1 #include "isl_equalities.h"
3 #include "isl_map_private.h"
6 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
8 isl_int
*t
= bmap
->eq
[a
];
9 bmap
->eq
[a
] = bmap
->eq
[b
];
13 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
16 isl_int
*t
= bmap
->ineq
[a
];
17 bmap
->ineq
[a
] = bmap
->ineq
[b
];
22 static void set_swap_inequality(struct isl_basic_set
*bset
, int a
, int b
)
24 swap_inequality((struct isl_basic_map
*)bset
, a
, b
);
27 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
29 isl_seq_cpy(c
, c
+ n
, rem
);
30 isl_seq_clr(c
+ rem
, n
);
33 /* Drop n dimensions starting at first.
35 * In principle, this frees up some extra variables as the number
36 * of columns remains constant, but we would have to extend
37 * the div array too as the number of rows in this array is assumed
38 * to be equal to extra.
40 struct isl_basic_set
*isl_basic_set_drop_dims(
41 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
48 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
53 bset
= isl_basic_set_cow(bset
);
57 for (i
= 0; i
< bset
->n_eq
; ++i
)
58 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
59 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
61 for (i
= 0; i
< bset
->n_ineq
; ++i
)
62 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
63 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
65 for (i
= 0; i
< bset
->n_div
; ++i
)
66 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
67 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
69 bset
->dim
= isl_dim_drop_outputs(bset
->dim
, first
, n
);
73 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
74 bset
= isl_basic_set_simplify(bset
);
75 return isl_basic_set_finalize(bset
);
77 isl_basic_set_free(bset
);
81 struct isl_set
*isl_set_drop_dims(
82 struct isl_set
*set
, unsigned first
, unsigned n
)
89 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
93 set
= isl_set_cow(set
);
96 set
->dim
= isl_dim_drop_outputs(set
->dim
, first
, n
);
100 for (i
= 0; i
< set
->n
; ++i
) {
101 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
106 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
113 /* Move "n" divs starting at "first" to the end of the list of divs.
115 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
116 unsigned first
, unsigned n
)
121 if (first
+ n
== bmap
->n_div
)
124 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
127 for (i
= 0; i
< n
; ++i
)
128 div
[i
] = bmap
->div
[first
+ i
];
129 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
130 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
131 for (i
= 0; i
< n
; ++i
)
132 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
136 isl_basic_map_free(bmap
);
140 /* Drop "n" dimensions of type "type" starting at "first".
142 * In principle, this frees up some extra variables as the number
143 * of columns remains constant, but we would have to extend
144 * the div array too as the number of rows in this array is assumed
145 * to be equal to extra.
147 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
148 enum isl_dim_type type
, unsigned first
, unsigned n
)
158 dim
= isl_basic_map_dim(bmap
, type
);
159 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
164 bmap
= isl_basic_map_cow(bmap
);
168 offset
= isl_basic_map_offset(bmap
, type
) + first
;
169 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
170 for (i
= 0; i
< bmap
->n_eq
; ++i
)
171 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
173 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
174 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
176 for (i
= 0; i
< bmap
->n_div
; ++i
)
177 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
179 if (type
== isl_dim_div
) {
180 bmap
= move_divs_last(bmap
, first
, n
);
183 isl_basic_map_free_div(bmap
, n
);
185 bmap
->dim
= isl_dim_drop(bmap
->dim
, type
, first
, n
);
189 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
190 bmap
= isl_basic_map_simplify(bmap
);
191 return isl_basic_map_finalize(bmap
);
193 isl_basic_map_free(bmap
);
197 struct isl_basic_map
*isl_basic_map_drop_inputs(
198 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
200 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
203 struct isl_map
*isl_map_drop(struct isl_map
*map
,
204 enum isl_dim_type type
, unsigned first
, unsigned n
)
211 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
215 map
= isl_map_cow(map
);
218 map
->dim
= isl_dim_drop(map
->dim
, type
, first
, n
);
222 for (i
= 0; i
< map
->n
; ++i
) {
223 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
227 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
235 struct isl_map
*isl_map_drop_inputs(
236 struct isl_map
*map
, unsigned first
, unsigned n
)
238 return isl_map_drop(map
, isl_dim_in
, first
, n
);
242 * We don't cow, as the div is assumed to be redundant.
244 static struct isl_basic_map
*isl_basic_map_drop_div(
245 struct isl_basic_map
*bmap
, unsigned div
)
253 pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
255 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
257 for (i
= 0; i
< bmap
->n_eq
; ++i
)
258 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
260 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
261 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
262 isl_basic_map_drop_inequality(bmap
, i
);
266 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
269 for (i
= 0; i
< bmap
->n_div
; ++i
)
270 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
272 if (div
!= bmap
->n_div
- 1) {
274 isl_int
*t
= bmap
->div
[div
];
276 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
277 bmap
->div
[j
] = bmap
->div
[j
+1];
279 bmap
->div
[bmap
->n_div
- 1] = t
;
281 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
282 isl_basic_map_free_div(bmap
, 1);
286 isl_basic_map_free(bmap
);
290 struct isl_basic_map
*isl_basic_map_normalize_constraints(
291 struct isl_basic_map
*bmap
)
295 unsigned total
= isl_basic_map_total_dim(bmap
);
298 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
299 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
300 if (isl_int_is_zero(gcd
)) {
301 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
302 bmap
= isl_basic_map_set_to_empty(bmap
);
305 isl_basic_map_drop_equality(bmap
, i
);
308 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
309 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
310 if (isl_int_is_one(gcd
))
312 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
313 bmap
= isl_basic_map_set_to_empty(bmap
);
316 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
319 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
320 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
321 if (isl_int_is_zero(gcd
)) {
322 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
323 bmap
= isl_basic_map_set_to_empty(bmap
);
326 isl_basic_map_drop_inequality(bmap
, i
);
329 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
330 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
331 if (isl_int_is_one(gcd
))
333 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
334 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
341 struct isl_basic_set
*isl_basic_set_normalize_constraints(
342 struct isl_basic_set
*bset
)
344 (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
345 (struct isl_basic_map
*)bset
);
348 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
, unsigned div
)
351 unsigned pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
353 len
= 1 + isl_basic_map_total_dim(bmap
);
355 for (i
= 0; i
< bmap
->n_eq
; ++i
)
356 if (bmap
->eq
[i
] != eq
)
357 isl_seq_elim(bmap
->eq
[i
], eq
, pos
, len
, NULL
);
359 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
360 isl_seq_elim(bmap
->ineq
[i
], eq
, pos
, len
, NULL
);
362 /* We need to be careful about circular definitions,
363 * so for now we just remove the definitions of other divs that
364 * depend on this div and (possibly) recompute them later.
