2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012-2014 Ecole Normale Superieure
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
8 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
10 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
13 #include <isl_ctx_private.h>
15 #include <isl_map_private.h>
16 #include <isl_local_space_private.h>
17 #include <isl_space_private.h>
18 #include <isl_mat_private.h>
19 #include <isl_aff_private.h>
20 #include <isl_vec_private.h>
21 #include <isl_point_private.h>
23 #include <isl_local.h>
25 isl_ctx
*isl_local_space_get_ctx(__isl_keep isl_local_space
*ls
)
27 return ls
? ls
->dim
->ctx
: NULL
;
30 /* Return a hash value that digests "ls".
32 uint32_t isl_local_space_get_hash(__isl_keep isl_local_space
*ls
)
34 uint32_t hash
, space_hash
, div_hash
;
39 hash
= isl_hash_init();
40 space_hash
= isl_space_get_hash(ls
->dim
);
41 isl_hash_hash(hash
, space_hash
);
42 div_hash
= isl_mat_get_hash(ls
->div
);
43 isl_hash_hash(hash
, div_hash
);
48 __isl_give isl_local_space
*isl_local_space_alloc_div(
49 __isl_take isl_space
*space
, __isl_take isl_mat
*div
)
52 isl_local_space
*ls
= NULL
;
57 ctx
= isl_space_get_ctx(space
);
58 ls
= isl_calloc_type(ctx
, struct isl_local_space
);
69 isl_space_free(space
);
70 isl_local_space_free(ls
);
74 __isl_give isl_local_space
*isl_local_space_alloc(__isl_take isl_space
*space
,
84 total
= isl_space_dim(space
, isl_dim_all
);
86 ctx
= isl_space_get_ctx(space
);
87 div
= isl_mat_alloc(ctx
, n_div
, 1 + 1 + total
+ n_div
);
88 return isl_local_space_alloc_div(space
, div
);
91 __isl_give isl_local_space
*isl_local_space_from_space(__isl_take isl_space
*dim
)
93 return isl_local_space_alloc(dim
, 0);
96 __isl_give isl_local_space
*isl_local_space_copy(__isl_keep isl_local_space
*ls
)
105 __isl_give isl_local_space
*isl_local_space_dup(__isl_keep isl_local_space
*ls
)
110 return isl_local_space_alloc_div(isl_space_copy(ls
->dim
),
111 isl_mat_copy(ls
->div
));
115 __isl_give isl_local_space
*isl_local_space_cow(__isl_take isl_local_space
*ls
)
123 return isl_local_space_dup(ls
);
126 __isl_null isl_local_space
*isl_local_space_free(
127 __isl_take isl_local_space
*ls
)
135 isl_space_free(ls
->dim
);
136 isl_mat_free(ls
->div
);
143 /* Is the local space that of a parameter domain?
145 isl_bool
isl_local_space_is_params(__isl_keep isl_local_space
*ls
)
148 return isl_bool_error
;
149 return isl_space_is_params(ls
->dim
);
152 /* Is the local space that of a set?
154 isl_bool
isl_local_space_is_set(__isl_keep isl_local_space
*ls
)
156 return ls
? isl_space_is_set(ls
->dim
) : isl_bool_error
;
159 /* Do "ls1" and "ls2" have the same space?
161 isl_bool
isl_local_space_has_equal_space(__isl_keep isl_local_space
*ls1
,
162 __isl_keep isl_local_space
*ls2
)
165 return isl_bool_error
;
167 return isl_space_is_equal(ls1
->dim
, ls2
->dim
);
170 /* Is the space of "ls" equal to "space"?
172 isl_bool
isl_local_space_has_space(__isl_keep isl_local_space
*ls
,
173 __isl_keep isl_space
*space
)
175 return isl_space_is_equal(isl_local_space_peek_space(ls
), space
);
178 /* Check that the space of "ls" is equal to "space".
180 static isl_stat
isl_local_space_check_has_space(__isl_keep isl_local_space
*ls
,
181 __isl_keep isl_space
*space
)
185 ok
= isl_local_space_has_space(ls
, space
);
187 return isl_stat_error
;
189 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
190 "spaces don't match", return isl_stat_error
);
194 /* Return true if the two local spaces are identical, with identical
195 * expressions for the integer divisions.
197 isl_bool
isl_local_space_is_equal(__isl_keep isl_local_space
*ls1
,
198 __isl_keep isl_local_space
*ls2
)
202 equal
= isl_local_space_has_equal_space(ls1
, ls2
);
203 if (equal
< 0 || !equal
)
206 if (!isl_local_space_divs_known(ls1
))
207 return isl_bool_false
;
208 if (!isl_local_space_divs_known(ls2
))
209 return isl_bool_false
;
211 return isl_mat_is_equal(ls1
->div
, ls2
->div
);
214 /* Compare two isl_local_spaces.
216 * Return -1 if "ls1" is "smaller" than "ls2", 1 if "ls1" is "greater"
217 * than "ls2" and 0 if they are equal.
219 int isl_local_space_cmp(__isl_keep isl_local_space
*ls1
,
220 __isl_keep isl_local_space
*ls2
)
231 cmp
= isl_space_cmp(ls1
->dim
, ls2
->dim
);
235 return isl_local_cmp(ls1
->div
, ls2
->div
);
238 int isl_local_space_dim(__isl_keep isl_local_space
*ls
,
239 enum isl_dim_type type
)
243 if (type
== isl_dim_div
)
244 return ls
->div
->n_row
;
245 if (type
== isl_dim_all
)
246 return isl_space_dim(ls
->dim
, isl_dim_all
) + ls
->div
->n_row
;
247 return isl_space_dim(ls
->dim
, type
);
250 unsigned isl_local_space_offset(__isl_keep isl_local_space
*ls
,
251 enum isl_dim_type type
)
260 case isl_dim_cst
: return 0;
261 case isl_dim_param
: return 1;
262 case isl_dim_in
: return 1 + space
->nparam
;
263 case isl_dim_out
: return 1 + space
->nparam
+ space
->n_in
;
265 return 1 + space
->nparam
+ space
->n_in
+ space
->n_out
;
270 /* Return the position of the dimension of the given type and name
272 * Return -1 if no such dimension can be found.
