2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Universiteit Leiden
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
8 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
10 * and Leiden Institute of Advanced Computer Science,
11 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
14 #include <isl_map_private.h>
15 #include <isl_aff_private.h>
16 #include <isl_dim_private.h>
17 #include <isl_local_space_private.h>
18 #include <isl_mat_private.h>
19 #include <isl/constraint.h>
23 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
24 __isl_take isl_vec *v)
31 aff = isl_calloc_type(v->ctx, struct isl_aff);
41 isl_local_space_free(ls);
46 __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
55 ctx = isl_local_space_get_ctx(ls);
56 if (!isl_local_space_divs_known(ls))
57 isl_die(ctx, isl_error_invalid, "local space has unknown divs",
60 total = isl_local_space_dim(ls, isl_dim_all);
61 v = isl_vec_alloc(ctx, 1 + 1 + total);
62 return isl_aff_alloc_vec(ls, v);
64 isl_local_space_free(ls);
68 __isl_give isl_aff *isl_aff_zero(__isl_take isl_local_space *ls)
72 aff = isl_aff_alloc(ls);
76 isl_int_set_si(aff->v->el[0], 1);
77 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
82 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
91 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
96 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
97 isl_vec_copy(aff->v));
100 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
108 return isl_aff_dup(aff);
111 void *isl_aff_free(__isl_take isl_aff *aff)
119 isl_local_space_free(aff->ls);
120 isl_vec_free(aff->v);
127 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
129 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
132 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
134 return aff ? isl_local_space_dim(aff->ls, type) : 0;
137 __isl_give isl_dim *isl_aff_get_dim(__isl_keep isl_aff *aff)
139 return aff ? isl_local_space_get_dim(aff->ls) : NULL;
142 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
144 return aff ? isl_local_space_copy(aff->ls) : NULL;
147 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
148 enum isl_dim_type type, unsigned pos)
150 return aff ? isl_local_space_get_dim_name(aff->ls, type, pos) : 0;
153 __isl_give isl_aff *isl_aff_reset_dim(__isl_take isl_aff *aff,
154 __isl_take isl_dim *dim)
156 aff = isl_aff_cow(aff);
160 aff->ls = isl_local_space_reset_dim(aff->ls, dim);
162 return isl_aff_free(aff);
171 /* Reorder the coefficients of the affine expression based
172 * on the given reodering.
173 * The reordering r is assumed to have been extended with the local
176 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
177 __isl_take isl_reordering *r, int n_div)
185 res = isl_vec_alloc(vec->ctx, 2 + isl_dim_total(r->dim) + n_div);
186 isl_seq_cpy(res->el, vec->el, 2);
187 isl_seq_clr(res->el + 2, res->size - 2);
188 for (i = 0; i < r->len; ++i)
189 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
191 isl_reordering_free(r);
196 isl_reordering_free(r);
200 /* Reorder the dimensions of "aff" according to the given reordering.
