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>
14 #include <isl_map_private.h>
15 #include <isl_local_space_private.h>
16 #include <isl_space_private.h>
17 #include <isl_mat_private.h>
18 #include <isl_aff_private.h>
19 #include <isl_vec_private.h>
21 #include <isl_local.h>
23 isl_ctx
*isl_local_space_get_ctx(__isl_keep isl_local_space
*ls
)
25 return ls
? ls
->dim
->ctx
: NULL
;
28 /* Return a hash value that digests "ls".
30 uint32_t isl_local_space_get_hash(__isl_keep isl_local_space
*ls
)
32 uint32_t hash
, space_hash
, div_hash
;
37 hash
= isl_hash_init();
38 space_hash
= isl_space_get_hash(ls
->dim
);
39 isl_hash_hash(hash
, space_hash
);
40 div_hash
= isl_mat_get_hash(ls
->div
);
41 isl_hash_hash(hash
, div_hash
);
46 __isl_give isl_local_space
*isl_local_space_alloc_div(__isl_take isl_space
*dim
,
47 __isl_take isl_mat
*div
)
50 isl_local_space
*ls
= NULL
;
55 ctx
= isl_space_get_ctx(dim
);
56 ls
= isl_calloc_type(ctx
, struct isl_local_space
);
68 isl_local_space_free(ls
);
72 __isl_give isl_local_space
*isl_local_space_alloc(__isl_take isl_space
*dim
,
82 total
= isl_space_dim(dim
, isl_dim_all
);
84 ctx
= isl_space_get_ctx(dim
);
85 div
= isl_mat_alloc(ctx
, n_div
, 1 + 1 + total
+ n_div
);
86 return isl_local_space_alloc_div(dim
, div
);
89 __isl_give isl_local_space
*isl_local_space_from_space(__isl_take isl_space
*dim
)
91 return isl_local_space_alloc(dim
, 0);
94 __isl_give isl_local_space
*isl_local_space_copy(__isl_keep isl_local_space
*ls
)
103 __isl_give isl_local_space
*isl_local_space_dup(__isl_keep isl_local_space
*ls
)
108 return isl_local_space_alloc_div(isl_space_copy(ls
->dim
),
109 isl_mat_copy(ls
->div
));
113 __isl_give isl_local_space
*isl_local_space_cow(__isl_take isl_local_space
*ls
)
121 return isl_local_space_dup(ls
);
124 __isl_null isl_local_space
*isl_local_space_free(
125 __isl_take isl_local_space
*ls
)
133 isl_space_free(ls
->dim
);
134 isl_mat_free(ls
->div
);
141 /* Is the local space that of a parameter domain?
143 isl_bool
isl_local_space_is_params(__isl_keep isl_local_space
*ls
)
146 return isl_bool_error
;
147 return isl_space_is_params(ls
->dim
);
150 /* Is the local space that of a set?
152 isl_bool
isl_local_space_is_set(__isl_keep isl_local_space
*ls
)
154 return ls
? isl_space_is_set(ls
->dim
) : isl_bool_error
;
157 /* Do "ls1" and "ls2" have the same space?
159 isl_bool
isl_local_space_has_equal_space(__isl_keep isl_local_space
*ls1
,
160 __isl_keep isl_local_space
*ls2
)
163 return isl_bool_error
;
165 return isl_space_is_equal(ls1
->dim
, ls2
->dim
);
168 /* Return true if the two local spaces are identical, with identical
169 * expressions for the integer divisions.
171 isl_bool
isl_local_space_is_equal(__isl_keep isl_local_space
*ls1
,
172 __isl_keep isl_local_space
*ls2
)
176 equal
= isl_local_space_has_equal_space(ls1
, ls2
);
177 if (equal
< 0 || !equal
)
180 if (!isl_local_space_divs_known(ls1
))
181 return isl_bool_false
;
182 if (!isl_local_space_divs_known(ls2
))
183 return isl_bool_false
;
185 return isl_mat_is_equal(ls1
->div
, ls2
->div
);
188 /* Compare two isl_local_spaces.
190 * Return -1 if "ls1" is "smaller" than "ls2", 1 if "ls1" is "greater"
191 * than "ls2" and 0 if they are equal.
193 int isl_local_space_cmp(__isl_keep isl_local_space
*ls1
,
194 __isl_keep isl_local_space
*ls2
)
205 cmp
= isl_space_cmp(ls1
->dim
, ls2
->dim
);
209 return isl_local_cmp(ls1
->div
, ls2
->div
);
212 int isl_local_space_dim(__isl_keep isl_local_space
*ls
,
213 enum isl_dim_type type
)
217 if (type
== isl_dim_div
)
218 return ls
->div
->n_row
;
219 if (type
== isl_dim_all
)
220 return isl_space_dim(ls
->dim
, isl_dim_all
) + ls
->div
->n_row
;
221 return isl_space_dim(ls
->dim
, type
);
224 unsigned isl_local_space_offset(__isl_keep isl_local_space
*ls
,
225 enum isl_dim_type type
)
234 case isl_dim_cst
: return 0;
235 case isl_dim_param
: return 1;
236 case isl_dim_in
: return 1 + dim
->nparam
;
237 case isl_dim_out
: return 1 + dim
->nparam
+ dim
->n_in
;
238 case isl_dim_div
: return 1 + dim
->nparam
+ dim
->n_in
+ dim
->n_out
;
243 /* Return the position of the dimension of the given type and name
245 * Return -1 if no such dimension can be found.
