2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012-2013 Ecole Normale Superieure
4 * Copyright 2014-2015 INRIA Rocquencourt
5 * Copyright 2016 Sven Verdoolaege
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
12 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
13 * B.P. 105 - 78153 Le Chesnay, France
16 #include <isl_ctx_private.h>
17 #include <isl_map_private.h>
18 #include "isl_equalities.h"
22 #include <isl_space_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_vec_private.h>
26 #include <bset_to_bmap.c>
27 #include <bset_from_bmap.c>
28 #include <set_to_map.c>
29 #include <set_from_map.c>
31 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
33 isl_int
*t
= bmap
->eq
[a
];
34 bmap
->eq
[a
] = bmap
->eq
[b
];
38 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
41 isl_int
*t
= bmap
->ineq
[a
];
42 bmap
->ineq
[a
] = bmap
->ineq
[b
];
47 __isl_give isl_basic_map
*isl_basic_map_normalize_constraints(
48 __isl_take isl_basic_map
*bmap
)
52 unsigned total
= isl_basic_map_total_dim(bmap
);
58 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
59 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
60 if (isl_int_is_zero(gcd
)) {
61 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
62 bmap
= isl_basic_map_set_to_empty(bmap
);
65 isl_basic_map_drop_equality(bmap
, i
);
68 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
69 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
70 if (isl_int_is_one(gcd
))
72 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
73 bmap
= isl_basic_map_set_to_empty(bmap
);
76 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
79 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
80 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
81 if (isl_int_is_zero(gcd
)) {
82 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
83 bmap
= isl_basic_map_set_to_empty(bmap
);
86 isl_basic_map_drop_inequality(bmap
, i
);
89 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
90 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
91 if (isl_int_is_one(gcd
))
93 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
94 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
101 __isl_give isl_basic_set
*isl_basic_set_normalize_constraints(
102 __isl_take isl_basic_set
*bset
)
104 isl_basic_map
*bmap
= bset_to_bmap(bset
);
105 return bset_from_bmap(isl_basic_map_normalize_constraints(bmap
));
108 /* Reduce the coefficient of the variable at position "pos"
109 * in integer division "div", such that it lies in the half-open
110 * interval (1/2,1/2], extracting any excess value from this integer division.
111 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
112 * corresponds to the constant term.
114 * That is, the integer division is of the form
116 * floor((... + (c * d + r) * x_pos + ...)/d)
118 * with -d < 2 * r <= d.
121 * floor((... + r * x_pos + ...)/d) + c * x_pos
123 * If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d).
124 * Otherwise, c = floor((c * d + r)/d) + 1.
126 * This is the same normalization that is performed by isl_aff_floor.
128 static __isl_give isl_basic_map
*reduce_coefficient_in_div(
129 __isl_take isl_basic_map
*bmap
, int div
, int pos
)
135 isl_int_fdiv_r(shift
, bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
136 isl_int_mul_ui(shift
, shift
, 2);
137 add_one
= isl_int_gt(shift
, bmap
->div
[div
][0]);
138 isl_int_fdiv_q(shift
, bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
140 isl_int_add_ui(shift
, shift
, 1);
141 isl_int_neg(shift
, shift
);
142 bmap
= isl_basic_map_shift_div(bmap
, div
, pos
, shift
);
143 isl_int_clear(shift
);
148 /* Does the coefficient of the variable at position "pos"
149 * in integer division "div" need to be reduced?
150 * That is, does it lie outside the half-open interval (1/2,1/2]?
151 * The coefficient c/d lies outside this interval if abs(2 * c) >= d and
154 static isl_bool
needs_reduction(__isl_keep isl_basic_map
*bmap
, int div
,
159 if (isl_int_is_zero(bmap
->div
[div
][1 + pos
]))
160 return isl_bool_false
;
162 isl_int_mul_ui(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][1 + pos
], 2);
163 r
= isl_int_abs_ge(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]) &&
164 !isl_int_eq(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
165 isl_int_divexact_ui(bmap
->div
[div
][1 + pos
],
166 bmap
->div
[div
][1 + pos
], 2);
171 /* Reduce the coefficients (including the constant term) of
172 * integer division "div", if needed.
173 * In particular, make sure all coefficients lie in
174 * the half-open interval (1/2,1/2].
176 static __isl_give isl_basic_map
*reduce_div_coefficients_of_div(
177 __isl_take isl_basic_map
*bmap
, int div
)
180 unsigned total
= 1 + isl_basic_map_total_dim(bmap
);
182 for (i
= 0; i
< total
; ++i
) {
185 reduce
= needs_reduction(bmap
, div
, i
);
187 return isl_basic_map_free(bmap
);
190 bmap
= reduce_coefficient_in_div(bmap
, div
, i
);
198 /* Reduce the coefficients (including the constant term) of
199 * the known integer divisions, if needed
200 * In particular, make sure all coefficients lie in
201 * the half-open interval (1/2,1/2].
203 static __isl_give isl_basic_map
*reduce_div_coefficients(
204 __isl_take isl_basic_map
*bmap
)
210 if (bmap
->n_div
== 0)
213 for (i
= 0; i
< bmap
->n_div
; ++i
) {
214 if (isl_int_is_zero(bmap
->div
[i
][0]))
216 bmap
= reduce_div_coefficients_of_div(bmap
, i
);
224 /* Remove any common factor in numerator and denominator of the div expression,
225 * not taking into account the constant term.
226 * That is, if the div is of the form
228 * floor((a + m f(x))/(m d))
232 * floor((floor(a/m) + f(x))/d)
234 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
235 * and can therefore not influence the result of the floor.
237 static __isl_give isl_basic_map
*normalize_div_expression(
238 __isl_take isl_basic_map
*bmap
, int div
)
240 unsigned total
= isl_basic_map_total_dim(bmap
);
241 isl_ctx
*ctx
= bmap
->ctx
;
243 if (isl_int_is_zero(bmap
->div
[div
][0]))
245 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
246 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
247 if (isl_int_is_one(ctx
->normalize_gcd
))
249 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
251 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
253 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
254 ctx
->normalize_gcd
, total
);
259 /* Remove any common factor in numerator and denominator of a div expression,
260 * not taking into account the constant term.
261 * That is, look for any div of the form
263 * floor((a + m f(x))/(m d))
267 * floor((floor(a/m) + f(x))/d)
269 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
270 * and can therefore not influence the result of the floor.
272 static __isl_give isl_basic_map
*normalize_div_expressions(
273 __isl_take isl_basic_map
*bmap
)
279 if (bmap
->n_div
== 0)
282 for (i
= 0; i
< bmap
->n_div
; ++i
)
283 bmap
= normalize_div_expression(bmap
, i
);
288 /* Assumes divs have been ordered if keep_divs is set.
290 static __isl_give isl_basic_map
*eliminate_var_using_equality(
291 __isl_take isl_basic_map
*bmap
,
292 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
299 total
= isl_basic_map_total_dim(bmap
);
300 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
302 return isl_basic_map_free(bmap
);
303 last_div
= isl_seq_last_non_zero(eq
+ 1 + v_div
, bmap
->n_div
);
304 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
305 if (bmap
->eq
[k
] == eq
)
307 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
311 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
312 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
315 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
316 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
320 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
321 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
322 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
323 ISL_F_CLR(bmap
, ISL_BASIC_MAP_SORTED
);
326 for (k
= 0; k
< bmap
->n_div
; ++k
) {
327 if (isl_int_is_zero(bmap
->div
[k
][0]))
329 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
333 /* We need to be careful about circular definitions,
334 * so for now we just remove the definition of div k
335 * if the equality contains any divs.
336 * If keep_divs is set, then the divs have been ordered
337 * and we can keep the definition as long as the result
340 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
341 isl_seq_elim(bmap
->div
[k
]+1, eq
,
342 1+pos
, 1+total
, &bmap
->div
[k
][0]);
343 bmap
= normalize_div_expression(bmap
, k
);
347 isl_seq_clr(bmap
->div
[k
], 1 + total
);
353 /* Assumes divs have been ordered if keep_divs is set.
355 static __isl_give isl_basic_map
*eliminate_div(__isl_take isl_basic_map
*bmap
,
356 isl_int
*eq
, unsigned div
, int keep_divs
)
361 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
363 return isl_basic_map_free(bmap
);
365 bmap
= eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
367 bmap
= isl_basic_map_drop_div(bmap
, div
);
372 /* Check if elimination of div "div" using equality "eq" would not
373 * result in a div depending on a later div.
375 static isl_bool
ok_to_eliminate_div(__isl_keep isl_basic_map
*bmap
, isl_int
*eq
,
383 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
385 return isl_bool_error
;
388 last_div
= isl_seq_last_non_zero(eq
+ 1 + v_div
, bmap
->n_div
);
389 if (last_div
< 0 || last_div
<= div
)
390 return isl_bool_true
;
392 for (k
= 0; k
<= last_div
; ++k
) {
393 if (isl_int_is_zero(bmap
->div
[k
][0]))
395 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
396 return isl_bool_false
;
399 return isl_bool_true
;
402 /* Eliminate divs based on equalities
404 static __isl_give isl_basic_map
*eliminate_divs_eq(
405 __isl_take isl_basic_map
*bmap
, int *progress
)
412 bmap
= isl_basic_map_order_divs(bmap
);
417 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
419 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
420 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
423 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
424 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
426 ok
= ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
);
428 return isl_basic_map_free(bmap
);
433 bmap
= eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
434 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
435 return isl_basic_map_free(bmap
);
440 return eliminate_divs_eq(bmap
, progress
);
444 /* Eliminate divs based on inequalities
446 static __isl_give isl_basic_map
*eliminate_divs_ineq(
447 __isl_take isl_basic_map
*bmap
, int *progress
)
458 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
460 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
461 for (i
= 0; i
< bmap
->n_eq
; ++i
)
462 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
466 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
467 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
469 if (i
< bmap
->n_ineq
)
472 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
473 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
475 bmap
= isl_basic_map_drop_div(bmap
, d
);
482 /* Does the equality constraint at position "eq" in "bmap" involve
483 * any local variables in the range [first, first + n)
484 * that are not marked as having an explicit representation?
