2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 #include <isl_ctx_private.h>
12 #include <isl_map_private.h>
13 #include "isl_equalities.h"
17 #include <isl_dim_private.h>
18 #include <isl_mat_private.h>
20 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
22 isl_int
*t
= bmap
->eq
[a
];
23 bmap
->eq
[a
] = bmap
->eq
[b
];
27 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
30 isl_int
*t
= bmap
->ineq
[a
];
31 bmap
->ineq
[a
] = bmap
->ineq
[b
];
36 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
38 isl_seq_cpy(c
, c
+ n
, rem
);
39 isl_seq_clr(c
+ rem
, n
);
42 /* Drop n dimensions starting at first.
44 * In principle, this frees up some extra variables as the number
45 * of columns remains constant, but we would have to extend
46 * the div array too as the number of rows in this array is assumed
47 * to be equal to extra.
49 struct isl_basic_set
*isl_basic_set_drop_dims(
50 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
57 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
59 if (n
== 0 && !isl_dim_get_tuple_name(bset
->dim
, isl_dim_set
))
62 bset
= isl_basic_set_cow(bset
);
66 for (i
= 0; i
< bset
->n_eq
; ++i
)
67 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
68 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
70 for (i
= 0; i
< bset
->n_ineq
; ++i
)
71 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
72 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
74 for (i
= 0; i
< bset
->n_div
; ++i
)
75 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
76 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
78 bset
->dim
= isl_dim_drop_outputs(bset
->dim
, first
, n
);
82 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
83 bset
= isl_basic_set_simplify(bset
);
84 return isl_basic_set_finalize(bset
);
86 isl_basic_set_free(bset
);
90 struct isl_set
*isl_set_drop_dims(
91 struct isl_set
*set
, unsigned first
, unsigned n
)
98 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
100 if (n
== 0 && !isl_dim_get_tuple_name(set
->dim
, isl_dim_set
))
102 set
= isl_set_cow(set
);
105 set
->dim
= isl_dim_drop_outputs(set
->dim
, first
, n
);
109 for (i
= 0; i
< set
->n
; ++i
) {
110 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
115 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
122 /* Move "n" divs starting at "first" to the end of the list of divs.
124 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
125 unsigned first
, unsigned n
)
130 if (first
+ n
== bmap
->n_div
)
133 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
136 for (i
= 0; i
< n
; ++i
)
137 div
[i
] = bmap
->div
[first
+ i
];
138 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
139 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
140 for (i
= 0; i
< n
; ++i
)
141 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
145 isl_basic_map_free(bmap
);
149 /* Drop "n" dimensions of type "type" starting at "first".
151 * In principle, this frees up some extra variables as the number
152 * of columns remains constant, but we would have to extend
153 * the div array too as the number of rows in this array is assumed
154 * to be equal to extra.
156 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
157 enum isl_dim_type type
, unsigned first
, unsigned n
)
167 dim
= isl_basic_map_dim(bmap
, type
);
168 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
170 if (n
== 0 && !isl_dim_is_named_or_nested(bmap
->dim
, type
))
173 bmap
= isl_basic_map_cow(bmap
);
177 offset
= isl_basic_map_offset(bmap
, type
) + first
;
178 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
179 for (i
= 0; i
< bmap
->n_eq
; ++i
)
180 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
182 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
183 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
185 for (i
= 0; i
< bmap
->n_div
; ++i
)
186 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
188 if (type
== isl_dim_div
) {
189 bmap
= move_divs_last(bmap
, first
, n
);
192 isl_basic_map_free_div(bmap
, n
);
194 bmap
->dim
= isl_dim_drop(bmap
->dim
, type
, first
, n
);
198 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
199 bmap
= isl_basic_map_simplify(bmap
);
200 return isl_basic_map_finalize(bmap
);
202 isl_basic_map_free(bmap
);
206 __isl_give isl_basic_set
*isl_basic_set_drop(__isl_take isl_basic_set
*bset
,
207 enum isl_dim_type type
, unsigned first
, unsigned n
)
209 return (isl_basic_set
*)isl_basic_map_drop((isl_basic_map
*)bset
,
213 struct isl_basic_map
*isl_basic_map_drop_inputs(
214 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
216 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
219 struct isl_map
*isl_map_drop(struct isl_map
*map
,
220 enum isl_dim_type type
, unsigned first
, unsigned n
)
227 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
229 if (n
== 0 && !isl_dim_get_tuple_name(map
->dim
, type
))
231 map
= isl_map_cow(map
);
234 map
->dim
= isl_dim_drop(map
->dim
, type
, first
, n
);
238 for (i
= 0; i
< map
->n
; ++i
) {
239 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
243 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
251 struct isl_set
*isl_set_drop(struct isl_set
*set
,
252 enum isl_dim_type type
, unsigned first
, unsigned n
)
254 return (isl_set
*)isl_map_drop((isl_map
*)set
, type
, first
, n
);
257 struct isl_map
*isl_map_drop_inputs(
258 struct isl_map
*map
, unsigned first
, unsigned n
)
260 return isl_map_drop(map
, isl_dim_in
, first
, n
);
264 * We don't cow, as the div is assumed to be redundant.
