2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012 Ecole Normale Superieure
5 * Use of this software is governed by the MIT 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 the div expression,
376 * not taking into account the constant term.
377 * That is, if the div is 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 void normalize_div_expression(__isl_keep isl_basic_map
*bmap
, int div
)
390 unsigned total
= isl_basic_map_total_dim(bmap
);
391 isl_ctx
*ctx
= bmap
->ctx
;
393 if (isl_int_is_zero(bmap
->div
[div
][0]))
395 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
396 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
397 if (isl_int_is_one(ctx
->normalize_gcd
))
399 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
401 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
403 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
404 ctx
->normalize_gcd
, total
);
407 /* Remove any common factor in numerator and denominator of a div expression,
408 * not taking into account the constant term.
409 * That is, look for any div of the form
411 * floor((a + m f(x))/(m d))
415 * floor((floor(a/m) + f(x))/d)
417 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
418 * and can therefore not influence the result of the floor.
420 static __isl_give isl_basic_map
*normalize_div_expressions(
421 __isl_take isl_basic_map
*bmap
)
427 if (bmap
->n_div
== 0)
430 for (i
= 0; i
< bmap
->n_div
; ++i
)
431 normalize_div_expression(bmap
, i
);
436 /* Assumes divs have been ordered if keep_divs is set.
438 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
439 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
442 unsigned space_total
;
446 total
= isl_basic_map_total_dim(bmap
);
447 space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
448 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
449 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
450 if (bmap
->eq
[k
] == eq
)
452 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
456 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
457 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
460 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
461 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
465 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
466 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
467 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
470 for (k
= 0; k
< bmap
->n_div
; ++k
) {
471 if (isl_int_is_zero(bmap
->div
[k
][0]))
473 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
477 /* We need to be careful about circular definitions,
478 * so for now we just remove the definition of div k
479 * if the equality contains any divs.
480 * If keep_divs is set, then the divs have been ordered
481 * and we can keep the definition as long as the result
484 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
485 isl_seq_elim(bmap
->div
[k
]+1, eq
,
486 1+pos
, 1+total
, &bmap
->div
[k
][0]);
487 normalize_div_expression(bmap
, k
);
489 isl_seq_clr(bmap
->div
[k
], 1 + total
);
490 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
494 /* Assumes divs have been ordered if keep_divs is set.
496 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
497 unsigned div
, int keep_divs
)
499 unsigned pos
= isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
501 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
503 isl_basic_map_drop_div(bmap
, div
);
506 /* Check if elimination of div "div" using equality "eq" would not
507 * result in a div depending on a later div.
509 static int ok_to_eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
514 unsigned space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
515 unsigned pos
= space_total
+ div
;
517 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
518 if (last_div
< 0 || last_div
<= div
)
521 for (k
= 0; k
<= last_div
; ++k
) {
522 if (isl_int_is_zero(bmap
->div
[k
][0]))
524 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
531 /* Elimininate divs based on equalities
533 static struct isl_basic_map
*eliminate_divs_eq(
534 struct isl_basic_map
*bmap
, int *progress
)
541 bmap
= isl_basic_map_order_divs(bmap
);
546 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
548 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
549 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
550 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
551 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
553 if (!ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
))
557 eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
558 isl_basic_map_drop_equality(bmap
, i
);
563 return eliminate_divs_eq(bmap
, progress
);
567 /* Elimininate divs based on inequalities
569 static struct isl_basic_map
*eliminate_divs_ineq(
570 struct isl_basic_map
*bmap
, int *progress
)
581 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
583 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
584 for (i
= 0; i
< bmap
->n_eq
; ++i
)
585 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
589 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
590 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
592 if (i
< bmap
->n_ineq
)
595 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
596 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
598 bmap
= isl_basic_map_drop_div(bmap
, d
);
605 struct isl_basic_map
*isl_basic_map_gauss(
606 struct isl_basic_map
*bmap
, int *progress
)
614 bmap
= isl_basic_map_order_divs(bmap
);
619 total
= isl_basic_map_total_dim(bmap
);
620 total_var
= total
- bmap
->n_div
;
622 last_var
= total
- 1;
623 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
624 for (; last_var
>= 0; --last_var
) {
625 for (k
= done
; k
< bmap
->n_eq
; ++k
)
626 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
634 swap_equality(bmap
, k
, done
);
635 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
636 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
638 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
641 if (last_var
>= total_var
&&
642 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
643 unsigned div
= last_var
- total_var
;
644 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
645 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
646 isl_int_set(bmap
->div
[div
][0],
647 bmap
->eq
[done
][1+last_var
]);
650 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
653 if (done
== bmap
->n_eq
)
655 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
656 if (isl_int_is_zero(bmap
->eq
[k
][0]))
658 return isl_basic_map_set_to_empty(bmap
);
660 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
664 struct isl_basic_set
*isl_basic_set_gauss(
665 struct isl_basic_set
*bset
, int *progress
)
667 return (struct isl_basic_set
*)isl_basic_map_gauss(
668 (struct isl_basic_map
*)bset
, progress
);
672 static unsigned int round_up(unsigned int v
)
683 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
684 struct isl_basic_map
*bmap
, int k
)
687 unsigned total
= isl_basic_map_total_dim(bmap
);
688 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
689 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
690 if (&bmap
->ineq
[k
] != index
[h
] &&
691 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
696 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
697 struct isl_basic_set
*bset
, int k
)
699 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
702 /* If we can eliminate more than one div, then we need to make
703 * sure we do it from last div to first div, in order not to
704 * change the position of the other divs that still need to
707 static struct isl_basic_map
*remove_duplicate_divs(
708 struct isl_basic_map
*bmap
, int *progress
)
720 bmap
= isl_basic_map_order_divs(bmap
);
721 if (!bmap
|| bmap
->n_div
<= 1)
724 total_var
= isl_space_dim(bmap
->dim
, isl_dim_all
);
725 total
= total_var
+ bmap
->n_div
;
728 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
729 if (!isl_int_is_zero(bmap
->div
[k
][0]))
734 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
735 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
736 bits
= ffs(size
) - 1;
737 index
= isl_calloc_array(ctx
, int, size
);
740 eq
= isl_blk_alloc(ctx
, 1+total
);
741 if (isl_blk_is_error(eq
))
744 isl_seq_clr(eq
.data
, 1+total
);
745 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
746 for (--k
; k
>= 0; --k
) {
749 if (isl_int_is_zero(bmap
->div
[k
][0]))
752 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
753 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
754 if (isl_seq_eq(bmap
->div
[k
],
755 bmap
->div
[index
[h
]-1], 2+total
))
764 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
768 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
769 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
770 eliminate_div(bmap
, eq
.data
, l
, 1);
771 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
772 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
775 isl_blk_free(ctx
, eq
);
782 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
787 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
788 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
789 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
793 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
799 /* Normalize divs that appear in equalities.
