2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
4 * Copyright 2012-2013 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,
11 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 #include <isl_ctx_private.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/constraint.h>
25 #include <isl_val_private.h>
26 #include <isl_config.h>
31 #include <isl_list_templ.c>
36 #include <isl_list_templ.c>
38 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
39 __isl_take isl_vec *v)
46 aff = isl_calloc_type(v->ctx, struct isl_aff);
56 isl_local_space_free(ls);
61 __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
70 ctx = isl_local_space_get_ctx(ls);
71 if (!isl_local_space_divs_known(ls))
72 isl_die(ctx, isl_error_invalid, "local space has unknown divs",
74 if (!isl_local_space_is_set(ls))
75 isl_die(ctx, isl_error_invalid,
76 "domain of affine expression should be a set",
79 total = isl_local_space_dim(ls, isl_dim_all);
80 v = isl_vec_alloc(ctx, 1 + 1 + total);
81 return isl_aff_alloc_vec(ls, v);
83 isl_local_space_free(ls);
87 __isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
91 aff = isl_aff_alloc(ls);
95 isl_int_set_si(aff->v->el[0], 1);
96 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
101 /* Return a piecewise affine expression defined on the specified domain
102 * that is equal to zero.
104 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(__isl_take isl_local_space *ls)
106 return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls));
109 /* Return an affine expression that is equal to the specified dimension
112 __isl_give isl_aff *isl_aff_var_on_domain(__isl_take isl_local_space *ls,
113 enum isl_dim_type type, unsigned pos)
121 space = isl_local_space_get_space(ls);
124 if (isl_space_is_map(space))
125 isl_die(isl_space_get_ctx(space), isl_error_invalid,
126 "expecting (parameter) set space", goto error);
127 if (pos >= isl_local_space_dim(ls, type))
128 isl_die(isl_space_get_ctx(space), isl_error_invalid,
129 "position out of bounds", goto error);
131 isl_space_free(space);
132 aff = isl_aff_alloc(ls);
136 pos += isl_local_space_offset(aff->ls, type);
138 isl_int_set_si(aff->v->el[0], 1);
139 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
140 isl_int_set_si(aff->v->el[1 + pos], 1);
144 isl_local_space_free(ls);
145 isl_space_free(space);
149 /* Return a piecewise affine expression that is equal to
150 * the specified dimension in "ls".
152 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(__isl_take isl_local_space *ls,
153 enum isl_dim_type type, unsigned pos)
155 return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls, type, pos));
158 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
167 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
172 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
173 isl_vec_copy(aff->v));
176 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
184 return isl_aff_dup(aff);
187 void *isl_aff_free(__isl_take isl_aff *aff)
195 isl_local_space_free(aff->ls);
196 isl_vec_free(aff->v);
203 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
205 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
208 /* Externally, an isl_aff has a map space, but internally, the
209 * ls field corresponds to the domain of that space.
211 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
215 if (type == isl_dim_out)
217 if (type == isl_dim_in)
219 return isl_local_space_dim(aff->ls, type);
222 __isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
224 return aff ? isl_local_space_get_space(aff->ls) : NULL;
227 __isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
232 space = isl_local_space_get_space(aff->ls);
233 space = isl_space_from_domain(space);
234 space = isl_space_add_dims(space, isl_dim_out, 1);
238 __isl_give isl_local_space *isl_aff_get_domain_local_space(
239 __isl_keep isl_aff *aff)
241 return aff ? isl_local_space_copy(aff->ls) : NULL;
244 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
249 ls = isl_local_space_copy(aff->ls);
250 ls = isl_local_space_from_domain(ls);
251 ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
255 /* Externally, an isl_aff has a map space, but internally, the
256 * ls field corresponds to the domain of that space.
258 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
259 enum isl_dim_type type, unsigned pos)
263 if (type == isl_dim_out)
265 if (type == isl_dim_in)
267 return isl_local_space_get_dim_name(aff->ls, type, pos);
270 __isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
271 __isl_take isl_space *dim)
273 aff = isl_aff_cow(aff);
277 aff->ls = isl_local_space_reset_space(aff->ls, dim);
279 return isl_aff_free(aff);
288 /* Reset the space of "aff". This function is called from isl_pw_templ.c
289 * and doesn't know if the space of an element object is represented
290 * directly or through its domain. It therefore passes along both.
292 __isl_give isl_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
293 __isl_take isl_space *space, __isl_take isl_space *domain)
295 isl_space_free(space);
296 return isl_aff_reset_domain_space(aff, domain);
299 /* Reorder the coefficients of the affine expression based
300 * on the given reodering.
301 * The reordering r is assumed to have been extended with the local
304 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
305 __isl_take isl_reordering *r, int n_div)
313 res = isl_vec_alloc(vec->ctx,
314 2 + isl_space_dim(r->dim, isl_dim_all) + n_div);
315 isl_seq_cpy(res->el, vec->el, 2);
316 isl_seq_clr(res->el + 2, res->size - 2);
317 for (i = 0; i < r->len; ++i)
318 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
320 isl_reordering_free(r);
325 isl_reordering_free(r);
329 /* Reorder the dimensions of the domain of "aff" according
330 * to the given reordering.
332 __isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
333 __isl_take isl_reordering *r)
335 aff = isl_aff_cow(aff);
339 r = isl_reordering_extend(r, aff->ls->div->n_row);
340 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
341 aff->ls->div->n_row);
342 aff->ls = isl_local_space_realign(aff->ls, r);
344 if (!aff->v || !aff->ls)
345 return isl_aff_free(aff);
350 isl_reordering_free(r);
354 __isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
355 __isl_take isl_space *model)
360 if (!isl_space_match(aff->ls->dim, isl_dim_param,
361 model, isl_dim_param)) {
364 model = isl_space_drop_dims(model, isl_dim_in,
365 0, isl_space_dim(model, isl_dim_in));
366 model = isl_space_drop_dims(model, isl_dim_out,
367 0, isl_space_dim(model, isl_dim_out));
368 exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
369 exp = isl_reordering_extend_space(exp,
370 isl_aff_get_domain_space(aff));
371 aff = isl_aff_realign_domain(aff, exp);
374 isl_space_free(model);
377 isl_space_free(model);
382 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
387 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
390 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
397 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
398 if (equal < 0 || !equal)
401 return isl_vec_is_equal(aff1->v, aff2->v);
404 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
408 isl_int_set(*v, aff->v->el[0]);
412 /* Return the common denominator of "aff".
414 __isl_give isl_val *isl_aff_get_denominator_val(__isl_keep isl_aff *aff)
421 ctx = isl_aff_get_ctx(aff);
422 return isl_val_int_from_isl_int(ctx, aff->v->el[0]);
425 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
429 isl_int_set(*v, aff->v->el[1]);
433 /* Return the constant term of "aff".
435 __isl_give isl_val *isl_aff_get_constant_val(__isl_keep isl_aff *aff)
443 ctx = isl_aff_get_ctx(aff);
444 v = isl_val_rat_from_isl_int(ctx, aff->v->el[1], aff->v->el[0]);
445 return isl_val_normalize(v);
448 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
449 enum isl_dim_type type, int pos, isl_int *v)
454 if (type == isl_dim_out)
455 isl_die(aff->v->ctx, isl_error_invalid,
456 "output/set dimension does not have a coefficient",
458 if (type == isl_dim_in)
461 if (pos >= isl_local_space_dim(aff->ls, type))
462 isl_die(aff->v->ctx, isl_error_invalid,
463 "position out of bounds", return -1);
465 pos += isl_local_space_offset(aff->ls, type);
466 isl_int_set(*v, aff->v->el[1 + pos]);
471 /* Return the coefficient of the variable of type "type" at position "pos"
474 __isl_give isl_val *isl_aff_get_coefficient_val(__isl_keep isl_aff *aff,
475 enum isl_dim_type type, int pos)
483 ctx = isl_aff_get_ctx(aff);
484 if (type == isl_dim_out)
485 isl_die(ctx, isl_error_invalid,
486 "output/set dimension does not have a coefficient",
488 if (type == isl_dim_in)
491 if (pos >= isl_local_space_dim(aff->ls, type))
492 isl_die(ctx, isl_error_invalid,
493 "position out of bounds", return NULL);
495 pos += isl_local_space_offset(aff->ls, type);
496 v = isl_val_rat_from_isl_int(ctx, aff->v->el[1 + pos], aff->v->el[0]);
497 return isl_val_normalize(v);
500 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
502 aff = isl_aff_cow(aff);
506 aff->v = isl_vec_cow(aff->v);
508 return isl_aff_free(aff);
510 isl_int_set(aff->v->el[0], v);
515 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
517 aff = isl_aff_cow(aff);
521 aff->v = isl_vec_cow(aff->v);
523 return isl_aff_free(aff);
525 isl_int_set(aff->v->el[1], v);
530 /* Replace the constant term of "aff" by "v".
532 __isl_give isl_aff *isl_aff_set_constant_val(__isl_take isl_aff *aff,
533 __isl_take isl_val *v)
538 if (!isl_val_is_rat(v))
539 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
540 "expecting rational value", goto error);
542 if (isl_int_eq(aff->v->el[1], v->n) &&
543 isl_int_eq(aff->v->el[0], v->d)) {
548 aff = isl_aff_cow(aff);
551 aff->v = isl_vec_cow(aff->v);
555 if (isl_int_eq(aff->v->el[0], v->d)) {
556 isl_int_set(aff->v->el[1], v->n);
557 } else if (isl_int_is_one(v->d)) {
558 isl_int_mul(aff->v->el[1], aff->v->el[0], v->n);
560 isl_seq_scale(aff->v->el + 1,
561 aff->v->el + 1, v->d, aff->v->size - 1);
562 isl_int_mul(aff->v->el[1], aff->v->el[0], v->n);
563 isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
564 aff->v = isl_vec_normalize(aff->v);
577 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
579 if (isl_int_is_zero(v))
582 aff = isl_aff_cow(aff);
586 aff->v = isl_vec_cow(aff->v);
588 return isl_aff_free(aff);
590 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
595 /* Add "v" to the constant term of "aff".
597 __isl_give isl_aff *isl_aff_add_constant_val(__isl_take isl_aff *aff,
598 __isl_take isl_val *v)
603 if (isl_val_is_zero(v)) {
608 if (!isl_val_is_rat(v))
609 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
610 "expecting rational value", goto error);
612 aff = isl_aff_cow(aff);
616 aff->v = isl_vec_cow(aff->v);
620 if (isl_int_is_one(v->d)) {
621 isl_int_addmul(aff->v->el[1], aff->v->el[0], v->n);
622 } else if (isl_int_eq(aff->v->el[0], v->d)) {
623 isl_int_add(aff->v->el[1], aff->v->el[1], v->n);
624 aff->v = isl_vec_normalize(aff->v);
628 isl_seq_scale(aff->v->el + 1,
629 aff->v->el + 1, v->d, aff->v->size - 1);
630 isl_int_addmul(aff->v->el[1], aff->v->el[0], v->n);
631 isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
632 aff->v = isl_vec_normalize(aff->v);
645 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
650 isl_int_set_si(t, v);
651 aff = isl_aff_add_constant(aff, t);
657 /* Add "v" to the numerator of the constant term of "aff".
659 __isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v)
661 if (isl_int_is_zero(v))
664 aff = isl_aff_cow(aff);
668 aff->v = isl_vec_cow(aff->v);
670 return isl_aff_free(aff);
672 isl_int_add(aff->v->el[1], aff->v->el[1], v);
677 /* Add "v" to the numerator of the constant term of "aff".
679 __isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v)
687 isl_int_set_si(t, v);
688 aff = isl_aff_add_constant_num(aff, t);
694 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
696 aff = isl_aff_cow(aff);
700 aff->v = isl_vec_cow(aff->v);
702 return isl_aff_free(aff);
704 isl_int_set_si(aff->v->el[1], v);
709 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
710 enum isl_dim_type type, int pos, isl_int v)
715 if (type == isl_dim_out)
716 isl_die(aff->v->ctx, isl_error_invalid,
717 "output/set dimension does not have a coefficient",
718 return isl_aff_free(aff));
719 if (type == isl_dim_in)
722 if (pos >= isl_local_space_dim(aff->ls, type))
723 isl_die(aff->v->ctx, isl_error_invalid,
724 "position out of bounds", return isl_aff_free(aff));
726 aff = isl_aff_cow(aff);
730 aff->v = isl_vec_cow(aff->v);
732 return isl_aff_free(aff);
734 pos += isl_local_space_offset(aff->ls, type);
735 isl_int_set(aff->v->el[1 + pos], v);
740 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
741 enum isl_dim_type type, int pos, int v)
746 if (type == isl_dim_out)
747 isl_die(aff->v->ctx, isl_error_invalid,
748 "output/set dimension does not have a coefficient",
749 return isl_aff_free(aff));
750 if (type == isl_dim_in)
753 if (pos >= isl_local_space_dim(aff->ls, type))
754 isl_die(aff->v->ctx, isl_error_invalid,
755 "position out of bounds", return isl_aff_free(aff));
757 aff = isl_aff_cow(aff);
761 aff->v = isl_vec_cow(aff->v);
763 return isl_aff_free(aff);
765 pos += isl_local_space_offset(aff->ls, type);
766 isl_int_set_si(aff->v->el[1 + pos], v);
771 /* Replace the coefficient of the variable of type "type" at position "pos"
774 __isl_give isl_aff *isl_aff_set_coefficient_val(__isl_take isl_aff *aff,
775 enum isl_dim_type type, int pos, __isl_take isl_val *v)
780 if (type == isl_dim_out)
781 isl_die(aff->v->ctx, isl_error_invalid,
782 "output/set dimension does not have a coefficient",
784 if (type == isl_dim_in)
787 if (pos >= isl_local_space_dim(aff->ls, type))
788 isl_die(aff->v->ctx, isl_error_invalid,
789 "position out of bounds", goto error);
791 if (!isl_val_is_rat(v))
792 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
793 "expecting rational value", goto error);
795 pos += isl_local_space_offset(aff->ls, type);
796 if (isl_int_eq(aff->v->el[1 + pos], v->n) &&
797 isl_int_eq(aff->v->el[0], v->d)) {
802 aff = isl_aff_cow(aff);
805 aff->v = isl_vec_cow(aff->v);
809 if (isl_int_eq(aff->v->el[0], v->d)) {
810 isl_int_set(aff->v->el[1 + pos], v->n);
811 } else if (isl_int_is_one(v->d)) {
812 isl_int_mul(aff->v->el[1 + pos], aff->v->el[0], v->n);
814 isl_seq_scale(aff->v->el + 1,
815 aff->v->el + 1, v->d, aff->v->size - 1);
816 isl_int_mul(aff->v->el[1 + pos], aff->v->el[0], v->n);
817 isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
818 aff->v = isl_vec_normalize(aff->v);
831 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
832 enum isl_dim_type type, int pos, isl_int v)
837 if (type == isl_dim_out)
838 isl_die(aff->v->ctx, isl_error_invalid,
839 "output/set dimension does not have a coefficient",
840 return isl_aff_free(aff));
841 if (type == isl_dim_in)
844 if (pos >= isl_local_space_dim(aff->ls, type))
845 isl_die(aff->v->ctx, isl_error_invalid,
846 "position out of bounds", return isl_aff_free(aff));
848 aff = isl_aff_cow(aff);
852 aff->v = isl_vec_cow(aff->v);
854 return isl_aff_free(aff);
856 pos += isl_local_space_offset(aff->ls, type);
857 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
862 /* Add "v" to the coefficient of the variable of type "type"
863 * at position "pos" of "aff".
