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 /* Given two affine expressions "p" of length p_len (including the
652 * denominator and the constant term) and "subs" of length subs_len,
653 * plug in "subs" for the variable at position "pos".
654 * The variables of "subs" and "p" are assumed to match up to subs_len,
655 * but "p" may have additional variables.
656 * "v" is an initialized isl_int that can be used internally.
658 * In particular, if "p" represents the expression
662 * with i the variable at position "pos" and "subs" represents the expression
666 * then the result represents the expression
671 void isl_seq_substitute(isl_int
*p
, int pos
, isl_int
*subs
,
672 int p_len
, int subs_len
, isl_int v
)
674 isl_int_set(v
, p
[1 + pos
]);
675 isl_int_set_si(p
[1 + pos
], 0);
676 isl_seq_combine(p
+ 1, subs
[0], p
+ 1, v
, subs
+ 1, subs_len
- 1);
677 isl_seq_scale(p
+ subs_len
, p
+ subs_len
, subs
[0], p_len
- subs_len
);
678 isl_int_mul(p
[0], p
[0], subs
[0]);
681 /* Look for any divs in the aff->ls with a denominator equal to one
682 * and plug them into the affine expression and any subsequent divs
683 * that may reference the div.
685 static __isl_give isl_aff
*plug_in_integral_divs(__isl_take isl_aff
*aff
)
697 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
699 for (i
= 0; i
< n
; ++i
) {
700 if (!isl_int_is_one(aff
->ls
->div
->row
[i
][0]))
702 ls
= isl_local_space_copy(aff
->ls
);
703 ls
= isl_local_space_substitute_seq(ls
, isl_dim_div
, i
,
704 aff
->ls
->div
->row
[i
], len
, i
+ 1);
705 vec
= isl_vec_copy(aff
->v
);
706 vec
= isl_vec_cow(vec
);
712 pos
= isl_local_space_offset(aff
->ls
, isl_dim_div
) + i
;
713 isl_seq_substitute(vec
->el
, pos
, aff
->ls
->div
->row
[i
],
718 isl_vec_free(aff
->v
);
720 isl_local_space_free(aff
->ls
);
727 isl_local_space_free(ls
);
728 return isl_aff_free(aff
);
731 /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
733 * Even though this function is only called on isl_affs with a single
734 * reference, we are careful to only change aff->v and aff->ls together.
736 static __isl_give isl_aff
*swap_div(__isl_take isl_aff
*aff
, int a
, int b
)
738 unsigned off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
742 ls
= isl_local_space_copy(aff
->ls
);
743 ls
= isl_local_space_swap_div(ls
, a
, b
);
744 v
= isl_vec_copy(aff
->v
);
749 isl_int_swap(v
->el
[1 + off
+ a
], v
->el
[1 + off
+ b
]);
750 isl_vec_free(aff
->v
);
752 isl_local_space_free(aff
->ls
);
758 isl_local_space_free(ls
);
759 return isl_aff_free(aff
);
762 /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
764 * We currently do not actually remove div "b", but simply add its
765 * coefficient to that of "a" and then zero it out.
767 static __isl_give isl_aff
*merge_divs(__isl_take isl_aff
*aff
, int a
, int b
)
769 unsigned off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
771 if (isl_int_is_zero(aff
->v
->el
[1 + off
+ b
]))
774 aff
->v
= isl_vec_cow(aff
->v
);
776 return isl_aff_free(aff
);
778 isl_int_add(aff
->v
->el
[1 + off
+ a
],
779 aff
->v
->el
[1 + off
+ a
], aff
->v
->el
[1 + off
+ b
]);
780 isl_int_set_si(aff
->v
->el
[1 + off
+ b
], 0);
785 /* Sort the divs in the local space of "aff" according to
786 * the comparison function "cmp_row" in isl_local_space.c,
787 * combining the coefficients of identical divs.
789 * Reordering divs does not change the semantics of "aff",
790 * so there is no need to call isl_aff_cow.
791 * Moreover, this function is currently only called on isl_affs
792 * with a single reference.
794 static __isl_give isl_aff
*sort_divs(__isl_take isl_aff
*aff
)
802 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
803 n
= isl_aff_dim(aff
, isl_dim_div
);
804 for (i
= 1; i
< n
; ++i
) {
805 for (j
= i
- 1; j
>= 0; --j
) {
806 int cmp
= isl_mat_cmp_div(aff
->ls
->div
, j
, j
+ 1);
810 aff
= merge_divs(aff
, j
, j
+ 1);
812 aff
= swap_div(aff
, j
, j
+ 1);
821 /* Normalize the representation of "aff".
823 * This function should only be called of "new" isl_affs, i.e.,
824 * with only a single reference. We therefore do not need to
825 * worry about affecting other instances.
827 __isl_give isl_aff
*isl_aff_normalize(__isl_take isl_aff
*aff
)
831 aff
->v
= isl_vec_normalize(aff
->v
);
833 return isl_aff_free(aff
);
834 aff
= plug_in_integral_divs(aff
);
835 aff
= sort_divs(aff
);
836 aff
= isl_aff_remove_unused_divs(aff
);
840 /* Given f, return floor(f).
841 * If f is an integer expression, then just return f.
842 * If f is a constant, then return the constant floor(f).
843 * Otherwise, if f = g/m, write g = q m + r,
844 * create a new div d = [r/m] and return the expression q + d.
845 * The coefficients in r are taken to lie between -m/2 and m/2.
847 __isl_give isl_aff
*isl_aff_floor(__isl_take isl_aff
*aff
)
857 if (isl_int_is_one(aff
->v
->el
[0]))
860 aff
= isl_aff_cow(aff
);
864 aff
->v
= isl_vec_cow(aff
->v
);
866 return isl_aff_free(aff
);
868 if (isl_aff_is_cst(aff
)) {
869 isl_int_fdiv_q(aff
->v
->el
[1], aff
->v
->el
[1], aff
->v
->el
[0]);
870 isl_int_set_si(aff
->v
->el
[0], 1);
874 div
= isl_vec_copy(aff
->v
);
875 div
= isl_vec_cow(div
);
877 return isl_aff_free(aff
);
879 ctx
= isl_aff_get_ctx(aff
);
880 isl_int_fdiv_q(aff
->v
->el
[0], aff
->v
->el
[0], ctx
->two
);
881 for (i
= 1; i
< aff
->v
->size
; ++i
) {
882 isl_int_fdiv_r(div
->el
[i
], div
->el
[i
], div
->el
[0]);
883 isl_int_fdiv_q(aff
->v
->el
[i
], aff
->v
->el
[i
], div
->el
[0]);
884 if (isl_int_gt(div
->el
[i
], aff
->v
->el
[0])) {
885 isl_int_sub(div
->el
[i
], div
->el
[i
], div
->el
[0]);
886 isl_int_add_ui(aff
->v
->el
[i
], aff
->v
->el
[i
], 1);
890 aff
->ls
= isl_local_space_add_div(aff
->ls
, div
);
892 return isl_aff_free(aff
);
895 aff
->v
= isl_vec_extend(aff
->v
, size
+ 1);
897 return isl_aff_free(aff
);
898 isl_int_set_si(aff
->v
->el
[0], 1);
899 isl_int_set_si(aff
->v
->el
[size
], 1);
906 * aff mod m = aff - m * floor(aff/m)
908 __isl_give isl_aff
*isl_aff_mod(__isl_take isl_aff
*aff
, isl_int m
)
912 res
= isl_aff_copy(aff
);
913 aff
= isl_aff_scale_down(aff
, m
);
914 aff
= isl_aff_floor(aff
);
915 aff
= isl_aff_scale(aff
, m
);
916 res
= isl_aff_sub(res
, aff
);
923 * pwaff mod m = pwaff - m * floor(pwaff/m)
925 __isl_give isl_pw_aff
*isl_pw_aff_mod(__isl_take isl_pw_aff
*pwaff
, isl_int m
)
929 res
= isl_pw_aff_copy(pwaff
);
930 pwaff
= isl_pw_aff_scale_down(pwaff
, m
);
931 pwaff
= isl_pw_aff_floor(pwaff
);
932 pwaff
= isl_pw_aff_scale(pwaff
, m
);
933 res
= isl_pw_aff_sub(res
, pwaff
);
938 /* Given f, return ceil(f).
939 * If f is an integer expression, then just return f.
940 * Otherwise, create a new div d = [-f] and return the expression -d.
942 __isl_give isl_aff
*isl_aff_ceil(__isl_take isl_aff
*aff
)
947 if (isl_int_is_one(aff
->v
->el
[0]))
950 aff
= isl_aff_neg(aff
);
951 aff
= isl_aff_floor(aff
);
952 aff
= isl_aff_neg(aff
);
957 /* Apply the expansion computed by isl_merge_divs.
958 * The expansion itself is given by "exp" while the resulting
959 * list of divs is given by "div".
961 __isl_give isl_aff
*isl_aff_expand_divs( __isl_take isl_aff
*aff
,
962 __isl_take isl_mat
*div
, int *exp
)
969 aff
= isl_aff_cow(aff
);
973 old_n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
974 new_n_div
= isl_mat_rows(div
);
975 if (new_n_div
< old_n_div
)
976 isl_die(isl_mat_get_ctx(div
), isl_error_invalid
,
977 "not an expansion", goto error
);
979 aff
->v
= isl_vec_extend(aff
->v
, aff
->v
->size
+ new_n_div
- old_n_div
);
983 offset
= 1 + isl_local_space_offset(aff
->ls
, isl_dim_div
);
985 for (i
= new_n_div
- 1; i
>= 0; --i
) {
986 if (j
>= 0 && exp
[j
] == i
) {
988 isl_int_swap(aff
->v
->el
[offset
+ i
],
989 aff
->v
->el
[offset
+ j
]);
992 isl_int_set_si(aff
->v
->el
[offset
+ i
], 0);
995 aff
->ls
= isl_local_space_replace_divs(aff
->ls
, isl_mat_copy(div
));
1006 /* Add two affine expressions that live in the same local space.