266 static struct isl_basic_map
*isl_basic_map_drop_div(
267 struct isl_basic_map
*bmap
, unsigned div
)
275 pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
277 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
279 for (i
= 0; i
< bmap
->n_eq
; ++i
)
280 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
282 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
283 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
284 isl_basic_map_drop_inequality(bmap
, i
);
288 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
291 for (i
= 0; i
< bmap
->n_div
; ++i
)
292 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
294 if (div
!= bmap
->n_div
- 1) {
296 isl_int
*t
= bmap
->div
[div
];
298 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
299 bmap
->div
[j
] = bmap
->div
[j
+1];
301 bmap
->div
[bmap
->n_div
- 1] = t
;
303 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
304 isl_basic_map_free_div(bmap
, 1);
308 isl_basic_map_free(bmap
);
312 struct isl_basic_map
*isl_basic_map_normalize_constraints(
313 struct isl_basic_map
*bmap
)
317 unsigned total
= isl_basic_map_total_dim(bmap
);
323 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
324 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
325 if (isl_int_is_zero(gcd
)) {
326 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
327 bmap
= isl_basic_map_set_to_empty(bmap
);
330 isl_basic_map_drop_equality(bmap
, i
);
333 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
334 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
335 if (isl_int_is_one(gcd
))
337 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
338 bmap
= isl_basic_map_set_to_empty(bmap
);
341 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
344 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
345 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
346 if (isl_int_is_zero(gcd
)) {
347 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
348 bmap
= isl_basic_map_set_to_empty(bmap
);
351 isl_basic_map_drop_inequality(bmap
, i
);
354 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
355 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
356 if (isl_int_is_one(gcd
))
358 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
359 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
366 struct isl_basic_set
*isl_basic_set_normalize_constraints(
367 struct isl_basic_set
*bset
)
369 return (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
370 (struct isl_basic_map
*)bset
);
373 /* Assumes divs have been ordered if keep_divs is set.
375 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
376 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
382 total
= isl_basic_map_total_dim(bmap
);
383 last_div
= isl_seq_last_non_zero(eq
+ 1 + isl_dim_total(bmap
->dim
),
385 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
386 if (bmap
->eq
[k
] == eq
)
388 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
392 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
393 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
396 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
397 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
401 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
402 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
403 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
406 for (k
= 0; k
< bmap
->n_div
; ++k
) {
407 if (isl_int_is_zero(bmap
->div
[k
][0]))
409 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
413 /* We need to be careful about circular definitions,
414 * so for now we just remove the definition of div k
415 * if the equality contains any divs.
416 * If keep_divs is set, then the divs have been ordered
417 * and we can keep the definition as long as the result
420 if (last_div
== -1 || (keep_divs
&& last_div
< k
))
421 isl_seq_elim(bmap
->div
[k
]+1, eq
,
422 1+pos
, 1+total
, &bmap
->div
[k
][0]);
424 isl_seq_clr(bmap
->div
[k
], 1 + total
);
425 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
429 /* Assumes divs have been ordered if keep_divs is set.
431 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
432 unsigned div
, int keep_divs
)
434 unsigned pos
= isl_dim_total(bmap
->dim
) + div
;
436 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
438 isl_basic_map_drop_div(bmap
, div
);
441 /* Check if elimination of div "div" using equality "eq" would not
442 * result in a div depending on a later div.
444 static int ok_to_eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
449 unsigned pos
= isl_dim_total(bmap
->dim
) + div
;
451 last_div
= isl_seq_last_non_zero(eq
+ 1 + isl_dim_total(bmap
->dim
),
453 if (last_div
< 0 || last_div
<= div
)
456 for (k
= 0; k
<= last_div
; ++k
) {
457 if (isl_int_is_zero(bmap
->div
[k
][0]))
459 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
466 /* Elimininate divs based on equalities
468 static struct isl_basic_map
*eliminate_divs_eq(
469 struct isl_basic_map
*bmap
, int *progress
)
476 bmap
= isl_basic_map_order_divs(bmap
);
481 off
= 1 + isl_dim_total(bmap
->dim
);
483 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
484 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
485 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
486 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
488 if (!ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
))
492 eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
493 isl_basic_map_drop_equality(bmap
, i
);
498 return eliminate_divs_eq(bmap
, progress
);
502 /* Elimininate divs based on inequalities
504 static struct isl_basic_map
*eliminate_divs_ineq(
505 struct isl_basic_map
*bmap
, int *progress
)
516 off
= 1 + isl_dim_total(bmap
->dim
);
518 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
519 for (i
= 0; i
< bmap
->n_eq
; ++i
)
520 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
524 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
525 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
527 if (i
< bmap
->n_ineq
)
530 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
531 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
533 bmap
= isl_basic_map_drop_div(bmap
, d
);
540 struct isl_basic_map
*isl_basic_map_gauss(
541 struct isl_basic_map
*bmap
, int *progress
)
549 bmap
= isl_basic_map_order_divs(bmap
);
554 total
= isl_basic_map_total_dim(bmap
);
555 total_var
= total
- bmap
->n_div
;
557 last_var
= total
- 1;
558 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
559 for (; last_var
>= 0; --last_var
) {
560 for (k
= done
; k
< bmap
->n_eq
; ++k
)
561 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
569 swap_equality(bmap
, k
, done
);
570 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
571 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
573 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
576 if (last_var
>= total_var
&&
577 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
578 unsigned div
= last_var
- total_var
;
579 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
580 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
581 isl_int_set(bmap
->div
[div
][0],
582 bmap
->eq
[done
][1+last_var
]);
583 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
586 if (done
== bmap
->n_eq
)
588 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
589 if (isl_int_is_zero(bmap
->eq
[k
][0]))
591 return isl_basic_map_set_to_empty(bmap
);
593 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
597 struct isl_basic_set
*isl_basic_set_gauss(
598 struct isl_basic_set
*bset
, int *progress
)
600 return (struct isl_basic_set
*)isl_basic_map_gauss(
601 (struct isl_basic_map
*)bset
, progress
);
605 static unsigned int round_up(unsigned int v
)
616 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
617 struct isl_basic_map
*bmap
, int k
)
620 unsigned total
= isl_basic_map_total_dim(bmap
);
621 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
622 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
623 if (&bmap
->ineq
[k
] != index
[h
] &&
624 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
629 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
630 struct isl_basic_set
*bset
, int k
)
632 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
635 /* If we can eliminate more than one div, then we need to make
636 * sure we do it from last div to first div, in order not to
637 * change the position of the other divs that still need to
640 static struct isl_basic_map
*remove_duplicate_divs(
641 struct isl_basic_map
*bmap
, int *progress
)
653 if (!bmap
|| bmap
->n_div
<= 1)
656 total_var
= isl_dim_total(bmap
->dim
);
657 total
= total_var
+ bmap
->n_div
;
660 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
661 if (!isl_int_is_zero(bmap
->div
[k
][0]))
666 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
667 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
668 bits
= ffs(size
) - 1;
669 index
= isl_calloc_array(ctx
, int, size
);
672 eq
= isl_blk_alloc(ctx
, 1+total
);
673 if (isl_blk_is_error(eq
))
676 isl_seq_clr(eq
.data
, 1+total
);
677 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
678 for (--k
; k
>= 0; --k
) {
681 if (isl_int_is_zero(bmap
->div
[k
][0]))
684 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
685 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
686 if (isl_seq_eq(bmap
->div
[k
],
687 bmap
->div
[index
[h
]-1], 2+total
))
696 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
700 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
701 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
702 eliminate_div(bmap
, eq
.data
, l
, 0);
703 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
704 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
707 isl_blk_free(ctx
, eq
);
714 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
719 total
= isl_dim_total(bmap
->dim
);
720 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
721 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
725 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
731 /* Normalize divs that appear in equalities.
