2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 #include "isl_equalities.h"
12 #include "isl_map_private.h"
15 #include <isl_dim_private.h>
17 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
19 isl_int
*t
= bmap
->eq
[a
];
20 bmap
->eq
[a
] = bmap
->eq
[b
];
24 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
27 isl_int
*t
= bmap
->ineq
[a
];
28 bmap
->ineq
[a
] = bmap
->ineq
[b
];
33 static void set_swap_inequality(struct isl_basic_set
*bset
, int a
, int b
)
35 swap_inequality((struct isl_basic_map
*)bset
, a
, b
);
38 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
40 isl_seq_cpy(c
, c
+ n
, rem
);
41 isl_seq_clr(c
+ rem
, n
);
44 /* Drop n dimensions starting at first.
46 * In principle, this frees up some extra variables as the number
47 * of columns remains constant, but we would have to extend
48 * the div array too as the number of rows in this array is assumed
49 * to be equal to extra.
51 struct isl_basic_set
*isl_basic_set_drop_dims(
52 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
59 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
61 if (n
== 0 && !isl_dim_get_tuple_name(bset
->dim
, isl_dim_set
))
64 bset
= isl_basic_set_cow(bset
);
68 for (i
= 0; i
< bset
->n_eq
; ++i
)
69 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
70 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
72 for (i
= 0; i
< bset
->n_ineq
; ++i
)
73 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
74 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
76 for (i
= 0; i
< bset
->n_div
; ++i
)
77 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
78 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
80 bset
->dim
= isl_dim_drop_outputs(bset
->dim
, first
, n
);
84 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
85 bset
= isl_basic_set_simplify(bset
);
86 return isl_basic_set_finalize(bset
);
88 isl_basic_set_free(bset
);
92 struct isl_set
*isl_set_drop_dims(
93 struct isl_set
*set
, unsigned first
, unsigned n
)
100 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
102 if (n
== 0 && !isl_dim_get_tuple_name(set
->dim
, isl_dim_set
))
104 set
= isl_set_cow(set
);
107 set
->dim
= isl_dim_drop_outputs(set
->dim
, first
, n
);
111 for (i
= 0; i
< set
->n
; ++i
) {
112 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
117 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
124 /* Move "n" divs starting at "first" to the end of the list of divs.
126 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
127 unsigned first
, unsigned n
)
132 if (first
+ n
== bmap
->n_div
)
135 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
138 for (i
= 0; i
< n
; ++i
)
139 div
[i
] = bmap
->div
[first
+ i
];
140 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
141 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
142 for (i
= 0; i
< n
; ++i
)
143 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
147 isl_basic_map_free(bmap
);
151 /* Drop "n" dimensions of type "type" starting at "first".
153 * In principle, this frees up some extra variables as the number
154 * of columns remains constant, but we would have to extend
155 * the div array too as the number of rows in this array is assumed
156 * to be equal to extra.
158 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
159 enum isl_dim_type type
, unsigned first
, unsigned n
)
169 dim
= isl_basic_map_dim(bmap
, type
);
170 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
172 if (n
== 0 && !isl_dim_get_tuple_name(bmap
->dim
, type
))
175 bmap
= isl_basic_map_cow(bmap
);
179 offset
= isl_basic_map_offset(bmap
, type
) + first
;
180 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
181 for (i
= 0; i
< bmap
->n_eq
; ++i
)
182 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
184 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
185 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
187 for (i
= 0; i
< bmap
->n_div
; ++i
)
188 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
190 if (type
== isl_dim_div
) {
191 bmap
= move_divs_last(bmap
, first
, n
);
194 isl_basic_map_free_div(bmap
, n
);
196 bmap
->dim
= isl_dim_drop(bmap
->dim
, type
, first
, n
);
200 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
201 bmap
= isl_basic_map_simplify(bmap
);
202 return isl_basic_map_finalize(bmap
);
204 isl_basic_map_free(bmap
);
208 __isl_give isl_basic_set
*isl_basic_set_drop(__isl_take isl_basic_set
*bset
,
209 enum isl_dim_type type
, unsigned first
, unsigned n
)
211 return (isl_basic_set
*)isl_basic_map_drop((isl_basic_map
*)bset
,
215 struct isl_basic_map
*isl_basic_map_drop_inputs(
216 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
218 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
221 struct isl_map
*isl_map_drop(struct isl_map
*map
,
222 enum isl_dim_type type
, unsigned first
, unsigned n
)
229 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
231 if (n
== 0 && !isl_dim_get_tuple_name(map
->dim
, type
))
233 map
= isl_map_cow(map
);
236 map
->dim
= isl_dim_drop(map
->dim
, type
, first
, n
);
240 for (i
= 0; i
< map
->n
; ++i
) {
241 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
245 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
253 struct isl_set
*isl_set_drop(struct isl_set
*set
,
254 enum isl_dim_type type
, unsigned first
, unsigned n
)
256 return (isl_set
*)isl_map_drop((isl_map
*)set
, type
, first
, n
);
259 struct isl_map
*isl_map_drop_inputs(
260 struct isl_map
*map
, unsigned first
, unsigned n
)
262 return isl_map_drop(map
, isl_dim_in
, first
, n
);
266 * We don't cow, as the div is assumed to be redundant.