801 * In particular, we assume that bmap contains some equalities
806 * and we want to replace the set of e_i by a minimal set and
807 * such that the new e_i have a canonical representation in terms
809 * If any of the equalities involves more than one divs, then
810 * we currently simply bail out.
812 * Let us first additionally assume that all equalities involve
813 * a div. The equalities then express modulo constraints on the
814 * remaining variables and we can use "parameter compression"
815 * to find a minimal set of constraints. The result is a transformation
817 * x = T(x') = x_0 + G x'
819 * with G a lower-triangular matrix with all elements below the diagonal
820 * non-negative and smaller than the diagonal element on the same row.
821 * We first normalize x_0 by making the same property hold in the affine
823 * The rows i of G with a 1 on the diagonal do not impose any modulo
824 * constraint and simply express x_i = x'_i.
825 * For each of the remaining rows i, we introduce a div and a corresponding
826 * equality. In particular
828 * g_ii e_j = x_i - g_i(x')
830 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
831 * corresponding div (if g_kk != 1).
833 * If there are any equalities not involving any div, then we
834 * first apply a variable compression on the variables x:
836 * x = C x'' x'' = C_2 x
838 * and perform the above parameter compression on A C instead of on A.
839 * The resulting compression is then of the form
841 * x'' = T(x') = x_0 + G x'
843 * and in constructing the new divs and the corresponding equalities,
844 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
845 * by the corresponding row from C_2.
847 static struct isl_basic_map
*normalize_divs(
848 struct isl_basic_map
*bmap
, int *progress
)
855 struct isl_mat
*T
= NULL
;
856 struct isl_mat
*C
= NULL
;
857 struct isl_mat
*C2
= NULL
;
865 if (bmap
->n_div
== 0)
871 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
874 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
875 div_eq
= n_pure_div_eq(bmap
);
879 if (div_eq
< bmap
->n_eq
) {
880 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
881 bmap
->n_eq
- div_eq
, 0, 1 + total
);
882 C
= isl_mat_variable_compression(B
, &C2
);
886 bmap
= isl_basic_map_set_to_empty(bmap
);
893 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
896 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
897 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
899 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
901 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
904 B
= isl_mat_product(B
, C
);
908 T
= isl_mat_parameter_compression(B
, d
);
912 bmap
= isl_basic_map_set_to_empty(bmap
);
918 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
919 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
920 if (isl_int_is_zero(v
))
922 isl_mat_col_submul(T
, 0, v
, 1 + i
);
925 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
928 /* We have to be careful because dropping equalities may reorder them */
930 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
931 for (i
= 0; i
< bmap
->n_eq
; ++i
)
932 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
934 if (i
< bmap
->n_eq
) {
935 bmap
= isl_basic_map_drop_div(bmap
, j
);
936 isl_basic_map_drop_equality(bmap
, i
);
942 for (i
= 1; i
< T
->n_row
; ++i
) {
943 if (isl_int_is_one(T
->row
[i
][i
]))
948 if (needed
> dropped
) {
949 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
954 for (i
= 1; i
< T
->n_row
; ++i
) {
955 if (isl_int_is_one(T
->row
[i
][i
]))
957 k
= isl_basic_map_alloc_div(bmap
);
958 pos
[i
] = 1 + total
+ k
;
959 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
960 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
962 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
964 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
965 for (j
= 0; j
< i
; ++j
) {
966 if (isl_int_is_zero(T
->row
[i
][j
]))
968 if (pos
[j
] < T
->n_row
&& C2
)
969 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
970 C2
->row
[pos
[j
]], 1 + total
);
972 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
975 j
= isl_basic_map_alloc_equality(bmap
);
976 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
977 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
986 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
996 static struct isl_basic_map
*set_div_from_lower_bound(
997 struct isl_basic_map
*bmap
, int div
, int ineq
)
999 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1001 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1002 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1003 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1004 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1005 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1010 /* Check whether it is ok to define a div based on an inequality.
1011 * To avoid the introduction of circular definitions of divs, we
1012 * do not allow such a definition if the resulting expression would refer to
1013 * any other undefined divs or if any known div is defined in
1014 * terms of the unknown div.
1016 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
1020 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1022 /* Not defined in terms of unknown divs */
1023 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1026 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1028 if (isl_int_is_zero(bmap
->div
[j
][0]))
1032 /* No other div defined in terms of this one => avoid loops */
1033 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1036 if (isl_int_is_zero(bmap
->div
[j
][0]))
1038 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1045 /* Given two constraints "k" and "l" that are opposite to each other,
1046 * except for the constant term, check if we can use them
1047 * to obtain an expression for one of the hitherto unknown divs.
1048 * "sum" is the sum of the constant terms of the constraints.
1049 * If this sum is strictly smaller than the coefficient of one
1050 * of the divs, then this pair can be used define the div.
1051 * To avoid the introduction of circular definitions of divs, we
1052 * do not use the pair if the resulting expression would refer to
1053 * any other undefined divs or if any known div is defined in
1054 * terms of the unknown div.
