1 #include "isl_equalities.h"
3 #include "isl_map_private.h"
7 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
9 isl_int
*t
= bmap
->eq
[a
];
10 bmap
->eq
[a
] = bmap
->eq
[b
];
14 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
17 isl_int
*t
= bmap
->ineq
[a
];
18 bmap
->ineq
[a
] = bmap
->ineq
[b
];
23 static void set_swap_inequality(struct isl_basic_set
*bset
, int a
, int b
)
25 swap_inequality((struct isl_basic_map
*)bset
, a
, b
);
28 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
30 isl_seq_cpy(c
, c
+ n
, rem
);
31 isl_seq_clr(c
+ rem
, n
);
34 /* Drop n dimensions starting at first.
36 * In principle, this frees up some extra variables as the number
37 * of columns remains constant, but we would have to extend
38 * the div array too as the number of rows in this array is assumed
39 * to be equal to extra.
41 struct isl_basic_set
*isl_basic_set_drop_dims(
42 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
49 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
54 bset
= isl_basic_set_cow(bset
);
58 for (i
= 0; i
< bset
->n_eq
; ++i
)
59 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
60 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
62 for (i
= 0; i
< bset
->n_ineq
; ++i
)
63 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
64 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
66 for (i
= 0; i
< bset
->n_div
; ++i
)
67 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
68 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
70 bset
->dim
= isl_dim_drop_outputs(bset
->dim
, first
, n
);
74 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
75 bset
= isl_basic_set_simplify(bset
);
76 return isl_basic_set_finalize(bset
);
78 isl_basic_set_free(bset
);
82 struct isl_set
*isl_set_drop_dims(
83 struct isl_set
*set
, unsigned first
, unsigned n
)
90 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
94 set
= isl_set_cow(set
);
97 set
->dim
= isl_dim_drop_outputs(set
->dim
, first
, n
);
101 for (i
= 0; i
< set
->n
; ++i
) {
102 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
107 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
114 /* Move "n" divs starting at "first" to the end of the list of divs.
116 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
117 unsigned first
, unsigned n
)
122 if (first
+ n
== bmap
->n_div
)
125 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
128 for (i
= 0; i
< n
; ++i
)
129 div
[i
] = bmap
->div
[first
+ i
];
130 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
131 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
132 for (i
= 0; i
< n
; ++i
)
133 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
137 isl_basic_map_free(bmap
);
141 /* Drop "n" dimensions of type "type" starting at "first".
143 * In principle, this frees up some extra variables as the number
144 * of columns remains constant, but we would have to extend
145 * the div array too as the number of rows in this array is assumed
146 * to be equal to extra.
148 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
149 enum isl_dim_type type
, unsigned first
, unsigned n
)
159 dim
= isl_basic_map_dim(bmap
, type
);
160 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
165 bmap
= isl_basic_map_cow(bmap
);
169 offset
= isl_basic_map_offset(bmap
, type
) + first
;
170 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
171 for (i
= 0; i
< bmap
->n_eq
; ++i
)
172 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
174 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
175 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
177 for (i
= 0; i
< bmap
->n_div
; ++i
)
178 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
180 if (type
== isl_dim_div
) {
181 bmap
= move_divs_last(bmap
, first
, n
);
184 isl_basic_map_free_div(bmap
, n
);
186 bmap
->dim
= isl_dim_drop(bmap
->dim
, type
, first
, n
);
190 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
191 bmap
= isl_basic_map_simplify(bmap
);
192 return isl_basic_map_finalize(bmap
);
194 isl_basic_map_free(bmap
);
198 struct isl_basic_map
*isl_basic_map_drop_inputs(
199 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
201 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
204 struct isl_map
*isl_map_drop(struct isl_map
*map
,
205 enum isl_dim_type type
, unsigned first
, unsigned n
)
212 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
216 map
= isl_map_cow(map
);
219 map
->dim
= isl_dim_drop(map
->dim
, type
, first
, n
);
223 for (i
= 0; i
< map
->n
; ++i
) {
224 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
228 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
236 struct isl_map
*isl_map_drop_inputs(
237 struct isl_map
*map
, unsigned first
, unsigned n
)
239 return isl_map_drop(map
, isl_dim_in
, first
, n
);
243 * We don't cow, as the div is assumed to be redundant.
245 static struct isl_basic_map
*isl_basic_map_drop_div(
246 struct isl_basic_map
*bmap
, unsigned div
)
254 pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
256 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
258 for (i
= 0; i
< bmap
->n_eq
; ++i
)
259 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
261 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
262 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
263 isl_basic_map_drop_inequality(bmap
, i
);
267 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
270 for (i
= 0; i
< bmap
->n_div
; ++i
)
271 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
273 if (div
!= bmap
->n_div
- 1) {
275 isl_int
*t
= bmap
->div
[div
];
277 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
278 bmap
->div
[j
] = bmap
->div
[j
+1];
280 bmap
->div
[bmap
->n_div
- 1] = t
;
282 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
283 isl_basic_map_free_div(bmap
, 1);
287 isl_basic_map_free(bmap
);
291 struct isl_basic_map
*isl_basic_map_normalize_constraints(
292 struct isl_basic_map
*bmap
)
296 unsigned total
= isl_basic_map_total_dim(bmap
);
299 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
300 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
301 if (isl_int_is_zero(gcd
)) {
302 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
303 bmap
= isl_basic_map_set_to_empty(bmap
);
306 isl_basic_map_drop_equality(bmap
, i
);
309 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
310 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
311 if (isl_int_is_one(gcd
))
313 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
314 bmap
= isl_basic_map_set_to_empty(bmap
);
317 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
320 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
321 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
322 if (isl_int_is_zero(gcd
)) {
323 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
324 bmap
= isl_basic_map_set_to_empty(bmap
);
327 isl_basic_map_drop_inequality(bmap
, i
);
330 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
331 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
332 if (isl_int_is_one(gcd
))
334 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
335 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
342 struct isl_basic_set
*isl_basic_set_normalize_constraints(
343 struct isl_basic_set
*bset
)
345 return (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
346 (struct isl_basic_map
*)bset
);
349 /* Assumes divs have been ordered if keep_divs is set.