268 static struct isl_basic_map
*isl_basic_map_drop_div(
269 struct isl_basic_map
*bmap
, unsigned div
)
277 pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
279 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
281 for (i
= 0; i
< bmap
->n_eq
; ++i
)
282 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
284 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
285 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
286 isl_basic_map_drop_inequality(bmap
, i
);
290 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
293 for (i
= 0; i
< bmap
->n_div
; ++i
)
294 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
296 if (div
!= bmap
->n_div
- 1) {
298 isl_int
*t
= bmap
->div
[div
];
300 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
301 bmap
->div
[j
] = bmap
->div
[j
+1];
303 bmap
->div
[bmap
->n_div
- 1] = t
;
305 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
306 isl_basic_map_free_div(bmap
, 1);
310 isl_basic_map_free(bmap
);
314 struct isl_basic_map
*isl_basic_map_normalize_constraints(
315 struct isl_basic_map
*bmap
)
319 unsigned total
= isl_basic_map_total_dim(bmap
);
325 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
326 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
327 if (isl_int_is_zero(gcd
)) {
328 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
329 bmap
= isl_basic_map_set_to_empty(bmap
);
332 isl_basic_map_drop_equality(bmap
, i
);
335 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
336 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
337 if (isl_int_is_one(gcd
))
339 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
340 bmap
= isl_basic_map_set_to_empty(bmap
);
343 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
346 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
347 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
348 if (isl_int_is_zero(gcd
)) {
349 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
350 bmap
= isl_basic_map_set_to_empty(bmap
);
353 isl_basic_map_drop_inequality(bmap
, i
);
356 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
357 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
358 if (isl_int_is_one(gcd
))
360 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
361 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
368 struct isl_basic_set
*isl_basic_set_normalize_constraints(
369 struct isl_basic_set
*bset
)
371 return (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
372 (struct isl_basic_map
*)bset
);
375 /* Assumes divs have been ordered if keep_divs is set.
377 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
378 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
384 total
= isl_basic_map_total_dim(bmap
);
385 last_div
= isl_seq_last_non_zero(eq
+ 1 + isl_dim_total(bmap
->dim
),
387 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
388 if (bmap
->eq
[k
] == eq
)
390 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
394 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
397 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
398 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
402 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
403 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
406 for (k
= 0; k
< bmap
->n_div
; ++k
) {
407 if (isl_int_is_zero(bmap
->div
[k
][0]))
409 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
413 /* We need to be careful about circular definitions,
414 * so for now we just remove the definition of div k
415 * if the equality contains any divs.
416 * If keep_divs is set, then the divs have been ordered
417 * and we can keep the definition as long as the result
420 if (last_div
== -1 || (keep_divs
&& last_div
< k
))
421 isl_seq_elim(bmap
->div
[k
]+1, eq
,
422 1+pos
, 1+total
, &bmap
->div
[k
][0]);
424 isl_seq_clr(bmap
->div
[k
], 1 + total
);
425 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
429 /* Assumes divs have been ordered if keep_divs is set.
431 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
432 unsigned div
, int keep_divs
)
434 unsigned pos
= isl_dim_total(bmap
->dim
) + div
;
436 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
438 isl_basic_map_drop_div(bmap
, div
);
441 /* Check if elimination of div "div" using equality "eq" would not
442 * result in a div depending on a later div.
444 static int ok_to_eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
449 unsigned pos
= isl_dim_total(bmap
->dim
) + div
;
451 last_div
= isl_seq_last_non_zero(eq
+ 1 + isl_dim_total(bmap
->dim
),
453 if (last_div
< 0 || last_div
<= div
)
456 for (k
= 0; k
<= last_div
; ++k
) {
457 if (isl_int_is_zero(bmap
->div
[k
][0]))
459 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
466 /* Elimininate divs based on equalities
468 static struct isl_basic_map
*eliminate_divs_eq(
469 struct isl_basic_map
*bmap
, int *progress
)
476 bmap
= isl_basic_map_order_divs(bmap
);
481 off
= 1 + isl_dim_total(bmap
->dim
);
483 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
484 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
485 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
486 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
488 if (!ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
))
492 eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
493 isl_basic_map_drop_equality(bmap
, i
);
498 return eliminate_divs_eq(bmap
, progress
);
502 /* Elimininate divs based on inequalities
504 static struct isl_basic_map
*eliminate_divs_ineq(
505 struct isl_basic_map
*bmap
, int *progress
)
516 off
= 1 + isl_dim_total(bmap
->dim
);
518 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
519 for (i
= 0; i
< bmap
->n_eq
; ++i
)
520 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
524 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
525 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
527 if (i
< bmap
->n_ineq
)
530 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
531 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
533 bmap
= isl_basic_map_drop_div(bmap
, d
);
540 struct isl_basic_map
*isl_basic_map_gauss(
541 struct isl_basic_map
*bmap
, int *progress
)
549 bmap
= isl_basic_map_order_divs(bmap
);
554 total
= isl_basic_map_total_dim(bmap
);
555 total_var
= total
- bmap
->n_div
;
557 last_var
= total
- 1;
558 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
559 for (; last_var
>= 0; --last_var
) {
560 for (k
= done
; k
< bmap
->n_eq
; ++k
)
561 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
569 swap_equality(bmap
, k
, done
);
570 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
571 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
573 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
576 if (last_var
>= total_var
&&
577 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
578 unsigned div
= last_var
- total_var
;
579 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
580 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
581 isl_int_set(bmap
->div
[div
][0],
582 bmap
->eq
[done
][1+last_var
]);
583 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
586 if (done
== bmap
->n_eq
)
588 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
589 if (isl_int_is_zero(bmap
->eq
[k
][0]))
591 return isl_basic_map_set_to_empty(bmap
);
593 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
597 struct isl_basic_set
*isl_basic_set_gauss(
598 struct isl_basic_set
*bset
, int *progress
)
600 return (struct isl_basic_set
*)isl_basic_map_gauss(
601 (struct isl_basic_map
*)bset
, progress
);
605 static unsigned int round_up(unsigned int v
)
616 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
617 struct isl_basic_map
*bmap
, int k
)
620 unsigned total
= isl_basic_map_total_dim(bmap
);
621 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
622 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
623 if (&bmap
->ineq
[k
] != index
[h
] &&
624 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
629 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
630 struct isl_basic_set
*bset
, int k
)
632 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
635 /* If we can eliminate more than one div, then we need to make
636 * sure we do it from last div to first div, in order not to
637 * change the position of the other divs that still need to
640 static struct isl_basic_map
*remove_duplicate_divs(
641 struct isl_basic_map
*bmap
, int *progress
)
653 if (!bmap
|| bmap
->n_div
<= 1)
656 total_var
= isl_dim_total(bmap
->dim
);
657 total
= total_var
+ bmap
->n_div
;
660 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
661 if (!isl_int_is_zero(bmap
->div
[k
][0]))
666 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
667 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
668 bits
= ffs(size
) - 1;
669 index
= isl_calloc_array(ctx
, int, size
);
672 eq
= isl_blk_alloc(ctx
, 1+total
);
673 if (isl_blk_is_error(eq
))
676 isl_seq_clr(eq
.data
, 1+total
);
677 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
678 for (--k
; k
>= 0; --k
) {
681 if (isl_int_is_zero(bmap
->div
[k
][0]))
684 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
685 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
686 if (isl_seq_eq(bmap
->div
[k
],
687 bmap
->div
[index
[h
]-1], 2+total
))
696 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
700 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
701 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
702 eliminate_div(bmap
, eq
.data
, l
, 0);
703 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
704 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
707 isl_blk_free(ctx
, eq
);
714 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
719 total
= isl_dim_total(bmap
->dim
);
720 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
721 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
725 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
731 /* Normalize divs that appear in equalities.
