2261 isl_ctx *ctx;
2262
2263 maff1 = isl_multi_aff_cow(maff1);
2264 if (!maff1 || !maff2)
2265 goto error;
2266
2267 ctx = isl_multi_aff_get_ctx(maff1);
2268 if (!isl_space_is_equal(maff1->space, maff2->space))
2269 isl_die(ctx, isl_error_invalid,
2270 "spaces don't match", goto error);
2271
2272 for (i = 0; i < maff1->n; ++i) {
2273 maff1->p[i] = isl_aff_add(maff1->p[i],
2274 isl_aff_copy(maff2->p[i]));
2275 if (!maff1->p[i])
2276 goto error;
2277 }
2278
2279 isl_multi_aff_free(maff2);
2280 return maff1;
2281 error:
2282 isl_multi_aff_free(maff1);
2283 isl_multi_aff_free(maff2);
2284 return NULL;
2285 }
2286
2287 /* Given two multi-affine expressions A -> B and C -> D,
2288 * construct a multi-affine expression [A -> C] -> [B -> D].
2289 */
2290 __isl_give isl_multi_aff *isl_multi_aff_product(
2291 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
2292 {
2293 int i;
2294 isl_aff *aff;
2295 isl_space *space;
2296 isl_multi_aff *res;
2297 int in1, in2, out1, out2;
2298
2299 in1 = isl_multi_aff_dim(ma1, isl_dim_in);
2300 in2 = isl_multi_aff_dim(ma2, isl_dim_in);
2301 out1 = isl_multi_aff_dim(ma1, isl_dim_out);
2302 out2 = isl_multi_aff_dim(ma2, isl_dim_out);
2303 space = isl_space_product(isl_multi_aff_get_space(ma1),
2304 isl_multi_aff_get_space(ma2));
2305 res = isl_multi_aff_alloc(isl_space_copy(space));
2306 space = isl_space_domain(space);
2307
2308 for (i = 0; i < out1; ++i) {
2309 aff = isl_multi_aff_get_aff(ma1, i);
2310 aff = isl_aff_insert_dims(aff, isl_dim_in, in1, in2);
2311 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
2312 res = isl_multi_aff_set_aff(res, i, aff);
2313 }
2314
2315 for (i = 0; i < out2; ++i) {
2316 aff = isl_multi_aff_get_aff(ma2, i);
2317 aff = isl_aff_insert_dims(aff, isl_dim_in, 0, in1);
2318 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
2319 res = isl_multi_aff_set_aff(res, out1 + i, aff);
2320 }
2321
2322 isl_space_free(space);
2323 isl_multi_aff_free(ma1);
2324 isl_multi_aff_free(ma2);
2325 return res;
2326 }
2327
2328 /* Exploit the equalities in "eq" to simplify the affine expressions.
2329 */
2330 static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
2331 __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
2332 {
2333 int i;
2334
2335 maff = isl_multi_aff_cow(maff);
2336 if (!maff || !eq)
2337 goto error;
2338
2339 for (i = 0; i < maff->n; ++i) {
2340 maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
2341 isl_basic_set_copy(eq));
2342 if (!maff->p[i])
2343 goto error;
2344 }
2345
2346 isl_basic_set_free(eq);
2347 return maff;
2348 error:
2349 isl_basic_set_free(eq);
2350 isl_multi_aff_free(maff);
2351 return NULL;
2352 }
2353
2354 __isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
2355 isl_int f)
2356 {
2357 int i;
2358
2359 maff = isl_multi_aff_cow(maff);
2360 if (!maff)
2361 return NULL;
2362
2363 for (i = 0; i < maff->n; ++i) {
2364 maff->p[i] = isl_aff_scale(maff->p[i], f);
2365 if (!maff->p[i])
2366 return isl_multi_aff_free(maff);
2367 }
2368
2369 return maff;
2370 }
2371
2372 __isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
2373 __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
2374 {
2375 maff1 = isl_multi_aff_add(maff1, maff2);
2376 maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
2377 return maff1;
2378 }
2379
2380 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
2381 {
2382 if (!maff)
2383 return -1;
2384
2385 return 0;
2386 }
2387
2388 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
2389 __isl_keep isl_multi_aff *maff2)
2390 {
2391 int i;
2392 int equal;
2393
2394 if (!maff1 || !maff2)
2395 return -1;
2396 if (maff1->n != maff2->n)
2397 return 0;
2398 equal = isl_space_is_equal(maff1->space, maff2->space);
2399 if (equal < 0 || !equal)
2400 return equal;
2401
2402 for (i = 0; i < maff1->n; ++i) {
2403 equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
2404 if (equal < 0 || !equal)
2405 return equal;
2406 }
2407
2408 return 1;
2409 }
2410
2411 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
2412 __isl_take isl_multi_aff *maff,
2413 enum isl_dim_type type, unsigned pos, const char *s)
2414 {
2415 int i;
2416
2417 maff = isl_multi_aff_cow(maff);
2418 if (!maff)
2419 return NULL;
2420
2421 maff->space = isl_space_set_dim_name(maff->space, type, pos, s);
2422 if (!maff->space)
2423 return isl_multi_aff_free(maff);
2424
2425 if (type == isl_dim_out)
2426 return maff;
2427 for (i = 0; i < maff->n; ++i) {
2428 maff->p[i] = isl_aff_set_dim_name(maff->p[i], type, pos, s);
2429 if (!maff->p[i])
2430 return isl_multi_aff_free(maff);
2431 }
2432
2433 return maff;
2434 }
2435
2436 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff,
2437 enum isl_dim_type type, unsigned first, unsigned n)
2438 {
2439 int i;
2440
2441 maff = isl_multi_aff_cow(maff);
2442 if (!maff)
2443 return NULL;
2444
2445 maff->space = isl_space_drop_dims(maff->space, type, first, n);
2446 if (!maff->space)
2447 return isl_multi_aff_free(maff);
2448
2449 if (type == isl_dim_out) {
2450 for (i = 0; i < n; ++i)
2451 isl_aff_free(maff->p[first + i]);
2452 for (i = first; i + n < maff->n; ++i)
2453 maff->p[i] = maff->p[i + n];
2454 maff->n -= n;
2455 return maff;
2456 }
2457
2458 for (i = 0; i < maff->n; ++i) {
2459 maff->p[i] = isl_aff_drop_dims(maff->p[i], type, first, n);
2460 if (!maff->p[i])
2461 return isl_multi_aff_free(maff);
2462 }
2463
2464 return maff;
2465 }
2466
2467 /* Return the set of domain elements where "ma1" is lexicographically
2468 * smaller than or equal to "ma2".