274 int isl_local_space_find_dim_by_name(__isl_keep isl_local_space
*ls
,
275 enum isl_dim_type type
, const char *name
)
279 if (type
== isl_dim_div
)
281 return isl_space_find_dim_by_name(ls
->dim
, type
, name
);
284 /* Does the given dimension have a name?
286 isl_bool
isl_local_space_has_dim_name(__isl_keep isl_local_space
*ls
,
287 enum isl_dim_type type
, unsigned pos
)
289 return ls
? isl_space_has_dim_name(ls
->dim
, type
, pos
) : isl_bool_error
;
292 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space
*ls
,
293 enum isl_dim_type type
, unsigned pos
)
295 return ls
? isl_space_get_dim_name(ls
->dim
, type
, pos
) : NULL
;
298 isl_bool
isl_local_space_has_dim_id(__isl_keep isl_local_space
*ls
,
299 enum isl_dim_type type
, unsigned pos
)
301 return ls
? isl_space_has_dim_id(ls
->dim
, type
, pos
) : isl_bool_error
;
304 __isl_give isl_id
*isl_local_space_get_dim_id(__isl_keep isl_local_space
*ls
,
305 enum isl_dim_type type
, unsigned pos
)
307 return ls
? isl_space_get_dim_id(ls
->dim
, type
, pos
) : NULL
;
310 /* Return the argument of the integer division at position "pos" in "ls".
311 * All local variables in "ls" are known to have a (complete) explicit
314 static __isl_give isl_aff
*extract_div(__isl_keep isl_local_space
*ls
, int pos
)
318 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
321 isl_seq_cpy(aff
->v
->el
, ls
->div
->row
[pos
], aff
->v
->size
);
325 /* Return the argument of the integer division at position "pos" in "ls".
326 * The integer division at that position is known to have a complete
327 * explicit representation, but some of the others do not.
328 * Remove them first because the domain of an isl_aff
329 * is not allowed to have unknown local variables.
331 static __isl_give isl_aff
*drop_unknown_divs_and_extract_div(
332 __isl_keep isl_local_space
*ls
, int pos
)
338 ls
= isl_local_space_copy(ls
);
339 n
= isl_local_space_dim(ls
, isl_dim_div
);
340 for (i
= n
- 1; i
>= 0; --i
) {
341 unknown
= isl_local_space_div_is_marked_unknown(ls
, i
);
343 ls
= isl_local_space_free(ls
);
346 ls
= isl_local_space_drop_dims(ls
, isl_dim_div
, i
, 1);
350 aff
= extract_div(ls
, pos
);
351 isl_local_space_free(ls
);
355 /* Return the argument of the integer division at position "pos" in "ls".
356 * The integer division is assumed to have a complete explicit
357 * representation. If some of the other integer divisions
358 * do not have an explicit representation, then they need
359 * to be removed first because the domain of an isl_aff
360 * is not allowed to have unknown local variables.
362 __isl_give isl_aff
*isl_local_space_get_div(__isl_keep isl_local_space
*ls
,
370 if (pos
< 0 || pos
>= ls
->div
->n_row
)
371 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
372 "index out of bounds", return NULL
);
374 known
= isl_local_space_div_is_known(ls
, pos
);
378 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
379 "expression of div unknown", return NULL
);
380 if (!isl_local_space_is_set(ls
))
381 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
382 "cannot represent divs of map spaces", return NULL
);
384 known
= isl_local_space_divs_known(ls
);
388 return extract_div(ls
, pos
);
390 return drop_unknown_divs_and_extract_div(ls
, pos
);
393 /* Return the space of "ls".
395 __isl_keep isl_space
*isl_local_space_peek_space(__isl_keep isl_local_space
*ls
)
403 __isl_give isl_space
*isl_local_space_get_space(__isl_keep isl_local_space
*ls
)
405 return isl_space_copy(isl_local_space_peek_space(ls
));
408 /* Return the space of "ls".
409 * This may be either a copy or the space itself
410 * if there is only one reference to "ls".
411 * This allows the space to be modified inplace
412 * if both the local space and its space have only a single reference.
413 * The caller is not allowed to modify "ls" between this call and
414 * a subsequent call to isl_local_space_restore_space.
415 * The only exception is that isl_local_space_free can be called instead.
417 __isl_give isl_space
*isl_local_space_take_space(__isl_keep isl_local_space
*ls
)
424 return isl_local_space_get_space(ls
);
430 /* Set the space of "ls" to "space", where the space of "ls" may be missing
431 * due to a preceding call to isl_local_space_take_space.
432 * However, in this case, "ls" only has a single reference and
433 * then the call to isl_local_space_cow has no effect.
435 __isl_give isl_local_space
*isl_local_space_restore_space(
436 __isl_take isl_local_space
*ls
, __isl_take isl_space
*space
)
441 if (ls
->dim
== space
) {
442 isl_space_free(space
);
446 ls
= isl_local_space_cow(ls
);
449 isl_space_free(ls
->dim
);
454 isl_local_space_free(ls
);
455 isl_space_free(space
);
459 /* Return the local variables of "ls".