733 * In particular, we assume that bmap contains some equalities
738 * and we want to replace the set of e_i by a minimal set and
739 * such that the new e_i have a canonical representation in terms
741 * If any of the equalities involves more than one divs, then
742 * we currently simply bail out.
744 * Let us first additionally assume that all equalities involve
745 * a div. The equalities then express modulo constraints on the
746 * remaining variables and we can use "parameter compression"
747 * to find a minimal set of constraints. The result is a transformation
749 * x = T(x') = x_0 + G x'
751 * with G a lower-triangular matrix with all elements below the diagonal
752 * non-negative and smaller than the diagonal element on the same row.
753 * We first normalize x_0 by making the same property hold in the affine
755 * The rows i of G with a 1 on the diagonal do not impose any modulo
756 * constraint and simply express x_i = x'_i.
757 * For each of the remaining rows i, we introduce a div and a corresponding
758 * equality. In particular
760 * g_ii e_j = x_i - g_i(x')
762 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
763 * corresponding div (if g_kk != 1).
765 * If there are any equalities not involving any div, then we
766 * first apply a variable compression on the variables x:
768 * x = C x'' x'' = C_2 x
770 * and perform the above parameter compression on A C instead of on A.
771 * The resulting compression is then of the form
773 * x'' = T(x') = x_0 + G x'
775 * and in constructing the new divs and the corresponding equalities,
776 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
777 * by the corresponding row from C_2.
779 static struct isl_basic_map
*normalize_divs(
780 struct isl_basic_map
*bmap
, int *progress
)
787 struct isl_mat
*T
= NULL
;
788 struct isl_mat
*C
= NULL
;
789 struct isl_mat
*C2
= NULL
;
797 if (bmap
->n_div
== 0)
803 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
806 total
= isl_dim_total(bmap
->dim
);
807 div_eq
= n_pure_div_eq(bmap
);
811 if (div_eq
< bmap
->n_eq
) {
812 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
813 bmap
->n_eq
- div_eq
, 0, 1 + total
);
814 C
= isl_mat_variable_compression(B
, &C2
);
818 bmap
= isl_basic_map_set_to_empty(bmap
);
825 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
828 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
829 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
831 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
833 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
836 B
= isl_mat_product(B
, C
);
840 T
= isl_mat_parameter_compression(B
, d
);
844 bmap
= isl_basic_map_set_to_empty(bmap
);
850 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
851 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
852 if (isl_int_is_zero(v
))
854 isl_mat_col_submul(T
, 0, v
, 1 + i
);
857 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
860 /* We have to be careful because dropping equalities may reorder them */
862 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
863 for (i
= 0; i
< bmap
->n_eq
; ++i
)
864 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
866 if (i
< bmap
->n_eq
) {
867 bmap
= isl_basic_map_drop_div(bmap
, j
);
868 isl_basic_map_drop_equality(bmap
, i
);
874 for (i
= 1; i
< T
->n_row
; ++i
) {
875 if (isl_int_is_one(T
->row
[i
][i
]))
880 if (needed
> dropped
) {
881 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
),
886 for (i
= 1; i
< T
->n_row
; ++i
) {
887 if (isl_int_is_one(T
->row
[i
][i
]))
889 k
= isl_basic_map_alloc_div(bmap
);
890 pos
[i
] = 1 + total
+ k
;
891 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
892 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
894 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
896 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
897 for (j
= 0; j
< i
; ++j
) {
898 if (isl_int_is_zero(T
->row
[i
][j
]))
900 if (pos
[j
] < T
->n_row
&& C2
)
901 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
902 C2
->row
[pos
[j
]], 1 + total
);
904 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
907 j
= isl_basic_map_alloc_equality(bmap
);
908 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
909 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
918 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
928 static struct isl_basic_map
*set_div_from_lower_bound(
929 struct isl_basic_map
*bmap
, int div
, int ineq
)
931 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
933 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
934 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
935 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
936 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
937 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
942 /* Check whether it is ok to define a div based on an inequality.
943 * To avoid the introduction of circular definitions of divs, we
944 * do not allow such a definition if the resulting expression would refer to
945 * any other undefined divs or if any known div is defined in
946 * terms of the unknown div.
948 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
952 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
954 /* Not defined in terms of unknown divs */
955 for (j
= 0; j
< bmap
->n_div
; ++j
) {
958 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
960 if (isl_int_is_zero(bmap
->div
[j
][0]))
964 /* No other div defined in terms of this one => avoid loops */
965 for (j
= 0; j
< bmap
->n_div
; ++j
) {
968 if (isl_int_is_zero(bmap
->div
[j
][0]))
970 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
977 /* Given two constraints "k" and "l" that are opposite to each other,
978 * except for the constant term, check if we can use them
979 * to obtain an expression for one of the hitherto unknown divs.