202 __isl_give isl_aff *isl_aff_realign(__isl_take isl_aff *aff,
203 __isl_take isl_reordering *r)
205 aff = isl_aff_cow(aff);
209 r = isl_reordering_extend(r, aff->ls->div->n_row);
210 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
211 aff->ls->div->n_row);
212 aff->ls = isl_local_space_realign(aff->ls, r);
214 if (!aff->v || !aff->ls)
215 return isl_aff_free(aff);
220 isl_reordering_free(r);
224 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
229 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
232 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
239 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
240 if (equal < 0 || !equal)
243 return isl_vec_is_equal(aff1->v, aff2->v);
246 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
250 isl_int_set(*v, aff->v->el[0]);
254 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
258 isl_int_set(*v, aff->v->el[1]);
262 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
263 enum isl_dim_type type, int pos, isl_int *v)
268 if (pos >= isl_local_space_dim(aff->ls, type))
269 isl_die(aff->v->ctx, isl_error_invalid,
270 "position out of bounds", return -1);
272 pos += isl_local_space_offset(aff->ls, type);
273 isl_int_set(*v, aff->v->el[1 + pos]);
278 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
280 aff = isl_aff_cow(aff);
284 aff->v = isl_vec_cow(aff->v);
286 return isl_aff_free(aff);
288 isl_int_set(aff->v->el[0], v);
293 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
295 aff = isl_aff_cow(aff);
299 aff->v = isl_vec_cow(aff->v);
301 return isl_aff_free(aff);
303 isl_int_set(aff->v->el[1], v);
308 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
310 if (isl_int_is_zero(v))
313 aff = isl_aff_cow(aff);
317 aff->v = isl_vec_cow(aff->v);
319 return isl_aff_free(aff);
321 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
326 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
331 isl_int_set_si(t, v);
332 aff = isl_aff_add_constant(aff, t);
338 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
340 aff = isl_aff_cow(aff);
344 aff->v = isl_vec_cow(aff->v);
346 return isl_aff_free(aff);
348 isl_int_set_si(aff->v->el[1], v);
353 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
354 enum isl_dim_type type, int pos, isl_int v)
359 if (pos >= isl_local_space_dim(aff->ls, type))
360 isl_die(aff->v->ctx, isl_error_invalid,
361 "position out of bounds", return isl_aff_free(aff));
363 aff = isl_aff_cow(aff);
367 aff->v = isl_vec_cow(aff->v);
369 return isl_aff_free(aff);
371 pos += isl_local_space_offset(aff->ls, type);
372 isl_int_set(aff->v->el[1 + pos], v);
377 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
378 enum isl_dim_type type, int pos, int v)
383 if (pos >= isl_local_space_dim(aff->ls, type))
384 isl_die(aff->v->ctx, isl_error_invalid,
385 "position out of bounds", return isl_aff_free(aff));
387 aff = isl_aff_cow(aff);
391 aff->v = isl_vec_cow(aff->v);
393 return isl_aff_free(aff);
395 pos += isl_local_space_offset(aff->ls, type);
396 isl_int_set_si(aff->v->el[1 + pos], v);
401 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
402 enum isl_dim_type type, int pos, isl_int v)
407 if (pos >= isl_local_space_dim(aff->ls, type))
408 isl_die(aff->v->ctx, isl_error_invalid,
409 "position out of bounds", return isl_aff_free(aff));
411 aff = isl_aff_cow(aff);
415 aff->v = isl_vec_cow(aff->v);
417 return isl_aff_free(aff);
419 pos += isl_local_space_offset(aff->ls, type);
420 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
425 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
426 enum isl_dim_type type, int pos, int v)
431 isl_int_set_si(t, v);
432 aff = isl_aff_add_coefficient(aff, type, pos, t);
438 __isl_give isl_div *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
443 return isl_local_space_get_div(aff->ls, pos);
446 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
448 aff = isl_aff_cow(aff);
451 aff->v = isl_vec_cow(aff->v);
453 return isl_aff_free(aff);
455 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
460 /* Given f, return floor(f).
461 * If f is an integer expression, then just return f.
462 * Otherwise, create a new div d = [f] and return the expression d.
464 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
472 if (isl_int_is_one(aff->v->el[0]))
475 aff = isl_aff_cow(aff);
479 aff->ls = isl_local_space_add_div(aff->ls, isl_vec_copy(aff->v));
481 return isl_aff_free(aff);
483 ctx = isl_aff_get_ctx(aff);
485 isl_vec_free(aff->v);
486 aff->v = isl_vec_alloc(ctx, size + 1);
487 aff->v = isl_vec_clr(aff->v);
489 return isl_aff_free(aff);
490 isl_int_set_si(aff->v->el[0], 1);
491 isl_int_set_si(aff->v->el[size], 1);
496 /* Given f, return ceil(f).
497 * If f is an integer expression, then just return f.
498 * Otherwise, create a new div d = [-f] and return the expression -d.
500 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
505 if (isl_int_is_one(aff->v->el[0]))
508 aff = isl_aff_neg(aff);
509 aff = isl_aff_floor(aff);
510 aff = isl_aff_neg(aff);
515 /* Apply the expansion computed by isl_merge_divs.
516 * The expansion itself is given by "exp" while the resulting
517 * list of divs is given by "div".
