add isl_multi_aff_pullback_multi_aff
[isl.git] / isl_aff.c
blobcfd08a7a69f7f752c430f6c0b911a39105ff4623
1 /*
2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
4 * Copyright 2012 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
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
14 #include <isl_ctx_private.h>
15 #define ISL_DIM_H
16 #include <isl_map_private.h>
17 #include <isl_union_map_private.h>
18 #include <isl_aff_private.h>
19 #include <isl_space_private.h>
20 #include <isl_local_space_private.h>
21 #include <isl_mat_private.h>
22 #include <isl_list_private.h>
23 #include <isl/constraint.h>
24 #include <isl/seq.h>
25 #include <isl/set.h>
26 #include <isl_config.h>
28 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
29 __isl_take isl_vec *v)
31 isl_aff *aff;
33 if (!ls || !v)
34 goto error;
36 aff = isl_calloc_type(v->ctx, struct isl_aff);
37 if (!aff)
38 goto error;
40 aff->ref = 1;
41 aff->ls = ls;
42 aff->v = v;
44 return aff;
45 error:
46 isl_local_space_free(ls);
47 isl_vec_free(v);
48 return NULL;
51 __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
53 isl_ctx *ctx;
54 isl_vec *v;
55 unsigned total;
57 if (!ls)
58 return NULL;
60 ctx = isl_local_space_get_ctx(ls);
61 if (!isl_local_space_divs_known(ls))
62 isl_die(ctx, isl_error_invalid, "local space has unknown divs",
63 goto error);
64 if (!isl_local_space_is_set(ls))
65 isl_die(ctx, isl_error_invalid,
66 "domain of affine expression should be a set",
67 goto error);
69 total = isl_local_space_dim(ls, isl_dim_all);
70 v = isl_vec_alloc(ctx, 1 + 1 + total);
71 return isl_aff_alloc_vec(ls, v);
72 error:
73 isl_local_space_free(ls);
74 return NULL;
77 __isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
79 isl_aff *aff;
81 aff = isl_aff_alloc(ls);
82 if (!aff)
83 return NULL;
85 isl_int_set_si(aff->v->el[0], 1);
86 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
88 return aff;
91 /* Return a piecewise affine expression defined on the specified domain
92 * that is equal to zero.
94 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(__isl_take isl_local_space *ls)
96 return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls));
99 /* Return an affine expression that is equal to the specified dimension
100 * in "ls".
102 __isl_give isl_aff *isl_aff_var_on_domain(__isl_take isl_local_space *ls,
103 enum isl_dim_type type, unsigned pos)
105 isl_space *space;
106 isl_aff *aff;
108 if (!ls)
109 return NULL;
111 space = isl_local_space_get_space(ls);
112 if (!space)
113 goto error;
114 if (isl_space_is_map(space))
115 isl_die(isl_space_get_ctx(space), isl_error_invalid,
116 "expecting (parameter) set space", goto error);
117 if (pos >= isl_local_space_dim(ls, type))
118 isl_die(isl_space_get_ctx(space), isl_error_invalid,
119 "position out of bounds", goto error);
121 isl_space_free(space);
122 aff = isl_aff_alloc(ls);
123 if (!aff)
124 return NULL;
126 pos += isl_local_space_offset(aff->ls, type);
128 isl_int_set_si(aff->v->el[0], 1);
129 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
130 isl_int_set_si(aff->v->el[1 + pos], 1);
132 return aff;
133 error:
134 isl_local_space_free(ls);
135 isl_space_free(space);
136 return NULL;
139 /* Return a piecewise affine expression that is equal to
140 * the specified dimension in "ls".
142 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(__isl_take isl_local_space *ls,
143 enum isl_dim_type type, unsigned pos)
145 return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls, type, pos));
148 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
150 if (!aff)
151 return NULL;
153 aff->ref++;
154 return aff;
157 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
159 if (!aff)
160 return NULL;
162 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
163 isl_vec_copy(aff->v));
166 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
168 if (!aff)
169 return NULL;
171 if (aff->ref == 1)
172 return aff;
173 aff->ref--;
174 return isl_aff_dup(aff);
177 void *isl_aff_free(__isl_take isl_aff *aff)
179 if (!aff)
180 return NULL;
182 if (--aff->ref > 0)
183 return NULL;
185 isl_local_space_free(aff->ls);
186 isl_vec_free(aff->v);
188 free(aff);
190 return NULL;
193 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
195 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
198 /* Externally, an isl_aff has a map space, but internally, the
199 * ls field corresponds to the domain of that space.
201 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
203 if (!aff)
204 return 0;
205 if (type == isl_dim_out)
206 return 1;
207 if (type == isl_dim_in)
208 type = isl_dim_set;
209 return isl_local_space_dim(aff->ls, type);
212 __isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
214 return aff ? isl_local_space_get_space(aff->ls) : NULL;
217 __isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
219 isl_space *space;
220 if (!aff)
221 return NULL;
222 space = isl_local_space_get_space(aff->ls);
223 space = isl_space_from_domain(space);
224 space = isl_space_add_dims(space, isl_dim_out, 1);
225 return space;
228 __isl_give isl_local_space *isl_aff_get_domain_local_space(
229 __isl_keep isl_aff *aff)
231 return aff ? isl_local_space_copy(aff->ls) : NULL;
234 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
236 isl_local_space *ls;
237 if (!aff)
238 return NULL;
239 ls = isl_local_space_copy(aff->ls);
240 ls = isl_local_space_from_domain(ls);
241 ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
242 return ls;
245 /* Externally, an isl_aff has a map space, but internally, the
246 * ls field corresponds to the domain of that space.
248 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
249 enum isl_dim_type type, unsigned pos)
251 if (!aff)
252 return NULL;
253 if (type == isl_dim_out)
254 return NULL;
255 if (type == isl_dim_in)
256 type = isl_dim_set;
257 return isl_local_space_get_dim_name(aff->ls, type, pos);
260 __isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
261 __isl_take isl_space *dim)
263 aff = isl_aff_cow(aff);
264 if (!aff || !dim)
265 goto error;
267 aff->ls = isl_local_space_reset_space(aff->ls, dim);
268 if (!aff->ls)
269 return isl_aff_free(aff);
271 return aff;
272 error:
273 isl_aff_free(aff);
274 isl_space_free(dim);
275 return NULL;
278 /* Reset the space of "aff". This function is called from isl_pw_templ.c
279 * and doesn't know if the space of an element object is represented
280 * directly or through its domain. It therefore passes along both.
282 __isl_give isl_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
283 __isl_take isl_space *space, __isl_take isl_space *domain)
285 isl_space_free(space);
286 return isl_aff_reset_domain_space(aff, domain);
289 /* Reorder the coefficients of the affine expression based
290 * on the given reodering.
291 * The reordering r is assumed to have been extended with the local
292 * variables.
294 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
295 __isl_take isl_reordering *r, int n_div)
297 isl_vec *res;
298 int i;
300 if (!vec || !r)
301 goto error;
303 res = isl_vec_alloc(vec->ctx,
304 2 + isl_space_dim(r->dim, isl_dim_all) + n_div);
305 isl_seq_cpy(res->el, vec->el, 2);
306 isl_seq_clr(res->el + 2, res->size - 2);
307 for (i = 0; i < r->len; ++i)
308 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
310 isl_reordering_free(r);
311 isl_vec_free(vec);
312 return res;
313 error:
314 isl_vec_free(vec);
315 isl_reordering_free(r);
316 return NULL;
319 /* Reorder the dimensions of the domain of "aff" according
320 * to the given reordering.
322 __isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
323 __isl_take isl_reordering *r)
325 aff = isl_aff_cow(aff);
326 if (!aff)
327 goto error;
329 r = isl_reordering_extend(r, aff->ls->div->n_row);
330 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
331 aff->ls->div->n_row);
332 aff->ls = isl_local_space_realign(aff->ls, r);
334 if (!aff->v || !aff->ls)
335 return isl_aff_free(aff);
337 return aff;
338 error:
339 isl_aff_free(aff);
340 isl_reordering_free(r);
341 return NULL;
344 __isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
345 __isl_take isl_space *model)
347 if (!aff || !model)
348 goto error;
350 if (!isl_space_match(aff->ls->dim, isl_dim_param,
351 model, isl_dim_param)) {
352 isl_reordering *exp;
354 model = isl_space_drop_dims(model, isl_dim_in,
355 0, isl_space_dim(model, isl_dim_in));
356 model = isl_space_drop_dims(model, isl_dim_out,
357 0, isl_space_dim(model, isl_dim_out));
358 exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
359 exp = isl_reordering_extend_space(exp,
360 isl_aff_get_domain_space(aff));
361 aff = isl_aff_realign_domain(aff, exp);
364 isl_space_free(model);
365 return aff;
366 error:
367 isl_space_free(model);
368 isl_aff_free(aff);
369 return NULL;
372 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
374 if (!aff)
375 return -1;
377 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
380 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
382 int equal;
384 if (!aff1 || !aff2)
385 return -1;
387 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
388 if (equal < 0 || !equal)
389 return equal;
391 return isl_vec_is_equal(aff1->v, aff2->v);
394 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
396 if (!aff)
397 return -1;
398 isl_int_set(*v, aff->v->el[0]);
399 return 0;
402 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
404 if (!aff)
405 return -1;
406 isl_int_set(*v, aff->v->el[1]);
407 return 0;
410 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
411 enum isl_dim_type type, int pos, isl_int *v)
413 if (!aff)
414 return -1;
416 if (type == isl_dim_out)
417 isl_die(aff->v->ctx, isl_error_invalid,
418 "output/set dimension does not have a coefficient",
419 return -1);
420 if (type == isl_dim_in)
421 type = isl_dim_set;
423 if (pos >= isl_local_space_dim(aff->ls, type))
424 isl_die(aff->v->ctx, isl_error_invalid,
425 "position out of bounds", return -1);
427 pos += isl_local_space_offset(aff->ls, type);
428 isl_int_set(*v, aff->v->el[1 + pos]);
430 return 0;
433 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
435 aff = isl_aff_cow(aff);
436 if (!aff)
437 return NULL;
439 aff->v = isl_vec_cow(aff->v);
440 if (!aff->v)
441 return isl_aff_free(aff);
443 isl_int_set(aff->v->el[0], v);
445 return aff;
448 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
450 aff = isl_aff_cow(aff);
451 if (!aff)
452 return NULL;
454 aff->v = isl_vec_cow(aff->v);
455 if (!aff->v)
456 return isl_aff_free(aff);
458 isl_int_set(aff->v->el[1], v);
460 return aff;
463 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
465 if (isl_int_is_zero(v))
466 return aff;
468 aff = isl_aff_cow(aff);
469 if (!aff)
470 return NULL;
472 aff->v = isl_vec_cow(aff->v);
473 if (!aff->v)
474 return isl_aff_free(aff);
476 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
478 return aff;
481 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
483 isl_int t;
485 isl_int_init(t);
486 isl_int_set_si(t, v);
487 aff = isl_aff_add_constant(aff, t);
488 isl_int_clear(t);
490 return aff;
493 /* Add "v" to the numerator of the constant term of "aff".
495 __isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v)
497 if (isl_int_is_zero(v))
498 return aff;
500 aff = isl_aff_cow(aff);
501 if (!aff)
502 return NULL;
504 aff->v = isl_vec_cow(aff->v);
505 if (!aff->v)
506 return isl_aff_free(aff);
508 isl_int_add(aff->v->el[1], aff->v->el[1], v);
510 return aff;
513 /* Add "v" to the numerator of the constant term of "aff".
515 __isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v)
517 isl_int t;
519 if (v == 0)
520 return aff;
522 isl_int_init(t);
523 isl_int_set_si(t, v);
524 aff = isl_aff_add_constant_num(aff, t);
525 isl_int_clear(t);
527 return aff;
530 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
532 aff = isl_aff_cow(aff);
533 if (!aff)
534 return NULL;
536 aff->v = isl_vec_cow(aff->v);
537 if (!aff->v)
538 return isl_aff_free(aff);
540 isl_int_set_si(aff->v->el[1], v);
542 return aff;
545 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
546 enum isl_dim_type type, int pos, isl_int v)
548 if (!aff)
549 return NULL;
551 if (type == isl_dim_out)
552 isl_die(aff->v->ctx, isl_error_invalid,
553 "output/set dimension does not have a coefficient",
554 return isl_aff_free(aff));
555 if (type == isl_dim_in)
556 type = isl_dim_set;
558 if (pos >= isl_local_space_dim(aff->ls, type))
559 isl_die(aff->v->ctx, isl_error_invalid,
560 "position out of bounds", return isl_aff_free(aff));
562 aff = isl_aff_cow(aff);
563 if (!aff)
564 return NULL;
566 aff->v = isl_vec_cow(aff->v);
567 if (!aff->v)
568 return isl_aff_free(aff);
570 pos += isl_local_space_offset(aff->ls, type);
571 isl_int_set(aff->v->el[1 + pos], v);
573 return aff;
576 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
577 enum isl_dim_type type, int pos, int v)
579 if (!aff)
580 return NULL;
582 if (type == isl_dim_out)
583 isl_die(aff->v->ctx, isl_error_invalid,
584 "output/set dimension does not have a coefficient",
585 return isl_aff_free(aff));
586 if (type == isl_dim_in)
587 type = isl_dim_set;
589 if (pos >= isl_local_space_dim(aff->ls, type))
590 isl_die(aff->v->ctx, isl_error_invalid,
591 "position out of bounds", return isl_aff_free(aff));
593 aff = isl_aff_cow(aff);
594 if (!aff)
595 return NULL;
597 aff->v = isl_vec_cow(aff->v);
598 if (!aff->v)
599 return isl_aff_free(aff);
601 pos += isl_local_space_offset(aff->ls, type);
602 isl_int_set_si(aff->v->el[1 + pos], v);
604 return aff;
607 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
608 enum isl_dim_type type, int pos, isl_int v)
610 if (!aff)
611 return NULL;
613 if (type == isl_dim_out)
614 isl_die(aff->v->ctx, isl_error_invalid,
615 "output/set dimension does not have a coefficient",
616 return isl_aff_free(aff));
617 if (type == isl_dim_in)
618 type = isl_dim_set;
620 if (pos >= isl_local_space_dim(aff->ls, type))
621 isl_die(aff->v->ctx, isl_error_invalid,
622 "position out of bounds", return isl_aff_free(aff));
624 aff = isl_aff_cow(aff);
625 if (!aff)
626 return NULL;
628 aff->v = isl_vec_cow(aff->v);
629 if (!aff->v)
630 return isl_aff_free(aff);
632 pos += isl_local_space_offset(aff->ls, type);
633 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
635 return aff;
638 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
639 enum isl_dim_type type, int pos, int v)
641 isl_int t;
643 isl_int_init(t);
644 isl_int_set_si(t, v);
645 aff = isl_aff_add_coefficient(aff, type, pos, t);
646 isl_int_clear(t);
648 return aff;
651 __isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
653 if (!aff)
654 return NULL;
656 return isl_local_space_get_div(aff->ls, pos);
659 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
661 aff = isl_aff_cow(aff);
662 if (!aff)
663 return NULL;
664 aff->v = isl_vec_cow(aff->v);
665 if (!aff->v)
666 return isl_aff_free(aff);
668 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
670 return aff;
673 /* Remove divs from the local space that do not appear in the affine
674 * expression.
