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isl_aff_ceil: compute ceil(e/m) as floor((e + m - 1)/m)
[isl.git] / isl_aff.c
blobc2e3f532e2b9d8d8d41160c29176e46a09f2cd87
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 /* Return a piecewise affine expression defined on the specified domain
92 * that is equal to zero.
93 */
94 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(__isl_take isl_local_space *ls)
95 {
96 return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls));
97 }
98
99 /* Return an affine expression that is equal to the specified dimension
100 * in "ls".
101 */
102 __isl_give isl_aff *isl_aff_var_on_domain(__isl_take isl_local_space *ls,
103 enum isl_dim_type type, unsigned pos)
104 {
105 isl_space *space;
106 isl_aff *aff;
107
108 if (!ls)
109 return NULL;
110
111 space = isl_local_space_get_space(ls);
112 if (!space)
113 goto error;
114 if (isl_space_is_map(space))
115 isl_die(isl_space_get_ctx(space), isl_error_invalid,
116 "expecting (parameter) set space", goto error);
117 if (pos >= isl_local_space_dim(ls, type))
118 isl_die(isl_space_get_ctx(space), isl_error_invalid,
119 "position out of bounds", goto error);
120
121 isl_space_free(space);
122 aff = isl_aff_alloc(ls);
123 if (!aff)
124 return NULL;
125
126 pos += isl_local_space_offset(aff->ls, type);
127
128 isl_int_set_si(aff->v->el[0], 1);
129 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
130 isl_int_set_si(aff->v->el[1 + pos], 1);
131
132 return aff;
133 error:
134 isl_local_space_free(ls);
135 isl_space_free(space);
136 return NULL;
137 }
138
139 /* Return a piecewise affine expression that is equal to
140 * the specified dimension in "ls".
141 */
142 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(__isl_take isl_local_space *ls,
143 enum isl_dim_type type, unsigned pos)
144 {
145 return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls, type, pos));
146 }
147
148 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
149 {
150 if (!aff)
151 return NULL;
152
153 aff->ref++;
154 return aff;
155 }
156
157 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
158 {
159 if (!aff)
160 return NULL;
161
162 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
163 isl_vec_copy(aff->v));
164 }
165
166 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
167 {
168 if (!aff)
169 return NULL;
170
171 if (aff->ref == 1)
172 return aff;
173 aff->ref--;
174 return isl_aff_dup(aff);
175 }
176
177 void *isl_aff_free(__isl_take isl_aff *aff)
178 {
179 if (!aff)
180 return NULL;
181
182 if (--aff->ref > 0)
183 return NULL;
184
185 isl_local_space_free(aff->ls);
186 isl_vec_free(aff->v);
187
188 free(aff);
189
190 return NULL;
191 }
192
193 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
194 {
195 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
196 }
197
198 /* Externally, an isl_aff has a map space, but internally, the
199 * ls field corresponds to the domain of that space.
200 */
201 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
202 {
203 if (!aff)
204 return 0;
205 if (type == isl_dim_out)
206 return 1;
207 if (type == isl_dim_in)
208 type = isl_dim_set;
209 return isl_local_space_dim(aff->ls, type);
210 }
211
212 __isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
213 {
214 return aff ? isl_local_space_get_space(aff->ls) : NULL;
215 }
216
217 __isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
218 {
219 isl_space *space;
220 if (!aff)
221 return NULL;
222 space = isl_local_space_get_space(aff->ls);
223 space = isl_space_from_domain(space);
224 space = isl_space_add_dims(space, isl_dim_out, 1);
225 return space;
226 }
227
228 __isl_give isl_local_space *isl_aff_get_domain_local_space(
229 __isl_keep isl_aff *aff)
230 {
231 return aff ? isl_local_space_copy(aff->ls) : NULL;
232 }
233
234 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
235 {
236 isl_local_space *ls;
237 if (!aff)
238 return NULL;
239 ls = isl_local_space_copy(aff->ls);
240 ls = isl_local_space_from_domain(ls);
241 ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
242 return ls;
243 }
244
245 /* Externally, an isl_aff has a map space, but internally, the
246 * ls field corresponds to the domain of that space.
247 */
248 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
249 enum isl_dim_type type, unsigned pos)
250 {
251 if (!aff)
252 return NULL;
253 if (type == isl_dim_out)
254 return NULL;
255 if (type == isl_dim_in)
256 type = isl_dim_set;
257 return isl_local_space_get_dim_name(aff->ls, type, pos);
258 }
259
260 __isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
261 __isl_take isl_space *dim)
262 {
263 aff = isl_aff_cow(aff);
264 if (!aff || !dim)
265 goto error;
266
267 aff->ls = isl_local_space_reset_space(aff->ls, dim);
268 if (!aff->ls)
269 return isl_aff_free(aff);
270
271 return aff;
272 error:
273 isl_aff_free(aff);
274 isl_space_free(dim);
275 return NULL;
276 }
277
278 /* Reset the space of "aff". This function is called from isl_pw_templ.c
279 * and doesn't know if the space of an element object is represented
280 * directly or through its domain. It therefore passes along both.
281 */
282 __isl_give isl_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
283 __isl_take isl_space *space, __isl_take isl_space *domain)
284 {
285 isl_space_free(space);
286 return isl_aff_reset_domain_space(aff, domain);
287 }
288
289 /* Reorder the coefficients of the affine expression based
290 * on the given reodering.
291 * The reordering r is assumed to have been extended with the local
292 * variables.
293 */
294 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
295 __isl_take isl_reordering *r, int n_div)
296 {
297 isl_vec *res;
298 int i;
299
300 if (!vec || !r)
301 goto error;
302
303 res = isl_vec_alloc(vec->ctx,
304 2 + isl_space_dim(r->dim, isl_dim_all) + n_div);
305 isl_seq_cpy(res->el, vec->el, 2);
306 isl_seq_clr(res->el + 2, res->size - 2);
307 for (i = 0; i < r->len; ++i)
308 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
309
310 isl_reordering_free(r);
311 isl_vec_free(vec);
312 return res;
313 error:
314 isl_vec_free(vec);
315 isl_reordering_free(r);
316 return NULL;
317 }
318
319 /* Reorder the dimensions of the domain of "aff" according
320 * to the given reordering.
321 */
322 __isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
323 __isl_take isl_reordering *r)
324 {
325 aff = isl_aff_cow(aff);
326 if (!aff)
327 goto error;
328
329 r = isl_reordering_extend(r, aff->ls->div->n_row);
330 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
331 aff->ls->div->n_row);
332 aff->ls = isl_local_space_realign(aff->ls, r);
333
334 if (!aff->v || !aff->ls)
335 return isl_aff_free(aff);
336
337 return aff;
338 error:
339 isl_aff_free(aff);
340 isl_reordering_free(r);
341 return NULL;
342 }
343
344 __isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
345 __isl_take isl_space *model)
346 {
347 if (!aff || !model)
348 goto error;
349
350 if (!isl_space_match(aff->ls->dim, isl_dim_param,
351 model, isl_dim_param)) {
352 isl_reordering *exp;
353
354 model = isl_space_drop_dims(model, isl_dim_in,
355 0, isl_space_dim(model, isl_dim_in));
356 model = isl_space_drop_dims(model, isl_dim_out,
357 0, isl_space_dim(model, isl_dim_out));
358 exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
359 exp = isl_reordering_extend_space(exp,
360 isl_aff_get_domain_space(aff));
361 aff = isl_aff_realign_domain(aff, exp);
362 }
363
364 isl_space_free(model);
365 return aff;
366 error:
367 isl_space_free(model);
368 isl_aff_free(aff);
369 return NULL;
370 }
371
372 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
373 {
374 if (!aff)
375 return -1;
376
377 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
378 }
379
380 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
381 {
382 int equal;
383
384 if (!aff1 || !aff2)
385 return -1;
386
387 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
388 if (equal < 0 || !equal)
389 return equal;
390
391 return isl_vec_is_equal(aff1->v, aff2->v);
392 }
393
394 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
395 {
396 if (!aff)
397 return -1;
398 isl_int_set(*v, aff->v->el[0]);
399 return 0;
400 }
401
402 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
403 {
404 if (!aff)
405 return -1;
406 isl_int_set(*v, aff->v->el[1]);
407 return 0;
408 }
409
410 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
411 enum isl_dim_type type, int pos, isl_int *v)
412 {
413 if (!aff)
414 return -1;
415
416 if (type == isl_dim_out)
417 isl_die(aff->v->ctx, isl_error_invalid,
418 "output/set dimension does not have a coefficient",
419 return -1);
420 if (type == isl_dim_in)
421 type = isl_dim_set;
422
423 if (pos >= isl_local_space_dim(aff->ls, type))
424 isl_die(aff->v->ctx, isl_error_invalid,
425 "position out of bounds", return -1);
426
427 pos += isl_local_space_offset(aff->ls, type);
428 isl_int_set(*v, aff->v->el[1 + pos]);
429
430 return 0;
431 }
432
433 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
434 {
435 aff = isl_aff_cow(aff);
436 if (!aff)
437 return NULL;
438
439 aff->v = isl_vec_cow(aff->v);
440 if (!aff->v)
441 return isl_aff_free(aff);
442
443 isl_int_set(aff->v->el[0], v);
444
445 return aff;
446 }
447
448 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
449 {
450 aff = isl_aff_cow(aff);
451 if (!aff)
452 return NULL;
453
454 aff->v = isl_vec_cow(aff->v);
455 if (!aff->v)
456 return isl_aff_free(aff);
457
458 isl_int_set(aff->v->el[1], v);
459
460 return aff;
461 }
462
463 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
464 {
465 if (isl_int_is_zero(v))
466 return aff;
467
468 aff = isl_aff_cow(aff);
469 if (!aff)
470 return NULL;
471
472 aff->v = isl_vec_cow(aff->v);
473 if (!aff->v)
474 return isl_aff_free(aff);
475
476 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
477
478 return aff;
479 }
480
481 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
482 {
483 isl_int t;
484
485 isl_int_init(t);
486 isl_int_set_si(t, v);
487 aff = isl_aff_add_constant(aff, t);
488 isl_int_clear(t);
489
490 return aff;
491 }
492
493 /* Add "v" to the numerator of the constant term of "aff".
494 */
495 __isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v)
496 {
497 if (isl_int_is_zero(v))
498 return aff;
499
500 aff = isl_aff_cow(aff);
501 if (!aff)
502 return NULL;
503
504 aff->v = isl_vec_cow(aff->v);
505 if (!aff->v)
506 return isl_aff_free(aff);
507
508 isl_int_add(aff->v->el[1], aff->v->el[1], v);
509
510 return aff;
511 }
512
513 /* Add "v" to the numerator of the constant term of "aff".
514 */
515 __isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v)
516 {
517 isl_int t;
518
519 if (v == 0)
520 return aff;
521
522 isl_int_init(t);
523 isl_int_set_si(t, v);
524 aff = isl_aff_add_constant_num(aff, t);
525 isl_int_clear(t);
526
527 return aff;
528 }
529
530 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
531 {
532 aff = isl_aff_cow(aff);
533 if (!aff)
534 return NULL;
535
536 aff->v = isl_vec_cow(aff->v);
537 if (!aff->v)
538 return isl_aff_free(aff);
539
540 isl_int_set_si(aff->v->el[1], v);
541
542 return aff;
543 }
544
545 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
546 enum isl_dim_type type, int pos, isl_int v)
547 {
548 if (!aff)
549 return NULL;
550
551 if (type == isl_dim_out)
552 isl_die(aff->v->ctx, isl_error_invalid,
553 "output/set dimension does not have a coefficient",
554 return isl_aff_free(aff));
555 if (type == isl_dim_in)
556 type = isl_dim_set;
557
558 if (pos >= isl_local_space_dim(aff->ls, type))
559 isl_die(aff->v->ctx, isl_error_invalid,
560 "position out of bounds", return isl_aff_free(aff));
561
562 aff = isl_aff_cow(aff);
563 if (!aff)
564 return NULL;
565
566 aff->v = isl_vec_cow(aff->v);
567 if (!aff->v)
568 return isl_aff_free(aff);
569
570 pos += isl_local_space_offset(aff->ls, type);
571 isl_int_set(aff->v->el[1 + pos], v);
572
573 return aff;
574 }
575
576 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
577 enum isl_dim_type type, int pos, int v)
578 {
579 if (!aff)
580 return NULL;
581
582 if (type == isl_dim_out)
583 isl_die(aff->v->ctx, isl_error_invalid,
584 "output/set dimension does not have a coefficient",
585 return isl_aff_free(aff));
586 if (type == isl_dim_in)
587 type = isl_dim_set;
588
589 if (pos >= isl_local_space_dim(aff->ls, type))
590 isl_die(aff->v->ctx, isl_error_invalid,
591 "position out of bounds", return isl_aff_free(aff));
592
593 aff = isl_aff_cow(aff);
594 if (!aff)
595 return NULL;
596
597 aff->v = isl_vec_cow(aff->v);
598 if (!aff->v)
599 return isl_aff_free(aff);
600
601 pos += isl_local_space_offset(aff->ls, type);
602 isl_int_set_si(aff->v->el[1 + pos], v);
603
604 return aff;
605 }
606
607 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
608 enum isl_dim_type type, int pos, isl_int v)
609 {
610 if (!aff)
611 return NULL;
612
613 if (type == isl_dim_out)
614 isl_die(aff->v->ctx, isl_error_invalid,
615 "output/set dimension does not have a coefficient",
616 return isl_aff_free(aff));
617 if (type == isl_dim_in)
618 type = isl_dim_set;
619
620 if (pos >= isl_local_space_dim(aff->ls, type))
621 isl_die(aff->v->ctx, isl_error_invalid,
622 "position out of bounds", return isl_aff_free(aff));
623
624 aff = isl_aff_cow(aff);
625 if (!aff)
626 return NULL;
627
628 aff->v = isl_vec_cow(aff->v);
629 if (!aff->v)
630 return isl_aff_free(aff);
631
632 pos += isl_local_space_offset(aff->ls, type);
633 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
634
635 return aff;
636 }
637
638 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
639 enum isl_dim_type type, int pos, int v)
640 {
641 isl_int t;
642
643 isl_int_init(t);
644 isl_int_set_si(t, v);
645 aff = isl_aff_add_coefficient(aff, type, pos, t);
646 isl_int_clear(t);
647
648 return aff;
649 }
650
651 __isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
652 {
653 if (!aff)
654 return NULL;
655
656 return isl_local_space_get_div(aff->ls, pos);
657 }
658
659 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
660 {
661 aff = isl_aff_cow(aff);
662 if (!aff)
663 return NULL;
664 aff->v = isl_vec_cow(aff->v);
665 if (!aff->v)
666 return isl_aff_free(aff);
667
668 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
669
670 return aff;
671 }
672
673 /* Remove divs from the local space that do not appear in the affine
674 * expression.
675 * We currently only remove divs at the end.
676 * Some intermediate divs may also not appear directly in the affine
677 * expression, but we would also need to check that no other divs are
678 * defined in terms of them.
679 */
680 __isl_give isl_aff *isl_aff_remove_unused_divs( __isl_take isl_aff *aff)
681 {
682 int pos;
683 int off;
684 int n;
685
686 if (!aff)
687 return NULL;
688
689 n = isl_local_space_dim(aff->ls, isl_dim_div);
690 off = isl_local_space_offset(aff->ls, isl_dim_div);
691
692 pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
693 if (pos == n)
694 return aff;
695
696 aff = isl_aff_cow(aff);
697 if (!aff)
698 return NULL;
699
700 aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
701 aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
702 if (!aff->ls || !aff->v)
703 return isl_aff_free(aff);
704
705 return aff;
706 }
707
708 /* Given two affine expressions "p" of length p_len (including the
709 * denominator and the constant term) and "subs" of length subs_len,
710 * plug in "subs" for the variable at position "pos".
711 * The variables of "subs" and "p" are assumed to match up to subs_len,
712 * but "p" may have additional variables.
713 * "v" is an initialized isl_int that can be used internally.
714 *
715 * In particular, if "p" represents the expression
716 *
717 * (a i + g)/m
718 *
719 * with i the variable at position "pos" and "subs" represents the expression
720 *
721 * f/d
722 *
723 * then the result represents the expression
724 *
725 * (a f + d g)/(m d)
726 *
727 */
728 void isl_seq_substitute(isl_int *p, int pos, isl_int *subs,
729 int p_len, int subs_len, isl_int v)
730 {
731 isl_int_set(v, p[1 + pos]);
732 isl_int_set_si(p[1 + pos], 0);
733 isl_seq_combine(p + 1, subs[0], p + 1, v, subs + 1, subs_len - 1);
734 isl_seq_scale(p + subs_len, p + subs_len, subs[0], p_len - subs_len);
735 isl_int_mul(p[0], p[0], subs[0]);
736 }
737
738 /* Look for any divs in the aff->ls with a denominator equal to one
739 * and plug them into the affine expression and any subsequent divs
740 * that may reference the div.