247 int isl_local_space_find_dim_by_name(__isl_keep isl_local_space
*ls
,
248 enum isl_dim_type type
, const char *name
)
252 if (type
== isl_dim_div
)
254 return isl_space_find_dim_by_name(ls
->dim
, type
, name
);
257 /* Does the given dimension have a name?
259 isl_bool
isl_local_space_has_dim_name(__isl_keep isl_local_space
*ls
,
260 enum isl_dim_type type
, unsigned pos
)
262 return ls
? isl_space_has_dim_name(ls
->dim
, type
, pos
) : isl_bool_error
;
265 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space
*ls
,
266 enum isl_dim_type type
, unsigned pos
)
268 return ls
? isl_space_get_dim_name(ls
->dim
, type
, pos
) : NULL
;
271 isl_bool
isl_local_space_has_dim_id(__isl_keep isl_local_space
*ls
,
272 enum isl_dim_type type
, unsigned pos
)
274 return ls
? isl_space_has_dim_id(ls
->dim
, type
, pos
) : isl_bool_error
;
277 __isl_give isl_id
*isl_local_space_get_dim_id(__isl_keep isl_local_space
*ls
,
278 enum isl_dim_type type
, unsigned pos
)
280 return ls
? isl_space_get_dim_id(ls
->dim
, type
, pos
) : NULL
;
283 /* Return the argument of the integer division at position "pos" in "ls".
284 * All local variables in "ls" are known to have a (complete) explicit
287 static __isl_give isl_aff
*extract_div(__isl_keep isl_local_space
*ls
, int pos
)
291 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
294 isl_seq_cpy(aff
->v
->el
, ls
->div
->row
[pos
], aff
->v
->size
);
298 /* Return the argument of the integer division at position "pos" in "ls".
299 * The integer division at that position is known to have a complete
300 * explicit representation, but some of the others do not.
301 * Remove them first because the domain of an isl_aff
302 * is not allowed to have unknown local variables.
304 static __isl_give isl_aff
*drop_unknown_divs_and_extract_div(
305 __isl_keep isl_local_space
*ls
, int pos
)
311 ls
= isl_local_space_copy(ls
);
312 n
= isl_local_space_dim(ls
, isl_dim_div
);
313 for (i
= n
- 1; i
>= 0; --i
) {
314 unknown
= isl_local_space_div_is_marked_unknown(ls
, i
);
316 ls
= isl_local_space_free(ls
);
319 ls
= isl_local_space_drop_dims(ls
, isl_dim_div
, i
, 1);
323 aff
= extract_div(ls
, pos
);
324 isl_local_space_free(ls
);
328 /* Return the argument of the integer division at position "pos" in "ls".
329 * The integer division is assumed to have a complete explicit
330 * representation. If some of the other integer divisions
331 * do not have an explicit representation, then they need
332 * to be removed first because the domain of an isl_aff
333 * is not allowed to have unknown local variables.
335 __isl_give isl_aff
*isl_local_space_get_div(__isl_keep isl_local_space
*ls
,
343 if (pos
< 0 || pos
>= ls
->div
->n_row
)
344 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
345 "index out of bounds", return NULL
);
347 known
= isl_local_space_div_is_known(ls
, pos
);
351 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
352 "expression of div unknown", return NULL
);
353 if (!isl_local_space_is_set(ls
))
354 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
355 "cannot represent divs of map spaces", return NULL
);
357 known
= isl_local_space_divs_known(ls
);
361 return extract_div(ls
, pos
);
363 return drop_unknown_divs_and_extract_div(ls
, pos
);
366 __isl_give isl_space
*isl_local_space_get_space(__isl_keep isl_local_space
*ls
)
371 return isl_space_copy(ls
->dim
);
374 /* Return the space of "ls".
375 * This may be either a copy or the space itself
376 * if there is only one reference to "ls".
377 * This allows the space to be modified inplace
378 * if both the local space and its space have only a single reference.
379 * The caller is not allowed to modify "ls" between this call and
380 * a subsequent call to isl_local_space_restore_space.
381 * The only exception is that isl_local_space_free can be called instead.
383 __isl_give isl_space
*isl_local_space_take_space(__isl_keep isl_local_space
*ls
)
390 return isl_local_space_get_space(ls
);
396 /* Set the space of "ls" to "space", where the space of "ls" may be missing
397 * due to a preceding call to isl_local_space_take_space.
398 * However, in this case, "ls" only has a single reference and
399 * then the call to isl_local_space_cow has no effect.
401 __isl_give isl_local_space
*isl_local_space_restore_space(
402 __isl_take isl_local_space
*ls
, __isl_take isl_space
*space
)
407 if (ls
->dim
== space
) {
408 isl_space_free(space
);
412 ls
= isl_local_space_cow(ls
);
415 isl_space_free(ls
->dim
);
420 isl_local_space_free(ls
);
421 isl_space_free(space
);
425 /* Replace the identifier of the tuple of type "type" by "id".