2469 */
2470 __isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
2471 __isl_take isl_multi_aff *ma2)
2472 {
2473 return isl_multi_aff_lex_ge_set(ma2, ma1);
2474 }
2475
2476 /* Return the set of domain elements where "ma1" is lexicographically
2477 * greater than or equal to "ma2".
2478 */
2479 __isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
2480 __isl_take isl_multi_aff *ma2)
2481 {
2482 isl_space *space;
2483 isl_map *map1, *map2;
2484 isl_map *map, *ge;
2485
2486 map1 = isl_map_from_multi_aff(ma1);
2487 map2 = isl_map_from_multi_aff(ma2);
2488 map = isl_map_range_product(map1, map2);
2489 space = isl_space_range(isl_map_get_space(map));
2490 space = isl_space_domain(isl_space_unwrap(space));
2491 ge = isl_map_lex_ge(space);
2492 map = isl_map_intersect_range(map, isl_map_wrap(ge));
2493
2494 return isl_map_domain(map);
2495 }
2496
2497 #undef PW
2498 #define PW isl_pw_multi_aff
2499 #undef EL
2500 #define EL isl_multi_aff
2501 #undef EL_IS_ZERO
2502 #define EL_IS_ZERO is_empty
2503 #undef ZERO
2504 #define ZERO empty
2505 #undef IS_ZERO
2506 #define IS_ZERO is_empty
2507 #undef FIELD
2508 #define FIELD maff
2509 #undef DEFAULT_IS_ZERO
2510 #define DEFAULT_IS_ZERO 0
2511
2512 #define NO_NEG
2513 #define NO_EVAL
2514 #define NO_OPT
2515 #define NO_INVOLVES_DIMS
2516 #define NO_MOVE_DIMS
2517 #define NO_INSERT_DIMS
2518 #define NO_LIFT
2519 #define NO_MORPH
2520
2521 #include <isl_pw_templ.c>
2522
2523 #undef UNION
2524 #define UNION isl_union_pw_multi_aff
2525 #undef PART
2526 #define PART isl_pw_multi_aff
2527 #undef PARTS
2528 #define PARTS pw_multi_aff
2529 #define ALIGN_DOMAIN
2530
2531 #define NO_EVAL
2532
2533 #include <isl_union_templ.c>
2534
2535 /* Given a function "cmp" that returns the set of elements where
2536 * "ma1" is "better" than "ma2", return the intersection of this
2537 * set with "dom1" and "dom2".
2538 */
2539 static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1,
2540 __isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1,
2541 __isl_keep isl_multi_aff *ma2,
2542 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
2543 __isl_take isl_multi_aff *ma2))
2544 {
2545 isl_set *common;
2546 isl_set *better;
2547 int is_empty;
2548
2549 common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2));
2550 is_empty = isl_set_plain_is_empty(common);
2551 if (is_empty >= 0 && is_empty)
2552 return common;
2553 if (is_empty < 0)
2554 return isl_set_free(common);
2555 better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2));
2556 better = isl_set_intersect(common, better);
2557
2558 return better;
2559 }
2560
2561 /* Given a function "cmp" that returns the set of elements where
2562 * "ma1" is "better" than "ma2", return a piecewise multi affine
2563 * expression defined on the union of the definition domains
2564 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
2565 * "pma2" on each cell. If only one of the two input functions
2566 * is defined on a given cell, then it is considered the best.