733 * In particular, we assume that bmap contains some equalities
738 * and we want to replace the set of e_i by a minimal set and
739 * such that the new e_i have a canonical representation in terms
741 * If any of the equalities involves more than one divs, then
742 * we currently simply bail out.
744 * Let us first additionally assume that all equalities involve
745 * a div. The equalities then express modulo constraints on the
746 * remaining variables and we can use "parameter compression"
747 * to find a minimal set of constraints. The result is a transformation
749 * x = T(x') = x_0 + G x'
751 * with G a lower-triangular matrix with all elements below the diagonal
752 * non-negative and smaller than the diagonal element on the same row.
753 * We first normalize x_0 by making the same property hold in the affine
755 * The rows i of G with a 1 on the diagonal do not impose any modulo
756 * constraint and simply express x_i = x'_i.
757 * For each of the remaining rows i, we introduce a div and a corresponding
758 * equality. In particular
760 * g_ii e_j = x_i - g_i(x')
762 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
763 * corresponding div (if g_kk != 1).
765 * If there are any equalities not involving any div, then we
766 * first apply a variable compression on the variables x:
768 * x = C x'' x'' = C_2 x
770 * and perform the above parameter compression on A C instead of on A.
771 * The resulting compression is then of the form
773 * x'' = T(x') = x_0 + G x'
775 * and in constructing the new divs and the corresponding equalities,
776 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
777 * by the corresponding row from C_2.
779 static struct isl_basic_map
*normalize_divs(
780 struct isl_basic_map
*bmap
, int *progress
)
787 struct isl_mat
*T
= NULL
;
788 struct isl_mat
*C
= NULL
;
789 struct isl_mat
*C2
= NULL
;
797 if (bmap
->n_div
== 0)
803 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
806 total
= isl_dim_total(bmap
->dim
);
807 div_eq
= n_pure_div_eq(bmap
);
811 if (div_eq
< bmap
->n_eq
) {
812 B
= isl_mat_sub_alloc(bmap
->ctx
, bmap
->eq
, div_eq
,
813 bmap
->n_eq
- div_eq
, 0, 1 + total
);
814 C
= isl_mat_variable_compression(B
, &C2
);
818 bmap
= isl_basic_map_set_to_empty(bmap
);
825 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
828 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
829 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
831 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
833 B
= isl_mat_sub_alloc(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
836 B
= isl_mat_product(B
, C
);
840 T
= isl_mat_parameter_compression(B
, d
);
844 bmap
= isl_basic_map_set_to_empty(bmap
);
850 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
851 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
852 if (isl_int_is_zero(v
))
854 isl_mat_col_submul(T
, 0, v
, 1 + i
);
857 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
860 /* We have to be careful because dropping equalities may reorder them */
862 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
863 for (i
= 0; i
< bmap
->n_eq
; ++i
)
864 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
866 if (i
< bmap
->n_eq
) {
867 bmap
= isl_basic_map_drop_div(bmap
, j
);
868 isl_basic_map_drop_equality(bmap
, i
);
874 for (i
= 1; i
< T
->n_row
; ++i
) {
875 if (isl_int_is_one(T
->row
[i
][i
]))
880 if (needed
> dropped
) {
881 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
),
886 for (i
= 1; i
< T
->n_row
; ++i
) {
887 if (isl_int_is_one(T
->row
[i
][i
]))
889 k
= isl_basic_map_alloc_div(bmap
);
890 pos
[i
] = 1 + total
+ k
;
891 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
892 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
894 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
896 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
897 for (j
= 0; j
< i
; ++j
) {
898 if (isl_int_is_zero(T
->row
[i
][j
]))
900 if (pos
[j
] < T
->n_row
&& C2
)
901 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
902 C2
->row
[pos
[j
]], 1 + total
);
904 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
907 j
= isl_basic_map_alloc_equality(bmap
);
908 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
909 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
918 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
928 static struct isl_basic_map
*set_div_from_lower_bound(
929 struct isl_basic_map
*bmap
, int div
, int ineq
)
931 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
933 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
934 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
935 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
936 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
937 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
942 /* Check whether it is ok to define a div based on an inequality.
943 * To avoid the introduction of circular definitions of divs, we
944 * do not allow such a definition if the resulting expression would refer to
945 * any other undefined divs or if any known div is defined in
946 * terms of the unknown div.
948 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
952 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
954 /* Not defined in terms of unknown divs */
955 for (j
= 0; j
< bmap
->n_div
; ++j
) {
958 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
960 if (isl_int_is_zero(bmap
->div
[j
][0]))
964 /* No other div defined in terms of this one => avoid loops */
965 for (j
= 0; j
< bmap
->n_div
; ++j
) {
968 if (isl_int_is_zero(bmap
->div
[j
][0]))
970 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
977 /* Given two constraints "k" and "l" that are opposite to each other,
978 * except for the constant term, check if we can use them
979 * to obtain an expression for one of the hitherto unknown divs.
980 * "sum" is the sum of the constant terms of the constraints.
981 * If this sum is strictly smaller than the coefficient of one
982 * of the divs, then this pair can be used define the div.
983 * To avoid the introduction of circular definitions of divs, we
984 * do not use the pair if the resulting expression would refer to
985 * any other undefined divs or if any known div is defined in
986 * terms of the unknown div.
