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 /* Does the (linear part of a) constraint "c" involve any of the "len"
1711 * "relevant" dimensions?
1713 static int is_related(isl_int
*c
, int len
, int *relevant
)
1717 for (i
= 0; i
< len
; ++i
) {
1720 if (!isl_int_is_zero(c
[i
]))
1727 /* Drop constraints from "bset" that do not involve any of
1728 * the dimensions marked "relevant".
1730 static __isl_give isl_basic_set
*drop_unrelated_constraints(
1731 __isl_take isl_basic_set
*bset
, int *relevant
)
1735 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1736 for (i
= 0; i
< dim
; ++i
)
1742 for (i
= bset
->n_eq
- 1; i
>= 0; --i
)
1743 if (!is_related(bset
->eq
[i
] + 1, dim
, relevant
))
1744 isl_basic_set_drop_equality(bset
, i
);
1746 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
)
1747 if (!is_related(bset
->ineq
[i
] + 1, dim
, relevant
))
1748 isl_basic_set_drop_inequality(bset
, i
);
1753 /* Update the groups in "group" based on the (linear part of a) constraint "c".
1755 * In particular, for any variable involved in the constraint,
1756 * find the actual group id from before and replace the group
1757 * of the corresponding variable by the minimal group of all
1758 * the variables involved in the constraint considered so far
1759 * (if this minimum is smaller) or replace the minimum by this group
1760 * (if the minimum is larger).
1762 * At the end, all the variables in "c" will (indirectly) point
1763 * to the minimal of the groups that they referred to originally.
1765 static void update_groups(int dim
, int *group
, isl_int
*c
)
1770 for (j
= 0; j
< dim
; ++j
) {
1771 if (isl_int_is_zero(c
[j
]))
1773 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
1774 group
[j
] = group
[group
[j
]];
1775 if (group
[j
] == min
)
1777 if (group
[j
] < min
) {
1778 if (min
>= 0 && min
< dim
)
1779 group
[min
] = group
[j
];
1782 group
[group
[j
]] = min
;
1786 /* Drop constraints from "context" that are irrelevant for computing
1787 * the gist of "bset".
1789 * In particular, drop constraints in variables that are not related
1790 * to any of the variables involved in the constraints of "bset"
1791 * in the sense that there is no sequence of constraints that connects them.
1793 * We construct groups of variables that collect variables that
1794 * (indirectly) appear in some common constraint of "context".
1795 * Each group is identified by the first variable in the group,
1796 * except for the special group of variables that appear in "bset"
1797 * (or are related to those variables), which is identified by -1.
1798 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
1799 * otherwise the group of i is the group of group[i].
1801 * We first initialize the -1 group with the variables that appear in "bset".
1802 * Then we initialize groups for the remaining variables.
1803 * Then we iterate over the constraints of "context" and update the
1804 * group of the variables in the constraint by the smallest group.
1805 * Finally, we resolve indirect references to groups by running over
1808 * After computing the groups, we drop constraints that do not involve
1809 * any variables in the -1 group.
1811 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
1812 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
1820 if (!context
|| !bset
)
1821 return isl_basic_set_free(context
);
1823 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1824 ctx
= isl_basic_set_get_ctx(bset
);
1825 group
= isl_calloc_array(ctx
, int, dim
);
1830 for (i
= 0; i
< dim
; ++i
) {
1831 for (j
= 0; j
< bset
->n_eq
; ++j
)
1832 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
1834 if (j
< bset
->n_eq
) {
1838 for (j
= 0; j
< bset
->n_ineq
; ++j
)
1839 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
1841 if (j
< bset
->n_ineq
)
1846 for (i
= 0; i
< dim
; ++i
)
1848 last
= group
[i
] = i
;
1854 for (i
= 0; i
< context
->n_eq
; ++i
)
1855 update_groups(dim
, group
, context
->eq
[i
] + 1);
1856 for (i
= 0; i
< context
->n_ineq
; ++i
)
1857 update_groups(dim
, group
, context
->ineq
[i
] + 1);
1859 for (i
= 0; i
< dim
; ++i
)
1861 group
[i
] = group
[group
[i
]];
1863 for (i
= 0; i
< dim
; ++i
)
1864 group
[i
] = group
[i
] == -1;
1866 context
= drop_unrelated_constraints(context
, group
);
1872 return isl_basic_set_free(context
);
1875 /* Remove all information from bset that is redundant in the context
1876 * of context. Both bset and context are assumed to be full-dimensional.