1056 static struct isl_basic_map
*check_for_div_constraints(
1057 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
1060 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1062 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1063 if (!isl_int_is_zero(bmap
->div
[i
][0]))
1065 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1067 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1069 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1071 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1072 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1074 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1082 static struct isl_basic_map
*remove_duplicate_constraints(
1083 struct isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1089 unsigned total
= isl_basic_map_total_dim(bmap
);
1093 if (!bmap
|| bmap
->n_ineq
<= 1)
1096 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
1097 bits
= ffs(size
) - 1;
1098 ctx
= isl_basic_map_get_ctx(bmap
);
1099 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1103 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
1104 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1105 h
= hash_index(index
, size
, bits
, bmap
, k
);
1107 index
[h
] = &bmap
->ineq
[k
];
1112 l
= index
[h
] - &bmap
->ineq
[0];
1113 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1114 swap_inequality(bmap
, k
, l
);
1115 isl_basic_map_drop_inequality(bmap
, k
);
1119 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1120 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1121 h
= hash_index(index
, size
, bits
, bmap
, k
);
1122 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1125 l
= index
[h
] - &bmap
->ineq
[0];
1126 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1127 if (isl_int_is_pos(sum
)) {
1129 bmap
= check_for_div_constraints(bmap
, k
, l
,
1133 if (isl_int_is_zero(sum
)) {
1134 /* We need to break out of the loop after these
1135 * changes since the contents of the hash
1136 * will no longer be valid.
1137 * Plus, we probably we want to regauss first.
1141 isl_basic_map_drop_inequality(bmap
, l
);
1142 isl_basic_map_inequality_to_equality(bmap
, k
);
1144 bmap
= isl_basic_map_set_to_empty(bmap
);
1154 /* Eliminate knowns divs from constraints where they appear with
1155 * a (positive or negative) unit coefficient.
1159 * floor(e/m) + f >= 0
1167 * -floor(e/m) + f >= 0
1171 * -e + m f + m - 1 >= 0
1173 * The first conversion is valid because floor(e/m) >= -f is equivalent
1174 * to e/m >= -f because -f is an integral expression.
1175 * The second conversion follows from the fact that
1177 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1180 * We skip integral divs, i.e., those with denominator 1, as we would
1181 * risk eliminating the div from the div constraints. We do not need
1182 * to handle those divs here anyway since the div constraints will turn
1183 * out to form an equality and this equality can then be use to eliminate
1184 * the div from all constraints.
1186 static __isl_give isl_basic_map
*eliminate_unit_divs(
1187 __isl_take isl_basic_map
*bmap
, int *progress
)
1196 ctx
= isl_basic_map_get_ctx(bmap
);
1197 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1199 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1200 if (isl_int_is_zero(bmap
->div
[i
][0]))
1202 if (isl_int_is_one(bmap
->div
[i
][0]))
1204 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1207 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1208 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1213 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1214 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1216 isl_seq_combine(bmap
->ineq
[j
],
1217 ctx
->negone
, bmap
->div
[i
] + 1,
1218 bmap
->div
[i
][0], bmap
->ineq
[j
],
1219 total
+ bmap
->n_div
);
1221 isl_seq_combine(bmap
->ineq
[j
],
1222 ctx
->one
, bmap
->div
[i
] + 1,
1223 bmap
->div
[i
][0], bmap
->ineq
[j
],
1224 total
+ bmap
->n_div
);
1226 isl_int_add(bmap
->ineq
[j
][0],
1227 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1228 isl_int_sub_ui(bmap
->ineq
[j
][0],
1229 bmap
->ineq
[j
][0], 1);
1237 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1244 bmap
= isl_basic_map_normalize_constraints(bmap
);
1245 bmap
= normalize_div_expressions(bmap
);
1246 bmap
= remove_duplicate_divs(bmap
, &progress
);
1247 bmap
= eliminate_unit_divs(bmap
, &progress
);
1248 bmap
= eliminate_divs_eq(bmap
, &progress
);
1249 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1250 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1251 /* requires equalities in normal form */
1252 bmap
= normalize_divs(bmap
, &progress
);
1253 bmap
= remove_duplicate_constraints(bmap
, &progress
, 1);
1258 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1260 return (struct isl_basic_set
*)
1261 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1265 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1266 isl_int
*constraint
, unsigned div
)
1273 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1275 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1277 isl_int_sub(bmap
->div
[div
][1],
1278 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1279 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1280 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1281 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1282 isl_int_add(bmap
->div
[div
][1],
1283 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1286 if (isl_seq_first_non_zero(constraint
+pos
+1,
1287 bmap
->n_div
-div
-1) != -1)
1289 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1290 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1292 if (isl_seq_first_non_zero(constraint
+pos
+1,
1293 bmap
->n_div
-div
-1) != -1)
1301 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1302 isl_int
*constraint
, unsigned div
)
1304 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1308 /* If the only constraints a div d=floor(f/m)
1309 * appears in are its two defining constraints
1312 * -(f - (m - 1)) + m d >= 0
1314 * then it can safely be removed.
1316 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1319 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1321 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1322 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1325 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1326 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1328 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1332 for (i
= 0; i
< bmap
->n_div
; ++i
)
1333 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1340 * Remove divs that don't occur in any of the constraints or other divs.
1341 * These can arise when dropping some of the variables in a quast
1342 * returned by piplib.
1344 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1351 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1352 if (!div_is_redundant(bmap
, i
))
1354 bmap
= isl_basic_map_drop_div(bmap
, i
);
1359 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1361 bmap
= remove_redundant_divs(bmap
);
1364 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1368 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1370 return (struct isl_basic_set
*)
1371 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1374 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1380 for (i
= 0; i
< set
->n
; ++i
) {
1381 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1391 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1397 for (i
= 0; i
< map
->n
; ++i
) {
1398 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1402 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1410 /* Remove definition of any div that is defined in terms of the given variable.
1411 * The div itself is not removed. Functions such as
1412 * eliminate_divs_ineq depend on the other divs remaining in place.