486 static isl_bool
bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map
*bmap
,
487 int eq
, unsigned first
, unsigned n
)
493 return isl_bool_error
;
495 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
496 for (i
= 0; i
< n
; ++i
) {
499 if (isl_int_is_zero(bmap
->eq
[eq
][o_div
+ first
+ i
]))
501 unknown
= isl_basic_map_div_is_marked_unknown(bmap
, first
+ i
);
503 return isl_bool_error
;
505 return isl_bool_true
;
508 return isl_bool_false
;
511 /* The last local variable involved in the equality constraint
512 * at position "eq" in "bmap" is the local variable at position "div".
513 * It can therefore be used to extract an explicit representation
515 * Do so unless the local variable already has an explicit representation or
516 * the explicit representation would involve any other local variables
517 * that in turn do not have an explicit representation.
518 * An equality constraint involving local variables without an explicit
519 * representation can be used in isl_basic_map_drop_redundant_divs
520 * to separate out an independent local variable. Introducing
521 * an explicit representation here would block this transformation,
522 * while the partial explicit representation in itself is not very useful.
523 * Set *progress if anything is changed.
525 * The equality constraint is of the form
529 * with n a positive number. The explicit representation derived from
534 static __isl_give isl_basic_map
*set_div_from_eq(__isl_take isl_basic_map
*bmap
,
535 int div
, int eq
, int *progress
)
537 unsigned total
, o_div
;
543 if (!isl_int_is_zero(bmap
->div
[div
][0]))
546 involves
= bmap_eq_involves_unknown_divs(bmap
, eq
, 0, div
);
548 return isl_basic_map_free(bmap
);
552 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
553 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
554 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->eq
[eq
], 1 + total
);
555 isl_int_set_si(bmap
->div
[div
][1 + o_div
+ div
], 0);
556 isl_int_set(bmap
->div
[div
][0], bmap
->eq
[eq
][o_div
+ div
]);
563 __isl_give isl_basic_map
*isl_basic_map_gauss(__isl_take isl_basic_map
*bmap
,
572 bmap
= isl_basic_map_order_divs(bmap
);
577 total
= isl_basic_map_total_dim(bmap
);
578 total_var
= total
- bmap
->n_div
;
580 last_var
= total
- 1;
581 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
582 for (; last_var
>= 0; --last_var
) {
583 for (k
= done
; k
< bmap
->n_eq
; ++k
)
584 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
592 swap_equality(bmap
, k
, done
);
593 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
594 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
596 bmap
= eliminate_var_using_equality(bmap
, last_var
,
597 bmap
->eq
[done
], 1, progress
);
599 if (last_var
>= total_var
)
600 bmap
= set_div_from_eq(bmap
, last_var
- total_var
,
605 if (done
== bmap
->n_eq
)
607 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
608 if (isl_int_is_zero(bmap
->eq
[k
][0]))
610 return isl_basic_map_set_to_empty(bmap
);
612 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
616 __isl_give isl_basic_set
*isl_basic_set_gauss(
617 __isl_take isl_basic_set
*bset
, int *progress
)
619 return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset
),
624 static unsigned int round_up(unsigned int v
)
635 /* Hash table of inequalities in a basic map.
636 * "index" is an array of addresses of inequalities in the basic map, some
637 * of which are NULL. The inequalities are hashed on the coefficients
638 * except the constant term.
639 * "size" is the number of elements in the array and is always a power of two
640 * "bits" is the number of bits need to represent an index into the array.
641 * "total" is the total dimension of the basic map.
643 struct isl_constraint_index
{
650 /* Fill in the "ci" data structure for holding the inequalities of "bmap".
652 static isl_stat
create_constraint_index(struct isl_constraint_index
*ci
,
653 __isl_keep isl_basic_map
*bmap
)
659 return isl_stat_error
;
660 ci
->total
= isl_basic_set_total_dim(bmap
);
661 if (bmap
->n_ineq
== 0)
663 ci
->size
= round_up(4 * (bmap
->n_ineq
+ 1) / 3 - 1);
664 ci
->bits
= ffs(ci
->size
) - 1;
665 ctx
= isl_basic_map_get_ctx(bmap
);
666 ci
->index
= isl_calloc_array(ctx
, isl_int
**, ci
->size
);
668 return isl_stat_error
;
673 /* Free the memory allocated by create_constraint_index.
675 static void constraint_index_free(struct isl_constraint_index
*ci
)
680 /* Return the position in ci->index that contains the address of
681 * an inequality that is equal to *ineq up to the constant term,
682 * provided this address is not identical to "ineq".
683 * If there is no such inequality, then return the position where
684 * such an inequality should be inserted.
686 static int hash_index_ineq(struct isl_constraint_index
*ci
, isl_int
**ineq
)
689 uint32_t hash
= isl_seq_get_hash_bits((*ineq
) + 1, ci
->total
, ci
->bits
);
690 for (h
= hash
; ci
->index
[h
]; h
= (h
+1) % ci
->size
)
691 if (ineq
!= ci
->index
[h
] &&
692 isl_seq_eq((*ineq
) + 1, ci
->index
[h
][0]+1, ci
->total
))
697 /* Return the position in ci->index that contains the address of
698 * an inequality that is equal to the k'th inequality of "bmap"
699 * up to the constant term, provided it does not point to the very
701 * If there is no such inequality, then return the position where
702 * such an inequality should be inserted.
704 static int hash_index(struct isl_constraint_index
*ci
,
705 __isl_keep isl_basic_map
*bmap
, int k
)
707 return hash_index_ineq(ci
, &bmap
->ineq
[k
]);
710 static int set_hash_index(struct isl_constraint_index
*ci
,
711 __isl_keep isl_basic_set
*bset
, int k
)
713 return hash_index(ci
, bset
, k
);
716 /* Fill in the "ci" data structure with the inequalities of "bset".
718 static isl_stat
setup_constraint_index(struct isl_constraint_index
*ci
,
719 __isl_keep isl_basic_set
*bset
)
723 if (create_constraint_index(ci
, bset
) < 0)
724 return isl_stat_error
;
726 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
727 h
= set_hash_index(ci
, bset
, k
);
728 ci
->index
[h
] = &bset
->ineq
[k
];
734 /* Is the inequality ineq (obviously) redundant with respect
735 * to the constraints in "ci"?
737 * Look for an inequality in "ci" with the same coefficients and then
738 * check if the contant term of "ineq" is greater than or equal
739 * to the constant term of that inequality. If so, "ineq" is clearly
742 * Note that hash_index_ineq ignores a stored constraint if it has
743 * the same address as the passed inequality. It is ok to pass
744 * the address of a local variable here since it will never be
745 * the same as the address of a constraint in "ci".
747 static isl_bool
constraint_index_is_redundant(struct isl_constraint_index
*ci
,
752 h
= hash_index_ineq(ci
, &ineq
);
754 return isl_bool_false
;
755 return isl_int_ge(ineq
[0], (*ci
->index
[h
])[0]);
758 /* If we can eliminate more than one div, then we need to make
759 * sure we do it from last div to first div, in order not to
760 * change the position of the other divs that still need to
763 static __isl_give isl_basic_map
*remove_duplicate_divs(
764 __isl_take isl_basic_map
*bmap
, int *progress
)
776 bmap
= isl_basic_map_order_divs(bmap
);
777 if (!bmap
|| bmap
->n_div
<= 1)
780 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
782 return isl_basic_map_free(bmap
);
783 total
= v_div
+ bmap
->n_div
;
786 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
787 if (!isl_int_is_zero(bmap
->div
[k
][0]))
792 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
795 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
796 bits
= ffs(size
) - 1;
797 index
= isl_calloc_array(ctx
, int, size
);
798 if (!elim_for
|| !index
)
800 eq
= isl_blk_alloc(ctx
, 1+total
);
801 if (isl_blk_is_error(eq
))
804 isl_seq_clr(eq
.data
, 1+total
);
805 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
806 for (--k
; k
>= 0; --k
) {
809 if (isl_int_is_zero(bmap
->div
[k
][0]))
812 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
813 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
814 if (isl_seq_eq(bmap
->div
[k
],
815 bmap
->div
[index
[h
]-1], 2+total
))
824 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
828 isl_int_set_si(eq
.data
[1 + v_div
+ k
], -1);
829 isl_int_set_si(eq
.data
[1 + v_div
+ l
], 1);
830 bmap
= eliminate_div(bmap
, eq
.data
, l
, 1);
833 isl_int_set_si(eq
.data
[1 + v_div
+ k
], 0);
834 isl_int_set_si(eq
.data
[1 + v_div
+ l
], 0);
837 isl_blk_free(ctx
, eq
);
844 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
849 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
852 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
853 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
857 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + v_div
, j
) != -1)
863 /* Normalize divs that appear in equalities.