1878 * We first remove the inequalities from "bset"
1879 * that are obviously redundant with respect to some inequality in "context".
1880 * Then we remove those constraints from "context" that have become
1881 * irrelevant for computing the gist of "bset".
1882 * Note that this removal of constraints cannot be replaced by
1883 * a factorization because factors in "bset" may still be connected
1884 * to each other through constraints in "context".
1886 * If there are any inequalities left, we construct a tableau for
1887 * the context and then add the inequalities of "bset".
1888 * Before adding these inequalities, we freeze all constraints such that
1889 * they won't be considered redundant in terms of the constraints of "bset".
1890 * Then we detect all redundant constraints (among the
1891 * constraints that weren't frozen), first by checking for redundancy in the
1892 * the tableau and then by checking if replacing a constraint by its negation
1893 * would lead to an empty set. This last step is fairly expensive
1894 * and could be optimized by more reuse of the tableau.
1895 * Finally, we update bset according to the results.
1897 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1898 __isl_take isl_basic_set
*context
)
1901 isl_basic_set
*combined
= NULL
;
1902 struct isl_tab
*tab
= NULL
;
1903 unsigned context_ineq
;
1906 if (!bset
|| !context
)
1909 if (isl_basic_set_is_universe(bset
)) {
1910 isl_basic_set_free(context
);
1914 if (isl_basic_set_is_universe(context
)) {
1915 isl_basic_set_free(context
);
1919 bset
= remove_shifted_constraints(bset
, context
);
1922 if (bset
->n_ineq
== 0)
1925 context
= drop_irrelevant_constraints(context
, bset
);
1928 if (isl_basic_set_is_universe(context
)) {
1929 isl_basic_set_free(context
);
1933 context_ineq
= context
->n_ineq
;
1934 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1935 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
1936 tab
= isl_tab_from_basic_set(combined
, 0);
1937 for (i
= 0; i
< context_ineq
; ++i
)
1938 if (isl_tab_freeze_constraint(tab
, i
) < 0)
1940 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1941 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1942 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
1944 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1948 if (isl_tab_detect_redundant(tab
) < 0)
1950 total
= isl_basic_set_total_dim(bset
);
1951 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
1953 if (tab
->con
[i
].is_redundant
)
1955 tab
->con
[i
].is_redundant
= 1;
1956 combined
= isl_basic_set_dup(bset
);
1957 combined
= isl_basic_set_update_from_tab(combined
, tab
);
1958 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
1959 k
= isl_basic_set_alloc_inequality(combined
);
1962 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
1963 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
1964 is_empty
= isl_basic_set_is_empty(combined
);
1967 isl_basic_set_free(combined
);
1970 tab
->con
[i
].is_redundant
= 0;
1972 for (i
= 0; i
< context_ineq
; ++i
)
1973 tab
->con
[i
].is_redundant
= 1;
1974 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1976 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1977 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1982 bset
= isl_basic_set_simplify(bset
);
1983 bset
= isl_basic_set_finalize(bset
);
1984 isl_basic_set_free(context
);
1988 isl_basic_set_free(combined
);
1989 isl_basic_set_free(context
);
1990 isl_basic_set_free(bset
);
1994 /* Remove all information from bset that is redundant in the context
1995 * of context. In particular, equalities that are linear combinations
1996 * of those in context are removed. Then the inequalities that are
1997 * redundant in the context of the equalities and inequalities of
1998 * context are removed.
2000 * First of all, we drop those constraints from "context"
2001 * that are irrelevant for computing the gist of "bset".
2002 * Alternatively, we could factorize the intersection of "context" and "bset".
2004 * We first compute the integer affine hull of the intersection,
2005 * compute the gist inside this affine hull and then add back
2006 * those equalities that are not implied by the context.
2008 * If two constraints are mutually redundant, then uset_gist_full
2009 * will remove the second of those constraints. We therefore first
2010 * sort the constraints so that constraints not involving existentially
2011 * quantified variables are given precedence over those that do.
2012 * We have to perform this sorting before the variable compression,
2013 * because that may effect the order of the variables.
