2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
4 * Copyright 2012-2013 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
9 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
11 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 #include <isl_ctx_private.h>
16 #include <isl_map_private.h>
17 #include <isl_union_map_private.h>
18 #include <isl_aff_private.h>
19 #include <isl_space_private.h>
20 #include <isl_local_space_private.h>
21 #include <isl_vec_private.h>
22 #include <isl_mat_private.h>
23 #include <isl/constraint.h>
26 #include <isl_val_private.h>
27 #include <isl/deprecated/aff_int.h>
28 #include <isl_config.h>
33 #include <isl_list_templ.c>
38 #include <isl_list_templ.c>
40 __isl_give isl_aff
*isl_aff_alloc_vec(__isl_take isl_local_space
*ls
,
41 __isl_take isl_vec
*v
)
48 aff
= isl_calloc_type(v
->ctx
, struct isl_aff
);
58 isl_local_space_free(ls
);
63 __isl_give isl_aff
*isl_aff_alloc(__isl_take isl_local_space
*ls
)
72 ctx
= isl_local_space_get_ctx(ls
);
73 if (!isl_local_space_divs_known(ls
))
74 isl_die(ctx
, isl_error_invalid
, "local space has unknown divs",
76 if (!isl_local_space_is_set(ls
))
77 isl_die(ctx
, isl_error_invalid
,
78 "domain of affine expression should be a set",
81 total
= isl_local_space_dim(ls
, isl_dim_all
);
82 v
= isl_vec_alloc(ctx
, 1 + 1 + total
);
83 return isl_aff_alloc_vec(ls
, v
);
85 isl_local_space_free(ls
);
89 __isl_give isl_aff
*isl_aff_zero_on_domain(__isl_take isl_local_space
*ls
)
93 aff
= isl_aff_alloc(ls
);
97 isl_int_set_si(aff
->v
->el
[0], 1);
98 isl_seq_clr(aff
->v
->el
+ 1, aff
->v
->size
- 1);
103 /* Return a piecewise affine expression defined on the specified domain
104 * that is equal to zero.
106 __isl_give isl_pw_aff
*isl_pw_aff_zero_on_domain(__isl_take isl_local_space
*ls
)
108 return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls
));
111 /* Return an affine expression that is equal to "val" on
112 * domain local space "ls".
114 __isl_give isl_aff
*isl_aff_val_on_domain(__isl_take isl_local_space
*ls
,
115 __isl_take isl_val
*val
)
121 if (!isl_val_is_rat(val
))
122 isl_die(isl_val_get_ctx(val
), isl_error_invalid
,
123 "expecting rational value", goto error
);
125 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
129 isl_seq_clr(aff
->v
->el
+ 2, aff
->v
->size
- 2);
130 isl_int_set(aff
->v
->el
[1], val
->n
);
131 isl_int_set(aff
->v
->el
[0], val
->d
);
133 isl_local_space_free(ls
);
137 isl_local_space_free(ls
);
142 /* Return an affine expression that is equal to the specified dimension
145 __isl_give isl_aff
*isl_aff_var_on_domain(__isl_take isl_local_space
*ls
,
146 enum isl_dim_type type
, unsigned pos
)
154 space
= isl_local_space_get_space(ls
);
157 if (isl_space_is_map(space
))
158 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
159 "expecting (parameter) set space", goto error
);
160 if (pos
>= isl_local_space_dim(ls
, type
))
161 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
162 "position out of bounds", goto error
);
164 isl_space_free(space
);
165 aff
= isl_aff_alloc(ls
);
169 pos
+= isl_local_space_offset(aff
->ls
, type
);
171 isl_int_set_si(aff
->v
->el
[0], 1);
172 isl_seq_clr(aff
->v
->el
+ 1, aff
->v
->size
- 1);
173 isl_int_set_si(aff
->v
->el
[1 + pos
], 1);
177 isl_local_space_free(ls
);
178 isl_space_free(space
);
182 /* Return a piecewise affine expression that is equal to
183 * the specified dimension in "ls".
185 __isl_give isl_pw_aff
*isl_pw_aff_var_on_domain(__isl_take isl_local_space
*ls
,
186 enum isl_dim_type type
, unsigned pos
)
188 return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls
, type
, pos
));
191 __isl_give isl_aff
*isl_aff_copy(__isl_keep isl_aff
*aff
)
200 __isl_give isl_aff
*isl_aff_dup(__isl_keep isl_aff
*aff
)
205 return isl_aff_alloc_vec(isl_local_space_copy(aff
->ls
),
206 isl_vec_copy(aff
->v
));
209 __isl_give isl_aff
*isl_aff_cow(__isl_take isl_aff
*aff
)
217 return isl_aff_dup(aff
);
220 void *isl_aff_free(__isl_take isl_aff
*aff
)
228 isl_local_space_free(aff
->ls
);
229 isl_vec_free(aff
->v
);
236 isl_ctx
*isl_aff_get_ctx(__isl_keep isl_aff
*aff
)
238 return aff
? isl_local_space_get_ctx(aff
->ls
) : NULL
;
241 /* Externally, an isl_aff has a map space, but internally, the
242 * ls field corresponds to the domain of that space.
244 int isl_aff_dim(__isl_keep isl_aff
*aff
, enum isl_dim_type type
)
248 if (type
== isl_dim_out
)
250 if (type
== isl_dim_in
)
252 return isl_local_space_dim(aff
->ls
, type
);
255 __isl_give isl_space
*isl_aff_get_domain_space(__isl_keep isl_aff
*aff
)
257 return aff
? isl_local_space_get_space(aff
->ls
) : NULL
;
260 __isl_give isl_space
*isl_aff_get_space(__isl_keep isl_aff
*aff
)
265 space
= isl_local_space_get_space(aff
->ls
);
266 space
= isl_space_from_domain(space
);
267 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
271 __isl_give isl_local_space
*isl_aff_get_domain_local_space(
272 __isl_keep isl_aff
*aff
)
274 return aff
? isl_local_space_copy(aff
->ls
) : NULL
;
277 __isl_give isl_local_space
*isl_aff_get_local_space(__isl_keep isl_aff
*aff
)
282 ls
= isl_local_space_copy(aff
->ls
);
283 ls
= isl_local_space_from_domain(ls
);
284 ls
= isl_local_space_add_dims(ls
, isl_dim_out
, 1);
288 /* Externally, an isl_aff has a map space, but internally, the
289 * ls field corresponds to the domain of that space.
291 const char *isl_aff_get_dim_name(__isl_keep isl_aff
*aff
,
292 enum isl_dim_type type
, unsigned pos
)
296 if (type
== isl_dim_out
)
298 if (type
== isl_dim_in
)
300 return isl_local_space_get_dim_name(aff
->ls
, type
, pos
);
303 __isl_give isl_aff
*isl_aff_reset_domain_space(__isl_take isl_aff
*aff
,
304 __isl_take isl_space
*dim
)
306 aff
= isl_aff_cow(aff
);
310 aff
->ls
= isl_local_space_reset_space(aff
->ls
, dim
);
312 return isl_aff_free(aff
);
321 /* Reset the space of "aff". This function is called from isl_pw_templ.c
322 * and doesn't know if the space of an element object is represented
323 * directly or through its domain. It therefore passes along both.
325 __isl_give isl_aff
*isl_aff_reset_space_and_domain(__isl_take isl_aff
*aff
,
326 __isl_take isl_space
*space
, __isl_take isl_space
*domain
)
328 isl_space_free(space
);
329 return isl_aff_reset_domain_space(aff
, domain
);
332 /* Reorder the coefficients of the affine expression based
333 * on the given reodering.
334 * The reordering r is assumed to have been extended with the local
337 static __isl_give isl_vec
*vec_reorder(__isl_take isl_vec
*vec
,
338 __isl_take isl_reordering
*r
, int n_div
)
346 res
= isl_vec_alloc(vec
->ctx
,
347 2 + isl_space_dim(r
->dim
, isl_dim_all
) + n_div
);
348 isl_seq_cpy(res
->el
, vec
->el
, 2);
349 isl_seq_clr(res
->el
+ 2, res
->size
- 2);
350 for (i
= 0; i
< r
->len
; ++i
)
351 isl_int_set(res
->el
[2 + r
->pos
[i
]], vec
->el
[2 + i
]);
353 isl_reordering_free(r
);
358 isl_reordering_free(r
);
362 /* Reorder the dimensions of the domain of "aff" according
363 * to the given reordering.
365 __isl_give isl_aff
*isl_aff_realign_domain(__isl_take isl_aff
*aff
,
366 __isl_take isl_reordering
*r
)
368 aff
= isl_aff_cow(aff
);
372 r
= isl_reordering_extend(r
, aff
->ls
->div
->n_row
);
373 aff
->v
= vec_reorder(aff
->v
, isl_reordering_copy(r
),
374 aff
->ls
->div
->n_row
);
375 aff
->ls
= isl_local_space_realign(aff
->ls
, r
);
377 if (!aff
->v
|| !aff
->ls
)
378 return isl_aff_free(aff
);
383 isl_reordering_free(r
);
387 __isl_give isl_aff
*isl_aff_align_params(__isl_take isl_aff
*aff
,
388 __isl_take isl_space
*model
)
393 if (!isl_space_match(aff
->ls
->dim
, isl_dim_param
,
394 model
, isl_dim_param
)) {
397 model
= isl_space_drop_dims(model
, isl_dim_in
,
398 0, isl_space_dim(model
, isl_dim_in
));
399 model
= isl_space_drop_dims(model
, isl_dim_out
,
400 0, isl_space_dim(model
, isl_dim_out
));
401 exp
= isl_parameter_alignment_reordering(aff
->ls
->dim
, model
);
402 exp
= isl_reordering_extend_space(exp
,
403 isl_aff_get_domain_space(aff
));
404 aff
= isl_aff_realign_domain(aff
, exp
);
407 isl_space_free(model
);
410 isl_space_free(model
);
415 int isl_aff_plain_is_zero(__isl_keep isl_aff
*aff
)
420 return isl_seq_first_non_zero(aff
->v
->el
+ 1, aff
->v
->size
- 1) < 0;
423 int isl_aff_plain_is_equal(__isl_keep isl_aff
*aff1
, __isl_keep isl_aff
*aff2
)
430 equal
= isl_local_space_is_equal(aff1
->ls
, aff2
->ls
);
431 if (equal
< 0 || !equal
)
434 return isl_vec_is_equal(aff1
->v
, aff2
->v
);
437 int isl_aff_get_denominator(__isl_keep isl_aff
*aff
, isl_int
*v
)
441 isl_int_set(*v
, aff
->v
->el
[0]);
445 /* Return the common denominator of "aff".
447 __isl_give isl_val
*isl_aff_get_denominator_val(__isl_keep isl_aff
*aff
)
454 ctx
= isl_aff_get_ctx(aff
);
455 return isl_val_int_from_isl_int(ctx
, aff
->v
->el
[0]);
458 int isl_aff_get_constant(__isl_keep isl_aff
*aff
, isl_int
*v
)
462 isl_int_set(*v
, aff
->v
->el
[1]);
466 /* Return the constant term of "aff".
468 __isl_give isl_val
*isl_aff_get_constant_val(__isl_keep isl_aff
*aff
)
476 ctx
= isl_aff_get_ctx(aff
);
477 v
= isl_val_rat_from_isl_int(ctx
, aff
->v
->el
[1], aff
->v
->el
[0]);
478 return isl_val_normalize(v
);
481 int isl_aff_get_coefficient(__isl_keep isl_aff
*aff
,
482 enum isl_dim_type type
, int pos
, isl_int
*v
)
487 if (type
== isl_dim_out
)
488 isl_die(aff
->v
->ctx
, isl_error_invalid
,
489 "output/set dimension does not have a coefficient",
491 if (type
== isl_dim_in
)
494 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
495 isl_die(aff
->v
->ctx
, isl_error_invalid
,
496 "position out of bounds", return -1);
498 pos
+= isl_local_space_offset(aff
->ls
, type
);
499 isl_int_set(*v
, aff
->v
->el
[1 + pos
]);
504 /* Return the coefficient of the variable of type "type" at position "pos"
507 __isl_give isl_val
*isl_aff_get_coefficient_val(__isl_keep isl_aff
*aff
,
508 enum isl_dim_type type
, int pos
)
516 ctx
= isl_aff_get_ctx(aff
);
517 if (type
== isl_dim_out
)
518 isl_die(ctx
, isl_error_invalid
,
519 "output/set dimension does not have a coefficient",
521 if (type
== isl_dim_in
)
524 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
525 isl_die(ctx
, isl_error_invalid
,
526 "position out of bounds", return NULL
);
528 pos
+= isl_local_space_offset(aff
->ls
, type
);
529 v
= isl_val_rat_from_isl_int(ctx
, aff
->v
->el
[1 + pos
], aff
->v
->el
[0]);
530 return isl_val_normalize(v
);
533 __isl_give isl_aff
*isl_aff_set_denominator(__isl_take isl_aff
*aff
, isl_int v
)
535 aff
= isl_aff_cow(aff
);
539 aff
->v
= isl_vec_cow(aff
->v
);
541 return isl_aff_free(aff
);
543 isl_int_set(aff
->v
->el
[0], v
);
548 __isl_give isl_aff
*isl_aff_set_constant(__isl_take isl_aff
*aff
, isl_int v
)
550 aff
= isl_aff_cow(aff
);
554 aff
->v
= isl_vec_cow(aff
->v
);
556 return isl_aff_free(aff
);
558 isl_int_set(aff
->v
->el
[1], v
);
563 /* Replace the constant term of "aff" by "v".
565 __isl_give isl_aff
*isl_aff_set_constant_val(__isl_take isl_aff
*aff
,
566 __isl_take isl_val
*v
)
571 if (!isl_val_is_rat(v
))
572 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
573 "expecting rational value", goto error
);
575 if (isl_int_eq(aff
->v
->el
[1], v
->n
) &&
576 isl_int_eq(aff
->v
->el
[0], v
->d
)) {
581 aff
= isl_aff_cow(aff
);
584 aff
->v
= isl_vec_cow(aff
->v
);
588 if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
589 isl_int_set(aff
->v
->el
[1], v
->n
);
590 } else if (isl_int_is_one(v
->d
)) {
591 isl_int_mul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
593 isl_seq_scale(aff
->v
->el
+ 1,
594 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
595 isl_int_mul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
596 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
597 aff
->v
= isl_vec_normalize(aff
->v
);
610 __isl_give isl_aff
*isl_aff_add_constant(__isl_take isl_aff
*aff
, isl_int v
)
612 if (isl_int_is_zero(v
))
615 aff
= isl_aff_cow(aff
);
619 aff
->v
= isl_vec_cow(aff
->v
);
621 return isl_aff_free(aff
);
623 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
);
628 /* Add "v" to the constant term of "aff".
630 __isl_give isl_aff
*isl_aff_add_constant_val(__isl_take isl_aff
*aff
,
631 __isl_take isl_val
*v
)
636 if (isl_val_is_zero(v
)) {
641 if (!isl_val_is_rat(v
))
642 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
643 "expecting rational value", goto error
);
645 aff
= isl_aff_cow(aff
);
649 aff
->v
= isl_vec_cow(aff
->v
);
653 if (isl_int_is_one(v
->d
)) {
654 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
655 } else if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
656 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], v
->n
);
657 aff
->v
= isl_vec_normalize(aff
->v
);
661 isl_seq_scale(aff
->v
->el
+ 1,
662 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
663 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
664 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
665 aff
->v
= isl_vec_normalize(aff
->v
);
678 __isl_give isl_aff
*isl_aff_add_constant_si(__isl_take isl_aff
*aff
, int v
)
683 isl_int_set_si(t
, v
);
684 aff
= isl_aff_add_constant(aff
, t
);
690 /* Add "v" to the numerator of the constant term of "aff".
692 __isl_give isl_aff
*isl_aff_add_constant_num(__isl_take isl_aff
*aff
, isl_int v
)
694 if (isl_int_is_zero(v
))
697 aff
= isl_aff_cow(aff
);
701 aff
->v
= isl_vec_cow(aff
->v
);
703 return isl_aff_free(aff
);
705 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], v
);
710 /* Add "v" to the numerator of the constant term of "aff".
712 __isl_give isl_aff
*isl_aff_add_constant_num_si(__isl_take isl_aff
*aff
, int v
)
720 isl_int_set_si(t
, v
);
721 aff
= isl_aff_add_constant_num(aff
, t
);
727 __isl_give isl_aff
*isl_aff_set_constant_si(__isl_take isl_aff
*aff
, int v
)
729 aff
= isl_aff_cow(aff
);
733 aff
->v
= isl_vec_cow(aff
->v
);
735 return isl_aff_free(aff
);
737 isl_int_set_si(aff
->v
->el
[1], v
);
742 __isl_give isl_aff
*isl_aff_set_coefficient(__isl_take isl_aff
*aff
,
743 enum isl_dim_type type
, int pos
, isl_int v
)
748 if (type
== isl_dim_out
)
749 isl_die(aff
->v
->ctx
, isl_error_invalid
,
750 "output/set dimension does not have a coefficient",
751 return isl_aff_free(aff
));
752 if (type
== isl_dim_in
)
755 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
756 isl_die(aff
->v
->ctx
, isl_error_invalid
,
757 "position out of bounds", return isl_aff_free(aff
));
759 aff
= isl_aff_cow(aff
);
763 aff
->v
= isl_vec_cow(aff
->v
);
765 return isl_aff_free(aff
);
767 pos
+= isl_local_space_offset(aff
->ls
, type
);
768 isl_int_set(aff
->v
->el
[1 + pos
], v
);
773 __isl_give isl_aff
*isl_aff_set_coefficient_si(__isl_take isl_aff
*aff
,
774 enum isl_dim_type type
, int pos
, int v
)
779 if (type
== isl_dim_out
)
780 isl_die(aff
->v
->ctx
, isl_error_invalid
,
781 "output/set dimension does not have a coefficient",
782 return isl_aff_free(aff
));
783 if (type
== isl_dim_in
)
786 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
787 isl_die(aff
->v
->ctx
, isl_error_invalid
,
788 "position out of bounds", return isl_aff_free(aff
));
790 aff
= isl_aff_cow(aff
);
794 aff
->v
= isl_vec_cow(aff
->v
);
796 return isl_aff_free(aff
);
798 pos
+= isl_local_space_offset(aff
->ls
, type
);
799 isl_int_set_si(aff
->v
->el
[1 + pos
], v
);
804 /* Replace the coefficient of the variable of type "type" at position "pos"
807 __isl_give isl_aff
*isl_aff_set_coefficient_val(__isl_take isl_aff
*aff
,
808 enum isl_dim_type type
, int pos
, __isl_take isl_val
*v
)
813 if (type
== isl_dim_out
)
814 isl_die(aff
->v
->ctx
, isl_error_invalid
,
815 "output/set dimension does not have a coefficient",
817 if (type
== isl_dim_in
)
820 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
821 isl_die(aff
->v
->ctx
, isl_error_invalid
,
822 "position out of bounds", goto error
);
824 if (!isl_val_is_rat(v
))
825 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
826 "expecting rational value", goto error
);
828 pos
+= isl_local_space_offset(aff
->ls
, type
);
829 if (isl_int_eq(aff
->v
->el
[1 + pos
], v
->n
) &&
830 isl_int_eq(aff
->v
->el
[0], v
->d
)) {
835 aff
= isl_aff_cow(aff
);
838 aff
->v
= isl_vec_cow(aff
->v
);
842 if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
843 isl_int_set(aff
->v
->el
[1 + pos
], v
->n
);
844 } else if (isl_int_is_one(v
->d
)) {
845 isl_int_mul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
847 isl_seq_scale(aff
->v
->el
+ 1,
848 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
849 isl_int_mul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
850 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
851 aff
->v
= isl_vec_normalize(aff
->v
);
864 __isl_give isl_aff
*isl_aff_add_coefficient(__isl_take isl_aff
*aff
,
865 enum isl_dim_type type
, int pos
, isl_int v
)
870 if (type
== isl_dim_out
)
871 isl_die(aff
->v
->ctx
, isl_error_invalid
,
872 "output/set dimension does not have a coefficient",
873 return isl_aff_free(aff
));
874 if (type
== isl_dim_in
)
877 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
878 isl_die(aff
->v
->ctx
, isl_error_invalid
,
879 "position out of bounds", return isl_aff_free(aff
));
881 aff
= isl_aff_cow(aff
);
885 aff
->v
= isl_vec_cow(aff
->v
);
887 return isl_aff_free(aff
);
889 pos
+= isl_local_space_offset(aff
->ls
, type
);
890 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
);
895 /* Add "v" to the coefficient of the variable of type "type"
896 * at position "pos" of "aff".