988 static struct isl_basic_map
*check_for_div_constraints(
989 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
992 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
994 for (i
= 0; i
< bmap
->n_div
; ++i
) {
995 if (!isl_int_is_zero(bmap
->div
[i
][0]))
997 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
999 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1001 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1003 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1004 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1006 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1014 static struct isl_basic_map
*remove_duplicate_constraints(
1015 struct isl_basic_map
*bmap
, int *progress
)
1021 unsigned total
= isl_basic_map_total_dim(bmap
);
1024 if (!bmap
|| bmap
->n_ineq
<= 1)
1027 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
1028 bits
= ffs(size
) - 1;
1029 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1033 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
1034 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1035 h
= hash_index(index
, size
, bits
, bmap
, k
);
1037 index
[h
] = &bmap
->ineq
[k
];
1042 l
= index
[h
] - &bmap
->ineq
[0];
1043 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1044 swap_inequality(bmap
, k
, l
);
1045 isl_basic_map_drop_inequality(bmap
, k
);
1049 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1050 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1051 h
= hash_index(index
, size
, bits
, bmap
, k
);
1052 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1055 l
= index
[h
] - &bmap
->ineq
[0];
1056 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1057 if (isl_int_is_pos(sum
)) {
1058 bmap
= check_for_div_constraints(bmap
, k
, l
, sum
,
1062 if (isl_int_is_zero(sum
)) {
1063 /* We need to break out of the loop after these
1064 * changes since the contents of the hash
1065 * will no longer be valid.
1066 * Plus, we probably we want to regauss first.
1070 isl_basic_map_drop_inequality(bmap
, l
);
1071 isl_basic_map_inequality_to_equality(bmap
, k
);
1073 bmap
= isl_basic_map_set_to_empty(bmap
);
1083 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1090 bmap
= isl_basic_map_normalize_constraints(bmap
);
1091 bmap
= remove_duplicate_divs(bmap
, &progress
);
1092 bmap
= eliminate_divs_eq(bmap
, &progress
);
1093 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1094 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1095 /* requires equalities in normal form */
1096 bmap
= normalize_divs(bmap
, &progress
);
1097 bmap
= remove_duplicate_constraints(bmap
, &progress
);
1102 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1104 return (struct isl_basic_set
*)
1105 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1109 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1110 isl_int
*constraint
, unsigned div
)
1117 pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
1119 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1121 isl_int_sub(bmap
->div
[div
][1],
1122 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1123 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1124 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1125 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1126 isl_int_add(bmap
->div
[div
][1],
1127 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1130 if (isl_seq_first_non_zero(constraint
+pos
+1,
1131 bmap
->n_div
-div
-1) != -1)
1133 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1134 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1136 if (isl_seq_first_non_zero(constraint
+pos
+1,
1137 bmap
->n_div
-div
-1) != -1)
1146 /* If the only constraints a div d=floor(f/m)
1147 * appears in are its two defining constraints
1150 * -(f - (m - 1)) + m d >= 0
1152 * then it can safely be removed.
1154 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1157 unsigned pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
1159 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1160 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1163 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1164 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1166 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1170 for (i
= 0; i
< bmap
->n_div
; ++i
)
1171 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1178 * Remove divs that don't occur in any of the constraints or other divs.
1179 * These can arise when dropping some of the variables in a quast
1180 * returned by piplib.
1182 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1189 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1190 if (!div_is_redundant(bmap
, i
))
1192 bmap
= isl_basic_map_drop_div(bmap
, i
);
1197 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1199 bmap
= remove_redundant_divs(bmap
);
1202 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1206 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1208 return (struct isl_basic_set
*)
1209 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1212 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1218 for (i
= 0; i
< set
->n
; ++i
) {
1219 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1229 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1235 for (i
= 0; i
< map
->n
; ++i
) {
1236 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1240 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1248 /* Remove definition of any div that is defined in terms of the given variable.
1249 * The div itself is not removed. Functions such as
1250 * eliminate_divs_ineq depend on the other divs remaining in place.
1252 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1257 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1258 if (isl_int_is_zero(bmap
->div
[i
][0]))
1260 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1262 isl_int_set_si(bmap
->div
[i
][0], 0);
1267 /* Eliminate the specified variables from the constraints using
1268 * Fourier-Motzkin. The variables themselves are not removed.
1270 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1271 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1281 total
= isl_basic_map_total_dim(bmap
);
1283 bmap
= isl_basic_map_cow(bmap
);
1284 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1285 bmap
= remove_dependent_vars(bmap
, d
);
1287 for (d
= pos
+ n
- 1;
1288 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1289 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1290 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1291 int n_lower
, n_upper
;
1294 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1295 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1297 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1298 isl_basic_map_drop_equality(bmap
, i
);
1305 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1306 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1308 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1311 bmap
= isl_basic_map_extend_constraints(bmap
,
1312 0, n_lower
* n_upper
);
1315 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1317 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1320 for (j
= 0; j
< i
; ++j
) {
1321 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1324 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1325 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1327 k
= isl_basic_map_alloc_inequality(bmap
);
1330 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1332 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1333 1+d
, 1+total
, NULL
);
1335 isl_basic_map_drop_inequality(bmap
, i
);
1338 if (n_lower
> 0 && n_upper
> 0) {
1339 bmap
= isl_basic_map_normalize_constraints(bmap
);
1340 bmap
= remove_duplicate_constraints(bmap
, NULL
);
1341 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1342 bmap
= isl_basic_map_remove_redundancies(bmap
);
1345 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1349 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1352 isl_basic_map_free(bmap
);
1356 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1357 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1359 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1360 (struct isl_basic_map
*)bset
, pos
, n
);
1363 /* Don't assume equalities are in order, because align_divs
1364 * may have changed the order of the divs.