980 * "sum" is the sum of the constant terms of the constraints.
981 * If this sum is strictly smaller than the coefficient of one
982 * of the divs, then this pair can be used define the div.
983 * To avoid the introduction of circular definitions of divs, we
984 * do not use the pair if the resulting expression would refer to
985 * any other undefined divs or if any known div is defined in
986 * terms of the unknown div.
988 static struct isl_basic_map
*check_for_div_constraints(
989 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
992 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
994 for (i
= 0; i
< bmap
->n_div
; ++i
) {
995 if (!isl_int_is_zero(bmap
->div
[i
][0]))
997 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
999 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1001 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1003 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1004 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1006 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1014 static struct isl_basic_map
*remove_duplicate_constraints(
1015 struct isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1021 unsigned total
= isl_basic_map_total_dim(bmap
);
1025 if (!bmap
|| bmap
->n_ineq
<= 1)
1028 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
1029 bits
= ffs(size
) - 1;
1030 ctx
= isl_basic_map_get_ctx(bmap
);
1031 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1035 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
1036 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1037 h
= hash_index(index
, size
, bits
, bmap
, k
);
1039 index
[h
] = &bmap
->ineq
[k
];
1044 l
= index
[h
] - &bmap
->ineq
[0];
1045 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1046 swap_inequality(bmap
, k
, l
);
1047 isl_basic_map_drop_inequality(bmap
, k
);
1051 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1052 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1053 h
= hash_index(index
, size
, bits
, bmap
, k
);
1054 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1057 l
= index
[h
] - &bmap
->ineq
[0];
1058 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1059 if (isl_int_is_pos(sum
)) {
1061 bmap
= check_for_div_constraints(bmap
, k
, l
,
1065 if (isl_int_is_zero(sum
)) {
1066 /* We need to break out of the loop after these
1067 * changes since the contents of the hash
1068 * will no longer be valid.
1069 * Plus, we probably we want to regauss first.
1073 isl_basic_map_drop_inequality(bmap
, l
);
1074 isl_basic_map_inequality_to_equality(bmap
, k
);
1076 bmap
= isl_basic_map_set_to_empty(bmap
);
1086 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1093 bmap
= isl_basic_map_normalize_constraints(bmap
);
1094 bmap
= remove_duplicate_divs(bmap
, &progress
);
1095 bmap
= eliminate_divs_eq(bmap
, &progress
);
1096 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1097 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1098 /* requires equalities in normal form */
1099 bmap
= normalize_divs(bmap
, &progress
);
1100 bmap
= remove_duplicate_constraints(bmap
, &progress
, 1);
1105 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1107 return (struct isl_basic_set
*)
1108 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1112 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1113 isl_int
*constraint
, unsigned div
)
1120 pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
1122 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1124 isl_int_sub(bmap
->div
[div
][1],
1125 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1126 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1127 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1128 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1129 isl_int_add(bmap
->div
[div
][1],
1130 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1133 if (isl_seq_first_non_zero(constraint
+pos
+1,
1134 bmap
->n_div
-div
-1) != -1)
1136 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1137 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1139 if (isl_seq_first_non_zero(constraint
+pos
+1,
1140 bmap
->n_div
-div
-1) != -1)
1149 /* If the only constraints a div d=floor(f/m)
1150 * appears in are its two defining constraints
1153 * -(f - (m - 1)) + m d >= 0
1155 * then it can safely be removed.
1157 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1160 unsigned pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
1162 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1163 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1166 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1167 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1169 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1173 for (i
= 0; i
< bmap
->n_div
; ++i
)
1174 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1181 * Remove divs that don't occur in any of the constraints or other divs.
1182 * These can arise when dropping some of the variables in a quast
1183 * returned by piplib.
1185 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1192 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1193 if (!div_is_redundant(bmap
, i
))
1195 bmap
= isl_basic_map_drop_div(bmap
, i
);
1200 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1202 bmap
= remove_redundant_divs(bmap
);
1205 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1209 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1211 return (struct isl_basic_set
*)
1212 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1215 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1221 for (i
= 0; i
< set
->n
; ++i
) {
1222 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1232 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1238 for (i
= 0; i
< map
->n
; ++i
) {
1239 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1243 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1251 /* Remove definition of any div that is defined in terms of the given variable.
1252 * The div itself is not removed. Functions such as
1253 * eliminate_divs_ineq depend on the other divs remaining in place.
1255 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1260 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1261 if (isl_int_is_zero(bmap
->div
[i
][0]))
1263 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1265 isl_int_set_si(bmap
->div
[i
][0], 0);
1270 /* Eliminate the specified variables from the constraints using
1271 * Fourier-Motzkin. The variables themselves are not removed.
1273 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1274 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1284 total
= isl_basic_map_total_dim(bmap
);
1286 bmap
= isl_basic_map_cow(bmap
);
1287 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1288 bmap
= remove_dependent_vars(bmap
, d
);
1290 for (d
= pos
+ n
- 1;
1291 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1292 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1293 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1294 int n_lower
, n_upper
;
1297 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1298 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1300 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1301 isl_basic_map_drop_equality(bmap
, i
);
1308 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1309 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1311 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1314 bmap
= isl_basic_map_extend_constraints(bmap
,
1315 0, n_lower
* n_upper
);
1318 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1320 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1323 for (j
= 0; j
< i
; ++j
) {
1324 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1327 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1328 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1330 k
= isl_basic_map_alloc_inequality(bmap
);
1333 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1335 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1336 1+d
, 1+total
, NULL
);
1338 isl_basic_map_drop_inequality(bmap
, i
);
1341 if (n_lower
> 0 && n_upper
> 0) {
1342 bmap
= isl_basic_map_normalize_constraints(bmap
);
1343 bmap
= remove_duplicate_constraints(bmap
, NULL
, 0);
1344 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1345 bmap
= isl_basic_map_remove_redundancies(bmap
);
1348 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1352 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1355 isl_basic_map_free(bmap
);
1359 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1360 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1362 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1363 (struct isl_basic_map
*)bset
, pos
, n
);
1366 /* Don't assume equalities are in order, because align_divs
1367 * may have changed the order of the divs.
