2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012 Ecole Normale Superieure
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * 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_equalities.h"
19 #include <isl_space_private.h>
20 #include <isl_mat_private.h>
21 #include <isl_vec_private.h>
23 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
25 isl_int
*t
= bmap
->eq
[a
];
26 bmap
->eq
[a
] = bmap
->eq
[b
];
30 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
33 isl_int
*t
= bmap
->ineq
[a
];
34 bmap
->ineq
[a
] = bmap
->ineq
[b
];
39 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
41 isl_seq_cpy(c
, c
+ n
, rem
);
42 isl_seq_clr(c
+ rem
, n
);
45 /* Drop n dimensions starting at first.
47 * In principle, this frees up some extra variables as the number
48 * of columns remains constant, but we would have to extend
49 * the div array too as the number of rows in this array is assumed
50 * to be equal to extra.
52 struct isl_basic_set
*isl_basic_set_drop_dims(
53 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
60 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
62 if (n
== 0 && !isl_space_get_tuple_name(bset
->dim
, isl_dim_set
))
65 bset
= isl_basic_set_cow(bset
);
69 for (i
= 0; i
< bset
->n_eq
; ++i
)
70 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
71 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
73 for (i
= 0; i
< bset
->n_ineq
; ++i
)
74 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
75 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
77 for (i
= 0; i
< bset
->n_div
; ++i
)
78 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
79 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
81 bset
->dim
= isl_space_drop_outputs(bset
->dim
, first
, n
);
85 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
86 bset
= isl_basic_set_simplify(bset
);
87 return isl_basic_set_finalize(bset
);
89 isl_basic_set_free(bset
);
93 struct isl_set
*isl_set_drop_dims(
94 struct isl_set
*set
, unsigned first
, unsigned n
)
101 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
103 if (n
== 0 && !isl_space_get_tuple_name(set
->dim
, isl_dim_set
))
105 set
= isl_set_cow(set
);
108 set
->dim
= isl_space_drop_outputs(set
->dim
, first
, n
);
112 for (i
= 0; i
< set
->n
; ++i
) {
113 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
118 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
125 /* Move "n" divs starting at "first" to the end of the list of divs.
127 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
128 unsigned first
, unsigned n
)
133 if (first
+ n
== bmap
->n_div
)
136 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
139 for (i
= 0; i
< n
; ++i
)
140 div
[i
] = bmap
->div
[first
+ i
];
141 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
142 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
143 for (i
= 0; i
< n
; ++i
)
144 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
148 isl_basic_map_free(bmap
);
152 /* Drop "n" dimensions of type "type" starting at "first".
154 * In principle, this frees up some extra variables as the number
155 * of columns remains constant, but we would have to extend
156 * the div array too as the number of rows in this array is assumed
157 * to be equal to extra.
159 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
160 enum isl_dim_type type
, unsigned first
, unsigned n
)
170 dim
= isl_basic_map_dim(bmap
, type
);
171 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
173 if (n
== 0 && !isl_space_is_named_or_nested(bmap
->dim
, type
))
176 bmap
= isl_basic_map_cow(bmap
);
180 offset
= isl_basic_map_offset(bmap
, type
) + first
;
181 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
182 for (i
= 0; i
< bmap
->n_eq
; ++i
)
183 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
185 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
186 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
188 for (i
= 0; i
< bmap
->n_div
; ++i
)
189 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
191 if (type
== isl_dim_div
) {
192 bmap
= move_divs_last(bmap
, first
, n
);
195 isl_basic_map_free_div(bmap
, n
);
197 bmap
->dim
= isl_space_drop_dims(bmap
->dim
, type
, first
, n
);
201 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
202 bmap
= isl_basic_map_simplify(bmap
);
203 return isl_basic_map_finalize(bmap
);
205 isl_basic_map_free(bmap
);
209 __isl_give isl_basic_set
*isl_basic_set_drop(__isl_take isl_basic_set
*bset
,
210 enum isl_dim_type type
, unsigned first
, unsigned n
)
212 return (isl_basic_set
*)isl_basic_map_drop((isl_basic_map
*)bset
,
216 struct isl_basic_map
*isl_basic_map_drop_inputs(
217 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
219 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
222 struct isl_map
*isl_map_drop(struct isl_map
*map
,
223 enum isl_dim_type type
, unsigned first
, unsigned n
)
230 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
232 if (n
== 0 && !isl_space_get_tuple_name(map
->dim
, type
))
234 map
= isl_map_cow(map
);
237 map
->dim
= isl_space_drop_dims(map
->dim
, type
, first
, n
);
241 for (i
= 0; i
< map
->n
; ++i
) {
242 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
246 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
254 struct isl_set
*isl_set_drop(struct isl_set
*set
,
255 enum isl_dim_type type
, unsigned first
, unsigned n
)
257 return (isl_set
*)isl_map_drop((isl_map
*)set
, type
, first
, n
);
260 struct isl_map
*isl_map_drop_inputs(
261 struct isl_map
*map
, unsigned first
, unsigned n
)
263 return isl_map_drop(map
, isl_dim_in
, first
, n
);
267 * We don't cow, as the div is assumed to be redundant.
269 static struct isl_basic_map
*isl_basic_map_drop_div(
270 struct isl_basic_map
*bmap
, unsigned div
)
278 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
280 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
282 for (i
= 0; i
< bmap
->n_eq
; ++i
)
283 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
285 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
286 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
287 isl_basic_map_drop_inequality(bmap
, i
);
291 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
294 for (i
= 0; i
< bmap
->n_div
; ++i
)
295 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
297 if (div
!= bmap
->n_div
- 1) {
299 isl_int
*t
= bmap
->div
[div
];
301 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
302 bmap
->div
[j
] = bmap
->div
[j
+1];
304 bmap
->div
[bmap
->n_div
- 1] = t
;
306 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
307 isl_basic_map_free_div(bmap
, 1);
311 isl_basic_map_free(bmap
);
315 struct isl_basic_map
*isl_basic_map_normalize_constraints(
316 struct isl_basic_map
*bmap
)
320 unsigned total
= isl_basic_map_total_dim(bmap
);
326 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
327 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
328 if (isl_int_is_zero(gcd
)) {
329 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
330 bmap
= isl_basic_map_set_to_empty(bmap
);
333 isl_basic_map_drop_equality(bmap
, i
);
336 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
337 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
338 if (isl_int_is_one(gcd
))
340 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
341 bmap
= isl_basic_map_set_to_empty(bmap
);
344 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
347 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
348 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
349 if (isl_int_is_zero(gcd
)) {
350 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
351 bmap
= isl_basic_map_set_to_empty(bmap
);
354 isl_basic_map_drop_inequality(bmap
, i
);
357 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
358 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
359 if (isl_int_is_one(gcd
))
361 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
362 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
369 struct isl_basic_set
*isl_basic_set_normalize_constraints(
370 struct isl_basic_set
*bset
)
372 return (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
373 (struct isl_basic_map
*)bset
);
376 /* Remove any common factor in numerator and denominator of the div expression,
377 * not taking into account the constant term.
378 * That is, if the div is of the form
380 * floor((a + m f(x))/(m d))
384 * floor((floor(a/m) + f(x))/d)
386 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
387 * and can therefore not influence the result of the floor.
389 static void normalize_div_expression(__isl_keep isl_basic_map
*bmap
, int div
)
391 unsigned total
= isl_basic_map_total_dim(bmap
);
392 isl_ctx
*ctx
= bmap
->ctx
;
394 if (isl_int_is_zero(bmap
->div
[div
][0]))
396 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
397 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
398 if (isl_int_is_one(ctx
->normalize_gcd
))
400 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
402 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
404 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
405 ctx
->normalize_gcd
, total
);
408 /* Remove any common factor in numerator and denominator of a div expression,
409 * not taking into account the constant term.