1366 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1371 total
= isl_dim_total(bmap
->dim
);
1372 for (d
= 0; d
< total
; ++d
)
1374 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1375 for (d
= total
- 1; d
>= 0; --d
) {
1376 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1384 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1386 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1389 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1390 struct isl_basic_map
*bmap
, int *elim
)
1396 total
= isl_dim_total(bmap
->dim
);
1397 for (d
= total
- 1; d
>= 0; --d
) {
1398 if (isl_int_is_zero(src
[1+d
]))
1403 isl_seq_cpy(dst
, src
, 1 + total
);
1406 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1411 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1412 struct isl_basic_set
*bset
, int *elim
)
1414 return reduced_using_equalities(dst
, src
,
1415 (struct isl_basic_map
*)bset
, elim
);
1418 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1419 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1424 if (!bset
|| !context
)
1427 if (context
->n_eq
== 0) {
1428 isl_basic_set_free(context
);
1432 bset
= isl_basic_set_cow(bset
);
1436 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1439 set_compute_elimination_index(context
, elim
);
1440 for (i
= 0; i
< bset
->n_eq
; ++i
)
1441 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1443 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1444 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1446 isl_basic_set_free(context
);
1448 bset
= isl_basic_set_simplify(bset
);
1449 bset
= isl_basic_set_finalize(bset
);
1452 isl_basic_set_free(bset
);
1453 isl_basic_set_free(context
);
1457 static struct isl_basic_set
*remove_shifted_constraints(
1458 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1468 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1469 bits
= ffs(size
) - 1;
1470 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1474 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1475 h
= set_hash_index(index
, size
, bits
, context
, k
);
1476 index
[h
] = &context
->ineq
[k
];
1478 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1479 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1482 l
= index
[h
] - &context
->ineq
[0];
1483 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1485 bset
= isl_basic_set_cow(bset
);
1488 isl_basic_set_drop_inequality(bset
, k
);
1498 /* Tighten (decrease) the constant terms of the inequalities based
1499 * on the equalities, without removing any integer points.
1500 * For example, if there is an equality
1508 * then we want to replace the inequality by
1512 * We do this by computing a variable compression and translating
1513 * the constraints to the compressed space.
1514 * If any constraint has coefficients (except the contant term)
1515 * with a common factor "f", then we can replace the constant term "c"
1522 * f * floor(c/f) - c = -fract(c/f)
1524 * and we can add the same value to the original constraint.
1526 * In the example, the compressed space only contains "j",
1527 * and the inequality translates to
1531 * We add -fract(-1/3) = -2 to the original constraint to obtain
1535 static struct isl_basic_set
*normalize_constraints_in_compressed_space(
1536 struct isl_basic_set
*bset
)
1540 struct isl_mat
*B
, *C
;
1546 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
))
1552 bset
= isl_basic_set_cow(bset
);
1556 total
= isl_basic_set_total_dim(bset
);
1557 B
= isl_mat_sub_alloc(bset
->ctx
, bset
->eq
, 0, bset
->n_eq
, 0, 1 + total
);
1558 C
= isl_mat_variable_compression(B
, NULL
);
1561 if (C
->n_col
== 0) {
1563 return isl_basic_set_set_to_empty(bset
);
1565 B
= isl_mat_sub_alloc(bset
->ctx
, bset
->ineq
,
1566 0, bset
->n_ineq
, 0, 1 + total
);
1567 C
= isl_mat_product(B
, C
);
1572 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1573 isl_seq_gcd(C
->row
[i
] + 1, C
->n_col
- 1, &gcd
);
1574 if (isl_int_is_one(gcd
))
1576 isl_int_fdiv_r(C
->row
[i
][0], C
->row
[i
][0], gcd
);
1577 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], C
->row
[i
][0]);
1586 /* Remove all information from bset that is redundant in the context
1587 * of context. Both bset and context are assumed to be full-dimensional.
1589 * We first * remove the inequalities from "bset"
1590 * that are obviously redundant with respect to some inequality in "context".
1592 * If there are any inequalities left, we construct a tableau for
1593 * the context and then add the inequalities of "bset".
1594 * Before adding these inequalities, we freeze all constraints such that
1595 * they won't be considered redundant in terms of the constraints of "bset".
1596 * Then we detect all redundant constraints (among the
1597 * constraints that weren't frozen), first by checking for redundancy in the
1598 * the tableau and then by checking if replacing a constraint by its negation
1599 * would lead to an empty set. This last step is fairly expensive
1600 * and could be optimized by more reuse of the tableau.
1601 * Finally, we update bset according to the results.
1603 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1604 __isl_take isl_basic_set
*context
)
1607 isl_basic_set
*combined
= NULL
;
1608 struct isl_tab
*tab
= NULL
;
1609 unsigned context_ineq
;
1612 if (!bset
|| !context
)
1615 if (isl_basic_set_is_universe(bset
)) {
1616 isl_basic_set_free(context
);
1620 if (isl_basic_set_is_universe(context
)) {
1621 isl_basic_set_free(context
);
1625 bset
= remove_shifted_constraints(bset
, context
);
1628 if (bset
->n_ineq
== 0)
1631 context_ineq
= context
->n_ineq
;
1632 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1633 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
1634 tab
= isl_tab_from_basic_set(combined
);
1635 for (i
= 0; i
< context_ineq
; ++i
)
1636 if (isl_tab_freeze_constraint(tab
, i
) < 0)
1638 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1639 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1640 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
1642 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1646 if (isl_tab_detect_redundant(tab
) < 0)
1648 total
= isl_basic_set_total_dim(bset
);
1649 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
1651 if (tab
->con
[i
].is_redundant
)
1653 tab
->con
[i
].is_redundant
= 1;
1654 combined
= isl_basic_set_dup(bset
);
1655 combined
= isl_basic_set_update_from_tab(combined
, tab
);
1656 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
1657 k
= isl_basic_set_alloc_inequality(combined
);
1660 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
1661 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
1662 is_empty
= isl_basic_set_is_empty(combined
);
1665 isl_basic_set_free(combined
);
1668 tab
->con
[i
].is_redundant
= 0;
1670 for (i
= 0; i
< context_ineq
; ++i
)
1671 tab
->con
[i
].is_redundant
= 1;
1672 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1674 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1675 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1680 bset
= isl_basic_set_simplify(bset
);
1681 bset
= isl_basic_set_finalize(bset
);
1682 isl_basic_set_free(context
);
1686 isl_basic_set_free(combined
);
1687 isl_basic_set_free(context
);
1688 isl_basic_set_free(bset
);
1692 /* Remove all information from bset that is redundant in the context
1693 * of context. In particular, equalities that are linear combinations
1694 * of those in context are removed. Then the inequalities that are
1695 * redundant in the context of the equalities and inequalities of
1696 * context are removed.