675 * We currently only remove divs at the end.
676 * Some intermediate divs may also not appear directly in the affine
677 * expression, but we would also need to check that no other divs are
678 * defined in terms of them.
680 __isl_give isl_aff *isl_aff_remove_unused_divs( __isl_take isl_aff *aff)
682 int pos;
683 int off;
684 int n;
686 if (!aff)
687 return NULL;
689 n = isl_local_space_dim(aff->ls, isl_dim_div);
690 off = isl_local_space_offset(aff->ls, isl_dim_div);
692 pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
693 if (pos == n)
694 return aff;
696 aff = isl_aff_cow(aff);
697 if (!aff)
698 return NULL;
700 aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
701 aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
702 if (!aff->ls || !aff->v)
703 return isl_aff_free(aff);
705 return aff;
708 /* Given two affine expressions "p" of length p_len (including the
709 * denominator and the constant term) and "subs" of length subs_len,
710 * plug in "subs" for the variable at position "pos".
711 * The variables of "subs" and "p" are assumed to match up to subs_len,
712 * but "p" may have additional variables.
713 * "v" is an initialized isl_int that can be used internally.
715 * In particular, if "p" represents the expression
717 * (a i + g)/m
719 * with i the variable at position "pos" and "subs" represents the expression
721 * f/d
723 * then the result represents the expression
725 * (a f + d g)/(m d)
728 void isl_seq_substitute(isl_int *p, int pos, isl_int *subs,
729 int p_len, int subs_len, isl_int v)
731 isl_int_set(v, p[1 + pos]);
732 isl_int_set_si(p[1 + pos], 0);
733 isl_seq_combine(p + 1, subs[0], p + 1, v, subs + 1, subs_len - 1);
734 isl_seq_scale(p + subs_len, p + subs_len, subs[0], p_len - subs_len);
735 isl_int_mul(p[0], p[0], subs[0]);
738 /* Look for any divs in the aff->ls with a denominator equal to one
739 * and plug them into the affine expression and any subsequent divs
740 * that may reference the div.
742 static __isl_give isl_aff *plug_in_integral_divs(__isl_take isl_aff *aff)
744 int i, n;
745 int len;
746 isl_int v;
747 isl_vec *vec;
748 isl_local_space *ls;
749 unsigned pos;
751 if (!aff)
752 return NULL;
754 n = isl_local_space_dim(aff->ls, isl_dim_div);
755 len = aff->v->size;
756 for (i = 0; i < n; ++i) {
757 if (!isl_int_is_one(aff->ls->div->row[i][0]))
758 continue;
759 ls = isl_local_space_copy(aff->ls);
760 ls = isl_local_space_substitute_seq(ls, isl_dim_div, i,
761 aff->ls->div->row[i], len, i + 1);
762 vec = isl_vec_copy(aff->v);
763 vec = isl_vec_cow(vec);
764 if (!ls || !vec)
765 goto error;
767 isl_int_init(v);
769 pos = isl_local_space_offset(aff->ls, isl_dim_div) + i;
770 isl_seq_substitute(vec->el, pos, aff->ls->div->row[i],
771 len, len, v);
773 isl_int_clear(v);
775 isl_vec_free(aff->v);
776 aff->v = vec;
777 isl_local_space_free(aff->ls);
778 aff->ls = ls;
781 return aff;
782 error:
783 isl_vec_free(vec);
784 isl_local_space_free(ls);
785 return isl_aff_free(aff);
788 /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
790 * Even though this function is only called on isl_affs with a single
791 * reference, we are careful to only change aff->v and aff->ls together.
793 static __isl_give isl_aff *swap_div(__isl_take isl_aff *aff, int a, int b)
795 unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
796 isl_local_space *ls;
797 isl_vec *v;
799 ls = isl_local_space_copy(aff->ls);
800 ls = isl_local_space_swap_div(ls, a, b);
801 v = isl_vec_copy(aff->v);
802 v = isl_vec_cow(v);
803 if (!ls || !v)
804 goto error;
806 isl_int_swap(v->el[1 + off + a], v->el[1 + off + b]);
807 isl_vec_free(aff->v);
808 aff->v = v;
809 isl_local_space_free(aff->ls);
810 aff->ls = ls;
812 return aff;
813 error:
814 isl_vec_free(v);
815 isl_local_space_free(ls);
816 return isl_aff_free(aff);
819 /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
821 * We currently do not actually remove div "b", but simply add its
822 * coefficient to that of "a" and then zero it out.
824 static __isl_give isl_aff *merge_divs(__isl_take isl_aff *aff, int a, int b)
826 unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
828 if (isl_int_is_zero(aff->v->el[1 + off + b]))
829 return aff;
831 aff->v = isl_vec_cow(aff->v);
832 if (!aff->v)
833 return isl_aff_free(aff);
835 isl_int_add(aff->v->el[1 + off + a],
836 aff->v->el[1 + off + a], aff->v->el[1 + off + b]);
837 isl_int_set_si(aff->v->el[1 + off + b], 0);
839 return aff;
842 /* Sort the divs in the local space of "aff" according to
843 * the comparison function "cmp_row" in isl_local_space.c,
844 * combining the coefficients of identical divs.
846 * Reordering divs does not change the semantics of "aff",
847 * so there is no need to call isl_aff_cow.
848 * Moreover, this function is currently only called on isl_affs
849 * with a single reference.
851 static __isl_give isl_aff *sort_divs(__isl_take isl_aff *aff)
853 int i, j, n;
854 unsigned off;
856 if (!aff)
857 return NULL;
859 off = isl_local_space_offset(aff->ls, isl_dim_div);
860 n = isl_aff_dim(aff, isl_dim_div);
861 for (i = 1; i < n; ++i) {
862 for (j = i - 1; j >= 0; --j) {
863 int cmp = isl_mat_cmp_div(aff->ls->div, j, j + 1);
864 if (cmp < 0)
865 break;
866 if (cmp == 0)
867 aff = merge_divs(aff, j, j + 1);
868 else
869 aff = swap_div(aff, j, j + 1);
870 if (!aff)
871 return NULL;
875 return aff;
878 /* Normalize the representation of "aff".
880 * This function should only be called of "new" isl_affs, i.e.,
881 * with only a single reference. We therefore do not need to
882 * worry about affecting other instances.
884 __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
886 if (!aff)
887 return NULL;
888 aff->v = isl_vec_normalize(aff->v);
889 if (!aff->v)
890 return isl_aff_free(aff);
891 aff = plug_in_integral_divs(aff);
892 aff = sort_divs(aff);
893 aff = isl_aff_remove_unused_divs(aff);
894 return aff;
897 /* Given f, return floor(f).
898 * If f is an integer expression, then just return f.
899 * If f is a constant, then return the constant floor(f).
900 * Otherwise, if f = g/m, write g = q m + r,
901 * create a new div d = [r/m] and return the expression q + d.
902 * The coefficients in r are taken to lie between -m/2 and m/2.
904 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
906 int i;
907 int size;
908 isl_ctx *ctx;
909 isl_vec *div;
911 if (!aff)
912 return NULL;
914 if (isl_int_is_one(aff->v->el[0]))
915 return aff;
917 aff = isl_aff_cow(aff);
918 if (!aff)
919 return NULL;
921 aff->v = isl_vec_cow(aff->v);
922 if (!aff->v)
923 return isl_aff_free(aff);
925 if (isl_aff_is_cst(aff)) {
926 isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
927 isl_int_set_si(aff->v->el[0], 1);
928 return aff;
931 div = isl_vec_copy(aff->v);
932 div = isl_vec_cow(div);
933 if (!div)
934 return isl_aff_free(aff);
936 ctx = isl_aff_get_ctx(aff);
937 isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
938 for (i = 1; i < aff->v->size; ++i) {
939 isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
940 isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
941 if (isl_int_gt(div->el[i], aff->v->el[0])) {
942 isl_int_sub(div->el[i], div->el[i], div->el[0]);
943 isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
947 aff->ls = isl_local_space_add_div(aff->ls, div);
948 if (!aff->ls)
949 return isl_aff_free(aff);
951 size = aff->v->size;
952 aff->v = isl_vec_extend(aff->v, size + 1);
953 if (!aff->v)
954 return isl_aff_free(aff);
955 isl_int_set_si(aff->v->el[0], 1);
956 isl_int_set_si(aff->v->el[size], 1);
958 return aff;
961 /* Compute
963 * aff mod m = aff - m * floor(aff/m)
965 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
967 isl_aff *res;
969 res = isl_aff_copy(aff);
970 aff = isl_aff_scale_down(aff, m);
971 aff = isl_aff_floor(aff);
972 aff = isl_aff_scale(aff, m);
973 res = isl_aff_sub(res, aff);
975 return res;
978 /* Compute
980 * pwaff mod m = pwaff - m * floor(pwaff/m)
982 __isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
984 isl_pw_aff *res;
986 res = isl_pw_aff_copy(pwaff);
987 pwaff = isl_pw_aff_scale_down(pwaff, m);
988 pwaff = isl_pw_aff_floor(pwaff);
989 pwaff = isl_pw_aff_scale(pwaff, m);
990 res = isl_pw_aff_sub(res, pwaff);
992 return res;
995 /* Given f, return ceil(f).
996 * If f is an integer expression, then just return f.
997 * Otherwise, create a new div d = [-f] and return the expression -d.
999 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
1001 if (!aff)
1002 return NULL;
1004 if (isl_int_is_one(aff->v->el[0]))
1005 return aff;
1007 aff = isl_aff_neg(aff);
1008 aff = isl_aff_floor(aff);
1009 aff = isl_aff_neg(aff);
1011 return aff;
1014 /* Apply the expansion computed by isl_merge_divs.
1015 * The expansion itself is given by "exp" while the resulting
1016 * list of divs is given by "div".
1018 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
1019 __isl_take isl_mat *div, int *exp)
1021 int i, j;
1022 int old_n_div;
1023 int new_n_div;
1024 int offset;
1026 aff = isl_aff_cow(aff);
1027 if (!aff || !div)
1028 goto error;
1030 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1031 new_n_div = isl_mat_rows(div);
1032 if (new_n_div < old_n_div)
1033 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
1034 "not an expansion", goto error);
1036 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
1037 if (!aff->v)
1038 goto error;
1040 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
1041 j = old_n_div - 1;
1042 for (i = new_n_div - 1; i >= 0; --i) {
1043 if (j >= 0 && exp[j] == i) {
1044 if (i != j)
1045 isl_int_swap(aff->v->el[offset + i],
1046 aff->v->el[offset + j]);
1047 j--;
1048 } else
1049 isl_int_set_si(aff->v->el[offset + i], 0);
1052 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
1053 if (!aff->ls)
1054 goto error;
1055 isl_mat_free(div);
1056 return aff;
1057 error:
1058 isl_aff_free(aff);
1059 isl_mat_free(div);
1060 return NULL;
1063 /* Add two affine expressions that live in the same local space.