519 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
520 __isl_take isl_mat *div, int *exp)
527 aff = isl_aff_cow(aff);
531 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
532 new_n_div = isl_mat_rows(div);
533 if (new_n_div < old_n_div)
534 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
535 "not an expansion", goto error);
537 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
541 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
543 for (i = new_n_div - 1; i >= 0; --i) {
544 if (j >= 0 && exp[j] == i) {
546 isl_int_swap(aff->v->el[offset + i],
547 aff->v->el[offset + j]);
550 isl_int_set_si(aff->v->el[offset + i], 0);
553 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
564 /* Add two affine expressions that live in the same local space.
566 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
567 __isl_take isl_aff *aff2)
571 aff1 = isl_aff_cow(aff1);
575 aff1->v = isl_vec_cow(aff1->v);
581 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
582 isl_int_divexact(f, aff2->v->el[0], gcd);
583 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
584 isl_int_divexact(f, aff1->v->el[0], gcd);
585 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
586 isl_int_divexact(f, aff2->v->el[0], gcd);
587 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
599 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
600 __isl_take isl_aff *aff2)
610 ctx = isl_aff_get_ctx(aff1);
611 if (!isl_dim_equal(aff1->ls->dim, aff2->ls->dim))
612 isl_die(ctx, isl_error_invalid,
613 "spaces don't match", goto error);
615 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
616 return add_expanded(aff1, aff2);
618 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
619 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
623 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
624 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
625 aff2 = isl_aff_expand_divs(aff2, div, exp2);
629 return add_expanded(aff1, aff2);
638 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
639 __isl_take isl_aff *aff2)
641 return isl_aff_add(aff1, isl_aff_neg(aff2));
644 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
648 if (isl_int_is_one(f))
651 aff = isl_aff_cow(aff);
654 aff->v = isl_vec_cow(aff->v);
656 return isl_aff_free(aff);
659 isl_int_gcd(gcd, aff->v->el[0], f);
660 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
661 isl_int_divexact(gcd, f, gcd);
662 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
668 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
672 if (isl_int_is_one(f))
675 aff = isl_aff_cow(aff);
678 aff->v = isl_vec_cow(aff->v);
680 return isl_aff_free(aff);
683 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
684 isl_int_gcd(gcd, gcd, f);
685 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
686 isl_int_divexact(gcd, f, gcd);
687 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
693 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
701 isl_int_set_ui(v, f);
702 aff = isl_aff_scale_down(aff, v);
708 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
709 enum isl_dim_type type, unsigned pos, const char *s)
711 aff = isl_aff_cow(aff);
714 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
716 return isl_aff_free(aff);
721 /* Exploit the equalities in "eq" to simplify the affine expression
722 * and the expressions of the integer divisions in the local space.
723 * The integer divisions in this local space are assumed to appear
724 * as regular dimensions in "eq".
726 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
727 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
736 isl_basic_set_free(eq);
740 aff = isl_aff_cow(aff);
744 aff->ls = isl_local_space_substitute_equalities(aff->ls,
745 isl_basic_set_copy(eq));
749 total = 1 + isl_dim_total(eq->dim);
751 for (i = 0; i < eq->n_eq; ++i) {
752 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
753 if (j < 0 || j == 0 || j >= total)
756 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
760 isl_basic_set_free(eq);
763 isl_basic_set_free(eq);
768 /* Exploit the equalities in "eq" to simplify the affine expression
769 * and the expressions of the integer divisions in the local space.
771 static __isl_give isl_aff *isl_aff_substitute_equalities(
772 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
778 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
780 eq = isl_basic_set_add(eq, isl_dim_set, n_div);
781 return isl_aff_substitute_equalities_lifted(aff, eq);
783 isl_basic_set_free(eq);
788 /* Look for equalities among the variables shared by context and aff
789 * and the integer divisions of aff, if any.
790 * The equalities are then used to eliminate coefficients and/or integer
791 * divisions from aff.