427 __isl_give isl_local_space
*isl_local_space_set_tuple_id(
428 __isl_take isl_local_space
*ls
,
429 enum isl_dim_type type
, __isl_take isl_id
*id
)
431 ls
= isl_local_space_cow(ls
);
434 ls
->dim
= isl_space_set_tuple_id(ls
->dim
, type
, id
);
436 return isl_local_space_free(ls
);
443 __isl_give isl_local_space
*isl_local_space_set_dim_name(
444 __isl_take isl_local_space
*ls
,
445 enum isl_dim_type type
, unsigned pos
, const char *s
)
447 ls
= isl_local_space_cow(ls
);
450 ls
->dim
= isl_space_set_dim_name(ls
->dim
, type
, pos
, s
);
452 return isl_local_space_free(ls
);
457 __isl_give isl_local_space
*isl_local_space_set_dim_id(
458 __isl_take isl_local_space
*ls
,
459 enum isl_dim_type type
, unsigned pos
, __isl_take isl_id
*id
)
461 ls
= isl_local_space_cow(ls
);
464 ls
->dim
= isl_space_set_dim_id(ls
->dim
, type
, pos
, id
);
466 return isl_local_space_free(ls
);
474 /* Construct a zero-dimensional local space with the given parameter domain.
476 __isl_give isl_local_space
*isl_local_space_set_from_params(
477 __isl_take isl_local_space
*ls
)
481 space
= isl_local_space_take_space(ls
);
482 space
= isl_space_set_from_params(space
);
483 ls
= isl_local_space_restore_space(ls
, space
);
488 __isl_give isl_local_space
*isl_local_space_reset_space(
489 __isl_take isl_local_space
*ls
, __isl_take isl_space
*dim
)
491 ls
= isl_local_space_cow(ls
);
495 isl_space_free(ls
->dim
);
500 isl_local_space_free(ls
);
505 /* Reorder the columns of the given div definitions according to the
507 * The order of the divs themselves is assumed not to change.
509 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
510 __isl_take isl_reordering
*r
)
519 extra
= isl_space_dim(r
->dim
, isl_dim_all
) + div
->n_row
- r
->len
;
520 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
524 for (i
= 0; i
< div
->n_row
; ++i
) {
525 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
526 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
527 for (j
= 0; j
< r
->len
; ++j
)
528 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
532 isl_reordering_free(r
);
536 isl_reordering_free(r
);
541 /* Reorder the dimensions of "ls" according to the given reordering.
542 * The reordering r is assumed to have been extended with the local
543 * variables, leaving them in the same order.
545 __isl_give isl_local_space
*isl_local_space_realign(
546 __isl_take isl_local_space
*ls
, __isl_take isl_reordering
*r
)
548 ls
= isl_local_space_cow(ls
);
552 ls
->div
= reorder_divs(ls
->div
, isl_reordering_copy(r
));
556 ls
= isl_local_space_reset_space(ls
, isl_space_copy(r
->dim
));
558 isl_reordering_free(r
);
561 isl_local_space_free(ls
);
562 isl_reordering_free(r
);
566 __isl_give isl_local_space
*isl_local_space_add_div(
567 __isl_take isl_local_space
*ls
, __isl_take isl_vec
*div
)
569 ls
= isl_local_space_cow(ls
);
573 if (ls
->div
->n_col
!= div
->size
)
574 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
575 "incompatible dimensions", goto error
);
577 ls
->div
= isl_mat_add_zero_cols(ls
->div
, 1);
578 ls
->div
= isl_mat_add_rows(ls
->div
, 1);
582 isl_seq_cpy(ls
->div
->row
[ls
->div
->n_row
- 1], div
->el
, div
->size
);
583 isl_int_set_si(ls
->div
->row
[ls
->div
->n_row
- 1][div
->size
], 0);
588 isl_local_space_free(ls
);
593 __isl_give isl_local_space
*isl_local_space_replace_divs(
594 __isl_take isl_local_space
*ls
, __isl_take isl_mat
*div
)
596 ls
= isl_local_space_cow(ls
);
601 isl_mat_free(ls
->div
);
606 isl_local_space_free(ls
);
610 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
613 static void expand_row(__isl_keep isl_mat
*dst
, int d
,
614 __isl_keep isl_mat
*src
, int s
, int *exp
)
617 unsigned c
= src
->n_col
- src
->n_row
;
619 isl_seq_cpy(dst
->row
[d
], src
->row
[s
], c
);
620 isl_seq_clr(dst
->row
[d
] + c
, dst
->n_col
- c
);
622 for (i
= 0; i
< s
; ++i
)
623 isl_int_set(dst
->row
[d
][c
+ exp
[i
]], src
->row
[s
][c
+ i
]);
626 /* Compare (known) divs.
627 * Return non-zero if at least one of the two divs is unknown.
628 * In particular, if both divs are unknown, we respect their
629 * current order. Otherwise, we sort the known div after the unknown
630 * div only if the known div depends on the unknown div.
632 static int cmp_row(isl_int
*row_i
, isl_int
*row_j
, int i
, int j
,
633 unsigned n_row
, unsigned n_col
)
636 int unknown_i
, unknown_j
;
638 unknown_i
= isl_int_is_zero(row_i
[0]);
639 unknown_j
= isl_int_is_zero(row_j
[0]);
641 if (unknown_i
&& unknown_j
)
645 li
= n_col
- n_row
+ i
;
647 li
= isl_seq_last_non_zero(row_i
, n_col
);
649 lj
= n_col
- n_row
+ j
;
651 lj
= isl_seq_last_non_zero(row_j
, n_col
);
656 return isl_seq_cmp(row_i
, row_j
, n_col
);
659 /* Call cmp_row for divs in a matrix.
661 int isl_mat_cmp_div(__isl_keep isl_mat
*div
, int i
, int j
)
663 return cmp_row(div
->row
[i
], div
->row
[j
], i
, j
, div
->n_row
, div
->n_col
);
666 /* Call cmp_row for divs in a basic map.