865 * In particular, we assume that bmap contains some equalities
870 * and we want to replace the set of e_i by a minimal set and
871 * such that the new e_i have a canonical representation in terms
873 * If any of the equalities involves more than one divs, then
874 * we currently simply bail out.
876 * Let us first additionally assume that all equalities involve
877 * a div. The equalities then express modulo constraints on the
878 * remaining variables and we can use "parameter compression"
879 * to find a minimal set of constraints. The result is a transformation
881 * x = T(x') = x_0 + G x'
883 * with G a lower-triangular matrix with all elements below the diagonal
884 * non-negative and smaller than the diagonal element on the same row.
885 * We first normalize x_0 by making the same property hold in the affine
887 * The rows i of G with a 1 on the diagonal do not impose any modulo
888 * constraint and simply express x_i = x'_i.
889 * For each of the remaining rows i, we introduce a div and a corresponding
890 * equality. In particular
892 * g_ii e_j = x_i - g_i(x')
894 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
895 * corresponding div (if g_kk != 1).
897 * If there are any equalities not involving any div, then we
898 * first apply a variable compression on the variables x:
900 * x = C x'' x'' = C_2 x
902 * and perform the above parameter compression on A C instead of on A.
903 * The resulting compression is then of the form
905 * x'' = T(x') = x_0 + G x'
907 * and in constructing the new divs and the corresponding equalities,
908 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
909 * by the corresponding row from C_2.
911 static __isl_give isl_basic_map
*normalize_divs(__isl_take isl_basic_map
*bmap
,
919 struct isl_mat
*T
= NULL
;
920 struct isl_mat
*C
= NULL
;
921 struct isl_mat
*C2
= NULL
;
929 if (bmap
->n_div
== 0)
935 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
938 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
939 div_eq
= n_pure_div_eq(bmap
);
940 if (v_div
< 0 || div_eq
< 0)
941 return isl_basic_map_free(bmap
);
945 if (div_eq
< bmap
->n_eq
) {
946 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
947 bmap
->n_eq
- div_eq
, 0, 1 + v_div
);
948 C
= isl_mat_variable_compression(B
, &C2
);
952 bmap
= isl_basic_map_set_to_empty(bmap
);
959 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
962 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
963 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
965 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + v_div
+ j
]);
967 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + v_div
);
970 B
= isl_mat_product(B
, C
);
974 T
= isl_mat_parameter_compression(B
, d
);
978 bmap
= isl_basic_map_set_to_empty(bmap
);
984 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
985 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
986 if (isl_int_is_zero(v
))
988 isl_mat_col_submul(T
, 0, v
, 1 + i
);
991 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
994 /* We have to be careful because dropping equalities may reorder them */
996 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
997 for (i
= 0; i
< bmap
->n_eq
; ++i
)
998 if (!isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
1000 if (i
< bmap
->n_eq
) {
1001 bmap
= isl_basic_map_drop_div(bmap
, j
);
1002 isl_basic_map_drop_equality(bmap
, i
);
1008 for (i
= 1; i
< T
->n_row
; ++i
) {
1009 if (isl_int_is_one(T
->row
[i
][i
]))
1014 if (needed
> dropped
) {
1015 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
1020 for (i
= 1; i
< T
->n_row
; ++i
) {
1021 if (isl_int_is_one(T
->row
[i
][i
]))
1023 k
= isl_basic_map_alloc_div(bmap
);
1024 pos
[i
] = 1 + v_div
+ k
;
1025 isl_seq_clr(bmap
->div
[k
] + 1, 1 + v_div
+ bmap
->n_div
);
1026 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
1028 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + v_div
);
1030 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
1031 for (j
= 0; j
< i
; ++j
) {
1032 if (isl_int_is_zero(T
->row
[i
][j
]))
1034 if (pos
[j
] < T
->n_row
&& C2
)
1035 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
1036 C2
->row
[pos
[j
]], 1 + v_div
);
1038 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
1041 j
= isl_basic_map_alloc_equality(bmap
);
1042 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+v_div
+bmap
->n_div
);
1043 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
1052 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
1063 static __isl_give isl_basic_map
*set_div_from_lower_bound(
1064 __isl_take isl_basic_map
*bmap
, int div
, int ineq
)
1066 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1068 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1069 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1070 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1071 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1072 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1077 /* Check whether it is ok to define a div based on an inequality.
1078 * To avoid the introduction of circular definitions of divs, we
1079 * do not allow such a definition if the resulting expression would refer to
1080 * any other undefined divs or if any known div is defined in
1081 * terms of the unknown div.
1083 static isl_bool
ok_to_set_div_from_bound(__isl_keep isl_basic_map
*bmap
,
1087 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1089 /* Not defined in terms of unknown divs */
1090 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1093 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1095 if (isl_int_is_zero(bmap
->div
[j
][0]))
1096 return isl_bool_false
;
1099 /* No other div defined in terms of this one => avoid loops */
1100 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1103 if (isl_int_is_zero(bmap
->div
[j
][0]))
1105 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1106 return isl_bool_false
;
1109 return isl_bool_true
;
1112 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1113 * be a better expression than the current one?
1115 * If we do not have any expression yet, then any expression would be better.
1116 * Otherwise we check if the last variable involved in the inequality
1117 * (disregarding the div that it would define) is in an earlier position
1118 * than the last variable involved in the current div expression.
1120 static isl_bool
better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1123 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1127 if (isl_int_is_zero(bmap
->div
[div
][0]))
1128 return isl_bool_true
;
1130 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1131 bmap
->n_div
- (div
+ 1)) >= 0)
1132 return isl_bool_false
;
1134 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1135 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1136 total
+ bmap
->n_div
);
1138 return last_ineq
< last_div
;
1141 /* Given two constraints "k" and "l" that are opposite to each other,
1142 * except for the constant term, check if we can use them
1143 * to obtain an expression for one of the hitherto unknown divs or
1144 * a "better" expression for a div for which we already have an expression.
1145 * "sum" is the sum of the constant terms of the constraints.
1146 * If this sum is strictly smaller than the coefficient of one
1147 * of the divs, then this pair can be used define the div.
1148 * To avoid the introduction of circular definitions of divs, we
1149 * do not use the pair if the resulting expression would refer to
1150 * any other undefined divs or if any known div is defined in
1151 * terms of the unknown div.
1153 static __isl_give isl_basic_map
*check_for_div_constraints(
1154 __isl_take isl_basic_map
*bmap
, int k
, int l
, isl_int sum
,
1158 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1160 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1163 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1165 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1167 set_div
= better_div_constraint(bmap
, i
, k
);
1168 if (set_div
>= 0 && set_div
)
1169 set_div
= ok_to_set_div_from_bound(bmap
, i
, k
);
1171 return isl_basic_map_free(bmap
);
1174 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1175 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1177 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1185 __isl_give isl_basic_map
*isl_basic_map_remove_duplicate_constraints(
1186 __isl_take isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1188 struct isl_constraint_index ci
;
1190 unsigned total
= isl_basic_map_total_dim(bmap
);
1193 if (!bmap
|| bmap
->n_ineq
<= 1)
1196 if (create_constraint_index(&ci
, bmap
) < 0)
1199 h
= isl_seq_get_hash_bits(bmap
->ineq
[0] + 1, total
, ci
.bits
);
1200 ci
.index
[h
] = &bmap
->ineq
[0];
1201 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1202 h
= hash_index(&ci
, bmap
, k
);
1204 ci
.index
[h
] = &bmap
->ineq
[k
];
1209 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1210 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1211 swap_inequality(bmap
, k
, l
);
1212 isl_basic_map_drop_inequality(bmap
, k
);
1216 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1217 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1218 h
= hash_index(&ci
, bmap
, k
);
1219 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1222 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1223 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1224 if (isl_int_is_pos(sum
)) {
1226 bmap
= check_for_div_constraints(bmap
, k
, l
,
1230 if (isl_int_is_zero(sum
)) {
1231 /* We need to break out of the loop after these
1232 * changes since the contents of the hash
1233 * will no longer be valid.
1234 * Plus, we probably we want to regauss first.
1238 isl_basic_map_drop_inequality(bmap
, l
);
1239 isl_basic_map_inequality_to_equality(bmap
, k
);
1241 bmap
= isl_basic_map_set_to_empty(bmap
);
1246 constraint_index_free(&ci
);
1250 /* Detect all pairs of inequalities that form an equality.
1252 * isl_basic_map_remove_duplicate_constraints detects at most one such pair.
1253 * Call it repeatedly while it is making progress.
1255 __isl_give isl_basic_map
*isl_basic_map_detect_inequality_pairs(
1256 __isl_take isl_basic_map
*bmap
, int *progress
)
1262 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1264 if (progress
&& duplicate
)
1266 } while (duplicate
);
1271 /* Eliminate knowns divs from constraints where they appear with
1272 * a (positive or negative) unit coefficient.
1276 * floor(e/m) + f >= 0
1284 * -floor(e/m) + f >= 0
1288 * -e + m f + m - 1 >= 0
1290 * The first conversion is valid because floor(e/m) >= -f is equivalent
1291 * to e/m >= -f because -f is an integral expression.
1292 * The second conversion follows from the fact that
1294 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1297 * Note that one of the div constraints may have been eliminated
1298 * due to being redundant with respect to the constraint that is
1299 * being modified by this function. The modified constraint may
1300 * no longer imply this div constraint, so we add it back to make
1301 * sure we do not lose any information.