1065 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
1066 __isl_take isl_aff *aff2)
1068 isl_int gcd, f;
1070 aff1 = isl_aff_cow(aff1);
1071 if (!aff1 || !aff2)
1072 goto error;
1074 aff1->v = isl_vec_cow(aff1->v);
1075 if (!aff1->v)
1076 goto error;
1078 isl_int_init(gcd);
1079 isl_int_init(f);
1080 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
1081 isl_int_divexact(f, aff2->v->el[0], gcd);
1082 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
1083 isl_int_divexact(f, aff1->v->el[0], gcd);
1084 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
1085 isl_int_divexact(f, aff2->v->el[0], gcd);
1086 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
1087 isl_int_clear(f);
1088 isl_int_clear(gcd);
1090 isl_aff_free(aff2);
1091 return aff1;
1092 error:
1093 isl_aff_free(aff1);
1094 isl_aff_free(aff2);
1095 return NULL;
1098 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
1099 __isl_take isl_aff *aff2)
1101 isl_ctx *ctx;
1102 int *exp1 = NULL;
1103 int *exp2 = NULL;
1104 isl_mat *div;
1106 if (!aff1 || !aff2)
1107 goto error;
1109 ctx = isl_aff_get_ctx(aff1);
1110 if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
1111 isl_die(ctx, isl_error_invalid,
1112 "spaces don't match", goto error);
1114 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
1115 return add_expanded(aff1, aff2);
1117 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
1118 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
1119 if (!exp1 || !exp2)
1120 goto error;
1122 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
1123 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
1124 aff2 = isl_aff_expand_divs(aff2, div, exp2);
1125 free(exp1);
1126 free(exp2);
1128 return add_expanded(aff1, aff2);
1129 error:
1130 free(exp1);
1131 free(exp2);
1132 isl_aff_free(aff1);
1133 isl_aff_free(aff2);
1134 return NULL;
1137 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
1138 __isl_take isl_aff *aff2)
1140 return isl_aff_add(aff1, isl_aff_neg(aff2));
1143 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
1145 isl_int gcd;
1147 if (isl_int_is_one(f))
1148 return aff;
1150 aff = isl_aff_cow(aff);
1151 if (!aff)
1152 return NULL;
1153 aff->v = isl_vec_cow(aff->v);
1154 if (!aff->v)
1155 return isl_aff_free(aff);
1157 isl_int_init(gcd);
1158 isl_int_gcd(gcd, aff->v->el[0], f);
1159 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
1160 isl_int_divexact(gcd, f, gcd);
1161 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
1162 isl_int_clear(gcd);
1164 return aff;
1167 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
1169 isl_int gcd;
1171 if (isl_int_is_one(f))
1172 return aff;
1174 aff = isl_aff_cow(aff);
1175 if (!aff)
1176 return NULL;
1178 if (isl_int_is_zero(f))
1179 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1180 "cannot scale down by zero", return isl_aff_free(aff));
1182 aff->v = isl_vec_cow(aff->v);
1183 if (!aff->v)
1184 return isl_aff_free(aff);
1186 isl_int_init(gcd);
1187 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
1188 isl_int_gcd(gcd, gcd, f);
1189 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
1190 isl_int_divexact(gcd, f, gcd);
1191 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
1192 isl_int_clear(gcd);
1194 return aff;
1197 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
1199 isl_int v;
1201 if (f == 1)
1202 return aff;
1204 isl_int_init(v);
1205 isl_int_set_ui(v, f);
1206 aff = isl_aff_scale_down(aff, v);
1207 isl_int_clear(v);
1209 return aff;
1212 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
1213 enum isl_dim_type type, unsigned pos, const char *s)
1215 aff = isl_aff_cow(aff);
1216 if (!aff)
1217 return NULL;
1218 if (type == isl_dim_out)
1219 isl_die(aff->v->ctx, isl_error_invalid,
1220 "cannot set name of output/set dimension",
1221 return isl_aff_free(aff));
1222 if (type == isl_dim_in)
1223 type = isl_dim_set;
1224 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
1225 if (!aff->ls)
1226 return isl_aff_free(aff);
1228 return aff;
1231 __isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
1232 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
1234 aff = isl_aff_cow(aff);
1235 if (!aff)
1236 return isl_id_free(id);
1237 if (type == isl_dim_out)
1238 isl_die(aff->v->ctx, isl_error_invalid,
1239 "cannot set name of output/set dimension",
1240 goto error);
1241 if (type == isl_dim_in)
1242 type = isl_dim_set;
1243 aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
1244 if (!aff->ls)
1245 return isl_aff_free(aff);
1247 return aff;
1248 error:
1249 isl_id_free(id);
1250 isl_aff_free(aff);
1251 return NULL;
1254 /* Exploit the equalities in "eq" to simplify the affine expression
1255 * and the expressions of the integer divisions in the local space.
1256 * The integer divisions in this local space are assumed to appear
1257 * as regular dimensions in "eq".
1259 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
1260 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1262 int i, j;
1263 unsigned total;
1264 unsigned n_div;
1266 if (!eq)
1267 goto error;
1268 if (eq->n_eq == 0) {
1269 isl_basic_set_free(eq);
1270 return aff;
1273 aff = isl_aff_cow(aff);
1274 if (!aff)
1275 goto error;
1277 aff->ls = isl_local_space_substitute_equalities(aff->ls,
1278 isl_basic_set_copy(eq));
1279 if (!aff->ls)
1280 goto error;
1282 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
1283 n_div = eq->n_div;
1284 for (i = 0; i < eq->n_eq; ++i) {
1285 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
1286 if (j < 0 || j == 0 || j >= total)
1287 continue;
1289 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
1290 &aff->v->el[0]);
1293 isl_basic_set_free(eq);
1294 aff = isl_aff_normalize(aff);
1295 return aff;
1296 error:
1297 isl_basic_set_free(eq);
1298 isl_aff_free(aff);
1299 return NULL;
1302 /* Exploit the equalities in "eq" to simplify the affine expression
1303 * and the expressions of the integer divisions in the local space.
1305 static __isl_give isl_aff *isl_aff_substitute_equalities(
1306 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1308 int n_div;
1310 if (!aff || !eq)
1311 goto error;
1312 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1313 if (n_div > 0)
1314 eq = isl_basic_set_add(eq, isl_dim_set, n_div);
1315 return isl_aff_substitute_equalities_lifted(aff, eq);
1316 error:
1317 isl_basic_set_free(eq);
1318 isl_aff_free(aff);
1319 return NULL;
1322 /* Look for equalities among the variables shared by context and aff
1323 * and the integer divisions of aff, if any.
1324 * The equalities are then used to eliminate coefficients and/or integer
1325 * divisions from aff.
1327 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
1328 __isl_take isl_set *context)
1330 isl_basic_set *hull;
1331 int n_div;
1333 if (!aff)
1334 goto error;
1335 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1336 if (n_div > 0) {
1337 isl_basic_set *bset;
1338 isl_local_space *ls;
1339 context = isl_set_add_dims(context, isl_dim_set, n_div);
1340 ls = isl_aff_get_domain_local_space(aff);
1341 bset = isl_basic_set_from_local_space(ls);
1342 bset = isl_basic_set_lift(bset);
1343 bset = isl_basic_set_flatten(bset);
1344 context = isl_set_intersect(context,
1345 isl_set_from_basic_set(bset));
1348 hull = isl_set_affine_hull(context);
1349 return isl_aff_substitute_equalities_lifted(aff, hull);
1350 error:
1351 isl_aff_free(aff);
1352 isl_set_free(context);
1353 return NULL;
1356 __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
1357 __isl_take isl_set *context)
1359 isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
1360 dom_context = isl_set_intersect_params(dom_context, context);
1361 return isl_aff_gist(aff, dom_context);
1364 /* Return a basic set containing those elements in the space
1365 * of aff where it is non-negative.
1366 * If "rational" is set, then return a rational basic set.
1368 static __isl_give isl_basic_set *aff_nonneg_basic_set(
1369 __isl_take isl_aff *aff, int rational)
1371 isl_constraint *ineq;
1372 isl_basic_set *bset;
1374 ineq = isl_inequality_from_aff(aff);
1376 bset = isl_basic_set_from_constraint(ineq);
1377 if (rational)
1378 bset = isl_basic_set_set_rational(bset);
1379 bset = isl_basic_set_simplify(bset);
1380 return bset;
1383 /* Return a basic set containing those elements in the space
1384 * of aff where it is non-negative.
1386 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
1388 return aff_nonneg_basic_set(aff, 0);
1391 /* Return a basic set containing those elements in the domain space
1392 * of aff where it is negative.
1394 __isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
1396 aff = isl_aff_neg(aff);
1397 aff = isl_aff_add_constant_num_si(aff, -1);
1398 return isl_aff_nonneg_basic_set(aff);
1401 /* Return a basic set containing those elements in the space
1402 * of aff where it is zero.
1403 * If "rational" is set, then return a rational basic set.
1405 static __isl_give isl_basic_set *aff_zero_basic_set(__isl_take isl_aff *aff,
1406 int rational)
1408 isl_constraint *ineq;
1409 isl_basic_set *bset;
1411 ineq = isl_equality_from_aff(aff);
1413 bset = isl_basic_set_from_constraint(ineq);
1414 if (rational)
1415 bset = isl_basic_set_set_rational(bset);
1416 bset = isl_basic_set_simplify(bset);
1417 return bset;
1420 /* Return a basic set containing those elements in the space
1421 * of aff where it is zero.
1423 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
1425 return aff_zero_basic_set(aff, 0);
1428 /* Return a basic set containing those elements in the shared space
1429 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1431 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
1432 __isl_take isl_aff *aff2)
1434 aff1 = isl_aff_sub(aff1, aff2);
1436 return isl_aff_nonneg_basic_set(aff1);
1439 /* Return a basic set containing those elements in the shared space
1440 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1442 __isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
1443 __isl_take isl_aff *aff2)
1445 return isl_aff_ge_basic_set(aff2, aff1);
1448 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
1449 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
1451 aff1 = isl_aff_add(aff1, aff2);
1452 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
1453 return aff1;
1456 int isl_aff_is_empty(__isl_keep isl_aff *aff)
1458 if (!aff)
1459 return -1;
1461 return 0;
1464 /* Check whether the given affine expression has non-zero coefficient
1465 * for any dimension in the given range or if any of these dimensions
1466 * appear with non-zero coefficients in any of the integer divisions
1467 * involved in the affine expression.
1469 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
1470 enum isl_dim_type type, unsigned first, unsigned n)
1472 int i;
1473 isl_ctx *ctx;
1474 int *active = NULL;
1475 int involves = 0;
1477 if (!aff)
1478 return -1;
1479 if (n == 0)
1480 return 0;
1482 ctx = isl_aff_get_ctx(aff);
1483 if (first + n > isl_aff_dim(aff, type))
1484 isl_die(ctx, isl_error_invalid,
1485 "range out of bounds", return -1);
1487 active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
1488 if (!active)
1489 goto error;
1491 first += isl_local_space_offset(aff->ls, type) - 1;
1492 for (i = 0; i < n; ++i)
1493 if (active[first + i]) {
1494 involves = 1;
1495 break;
1498 free(active);
1500 return involves;
1501 error:
1502 free(active);
1503 return -1;
1506 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
1507 enum isl_dim_type type, unsigned first, unsigned n)
1509 isl_ctx *ctx;
1511 if (!aff)
1512 return NULL;
1513 if (type == isl_dim_out)
1514 isl_die(aff->v->ctx, isl_error_invalid,
1515 "cannot drop output/set dimension",
1516 return isl_aff_free(aff));
1517 if (type == isl_dim_in)
1518 type = isl_dim_set;
1519 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1520 return aff;
1522 ctx = isl_aff_get_ctx(aff);
1523 if (first + n > isl_local_space_dim(aff->ls, type))
1524 isl_die(ctx, isl_error_invalid, "range out of bounds",
1525 return isl_aff_free(aff));
1527 aff = isl_aff_cow(aff);
1528 if (!aff)
1529 return NULL;
1531 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
1532 if (!aff->ls)
1533 return isl_aff_free(aff);
1535 first += 1 + isl_local_space_offset(aff->ls, type);
1536 aff->v = isl_vec_drop_els(aff->v, first, n);
1537 if (!aff->v)
1538 return isl_aff_free(aff);
1540 return aff;
1543 /* Project the domain of the affine expression onto its parameter space.
1544 * The affine expression may not involve any of the domain dimensions.
1546 __isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
1548 isl_space *space;
1549 unsigned n;
1550 int involves;
1552 n = isl_aff_dim(aff, isl_dim_in);
1553 involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
1554 if (involves < 0)
1555 return isl_aff_free(aff);
1556 if (involves)
1557 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1558 "affine expression involves some of the domain dimensions",
1559 return isl_aff_free(aff));
1560 aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
1561 space = isl_aff_get_domain_space(aff);
1562 space = isl_space_params(space);
1563 aff = isl_aff_reset_domain_space(aff, space);
1564 return aff;
1567 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
1568 enum isl_dim_type type, unsigned first, unsigned n)
1570 isl_ctx *ctx;
1572 if (!aff)
1573 return NULL;
1574 if (type == isl_dim_out)
1575 isl_die(aff->v->ctx, isl_error_invalid,
1576 "cannot insert output/set dimensions",
1577 return isl_aff_free(aff));
1578 if (type == isl_dim_in)
1579 type = isl_dim_set;
1580 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1581 return aff;
1583 ctx = isl_aff_get_ctx(aff);
1584 if (first > isl_local_space_dim(aff->ls, type))
1585 isl_die(ctx, isl_error_invalid, "position out of bounds",
1586 return isl_aff_free(aff));
1588 aff = isl_aff_cow(aff);
1589 if (!aff)
1590 return NULL;
1592 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
1593 if (!aff->ls)
1594 return isl_aff_free(aff);
1596 first += 1 + isl_local_space_offset(aff->ls, type);
1597 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
1598 if (!aff->v)
1599 return isl_aff_free(aff);
1601 return aff;
1604 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
1605 enum isl_dim_type type, unsigned n)
1607 unsigned pos;
1609 pos = isl_aff_dim(aff, type);
1611 return isl_aff_insert_dims(aff, type, pos, n);
1614 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
1615 enum isl_dim_type type, unsigned n)
1617 unsigned pos;
1619 pos = isl_pw_aff_dim(pwaff, type);
1621 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
1624 __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
1626 isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
1627 return isl_pw_aff_alloc(dom, aff);
1630 #undef PW
1631 #define PW isl_pw_aff
1632 #undef EL
1633 #define EL isl_aff
1634 #undef EL_IS_ZERO
1635 #define EL_IS_ZERO is_empty
1636 #undef ZERO
1637 #define ZERO empty
1638 #undef IS_ZERO
1639 #define IS_ZERO is_empty
1640 #undef FIELD
1641 #define FIELD aff
1642 #undef DEFAULT_IS_ZERO
1643 #define DEFAULT_IS_ZERO 0
1645 #define NO_EVAL
1646 #define NO_OPT
1647 #define NO_MOVE_DIMS
1648 #define NO_LIFT
1649 #define NO_MORPH
1651 #include <isl_pw_templ.c>
1653 static __isl_give isl_set *align_params_pw_pw_set_and(
1654 __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
1655 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1656 __isl_take isl_pw_aff *pwaff2))
1658 if (!pwaff1 || !pwaff2)
1659 goto error;
1660 if (isl_space_match(pwaff1->dim, isl_dim_param,
1661 pwaff2->dim, isl_dim_param))
1662 return fn(pwaff1, pwaff2);
1663 if (!isl_space_has_named_params(pwaff1->dim) ||
1664 !isl_space_has_named_params(pwaff2->dim))
1665 isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
1666 "unaligned unnamed parameters", goto error);
1667 pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
1668 pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
1669 return fn(pwaff1, pwaff2);
1670 error:
1671 isl_pw_aff_free(pwaff1);
1672 isl_pw_aff_free(pwaff2);
1673 return NULL;
1676 /* Compute a piecewise quasi-affine expression with a domain that
1677 * is the union of those of pwaff1 and pwaff2 and such that on each
1678 * cell, the quasi-affine expression is the better (according to cmp)
1679 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
1680 * is defined on a given cell, then the associated expression
1681 * is the defined one.
