2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012 Ecole Normale Superieure
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include "isl_equalities.h"
19 #include <isl_space_private.h>
20 #include <isl_mat_private.h>
22 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
24 isl_int
*t
= bmap
->eq
[a
];
25 bmap
->eq
[a
] = bmap
->eq
[b
];
29 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
32 isl_int
*t
= bmap
->ineq
[a
];
33 bmap
->ineq
[a
] = bmap
->ineq
[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_space_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_space_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_space_get_tuple_name(set
->dim
, isl_dim_set
))
104 set
= isl_set_cow(set
);
107 set
->dim
= isl_space_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_space_is_named_or_nested(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_space_drop_dims(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_space_get_tuple_name(map
->dim
, type
))
233 map
= isl_map_cow(map
);
236 map
->dim
= isl_space_drop_dims(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_space_dim(bmap
->dim
, isl_dim_all
) + 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 /* Remove any common factor in numerator and denominator of a div expression,
376 * not taking into account the constant term.
377 * That is, look for any div of the form
379 * floor((a + m f(x))/(m d))
383 * floor((floor(a/m) + f(x))/d)
385 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
386 * and can therefore not influence the result of the floor.
388 static __isl_give isl_basic_map
*normalize_div_expressions(
389 __isl_take isl_basic_map
*bmap
)
393 unsigned total
= isl_basic_map_total_dim(bmap
);
397 if (bmap
->n_div
== 0)
401 for (i
= 0; i
< bmap
->n_div
; ++i
) {
402 if (isl_int_is_zero(bmap
->div
[i
][0]))
404 isl_seq_gcd(bmap
->div
[i
] + 2, total
, &gcd
);
405 isl_int_gcd(gcd
, gcd
, bmap
->div
[i
][0]);
406 if (isl_int_is_one(gcd
))
408 isl_int_fdiv_q(bmap
->div
[i
][1], bmap
->div
[i
][1], gcd
);
409 isl_int_divexact(bmap
->div
[i
][0], bmap
->div
[i
][0], gcd
);
410 isl_seq_scale_down(bmap
->div
[i
] + 2, bmap
->div
[i
] + 2, gcd
,
418 /* Assumes divs have been ordered if keep_divs is set.
420 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
421 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
424 unsigned space_total
;
428 total
= isl_basic_map_total_dim(bmap
);
429 space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
430 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
431 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
432 if (bmap
->eq
[k
] == eq
)
434 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
438 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
439 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
442 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
443 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
447 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
448 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
449 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
452 for (k
= 0; k
< bmap
->n_div
; ++k
) {
453 if (isl_int_is_zero(bmap
->div
[k
][0]))
455 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
459 /* We need to be careful about circular definitions,
460 * so for now we just remove the definition of div k
461 * if the equality contains any divs.
462 * If keep_divs is set, then the divs have been ordered
463 * and we can keep the definition as long as the result
466 if (last_div
== -1 || (keep_divs
&& last_div
< k
))
467 isl_seq_elim(bmap
->div
[k
]+1, eq
,
468 1+pos
, 1+total
, &bmap
->div
[k
][0]);
470 isl_seq_clr(bmap
->div
[k
], 1 + total
);
471 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
475 /* Assumes divs have been ordered if keep_divs is set.
477 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
478 unsigned div
, int keep_divs
)
480 unsigned pos
= isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
482 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
484 isl_basic_map_drop_div(bmap
, div
);
487 /* Check if elimination of div "div" using equality "eq" would not
488 * result in a div depending on a later div.
490 static int ok_to_eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
495 unsigned space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
496 unsigned pos
= space_total
+ div
;
498 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
499 if (last_div
< 0 || last_div
<= div
)
502 for (k
= 0; k
<= last_div
; ++k
) {
503 if (isl_int_is_zero(bmap
->div
[k
][0]))
505 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
512 /* Elimininate divs based on equalities
514 static struct isl_basic_map
*eliminate_divs_eq(
515 struct isl_basic_map
*bmap
, int *progress
)
522 bmap
= isl_basic_map_order_divs(bmap
);
527 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
529 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
530 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
531 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
532 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
534 if (!ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
))
538 eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
539 isl_basic_map_drop_equality(bmap
, i
);
544 return eliminate_divs_eq(bmap
, progress
);
548 /* Elimininate divs based on inequalities
550 static struct isl_basic_map
*eliminate_divs_ineq(
551 struct isl_basic_map
*bmap
, int *progress
)
562 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
564 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
565 for (i
= 0; i
< bmap
->n_eq
; ++i
)
566 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
570 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
571 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
573 if (i
< bmap
->n_ineq
)
576 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
577 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
579 bmap
= isl_basic_map_drop_div(bmap
, d
);
586 struct isl_basic_map
*isl_basic_map_gauss(
587 struct isl_basic_map
*bmap
, int *progress
)
595 bmap
= isl_basic_map_order_divs(bmap
);
600 total
= isl_basic_map_total_dim(bmap
);
601 total_var
= total
- bmap
->n_div
;
603 last_var
= total
- 1;
604 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
605 for (; last_var
>= 0; --last_var
) {
606 for (k
= done
; k
< bmap
->n_eq
; ++k
)
607 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
615 swap_equality(bmap
, k
, done
);
616 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
617 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
619 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
622 if (last_var
>= total_var
&&
623 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
624 unsigned div
= last_var
- total_var
;
625 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
626 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
627 isl_int_set(bmap
->div
[div
][0],
628 bmap
->eq
[done
][1+last_var
]);
629 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
632 if (done
== bmap
->n_eq
)
634 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
635 if (isl_int_is_zero(bmap
->eq
[k
][0]))
637 return isl_basic_map_set_to_empty(bmap
);
639 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
643 struct isl_basic_set
*isl_basic_set_gauss(
644 struct isl_basic_set
*bset
, int *progress
)