1008 static __isl_give isl_aff
*add_expanded(__isl_take isl_aff
*aff1
,
1009 __isl_take isl_aff
*aff2
)
1013 aff1
= isl_aff_cow(aff1
);
1017 aff1
->v
= isl_vec_cow(aff1
->v
);
1023 isl_int_gcd(gcd
, aff1
->v
->el
[0], aff2
->v
->el
[0]);
1024 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
1025 isl_seq_scale(aff1
->v
->el
+ 1, aff1
->v
->el
+ 1, f
, aff1
->v
->size
- 1);
1026 isl_int_divexact(f
, aff1
->v
->el
[0], gcd
);
1027 isl_seq_addmul(aff1
->v
->el
+ 1, f
, aff2
->v
->el
+ 1, aff1
->v
->size
- 1);
1028 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
1029 isl_int_mul(aff1
->v
->el
[0], aff1
->v
->el
[0], f
);
1041 __isl_give isl_aff
*isl_aff_add(__isl_take isl_aff
*aff1
,
1042 __isl_take isl_aff
*aff2
)
1052 ctx
= isl_aff_get_ctx(aff1
);
1053 if (!isl_space_is_equal(aff1
->ls
->dim
, aff2
->ls
->dim
))
1054 isl_die(ctx
, isl_error_invalid
,
1055 "spaces don't match", goto error
);
1057 if (aff1
->ls
->div
->n_row
== 0 && aff2
->ls
->div
->n_row
== 0)
1058 return add_expanded(aff1
, aff2
);
1060 exp1
= isl_alloc_array(ctx
, int, aff1
->ls
->div
->n_row
);
1061 exp2
= isl_alloc_array(ctx
, int, aff2
->ls
->div
->n_row
);
1065 div
= isl_merge_divs(aff1
->ls
->div
, aff2
->ls
->div
, exp1
, exp2
);
1066 aff1
= isl_aff_expand_divs(aff1
, isl_mat_copy(div
), exp1
);
1067 aff2
= isl_aff_expand_divs(aff2
, div
, exp2
);
1071 return add_expanded(aff1
, aff2
);
1080 __isl_give isl_aff
*isl_aff_sub(__isl_take isl_aff
*aff1
,
1081 __isl_take isl_aff
*aff2
)
1083 return isl_aff_add(aff1
, isl_aff_neg(aff2
));
1086 __isl_give isl_aff
*isl_aff_scale(__isl_take isl_aff
*aff
, isl_int f
)
1090 if (isl_int_is_one(f
))
1093 aff
= isl_aff_cow(aff
);
1096 aff
->v
= isl_vec_cow(aff
->v
);
1098 return isl_aff_free(aff
);
1101 isl_int_gcd(gcd
, aff
->v
->el
[0], f
);
1102 isl_int_divexact(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
1103 isl_int_divexact(gcd
, f
, gcd
);
1104 isl_seq_scale(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
1110 __isl_give isl_aff
*isl_aff_scale_down(__isl_take isl_aff
*aff
, isl_int f
)
1114 if (isl_int_is_one(f
))
1117 aff
= isl_aff_cow(aff
);
1121 if (isl_int_is_zero(f
))
1122 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1123 "cannot scale down by zero", return isl_aff_free(aff
));
1125 aff
->v
= isl_vec_cow(aff
->v
);
1127 return isl_aff_free(aff
);
1130 isl_seq_gcd(aff
->v
->el
+ 1, aff
->v
->size
- 1, &gcd
);
1131 isl_int_gcd(gcd
, gcd
, f
);
1132 isl_seq_scale_down(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
1133 isl_int_divexact(gcd
, f
, gcd
);
1134 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
1140 __isl_give isl_aff
*isl_aff_scale_down_ui(__isl_take isl_aff
*aff
, unsigned f
)
1148 isl_int_set_ui(v
, f
);
1149 aff
= isl_aff_scale_down(aff
, v
);
1155 __isl_give isl_aff
*isl_aff_set_dim_name(__isl_take isl_aff
*aff
,
1156 enum isl_dim_type type
, unsigned pos
, const char *s
)
1158 aff
= isl_aff_cow(aff
);
1161 if (type
== isl_dim_out
)
1162 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1163 "cannot set name of output/set dimension",
1164 return isl_aff_free(aff
));
1165 if (type
== isl_dim_in
)
1167 aff
->ls
= isl_local_space_set_dim_name(aff
->ls
, type
, pos
, s
);
1169 return isl_aff_free(aff
);
1174 __isl_give isl_aff
*isl_aff_set_dim_id(__isl_take isl_aff
*aff
,
1175 enum isl_dim_type type
, unsigned pos
, __isl_take isl_id
*id
)
1177 aff
= isl_aff_cow(aff
);
1179 return isl_id_free(id
);
1180 if (type
== isl_dim_out
)
1181 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1182 "cannot set name of output/set dimension",
1184 if (type
== isl_dim_in
)
1186 aff
->ls
= isl_local_space_set_dim_id(aff
->ls
, type
, pos
, id
);
1188 return isl_aff_free(aff
);
1197 /* Exploit the equalities in "eq" to simplify the affine expression
1198 * and the expressions of the integer divisions in the local space.
1199 * The integer divisions in this local space are assumed to appear
1200 * as regular dimensions in "eq".
1202 static __isl_give isl_aff
*isl_aff_substitute_equalities_lifted(
1203 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
1211 if (eq
->n_eq
== 0) {
1212 isl_basic_set_free(eq
);
1216 aff
= isl_aff_cow(aff
);
1220 aff
->ls
= isl_local_space_substitute_equalities(aff
->ls
,
1221 isl_basic_set_copy(eq
));
1225 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
1227 for (i
= 0; i
< eq
->n_eq
; ++i
) {
1228 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
1229 if (j
< 0 || j
== 0 || j
>= total
)
1232 isl_seq_elim(aff
->v
->el
+ 1, eq
->eq
[i
], j
, total
,
1236 isl_basic_set_free(eq
);
1237 aff
= isl_aff_normalize(aff
);
1240 isl_basic_set_free(eq
);
1245 /* Exploit the equalities in "eq" to simplify the affine expression
1246 * and the expressions of the integer divisions in the local space.
1248 static __isl_give isl_aff
*isl_aff_substitute_equalities(
1249 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
1255 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1257 eq
= isl_basic_set_add(eq
, isl_dim_set
, n_div
);
1258 return isl_aff_substitute_equalities_lifted(aff
, eq
);
1260 isl_basic_set_free(eq
);
1265 /* Look for equalities among the variables shared by context and aff
1266 * and the integer divisions of aff, if any.
1267 * The equalities are then used to eliminate coefficients and/or integer
1268 * divisions from aff.
1270 __isl_give isl_aff
*isl_aff_gist(__isl_take isl_aff
*aff
,
1271 __isl_take isl_set
*context
)
1273 isl_basic_set
*hull
;
1278 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1280 isl_basic_set
*bset
;
1281 isl_local_space
*ls
;
1282 context
= isl_set_add_dims(context
, isl_dim_set
, n_div
);
1283 ls
= isl_aff_get_domain_local_space(aff
);
1284 bset
= isl_basic_set_from_local_space(ls
);
1285 bset
= isl_basic_set_lift(bset
);
1286 bset
= isl_basic_set_flatten(bset
);
1287 context
= isl_set_intersect(context
,
1288 isl_set_from_basic_set(bset
));
1291 hull
= isl_set_affine_hull(context
);
1292 return isl_aff_substitute_equalities_lifted(aff
, hull
);
1295 isl_set_free(context
);
1299 __isl_give isl_aff
*isl_aff_gist_params(__isl_take isl_aff
*aff
,
1300 __isl_take isl_set
*context
)
1302 isl_set
*dom_context
= isl_set_universe(isl_aff_get_domain_space(aff
));
1303 dom_context
= isl_set_intersect_params(dom_context
, context
);
1304 return isl_aff_gist(aff
, dom_context
);
1307 /* Return a basic set containing those elements in the space
1308 * of aff where it is non-negative.
1310 __isl_give isl_basic_set
*isl_aff_nonneg_basic_set(__isl_take isl_aff
*aff
)
1312 isl_constraint
*ineq
;
1313 isl_basic_set
*bset
;
1315 ineq
= isl_inequality_from_aff(aff
);
1317 bset
= isl_basic_set_from_constraint(ineq
);
1318 bset
= isl_basic_set_simplify(bset
);
1322 /* Return a basic set containing those elements in the domain space
1323 * of aff where it is negative.
1325 __isl_give isl_basic_set
*isl_aff_neg_basic_set(__isl_take isl_aff
*aff
)
1327 aff
= isl_aff_neg(aff
);
1328 aff
= isl_aff_add_constant_num_si(aff
, -1);
1329 return isl_aff_nonneg_basic_set(aff
);
1332 /* Return a basic set containing those elements in the space
1333 * of aff where it is zero.
1335 __isl_give isl_basic_set
*isl_aff_zero_basic_set(__isl_take isl_aff
*aff
)
1337 isl_constraint
*ineq
;
1338 isl_basic_set
*bset
;
1340 ineq
= isl_equality_from_aff(aff
);
1342 bset
= isl_basic_set_from_constraint(ineq
);
1343 bset
= isl_basic_set_simplify(bset
);
1347 /* Return a basic set containing those elements in the shared space
1348 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1350 __isl_give isl_basic_set
*isl_aff_ge_basic_set(__isl_take isl_aff
*aff1
,
1351 __isl_take isl_aff
*aff2
)
1353 aff1
= isl_aff_sub(aff1
, aff2
);
1355 return isl_aff_nonneg_basic_set(aff1
);
1358 /* Return a basic set containing those elements in the shared space
1359 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1361 __isl_give isl_basic_set
*isl_aff_le_basic_set(__isl_take isl_aff
*aff1
,
1362 __isl_take isl_aff
*aff2
)
1364 return isl_aff_ge_basic_set(aff2
, aff1
);
1367 __isl_give isl_aff
*isl_aff_add_on_domain(__isl_keep isl_set
*dom
,
1368 __isl_take isl_aff
*aff1
, __isl_take isl_aff
*aff2
)
1370 aff1
= isl_aff_add(aff1
, aff2
);
1371 aff1
= isl_aff_gist(aff1
, isl_set_copy(dom
));
1375 int isl_aff_is_empty(__isl_keep isl_aff
*aff
)
1383 /* Check whether the given affine expression has non-zero coefficient
1384 * for any dimension in the given range or if any of these dimensions
1385 * appear with non-zero coefficients in any of the integer divisions
1386 * involved in the affine expression.
1388 int isl_aff_involves_dims(__isl_keep isl_aff
*aff
,
1389 enum isl_dim_type type
, unsigned first
, unsigned n
)
1401 ctx
= isl_aff_get_ctx(aff
);
1402 if (first
+ n
> isl_aff_dim(aff
, type
))
1403 isl_die(ctx
, isl_error_invalid
,
1404 "range out of bounds", return -1);
1406 active
= isl_local_space_get_active(aff
->ls
, aff
->v
->el
+ 2);
1410 first
+= isl_local_space_offset(aff
->ls
, type
) - 1;
1411 for (i
= 0; i
< n
; ++i
)
1412 if (active
[first
+ i
]) {
1425 __isl_give isl_aff
*isl_aff_drop_dims(__isl_take isl_aff
*aff
,
1426 enum isl_dim_type type
, unsigned first
, unsigned n
)
1432 if (type
== isl_dim_out
)
1433 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1434 "cannot drop output/set dimension",
1435 return isl_aff_free(aff
));
1436 if (type
== isl_dim_in
)
1438 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
1441 ctx
= isl_aff_get_ctx(aff
);
1442 if (first
+ n
> isl_local_space_dim(aff
->ls
, type
))
1443 isl_die(ctx
, isl_error_invalid
, "range out of bounds",
1444 return isl_aff_free(aff
));
1446 aff
= isl_aff_cow(aff
);
1450 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, type
, first
, n
);
1452 return isl_aff_free(aff
);
1454 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
1455 aff
->v
= isl_vec_drop_els(aff
->v
, first
, n
);
1457 return isl_aff_free(aff
);
1462 /* Project the domain of the affine expression onto its parameter space.
1463 * The affine expression may not involve any of the domain dimensions.