1698 * We first compute the integer affine hull of the intersection,
1699 * compute the gist inside this affine hull and then add back
1700 * those equalities that are not implied by the context.
1702 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
1703 __isl_take isl_basic_set
*context
)
1708 isl_basic_set
*aff_context
;
1711 if (!bset
|| !context
)
1714 bset
= isl_basic_set_intersect(bset
, isl_basic_set_copy(context
));
1715 if (isl_basic_set_fast_is_empty(bset
)) {
1716 isl_basic_set_free(context
);
1719 aff
= isl_basic_set_affine_hull(isl_basic_set_copy(bset
));
1722 if (isl_basic_set_fast_is_empty(aff
)) {
1723 isl_basic_set_free(aff
);
1724 isl_basic_set_free(context
);
1727 if (aff
->n_eq
== 0) {
1728 isl_basic_set_free(aff
);
1729 return uset_gist_full(bset
, context
);
1731 total
= isl_basic_set_total_dim(bset
);
1732 eq
= isl_mat_sub_alloc(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
1733 eq
= isl_mat_cow(eq
);
1734 T
= isl_mat_variable_compression(eq
, &T2
);
1735 if (T
&& T
->n_col
== 0) {
1738 isl_basic_set_free(context
);
1739 isl_basic_set_free(aff
);
1740 return isl_basic_set_set_to_empty(bset
);
1743 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
1745 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
1746 context
= isl_basic_set_preimage(context
, T
);
1748 bset
= uset_gist_full(bset
, context
);
1749 bset
= isl_basic_set_preimage(bset
, T2
);
1750 bset
= isl_basic_set_intersect(bset
, aff
);
1751 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
1754 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1755 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1760 isl_basic_set_free(bset
);
1761 isl_basic_set_free(context
);
1765 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1766 * We simply add the equalities in context to bmap and then do a regular
1767 * div normalizations. Better results can be obtained by normalizing
1768 * only the divs in bmap than do not also appear in context.
1769 * We need to be careful to reduce the divs using the equalities
1770 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1771 * spurious constraints.
1773 static struct isl_basic_map
*normalize_divs_in_context(
1774 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
1777 unsigned total_context
;
1780 div_eq
= n_pure_div_eq(bmap
);
1784 if (context
->n_div
> 0)
1785 bmap
= isl_basic_map_align_divs(bmap
, context
);
1787 total_context
= isl_basic_map_total_dim(context
);
1788 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
1789 for (i
= 0; i
< context
->n_eq
; ++i
) {
1791 k
= isl_basic_map_alloc_equality(bmap
);
1792 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
1793 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
1794 isl_basic_map_total_dim(bmap
) - total_context
);
1796 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1797 bmap
= normalize_divs(bmap
, NULL
);
1798 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1802 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
1803 struct isl_basic_map
*context
)
1805 struct isl_basic_set
*bset
;
1807 if (!bmap
|| !context
)
1810 if (isl_basic_map_is_universe(context
)) {
1811 isl_basic_map_free(context
);
1814 if (isl_basic_map_is_universe(bmap
)) {
1815 isl_basic_map_free(context
);
1818 if (isl_basic_map_fast_is_empty(context
)) {
1819 struct isl_dim
*dim
= isl_dim_copy(bmap
->dim
);
1820 isl_basic_map_free(context
);
1821 isl_basic_map_free(bmap
);
1822 return isl_basic_map_universe(dim
);
1824 if (isl_basic_map_fast_is_empty(bmap
)) {
1825 isl_basic_map_free(context
);
1829 bmap
= isl_basic_map_remove_redundancies(bmap
);
1830 context
= isl_basic_map_remove_redundancies(context
);
1833 bmap
= normalize_divs_in_context(bmap
, context
);
1835 context
= isl_basic_map_align_divs(context
, bmap
);
1836 bmap
= isl_basic_map_align_divs(bmap
, context
);
1838 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
1839 isl_basic_map_underlying_set(context
));
1841 return isl_basic_map_overlying_set(bset
, bmap
);
1843 isl_basic_map_free(bmap
);
1844 isl_basic_map_free(context
);
1849 * Assumes context has no implicit divs.
1851 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
1852 __isl_take isl_basic_map
*context
)
1856 if (!map
|| !context
)
1859 if (isl_basic_map_is_universe(context
)) {
1860 isl_basic_map_free(context
);
1863 if (isl_basic_map_fast_is_empty(context
)) {
1864 struct isl_dim
*dim
= isl_dim_copy(map
->dim
);
1865 isl_basic_map_free(context
);
1867 return isl_map_universe(dim
);
1870 context
= isl_basic_map_remove_redundancies(context
);
1871 map
= isl_map_cow(map
);
1872 if (!map
|| !context
)
1874 isl_assert(map
->ctx
, isl_dim_equal(map
->dim
, context
->dim
), goto error
);
1875 map
= isl_map_compute_divs(map
);
1876 for (i
= 0; i
< map
->n
; ++i
)
1877 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
1878 for (i
= 0; i
< map
->n
; ++i
) {
1879 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
1880 isl_basic_map_copy(context
));
1884 isl_basic_map_free(context
);
1885 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1889 isl_basic_map_free(context
);
1893 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
1894 __isl_take isl_map
*context
)
1896 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
1899 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
1900 struct isl_basic_set
*context
)
1902 return (struct isl_basic_set
*)isl_basic_map_gist(
1903 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
1906 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
1907 __isl_take isl_basic_set
*context
)
1909 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
1910 (struct isl_basic_map
*)context
);
1913 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
1914 __isl_take isl_set
*context
)
1916 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
1917 (struct isl_map
*)context
);
1920 /* Quick check to see if two basic maps are disjoint.
1921 * In particular, we reduce the equalities and inequalities of
1922 * one basic map in the context of the equalities of the other
1923 * basic map and check if we get a contradiction.