898 __isl_give isl_aff
*isl_aff_add_coefficient_val(__isl_take isl_aff
*aff
,
899 enum isl_dim_type type
, int pos
, __isl_take isl_val
*v
)
904 if (isl_val_is_zero(v
)) {
909 if (type
== isl_dim_out
)
910 isl_die(aff
->v
->ctx
, isl_error_invalid
,
911 "output/set dimension does not have a coefficient",
913 if (type
== isl_dim_in
)
916 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
917 isl_die(aff
->v
->ctx
, isl_error_invalid
,
918 "position out of bounds", goto error
);
920 if (!isl_val_is_rat(v
))
921 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
922 "expecting rational value", goto error
);
924 aff
= isl_aff_cow(aff
);
928 aff
->v
= isl_vec_cow(aff
->v
);
932 pos
+= isl_local_space_offset(aff
->ls
, type
);
933 if (isl_int_is_one(v
->d
)) {
934 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
935 } else if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
936 isl_int_add(aff
->v
->el
[1 + pos
], aff
->v
->el
[1 + pos
], v
->n
);
937 aff
->v
= isl_vec_normalize(aff
->v
);
941 isl_seq_scale(aff
->v
->el
+ 1,
942 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
943 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
944 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
945 aff
->v
= isl_vec_normalize(aff
->v
);
958 __isl_give isl_aff
*isl_aff_add_coefficient_si(__isl_take isl_aff
*aff
,
959 enum isl_dim_type type
, int pos
, int v
)
964 isl_int_set_si(t
, v
);
965 aff
= isl_aff_add_coefficient(aff
, type
, pos
, t
);
971 __isl_give isl_aff
*isl_aff_get_div(__isl_keep isl_aff
*aff
, int pos
)
976 return isl_local_space_get_div(aff
->ls
, pos
);
979 __isl_give isl_aff
*isl_aff_neg(__isl_take isl_aff
*aff
)
981 aff
= isl_aff_cow(aff
);
984 aff
->v
= isl_vec_cow(aff
->v
);
986 return isl_aff_free(aff
);
988 isl_seq_neg(aff
->v
->el
+ 1, aff
->v
->el
+ 1, aff
->v
->size
- 1);
993 /* Remove divs from the local space that do not appear in the affine
995 * We currently only remove divs at the end.
996 * Some intermediate divs may also not appear directly in the affine
997 * expression, but we would also need to check that no other divs are
998 * defined in terms of them.
1000 __isl_give isl_aff
*isl_aff_remove_unused_divs( __isl_take isl_aff
*aff
)
1009 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1010 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1012 pos
= isl_seq_last_non_zero(aff
->v
->el
+ 1 + off
, n
) + 1;
1016 aff
= isl_aff_cow(aff
);
1020 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, isl_dim_div
, pos
, n
- pos
);
1021 aff
->v
= isl_vec_drop_els(aff
->v
, 1 + off
+ pos
, n
- pos
);
1022 if (!aff
->ls
|| !aff
->v
)
1023 return isl_aff_free(aff
);
1028 /* Given two affine expressions "p" of length p_len (including the
1029 * denominator and the constant term) and "subs" of length subs_len,
1030 * plug in "subs" for the variable at position "pos".
1031 * The variables of "subs" and "p" are assumed to match up to subs_len,
1032 * but "p" may have additional variables.
1033 * "v" is an initialized isl_int that can be used internally.
1035 * In particular, if "p" represents the expression
1039 * with i the variable at position "pos" and "subs" represents the expression
1043 * then the result represents the expression
1048 void isl_seq_substitute(isl_int
*p
, int pos
, isl_int
*subs
,
1049 int p_len
, int subs_len
, isl_int v
)
1051 isl_int_set(v
, p
[1 + pos
]);
1052 isl_int_set_si(p
[1 + pos
], 0);
1053 isl_seq_combine(p
+ 1, subs
[0], p
+ 1, v
, subs
+ 1, subs_len
- 1);
1054 isl_seq_scale(p
+ subs_len
, p
+ subs_len
, subs
[0], p_len
- subs_len
);
1055 isl_int_mul(p
[0], p
[0], subs
[0]);
1058 /* Look for any divs in the aff->ls with a denominator equal to one
1059 * and plug them into the affine expression and any subsequent divs
1060 * that may reference the div.
1062 static __isl_give isl_aff
*plug_in_integral_divs(__isl_take isl_aff
*aff
)
1068 isl_local_space
*ls
;
1074 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1076 for (i
= 0; i
< n
; ++i
) {
1077 if (!isl_int_is_one(aff
->ls
->div
->row
[i
][0]))
1079 ls
= isl_local_space_copy(aff
->ls
);
1080 ls
= isl_local_space_substitute_seq(ls
, isl_dim_div
, i
,
1081 aff
->ls
->div
->row
[i
], len
, i
+ 1, n
- (i
+ 1));
1082 vec
= isl_vec_copy(aff
->v
);
1083 vec
= isl_vec_cow(vec
);
1089 pos
= isl_local_space_offset(aff
->ls
, isl_dim_div
) + i
;
1090 isl_seq_substitute(vec
->el
, pos
, aff
->ls
->div
->row
[i
],
1095 isl_vec_free(aff
->v
);
1097 isl_local_space_free(aff
->ls
);
1104 isl_local_space_free(ls
);
1105 return isl_aff_free(aff
);
1108 /* Look for any divs j that appear with a unit coefficient inside
1109 * the definitions of other divs i and plug them into the definitions
1112 * In particular, an expression of the form
1114 * floor((f(..) + floor(g(..)/n))/m)
1118 * floor((n * f(..) + g(..))/(n * m))
1120 * This simplification is correct because we can move the expression
1121 * f(..) into the inner floor in the original expression to obtain
1123 * floor(floor((n * f(..) + g(..))/n)/m)
1125 * from which we can derive the simplified expression.
1127 static __isl_give isl_aff
*plug_in_unit_divs(__isl_take isl_aff
*aff
)
1135 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1136 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1137 for (i
= 1; i
< n
; ++i
) {
1138 for (j
= 0; j
< i
; ++j
) {
1139 if (!isl_int_is_one(aff
->ls
->div
->row
[i
][1 + off
+ j
]))
1141 aff
->ls
= isl_local_space_substitute_seq(aff
->ls
,
1142 isl_dim_div
, j
, aff
->ls
->div
->row
[j
],
1143 aff
->v
->size
, i
, 1);
1145 return isl_aff_free(aff
);
1152 /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
1154 * Even though this function is only called on isl_affs with a single
1155 * reference, we are careful to only change aff->v and aff->ls together.
1157 static __isl_give isl_aff
*swap_div(__isl_take isl_aff
*aff
, int a
, int b
)
1159 unsigned off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1160 isl_local_space
*ls
;
1163 ls
= isl_local_space_copy(aff
->ls
);
1164 ls
= isl_local_space_swap_div(ls
, a
, b
);
1165 v
= isl_vec_copy(aff
->v
);
1170 isl_int_swap(v
->el
[1 + off
+ a
], v
->el
[1 + off
+ b
]);
1171 isl_vec_free(aff
->v
);
1173 isl_local_space_free(aff
->ls
);
1179 isl_local_space_free(ls
);
1180 return isl_aff_free(aff
);
1183 /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
1185 * We currently do not actually remove div "b", but simply add its
1186 * coefficient to that of "a" and then zero it out.
1188 static __isl_give isl_aff
*merge_divs(__isl_take isl_aff
*aff
, int a
, int b
)
1190 unsigned off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1192 if (isl_int_is_zero(aff
->v
->el
[1 + off
+ b
]))
1195 aff
->v
= isl_vec_cow(aff
->v
);
1197 return isl_aff_free(aff
);
1199 isl_int_add(aff
->v
->el
[1 + off
+ a
],
1200 aff
->v
->el
[1 + off
+ a
], aff
->v
->el
[1 + off
+ b
]);
1201 isl_int_set_si(aff
->v
->el
[1 + off
+ b
], 0);
1206 /* Sort the divs in the local space of "aff" according to
1207 * the comparison function "cmp_row" in isl_local_space.c,
1208 * combining the coefficients of identical divs.
1210 * Reordering divs does not change the semantics of "aff",
1211 * so there is no need to call isl_aff_cow.
1212 * Moreover, this function is currently only called on isl_affs
1213 * with a single reference.
1215 static __isl_give isl_aff
*sort_divs(__isl_take isl_aff
*aff
)
1223 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1224 n
= isl_aff_dim(aff
, isl_dim_div
);
1225 for (i
= 1; i
< n
; ++i
) {
1226 for (j
= i
- 1; j
>= 0; --j
) {
1227 int cmp
= isl_mat_cmp_div(aff
->ls
->div
, j
, j
+ 1);
1231 aff
= merge_divs(aff
, j
, j
+ 1);
1233 aff
= swap_div(aff
, j
, j
+ 1);
1242 /* Normalize the representation of "aff".
1244 * This function should only be called of "new" isl_affs, i.e.,
1245 * with only a single reference. We therefore do not need to
1246 * worry about affecting other instances.
1248 __isl_give isl_aff
*isl_aff_normalize(__isl_take isl_aff
*aff
)
1252 aff
->v
= isl_vec_normalize(aff
->v
);
1254 return isl_aff_free(aff
);
1255 aff
= plug_in_integral_divs(aff
);
1256 aff
= plug_in_unit_divs(aff
);
1257 aff
= sort_divs(aff
);
1258 aff
= isl_aff_remove_unused_divs(aff
);
1262 /* Given f, return floor(f).
1263 * If f is an integer expression, then just return f.
1264 * If f is a constant, then return the constant floor(f).
1265 * Otherwise, if f = g/m, write g = q m + r,
1266 * create a new div d = [r/m] and return the expression q + d.
1267 * The coefficients in r are taken to lie between -m/2 and m/2.
1269 __isl_give isl_aff
*isl_aff_floor(__isl_take isl_aff
*aff
)
1279 if (isl_int_is_one(aff
->v
->el
[0]))
1282 aff
= isl_aff_cow(aff
);
1286 aff
->v
= isl_vec_cow(aff
->v
);
1288 return isl_aff_free(aff
);
1290 if (isl_aff_is_cst(aff
)) {
1291 isl_int_fdiv_q(aff
->v
->el
[1], aff
->v
->el
[1], aff
->v
->el
[0]);
1292 isl_int_set_si(aff
->v
->el
[0], 1);
1296 div
= isl_vec_copy(aff
->v
);
1297 div
= isl_vec_cow(div
);
1299 return isl_aff_free(aff
);
1301 ctx
= isl_aff_get_ctx(aff
);
1302 isl_int_fdiv_q(aff
->v
->el
[0], aff
->v
->el
[0], ctx
->two
);
1303 for (i
= 1; i
< aff
->v
->size
; ++i
) {
1304 isl_int_fdiv_r(div
->el
[i
], div
->el
[i
], div
->el
[0]);
1305 isl_int_fdiv_q(aff
->v
->el
[i
], aff
->v
->el
[i
], div
->el
[0]);
1306 if (isl_int_gt(div
->el
[i
], aff
->v
->el
[0])) {
1307 isl_int_sub(div
->el
[i
], div
->el
[i
], div
->el
[0]);
1308 isl_int_add_ui(aff
->v
->el
[i
], aff
->v
->el
[i
], 1);
1312 aff
->ls
= isl_local_space_add_div(aff
->ls
, div
);
1314 return isl_aff_free(aff
);
1316 size
= aff
->v
->size
;
1317 aff
->v
= isl_vec_extend(aff
->v
, size
+ 1);
1319 return isl_aff_free(aff
);
1320 isl_int_set_si(aff
->v
->el
[0], 1);
1321 isl_int_set_si(aff
->v
->el
[size
], 1);
1323 aff
= isl_aff_normalize(aff
);
1330 * aff mod m = aff - m * floor(aff/m)
1332 __isl_give isl_aff
*isl_aff_mod(__isl_take isl_aff
*aff
, isl_int m
)
1336 res
= isl_aff_copy(aff
);
1337 aff
= isl_aff_scale_down(aff
, m
);
1338 aff
= isl_aff_floor(aff
);
1339 aff
= isl_aff_scale(aff
, m
);
1340 res
= isl_aff_sub(res
, aff
);
1347 * aff mod m = aff - m * floor(aff/m)
1349 * with m an integer value.
1351 __isl_give isl_aff
*isl_aff_mod_val(__isl_take isl_aff
*aff
,
1352 __isl_take isl_val
*m
)
1359 if (!isl_val_is_int(m
))
1360 isl_die(isl_val_get_ctx(m
), isl_error_invalid
,
1361 "expecting integer modulo", goto error
);
1363 res
= isl_aff_copy(aff
);
1364 aff
= isl_aff_scale_down_val(aff
, isl_val_copy(m
));
1365 aff
= isl_aff_floor(aff
);
1366 aff
= isl_aff_scale_val(aff
, m
);
1367 res
= isl_aff_sub(res
, aff
);
1378 * pwaff mod m = pwaff - m * floor(pwaff/m)
1380 __isl_give isl_pw_aff
*isl_pw_aff_mod(__isl_take isl_pw_aff
*pwaff
, isl_int m
)
1384 res
= isl_pw_aff_copy(pwaff
);
1385 pwaff
= isl_pw_aff_scale_down(pwaff
, m
);
1386 pwaff
= isl_pw_aff_floor(pwaff
);
1387 pwaff
= isl_pw_aff_scale(pwaff
, m
);
1388 res
= isl_pw_aff_sub(res
, pwaff
);
1395 * pa mod m = pa - m * floor(pa/m)
1397 * with m an integer value.
1399 __isl_give isl_pw_aff
*isl_pw_aff_mod_val(__isl_take isl_pw_aff
*pa
,
1400 __isl_take isl_val
*m
)
1404 if (!isl_val_is_int(m
))
1405 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
1406 "expecting integer modulo", goto error
);
1407 pa
= isl_pw_aff_mod(pa
, m
->n
);
1411 isl_pw_aff_free(pa
);
1416 /* Given f, return ceil(f).
1417 * If f is an integer expression, then just return f.
1418 * Otherwise, let f be the expression
1424 * floor((e + m - 1)/m)
1426 __isl_give isl_aff
*isl_aff_ceil(__isl_take isl_aff
*aff
)
1431 if (isl_int_is_one(aff
->v
->el
[0]))
1434 aff
= isl_aff_cow(aff
);
1437 aff
->v
= isl_vec_cow(aff
->v
);
1439 return isl_aff_free(aff
);
1441 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], aff
->v
->el
[0]);
1442 isl_int_sub_ui(aff
->v
->el
[1], aff
->v
->el
[1], 1);
1443 aff
= isl_aff_floor(aff
);
1448 /* Apply the expansion computed by isl_merge_divs.
1449 * The expansion itself is given by "exp" while the resulting
1450 * list of divs is given by "div".
1452 __isl_give isl_aff
*isl_aff_expand_divs( __isl_take isl_aff
*aff
,
1453 __isl_take isl_mat
*div
, int *exp
)
1460 aff
= isl_aff_cow(aff
);
1464 old_n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1465 new_n_div
= isl_mat_rows(div
);
1466 if (new_n_div
< old_n_div
)
1467 isl_die(isl_mat_get_ctx(div
), isl_error_invalid
,
1468 "not an expansion", goto error
);
1470 aff
->v
= isl_vec_extend(aff
->v
, aff
->v
->size
+ new_n_div
- old_n_div
);
1474 offset
= 1 + isl_local_space_offset(aff
->ls
, isl_dim_div
);
1476 for (i
= new_n_div
- 1; i
>= 0; --i
) {
1477 if (j
>= 0 && exp
[j
] == i
) {
1479 isl_int_swap(aff
->v
->el
[offset
+ i
],
1480 aff
->v
->el
[offset
+ j
]);
1483 isl_int_set_si(aff
->v
->el
[offset
+ i
], 0);
1486 aff
->ls
= isl_local_space_replace_divs(aff
->ls
, isl_mat_copy(div
));
1497 /* Add two affine expressions that live in the same local space.
1499 static __isl_give isl_aff
*add_expanded(__isl_take isl_aff
*aff1
,
1500 __isl_take isl_aff
*aff2
)
1504 aff1
= isl_aff_cow(aff1
);
1508 aff1
->v
= isl_vec_cow(aff1
->v
);
1514 isl_int_gcd(gcd
, aff1
->v
->el
[0], aff2
->v
->el
[0]);
1515 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
1516 isl_seq_scale(aff1
->v
->el
+ 1, aff1
->v
->el
+ 1, f
, aff1
->v
->size
- 1);
1517 isl_int_divexact(f
, aff1
->v
->el
[0], gcd
);
1518 isl_seq_addmul(aff1
->v
->el
+ 1, f
, aff2
->v
->el
+ 1, aff1
->v
->size
- 1);
1519 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
1520 isl_int_mul(aff1
->v
->el
[0], aff1
->v
->el
[0], f
);
1532 __isl_give isl_aff
*isl_aff_add(__isl_take isl_aff
*aff1
,
1533 __isl_take isl_aff
*aff2
)
1544 ctx
= isl_aff_get_ctx(aff1
);
1545 if (!isl_space_is_equal(aff1
->ls
->dim
, aff2
->ls
->dim
))
1546 isl_die(ctx
, isl_error_invalid
,
1547 "spaces don't match", goto error
);
1549 n_div1
= isl_aff_dim(aff1
, isl_dim_div
);
1550 n_div2
= isl_aff_dim(aff2
, isl_dim_div
);
1551 if (n_div1
== 0 && n_div2
== 0)
1552 return add_expanded(aff1
, aff2
);
1554 exp1
= isl_alloc_array(ctx
, int, n_div1
);
1555 exp2
= isl_alloc_array(ctx
, int, n_div2
);
1556 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1559 div
= isl_merge_divs(aff1
->ls
->div
, aff2
->ls
->div
, exp1
, exp2
);
1560 aff1
= isl_aff_expand_divs(aff1
, isl_mat_copy(div
), exp1
);
1561 aff2
= isl_aff_expand_divs(aff2
, div
, exp2
);
1565 return add_expanded(aff1
, aff2
);
1574 __isl_give isl_aff
*isl_aff_sub(__isl_take isl_aff
*aff1
,
1575 __isl_take isl_aff
*aff2
)
1577 return isl_aff_add(aff1
, isl_aff_neg(aff2
));
1580 __isl_give isl_aff
*isl_aff_scale(__isl_take isl_aff
*aff
, isl_int f
)
1584 if (isl_int_is_one(f
))
1587 aff
= isl_aff_cow(aff
);
1590 aff
->v
= isl_vec_cow(aff
->v
);
1592 return isl_aff_free(aff
);
1594 if (isl_int_is_pos(f
) && isl_int_is_divisible_by(aff
->v
->el
[0], f
)) {
1595 isl_int_divexact(aff
->v
->el
[0], aff
->v
->el
[0], f
);
1600 isl_int_gcd(gcd
, aff
->v
->el
[0], f
);
1601 isl_int_divexact(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
1602 isl_int_divexact(gcd
, f
, gcd
);
1603 isl_seq_scale(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
1609 /* Multiple "aff" by "v".
1611 __isl_give isl_aff
*isl_aff_scale_val(__isl_take isl_aff
*aff
,
1612 __isl_take isl_val
*v
)
1617 if (isl_val_is_one(v
)) {
1622 if (!isl_val_is_rat(v
))
1623 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1624 "expecting rational factor", goto error
);
1626 aff
= isl_aff_scale(aff
, v
->n
);
1627 aff
= isl_aff_scale_down(aff
, v
->d
);
1637 __isl_give isl_aff
*isl_aff_scale_down(__isl_take isl_aff
*aff
, isl_int f
)
1641 if (isl_int_is_one(f
))
1644 aff
= isl_aff_cow(aff
);
1648 if (isl_int_is_zero(f
))
1649 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1650 "cannot scale down by zero", return isl_aff_free(aff
));
1652 aff
->v
= isl_vec_cow(aff
->v
);
1654 return isl_aff_free(aff
);
1657 isl_seq_gcd(aff
->v
->el
+ 1, aff
->v
->size
- 1, &gcd
);
1658 isl_int_gcd(gcd
, gcd
, f
);
1659 isl_seq_scale_down(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
1660 isl_int_divexact(gcd
, f
, gcd
);
1661 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
1667 /* Divide "aff" by "v".