1303 * We skip integral divs, i.e., those with denominator 1, as we would
1304 * risk eliminating the div from the div constraints. We do not need
1305 * to handle those divs here anyway since the div constraints will turn
1306 * out to form an equality and this equality can then be used to eliminate
1307 * the div from all constraints.
1309 static __isl_give isl_basic_map
*eliminate_unit_divs(
1310 __isl_take isl_basic_map
*bmap
, int *progress
)
1319 ctx
= isl_basic_map_get_ctx(bmap
);
1320 total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1322 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1323 if (isl_int_is_zero(bmap
->div
[i
][0]))
1325 if (isl_int_is_one(bmap
->div
[i
][0]))
1327 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1330 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1331 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1336 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1337 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1339 isl_seq_combine(bmap
->ineq
[j
],
1340 ctx
->negone
, bmap
->div
[i
] + 1,
1341 bmap
->div
[i
][0], bmap
->ineq
[j
],
1342 total
+ bmap
->n_div
);
1344 isl_seq_combine(bmap
->ineq
[j
],
1345 ctx
->one
, bmap
->div
[i
] + 1,
1346 bmap
->div
[i
][0], bmap
->ineq
[j
],
1347 total
+ bmap
->n_div
);
1349 isl_int_add(bmap
->ineq
[j
][0],
1350 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1351 isl_int_sub_ui(bmap
->ineq
[j
][0],
1352 bmap
->ineq
[j
][0], 1);
1355 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
1356 bmap
= isl_basic_map_add_div_constraint(bmap
, i
, s
);
1365 __isl_give isl_basic_map
*isl_basic_map_simplify(__isl_take isl_basic_map
*bmap
)
1374 empty
= isl_basic_map_plain_is_empty(bmap
);
1376 return isl_basic_map_free(bmap
);
1379 bmap
= isl_basic_map_normalize_constraints(bmap
);
1380 bmap
= reduce_div_coefficients(bmap
);
1381 bmap
= normalize_div_expressions(bmap
);
1382 bmap
= remove_duplicate_divs(bmap
, &progress
);
1383 bmap
= eliminate_unit_divs(bmap
, &progress
);
1384 bmap
= eliminate_divs_eq(bmap
, &progress
);
1385 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1386 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1387 /* requires equalities in normal form */
1388 bmap
= normalize_divs(bmap
, &progress
);
1389 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1391 if (bmap
&& progress
)
1392 ISL_F_CLR(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
1397 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1399 return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset
)));
1403 isl_bool
isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1404 isl_int
*constraint
, unsigned div
)
1409 return isl_bool_error
;
1411 pos
= isl_basic_map_offset(bmap
, isl_dim_div
) + div
;
1413 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1415 isl_int_sub(bmap
->div
[div
][1],
1416 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1417 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1418 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1419 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1420 isl_int_add(bmap
->div
[div
][1],
1421 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1423 return isl_bool_false
;
1424 if (isl_seq_first_non_zero(constraint
+pos
+1,
1425 bmap
->n_div
-div
-1) != -1)
1426 return isl_bool_false
;
1427 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1428 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1429 return isl_bool_false
;
1430 if (isl_seq_first_non_zero(constraint
+pos
+1,
1431 bmap
->n_div
-div
-1) != -1)
1432 return isl_bool_false
;
1434 return isl_bool_false
;
1436 return isl_bool_true
;
1439 isl_bool
isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1440 isl_int
*constraint
, unsigned div
)
1442 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1446 /* If the only constraints a div d=floor(f/m)
1447 * appears in are its two defining constraints
1450 * -(f - (m - 1)) + m d >= 0
1452 * then it can safely be removed.
1454 static isl_bool
div_is_redundant(__isl_keep isl_basic_map
*bmap
, int div
)
1457 unsigned pos
= isl_basic_map_offset(bmap
, isl_dim_div
) + div
;
1459 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1460 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1461 return isl_bool_false
;
1463 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1466 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1468 red
= isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
);
1469 if (red
< 0 || !red
)
1473 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1474 if (isl_int_is_zero(bmap
->div
[i
][0]))
1476 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1477 return isl_bool_false
;
1480 return isl_bool_true
;
1484 * Remove divs that don't occur in any of the constraints or other divs.
1485 * These can arise when dropping constraints from a basic map or
1486 * when the divs of a basic map have been temporarily aligned
1487 * with the divs of another basic map.
1489 static __isl_give isl_basic_map
*remove_redundant_divs(
1490 __isl_take isl_basic_map
*bmap
)
1495 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1497 return isl_basic_map_free(bmap
);
1499 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1502 redundant
= div_is_redundant(bmap
, i
);
1504 return isl_basic_map_free(bmap
);
1507 bmap
= isl_basic_map_drop_constraints_involving(bmap
,
1509 bmap
= isl_basic_map_drop_div(bmap
, i
);
1514 /* Mark "bmap" as final, without checking for obviously redundant
1515 * integer divisions. This function should be used when "bmap"
1516 * is known not to involve any such integer divisions.
1518 __isl_give isl_basic_map
*isl_basic_map_mark_final(
1519 __isl_take isl_basic_map
*bmap
)
1523 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1527 /* Mark "bmap" as final, after removing obviously redundant integer divisions.
1529 __isl_give isl_basic_map
*isl_basic_map_finalize(__isl_take isl_basic_map
*bmap
)
1531 bmap
= remove_redundant_divs(bmap
);
1532 bmap
= isl_basic_map_mark_final(bmap
);
1536 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1538 return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset
)));
1541 /* Remove definition of any div that is defined in terms of the given variable.
1542 * The div itself is not removed. Functions such as
1543 * eliminate_divs_ineq depend on the other divs remaining in place.
1545 static __isl_give isl_basic_map
*remove_dependent_vars(
1546 __isl_take isl_basic_map
*bmap
, int pos
)
1553 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1554 if (isl_int_is_zero(bmap
->div
[i
][0]))
1556 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1558 bmap
= isl_basic_map_mark_div_unknown(bmap
, i
);
1565 /* Eliminate the specified variables from the constraints using
1566 * Fourier-Motzkin. The variables themselves are not removed.
1568 __isl_give isl_basic_map
*isl_basic_map_eliminate_vars(
1569 __isl_take isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1580 total
= isl_basic_map_total_dim(bmap
);
1582 bmap
= isl_basic_map_cow(bmap
);
1583 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1584 bmap
= remove_dependent_vars(bmap
, d
);
1588 for (d
= pos
+ n
- 1;
1589 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1590 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1591 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1592 int n_lower
, n_upper
;
1595 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1596 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1598 bmap
= eliminate_var_using_equality(bmap
, d
,
1599 bmap
->eq
[i
], 0, NULL
);
1600 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
1601 return isl_basic_map_free(bmap
);
1609 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1610 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1612 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1615 bmap
= isl_basic_map_extend_constraints(bmap
,
1616 0, n_lower
* n_upper
);
1619 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1621 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1624 for (j
= 0; j
< i
; ++j
) {
1625 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1628 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1629 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1631 k
= isl_basic_map_alloc_inequality(bmap
);
1634 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1636 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1637 1+d
, 1+total
, NULL
);
1639 isl_basic_map_drop_inequality(bmap
, i
);
1642 if (n_lower
> 0 && n_upper
> 0) {
1643 bmap
= isl_basic_map_normalize_constraints(bmap
);
1644 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1646 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1647 bmap
= isl_basic_map_remove_redundancies(bmap
);
1651 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1656 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1659 isl_basic_map_free(bmap
);
1663 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1664 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1666 return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset
),
1670 /* Eliminate the specified n dimensions starting at first from the
1671 * constraints, without removing the dimensions from the space.
1672 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1673 * Otherwise, they are projected out and the original space is restored.
1675 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1676 __isl_take isl_basic_map
*bmap
,
1677 enum isl_dim_type type
, unsigned first
, unsigned n
)
1686 if (isl_basic_map_check_range(bmap
, type
, first
, n
) < 0)
1687 return isl_basic_map_free(bmap
);
1689 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1690 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1691 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1692 return isl_basic_map_finalize(bmap
);
1695 space
= isl_basic_map_get_space(bmap
);
1696 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1697 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1698 bmap
= isl_basic_map_reset_space(bmap
, space
);
1702 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1703 __isl_take isl_basic_set
*bset
,
1704 enum isl_dim_type type
, unsigned first
, unsigned n
)
1706 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1709 /* Remove all constraints from "bmap" that reference any unknown local
1710 * variables (directly or indirectly).
1712 * Dropping all constraints on a local variable will make it redundant,
1713 * so it will get removed implicitly by
1714 * isl_basic_map_drop_constraints_involving_dims. Some other local
1715 * variables may also end up becoming redundant if they only appear
1716 * in constraints together with the unknown local variable.
1717 * Therefore, start over after calling
1718 * isl_basic_map_drop_constraints_involving_dims.
1720 __isl_give isl_basic_map
*isl_basic_map_drop_constraint_involving_unknown_divs(
1721 __isl_take isl_basic_map
*bmap
)
1724 int i
, n_div
, o_div
;
1726 known
= isl_basic_map_divs_known(bmap
);
1728 return isl_basic_map_free(bmap
);
1732 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1733 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
) - 1;
1735 for (i
= 0; i
< n_div
; ++i
) {
1736 known
= isl_basic_map_div_is_known(bmap
, i
);
1738 return isl_basic_map_free(bmap
);
1741 bmap
= remove_dependent_vars(bmap
, o_div
+ i
);
1742 bmap
= isl_basic_map_drop_constraints_involving_dims(bmap
,
1746 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1753 /* Remove all constraints from "map" that reference any unknown local
1754 * variables (directly or indirectly).