410 * That is, look for any div of the form
412 * floor((a + m f(x))/(m d))
416 * floor((floor(a/m) + f(x))/d)
418 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
419 * and can therefore not influence the result of the floor.
421 static __isl_give isl_basic_map
*normalize_div_expressions(
422 __isl_take isl_basic_map
*bmap
)
428 if (bmap
->n_div
== 0)
431 for (i
= 0; i
< bmap
->n_div
; ++i
)
432 normalize_div_expression(bmap
, i
);
437 /* Assumes divs have been ordered if keep_divs is set.
439 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
440 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
443 unsigned space_total
;
447 total
= isl_basic_map_total_dim(bmap
);
448 space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
449 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
450 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
451 if (bmap
->eq
[k
] == eq
)
453 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
457 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
458 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
461 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
462 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
466 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
467 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
468 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
471 for (k
= 0; k
< bmap
->n_div
; ++k
) {
472 if (isl_int_is_zero(bmap
->div
[k
][0]))
474 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
478 /* We need to be careful about circular definitions,
479 * so for now we just remove the definition of div k
480 * if the equality contains any divs.
481 * If keep_divs is set, then the divs have been ordered
482 * and we can keep the definition as long as the result
485 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
486 isl_seq_elim(bmap
->div
[k
]+1, eq
,
487 1+pos
, 1+total
, &bmap
->div
[k
][0]);
488 normalize_div_expression(bmap
, k
);
490 isl_seq_clr(bmap
->div
[k
], 1 + total
);
491 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
495 /* Assumes divs have been ordered if keep_divs is set.
497 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
498 unsigned div
, int keep_divs
)
500 unsigned pos
= isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
502 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
504 isl_basic_map_drop_div(bmap
, div
);
507 /* Check if elimination of div "div" using equality "eq" would not
508 * result in a div depending on a later div.
510 static int ok_to_eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
515 unsigned space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
516 unsigned pos
= space_total
+ div
;
518 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
519 if (last_div
< 0 || last_div
<= div
)
522 for (k
= 0; k
<= last_div
; ++k
) {
523 if (isl_int_is_zero(bmap
->div
[k
][0]))
525 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
532 /* Elimininate divs based on equalities
534 static struct isl_basic_map
*eliminate_divs_eq(
535 struct isl_basic_map
*bmap
, int *progress
)
542 bmap
= isl_basic_map_order_divs(bmap
);
547 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
549 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
550 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
551 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
552 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
554 if (!ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
))
558 eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
559 isl_basic_map_drop_equality(bmap
, i
);
564 return eliminate_divs_eq(bmap
, progress
);
568 /* Elimininate divs based on inequalities
570 static struct isl_basic_map
*eliminate_divs_ineq(
571 struct isl_basic_map
*bmap
, int *progress
)
582 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
584 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
585 for (i
= 0; i
< bmap
->n_eq
; ++i
)
586 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
590 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
591 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
593 if (i
< bmap
->n_ineq
)
596 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
597 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
599 bmap
= isl_basic_map_drop_div(bmap
, d
);
606 struct isl_basic_map
*isl_basic_map_gauss(
607 struct isl_basic_map
*bmap
, int *progress
)
615 bmap
= isl_basic_map_order_divs(bmap
);
620 total
= isl_basic_map_total_dim(bmap
);
621 total_var
= total
- bmap
->n_div
;
623 last_var
= total
- 1;
624 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
625 for (; last_var
>= 0; --last_var
) {
626 for (k
= done
; k
< bmap
->n_eq
; ++k
)
627 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
635 swap_equality(bmap
, k
, done
);
636 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
637 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
639 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
642 if (last_var
>= total_var
&&
643 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
644 unsigned div
= last_var
- total_var
;
645 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
646 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
647 isl_int_set(bmap
->div
[div
][0],
648 bmap
->eq
[done
][1+last_var
]);
651 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
654 if (done
== bmap
->n_eq
)
656 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
657 if (isl_int_is_zero(bmap
->eq
[k
][0]))
659 return isl_basic_map_set_to_empty(bmap
);
661 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
665 struct isl_basic_set
*isl_basic_set_gauss(
666 struct isl_basic_set
*bset
, int *progress
)
668 return (struct isl_basic_set
*)isl_basic_map_gauss(
669 (struct isl_basic_map
*)bset
, progress
);
673 static unsigned int round_up(unsigned int v
)
684 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
685 struct isl_basic_map
*bmap
, int k
)
688 unsigned total
= isl_basic_map_total_dim(bmap
);
689 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
690 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
691 if (&bmap
->ineq
[k
] != index
[h
] &&
692 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
697 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
698 struct isl_basic_set
*bset
, int k
)
700 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
703 /* If we can eliminate more than one div, then we need to make
704 * sure we do it from last div to first div, in order not to
705 * change the position of the other divs that still need to
708 static struct isl_basic_map
*remove_duplicate_divs(
709 struct isl_basic_map
*bmap
, int *progress
)
721 bmap
= isl_basic_map_order_divs(bmap
);
722 if (!bmap
|| bmap
->n_div
<= 1)
725 total_var
= isl_space_dim(bmap
->dim
, isl_dim_all
);
726 total
= total_var
+ bmap
->n_div
;
729 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
730 if (!isl_int_is_zero(bmap
->div
[k
][0]))
735 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
736 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
737 bits
= ffs(size
) - 1;
738 index
= isl_calloc_array(ctx
, int, size
);
741 eq
= isl_blk_alloc(ctx
, 1+total
);
742 if (isl_blk_is_error(eq
))
745 isl_seq_clr(eq
.data
, 1+total
);
746 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
747 for (--k
; k
>= 0; --k
) {
750 if (isl_int_is_zero(bmap
->div
[k
][0]))
753 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
754 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
755 if (isl_seq_eq(bmap
->div
[k
],
756 bmap
->div
[index
[h
]-1], 2+total
))
765 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
769 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
770 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
771 eliminate_div(bmap
, eq
.data
, l
, 1);
772 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
773 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
776 isl_blk_free(ctx
, eq
);
783 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
788 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
789 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
790 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
794 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
800 /* Normalize divs that appear in equalities.
802 * In particular, we assume that bmap contains some equalities
807 * and we want to replace the set of e_i by a minimal set and
808 * such that the new e_i have a canonical representation in terms
810 * If any of the equalities involves more than one divs, then
811 * we currently simply bail out.
813 * Let us first additionally assume that all equalities involve
814 * a div. The equalities then express modulo constraints on the
815 * remaining variables and we can use "parameter compression"
816 * to find a minimal set of constraints. The result is a transformation
818 * x = T(x') = x_0 + G x'
820 * with G a lower-triangular matrix with all elements below the diagonal
821 * non-negative and smaller than the diagonal element on the same row.
822 * We first normalize x_0 by making the same property hold in the affine
824 * The rows i of G with a 1 on the diagonal do not impose any modulo
825 * constraint and simply express x_i = x'_i.
826 * For each of the remaining rows i, we introduce a div and a corresponding
827 * equality. In particular
829 * g_ii e_j = x_i - g_i(x')
831 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
832 * corresponding div (if g_kk != 1).
834 * If there are any equalities not involving any div, then we
835 * first apply a variable compression on the variables x:
837 * x = C x'' x'' = C_2 x
839 * and perform the above parameter compression on A C instead of on A.