793 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
794 __isl_take isl_set *context)
801 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
804 context = isl_set_add_dims(context, isl_dim_set, n_div);
805 bset = isl_basic_set_from_local_space(
806 isl_aff_get_local_space(aff));
807 bset = isl_basic_set_lift(bset);
808 bset = isl_basic_set_flatten(bset);
809 context = isl_set_intersect(context,
810 isl_set_from_basic_set(bset));
813 hull = isl_set_affine_hull(context);
814 return isl_aff_substitute_equalities_lifted(aff, hull);
817 isl_set_free(context);
821 /* Return a basic set containing those elements in the space
822 * of aff where it is non-negative.
824 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
826 isl_constraint *ineq;
828 ineq = isl_inequality_from_aff(aff);
830 return isl_basic_set_from_constraint(ineq);
833 /* Return a basic set containing those elements in the space
834 * of aff where it is zero.
836 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
838 isl_constraint *ineq;
840 ineq = isl_equality_from_aff(aff);
842 return isl_basic_set_from_constraint(ineq);
845 /* Return a basic set containing those elements in the shared space
846 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
848 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
849 __isl_take isl_aff *aff2)
851 aff1 = isl_aff_sub(aff1, aff2);
853 return isl_aff_nonneg_basic_set(aff1);
856 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
857 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
859 aff1 = isl_aff_add(aff1, aff2);
860 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
864 int isl_aff_is_empty(__isl_keep isl_aff *aff)
872 /* Set active[i] to 1 if the dimension at position i is involved
873 * in the affine expression.
875 static int set_active(__isl_keep isl_aff *aff, int *active)
884 total = aff->v->size - 2;
885 for (i = 0; i < total; ++i)
886 active[i] = !isl_int_is_zero(aff->v->el[2 + i]);
888 offset = isl_local_space_offset(aff->ls, isl_dim_div) - 1;
889 for (i = aff->ls->div->n_row - 1; i >= 0; --i) {
890 if (!active[offset + i])
892 for (j = 0; j < total; ++j)
894 !isl_int_is_zero(aff->ls->div->row[i][2 + j]);
900 /* Check whether the given affine expression has non-zero coefficient
901 * for any dimension in the given range or if any of these dimensions
902 * appear with non-zero coefficients in any of the integer divisions
903 * involved in the affine expression.
905 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
906 enum isl_dim_type type, unsigned first, unsigned n)
918 ctx = isl_aff_get_ctx(aff);
919 if (first + n > isl_aff_dim(aff, type))
920 isl_die(ctx, isl_error_invalid,
921 "range out of bounds", return -1);
923 active = isl_calloc_array(ctx, int,
924 isl_local_space_dim(aff->ls, isl_dim_all));
925 if (set_active(aff, active) < 0)
928 first += isl_local_space_offset(aff->ls, type) - 1;
929 for (i = 0; i < n; ++i)
930 if (active[first + i]) {
943 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
944 enum isl_dim_type type, unsigned first, unsigned n)
950 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
953 ctx = isl_aff_get_ctx(aff);
954 if (first + n > isl_aff_dim(aff, type))
955 isl_die(ctx, isl_error_invalid, "range out of bounds",
956 return isl_aff_free(aff));
958 aff = isl_aff_cow(aff);
962 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
964 return isl_aff_free(aff);
966 first += 1 + isl_local_space_offset(aff->ls, type);
967 aff->v = isl_vec_drop_els(aff->v, first, n);
969 return isl_aff_free(aff);
974 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
975 enum isl_dim_type type, unsigned first, unsigned n)
981 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
984 ctx = isl_aff_get_ctx(aff);
985 if (first > isl_aff_dim(aff, type))
986 isl_die(ctx, isl_error_invalid, "position out of bounds",
987 return isl_aff_free(aff));
989 aff = isl_aff_cow(aff);
993 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
995 return isl_aff_free(aff);