2567 */
2568 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt(
2569 __isl_take isl_pw_multi_aff *pma1,
2570 __isl_take isl_pw_multi_aff *pma2,
2571 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
2572 __isl_take isl_multi_aff *ma2))
2573 {
2574 int i, j, n;
2575 isl_pw_multi_aff *res = NULL;
2576 isl_ctx *ctx;
2577 isl_set *set = NULL;
2578
2579 if (!pma1 || !pma2)
2580 goto error;
2581
2582 ctx = isl_space_get_ctx(pma1->dim);
2583 if (!isl_space_is_equal(pma1->dim, pma2->dim))
2584 isl_die(ctx, isl_error_invalid,
2585 "arguments should live in the same space", goto error);
2586
2587 if (isl_pw_multi_aff_is_empty(pma1)) {
2588 isl_pw_multi_aff_free(pma1);
2589 return pma2;
2590 }
2591
2592 if (isl_pw_multi_aff_is_empty(pma2)) {
2593 isl_pw_multi_aff_free(pma2);
2594 return pma1;
2595 }
2596
2597 n = 2 * (pma1->n + 1) * (pma2->n + 1);
2598 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n);
2599
2600 for (i = 0; i < pma1->n; ++i) {
2601 set = isl_set_copy(pma1->p[i].set);
2602 for (j = 0; j < pma2->n; ++j) {
2603 isl_set *better;
2604 int is_empty;
2605
2606 better = shared_and_better(pma2->p[j].set,
2607 pma1->p[i].set, pma2->p[j].maff,
2608 pma1->p[i].maff, cmp);
2609 is_empty = isl_set_plain_is_empty(better);
2610 if (is_empty < 0 || is_empty) {
2611 isl_set_free(better);
2612 if (is_empty < 0)
2613 goto error;
2614 continue;
2615 }
2616 set = isl_set_subtract(set, isl_set_copy(better));
2617
2618 res = isl_pw_multi_aff_add_piece(res, better,
2619 isl_multi_aff_copy(pma2->p[j].maff));
2620 }
2621 res = isl_pw_multi_aff_add_piece(res, set,
2622 isl_multi_aff_copy(pma1->p[i].maff));
2623 }
2624
2625 for (j = 0; j < pma2->n; ++j) {
2626 set = isl_set_copy(pma2->p[j].set);
2627 for (i = 0; i < pma1->n; ++i)
2628 set = isl_set_subtract(set,
2629 isl_set_copy(pma1->p[i].set));
2630 res = isl_pw_multi_aff_add_piece(res, set,
2631 isl_multi_aff_copy(pma2->p[j].maff));
2632 }
2633
2634 isl_pw_multi_aff_free(pma1);
2635 isl_pw_multi_aff_free(pma2);
2636
2637 return res;
2638 error:
2639 isl_pw_multi_aff_free(pma1);
2640 isl_pw_multi_aff_free(pma2);
2641 isl_set_free(set);
2642 return isl_pw_multi_aff_free(res);
2643 }
2644
2645 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
2646 __isl_take isl_pw_multi_aff *pma1,
2647 __isl_take isl_pw_multi_aff *pma2)
2648 {
2649 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_ge_set);
2650 }
2651
2652 /* Given two piecewise multi affine expressions, return a piecewise
2653 * multi-affine expression defined on the union of the definition domains
2654 * of the inputs that is equal to the lexicographic maximum of the two
2655 * inputs on each cell. If only one of the two inputs is defined on
2656 * a given cell, then it is considered to be the maximum.
2657 */
2658 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
2659 __isl_take isl_pw_multi_aff *pma1,
2660 __isl_take isl_pw_multi_aff *pma2)
2661 {
2662 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2663 &pw_multi_aff_union_lexmax);
2664 }
2665
2666 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
2667 __isl_take isl_pw_multi_aff *pma1,
2668 __isl_take isl_pw_multi_aff *pma2)
2669 {
2670 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_set);
2671 }
2672
2673 /* Given two piecewise multi affine expressions, return a piecewise
2674 * multi-affine expression defined on the union of the definition domains
2675 * of the inputs that is equal to the lexicographic minimum of the two
2676 * inputs on each cell. If only one of the two inputs is defined on
2677 * a given cell, then it is considered to be the minimum.
2678 */
2679 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
2680 __isl_take isl_pw_multi_aff *pma1,
2681 __isl_take isl_pw_multi_aff *pma2)
2682 {
2683 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2684 &pw_multi_aff_union_lexmin);
2685 }
2686
2687 static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
2688 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2689 {
2690 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
2691 &isl_multi_aff_add);
2692 }
2693
2694 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
2695 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2696 {
2697 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2698 &pw_multi_aff_add);
2699 }
2700
2701 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
2702 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2703 {
2704 return isl_pw_multi_aff_union_add_(pma1, pma2);
2705 }
2706
2707 /* Given two piecewise multi-affine expressions A -> B and C -> D,
2708 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
2709 */
2710 static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
2711 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2712 {
2713 int i, j, n;
2714 isl_space *space;
2715 isl_pw_multi_aff *res;
2716
2717 if (!pma1 || !pma2)
2718 goto error;
2719
2720 n = pma1->n * pma2->n;
2721 space = isl_space_product(isl_space_copy(pma1->dim),
2722 isl_space_copy(pma2->dim));
2723 res = isl_pw_multi_aff_alloc_size(space, n);
2724
2725 for (i = 0; i < pma1->n; ++i) {
2726 for (j = 0; j < pma2->n; ++j) {
2727 isl_set *domain;
2728 isl_multi_aff *ma;
2729
2730 domain = isl_set_product(isl_set_copy(pma1->p[i].set),
2731 isl_set_copy(pma2->p[j].set));
2732 ma = isl_multi_aff_product(
2733 isl_multi_aff_copy(pma1->p[i].maff),
2734 isl_multi_aff_copy(pma2->p[i].maff));
2735 res = isl_pw_multi_aff_add_piece(res, domain, ma);
2736 }
2737 }
2738
2739 isl_pw_multi_aff_free(pma1);
2740 isl_pw_multi_aff_free(pma2);
2741 return res;
2742 error:
2743 isl_pw_multi_aff_free(pma1);
2744 isl_pw_multi_aff_free(pma2);
2745 return NULL;
2746 }
2747
2748 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
2749 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2750 {
2751 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2752 &pw_multi_aff_product);
2753 }
2754
2755 /* Construct a map mapping the domain of the piecewise multi-affine expression
2756 * to its range, with each dimension in the range equated to the
2757 * corresponding affine expression on its cell.
