2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
4 * Copyright 2012 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
9 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
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_list_private.h>
23 #include <isl/constraint.h>
26 #include <isl_config.h>
28 __isl_give isl_aff
*isl_aff_alloc_vec(__isl_take isl_local_space
*ls
,
29 __isl_take isl_vec
*v
)
36 aff
= isl_calloc_type(v
->ctx
, struct isl_aff
);
46 isl_local_space_free(ls
);
51 __isl_give isl_aff
*isl_aff_alloc(__isl_take isl_local_space
*ls
)
60 ctx
= isl_local_space_get_ctx(ls
);
61 if (!isl_local_space_divs_known(ls
))
62 isl_die(ctx
, isl_error_invalid
, "local space has unknown divs",
64 if (!isl_local_space_is_set(ls
))
65 isl_die(ctx
, isl_error_invalid
,
66 "domain of affine expression should be a set",
69 total
= isl_local_space_dim(ls
, isl_dim_all
);
70 v
= isl_vec_alloc(ctx
, 1 + 1 + total
);
71 return isl_aff_alloc_vec(ls
, v
);
73 isl_local_space_free(ls
);
77 __isl_give isl_aff
*isl_aff_zero_on_domain(__isl_take isl_local_space
*ls
)
81 aff
= isl_aff_alloc(ls
);
85 isl_int_set_si(aff
->v
->el
[0], 1);
86 isl_seq_clr(aff
->v
->el
+ 1, aff
->v
->size
- 1);
91 __isl_give isl_aff
*isl_aff_copy(__isl_keep isl_aff
*aff
)
100 __isl_give isl_aff
*isl_aff_dup(__isl_keep isl_aff
*aff
)
105 return isl_aff_alloc_vec(isl_local_space_copy(aff
->ls
),
106 isl_vec_copy(aff
->v
));
109 __isl_give isl_aff
*isl_aff_cow(__isl_take isl_aff
*aff
)
117 return isl_aff_dup(aff
);
120 void *isl_aff_free(__isl_take isl_aff
*aff
)
128 isl_local_space_free(aff
->ls
);
129 isl_vec_free(aff
->v
);
136 isl_ctx
*isl_aff_get_ctx(__isl_keep isl_aff
*aff
)
138 return aff
? isl_local_space_get_ctx(aff
->ls
) : NULL
;
141 /* Externally, an isl_aff has a map space, but internally, the
142 * ls field corresponds to the domain of that space.
144 int isl_aff_dim(__isl_keep isl_aff
*aff
, enum isl_dim_type type
)
148 if (type
== isl_dim_out
)
150 if (type
== isl_dim_in
)
152 return isl_local_space_dim(aff
->ls
, type
);
155 __isl_give isl_space
*isl_aff_get_domain_space(__isl_keep isl_aff
*aff
)
157 return aff
? isl_local_space_get_space(aff
->ls
) : NULL
;
160 __isl_give isl_space
*isl_aff_get_space(__isl_keep isl_aff
*aff
)
165 space
= isl_local_space_get_space(aff
->ls
);
166 space
= isl_space_from_domain(space
);
167 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
171 __isl_give isl_local_space
*isl_aff_get_domain_local_space(
172 __isl_keep isl_aff
*aff
)
174 return aff
? isl_local_space_copy(aff
->ls
) : NULL
;
177 __isl_give isl_local_space
*isl_aff_get_local_space(__isl_keep isl_aff
*aff
)
182 ls
= isl_local_space_copy(aff
->ls
);
183 ls
= isl_local_space_from_domain(ls
);
184 ls
= isl_local_space_add_dims(ls
, isl_dim_out
, 1);
188 /* Externally, an isl_aff has a map space, but internally, the
189 * ls field corresponds to the domain of that space.
191 const char *isl_aff_get_dim_name(__isl_keep isl_aff
*aff
,
192 enum isl_dim_type type
, unsigned pos
)
196 if (type
== isl_dim_out
)
198 if (type
== isl_dim_in
)
200 return isl_local_space_get_dim_name(aff
->ls
, type
, pos
);
203 __isl_give isl_aff
*isl_aff_reset_domain_space(__isl_take isl_aff
*aff
,
204 __isl_take isl_space
*dim
)
206 aff
= isl_aff_cow(aff
);
210 aff
->ls
= isl_local_space_reset_space(aff
->ls
, dim
);
212 return isl_aff_free(aff
);
221 /* Reset the space of "aff". This function is called from isl_pw_templ.c
222 * and doesn't know if the space of an element object is represented
223 * directly or through its domain. It therefore passes along both.
225 __isl_give isl_aff
*isl_aff_reset_space_and_domain(__isl_take isl_aff
*aff
,
226 __isl_take isl_space
*space
, __isl_take isl_space
*domain
)
228 isl_space_free(space
);
229 return isl_aff_reset_domain_space(aff
, domain
);
232 /* Reorder the coefficients of the affine expression based
233 * on the given reodering.
234 * The reordering r is assumed to have been extended with the local
237 static __isl_give isl_vec
*vec_reorder(__isl_take isl_vec
*vec
,
238 __isl_take isl_reordering
*r
, int n_div
)
246 res
= isl_vec_alloc(vec
->ctx
,
247 2 + isl_space_dim(r
->dim
, isl_dim_all
) + n_div
);
248 isl_seq_cpy(res
->el
, vec
->el
, 2);
249 isl_seq_clr(res
->el
+ 2, res
->size
- 2);
250 for (i
= 0; i
< r
->len
; ++i
)
251 isl_int_set(res
->el
[2 + r
->pos
[i
]], vec
->el
[2 + i
]);
253 isl_reordering_free(r
);
258 isl_reordering_free(r
);
262 /* Reorder the dimensions of the domain of "aff" according
263 * to the given reordering.
265 __isl_give isl_aff
*isl_aff_realign_domain(__isl_take isl_aff
*aff
,
266 __isl_take isl_reordering
*r
)
268 aff
= isl_aff_cow(aff
);
272 r
= isl_reordering_extend(r
, aff
->ls
->div
->n_row
);
273 aff
->v
= vec_reorder(aff
->v
, isl_reordering_copy(r
),
274 aff
->ls
->div
->n_row
);
275 aff
->ls
= isl_local_space_realign(aff
->ls
, r
);
277 if (!aff
->v
|| !aff
->ls
)
278 return isl_aff_free(aff
);
283 isl_reordering_free(r
);
287 __isl_give isl_aff
*isl_aff_align_params(__isl_take isl_aff
*aff
,
288 __isl_take isl_space
*model
)
293 if (!isl_space_match(aff
->ls
->dim
, isl_dim_param
,
294 model
, isl_dim_param
)) {
297 model
= isl_space_drop_dims(model
, isl_dim_in
,
298 0, isl_space_dim(model
, isl_dim_in
));
299 model
= isl_space_drop_dims(model
, isl_dim_out
,
300 0, isl_space_dim(model
, isl_dim_out
));
301 exp
= isl_parameter_alignment_reordering(aff
->ls
->dim
, model
);
302 exp
= isl_reordering_extend_space(exp
,
303 isl_aff_get_domain_space(aff
));
304 aff
= isl_aff_realign_domain(aff
, exp
);
307 isl_space_free(model
);
310 isl_space_free(model
);
315 int isl_aff_plain_is_zero(__isl_keep isl_aff
*aff
)
320 return isl_seq_first_non_zero(aff
->v
->el
+ 1, aff
->v
->size
- 1) < 0;
323 int isl_aff_plain_is_equal(__isl_keep isl_aff
*aff1
, __isl_keep isl_aff
*aff2
)
330 equal
= isl_local_space_is_equal(aff1
->ls
, aff2
->ls
);
331 if (equal
< 0 || !equal
)
334 return isl_vec_is_equal(aff1
->v
, aff2
->v
);
337 int isl_aff_get_denominator(__isl_keep isl_aff
*aff
, isl_int
*v
)
341 isl_int_set(*v
, aff
->v
->el
[0]);
345 int isl_aff_get_constant(__isl_keep isl_aff
*aff
, isl_int
*v
)
349 isl_int_set(*v
, aff
->v
->el
[1]);
353 int isl_aff_get_coefficient(__isl_keep isl_aff
*aff
,
354 enum isl_dim_type type
, int pos
, isl_int
*v
)
359 if (type
== isl_dim_out
)
360 isl_die(aff
->v
->ctx
, isl_error_invalid
,
361 "output/set dimension does not have a coefficient",
363 if (type
== isl_dim_in
)
366 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
367 isl_die(aff
->v
->ctx
, isl_error_invalid
,
368 "position out of bounds", return -1);
370 pos
+= isl_local_space_offset(aff
->ls
, type
);
371 isl_int_set(*v
, aff
->v
->el
[1 + pos
]);
376 __isl_give isl_aff
*isl_aff_set_denominator(__isl_take isl_aff
*aff
, isl_int v
)
378 aff
= isl_aff_cow(aff
);
382 aff
->v
= isl_vec_cow(aff
->v
);
384 return isl_aff_free(aff
);
386 isl_int_set(aff
->v
->el
[0], v
);
391 __isl_give isl_aff
*isl_aff_set_constant(__isl_take isl_aff
*aff
, isl_int v
)
393 aff
= isl_aff_cow(aff
);
397 aff
->v
= isl_vec_cow(aff
->v
);
399 return isl_aff_free(aff
);
401 isl_int_set(aff
->v
->el
[1], v
);
406 __isl_give isl_aff
*isl_aff_add_constant(__isl_take isl_aff
*aff
, isl_int v
)
408 if (isl_int_is_zero(v
))
411 aff
= isl_aff_cow(aff
);
415 aff
->v
= isl_vec_cow(aff
->v
);
417 return isl_aff_free(aff
);
419 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
);
424 __isl_give isl_aff
*isl_aff_add_constant_si(__isl_take isl_aff
*aff
, int v
)
429 isl_int_set_si(t
, v
);
430 aff
= isl_aff_add_constant(aff
, t
);
436 /* Add "v" to the numerator of the constant term of "aff".
438 __isl_give isl_aff
*isl_aff_add_constant_num(__isl_take isl_aff
*aff
, isl_int v
)
440 if (isl_int_is_zero(v
))
443 aff
= isl_aff_cow(aff
);
447 aff
->v
= isl_vec_cow(aff
->v
);
449 return isl_aff_free(aff
);
451 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], v
);
456 /* Add "v" to the numerator of the constant term of "aff".
458 __isl_give isl_aff
*isl_aff_add_constant_num_si(__isl_take isl_aff
*aff
, int v
)
466 isl_int_set_si(t
, v
);
467 aff
= isl_aff_add_constant_num(aff
, t
);
473 __isl_give isl_aff
*isl_aff_set_constant_si(__isl_take isl_aff
*aff
, int v
)
475 aff
= isl_aff_cow(aff
);
479 aff
->v
= isl_vec_cow(aff
->v
);
481 return isl_aff_free(aff
);
483 isl_int_set_si(aff
->v
->el
[1], v
);
488 __isl_give isl_aff
*isl_aff_set_coefficient(__isl_take isl_aff
*aff
,
489 enum isl_dim_type type
, int pos
, isl_int v
)
494 if (type
== isl_dim_out
)
495 isl_die(aff
->v
->ctx
, isl_error_invalid
,
496 "output/set dimension does not have a coefficient",
497 return isl_aff_free(aff
));
498 if (type
== isl_dim_in
)
501 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
502 isl_die(aff
->v
->ctx
, isl_error_invalid
,
503 "position out of bounds", return isl_aff_free(aff
));
505 aff
= isl_aff_cow(aff
);
509 aff
->v
= isl_vec_cow(aff
->v
);
511 return isl_aff_free(aff
);
513 pos
+= isl_local_space_offset(aff
->ls
, type
);
514 isl_int_set(aff
->v
->el
[1 + pos
], v
);
519 __isl_give isl_aff
*isl_aff_set_coefficient_si(__isl_take isl_aff
*aff
,
520 enum isl_dim_type type
, int pos
, int v
)
525 if (type
== isl_dim_out
)
526 isl_die(aff
->v
->ctx
, isl_error_invalid
,
527 "output/set dimension does not have a coefficient",
528 return isl_aff_free(aff
));
529 if (type
== isl_dim_in
)
532 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
533 isl_die(aff
->v
->ctx
, isl_error_invalid
,
534 "position out of bounds", return isl_aff_free(aff
));
536 aff
= isl_aff_cow(aff
);
540 aff
->v
= isl_vec_cow(aff
->v
);
542 return isl_aff_free(aff
);
544 pos
+= isl_local_space_offset(aff
->ls
, type
);
545 isl_int_set_si(aff
->v
->el
[1 + pos
], v
);
550 __isl_give isl_aff
*isl_aff_add_coefficient(__isl_take isl_aff
*aff
,
551 enum isl_dim_type type
, int pos
, isl_int v
)
556 if (type
== isl_dim_out
)
557 isl_die(aff
->v
->ctx
, isl_error_invalid
,
558 "output/set dimension does not have a coefficient",
559 return isl_aff_free(aff
));
560 if (type
== isl_dim_in
)
563 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
564 isl_die(aff
->v
->ctx
, isl_error_invalid
,
565 "position out of bounds", return isl_aff_free(aff
));
567 aff
= isl_aff_cow(aff
);
571 aff
->v
= isl_vec_cow(aff
->v
);
573 return isl_aff_free(aff
);
575 pos
+= isl_local_space_offset(aff
->ls
, type
);
576 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
);
581 __isl_give isl_aff
*isl_aff_add_coefficient_si(__isl_take isl_aff
*aff
,
582 enum isl_dim_type type
, int pos
, int v
)
587 isl_int_set_si(t
, v
);
588 aff
= isl_aff_add_coefficient(aff
, type
, pos
, t
);
594 __isl_give isl_aff
*isl_aff_get_div(__isl_keep isl_aff
*aff
, int pos
)
599 return isl_local_space_get_div(aff
->ls
, pos
);
602 __isl_give isl_aff
*isl_aff_neg(__isl_take isl_aff
*aff
)
604 aff
= isl_aff_cow(aff
);
607 aff
->v
= isl_vec_cow(aff
->v
);
609 return isl_aff_free(aff
);
611 isl_seq_neg(aff
->v
->el
+ 1, aff
->v
->el
+ 1, aff
->v
->size
- 1);
616 /* Remove divs from the local space that do not appear in the affine
618 * We currently only remove divs at the end.