1369 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1374 total
= isl_dim_total(bmap
->dim
);
1375 for (d
= 0; d
< total
; ++d
)
1377 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1378 for (d
= total
- 1; d
>= 0; --d
) {
1379 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1387 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1389 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1392 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1393 struct isl_basic_map
*bmap
, int *elim
)
1399 total
= isl_dim_total(bmap
->dim
);
1400 for (d
= total
- 1; d
>= 0; --d
) {
1401 if (isl_int_is_zero(src
[1+d
]))
1406 isl_seq_cpy(dst
, src
, 1 + total
);
1409 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1414 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1415 struct isl_basic_set
*bset
, int *elim
)
1417 return reduced_using_equalities(dst
, src
,
1418 (struct isl_basic_map
*)bset
, elim
);
1421 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1422 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1427 if (!bset
|| !context
)
1430 if (context
->n_eq
== 0) {
1431 isl_basic_set_free(context
);
1435 bset
= isl_basic_set_cow(bset
);
1439 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1442 set_compute_elimination_index(context
, elim
);
1443 for (i
= 0; i
< bset
->n_eq
; ++i
)
1444 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1446 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1447 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1449 isl_basic_set_free(context
);
1451 bset
= isl_basic_set_simplify(bset
);
1452 bset
= isl_basic_set_finalize(bset
);
1455 isl_basic_set_free(bset
);
1456 isl_basic_set_free(context
);
1460 static struct isl_basic_set
*remove_shifted_constraints(
1461 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1472 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1473 bits
= ffs(size
) - 1;
1474 ctx
= isl_basic_set_get_ctx(bset
);
1475 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1479 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1480 h
= set_hash_index(index
, size
, bits
, context
, k
);
1481 index
[h
] = &context
->ineq
[k
];
1483 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1484 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1487 l
= index
[h
] - &context
->ineq
[0];
1488 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1490 bset
= isl_basic_set_cow(bset
);
1493 isl_basic_set_drop_inequality(bset
, k
);
1503 /* Remove all information from bset that is redundant in the context
1504 * of context. Both bset and context are assumed to be full-dimensional.
1506 * We first * remove the inequalities from "bset"
1507 * that are obviously redundant with respect to some inequality in "context".
1509 * If there are any inequalities left, we construct a tableau for
1510 * the context and then add the inequalities of "bset".
1511 * Before adding these inequalities, we freeze all constraints such that
1512 * they won't be considered redundant in terms of the constraints of "bset".
1513 * Then we detect all redundant constraints (among the
1514 * constraints that weren't frozen), first by checking for redundancy in the
1515 * the tableau and then by checking if replacing a constraint by its negation
1516 * would lead to an empty set. This last step is fairly expensive
1517 * and could be optimized by more reuse of the tableau.
1518 * Finally, we update bset according to the results.
1520 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1521 __isl_take isl_basic_set
*context
)
1524 isl_basic_set
*combined
= NULL
;
1525 struct isl_tab
*tab
= NULL
;
1526 unsigned context_ineq
;
1529 if (!bset
|| !context
)
1532 if (isl_basic_set_is_universe(bset
)) {
1533 isl_basic_set_free(context
);
1537 if (isl_basic_set_is_universe(context
)) {
1538 isl_basic_set_free(context
);
1542 bset
= remove_shifted_constraints(bset
, context
);
1545 if (bset
->n_ineq
== 0)
1548 context_ineq
= context
->n_ineq
;
1549 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1550 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
1551 tab
= isl_tab_from_basic_set(combined
);
1552 for (i
= 0; i
< context_ineq
; ++i
)
1553 if (isl_tab_freeze_constraint(tab
, i
) < 0)
1555 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1556 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1557 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
1559 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1563 if (isl_tab_detect_redundant(tab
) < 0)
1565 total
= isl_basic_set_total_dim(bset
);
1566 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
1568 if (tab
->con
[i
].is_redundant
)
1570 tab
->con
[i
].is_redundant
= 1;
1571 combined
= isl_basic_set_dup(bset
);
1572 combined
= isl_basic_set_update_from_tab(combined
, tab
);
1573 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
1574 k
= isl_basic_set_alloc_inequality(combined
);
1577 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
1578 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
1579 is_empty
= isl_basic_set_is_empty(combined
);
1582 isl_basic_set_free(combined
);
1585 tab
->con
[i
].is_redundant
= 0;
1587 for (i
= 0; i
< context_ineq
; ++i
)
1588 tab
->con
[i
].is_redundant
= 1;
1589 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1591 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1592 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1597 bset
= isl_basic_set_simplify(bset
);
1598 bset
= isl_basic_set_finalize(bset
);
1599 isl_basic_set_free(context
);
1603 isl_basic_set_free(combined
);
1604 isl_basic_set_free(context
);
1605 isl_basic_set_free(bset
);
1609 /* Remove all information from bset that is redundant in the context
1610 * of context. In particular, equalities that are linear combinations
1611 * of those in context are removed. Then the inequalities that are
1612 * redundant in the context of the equalities and inequalities of
1613 * context are removed.
1615 * We first compute the integer affine hull of the intersection,
1616 * compute the gist inside this affine hull and then add back
1617 * those equalities that are not implied by the context.
1619 * If two constraints are mutually redundant, then uset_gist_full
1620 * will remove the second of those constraints. We therefore first
1621 * sort the constraints so that constraints not involving existentially
1622 * quantified variables are given precedence over those that do.