351 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
352 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
358 total
= isl_basic_map_total_dim(bmap
);
359 last_div
= isl_seq_last_non_zero(eq
+ 1 + isl_dim_total(bmap
->dim
),
361 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
362 if (bmap
->eq
[k
] == eq
)
364 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
368 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
371 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
372 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
376 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
377 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
380 for (k
= 0; k
< bmap
->n_div
; ++k
) {
381 if (isl_int_is_zero(bmap
->div
[k
][0]))
383 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
387 /* We need to be careful about circular definitions,
388 * so for now we just remove the definition of div k
389 * if the equality contains any divs.
390 * If keep_divs is set, then the divs have been ordered
391 * and we can keep the definition as long as the result
394 if (last_div
== -1 || (keep_divs
&& last_div
< k
))
395 isl_seq_elim(bmap
->div
[k
]+1, eq
,
396 1+pos
, 1+total
, &bmap
->div
[k
][0]);
398 isl_seq_clr(bmap
->div
[k
], 1 + total
);
399 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
403 /* Assumes divs have been ordered if keep_divs is set.
405 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
406 unsigned div
, int keep_divs
)
408 unsigned pos
= isl_dim_total(bmap
->dim
) + div
;
410 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
412 isl_basic_map_drop_div(bmap
, div
);
415 /* Elimininate divs based on equalities
417 static struct isl_basic_map
*eliminate_divs_eq(
418 struct isl_basic_map
*bmap
, int *progress
)
425 bmap
= isl_basic_map_order_divs(bmap
);
430 off
= 1 + isl_dim_total(bmap
->dim
);
432 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
433 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
434 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
435 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
439 eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
440 isl_basic_map_drop_equality(bmap
, i
);
445 return eliminate_divs_eq(bmap
, progress
);
449 /* Elimininate divs based on inequalities
451 static struct isl_basic_map
*eliminate_divs_ineq(
452 struct isl_basic_map
*bmap
, int *progress
)
463 off
= 1 + isl_dim_total(bmap
->dim
);
465 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
466 for (i
= 0; i
< bmap
->n_eq
; ++i
)
467 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
471 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
472 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
474 if (i
< bmap
->n_ineq
)
477 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
478 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
480 bmap
= isl_basic_map_drop_div(bmap
, d
);
487 struct isl_basic_map
*isl_basic_map_gauss(
488 struct isl_basic_map
*bmap
, int *progress
)
496 bmap
= isl_basic_map_order_divs(bmap
);
501 total
= isl_basic_map_total_dim(bmap
);
502 total_var
= total
- bmap
->n_div
;
504 last_var
= total
- 1;
505 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
506 for (; last_var
>= 0; --last_var
) {
507 for (k
= done
; k
< bmap
->n_eq
; ++k
)
508 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
516 swap_equality(bmap
, k
, done
);
517 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
518 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
520 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
523 if (last_var
>= total_var
&&
524 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
525 unsigned div
= last_var
- total_var
;
526 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
527 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
528 isl_int_set(bmap
->div
[div
][0],
529 bmap
->eq
[done
][1+last_var
]);
530 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
533 if (done
== bmap
->n_eq
)
535 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
536 if (isl_int_is_zero(bmap
->eq
[k
][0]))
538 return isl_basic_map_set_to_empty(bmap
);
540 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
544 struct isl_basic_set
*isl_basic_set_gauss(
545 struct isl_basic_set
*bset
, int *progress
)
547 return (struct isl_basic_set
*)isl_basic_map_gauss(
548 (struct isl_basic_map
*)bset
, progress
);
552 static unsigned int round_up(unsigned int v
)
563 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
564 struct isl_basic_map
*bmap
, int k
)
567 unsigned total
= isl_basic_map_total_dim(bmap
);
568 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
569 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
570 if (&bmap
->ineq
[k
] != index
[h
] &&
571 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
576 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
577 struct isl_basic_set
*bset
, int k
)
579 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
582 /* If we can eliminate more than one div, then we need to make
583 * sure we do it from last div to first div, in order not to
584 * change the position of the other divs that still need to
587 static struct isl_basic_map
*remove_duplicate_divs(
588 struct isl_basic_map
*bmap
, int *progress
)
596 unsigned total_var
= isl_dim_total(bmap
->dim
);
597 unsigned total
= total_var
+ bmap
->n_div
;
600 if (bmap
->n_div
<= 1)
604 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
605 if (!isl_int_is_zero(bmap
->div
[k
][0]))
610 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
611 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
612 bits
= ffs(size
) - 1;
613 index
= isl_calloc_array(ctx
, int, size
);
616 eq
= isl_blk_alloc(ctx
, 1+total
);
617 if (isl_blk_is_error(eq
))
620 isl_seq_clr(eq
.data
, 1+total
);
621 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
622 for (--k
; k
>= 0; --k
) {
625 if (isl_int_is_zero(bmap
->div
[k
][0]))
628 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
629 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
630 if (isl_seq_eq(bmap
->div
[k
],
631 bmap
->div
[index
[h
]-1], 2+total
))
640 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
644 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
645 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
646 eliminate_div(bmap
, eq
.data
, l
, 0);
647 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
648 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
651 isl_blk_free(ctx
, eq
);
658 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
663 total
= isl_dim_total(bmap
->dim
);
664 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
665 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
669 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
675 /* Normalize divs that appear in equalities.