2015 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2016 __isl_take isl_basic_set
*context
)
2021 isl_basic_set
*aff_context
;
2024 if (!bset
|| !context
)
2027 context
= drop_irrelevant_constraints(context
, bset
);
2029 bset
= isl_basic_set_intersect(bset
, isl_basic_set_copy(context
));
2030 if (isl_basic_set_plain_is_empty(bset
)) {
2031 isl_basic_set_free(context
);
2034 bset
= isl_basic_set_sort_constraints(bset
);
2035 aff
= isl_basic_set_affine_hull(isl_basic_set_copy(bset
));
2038 if (isl_basic_set_plain_is_empty(aff
)) {
2039 isl_basic_set_free(aff
);
2040 isl_basic_set_free(context
);
2043 if (aff
->n_eq
== 0) {
2044 isl_basic_set_free(aff
);
2045 return uset_gist_full(bset
, context
);
2047 total
= isl_basic_set_total_dim(bset
);
2048 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2049 eq
= isl_mat_cow(eq
);
2050 T
= isl_mat_variable_compression(eq
, &T2
);
2051 if (T
&& T
->n_col
== 0) {
2054 isl_basic_set_free(context
);
2055 isl_basic_set_free(aff
);
2056 return isl_basic_set_set_to_empty(bset
);
2059 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2061 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
2062 context
= isl_basic_set_preimage(context
, T
);
2064 bset
= uset_gist_full(bset
, context
);
2065 bset
= isl_basic_set_preimage(bset
, T2
);
2066 bset
= isl_basic_set_intersect(bset
, aff
);
2067 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2070 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2071 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2076 isl_basic_set_free(bset
);
2077 isl_basic_set_free(context
);
2081 /* Normalize the divs in "bmap" in the context of the equalities in "context".
2082 * We simply add the equalities in context to bmap and then do a regular
2083 * div normalizations. Better results can be obtained by normalizing
2084 * only the divs in bmap than do not also appear in context.
2085 * We need to be careful to reduce the divs using the equalities
2086 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
2087 * spurious constraints.
2089 static struct isl_basic_map
*normalize_divs_in_context(
2090 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
2093 unsigned total_context
;
2096 div_eq
= n_pure_div_eq(bmap
);
2100 if (context
->n_div
> 0)
2101 bmap
= isl_basic_map_align_divs(bmap
, context
);
2103 total_context
= isl_basic_map_total_dim(context
);
2104 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
2105 for (i
= 0; i
< context
->n_eq
; ++i
) {
2107 k
= isl_basic_map_alloc_equality(bmap
);
2108 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
2109 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
2110 isl_basic_map_total_dim(bmap
) - total_context
);
2112 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2113 bmap
= normalize_divs(bmap
, NULL
);
2114 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2118 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
2119 struct isl_basic_map
*context
)
2121 struct isl_basic_set
*bset
;
2123 if (!bmap
|| !context
)
2126 if (isl_basic_map_is_universe(bmap
)) {
2127 isl_basic_map_free(context
);
2130 if (isl_basic_map_plain_is_empty(context
)) {
2131 isl_basic_map_free(bmap
);
2134 if (isl_basic_map_plain_is_empty(bmap
)) {
2135 isl_basic_map_free(context
);
2139 bmap
= isl_basic_map_remove_redundancies(bmap
);
2140 context
= isl_basic_map_remove_redundancies(context
);
2143 bmap
= normalize_divs_in_context(bmap
, context
);
2145 context
= isl_basic_map_align_divs(context
, bmap
);
2146 bmap
= isl_basic_map_align_divs(bmap
, context
);
2148 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
2149 isl_basic_map_underlying_set(context
));
2151 return isl_basic_map_overlying_set(bset
, bmap
);
2153 isl_basic_map_free(bmap
);
2154 isl_basic_map_free(context
);
2159 * Assumes context has no implicit divs.
2161 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
2162 __isl_take isl_basic_map
*context
)
2166 if (!map
|| !context
)
2169 if (isl_basic_map_plain_is_empty(context
)) {
2171 return isl_map_from_basic_map(context
);
2174 context
= isl_basic_map_remove_redundancies(context
);
2175 map
= isl_map_cow(map
);
2176 if (!map
|| !context
)
2178 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
2179 map
= isl_map_compute_divs(map
);
2180 for (i
= 0; i
< map
->n
; ++i
)
2181 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
2182 for (i
= map
->n
- 1; i
>= 0; --i
) {
2183 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
2184 isl_basic_map_copy(context
));
2187 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
2188 isl_basic_map_free(map
->p
[i
]);
2189 if (i
!= map
->n
- 1)
2190 map
->p
[i
] = map
->p
[map
->n
- 1];
2194 isl_basic_map_free(context
);
2195 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2199 isl_basic_map_free(context
);
2203 /* Return a map that has the same intersection with "context" as "map"
2204 * and that as "simple" as possible.