840 * The resulting compression is then of the form
842 * x'' = T(x') = x_0 + G x'
844 * and in constructing the new divs and the corresponding equalities,
845 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
846 * by the corresponding row from C_2.
848 static struct isl_basic_map
*normalize_divs(
849 struct isl_basic_map
*bmap
, int *progress
)
856 struct isl_mat
*T
= NULL
;
857 struct isl_mat
*C
= NULL
;
858 struct isl_mat
*C2
= NULL
;
866 if (bmap
->n_div
== 0)
872 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
875 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
876 div_eq
= n_pure_div_eq(bmap
);
880 if (div_eq
< bmap
->n_eq
) {
881 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
882 bmap
->n_eq
- div_eq
, 0, 1 + total
);
883 C
= isl_mat_variable_compression(B
, &C2
);
887 bmap
= isl_basic_map_set_to_empty(bmap
);
894 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
897 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
898 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
900 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
902 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
905 B
= isl_mat_product(B
, C
);
909 T
= isl_mat_parameter_compression(B
, d
);
913 bmap
= isl_basic_map_set_to_empty(bmap
);
919 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
920 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
921 if (isl_int_is_zero(v
))
923 isl_mat_col_submul(T
, 0, v
, 1 + i
);
926 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
929 /* We have to be careful because dropping equalities may reorder them */
931 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
932 for (i
= 0; i
< bmap
->n_eq
; ++i
)
933 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
935 if (i
< bmap
->n_eq
) {
936 bmap
= isl_basic_map_drop_div(bmap
, j
);
937 isl_basic_map_drop_equality(bmap
, i
);
943 for (i
= 1; i
< T
->n_row
; ++i
) {
944 if (isl_int_is_one(T
->row
[i
][i
]))
949 if (needed
> dropped
) {
950 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
955 for (i
= 1; i
< T
->n_row
; ++i
) {
956 if (isl_int_is_one(T
->row
[i
][i
]))
958 k
= isl_basic_map_alloc_div(bmap
);
959 pos
[i
] = 1 + total
+ k
;
960 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
961 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
963 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
965 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
966 for (j
= 0; j
< i
; ++j
) {
967 if (isl_int_is_zero(T
->row
[i
][j
]))
969 if (pos
[j
] < T
->n_row
&& C2
)
970 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
971 C2
->row
[pos
[j
]], 1 + total
);
973 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
976 j
= isl_basic_map_alloc_equality(bmap
);
977 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
978 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
987 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
997 static struct isl_basic_map
*set_div_from_lower_bound(
998 struct isl_basic_map
*bmap
, int div
, int ineq
)
1000 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1002 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1003 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1004 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1005 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1006 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1011 /* Check whether it is ok to define a div based on an inequality.
1012 * To avoid the introduction of circular definitions of divs, we
1013 * do not allow such a definition if the resulting expression would refer to
1014 * any other undefined divs or if any known div is defined in
1015 * terms of the unknown div.
1017 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
1021 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1023 /* Not defined in terms of unknown divs */
1024 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1027 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1029 if (isl_int_is_zero(bmap
->div
[j
][0]))
1033 /* No other div defined in terms of this one => avoid loops */
1034 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1037 if (isl_int_is_zero(bmap
->div
[j
][0]))
1039 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1046 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1047 * be a better expression than the current one?
1049 * If we do not have any expression yet, then any expression would be better.
1050 * Otherwise we check if the last variable involved in the inequality
1051 * (disregarding the div that it would define) is in an earlier position
1052 * than the last variable involved in the current div expression.
1054 static int better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1057 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1061 if (isl_int_is_zero(bmap
->div
[div
][0]))
1064 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1065 bmap
->n_div
- (div
+ 1)) >= 0)
1068 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1069 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1070 total
+ bmap
->n_div
);
1072 return last_ineq
< last_div
;
1075 /* Given two constraints "k" and "l" that are opposite to each other,
1076 * except for the constant term, check if we can use them
1077 * to obtain an expression for one of the hitherto unknown divs or
1078 * a "better" expression for a div for which we already have an expression.
1079 * "sum" is the sum of the constant terms of the constraints.
1080 * If this sum is strictly smaller than the coefficient of one
1081 * of the divs, then this pair can be used define the div.
1082 * To avoid the introduction of circular definitions of divs, we
1083 * do not use the pair if the resulting expression would refer to
1084 * any other undefined divs or if any known div is defined in
1085 * terms of the unknown div.
1087 static struct isl_basic_map
*check_for_div_constraints(
1088 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
1091 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1093 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1094 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1096 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1098 if (!better_div_constraint(bmap
, i
, k
))
1100 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1102 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1103 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1105 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1113 static struct isl_basic_map
*remove_duplicate_constraints(
1114 struct isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1120 unsigned total
= isl_basic_map_total_dim(bmap
);
1124 if (!bmap
|| bmap
->n_ineq
<= 1)
1127 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
1128 bits
= ffs(size
) - 1;
1129 ctx
= isl_basic_map_get_ctx(bmap
);
1130 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1134 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
1135 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1136 h
= hash_index(index
, size
, bits
, bmap
, k
);
1138 index
[h
] = &bmap
->ineq
[k
];
1143 l
= index
[h
] - &bmap
->ineq
[0];
1144 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1145 swap_inequality(bmap
, k
, l
);
1146 isl_basic_map_drop_inequality(bmap
, k
);
1150 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1151 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1152 h
= hash_index(index
, size
, bits
, bmap
, k
);
1153 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1156 l
= index
[h
] - &bmap
->ineq
[0];
1157 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1158 if (isl_int_is_pos(sum
)) {
1160 bmap
= check_for_div_constraints(bmap
, k
, l
,
1164 if (isl_int_is_zero(sum
)) {
1165 /* We need to break out of the loop after these
1166 * changes since the contents of the hash
1167 * will no longer be valid.
1168 * Plus, we probably we want to regauss first.
1172 isl_basic_map_drop_inequality(bmap
, l
);
1173 isl_basic_map_inequality_to_equality(bmap
, k
);
1175 bmap
= isl_basic_map_set_to_empty(bmap
);
1185 /* Eliminate knowns divs from constraints where they appear with
1186 * a (positive or negative) unit coefficient.
1190 * floor(e/m) + f >= 0
1198 * -floor(e/m) + f >= 0
1202 * -e + m f + m - 1 >= 0
1204 * The first conversion is valid because floor(e/m) >= -f is equivalent
1205 * to e/m >= -f because -f is an integral expression.
1206 * The second conversion follows from the fact that
1208 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1211 * We skip integral divs, i.e., those with denominator 1, as we would
1212 * risk eliminating the div from the div constraints. We do not need
1213 * to handle those divs here anyway since the div constraints will turn
1214 * out to form an equality and this equality can then be use to eliminate
1215 * the div from all constraints.