677 * In particular, we assume that bmap contains some equalities
682 * and we want to replace the set of e_i by a minimal set and
683 * such that the new e_i have a canonical representation in terms
685 * If any of the equalities involves more than one divs, then
686 * we currently simply bail out.
688 * Let us first additionally assume that all equalities involve
689 * a div. The equalities then express modulo constraints on the
690 * remaining variables and we can use "parameter compression"
691 * to find a minimal set of constraints. The result is a transformation
693 * x = T(x') = x_0 + G x'
695 * with G a lower-triangular matrix with all elements below the diagonal
696 * non-negative and smaller than the diagonal element on the same row.
697 * We first normalize x_0 by making the same property hold in the affine
699 * The rows i of G with a 1 on the diagonal do not impose any modulo
700 * constraint and simply express x_i = x'_i.
701 * For each of the remaining rows i, we introduce a div and a corresponding
702 * equality. In particular
704 * g_ii e_j = x_i - g_i(x')
706 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
707 * corresponding div (if g_kk != 1).
709 * If there are any equalities not involving any div, then we
710 * first apply a variable compression on the variables x:
712 * x = C x'' x'' = C_2 x
714 * and perform the above parameter compression on A C instead of on A.
715 * The resulting compression is then of the form
717 * x'' = T(x') = x_0 + G x'
719 * and in constructing the new divs and the corresponding equalities,
720 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
721 * by the corresponding row from C_2.
723 static struct isl_basic_map
*normalize_divs(
724 struct isl_basic_map
*bmap
, int *progress
)
731 struct isl_mat
*T
= NULL
;
732 struct isl_mat
*C
= NULL
;
733 struct isl_mat
*C2
= NULL
;
741 if (bmap
->n_div
== 0)
747 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
750 total
= isl_dim_total(bmap
->dim
);
751 div_eq
= n_pure_div_eq(bmap
);
755 if (div_eq
< bmap
->n_eq
) {
756 B
= isl_mat_sub_alloc(bmap
->ctx
, bmap
->eq
, div_eq
,
757 bmap
->n_eq
- div_eq
, 0, 1 + total
);
758 C
= isl_mat_variable_compression(B
, &C2
);
762 bmap
= isl_basic_map_set_to_empty(bmap
);
769 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
772 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
773 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
775 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
777 B
= isl_mat_sub_alloc(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
780 B
= isl_mat_product(B
, C
);
784 T
= isl_mat_parameter_compression(B
, d
);
788 bmap
= isl_basic_map_set_to_empty(bmap
);
794 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
795 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
796 if (isl_int_is_zero(v
))
798 isl_mat_col_submul(T
, 0, v
, 1 + i
);
801 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
802 /* We have to be careful because dropping equalities may reorder them */
804 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
805 for (i
= 0; i
< bmap
->n_eq
; ++i
)
806 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
808 if (i
< bmap
->n_eq
) {
809 bmap
= isl_basic_map_drop_div(bmap
, j
);
810 isl_basic_map_drop_equality(bmap
, i
);
816 for (i
= 1; i
< T
->n_row
; ++i
) {
817 if (isl_int_is_one(T
->row
[i
][i
]))
822 if (needed
> dropped
) {
823 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
),
828 for (i
= 1; i
< T
->n_row
; ++i
) {
829 if (isl_int_is_one(T
->row
[i
][i
]))
831 k
= isl_basic_map_alloc_div(bmap
);
832 pos
[i
] = 1 + total
+ k
;
833 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
834 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
836 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
838 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
839 for (j
= 0; j
< i
; ++j
) {
840 if (isl_int_is_zero(T
->row
[i
][j
]))
842 if (pos
[j
] < T
->n_row
&& C2
)
843 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
844 C2
->row
[pos
[j
]], 1 + total
);
846 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
849 j
= isl_basic_map_alloc_equality(bmap
);
850 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
851 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
860 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
870 static struct isl_basic_map
*set_div_from_lower_bound(
871 struct isl_basic_map
*bmap
, int div
, int ineq
)
873 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
875 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
876 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
877 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
878 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
879 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
884 /* Check whether it is ok to define a div based on an inequality.
885 * To avoid the introduction of circular definitions of divs, we
886 * do not allow such a definition if the resulting expression would refer to
887 * any other undefined divs or if any known div is defined in
888 * terms of the unknown div.
890 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
894 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
896 /* Not defined in terms of unknown divs */
897 for (j
= 0; j
< bmap
->n_div
; ++j
) {
900 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
902 if (isl_int_is_zero(bmap
->div
[j
][0]))
906 /* No other div defined in terms of this one => avoid loops */
907 for (j
= 0; j
< bmap
->n_div
; ++j
) {
910 if (isl_int_is_zero(bmap
->div
[j
][0]))
912 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
919 /* Given two constraints "k" and "l" that are opposite to each other,
920 * except for the constant term, check if we can use them
921 * to obtain an expression for one of the hitherto unknown divs.
922 * "sum" is the sum of the constant terms of the constraints.
923 * If this sum is strictly smaller than the coefficient of one
924 * of the divs, then this pair can be used define the div.
925 * To avoid the introduction of circular definitions of divs, we
926 * do not use the pair if the resulting expression would refer to
927 * any other undefined divs or if any known div is defined in
928 * terms of the unknown div.