1683 static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1684 __isl_take isl_pw_aff *pwaff2,
1685 __isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
1686 __isl_take isl_aff *aff2))
1688 int i, j, n;
1689 isl_pw_aff *res;
1690 isl_ctx *ctx;
1691 isl_set *set;
1693 if (!pwaff1 || !pwaff2)
1694 goto error;
1696 ctx = isl_space_get_ctx(pwaff1->dim);
1697 if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
1698 isl_die(ctx, isl_error_invalid,
1699 "arguments should live in same space", goto error);
1701 if (isl_pw_aff_is_empty(pwaff1)) {
1702 isl_pw_aff_free(pwaff1);
1703 return pwaff2;
1706 if (isl_pw_aff_is_empty(pwaff2)) {
1707 isl_pw_aff_free(pwaff2);
1708 return pwaff1;
1711 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
1712 res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
1714 for (i = 0; i < pwaff1->n; ++i) {
1715 set = isl_set_copy(pwaff1->p[i].set);
1716 for (j = 0; j < pwaff2->n; ++j) {
1717 struct isl_set *common;
1718 isl_set *better;
1720 common = isl_set_intersect(
1721 isl_set_copy(pwaff1->p[i].set),
1722 isl_set_copy(pwaff2->p[j].set));
1723 better = isl_set_from_basic_set(cmp(
1724 isl_aff_copy(pwaff2->p[j].aff),
1725 isl_aff_copy(pwaff1->p[i].aff)));
1726 better = isl_set_intersect(common, better);
1727 if (isl_set_plain_is_empty(better)) {
1728 isl_set_free(better);
1729 continue;
1731 set = isl_set_subtract(set, isl_set_copy(better));
1733 res = isl_pw_aff_add_piece(res, better,
1734 isl_aff_copy(pwaff2->p[j].aff));
1736 res = isl_pw_aff_add_piece(res, set,
1737 isl_aff_copy(pwaff1->p[i].aff));
1740 for (j = 0; j < pwaff2->n; ++j) {
1741 set = isl_set_copy(pwaff2->p[j].set);
1742 for (i = 0; i < pwaff1->n; ++i)
1743 set = isl_set_subtract(set,
1744 isl_set_copy(pwaff1->p[i].set));
1745 res = isl_pw_aff_add_piece(res, set,
1746 isl_aff_copy(pwaff2->p[j].aff));
1749 isl_pw_aff_free(pwaff1);
1750 isl_pw_aff_free(pwaff2);
1752 return res;
1753 error:
1754 isl_pw_aff_free(pwaff1);
1755 isl_pw_aff_free(pwaff2);
1756 return NULL;
1759 /* Compute a piecewise quasi-affine expression with a domain that
1760 * is the union of those of pwaff1 and pwaff2 and such that on each
1761 * cell, the quasi-affine expression is the maximum of those of pwaff1
1762 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1763 * cell, then the associated expression is the defined one.
1765 static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1766 __isl_take isl_pw_aff *pwaff2)
1768 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
1771 __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1772 __isl_take isl_pw_aff *pwaff2)
1774 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1775 &pw_aff_union_max);
1778 /* Compute a piecewise quasi-affine expression with a domain that
1779 * is the union of those of pwaff1 and pwaff2 and such that on each
1780 * cell, the quasi-affine expression is the minimum of those of pwaff1
1781 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1782 * cell, then the associated expression is the defined one.
1784 static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1785 __isl_take isl_pw_aff *pwaff2)
1787 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
1790 __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1791 __isl_take isl_pw_aff *pwaff2)
1793 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1794 &pw_aff_union_min);
1797 __isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1798 __isl_take isl_pw_aff *pwaff2, int max)
1800 if (max)
1801 return isl_pw_aff_union_max(pwaff1, pwaff2);
1802 else
1803 return isl_pw_aff_union_min(pwaff1, pwaff2);
1806 /* Construct a map with as domain the domain of pwaff and
1807 * one-dimensional range corresponding to the affine expressions.
1809 static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1811 int i;
1812 isl_space *dim;
1813 isl_map *map;
1815 if (!pwaff)
1816 return NULL;
1818 dim = isl_pw_aff_get_space(pwaff);
1819 map = isl_map_empty(dim);
1821 for (i = 0; i < pwaff->n; ++i) {
1822 isl_basic_map *bmap;
1823 isl_map *map_i;
1825 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
1826 map_i = isl_map_from_basic_map(bmap);
1827 map_i = isl_map_intersect_domain(map_i,
1828 isl_set_copy(pwaff->p[i].set));
1829 map = isl_map_union_disjoint(map, map_i);
1832 isl_pw_aff_free(pwaff);
1834 return map;
1837 /* Construct a map with as domain the domain of pwaff and
1838 * one-dimensional range corresponding to the affine expressions.
1840 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1842 if (!pwaff)
1843 return NULL;
1844 if (isl_space_is_set(pwaff->dim))
1845 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1846 "space of input is not a map",
1847 return isl_pw_aff_free(pwaff));
1848 return map_from_pw_aff(pwaff);
1851 /* Construct a one-dimensional set with as parameter domain
1852 * the domain of pwaff and the single set dimension
1853 * corresponding to the affine expressions.
1855 __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1857 if (!pwaff)
1858 return NULL;
1859 if (!isl_space_is_set(pwaff->dim))
1860 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1861 "space of input is not a set",
1862 return isl_pw_aff_free(pwaff));
1863 return map_from_pw_aff(pwaff);
1866 /* Return a set containing those elements in the domain
1867 * of pwaff where it is non-negative.
1869 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
1871 int i;
1872 isl_set *set;
1874 if (!pwaff)
1875 return NULL;
1877 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1879 for (i = 0; i < pwaff->n; ++i) {
1880 isl_basic_set *bset;
1881 isl_set *set_i;
1882 int rational;
1884 rational = isl_set_has_rational(pwaff->p[i].set);
1885 bset = aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff),
1886 rational);
1887 set_i = isl_set_from_basic_set(bset);
1888 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1889 set = isl_set_union_disjoint(set, set_i);
1892 isl_pw_aff_free(pwaff);
1894 return set;
1897 /* Return a set containing those elements in the domain
1898 * of pwaff where it is zero (if complement is 0) or not zero
1899 * (if complement is 1).
1901 static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
1902 int complement)
1904 int i;
1905 isl_set *set;
1907 if (!pwaff)
1908 return NULL;
1910 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1912 for (i = 0; i < pwaff->n; ++i) {
1913 isl_basic_set *bset;
1914 isl_set *set_i, *zero;
1915 int rational;
1917 rational = isl_set_has_rational(pwaff->p[i].set);
1918 bset = aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff),
1919 rational);
1920 zero = isl_set_from_basic_set(bset);
1921 set_i = isl_set_copy(pwaff->p[i].set);
1922 if (complement)
1923 set_i = isl_set_subtract(set_i, zero);
1924 else
1925 set_i = isl_set_intersect(set_i, zero);
1926 set = isl_set_union_disjoint(set, set_i);
1929 isl_pw_aff_free(pwaff);
1931 return set;
1934 /* Return a set containing those elements in the domain
1935 * of pwaff where it is zero.
1937 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
1939 return pw_aff_zero_set(pwaff, 0);
1942 /* Return a set containing those elements in the domain
1943 * of pwaff where it is not zero.
1945 __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
1947 return pw_aff_zero_set(pwaff, 1);
1950 /* Return a set containing those elements in the shared domain
1951 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1953 * We compute the difference on the shared domain and then construct
1954 * the set of values where this difference is non-negative.
1955 * If strict is set, we first subtract 1 from the difference.
1956 * If equal is set, we only return the elements where pwaff1 and pwaff2
1957 * are equal.
1959 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
1960 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
1962 isl_set *set1, *set2;
1964 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
1965 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
1966 set1 = isl_set_intersect(set1, set2);
1967 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
1968 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
1969 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
1971 if (strict) {
1972 isl_space *dim = isl_set_get_space(set1);
1973 isl_aff *aff;
1974 aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
1975 aff = isl_aff_add_constant_si(aff, -1);
1976 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
1977 } else
1978 isl_set_free(set1);
1980 if (equal)
1981 return isl_pw_aff_zero_set(pwaff1);
1982 return isl_pw_aff_nonneg_set(pwaff1);
1985 /* Return a set containing those elements in the shared domain
1986 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1988 static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1989 __isl_take isl_pw_aff *pwaff2)
1991 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
1994 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1995 __isl_take isl_pw_aff *pwaff2)
1997 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
2000 /* Return a set containing those elements in the shared domain
2001 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
2003 static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
2004 __isl_take isl_pw_aff *pwaff2)
2006 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
2009 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
2010 __isl_take isl_pw_aff *pwaff2)
2012 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
2015 /* Return a set containing those elements in the shared domain
2016 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
2018 static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
2019 __isl_take isl_pw_aff *pwaff2)
2021 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
2024 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
2025 __isl_take isl_pw_aff *pwaff2)
2027 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
2030 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
2031 __isl_take isl_pw_aff *pwaff2)
2033 return isl_pw_aff_ge_set(pwaff2, pwaff1);
2036 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
2037 __isl_take isl_pw_aff *pwaff2)
2039 return isl_pw_aff_gt_set(pwaff2, pwaff1);
2042 /* Return a set containing those elements in the shared domain
2043 * of the elements of list1 and list2 where each element in list1
2044 * has the relation specified by "fn" with each element in list2.
2046 static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
2047 __isl_take isl_pw_aff_list *list2,
2048 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
2049 __isl_take isl_pw_aff *pwaff2))
2051 int i, j;
2052 isl_ctx *ctx;
2053 isl_set *set;
2055 if (!list1 || !list2)
2056 goto error;
2058 ctx = isl_pw_aff_list_get_ctx(list1);
2059 if (list1->n < 1 || list2->n < 1)
2060 isl_die(ctx, isl_error_invalid,
2061 "list should contain at least one element", goto error);
2063 set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
2064 for (i = 0; i < list1->n; ++i)
2065 for (j = 0; j < list2->n; ++j) {
2066 isl_set *set_ij;
2068 set_ij = fn(isl_pw_aff_copy(list1->p[i]),
2069 isl_pw_aff_copy(list2->p[j]));
2070 set = isl_set_intersect(set, set_ij);
2073 isl_pw_aff_list_free(list1);
2074 isl_pw_aff_list_free(list2);
2075 return set;
2076 error:
2077 isl_pw_aff_list_free(list1);
2078 isl_pw_aff_list_free(list2);
2079 return NULL;
2082 /* Return a set containing those elements in the shared domain
2083 * of the elements of list1 and list2 where each element in list1
2084 * is equal to each element in list2.
2086 __isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
2087 __isl_take isl_pw_aff_list *list2)
2089 return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
2092 __isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
2093 __isl_take isl_pw_aff_list *list2)
2095 return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
2098 /* Return a set containing those elements in the shared domain
2099 * of the elements of list1 and list2 where each element in list1
2100 * is less than or equal to each element in list2.
2102 __isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
2103 __isl_take isl_pw_aff_list *list2)
2105 return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
2108 __isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
2109 __isl_take isl_pw_aff_list *list2)
2111 return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
2114 __isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
2115 __isl_take isl_pw_aff_list *list2)
2117 return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
2120 __isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
2121 __isl_take isl_pw_aff_list *list2)
2123 return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
2127 /* Return a set containing those elements in the shared domain
2128 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
2130 static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
2131 __isl_take isl_pw_aff *pwaff2)
2133 isl_set *set_lt, *set_gt;
2135 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
2136 isl_pw_aff_copy(pwaff2));
2137 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
2138 return isl_set_union_disjoint(set_lt, set_gt);
2141 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
2142 __isl_take isl_pw_aff *pwaff2)
2144 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
2147 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
2148 isl_int v)
2150 int i;
2152 if (isl_int_is_one(v))
2153 return pwaff;
2154 if (!isl_int_is_pos(v))
2155 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
2156 "factor needs to be positive",
2157 return isl_pw_aff_free(pwaff));
2158 pwaff = isl_pw_aff_cow(pwaff);
2159 if (!pwaff)
2160 return NULL;
2161 if (pwaff->n == 0)
2162 return pwaff;
2164 for (i = 0; i < pwaff->n; ++i) {
2165 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
2166 if (!pwaff->p[i].aff)
2167 return isl_pw_aff_free(pwaff);
2170 return pwaff;
2173 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
2175 int i;
2177 pwaff = isl_pw_aff_cow(pwaff);
2178 if (!pwaff)
2179 return NULL;
2180 if (pwaff->n == 0)
2181 return pwaff;
2183 for (i = 0; i < pwaff->n; ++i) {
2184 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
2185 if (!pwaff->p[i].aff)
2186 return isl_pw_aff_free(pwaff);
2189 return pwaff;
2192 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
2194 int i;
2196 pwaff = isl_pw_aff_cow(pwaff);
2197 if (!pwaff)
2198 return NULL;
2199 if (pwaff->n == 0)
2200 return pwaff;
2202 for (i = 0; i < pwaff->n; ++i) {
2203 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
2204 if (!pwaff->p[i].aff)
2205 return isl_pw_aff_free(pwaff);
2208 return pwaff;
2211 /* Assuming that "cond1" and "cond2" are disjoint,
2212 * return an affine expression that is equal to pwaff1 on cond1
2213 * and to pwaff2 on cond2.