865 __isl_give isl_aff *isl_aff_add_coefficient_val(__isl_take isl_aff *aff,
866 enum isl_dim_type type, int pos, __isl_take isl_val *v)
871 if (isl_val_is_zero(v)) {
876 if (type == isl_dim_out)
877 isl_die(aff->v->ctx, isl_error_invalid,
878 "output/set dimension does not have a coefficient",
880 if (type == isl_dim_in)
883 if (pos >= isl_local_space_dim(aff->ls, type))
884 isl_die(aff->v->ctx, isl_error_invalid,
885 "position out of bounds", goto error);
887 if (!isl_val_is_rat(v))
888 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
889 "expecting rational value", goto error);
891 aff = isl_aff_cow(aff);
895 aff->v = isl_vec_cow(aff->v);
899 pos += isl_local_space_offset(aff->ls, type);
900 if (isl_int_is_one(v->d)) {
901 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v->n);
902 } else if (isl_int_eq(aff->v->el[0], v->d)) {
903 isl_int_add(aff->v->el[1 + pos], aff->v->el[1 + pos], v->n);
904 aff->v = isl_vec_normalize(aff->v);
908 isl_seq_scale(aff->v->el + 1,
909 aff->v->el + 1, v->d, aff->v->size - 1);
910 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v->n);
911 isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
912 aff->v = isl_vec_normalize(aff->v);
925 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
926 enum isl_dim_type type, int pos, int v)
931 isl_int_set_si(t, v);
932 aff = isl_aff_add_coefficient(aff, type, pos, t);
938 __isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
943 return isl_local_space_get_div(aff->ls, pos);
946 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
948 aff = isl_aff_cow(aff);
951 aff->v = isl_vec_cow(aff->v);
953 return isl_aff_free(aff);
955 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
960 /* Remove divs from the local space that do not appear in the affine
962 * We currently only remove divs at the end.
963 * Some intermediate divs may also not appear directly in the affine
964 * expression, but we would also need to check that no other divs are
965 * defined in terms of them.
967 __isl_give isl_aff *isl_aff_remove_unused_divs( __isl_take isl_aff *aff)
976 n = isl_local_space_dim(aff->ls, isl_dim_div);
977 off = isl_local_space_offset(aff->ls, isl_dim_div);
979 pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
983 aff = isl_aff_cow(aff);
987 aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
988 aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
989 if (!aff->ls || !aff->v)
990 return isl_aff_free(aff);
995 /* Given two affine expressions "p" of length p_len (including the
996 * denominator and the constant term) and "subs" of length subs_len,
997 * plug in "subs" for the variable at position "pos".
998 * The variables of "subs" and "p" are assumed to match up to subs_len,
999 * but "p" may have additional variables.
1000 * "v" is an initialized isl_int that can be used internally.
1002 * In particular, if "p" represents the expression
1006 * with i the variable at position "pos" and "subs" represents the expression
1010 * then the result represents the expression
1015 void isl_seq_substitute(isl_int *p, int pos, isl_int *subs,
1016 int p_len, int subs_len, isl_int v)
1018 isl_int_set(v, p[1 + pos]);
1019 isl_int_set_si(p[1 + pos], 0);
1020 isl_seq_combine(p + 1, subs[0], p + 1, v, subs + 1, subs_len - 1);
1021 isl_seq_scale(p + subs_len, p + subs_len, subs[0], p_len - subs_len);
1022 isl_int_mul(p[0], p[0], subs[0]);
1025 /* Look for any divs in the aff->ls with a denominator equal to one
1026 * and plug them into the affine expression and any subsequent divs
1027 * that may reference the div.
1029 static __isl_give isl_aff *plug_in_integral_divs(__isl_take isl_aff *aff)
1035 isl_local_space *ls;
1041 n = isl_local_space_dim(aff->ls, isl_dim_div);
1043 for (i = 0; i < n; ++i) {
1044 if (!isl_int_is_one(aff->ls->div->row[i][0]))
1046 ls = isl_local_space_copy(aff->ls);
1047 ls = isl_local_space_substitute_seq(ls, isl_dim_div, i,
1048 aff->ls->div->row[i], len, i + 1, n - (i + 1));
1049 vec = isl_vec_copy(aff->v);
1050 vec = isl_vec_cow(vec);
1056 pos = isl_local_space_offset(aff->ls, isl_dim_div) + i;
1057 isl_seq_substitute(vec->el, pos, aff->ls->div->row[i],
1062 isl_vec_free(aff->v);
1064 isl_local_space_free(aff->ls);
1071 isl_local_space_free(ls);
1072 return isl_aff_free(aff);
1075 /* Look for any divs j that appear with a unit coefficient inside
1076 * the definitions of other divs i and plug them into the definitions
1079 * In particular, an expression of the form
1081 * floor((f(..) + floor(g(..)/n))/m)
1085 * floor((n * f(..) + g(..))/(n * m))
1087 * This simplification is correct because we can move the expression
1088 * f(..) into the inner floor in the original expression to obtain
1090 * floor(floor((n * f(..) + g(..))/n)/m)
1092 * from which we can derive the simplified expression.
1094 static __isl_give isl_aff *plug_in_unit_divs(__isl_take isl_aff *aff)
1102 n = isl_local_space_dim(aff->ls, isl_dim_div);
1103 off = isl_local_space_offset(aff->ls, isl_dim_div);
1104 for (i = 1; i < n; ++i) {
1105 for (j = 0; j < i; ++j) {
1106 if (!isl_int_is_one(aff->ls->div->row[i][1 + off + j]))
1108 aff->ls = isl_local_space_substitute_seq(aff->ls,
1109 isl_dim_div, j, aff->ls->div->row[j],
1110 aff->v->size, i, 1);
1112 return isl_aff_free(aff);
1119 /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
1121 * Even though this function is only called on isl_affs with a single
1122 * reference, we are careful to only change aff->v and aff->ls together.
1124 static __isl_give isl_aff *swap_div(__isl_take isl_aff *aff, int a, int b)
1126 unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
1127 isl_local_space *ls;
1130 ls = isl_local_space_copy(aff->ls);
1131 ls = isl_local_space_swap_div(ls, a, b);
1132 v = isl_vec_copy(aff->v);
1137 isl_int_swap(v->el[1 + off + a], v->el[1 + off + b]);
1138 isl_vec_free(aff->v);
1140 isl_local_space_free(aff->ls);
1146 isl_local_space_free(ls);
1147 return isl_aff_free(aff);
1150 /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
1152 * We currently do not actually remove div "b", but simply add its
1153 * coefficient to that of "a" and then zero it out.
1155 static __isl_give isl_aff *merge_divs(__isl_take isl_aff *aff, int a, int b)
1157 unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
1159 if (isl_int_is_zero(aff->v->el[1 + off + b]))
1162 aff->v = isl_vec_cow(aff->v);
1164 return isl_aff_free(aff);
1166 isl_int_add(aff->v->el[1 + off + a],
1167 aff->v->el[1 + off + a], aff->v->el[1 + off + b]);
1168 isl_int_set_si(aff->v->el[1 + off + b], 0);
1173 /* Sort the divs in the local space of "aff" according to
1174 * the comparison function "cmp_row" in isl_local_space.c,
1175 * combining the coefficients of identical divs.
1177 * Reordering divs does not change the semantics of "aff",
1178 * so there is no need to call isl_aff_cow.
1179 * Moreover, this function is currently only called on isl_affs
1180 * with a single reference.
1182 static __isl_give isl_aff *sort_divs(__isl_take isl_aff *aff)
1190 off = isl_local_space_offset(aff->ls, isl_dim_div);
1191 n = isl_aff_dim(aff, isl_dim_div);
1192 for (i = 1; i < n; ++i) {
1193 for (j = i - 1; j >= 0; --j) {
1194 int cmp = isl_mat_cmp_div(aff->ls->div, j, j + 1);
1198 aff = merge_divs(aff, j, j + 1);
1200 aff = swap_div(aff, j, j + 1);
1209 /* Normalize the representation of "aff".
1211 * This function should only be called of "new" isl_affs, i.e.,
1212 * with only a single reference. We therefore do not need to
1213 * worry about affecting other instances.
1215 __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
1219 aff->v = isl_vec_normalize(aff->v);
1221 return isl_aff_free(aff);
1222 aff = plug_in_integral_divs(aff);
1223 aff = plug_in_unit_divs(aff);
1224 aff = sort_divs(aff);
1225 aff = isl_aff_remove_unused_divs(aff);
1229 /* Given f, return floor(f).
1230 * If f is an integer expression, then just return f.
1231 * If f is a constant, then return the constant floor(f).
1232 * Otherwise, if f = g/m, write g = q m + r,
1233 * create a new div d = [r/m] and return the expression q + d.
1234 * The coefficients in r are taken to lie between -m/2 and m/2.
1236 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
1246 if (isl_int_is_one(aff->v->el[0]))
1249 aff = isl_aff_cow(aff);
1253 aff->v = isl_vec_cow(aff->v);
1255 return isl_aff_free(aff);
1257 if (isl_aff_is_cst(aff)) {
1258 isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
1259 isl_int_set_si(aff->v->el[0], 1);
1263 div = isl_vec_copy(aff->v);
1264 div = isl_vec_cow(div);
1266 return isl_aff_free(aff);
1268 ctx = isl_aff_get_ctx(aff);
1269 isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
1270 for (i = 1; i < aff->v->size; ++i) {
1271 isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
1272 isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
1273 if (isl_int_gt(div->el[i], aff->v->el[0])) {
1274 isl_int_sub(div->el[i], div->el[i], div->el[0]);
1275 isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
1279 aff->ls = isl_local_space_add_div(aff->ls, div);
1281 return isl_aff_free(aff);
1283 size = aff->v->size;
1284 aff->v = isl_vec_extend(aff->v, size + 1);
1286 return isl_aff_free(aff);
1287 isl_int_set_si(aff->v->el[0], 1);
1288 isl_int_set_si(aff->v->el[size], 1);
1290 aff = isl_aff_normalize(aff);
1297 * aff mod m = aff - m * floor(aff/m)
1299 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
1303 res = isl_aff_copy(aff);
1304 aff = isl_aff_scale_down(aff, m);
1305 aff = isl_aff_floor(aff);
1306 aff = isl_aff_scale(aff, m);
1307 res = isl_aff_sub(res, aff);
1314 * aff mod m = aff - m * floor(aff/m)
1316 * with m an integer value.
1318 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
1319 __isl_take isl_val *m)
1326 if (!isl_val_is_int(m))
1327 isl_die(isl_val_get_ctx(m), isl_error_invalid,
1328 "expecting integer modulo", goto error);
1330 res = isl_aff_copy(aff);
1331 aff = isl_aff_scale_down_val(aff, isl_val_copy(m));
1332 aff = isl_aff_floor(aff);
1333 aff = isl_aff_scale_val(aff, m);
1334 res = isl_aff_sub(res, aff);
1345 * pwaff mod m = pwaff - m * floor(pwaff/m)
1347 __isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
1351 res = isl_pw_aff_copy(pwaff);
1352 pwaff = isl_pw_aff_scale_down(pwaff, m);
1353 pwaff = isl_pw_aff_floor(pwaff);
1354 pwaff = isl_pw_aff_scale(pwaff, m);
1355 res = isl_pw_aff_sub(res, pwaff);
1360 /* Given f, return ceil(f).
1361 * If f is an integer expression, then just return f.
1362 * Otherwise, let f be the expression
1368 * floor((e + m - 1)/m)
1370 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
1375 if (isl_int_is_one(aff->v->el[0]))
1378 aff = isl_aff_cow(aff);
1381 aff->v = isl_vec_cow(aff->v);
1383 return isl_aff_free(aff);
1385 isl_int_add(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
1386 isl_int_sub_ui(aff->v->el[1], aff->v->el[1], 1);
1387 aff = isl_aff_floor(aff);
1392 /* Apply the expansion computed by isl_merge_divs.
1393 * The expansion itself is given by "exp" while the resulting
1394 * list of divs is given by "div".
1396 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
1397 __isl_take isl_mat *div, int *exp)
1404 aff = isl_aff_cow(aff);
1408 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1409 new_n_div = isl_mat_rows(div);
1410 if (new_n_div < old_n_div)
1411 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
1412 "not an expansion", goto error);
1414 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
1418 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
1420 for (i = new_n_div - 1; i >= 0; --i) {
1421 if (j >= 0 && exp[j] == i) {
1423 isl_int_swap(aff->v->el[offset + i],
1424 aff->v->el[offset + j]);
1427 isl_int_set_si(aff->v->el[offset + i], 0);
1430 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
1441 /* Add two affine expressions that live in the same local space.