1414 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1419 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1420 if (isl_int_is_zero(bmap
->div
[i
][0]))
1422 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1424 isl_int_set_si(bmap
->div
[i
][0], 0);
1429 /* Eliminate the specified variables from the constraints using
1430 * Fourier-Motzkin. The variables themselves are not removed.
1432 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1433 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1444 total
= isl_basic_map_total_dim(bmap
);
1446 bmap
= isl_basic_map_cow(bmap
);
1447 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1448 bmap
= remove_dependent_vars(bmap
, d
);
1450 for (d
= pos
+ n
- 1;
1451 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1452 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1453 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1454 int n_lower
, n_upper
;
1457 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1458 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1460 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1461 isl_basic_map_drop_equality(bmap
, i
);
1469 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1470 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1472 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1475 bmap
= isl_basic_map_extend_constraints(bmap
,
1476 0, n_lower
* n_upper
);
1479 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1481 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1484 for (j
= 0; j
< i
; ++j
) {
1485 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1488 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1489 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1491 k
= isl_basic_map_alloc_inequality(bmap
);
1494 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1496 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1497 1+d
, 1+total
, NULL
);
1499 isl_basic_map_drop_inequality(bmap
, i
);
1502 if (n_lower
> 0 && n_upper
> 0) {
1503 bmap
= isl_basic_map_normalize_constraints(bmap
);
1504 bmap
= remove_duplicate_constraints(bmap
, NULL
, 0);
1505 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1506 bmap
= isl_basic_map_remove_redundancies(bmap
);
1510 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1514 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1516 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1519 isl_basic_map_free(bmap
);
1523 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1524 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1526 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1527 (struct isl_basic_map
*)bset
, pos
, n
);
1530 /* Eliminate the specified n dimensions starting at first from the
1531 * constraints, without removing the dimensions from the space.
1532 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1533 * Otherwise, they are projected out and the original space is restored.
1535 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1536 __isl_take isl_basic_map
*bmap
,
1537 enum isl_dim_type type
, unsigned first
, unsigned n
)
1546 if (first
+ n
> isl_basic_map_dim(bmap
, type
) || first
+ n
< first
)
1547 isl_die(bmap
->ctx
, isl_error_invalid
,
1548 "index out of bounds", goto error
);
1550 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1551 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1552 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1553 return isl_basic_map_finalize(bmap
);
1556 space
= isl_basic_map_get_space(bmap
);
1557 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1558 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1559 bmap
= isl_basic_map_reset_space(bmap
, space
);
1562 isl_basic_map_free(bmap
);
1566 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1567 __isl_take isl_basic_set
*bset
,
1568 enum isl_dim_type type
, unsigned first
, unsigned n
)
1570 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1573 /* Don't assume equalities are in order, because align_divs
1574 * may have changed the order of the divs.
1576 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1581 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1582 for (d
= 0; d
< total
; ++d
)
1584 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1585 for (d
= total
- 1; d
>= 0; --d
) {
1586 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1594 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1596 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1599 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1600 struct isl_basic_map
*bmap
, int *elim
)
1606 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1607 for (d
= total
- 1; d
>= 0; --d
) {
1608 if (isl_int_is_zero(src
[1+d
]))
1613 isl_seq_cpy(dst
, src
, 1 + total
);
1616 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1621 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1622 struct isl_basic_set
*bset
, int *elim
)
1624 return reduced_using_equalities(dst
, src
,
1625 (struct isl_basic_map
*)bset
, elim
);
1628 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1629 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1634 if (!bset
|| !context
)
1637 if (context
->n_eq
== 0) {
1638 isl_basic_set_free(context
);
1642 bset
= isl_basic_set_cow(bset
);
1646 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1649 set_compute_elimination_index(context
, elim
);
1650 for (i
= 0; i
< bset
->n_eq
; ++i
)
1651 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1653 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1654 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1656 isl_basic_set_free(context
);
1658 bset
= isl_basic_set_simplify(bset
);
1659 bset
= isl_basic_set_finalize(bset
);
1662 isl_basic_set_free(bset
);
1663 isl_basic_set_free(context
);
1667 static struct isl_basic_set
*remove_shifted_constraints(
1668 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1679 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1680 bits
= ffs(size
) - 1;
1681 ctx
= isl_basic_set_get_ctx(bset
);
1682 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1686 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1687 h
= set_hash_index(index
, size
, bits
, context
, k
);
1688 index
[h
] = &context
->ineq
[k
];
1690 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1691 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1694 l
= index
[h
] - &context
->ineq
[0];
1695 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1697 bset
= isl_basic_set_cow(bset
);
1700 isl_basic_set_drop_inequality(bset
, k
);
1710 /* Remove all information from bset that is redundant in the context
1711 * of context. Both bset and context are assumed to be full-dimensional.
1713 * We first * remove the inequalities from "bset"
1714 * that are obviously redundant with respect to some inequality in "context".
1716 * If there are any inequalities left, we construct a tableau for
1717 * the context and then add the inequalities of "bset".
1718 * Before adding these inequalities, we freeze all constraints such that
1719 * they won't be considered redundant in terms of the constraints of "bset".
1720 * Then we detect all redundant constraints (among the
1721 * constraints that weren't frozen), first by checking for redundancy in the
1722 * the tableau and then by checking if replacing a constraint by its negation
1723 * would lead to an empty set. This last step is fairly expensive
1724 * and could be optimized by more reuse of the tableau.
1725 * Finally, we update bset according to the results.