2215 static __isl_give isl_pw_aff *isl_pw_aff_select(
2216 __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
2217 __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
2219 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
2220 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
2222 return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
2225 /* Return an affine expression that is equal to pwaff_true for elements
2226 * where "cond" is non-zero and to pwaff_false for elements where "cond"
2227 * is zero.
2228 * That is, return cond ? pwaff_true : pwaff_false;
2230 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
2231 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
2233 isl_set *cond_true, *cond_false;
2235 cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
2236 cond_false = isl_pw_aff_zero_set(cond);
2237 return isl_pw_aff_select(cond_true, pwaff_true,
2238 cond_false, pwaff_false);
2241 int isl_aff_is_cst(__isl_keep isl_aff *aff)
2243 if (!aff)
2244 return -1;
2246 return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
2249 /* Check whether pwaff is a piecewise constant.
2251 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
2253 int i;
2255 if (!pwaff)
2256 return -1;
2258 for (i = 0; i < pwaff->n; ++i) {
2259 int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
2260 if (is_cst < 0 || !is_cst)
2261 return is_cst;
2264 return 1;
2267 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2268 __isl_take isl_aff *aff2)
2270 if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
2271 return isl_aff_mul(aff2, aff1);
2273 if (!isl_aff_is_cst(aff2))
2274 isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
2275 "at least one affine expression should be constant",
2276 goto error);
2278 aff1 = isl_aff_cow(aff1);
2279 if (!aff1 || !aff2)
2280 goto error;
2282 aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
2283 aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
2285 isl_aff_free(aff2);
2286 return aff1;
2287 error:
2288 isl_aff_free(aff1);
2289 isl_aff_free(aff2);
2290 return NULL;
2293 /* Divide "aff1" by "aff2", assuming "aff2" is a piecewise constant.
2295 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
2296 __isl_take isl_aff *aff2)
2298 int is_cst;
2299 int neg;
2301 is_cst = isl_aff_is_cst(aff2);
2302 if (is_cst < 0)
2303 goto error;
2304 if (!is_cst)
2305 isl_die(isl_aff_get_ctx(aff2), isl_error_invalid,
2306 "second argument should be a constant", goto error);
2308 if (!aff2)
2309 goto error;
2311 neg = isl_int_is_neg(aff2->v->el[1]);
2312 if (neg) {
2313 isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
2314 isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
2317 aff1 = isl_aff_scale(aff1, aff2->v->el[0]);
2318 aff1 = isl_aff_scale_down(aff1, aff2->v->el[1]);
2320 if (neg) {
2321 isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
2322 isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
2325 isl_aff_free(aff2);
2326 return aff1;
2327 error:
2328 isl_aff_free(aff1);
2329 isl_aff_free(aff2);
2330 return NULL;
2333 static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2334 __isl_take isl_pw_aff *pwaff2)
2336 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
2339 __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2340 __isl_take isl_pw_aff *pwaff2)
2342 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
2345 __isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
2346 __isl_take isl_pw_aff *pwaff2)
2348 return isl_pw_aff_union_add_(pwaff1, pwaff2);
2351 static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2352 __isl_take isl_pw_aff *pwaff2)
2354 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
2357 __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2358 __isl_take isl_pw_aff *pwaff2)
2360 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
2363 static __isl_give isl_pw_aff *pw_aff_div(__isl_take isl_pw_aff *pa1,
2364 __isl_take isl_pw_aff *pa2)
2366 return isl_pw_aff_on_shared_domain(pa1, pa2, &isl_aff_div);
2369 /* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
2371 __isl_give isl_pw_aff *isl_pw_aff_div(__isl_take isl_pw_aff *pa1,
2372 __isl_take isl_pw_aff *pa2)
2374 int is_cst;
2376 is_cst = isl_pw_aff_is_cst(pa2);
2377 if (is_cst < 0)
2378 goto error;
2379 if (!is_cst)
2380 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2381 "second argument should be a piecewise constant",
2382 goto error);
2383 return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_aff_div);
2384 error:
2385 isl_pw_aff_free(pa1);
2386 isl_pw_aff_free(pa2);
2387 return NULL;
2390 /* Compute the quotient of the integer division of "pa1" by "pa2"
2391 * with rounding towards zero.
2392 * "pa2" is assumed to be a piecewise constant.
2394 * In particular, return
2396 * pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
2399 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(__isl_take isl_pw_aff *pa1,
2400 __isl_take isl_pw_aff *pa2)
2402 int is_cst;
2403 isl_set *cond;
2404 isl_pw_aff *f, *c;
2406 is_cst = isl_pw_aff_is_cst(pa2);
2407 if (is_cst < 0)
2408 goto error;
2409 if (!is_cst)
2410 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2411 "second argument should be a piecewise constant",
2412 goto error);
2414 pa1 = isl_pw_aff_div(pa1, pa2);
2416 cond = isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1));
2417 f = isl_pw_aff_floor(isl_pw_aff_copy(pa1));
2418 c = isl_pw_aff_ceil(pa1);
2419 return isl_pw_aff_cond(isl_set_indicator_function(cond), f, c);
2420 error:
2421 isl_pw_aff_free(pa1);
2422 isl_pw_aff_free(pa2);
2423 return NULL;
2426 /* Compute the remainder of the integer division of "pa1" by "pa2"
2427 * with rounding towards zero.
2428 * "pa2" is assumed to be a piecewise constant.
2430 * In particular, return
2432 * pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
2435 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(__isl_take isl_pw_aff *pa1,
2436 __isl_take isl_pw_aff *pa2)
2438 int is_cst;
2439 isl_pw_aff *res;
2441 is_cst = isl_pw_aff_is_cst(pa2);
2442 if (is_cst < 0)
2443 goto error;
2444 if (!is_cst)
2445 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2446 "second argument should be a piecewise constant",
2447 goto error);
2448 res = isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1), isl_pw_aff_copy(pa2));
2449 res = isl_pw_aff_mul(pa2, res);
2450 res = isl_pw_aff_sub(pa1, res);
2451 return res;
2452 error:
2453 isl_pw_aff_free(pa1);
2454 isl_pw_aff_free(pa2);
2455 return NULL;
2458 static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2459 __isl_take isl_pw_aff *pwaff2)
2461 isl_set *le;
2462 isl_set *dom;
2464 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2465 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2466 le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
2467 isl_pw_aff_copy(pwaff2));
2468 dom = isl_set_subtract(dom, isl_set_copy(le));
2469 return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
2472 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2473 __isl_take isl_pw_aff *pwaff2)
2475 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
2478 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2479 __isl_take isl_pw_aff *pwaff2)
2481 isl_set *ge;
2482 isl_set *dom;
2484 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2485 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2486 ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
2487 isl_pw_aff_copy(pwaff2));
2488 dom = isl_set_subtract(dom, isl_set_copy(ge));
2489 return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
2492 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2493 __isl_take isl_pw_aff *pwaff2)
2495 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
2498 static __isl_give isl_pw_aff *pw_aff_list_reduce(
2499 __isl_take isl_pw_aff_list *list,
2500 __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
2501 __isl_take isl_pw_aff *pwaff2))
2503 int i;
2504 isl_ctx *ctx;
2505 isl_pw_aff *res;
2507 if (!list)
2508 return NULL;
2510 ctx = isl_pw_aff_list_get_ctx(list);
2511 if (list->n < 1)
2512 isl_die(ctx, isl_error_invalid,
2513 "list should contain at least one element",
2514 return isl_pw_aff_list_free(list));
2516 res = isl_pw_aff_copy(list->p[0]);
2517 for (i = 1; i < list->n; ++i)
2518 res = fn(res, isl_pw_aff_copy(list->p[i]));
2520 isl_pw_aff_list_free(list);
2521 return res;
2524 /* Return an isl_pw_aff that maps each element in the intersection of the
2525 * domains of the elements of list to the minimal corresponding affine
2526 * expression.
2528 __isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
2530 return pw_aff_list_reduce(list, &isl_pw_aff_min);
2533 /* Return an isl_pw_aff that maps each element in the intersection of the
2534 * domains of the elements of list to the maximal corresponding affine
2535 * expression.
2537 __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
2539 return pw_aff_list_reduce(list, &isl_pw_aff_max);
2542 /* Mark the domains of "pwaff" as rational.
2544 __isl_give isl_pw_aff *isl_pw_aff_set_rational(__isl_take isl_pw_aff *pwaff)
2546 int i;
2548 pwaff = isl_pw_aff_cow(pwaff);
2549 if (!pwaff)
2550 return NULL;
2551 if (pwaff->n == 0)
2552 return pwaff;
2554 for (i = 0; i < pwaff->n; ++i) {
2555 pwaff->p[i].set = isl_set_set_rational(pwaff->p[i].set);
2556 if (!pwaff->p[i].set)
2557 return isl_pw_aff_free(pwaff);
2560 return pwaff;
2563 /* Mark the domains of the elements of "list" as rational.
2565 __isl_give isl_pw_aff_list *isl_pw_aff_list_set_rational(
2566 __isl_take isl_pw_aff_list *list)
2568 int i;
2570 if (!list)
2571 return NULL;
2572 if (list->n == 0)
2573 return list;
2575 for (i = 0; i < list->n; ++i) {
2576 isl_pw_aff *pa;
2578 pa = isl_pw_aff_list_get_pw_aff(list, i);
2579 pa = isl_pw_aff_set_rational(pa);
2580 list = isl_pw_aff_list_set_pw_aff(list, i, pa);
2583 return list;
2586 #undef BASE
2587 #define BASE aff
2589 #include <isl_multi_templ.c>
2591 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
2592 * domain.
2594 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
2595 __isl_take isl_multi_aff *ma)
2597 isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
2598 return isl_pw_multi_aff_alloc(dom, ma);
2601 /* Create a piecewise multi-affine expression in the given space that maps each
2602 * input dimension to the corresponding output dimension.
2604 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2605 __isl_take isl_space *space)
2607 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space));
2610 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
2611 __isl_take isl_multi_aff *maff2)
2613 int i;
2614 isl_ctx *ctx;
2616 maff1 = isl_multi_aff_cow(maff1);
2617 if (!maff1 || !maff2)
2618 goto error;
2620 ctx = isl_multi_aff_get_ctx(maff1);
2621 if (!isl_space_is_equal(maff1->space, maff2->space))
2622 isl_die(ctx, isl_error_invalid,
2623 "spaces don't match", goto error);
2625 for (i = 0; i < maff1->n; ++i) {
2626 maff1->p[i] = isl_aff_add(maff1->p[i],
2627 isl_aff_copy(maff2->p[i]));
2628 if (!maff1->p[i])
2629 goto error;
2632 isl_multi_aff_free(maff2);
2633 return maff1;
2634 error:
2635 isl_multi_aff_free(maff1);
2636 isl_multi_aff_free(maff2);
2637 return NULL;
2640 /* Given two multi-affine expressions A -> B and C -> D,
2641 * construct a multi-affine expression [A -> C] -> [B -> D].
2643 __isl_give isl_multi_aff *isl_multi_aff_product(
2644 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
2646 int i;
2647 isl_aff *aff;
2648 isl_space *space;
2649 isl_multi_aff *res;
2650 int in1, in2, out1, out2;
2652 in1 = isl_multi_aff_dim(ma1, isl_dim_in);
2653 in2 = isl_multi_aff_dim(ma2, isl_dim_in);
2654 out1 = isl_multi_aff_dim(ma1, isl_dim_out);
2655 out2 = isl_multi_aff_dim(ma2, isl_dim_out);
2656 space = isl_space_product(isl_multi_aff_get_space(ma1),
2657 isl_multi_aff_get_space(ma2));
2658 res = isl_multi_aff_alloc(isl_space_copy(space));
2659 space = isl_space_domain(space);
2661 for (i = 0; i < out1; ++i) {
2662 aff = isl_multi_aff_get_aff(ma1, i);
2663 aff = isl_aff_insert_dims(aff, isl_dim_in, in1, in2);
2664 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
2665 res = isl_multi_aff_set_aff(res, i, aff);
2668 for (i = 0; i < out2; ++i) {
2669 aff = isl_multi_aff_get_aff(ma2, i);
2670 aff = isl_aff_insert_dims(aff, isl_dim_in, 0, in1);
2671 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
2672 res = isl_multi_aff_set_aff(res, out1 + i, aff);
2675 isl_space_free(space);
2676 isl_multi_aff_free(ma1);
2677 isl_multi_aff_free(ma2);
2678 return res;
2681 /* Exploit the equalities in "eq" to simplify the affine expressions.