619 * Some intermediate divs may also not appear directly in the affine
620 * expression, but we would also need to check that no other divs are
621 * defined in terms of them.
623 __isl_give isl_aff
*isl_aff_remove_unused_divs( __isl_take isl_aff
*aff
)
632 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
633 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
635 pos
= isl_seq_last_non_zero(aff
->v
->el
+ 1 + off
, n
) + 1;
639 aff
= isl_aff_cow(aff
);
643 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, isl_dim_div
, pos
, n
- pos
);
644 aff
->v
= isl_vec_drop_els(aff
->v
, 1 + off
+ pos
, n
- pos
);
645 if (!aff
->ls
|| !aff
->v
)
646 return isl_aff_free(aff
);
651 __isl_give isl_aff
*isl_aff_normalize(__isl_take isl_aff
*aff
)
655 aff
->v
= isl_vec_normalize(aff
->v
);
657 return isl_aff_free(aff
);
658 aff
= isl_aff_remove_unused_divs(aff
);
662 /* Given f, return floor(f).
663 * If f is an integer expression, then just return f.
664 * If f is a constant, then return the constant floor(f).
665 * Otherwise, if f = g/m, write g = q m + r,
666 * create a new div d = [r/m] and return the expression q + d.
667 * The coefficients in r are taken to lie between -m/2 and m/2.
669 __isl_give isl_aff
*isl_aff_floor(__isl_take isl_aff
*aff
)
679 if (isl_int_is_one(aff
->v
->el
[0]))
682 aff
= isl_aff_cow(aff
);
686 aff
->v
= isl_vec_cow(aff
->v
);
688 return isl_aff_free(aff
);
690 if (isl_aff_is_cst(aff
)) {
691 isl_int_fdiv_q(aff
->v
->el
[1], aff
->v
->el
[1], aff
->v
->el
[0]);
692 isl_int_set_si(aff
->v
->el
[0], 1);
696 div
= isl_vec_copy(aff
->v
);
697 div
= isl_vec_cow(div
);
699 return isl_aff_free(aff
);
701 ctx
= isl_aff_get_ctx(aff
);
702 isl_int_fdiv_q(aff
->v
->el
[0], aff
->v
->el
[0], ctx
->two
);
703 for (i
= 1; i
< aff
->v
->size
; ++i
) {
704 isl_int_fdiv_r(div
->el
[i
], div
->el
[i
], div
->el
[0]);
705 isl_int_fdiv_q(aff
->v
->el
[i
], aff
->v
->el
[i
], div
->el
[0]);
706 if (isl_int_gt(div
->el
[i
], aff
->v
->el
[0])) {
707 isl_int_sub(div
->el
[i
], div
->el
[i
], div
->el
[0]);
708 isl_int_add_ui(aff
->v
->el
[i
], aff
->v
->el
[i
], 1);
712 aff
->ls
= isl_local_space_add_div(aff
->ls
, div
);
714 return isl_aff_free(aff
);
717 aff
->v
= isl_vec_extend(aff
->v
, size
+ 1);
719 return isl_aff_free(aff
);
720 isl_int_set_si(aff
->v
->el
[0], 1);
721 isl_int_set_si(aff
->v
->el
[size
], 1);
728 * aff mod m = aff - m * floor(aff/m)
730 __isl_give isl_aff
*isl_aff_mod(__isl_take isl_aff
*aff
, isl_int m
)
734 res
= isl_aff_copy(aff
);
735 aff
= isl_aff_scale_down(aff
, m
);
736 aff
= isl_aff_floor(aff
);
737 aff
= isl_aff_scale(aff
, m
);
738 res
= isl_aff_sub(res
, aff
);
745 * pwaff mod m = pwaff - m * floor(pwaff/m)
747 __isl_give isl_pw_aff
*isl_pw_aff_mod(__isl_take isl_pw_aff
*pwaff
, isl_int m
)
751 res
= isl_pw_aff_copy(pwaff
);
752 pwaff
= isl_pw_aff_scale_down(pwaff
, m
);
753 pwaff
= isl_pw_aff_floor(pwaff
);
754 pwaff
= isl_pw_aff_scale(pwaff
, m
);
755 res
= isl_pw_aff_sub(res
, pwaff
);
760 /* Given f, return ceil(f).
761 * If f is an integer expression, then just return f.
762 * Otherwise, create a new div d = [-f] and return the expression -d.
764 __isl_give isl_aff
*isl_aff_ceil(__isl_take isl_aff
*aff
)
769 if (isl_int_is_one(aff
->v
->el
[0]))
772 aff
= isl_aff_neg(aff
);
773 aff
= isl_aff_floor(aff
);
774 aff
= isl_aff_neg(aff
);
779 /* Apply the expansion computed by isl_merge_divs.
780 * The expansion itself is given by "exp" while the resulting
781 * list of divs is given by "div".
783 __isl_give isl_aff
*isl_aff_expand_divs( __isl_take isl_aff
*aff
,
784 __isl_take isl_mat
*div
, int *exp
)
791 aff
= isl_aff_cow(aff
);
795 old_n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
796 new_n_div
= isl_mat_rows(div
);
797 if (new_n_div
< old_n_div
)
798 isl_die(isl_mat_get_ctx(div
), isl_error_invalid
,
799 "not an expansion", goto error
);
801 aff
->v
= isl_vec_extend(aff
->v
, aff
->v
->size
+ new_n_div
- old_n_div
);
805 offset
= 1 + isl_local_space_offset(aff
->ls
, isl_dim_div
);
807 for (i
= new_n_div
- 1; i
>= 0; --i
) {
808 if (j
>= 0 && exp
[j
] == i
) {
810 isl_int_swap(aff
->v
->el
[offset
+ i
],
811 aff
->v
->el
[offset
+ j
]);
814 isl_int_set_si(aff
->v
->el
[offset
+ i
], 0);
817 aff
->ls
= isl_local_space_replace_divs(aff
->ls
, isl_mat_copy(div
));
828 /* Add two affine expressions that live in the same local space.
830 static __isl_give isl_aff
*add_expanded(__isl_take isl_aff
*aff1
,
831 __isl_take isl_aff
*aff2
)
835 aff1
= isl_aff_cow(aff1
);
839 aff1
->v
= isl_vec_cow(aff1
->v
);
845 isl_int_gcd(gcd
, aff1
->v
->el
[0], aff2
->v
->el
[0]);
846 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
847 isl_seq_scale(aff1
->v
->el
+ 1, aff1
->v
->el
+ 1, f
, aff1
->v
->size
- 1);
848 isl_int_divexact(f
, aff1
->v
->el
[0], gcd
);
849 isl_seq_addmul(aff1
->v
->el
+ 1, f
, aff2
->v
->el
+ 1, aff1
->v
->size
- 1);
850 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
851 isl_int_mul(aff1
->v
->el
[0], aff1
->v
->el
[0], f
);
863 __isl_give isl_aff
*isl_aff_add(__isl_take isl_aff
*aff1
,
864 __isl_take isl_aff
*aff2
)
874 ctx
= isl_aff_get_ctx(aff1
);
875 if (!isl_space_is_equal(aff1
->ls
->dim
, aff2
->ls
->dim
))
876 isl_die(ctx
, isl_error_invalid
,
877 "spaces don't match", goto error
);
879 if (aff1
->ls
->div
->n_row
== 0 && aff2
->ls
->div
->n_row
== 0)
880 return add_expanded(aff1
, aff2
);
882 exp1
= isl_alloc_array(ctx
, int, aff1
->ls
->div
->n_row
);
883 exp2
= isl_alloc_array(ctx
, int, aff2
->ls
->div
->n_row
);
887 div
= isl_merge_divs(aff1
->ls
->div
, aff2
->ls
->div
, exp1
, exp2
);
888 aff1
= isl_aff_expand_divs(aff1
, isl_mat_copy(div
), exp1
);
889 aff2
= isl_aff_expand_divs(aff2
, div
, exp2
);
893 return add_expanded(aff1
, aff2
);
902 __isl_give isl_aff
*isl_aff_sub(__isl_take isl_aff
*aff1
,
903 __isl_take isl_aff
*aff2
)
905 return isl_aff_add(aff1
, isl_aff_neg(aff2
));
908 __isl_give isl_aff
*isl_aff_scale(__isl_take isl_aff
*aff
, isl_int f
)
912 if (isl_int_is_one(f
))
915 aff
= isl_aff_cow(aff
);
918 aff
->v
= isl_vec_cow(aff
->v
);
920 return isl_aff_free(aff
);
923 isl_int_gcd(gcd
, aff
->v
->el
[0], f
);
924 isl_int_divexact(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
925 isl_int_divexact(gcd
, f
, gcd
);
926 isl_seq_scale(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
932 __isl_give isl_aff
*isl_aff_scale_down(__isl_take isl_aff
*aff
, isl_int f
)
936 if (isl_int_is_one(f
))
939 aff
= isl_aff_cow(aff
);
943 if (isl_int_is_zero(f
))
944 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
945 "cannot scale down by zero", return isl_aff_free(aff
));
947 aff
->v
= isl_vec_cow(aff
->v
);
949 return isl_aff_free(aff
);
952 isl_seq_gcd(aff
->v
->el
+ 1, aff
->v
->size
- 1, &gcd
);
953 isl_int_gcd(gcd
, gcd
, f
);
954 isl_seq_scale_down(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
955 isl_int_divexact(gcd
, f
, gcd
);
956 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
962 __isl_give isl_aff
*isl_aff_scale_down_ui(__isl_take isl_aff
*aff
, unsigned f
)
970 isl_int_set_ui(v
, f
);
971 aff
= isl_aff_scale_down(aff
, v
);
977 __isl_give isl_aff
*isl_aff_set_dim_name(__isl_take isl_aff
*aff
,
978 enum isl_dim_type type
, unsigned pos
, const char *s
)
980 aff
= isl_aff_cow(aff
);
983 if (type
== isl_dim_out
)
984 isl_die(aff
->v
->ctx
, isl_error_invalid
,
985 "cannot set name of output/set dimension",
986 return isl_aff_free(aff
));
987 if (type
== isl_dim_in
)
989 aff
->ls
= isl_local_space_set_dim_name(aff
->ls
, type
, pos
, s
);
991 return isl_aff_free(aff
);
996 __isl_give isl_aff
*isl_aff_set_dim_id(__isl_take isl_aff
*aff
,
997 enum isl_dim_type type
, unsigned pos
, __isl_take isl_id
*id
)
999 aff
= isl_aff_cow(aff
);
1001 return isl_id_free(id
);
1002 if (type
== isl_dim_out
)
1003 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1004 "cannot set name of output/set dimension",
1006 if (type
== isl_dim_in
)
1008 aff
->ls
= isl_local_space_set_dim_id(aff
->ls
, type
, pos
, id
);
1010 return isl_aff_free(aff
);
1019 /* Exploit the equalities in "eq" to simplify the affine expression
1020 * and the expressions of the integer divisions in the local space.