2206 * If "map" is already the universe, then we cannot make it any simpler.
2207 * Similarly, if "context" is the universe, then we cannot exploit it
2209 * If "map" and "context" are identical to each other, then we can
2210 * return the corresponding universe.
2212 * If none of these cases apply, we have to work a bit harder.
2214 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
2215 __isl_take isl_map
*context
)
2220 is_universe
= isl_map_plain_is_universe(map
);
2221 if (is_universe
>= 0 && !is_universe
)
2222 is_universe
= isl_map_plain_is_universe(context
);
2223 if (is_universe
< 0)
2226 isl_map_free(context
);
2230 equal
= isl_map_plain_is_equal(map
, context
);
2234 isl_map
*res
= isl_map_universe(isl_map_get_space(map
));
2236 isl_map_free(context
);
2240 context
= isl_map_compute_divs(context
);
2241 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
2244 isl_map_free(context
);
2248 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
2249 __isl_take isl_map
*context
)
2251 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2254 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2255 struct isl_basic_set
*context
)
2257 return (struct isl_basic_set
*)isl_basic_map_gist(
2258 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2261 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2262 __isl_take isl_basic_set
*context
)
2264 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2265 (struct isl_basic_map
*)context
);
2268 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2269 __isl_take isl_basic_set
*context
)
2271 isl_space
*space
= isl_set_get_space(set
);
2272 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2273 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2274 return isl_set_gist_basic_set(set
, dom_context
);
2277 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2278 __isl_take isl_set
*context
)
2280 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2281 (struct isl_map
*)context
);
2284 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2285 __isl_take isl_set
*context
)
2287 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2288 map_context
= isl_map_intersect_domain(map_context
, context
);
2289 return isl_map_gist(map
, map_context
);
2292 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2293 __isl_take isl_set
*context
)
2295 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2296 map_context
= isl_map_intersect_range(map_context
, context
);
2297 return isl_map_gist(map
, map_context
);
2300 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2301 __isl_take isl_set
*context
)
2303 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2304 map_context
= isl_map_intersect_params(map_context
, context
);
2305 return isl_map_gist(map
, map_context
);
2308 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2309 __isl_take isl_set
*context
)
2311 return isl_map_gist_params(set
, context
);
2314 /* Quick check to see if two basic maps are disjoint.
2315 * In particular, we reduce the equalities and inequalities of
2316 * one basic map in the context of the equalities of the other
2317 * basic map and check if we get a contradiction.
2319 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2320 __isl_keep isl_basic_map
*bmap2
)
2322 struct isl_vec
*v
= NULL
;
2327 if (!bmap1
|| !bmap2
)
2329 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
2331 if (bmap1
->n_div
|| bmap2
->n_div
)
2333 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
2336 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
2339 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
2342 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
2345 compute_elimination_index(bmap1
, elim
);
2346 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
2348 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
2350 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
2351 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2354 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
2356 reduced
= reduced_using_equalities(v
->block
.data
,
2357 bmap2
->ineq
[i
], bmap1
, elim
);
2358 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2359 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2362 compute_elimination_index(bmap2
, elim
);
2363 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
2365 reduced
= reduced_using_equalities(v
->block
.data
,
2366 bmap1
->ineq
[i
], bmap2
, elim
);
2367 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2368 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2384 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2385 __isl_keep isl_basic_set
*bset2
)
2387 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
2388 (struct isl_basic_map
*)bset2
);
2391 /* Are "map1" and "map2" obviously disjoint?
2393 * If one of them is empty or if they live in different spaces (ignoring
2394 * parameters), then they are clearly disjoint.
2396 * If they have different parameters, then we skip any further tests.
2398 * If they are obviously equal, but not obviously empty, then we will
2399 * not be able to detect if they are disjoint.
2401 * Otherwise we check if each basic map in "map1" is obviously disjoint
2402 * from each basic map in "map2".