1623 * We have to perform this sorting before the variable compression,
1624 * because that may effect the order of the variables.
1626 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
1627 __isl_take isl_basic_set
*context
)
1632 isl_basic_set
*aff_context
;
1635 if (!bset
|| !context
)
1638 bset
= isl_basic_set_intersect(bset
, isl_basic_set_copy(context
));
1639 if (isl_basic_set_plain_is_empty(bset
)) {
1640 isl_basic_set_free(context
);
1643 bset
= isl_basic_set_sort_constraints(bset
);
1644 aff
= isl_basic_set_affine_hull(isl_basic_set_copy(bset
));
1647 if (isl_basic_set_plain_is_empty(aff
)) {
1648 isl_basic_set_free(aff
);
1649 isl_basic_set_free(context
);
1652 if (aff
->n_eq
== 0) {
1653 isl_basic_set_free(aff
);
1654 return uset_gist_full(bset
, context
);
1656 total
= isl_basic_set_total_dim(bset
);
1657 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
1658 eq
= isl_mat_cow(eq
);
1659 T
= isl_mat_variable_compression(eq
, &T2
);
1660 if (T
&& T
->n_col
== 0) {
1663 isl_basic_set_free(context
);
1664 isl_basic_set_free(aff
);
1665 return isl_basic_set_set_to_empty(bset
);
1668 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
1670 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
1671 context
= isl_basic_set_preimage(context
, T
);
1673 bset
= uset_gist_full(bset
, context
);
1674 bset
= isl_basic_set_preimage(bset
, T2
);
1675 bset
= isl_basic_set_intersect(bset
, aff
);
1676 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
1679 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1680 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1685 isl_basic_set_free(bset
);
1686 isl_basic_set_free(context
);
1690 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1691 * We simply add the equalities in context to bmap and then do a regular
1692 * div normalizations. Better results can be obtained by normalizing
1693 * only the divs in bmap than do not also appear in context.
1694 * We need to be careful to reduce the divs using the equalities
1695 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1696 * spurious constraints.
1698 static struct isl_basic_map
*normalize_divs_in_context(
1699 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
1702 unsigned total_context
;
1705 div_eq
= n_pure_div_eq(bmap
);
1709 if (context
->n_div
> 0)
1710 bmap
= isl_basic_map_align_divs(bmap
, context
);
1712 total_context
= isl_basic_map_total_dim(context
);
1713 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
1714 for (i
= 0; i
< context
->n_eq
; ++i
) {
1716 k
= isl_basic_map_alloc_equality(bmap
);
1717 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
1718 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
1719 isl_basic_map_total_dim(bmap
) - total_context
);
1721 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1722 bmap
= normalize_divs(bmap
, NULL
);
1723 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1727 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
1728 struct isl_basic_map
*context
)
1730 struct isl_basic_set
*bset
;
1732 if (!bmap
|| !context
)
1735 if (isl_basic_map_is_universe(bmap
)) {
1736 isl_basic_map_free(context
);
1739 if (isl_basic_map_plain_is_empty(context
)) {
1740 struct isl_dim
*dim
= isl_dim_copy(bmap
->dim
);
1741 isl_basic_map_free(context
);
1742 isl_basic_map_free(bmap
);
1743 return isl_basic_map_universe(dim
);
1745 if (isl_basic_map_plain_is_empty(bmap
)) {
1746 isl_basic_map_free(context
);
1750 bmap
= isl_basic_map_remove_redundancies(bmap
);
1751 context
= isl_basic_map_remove_redundancies(context
);
1754 bmap
= normalize_divs_in_context(bmap
, context
);
1756 context
= isl_basic_map_align_divs(context
, bmap
);
1757 bmap
= isl_basic_map_align_divs(bmap
, context
);
1759 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
1760 isl_basic_map_underlying_set(context
));
1762 return isl_basic_map_overlying_set(bset
, bmap
);
1764 isl_basic_map_free(bmap
);
1765 isl_basic_map_free(context
);
1770 * Assumes context has no implicit divs.
1772 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
1773 __isl_take isl_basic_map
*context
)
1777 if (!map
|| !context
)
1780 if (isl_basic_map_plain_is_empty(context
)) {
1781 struct isl_dim
*dim
= isl_dim_copy(map
->dim
);
1782 isl_basic_map_free(context
);
1784 return isl_map_universe(dim
);
1787 context
= isl_basic_map_remove_redundancies(context
);
1788 map
= isl_map_cow(map
);
1789 if (!map
|| !context
)
1791 isl_assert(map
->ctx
, isl_dim_equal(map
->dim
, context
->dim
), goto error
);
1792 map
= isl_map_compute_divs(map
);
1793 for (i
= 0; i
< map
->n
; ++i
)
1794 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
1795 for (i
= map
->n
- 1; i
>= 0; --i
) {
1796 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
1797 isl_basic_map_copy(context
));
1800 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
1801 isl_basic_map_free(map
->p
[i
]);
1802 if (i
!= map
->n
- 1)
1803 map
->p
[i
] = map
->p
[map
->n
- 1];
1807 isl_basic_map_free(context
);
1808 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1812 isl_basic_map_free(context
);
1816 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
1817 __isl_take isl_map
*context
)
1819 context
= isl_map_compute_divs(context
);
1820 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
1823 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
1824 struct isl_basic_set
*context
)
1826 return (struct isl_basic_set
*)isl_basic_map_gist(
1827 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
1830 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
1831 __isl_take isl_basic_set
*context
)
1833 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
1834 (struct isl_basic_map
*)context
);
1837 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
1838 __isl_take isl_set
*context
)
1840 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
1841 (struct isl_map
*)context
);
1844 /* Quick check to see if two basic maps are disjoint.
1845 * In particular, we reduce the equalities and inequalities of
1846 * one basic map in the context of the equalities of the other
1847 * basic map and check if we get a contradiction.