1021 * The integer divisions in this local space are assumed to appear
1022 * as regular dimensions in "eq".
1024 static __isl_give isl_aff
*isl_aff_substitute_equalities_lifted(
1025 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
1033 if (eq
->n_eq
== 0) {
1034 isl_basic_set_free(eq
);
1038 aff
= isl_aff_cow(aff
);
1042 aff
->ls
= isl_local_space_substitute_equalities(aff
->ls
,
1043 isl_basic_set_copy(eq
));
1047 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
1049 for (i
= 0; i
< eq
->n_eq
; ++i
) {
1050 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
1051 if (j
< 0 || j
== 0 || j
>= total
)
1054 isl_seq_elim(aff
->v
->el
+ 1, eq
->eq
[i
], j
, total
,
1058 isl_basic_set_free(eq
);
1059 aff
= isl_aff_normalize(aff
);
1062 isl_basic_set_free(eq
);
1067 /* Exploit the equalities in "eq" to simplify the affine expression
1068 * and the expressions of the integer divisions in the local space.
1070 static __isl_give isl_aff
*isl_aff_substitute_equalities(
1071 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
1077 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1079 eq
= isl_basic_set_add(eq
, isl_dim_set
, n_div
);
1080 return isl_aff_substitute_equalities_lifted(aff
, eq
);
1082 isl_basic_set_free(eq
);
1087 /* Look for equalities among the variables shared by context and aff
1088 * and the integer divisions of aff, if any.
1089 * The equalities are then used to eliminate coefficients and/or integer
1090 * divisions from aff.
1092 __isl_give isl_aff
*isl_aff_gist(__isl_take isl_aff
*aff
,
1093 __isl_take isl_set
*context
)
1095 isl_basic_set
*hull
;
1100 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1102 isl_basic_set
*bset
;
1103 isl_local_space
*ls
;
1104 context
= isl_set_add_dims(context
, isl_dim_set
, n_div
);
1105 ls
= isl_aff_get_domain_local_space(aff
);
1106 bset
= isl_basic_set_from_local_space(ls
);
1107 bset
= isl_basic_set_lift(bset
);
1108 bset
= isl_basic_set_flatten(bset
);
1109 context
= isl_set_intersect(context
,
1110 isl_set_from_basic_set(bset
));
1113 hull
= isl_set_affine_hull(context
);
1114 return isl_aff_substitute_equalities_lifted(aff
, hull
);
1117 isl_set_free(context
);
1121 __isl_give isl_aff
*isl_aff_gist_params(__isl_take isl_aff
*aff
,
1122 __isl_take isl_set
*context
)
1124 isl_set
*dom_context
= isl_set_universe(isl_aff_get_domain_space(aff
));
1125 dom_context
= isl_set_intersect_params(dom_context
, context
);
1126 return isl_aff_gist(aff
, dom_context
);
1129 /* Return a basic set containing those elements in the space
1130 * of aff where it is non-negative.
1132 __isl_give isl_basic_set
*isl_aff_nonneg_basic_set(__isl_take isl_aff
*aff
)
1134 isl_constraint
*ineq
;
1135 isl_basic_set
*bset
;
1137 ineq
= isl_inequality_from_aff(aff
);
1139 bset
= isl_basic_set_from_constraint(ineq
);
1140 bset
= isl_basic_set_simplify(bset
);
1144 /* Return a basic set containing those elements in the domain space
1145 * of aff where it is negative.
1147 __isl_give isl_basic_set
*isl_aff_neg_basic_set(__isl_take isl_aff
*aff
)
1149 aff
= isl_aff_neg(aff
);
1150 aff
= isl_aff_add_constant_num_si(aff
, -1);
1151 return isl_aff_nonneg_basic_set(aff
);
1154 /* Return a basic set containing those elements in the space
1155 * of aff where it is zero.
1157 __isl_give isl_basic_set
*isl_aff_zero_basic_set(__isl_take isl_aff
*aff
)
1159 isl_constraint
*ineq
;
1160 isl_basic_set
*bset
;
1162 ineq
= isl_equality_from_aff(aff
);
1164 bset
= isl_basic_set_from_constraint(ineq
);
1165 bset
= isl_basic_set_simplify(bset
);
1169 /* Return a basic set containing those elements in the shared space
1170 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1172 __isl_give isl_basic_set
*isl_aff_ge_basic_set(__isl_take isl_aff
*aff1
,
1173 __isl_take isl_aff
*aff2
)
1175 aff1
= isl_aff_sub(aff1
, aff2
);
1177 return isl_aff_nonneg_basic_set(aff1
);
1180 /* Return a basic set containing those elements in the shared space
1181 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1183 __isl_give isl_basic_set
*isl_aff_le_basic_set(__isl_take isl_aff
*aff1
,
1184 __isl_take isl_aff
*aff2
)
1186 return isl_aff_ge_basic_set(aff2
, aff1
);
1189 __isl_give isl_aff
*isl_aff_add_on_domain(__isl_keep isl_set
*dom
,
1190 __isl_take isl_aff
*aff1
, __isl_take isl_aff
*aff2
)
1192 aff1
= isl_aff_add(aff1
, aff2
);
1193 aff1
= isl_aff_gist(aff1
, isl_set_copy(dom
));
1197 int isl_aff_is_empty(__isl_keep isl_aff
*aff
)
1205 /* Check whether the given affine expression has non-zero coefficient
1206 * for any dimension in the given range or if any of these dimensions
1207 * appear with non-zero coefficients in any of the integer divisions
1208 * involved in the affine expression.
1210 int isl_aff_involves_dims(__isl_keep isl_aff
*aff
,
1211 enum isl_dim_type type
, unsigned first
, unsigned n
)
1223 ctx
= isl_aff_get_ctx(aff
);
1224 if (first
+ n
> isl_aff_dim(aff
, type
))
1225 isl_die(ctx
, isl_error_invalid
,
1226 "range out of bounds", return -1);
1228 active
= isl_local_space_get_active(aff
->ls
, aff
->v
->el
+ 2);
1232 first
+= isl_local_space_offset(aff
->ls
, type
) - 1;
1233 for (i
= 0; i
< n
; ++i
)
1234 if (active
[first
+ i
]) {
1247 __isl_give isl_aff
*isl_aff_drop_dims(__isl_take isl_aff
*aff
,
1248 enum isl_dim_type type
, unsigned first
, unsigned n
)
1254 if (type
== isl_dim_out
)
1255 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1256 "cannot drop output/set dimension",
1257 return isl_aff_free(aff
));
1258 if (type
== isl_dim_in
)
1260 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
1263 ctx
= isl_aff_get_ctx(aff
);
1264 if (first
+ n
> isl_local_space_dim(aff
->ls
, type
))
1265 isl_die(ctx
, isl_error_invalid
, "range out of bounds",
1266 return isl_aff_free(aff
));
1268 aff
= isl_aff_cow(aff
);
1272 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, type
, first
, n
);
1274 return isl_aff_free(aff
);
1276 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
1277 aff
->v
= isl_vec_drop_els(aff
->v
, first
, n
);
1279 return isl_aff_free(aff
);
1284 /* Project the domain of the affine expression onto its parameter space.
1285 * The affine expression may not involve any of the domain dimensions.
1287 __isl_give isl_aff
*isl_aff_project_domain_on_params(__isl_take isl_aff
*aff
)
1293 n
= isl_aff_dim(aff
, isl_dim_in
);
1294 involves
= isl_aff_involves_dims(aff
, isl_dim_in
, 0, n
);
1296 return isl_aff_free(aff
);
1298 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1299 "affine expression involves some of the domain dimensions",
1300 return isl_aff_free(aff
));
1301 aff
= isl_aff_drop_dims(aff
, isl_dim_in
, 0, n
);
1302 space
= isl_aff_get_domain_space(aff
);
1303 space
= isl_space_params(space
);
1304 aff
= isl_aff_reset_domain_space(aff
, space
);
1308 __isl_give isl_aff
*isl_aff_insert_dims(__isl_take isl_aff
*aff
,
1309 enum isl_dim_type type
, unsigned first
, unsigned n
)
1315 if (type
== isl_dim_out
)
1316 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1317 "cannot insert output/set dimensions",
1318 return isl_aff_free(aff
));
1319 if (type
== isl_dim_in
)
1321 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
1324 ctx
= isl_aff_get_ctx(aff
);
1325 if (first
> isl_local_space_dim(aff
->ls
, type
))
1326 isl_die(ctx
, isl_error_invalid
, "position out of bounds",
1327 return isl_aff_free(aff
));
1329 aff
= isl_aff_cow(aff
);
1333 aff
->ls
= isl_local_space_insert_dims(aff
->ls
, type
, first
, n
);
1335 return isl_aff_free(aff
);
1337 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
1338 aff
->v
= isl_vec_insert_zero_els(aff
->v
, first
, n
);
1340 return isl_aff_free(aff
);
1345 __isl_give isl_aff
*isl_aff_add_dims(__isl_take isl_aff
*aff
,
1346 enum isl_dim_type type
, unsigned n
)
1350 pos
= isl_aff_dim(aff
, type
);
1352 return isl_aff_insert_dims(aff
, type
, pos
, n
);
1355 __isl_give isl_pw_aff
*isl_pw_aff_add_dims(__isl_take isl_pw_aff
*pwaff
,
1356 enum isl_dim_type type
, unsigned n
)
1360 pos
= isl_pw_aff_dim(pwaff
, type
);
1362 return isl_pw_aff_insert_dims(pwaff
, type
, pos
, n
);
1365 __isl_give isl_pw_aff
*isl_pw_aff_from_aff(__isl_take isl_aff
*aff
)
1367 isl_set
*dom
= isl_set_universe(isl_aff_get_domain_space(aff
));
1368 return isl_pw_aff_alloc(dom
, aff
);
1372 #define PW isl_pw_aff
1376 #define EL_IS_ZERO is_empty
1380 #define IS_ZERO is_empty
1383 #undef DEFAULT_IS_ZERO
1384 #define DEFAULT_IS_ZERO 0
1388 #define NO_MOVE_DIMS
1392 #include <isl_pw_templ.c>
1394 static __isl_give isl_set
*align_params_pw_pw_set_and(
1395 __isl_take isl_pw_aff
*pwaff1
, __isl_take isl_pw_aff
*pwaff2
,
1396 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
1397 __isl_take isl_pw_aff
*pwaff2
))
1399 if (!pwaff1
|| !pwaff2
)
1401 if (isl_space_match(pwaff1
->dim
, isl_dim_param
,
1402 pwaff2
->dim
, isl_dim_param
))
1403 return fn(pwaff1
, pwaff2
);
1404 if (!isl_space_has_named_params(pwaff1
->dim
) ||
1405 !isl_space_has_named_params(pwaff2
->dim
))
1406 isl_die(isl_pw_aff_get_ctx(pwaff1
), isl_error_invalid
,
1407 "unaligned unnamed parameters", goto error
);
1408 pwaff1
= isl_pw_aff_align_params(pwaff1
, isl_pw_aff_get_space(pwaff2
));
1409 pwaff2
= isl_pw_aff_align_params(pwaff2
, isl_pw_aff_get_space(pwaff1
));
1410 return fn(pwaff1
, pwaff2
);
1412 isl_pw_aff_free(pwaff1
);
1413 isl_pw_aff_free(pwaff2
);
1417 /* Compute a piecewise quasi-affine expression with a domain that
1418 * is the union of those of pwaff1 and pwaff2 and such that on each
1419 * cell, the quasi-affine expression is the better (according to cmp)
1420 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
1421 * is defined on a given cell, then the associated expression
1422 * is the defined one.