461 __isl_keep isl_local
*isl_local_space_peek_local(__isl_keep isl_local_space
*ls
)
463 return ls
? ls
->div
: NULL
;
466 /* Replace the identifier of the tuple of type "type" by "id".
468 __isl_give isl_local_space
*isl_local_space_set_tuple_id(
469 __isl_take isl_local_space
*ls
,
470 enum isl_dim_type type
, __isl_take isl_id
*id
)
472 ls
= isl_local_space_cow(ls
);
475 ls
->dim
= isl_space_set_tuple_id(ls
->dim
, type
, id
);
477 return isl_local_space_free(ls
);
484 __isl_give isl_local_space
*isl_local_space_set_dim_name(
485 __isl_take isl_local_space
*ls
,
486 enum isl_dim_type type
, unsigned pos
, const char *s
)
488 ls
= isl_local_space_cow(ls
);
491 ls
->dim
= isl_space_set_dim_name(ls
->dim
, type
, pos
, s
);
493 return isl_local_space_free(ls
);
498 __isl_give isl_local_space
*isl_local_space_set_dim_id(
499 __isl_take isl_local_space
*ls
,
500 enum isl_dim_type type
, unsigned pos
, __isl_take isl_id
*id
)
502 ls
= isl_local_space_cow(ls
);
505 ls
->dim
= isl_space_set_dim_id(ls
->dim
, type
, pos
, id
);
507 return isl_local_space_free(ls
);
515 /* Construct a zero-dimensional local space with the given parameter domain.
517 __isl_give isl_local_space
*isl_local_space_set_from_params(
518 __isl_take isl_local_space
*ls
)
522 space
= isl_local_space_take_space(ls
);
523 space
= isl_space_set_from_params(space
);
524 ls
= isl_local_space_restore_space(ls
, space
);
529 __isl_give isl_local_space
*isl_local_space_reset_space(
530 __isl_take isl_local_space
*ls
, __isl_take isl_space
*dim
)
532 ls
= isl_local_space_cow(ls
);
536 isl_space_free(ls
->dim
);
541 isl_local_space_free(ls
);
546 /* Reorder the dimensions of "ls" according to the given reordering.
547 * The reordering r is assumed to have been extended with the local
548 * variables, leaving them in the same order.
550 __isl_give isl_local_space
*isl_local_space_realign(
551 __isl_take isl_local_space
*ls
, __isl_take isl_reordering
*r
)
553 ls
= isl_local_space_cow(ls
);
557 ls
->div
= isl_local_reorder(ls
->div
, isl_reordering_copy(r
));
561 ls
= isl_local_space_reset_space(ls
, isl_reordering_get_space(r
));
563 isl_reordering_free(r
);
566 isl_local_space_free(ls
);
567 isl_reordering_free(r
);
571 __isl_give isl_local_space
*isl_local_space_add_div(
572 __isl_take isl_local_space
*ls
, __isl_take isl_vec
*div
)
574 ls
= isl_local_space_cow(ls
);
578 if (ls
->div
->n_col
!= div
->size
)
579 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
580 "incompatible dimensions", goto error
);
582 ls
->div
= isl_mat_add_zero_cols(ls
->div
, 1);
583 ls
->div
= isl_mat_add_rows(ls
->div
, 1);
587 isl_seq_cpy(ls
->div
->row
[ls
->div
->n_row
- 1], div
->el
, div
->size
);
588 isl_int_set_si(ls
->div
->row
[ls
->div
->n_row
- 1][div
->size
], 0);
593 isl_local_space_free(ls
);
598 __isl_give isl_local_space
*isl_local_space_replace_divs(
599 __isl_take isl_local_space
*ls
, __isl_take isl_mat
*div
)
601 ls
= isl_local_space_cow(ls
);
606 isl_mat_free(ls
->div
);
611 isl_local_space_free(ls
);
615 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
618 static void expand_row(__isl_keep isl_mat
*dst
, int d
,
619 __isl_keep isl_mat
*src
, int s
, int *exp
)
622 unsigned c
= src
->n_col
- src
->n_row
;
624 isl_seq_cpy(dst
->row
[d
], src
->row
[s
], c
);
625 isl_seq_clr(dst
->row
[d
] + c
, dst
->n_col
- c
);
627 for (i
= 0; i
< s
; ++i
)
628 isl_int_set(dst
->row
[d
][c
+ exp
[i
]], src
->row
[s
][c
+ i
]);
631 /* Compare (known) divs.
632 * Return non-zero if at least one of the two divs is unknown.
633 * In particular, if both divs are unknown, we respect their
634 * current order. Otherwise, we sort the known div after the unknown
635 * div only if the known div depends on the unknown div.
637 static int cmp_row(isl_int
*row_i
, isl_int
*row_j
, int i
, int j
,
638 unsigned n_row
, unsigned n_col
)
641 int unknown_i
, unknown_j
;
643 unknown_i
= isl_int_is_zero(row_i
[0]);
644 unknown_j
= isl_int_is_zero(row_j
[0]);
646 if (unknown_i
&& unknown_j
)
650 li
= n_col
- n_row
+ i
;
652 li
= isl_seq_last_non_zero(row_i
, n_col
);
654 lj
= n_col
- n_row
+ j
;
656 lj
= isl_seq_last_non_zero(row_j
, n_col
);
661 return isl_seq_cmp(row_i
, row_j
, n_col
);
664 /* Call cmp_row for divs in a matrix.
666 int isl_mat_cmp_div(__isl_keep isl_mat
*div
, int i
, int j
)
668 return cmp_row(div
->row
[i
], div
->row
[j
], i
, j
, div
->n_row
, div
->n_col
);
671 /* Call cmp_row for divs in a basic map.