2683 static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
2684 __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
2686 int i;
2688 maff = isl_multi_aff_cow(maff);
2689 if (!maff || !eq)
2690 goto error;
2692 for (i = 0; i < maff->n; ++i) {
2693 maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
2694 isl_basic_set_copy(eq));
2695 if (!maff->p[i])
2696 goto error;
2699 isl_basic_set_free(eq);
2700 return maff;
2701 error:
2702 isl_basic_set_free(eq);
2703 isl_multi_aff_free(maff);
2704 return NULL;
2707 __isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
2708 isl_int f)
2710 int i;
2712 maff = isl_multi_aff_cow(maff);
2713 if (!maff)
2714 return NULL;
2716 for (i = 0; i < maff->n; ++i) {
2717 maff->p[i] = isl_aff_scale(maff->p[i], f);
2718 if (!maff->p[i])
2719 return isl_multi_aff_free(maff);
2722 return maff;
2725 __isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
2726 __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
2728 maff1 = isl_multi_aff_add(maff1, maff2);
2729 maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
2730 return maff1;
2733 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
2735 if (!maff)
2736 return -1;
2738 return 0;
2741 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
2742 __isl_keep isl_multi_aff *maff2)
2744 int i;
2745 int equal;
2747 if (!maff1 || !maff2)
2748 return -1;
2749 if (maff1->n != maff2->n)
2750 return 0;
2751 equal = isl_space_is_equal(maff1->space, maff2->space);
2752 if (equal < 0 || !equal)
2753 return equal;
2755 for (i = 0; i < maff1->n; ++i) {
2756 equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
2757 if (equal < 0 || !equal)
2758 return equal;
2761 return 1;
2764 /* Return the set of domain elements where "ma1" is lexicographically
2765 * smaller than or equal to "ma2".
2767 __isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
2768 __isl_take isl_multi_aff *ma2)
2770 return isl_multi_aff_lex_ge_set(ma2, ma1);
2773 /* Return the set of domain elements where "ma1" is lexicographically
2774 * greater than or equal to "ma2".
2776 __isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
2777 __isl_take isl_multi_aff *ma2)
2779 isl_space *space;
2780 isl_map *map1, *map2;
2781 isl_map *map, *ge;
2783 map1 = isl_map_from_multi_aff(ma1);
2784 map2 = isl_map_from_multi_aff(ma2);
2785 map = isl_map_range_product(map1, map2);
2786 space = isl_space_range(isl_map_get_space(map));
2787 space = isl_space_domain(isl_space_unwrap(space));
2788 ge = isl_map_lex_ge(space);
2789 map = isl_map_intersect_range(map, isl_map_wrap(ge));
2791 return isl_map_domain(map);
2794 #undef PW
2795 #define PW isl_pw_multi_aff
2796 #undef EL
2797 #define EL isl_multi_aff
2798 #undef EL_IS_ZERO
2799 #define EL_IS_ZERO is_empty
2800 #undef ZERO
2801 #define ZERO empty
2802 #undef IS_ZERO
2803 #define IS_ZERO is_empty
2804 #undef FIELD
2805 #define FIELD maff
2806 #undef DEFAULT_IS_ZERO
2807 #define DEFAULT_IS_ZERO 0
2809 #define NO_NEG
2810 #define NO_EVAL
2811 #define NO_OPT
2812 #define NO_INVOLVES_DIMS
2813 #define NO_MOVE_DIMS
2814 #define NO_INSERT_DIMS
2815 #define NO_LIFT
2816 #define NO_MORPH
2818 #include <isl_pw_templ.c>
2820 #undef UNION
2821 #define UNION isl_union_pw_multi_aff
2822 #undef PART
2823 #define PART isl_pw_multi_aff
2824 #undef PARTS
2825 #define PARTS pw_multi_aff
2826 #define ALIGN_DOMAIN
2828 #define NO_EVAL
2830 #include <isl_union_templ.c>
2832 /* Given a function "cmp" that returns the set of elements where
2833 * "ma1" is "better" than "ma2", return the intersection of this
2834 * set with "dom1" and "dom2".
2836 static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1,
2837 __isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1,
2838 __isl_keep isl_multi_aff *ma2,
2839 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
2840 __isl_take isl_multi_aff *ma2))
2842 isl_set *common;
2843 isl_set *better;
2844 int is_empty;
2846 common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2));
2847 is_empty = isl_set_plain_is_empty(common);
2848 if (is_empty >= 0 && is_empty)
2849 return common;
2850 if (is_empty < 0)
2851 return isl_set_free(common);
2852 better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2));
2853 better = isl_set_intersect(common, better);
2855 return better;
2858 /* Given a function "cmp" that returns the set of elements where
2859 * "ma1" is "better" than "ma2", return a piecewise multi affine
2860 * expression defined on the union of the definition domains
2861 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
2862 * "pma2" on each cell. If only one of the two input functions
2863 * is defined on a given cell, then it is considered the best.
2865 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt(
2866 __isl_take isl_pw_multi_aff *pma1,
2867 __isl_take isl_pw_multi_aff *pma2,
2868 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
2869 __isl_take isl_multi_aff *ma2))
2871 int i, j, n;
2872 isl_pw_multi_aff *res = NULL;
2873 isl_ctx *ctx;
2874 isl_set *set = NULL;
2876 if (!pma1 || !pma2)
2877 goto error;
2879 ctx = isl_space_get_ctx(pma1->dim);
2880 if (!isl_space_is_equal(pma1->dim, pma2->dim))
2881 isl_die(ctx, isl_error_invalid,
2882 "arguments should live in the same space", goto error);
2884 if (isl_pw_multi_aff_is_empty(pma1)) {
2885 isl_pw_multi_aff_free(pma1);
2886 return pma2;
2889 if (isl_pw_multi_aff_is_empty(pma2)) {
2890 isl_pw_multi_aff_free(pma2);
2891 return pma1;
2894 n = 2 * (pma1->n + 1) * (pma2->n + 1);
2895 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n);
2897 for (i = 0; i < pma1->n; ++i) {
2898 set = isl_set_copy(pma1->p[i].set);
2899 for (j = 0; j < pma2->n; ++j) {
2900 isl_set *better;
2901 int is_empty;
2903 better = shared_and_better(pma2->p[j].set,
2904 pma1->p[i].set, pma2->p[j].maff,
2905 pma1->p[i].maff, cmp);
2906 is_empty = isl_set_plain_is_empty(better);
2907 if (is_empty < 0 || is_empty) {
2908 isl_set_free(better);
2909 if (is_empty < 0)
2910 goto error;
2911 continue;
2913 set = isl_set_subtract(set, isl_set_copy(better));
2915 res = isl_pw_multi_aff_add_piece(res, better,
2916 isl_multi_aff_copy(pma2->p[j].maff));
2918 res = isl_pw_multi_aff_add_piece(res, set,
2919 isl_multi_aff_copy(pma1->p[i].maff));
2922 for (j = 0; j < pma2->n; ++j) {
2923 set = isl_set_copy(pma2->p[j].set);
2924 for (i = 0; i < pma1->n; ++i)
2925 set = isl_set_subtract(set,
2926 isl_set_copy(pma1->p[i].set));
2927 res = isl_pw_multi_aff_add_piece(res, set,
2928 isl_multi_aff_copy(pma2->p[j].maff));
2931 isl_pw_multi_aff_free(pma1);
2932 isl_pw_multi_aff_free(pma2);
2934 return res;
2935 error:
2936 isl_pw_multi_aff_free(pma1);
2937 isl_pw_multi_aff_free(pma2);
2938 isl_set_free(set);
2939 return isl_pw_multi_aff_free(res);
2942 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
2943 __isl_take isl_pw_multi_aff *pma1,
2944 __isl_take isl_pw_multi_aff *pma2)
2946 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_ge_set);
2949 /* Given two piecewise multi affine expressions, return a piecewise
2950 * multi-affine expression defined on the union of the definition domains
2951 * of the inputs that is equal to the lexicographic maximum of the two
2952 * inputs on each cell. If only one of the two inputs is defined on
2953 * a given cell, then it is considered to be the maximum.
2955 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
2956 __isl_take isl_pw_multi_aff *pma1,
2957 __isl_take isl_pw_multi_aff *pma2)
2959 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2960 &pw_multi_aff_union_lexmax);
2963 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
2964 __isl_take isl_pw_multi_aff *pma1,
2965 __isl_take isl_pw_multi_aff *pma2)
2967 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_set);
2970 /* Given two piecewise multi affine expressions, return a piecewise
2971 * multi-affine expression defined on the union of the definition domains
2972 * of the inputs that is equal to the lexicographic minimum of the two
2973 * inputs on each cell. If only one of the two inputs is defined on
2974 * a given cell, then it is considered to be the minimum.
2976 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
2977 __isl_take isl_pw_multi_aff *pma1,
2978 __isl_take isl_pw_multi_aff *pma2)
2980 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2981 &pw_multi_aff_union_lexmin);
2984 static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
2985 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2987 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
2988 &isl_multi_aff_add);
2991 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
2992 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2994 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2995 &pw_multi_aff_add);
2998 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
2999 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3001 return isl_pw_multi_aff_union_add_(pma1, pma2);
3004 /* Given two piecewise multi-affine expressions A -> B and C -> D,
3005 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
3007 static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
3008 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3010 int i, j, n;
3011 isl_space *space;
3012 isl_pw_multi_aff *res;
3014 if (!pma1 || !pma2)
3015 goto error;
3017 n = pma1->n * pma2->n;
3018 space = isl_space_product(isl_space_copy(pma1->dim),
3019 isl_space_copy(pma2->dim));
3020 res = isl_pw_multi_aff_alloc_size(space, n);
3022 for (i = 0; i < pma1->n; ++i) {
3023 for (j = 0; j < pma2->n; ++j) {
3024 isl_set *domain;
3025 isl_multi_aff *ma;
3027 domain = isl_set_product(isl_set_copy(pma1->p[i].set),
3028 isl_set_copy(pma2->p[j].set));
3029 ma = isl_multi_aff_product(
3030 isl_multi_aff_copy(pma1->p[i].maff),
3031 isl_multi_aff_copy(pma2->p[i].maff));
3032 res = isl_pw_multi_aff_add_piece(res, domain, ma);
3036 isl_pw_multi_aff_free(pma1);
3037 isl_pw_multi_aff_free(pma2);
3038 return res;
3039 error:
3040 isl_pw_multi_aff_free(pma1);
3041 isl_pw_multi_aff_free(pma2);
3042 return NULL;
3045 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3046 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3048 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3049 &pw_multi_aff_product);
3052 /* Construct a map mapping the domain of the piecewise multi-affine expression
3053 * to its range, with each dimension in the range equated to the
3054 * corresponding affine expression on its cell.
3056 __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
3058 int i;
3059 isl_map *map;
3061 if (!pma)
3062 return NULL;
3064 map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
3066 for (i = 0; i < pma->n; ++i) {
3067 isl_multi_aff *maff;
3068 isl_basic_map *bmap;
3069 isl_map *map_i;
3071 maff = isl_multi_aff_copy(pma->p[i].maff);
3072 bmap = isl_basic_map_from_multi_aff(maff);
3073 map_i = isl_map_from_basic_map(bmap);
3074 map_i = isl_map_intersect_domain(map_i,
3075 isl_set_copy(pma->p[i].set));
3076 map = isl_map_union_disjoint(map, map_i);
3079 isl_pw_multi_aff_free(pma);
3080 return map;
3083 __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
3085 if (!pma)
3086 return NULL;
3088 if (!isl_space_is_set(pma->dim))
3089 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3090 "isl_pw_multi_aff cannot be converted into an isl_set",
3091 return isl_pw_multi_aff_free(pma));
3093 return isl_map_from_pw_multi_aff(pma);
3096 /* Given a basic map with a single output dimension that is defined
3097 * in terms of the parameters and input dimensions using an equality,
3098 * extract an isl_aff that expresses the output dimension in terms
3099 * of the parameters and input dimensions.
3101 * Since some applications expect the result of isl_pw_multi_aff_from_map
3102 * to only contain integer affine expressions, we compute the floor
3103 * of the expression before returning.
3105 * This function shares some similarities with
3106 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
3108 static __isl_give isl_aff *extract_isl_aff_from_basic_map(
3109 __isl_take isl_basic_map *bmap)
3111 int i;
3112 unsigned offset;
3113 unsigned total;
3114 isl_local_space *ls;
3115 isl_aff *aff;
3117 if (!bmap)
3118 return NULL;
3119 if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
3120 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3121 "basic map should have a single output dimension",
3122 goto error);
3123 offset = isl_basic_map_offset(bmap, isl_dim_out);
3124 total = isl_basic_map_total_dim(bmap);
3125 for (i = 0; i < bmap->n_eq; ++i) {
3126 if (isl_int_is_zero(bmap->eq[i][offset]))
3127 continue;
3128 if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
3129 1 + total - (offset + 1)) != -1)
3130 continue;
3131 break;
3133 if (i >= bmap->n_eq)
3134 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3135 "unable to find suitable equality", goto error);
3136 ls = isl_basic_map_get_local_space(bmap);
3137 aff = isl_aff_alloc(isl_local_space_domain(ls));
3138 if (!aff)
3139 goto error;
3140 if (isl_int_is_neg(bmap->eq[i][offset]))
3141 isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
3142 else
3143 isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
3144 isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
3145 isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
3146 isl_basic_map_free(bmap);
3148 aff = isl_aff_remove_unused_divs(aff);
3149 aff = isl_aff_floor(aff);
3150 return aff;
3151 error:
3152 isl_basic_map_free(bmap);
3153 return NULL;
3156 /* Given a basic map where each output dimension is defined
3157 * in terms of the parameters and input dimensions using an equality,
3158 * extract an isl_multi_aff that expresses the output dimensions in terms
3159 * of the parameters and input dimensions.