2404 int isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
2405 __isl_keep isl_map
*map2
)
2415 disjoint
= isl_map_plain_is_empty(map1
);
2416 if (disjoint
< 0 || disjoint
)
2419 disjoint
= isl_map_plain_is_empty(map2
);
2420 if (disjoint
< 0 || disjoint
)
2423 match
= isl_space_tuple_match(map1
->dim
, isl_dim_in
,
2424 map2
->dim
, isl_dim_in
);
2425 if (match
< 0 || !match
)
2426 return match
< 0 ? -1 : 1;
2428 match
= isl_space_tuple_match(map1
->dim
, isl_dim_out
,
2429 map2
->dim
, isl_dim_out
);
2430 if (match
< 0 || !match
)
2431 return match
< 0 ? -1 : 1;
2433 match
= isl_space_match(map1
->dim
, isl_dim_param
,
2434 map2
->dim
, isl_dim_param
);
2435 if (match
< 0 || !match
)
2436 return match
< 0 ? -1 : 0;
2438 intersect
= isl_map_plain_is_equal(map1
, map2
);
2439 if (intersect
< 0 || intersect
)
2440 return intersect
< 0 ? -1 : 0;
2442 for (i
= 0; i
< map1
->n
; ++i
) {
2443 for (j
= 0; j
< map2
->n
; ++j
) {
2444 int d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
2453 /* Are "map1" and "map2" disjoint?
2455 * They are disjoint if they are "obviously disjoint" or if one of them
2456 * is empty. Otherwise, they are not disjoint if one of them is universal.
2457 * If none of these cases apply, we compute the intersection and see if
2458 * the result is empty.
2460 int isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
2466 disjoint
= isl_map_plain_is_disjoint(map1
, map2
);
2467 if (disjoint
< 0 || disjoint
)
2470 disjoint
= isl_map_is_empty(map1
);
2471 if (disjoint
< 0 || disjoint
)
2474 disjoint
= isl_map_is_empty(map2
);
2475 if (disjoint
< 0 || disjoint
)
2478 intersect
= isl_map_plain_is_universe(map1
);
2479 if (intersect
< 0 || intersect
)
2480 return intersect
< 0 ? -1 : 0;
2482 intersect
= isl_map_plain_is_universe(map2
);
2483 if (intersect
< 0 || intersect
)
2484 return intersect
< 0 ? -1 : 0;
2486 test
= isl_map_intersect(isl_map_copy(map1
), isl_map_copy(map2
));
2487 disjoint
= isl_map_is_empty(test
);
2493 int isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
2494 __isl_keep isl_set
*set2
)
2496 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
2497 (struct isl_map
*)set2
);
2500 /* Are "set1" and "set2" disjoint?
2502 int isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2504 return isl_map_is_disjoint(set1
, set2
);
2507 int isl_set_fast_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2509 return isl_set_plain_is_disjoint(set1
, set2
);
2512 /* Check if we can combine a given div with lower bound l and upper
2513 * bound u with some other div and if so return that other div.
2514 * Otherwise return -1.
2516 * We first check that
2517 * - the bounds are opposites of each other (except for the constant
2519 * - the bounds do not reference any other div
2520 * - no div is defined in terms of this div
2522 * Let m be the size of the range allowed on the div by the bounds.
2523 * That is, the bounds are of the form
2525 * e <= a <= e + m - 1
2527 * with e some expression in the other variables.
2528 * We look for another div b such that no third div is defined in terms
2529 * of this second div b and such that in any constraint that contains
2530 * a (except for the given lower and upper bound), also contains b
2531 * with a coefficient that is m times that of b.
2532 * That is, all constraints (execpt for the lower and upper bound)
2535 * e + f (a + m b) >= 0
2537 * If so, we return b so that "a + m b" can be replaced by
2538 * a single div "c = a + m b".