930 static struct isl_basic_map
*check_for_div_constraints(
931 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
934 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
936 for (i
= 0; i
< bmap
->n_div
; ++i
) {
937 if (!isl_int_is_zero(bmap
->div
[i
][0]))
939 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
941 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
943 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
945 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
946 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
948 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
956 static struct isl_basic_map
*remove_duplicate_constraints(
957 struct isl_basic_map
*bmap
, int *progress
)
963 unsigned total
= isl_basic_map_total_dim(bmap
);
966 if (bmap
->n_ineq
<= 1)
969 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
970 bits
= ffs(size
) - 1;
971 index
= isl_calloc_array(ctx
, isl_int
**, size
);
975 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
976 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
977 h
= hash_index(index
, size
, bits
, bmap
, k
);
979 index
[h
] = &bmap
->ineq
[k
];
984 l
= index
[h
] - &bmap
->ineq
[0];
985 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
986 swap_inequality(bmap
, k
, l
);
987 isl_basic_map_drop_inequality(bmap
, k
);
991 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
992 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
993 h
= hash_index(index
, size
, bits
, bmap
, k
);
994 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
997 l
= index
[h
] - &bmap
->ineq
[0];
998 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
999 if (isl_int_is_pos(sum
)) {
1000 bmap
= check_for_div_constraints(bmap
, k
, l
, sum
,
1004 if (isl_int_is_zero(sum
)) {
1005 /* We need to break out of the loop after these
1006 * changes since the contents of the hash
1007 * will no longer be valid.
1008 * Plus, we probably we want to regauss first.
1010 isl_basic_map_drop_inequality(bmap
, l
);
1011 isl_basic_map_inequality_to_equality(bmap
, k
);
1013 bmap
= isl_basic_map_set_to_empty(bmap
);
1023 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1030 bmap
= isl_basic_map_normalize_constraints(bmap
);
1031 bmap
= remove_duplicate_divs(bmap
, &progress
);
1032 bmap
= eliminate_divs_eq(bmap
, &progress
);
1033 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1034 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1035 /* requires equalities in normal form */
1036 bmap
= normalize_divs(bmap
, &progress
);
1037 bmap
= remove_duplicate_constraints(bmap
, &progress
);
1042 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1044 return (struct isl_basic_set
*)
1045 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1049 /* If the only constraints a div d=floor(f/m)
1050 * appears in are its two defining constraints
1053 * -(f - (m - 1)) + m d >= 0
1055 * then it can safely be removed.
1057 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1060 unsigned pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
1062 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1063 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1066 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1067 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1069 if (isl_int_eq(bmap
->ineq
[i
][pos
], bmap
->div
[div
][0])) {
1071 isl_int_sub(bmap
->div
[div
][1],
1072 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1073 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1074 neg
= isl_seq_is_neg(bmap
->ineq
[i
], bmap
->div
[div
]+1, pos
);
1075 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1076 isl_int_add(bmap
->div
[div
][1],
1077 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1080 if (isl_seq_first_non_zero(bmap
->ineq
[i
]+pos
+1,
1081 bmap
->n_div
-div
-1) != -1)
1083 } else if (isl_int_abs_eq(bmap
->ineq
[i
][pos
], bmap
->div
[div
][0])) {
1084 if (!isl_seq_eq(bmap
->ineq
[i
], bmap
->div
[div
]+1, pos
))
1086 if (isl_seq_first_non_zero(bmap
->ineq
[i
]+pos
+1,
1087 bmap
->n_div
-div
-1) != -1)
1093 for (i
= 0; i
< bmap
->n_div
; ++i
)
1094 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1101 * Remove divs that don't occur in any of the constraints or other divs.
1102 * These can arise when dropping some of the variables in a quast
1103 * returned by piplib.
1105 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1112 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1113 if (!div_is_redundant(bmap
, i
))
1115 bmap
= isl_basic_map_drop_div(bmap
, i
);
1120 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1122 bmap
= remove_redundant_divs(bmap
);
1125 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1129 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1131 return (struct isl_basic_set
*)
1132 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1135 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1141 for (i
= 0; i
< set
->n
; ++i
) {
1142 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1152 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1158 for (i
= 0; i
< map
->n
; ++i
) {
1159 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1163 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1171 /* Remove definition of any div that is defined in terms of the given variable.
1172 * The div itself is not removed. Functions such as
1173 * eliminate_divs_ineq depend on the other divs remaining in place.
1175 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1180 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1181 if (isl_int_is_zero(bmap
->div
[i
][0]))
1183 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1185 isl_int_set_si(bmap
->div
[i
][0], 0);
1190 /* Eliminate the specified variables from the constraints using
1191 * Fourier-Motzkin. The variables themselves are not removed.
1193 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1194 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1204 total
= isl_basic_map_total_dim(bmap
);
1206 bmap
= isl_basic_map_cow(bmap
);
1207 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1208 bmap
= remove_dependent_vars(bmap
, d
);
1210 for (d
= pos
+ n
- 1;
1211 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1212 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1213 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1214 int n_lower
, n_upper
;
1217 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1218 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1220 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1221 isl_basic_map_drop_equality(bmap
, i
);
1228 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1229 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1231 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1234 bmap
= isl_basic_map_extend_constraints(bmap
,
1235 0, n_lower
* n_upper
);
1236 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1238 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1241 for (j
= 0; j
< i
; ++j
) {
1242 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1245 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1246 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1248 k
= isl_basic_map_alloc_inequality(bmap
);
1251 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1253 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1254 1+d
, 1+total
, NULL
);
1256 isl_basic_map_drop_inequality(bmap
, i
);
1259 if (n_lower
> 0 && n_upper
> 0) {
1260 bmap
= isl_basic_map_normalize_constraints(bmap
);
1261 bmap
= remove_duplicate_constraints(bmap
, NULL
);
1262 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1263 bmap
= isl_basic_map_convex_hull(bmap
);
1266 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1270 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1273 isl_basic_map_free(bmap
);
1277 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1278 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1280 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1281 (struct isl_basic_map
*)bset
, pos
, n
);
1284 /* Don't assume equalities are in order, because align_divs
1285 * may have changed the order of the divs.