1756 * Since constraints may get dropped from the basic maps,
1757 * they may no longer be disjoint from each other.
1759 __isl_give isl_map
*isl_map_drop_constraint_involving_unknown_divs(
1760 __isl_take isl_map
*map
)
1765 known
= isl_map_divs_known(map
);
1767 return isl_map_free(map
);
1771 map
= isl_map_cow(map
);
1775 for (i
= 0; i
< map
->n
; ++i
) {
1777 isl_basic_map_drop_constraint_involving_unknown_divs(
1780 return isl_map_free(map
);
1784 ISL_F_CLR(map
, ISL_MAP_DISJOINT
);
1789 /* Don't assume equalities are in order, because align_divs
1790 * may have changed the order of the divs.
1792 static void compute_elimination_index(__isl_keep isl_basic_map
*bmap
, int *elim
)
1797 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1798 for (d
= 0; d
< total
; ++d
)
1800 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1801 for (d
= total
- 1; d
>= 0; --d
) {
1802 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1810 static void set_compute_elimination_index(__isl_keep isl_basic_set
*bset
,
1813 compute_elimination_index(bset_to_bmap(bset
), elim
);
1816 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1817 __isl_keep isl_basic_map
*bmap
, int *elim
)
1823 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1824 for (d
= total
- 1; d
>= 0; --d
) {
1825 if (isl_int_is_zero(src
[1+d
]))
1830 isl_seq_cpy(dst
, src
, 1 + total
);
1833 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1838 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1839 __isl_keep isl_basic_set
*bset
, int *elim
)
1841 return reduced_using_equalities(dst
, src
,
1842 bset_to_bmap(bset
), elim
);
1845 static __isl_give isl_basic_set
*isl_basic_set_reduce_using_equalities(
1846 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
1851 if (!bset
|| !context
)
1854 if (context
->n_eq
== 0) {
1855 isl_basic_set_free(context
);
1859 bset
= isl_basic_set_cow(bset
);
1863 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1866 set_compute_elimination_index(context
, elim
);
1867 for (i
= 0; i
< bset
->n_eq
; ++i
)
1868 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1870 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1871 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1873 isl_basic_set_free(context
);
1875 bset
= isl_basic_set_simplify(bset
);
1876 bset
= isl_basic_set_finalize(bset
);
1879 isl_basic_set_free(bset
);
1880 isl_basic_set_free(context
);
1884 /* For each inequality in "ineq" that is a shifted (more relaxed)
1885 * copy of an inequality in "context", mark the corresponding entry
1887 * If an inequality only has a non-negative constant term, then
1890 static isl_stat
mark_shifted_constraints(__isl_keep isl_mat
*ineq
,
1891 __isl_keep isl_basic_set
*context
, int *row
)
1893 struct isl_constraint_index ci
;
1898 if (!ineq
|| !context
)
1899 return isl_stat_error
;
1900 if (context
->n_ineq
== 0)
1902 if (setup_constraint_index(&ci
, context
) < 0)
1903 return isl_stat_error
;
1905 n_ineq
= isl_mat_rows(ineq
);
1906 total
= isl_mat_cols(ineq
) - 1;
1907 for (k
= 0; k
< n_ineq
; ++k
) {
1911 l
= isl_seq_first_non_zero(ineq
->row
[k
] + 1, total
);
1912 if (l
< 0 && isl_int_is_nonneg(ineq
->row
[k
][0])) {
1916 redundant
= constraint_index_is_redundant(&ci
, ineq
->row
[k
]);
1923 constraint_index_free(&ci
);
1926 constraint_index_free(&ci
);
1927 return isl_stat_error
;
1930 static __isl_give isl_basic_set
*remove_shifted_constraints(
1931 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*context
)
1933 struct isl_constraint_index ci
;
1936 if (!bset
|| !context
)
1939 if (context
->n_ineq
== 0)
1941 if (setup_constraint_index(&ci
, context
) < 0)
1944 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1947 redundant
= constraint_index_is_redundant(&ci
, bset
->ineq
[k
]);
1952 bset
= isl_basic_set_cow(bset
);
1955 isl_basic_set_drop_inequality(bset
, k
);
1958 constraint_index_free(&ci
);
1961 constraint_index_free(&ci
);
1965 /* Remove constraints from "bmap" that are identical to constraints
1966 * in "context" or that are more relaxed (greater constant term).
1968 * We perform the test for shifted copies on the pure constraints
1969 * in remove_shifted_constraints.
1971 static __isl_give isl_basic_map
*isl_basic_map_remove_shifted_constraints(
1972 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
1974 isl_basic_set
*bset
, *bset_context
;
1976 if (!bmap
|| !context
)
1979 if (bmap
->n_ineq
== 0 || context
->n_ineq
== 0) {
1980 isl_basic_map_free(context
);
1984 context
= isl_basic_map_align_divs(context
, bmap
);
1985 bmap
= isl_basic_map_align_divs(bmap
, context
);
1987 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
1988 bset_context
= isl_basic_map_underlying_set(context
);
1989 bset
= remove_shifted_constraints(bset
, bset_context
);
1990 isl_basic_set_free(bset_context
);
1992 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
1996 isl_basic_map_free(bmap
);
1997 isl_basic_map_free(context
);
2001 /* Does the (linear part of a) constraint "c" involve any of the "len"
2002 * "relevant" dimensions?
2004 static int is_related(isl_int
*c
, int len
, int *relevant
)
2008 for (i
= 0; i
< len
; ++i
) {
2011 if (!isl_int_is_zero(c
[i
]))
2018 /* Drop constraints from "bmap" that do not involve any of
2019 * the dimensions marked "relevant".
2021 static __isl_give isl_basic_map
*drop_unrelated_constraints(
2022 __isl_take isl_basic_map
*bmap
, int *relevant
)
2026 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
2027 for (i
= 0; i
< dim
; ++i
)
2033 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
)
2034 if (!is_related(bmap
->eq
[i
] + 1, dim
, relevant
)) {
2035 bmap
= isl_basic_map_cow(bmap
);
2036 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
2037 return isl_basic_map_free(bmap
);
2040 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
)
2041 if (!is_related(bmap
->ineq
[i
] + 1, dim
, relevant
)) {
2042 bmap
= isl_basic_map_cow(bmap
);
2043 if (isl_basic_map_drop_inequality(bmap
, i
) < 0)
2044 return isl_basic_map_free(bmap
);
2050 /* Update the groups in "group" based on the (linear part of a) constraint "c".
2052 * In particular, for any variable involved in the constraint,
2053 * find the actual group id from before and replace the group
2054 * of the corresponding variable by the minimal group of all
2055 * the variables involved in the constraint considered so far
2056 * (if this minimum is smaller) or replace the minimum by this group
2057 * (if the minimum is larger).
2059 * At the end, all the variables in "c" will (indirectly) point
2060 * to the minimal of the groups that they referred to originally.
2062 static void update_groups(int dim
, int *group
, isl_int
*c
)
2067 for (j
= 0; j
< dim
; ++j
) {
2068 if (isl_int_is_zero(c
[j
]))
2070 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
2071 group
[j
] = group
[group
[j
]];
2072 if (group
[j
] == min
)
2074 if (group
[j
] < min
) {
2075 if (min
>= 0 && min
< dim
)
2076 group
[min
] = group
[j
];
2079 group
[group
[j
]] = min
;
2083 /* Allocate an array of groups of variables, one for each variable
2084 * in "context", initialized to zero.
2086 static int *alloc_groups(__isl_keep isl_basic_set
*context
)
2091 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2092 ctx
= isl_basic_set_get_ctx(context
);
2093 return isl_calloc_array(ctx
, int, dim
);
2096 /* Drop constraints from "bmap" that only involve variables that are
2097 * not related to any of the variables marked with a "-1" in "group".
2099 * We construct groups of variables that collect variables that
2100 * (indirectly) appear in some common constraint of "bmap".
2101 * Each group is identified by the first variable in the group,
2102 * except for the special group of variables that was already identified
2103 * in the input as -1 (or are related to those variables).
2104 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
2105 * otherwise the group of i is the group of group[i].
2107 * We first initialize groups for the remaining variables.
2108 * Then we iterate over the constraints of "bmap" and update the
2109 * group of the variables in the constraint by the smallest group.
2110 * Finally, we resolve indirect references to groups by running over
2113 * After computing the groups, we drop constraints that do not involve
2114 * any variables in the -1 group.
2116 __isl_give isl_basic_map
*isl_basic_map_drop_unrelated_constraints(
2117 __isl_take isl_basic_map
*bmap
, __isl_take
int *group
)
2126 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
2129 for (i
= 0; i
< dim
; ++i
)
2131 last
= group
[i
] = i
;
2137 for (i
= 0; i
< bmap
->n_eq
; ++i
)
2138 update_groups(dim
, group
, bmap
->eq
[i
] + 1);
2139 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
2140 update_groups(dim
, group
, bmap
->ineq
[i
] + 1);
2142 for (i
= 0; i
< dim
; ++i
)
2144 group
[i
] = group
[group
[i
]];
2146 for (i
= 0; i
< dim
; ++i
)
2147 group
[i
] = group
[i
] == -1;
2149 bmap
= drop_unrelated_constraints(bmap
, group
);
2155 /* Drop constraints from "context" that are irrelevant for computing
2156 * the gist of "bset".