741 */
742 static __isl_give isl_aff *plug_in_integral_divs(__isl_take isl_aff *aff)
743 {
744 int i, n;
745 int len;
746 isl_int v;
747 isl_vec *vec;
748 isl_local_space *ls;
749 unsigned pos;
750
751 if (!aff)
752 return NULL;
753
754 n = isl_local_space_dim(aff->ls, isl_dim_div);
755 len = aff->v->size;
756 for (i = 0; i < n; ++i) {
757 if (!isl_int_is_one(aff->ls->div->row[i][0]))
758 continue;
759 ls = isl_local_space_copy(aff->ls);
760 ls = isl_local_space_substitute_seq(ls, isl_dim_div, i,
761 aff->ls->div->row[i], len, i + 1);
762 vec = isl_vec_copy(aff->v);
763 vec = isl_vec_cow(vec);
764 if (!ls || !vec)
765 goto error;
766
767 isl_int_init(v);
768
769 pos = isl_local_space_offset(aff->ls, isl_dim_div) + i;
770 isl_seq_substitute(vec->el, pos, aff->ls->div->row[i],
771 len, len, v);
772
773 isl_int_clear(v);
774
775 isl_vec_free(aff->v);
776 aff->v = vec;
777 isl_local_space_free(aff->ls);
778 aff->ls = ls;
779 }
780
781 return aff;
782 error:
783 isl_vec_free(vec);
784 isl_local_space_free(ls);
785 return isl_aff_free(aff);
786 }
787
788 /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
789 *
790 * Even though this function is only called on isl_affs with a single
791 * reference, we are careful to only change aff->v and aff->ls together.
792 */
793 static __isl_give isl_aff *swap_div(__isl_take isl_aff *aff, int a, int b)
794 {
795 unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
796 isl_local_space *ls;
797 isl_vec *v;
798
799 ls = isl_local_space_copy(aff->ls);
800 ls = isl_local_space_swap_div(ls, a, b);
801 v = isl_vec_copy(aff->v);
802 v = isl_vec_cow(v);
803 if (!ls || !v)
804 goto error;
805
806 isl_int_swap(v->el[1 + off + a], v->el[1 + off + b]);
807 isl_vec_free(aff->v);
808 aff->v = v;
809 isl_local_space_free(aff->ls);
810 aff->ls = ls;
811
812 return aff;
813 error:
814 isl_vec_free(v);
815 isl_local_space_free(ls);
816 return isl_aff_free(aff);
817 }
818
819 /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
820 *
821 * We currently do not actually remove div "b", but simply add its
822 * coefficient to that of "a" and then zero it out.
823 */
824 static __isl_give isl_aff *merge_divs(__isl_take isl_aff *aff, int a, int b)
825 {
826 unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
827
828 if (isl_int_is_zero(aff->v->el[1 + off + b]))
829 return aff;
830
831 aff->v = isl_vec_cow(aff->v);
832 if (!aff->v)
833 return isl_aff_free(aff);
834
835 isl_int_add(aff->v->el[1 + off + a],
836 aff->v->el[1 + off + a], aff->v->el[1 + off + b]);
837 isl_int_set_si(aff->v->el[1 + off + b], 0);
838
839 return aff;
840 }
841
842 /* Sort the divs in the local space of "aff" according to
843 * the comparison function "cmp_row" in isl_local_space.c,
844 * combining the coefficients of identical divs.
845 *
846 * Reordering divs does not change the semantics of "aff",
847 * so there is no need to call isl_aff_cow.
848 * Moreover, this function is currently only called on isl_affs
849 * with a single reference.
850 */
851 static __isl_give isl_aff *sort_divs(__isl_take isl_aff *aff)
852 {
853 int i, j, n;
854 unsigned off;
855
856 if (!aff)
857 return NULL;
858
859 off = isl_local_space_offset(aff->ls, isl_dim_div);
860 n = isl_aff_dim(aff, isl_dim_div);
861 for (i = 1; i < n; ++i) {
862 for (j = i - 1; j >= 0; --j) {
863 int cmp = isl_mat_cmp_div(aff->ls->div, j, j + 1);
864 if (cmp < 0)
865 break;
866 if (cmp == 0)
867 aff = merge_divs(aff, j, j + 1);
868 else
869 aff = swap_div(aff, j, j + 1);
870 if (!aff)
871 return NULL;
872 }
873 }
874
875 return aff;
876 }
877
878 /* Normalize the representation of "aff".
879 *
880 * This function should only be called of "new" isl_affs, i.e.,
881 * with only a single reference. We therefore do not need to
882 * worry about affecting other instances.
883 */
884 __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
885 {
886 if (!aff)
887 return NULL;
888 aff->v = isl_vec_normalize(aff->v);
889 if (!aff->v)
890 return isl_aff_free(aff);
891 aff = plug_in_integral_divs(aff);
892 aff = sort_divs(aff);
893 aff = isl_aff_remove_unused_divs(aff);
894 return aff;
895 }
896
897 /* Given f, return floor(f).
898 * If f is an integer expression, then just return f.
899 * If f is a constant, then return the constant floor(f).
900 * Otherwise, if f = g/m, write g = q m + r,
901 * create a new div d = [r/m] and return the expression q + d.
902 * The coefficients in r are taken to lie between -m/2 and m/2.
903 */
904 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
905 {
906 int i;
907 int size;
908 isl_ctx *ctx;
909 isl_vec *div;
910
911 if (!aff)
912 return NULL;
913
914 if (isl_int_is_one(aff->v->el[0]))
915 return aff;
916
917 aff = isl_aff_cow(aff);
918 if (!aff)
919 return NULL;
920
921 aff->v = isl_vec_cow(aff->v);
922 if (!aff->v)
923 return isl_aff_free(aff);
924
925 if (isl_aff_is_cst(aff)) {
926 isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
927 isl_int_set_si(aff->v->el[0], 1);
928 return aff;
929 }
930
931 div = isl_vec_copy(aff->v);
932 div = isl_vec_cow(div);
933 if (!div)
934 return isl_aff_free(aff);
935
936 ctx = isl_aff_get_ctx(aff);
937 isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
938 for (i = 1; i < aff->v->size; ++i) {
939 isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
940 isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
941 if (isl_int_gt(div->el[i], aff->v->el[0])) {
942 isl_int_sub(div->el[i], div->el[i], div->el[0]);
943 isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
944 }
945 }
946
947 aff->ls = isl_local_space_add_div(aff->ls, div);
948 if (!aff->ls)
949 return isl_aff_free(aff);
950
951 size = aff->v->size;
952 aff->v = isl_vec_extend(aff->v, size + 1);
953 if (!aff->v)
954 return isl_aff_free(aff);
955 isl_int_set_si(aff->v->el[0], 1);
956 isl_int_set_si(aff->v->el[size], 1);
957
958 return aff;
959 }
960
961 /* Compute
962 *
963 * aff mod m = aff - m * floor(aff/m)
964 */
965 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
966 {
967 isl_aff *res;
968
969 res = isl_aff_copy(aff);
970 aff = isl_aff_scale_down(aff, m);
971 aff = isl_aff_floor(aff);
972 aff = isl_aff_scale(aff, m);
973 res = isl_aff_sub(res, aff);
974
975 return res;
976 }
977
978 /* Compute
979 *
980 * pwaff mod m = pwaff - m * floor(pwaff/m)
981 */
982 __isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
983 {
984 isl_pw_aff *res;
985
986 res = isl_pw_aff_copy(pwaff);
987 pwaff = isl_pw_aff_scale_down(pwaff, m);
988 pwaff = isl_pw_aff_floor(pwaff);
989 pwaff = isl_pw_aff_scale(pwaff, m);
990 res = isl_pw_aff_sub(res, pwaff);
991
992 return res;
993 }
994
995 /* Given f, return ceil(f).
996 * If f is an integer expression, then just return f.
997 * Otherwise, let f be the expression
998 *
999 * e/m
1000 *
1001 * then return
1002 *
1003 * floor((e + m - 1)/m)
1004 */
1005 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
1006 {
1007 if (!aff)
1008 return NULL;
1009
1010 if (isl_int_is_one(aff->v->el[0]))
1011 return aff;
1012
1013 aff = isl_aff_cow(aff);
1014 if (!aff)
1015 return NULL;
1016 aff->v = isl_vec_cow(aff->v);
1017 if (!aff->v)
1018 return isl_aff_free(aff);
1019
1020 isl_int_add(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
1021 isl_int_sub_ui(aff->v->el[1], aff->v->el[1], 1);
1022 aff = isl_aff_floor(aff);
1023
1024 return aff;
1025 }
1026
1027 /* Apply the expansion computed by isl_merge_divs.
1028 * The expansion itself is given by "exp" while the resulting
1029 * list of divs is given by "div".
1030 */
1031 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
1032 __isl_take isl_mat *div, int *exp)
1033 {
1034 int i, j;
1035 int old_n_div;
1036 int new_n_div;
1037 int offset;
1038
1039 aff = isl_aff_cow(aff);
1040 if (!aff || !div)
1041 goto error;
1042
1043 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1044 new_n_div = isl_mat_rows(div);
1045 if (new_n_div < old_n_div)
1046 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
1047 "not an expansion", goto error);
1048
1049 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
1050 if (!aff->v)
1051 goto error;
1052
1053 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
1054 j = old_n_div - 1;
1055 for (i = new_n_div - 1; i >= 0; --i) {
1056 if (j >= 0 && exp[j] == i) {
1057 if (i != j)
1058 isl_int_swap(aff->v->el[offset + i],
1059 aff->v->el[offset + j]);
1060 j--;
1061 } else
1062 isl_int_set_si(aff->v->el[offset + i], 0);
1063 }
1064
1065 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
1066 if (!aff->ls)
1067 goto error;
1068 isl_mat_free(div);
1069 return aff;
1070 error:
1071 isl_aff_free(aff);
1072 isl_mat_free(div);
1073 return NULL;
1074 }
1075
1076 /* Add two affine expressions that live in the same local space.
1077 */
1078 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
1079 __isl_take isl_aff *aff2)
1080 {
1081 isl_int gcd, f;
1082
1083 aff1 = isl_aff_cow(aff1);
1084 if (!aff1 || !aff2)
1085 goto error;
1086
1087 aff1->v = isl_vec_cow(aff1->v);
1088 if (!aff1->v)
1089 goto error;
1090
1091 isl_int_init(gcd);
1092 isl_int_init(f);
1093 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
1094 isl_int_divexact(f, aff2->v->el[0], gcd);
1095 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
1096 isl_int_divexact(f, aff1->v->el[0], gcd);
1097 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
1098 isl_int_divexact(f, aff2->v->el[0], gcd);
1099 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
1100 isl_int_clear(f);
1101 isl_int_clear(gcd);
1102
1103 isl_aff_free(aff2);
1104 return aff1;
1105 error:
1106 isl_aff_free(aff1);
1107 isl_aff_free(aff2);
1108 return NULL;
1109 }
1110
1111 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
1112 __isl_take isl_aff *aff2)
1113 {
1114 isl_ctx *ctx;
1115 int *exp1 = NULL;
1116 int *exp2 = NULL;
1117 isl_mat *div;
1118
1119 if (!aff1 || !aff2)
1120 goto error;
1121
1122 ctx = isl_aff_get_ctx(aff1);
1123 if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
1124 isl_die(ctx, isl_error_invalid,
1125 "spaces don't match", goto error);
1126
1127 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
1128 return add_expanded(aff1, aff2);
1129
1130 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
1131 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
1132 if (!exp1 || !exp2)
1133 goto error;
1134
1135 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
1136 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
1137 aff2 = isl_aff_expand_divs(aff2, div, exp2);
1138 free(exp1);
1139 free(exp2);
1140
1141 return add_expanded(aff1, aff2);
1142 error:
1143 free(exp1);
1144 free(exp2);
1145 isl_aff_free(aff1);
1146 isl_aff_free(aff2);
1147 return NULL;
1148 }
1149
1150 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
1151 __isl_take isl_aff *aff2)
1152 {
1153 return isl_aff_add(aff1, isl_aff_neg(aff2));
1154 }
1155
1156 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
1157 {
1158 isl_int gcd;
1159
1160 if (isl_int_is_one(f))
1161 return aff;
1162
1163 aff = isl_aff_cow(aff);
1164 if (!aff)
1165 return NULL;
1166 aff->v = isl_vec_cow(aff->v);
1167 if (!aff->v)
1168 return isl_aff_free(aff);
1169
1170 isl_int_init(gcd);
1171 isl_int_gcd(gcd, aff->v->el[0], f);
1172 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
1173 isl_int_divexact(gcd, f, gcd);
1174 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
1175 isl_int_clear(gcd);
1176
1177 return aff;
1178 }
1179
1180 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
1181 {
1182 isl_int gcd;
1183
1184 if (isl_int_is_one(f))
1185 return aff;
1186
1187 aff = isl_aff_cow(aff);
1188 if (!aff)
1189 return NULL;
1190
1191 if (isl_int_is_zero(f))
1192 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1193 "cannot scale down by zero", return isl_aff_free(aff));
1194
1195 aff->v = isl_vec_cow(aff->v);
1196 if (!aff->v)
1197 return isl_aff_free(aff);
1198
1199 isl_int_init(gcd);
1200 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
1201 isl_int_gcd(gcd, gcd, f);
1202 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
1203 isl_int_divexact(gcd, f, gcd);
1204 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
1205 isl_int_clear(gcd);
1206
1207 return aff;
1208 }
1209
1210 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
1211 {
1212 isl_int v;
1213
1214 if (f == 1)
1215 return aff;
1216
1217 isl_int_init(v);
1218 isl_int_set_ui(v, f);
1219 aff = isl_aff_scale_down(aff, v);
1220 isl_int_clear(v);
1221
1222 return aff;
1223 }
1224
1225 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
1226 enum isl_dim_type type, unsigned pos, const char *s)
1227 {
1228 aff = isl_aff_cow(aff);
1229 if (!aff)
1230 return NULL;
1231 if (type == isl_dim_out)
1232 isl_die(aff->v->ctx, isl_error_invalid,
1233 "cannot set name of output/set dimension",
1234 return isl_aff_free(aff));
1235 if (type == isl_dim_in)
1236 type = isl_dim_set;
1237 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
1238 if (!aff->ls)
1239 return isl_aff_free(aff);
1240
1241 return aff;
1242 }
1243
1244 __isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
1245 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
1246 {
1247 aff = isl_aff_cow(aff);
1248 if (!aff)
1249 return isl_id_free(id);
1250 if (type == isl_dim_out)
1251 isl_die(aff->v->ctx, isl_error_invalid,
1252 "cannot set name of output/set dimension",
1253 goto error);
1254 if (type == isl_dim_in)
1255 type = isl_dim_set;
1256 aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
1257 if (!aff->ls)
1258 return isl_aff_free(aff);
1259
1260 return aff;
1261 error:
1262 isl_id_free(id);
1263 isl_aff_free(aff);
1264 return NULL;
1265 }
1266
1267 /* Exploit the equalities in "eq" to simplify the affine expression
1268 * and the expressions of the integer divisions in the local space.
1269 * The integer divisions in this local space are assumed to appear
1270 * as regular dimensions in "eq".
1271 */
1272 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
1273 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1274 {
1275 int i, j;
1276 unsigned total;
1277 unsigned n_div;
1278
1279 if (!eq)
1280 goto error;
1281 if (eq->n_eq == 0) {
1282 isl_basic_set_free(eq);
1283 return aff;
1284 }
1285
1286 aff = isl_aff_cow(aff);
1287 if (!aff)
1288 goto error;
1289
1290 aff->ls = isl_local_space_substitute_equalities(aff->ls,
1291 isl_basic_set_copy(eq));
1292 aff->v = isl_vec_cow(aff->v);
1293 if (!aff->ls || !aff->v)
1294 goto error;
1295
1296 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
1297 n_div = eq->n_div;
1298 for (i = 0; i < eq->n_eq; ++i) {
1299 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
1300 if (j < 0 || j == 0 || j >= total)
1301 continue;
1302
1303 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
1304 &aff->v->el[0]);
1305 }
1306
1307 isl_basic_set_free(eq);
1308 aff = isl_aff_normalize(aff);
1309 return aff;
1310 error:
1311 isl_basic_set_free(eq);
1312 isl_aff_free(aff);
1313 return NULL;
1314 }
1315
1316 /* Exploit the equalities in "eq" to simplify the affine expression
1317 * and the expressions of the integer divisions in the local space.