1217 static __isl_give isl_basic_map
*eliminate_unit_divs(
1218 __isl_take isl_basic_map
*bmap
, int *progress
)
1227 ctx
= isl_basic_map_get_ctx(bmap
);
1228 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1230 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1231 if (isl_int_is_zero(bmap
->div
[i
][0]))
1233 if (isl_int_is_one(bmap
->div
[i
][0]))
1235 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1238 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1239 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1244 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1245 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1247 isl_seq_combine(bmap
->ineq
[j
],
1248 ctx
->negone
, bmap
->div
[i
] + 1,
1249 bmap
->div
[i
][0], bmap
->ineq
[j
],
1250 total
+ bmap
->n_div
);
1252 isl_seq_combine(bmap
->ineq
[j
],
1253 ctx
->one
, bmap
->div
[i
] + 1,
1254 bmap
->div
[i
][0], bmap
->ineq
[j
],
1255 total
+ bmap
->n_div
);
1257 isl_int_add(bmap
->ineq
[j
][0],
1258 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1259 isl_int_sub_ui(bmap
->ineq
[j
][0],
1260 bmap
->ineq
[j
][0], 1);
1268 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1277 if (isl_basic_map_plain_is_empty(bmap
))
1279 bmap
= isl_basic_map_normalize_constraints(bmap
);
1280 bmap
= normalize_div_expressions(bmap
);
1281 bmap
= remove_duplicate_divs(bmap
, &progress
);
1282 bmap
= eliminate_unit_divs(bmap
, &progress
);
1283 bmap
= eliminate_divs_eq(bmap
, &progress
);
1284 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1285 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1286 /* requires equalities in normal form */
1287 bmap
= normalize_divs(bmap
, &progress
);
1288 bmap
= remove_duplicate_constraints(bmap
, &progress
, 1);
1293 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1295 return (struct isl_basic_set
*)
1296 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1300 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1301 isl_int
*constraint
, unsigned div
)
1308 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1310 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1312 isl_int_sub(bmap
->div
[div
][1],
1313 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1314 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1315 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1316 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1317 isl_int_add(bmap
->div
[div
][1],
1318 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1321 if (isl_seq_first_non_zero(constraint
+pos
+1,
1322 bmap
->n_div
-div
-1) != -1)
1324 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1325 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1327 if (isl_seq_first_non_zero(constraint
+pos
+1,
1328 bmap
->n_div
-div
-1) != -1)
1336 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1337 isl_int
*constraint
, unsigned div
)
1339 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1343 /* If the only constraints a div d=floor(f/m)
1344 * appears in are its two defining constraints
1347 * -(f - (m - 1)) + m d >= 0
1349 * then it can safely be removed.
1351 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1354 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1356 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1357 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1360 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1361 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1363 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1367 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1368 if (isl_int_is_zero(bmap
->div
[i
][0]))
1370 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1378 * Remove divs that don't occur in any of the constraints or other divs.
1379 * These can arise when dropping some of the variables in a quast
1380 * returned by piplib.
1382 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1389 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1390 if (!div_is_redundant(bmap
, i
))
1392 bmap
= isl_basic_map_drop_div(bmap
, i
);
1397 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1399 bmap
= remove_redundant_divs(bmap
);
1402 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1406 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1408 return (struct isl_basic_set
*)
1409 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1412 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1418 for (i
= 0; i
< set
->n
; ++i
) {
1419 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1429 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1435 for (i
= 0; i
< map
->n
; ++i
) {
1436 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1440 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1448 /* Remove definition of any div that is defined in terms of the given variable.
1449 * The div itself is not removed. Functions such as
1450 * eliminate_divs_ineq depend on the other divs remaining in place.
1452 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1460 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1461 if (isl_int_is_zero(bmap
->div
[i
][0]))
1463 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1465 isl_int_set_si(bmap
->div
[i
][0], 0);
1470 /* Eliminate the specified variables from the constraints using
1471 * Fourier-Motzkin. The variables themselves are not removed.
1473 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1474 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1485 total
= isl_basic_map_total_dim(bmap
);
1487 bmap
= isl_basic_map_cow(bmap
);
1488 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1489 bmap
= remove_dependent_vars(bmap
, d
);
1493 for (d
= pos
+ n
- 1;
1494 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1495 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1496 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1497 int n_lower
, n_upper
;
1500 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1501 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1503 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1504 isl_basic_map_drop_equality(bmap
, i
);
1512 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1513 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1515 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1518 bmap
= isl_basic_map_extend_constraints(bmap
,
1519 0, n_lower
* n_upper
);
1522 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1524 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1527 for (j
= 0; j
< i
; ++j
) {
1528 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1531 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1532 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1534 k
= isl_basic_map_alloc_inequality(bmap
);
1537 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1539 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1540 1+d
, 1+total
, NULL
);
1542 isl_basic_map_drop_inequality(bmap
, i
);
1545 if (n_lower
> 0 && n_upper
> 0) {
1546 bmap
= isl_basic_map_normalize_constraints(bmap
);
1547 bmap
= remove_duplicate_constraints(bmap
, NULL
, 0);
1548 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1549 bmap
= isl_basic_map_remove_redundancies(bmap
);
1553 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1557 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1559 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1562 isl_basic_map_free(bmap
);
1566 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1567 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1569 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1570 (struct isl_basic_map
*)bset
, pos
, n
);
1573 /* Eliminate the specified n dimensions starting at first from the
1574 * constraints, without removing the dimensions from the space.
1575 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1576 * Otherwise, they are projected out and the original space is restored.
1578 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1579 __isl_take isl_basic_map
*bmap
,
1580 enum isl_dim_type type
, unsigned first
, unsigned n
)
1589 if (first
+ n
> isl_basic_map_dim(bmap
, type
) || first
+ n
< first
)
1590 isl_die(bmap
->ctx
, isl_error_invalid
,
1591 "index out of bounds", goto error
);
1593 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1594 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1595 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1596 return isl_basic_map_finalize(bmap
);
1599 space
= isl_basic_map_get_space(bmap
);
1600 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1601 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1602 bmap
= isl_basic_map_reset_space(bmap
, space
);
1605 isl_basic_map_free(bmap
);
1609 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1610 __isl_take isl_basic_set
*bset
,
1611 enum isl_dim_type type
, unsigned first
, unsigned n
)
1613 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1616 /* Don't assume equalities are in order, because align_divs
1617 * may have changed the order of the divs.
1619 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1624 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1625 for (d
= 0; d
< total
; ++d
)
1627 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1628 for (d
= total
- 1; d
>= 0; --d
) {
1629 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1637 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1639 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1642 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1643 struct isl_basic_map
*bmap
, int *elim
)
1649 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1650 for (d
= total
- 1; d
>= 0; --d
) {
1651 if (isl_int_is_zero(src
[1+d
]))
1656 isl_seq_cpy(dst
, src
, 1 + total
);
1659 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1664 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1665 struct isl_basic_set
*bset
, int *elim
)
1667 return reduced_using_equalities(dst
, src
,
1668 (struct isl_basic_map
*)bset
, elim
);
1671 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1672 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1677 if (!bset
|| !context
)
1680 if (context
->n_eq
== 0) {
1681 isl_basic_set_free(context
);
1685 bset
= isl_basic_set_cow(bset
);
1689 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1692 set_compute_elimination_index(context
, elim
);
1693 for (i
= 0; i
< bset
->n_eq
; ++i
)
1694 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1696 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1697 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1699 isl_basic_set_free(context
);
1701 bset
= isl_basic_set_simplify(bset
);
1702 bset
= isl_basic_set_finalize(bset
);
1705 isl_basic_set_free(bset
);
1706 isl_basic_set_free(context
);
1710 static struct isl_basic_set
*remove_shifted_constraints(
1711 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1722 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1723 bits
= ffs(size
) - 1;
1724 ctx
= isl_basic_set_get_ctx(bset
);
1725 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1729 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1730 h
= set_hash_index(index
, size
, bits
, context
, k
);
1731 index
[h
] = &context
->ineq
[k
];
1733 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1734 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1737 l
= index
[h
] - &context
->ineq
[0];
1738 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1740 bset
= isl_basic_set_cow(bset
);
1743 isl_basic_set_drop_inequality(bset
, k
);
1753 /* Does the (linear part of a) constraint "c" involve any of the "len"
1754 * "relevant" dimensions?
