?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
add isl_multi_pw_aff_intersect_domain
[isl.git] / isl_aff.c
blob481cc4335234719f79cb992b540fb968d654f1a9
1 /*
2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
4 * Copyright 2012-2013 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_vec_private.h>
22 #include <isl_mat_private.h>
23 #include <isl/constraint.h>
24 #include <isl_seq.h>
25 #include <isl/set.h>
26 #include <isl_val_private.h>
27 #include <isl/deprecated/aff_int.h>
28 #include <isl_config.h>
29
30 #undef BASE
31 #define BASE aff
32
33 #include <isl_list_templ.c>
34
35 #undef BASE
36 #define BASE pw_aff
37
38 #include <isl_list_templ.c>
39
40 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
41 __isl_take isl_vec *v)
42 {
43 isl_aff *aff;
44
45 if (!ls || !v)
46 goto error;
47
48 aff = isl_calloc_type(v->ctx, struct isl_aff);
49 if (!aff)
50 goto error;
51
52 aff->ref = 1;
53 aff->ls = ls;
54 aff->v = v;
55
56 return aff;
57 error:
58 isl_local_space_free(ls);
59 isl_vec_free(v);
60 return NULL;
61 }
62
63 __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
64 {
65 isl_ctx *ctx;
66 isl_vec *v;
67 unsigned total;
68
69 if (!ls)
70 return NULL;
71
72 ctx = isl_local_space_get_ctx(ls);
73 if (!isl_local_space_divs_known(ls))
74 isl_die(ctx, isl_error_invalid, "local space has unknown divs",
75 goto error);
76 if (!isl_local_space_is_set(ls))
77 isl_die(ctx, isl_error_invalid,
78 "domain of affine expression should be a set",
79 goto error);
80
81 total = isl_local_space_dim(ls, isl_dim_all);
82 v = isl_vec_alloc(ctx, 1 + 1 + total);
83 return isl_aff_alloc_vec(ls, v);
84 error:
85 isl_local_space_free(ls);
86 return NULL;
87 }
88
89 __isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
90 {
91 isl_aff *aff;
92
93 aff = isl_aff_alloc(ls);
94 if (!aff)
95 return NULL;
96
97 isl_int_set_si(aff->v->el[0], 1);
98 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
99
100 return aff;
101 }
102
103 /* Return a piecewise affine expression defined on the specified domain
104 * that is equal to zero.
105 */
106 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(__isl_take isl_local_space *ls)
107 {
108 return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls));
109 }
110
111 /* Return an affine expression that is equal to "val" on
112 * domain local space "ls".
113 */
114 __isl_give isl_aff *isl_aff_val_on_domain(__isl_take isl_local_space *ls,
115 __isl_take isl_val *val)
116 {
117 isl_aff *aff;
118
119 if (!ls || !val)
120 goto error;
121 if (!isl_val_is_rat(val))
122 isl_die(isl_val_get_ctx(val), isl_error_invalid,
123 "expecting rational value", goto error);
124
125 aff = isl_aff_alloc(isl_local_space_copy(ls));
126 if (!aff)
127 goto error;
128
129 isl_seq_clr(aff->v->el + 2, aff->v->size - 2);
130 isl_int_set(aff->v->el[1], val->n);
131 isl_int_set(aff->v->el[0], val->d);
132
133 isl_local_space_free(ls);
134 isl_val_free(val);
135 return aff;
136 error:
137 isl_local_space_free(ls);
138 isl_val_free(val);
139 return NULL;
140 }
141
142 /* Return an affine expression that is equal to the specified dimension
143 * in "ls".
144 */
145 __isl_give isl_aff *isl_aff_var_on_domain(__isl_take isl_local_space *ls,
146 enum isl_dim_type type, unsigned pos)
147 {
148 isl_space *space;
149 isl_aff *aff;
150
151 if (!ls)
152 return NULL;
153
154 space = isl_local_space_get_space(ls);
155 if (!space)
156 goto error;
157 if (isl_space_is_map(space))
158 isl_die(isl_space_get_ctx(space), isl_error_invalid,
159 "expecting (parameter) set space", goto error);
160 if (pos >= isl_local_space_dim(ls, type))
161 isl_die(isl_space_get_ctx(space), isl_error_invalid,
162 "position out of bounds", goto error);
163
164 isl_space_free(space);
165 aff = isl_aff_alloc(ls);
166 if (!aff)
167 return NULL;
168
169 pos += isl_local_space_offset(aff->ls, type);
170
171 isl_int_set_si(aff->v->el[0], 1);
172 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
173 isl_int_set_si(aff->v->el[1 + pos], 1);
174
175 return aff;
176 error:
177 isl_local_space_free(ls);
178 isl_space_free(space);
179 return NULL;
180 }
181
182 /* Return a piecewise affine expression that is equal to
183 * the specified dimension in "ls".
184 */
185 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(__isl_take isl_local_space *ls,
186 enum isl_dim_type type, unsigned pos)
187 {
188 return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls, type, pos));
189 }
190
191 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
192 {
193 if (!aff)
194 return NULL;
195
196 aff->ref++;
197 return aff;
198 }
199
200 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
201 {
202 if (!aff)
203 return NULL;
204
205 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
206 isl_vec_copy(aff->v));
207 }
208
209 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
210 {
211 if (!aff)
212 return NULL;
213
214 if (aff->ref == 1)
215 return aff;
216 aff->ref--;
217 return isl_aff_dup(aff);
218 }
219
220 void *isl_aff_free(__isl_take isl_aff *aff)
221 {
222 if (!aff)
223 return NULL;
224
225 if (--aff->ref > 0)
226 return NULL;
227
228 isl_local_space_free(aff->ls);
229 isl_vec_free(aff->v);
230
231 free(aff);
232
233 return NULL;
234 }
235
236 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
237 {
238 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
239 }
240
241 /* Externally, an isl_aff has a map space, but internally, the
242 * ls field corresponds to the domain of that space.
243 */
244 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
245 {
246 if (!aff)
247 return 0;
248 if (type == isl_dim_out)
249 return 1;
250 if (type == isl_dim_in)
251 type = isl_dim_set;
252 return isl_local_space_dim(aff->ls, type);
253 }
254
255 __isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
256 {
257 return aff ? isl_local_space_get_space(aff->ls) : NULL;
258 }
259
260 __isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
261 {
262 isl_space *space;
263 if (!aff)
264 return NULL;
265 space = isl_local_space_get_space(aff->ls);
266 space = isl_space_from_domain(space);
267 space = isl_space_add_dims(space, isl_dim_out, 1);
268 return space;
269 }
270
271 __isl_give isl_local_space *isl_aff_get_domain_local_space(
272 __isl_keep isl_aff *aff)
273 {
274 return aff ? isl_local_space_copy(aff->ls) : NULL;
275 }
276
277 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
278 {
279 isl_local_space *ls;
280 if (!aff)
281 return NULL;
282 ls = isl_local_space_copy(aff->ls);
283 ls = isl_local_space_from_domain(ls);
284 ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
285 return ls;
286 }
287
288 /* Externally, an isl_aff has a map space, but internally, the
289 * ls field corresponds to the domain of that space.
290 */
291 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
292 enum isl_dim_type type, unsigned pos)
293 {
294 if (!aff)
295 return NULL;
296 if (type == isl_dim_out)
297 return NULL;
298 if (type == isl_dim_in)
299 type = isl_dim_set;
300 return isl_local_space_get_dim_name(aff->ls, type, pos);
301 }
302
303 __isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
304 __isl_take isl_space *dim)
305 {
306 aff = isl_aff_cow(aff);
307 if (!aff || !dim)
308 goto error;
309
310 aff->ls = isl_local_space_reset_space(aff->ls, dim);
311 if (!aff->ls)
312 return isl_aff_free(aff);
313
314 return aff;
315 error:
316 isl_aff_free(aff);
317 isl_space_free(dim);
318 return NULL;
319 }
320
321 /* Reset the space of "aff". This function is called from isl_pw_templ.c
322 * and doesn't know if the space of an element object is represented
323 * directly or through its domain. It therefore passes along both.
324 */
325 __isl_give isl_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
326 __isl_take isl_space *space, __isl_take isl_space *domain)
327 {
328 isl_space_free(space);
329 return isl_aff_reset_domain_space(aff, domain);
330 }
331
332 /* Reorder the coefficients of the affine expression based
333 * on the given reodering.
334 * The reordering r is assumed to have been extended with the local
335 * variables.
336 */
337 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
338 __isl_take isl_reordering *r, int n_div)
339 {
340 isl_vec *res;
341 int i;
342
343 if (!vec || !r)
344 goto error;
345
346 res = isl_vec_alloc(vec->ctx,
347 2 + isl_space_dim(r->dim, isl_dim_all) + n_div);
348 isl_seq_cpy(res->el, vec->el, 2);
349 isl_seq_clr(res->el + 2, res->size - 2);
350 for (i = 0; i < r->len; ++i)
351 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
352
353 isl_reordering_free(r);
354 isl_vec_free(vec);
355 return res;
356 error:
357 isl_vec_free(vec);
358 isl_reordering_free(r);
359 return NULL;
360 }
361
362 /* Reorder the dimensions of the domain of "aff" according
363 * to the given reordering.
364 */
365 __isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
366 __isl_take isl_reordering *r)
367 {
368 aff = isl_aff_cow(aff);
369 if (!aff)
370 goto error;
371
372 r = isl_reordering_extend(r, aff->ls->div->n_row);
373 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
374 aff->ls->div->n_row);
375 aff->ls = isl_local_space_realign(aff->ls, r);
376
377 if (!aff->v || !aff->ls)
378 return isl_aff_free(aff);
379
380 return aff;
381 error:
382 isl_aff_free(aff);
383 isl_reordering_free(r);
384 return NULL;
385 }
386
387 __isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
388 __isl_take isl_space *model)
389 {
390 if (!aff || !model)
391 goto error;
392
393 if (!isl_space_match(aff->ls->dim, isl_dim_param,
394 model, isl_dim_param)) {
395 isl_reordering *exp;
396
397 model = isl_space_drop_dims(model, isl_dim_in,
398 0, isl_space_dim(model, isl_dim_in));
399 model = isl_space_drop_dims(model, isl_dim_out,
400 0, isl_space_dim(model, isl_dim_out));
401 exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
402 exp = isl_reordering_extend_space(exp,
403 isl_aff_get_domain_space(aff));
404 aff = isl_aff_realign_domain(aff, exp);
405 }
406
407 isl_space_free(model);
408 return aff;
409 error:
410 isl_space_free(model);
411 isl_aff_free(aff);
412 return NULL;
413 }
414
415 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
416 {
417 if (!aff)
418 return -1;
419
420 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
421 }
422
423 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
424 {
425 int equal;
426
427 if (!aff1 || !aff2)
428 return -1;
429
430 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
431 if (equal < 0 || !equal)
432 return equal;
433
434 return isl_vec_is_equal(aff1->v, aff2->v);
435 }
436
437 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
438 {
439 if (!aff)
440 return -1;
441 isl_int_set(*v, aff->v->el[0]);
442 return 0;
443 }
444
445 /* Return the common denominator of "aff".
446 */
447 __isl_give isl_val *isl_aff_get_denominator_val(__isl_keep isl_aff *aff)
448 {
449 isl_ctx *ctx;
450
451 if (!aff)
452 return NULL;
453
454 ctx = isl_aff_get_ctx(aff);
455 return isl_val_int_from_isl_int(ctx, aff->v->el[0]);
456 }
457
458 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
459 {
460 if (!aff)
461 return -1;
462 isl_int_set(*v, aff->v->el[1]);
463 return 0;
464 }
465
466 /* Return the constant term of "aff".
467 */
468 __isl_give isl_val *isl_aff_get_constant_val(__isl_keep isl_aff *aff)
469 {
470 isl_ctx *ctx;
471 isl_val *v;
472
473 if (!aff)
474 return NULL;
475
476 ctx = isl_aff_get_ctx(aff);
477 v = isl_val_rat_from_isl_int(ctx, aff->v->el[1], aff->v->el[0]);
478 return isl_val_normalize(v);
479 }
480
481 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
482 enum isl_dim_type type, int pos, isl_int *v)
483 {
484 if (!aff)
485 return -1;
486
487 if (type == isl_dim_out)
488 isl_die(aff->v->ctx, isl_error_invalid,
489 "output/set dimension does not have a coefficient",
490 return -1);
491 if (type == isl_dim_in)
492 type = isl_dim_set;
493
494 if (pos >= isl_local_space_dim(aff->ls, type))
495 isl_die(aff->v->ctx, isl_error_invalid,
496 "position out of bounds", return -1);
497
498 pos += isl_local_space_offset(aff->ls, type);
499 isl_int_set(*v, aff->v->el[1 + pos]);
500
501 return 0;
502 }
503
504 /* Return the coefficient of the variable of type "type" at position "pos"
505 * of "aff".
506 */
507 __isl_give isl_val *isl_aff_get_coefficient_val(__isl_keep isl_aff *aff,
508 enum isl_dim_type type, int pos)
509 {
510 isl_ctx *ctx;
511 isl_val *v;
512
513 if (!aff)
514 return NULL;
515
516 ctx = isl_aff_get_ctx(aff);
517 if (type == isl_dim_out)
518 isl_die(ctx, isl_error_invalid,
519 "output/set dimension does not have a coefficient",
520 return NULL);
521 if (type == isl_dim_in)
522 type = isl_dim_set;
523
524 if (pos >= isl_local_space_dim(aff->ls, type))
525 isl_die(ctx, isl_error_invalid,
526 "position out of bounds", return NULL);
527
528 pos += isl_local_space_offset(aff->ls, type);
529 v = isl_val_rat_from_isl_int(ctx, aff->v->el[1 + pos], aff->v->el[0]);
530 return isl_val_normalize(v);
531 }
532
533 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
534 {
535 aff = isl_aff_cow(aff);
536 if (!aff)
537 return NULL;
538
539 aff->v = isl_vec_cow(aff->v);
540 if (!aff->v)
541 return isl_aff_free(aff);
542
543 isl_int_set(aff->v->el[0], v);
544
545 return aff;
546 }
547
548 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
549 {
550 aff = isl_aff_cow(aff);
551 if (!aff)
552 return NULL;
553
554 aff->v = isl_vec_cow(aff->v);
555 if (!aff->v)
556 return isl_aff_free(aff);
557
558 isl_int_set(aff->v->el[1], v);
559
560 return aff;
561 }
562
563 /* Replace the constant term of "aff" by "v".
564 */
565 __isl_give isl_aff *isl_aff_set_constant_val(__isl_take isl_aff *aff,
566 __isl_take isl_val *v)
567 {
568 if (!aff || !v)
569 goto error;
570
571 if (!isl_val_is_rat(v))
572 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
573 "expecting rational value", goto error);
574
575 if (isl_int_eq(aff->v->el[1], v->n) &&
576 isl_int_eq(aff->v->el[0], v->d)) {
577 isl_val_free(v);
578 return aff;
579 }
580
581 aff = isl_aff_cow(aff);
582 if (!aff)
583 goto error;
584 aff->v = isl_vec_cow(aff->v);
585 if (!aff->v)
586 goto error;
587
588 if (isl_int_eq(aff->v->el[0], v->d)) {
589 isl_int_set(aff->v->el[1], v->n);
590 } else if (isl_int_is_one(v->d)) {
591 isl_int_mul(aff->v->el[1], aff->v->el[0], v->n);
592 } else {
593 isl_seq_scale(aff->v->el + 1,
594 aff->v->el + 1, v->d, aff->v->size - 1);
595 isl_int_mul(aff->v->el[1], aff->v->el[0], v->n);
596 isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
597 aff->v = isl_vec_normalize(aff->v);
598 if (!aff->v)
599 goto error;
600 }
601
602 isl_val_free(v);
603 return aff;
604 error:
605 isl_aff_free(aff);
606 isl_val_free(v);
607 return NULL;
608 }
609
610 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
611 {
612 if (isl_int_is_zero(v))
613 return aff;
614
615 aff = isl_aff_cow(aff);
616 if (!aff)
617 return NULL;
618
619 aff->v = isl_vec_cow(aff->v);
620 if (!aff->v)
621 return isl_aff_free(aff);
622
623 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
624
625 return aff;
626 }
627
628 /* Add "v" to the constant term of "aff".
629 */
630 __isl_give isl_aff *isl_aff_add_constant_val(__isl_take isl_aff *aff,
631 __isl_take isl_val *v)
632 {
633 if (!aff || !v)
634 goto error;
635
636 if (isl_val_is_zero(v)) {
637 isl_val_free(v);
638 return aff;
639 }
640
641 if (!isl_val_is_rat(v))
642 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
643 "expecting rational value", goto error);
644
645 aff = isl_aff_cow(aff);
646 if (!aff)
647 goto error;
648
649 aff->v = isl_vec_cow(aff->v);
650 if (!aff->v)
651 goto error;
652
653 if (isl_int_is_one(v->d)) {
654 isl_int_addmul(aff->v->el[1], aff->v->el[0], v->n);
655 } else if (isl_int_eq(aff->v->el[0], v->d)) {
656 isl_int_add(aff->v->el[1], aff->v->el[1], v->n);
657 aff->v = isl_vec_normalize(aff->v);
658 if (!aff->v)
659 goto error;
660 } else {
661 isl_seq_scale(aff->v->el + 1,
662 aff->v->el + 1, v->d, aff->v->size - 1);
663 isl_int_addmul(aff->v->el[1], aff->v->el[0], v->n);
664 isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
665 aff->v = isl_vec_normalize(aff->v);
666 if (!aff->v)
667 goto error;
668 }
669
670 isl_val_free(v);
671 return aff;
672 error:
673 isl_aff_free(aff);
674 isl_val_free(v);
675 return NULL;
676 }
677
678 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
679 {
680 isl_int t;
681
682 isl_int_init(t);
683 isl_int_set_si(t, v);
684 aff = isl_aff_add_constant(aff, t);
685 isl_int_clear(t);
686
687 return aff;
688 }
689
690 /* Add "v" to the numerator of the constant term of "aff".
691 */
692 __isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v)
693 {
694 if (isl_int_is_zero(v))
695 return aff;
696
697 aff = isl_aff_cow(aff);
698 if (!aff)
699 return NULL;
700
701 aff->v = isl_vec_cow(aff->v);
702 if (!aff->v)
703 return isl_aff_free(aff);
704
705 isl_int_add(aff->v->el[1], aff->v->el[1], v);
706
707 return aff;
708 }
709
710 /* Add "v" to the numerator of the constant term of "aff".
711 */
712 __isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v)
713 {
714 isl_int t;
715
716 if (v == 0)
717 return aff;
718
719 isl_int_init(t);
720 isl_int_set_si(t, v);
721 aff = isl_aff_add_constant_num(aff, t);
722 isl_int_clear(t);
723
724 return aff;
725 }
726
727 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
728 {
729 aff = isl_aff_cow(aff);
730 if (!aff)
731 return NULL;
732
733 aff->v = isl_vec_cow(aff->v);
734 if (!aff->v)
735 return isl_aff_free(aff);
736
737 isl_int_set_si(aff->v->el[1], v);
738
739 return aff;
740 }
741
742 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
743 enum isl_dim_type type, int pos, isl_int v)
744 {
745 if (!aff)
746 return NULL;
747
748 if (type == isl_dim_out)
749 isl_die(aff->v->ctx, isl_error_invalid,
750 "output/set dimension does not have a coefficient",
751 return isl_aff_free(aff));
752 if (type == isl_dim_in)
753 type = isl_dim_set;
754
755 if (pos >= isl_local_space_dim(aff->ls, type))
756 isl_die(aff->v->ctx, isl_error_invalid,
757 "position out of bounds", return isl_aff_free(aff));
758
759 aff = isl_aff_cow(aff);
760 if (!aff)
761 return NULL;
762
763 aff->v = isl_vec_cow(aff->v);
764 if (!aff->v)
765 return isl_aff_free(aff);
766
767 pos += isl_local_space_offset(aff->ls, type);
768 isl_int_set(aff->v->el[1 + pos], v);
769
770 return aff;
771 }
772
773 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
774 enum isl_dim_type type, int pos, int v)
775 {
776 if (!aff)
777 return NULL;
778
779 if (type == isl_dim_out)
780 isl_die(aff->v->ctx, isl_error_invalid,
781 "output/set dimension does not have a coefficient",
782 return isl_aff_free(aff));
783 if (type == isl_dim_in)
784 type = isl_dim_set;
785
786 if (pos >= isl_local_space_dim(aff->ls, type))
787 isl_die(aff->v->ctx, isl_error_invalid,
788 "position out of bounds", return isl_aff_free(aff));
789
790 aff = isl_aff_cow(aff);
791 if (!aff)
792 return NULL;
793
794 aff->v = isl_vec_cow(aff->v);
795 if (!aff->v)
796 return isl_aff_free(aff);
797
798 pos += isl_local_space_offset(aff->ls, type);
799 isl_int_set_si(aff->v->el[1 + pos], v);
800
801 return aff;
802 }
803
804 /* Replace the coefficient of the variable of type "type" at position "pos"
805 * of "aff" by "v".