366 for (i
= 0; i
< bmap
->n_div
; ++i
)
367 if (!isl_int_is_zero(bmap
->div
[i
][0]) &&
368 !isl_int_is_zero(bmap
->div
[i
][1 + pos
]))
369 isl_seq_clr(bmap
->div
[i
], 1 + len
);
371 isl_basic_map_drop_div(bmap
, div
);
374 /* Elimininate divs based on equalities
376 static struct isl_basic_map
*eliminate_divs_eq(
377 struct isl_basic_map
*bmap
, int *progress
)
387 off
= 1 + isl_dim_total(bmap
->dim
);
389 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
390 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
391 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
392 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
396 eliminate_div(bmap
, bmap
->eq
[i
], d
);
397 isl_basic_map_drop_equality(bmap
, i
);
402 return eliminate_divs_eq(bmap
, progress
);
406 /* Elimininate divs based on inequalities
408 static struct isl_basic_map
*eliminate_divs_ineq(
409 struct isl_basic_map
*bmap
, int *progress
)
420 off
= 1 + isl_dim_total(bmap
->dim
);
422 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
423 for (i
= 0; i
< bmap
->n_eq
; ++i
)
424 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
428 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
429 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
431 if (i
< bmap
->n_ineq
)
434 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
435 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
437 bmap
= isl_basic_map_drop_div(bmap
, d
);
444 /* Assumes divs have been ordered if keep_divs is set.
446 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
447 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
453 total
= isl_basic_map_total_dim(bmap
);
454 last_div
= isl_seq_last_non_zero(eq
+ 1 + isl_dim_total(bmap
->dim
),
456 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
457 if (bmap
->eq
[k
] == eq
)
459 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
463 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
466 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
467 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
471 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
472 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
475 for (k
= 0; k
< bmap
->n_div
; ++k
) {
476 if (isl_int_is_zero(bmap
->div
[k
][0]))
478 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
482 /* We need to be careful about circular definitions,
483 * so for now we just remove the definition of div k
484 * if the equality contains any divs.
485 * If keep_divs is set, then the divs have been ordered
486 * and we can keep the definition as long as the result
489 if (last_div
== -1 || (keep_divs
&& last_div
< k
))
490 isl_seq_elim(bmap
->div
[k
]+1, eq
,
491 1+pos
, 1+total
, &bmap
->div
[k
][0]);
493 isl_seq_clr(bmap
->div
[k
], 1 + total
);
494 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
498 struct isl_basic_map
*isl_basic_map_gauss(
499 struct isl_basic_map
*bmap
, int *progress
)
507 bmap
= isl_basic_map_order_divs(bmap
);
512 total
= isl_basic_map_total_dim(bmap
);
513 total_var
= total
- bmap
->n_div
;
515 last_var
= total
- 1;
516 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
517 for (; last_var
>= 0; --last_var
) {
518 for (k
= done
; k
< bmap
->n_eq
; ++k
)
519 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
527 swap_equality(bmap
, k
, done
);
528 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
529 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
531 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
534 if (last_var
>= total_var
&&
535 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
536 unsigned div
= last_var
- total_var
;
537 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
538 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
539 isl_int_set(bmap
->div
[div
][0],
540 bmap
->eq
[done
][1+last_var
]);
541 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
544 if (done
== bmap
->n_eq
)
546 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
547 if (isl_int_is_zero(bmap
->eq
[k
][0]))
549 return isl_basic_map_set_to_empty(bmap
);
551 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
555 struct isl_basic_set
*isl_basic_set_gauss(
556 struct isl_basic_set
*bset
, int *progress
)
558 return (struct isl_basic_set
*)isl_basic_map_gauss(
559 (struct isl_basic_map
*)bset
, progress
);
563 static unsigned int round_up(unsigned int v
)
574 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
575 struct isl_basic_map
*bmap
, int k
)
578 unsigned total
= isl_basic_map_total_dim(bmap
);
579 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
580 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
581 if (&bmap
->ineq
[k
] != index
[h
] &&
582 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
587 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
588 struct isl_basic_set
*bset
, int k
)
590 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
593 /* If we can eliminate more than one div, then we need to make
594 * sure we do it from last div to first div, in order not to
595 * change the position of the other divs that still need to
598 static struct isl_basic_map
*remove_duplicate_divs(
599 struct isl_basic_map
*bmap
, int *progress
)
607 unsigned total_var
= isl_dim_total(bmap
->dim
);
608 unsigned total
= total_var
+ bmap
->n_div
;
611 if (bmap
->n_div
<= 1)
615 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
616 if (!isl_int_is_zero(bmap
->div
[k
][0]))
621 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
622 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
623 bits
= ffs(size
) - 1;
624 index
= isl_calloc_array(ctx
, int, size
);
627 eq
= isl_blk_alloc(ctx
, 1+total
);
628 if (isl_blk_is_error(eq
))
631 isl_seq_clr(eq
.data
, 1+total
);
632 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
633 for (--k
; k
>= 0; --k
) {
636 if (isl_int_is_zero(bmap
->div
[k
][0]))
639 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
640 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
641 if (isl_seq_eq(bmap
->div
[k
],
642 bmap
->div
[index
[h
]-1], 2+total
))
651 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
655 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
656 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
657 eliminate_div(bmap
, eq
.data
, l
);
658 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
659 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
662 isl_blk_free(ctx
, eq
);
669 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
674 total
= isl_dim_total(bmap
->dim
);
675 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
676 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
680 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
686 /* Normalize divs that appear in equalities.