2540 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2541 unsigned div
, unsigned l
, unsigned u
)
2547 if (bmap
->n_div
<= 1)
2549 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2550 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2552 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2553 bmap
->n_div
- div
- 1) != -1)
2555 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2559 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2560 if (isl_int_is_zero(bmap
->div
[i
][0]))
2562 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2566 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2567 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2568 isl_int_sub(bmap
->ineq
[l
][0],
2569 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2570 bmap
= isl_basic_map_copy(bmap
);
2571 bmap
= isl_basic_map_set_to_empty(bmap
);
2572 isl_basic_map_free(bmap
);
2575 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2576 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2581 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2582 if (isl_int_is_zero(bmap
->div
[j
][0]))
2584 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2587 if (j
< bmap
->n_div
)
2589 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2591 if (j
== l
|| j
== u
)
2593 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2595 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2597 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2598 bmap
->ineq
[j
][1 + dim
+ div
],
2600 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2601 bmap
->ineq
[j
][1 + dim
+ i
]);
2602 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2603 bmap
->ineq
[j
][1 + dim
+ div
],
2608 if (j
< bmap
->n_ineq
)
2613 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2614 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2618 /* Given a lower and an upper bound on div i, construct an inequality
2619 * that when nonnegative ensures that this pair of bounds always allows
2620 * for an integer value of the given div.
2621 * The lower bound is inequality l, while the upper bound is inequality u.
2622 * The constructed inequality is stored in ineq.
2623 * g, fl, fu are temporary scalars.
2625 * Let the upper bound be
2629 * and the lower bound
2633 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2636 * - f_u e_l <= f_u f_l g a <= f_l e_u
2638 * Since all variables are integer valued, this is equivalent to
2640 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2642 * If this interval is at least f_u f_l g, then it contains at least
2643 * one integer value for a.
2644 * That is, the test constraint is
2646 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2648 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2649 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2652 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2654 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2655 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2656 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2657 isl_int_neg(fu
, fu
);
2658 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2659 1 + dim
+ bmap
->n_div
);
2660 isl_int_add(ineq
[0], ineq
[0], fl
);
2661 isl_int_add(ineq
[0], ineq
[0], fu
);
2662 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2663 isl_int_mul(g
, g
, fl
);
2664 isl_int_mul(g
, g
, fu
);
2665 isl_int_sub(ineq
[0], ineq
[0], g
);
2668 /* Remove more kinds of divs that are not strictly needed.
2669 * In particular, if all pairs of lower and upper bounds on a div
2670 * are such that they allow at least one integer value of the div,
2671 * the we can eliminate the div using Fourier-Motzkin without
2672 * introducing any spurious solutions.
2674 static struct isl_basic_map
*drop_more_redundant_divs(
2675 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2677 struct isl_tab
*tab
= NULL
;
2678 struct isl_vec
*vec
= NULL
;
2690 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2691 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2695 tab
= isl_tab_from_basic_map(bmap
, 0);
2700 enum isl_lp_result res
;
2702 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2705 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2711 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2712 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2714 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2715 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2717 construct_test_ineq(bmap
, i
, l
, u
,
2718 vec
->el
, g
, fl
, fu
);
2719 res
= isl_tab_min(tab
, vec
->el
,
2720 bmap
->ctx
->one
, &g
, NULL
, 0);
2721 if (res
== isl_lp_error
)
2723 if (res
== isl_lp_empty
) {
2724 bmap
= isl_basic_map_set_to_empty(bmap
);
2727 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2730 if (u
< bmap
->n_ineq
)
2733 if (l
== bmap
->n_ineq
) {
2753 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
2754 return isl_basic_map_drop_redundant_divs(bmap
);
2757 isl_basic_map_free(bmap
);
2766 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2767 * and the upper bound u, div1 always occurs together with div2 in the form
2768 * (div1 + m div2), where m is the constant range on the variable div1
2769 * allowed by l and u, replace the pair div1 and div2 by a single
2770 * div that is equal to div1 + m div2.
2772 * The new div will appear in the location that contains div2.
2773 * We need to modify all constraints that contain
2774 * div2 = (div - div1) / m
2775 * (If a constraint does not contain div2, it will also not contain div1.)
2776 * If the constraint also contains div1, then we know they appear
2777 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2778 * i.e., the coefficient of div is f.
2780 * Otherwise, we first need to introduce div1 into the constraint.
2789 * A lower bound on div2
2793 * can be replaced by
2795 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2797 * with g = gcd(m,n).
2802 * can be replaced by
2804 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2806 * These constraint are those that we would obtain from eliminating
2807 * div1 using Fourier-Motzkin.
2809 * After all constraints have been modified, we drop the lower and upper
2810 * bound and then drop div1.