646 return (struct isl_basic_set
*)isl_basic_map_gauss(
647 (struct isl_basic_map
*)bset
, progress
);
651 static unsigned int round_up(unsigned int v
)
662 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
663 struct isl_basic_map
*bmap
, int k
)
666 unsigned total
= isl_basic_map_total_dim(bmap
);
667 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
668 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
669 if (&bmap
->ineq
[k
] != index
[h
] &&
670 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
675 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
676 struct isl_basic_set
*bset
, int k
)
678 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
681 /* If we can eliminate more than one div, then we need to make
682 * sure we do it from last div to first div, in order not to
683 * change the position of the other divs that still need to
686 static struct isl_basic_map
*remove_duplicate_divs(
687 struct isl_basic_map
*bmap
, int *progress
)
699 if (!bmap
|| bmap
->n_div
<= 1)
702 total_var
= isl_space_dim(bmap
->dim
, isl_dim_all
);
703 total
= total_var
+ bmap
->n_div
;
706 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
707 if (!isl_int_is_zero(bmap
->div
[k
][0]))
712 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
713 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
714 bits
= ffs(size
) - 1;
715 index
= isl_calloc_array(ctx
, int, size
);
718 eq
= isl_blk_alloc(ctx
, 1+total
);
719 if (isl_blk_is_error(eq
))
722 isl_seq_clr(eq
.data
, 1+total
);
723 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
724 for (--k
; k
>= 0; --k
) {
727 if (isl_int_is_zero(bmap
->div
[k
][0]))
730 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
731 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
732 if (isl_seq_eq(bmap
->div
[k
],
733 bmap
->div
[index
[h
]-1], 2+total
))
742 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
746 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
747 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
748 eliminate_div(bmap
, eq
.data
, l
, 0);
749 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
750 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
753 isl_blk_free(ctx
, eq
);
760 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
765 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
766 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
767 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
771 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
777 /* Normalize divs that appear in equalities.
779 * In particular, we assume that bmap contains some equalities
784 * and we want to replace the set of e_i by a minimal set and
785 * such that the new e_i have a canonical representation in terms
787 * If any of the equalities involves more than one divs, then
788 * we currently simply bail out.
790 * Let us first additionally assume that all equalities involve
791 * a div. The equalities then express modulo constraints on the
792 * remaining variables and we can use "parameter compression"
793 * to find a minimal set of constraints. The result is a transformation
795 * x = T(x') = x_0 + G x'
797 * with G a lower-triangular matrix with all elements below the diagonal
798 * non-negative and smaller than the diagonal element on the same row.
799 * We first normalize x_0 by making the same property hold in the affine
801 * The rows i of G with a 1 on the diagonal do not impose any modulo
802 * constraint and simply express x_i = x'_i.
803 * For each of the remaining rows i, we introduce a div and a corresponding
804 * equality. In particular
806 * g_ii e_j = x_i - g_i(x')
808 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
809 * corresponding div (if g_kk != 1).
811 * If there are any equalities not involving any div, then we
812 * first apply a variable compression on the variables x:
814 * x = C x'' x'' = C_2 x
816 * and perform the above parameter compression on A C instead of on A.
817 * The resulting compression is then of the form
819 * x'' = T(x') = x_0 + G x'
821 * and in constructing the new divs and the corresponding equalities,
822 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
823 * by the corresponding row from C_2.
825 static struct isl_basic_map
*normalize_divs(
826 struct isl_basic_map
*bmap
, int *progress
)
833 struct isl_mat
*T
= NULL
;
834 struct isl_mat
*C
= NULL
;
835 struct isl_mat
*C2
= NULL
;
843 if (bmap
->n_div
== 0)
849 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
852 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
853 div_eq
= n_pure_div_eq(bmap
);
857 if (div_eq
< bmap
->n_eq
) {
858 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
859 bmap
->n_eq
- div_eq
, 0, 1 + total
);
860 C
= isl_mat_variable_compression(B
, &C2
);
864 bmap
= isl_basic_map_set_to_empty(bmap
);
871 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
874 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
875 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
877 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
879 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
882 B
= isl_mat_product(B
, C
);
886 T
= isl_mat_parameter_compression(B
, d
);
890 bmap
= isl_basic_map_set_to_empty(bmap
);
896 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
897 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
898 if (isl_int_is_zero(v
))
900 isl_mat_col_submul(T
, 0, v
, 1 + i
);
903 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
906 /* We have to be careful because dropping equalities may reorder them */
908 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
909 for (i
= 0; i
< bmap
->n_eq
; ++i
)
910 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
912 if (i
< bmap
->n_eq
) {
913 bmap
= isl_basic_map_drop_div(bmap
, j
);
914 isl_basic_map_drop_equality(bmap
, i
);
920 for (i
= 1; i
< T
->n_row
; ++i
) {
921 if (isl_int_is_one(T
->row
[i
][i
]))
926 if (needed
> dropped
) {
927 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
932 for (i
= 1; i
< T
->n_row
; ++i
) {
933 if (isl_int_is_one(T
->row
[i
][i
]))
935 k
= isl_basic_map_alloc_div(bmap
);
936 pos
[i
] = 1 + total
+ k
;
937 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
938 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
940 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
942 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
943 for (j
= 0; j
< i
; ++j
) {
944 if (isl_int_is_zero(T
->row
[i
][j
]))
946 if (pos
[j
] < T
->n_row
&& C2
)
947 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
948 C2
->row
[pos
[j
]], 1 + total
);
950 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
953 j
= isl_basic_map_alloc_equality(bmap
);
954 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
955 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
964 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
974 static struct isl_basic_map
*set_div_from_lower_bound(
975 struct isl_basic_map
*bmap
, int div
, int ineq
)
977 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
979 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
980 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
981 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
982 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
983 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
988 /* Check whether it is ok to define a div based on an inequality.