806 */
807 __isl_give isl_aff *isl_aff_set_coefficient_val(__isl_take isl_aff *aff,
808 enum isl_dim_type type, int pos, __isl_take isl_val *v)
809 {
810 if (!aff || !v)
811 goto error;
812
813 if (type == isl_dim_out)
814 isl_die(aff->v->ctx, isl_error_invalid,
815 "output/set dimension does not have a coefficient",
816 goto error);
817 if (type == isl_dim_in)
818 type = isl_dim_set;
819
820 if (pos >= isl_local_space_dim(aff->ls, type))
821 isl_die(aff->v->ctx, isl_error_invalid,
822 "position out of bounds", goto error);
823
824 if (!isl_val_is_rat(v))
825 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
826 "expecting rational value", goto error);
827
828 pos += isl_local_space_offset(aff->ls, type);
829 if (isl_int_eq(aff->v->el[1 + pos], v->n) &&
830 isl_int_eq(aff->v->el[0], v->d)) {
831 isl_val_free(v);
832 return aff;
833 }
834
835 aff = isl_aff_cow(aff);
836 if (!aff)
837 goto error;
838 aff->v = isl_vec_cow(aff->v);
839 if (!aff->v)
840 goto error;
841
842 if (isl_int_eq(aff->v->el[0], v->d)) {
843 isl_int_set(aff->v->el[1 + pos], v->n);
844 } else if (isl_int_is_one(v->d)) {
845 isl_int_mul(aff->v->el[1 + pos], aff->v->el[0], v->n);
846 } else {
847 isl_seq_scale(aff->v->el + 1,
848 aff->v->el + 1, v->d, aff->v->size - 1);
849 isl_int_mul(aff->v->el[1 + pos], aff->v->el[0], v->n);
850 isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
851 aff->v = isl_vec_normalize(aff->v);
852 if (!aff->v)
853 goto error;
854 }
855
856 isl_val_free(v);
857 return aff;
858 error:
859 isl_aff_free(aff);
860 isl_val_free(v);
861 return NULL;
862 }
863
864 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
865 enum isl_dim_type type, int pos, isl_int v)
866 {
867 if (!aff)
868 return NULL;
869
870 if (type == isl_dim_out)
871 isl_die(aff->v->ctx, isl_error_invalid,
872 "output/set dimension does not have a coefficient",
873 return isl_aff_free(aff));
874 if (type == isl_dim_in)
875 type = isl_dim_set;
876
877 if (pos >= isl_local_space_dim(aff->ls, type))
878 isl_die(aff->v->ctx, isl_error_invalid,
879 "position out of bounds", return isl_aff_free(aff));
880
881 aff = isl_aff_cow(aff);
882 if (!aff)
883 return NULL;
884
885 aff->v = isl_vec_cow(aff->v);
886 if (!aff->v)
887 return isl_aff_free(aff);
888
889 pos += isl_local_space_offset(aff->ls, type);
890 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
891
892 return aff;
893 }
894
895 /* Add "v" to the coefficient of the variable of type "type"
896 * at position "pos" of "aff".
897 */
898 __isl_give isl_aff *isl_aff_add_coefficient_val(__isl_take isl_aff *aff,
899 enum isl_dim_type type, int pos, __isl_take isl_val *v)
900 {
901 if (!aff || !v)
902 goto error;
903
904 if (isl_val_is_zero(v)) {
905 isl_val_free(v);
906 return aff;
907 }
908
909 if (type == isl_dim_out)
910 isl_die(aff->v->ctx, isl_error_invalid,
911 "output/set dimension does not have a coefficient",
912 goto error);
913 if (type == isl_dim_in)
914 type = isl_dim_set;
915
916 if (pos >= isl_local_space_dim(aff->ls, type))
917 isl_die(aff->v->ctx, isl_error_invalid,
918 "position out of bounds", goto error);
919
920 if (!isl_val_is_rat(v))
921 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
922 "expecting rational value", goto error);
923
924 aff = isl_aff_cow(aff);
925 if (!aff)
926 goto error;
927
928 aff->v = isl_vec_cow(aff->v);
929 if (!aff->v)
930 goto error;
931
932 pos += isl_local_space_offset(aff->ls, type);
933 if (isl_int_is_one(v->d)) {
934 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v->n);
935 } else if (isl_int_eq(aff->v->el[0], v->d)) {
936 isl_int_add(aff->v->el[1 + pos], aff->v->el[1 + pos], v->n);
937 aff->v = isl_vec_normalize(aff->v);
938 if (!aff->v)
939 goto error;
940 } else {
941 isl_seq_scale(aff->v->el + 1,
942 aff->v->el + 1, v->d, aff->v->size - 1);
943 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v->n);
944 isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
945 aff->v = isl_vec_normalize(aff->v);
946 if (!aff->v)
947 goto error;
948 }
949
950 isl_val_free(v);
951 return aff;
952 error:
953 isl_aff_free(aff);
954 isl_val_free(v);
955 return NULL;
956 }
957
958 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
959 enum isl_dim_type type, int pos, int v)
960 {
961 isl_int t;
962
963 isl_int_init(t);
964 isl_int_set_si(t, v);
965 aff = isl_aff_add_coefficient(aff, type, pos, t);
966 isl_int_clear(t);
967
968 return aff;
969 }
970
971 __isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
972 {
973 if (!aff)
974 return NULL;
975
976 return isl_local_space_get_div(aff->ls, pos);
977 }
978
979 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
980 {
981 aff = isl_aff_cow(aff);
982 if (!aff)
983 return NULL;
984 aff->v = isl_vec_cow(aff->v);
985 if (!aff->v)
986 return isl_aff_free(aff);
987
988 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
989
990 return aff;
991 }
992
993 /* Remove divs from the local space that do not appear in the affine
994 * expression.
995 * We currently only remove divs at the end.
996 * Some intermediate divs may also not appear directly in the affine
997 * expression, but we would also need to check that no other divs are
998 * defined in terms of them.
999 */
1000 __isl_give isl_aff *isl_aff_remove_unused_divs( __isl_take isl_aff *aff)
1001 {
1002 int pos;
1003 int off;
1004 int n;
1005
1006 if (!aff)
1007 return NULL;
1008
1009 n = isl_local_space_dim(aff->ls, isl_dim_div);
1010 off = isl_local_space_offset(aff->ls, isl_dim_div);
1011
1012 pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
1013 if (pos == n)
1014 return aff;
1015
1016 aff = isl_aff_cow(aff);
1017 if (!aff)
1018 return NULL;
1019
1020 aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
1021 aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
1022 if (!aff->ls || !aff->v)
1023 return isl_aff_free(aff);
1024
1025 return aff;
1026 }
1027
1028 /* Given two affine expressions "p" of length p_len (including the
1029 * denominator and the constant term) and "subs" of length subs_len,
1030 * plug in "subs" for the variable at position "pos".
1031 * The variables of "subs" and "p" are assumed to match up to subs_len,
1032 * but "p" may have additional variables.
1033 * "v" is an initialized isl_int that can be used internally.
1034 *
1035 * In particular, if "p" represents the expression
1036 *
1037 * (a i + g)/m
1038 *
1039 * with i the variable at position "pos" and "subs" represents the expression
1040 *
1041 * f/d
1042 *
1043 * then the result represents the expression
1044 *
1045 * (a f + d g)/(m d)
1046 *
1047 */
1048 void isl_seq_substitute(isl_int *p, int pos, isl_int *subs,
1049 int p_len, int subs_len, isl_int v)
1050 {
1051 isl_int_set(v, p[1 + pos]);
1052 isl_int_set_si(p[1 + pos], 0);
1053 isl_seq_combine(p + 1, subs[0], p + 1, v, subs + 1, subs_len - 1);
1054 isl_seq_scale(p + subs_len, p + subs_len, subs[0], p_len - subs_len);
1055 isl_int_mul(p[0], p[0], subs[0]);
1056 }
1057
1058 /* Look for any divs in the aff->ls with a denominator equal to one
1059 * and plug them into the affine expression and any subsequent divs
1060 * that may reference the div.
1061 */
1062 static __isl_give isl_aff *plug_in_integral_divs(__isl_take isl_aff *aff)
1063 {
1064 int i, n;
1065 int len;
1066 isl_int v;
1067 isl_vec *vec;
1068 isl_local_space *ls;
1069 unsigned pos;
1070
1071 if (!aff)
1072 return NULL;
1073
1074 n = isl_local_space_dim(aff->ls, isl_dim_div);
1075 len = aff->v->size;
1076 for (i = 0; i < n; ++i) {
1077 if (!isl_int_is_one(aff->ls->div->row[i][0]))
1078 continue;
1079 ls = isl_local_space_copy(aff->ls);
1080 ls = isl_local_space_substitute_seq(ls, isl_dim_div, i,
1081 aff->ls->div->row[i], len, i + 1, n - (i + 1));
1082 vec = isl_vec_copy(aff->v);
1083 vec = isl_vec_cow(vec);
1084 if (!ls || !vec)
1085 goto error;
1086
1087 isl_int_init(v);
1088
1089 pos = isl_local_space_offset(aff->ls, isl_dim_div) + i;
1090 isl_seq_substitute(vec->el, pos, aff->ls->div->row[i],
1091 len, len, v);
1092
1093 isl_int_clear(v);
1094
1095 isl_vec_free(aff->v);
1096 aff->v = vec;
1097 isl_local_space_free(aff->ls);
1098 aff->ls = ls;
1099 }
1100
1101 return aff;
1102 error:
1103 isl_vec_free(vec);
1104 isl_local_space_free(ls);
1105 return isl_aff_free(aff);
1106 }
1107
1108 /* Look for any divs j that appear with a unit coefficient inside
1109 * the definitions of other divs i and plug them into the definitions
1110 * of the divs i.
1111 *
1112 * In particular, an expression of the form
1113 *
1114 * floor((f(..) + floor(g(..)/n))/m)
1115 *
1116 * is simplified to
1117 *
1118 * floor((n * f(..) + g(..))/(n * m))
1119 *
1120 * This simplification is correct because we can move the expression
1121 * f(..) into the inner floor in the original expression to obtain
1122 *
1123 * floor(floor((n * f(..) + g(..))/n)/m)
1124 *
1125 * from which we can derive the simplified expression.
1126 */
1127 static __isl_give isl_aff *plug_in_unit_divs(__isl_take isl_aff *aff)
1128 {
1129 int i, j, n;
1130 int off;
1131
1132 if (!aff)
1133 return NULL;
1134
1135 n = isl_local_space_dim(aff->ls, isl_dim_div);
1136 off = isl_local_space_offset(aff->ls, isl_dim_div);
1137 for (i = 1; i < n; ++i) {
1138 for (j = 0; j < i; ++j) {
1139 if (!isl_int_is_one(aff->ls->div->row[i][1 + off + j]))
1140 continue;
1141 aff->ls = isl_local_space_substitute_seq(aff->ls,
1142 isl_dim_div, j, aff->ls->div->row[j],
1143 aff->v->size, i, 1);
1144 if (!aff->ls)
1145 return isl_aff_free(aff);
1146 }
1147 }
1148
1149 return aff;
1150 }
1151
1152 /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
1153 *
1154 * Even though this function is only called on isl_affs with a single
1155 * reference, we are careful to only change aff->v and aff->ls together.
1156 */
1157 static __isl_give isl_aff *swap_div(__isl_take isl_aff *aff, int a, int b)
1158 {
1159 unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
1160 isl_local_space *ls;
1161 isl_vec *v;
1162
1163 ls = isl_local_space_copy(aff->ls);
1164 ls = isl_local_space_swap_div(ls, a, b);
1165 v = isl_vec_copy(aff->v);
1166 v = isl_vec_cow(v);
1167 if (!ls || !v)
1168 goto error;
1169
1170 isl_int_swap(v->el[1 + off + a], v->el[1 + off + b]);
1171 isl_vec_free(aff->v);
1172 aff->v = v;
1173 isl_local_space_free(aff->ls);
1174 aff->ls = ls;
1175
1176 return aff;
1177 error:
1178 isl_vec_free(v);
1179 isl_local_space_free(ls);
1180 return isl_aff_free(aff);
1181 }
1182
1183 /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
1184 *
1185 * We currently do not actually remove div "b", but simply add its
1186 * coefficient to that of "a" and then zero it out.
1187 */
1188 static __isl_give isl_aff *merge_divs(__isl_take isl_aff *aff, int a, int b)
1189 {
1190 unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
1191
1192 if (isl_int_is_zero(aff->v->el[1 + off + b]))
1193 return aff;
1194
1195 aff->v = isl_vec_cow(aff->v);
1196 if (!aff->v)
1197 return isl_aff_free(aff);
1198
1199 isl_int_add(aff->v->el[1 + off + a],
1200 aff->v->el[1 + off + a], aff->v->el[1 + off + b]);
1201 isl_int_set_si(aff->v->el[1 + off + b], 0);
1202
1203 return aff;
1204 }
1205
1206 /* Sort the divs in the local space of "aff" according to
1207 * the comparison function "cmp_row" in isl_local_space.c,
1208 * combining the coefficients of identical divs.
1209 *
1210 * Reordering divs does not change the semantics of "aff",
1211 * so there is no need to call isl_aff_cow.
1212 * Moreover, this function is currently only called on isl_affs
1213 * with a single reference.
1214 */
1215 static __isl_give isl_aff *sort_divs(__isl_take isl_aff *aff)
1216 {
1217 int i, j, n;
1218 unsigned off;
1219
1220 if (!aff)
1221 return NULL;
1222
1223 off = isl_local_space_offset(aff->ls, isl_dim_div);
1224 n = isl_aff_dim(aff, isl_dim_div);
1225 for (i = 1; i < n; ++i) {
1226 for (j = i - 1; j >= 0; --j) {
1227 int cmp = isl_mat_cmp_div(aff->ls->div, j, j + 1);
1228 if (cmp < 0)
1229 break;
1230 if (cmp == 0)
1231 aff = merge_divs(aff, j, j + 1);
1232 else
1233 aff = swap_div(aff, j, j + 1);
1234 if (!aff)
1235 return NULL;
1236 }
1237 }
1238
1239 return aff;
1240 }
1241
1242 /* Normalize the representation of "aff".
1243 *
1244 * This function should only be called of "new" isl_affs, i.e.,
1245 * with only a single reference. We therefore do not need to
1246 * worry about affecting other instances.
1247 */
1248 __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
1249 {
1250 if (!aff)
1251 return NULL;
1252 aff->v = isl_vec_normalize(aff->v);
1253 if (!aff->v)
1254 return isl_aff_free(aff);
1255 aff = plug_in_integral_divs(aff);
1256 aff = plug_in_unit_divs(aff);
1257 aff = sort_divs(aff);
1258 aff = isl_aff_remove_unused_divs(aff);
1259 return aff;
1260 }
1261
1262 /* Given f, return floor(f).
1263 * If f is an integer expression, then just return f.
1264 * If f is a constant, then return the constant floor(f).
1265 * Otherwise, if f = g/m, write g = q m + r,
1266 * create a new div d = [r/m] and return the expression q + d.
1267 * The coefficients in r are taken to lie between -m/2 and m/2.
1268 */
1269 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
1270 {
1271 int i;
1272 int size;
1273 isl_ctx *ctx;
1274 isl_vec *div;
1275
1276 if (!aff)
1277 return NULL;
1278
1279 if (isl_int_is_one(aff->v->el[0]))
1280 return aff;
1281
1282 aff = isl_aff_cow(aff);
1283 if (!aff)
1284 return NULL;
1285
1286 aff->v = isl_vec_cow(aff->v);
1287 if (!aff->v)
1288 return isl_aff_free(aff);
1289
1290 if (isl_aff_is_cst(aff)) {
1291 isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
1292 isl_int_set_si(aff->v->el[0], 1);
1293 return aff;
1294 }
1295
1296 div = isl_vec_copy(aff->v);
1297 div = isl_vec_cow(div);
1298 if (!div)
1299 return isl_aff_free(aff);
1300
1301 ctx = isl_aff_get_ctx(aff);
1302 isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
1303 for (i = 1; i < aff->v->size; ++i) {
1304 isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
1305 isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
1306 if (isl_int_gt(div->el[i], aff->v->el[0])) {
1307 isl_int_sub(div->el[i], div->el[i], div->el[0]);
1308 isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
1309 }
1310 }
1311
1312 aff->ls = isl_local_space_add_div(aff->ls, div);
1313 if (!aff->ls)
1314 return isl_aff_free(aff);
1315
1316 size = aff->v->size;
1317 aff->v = isl_vec_extend(aff->v, size + 1);
1318 if (!aff->v)
1319 return isl_aff_free(aff);
1320 isl_int_set_si(aff->v->el[0], 1);
1321 isl_int_set_si(aff->v->el[size], 1);
1322
1323 aff = isl_aff_normalize(aff);
1324
1325 return aff;
1326 }
1327
1328 /* Compute
1329 *
1330 * aff mod m = aff - m * floor(aff/m)
1331 */
1332 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
1333 {
1334 isl_aff *res;
1335
1336 res = isl_aff_copy(aff);
1337 aff = isl_aff_scale_down(aff, m);
1338 aff = isl_aff_floor(aff);
1339 aff = isl_aff_scale(aff, m);
1340 res = isl_aff_sub(res, aff);
1341
1342 return res;
1343 }
1344
1345 /* Compute
1346 *
1347 * aff mod m = aff - m * floor(aff/m)
1348 *
1349 * with m an integer value.
1350 */
1351 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
1352 __isl_take isl_val *m)
1353 {
1354 isl_aff *res;
1355
1356 if (!aff || !m)
1357 goto error;
1358
1359 if (!isl_val_is_int(m))
1360 isl_die(isl_val_get_ctx(m), isl_error_invalid,
1361 "expecting integer modulo", goto error);
1362
1363 res = isl_aff_copy(aff);
1364 aff = isl_aff_scale_down_val(aff, isl_val_copy(m));
1365 aff = isl_aff_floor(aff);
1366 aff = isl_aff_scale_val(aff, m);
1367 res = isl_aff_sub(res, aff);
1368
1369 return res;
1370 error:
1371 isl_aff_free(aff);
1372 isl_val_free(m);
1373 return NULL;
1374 }
1375
1376 /* Compute
1377 *
1378 * pwaff mod m = pwaff - m * floor(pwaff/m)
1379 */
1380 __isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
1381 {
1382 isl_pw_aff *res;
1383
1384 res = isl_pw_aff_copy(pwaff);
1385 pwaff = isl_pw_aff_scale_down(pwaff, m);
1386 pwaff = isl_pw_aff_floor(pwaff);
1387 pwaff = isl_pw_aff_scale(pwaff, m);
1388 res = isl_pw_aff_sub(res, pwaff);
1389
1390 return res;
1391 }
1392
1393 /* Compute
1394 *
1395 * pa mod m = pa - m * floor(pa/m)
1396 *
1397 * with m an integer value.
1398 */
1399 __isl_give isl_pw_aff *isl_pw_aff_mod_val(__isl_take isl_pw_aff *pa,
1400 __isl_take isl_val *m)
1401 {
1402 if (!pa || !m)
1403 goto error;
1404 if (!isl_val_is_int(m))
1405 isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
1406 "expecting integer modulo", goto error);
1407 pa = isl_pw_aff_mod(pa, m->n);
1408 isl_val_free(m);
1409 return pa;
1410 error:
1411 isl_pw_aff_free(pa);
1412 isl_val_free(m);
1413 return NULL;
1414 }
1415
1416 /* Given f, return ceil(f).
1417 * If f is an integer expression, then just return f.
1418 * Otherwise, let f be the expression
1419 *
1420 * e/m
1421 *
1422 * then return
1423 *
1424 * floor((e + m - 1)/m)
1425 */
1426 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
1427 {
1428 if (!aff)
1429 return NULL;
1430
1431 if (isl_int_is_one(aff->v->el[0]))
1432 return aff;
1433
1434 aff = isl_aff_cow(aff);
1435 if (!aff)
1436 return NULL;
1437 aff->v = isl_vec_cow(aff->v);
1438 if (!aff->v)
1439 return isl_aff_free(aff);
1440
1441 isl_int_add(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
1442 isl_int_sub_ui(aff->v->el[1], aff->v->el[1], 1);
1443 aff = isl_aff_floor(aff);
1444
1445 return aff;
1446 }
1447
1448 /* Apply the expansion computed by isl_merge_divs.
1449 * The expansion itself is given by "exp" while the resulting
1450 * list of divs is given by "div".
1451 */
1452 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
1453 __isl_take isl_mat *div, int *exp)
1454 {
1455 int i, j;
1456 int old_n_div;
1457 int new_n_div;
1458 int offset;
1459
1460 aff = isl_aff_cow(aff);
1461 if (!aff || !div)
1462 goto error;
1463
1464 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1465 new_n_div = isl_mat_rows(div);
1466 if (new_n_div < old_n_div)
1467 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
1468 "not an expansion", goto error);
1469
1470 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
1471 if (!aff->v)
1472 goto error;
1473
1474 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
1475 j = old_n_div - 1;
1476 for (i = new_n_div - 1; i >= 0; --i) {
1477 if (j >= 0 && exp[j] == i) {
1478 if (i != j)
1479 isl_int_swap(aff->v->el[offset + i],
1480 aff->v->el[offset + j]);
1481 j--;
1482 } else
1483 isl_int_set_si(aff->v->el[offset + i], 0);
1484 }
1485
1486 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
1487 if (!aff->ls)
1488 goto error;
1489 isl_mat_free(div);
1490 return aff;
1491 error:
1492 isl_aff_free(aff);
1493 isl_mat_free(div);
1494 return NULL;
1495 }
1496
1497 /* Add two affine expressions that live in the same local space.