1318 */
1319 static __isl_give isl_aff *isl_aff_substitute_equalities(
1320 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1321 {
1322 int n_div;
1323
1324 if (!aff || !eq)
1325 goto error;
1326 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1327 if (n_div > 0)
1328 eq = isl_basic_set_add(eq, isl_dim_set, n_div);
1329 return isl_aff_substitute_equalities_lifted(aff, eq);
1330 error:
1331 isl_basic_set_free(eq);
1332 isl_aff_free(aff);
1333 return NULL;
1334 }
1335
1336 /* Look for equalities among the variables shared by context and aff
1337 * and the integer divisions of aff, if any.
1338 * The equalities are then used to eliminate coefficients and/or integer
1339 * divisions from aff.
1340 */
1341 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
1342 __isl_take isl_set *context)
1343 {
1344 isl_basic_set *hull;
1345 int n_div;
1346
1347 if (!aff)
1348 goto error;
1349 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1350 if (n_div > 0) {
1351 isl_basic_set *bset;
1352 isl_local_space *ls;
1353 context = isl_set_add_dims(context, isl_dim_set, n_div);
1354 ls = isl_aff_get_domain_local_space(aff);
1355 bset = isl_basic_set_from_local_space(ls);
1356 bset = isl_basic_set_lift(bset);
1357 bset = isl_basic_set_flatten(bset);
1358 context = isl_set_intersect(context,
1359 isl_set_from_basic_set(bset));
1360 }
1361
1362 hull = isl_set_affine_hull(context);
1363 return isl_aff_substitute_equalities_lifted(aff, hull);
1364 error:
1365 isl_aff_free(aff);
1366 isl_set_free(context);
1367 return NULL;
1368 }
1369
1370 __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
1371 __isl_take isl_set *context)
1372 {
1373 isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
1374 dom_context = isl_set_intersect_params(dom_context, context);
1375 return isl_aff_gist(aff, dom_context);
1376 }
1377
1378 /* Return a basic set containing those elements in the space
1379 * of aff where it is non-negative.
1380 * If "rational" is set, then return a rational basic set.
1381 */
1382 static __isl_give isl_basic_set *aff_nonneg_basic_set(
1383 __isl_take isl_aff *aff, int rational)
1384 {
1385 isl_constraint *ineq;
1386 isl_basic_set *bset;
1387
1388 ineq = isl_inequality_from_aff(aff);
1389
1390 bset = isl_basic_set_from_constraint(ineq);
1391 if (rational)
1392 bset = isl_basic_set_set_rational(bset);
1393 bset = isl_basic_set_simplify(bset);
1394 return bset;
1395 }
1396
1397 /* Return a basic set containing those elements in the space
1398 * of aff where it is non-negative.
1399 */
1400 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
1401 {
1402 return aff_nonneg_basic_set(aff, 0);
1403 }
1404
1405 /* Return a basic set containing those elements in the domain space
1406 * of aff where it is negative.
1407 */
1408 __isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
1409 {
1410 aff = isl_aff_neg(aff);
1411 aff = isl_aff_add_constant_num_si(aff, -1);
1412 return isl_aff_nonneg_basic_set(aff);
1413 }
1414
1415 /* Return a basic set containing those elements in the space
1416 * of aff where it is zero.
1417 * If "rational" is set, then return a rational basic set.
1418 */
1419 static __isl_give isl_basic_set *aff_zero_basic_set(__isl_take isl_aff *aff,
1420 int rational)
1421 {
1422 isl_constraint *ineq;
1423 isl_basic_set *bset;
1424
1425 ineq = isl_equality_from_aff(aff);
1426
1427 bset = isl_basic_set_from_constraint(ineq);
1428 if (rational)
1429 bset = isl_basic_set_set_rational(bset);
1430 bset = isl_basic_set_simplify(bset);
1431 return bset;
1432 }
1433
1434 /* Return a basic set containing those elements in the space
1435 * of aff where it is zero.
1436 */
1437 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
1438 {
1439 return aff_zero_basic_set(aff, 0);
1440 }
1441
1442 /* Return a basic set containing those elements in the shared space
1443 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1444 */
1445 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
1446 __isl_take isl_aff *aff2)
1447 {
1448 aff1 = isl_aff_sub(aff1, aff2);
1449
1450 return isl_aff_nonneg_basic_set(aff1);
1451 }
1452
1453 /* Return a basic set containing those elements in the shared space
1454 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1455 */
1456 __isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
1457 __isl_take isl_aff *aff2)
1458 {
1459 return isl_aff_ge_basic_set(aff2, aff1);
1460 }
1461
1462 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
1463 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
1464 {
1465 aff1 = isl_aff_add(aff1, aff2);
1466 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
1467 return aff1;
1468 }
1469
1470 int isl_aff_is_empty(__isl_keep isl_aff *aff)
1471 {
1472 if (!aff)
1473 return -1;
1474
1475 return 0;
1476 }
1477
1478 /* Check whether the given affine expression has non-zero coefficient
1479 * for any dimension in the given range or if any of these dimensions
1480 * appear with non-zero coefficients in any of the integer divisions
1481 * involved in the affine expression.
1482 */
1483 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
1484 enum isl_dim_type type, unsigned first, unsigned n)
1485 {
1486 int i;
1487 isl_ctx *ctx;
1488 int *active = NULL;
1489 int involves = 0;
1490
1491 if (!aff)
1492 return -1;
1493 if (n == 0)
1494 return 0;
1495
1496 ctx = isl_aff_get_ctx(aff);
1497 if (first + n > isl_aff_dim(aff, type))
1498 isl_die(ctx, isl_error_invalid,
1499 "range out of bounds", return -1);
1500
1501 active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
1502 if (!active)
1503 goto error;
1504
1505 first += isl_local_space_offset(aff->ls, type) - 1;
1506 for (i = 0; i < n; ++i)
1507 if (active[first + i]) {
1508 involves = 1;
1509 break;
1510 }
1511
1512 free(active);
1513
1514 return involves;
1515 error:
1516 free(active);
1517 return -1;
1518 }
1519
1520 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
1521 enum isl_dim_type type, unsigned first, unsigned n)
1522 {
1523 isl_ctx *ctx;
1524
1525 if (!aff)
1526 return NULL;
1527 if (type == isl_dim_out)
1528 isl_die(aff->v->ctx, isl_error_invalid,
1529 "cannot drop output/set dimension",
1530 return isl_aff_free(aff));
1531 if (type == isl_dim_in)
1532 type = isl_dim_set;
1533 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1534 return aff;
1535
1536 ctx = isl_aff_get_ctx(aff);
1537 if (first + n > isl_local_space_dim(aff->ls, type))
1538 isl_die(ctx, isl_error_invalid, "range out of bounds",
1539 return isl_aff_free(aff));
1540
1541 aff = isl_aff_cow(aff);
1542 if (!aff)
1543 return NULL;
1544
1545 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
1546 if (!aff->ls)
1547 return isl_aff_free(aff);
1548
1549 first += 1 + isl_local_space_offset(aff->ls, type);
1550 aff->v = isl_vec_drop_els(aff->v, first, n);
1551 if (!aff->v)
1552 return isl_aff_free(aff);
1553
1554 return aff;
1555 }
1556
1557 /* Project the domain of the affine expression onto its parameter space.
1558 * The affine expression may not involve any of the domain dimensions.
1559 */
1560 __isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
1561 {
1562 isl_space *space;
1563 unsigned n;
1564 int involves;
1565
1566 n = isl_aff_dim(aff, isl_dim_in);
1567 involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
1568 if (involves < 0)
1569 return isl_aff_free(aff);
1570 if (involves)
1571 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1572 "affine expression involves some of the domain dimensions",
1573 return isl_aff_free(aff));
1574 aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
1575 space = isl_aff_get_domain_space(aff);
1576 space = isl_space_params(space);
1577 aff = isl_aff_reset_domain_space(aff, space);
1578 return aff;
1579 }
1580
1581 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
1582 enum isl_dim_type type, unsigned first, unsigned n)
1583 {
1584 isl_ctx *ctx;
1585
1586 if (!aff)
1587 return NULL;
1588 if (type == isl_dim_out)
1589 isl_die(aff->v->ctx, isl_error_invalid,
1590 "cannot insert output/set dimensions",
1591 return isl_aff_free(aff));
1592 if (type == isl_dim_in)
1593 type = isl_dim_set;
1594 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1595 return aff;
1596
1597 ctx = isl_aff_get_ctx(aff);
1598 if (first > isl_local_space_dim(aff->ls, type))
1599 isl_die(ctx, isl_error_invalid, "position out of bounds",
1600 return isl_aff_free(aff));
1601
1602 aff = isl_aff_cow(aff);
1603 if (!aff)
1604 return NULL;
1605
1606 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
1607 if (!aff->ls)
1608 return isl_aff_free(aff);
1609
1610 first += 1 + isl_local_space_offset(aff->ls, type);
1611 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
1612 if (!aff->v)
1613 return isl_aff_free(aff);
1614
1615 return aff;
1616 }
1617
1618 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
1619 enum isl_dim_type type, unsigned n)
1620 {
1621 unsigned pos;
1622
1623 pos = isl_aff_dim(aff, type);
1624
1625 return isl_aff_insert_dims(aff, type, pos, n);
1626 }
1627
1628 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
1629 enum isl_dim_type type, unsigned n)
1630 {
1631 unsigned pos;
1632
1633 pos = isl_pw_aff_dim(pwaff, type);
1634
1635 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
1636 }
1637
1638 __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
1639 {
1640 isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
1641 return isl_pw_aff_alloc(dom, aff);
1642 }
1643
1644 #undef PW
1645 #define PW isl_pw_aff
1646 #undef EL
1647 #define EL isl_aff
1648 #undef EL_IS_ZERO
1649 #define EL_IS_ZERO is_empty
1650 #undef ZERO
1651 #define ZERO empty
1652 #undef IS_ZERO
1653 #define IS_ZERO is_empty
1654 #undef FIELD
1655 #define FIELD aff
1656 #undef DEFAULT_IS_ZERO
1657 #define DEFAULT_IS_ZERO 0
1658
1659 #define NO_EVAL
1660 #define NO_OPT
1661 #define NO_MOVE_DIMS
1662 #define NO_LIFT
1663 #define NO_MORPH
1664
1665 #include <isl_pw_templ.c>
1666
1667 static __isl_give isl_set *align_params_pw_pw_set_and(
1668 __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
1669 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1670 __isl_take isl_pw_aff *pwaff2))
1671 {
1672 if (!pwaff1 || !pwaff2)
1673 goto error;
1674 if (isl_space_match(pwaff1->dim, isl_dim_param,
1675 pwaff2->dim, isl_dim_param))
1676 return fn(pwaff1, pwaff2);
1677 if (!isl_space_has_named_params(pwaff1->dim) ||
1678 !isl_space_has_named_params(pwaff2->dim))
1679 isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
1680 "unaligned unnamed parameters", goto error);
1681 pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
1682 pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
1683 return fn(pwaff1, pwaff2);
1684 error:
1685 isl_pw_aff_free(pwaff1);
1686 isl_pw_aff_free(pwaff2);
1687 return NULL;
1688 }
1689
1690 /* Compute a piecewise quasi-affine expression with a domain that
1691 * is the union of those of pwaff1 and pwaff2 and such that on each
1692 * cell, the quasi-affine expression is the better (according to cmp)
1693 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
1694 * is defined on a given cell, then the associated expression
1695 * is the defined one.
1696 */
1697 static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1698 __isl_take isl_pw_aff *pwaff2,
1699 __isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
1700 __isl_take isl_aff *aff2))
1701 {
1702 int i, j, n;
1703 isl_pw_aff *res;
1704 isl_ctx *ctx;
1705 isl_set *set;
1706
1707 if (!pwaff1 || !pwaff2)
1708 goto error;
1709
1710 ctx = isl_space_get_ctx(pwaff1->dim);
1711 if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
1712 isl_die(ctx, isl_error_invalid,
1713 "arguments should live in same space", goto error);
1714
1715 if (isl_pw_aff_is_empty(pwaff1)) {
1716 isl_pw_aff_free(pwaff1);
1717 return pwaff2;
1718 }
1719
1720 if (isl_pw_aff_is_empty(pwaff2)) {
1721 isl_pw_aff_free(pwaff2);
1722 return pwaff1;
1723 }
1724
1725 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
1726 res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
1727
1728 for (i = 0; i < pwaff1->n; ++i) {
1729 set = isl_set_copy(pwaff1->p[i].set);
1730 for (j = 0; j < pwaff2->n; ++j) {
1731 struct isl_set *common;
1732 isl_set *better;
1733
1734 common = isl_set_intersect(
1735 isl_set_copy(pwaff1->p[i].set),
1736 isl_set_copy(pwaff2->p[j].set));
1737 better = isl_set_from_basic_set(cmp(
1738 isl_aff_copy(pwaff2->p[j].aff),
1739 isl_aff_copy(pwaff1->p[i].aff)));
1740 better = isl_set_intersect(common, better);
1741 if (isl_set_plain_is_empty(better)) {
1742 isl_set_free(better);
1743 continue;
1744 }
1745 set = isl_set_subtract(set, isl_set_copy(better));
1746
1747 res = isl_pw_aff_add_piece(res, better,
1748 isl_aff_copy(pwaff2->p[j].aff));
1749 }
1750 res = isl_pw_aff_add_piece(res, set,
1751 isl_aff_copy(pwaff1->p[i].aff));
1752 }
1753
1754 for (j = 0; j < pwaff2->n; ++j) {
1755 set = isl_set_copy(pwaff2->p[j].set);
1756 for (i = 0; i < pwaff1->n; ++i)
1757 set = isl_set_subtract(set,
1758 isl_set_copy(pwaff1->p[i].set));
1759 res = isl_pw_aff_add_piece(res, set,
1760 isl_aff_copy(pwaff2->p[j].aff));
1761 }
1762
1763 isl_pw_aff_free(pwaff1);
1764 isl_pw_aff_free(pwaff2);
1765
1766 return res;
1767 error:
1768 isl_pw_aff_free(pwaff1);
1769 isl_pw_aff_free(pwaff2);
1770 return NULL;
1771 }
1772
1773 /* Compute a piecewise quasi-affine expression with a domain that
1774 * is the union of those of pwaff1 and pwaff2 and such that on each
1775 * cell, the quasi-affine expression is the maximum of those of pwaff1
1776 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1777 * cell, then the associated expression is the defined one.
1778 */
1779 static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1780 __isl_take isl_pw_aff *pwaff2)
1781 {
1782 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
1783 }
1784
1785 __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1786 __isl_take isl_pw_aff *pwaff2)
1787 {
1788 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1789 &pw_aff_union_max);
1790 }
1791
1792 /* Compute a piecewise quasi-affine expression with a domain that
1793 * is the union of those of pwaff1 and pwaff2 and such that on each
1794 * cell, the quasi-affine expression is the minimum of those of pwaff1
1795 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1796 * cell, then the associated expression is the defined one.
1797 */
1798 static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1799 __isl_take isl_pw_aff *pwaff2)
1800 {
1801 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
1802 }
1803
1804 __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1805 __isl_take isl_pw_aff *pwaff2)
1806 {
1807 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1808 &pw_aff_union_min);
1809 }
1810
1811 __isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1812 __isl_take isl_pw_aff *pwaff2, int max)
1813 {
1814 if (max)
1815 return isl_pw_aff_union_max(pwaff1, pwaff2);
1816 else
1817 return isl_pw_aff_union_min(pwaff1, pwaff2);
1818 }
1819
1820 /* Construct a map with as domain the domain of pwaff and
1821 * one-dimensional range corresponding to the affine expressions.
1822 */
1823 static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1824 {
1825 int i;
1826 isl_space *dim;
1827 isl_map *map;
1828
1829 if (!pwaff)
1830 return NULL;
1831
1832 dim = isl_pw_aff_get_space(pwaff);
1833 map = isl_map_empty(dim);
1834
1835 for (i = 0; i < pwaff->n; ++i) {
1836 isl_basic_map *bmap;
1837 isl_map *map_i;
1838
1839 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
1840 map_i = isl_map_from_basic_map(bmap);
1841 map_i = isl_map_intersect_domain(map_i,
1842 isl_set_copy(pwaff->p[i].set));
1843 map = isl_map_union_disjoint(map, map_i);
1844 }
1845
1846 isl_pw_aff_free(pwaff);
1847
1848 return map;
1849 }
1850
1851 /* Construct a map with as domain the domain of pwaff and
1852 * one-dimensional range corresponding to the affine expressions.
1853 */
1854 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1855 {
1856 if (!pwaff)
1857 return NULL;
1858 if (isl_space_is_set(pwaff->dim))
1859 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1860 "space of input is not a map",
1861 return isl_pw_aff_free(pwaff));
1862 return map_from_pw_aff(pwaff);
1863 }
1864
1865 /* Construct a one-dimensional set with as parameter domain
1866 * the domain of pwaff and the single set dimension
1867 * corresponding to the affine expressions.