1287 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1292 total
= isl_dim_total(bmap
->dim
);
1293 for (d
= 0; d
< total
; ++d
)
1295 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1296 for (d
= total
- 1; d
>= 0; --d
) {
1297 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1305 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1307 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1310 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1311 struct isl_basic_map
*bmap
, int *elim
)
1317 total
= isl_dim_total(bmap
->dim
);
1318 for (d
= total
- 1; d
>= 0; --d
) {
1319 if (isl_int_is_zero(src
[1+d
]))
1324 isl_seq_cpy(dst
, src
, 1 + total
);
1327 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1332 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1333 struct isl_basic_set
*bset
, int *elim
)
1335 return reduced_using_equalities(dst
, src
,
1336 (struct isl_basic_map
*)bset
, elim
);
1339 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1340 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1345 if (!bset
|| !context
)
1348 bset
= isl_basic_set_cow(bset
);
1352 elim
= isl_alloc_array(ctx
, int, isl_basic_set_n_dim(bset
));
1355 set_compute_elimination_index(context
, elim
);
1356 for (i
= 0; i
< bset
->n_eq
; ++i
)
1357 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1359 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1360 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1362 isl_basic_set_free(context
);
1364 bset
= isl_basic_set_simplify(bset
);
1365 bset
= isl_basic_set_finalize(bset
);
1368 isl_basic_set_free(bset
);
1369 isl_basic_set_free(context
);
1373 static struct isl_basic_set
*remove_shifted_constraints(
1374 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1384 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1385 bits
= ffs(size
) - 1;
1386 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1390 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1391 h
= set_hash_index(index
, size
, bits
, context
, k
);
1392 index
[h
] = &context
->ineq
[k
];
1394 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1395 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1398 l
= index
[h
] - &context
->ineq
[0];
1399 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1401 bset
= isl_basic_set_cow(bset
);
1404 isl_basic_set_drop_inequality(bset
, k
);
1414 /* Tighten (decrease) the constant terms of the inequalities based
1415 * on the equalities, without removing any integer points.
1416 * For example, if there is an equality
1424 * then we want to replace the inequality by
1428 * We do this by computing a variable compression and translating
1429 * the constraints to the compressed space.
1430 * If any constraint has coefficients (except the contant term)
1431 * with a common factor "f", then we can replace the constant term "c"
1438 * f * floor(c/f) - c = -fract(c/f)
1440 * and we can add the same value to the original constraint.
1442 * In the example, the compressed space only contains "j",
1443 * and the inequality translates to
1447 * We add -fract(-1/3) = -2 to the original constraint to obtain
1451 static struct isl_basic_set
*normalize_constraints_in_compressed_space(
1452 struct isl_basic_set
*bset
)
1456 struct isl_mat
*B
, *C
;
1462 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
))
1468 bset
= isl_basic_set_cow(bset
);
1472 total
= isl_basic_set_total_dim(bset
);
1473 B
= isl_mat_sub_alloc(bset
->ctx
, bset
->eq
, 0, bset
->n_eq
, 0, 1 + total
);
1474 C
= isl_mat_variable_compression(B
, NULL
);
1477 if (C
->n_col
== 0) {
1479 return isl_basic_set_set_to_empty(bset
);
1481 B
= isl_mat_sub_alloc(bset
->ctx
, bset
->ineq
,
1482 0, bset
->n_ineq
, 0, 1 + total
);
1483 C
= isl_mat_product(B
, C
);
1488 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1489 isl_seq_gcd(C
->row
[i
] + 1, C
->n_col
- 1, &gcd
);
1490 if (isl_int_is_one(gcd
))
1492 isl_int_fdiv_r(C
->row
[i
][0], C
->row
[i
][0], gcd
);
1493 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], C
->row
[i
][0]);
1502 /* Remove all information from bset that is redundant in the context
1503 * of context. In particular, equalities that are linear combinations
1504 * of those in context are removed. Then the inequalities that are
1505 * redundant in the context of the equalities and inequalities of
1506 * context are removed.
1508 * We first simplify the constraints of "bset" in the context of the
1509 * equalities of "context".
1510 * Then we simplify the inequalities of the context in the context
1511 * of the equalities of bset and remove the inequalities from "bset"
1512 * that are obviously redundant with respect to some inequality in "context".
1514 * If there are any inequalities left, we construct a tableau for
1515 * the context and then add the inequalities of "bset".
1516 * Before adding these equalities, we freeze all constraints such that
1517 * they won't be considered redundant in terms of the constraints of "bset".
1518 * Then we detect all equalities and redundant constraints (among the
1519 * constraints that weren't frozen) and update bset according to the results.
1520 * We have to be careful here because we don't want any of the context
1521 * constraints to remain and because we haven't added the equalities of "bset"
1522 * to the tableau so we temporarily have to pretend that there were no
1525 static struct isl_basic_set
*uset_gist(struct isl_basic_set
*bset
,
1526 struct isl_basic_set
*context
)
1529 struct isl_tab
*tab
;
1530 unsigned context_ineq
;
1531 struct isl_basic_set
*combined
= NULL
;
1533 if (!context
|| !bset
)
1536 if (context
->n_eq
> 0)
1537 bset
= isl_basic_set_reduce_using_equalities(bset
,
1538 isl_basic_set_copy(context
));
1541 if (isl_basic_set_fast_is_empty(bset
))
1546 if (bset
->n_eq
> 0) {
1547 struct isl_basic_set
*affine_hull
;
1548 affine_hull
= isl_basic_set_copy(bset
);
1549 affine_hull
= isl_basic_set_cow(affine_hull
);
1552 isl_basic_set_free_inequality(affine_hull
, affine_hull
->n_ineq
);
1553 context
= isl_basic_set_intersect(context
, affine_hull
);
1554 context
= isl_basic_set_gauss(context
, NULL
);
1555 context
= normalize_constraints_in_compressed_space(context
);
1559 if (ISL_F_ISSET(context
, ISL_BASIC_SET_EMPTY
)) {
1560 isl_basic_set_free(bset
);
1563 if (!context
->n_ineq
)
1565 bset
= remove_shifted_constraints(bset
, context
);
1568 isl_basic_set_free_equality(context
, context
->n_eq
);
1569 context_ineq
= context
->n_ineq
;
1570 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1571 combined
= isl_basic_set_extend_constraints(combined
,
1572 bset
->n_eq
, bset
->n_ineq
);
1573 tab
= isl_tab_from_basic_set(combined
);
1576 for (i
= 0; i
< context_ineq
; ++i
)
1577 tab
->con
[i
].frozen
= 1;
1578 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1581 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1582 tab
= isl_tab_add_ineq(tab
, bset
->ineq
[i
]);
1583 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1584 tab
= isl_tab_detect_implicit_equalities(tab
);
1585 tab
= isl_tab_detect_redundant(tab
);
1588 for (i
= 0; i
< context_ineq
; ++i
) {
1589 tab
->con
[i
].is_zero
= 0;
1590 tab
->con
[i
].is_redundant
= 1;
1592 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1594 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1595 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
);
1602 isl_basic_set_free(combined
);
1604 isl_basic_set_free(bset
);
1605 isl_basic_set_free(context
);
1609 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1610 * We simply add the equalities in context to bmap and then do a regular
1611 * div normalizations. Better results can be obtained by normalizing
1612 * only the divs in bmap than do not also appear in context.