1498 */
1499 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
1500 __isl_take isl_aff *aff2)
1501 {
1502 isl_int gcd, f;
1503
1504 aff1 = isl_aff_cow(aff1);
1505 if (!aff1 || !aff2)
1506 goto error;
1507
1508 aff1->v = isl_vec_cow(aff1->v);
1509 if (!aff1->v)
1510 goto error;
1511
1512 isl_int_init(gcd);
1513 isl_int_init(f);
1514 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
1515 isl_int_divexact(f, aff2->v->el[0], gcd);
1516 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
1517 isl_int_divexact(f, aff1->v->el[0], gcd);
1518 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
1519 isl_int_divexact(f, aff2->v->el[0], gcd);
1520 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
1521 isl_int_clear(f);
1522 isl_int_clear(gcd);
1523
1524 isl_aff_free(aff2);
1525 return aff1;
1526 error:
1527 isl_aff_free(aff1);
1528 isl_aff_free(aff2);
1529 return NULL;
1530 }
1531
1532 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
1533 __isl_take isl_aff *aff2)
1534 {
1535 isl_ctx *ctx;
1536 int *exp1 = NULL;
1537 int *exp2 = NULL;
1538 isl_mat *div;
1539 int n_div1, n_div2;
1540
1541 if (!aff1 || !aff2)
1542 goto error;
1543
1544 ctx = isl_aff_get_ctx(aff1);
1545 if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
1546 isl_die(ctx, isl_error_invalid,
1547 "spaces don't match", goto error);
1548
1549 n_div1 = isl_aff_dim(aff1, isl_dim_div);
1550 n_div2 = isl_aff_dim(aff2, isl_dim_div);
1551 if (n_div1 == 0 && n_div2 == 0)
1552 return add_expanded(aff1, aff2);
1553
1554 exp1 = isl_alloc_array(ctx, int, n_div1);
1555 exp2 = isl_alloc_array(ctx, int, n_div2);
1556 if ((n_div1 && !exp1) || (n_div2 && !exp2))
1557 goto error;
1558
1559 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
1560 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
1561 aff2 = isl_aff_expand_divs(aff2, div, exp2);
1562 free(exp1);
1563 free(exp2);
1564
1565 return add_expanded(aff1, aff2);
1566 error:
1567 free(exp1);
1568 free(exp2);
1569 isl_aff_free(aff1);
1570 isl_aff_free(aff2);
1571 return NULL;
1572 }
1573
1574 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
1575 __isl_take isl_aff *aff2)
1576 {
1577 return isl_aff_add(aff1, isl_aff_neg(aff2));
1578 }
1579
1580 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
1581 {
1582 isl_int gcd;
1583
1584 if (isl_int_is_one(f))
1585 return aff;
1586
1587 aff = isl_aff_cow(aff);
1588 if (!aff)
1589 return NULL;
1590 aff->v = isl_vec_cow(aff->v);
1591 if (!aff->v)
1592 return isl_aff_free(aff);
1593
1594 if (isl_int_is_pos(f) && isl_int_is_divisible_by(aff->v->el[0], f)) {
1595 isl_int_divexact(aff->v->el[0], aff->v->el[0], f);
1596 return aff;
1597 }
1598
1599 isl_int_init(gcd);
1600 isl_int_gcd(gcd, aff->v->el[0], f);
1601 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
1602 isl_int_divexact(gcd, f, gcd);
1603 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
1604 isl_int_clear(gcd);
1605
1606 return aff;
1607 }
1608
1609 /* Multiple "aff" by "v".
1610 */
1611 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
1612 __isl_take isl_val *v)
1613 {
1614 if (!aff || !v)
1615 goto error;
1616
1617 if (isl_val_is_one(v)) {
1618 isl_val_free(v);
1619 return aff;
1620 }
1621
1622 if (!isl_val_is_rat(v))
1623 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1624 "expecting rational factor", goto error);
1625
1626 aff = isl_aff_scale(aff, v->n);
1627 aff = isl_aff_scale_down(aff, v->d);
1628
1629 isl_val_free(v);
1630 return aff;
1631 error:
1632 isl_aff_free(aff);
1633 isl_val_free(v);
1634 return NULL;
1635 }
1636
1637 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
1638 {
1639 isl_int gcd;
1640
1641 if (isl_int_is_one(f))
1642 return aff;
1643
1644 aff = isl_aff_cow(aff);
1645 if (!aff)
1646 return NULL;
1647
1648 if (isl_int_is_zero(f))
1649 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1650 "cannot scale down by zero", return isl_aff_free(aff));
1651
1652 aff->v = isl_vec_cow(aff->v);
1653 if (!aff->v)
1654 return isl_aff_free(aff);
1655
1656 isl_int_init(gcd);
1657 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
1658 isl_int_gcd(gcd, gcd, f);
1659 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
1660 isl_int_divexact(gcd, f, gcd);
1661 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
1662 isl_int_clear(gcd);
1663
1664 return aff;
1665 }
1666
1667 /* Divide "aff" by "v".
1668 */
1669 __isl_give isl_aff *isl_aff_scale_down_val(__isl_take isl_aff *aff,
1670 __isl_take isl_val *v)
1671 {
1672 if (!aff || !v)
1673 goto error;
1674
1675 if (isl_val_is_one(v)) {
1676 isl_val_free(v);
1677 return aff;
1678 }
1679
1680 if (!isl_val_is_rat(v))
1681 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1682 "expecting rational factor", goto error);
1683 if (!isl_val_is_pos(v))
1684 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1685 "factor needs to be positive", goto error);
1686
1687 aff = isl_aff_scale(aff, v->d);
1688 aff = isl_aff_scale_down(aff, v->n);
1689
1690 isl_val_free(v);
1691 return aff;
1692 error:
1693 isl_aff_free(aff);
1694 isl_val_free(v);
1695 return NULL;
1696 }
1697
1698 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
1699 {
1700 isl_int v;
1701
1702 if (f == 1)
1703 return aff;
1704
1705 isl_int_init(v);
1706 isl_int_set_ui(v, f);
1707 aff = isl_aff_scale_down(aff, v);
1708 isl_int_clear(v);
1709
1710 return aff;
1711 }
1712
1713 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
1714 enum isl_dim_type type, unsigned pos, const char *s)
1715 {
1716 aff = isl_aff_cow(aff);
1717 if (!aff)
1718 return NULL;
1719 if (type == isl_dim_out)
1720 isl_die(aff->v->ctx, isl_error_invalid,
1721 "cannot set name of output/set dimension",
1722 return isl_aff_free(aff));
1723 if (type == isl_dim_in)
1724 type = isl_dim_set;
1725 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
1726 if (!aff->ls)
1727 return isl_aff_free(aff);
1728
1729 return aff;
1730 }
1731
1732 __isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
1733 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
1734 {
1735 aff = isl_aff_cow(aff);
1736 if (!aff)
1737 return isl_id_free(id);
1738 if (type == isl_dim_out)
1739 isl_die(aff->v->ctx, isl_error_invalid,
1740 "cannot set name of output/set dimension",
1741 goto error);
1742 if (type == isl_dim_in)
1743 type = isl_dim_set;
1744 aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
1745 if (!aff->ls)
1746 return isl_aff_free(aff);
1747
1748 return aff;
1749 error:
1750 isl_id_free(id);
1751 isl_aff_free(aff);
1752 return NULL;
1753 }
1754
1755 /* Exploit the equalities in "eq" to simplify the affine expression
1756 * and the expressions of the integer divisions in the local space.
1757 * The integer divisions in this local space are assumed to appear
1758 * as regular dimensions in "eq".
1759 */
1760 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
1761 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1762 {
1763 int i, j;
1764 unsigned total;
1765 unsigned n_div;
1766
1767 if (!eq)
1768 goto error;
1769 if (eq->n_eq == 0) {
1770 isl_basic_set_free(eq);
1771 return aff;
1772 }
1773
1774 aff = isl_aff_cow(aff);
1775 if (!aff)
1776 goto error;
1777
1778 aff->ls = isl_local_space_substitute_equalities(aff->ls,
1779 isl_basic_set_copy(eq));
1780 aff->v = isl_vec_cow(aff->v);
1781 if (!aff->ls || !aff->v)
1782 goto error;
1783
1784 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
1785 n_div = eq->n_div;
1786 for (i = 0; i < eq->n_eq; ++i) {
1787 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
1788 if (j < 0 || j == 0 || j >= total)
1789 continue;
1790
1791 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
1792 &aff->v->el[0]);
1793 }
1794
1795 isl_basic_set_free(eq);
1796 aff = isl_aff_normalize(aff);
1797 return aff;
1798 error:
1799 isl_basic_set_free(eq);
1800 isl_aff_free(aff);
1801 return NULL;
1802 }
1803
1804 /* Exploit the equalities in "eq" to simplify the affine expression
1805 * and the expressions of the integer divisions in the local space.
1806 */
1807 static __isl_give isl_aff *isl_aff_substitute_equalities(
1808 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1809 {
1810 int n_div;
1811
1812 if (!aff || !eq)
1813 goto error;
1814 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1815 if (n_div > 0)
1816 eq = isl_basic_set_add_dims(eq, isl_dim_set, n_div);
1817 return isl_aff_substitute_equalities_lifted(aff, eq);
1818 error:
1819 isl_basic_set_free(eq);
1820 isl_aff_free(aff);
1821 return NULL;
1822 }
1823
1824 /* Look for equalities among the variables shared by context and aff
1825 * and the integer divisions of aff, if any.
1826 * The equalities are then used to eliminate coefficients and/or integer
1827 * divisions from aff.
1828 */
1829 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
1830 __isl_take isl_set *context)
1831 {
1832 isl_basic_set *hull;
1833 int n_div;
1834
1835 if (!aff)
1836 goto error;
1837 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1838 if (n_div > 0) {
1839 isl_basic_set *bset;
1840 isl_local_space *ls;
1841 context = isl_set_add_dims(context, isl_dim_set, n_div);
1842 ls = isl_aff_get_domain_local_space(aff);
1843 bset = isl_basic_set_from_local_space(ls);
1844 bset = isl_basic_set_lift(bset);
1845 bset = isl_basic_set_flatten(bset);
1846 context = isl_set_intersect(context,
1847 isl_set_from_basic_set(bset));
1848 }
1849
1850 hull = isl_set_affine_hull(context);
1851 return isl_aff_substitute_equalities_lifted(aff, hull);
1852 error:
1853 isl_aff_free(aff);
1854 isl_set_free(context);
1855 return NULL;
1856 }
1857
1858 __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
1859 __isl_take isl_set *context)
1860 {
1861 isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
1862 dom_context = isl_set_intersect_params(dom_context, context);
1863 return isl_aff_gist(aff, dom_context);
1864 }
1865
1866 /* Return a basic set containing those elements in the space
1867 * of aff where it is non-negative.
1868 * If "rational" is set, then return a rational basic set.
1869 */
1870 static __isl_give isl_basic_set *aff_nonneg_basic_set(
1871 __isl_take isl_aff *aff, int rational)
1872 {
1873 isl_constraint *ineq;
1874 isl_basic_set *bset;
1875
1876 ineq = isl_inequality_from_aff(aff);
1877
1878 bset = isl_basic_set_from_constraint(ineq);
1879 if (rational)
1880 bset = isl_basic_set_set_rational(bset);
1881 bset = isl_basic_set_simplify(bset);
1882 return bset;
1883 }
1884
1885 /* Return a basic set containing those elements in the space
1886 * of aff where it is non-negative.
1887 */
1888 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
1889 {
1890 return aff_nonneg_basic_set(aff, 0);
1891 }
1892
1893 /* Return a basic set containing those elements in the domain space
1894 * of aff where it is negative.
1895 */
1896 __isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
1897 {
1898 aff = isl_aff_neg(aff);
1899 aff = isl_aff_add_constant_num_si(aff, -1);
1900 return isl_aff_nonneg_basic_set(aff);
1901 }
1902
1903 /* Return a basic set containing those elements in the space
1904 * of aff where it is zero.
1905 * If "rational" is set, then return a rational basic set.
1906 */
1907 static __isl_give isl_basic_set *aff_zero_basic_set(__isl_take isl_aff *aff,
1908 int rational)
1909 {
1910 isl_constraint *ineq;
1911 isl_basic_set *bset;
1912
1913 ineq = isl_equality_from_aff(aff);
1914
1915 bset = isl_basic_set_from_constraint(ineq);
1916 if (rational)
1917 bset = isl_basic_set_set_rational(bset);
1918 bset = isl_basic_set_simplify(bset);
1919 return bset;
1920 }
1921
1922 /* Return a basic set containing those elements in the space
1923 * of aff where it is zero.
1924 */
1925 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
1926 {
1927 return aff_zero_basic_set(aff, 0);
1928 }
1929
1930 /* Return a basic set containing those elements in the shared space
1931 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1932 */
1933 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
1934 __isl_take isl_aff *aff2)
1935 {
1936 aff1 = isl_aff_sub(aff1, aff2);
1937
1938 return isl_aff_nonneg_basic_set(aff1);
1939 }
1940
1941 /* Return a basic set containing those elements in the shared space
1942 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1943 */
1944 __isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
1945 __isl_take isl_aff *aff2)
1946 {
1947 return isl_aff_ge_basic_set(aff2, aff1);
1948 }
1949
1950 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
1951 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
1952 {
1953 aff1 = isl_aff_add(aff1, aff2);
1954 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
1955 return aff1;
1956 }
1957
1958 int isl_aff_is_empty(__isl_keep isl_aff *aff)
1959 {
1960 if (!aff)
1961 return -1;
1962
1963 return 0;
1964 }
1965
1966 /* Check whether the given affine expression has non-zero coefficient
1967 * for any dimension in the given range or if any of these dimensions
1968 * appear with non-zero coefficients in any of the integer divisions
1969 * involved in the affine expression.
1970 */
1971 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
1972 enum isl_dim_type type, unsigned first, unsigned n)
1973 {
1974 int i;
1975 isl_ctx *ctx;
1976 int *active = NULL;
1977 int involves = 0;
1978
1979 if (!aff)
1980 return -1;
1981 if (n == 0)
1982 return 0;
1983
1984 ctx = isl_aff_get_ctx(aff);
1985 if (first + n > isl_aff_dim(aff, type))
1986 isl_die(ctx, isl_error_invalid,
1987 "range out of bounds", return -1);
1988
1989 active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
1990 if (!active)
1991 goto error;
1992
1993 first += isl_local_space_offset(aff->ls, type) - 1;
1994 for (i = 0; i < n; ++i)
1995 if (active[first + i]) {
1996 involves = 1;
1997 break;
1998 }
1999
2000 free(active);
2001
2002 return involves;
2003 error:
2004 free(active);
2005 return -1;
2006 }
2007
2008 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
2009 enum isl_dim_type type, unsigned first, unsigned n)
2010 {
2011 isl_ctx *ctx;
2012
2013 if (!aff)
2014 return NULL;
2015 if (type == isl_dim_out)
2016 isl_die(aff->v->ctx, isl_error_invalid,
2017 "cannot drop output/set dimension",
2018 return isl_aff_free(aff));
2019 if (type == isl_dim_in)
2020 type = isl_dim_set;
2021 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
2022 return aff;
2023
2024 ctx = isl_aff_get_ctx(aff);
2025 if (first + n > isl_local_space_dim(aff->ls, type))
2026 isl_die(ctx, isl_error_invalid, "range out of bounds",
2027 return isl_aff_free(aff));
2028
2029 aff = isl_aff_cow(aff);
2030 if (!aff)
2031 return NULL;
2032
2033 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
2034 if (!aff->ls)
2035 return isl_aff_free(aff);
2036
2037 first += 1 + isl_local_space_offset(aff->ls, type);
2038 aff->v = isl_vec_drop_els(aff->v, first, n);
2039 if (!aff->v)
2040 return isl_aff_free(aff);
2041
2042 return aff;
2043 }
2044
2045 /* Project the domain of the affine expression onto its parameter space.
2046 * The affine expression may not involve any of the domain dimensions.
2047 */
2048 __isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
2049 {
2050 isl_space *space;
2051 unsigned n;
2052 int involves;
2053
2054 n = isl_aff_dim(aff, isl_dim_in);
2055 involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
2056 if (involves < 0)
2057 return isl_aff_free(aff);
2058 if (involves)
2059 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
2060 "affine expression involves some of the domain dimensions",
2061 return isl_aff_free(aff));
2062 aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
2063 space = isl_aff_get_domain_space(aff);
2064 space = isl_space_params(space);
2065 aff = isl_aff_reset_domain_space(aff, space);
2066 return aff;
2067 }
2068
2069 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
2070 enum isl_dim_type type, unsigned first, unsigned n)
2071 {
2072 isl_ctx *ctx;
2073
2074 if (!aff)
2075 return NULL;
2076 if (type == isl_dim_out)
2077 isl_die(aff->v->ctx, isl_error_invalid,
2078 "cannot insert output/set dimensions",
2079 return isl_aff_free(aff));
2080 if (type == isl_dim_in)
2081 type = isl_dim_set;
2082 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
2083 return aff;
2084
2085 ctx = isl_aff_get_ctx(aff);
2086 if (first > isl_local_space_dim(aff->ls, type))
2087 isl_die(ctx, isl_error_invalid, "position out of bounds",
2088 return isl_aff_free(aff));
2089
2090 aff = isl_aff_cow(aff);
2091 if (!aff)
2092 return NULL;
2093
2094 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
2095 if (!aff->ls)
2096 return isl_aff_free(aff);
2097
2098 first += 1 + isl_local_space_offset(aff->ls, type);
2099 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
2100 if (!aff->v)
2101 return isl_aff_free(aff);
2102
2103 return aff;
2104 }
2105
2106 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
2107 enum isl_dim_type type, unsigned n)
2108 {
2109 unsigned pos;
2110
2111 pos = isl_aff_dim(aff, type);
2112
2113 return isl_aff_insert_dims(aff, type, pos, n);
2114 }
2115
2116 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
2117 enum isl_dim_type type, unsigned n)
2118 {
2119 unsigned pos;
2120
2121 pos = isl_pw_aff_dim(pwaff, type);
2122
2123 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
2124 }
2125
2126 /* Move the "n" dimensions of "src_type" starting at "src_pos" of "aff"
2127 * to dimensions of "dst_type" at "dst_pos".
2128 *
2129 * We only support moving input dimensions to parameters and vice versa.
2130 */
2131 __isl_give isl_aff *isl_aff_move_dims(__isl_take isl_aff *aff,
2132 enum isl_dim_type dst_type, unsigned dst_pos,
2133 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2134 {
2135 unsigned g_dst_pos;
2136 unsigned g_src_pos;
2137
2138 if (!aff)
2139 return NULL;
2140 if (n == 0 &&
2141 !isl_local_space_is_named_or_nested(aff->ls, src_type) &&
2142 !isl_local_space_is_named_or_nested(aff->ls, dst_type))
2143 return aff;
2144
2145 if (dst_type == isl_dim_out || src_type == isl_dim_out)
2146 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
2147 "cannot move output/set dimension", isl_aff_free(aff));
2148 if (dst_type == isl_dim_div || src_type == isl_dim_div)
2149 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
2150 "cannot move divs", isl_aff_free(aff));
2151 if (dst_type == isl_dim_in)
2152 dst_type = isl_dim_set;
2153 if (src_type == isl_dim_in)
2154 src_type = isl_dim_set;
2155
2156 if (src_pos + n > isl_local_space_dim(aff->ls, src_type))
2157 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
2158 "range out of bounds", isl_aff_free(aff));
2159 if (dst_type == src_type)
2160 isl_die(isl_aff_get_ctx(aff), isl_error_unsupported,
2161 "moving dims within the same type not supported",
2162 isl_aff_free(aff));
2163
2164 aff = isl_aff_cow(aff);
2165 if (!aff)
2166 return NULL;
2167
2168 g_src_pos = 1 + isl_local_space_offset(aff->ls, src_type) + src_pos;
2169 g_dst_pos = 1 + isl_local_space_offset(aff->ls, dst_type) + dst_pos;
2170 if (dst_type > src_type)
2171 g_dst_pos -= n;
2172
2173 aff->v = isl_vec_move_els(aff->v, g_dst_pos, g_src_pos, n);
2174 aff->ls = isl_local_space_move_dims(aff->ls, dst_type, dst_pos,
2175 src_type, src_pos, n);
2176 if (!aff->v || !aff->ls)
2177 return isl_aff_free(aff);
2178
2179 aff = sort_divs(aff);
2180
2181 return aff;
2182 }
2183
2184 __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
2185 {
2186 isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
2187 return isl_pw_aff_alloc(dom, aff);
2188 }
2189
2190 #undef PW
2191 #define PW isl_pw_aff
2192 #undef EL
2193 #define EL isl_aff
2194 #undef EL_IS_ZERO
2195 #define EL_IS_ZERO is_empty
2196 #undef ZERO
2197 #define ZERO empty
2198 #undef IS_ZERO
2199 #define IS_ZERO is_empty
2200 #undef FIELD
2201 #define FIELD aff
2202 #undef DEFAULT_IS_ZERO
2203 #define DEFAULT_IS_ZERO 0
2204
2205 #define NO_EVAL
2206 #define NO_OPT
2207 #define NO_LIFT
2208 #define NO_MORPH
2209
2210 #include <isl_pw_templ.c>
2211
2212 static __isl_give isl_set *align_params_pw_pw_set_and(
2213 __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
2214 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
2215 __isl_take isl_pw_aff *pwaff2))
2216 {
2217 if (!pwaff1 || !pwaff2)
2218 goto error;
2219 if (isl_space_match(pwaff1->dim, isl_dim_param,
2220 pwaff2->dim, isl_dim_param))
2221 return fn(pwaff1, pwaff2);
2222 if (!isl_space_has_named_params(pwaff1->dim) ||
2223 !isl_space_has_named_params(pwaff2->dim))
2224 isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
2225 "unaligned unnamed parameters", goto error);
2226 pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
2227 pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
2228 return fn(pwaff1, pwaff2);
2229 error:
2230 isl_pw_aff_free(pwaff1);
2231 isl_pw_aff_free(pwaff2);
2232 return NULL;
2233 }
2234
2235 /* Compute a piecewise quasi-affine expression with a domain that
2236 * is the union of those of pwaff1 and pwaff2 and such that on each
2237 * cell, the quasi-affine expression is the better (according to cmp)
2238 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
2239 * is defined on a given cell, then the associated expression
2240 * is the defined one.