1443 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
1444 __isl_take isl_aff *aff2)
1448 aff1 = isl_aff_cow(aff1);
1452 aff1->v = isl_vec_cow(aff1->v);
1458 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
1459 isl_int_divexact(f, aff2->v->el[0], gcd);
1460 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
1461 isl_int_divexact(f, aff1->v->el[0], gcd);
1462 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
1463 isl_int_divexact(f, aff2->v->el[0], gcd);
1464 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
1476 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
1477 __isl_take isl_aff *aff2)
1487 ctx = isl_aff_get_ctx(aff1);
1488 if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
1489 isl_die(ctx, isl_error_invalid,
1490 "spaces don't match", goto error);
1492 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
1493 return add_expanded(aff1, aff2);
1495 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
1496 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
1500 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
1501 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
1502 aff2 = isl_aff_expand_divs(aff2, div, exp2);
1506 return add_expanded(aff1, aff2);
1515 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
1516 __isl_take isl_aff *aff2)
1518 return isl_aff_add(aff1, isl_aff_neg(aff2));
1521 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
1525 if (isl_int_is_one(f))
1528 aff = isl_aff_cow(aff);
1531 aff->v = isl_vec_cow(aff->v);
1533 return isl_aff_free(aff);
1535 if (isl_int_is_pos(f) && isl_int_is_divisible_by(aff->v->el[0], f)) {
1536 isl_int_divexact(aff->v->el[0], aff->v->el[0], f);
1541 isl_int_gcd(gcd, aff->v->el[0], f);
1542 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
1543 isl_int_divexact(gcd, f, gcd);
1544 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
1550 /* Multiple "aff" by "v".
1552 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
1553 __isl_take isl_val *v)
1558 if (isl_val_is_one(v)) {
1563 if (!isl_val_is_rat(v))
1564 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1565 "expecting rational factor", goto error);
1567 aff = isl_aff_scale(aff, v->n);
1568 aff = isl_aff_scale_down(aff, v->d);
1578 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
1582 if (isl_int_is_one(f))
1585 aff = isl_aff_cow(aff);
1589 if (isl_int_is_zero(f))
1590 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1591 "cannot scale down by zero", return isl_aff_free(aff));
1593 aff->v = isl_vec_cow(aff->v);
1595 return isl_aff_free(aff);
1598 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
1599 isl_int_gcd(gcd, gcd, f);
1600 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
1601 isl_int_divexact(gcd, f, gcd);
1602 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
1608 /* Divide "aff" by "v".
1610 __isl_give isl_aff *isl_aff_scale_down_val(__isl_take isl_aff *aff,
1611 __isl_take isl_val *v)
1616 if (isl_val_is_one(v)) {
1621 if (!isl_val_is_rat(v))
1622 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1623 "expecting rational factor", goto error);
1624 if (!isl_val_is_pos(v))
1625 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1626 "factor needs to be positive", goto error);
1628 aff = isl_aff_scale(aff, v->d);
1629 aff = isl_aff_scale_down(aff, v->n);
1639 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
1647 isl_int_set_ui(v, f);
1648 aff = isl_aff_scale_down(aff, v);
1654 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
1655 enum isl_dim_type type, unsigned pos, const char *s)
1657 aff = isl_aff_cow(aff);
1660 if (type == isl_dim_out)
1661 isl_die(aff->v->ctx, isl_error_invalid,
1662 "cannot set name of output/set dimension",
1663 return isl_aff_free(aff));
1664 if (type == isl_dim_in)
1666 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
1668 return isl_aff_free(aff);
1673 __isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
1674 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
1676 aff = isl_aff_cow(aff);
1678 return isl_id_free(id);
1679 if (type == isl_dim_out)
1680 isl_die(aff->v->ctx, isl_error_invalid,
1681 "cannot set name of output/set dimension",
1683 if (type == isl_dim_in)
1685 aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
1687 return isl_aff_free(aff);
1696 /* Exploit the equalities in "eq" to simplify the affine expression
1697 * and the expressions of the integer divisions in the local space.
1698 * The integer divisions in this local space are assumed to appear
1699 * as regular dimensions in "eq".
1701 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
1702 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1710 if (eq->n_eq == 0) {
1711 isl_basic_set_free(eq);
1715 aff = isl_aff_cow(aff);
1719 aff->ls = isl_local_space_substitute_equalities(aff->ls,
1720 isl_basic_set_copy(eq));
1721 aff->v = isl_vec_cow(aff->v);
1722 if (!aff->ls || !aff->v)
1725 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
1727 for (i = 0; i < eq->n_eq; ++i) {
1728 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
1729 if (j < 0 || j == 0 || j >= total)
1732 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
1736 isl_basic_set_free(eq);
1737 aff = isl_aff_normalize(aff);
1740 isl_basic_set_free(eq);
1745 /* Exploit the equalities in "eq" to simplify the affine expression
1746 * and the expressions of the integer divisions in the local space.
1748 static __isl_give isl_aff *isl_aff_substitute_equalities(
1749 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
1755 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1757 eq = isl_basic_set_add_dims(eq, isl_dim_set, n_div);
1758 return isl_aff_substitute_equalities_lifted(aff, eq);
1760 isl_basic_set_free(eq);
1765 /* Look for equalities among the variables shared by context and aff
1766 * and the integer divisions of aff, if any.
1767 * The equalities are then used to eliminate coefficients and/or integer
1768 * divisions from aff.
1770 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
1771 __isl_take isl_set *context)
1773 isl_basic_set *hull;
1778 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1780 isl_basic_set *bset;
1781 isl_local_space *ls;
1782 context = isl_set_add_dims(context, isl_dim_set, n_div);
1783 ls = isl_aff_get_domain_local_space(aff);
1784 bset = isl_basic_set_from_local_space(ls);
1785 bset = isl_basic_set_lift(bset);
1786 bset = isl_basic_set_flatten(bset);
1787 context = isl_set_intersect(context,
1788 isl_set_from_basic_set(bset));
1791 hull = isl_set_affine_hull(context);
1792 return isl_aff_substitute_equalities_lifted(aff, hull);
1795 isl_set_free(context);
1799 __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
1800 __isl_take isl_set *context)
1802 isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
1803 dom_context = isl_set_intersect_params(dom_context, context);
1804 return isl_aff_gist(aff, dom_context);
1807 /* Return a basic set containing those elements in the space
1808 * of aff where it is non-negative.
1809 * If "rational" is set, then return a rational basic set.
1811 static __isl_give isl_basic_set *aff_nonneg_basic_set(
1812 __isl_take isl_aff *aff, int rational)
1814 isl_constraint *ineq;
1815 isl_basic_set *bset;
1817 ineq = isl_inequality_from_aff(aff);
1819 bset = isl_basic_set_from_constraint(ineq);
1821 bset = isl_basic_set_set_rational(bset);
1822 bset = isl_basic_set_simplify(bset);
1826 /* Return a basic set containing those elements in the space
1827 * of aff where it is non-negative.
1829 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
1831 return aff_nonneg_basic_set(aff, 0);
1834 /* Return a basic set containing those elements in the domain space
1835 * of aff where it is negative.
1837 __isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
1839 aff = isl_aff_neg(aff);
1840 aff = isl_aff_add_constant_num_si(aff, -1);
1841 return isl_aff_nonneg_basic_set(aff);
1844 /* Return a basic set containing those elements in the space
1845 * of aff where it is zero.
1846 * If "rational" is set, then return a rational basic set.
1848 static __isl_give isl_basic_set *aff_zero_basic_set(__isl_take isl_aff *aff,
1851 isl_constraint *ineq;
1852 isl_basic_set *bset;
1854 ineq = isl_equality_from_aff(aff);
1856 bset = isl_basic_set_from_constraint(ineq);
1858 bset = isl_basic_set_set_rational(bset);
1859 bset = isl_basic_set_simplify(bset);
1863 /* Return a basic set containing those elements in the space
1864 * of aff where it is zero.
1866 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
1868 return aff_zero_basic_set(aff, 0);
1871 /* Return a basic set containing those elements in the shared space
1872 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1874 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
1875 __isl_take isl_aff *aff2)
1877 aff1 = isl_aff_sub(aff1, aff2);
1879 return isl_aff_nonneg_basic_set(aff1);
1882 /* Return a basic set containing those elements in the shared space
1883 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1885 __isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
1886 __isl_take isl_aff *aff2)
1888 return isl_aff_ge_basic_set(aff2, aff1);
1891 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
1892 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
1894 aff1 = isl_aff_add(aff1, aff2);
1895 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
1899 int isl_aff_is_empty(__isl_keep isl_aff *aff)
1907 /* Check whether the given affine expression has non-zero coefficient
1908 * for any dimension in the given range or if any of these dimensions
1909 * appear with non-zero coefficients in any of the integer divisions
1910 * involved in the affine expression.
1912 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
1913 enum isl_dim_type type, unsigned first, unsigned n)
1925 ctx = isl_aff_get_ctx(aff);
1926 if (first + n > isl_aff_dim(aff, type))
1927 isl_die(ctx, isl_error_invalid,
1928 "range out of bounds", return -1);
1930 active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
1934 first += isl_local_space_offset(aff->ls, type) - 1;
1935 for (i = 0; i < n; ++i)
1936 if (active[first + i]) {
1949 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
1950 enum isl_dim_type type, unsigned first, unsigned n)
1956 if (type == isl_dim_out)
1957 isl_die(aff->v->ctx, isl_error_invalid,
1958 "cannot drop output/set dimension",
1959 return isl_aff_free(aff));
1960 if (type == isl_dim_in)
1962 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1965 ctx = isl_aff_get_ctx(aff);
1966 if (first + n > isl_local_space_dim(aff->ls, type))
1967 isl_die(ctx, isl_error_invalid, "range out of bounds",
1968 return isl_aff_free(aff));
1970 aff = isl_aff_cow(aff);
1974 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
1976 return isl_aff_free(aff);
1978 first += 1 + isl_local_space_offset(aff->ls, type);
1979 aff->v = isl_vec_drop_els(aff->v, first, n);
1981 return isl_aff_free(aff);
1986 /* Project the domain of the affine expression onto its parameter space.
1987 * The affine expression may not involve any of the domain dimensions.
1989 __isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
1995 n = isl_aff_dim(aff, isl_dim_in);
1996 involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
1998 return isl_aff_free(aff);
2000 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
2001 "affine expression involves some of the domain dimensions",
2002 return isl_aff_free(aff));
2003 aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
2004 space = isl_aff_get_domain_space(aff);
2005 space = isl_space_params(space);
2006 aff = isl_aff_reset_domain_space(aff, space);
2010 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
2011 enum isl_dim_type type, unsigned first, unsigned n)
2017 if (type == isl_dim_out)
2018 isl_die(aff->v->ctx, isl_error_invalid,
2019 "cannot insert output/set dimensions",
2020 return isl_aff_free(aff));
2021 if (type == isl_dim_in)
2023 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
2026 ctx = isl_aff_get_ctx(aff);
2027 if (first > isl_local_space_dim(aff->ls, type))
2028 isl_die(ctx, isl_error_invalid, "position out of bounds",
2029 return isl_aff_free(aff));
2031 aff = isl_aff_cow(aff);
2035 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
2037 return isl_aff_free(aff);
2039 first += 1 + isl_local_space_offset(aff->ls, type);
2040 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
2042 return isl_aff_free(aff);
2047 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
2048 enum isl_dim_type type, unsigned n)
2052 pos = isl_aff_dim(aff, type);
2054 return isl_aff_insert_dims(aff, type, pos, n);
2057 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
2058 enum isl_dim_type type, unsigned n)
2062 pos = isl_pw_aff_dim(pwaff, type);
2064 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
2067 __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
2069 isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
2070 return isl_pw_aff_alloc(dom, aff);
2074 #define PW isl_pw_aff
2078 #define EL_IS_ZERO is_empty
2082 #define IS_ZERO is_empty
2085 #undef DEFAULT_IS_ZERO
2086 #define DEFAULT_IS_ZERO 0
2090 #define NO_MOVE_DIMS
2094 #include <isl_pw_templ.c>
2096 static __isl_give isl_set *align_params_pw_pw_set_and(
2097 __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
2098 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
2099 __isl_take isl_pw_aff *pwaff2))
2101 if (!pwaff1 || !pwaff2)
2103 if (isl_space_match(pwaff1->dim, isl_dim_param,
2104 pwaff2->dim, isl_dim_param))
2105 return fn(pwaff1, pwaff2);
2106 if (!isl_space_has_named_params(pwaff1->dim) ||
2107 !isl_space_has_named_params(pwaff2->dim))
2108 isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
2109 "unaligned unnamed parameters", goto error);
2110 pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
2111 pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
2112 return fn(pwaff1, pwaff2);
2114 isl_pw_aff_free(pwaff1);
2115 isl_pw_aff_free(pwaff2);
2119 /* Compute a piecewise quasi-affine expression with a domain that
2120 * is the union of those of pwaff1 and pwaff2 and such that on each
2121 * cell, the quasi-affine expression is the better (according to cmp)
2122 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
2123 * is defined on a given cell, then the associated expression
2124 * is the defined one.
2126 static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
2127 __isl_take isl_pw_aff *pwaff2,
2128 __isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
2129 __isl_take isl_aff *aff2))
2136 if (!pwaff1 || !pwaff2)
2139 ctx = isl_space_get_ctx(pwaff1->dim);
2140 if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
2141 isl_die(ctx, isl_error_invalid,
2142 "arguments should live in same space", goto error);
2144 if (isl_pw_aff_is_empty(pwaff1)) {
2145 isl_pw_aff_free(pwaff1);
2149 if (isl_pw_aff_is_empty(pwaff2)) {
2150 isl_pw_aff_free(pwaff2);
2154 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
2155 res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
2157 for (i = 0; i < pwaff1->n; ++i) {
2158 set = isl_set_copy(pwaff1->p[i].set);
2159 for (j = 0; j < pwaff2->n; ++j) {
2160 struct isl_set *common;
2163 common = isl_set_intersect(
2164 isl_set_copy(pwaff1->p[i].set),
2165 isl_set_copy(pwaff2->p[j].set));
2166 better = isl_set_from_basic_set(cmp(
2167 isl_aff_copy(pwaff2->p[j].aff),
2168 isl_aff_copy(pwaff1->p[i].aff)));
2169 better = isl_set_intersect(common, better);
2170 if (isl_set_plain_is_empty(better)) {
2171 isl_set_free(better);
2174 set = isl_set_subtract(set, isl_set_copy(better));
2176 res = isl_pw_aff_add_piece(res, better,
2177 isl_aff_copy(pwaff2->p[j].aff));
2179 res = isl_pw_aff_add_piece(res, set,
2180 isl_aff_copy(pwaff1->p[i].aff));
2183 for (j = 0; j < pwaff2->n; ++j) {
2184 set = isl_set_copy(pwaff2->p[j].set);
2185 for (i = 0; i < pwaff1->n; ++i)
2186 set = isl_set_subtract(set,
2187 isl_set_copy(pwaff1->p[i].set));
2188 res = isl_pw_aff_add_piece(res, set,
2189 isl_aff_copy(pwaff2->p[j].aff));
2192 isl_pw_aff_free(pwaff1);
2193 isl_pw_aff_free(pwaff2);
2197 isl_pw_aff_free(pwaff1);
2198 isl_pw_aff_free(pwaff2);
2202 /* Compute a piecewise quasi-affine expression with a domain that
2203 * is the union of those of pwaff1 and pwaff2 and such that on each
2204 * cell, the quasi-affine expression is the maximum of those of pwaff1
2205 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2206 * cell, then the associated expression is the defined one.