1613 * We need to be careful to reduce the divs using the equalities
1614 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1615 * spurious constraints.
1617 static struct isl_basic_map
*normalize_divs_in_context(
1618 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
1621 unsigned total_context
;
1624 div_eq
= n_pure_div_eq(bmap
);
1628 if (context
->n_div
> 0)
1629 bmap
= isl_basic_map_align_divs(bmap
, context
);
1631 total_context
= isl_basic_map_total_dim(context
);
1632 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
1633 for (i
= 0; i
< context
->n_eq
; ++i
) {
1635 k
= isl_basic_map_alloc_equality(bmap
);
1636 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
1637 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
1638 isl_basic_map_total_dim(bmap
) - total_context
);
1640 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1641 bmap
= normalize_divs(bmap
, NULL
);
1642 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1646 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
1647 struct isl_basic_map
*context
)
1649 struct isl_basic_set
*bset
;
1651 if (!bmap
|| !context
)
1654 if (isl_basic_map_is_universe(context
)) {
1655 isl_basic_map_free(context
);
1658 if (isl_basic_map_is_universe(bmap
)) {
1659 isl_basic_map_free(context
);
1662 if (isl_basic_map_fast_is_empty(context
)) {
1663 struct isl_dim
*dim
= isl_dim_copy(bmap
->dim
);
1664 isl_basic_map_free(context
);
1665 isl_basic_map_free(bmap
);
1666 return isl_basic_map_universe(dim
);
1668 if (isl_basic_map_fast_is_empty(bmap
)) {
1669 isl_basic_map_free(context
);
1673 bmap
= isl_basic_map_convex_hull(bmap
);
1674 context
= isl_basic_map_convex_hull(context
);
1677 bmap
= normalize_divs_in_context(bmap
, context
);
1679 context
= isl_basic_map_align_divs(context
, bmap
);
1680 bmap
= isl_basic_map_align_divs(bmap
, context
);
1682 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
1683 isl_basic_map_underlying_set(context
));
1685 return isl_basic_map_overlying_set(bset
, bmap
);
1687 isl_basic_map_free(bmap
);
1688 isl_basic_map_free(context
);
1693 * Assumes context has no implicit divs.
1695 struct isl_map
*isl_map_gist(struct isl_map
*map
, struct isl_basic_map
*context
)
1699 if (!map
|| !context
)
1702 if (isl_basic_map_is_universe(context
)) {
1703 isl_basic_map_free(context
);
1706 if (isl_basic_map_fast_is_empty(context
)) {
1707 struct isl_dim
*dim
= isl_dim_copy(map
->dim
);
1708 isl_basic_map_free(context
);
1710 return isl_map_universe(dim
);
1713 context
= isl_basic_map_convex_hull(context
);
1714 map
= isl_map_cow(map
);
1715 if (!map
|| !context
)
1717 isl_assert(map
->ctx
, isl_dim_equal(map
->dim
, context
->dim
), goto error
);
1718 map
= isl_map_compute_divs(map
);
1719 for (i
= 0; i
< map
->n
; ++i
)
1720 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
1721 for (i
= 0; i
< map
->n
; ++i
) {
1722 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
1723 isl_basic_map_copy(context
));
1727 isl_basic_map_free(context
);
1728 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1732 isl_basic_map_free(context
);
1736 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
1737 struct isl_basic_set
*context
)
1739 return (struct isl_basic_set
*)isl_basic_map_gist(
1740 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
1743 struct isl_set
*isl_set_gist(struct isl_set
*set
, struct isl_basic_set
*context
)
1745 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
1746 (struct isl_basic_map
*)context
);
1749 /* Quick check to see if two basic maps are disjoint.
1750 * In particular, we reduce the equalities and inequalities of
1751 * one basic map in the context of the equalities of the other
1752 * basic map and check if we get a contradiction.