1925 int isl_basic_map_fast_is_disjoint(struct isl_basic_map
*bmap1
,
1926 struct isl_basic_map
*bmap2
)
1928 struct isl_vec
*v
= NULL
;
1933 if (!bmap1
|| !bmap2
)
1935 isl_assert(bmap1
->ctx
, isl_dim_equal(bmap1
->dim
, bmap2
->dim
),
1937 if (bmap1
->n_div
|| bmap2
->n_div
)
1939 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
1942 total
= isl_dim_total(bmap1
->dim
);
1945 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
1948 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
1951 compute_elimination_index(bmap1
, elim
);
1952 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
1954 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
1956 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
1957 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1960 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
1962 reduced
= reduced_using_equalities(v
->block
.data
,
1963 bmap2
->ineq
[i
], bmap1
, elim
);
1964 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1965 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1968 compute_elimination_index(bmap2
, elim
);
1969 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
1971 reduced
= reduced_using_equalities(v
->block
.data
,
1972 bmap1
->ineq
[i
], bmap2
, elim
);
1973 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1974 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1990 int isl_basic_set_fast_is_disjoint(struct isl_basic_set
*bset1
,
1991 struct isl_basic_set
*bset2
)
1993 return isl_basic_map_fast_is_disjoint((struct isl_basic_map
*)bset1
,
1994 (struct isl_basic_map
*)bset2
);
1997 int isl_map_fast_is_disjoint(struct isl_map
*map1
, struct isl_map
*map2
)
2004 if (isl_map_fast_is_equal(map1
, map2
))
2007 for (i
= 0; i
< map1
->n
; ++i
) {
2008 for (j
= 0; j
< map2
->n
; ++j
) {
2009 int d
= isl_basic_map_fast_is_disjoint(map1
->p
[i
],
2018 int isl_set_fast_is_disjoint(struct isl_set
*set1
, struct isl_set
*set2
)
2020 return isl_map_fast_is_disjoint((struct isl_map
*)set1
,
2021 (struct isl_map
*)set2
);
2024 /* Check if we can combine a given div with lower bound l and upper
2025 * bound u with some other div and if so return that other div.
2026 * Otherwise return -1.
2028 * We first check that
2029 * - the bounds are opposites of each other (except for the constant
2031 * - the bounds do not reference any other div
2032 * - no div is defined in terms of this div
2034 * Let m be the size of the range allowed on the div by the bounds.
2035 * That is, the bounds are of the form
2037 * e <= a <= e + m - 1
2039 * with e some expression in the other variables.
2040 * We look for another div b such that no third div is defined in terms
2041 * of this second div b and such that in any constraint that contains
2042 * a (except for the given lower and upper bound), also contains b
2043 * with a coefficient that is m times that of b.
2044 * That is, all constraints (execpt for the lower and upper bound)
2047 * e + f (a + m b) >= 0
2049 * If so, we return b so that "a + m b" can be replaced by
2050 * a single div "c = a + m b".
2052 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2053 unsigned div
, unsigned l
, unsigned u
)
2059 if (bmap
->n_div
<= 1)
2061 dim
= isl_dim_total(bmap
->dim
);
2062 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2064 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2065 bmap
->n_div
- div
- 1) != -1)
2067 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2071 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2072 if (isl_int_is_zero(bmap
->div
[i
][0]))
2074 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2078 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2079 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2080 isl_int_sub(bmap
->ineq
[l
][0],
2081 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2082 bmap
= isl_basic_map_copy(bmap
);
2083 bmap
= isl_basic_map_set_to_empty(bmap
);
2084 isl_basic_map_free(bmap
);
2087 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2088 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2093 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2094 if (isl_int_is_zero(bmap
->div
[j
][0]))
2096 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2099 if (j
< bmap
->n_div
)
2101 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2103 if (j
== l
|| j
== u
)
2105 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2107 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2109 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2110 bmap
->ineq
[j
][1 + dim
+ div
],
2112 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2113 bmap
->ineq
[j
][1 + dim
+ i
]);
2114 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2115 bmap
->ineq
[j
][1 + dim
+ div
],
2120 if (j
< bmap
->n_ineq
)
2125 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2126 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2130 /* Given a lower and an upper bound on div i, construct an inequality
2131 * that when nonnegative ensures that this pair of bounds always allows
2132 * for an integer value of the given div.
2133 * The lower bound is inequality l, while the upper bound is inequality u.
2134 * The constructed inequality is stored in ineq.
2135 * g, fl, fu are temporary scalars.
2137 * Let the upper bound be
2141 * and the lower bound
2145 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2148 * - f_u e_l <= f_u f_l g a <= f_l e_u
2150 * Since all variables are integer valued, this is equivalent to
2152 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2154 * If this interval is at least f_u f_l g, then it contains at least
2155 * one integer value for a.
2156 * That is, the test constraint is
2158 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2160 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2161 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2164 dim
= isl_dim_total(bmap
->dim
);
2166 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2167 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2168 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2169 isl_int_neg(fu
, fu
);
2170 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2171 1 + dim
+ bmap
->n_div
);
2172 isl_int_add(ineq
[0], ineq
[0], fl
);
2173 isl_int_add(ineq
[0], ineq
[0], fu
);
2174 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2175 isl_int_mul(g
, g
, fl
);
2176 isl_int_mul(g
, g
, fu
);
2177 isl_int_sub(ineq
[0], ineq
[0], g
);
2180 /* Remove more kinds of divs that are not strictly needed.
2181 * In particular, if all pairs of lower and upper bounds on a div
2182 * are such that they allow at least one integer value of the div,
2183 * the we can eliminate the div using Fourier-Motzkin without
2184 * introducing any spurious solutions.