1849 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
1850 __isl_keep isl_basic_map
*bmap2
)
1852 struct isl_vec
*v
= NULL
;
1857 if (!bmap1
|| !bmap2
)
1859 isl_assert(bmap1
->ctx
, isl_dim_equal(bmap1
->dim
, bmap2
->dim
),
1861 if (bmap1
->n_div
|| bmap2
->n_div
)
1863 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
1866 total
= isl_dim_total(bmap1
->dim
);
1869 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
1872 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
1875 compute_elimination_index(bmap1
, elim
);
1876 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
1878 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
1880 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
1881 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1884 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
1886 reduced
= reduced_using_equalities(v
->block
.data
,
1887 bmap2
->ineq
[i
], bmap1
, elim
);
1888 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1889 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1892 compute_elimination_index(bmap2
, elim
);
1893 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
1895 reduced
= reduced_using_equalities(v
->block
.data
,
1896 bmap1
->ineq
[i
], bmap2
, elim
);
1897 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1898 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1914 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
1915 __isl_keep isl_basic_set
*bset2
)
1917 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
1918 (struct isl_basic_map
*)bset2
);
1921 int isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
1922 __isl_keep isl_map
*map2
)
1929 if (isl_map_plain_is_equal(map1
, map2
))
1932 for (i
= 0; i
< map1
->n
; ++i
) {
1933 for (j
= 0; j
< map2
->n
; ++j
) {
1934 int d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
1943 int isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
1944 __isl_keep isl_set
*set2
)
1946 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
1947 (struct isl_map
*)set2
);
1950 int isl_set_fast_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
1952 return isl_set_plain_is_disjoint(set1
, set2
);
1955 /* Check if we can combine a given div with lower bound l and upper
1956 * bound u with some other div and if so return that other div.
1957 * Otherwise return -1.
1959 * We first check that
1960 * - the bounds are opposites of each other (except for the constant
1962 * - the bounds do not reference any other div
1963 * - no div is defined in terms of this div
1965 * Let m be the size of the range allowed on the div by the bounds.
1966 * That is, the bounds are of the form
1968 * e <= a <= e + m - 1
1970 * with e some expression in the other variables.
1971 * We look for another div b such that no third div is defined in terms
1972 * of this second div b and such that in any constraint that contains
1973 * a (except for the given lower and upper bound), also contains b
1974 * with a coefficient that is m times that of b.
1975 * That is, all constraints (execpt for the lower and upper bound)
1978 * e + f (a + m b) >= 0
1980 * If so, we return b so that "a + m b" can be replaced by
1981 * a single div "c = a + m b".
1983 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
1984 unsigned div
, unsigned l
, unsigned u
)
1990 if (bmap
->n_div
<= 1)
1992 dim
= isl_dim_total(bmap
->dim
);
1993 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
1995 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
1996 bmap
->n_div
- div
- 1) != -1)
1998 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2002 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2003 if (isl_int_is_zero(bmap
->div
[i
][0]))
2005 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2009 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2010 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2011 isl_int_sub(bmap
->ineq
[l
][0],
2012 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2013 bmap
= isl_basic_map_copy(bmap
);
2014 bmap
= isl_basic_map_set_to_empty(bmap
);
2015 isl_basic_map_free(bmap
);
2018 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2019 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2024 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2025 if (isl_int_is_zero(bmap
->div
[j
][0]))
2027 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2030 if (j
< bmap
->n_div
)
2032 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2034 if (j
== l
|| j
== u
)
2036 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2038 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2040 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2041 bmap
->ineq
[j
][1 + dim
+ div
],
2043 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2044 bmap
->ineq
[j
][1 + dim
+ i
]);
2045 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2046 bmap
->ineq
[j
][1 + dim
+ div
],
2051 if (j
< bmap
->n_ineq
)
2056 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2057 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2061 /* Given a lower and an upper bound on div i, construct an inequality
2062 * that when nonnegative ensures that this pair of bounds always allows
2063 * for an integer value of the given div.
2064 * The lower bound is inequality l, while the upper bound is inequality u.
2065 * The constructed inequality is stored in ineq.
2066 * g, fl, fu are temporary scalars.
2068 * Let the upper bound be
2072 * and the lower bound
2076 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2079 * - f_u e_l <= f_u f_l g a <= f_l e_u
2081 * Since all variables are integer valued, this is equivalent to
2083 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2085 * If this interval is at least f_u f_l g, then it contains at least
2086 * one integer value for a.
2087 * That is, the test constraint is
2089 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2091 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2092 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2095 dim
= isl_dim_total(bmap
->dim
);
2097 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2098 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2099 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2100 isl_int_neg(fu
, fu
);
2101 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2102 1 + dim
+ bmap
->n_div
);
2103 isl_int_add(ineq
[0], ineq
[0], fl
);
2104 isl_int_add(ineq
[0], ineq
[0], fu
);
2105 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2106 isl_int_mul(g
, g
, fl
);
2107 isl_int_mul(g
, g
, fu
);
2108 isl_int_sub(ineq
[0], ineq
[0], g
);
2111 /* Remove more kinds of divs that are not strictly needed.
2112 * In particular, if all pairs of lower and upper bounds on a div
2113 * are such that they allow at least one integer value of the div,
2114 * the we can eliminate the div using Fourier-Motzkin without
2115 * introducing any spurious solutions.