1424 static __isl_give isl_pw_aff
*pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
1425 __isl_take isl_pw_aff
*pwaff2
,
1426 __isl_give isl_basic_set
*(*cmp
)(__isl_take isl_aff
*aff1
,
1427 __isl_take isl_aff
*aff2
))
1434 if (!pwaff1
|| !pwaff2
)
1437 ctx
= isl_space_get_ctx(pwaff1
->dim
);
1438 if (!isl_space_is_equal(pwaff1
->dim
, pwaff2
->dim
))
1439 isl_die(ctx
, isl_error_invalid
,
1440 "arguments should live in same space", goto error
);
1442 if (isl_pw_aff_is_empty(pwaff1
)) {
1443 isl_pw_aff_free(pwaff1
);
1447 if (isl_pw_aff_is_empty(pwaff2
)) {
1448 isl_pw_aff_free(pwaff2
);
1452 n
= 2 * (pwaff1
->n
+ 1) * (pwaff2
->n
+ 1);
1453 res
= isl_pw_aff_alloc_size(isl_space_copy(pwaff1
->dim
), n
);
1455 for (i
= 0; i
< pwaff1
->n
; ++i
) {
1456 set
= isl_set_copy(pwaff1
->p
[i
].set
);
1457 for (j
= 0; j
< pwaff2
->n
; ++j
) {
1458 struct isl_set
*common
;
1461 common
= isl_set_intersect(
1462 isl_set_copy(pwaff1
->p
[i
].set
),
1463 isl_set_copy(pwaff2
->p
[j
].set
));
1464 better
= isl_set_from_basic_set(cmp(
1465 isl_aff_copy(pwaff2
->p
[j
].aff
),
1466 isl_aff_copy(pwaff1
->p
[i
].aff
)));
1467 better
= isl_set_intersect(common
, better
);
1468 if (isl_set_plain_is_empty(better
)) {
1469 isl_set_free(better
);
1472 set
= isl_set_subtract(set
, isl_set_copy(better
));
1474 res
= isl_pw_aff_add_piece(res
, better
,
1475 isl_aff_copy(pwaff2
->p
[j
].aff
));
1477 res
= isl_pw_aff_add_piece(res
, set
,
1478 isl_aff_copy(pwaff1
->p
[i
].aff
));
1481 for (j
= 0; j
< pwaff2
->n
; ++j
) {
1482 set
= isl_set_copy(pwaff2
->p
[j
].set
);
1483 for (i
= 0; i
< pwaff1
->n
; ++i
)
1484 set
= isl_set_subtract(set
,
1485 isl_set_copy(pwaff1
->p
[i
].set
));
1486 res
= isl_pw_aff_add_piece(res
, set
,
1487 isl_aff_copy(pwaff2
->p
[j
].aff
));
1490 isl_pw_aff_free(pwaff1
);
1491 isl_pw_aff_free(pwaff2
);
1495 isl_pw_aff_free(pwaff1
);
1496 isl_pw_aff_free(pwaff2
);
1500 /* Compute a piecewise quasi-affine expression with a domain that
1501 * is the union of those of pwaff1 and pwaff2 and such that on each
1502 * cell, the quasi-affine expression is the maximum of those of pwaff1
1503 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1504 * cell, then the associated expression is the defined one.
1506 static __isl_give isl_pw_aff
*pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
1507 __isl_take isl_pw_aff
*pwaff2
)
1509 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_ge_basic_set
);
1512 __isl_give isl_pw_aff
*isl_pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
1513 __isl_take isl_pw_aff
*pwaff2
)
1515 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
1519 /* Compute a piecewise quasi-affine expression with a domain that
1520 * is the union of those of pwaff1 and pwaff2 and such that on each
1521 * cell, the quasi-affine expression is the minimum of those of pwaff1
1522 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1523 * cell, then the associated expression is the defined one.
1525 static __isl_give isl_pw_aff
*pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
1526 __isl_take isl_pw_aff
*pwaff2
)
1528 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_le_basic_set
);
1531 __isl_give isl_pw_aff
*isl_pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
1532 __isl_take isl_pw_aff
*pwaff2
)
1534 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
1538 __isl_give isl_pw_aff
*isl_pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
1539 __isl_take isl_pw_aff
*pwaff2
, int max
)
1542 return isl_pw_aff_union_max(pwaff1
, pwaff2
);
1544 return isl_pw_aff_union_min(pwaff1
, pwaff2
);
1547 /* Construct a map with as domain the domain of pwaff and
1548 * one-dimensional range corresponding to the affine expressions.
1550 static __isl_give isl_map
*map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
1559 dim
= isl_pw_aff_get_space(pwaff
);
1560 map
= isl_map_empty(dim
);
1562 for (i
= 0; i
< pwaff
->n
; ++i
) {
1563 isl_basic_map
*bmap
;
1566 bmap
= isl_basic_map_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
1567 map_i
= isl_map_from_basic_map(bmap
);
1568 map_i
= isl_map_intersect_domain(map_i
,
1569 isl_set_copy(pwaff
->p
[i
].set
));
1570 map
= isl_map_union_disjoint(map
, map_i
);
1573 isl_pw_aff_free(pwaff
);
1578 /* Construct a map with as domain the domain of pwaff and
1579 * one-dimensional range corresponding to the affine expressions.
1581 __isl_give isl_map
*isl_map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
1585 if (isl_space_is_set(pwaff
->dim
))
1586 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
1587 "space of input is not a map",
1588 return isl_pw_aff_free(pwaff
));
1589 return map_from_pw_aff(pwaff
);
1592 /* Construct a one-dimensional set with as parameter domain
1593 * the domain of pwaff and the single set dimension
1594 * corresponding to the affine expressions.
1596 __isl_give isl_set
*isl_set_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
1600 if (!isl_space_is_set(pwaff
->dim
))
1601 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
1602 "space of input is not a set",
1603 return isl_pw_aff_free(pwaff
));
1604 return map_from_pw_aff(pwaff
);
1607 /* Return a set containing those elements in the domain
1608 * of pwaff where it is non-negative.
1610 __isl_give isl_set
*isl_pw_aff_nonneg_set(__isl_take isl_pw_aff
*pwaff
)
1618 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
1620 for (i
= 0; i
< pwaff
->n
; ++i
) {
1621 isl_basic_set
*bset
;
1624 bset
= isl_aff_nonneg_basic_set(isl_aff_copy(pwaff
->p
[i
].aff
));
1625 set_i
= isl_set_from_basic_set(bset
);
1626 set_i
= isl_set_intersect(set_i
, isl_set_copy(pwaff
->p
[i
].set
));
1627 set
= isl_set_union_disjoint(set
, set_i
);
1630 isl_pw_aff_free(pwaff
);
1635 /* Return a set containing those elements in the domain
1636 * of pwaff where it is zero (if complement is 0) or not zero
1637 * (if complement is 1).
1639 static __isl_give isl_set
*pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
,
1648 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
1650 for (i
= 0; i
< pwaff
->n
; ++i
) {
1651 isl_basic_set
*bset
;
1652 isl_set
*set_i
, *zero
;
1654 bset
= isl_aff_zero_basic_set(isl_aff_copy(pwaff
->p
[i
].aff
));
1655 zero
= isl_set_from_basic_set(bset
);
1656 set_i
= isl_set_copy(pwaff
->p
[i
].set
);
1658 set_i
= isl_set_subtract(set_i
, zero
);
1660 set_i
= isl_set_intersect(set_i
, zero
);
1661 set
= isl_set_union_disjoint(set
, set_i
);
1664 isl_pw_aff_free(pwaff
);
1669 /* Return a set containing those elements in the domain
1670 * of pwaff where it is zero.
1672 __isl_give isl_set
*isl_pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
)
1674 return pw_aff_zero_set(pwaff
, 0);
1677 /* Return a set containing those elements in the domain
1678 * of pwaff where it is not zero.
1680 __isl_give isl_set
*isl_pw_aff_non_zero_set(__isl_take isl_pw_aff
*pwaff
)
1682 return pw_aff_zero_set(pwaff
, 1);
1685 /* Return a set containing those elements in the shared domain
1686 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1688 * We compute the difference on the shared domain and then construct
1689 * the set of values where this difference is non-negative.
1690 * If strict is set, we first subtract 1 from the difference.
1691 * If equal is set, we only return the elements where pwaff1 and pwaff2
1694 static __isl_give isl_set
*pw_aff_gte_set(__isl_take isl_pw_aff
*pwaff1
,
1695 __isl_take isl_pw_aff
*pwaff2
, int strict
, int equal
)
1697 isl_set
*set1
, *set2
;
1699 set1
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
));
1700 set2
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
));
1701 set1
= isl_set_intersect(set1
, set2
);
1702 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, isl_set_copy(set1
));
1703 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, isl_set_copy(set1
));
1704 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_neg(pwaff2
));
1707 isl_space
*dim
= isl_set_get_space(set1
);
1709 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(dim
));
1710 aff
= isl_aff_add_constant_si(aff
, -1);
1711 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_alloc(set1
, aff
));
1716 return isl_pw_aff_zero_set(pwaff1
);
1717 return isl_pw_aff_nonneg_set(pwaff1
);
1720 /* Return a set containing those elements in the shared domain
1721 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1723 static __isl_give isl_set
*pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
1724 __isl_take isl_pw_aff
*pwaff2
)
1726 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 1);
1729 __isl_give isl_set
*isl_pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
1730 __isl_take isl_pw_aff
*pwaff2
)
1732 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_eq_set
);
1735 /* Return a set containing those elements in the shared domain
1736 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
1738 static __isl_give isl_set
*pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
1739 __isl_take isl_pw_aff
*pwaff2
)
1741 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 0);
1744 __isl_give isl_set
*isl_pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
1745 __isl_take isl_pw_aff
*pwaff2
)
1747 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ge_set
);
1750 /* Return a set containing those elements in the shared domain
1751 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
1753 static __isl_give isl_set
*pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
1754 __isl_take isl_pw_aff
*pwaff2
)
1756 return pw_aff_gte_set(pwaff1
, pwaff2
, 1, 0);
1759 __isl_give isl_set
*isl_pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
1760 __isl_take isl_pw_aff
*pwaff2
)
1762 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_gt_set
);
1765 __isl_give isl_set
*isl_pw_aff_le_set(__isl_take isl_pw_aff
*pwaff1
,
1766 __isl_take isl_pw_aff
*pwaff2
)
1768 return isl_pw_aff_ge_set(pwaff2
, pwaff1
);
1771 __isl_give isl_set
*isl_pw_aff_lt_set(__isl_take isl_pw_aff
*pwaff1
,
1772 __isl_take isl_pw_aff
*pwaff2
)
1774 return isl_pw_aff_gt_set(pwaff2
, pwaff1
);
1777 /* Return a set containing those elements in the shared domain
1778 * of the elements of list1 and list2 where each element in list1
1779 * has the relation specified by "fn" with each element in list2.
1781 static __isl_give isl_set
*pw_aff_list_set(__isl_take isl_pw_aff_list
*list1
,
1782 __isl_take isl_pw_aff_list
*list2
,
1783 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
1784 __isl_take isl_pw_aff
*pwaff2
))
1790 if (!list1
|| !list2
)
1793 ctx
= isl_pw_aff_list_get_ctx(list1
);
1794 if (list1
->n
< 1 || list2
->n
< 1)
1795 isl_die(ctx
, isl_error_invalid
,
1796 "list should contain at least one element", goto error
);
1798 set
= isl_set_universe(isl_pw_aff_get_domain_space(list1
->p
[0]));
1799 for (i
= 0; i
< list1
->n
; ++i
)
1800 for (j
= 0; j
< list2
->n
; ++j
) {
1803 set_ij
= fn(isl_pw_aff_copy(list1
->p
[i
]),
1804 isl_pw_aff_copy(list2
->p
[j
]));
1805 set
= isl_set_intersect(set
, set_ij
);
1808 isl_pw_aff_list_free(list1
);
1809 isl_pw_aff_list_free(list2
);
1812 isl_pw_aff_list_free(list1
);
1813 isl_pw_aff_list_free(list2
);
1817 /* Return a set containing those elements in the shared domain
1818 * of the elements of list1 and list2 where each element in list1
1819 * is equal to each element in list2.
1821 __isl_give isl_set
*isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list
*list1
,
1822 __isl_take isl_pw_aff_list
*list2
)
1824 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_eq_set
);
1827 __isl_give isl_set
*isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list
*list1
,
1828 __isl_take isl_pw_aff_list
*list2
)
1830 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ne_set
);
1833 /* Return a set containing those elements in the shared domain
1834 * of the elements of list1 and list2 where each element in list1
1835 * is less than or equal to each element in list2.