673 static int bmap_cmp_row(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
676 return cmp_row(bmap
->div
[i
], bmap
->div
[j
], i
, j
, bmap
->n_div
, total
);
679 /* Sort the divs in "bmap".
681 * We first make sure divs are placed after divs on which they depend.
682 * Then we perform a simple insertion sort based on the same ordering
683 * that is used in isl_merge_divs.
685 __isl_give isl_basic_map
*isl_basic_map_sort_divs(
686 __isl_take isl_basic_map
*bmap
)
691 bmap
= isl_basic_map_order_divs(bmap
);
694 if (bmap
->n_div
<= 1)
697 total
= 2 + isl_basic_map_total_dim(bmap
);
698 for (i
= 1; i
< bmap
->n_div
; ++i
) {
699 for (j
= i
- 1; j
>= 0; --j
) {
700 if (bmap_cmp_row(bmap
, j
, j
+ 1, total
) <= 0)
702 isl_basic_map_swap_div(bmap
, j
, j
+ 1);
709 /* Sort the divs in the basic maps of "map".
711 __isl_give isl_map
*isl_map_sort_divs(__isl_take isl_map
*map
)
713 return isl_map_inline_foreach_basic_map(map
, &isl_basic_map_sort_divs
);
716 /* Combine the two lists of divs into a single list.
717 * For each row i in div1, exp1[i] is set to the position of the corresponding
718 * row in the result. Similarly for div2 and exp2.
719 * This function guarantees
721 * exp1[i+1] > exp1[i]
722 * For optimal merging, the two input list should have been sorted.
724 __isl_give isl_mat
*isl_merge_divs(__isl_keep isl_mat
*div1
,
725 __isl_keep isl_mat
*div2
, int *exp1
, int *exp2
)
734 d
= div1
->n_col
- div1
->n_row
;
735 div
= isl_mat_alloc(div1
->ctx
, 1 + div1
->n_row
+ div2
->n_row
,
736 d
+ div1
->n_row
+ div2
->n_row
);
740 for (i
= 0, j
= 0, k
= 0; i
< div1
->n_row
&& j
< div2
->n_row
; ++k
) {
743 expand_row(div
, k
, div1
, i
, exp1
);
744 expand_row(div
, k
+ 1, div2
, j
, exp2
);
746 cmp
= isl_mat_cmp_div(div
, k
, k
+ 1);
750 } else if (cmp
< 0) {
754 isl_seq_cpy(div
->row
[k
], div
->row
[k
+ 1], div
->n_col
);
757 for (; i
< div1
->n_row
; ++i
, ++k
) {
758 expand_row(div
, k
, div1
, i
, exp1
);
761 for (; j
< div2
->n_row
; ++j
, ++k
) {
762 expand_row(div
, k
, div2
, j
, exp2
);
772 /* Swap divs "a" and "b" in "ls".
774 __isl_give isl_local_space
*isl_local_space_swap_div(
775 __isl_take isl_local_space
*ls
, int a
, int b
)
779 ls
= isl_local_space_cow(ls
);
782 if (a
< 0 || a
>= ls
->div
->n_row
|| b
< 0 || b
>= ls
->div
->n_row
)
783 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
784 "index out of bounds", return isl_local_space_free(ls
));
785 offset
= ls
->div
->n_col
- ls
->div
->n_row
;
786 ls
->div
= isl_mat_swap_cols(ls
->div
, offset
+ a
, offset
+ b
);
787 ls
->div
= isl_mat_swap_rows(ls
->div
, a
, b
);
789 return isl_local_space_free(ls
);
793 /* Construct a local space that contains all the divs in either
796 __isl_give isl_local_space
*isl_local_space_intersect(
797 __isl_take isl_local_space
*ls1
, __isl_take isl_local_space
*ls2
)
808 ctx
= isl_local_space_get_ctx(ls1
);
809 if (!isl_space_is_equal(ls1
->dim
, ls2
->dim
))
810 isl_die(ctx
, isl_error_invalid
,
811 "spaces should be identical", goto error
);
813 if (ls2
->div
->n_row
== 0) {
814 isl_local_space_free(ls2
);
818 if (ls1
->div
->n_row
== 0) {
819 isl_local_space_free(ls1
);
823 exp1
= isl_alloc_array(ctx
, int, ls1
->div
->n_row
);
824 exp2
= isl_alloc_array(ctx
, int, ls2
->div
->n_row
);
828 div
= isl_merge_divs(ls1
->div
, ls2
->div
, exp1
, exp2
);
832 equal
= isl_mat_is_equal(ls1
->div
, div
);
836 ls1
= isl_local_space_cow(ls1
);
842 isl_local_space_free(ls2
);
843 isl_mat_free(ls1
->div
);
851 isl_local_space_free(ls1
);
852 isl_local_space_free(ls2
);
856 /* Is the local variable "div" of "ls" marked as not having
857 * an explicit representation?
858 * Note that even if this variable is not marked in this way and therefore
859 * does have an explicit representation, this representation may still
860 * depend (indirectly) on other local variables that do not
861 * have an explicit representation.
863 isl_bool
isl_local_space_div_is_marked_unknown(__isl_keep isl_local_space
*ls
,
867 return isl_bool_error
;
868 return isl_local_div_is_marked_unknown(ls
->div
, div
);
871 /* Does "ls" have a complete explicit representation for div "div"?
873 isl_bool
isl_local_space_div_is_known(__isl_keep isl_local_space
*ls
, int div
)
876 return isl_bool_error
;
877 return isl_local_div_is_known(ls
->div
, div
);
880 /* Does "ls" have an explicit representation for all local variables?