997 first += 1 + isl_local_space_offset(aff->ls, type);
998 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
1000 return isl_aff_free(aff);
1005 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
1006 enum isl_dim_type type, unsigned n)
1010 pos = isl_aff_dim(aff, type);
1012 return isl_aff_insert_dims(aff, type, pos, n);
1015 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
1016 enum isl_dim_type type, unsigned n)
1020 pos = isl_pw_aff_dim(pwaff, type);
1022 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
1025 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(__isl_take isl_pw_aff *pwaff,
1026 __isl_take isl_id *id)
1030 dim = isl_pw_aff_get_dim(pwaff);
1031 dim = isl_dim_set_tuple_id(dim, isl_dim_set, id);
1033 return isl_pw_aff_reset_dim(pwaff, dim);
1037 #define PW isl_pw_aff
1041 #define EL_IS_ZERO is_empty
1045 #define IS_ZERO is_empty
1051 #define NO_MOVE_DIMS
1055 #include <isl_pw_templ.c>
1057 static __isl_give isl_set *align_params_pw_pw_set_and(
1058 __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
1059 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1060 __isl_take isl_pw_aff *pwaff2))
1062 if (!pwaff1 || !pwaff2)
1064 if (isl_dim_match(pwaff1->dim, isl_dim_param,
1065 pwaff2->dim, isl_dim_param))
1066 return fn(pwaff1, pwaff2);
1067 if (!isl_dim_has_named_params(pwaff1->dim) ||
1068 !isl_dim_has_named_params(pwaff2->dim))
1069 isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
1070 "unaligned unnamed parameters", goto error);
1071 pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_dim(pwaff2));
1072 pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_dim(pwaff1));
1073 return fn(pwaff1, pwaff2);
1075 isl_pw_aff_free(pwaff1);
1076 isl_pw_aff_free(pwaff2);
1080 /* Compute a piecewise quasi-affine expression with a domain that
1081 * is the union of those of pwaff1 and pwaff2 and such that on each
1082 * cell, the quasi-affine expression is the maximum of those of pwaff1
1083 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1084 * cell, then the associated expression is the defined one.
1086 static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1087 __isl_take isl_pw_aff *pwaff2)
1094 if (!pwaff1 || !pwaff2)
1097 ctx = isl_dim_get_ctx(pwaff1->dim);
1098 if (!isl_dim_equal(pwaff1->dim, pwaff2->dim))
1099 isl_die(ctx, isl_error_invalid,
1100 "arguments should live in same space", goto error);
1102 if (isl_pw_aff_is_empty(pwaff1)) {
1103 isl_pw_aff_free(pwaff1);
1107 if (isl_pw_aff_is_empty(pwaff2)) {
1108 isl_pw_aff_free(pwaff2);
1112 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
1113 res = isl_pw_aff_alloc_(isl_dim_copy(pwaff1->dim), n);
1115 for (i = 0; i < pwaff1->n; ++i) {
1116 set = isl_set_copy(pwaff1->p[i].set);
1117 for (j = 0; j < pwaff2->n; ++j) {
1118 struct isl_set *common;
1121 common = isl_set_intersect(
1122 isl_set_copy(pwaff1->p[i].set),
1123 isl_set_copy(pwaff2->p[j].set));
1124 ge = isl_set_from_basic_set(isl_aff_ge_basic_set(
1125 isl_aff_copy(pwaff2->p[j].aff),
1126 isl_aff_copy(pwaff1->p[i].aff)));
1127 ge = isl_set_intersect(common, ge);
1128 if (isl_set_plain_is_empty(ge)) {
1132 set = isl_set_subtract(set, isl_set_copy(ge));
1134 res = isl_pw_aff_add_piece(res, ge,
1135 isl_aff_copy(pwaff2->p[j].aff));
1137 res = isl_pw_aff_add_piece(res, set,
1138 isl_aff_copy(pwaff1->p[i].aff));
1141 for (j = 0; j < pwaff2->n; ++j) {
1142 set = isl_set_copy(pwaff2->p[j].set);
1143 for (i = 0; i < pwaff1->n; ++i)
1144 set = isl_set_subtract(set,
1145 isl_set_copy(pwaff1->p[i].set));
1146 res = isl_pw_aff_add_piece(res, set,
1147 isl_aff_copy(pwaff2->p[j].aff));
1150 isl_pw_aff_free(pwaff1);
1151 isl_pw_aff_free(pwaff2);
1155 isl_pw_aff_free(pwaff1);
1156 isl_pw_aff_free(pwaff2);
1160 __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1161 __isl_take isl_pw_aff *pwaff2)
1163 return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_union_max);
1166 /* Construct a map with as domain the domain of pwaff and
1167 * one-dimensional range corresponding to the affine expressions.