3161 static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
3162 __isl_take isl_basic_map *bmap)
3164 int i;
3165 unsigned n_out;
3166 isl_multi_aff *ma;
3168 if (!bmap)
3169 return NULL;
3171 ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
3172 n_out = isl_basic_map_dim(bmap, isl_dim_out);
3174 for (i = 0; i < n_out; ++i) {
3175 isl_basic_map *bmap_i;
3176 isl_aff *aff;
3178 bmap_i = isl_basic_map_copy(bmap);
3179 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
3180 i + 1, n_out - (1 + i));
3181 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
3182 aff = extract_isl_aff_from_basic_map(bmap_i);
3183 ma = isl_multi_aff_set_aff(ma, i, aff);
3186 isl_basic_map_free(bmap);
3188 return ma;
3191 /* Create an isl_pw_multi_aff that is equivalent to
3192 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
3193 * The given basic map is such that each output dimension is defined
3194 * in terms of the parameters and input dimensions using an equality.
3196 static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
3197 __isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
3199 isl_multi_aff *ma;
3201 ma = extract_isl_multi_aff_from_basic_map(bmap);
3202 return isl_pw_multi_aff_alloc(domain, ma);
3205 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3206 * This obviously only works if the input "map" is single-valued.
3207 * If so, we compute the lexicographic minimum of the image in the form
3208 * of an isl_pw_multi_aff. Since the image is unique, it is equal
3209 * to its lexicographic minimum.
3210 * If the input is not single-valued, we produce an error.
3212 * As a special case, we first check if all output dimensions are uniquely
3213 * defined in terms of the parameters and input dimensions over the entire
3214 * domain. If so, we extract the desired isl_pw_multi_aff directly
3215 * from the affine hull of "map" and its domain.
3217 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
3219 int i;
3220 int sv;
3221 isl_pw_multi_aff *pma;
3222 isl_basic_map *hull;
3224 if (!map)
3225 return NULL;
3227 hull = isl_map_affine_hull(isl_map_copy(map));
3228 sv = isl_basic_map_plain_is_single_valued(hull);
3229 if (sv >= 0 && sv)
3230 return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
3231 isl_basic_map_free(hull);
3232 if (sv < 0)
3233 goto error;
3235 sv = isl_map_is_single_valued(map);
3236 if (sv < 0)
3237 goto error;
3238 if (!sv)
3239 isl_die(isl_map_get_ctx(map), isl_error_invalid,
3240 "map is not single-valued", goto error);
3241 map = isl_map_make_disjoint(map);
3242 if (!map)
3243 return NULL;
3245 pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
3247 for (i = 0; i < map->n; ++i) {
3248 isl_pw_multi_aff *pma_i;
3249 isl_basic_map *bmap;
3250 bmap = isl_basic_map_copy(map->p[i]);
3251 pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
3252 pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
3255 isl_map_free(map);
3256 return pma;
3257 error:
3258 isl_map_free(map);
3259 return NULL;
3262 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
3264 return isl_pw_multi_aff_from_map(set);
3267 /* Return the piecewise affine expression "set ? 1 : 0".
3269 __isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
3271 isl_pw_aff *pa;
3272 isl_space *space = isl_set_get_space(set);
3273 isl_local_space *ls = isl_local_space_from_space(space);
3274 isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
3275 isl_aff *one = isl_aff_zero_on_domain(ls);
3277 one = isl_aff_add_constant_si(one, 1);
3278 pa = isl_pw_aff_alloc(isl_set_copy(set), one);
3279 set = isl_set_complement(set);
3280 pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
3282 return pa;
3285 /* Plug in "subs" for dimension "type", "pos" of "aff".
3287 * Let i be the dimension to replace and let "subs" be of the form
3289 * f/d
3291 * and "aff" of the form
3293 * (a i + g)/m
3295 * The result is
3297 * (a f + d g')/(m d)
3299 * where g' is the result of plugging in "subs" in each of the integer
3300 * divisions in g.
3302 __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
3303 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
3305 isl_ctx *ctx;
3306 isl_int v;
3308 aff = isl_aff_cow(aff);
3309 if (!aff || !subs)
3310 return isl_aff_free(aff);
3312 ctx = isl_aff_get_ctx(aff);
3313 if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
3314 isl_die(ctx, isl_error_invalid,
3315 "spaces don't match", return isl_aff_free(aff));
3316 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
3317 isl_die(ctx, isl_error_unsupported,
3318 "cannot handle divs yet", return isl_aff_free(aff));
3320 aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
3321 if (!aff->ls)
3322 return isl_aff_free(aff);
3324 aff->v = isl_vec_cow(aff->v);
3325 if (!aff->v)
3326 return isl_aff_free(aff);
3328 pos += isl_local_space_offset(aff->ls, type);
3330 isl_int_init(v);
3331 isl_seq_substitute(aff->v->el, pos, subs->v->el,
3332 aff->v->size, subs->v->size, v);
3333 isl_int_clear(v);
3335 return aff;
3338 /* Plug in "subs" for dimension "type", "pos" in each of the affine
3339 * expressions in "maff".
3341 __isl_give isl_multi_aff *isl_multi_aff_substitute(
3342 __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
3343 __isl_keep isl_aff *subs)
3345 int i;
3347 maff = isl_multi_aff_cow(maff);
3348 if (!maff || !subs)
3349 return isl_multi_aff_free(maff);
3351 if (type == isl_dim_in)
3352 type = isl_dim_set;
3354 for (i = 0; i < maff->n; ++i) {
3355 maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
3356 if (!maff->p[i])
3357 return isl_multi_aff_free(maff);
3360 return maff;
3363 /* Plug in "subs" for dimension "type", "pos" of "pma".
3365 * pma is of the form
3367 * A_i(v) -> M_i(v)
3369 * while subs is of the form
3371 * v' = B_j(v) -> S_j
3373 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
3374 * has a contribution in the result, in particular
3376 * C_ij(S_j) -> M_i(S_j)
3378 * Note that plugging in S_j in C_ij may also result in an empty set
3379 * and this contribution should simply be discarded.
3381 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
3382 __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
3383 __isl_keep isl_pw_aff *subs)
3385 int i, j, n;
3386 isl_pw_multi_aff *res;
3388 if (!pma || !subs)
3389 return isl_pw_multi_aff_free(pma);
3391 n = pma->n * subs->n;
3392 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
3394 for (i = 0; i < pma->n; ++i) {
3395 for (j = 0; j < subs->n; ++j) {
3396 isl_set *common;
3397 isl_multi_aff *res_ij;
3398 common = isl_set_intersect(
3399 isl_set_copy(pma->p[i].set),
3400 isl_set_copy(subs->p[j].set));
3401 common = isl_set_substitute(common,
3402 type, pos, subs->p[j].aff);
3403 if (isl_set_plain_is_empty(common)) {
3404 isl_set_free(common);
3405 continue;
3408 res_ij = isl_multi_aff_substitute(
3409 isl_multi_aff_copy(pma->p[i].maff),
3410 type, pos, subs->p[j].aff);
3412 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
3416 isl_pw_multi_aff_free(pma);
3417 return res;
3420 /* Compute the preimage of the affine expression "src" under "ma"
3421 * and put the result in "dst". If "has_denom" is set (to one),
3422 * then "src" and "dst" have an extra initial denominator.
3423 * "n_div_ma" is the number of existentials in "ma"
3424 * "n_div_bset" is the number of existentials in "src"
3425 * The resulting "dst" (which is assumed to have been allocated by
3426 * the caller) contains coefficients for both sets of existentials,
3427 * first those in "ma" and then those in "src".
3428 * f, c1, c2 and g are temporary objects that have been initialized
3429 * by the caller.
3431 * Let src represent the expression
3433 * (a(p) + b x + c(divs))/d
3435 * and let ma represent the expressions
3437 * x_i = (r_i(p) + s_i(y) + t_i(divs'))/m_i
3439 * We start out with the following expression for dst:
3441 * (a(p) + 0 y + 0 divs' + f \sum_i b_i x_i + c(divs))/d
3443 * with the multiplication factor f initially equal to 1.
3444 * For each x_i that we substitute, we multiply the numerator
3445 * (and denominator) of dst by c_1 = m_i and add the numerator
3446 * of the x_i expression multiplied by c_2 = f b_i,
3447 * after removing the common factors of c_1 and c_2.
3448 * The multiplication factor f also needs to be multiplied by c_1
3449 * for the next x_j, j > i.
3451 void isl_seq_preimage(isl_int *dst, isl_int *src,
3452 __isl_keep isl_multi_aff *ma, int n_div_ma, int n_div_bset,
3453 isl_int f, isl_int c1, isl_int c2, isl_int g, int has_denom)
3455 int i;
3456 int n_param, n_in, n_out;
3457 int o_div_bset;
3459 n_param = isl_multi_aff_dim(ma, isl_dim_param);
3460 n_in = isl_multi_aff_dim(ma, isl_dim_in);
3461 n_out = isl_multi_aff_dim(ma, isl_dim_out);
3463 o_div_bset = has_denom + 1 + n_param + n_in + n_div_ma;
3465 isl_seq_cpy(dst, src, has_denom + 1 + n_param);
3466 isl_seq_clr(dst + has_denom + 1 + n_param, n_in + n_div_ma);
3467 isl_seq_cpy(dst + o_div_bset,
3468 src + has_denom + 1 + n_param + n_out, n_div_bset);
3470 isl_int_set_si(f, 1);
3472 for (i = 0; i < n_out; ++i) {
3473 if (isl_int_is_zero(src[has_denom + 1 + n_param + i]))
3474 continue;
3475 isl_int_set(c1, ma->p[i]->v->el[0]);
3476 isl_int_mul(c2, f, src[has_denom + 1 + n_param + i]);
3477 isl_int_gcd(g, c1, c2);
3478 isl_int_divexact(c1, c1, g);
3479 isl_int_divexact(c2, c2, g);
3481 isl_int_mul(f, f, c1);
3482 isl_seq_combine(dst + has_denom, c1, dst + has_denom,
3483 c2, ma->p[i]->v->el + 1, ma->p[i]->v->size - 1);
3484 isl_seq_scale(dst + o_div_bset,
3485 dst + o_div_bset, c1, n_div_bset);
3486 if (has_denom)
3487 isl_int_mul(dst[0], dst[0], c1);
3491 /* Compute the pullback of "aff" by the function represented by "ma".
3492 * In other words, plug in "ma" in "aff". The result is an affine expression
3493 * defined over the domain space of "ma".
3495 * If "aff" is represented by
3497 * (a(p) + b x + c(divs))/d
3499 * and ma is represented by
3501 * x = D(p) + F(y) + G(divs')
3503 * then the result is
3505 * (a(p) + b D(p) + b F(y) + b G(divs') + c(divs))/d
3507 * The divs in the local space of the input are similarly adjusted
3508 * through a call to isl_local_space_preimage_multi_aff.
3510 __isl_give isl_aff *isl_aff_pullback_multi_aff(__isl_take isl_aff *aff,
3511 __isl_take isl_multi_aff *ma)
3513 isl_aff *res = NULL;
3514 isl_local_space *ls;
3515 int n_div_aff, n_div_ma;
3516 isl_int f, c1, c2, g;
3518 ma = isl_multi_aff_align_divs(ma);
3519 if (!aff || !ma)
3520 goto error;
3522 n_div_aff = isl_aff_dim(aff, isl_dim_div);
3523 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
3525 ls = isl_aff_get_domain_local_space(aff);
3526 ls = isl_local_space_preimage_multi_aff(ls, isl_multi_aff_copy(ma));
3527 res = isl_aff_alloc(ls);
3528 if (!res)
3529 goto error;
3531 isl_int_init(f);
3532 isl_int_init(c1);
3533 isl_int_init(c2);
3534 isl_int_init(g);
3536 isl_seq_preimage(res->v->el, aff->v->el, ma, n_div_ma, n_div_aff,
3537 f, c1, c2, g, 1);
3539 isl_int_clear(f);
3540 isl_int_clear(c1);
3541 isl_int_clear(c2);
3542 isl_int_clear(g);
3544 isl_aff_free(aff);
3545 isl_multi_aff_free(ma);
3546 res = isl_aff_normalize(res);
3547 return res;
3548 error:
3549 isl_aff_free(aff);
3550 isl_multi_aff_free(ma);
3551 isl_aff_free(res);
3552 return NULL;
3555 /* Compute the pullback of "ma1" by the function represented by "ma2".
3556 * In other words, plug in "ma2" in "ma1".
3558 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
3559 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
3561 int i;
3562 isl_space *space = NULL;
3564 ma2 = isl_multi_aff_align_divs(ma2);
3565 ma1 = isl_multi_aff_cow(ma1);
3566 if (!ma1 || !ma2)
3567 goto error;
3569 space = isl_space_join(isl_multi_aff_get_space(ma2),
3570 isl_multi_aff_get_space(ma1));
3572 for (i = 0; i < ma1->n; ++i) {
3573 ma1->p[i] = isl_aff_pullback_multi_aff(ma1->p[i],
3574 isl_multi_aff_copy(ma2));
3575 if (!ma1->p[i])
3576 goto error;
3579 ma1 = isl_multi_aff_reset_space(ma1, space);
3580 isl_multi_aff_free(ma2);
3581 return ma1;
3582 error:
3583 isl_space_free(space);
3584 isl_multi_aff_free(ma2);
3585 isl_multi_aff_free(ma1);
3586 return NULL;
3589 /* Extend the local space of "dst" to include the divs
3590 * in the local space of "src".