2158 * In particular, drop constraints in variables that are not related
2159 * to any of the variables involved in the constraints of "bset"
2160 * in the sense that there is no sequence of constraints that connects them.
2162 * We first mark all variables that appear in "bset" as belonging
2163 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2165 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
2166 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
2172 if (!context
|| !bset
)
2173 return isl_basic_set_free(context
);
2175 group
= alloc_groups(context
);
2178 return isl_basic_set_free(context
);
2180 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2181 for (i
= 0; i
< dim
; ++i
) {
2182 for (j
= 0; j
< bset
->n_eq
; ++j
)
2183 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
2185 if (j
< bset
->n_eq
) {
2189 for (j
= 0; j
< bset
->n_ineq
; ++j
)
2190 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
2192 if (j
< bset
->n_ineq
)
2196 return isl_basic_map_drop_unrelated_constraints(context
, group
);
2199 /* Drop constraints from "context" that are irrelevant for computing
2200 * the gist of the inequalities "ineq".
2201 * Inequalities in "ineq" for which the corresponding element of row
2202 * is set to -1 have already been marked for removal and should be ignored.
2204 * In particular, drop constraints in variables that are not related
2205 * to any of the variables involved in "ineq"
2206 * in the sense that there is no sequence of constraints that connects them.
2208 * We first mark all variables that appear in "bset" as belonging
2209 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2211 static __isl_give isl_basic_set
*drop_irrelevant_constraints_marked(
2212 __isl_take isl_basic_set
*context
, __isl_keep isl_mat
*ineq
, int *row
)
2218 if (!context
|| !ineq
)
2219 return isl_basic_set_free(context
);
2221 group
= alloc_groups(context
);
2224 return isl_basic_set_free(context
);
2226 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2227 n
= isl_mat_rows(ineq
);
2228 for (i
= 0; i
< dim
; ++i
) {
2229 for (j
= 0; j
< n
; ++j
) {
2232 if (!isl_int_is_zero(ineq
->row
[j
][1 + i
]))
2239 return isl_basic_map_drop_unrelated_constraints(context
, group
);
2242 /* Do all "n" entries of "row" contain a negative value?
2244 static int all_neg(int *row
, int n
)
2248 for (i
= 0; i
< n
; ++i
)
2255 /* Update the inequalities in "bset" based on the information in "row"
2258 * In particular, the array "row" contains either -1, meaning that
2259 * the corresponding inequality of "bset" is redundant, or the index
2260 * of an inequality in "tab".
2262 * If the row entry is -1, then drop the inequality.
2263 * Otherwise, if the constraint is marked redundant in the tableau,
2264 * then drop the inequality. Similarly, if it is marked as an equality
2265 * in the tableau, then turn the inequality into an equality and
2266 * perform Gaussian elimination.
2268 static __isl_give isl_basic_set
*update_ineq(__isl_take isl_basic_set
*bset
,
2269 __isl_keep
int *row
, struct isl_tab
*tab
)
2274 int found_equality
= 0;
2278 if (tab
&& tab
->empty
)
2279 return isl_basic_set_set_to_empty(bset
);
2281 n_ineq
= bset
->n_ineq
;
2282 for (i
= n_ineq
- 1; i
>= 0; --i
) {
2284 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2285 return isl_basic_set_free(bset
);
2291 if (isl_tab_is_equality(tab
, n_eq
+ row
[i
])) {
2292 isl_basic_map_inequality_to_equality(bset
, i
);
2294 } else if (isl_tab_is_redundant(tab
, n_eq
+ row
[i
])) {
2295 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2296 return isl_basic_set_free(bset
);
2301 bset
= isl_basic_set_gauss(bset
, NULL
);
2302 bset
= isl_basic_set_finalize(bset
);
2306 /* Update the inequalities in "bset" based on the information in "row"
2307 * and "tab" and free all arguments (other than "bset").
2309 static __isl_give isl_basic_set
*update_ineq_free(
2310 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*ineq
,
2311 __isl_take isl_basic_set
*context
, __isl_take
int *row
,
2312 struct isl_tab
*tab
)
2315 isl_basic_set_free(context
);
2317 bset
= update_ineq(bset
, row
, tab
);
2324 /* Remove all information from bset that is redundant in the context
2326 * "ineq" contains the (possibly transformed) inequalities of "bset",
2327 * in the same order.
2328 * The (explicit) equalities of "bset" are assumed to have been taken
2329 * into account by the transformation such that only the inequalities
2331 * "context" is assumed not to be empty.
2333 * "row" keeps track of the constraint index of a "bset" inequality in "tab".
2334 * A value of -1 means that the inequality is obviously redundant and may
2335 * not even appear in "tab".
2337 * We first mark the inequalities of "bset"
2338 * that are obviously redundant with respect to some inequality in "context".
2339 * Then we remove those constraints from "context" that have become
2340 * irrelevant for computing the gist of "bset".
2341 * Note that this removal of constraints cannot be replaced by
2342 * a factorization because factors in "bset" may still be connected
2343 * to each other through constraints in "context".
2345 * If there are any inequalities left, we construct a tableau for
2346 * the context and then add the inequalities of "bset".
2347 * Before adding these inequalities, we freeze all constraints such that
2348 * they won't be considered redundant in terms of the constraints of "bset".
2349 * Then we detect all redundant constraints (among the
2350 * constraints that weren't frozen), first by checking for redundancy in the
2351 * the tableau and then by checking if replacing a constraint by its negation
2352 * would lead to an empty set. This last step is fairly expensive
2353 * and could be optimized by more reuse of the tableau.
2354 * Finally, we update bset according to the results.
2356 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
2357 __isl_take isl_mat
*ineq
, __isl_take isl_basic_set
*context
)
2362 isl_basic_set
*combined
= NULL
;
2363 struct isl_tab
*tab
= NULL
;
2364 unsigned n_eq
, context_ineq
;
2366 if (!bset
|| !ineq
|| !context
)
2369 if (bset
->n_ineq
== 0 || isl_basic_set_plain_is_universe(context
)) {
2370 isl_basic_set_free(context
);
2375 ctx
= isl_basic_set_get_ctx(context
);
2376 row
= isl_calloc_array(ctx
, int, bset
->n_ineq
);
2380 if (mark_shifted_constraints(ineq
, context
, row
) < 0)
2382 if (all_neg(row
, bset
->n_ineq
))
2383 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
2385 context
= drop_irrelevant_constraints_marked(context
, ineq
, row
);
2388 if (isl_basic_set_plain_is_universe(context
))
2389 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
2391 n_eq
= context
->n_eq
;
2392 context_ineq
= context
->n_ineq
;
2393 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
2394 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
2395 tab
= isl_tab_from_basic_set(combined
, 0);
2396 for (i
= 0; i
< context_ineq
; ++i
)
2397 if (isl_tab_freeze_constraint(tab
, n_eq
+ i
) < 0)
2399 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
2402 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2405 combined
= isl_basic_set_add_ineq(combined
, ineq
->row
[i
]);
2406 if (isl_tab_add_ineq(tab
, ineq
->row
[i
]) < 0)
2410 if (isl_tab_detect_implicit_equalities(tab
) < 0)
2412 if (isl_tab_detect_redundant(tab
) < 0)
2414 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
2415 isl_basic_set
*test
;
2421 if (tab
->con
[n_eq
+ r
].is_redundant
)
2423 test
= isl_basic_set_dup(combined
);
2424 test
= isl_inequality_negate(test
, r
);
2425 test
= isl_basic_set_update_from_tab(test
, tab
);
2426 is_empty
= isl_basic_set_is_empty(test
);
2427 isl_basic_set_free(test
);
2431 tab
->con
[n_eq
+ r
].is_redundant
= 1;
2433 bset
= update_ineq_free(bset
, ineq
, context
, row
, tab
);
2435 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2436 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2439 isl_basic_set_free(combined
);
2445 isl_basic_set_free(combined
);
2446 isl_basic_set_free(context
);
2447 isl_basic_set_free(bset
);
2451 /* Extract the inequalities of "bset" as an isl_mat.
2453 static __isl_give isl_mat
*extract_ineq(__isl_keep isl_basic_set
*bset
)
2462 ctx
= isl_basic_set_get_ctx(bset
);
2463 total
= isl_basic_set_total_dim(bset
);
2464 ineq
= isl_mat_sub_alloc6(ctx
, bset
->ineq
, 0, bset
->n_ineq
,
2470 /* Remove all information from "bset" that is redundant in the context
2471 * of "context", for the case where both "bset" and "context" are
2474 static __isl_give isl_basic_set
*uset_gist_uncompressed(
2475 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
2479 ineq
= extract_ineq(bset
);
2480 return uset_gist_full(bset
, ineq
, context
);
2483 /* Remove all information from "bset" that is redundant in the context
2484 * of "context", for the case where the combined equalities of
2485 * "bset" and "context" allow for a compression that can be obtained
2486 * by preapplication of "T".
2488 * "bset" itself is not transformed by "T". Instead, the inequalities
2489 * are extracted from "bset" and those are transformed by "T".
2490 * uset_gist_full then determines which of the transformed inequalities
2491 * are redundant with respect to the transformed "context" and removes
2492 * the corresponding inequalities from "bset".
2494 * After preapplying "T" to the inequalities, any common factor is
2495 * removed from the coefficients. If this results in a tightening
2496 * of the constant term, then the same tightening is applied to
2497 * the corresponding untransformed inequality in "bset".