1169 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1178 dim = isl_pw_aff_get_dim(pwaff);
1179 dim = isl_dim_from_domain(dim);
1180 dim = isl_dim_add(dim, isl_dim_out, 1);
1181 map = isl_map_empty(dim);
1183 for (i = 0; i < pwaff->n; ++i) {
1184 isl_basic_map *bmap;
1187 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
1188 map_i = isl_map_from_basic_map(bmap);
1189 map_i = isl_map_intersect_domain(map_i,
1190 isl_set_copy(pwaff->p[i].set));
1191 map = isl_map_union_disjoint(map, map_i);
1194 isl_pw_aff_free(pwaff);
1199 /* Return a set containing those elements in the domain
1200 * of pwaff where it is non-negative.
1202 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
1210 set = isl_set_empty(isl_pw_aff_get_dim(pwaff));
1212 for (i = 0; i < pwaff->n; ++i) {
1213 isl_basic_set *bset;
1216 bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff));
1217 set_i = isl_set_from_basic_set(bset);
1218 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1219 set = isl_set_union_disjoint(set, set_i);
1222 isl_pw_aff_free(pwaff);
1227 /* Return a set containing those elements in the domain
1228 * of pwaff where it is zero.
1230 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
1238 set = isl_set_empty(isl_pw_aff_get_dim(pwaff));
1240 for (i = 0; i < pwaff->n; ++i) {
1241 isl_basic_set *bset;
1244 bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
1245 set_i = isl_set_from_basic_set(bset);
1246 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1247 set = isl_set_union_disjoint(set, set_i);
1250 isl_pw_aff_free(pwaff);
1255 /* Return a set containing those elements in the domain
1256 * of pwaff where it is not zero.
1258 __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
1260 return isl_set_complement(isl_pw_aff_zero_set(pwaff));
1263 /* Return a set containing those elements in the shared domain
1264 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1266 * We compute the difference on the shared domain and then construct
1267 * the set of values where this difference is non-negative.
1268 * If strict is set, we first subtract 1 from the difference.
1269 * If equal is set, we only return the elements where pwaff1 and pwaff2
1272 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
1273 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
1275 isl_set *set1, *set2;
1277 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
1278 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
1279 set1 = isl_set_intersect(set1, set2);
1280 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
1281 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
1282 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
1285 isl_dim *dim = isl_set_get_dim(set1);
1287 aff = isl_aff_zero(isl_local_space_from_dim(dim));
1288 aff = isl_aff_add_constant_si(aff, -1);
1289 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
1294 return isl_pw_aff_zero_set(pwaff1);
1295 return isl_pw_aff_nonneg_set(pwaff1);
1298 /* Return a set containing those elements in the shared domain
1299 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1301 static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1302 __isl_take isl_pw_aff *pwaff2)
1304 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
1307 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1308 __isl_take isl_pw_aff *pwaff2)
1310 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
1313 /* Return a set containing those elements in the shared domain
1314 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
1316 static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1317 __isl_take isl_pw_aff *pwaff2)
1319 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
1322 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1323 __isl_take isl_pw_aff *pwaff2)
1325 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
1328 /* Return a set containing those elements in the shared domain
1329 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
1331 static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1332 __isl_take isl_pw_aff *pwaff2)
1334 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
1337 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1338 __isl_take isl_pw_aff *pwaff2)
1340 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
1343 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
1344 __isl_take isl_pw_aff *pwaff2)
1346 return isl_pw_aff_ge_set(pwaff2, pwaff1);
1349 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
1350 __isl_take isl_pw_aff *pwaff2)
1352 return isl_pw_aff_gt_set(pwaff2, pwaff1);
1355 /* Return a set containing those elements in the shared domain
1356 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
1358 static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1359 __isl_take isl_pw_aff *pwaff2)
1361 isl_set *set_lt, *set_gt;
1363 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
1364 isl_pw_aff_copy(pwaff2));
1365 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
1366 return isl_set_union_disjoint(set_lt, set_gt);
1369 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1370 __isl_take isl_pw_aff *pwaff2)
1372 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
1375 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
1380 if (isl_int_is_one(v))
1382 if (!isl_int_is_pos(v))
1383 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1384 "factor needs to be positive",
1385 return isl_pw_aff_free(pwaff));
1386 pwaff = isl_pw_aff_cow(pwaff);
1392 for (i = 0; i < pwaff->n; ++i) {
1393 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
1394 if (!pwaff->p[i].aff)
1395 return isl_pw_aff_free(pwaff);
1401 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
1405 pwaff = isl_pw_aff_cow(pwaff);
1411 for (i = 0; i < pwaff->n; ++i) {
1412 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
1413 if (!pwaff->p[i].aff)
1414 return isl_pw_aff_free(pwaff);
1420 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
1424 pwaff = isl_pw_aff_cow(pwaff);
1430 for (i = 0; i < pwaff->n; ++i) {
1431 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
1432 if (!pwaff->p[i].aff)
1433 return isl_pw_aff_free(pwaff);
1439 /* Return an affine expression that is equal to pwaff_true for elements
1440 * in "cond" and to pwaff_false for elements not in "cond".