1465 __isl_give isl_aff
*isl_aff_project_domain_on_params(__isl_take isl_aff
*aff
)
1471 n
= isl_aff_dim(aff
, isl_dim_in
);
1472 involves
= isl_aff_involves_dims(aff
, isl_dim_in
, 0, n
);
1474 return isl_aff_free(aff
);
1476 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1477 "affine expression involves some of the domain dimensions",
1478 return isl_aff_free(aff
));
1479 aff
= isl_aff_drop_dims(aff
, isl_dim_in
, 0, n
);
1480 space
= isl_aff_get_domain_space(aff
);
1481 space
= isl_space_params(space
);
1482 aff
= isl_aff_reset_domain_space(aff
, space
);
1486 __isl_give isl_aff
*isl_aff_insert_dims(__isl_take isl_aff
*aff
,
1487 enum isl_dim_type type
, unsigned first
, unsigned n
)
1493 if (type
== isl_dim_out
)
1494 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1495 "cannot insert output/set dimensions",
1496 return isl_aff_free(aff
));
1497 if (type
== isl_dim_in
)
1499 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
1502 ctx
= isl_aff_get_ctx(aff
);
1503 if (first
> isl_local_space_dim(aff
->ls
, type
))
1504 isl_die(ctx
, isl_error_invalid
, "position out of bounds",
1505 return isl_aff_free(aff
));
1507 aff
= isl_aff_cow(aff
);
1511 aff
->ls
= isl_local_space_insert_dims(aff
->ls
, type
, first
, n
);
1513 return isl_aff_free(aff
);
1515 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
1516 aff
->v
= isl_vec_insert_zero_els(aff
->v
, first
, n
);
1518 return isl_aff_free(aff
);
1523 __isl_give isl_aff
*isl_aff_add_dims(__isl_take isl_aff
*aff
,
1524 enum isl_dim_type type
, unsigned n
)
1528 pos
= isl_aff_dim(aff
, type
);
1530 return isl_aff_insert_dims(aff
, type
, pos
, n
);
1533 __isl_give isl_pw_aff
*isl_pw_aff_add_dims(__isl_take isl_pw_aff
*pwaff
,
1534 enum isl_dim_type type
, unsigned n
)
1538 pos
= isl_pw_aff_dim(pwaff
, type
);
1540 return isl_pw_aff_insert_dims(pwaff
, type
, pos
, n
);
1543 __isl_give isl_pw_aff
*isl_pw_aff_from_aff(__isl_take isl_aff
*aff
)
1545 isl_set
*dom
= isl_set_universe(isl_aff_get_domain_space(aff
));
1546 return isl_pw_aff_alloc(dom
, aff
);
1550 #define PW isl_pw_aff
1554 #define EL_IS_ZERO is_empty
1558 #define IS_ZERO is_empty
1561 #undef DEFAULT_IS_ZERO
1562 #define DEFAULT_IS_ZERO 0
1566 #define NO_MOVE_DIMS
1570 #include <isl_pw_templ.c>
1572 static __isl_give isl_set
*align_params_pw_pw_set_and(
1573 __isl_take isl_pw_aff
*pwaff1
, __isl_take isl_pw_aff
*pwaff2
,
1574 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
1575 __isl_take isl_pw_aff
*pwaff2
))
1577 if (!pwaff1
|| !pwaff2
)
1579 if (isl_space_match(pwaff1
->dim
, isl_dim_param
,
1580 pwaff2
->dim
, isl_dim_param
))
1581 return fn(pwaff1
, pwaff2
);
1582 if (!isl_space_has_named_params(pwaff1
->dim
) ||
1583 !isl_space_has_named_params(pwaff2
->dim
))
1584 isl_die(isl_pw_aff_get_ctx(pwaff1
), isl_error_invalid
,
1585 "unaligned unnamed parameters", goto error
);
1586 pwaff1
= isl_pw_aff_align_params(pwaff1
, isl_pw_aff_get_space(pwaff2
));
1587 pwaff2
= isl_pw_aff_align_params(pwaff2
, isl_pw_aff_get_space(pwaff1
));
1588 return fn(pwaff1
, pwaff2
);
1590 isl_pw_aff_free(pwaff1
);
1591 isl_pw_aff_free(pwaff2
);
1595 /* Compute a piecewise quasi-affine expression with a domain that
1596 * is the union of those of pwaff1 and pwaff2 and such that on each
1597 * cell, the quasi-affine expression is the better (according to cmp)
1598 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
1599 * is defined on a given cell, then the associated expression
1600 * is the defined one.
1602 static __isl_give isl_pw_aff
*pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
1603 __isl_take isl_pw_aff
*pwaff2
,
1604 __isl_give isl_basic_set
*(*cmp
)(__isl_take isl_aff
*aff1
,
1605 __isl_take isl_aff
*aff2
))
1612 if (!pwaff1
|| !pwaff2
)
1615 ctx
= isl_space_get_ctx(pwaff1
->dim
);
1616 if (!isl_space_is_equal(pwaff1
->dim
, pwaff2
->dim
))
1617 isl_die(ctx
, isl_error_invalid
,
1618 "arguments should live in same space", goto error
);
1620 if (isl_pw_aff_is_empty(pwaff1
)) {
1621 isl_pw_aff_free(pwaff1
);
1625 if (isl_pw_aff_is_empty(pwaff2
)) {
1626 isl_pw_aff_free(pwaff2
);
1630 n
= 2 * (pwaff1
->n
+ 1) * (pwaff2
->n
+ 1);
1631 res
= isl_pw_aff_alloc_size(isl_space_copy(pwaff1
->dim
), n
);
1633 for (i
= 0; i
< pwaff1
->n
; ++i
) {
1634 set
= isl_set_copy(pwaff1
->p
[i
].set
);
1635 for (j
= 0; j
< pwaff2
->n
; ++j
) {
1636 struct isl_set
*common
;
1639 common
= isl_set_intersect(
1640 isl_set_copy(pwaff1
->p
[i
].set
),
1641 isl_set_copy(pwaff2
->p
[j
].set
));
1642 better
= isl_set_from_basic_set(cmp(
1643 isl_aff_copy(pwaff2
->p
[j
].aff
),
1644 isl_aff_copy(pwaff1
->p
[i
].aff
)));
1645 better
= isl_set_intersect(common
, better
);
1646 if (isl_set_plain_is_empty(better
)) {
1647 isl_set_free(better
);
1650 set
= isl_set_subtract(set
, isl_set_copy(better
));
1652 res
= isl_pw_aff_add_piece(res
, better
,
1653 isl_aff_copy(pwaff2
->p
[j
].aff
));
1655 res
= isl_pw_aff_add_piece(res
, set
,
1656 isl_aff_copy(pwaff1
->p
[i
].aff
));
1659 for (j
= 0; j
< pwaff2
->n
; ++j
) {
1660 set
= isl_set_copy(pwaff2
->p
[j
].set
);
1661 for (i
= 0; i
< pwaff1
->n
; ++i
)
1662 set
= isl_set_subtract(set
,
1663 isl_set_copy(pwaff1
->p
[i
].set
));
1664 res
= isl_pw_aff_add_piece(res
, set
,
1665 isl_aff_copy(pwaff2
->p
[j
].aff
));
1668 isl_pw_aff_free(pwaff1
);
1669 isl_pw_aff_free(pwaff2
);
1673 isl_pw_aff_free(pwaff1
);
1674 isl_pw_aff_free(pwaff2
);
1678 /* Compute a piecewise quasi-affine expression with a domain that
1679 * is the union of those of pwaff1 and pwaff2 and such that on each
1680 * cell, the quasi-affine expression is the maximum of those of pwaff1
1681 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1682 * cell, then the associated expression is the defined one.
1684 static __isl_give isl_pw_aff
*pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
1685 __isl_take isl_pw_aff
*pwaff2
)
1687 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_ge_basic_set
);
1690 __isl_give isl_pw_aff
*isl_pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
1691 __isl_take isl_pw_aff
*pwaff2
)
1693 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
1697 /* Compute a piecewise quasi-affine expression with a domain that
1698 * is the union of those of pwaff1 and pwaff2 and such that on each
1699 * cell, the quasi-affine expression is the minimum of those of pwaff1
1700 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1701 * cell, then the associated expression is the defined one.
1703 static __isl_give isl_pw_aff
*pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
1704 __isl_take isl_pw_aff
*pwaff2
)
1706 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_le_basic_set
);
1709 __isl_give isl_pw_aff
*isl_pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
1710 __isl_take isl_pw_aff
*pwaff2
)
1712 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
1716 __isl_give isl_pw_aff
*isl_pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
1717 __isl_take isl_pw_aff
*pwaff2
, int max
)
1720 return isl_pw_aff_union_max(pwaff1
, pwaff2
);
1722 return isl_pw_aff_union_min(pwaff1
, pwaff2
);
1725 /* Construct a map with as domain the domain of pwaff and
1726 * one-dimensional range corresponding to the affine expressions.
1728 static __isl_give isl_map
*map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
1737 dim
= isl_pw_aff_get_space(pwaff
);
1738 map
= isl_map_empty(dim
);
1740 for (i
= 0; i
< pwaff
->n
; ++i
) {
1741 isl_basic_map
*bmap
;
1744 bmap
= isl_basic_map_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
1745 map_i
= isl_map_from_basic_map(bmap
);
1746 map_i
= isl_map_intersect_domain(map_i
,
1747 isl_set_copy(pwaff
->p
[i
].set
));
1748 map
= isl_map_union_disjoint(map
, map_i
);
1751 isl_pw_aff_free(pwaff
);
1756 /* Construct a map with as domain the domain of pwaff and
1757 * one-dimensional range corresponding to the affine expressions.
1759 __isl_give isl_map
*isl_map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
1763 if (isl_space_is_set(pwaff
->dim
))
1764 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
1765 "space of input is not a map",
1766 return isl_pw_aff_free(pwaff
));
1767 return map_from_pw_aff(pwaff
);
1770 /* Construct a one-dimensional set with as parameter domain
1771 * the domain of pwaff and the single set dimension
1772 * corresponding to the affine expressions.
1774 __isl_give isl_set
*isl_set_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
1778 if (!isl_space_is_set(pwaff
->dim
))
1779 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
1780 "space of input is not a set",
1781 return isl_pw_aff_free(pwaff
));
1782 return map_from_pw_aff(pwaff
);
1785 /* Return a set containing those elements in the domain
1786 * of pwaff where it is non-negative.
1788 __isl_give isl_set
*isl_pw_aff_nonneg_set(__isl_take isl_pw_aff
*pwaff
)
1796 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
1798 for (i
= 0; i
< pwaff
->n
; ++i
) {
1799 isl_basic_set
*bset
;
1802 bset
= isl_aff_nonneg_basic_set(isl_aff_copy(pwaff
->p
[i
].aff
));
1803 set_i
= isl_set_from_basic_set(bset
);
1804 set_i
= isl_set_intersect(set_i
, isl_set_copy(pwaff
->p
[i
].set
));
1805 set
= isl_set_union_disjoint(set
, set_i
);
1808 isl_pw_aff_free(pwaff
);
1813 /* Return a set containing those elements in the domain
1814 * of pwaff where it is zero (if complement is 0) or not zero
1815 * (if complement is 1).
1817 static __isl_give isl_set
*pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
,
1826 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
1828 for (i
= 0; i
< pwaff
->n
; ++i
) {
1829 isl_basic_set
*bset
;
1830 isl_set
*set_i
, *zero
;
1832 bset
= isl_aff_zero_basic_set(isl_aff_copy(pwaff
->p
[i
].aff
));
1833 zero
= isl_set_from_basic_set(bset
);
1834 set_i
= isl_set_copy(pwaff
->p
[i
].set
);
1836 set_i
= isl_set_subtract(set_i
, zero
);
1838 set_i
= isl_set_intersect(set_i
, zero
);
1839 set
= isl_set_union_disjoint(set
, set_i
);
1842 isl_pw_aff_free(pwaff
);
1847 /* Return a set containing those elements in the domain
1848 * of pwaff where it is zero.
1850 __isl_give isl_set
*isl_pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
)
1852 return pw_aff_zero_set(pwaff
, 0);
1855 /* Return a set containing those elements in the domain
1856 * of pwaff where it is not zero.
1858 __isl_give isl_set
*isl_pw_aff_non_zero_set(__isl_take isl_pw_aff
*pwaff
)
1860 return pw_aff_zero_set(pwaff
, 1);
1863 /* Return a set containing those elements in the shared domain
1864 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1866 * We compute the difference on the shared domain and then construct
1867 * the set of values where this difference is non-negative.