1754 int isl_basic_map_fast_is_disjoint(struct isl_basic_map
*bmap1
,
1755 struct isl_basic_map
*bmap2
)
1757 struct isl_vec
*v
= NULL
;
1762 if (!bmap1
|| !bmap2
)
1764 isl_assert(bmap1
->ctx
, isl_dim_equal(bmap1
->dim
, bmap2
->dim
),
1766 if (bmap1
->n_div
|| bmap2
->n_div
)
1768 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
1771 total
= isl_dim_total(bmap1
->dim
);
1774 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
1777 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
1780 compute_elimination_index(bmap1
, elim
);
1781 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
1783 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
1785 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
1786 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1789 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
1791 reduced
= reduced_using_equalities(v
->block
.data
,
1792 bmap2
->ineq
[i
], bmap1
, elim
);
1793 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1794 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1797 compute_elimination_index(bmap2
, elim
);
1798 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
1800 reduced
= reduced_using_equalities(v
->block
.data
,
1801 bmap1
->ineq
[i
], bmap2
, elim
);
1802 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1803 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1819 int isl_basic_set_fast_is_disjoint(struct isl_basic_set
*bset1
,
1820 struct isl_basic_set
*bset2
)
1822 return isl_basic_map_fast_is_disjoint((struct isl_basic_map
*)bset1
,
1823 (struct isl_basic_map
*)bset2
);
1826 int isl_map_fast_is_disjoint(struct isl_map
*map1
, struct isl_map
*map2
)
1833 if (isl_map_fast_is_equal(map1
, map2
))
1836 for (i
= 0; i
< map1
->n
; ++i
) {
1837 for (j
= 0; j
< map2
->n
; ++j
) {
1838 int d
= isl_basic_map_fast_is_disjoint(map1
->p
[i
],
1847 int isl_set_fast_is_disjoint(struct isl_set
*set1
, struct isl_set
*set2
)
1849 return isl_map_fast_is_disjoint((struct isl_map
*)set1
,
1850 (struct isl_map
*)set2
);
1853 /* Check if we can combine a given div with lower bound l and upper
1854 * bound u with some other div and if so return that other div.
1855 * Otherwise return -1.
1857 * We first check that
1858 * - the bounds are opposites of each other (except for the constant
1860 * - the bounds do not reference any other div
1861 * - no div is defined in terms of this div
1863 * Let m be the size of the range allowed on the div by the bounds.
1864 * That is, the bounds are of the form
1866 * e <= a <= e + m - 1
1868 * with e some expression in the other variables.
1869 * We look for another div b such that no third div is defined in terms
1870 * of this second div b and such that in any constraint that contains
1871 * a (except for the given lower and upper bound), also contains b
1872 * with a coefficient that is m times that of b.
1873 * That is, all constraints (execpt for the lower and upper bound)
1876 * e + f (a + m b) >= 0
1878 * If so, we return b so that "a + m b" can be replaced by
1879 * a single div "c = a + m b".
1881 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
1882 unsigned div
, unsigned l
, unsigned u
)
1888 if (bmap
->n_div
<= 1)
1890 dim
= isl_dim_total(bmap
->dim
);
1891 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
1893 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
1894 bmap
->n_div
- div
- 1) != -1)
1896 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
1900 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1901 if (isl_int_is_zero(bmap
->div
[i
][0]))
1903 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
1907 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
1908 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
1909 isl_int_sub(bmap
->ineq
[l
][0],
1910 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
1911 bmap
= isl_basic_map_copy(bmap
);
1912 bmap
= isl_basic_map_set_to_empty(bmap
);
1913 isl_basic_map_free(bmap
);
1916 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
1917 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1922 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1923 if (isl_int_is_zero(bmap
->div
[j
][0]))
1925 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
1928 if (j
< bmap
->n_div
)
1930 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1932 if (j
== l
|| j
== u
)
1934 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
1936 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
1938 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
1939 bmap
->ineq
[j
][1 + dim
+ div
],
1941 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
1942 bmap
->ineq
[j
][1 + dim
+ i
]);
1943 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
1944 bmap
->ineq
[j
][1 + dim
+ div
],
1949 if (j
< bmap
->n_ineq
)
1954 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
1955 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
1959 /* Given a lower and an upper bound on div i, construct an inequality
1960 * that when nonnegative ensures that this pair of bounds always allows
1961 * for an integer value of the given div.
1962 * The lower bound is inequality l, while the upper bound is inequality u.
1963 * The constructed inequality is stored in ineq.
1964 * g, fl, fu are temporary scalars.
1966 * Let the upper bound be
1970 * and the lower bound
1974 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1977 * - f_u e_l <= f_u f_l g a <= f_l e_u
1979 * Since all variables are integer valued, this is equivalent to
1981 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1983 * If this interval is at least f_u f_l g, then it contains at least
1984 * one integer value for a.
1985 * That is, the test constraint is
1987 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
1989 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
1990 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
1993 dim
= isl_dim_total(bmap
->dim
);
1995 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
1996 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
1997 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
1998 isl_int_neg(fu
, fu
);
1999 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2000 1 + dim
+ bmap
->n_div
);
2001 isl_int_add(ineq
[0], ineq
[0], fl
);
2002 isl_int_add(ineq
[0], ineq
[0], fu
);
2003 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2004 isl_int_mul(g
, g
, fl
);
2005 isl_int_mul(g
, g
, fu
);
2006 isl_int_sub(ineq
[0], ineq
[0], g
);
2009 /* Remove more kinds of divs that are not strictly needed.
2010 * In particular, if all pairs of lower and upper bounds on a div
2011 * are such that they allow at least one integer value of the div,
2012 * the we can eliminate the div using Fourier-Motzkin without
2013 * introducing any spurious solutions.
2015 static struct isl_basic_map
*drop_more_redundant_divs(
2016 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2018 struct isl_tab
*tab
= NULL
;
2019 struct isl_vec
*vec
= NULL
;
2031 dim
= isl_dim_total(bmap
->dim
);
2032 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2036 tab
= isl_tab_from_basic_map(bmap
);
2041 enum isl_lp_result res
;
2043 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2046 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2052 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2053 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2055 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2056 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2058 construct_test_ineq(bmap
, i
, l
, u
,
2059 vec
->el
, g
, fl
, fu
);
2060 res
= isl_tab_min(tab
, vec
->el
,
2061 bmap
->ctx
->one
, &g
, NULL
, 0);
2062 if (res
== isl_lp_error
)
2064 if (res
== isl_lp_empty
) {
2065 bmap
= isl_basic_map_set_to_empty(bmap
);
2068 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2071 if (u
< bmap
->n_ineq
)
2074 if (l
== bmap
->n_ineq
) {
2094 bmap
= isl_basic_map_remove(bmap
, isl_dim_div
, remove
, 1);
2095 return isl_basic_map_drop_redundant_divs(bmap
);
2098 isl_basic_map_free(bmap
);
2107 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2108 * and the upper bound u, div1 always occurs together with div2 in the form
2109 * (div1 + m div2), where m is the constant range on the variable div1
2110 * allowed by l and u, replace the pair div1 and div2 by a single
2111 * div that is equal to div1 + m div2.