1669 __isl_give isl_aff
*isl_aff_scale_down_val(__isl_take isl_aff
*aff
,
1670 __isl_take isl_val
*v
)
1675 if (isl_val_is_one(v
)) {
1680 if (!isl_val_is_rat(v
))
1681 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1682 "expecting rational factor", goto error
);
1683 if (!isl_val_is_pos(v
))
1684 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1685 "factor needs to be positive", goto error
);
1687 aff
= isl_aff_scale(aff
, v
->d
);
1688 aff
= isl_aff_scale_down(aff
, v
->n
);
1698 __isl_give isl_aff
*isl_aff_scale_down_ui(__isl_take isl_aff
*aff
, unsigned f
)
1706 isl_int_set_ui(v
, f
);
1707 aff
= isl_aff_scale_down(aff
, v
);
1713 __isl_give isl_aff
*isl_aff_set_dim_name(__isl_take isl_aff
*aff
,
1714 enum isl_dim_type type
, unsigned pos
, const char *s
)
1716 aff
= isl_aff_cow(aff
);
1719 if (type
== isl_dim_out
)
1720 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1721 "cannot set name of output/set dimension",
1722 return isl_aff_free(aff
));
1723 if (type
== isl_dim_in
)
1725 aff
->ls
= isl_local_space_set_dim_name(aff
->ls
, type
, pos
, s
);
1727 return isl_aff_free(aff
);
1732 __isl_give isl_aff
*isl_aff_set_dim_id(__isl_take isl_aff
*aff
,
1733 enum isl_dim_type type
, unsigned pos
, __isl_take isl_id
*id
)
1735 aff
= isl_aff_cow(aff
);
1737 return isl_id_free(id
);
1738 if (type
== isl_dim_out
)
1739 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1740 "cannot set name of output/set dimension",
1742 if (type
== isl_dim_in
)
1744 aff
->ls
= isl_local_space_set_dim_id(aff
->ls
, type
, pos
, id
);
1746 return isl_aff_free(aff
);
1755 /* Exploit the equalities in "eq" to simplify the affine expression
1756 * and the expressions of the integer divisions in the local space.
1757 * The integer divisions in this local space are assumed to appear
1758 * as regular dimensions in "eq".
1760 static __isl_give isl_aff
*isl_aff_substitute_equalities_lifted(
1761 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
1769 if (eq
->n_eq
== 0) {
1770 isl_basic_set_free(eq
);
1774 aff
= isl_aff_cow(aff
);
1778 aff
->ls
= isl_local_space_substitute_equalities(aff
->ls
,
1779 isl_basic_set_copy(eq
));
1780 aff
->v
= isl_vec_cow(aff
->v
);
1781 if (!aff
->ls
|| !aff
->v
)
1784 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
1786 for (i
= 0; i
< eq
->n_eq
; ++i
) {
1787 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
1788 if (j
< 0 || j
== 0 || j
>= total
)
1791 isl_seq_elim(aff
->v
->el
+ 1, eq
->eq
[i
], j
, total
,
1795 isl_basic_set_free(eq
);
1796 aff
= isl_aff_normalize(aff
);
1799 isl_basic_set_free(eq
);
1804 /* Exploit the equalities in "eq" to simplify the affine expression
1805 * and the expressions of the integer divisions in the local space.
1807 static __isl_give isl_aff
*isl_aff_substitute_equalities(
1808 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
1814 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1816 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, n_div
);
1817 return isl_aff_substitute_equalities_lifted(aff
, eq
);
1819 isl_basic_set_free(eq
);
1824 /* Look for equalities among the variables shared by context and aff
1825 * and the integer divisions of aff, if any.
1826 * The equalities are then used to eliminate coefficients and/or integer
1827 * divisions from aff.
1829 __isl_give isl_aff
*isl_aff_gist(__isl_take isl_aff
*aff
,
1830 __isl_take isl_set
*context
)
1832 isl_basic_set
*hull
;
1837 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1839 isl_basic_set
*bset
;
1840 isl_local_space
*ls
;
1841 context
= isl_set_add_dims(context
, isl_dim_set
, n_div
);
1842 ls
= isl_aff_get_domain_local_space(aff
);
1843 bset
= isl_basic_set_from_local_space(ls
);
1844 bset
= isl_basic_set_lift(bset
);
1845 bset
= isl_basic_set_flatten(bset
);
1846 context
= isl_set_intersect(context
,
1847 isl_set_from_basic_set(bset
));
1850 hull
= isl_set_affine_hull(context
);
1851 return isl_aff_substitute_equalities_lifted(aff
, hull
);
1854 isl_set_free(context
);
1858 __isl_give isl_aff
*isl_aff_gist_params(__isl_take isl_aff
*aff
,
1859 __isl_take isl_set
*context
)
1861 isl_set
*dom_context
= isl_set_universe(isl_aff_get_domain_space(aff
));
1862 dom_context
= isl_set_intersect_params(dom_context
, context
);
1863 return isl_aff_gist(aff
, dom_context
);
1866 /* Return a basic set containing those elements in the space
1867 * of aff where it is non-negative.
1868 * If "rational" is set, then return a rational basic set.
1870 static __isl_give isl_basic_set
*aff_nonneg_basic_set(
1871 __isl_take isl_aff
*aff
, int rational
)
1873 isl_constraint
*ineq
;
1874 isl_basic_set
*bset
;
1876 ineq
= isl_inequality_from_aff(aff
);
1878 bset
= isl_basic_set_from_constraint(ineq
);
1880 bset
= isl_basic_set_set_rational(bset
);
1881 bset
= isl_basic_set_simplify(bset
);
1885 /* Return a basic set containing those elements in the space
1886 * of aff where it is non-negative.
1888 __isl_give isl_basic_set
*isl_aff_nonneg_basic_set(__isl_take isl_aff
*aff
)
1890 return aff_nonneg_basic_set(aff
, 0);
1893 /* Return a basic set containing those elements in the domain space
1894 * of aff where it is negative.
1896 __isl_give isl_basic_set
*isl_aff_neg_basic_set(__isl_take isl_aff
*aff
)
1898 aff
= isl_aff_neg(aff
);
1899 aff
= isl_aff_add_constant_num_si(aff
, -1);
1900 return isl_aff_nonneg_basic_set(aff
);
1903 /* Return a basic set containing those elements in the space
1904 * of aff where it is zero.
1905 * If "rational" is set, then return a rational basic set.
1907 static __isl_give isl_basic_set
*aff_zero_basic_set(__isl_take isl_aff
*aff
,
1910 isl_constraint
*ineq
;
1911 isl_basic_set
*bset
;
1913 ineq
= isl_equality_from_aff(aff
);
1915 bset
= isl_basic_set_from_constraint(ineq
);
1917 bset
= isl_basic_set_set_rational(bset
);
1918 bset
= isl_basic_set_simplify(bset
);
1922 /* Return a basic set containing those elements in the space
1923 * of aff where it is zero.
1925 __isl_give isl_basic_set
*isl_aff_zero_basic_set(__isl_take isl_aff
*aff
)
1927 return aff_zero_basic_set(aff
, 0);
1930 /* Return a basic set containing those elements in the shared space
1931 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1933 __isl_give isl_basic_set
*isl_aff_ge_basic_set(__isl_take isl_aff
*aff1
,
1934 __isl_take isl_aff
*aff2
)
1936 aff1
= isl_aff_sub(aff1
, aff2
);
1938 return isl_aff_nonneg_basic_set(aff1
);
1941 /* Return a basic set containing those elements in the shared space
1942 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1944 __isl_give isl_basic_set
*isl_aff_le_basic_set(__isl_take isl_aff
*aff1
,
1945 __isl_take isl_aff
*aff2
)
1947 return isl_aff_ge_basic_set(aff2
, aff1
);
1950 __isl_give isl_aff
*isl_aff_add_on_domain(__isl_keep isl_set
*dom
,
1951 __isl_take isl_aff
*aff1
, __isl_take isl_aff
*aff2
)
1953 aff1
= isl_aff_add(aff1
, aff2
);
1954 aff1
= isl_aff_gist(aff1
, isl_set_copy(dom
));
1958 int isl_aff_is_empty(__isl_keep isl_aff
*aff
)
1966 /* Check whether the given affine expression has non-zero coefficient
1967 * for any dimension in the given range or if any of these dimensions
1968 * appear with non-zero coefficients in any of the integer divisions
1969 * involved in the affine expression.
1971 int isl_aff_involves_dims(__isl_keep isl_aff
*aff
,
1972 enum isl_dim_type type
, unsigned first
, unsigned n
)
1984 ctx
= isl_aff_get_ctx(aff
);
1985 if (first
+ n
> isl_aff_dim(aff
, type
))
1986 isl_die(ctx
, isl_error_invalid
,
1987 "range out of bounds", return -1);
1989 active
= isl_local_space_get_active(aff
->ls
, aff
->v
->el
+ 2);
1993 first
+= isl_local_space_offset(aff
->ls
, type
) - 1;
1994 for (i
= 0; i
< n
; ++i
)
1995 if (active
[first
+ i
]) {
2008 __isl_give isl_aff
*isl_aff_drop_dims(__isl_take isl_aff
*aff
,
2009 enum isl_dim_type type
, unsigned first
, unsigned n
)
2015 if (type
== isl_dim_out
)
2016 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2017 "cannot drop output/set dimension",
2018 return isl_aff_free(aff
));
2019 if (type
== isl_dim_in
)
2021 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
2024 ctx
= isl_aff_get_ctx(aff
);
2025 if (first
+ n
> isl_local_space_dim(aff
->ls
, type
))
2026 isl_die(ctx
, isl_error_invalid
, "range out of bounds",
2027 return isl_aff_free(aff
));
2029 aff
= isl_aff_cow(aff
);
2033 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, type
, first
, n
);
2035 return isl_aff_free(aff
);
2037 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
2038 aff
->v
= isl_vec_drop_els(aff
->v
, first
, n
);
2040 return isl_aff_free(aff
);
2045 /* Project the domain of the affine expression onto its parameter space.
2046 * The affine expression may not involve any of the domain dimensions.
2048 __isl_give isl_aff
*isl_aff_project_domain_on_params(__isl_take isl_aff
*aff
)
2054 n
= isl_aff_dim(aff
, isl_dim_in
);
2055 involves
= isl_aff_involves_dims(aff
, isl_dim_in
, 0, n
);
2057 return isl_aff_free(aff
);
2059 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2060 "affine expression involves some of the domain dimensions",
2061 return isl_aff_free(aff
));
2062 aff
= isl_aff_drop_dims(aff
, isl_dim_in
, 0, n
);
2063 space
= isl_aff_get_domain_space(aff
);
2064 space
= isl_space_params(space
);
2065 aff
= isl_aff_reset_domain_space(aff
, space
);
2069 __isl_give isl_aff
*isl_aff_insert_dims(__isl_take isl_aff
*aff
,
2070 enum isl_dim_type type
, unsigned first
, unsigned n
)
2076 if (type
== isl_dim_out
)
2077 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2078 "cannot insert output/set dimensions",
2079 return isl_aff_free(aff
));
2080 if (type
== isl_dim_in
)
2082 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
2085 ctx
= isl_aff_get_ctx(aff
);
2086 if (first
> isl_local_space_dim(aff
->ls
, type
))
2087 isl_die(ctx
, isl_error_invalid
, "position out of bounds",
2088 return isl_aff_free(aff
));
2090 aff
= isl_aff_cow(aff
);
2094 aff
->ls
= isl_local_space_insert_dims(aff
->ls
, type
, first
, n
);
2096 return isl_aff_free(aff
);
2098 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
2099 aff
->v
= isl_vec_insert_zero_els(aff
->v
, first
, n
);
2101 return isl_aff_free(aff
);
2106 __isl_give isl_aff
*isl_aff_add_dims(__isl_take isl_aff
*aff
,
2107 enum isl_dim_type type
, unsigned n
)
2111 pos
= isl_aff_dim(aff
, type
);
2113 return isl_aff_insert_dims(aff
, type
, pos
, n
);
2116 __isl_give isl_pw_aff
*isl_pw_aff_add_dims(__isl_take isl_pw_aff
*pwaff
,
2117 enum isl_dim_type type
, unsigned n
)
2121 pos
= isl_pw_aff_dim(pwaff
, type
);
2123 return isl_pw_aff_insert_dims(pwaff
, type
, pos
, n
);
2126 /* Move the "n" dimensions of "src_type" starting at "src_pos" of "aff"
2127 * to dimensions of "dst_type" at "dst_pos".
2129 * We only support moving input dimensions to parameters and vice versa.
2131 __isl_give isl_aff
*isl_aff_move_dims(__isl_take isl_aff
*aff
,
2132 enum isl_dim_type dst_type
, unsigned dst_pos
,
2133 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2141 !isl_local_space_is_named_or_nested(aff
->ls
, src_type
) &&
2142 !isl_local_space_is_named_or_nested(aff
->ls
, dst_type
))
2145 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
2146 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2147 "cannot move output/set dimension", isl_aff_free(aff
));
2148 if (dst_type
== isl_dim_div
|| src_type
== isl_dim_div
)
2149 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2150 "cannot move divs", isl_aff_free(aff
));
2151 if (dst_type
== isl_dim_in
)
2152 dst_type
= isl_dim_set
;
2153 if (src_type
== isl_dim_in
)
2154 src_type
= isl_dim_set
;
2156 if (src_pos
+ n
> isl_local_space_dim(aff
->ls
, src_type
))
2157 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2158 "range out of bounds", isl_aff_free(aff
));
2159 if (dst_type
== src_type
)
2160 isl_die(isl_aff_get_ctx(aff
), isl_error_unsupported
,
2161 "moving dims within the same type not supported",
2164 aff
= isl_aff_cow(aff
);
2168 g_src_pos
= 1 + isl_local_space_offset(aff
->ls
, src_type
) + src_pos
;
2169 g_dst_pos
= 1 + isl_local_space_offset(aff
->ls
, dst_type
) + dst_pos
;
2170 if (dst_type
> src_type
)
2173 aff
->v
= isl_vec_move_els(aff
->v
, g_dst_pos
, g_src_pos
, n
);
2174 aff
->ls
= isl_local_space_move_dims(aff
->ls
, dst_type
, dst_pos
,
2175 src_type
, src_pos
, n
);
2176 if (!aff
->v
|| !aff
->ls
)
2177 return isl_aff_free(aff
);
2179 aff
= sort_divs(aff
);
2184 __isl_give isl_pw_aff
*isl_pw_aff_from_aff(__isl_take isl_aff
*aff
)
2186 isl_set
*dom
= isl_set_universe(isl_aff_get_domain_space(aff
));
2187 return isl_pw_aff_alloc(dom
, aff
);
2191 #define PW isl_pw_aff
2195 #define EL_IS_ZERO is_empty
2199 #define IS_ZERO is_empty
2202 #undef DEFAULT_IS_ZERO
2203 #define DEFAULT_IS_ZERO 0
2210 #include <isl_pw_templ.c>
2212 static __isl_give isl_set
*align_params_pw_pw_set_and(
2213 __isl_take isl_pw_aff
*pwaff1
, __isl_take isl_pw_aff
*pwaff2
,
2214 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
2215 __isl_take isl_pw_aff
*pwaff2
))
2217 if (!pwaff1
|| !pwaff2
)
2219 if (isl_space_match(pwaff1
->dim
, isl_dim_param
,
2220 pwaff2
->dim
, isl_dim_param
))
2221 return fn(pwaff1
, pwaff2
);
2222 if (!isl_space_has_named_params(pwaff1
->dim
) ||
2223 !isl_space_has_named_params(pwaff2
->dim
))
2224 isl_die(isl_pw_aff_get_ctx(pwaff1
), isl_error_invalid
,
2225 "unaligned unnamed parameters", goto error
);
2226 pwaff1
= isl_pw_aff_align_params(pwaff1
, isl_pw_aff_get_space(pwaff2
));
2227 pwaff2
= isl_pw_aff_align_params(pwaff2
, isl_pw_aff_get_space(pwaff1
));
2228 return fn(pwaff1
, pwaff2
);
2230 isl_pw_aff_free(pwaff1
);
2231 isl_pw_aff_free(pwaff2
);
2235 /* Compute a piecewise quasi-affine expression with a domain that
2236 * is the union of those of pwaff1 and pwaff2 and such that on each
2237 * cell, the quasi-affine expression is the better (according to cmp)
2238 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
2239 * is defined on a given cell, then the associated expression
2240 * is the defined one.
2242 static __isl_give isl_pw_aff
*pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
2243 __isl_take isl_pw_aff
*pwaff2
,
2244 __isl_give isl_basic_set
*(*cmp
)(__isl_take isl_aff
*aff1
,
2245 __isl_take isl_aff
*aff2
))
2252 if (!pwaff1
|| !pwaff2
)
2255 ctx
= isl_space_get_ctx(pwaff1
->dim
);
2256 if (!isl_space_is_equal(pwaff1
->dim
, pwaff2
->dim
))
2257 isl_die(ctx
, isl_error_invalid
,
2258 "arguments should live in same space", goto error
);
2260 if (isl_pw_aff_is_empty(pwaff1
)) {
2261 isl_pw_aff_free(pwaff1
);
2265 if (isl_pw_aff_is_empty(pwaff2
)) {
2266 isl_pw_aff_free(pwaff2
);
2270 n
= 2 * (pwaff1
->n
+ 1) * (pwaff2
->n
+ 1);
2271 res
= isl_pw_aff_alloc_size(isl_space_copy(pwaff1
->dim
), n
);
2273 for (i
= 0; i
< pwaff1
->n
; ++i
) {
2274 set
= isl_set_copy(pwaff1
->p
[i
].set
);
2275 for (j
= 0; j
< pwaff2
->n
; ++j
) {
2276 struct isl_set
*common
;
2279 common
= isl_set_intersect(
2280 isl_set_copy(pwaff1
->p
[i
].set
),
2281 isl_set_copy(pwaff2
->p
[j
].set
));
2282 better
= isl_set_from_basic_set(cmp(
2283 isl_aff_copy(pwaff2
->p
[j
].aff
),
2284 isl_aff_copy(pwaff1
->p
[i
].aff
)));
2285 better
= isl_set_intersect(common
, better
);
2286 if (isl_set_plain_is_empty(better
)) {
2287 isl_set_free(better
);
2290 set
= isl_set_subtract(set
, isl_set_copy(better
));
2292 res
= isl_pw_aff_add_piece(res
, better
,
2293 isl_aff_copy(pwaff2
->p
[j
].aff
));
2295 res
= isl_pw_aff_add_piece(res
, set
,
2296 isl_aff_copy(pwaff1
->p
[i
].aff
));
2299 for (j
= 0; j
< pwaff2
->n
; ++j
) {
2300 set
= isl_set_copy(pwaff2
->p
[j
].set
);
2301 for (i
= 0; i
< pwaff1
->n
; ++i
)
2302 set
= isl_set_subtract(set
,
2303 isl_set_copy(pwaff1
->p
[i
].set
));
2304 res
= isl_pw_aff_add_piece(res
, set
,
2305 isl_aff_copy(pwaff2
->p
[j
].aff
));
2308 isl_pw_aff_free(pwaff1
);
2309 isl_pw_aff_free(pwaff2
);
2313 isl_pw_aff_free(pwaff1
);
2314 isl_pw_aff_free(pwaff2
);
2318 /* Compute a piecewise quasi-affine expression with a domain that
2319 * is the union of those of pwaff1 and pwaff2 and such that on each
2320 * cell, the quasi-affine expression is the maximum of those of pwaff1
2321 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2322 * cell, then the associated expression is the defined one.
2324 static __isl_give isl_pw_aff
*pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
2325 __isl_take isl_pw_aff
*pwaff2
)
2327 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_ge_basic_set
);
2330 __isl_give isl_pw_aff
*isl_pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
2331 __isl_take isl_pw_aff
*pwaff2
)
2333 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
2337 /* Compute a piecewise quasi-affine expression with a domain that
2338 * is the union of those of pwaff1 and pwaff2 and such that on each
2339 * cell, the quasi-affine expression is the minimum of those of pwaff1
2340 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2341 * cell, then the associated expression is the defined one.
2343 static __isl_give isl_pw_aff
*pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
2344 __isl_take isl_pw_aff
*pwaff2
)
2346 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_le_basic_set
);
2349 __isl_give isl_pw_aff
*isl_pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
2350 __isl_take isl_pw_aff
*pwaff2
)
2352 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
2356 __isl_give isl_pw_aff
*isl_pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
2357 __isl_take isl_pw_aff
*pwaff2
, int max
)
2360 return isl_pw_aff_union_max(pwaff1
, pwaff2
);
2362 return isl_pw_aff_union_min(pwaff1
, pwaff2
);
2365 /* Construct a map with as domain the domain of pwaff and
2366 * one-dimensional range corresponding to the affine expressions.
2368 static __isl_give isl_map
*map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2377 dim
= isl_pw_aff_get_space(pwaff
);
2378 map
= isl_map_empty(dim
);
2380 for (i
= 0; i
< pwaff
->n
; ++i
) {
2381 isl_basic_map
*bmap
;
2384 bmap
= isl_basic_map_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
2385 map_i
= isl_map_from_basic_map(bmap
);
2386 map_i
= isl_map_intersect_domain(map_i
,
2387 isl_set_copy(pwaff
->p
[i
].set
));
2388 map
= isl_map_union_disjoint(map
, map_i
);
2391 isl_pw_aff_free(pwaff
);
2396 /* Construct a map with as domain the domain of pwaff and
2397 * one-dimensional range corresponding to the affine expressions.