1837 __isl_give isl_set
*isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list
*list1
,
1838 __isl_take isl_pw_aff_list
*list2
)
1840 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_le_set
);
1843 __isl_give isl_set
*isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list
*list1
,
1844 __isl_take isl_pw_aff_list
*list2
)
1846 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_lt_set
);
1849 __isl_give isl_set
*isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list
*list1
,
1850 __isl_take isl_pw_aff_list
*list2
)
1852 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ge_set
);
1855 __isl_give isl_set
*isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list
*list1
,
1856 __isl_take isl_pw_aff_list
*list2
)
1858 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_gt_set
);
1862 /* Return a set containing those elements in the shared domain
1863 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
1865 static __isl_give isl_set
*pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
1866 __isl_take isl_pw_aff
*pwaff2
)
1868 isl_set
*set_lt
, *set_gt
;
1870 set_lt
= isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1
),
1871 isl_pw_aff_copy(pwaff2
));
1872 set_gt
= isl_pw_aff_gt_set(pwaff1
, pwaff2
);
1873 return isl_set_union_disjoint(set_lt
, set_gt
);
1876 __isl_give isl_set
*isl_pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
1877 __isl_take isl_pw_aff
*pwaff2
)
1879 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ne_set
);
1882 __isl_give isl_pw_aff
*isl_pw_aff_scale_down(__isl_take isl_pw_aff
*pwaff
,
1887 if (isl_int_is_one(v
))
1889 if (!isl_int_is_pos(v
))
1890 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
1891 "factor needs to be positive",
1892 return isl_pw_aff_free(pwaff
));
1893 pwaff
= isl_pw_aff_cow(pwaff
);
1899 for (i
= 0; i
< pwaff
->n
; ++i
) {
1900 pwaff
->p
[i
].aff
= isl_aff_scale_down(pwaff
->p
[i
].aff
, v
);
1901 if (!pwaff
->p
[i
].aff
)
1902 return isl_pw_aff_free(pwaff
);
1908 __isl_give isl_pw_aff
*isl_pw_aff_floor(__isl_take isl_pw_aff
*pwaff
)
1912 pwaff
= isl_pw_aff_cow(pwaff
);
1918 for (i
= 0; i
< pwaff
->n
; ++i
) {
1919 pwaff
->p
[i
].aff
= isl_aff_floor(pwaff
->p
[i
].aff
);
1920 if (!pwaff
->p
[i
].aff
)
1921 return isl_pw_aff_free(pwaff
);
1927 __isl_give isl_pw_aff
*isl_pw_aff_ceil(__isl_take isl_pw_aff
*pwaff
)
1931 pwaff
= isl_pw_aff_cow(pwaff
);
1937 for (i
= 0; i
< pwaff
->n
; ++i
) {
1938 pwaff
->p
[i
].aff
= isl_aff_ceil(pwaff
->p
[i
].aff
);
1939 if (!pwaff
->p
[i
].aff
)
1940 return isl_pw_aff_free(pwaff
);
1946 /* Assuming that "cond1" and "cond2" are disjoint,
1947 * return an affine expression that is equal to pwaff1 on cond1
1948 * and to pwaff2 on cond2.
1950 static __isl_give isl_pw_aff
*isl_pw_aff_select(
1951 __isl_take isl_set
*cond1
, __isl_take isl_pw_aff
*pwaff1
,
1952 __isl_take isl_set
*cond2
, __isl_take isl_pw_aff
*pwaff2
)
1954 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, cond1
);
1955 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, cond2
);
1957 return isl_pw_aff_add_disjoint(pwaff1
, pwaff2
);
1960 /* Return an affine expression that is equal to pwaff_true for elements
1961 * where "cond" is non-zero and to pwaff_false for elements where "cond"
1963 * That is, return cond ? pwaff_true : pwaff_false;
1965 __isl_give isl_pw_aff
*isl_pw_aff_cond(__isl_take isl_pw_aff
*cond
,
1966 __isl_take isl_pw_aff
*pwaff_true
, __isl_take isl_pw_aff
*pwaff_false
)
1968 isl_set
*cond_true
, *cond_false
;
1970 cond_true
= isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond
));
1971 cond_false
= isl_pw_aff_zero_set(cond
);
1972 return isl_pw_aff_select(cond_true
, pwaff_true
,
1973 cond_false
, pwaff_false
);
1976 int isl_aff_is_cst(__isl_keep isl_aff
*aff
)
1981 return isl_seq_first_non_zero(aff
->v
->el
+ 2, aff
->v
->size
- 2) == -1;
1984 /* Check whether pwaff is a piecewise constant.
1986 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff
*pwaff
)
1993 for (i
= 0; i
< pwaff
->n
; ++i
) {
1994 int is_cst
= isl_aff_is_cst(pwaff
->p
[i
].aff
);
1995 if (is_cst
< 0 || !is_cst
)
2002 __isl_give isl_aff
*isl_aff_mul(__isl_take isl_aff
*aff1
,
2003 __isl_take isl_aff
*aff2
)
2005 if (!isl_aff_is_cst(aff2
) && isl_aff_is_cst(aff1
))
2006 return isl_aff_mul(aff2
, aff1
);
2008 if (!isl_aff_is_cst(aff2
))
2009 isl_die(isl_aff_get_ctx(aff1
), isl_error_invalid
,
2010 "at least one affine expression should be constant",
2013 aff1
= isl_aff_cow(aff1
);
2017 aff1
= isl_aff_scale(aff1
, aff2
->v
->el
[1]);
2018 aff1
= isl_aff_scale_down(aff1
, aff2
->v
->el
[0]);
2028 static __isl_give isl_pw_aff
*pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
2029 __isl_take isl_pw_aff
*pwaff2
)
2031 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_add
);
2034 __isl_give isl_pw_aff
*isl_pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
2035 __isl_take isl_pw_aff
*pwaff2
)
2037 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_add
);
2040 __isl_give isl_pw_aff
*isl_pw_aff_union_add(__isl_take isl_pw_aff
*pwaff1
,
2041 __isl_take isl_pw_aff
*pwaff2
)
2043 return isl_pw_aff_union_add_(pwaff1
, pwaff2
);
2046 static __isl_give isl_pw_aff
*pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
2047 __isl_take isl_pw_aff
*pwaff2
)
2049 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_mul
);
2052 __isl_give isl_pw_aff
*isl_pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
2053 __isl_take isl_pw_aff
*pwaff2
)
2055 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_mul
);
2058 static __isl_give isl_pw_aff
*pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
2059 __isl_take isl_pw_aff
*pwaff2
)
2064 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
2065 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
2066 le
= isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1
),
2067 isl_pw_aff_copy(pwaff2
));
2068 dom
= isl_set_subtract(dom
, isl_set_copy(le
));
2069 return isl_pw_aff_select(le
, pwaff1
, dom
, pwaff2
);
2072 __isl_give isl_pw_aff
*isl_pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
2073 __isl_take isl_pw_aff
*pwaff2
)
2075 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_min
);
2078 static __isl_give isl_pw_aff
*pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
2079 __isl_take isl_pw_aff
*pwaff2
)
2084 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
2085 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
2086 ge
= isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1
),
2087 isl_pw_aff_copy(pwaff2
));
2088 dom
= isl_set_subtract(dom
, isl_set_copy(ge
));
2089 return isl_pw_aff_select(ge
, pwaff1
, dom
, pwaff2
);
2092 __isl_give isl_pw_aff
*isl_pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
2093 __isl_take isl_pw_aff
*pwaff2
)
2095 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_max
);
2098 static __isl_give isl_pw_aff
*pw_aff_list_reduce(
2099 __isl_take isl_pw_aff_list
*list
,
2100 __isl_give isl_pw_aff
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
2101 __isl_take isl_pw_aff
*pwaff2
))
2110 ctx
= isl_pw_aff_list_get_ctx(list
);
2112 isl_die(ctx
, isl_error_invalid
,
2113 "list should contain at least one element",
2114 return isl_pw_aff_list_free(list
));
2116 res
= isl_pw_aff_copy(list
->p
[0]);
2117 for (i
= 1; i
< list
->n
; ++i
)
2118 res
= fn(res
, isl_pw_aff_copy(list
->p
[i
]));
2120 isl_pw_aff_list_free(list
);
2124 /* Return an isl_pw_aff that maps each element in the intersection of the
2125 * domains of the elements of list to the minimal corresponding affine
2128 __isl_give isl_pw_aff
*isl_pw_aff_list_min(__isl_take isl_pw_aff_list
*list
)
2130 return pw_aff_list_reduce(list
, &isl_pw_aff_min
);
2133 /* Return an isl_pw_aff that maps each element in the intersection of the
2134 * domains of the elements of list to the maximal corresponding affine
2137 __isl_give isl_pw_aff
*isl_pw_aff_list_max(__isl_take isl_pw_aff_list
*list
)
2139 return pw_aff_list_reduce(list
, &isl_pw_aff_max
);
2145 #include <isl_multi_templ.c>
2147 /* Construct an isl_multi_aff in the given space with value zero in
2148 * each of the output dimensions.
2150 __isl_give isl_multi_aff
*isl_multi_aff_zero(__isl_take isl_space
*space
)
2158 n
= isl_space_dim(space
, isl_dim_out
);
2159 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
2162 isl_space_free(space
);
2165 isl_local_space
*ls
;
2168 space
= isl_space_domain(space
);
2169 ls
= isl_local_space_from_space(space
);
2170 aff
= isl_aff_zero_on_domain(ls
);
2172 for (i
= 0; i
< n
; ++i
)
2173 ma
= isl_multi_aff_set_aff(ma
, i
, isl_aff_copy(aff
));
2181 /* Create an isl_multi_aff in the given space that maps each
2182 * input dimension to the corresponding output dimension.
2184 __isl_give isl_multi_aff
*isl_multi_aff_identity(__isl_take isl_space
*space
)
2192 if (isl_space_is_set(space
))
2193 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
2194 "expecting map space", goto error
);
2196 n
= isl_space_dim(space
, isl_dim_out
);
2197 if (n
!= isl_space_dim(space
, isl_dim_in
))
2198 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
2199 "number of input and output dimensions needs to be "
2200 "the same", goto error
);
2202 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
2205 isl_space_free(space
);
2208 isl_local_space
*ls
;
2211 space
= isl_space_domain(space
);
2212 ls
= isl_local_space_from_space(space
);
2213 aff
= isl_aff_zero_on_domain(ls
);
2215 for (i
= 0; i
< n
; ++i
) {
2217 aff_i
= isl_aff_copy(aff
);
2218 aff_i
= isl_aff_add_coefficient_si(aff_i
,
2220 ma
= isl_multi_aff_set_aff(ma
, i
, aff_i
);
2228 isl_space_free(space
);
2232 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
2235 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_multi_aff(
2236 __isl_take isl_multi_aff
*ma
)
2238 isl_set
*dom
= isl_set_universe(isl_multi_aff_get_domain_space(ma
));
2239 return isl_pw_multi_aff_alloc(dom
, ma
);
2242 __isl_give isl_multi_aff
*isl_multi_aff_add(__isl_take isl_multi_aff
*maff1
,
2243 __isl_take isl_multi_aff
*maff2
)
2248 maff1
= isl_multi_aff_cow(maff1
);
2249 if (!maff1
|| !maff2
)
2252 ctx
= isl_multi_aff_get_ctx(maff1
);
2253 if (!isl_space_is_equal(maff1
->space
, maff2
->space
))
2254 isl_die(ctx
, isl_error_invalid
,
2255 "spaces don't match", goto error
);
2257 for (i
= 0; i
< maff1
->n
; ++i
) {
2258 maff1
->p
[i
] = isl_aff_add(maff1
->p
[i
],
2259 isl_aff_copy(maff2
->p
[i
]));
2264 isl_multi_aff_free(maff2
);
2267 isl_multi_aff_free(maff1
);
2268 isl_multi_aff_free(maff2
);
2272 /* Given two multi-affine expressions A -> B and C -> D,
2273 * construct a multi-affine expression [A -> C] -> [B -> D].