2758 */
2759 __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
2760 {
2761 int i;
2762 isl_map *map;
2763
2764 if (!pma)
2765 return NULL;
2766
2767 map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
2768
2769 for (i = 0; i < pma->n; ++i) {
2770 isl_multi_aff *maff;
2771 isl_basic_map *bmap;
2772 isl_map *map_i;
2773
2774 maff = isl_multi_aff_copy(pma->p[i].maff);
2775 bmap = isl_basic_map_from_multi_aff(maff);
2776 map_i = isl_map_from_basic_map(bmap);
2777 map_i = isl_map_intersect_domain(map_i,
2778 isl_set_copy(pma->p[i].set));
2779 map = isl_map_union_disjoint(map, map_i);
2780 }
2781
2782 isl_pw_multi_aff_free(pma);
2783 return map;
2784 }
2785
2786 __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
2787 {
2788 if (!isl_space_is_set(pma->dim))
2789 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
2790 "isl_pw_multi_aff cannot be converted into an isl_set",
2791 return isl_pw_multi_aff_free(pma));
2792
2793 return isl_map_from_pw_multi_aff(pma);
2794 }
2795
2796 /* Given a basic map with a single output dimension that is defined
2797 * in terms of the parameters and input dimensions using an equality,
2798 * extract an isl_aff that expresses the output dimension in terms
2799 * of the parameters and input dimensions.
2800 *
2801 * Since some applications expect the result of isl_pw_multi_aff_from_map
2802 * to only contain integer affine expressions, we compute the floor
2803 * of the expression before returning.
2804 *
2805 * This function shares some similarities with
2806 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
2807 */
2808 static __isl_give isl_aff *extract_isl_aff_from_basic_map(
2809 __isl_take isl_basic_map *bmap)
2810 {
2811 int i;
2812 unsigned offset;
2813 unsigned total;
2814 isl_local_space *ls;
2815 isl_aff *aff;
2816
2817 if (!bmap)
2818 return NULL;
2819 if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
2820 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
2821 "basic map should have a single output dimension",
2822 goto error);
2823 offset = isl_basic_map_offset(bmap, isl_dim_out);
2824 total = isl_basic_map_total_dim(bmap);
2825 for (i = 0; i < bmap->n_eq; ++i) {
2826 if (isl_int_is_zero(bmap->eq[i][offset]))
2827 continue;
2828 if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
2829 1 + total - (offset + 1)) != -1)
2830 continue;
2831 break;
2832 }
2833 if (i >= bmap->n_eq)
2834 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
2835 "unable to find suitable equality", goto error);
2836 ls = isl_basic_map_get_local_space(bmap);
2837 aff = isl_aff_alloc(isl_local_space_domain(ls));
2838 if (!aff)
2839 goto error;
2840 if (isl_int_is_neg(bmap->eq[i][offset]))
2841 isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
2842 else
2843 isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
2844 isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
2845 isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
2846 isl_basic_map_free(bmap);
2847
2848 aff = isl_aff_remove_unused_divs(aff);
2849 aff = isl_aff_floor(aff);
2850 return aff;
2851 error:
2852 isl_basic_map_free(bmap);
2853 return NULL;
2854 }
2855
2856 /* Given a basic map where each output dimension is defined
2857 * in terms of the parameters and input dimensions using an equality,
2858 * extract an isl_multi_aff that expresses the output dimensions in terms
2859 * of the parameters and input dimensions.
2860 */
2861 static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
2862 __isl_take isl_basic_map *bmap)
2863 {
2864 int i;
2865 unsigned n_out;
2866 isl_multi_aff *ma;
2867
2868 if (!bmap)
2869 return NULL;
2870
2871 ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
2872 n_out = isl_basic_map_dim(bmap, isl_dim_out);
2873
2874 for (i = 0; i < n_out; ++i) {
2875 isl_basic_map *bmap_i;
2876 isl_aff *aff;
2877
2878 bmap_i = isl_basic_map_copy(bmap);
2879 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
2880 i + 1, n_out - (1 + i));
2881 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
2882 aff = extract_isl_aff_from_basic_map(bmap_i);
2883 ma = isl_multi_aff_set_aff(ma, i, aff);
2884 }
2885
2886 isl_basic_map_free(bmap);
2887
2888 return ma;
2889 }
2890
2891 /* Create an isl_pw_multi_aff that is equivalent to
2892 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
2893 * The given basic map is such that each output dimension is defined
2894 * in terms of the parameters and input dimensions using an equality.
2895 */
2896 static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
2897 __isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
2898 {
2899 isl_multi_aff *ma;
2900
2901 ma = extract_isl_multi_aff_from_basic_map(bmap);
2902 return isl_pw_multi_aff_alloc(domain, ma);
2903 }
2904
2905 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
2906 * This obivously only works if the input "map" is single-valued.
2907 * If so, we compute the lexicographic minimum of the image in the form
2908 * of an isl_pw_multi_aff. Since the image is unique, it is equal
2909 * to its lexicographic minimum.
2910 * If the input is not single-valued, we produce an error.
2911 *
2912 * As a special case, we first check if all output dimensions are uniquely
2913 * defined in terms of the parameters and input dimensions over the entire
2914 * domain. If so, we extract the desired isl_pw_multi_aff directly
2915 * from the affine hull of "map" and its domain.