2498 * That is, if after plugging in T, a constraint f(x) >= 0 is of the form
2502 * with 0 <= r < g, then it is equivalent to
2506 * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
2507 * subspace compressed by T since the latter would be transformed to
2511 static __isl_give isl_basic_set
*uset_gist_compressed(
2512 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
,
2513 __isl_take isl_mat
*T
)
2517 int i
, n_row
, n_col
;
2520 ineq
= extract_ineq(bset
);
2521 ineq
= isl_mat_product(ineq
, isl_mat_copy(T
));
2522 context
= isl_basic_set_preimage(context
, T
);
2524 if (!ineq
|| !context
)
2526 if (isl_basic_set_plain_is_empty(context
)) {
2528 isl_basic_set_free(context
);
2529 return isl_basic_set_set_to_empty(bset
);
2532 ctx
= isl_mat_get_ctx(ineq
);
2533 n_row
= isl_mat_rows(ineq
);
2534 n_col
= isl_mat_cols(ineq
);
2536 for (i
= 0; i
< n_row
; ++i
) {
2537 isl_seq_gcd(ineq
->row
[i
] + 1, n_col
- 1, &ctx
->normalize_gcd
);
2538 if (isl_int_is_zero(ctx
->normalize_gcd
))
2540 if (isl_int_is_one(ctx
->normalize_gcd
))
2542 isl_seq_scale_down(ineq
->row
[i
] + 1, ineq
->row
[i
] + 1,
2543 ctx
->normalize_gcd
, n_col
- 1);
2544 isl_int_fdiv_r(rem
, ineq
->row
[i
][0], ctx
->normalize_gcd
);
2545 isl_int_fdiv_q(ineq
->row
[i
][0],
2546 ineq
->row
[i
][0], ctx
->normalize_gcd
);
2547 if (isl_int_is_zero(rem
))
2549 bset
= isl_basic_set_cow(bset
);
2552 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], rem
);
2556 return uset_gist_full(bset
, ineq
, context
);
2559 isl_basic_set_free(context
);
2560 isl_basic_set_free(bset
);
2564 /* Project "bset" onto the variables that are involved in "template".
2566 static __isl_give isl_basic_set
*project_onto_involved(
2567 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*template)
2571 if (!bset
|| !template)
2572 return isl_basic_set_free(bset
);
2574 n
= isl_basic_set_dim(template, isl_dim_set
);
2576 for (i
= 0; i
< n
; ++i
) {
2579 involved
= isl_basic_set_involves_dims(template,
2582 return isl_basic_set_free(bset
);
2585 bset
= isl_basic_set_eliminate_vars(bset
, i
, 1);
2591 /* Remove all information from bset that is redundant in the context
2592 * of context. In particular, equalities that are linear combinations
2593 * of those in context are removed. Then the inequalities that are
2594 * redundant in the context of the equalities and inequalities of
2595 * context are removed.
2597 * First of all, we drop those constraints from "context"
2598 * that are irrelevant for computing the gist of "bset".
2599 * Alternatively, we could factorize the intersection of "context" and "bset".
2601 * We first compute the intersection of the integer affine hulls
2602 * of "bset" and "context",
2603 * compute the gist inside this intersection and then reduce
2604 * the constraints with respect to the equalities of the context
2605 * that only involve variables already involved in the input.
2607 * If two constraints are mutually redundant, then uset_gist_full
2608 * will remove the second of those constraints. We therefore first
2609 * sort the constraints so that constraints not involving existentially
2610 * quantified variables are given precedence over those that do.
2611 * We have to perform this sorting before the variable compression,
2612 * because that may effect the order of the variables.
2614 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2615 __isl_take isl_basic_set
*context
)
2620 isl_basic_set
*aff_context
;
2623 if (!bset
|| !context
)
2626 context
= drop_irrelevant_constraints(context
, bset
);
2628 bset
= isl_basic_set_detect_equalities(bset
);
2629 aff
= isl_basic_set_copy(bset
);
2630 aff
= isl_basic_set_plain_affine_hull(aff
);
2631 context
= isl_basic_set_detect_equalities(context
);
2632 aff_context
= isl_basic_set_copy(context
);
2633 aff_context
= isl_basic_set_plain_affine_hull(aff_context
);
2634 aff
= isl_basic_set_intersect(aff
, aff_context
);
2637 if (isl_basic_set_plain_is_empty(aff
)) {
2638 isl_basic_set_free(bset
);
2639 isl_basic_set_free(context
);
2642 bset
= isl_basic_set_sort_constraints(bset
);
2643 if (aff
->n_eq
== 0) {
2644 isl_basic_set_free(aff
);
2645 return uset_gist_uncompressed(bset
, context
);
2647 total
= isl_basic_set_total_dim(bset
);
2648 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2649 eq
= isl_mat_cow(eq
);
2650 T
= isl_mat_variable_compression(eq
, NULL
);
2651 isl_basic_set_free(aff
);
2652 if (T
&& T
->n_col
== 0) {
2654 isl_basic_set_free(context
);
2655 return isl_basic_set_set_to_empty(bset
);
2658 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2659 aff_context
= project_onto_involved(aff_context
, bset
);
2661 bset
= uset_gist_compressed(bset
, context
, T
);
2662 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2665 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2666 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2671 isl_basic_set_free(bset
);
2672 isl_basic_set_free(context
);
2676 /* Return the number of equality constraints in "bmap" that involve
2677 * local variables. This function assumes that Gaussian elimination
2678 * has been applied to the equality constraints.
2680 static int n_div_eq(__isl_keep isl_basic_map
*bmap
)
2688 if (bmap
->n_eq
== 0)
2691 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2692 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2695 for (i
= 0; i
< bmap
->n_eq
; ++i
)
2696 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
,
2703 /* Construct a basic map in "space" defined by the equality constraints in "eq".
2704 * The constraints are assumed not to involve any local variables.
2706 static __isl_give isl_basic_map
*basic_map_from_equalities(
2707 __isl_take isl_space
*space
, __isl_take isl_mat
*eq
)
2710 isl_basic_map
*bmap
= NULL
;
2715 if (1 + isl_space_dim(space
, isl_dim_all
) != eq
->n_col
)
2716 isl_die(isl_space_get_ctx(space
), isl_error_internal
,
2717 "unexpected number of columns", goto error
);
2719 bmap
= isl_basic_map_alloc_space(isl_space_copy(space
),
2721 for (i
= 0; i
< eq
->n_row
; ++i
) {
2722 k
= isl_basic_map_alloc_equality(bmap
);
2725 isl_seq_cpy(bmap
->eq
[k
], eq
->row
[i
], eq
->n_col
);
2728 isl_space_free(space
);
2732 isl_space_free(space
);
2734 isl_basic_map_free(bmap
);
2738 /* Construct and return a variable compression based on the equality
2739 * constraints in "bmap1" and "bmap2" that do not involve the local variables.
2740 * "n1" is the number of (initial) equality constraints in "bmap1"
2741 * that do involve local variables.
2742 * "n2" is the number of (initial) equality constraints in "bmap2"
2743 * that do involve local variables.
2744 * "total" is the total number of other variables.
2745 * This function assumes that Gaussian elimination
2746 * has been applied to the equality constraints in both "bmap1" and "bmap2"
2747 * such that the equality constraints not involving local variables
2748 * are those that start at "n1" or "n2".
2750 * If either of "bmap1" and "bmap2" does not have such equality constraints,
2751 * then simply compute the compression based on the equality constraints
2752 * in the other basic map.
2753 * Otherwise, combine the equality constraints from both into a new
2754 * basic map such that Gaussian elimination can be applied to this combination
2755 * and then construct a variable compression from the resulting
2756 * equality constraints.
2758 static __isl_give isl_mat
*combined_variable_compression(
2759 __isl_keep isl_basic_map
*bmap1
, int n1
,
2760 __isl_keep isl_basic_map
*bmap2
, int n2
, int total
)
2763 isl_mat
*E1
, *E2
, *V
;
2764 isl_basic_map
*bmap
;
2766 ctx
= isl_basic_map_get_ctx(bmap1
);
2767 if (bmap1
->n_eq
== n1
) {
2768 E2
= isl_mat_sub_alloc6(ctx
, bmap2
->eq
,
2769 n2
, bmap2
->n_eq
- n2
, 0, 1 + total
);
2770 return isl_mat_variable_compression(E2
, NULL
);
2772 if (bmap2
->n_eq
== n2
) {
2773 E1
= isl_mat_sub_alloc6(ctx
, bmap1
->eq
,
2774 n1
, bmap1
->n_eq
- n1
, 0, 1 + total
);
2775 return isl_mat_variable_compression(E1
, NULL
);
2777 E1
= isl_mat_sub_alloc6(ctx
, bmap1
->eq
,
2778 n1
, bmap1
->n_eq
- n1
, 0, 1 + total
);
2779 E2
= isl_mat_sub_alloc6(ctx
, bmap2
->eq
,
2780 n2
, bmap2
->n_eq
- n2
, 0, 1 + total
);
2781 E1
= isl_mat_concat(E1
, E2
);
2782 bmap
= basic_map_from_equalities(isl_basic_map_get_space(bmap1
), E1
);
2783 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2786 E1
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
, 0, 1 + total
);
2787 V
= isl_mat_variable_compression(E1
, NULL
);
2788 isl_basic_map_free(bmap
);
2793 /* Extract the stride constraints from "bmap", compressed
2794 * with respect to both the stride constraints in "context" and
2795 * the remaining equality constraints in both "bmap" and "context".