2275 __isl_give isl_multi_aff
*isl_multi_aff_product(
2276 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
2282 int in1
, in2
, out1
, out2
;
2284 in1
= isl_multi_aff_dim(ma1
, isl_dim_in
);
2285 in2
= isl_multi_aff_dim(ma2
, isl_dim_in
);
2286 out1
= isl_multi_aff_dim(ma1
, isl_dim_out
);
2287 out2
= isl_multi_aff_dim(ma2
, isl_dim_out
);
2288 space
= isl_space_product(isl_multi_aff_get_space(ma1
),
2289 isl_multi_aff_get_space(ma2
));
2290 res
= isl_multi_aff_alloc(isl_space_copy(space
));
2291 space
= isl_space_domain(space
);
2293 for (i
= 0; i
< out1
; ++i
) {
2294 aff
= isl_multi_aff_get_aff(ma1
, i
);
2295 aff
= isl_aff_insert_dims(aff
, isl_dim_in
, in1
, in2
);
2296 aff
= isl_aff_reset_domain_space(aff
, isl_space_copy(space
));
2297 res
= isl_multi_aff_set_aff(res
, i
, aff
);
2300 for (i
= 0; i
< out2
; ++i
) {
2301 aff
= isl_multi_aff_get_aff(ma2
, i
);
2302 aff
= isl_aff_insert_dims(aff
, isl_dim_in
, 0, in1
);
2303 aff
= isl_aff_reset_domain_space(aff
, isl_space_copy(space
));
2304 res
= isl_multi_aff_set_aff(res
, out1
+ i
, aff
);
2307 isl_space_free(space
);
2308 isl_multi_aff_free(ma1
);
2309 isl_multi_aff_free(ma2
);
2313 /* Exploit the equalities in "eq" to simplify the affine expressions.
2315 static __isl_give isl_multi_aff
*isl_multi_aff_substitute_equalities(
2316 __isl_take isl_multi_aff
*maff
, __isl_take isl_basic_set
*eq
)
2320 maff
= isl_multi_aff_cow(maff
);
2324 for (i
= 0; i
< maff
->n
; ++i
) {
2325 maff
->p
[i
] = isl_aff_substitute_equalities(maff
->p
[i
],
2326 isl_basic_set_copy(eq
));
2331 isl_basic_set_free(eq
);
2334 isl_basic_set_free(eq
);
2335 isl_multi_aff_free(maff
);
2339 __isl_give isl_multi_aff
*isl_multi_aff_scale(__isl_take isl_multi_aff
*maff
,
2344 maff
= isl_multi_aff_cow(maff
);
2348 for (i
= 0; i
< maff
->n
; ++i
) {
2349 maff
->p
[i
] = isl_aff_scale(maff
->p
[i
], f
);
2351 return isl_multi_aff_free(maff
);
2357 __isl_give isl_multi_aff
*isl_multi_aff_add_on_domain(__isl_keep isl_set
*dom
,
2358 __isl_take isl_multi_aff
*maff1
, __isl_take isl_multi_aff
*maff2
)
2360 maff1
= isl_multi_aff_add(maff1
, maff2
);
2361 maff1
= isl_multi_aff_gist(maff1
, isl_set_copy(dom
));
2365 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff
*maff
)
2373 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff
*maff1
,
2374 __isl_keep isl_multi_aff
*maff2
)
2379 if (!maff1
|| !maff2
)
2381 if (maff1
->n
!= maff2
->n
)
2383 equal
= isl_space_is_equal(maff1
->space
, maff2
->space
);
2384 if (equal
< 0 || !equal
)
2387 for (i
= 0; i
< maff1
->n
; ++i
) {
2388 equal
= isl_aff_plain_is_equal(maff1
->p
[i
], maff2
->p
[i
]);
2389 if (equal
< 0 || !equal
)
2396 __isl_give isl_multi_aff
*isl_multi_aff_set_dim_name(
2397 __isl_take isl_multi_aff
*maff
,
2398 enum isl_dim_type type
, unsigned pos
, const char *s
)
2402 maff
= isl_multi_aff_cow(maff
);
2406 maff
->space
= isl_space_set_dim_name(maff
->space
, type
, pos
, s
);
2408 return isl_multi_aff_free(maff
);
2410 if (type
== isl_dim_out
)
2412 for (i
= 0; i
< maff
->n
; ++i
) {
2413 maff
->p
[i
] = isl_aff_set_dim_name(maff
->p
[i
], type
, pos
, s
);
2415 return isl_multi_aff_free(maff
);
2421 __isl_give isl_multi_aff
*isl_multi_aff_drop_dims(__isl_take isl_multi_aff
*maff
,
2422 enum isl_dim_type type
, unsigned first
, unsigned n
)
2426 maff
= isl_multi_aff_cow(maff
);
2430 maff
->space
= isl_space_drop_dims(maff
->space
, type
, first
, n
);
2432 return isl_multi_aff_free(maff
);
2434 if (type
== isl_dim_out
) {
2435 for (i
= 0; i
< n
; ++i
)
2436 isl_aff_free(maff
->p
[first
+ i
]);
2437 for (i
= first
; i
+ n
< maff
->n
; ++i
)
2438 maff
->p
[i
] = maff
->p
[i
+ n
];
2443 for (i
= 0; i
< maff
->n
; ++i
) {
2444 maff
->p
[i
] = isl_aff_drop_dims(maff
->p
[i
], type
, first
, n
);
2446 return isl_multi_aff_free(maff
);
2452 /* Return the set of domain elements where "ma1" is lexicographically
2453 * smaller than or equal to "ma2".
2455 __isl_give isl_set
*isl_multi_aff_lex_le_set(__isl_take isl_multi_aff
*ma1
,
2456 __isl_take isl_multi_aff
*ma2
)
2458 return isl_multi_aff_lex_ge_set(ma2
, ma1
);
2461 /* Return the set of domain elements where "ma1" is lexicographically
2462 * greater than or equal to "ma2".
2464 __isl_give isl_set
*isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff
*ma1
,
2465 __isl_take isl_multi_aff
*ma2
)
2468 isl_map
*map1
, *map2
;
2471 map1
= isl_map_from_multi_aff(ma1
);
2472 map2
= isl_map_from_multi_aff(ma2
);
2473 map
= isl_map_range_product(map1
, map2
);
2474 space
= isl_space_range(isl_map_get_space(map
));
2475 space
= isl_space_domain(isl_space_unwrap(space
));
2476 ge
= isl_map_lex_ge(space
);
2477 map
= isl_map_intersect_range(map
, isl_map_wrap(ge
));
2479 return isl_map_domain(map
);
2483 #define PW isl_pw_multi_aff
2485 #define EL isl_multi_aff
2487 #define EL_IS_ZERO is_empty
2491 #define IS_ZERO is_empty
2494 #undef DEFAULT_IS_ZERO
2495 #define DEFAULT_IS_ZERO 0
2500 #define NO_INVOLVES_DIMS
2501 #define NO_MOVE_DIMS
2502 #define NO_INSERT_DIMS
2506 #include <isl_pw_templ.c>
2509 #define UNION isl_union_pw_multi_aff
2511 #define PART isl_pw_multi_aff
2513 #define PARTS pw_multi_aff
2514 #define ALIGN_DOMAIN
2518 #include <isl_union_templ.c>
2520 /* Given a function "cmp" that returns the set of elements where
2521 * "ma1" is "better" than "ma2", return the intersection of this
2522 * set with "dom1" and "dom2".
2524 static __isl_give isl_set
*shared_and_better(__isl_keep isl_set
*dom1
,
2525 __isl_keep isl_set
*dom2
, __isl_keep isl_multi_aff
*ma1
,
2526 __isl_keep isl_multi_aff
*ma2
,
2527 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
2528 __isl_take isl_multi_aff
*ma2
))
2534 common
= isl_set_intersect(isl_set_copy(dom1
), isl_set_copy(dom2
));
2535 is_empty
= isl_set_plain_is_empty(common
);
2536 if (is_empty
>= 0 && is_empty
)
2539 return isl_set_free(common
);
2540 better
= cmp(isl_multi_aff_copy(ma1
), isl_multi_aff_copy(ma2
));
2541 better
= isl_set_intersect(common
, better
);
2546 /* Given a function "cmp" that returns the set of elements where
2547 * "ma1" is "better" than "ma2", return a piecewise multi affine
2548 * expression defined on the union of the definition domains
2549 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
2550 * "pma2" on each cell. If only one of the two input functions
2551 * is defined on a given cell, then it is considered the best.
2553 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_opt(
2554 __isl_take isl_pw_multi_aff
*pma1
,
2555 __isl_take isl_pw_multi_aff
*pma2
,
2556 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
2557 __isl_take isl_multi_aff
*ma2
))
2560 isl_pw_multi_aff
*res
= NULL
;
2562 isl_set
*set
= NULL
;
2567 ctx
= isl_space_get_ctx(pma1
->dim
);
2568 if (!isl_space_is_equal(pma1
->dim
, pma2
->dim
))
2569 isl_die(ctx
, isl_error_invalid
,
2570 "arguments should live in the same space", goto error
);
2572 if (isl_pw_multi_aff_is_empty(pma1
)) {
2573 isl_pw_multi_aff_free(pma1
);
2577 if (isl_pw_multi_aff_is_empty(pma2
)) {
2578 isl_pw_multi_aff_free(pma2
);
2582 n
= 2 * (pma1
->n
+ 1) * (pma2
->n
+ 1);
2583 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma1
->dim
), n
);
2585 for (i
= 0; i
< pma1
->n
; ++i
) {
2586 set
= isl_set_copy(pma1
->p
[i
].set
);
2587 for (j
= 0; j
< pma2
->n
; ++j
) {
2591 better
= shared_and_better(pma2
->p
[j
].set
,
2592 pma1
->p
[i
].set
, pma2
->p
[j
].maff
,
2593 pma1
->p
[i
].maff
, cmp
);
2594 is_empty
= isl_set_plain_is_empty(better
);
2595 if (is_empty
< 0 || is_empty
) {
2596 isl_set_free(better
);
2601 set
= isl_set_subtract(set
, isl_set_copy(better
));
2603 res
= isl_pw_multi_aff_add_piece(res
, better
,
2604 isl_multi_aff_copy(pma2
->p
[j
].maff
));
2606 res
= isl_pw_multi_aff_add_piece(res
, set
,
2607 isl_multi_aff_copy(pma1
->p
[i
].maff
));
2610 for (j
= 0; j
< pma2
->n
; ++j
) {
2611 set
= isl_set_copy(pma2
->p
[j
].set
);
2612 for (i
= 0; i
< pma1
->n
; ++i
)
2613 set
= isl_set_subtract(set
,
2614 isl_set_copy(pma1
->p
[i
].set
));
2615 res
= isl_pw_multi_aff_add_piece(res
, set
,
2616 isl_multi_aff_copy(pma2
->p
[j
].maff
));
2619 isl_pw_multi_aff_free(pma1
);
2620 isl_pw_multi_aff_free(pma2
);
2624 isl_pw_multi_aff_free(pma1
);
2625 isl_pw_multi_aff_free(pma2
);
2627 return isl_pw_multi_aff_free(res
);
2630 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmax(
2631 __isl_take isl_pw_multi_aff
*pma1
,
2632 __isl_take isl_pw_multi_aff
*pma2
)
2634 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_ge_set
);
2637 /* Given two piecewise multi affine expressions, return a piecewise
2638 * multi-affine expression defined on the union of the definition domains
2639 * of the inputs that is equal to the lexicographic maximum of the two
2640 * inputs on each cell. If only one of the two inputs is defined on
2641 * a given cell, then it is considered to be the maximum.
2643 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmax(
2644 __isl_take isl_pw_multi_aff
*pma1
,
2645 __isl_take isl_pw_multi_aff
*pma2
)
2647 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
2648 &pw_multi_aff_union_lexmax
);
2651 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmin(
2652 __isl_take isl_pw_multi_aff
*pma1
,
2653 __isl_take isl_pw_multi_aff
*pma2
)
2655 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_le_set
);
2658 /* Given two piecewise multi affine expressions, return a piecewise
2659 * multi-affine expression defined on the union of the definition domains
2660 * of the inputs that is equal to the lexicographic minimum of the two
2661 * inputs on each cell. If only one of the two inputs is defined on
2662 * a given cell, then it is considered to be the minimum.