668 static int bmap_cmp_row(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
671 return cmp_row(bmap
->div
[i
], bmap
->div
[j
], i
, j
, bmap
->n_div
, total
);
674 /* Sort the divs in "bmap".
676 * We first make sure divs are placed after divs on which they depend.
677 * Then we perform a simple insertion sort based on the same ordering
678 * that is used in isl_merge_divs.
680 __isl_give isl_basic_map
*isl_basic_map_sort_divs(
681 __isl_take isl_basic_map
*bmap
)
686 bmap
= isl_basic_map_order_divs(bmap
);
689 if (bmap
->n_div
<= 1)
692 total
= 2 + isl_basic_map_total_dim(bmap
);
693 for (i
= 1; i
< bmap
->n_div
; ++i
) {
694 for (j
= i
- 1; j
>= 0; --j
) {
695 if (bmap_cmp_row(bmap
, j
, j
+ 1, total
) <= 0)
697 isl_basic_map_swap_div(bmap
, j
, j
+ 1);
704 /* Sort the divs in the basic maps of "map".
706 __isl_give isl_map
*isl_map_sort_divs(__isl_take isl_map
*map
)
708 return isl_map_inline_foreach_basic_map(map
, &isl_basic_map_sort_divs
);
711 /* Combine the two lists of divs into a single list.
712 * For each row i in div1, exp1[i] is set to the position of the corresponding
713 * row in the result. Similarly for div2 and exp2.
714 * This function guarantees
716 * exp1[i+1] > exp1[i]
717 * For optimal merging, the two input list should have been sorted.
719 __isl_give isl_mat
*isl_merge_divs(__isl_keep isl_mat
*div1
,
720 __isl_keep isl_mat
*div2
, int *exp1
, int *exp2
)
729 d
= div1
->n_col
- div1
->n_row
;
730 div
= isl_mat_alloc(div1
->ctx
, 1 + div1
->n_row
+ div2
->n_row
,
731 d
+ div1
->n_row
+ div2
->n_row
);
735 for (i
= 0, j
= 0, k
= 0; i
< div1
->n_row
&& j
< div2
->n_row
; ++k
) {
738 expand_row(div
, k
, div1
, i
, exp1
);
739 expand_row(div
, k
+ 1, div2
, j
, exp2
);
741 cmp
= isl_mat_cmp_div(div
, k
, k
+ 1);
745 } else if (cmp
< 0) {
749 isl_seq_cpy(div
->row
[k
], div
->row
[k
+ 1], div
->n_col
);
752 for (; i
< div1
->n_row
; ++i
, ++k
) {
753 expand_row(div
, k
, div1
, i
, exp1
);
756 for (; j
< div2
->n_row
; ++j
, ++k
) {
757 expand_row(div
, k
, div2
, j
, exp2
);
767 /* Swap divs "a" and "b" in "ls".
769 __isl_give isl_local_space
*isl_local_space_swap_div(
770 __isl_take isl_local_space
*ls
, int a
, int b
)
774 ls
= isl_local_space_cow(ls
);
777 if (a
< 0 || a
>= ls
->div
->n_row
|| b
< 0 || b
>= ls
->div
->n_row
)
778 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
779 "index out of bounds", return isl_local_space_free(ls
));
780 offset
= ls
->div
->n_col
- ls
->div
->n_row
;
781 ls
->div
= isl_mat_swap_cols(ls
->div
, offset
+ a
, offset
+ b
);
782 ls
->div
= isl_mat_swap_rows(ls
->div
, a
, b
);
784 return isl_local_space_free(ls
);
788 /* Construct a local space that contains all the divs in either
791 __isl_give isl_local_space
*isl_local_space_intersect(
792 __isl_take isl_local_space
*ls1
, __isl_take isl_local_space
*ls2
)
803 ctx
= isl_local_space_get_ctx(ls1
);
804 if (!isl_space_is_equal(ls1
->dim
, ls2
->dim
))
805 isl_die(ctx
, isl_error_invalid
,
806 "spaces should be identical", goto error
);
808 if (ls2
->div
->n_row
== 0) {
809 isl_local_space_free(ls2
);
813 if (ls1
->div
->n_row
== 0) {
814 isl_local_space_free(ls1
);
818 exp1
= isl_alloc_array(ctx
, int, ls1
->div
->n_row
);
819 exp2
= isl_alloc_array(ctx
, int, ls2
->div
->n_row
);
823 div
= isl_merge_divs(ls1
->div
, ls2
->div
, exp1
, exp2
);
827 equal
= isl_mat_is_equal(ls1
->div
, div
);
831 ls1
= isl_local_space_cow(ls1
);
837 isl_local_space_free(ls2
);
838 isl_mat_free(ls1
->div
);
846 isl_local_space_free(ls1
);
847 isl_local_space_free(ls2
);
851 /* Is the local variable "div" of "ls" marked as not having
852 * an explicit representation?
853 * Note that even if this variable is not marked in this way and therefore
854 * does have an explicit representation, this representation may still
855 * depend (indirectly) on other local variables that do not
856 * have an explicit representation.
858 isl_bool
isl_local_space_div_is_marked_unknown(__isl_keep isl_local_space
*ls
,
862 return isl_bool_error
;
863 return isl_local_div_is_marked_unknown(ls
->div
, div
);
866 /* Does "ls" have a complete explicit representation for div "div"?