1868 * If strict is set, we first subtract 1 from the difference.
1869 * If equal is set, we only return the elements where pwaff1 and pwaff2
1872 static __isl_give isl_set
*pw_aff_gte_set(__isl_take isl_pw_aff
*pwaff1
,
1873 __isl_take isl_pw_aff
*pwaff2
, int strict
, int equal
)
1875 isl_set
*set1
, *set2
;
1877 set1
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
));
1878 set2
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
));
1879 set1
= isl_set_intersect(set1
, set2
);
1880 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, isl_set_copy(set1
));
1881 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, isl_set_copy(set1
));
1882 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_neg(pwaff2
));
1885 isl_space
*dim
= isl_set_get_space(set1
);
1887 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(dim
));
1888 aff
= isl_aff_add_constant_si(aff
, -1);
1889 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_alloc(set1
, aff
));
1894 return isl_pw_aff_zero_set(pwaff1
);
1895 return isl_pw_aff_nonneg_set(pwaff1
);
1898 /* Return a set containing those elements in the shared domain
1899 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1901 static __isl_give isl_set
*pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
1902 __isl_take isl_pw_aff
*pwaff2
)
1904 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 1);
1907 __isl_give isl_set
*isl_pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
1908 __isl_take isl_pw_aff
*pwaff2
)
1910 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_eq_set
);
1913 /* Return a set containing those elements in the shared domain
1914 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
1916 static __isl_give isl_set
*pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
1917 __isl_take isl_pw_aff
*pwaff2
)
1919 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 0);
1922 __isl_give isl_set
*isl_pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
1923 __isl_take isl_pw_aff
*pwaff2
)
1925 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ge_set
);
1928 /* Return a set containing those elements in the shared domain
1929 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
1931 static __isl_give isl_set
*pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
1932 __isl_take isl_pw_aff
*pwaff2
)
1934 return pw_aff_gte_set(pwaff1
, pwaff2
, 1, 0);
1937 __isl_give isl_set
*isl_pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
1938 __isl_take isl_pw_aff
*pwaff2
)
1940 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_gt_set
);
1943 __isl_give isl_set
*isl_pw_aff_le_set(__isl_take isl_pw_aff
*pwaff1
,
1944 __isl_take isl_pw_aff
*pwaff2
)
1946 return isl_pw_aff_ge_set(pwaff2
, pwaff1
);
1949 __isl_give isl_set
*isl_pw_aff_lt_set(__isl_take isl_pw_aff
*pwaff1
,
1950 __isl_take isl_pw_aff
*pwaff2
)
1952 return isl_pw_aff_gt_set(pwaff2
, pwaff1
);
1955 /* Return a set containing those elements in the shared domain
1956 * of the elements of list1 and list2 where each element in list1
1957 * has the relation specified by "fn" with each element in list2.
1959 static __isl_give isl_set
*pw_aff_list_set(__isl_take isl_pw_aff_list
*list1
,
1960 __isl_take isl_pw_aff_list
*list2
,
1961 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
1962 __isl_take isl_pw_aff
*pwaff2
))
1968 if (!list1
|| !list2
)
1971 ctx
= isl_pw_aff_list_get_ctx(list1
);
1972 if (list1
->n
< 1 || list2
->n
< 1)
1973 isl_die(ctx
, isl_error_invalid
,
1974 "list should contain at least one element", goto error
);
1976 set
= isl_set_universe(isl_pw_aff_get_domain_space(list1
->p
[0]));
1977 for (i
= 0; i
< list1
->n
; ++i
)
1978 for (j
= 0; j
< list2
->n
; ++j
) {
1981 set_ij
= fn(isl_pw_aff_copy(list1
->p
[i
]),
1982 isl_pw_aff_copy(list2
->p
[j
]));
1983 set
= isl_set_intersect(set
, set_ij
);
1986 isl_pw_aff_list_free(list1
);
1987 isl_pw_aff_list_free(list2
);
1990 isl_pw_aff_list_free(list1
);
1991 isl_pw_aff_list_free(list2
);
1995 /* Return a set containing those elements in the shared domain
1996 * of the elements of list1 and list2 where each element in list1
1997 * is equal to each element in list2.
1999 __isl_give isl_set
*isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list
*list1
,
2000 __isl_take isl_pw_aff_list
*list2
)
2002 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_eq_set
);
2005 __isl_give isl_set
*isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list
*list1
,
2006 __isl_take isl_pw_aff_list
*list2
)
2008 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ne_set
);
2011 /* Return a set containing those elements in the shared domain
2012 * of the elements of list1 and list2 where each element in list1
2013 * is less than or equal to each element in list2.
2015 __isl_give isl_set
*isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list
*list1
,
2016 __isl_take isl_pw_aff_list
*list2
)
2018 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_le_set
);
2021 __isl_give isl_set
*isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list
*list1
,
2022 __isl_take isl_pw_aff_list
*list2
)
2024 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_lt_set
);
2027 __isl_give isl_set
*isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list
*list1
,
2028 __isl_take isl_pw_aff_list
*list2
)
2030 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ge_set
);
2033 __isl_give isl_set
*isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list
*list1
,
2034 __isl_take isl_pw_aff_list
*list2
)
2036 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_gt_set
);
2040 /* Return a set containing those elements in the shared domain
2041 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
2043 static __isl_give isl_set
*pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
2044 __isl_take isl_pw_aff
*pwaff2
)
2046 isl_set
*set_lt
, *set_gt
;
2048 set_lt
= isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1
),
2049 isl_pw_aff_copy(pwaff2
));
2050 set_gt
= isl_pw_aff_gt_set(pwaff1
, pwaff2
);
2051 return isl_set_union_disjoint(set_lt
, set_gt
);
2054 __isl_give isl_set
*isl_pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
2055 __isl_take isl_pw_aff
*pwaff2
)
2057 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ne_set
);
2060 __isl_give isl_pw_aff
*isl_pw_aff_scale_down(__isl_take isl_pw_aff
*pwaff
,
2065 if (isl_int_is_one(v
))
2067 if (!isl_int_is_pos(v
))
2068 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
2069 "factor needs to be positive",
2070 return isl_pw_aff_free(pwaff
));
2071 pwaff
= isl_pw_aff_cow(pwaff
);
2077 for (i
= 0; i
< pwaff
->n
; ++i
) {
2078 pwaff
->p
[i
].aff
= isl_aff_scale_down(pwaff
->p
[i
].aff
, v
);
2079 if (!pwaff
->p
[i
].aff
)
2080 return isl_pw_aff_free(pwaff
);
2086 __isl_give isl_pw_aff
*isl_pw_aff_floor(__isl_take isl_pw_aff
*pwaff
)
2090 pwaff
= isl_pw_aff_cow(pwaff
);
2096 for (i
= 0; i
< pwaff
->n
; ++i
) {
2097 pwaff
->p
[i
].aff
= isl_aff_floor(pwaff
->p
[i
].aff
);
2098 if (!pwaff
->p
[i
].aff
)
2099 return isl_pw_aff_free(pwaff
);
2105 __isl_give isl_pw_aff
*isl_pw_aff_ceil(__isl_take isl_pw_aff
*pwaff
)
2109 pwaff
= isl_pw_aff_cow(pwaff
);
2115 for (i
= 0; i
< pwaff
->n
; ++i
) {
2116 pwaff
->p
[i
].aff
= isl_aff_ceil(pwaff
->p
[i
].aff
);
2117 if (!pwaff
->p
[i
].aff
)
2118 return isl_pw_aff_free(pwaff
);
2124 /* Assuming that "cond1" and "cond2" are disjoint,
2125 * return an affine expression that is equal to pwaff1 on cond1
2126 * and to pwaff2 on cond2.
2128 static __isl_give isl_pw_aff
*isl_pw_aff_select(
2129 __isl_take isl_set
*cond1
, __isl_take isl_pw_aff
*pwaff1
,
2130 __isl_take isl_set
*cond2
, __isl_take isl_pw_aff
*pwaff2
)
2132 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, cond1
);
2133 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, cond2
);
2135 return isl_pw_aff_add_disjoint(pwaff1
, pwaff2
);
2138 /* Return an affine expression that is equal to pwaff_true for elements
2139 * where "cond" is non-zero and to pwaff_false for elements where "cond"
2141 * That is, return cond ? pwaff_true : pwaff_false;
2143 __isl_give isl_pw_aff
*isl_pw_aff_cond(__isl_take isl_pw_aff
*cond
,
2144 __isl_take isl_pw_aff
*pwaff_true
, __isl_take isl_pw_aff
*pwaff_false
)
2146 isl_set
*cond_true
, *cond_false
;
2148 cond_true
= isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond
));
2149 cond_false
= isl_pw_aff_zero_set(cond
);
2150 return isl_pw_aff_select(cond_true
, pwaff_true
,
2151 cond_false
, pwaff_false
);
2154 int isl_aff_is_cst(__isl_keep isl_aff
*aff
)
2159 return isl_seq_first_non_zero(aff
->v
->el
+ 2, aff
->v
->size
- 2) == -1;
2162 /* Check whether pwaff is a piecewise constant.
2164 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff
*pwaff
)
2171 for (i
= 0; i
< pwaff
->n
; ++i
) {
2172 int is_cst
= isl_aff_is_cst(pwaff
->p
[i
].aff
);
2173 if (is_cst
< 0 || !is_cst
)
2180 __isl_give isl_aff
*isl_aff_mul(__isl_take isl_aff
*aff1
,
2181 __isl_take isl_aff
*aff2
)
2183 if (!isl_aff_is_cst(aff2
) && isl_aff_is_cst(aff1
))
2184 return isl_aff_mul(aff2
, aff1
);
2186 if (!isl_aff_is_cst(aff2
))
2187 isl_die(isl_aff_get_ctx(aff1
), isl_error_invalid
,
2188 "at least one affine expression should be constant",
2191 aff1
= isl_aff_cow(aff1
);
2195 aff1
= isl_aff_scale(aff1
, aff2
->v
->el
[1]);
2196 aff1
= isl_aff_scale_down(aff1
, aff2
->v
->el
[0]);
2206 static __isl_give isl_pw_aff
*pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
2207 __isl_take isl_pw_aff
*pwaff2
)
2209 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_add
);
2212 __isl_give isl_pw_aff
*isl_pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
2213 __isl_take isl_pw_aff
*pwaff2
)
2215 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_add
);
2218 __isl_give isl_pw_aff
*isl_pw_aff_union_add(__isl_take isl_pw_aff
*pwaff1
,
2219 __isl_take isl_pw_aff
*pwaff2
)
2221 return isl_pw_aff_union_add_(pwaff1
, pwaff2
);
2224 static __isl_give isl_pw_aff
*pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
2225 __isl_take isl_pw_aff
*pwaff2
)
2227 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_mul
);
2230 __isl_give isl_pw_aff
*isl_pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
2231 __isl_take isl_pw_aff
*pwaff2
)
2233 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_mul
);
2236 static __isl_give isl_pw_aff
*pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
2237 __isl_take isl_pw_aff
*pwaff2
)
2242 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
2243 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
2244 le
= isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1
),
2245 isl_pw_aff_copy(pwaff2
));
2246 dom
= isl_set_subtract(dom
, isl_set_copy(le
));
2247 return isl_pw_aff_select(le
, pwaff1
, dom
, pwaff2
);
2250 __isl_give isl_pw_aff
*isl_pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
2251 __isl_take isl_pw_aff
*pwaff2
)
2253 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_min
);
2256 static __isl_give isl_pw_aff
*pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
2257 __isl_take isl_pw_aff
*pwaff2
)
2262 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
2263 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
2264 ge
= isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1
),
2265 isl_pw_aff_copy(pwaff2
));
2266 dom
= isl_set_subtract(dom
, isl_set_copy(ge
));
2267 return isl_pw_aff_select(ge
, pwaff1
, dom
, pwaff2
);
2270 __isl_give isl_pw_aff
*isl_pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
2271 __isl_take isl_pw_aff
*pwaff2
)
2273 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_max
);
2276 static __isl_give isl_pw_aff
*pw_aff_list_reduce(
2277 __isl_take isl_pw_aff_list
*list
,
2278 __isl_give isl_pw_aff
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
2279 __isl_take isl_pw_aff
*pwaff2
))
2288 ctx
= isl_pw_aff_list_get_ctx(list
);
2290 isl_die(ctx
, isl_error_invalid
,
2291 "list should contain at least one element",
2292 return isl_pw_aff_list_free(list
));
2294 res
= isl_pw_aff_copy(list
->p
[0]);
2295 for (i
= 1; i
< list
->n
; ++i
)
2296 res
= fn(res
, isl_pw_aff_copy(list
->p
[i
]));
2298 isl_pw_aff_list_free(list
);
2302 /* Return an isl_pw_aff that maps each element in the intersection of the
2303 * domains of the elements of list to the minimal corresponding affine
2306 __isl_give isl_pw_aff
*isl_pw_aff_list_min(__isl_take isl_pw_aff_list
*list
)
2308 return pw_aff_list_reduce(list
, &isl_pw_aff_min
);
2311 /* Return an isl_pw_aff that maps each element in the intersection of the
2312 * domains of the elements of list to the maximal corresponding affine
2315 __isl_give isl_pw_aff
*isl_pw_aff_list_max(__isl_take isl_pw_aff_list
*list
)
2317 return pw_aff_list_reduce(list
, &isl_pw_aff_max
);
2323 #include <isl_multi_templ.c>
2325 /* Construct an isl_multi_aff in the given space with value zero in
2326 * each of the output dimensions.