2812 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2813 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2818 unsigned dim
, total
;
2821 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2822 total
= 1 + dim
+ bmap
->n_div
;
2827 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2828 isl_int_add_ui(m
, m
, 1);
2830 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2831 if (i
== l
|| i
== u
)
2833 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2835 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2836 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2837 isl_int_divexact(a
, m
, b
);
2838 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2839 if (isl_int_is_pos(b
)) {
2840 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2841 b
, bmap
->ineq
[l
], total
);
2844 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2845 b
, bmap
->ineq
[u
], total
);
2848 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2849 bmap
->ineq
[i
][1 + dim
+ div1
]);
2850 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2857 isl_basic_map_drop_inequality(bmap
, l
);
2858 isl_basic_map_drop_inequality(bmap
, u
);
2860 isl_basic_map_drop_inequality(bmap
, u
);
2861 isl_basic_map_drop_inequality(bmap
, l
);
2863 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2867 /* First check if we can coalesce any pair of divs and
2868 * then continue with dropping more redundant divs.
2870 * We loop over all pairs of lower and upper bounds on a div
2871 * with coefficient 1 and -1, respectively, check if there
2872 * is any other div "c" with which we can coalesce the div
2873 * and if so, perform the coalescing.
2875 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2876 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2881 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2883 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2886 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2887 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2889 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2892 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2894 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2898 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2899 return isl_basic_map_drop_redundant_divs(bmap
);
2904 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2907 return drop_more_redundant_divs(bmap
, pairs
, n
);
2910 /* Remove divs that are not strictly needed.
2911 * In particular, if a div only occurs positively (or negatively)
2912 * in constraints, then it can simply be dropped.
2913 * Also, if a div occurs in only two constraints and if moreover
2914 * those two constraints are opposite to each other, except for the constant
2915 * term and if the sum of the constant terms is such that for any value
2916 * of the other values, there is always at least one integer value of the
2917 * div, i.e., if one plus this sum is greater than or equal to
2918 * the (absolute value) of the coefficent of the div in the constraints,
2919 * then we can also simply drop the div.
2921 * We skip divs that appear in equalities or in the definition of other divs.
2922 * Divs that appear in the definition of other divs usually occur in at least
2923 * 4 constraints, but the constraints may have been simplified.
2925 * If any divs are left after these simple checks then we move on
2926 * to more complicated cases in drop_more_redundant_divs.
2928 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2929 struct isl_basic_map
*bmap
)
2939 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2940 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2944 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2946 int last_pos
, last_neg
;
2950 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2951 for (j
= i
; j
< bmap
->n_div
; ++j
)
2952 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
2954 if (j
< bmap
->n_div
)
2956 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2957 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2963 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2964 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2968 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2973 pairs
[i
] = pos
* neg
;
2974 if (pairs
[i
] == 0) {
2975 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2976 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2977 isl_basic_map_drop_inequality(bmap
, j
);
2978 bmap
= isl_basic_map_drop_div(bmap
, i
);
2980 return isl_basic_map_drop_redundant_divs(bmap
);
2984 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2985 bmap
->ineq
[last_neg
] + 1,
2989 isl_int_add(bmap
->ineq
[last_pos
][0],
2990 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2991 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2992 bmap
->ineq
[last_pos
][0], 1);
2993 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2994 bmap
->ineq
[last_pos
][1+off
+i
]);
2995 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2996 bmap
->ineq
[last_pos
][0], 1);
2997 isl_int_sub(bmap
->ineq
[last_pos
][0],
2998 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3001 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
3006 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
3007 bmap
= isl_basic_map_simplify(bmap
);
3009 return isl_basic_map_drop_redundant_divs(bmap
);
3011 if (last_pos
> last_neg
) {
3012 isl_basic_map_drop_inequality(bmap
, last_pos
);
3013 isl_basic_map_drop_inequality(bmap
, last_neg
);
3015 isl_basic_map_drop_inequality(bmap
, last_neg
);
3016 isl_basic_map_drop_inequality(bmap
, last_pos
);
3018 bmap
= isl_basic_map_drop_div(bmap
, i
);
3020 return isl_basic_map_drop_redundant_divs(bmap
);
3024 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
3030 isl_basic_map_free(bmap
);
3034 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
3035 struct isl_basic_set
*bset
)
3037 return (struct isl_basic_set
*)
3038 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
3041 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
3047 for (i
= 0; i
< map
->n
; ++i
) {
3048 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
3052 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3059 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
3061 return (struct isl_set
*)
3062 isl_map_drop_redundant_divs((struct isl_map
*)set
);