2241 */
2242 static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
2243 __isl_take isl_pw_aff *pwaff2,
2244 __isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
2245 __isl_take isl_aff *aff2))
2246 {
2247 int i, j, n;
2248 isl_pw_aff *res;
2249 isl_ctx *ctx;
2250 isl_set *set;
2251
2252 if (!pwaff1 || !pwaff2)
2253 goto error;
2254
2255 ctx = isl_space_get_ctx(pwaff1->dim);
2256 if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
2257 isl_die(ctx, isl_error_invalid,
2258 "arguments should live in same space", goto error);
2259
2260 if (isl_pw_aff_is_empty(pwaff1)) {
2261 isl_pw_aff_free(pwaff1);
2262 return pwaff2;
2263 }
2264
2265 if (isl_pw_aff_is_empty(pwaff2)) {
2266 isl_pw_aff_free(pwaff2);
2267 return pwaff1;
2268 }
2269
2270 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
2271 res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
2272
2273 for (i = 0; i < pwaff1->n; ++i) {
2274 set = isl_set_copy(pwaff1->p[i].set);
2275 for (j = 0; j < pwaff2->n; ++j) {
2276 struct isl_set *common;
2277 isl_set *better;
2278
2279 common = isl_set_intersect(
2280 isl_set_copy(pwaff1->p[i].set),
2281 isl_set_copy(pwaff2->p[j].set));
2282 better = isl_set_from_basic_set(cmp(
2283 isl_aff_copy(pwaff2->p[j].aff),
2284 isl_aff_copy(pwaff1->p[i].aff)));
2285 better = isl_set_intersect(common, better);
2286 if (isl_set_plain_is_empty(better)) {
2287 isl_set_free(better);
2288 continue;
2289 }
2290 set = isl_set_subtract(set, isl_set_copy(better));
2291
2292 res = isl_pw_aff_add_piece(res, better,
2293 isl_aff_copy(pwaff2->p[j].aff));
2294 }
2295 res = isl_pw_aff_add_piece(res, set,
2296 isl_aff_copy(pwaff1->p[i].aff));
2297 }
2298
2299 for (j = 0; j < pwaff2->n; ++j) {
2300 set = isl_set_copy(pwaff2->p[j].set);
2301 for (i = 0; i < pwaff1->n; ++i)
2302 set = isl_set_subtract(set,
2303 isl_set_copy(pwaff1->p[i].set));
2304 res = isl_pw_aff_add_piece(res, set,
2305 isl_aff_copy(pwaff2->p[j].aff));
2306 }
2307
2308 isl_pw_aff_free(pwaff1);
2309 isl_pw_aff_free(pwaff2);
2310
2311 return res;
2312 error:
2313 isl_pw_aff_free(pwaff1);
2314 isl_pw_aff_free(pwaff2);
2315 return NULL;
2316 }
2317
2318 /* Compute a piecewise quasi-affine expression with a domain that
2319 * is the union of those of pwaff1 and pwaff2 and such that on each
2320 * cell, the quasi-affine expression is the maximum of those of pwaff1
2321 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2322 * cell, then the associated expression is the defined one.
2323 */
2324 static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
2325 __isl_take isl_pw_aff *pwaff2)
2326 {
2327 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
2328 }
2329
2330 __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
2331 __isl_take isl_pw_aff *pwaff2)
2332 {
2333 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
2334 &pw_aff_union_max);
2335 }
2336
2337 /* Compute a piecewise quasi-affine expression with a domain that
2338 * is the union of those of pwaff1 and pwaff2 and such that on each
2339 * cell, the quasi-affine expression is the minimum of those of pwaff1
2340 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2341 * cell, then the associated expression is the defined one.
2342 */
2343 static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
2344 __isl_take isl_pw_aff *pwaff2)
2345 {
2346 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
2347 }
2348
2349 __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
2350 __isl_take isl_pw_aff *pwaff2)
2351 {
2352 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
2353 &pw_aff_union_min);
2354 }
2355
2356 __isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
2357 __isl_take isl_pw_aff *pwaff2, int max)
2358 {
2359 if (max)
2360 return isl_pw_aff_union_max(pwaff1, pwaff2);
2361 else
2362 return isl_pw_aff_union_min(pwaff1, pwaff2);
2363 }
2364
2365 /* Construct a map with as domain the domain of pwaff and
2366 * one-dimensional range corresponding to the affine expressions.
2367 */
2368 static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
2369 {
2370 int i;
2371 isl_space *dim;
2372 isl_map *map;
2373
2374 if (!pwaff)
2375 return NULL;
2376
2377 dim = isl_pw_aff_get_space(pwaff);
2378 map = isl_map_empty(dim);
2379
2380 for (i = 0; i < pwaff->n; ++i) {
2381 isl_basic_map *bmap;
2382 isl_map *map_i;
2383
2384 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
2385 map_i = isl_map_from_basic_map(bmap);
2386 map_i = isl_map_intersect_domain(map_i,
2387 isl_set_copy(pwaff->p[i].set));
2388 map = isl_map_union_disjoint(map, map_i);
2389 }
2390
2391 isl_pw_aff_free(pwaff);
2392
2393 return map;
2394 }
2395
2396 /* Construct a map with as domain the domain of pwaff and
2397 * one-dimensional range corresponding to the affine expressions.
2398 */
2399 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
2400 {
2401 if (!pwaff)
2402 return NULL;
2403 if (isl_space_is_set(pwaff->dim))
2404 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
2405 "space of input is not a map",
2406 return isl_pw_aff_free(pwaff));
2407 return map_from_pw_aff(pwaff);
2408 }
2409
2410 /* Construct a one-dimensional set with as parameter domain
2411 * the domain of pwaff and the single set dimension
2412 * corresponding to the affine expressions.
2413 */
2414 __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
2415 {
2416 if (!pwaff)
2417 return NULL;
2418 if (!isl_space_is_set(pwaff->dim))
2419 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
2420 "space of input is not a set",
2421 return isl_pw_aff_free(pwaff));
2422 return map_from_pw_aff(pwaff);
2423 }
2424
2425 /* Return a set containing those elements in the domain
2426 * of pwaff where it is non-negative.
2427 */
2428 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
2429 {
2430 int i;
2431 isl_set *set;
2432
2433 if (!pwaff)
2434 return NULL;
2435
2436 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
2437
2438 for (i = 0; i < pwaff->n; ++i) {
2439 isl_basic_set *bset;
2440 isl_set *set_i;
2441 int rational;
2442
2443 rational = isl_set_has_rational(pwaff->p[i].set);
2444 bset = aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff),
2445 rational);
2446 set_i = isl_set_from_basic_set(bset);
2447 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
2448 set = isl_set_union_disjoint(set, set_i);
2449 }
2450
2451 isl_pw_aff_free(pwaff);
2452
2453 return set;
2454 }
2455
2456 /* Return a set containing those elements in the domain
2457 * of pwaff where it is zero (if complement is 0) or not zero
2458 * (if complement is 1).
2459 */
2460 static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
2461 int complement)
2462 {
2463 int i;
2464 isl_set *set;
2465
2466 if (!pwaff)
2467 return NULL;
2468
2469 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
2470
2471 for (i = 0; i < pwaff->n; ++i) {
2472 isl_basic_set *bset;
2473 isl_set *set_i, *zero;
2474 int rational;
2475
2476 rational = isl_set_has_rational(pwaff->p[i].set);
2477 bset = aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff),
2478 rational);
2479 zero = isl_set_from_basic_set(bset);
2480 set_i = isl_set_copy(pwaff->p[i].set);
2481 if (complement)
2482 set_i = isl_set_subtract(set_i, zero);
2483 else
2484 set_i = isl_set_intersect(set_i, zero);
2485 set = isl_set_union_disjoint(set, set_i);
2486 }
2487
2488 isl_pw_aff_free(pwaff);
2489
2490 return set;
2491 }
2492
2493 /* Return a set containing those elements in the domain
2494 * of pwaff where it is zero.
2495 */
2496 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
2497 {
2498 return pw_aff_zero_set(pwaff, 0);
2499 }
2500
2501 /* Return a set containing those elements in the domain
2502 * of pwaff where it is not zero.
2503 */
2504 __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
2505 {
2506 return pw_aff_zero_set(pwaff, 1);
2507 }
2508
2509 /* Return a set containing those elements in the shared domain
2510 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
2511 *
2512 * We compute the difference on the shared domain and then construct
2513 * the set of values where this difference is non-negative.
2514 * If strict is set, we first subtract 1 from the difference.
2515 * If equal is set, we only return the elements where pwaff1 and pwaff2
2516 * are equal.
2517 */
2518 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
2519 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
2520 {
2521 isl_set *set1, *set2;
2522
2523 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
2524 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
2525 set1 = isl_set_intersect(set1, set2);
2526 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
2527 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
2528 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
2529
2530 if (strict) {
2531 isl_space *dim = isl_set_get_space(set1);
2532 isl_aff *aff;
2533 aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
2534 aff = isl_aff_add_constant_si(aff, -1);
2535 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
2536 } else
2537 isl_set_free(set1);
2538
2539 if (equal)
2540 return isl_pw_aff_zero_set(pwaff1);
2541 return isl_pw_aff_nonneg_set(pwaff1);
2542 }
2543
2544 /* Return a set containing those elements in the shared domain
2545 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
2546 */
2547 static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
2548 __isl_take isl_pw_aff *pwaff2)
2549 {
2550 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
2551 }
2552
2553 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
2554 __isl_take isl_pw_aff *pwaff2)
2555 {
2556 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
2557 }
2558
2559 /* Return a set containing those elements in the shared domain
2560 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
2561 */
2562 static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
2563 __isl_take isl_pw_aff *pwaff2)
2564 {
2565 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
2566 }
2567
2568 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
2569 __isl_take isl_pw_aff *pwaff2)
2570 {
2571 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
2572 }
2573
2574 /* Return a set containing those elements in the shared domain
2575 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
2576 */
2577 static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
2578 __isl_take isl_pw_aff *pwaff2)
2579 {
2580 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
2581 }
2582
2583 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
2584 __isl_take isl_pw_aff *pwaff2)
2585 {
2586 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
2587 }
2588
2589 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
2590 __isl_take isl_pw_aff *pwaff2)
2591 {
2592 return isl_pw_aff_ge_set(pwaff2, pwaff1);
2593 }
2594
2595 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
2596 __isl_take isl_pw_aff *pwaff2)
2597 {
2598 return isl_pw_aff_gt_set(pwaff2, pwaff1);
2599 }
2600
2601 /* Return a set containing those elements in the shared domain
2602 * of the elements of list1 and list2 where each element in list1
2603 * has the relation specified by "fn" with each element in list2.
2604 */
2605 static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
2606 __isl_take isl_pw_aff_list *list2,
2607 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
2608 __isl_take isl_pw_aff *pwaff2))
2609 {
2610 int i, j;
2611 isl_ctx *ctx;
2612 isl_set *set;
2613
2614 if (!list1 || !list2)
2615 goto error;
2616
2617 ctx = isl_pw_aff_list_get_ctx(list1);
2618 if (list1->n < 1 || list2->n < 1)
2619 isl_die(ctx, isl_error_invalid,
2620 "list should contain at least one element", goto error);
2621
2622 set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
2623 for (i = 0; i < list1->n; ++i)
2624 for (j = 0; j < list2->n; ++j) {
2625 isl_set *set_ij;
2626
2627 set_ij = fn(isl_pw_aff_copy(list1->p[i]),
2628 isl_pw_aff_copy(list2->p[j]));
2629 set = isl_set_intersect(set, set_ij);
2630 }
2631
2632 isl_pw_aff_list_free(list1);
2633 isl_pw_aff_list_free(list2);
2634 return set;
2635 error:
2636 isl_pw_aff_list_free(list1);
2637 isl_pw_aff_list_free(list2);
2638 return NULL;
2639 }
2640
2641 /* Return a set containing those elements in the shared domain
2642 * of the elements of list1 and list2 where each element in list1
2643 * is equal to each element in list2.
2644 */
2645 __isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
2646 __isl_take isl_pw_aff_list *list2)
2647 {
2648 return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
2649 }
2650
2651 __isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
2652 __isl_take isl_pw_aff_list *list2)
2653 {
2654 return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
2655 }
2656
2657 /* Return a set containing those elements in the shared domain
2658 * of the elements of list1 and list2 where each element in list1
2659 * is less than or equal to each element in list2.
2660 */
2661 __isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
2662 __isl_take isl_pw_aff_list *list2)
2663 {
2664 return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
2665 }
2666
2667 __isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
2668 __isl_take isl_pw_aff_list *list2)
2669 {
2670 return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
2671 }
2672
2673 __isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
2674 __isl_take isl_pw_aff_list *list2)
2675 {
2676 return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
2677 }
2678
2679 __isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
2680 __isl_take isl_pw_aff_list *list2)
2681 {
2682 return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
2683 }
2684
2685
2686 /* Return a set containing those elements in the shared domain
2687 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
2688 */
2689 static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
2690 __isl_take isl_pw_aff *pwaff2)
2691 {
2692 isl_set *set_lt, *set_gt;
2693
2694 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
2695 isl_pw_aff_copy(pwaff2));
2696 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
2697 return isl_set_union_disjoint(set_lt, set_gt);
2698 }
2699
2700 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
2701 __isl_take isl_pw_aff *pwaff2)
2702 {
2703 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
2704 }
2705
2706 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
2707 isl_int v)
2708 {
2709 int i;
2710
2711 if (isl_int_is_one(v))
2712 return pwaff;
2713 if (!isl_int_is_pos(v))
2714 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
2715 "factor needs to be positive",
2716 return isl_pw_aff_free(pwaff));
2717 pwaff = isl_pw_aff_cow(pwaff);
2718 if (!pwaff)
2719 return NULL;
2720 if (pwaff->n == 0)
2721 return pwaff;
2722
2723 for (i = 0; i < pwaff->n; ++i) {
2724 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
2725 if (!pwaff->p[i].aff)
2726 return isl_pw_aff_free(pwaff);
2727 }
2728
2729 return pwaff;
2730 }
2731
2732 /* Divide "pa" by "f".
2733 */
2734 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(__isl_take isl_pw_aff *pa,
2735 __isl_take isl_val *f)
2736 {
2737 int i;
2738
2739 if (!pa || !f)
2740 goto error;
2741
2742 if (isl_val_is_one(f)) {
2743 isl_val_free(f);
2744 return pa;
2745 }
2746
2747 if (!isl_val_is_rat(f))
2748 isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
2749 "expecting rational factor", goto error);
2750 if (!isl_val_is_pos(f))
2751 isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
2752 "factor needs to be positive", goto error);
2753
2754 pa = isl_pw_aff_cow(pa);
2755 if (!pa)
2756 return NULL;
2757 if (pa->n == 0)
2758 return pa;
2759
2760 for (i = 0; i < pa->n; ++i) {
2761 pa->p[i].aff = isl_aff_scale_down_val(pa->p[i].aff,
2762 isl_val_copy(f));
2763 if (!pa->p[i].aff)
2764 goto error;
2765 }
2766
2767 isl_val_free(f);
2768 return pa;
2769 error:
2770 isl_pw_aff_free(pa);
2771 isl_val_free(f);
2772 return NULL;
2773 }
2774
2775 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
2776 {
2777 int i;
2778
2779 pwaff = isl_pw_aff_cow(pwaff);
2780 if (!pwaff)
2781 return NULL;
2782 if (pwaff->n == 0)
2783 return pwaff;
2784
2785 for (i = 0; i < pwaff->n; ++i) {
2786 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
2787 if (!pwaff->p[i].aff)
2788 return isl_pw_aff_free(pwaff);
2789 }
2790
2791 return pwaff;
2792 }
2793
2794 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
2795 {
2796 int i;
2797
2798 pwaff = isl_pw_aff_cow(pwaff);
2799 if (!pwaff)
2800 return NULL;
2801 if (pwaff->n == 0)
2802 return pwaff;
2803
2804 for (i = 0; i < pwaff->n; ++i) {
2805 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
2806 if (!pwaff->p[i].aff)
2807 return isl_pw_aff_free(pwaff);
2808 }
2809
2810 return pwaff;
2811 }
2812
2813 /* Assuming that "cond1" and "cond2" are disjoint,
2814 * return an affine expression that is equal to pwaff1 on cond1
2815 * and to pwaff2 on cond2.
2816 */
2817 static __isl_give isl_pw_aff *isl_pw_aff_select(
2818 __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
2819 __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
2820 {
2821 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
2822 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
2823
2824 return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
2825 }
2826
2827 /* Return an affine expression that is equal to pwaff_true for elements
2828 * where "cond" is non-zero and to pwaff_false for elements where "cond"
2829 * is zero.
2830 * That is, return cond ? pwaff_true : pwaff_false;
2831 */
2832 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
2833 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
2834 {
2835 isl_set *cond_true, *cond_false;
2836
2837 cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
2838 cond_false = isl_pw_aff_zero_set(cond);
2839 return isl_pw_aff_select(cond_true, pwaff_true,
2840 cond_false, pwaff_false);
2841 }
2842
2843 int isl_aff_is_cst(__isl_keep isl_aff *aff)
2844 {
2845 if (!aff)
2846 return -1;
2847
2848 return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
2849 }
2850
2851 /* Check whether pwaff is a piecewise constant.
2852 */
2853 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
2854 {
2855 int i;
2856
2857 if (!pwaff)
2858 return -1;
2859
2860 for (i = 0; i < pwaff->n; ++i) {
2861 int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
2862 if (is_cst < 0 || !is_cst)
2863 return is_cst;
2864 }
2865
2866 return 1;
2867 }
2868
2869 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2870 __isl_take isl_aff *aff2)
2871 {
2872 if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
2873 return isl_aff_mul(aff2, aff1);
2874
2875 if (!isl_aff_is_cst(aff2))
2876 isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
2877 "at least one affine expression should be constant",
2878 goto error);
2879
2880 aff1 = isl_aff_cow(aff1);
2881 if (!aff1 || !aff2)
2882 goto error;
2883
2884 aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
2885 aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
2886
2887 isl_aff_free(aff2);
2888 return aff1;
2889 error:
2890 isl_aff_free(aff1);
2891 isl_aff_free(aff2);
2892 return NULL;
2893 }
2894
2895 /* Divide "aff1" by "aff2", assuming "aff2" is a piecewise constant.
2896 */
2897 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
2898 __isl_take isl_aff *aff2)
2899 {
2900 int is_cst;
2901 int neg;
2902
2903 is_cst = isl_aff_is_cst(aff2);
2904 if (is_cst < 0)
2905 goto error;
2906 if (!is_cst)
2907 isl_die(isl_aff_get_ctx(aff2), isl_error_invalid,
2908 "second argument should be a constant", goto error);
2909
2910 if (!aff2)
2911 goto error;
2912
2913 neg = isl_int_is_neg(aff2->v->el[1]);
2914 if (neg) {
2915 isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
2916 isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
2917 }
2918
2919 aff1 = isl_aff_scale(aff1, aff2->v->el[0]);
2920 aff1 = isl_aff_scale_down(aff1, aff2->v->el[1]);
2921
2922 if (neg) {
2923 isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
2924 isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
2925 }
2926
2927 isl_aff_free(aff2);
2928 return aff1;
2929 error:
2930 isl_aff_free(aff1);
2931 isl_aff_free(aff2);
2932 return NULL;
2933 }
2934
2935 static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2936 __isl_take isl_pw_aff *pwaff2)
2937 {
2938 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
2939 }
2940
2941 __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2942 __isl_take isl_pw_aff *pwaff2)
2943 {
2944 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
2945 }
2946
2947 __isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
2948 __isl_take isl_pw_aff *pwaff2)
2949 {
2950 return isl_pw_aff_union_add_(pwaff1, pwaff2);
2951 }
2952
2953 static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2954 __isl_take isl_pw_aff *pwaff2)
2955 {
2956 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
2957 }
2958
2959 __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2960 __isl_take isl_pw_aff *pwaff2)
2961 {
2962 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
2963 }
2964
2965 static __isl_give isl_pw_aff *pw_aff_div(__isl_take isl_pw_aff *pa1,
2966 __isl_take isl_pw_aff *pa2)
2967 {
2968 return isl_pw_aff_on_shared_domain(pa1, pa2, &isl_aff_div);
2969 }
2970
2971 /* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
2972 */
2973 __isl_give isl_pw_aff *isl_pw_aff_div(__isl_take isl_pw_aff *pa1,
2974 __isl_take isl_pw_aff *pa2)
2975 {
2976 int is_cst;
2977
2978 is_cst = isl_pw_aff_is_cst(pa2);
2979 if (is_cst < 0)
2980 goto error;
2981 if (!is_cst)
2982 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2983 "second argument should be a piecewise constant",
2984 goto error);
2985 return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_aff_div);
2986 error:
2987 isl_pw_aff_free(pa1);
2988 isl_pw_aff_free(pa2);
2989 return NULL;
2990 }
2991
2992 /* Compute the quotient of the integer division of "pa1" by "pa2"
2993 * with rounding towards zero.
2994 * "pa2" is assumed to be a piecewise constant.
2995 *
2996 * In particular, return
2997 *
2998 * pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
2999 *
3000 */
3001 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(__isl_take isl_pw_aff *pa1,
3002 __isl_take isl_pw_aff *pa2)
3003 {
3004 int is_cst;
3005 isl_set *cond;
3006 isl_pw_aff *f, *c;
3007
3008 is_cst = isl_pw_aff_is_cst(pa2);
3009 if (is_cst < 0)
3010 goto error;
3011 if (!is_cst)
3012 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
3013 "second argument should be a piecewise constant",
3014 goto error);
3015
3016 pa1 = isl_pw_aff_div(pa1, pa2);
3017
3018 cond = isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1));
3019 f = isl_pw_aff_floor(isl_pw_aff_copy(pa1));
3020 c = isl_pw_aff_ceil(pa1);
3021 return isl_pw_aff_cond(isl_set_indicator_function(cond), f, c);
3022 error:
3023 isl_pw_aff_free(pa1);
3024 isl_pw_aff_free(pa2);
3025 return NULL;
3026 }
3027
3028 /* Compute the remainder of the integer division of "pa1" by "pa2"
3029 * with rounding towards zero.
3030 * "pa2" is assumed to be a piecewise constant.