1441 * That is, return cond ? pwaff_true : pwaff_false;
1443 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_set *cond,
1444 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
1448 comp = isl_set_complement(isl_set_copy(cond));
1449 pwaff_true = isl_pw_aff_intersect_domain(pwaff_true, cond);
1450 pwaff_false = isl_pw_aff_intersect_domain(pwaff_false, comp);
1452 return isl_pw_aff_add_disjoint(pwaff_true, pwaff_false);
1455 int isl_aff_is_cst(__isl_keep isl_aff *aff)
1460 return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
1463 /* Check whether pwaff is a piecewise constant.
1465 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
1472 for (i = 0; i < pwaff->n; ++i) {
1473 int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
1474 if (is_cst < 0 || !is_cst)
1481 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
1482 __isl_take isl_aff *aff2)
1484 if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
1485 return isl_aff_mul(aff2, aff1);
1487 if (!isl_aff_is_cst(aff2))
1488 isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
1489 "at least one affine expression should be constant",
1492 aff1 = isl_aff_cow(aff1);
1496 aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
1497 aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
1507 static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
1508 __isl_take isl_pw_aff *pwaff2)
1513 if (!pwaff1 || !pwaff2)
1516 n = pwaff1->n * pwaff2->n;
1517 res = isl_pw_aff_alloc_(isl_dim_copy(pwaff1->dim), n);
1519 for (i = 0; i < pwaff1->n; ++i) {
1520 for (j = 0; j < pwaff2->n; ++j) {
1523 common = isl_set_intersect(
1524 isl_set_copy(pwaff1->p[i].set),
1525 isl_set_copy(pwaff2->p[j].set));
1526 if (isl_set_plain_is_empty(common)) {
1527 isl_set_free(common);
1531 prod = isl_aff_mul(isl_aff_copy(pwaff1->p[i].aff),
1532 isl_aff_copy(pwaff2->p[j].aff));
1534 res = isl_pw_aff_add_piece(res, common, prod);
1538 isl_pw_aff_free(pwaff1);
1539 isl_pw_aff_free(pwaff2);
1542 isl_pw_aff_free(pwaff1);
1543 isl_pw_aff_free(pwaff2);
1547 __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
1548 __isl_take isl_pw_aff *pwaff2)
1550 return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
1553 static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
1554 __isl_take isl_pw_aff *pwaff2)
1558 le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
1559 isl_pw_aff_copy(pwaff2));
1560 return isl_pw_aff_cond(le, pwaff1, pwaff2);
1563 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
1564 __isl_take isl_pw_aff *pwaff2)
1566 return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
1569 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
1570 __isl_take isl_pw_aff *pwaff2)
1574 le = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
1575 isl_pw_aff_copy(pwaff2));
1576 return isl_pw_aff_cond(le, pwaff1, pwaff2);
1579 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
1580 __isl_take isl_pw_aff *pwaff2)
1582 return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);