868 isl_bool
isl_local_space_div_is_known(__isl_keep isl_local_space
*ls
, int div
)
871 return isl_bool_error
;
872 return isl_local_div_is_known(ls
->div
, div
);
875 /* Does "ls" have an explicit representation for all local variables?
877 isl_bool
isl_local_space_divs_known(__isl_keep isl_local_space
*ls
)
882 return isl_bool_error
;
884 for (i
= 0; i
< ls
->div
->n_row
; ++i
) {
885 isl_bool unknown
= isl_local_space_div_is_marked_unknown(ls
, i
);
886 if (unknown
< 0 || unknown
)
887 return isl_bool_not(unknown
);
890 return isl_bool_true
;
893 __isl_give isl_local_space
*isl_local_space_domain(
894 __isl_take isl_local_space
*ls
)
896 ls
= isl_local_space_drop_dims(ls
, isl_dim_out
,
897 0, isl_local_space_dim(ls
, isl_dim_out
));
898 ls
= isl_local_space_cow(ls
);
901 ls
->dim
= isl_space_domain(ls
->dim
);
903 return isl_local_space_free(ls
);
907 __isl_give isl_local_space
*isl_local_space_range(
908 __isl_take isl_local_space
*ls
)
910 ls
= isl_local_space_drop_dims(ls
, isl_dim_in
,
911 0, isl_local_space_dim(ls
, isl_dim_in
));
912 ls
= isl_local_space_cow(ls
);
916 ls
->dim
= isl_space_range(ls
->dim
);
918 return isl_local_space_free(ls
);
922 /* Construct a local space for a map that has the given local
923 * space as domain and that has a zero-dimensional range.
925 __isl_give isl_local_space
*isl_local_space_from_domain(
926 __isl_take isl_local_space
*ls
)
928 ls
= isl_local_space_cow(ls
);
931 ls
->dim
= isl_space_from_domain(ls
->dim
);
933 return isl_local_space_free(ls
);
937 __isl_give isl_local_space
*isl_local_space_add_dims(
938 __isl_take isl_local_space
*ls
, enum isl_dim_type type
, unsigned n
)
944 pos
= isl_local_space_dim(ls
, type
);
945 return isl_local_space_insert_dims(ls
, type
, pos
, n
);
948 /* Remove common factor of non-constant terms and denominator.
950 static void normalize_div(__isl_keep isl_local_space
*ls
, int div
)
952 isl_ctx
*ctx
= ls
->div
->ctx
;
953 unsigned total
= ls
->div
->n_col
- 2;
955 isl_seq_gcd(ls
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
956 isl_int_gcd(ctx
->normalize_gcd
,
957 ctx
->normalize_gcd
, ls
->div
->row
[div
][0]);
958 if (isl_int_is_one(ctx
->normalize_gcd
))
961 isl_seq_scale_down(ls
->div
->row
[div
] + 2, ls
->div
->row
[div
] + 2,
962 ctx
->normalize_gcd
, total
);
963 isl_int_divexact(ls
->div
->row
[div
][0], ls
->div
->row
[div
][0],
965 isl_int_fdiv_q(ls
->div
->row
[div
][1], ls
->div
->row
[div
][1],
969 /* Exploit the equalities in "eq" to simplify the expressions of
970 * the integer divisions in "ls".
971 * The integer divisions in "ls" are assumed to appear as regular
972 * dimensions in "eq".
974 __isl_give isl_local_space
*isl_local_space_substitute_equalities(
975 __isl_take isl_local_space
*ls
, __isl_take isl_basic_set
*eq
)
984 total
= isl_space_dim(eq
->dim
, isl_dim_all
);
985 if (isl_local_space_dim(ls
, isl_dim_all
) != total
)
986 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
987 "spaces don't match", goto error
);
990 for (i
= 0; i
< eq
->n_eq
; ++i
) {
991 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
992 if (j
< 0 || j
== 0 || j
>= total
)
995 for (k
= 0; k
< ls
->div
->n_row
; ++k
) {
996 if (isl_int_is_zero(ls
->div
->row
[k
][1 + j
]))
998 ls
= isl_local_space_cow(ls
);
1001 ls
->div
= isl_mat_cow(ls
->div
);
1004 isl_seq_elim(ls
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
1005 &ls
->div
->row
[k
][0]);
1006 normalize_div(ls
, k
);
1010 isl_basic_set_free(eq
);
1013 isl_basic_set_free(eq
);
1014 isl_local_space_free(ls
);
1018 /* Plug in the affine expressions "subs" of length "subs_len" (including
1019 * the denominator and the constant term) into the variable at position "pos"
1020 * of the "n" div expressions starting at "first".