1868 */
1869 __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1870 {
1871 if (!pwaff)
1872 return NULL;
1873 if (!isl_space_is_set(pwaff->dim))
1874 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1875 "space of input is not a set",
1876 return isl_pw_aff_free(pwaff));
1877 return map_from_pw_aff(pwaff);
1878 }
1879
1880 /* Return a set containing those elements in the domain
1881 * of pwaff where it is non-negative.
1882 */
1883 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
1884 {
1885 int i;
1886 isl_set *set;
1887
1888 if (!pwaff)
1889 return NULL;
1890
1891 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1892
1893 for (i = 0; i < pwaff->n; ++i) {
1894 isl_basic_set *bset;
1895 isl_set *set_i;
1896 int rational;
1897
1898 rational = isl_set_has_rational(pwaff->p[i].set);
1899 bset = aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff),
1900 rational);
1901 set_i = isl_set_from_basic_set(bset);
1902 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1903 set = isl_set_union_disjoint(set, set_i);
1904 }
1905
1906 isl_pw_aff_free(pwaff);
1907
1908 return set;
1909 }
1910
1911 /* Return a set containing those elements in the domain
1912 * of pwaff where it is zero (if complement is 0) or not zero
1913 * (if complement is 1).
1914 */
1915 static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
1916 int complement)
1917 {
1918 int i;
1919 isl_set *set;
1920
1921 if (!pwaff)
1922 return NULL;
1923
1924 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1925
1926 for (i = 0; i < pwaff->n; ++i) {
1927 isl_basic_set *bset;
1928 isl_set *set_i, *zero;
1929 int rational;
1930
1931 rational = isl_set_has_rational(pwaff->p[i].set);
1932 bset = aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff),
1933 rational);
1934 zero = isl_set_from_basic_set(bset);
1935 set_i = isl_set_copy(pwaff->p[i].set);
1936 if (complement)
1937 set_i = isl_set_subtract(set_i, zero);
1938 else
1939 set_i = isl_set_intersect(set_i, zero);
1940 set = isl_set_union_disjoint(set, set_i);
1941 }
1942
1943 isl_pw_aff_free(pwaff);
1944
1945 return set;
1946 }
1947
1948 /* Return a set containing those elements in the domain
1949 * of pwaff where it is zero.
1950 */
1951 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
1952 {
1953 return pw_aff_zero_set(pwaff, 0);
1954 }
1955
1956 /* Return a set containing those elements in the domain
1957 * of pwaff where it is not zero.
1958 */
1959 __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
1960 {
1961 return pw_aff_zero_set(pwaff, 1);
1962 }
1963
1964 /* Return a set containing those elements in the shared domain
1965 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1966 *
1967 * We compute the difference on the shared domain and then construct
1968 * the set of values where this difference is non-negative.
1969 * If strict is set, we first subtract 1 from the difference.
1970 * If equal is set, we only return the elements where pwaff1 and pwaff2
1971 * are equal.
1972 */
1973 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
1974 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
1975 {
1976 isl_set *set1, *set2;
1977
1978 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
1979 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
1980 set1 = isl_set_intersect(set1, set2);
1981 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
1982 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
1983 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
1984
1985 if (strict) {
1986 isl_space *dim = isl_set_get_space(set1);
1987 isl_aff *aff;
1988 aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
1989 aff = isl_aff_add_constant_si(aff, -1);
1990 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
1991 } else
1992 isl_set_free(set1);
1993
1994 if (equal)
1995 return isl_pw_aff_zero_set(pwaff1);
1996 return isl_pw_aff_nonneg_set(pwaff1);
1997 }
1998
1999 /* Return a set containing those elements in the shared domain
2000 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
2001 */
2002 static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
2003 __isl_take isl_pw_aff *pwaff2)
2004 {
2005 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
2006 }
2007
2008 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
2009 __isl_take isl_pw_aff *pwaff2)
2010 {
2011 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
2012 }
2013
2014 /* Return a set containing those elements in the shared domain
2015 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
2016 */
2017 static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
2018 __isl_take isl_pw_aff *pwaff2)
2019 {
2020 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
2021 }
2022
2023 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
2024 __isl_take isl_pw_aff *pwaff2)
2025 {
2026 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
2027 }
2028
2029 /* Return a set containing those elements in the shared domain
2030 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
2031 */
2032 static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
2033 __isl_take isl_pw_aff *pwaff2)
2034 {
2035 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
2036 }
2037
2038 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
2039 __isl_take isl_pw_aff *pwaff2)
2040 {
2041 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
2042 }
2043
2044 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
2045 __isl_take isl_pw_aff *pwaff2)
2046 {
2047 return isl_pw_aff_ge_set(pwaff2, pwaff1);
2048 }
2049
2050 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
2051 __isl_take isl_pw_aff *pwaff2)
2052 {
2053 return isl_pw_aff_gt_set(pwaff2, pwaff1);
2054 }
2055
2056 /* Return a set containing those elements in the shared domain
2057 * of the elements of list1 and list2 where each element in list1
2058 * has the relation specified by "fn" with each element in list2.
2059 */
2060 static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
2061 __isl_take isl_pw_aff_list *list2,
2062 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
2063 __isl_take isl_pw_aff *pwaff2))
2064 {
2065 int i, j;
2066 isl_ctx *ctx;
2067 isl_set *set;
2068
2069 if (!list1 || !list2)
2070 goto error;
2071
2072 ctx = isl_pw_aff_list_get_ctx(list1);
2073 if (list1->n < 1 || list2->n < 1)
2074 isl_die(ctx, isl_error_invalid,
2075 "list should contain at least one element", goto error);
2076
2077 set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
2078 for (i = 0; i < list1->n; ++i)
2079 for (j = 0; j < list2->n; ++j) {
2080 isl_set *set_ij;
2081
2082 set_ij = fn(isl_pw_aff_copy(list1->p[i]),
2083 isl_pw_aff_copy(list2->p[j]));
2084 set = isl_set_intersect(set, set_ij);
2085 }
2086
2087 isl_pw_aff_list_free(list1);
2088 isl_pw_aff_list_free(list2);
2089 return set;
2090 error:
2091 isl_pw_aff_list_free(list1);
2092 isl_pw_aff_list_free(list2);
2093 return NULL;
2094 }
2095
2096 /* Return a set containing those elements in the shared domain
2097 * of the elements of list1 and list2 where each element in list1
2098 * is equal to each element in list2.
2099 */
2100 __isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
2101 __isl_take isl_pw_aff_list *list2)
2102 {
2103 return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
2104 }
2105
2106 __isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
2107 __isl_take isl_pw_aff_list *list2)
2108 {
2109 return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
2110 }
2111
2112 /* Return a set containing those elements in the shared domain
2113 * of the elements of list1 and list2 where each element in list1
2114 * is less than or equal to each element in list2.
2115 */
2116 __isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
2117 __isl_take isl_pw_aff_list *list2)
2118 {
2119 return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
2120 }
2121
2122 __isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
2123 __isl_take isl_pw_aff_list *list2)
2124 {
2125 return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
2126 }
2127
2128 __isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
2129 __isl_take isl_pw_aff_list *list2)
2130 {
2131 return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
2132 }
2133
2134 __isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
2135 __isl_take isl_pw_aff_list *list2)
2136 {
2137 return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
2138 }
2139
2140
2141 /* Return a set containing those elements in the shared domain
2142 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
2143 */
2144 static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
2145 __isl_take isl_pw_aff *pwaff2)
2146 {
2147 isl_set *set_lt, *set_gt;
2148
2149 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
2150 isl_pw_aff_copy(pwaff2));
2151 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
2152 return isl_set_union_disjoint(set_lt, set_gt);
2153 }
2154
2155 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
2156 __isl_take isl_pw_aff *pwaff2)
2157 {
2158 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
2159 }
2160
2161 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
2162 isl_int v)
2163 {
2164 int i;
2165
2166 if (isl_int_is_one(v))
2167 return pwaff;
2168 if (!isl_int_is_pos(v))
2169 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
2170 "factor needs to be positive",
2171 return isl_pw_aff_free(pwaff));
2172 pwaff = isl_pw_aff_cow(pwaff);
2173 if (!pwaff)
2174 return NULL;
2175 if (pwaff->n == 0)
2176 return pwaff;
2177
2178 for (i = 0; i < pwaff->n; ++i) {
2179 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
2180 if (!pwaff->p[i].aff)
2181 return isl_pw_aff_free(pwaff);
2182 }
2183
2184 return pwaff;
2185 }
2186
2187 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
2188 {
2189 int i;
2190
2191 pwaff = isl_pw_aff_cow(pwaff);
2192 if (!pwaff)
2193 return NULL;
2194 if (pwaff->n == 0)
2195 return pwaff;
2196
2197 for (i = 0; i < pwaff->n; ++i) {
2198 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
2199 if (!pwaff->p[i].aff)
2200 return isl_pw_aff_free(pwaff);
2201 }
2202
2203 return pwaff;
2204 }
2205
2206 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
2207 {
2208 int i;
2209
2210 pwaff = isl_pw_aff_cow(pwaff);
2211 if (!pwaff)
2212 return NULL;
2213 if (pwaff->n == 0)
2214 return pwaff;
2215
2216 for (i = 0; i < pwaff->n; ++i) {
2217 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
2218 if (!pwaff->p[i].aff)
2219 return isl_pw_aff_free(pwaff);
2220 }
2221
2222 return pwaff;
2223 }
2224
2225 /* Assuming that "cond1" and "cond2" are disjoint,
2226 * return an affine expression that is equal to pwaff1 on cond1
2227 * and to pwaff2 on cond2.
2228 */
2229 static __isl_give isl_pw_aff *isl_pw_aff_select(
2230 __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
2231 __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
2232 {
2233 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
2234 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
2235
2236 return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
2237 }
2238
2239 /* Return an affine expression that is equal to pwaff_true for elements
2240 * where "cond" is non-zero and to pwaff_false for elements where "cond"
2241 * is zero.
2242 * That is, return cond ? pwaff_true : pwaff_false;
2243 */
2244 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
2245 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
2246 {
2247 isl_set *cond_true, *cond_false;
2248
2249 cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
2250 cond_false = isl_pw_aff_zero_set(cond);
2251 return isl_pw_aff_select(cond_true, pwaff_true,
2252 cond_false, pwaff_false);
2253 }
2254
2255 int isl_aff_is_cst(__isl_keep isl_aff *aff)
2256 {
2257 if (!aff)
2258 return -1;
2259
2260 return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
2261 }
2262
2263 /* Check whether pwaff is a piecewise constant.
2264 */
2265 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
2266 {
2267 int i;
2268
2269 if (!pwaff)
2270 return -1;
2271
2272 for (i = 0; i < pwaff->n; ++i) {
2273 int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
2274 if (is_cst < 0 || !is_cst)
2275 return is_cst;
2276 }
2277
2278 return 1;
2279 }
2280
2281 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2282 __isl_take isl_aff *aff2)
2283 {
2284 if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
2285 return isl_aff_mul(aff2, aff1);
2286
2287 if (!isl_aff_is_cst(aff2))
2288 isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
2289 "at least one affine expression should be constant",
2290 goto error);
2291
2292 aff1 = isl_aff_cow(aff1);
2293 if (!aff1 || !aff2)
2294 goto error;
2295
2296 aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
2297 aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
2298
2299 isl_aff_free(aff2);
2300 return aff1;
2301 error:
2302 isl_aff_free(aff1);
2303 isl_aff_free(aff2);
2304 return NULL;
2305 }
2306
2307 /* Divide "aff1" by "aff2", assuming "aff2" is a piecewise constant.
2308 */
2309 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
2310 __isl_take isl_aff *aff2)
2311 {
2312 int is_cst;
2313 int neg;
2314
2315 is_cst = isl_aff_is_cst(aff2);
2316 if (is_cst < 0)
2317 goto error;
2318 if (!is_cst)
2319 isl_die(isl_aff_get_ctx(aff2), isl_error_invalid,
2320 "second argument should be a constant", goto error);
2321
2322 if (!aff2)
2323 goto error;
2324
2325 neg = isl_int_is_neg(aff2->v->el[1]);
2326 if (neg) {
2327 isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
2328 isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
2329 }
2330
2331 aff1 = isl_aff_scale(aff1, aff2->v->el[0]);
2332 aff1 = isl_aff_scale_down(aff1, aff2->v->el[1]);
2333
2334 if (neg) {
2335 isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
2336 isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
2337 }
2338
2339 isl_aff_free(aff2);
2340 return aff1;
2341 error:
2342 isl_aff_free(aff1);
2343 isl_aff_free(aff2);
2344 return NULL;
2345 }
2346
2347 static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2348 __isl_take isl_pw_aff *pwaff2)
2349 {
2350 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
2351 }
2352
2353 __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2354 __isl_take isl_pw_aff *pwaff2)
2355 {
2356 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
2357 }
2358
2359 __isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
2360 __isl_take isl_pw_aff *pwaff2)
2361 {
2362 return isl_pw_aff_union_add_(pwaff1, pwaff2);
2363 }
2364
2365 static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2366 __isl_take isl_pw_aff *pwaff2)
2367 {
2368 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
2369 }
2370
2371 __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2372 __isl_take isl_pw_aff *pwaff2)
2373 {
2374 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
2375 }
2376
2377 static __isl_give isl_pw_aff *pw_aff_div(__isl_take isl_pw_aff *pa1,
2378 __isl_take isl_pw_aff *pa2)
2379 {
2380 return isl_pw_aff_on_shared_domain(pa1, pa2, &isl_aff_div);
2381 }
2382
2383 /* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
2384 */
2385 __isl_give isl_pw_aff *isl_pw_aff_div(__isl_take isl_pw_aff *pa1,
2386 __isl_take isl_pw_aff *pa2)
2387 {
2388 int is_cst;
2389
2390 is_cst = isl_pw_aff_is_cst(pa2);
2391 if (is_cst < 0)
2392 goto error;
2393 if (!is_cst)
2394 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2395 "second argument should be a piecewise constant",
2396 goto error);
2397 return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_aff_div);
2398 error:
2399 isl_pw_aff_free(pa1);
2400 isl_pw_aff_free(pa2);
2401 return NULL;
2402 }
2403
2404 /* Compute the quotient of the integer division of "pa1" by "pa2"
2405 * with rounding towards zero.
2406 * "pa2" is assumed to be a piecewise constant.
2407 *
2408 * In particular, return
2409 *
2410 * pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
2411 *
2412 */
2413 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(__isl_take isl_pw_aff *pa1,
2414 __isl_take isl_pw_aff *pa2)
2415 {
2416 int is_cst;
2417 isl_set *cond;
2418 isl_pw_aff *f, *c;
2419
2420 is_cst = isl_pw_aff_is_cst(pa2);
2421 if (is_cst < 0)
2422 goto error;
2423 if (!is_cst)
2424 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2425 "second argument should be a piecewise constant",
2426 goto error);
2427
2428 pa1 = isl_pw_aff_div(pa1, pa2);
2429
2430 cond = isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1));
2431 f = isl_pw_aff_floor(isl_pw_aff_copy(pa1));
2432 c = isl_pw_aff_ceil(pa1);
2433 return isl_pw_aff_cond(isl_set_indicator_function(cond), f, c);
2434 error:
2435 isl_pw_aff_free(pa1);
2436 isl_pw_aff_free(pa2);
2437 return NULL;
2438 }
2439
2440 /* Compute the remainder of the integer division of "pa1" by "pa2"
2441 * with rounding towards zero.
2442 * "pa2" is assumed to be a piecewise constant.