989 * To avoid the introduction of circular definitions of divs, we
990 * do not allow such a definition if the resulting expression would refer to
991 * any other undefined divs or if any known div is defined in
992 * terms of the unknown div.
994 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
998 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1000 /* Not defined in terms of unknown divs */
1001 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1004 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1006 if (isl_int_is_zero(bmap
->div
[j
][0]))
1010 /* No other div defined in terms of this one => avoid loops */
1011 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1014 if (isl_int_is_zero(bmap
->div
[j
][0]))
1016 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1023 /* Given two constraints "k" and "l" that are opposite to each other,
1024 * except for the constant term, check if we can use them
1025 * to obtain an expression for one of the hitherto unknown divs.
1026 * "sum" is the sum of the constant terms of the constraints.
1027 * If this sum is strictly smaller than the coefficient of one
1028 * of the divs, then this pair can be used define the div.
1029 * To avoid the introduction of circular definitions of divs, we
1030 * do not use the pair if the resulting expression would refer to
1031 * any other undefined divs or if any known div is defined in
1032 * terms of the unknown div.
1034 static struct isl_basic_map
*check_for_div_constraints(
1035 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
1038 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1040 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1041 if (!isl_int_is_zero(bmap
->div
[i
][0]))
1043 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1045 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1047 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1049 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1050 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1052 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1060 static struct isl_basic_map
*remove_duplicate_constraints(
1061 struct isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1067 unsigned total
= isl_basic_map_total_dim(bmap
);
1071 if (!bmap
|| bmap
->n_ineq
<= 1)
1074 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
1075 bits
= ffs(size
) - 1;
1076 ctx
= isl_basic_map_get_ctx(bmap
);
1077 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1081 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
1082 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1083 h
= hash_index(index
, size
, bits
, bmap
, k
);
1085 index
[h
] = &bmap
->ineq
[k
];
1090 l
= index
[h
] - &bmap
->ineq
[0];
1091 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1092 swap_inequality(bmap
, k
, l
);
1093 isl_basic_map_drop_inequality(bmap
, k
);
1097 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1098 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1099 h
= hash_index(index
, size
, bits
, bmap
, k
);
1100 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1103 l
= index
[h
] - &bmap
->ineq
[0];
1104 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1105 if (isl_int_is_pos(sum
)) {
1107 bmap
= check_for_div_constraints(bmap
, k
, l
,
1111 if (isl_int_is_zero(sum
)) {
1112 /* We need to break out of the loop after these
1113 * changes since the contents of the hash
1114 * will no longer be valid.
1115 * Plus, we probably we want to regauss first.
1119 isl_basic_map_drop_inequality(bmap
, l
);
1120 isl_basic_map_inequality_to_equality(bmap
, k
);
1122 bmap
= isl_basic_map_set_to_empty(bmap
);
1132 /* Eliminate knowns divs from constraints where they appear with
1133 * a (positive or negative) unit coefficient.
1137 * floor(e/m) + f >= 0
1145 * -floor(e/m) + f >= 0
1149 * -e + m f + m - 1 >= 0
1151 * The first conversion is valid because floor(e/m) >= -f is equivalent
1152 * to e/m >= -f because -f is an integral expression.
1153 * The second conversion follows from the fact that
1155 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1158 * We skip integral divs, i.e., those with denominator 1, as we would
1159 * risk eliminating the div from the div constraints. We do not need
1160 * to handle those divs here anyway since the div constraints will turn
1161 * out to form an equality and this equality can then be use to eliminate
1162 * the div from all constraints.
1164 static __isl_give isl_basic_map
*eliminate_unit_divs(
1165 __isl_take isl_basic_map
*bmap
, int *progress
)
1174 ctx
= isl_basic_map_get_ctx(bmap
);
1175 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1177 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1178 if (isl_int_is_zero(bmap
->div
[i
][0]))
1180 if (isl_int_is_one(bmap
->div
[i
][0]))
1182 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1185 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1186 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1191 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1192 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1194 isl_seq_combine(bmap
->ineq
[j
],
1195 ctx
->negone
, bmap
->div
[i
] + 1,
1196 bmap
->div
[i
][0], bmap
->ineq
[j
],
1197 total
+ bmap
->n_div
);
1199 isl_seq_combine(bmap
->ineq
[j
],
1200 ctx
->one
, bmap
->div
[i
] + 1,
1201 bmap
->div
[i
][0], bmap
->ineq
[j
],
1202 total
+ bmap
->n_div
);
1204 isl_int_add(bmap
->ineq
[j
][0],
1205 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1206 isl_int_sub_ui(bmap
->ineq
[j
][0],
1207 bmap
->ineq
[j
][0], 1);
1215 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1222 bmap
= isl_basic_map_normalize_constraints(bmap
);
1223 bmap
= normalize_div_expressions(bmap
);
1224 bmap
= remove_duplicate_divs(bmap
, &progress
);
1225 bmap
= eliminate_unit_divs(bmap
, &progress
);
1226 bmap
= eliminate_divs_eq(bmap
, &progress
);
1227 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1228 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1229 /* requires equalities in normal form */
1230 bmap
= normalize_divs(bmap
, &progress
);
1231 bmap
= remove_duplicate_constraints(bmap
, &progress
, 1);
1236 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1238 return (struct isl_basic_set
*)
1239 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1243 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1244 isl_int
*constraint
, unsigned div
)
1251 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1253 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1255 isl_int_sub(bmap
->div
[div
][1],
1256 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1257 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1258 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1259 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1260 isl_int_add(bmap
->div
[div
][1],
1261 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1264 if (isl_seq_first_non_zero(constraint
+pos
+1,
1265 bmap
->n_div
-div
-1) != -1)
1267 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1268 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1270 if (isl_seq_first_non_zero(constraint
+pos
+1,
1271 bmap
->n_div
-div
-1) != -1)
1279 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1280 isl_int
*constraint
, unsigned div
)
1282 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1286 /* If the only constraints a div d=floor(f/m)
1287 * appears in are its two defining constraints
1290 * -(f - (m - 1)) + m d >= 0
1292 * then it can safely be removed.