688 * In particular, we assume that bmap contains some equalities
693 * and we want to replace the set of e_i by a minimal set and
694 * such that the new e_i have a canonical representation in terms
696 * If any of the equalities involves more than one divs, then
697 * we currently simply bail out.
699 * Let us first additionally assume that all equalities involve
700 * a div. The equalities then express modulo constraints on the
701 * remaining variables and we can use "parameter compression"
702 * to find a minimal set of constraints. The result is a transformation
704 * x = T(x') = x_0 + G x'
706 * with G a lower-triangular matrix with all elements below the diagonal
707 * non-negative and smaller than the diagonal element on the same row.
708 * We first normalize x_0 by making the same property hold in the affine
710 * The rows i of G with a 1 on the diagonal do not impose any modulo
711 * constraint and simply express x_i = x'_i.
712 * For each of the remaining rows i, we introduce a div and a corresponding
713 * equality. In particular
715 * g_ii e_j = x_i - g_i(x')
717 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
718 * corresponding div (if g_kk != 1).
720 * If there are any equalities not involving any div, then we
721 * first apply a variable compression on the variables x:
723 * x = C x'' x'' = C_2 x
725 * and perform the above parameter compression on A C instead of on A.
726 * The resulting compression is then of the form
728 * x'' = T(x') = x_0 + G x'
730 * and in constructing the new divs and the corresponding equalities,
731 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
732 * by the corresponding row from C_2.
734 static struct isl_basic_map
*normalize_divs(
735 struct isl_basic_map
*bmap
, int *progress
)
742 struct isl_mat
*T
= NULL
;
743 struct isl_mat
*C
= NULL
;
744 struct isl_mat
*C2
= NULL
;
752 if (bmap
->n_div
== 0)
758 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
761 total
= isl_dim_total(bmap
->dim
);
762 div_eq
= n_pure_div_eq(bmap
);
766 if (div_eq
< bmap
->n_eq
) {
767 B
= isl_mat_sub_alloc(bmap
->ctx
, bmap
->eq
, div_eq
,
768 bmap
->n_eq
- div_eq
, 0, 1 + total
);
769 C
= isl_mat_variable_compression(B
, &C2
);
773 bmap
= isl_basic_map_set_to_empty(bmap
);
780 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
783 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
784 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
786 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
788 B
= isl_mat_sub_alloc(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
791 B
= isl_mat_product(B
, C
);
795 T
= isl_mat_parameter_compression(B
, d
);
799 bmap
= isl_basic_map_set_to_empty(bmap
);
805 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
806 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
807 if (isl_int_is_zero(v
))
809 isl_mat_col_submul(T
, 0, v
, 1 + i
);
812 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
813 /* We have to be careful because dropping equalities may reorder them */
815 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
816 for (i
= 0; i
< bmap
->n_eq
; ++i
)
817 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
819 if (i
< bmap
->n_eq
) {
820 bmap
= isl_basic_map_drop_div(bmap
, j
);
821 isl_basic_map_drop_equality(bmap
, i
);
827 for (i
= 1; i
< T
->n_row
; ++i
) {
828 if (isl_int_is_one(T
->row
[i
][i
]))
833 if (needed
> dropped
) {
834 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
),
839 for (i
= 1; i
< T
->n_row
; ++i
) {
840 if (isl_int_is_one(T
->row
[i
][i
]))
842 k
= isl_basic_map_alloc_div(bmap
);
843 pos
[i
] = 1 + total
+ k
;
844 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
845 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
847 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
849 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
850 for (j
= 0; j
< i
; ++j
) {
851 if (isl_int_is_zero(T
->row
[i
][j
]))
853 if (pos
[j
] < T
->n_row
&& C2
)
854 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
855 C2
->row
[pos
[j
]], 1 + total
);
857 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
860 j
= isl_basic_map_alloc_equality(bmap
);
861 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
862 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
871 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
881 static struct isl_basic_map
*set_div_from_lower_bound(
882 struct isl_basic_map
*bmap
, int div
, int ineq
)
884 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
886 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
887 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
888 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
889 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
890 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
895 /* Check whether it is ok to define a div based on an inequality.
896 * To avoid the introduction of circular definitions of divs, we
897 * do not allow such a definition if the resulting expression would refer to
898 * any other undefined divs or if any known div is defined in
899 * terms of the unknown div.
901 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
905 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
907 /* Not defined in terms of unknown divs */
908 for (j
= 0; j
< bmap
->n_div
; ++j
) {
911 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
913 if (isl_int_is_zero(bmap
->div
[j
][0]))
917 /* No other div defined in terms of this one => avoid loops */
918 for (j
= 0; j
< bmap
->n_div
; ++j
) {
921 if (isl_int_is_zero(bmap
->div
[j
][0]))
923 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
930 /* Given two constraints "k" and "l" that are opposite to each other,
931 * except for the constant term, check if we can use them
932 * to obtain an expression for one of the hitherto unknown divs.
933 * "sum" is the sum of the constant terms of the constraints.
934 * If this sum is strictly smaller than the coefficient of one
935 * of the divs, then this pair can be used define the div.
936 * To avoid the introduction of circular definitions of divs, we
937 * do not use the pair if the resulting expression would refer to
938 * any other undefined divs or if any known div is defined in
939 * terms of the unknown div.