2443 *
2444 * In particular, return
2445 *
2446 * pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
2447 *
2448 */
2449 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(__isl_take isl_pw_aff *pa1,
2450 __isl_take isl_pw_aff *pa2)
2451 {
2452 int is_cst;
2453 isl_pw_aff *res;
2454
2455 is_cst = isl_pw_aff_is_cst(pa2);
2456 if (is_cst < 0)
2457 goto error;
2458 if (!is_cst)
2459 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2460 "second argument should be a piecewise constant",
2461 goto error);
2462 res = isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1), isl_pw_aff_copy(pa2));
2463 res = isl_pw_aff_mul(pa2, res);
2464 res = isl_pw_aff_sub(pa1, res);
2465 return res;
2466 error:
2467 isl_pw_aff_free(pa1);
2468 isl_pw_aff_free(pa2);
2469 return NULL;
2470 }
2471
2472 static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2473 __isl_take isl_pw_aff *pwaff2)
2474 {
2475 isl_set *le;
2476 isl_set *dom;
2477
2478 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2479 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2480 le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
2481 isl_pw_aff_copy(pwaff2));
2482 dom = isl_set_subtract(dom, isl_set_copy(le));
2483 return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
2484 }
2485
2486 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2487 __isl_take isl_pw_aff *pwaff2)
2488 {
2489 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
2490 }
2491
2492 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2493 __isl_take isl_pw_aff *pwaff2)
2494 {
2495 isl_set *ge;
2496 isl_set *dom;
2497
2498 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2499 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2500 ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
2501 isl_pw_aff_copy(pwaff2));
2502 dom = isl_set_subtract(dom, isl_set_copy(ge));
2503 return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
2504 }
2505
2506 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2507 __isl_take isl_pw_aff *pwaff2)
2508 {
2509 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
2510 }
2511
2512 static __isl_give isl_pw_aff *pw_aff_list_reduce(
2513 __isl_take isl_pw_aff_list *list,
2514 __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
2515 __isl_take isl_pw_aff *pwaff2))
2516 {
2517 int i;
2518 isl_ctx *ctx;
2519 isl_pw_aff *res;
2520
2521 if (!list)
2522 return NULL;
2523
2524 ctx = isl_pw_aff_list_get_ctx(list);
2525 if (list->n < 1)
2526 isl_die(ctx, isl_error_invalid,
2527 "list should contain at least one element",
2528 return isl_pw_aff_list_free(list));
2529
2530 res = isl_pw_aff_copy(list->p[0]);
2531 for (i = 1; i < list->n; ++i)
2532 res = fn(res, isl_pw_aff_copy(list->p[i]));
2533
2534 isl_pw_aff_list_free(list);
2535 return res;
2536 }
2537
2538 /* Return an isl_pw_aff that maps each element in the intersection of the
2539 * domains of the elements of list to the minimal corresponding affine
2540 * expression.
2541 */
2542 __isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
2543 {
2544 return pw_aff_list_reduce(list, &isl_pw_aff_min);
2545 }
2546
2547 /* Return an isl_pw_aff that maps each element in the intersection of the
2548 * domains of the elements of list to the maximal corresponding affine
2549 * expression.
2550 */
2551 __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
2552 {
2553 return pw_aff_list_reduce(list, &isl_pw_aff_max);
2554 }
2555
2556 /* Mark the domains of "pwaff" as rational.
2557 */
2558 __isl_give isl_pw_aff *isl_pw_aff_set_rational(__isl_take isl_pw_aff *pwaff)
2559 {
2560 int i;
2561
2562 pwaff = isl_pw_aff_cow(pwaff);
2563 if (!pwaff)
2564 return NULL;
2565 if (pwaff->n == 0)
2566 return pwaff;
2567
2568 for (i = 0; i < pwaff->n; ++i) {
2569 pwaff->p[i].set = isl_set_set_rational(pwaff->p[i].set);
2570 if (!pwaff->p[i].set)
2571 return isl_pw_aff_free(pwaff);
2572 }
2573
2574 return pwaff;
2575 }
2576
2577 /* Mark the domains of the elements of "list" as rational.
2578 */
2579 __isl_give isl_pw_aff_list *isl_pw_aff_list_set_rational(
2580 __isl_take isl_pw_aff_list *list)
2581 {
2582 int i;
2583
2584 if (!list)
2585 return NULL;
2586 if (list->n == 0)
2587 return list;
2588
2589 for (i = 0; i < list->n; ++i) {
2590 isl_pw_aff *pa;
2591
2592 pa = isl_pw_aff_list_get_pw_aff(list, i);
2593 pa = isl_pw_aff_set_rational(pa);
2594 list = isl_pw_aff_list_set_pw_aff(list, i, pa);
2595 }
2596
2597 return list;
2598 }
2599
2600 #undef BASE
2601 #define BASE aff
2602
2603 #include <isl_multi_templ.c>
2604
2605 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
2606 * domain.
2607 */
2608 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
2609 __isl_take isl_multi_aff *ma)
2610 {
2611 isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
2612 return isl_pw_multi_aff_alloc(dom, ma);
2613 }
2614
2615 /* Create a piecewise multi-affine expression in the given space that maps each
2616 * input dimension to the corresponding output dimension.
2617 */
2618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2619 __isl_take isl_space *space)
2620 {
2621 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space));
2622 }
2623
2624 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
2625 __isl_take isl_multi_aff *maff2)
2626 {
2627 int i;
2628 isl_ctx *ctx;
2629
2630 maff1 = isl_multi_aff_cow(maff1);
2631 if (!maff1 || !maff2)
2632 goto error;
2633
2634 ctx = isl_multi_aff_get_ctx(maff1);
2635 if (!isl_space_is_equal(maff1->space, maff2->space))
2636 isl_die(ctx, isl_error_invalid,
2637 "spaces don't match", goto error);
2638
2639 for (i = 0; i < maff1->n; ++i) {
2640 maff1->p[i] = isl_aff_add(maff1->p[i],
2641 isl_aff_copy(maff2->p[i]));
2642 if (!maff1->p[i])
2643 goto error;
2644 }
2645
2646 isl_multi_aff_free(maff2);
2647 return maff1;
2648 error:
2649 isl_multi_aff_free(maff1);
2650 isl_multi_aff_free(maff2);
2651 return NULL;
2652 }
2653
2654 /* Given two multi-affine expressions A -> B and C -> D,
2655 * construct a multi-affine expression [A -> C] -> [B -> D].
2656 */
2657 __isl_give isl_multi_aff *isl_multi_aff_product(
2658 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
2659 {
2660 int i;
2661 isl_aff *aff;
2662 isl_space *space;
2663 isl_multi_aff *res;
2664 int in1, in2, out1, out2;
2665
2666 in1 = isl_multi_aff_dim(ma1, isl_dim_in);
2667 in2 = isl_multi_aff_dim(ma2, isl_dim_in);
2668 out1 = isl_multi_aff_dim(ma1, isl_dim_out);
2669 out2 = isl_multi_aff_dim(ma2, isl_dim_out);
2670 space = isl_space_product(isl_multi_aff_get_space(ma1),
2671 isl_multi_aff_get_space(ma2));
2672 res = isl_multi_aff_alloc(isl_space_copy(space));
2673 space = isl_space_domain(space);
2674
2675 for (i = 0; i < out1; ++i) {
2676 aff = isl_multi_aff_get_aff(ma1, i);
2677 aff = isl_aff_insert_dims(aff, isl_dim_in, in1, in2);
2678 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
2679 res = isl_multi_aff_set_aff(res, i, aff);
2680 }
2681
2682 for (i = 0; i < out2; ++i) {
2683 aff = isl_multi_aff_get_aff(ma2, i);
2684 aff = isl_aff_insert_dims(aff, isl_dim_in, 0, in1);
2685 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
2686 res = isl_multi_aff_set_aff(res, out1 + i, aff);
2687 }
2688
2689 isl_space_free(space);
2690 isl_multi_aff_free(ma1);
2691 isl_multi_aff_free(ma2);
2692 return res;
2693 }
2694
2695 /* Exploit the equalities in "eq" to simplify the affine expressions.
2696 */
2697 static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
2698 __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
2699 {
2700 int i;
2701
2702 maff = isl_multi_aff_cow(maff);
2703 if (!maff || !eq)
2704 goto error;
2705
2706 for (i = 0; i < maff->n; ++i) {
2707 maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
2708 isl_basic_set_copy(eq));
2709 if (!maff->p[i])
2710 goto error;
2711 }
2712
2713 isl_basic_set_free(eq);
2714 return maff;
2715 error:
2716 isl_basic_set_free(eq);
2717 isl_multi_aff_free(maff);
2718 return NULL;
2719 }
2720
2721 __isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
2722 isl_int f)
2723 {
2724 int i;
2725
2726 maff = isl_multi_aff_cow(maff);
2727 if (!maff)
2728 return NULL;
2729
2730 for (i = 0; i < maff->n; ++i) {
2731 maff->p[i] = isl_aff_scale(maff->p[i], f);
2732 if (!maff->p[i])
2733 return isl_multi_aff_free(maff);
2734 }
2735
2736 return maff;
2737 }
2738
2739 __isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
2740 __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
2741 {
2742 maff1 = isl_multi_aff_add(maff1, maff2);
2743 maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
2744 return maff1;
2745 }
2746
2747 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
2748 {
2749 if (!maff)
2750 return -1;
2751
2752 return 0;
2753 }
2754
2755 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
2756 __isl_keep isl_multi_aff *maff2)
2757 {
2758 int i;
2759 int equal;
2760
2761 if (!maff1 || !maff2)
2762 return -1;
2763 if (maff1->n != maff2->n)
2764 return 0;
2765 equal = isl_space_is_equal(maff1->space, maff2->space);
2766 if (equal < 0 || !equal)
2767 return equal;
2768
2769 for (i = 0; i < maff1->n; ++i) {
2770 equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
2771 if (equal < 0 || !equal)
2772 return equal;
2773 }
2774
2775 return 1;
2776 }
2777
2778 /* Return the set of domain elements where "ma1" is lexicographically
2779 * smaller than or equal to "ma2".
2780 */
2781 __isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
2782 __isl_take isl_multi_aff *ma2)
2783 {
2784 return isl_multi_aff_lex_ge_set(ma2, ma1);
2785 }
2786
2787 /* Return the set of domain elements where "ma1" is lexicographically
2788 * greater than or equal to "ma2".
2789 */
2790 __isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
2791 __isl_take isl_multi_aff *ma2)
2792 {
2793 isl_space *space;
2794 isl_map *map1, *map2;
2795 isl_map *map, *ge;
2796
2797 map1 = isl_map_from_multi_aff(ma1);
2798 map2 = isl_map_from_multi_aff(ma2);
2799 map = isl_map_range_product(map1, map2);
2800 space = isl_space_range(isl_map_get_space(map));
2801 space = isl_space_domain(isl_space_unwrap(space));
2802 ge = isl_map_lex_ge(space);
2803 map = isl_map_intersect_range(map, isl_map_wrap(ge));
2804
2805 return isl_map_domain(map);
2806 }
2807
2808 #undef PW
2809 #define PW isl_pw_multi_aff
2810 #undef EL
2811 #define EL isl_multi_aff
2812 #undef EL_IS_ZERO
2813 #define EL_IS_ZERO is_empty
2814 #undef ZERO
2815 #define ZERO empty
2816 #undef IS_ZERO
2817 #define IS_ZERO is_empty
2818 #undef FIELD
2819 #define FIELD maff
2820 #undef DEFAULT_IS_ZERO
2821 #define DEFAULT_IS_ZERO 0
2822
2823 #define NO_NEG
2824 #define NO_EVAL
2825 #define NO_OPT
2826 #define NO_INVOLVES_DIMS
2827 #define NO_MOVE_DIMS
2828 #define NO_INSERT_DIMS
2829 #define NO_LIFT
2830 #define NO_MORPH
2831
2832 #include <isl_pw_templ.c>
2833
2834 #undef UNION
2835 #define UNION isl_union_pw_multi_aff
2836 #undef PART
2837 #define PART isl_pw_multi_aff
2838 #undef PARTS
2839 #define PARTS pw_multi_aff
2840 #define ALIGN_DOMAIN
2841
2842 #define NO_EVAL
2843
2844 #include <isl_union_templ.c>
2845
2846 /* Given a function "cmp" that returns the set of elements where
2847 * "ma1" is "better" than "ma2", return the intersection of this
2848 * set with "dom1" and "dom2".
2849 */
2850 static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1,
2851 __isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1,
2852 __isl_keep isl_multi_aff *ma2,
2853 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
2854 __isl_take isl_multi_aff *ma2))
2855 {
2856 isl_set *common;
2857 isl_set *better;
2858 int is_empty;
2859
2860 common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2));
2861 is_empty = isl_set_plain_is_empty(common);
2862 if (is_empty >= 0 && is_empty)
2863 return common;
2864 if (is_empty < 0)
2865 return isl_set_free(common);
2866 better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2));
2867 better = isl_set_intersect(common, better);
2868
2869 return better;
2870 }
2871
2872 /* Given a function "cmp" that returns the set of elements where
2873 * "ma1" is "better" than "ma2", return a piecewise multi affine
2874 * expression defined on the union of the definition domains
2875 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
2876 * "pma2" on each cell. If only one of the two input functions
2877 * is defined on a given cell, then it is considered the best.
2878 */
2879 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt(
2880 __isl_take isl_pw_multi_aff *pma1,
2881 __isl_take isl_pw_multi_aff *pma2,
2882 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
2883 __isl_take isl_multi_aff *ma2))
2884 {
2885 int i, j, n;
2886 isl_pw_multi_aff *res = NULL;
2887 isl_ctx *ctx;
2888 isl_set *set = NULL;
2889
2890 if (!pma1 || !pma2)
2891 goto error;
2892
2893 ctx = isl_space_get_ctx(pma1->dim);
2894 if (!isl_space_is_equal(pma1->dim, pma2->dim))
2895 isl_die(ctx, isl_error_invalid,
2896 "arguments should live in the same space", goto error);
2897
2898 if (isl_pw_multi_aff_is_empty(pma1)) {
2899 isl_pw_multi_aff_free(pma1);
2900 return pma2;
2901 }
2902
2903 if (isl_pw_multi_aff_is_empty(pma2)) {
2904 isl_pw_multi_aff_free(pma2);
2905 return pma1;
2906 }
2907
2908 n = 2 * (pma1->n + 1) * (pma2->n + 1);
2909 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n);
2910
2911 for (i = 0; i < pma1->n; ++i) {
2912 set = isl_set_copy(pma1->p[i].set);
2913 for (j = 0; j < pma2->n; ++j) {
2914 isl_set *better;
2915 int is_empty;
2916
2917 better = shared_and_better(pma2->p[j].set,
2918 pma1->p[i].set, pma2->p[j].maff,
2919 pma1->p[i].maff, cmp);
2920 is_empty = isl_set_plain_is_empty(better);
2921 if (is_empty < 0 || is_empty) {
2922 isl_set_free(better);
2923 if (is_empty < 0)
2924 goto error;
2925 continue;
2926 }
2927 set = isl_set_subtract(set, isl_set_copy(better));
2928
2929 res = isl_pw_multi_aff_add_piece(res, better,
2930 isl_multi_aff_copy(pma2->p[j].maff));
2931 }
2932 res = isl_pw_multi_aff_add_piece(res, set,
2933 isl_multi_aff_copy(pma1->p[i].maff));
2934 }
2935
2936 for (j = 0; j < pma2->n; ++j) {
2937 set = isl_set_copy(pma2->p[j].set);
2938 for (i = 0; i < pma1->n; ++i)
2939 set = isl_set_subtract(set,
2940 isl_set_copy(pma1->p[i].set));
2941 res = isl_pw_multi_aff_add_piece(res, set,
2942 isl_multi_aff_copy(pma2->p[j].maff));
2943 }
2944
2945 isl_pw_multi_aff_free(pma1);
2946 isl_pw_multi_aff_free(pma2);
2947
2948 return res;
2949 error:
2950 isl_pw_multi_aff_free(pma1);
2951 isl_pw_multi_aff_free(pma2);
2952 isl_set_free(set);
2953 return isl_pw_multi_aff_free(res);
2954 }
2955
2956 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
2957 __isl_take isl_pw_multi_aff *pma1,
2958 __isl_take isl_pw_multi_aff *pma2)
2959 {
2960 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_ge_set);
2961 }
2962
2963 /* Given two piecewise multi affine expressions, return a piecewise
2964 * multi-affine expression defined on the union of the definition domains
2965 * of the inputs that is equal to the lexicographic maximum of the two
2966 * inputs on each cell. If only one of the two inputs is defined on
2967 * a given cell, then it is considered to be the maximum.
2968 */
2969 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
2970 __isl_take isl_pw_multi_aff *pma1,
2971 __isl_take isl_pw_multi_aff *pma2)
2972 {
2973 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2974 &pw_multi_aff_union_lexmax);
2975 }
2976
2977 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
2978 __isl_take isl_pw_multi_aff *pma1,
2979 __isl_take isl_pw_multi_aff *pma2)
2980 {
2981 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_set);
2982 }
2983
2984 /* Given two piecewise multi affine expressions, return a piecewise
2985 * multi-affine expression defined on the union of the definition domains
2986 * of the inputs that is equal to the lexicographic minimum of the two
2987 * inputs on each cell. If only one of the two inputs is defined on
2988 * a given cell, then it is considered to be the minimum.