2399 __isl_give isl_map
*isl_map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2403 if (isl_space_is_set(pwaff
->dim
))
2404 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
2405 "space of input is not a map",
2406 return isl_pw_aff_free(pwaff
));
2407 return map_from_pw_aff(pwaff
);
2410 /* Construct a one-dimensional set with as parameter domain
2411 * the domain of pwaff and the single set dimension
2412 * corresponding to the affine expressions.
2414 __isl_give isl_set
*isl_set_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2418 if (!isl_space_is_set(pwaff
->dim
))
2419 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
2420 "space of input is not a set",
2421 return isl_pw_aff_free(pwaff
));
2422 return map_from_pw_aff(pwaff
);
2425 /* Return a set containing those elements in the domain
2426 * of pwaff where it is non-negative.
2428 __isl_give isl_set
*isl_pw_aff_nonneg_set(__isl_take isl_pw_aff
*pwaff
)
2436 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
2438 for (i
= 0; i
< pwaff
->n
; ++i
) {
2439 isl_basic_set
*bset
;
2443 rational
= isl_set_has_rational(pwaff
->p
[i
].set
);
2444 bset
= aff_nonneg_basic_set(isl_aff_copy(pwaff
->p
[i
].aff
),
2446 set_i
= isl_set_from_basic_set(bset
);
2447 set_i
= isl_set_intersect(set_i
, isl_set_copy(pwaff
->p
[i
].set
));
2448 set
= isl_set_union_disjoint(set
, set_i
);
2451 isl_pw_aff_free(pwaff
);
2456 /* Return a set containing those elements in the domain
2457 * of pwaff where it is zero (if complement is 0) or not zero
2458 * (if complement is 1).
2460 static __isl_give isl_set
*pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
,
2469 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
2471 for (i
= 0; i
< pwaff
->n
; ++i
) {
2472 isl_basic_set
*bset
;
2473 isl_set
*set_i
, *zero
;
2476 rational
= isl_set_has_rational(pwaff
->p
[i
].set
);
2477 bset
= aff_zero_basic_set(isl_aff_copy(pwaff
->p
[i
].aff
),
2479 zero
= isl_set_from_basic_set(bset
);
2480 set_i
= isl_set_copy(pwaff
->p
[i
].set
);
2482 set_i
= isl_set_subtract(set_i
, zero
);
2484 set_i
= isl_set_intersect(set_i
, zero
);
2485 set
= isl_set_union_disjoint(set
, set_i
);
2488 isl_pw_aff_free(pwaff
);
2493 /* Return a set containing those elements in the domain
2494 * of pwaff where it is zero.
2496 __isl_give isl_set
*isl_pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
)
2498 return pw_aff_zero_set(pwaff
, 0);
2501 /* Return a set containing those elements in the domain
2502 * of pwaff where it is not zero.
2504 __isl_give isl_set
*isl_pw_aff_non_zero_set(__isl_take isl_pw_aff
*pwaff
)
2506 return pw_aff_zero_set(pwaff
, 1);
2509 /* Return a set containing those elements in the shared domain
2510 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
2512 * We compute the difference on the shared domain and then construct
2513 * the set of values where this difference is non-negative.
2514 * If strict is set, we first subtract 1 from the difference.
2515 * If equal is set, we only return the elements where pwaff1 and pwaff2
2518 static __isl_give isl_set
*pw_aff_gte_set(__isl_take isl_pw_aff
*pwaff1
,
2519 __isl_take isl_pw_aff
*pwaff2
, int strict
, int equal
)
2521 isl_set
*set1
, *set2
;
2523 set1
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
));
2524 set2
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
));
2525 set1
= isl_set_intersect(set1
, set2
);
2526 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, isl_set_copy(set1
));
2527 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, isl_set_copy(set1
));
2528 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_neg(pwaff2
));
2531 isl_space
*dim
= isl_set_get_space(set1
);
2533 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(dim
));
2534 aff
= isl_aff_add_constant_si(aff
, -1);
2535 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_alloc(set1
, aff
));
2540 return isl_pw_aff_zero_set(pwaff1
);
2541 return isl_pw_aff_nonneg_set(pwaff1
);
2544 /* Return a set containing those elements in the shared domain
2545 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
2547 static __isl_give isl_set
*pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
2548 __isl_take isl_pw_aff
*pwaff2
)
2550 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 1);
2553 __isl_give isl_set
*isl_pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
2554 __isl_take isl_pw_aff
*pwaff2
)
2556 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_eq_set
);
2559 /* Return a set containing those elements in the shared domain
2560 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
2562 static __isl_give isl_set
*pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
2563 __isl_take isl_pw_aff
*pwaff2
)
2565 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 0);
2568 __isl_give isl_set
*isl_pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
2569 __isl_take isl_pw_aff
*pwaff2
)
2571 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ge_set
);
2574 /* Return a set containing those elements in the shared domain
2575 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
2577 static __isl_give isl_set
*pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
2578 __isl_take isl_pw_aff
*pwaff2
)
2580 return pw_aff_gte_set(pwaff1
, pwaff2
, 1, 0);
2583 __isl_give isl_set
*isl_pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
2584 __isl_take isl_pw_aff
*pwaff2
)
2586 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_gt_set
);
2589 __isl_give isl_set
*isl_pw_aff_le_set(__isl_take isl_pw_aff
*pwaff1
,
2590 __isl_take isl_pw_aff
*pwaff2
)
2592 return isl_pw_aff_ge_set(pwaff2
, pwaff1
);
2595 __isl_give isl_set
*isl_pw_aff_lt_set(__isl_take isl_pw_aff
*pwaff1
,
2596 __isl_take isl_pw_aff
*pwaff2
)
2598 return isl_pw_aff_gt_set(pwaff2
, pwaff1
);
2601 /* Return a set containing those elements in the shared domain
2602 * of the elements of list1 and list2 where each element in list1
2603 * has the relation specified by "fn" with each element in list2.
2605 static __isl_give isl_set
*pw_aff_list_set(__isl_take isl_pw_aff_list
*list1
,
2606 __isl_take isl_pw_aff_list
*list2
,
2607 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
2608 __isl_take isl_pw_aff
*pwaff2
))
2614 if (!list1
|| !list2
)
2617 ctx
= isl_pw_aff_list_get_ctx(list1
);
2618 if (list1
->n
< 1 || list2
->n
< 1)
2619 isl_die(ctx
, isl_error_invalid
,
2620 "list should contain at least one element", goto error
);
2622 set
= isl_set_universe(isl_pw_aff_get_domain_space(list1
->p
[0]));
2623 for (i
= 0; i
< list1
->n
; ++i
)
2624 for (j
= 0; j
< list2
->n
; ++j
) {
2627 set_ij
= fn(isl_pw_aff_copy(list1
->p
[i
]),
2628 isl_pw_aff_copy(list2
->p
[j
]));
2629 set
= isl_set_intersect(set
, set_ij
);
2632 isl_pw_aff_list_free(list1
);
2633 isl_pw_aff_list_free(list2
);
2636 isl_pw_aff_list_free(list1
);
2637 isl_pw_aff_list_free(list2
);
2641 /* Return a set containing those elements in the shared domain
2642 * of the elements of list1 and list2 where each element in list1
2643 * is equal to each element in list2.
2645 __isl_give isl_set
*isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list
*list1
,
2646 __isl_take isl_pw_aff_list
*list2
)
2648 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_eq_set
);
2651 __isl_give isl_set
*isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list
*list1
,
2652 __isl_take isl_pw_aff_list
*list2
)
2654 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ne_set
);
2657 /* Return a set containing those elements in the shared domain
2658 * of the elements of list1 and list2 where each element in list1
2659 * is less than or equal to each element in list2.
2661 __isl_give isl_set
*isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list
*list1
,
2662 __isl_take isl_pw_aff_list
*list2
)
2664 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_le_set
);
2667 __isl_give isl_set
*isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list
*list1
,
2668 __isl_take isl_pw_aff_list
*list2
)
2670 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_lt_set
);
2673 __isl_give isl_set
*isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list
*list1
,
2674 __isl_take isl_pw_aff_list
*list2
)
2676 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ge_set
);
2679 __isl_give isl_set
*isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list
*list1
,
2680 __isl_take isl_pw_aff_list
*list2
)
2682 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_gt_set
);
2686 /* Return a set containing those elements in the shared domain
2687 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
2689 static __isl_give isl_set
*pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
2690 __isl_take isl_pw_aff
*pwaff2
)
2692 isl_set
*set_lt
, *set_gt
;
2694 set_lt
= isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1
),
2695 isl_pw_aff_copy(pwaff2
));
2696 set_gt
= isl_pw_aff_gt_set(pwaff1
, pwaff2
);
2697 return isl_set_union_disjoint(set_lt
, set_gt
);
2700 __isl_give isl_set
*isl_pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
2701 __isl_take isl_pw_aff
*pwaff2
)
2703 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ne_set
);
2706 __isl_give isl_pw_aff
*isl_pw_aff_scale_down(__isl_take isl_pw_aff
*pwaff
,
2711 if (isl_int_is_one(v
))
2713 if (!isl_int_is_pos(v
))
2714 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
2715 "factor needs to be positive",
2716 return isl_pw_aff_free(pwaff
));
2717 pwaff
= isl_pw_aff_cow(pwaff
);
2723 for (i
= 0; i
< pwaff
->n
; ++i
) {
2724 pwaff
->p
[i
].aff
= isl_aff_scale_down(pwaff
->p
[i
].aff
, v
);
2725 if (!pwaff
->p
[i
].aff
)
2726 return isl_pw_aff_free(pwaff
);
2732 /* Divide "pa" by "f".
2734 __isl_give isl_pw_aff
*isl_pw_aff_scale_down_val(__isl_take isl_pw_aff
*pa
,
2735 __isl_take isl_val
*f
)
2742 if (isl_val_is_one(f
)) {
2747 if (!isl_val_is_rat(f
))
2748 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
2749 "expecting rational factor", goto error
);
2750 if (!isl_val_is_pos(f
))
2751 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
2752 "factor needs to be positive", goto error
);
2754 pa
= isl_pw_aff_cow(pa
);
2760 for (i
= 0; i
< pa
->n
; ++i
) {
2761 pa
->p
[i
].aff
= isl_aff_scale_down_val(pa
->p
[i
].aff
,
2770 isl_pw_aff_free(pa
);
2775 __isl_give isl_pw_aff
*isl_pw_aff_floor(__isl_take isl_pw_aff
*pwaff
)
2779 pwaff
= isl_pw_aff_cow(pwaff
);
2785 for (i
= 0; i
< pwaff
->n
; ++i
) {
2786 pwaff
->p
[i
].aff
= isl_aff_floor(pwaff
->p
[i
].aff
);
2787 if (!pwaff
->p
[i
].aff
)
2788 return isl_pw_aff_free(pwaff
);
2794 __isl_give isl_pw_aff
*isl_pw_aff_ceil(__isl_take isl_pw_aff
*pwaff
)
2798 pwaff
= isl_pw_aff_cow(pwaff
);
2804 for (i
= 0; i
< pwaff
->n
; ++i
) {
2805 pwaff
->p
[i
].aff
= isl_aff_ceil(pwaff
->p
[i
].aff
);
2806 if (!pwaff
->p
[i
].aff
)
2807 return isl_pw_aff_free(pwaff
);
2813 /* Assuming that "cond1" and "cond2" are disjoint,
2814 * return an affine expression that is equal to pwaff1 on cond1
2815 * and to pwaff2 on cond2.
2817 static __isl_give isl_pw_aff
*isl_pw_aff_select(
2818 __isl_take isl_set
*cond1
, __isl_take isl_pw_aff
*pwaff1
,
2819 __isl_take isl_set
*cond2
, __isl_take isl_pw_aff
*pwaff2
)
2821 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, cond1
);
2822 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, cond2
);
2824 return isl_pw_aff_add_disjoint(pwaff1
, pwaff2
);
2827 /* Return an affine expression that is equal to pwaff_true for elements
2828 * where "cond" is non-zero and to pwaff_false for elements where "cond"
2830 * That is, return cond ? pwaff_true : pwaff_false;
2832 __isl_give isl_pw_aff
*isl_pw_aff_cond(__isl_take isl_pw_aff
*cond
,
2833 __isl_take isl_pw_aff
*pwaff_true
, __isl_take isl_pw_aff
*pwaff_false
)
2835 isl_set
*cond_true
, *cond_false
;
2837 cond_true
= isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond
));
2838 cond_false
= isl_pw_aff_zero_set(cond
);
2839 return isl_pw_aff_select(cond_true
, pwaff_true
,
2840 cond_false
, pwaff_false
);
2843 int isl_aff_is_cst(__isl_keep isl_aff
*aff
)
2848 return isl_seq_first_non_zero(aff
->v
->el
+ 2, aff
->v
->size
- 2) == -1;
2851 /* Check whether pwaff is a piecewise constant.
2853 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff
*pwaff
)
2860 for (i
= 0; i
< pwaff
->n
; ++i
) {
2861 int is_cst
= isl_aff_is_cst(pwaff
->p
[i
].aff
);
2862 if (is_cst
< 0 || !is_cst
)
2869 __isl_give isl_aff
*isl_aff_mul(__isl_take isl_aff
*aff1
,
2870 __isl_take isl_aff
*aff2
)
2872 if (!isl_aff_is_cst(aff2
) && isl_aff_is_cst(aff1
))
2873 return isl_aff_mul(aff2
, aff1
);
2875 if (!isl_aff_is_cst(aff2
))
2876 isl_die(isl_aff_get_ctx(aff1
), isl_error_invalid
,
2877 "at least one affine expression should be constant",
2880 aff1
= isl_aff_cow(aff1
);
2884 aff1
= isl_aff_scale(aff1
, aff2
->v
->el
[1]);
2885 aff1
= isl_aff_scale_down(aff1
, aff2
->v
->el
[0]);
2895 /* Divide "aff1" by "aff2", assuming "aff2" is a piecewise constant.
2897 __isl_give isl_aff
*isl_aff_div(__isl_take isl_aff
*aff1
,
2898 __isl_take isl_aff
*aff2
)
2903 is_cst
= isl_aff_is_cst(aff2
);
2907 isl_die(isl_aff_get_ctx(aff2
), isl_error_invalid
,
2908 "second argument should be a constant", goto error
);
2913 neg
= isl_int_is_neg(aff2
->v
->el
[1]);
2915 isl_int_neg(aff2
->v
->el
[0], aff2
->v
->el
[0]);
2916 isl_int_neg(aff2
->v
->el
[1], aff2
->v
->el
[1]);
2919 aff1
= isl_aff_scale(aff1
, aff2
->v
->el
[0]);
2920 aff1
= isl_aff_scale_down(aff1
, aff2
->v
->el
[1]);
2923 isl_int_neg(aff2
->v
->el
[0], aff2
->v
->el
[0]);
2924 isl_int_neg(aff2
->v
->el
[1], aff2
->v
->el
[1]);
2935 static __isl_give isl_pw_aff
*pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
2936 __isl_take isl_pw_aff
*pwaff2
)
2938 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_add
);
2941 __isl_give isl_pw_aff
*isl_pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
2942 __isl_take isl_pw_aff
*pwaff2
)
2944 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_add
);
2947 __isl_give isl_pw_aff
*isl_pw_aff_union_add(__isl_take isl_pw_aff
*pwaff1
,
2948 __isl_take isl_pw_aff
*pwaff2
)
2950 return isl_pw_aff_union_add_(pwaff1
, pwaff2
);
2953 static __isl_give isl_pw_aff
*pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
2954 __isl_take isl_pw_aff
*pwaff2
)
2956 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_mul
);
2959 __isl_give isl_pw_aff
*isl_pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
2960 __isl_take isl_pw_aff
*pwaff2
)
2962 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_mul
);
2965 static __isl_give isl_pw_aff
*pw_aff_div(__isl_take isl_pw_aff
*pa1
,
2966 __isl_take isl_pw_aff
*pa2
)
2968 return isl_pw_aff_on_shared_domain(pa1
, pa2
, &isl_aff_div
);
2971 /* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
2973 __isl_give isl_pw_aff
*isl_pw_aff_div(__isl_take isl_pw_aff
*pa1
,
2974 __isl_take isl_pw_aff
*pa2
)
2978 is_cst
= isl_pw_aff_is_cst(pa2
);
2982 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
2983 "second argument should be a piecewise constant",
2985 return isl_pw_aff_align_params_pw_pw_and(pa1
, pa2
, &pw_aff_div
);
2987 isl_pw_aff_free(pa1
);
2988 isl_pw_aff_free(pa2
);
2992 /* Compute the quotient of the integer division of "pa1" by "pa2"
2993 * with rounding towards zero.
2994 * "pa2" is assumed to be a piecewise constant.
2996 * In particular, return
2998 * pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
3001 __isl_give isl_pw_aff
*isl_pw_aff_tdiv_q(__isl_take isl_pw_aff
*pa1
,
3002 __isl_take isl_pw_aff
*pa2
)
3008 is_cst
= isl_pw_aff_is_cst(pa2
);
3012 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
3013 "second argument should be a piecewise constant",
3016 pa1
= isl_pw_aff_div(pa1
, pa2
);
3018 cond
= isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1
));
3019 f
= isl_pw_aff_floor(isl_pw_aff_copy(pa1
));
3020 c
= isl_pw_aff_ceil(pa1
);
3021 return isl_pw_aff_cond(isl_set_indicator_function(cond
), f
, c
);
3023 isl_pw_aff_free(pa1
);
3024 isl_pw_aff_free(pa2
);
3028 /* Compute the remainder of the integer division of "pa1" by "pa2"
3029 * with rounding towards zero.
3030 * "pa2" is assumed to be a piecewise constant.
3032 * In particular, return
3034 * pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
3037 __isl_give isl_pw_aff
*isl_pw_aff_tdiv_r(__isl_take isl_pw_aff
*pa1
,
3038 __isl_take isl_pw_aff
*pa2
)
3043 is_cst
= isl_pw_aff_is_cst(pa2
);
3047 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
3048 "second argument should be a piecewise constant",
3050 res
= isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1
), isl_pw_aff_copy(pa2
));
3051 res
= isl_pw_aff_mul(pa2
, res
);
3052 res
= isl_pw_aff_sub(pa1
, res
);
3055 isl_pw_aff_free(pa1
);
3056 isl_pw_aff_free(pa2
);
3060 static __isl_give isl_pw_aff
*pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
3061 __isl_take isl_pw_aff
*pwaff2
)
3066 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
3067 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
3068 le
= isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1
),
3069 isl_pw_aff_copy(pwaff2
));
3070 dom
= isl_set_subtract(dom
, isl_set_copy(le
));
3071 return isl_pw_aff_select(le
, pwaff1
, dom
, pwaff2
);
3074 __isl_give isl_pw_aff
*isl_pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
3075 __isl_take isl_pw_aff
*pwaff2
)
3077 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_min
);
3080 static __isl_give isl_pw_aff
*pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
3081 __isl_take isl_pw_aff
*pwaff2
)
3086 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
3087 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
3088 ge
= isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1
),
3089 isl_pw_aff_copy(pwaff2
));
3090 dom
= isl_set_subtract(dom
, isl_set_copy(ge
));
3091 return isl_pw_aff_select(ge
, pwaff1
, dom
, pwaff2
);
3094 __isl_give isl_pw_aff
*isl_pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
3095 __isl_take isl_pw_aff
*pwaff2
)
3097 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_max
);
3100 static __isl_give isl_pw_aff
*pw_aff_list_reduce(
3101 __isl_take isl_pw_aff_list
*list
,
3102 __isl_give isl_pw_aff
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
3103 __isl_take isl_pw_aff
*pwaff2
))
3112 ctx
= isl_pw_aff_list_get_ctx(list
);
3114 isl_die(ctx
, isl_error_invalid
,
3115 "list should contain at least one element",
3116 return isl_pw_aff_list_free(list
));
3118 res
= isl_pw_aff_copy(list
->p
[0]);
3119 for (i
= 1; i
< list
->n
; ++i
)
3120 res
= fn(res
, isl_pw_aff_copy(list
->p
[i
]));
3122 isl_pw_aff_list_free(list
);
3126 /* Return an isl_pw_aff that maps each element in the intersection of the
3127 * domains of the elements of list to the minimal corresponding affine
3130 __isl_give isl_pw_aff
*isl_pw_aff_list_min(__isl_take isl_pw_aff_list
*list
)
3132 return pw_aff_list_reduce(list
, &isl_pw_aff_min
);
3135 /* Return an isl_pw_aff that maps each element in the intersection of the
3136 * domains of the elements of list to the maximal corresponding affine
3139 __isl_give isl_pw_aff
*isl_pw_aff_list_max(__isl_take isl_pw_aff_list
*list
)
3141 return pw_aff_list_reduce(list
, &isl_pw_aff_max
);
3144 /* Mark the domains of "pwaff" as rational.