1294 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1297 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1299 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1300 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1303 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1304 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1306 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1310 for (i
= 0; i
< bmap
->n_div
; ++i
)
1311 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1318 * Remove divs that don't occur in any of the constraints or other divs.
1319 * These can arise when dropping some of the variables in a quast
1320 * returned by piplib.
1322 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1329 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1330 if (!div_is_redundant(bmap
, i
))
1332 bmap
= isl_basic_map_drop_div(bmap
, i
);
1337 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1339 bmap
= remove_redundant_divs(bmap
);
1342 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1346 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1348 return (struct isl_basic_set
*)
1349 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1352 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1358 for (i
= 0; i
< set
->n
; ++i
) {
1359 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1369 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1375 for (i
= 0; i
< map
->n
; ++i
) {
1376 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1380 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1388 /* Remove definition of any div that is defined in terms of the given variable.
1389 * The div itself is not removed. Functions such as
1390 * eliminate_divs_ineq depend on the other divs remaining in place.
1392 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1397 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1398 if (isl_int_is_zero(bmap
->div
[i
][0]))
1400 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1402 isl_int_set_si(bmap
->div
[i
][0], 0);
1407 /* Eliminate the specified variables from the constraints using
1408 * Fourier-Motzkin. The variables themselves are not removed.
1410 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1411 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1422 total
= isl_basic_map_total_dim(bmap
);
1424 bmap
= isl_basic_map_cow(bmap
);
1425 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1426 bmap
= remove_dependent_vars(bmap
, d
);
1428 for (d
= pos
+ n
- 1;
1429 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1430 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1431 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1432 int n_lower
, n_upper
;
1435 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1436 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1438 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1439 isl_basic_map_drop_equality(bmap
, i
);
1447 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1448 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1450 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1453 bmap
= isl_basic_map_extend_constraints(bmap
,
1454 0, n_lower
* n_upper
);
1457 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1459 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1462 for (j
= 0; j
< i
; ++j
) {
1463 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1466 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1467 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1469 k
= isl_basic_map_alloc_inequality(bmap
);
1472 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1474 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1475 1+d
, 1+total
, NULL
);
1477 isl_basic_map_drop_inequality(bmap
, i
);
1480 if (n_lower
> 0 && n_upper
> 0) {
1481 bmap
= isl_basic_map_normalize_constraints(bmap
);
1482 bmap
= remove_duplicate_constraints(bmap
, NULL
, 0);
1483 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1484 bmap
= isl_basic_map_remove_redundancies(bmap
);
1488 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1492 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1494 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1497 isl_basic_map_free(bmap
);
1501 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1502 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1504 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1505 (struct isl_basic_map
*)bset
, pos
, n
);
1508 /* Eliminate the specified n dimensions starting at first from the
1509 * constraints, without removing the dimensions from the space.
1510 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1511 * Otherwise, they are projected out and the original space is restored.
1513 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1514 __isl_take isl_basic_map
*bmap
,
1515 enum isl_dim_type type
, unsigned first
, unsigned n
)
1524 if (first
+ n
> isl_basic_map_dim(bmap
, type
) || first
+ n
< first
)
1525 isl_die(bmap
->ctx
, isl_error_invalid
,
1526 "index out of bounds", goto error
);
1528 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1529 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1530 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1531 return isl_basic_map_finalize(bmap
);
1534 space
= isl_basic_map_get_space(bmap
);
1535 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1536 bmap
= isl_basic_map_insert(bmap
, type
, first
, n
);
1537 bmap
= isl_basic_map_reset_space(bmap
, space
);
1540 isl_basic_map_free(bmap
);
1544 /* Don't assume equalities are in order, because align_divs
1545 * may have changed the order of the divs.