2989 */
2990 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
2991 __isl_take isl_pw_multi_aff *pma1,
2992 __isl_take isl_pw_multi_aff *pma2)
2993 {
2994 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2995 &pw_multi_aff_union_lexmin);
2996 }
2997
2998 static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
2999 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3000 {
3001 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
3002 &isl_multi_aff_add);
3003 }
3004
3005 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3006 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3007 {
3008 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3009 &pw_multi_aff_add);
3010 }
3011
3012 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3013 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3014 {
3015 return isl_pw_multi_aff_union_add_(pma1, pma2);
3016 }
3017
3018 /* Given two piecewise multi-affine expressions A -> B and C -> D,
3019 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
3020 */
3021 static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
3022 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3023 {
3024 int i, j, n;
3025 isl_space *space;
3026 isl_pw_multi_aff *res;
3027
3028 if (!pma1 || !pma2)
3029 goto error;
3030
3031 n = pma1->n * pma2->n;
3032 space = isl_space_product(isl_space_copy(pma1->dim),
3033 isl_space_copy(pma2->dim));
3034 res = isl_pw_multi_aff_alloc_size(space, n);
3035
3036 for (i = 0; i < pma1->n; ++i) {
3037 for (j = 0; j < pma2->n; ++j) {
3038 isl_set *domain;
3039 isl_multi_aff *ma;
3040
3041 domain = isl_set_product(isl_set_copy(pma1->p[i].set),
3042 isl_set_copy(pma2->p[j].set));
3043 ma = isl_multi_aff_product(
3044 isl_multi_aff_copy(pma1->p[i].maff),
3045 isl_multi_aff_copy(pma2->p[i].maff));
3046 res = isl_pw_multi_aff_add_piece(res, domain, ma);
3047 }
3048 }
3049
3050 isl_pw_multi_aff_free(pma1);
3051 isl_pw_multi_aff_free(pma2);
3052 return res;
3053 error:
3054 isl_pw_multi_aff_free(pma1);
3055 isl_pw_multi_aff_free(pma2);
3056 return NULL;
3057 }
3058
3059 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3060 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3061 {
3062 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3063 &pw_multi_aff_product);
3064 }
3065
3066 /* Construct a map mapping the domain of the piecewise multi-affine expression
3067 * to its range, with each dimension in the range equated to the
3068 * corresponding affine expression on its cell.
3069 */
3070 __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
3071 {
3072 int i;
3073 isl_map *map;
3074
3075 if (!pma)
3076 return NULL;
3077
3078 map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
3079
3080 for (i = 0; i < pma->n; ++i) {
3081 isl_multi_aff *maff;
3082 isl_basic_map *bmap;
3083 isl_map *map_i;
3084
3085 maff = isl_multi_aff_copy(pma->p[i].maff);
3086 bmap = isl_basic_map_from_multi_aff(maff);
3087 map_i = isl_map_from_basic_map(bmap);
3088 map_i = isl_map_intersect_domain(map_i,
3089 isl_set_copy(pma->p[i].set));
3090 map = isl_map_union_disjoint(map, map_i);
3091 }
3092
3093 isl_pw_multi_aff_free(pma);
3094 return map;
3095 }
3096
3097 __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
3098 {
3099 if (!pma)
3100 return NULL;
3101
3102 if (!isl_space_is_set(pma->dim))
3103 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3104 "isl_pw_multi_aff cannot be converted into an isl_set",
3105 return isl_pw_multi_aff_free(pma));
3106
3107 return isl_map_from_pw_multi_aff(pma);
3108 }
3109
3110 /* Given a basic map with a single output dimension that is defined
3111 * in terms of the parameters and input dimensions using an equality,
3112 * extract an isl_aff that expresses the output dimension in terms
3113 * of the parameters and input dimensions.
3114 *
3115 * Since some applications expect the result of isl_pw_multi_aff_from_map
3116 * to only contain integer affine expressions, we compute the floor
3117 * of the expression before returning.
3118 *
3119 * This function shares some similarities with
3120 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
3121 */
3122 static __isl_give isl_aff *extract_isl_aff_from_basic_map(
3123 __isl_take isl_basic_map *bmap)
3124 {
3125 int i;
3126 unsigned offset;
3127 unsigned total;
3128 isl_local_space *ls;
3129 isl_aff *aff;
3130
3131 if (!bmap)
3132 return NULL;
3133 if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
3134 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3135 "basic map should have a single output dimension",
3136 goto error);
3137 offset = isl_basic_map_offset(bmap, isl_dim_out);
3138 total = isl_basic_map_total_dim(bmap);
3139 for (i = 0; i < bmap->n_eq; ++i) {
3140 if (isl_int_is_zero(bmap->eq[i][offset]))
3141 continue;
3142 if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
3143 1 + total - (offset + 1)) != -1)
3144 continue;
3145 break;
3146 }
3147 if (i >= bmap->n_eq)
3148 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3149 "unable to find suitable equality", goto error);
3150 ls = isl_basic_map_get_local_space(bmap);
3151 aff = isl_aff_alloc(isl_local_space_domain(ls));
3152 if (!aff)
3153 goto error;
3154 if (isl_int_is_neg(bmap->eq[i][offset]))
3155 isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
3156 else
3157 isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
3158 isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
3159 isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
3160 isl_basic_map_free(bmap);
3161
3162 aff = isl_aff_remove_unused_divs(aff);
3163 aff = isl_aff_floor(aff);
3164 return aff;
3165 error:
3166 isl_basic_map_free(bmap);
3167 return NULL;
3168 }
3169
3170 /* Given a basic map where each output dimension is defined
3171 * in terms of the parameters and input dimensions using an equality,
3172 * extract an isl_multi_aff that expresses the output dimensions in terms
3173 * of the parameters and input dimensions.
3174 */
3175 static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
3176 __isl_take isl_basic_map *bmap)
3177 {
3178 int i;
3179 unsigned n_out;
3180 isl_multi_aff *ma;
3181
3182 if (!bmap)
3183 return NULL;
3184
3185 ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
3186 n_out = isl_basic_map_dim(bmap, isl_dim_out);
3187
3188 for (i = 0; i < n_out; ++i) {
3189 isl_basic_map *bmap_i;
3190 isl_aff *aff;
3191
3192 bmap_i = isl_basic_map_copy(bmap);
3193 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
3194 i + 1, n_out - (1 + i));
3195 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
3196 aff = extract_isl_aff_from_basic_map(bmap_i);
3197 ma = isl_multi_aff_set_aff(ma, i, aff);
3198 }
3199
3200 isl_basic_map_free(bmap);
3201
3202 return ma;
3203 }
3204
3205 /* Create an isl_pw_multi_aff that is equivalent to
3206 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
3207 * The given basic map is such that each output dimension is defined
3208 * in terms of the parameters and input dimensions using an equality.
3209 */
3210 static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
3211 __isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
3212 {
3213 isl_multi_aff *ma;
3214
3215 ma = extract_isl_multi_aff_from_basic_map(bmap);
3216 return isl_pw_multi_aff_alloc(domain, ma);
3217 }
3218
3219 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3220 * This obviously only works if the input "map" is single-valued.
3221 * If so, we compute the lexicographic minimum of the image in the form
3222 * of an isl_pw_multi_aff. Since the image is unique, it is equal
3223 * to its lexicographic minimum.
3224 * If the input is not single-valued, we produce an error.
3225 */
3226 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_base(
3227 __isl_take isl_map *map)
3228 {
3229 int i;
3230 int sv;
3231 isl_pw_multi_aff *pma;
3232
3233 sv = isl_map_is_single_valued(map);
3234 if (sv < 0)
3235 goto error;
3236 if (!sv)
3237 isl_die(isl_map_get_ctx(map), isl_error_invalid,
3238 "map is not single-valued", goto error);
3239 map = isl_map_make_disjoint(map);
3240 if (!map)
3241 return NULL;
3242
3243 pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
3244
3245 for (i = 0; i < map->n; ++i) {
3246 isl_pw_multi_aff *pma_i;
3247 isl_basic_map *bmap;
3248 bmap = isl_basic_map_copy(map->p[i]);
3249 pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
3250 pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
3251 }
3252
3253 isl_map_free(map);
3254 return pma;
3255 error:
3256 isl_map_free(map);
3257 return NULL;
3258 }
3259
3260 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
3261 * taking into account that the output dimension at position "d"
3262 * can be represented as
3263 *
3264 * x = floor((e(...) + c1) / m)
3265 *
3266 * given that constraint "i" is of the form
3267 *
3268 * e(...) + c1 - m x >= 0
3269 *
3270 *
3271 * Let "map" be of the form
3272 *
3273 * A -> B
3274 *
3275 * We construct a mapping
3276 *
3277 * A -> [A -> x = floor(...)]
3278 *
3279 * apply that to the map, obtaining
3280 *
3281 * [A -> x = floor(...)] -> B
3282 *
3283 * and equate dimension "d" to x.
3284 * We then compute a isl_pw_multi_aff representation of the resulting map
3285 * and plug in the mapping above.
3286 */
3287 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_div(
3288 __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i)
3289 {
3290 isl_ctx *ctx;
3291 isl_space *space;
3292 isl_local_space *ls;
3293 isl_multi_aff *ma;
3294 isl_aff *aff;
3295 isl_vec *v;
3296 isl_map *insert;
3297 int offset;
3298 int n;
3299 int n_in;
3300 isl_pw_multi_aff *pma;
3301 int is_set;
3302
3303 is_set = isl_map_is_set(map);
3304
3305 offset = isl_basic_map_offset(hull, isl_dim_out);
3306 ctx = isl_map_get_ctx(map);
3307 space = isl_space_domain(isl_map_get_space(map));
3308 n_in = isl_space_dim(space, isl_dim_set);
3309 n = isl_space_dim(space, isl_dim_all);
3310
3311 v = isl_vec_alloc(ctx, 1 + 1 + n);
3312 if (v) {
3313 isl_int_neg(v->el[0], hull->ineq[i][offset + d]);
3314 isl_seq_cpy(v->el + 1, hull->ineq[i], 1 + n);
3315 }
3316 isl_basic_map_free(hull);
3317
3318 ls = isl_local_space_from_space(isl_space_copy(space));
3319 aff = isl_aff_alloc_vec(ls, v);
3320 aff = isl_aff_floor(aff);
3321 if (is_set) {
3322 isl_space_free(space);
3323 ma = isl_multi_aff_from_aff(aff);
3324 } else {
3325 ma = isl_multi_aff_identity(isl_space_map_from_set(space));
3326 ma = isl_multi_aff_range_product(ma,
3327 isl_multi_aff_from_aff(aff));
3328 }
3329
3330 insert = isl_map_from_multi_aff(isl_multi_aff_copy(ma));
3331 map = isl_map_apply_domain(map, insert);
3332 map = isl_map_equate(map, isl_dim_in, n_in, isl_dim_out, d);
3333 pma = isl_pw_multi_aff_from_map(map);
3334 pma = isl_pw_multi_aff_pullback_multi_aff(pma, ma);
3335
3336 return pma;
3337 }
3338
3339 /* Is constraint "c" of the form
3340 *
3341 * e(...) + c1 - m x >= 0
3342 *
3343 * or
3344 *
3345 * -e(...) + c2 + m x >= 0
3346 *
3347 * where m > 1 and e only depends on parameters and input dimemnsions?
3348 *
3349 * "offset" is the offset of the output dimensions
3350 * "pos" is the position of output dimension x.
3351 */
3352 static int is_potential_div_constraint(isl_int *c, int offset, int d, int total)
3353 {
3354 if (isl_int_is_zero(c[offset + d]))
3355 return 0;
3356 if (isl_int_is_one(c[offset + d]))
3357 return 0;
3358 if (isl_int_is_negone(c[offset + d]))
3359 return 0;
3360 if (isl_seq_first_non_zero(c + offset, d) != -1)
3361 return 0;
3362 if (isl_seq_first_non_zero(c + offset + d + 1,
3363 total - (offset + d + 1)) != -1)
3364 return 0;
3365 return 1;
3366 }
3367
3368 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3369 *
3370 * As a special case, we first check if there is any pair of constraints,
3371 * shared by all the basic maps in "map" that force a given dimension
3372 * to be equal to the floor of some affine combination of the input dimensions.
3373 *
3374 * In particular, if we can find two constraints
3375 *
3376 * e(...) + c1 - m x >= 0 i.e., m x <= e(...) + c1
3377 *
3378 * and
3379 *
3380 * -e(...) + c2 + m x >= 0 i.e., m x >= e(...) - c2
3381 *
3382 * where m > 1 and e only depends on parameters and input dimemnsions,
3383 * and such that
3384 *
3385 * c1 + c2 < m i.e., -c2 >= c1 - (m - 1)
3386 *
3387 * then we know that we can take
3388 *
3389 * x = floor((e(...) + c1) / m)
3390 *
3391 * without having to perform any computation.
3392 *
3393 * Note that we know that
3394 *
3395 * c1 + c2 >= 1
3396 *
3397 * If c1 + c2 were 0, then we would have detected an equality during
3398 * simplification. If c1 + c2 were negative, then we would have detected
3399 * a contradiction.
3400 */
3401 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_check_div(
3402 __isl_take isl_map *map)
3403 {
3404 int d, dim;
3405 int i, j, n;
3406 int offset, total;
3407 isl_int sum;
3408 isl_basic_map *hull;
3409
3410 hull = isl_map_unshifted_simple_hull(isl_map_copy(map));
3411 if (!hull)
3412 goto error;
3413
3414 isl_int_init(sum);
3415 dim = isl_map_dim(map, isl_dim_out);
3416 offset = isl_basic_map_offset(hull, isl_dim_out);
3417 total = 1 + isl_basic_map_total_dim(hull);
3418 n = hull->n_ineq;
3419 for (d = 0; d < dim; ++d) {
3420 for (i = 0; i < n; ++i) {
3421 if (!is_potential_div_constraint(hull->ineq[i],
3422 offset, d, total))
3423 continue;
3424 for (j = i + 1; j < n; ++j) {
3425 if (!isl_seq_is_neg(hull->ineq[i] + 1,
3426 hull->ineq[j] + 1, total - 1))
3427 continue;
3428 isl_int_add(sum, hull->ineq[i][0],
3429 hull->ineq[j][0]);
3430 if (isl_int_abs_lt(sum,
3431 hull->ineq[i][offset + d]))
3432 break;
3433
3434 }
3435 if (j >= n)
3436 continue;
3437 isl_int_clear(sum);
3438 if (isl_int_is_pos(hull->ineq[j][offset + d]))
3439 j = i;
3440 return pw_multi_aff_from_map_div(map, hull, d, j);
3441 }
3442 }
3443 isl_int_clear(sum);
3444 isl_basic_map_free(hull);
3445 return pw_multi_aff_from_map_base(map);
3446 error:
3447 isl_map_free(map);
3448 isl_basic_map_free(hull);
3449 return NULL;
3450 }
3451
3452 /* Given an affine expression
3453 *
3454 * [A -> B] -> f(A,B)
3455 *
3456 * construct an isl_multi_aff
3457 *
3458 * [A -> B] -> B'
3459 *
3460 * such that dimension "d" in B' is set to "aff" and the remaining
3461 * dimensions are set equal to the corresponding dimensions in B.
3462 * "n_in" is the dimension of the space A.
3463 * "n_out" is the dimension of the space B.
3464 *
3465 * If "is_set" is set, then the affine expression is of the form
3466 *
3467 * [B] -> f(B)
3468 *
3469 * and we construct an isl_multi_aff
3470 *
3471 * B -> B'
3472 */
3473 static __isl_give isl_multi_aff *range_map(__isl_take isl_aff *aff, int d,
3474 unsigned n_in, unsigned n_out, int is_set)
3475 {
3476 int i;
3477 isl_multi_aff *ma;
3478 isl_space *space, *space2;
3479 isl_local_space *ls;
3480
3481 space = isl_aff_get_domain_space(aff);
3482 ls = isl_local_space_from_space(isl_space_copy(space));
3483 space2 = isl_space_copy(space);
3484 if (!is_set)
3485 space2 = isl_space_range(isl_space_unwrap(space2));
3486 space = isl_space_map_from_domain_and_range(space, space2);
3487 ma = isl_multi_aff_alloc(space);
3488 ma = isl_multi_aff_set_aff(ma, d, aff);
3489
3490 for (i = 0; i < n_out; ++i) {
3491 if (i == d)
3492 continue;
3493 aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
3494 isl_dim_set, n_in + i);
3495 ma = isl_multi_aff_set_aff(ma, i, aff);
3496 }
3497
3498 isl_local_space_free(ls);
3499
3500 return ma;
3501 }
3502
3503 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
3504 * taking into account that the dimension at position "d" can be written as
3505 *
3506 * x = m a + f(..) (1)
3507 *
3508 * where m is equal to "gcd".
3509 * "i" is the index of the equality in "hull" that defines f(..).
3510 * In particular, the equality is of the form
3511 *
3512 * f(..) - x + m g(existentials) = 0
3513 *
3514 * or
3515 *
3516 * -f(..) + x + m g(existentials) = 0
3517 *
3518 * We basically plug (1) into "map", resulting in a map with "a"
3519 * in the range instead of "x". The corresponding isl_pw_multi_aff
3520 * defining "a" is then plugged back into (1) to obtain a definition fro "x".
3521 *
3522 * Specifically, given the input map
3523 *
3524 * A -> B
3525 *
3526 * We first wrap it into a set
3527 *
3528 * [A -> B]
3529 *
3530 * and define (1) on top of the corresponding space, resulting in "aff".