882 isl_bool
isl_local_space_divs_known(__isl_keep isl_local_space
*ls
)
885 return isl_bool_error
;
886 return isl_local_divs_known(ls
->div
);
889 __isl_give isl_local_space
*isl_local_space_domain(
890 __isl_take isl_local_space
*ls
)
892 ls
= isl_local_space_drop_dims(ls
, isl_dim_out
,
893 0, isl_local_space_dim(ls
, isl_dim_out
));
894 ls
= isl_local_space_cow(ls
);
897 ls
->dim
= isl_space_domain(ls
->dim
);
899 return isl_local_space_free(ls
);
903 __isl_give isl_local_space
*isl_local_space_range(
904 __isl_take isl_local_space
*ls
)
906 ls
= isl_local_space_drop_dims(ls
, isl_dim_in
,
907 0, isl_local_space_dim(ls
, isl_dim_in
));
908 ls
= isl_local_space_cow(ls
);
912 ls
->dim
= isl_space_range(ls
->dim
);
914 return isl_local_space_free(ls
);
918 /* Construct a local space for a map that has the given local
919 * space as domain and that has a zero-dimensional range.
921 __isl_give isl_local_space
*isl_local_space_from_domain(
922 __isl_take isl_local_space
*ls
)
924 ls
= isl_local_space_cow(ls
);
927 ls
->dim
= isl_space_from_domain(ls
->dim
);
929 return isl_local_space_free(ls
);
933 __isl_give isl_local_space
*isl_local_space_add_dims(
934 __isl_take isl_local_space
*ls
, enum isl_dim_type type
, unsigned n
)
940 pos
= isl_local_space_dim(ls
, type
);
941 return isl_local_space_insert_dims(ls
, type
, pos
, n
);
944 /* Remove common factor of non-constant terms and denominator.
946 static void normalize_div(__isl_keep isl_local_space
*ls
, int div
)
948 isl_ctx
*ctx
= ls
->div
->ctx
;
949 unsigned total
= ls
->div
->n_col
- 2;
951 isl_seq_gcd(ls
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
952 isl_int_gcd(ctx
->normalize_gcd
,
953 ctx
->normalize_gcd
, ls
->div
->row
[div
][0]);
954 if (isl_int_is_one(ctx
->normalize_gcd
))
957 isl_seq_scale_down(ls
->div
->row
[div
] + 2, ls
->div
->row
[div
] + 2,
958 ctx
->normalize_gcd
, total
);
959 isl_int_divexact(ls
->div
->row
[div
][0], ls
->div
->row
[div
][0],
961 isl_int_fdiv_q(ls
->div
->row
[div
][1], ls
->div
->row
[div
][1],
965 /* Exploit the equalities in "eq" to simplify the expressions of
966 * the integer divisions in "ls".
967 * The integer divisions in "ls" are assumed to appear as regular
968 * dimensions in "eq".
970 __isl_give isl_local_space
*isl_local_space_substitute_equalities(
971 __isl_take isl_local_space
*ls
, __isl_take isl_basic_set
*eq
)
980 total
= isl_space_dim(eq
->dim
, isl_dim_all
);
981 if (isl_local_space_dim(ls
, isl_dim_all
) != total
)
982 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
983 "spaces don't match", goto error
);
986 for (i
= 0; i
< eq
->n_eq
; ++i
) {
987 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
988 if (j
< 0 || j
== 0 || j
>= total
)
991 for (k
= 0; k
< ls
->div
->n_row
; ++k
) {
992 if (isl_int_is_zero(ls
->div
->row
[k
][1 + j
]))
994 ls
= isl_local_space_cow(ls
);
997 ls
->div
= isl_mat_cow(ls
->div
);
1000 isl_seq_elim(ls
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
1001 &ls
->div
->row
[k
][0]);
1002 normalize_div(ls
, k
);
1006 isl_basic_set_free(eq
);
1009 isl_basic_set_free(eq
);
1010 isl_local_space_free(ls
);
1014 /* Plug in the affine expressions "subs" of length "subs_len" (including
1015 * the denominator and the constant term) into the variable at position "pos"
1016 * of the "n" div expressions starting at "first".