1547 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1552 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1553 for (d
= 0; d
< total
; ++d
)
1555 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1556 for (d
= total
- 1; d
>= 0; --d
) {
1557 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1565 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1567 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1570 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1571 struct isl_basic_map
*bmap
, int *elim
)
1577 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1578 for (d
= total
- 1; d
>= 0; --d
) {
1579 if (isl_int_is_zero(src
[1+d
]))
1584 isl_seq_cpy(dst
, src
, 1 + total
);
1587 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1592 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1593 struct isl_basic_set
*bset
, int *elim
)
1595 return reduced_using_equalities(dst
, src
,
1596 (struct isl_basic_map
*)bset
, elim
);
1599 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1600 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1605 if (!bset
|| !context
)
1608 if (context
->n_eq
== 0) {
1609 isl_basic_set_free(context
);
1613 bset
= isl_basic_set_cow(bset
);
1617 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1620 set_compute_elimination_index(context
, elim
);
1621 for (i
= 0; i
< bset
->n_eq
; ++i
)
1622 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1624 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1625 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1627 isl_basic_set_free(context
);
1629 bset
= isl_basic_set_simplify(bset
);
1630 bset
= isl_basic_set_finalize(bset
);
1633 isl_basic_set_free(bset
);
1634 isl_basic_set_free(context
);
1638 static struct isl_basic_set
*remove_shifted_constraints(
1639 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1650 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1651 bits
= ffs(size
) - 1;
1652 ctx
= isl_basic_set_get_ctx(bset
);
1653 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1657 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1658 h
= set_hash_index(index
, size
, bits
, context
, k
);
1659 index
[h
] = &context
->ineq
[k
];
1661 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1662 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1665 l
= index
[h
] - &context
->ineq
[0];
1666 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1668 bset
= isl_basic_set_cow(bset
);
1671 isl_basic_set_drop_inequality(bset
, k
);
1681 /* Remove all information from bset that is redundant in the context
1682 * of context. Both bset and context are assumed to be full-dimensional.
1684 * We first * remove the inequalities from "bset"
1685 * that are obviously redundant with respect to some inequality in "context".
1687 * If there are any inequalities left, we construct a tableau for
1688 * the context and then add the inequalities of "bset".
1689 * Before adding these inequalities, we freeze all constraints such that
1690 * they won't be considered redundant in terms of the constraints of "bset".
1691 * Then we detect all redundant constraints (among the
1692 * constraints that weren't frozen), first by checking for redundancy in the
1693 * the tableau and then by checking if replacing a constraint by its negation
1694 * would lead to an empty set. This last step is fairly expensive
1695 * and could be optimized by more reuse of the tableau.
1696 * Finally, we update bset according to the results.
1698 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1699 __isl_take isl_basic_set
*context
)
1702 isl_basic_set
*combined
= NULL
;
1703 struct isl_tab
*tab
= NULL
;
1704 unsigned context_ineq
;
1707 if (!bset
|| !context
)
1710 if (isl_basic_set_is_universe(bset
)) {
1711 isl_basic_set_free(context
);
1715 if (isl_basic_set_is_universe(context
)) {
1716 isl_basic_set_free(context
);
1720 bset
= remove_shifted_constraints(bset
, context
);
1723 if (bset
->n_ineq
== 0)
1726 context_ineq
= context
->n_ineq
;
1727 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1728 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
1729 tab
= isl_tab_from_basic_set(combined
, 0);
1730 for (i
= 0; i
< context_ineq
; ++i
)
1731 if (isl_tab_freeze_constraint(tab
, i
) < 0)
1733 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1734 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1735 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
1737 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1741 if (isl_tab_detect_redundant(tab
) < 0)
1743 total
= isl_basic_set_total_dim(bset
);
1744 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
1746 if (tab
->con
[i
].is_redundant
)
1748 tab
->con
[i
].is_redundant
= 1;
1749 combined
= isl_basic_set_dup(bset
);
1750 combined
= isl_basic_set_update_from_tab(combined
, tab
);
1751 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
1752 k
= isl_basic_set_alloc_inequality(combined
);
1755 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
1756 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
1757 is_empty
= isl_basic_set_is_empty(combined
);
1760 isl_basic_set_free(combined
);
1763 tab
->con
[i
].is_redundant
= 0;
1765 for (i
= 0; i
< context_ineq
; ++i
)
1766 tab
->con
[i
].is_redundant
= 1;
1767 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1769 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1770 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1775 bset
= isl_basic_set_simplify(bset
);
1776 bset
= isl_basic_set_finalize(bset
);
1777 isl_basic_set_free(context
);
1781 isl_basic_set_free(combined
);
1782 isl_basic_set_free(context
);
1783 isl_basic_set_free(bset
);
1787 /* Remove all information from bset that is redundant in the context
1788 * of context. In particular, equalities that are linear combinations
1789 * of those in context are removed. Then the inequalities that are
1790 * redundant in the context of the equalities and inequalities of
1791 * context are removed.
1793 * We first compute the integer affine hull of the intersection,
1794 * compute the gist inside this affine hull and then add back
1795 * those equalities that are not implied by the context.
1797 * If two constraints are mutually redundant, then uset_gist_full
1798 * will remove the second of those constraints. We therefore first
1799 * sort the constraints so that constraints not involving existentially
1800 * quantified variables are given precedence over those that do.
1801 * We have to perform this sorting before the variable compression,
1802 * because that may effect the order of the variables.
1804 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
1805 __isl_take isl_basic_set
*context
)
1810 isl_basic_set
*aff_context
;
1813 if (!bset
|| !context
)
1816 bset
= isl_basic_set_intersect(bset
, isl_basic_set_copy(context
));
1817 if (isl_basic_set_plain_is_empty(bset
)) {
1818 isl_basic_set_free(context
);
1821 bset
= isl_basic_set_sort_constraints(bset
);
1822 aff
= isl_basic_set_affine_hull(isl_basic_set_copy(bset
));
1825 if (isl_basic_set_plain_is_empty(aff
)) {
1826 isl_basic_set_free(aff
);
1827 isl_basic_set_free(context
);
1830 if (aff
->n_eq
== 0) {
1831 isl_basic_set_free(aff
);
1832 return uset_gist_full(bset
, context
);
1834 total
= isl_basic_set_total_dim(bset
);
1835 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
1836 eq
= isl_mat_cow(eq
);
1837 T
= isl_mat_variable_compression(eq
, &T2
);
1838 if (T
&& T
->n_col
== 0) {
1841 isl_basic_set_free(context
);
1842 isl_basic_set_free(aff
);
1843 return isl_basic_set_set_to_empty(bset
);
1846 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
1848 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
1849 context
= isl_basic_set_preimage(context
, T
);
1851 bset
= uset_gist_full(bset
, context
);
1852 bset
= isl_basic_set_preimage(bset
, T2
);
1853 bset
= isl_basic_set_intersect(bset
, aff
);
1854 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
1857 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1858 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1863 isl_basic_set_free(bset
);
1864 isl_basic_set_free(context
);
1868 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1869 * We simply add the equalities in context to bmap and then do a regular
1870 * div normalizations. Better results can be obtained by normalizing
1871 * only the divs in bmap than do not also appear in context.