2916 */
2917 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
2918 {
2919 int i;
2920 int sv;
2921 isl_pw_multi_aff *pma;
2922 isl_basic_map *hull;
2923
2924 if (!map)
2925 return NULL;
2926
2927 hull = isl_map_affine_hull(isl_map_copy(map));
2928 sv = isl_basic_map_plain_is_single_valued(hull);
2929 if (sv >= 0 && sv)
2930 return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
2931 isl_basic_map_free(hull);
2932 if (sv < 0)
2933 goto error;
2934
2935 sv = isl_map_is_single_valued(map);
2936 if (sv < 0)
2937 goto error;
2938 if (!sv)
2939 isl_die(isl_map_get_ctx(map), isl_error_invalid,
2940 "map is not single-valued", goto error);
2941 map = isl_map_make_disjoint(map);
2942 if (!map)
2943 return NULL;
2944
2945 pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
2946
2947 for (i = 0; i < map->n; ++i) {
2948 isl_pw_multi_aff *pma_i;
2949 isl_basic_map *bmap;
2950 bmap = isl_basic_map_copy(map->p[i]);
2951 pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
2952 pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
2953 }
2954
2955 isl_map_free(map);
2956 return pma;
2957 error:
2958 isl_map_free(map);
2959 return NULL;
2960 }
2961
2962 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
2963 {
2964 return isl_pw_multi_aff_from_map(set);
2965 }
2966
2967 /* Return the piecewise affine expression "set ? 1 : 0".
2968 */
2969 __isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
2970 {
2971 isl_pw_aff *pa;
2972 isl_space *space = isl_set_get_space(set);
2973 isl_local_space *ls = isl_local_space_from_space(space);
2974 isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
2975 isl_aff *one = isl_aff_zero_on_domain(ls);
2976
2977 one = isl_aff_add_constant_si(one, 1);
2978 pa = isl_pw_aff_alloc(isl_set_copy(set), one);
2979 set = isl_set_complement(set);
2980 pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
2981
2982 return pa;
2983 }
2984
2985 /* Plug in "subs" for dimension "type", "pos" of "aff".
2986 *
2987 * Let i be the dimension to replace and let "subs" be of the form
2988 *
2989 * f/d
2990 *
2991 * and "aff" of the form
2992 *
2993 * (a i + g)/m
2994 *
2995 * The result is
2996 *
2997 * (a f + d g')/(m d)
2998 *
2999 * where g' is the result of plugging in "subs" in each of the integer
3000 * divisions in g.
3001 */
3002 __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
3003 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
3004 {
3005 isl_ctx *ctx;
3006 isl_int v;
3007
3008 aff = isl_aff_cow(aff);
3009 if (!aff || !subs)
3010 return isl_aff_free(aff);
3011
3012 ctx = isl_aff_get_ctx(aff);
3013 if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
3014 isl_die(ctx, isl_error_invalid,
3015 "spaces don't match", return isl_aff_free(aff));
3016 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
3017 isl_die(ctx, isl_error_unsupported,
3018 "cannot handle divs yet", return isl_aff_free(aff));
3019
3020 aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
3021 if (!aff->ls)
3022 return isl_aff_free(aff);
3023
3024 aff->v = isl_vec_cow(aff->v);
3025 if (!aff->v)
3026 return isl_aff_free(aff);
3027
3028 pos += isl_local_space_offset(aff->ls, type);
3029
3030 isl_int_init(v);
3031 isl_int_set(v, aff->v->el[1 + pos]);
3032 isl_int_set_si(aff->v->el[1 + pos], 0);
3033 isl_seq_combine(aff->v->el + 1, subs->v->el[0], aff->v->el + 1,
3034 v, subs->v->el + 1, subs->v->size - 1);
3035 isl_int_mul(aff->v->el[0], aff->v->el[0], subs->v->el[0]);
3036 isl_int_clear(v);
3037
3038 return aff;
3039 }
3040
3041 /* Plug in "subs" for dimension "type", "pos" in each of the affine
3042 * expressions in "maff".
3043 */
3044 __isl_give isl_multi_aff *isl_multi_aff_substitute(
3045 __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
3046 __isl_keep isl_aff *subs)
3047 {
3048 int i;
3049
3050 maff = isl_multi_aff_cow(maff);
3051 if (!maff || !subs)
3052 return isl_multi_aff_free(maff);
3053
3054 if (type == isl_dim_in)
3055 type = isl_dim_set;
3056
3057 for (i = 0; i < maff->n; ++i) {
3058 maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
3059 if (!maff->p[i])
3060 return isl_multi_aff_free(maff);
3061 }
3062
3063 return maff;
3064 }
3065
3066 /* Plug in "subs" for dimension "type", "pos" of "pma".
3067 *
3068 * pma is of the form
3069 *
3070 * A_i(v) -> M_i(v)
3071 *
3072 * while subs is of the form
3073 *
3074 * v' = B_j(v) -> S_j
3075 *
3076 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
3077 * has a contribution in the result, in particular
3078 *
3079 * C_ij(S_j) -> M_i(S_j)
3080 *
3081 * Note that plugging in S_j in C_ij may also result in an empty set
3082 * and this contribution should simply be discarded.
3083 */
3084 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
3085 __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
3086 __isl_keep isl_pw_aff *subs)
3087 {
3088 int i, j, n;
3089 isl_pw_multi_aff *res;
3090
3091 if (!pma || !subs)
3092 return isl_pw_multi_aff_free(pma);
3093
3094 n = pma->n * subs->n;
3095 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
3096
3097 for (i = 0; i < pma->n; ++i) {
3098 for (j = 0; j < subs->n; ++j) {
3099 isl_set *common;
3100 isl_multi_aff *res_ij;
3101 common = isl_set_intersect(
3102 isl_set_copy(pma->p[i].set),
3103 isl_set_copy(subs->p[j].set));
3104 common = isl_set_substitute(common,
3105 type, pos, subs->p[j].aff);
3106 if (isl_set_plain_is_empty(common)) {
3107 isl_set_free(common);
3108 continue;
3109 }
3110
3111 res_ij = isl_multi_aff_substitute(
3112 isl_multi_aff_copy(pma->p[i].maff),
3113 type, pos, subs->p[j].aff);
3114
3115 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
3116 }
3117 }
3118
3119 isl_pw_multi_aff_free(pma);
3120 return res;
3121 }
3122
3123 /* Extend the local space of "dst" to include the divs
3124 * in the local space of "src".