2664 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmin(
2665 __isl_take isl_pw_multi_aff
*pma1
,
2666 __isl_take isl_pw_multi_aff
*pma2
)
2668 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
2669 &pw_multi_aff_union_lexmin
);
2672 static __isl_give isl_pw_multi_aff
*pw_multi_aff_add(
2673 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2675 return isl_pw_multi_aff_on_shared_domain(pma1
, pma2
,
2676 &isl_multi_aff_add
);
2679 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_add(
2680 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2682 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
2686 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_add(
2687 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2689 return isl_pw_multi_aff_union_add_(pma1
, pma2
);
2692 /* Given two piecewise multi-affine expressions A -> B and C -> D,
2693 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
2695 static __isl_give isl_pw_multi_aff
*pw_multi_aff_product(
2696 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2700 isl_pw_multi_aff
*res
;
2705 n
= pma1
->n
* pma2
->n
;
2706 space
= isl_space_product(isl_space_copy(pma1
->dim
),
2707 isl_space_copy(pma2
->dim
));
2708 res
= isl_pw_multi_aff_alloc_size(space
, n
);
2710 for (i
= 0; i
< pma1
->n
; ++i
) {
2711 for (j
= 0; j
< pma2
->n
; ++j
) {
2715 domain
= isl_set_product(isl_set_copy(pma1
->p
[i
].set
),
2716 isl_set_copy(pma2
->p
[j
].set
));
2717 ma
= isl_multi_aff_product(
2718 isl_multi_aff_copy(pma1
->p
[i
].maff
),
2719 isl_multi_aff_copy(pma2
->p
[i
].maff
));
2720 res
= isl_pw_multi_aff_add_piece(res
, domain
, ma
);
2724 isl_pw_multi_aff_free(pma1
);
2725 isl_pw_multi_aff_free(pma2
);
2728 isl_pw_multi_aff_free(pma1
);
2729 isl_pw_multi_aff_free(pma2
);
2733 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_product(
2734 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2736 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
2737 &pw_multi_aff_product
);
2740 /* Construct a map mapping the domain of the piecewise multi-affine expression
2741 * to its range, with each dimension in the range equated to the
2742 * corresponding affine expression on its cell.
2744 __isl_give isl_map
*isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
2752 map
= isl_map_empty(isl_pw_multi_aff_get_space(pma
));
2754 for (i
= 0; i
< pma
->n
; ++i
) {
2755 isl_multi_aff
*maff
;
2756 isl_basic_map
*bmap
;
2759 maff
= isl_multi_aff_copy(pma
->p
[i
].maff
);
2760 bmap
= isl_basic_map_from_multi_aff(maff
);
2761 map_i
= isl_map_from_basic_map(bmap
);
2762 map_i
= isl_map_intersect_domain(map_i
,
2763 isl_set_copy(pma
->p
[i
].set
));
2764 map
= isl_map_union_disjoint(map
, map_i
);
2767 isl_pw_multi_aff_free(pma
);
2771 __isl_give isl_set
*isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
2773 if (!isl_space_is_set(pma
->dim
))
2774 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
2775 "isl_pw_multi_aff cannot be converted into an isl_set",
2776 return isl_pw_multi_aff_free(pma
));
2778 return isl_map_from_pw_multi_aff(pma
);
2781 /* Given a basic map with a single output dimension that is defined
2782 * in terms of the parameters and input dimensions using an equality,
2783 * extract an isl_aff that expresses the output dimension in terms
2784 * of the parameters and input dimensions.
2786 * Since some applications expect the result of isl_pw_multi_aff_from_map
2787 * to only contain integer affine expressions, we compute the floor
2788 * of the expression before returning.
2790 * This function shares some similarities with
2791 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
2793 static __isl_give isl_aff
*extract_isl_aff_from_basic_map(
2794 __isl_take isl_basic_map
*bmap
)
2799 isl_local_space
*ls
;
2804 if (isl_basic_map_dim(bmap
, isl_dim_out
) != 1)
2805 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
2806 "basic map should have a single output dimension",
2808 offset
= isl_basic_map_offset(bmap
, isl_dim_out
);
2809 total
= isl_basic_map_total_dim(bmap
);
2810 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2811 if (isl_int_is_zero(bmap
->eq
[i
][offset
]))
2813 if (isl_seq_first_non_zero(bmap
->eq
[i
] + offset
+ 1,
2814 1 + total
- (offset
+ 1)) != -1)
2818 if (i
>= bmap
->n_eq
)
2819 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
2820 "unable to find suitable equality", goto error
);
2821 ls
= isl_basic_map_get_local_space(bmap
);
2822 aff
= isl_aff_alloc(isl_local_space_domain(ls
));
2825 if (isl_int_is_neg(bmap
->eq
[i
][offset
]))
2826 isl_seq_cpy(aff
->v
->el
+ 1, bmap
->eq
[i
], offset
);
2828 isl_seq_neg(aff
->v
->el
+ 1, bmap
->eq
[i
], offset
);
2829 isl_seq_clr(aff
->v
->el
+ 1 + offset
, aff
->v
->size
- (1 + offset
));
2830 isl_int_abs(aff
->v
->el
[0], bmap
->eq
[i
][offset
]);
2831 isl_basic_map_free(bmap
);
2833 aff
= isl_aff_remove_unused_divs(aff
);
2834 aff
= isl_aff_floor(aff
);
2837 isl_basic_map_free(bmap
);
2841 /* Given a basic map where each output dimension is defined
2842 * in terms of the parameters and input dimensions using an equality,
2843 * extract an isl_multi_aff that expresses the output dimensions in terms
2844 * of the parameters and input dimensions.
2846 static __isl_give isl_multi_aff
*extract_isl_multi_aff_from_basic_map(
2847 __isl_take isl_basic_map
*bmap
)
2856 ma
= isl_multi_aff_alloc(isl_basic_map_get_space(bmap
));
2857 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
2859 for (i
= 0; i
< n_out
; ++i
) {
2860 isl_basic_map
*bmap_i
;
2863 bmap_i
= isl_basic_map_copy(bmap
);
2864 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
,
2865 i
+ 1, n_out
- (1 + i
));
2866 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
, 0, i
);
2867 aff
= extract_isl_aff_from_basic_map(bmap_i
);
2868 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
2871 isl_basic_map_free(bmap
);
2876 /* Create an isl_pw_multi_aff that is equivalent to
2877 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
2878 * The given basic map is such that each output dimension is defined
2879 * in terms of the parameters and input dimensions using an equality.
2881 static __isl_give isl_pw_multi_aff
*plain_pw_multi_aff_from_map(
2882 __isl_take isl_set
*domain
, __isl_take isl_basic_map
*bmap
)
2886 ma
= extract_isl_multi_aff_from_basic_map(bmap
);
2887 return isl_pw_multi_aff_alloc(domain
, ma
);
2890 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
2891 * This obivously only works if the input "map" is single-valued.
2892 * If so, we compute the lexicographic minimum of the image in the form
2893 * of an isl_pw_multi_aff. Since the image is unique, it is equal
2894 * to its lexicographic minimum.
2895 * If the input is not single-valued, we produce an error.
2897 * As a special case, we first check if all output dimensions are uniquely
2898 * defined in terms of the parameters and input dimensions over the entire
2899 * domain. If so, we extract the desired isl_pw_multi_aff directly
2900 * from the affine hull of "map" and its domain.
2902 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_map(__isl_take isl_map
*map
)
2906 isl_pw_multi_aff
*pma
;
2907 isl_basic_map
*hull
;
2912 hull
= isl_map_affine_hull(isl_map_copy(map
));
2913 sv
= isl_basic_map_plain_is_single_valued(hull
);
2915 return plain_pw_multi_aff_from_map(isl_map_domain(map
), hull
);
2916 isl_basic_map_free(hull
);
2920 sv
= isl_map_is_single_valued(map
);
2924 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
2925 "map is not single-valued", goto error
);
2926 map
= isl_map_make_disjoint(map
);
2930 pma
= isl_pw_multi_aff_empty(isl_map_get_space(map
));
2932 for (i
= 0; i
< map
->n
; ++i
) {
2933 isl_pw_multi_aff
*pma_i
;
2934 isl_basic_map
*bmap
;
2935 bmap
= isl_basic_map_copy(map
->p
[i
]);
2936 pma_i
= isl_basic_map_lexmin_pw_multi_aff(bmap
);
2937 pma
= isl_pw_multi_aff_add_disjoint(pma
, pma_i
);
2947 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_set(__isl_take isl_set
*set
)
2949 return isl_pw_multi_aff_from_map(set
);
2952 /* Return the piecewise affine expression "set ? 1 : 0".
2954 __isl_give isl_pw_aff
*isl_set_indicator_function(__isl_take isl_set
*set
)
2957 isl_space
*space
= isl_set_get_space(set
);
2958 isl_local_space
*ls
= isl_local_space_from_space(space
);
2959 isl_aff
*zero
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
2960 isl_aff
*one
= isl_aff_zero_on_domain(ls
);
2962 one
= isl_aff_add_constant_si(one
, 1);
2963 pa
= isl_pw_aff_alloc(isl_set_copy(set
), one
);
2964 set
= isl_set_complement(set
);
2965 pa
= isl_pw_aff_add_disjoint(pa
, isl_pw_aff_alloc(set
, zero
));
2970 /* Plug in "subs" for dimension "type", "pos" of "aff".
2972 * Let i be the dimension to replace and let "subs" be of the form
2976 * and "aff" of the form
2982 * floor((a f + d g')/(m d))
2984 * where g' is the result of plugging in "subs" in each of the integer
2987 __isl_give isl_aff
*isl_aff_substitute(__isl_take isl_aff
*aff
,
2988 enum isl_dim_type type
, unsigned pos
, __isl_keep isl_aff
*subs
)
2993 aff
= isl_aff_cow(aff
);
2995 return isl_aff_free(aff
);
2997 ctx
= isl_aff_get_ctx(aff
);
2998 if (!isl_space_is_equal(aff
->ls
->dim
, subs
->ls
->dim
))
2999 isl_die(ctx
, isl_error_invalid
,
3000 "spaces don't match", return isl_aff_free(aff
));
3001 if (isl_local_space_dim(subs
->ls
, isl_dim_div
) != 0)
3002 isl_die(ctx
, isl_error_unsupported
,
3003 "cannot handle divs yet", return isl_aff_free(aff
));
3005 aff
->ls
= isl_local_space_substitute(aff
->ls
, type
, pos
, subs
);
3007 return isl_aff_free(aff
);
3009 aff
->v
= isl_vec_cow(aff
->v
);
3011 return isl_aff_free(aff
);
3013 pos
+= isl_local_space_offset(aff
->ls
, type
);
3016 isl_int_set(v
, aff
->v
->el
[1 + pos
]);
3017 isl_int_set_si(aff
->v
->el
[1 + pos
], 0);
3018 isl_seq_combine(aff
->v
->el
+ 1, subs
->v
->el
[0], aff
->v
->el
+ 1,
3019 v
, subs
->v
->el
+ 1, subs
->v
->size
- 1);
3020 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], subs
->v
->el
[0]);
3026 /* Plug in "subs" for dimension "type", "pos" in each of the affine
3027 * expressions in "maff".
3029 __isl_give isl_multi_aff
*isl_multi_aff_substitute(
3030 __isl_take isl_multi_aff
*maff
, enum isl_dim_type type
, unsigned pos
,
3031 __isl_keep isl_aff
*subs
)
3035 maff
= isl_multi_aff_cow(maff
);
3037 return isl_multi_aff_free(maff
);
3039 if (type
== isl_dim_in
)
3042 for (i
= 0; i
< maff
->n
; ++i
) {
3043 maff
->p
[i
] = isl_aff_substitute(maff
->p
[i
], type
, pos
, subs
);
3045 return isl_multi_aff_free(maff
);
3051 /* Plug in "subs" for dimension "type", "pos" of "pma".
3053 * pma is of the form
3057 * while subs is of the form
3059 * v' = B_j(v) -> S_j
3061 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
3062 * has a contribution in the result, in particular
3064 * C_ij(S_j) -> M_i(S_j)
3066 * Note that plugging in S_j in C_ij may also result in an empty set
3067 * and this contribution should simply be discarded.
3069 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_substitute(
3070 __isl_take isl_pw_multi_aff
*pma
, enum isl_dim_type type
, unsigned pos
,
3071 __isl_keep isl_pw_aff
*subs
)
3074 isl_pw_multi_aff
*res
;
3077 return isl_pw_multi_aff_free(pma
);
3079 n
= pma
->n
* subs
->n
;
3080 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma
->dim
), n
);
3082 for (i
= 0; i
< pma
->n
; ++i
) {
3083 for (j
= 0; j
< subs
->n
; ++j
) {
3085 isl_multi_aff
*res_ij
;
3086 common
= isl_set_intersect(
3087 isl_set_copy(pma
->p
[i
].set
),
3088 isl_set_copy(subs
->p
[j
].set
));
3089 common
= isl_set_substitute(common
,
3090 type
, pos
, subs
->p
[j
].aff
);
3091 if (isl_set_plain_is_empty(common
)) {
3092 isl_set_free(common
);
3096 res_ij
= isl_multi_aff_substitute(
3097 isl_multi_aff_copy(pma
->p
[i
].maff
),
3098 type
, pos
, subs
->p
[j
].aff
);
3100 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
3104 isl_pw_multi_aff_free(pma
);
3108 /* Extend the local space of "dst" to include the divs
3109 * in the local space of "src".