1872 * We need to be careful to reduce the divs using the equalities
1873 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1874 * spurious constraints.
1876 static struct isl_basic_map
*normalize_divs_in_context(
1877 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
1880 unsigned total_context
;
1883 div_eq
= n_pure_div_eq(bmap
);
1887 if (context
->n_div
> 0)
1888 bmap
= isl_basic_map_align_divs(bmap
, context
);
1890 total_context
= isl_basic_map_total_dim(context
);
1891 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
1892 for (i
= 0; i
< context
->n_eq
; ++i
) {
1894 k
= isl_basic_map_alloc_equality(bmap
);
1895 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
1896 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
1897 isl_basic_map_total_dim(bmap
) - total_context
);
1899 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1900 bmap
= normalize_divs(bmap
, NULL
);
1901 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1905 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
1906 struct isl_basic_map
*context
)
1908 struct isl_basic_set
*bset
;
1910 if (!bmap
|| !context
)
1913 if (isl_basic_map_is_universe(bmap
)) {
1914 isl_basic_map_free(context
);
1917 if (isl_basic_map_plain_is_empty(context
)) {
1918 isl_basic_map_free(bmap
);
1921 if (isl_basic_map_plain_is_empty(bmap
)) {
1922 isl_basic_map_free(context
);
1926 bmap
= isl_basic_map_remove_redundancies(bmap
);
1927 context
= isl_basic_map_remove_redundancies(context
);
1930 bmap
= normalize_divs_in_context(bmap
, context
);
1932 context
= isl_basic_map_align_divs(context
, bmap
);
1933 bmap
= isl_basic_map_align_divs(bmap
, context
);
1935 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
1936 isl_basic_map_underlying_set(context
));
1938 return isl_basic_map_overlying_set(bset
, bmap
);
1940 isl_basic_map_free(bmap
);
1941 isl_basic_map_free(context
);
1946 * Assumes context has no implicit divs.
1948 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
1949 __isl_take isl_basic_map
*context
)
1953 if (!map
|| !context
)
1956 if (isl_basic_map_plain_is_empty(context
)) {
1958 return isl_map_from_basic_map(context
);
1961 context
= isl_basic_map_remove_redundancies(context
);
1962 map
= isl_map_cow(map
);
1963 if (!map
|| !context
)
1965 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
1966 map
= isl_map_compute_divs(map
);
1967 for (i
= 0; i
< map
->n
; ++i
)
1968 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
1969 for (i
= map
->n
- 1; i
>= 0; --i
) {
1970 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
1971 isl_basic_map_copy(context
));
1974 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
1975 isl_basic_map_free(map
->p
[i
]);
1976 if (i
!= map
->n
- 1)
1977 map
->p
[i
] = map
->p
[map
->n
- 1];
1981 isl_basic_map_free(context
);
1982 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1986 isl_basic_map_free(context
);
1990 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
1991 __isl_take isl_map
*context
)
1993 context
= isl_map_compute_divs(context
);
1994 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
1997 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
1998 __isl_take isl_map
*context
)
2000 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2003 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2004 struct isl_basic_set
*context
)
2006 return (struct isl_basic_set
*)isl_basic_map_gist(
2007 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2010 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2011 __isl_take isl_basic_set
*context
)
2013 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2014 (struct isl_basic_map
*)context
);
2017 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2018 __isl_take isl_basic_set
*context
)
2020 isl_space
*space
= isl_set_get_space(set
);
2021 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2022 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2023 return isl_set_gist_basic_set(set
, dom_context
);
2026 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2027 __isl_take isl_set
*context
)
2029 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2030 (struct isl_map
*)context
);
2033 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2034 __isl_take isl_set
*context
)
2036 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2037 map_context
= isl_map_intersect_domain(map_context
, context
);
2038 return isl_map_gist(map
, map_context
);
2041 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2042 __isl_take isl_set
*context
)
2044 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2045 map_context
= isl_map_intersect_range(map_context
, context
);
2046 return isl_map_gist(map
, map_context
);
2049 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2050 __isl_take isl_set
*context
)
2052 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2053 map_context
= isl_map_intersect_params(map_context
, context
);
2054 return isl_map_gist(map
, map_context
);
2057 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2058 __isl_take isl_set
*context
)
2060 return isl_map_gist_params(set
, context
);
2063 /* Quick check to see if two basic maps are disjoint.
2064 * In particular, we reduce the equalities and inequalities of
2065 * one basic map in the context of the equalities of the other
2066 * basic map and check if we get a contradiction.