1727 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1728 __isl_take isl_basic_set
*context
)
1731 isl_basic_set
*combined
= NULL
;
1732 struct isl_tab
*tab
= NULL
;
1733 unsigned context_ineq
;
1736 if (!bset
|| !context
)
1739 if (isl_basic_set_is_universe(bset
)) {
1740 isl_basic_set_free(context
);
1744 if (isl_basic_set_is_universe(context
)) {
1745 isl_basic_set_free(context
);
1749 bset
= remove_shifted_constraints(bset
, context
);
1752 if (bset
->n_ineq
== 0)
1755 context_ineq
= context
->n_ineq
;
1756 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1757 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
1758 tab
= isl_tab_from_basic_set(combined
, 0);
1759 for (i
= 0; i
< context_ineq
; ++i
)
1760 if (isl_tab_freeze_constraint(tab
, i
) < 0)
1762 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1763 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1764 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
1766 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1770 if (isl_tab_detect_redundant(tab
) < 0)
1772 total
= isl_basic_set_total_dim(bset
);
1773 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
1775 if (tab
->con
[i
].is_redundant
)
1777 tab
->con
[i
].is_redundant
= 1;
1778 combined
= isl_basic_set_dup(bset
);
1779 combined
= isl_basic_set_update_from_tab(combined
, tab
);
1780 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
1781 k
= isl_basic_set_alloc_inequality(combined
);
1784 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
1785 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
1786 is_empty
= isl_basic_set_is_empty(combined
);
1789 isl_basic_set_free(combined
);
1792 tab
->con
[i
].is_redundant
= 0;
1794 for (i
= 0; i
< context_ineq
; ++i
)
1795 tab
->con
[i
].is_redundant
= 1;
1796 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1798 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1799 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1804 bset
= isl_basic_set_simplify(bset
);
1805 bset
= isl_basic_set_finalize(bset
);
1806 isl_basic_set_free(context
);
1810 isl_basic_set_free(combined
);
1811 isl_basic_set_free(context
);
1812 isl_basic_set_free(bset
);
1816 /* Remove all information from bset that is redundant in the context
1817 * of context. In particular, equalities that are linear combinations
1818 * of those in context are removed. Then the inequalities that are
1819 * redundant in the context of the equalities and inequalities of
1820 * context are removed.
1822 * We first compute the integer affine hull of the intersection,
1823 * compute the gist inside this affine hull and then add back
1824 * those equalities that are not implied by the context.
1826 * If two constraints are mutually redundant, then uset_gist_full
1827 * will remove the second of those constraints. We therefore first
1828 * sort the constraints so that constraints not involving existentially
1829 * quantified variables are given precedence over those that do.
1830 * We have to perform this sorting before the variable compression,
1831 * because that may effect the order of the variables.
1833 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
1834 __isl_take isl_basic_set
*context
)
1839 isl_basic_set
*aff_context
;
1842 if (!bset
|| !context
)
1845 bset
= isl_basic_set_intersect(bset
, isl_basic_set_copy(context
));
1846 if (isl_basic_set_plain_is_empty(bset
)) {
1847 isl_basic_set_free(context
);
1850 bset
= isl_basic_set_sort_constraints(bset
);
1851 aff
= isl_basic_set_affine_hull(isl_basic_set_copy(bset
));
1854 if (isl_basic_set_plain_is_empty(aff
)) {
1855 isl_basic_set_free(aff
);
1856 isl_basic_set_free(context
);
1859 if (aff
->n_eq
== 0) {
1860 isl_basic_set_free(aff
);
1861 return uset_gist_full(bset
, context
);
1863 total
= isl_basic_set_total_dim(bset
);
1864 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
1865 eq
= isl_mat_cow(eq
);
1866 T
= isl_mat_variable_compression(eq
, &T2
);
1867 if (T
&& T
->n_col
== 0) {
1870 isl_basic_set_free(context
);
1871 isl_basic_set_free(aff
);
1872 return isl_basic_set_set_to_empty(bset
);
1875 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
1877 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
1878 context
= isl_basic_set_preimage(context
, T
);
1880 bset
= uset_gist_full(bset
, context
);
1881 bset
= isl_basic_set_preimage(bset
, T2
);
1882 bset
= isl_basic_set_intersect(bset
, aff
);
1883 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
1886 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1887 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1892 isl_basic_set_free(bset
);
1893 isl_basic_set_free(context
);
1897 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1898 * We simply add the equalities in context to bmap and then do a regular
1899 * div normalizations. Better results can be obtained by normalizing
1900 * only the divs in bmap than do not also appear in context.
1901 * We need to be careful to reduce the divs using the equalities
1902 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1903 * spurious constraints.
1905 static struct isl_basic_map
*normalize_divs_in_context(
1906 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
1909 unsigned total_context
;
1912 div_eq
= n_pure_div_eq(bmap
);
1916 if (context
->n_div
> 0)
1917 bmap
= isl_basic_map_align_divs(bmap
, context
);
1919 total_context
= isl_basic_map_total_dim(context
);
1920 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
1921 for (i
= 0; i
< context
->n_eq
; ++i
) {
1923 k
= isl_basic_map_alloc_equality(bmap
);
1924 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
1925 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
1926 isl_basic_map_total_dim(bmap
) - total_context
);
1928 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1929 bmap
= normalize_divs(bmap
, NULL
);
1930 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1934 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
1935 struct isl_basic_map
*context
)
1937 struct isl_basic_set
*bset
;
1939 if (!bmap
|| !context
)
1942 if (isl_basic_map_is_universe(bmap
)) {
1943 isl_basic_map_free(context
);
1946 if (isl_basic_map_plain_is_empty(context
)) {
1947 isl_basic_map_free(bmap
);
1950 if (isl_basic_map_plain_is_empty(bmap
)) {
1951 isl_basic_map_free(context
);
1955 bmap
= isl_basic_map_remove_redundancies(bmap
);
1956 context
= isl_basic_map_remove_redundancies(context
);
1959 bmap
= normalize_divs_in_context(bmap
, context
);
1961 context
= isl_basic_map_align_divs(context
, bmap
);
1962 bmap
= isl_basic_map_align_divs(bmap
, context
);
1964 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
1965 isl_basic_map_underlying_set(context
));
1967 return isl_basic_map_overlying_set(bset
, bmap
);
1969 isl_basic_map_free(bmap
);
1970 isl_basic_map_free(context
);
1975 * Assumes context has no implicit divs.