3531 * We use this to create an isl_multi_aff that maps the output position "d"
3532 * from "a" to "x", leaving all other (intput and output) dimensions unchanged.
3533 * We plug this into the wrapped map, unwrap the result and compute the
3534 * corresponding isl_pw_multi_aff.
3535 * The result is an expression
3536 *
3537 * A -> T(A)
3538 *
3539 * We adjust that to
3540 *
3541 * A -> [A -> T(A)]
3542 *
3543 * so that we can plug that into "aff", after extending the latter to
3544 * a mapping
3545 *
3546 * [A -> B] -> B'
3547 *
3548 *
3549 * If "map" is actually a set, then there is no "A" space, meaning
3550 * that we do not need to perform any wrapping, and that the result
3551 * of the recursive call is of the form
3552 *
3553 * [T]
3554 *
3555 * which is plugged into a mapping of the form
3556 *
3557 * B -> B'
3558 */
3559 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_stride(
3560 __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i,
3561 isl_int gcd)
3562 {
3563 isl_set *set;
3564 isl_space *space;
3565 isl_local_space *ls;
3566 isl_aff *aff;
3567 isl_multi_aff *ma;
3568 isl_pw_multi_aff *pma, *id;
3569 unsigned n_in;
3570 unsigned o_out;
3571 unsigned n_out;
3572 int is_set;
3573
3574 is_set = isl_map_is_set(map);
3575
3576 n_in = isl_basic_map_dim(hull, isl_dim_in);
3577 n_out = isl_basic_map_dim(hull, isl_dim_out);
3578 o_out = isl_basic_map_offset(hull, isl_dim_out);
3579
3580 if (is_set)
3581 set = map;
3582 else
3583 set = isl_map_wrap(map);
3584 space = isl_space_map_from_set(isl_set_get_space(set));
3585 ma = isl_multi_aff_identity(space);
3586 ls = isl_local_space_from_space(isl_set_get_space(set));
3587 aff = isl_aff_alloc(ls);
3588 if (aff) {
3589 isl_int_set_si(aff->v->el[0], 1);
3590 if (isl_int_is_one(hull->eq[i][o_out + d]))
3591 isl_seq_neg(aff->v->el + 1, hull->eq[i],
3592 aff->v->size - 1);
3593 else
3594 isl_seq_cpy(aff->v->el + 1, hull->eq[i],
3595 aff->v->size - 1);
3596 isl_int_set(aff->v->el[1 + o_out + d], gcd);
3597 }
3598 ma = isl_multi_aff_set_aff(ma, n_in + d, isl_aff_copy(aff));
3599 set = isl_set_preimage_multi_aff(set, ma);
3600
3601 ma = range_map(aff, d, n_in, n_out, is_set);
3602
3603 if (is_set)
3604 map = set;
3605 else
3606 map = isl_set_unwrap(set);
3607 pma = isl_pw_multi_aff_from_map(set);
3608
3609 if (!is_set) {
3610 space = isl_pw_multi_aff_get_domain_space(pma);
3611 space = isl_space_map_from_set(space);
3612 id = isl_pw_multi_aff_identity(space);
3613 pma = isl_pw_multi_aff_range_product(id, pma);
3614 }
3615 id = isl_pw_multi_aff_from_multi_aff(ma);
3616 pma = isl_pw_multi_aff_pullback_pw_multi_aff(id, pma);
3617
3618 isl_basic_map_free(hull);
3619 return pma;
3620 }
3621
3622 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3623 *
3624 * As a special case, we first check if all output dimensions are uniquely
3625 * defined in terms of the parameters and input dimensions over the entire
3626 * domain. If so, we extract the desired isl_pw_multi_aff directly
3627 * from the affine hull of "map" and its domain.
3628 *
3629 * Otherwise, we check if any of the output dimensions is "strided".
3630 * That is, we check if can be written as
3631 *
3632 * x = m a + f(..)
3633 *
3634 * with m greater than 1, a some combination of existentiall quantified
3635 * variables and f and expression in the parameters and input dimensions.
3636 * If so, we remove the stride in pw_multi_aff_from_map_stride.
3637 *
3638 * Otherwise, we continue with pw_multi_aff_from_map_check_div for a further
3639 * special case.
3640 */
3641 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
3642 {
3643 int i, j;
3644 int sv;
3645 isl_basic_map *hull;
3646 unsigned n_out;
3647 unsigned o_out;
3648 unsigned n_div;
3649 unsigned o_div;
3650 isl_int gcd;
3651
3652 if (!map)
3653 return NULL;
3654
3655 hull = isl_map_affine_hull(isl_map_copy(map));
3656 sv = isl_basic_map_plain_is_single_valued(hull);
3657 if (sv >= 0 && sv)
3658 return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
3659 if (sv < 0)
3660 hull = isl_basic_map_free(hull);
3661 if (!hull)
3662 goto error;
3663
3664 n_div = isl_basic_map_dim(hull, isl_dim_div);
3665 o_div = isl_basic_map_offset(hull, isl_dim_div);
3666
3667 if (n_div == 0) {
3668 isl_basic_map_free(hull);
3669 return pw_multi_aff_from_map_check_div(map);
3670 }
3671
3672 isl_int_init(gcd);
3673
3674 n_out = isl_basic_map_dim(hull, isl_dim_out);
3675 o_out = isl_basic_map_offset(hull, isl_dim_out);
3676
3677 for (i = 0; i < n_out; ++i) {
3678 for (j = 0; j < hull->n_eq; ++j) {
3679 isl_int *eq = hull->eq[j];
3680 isl_pw_multi_aff *res;
3681
3682 if (!isl_int_is_one(eq[o_out + i]) &&
3683 !isl_int_is_negone(eq[o_out + i]))
3684 continue;
3685 if (isl_seq_first_non_zero(eq + o_out, i) != -1)
3686 continue;
3687 if (isl_seq_first_non_zero(eq + o_out + i + 1,
3688 n_out - (i + 1)) != -1)
3689 continue;
3690 isl_seq_gcd(eq + o_div, n_div, &gcd);
3691 if (isl_int_is_zero(gcd))
3692 continue;
3693 if (isl_int_is_one(gcd))
3694 continue;
3695
3696 res = pw_multi_aff_from_map_stride(map, hull,
3697 i, j, gcd);
3698 isl_int_clear(gcd);
3699 return res;
3700 }
3701 }
3702
3703 isl_int_clear(gcd);
3704 isl_basic_map_free(hull);
3705 return pw_multi_aff_from_map_check_div(map);
3706 error:
3707 isl_map_free(map);
3708 return NULL;
3709 }
3710
3711 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
3712 {
3713 return isl_pw_multi_aff_from_map(set);
3714 }
3715
3716 /* Return the piecewise affine expression "set ? 1 : 0".
3717 */
3718 __isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
3719 {
3720 isl_pw_aff *pa;
3721 isl_space *space = isl_set_get_space(set);
3722 isl_local_space *ls = isl_local_space_from_space(space);
3723 isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
3724 isl_aff *one = isl_aff_zero_on_domain(ls);
3725
3726 one = isl_aff_add_constant_si(one, 1);
3727 pa = isl_pw_aff_alloc(isl_set_copy(set), one);
3728 set = isl_set_complement(set);
3729 pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
3730
3731 return pa;
3732 }
3733
3734 /* Plug in "subs" for dimension "type", "pos" of "aff".
3735 *
3736 * Let i be the dimension to replace and let "subs" be of the form
3737 *
3738 * f/d
3739 *
3740 * and "aff" of the form
3741 *
3742 * (a i + g)/m
3743 *
3744 * The result is
3745 *
3746 * (a f + d g')/(m d)
3747 *
3748 * where g' is the result of plugging in "subs" in each of the integer
3749 * divisions in g.
3750 */
3751 __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
3752 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
3753 {
3754 isl_ctx *ctx;
3755 isl_int v;
3756
3757 aff = isl_aff_cow(aff);
3758 if (!aff || !subs)
3759 return isl_aff_free(aff);
3760
3761 ctx = isl_aff_get_ctx(aff);
3762 if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
3763 isl_die(ctx, isl_error_invalid,
3764 "spaces don't match", return isl_aff_free(aff));
3765 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
3766 isl_die(ctx, isl_error_unsupported,
3767 "cannot handle divs yet", return isl_aff_free(aff));
3768
3769 aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
3770 if (!aff->ls)
3771 return isl_aff_free(aff);
3772
3773 aff->v = isl_vec_cow(aff->v);
3774 if (!aff->v)
3775 return isl_aff_free(aff);
3776
3777 pos += isl_local_space_offset(aff->ls, type);
3778
3779 isl_int_init(v);
3780 isl_seq_substitute(aff->v->el, pos, subs->v->el,
3781 aff->v->size, subs->v->size, v);
3782 isl_int_clear(v);
3783
3784 return aff;
3785 }
3786
3787 /* Plug in "subs" for dimension "type", "pos" in each of the affine
3788 * expressions in "maff".
3789 */
3790 __isl_give isl_multi_aff *isl_multi_aff_substitute(
3791 __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
3792 __isl_keep isl_aff *subs)
3793 {
3794 int i;
3795
3796 maff = isl_multi_aff_cow(maff);
3797 if (!maff || !subs)
3798 return isl_multi_aff_free(maff);
3799
3800 if (type == isl_dim_in)
3801 type = isl_dim_set;
3802
3803 for (i = 0; i < maff->n; ++i) {
3804 maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
3805 if (!maff->p[i])
3806 return isl_multi_aff_free(maff);
3807 }
3808
3809 return maff;
3810 }
3811
3812 /* Plug in "subs" for dimension "type", "pos" of "pma".
3813 *
3814 * pma is of the form
3815 *
3816 * A_i(v) -> M_i(v)
3817 *
3818 * while subs is of the form
3819 *
3820 * v' = B_j(v) -> S_j
3821 *
3822 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
3823 * has a contribution in the result, in particular
3824 *
3825 * C_ij(S_j) -> M_i(S_j)
3826 *
3827 * Note that plugging in S_j in C_ij may also result in an empty set
3828 * and this contribution should simply be discarded.
3829 */
3830 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
3831 __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
3832 __isl_keep isl_pw_aff *subs)
3833 {
3834 int i, j, n;
3835 isl_pw_multi_aff *res;
3836
3837 if (!pma || !subs)
3838 return isl_pw_multi_aff_free(pma);
3839
3840 n = pma->n * subs->n;
3841 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
3842
3843 for (i = 0; i < pma->n; ++i) {
3844 for (j = 0; j < subs->n; ++j) {
3845 isl_set *common;
3846 isl_multi_aff *res_ij;
3847 int empty;
3848
3849 common = isl_set_intersect(
3850 isl_set_copy(pma->p[i].set),
3851 isl_set_copy(subs->p[j].set));
3852 common = isl_set_substitute(common,
3853 type, pos, subs->p[j].aff);
3854 empty = isl_set_plain_is_empty(common);
3855 if (empty < 0 || empty) {
3856 isl_set_free(common);
3857 if (empty < 0)
3858 goto error;
3859 continue;
3860 }
3861
3862 res_ij = isl_multi_aff_substitute(
3863 isl_multi_aff_copy(pma->p[i].maff),
3864 type, pos, subs->p[j].aff);
3865
3866 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
3867 }
3868 }
3869
3870 isl_pw_multi_aff_free(pma);
3871 return res;
3872 error:
3873 isl_pw_multi_aff_free(pma);
3874 isl_pw_multi_aff_free(res);
3875 return NULL;
3876 }
3877
3878 /* Compute the preimage of the affine expression "src" under "ma"
3879 * and put the result in "dst". If "has_denom" is set (to one),
3880 * then "src" and "dst" have an extra initial denominator.
3881 * "n_div_ma" is the number of existentials in "ma"
3882 * "n_div_bset" is the number of existentials in "src"
3883 * The resulting "dst" (which is assumed to have been allocated by
3884 * the caller) contains coefficients for both sets of existentials,
3885 * first those in "ma" and then those in "src".
3886 * f, c1, c2 and g are temporary objects that have been initialized
3887 * by the caller.
3888 *
3889 * Let src represent the expression
3890 *
3891 * (a(p) + b x + c(divs))/d
3892 *
3893 * and let ma represent the expressions
3894 *
3895 * x_i = (r_i(p) + s_i(y) + t_i(divs'))/m_i
3896 *
3897 * We start out with the following expression for dst:
3898 *
3899 * (a(p) + 0 y + 0 divs' + f \sum_i b_i x_i + c(divs))/d
3900 *
3901 * with the multiplication factor f initially equal to 1.
3902 * For each x_i that we substitute, we multiply the numerator
3903 * (and denominator) of dst by c_1 = m_i and add the numerator
3904 * of the x_i expression multiplied by c_2 = f b_i,
3905 * after removing the common factors of c_1 and c_2.
3906 * The multiplication factor f also needs to be multiplied by c_1
3907 * for the next x_j, j > i.
3908 */
3909 void isl_seq_preimage(isl_int *dst, isl_int *src,
3910 __isl_keep isl_multi_aff *ma, int n_div_ma, int n_div_bset,
3911 isl_int f, isl_int c1, isl_int c2, isl_int g, int has_denom)
3912 {
3913 int i;
3914 int n_param, n_in, n_out;
3915 int o_div_bset;
3916
3917 n_param = isl_multi_aff_dim(ma, isl_dim_param);
3918 n_in = isl_multi_aff_dim(ma, isl_dim_in);
3919 n_out = isl_multi_aff_dim(ma, isl_dim_out);
3920
3921 o_div_bset = has_denom + 1 + n_param + n_in + n_div_ma;
3922
3923 isl_seq_cpy(dst, src, has_denom + 1 + n_param);
3924 isl_seq_clr(dst + has_denom + 1 + n_param, n_in + n_div_ma);
3925 isl_seq_cpy(dst + o_div_bset,
3926 src + has_denom + 1 + n_param + n_out, n_div_bset);
3927
3928 isl_int_set_si(f, 1);
3929
3930 for (i = 0; i < n_out; ++i) {
3931 if (isl_int_is_zero(src[has_denom + 1 + n_param + i]))
3932 continue;
3933 isl_int_set(c1, ma->p[i]->v->el[0]);
3934 isl_int_mul(c2, f, src[has_denom + 1 + n_param + i]);
3935 isl_int_gcd(g, c1, c2);
3936 isl_int_divexact(c1, c1, g);
3937 isl_int_divexact(c2, c2, g);
3938
3939 isl_int_mul(f, f, c1);
3940 isl_seq_combine(dst + has_denom, c1, dst + has_denom,
3941 c2, ma->p[i]->v->el + 1, ma->p[i]->v->size - 1);
3942 isl_seq_scale(dst + o_div_bset,
3943 dst + o_div_bset, c1, n_div_bset);
3944 if (has_denom)
3945 isl_int_mul(dst[0], dst[0], c1);
3946 }
3947 }
3948
3949 /* Compute the pullback of "aff" by the function represented by "ma".
3950 * In other words, plug in "ma" in "aff". The result is an affine expression
3951 * defined over the domain space of "ma".
3952 *
3953 * If "aff" is represented by
3954 *
3955 * (a(p) + b x + c(divs))/d
3956 *
3957 * and ma is represented by
3958 *
3959 * x = D(p) + F(y) + G(divs')
3960 *
3961 * then the result is
3962 *
3963 * (a(p) + b D(p) + b F(y) + b G(divs') + c(divs))/d
3964 *
3965 * The divs in the local space of the input are similarly adjusted
3966 * through a call to isl_local_space_preimage_multi_aff.
3967 */
3968 __isl_give isl_aff *isl_aff_pullback_multi_aff(__isl_take isl_aff *aff,
3969 __isl_take isl_multi_aff *ma)
3970 {
3971 isl_aff *res = NULL;
3972 isl_local_space *ls;
3973 int n_div_aff, n_div_ma;
3974 isl_int f, c1, c2, g;
3975
3976 ma = isl_multi_aff_align_divs(ma);
3977 if (!aff || !ma)
3978 goto error;
3979
3980 n_div_aff = isl_aff_dim(aff, isl_dim_div);
3981 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
3982
3983 ls = isl_aff_get_domain_local_space(aff);
3984 ls = isl_local_space_preimage_multi_aff(ls, isl_multi_aff_copy(ma));
3985 res = isl_aff_alloc(ls);
3986 if (!res)
3987 goto error;
3988
3989 isl_int_init(f);
3990 isl_int_init(c1);
3991 isl_int_init(c2);
3992 isl_int_init(g);
3993
3994 isl_seq_preimage(res->v->el, aff->v->el, ma, n_div_ma, n_div_aff,
3995 f, c1, c2, g, 1);
3996
3997 isl_int_clear(f);
3998 isl_int_clear(c1);
3999 isl_int_clear(c2);
4000 isl_int_clear(g);
4001
4002 isl_aff_free(aff);
4003 isl_multi_aff_free(ma);
4004 res = isl_aff_normalize(res);
4005 return res;
4006 error:
4007 isl_aff_free(aff);
4008 isl_multi_aff_free(ma);
4009 isl_aff_free(res);
4010 return NULL;
4011 }
4012
4013 /* Compute the pullback of "ma1" by the function represented by "ma2".