1756 static int is_related(isl_int
*c
, int len
, int *relevant
)
1760 for (i
= 0; i
< len
; ++i
) {
1763 if (!isl_int_is_zero(c
[i
]))
1770 /* Drop constraints from "bset" that do not involve any of
1771 * the dimensions marked "relevant".
1773 static __isl_give isl_basic_set
*drop_unrelated_constraints(
1774 __isl_take isl_basic_set
*bset
, int *relevant
)
1778 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1779 for (i
= 0; i
< dim
; ++i
)
1785 for (i
= bset
->n_eq
- 1; i
>= 0; --i
)
1786 if (!is_related(bset
->eq
[i
] + 1, dim
, relevant
))
1787 isl_basic_set_drop_equality(bset
, i
);
1789 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
)
1790 if (!is_related(bset
->ineq
[i
] + 1, dim
, relevant
))
1791 isl_basic_set_drop_inequality(bset
, i
);
1796 /* Update the groups in "group" based on the (linear part of a) constraint "c".
1798 * In particular, for any variable involved in the constraint,
1799 * find the actual group id from before and replace the group
1800 * of the corresponding variable by the minimal group of all
1801 * the variables involved in the constraint considered so far
1802 * (if this minimum is smaller) or replace the minimum by this group
1803 * (if the minimum is larger).
1805 * At the end, all the variables in "c" will (indirectly) point
1806 * to the minimal of the groups that they referred to originally.
1808 static void update_groups(int dim
, int *group
, isl_int
*c
)
1813 for (j
= 0; j
< dim
; ++j
) {
1814 if (isl_int_is_zero(c
[j
]))
1816 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
1817 group
[j
] = group
[group
[j
]];
1818 if (group
[j
] == min
)
1820 if (group
[j
] < min
) {
1821 if (min
>= 0 && min
< dim
)
1822 group
[min
] = group
[j
];
1825 group
[group
[j
]] = min
;
1829 /* Drop constraints from "context" that are irrelevant for computing
1830 * the gist of "bset".
1832 * In particular, drop constraints in variables that are not related
1833 * to any of the variables involved in the constraints of "bset"
1834 * in the sense that there is no sequence of constraints that connects them.
1836 * We construct groups of variables that collect variables that
1837 * (indirectly) appear in some common constraint of "context".
1838 * Each group is identified by the first variable in the group,
1839 * except for the special group of variables that appear in "bset"
1840 * (or are related to those variables), which is identified by -1.
1841 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
1842 * otherwise the group of i is the group of group[i].
1844 * We first initialize the -1 group with the variables that appear in "bset".
1845 * Then we initialize groups for the remaining variables.
1846 * Then we iterate over the constraints of "context" and update the
1847 * group of the variables in the constraint by the smallest group.
1848 * Finally, we resolve indirect references to groups by running over
1851 * After computing the groups, we drop constraints that do not involve
1852 * any variables in the -1 group.
1854 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
1855 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
1863 if (!context
|| !bset
)
1864 return isl_basic_set_free(context
);
1866 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1867 ctx
= isl_basic_set_get_ctx(bset
);
1868 group
= isl_calloc_array(ctx
, int, dim
);
1873 for (i
= 0; i
< dim
; ++i
) {
1874 for (j
= 0; j
< bset
->n_eq
; ++j
)
1875 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
1877 if (j
< bset
->n_eq
) {
1881 for (j
= 0; j
< bset
->n_ineq
; ++j
)
1882 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
1884 if (j
< bset
->n_ineq
)
1889 for (i
= 0; i
< dim
; ++i
)
1891 last
= group
[i
] = i
;
1897 for (i
= 0; i
< context
->n_eq
; ++i
)
1898 update_groups(dim
, group
, context
->eq
[i
] + 1);
1899 for (i
= 0; i
< context
->n_ineq
; ++i
)
1900 update_groups(dim
, group
, context
->ineq
[i
] + 1);
1902 for (i
= 0; i
< dim
; ++i
)
1904 group
[i
] = group
[group
[i
]];
1906 for (i
= 0; i
< dim
; ++i
)
1907 group
[i
] = group
[i
] == -1;
1909 context
= drop_unrelated_constraints(context
, group
);
1915 return isl_basic_set_free(context
);
1918 /* Remove all information from bset that is redundant in the context
1919 * of context. Both bset and context are assumed to be full-dimensional.
1921 * We first remove the inequalities from "bset"
1922 * that are obviously redundant with respect to some inequality in "context".
1923 * Then we remove those constraints from "context" that have become
1924 * irrelevant for computing the gist of "bset".
1925 * Note that this removal of constraints cannot be replaced by
1926 * a factorization because factors in "bset" may still be connected
1927 * to each other through constraints in "context".
1929 * If there are any inequalities left, we construct a tableau for
1930 * the context and then add the inequalities of "bset".
1931 * Before adding these inequalities, we freeze all constraints such that
1932 * they won't be considered redundant in terms of the constraints of "bset".
1933 * Then we detect all redundant constraints (among the
1934 * constraints that weren't frozen), first by checking for redundancy in the
1935 * the tableau and then by checking if replacing a constraint by its negation
1936 * would lead to an empty set. This last step is fairly expensive
1937 * and could be optimized by more reuse of the tableau.
1938 * Finally, we update bset according to the results.
1940 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1941 __isl_take isl_basic_set
*context
)
1944 isl_basic_set
*combined
= NULL
;
1945 struct isl_tab
*tab
= NULL
;
1946 unsigned context_ineq
;
1949 if (!bset
|| !context
)
1952 if (isl_basic_set_is_universe(bset
)) {
1953 isl_basic_set_free(context
);
1957 if (isl_basic_set_is_universe(context
)) {
1958 isl_basic_set_free(context
);
1962 bset
= remove_shifted_constraints(bset
, context
);
1965 if (bset
->n_ineq
== 0)
1968 context
= drop_irrelevant_constraints(context
, bset
);
1971 if (isl_basic_set_is_universe(context
)) {
1972 isl_basic_set_free(context
);
1976 context_ineq
= context
->n_ineq
;
1977 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1978 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
1979 tab
= isl_tab_from_basic_set(combined
, 0);
1980 for (i
= 0; i
< context_ineq
; ++i
)
1981 if (isl_tab_freeze_constraint(tab
, i
) < 0)
1983 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1984 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1985 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
1987 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1991 if (isl_tab_detect_redundant(tab
) < 0)
1993 total
= isl_basic_set_total_dim(bset
);
1994 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
1996 if (tab
->con
[i
].is_redundant
)
1998 tab
->con
[i
].is_redundant
= 1;
1999 combined
= isl_basic_set_dup(bset
);
2000 combined
= isl_basic_set_update_from_tab(combined
, tab
);
2001 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
2002 k
= isl_basic_set_alloc_inequality(combined
);
2005 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
2006 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
2007 is_empty
= isl_basic_set_is_empty(combined
);
2010 isl_basic_set_free(combined
);
2013 tab
->con
[i
].is_redundant
= 0;
2015 for (i
= 0; i
< context_ineq
; ++i
)
2016 tab
->con
[i
].is_redundant
= 1;
2017 bset
= isl_basic_set_update_from_tab(bset
, tab
);
2019 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2020 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2025 bset
= isl_basic_set_simplify(bset
);
2026 bset
= isl_basic_set_finalize(bset
);
2027 isl_basic_set_free(context
);
2031 isl_basic_set_free(combined
);
2032 isl_basic_set_free(context
);
2033 isl_basic_set_free(bset
);
2037 /* Remove all information from bset that is redundant in the context
2038 * of context. In particular, equalities that are linear combinations
2039 * of those in context are removed. Then the inequalities that are
2040 * redundant in the context of the equalities and inequalities of
2041 * context are removed.