1977 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
1978 __isl_take isl_basic_map
*context
)
1982 if (!map
|| !context
)
1985 if (isl_basic_map_plain_is_empty(context
)) {
1987 return isl_map_from_basic_map(context
);
1990 context
= isl_basic_map_remove_redundancies(context
);
1991 map
= isl_map_cow(map
);
1992 if (!map
|| !context
)
1994 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
1995 map
= isl_map_compute_divs(map
);
1996 for (i
= 0; i
< map
->n
; ++i
)
1997 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
1998 for (i
= map
->n
- 1; i
>= 0; --i
) {
1999 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
2000 isl_basic_map_copy(context
));
2003 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
2004 isl_basic_map_free(map
->p
[i
]);
2005 if (i
!= map
->n
- 1)
2006 map
->p
[i
] = map
->p
[map
->n
- 1];
2010 isl_basic_map_free(context
);
2011 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2015 isl_basic_map_free(context
);
2019 /* Return a map that has the same intersection with "context" as "map"
2020 * and that as "simple" as possible.
2022 * If "map" is already the universe, then we cannot make it any simpler.
2023 * Similarly, if "context" is the universe, then we cannot exploit it
2025 * If "map" and "context" are identical to each other, then we can
2026 * return the corresponding universe.
2028 * If none of these cases apply, we have to work a bit harder.
2030 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
2031 __isl_take isl_map
*context
)
2036 is_universe
= isl_map_plain_is_universe(map
);
2037 if (is_universe
>= 0 && !is_universe
)
2038 is_universe
= isl_map_plain_is_universe(context
);
2039 if (is_universe
< 0)
2042 isl_map_free(context
);
2046 equal
= isl_map_plain_is_equal(map
, context
);
2050 isl_map
*res
= isl_map_universe(isl_map_get_space(map
));
2052 isl_map_free(context
);
2056 context
= isl_map_compute_divs(context
);
2057 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
2060 isl_map_free(context
);
2064 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
2065 __isl_take isl_map
*context
)
2067 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2070 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2071 struct isl_basic_set
*context
)
2073 return (struct isl_basic_set
*)isl_basic_map_gist(
2074 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2077 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2078 __isl_take isl_basic_set
*context
)
2080 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2081 (struct isl_basic_map
*)context
);
2084 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2085 __isl_take isl_basic_set
*context
)
2087 isl_space
*space
= isl_set_get_space(set
);
2088 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2089 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2090 return isl_set_gist_basic_set(set
, dom_context
);
2093 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2094 __isl_take isl_set
*context
)
2096 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2097 (struct isl_map
*)context
);
2100 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2101 __isl_take isl_set
*context
)
2103 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2104 map_context
= isl_map_intersect_domain(map_context
, context
);
2105 return isl_map_gist(map
, map_context
);
2108 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2109 __isl_take isl_set
*context
)
2111 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2112 map_context
= isl_map_intersect_range(map_context
, context
);
2113 return isl_map_gist(map
, map_context
);
2116 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2117 __isl_take isl_set
*context
)
2119 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2120 map_context
= isl_map_intersect_params(map_context
, context
);
2121 return isl_map_gist(map
, map_context
);
2124 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2125 __isl_take isl_set
*context
)
2127 return isl_map_gist_params(set
, context
);
2130 /* Quick check to see if two basic maps are disjoint.
2131 * In particular, we reduce the equalities and inequalities of
2132 * one basic map in the context of the equalities of the other
2133 * basic map and check if we get a contradiction.
2135 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2136 __isl_keep isl_basic_map
*bmap2
)
2138 struct isl_vec
*v
= NULL
;
2143 if (!bmap1
|| !bmap2
)
2145 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
2147 if (bmap1
->n_div
|| bmap2
->n_div
)
2149 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
2152 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
2155 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
2158 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
2161 compute_elimination_index(bmap1
, elim
);
2162 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
2164 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
2166 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
2167 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2170 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
2172 reduced
= reduced_using_equalities(v
->block
.data
,
2173 bmap2
->ineq
[i
], bmap1
, elim
);
2174 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2175 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2178 compute_elimination_index(bmap2
, elim
);
2179 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
2181 reduced
= reduced_using_equalities(v
->block
.data
,
2182 bmap1
->ineq
[i
], bmap2
, elim
);
2183 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2184 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2200 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2201 __isl_keep isl_basic_set
*bset2
)
2203 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
2204 (struct isl_basic_map
*)bset2
);
2207 /* Are "map1" and "map2" obviously disjoint?
2209 * If one of them is empty or if they live in different spaces (ignoring
2210 * parameters), then they are clearly disjoint.
2212 * If they have different parameters, then we skip any further tests.
2214 * If they are obviously equal, but not obviously empty, then we will
2215 * not be able to detect if they are disjoint.
2217 * Otherwise we check if each basic map in "map1" is obviously disjoint
2218 * from each basic map in "map2".
2220 int isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
2221 __isl_keep isl_map
*map2
)
2231 disjoint
= isl_map_plain_is_empty(map1
);
2232 if (disjoint
< 0 || disjoint
)
2235 disjoint
= isl_map_plain_is_empty(map2
);
2236 if (disjoint
< 0 || disjoint
)
2239 match
= isl_space_tuple_match(map1
->dim
, isl_dim_in
,
2240 map2
->dim
, isl_dim_in
);
2241 if (match
< 0 || !match
)
2242 return match
< 0 ? -1 : 1;
2244 match
= isl_space_tuple_match(map1
->dim
, isl_dim_out
,
2245 map2
->dim
, isl_dim_out
);
2246 if (match
< 0 || !match
)
2247 return match
< 0 ? -1 : 1;
2249 match
= isl_space_match(map1
->dim
, isl_dim_param
,
2250 map2
->dim
, isl_dim_param
);
2251 if (match
< 0 || !match
)
2252 return match
< 0 ? -1 : 0;
2254 intersect
= isl_map_plain_is_equal(map1
, map2
);
2255 if (intersect
< 0 || intersect
)
2256 return intersect
< 0 ? -1 : 0;
2258 for (i
= 0; i
< map1
->n
; ++i
) {
2259 for (j
= 0; j
< map2
->n
; ++j
) {
2260 int d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
2269 /* Are "map1" and "map2" disjoint?