4014 * In other words, plug in "ma2" in "ma1".
4015 */
4016 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4017 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
4018 {
4019 int i;
4020 isl_space *space = NULL;
4021
4022 ma2 = isl_multi_aff_align_divs(ma2);
4023 ma1 = isl_multi_aff_cow(ma1);
4024 if (!ma1 || !ma2)
4025 goto error;
4026
4027 space = isl_space_join(isl_multi_aff_get_space(ma2),
4028 isl_multi_aff_get_space(ma1));
4029
4030 for (i = 0; i < ma1->n; ++i) {
4031 ma1->p[i] = isl_aff_pullback_multi_aff(ma1->p[i],
4032 isl_multi_aff_copy(ma2));
4033 if (!ma1->p[i])
4034 goto error;
4035 }
4036
4037 ma1 = isl_multi_aff_reset_space(ma1, space);
4038 isl_multi_aff_free(ma2);
4039 return ma1;
4040 error:
4041 isl_space_free(space);
4042 isl_multi_aff_free(ma2);
4043 isl_multi_aff_free(ma1);
4044 return NULL;
4045 }
4046
4047 /* Extend the local space of "dst" to include the divs
4048 * in the local space of "src".
4049 */
4050 __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
4051 __isl_keep isl_aff *src)
4052 {
4053 isl_ctx *ctx;
4054 int *exp1 = NULL;
4055 int *exp2 = NULL;
4056 isl_mat *div;
4057
4058 if (!src || !dst)
4059 return isl_aff_free(dst);
4060
4061 ctx = isl_aff_get_ctx(src);
4062 if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
4063 isl_die(ctx, isl_error_invalid,
4064 "spaces don't match", goto error);
4065
4066 if (src->ls->div->n_row == 0)
4067 return dst;
4068
4069 exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
4070 exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
4071 if (!exp1 || !exp2)
4072 goto error;
4073
4074 div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
4075 dst = isl_aff_expand_divs(dst, div, exp2);
4076 free(exp1);
4077 free(exp2);
4078
4079 return dst;
4080 error:
4081 free(exp1);
4082 free(exp2);
4083 return isl_aff_free(dst);
4084 }
4085
4086 /* Adjust the local spaces of the affine expressions in "maff"
4087 * such that they all have the save divs.
4088 */
4089 __isl_give isl_multi_aff *isl_multi_aff_align_divs(
4090 __isl_take isl_multi_aff *maff)
4091 {
4092 int i;
4093
4094 if (!maff)
4095 return NULL;
4096 if (maff->n == 0)
4097 return maff;
4098 maff = isl_multi_aff_cow(maff);
4099 if (!maff)
4100 return NULL;
4101
4102 for (i = 1; i < maff->n; ++i)
4103 maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
4104 for (i = 1; i < maff->n; ++i) {
4105 maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
4106 if (!maff->p[i])
4107 return isl_multi_aff_free(maff);
4108 }
4109
4110 return maff;
4111 }
4112
4113 __isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
4114 {
4115 aff = isl_aff_cow(aff);
4116 if (!aff)
4117 return NULL;
4118
4119 aff->ls = isl_local_space_lift(aff->ls);
4120 if (!aff->ls)
4121 return isl_aff_free(aff);
4122
4123 return aff;
4124 }
4125
4126 /* Lift "maff" to a space with extra dimensions such that the result
4127 * has no more existentially quantified variables.
4128 * If "ls" is not NULL, then *ls is assigned the local space that lies
4129 * at the basis of the lifting applied to "maff".
4130 */
4131 __isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
4132 __isl_give isl_local_space **ls)
4133 {
4134 int i;
4135 isl_space *space;
4136 unsigned n_div;
4137
4138 if (ls)
4139 *ls = NULL;
4140
4141 if (!maff)
4142 return NULL;
4143
4144 if (maff->n == 0) {
4145 if (ls) {
4146 isl_space *space = isl_multi_aff_get_domain_space(maff);
4147 *ls = isl_local_space_from_space(space);
4148 if (!*ls)
4149 return isl_multi_aff_free(maff);
4150 }
4151 return maff;
4152 }
4153
4154 maff = isl_multi_aff_cow(maff);
4155 maff = isl_multi_aff_align_divs(maff);
4156 if (!maff)
4157 return NULL;
4158
4159 n_div = isl_aff_dim(maff->p[0], isl_dim_div);
4160 space = isl_multi_aff_get_space(maff);
4161 space = isl_space_lift(isl_space_domain(space), n_div);
4162 space = isl_space_extend_domain_with_range(space,
4163 isl_multi_aff_get_space(maff));
4164 if (!space)
4165 return isl_multi_aff_free(maff);
4166 isl_space_free(maff->space);
4167 maff->space = space;
4168
4169 if (ls) {
4170 *ls = isl_aff_get_domain_local_space(maff->p[0]);
4171 if (!*ls)
4172 return isl_multi_aff_free(maff);
4173 }
4174
4175 for (i = 0; i < maff->n; ++i) {
4176 maff->p[i] = isl_aff_lift(maff->p[i]);
4177 if (!maff->p[i])
4178 goto error;
4179 }
4180
4181 return maff;
4182 error:
4183 if (ls)
4184 isl_local_space_free(*ls);
4185 return isl_multi_aff_free(maff);
4186 }
4187
4188
4189 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
4190 */
4191 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4192 __isl_keep isl_pw_multi_aff *pma, int pos)
4193 {
4194 int i;
4195 int n_out;
4196 isl_space *space;
4197 isl_pw_aff *pa;
4198
4199 if (!pma)
4200 return NULL;
4201
4202 n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
4203 if (pos < 0 || pos >= n_out)
4204 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
4205 "index out of bounds", return NULL);
4206
4207 space = isl_pw_multi_aff_get_space(pma);
4208 space = isl_space_drop_dims(space, isl_dim_out,
4209 pos + 1, n_out - pos - 1);
4210 space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
4211
4212 pa = isl_pw_aff_alloc_size(space, pma->n);
4213 for (i = 0; i < pma->n; ++i) {
4214 isl_aff *aff;
4215 aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
4216 pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
4217 }
4218
4219 return pa;
4220 }
4221
4222 /* Return an isl_pw_multi_aff with the given "set" as domain and
4223 * an unnamed zero-dimensional range.
4224 */
4225 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4226 __isl_take isl_set *set)
4227 {
4228 isl_multi_aff *ma;
4229 isl_space *space;
4230
4231 space = isl_set_get_space(set);
4232 space = isl_space_from_domain(space);
4233 ma = isl_multi_aff_zero(space);
4234 return isl_pw_multi_aff_alloc(set, ma);
4235 }
4236
4237 /* Add an isl_pw_multi_aff with the given "set" as domain and
4238 * an unnamed zero-dimensional range to *user.
4239 */
4240 static int add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user)
4241 {
4242 isl_union_pw_multi_aff **upma = user;
4243 isl_pw_multi_aff *pma;
4244
4245 pma = isl_pw_multi_aff_from_domain(set);
4246 *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
4247
4248 return 0;
4249 }
4250
4251 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
4252 * an unnamed zero-dimensional range.
4253 */
4254 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain(
4255 __isl_take isl_union_set *uset)
4256 {
4257 isl_space *space;
4258 isl_union_pw_multi_aff *upma;
4259
4260 if (!uset)
4261 return NULL;
4262
4263 space = isl_union_set_get_space(uset);
4264 upma = isl_union_pw_multi_aff_empty(space);
4265
4266 if (isl_union_set_foreach_set(uset,
4267 &add_pw_multi_aff_from_domain, &upma) < 0)
4268 goto error;
4269
4270 isl_union_set_free(uset);
4271 return upma;
4272 error:
4273 isl_union_set_free(uset);
4274 isl_union_pw_multi_aff_free(upma);
4275 return NULL;
4276 }
4277
4278 /* Convert "pma" to an isl_map and add it to *umap.
4279 */
4280 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
4281 {
4282 isl_union_map **umap = user;
4283 isl_map *map;
4284
4285 map = isl_map_from_pw_multi_aff(pma);
4286 *umap = isl_union_map_add_map(*umap, map);
4287
4288 return 0;
4289 }
4290
4291 /* Construct a union map mapping the domain of the union
4292 * piecewise multi-affine expression to its range, with each dimension
4293 * in the range equated to the corresponding affine expression on its cell.
4294 */
4295 __isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff(
4296 __isl_take isl_union_pw_multi_aff *upma)
4297 {
4298 isl_space *space;
4299 isl_union_map *umap;
4300
4301 if (!upma)
4302 return NULL;
4303
4304 space = isl_union_pw_multi_aff_get_space(upma);
4305 umap = isl_union_map_empty(space);
4306
4307 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
4308 &map_from_pw_multi_aff, &umap) < 0)
4309 goto error;
4310
4311 isl_union_pw_multi_aff_free(upma);
4312 return umap;
4313 error:
4314 isl_union_pw_multi_aff_free(upma);
4315 isl_union_map_free(umap);
4316 return NULL;
4317 }
4318
4319 /* Local data for bin_entry and the callback "fn".
4320 */
4321 struct isl_union_pw_multi_aff_bin_data {
4322 isl_union_pw_multi_aff *upma2;
4323 isl_union_pw_multi_aff *res;
4324 isl_pw_multi_aff *pma;
4325 int (*fn)(void **entry, void *user);
4326 };
4327
4328 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
4329 * and call data->fn for each isl_pw_multi_aff in data->upma2.
4330 */
4331 static int bin_entry(void **entry, void *user)
4332 {
4333 struct isl_union_pw_multi_aff_bin_data *data = user;
4334 isl_pw_multi_aff *pma = *entry;
4335
4336 data->pma = pma;
4337 if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
4338 data->fn, data) < 0)
4339 return -1;
4340
4341 return 0;
4342 }
4343
4344 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
4345 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
4346 * passed as user field) and the isl_pw_multi_aff from upma2 is available
4347 * as *entry. The callback should adjust data->res if desired.
4348 */
4349 static __isl_give isl_union_pw_multi_aff *bin_op(
4350 __isl_take isl_union_pw_multi_aff *upma1,
4351 __isl_take isl_union_pw_multi_aff *upma2,
4352 int (*fn)(void **entry, void *user))
4353 {
4354 isl_space *space;
4355 struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
4356
4357 space = isl_union_pw_multi_aff_get_space(upma2);
4358 upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
4359 space = isl_union_pw_multi_aff_get_space(upma1);
4360 upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
4361
4362 if (!upma1 || !upma2)
4363 goto error;
4364
4365 data.upma2 = upma2;
4366 data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
4367 upma1->table.n);
4368 if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
4369 &bin_entry, &data) < 0)
4370 goto error;
4371
4372 isl_union_pw_multi_aff_free(upma1);
4373 isl_union_pw_multi_aff_free(upma2);
4374 return data.res;
4375 error:
4376 isl_union_pw_multi_aff_free(upma1);
4377 isl_union_pw_multi_aff_free(upma2);
4378 isl_union_pw_multi_aff_free(data.res);
4379 return NULL;
4380 }
4381
4382 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
4383 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
4384 */
4385 static __isl_give isl_pw_multi_aff *pw_multi_aff_range_product(
4386 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
4387 {
4388 isl_space *space;
4389
4390 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
4391 isl_pw_multi_aff_get_space(pma2));
4392 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
4393 &isl_multi_aff_range_product);
4394 }
4395
4396 /* Given two isl_pw_multi_affs A -> B and C -> D,
4397 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
4398 */
4399 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_product(
4400 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
4401 {
4402 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
4403 &pw_multi_aff_range_product);
4404 }
4405
4406 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
4407 * construct an isl_pw_multi_aff (A * C) -> (B, D).
4408 */
4409 static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
4410 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
4411 {
4412 isl_space *space;
4413
4414 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
4415 isl_pw_multi_aff_get_space(pma2));
4416 space = isl_space_flatten_range(space);
4417 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
4418 &isl_multi_aff_flat_range_product);
4419 }
4420
4421 /* Given two isl_pw_multi_affs A -> B and C -> D,
4422 * construct an isl_pw_multi_aff (A * C) -> (B, D).
4423 */
4424 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
4425 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
4426 {
4427 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
4428 &pw_multi_aff_flat_range_product);
4429 }
4430
4431 /* If data->pma and *entry have the same domain space, then compute
4432 * their flat range product and the result to data->res.
4433 */
4434 static int flat_range_product_entry(void **entry, void *user)
4435 {
4436 struct isl_union_pw_multi_aff_bin_data *data = user;
4437 isl_pw_multi_aff *pma2 = *entry;
4438
4439 if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
4440 pma2->dim, isl_dim_in))
4441 return 0;
4442
4443 pma2 = isl_pw_multi_aff_flat_range_product(
4444 isl_pw_multi_aff_copy(data->pma),
4445 isl_pw_multi_aff_copy(pma2));
4446
4447 data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
4448
4449 return 0;
4450 }
4451
4452 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
4453 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
4454 */
4455 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
4456 __isl_take isl_union_pw_multi_aff *upma1,
4457 __isl_take isl_union_pw_multi_aff *upma2)
4458 {
4459 return bin_op(upma1, upma2, &flat_range_product_entry);
4460 }
4461
4462 /* Replace the affine expressions at position "pos" in "pma" by "pa".
4463 * The parameters are assumed to have been aligned.
4464 *
4465 * The implementation essentially performs an isl_pw_*_on_shared_domain,
4466 * except that it works on two different isl_pw_* types.
4467 */
4468 static __isl_give isl_pw_multi_aff *pw_multi_aff_set_pw_aff(
4469 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4470 __isl_take isl_pw_aff *pa)
4471 {
4472 int i, j, n;
4473 isl_pw_multi_aff *res = NULL;
4474
4475 if (!pma || !pa)
4476 goto error;
4477
4478 if (!isl_space_tuple_match(pma->dim, isl_dim_in, pa->dim, isl_dim_in))
4479 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
4480 "domains don't match", goto error);
4481 if (pos >= isl_pw_multi_aff_dim(pma, isl_dim_out))
4482 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
4483 "index out of bounds", goto error);
4484
4485 n = pma->n * pa->n;
4486 res = isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma), n);
4487
4488 for (i = 0; i < pma->n; ++i) {
4489 for (j = 0; j < pa->n; ++j) {
4490 isl_set *common;
4491 isl_multi_aff *res_ij;
4492 int empty;
4493
4494 common = isl_set_intersect(isl_set_copy(pma->p[i].set),
4495 isl_set_copy(pa->p[j].set));
4496 empty = isl_set_plain_is_empty(common);
4497 if (empty < 0 || empty) {
4498 isl_set_free(common);
4499 if (empty < 0)
4500 goto error;
4501 continue;
4502 }
4503
4504 res_ij = isl_multi_aff_set_aff(
4505 isl_multi_aff_copy(pma->p[i].maff), pos,
4506 isl_aff_copy(pa->p[j].aff));
4507 res_ij = isl_multi_aff_gist(res_ij,
4508 isl_set_copy(common));
4509
4510 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
4511 }
4512 }
4513
4514 isl_pw_multi_aff_free(pma);
4515 isl_pw_aff_free(pa);
4516 return res;
4517 error:
4518 isl_pw_multi_aff_free(pma);
4519 isl_pw_aff_free(pa);
4520 return isl_pw_multi_aff_free(res);
4521 }
4522
4523 /* Replace the affine expressions at position "pos" in "pma" by "pa".
4524 */
4525 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4526 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4527 __isl_take isl_pw_aff *pa)
4528 {
4529 if (!pma || !pa)
4530 goto error;
4531 if (isl_space_match(pma->dim, isl_dim_param, pa->dim, isl_dim_param))
4532 return pw_multi_aff_set_pw_aff(pma, pos, pa);
4533 if (!isl_space_has_named_params(pma->dim) ||
4534 !isl_space_has_named_params(pa->dim))
4535 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
4536 "unaligned unnamed parameters", goto error);
4537 pma = isl_pw_multi_aff_align_params(pma, isl_pw_aff_get_space(pa));
4538 pa = isl_pw_aff_align_params(pa, isl_pw_multi_aff_get_space(pma));
4539 return pw_multi_aff_set_pw_aff(pma, pos, pa);
4540 error:
4541 isl_pw_multi_aff_free(pma);
4542 isl_pw_aff_free(pa);
4543 return NULL;
4544 }
4545
4546 #undef BASE
4547 #define BASE pw_aff
4548
4549 #include <isl_multi_templ.c>
Integer set library