3125 */
3126 __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
3127 __isl_keep isl_aff *src)
3128 {
3129 isl_ctx *ctx;
3130 int *exp1 = NULL;
3131 int *exp2 = NULL;
3132 isl_mat *div;
3133
3134 if (!src || !dst)
3135 return isl_aff_free(dst);
3136
3137 ctx = isl_aff_get_ctx(src);
3138 if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
3139 isl_die(ctx, isl_error_invalid,
3140 "spaces don't match", goto error);
3141
3142 if (src->ls->div->n_row == 0)
3143 return dst;
3144
3145 exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
3146 exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
3147 if (!exp1 || !exp2)
3148 goto error;
3149
3150 div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
3151 dst = isl_aff_expand_divs(dst, div, exp2);
3152 free(exp1);
3153 free(exp2);
3154
3155 return dst;
3156 error:
3157 free(exp1);
3158 free(exp2);
3159 return isl_aff_free(dst);
3160 }
3161
3162 /* Adjust the local spaces of the affine expressions in "maff"
3163 * such that they all have the save divs.
3164 */
3165 __isl_give isl_multi_aff *isl_multi_aff_align_divs(
3166 __isl_take isl_multi_aff *maff)
3167 {
3168 int i;
3169
3170 if (!maff)
3171 return NULL;
3172 if (maff->n == 0)
3173 return maff;
3174 maff = isl_multi_aff_cow(maff);
3175 if (!maff)
3176 return NULL;
3177
3178 for (i = 1; i < maff->n; ++i)
3179 maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
3180 for (i = 1; i < maff->n; ++i) {
3181 maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
3182 if (!maff->p[i])
3183 return isl_multi_aff_free(maff);
3184 }
3185
3186 return maff;
3187 }
3188
3189 __isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
3190 {
3191 aff = isl_aff_cow(aff);
3192 if (!aff)
3193 return NULL;
3194
3195 aff->ls = isl_local_space_lift(aff->ls);
3196 if (!aff->ls)
3197 return isl_aff_free(aff);
3198
3199 return aff;
3200 }
3201
3202 /* Lift "maff" to a space with extra dimensions such that the result
3203 * has no more existentially quantified variables.
3204 * If "ls" is not NULL, then *ls is assigned the local space that lies
3205 * at the basis of the lifting applied to "maff".
3206 */
3207 __isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
3208 __isl_give isl_local_space **ls)
3209 {
3210 int i;
3211 isl_space *space;
3212 unsigned n_div;
3213
3214 if (ls)
3215 *ls = NULL;
3216
3217 if (!maff)
3218 return NULL;
3219
3220 if (maff->n == 0) {
3221 if (ls) {
3222 isl_space *space = isl_multi_aff_get_domain_space(maff);
3223 *ls = isl_local_space_from_space(space);
3224 if (!*ls)
3225 return isl_multi_aff_free(maff);
3226 }
3227 return maff;
3228 }
3229
3230 maff = isl_multi_aff_cow(maff);
3231 maff = isl_multi_aff_align_divs(maff);
3232 if (!maff)
3233 return NULL;
3234
3235 n_div = isl_aff_dim(maff->p[0], isl_dim_div);
3236 space = isl_multi_aff_get_space(maff);
3237 space = isl_space_lift(isl_space_domain(space), n_div);
3238 space = isl_space_extend_domain_with_range(space,
3239 isl_multi_aff_get_space(maff));
3240 if (!space)
3241 return isl_multi_aff_free(maff);
3242 isl_space_free(maff->space);
3243 maff->space = space;
3244
3245 if (ls) {
3246 *ls = isl_aff_get_domain_local_space(maff->p[0]);
3247 if (!*ls)
3248 return isl_multi_aff_free(maff);
3249 }
3250
3251 for (i = 0; i < maff->n; ++i) {
3252 maff->p[i] = isl_aff_lift(maff->p[i]);
3253 if (!maff->p[i])
3254 goto error;
3255 }
3256
3257 return maff;
3258 error:
3259 if (ls)
3260 isl_local_space_free(*ls);
3261 return isl_multi_aff_free(maff);
3262 }
3263
3264
3265 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
3266 */
3267 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3268 __isl_keep isl_pw_multi_aff *pma, int pos)
3269 {
3270 int i;
3271 int n_out;
3272 isl_space *space;
3273 isl_pw_aff *pa;
3274
3275 if (!pma)
3276 return NULL;
3277
3278 n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
3279 if (pos < 0 || pos >= n_out)
3280 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3281 "index out of bounds", return NULL);
3282
3283 space = isl_pw_multi_aff_get_space(pma);
3284 space = isl_space_drop_dims(space, isl_dim_out,
3285 pos + 1, n_out - pos - 1);
3286 space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
3287
3288 pa = isl_pw_aff_alloc_size(space, pma->n);
3289 for (i = 0; i < pma->n; ++i) {
3290 isl_aff *aff;
3291 aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
3292 pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
3293 }
3294
3295 return pa;
3296 }
3297
3298 /* Return an isl_pw_multi_aff with the given "set" as domain and
3299 * an unnamed zero-dimensional range.