2043 * First of all, we drop those constraints from "context"
2044 * that are irrelevant for computing the gist of "bset".
2045 * Alternatively, we could factorize the intersection of "context" and "bset".
2047 * We first compute the integer affine hull of the intersection,
2048 * compute the gist inside this affine hull and then add back
2049 * those equalities that are not implied by the context.
2051 * If two constraints are mutually redundant, then uset_gist_full
2052 * will remove the second of those constraints. We therefore first
2053 * sort the constraints so that constraints not involving existentially
2054 * quantified variables are given precedence over those that do.
2055 * We have to perform this sorting before the variable compression,
2056 * because that may effect the order of the variables.
2058 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2059 __isl_take isl_basic_set
*context
)
2064 isl_basic_set
*aff_context
;
2067 if (!bset
|| !context
)
2070 context
= drop_irrelevant_constraints(context
, bset
);
2072 bset
= isl_basic_set_intersect(bset
, isl_basic_set_copy(context
));
2073 if (isl_basic_set_plain_is_empty(bset
)) {
2074 isl_basic_set_free(context
);
2077 bset
= isl_basic_set_sort_constraints(bset
);
2078 aff
= isl_basic_set_affine_hull(isl_basic_set_copy(bset
));
2081 if (isl_basic_set_plain_is_empty(aff
)) {
2082 isl_basic_set_free(aff
);
2083 isl_basic_set_free(context
);
2086 if (aff
->n_eq
== 0) {
2087 isl_basic_set_free(aff
);
2088 return uset_gist_full(bset
, context
);
2090 total
= isl_basic_set_total_dim(bset
);
2091 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2092 eq
= isl_mat_cow(eq
);
2093 T
= isl_mat_variable_compression(eq
, &T2
);
2094 if (T
&& T
->n_col
== 0) {
2097 isl_basic_set_free(context
);
2098 isl_basic_set_free(aff
);
2099 return isl_basic_set_set_to_empty(bset
);
2102 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2104 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
2105 context
= isl_basic_set_preimage(context
, T
);
2107 bset
= uset_gist_full(bset
, context
);
2108 bset
= isl_basic_set_preimage(bset
, T2
);
2109 bset
= isl_basic_set_intersect(bset
, aff
);
2110 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2113 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2114 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2119 isl_basic_set_free(bset
);
2120 isl_basic_set_free(context
);
2124 /* Normalize the divs in "bmap" in the context of the equalities in "context".
2125 * We simply add the equalities in context to bmap and then do a regular
2126 * div normalizations. Better results can be obtained by normalizing
2127 * only the divs in bmap than do not also appear in context.
2128 * We need to be careful to reduce the divs using the equalities
2129 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
2130 * spurious constraints.
2132 static struct isl_basic_map
*normalize_divs_in_context(
2133 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
2136 unsigned total_context
;
2139 div_eq
= n_pure_div_eq(bmap
);
2143 if (context
->n_div
> 0)
2144 bmap
= isl_basic_map_align_divs(bmap
, context
);
2146 total_context
= isl_basic_map_total_dim(context
);
2147 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
2148 for (i
= 0; i
< context
->n_eq
; ++i
) {
2150 k
= isl_basic_map_alloc_equality(bmap
);
2152 return isl_basic_map_free(bmap
);
2153 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
2154 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
2155 isl_basic_map_total_dim(bmap
) - total_context
);
2157 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2158 bmap
= normalize_divs(bmap
, NULL
);
2159 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2163 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
2164 struct isl_basic_map
*context
)
2166 struct isl_basic_set
*bset
;
2168 if (!bmap
|| !context
)
2171 if (isl_basic_map_is_universe(bmap
)) {
2172 isl_basic_map_free(context
);
2175 if (isl_basic_map_plain_is_empty(context
)) {
2176 isl_basic_map_free(bmap
);
2179 if (isl_basic_map_plain_is_empty(bmap
)) {
2180 isl_basic_map_free(context
);
2184 bmap
= isl_basic_map_remove_redundancies(bmap
);
2185 context
= isl_basic_map_remove_redundancies(context
);
2190 bmap
= normalize_divs_in_context(bmap
, context
);
2192 context
= isl_basic_map_align_divs(context
, bmap
);
2193 bmap
= isl_basic_map_align_divs(bmap
, context
);
2195 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
2196 isl_basic_map_underlying_set(context
));
2198 return isl_basic_map_overlying_set(bset
, bmap
);
2200 isl_basic_map_free(bmap
);
2201 isl_basic_map_free(context
);
2206 * Assumes context has no implicit divs.
2208 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
2209 __isl_take isl_basic_map
*context
)
2213 if (!map
|| !context
)
2216 if (isl_basic_map_plain_is_empty(context
)) {
2218 return isl_map_from_basic_map(context
);
2221 context
= isl_basic_map_remove_redundancies(context
);
2222 map
= isl_map_cow(map
);
2223 if (!map
|| !context
)
2225 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
2226 map
= isl_map_compute_divs(map
);
2229 for (i
= map
->n
- 1; i
>= 0; --i
) {
2230 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
2231 isl_basic_map_copy(context
));
2234 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
2235 isl_basic_map_free(map
->p
[i
]);
2236 if (i
!= map
->n
- 1)
2237 map
->p
[i
] = map
->p
[map
->n
- 1];
2241 isl_basic_map_free(context
);
2242 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2246 isl_basic_map_free(context
);
2250 /* Return a map that has the same intersection with "context" as "map"
2251 * and that as "simple" as possible.
2253 * If "map" is already the universe, then we cannot make it any simpler.
2254 * Similarly, if "context" is the universe, then we cannot exploit it
2256 * If "map" and "context" are identical to each other, then we can
2257 * return the corresponding universe.
2259 * If none of these cases apply, we have to work a bit harder.
2261 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
2262 __isl_take isl_map
*context
)
2267 is_universe
= isl_map_plain_is_universe(map
);
2268 if (is_universe
>= 0 && !is_universe
)
2269 is_universe
= isl_map_plain_is_universe(context
);
2270 if (is_universe
< 0)
2273 isl_map_free(context
);
2277 equal
= isl_map_plain_is_equal(map
, context
);
2281 isl_map
*res
= isl_map_universe(isl_map_get_space(map
));
2283 isl_map_free(context
);
2287 context
= isl_map_compute_divs(context
);
2288 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
2291 isl_map_free(context
);
2295 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
2296 __isl_take isl_map
*context
)
2298 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2301 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2302 struct isl_basic_set
*context
)
2304 return (struct isl_basic_set
*)isl_basic_map_gist(
2305 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2308 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2309 __isl_take isl_basic_set
*context
)
2311 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2312 (struct isl_basic_map
*)context
);
2315 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2316 __isl_take isl_basic_set
*context
)
2318 isl_space
*space
= isl_set_get_space(set
);
2319 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2320 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2321 return isl_set_gist_basic_set(set
, dom_context
);
2324 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2325 __isl_take isl_set
*context
)
2327 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2328 (struct isl_map
*)context
);
2331 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2332 __isl_take isl_set
*context
)
2334 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2335 map_context
= isl_map_intersect_domain(map_context
, context
);
2336 return isl_map_gist(map
, map_context
);
2339 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2340 __isl_take isl_set
*context
)
2342 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2343 map_context
= isl_map_intersect_range(map_context
, context
);
2344 return isl_map_gist(map
, map_context
);
2347 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2348 __isl_take isl_set
*context
)
2350 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2351 map_context
= isl_map_intersect_params(map_context
, context
);
2352 return isl_map_gist(map
, map_context
);
2355 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2356 __isl_take isl_set
*context
)
2358 return isl_map_gist_params(set
, context
);
2361 /* Quick check to see if two basic maps are disjoint.