1018 * Let i be the dimension to replace and let "subs" be of the form
1022 * Any integer division starting at "first" with a non-zero coefficient for i,
1024 * floor((a i + g)/m)
1028 * floor((a f + d g)/(m d))
1030 __isl_give isl_local_space
*isl_local_space_substitute_seq(
1031 __isl_take isl_local_space
*ls
,
1032 enum isl_dim_type type
, unsigned pos
, isl_int
*subs
, int subs_len
,
1040 ls
= isl_local_space_cow(ls
);
1043 ls
->div
= isl_mat_cow(ls
->div
);
1045 return isl_local_space_free(ls
);
1047 if (first
+ n
> ls
->div
->n_row
)
1048 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1049 "index out of bounds", return isl_local_space_free(ls
));
1051 pos
+= isl_local_space_offset(ls
, type
);
1054 for (i
= first
; i
< first
+ n
; ++i
) {
1055 if (isl_int_is_zero(ls
->div
->row
[i
][1 + pos
]))
1057 isl_seq_substitute(ls
->div
->row
[i
], pos
, subs
,
1058 ls
->div
->n_col
, subs_len
, v
);
1059 normalize_div(ls
, i
);
1066 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
1069 * Let i be the dimension to replace and let "subs" be of the form
1073 * Any integer division with a non-zero coefficient for i,
1075 * floor((a i + g)/m)
1079 * floor((a f + d g)/(m d))
1081 __isl_give isl_local_space
*isl_local_space_substitute(
1082 __isl_take isl_local_space
*ls
,
1083 enum isl_dim_type type
, unsigned pos
, __isl_keep isl_aff
*subs
)
1085 ls
= isl_local_space_cow(ls
);
1087 return isl_local_space_free(ls
);
1089 if (!isl_space_is_equal(ls
->dim
, subs
->ls
->dim
))
1090 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1091 "spaces don't match", return isl_local_space_free(ls
));
1092 if (isl_local_space_dim(subs
->ls
, isl_dim_div
) != 0)
1093 isl_die(isl_local_space_get_ctx(ls
), isl_error_unsupported
,
1094 "cannot handle divs yet",
1095 return isl_local_space_free(ls
));
1097 return isl_local_space_substitute_seq(ls
, type
, pos
, subs
->v
->el
,
1098 subs
->v
->size
, 0, ls
->div
->n_row
);
1101 isl_bool
isl_local_space_is_named_or_nested(__isl_keep isl_local_space
*ls
,
1102 enum isl_dim_type type
)
1105 return isl_bool_error
;
1106 return isl_space_is_named_or_nested(ls
->dim
, type
);
1109 __isl_give isl_local_space
*isl_local_space_drop_dims(
1110 __isl_take isl_local_space
*ls
,
1111 enum isl_dim_type type
, unsigned first
, unsigned n
)
1117 if (n
== 0 && !isl_local_space_is_named_or_nested(ls
, type
))
1120 ctx
= isl_local_space_get_ctx(ls
);
1121 if (first
+ n
> isl_local_space_dim(ls
, type
))
1122 isl_die(ctx
, isl_error_invalid
, "range out of bounds",
1123 return isl_local_space_free(ls
));
1125 ls
= isl_local_space_cow(ls
);
1129 if (type
== isl_dim_div
) {
1130 ls
->div
= isl_mat_drop_rows(ls
->div
, first
, n
);
1132 ls
->dim
= isl_space_drop_dims(ls
->dim
, type
, first
, n
);
1134 return isl_local_space_free(ls
);
1137 first
+= 1 + isl_local_space_offset(ls
, type
);
1138 ls
->div
= isl_mat_drop_cols(ls
->div
, first
, n
);
1140 return isl_local_space_free(ls
);
1145 __isl_give isl_local_space
*isl_local_space_insert_dims(
1146 __isl_take isl_local_space
*ls
,
1147 enum isl_dim_type type
, unsigned first
, unsigned n
)
1153 if (n
== 0 && !isl_local_space_is_named_or_nested(ls
, type
))
1156 ctx
= isl_local_space_get_ctx(ls
);
1157 if (first
> isl_local_space_dim(ls
, type
))
1158 isl_die(ctx
, isl_error_invalid
, "position out of bounds",
1159 return isl_local_space_free(ls
));
1161 ls
= isl_local_space_cow(ls
);
1165 if (type
== isl_dim_div
) {
1166 ls
->div
= isl_mat_insert_zero_rows(ls
->div
, first
, n
);
1168 ls
->dim
= isl_space_insert_dims(ls
->dim
, type
, first
, n
);
1170 return isl_local_space_free(ls
);
1173 first
+= 1 + isl_local_space_offset(ls
, type
);
1174 ls
->div
= isl_mat_insert_zero_cols(ls
->div
, first
, n
);
1176 return isl_local_space_free(ls
);
1181 /* Does the linear part of "constraint" correspond to
1182 * integer division "div" in "ls"?
1184 * That is, given div = floor((c + f)/m), is the constraint of the form
1186 * f - m d + c' >= 0 [sign = 1]
1188 * -f + m d + c'' >= 0 [sign = -1]
1190 * If so, set *sign to the corresponding value.
1192 static isl_bool
is_linear_div_constraint(__isl_keep isl_local_space
*ls
,
1193 isl_int
*constraint
, unsigned div
, int *sign
)
1198 unknown
= isl_local_space_div_is_marked_unknown(ls
, div
);
1200 return isl_bool_error
;
1202 return isl_bool_false
;
1204 pos
= isl_local_space_offset(ls
, isl_dim_div
) + div
;
1206 if (isl_int_eq(constraint
[pos
], ls
->div
->row
[div
][0])) {
1208 if (!isl_seq_is_neg(constraint
+ 1,
1209 ls
->div
->row
[div
] + 2, pos
- 1))
1210 return isl_bool_false
;
1211 } else if (isl_int_abs_eq(constraint
[pos
], ls
->div
->row
[div
][0])) {
1213 if (!isl_seq_eq(constraint
+ 1, ls
->div
->row
[div
] + 2, pos
- 1))
1214 return isl_bool_false
;
1216 return isl_bool_false
;
1218 if (isl_seq_first_non_zero(constraint
+ pos
+ 1,
1219 ls
->div
->n_row
- div
- 1) != -1)
1220 return isl_bool_false
;
1221 return isl_bool_true
;
1224 /* Check if the constraints pointed to by "constraint" is a div
1225 * constraint corresponding to div "div" in "ls".
1227 * That is, if div = floor(f/m), then check if the constraint is
1231 * -(f-(m-1)) + m d >= 0
1233 * First check if the linear part is of the right form and
1234 * then check the constant term.