2328 __isl_give isl_multi_aff
*isl_multi_aff_zero(__isl_take isl_space
*space
)
2336 n
= isl_space_dim(space
, isl_dim_out
);
2337 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
2340 isl_space_free(space
);
2343 isl_local_space
*ls
;
2346 space
= isl_space_domain(space
);
2347 ls
= isl_local_space_from_space(space
);
2348 aff
= isl_aff_zero_on_domain(ls
);
2350 for (i
= 0; i
< n
; ++i
)
2351 ma
= isl_multi_aff_set_aff(ma
, i
, isl_aff_copy(aff
));
2359 /* Create an isl_multi_aff in the given space that maps each
2360 * input dimension to the corresponding output dimension.
2362 __isl_give isl_multi_aff
*isl_multi_aff_identity(__isl_take isl_space
*space
)
2370 if (isl_space_is_set(space
))
2371 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
2372 "expecting map space", goto error
);
2374 n
= isl_space_dim(space
, isl_dim_out
);
2375 if (n
!= isl_space_dim(space
, isl_dim_in
))
2376 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
2377 "number of input and output dimensions needs to be "
2378 "the same", goto error
);
2380 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
2383 isl_space_free(space
);
2386 isl_local_space
*ls
;
2389 space
= isl_space_domain(space
);
2390 ls
= isl_local_space_from_space(space
);
2391 aff
= isl_aff_zero_on_domain(ls
);
2393 for (i
= 0; i
< n
; ++i
) {
2395 aff_i
= isl_aff_copy(aff
);
2396 aff_i
= isl_aff_add_coefficient_si(aff_i
,
2398 ma
= isl_multi_aff_set_aff(ma
, i
, aff_i
);
2406 isl_space_free(space
);
2410 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
2413 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_multi_aff(
2414 __isl_take isl_multi_aff
*ma
)
2416 isl_set
*dom
= isl_set_universe(isl_multi_aff_get_domain_space(ma
));
2417 return isl_pw_multi_aff_alloc(dom
, ma
);
2420 /* Create a piecewise multi-affine expression in the given space that maps each
2421 * input dimension to the corresponding output dimension.
2423 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_identity(
2424 __isl_take isl_space
*space
)
2426 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space
));
2429 __isl_give isl_multi_aff
*isl_multi_aff_add(__isl_take isl_multi_aff
*maff1
,
2430 __isl_take isl_multi_aff
*maff2
)
2435 maff1
= isl_multi_aff_cow(maff1
);
2436 if (!maff1
|| !maff2
)
2439 ctx
= isl_multi_aff_get_ctx(maff1
);
2440 if (!isl_space_is_equal(maff1
->space
, maff2
->space
))
2441 isl_die(ctx
, isl_error_invalid
,
2442 "spaces don't match", goto error
);
2444 for (i
= 0; i
< maff1
->n
; ++i
) {
2445 maff1
->p
[i
] = isl_aff_add(maff1
->p
[i
],
2446 isl_aff_copy(maff2
->p
[i
]));
2451 isl_multi_aff_free(maff2
);
2454 isl_multi_aff_free(maff1
);
2455 isl_multi_aff_free(maff2
);
2459 /* Given two multi-affine expressions A -> B and C -> D,
2460 * construct a multi-affine expression [A -> C] -> [B -> D].
2462 __isl_give isl_multi_aff
*isl_multi_aff_product(
2463 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
2469 int in1
, in2
, out1
, out2
;
2471 in1
= isl_multi_aff_dim(ma1
, isl_dim_in
);
2472 in2
= isl_multi_aff_dim(ma2
, isl_dim_in
);
2473 out1
= isl_multi_aff_dim(ma1
, isl_dim_out
);
2474 out2
= isl_multi_aff_dim(ma2
, isl_dim_out
);
2475 space
= isl_space_product(isl_multi_aff_get_space(ma1
),
2476 isl_multi_aff_get_space(ma2
));
2477 res
= isl_multi_aff_alloc(isl_space_copy(space
));
2478 space
= isl_space_domain(space
);
2480 for (i
= 0; i
< out1
; ++i
) {
2481 aff
= isl_multi_aff_get_aff(ma1
, i
);
2482 aff
= isl_aff_insert_dims(aff
, isl_dim_in
, in1
, in2
);
2483 aff
= isl_aff_reset_domain_space(aff
, isl_space_copy(space
));
2484 res
= isl_multi_aff_set_aff(res
, i
, aff
);
2487 for (i
= 0; i
< out2
; ++i
) {
2488 aff
= isl_multi_aff_get_aff(ma2
, i
);
2489 aff
= isl_aff_insert_dims(aff
, isl_dim_in
, 0, in1
);
2490 aff
= isl_aff_reset_domain_space(aff
, isl_space_copy(space
));
2491 res
= isl_multi_aff_set_aff(res
, out1
+ i
, aff
);
2494 isl_space_free(space
);
2495 isl_multi_aff_free(ma1
);
2496 isl_multi_aff_free(ma2
);
2500 /* Exploit the equalities in "eq" to simplify the affine expressions.
2502 static __isl_give isl_multi_aff
*isl_multi_aff_substitute_equalities(
2503 __isl_take isl_multi_aff
*maff
, __isl_take isl_basic_set
*eq
)
2507 maff
= isl_multi_aff_cow(maff
);
2511 for (i
= 0; i
< maff
->n
; ++i
) {
2512 maff
->p
[i
] = isl_aff_substitute_equalities(maff
->p
[i
],
2513 isl_basic_set_copy(eq
));
2518 isl_basic_set_free(eq
);
2521 isl_basic_set_free(eq
);
2522 isl_multi_aff_free(maff
);
2526 __isl_give isl_multi_aff
*isl_multi_aff_scale(__isl_take isl_multi_aff
*maff
,
2531 maff
= isl_multi_aff_cow(maff
);
2535 for (i
= 0; i
< maff
->n
; ++i
) {
2536 maff
->p
[i
] = isl_aff_scale(maff
->p
[i
], f
);
2538 return isl_multi_aff_free(maff
);
2544 __isl_give isl_multi_aff
*isl_multi_aff_add_on_domain(__isl_keep isl_set
*dom
,
2545 __isl_take isl_multi_aff
*maff1
, __isl_take isl_multi_aff
*maff2
)
2547 maff1
= isl_multi_aff_add(maff1
, maff2
);
2548 maff1
= isl_multi_aff_gist(maff1
, isl_set_copy(dom
));
2552 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff
*maff
)
2560 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff
*maff1
,
2561 __isl_keep isl_multi_aff
*maff2
)
2566 if (!maff1
|| !maff2
)
2568 if (maff1
->n
!= maff2
->n
)
2570 equal
= isl_space_is_equal(maff1
->space
, maff2
->space
);
2571 if (equal
< 0 || !equal
)
2574 for (i
= 0; i
< maff1
->n
; ++i
) {
2575 equal
= isl_aff_plain_is_equal(maff1
->p
[i
], maff2
->p
[i
]);
2576 if (equal
< 0 || !equal
)
2583 __isl_give isl_multi_aff
*isl_multi_aff_set_dim_name(
2584 __isl_take isl_multi_aff
*maff
,
2585 enum isl_dim_type type
, unsigned pos
, const char *s
)
2589 maff
= isl_multi_aff_cow(maff
);
2593 maff
->space
= isl_space_set_dim_name(maff
->space
, type
, pos
, s
);
2595 return isl_multi_aff_free(maff
);
2597 if (type
== isl_dim_out
)
2599 for (i
= 0; i
< maff
->n
; ++i
) {
2600 maff
->p
[i
] = isl_aff_set_dim_name(maff
->p
[i
], type
, pos
, s
);
2602 return isl_multi_aff_free(maff
);
2608 __isl_give isl_multi_aff
*isl_multi_aff_drop_dims(__isl_take isl_multi_aff
*maff
,
2609 enum isl_dim_type type
, unsigned first
, unsigned n
)
2613 maff
= isl_multi_aff_cow(maff
);
2617 maff
->space
= isl_space_drop_dims(maff
->space
, type
, first
, n
);
2619 return isl_multi_aff_free(maff
);
2621 if (type
== isl_dim_out
) {
2622 for (i
= 0; i
< n
; ++i
)
2623 isl_aff_free(maff
->p
[first
+ i
]);
2624 for (i
= first
; i
+ n
< maff
->n
; ++i
)
2625 maff
->p
[i
] = maff
->p
[i
+ n
];
2630 for (i
= 0; i
< maff
->n
; ++i
) {
2631 maff
->p
[i
] = isl_aff_drop_dims(maff
->p
[i
], type
, first
, n
);
2633 return isl_multi_aff_free(maff
);
2639 /* Return the set of domain elements where "ma1" is lexicographically
2640 * smaller than or equal to "ma2".
2642 __isl_give isl_set
*isl_multi_aff_lex_le_set(__isl_take isl_multi_aff
*ma1
,
2643 __isl_take isl_multi_aff
*ma2
)
2645 return isl_multi_aff_lex_ge_set(ma2
, ma1
);
2648 /* Return the set of domain elements where "ma1" is lexicographically
2649 * greater than or equal to "ma2".