3146 __isl_give isl_pw_aff
*isl_pw_aff_set_rational(__isl_take isl_pw_aff
*pwaff
)
3150 pwaff
= isl_pw_aff_cow(pwaff
);
3156 for (i
= 0; i
< pwaff
->n
; ++i
) {
3157 pwaff
->p
[i
].set
= isl_set_set_rational(pwaff
->p
[i
].set
);
3158 if (!pwaff
->p
[i
].set
)
3159 return isl_pw_aff_free(pwaff
);
3165 /* Mark the domains of the elements of "list" as rational.
3167 __isl_give isl_pw_aff_list
*isl_pw_aff_list_set_rational(
3168 __isl_take isl_pw_aff_list
*list
)
3178 for (i
= 0; i
< n
; ++i
) {
3181 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
3182 pa
= isl_pw_aff_set_rational(pa
);
3183 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
3189 /* Do the parameters of "aff" match those of "space"?
3191 int isl_aff_matching_params(__isl_keep isl_aff
*aff
,
3192 __isl_keep isl_space
*space
)
3194 isl_space
*aff_space
;
3200 aff_space
= isl_aff_get_domain_space(aff
);
3202 match
= isl_space_match(space
, isl_dim_param
, aff_space
, isl_dim_param
);
3204 isl_space_free(aff_space
);
3208 /* Check that the domain space of "aff" matches "space".
3210 * Return 0 on success and -1 on error.
3212 int isl_aff_check_match_domain_space(__isl_keep isl_aff
*aff
,
3213 __isl_keep isl_space
*space
)
3215 isl_space
*aff_space
;
3221 aff_space
= isl_aff_get_domain_space(aff
);
3223 match
= isl_space_match(space
, isl_dim_param
, aff_space
, isl_dim_param
);
3227 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
3228 "parameters don't match", goto error
);
3229 match
= isl_space_tuple_match(space
, isl_dim_in
,
3230 aff_space
, isl_dim_set
);
3234 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
3235 "domains don't match", goto error
);
3236 isl_space_free(aff_space
);
3239 isl_space_free(aff_space
);
3245 #define NO_INTERSECT_DOMAIN
3248 #include <isl_multi_templ.c>
3251 #undef NO_INTERSECT_DOMAIN
3253 /* Given a map space, return an isl_multi_aff that maps a wrapped copy
3254 * of the space to its domain.
3256 __isl_give isl_multi_aff
*isl_multi_aff_domain_map(__isl_take isl_space
*space
)
3259 isl_local_space
*ls
;
3264 if (!isl_space_is_map(space
))
3265 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3266 "not a map space", goto error
);
3268 n_in
= isl_space_dim(space
, isl_dim_in
);
3269 space
= isl_space_domain_map(space
);
3271 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3273 isl_space_free(space
);
3277 space
= isl_space_domain(space
);
3278 ls
= isl_local_space_from_space(space
);
3279 for (i
= 0; i
< n_in
; ++i
) {
3282 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3284 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3286 isl_local_space_free(ls
);
3289 isl_space_free(space
);
3293 /* Given a map space, return an isl_multi_aff that maps a wrapped copy
3294 * of the space to its range.
3296 __isl_give isl_multi_aff
*isl_multi_aff_range_map(__isl_take isl_space
*space
)
3299 isl_local_space
*ls
;
3304 if (!isl_space_is_map(space
))
3305 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3306 "not a map space", goto error
);
3308 n_in
= isl_space_dim(space
, isl_dim_in
);
3309 n_out
= isl_space_dim(space
, isl_dim_out
);
3310 space
= isl_space_range_map(space
);
3312 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3314 isl_space_free(space
);
3318 space
= isl_space_domain(space
);
3319 ls
= isl_local_space_from_space(space
);
3320 for (i
= 0; i
< n_out
; ++i
) {
3323 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3324 isl_dim_set
, n_in
+ i
);
3325 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3327 isl_local_space_free(ls
);
3330 isl_space_free(space
);
3334 /* Given the space of a set and a range of set dimensions,
3335 * construct an isl_multi_aff that projects out those dimensions.
3337 __isl_give isl_multi_aff
*isl_multi_aff_project_out_map(
3338 __isl_take isl_space
*space
, enum isl_dim_type type
,
3339 unsigned first
, unsigned n
)
3342 isl_local_space
*ls
;
3347 if (!isl_space_is_set(space
))
3348 isl_die(isl_space_get_ctx(space
), isl_error_unsupported
,
3349 "expecting set space", goto error
);
3350 if (type
!= isl_dim_set
)
3351 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3352 "only set dimensions can be projected out", goto error
);
3354 dim
= isl_space_dim(space
, isl_dim_set
);
3355 if (first
+ n
> dim
)
3356 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3357 "range out of bounds", goto error
);
3359 space
= isl_space_from_domain(space
);
3360 space
= isl_space_add_dims(space
, isl_dim_out
, dim
- n
);
3363 return isl_multi_aff_alloc(space
);
3365 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3366 space
= isl_space_domain(space
);
3367 ls
= isl_local_space_from_space(space
);
3369 for (i
= 0; i
< first
; ++i
) {
3372 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3374 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3377 for (i
= 0; i
< dim
- (first
+ n
); ++i
) {
3380 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3381 isl_dim_set
, first
+ n
+ i
);
3382 ma
= isl_multi_aff_set_aff(ma
, first
+ i
, aff
);
3385 isl_local_space_free(ls
);
3388 isl_space_free(space
);
3392 /* Given the space of a set and a range of set dimensions,
3393 * construct an isl_pw_multi_aff that projects out those dimensions.
3395 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_project_out_map(
3396 __isl_take isl_space
*space
, enum isl_dim_type type
,
3397 unsigned first
, unsigned n
)
3401 ma
= isl_multi_aff_project_out_map(space
, type
, first
, n
);
3402 return isl_pw_multi_aff_from_multi_aff(ma
);
3405 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
3408 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_multi_aff(
3409 __isl_take isl_multi_aff
*ma
)
3411 isl_set
*dom
= isl_set_universe(isl_multi_aff_get_domain_space(ma
));
3412 return isl_pw_multi_aff_alloc(dom
, ma
);
3415 /* Create a piecewise multi-affine expression in the given space that maps each
3416 * input dimension to the corresponding output dimension.
3418 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_identity(
3419 __isl_take isl_space
*space
)
3421 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space
));
3424 /* Add "ma2" to "ma1" and return the result.
3426 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
3428 static __isl_give isl_multi_aff
*isl_multi_aff_add_aligned(
3429 __isl_take isl_multi_aff
*maff1
, __isl_take isl_multi_aff
*maff2
)
3431 return isl_multi_aff_bin_op(maff1
, maff2
, &isl_aff_add
);
3434 /* Add "ma2" to "ma1" and return the result.
3436 __isl_give isl_multi_aff
*isl_multi_aff_add(__isl_take isl_multi_aff
*ma1
,
3437 __isl_take isl_multi_aff
*ma2
)
3439 return isl_multi_aff_align_params_multi_multi_and(ma1
, ma2
,
3440 &isl_multi_aff_add_aligned
);
3443 /* Subtract "ma2" from "ma1" and return the result.
3445 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
3447 static __isl_give isl_multi_aff
*isl_multi_aff_sub_aligned(
3448 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
3450 return isl_multi_aff_bin_op(ma1
, ma2
, &isl_aff_sub
);
3453 /* Subtract "ma2" from "ma1" and return the result.
3455 __isl_give isl_multi_aff
*isl_multi_aff_sub(__isl_take isl_multi_aff
*ma1
,
3456 __isl_take isl_multi_aff
*ma2
)
3458 return isl_multi_aff_align_params_multi_multi_and(ma1
, ma2
,
3459 &isl_multi_aff_sub_aligned
);
3462 /* Exploit the equalities in "eq" to simplify the affine expressions.
3464 static __isl_give isl_multi_aff
*isl_multi_aff_substitute_equalities(
3465 __isl_take isl_multi_aff
*maff
, __isl_take isl_basic_set
*eq
)
3469 maff
= isl_multi_aff_cow(maff
);
3473 for (i
= 0; i
< maff
->n
; ++i
) {
3474 maff
->p
[i
] = isl_aff_substitute_equalities(maff
->p
[i
],
3475 isl_basic_set_copy(eq
));
3480 isl_basic_set_free(eq
);
3483 isl_basic_set_free(eq
);
3484 isl_multi_aff_free(maff
);
3488 __isl_give isl_multi_aff
*isl_multi_aff_scale(__isl_take isl_multi_aff
*maff
,
3493 maff
= isl_multi_aff_cow(maff
);
3497 for (i
= 0; i
< maff
->n
; ++i
) {
3498 maff
->p
[i
] = isl_aff_scale(maff
->p
[i
], f
);
3500 return isl_multi_aff_free(maff
);
3506 __isl_give isl_multi_aff
*isl_multi_aff_add_on_domain(__isl_keep isl_set
*dom
,
3507 __isl_take isl_multi_aff
*maff1
, __isl_take isl_multi_aff
*maff2
)
3509 maff1
= isl_multi_aff_add(maff1
, maff2
);
3510 maff1
= isl_multi_aff_gist(maff1
, isl_set_copy(dom
));
3514 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff
*maff
)
3522 /* Return the set of domain elements where "ma1" is lexicographically
3523 * smaller than or equal to "ma2".
3525 __isl_give isl_set
*isl_multi_aff_lex_le_set(__isl_take isl_multi_aff
*ma1
,
3526 __isl_take isl_multi_aff
*ma2
)
3528 return isl_multi_aff_lex_ge_set(ma2
, ma1
);
3531 /* Return the set of domain elements where "ma1" is lexicographically
3532 * greater than or equal to "ma2".
3534 __isl_give isl_set
*isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff
*ma1
,
3535 __isl_take isl_multi_aff
*ma2
)
3538 isl_map
*map1
, *map2
;
3541 map1
= isl_map_from_multi_aff(ma1
);
3542 map2
= isl_map_from_multi_aff(ma2
);
3543 map
= isl_map_range_product(map1
, map2
);
3544 space
= isl_space_range(isl_map_get_space(map
));
3545 space
= isl_space_domain(isl_space_unwrap(space
));
3546 ge
= isl_map_lex_ge(space
);
3547 map
= isl_map_intersect_range(map
, isl_map_wrap(ge
));
3549 return isl_map_domain(map
);
3553 #define PW isl_pw_multi_aff
3555 #define EL isl_multi_aff
3557 #define EL_IS_ZERO is_empty
3561 #define IS_ZERO is_empty
3564 #undef DEFAULT_IS_ZERO
3565 #define DEFAULT_IS_ZERO 0
3570 #define NO_INVOLVES_DIMS
3571 #define NO_INSERT_DIMS
3575 #include <isl_pw_templ.c>
3578 #define UNION isl_union_pw_multi_aff
3580 #define PART isl_pw_multi_aff
3582 #define PARTS pw_multi_aff
3583 #define ALIGN_DOMAIN
3587 #include <isl_union_templ.c>
3589 /* Given a function "cmp" that returns the set of elements where
3590 * "ma1" is "better" than "ma2", return the intersection of this
3591 * set with "dom1" and "dom2".
3593 static __isl_give isl_set
*shared_and_better(__isl_keep isl_set
*dom1
,
3594 __isl_keep isl_set
*dom2
, __isl_keep isl_multi_aff
*ma1
,
3595 __isl_keep isl_multi_aff
*ma2
,
3596 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
3597 __isl_take isl_multi_aff
*ma2
))
3603 common
= isl_set_intersect(isl_set_copy(dom1
), isl_set_copy(dom2
));
3604 is_empty
= isl_set_plain_is_empty(common
);
3605 if (is_empty
>= 0 && is_empty
)
3608 return isl_set_free(common
);
3609 better
= cmp(isl_multi_aff_copy(ma1
), isl_multi_aff_copy(ma2
));
3610 better
= isl_set_intersect(common
, better
);
3615 /* Given a function "cmp" that returns the set of elements where
3616 * "ma1" is "better" than "ma2", return a piecewise multi affine
3617 * expression defined on the union of the definition domains
3618 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
3619 * "pma2" on each cell. If only one of the two input functions
3620 * is defined on a given cell, then it is considered the best.
3622 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_opt(
3623 __isl_take isl_pw_multi_aff
*pma1
,
3624 __isl_take isl_pw_multi_aff
*pma2
,
3625 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
3626 __isl_take isl_multi_aff
*ma2
))
3629 isl_pw_multi_aff
*res
= NULL
;
3631 isl_set
*set
= NULL
;
3636 ctx
= isl_space_get_ctx(pma1
->dim
);
3637 if (!isl_space_is_equal(pma1
->dim
, pma2
->dim
))
3638 isl_die(ctx
, isl_error_invalid
,
3639 "arguments should live in the same space", goto error
);
3641 if (isl_pw_multi_aff_is_empty(pma1
)) {
3642 isl_pw_multi_aff_free(pma1
);
3646 if (isl_pw_multi_aff_is_empty(pma2
)) {
3647 isl_pw_multi_aff_free(pma2
);
3651 n
= 2 * (pma1
->n
+ 1) * (pma2
->n
+ 1);
3652 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma1
->dim
), n
);
3654 for (i
= 0; i
< pma1
->n
; ++i
) {
3655 set
= isl_set_copy(pma1
->p
[i
].set
);
3656 for (j
= 0; j
< pma2
->n
; ++j
) {
3660 better
= shared_and_better(pma2
->p
[j
].set
,
3661 pma1
->p
[i
].set
, pma2
->p
[j
].maff
,
3662 pma1
->p
[i
].maff
, cmp
);
3663 is_empty
= isl_set_plain_is_empty(better
);
3664 if (is_empty
< 0 || is_empty
) {
3665 isl_set_free(better
);
3670 set
= isl_set_subtract(set
, isl_set_copy(better
));
3672 res
= isl_pw_multi_aff_add_piece(res
, better
,
3673 isl_multi_aff_copy(pma2
->p
[j
].maff
));
3675 res
= isl_pw_multi_aff_add_piece(res
, set
,
3676 isl_multi_aff_copy(pma1
->p
[i
].maff
));
3679 for (j
= 0; j
< pma2
->n
; ++j
) {
3680 set
= isl_set_copy(pma2
->p
[j
].set
);
3681 for (i
= 0; i
< pma1
->n
; ++i
)
3682 set
= isl_set_subtract(set
,
3683 isl_set_copy(pma1
->p
[i
].set
));
3684 res
= isl_pw_multi_aff_add_piece(res
, set
,
3685 isl_multi_aff_copy(pma2
->p
[j
].maff
));
3688 isl_pw_multi_aff_free(pma1
);
3689 isl_pw_multi_aff_free(pma2
);
3693 isl_pw_multi_aff_free(pma1
);
3694 isl_pw_multi_aff_free(pma2
);
3696 return isl_pw_multi_aff_free(res
);
3699 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmax(
3700 __isl_take isl_pw_multi_aff
*pma1
,
3701 __isl_take isl_pw_multi_aff
*pma2
)
3703 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_ge_set
);
3706 /* Given two piecewise multi affine expressions, return a piecewise
3707 * multi-affine expression defined on the union of the definition domains
3708 * of the inputs that is equal to the lexicographic maximum of the two
3709 * inputs on each cell. If only one of the two inputs is defined on
3710 * a given cell, then it is considered to be the maximum.
3712 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmax(
3713 __isl_take isl_pw_multi_aff
*pma1
,
3714 __isl_take isl_pw_multi_aff
*pma2
)
3716 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
3717 &pw_multi_aff_union_lexmax
);
3720 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmin(
3721 __isl_take isl_pw_multi_aff
*pma1
,
3722 __isl_take isl_pw_multi_aff
*pma2
)
3724 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_le_set
);
3727 /* Given two piecewise multi affine expressions, return a piecewise
3728 * multi-affine expression defined on the union of the definition domains
3729 * of the inputs that is equal to the lexicographic minimum of the two
3730 * inputs on each cell. If only one of the two inputs is defined on
3731 * a given cell, then it is considered to be the minimum.
3733 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmin(
3734 __isl_take isl_pw_multi_aff
*pma1
,
3735 __isl_take isl_pw_multi_aff
*pma2
)
3737 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
3738 &pw_multi_aff_union_lexmin
);
3741 static __isl_give isl_pw_multi_aff
*pw_multi_aff_add(
3742 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3744 return isl_pw_multi_aff_on_shared_domain(pma1
, pma2
,
3745 &isl_multi_aff_add
);
3748 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_add(
3749 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3751 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
3755 static __isl_give isl_pw_multi_aff
*pw_multi_aff_sub(
3756 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3758 return isl_pw_multi_aff_on_shared_domain(pma1
, pma2
,
3759 &isl_multi_aff_sub
);
3762 /* Subtract "pma2" from "pma1" and return the result.
3764 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_sub(
3765 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3767 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
3771 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_add(
3772 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3774 return isl_pw_multi_aff_union_add_(pma1
, pma2
);
3777 /* Given two piecewise multi-affine expressions A -> B and C -> D,
3778 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
3780 static __isl_give isl_pw_multi_aff
*pw_multi_aff_product(
3781 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3785 isl_pw_multi_aff
*res
;
3790 n
= pma1
->n
* pma2
->n
;
3791 space
= isl_space_product(isl_space_copy(pma1
->dim
),
3792 isl_space_copy(pma2
->dim
));
3793 res
= isl_pw_multi_aff_alloc_size(space
, n
);
3795 for (i
= 0; i
< pma1
->n
; ++i
) {
3796 for (j
= 0; j
< pma2
->n
; ++j
) {
3800 domain
= isl_set_product(isl_set_copy(pma1
->p
[i
].set
),
3801 isl_set_copy(pma2
->p
[j
].set
));
3802 ma
= isl_multi_aff_product(
3803 isl_multi_aff_copy(pma1
->p
[i
].maff
),
3804 isl_multi_aff_copy(pma2
->p
[j
].maff
));
3805 res
= isl_pw_multi_aff_add_piece(res
, domain
, ma
);
3809 isl_pw_multi_aff_free(pma1
);
3810 isl_pw_multi_aff_free(pma2
);
3813 isl_pw_multi_aff_free(pma1
);
3814 isl_pw_multi_aff_free(pma2
);
3818 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_product(
3819 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
3821 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
3822 &pw_multi_aff_product
);
3825 /* Construct a map mapping the domain of the piecewise multi-affine expression
3826 * to its range, with each dimension in the range equated to the
3827 * corresponding affine expression on its cell.
3829 __isl_give isl_map
*isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
3837 map
= isl_map_empty(isl_pw_multi_aff_get_space(pma
));
3839 for (i
= 0; i
< pma
->n
; ++i
) {
3840 isl_multi_aff
*maff
;
3841 isl_basic_map
*bmap
;
3844 maff
= isl_multi_aff_copy(pma
->p
[i
].maff
);
3845 bmap
= isl_basic_map_from_multi_aff(maff
);
3846 map_i
= isl_map_from_basic_map(bmap
);
3847 map_i
= isl_map_intersect_domain(map_i
,
3848 isl_set_copy(pma
->p
[i
].set
));
3849 map
= isl_map_union_disjoint(map
, map_i
);
3852 isl_pw_multi_aff_free(pma
);
3856 __isl_give isl_set
*isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
3861 if (!isl_space_is_set(pma
->dim
))
3862 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
3863 "isl_pw_multi_aff cannot be converted into an isl_set",
3864 return isl_pw_multi_aff_free(pma
));
3866 return isl_map_from_pw_multi_aff(pma
);
3869 /* Given a basic map with a single output dimension that is defined
3870 * in terms of the parameters and input dimensions using an equality,
3871 * extract an isl_aff that expresses the output dimension in terms
3872 * of the parameters and input dimensions.
3874 * Since some applications expect the result of isl_pw_multi_aff_from_map
3875 * to only contain integer affine expressions, we compute the floor
3876 * of the expression before returning.
3878 * This function shares some similarities with
3879 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
3881 static __isl_give isl_aff
*extract_isl_aff_from_basic_map(
3882 __isl_take isl_basic_map
*bmap
)
3887 isl_local_space
*ls
;
3892 if (isl_basic_map_dim(bmap
, isl_dim_out
) != 1)
3893 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
3894 "basic map should have a single output dimension",
3896 offset
= isl_basic_map_offset(bmap
, isl_dim_out
);
3897 total
= isl_basic_map_total_dim(bmap
);
3898 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
3899 if (isl_int_is_zero(bmap
->eq
[i
][offset
]))
3901 if (isl_seq_first_non_zero(bmap
->eq
[i
] + offset
+ 1,
3902 1 + total
- (offset
+ 1)) != -1)
3906 if (i
>= bmap
->n_eq
)
3907 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
3908 "unable to find suitable equality", goto error
);
3909 ls
= isl_basic_map_get_local_space(bmap
);
3910 aff
= isl_aff_alloc(isl_local_space_domain(ls
));
3913 if (isl_int_is_neg(bmap
->eq
[i
][offset
]))
3914 isl_seq_cpy(aff
->v
->el
+ 1, bmap
->eq
[i
], offset
);
3916 isl_seq_neg(aff
->v
->el
+ 1, bmap
->eq
[i
], offset
);
3917 isl_seq_clr(aff
->v
->el
+ 1 + offset
, aff
->v
->size
- (1 + offset
));
3918 isl_int_abs(aff
->v
->el
[0], bmap
->eq
[i
][offset
]);
3919 isl_basic_map_free(bmap
);
3921 aff
= isl_aff_remove_unused_divs(aff
);
3922 aff
= isl_aff_floor(aff
);
3925 isl_basic_map_free(bmap
);
3929 /* Given a basic map where each output dimension is defined
3930 * in terms of the parameters and input dimensions using an equality,
3931 * extract an isl_multi_aff that expresses the output dimensions in terms
3932 * of the parameters and input dimensions.