1236 isl_bool
isl_local_space_is_div_constraint(__isl_keep isl_local_space
*ls
,
1237 isl_int
*constraint
, unsigned div
)
1242 linear
= is_linear_div_constraint(ls
, constraint
, div
, &sign
);
1243 if (linear
< 0 || !linear
)
1248 isl_int_sub(ls
->div
->row
[div
][1],
1249 ls
->div
->row
[div
][1], ls
->div
->row
[div
][0]);
1250 isl_int_add_ui(ls
->div
->row
[div
][1], ls
->div
->row
[div
][1], 1);
1251 neg
= isl_seq_is_neg(constraint
, ls
->div
->row
[div
] + 1, 1);
1252 isl_int_sub_ui(ls
->div
->row
[div
][1], ls
->div
->row
[div
][1], 1);
1253 isl_int_add(ls
->div
->row
[div
][1],
1254 ls
->div
->row
[div
][1], ls
->div
->row
[div
][0]);
1256 return isl_bool_false
;
1258 if (!isl_int_eq(constraint
[0], ls
->div
->row
[div
][1]))
1259 return isl_bool_false
;
1262 return isl_bool_true
;
1265 /* Is the constraint pointed to by "constraint" one
1266 * of an equality that corresponds to integer division "div" in "ls"?
1268 * That is, given an integer division of the form
1270 * a = floor((f + c)/m)
1272 * is the equality of the form
1276 * Note that the constant term is not checked explicitly, but given
1277 * that this is a valid equality constraint, the constant c' necessarily
1278 * has a value close to -c.
1280 isl_bool
isl_local_space_is_div_equality(__isl_keep isl_local_space
*ls
,
1281 isl_int
*constraint
, unsigned div
)
1286 linear
= is_linear_div_constraint(ls
, constraint
, div
, &sign
);
1287 if (linear
< 0 || !linear
)
1294 * Set active[i] to 1 if the dimension at position i is involved
1295 * in the linear expression l.
1297 int *isl_local_space_get_active(__isl_keep isl_local_space
*ls
, isl_int
*l
)
1305 ctx
= isl_local_space_get_ctx(ls
);
1306 total
= isl_local_space_dim(ls
, isl_dim_all
);
1307 active
= isl_calloc_array(ctx
, int, total
);
1308 if (total
&& !active
)
1311 for (i
= 0; i
< total
; ++i
)
1312 active
[i
] = !isl_int_is_zero(l
[i
]);
1314 offset
= isl_local_space_offset(ls
, isl_dim_div
) - 1;
1315 for (i
= ls
->div
->n_row
- 1; i
>= 0; --i
) {
1316 if (!active
[offset
+ i
])
1318 for (j
= 0; j
< total
; ++j
)
1319 active
[j
] |= !isl_int_is_zero(ls
->div
->row
[i
][2 + j
]);
1325 /* Given a local space "ls" of a set, create a local space
1326 * for the lift of the set. In particular, the result
1327 * is of the form [dim -> local[..]], with ls->div->n_row variables in the
1328 * range of the wrapped map.
1330 __isl_give isl_local_space
*isl_local_space_lift(
1331 __isl_take isl_local_space
*ls
)
1333 ls
= isl_local_space_cow(ls
);
1337 ls
->dim
= isl_space_lift(ls
->dim
, ls
->div
->n_row
);
1338 ls
->div
= isl_mat_drop_rows(ls
->div
, 0, ls
->div
->n_row
);
1339 if (!ls
->dim
|| !ls
->div
)
1340 return isl_local_space_free(ls
);
1345 /* Construct a basic map that maps a set living in local space "ls"
1346 * to the corresponding lifted local space.
1348 __isl_give isl_basic_map
*isl_local_space_lifting(
1349 __isl_take isl_local_space
*ls
)
1351 isl_basic_map
*lifting
;
1352 isl_basic_set
*bset
;
1356 if (!isl_local_space_is_set(ls
))
1357 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1358 "lifting only defined on set spaces", goto error
);
1360 bset
= isl_basic_set_from_local_space(ls
);
1361 lifting
= isl_basic_set_unwrap(isl_basic_set_lift(bset
));
1362 lifting
= isl_basic_map_domain_map(lifting
);
1363 lifting
= isl_basic_map_reverse(lifting
);
1367 isl_local_space_free(ls
);
1371 /* Compute the preimage of "ls" under the function represented by "ma".
1372 * In other words, plug in "ma" in "ls". The result is a local space
1373 * that is part of the domain space of "ma".
1375 * If the divs in "ls" are represented as
1377 * floor((a_i(p) + b_i x + c_i(divs))/n_i)
1379 * and ma is represented by
1381 * x = D(p) + F(y) + G(divs')
1383 * then the resulting divs are
1385 * floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
1387 * We first copy over the divs from "ma" and then
1388 * we add the modified divs from "ls".
1390 __isl_give isl_local_space
*isl_local_space_preimage_multi_aff(
1391 __isl_take isl_local_space
*ls
, __isl_take isl_multi_aff
*ma
)
1395 isl_local_space
*res
= NULL
;
1396 int n_div_ls
, n_div_ma
;
1397 isl_int f
, c1
, c2
, g
;
1399 ma
= isl_multi_aff_align_divs(ma
);
1402 if (!isl_space_is_range_internal(ls
->dim
, ma
->space
))
1403 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1404 "spaces don't match", goto error
);
1406 n_div_ls
= isl_local_space_dim(ls
, isl_dim_div
);
1407 n_div_ma
= ma
->n
? isl_aff_dim(ma
->u
.p
[0], isl_dim_div
) : 0;
1409 space
= isl_space_domain(isl_multi_aff_get_space(ma
));
1410 res
= isl_local_space_alloc(space
, n_div_ma
+ n_div_ls
);
1415 isl_mat_free(res
->div
);
1416 res
->div
= isl_mat_copy(ma
->u
.p
[0]->ls
->div
);
1417 res
->div
= isl_mat_add_zero_cols(res
->div
, n_div_ls
);
1418 res
->div
= isl_mat_add_rows(res
->div
, n_div_ls
);
1428 for (i
= 0; i
< ls
->div
->n_row
; ++i
) {
1429 if (isl_int_is_zero(ls
->div
->row
[i
][0])) {
1430 isl_int_set_si(res
->div
->row
[n_div_ma
+ i
][0], 0);
1433 isl_seq_preimage(res
->div
->row
[n_div_ma
+ i
], ls
->div
->row
[i
],
1434 ma
, 0, 0, n_div_ma
, n_div_ls
, f
, c1
, c2
, g
, 1);
1435 normalize_div(res
, n_div_ma
+ i
);
1443 isl_local_space_free(ls
);
1444 isl_multi_aff_free(ma
);
1447 isl_local_space_free(ls
);
1448 isl_multi_aff_free(ma
);
1449 isl_local_space_free(res
);
1453 /* Move the "n" dimensions of "src_type" starting at "src_pos" of "ls"
1454 * to dimensions of "dst_type" at "dst_pos".