2271 * They are disjoint if they are "obviously disjoint" or if one of them
2272 * is empty. Otherwise, they are not disjoint if one of them is universal.
2273 * If none of these cases apply, we compute the intersection and see if
2274 * the result is empty.
2276 int isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
2282 disjoint
= isl_map_plain_is_disjoint(map1
, map2
);
2283 if (disjoint
< 0 || disjoint
)
2286 disjoint
= isl_map_is_empty(map1
);
2287 if (disjoint
< 0 || disjoint
)
2290 disjoint
= isl_map_is_empty(map2
);
2291 if (disjoint
< 0 || disjoint
)
2294 intersect
= isl_map_plain_is_universe(map1
);
2295 if (intersect
< 0 || intersect
)
2296 return intersect
< 0 ? -1 : 0;
2298 intersect
= isl_map_plain_is_universe(map2
);
2299 if (intersect
< 0 || intersect
)
2300 return intersect
< 0 ? -1 : 0;
2302 test
= isl_map_intersect(isl_map_copy(map1
), isl_map_copy(map2
));
2303 disjoint
= isl_map_is_empty(test
);
2309 int isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
2310 __isl_keep isl_set
*set2
)
2312 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
2313 (struct isl_map
*)set2
);
2316 /* Are "set1" and "set2" disjoint?
2318 int isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2320 return isl_map_is_disjoint(set1
, set2
);
2323 int isl_set_fast_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2325 return isl_set_plain_is_disjoint(set1
, set2
);
2328 /* Check if we can combine a given div with lower bound l and upper
2329 * bound u with some other div and if so return that other div.
2330 * Otherwise return -1.
2332 * We first check that
2333 * - the bounds are opposites of each other (except for the constant
2335 * - the bounds do not reference any other div
2336 * - no div is defined in terms of this div
2338 * Let m be the size of the range allowed on the div by the bounds.
2339 * That is, the bounds are of the form
2341 * e <= a <= e + m - 1
2343 * with e some expression in the other variables.
2344 * We look for another div b such that no third div is defined in terms
2345 * of this second div b and such that in any constraint that contains
2346 * a (except for the given lower and upper bound), also contains b
2347 * with a coefficient that is m times that of b.
2348 * That is, all constraints (execpt for the lower and upper bound)
2351 * e + f (a + m b) >= 0
2353 * If so, we return b so that "a + m b" can be replaced by
2354 * a single div "c = a + m b".
2356 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2357 unsigned div
, unsigned l
, unsigned u
)
2363 if (bmap
->n_div
<= 1)
2365 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2366 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2368 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2369 bmap
->n_div
- div
- 1) != -1)
2371 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2375 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2376 if (isl_int_is_zero(bmap
->div
[i
][0]))
2378 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2382 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2383 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2384 isl_int_sub(bmap
->ineq
[l
][0],
2385 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2386 bmap
= isl_basic_map_copy(bmap
);
2387 bmap
= isl_basic_map_set_to_empty(bmap
);
2388 isl_basic_map_free(bmap
);
2391 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2392 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2397 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2398 if (isl_int_is_zero(bmap
->div
[j
][0]))
2400 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2403 if (j
< bmap
->n_div
)
2405 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2407 if (j
== l
|| j
== u
)
2409 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2411 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2413 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2414 bmap
->ineq
[j
][1 + dim
+ div
],
2416 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2417 bmap
->ineq
[j
][1 + dim
+ i
]);
2418 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2419 bmap
->ineq
[j
][1 + dim
+ div
],
2424 if (j
< bmap
->n_ineq
)
2429 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2430 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2434 /* Given a lower and an upper bound on div i, construct an inequality
2435 * that when nonnegative ensures that this pair of bounds always allows
2436 * for an integer value of the given div.
2437 * The lower bound is inequality l, while the upper bound is inequality u.
2438 * The constructed inequality is stored in ineq.
2439 * g, fl, fu are temporary scalars.
2441 * Let the upper bound be
2445 * and the lower bound
2449 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2452 * - f_u e_l <= f_u f_l g a <= f_l e_u
2454 * Since all variables are integer valued, this is equivalent to
2456 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2458 * If this interval is at least f_u f_l g, then it contains at least
2459 * one integer value for a.
2460 * That is, the test constraint is
2462 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2464 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2465 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2468 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2470 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2471 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2472 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2473 isl_int_neg(fu
, fu
);
2474 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2475 1 + dim
+ bmap
->n_div
);
2476 isl_int_add(ineq
[0], ineq
[0], fl
);
2477 isl_int_add(ineq
[0], ineq
[0], fu
);
2478 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2479 isl_int_mul(g
, g
, fl
);
2480 isl_int_mul(g
, g
, fu
);
2481 isl_int_sub(ineq
[0], ineq
[0], g
);
2484 /* Remove more kinds of divs that are not strictly needed.
2485 * In particular, if all pairs of lower and upper bounds on a div
2486 * are such that they allow at least one integer value of the div,
2487 * the we can eliminate the div using Fourier-Motzkin without
2488 * introducing any spurious solutions.