2208 static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
2209 __isl_take isl_pw_aff *pwaff2)
2211 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
2214 __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
2215 __isl_take isl_pw_aff *pwaff2)
2217 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
2221 /* Compute a piecewise quasi-affine expression with a domain that
2222 * is the union of those of pwaff1 and pwaff2 and such that on each
2223 * cell, the quasi-affine expression is the minimum of those of pwaff1
2224 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2225 * cell, then the associated expression is the defined one.
2227 static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
2228 __isl_take isl_pw_aff *pwaff2)
2230 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
2233 __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
2234 __isl_take isl_pw_aff *pwaff2)
2236 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
2240 __isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
2241 __isl_take isl_pw_aff *pwaff2, int max)
2244 return isl_pw_aff_union_max(pwaff1, pwaff2);
2246 return isl_pw_aff_union_min(pwaff1, pwaff2);
2249 /* Construct a map with as domain the domain of pwaff and
2250 * one-dimensional range corresponding to the affine expressions.
2252 static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
2261 dim = isl_pw_aff_get_space(pwaff);
2262 map = isl_map_empty(dim);
2264 for (i = 0; i < pwaff->n; ++i) {
2265 isl_basic_map *bmap;
2268 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
2269 map_i = isl_map_from_basic_map(bmap);
2270 map_i = isl_map_intersect_domain(map_i,
2271 isl_set_copy(pwaff->p[i].set));
2272 map = isl_map_union_disjoint(map, map_i);
2275 isl_pw_aff_free(pwaff);
2280 /* Construct a map with as domain the domain of pwaff and
2281 * one-dimensional range corresponding to the affine expressions.
2283 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
2287 if (isl_space_is_set(pwaff->dim))
2288 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
2289 "space of input is not a map",
2290 return isl_pw_aff_free(pwaff));
2291 return map_from_pw_aff(pwaff);
2294 /* Construct a one-dimensional set with as parameter domain
2295 * the domain of pwaff and the single set dimension
2296 * corresponding to the affine expressions.
2298 __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
2302 if (!isl_space_is_set(pwaff->dim))
2303 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
2304 "space of input is not a set",
2305 return isl_pw_aff_free(pwaff));
2306 return map_from_pw_aff(pwaff);
2309 /* Return a set containing those elements in the domain
2310 * of pwaff where it is non-negative.
2312 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
2320 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
2322 for (i = 0; i < pwaff->n; ++i) {
2323 isl_basic_set *bset;
2327 rational = isl_set_has_rational(pwaff->p[i].set);
2328 bset = aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff),
2330 set_i = isl_set_from_basic_set(bset);
2331 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
2332 set = isl_set_union_disjoint(set, set_i);
2335 isl_pw_aff_free(pwaff);
2340 /* Return a set containing those elements in the domain
2341 * of pwaff where it is zero (if complement is 0) or not zero
2342 * (if complement is 1).
2344 static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
2353 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
2355 for (i = 0; i < pwaff->n; ++i) {
2356 isl_basic_set *bset;
2357 isl_set *set_i, *zero;
2360 rational = isl_set_has_rational(pwaff->p[i].set);
2361 bset = aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff),
2363 zero = isl_set_from_basic_set(bset);
2364 set_i = isl_set_copy(pwaff->p[i].set);
2366 set_i = isl_set_subtract(set_i, zero);
2368 set_i = isl_set_intersect(set_i, zero);
2369 set = isl_set_union_disjoint(set, set_i);
2372 isl_pw_aff_free(pwaff);
2377 /* Return a set containing those elements in the domain
2378 * of pwaff where it is zero.
2380 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
2382 return pw_aff_zero_set(pwaff, 0);
2385 /* Return a set containing those elements in the domain
2386 * of pwaff where it is not zero.
2388 __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
2390 return pw_aff_zero_set(pwaff, 1);
2393 /* Return a set containing those elements in the shared domain
2394 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
2396 * We compute the difference on the shared domain and then construct
2397 * the set of values where this difference is non-negative.
2398 * If strict is set, we first subtract 1 from the difference.
2399 * If equal is set, we only return the elements where pwaff1 and pwaff2
2402 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
2403 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
2405 isl_set *set1, *set2;
2407 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
2408 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
2409 set1 = isl_set_intersect(set1, set2);
2410 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
2411 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
2412 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
2415 isl_space *dim = isl_set_get_space(set1);
2417 aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
2418 aff = isl_aff_add_constant_si(aff, -1);
2419 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
2424 return isl_pw_aff_zero_set(pwaff1);
2425 return isl_pw_aff_nonneg_set(pwaff1);
2428 /* Return a set containing those elements in the shared domain
2429 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
2431 static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
2432 __isl_take isl_pw_aff *pwaff2)
2434 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
2437 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
2438 __isl_take isl_pw_aff *pwaff2)
2440 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
2443 /* Return a set containing those elements in the shared domain
2444 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
2446 static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
2447 __isl_take isl_pw_aff *pwaff2)
2449 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
2452 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
2453 __isl_take isl_pw_aff *pwaff2)
2455 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
2458 /* Return a set containing those elements in the shared domain
2459 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
2461 static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
2462 __isl_take isl_pw_aff *pwaff2)
2464 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
2467 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
2468 __isl_take isl_pw_aff *pwaff2)
2470 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
2473 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
2474 __isl_take isl_pw_aff *pwaff2)
2476 return isl_pw_aff_ge_set(pwaff2, pwaff1);
2479 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
2480 __isl_take isl_pw_aff *pwaff2)
2482 return isl_pw_aff_gt_set(pwaff2, pwaff1);
2485 /* Return a set containing those elements in the shared domain
2486 * of the elements of list1 and list2 where each element in list1
2487 * has the relation specified by "fn" with each element in list2.
2489 static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
2490 __isl_take isl_pw_aff_list *list2,
2491 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
2492 __isl_take isl_pw_aff *pwaff2))
2498 if (!list1 || !list2)
2501 ctx = isl_pw_aff_list_get_ctx(list1);
2502 if (list1->n < 1 || list2->n < 1)
2503 isl_die(ctx, isl_error_invalid,
2504 "list should contain at least one element", goto error);
2506 set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
2507 for (i = 0; i < list1->n; ++i)
2508 for (j = 0; j < list2->n; ++j) {
2511 set_ij = fn(isl_pw_aff_copy(list1->p[i]),
2512 isl_pw_aff_copy(list2->p[j]));
2513 set = isl_set_intersect(set, set_ij);
2516 isl_pw_aff_list_free(list1);
2517 isl_pw_aff_list_free(list2);
2520 isl_pw_aff_list_free(list1);
2521 isl_pw_aff_list_free(list2);
2525 /* Return a set containing those elements in the shared domain
2526 * of the elements of list1 and list2 where each element in list1
2527 * is equal to each element in list2.
2529 __isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
2530 __isl_take isl_pw_aff_list *list2)
2532 return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
2535 __isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
2536 __isl_take isl_pw_aff_list *list2)
2538 return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
2541 /* Return a set containing those elements in the shared domain
2542 * of the elements of list1 and list2 where each element in list1
2543 * is less than or equal to each element in list2.
2545 __isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
2546 __isl_take isl_pw_aff_list *list2)
2548 return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
2551 __isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
2552 __isl_take isl_pw_aff_list *list2)
2554 return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
2557 __isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
2558 __isl_take isl_pw_aff_list *list2)
2560 return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
2563 __isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
2564 __isl_take isl_pw_aff_list *list2)
2566 return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
2570 /* Return a set containing those elements in the shared domain
2571 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
2573 static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
2574 __isl_take isl_pw_aff *pwaff2)
2576 isl_set *set_lt, *set_gt;
2578 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
2579 isl_pw_aff_copy(pwaff2));
2580 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
2581 return isl_set_union_disjoint(set_lt, set_gt);
2584 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
2585 __isl_take isl_pw_aff *pwaff2)
2587 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
2590 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
2595 if (isl_int_is_one(v))
2597 if (!isl_int_is_pos(v))
2598 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
2599 "factor needs to be positive",
2600 return isl_pw_aff_free(pwaff));
2601 pwaff = isl_pw_aff_cow(pwaff);
2607 for (i = 0; i < pwaff->n; ++i) {
2608 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
2609 if (!pwaff->p[i].aff)
2610 return isl_pw_aff_free(pwaff);
2616 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
2620 pwaff = isl_pw_aff_cow(pwaff);
2626 for (i = 0; i < pwaff->n; ++i) {
2627 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
2628 if (!pwaff->p[i].aff)
2629 return isl_pw_aff_free(pwaff);
2635 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
2639 pwaff = isl_pw_aff_cow(pwaff);
2645 for (i = 0; i < pwaff->n; ++i) {
2646 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
2647 if (!pwaff->p[i].aff)
2648 return isl_pw_aff_free(pwaff);
2654 /* Assuming that "cond1" and "cond2" are disjoint,
2655 * return an affine expression that is equal to pwaff1 on cond1
2656 * and to pwaff2 on cond2.
2658 static __isl_give isl_pw_aff *isl_pw_aff_select(
2659 __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
2660 __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
2662 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
2663 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
2665 return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
2668 /* Return an affine expression that is equal to pwaff_true for elements
2669 * where "cond" is non-zero and to pwaff_false for elements where "cond"
2671 * That is, return cond ? pwaff_true : pwaff_false;
2673 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
2674 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
2676 isl_set *cond_true, *cond_false;
2678 cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
2679 cond_false = isl_pw_aff_zero_set(cond);
2680 return isl_pw_aff_select(cond_true, pwaff_true,
2681 cond_false, pwaff_false);
2684 int isl_aff_is_cst(__isl_keep isl_aff *aff)
2689 return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
2692 /* Check whether pwaff is a piecewise constant.
2694 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
2701 for (i = 0; i < pwaff->n; ++i) {
2702 int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
2703 if (is_cst < 0 || !is_cst)
2710 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2711 __isl_take isl_aff *aff2)
2713 if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
2714 return isl_aff_mul(aff2, aff1);
2716 if (!isl_aff_is_cst(aff2))
2717 isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
2718 "at least one affine expression should be constant",
2721 aff1 = isl_aff_cow(aff1);
2725 aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
2726 aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
2736 /* Divide "aff1" by "aff2", assuming "aff2" is a piecewise constant.
2738 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
2739 __isl_take isl_aff *aff2)
2744 is_cst = isl_aff_is_cst(aff2);
2748 isl_die(isl_aff_get_ctx(aff2), isl_error_invalid,
2749 "second argument should be a constant", goto error);
2754 neg = isl_int_is_neg(aff2->v->el[1]);
2756 isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
2757 isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
2760 aff1 = isl_aff_scale(aff1, aff2->v->el[0]);
2761 aff1 = isl_aff_scale_down(aff1, aff2->v->el[1]);
2764 isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
2765 isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
2776 static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2777 __isl_take isl_pw_aff *pwaff2)
2779 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
2782 __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
2783 __isl_take isl_pw_aff *pwaff2)
2785 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
2788 __isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
2789 __isl_take isl_pw_aff *pwaff2)
2791 return isl_pw_aff_union_add_(pwaff1, pwaff2);
2794 static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2795 __isl_take isl_pw_aff *pwaff2)
2797 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
2800 __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
2801 __isl_take isl_pw_aff *pwaff2)
2803 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
2806 static __isl_give isl_pw_aff *pw_aff_div(__isl_take isl_pw_aff *pa1,
2807 __isl_take isl_pw_aff *pa2)
2809 return isl_pw_aff_on_shared_domain(pa1, pa2, &isl_aff_div);
2812 /* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
2814 __isl_give isl_pw_aff *isl_pw_aff_div(__isl_take isl_pw_aff *pa1,
2815 __isl_take isl_pw_aff *pa2)
2819 is_cst = isl_pw_aff_is_cst(pa2);
2823 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2824 "second argument should be a piecewise constant",
2826 return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_aff_div);
2828 isl_pw_aff_free(pa1);
2829 isl_pw_aff_free(pa2);
2833 /* Compute the quotient of the integer division of "pa1" by "pa2"
2834 * with rounding towards zero.
2835 * "pa2" is assumed to be a piecewise constant.
2837 * In particular, return
2839 * pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
2842 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(__isl_take isl_pw_aff *pa1,
2843 __isl_take isl_pw_aff *pa2)
2849 is_cst = isl_pw_aff_is_cst(pa2);
2853 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2854 "second argument should be a piecewise constant",
2857 pa1 = isl_pw_aff_div(pa1, pa2);
2859 cond = isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1));
2860 f = isl_pw_aff_floor(isl_pw_aff_copy(pa1));
2861 c = isl_pw_aff_ceil(pa1);
2862 return isl_pw_aff_cond(isl_set_indicator_function(cond), f, c);
2864 isl_pw_aff_free(pa1);
2865 isl_pw_aff_free(pa2);
2869 /* Compute the remainder of the integer division of "pa1" by "pa2"
2870 * with rounding towards zero.
2871 * "pa2" is assumed to be a piecewise constant.