2651 __isl_give isl_set
*isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff
*ma1
,
2652 __isl_take isl_multi_aff
*ma2
)
2655 isl_map
*map1
, *map2
;
2658 map1
= isl_map_from_multi_aff(ma1
);
2659 map2
= isl_map_from_multi_aff(ma2
);
2660 map
= isl_map_range_product(map1
, map2
);
2661 space
= isl_space_range(isl_map_get_space(map
));
2662 space
= isl_space_domain(isl_space_unwrap(space
));
2663 ge
= isl_map_lex_ge(space
);
2664 map
= isl_map_intersect_range(map
, isl_map_wrap(ge
));
2666 return isl_map_domain(map
);
2670 #define PW isl_pw_multi_aff
2672 #define EL isl_multi_aff
2674 #define EL_IS_ZERO is_empty
2678 #define IS_ZERO is_empty
2681 #undef DEFAULT_IS_ZERO
2682 #define DEFAULT_IS_ZERO 0
2687 #define NO_INVOLVES_DIMS
2688 #define NO_MOVE_DIMS
2689 #define NO_INSERT_DIMS
2693 #include <isl_pw_templ.c>
2696 #define UNION isl_union_pw_multi_aff
2698 #define PART isl_pw_multi_aff
2700 #define PARTS pw_multi_aff
2701 #define ALIGN_DOMAIN
2705 #include <isl_union_templ.c>
2707 /* Given a function "cmp" that returns the set of elements where
2708 * "ma1" is "better" than "ma2", return the intersection of this
2709 * set with "dom1" and "dom2".
2711 static __isl_give isl_set
*shared_and_better(__isl_keep isl_set
*dom1
,
2712 __isl_keep isl_set
*dom2
, __isl_keep isl_multi_aff
*ma1
,
2713 __isl_keep isl_multi_aff
*ma2
,
2714 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
2715 __isl_take isl_multi_aff
*ma2
))
2721 common
= isl_set_intersect(isl_set_copy(dom1
), isl_set_copy(dom2
));
2722 is_empty
= isl_set_plain_is_empty(common
);
2723 if (is_empty
>= 0 && is_empty
)
2726 return isl_set_free(common
);
2727 better
= cmp(isl_multi_aff_copy(ma1
), isl_multi_aff_copy(ma2
));
2728 better
= isl_set_intersect(common
, better
);
2733 /* Given a function "cmp" that returns the set of elements where
2734 * "ma1" is "better" than "ma2", return a piecewise multi affine
2735 * expression defined on the union of the definition domains
2736 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
2737 * "pma2" on each cell. If only one of the two input functions
2738 * is defined on a given cell, then it is considered the best.
2740 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_opt(
2741 __isl_take isl_pw_multi_aff
*pma1
,
2742 __isl_take isl_pw_multi_aff
*pma2
,
2743 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
2744 __isl_take isl_multi_aff
*ma2
))
2747 isl_pw_multi_aff
*res
= NULL
;
2749 isl_set
*set
= NULL
;
2754 ctx
= isl_space_get_ctx(pma1
->dim
);
2755 if (!isl_space_is_equal(pma1
->dim
, pma2
->dim
))
2756 isl_die(ctx
, isl_error_invalid
,
2757 "arguments should live in the same space", goto error
);
2759 if (isl_pw_multi_aff_is_empty(pma1
)) {
2760 isl_pw_multi_aff_free(pma1
);
2764 if (isl_pw_multi_aff_is_empty(pma2
)) {
2765 isl_pw_multi_aff_free(pma2
);
2769 n
= 2 * (pma1
->n
+ 1) * (pma2
->n
+ 1);
2770 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma1
->dim
), n
);
2772 for (i
= 0; i
< pma1
->n
; ++i
) {
2773 set
= isl_set_copy(pma1
->p
[i
].set
);
2774 for (j
= 0; j
< pma2
->n
; ++j
) {
2778 better
= shared_and_better(pma2
->p
[j
].set
,
2779 pma1
->p
[i
].set
, pma2
->p
[j
].maff
,
2780 pma1
->p
[i
].maff
, cmp
);
2781 is_empty
= isl_set_plain_is_empty(better
);
2782 if (is_empty
< 0 || is_empty
) {
2783 isl_set_free(better
);
2788 set
= isl_set_subtract(set
, isl_set_copy(better
));
2790 res
= isl_pw_multi_aff_add_piece(res
, better
,
2791 isl_multi_aff_copy(pma2
->p
[j
].maff
));
2793 res
= isl_pw_multi_aff_add_piece(res
, set
,
2794 isl_multi_aff_copy(pma1
->p
[i
].maff
));
2797 for (j
= 0; j
< pma2
->n
; ++j
) {
2798 set
= isl_set_copy(pma2
->p
[j
].set
);
2799 for (i
= 0; i
< pma1
->n
; ++i
)
2800 set
= isl_set_subtract(set
,
2801 isl_set_copy(pma1
->p
[i
].set
));
2802 res
= isl_pw_multi_aff_add_piece(res
, set
,
2803 isl_multi_aff_copy(pma2
->p
[j
].maff
));
2806 isl_pw_multi_aff_free(pma1
);
2807 isl_pw_multi_aff_free(pma2
);
2811 isl_pw_multi_aff_free(pma1
);
2812 isl_pw_multi_aff_free(pma2
);
2814 return isl_pw_multi_aff_free(res
);
2817 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmax(
2818 __isl_take isl_pw_multi_aff
*pma1
,
2819 __isl_take isl_pw_multi_aff
*pma2
)
2821 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_ge_set
);
2824 /* Given two piecewise multi affine expressions, return a piecewise
2825 * multi-affine expression defined on the union of the definition domains
2826 * of the inputs that is equal to the lexicographic maximum of the two
2827 * inputs on each cell. If only one of the two inputs is defined on
2828 * a given cell, then it is considered to be the maximum.
2830 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmax(
2831 __isl_take isl_pw_multi_aff
*pma1
,
2832 __isl_take isl_pw_multi_aff
*pma2
)
2834 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
2835 &pw_multi_aff_union_lexmax
);
2838 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmin(
2839 __isl_take isl_pw_multi_aff
*pma1
,
2840 __isl_take isl_pw_multi_aff
*pma2
)
2842 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_le_set
);
2845 /* Given two piecewise multi affine expressions, return a piecewise
2846 * multi-affine expression defined on the union of the definition domains
2847 * of the inputs that is equal to the lexicographic minimum of the two
2848 * inputs on each cell. If only one of the two inputs is defined on
2849 * a given cell, then it is considered to be the minimum.
2851 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmin(
2852 __isl_take isl_pw_multi_aff
*pma1
,
2853 __isl_take isl_pw_multi_aff
*pma2
)
2855 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
2856 &pw_multi_aff_union_lexmin
);
2859 static __isl_give isl_pw_multi_aff
*pw_multi_aff_add(
2860 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2862 return isl_pw_multi_aff_on_shared_domain(pma1
, pma2
,
2863 &isl_multi_aff_add
);
2866 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_add(
2867 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2869 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
2873 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_add(
2874 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2876 return isl_pw_multi_aff_union_add_(pma1
, pma2
);
2879 /* Given two piecewise multi-affine expressions A -> B and C -> D,
2880 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
2882 static __isl_give isl_pw_multi_aff
*pw_multi_aff_product(
2883 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2887 isl_pw_multi_aff
*res
;
2892 n
= pma1
->n
* pma2
->n
;
2893 space
= isl_space_product(isl_space_copy(pma1
->dim
),
2894 isl_space_copy(pma2
->dim
));
2895 res
= isl_pw_multi_aff_alloc_size(space
, n
);
2897 for (i
= 0; i
< pma1
->n
; ++i
) {
2898 for (j
= 0; j
< pma2
->n
; ++j
) {
2902 domain
= isl_set_product(isl_set_copy(pma1
->p
[i
].set
),
2903 isl_set_copy(pma2
->p
[j
].set
));
2904 ma
= isl_multi_aff_product(
2905 isl_multi_aff_copy(pma1
->p
[i
].maff
),
2906 isl_multi_aff_copy(pma2
->p
[i
].maff
));
2907 res
= isl_pw_multi_aff_add_piece(res
, domain
, ma
);
2911 isl_pw_multi_aff_free(pma1
);
2912 isl_pw_multi_aff_free(pma2
);
2915 isl_pw_multi_aff_free(pma1
);
2916 isl_pw_multi_aff_free(pma2
);
2920 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_product(
2921 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
2923 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
2924 &pw_multi_aff_product
);
2927 /* Construct a map mapping the domain of the piecewise multi-affine expression
2928 * to its range, with each dimension in the range equated to the
2929 * corresponding affine expression on its cell.
2931 __isl_give isl_map
*isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
2939 map
= isl_map_empty(isl_pw_multi_aff_get_space(pma
));
2941 for (i
= 0; i
< pma
->n
; ++i
) {
2942 isl_multi_aff
*maff
;
2943 isl_basic_map
*bmap
;
2946 maff
= isl_multi_aff_copy(pma
->p
[i
].maff
);
2947 bmap
= isl_basic_map_from_multi_aff(maff
);
2948 map_i
= isl_map_from_basic_map(bmap
);
2949 map_i
= isl_map_intersect_domain(map_i
,
2950 isl_set_copy(pma
->p
[i
].set
));
2951 map
= isl_map_union_disjoint(map
, map_i
);
2954 isl_pw_multi_aff_free(pma
);
2958 __isl_give isl_set
*isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
2960 if (!isl_space_is_set(pma
->dim
))
2961 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
2962 "isl_pw_multi_aff cannot be converted into an isl_set",
2963 return isl_pw_multi_aff_free(pma
));
2965 return isl_map_from_pw_multi_aff(pma
);
2968 /* Given a basic map with a single output dimension that is defined
2969 * in terms of the parameters and input dimensions using an equality,
2970 * extract an isl_aff that expresses the output dimension in terms
2971 * of the parameters and input dimensions.
2973 * Since some applications expect the result of isl_pw_multi_aff_from_map
2974 * to only contain integer affine expressions, we compute the floor
2975 * of the expression before returning.
2977 * This function shares some similarities with
2978 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
2980 static __isl_give isl_aff
*extract_isl_aff_from_basic_map(
2981 __isl_take isl_basic_map
*bmap
)
2986 isl_local_space
*ls
;
2991 if (isl_basic_map_dim(bmap
, isl_dim_out
) != 1)
2992 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
2993 "basic map should have a single output dimension",
2995 offset
= isl_basic_map_offset(bmap
, isl_dim_out
);
2996 total
= isl_basic_map_total_dim(bmap
);
2997 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2998 if (isl_int_is_zero(bmap
->eq
[i
][offset
]))
3000 if (isl_seq_first_non_zero(bmap
->eq
[i
] + offset
+ 1,
3001 1 + total
- (offset
+ 1)) != -1)
3005 if (i
>= bmap
->n_eq
)
3006 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
3007 "unable to find suitable equality", goto error
);
3008 ls
= isl_basic_map_get_local_space(bmap
);
3009 aff
= isl_aff_alloc(isl_local_space_domain(ls
));
3012 if (isl_int_is_neg(bmap
->eq
[i
][offset
]))
3013 isl_seq_cpy(aff
->v
->el
+ 1, bmap
->eq
[i
], offset
);
3015 isl_seq_neg(aff
->v
->el
+ 1, bmap
->eq
[i
], offset
);
3016 isl_seq_clr(aff
->v
->el
+ 1 + offset
, aff
->v
->size
- (1 + offset
));
3017 isl_int_abs(aff
->v
->el
[0], bmap
->eq
[i
][offset
]);
3018 isl_basic_map_free(bmap
);
3020 aff
= isl_aff_remove_unused_divs(aff
);
3021 aff
= isl_aff_floor(aff
);
3024 isl_basic_map_free(bmap
);
3028 /* Given a basic map where each output dimension is defined
3029 * in terms of the parameters and input dimensions using an equality,
3030 * extract an isl_multi_aff that expresses the output dimensions in terms
3031 * of the parameters and input dimensions.