3111 __isl_give isl_aff
*isl_aff_align_divs(__isl_take isl_aff
*dst
,
3112 __isl_keep isl_aff
*src
)
3120 return isl_aff_free(dst
);
3122 ctx
= isl_aff_get_ctx(src
);
3123 if (!isl_space_is_equal(src
->ls
->dim
, dst
->ls
->dim
))
3124 isl_die(ctx
, isl_error_invalid
,
3125 "spaces don't match", goto error
);
3127 if (src
->ls
->div
->n_row
== 0)
3130 exp1
= isl_alloc_array(ctx
, int, src
->ls
->div
->n_row
);
3131 exp2
= isl_alloc_array(ctx
, int, dst
->ls
->div
->n_row
);
3135 div
= isl_merge_divs(src
->ls
->div
, dst
->ls
->div
, exp1
, exp2
);
3136 dst
= isl_aff_expand_divs(dst
, div
, exp2
);
3144 return isl_aff_free(dst
);
3147 /* Adjust the local spaces of the affine expressions in "maff"
3148 * such that they all have the save divs.
3150 __isl_give isl_multi_aff
*isl_multi_aff_align_divs(
3151 __isl_take isl_multi_aff
*maff
)
3159 maff
= isl_multi_aff_cow(maff
);
3163 for (i
= 1; i
< maff
->n
; ++i
)
3164 maff
->p
[0] = isl_aff_align_divs(maff
->p
[0], maff
->p
[i
]);
3165 for (i
= 1; i
< maff
->n
; ++i
) {
3166 maff
->p
[i
] = isl_aff_align_divs(maff
->p
[i
], maff
->p
[0]);
3168 return isl_multi_aff_free(maff
);
3174 __isl_give isl_aff
*isl_aff_lift(__isl_take isl_aff
*aff
)
3176 aff
= isl_aff_cow(aff
);
3180 aff
->ls
= isl_local_space_lift(aff
->ls
);
3182 return isl_aff_free(aff
);
3187 /* Lift "maff" to a space with extra dimensions such that the result
3188 * has no more existentially quantified variables.
3189 * If "ls" is not NULL, then *ls is assigned the local space that lies
3190 * at the basis of the lifting applied to "maff".
3192 __isl_give isl_multi_aff
*isl_multi_aff_lift(__isl_take isl_multi_aff
*maff
,
3193 __isl_give isl_local_space
**ls
)
3207 isl_space
*space
= isl_multi_aff_get_domain_space(maff
);
3208 *ls
= isl_local_space_from_space(space
);
3210 return isl_multi_aff_free(maff
);
3215 maff
= isl_multi_aff_cow(maff
);
3216 maff
= isl_multi_aff_align_divs(maff
);
3220 n_div
= isl_aff_dim(maff
->p
[0], isl_dim_div
);
3221 space
= isl_multi_aff_get_space(maff
);
3222 space
= isl_space_lift(isl_space_domain(space
), n_div
);
3223 space
= isl_space_extend_domain_with_range(space
,
3224 isl_multi_aff_get_space(maff
));
3226 return isl_multi_aff_free(maff
);
3227 isl_space_free(maff
->space
);
3228 maff
->space
= space
;
3231 *ls
= isl_aff_get_domain_local_space(maff
->p
[0]);
3233 return isl_multi_aff_free(maff
);
3236 for (i
= 0; i
< maff
->n
; ++i
) {
3237 maff
->p
[i
] = isl_aff_lift(maff
->p
[i
]);
3245 isl_local_space_free(*ls
);
3246 return isl_multi_aff_free(maff
);
3250 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
3252 __isl_give isl_pw_aff
*isl_pw_multi_aff_get_pw_aff(
3253 __isl_keep isl_pw_multi_aff
*pma
, int pos
)
3263 n_out
= isl_pw_multi_aff_dim(pma
, isl_dim_out
);
3264 if (pos
< 0 || pos
>= n_out
)
3265 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
3266 "index out of bounds", return NULL
);
3268 space
= isl_pw_multi_aff_get_space(pma
);
3269 space
= isl_space_drop_dims(space
, isl_dim_out
,
3270 pos
+ 1, n_out
- pos
- 1);
3271 space
= isl_space_drop_dims(space
, isl_dim_out
, 0, pos
);
3273 pa
= isl_pw_aff_alloc_size(space
, pma
->n
);
3274 for (i
= 0; i
< pma
->n
; ++i
) {
3276 aff
= isl_multi_aff_get_aff(pma
->p
[i
].maff
, pos
);
3277 pa
= isl_pw_aff_add_piece(pa
, isl_set_copy(pma
->p
[i
].set
), aff
);
3283 /* Return an isl_pw_multi_aff with the given "set" as domain and
3284 * an unnamed zero-dimensional range.
3286 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_domain(
3287 __isl_take isl_set
*set
)
3292 space
= isl_set_get_space(set
);
3293 space
= isl_space_from_domain(space
);
3294 ma
= isl_multi_aff_zero(space
);
3295 return isl_pw_multi_aff_alloc(set
, ma
);
3298 /* Add an isl_pw_multi_aff with the given "set" as domain and
3299 * an unnamed zero-dimensional range to *user.
3301 static int add_pw_multi_aff_from_domain(__isl_take isl_set
*set
, void *user
)
3303 isl_union_pw_multi_aff
**upma
= user
;
3304 isl_pw_multi_aff
*pma
;
3306 pma
= isl_pw_multi_aff_from_domain(set
);
3307 *upma
= isl_union_pw_multi_aff_add_pw_multi_aff(*upma
, pma
);
3312 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
3313 * an unnamed zero-dimensional range.
3315 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_domain(
3316 __isl_take isl_union_set
*uset
)
3319 isl_union_pw_multi_aff
*upma
;
3324 space
= isl_union_set_get_space(uset
);
3325 upma
= isl_union_pw_multi_aff_empty(space
);
3327 if (isl_union_set_foreach_set(uset
,
3328 &add_pw_multi_aff_from_domain
, &upma
) < 0)
3331 isl_union_set_free(uset
);
3334 isl_union_set_free(uset
);
3335 isl_union_pw_multi_aff_free(upma
);
3339 /* Convert "pma" to an isl_map and add it to *umap.
3341 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
, void *user
)
3343 isl_union_map
**umap
= user
;
3346 map
= isl_map_from_pw_multi_aff(pma
);
3347 *umap
= isl_union_map_add_map(*umap
, map
);
3352 /* Construct a union map mapping the domain of the union
3353 * piecewise multi-affine expression to its range, with each dimension
3354 * in the range equated to the corresponding affine expression on its cell.
3356 __isl_give isl_union_map
*isl_union_map_from_union_pw_multi_aff(
3357 __isl_take isl_union_pw_multi_aff
*upma
)
3360 isl_union_map
*umap
;
3365 space
= isl_union_pw_multi_aff_get_space(upma
);
3366 umap
= isl_union_map_empty(space
);
3368 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
3369 &map_from_pw_multi_aff
, &umap
) < 0)
3372 isl_union_pw_multi_aff_free(upma
);
3375 isl_union_pw_multi_aff_free(upma
);
3376 isl_union_map_free(umap
);
3380 /* Local data for bin_entry and the callback "fn".
3382 struct isl_union_pw_multi_aff_bin_data
{
3383 isl_union_pw_multi_aff
*upma2
;
3384 isl_union_pw_multi_aff
*res
;
3385 isl_pw_multi_aff
*pma
;
3386 int (*fn
)(void **entry
, void *user
);
3389 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
3390 * and call data->fn for each isl_pw_multi_aff in data->upma2.
3392 static int bin_entry(void **entry
, void *user
)
3394 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
3395 isl_pw_multi_aff
*pma
= *entry
;
3398 if (isl_hash_table_foreach(data
->upma2
->dim
->ctx
, &data
->upma2
->table
,
3399 data
->fn
, data
) < 0)
3405 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
3406 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
3407 * passed as user field) and the isl_pw_multi_aff from upma2 is available
3408 * as *entry. The callback should adjust data->res if desired.
3410 static __isl_give isl_union_pw_multi_aff
*bin_op(
3411 __isl_take isl_union_pw_multi_aff
*upma1
,
3412 __isl_take isl_union_pw_multi_aff
*upma2
,
3413 int (*fn
)(void **entry
, void *user
))
3416 struct isl_union_pw_multi_aff_bin_data data
= { NULL
, NULL
, NULL
, fn
};
3418 space
= isl_union_pw_multi_aff_get_space(upma2
);
3419 upma1
= isl_union_pw_multi_aff_align_params(upma1
, space
);
3420 space
= isl_union_pw_multi_aff_get_space(upma1
);
3421 upma2
= isl_union_pw_multi_aff_align_params(upma2
, space
);
3423 if (!upma1
|| !upma2
)
3427 data
.res
= isl_union_pw_multi_aff_alloc(isl_space_copy(upma1
->dim
),
3429 if (isl_hash_table_foreach(upma1
->dim
->ctx
, &upma1
->table
,
3430 &bin_entry
, &data
) < 0)
3433 isl_union_pw_multi_aff_free(upma1
);
3434 isl_union_pw_multi_aff_free(upma2
);
3437 isl_union_pw_multi_aff_free(upma1
);
3438 isl_union_pw_multi_aff_free(upma2
);
3439 isl_union_pw_multi_aff_free(data
.res
);
3443 /* Given two isl_multi_affs A -> B and C -> D,
3444 * construct an isl_multi_aff (A * C) -> (B, D).
3446 __isl_give isl_multi_aff
*isl_multi_aff_flat_range_product(
3447 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
3457 space
= isl_space_range_product(isl_multi_aff_get_space(ma1
),
3458 isl_multi_aff_get_space(ma2
));
3459 space
= isl_space_flatten_range(space
);
3460 res
= isl_multi_aff_alloc(space
);
3462 n1
= isl_multi_aff_dim(ma1
, isl_dim_out
);
3463 n2
= isl_multi_aff_dim(ma2
, isl_dim_out
);
3465 for (i
= 0; i
< n1
; ++i
) {
3466 aff
= isl_multi_aff_get_aff(ma1
, i
);
3467 res
= isl_multi_aff_set_aff(res
, i
, aff
);
3470 for (i
= 0; i
< n2
; ++i
) {
3471 aff
= isl_multi_aff_get_aff(ma2
, i
);
3472 res
= isl_multi_aff_set_aff(res
, n1
+ i
, aff
);
3475 isl_multi_aff_free(ma1
);
3476 isl_multi_aff_free(ma2
);
3479 isl_multi_aff_free(ma1
);
3480 isl_multi_aff_free(ma2
);
3484 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
3485 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3487 static __isl_give isl_pw_multi_aff
*pw_multi_aff_flat_range_product(
3488 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3492 space
= isl_space_range_product(isl_pw_multi_aff_get_space(pma1
),
3493 isl_pw_multi_aff_get_space(pma2
));
3494 space
= isl_space_flatten_range(space
);
3495 return isl_pw_multi_aff_on_shared_domain_in(pma1
, pma2
, space
,
3496 &isl_multi_aff_flat_range_product
);
3499 /* Given two isl_pw_multi_affs A -> B and C -> D,
3500 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3502 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_flat_range_product(
3503 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3505 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
3506 &pw_multi_aff_flat_range_product
);
3509 /* If data->pma and *entry have the same domain space, then compute
3510 * their flat range product and the result to data->res.
3512 static int flat_range_product_entry(void **entry
, void *user
)
3514 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
3515 isl_pw_multi_aff
*pma2
= *entry
;
3517 if (!isl_space_tuple_match(data
->pma
->dim
, isl_dim_in
,
3518 pma2
->dim
, isl_dim_in
))
3521 pma2
= isl_pw_multi_aff_flat_range_product(
3522 isl_pw_multi_aff_copy(data
->pma
),
3523 isl_pw_multi_aff_copy(pma2
));
3525 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma2
);
3530 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
3531 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
3533 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_flat_range_product(
3534 __isl_take isl_union_pw_multi_aff
*upma1
,
3535 __isl_take isl_union_pw_multi_aff
*upma2
)
3537 return bin_op(upma1
, upma2
, &flat_range_product_entry
);