2068 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2069 __isl_keep isl_basic_map
*bmap2
)
2071 struct isl_vec
*v
= NULL
;
2076 if (!bmap1
|| !bmap2
)
2078 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
2080 if (bmap1
->n_div
|| bmap2
->n_div
)
2082 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
2085 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
2088 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
2091 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
2094 compute_elimination_index(bmap1
, elim
);
2095 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
2097 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
2099 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
2100 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2103 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
2105 reduced
= reduced_using_equalities(v
->block
.data
,
2106 bmap2
->ineq
[i
], bmap1
, elim
);
2107 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2108 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2111 compute_elimination_index(bmap2
, elim
);
2112 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
2114 reduced
= reduced_using_equalities(v
->block
.data
,
2115 bmap1
->ineq
[i
], bmap2
, elim
);
2116 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2117 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2133 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2134 __isl_keep isl_basic_set
*bset2
)
2136 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
2137 (struct isl_basic_map
*)bset2
);
2140 int isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
2141 __isl_keep isl_map
*map2
)
2148 if (isl_map_plain_is_equal(map1
, map2
))
2151 for (i
= 0; i
< map1
->n
; ++i
) {
2152 for (j
= 0; j
< map2
->n
; ++j
) {
2153 int d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
2162 int isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
2163 __isl_keep isl_set
*set2
)
2165 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
2166 (struct isl_map
*)set2
);
2169 int isl_set_fast_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2171 return isl_set_plain_is_disjoint(set1
, set2
);
2174 /* Check if we can combine a given div with lower bound l and upper
2175 * bound u with some other div and if so return that other div.
2176 * Otherwise return -1.
2178 * We first check that
2179 * - the bounds are opposites of each other (except for the constant
2181 * - the bounds do not reference any other div
2182 * - no div is defined in terms of this div
2184 * Let m be the size of the range allowed on the div by the bounds.
2185 * That is, the bounds are of the form
2187 * e <= a <= e + m - 1
2189 * with e some expression in the other variables.
2190 * We look for another div b such that no third div is defined in terms
2191 * of this second div b and such that in any constraint that contains
2192 * a (except for the given lower and upper bound), also contains b
2193 * with a coefficient that is m times that of b.
2194 * That is, all constraints (execpt for the lower and upper bound)
2197 * e + f (a + m b) >= 0
2199 * If so, we return b so that "a + m b" can be replaced by
2200 * a single div "c = a + m b".
2202 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2203 unsigned div
, unsigned l
, unsigned u
)
2209 if (bmap
->n_div
<= 1)
2211 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2212 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2214 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2215 bmap
->n_div
- div
- 1) != -1)
2217 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2221 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2222 if (isl_int_is_zero(bmap
->div
[i
][0]))
2224 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2228 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2229 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2230 isl_int_sub(bmap
->ineq
[l
][0],
2231 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2232 bmap
= isl_basic_map_copy(bmap
);
2233 bmap
= isl_basic_map_set_to_empty(bmap
);
2234 isl_basic_map_free(bmap
);
2237 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2238 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2243 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2244 if (isl_int_is_zero(bmap
->div
[j
][0]))
2246 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2249 if (j
< bmap
->n_div
)
2251 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2253 if (j
== l
|| j
== u
)
2255 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2257 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2259 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2260 bmap
->ineq
[j
][1 + dim
+ div
],
2262 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2263 bmap
->ineq
[j
][1 + dim
+ i
]);
2264 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2265 bmap
->ineq
[j
][1 + dim
+ div
],
2270 if (j
< bmap
->n_ineq
)
2275 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2276 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2280 /* Given a lower and an upper bound on div i, construct an inequality
2281 * that when nonnegative ensures that this pair of bounds always allows
2282 * for an integer value of the given div.
2283 * The lower bound is inequality l, while the upper bound is inequality u.
2284 * The constructed inequality is stored in ineq.
2285 * g, fl, fu are temporary scalars.
2287 * Let the upper bound be
2291 * and the lower bound
2295 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2298 * - f_u e_l <= f_u f_l g a <= f_l e_u
2300 * Since all variables are integer valued, this is equivalent to
2302 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2304 * If this interval is at least f_u f_l g, then it contains at least
2305 * one integer value for a.
2306 * That is, the test constraint is
2308 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2310 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2311 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2314 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2316 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2317 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2318 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2319 isl_int_neg(fu
, fu
);
2320 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2321 1 + dim
+ bmap
->n_div
);
2322 isl_int_add(ineq
[0], ineq
[0], fl
);
2323 isl_int_add(ineq
[0], ineq
[0], fu
);
2324 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2325 isl_int_mul(g
, g
, fl
);
2326 isl_int_mul(g
, g
, fu
);
2327 isl_int_sub(ineq
[0], ineq
[0], g
);
2330 /* Remove more kinds of divs that are not strictly needed.
2331 * In particular, if all pairs of lower and upper bounds on a div
2332 * are such that they allow at least one integer value of the div,
2333 * the we can eliminate the div using Fourier-Motzkin without
2334 * introducing any spurious solutions.
2336 static struct isl_basic_map
*drop_more_redundant_divs(
2337 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2339 struct isl_tab
*tab
= NULL
;
2340 struct isl_vec
*vec
= NULL
;
2352 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2353 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2357 tab
= isl_tab_from_basic_map(bmap
, 0);
2362 enum isl_lp_result res
;
2364 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2367 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2373 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2374 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2376 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2377 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2379 construct_test_ineq(bmap
, i
, l
, u
,
2380 vec
->el
, g
, fl
, fu
);
2381 res
= isl_tab_min(tab
, vec
->el
,
2382 bmap
->ctx
->one
, &g
, NULL
, 0);
2383 if (res
== isl_lp_error
)
2385 if (res
== isl_lp_empty
) {
2386 bmap
= isl_basic_map_set_to_empty(bmap
);
2389 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2392 if (u
< bmap
->n_ineq
)
2395 if (l
== bmap
->n_ineq
) {
2415 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
2416 return isl_basic_map_drop_redundant_divs(bmap
);
2419 isl_basic_map_free(bmap
);
2428 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2429 * and the upper bound u, div1 always occurs together with div2 in the form
2430 * (div1 + m div2), where m is the constant range on the variable div1
2431 * allowed by l and u, replace the pair div1 and div2 by a single
2432 * div that is equal to div1 + m div2.