2362 * In particular, we reduce the equalities and inequalities of
2363 * one basic map in the context of the equalities of the other
2364 * basic map and check if we get a contradiction.
2366 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2367 __isl_keep isl_basic_map
*bmap2
)
2369 struct isl_vec
*v
= NULL
;
2374 if (!bmap1
|| !bmap2
)
2376 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
2378 if (bmap1
->n_div
|| bmap2
->n_div
)
2380 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
2383 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
2386 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
2389 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
2392 compute_elimination_index(bmap1
, elim
);
2393 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
2395 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
2397 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
2398 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2401 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
2403 reduced
= reduced_using_equalities(v
->block
.data
,
2404 bmap2
->ineq
[i
], bmap1
, elim
);
2405 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2406 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2409 compute_elimination_index(bmap2
, elim
);
2410 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
2412 reduced
= reduced_using_equalities(v
->block
.data
,
2413 bmap1
->ineq
[i
], bmap2
, elim
);
2414 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2415 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2431 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2432 __isl_keep isl_basic_set
*bset2
)
2434 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
2435 (struct isl_basic_map
*)bset2
);
2438 /* Are "map1" and "map2" obviously disjoint?
2440 * If one of them is empty or if they live in different spaces (ignoring
2441 * parameters), then they are clearly disjoint.
2443 * If they have different parameters, then we skip any further tests.
2445 * If they are obviously equal, but not obviously empty, then we will
2446 * not be able to detect if they are disjoint.
2448 * Otherwise we check if each basic map in "map1" is obviously disjoint
2449 * from each basic map in "map2".
2451 int isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
2452 __isl_keep isl_map
*map2
)
2462 disjoint
= isl_map_plain_is_empty(map1
);
2463 if (disjoint
< 0 || disjoint
)
2466 disjoint
= isl_map_plain_is_empty(map2
);
2467 if (disjoint
< 0 || disjoint
)
2470 match
= isl_space_tuple_match(map1
->dim
, isl_dim_in
,
2471 map2
->dim
, isl_dim_in
);
2472 if (match
< 0 || !match
)
2473 return match
< 0 ? -1 : 1;
2475 match
= isl_space_tuple_match(map1
->dim
, isl_dim_out
,
2476 map2
->dim
, isl_dim_out
);
2477 if (match
< 0 || !match
)
2478 return match
< 0 ? -1 : 1;
2480 match
= isl_space_match(map1
->dim
, isl_dim_param
,
2481 map2
->dim
, isl_dim_param
);
2482 if (match
< 0 || !match
)
2483 return match
< 0 ? -1 : 0;
2485 intersect
= isl_map_plain_is_equal(map1
, map2
);
2486 if (intersect
< 0 || intersect
)
2487 return intersect
< 0 ? -1 : 0;
2489 for (i
= 0; i
< map1
->n
; ++i
) {
2490 for (j
= 0; j
< map2
->n
; ++j
) {
2491 int d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
2500 /* Are "map1" and "map2" disjoint?
2502 * They are disjoint if they are "obviously disjoint" or if one of them
2503 * is empty. Otherwise, they are not disjoint if one of them is universal.
2504 * If none of these cases apply, we compute the intersection and see if
2505 * the result is empty.
2507 int isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
2513 disjoint
= isl_map_plain_is_disjoint(map1
, map2
);
2514 if (disjoint
< 0 || disjoint
)
2517 disjoint
= isl_map_is_empty(map1
);
2518 if (disjoint
< 0 || disjoint
)
2521 disjoint
= isl_map_is_empty(map2
);
2522 if (disjoint
< 0 || disjoint
)
2525 intersect
= isl_map_plain_is_universe(map1
);
2526 if (intersect
< 0 || intersect
)
2527 return intersect
< 0 ? -1 : 0;
2529 intersect
= isl_map_plain_is_universe(map2
);
2530 if (intersect
< 0 || intersect
)
2531 return intersect
< 0 ? -1 : 0;
2533 test
= isl_map_intersect(isl_map_copy(map1
), isl_map_copy(map2
));
2534 disjoint
= isl_map_is_empty(test
);
2540 int isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
2541 __isl_keep isl_set
*set2
)
2543 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
2544 (struct isl_map
*)set2
);
2547 /* Are "set1" and "set2" disjoint?
2549 int isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2551 return isl_map_is_disjoint(set1
, set2
);
2554 int isl_set_fast_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2556 return isl_set_plain_is_disjoint(set1
, set2
);
2559 /* Check if we can combine a given div with lower bound l and upper
2560 * bound u with some other div and if so return that other div.
2561 * Otherwise return -1.
2563 * We first check that
2564 * - the bounds are opposites of each other (except for the constant
2566 * - the bounds do not reference any other div
2567 * - no div is defined in terms of this div
2569 * Let m be the size of the range allowed on the div by the bounds.
2570 * That is, the bounds are of the form
2572 * e <= a <= e + m - 1
2574 * with e some expression in the other variables.
2575 * We look for another div b such that no third div is defined in terms
2576 * of this second div b and such that in any constraint that contains
2577 * a (except for the given lower and upper bound), also contains b
2578 * with a coefficient that is m times that of b.
2579 * That is, all constraints (execpt for the lower and upper bound)
2582 * e + f (a + m b) >= 0
2584 * If so, we return b so that "a + m b" can be replaced by
2585 * a single div "c = a + m b".
2587 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2588 unsigned div
, unsigned l
, unsigned u
)
2594 if (bmap
->n_div
<= 1)
2596 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2597 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2599 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2600 bmap
->n_div
- div
- 1) != -1)
2602 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2606 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2607 if (isl_int_is_zero(bmap
->div
[i
][0]))
2609 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2613 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2614 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2615 isl_int_sub(bmap
->ineq
[l
][0],
2616 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2617 bmap
= isl_basic_map_copy(bmap
);
2618 bmap
= isl_basic_map_set_to_empty(bmap
);
2619 isl_basic_map_free(bmap
);
2622 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2623 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2628 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2629 if (isl_int_is_zero(bmap
->div
[j
][0]))
2631 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2634 if (j
< bmap
->n_div
)
2636 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2638 if (j
== l
|| j
== u
)
2640 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2642 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2644 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2645 bmap
->ineq
[j
][1 + dim
+ div
],
2647 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2648 bmap
->ineq
[j
][1 + dim
+ i
]);
2649 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2650 bmap
->ineq
[j
][1 + dim
+ div
],
2655 if (j
< bmap
->n_ineq
)
2660 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2661 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2665 /* Given a lower and an upper bound on div i, construct an inequality
2666 * that when nonnegative ensures that this pair of bounds always allows
2667 * for an integer value of the given div.
2668 * The lower bound is inequality l, while the upper bound is inequality u.
2669 * The constructed inequality is stored in ineq.
2670 * g, fl, fu are temporary scalars.
2672 * Let the upper bound be
2676 * and the lower bound
2680 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2683 * - f_u e_l <= f_u f_l g a <= f_l e_u
2685 * Since all variables are integer valued, this is equivalent to
2687 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2689 * If this interval is at least f_u f_l g, then it contains at least
2690 * one integer value for a.