941 static struct isl_basic_map
*check_for_div_constraints(
942 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
945 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
947 for (i
= 0; i
< bmap
->n_div
; ++i
) {
948 if (!isl_int_is_zero(bmap
->div
[i
][0]))
950 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
952 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
954 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
956 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
957 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
959 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
967 static struct isl_basic_map
*remove_duplicate_constraints(
968 struct isl_basic_map
*bmap
, int *progress
)
974 unsigned total
= isl_basic_map_total_dim(bmap
);
977 if (bmap
->n_ineq
<= 1)
980 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
981 bits
= ffs(size
) - 1;
982 index
= isl_calloc_array(ctx
, isl_int
**, size
);
986 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
987 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
988 h
= hash_index(index
, size
, bits
, bmap
, k
);
990 index
[h
] = &bmap
->ineq
[k
];
995 l
= index
[h
] - &bmap
->ineq
[0];
996 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
997 swap_inequality(bmap
, k
, l
);
998 isl_basic_map_drop_inequality(bmap
, k
);
1002 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1003 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1004 h
= hash_index(index
, size
, bits
, bmap
, k
);
1005 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1008 l
= index
[h
] - &bmap
->ineq
[0];
1009 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1010 if (isl_int_is_pos(sum
)) {
1011 bmap
= check_for_div_constraints(bmap
, k
, l
, sum
,
1015 if (isl_int_is_zero(sum
)) {
1016 /* We need to break out of the loop after these
1017 * changes since the contents of the hash
1018 * will no longer be valid.
1019 * Plus, we probably we want to regauss first.
1021 isl_basic_map_drop_inequality(bmap
, l
);
1022 isl_basic_map_inequality_to_equality(bmap
, k
);
1024 bmap
= isl_basic_map_set_to_empty(bmap
);
1034 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1041 bmap
= isl_basic_map_normalize_constraints(bmap
);
1042 bmap
= remove_duplicate_divs(bmap
, &progress
);
1043 bmap
= eliminate_divs_eq(bmap
, &progress
);
1044 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1045 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1046 /* requires equalities in normal form */
1047 bmap
= normalize_divs(bmap
, &progress
);
1048 bmap
= remove_duplicate_constraints(bmap
, &progress
);
1053 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1055 return (struct isl_basic_set
*)
1056 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1060 /* If the only constraints a div d=floor(f/m)
1061 * appears in are its two defining constraints
1064 * -(f - (m - 1)) + m d >= 0
1066 * then it can safely be removed.
1068 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1071 unsigned pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
1073 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1074 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1077 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1078 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1080 if (isl_int_eq(bmap
->ineq
[i
][pos
], bmap
->div
[div
][0])) {
1082 isl_int_sub(bmap
->div
[div
][1],
1083 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1084 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1085 neg
= isl_seq_is_neg(bmap
->ineq
[i
], bmap
->div
[div
]+1, pos
);
1086 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1087 isl_int_add(bmap
->div
[div
][1],
1088 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1091 if (isl_seq_first_non_zero(bmap
->ineq
[i
]+pos
+1,
1092 bmap
->n_div
-div
-1) != -1)
1094 } else if (isl_int_abs_eq(bmap
->ineq
[i
][pos
], bmap
->div
[div
][0])) {
1095 if (!isl_seq_eq(bmap
->ineq
[i
], bmap
->div
[div
]+1, pos
))
1097 if (isl_seq_first_non_zero(bmap
->ineq
[i
]+pos
+1,
1098 bmap
->n_div
-div
-1) != -1)
1104 for (i
= 0; i
< bmap
->n_div
; ++i
)
1105 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1112 * Remove divs that don't occur in any of the constraints or other divs.
1113 * These can arise when dropping some of the variables in a quast
1114 * returned by piplib.
1116 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1123 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1124 if (!div_is_redundant(bmap
, i
))
1126 bmap
= isl_basic_map_drop_div(bmap
, i
);
1131 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1133 bmap
= remove_redundant_divs(bmap
);
1136 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1140 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1142 return (struct isl_basic_set
*)
1143 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1146 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1152 for (i
= 0; i
< set
->n
; ++i
) {
1153 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1163 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1169 for (i
= 0; i
< map
->n
; ++i
) {
1170 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1174 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1182 /* Remove definition of any div that is defined in terms of the given variable.
1183 * The div itself is not removed. Functions such as
1184 * eliminate_divs_ineq depend on the other divs remaining in place.
1186 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1190 unsigned dim
= isl_dim_total(bmap
->dim
);
1192 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1193 if (isl_int_is_zero(bmap
->div
[i
][0]))
1195 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1197 isl_int_set_si(bmap
->div
[i
][0], 0);
1202 /* Eliminate the specified variables from the constraints using
1203 * Fourier-Motzkin. The variables themselves are not removed.
1205 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1206 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1216 total
= isl_basic_map_total_dim(bmap
);
1218 bmap
= isl_basic_map_cow(bmap
);
1219 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1220 bmap
= remove_dependent_vars(bmap
, d
);
1222 for (d
= pos
+ n
- 1;
1223 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1224 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1225 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1226 int n_lower
, n_upper
;
1229 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1230 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1232 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1233 isl_basic_map_drop_equality(bmap
, i
);
1240 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1241 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1243 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1246 bmap
= isl_basic_map_extend_constraints(bmap
,
1247 0, n_lower
* n_upper
);
1248 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1250 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1253 for (j
= 0; j
< i
; ++j
) {
1254 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1257 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1258 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1260 k
= isl_basic_map_alloc_inequality(bmap
);
1263 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1265 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1266 1+d
, 1+total
, NULL
);
1268 isl_basic_map_drop_inequality(bmap
, i
);
1271 if (n_lower
> 0 && n_upper
> 0) {
1272 bmap
= isl_basic_map_normalize_constraints(bmap
);
1273 bmap
= remove_duplicate_constraints(bmap
, NULL
);
1274 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1275 bmap
= isl_basic_map_convex_hull(bmap
);
1278 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1282 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1285 isl_basic_map_free(bmap
);
1289 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1290 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1292 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1293 (struct isl_basic_map
*)bset
, pos
, n
);
1296 /* Don't assume equalities are in order, because align_divs
1297 * may have changed the order of the divs.