2873 * In particular, return
2875 * pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
2878 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(__isl_take isl_pw_aff *pa1,
2879 __isl_take isl_pw_aff *pa2)
2884 is_cst = isl_pw_aff_is_cst(pa2);
2888 isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
2889 "second argument should be a piecewise constant",
2891 res = isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1), isl_pw_aff_copy(pa2));
2892 res = isl_pw_aff_mul(pa2, res);
2893 res = isl_pw_aff_sub(pa1, res);
2896 isl_pw_aff_free(pa1);
2897 isl_pw_aff_free(pa2);
2901 static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2902 __isl_take isl_pw_aff *pwaff2)
2907 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2908 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2909 le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
2910 isl_pw_aff_copy(pwaff2));
2911 dom = isl_set_subtract(dom, isl_set_copy(le));
2912 return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
2915 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
2916 __isl_take isl_pw_aff *pwaff2)
2918 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
2921 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2922 __isl_take isl_pw_aff *pwaff2)
2927 dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
2928 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
2929 ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
2930 isl_pw_aff_copy(pwaff2));
2931 dom = isl_set_subtract(dom, isl_set_copy(ge));
2932 return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
2935 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
2936 __isl_take isl_pw_aff *pwaff2)
2938 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
2941 static __isl_give isl_pw_aff *pw_aff_list_reduce(
2942 __isl_take isl_pw_aff_list *list,
2943 __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
2944 __isl_take isl_pw_aff *pwaff2))
2953 ctx = isl_pw_aff_list_get_ctx(list);
2955 isl_die(ctx, isl_error_invalid,
2956 "list should contain at least one element",
2957 return isl_pw_aff_list_free(list));
2959 res = isl_pw_aff_copy(list->p[0]);
2960 for (i = 1; i < list->n; ++i)
2961 res = fn(res, isl_pw_aff_copy(list->p[i]));
2963 isl_pw_aff_list_free(list);
2967 /* Return an isl_pw_aff that maps each element in the intersection of the
2968 * domains of the elements of list to the minimal corresponding affine
2971 __isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
2973 return pw_aff_list_reduce(list, &isl_pw_aff_min);
2976 /* Return an isl_pw_aff that maps each element in the intersection of the
2977 * domains of the elements of list to the maximal corresponding affine
2980 __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
2982 return pw_aff_list_reduce(list, &isl_pw_aff_max);
2985 /* Mark the domains of "pwaff" as rational.
2987 __isl_give isl_pw_aff *isl_pw_aff_set_rational(__isl_take isl_pw_aff *pwaff)
2991 pwaff = isl_pw_aff_cow(pwaff);
2997 for (i = 0; i < pwaff->n; ++i) {
2998 pwaff->p[i].set = isl_set_set_rational(pwaff->p[i].set);
2999 if (!pwaff->p[i].set)
3000 return isl_pw_aff_free(pwaff);
3006 /* Mark the domains of the elements of "list" as rational.
3008 __isl_give isl_pw_aff_list *isl_pw_aff_list_set_rational(
3009 __isl_take isl_pw_aff_list *list)
3019 for (i = 0; i < n; ++i) {
3022 pa = isl_pw_aff_list_get_pw_aff(list, i);
3023 pa = isl_pw_aff_set_rational(pa);
3024 list = isl_pw_aff_list_set_pw_aff(list, i, pa);
3030 /* Check that the domain space of "aff" matches "space".
3032 * Return 0 on success and -1 on error.
3034 int isl_aff_check_match_domain_space(__isl_keep isl_aff *aff,
3035 __isl_keep isl_space *space)
3037 isl_space *aff_space;
3043 aff_space = isl_aff_get_domain_space(aff);
3045 match = isl_space_match(space, isl_dim_param, aff_space, isl_dim_param);
3049 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
3050 "parameters don't match", goto error);
3051 match = isl_space_tuple_match(space, isl_dim_in,
3052 aff_space, isl_dim_set);
3056 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
3057 "domains don't match", goto error);
3058 isl_space_free(aff_space);
3061 isl_space_free(aff_space);
3068 #include <isl_multi_templ.c>
3070 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
3073 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
3074 __isl_take isl_multi_aff *ma)
3076 isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
3077 return isl_pw_multi_aff_alloc(dom, ma);
3080 /* Create a piecewise multi-affine expression in the given space that maps each
3081 * input dimension to the corresponding output dimension.
3083 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3084 __isl_take isl_space *space)
3086 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space));
3089 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
3090 __isl_take isl_multi_aff *maff2)
3092 return isl_multi_aff_bin_op(maff1, maff2, &isl_aff_add);
3095 /* Subtract "ma2" from "ma1" and return the result.
3097 __isl_give isl_multi_aff *isl_multi_aff_sub(__isl_take isl_multi_aff *ma1,
3098 __isl_take isl_multi_aff *ma2)
3100 return isl_multi_aff_bin_op(ma1, ma2, &isl_aff_sub);
3103 /* Given two multi-affine expressions A -> B and C -> D,
3104 * construct a multi-affine expression [A -> C] -> [B -> D].
3106 __isl_give isl_multi_aff *isl_multi_aff_product(
3107 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
3113 int in1, in2, out1, out2;
3115 in1 = isl_multi_aff_dim(ma1, isl_dim_in);
3116 in2 = isl_multi_aff_dim(ma2, isl_dim_in);
3117 out1 = isl_multi_aff_dim(ma1, isl_dim_out);
3118 out2 = isl_multi_aff_dim(ma2, isl_dim_out);
3119 space = isl_space_product(isl_multi_aff_get_space(ma1),
3120 isl_multi_aff_get_space(ma2));
3121 res = isl_multi_aff_alloc(isl_space_copy(space));
3122 space = isl_space_domain(space);
3124 for (i = 0; i < out1; ++i) {
3125 aff = isl_multi_aff_get_aff(ma1, i);
3126 aff = isl_aff_insert_dims(aff, isl_dim_in, in1, in2);
3127 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
3128 res = isl_multi_aff_set_aff(res, i, aff);
3131 for (i = 0; i < out2; ++i) {
3132 aff = isl_multi_aff_get_aff(ma2, i);
3133 aff = isl_aff_insert_dims(aff, isl_dim_in, 0, in1);
3134 aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
3135 res = isl_multi_aff_set_aff(res, out1 + i, aff);
3138 isl_space_free(space);
3139 isl_multi_aff_free(ma1);
3140 isl_multi_aff_free(ma2);
3144 /* Exploit the equalities in "eq" to simplify the affine expressions.
3146 static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
3147 __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
3151 maff = isl_multi_aff_cow(maff);
3155 for (i = 0; i < maff->n; ++i) {
3156 maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
3157 isl_basic_set_copy(eq));
3162 isl_basic_set_free(eq);
3165 isl_basic_set_free(eq);
3166 isl_multi_aff_free(maff);
3170 __isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
3175 maff = isl_multi_aff_cow(maff);
3179 for (i = 0; i < maff->n; ++i) {
3180 maff->p[i] = isl_aff_scale(maff->p[i], f);
3182 return isl_multi_aff_free(maff);
3188 __isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
3189 __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
3191 maff1 = isl_multi_aff_add(maff1, maff2);
3192 maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
3196 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
3204 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3205 __isl_keep isl_multi_aff *maff2)
3210 if (!maff1 || !maff2)
3212 if (maff1->n != maff2->n)
3214 equal = isl_space_is_equal(maff1->space, maff2->space);
3215 if (equal < 0 || !equal)
3218 for (i = 0; i < maff1->n; ++i) {
3219 equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
3220 if (equal < 0 || !equal)
3227 /* Return the set of domain elements where "ma1" is lexicographically
3228 * smaller than or equal to "ma2".
3230 __isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
3231 __isl_take isl_multi_aff *ma2)
3233 return isl_multi_aff_lex_ge_set(ma2, ma1);
3236 /* Return the set of domain elements where "ma1" is lexicographically
3237 * greater than or equal to "ma2".
3239 __isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
3240 __isl_take isl_multi_aff *ma2)
3243 isl_map *map1, *map2;
3246 map1 = isl_map_from_multi_aff(ma1);
3247 map2 = isl_map_from_multi_aff(ma2);
3248 map = isl_map_range_product(map1, map2);
3249 space = isl_space_range(isl_map_get_space(map));
3250 space = isl_space_domain(isl_space_unwrap(space));
3251 ge = isl_map_lex_ge(space);
3252 map = isl_map_intersect_range(map, isl_map_wrap(ge));
3254 return isl_map_domain(map);
3258 #define PW isl_pw_multi_aff
3260 #define EL isl_multi_aff
3262 #define EL_IS_ZERO is_empty
3266 #define IS_ZERO is_empty
3269 #undef DEFAULT_IS_ZERO
3270 #define DEFAULT_IS_ZERO 0
3275 #define NO_INVOLVES_DIMS
3276 #define NO_MOVE_DIMS
3277 #define NO_INSERT_DIMS
3281 #include <isl_pw_templ.c>
3284 #define UNION isl_union_pw_multi_aff
3286 #define PART isl_pw_multi_aff
3288 #define PARTS pw_multi_aff
3289 #define ALIGN_DOMAIN
3293 #include <isl_union_templ.c>
3295 /* Given a function "cmp" that returns the set of elements where
3296 * "ma1" is "better" than "ma2", return the intersection of this
3297 * set with "dom1" and "dom2".
3299 static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1,
3300 __isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1,
3301 __isl_keep isl_multi_aff *ma2,
3302 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
3303 __isl_take isl_multi_aff *ma2))
3309 common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2));
3310 is_empty = isl_set_plain_is_empty(common);
3311 if (is_empty >= 0 && is_empty)
3314 return isl_set_free(common);
3315 better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2));
3316 better = isl_set_intersect(common, better);
3321 /* Given a function "cmp" that returns the set of elements where
3322 * "ma1" is "better" than "ma2", return a piecewise multi affine
3323 * expression defined on the union of the definition domains
3324 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
3325 * "pma2" on each cell. If only one of the two input functions
3326 * is defined on a given cell, then it is considered the best.
3328 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt(
3329 __isl_take isl_pw_multi_aff *pma1,
3330 __isl_take isl_pw_multi_aff *pma2,
3331 __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
3332 __isl_take isl_multi_aff *ma2))
3335 isl_pw_multi_aff *res = NULL;
3337 isl_set *set = NULL;
3342 ctx = isl_space_get_ctx(pma1->dim);
3343 if (!isl_space_is_equal(pma1->dim, pma2->dim))
3344 isl_die(ctx, isl_error_invalid,
3345 "arguments should live in the same space", goto error);
3347 if (isl_pw_multi_aff_is_empty(pma1)) {
3348 isl_pw_multi_aff_free(pma1);
3352 if (isl_pw_multi_aff_is_empty(pma2)) {
3353 isl_pw_multi_aff_free(pma2);
3357 n = 2 * (pma1->n + 1) * (pma2->n + 1);
3358 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n);
3360 for (i = 0; i < pma1->n; ++i) {
3361 set = isl_set_copy(pma1->p[i].set);
3362 for (j = 0; j < pma2->n; ++j) {
3366 better = shared_and_better(pma2->p[j].set,
3367 pma1->p[i].set, pma2->p[j].maff,
3368 pma1->p[i].maff, cmp);
3369 is_empty = isl_set_plain_is_empty(better);
3370 if (is_empty < 0 || is_empty) {
3371 isl_set_free(better);
3376 set = isl_set_subtract(set, isl_set_copy(better));
3378 res = isl_pw_multi_aff_add_piece(res, better,
3379 isl_multi_aff_copy(pma2->p[j].maff));
3381 res = isl_pw_multi_aff_add_piece(res, set,
3382 isl_multi_aff_copy(pma1->p[i].maff));
3385 for (j = 0; j < pma2->n; ++j) {
3386 set = isl_set_copy(pma2->p[j].set);
3387 for (i = 0; i < pma1->n; ++i)
3388 set = isl_set_subtract(set,
3389 isl_set_copy(pma1->p[i].set));
3390 res = isl_pw_multi_aff_add_piece(res, set,
3391 isl_multi_aff_copy(pma2->p[j].maff));
3394 isl_pw_multi_aff_free(pma1);
3395 isl_pw_multi_aff_free(pma2);
3399 isl_pw_multi_aff_free(pma1);
3400 isl_pw_multi_aff_free(pma2);
3402 return isl_pw_multi_aff_free(res);
3405 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
3406 __isl_take isl_pw_multi_aff *pma1,
3407 __isl_take isl_pw_multi_aff *pma2)
3409 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_ge_set);
3412 /* Given two piecewise multi affine expressions, return a piecewise
3413 * multi-affine expression defined on the union of the definition domains
3414 * of the inputs that is equal to the lexicographic maximum of the two
3415 * inputs on each cell. If only one of the two inputs is defined on
3416 * a given cell, then it is considered to be the maximum.
3418 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3419 __isl_take isl_pw_multi_aff *pma1,
3420 __isl_take isl_pw_multi_aff *pma2)
3422 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3423 &pw_multi_aff_union_lexmax);
3426 static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
3427 __isl_take isl_pw_multi_aff *pma1,
3428 __isl_take isl_pw_multi_aff *pma2)
3430 return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_set);
3433 /* Given two piecewise multi affine expressions, return a piecewise
3434 * multi-affine expression defined on the union of the definition domains
3435 * of the inputs that is equal to the lexicographic minimum of the two
3436 * inputs on each cell. If only one of the two inputs is defined on
3437 * a given cell, then it is considered to be the minimum.
3439 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3440 __isl_take isl_pw_multi_aff *pma1,
3441 __isl_take isl_pw_multi_aff *pma2)
3443 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3444 &pw_multi_aff_union_lexmin);
3447 static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
3448 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3450 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
3451 &isl_multi_aff_add);
3454 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3455 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3457 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3461 static __isl_give isl_pw_multi_aff *pw_multi_aff_sub(
3462 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3464 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
3465 &isl_multi_aff_sub);
3468 /* Subtract "pma2" from "pma1" and return the result.