3934 static __isl_give isl_multi_aff
*extract_isl_multi_aff_from_basic_map(
3935 __isl_take isl_basic_map
*bmap
)
3944 ma
= isl_multi_aff_alloc(isl_basic_map_get_space(bmap
));
3945 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
3947 for (i
= 0; i
< n_out
; ++i
) {
3948 isl_basic_map
*bmap_i
;
3951 bmap_i
= isl_basic_map_copy(bmap
);
3952 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
,
3953 i
+ 1, n_out
- (1 + i
));
3954 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
, 0, i
);
3955 aff
= extract_isl_aff_from_basic_map(bmap_i
);
3956 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3959 isl_basic_map_free(bmap
);
3964 /* Create an isl_pw_multi_aff that is equivalent to
3965 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
3966 * The given basic map is such that each output dimension is defined
3967 * in terms of the parameters and input dimensions using an equality.
3969 static __isl_give isl_pw_multi_aff
*plain_pw_multi_aff_from_map(
3970 __isl_take isl_set
*domain
, __isl_take isl_basic_map
*bmap
)
3974 ma
= extract_isl_multi_aff_from_basic_map(bmap
);
3975 return isl_pw_multi_aff_alloc(domain
, ma
);
3978 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
3979 * This obviously only works if the input "map" is single-valued.
3980 * If so, we compute the lexicographic minimum of the image in the form
3981 * of an isl_pw_multi_aff. Since the image is unique, it is equal
3982 * to its lexicographic minimum.
3983 * If the input is not single-valued, we produce an error.
3985 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_base(
3986 __isl_take isl_map
*map
)
3990 isl_pw_multi_aff
*pma
;
3992 sv
= isl_map_is_single_valued(map
);
3996 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
3997 "map is not single-valued", goto error
);
3998 map
= isl_map_make_disjoint(map
);
4002 pma
= isl_pw_multi_aff_empty(isl_map_get_space(map
));
4004 for (i
= 0; i
< map
->n
; ++i
) {
4005 isl_pw_multi_aff
*pma_i
;
4006 isl_basic_map
*bmap
;
4007 bmap
= isl_basic_map_copy(map
->p
[i
]);
4008 pma_i
= isl_basic_map_lexmin_pw_multi_aff(bmap
);
4009 pma
= isl_pw_multi_aff_add_disjoint(pma
, pma_i
);
4019 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
4020 * taking into account that the output dimension at position "d"
4021 * can be represented as
4023 * x = floor((e(...) + c1) / m)
4025 * given that constraint "i" is of the form
4027 * e(...) + c1 - m x >= 0
4030 * Let "map" be of the form
4034 * We construct a mapping
4036 * A -> [A -> x = floor(...)]
4038 * apply that to the map, obtaining
4040 * [A -> x = floor(...)] -> B
4042 * and equate dimension "d" to x.
4043 * We then compute a isl_pw_multi_aff representation of the resulting map
4044 * and plug in the mapping above.
4046 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_div(
4047 __isl_take isl_map
*map
, __isl_take isl_basic_map
*hull
, int d
, int i
)
4051 isl_local_space
*ls
;
4059 isl_pw_multi_aff
*pma
;
4062 is_set
= isl_map_is_set(map
);
4064 offset
= isl_basic_map_offset(hull
, isl_dim_out
);
4065 ctx
= isl_map_get_ctx(map
);
4066 space
= isl_space_domain(isl_map_get_space(map
));
4067 n_in
= isl_space_dim(space
, isl_dim_set
);
4068 n
= isl_space_dim(space
, isl_dim_all
);
4070 v
= isl_vec_alloc(ctx
, 1 + 1 + n
);
4072 isl_int_neg(v
->el
[0], hull
->ineq
[i
][offset
+ d
]);
4073 isl_seq_cpy(v
->el
+ 1, hull
->ineq
[i
], 1 + n
);
4075 isl_basic_map_free(hull
);
4077 ls
= isl_local_space_from_space(isl_space_copy(space
));
4078 aff
= isl_aff_alloc_vec(ls
, v
);
4079 aff
= isl_aff_floor(aff
);
4081 isl_space_free(space
);
4082 ma
= isl_multi_aff_from_aff(aff
);
4084 ma
= isl_multi_aff_identity(isl_space_map_from_set(space
));
4085 ma
= isl_multi_aff_range_product(ma
,
4086 isl_multi_aff_from_aff(aff
));
4089 insert
= isl_map_from_multi_aff(isl_multi_aff_copy(ma
));
4090 map
= isl_map_apply_domain(map
, insert
);
4091 map
= isl_map_equate(map
, isl_dim_in
, n_in
, isl_dim_out
, d
);
4092 pma
= isl_pw_multi_aff_from_map(map
);
4093 pma
= isl_pw_multi_aff_pullback_multi_aff(pma
, ma
);
4098 /* Is constraint "c" of the form
4100 * e(...) + c1 - m x >= 0
4104 * -e(...) + c2 + m x >= 0
4106 * where m > 1 and e only depends on parameters and input dimemnsions?
4108 * "offset" is the offset of the output dimensions
4109 * "pos" is the position of output dimension x.
4111 static int is_potential_div_constraint(isl_int
*c
, int offset
, int d
, int total
)
4113 if (isl_int_is_zero(c
[offset
+ d
]))
4115 if (isl_int_is_one(c
[offset
+ d
]))
4117 if (isl_int_is_negone(c
[offset
+ d
]))
4119 if (isl_seq_first_non_zero(c
+ offset
, d
) != -1)
4121 if (isl_seq_first_non_zero(c
+ offset
+ d
+ 1,
4122 total
- (offset
+ d
+ 1)) != -1)
4127 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4129 * As a special case, we first check if there is any pair of constraints,
4130 * shared by all the basic maps in "map" that force a given dimension
4131 * to be equal to the floor of some affine combination of the input dimensions.
4133 * In particular, if we can find two constraints
4135 * e(...) + c1 - m x >= 0 i.e., m x <= e(...) + c1
4139 * -e(...) + c2 + m x >= 0 i.e., m x >= e(...) - c2
4141 * where m > 1 and e only depends on parameters and input dimemnsions,
4144 * c1 + c2 < m i.e., -c2 >= c1 - (m - 1)
4146 * then we know that we can take
4148 * x = floor((e(...) + c1) / m)
4150 * without having to perform any computation.
4152 * Note that we know that
4156 * If c1 + c2 were 0, then we would have detected an equality during
4157 * simplification. If c1 + c2 were negative, then we would have detected
4160 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_check_div(
4161 __isl_take isl_map
*map
)
4167 isl_basic_map
*hull
;
4169 hull
= isl_map_unshifted_simple_hull(isl_map_copy(map
));
4174 dim
= isl_map_dim(map
, isl_dim_out
);
4175 offset
= isl_basic_map_offset(hull
, isl_dim_out
);
4176 total
= 1 + isl_basic_map_total_dim(hull
);
4178 for (d
= 0; d
< dim
; ++d
) {
4179 for (i
= 0; i
< n
; ++i
) {
4180 if (!is_potential_div_constraint(hull
->ineq
[i
],
4183 for (j
= i
+ 1; j
< n
; ++j
) {
4184 if (!isl_seq_is_neg(hull
->ineq
[i
] + 1,
4185 hull
->ineq
[j
] + 1, total
- 1))
4187 isl_int_add(sum
, hull
->ineq
[i
][0],
4189 if (isl_int_abs_lt(sum
,
4190 hull
->ineq
[i
][offset
+ d
]))
4197 if (isl_int_is_pos(hull
->ineq
[j
][offset
+ d
]))
4199 return pw_multi_aff_from_map_div(map
, hull
, d
, j
);
4203 isl_basic_map_free(hull
);
4204 return pw_multi_aff_from_map_base(map
);
4207 isl_basic_map_free(hull
);
4211 /* Given an affine expression
4213 * [A -> B] -> f(A,B)
4215 * construct an isl_multi_aff
4219 * such that dimension "d" in B' is set to "aff" and the remaining
4220 * dimensions are set equal to the corresponding dimensions in B.
4221 * "n_in" is the dimension of the space A.
4222 * "n_out" is the dimension of the space B.
4224 * If "is_set" is set, then the affine expression is of the form
4228 * and we construct an isl_multi_aff
4232 static __isl_give isl_multi_aff
*range_map(__isl_take isl_aff
*aff
, int d
,
4233 unsigned n_in
, unsigned n_out
, int is_set
)
4237 isl_space
*space
, *space2
;
4238 isl_local_space
*ls
;
4240 space
= isl_aff_get_domain_space(aff
);
4241 ls
= isl_local_space_from_space(isl_space_copy(space
));
4242 space2
= isl_space_copy(space
);
4244 space2
= isl_space_range(isl_space_unwrap(space2
));
4245 space
= isl_space_map_from_domain_and_range(space
, space2
);
4246 ma
= isl_multi_aff_alloc(space
);
4247 ma
= isl_multi_aff_set_aff(ma
, d
, aff
);
4249 for (i
= 0; i
< n_out
; ++i
) {
4252 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
4253 isl_dim_set
, n_in
+ i
);
4254 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
4257 isl_local_space_free(ls
);
4262 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
4263 * taking into account that the dimension at position "d" can be written as
4265 * x = m a + f(..) (1)
4267 * where m is equal to "gcd".
4268 * "i" is the index of the equality in "hull" that defines f(..).
4269 * In particular, the equality is of the form
4271 * f(..) - x + m g(existentials) = 0
4275 * -f(..) + x + m g(existentials) = 0
4277 * We basically plug (1) into "map", resulting in a map with "a"
4278 * in the range instead of "x". The corresponding isl_pw_multi_aff
4279 * defining "a" is then plugged back into (1) to obtain a definition fro "x".
4281 * Specifically, given the input map
4285 * We first wrap it into a set
4289 * and define (1) on top of the corresponding space, resulting in "aff".
4290 * We use this to create an isl_multi_aff that maps the output position "d"
4291 * from "a" to "x", leaving all other (intput and output) dimensions unchanged.
4292 * We plug this into the wrapped map, unwrap the result and compute the
4293 * corresponding isl_pw_multi_aff.
4294 * The result is an expression
4302 * so that we can plug that into "aff", after extending the latter to
4308 * If "map" is actually a set, then there is no "A" space, meaning
4309 * that we do not need to perform any wrapping, and that the result
4310 * of the recursive call is of the form
4314 * which is plugged into a mapping of the form
4318 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_stride(
4319 __isl_take isl_map
*map
, __isl_take isl_basic_map
*hull
, int d
, int i
,
4324 isl_local_space
*ls
;
4327 isl_pw_multi_aff
*pma
, *id
;
4333 is_set
= isl_map_is_set(map
);
4335 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
4336 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
4337 o_out
= isl_basic_map_offset(hull
, isl_dim_out
);
4342 set
= isl_map_wrap(map
);
4343 space
= isl_space_map_from_set(isl_set_get_space(set
));
4344 ma
= isl_multi_aff_identity(space
);
4345 ls
= isl_local_space_from_space(isl_set_get_space(set
));
4346 aff
= isl_aff_alloc(ls
);
4348 isl_int_set_si(aff
->v
->el
[0], 1);
4349 if (isl_int_is_one(hull
->eq
[i
][o_out
+ d
]))
4350 isl_seq_neg(aff
->v
->el
+ 1, hull
->eq
[i
],
4353 isl_seq_cpy(aff
->v
->el
+ 1, hull
->eq
[i
],
4355 isl_int_set(aff
->v
->el
[1 + o_out
+ d
], gcd
);
4357 ma
= isl_multi_aff_set_aff(ma
, n_in
+ d
, isl_aff_copy(aff
));
4358 set
= isl_set_preimage_multi_aff(set
, ma
);
4360 ma
= range_map(aff
, d
, n_in
, n_out
, is_set
);
4365 map
= isl_set_unwrap(set
);
4366 pma
= isl_pw_multi_aff_from_map(set
);
4369 space
= isl_pw_multi_aff_get_domain_space(pma
);
4370 space
= isl_space_map_from_set(space
);
4371 id
= isl_pw_multi_aff_identity(space
);
4372 pma
= isl_pw_multi_aff_range_product(id
, pma
);
4374 id
= isl_pw_multi_aff_from_multi_aff(ma
);
4375 pma
= isl_pw_multi_aff_pullback_pw_multi_aff(id
, pma
);
4377 isl_basic_map_free(hull
);
4381 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4383 * As a special case, we first check if all output dimensions are uniquely
4384 * defined in terms of the parameters and input dimensions over the entire
4385 * domain. If so, we extract the desired isl_pw_multi_aff directly
4386 * from the affine hull of "map" and its domain.
4388 * Otherwise, we check if any of the output dimensions is "strided".
4389 * That is, we check if can be written as
4393 * with m greater than 1, a some combination of existentiall quantified
4394 * variables and f and expression in the parameters and input dimensions.
4395 * If so, we remove the stride in pw_multi_aff_from_map_stride.
4397 * Otherwise, we continue with pw_multi_aff_from_map_check_div for a further
4400 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_map(__isl_take isl_map
*map
)
4404 isl_basic_map
*hull
;
4414 hull
= isl_map_affine_hull(isl_map_copy(map
));
4415 sv
= isl_basic_map_plain_is_single_valued(hull
);
4417 return plain_pw_multi_aff_from_map(isl_map_domain(map
), hull
);
4419 hull
= isl_basic_map_free(hull
);
4423 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
4424 o_div
= isl_basic_map_offset(hull
, isl_dim_div
);
4427 isl_basic_map_free(hull
);
4428 return pw_multi_aff_from_map_check_div(map
);
4433 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
4434 o_out
= isl_basic_map_offset(hull
, isl_dim_out
);
4436 for (i
= 0; i
< n_out
; ++i
) {
4437 for (j
= 0; j
< hull
->n_eq
; ++j
) {
4438 isl_int
*eq
= hull
->eq
[j
];
4439 isl_pw_multi_aff
*res
;
4441 if (!isl_int_is_one(eq
[o_out
+ i
]) &&
4442 !isl_int_is_negone(eq
[o_out
+ i
]))
4444 if (isl_seq_first_non_zero(eq
+ o_out
, i
) != -1)
4446 if (isl_seq_first_non_zero(eq
+ o_out
+ i
+ 1,
4447 n_out
- (i
+ 1)) != -1)
4449 isl_seq_gcd(eq
+ o_div
, n_div
, &gcd
);
4450 if (isl_int_is_zero(gcd
))
4452 if (isl_int_is_one(gcd
))
4455 res
= pw_multi_aff_from_map_stride(map
, hull
,
4463 isl_basic_map_free(hull
);
4464 return pw_multi_aff_from_map_check_div(map
);
4470 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_set(__isl_take isl_set
*set
)
4472 return isl_pw_multi_aff_from_map(set
);
4475 /* Convert "map" into an isl_pw_multi_aff (if possible) and
4478 static int pw_multi_aff_from_map(__isl_take isl_map
*map
, void *user
)
4480 isl_union_pw_multi_aff
**upma
= user
;
4481 isl_pw_multi_aff
*pma
;
4483 pma
= isl_pw_multi_aff_from_map(map
);
4484 *upma
= isl_union_pw_multi_aff_add_pw_multi_aff(*upma
, pma
);
4486 return *upma
? 0 : -1;
4489 /* Try and create an isl_union_pw_multi_aff that is equivalent
4490 * to the given isl_union_map.
4491 * The isl_union_map is required to be single-valued in each space.
4492 * Otherwise, an error is produced.
4494 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_union_map(
4495 __isl_take isl_union_map
*umap
)
4498 isl_union_pw_multi_aff
*upma
;
4500 space
= isl_union_map_get_space(umap
);
4501 upma
= isl_union_pw_multi_aff_empty(space
);
4502 if (isl_union_map_foreach_map(umap
, &pw_multi_aff_from_map
, &upma
) < 0)
4503 upma
= isl_union_pw_multi_aff_free(upma
);
4504 isl_union_map_free(umap
);
4509 /* Try and create an isl_union_pw_multi_aff that is equivalent
4510 * to the given isl_union_set.
4511 * The isl_union_set is required to be a singleton in each space.
4512 * Otherwise, an error is produced.
4514 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_union_set(
4515 __isl_take isl_union_set
*uset
)
4517 return isl_union_pw_multi_aff_from_union_map(uset
);
4520 /* Return the piecewise affine expression "set ? 1 : 0".
4522 __isl_give isl_pw_aff
*isl_set_indicator_function(__isl_take isl_set
*set
)
4525 isl_space
*space
= isl_set_get_space(set
);
4526 isl_local_space
*ls
= isl_local_space_from_space(space
);
4527 isl_aff
*zero
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
4528 isl_aff
*one
= isl_aff_zero_on_domain(ls
);
4530 one
= isl_aff_add_constant_si(one
, 1);
4531 pa
= isl_pw_aff_alloc(isl_set_copy(set
), one
);
4532 set
= isl_set_complement(set
);
4533 pa
= isl_pw_aff_add_disjoint(pa
, isl_pw_aff_alloc(set
, zero
));
4538 /* Plug in "subs" for dimension "type", "pos" of "aff".
4540 * Let i be the dimension to replace and let "subs" be of the form
4544 * and "aff" of the form
4550 * (a f + d g')/(m d)
4552 * where g' is the result of plugging in "subs" in each of the integer
4555 __isl_give isl_aff
*isl_aff_substitute(__isl_take isl_aff
*aff
,
4556 enum isl_dim_type type
, unsigned pos
, __isl_keep isl_aff
*subs
)
4561 aff
= isl_aff_cow(aff
);
4563 return isl_aff_free(aff
);
4565 ctx
= isl_aff_get_ctx(aff
);
4566 if (!isl_space_is_equal(aff
->ls
->dim
, subs
->ls
->dim
))
4567 isl_die(ctx
, isl_error_invalid
,
4568 "spaces don't match", return isl_aff_free(aff
));
4569 if (isl_local_space_dim(subs
->ls
, isl_dim_div
) != 0)
4570 isl_die(ctx
, isl_error_unsupported
,
4571 "cannot handle divs yet", return isl_aff_free(aff
));
4573 aff
->ls
= isl_local_space_substitute(aff
->ls
, type
, pos
, subs
);
4575 return isl_aff_free(aff
);
4577 aff
->v
= isl_vec_cow(aff
->v
);
4579 return isl_aff_free(aff
);
4581 pos
+= isl_local_space_offset(aff
->ls
, type
);
4584 isl_seq_substitute(aff
->v
->el
, pos
, subs
->v
->el
,
4585 aff
->v
->size
, subs
->v
->size
, v
);
4591 /* Plug in "subs" for dimension "type", "pos" in each of the affine
4592 * expressions in "maff".
4594 __isl_give isl_multi_aff
*isl_multi_aff_substitute(
4595 __isl_take isl_multi_aff
*maff
, enum isl_dim_type type
, unsigned pos
,
4596 __isl_keep isl_aff
*subs
)
4600 maff
= isl_multi_aff_cow(maff
);
4602 return isl_multi_aff_free(maff
);
4604 if (type
== isl_dim_in
)
4607 for (i
= 0; i
< maff
->n
; ++i
) {
4608 maff
->p
[i
] = isl_aff_substitute(maff
->p
[i
], type
, pos
, subs
);
4610 return isl_multi_aff_free(maff
);
4616 /* Plug in "subs" for dimension "type", "pos" of "pma".
4618 * pma is of the form
4622 * while subs is of the form
4624 * v' = B_j(v) -> S_j
4626 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
4627 * has a contribution in the result, in particular
4629 * C_ij(S_j) -> M_i(S_j)
4631 * Note that plugging in S_j in C_ij may also result in an empty set
4632 * and this contribution should simply be discarded.