1299 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1304 total
= isl_dim_total(bmap
->dim
);
1305 for (d
= 0; d
< total
; ++d
)
1307 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1308 for (d
= total
- 1; d
>= 0; --d
) {
1309 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1317 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1319 return compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1322 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1323 struct isl_basic_map
*bmap
, int *elim
)
1329 total
= isl_dim_total(bmap
->dim
);
1330 for (d
= total
- 1; d
>= 0; --d
) {
1331 if (isl_int_is_zero(src
[1+d
]))
1336 isl_seq_cpy(dst
, src
, 1 + total
);
1339 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1344 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1345 struct isl_basic_set
*bset
, int *elim
)
1347 return reduced_using_equalities(dst
, src
,
1348 (struct isl_basic_map
*)bset
, elim
);
1351 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1352 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1357 if (!bset
|| !context
)
1360 bset
= isl_basic_set_cow(bset
);
1364 elim
= isl_alloc_array(ctx
, int, isl_basic_set_n_dim(bset
));
1367 set_compute_elimination_index(context
, elim
);
1368 for (i
= 0; i
< bset
->n_eq
; ++i
)
1369 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1371 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1372 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1374 isl_basic_set_free(context
);
1376 bset
= isl_basic_set_simplify(bset
);
1377 bset
= isl_basic_set_finalize(bset
);
1380 isl_basic_set_free(bset
);
1381 isl_basic_set_free(context
);
1385 static struct isl_basic_set
*remove_shifted_constraints(
1386 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1396 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1397 bits
= ffs(size
) - 1;
1398 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1402 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1403 h
= set_hash_index(index
, size
, bits
, context
, k
);
1404 index
[h
] = &context
->ineq
[k
];
1406 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1407 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1410 l
= index
[h
] - &context
->ineq
[0];
1411 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1413 bset
= isl_basic_set_cow(bset
);
1416 isl_basic_set_drop_inequality(bset
, k
);
1426 /* Tighten (decrease) the constant terms of the inequalities based
1427 * on the equalities, without removing any integer points.
1428 * For example, if there is an equality
1436 * then we want to replace the inequality by
1440 * We do this by computing a variable compression and translating
1441 * the constraints to the compressed space.
1442 * If any constraint has coefficients (except the contant term)
1443 * with a common factor "f", then we can replace the constant term "c"
1450 * f * floor(c/f) - c = -fract(c/f)
1452 * and we can add the same value to the original constraint.
1454 * In the example, the compressed space only contains "j",
1455 * and the inequality translates to
1459 * We add -fract(-1/3) = -2 to the original constraint to obtain
1463 static struct isl_basic_set
*normalize_constraints_in_compressed_space(
1464 struct isl_basic_set
*bset
)
1468 struct isl_mat
*B
, *C
;
1474 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
))
1480 bset
= isl_basic_set_cow(bset
);
1484 total
= isl_basic_set_total_dim(bset
);
1485 B
= isl_mat_sub_alloc(bset
->ctx
, bset
->eq
, 0, bset
->n_eq
, 0, 1 + total
);
1486 C
= isl_mat_variable_compression(B
, NULL
);
1489 if (C
->n_col
== 0) {
1491 return isl_basic_set_set_to_empty(bset
);
1493 B
= isl_mat_sub_alloc(bset
->ctx
, bset
->ineq
,
1494 0, bset
->n_ineq
, 0, 1 + total
);
1495 C
= isl_mat_product(B
, C
);
1500 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1501 isl_seq_gcd(C
->row
[i
] + 1, C
->n_col
- 1, &gcd
);
1502 if (isl_int_is_one(gcd
))
1504 isl_int_fdiv_r(C
->row
[i
][0], C
->row
[i
][0], gcd
);
1505 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], C
->row
[i
][0]);
1514 /* Remove all information from bset that is redundant in the context
1515 * of context. In particular, equalities that are linear combinations
1516 * of those in context are removed. Then the inequalities that are
1517 * redundant in the context of the equalities and inequalities of
1518 * context are removed.
1520 * We first simplify the constraints of "bset" in the context of the
1521 * equalities of "context".
1522 * Then we simplify the inequalities of the context in the context
1523 * of the equalities of bset and remove the inequalities from "bset"
1524 * that are obviously redundant with respect to some inequality in "context".
1526 * If there are any inequalities left, we construct a tableau for
1527 * the context and then add the inequalities of "bset".
1528 * Before adding these equalities, we freeze all constraints such that
1529 * they won't be considered redundant in terms of the constraints of "bset".
1530 * Then we detect all equalities and redundant constraints (among the
1531 * constraints that weren't frozen) and update bset according to the results.