3470 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
3471 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3473 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3477 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3478 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3480 return isl_pw_multi_aff_union_add_(pma1, pma2);
3483 /* Given two piecewise multi-affine expressions A -> B and C -> D,
3484 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
3486 static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
3487 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3491 isl_pw_multi_aff *res;
3496 n = pma1->n * pma2->n;
3497 space = isl_space_product(isl_space_copy(pma1->dim),
3498 isl_space_copy(pma2->dim));
3499 res = isl_pw_multi_aff_alloc_size(space, n);
3501 for (i = 0; i < pma1->n; ++i) {
3502 for (j = 0; j < pma2->n; ++j) {
3506 domain = isl_set_product(isl_set_copy(pma1->p[i].set),
3507 isl_set_copy(pma2->p[j].set));
3508 ma = isl_multi_aff_product(
3509 isl_multi_aff_copy(pma1->p[i].maff),
3510 isl_multi_aff_copy(pma2->p[i].maff));
3511 res = isl_pw_multi_aff_add_piece(res, domain, ma);
3515 isl_pw_multi_aff_free(pma1);
3516 isl_pw_multi_aff_free(pma2);
3519 isl_pw_multi_aff_free(pma1);
3520 isl_pw_multi_aff_free(pma2);
3524 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3525 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
3527 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
3528 &pw_multi_aff_product);
3531 /* Construct a map mapping the domain of the piecewise multi-affine expression
3532 * to its range, with each dimension in the range equated to the
3533 * corresponding affine expression on its cell.
3535 __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
3543 map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
3545 for (i = 0; i < pma->n; ++i) {
3546 isl_multi_aff *maff;
3547 isl_basic_map *bmap;
3550 maff = isl_multi_aff_copy(pma->p[i].maff);
3551 bmap = isl_basic_map_from_multi_aff(maff);
3552 map_i = isl_map_from_basic_map(bmap);
3553 map_i = isl_map_intersect_domain(map_i,
3554 isl_set_copy(pma->p[i].set));
3555 map = isl_map_union_disjoint(map, map_i);
3558 isl_pw_multi_aff_free(pma);
3562 __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
3567 if (!isl_space_is_set(pma->dim))
3568 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
3569 "isl_pw_multi_aff cannot be converted into an isl_set",
3570 return isl_pw_multi_aff_free(pma));
3572 return isl_map_from_pw_multi_aff(pma);
3575 /* Given a basic map with a single output dimension that is defined
3576 * in terms of the parameters and input dimensions using an equality,
3577 * extract an isl_aff that expresses the output dimension in terms
3578 * of the parameters and input dimensions.
3580 * Since some applications expect the result of isl_pw_multi_aff_from_map
3581 * to only contain integer affine expressions, we compute the floor
3582 * of the expression before returning.
3584 * This function shares some similarities with
3585 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
3587 static __isl_give isl_aff *extract_isl_aff_from_basic_map(
3588 __isl_take isl_basic_map *bmap)
3593 isl_local_space *ls;
3598 if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
3599 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3600 "basic map should have a single output dimension",
3602 offset = isl_basic_map_offset(bmap, isl_dim_out);
3603 total = isl_basic_map_total_dim(bmap);
3604 for (i = 0; i < bmap->n_eq; ++i) {
3605 if (isl_int_is_zero(bmap->eq[i][offset]))
3607 if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
3608 1 + total - (offset + 1)) != -1)
3612 if (i >= bmap->n_eq)
3613 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
3614 "unable to find suitable equality", goto error);
3615 ls = isl_basic_map_get_local_space(bmap);
3616 aff = isl_aff_alloc(isl_local_space_domain(ls));
3619 if (isl_int_is_neg(bmap->eq[i][offset]))
3620 isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
3622 isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
3623 isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
3624 isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
3625 isl_basic_map_free(bmap);
3627 aff = isl_aff_remove_unused_divs(aff);
3628 aff = isl_aff_floor(aff);
3631 isl_basic_map_free(bmap);
3635 /* Given a basic map where each output dimension is defined
3636 * in terms of the parameters and input dimensions using an equality,
3637 * extract an isl_multi_aff that expresses the output dimensions in terms
3638 * of the parameters and input dimensions.
3640 static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
3641 __isl_take isl_basic_map *bmap)
3650 ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
3651 n_out = isl_basic_map_dim(bmap, isl_dim_out);
3653 for (i = 0; i < n_out; ++i) {
3654 isl_basic_map *bmap_i;
3657 bmap_i = isl_basic_map_copy(bmap);
3658 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
3659 i + 1, n_out - (1 + i));
3660 bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
3661 aff = extract_isl_aff_from_basic_map(bmap_i);
3662 ma = isl_multi_aff_set_aff(ma, i, aff);
3665 isl_basic_map_free(bmap);
3670 /* Create an isl_pw_multi_aff that is equivalent to
3671 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
3672 * The given basic map is such that each output dimension is defined
3673 * in terms of the parameters and input dimensions using an equality.
3675 static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
3676 __isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
3680 ma = extract_isl_multi_aff_from_basic_map(bmap);
3681 return isl_pw_multi_aff_alloc(domain, ma);
3684 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3685 * This obviously only works if the input "map" is single-valued.
3686 * If so, we compute the lexicographic minimum of the image in the form
3687 * of an isl_pw_multi_aff. Since the image is unique, it is equal
3688 * to its lexicographic minimum.
3689 * If the input is not single-valued, we produce an error.
3691 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_base(
3692 __isl_take isl_map *map)
3696 isl_pw_multi_aff *pma;
3698 sv = isl_map_is_single_valued(map);
3702 isl_die(isl_map_get_ctx(map), isl_error_invalid,
3703 "map is not single-valued", goto error);
3704 map = isl_map_make_disjoint(map);
3708 pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
3710 for (i = 0; i < map->n; ++i) {
3711 isl_pw_multi_aff *pma_i;
3712 isl_basic_map *bmap;
3713 bmap = isl_basic_map_copy(map->p[i]);
3714 pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
3715 pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
3725 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
3726 * taking into account that the output dimension at position "d"
3727 * can be represented as
3729 * x = floor((e(...) + c1) / m)
3731 * given that constraint "i" is of the form
3733 * e(...) + c1 - m x >= 0
3736 * Let "map" be of the form
3740 * We construct a mapping
3742 * A -> [A -> x = floor(...)]
3744 * apply that to the map, obtaining
3746 * [A -> x = floor(...)] -> B
3748 * and equate dimension "d" to x.
3749 * We then compute a isl_pw_multi_aff representation of the resulting map
3750 * and plug in the mapping above.
3752 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_div(
3753 __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i)
3757 isl_local_space *ls;
3765 isl_pw_multi_aff *pma;
3768 is_set = isl_map_is_set(map);
3770 offset = isl_basic_map_offset(hull, isl_dim_out);
3771 ctx = isl_map_get_ctx(map);
3772 space = isl_space_domain(isl_map_get_space(map));
3773 n_in = isl_space_dim(space, isl_dim_set);
3774 n = isl_space_dim(space, isl_dim_all);
3776 v = isl_vec_alloc(ctx, 1 + 1 + n);
3778 isl_int_neg(v->el[0], hull->ineq[i][offset + d]);
3779 isl_seq_cpy(v->el + 1, hull->ineq[i], 1 + n);
3781 isl_basic_map_free(hull);
3783 ls = isl_local_space_from_space(isl_space_copy(space));
3784 aff = isl_aff_alloc_vec(ls, v);
3785 aff = isl_aff_floor(aff);
3787 isl_space_free(space);
3788 ma = isl_multi_aff_from_aff(aff);
3790 ma = isl_multi_aff_identity(isl_space_map_from_set(space));
3791 ma = isl_multi_aff_range_product(ma,
3792 isl_multi_aff_from_aff(aff));
3795 insert = isl_map_from_multi_aff(isl_multi_aff_copy(ma));
3796 map = isl_map_apply_domain(map, insert);
3797 map = isl_map_equate(map, isl_dim_in, n_in, isl_dim_out, d);
3798 pma = isl_pw_multi_aff_from_map(map);
3799 pma = isl_pw_multi_aff_pullback_multi_aff(pma, ma);
3804 /* Is constraint "c" of the form
3806 * e(...) + c1 - m x >= 0
3810 * -e(...) + c2 + m x >= 0
3812 * where m > 1 and e only depends on parameters and input dimemnsions?
3814 * "offset" is the offset of the output dimensions
3815 * "pos" is the position of output dimension x.
3817 static int is_potential_div_constraint(isl_int *c, int offset, int d, int total)
3819 if (isl_int_is_zero(c[offset + d]))
3821 if (isl_int_is_one(c[offset + d]))
3823 if (isl_int_is_negone(c[offset + d]))
3825 if (isl_seq_first_non_zero(c + offset, d) != -1)
3827 if (isl_seq_first_non_zero(c + offset + d + 1,
3828 total - (offset + d + 1)) != -1)
3833 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3835 * As a special case, we first check if there is any pair of constraints,
3836 * shared by all the basic maps in "map" that force a given dimension
3837 * to be equal to the floor of some affine combination of the input dimensions.
3839 * In particular, if we can find two constraints
3841 * e(...) + c1 - m x >= 0 i.e., m x <= e(...) + c1
3845 * -e(...) + c2 + m x >= 0 i.e., m x >= e(...) - c2
3847 * where m > 1 and e only depends on parameters and input dimemnsions,
3850 * c1 + c2 < m i.e., -c2 >= c1 - (m - 1)
3852 * then we know that we can take
3854 * x = floor((e(...) + c1) / m)
3856 * without having to perform any computation.
3858 * Note that we know that
3862 * If c1 + c2 were 0, then we would have detected an equality during
3863 * simplification. If c1 + c2 were negative, then we would have detected
3866 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_check_div(
3867 __isl_take isl_map *map)
3873 isl_basic_map *hull;
3875 hull = isl_map_unshifted_simple_hull(isl_map_copy(map));
3880 dim = isl_map_dim(map, isl_dim_out);
3881 offset = isl_basic_map_offset(hull, isl_dim_out);
3882 total = 1 + isl_basic_map_total_dim(hull);
3884 for (d = 0; d < dim; ++d) {
3885 for (i = 0; i < n; ++i) {
3886 if (!is_potential_div_constraint(hull->ineq[i],
3889 for (j = i + 1; j < n; ++j) {
3890 if (!isl_seq_is_neg(hull->ineq[i] + 1,
3891 hull->ineq[j] + 1, total - 1))
3893 isl_int_add(sum, hull->ineq[i][0],
3895 if (isl_int_abs_lt(sum,
3896 hull->ineq[i][offset + d]))
3903 if (isl_int_is_pos(hull->ineq[j][offset + d]))
3905 return pw_multi_aff_from_map_div(map, hull, d, j);
3909 isl_basic_map_free(hull);
3910 return pw_multi_aff_from_map_base(map);
3913 isl_basic_map_free(hull);
3917 /* Given an affine expression
3919 * [A -> B] -> f(A,B)
3921 * construct an isl_multi_aff
3925 * such that dimension "d" in B' is set to "aff" and the remaining
3926 * dimensions are set equal to the corresponding dimensions in B.
3927 * "n_in" is the dimension of the space A.
3928 * "n_out" is the dimension of the space B.
3930 * If "is_set" is set, then the affine expression is of the form
3934 * and we construct an isl_multi_aff
3938 static __isl_give isl_multi_aff *range_map(__isl_take isl_aff *aff, int d,
3939 unsigned n_in, unsigned n_out, int is_set)
3943 isl_space *space, *space2;
3944 isl_local_space *ls;
3946 space = isl_aff_get_domain_space(aff);
3947 ls = isl_local_space_from_space(isl_space_copy(space));
3948 space2 = isl_space_copy(space);
3950 space2 = isl_space_range(isl_space_unwrap(space2));
3951 space = isl_space_map_from_domain_and_range(space, space2);
3952 ma = isl_multi_aff_alloc(space);
3953 ma = isl_multi_aff_set_aff(ma, d, aff);
3955 for (i = 0; i < n_out; ++i) {
3958 aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
3959 isl_dim_set, n_in + i);
3960 ma = isl_multi_aff_set_aff(ma, i, aff);
3963 isl_local_space_free(ls);
3968 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
3969 * taking into account that the dimension at position "d" can be written as
3971 * x = m a + f(..) (1)
3973 * where m is equal to "gcd".
3974 * "i" is the index of the equality in "hull" that defines f(..).
3975 * In particular, the equality is of the form
3977 * f(..) - x + m g(existentials) = 0
3981 * -f(..) + x + m g(existentials) = 0
3983 * We basically plug (1) into "map", resulting in a map with "a"
3984 * in the range instead of "x". The corresponding isl_pw_multi_aff
3985 * defining "a" is then plugged back into (1) to obtain a definition fro "x".
3987 * Specifically, given the input map
3991 * We first wrap it into a set
3995 * and define (1) on top of the corresponding space, resulting in "aff".
3996 * We use this to create an isl_multi_aff that maps the output position "d"
3997 * from "a" to "x", leaving all other (intput and output) dimensions unchanged.
3998 * We plug this into the wrapped map, unwrap the result and compute the
3999 * corresponding isl_pw_multi_aff.
4000 * The result is an expression
4008 * so that we can plug that into "aff", after extending the latter to
4014 * If "map" is actually a set, then there is no "A" space, meaning
4015 * that we do not need to perform any wrapping, and that the result
4016 * of the recursive call is of the form
4020 * which is plugged into a mapping of the form
4024 static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_stride(
4025 __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i,
4030 isl_local_space *ls;
4033 isl_pw_multi_aff *pma, *id;
4039 is_set = isl_map_is_set(map);
4041 n_in = isl_basic_map_dim(hull, isl_dim_in);
4042 n_out = isl_basic_map_dim(hull, isl_dim_out);
4043 o_out = isl_basic_map_offset(hull, isl_dim_out);
4048 set = isl_map_wrap(map);
4049 space = isl_space_map_from_set(isl_set_get_space(set));
4050 ma = isl_multi_aff_identity(space);
4051 ls = isl_local_space_from_space(isl_set_get_space(set));
4052 aff = isl_aff_alloc(ls);
4054 isl_int_set_si(aff->v->el[0], 1);
4055 if (isl_int_is_one(hull->eq[i][o_out + d]))
4056 isl_seq_neg(aff->v->el + 1, hull->eq[i],
4059 isl_seq_cpy(aff->v->el + 1, hull->eq[i],
4061 isl_int_set(aff->v->el[1 + o_out + d], gcd);
4063 ma = isl_multi_aff_set_aff(ma, n_in + d, isl_aff_copy(aff));
4064 set = isl_set_preimage_multi_aff(set, ma);
4066 ma = range_map(aff, d, n_in, n_out, is_set);
4071 map = isl_set_unwrap(set);
4072 pma = isl_pw_multi_aff_from_map(set);
4075 space = isl_pw_multi_aff_get_domain_space(pma);
4076 space = isl_space_map_from_set(space);
4077 id = isl_pw_multi_aff_identity(space);
4078 pma = isl_pw_multi_aff_range_product(id, pma);
4080 id = isl_pw_multi_aff_from_multi_aff(ma);
4081 pma = isl_pw_multi_aff_pullback_pw_multi_aff(id, pma);
4083 isl_basic_map_free(hull);
4087 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4089 * As a special case, we first check if all output dimensions are uniquely
4090 * defined in terms of the parameters and input dimensions over the entire
4091 * domain. If so, we extract the desired isl_pw_multi_aff directly
4092 * from the affine hull of "map" and its domain.