4634 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_substitute(
4635 __isl_take isl_pw_multi_aff
*pma
, enum isl_dim_type type
, unsigned pos
,
4636 __isl_keep isl_pw_aff
*subs
)
4639 isl_pw_multi_aff
*res
;
4642 return isl_pw_multi_aff_free(pma
);
4644 n
= pma
->n
* subs
->n
;
4645 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma
->dim
), n
);
4647 for (i
= 0; i
< pma
->n
; ++i
) {
4648 for (j
= 0; j
< subs
->n
; ++j
) {
4650 isl_multi_aff
*res_ij
;
4653 common
= isl_set_intersect(
4654 isl_set_copy(pma
->p
[i
].set
),
4655 isl_set_copy(subs
->p
[j
].set
));
4656 common
= isl_set_substitute(common
,
4657 type
, pos
, subs
->p
[j
].aff
);
4658 empty
= isl_set_plain_is_empty(common
);
4659 if (empty
< 0 || empty
) {
4660 isl_set_free(common
);
4666 res_ij
= isl_multi_aff_substitute(
4667 isl_multi_aff_copy(pma
->p
[i
].maff
),
4668 type
, pos
, subs
->p
[j
].aff
);
4670 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
4674 isl_pw_multi_aff_free(pma
);
4677 isl_pw_multi_aff_free(pma
);
4678 isl_pw_multi_aff_free(res
);
4682 /* Compute the preimage of a range of dimensions in the affine expression "src"
4683 * under "ma" and put the result in "dst". The number of dimensions in "src"
4684 * that precede the range is given by "n_before". The number of dimensions
4685 * in the range is given by the number of output dimensions of "ma".
4686 * The number of dimensions that follow the range is given by "n_after".
4687 * If "has_denom" is set (to one),
4688 * then "src" and "dst" have an extra initial denominator.
4689 * "n_div_ma" is the number of existentials in "ma"
4690 * "n_div_bset" is the number of existentials in "src"
4691 * The resulting "dst" (which is assumed to have been allocated by
4692 * the caller) contains coefficients for both sets of existentials,
4693 * first those in "ma" and then those in "src".
4694 * f, c1, c2 and g are temporary objects that have been initialized
4697 * Let src represent the expression
4699 * (a(p) + f_u u + b v + f_w w + c(divs))/d
4701 * and let ma represent the expressions
4703 * v_i = (r_i(p) + s_i(y) + t_i(divs'))/m_i
4705 * We start out with the following expression for dst:
4707 * (a(p) + f_u u + 0 y + f_w w + 0 divs' + c(divs) + f \sum_i b_i v_i)/d
4709 * with the multiplication factor f initially equal to 1
4710 * and f \sum_i b_i v_i kept separately.
4711 * For each x_i that we substitute, we multiply the numerator
4712 * (and denominator) of dst by c_1 = m_i and add the numerator
4713 * of the x_i expression multiplied by c_2 = f b_i,
4714 * after removing the common factors of c_1 and c_2.
4715 * The multiplication factor f also needs to be multiplied by c_1
4716 * for the next x_j, j > i.
4718 void isl_seq_preimage(isl_int
*dst
, isl_int
*src
,
4719 __isl_keep isl_multi_aff
*ma
, int n_before
, int n_after
,
4720 int n_div_ma
, int n_div_bmap
,
4721 isl_int f
, isl_int c1
, isl_int c2
, isl_int g
, int has_denom
)
4724 int n_param
, n_in
, n_out
;
4727 n_param
= isl_multi_aff_dim(ma
, isl_dim_param
);
4728 n_in
= isl_multi_aff_dim(ma
, isl_dim_in
);
4729 n_out
= isl_multi_aff_dim(ma
, isl_dim_out
);
4731 isl_seq_cpy(dst
, src
, has_denom
+ 1 + n_param
+ n_before
);
4732 o_dst
= o_src
= has_denom
+ 1 + n_param
+ n_before
;
4733 isl_seq_clr(dst
+ o_dst
, n_in
);
4736 isl_seq_cpy(dst
+ o_dst
, src
+ o_src
, n_after
);
4739 isl_seq_clr(dst
+ o_dst
, n_div_ma
);
4741 isl_seq_cpy(dst
+ o_dst
, src
+ o_src
, n_div_bmap
);
4743 isl_int_set_si(f
, 1);
4745 for (i
= 0; i
< n_out
; ++i
) {
4746 int offset
= has_denom
+ 1 + n_param
+ n_before
+ i
;
4748 if (isl_int_is_zero(src
[offset
]))
4750 isl_int_set(c1
, ma
->p
[i
]->v
->el
[0]);
4751 isl_int_mul(c2
, f
, src
[offset
]);
4752 isl_int_gcd(g
, c1
, c2
);
4753 isl_int_divexact(c1
, c1
, g
);
4754 isl_int_divexact(c2
, c2
, g
);
4756 isl_int_mul(f
, f
, c1
);
4759 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
4760 c2
, ma
->p
[i
]->v
->el
+ o_src
, 1 + n_param
);
4761 o_dst
+= 1 + n_param
;
4762 o_src
+= 1 + n_param
;
4763 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_before
);
4765 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
4766 c2
, ma
->p
[i
]->v
->el
+ o_src
, n_in
);
4769 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_after
);
4771 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
4772 c2
, ma
->p
[i
]->v
->el
+ o_src
, n_div_ma
);
4775 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_div_bmap
);
4777 isl_int_mul(dst
[0], dst
[0], c1
);
4781 /* Compute the pullback of "aff" by the function represented by "ma".
4782 * In other words, plug in "ma" in "aff". The result is an affine expression
4783 * defined over the domain space of "ma".
4785 * If "aff" is represented by
4787 * (a(p) + b x + c(divs))/d
4789 * and ma is represented by
4791 * x = D(p) + F(y) + G(divs')
4793 * then the result is
4795 * (a(p) + b D(p) + b F(y) + b G(divs') + c(divs))/d
4797 * The divs in the local space of the input are similarly adjusted
4798 * through a call to isl_local_space_preimage_multi_aff.
4800 __isl_give isl_aff
*isl_aff_pullback_multi_aff(__isl_take isl_aff
*aff
,
4801 __isl_take isl_multi_aff
*ma
)
4803 isl_aff
*res
= NULL
;
4804 isl_local_space
*ls
;
4805 int n_div_aff
, n_div_ma
;
4806 isl_int f
, c1
, c2
, g
;
4808 ma
= isl_multi_aff_align_divs(ma
);
4812 n_div_aff
= isl_aff_dim(aff
, isl_dim_div
);
4813 n_div_ma
= ma
->n
? isl_aff_dim(ma
->p
[0], isl_dim_div
) : 0;
4815 ls
= isl_aff_get_domain_local_space(aff
);
4816 ls
= isl_local_space_preimage_multi_aff(ls
, isl_multi_aff_copy(ma
));
4817 res
= isl_aff_alloc(ls
);
4826 isl_seq_preimage(res
->v
->el
, aff
->v
->el
, ma
, 0, 0, n_div_ma
, n_div_aff
,
4835 isl_multi_aff_free(ma
);
4836 res
= isl_aff_normalize(res
);
4840 isl_multi_aff_free(ma
);
4845 /* Compute the pullback of "aff1" by the function represented by "aff2".
4846 * In other words, plug in "aff2" in "aff1". The result is an affine expression
4847 * defined over the domain space of "aff1".
4849 * The domain of "aff1" should match the range of "aff2", which means
4850 * that it should be single-dimensional.
4852 __isl_give isl_aff
*isl_aff_pullback_aff(__isl_take isl_aff
*aff1
,
4853 __isl_take isl_aff
*aff2
)
4857 ma
= isl_multi_aff_from_aff(aff2
);
4858 return isl_aff_pullback_multi_aff(aff1
, ma
);
4861 /* Compute the pullback of "ma1" by the function represented by "ma2".
4862 * In other words, plug in "ma2" in "ma1".
4864 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
4866 static __isl_give isl_multi_aff
*isl_multi_aff_pullback_multi_aff_aligned(
4867 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
4870 isl_space
*space
= NULL
;
4872 ma2
= isl_multi_aff_align_divs(ma2
);
4873 ma1
= isl_multi_aff_cow(ma1
);
4877 space
= isl_space_join(isl_multi_aff_get_space(ma2
),
4878 isl_multi_aff_get_space(ma1
));
4880 for (i
= 0; i
< ma1
->n
; ++i
) {
4881 ma1
->p
[i
] = isl_aff_pullback_multi_aff(ma1
->p
[i
],
4882 isl_multi_aff_copy(ma2
));
4887 ma1
= isl_multi_aff_reset_space(ma1
, space
);
4888 isl_multi_aff_free(ma2
);
4891 isl_space_free(space
);
4892 isl_multi_aff_free(ma2
);
4893 isl_multi_aff_free(ma1
);
4897 /* Compute the pullback of "ma1" by the function represented by "ma2".
4898 * In other words, plug in "ma2" in "ma1".
4900 __isl_give isl_multi_aff
*isl_multi_aff_pullback_multi_aff(
4901 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
4903 return isl_multi_aff_align_params_multi_multi_and(ma1
, ma2
,
4904 &isl_multi_aff_pullback_multi_aff_aligned
);
4907 /* Extend the local space of "dst" to include the divs
4908 * in the local space of "src".
4910 __isl_give isl_aff
*isl_aff_align_divs(__isl_take isl_aff
*dst
,
4911 __isl_keep isl_aff
*src
)
4919 return isl_aff_free(dst
);
4921 ctx
= isl_aff_get_ctx(src
);
4922 if (!isl_space_is_equal(src
->ls
->dim
, dst
->ls
->dim
))
4923 isl_die(ctx
, isl_error_invalid
,
4924 "spaces don't match", goto error
);
4926 if (src
->ls
->div
->n_row
== 0)
4929 exp1
= isl_alloc_array(ctx
, int, src
->ls
->div
->n_row
);
4930 exp2
= isl_alloc_array(ctx
, int, dst
->ls
->div
->n_row
);
4931 if (!exp1
|| (dst
->ls
->div
->n_row
&& !exp2
))
4934 div
= isl_merge_divs(src
->ls
->div
, dst
->ls
->div
, exp1
, exp2
);
4935 dst
= isl_aff_expand_divs(dst
, div
, exp2
);
4943 return isl_aff_free(dst
);
4946 /* Adjust the local spaces of the affine expressions in "maff"
4947 * such that they all have the save divs.
4949 __isl_give isl_multi_aff
*isl_multi_aff_align_divs(
4950 __isl_take isl_multi_aff
*maff
)
4958 maff
= isl_multi_aff_cow(maff
);
4962 for (i
= 1; i
< maff
->n
; ++i
)
4963 maff
->p
[0] = isl_aff_align_divs(maff
->p
[0], maff
->p
[i
]);
4964 for (i
= 1; i
< maff
->n
; ++i
) {
4965 maff
->p
[i
] = isl_aff_align_divs(maff
->p
[i
], maff
->p
[0]);
4967 return isl_multi_aff_free(maff
);
4973 __isl_give isl_aff
*isl_aff_lift(__isl_take isl_aff
*aff
)
4975 aff
= isl_aff_cow(aff
);
4979 aff
->ls
= isl_local_space_lift(aff
->ls
);
4981 return isl_aff_free(aff
);
4986 /* Lift "maff" to a space with extra dimensions such that the result
4987 * has no more existentially quantified variables.
4988 * If "ls" is not NULL, then *ls is assigned the local space that lies
4989 * at the basis of the lifting applied to "maff".
4991 __isl_give isl_multi_aff
*isl_multi_aff_lift(__isl_take isl_multi_aff
*maff
,
4992 __isl_give isl_local_space
**ls
)
5006 isl_space
*space
= isl_multi_aff_get_domain_space(maff
);
5007 *ls
= isl_local_space_from_space(space
);
5009 return isl_multi_aff_free(maff
);
5014 maff
= isl_multi_aff_cow(maff
);
5015 maff
= isl_multi_aff_align_divs(maff
);
5019 n_div
= isl_aff_dim(maff
->p
[0], isl_dim_div
);
5020 space
= isl_multi_aff_get_space(maff
);
5021 space
= isl_space_lift(isl_space_domain(space
), n_div
);
5022 space
= isl_space_extend_domain_with_range(space
,
5023 isl_multi_aff_get_space(maff
));
5025 return isl_multi_aff_free(maff
);
5026 isl_space_free(maff
->space
);
5027 maff
->space
= space
;
5030 *ls
= isl_aff_get_domain_local_space(maff
->p
[0]);
5032 return isl_multi_aff_free(maff
);
5035 for (i
= 0; i
< maff
->n
; ++i
) {
5036 maff
->p
[i
] = isl_aff_lift(maff
->p
[i
]);
5044 isl_local_space_free(*ls
);
5045 return isl_multi_aff_free(maff
);
5049 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
5051 __isl_give isl_pw_aff
*isl_pw_multi_aff_get_pw_aff(
5052 __isl_keep isl_pw_multi_aff
*pma
, int pos
)
5062 n_out
= isl_pw_multi_aff_dim(pma
, isl_dim_out
);
5063 if (pos
< 0 || pos
>= n_out
)
5064 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5065 "index out of bounds", return NULL
);
5067 space
= isl_pw_multi_aff_get_space(pma
);
5068 space
= isl_space_drop_dims(space
, isl_dim_out
,
5069 pos
+ 1, n_out
- pos
- 1);
5070 space
= isl_space_drop_dims(space
, isl_dim_out
, 0, pos
);
5072 pa
= isl_pw_aff_alloc_size(space
, pma
->n
);
5073 for (i
= 0; i
< pma
->n
; ++i
) {
5075 aff
= isl_multi_aff_get_aff(pma
->p
[i
].maff
, pos
);
5076 pa
= isl_pw_aff_add_piece(pa
, isl_set_copy(pma
->p
[i
].set
), aff
);
5082 /* Return an isl_pw_multi_aff with the given "set" as domain and
5083 * an unnamed zero-dimensional range.
5085 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_domain(
5086 __isl_take isl_set
*set
)
5091 space
= isl_set_get_space(set
);
5092 space
= isl_space_from_domain(space
);
5093 ma
= isl_multi_aff_zero(space
);
5094 return isl_pw_multi_aff_alloc(set
, ma
);
5097 /* Add an isl_pw_multi_aff with the given "set" as domain and
5098 * an unnamed zero-dimensional range to *user.
5100 static int add_pw_multi_aff_from_domain(__isl_take isl_set
*set
, void *user
)
5102 isl_union_pw_multi_aff
**upma
= user
;
5103 isl_pw_multi_aff
*pma
;
5105 pma
= isl_pw_multi_aff_from_domain(set
);
5106 *upma
= isl_union_pw_multi_aff_add_pw_multi_aff(*upma
, pma
);
5111 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
5112 * an unnamed zero-dimensional range.
5114 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_domain(
5115 __isl_take isl_union_set
*uset
)
5118 isl_union_pw_multi_aff
*upma
;
5123 space
= isl_union_set_get_space(uset
);
5124 upma
= isl_union_pw_multi_aff_empty(space
);
5126 if (isl_union_set_foreach_set(uset
,
5127 &add_pw_multi_aff_from_domain
, &upma
) < 0)
5130 isl_union_set_free(uset
);
5133 isl_union_set_free(uset
);
5134 isl_union_pw_multi_aff_free(upma
);
5138 /* Convert "pma" to an isl_map and add it to *umap.
5140 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
, void *user
)
5142 isl_union_map
**umap
= user
;
5145 map
= isl_map_from_pw_multi_aff(pma
);
5146 *umap
= isl_union_map_add_map(*umap
, map
);
5151 /* Construct a union map mapping the domain of the union
5152 * piecewise multi-affine expression to its range, with each dimension
5153 * in the range equated to the corresponding affine expression on its cell.
5155 __isl_give isl_union_map
*isl_union_map_from_union_pw_multi_aff(
5156 __isl_take isl_union_pw_multi_aff
*upma
)
5159 isl_union_map
*umap
;
5164 space
= isl_union_pw_multi_aff_get_space(upma
);
5165 umap
= isl_union_map_empty(space
);
5167 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
5168 &map_from_pw_multi_aff
, &umap
) < 0)
5171 isl_union_pw_multi_aff_free(upma
);
5174 isl_union_pw_multi_aff_free(upma
);
5175 isl_union_map_free(umap
);
5179 /* Local data for bin_entry and the callback "fn".
5181 struct isl_union_pw_multi_aff_bin_data
{
5182 isl_union_pw_multi_aff
*upma2
;
5183 isl_union_pw_multi_aff
*res
;
5184 isl_pw_multi_aff
*pma
;
5185 int (*fn
)(void **entry
, void *user
);
5188 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
5189 * and call data->fn for each isl_pw_multi_aff in data->upma2.
5191 static int bin_entry(void **entry
, void *user
)
5193 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
5194 isl_pw_multi_aff
*pma
= *entry
;
5197 if (isl_hash_table_foreach(data
->upma2
->dim
->ctx
, &data
->upma2
->table
,
5198 data
->fn
, data
) < 0)
5204 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
5205 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
5206 * passed as user field) and the isl_pw_multi_aff from upma2 is available
5207 * as *entry. The callback should adjust data->res if desired.
5209 static __isl_give isl_union_pw_multi_aff
*bin_op(
5210 __isl_take isl_union_pw_multi_aff
*upma1
,
5211 __isl_take isl_union_pw_multi_aff
*upma2
,
5212 int (*fn
)(void **entry
, void *user
))
5215 struct isl_union_pw_multi_aff_bin_data data
= { NULL
, NULL
, NULL
, fn
};
5217 space
= isl_union_pw_multi_aff_get_space(upma2
);
5218 upma1
= isl_union_pw_multi_aff_align_params(upma1
, space
);
5219 space
= isl_union_pw_multi_aff_get_space(upma1
);
5220 upma2
= isl_union_pw_multi_aff_align_params(upma2
, space
);
5222 if (!upma1
|| !upma2
)
5226 data
.res
= isl_union_pw_multi_aff_alloc(isl_space_copy(upma1
->dim
),
5228 if (isl_hash_table_foreach(upma1
->dim
->ctx
, &upma1
->table
,
5229 &bin_entry
, &data
) < 0)
5232 isl_union_pw_multi_aff_free(upma1
);
5233 isl_union_pw_multi_aff_free(upma2
);
5236 isl_union_pw_multi_aff_free(upma1
);
5237 isl_union_pw_multi_aff_free(upma2
);
5238 isl_union_pw_multi_aff_free(data
.res
);
5242 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
5243 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
5245 static __isl_give isl_pw_multi_aff
*pw_multi_aff_range_product(
5246 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5250 space
= isl_space_range_product(isl_pw_multi_aff_get_space(pma1
),
5251 isl_pw_multi_aff_get_space(pma2
));
5252 return isl_pw_multi_aff_on_shared_domain_in(pma1
, pma2
, space
,
5253 &isl_multi_aff_range_product
);
5256 /* Given two isl_pw_multi_affs A -> B and C -> D,
5257 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
5259 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_range_product(
5260 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5262 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
5263 &pw_multi_aff_range_product
);
5266 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
5267 * construct an isl_pw_multi_aff (A * C) -> (B, D).
5269 static __isl_give isl_pw_multi_aff
*pw_multi_aff_flat_range_product(
5270 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5274 space
= isl_space_range_product(isl_pw_multi_aff_get_space(pma1
),
5275 isl_pw_multi_aff_get_space(pma2
));
5276 space
= isl_space_flatten_range(space
);
5277 return isl_pw_multi_aff_on_shared_domain_in(pma1
, pma2
, space
,
5278 &isl_multi_aff_flat_range_product
);
5281 /* Given two isl_pw_multi_affs A -> B and C -> D,
5282 * construct an isl_pw_multi_aff (A * C) -> (B, D).
5284 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_flat_range_product(
5285 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5287 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
5288 &pw_multi_aff_flat_range_product
);
5291 /* If data->pma and *entry have the same domain space, then compute
5292 * their flat range product and the result to data->res.
5294 static int flat_range_product_entry(void **entry
, void *user
)
5296 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
5297 isl_pw_multi_aff
*pma2
= *entry
;
5299 if (!isl_space_tuple_match(data
->pma
->dim
, isl_dim_in
,
5300 pma2
->dim
, isl_dim_in
))
5303 pma2
= isl_pw_multi_aff_flat_range_product(
5304 isl_pw_multi_aff_copy(data
->pma
),
5305 isl_pw_multi_aff_copy(pma2
));
5307 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma2
);
5312 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
5313 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
5315 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_flat_range_product(
5316 __isl_take isl_union_pw_multi_aff
*upma1
,
5317 __isl_take isl_union_pw_multi_aff
*upma2
)
5319 return bin_op(upma1
, upma2
, &flat_range_product_entry
);
5322 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5323 * The parameters are assumed to have been aligned.
5325 * The implementation essentially performs an isl_pw_*_on_shared_domain,
5326 * except that it works on two different isl_pw_* types.