1022 * Let i be the dimension to replace and let "subs" be of the form
1026 * Any integer division starting at "first" with a non-zero coefficient for i,
1028 * floor((a i + g)/m)
1032 * floor((a f + d g)/(m d))
1034 __isl_give isl_local_space
*isl_local_space_substitute_seq(
1035 __isl_take isl_local_space
*ls
,
1036 enum isl_dim_type type
, unsigned pos
, isl_int
*subs
, int subs_len
,
1044 ls
= isl_local_space_cow(ls
);
1047 ls
->div
= isl_mat_cow(ls
->div
);
1049 return isl_local_space_free(ls
);
1051 if (first
+ n
> ls
->div
->n_row
)
1052 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1053 "index out of bounds", return isl_local_space_free(ls
));
1055 pos
+= isl_local_space_offset(ls
, type
);
1058 for (i
= first
; i
< first
+ n
; ++i
) {
1059 if (isl_int_is_zero(ls
->div
->row
[i
][1 + pos
]))
1061 isl_seq_substitute(ls
->div
->row
[i
], pos
, subs
,
1062 ls
->div
->n_col
, subs_len
, v
);
1063 normalize_div(ls
, i
);
1070 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
1073 * Let i be the dimension to replace and let "subs" be of the form
1077 * Any integer division with a non-zero coefficient for i,
1079 * floor((a i + g)/m)
1083 * floor((a f + d g)/(m d))
1085 __isl_give isl_local_space
*isl_local_space_substitute(
1086 __isl_take isl_local_space
*ls
,
1087 enum isl_dim_type type
, unsigned pos
, __isl_keep isl_aff
*subs
)
1089 ls
= isl_local_space_cow(ls
);
1091 return isl_local_space_free(ls
);
1093 if (!isl_space_is_equal(ls
->dim
, subs
->ls
->dim
))
1094 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1095 "spaces don't match", return isl_local_space_free(ls
));
1096 if (isl_local_space_dim(subs
->ls
, isl_dim_div
) != 0)
1097 isl_die(isl_local_space_get_ctx(ls
), isl_error_unsupported
,
1098 "cannot handle divs yet",
1099 return isl_local_space_free(ls
));
1101 return isl_local_space_substitute_seq(ls
, type
, pos
, subs
->v
->el
,
1102 subs
->v
->size
, 0, ls
->div
->n_row
);
1105 isl_bool
isl_local_space_is_named_or_nested(__isl_keep isl_local_space
*ls
,
1106 enum isl_dim_type type
)
1109 return isl_bool_error
;
1110 return isl_space_is_named_or_nested(ls
->dim
, type
);
1113 __isl_give isl_local_space
*isl_local_space_drop_dims(
1114 __isl_take isl_local_space
*ls
,
1115 enum isl_dim_type type
, unsigned first
, unsigned n
)
1121 if (n
== 0 && !isl_local_space_is_named_or_nested(ls
, type
))
1124 ctx
= isl_local_space_get_ctx(ls
);
1125 if (first
+ n
> isl_local_space_dim(ls
, type
))
1126 isl_die(ctx
, isl_error_invalid
, "range out of bounds",
1127 return isl_local_space_free(ls
));
1129 ls
= isl_local_space_cow(ls
);
1133 if (type
== isl_dim_div
) {
1134 ls
->div
= isl_mat_drop_rows(ls
->div
, first
, n
);
1136 ls
->dim
= isl_space_drop_dims(ls
->dim
, type
, first
, n
);
1138 return isl_local_space_free(ls
);
1141 first
+= 1 + isl_local_space_offset(ls
, type
);
1142 ls
->div
= isl_mat_drop_cols(ls
->div
, first
, n
);
1144 return isl_local_space_free(ls
);
1149 __isl_give isl_local_space
*isl_local_space_insert_dims(
1150 __isl_take isl_local_space
*ls
,
1151 enum isl_dim_type type
, unsigned first
, unsigned n
)
1157 if (n
== 0 && !isl_local_space_is_named_or_nested(ls
, type
))
1160 ctx
= isl_local_space_get_ctx(ls
);
1161 if (first
> isl_local_space_dim(ls
, type
))
1162 isl_die(ctx
, isl_error_invalid
, "position out of bounds",
1163 return isl_local_space_free(ls
));
1165 ls
= isl_local_space_cow(ls
);
1169 if (type
== isl_dim_div
) {
1170 ls
->div
= isl_mat_insert_zero_rows(ls
->div
, first
, n
);
1172 ls
->dim
= isl_space_insert_dims(ls
->dim
, type
, first
, n
);
1174 return isl_local_space_free(ls
);
1177 first
+= 1 + isl_local_space_offset(ls
, type
);
1178 ls
->div
= isl_mat_insert_zero_cols(ls
->div
, first
, n
);
1180 return isl_local_space_free(ls
);
1185 /* Does the linear part of "constraint" correspond to
1186 * integer division "div" in "ls"?
1188 * That is, given div = floor((c + f)/m), is the constraint of the form
1190 * f - m d + c' >= 0 [sign = 1]
1192 * -f + m d + c'' >= 0 [sign = -1]
1194 * If so, set *sign to the corresponding value.
1196 static isl_bool
is_linear_div_constraint(__isl_keep isl_local_space
*ls
,
1197 isl_int
*constraint
, unsigned div
, int *sign
)
1202 unknown
= isl_local_space_div_is_marked_unknown(ls
, div
);
1204 return isl_bool_error
;
1206 return isl_bool_false
;
1208 pos
= isl_local_space_offset(ls
, isl_dim_div
) + div
;
1210 if (isl_int_eq(constraint
[pos
], ls
->div
->row
[div
][0])) {
1212 if (!isl_seq_is_neg(constraint
+ 1,
1213 ls
->div
->row
[div
] + 2, pos
- 1))
1214 return isl_bool_false
;
1215 } else if (isl_int_abs_eq(constraint
[pos
], ls
->div
->row
[div
][0])) {
1217 if (!isl_seq_eq(constraint
+ 1, ls
->div
->row
[div
] + 2, pos
- 1))
1218 return isl_bool_false
;
1220 return isl_bool_false
;
1222 if (isl_seq_first_non_zero(constraint
+ pos
+ 1,
1223 ls
->div
->n_row
- div
- 1) != -1)
1224 return isl_bool_false
;
1225 return isl_bool_true
;
1228 /* Check if the constraints pointed to by "constraint" is a div
1229 * constraint corresponding to div "div" in "ls".