1532 * We have to be careful here because we don't want any of the context
1533 * constraints to remain and because we haven't added the equalities of "bset"
1534 * to the tableau so we temporarily have to pretend that there were no
1537 static struct isl_basic_set
*uset_gist(struct isl_basic_set
*bset
,
1538 struct isl_basic_set
*context
)
1541 struct isl_tab
*tab
;
1542 unsigned context_ineq
;
1543 struct isl_basic_set
*combined
= NULL
;
1545 if (!context
|| !bset
)
1548 if (context
->n_eq
> 0)
1549 bset
= isl_basic_set_reduce_using_equalities(bset
,
1550 isl_basic_set_copy(context
));
1553 if (isl_basic_set_fast_is_empty(bset
))
1558 if (bset
->n_eq
> 0) {
1559 struct isl_basic_set
*affine_hull
;
1560 affine_hull
= isl_basic_set_copy(bset
);
1561 affine_hull
= isl_basic_set_cow(affine_hull
);
1564 isl_basic_set_free_inequality(affine_hull
, affine_hull
->n_ineq
);
1565 context
= isl_basic_set_intersect(context
, affine_hull
);
1566 context
= isl_basic_set_gauss(context
, NULL
);
1567 context
= normalize_constraints_in_compressed_space(context
);
1571 if (ISL_F_ISSET(context
, ISL_BASIC_SET_EMPTY
)) {
1572 isl_basic_set_free(bset
);
1575 if (!context
->n_ineq
)
1577 bset
= remove_shifted_constraints(bset
, context
);
1580 isl_basic_set_free_equality(context
, context
->n_eq
);
1581 context_ineq
= context
->n_ineq
;
1582 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1583 combined
= isl_basic_set_extend_constraints(combined
,
1584 bset
->n_eq
, bset
->n_ineq
);
1585 tab
= isl_tab_from_basic_set(combined
);
1588 for (i
= 0; i
< context_ineq
; ++i
)
1589 tab
->con
[i
].frozen
= 1;
1590 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1593 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1594 tab
= isl_tab_add_ineq(tab
, bset
->ineq
[i
]);
1595 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1596 tab
= isl_tab_detect_equalities(tab
);
1597 tab
= isl_tab_detect_redundant(tab
);
1600 for (i
= 0; i
< context_ineq
; ++i
) {
1601 tab
->con
[i
].is_zero
= 0;
1602 tab
->con
[i
].is_redundant
= 1;
1604 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1606 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1607 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1609 bset
= isl_basic_set_simplify(bset
);
1610 bset
= isl_basic_set_finalize(bset
);
1611 isl_basic_set_free(context
);
1614 isl_basic_set_free(combined
);
1616 isl_basic_set_free(bset
);
1617 isl_basic_set_free(context
);
1621 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1622 * We simply add the equalities in context to bmap and then do a regular
1623 * div normalizations. Better results can be obtained by normalizing
1624 * only the divs in bmap than do not also appear in context.
1625 * We need to be careful to reduce the divs using the equalities
1626 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1627 * spurious constraints.
1629 static struct isl_basic_map
*normalize_divs_in_context(
1630 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
1633 unsigned total_context
;
1636 div_eq
= n_pure_div_eq(bmap
);
1640 if (context
->n_div
> 0)
1641 bmap
= isl_basic_map_align_divs(bmap
, context
);
1643 total_context
= isl_basic_map_total_dim(context
);
1644 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
1645 for (i
= 0; i
< context
->n_eq
; ++i
) {
1647 k
= isl_basic_map_alloc_equality(bmap
);
1648 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
1649 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
1650 isl_basic_map_total_dim(bmap
) - total_context
);
1652 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1653 bmap
= normalize_divs(bmap
, NULL
);
1654 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1658 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
1659 struct isl_basic_map
*context
)
1661 struct isl_basic_set
*bset
;
1663 if (!bmap
|| !context
)
1666 if (isl_basic_map_is_universe(context
)) {
1667 isl_basic_map_free(context
);
1670 if (isl_basic_map_is_universe(bmap
)) {
1671 isl_basic_map_free(context
);
1674 if (isl_basic_map_fast_is_empty(context
)) {
1675 struct isl_dim
*dim
= isl_dim_copy(bmap
->dim
);
1676 isl_basic_map_free(context
);
1677 isl_basic_map_free(bmap
);
1678 return isl_basic_map_universe(dim
);
1680 if (isl_basic_map_fast_is_empty(bmap
)) {
1681 isl_basic_map_free(context
);
1685 bmap
= isl_basic_map_convex_hull(bmap
);
1686 context
= isl_basic_map_convex_hull(context
);
1689 bmap
= normalize_divs_in_context(bmap
, context
);
1691 context
= isl_basic_map_align_divs(context
, bmap
);
1692 bmap
= isl_basic_map_align_divs(bmap
, context
);
1694 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
1695 isl_basic_map_underlying_set(context
));
1697 return isl_basic_map_overlying_set(bset
, bmap
);
1699 isl_basic_map_free(bmap
);
1700 isl_basic_map_free(context
);
1705 * Assumes context has no implicit divs.
1707 struct isl_map
*isl_map_gist(struct isl_map
*map
, struct isl_basic_map
*context
)
1711 if (!map
|| !context
)
1714 if (isl_basic_map_is_universe(context
)) {
1715 isl_basic_map_free(context
);
1718 if (isl_basic_map_fast_is_empty(context
)) {
1719 struct isl_dim
*dim
= isl_dim_copy(map
->dim
);
1720 isl_basic_map_free(context
);
1722 return isl_map_universe(dim
);
1725 context
= isl_basic_map_convex_hull(context
);
1726 map
= isl_map_cow(map
);
1727 if (!map
|| !context
)
1729 isl_assert(map
->ctx
, isl_dim_equal(map
->dim
, context
->dim
), goto error
);
1730 map
= isl_map_compute_divs(map
);
1731 for (i
= 0; i
< map
->n
; ++i
)
1732 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
1733 for (i
= 0; i
< map
->n
; ++i
) {
1734 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
1735 isl_basic_map_copy(context
));
1739 isl_basic_map_free(context
);
1740 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1744 isl_basic_map_free(context
);
1748 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
1749 struct isl_basic_set
*context
)
1751 return (struct isl_basic_set
*)isl_basic_map_gist(
1752 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
1755 struct isl_set
*isl_set_gist(struct isl_set
*set
, struct isl_basic_set
*context
)
1757 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
1758 (struct isl_basic_map
*)context
);
1761 /* Quick check to see if two basic maps are disjoint.
1762 * In particular, we reduce the equalities and inequalities of
1763 * one basic map in the context of the equalities of the other
1764 * basic map and check if we get a contradiction.