2113 * The new div will appear in the location that contains div2.
2114 * We need to modify all constraints that contain
2115 * div2 = (div - div1) / m
2116 * (If a constraint does not contain div2, it will also not contain div1.)
2117 * If the constraint also contains div1, then we know they appear
2118 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2119 * i.e., the coefficient of div is f.
2121 * Otherwise, we first need to introduce div1 into the constraint.
2130 * A lower bound on div2
2134 * can be replaced by
2136 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2138 * with g = gcd(m,n).
2143 * can be replaced by
2145 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2147 * These constraint are those that we would obtain from eliminating
2148 * div1 using Fourier-Motzkin.
2150 * After all constraints have been modified, we drop the lower and upper
2151 * bound and then drop div1.
2153 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2154 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2159 unsigned dim
, total
;
2162 dim
= isl_dim_total(bmap
->dim
);
2163 total
= 1 + dim
+ bmap
->n_div
;
2168 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2169 isl_int_add_ui(m
, m
, 1);
2171 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2172 if (i
== l
|| i
== u
)
2174 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2176 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2177 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2178 isl_int_divexact(a
, m
, b
);
2179 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2180 if (isl_int_is_pos(b
)) {
2181 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2182 b
, bmap
->ineq
[l
], total
);
2185 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2186 b
, bmap
->ineq
[u
], total
);
2189 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2190 bmap
->ineq
[i
][1 + dim
+ div1
]);
2191 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2198 isl_basic_map_drop_inequality(bmap
, l
);
2199 isl_basic_map_drop_inequality(bmap
, u
);
2201 isl_basic_map_drop_inequality(bmap
, u
);
2202 isl_basic_map_drop_inequality(bmap
, l
);
2204 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2208 /* First check if we can coalesce any pair of divs and
2209 * then continue with dropping more redundant divs.
2211 * We loop over all pairs of lower and upper bounds on a div
2212 * with coefficient 1 and -1, respectively, check if there
2213 * is any other div "c" with which we can coalesce the div
2214 * and if so, perform the coalescing.
2216 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2217 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2222 dim
= isl_dim_total(bmap
->dim
);
2224 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2227 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2228 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2230 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2233 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2235 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2239 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2240 return isl_basic_map_drop_redundant_divs(bmap
);
2245 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2248 return drop_more_redundant_divs(bmap
, pairs
, n
);
2251 /* Remove divs that are not strictly needed.
2252 * In particular, if a div only occurs positively (or negatively)
2253 * in constraints, then it can simply be dropped.
2254 * Also, if a div occurs only occurs in two constraints and if moreover
2255 * those two constraints are opposite to each other, except for the constant
2256 * term and if the sum of the constant terms is such that for any value
2257 * of the other values, there is always at least one integer value of the
2258 * div, i.e., if one plus this sum is greater than or equal to
2259 * the (absolute value) of the coefficent of the div in the constraints,
2260 * then we can also simply drop the div.
2262 * If any divs are left after these simple checks then we move on
2263 * to more complicated cases in drop_more_redundant_divs.
2265 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2266 struct isl_basic_map
*bmap
)
2276 off
= isl_dim_total(bmap
->dim
);
2277 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2281 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2283 int last_pos
, last_neg
;
2287 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2288 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2289 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2295 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2296 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2300 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2305 pairs
[i
] = pos
* neg
;
2306 if (pairs
[i
] == 0) {
2307 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2308 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2309 isl_basic_map_drop_inequality(bmap
, j
);
2310 bmap
= isl_basic_map_drop_div(bmap
, i
);
2312 return isl_basic_map_drop_redundant_divs(bmap
);
2316 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2317 bmap
->ineq
[last_neg
] + 1,
2321 isl_int_add(bmap
->ineq
[last_pos
][0],
2322 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2323 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2324 bmap
->ineq
[last_pos
][0], 1);
2325 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2326 bmap
->ineq
[last_pos
][1+off
+i
]);
2327 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2328 bmap
->ineq
[last_pos
][0], 1);
2329 isl_int_sub(bmap
->ineq
[last_pos
][0],
2330 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2333 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
2338 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
2339 bmap
= isl_basic_map_simplify(bmap
);
2341 return isl_basic_map_drop_redundant_divs(bmap
);
2343 if (last_pos
> last_neg
) {
2344 isl_basic_map_drop_inequality(bmap
, last_pos
);
2345 isl_basic_map_drop_inequality(bmap
, last_neg
);
2347 isl_basic_map_drop_inequality(bmap
, last_neg
);
2348 isl_basic_map_drop_inequality(bmap
, last_pos
);
2350 bmap
= isl_basic_map_drop_div(bmap
, i
);
2352 return isl_basic_map_drop_redundant_divs(bmap
);
2356 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
2362 isl_basic_map_free(bmap
);
2366 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
2367 struct isl_basic_set
*bset
)
2369 return (struct isl_basic_set
*)
2370 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
2373 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
2379 for (i
= 0; i
< map
->n
; ++i
) {
2380 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
2384 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2391 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
2393 return (struct isl_set
*)
2394 isl_map_drop_redundant_divs((struct isl_map
*)set
);