1231 * That is, if div = floor(f/m), then check if the constraint is
1235 * -(f-(m-1)) + m d >= 0
1237 * First check if the linear part is of the right form and
1238 * then check the constant term.
1240 isl_bool
isl_local_space_is_div_constraint(__isl_keep isl_local_space
*ls
,
1241 isl_int
*constraint
, unsigned div
)
1246 linear
= is_linear_div_constraint(ls
, constraint
, div
, &sign
);
1247 if (linear
< 0 || !linear
)
1252 isl_int_sub(ls
->div
->row
[div
][1],
1253 ls
->div
->row
[div
][1], ls
->div
->row
[div
][0]);
1254 isl_int_add_ui(ls
->div
->row
[div
][1], ls
->div
->row
[div
][1], 1);
1255 neg
= isl_seq_is_neg(constraint
, ls
->div
->row
[div
] + 1, 1);
1256 isl_int_sub_ui(ls
->div
->row
[div
][1], ls
->div
->row
[div
][1], 1);
1257 isl_int_add(ls
->div
->row
[div
][1],
1258 ls
->div
->row
[div
][1], ls
->div
->row
[div
][0]);
1260 return isl_bool_false
;
1262 if (!isl_int_eq(constraint
[0], ls
->div
->row
[div
][1]))
1263 return isl_bool_false
;
1266 return isl_bool_true
;
1269 /* Is the constraint pointed to by "constraint" one
1270 * of an equality that corresponds to integer division "div" in "ls"?
1272 * That is, given an integer division of the form
1274 * a = floor((f + c)/m)
1276 * is the equality of the form
1280 * Note that the constant term is not checked explicitly, but given
1281 * that this is a valid equality constraint, the constant c' necessarily
1282 * has a value close to -c.
1284 isl_bool
isl_local_space_is_div_equality(__isl_keep isl_local_space
*ls
,
1285 isl_int
*constraint
, unsigned div
)
1290 linear
= is_linear_div_constraint(ls
, constraint
, div
, &sign
);
1291 if (linear
< 0 || !linear
)
1298 * Set active[i] to 1 if the dimension at position i is involved
1299 * in the linear expression l.
1301 int *isl_local_space_get_active(__isl_keep isl_local_space
*ls
, isl_int
*l
)
1309 ctx
= isl_local_space_get_ctx(ls
);
1310 total
= isl_local_space_dim(ls
, isl_dim_all
);
1311 active
= isl_calloc_array(ctx
, int, total
);
1312 if (total
&& !active
)
1315 for (i
= 0; i
< total
; ++i
)
1316 active
[i
] = !isl_int_is_zero(l
[i
]);
1318 offset
= isl_local_space_offset(ls
, isl_dim_div
) - 1;
1319 for (i
= ls
->div
->n_row
- 1; i
>= 0; --i
) {
1320 if (!active
[offset
+ i
])
1322 for (j
= 0; j
< total
; ++j
)
1323 active
[j
] |= !isl_int_is_zero(ls
->div
->row
[i
][2 + j
]);
1329 /* Given a local space "ls" of a set, create a local space
1330 * for the lift of the set. In particular, the result
1331 * is of the form [dim -> local[..]], with ls->div->n_row variables in the
1332 * range of the wrapped map.
1334 __isl_give isl_local_space
*isl_local_space_lift(
1335 __isl_take isl_local_space
*ls
)
1337 ls
= isl_local_space_cow(ls
);
1341 ls
->dim
= isl_space_lift(ls
->dim
, ls
->div
->n_row
);
1342 ls
->div
= isl_mat_drop_rows(ls
->div
, 0, ls
->div
->n_row
);
1343 if (!ls
->dim
|| !ls
->div
)
1344 return isl_local_space_free(ls
);
1349 /* Construct a basic map that maps a set living in local space "ls"
1350 * to the corresponding lifted local space.
1352 __isl_give isl_basic_map
*isl_local_space_lifting(
1353 __isl_take isl_local_space
*ls
)
1355 isl_basic_map
*lifting
;
1356 isl_basic_set
*bset
;
1360 if (!isl_local_space_is_set(ls
))
1361 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1362 "lifting only defined on set spaces", goto error
);
1364 bset
= isl_basic_set_from_local_space(ls
);
1365 lifting
= isl_basic_set_unwrap(isl_basic_set_lift(bset
));
1366 lifting
= isl_basic_map_domain_map(lifting
);
1367 lifting
= isl_basic_map_reverse(lifting
);
1371 isl_local_space_free(ls
);
1375 /* Compute the preimage of "ls" under the function represented by "ma".
1376 * In other words, plug in "ma" in "ls". The result is a local space
1377 * that is part of the domain space of "ma".
1379 * If the divs in "ls" are represented as
1381 * floor((a_i(p) + b_i x + c_i(divs))/n_i)
1383 * and ma is represented by
1385 * x = D(p) + F(y) + G(divs')
1387 * then the resulting divs are
1389 * floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
1391 * We first copy over the divs from "ma" and then
1392 * we add the modified divs from "ls".