1456 * Moving to/from local dimensions is not allowed.
1457 * We currently assume that the dimension type changes.
1459 __isl_give isl_local_space
*isl_local_space_move_dims(
1460 __isl_take isl_local_space
*ls
,
1461 enum isl_dim_type dst_type
, unsigned dst_pos
,
1462 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
1470 !isl_local_space_is_named_or_nested(ls
, src_type
) &&
1471 !isl_local_space_is_named_or_nested(ls
, dst_type
))
1474 if (src_pos
+ n
> isl_local_space_dim(ls
, src_type
))
1475 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1476 "range out of bounds", return isl_local_space_free(ls
));
1477 if (dst_pos
> isl_local_space_dim(ls
, dst_type
))
1478 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1479 "position out of bounds",
1480 return isl_local_space_free(ls
));
1481 if (src_type
== isl_dim_div
)
1482 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1483 "cannot move divs", return isl_local_space_free(ls
));
1484 if (dst_type
== isl_dim_div
)
1485 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1486 "cannot move to divs", return isl_local_space_free(ls
));
1487 if (dst_type
== src_type
&& dst_pos
== src_pos
)
1489 if (dst_type
== src_type
)
1490 isl_die(isl_local_space_get_ctx(ls
), isl_error_unsupported
,
1491 "moving dims within the same type not supported",
1492 return isl_local_space_free(ls
));
1494 ls
= isl_local_space_cow(ls
);
1498 g_src_pos
= 1 + isl_local_space_offset(ls
, src_type
) + src_pos
;
1499 g_dst_pos
= 1 + isl_local_space_offset(ls
, dst_type
) + dst_pos
;
1500 if (dst_type
> src_type
)
1502 ls
->div
= isl_mat_move_cols(ls
->div
, g_dst_pos
, g_src_pos
, n
);
1504 return isl_local_space_free(ls
);
1505 ls
->dim
= isl_space_move_dims(ls
->dim
, dst_type
, dst_pos
,
1506 src_type
, src_pos
, n
);
1508 return isl_local_space_free(ls
);
1513 /* Remove any internal structure of the domain of "ls".
1514 * If there is any such internal structure in the input,
1515 * then the name of the corresponding space is also removed.
1517 __isl_give isl_local_space
*isl_local_space_flatten_domain(
1518 __isl_take isl_local_space
*ls
)
1523 if (!ls
->dim
->nested
[0])
1526 ls
= isl_local_space_cow(ls
);
1530 ls
->dim
= isl_space_flatten_domain(ls
->dim
);
1532 return isl_local_space_free(ls
);
1537 /* Remove any internal structure of the range of "ls".
1538 * If there is any such internal structure in the input,
1539 * then the name of the corresponding space is also removed.
1541 __isl_give isl_local_space
*isl_local_space_flatten_range(
1542 __isl_take isl_local_space
*ls
)
1547 if (!ls
->dim
->nested
[1])
1550 ls
= isl_local_space_cow(ls
);
1554 ls
->dim
= isl_space_flatten_range(ls
->dim
);
1556 return isl_local_space_free(ls
);
1561 /* Given the local space "ls" of a map, return the local space of a set
1562 * that lives in a space that wraps the space of "ls" and that has
1565 __isl_give isl_local_space
*isl_local_space_wrap(__isl_take isl_local_space
*ls
)
1567 ls
= isl_local_space_cow(ls
);
1571 ls
->dim
= isl_space_wrap(ls
->dim
);
1573 return isl_local_space_free(ls
);
1578 /* Lift the point "pnt", living in the space of "ls"
1579 * to live in a space with extra coordinates corresponding
1580 * to the local variables of "ls".
1582 __isl_give isl_point
*isl_local_space_lift_point(__isl_take isl_local_space
*ls
,
1583 __isl_take isl_point
*pnt
)
1590 if (isl_local_space_check_has_space(ls
, isl_point_peek_space(pnt
)) < 0)
1593 local
= isl_local_space_peek_local(ls
);
1594 n_local
= isl_local_space_dim(ls
, isl_dim_div
);
1596 space
= isl_point_take_space(pnt
);
1597 vec
= isl_point_take_vec(pnt
);
1599 space
= isl_space_lift(space
, n_local
);
1600 vec
= isl_local_extend_point_vec(local
, vec
);
1602 pnt
= isl_point_restore_vec(pnt
, vec
);
1603 pnt
= isl_point_restore_space(pnt
, space
);
1605 isl_local_space_free(ls
);
1609 isl_local_space_free(ls
);
1610 isl_point_free(pnt
);