1766 int isl_basic_map_fast_is_disjoint(struct isl_basic_map
*bmap1
,
1767 struct isl_basic_map
*bmap2
)
1769 struct isl_vec
*v
= NULL
;
1774 if (!bmap1
|| !bmap2
)
1776 isl_assert(bmap1
->ctx
, isl_dim_equal(bmap1
->dim
, bmap2
->dim
),
1778 if (bmap1
->n_div
|| bmap2
->n_div
)
1780 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
1783 total
= isl_dim_total(bmap1
->dim
);
1786 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
1789 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
1792 compute_elimination_index(bmap1
, elim
);
1793 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
1795 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
1797 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
1798 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1801 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
1803 reduced
= reduced_using_equalities(v
->block
.data
,
1804 bmap2
->ineq
[i
], bmap1
, elim
);
1805 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1806 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1809 compute_elimination_index(bmap2
, elim
);
1810 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
1812 reduced
= reduced_using_equalities(v
->block
.data
,
1813 bmap1
->ineq
[i
], bmap2
, elim
);
1814 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1815 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1831 int isl_basic_set_fast_is_disjoint(struct isl_basic_set
*bset1
,
1832 struct isl_basic_set
*bset2
)
1834 return isl_basic_map_fast_is_disjoint((struct isl_basic_map
*)bset1
,
1835 (struct isl_basic_map
*)bset2
);
1838 int isl_map_fast_is_disjoint(struct isl_map
*map1
, struct isl_map
*map2
)
1845 if (isl_map_fast_is_equal(map1
, map2
))
1848 for (i
= 0; i
< map1
->n
; ++i
) {
1849 for (j
= 0; j
< map2
->n
; ++j
) {
1850 int d
= isl_basic_map_fast_is_disjoint(map1
->p
[i
],
1859 int isl_set_fast_is_disjoint(struct isl_set
*set1
, struct isl_set
*set2
)
1861 return isl_map_fast_is_disjoint((struct isl_map
*)set1
,
1862 (struct isl_map
*)set2
);
1865 /* Check if we can combine a given div with lower bound l and upper
1866 * bound u with some other div and if so return that other div.
1867 * Otherwise return -1.
1869 * We first check that
1870 * - the bounds are opposites of each other (except for the constant
1872 * - the bounds do not reference any other div
1873 * - no div is defined in terms of this div
1875 * Let m be the size of the range allowed on the div by the bounds.
1876 * That is, the bounds are of the form
1878 * e <= a <= e + m - 1
1880 * with e some expression in the other variables.
1881 * We look for another div b such that no third div is defined in terms
1882 * of this second div b and such that in any constraint that contains
1883 * a (except for the given lower and upper bound), also contains b
1884 * with a coefficient that is m times that of b.
1885 * That is, all constraints (execpt for the lower and upper bound)
1888 * e + f (a + m b) >= 0
1890 * If so, we return b so that "a + m b" can be replaced by
1891 * a single div "c = a + m b".
1893 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
1894 unsigned div
, unsigned l
, unsigned u
)
1900 if (bmap
->n_div
<= 1)
1902 dim
= isl_dim_total(bmap
->dim
);
1903 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
1905 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
1906 bmap
->n_div
- div
- 1) != -1)
1908 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
1912 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1913 if (isl_int_is_zero(bmap
->div
[i
][0]))
1915 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
1919 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
1920 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
1921 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1926 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1927 if (isl_int_is_zero(bmap
->div
[j
][0]))
1929 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
1932 if (j
< bmap
->n_div
)
1934 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1936 if (j
== l
|| j
== u
)
1938 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
1940 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
1942 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
1943 bmap
->ineq
[j
][1 + dim
+ div
],
1945 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
1946 bmap
->ineq
[j
][1 + dim
+ i
]);
1947 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
1948 bmap
->ineq
[j
][1 + dim
+ div
],
1953 if (j
< bmap
->n_ineq
)
1958 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
1959 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
1963 /* Given a lower and an upper bound on div i, construct an inequality
1964 * that when nonnegative ensures that this pair of bounds always allows
1965 * for an integer value of the given div.
1966 * The lower bound is inequality l, while the upper bound is inequality u.
1967 * The constructed inequality is stored in ineq.
1968 * g, fl, fu are temporary scalars.
1970 * Let the upper bound be
1974 * and the lower bound
1978 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1981 * - f_u e_l <= f_u f_l g a <= f_l e_u
1983 * Since all variables are integer valued, this is equivalent to
1985 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1987 * If this interval is at least f_u f_l g, then it contains at least
1988 * one integer value for a.
1989 * That is, the test constraint is
1991 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
1993 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
1994 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
1997 dim
= isl_dim_total(bmap
->dim
);
1999 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2000 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2001 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2002 isl_int_neg(fu
, fu
);
2003 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2004 1 + dim
+ bmap
->n_div
);
2005 isl_int_add(ineq
[0], ineq
[0], fl
);
2006 isl_int_add(ineq
[0], ineq
[0], fu
);
2007 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2008 isl_int_mul(g
, g
, fl
);
2009 isl_int_mul(g
, g
, fu
);
2010 isl_int_sub(ineq
[0], ineq
[0], g
);
2013 /* Remove more kinds of divs that are not strictly needed.
2014 * In particular, if all pairs of lower and upper bounds on a div
2015 * are such that they allow at least one integer value of the div,
2016 * the we can eliminate the div using Fourier-Motzkin without
2017 * introducing any spurious solutions.