4094 * Otherwise, we check if any of the output dimensions is "strided".
4095 * That is, we check if can be written as
4099 * with m greater than 1, a some combination of existentiall quantified
4100 * variables and f and expression in the parameters and input dimensions.
4101 * If so, we remove the stride in pw_multi_aff_from_map_stride.
4103 * Otherwise, we continue with pw_multi_aff_from_map_check_div for a further
4106 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
4110 isl_basic_map *hull;
4120 hull = isl_map_affine_hull(isl_map_copy(map));
4121 sv = isl_basic_map_plain_is_single_valued(hull);
4123 return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
4125 hull = isl_basic_map_free(hull);
4129 n_div = isl_basic_map_dim(hull, isl_dim_div);
4130 o_div = isl_basic_map_offset(hull, isl_dim_div);
4133 isl_basic_map_free(hull);
4134 return pw_multi_aff_from_map_check_div(map);
4139 n_out = isl_basic_map_dim(hull, isl_dim_out);
4140 o_out = isl_basic_map_offset(hull, isl_dim_out);
4142 for (i = 0; i < n_out; ++i) {
4143 for (j = 0; j < hull->n_eq; ++j) {
4144 isl_int *eq = hull->eq[j];
4145 isl_pw_multi_aff *res;
4147 if (!isl_int_is_one(eq[o_out + i]) &&
4148 !isl_int_is_negone(eq[o_out + i]))
4150 if (isl_seq_first_non_zero(eq + o_out, i) != -1)
4152 if (isl_seq_first_non_zero(eq + o_out + i + 1,
4153 n_out - (i + 1)) != -1)
4155 isl_seq_gcd(eq + o_div, n_div, &gcd);
4156 if (isl_int_is_zero(gcd))
4158 if (isl_int_is_one(gcd))
4161 res = pw_multi_aff_from_map_stride(map, hull,
4169 isl_basic_map_free(hull);
4170 return pw_multi_aff_from_map_check_div(map);
4176 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
4178 return isl_pw_multi_aff_from_map(set);
4181 /* Convert "map" into an isl_pw_multi_aff (if possible) and
4184 static int pw_multi_aff_from_map(__isl_take isl_map *map, void *user)
4186 isl_union_pw_multi_aff **upma = user;
4187 isl_pw_multi_aff *pma;
4189 pma = isl_pw_multi_aff_from_map(map);
4190 *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
4192 return *upma ? 0 : -1;
4195 /* Try and create an isl_union_pw_multi_aff that is equivalent
4196 * to the given isl_union_map.
4197 * The isl_union_map is required to be single-valued in each space.
4198 * Otherwise, an error is produced.
4200 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_map(
4201 __isl_take isl_union_map *umap)
4204 isl_union_pw_multi_aff *upma;
4206 space = isl_union_map_get_space(umap);
4207 upma = isl_union_pw_multi_aff_empty(space);
4208 if (isl_union_map_foreach_map(umap, &pw_multi_aff_from_map, &upma) < 0)
4209 upma = isl_union_pw_multi_aff_free(upma);
4210 isl_union_map_free(umap);
4215 /* Try and create an isl_union_pw_multi_aff that is equivalent
4216 * to the given isl_union_set.
4217 * The isl_union_set is required to be a singleton in each space.
4218 * Otherwise, an error is produced.
4220 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_set(
4221 __isl_take isl_union_set *uset)
4223 return isl_union_pw_multi_aff_from_union_map(uset);
4226 /* Return the piecewise affine expression "set ? 1 : 0".
4228 __isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
4231 isl_space *space = isl_set_get_space(set);
4232 isl_local_space *ls = isl_local_space_from_space(space);
4233 isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
4234 isl_aff *one = isl_aff_zero_on_domain(ls);
4236 one = isl_aff_add_constant_si(one, 1);
4237 pa = isl_pw_aff_alloc(isl_set_copy(set), one);
4238 set = isl_set_complement(set);
4239 pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
4244 /* Plug in "subs" for dimension "type", "pos" of "aff".
4246 * Let i be the dimension to replace and let "subs" be of the form
4250 * and "aff" of the form
4256 * (a f + d g')/(m d)
4258 * where g' is the result of plugging in "subs" in each of the integer
4261 __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
4262 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
4267 aff = isl_aff_cow(aff);
4269 return isl_aff_free(aff);
4271 ctx = isl_aff_get_ctx(aff);
4272 if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
4273 isl_die(ctx, isl_error_invalid,
4274 "spaces don't match", return isl_aff_free(aff));
4275 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
4276 isl_die(ctx, isl_error_unsupported,
4277 "cannot handle divs yet", return isl_aff_free(aff));
4279 aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
4281 return isl_aff_free(aff);
4283 aff->v = isl_vec_cow(aff->v);
4285 return isl_aff_free(aff);
4287 pos += isl_local_space_offset(aff->ls, type);
4290 isl_seq_substitute(aff->v->el, pos, subs->v->el,
4291 aff->v->size, subs->v->size, v);
4297 /* Plug in "subs" for dimension "type", "pos" in each of the affine
4298 * expressions in "maff".
4300 __isl_give isl_multi_aff *isl_multi_aff_substitute(
4301 __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
4302 __isl_keep isl_aff *subs)
4306 maff = isl_multi_aff_cow(maff);
4308 return isl_multi_aff_free(maff);
4310 if (type == isl_dim_in)
4313 for (i = 0; i < maff->n; ++i) {
4314 maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
4316 return isl_multi_aff_free(maff);
4322 /* Plug in "subs" for dimension "type", "pos" of "pma".
4324 * pma is of the form
4328 * while subs is of the form
4330 * v' = B_j(v) -> S_j
4332 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
4333 * has a contribution in the result, in particular
4335 * C_ij(S_j) -> M_i(S_j)
4337 * Note that plugging in S_j in C_ij may also result in an empty set
4338 * and this contribution should simply be discarded.
4340 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
4341 __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
4342 __isl_keep isl_pw_aff *subs)
4345 isl_pw_multi_aff *res;
4348 return isl_pw_multi_aff_free(pma);
4350 n = pma->n * subs->n;
4351 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
4353 for (i = 0; i < pma->n; ++i) {
4354 for (j = 0; j < subs->n; ++j) {
4356 isl_multi_aff *res_ij;
4359 common = isl_set_intersect(
4360 isl_set_copy(pma->p[i].set),
4361 isl_set_copy(subs->p[j].set));
4362 common = isl_set_substitute(common,
4363 type, pos, subs->p[j].aff);
4364 empty = isl_set_plain_is_empty(common);
4365 if (empty < 0 || empty) {
4366 isl_set_free(common);
4372 res_ij = isl_multi_aff_substitute(
4373 isl_multi_aff_copy(pma->p[i].maff),
4374 type, pos, subs->p[j].aff);
4376 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
4380 isl_pw_multi_aff_free(pma);
4383 isl_pw_multi_aff_free(pma);
4384 isl_pw_multi_aff_free(res);
4388 /* Compute the preimage of a range of dimensions in the affine expression "src"
4389 * under "ma" and put the result in "dst". The number of dimensions in "src"
4390 * that precede the range is given by "n_before". The number of dimensions
4391 * in the range is given by the number of output dimensions of "ma".
4392 * The number of dimensions that follow the range is given by "n_after".
4393 * If "has_denom" is set (to one),
4394 * then "src" and "dst" have an extra initial denominator.
4395 * "n_div_ma" is the number of existentials in "ma"
4396 * "n_div_bset" is the number of existentials in "src"
4397 * The resulting "dst" (which is assumed to have been allocated by
4398 * the caller) contains coefficients for both sets of existentials,
4399 * first those in "ma" and then those in "src".
4400 * f, c1, c2 and g are temporary objects that have been initialized
4403 * Let src represent the expression
4405 * (a(p) + f_u u + b v + f_w w + c(divs))/d
4407 * and let ma represent the expressions
4409 * v_i = (r_i(p) + s_i(y) + t_i(divs'))/m_i
4411 * We start out with the following expression for dst:
4413 * (a(p) + f_u u + 0 y + f_w w + 0 divs' + c(divs) + f \sum_i b_i v_i)/d
4415 * with the multiplication factor f initially equal to 1
4416 * and f \sum_i b_i v_i kept separately.
4417 * For each x_i that we substitute, we multiply the numerator
4418 * (and denominator) of dst by c_1 = m_i and add the numerator
4419 * of the x_i expression multiplied by c_2 = f b_i,
4420 * after removing the common factors of c_1 and c_2.
4421 * The multiplication factor f also needs to be multiplied by c_1
4422 * for the next x_j, j > i.
4424 void isl_seq_preimage(isl_int *dst, isl_int *src,
4425 __isl_keep isl_multi_aff *ma, int n_before, int n_after,
4426 int n_div_ma, int n_div_bmap,
4427 isl_int f, isl_int c1, isl_int c2, isl_int g, int has_denom)
4430 int n_param, n_in, n_out;
4433 n_param = isl_multi_aff_dim(ma, isl_dim_param);
4434 n_in = isl_multi_aff_dim(ma, isl_dim_in);
4435 n_out = isl_multi_aff_dim(ma, isl_dim_out);
4437 isl_seq_cpy(dst, src, has_denom + 1 + n_param + n_before);
4438 o_dst = o_src = has_denom + 1 + n_param + n_before;
4439 isl_seq_clr(dst + o_dst, n_in);
4442 isl_seq_cpy(dst + o_dst, src + o_src, n_after);
4445 isl_seq_clr(dst + o_dst, n_div_ma);
4447 isl_seq_cpy(dst + o_dst, src + o_src, n_div_bmap);
4449 isl_int_set_si(f, 1);
4451 for (i = 0; i < n_out; ++i) {
4452 int offset = has_denom + 1 + n_param + n_before + i;
4454 if (isl_int_is_zero(src[offset]))
4456 isl_int_set(c1, ma->p[i]->v->el[0]);
4457 isl_int_mul(c2, f, src[offset]);
4458 isl_int_gcd(g, c1, c2);
4459 isl_int_divexact(c1, c1, g);
4460 isl_int_divexact(c2, c2, g);
4462 isl_int_mul(f, f, c1);
4465 isl_seq_combine(dst + o_dst, c1, dst + o_dst,
4466 c2, ma->p[i]->v->el + o_src, 1 + n_param);
4467 o_dst += 1 + n_param;
4468 o_src += 1 + n_param;
4469 isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_before);
4471 isl_seq_combine(dst + o_dst, c1, dst + o_dst,
4472 c2, ma->p[i]->v->el + o_src, n_in);
4475 isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_after);
4477 isl_seq_combine(dst + o_dst, c1, dst + o_dst,
4478 c2, ma->p[i]->v->el + o_src, n_div_ma);
4481 isl_seq_scale(dst + o_dst, dst + o_dst, c1, n_div_bmap);
4483 isl_int_mul(dst[0], dst[0], c1);
4487 /* Compute the pullback of "aff" by the function represented by "ma".
4488 * In other words, plug in "ma" in "aff". The result is an affine expression
4489 * defined over the domain space of "ma".
4491 * If "aff" is represented by
4493 * (a(p) + b x + c(divs))/d
4495 * and ma is represented by
4497 * x = D(p) + F(y) + G(divs')
4499 * then the result is
4501 * (a(p) + b D(p) + b F(y) + b G(divs') + c(divs))/d
4503 * The divs in the local space of the input are similarly adjusted
4504 * through a call to isl_local_space_preimage_multi_aff.
4506 __isl_give isl_aff *isl_aff_pullback_multi_aff(__isl_take isl_aff *aff,
4507 __isl_take isl_multi_aff *ma)
4509 isl_aff *res = NULL;
4510 isl_local_space *ls;
4511 int n_div_aff, n_div_ma;
4512 isl_int f, c1, c2, g;
4514 ma = isl_multi_aff_align_divs(ma);
4518 n_div_aff = isl_aff_dim(aff, isl_dim_div);
4519 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
4521 ls = isl_aff_get_domain_local_space(aff);
4522 ls = isl_local_space_preimage_multi_aff(ls, isl_multi_aff_copy(ma));
4523 res = isl_aff_alloc(ls);
4532 isl_seq_preimage(res->v->el, aff->v->el, ma, 0, 0, n_div_ma, n_div_aff,
4541 isl_multi_aff_free(ma);
4542 res = isl_aff_normalize(res);
4546 isl_multi_aff_free(ma);
4551 /* Compute the pullback of "ma1" by the function represented by "ma2".
4552 * In other words, plug in "ma2" in "ma1".
4554 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4555 __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
4558 isl_space *space = NULL;
4560 ma2 = isl_multi_aff_align_divs(ma2);
4561 ma1 = isl_multi_aff_cow(ma1);
4565 space = isl_space_join(isl_multi_aff_get_space(ma2),
4566 isl_multi_aff_get_space(ma1));
4568 for (i = 0; i < ma1->n; ++i) {
4569 ma1->p[i] = isl_aff_pullback_multi_aff(ma1->p[i],
4570 isl_multi_aff_copy(ma2));
4575 ma1 = isl_multi_aff_reset_space(ma1, space);
4576 isl_multi_aff_free(ma2);
4579 isl_space_free(space);
4580 isl_multi_aff_free(ma2);
4581 isl_multi_aff_free(ma1);
4585 /* Extend the local space of "dst" to include the divs
4586 * in the local space of "src".