2434 * The new div will appear in the location that contains div2.
2435 * We need to modify all constraints that contain
2436 * div2 = (div - div1) / m
2437 * (If a constraint does not contain div2, it will also not contain div1.)
2438 * If the constraint also contains div1, then we know they appear
2439 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2440 * i.e., the coefficient of div is f.
2442 * Otherwise, we first need to introduce div1 into the constraint.
2451 * A lower bound on div2
2455 * can be replaced by
2457 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2459 * with g = gcd(m,n).
2464 * can be replaced by
2466 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2468 * These constraint are those that we would obtain from eliminating
2469 * div1 using Fourier-Motzkin.
2471 * After all constraints have been modified, we drop the lower and upper
2472 * bound and then drop div1.
2474 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2475 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2480 unsigned dim
, total
;
2483 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2484 total
= 1 + dim
+ bmap
->n_div
;
2489 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2490 isl_int_add_ui(m
, m
, 1);
2492 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2493 if (i
== l
|| i
== u
)
2495 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2497 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2498 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2499 isl_int_divexact(a
, m
, b
);
2500 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2501 if (isl_int_is_pos(b
)) {
2502 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2503 b
, bmap
->ineq
[l
], total
);
2506 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2507 b
, bmap
->ineq
[u
], total
);
2510 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2511 bmap
->ineq
[i
][1 + dim
+ div1
]);
2512 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2519 isl_basic_map_drop_inequality(bmap
, l
);
2520 isl_basic_map_drop_inequality(bmap
, u
);
2522 isl_basic_map_drop_inequality(bmap
, u
);
2523 isl_basic_map_drop_inequality(bmap
, l
);
2525 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2529 /* First check if we can coalesce any pair of divs and
2530 * then continue with dropping more redundant divs.
2532 * We loop over all pairs of lower and upper bounds on a div
2533 * with coefficient 1 and -1, respectively, check if there
2534 * is any other div "c" with which we can coalesce the div
2535 * and if so, perform the coalescing.
2537 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2538 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2543 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2545 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2548 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2549 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2551 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2554 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2556 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2560 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2561 return isl_basic_map_drop_redundant_divs(bmap
);
2566 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2569 return drop_more_redundant_divs(bmap
, pairs
, n
);
2572 /* Remove divs that are not strictly needed.
2573 * In particular, if a div only occurs positively (or negatively)
2574 * in constraints, then it can simply be dropped.
2575 * Also, if a div occurs only occurs in two constraints and if moreover
2576 * those two constraints are opposite to each other, except for the constant
2577 * term and if the sum of the constant terms is such that for any value
2578 * of the other values, there is always at least one integer value of the
2579 * div, i.e., if one plus this sum is greater than or equal to
2580 * the (absolute value) of the coefficent of the div in the constraints,
2581 * then we can also simply drop the div.
2583 * If any divs are left after these simple checks then we move on
2584 * to more complicated cases in drop_more_redundant_divs.
2586 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2587 struct isl_basic_map
*bmap
)
2597 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2598 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2602 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2604 int last_pos
, last_neg
;
2608 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2609 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2610 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2616 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2617 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2621 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2626 pairs
[i
] = pos
* neg
;
2627 if (pairs
[i
] == 0) {
2628 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2629 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2630 isl_basic_map_drop_inequality(bmap
, j
);
2631 bmap
= isl_basic_map_drop_div(bmap
, i
);
2633 return isl_basic_map_drop_redundant_divs(bmap
);
2637 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2638 bmap
->ineq
[last_neg
] + 1,
2642 isl_int_add(bmap
->ineq
[last_pos
][0],
2643 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2644 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2645 bmap
->ineq
[last_pos
][0], 1);
2646 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2647 bmap
->ineq
[last_pos
][1+off
+i
]);
2648 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2649 bmap
->ineq
[last_pos
][0], 1);
2650 isl_int_sub(bmap
->ineq
[last_pos
][0],
2651 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2654 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
2659 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
2660 bmap
= isl_basic_map_simplify(bmap
);
2662 return isl_basic_map_drop_redundant_divs(bmap
);
2664 if (last_pos
> last_neg
) {
2665 isl_basic_map_drop_inequality(bmap
, last_pos
);
2666 isl_basic_map_drop_inequality(bmap
, last_neg
);
2668 isl_basic_map_drop_inequality(bmap
, last_neg
);
2669 isl_basic_map_drop_inequality(bmap
, last_pos
);
2671 bmap
= isl_basic_map_drop_div(bmap
, i
);
2673 return isl_basic_map_drop_redundant_divs(bmap
);
2677 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
2683 isl_basic_map_free(bmap
);
2687 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
2688 struct isl_basic_set
*bset
)
2690 return (struct isl_basic_set
*)
2691 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
2694 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
2700 for (i
= 0; i
< map
->n
; ++i
) {
2701 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
2705 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2712 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
2714 return (struct isl_set
*)
2715 isl_map_drop_redundant_divs((struct isl_map
*)set
);