3031 *
3032 * In particular, return
3033 *
3034 * pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
3035 *
3036 */
3037 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(__isl_take isl_pw_aff *pa1,
3038 __isl_take isl_pw_aff *pa2)
3039 {
3040 int is_cst;
3041 isl_pw_aff *res;
3042
3043 is_cst = isl_pw_aff_is_cst(pa2);
3044 if (is_cst < 0)
3045 goto error;
3046 if (!is_cst)
3047 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
3048 "second argument should be a piecewise constant",
3049 goto error);
3050 res = isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1), isl_pw_aff_copy(pa2));
3051 res = isl_pw_aff_mul(pa2, res);
3052 res = isl_pw_aff_sub(pa1, res);
3053 return res;
3054 error:
3055 isl_pw_aff_free(pa1);
3056 isl_pw_aff_free(pa2);
3057 return NULL;
3058 }
3059
3060 static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
3061 __isl_take isl_pw_aff *pwaff2)
3062 {
3063 isl_set *le;
3064 isl_set *dom;
3065
3066 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
3067 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
3068 le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
3069 isl_pw_aff_copy(pwaff2));
3070 dom = isl_set_subtract(dom, isl_set_copy(le));
3071 return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
3072 }
3073
3074 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
3075 __isl_take isl_pw_aff *pwaff2)
3076 {
3077 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
3078 }
3079
3080 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
3081 __isl_take isl_pw_aff *pwaff2)
3082 {
3083 isl_set *ge;
3084 isl_set *dom;
3085
3086 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
3087 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
3088 ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
3089 isl_pw_aff_copy(pwaff2));
3090 dom = isl_set_subtract(dom, isl_set_copy(ge));
3091 return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
3092 }
3093
3094 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
3095 __isl_take isl_pw_aff *pwaff2)
3096 {
3097 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
3098 }
3099
3100 static __isl_give isl_pw_aff *pw_aff_list_reduce(
3101 __isl_take isl_pw_aff_list *list,
3102 __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
3103 __isl_take isl_pw_aff *pwaff2))
3104 {
3105 int i;
3106 isl_ctx *ctx;
3107 isl_pw_aff *res;
3108
3109 if (!list)
3110 return NULL;
3111
3112 ctx = isl_pw_aff_list_get_ctx(list);
3113 if (list->n < 1)
3114 isl_die(ctx, isl_error_invalid,
3115 "list should contain at least one element",
3116 return isl_pw_aff_list_free(list));
3117
3118 res = isl_pw_aff_copy(list->p[0]);
3119 for (i = 1; i < list->n; ++i)
3120 res = fn(res, isl_pw_aff_copy(list->p[i]));
3121
3122 isl_pw_aff_list_free(list);
3123 return res;
3124 }
3125
3126 /* Return an isl_pw_aff that maps each element in the intersection of the
3127 * domains of the elements of list to the minimal corresponding affine
3128 * expression.
3129 */
3130 __isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
3131 {
3132 return pw_aff_list_reduce(list, &isl_pw_aff_min);
3133 }
3134
3135 /* Return an isl_pw_aff that maps each element in the intersection of the
3136 * domains of the elements of list to the maximal corresponding affine
3137 * expression.
3138 */
3139 __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
3140 {
3141 return pw_aff_list_reduce(list, &isl_pw_aff_max);
3142 }
3143
3144 /* Mark the domains of "pwaff" as rational.
3145 */
3146 __isl_give isl_pw_aff *isl_pw_aff_set_rational(__isl_take isl_pw_aff *pwaff)
3147 {
3148 int i;
3149
3150 pwaff = isl_pw_aff_cow(pwaff);
3151 if (!pwaff)
3152 return NULL;
3153 if (pwaff->n == 0)
3154 return pwaff;
3155
3156 for (i = 0; i < pwaff->n; ++i) {
3157 pwaff->p[i].set = isl_set_set_rational(pwaff->p[i].set);
3158 if (!pwaff->p[i].set)
3159 return isl_pw_aff_free(pwaff);
3160 }
3161
3162 return pwaff;
3163 }
3164
3165 /* Mark the domains of the elements of "list" as rational.
3166 */
3167 __isl_give isl_pw_aff_list *isl_pw_aff_list_set_rational(
3168 __isl_take isl_pw_aff_list *list)
3169 {
3170 int i, n;
3171
3172 if (!list)
3173 return NULL;
3174 if (list->n == 0)
3175 return list;
3176
3177 n = list->n;
3178 for (i = 0; i < n; ++i) {
3179 isl_pw_aff *pa;
3180
3181 pa = isl_pw_aff_list_get_pw_aff(list, i);
3182 pa = isl_pw_aff_set_rational(pa);
3183 list = isl_pw_aff_list_set_pw_aff(list, i, pa);
3184 }
3185
3186 return list;
3187 }
3188
3189 /* Do the parameters of "aff" match those of "space"?
3190 */
3191 int isl_aff_matching_params(__isl_keep isl_aff *aff,
3192 __isl_keep isl_space *space)
3193 {
3194 isl_space *aff_space;
3195 int match;
3196
3197 if (!aff || !space)
3198 return -1;
3199
3200 aff_space = isl_aff_get_domain_space(aff);
3201
3202 match = isl_space_match(space, isl_dim_param, aff_space, isl_dim_param);
3203
3204 isl_space_free(aff_space);
3205 return match;
3206 }
3207
3208 /* Check that the domain space of "aff" matches "space".
3209 *
3210 * Return 0 on success and -1 on error.
3211 */
3212 int isl_aff_check_match_domain_space(__isl_keep isl_aff *aff,
3213 __isl_keep isl_space *space)
3214 {
3215 isl_space *aff_space;
3216 int match;
3217
3218 if (!aff || !space)
3219 return -1;
3220
3221 aff_space = isl_aff_get_domain_space(aff);
3222
3223 match = isl_space_match(space, isl_dim_param, aff_space, isl_dim_param);
3224 if (match < 0)
3225 goto error;
3226 if (!match)
3227 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
3228 "parameters don't match", goto error);
3229 match = isl_space_tuple_match(space, isl_dim_in,
3230 aff_space, isl_dim_set);
3231 if (match < 0)
3232 goto error;
3233 if (!match)
3234 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
3235 "domains don't match", goto error);
3236 isl_space_free(aff_space);
3237 return 0;
3238 error:
3239 isl_space_free(aff_space);
3240 return -1;
3241 }
3242
3243 #undef BASE
3244 #define BASE aff
3245 #define NO_INTERSECT_DOMAIN
3246
3247 #include <isl_multi_templ.c>
3248
3249 #undef NO_INTERSECT_DOMAIN
3250
3251 /* Given a map space, return an isl_multi_aff that maps a wrapped copy
3252 * of the space to its domain.
3253 */
3254 __isl_give isl_multi_aff *isl_multi_aff_domain_map(__isl_take isl_space *space)
3255 {
3256 int i, n_in;
3257 isl_local_space *ls;
3258 isl_multi_aff *ma;
3259
3260 if (!space)
3261 return NULL;
3262 if (!isl_space_is_map(space))
3263 isl_die(isl_space_get_ctx(space), isl_error_invalid,
3264 "not a map space", goto error);
3265
3266 n_in = isl_space_dim(space, isl_dim_in);
3267 space = isl_space_domain_map(space);
3268
3269 ma = isl_multi_aff_alloc(isl_space_copy(space));
3270 if (n_in == 0) {
3271 isl_space_free(space);
3272 return ma;
3273 }
3274
3275 space = isl_space_domain(space);
3276 ls = isl_local_space_from_space(space);
3277 for (i = 0; i < n_in; ++i) {
3278 isl_aff *aff;
3279
3280 aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
3281 isl_dim_set, i);
3282 ma = isl_multi_aff_set_aff(ma, i, aff);
3283 }
3284 isl_local_space_free(ls);
3285 return ma;
3286 error:
3287 isl_space_free(space);
3288 return NULL;
3289 }
3290
3291 /* Given a map space, return an isl_multi_aff that maps a wrapped copy
3292 * of the space to its range.
3293 */
3294 __isl_give isl_multi_aff *isl_multi_aff_range_map(__isl_take isl_space *space)
3295 {
3296 int i, n_in, n_out;
3297 isl_local_space *ls;
3298 isl_multi_aff *ma;
3299
3300 if (!space)
3301 return NULL;
3302 if (!isl_space_is_map(space))
3303 isl_die(isl_space_get_ctx(space), isl_error_invalid,
3304 "not a map space", goto error);
3305
3306 n_in = isl_space_dim(space, isl_dim_in);
3307 n_out = isl_space_dim(space, isl_dim_out);
3308 space = isl_space_range_map(space);
3309
3310 ma = isl_multi_aff_alloc(isl_space_copy(space));
3311 if (n_out == 0) {
3312 isl_space_free(space);
3313 return ma;
3314 }
3315
3316 space = isl_space_domain(space);
3317 ls = isl_local_space_from_space(space);
3318 for (i = 0; i < n_out; ++i) {
3319 isl_aff *aff;
3320
3321 aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
3322 isl_dim_set, n_in + i);
3323 ma = isl_multi_aff_set_aff(ma, i, aff);
3324 }
3325 isl_local_space_free(ls);
3326 return ma;
3327 error:
3328 isl_space_free(space);
3329 return NULL;
3330 }
3331
3332 /* Given the space of a set and a range of set dimensions,
3333 * construct an isl_multi_aff that projects out those dimensions.
3334 */
3335 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
3336 __isl_take isl_space *space, enum isl_dim_type type,
3337 unsigned first, unsigned n)
3338 {
3339 int i, dim;
3340 isl_local_space *ls;
3341 isl_multi_aff *ma;
3342
3343 if (!space)
3344 return NULL;
3345 if (!isl_space_is_set(space))
3346 isl_die(isl_space_get_ctx(space), isl_error_unsupported,
3347 "expecting set space", goto error);
3348 if (type != isl_dim_set)
3349 isl_die(isl_space_get_ctx(space), isl_error_invalid,
3350 "only set dimensions can be projected out", goto error);
3351
3352 dim = isl_space_dim(space, isl_dim_set);
3353 if (first + n > dim)
3354 isl_die(isl_space_get_ctx(space), isl_error_invalid,
3355 "range out of bounds", goto error);
3356
3357 space = isl_space_from_domain(space);
3358 space = isl_space_add_dims(space, isl_dim_out, dim - n);
3359
3360 if (dim == n)
3361 return isl_multi_aff_alloc(space);
3362
3363 ma = isl_multi_aff_alloc(isl_space_copy(space));
3364 space = isl_space_domain(space);
3365 ls = isl_local_space_from_space(space);
3366
3367 for (i = 0; i < first; ++i) {
3368 isl_aff *aff;
3369
3370 aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
3371 isl_dim_set, i);
3372 ma = isl_multi_aff_set_aff(ma, i, aff);
3373 }
3374
3375 for (i = 0; i < dim - (first + n); ++i) {
3376 isl_aff *aff;
3377
3378 aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
3379 isl_dim_set, first + n + i);
3380 ma = isl_multi_aff_set_aff(ma, first + i, aff);
3381 }
3382
3383 isl_local_space_free(ls);
3384 return ma;
3385 error:
3386 isl_space_free(space);
3387 return NULL;
3388 }
3389
3390 /* Given the space of a set and a range of set dimensions,
3391 * construct an isl_pw_multi_aff that projects out those dimensions.
3392 */
3393 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_project_out_map(
3394 __isl_take isl_space *space, enum isl_dim_type type,
3395 unsigned first, unsigned n)
3396 {
3397 isl_multi_aff *ma;
3398
3399 ma = isl_multi_aff_project_out_map(space, type, first, n);
3400 return isl_pw_multi_aff_from_multi_aff(ma);
3401 }
3402
3403 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
3404 * domain.
3405 */
3406 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
3407 __isl_take isl_multi_aff *ma)
3408 {
3409 isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
3410 return isl_pw_multi_aff_alloc(dom, ma);
3411 }
3412
3413 /* Create a piecewise multi-affine expression in the given space that maps each
3414 * input dimension to the corresponding output dimension.
3415 */
3416 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3417 __isl_take isl_space *space)
3418 {
3419 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space));
3420 }
3421
3422 /* Add "ma2" to "ma1" and return the result.
3423 *
3424 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
3425 */
3426 static __isl_give isl_multi_aff *isl_multi_aff_add_aligned(
3427 __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
3428 {
3429 return isl_multi_aff_bin_op(maff1, maff2, &isl_aff_add);
3430 }
3431
3432 /* Add "ma2" to "ma1" and return the result.
3433 */
3434 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *ma1,
3435 __isl_take isl_multi_aff *ma2)
3436 {
3437 return isl_multi_aff_align_params_multi_multi_and(ma1, ma2,
3438 &isl_multi_aff_add_aligned);
3439 }
3440
3441 /* Subtract "ma2" from "ma1" and return the result.
3442 *
3443 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
3444 */
3445 static __isl_give isl_multi_aff *isl_multi_aff_sub_aligned(
3446 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
3447 {
3448 return isl_multi_aff_bin_op(ma1, ma2, &isl_aff_sub);
3449 }
3450
3451 /* Subtract "ma2" from "ma1" and return the result.
3452 */
3453 __isl_give isl_multi_aff *isl_multi_aff_sub(__isl_take isl_multi_aff *ma1,
3454 __isl_take isl_multi_aff *ma2)
3455 {
3456 return isl_multi_aff_align_params_multi_multi_and(ma1, ma2,
3457 &isl_multi_aff_sub_aligned);
3458 }
3459
3460 /* Exploit the equalities in "eq" to simplify the affine expressions.
3461 */
3462 static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
3463 __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
3464 {
3465 int i;
3466
3467 maff = isl_multi_aff_cow(maff);
3468 if (!maff || !eq)
3469 goto error;
3470
3471 for (i = 0; i < maff->n; ++i) {
3472 maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
3473 isl_basic_set_copy(eq));
3474 if (!maff->p[i])
3475 goto error;
3476 }
3477
3478 isl_basic_set_free(eq);
3479 return maff;
3480 error:
3481 isl_basic_set_free(eq);
3482 isl_multi_aff_free(maff);
3483 return NULL;
3484 }
3485
3486 __isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
3487 isl_int f)
3488 {
3489 int i;
3490
3491 maff = isl_multi_aff_cow(maff);
3492 if (!maff)
3493 return NULL;
3494
3495 for (i = 0; i < maff->n; ++i) {
3496 maff->p[i] = isl_aff_scale(maff->p[i], f);
3497 if (!maff->p[i])
3498 return isl_multi_aff_free(maff);
3499 }
3500
3501 return maff;
3502 }
3503
3504 __isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
3505 __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
3506 {
3507 maff1 = isl_multi_aff_add(maff1, maff2);
3508 maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
3509 return maff1;
3510 }
3511
3512 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
3513 {
3514 if (!maff)
3515 return -1;
3516
3517 return 0;
3518 }
3519
3520 /* Return the set of domain elements where "ma1" is lexicographically
3521 * smaller than or equal to "ma2".
3522 */
3523 __isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
3524 __isl_take isl_multi_aff *ma2)
3525 {
3526 return isl_multi_aff_lex_ge_set(ma2, ma1);
3527 }
3528
3529 /* Return the set of domain elements where "ma1" is lexicographically
3530 * greater than or equal to "ma2".
3531 */
3532 __isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
3533 __isl_take isl_multi_aff *ma2)
3534 {
3535 isl_space *space;
3536 isl_map *map1, *map2;
3537 isl_map *map, *ge;
3538
3539 map1 = isl_map_from_multi_aff(ma1);
3540 map2 = isl_map_from_multi_aff(ma2);
3541 map = isl_map_range_product(map1, map2);
3542 space = isl_space_range(isl_map_get_space(map));
3543 space = isl_space_domain(isl_space_unwrap(space));
3544 ge = isl_map_lex_ge(space);
3545 map = isl_map_intersect_range(map, isl_map_wrap(ge));
3546
3547 return isl_map_domain(map);
3548 }
3549
3550 #undef PW
3551 #define PW isl_pw_multi_aff
3552 #undef EL
3553 #define EL isl_multi_aff
3554 #undef EL_IS_ZERO
3555 #define EL_IS_ZERO is_empty
3556 #undef ZERO
3557 #define ZERO empty
3558 #undef IS_ZERO
3559 #define IS_ZERO is_empty
3560 #undef FIELD
3561 #define FIELD maff
3562 #undef DEFAULT_IS_ZERO
3563 #define DEFAULT_IS_ZERO 0
3564
3565 #define NO_NEG
3566 #define NO_EVAL
3567 #define NO_OPT
3568 #define NO_INVOLVES_DIMS
3569 #define NO_INSERT_DIMS
3570 #define NO_LIFT
3571 #define NO_MORPH
3572
3573 #include <isl_pw_templ.c>
3574
3575 #undef UNION
3576 #define UNION isl_union_pw_multi_aff
3577 #undef PART
3578 #define PART isl_pw_multi_aff
3579 #undef PARTS
3580 #define PARTS pw_multi_aff
3581 #define ALIGN_DOMAIN
3582
3583 #define NO_EVAL
3584
3585 #include <isl_union_templ.c>
3586
3587 /* Given a function "cmp" that returns the set of elements where
3588 * "ma1" is "better" than "ma2", return the intersection of this
3589 * set with "dom1" and "dom2".
3590 */
3591 static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1,
3592 __isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1,
3593 __isl_keep isl_multi_aff *ma2,
3594 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
3595 __isl_take isl_multi_aff *ma2))
3596 {
3597 isl_set *common;
3598 isl_set *better;
3599 int is_empty;
3600
3601 common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2));
3602 is_empty = isl_set_plain_is_empty(common);
3603 if (is_empty >= 0 && is_empty)
3604 return common;
3605 if (is_empty < 0)
3606 return isl_set_free(common);
3607 better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2));
3608 better = isl_set_intersect(common, better);
3609
3610 return better;
3611 }
3612
3613 /* Given a function "cmp" that returns the set of elements where
3614 * "ma1" is "better" than "ma2", return a piecewise multi affine
3615 * expression defined on the union of the definition domains
3616 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
3617 * "pma2" on each cell. If only one of the two input functions
3618 * is defined on a given cell, then it is considered the best.
3619 */
3620 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt(
3621 __isl_take isl_pw_multi_aff *pma1,
3622 __isl_take isl_pw_multi_aff *pma2,
3623 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
3624 __isl_take isl_multi_aff *ma2))
3625 {
3626 int i, j, n;
3627 isl_pw_multi_aff *res = NULL;
3628 isl_ctx *ctx;
3629 isl_set *set = NULL;
3630
3631 if (!pma1 || !pma2)
3632 goto error;
3633
3634 ctx = isl_space_get_ctx(pma1->dim);
3635 if (!isl_space_is_equal(pma1->dim, pma2->dim))
3636 isl_die(ctx, isl_error_invalid,
3637 "arguments should live in the same space", goto error);
3638
3639 if (isl_pw_multi_aff_is_empty(pma1)) {
3640 isl_pw_multi_aff_free(pma1);
3641 return pma2;
3642 }
3643
3644 if (isl_pw_multi_aff_is_empty(pma2)) {
3645 isl_pw_multi_aff_free(pma2);
3646 return pma1;
3647 }
3648
3649 n = 2 * (pma1->n + 1) * (pma2->n + 1);
3650 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n);
3651
3652 for (i = 0; i < pma1->n; ++i) {
3653 set = isl_set_copy(pma1->p[i].set);
3654 for (j = 0; j < pma2->n; ++j) {
3655 isl_set *better;
3656 int is_empty;
3657
3658 better = shared_and_better(pma2->p[j].set,
3659 pma1->p[i].set, pma2->p[j].maff,
3660 pma1->p[i].maff, cmp);
3661 is_empty = isl_set_plain_is_empty(better);
3662 if (is_empty < 0 || is_empty) {
3663 isl_set_free(better);
3664 if (is_empty < 0)
3665 goto error;
3666 continue;
3667 }
3668 set = isl_set_subtract(set, isl_set_copy(better));
3669
3670 res = isl_pw_multi_aff_add_piece(res, better,
3671 isl_multi_aff_copy(pma2->p[j].maff));
3672 }
3673 res = isl_pw_multi_aff_add_piece(res, set,
3674 isl_multi_aff_copy(pma1->p[i].maff));
3675 }
3676
3677 for (j = 0; j < pma2->n; ++j) {
3678 set = isl_set_copy(pma2->p[j].set);
3679 for (i = 0; i < pma1->n; ++i)
3680 set = isl_set_subtract(set,
3681 isl_set_copy(pma1->p[i].set));
3682 res = isl_pw_multi_aff_add_piece(res, set,
3683 isl_multi_aff_copy(pma2->p[j].maff));
3684 }
3685
3686 isl_pw_multi_aff_free(pma1);
3687 isl_pw_multi_aff_free(pma2);
3688
3689 return res;
3690 error:
3691 isl_pw_multi_aff_free(pma1);
3692 isl_pw_multi_aff_free(pma2);
3693 isl_set_free(set);
3694 return isl_pw_multi_aff_free(res);
3695 }
3696
3697 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
3698 __isl_take isl_pw_multi_aff *pma1,
3699 __isl_take isl_pw_multi_aff *pma2)
3700 {
3701 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_ge_set);
3702 }
3703
3704 /* Given two piecewise multi affine expressions, return a piecewise
3705 * multi-affine expression defined on the union of the definition domains
3706 * of the inputs that is equal to the lexicographic maximum of the two
3707 * inputs on each cell. If only one of the two inputs is defined on
3708 * a given cell, then it is considered to be the maximum.
3709 */
3710 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3711 __isl_take isl_pw_multi_aff *pma1,
3712 __isl_take isl_pw_multi_aff *pma2)
3713 {
3714 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3715 &pw_multi_aff_union_lexmax);
3716 }
3717
3718 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
3719 __isl_take isl_pw_multi_aff *pma1,
3720 __isl_take isl_pw_multi_aff *pma2)
3721 {
3722 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_set);
3723 }
3724
3725 /* Given two piecewise multi affine expressions, return a piecewise
3726 * multi-affine expression defined on the union of the definition domains
3727 * of the inputs that is equal to the lexicographic minimum of the two
3728 * inputs on each cell. If only one of the two inputs is defined on
3729 * a given cell, then it is considered to be the minimum.