4588 __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
4589 __isl_keep isl_aff *src)
4597 return isl_aff_free(dst);
4599 ctx = isl_aff_get_ctx(src);
4600 if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
4601 isl_die(ctx, isl_error_invalid,
4602 "spaces don't match", goto error);
4604 if (src->ls->div->n_row == 0)
4607 exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
4608 exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
4612 div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
4613 dst = isl_aff_expand_divs(dst, div, exp2);
4621 return isl_aff_free(dst);
4624 /* Adjust the local spaces of the affine expressions in "maff"
4625 * such that they all have the save divs.
4627 __isl_give isl_multi_aff *isl_multi_aff_align_divs(
4628 __isl_take isl_multi_aff *maff)
4636 maff = isl_multi_aff_cow(maff);
4640 for (i = 1; i < maff->n; ++i)
4641 maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
4642 for (i = 1; i < maff->n; ++i) {
4643 maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
4645 return isl_multi_aff_free(maff);
4651 __isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
4653 aff = isl_aff_cow(aff);
4657 aff->ls = isl_local_space_lift(aff->ls);
4659 return isl_aff_free(aff);
4664 /* Lift "maff" to a space with extra dimensions such that the result
4665 * has no more existentially quantified variables.
4666 * If "ls" is not NULL, then *ls is assigned the local space that lies
4667 * at the basis of the lifting applied to "maff".
4669 __isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
4670 __isl_give isl_local_space **ls)
4684 isl_space *space = isl_multi_aff_get_domain_space(maff);
4685 *ls = isl_local_space_from_space(space);
4687 return isl_multi_aff_free(maff);
4692 maff = isl_multi_aff_cow(maff);
4693 maff = isl_multi_aff_align_divs(maff);
4697 n_div = isl_aff_dim(maff->p[0], isl_dim_div);
4698 space = isl_multi_aff_get_space(maff);
4699 space = isl_space_lift(isl_space_domain(space), n_div);
4700 space = isl_space_extend_domain_with_range(space,
4701 isl_multi_aff_get_space(maff));
4703 return isl_multi_aff_free(maff);
4704 isl_space_free(maff->space);
4705 maff->space = space;
4708 *ls = isl_aff_get_domain_local_space(maff->p[0]);
4710 return isl_multi_aff_free(maff);
4713 for (i = 0; i < maff->n; ++i) {
4714 maff->p[i] = isl_aff_lift(maff->p[i]);
4722 isl_local_space_free(*ls);
4723 return isl_multi_aff_free(maff);
4727 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
4729 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4730 __isl_keep isl_pw_multi_aff *pma, int pos)
4740 n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
4741 if (pos < 0 || pos >= n_out)
4742 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
4743 "index out of bounds", return NULL);
4745 space = isl_pw_multi_aff_get_space(pma);
4746 space = isl_space_drop_dims(space, isl_dim_out,
4747 pos + 1, n_out - pos - 1);
4748 space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
4750 pa = isl_pw_aff_alloc_size(space, pma->n);
4751 for (i = 0; i < pma->n; ++i) {
4753 aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
4754 pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
4760 /* Return an isl_pw_multi_aff with the given "set" as domain and
4761 * an unnamed zero-dimensional range.
4763 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4764 __isl_take isl_set *set)
4769 space = isl_set_get_space(set);
4770 space = isl_space_from_domain(space);
4771 ma = isl_multi_aff_zero(space);
4772 return isl_pw_multi_aff_alloc(set, ma);
4775 /* Add an isl_pw_multi_aff with the given "set" as domain and
4776 * an unnamed zero-dimensional range to *user.
4778 static int add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user)
4780 isl_union_pw_multi_aff **upma = user;
4781 isl_pw_multi_aff *pma;
4783 pma = isl_pw_multi_aff_from_domain(set);
4784 *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
4789 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
4790 * an unnamed zero-dimensional range.
4792 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain(
4793 __isl_take isl_union_set *uset)
4796 isl_union_pw_multi_aff *upma;
4801 space = isl_union_set_get_space(uset);
4802 upma = isl_union_pw_multi_aff_empty(space);
4804 if (isl_union_set_foreach_set(uset,
4805 &add_pw_multi_aff_from_domain, &upma) < 0)
4808 isl_union_set_free(uset);
4811 isl_union_set_free(uset);
4812 isl_union_pw_multi_aff_free(upma);
4816 /* Convert "pma" to an isl_map and add it to *umap.
4818 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
4820 isl_union_map **umap = user;
4823 map = isl_map_from_pw_multi_aff(pma);
4824 *umap = isl_union_map_add_map(*umap, map);
4829 /* Construct a union map mapping the domain of the union
4830 * piecewise multi-affine expression to its range, with each dimension
4831 * in the range equated to the corresponding affine expression on its cell.
4833 __isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff(
4834 __isl_take isl_union_pw_multi_aff *upma)
4837 isl_union_map *umap;
4842 space = isl_union_pw_multi_aff_get_space(upma);
4843 umap = isl_union_map_empty(space);
4845 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
4846 &map_from_pw_multi_aff, &umap) < 0)
4849 isl_union_pw_multi_aff_free(upma);
4852 isl_union_pw_multi_aff_free(upma);
4853 isl_union_map_free(umap);
4857 /* Local data for bin_entry and the callback "fn".
4859 struct isl_union_pw_multi_aff_bin_data {
4860 isl_union_pw_multi_aff *upma2;
4861 isl_union_pw_multi_aff *res;
4862 isl_pw_multi_aff *pma;
4863 int (*fn)(void **entry, void *user);
4866 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
4867 * and call data->fn for each isl_pw_multi_aff in data->upma2.
4869 static int bin_entry(void **entry, void *user)
4871 struct isl_union_pw_multi_aff_bin_data *data = user;
4872 isl_pw_multi_aff *pma = *entry;
4875 if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
4876 data->fn, data) < 0)
4882 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
4883 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
4884 * passed as user field) and the isl_pw_multi_aff from upma2 is available
4885 * as *entry. The callback should adjust data->res if desired.
4887 static __isl_give isl_union_pw_multi_aff *bin_op(
4888 __isl_take isl_union_pw_multi_aff *upma1,
4889 __isl_take isl_union_pw_multi_aff *upma2,
4890 int (*fn)(void **entry, void *user))
4893 struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
4895 space = isl_union_pw_multi_aff_get_space(upma2);
4896 upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
4897 space = isl_union_pw_multi_aff_get_space(upma1);
4898 upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
4900 if (!upma1 || !upma2)
4904 data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
4906 if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
4907 &bin_entry, &data) < 0)
4910 isl_union_pw_multi_aff_free(upma1);
4911 isl_union_pw_multi_aff_free(upma2);
4914 isl_union_pw_multi_aff_free(upma1);
4915 isl_union_pw_multi_aff_free(upma2);
4916 isl_union_pw_multi_aff_free(data.res);
4920 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
4921 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
4923 static __isl_give isl_pw_multi_aff *pw_multi_aff_range_product(
4924 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
4928 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
4929 isl_pw_multi_aff_get_space(pma2));
4930 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
4931 &isl_multi_aff_range_product);
4934 /* Given two isl_pw_multi_affs A -> B and C -> D,
4935 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
4937 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_product(
4938 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
4940 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
4941 &pw_multi_aff_range_product);
4944 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
4945 * construct an isl_pw_multi_aff (A * C) -> (B, D).
4947 static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
4948 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
4952 space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
4953 isl_pw_multi_aff_get_space(pma2));
4954 space = isl_space_flatten_range(space);
4955 return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
4956 &isl_multi_aff_flat_range_product);
4959 /* Given two isl_pw_multi_affs A -> B and C -> D,
4960 * construct an isl_pw_multi_aff (A * C) -> (B, D).
4962 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
4963 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
4965 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
4966 &pw_multi_aff_flat_range_product);
4969 /* If data->pma and *entry have the same domain space, then compute
4970 * their flat range product and the result to data->res.
4972 static int flat_range_product_entry(void **entry, void *user)
4974 struct isl_union_pw_multi_aff_bin_data *data = user;
4975 isl_pw_multi_aff *pma2 = *entry;
4977 if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
4978 pma2->dim, isl_dim_in))
4981 pma2 = isl_pw_multi_aff_flat_range_product(
4982 isl_pw_multi_aff_copy(data->pma),
4983 isl_pw_multi_aff_copy(pma2));
4985 data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
4990 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
4991 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
4993 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
4994 __isl_take isl_union_pw_multi_aff *upma1,
4995 __isl_take isl_union_pw_multi_aff *upma2)
4997 return bin_op(upma1, upma2, &flat_range_product_entry);
5000 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5001 * The parameters are assumed to have been aligned.
5003 * The implementation essentially performs an isl_pw_*_on_shared_domain,
5004 * except that it works on two different isl_pw_* types.
5006 static __isl_give isl_pw_multi_aff *pw_multi_aff_set_pw_aff(
5007 __isl_take isl_pw_multi_aff *pma, unsigned pos,
5008 __isl_take isl_pw_aff *pa)
5011 isl_pw_multi_aff *res = NULL;
5016 if (!isl_space_tuple_match(pma->dim, isl_dim_in, pa->dim, isl_dim_in))
5017 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
5018 "domains don't match", goto error);
5019 if (pos >= isl_pw_multi_aff_dim(pma, isl_dim_out))
5020 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
5021 "index out of bounds", goto error);
5024 res = isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma), n);
5026 for (i = 0; i < pma->n; ++i) {
5027 for (j = 0; j < pa->n; ++j) {
5029 isl_multi_aff *res_ij;
5032 common = isl_set_intersect(isl_set_copy(pma->p[i].set),
5033 isl_set_copy(pa->p[j].set));
5034 empty = isl_set_plain_is_empty(common);
5035 if (empty < 0 || empty) {
5036 isl_set_free(common);
5042 res_ij = isl_multi_aff_set_aff(
5043 isl_multi_aff_copy(pma->p[i].maff), pos,
5044 isl_aff_copy(pa->p[j].aff));
5045 res_ij = isl_multi_aff_gist(res_ij,
5046 isl_set_copy(common));
5048 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
5052 isl_pw_multi_aff_free(pma);
5053 isl_pw_aff_free(pa);
5056 isl_pw_multi_aff_free(pma);
5057 isl_pw_aff_free(pa);
5058 return isl_pw_multi_aff_free(res);
5061 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5063 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
5064 __isl_take isl_pw_multi_aff *pma, unsigned pos,
5065 __isl_take isl_pw_aff *pa)
5069 if (isl_space_match(pma->dim, isl_dim_param, pa->dim, isl_dim_param))
5070 return pw_multi_aff_set_pw_aff(pma, pos, pa);
5071 if (!isl_space_has_named_params(pma->dim) ||
5072 !isl_space_has_named_params(pa->dim))
5073 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
5074 "unaligned unnamed parameters", goto error);
5075 pma = isl_pw_multi_aff_align_params(pma, isl_pw_aff_get_space(pa));
5076 pa = isl_pw_aff_align_params(pa, isl_pw_multi_aff_get_space(pma));
5077 return pw_multi_aff_set_pw_aff(pma, pos, pa);
5079 isl_pw_multi_aff_free(pma);
5080 isl_pw_aff_free(pa);
5084 /* Check that the domain space of "pa" matches "space".
5086 * Return 0 on success and -1 on error.
5088 int isl_pw_aff_check_match_domain_space(__isl_keep isl_pw_aff *pa,
5089 __isl_keep isl_space *space)
5091 isl_space *pa_space;
5097 pa_space = isl_pw_aff_get_space(pa);
5099 match = isl_space_match(space, isl_dim_param, pa_space, isl_dim_param);
5103 isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
5104 "parameters don't match", goto error);
5105 match = isl_space_tuple_match(space, isl_dim_in, pa_space, isl_dim_in);
5109 isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
5110 "domains don't match", goto error);
5111 isl_space_free(pa_space);
5114 isl_space_free(pa_space);
5121 #include <isl_multi_templ.c>
5123 /* Scale the first elements of "ma" by the corresponding elements of "vec".
5125 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(__isl_take isl_multi_aff *ma,
5126 __isl_take isl_vec *vec)
5134 n = isl_multi_aff_dim(ma, isl_dim_out);
5135 if (isl_vec_size(vec) < n)
5136 n = isl_vec_size(vec);
5139 for (i = 0; i < n; ++i) {
5142 isl_vec_get_element(vec, i, &v);
5144 aff = isl_multi_aff_get_aff(ma, i);
5145 aff = isl_aff_scale(aff, v);
5146 ma = isl_multi_aff_set_aff(ma, i, aff);
5154 isl_multi_aff_free(ma);
5158 /* Scale the first elements of "pma" by the corresponding elements of "vec".
5160 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
5161 __isl_take isl_pw_multi_aff *pma, __isl_take isl_vec *v)
5165 pma = isl_pw_multi_aff_cow(pma);
5169 for (i = 0; i < pma->n; ++i) {
5170 pma->p[i].maff = isl_multi_aff_scale_vec(pma->p[i].maff,
5172 if (!pma->p[i].maff)
5180 isl_pw_multi_aff_free(pma);
5184 /* This function is called for each entry of an isl_union_pw_multi_aff.
5185 * Replace the entry by the result of applying isl_pw_multi_aff_scale_vec
5186 * to the original entry with the isl_vec in "user" as extra argument.
5188 static int union_pw_multi_aff_scale_vec_entry(void **entry, void *user)
5190 isl_pw_multi_aff **pma = (isl_pw_multi_aff **) entry;
5193 *pma = isl_pw_multi_aff_scale_vec(*pma, isl_vec_copy(v));
5200 /* Scale the first elements of "upma" by the corresponding elements of "vec".
5202 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
5203 __isl_take isl_union_pw_multi_aff *upma, __isl_take isl_vec *v)
5205 upma = isl_union_pw_multi_aff_cow(upma);
5209 if (isl_hash_table_foreach(upma->dim->ctx, &upma->table,
5210 &union_pw_multi_aff_scale_vec_entry, v) < 0)
5217 isl_union_pw_multi_aff_free(upma);