2186 static struct isl_basic_map
*drop_more_redundant_divs(
2187 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2189 struct isl_tab
*tab
= NULL
;
2190 struct isl_vec
*vec
= NULL
;
2202 dim
= isl_dim_total(bmap
->dim
);
2203 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2207 tab
= isl_tab_from_basic_map(bmap
);
2212 enum isl_lp_result res
;
2214 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2217 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2223 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2224 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2226 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2227 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2229 construct_test_ineq(bmap
, i
, l
, u
,
2230 vec
->el
, g
, fl
, fu
);
2231 res
= isl_tab_min(tab
, vec
->el
,
2232 bmap
->ctx
->one
, &g
, NULL
, 0);
2233 if (res
== isl_lp_error
)
2235 if (res
== isl_lp_empty
) {
2236 bmap
= isl_basic_map_set_to_empty(bmap
);
2239 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2242 if (u
< bmap
->n_ineq
)
2245 if (l
== bmap
->n_ineq
) {
2265 bmap
= isl_basic_map_remove(bmap
, isl_dim_div
, remove
, 1);
2266 return isl_basic_map_drop_redundant_divs(bmap
);
2269 isl_basic_map_free(bmap
);
2278 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2279 * and the upper bound u, div1 always occurs together with div2 in the form
2280 * (div1 + m div2), where m is the constant range on the variable div1
2281 * allowed by l and u, replace the pair div1 and div2 by a single
2282 * div that is equal to div1 + m div2.
2284 * The new div will appear in the location that contains div2.
2285 * We need to modify all constraints that contain
2286 * div2 = (div - div1) / m
2287 * (If a constraint does not contain div2, it will also not contain div1.)
2288 * If the constraint also contains div1, then we know they appear
2289 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2290 * i.e., the coefficient of div is f.
2292 * Otherwise, we first need to introduce div1 into the constraint.
2301 * A lower bound on div2
2305 * can be replaced by
2307 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2309 * with g = gcd(m,n).
2314 * can be replaced by
2316 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2318 * These constraint are those that we would obtain from eliminating
2319 * div1 using Fourier-Motzkin.
2321 * After all constraints have been modified, we drop the lower and upper
2322 * bound and then drop div1.
2324 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2325 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2330 unsigned dim
, total
;
2333 dim
= isl_dim_total(bmap
->dim
);
2334 total
= 1 + dim
+ bmap
->n_div
;
2339 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2340 isl_int_add_ui(m
, m
, 1);
2342 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2343 if (i
== l
|| i
== u
)
2345 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2347 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2348 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2349 isl_int_divexact(a
, m
, b
);
2350 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2351 if (isl_int_is_pos(b
)) {
2352 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2353 b
, bmap
->ineq
[l
], total
);
2356 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2357 b
, bmap
->ineq
[u
], total
);
2360 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2361 bmap
->ineq
[i
][1 + dim
+ div1
]);
2362 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2369 isl_basic_map_drop_inequality(bmap
, l
);
2370 isl_basic_map_drop_inequality(bmap
, u
);
2372 isl_basic_map_drop_inequality(bmap
, u
);
2373 isl_basic_map_drop_inequality(bmap
, l
);
2375 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2379 /* First check if we can coalesce any pair of divs and
2380 * then continue with dropping more redundant divs.
2382 * We loop over all pairs of lower and upper bounds on a div
2383 * with coefficient 1 and -1, respectively, check if there
2384 * is any other div "c" with which we can coalesce the div
2385 * and if so, perform the coalescing.
2387 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2388 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2393 dim
= isl_dim_total(bmap
->dim
);
2395 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2398 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2399 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2401 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2404 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2406 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2410 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2411 return isl_basic_map_drop_redundant_divs(bmap
);
2416 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2419 return drop_more_redundant_divs(bmap
, pairs
, n
);
2422 /* Remove divs that are not strictly needed.
2423 * In particular, if a div only occurs positively (or negatively)
2424 * in constraints, then it can simply be dropped.
2425 * Also, if a div occurs only occurs in two constraints and if moreover
2426 * those two constraints are opposite to each other, except for the constant
2427 * term and if the sum of the constant terms is such that for any value
2428 * of the other values, there is always at least one integer value of the
2429 * div, i.e., if one plus this sum is greater than or equal to
2430 * the (absolute value) of the coefficent of the div in the constraints,
2431 * then we can also simply drop the div.
2433 * If any divs are left after these simple checks then we move on
2434 * to more complicated cases in drop_more_redundant_divs.
2436 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2437 struct isl_basic_map
*bmap
)
2447 off
= isl_dim_total(bmap
->dim
);
2448 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2452 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2454 int last_pos
, last_neg
;
2458 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2459 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2460 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2466 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2467 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2471 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2476 pairs
[i
] = pos
* neg
;
2477 if (pairs
[i
] == 0) {
2478 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2479 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2480 isl_basic_map_drop_inequality(bmap
, j
);
2481 bmap
= isl_basic_map_drop_div(bmap
, i
);
2483 return isl_basic_map_drop_redundant_divs(bmap
);
2487 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2488 bmap
->ineq
[last_neg
] + 1,
2492 isl_int_add(bmap
->ineq
[last_pos
][0],
2493 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2494 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2495 bmap
->ineq
[last_pos
][0], 1);
2496 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2497 bmap
->ineq
[last_pos
][1+off
+i
]);
2498 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2499 bmap
->ineq
[last_pos
][0], 1);
2500 isl_int_sub(bmap
->ineq
[last_pos
][0],
2501 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2504 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
2509 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
2510 bmap
= isl_basic_map_simplify(bmap
);
2512 return isl_basic_map_drop_redundant_divs(bmap
);
2514 if (last_pos
> last_neg
) {
2515 isl_basic_map_drop_inequality(bmap
, last_pos
);
2516 isl_basic_map_drop_inequality(bmap
, last_neg
);
2518 isl_basic_map_drop_inequality(bmap
, last_neg
);
2519 isl_basic_map_drop_inequality(bmap
, last_pos
);
2521 bmap
= isl_basic_map_drop_div(bmap
, i
);
2523 return isl_basic_map_drop_redundant_divs(bmap
);
2527 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
2533 isl_basic_map_free(bmap
);
2537 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
2538 struct isl_basic_set
*bset
)
2540 return (struct isl_basic_set
*)
2541 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
2544 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
2550 for (i
= 0; i
< map
->n
; ++i
) {
2551 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
2555 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2562 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
2564 return (struct isl_set
*)
2565 isl_map_drop_redundant_divs((struct isl_map
*)set
);