3033 static __isl_give isl_multi_aff
*extract_isl_multi_aff_from_basic_map(
3034 __isl_take isl_basic_map
*bmap
)
3043 ma
= isl_multi_aff_alloc(isl_basic_map_get_space(bmap
));
3044 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
3046 for (i
= 0; i
< n_out
; ++i
) {
3047 isl_basic_map
*bmap_i
;
3050 bmap_i
= isl_basic_map_copy(bmap
);
3051 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
,
3052 i
+ 1, n_out
- (1 + i
));
3053 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
, 0, i
);
3054 aff
= extract_isl_aff_from_basic_map(bmap_i
);
3055 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3058 isl_basic_map_free(bmap
);
3063 /* Create an isl_pw_multi_aff that is equivalent to
3064 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
3065 * The given basic map is such that each output dimension is defined
3066 * in terms of the parameters and input dimensions using an equality.
3068 static __isl_give isl_pw_multi_aff
*plain_pw_multi_aff_from_map(
3069 __isl_take isl_set
*domain
, __isl_take isl_basic_map
*bmap
)
3073 ma
= extract_isl_multi_aff_from_basic_map(bmap
);
3074 return isl_pw_multi_aff_alloc(domain
, ma
);
3077 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3078 * This obviously only works if the input "map" is single-valued.
3079 * If so, we compute the lexicographic minimum of the image in the form
3080 * of an isl_pw_multi_aff. Since the image is unique, it is equal
3081 * to its lexicographic minimum.
3082 * If the input is not single-valued, we produce an error.
3084 * As a special case, we first check if all output dimensions are uniquely
3085 * defined in terms of the parameters and input dimensions over the entire
3086 * domain. If so, we extract the desired isl_pw_multi_aff directly
3087 * from the affine hull of "map" and its domain.
3089 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_map(__isl_take isl_map
*map
)
3093 isl_pw_multi_aff
*pma
;
3094 isl_basic_map
*hull
;
3099 hull
= isl_map_affine_hull(isl_map_copy(map
));
3100 sv
= isl_basic_map_plain_is_single_valued(hull
);
3102 return plain_pw_multi_aff_from_map(isl_map_domain(map
), hull
);
3103 isl_basic_map_free(hull
);
3107 sv
= isl_map_is_single_valued(map
);
3111 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
3112 "map is not single-valued", goto error
);
3113 map
= isl_map_make_disjoint(map
);
3117 pma
= isl_pw_multi_aff_empty(isl_map_get_space(map
));
3119 for (i
= 0; i
< map
->n
; ++i
) {
3120 isl_pw_multi_aff
*pma_i
;
3121 isl_basic_map
*bmap
;
3122 bmap
= isl_basic_map_copy(map
->p
[i
]);
3123 pma_i
= isl_basic_map_lexmin_pw_multi_aff(bmap
);
3124 pma
= isl_pw_multi_aff_add_disjoint(pma
, pma_i
);
3134 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_set(__isl_take isl_set
*set
)
3136 return isl_pw_multi_aff_from_map(set
);
3139 /* Return the piecewise affine expression "set ? 1 : 0".
3141 __isl_give isl_pw_aff
*isl_set_indicator_function(__isl_take isl_set
*set
)
3144 isl_space
*space
= isl_set_get_space(set
);
3145 isl_local_space
*ls
= isl_local_space_from_space(space
);
3146 isl_aff
*zero
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
3147 isl_aff
*one
= isl_aff_zero_on_domain(ls
);
3149 one
= isl_aff_add_constant_si(one
, 1);
3150 pa
= isl_pw_aff_alloc(isl_set_copy(set
), one
);
3151 set
= isl_set_complement(set
);
3152 pa
= isl_pw_aff_add_disjoint(pa
, isl_pw_aff_alloc(set
, zero
));
3157 /* Plug in "subs" for dimension "type", "pos" of "aff".
3159 * Let i be the dimension to replace and let "subs" be of the form
3163 * and "aff" of the form
3169 * (a f + d g')/(m d)
3171 * where g' is the result of plugging in "subs" in each of the integer
3174 __isl_give isl_aff
*isl_aff_substitute(__isl_take isl_aff
*aff
,
3175 enum isl_dim_type type
, unsigned pos
, __isl_keep isl_aff
*subs
)
3180 aff
= isl_aff_cow(aff
);
3182 return isl_aff_free(aff
);
3184 ctx
= isl_aff_get_ctx(aff
);
3185 if (!isl_space_is_equal(aff
->ls
->dim
, subs
->ls
->dim
))
3186 isl_die(ctx
, isl_error_invalid
,
3187 "spaces don't match", return isl_aff_free(aff
));
3188 if (isl_local_space_dim(subs
->ls
, isl_dim_div
) != 0)
3189 isl_die(ctx
, isl_error_unsupported
,
3190 "cannot handle divs yet", return isl_aff_free(aff
));
3192 aff
->ls
= isl_local_space_substitute(aff
->ls
, type
, pos
, subs
);
3194 return isl_aff_free(aff
);
3196 aff
->v
= isl_vec_cow(aff
->v
);
3198 return isl_aff_free(aff
);
3200 pos
+= isl_local_space_offset(aff
->ls
, type
);
3203 isl_seq_substitute(aff
->v
->el
, pos
, subs
->v
->el
,
3204 aff
->v
->size
, subs
->v
->size
, v
);
3210 /* Plug in "subs" for dimension "type", "pos" in each of the affine
3211 * expressions in "maff".
3213 __isl_give isl_multi_aff
*isl_multi_aff_substitute(
3214 __isl_take isl_multi_aff
*maff
, enum isl_dim_type type
, unsigned pos
,
3215 __isl_keep isl_aff
*subs
)
3219 maff
= isl_multi_aff_cow(maff
);
3221 return isl_multi_aff_free(maff
);
3223 if (type
== isl_dim_in
)
3226 for (i
= 0; i
< maff
->n
; ++i
) {
3227 maff
->p
[i
] = isl_aff_substitute(maff
->p
[i
], type
, pos
, subs
);
3229 return isl_multi_aff_free(maff
);
3235 /* Plug in "subs" for dimension "type", "pos" of "pma".
3237 * pma is of the form
3241 * while subs is of the form
3243 * v' = B_j(v) -> S_j
3245 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
3246 * has a contribution in the result, in particular
3248 * C_ij(S_j) -> M_i(S_j)
3250 * Note that plugging in S_j in C_ij may also result in an empty set
3251 * and this contribution should simply be discarded.
3253 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_substitute(
3254 __isl_take isl_pw_multi_aff
*pma
, enum isl_dim_type type
, unsigned pos
,
3255 __isl_keep isl_pw_aff
*subs
)
3258 isl_pw_multi_aff
*res
;
3261 return isl_pw_multi_aff_free(pma
);
3263 n
= pma
->n
* subs
->n
;
3264 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma
->dim
), n
);
3266 for (i
= 0; i
< pma
->n
; ++i
) {
3267 for (j
= 0; j
< subs
->n
; ++j
) {
3269 isl_multi_aff
*res_ij
;
3270 common
= isl_set_intersect(
3271 isl_set_copy(pma
->p
[i
].set
),
3272 isl_set_copy(subs
->p
[j
].set
));
3273 common
= isl_set_substitute(common
,
3274 type
, pos
, subs
->p
[j
].aff
);
3275 if (isl_set_plain_is_empty(common
)) {
3276 isl_set_free(common
);
3280 res_ij
= isl_multi_aff_substitute(
3281 isl_multi_aff_copy(pma
->p
[i
].maff
),
3282 type
, pos
, subs
->p
[j
].aff
);
3284 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
3288 isl_pw_multi_aff_free(pma
);
3292 /* Extend the local space of "dst" to include the divs
3293 * in the local space of "src".
3295 __isl_give isl_aff
*isl_aff_align_divs(__isl_take isl_aff
*dst
,
3296 __isl_keep isl_aff
*src
)
3304 return isl_aff_free(dst
);
3306 ctx
= isl_aff_get_ctx(src
);
3307 if (!isl_space_is_equal(src
->ls
->dim
, dst
->ls
->dim
))
3308 isl_die(ctx
, isl_error_invalid
,
3309 "spaces don't match", goto error
);
3311 if (src
->ls
->div
->n_row
== 0)
3314 exp1
= isl_alloc_array(ctx
, int, src
->ls
->div
->n_row
);
3315 exp2
= isl_alloc_array(ctx
, int, dst
->ls
->div
->n_row
);
3319 div
= isl_merge_divs(src
->ls
->div
, dst
->ls
->div
, exp1
, exp2
);
3320 dst
= isl_aff_expand_divs(dst
, div
, exp2
);
3328 return isl_aff_free(dst
);
3331 /* Adjust the local spaces of the affine expressions in "maff"
3332 * such that they all have the save divs.
3334 __isl_give isl_multi_aff
*isl_multi_aff_align_divs(
3335 __isl_take isl_multi_aff
*maff
)
3343 maff
= isl_multi_aff_cow(maff
);
3347 for (i
= 1; i
< maff
->n
; ++i
)
3348 maff
->p
[0] = isl_aff_align_divs(maff
->p
[0], maff
->p
[i
]);
3349 for (i
= 1; i
< maff
->n
; ++i
) {
3350 maff
->p
[i
] = isl_aff_align_divs(maff
->p
[i
], maff
->p
[0]);
3352 return isl_multi_aff_free(maff
);
3358 __isl_give isl_aff
*isl_aff_lift(__isl_take isl_aff
*aff
)
3360 aff
= isl_aff_cow(aff
);
3364 aff
->ls
= isl_local_space_lift(aff
->ls
);
3366 return isl_aff_free(aff
);
3371 /* Lift "maff" to a space with extra dimensions such that the result
3372 * has no more existentially quantified variables.
3373 * If "ls" is not NULL, then *ls is assigned the local space that lies
3374 * at the basis of the lifting applied to "maff".
3376 __isl_give isl_multi_aff
*isl_multi_aff_lift(__isl_take isl_multi_aff
*maff
,
3377 __isl_give isl_local_space
**ls
)
3391 isl_space
*space
= isl_multi_aff_get_domain_space(maff
);
3392 *ls
= isl_local_space_from_space(space
);
3394 return isl_multi_aff_free(maff
);
3399 maff
= isl_multi_aff_cow(maff
);
3400 maff
= isl_multi_aff_align_divs(maff
);
3404 n_div
= isl_aff_dim(maff
->p
[0], isl_dim_div
);
3405 space
= isl_multi_aff_get_space(maff
);
3406 space
= isl_space_lift(isl_space_domain(space
), n_div
);
3407 space
= isl_space_extend_domain_with_range(space
,
3408 isl_multi_aff_get_space(maff
));
3410 return isl_multi_aff_free(maff
);
3411 isl_space_free(maff
->space
);
3412 maff
->space
= space
;
3415 *ls
= isl_aff_get_domain_local_space(maff
->p
[0]);
3417 return isl_multi_aff_free(maff
);
3420 for (i
= 0; i
< maff
->n
; ++i
) {
3421 maff
->p
[i
] = isl_aff_lift(maff
->p
[i
]);
3429 isl_local_space_free(*ls
);
3430 return isl_multi_aff_free(maff
);
3434 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
3436 __isl_give isl_pw_aff
*isl_pw_multi_aff_get_pw_aff(
3437 __isl_keep isl_pw_multi_aff
*pma
, int pos
)
3447 n_out
= isl_pw_multi_aff_dim(pma
, isl_dim_out
);
3448 if (pos
< 0 || pos
>= n_out
)
3449 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
3450 "index out of bounds", return NULL
);
3452 space
= isl_pw_multi_aff_get_space(pma
);
3453 space
= isl_space_drop_dims(space
, isl_dim_out
,
3454 pos
+ 1, n_out
- pos
- 1);
3455 space
= isl_space_drop_dims(space
, isl_dim_out
, 0, pos
);
3457 pa
= isl_pw_aff_alloc_size(space
, pma
->n
);
3458 for (i
= 0; i
< pma
->n
; ++i
) {
3460 aff
= isl_multi_aff_get_aff(pma
->p
[i
].maff
, pos
);
3461 pa
= isl_pw_aff_add_piece(pa
, isl_set_copy(pma
->p
[i
].set
), aff
);
3467 /* Return an isl_pw_multi_aff with the given "set" as domain and
3468 * an unnamed zero-dimensional range.