2117 static struct isl_basic_map
*drop_more_redundant_divs(
2118 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2120 struct isl_tab
*tab
= NULL
;
2121 struct isl_vec
*vec
= NULL
;
2133 dim
= isl_dim_total(bmap
->dim
);
2134 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2138 tab
= isl_tab_from_basic_map(bmap
);
2143 enum isl_lp_result res
;
2145 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2148 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2154 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2155 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2157 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2158 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2160 construct_test_ineq(bmap
, i
, l
, u
,
2161 vec
->el
, g
, fl
, fu
);
2162 res
= isl_tab_min(tab
, vec
->el
,
2163 bmap
->ctx
->one
, &g
, NULL
, 0);
2164 if (res
== isl_lp_error
)
2166 if (res
== isl_lp_empty
) {
2167 bmap
= isl_basic_map_set_to_empty(bmap
);
2170 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2173 if (u
< bmap
->n_ineq
)
2176 if (l
== bmap
->n_ineq
) {
2196 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
2197 return isl_basic_map_drop_redundant_divs(bmap
);
2200 isl_basic_map_free(bmap
);
2209 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2210 * and the upper bound u, div1 always occurs together with div2 in the form
2211 * (div1 + m div2), where m is the constant range on the variable div1
2212 * allowed by l and u, replace the pair div1 and div2 by a single
2213 * div that is equal to div1 + m div2.
2215 * The new div will appear in the location that contains div2.
2216 * We need to modify all constraints that contain
2217 * div2 = (div - div1) / m
2218 * (If a constraint does not contain div2, it will also not contain div1.)
2219 * If the constraint also contains div1, then we know they appear
2220 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2221 * i.e., the coefficient of div is f.
2223 * Otherwise, we first need to introduce div1 into the constraint.
2232 * A lower bound on div2
2236 * can be replaced by
2238 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2240 * with g = gcd(m,n).
2245 * can be replaced by
2247 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2249 * These constraint are those that we would obtain from eliminating
2250 * div1 using Fourier-Motzkin.
2252 * After all constraints have been modified, we drop the lower and upper
2253 * bound and then drop div1.
2255 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2256 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2261 unsigned dim
, total
;
2264 dim
= isl_dim_total(bmap
->dim
);
2265 total
= 1 + dim
+ bmap
->n_div
;
2270 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2271 isl_int_add_ui(m
, m
, 1);
2273 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2274 if (i
== l
|| i
== u
)
2276 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2278 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2279 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2280 isl_int_divexact(a
, m
, b
);
2281 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2282 if (isl_int_is_pos(b
)) {
2283 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2284 b
, bmap
->ineq
[l
], total
);
2287 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2288 b
, bmap
->ineq
[u
], total
);
2291 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2292 bmap
->ineq
[i
][1 + dim
+ div1
]);
2293 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2300 isl_basic_map_drop_inequality(bmap
, l
);
2301 isl_basic_map_drop_inequality(bmap
, u
);
2303 isl_basic_map_drop_inequality(bmap
, u
);
2304 isl_basic_map_drop_inequality(bmap
, l
);
2306 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2310 /* First check if we can coalesce any pair of divs and
2311 * then continue with dropping more redundant divs.
2313 * We loop over all pairs of lower and upper bounds on a div
2314 * with coefficient 1 and -1, respectively, check if there
2315 * is any other div "c" with which we can coalesce the div
2316 * and if so, perform the coalescing.
2318 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2319 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2324 dim
= isl_dim_total(bmap
->dim
);
2326 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2329 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2330 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2332 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2335 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2337 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2341 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2342 return isl_basic_map_drop_redundant_divs(bmap
);
2347 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2350 return drop_more_redundant_divs(bmap
, pairs
, n
);
2353 /* Remove divs that are not strictly needed.
2354 * In particular, if a div only occurs positively (or negatively)
2355 * in constraints, then it can simply be dropped.
2356 * Also, if a div occurs only occurs in two constraints and if moreover
2357 * those two constraints are opposite to each other, except for the constant
2358 * term and if the sum of the constant terms is such that for any value
2359 * of the other values, there is always at least one integer value of the
2360 * div, i.e., if one plus this sum is greater than or equal to
2361 * the (absolute value) of the coefficent of the div in the constraints,
2362 * then we can also simply drop the div.
2364 * If any divs are left after these simple checks then we move on
2365 * to more complicated cases in drop_more_redundant_divs.
2367 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2368 struct isl_basic_map
*bmap
)
2378 off
= isl_dim_total(bmap
->dim
);
2379 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2383 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2385 int last_pos
, last_neg
;
2389 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2390 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2391 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2397 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2398 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2402 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2407 pairs
[i
] = pos
* neg
;
2408 if (pairs
[i
] == 0) {
2409 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2410 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2411 isl_basic_map_drop_inequality(bmap
, j
);
2412 bmap
= isl_basic_map_drop_div(bmap
, i
);
2414 return isl_basic_map_drop_redundant_divs(bmap
);
2418 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2419 bmap
->ineq
[last_neg
] + 1,
2423 isl_int_add(bmap
->ineq
[last_pos
][0],
2424 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2425 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2426 bmap
->ineq
[last_pos
][0], 1);
2427 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2428 bmap
->ineq
[last_pos
][1+off
+i
]);
2429 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2430 bmap
->ineq
[last_pos
][0], 1);
2431 isl_int_sub(bmap
->ineq
[last_pos
][0],
2432 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2435 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
2440 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
2441 bmap
= isl_basic_map_simplify(bmap
);
2443 return isl_basic_map_drop_redundant_divs(bmap
);
2445 if (last_pos
> last_neg
) {
2446 isl_basic_map_drop_inequality(bmap
, last_pos
);
2447 isl_basic_map_drop_inequality(bmap
, last_neg
);
2449 isl_basic_map_drop_inequality(bmap
, last_neg
);
2450 isl_basic_map_drop_inequality(bmap
, last_pos
);
2452 bmap
= isl_basic_map_drop_div(bmap
, i
);
2454 return isl_basic_map_drop_redundant_divs(bmap
);
2458 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
2464 isl_basic_map_free(bmap
);
2468 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
2469 struct isl_basic_set
*bset
)
2471 return (struct isl_basic_set
*)
2472 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
2475 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
2481 for (i
= 0; i
< map
->n
; ++i
) {
2482 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
2486 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2493 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
2495 return (struct isl_set
*)
2496 isl_map_drop_redundant_divs((struct isl_map
*)set
);