3730 */
3731 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3732 __isl_take isl_pw_multi_aff *pma1,
3733 __isl_take isl_pw_multi_aff *pma2)
3734 {
3735 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3736 &pw_multi_aff_union_lexmin);
3737 }
3738
3739 static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
3740 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3741 {
3742 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
3743 &isl_multi_aff_add);
3744 }
3745
3746 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3747 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3748 {
3749 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3750 &pw_multi_aff_add);
3751 }
3752
3753 static __isl_give isl_pw_multi_aff *pw_multi_aff_sub(
3754 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3755 {
3756 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
3757 &isl_multi_aff_sub);
3758 }
3759
3760 /* Subtract "pma2" from "pma1" and return the result.
3761 */
3762 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
3763 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3764 {
3765 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3766 &pw_multi_aff_sub);
3767 }
3768
3769 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3770 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3771 {
3772 return isl_pw_multi_aff_union_add_(pma1, pma2);
3773 }
3774
3775 /* Given two piecewise multi-affine expressions A -> B and C -> D,
3776 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
3777 */
3778 static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
3779 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3780 {
3781 int i, j, n;
3782 isl_space *space;
3783 isl_pw_multi_aff *res;
3784
3785 if (!pma1 || !pma2)
3786 goto error;
3787
3788 n = pma1->n * pma2->n;
3789 space = isl_space_product(isl_space_copy(pma1->dim),
3790 isl_space_copy(pma2->dim));
3791 res = isl_pw_multi_aff_alloc_size(space, n);
3792
3793 for (i = 0; i < pma1->n; ++i) {
3794 for (j = 0; j < pma2->n; ++j) {
3795 isl_set *domain;
3796 isl_multi_aff *ma;
3797
3798 domain = isl_set_product(isl_set_copy(pma1->p[i].set),
3799 isl_set_copy(pma2->p[j].set));
3800 ma = isl_multi_aff_product(
3801 isl_multi_aff_copy(pma1->p[i].maff),
3802 isl_multi_aff_copy(pma2->p[j].maff));
3803 res = isl_pw_multi_aff_add_piece(res, domain, ma);
3804 }
3805 }
3806
3807 isl_pw_multi_aff_free(pma1);
3808 isl_pw_multi_aff_free(pma2);
3809 return res;
3810 error:
3811 isl_pw_multi_aff_free(pma1);
3812 isl_pw_multi_aff_free(pma2);
3813 return NULL;
3814 }
3815
3816 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3817 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3818 {
3819 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3820 &pw_multi_aff_product);
3821 }
3822
3823 /* Construct a map mapping the domain of the piecewise multi-affine expression
3824 * to its range, with each dimension in the range equated to the
3825 * corresponding affine expression on its cell.
3826 */
3827 __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
3828 {
3829 int i;
3830 isl_map *map;
3831
3832 if (!pma)
3833 return NULL;
3834
3835 map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
3836
3837 for (i = 0; i < pma->n; ++i) {
3838 isl_multi_aff *maff;
3839 isl_basic_map *bmap;
3840 isl_map *map_i;
3841
3842 maff = isl_multi_aff_copy(pma->p[i].maff);
3843 bmap = isl_basic_map_from_multi_aff(maff);
3844 map_i = isl_map_from_basic_map(bmap);
3845 map_i = isl_map_intersect_domain(map_i,
3846 isl_set_copy(pma->p[i].set));
3847 map = isl_map_union_disjoint(map, map_i);
3848 }
3849
3850 isl_pw_multi_aff_free(pma);
3851 return map;
3852 }
3853
3854 __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
3855 {
3856 if (!pma)
3857 return NULL;
3858
3859 if (!isl_space_is_set(pma->dim))
3860 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3861 "isl_pw_multi_aff cannot be converted into an isl_set",
3862 return isl_pw_multi_aff_free(pma));
3863
3864 return isl_map_from_pw_multi_aff(pma);
3865 }
3866
3867 /* Given a basic map with a single output dimension that is defined
3868 * in terms of the parameters and input dimensions using an equality,
3869 * extract an isl_aff that expresses the output dimension in terms
3870 * of the parameters and input dimensions.
3871 *
3872 * Since some applications expect the result of isl_pw_multi_aff_from_map
3873 * to only contain integer affine expressions, we compute the floor
3874 * of the expression before returning.
3875 *
3876 * This function shares some similarities with
3877 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
3878 */
3879 static __isl_give isl_aff *extract_isl_aff_from_basic_map(
3880 __isl_take isl_basic_map *bmap)
3881 {
3882 int i;
3883 unsigned offset;
3884 unsigned total;
3885 isl_local_space *ls;
3886 isl_aff *aff;
3887
3888 if (!bmap)
3889 return NULL;
3890 if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
3891 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3892 "basic map should have a single output dimension",
3893 goto error);
3894 offset = isl_basic_map_offset(bmap, isl_dim_out);
3895 total = isl_basic_map_total_dim(bmap);
3896 for (i = 0; i < bmap->n_eq; ++i) {
3897 if (isl_int_is_zero(bmap->eq[i][offset]))
3898 continue;
3899 if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
3900 1 + total - (offset + 1)) != -1)
3901 continue;
3902 break;
3903 }
3904 if (i >= bmap->n_eq)
3905 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3906 "unable to find suitable equality", goto error);
3907 ls = isl_basic_map_get_local_space(bmap);
3908 aff = isl_aff_alloc(isl_local_space_domain(ls));
3909 if (!aff)
3910 goto error;
3911 if (isl_int_is_neg(bmap->eq[i][offset]))
3912 isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
3913 else
3914 isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
3915 isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
3916 isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
3917 isl_basic_map_free(bmap);
3918
3919 aff = isl_aff_remove_unused_divs(aff);
3920 aff = isl_aff_floor(aff);
3921 return aff;
3922 error:
3923 isl_basic_map_free(bmap);
3924 return NULL;
3925 }
3926
3927 /* Given a basic map where each output dimension is defined
3928 * in terms of the parameters and input dimensions using an equality,
3929 * extract an isl_multi_aff that expresses the output dimensions in terms
3930 * of the parameters and input dimensions.
3931 */
3932 static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
3933 __isl_take isl_basic_map *bmap)
3934 {
3935 int i;
3936 unsigned n_out;
3937 isl_multi_aff *ma;
3938
3939 if (!bmap)
3940 return NULL;
3941
3942 ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
3943 n_out = isl_basic_map_dim(bmap, isl_dim_out);
3944
3945 for (i = 0; i < n_out; ++i) {
3946 isl_basic_map *bmap_i;
3947 isl_aff *aff;
3948
3949 bmap_i = isl_basic_map_copy(bmap);
3950 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
3951 i + 1, n_out - (1 + i));
3952 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
3953 aff = extract_isl_aff_from_basic_map(bmap_i);
3954 ma = isl_multi_aff_set_aff(ma, i, aff);
3955 }
3956
3957 isl_basic_map_free(bmap);
3958
3959 return ma;
3960 }
3961
3962 /* Create an isl_pw_multi_aff that is equivalent to
3963 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
3964 * The given basic map is such that each output dimension is defined
3965 * in terms of the parameters and input dimensions using an equality.
3966 */
3967 static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
3968 __isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
3969 {
3970 isl_multi_aff *ma;
3971
3972 ma = extract_isl_multi_aff_from_basic_map(bmap);
3973 return isl_pw_multi_aff_alloc(domain, ma);
3974 }
3975
3976 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3977 * This obviously only works if the input "map" is single-valued.
3978 * If so, we compute the lexicographic minimum of the image in the form
3979 * of an isl_pw_multi_aff. Since the image is unique, it is equal
3980 * to its lexicographic minimum.
3981 * If the input is not single-valued, we produce an error.
3982 */
3983 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_base(
3984 __isl_take isl_map *map)
3985 {
3986 int i;
3987 int sv;
3988 isl_pw_multi_aff *pma;
3989
3990 sv = isl_map_is_single_valued(map);
3991 if (sv < 0)
3992 goto error;
3993 if (!sv)
3994 isl_die(isl_map_get_ctx(map), isl_error_invalid,
3995 "map is not single-valued", goto error);
3996 map = isl_map_make_disjoint(map);
3997 if (!map)
3998 return NULL;
3999
4000 pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
4001
4002 for (i = 0; i < map->n; ++i) {
4003 isl_pw_multi_aff *pma_i;
4004 isl_basic_map *bmap;
4005 bmap = isl_basic_map_copy(map->p[i]);
4006 pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
4007 pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
4008 }
4009
4010 isl_map_free(map);
4011 return pma;
4012 error:
4013 isl_map_free(map);
4014 return NULL;
4015 }
4016
4017 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
4018 * taking into account that the output dimension at position "d"
4019 * can be represented as
4020 *
4021 * x = floor((e(...) + c1) / m)
4022 *
4023 * given that constraint "i" is of the form
4024 *
4025 * e(...) + c1 - m x >= 0
4026 *
4027 *
4028 * Let "map" be of the form
4029 *
4030 * A -> B
4031 *
4032 * We construct a mapping
4033 *
4034 * A -> [A -> x = floor(...)]
4035 *
4036 * apply that to the map, obtaining
4037 *
4038 * [A -> x = floor(...)] -> B
4039 *
4040 * and equate dimension "d" to x.
4041 * We then compute a isl_pw_multi_aff representation of the resulting map
4042 * and plug in the mapping above.
4043 */
4044 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_div(
4045 __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i)
4046 {
4047 isl_ctx *ctx;
4048 isl_space *space;
4049 isl_local_space *ls;
4050 isl_multi_aff *ma;
4051 isl_aff *aff;
4052 isl_vec *v;
4053 isl_map *insert;
4054 int offset;
4055 int n;
4056 int n_in;
4057 isl_pw_multi_aff *pma;
4058 int is_set;
4059
4060 is_set = isl_map_is_set(map);
4061
4062 offset = isl_basic_map_offset(hull, isl_dim_out);
4063 ctx = isl_map_get_ctx(map);
4064 space = isl_space_domain(isl_map_get_space(map));
4065 n_in = isl_space_dim(space, isl_dim_set);
4066 n = isl_space_dim(space, isl_dim_all);
4067
4068 v = isl_vec_alloc(ctx, 1 + 1 + n);
4069 if (v) {
4070 isl_int_neg(v->el[0], hull->ineq[i][offset + d]);
4071 isl_seq_cpy(v->el + 1, hull->ineq[i], 1 + n);
4072 }
4073 isl_basic_map_free(hull);
4074
4075 ls = isl_local_space_from_space(isl_space_copy(space));
4076 aff = isl_aff_alloc_vec(ls, v);
4077 aff = isl_aff_floor(aff);
4078 if (is_set) {
4079 isl_space_free(space);
4080 ma = isl_multi_aff_from_aff(aff);
4081 } else {
4082 ma = isl_multi_aff_identity(isl_space_map_from_set(space));
4083 ma = isl_multi_aff_range_product(ma,
4084 isl_multi_aff_from_aff(aff));
4085 }
4086
4087 insert = isl_map_from_multi_aff(isl_multi_aff_copy(ma));
4088 map = isl_map_apply_domain(map, insert);
4089 map = isl_map_equate(map, isl_dim_in, n_in, isl_dim_out, d);
4090 pma = isl_pw_multi_aff_from_map(map);
4091 pma = isl_pw_multi_aff_pullback_multi_aff(pma, ma);
4092
4093 return pma;
4094 }
4095
4096 /* Is constraint "c" of the form
4097 *
4098 * e(...) + c1 - m x >= 0
4099 *
4100 * or
4101 *
4102 * -e(...) + c2 + m x >= 0
4103 *
4104 * where m > 1 and e only depends on parameters and input dimemnsions?
4105 *
4106 * "offset" is the offset of the output dimensions
4107 * "pos" is the position of output dimension x.
4108 */
4109 static int is_potential_div_constraint(isl_int *c, int offset, int d, int total)
4110 {
4111 if (isl_int_is_zero(c[offset + d]))
4112 return 0;
4113 if (isl_int_is_one(c[offset + d]))
4114 return 0;
4115 if (isl_int_is_negone(c[offset + d]))
4116 return 0;
4117 if (isl_seq_first_non_zero(c + offset, d) != -1)
4118 return 0;
4119 if (isl_seq_first_non_zero(c + offset + d + 1,
4120 total - (offset + d + 1)) != -1)
4121 return 0;
4122 return 1;
4123 }
4124
4125 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4126 *
4127 * As a special case, we first check if there is any pair of constraints,
4128 * shared by all the basic maps in "map" that force a given dimension
4129 * to be equal to the floor of some affine combination of the input dimensions.
4130 *
4131 * In particular, if we can find two constraints
4132 *
4133 * e(...) + c1 - m x >= 0 i.e., m x <= e(...) + c1
4134 *
4135 * and
4136 *
4137 * -e(...) + c2 + m x >= 0 i.e., m x >= e(...) - c2
4138 *
4139 * where m > 1 and e only depends on parameters and input dimemnsions,
4140 * and such that
4141 *
4142 * c1 + c2 < m i.e., -c2 >= c1 - (m - 1)
4143 *
4144 * then we know that we can take
4145 *
4146 * x = floor((e(...) + c1) / m)
4147 *
4148 * without having to perform any computation.
4149 *
4150 * Note that we know that
4151 *
4152 * c1 + c2 >= 1
4153 *
4154 * If c1 + c2 were 0, then we would have detected an equality during
4155 * simplification. If c1 + c2 were negative, then we would have detected
4156 * a contradiction.
4157 */
4158 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_check_div(
4159 __isl_take isl_map *map)
4160 {
4161 int d, dim;
4162 int i, j, n;
4163 int offset, total;
4164 isl_int sum;
4165 isl_basic_map *hull;
4166
4167 hull = isl_map_unshifted_simple_hull(isl_map_copy(map));
4168 if (!hull)
4169 goto error;
4170
4171 isl_int_init(sum);
4172 dim = isl_map_dim(map, isl_dim_out);
4173 offset = isl_basic_map_offset(hull, isl_dim_out);
4174 total = 1 + isl_basic_map_total_dim(hull);
4175 n = hull->n_ineq;
4176 for (d = 0; d < dim; ++d) {
4177 for (i = 0; i < n; ++i) {
4178 if (!is_potential_div_constraint(hull->ineq[i],
4179 offset, d, total))
4180 continue;
4181 for (j = i + 1; j < n; ++j) {
4182 if (!isl_seq_is_neg(hull->ineq[i] + 1,
4183 hull->ineq[j] + 1, total - 1))
4184 continue;
4185 isl_int_add(sum, hull->ineq[i][0],
4186 hull->ineq[j][0]);
4187 if (isl_int_abs_lt(sum,
4188 hull->ineq[i][offset + d]))
4189 break;
4190
4191 }
4192 if (j >= n)
4193 continue;
4194 isl_int_clear(sum);
4195 if (isl_int_is_pos(hull->ineq[j][offset + d]))
4196 j = i;
4197 return pw_multi_aff_from_map_div(map, hull, d, j);
4198 }
4199 }
4200 isl_int_clear(sum);
4201 isl_basic_map_free(hull);
4202 return pw_multi_aff_from_map_base(map);
4203 error:
4204 isl_map_free(map);
4205 isl_basic_map_free(hull);
4206 return NULL;
4207 }
4208
4209 /* Given an affine expression
4210 *
4211 * [A -> B] -> f(A,B)
4212 *
4213 * construct an isl_multi_aff
4214 *
4215 * [A -> B] -> B'
4216 *
4217 * such that dimension "d" in B' is set to "aff" and the remaining
4218 * dimensions are set equal to the corresponding dimensions in B.
4219 * "n_in" is the dimension of the space A.
4220 * "n_out" is the dimension of the space B.
4221 *
4222 * If "is_set" is set, then the affine expression is of the form
4223 *
4224 * [B] -> f(B)
4225 *
4226 * and we construct an isl_multi_aff
4227 *
4228 * B -> B'
4229 */
4230 static __isl_give isl_multi_aff *range_map(__isl_take isl_aff *aff, int d,
4231 unsigned n_in, unsigned n_out, int is_set)
4232 {
4233 int i;
4234 isl_multi_aff *ma;
4235 isl_space *space, *space2;
4236 isl_local_space *ls;
4237
4238 space = isl_aff_get_domain_space(aff);
4239 ls = isl_local_space_from_space(isl_space_copy(space));
4240 space2 = isl_space_copy(space);
4241 if (!is_set)
4242 space2 = isl_space_range(isl_space_unwrap(space2));
4243 space = isl_space_map_from_domain_and_range(space, space2);
4244 ma = isl_multi_aff_alloc(space);
4245 ma = isl_multi_aff_set_aff(ma, d, aff);
4246
4247 for (i = 0; i < n_out; ++i) {
4248 if (i == d)
4249 continue;
4250 aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
4251 isl_dim_set, n_in + i);
4252 ma = isl_multi_aff_set_aff(ma, i, aff);
4253 }
4254
4255 isl_local_space_free(ls);
4256
4257 return ma;
4258 }
4259
4260 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
4261 * taking into account that the dimension at position "d" can be written as
4262 *
4263 * x = m a + f(..) (1)
4264 *
4265 * where m is equal to "gcd".
4266 * "i" is the index of the equality in "hull" that defines f(..).
4267 * In particular, the equality is of the form
4268 *
4269 * f(..) - x + m g(existentials) = 0
4270 *
4271 * or
4272 *
4273 * -f(..) + x + m g(existentials) = 0
4274 *
4275 * We basically plug (1) into "map", resulting in a map with "a"
4276 * in the range instead of "x". The corresponding isl_pw_multi_aff
4277 * defining "a" is then plugged back into (1) to obtain a definition fro "x".
4278 *
4279 * Specifically, given the input map
4280 *
4281 * A -> B
4282 *
4283 * We first wrap it into a set
4284 *
4285 * [A -> B]
4286 *
4287 * and define (1) on top of the corresponding space, resulting in "aff".
4288 * We use this to create an isl_multi_aff that maps the output position "d"
4289 * from "a" to "x", leaving all other (intput and output) dimensions unchanged.
4290 * We plug this into the wrapped map, unwrap the result and compute the
4291 * corresponding isl_pw_multi_aff.
4292 * The result is an expression
4293 *
4294 * A -> T(A)
4295 *
4296 * We adjust that to
4297 *
4298 * A -> [A -> T(A)]
4299 *
4300 * so that we can plug that into "aff", after extending the latter to
4301 * a mapping
4302 *
4303 * [A -> B] -> B'
4304 *
4305 *
4306 * If "map" is actually a set, then there is no "A" space, meaning
4307 * that we do not need to perform any wrapping, and that the result
4308 * of the recursive call is of the form
4309 *
4310 * [T]
4311 *
4312 * which is plugged into a mapping of the form
4313 *
4314 * B -> B'
4315 */
4316 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_stride(
4317 __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i,
4318 isl_int gcd)
4319 {
4320 isl_set *set;
4321 isl_space *space;
4322 isl_local_space *ls;
4323 isl_aff *aff;
4324 isl_multi_aff *ma;
4325 isl_pw_multi_aff *pma, *id;
4326 unsigned n_in;
4327 unsigned o_out;
4328 unsigned n_out;
4329 int is_set;
4330
4331 is_set = isl_map_is_set(map);
4332
4333 n_in = isl_basic_map_dim(hull, isl_dim_in);
4334 n_out = isl_basic_map_dim(hull, isl_dim_out);
4335 o_out = isl_basic_map_offset(hull, isl_dim_out);
4336
4337 if (is_set)
4338 set = map;
4339 else
4340 set = isl_map_wrap(map);
4341 space = isl_space_map_from_set(isl_set_get_space(set));
4342 ma = isl_multi_aff_identity(space);
4343 ls = isl_local_space_from_space(isl_set_get_space(set));
4344 aff = isl_aff_alloc(ls);
4345 if (aff) {
4346 isl_int_set_si(aff->v->el[0], 1);
4347 if (isl_int_is_one(hull->eq[i][o_out + d]))
4348 isl_seq_neg(aff->v->el + 1, hull->eq[i],
4349 aff->v->size - 1);
4350 else
4351 isl_seq_cpy(aff->v->el + 1, hull->eq[i],
4352 aff->v->size - 1);
4353 isl_int_set(aff->v->el[1 + o_out + d], gcd);
4354 }
4355 ma = isl_multi_aff_set_aff(ma, n_in + d, isl_aff_copy(aff));
4356 set = isl_set_preimage_multi_aff(set, ma);
4357
4358 ma = range_map(aff, d, n_in, n_out, is_set);
4359
4360 if (is_set)
4361 map = set;
4362 else
4363 map = isl_set_unwrap(set);
4364 pma = isl_pw_multi_aff_from_map(set);
4365
4366 if (!is_set) {
4367 space = isl_pw_multi_aff_get_domain_space(pma);
4368 space = isl_space_map_from_set(space);
4369 id = isl_pw_multi_aff_identity(space);
4370 pma = isl_pw_multi_aff_range_product(id, pma);
4371 }
4372 id = isl_pw_multi_aff_from_multi_aff(ma);
4373 pma = isl_pw_multi_aff_pullback_pw_multi_aff(id, pma);
4374
4375 isl_basic_map_free(hull);
4376 return pma;
4377 }
4378
4379 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4380 *
4381 * As a special case, we first check if all output dimensions are uniquely
4382 * defined in terms of the parameters and input dimensions over the entire
4383 * domain. If so, we extract the desired isl_pw_multi_aff directly
4384 * from the affine hull of "map" and its domain.
4385 *
4386 * Otherwise, we check if any of the output dimensions is "strided".
4387 * That is, we check if can be written as
4388 *
4389 * x = m a + f(..)
4390 *
4391 * with m greater than 1, a some combination of existentiall quantified
4392 * variables and f and expression in the parameters and input dimensions.
4393 * If so, we remove the stride in pw_multi_aff_from_map_stride.
4394 *
4395 * Otherwise, we continue with pw_multi_aff_from_map_check_div for a further
4396 * special case.