5328 static __isl_give isl_pw_multi_aff
*pw_multi_aff_set_pw_aff(
5329 __isl_take isl_pw_multi_aff
*pma
, unsigned pos
,
5330 __isl_take isl_pw_aff
*pa
)
5333 isl_pw_multi_aff
*res
= NULL
;
5338 if (!isl_space_tuple_match(pma
->dim
, isl_dim_in
, pa
->dim
, isl_dim_in
))
5339 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5340 "domains don't match", goto error
);
5341 if (pos
>= isl_pw_multi_aff_dim(pma
, isl_dim_out
))
5342 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5343 "index out of bounds", goto error
);
5346 res
= isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma
), n
);
5348 for (i
= 0; i
< pma
->n
; ++i
) {
5349 for (j
= 0; j
< pa
->n
; ++j
) {
5351 isl_multi_aff
*res_ij
;
5354 common
= isl_set_intersect(isl_set_copy(pma
->p
[i
].set
),
5355 isl_set_copy(pa
->p
[j
].set
));
5356 empty
= isl_set_plain_is_empty(common
);
5357 if (empty
< 0 || empty
) {
5358 isl_set_free(common
);
5364 res_ij
= isl_multi_aff_set_aff(
5365 isl_multi_aff_copy(pma
->p
[i
].maff
), pos
,
5366 isl_aff_copy(pa
->p
[j
].aff
));
5367 res_ij
= isl_multi_aff_gist(res_ij
,
5368 isl_set_copy(common
));
5370 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
5374 isl_pw_multi_aff_free(pma
);
5375 isl_pw_aff_free(pa
);
5378 isl_pw_multi_aff_free(pma
);
5379 isl_pw_aff_free(pa
);
5380 return isl_pw_multi_aff_free(res
);
5383 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5385 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_set_pw_aff(
5386 __isl_take isl_pw_multi_aff
*pma
, unsigned pos
,
5387 __isl_take isl_pw_aff
*pa
)
5391 if (isl_space_match(pma
->dim
, isl_dim_param
, pa
->dim
, isl_dim_param
))
5392 return pw_multi_aff_set_pw_aff(pma
, pos
, pa
);
5393 if (!isl_space_has_named_params(pma
->dim
) ||
5394 !isl_space_has_named_params(pa
->dim
))
5395 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5396 "unaligned unnamed parameters", goto error
);
5397 pma
= isl_pw_multi_aff_align_params(pma
, isl_pw_aff_get_space(pa
));
5398 pa
= isl_pw_aff_align_params(pa
, isl_pw_multi_aff_get_space(pma
));
5399 return pw_multi_aff_set_pw_aff(pma
, pos
, pa
);
5401 isl_pw_multi_aff_free(pma
);
5402 isl_pw_aff_free(pa
);
5406 /* Do the parameters of "pa" match those of "space"?
5408 int isl_pw_aff_matching_params(__isl_keep isl_pw_aff
*pa
,
5409 __isl_keep isl_space
*space
)
5411 isl_space
*pa_space
;
5417 pa_space
= isl_pw_aff_get_space(pa
);
5419 match
= isl_space_match(space
, isl_dim_param
, pa_space
, isl_dim_param
);
5421 isl_space_free(pa_space
);
5425 /* Check that the domain space of "pa" matches "space".
5427 * Return 0 on success and -1 on error.
5429 int isl_pw_aff_check_match_domain_space(__isl_keep isl_pw_aff
*pa
,
5430 __isl_keep isl_space
*space
)
5432 isl_space
*pa_space
;
5438 pa_space
= isl_pw_aff_get_space(pa
);
5440 match
= isl_space_match(space
, isl_dim_param
, pa_space
, isl_dim_param
);
5444 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
5445 "parameters don't match", goto error
);
5446 match
= isl_space_tuple_match(space
, isl_dim_in
, pa_space
, isl_dim_in
);
5450 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
5451 "domains don't match", goto error
);
5452 isl_space_free(pa_space
);
5455 isl_space_free(pa_space
);
5462 #include <isl_multi_templ.c>
5464 /* Scale the elements of "pma" by the corresponding elements of "mv".
5466 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_scale_multi_val(
5467 __isl_take isl_pw_multi_aff
*pma
, __isl_take isl_multi_val
*mv
)
5471 pma
= isl_pw_multi_aff_cow(pma
);
5474 if (!isl_space_tuple_match(pma
->dim
, isl_dim_out
,
5475 mv
->space
, isl_dim_set
))
5476 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5477 "spaces don't match", goto error
);
5478 if (!isl_space_match(pma
->dim
, isl_dim_param
,
5479 mv
->space
, isl_dim_param
)) {
5480 pma
= isl_pw_multi_aff_align_params(pma
,
5481 isl_multi_val_get_space(mv
));
5482 mv
= isl_multi_val_align_params(mv
,
5483 isl_pw_multi_aff_get_space(pma
));
5488 for (i
= 0; i
< pma
->n
; ++i
) {
5489 pma
->p
[i
].maff
= isl_multi_aff_scale_multi_val(pma
->p
[i
].maff
,
5490 isl_multi_val_copy(mv
));
5491 if (!pma
->p
[i
].maff
)
5495 isl_multi_val_free(mv
);
5498 isl_multi_val_free(mv
);
5499 isl_pw_multi_aff_free(pma
);
5503 /* Internal data structure for isl_union_pw_multi_aff_scale_multi_val.
5504 * mv contains the mv argument.
5505 * res collects the results.
5507 struct isl_union_pw_multi_aff_scale_multi_val_data
{
5509 isl_union_pw_multi_aff
*res
;
5512 /* This function is called for each entry of an isl_union_pw_multi_aff.
5513 * If the space of the entry matches that of data->mv,
5514 * then apply isl_pw_multi_aff_scale_multi_val and add the result
5517 static int union_pw_multi_aff_scale_multi_val_entry(void **entry
, void *user
)
5519 struct isl_union_pw_multi_aff_scale_multi_val_data
*data
= user
;
5520 isl_pw_multi_aff
*pma
= *entry
;
5524 if (!isl_space_tuple_match(pma
->dim
, isl_dim_out
,
5525 data
->mv
->space
, isl_dim_set
))
5528 pma
= isl_pw_multi_aff_copy(pma
);
5529 pma
= isl_pw_multi_aff_scale_multi_val(pma
,
5530 isl_multi_val_copy(data
->mv
));
5531 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma
);
5538 /* Scale the elements of "upma" by the corresponding elements of "mv",
5539 * for those entries that match the space of "mv".
5541 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_scale_multi_val(
5542 __isl_take isl_union_pw_multi_aff
*upma
, __isl_take isl_multi_val
*mv
)
5544 struct isl_union_pw_multi_aff_scale_multi_val_data data
;
5546 upma
= isl_union_pw_multi_aff_align_params(upma
,
5547 isl_multi_val_get_space(mv
));
5548 mv
= isl_multi_val_align_params(mv
,
5549 isl_union_pw_multi_aff_get_space(upma
));
5554 data
.res
= isl_union_pw_multi_aff_alloc(isl_space_copy(upma
->dim
),
5556 if (isl_hash_table_foreach(upma
->dim
->ctx
, &upma
->table
,
5557 &union_pw_multi_aff_scale_multi_val_entry
, &data
) < 0)
5560 isl_multi_val_free(mv
);
5561 isl_union_pw_multi_aff_free(upma
);
5564 isl_multi_val_free(mv
);
5565 isl_union_pw_multi_aff_free(upma
);
5569 /* Construct and return a piecewise multi affine expression
5570 * in the given space with value zero in each of the output dimensions and
5571 * a universe domain.
5573 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_zero(__isl_take isl_space
*space
)
5575 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_zero(space
));
5578 /* Construct and return a piecewise multi affine expression
5579 * that is equal to the given piecewise affine expression.
5581 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_pw_aff(
5582 __isl_take isl_pw_aff
*pa
)
5586 isl_pw_multi_aff
*pma
;
5591 space
= isl_pw_aff_get_space(pa
);
5592 pma
= isl_pw_multi_aff_alloc_size(space
, pa
->n
);
5594 for (i
= 0; i
< pa
->n
; ++i
) {
5598 set
= isl_set_copy(pa
->p
[i
].set
);
5599 ma
= isl_multi_aff_from_aff(isl_aff_copy(pa
->p
[i
].aff
));
5600 pma
= isl_pw_multi_aff_add_piece(pma
, set
, ma
);
5603 isl_pw_aff_free(pa
);
5607 /* Construct a set or map mapping the shared (parameter) domain
5608 * of the piecewise affine expressions to the range of "mpa"
5609 * with each dimension in the range equated to the
5610 * corresponding piecewise affine expression.
5612 static __isl_give isl_map
*map_from_multi_pw_aff(
5613 __isl_take isl_multi_pw_aff
*mpa
)
5622 if (isl_space_dim(mpa
->space
, isl_dim_out
) != mpa
->n
)
5623 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
5624 "invalid space", return isl_multi_pw_aff_free(mpa
));
5626 space
= isl_multi_pw_aff_get_domain_space(mpa
);
5627 map
= isl_map_universe(isl_space_from_domain(space
));
5629 for (i
= 0; i
< mpa
->n
; ++i
) {
5633 pa
= isl_pw_aff_copy(mpa
->p
[i
]);
5634 map_i
= map_from_pw_aff(pa
);
5636 map
= isl_map_flat_range_product(map
, map_i
);
5639 map
= isl_map_reset_space(map
, isl_multi_pw_aff_get_space(mpa
));
5641 isl_multi_pw_aff_free(mpa
);
5645 /* Construct a map mapping the shared domain
5646 * of the piecewise affine expressions to the range of "mpa"
5647 * with each dimension in the range equated to the
5648 * corresponding piecewise affine expression.
5650 __isl_give isl_map
*isl_map_from_multi_pw_aff(__isl_take isl_multi_pw_aff
*mpa
)
5654 if (isl_space_is_set(mpa
->space
))
5655 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
5656 "space of input is not a map", goto error
);
5658 return map_from_multi_pw_aff(mpa
);
5660 isl_multi_pw_aff_free(mpa
);
5664 /* Construct a set mapping the shared parameter domain
5665 * of the piecewise affine expressions to the space of "mpa"
5666 * with each dimension in the range equated to the
5667 * corresponding piecewise affine expression.
5669 __isl_give isl_set
*isl_set_from_multi_pw_aff(__isl_take isl_multi_pw_aff
*mpa
)
5673 if (!isl_space_is_set(mpa
->space
))
5674 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
5675 "space of input is not a set", goto error
);
5677 return map_from_multi_pw_aff(mpa
);
5679 isl_multi_pw_aff_free(mpa
);
5683 /* Construct and return a piecewise multi affine expression
5684 * that is equal to the given multi piecewise affine expression
5685 * on the shared domain of the piecewise affine expressions.
5687 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_multi_pw_aff(
5688 __isl_take isl_multi_pw_aff
*mpa
)
5693 isl_pw_multi_aff
*pma
;
5698 space
= isl_multi_pw_aff_get_space(mpa
);
5701 isl_multi_pw_aff_free(mpa
);
5702 return isl_pw_multi_aff_zero(space
);
5705 pa
= isl_multi_pw_aff_get_pw_aff(mpa
, 0);
5706 pma
= isl_pw_multi_aff_from_pw_aff(pa
);
5708 for (i
= 1; i
< mpa
->n
; ++i
) {
5709 isl_pw_multi_aff
*pma_i
;
5711 pa
= isl_multi_pw_aff_get_pw_aff(mpa
, i
);
5712 pma_i
= isl_pw_multi_aff_from_pw_aff(pa
);
5713 pma
= isl_pw_multi_aff_range_product(pma
, pma_i
);
5716 pma
= isl_pw_multi_aff_reset_space(pma
, space
);
5718 isl_multi_pw_aff_free(mpa
);
5722 /* Construct and return a multi piecewise affine expression
5723 * that is equal to the given multi affine expression.
5725 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_from_multi_aff(
5726 __isl_take isl_multi_aff
*ma
)
5729 isl_multi_pw_aff
*mpa
;
5734 n
= isl_multi_aff_dim(ma
, isl_dim_out
);
5735 mpa
= isl_multi_pw_aff_alloc(isl_multi_aff_get_space(ma
));
5737 for (i
= 0; i
< n
; ++i
) {
5740 pa
= isl_pw_aff_from_aff(isl_multi_aff_get_aff(ma
, i
));
5741 mpa
= isl_multi_pw_aff_set_pw_aff(mpa
, i
, pa
);
5744 isl_multi_aff_free(ma
);
5748 /* Construct and return a multi piecewise affine expression
5749 * that is equal to the given piecewise multi affine expression.
5751 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_from_pw_multi_aff(
5752 __isl_take isl_pw_multi_aff
*pma
)
5756 isl_multi_pw_aff
*mpa
;
5761 n
= isl_pw_multi_aff_dim(pma
, isl_dim_out
);
5762 space
= isl_pw_multi_aff_get_space(pma
);
5763 mpa
= isl_multi_pw_aff_alloc(space
);
5765 for (i
= 0; i
< n
; ++i
) {
5768 pa
= isl_pw_multi_aff_get_pw_aff(pma
, i
);
5769 mpa
= isl_multi_pw_aff_set_pw_aff(mpa
, i
, pa
);
5772 isl_pw_multi_aff_free(pma
);
5776 /* Do "pa1" and "pa2" represent the same function?
5778 * We first check if they are obviously equal.
5779 * If not, we convert them to maps and check if those are equal.
5781 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff
*pa1
, __isl_keep isl_pw_aff
*pa2
)
5784 isl_map
*map1
, *map2
;
5789 equal
= isl_pw_aff_plain_is_equal(pa1
, pa2
);
5790 if (equal
< 0 || equal
)
5793 map1
= map_from_pw_aff(isl_pw_aff_copy(pa1
));
5794 map2
= map_from_pw_aff(isl_pw_aff_copy(pa2
));
5795 equal
= isl_map_is_equal(map1
, map2
);
5802 /* Do "mpa1" and "mpa2" represent the same function?
5804 * Note that we cannot convert the entire isl_multi_pw_aff
5805 * to a map because the domains of the piecewise affine expressions
5806 * may not be the same.
5808 int isl_multi_pw_aff_is_equal(__isl_keep isl_multi_pw_aff
*mpa1
,
5809 __isl_keep isl_multi_pw_aff
*mpa2
)
5817 if (!isl_space_match(mpa1
->space
, isl_dim_param
,
5818 mpa2
->space
, isl_dim_param
)) {
5819 if (!isl_space_has_named_params(mpa1
->space
))
5821 if (!isl_space_has_named_params(mpa2
->space
))
5823 mpa1
= isl_multi_pw_aff_copy(mpa1
);
5824 mpa2
= isl_multi_pw_aff_copy(mpa2
);
5825 mpa1
= isl_multi_pw_aff_align_params(mpa1
,
5826 isl_multi_pw_aff_get_space(mpa2
));
5827 mpa2
= isl_multi_pw_aff_align_params(mpa2
,
5828 isl_multi_pw_aff_get_space(mpa1
));
5829 equal
= isl_multi_pw_aff_is_equal(mpa1
, mpa2
);
5830 isl_multi_pw_aff_free(mpa1
);
5831 isl_multi_pw_aff_free(mpa2
);
5835 equal
= isl_space_is_equal(mpa1
->space
, mpa2
->space
);
5836 if (equal
< 0 || !equal
)
5839 for (i
= 0; i
< mpa1
->n
; ++i
) {
5840 equal
= isl_pw_aff_is_equal(mpa1
->p
[i
], mpa2
->p
[i
]);
5841 if (equal
< 0 || !equal
)
5848 /* Coalesce the elements of "mpa".
5850 * Note that such coalescing does not change the meaning of "mpa"
5851 * so there is no need to cow. We do need to be careful not to
5852 * destroy any other copies of "mpa" in case of failure.
5854 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_coalesce(
5855 __isl_take isl_multi_pw_aff
*mpa
)
5862 for (i
= 0; i
< mpa
->n
; ++i
) {
5863 isl_pw_aff
*pa
= isl_pw_aff_copy(mpa
->p
[i
]);
5864 pa
= isl_pw_aff_coalesce(pa
);
5866 return isl_multi_pw_aff_free(mpa
);
5867 isl_pw_aff_free(mpa
->p
[i
]);
5874 /* Compute the pullback of "mpa" by the function represented by "ma".
5875 * In other words, plug in "ma" in "mpa".
5877 * The parameters of "mpa" and "ma" are assumed to have been aligned.
5879 static __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_aff_aligned(
5880 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_multi_aff
*ma
)
5883 isl_space
*space
= NULL
;
5885 mpa
= isl_multi_pw_aff_cow(mpa
);
5889 space
= isl_space_join(isl_multi_aff_get_space(ma
),
5890 isl_multi_pw_aff_get_space(mpa
));
5894 for (i
= 0; i
< mpa
->n
; ++i
) {
5895 mpa
->p
[i
] = isl_pw_aff_pullback_multi_aff(mpa
->p
[i
],
5896 isl_multi_aff_copy(ma
));
5901 isl_multi_aff_free(ma
);
5902 isl_space_free(mpa
->space
);
5906 isl_space_free(space
);
5907 isl_multi_pw_aff_free(mpa
);
5908 isl_multi_aff_free(ma
);
5912 /* Compute the pullback of "mpa" by the function represented by "ma".
5913 * In other words, plug in "ma" in "mpa".
5915 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_aff(
5916 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_multi_aff
*ma
)
5920 if (isl_space_match(mpa
->space
, isl_dim_param
,
5921 ma
->space
, isl_dim_param
))
5922 return isl_multi_pw_aff_pullback_multi_aff_aligned(mpa
, ma
);
5923 mpa
= isl_multi_pw_aff_align_params(mpa
, isl_multi_aff_get_space(ma
));
5924 ma
= isl_multi_aff_align_params(ma
, isl_multi_pw_aff_get_space(mpa
));
5925 return isl_multi_pw_aff_pullback_multi_aff_aligned(mpa
, ma
);
5927 isl_multi_pw_aff_free(mpa
);
5928 isl_multi_aff_free(ma
);
5932 /* Compute the pullback of "mpa" by the function represented by "pma".
5933 * In other words, plug in "pma" in "mpa".
5935 * The parameters of "mpa" and "mpa" are assumed to have been aligned.
5937 static __isl_give isl_multi_pw_aff
*
5938 isl_multi_pw_aff_pullback_pw_multi_aff_aligned(
5939 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_multi_aff
*pma
)
5942 isl_space
*space
= NULL
;
5944 mpa
= isl_multi_pw_aff_cow(mpa
);
5948 space
= isl_space_join(isl_pw_multi_aff_get_space(pma
),
5949 isl_multi_pw_aff_get_space(mpa
));
5951 for (i
= 0; i
< mpa
->n
; ++i
) {
5952 mpa
->p
[i
] = isl_pw_aff_pullback_pw_multi_aff_aligned(mpa
->p
[i
],
5953 isl_pw_multi_aff_copy(pma
));
5958 isl_pw_multi_aff_free(pma
);
5959 isl_space_free(mpa
->space
);
5963 isl_space_free(space
);
5964 isl_multi_pw_aff_free(mpa
);
5965 isl_pw_multi_aff_free(pma
);
5969 /* Compute the pullback of "mpa" by the function represented by "pma".
5970 * In other words, plug in "pma" in "mpa".
5972 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_pw_multi_aff(
5973 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_multi_aff
*pma
)
5977 if (isl_space_match(mpa
->space
, isl_dim_param
, pma
->dim
, isl_dim_param
))
5978 return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa
, pma
);
5979 mpa
= isl_multi_pw_aff_align_params(mpa
,
5980 isl_pw_multi_aff_get_space(pma
));
5981 pma
= isl_pw_multi_aff_align_params(pma
,
5982 isl_multi_pw_aff_get_space(mpa
));
5983 return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa
, pma
);
5985 isl_multi_pw_aff_free(mpa
);
5986 isl_pw_multi_aff_free(pma
);
5990 /* Compute the pullback of "mpa1" by the function represented by "mpa2".
5991 * In other words, plug in "mpa2" in "mpa1".
5993 * The parameters of "mpa1" and "mpa2" are assumed to have been aligned.
5995 static __isl_give isl_multi_pw_aff
*
5996 isl_multi_pw_aff_pullback_multi_pw_aff_aligned(
5997 __isl_take isl_multi_pw_aff
*mpa1
, __isl_take isl_multi_pw_aff
*mpa2
)
5999 isl_pw_multi_aff
*pma
;
6001 pma
= isl_pw_multi_aff_from_multi_pw_aff(mpa2
);
6002 return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa1
, pma
);
6005 /* Compute the pullback of "mpa1" by the function represented by "mpa2".
6006 * In other words, plug in "mpa2" in "mpa1".
6008 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_pw_aff(
6009 __isl_take isl_multi_pw_aff
*mpa1
, __isl_take isl_multi_pw_aff
*mpa2
)
6011 return isl_multi_pw_aff_align_params_multi_multi_and(mpa1
, mpa2
,
6012 &isl_multi_pw_aff_pullback_multi_pw_aff_aligned
);