3300 */
3301 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3302 __isl_take isl_set *set)
3303 {
3304 isl_multi_aff *ma;
3305 isl_space *space;
3306
3307 space = isl_set_get_space(set);
3308 space = isl_space_from_domain(space);
3309 ma = isl_multi_aff_zero(space);
3310 return isl_pw_multi_aff_alloc(set, ma);
3311 }
3312
3313 /* Add an isl_pw_multi_aff with the given "set" as domain and
3314 * an unnamed zero-dimensional range to *user.
3315 */
3316 static int add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user)
3317 {
3318 isl_union_pw_multi_aff **upma = user;
3319 isl_pw_multi_aff *pma;
3320
3321 pma = isl_pw_multi_aff_from_domain(set);
3322 *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
3323
3324 return 0;
3325 }
3326
3327 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
3328 * an unnamed zero-dimensional range.
3329 */
3330 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain(
3331 __isl_take isl_union_set *uset)
3332 {
3333 isl_space *space;
3334 isl_union_pw_multi_aff *upma;
3335
3336 if (!uset)
3337 return NULL;
3338
3339 space = isl_union_set_get_space(uset);
3340 upma = isl_union_pw_multi_aff_empty(space);
3341
3342 if (isl_union_set_foreach_set(uset,
3343 &add_pw_multi_aff_from_domain, &upma) < 0)
3344 goto error;
3345
3346 isl_union_set_free(uset);
3347 return upma;
3348 error:
3349 isl_union_set_free(uset);
3350 isl_union_pw_multi_aff_free(upma);
3351 return NULL;
3352 }
3353
3354 /* Convert "pma" to an isl_map and add it to *umap.
3355 */
3356 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
3357 {
3358 isl_union_map **umap = user;
3359 isl_map *map;
3360
3361 map = isl_map_from_pw_multi_aff(pma);
3362 *umap = isl_union_map_add_map(*umap, map);
3363
3364 return 0;
3365 }
3366
3367 /* Construct a union map mapping the domain of the union
3368 * piecewise multi-affine expression to its range, with each dimension
3369 * in the range equated to the corresponding affine expression on its cell.
3370 */
3371 __isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff(
3372 __isl_take isl_union_pw_multi_aff *upma)
3373 {
3374 isl_space *space;
3375 isl_union_map *umap;
3376
3377 if (!upma)
3378 return NULL;
3379
3380 space = isl_union_pw_multi_aff_get_space(upma);
3381 umap = isl_union_map_empty(space);
3382
3383 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
3384 &map_from_pw_multi_aff, &umap) < 0)
3385 goto error;
3386
3387 isl_union_pw_multi_aff_free(upma);
3388 return umap;
3389 error:
3390 isl_union_pw_multi_aff_free(upma);
3391 isl_union_map_free(umap);
3392 return NULL;
3393 }
3394
3395 /* Local data for bin_entry and the callback "fn".
3396 */
3397 struct isl_union_pw_multi_aff_bin_data {
3398 isl_union_pw_multi_aff *upma2;
3399 isl_union_pw_multi_aff *res;
3400 isl_pw_multi_aff *pma;
3401 int (*fn)(void **entry, void *user);
3402 };
3403
3404 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
3405 * and call data->fn for each isl_pw_multi_aff in data->upma2.
3406 */
3407 static int bin_entry(void **entry, void *user)
3408 {
3409 struct isl_union_pw_multi_aff_bin_data *data = user;
3410 isl_pw_multi_aff *pma = *entry;
3411
3412 data->pma = pma;
3413 if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
3414 data->fn, data) < 0)
3415 return -1;
3416
3417 return 0;
3418 }
3419
3420 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
3421 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
3422 * passed as user field) and the isl_pw_multi_aff from upma2 is available
3423 * as *entry. The callback should adjust data->res if desired.
3424 */
3425 static __isl_give isl_union_pw_multi_aff *bin_op(
3426 __isl_take isl_union_pw_multi_aff *upma1,
3427 __isl_take isl_union_pw_multi_aff *upma2,
3428 int (*fn)(void **entry, void *user))
3429 {
3430 isl_space *space;
3431 struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
3432
3433 space = isl_union_pw_multi_aff_get_space(upma2);
3434 upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
3435 space = isl_union_pw_multi_aff_get_space(upma1);
3436 upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
3437
3438 if (!upma1 || !upma2)
3439 goto error;
3440
3441 data.upma2 = upma2;
3442 data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
3443 upma1->table.n);
3444 if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
3445 &bin_entry, &data) < 0)
3446 goto error;
3447
3448 isl_union_pw_multi_aff_free(upma1);
3449 isl_union_pw_multi_aff_free(upma2);
3450 return data.res;
3451 error:
3452 isl_union_pw_multi_aff_free(upma1);
3453 isl_union_pw_multi_aff_free(upma2);
3454 isl_union_pw_multi_aff_free(data.res);
3455 return NULL;
3456 }
3457
3458 /* Given two isl_multi_affs A -> B and C -> D,
3459 * construct an isl_multi_aff (A * C) -> (B, D).