1394 __isl_give isl_local_space
*isl_local_space_preimage_multi_aff(
1395 __isl_take isl_local_space
*ls
, __isl_take isl_multi_aff
*ma
)
1399 isl_local_space
*res
= NULL
;
1400 int n_div_ls
, n_div_ma
;
1401 isl_int f
, c1
, c2
, g
;
1403 ma
= isl_multi_aff_align_divs(ma
);
1406 if (!isl_space_is_range_internal(ls
->dim
, ma
->space
))
1407 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1408 "spaces don't match", goto error
);
1410 n_div_ls
= isl_local_space_dim(ls
, isl_dim_div
);
1411 n_div_ma
= ma
->n
? isl_aff_dim(ma
->p
[0], isl_dim_div
) : 0;
1413 space
= isl_space_domain(isl_multi_aff_get_space(ma
));
1414 res
= isl_local_space_alloc(space
, n_div_ma
+ n_div_ls
);
1419 isl_mat_free(res
->div
);
1420 res
->div
= isl_mat_copy(ma
->p
[0]->ls
->div
);
1421 res
->div
= isl_mat_add_zero_cols(res
->div
, n_div_ls
);
1422 res
->div
= isl_mat_add_rows(res
->div
, n_div_ls
);
1432 for (i
= 0; i
< ls
->div
->n_row
; ++i
) {
1433 if (isl_int_is_zero(ls
->div
->row
[i
][0])) {
1434 isl_int_set_si(res
->div
->row
[n_div_ma
+ i
][0], 0);
1437 isl_seq_preimage(res
->div
->row
[n_div_ma
+ i
], ls
->div
->row
[i
],
1438 ma
, 0, 0, n_div_ma
, n_div_ls
, f
, c1
, c2
, g
, 1);
1439 normalize_div(res
, n_div_ma
+ i
);
1447 isl_local_space_free(ls
);
1448 isl_multi_aff_free(ma
);
1451 isl_local_space_free(ls
);
1452 isl_multi_aff_free(ma
);
1453 isl_local_space_free(res
);
1457 /* Move the "n" dimensions of "src_type" starting at "src_pos" of "ls"
1458 * to dimensions of "dst_type" at "dst_pos".
1460 * Moving to/from local dimensions is not allowed.
1461 * We currently assume that the dimension type changes.
1463 __isl_give isl_local_space
*isl_local_space_move_dims(
1464 __isl_take isl_local_space
*ls
,
1465 enum isl_dim_type dst_type
, unsigned dst_pos
,
1466 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
1474 !isl_local_space_is_named_or_nested(ls
, src_type
) &&
1475 !isl_local_space_is_named_or_nested(ls
, dst_type
))
1478 if (src_pos
+ n
> isl_local_space_dim(ls
, src_type
))
1479 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1480 "range out of bounds", return isl_local_space_free(ls
));
1481 if (dst_pos
> isl_local_space_dim(ls
, dst_type
))
1482 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1483 "position out of bounds",
1484 return isl_local_space_free(ls
));
1485 if (src_type
== isl_dim_div
)
1486 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1487 "cannot move divs", return isl_local_space_free(ls
));
1488 if (dst_type
== isl_dim_div
)
1489 isl_die(isl_local_space_get_ctx(ls
), isl_error_invalid
,
1490 "cannot move to divs", return isl_local_space_free(ls
));
1491 if (dst_type
== src_type
&& dst_pos
== src_pos
)
1493 if (dst_type
== src_type
)
1494 isl_die(isl_local_space_get_ctx(ls
), isl_error_unsupported
,
1495 "moving dims within the same type not supported",
1496 return isl_local_space_free(ls
));
1498 ls
= isl_local_space_cow(ls
);
1502 g_src_pos
= 1 + isl_local_space_offset(ls
, src_type
) + src_pos
;
1503 g_dst_pos
= 1 + isl_local_space_offset(ls
, dst_type
) + dst_pos
;
1504 if (dst_type
> src_type
)
1506 ls
->div
= isl_mat_move_cols(ls
->div
, g_dst_pos
, g_src_pos
, n
);
1508 return isl_local_space_free(ls
);
1509 ls
->dim
= isl_space_move_dims(ls
->dim
, dst_type
, dst_pos
,
1510 src_type
, src_pos
, n
);
1512 return isl_local_space_free(ls
);
1517 /* Remove any internal structure of the domain of "ls".
1518 * If there is any such internal structure in the input,
1519 * then the name of the corresponding space is also removed.
1521 __isl_give isl_local_space
*isl_local_space_flatten_domain(
1522 __isl_take isl_local_space
*ls
)
1527 if (!ls
->dim
->nested
[0])
1530 ls
= isl_local_space_cow(ls
);
1534 ls
->dim
= isl_space_flatten_domain(ls
->dim
);
1536 return isl_local_space_free(ls
);
1541 /* Remove any internal structure of the range of "ls".
1542 * If there is any such internal structure in the input,
1543 * then the name of the corresponding space is also removed.
1545 __isl_give isl_local_space
*isl_local_space_flatten_range(
1546 __isl_take isl_local_space
*ls
)
1551 if (!ls
->dim
->nested
[1])
1554 ls
= isl_local_space_cow(ls
);
1558 ls
->dim
= isl_space_flatten_range(ls
->dim
);
1560 return isl_local_space_free(ls
);
1565 /* Given the local space "ls" of a map, return the local space of a set
1566 * that lives in a space that wraps the space of "ls" and that has
1569 __isl_give isl_local_space
*isl_local_space_wrap(__isl_take isl_local_space
*ls
)
1571 ls
= isl_local_space_cow(ls
);
1575 ls
->dim
= isl_space_wrap(ls
->dim
);
1577 return isl_local_space_free(ls
);