2490 static struct isl_basic_map
*drop_more_redundant_divs(
2491 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2493 struct isl_tab
*tab
= NULL
;
2494 struct isl_vec
*vec
= NULL
;
2506 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2507 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2511 tab
= isl_tab_from_basic_map(bmap
, 0);
2516 enum isl_lp_result res
;
2518 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2521 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2527 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2528 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2530 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2531 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2533 construct_test_ineq(bmap
, i
, l
, u
,
2534 vec
->el
, g
, fl
, fu
);
2535 res
= isl_tab_min(tab
, vec
->el
,
2536 bmap
->ctx
->one
, &g
, NULL
, 0);
2537 if (res
== isl_lp_error
)
2539 if (res
== isl_lp_empty
) {
2540 bmap
= isl_basic_map_set_to_empty(bmap
);
2543 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2546 if (u
< bmap
->n_ineq
)
2549 if (l
== bmap
->n_ineq
) {
2569 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
2570 return isl_basic_map_drop_redundant_divs(bmap
);
2573 isl_basic_map_free(bmap
);
2582 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2583 * and the upper bound u, div1 always occurs together with div2 in the form
2584 * (div1 + m div2), where m is the constant range on the variable div1
2585 * allowed by l and u, replace the pair div1 and div2 by a single
2586 * div that is equal to div1 + m div2.
2588 * The new div will appear in the location that contains div2.
2589 * We need to modify all constraints that contain
2590 * div2 = (div - div1) / m
2591 * (If a constraint does not contain div2, it will also not contain div1.)
2592 * If the constraint also contains div1, then we know they appear
2593 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2594 * i.e., the coefficient of div is f.
2596 * Otherwise, we first need to introduce div1 into the constraint.
2605 * A lower bound on div2
2609 * can be replaced by
2611 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2613 * with g = gcd(m,n).
2618 * can be replaced by
2620 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2622 * These constraint are those that we would obtain from eliminating
2623 * div1 using Fourier-Motzkin.
2625 * After all constraints have been modified, we drop the lower and upper
2626 * bound and then drop div1.
2628 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2629 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2634 unsigned dim
, total
;
2637 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2638 total
= 1 + dim
+ bmap
->n_div
;
2643 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2644 isl_int_add_ui(m
, m
, 1);
2646 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2647 if (i
== l
|| i
== u
)
2649 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2651 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2652 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2653 isl_int_divexact(a
, m
, b
);
2654 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2655 if (isl_int_is_pos(b
)) {
2656 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2657 b
, bmap
->ineq
[l
], total
);
2660 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2661 b
, bmap
->ineq
[u
], total
);
2664 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2665 bmap
->ineq
[i
][1 + dim
+ div1
]);
2666 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2673 isl_basic_map_drop_inequality(bmap
, l
);
2674 isl_basic_map_drop_inequality(bmap
, u
);
2676 isl_basic_map_drop_inequality(bmap
, u
);
2677 isl_basic_map_drop_inequality(bmap
, l
);
2679 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2683 /* First check if we can coalesce any pair of divs and
2684 * then continue with dropping more redundant divs.
2686 * We loop over all pairs of lower and upper bounds on a div
2687 * with coefficient 1 and -1, respectively, check if there
2688 * is any other div "c" with which we can coalesce the div
2689 * and if so, perform the coalescing.
2691 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2692 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2697 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2699 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2702 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2703 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2705 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2708 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2710 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2714 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2715 return isl_basic_map_drop_redundant_divs(bmap
);
2720 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2723 return drop_more_redundant_divs(bmap
, pairs
, n
);
2726 /* Remove divs that are not strictly needed.
2727 * In particular, if a div only occurs positively (or negatively)
2728 * in constraints, then it can simply be dropped.
2729 * Also, if a div occurs in only two constraints and if moreover
2730 * those two constraints are opposite to each other, except for the constant
2731 * term and if the sum of the constant terms is such that for any value
2732 * of the other values, there is always at least one integer value of the
2733 * div, i.e., if one plus this sum is greater than or equal to
2734 * the (absolute value) of the coefficent of the div in the constraints,
2735 * then we can also simply drop the div.
2737 * We skip divs that appear in equalities or in the definition of other divs.
2738 * Divs that appear in the definition of other divs usually occur in at least
2739 * 4 constraints, but the constraints may have been simplified.
2741 * If any divs are left after these simple checks then we move on
2742 * to more complicated cases in drop_more_redundant_divs.
2744 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2745 struct isl_basic_map
*bmap
)
2755 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2756 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2760 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2762 int last_pos
, last_neg
;
2766 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2767 for (j
= i
; j
< bmap
->n_div
; ++j
)
2768 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
2770 if (j
< bmap
->n_div
)
2772 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2773 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2779 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2780 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2784 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2789 pairs
[i
] = pos
* neg
;
2790 if (pairs
[i
] == 0) {
2791 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2792 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2793 isl_basic_map_drop_inequality(bmap
, j
);
2794 bmap
= isl_basic_map_drop_div(bmap
, i
);
2796 return isl_basic_map_drop_redundant_divs(bmap
);
2800 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2801 bmap
->ineq
[last_neg
] + 1,
2805 isl_int_add(bmap
->ineq
[last_pos
][0],
2806 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2807 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2808 bmap
->ineq
[last_pos
][0], 1);
2809 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2810 bmap
->ineq
[last_pos
][1+off
+i
]);
2811 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2812 bmap
->ineq
[last_pos
][0], 1);
2813 isl_int_sub(bmap
->ineq
[last_pos
][0],
2814 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2817 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
2822 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
2823 bmap
= isl_basic_map_simplify(bmap
);
2825 return isl_basic_map_drop_redundant_divs(bmap
);
2827 if (last_pos
> last_neg
) {
2828 isl_basic_map_drop_inequality(bmap
, last_pos
);
2829 isl_basic_map_drop_inequality(bmap
, last_neg
);
2831 isl_basic_map_drop_inequality(bmap
, last_neg
);
2832 isl_basic_map_drop_inequality(bmap
, last_pos
);
2834 bmap
= isl_basic_map_drop_div(bmap
, i
);
2836 return isl_basic_map_drop_redundant_divs(bmap
);
2840 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
2846 isl_basic_map_free(bmap
);
2850 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
2851 struct isl_basic_set
*bset
)
2853 return (struct isl_basic_set
*)
2854 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
2857 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
2863 for (i
= 0; i
< map
->n
; ++i
) {
2864 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
2868 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2875 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
2877 return (struct isl_set
*)
2878 isl_map_drop_redundant_divs((struct isl_map
*)set
);