2019 static struct isl_basic_map
*drop_more_redundant_divs(
2020 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2022 struct isl_tab
*tab
= NULL
;
2023 struct isl_vec
*vec
= NULL
;
2035 dim
= isl_dim_total(bmap
->dim
);
2036 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2040 tab
= isl_tab_from_basic_map(bmap
);
2045 enum isl_lp_result res
;
2047 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2050 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2056 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2057 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2059 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2060 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2062 construct_test_ineq(bmap
, i
, l
, u
,
2063 vec
->el
, g
, fl
, fu
);
2064 res
= isl_tab_min(tab
, vec
->el
,
2065 bmap
->ctx
->one
, &g
, NULL
, 0);
2066 if (res
== isl_lp_error
)
2068 if (res
== isl_lp_empty
) {
2069 bmap
= isl_basic_map_set_to_empty(bmap
);
2072 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2075 if (u
< bmap
->n_ineq
)
2078 if (l
== bmap
->n_ineq
) {
2098 bmap
= isl_basic_map_remove(bmap
, isl_dim_div
, remove
, 1);
2099 return isl_basic_map_drop_redundant_divs(bmap
);
2102 isl_basic_map_free(bmap
);
2111 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2112 * and the upper bound u, div1 always occurs together with div2 in the form
2113 * (div1 + m div2), where m is the constant range on the variable div1
2114 * allowed by l and u, replace the pair div1 and div2 by a single
2115 * div that is equal to div1 + m div2.
2117 * The new div will appear in the location that contains div2.
2118 * We need to modify all constraints that contain
2119 * div2 = (div - div1) / m
2120 * (If a constraint does not contain div2, it will also not contain div1.)
2121 * If the constraint also contains div1, then we know they appear
2122 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2123 * i.e., the coefficient of div is f.
2125 * Otherwise, we first need to introduce div1 into the constraint.
2134 * A lower bound on div2
2138 * can be replaced by
2140 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2142 * with g = gcd(m,n).
2147 * can be replaced by
2149 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2151 * These constraint are those that we would obtain from eliminating
2152 * div1 using Fourier-Motzkin.
2154 * After all constraints have been modified, we drop the lower and upper
2155 * bound and then drop div1.
2157 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2158 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2163 unsigned dim
, total
;
2166 dim
= isl_dim_total(bmap
->dim
);
2167 total
= 1 + dim
+ bmap
->n_div
;
2172 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2173 isl_int_add_ui(m
, m
, 1);
2175 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2176 if (i
== l
|| i
== u
)
2178 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2180 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2181 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2182 isl_int_divexact(a
, m
, b
);
2183 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2184 if (isl_int_is_pos(b
)) {
2185 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2186 b
, bmap
->ineq
[l
], total
);
2189 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2190 b
, bmap
->ineq
[u
], total
);
2193 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2194 bmap
->ineq
[i
][1 + dim
+ div1
]);
2195 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2202 isl_basic_map_drop_inequality(bmap
, l
);
2203 isl_basic_map_drop_inequality(bmap
, u
);
2205 isl_basic_map_drop_inequality(bmap
, u
);
2206 isl_basic_map_drop_inequality(bmap
, l
);
2208 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2212 /* First check if we can coalesce any pair of divs and
2213 * then continue with dropping more redundant divs.
2215 * We loop over all pairs of lower and upper bounds on a div
2216 * with coefficient 1 and -1, respectively, check if there
2217 * is any other div "c" with which we can coalesce the div
2218 * and if so, perform the coalescing.
2220 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2221 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2226 dim
= isl_dim_total(bmap
->dim
);
2228 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2231 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2232 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2234 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2237 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2239 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2243 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2244 return isl_basic_map_drop_redundant_divs(bmap
);
2249 return drop_more_redundant_divs(bmap
, pairs
, n
);
2252 /* Remove divs that are not strictly needed.
2253 * In particular, if a div only occurs positively (or negatively)
2254 * in constraints, then it can simply be dropped.
2255 * Also, if a div occurs only occurs in two constraints and if moreover
2256 * those two constraints are opposite to each other, except for the constant
2257 * term and if the sum of the constant terms is such that for any value
2258 * of the other values, there is always at least one integer value of the
2259 * div, i.e., if one plus this sum is greater than or equal to
2260 * the (absolute value) of the coefficent of the div in the constraints,
2261 * then we can also simply drop the div.
2263 * If any divs are left after these simple checks then we move on
2264 * to more complicated cases in drop_more_redundant_divs.
2266 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2267 struct isl_basic_map
*bmap
)
2277 off
= isl_dim_total(bmap
->dim
);
2278 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2282 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2284 int last_pos
, last_neg
;
2288 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2289 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2290 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2296 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2297 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2301 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2306 pairs
[i
] = pos
* neg
;
2307 if (pairs
[i
] == 0) {
2308 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2309 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2310 isl_basic_map_drop_inequality(bmap
, j
);
2311 bmap
= isl_basic_map_drop_div(bmap
, i
);
2313 return isl_basic_map_drop_redundant_divs(bmap
);
2317 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2318 bmap
->ineq
[last_neg
] + 1,
2322 isl_int_add(bmap
->ineq
[last_pos
][0],
2323 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2324 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2325 bmap
->ineq
[last_pos
][0], 1);
2326 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2327 bmap
->ineq
[last_pos
][1+off
+i
]);
2328 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2329 bmap
->ineq
[last_pos
][0], 1);
2330 isl_int_sub(bmap
->ineq
[last_pos
][0],
2331 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2334 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
2339 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
2340 bmap
= isl_basic_map_simplify(bmap
);
2342 return isl_basic_map_drop_redundant_divs(bmap
);
2344 if (last_pos
> last_neg
) {
2345 isl_basic_map_drop_inequality(bmap
, last_pos
);
2346 isl_basic_map_drop_inequality(bmap
, last_neg
);
2348 isl_basic_map_drop_inequality(bmap
, last_neg
);
2349 isl_basic_map_drop_inequality(bmap
, last_pos
);
2351 bmap
= isl_basic_map_drop_div(bmap
, i
);
2353 return isl_basic_map_drop_redundant_divs(bmap
);
2357 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
2363 isl_basic_map_free(bmap
);
2367 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
2368 struct isl_basic_set
*bset
)
2370 return (struct isl_basic_set
*)
2371 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
2374 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
2380 for (i
= 0; i
< map
->n
; ++i
) {
2381 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
2385 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2392 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
2394 return (struct isl_set
*)
2395 isl_map_drop_redundant_divs((struct isl_map
*)set
);