2691 * That is, the test constraint is
2693 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2695 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2696 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2699 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2701 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2702 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2703 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2704 isl_int_neg(fu
, fu
);
2705 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2706 1 + dim
+ bmap
->n_div
);
2707 isl_int_add(ineq
[0], ineq
[0], fl
);
2708 isl_int_add(ineq
[0], ineq
[0], fu
);
2709 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2710 isl_int_mul(g
, g
, fl
);
2711 isl_int_mul(g
, g
, fu
);
2712 isl_int_sub(ineq
[0], ineq
[0], g
);
2715 /* Remove more kinds of divs that are not strictly needed.
2716 * In particular, if all pairs of lower and upper bounds on a div
2717 * are such that they allow at least one integer value of the div,
2718 * the we can eliminate the div using Fourier-Motzkin without
2719 * introducing any spurious solutions.
2721 static struct isl_basic_map
*drop_more_redundant_divs(
2722 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2724 struct isl_tab
*tab
= NULL
;
2725 struct isl_vec
*vec
= NULL
;
2737 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2738 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2742 tab
= isl_tab_from_basic_map(bmap
, 0);
2747 enum isl_lp_result res
;
2749 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2752 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2758 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2759 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2761 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2762 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2764 construct_test_ineq(bmap
, i
, l
, u
,
2765 vec
->el
, g
, fl
, fu
);
2766 res
= isl_tab_min(tab
, vec
->el
,
2767 bmap
->ctx
->one
, &g
, NULL
, 0);
2768 if (res
== isl_lp_error
)
2770 if (res
== isl_lp_empty
) {
2771 bmap
= isl_basic_map_set_to_empty(bmap
);
2774 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2777 if (u
< bmap
->n_ineq
)
2780 if (l
== bmap
->n_ineq
) {
2800 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
2801 return isl_basic_map_drop_redundant_divs(bmap
);
2804 isl_basic_map_free(bmap
);
2813 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2814 * and the upper bound u, div1 always occurs together with div2 in the form
2815 * (div1 + m div2), where m is the constant range on the variable div1
2816 * allowed by l and u, replace the pair div1 and div2 by a single
2817 * div that is equal to div1 + m div2.
2819 * The new div will appear in the location that contains div2.
2820 * We need to modify all constraints that contain
2821 * div2 = (div - div1) / m
2822 * (If a constraint does not contain div2, it will also not contain div1.)
2823 * If the constraint also contains div1, then we know they appear
2824 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2825 * i.e., the coefficient of div is f.
2827 * Otherwise, we first need to introduce div1 into the constraint.
2836 * A lower bound on div2
2840 * can be replaced by
2842 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2844 * with g = gcd(m,n).
2849 * can be replaced by
2851 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2853 * These constraint are those that we would obtain from eliminating
2854 * div1 using Fourier-Motzkin.
2856 * After all constraints have been modified, we drop the lower and upper
2857 * bound and then drop div1.
2859 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2860 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2865 unsigned dim
, total
;
2868 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2869 total
= 1 + dim
+ bmap
->n_div
;
2874 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2875 isl_int_add_ui(m
, m
, 1);
2877 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2878 if (i
== l
|| i
== u
)
2880 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2882 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2883 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2884 isl_int_divexact(a
, m
, b
);
2885 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2886 if (isl_int_is_pos(b
)) {
2887 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2888 b
, bmap
->ineq
[l
], total
);
2891 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2892 b
, bmap
->ineq
[u
], total
);
2895 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2896 bmap
->ineq
[i
][1 + dim
+ div1
]);
2897 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2904 isl_basic_map_drop_inequality(bmap
, l
);
2905 isl_basic_map_drop_inequality(bmap
, u
);
2907 isl_basic_map_drop_inequality(bmap
, u
);
2908 isl_basic_map_drop_inequality(bmap
, l
);
2910 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2914 /* First check if we can coalesce any pair of divs and
2915 * then continue with dropping more redundant divs.
2917 * We loop over all pairs of lower and upper bounds on a div
2918 * with coefficient 1 and -1, respectively, check if there
2919 * is any other div "c" with which we can coalesce the div
2920 * and if so, perform the coalescing.
2922 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2923 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2928 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2930 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2933 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2934 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2936 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2939 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2941 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2945 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2946 return isl_basic_map_drop_redundant_divs(bmap
);
2951 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2954 return drop_more_redundant_divs(bmap
, pairs
, n
);
2957 /* Remove divs that are not strictly needed.
2958 * In particular, if a div only occurs positively (or negatively)
2959 * in constraints, then it can simply be dropped.
2960 * Also, if a div occurs in only two constraints and if moreover
2961 * those two constraints are opposite to each other, except for the constant
2962 * term and if the sum of the constant terms is such that for any value
2963 * of the other values, there is always at least one integer value of the
2964 * div, i.e., if one plus this sum is greater than or equal to
2965 * the (absolute value) of the coefficent of the div in the constraints,
2966 * then we can also simply drop the div.
2968 * We skip divs that appear in equalities or in the definition of other divs.
2969 * Divs that appear in the definition of other divs usually occur in at least
2970 * 4 constraints, but the constraints may have been simplified.
2972 * If any divs are left after these simple checks then we move on
2973 * to more complicated cases in drop_more_redundant_divs.
2975 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2976 struct isl_basic_map
*bmap
)
2986 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2987 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2991 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2993 int last_pos
, last_neg
;
2997 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2998 for (j
= i
; j
< bmap
->n_div
; ++j
)
2999 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
3001 if (j
< bmap
->n_div
)
3003 for (j
= 0; j
< bmap
->n_eq
; ++j
)
3004 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
3010 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
3011 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
3015 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
3020 pairs
[i
] = pos
* neg
;
3021 if (pairs
[i
] == 0) {
3022 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
3023 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
3024 isl_basic_map_drop_inequality(bmap
, j
);
3025 bmap
= isl_basic_map_drop_div(bmap
, i
);
3027 return isl_basic_map_drop_redundant_divs(bmap
);
3031 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
3032 bmap
->ineq
[last_neg
] + 1,
3036 isl_int_add(bmap
->ineq
[last_pos
][0],
3037 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3038 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
3039 bmap
->ineq
[last_pos
][0], 1);
3040 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
3041 bmap
->ineq
[last_pos
][1+off
+i
]);
3042 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
3043 bmap
->ineq
[last_pos
][0], 1);
3044 isl_int_sub(bmap
->ineq
[last_pos
][0],
3045 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3048 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
3053 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
3054 bmap
= isl_basic_map_simplify(bmap
);
3056 return isl_basic_map_drop_redundant_divs(bmap
);
3058 if (last_pos
> last_neg
) {
3059 isl_basic_map_drop_inequality(bmap
, last_pos
);
3060 isl_basic_map_drop_inequality(bmap
, last_neg
);
3062 isl_basic_map_drop_inequality(bmap
, last_neg
);
3063 isl_basic_map_drop_inequality(bmap
, last_pos
);
3065 bmap
= isl_basic_map_drop_div(bmap
, i
);
3067 return isl_basic_map_drop_redundant_divs(bmap
);
3071 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
3077 isl_basic_map_free(bmap
);
3081 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
3082 struct isl_basic_set
*bset
)
3084 return (struct isl_basic_set
*)
3085 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
3088 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
3094 for (i
= 0; i
< map
->n
; ++i
) {
3095 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
3099 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3106 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
3108 return (struct isl_set
*)
3109 isl_map_drop_redundant_divs((struct isl_map
*)set
);