3460 */
3461 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3462 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
3463 {
3464 int i, n1, n2;
3465 isl_aff *aff;
3466 isl_space *space;
3467 isl_multi_aff *res;
3468
3469 if (!ma1 || !ma2)
3470 goto error;
3471
3472 space = isl_space_range_product(isl_multi_aff_get_space(ma1),
3473 isl_multi_aff_get_space(ma2));
3474 space = isl_space_flatten_range(space);
3475 res = isl_multi_aff_alloc(space);
3476
3477 n1 = isl_multi_aff_dim(ma1, isl_dim_out);
3478 n2 = isl_multi_aff_dim(ma2, isl_dim_out);
3479
3480 for (i = 0; i < n1; ++i) {
3481 aff = isl_multi_aff_get_aff(ma1, i);
3482 res = isl_multi_aff_set_aff(res, i, aff);
3483 }
3484
3485 for (i = 0; i < n2; ++i) {
3486 aff = isl_multi_aff_get_aff(ma2, i);
3487 res = isl_multi_aff_set_aff(res, n1 + i, aff);
3488 }
3489
3490 isl_multi_aff_free(ma1);
3491 isl_multi_aff_free(ma2);
3492 return res;
3493 error:
3494 isl_multi_aff_free(ma1);
3495 isl_multi_aff_free(ma2);
3496 return NULL;
3497 }
3498
3499 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
3500 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3501 */
3502 static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
3503 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3504 {
3505 isl_space *space;
3506
3507 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
3508 isl_pw_multi_aff_get_space(pma2));
3509 space = isl_space_flatten_range(space);
3510 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
3511 &isl_multi_aff_flat_range_product);
3512 }
3513
3514 /* Given two isl_pw_multi_affs A -> B and C -> D,
3515 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3516 */
3517 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
3518 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3519 {
3520 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3521 &pw_multi_aff_flat_range_product);
3522 }
3523
3524 /* If data->pma and *entry have the same domain space, then compute
3525 * their flat range product and the result to data->res.
3526 */
3527 static int flat_range_product_entry(void **entry, void *user)
3528 {
3529 struct isl_union_pw_multi_aff_bin_data *data = user;
3530 isl_pw_multi_aff *pma2 = *entry;
3531
3532 if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
3533 pma2->dim, isl_dim_in))
3534 return 0;
3535
3536 pma2 = isl_pw_multi_aff_flat_range_product(
3537 isl_pw_multi_aff_copy(data->pma),
3538 isl_pw_multi_aff_copy(pma2));
3539
3540 data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
3541
3542 return 0;
3543 }
3544
3545 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
3546 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
3547 */
3548 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
3549 __isl_take isl_union_pw_multi_aff *upma1,
3550 __isl_take isl_union_pw_multi_aff *upma2)
3551 {
3552 return bin_op(upma1, upma2, &flat_range_product_entry);
3553 }
3554
3555 /* Replace the affine expressions at position "pos" in "pma" by "pa".
3556 * The parameters are assumed to have been aligned.
3557 *
3558 * The implementation essentially performs an isl_pw_*_on_shared_domain,
3559 * except that it works on two different isl_pw_* types.
3560 */
3561 static __isl_give isl_pw_multi_aff *pw_multi_aff_set_pw_aff(
3562 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3563 __isl_take isl_pw_aff *pa)
3564 {
3565 int i, j, n;
3566 isl_pw_multi_aff *res = NULL;
3567
3568 if (!pma || !pa)
3569 goto error;
3570
3571 if (!isl_space_tuple_match(pma->dim, isl_dim_in, pa->dim, isl_dim_in))
3572 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3573 "domains don't match", goto error);
3574 if (pos >= isl_pw_multi_aff_dim(pma, isl_dim_out))
3575 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3576 "index out of bounds", goto error);
3577
3578 n = pma->n * pa->n;
3579 res = isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma), n);
3580
3581 for (i = 0; i < pma->n; ++i) {
3582 for (j = 0; j < pa->n; ++j) {
3583 isl_set *common;
3584 isl_multi_aff *res_ij;
3585 int empty;
3586
3587 common = isl_set_intersect(isl_set_copy(pma->p[i].set),
3588 isl_set_copy(pa->p[j].set));
3589 empty = isl_set_plain_is_empty(common);
3590 if (empty < 0 || empty) {
3591 isl_set_free(common);
3592 if (empty < 0)
3593 goto error;
3594 continue;
3595 }
3596
3597 res_ij = isl_multi_aff_set_aff(
3598 isl_multi_aff_copy(pma->p[i].maff), pos,
3599 isl_aff_copy(pa->p[j].aff));
3600 res_ij = isl_multi_aff_gist(res_ij,
3601 isl_set_copy(common));
3602
3603 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
3604 }
3605 }
3606
3607 isl_pw_multi_aff_free(pma);
3608 isl_pw_aff_free(pa);
3609 return res;
3610 error:
3611 isl_pw_multi_aff_free(pma);
3612 isl_pw_aff_free(pa);
3613 return isl_pw_multi_aff_free(res);
3614 }
3615
3616 /* Replace the affine expressions at position "pos" in "pma" by "pa".
3617 */
3618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3619 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3620 __isl_take isl_pw_aff *pa)
3621 {
3622 if (!pma || !pa)
3623 goto error;
3624 if (isl_space_match(pma->dim, isl_dim_param, pa->dim, isl_dim_param))
3625 return pw_multi_aff_set_pw_aff(pma, pos, pa);
3626 if (!isl_space_has_named_params(pma->dim) ||
3627 !isl_space_has_named_params(pa->dim))
3628 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3629 "unaligned unnamed parameters", goto error);
3630 pma = isl_pw_multi_aff_align_params(pma, isl_pw_aff_get_space(pa));
3631 pa = isl_pw_aff_align_params(pa, isl_pw_multi_aff_get_space(pma));
3632 return pw_multi_aff_set_pw_aff(pma, pos, pa);
3633 error:
3634 isl_pw_multi_aff_free(pma);
3635 isl_pw_aff_free(pa);
3636 return NULL;
3637 }
Integer set library