4397 */
4398 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
4399 {
4400 int i, j;
4401 int sv;
4402 isl_basic_map *hull;
4403 unsigned n_out;
4404 unsigned o_out;
4405 unsigned n_div;
4406 unsigned o_div;
4407 isl_int gcd;
4408
4409 if (!map)
4410 return NULL;
4411
4412 hull = isl_map_affine_hull(isl_map_copy(map));
4413 sv = isl_basic_map_plain_is_single_valued(hull);
4414 if (sv >= 0 && sv)
4415 return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
4416 if (sv < 0)
4417 hull = isl_basic_map_free(hull);
4418 if (!hull)
4419 goto error;
4420
4421 n_div = isl_basic_map_dim(hull, isl_dim_div);
4422 o_div = isl_basic_map_offset(hull, isl_dim_div);
4423
4424 if (n_div == 0) {
4425 isl_basic_map_free(hull);
4426 return pw_multi_aff_from_map_check_div(map);
4427 }
4428
4429 isl_int_init(gcd);
4430
4431 n_out = isl_basic_map_dim(hull, isl_dim_out);
4432 o_out = isl_basic_map_offset(hull, isl_dim_out);
4433
4434 for (i = 0; i < n_out; ++i) {
4435 for (j = 0; j < hull->n_eq; ++j) {
4436 isl_int *eq = hull->eq[j];
4437 isl_pw_multi_aff *res;
4438
4439 if (!isl_int_is_one(eq[o_out + i]) &&
4440 !isl_int_is_negone(eq[o_out + i]))
4441 continue;
4442 if (isl_seq_first_non_zero(eq + o_out, i) != -1)
4443 continue;
4444 if (isl_seq_first_non_zero(eq + o_out + i + 1,
4445 n_out - (i + 1)) != -1)
4446 continue;
4447 isl_seq_gcd(eq + o_div, n_div, &gcd);
4448 if (isl_int_is_zero(gcd))
4449 continue;
4450 if (isl_int_is_one(gcd))
4451 continue;
4452
4453 res = pw_multi_aff_from_map_stride(map, hull,
4454 i, j, gcd);
4455 isl_int_clear(gcd);
4456 return res;
4457 }
4458 }
4459
4460 isl_int_clear(gcd);
4461 isl_basic_map_free(hull);
4462 return pw_multi_aff_from_map_check_div(map);
4463 error:
4464 isl_map_free(map);
4465 return NULL;
4466 }
4467
4468 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
4469 {
4470 return isl_pw_multi_aff_from_map(set);
4471 }
4472
4473 /* Convert "map" into an isl_pw_multi_aff (if possible) and
4474 * add it to *user.
4475 */
4476 static int pw_multi_aff_from_map(__isl_take isl_map *map, void *user)
4477 {
4478 isl_union_pw_multi_aff **upma = user;
4479 isl_pw_multi_aff *pma;
4480
4481 pma = isl_pw_multi_aff_from_map(map);
4482 *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
4483
4484 return *upma ? 0 : -1;
4485 }
4486
4487 /* Try and create an isl_union_pw_multi_aff that is equivalent
4488 * to the given isl_union_map.
4489 * The isl_union_map is required to be single-valued in each space.
4490 * Otherwise, an error is produced.
4491 */
4492 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_map(
4493 __isl_take isl_union_map *umap)
4494 {
4495 isl_space *space;
4496 isl_union_pw_multi_aff *upma;
4497
4498 space = isl_union_map_get_space(umap);
4499 upma = isl_union_pw_multi_aff_empty(space);
4500 if (isl_union_map_foreach_map(umap, &pw_multi_aff_from_map, &upma) < 0)
4501 upma = isl_union_pw_multi_aff_free(upma);
4502 isl_union_map_free(umap);
4503
4504 return upma;
4505 }
4506
4507 /* Try and create an isl_union_pw_multi_aff that is equivalent
4508 * to the given isl_union_set.
4509 * The isl_union_set is required to be a singleton in each space.
4510 * Otherwise, an error is produced.
4511 */
4512 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_set(
4513 __isl_take isl_union_set *uset)
4514 {
4515 return isl_union_pw_multi_aff_from_union_map(uset);
4516 }
4517
4518 /* Return the piecewise affine expression "set ? 1 : 0".
4519 */
4520 __isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
4521 {
4522 isl_pw_aff *pa;
4523 isl_space *space = isl_set_get_space(set);
4524 isl_local_space *ls = isl_local_space_from_space(space);
4525 isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
4526 isl_aff *one = isl_aff_zero_on_domain(ls);
4527
4528 one = isl_aff_add_constant_si(one, 1);
4529 pa = isl_pw_aff_alloc(isl_set_copy(set), one);
4530 set = isl_set_complement(set);
4531 pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
4532
4533 return pa;
4534 }
4535
4536 /* Plug in "subs" for dimension "type", "pos" of "aff".
4537 *
4538 * Let i be the dimension to replace and let "subs" be of the form
4539 *
4540 * f/d
4541 *
4542 * and "aff" of the form
4543 *
4544 * (a i + g)/m
4545 *
4546 * The result is
4547 *
4548 * (a f + d g')/(m d)
4549 *
4550 * where g' is the result of plugging in "subs" in each of the integer
4551 * divisions in g.
4552 */
4553 __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
4554 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
4555 {
4556 isl_ctx *ctx;
4557 isl_int v;
4558
4559 aff = isl_aff_cow(aff);
4560 if (!aff || !subs)
4561 return isl_aff_free(aff);
4562
4563 ctx = isl_aff_get_ctx(aff);
4564 if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
4565 isl_die(ctx, isl_error_invalid,
4566 "spaces don't match", return isl_aff_free(aff));
4567 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
4568 isl_die(ctx, isl_error_unsupported,
4569 "cannot handle divs yet", return isl_aff_free(aff));
4570
4571 aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
4572 if (!aff->ls)
4573 return isl_aff_free(aff);
4574
4575 aff->v = isl_vec_cow(aff->v);
4576 if (!aff->v)
4577 return isl_aff_free(aff);
4578
4579 pos += isl_local_space_offset(aff->ls, type);
4580
4581 isl_int_init(v);
4582 isl_seq_substitute(aff->v->el, pos, subs->v->el,
4583 aff->v->size, subs->v->size, v);
4584 isl_int_clear(v);
4585
4586 return aff;
4587 }
4588
4589 /* Plug in "subs" for dimension "type", "pos" in each of the affine
4590 * expressions in "maff".
4591 */
4592 __isl_give isl_multi_aff *isl_multi_aff_substitute(
4593 __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
4594 __isl_keep isl_aff *subs)
4595 {
4596 int i;
4597
4598 maff = isl_multi_aff_cow(maff);
4599 if (!maff || !subs)
4600 return isl_multi_aff_free(maff);
4601
4602 if (type == isl_dim_in)
4603 type = isl_dim_set;
4604
4605 for (i = 0; i < maff->n; ++i) {
4606 maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
4607 if (!maff->p[i])
4608 return isl_multi_aff_free(maff);
4609 }
4610
4611 return maff;
4612 }
4613
4614 /* Plug in "subs" for dimension "type", "pos" of "pma".
4615 *
4616 * pma is of the form
4617 *
4618 * A_i(v) -> M_i(v)
4619 *
4620 * while subs is of the form
4621 *
4622 * v' = B_j(v) -> S_j
4623 *
4624 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
4625 * has a contribution in the result, in particular
4626 *
4627 * C_ij(S_j) -> M_i(S_j)
4628 *
4629 * Note that plugging in S_j in C_ij may also result in an empty set
4630 * and this contribution should simply be discarded.
4631 */
4632 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
4633 __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
4634 __isl_keep isl_pw_aff *subs)
4635 {
4636 int i, j, n;
4637 isl_pw_multi_aff *res;
4638
4639 if (!pma || !subs)
4640 return isl_pw_multi_aff_free(pma);
4641
4642 n = pma->n * subs->n;
4643 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
4644
4645 for (i = 0; i < pma->n; ++i) {
4646 for (j = 0; j < subs->n; ++j) {
4647 isl_set *common;
4648 isl_multi_aff *res_ij;
4649 int empty;
4650
4651 common = isl_set_intersect(
4652 isl_set_copy(pma->p[i].set),
4653 isl_set_copy(subs->p[j].set));
4654 common = isl_set_substitute(common,
4655 type, pos, subs->p[j].aff);
4656 empty = isl_set_plain_is_empty(common);
4657 if (empty < 0 || empty) {
4658 isl_set_free(common);
4659 if (empty < 0)
4660 goto error;
4661 continue;
4662 }
4663
4664 res_ij = isl_multi_aff_substitute(
4665 isl_multi_aff_copy(pma->p[i].maff),
4666 type, pos, subs->p[j].aff);
4667
4668 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
4669 }
4670 }
4671
4672 isl_pw_multi_aff_free(pma);
4673 return res;
4674 error:
4675 isl_pw_multi_aff_free(pma);
4676 isl_pw_multi_aff_free(res);
4677 return NULL;
4678 }
4679
4680 /* Compute the preimage of a range of dimensions in the affine expression "src"
4681 * under "ma" and put the result in "dst". The number of dimensions in "src"
4682 * that precede the range is given by "n_before". The number of dimensions
4683 * in the range is given by the number of output dimensions of "ma".
4684 * The number of dimensions that follow the range is given by "n_after".
4685 * If "has_denom" is set (to one),
4686 * then "src" and "dst" have an extra initial denominator.
4687 * "n_div_ma" is the number of existentials in "ma"
4688 * "n_div_bset" is the number of existentials in "src"
4689 * The resulting "dst" (which is assumed to have been allocated by
4690 * the caller) contains coefficients for both sets of existentials,
4691 * first those in "ma" and then those in "src".
4692 * f, c1, c2 and g are temporary objects that have been initialized
4693 * by the caller.
4694 *
4695 * Let src represent the expression
4696 *
4697 * (a(p) + f_u u + b v + f_w w + c(divs))/d
4698 *
4699 * and let ma represent the expressions
4700 *
4701 * v_i = (r_i(p) + s_i(y) + t_i(divs'))/m_i
4702 *
4703 * We start out with the following expression for dst:
4704 *
4705 * (a(p) + f_u u + 0 y + f_w w + 0 divs' + c(divs) + f \sum_i b_i v_i)/d
4706 *
4707 * with the multiplication factor f initially equal to 1
4708 * and f \sum_i b_i v_i kept separately.
4709 * For each x_i that we substitute, we multiply the numerator
4710 * (and denominator) of dst by c_1 = m_i and add the numerator
4711 * of the x_i expression multiplied by c_2 = f b_i,
4712 * after removing the common factors of c_1 and c_2.
4713 * The multiplication factor f also needs to be multiplied by c_1
4714 * for the next x_j, j > i.
4715 */
4716 void isl_seq_preimage(isl_int *dst, isl_int *src,
4717 __isl_keep isl_multi_aff *ma, int n_before, int n_after,
4718 int n_div_ma, int n_div_bmap,
4719 isl_int f, isl_int c1, isl_int c2, isl_int g, int has_denom)
4720 {
4721 int i;
4722 int n_param, n_in, n_out;
4723 int o_dst, o_src;
4724
4725 n_param = isl_multi_aff_dim(ma, isl_dim_param);
4726 n_in = isl_multi_aff_dim(ma, isl_dim_in);
4727 n_out = isl_multi_aff_dim(ma, isl_dim_out);
4728
4729 isl_seq_cpy(dst, src, has_denom + 1 + n_param + n_before);
4730 o_dst = o_src = has_denom + 1 + n_param + n_before;
4731 isl_seq_clr(dst + o_dst, n_in);
4732 o_dst += n_in;
4733 o_src += n_out;
4734 isl_seq_cpy(dst + o_dst, src + o_src, n_after);
4735 o_dst += n_after;
4736 o_src += n_after;
4737 isl_seq_clr(dst + o_dst, n_div_ma);
4738 o_dst += n_div_ma;
4739 isl_seq_cpy(dst + o_dst, src + o_src, n_div_bmap);
4740
4741 isl_int_set_si(f, 1);
4742
4743 for (i = 0; i < n_out; ++i) {
4744 int offset = has_denom + 1 + n_param + n_before + i;
4745
4746 if (isl_int_is_zero(src[offset]))
4747 continue;
4748 isl_int_set(c1, ma->p[i]->v->el[0]);
4749 isl_int_mul(c2, f, src[offset]);
4750 isl_int_gcd(g, c1, c2);
4751 isl_int_divexact(c1, c1, g);
4752 isl_int_divexact(c2, c2, g);
4753
4754 isl_int_mul(f, f, c1);
4755 o_dst = has_denom;
4756 o_src = 1;
4757 isl_seq_combine(dst + o_dst, c1, dst + o_dst,
4758 c2, ma->p[i]->v->el + o_src, 1 + n_param);
4759 o_dst += 1 + n_param;
4760 o_src += 1 + n_param;
4761 isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_before);
4762 o_dst += n_before;
4763 isl_seq_combine(dst + o_dst, c1, dst + o_dst,
4764 c2, ma->p[i]->v->el + o_src, n_in);
4765 o_dst += n_in;
4766 o_src += n_in;
4767 isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_after);
4768 o_dst += n_after;
4769 isl_seq_combine(dst + o_dst, c1, dst + o_dst,
4770 c2, ma->p[i]->v->el + o_src, n_div_ma);
4771 o_dst += n_div_ma;
4772 o_src += n_div_ma;
4773 isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_div_bmap);
4774 if (has_denom)
4775 isl_int_mul(dst[0], dst[0], c1);
4776 }
4777 }
4778
4779 /* Compute the pullback of "aff" by the function represented by "ma".
4780 * In other words, plug in "ma" in "aff". The result is an affine expression
4781 * defined over the domain space of "ma".
4782 *
4783 * If "aff" is represented by
4784 *
4785 * (a(p) + b x + c(divs))/d
4786 *
4787 * and ma is represented by
4788 *
4789 * x = D(p) + F(y) + G(divs')
4790 *
4791 * then the result is
4792 *
4793 * (a(p) + b D(p) + b F(y) + b G(divs') + c(divs))/d
4794 *
4795 * The divs in the local space of the input are similarly adjusted
4796 * through a call to isl_local_space_preimage_multi_aff.
4797 */
4798 __isl_give isl_aff *isl_aff_pullback_multi_aff(__isl_take isl_aff *aff,
4799 __isl_take isl_multi_aff *ma)
4800 {
4801 isl_aff *res = NULL;
4802 isl_local_space *ls;
4803 int n_div_aff, n_div_ma;
4804 isl_int f, c1, c2, g;
4805
4806 ma = isl_multi_aff_align_divs(ma);
4807 if (!aff || !ma)
4808 goto error;
4809
4810 n_div_aff = isl_aff_dim(aff, isl_dim_div);
4811 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
4812
4813 ls = isl_aff_get_domain_local_space(aff);
4814 ls = isl_local_space_preimage_multi_aff(ls, isl_multi_aff_copy(ma));
4815 res = isl_aff_alloc(ls);
4816 if (!res)
4817 goto error;
4818
4819 isl_int_init(f);
4820 isl_int_init(c1);
4821 isl_int_init(c2);
4822 isl_int_init(g);
4823
4824 isl_seq_preimage(res->v->el, aff->v->el, ma, 0, 0, n_div_ma, n_div_aff,
4825 f, c1, c2, g, 1);
4826
4827 isl_int_clear(f);
4828 isl_int_clear(c1);
4829 isl_int_clear(c2);
4830 isl_int_clear(g);
4831
4832 isl_aff_free(aff);
4833 isl_multi_aff_free(ma);
4834 res = isl_aff_normalize(res);
4835 return res;
4836 error:
4837 isl_aff_free(aff);
4838 isl_multi_aff_free(ma);
4839 isl_aff_free(res);
4840 return NULL;
4841 }
4842
4843 /* Compute the pullback of "ma1" by the function represented by "ma2".
4844 * In other words, plug in "ma2" in "ma1".
4845 *
4846 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
4847 */
4848 static __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff_aligned(
4849 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
4850 {
4851 int i;
4852 isl_space *space = NULL;
4853
4854 ma2 = isl_multi_aff_align_divs(ma2);
4855 ma1 = isl_multi_aff_cow(ma1);
4856 if (!ma1 || !ma2)
4857 goto error;
4858
4859 space = isl_space_join(isl_multi_aff_get_space(ma2),
4860 isl_multi_aff_get_space(ma1));
4861
4862 for (i = 0; i < ma1->n; ++i) {
4863 ma1->p[i] = isl_aff_pullback_multi_aff(ma1->p[i],
4864 isl_multi_aff_copy(ma2));
4865 if (!ma1->p[i])
4866 goto error;
4867 }
4868
4869 ma1 = isl_multi_aff_reset_space(ma1, space);
4870 isl_multi_aff_free(ma2);
4871 return ma1;
4872 error:
4873 isl_space_free(space);
4874 isl_multi_aff_free(ma2);
4875 isl_multi_aff_free(ma1);
4876 return NULL;
4877 }
4878
4879 /* Compute the pullback of "ma1" by the function represented by "ma2".
4880 * In other words, plug in "ma2" in "ma1".
4881 */
4882 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4883 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
4884 {
4885 return isl_multi_aff_align_params_multi_multi_and(ma1, ma2,
4886 &isl_multi_aff_pullback_multi_aff_aligned);
4887 }
4888
4889 /* Extend the local space of "dst" to include the divs
4890 * in the local space of "src".
4891 */
4892 __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
4893 __isl_keep isl_aff *src)
4894 {
4895 isl_ctx *ctx;
4896 int *exp1 = NULL;
4897 int *exp2 = NULL;
4898 isl_mat *div;
4899
4900 if (!src || !dst)
4901 return isl_aff_free(dst);
4902
4903 ctx = isl_aff_get_ctx(src);
4904 if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
4905 isl_die(ctx, isl_error_invalid,
4906 "spaces don't match", goto error);
4907
4908 if (src->ls->div->n_row == 0)
4909 return dst;
4910
4911 exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
4912 exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
4913 if (!exp1 || (dst->ls->div->n_row && !exp2))
4914 goto error;
4915
4916 div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
4917 dst = isl_aff_expand_divs(dst, div, exp2);
4918 free(exp1);
4919 free(exp2);
4920
4921 return dst;
4922 error:
4923 free(exp1);
4924 free(exp2);
4925 return isl_aff_free(dst);
4926 }
4927
4928 /* Adjust the local spaces of the affine expressions in "maff"
4929 * such that they all have the save divs.
4930 */
4931 __isl_give isl_multi_aff *isl_multi_aff_align_divs(
4932 __isl_take isl_multi_aff *maff)
4933 {
4934 int i;
4935
4936 if (!maff)
4937 return NULL;
4938 if (maff->n == 0)
4939 return maff;
4940 maff = isl_multi_aff_cow(maff);
4941 if (!maff)
4942 return NULL;
4943
4944 for (i = 1; i < maff->n; ++i)
4945 maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
4946 for (i = 1; i < maff->n; ++i) {
4947 maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
4948 if (!maff->p[i])
4949 return isl_multi_aff_free(maff);
4950 }
4951
4952 return maff;
4953 }
4954
4955 __isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
4956 {
4957 aff = isl_aff_cow(aff);
4958 if (!aff)
4959 return NULL;
4960
4961 aff->ls = isl_local_space_lift(aff->ls);
4962 if (!aff->ls)
4963 return isl_aff_free(aff);
4964
4965 return aff;
4966 }
4967
4968 /* Lift "maff" to a space with extra dimensions such that the result
4969 * has no more existentially quantified variables.
4970 * If "ls" is not NULL, then *ls is assigned the local space that lies
4971 * at the basis of the lifting applied to "maff".
4972 */
4973 __isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
4974 __isl_give isl_local_space **ls)
4975 {
4976 int i;
4977 isl_space *space;
4978 unsigned n_div;
4979
4980 if (ls)
4981 *ls = NULL;
4982
4983 if (!maff)
4984 return NULL;
4985
4986 if (maff->n == 0) {
4987 if (ls) {
4988 isl_space *space = isl_multi_aff_get_domain_space(maff);
4989 *ls = isl_local_space_from_space(space);
4990 if (!*ls)
4991 return isl_multi_aff_free(maff);
4992 }
4993 return maff;
4994 }
4995
4996 maff = isl_multi_aff_cow(maff);
4997 maff = isl_multi_aff_align_divs(maff);
4998 if (!maff)
4999 return NULL;
5000
5001 n_div = isl_aff_dim(maff->p[0], isl_dim_div);
5002 space = isl_multi_aff_get_space(maff);
5003 space = isl_space_lift(isl_space_domain(space), n_div);
5004 space = isl_space_extend_domain_with_range(space,
5005 isl_multi_aff_get_space(maff));
5006 if (!space)
5007 return isl_multi_aff_free(maff);
5008 isl_space_free(maff->space);
5009 maff->space = space;
5010
5011 if (ls) {
5012 *ls = isl_aff_get_domain_local_space(maff->p[0]);
5013 if (!*ls)
5014 return isl_multi_aff_free(maff);
5015 }
5016
5017 for (i = 0; i < maff->n; ++i) {
5018 maff->p[i] = isl_aff_lift(maff->p[i]);
5019 if (!maff->p[i])
5020 goto error;
5021 }
5022
5023 return maff;
5024 error:
5025 if (ls)
5026 isl_local_space_free(*ls);
5027 return isl_multi_aff_free(maff);
5028 }
5029
5030
5031 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
5032 */
5033 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
5034 __isl_keep isl_pw_multi_aff *pma, int pos)
5035 {
5036 int i;
5037 int n_out;
5038 isl_space *space;
5039 isl_pw_aff *pa;
5040
5041 if (!pma)
5042 return NULL;
5043
5044 n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
5045 if (pos < 0 || pos >= n_out)
5046 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
5047 "index out of bounds", return NULL);
5048
5049 space = isl_pw_multi_aff_get_space(pma);
5050 space = isl_space_drop_dims(space, isl_dim_out,
5051 pos + 1, n_out - pos - 1);
5052 space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
5053
5054 pa = isl_pw_aff_alloc_size(space, pma->n);
5055 for (i = 0; i < pma->n; ++i) {
5056 isl_aff *aff;
5057 aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
5058 pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
5059 }
5060
5061 return pa;
5062 }
5063
5064 /* Return an isl_pw_multi_aff with the given "set" as domain and
5065 * an unnamed zero-dimensional range.