3470 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_domain(
3471 __isl_take isl_set
*set
)
3476 space
= isl_set_get_space(set
);
3477 space
= isl_space_from_domain(space
);
3478 ma
= isl_multi_aff_zero(space
);
3479 return isl_pw_multi_aff_alloc(set
, ma
);
3482 /* Add an isl_pw_multi_aff with the given "set" as domain and
3483 * an unnamed zero-dimensional range to *user.
3485 static int add_pw_multi_aff_from_domain(__isl_take isl_set
*set
, void *user
)
3487 isl_union_pw_multi_aff
**upma
= user
;
3488 isl_pw_multi_aff
*pma
;
3490 pma
= isl_pw_multi_aff_from_domain(set
);
3491 *upma
= isl_union_pw_multi_aff_add_pw_multi_aff(*upma
, pma
);
3496 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
3497 * an unnamed zero-dimensional range.
3499 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_domain(
3500 __isl_take isl_union_set
*uset
)
3503 isl_union_pw_multi_aff
*upma
;
3508 space
= isl_union_set_get_space(uset
);
3509 upma
= isl_union_pw_multi_aff_empty(space
);
3511 if (isl_union_set_foreach_set(uset
,
3512 &add_pw_multi_aff_from_domain
, &upma
) < 0)
3515 isl_union_set_free(uset
);
3518 isl_union_set_free(uset
);
3519 isl_union_pw_multi_aff_free(upma
);
3523 /* Convert "pma" to an isl_map and add it to *umap.
3525 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
, void *user
)
3527 isl_union_map
**umap
= user
;
3530 map
= isl_map_from_pw_multi_aff(pma
);
3531 *umap
= isl_union_map_add_map(*umap
, map
);
3536 /* Construct a union map mapping the domain of the union
3537 * piecewise multi-affine expression to its range, with each dimension
3538 * in the range equated to the corresponding affine expression on its cell.
3540 __isl_give isl_union_map
*isl_union_map_from_union_pw_multi_aff(
3541 __isl_take isl_union_pw_multi_aff
*upma
)
3544 isl_union_map
*umap
;
3549 space
= isl_union_pw_multi_aff_get_space(upma
);
3550 umap
= isl_union_map_empty(space
);
3552 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
3553 &map_from_pw_multi_aff
, &umap
) < 0)
3556 isl_union_pw_multi_aff_free(upma
);
3559 isl_union_pw_multi_aff_free(upma
);
3560 isl_union_map_free(umap
);
3564 /* Local data for bin_entry and the callback "fn".
3566 struct isl_union_pw_multi_aff_bin_data
{
3567 isl_union_pw_multi_aff
*upma2
;
3568 isl_union_pw_multi_aff
*res
;
3569 isl_pw_multi_aff
*pma
;
3570 int (*fn
)(void **entry
, void *user
);
3573 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
3574 * and call data->fn for each isl_pw_multi_aff in data->upma2.
3576 static int bin_entry(void **entry
, void *user
)
3578 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
3579 isl_pw_multi_aff
*pma
= *entry
;
3582 if (isl_hash_table_foreach(data
->upma2
->dim
->ctx
, &data
->upma2
->table
,
3583 data
->fn
, data
) < 0)
3589 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
3590 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
3591 * passed as user field) and the isl_pw_multi_aff from upma2 is available
3592 * as *entry. The callback should adjust data->res if desired.
3594 static __isl_give isl_union_pw_multi_aff
*bin_op(
3595 __isl_take isl_union_pw_multi_aff
*upma1
,
3596 __isl_take isl_union_pw_multi_aff
*upma2
,
3597 int (*fn
)(void **entry
, void *user
))
3600 struct isl_union_pw_multi_aff_bin_data data
= { NULL
, NULL
, NULL
, fn
};
3602 space
= isl_union_pw_multi_aff_get_space(upma2
);
3603 upma1
= isl_union_pw_multi_aff_align_params(upma1
, space
);
3604 space
= isl_union_pw_multi_aff_get_space(upma1
);
3605 upma2
= isl_union_pw_multi_aff_align_params(upma2
, space
);
3607 if (!upma1
|| !upma2
)
3611 data
.res
= isl_union_pw_multi_aff_alloc(isl_space_copy(upma1
->dim
),
3613 if (isl_hash_table_foreach(upma1
->dim
->ctx
, &upma1
->table
,
3614 &bin_entry
, &data
) < 0)
3617 isl_union_pw_multi_aff_free(upma1
);
3618 isl_union_pw_multi_aff_free(upma2
);
3621 isl_union_pw_multi_aff_free(upma1
);
3622 isl_union_pw_multi_aff_free(upma2
);
3623 isl_union_pw_multi_aff_free(data
.res
);
3627 /* Given two isl_multi_affs A -> B and C -> D,
3628 * construct an isl_multi_aff (A * C) -> (B, D).
3630 __isl_give isl_multi_aff
*isl_multi_aff_flat_range_product(
3631 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
3641 space
= isl_space_range_product(isl_multi_aff_get_space(ma1
),
3642 isl_multi_aff_get_space(ma2
));
3643 space
= isl_space_flatten_range(space
);
3644 res
= isl_multi_aff_alloc(space
);
3646 n1
= isl_multi_aff_dim(ma1
, isl_dim_out
);
3647 n2
= isl_multi_aff_dim(ma2
, isl_dim_out
);
3649 for (i
= 0; i
< n1
; ++i
) {
3650 aff
= isl_multi_aff_get_aff(ma1
, i
);
3651 res
= isl_multi_aff_set_aff(res
, i
, aff
);
3654 for (i
= 0; i
< n2
; ++i
) {
3655 aff
= isl_multi_aff_get_aff(ma2
, i
);
3656 res
= isl_multi_aff_set_aff(res
, n1
+ i
, aff
);
3659 isl_multi_aff_free(ma1
);
3660 isl_multi_aff_free(ma2
);
3663 isl_multi_aff_free(ma1
);
3664 isl_multi_aff_free(ma2
);
3668 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
3669 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3671 static __isl_give isl_pw_multi_aff
*pw_multi_aff_flat_range_product(
3672 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3676 space
= isl_space_range_product(isl_pw_multi_aff_get_space(pma1
),
3677 isl_pw_multi_aff_get_space(pma2
));
3678 space
= isl_space_flatten_range(space
);
3679 return isl_pw_multi_aff_on_shared_domain_in(pma1
, pma2
, space
,
3680 &isl_multi_aff_flat_range_product
);
3683 /* Given two isl_pw_multi_affs A -> B and C -> D,
3684 * construct an isl_pw_multi_aff (A * C) -> (B, D).
3686 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_flat_range_product(
3687 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3689 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
3690 &pw_multi_aff_flat_range_product
);
3693 /* If data->pma and *entry have the same domain space, then compute
3694 * their flat range product and the result to data->res.
3696 static int flat_range_product_entry(void **entry
, void *user
)
3698 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
3699 isl_pw_multi_aff
*pma2
= *entry
;
3701 if (!isl_space_tuple_match(data
->pma
->dim
, isl_dim_in
,
3702 pma2
->dim
, isl_dim_in
))
3705 pma2
= isl_pw_multi_aff_flat_range_product(
3706 isl_pw_multi_aff_copy(data
->pma
),
3707 isl_pw_multi_aff_copy(pma2
));
3709 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma2
);
3714 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
3715 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
3717 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_flat_range_product(
3718 __isl_take isl_union_pw_multi_aff
*upma1
,
3719 __isl_take isl_union_pw_multi_aff
*upma2
)
3721 return bin_op(upma1
, upma2
, &flat_range_product_entry
);
3724 /* Replace the affine expressions at position "pos" in "pma" by "pa".
3725 * The parameters are assumed to have been aligned.
3727 * The implementation essentially performs an isl_pw_*_on_shared_domain,
3728 * except that it works on two different isl_pw_* types.
3730 static __isl_give isl_pw_multi_aff
*pw_multi_aff_set_pw_aff(
3731 __isl_take isl_pw_multi_aff
*pma
, unsigned pos
,
3732 __isl_take isl_pw_aff
*pa
)
3735 isl_pw_multi_aff
*res
= NULL
;
3740 if (!isl_space_tuple_match(pma
->dim
, isl_dim_in
, pa
->dim
, isl_dim_in
))
3741 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
3742 "domains don't match", goto error
);
3743 if (pos
>= isl_pw_multi_aff_dim(pma
, isl_dim_out
))
3744 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
3745 "index out of bounds", goto error
);
3748 res
= isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma
), n
);
3750 for (i
= 0; i
< pma
->n
; ++i
) {
3751 for (j
= 0; j
< pa
->n
; ++j
) {
3753 isl_multi_aff
*res_ij
;
3756 common
= isl_set_intersect(isl_set_copy(pma
->p
[i
].set
),
3757 isl_set_copy(pa
->p
[j
].set
));
3758 empty
= isl_set_plain_is_empty(common
);
3759 if (empty
< 0 || empty
) {
3760 isl_set_free(common
);
3766 res_ij
= isl_multi_aff_set_aff(
3767 isl_multi_aff_copy(pma
->p
[i
].maff
), pos
,
3768 isl_aff_copy(pa
->p
[j
].aff
));
3769 res_ij
= isl_multi_aff_gist(res_ij
,
3770 isl_set_copy(common
));
3772 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
3776 isl_pw_multi_aff_free(pma
);
3777 isl_pw_aff_free(pa
);
3780 isl_pw_multi_aff_free(pma
);
3781 isl_pw_aff_free(pa
);
3782 return isl_pw_multi_aff_free(res
);
3785 /* Replace the affine expressions at position "pos" in "pma" by "pa".
3787 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_set_pw_aff(
3788 __isl_take isl_pw_multi_aff
*pma
, unsigned pos
,
3789 __isl_take isl_pw_aff
*pa
)
3793 if (isl_space_match(pma
->dim
, isl_dim_param
, pa
->dim
, isl_dim_param
))
3794 return pw_multi_aff_set_pw_aff(pma
, pos
, pa
);
3795 if (!isl_space_has_named_params(pma
->dim
) ||
3796 !isl_space_has_named_params(pa
->dim
))
3797 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
3798 "unaligned unnamed parameters", goto error
);
3799 pma
= isl_pw_multi_aff_align_params(pma
, isl_pw_aff_get_space(pa
));
3800 pa
= isl_pw_aff_align_params(pa
, isl_pw_multi_aff_get_space(pma
));
3801 return pw_multi_aff_set_pw_aff(pma
, pos
, pa
);
3803 isl_pw_multi_aff_free(pma
);
3804 isl_pw_aff_free(pa
);