3592 __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
3593 __isl_keep isl_aff *src)
3595 isl_ctx *ctx;
3596 int *exp1 = NULL;
3597 int *exp2 = NULL;
3598 isl_mat *div;
3600 if (!src || !dst)
3601 return isl_aff_free(dst);
3603 ctx = isl_aff_get_ctx(src);
3604 if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
3605 isl_die(ctx, isl_error_invalid,
3606 "spaces don't match", goto error);
3608 if (src->ls->div->n_row == 0)
3609 return dst;
3611 exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
3612 exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
3613 if (!exp1 || !exp2)
3614 goto error;
3616 div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
3617 dst = isl_aff_expand_divs(dst, div, exp2);
3618 free(exp1);
3619 free(exp2);
3621 return dst;
3622 error:
3623 free(exp1);
3624 free(exp2);
3625 return isl_aff_free(dst);
3628 /* Adjust the local spaces of the affine expressions in "maff"
3629 * such that they all have the save divs.
3631 __isl_give isl_multi_aff *isl_multi_aff_align_divs(
3632 __isl_take isl_multi_aff *maff)
3634 int i;
3636 if (!maff)
3637 return NULL;
3638 if (maff->n == 0)
3639 return maff;
3640 maff = isl_multi_aff_cow(maff);
3641 if (!maff)
3642 return NULL;
3644 for (i = 1; i < maff->n; ++i)
3645 maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
3646 for (i = 1; i < maff->n; ++i) {
3647 maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
3648 if (!maff->p[i])
3649 return isl_multi_aff_free(maff);
3652 return maff;
3655 __isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
3657 aff = isl_aff_cow(aff);
3658 if (!aff)
3659 return NULL;
3661 aff->ls = isl_local_space_lift(aff->ls);
3662 if (!aff->ls)
3663 return isl_aff_free(aff);
3665 return aff;
3668 /* Lift "maff" to a space with extra dimensions such that the result
3669 * has no more existentially quantified variables.
3670 * If "ls" is not NULL, then *ls is assigned the local space that lies
3671 * at the basis of the lifting applied to "maff".
3673 __isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
3674 __isl_give isl_local_space **ls)
3676 int i;
3677 isl_space *space;
3678 unsigned n_div;
3680 if (ls)
3681 *ls = NULL;
3683 if (!maff)
3684 return NULL;
3686 if (maff->n == 0) {
3687 if (ls) {
3688 isl_space *space = isl_multi_aff_get_domain_space(maff);
3689 *ls = isl_local_space_from_space(space);
3690 if (!*ls)
3691 return isl_multi_aff_free(maff);
3693 return maff;
3696 maff = isl_multi_aff_cow(maff);
3697 maff = isl_multi_aff_align_divs(maff);
3698 if (!maff)
3699 return NULL;
3701 n_div = isl_aff_dim(maff->p[0], isl_dim_div);
3702 space = isl_multi_aff_get_space(maff);
3703 space = isl_space_lift(isl_space_domain(space), n_div);
3704 space = isl_space_extend_domain_with_range(space,
3705 isl_multi_aff_get_space(maff));
3706 if (!space)
3707 return isl_multi_aff_free(maff);
3708 isl_space_free(maff->space);
3709 maff->space = space;
3711 if (ls) {
3712 *ls = isl_aff_get_domain_local_space(maff->p[0]);
3713 if (!*ls)
3714 return isl_multi_aff_free(maff);
3717 for (i = 0; i < maff->n; ++i) {
3718 maff->p[i] = isl_aff_lift(maff->p[i]);
3719 if (!maff->p[i])
3720 goto error;
3723 return maff;
3724 error:
3725 if (ls)
3726 isl_local_space_free(*ls);
3727 return isl_multi_aff_free(maff);
3731 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
3733 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3734 __isl_keep isl_pw_multi_aff *pma, int pos)
3736 int i;
3737 int n_out;
3738 isl_space *space;
3739 isl_pw_aff *pa;
3741 if (!pma)
3742 return NULL;
3744 n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
3745 if (pos < 0 || pos >= n_out)
3746 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3747 "index out of bounds", return NULL);
3749 space = isl_pw_multi_aff_get_space(pma);
3750 space = isl_space_drop_dims(space, isl_dim_out,
3751 pos + 1, n_out - pos - 1);
3752 space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
3754 pa = isl_pw_aff_alloc_size(space, pma->n);
3755 for (i = 0; i < pma->n; ++i) {
3756 isl_aff *aff;
3757 aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
3758 pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
3761 return pa;
3764 /* Return an isl_pw_multi_aff with the given "set" as domain and
3765 * an unnamed zero-dimensional range.
3767 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3768 __isl_take isl_set *set)
3770 isl_multi_aff *ma;
3771 isl_space *space;
3773 space = isl_set_get_space(set);
3774 space = isl_space_from_domain(space);
3775 ma = isl_multi_aff_zero(space);
3776 return isl_pw_multi_aff_alloc(set, ma);
3779 /* Add an isl_pw_multi_aff with the given "set" as domain and
3780 * an unnamed zero-dimensional range to *user.
3782 static int add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user)
3784 isl_union_pw_multi_aff **upma = user;
3785 isl_pw_multi_aff *pma;
3787 pma = isl_pw_multi_aff_from_domain(set);
3788 *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
3790 return 0;
3793 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
3794 * an unnamed zero-dimensional range.
3796 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain(
3797 __isl_take isl_union_set *uset)
3799 isl_space *space;
3800 isl_union_pw_multi_aff *upma;
3802 if (!uset)
3803 return NULL;
3805 space = isl_union_set_get_space(uset);
3806 upma = isl_union_pw_multi_aff_empty(space);
3808 if (isl_union_set_foreach_set(uset,
3809 &add_pw_multi_aff_from_domain, &upma) < 0)
3810 goto error;
3812 isl_union_set_free(uset);
3813 return upma;
3814 error:
3815 isl_union_set_free(uset);
3816 isl_union_pw_multi_aff_free(upma);
3817 return NULL;
3820 /* Convert "pma" to an isl_map and add it to *umap.
3822 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
3824 isl_union_map **umap = user;
3825 isl_map *map;
3827 map = isl_map_from_pw_multi_aff(pma);
3828 *umap = isl_union_map_add_map(*umap, map);
3830 return 0;
3833 /* Construct a union map mapping the domain of the union
3834 * piecewise multi-affine expression to its range, with each dimension
3835 * in the range equated to the corresponding affine expression on its cell.
3837 __isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff(
3838 __isl_take isl_union_pw_multi_aff *upma)
3840 isl_space *space;
3841 isl_union_map *umap;
3843 if (!upma)
3844 return NULL;
3846 space = isl_union_pw_multi_aff_get_space(upma);
3847 umap = isl_union_map_empty(space);
3849 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
3850 &map_from_pw_multi_aff, &umap) < 0)
3851 goto error;
3853 isl_union_pw_multi_aff_free(upma);
3854 return umap;
3855 error:
3856 isl_union_pw_multi_aff_free(upma);
3857 isl_union_map_free(umap);
3858 return NULL;
3861 /* Local data for bin_entry and the callback "fn".
3863 struct isl_union_pw_multi_aff_bin_data {
3864 isl_union_pw_multi_aff *upma2;
3865 isl_union_pw_multi_aff *res;
3866 isl_pw_multi_aff *pma;
3867 int (*fn)(void **entry, void *user);
3870 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
3871 * and call data->fn for each isl_pw_multi_aff in data->upma2.
3873 static int bin_entry(void **entry, void *user)
3875 struct isl_union_pw_multi_aff_bin_data *data = user;
3876 isl_pw_multi_aff *pma = *entry;
3878 data->pma = pma;
3879 if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
3880 data->fn, data) < 0)
3881 return -1;
3883 return 0;
3886 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
3887 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
3888 * passed as user field) and the isl_pw_multi_aff from upma2 is available
3889 * as *entry. The callback should adjust data->res if desired.
3891 static __isl_give isl_union_pw_multi_aff *bin_op(
3892 __isl_take isl_union_pw_multi_aff *upma1,
3893 __isl_take isl_union_pw_multi_aff *upma2,
3894 int (*fn)(void **entry, void *user))
3896 isl_space *space;
3897 struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
3899 space = isl_union_pw_multi_aff_get_space(upma2);
3900 upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
3901 space = isl_union_pw_multi_aff_get_space(upma1);
3902 upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
3904 if (!upma1 || !upma2)
3905 goto error;
3907 data.upma2 = upma2;
3908 data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
3909 upma1->table.n);
3910 if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
3911 &bin_entry, &data) < 0)
3912 goto error;
3914 isl_union_pw_multi_aff_free(upma1);
3915 isl_union_pw_multi_aff_free(upma2);
3916 return data.res;
3917 error:
3918 isl_union_pw_multi_aff_free(upma1);
3919 isl_union_pw_multi_aff_free(upma2);
3920 isl_union_pw_multi_aff_free(data.res);
3921 return NULL;
3924 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
3925 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
3927 static __isl_give isl_pw_multi_aff *pw_multi_aff_range_product(
3928 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3930 isl_space *space;
3932 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
3933 isl_pw_multi_aff_get_space(pma2));
3934 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
3935 &isl_multi_aff_range_product);
3938 /* Given two isl_pw_multi_affs A -> B and C -> D,
3939 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
3941 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_product(
3942 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3944 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3945 &pw_multi_aff_range_product);
3948 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
3949 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3951 static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
3952 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3954 isl_space *space;
3956 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
3957 isl_pw_multi_aff_get_space(pma2));
3958 space = isl_space_flatten_range(space);
3959 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
3960 &isl_multi_aff_flat_range_product);
3963 /* Given two isl_pw_multi_affs A -> B and C -> D,
3964 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3966 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
3967 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3969 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3970 &pw_multi_aff_flat_range_product);
3973 /* If data->pma and *entry have the same domain space, then compute
3974 * their flat range product and the result to data->res.
3976 static int flat_range_product_entry(void **entry, void *user)
3978 struct isl_union_pw_multi_aff_bin_data *data = user;
3979 isl_pw_multi_aff *pma2 = *entry;
3981 if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
3982 pma2->dim, isl_dim_in))
3983 return 0;
3985 pma2 = isl_pw_multi_aff_flat_range_product(
3986 isl_pw_multi_aff_copy(data->pma),
3987 isl_pw_multi_aff_copy(pma2));
3989 data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
3991 return 0;
3994 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
3995 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
3997 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
3998 __isl_take isl_union_pw_multi_aff *upma1,
3999 __isl_take isl_union_pw_multi_aff *upma2)
4001 return bin_op(upma1, upma2, &flat_range_product_entry);
4004 /* Replace the affine expressions at position "pos" in "pma" by "pa".
4005 * The parameters are assumed to have been aligned.
4007 * The implementation essentially performs an isl_pw_*_on_shared_domain,
4008 * except that it works on two different isl_pw_* types.
4010 static __isl_give isl_pw_multi_aff *pw_multi_aff_set_pw_aff(
4011 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4012 __isl_take isl_pw_aff *pa)
4014 int i, j, n;
4015 isl_pw_multi_aff *res = NULL;
4017 if (!pma || !pa)
4018 goto error;
4020 if (!isl_space_tuple_match(pma->dim, isl_dim_in, pa->dim, isl_dim_in))
4021 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
4022 "domains don't match", goto error);
4023 if (pos >= isl_pw_multi_aff_dim(pma, isl_dim_out))
4024 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
4025 "index out of bounds", goto error);
4027 n = pma->n * pa->n;
4028 res = isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma), n);
4030 for (i = 0; i < pma->n; ++i) {
4031 for (j = 0; j < pa->n; ++j) {
4032 isl_set *common;
4033 isl_multi_aff *res_ij;
4034 int empty;
4036 common = isl_set_intersect(isl_set_copy(pma->p[i].set),
4037 isl_set_copy(pa->p[j].set));
4038 empty = isl_set_plain_is_empty(common);
4039 if (empty < 0 || empty) {
4040 isl_set_free(common);
4041 if (empty < 0)
4042 goto error;
4043 continue;
4046 res_ij = isl_multi_aff_set_aff(
4047 isl_multi_aff_copy(pma->p[i].maff), pos,
4048 isl_aff_copy(pa->p[j].aff));
4049 res_ij = isl_multi_aff_gist(res_ij,
4050 isl_set_copy(common));
4052 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
4056 isl_pw_multi_aff_free(pma);
4057 isl_pw_aff_free(pa);
4058 return res;
4059 error:
4060 isl_pw_multi_aff_free(pma);
4061 isl_pw_aff_free(pa);
4062 return isl_pw_multi_aff_free(res);
4065 /* Replace the affine expressions at position "pos" in "pma" by "pa".
4067 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4068 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4069 __isl_take isl_pw_aff *pa)
4071 if (!pma || !pa)
4072 goto error;
4073 if (isl_space_match(pma->dim, isl_dim_param, pa->dim, isl_dim_param))
4074 return pw_multi_aff_set_pw_aff(pma, pos, pa);
4075 if (!isl_space_has_named_params(pma->dim) ||
4076 !isl_space_has_named_params(pa->dim))
4077 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
4078 "unaligned unnamed parameters", goto error);
4079 pma = isl_pw_multi_aff_align_params(pma, isl_pw_aff_get_space(pa));
4080 pa = isl_pw_aff_align_params(pa, isl_pw_multi_aff_get_space(pma));
4081 return pw_multi_aff_set_pw_aff(pma, pos, pa);
4082 error:
4083 isl_pw_multi_aff_free(pma);
4084 isl_pw_aff_free(pa);
4085 return NULL;
4088 #undef BASE
4089 #define BASE pw_aff
4091 #include <isl_multi_templ.c>