5066 */
5067 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5068 __isl_take isl_set *set)
5069 {
5070 isl_multi_aff *ma;
5071 isl_space *space;
5072
5073 space = isl_set_get_space(set);
5074 space = isl_space_from_domain(space);
5075 ma = isl_multi_aff_zero(space);
5076 return isl_pw_multi_aff_alloc(set, ma);
5077 }
5078
5079 /* Add an isl_pw_multi_aff with the given "set" as domain and
5080 * an unnamed zero-dimensional range to *user.
5081 */
5082 static int add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user)
5083 {
5084 isl_union_pw_multi_aff **upma = user;
5085 isl_pw_multi_aff *pma;
5086
5087 pma = isl_pw_multi_aff_from_domain(set);
5088 *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
5089
5090 return 0;
5091 }
5092
5093 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
5094 * an unnamed zero-dimensional range.
5095 */
5096 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain(
5097 __isl_take isl_union_set *uset)
5098 {
5099 isl_space *space;
5100 isl_union_pw_multi_aff *upma;
5101
5102 if (!uset)
5103 return NULL;
5104
5105 space = isl_union_set_get_space(uset);
5106 upma = isl_union_pw_multi_aff_empty(space);
5107
5108 if (isl_union_set_foreach_set(uset,
5109 &add_pw_multi_aff_from_domain, &upma) < 0)
5110 goto error;
5111
5112 isl_union_set_free(uset);
5113 return upma;
5114 error:
5115 isl_union_set_free(uset);
5116 isl_union_pw_multi_aff_free(upma);
5117 return NULL;
5118 }
5119
5120 /* Convert "pma" to an isl_map and add it to *umap.
5121 */
5122 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
5123 {
5124 isl_union_map **umap = user;
5125 isl_map *map;
5126
5127 map = isl_map_from_pw_multi_aff(pma);
5128 *umap = isl_union_map_add_map(*umap, map);
5129
5130 return 0;
5131 }
5132
5133 /* Construct a union map mapping the domain of the union
5134 * piecewise multi-affine expression to its range, with each dimension
5135 * in the range equated to the corresponding affine expression on its cell.
5136 */
5137 __isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff(
5138 __isl_take isl_union_pw_multi_aff *upma)
5139 {
5140 isl_space *space;
5141 isl_union_map *umap;
5142
5143 if (!upma)
5144 return NULL;
5145
5146 space = isl_union_pw_multi_aff_get_space(upma);
5147 umap = isl_union_map_empty(space);
5148
5149 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
5150 &map_from_pw_multi_aff, &umap) < 0)
5151 goto error;
5152
5153 isl_union_pw_multi_aff_free(upma);
5154 return umap;
5155 error:
5156 isl_union_pw_multi_aff_free(upma);
5157 isl_union_map_free(umap);
5158 return NULL;
5159 }
5160
5161 /* Local data for bin_entry and the callback "fn".
5162 */
5163 struct isl_union_pw_multi_aff_bin_data {
5164 isl_union_pw_multi_aff *upma2;
5165 isl_union_pw_multi_aff *res;
5166 isl_pw_multi_aff *pma;
5167 int (*fn)(void **entry, void *user);
5168 };
5169
5170 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
5171 * and call data->fn for each isl_pw_multi_aff in data->upma2.
5172 */
5173 static int bin_entry(void **entry, void *user)
5174 {
5175 struct isl_union_pw_multi_aff_bin_data *data = user;
5176 isl_pw_multi_aff *pma = *entry;
5177
5178 data->pma = pma;
5179 if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
5180 data->fn, data) < 0)
5181 return -1;
5182
5183 return 0;
5184 }
5185
5186 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
5187 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
5188 * passed as user field) and the isl_pw_multi_aff from upma2 is available
5189 * as *entry. The callback should adjust data->res if desired.
5190 */
5191 static __isl_give isl_union_pw_multi_aff *bin_op(
5192 __isl_take isl_union_pw_multi_aff *upma1,
5193 __isl_take isl_union_pw_multi_aff *upma2,
5194 int (*fn)(void **entry, void *user))
5195 {
5196 isl_space *space;
5197 struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
5198
5199 space = isl_union_pw_multi_aff_get_space(upma2);
5200 upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
5201 space = isl_union_pw_multi_aff_get_space(upma1);
5202 upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
5203
5204 if (!upma1 || !upma2)
5205 goto error;
5206
5207 data.upma2 = upma2;
5208 data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
5209 upma1->table.n);
5210 if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
5211 &bin_entry, &data) < 0)
5212 goto error;
5213
5214 isl_union_pw_multi_aff_free(upma1);
5215 isl_union_pw_multi_aff_free(upma2);
5216 return data.res;
5217 error:
5218 isl_union_pw_multi_aff_free(upma1);
5219 isl_union_pw_multi_aff_free(upma2);
5220 isl_union_pw_multi_aff_free(data.res);
5221 return NULL;
5222 }
5223
5224 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
5225 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
5226 */
5227 static __isl_give isl_pw_multi_aff *pw_multi_aff_range_product(
5228 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
5229 {
5230 isl_space *space;
5231
5232 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
5233 isl_pw_multi_aff_get_space(pma2));
5234 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
5235 &isl_multi_aff_range_product);
5236 }
5237
5238 /* Given two isl_pw_multi_affs A -> B and C -> D,
5239 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
5240 */
5241 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_product(
5242 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
5243 {
5244 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
5245 &pw_multi_aff_range_product);
5246 }
5247
5248 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
5249 * construct an isl_pw_multi_aff (A * C) -> (B, D).
5250 */
5251 static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
5252 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
5253 {
5254 isl_space *space;
5255
5256 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
5257 isl_pw_multi_aff_get_space(pma2));
5258 space = isl_space_flatten_range(space);
5259 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
5260 &isl_multi_aff_flat_range_product);
5261 }
5262
5263 /* Given two isl_pw_multi_affs A -> B and C -> D,
5264 * construct an isl_pw_multi_aff (A * C) -> (B, D).
5265 */
5266 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
5267 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
5268 {
5269 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
5270 &pw_multi_aff_flat_range_product);
5271 }
5272
5273 /* If data->pma and *entry have the same domain space, then compute
5274 * their flat range product and the result to data->res.
5275 */
5276 static int flat_range_product_entry(void **entry, void *user)
5277 {
5278 struct isl_union_pw_multi_aff_bin_data *data = user;
5279 isl_pw_multi_aff *pma2 = *entry;
5280
5281 if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
5282 pma2->dim, isl_dim_in))
5283 return 0;
5284
5285 pma2 = isl_pw_multi_aff_flat_range_product(
5286 isl_pw_multi_aff_copy(data->pma),
5287 isl_pw_multi_aff_copy(pma2));
5288
5289 data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
5290
5291 return 0;
5292 }
5293
5294 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
5295 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
5296 */
5297 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
5298 __isl_take isl_union_pw_multi_aff *upma1,
5299 __isl_take isl_union_pw_multi_aff *upma2)
5300 {
5301 return bin_op(upma1, upma2, &flat_range_product_entry);
5302 }
5303
5304 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5305 * The parameters are assumed to have been aligned.
5306 *
5307 * The implementation essentially performs an isl_pw_*_on_shared_domain,
5308 * except that it works on two different isl_pw_* types.
5309 */
5310 static __isl_give isl_pw_multi_aff *pw_multi_aff_set_pw_aff(
5311 __isl_take isl_pw_multi_aff *pma, unsigned pos,
5312 __isl_take isl_pw_aff *pa)
5313 {
5314 int i, j, n;
5315 isl_pw_multi_aff *res = NULL;
5316
5317 if (!pma || !pa)
5318 goto error;
5319
5320 if (!isl_space_tuple_match(pma->dim, isl_dim_in, pa->dim, isl_dim_in))
5321 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
5322 "domains don't match", goto error);
5323 if (pos >= isl_pw_multi_aff_dim(pma, isl_dim_out))
5324 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
5325 "index out of bounds", goto error);
5326
5327 n = pma->n * pa->n;
5328 res = isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma), n);
5329
5330 for (i = 0; i < pma->n; ++i) {
5331 for (j = 0; j < pa->n; ++j) {
5332 isl_set *common;
5333 isl_multi_aff *res_ij;
5334 int empty;
5335
5336 common = isl_set_intersect(isl_set_copy(pma->p[i].set),
5337 isl_set_copy(pa->p[j].set));
5338 empty = isl_set_plain_is_empty(common);
5339 if (empty < 0 || empty) {
5340 isl_set_free(common);
5341 if (empty < 0)
5342 goto error;
5343 continue;
5344 }
5345
5346 res_ij = isl_multi_aff_set_aff(
5347 isl_multi_aff_copy(pma->p[i].maff), pos,
5348 isl_aff_copy(pa->p[j].aff));
5349 res_ij = isl_multi_aff_gist(res_ij,
5350 isl_set_copy(common));
5351
5352 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
5353 }
5354 }
5355
5356 isl_pw_multi_aff_free(pma);
5357 isl_pw_aff_free(pa);
5358 return res;
5359 error:
5360 isl_pw_multi_aff_free(pma);
5361 isl_pw_aff_free(pa);
5362 return isl_pw_multi_aff_free(res);
5363 }
5364
5365 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5366 */
5367 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
5368 __isl_take isl_pw_multi_aff *pma, unsigned pos,
5369 __isl_take isl_pw_aff *pa)
5370 {
5371 if (!pma || !pa)
5372 goto error;
5373 if (isl_space_match(pma->dim, isl_dim_param, pa->dim, isl_dim_param))
5374 return pw_multi_aff_set_pw_aff(pma, pos, pa);
5375 if (!isl_space_has_named_params(pma->dim) ||
5376 !isl_space_has_named_params(pa->dim))
5377 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
5378 "unaligned unnamed parameters", goto error);
5379 pma = isl_pw_multi_aff_align_params(pma, isl_pw_aff_get_space(pa));
5380 pa = isl_pw_aff_align_params(pa, isl_pw_multi_aff_get_space(pma));
5381 return pw_multi_aff_set_pw_aff(pma, pos, pa);
5382 error:
5383 isl_pw_multi_aff_free(pma);
5384 isl_pw_aff_free(pa);
5385 return NULL;
5386 }
5387
5388 /* Do the parameters of "pa" match those of "space"?
5389 */
5390 int isl_pw_aff_matching_params(__isl_keep isl_pw_aff *pa,
5391 __isl_keep isl_space *space)
5392 {
5393 isl_space *pa_space;
5394 int match;
5395
5396 if (!pa || !space)
5397 return -1;
5398
5399 pa_space = isl_pw_aff_get_space(pa);
5400
5401 match = isl_space_match(space, isl_dim_param, pa_space, isl_dim_param);
5402
5403 isl_space_free(pa_space);
5404 return match;
5405 }
5406
5407 /* Check that the domain space of "pa" matches "space".
5408 *
5409 * Return 0 on success and -1 on error.
5410 */
5411 int isl_pw_aff_check_match_domain_space(__isl_keep isl_pw_aff *pa,
5412 __isl_keep isl_space *space)
5413 {
5414 isl_space *pa_space;
5415 int match;
5416
5417 if (!pa || !space)
5418 return -1;
5419
5420 pa_space = isl_pw_aff_get_space(pa);
5421
5422 match = isl_space_match(space, isl_dim_param, pa_space, isl_dim_param);
5423 if (match < 0)
5424 goto error;
5425 if (!match)
5426 isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
5427 "parameters don't match", goto error);
5428 match = isl_space_tuple_match(space, isl_dim_in, pa_space, isl_dim_in);
5429 if (match < 0)
5430 goto error;
5431 if (!match)
5432 isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
5433 "domains don't match", goto error);
5434 isl_space_free(pa_space);
5435 return 0;
5436 error:
5437 isl_space_free(pa_space);
5438 return -1;
5439 }
5440
5441 #undef BASE
5442 #define BASE pw_aff
5443
5444 #include <isl_multi_templ.c>
5445
5446 /* Scale the elements of "pma" by the corresponding elements of "mv".
5447 */
5448 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_multi_val(
5449 __isl_take isl_pw_multi_aff *pma, __isl_take isl_multi_val *mv)
5450 {
5451 int i;
5452
5453 pma = isl_pw_multi_aff_cow(pma);
5454 if (!pma || !mv)
5455 goto error;
5456 if (!isl_space_tuple_match(pma->dim, isl_dim_out,
5457 mv->space, isl_dim_set))
5458 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
5459 "spaces don't match", goto error);
5460 if (!isl_space_match(pma->dim, isl_dim_param,
5461 mv->space, isl_dim_param)) {
5462 pma = isl_pw_multi_aff_align_params(pma,
5463 isl_multi_val_get_space(mv));
5464 mv = isl_multi_val_align_params(mv,
5465 isl_pw_multi_aff_get_space(pma));
5466 if (!pma || !mv)
5467 goto error;
5468 }
5469
5470 for (i = 0; i < pma->n; ++i) {
5471 pma->p[i].maff = isl_multi_aff_scale_multi_val(pma->p[i].maff,
5472 isl_multi_val_copy(mv));
5473 if (!pma->p[i].maff)
5474 goto error;
5475 }
5476
5477 isl_multi_val_free(mv);
5478 return pma;
5479 error:
5480 isl_multi_val_free(mv);
5481 isl_pw_multi_aff_free(pma);
5482 return NULL;
5483 }
5484
5485 /* Internal data structure for isl_union_pw_multi_aff_scale_multi_val.
5486 * mv contains the mv argument.
5487 * res collects the results.
5488 */
5489 struct isl_union_pw_multi_aff_scale_multi_val_data {
5490 isl_multi_val *mv;
5491 isl_union_pw_multi_aff *res;
5492 };
5493
5494 /* This function is called for each entry of an isl_union_pw_multi_aff.
5495 * If the space of the entry matches that of data->mv,
5496 * then apply isl_pw_multi_aff_scale_multi_val and add the result
5497 * to data->res.
5498 */
5499 static int union_pw_multi_aff_scale_multi_val_entry(void **entry, void *user)
5500 {
5501 struct isl_union_pw_multi_aff_scale_multi_val_data *data = user;
5502 isl_pw_multi_aff *pma = *entry;
5503
5504 if (!pma)
5505 return -1;
5506 if (!isl_space_tuple_match(pma->dim, isl_dim_out,
5507 data->mv->space, isl_dim_set))
5508 return 0;
5509
5510 pma = isl_pw_multi_aff_copy(pma);
5511 pma = isl_pw_multi_aff_scale_multi_val(pma,
5512 isl_multi_val_copy(data->mv));
5513 data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma);
5514 if (!data->res)
5515 return -1;
5516
5517 return 0;
5518 }
5519
5520 /* Scale the elements of "upma" by the corresponding elements of "mv",
5521 * for those entries that match the space of "mv".
5522 */
5523 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_multi_val(
5524 __isl_take isl_union_pw_multi_aff *upma, __isl_take isl_multi_val *mv)
5525 {
5526 struct isl_union_pw_multi_aff_scale_multi_val_data data;
5527
5528 upma = isl_union_pw_multi_aff_align_params(upma,
5529 isl_multi_val_get_space(mv));
5530 mv = isl_multi_val_align_params(mv,
5531 isl_union_pw_multi_aff_get_space(upma));
5532 if (!upma || !mv)
5533 goto error;
5534
5535 data.mv = mv;
5536 data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma->dim),
5537 upma->table.n);
5538 if (isl_hash_table_foreach(upma->dim->ctx, &upma->table,
5539 &union_pw_multi_aff_scale_multi_val_entry, &data) < 0)
5540 goto error;
5541
5542 isl_multi_val_free(mv);
5543 isl_union_pw_multi_aff_free(upma);
5544 return data.res;
5545 error:
5546 isl_multi_val_free(mv);
5547 isl_union_pw_multi_aff_free(upma);
5548 return NULL;
5549 }
5550
5551 /* Construct and return a piecewise multi affine expression
5552 * in the given space with value zero in each of the output dimensions and
5553 * a universe domain.
5554 */
5555 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(__isl_take isl_space *space)
5556 {
5557 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_zero(space));
5558 }
5559
5560 /* Construct and return a piecewise multi affine expression
5561 * that is equal to the given piecewise affine expression.
5562 */
5563 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
5564 __isl_take isl_pw_aff *pa)
5565 {
5566 int i;
5567 isl_space *space;
5568 isl_pw_multi_aff *pma;
5569
5570 if (!pa)
5571 return NULL;
5572
5573 space = isl_pw_aff_get_space(pa);
5574 pma = isl_pw_multi_aff_alloc_size(space, pa->n);
5575
5576 for (i = 0; i < pa->n; ++i) {
5577 isl_set *set;
5578 isl_multi_aff *ma;
5579
5580 set = isl_set_copy(pa->p[i].set);
5581 ma = isl_multi_aff_from_aff(isl_aff_copy(pa->p[i].aff));
5582 pma = isl_pw_multi_aff_add_piece(pma, set, ma);
5583 }
5584
5585 isl_pw_aff_free(pa);
5586 return pma;
5587 }
5588
5589 /* Construct and return a piecewise multi affine expression
5590 * that is equal to the given multi piecewise affine expression
5591 * on the shared domain of the piecewise affine expressions.
5592 */
5593 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_pw_aff(
5594 __isl_take isl_multi_pw_aff *mpa)
5595 {
5596 int i;
5597 isl_space *space;
5598 isl_pw_aff *pa;
5599 isl_pw_multi_aff *pma;
5600
5601 if (!mpa)
5602 return NULL;
5603
5604 space = isl_multi_pw_aff_get_space(mpa);
5605
5606 if (mpa->n == 0) {
5607 isl_multi_pw_aff_free(mpa);
5608 return isl_pw_multi_aff_zero(space);
5609 }
5610
5611 pa = isl_multi_pw_aff_get_pw_aff(mpa, 0);
5612 pma = isl_pw_multi_aff_from_pw_aff(pa);
5613
5614 for (i = 1; i < mpa->n; ++i) {
5615 isl_pw_multi_aff *pma_i;
5616
5617 pa = isl_multi_pw_aff_get_pw_aff(mpa, i);
5618 pma_i = isl_pw_multi_aff_from_pw_aff(pa);
5619 pma = isl_pw_multi_aff_range_product(pma, pma_i);
5620 }
5621
5622 pma = isl_pw_multi_aff_reset_space(pma, space);
5623
5624 isl_multi_pw_aff_free(mpa);
5625 return pma;
5626 }
5627
5628 /* Do "pa1" and "pa2" represent the same function?
5629 *
5630 * We first check if they are obviously equal.
5631 * If not, we convert them to maps and check if those are equal.
5632 */
5633 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1, __isl_keep isl_pw_aff *pa2)
5634 {
5635 int equal;
5636 isl_map *map1, *map2;
5637
5638 if (!pa1 || !pa2)
5639 return -1;
5640
5641 equal = isl_pw_aff_plain_is_equal(pa1, pa2);
5642 if (equal < 0 || equal)
5643 return equal;
5644
5645 map1 = map_from_pw_aff(isl_pw_aff_copy(pa1));
5646 map2 = map_from_pw_aff(isl_pw_aff_copy(pa2));
5647 equal = isl_map_is_equal(map1, map2);
5648 isl_map_free(map1);
5649 isl_map_free(map2);
5650
5651 return equal;
5652 }
5653
5654 /* Do "mpa1" and "mpa2" represent the same function?
5655 *
5656 * Note that we cannot convert the entire isl_multi_pw_aff
5657 * to a map because the domains of the piecewise affine expressions
5658 * may not be the same.
5659 */
5660 int isl_multi_pw_aff_is_equal(__isl_keep isl_multi_pw_aff *mpa1,
5661 __isl_keep isl_multi_pw_aff *mpa2)
5662 {
5663 int i;
5664 int equal;
5665
5666 if (!mpa1 || !mpa2)
5667 return -1;
5668
5669 if (!isl_space_match(mpa1->space, isl_dim_param,
5670 mpa2->space, isl_dim_param)) {
5671 if (!isl_space_has_named_params(mpa1->space))
5672 return 0;
5673 if (!isl_space_has_named_params(mpa2->space))
5674 return 0;
5675 mpa1 = isl_multi_pw_aff_copy(mpa1);
5676 mpa2 = isl_multi_pw_aff_copy(mpa2);
5677 mpa1 = isl_multi_pw_aff_align_params(mpa1,
5678 isl_multi_pw_aff_get_space(mpa2));
5679 mpa2 = isl_multi_pw_aff_align_params(mpa2,
5680 isl_multi_pw_aff_get_space(mpa1));
5681 equal = isl_multi_pw_aff_is_equal(mpa1, mpa2);
5682 isl_multi_pw_aff_free(mpa1);
5683 isl_multi_pw_aff_free(mpa2);
5684 return equal;
5685 }
5686
5687 equal = isl_space_is_equal(mpa1->space, mpa2->space);
5688 if (equal < 0 || !equal)
5689 return equal;
5690
5691 for (i = 0; i < mpa1->n; ++i) {
5692 equal = isl_pw_aff_is_equal(mpa1->p[i], mpa2->p[i]);
5693 if (equal < 0 || !equal)
5694 return equal;
5695 }
5696
5697 return 1;
5698 }
5699
5700 /* Coalesce the elements of "mpa".
5701 *
5702 * Note that such coalescing does not change the meaning of "mpa"
5703 * so there is no need to cow. We do need to be careful not to
5704 * destroy any other copies of "mpa" in case of failure.
5705 */
5706 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5707 __isl_take isl_multi_pw_aff *mpa)
5708 {
5709 int i;
5710
5711 if (!mpa)
5712 return NULL;
5713
5714 for (i = 0; i < mpa->n; ++i) {
5715 isl_pw_aff *pa = isl_pw_aff_copy(mpa->p[i]);
5716 pa = isl_pw_aff_coalesce(pa);
5717 if (!pa)
5718 return isl_multi_pw_aff_free(mpa);
5719 isl_pw_aff_free(mpa->p[i]);
5720 mpa->p[i] = pa;
5721 }
5722
5723 return mpa;
5724 }
Integer set library