2796 * "bmap_n_eq" is the number of (initial) stride constraints in "bmap".
2797 * "context_n_eq" is the number of (initial) stride constraints in "context".
2799 * Let x be all variables in "bmap" (and "context") other than the local
2800 * variables. First compute a variable compression
2804 * based on the non-stride equality constraints in "bmap" and "context".
2805 * Consider the stride constraints of "context",
2809 * with y the local variables and plug in the variable compression,
2812 * A(V x') + B(y) = 0
2814 * Use these constraints to compute a parameter compression on x'
2818 * Now consider the stride constraints of "bmap"
2822 * and plug in x = V*T x''.
2823 * That is, return A = [C*V*T D].
2825 static __isl_give isl_mat
*extract_compressed_stride_constraints(
2826 __isl_keep isl_basic_map
*bmap
, int bmap_n_eq
,
2827 __isl_keep isl_basic_map
*context
, int context_n_eq
)
2831 isl_mat
*A
, *B
, *T
, *V
;
2833 total
= isl_basic_map_dim(context
, isl_dim_all
);
2834 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
2837 ctx
= isl_basic_map_get_ctx(bmap
);
2839 V
= combined_variable_compression(bmap
, bmap_n_eq
,
2840 context
, context_n_eq
, total
);
2842 A
= isl_mat_sub_alloc6(ctx
, context
->eq
, 0, context_n_eq
, 0, 1 + total
);
2843 B
= isl_mat_sub_alloc6(ctx
, context
->eq
,
2844 0, context_n_eq
, 1 + total
, n_div
);
2845 A
= isl_mat_product(A
, isl_mat_copy(V
));
2846 T
= isl_mat_parameter_compression_ext(A
, B
);
2847 T
= isl_mat_product(V
, T
);
2849 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2850 T
= isl_mat_diagonal(T
, isl_mat_identity(ctx
, n_div
));
2852 A
= isl_mat_sub_alloc6(ctx
, bmap
->eq
,
2853 0, bmap_n_eq
, 0, 1 + total
+ n_div
);
2854 A
= isl_mat_product(A
, T
);
2859 /* Remove the prime factors from *g that have an exponent that
2860 * is strictly smaller than the exponent in "c".
2861 * All exponents in *g are known to be smaller than or equal
2864 * That is, if *g is equal to
2866 * p_1^{e_1} p_2^{e_2} ... p_n^{e_n}
2868 * and "c" is equal to
2870 * p_1^{f_1} p_2^{f_2} ... p_n^{f_n}
2874 * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ...
2875 * p_n^{e_n * (e_n = f_n)}
2877 * If e_i = f_i, then c / *g does not have any p_i factors and therefore
2878 * neither does the gcd of *g and c / *g.
2879 * If e_i < f_i, then the gcd of *g and c / *g has a positive
2880 * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors.
2881 * Dividing *g by this gcd therefore strictly reduces the exponent
2882 * of the prime factors that need to be removed, while leaving the
2883 * other prime factors untouched.
2884 * Repeating this process until gcd(*g, c / *g) = 1 therefore
2885 * removes all undesired factors, without removing any others.
2887 static void remove_incomplete_powers(isl_int
*g
, isl_int c
)
2893 isl_int_divexact(t
, c
, *g
);
2894 isl_int_gcd(t
, t
, *g
);
2895 if (isl_int_is_one(t
))
2897 isl_int_divexact(*g
, *g
, t
);
2902 /* Reduce the "n" stride constraints in "bmap" based on a copy "A"
2903 * of the same stride constraints in a compressed space that exploits
2904 * all equalities in the context and the other equalities in "bmap".
2906 * If the stride constraints of "bmap" are of the form
2910 * then A is of the form
2914 * If any of these constraints involves only a single local variable y,
2915 * then the constraint appears as
2925 * Let g be the gcd of m and the coefficients of h.
2926 * Then, in particular, g is a divisor of the coefficients of h and
2930 * is known to be a multiple of g.
2931 * If some prime factor in m appears with the same exponent in g,
2932 * then it can be removed from m because f(x) is already known
2933 * to be a multiple of g and therefore in particular of this power
2934 * of the prime factors.
2935 * Prime factors that appear with a smaller exponent in g cannot
2936 * be removed from m.
2937 * Let g' be the divisor of g containing all prime factors that
2938 * appear with the same exponent in m and g, then
2942 * can be replaced by
2944 * f(x) + m/g' y_i' = 0
2946 * Note that (if g' != 1) this changes the explicit representation
2947 * of y_i to that of y_i', so the integer division at position i
2948 * is marked unknown and later recomputed by a call to
2949 * isl_basic_map_gauss.
2951 static __isl_give isl_basic_map
*reduce_stride_constraints(
2952 __isl_take isl_basic_map
*bmap
, int n
, __isl_keep isl_mat
*A
)
2960 return isl_basic_map_free(bmap
);
2962 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2963 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2967 for (i
= 0; i
< n
; ++i
) {
2970 div
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, n_div
);
2972 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2973 "equality constraints modified unexpectedly",
2975 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
+ div
+ 1,
2976 n_div
- div
- 1) != -1)
2978 if (isl_mat_row_gcd(A
, i
, &gcd
) < 0)
2980 if (isl_int_is_one(gcd
))
2982 remove_incomplete_powers(&gcd
, bmap
->eq
[i
][1 + total
+ div
]);
2983 if (isl_int_is_one(gcd
))
2985 isl_int_divexact(bmap
->eq
[i
][1 + total
+ div
],
2986 bmap
->eq
[i
][1 + total
+ div
], gcd
);
2987 bmap
= isl_basic_map_mark_div_unknown(bmap
, div
);
2995 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3000 isl_basic_map_free(bmap
);
3004 /* Simplify the stride constraints in "bmap" based on
3005 * the remaining equality constraints in "bmap" and all equality
3006 * constraints in "context".
3007 * Only do this if both "bmap" and "context" have stride constraints.
3009 * First extract a copy of the stride constraints in "bmap" in a compressed
3010 * space exploiting all the other equality constraints and then
3011 * use this compressed copy to simplify the original stride constraints.
3013 static __isl_give isl_basic_map
*gist_strides(__isl_take isl_basic_map
*bmap
,
3014 __isl_keep isl_basic_map
*context
)
3016 int bmap_n_eq
, context_n_eq
;
3019 if (!bmap
|| !context
)
3020 return isl_basic_map_free(bmap
);
3022 bmap_n_eq
= n_div_eq(bmap
);
3023 context_n_eq
= n_div_eq(context
);
3025 if (bmap_n_eq
< 0 || context_n_eq
< 0)
3026 return isl_basic_map_free(bmap
);
3027 if (bmap_n_eq
== 0 || context_n_eq
== 0)
3030 A
= extract_compressed_stride_constraints(bmap
, bmap_n_eq
,
3031 context
, context_n_eq
);
3032 bmap
= reduce_stride_constraints(bmap
, bmap_n_eq
, A
);
3039 /* Return a basic map that has the same intersection with "context" as "bmap"
3040 * and that is as "simple" as possible.
3042 * The core computation is performed on the pure constraints.
3043 * When we add back the meaning of the integer divisions, we need
3044 * to (re)introduce the div constraints. If we happen to have
3045 * discovered that some of these integer divisions are equal to
3046 * some affine combination of other variables, then these div
3047 * constraints may end up getting simplified in terms of the equalities,
3048 * resulting in extra inequalities on the other variables that
3049 * may have been removed already or that may not even have been
3050 * part of the input. We try and remove those constraints of
3051 * this form that are most obviously redundant with respect to
3052 * the context. We also remove those div constraints that are
3053 * redundant with respect to the other constraints in the result.
3055 * The stride constraints among the equality constraints in "bmap" are
3056 * also simplified with respecting to the other equality constraints
3057 * in "bmap" and with respect to all equality constraints in "context".
3059 __isl_give isl_basic_map
*isl_basic_map_gist(__isl_take isl_basic_map
*bmap
,
3060 __isl_take isl_basic_map
*context
)
3062 isl_basic_set
*bset
, *eq
;
3063 isl_basic_map
*eq_bmap
;
3064 unsigned total
, n_div
, extra
, n_eq
, n_ineq
;
3066 if (!bmap
|| !context
)
3069 if (isl_basic_map_plain_is_universe(bmap
)) {
3070 isl_basic_map_free(context
);
3073 if (isl_basic_map_plain_is_empty(context
)) {
3074 isl_space
*space
= isl_basic_map_get_space(bmap
);
3075 isl_basic_map_free(bmap
);
3076 isl_basic_map_free(context
);
3077 return isl_basic_map_universe(space
);
3079 if (isl_basic_map_plain_is_empty(bmap
)) {
3080 isl_basic_map_free(context
);
3084 bmap
= isl_basic_map_remove_redundancies(bmap
);
3085 context
= isl_basic_map_remove_redundancies(context
);
3086 context
= isl_basic_map_align_divs(context
, bmap
);
3090 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
3091 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3092 extra
= n_div
- isl_basic_map_dim(bmap
, isl_dim_div
);
3094 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
3095 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, extra
);
3096 bset
= uset_gist(bset
,
3097 isl_basic_map_underlying_set(isl_basic_map_copy(context
)));
3098 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, total
, extra
);
3100 if (!bset
|| bset
->n_eq
== 0 || n_div
== 0 ||
3101 isl_basic_set_plain_is_empty(bset
)) {
3102 isl_basic_map_free(context
);
3103 return isl_basic_map_overlying_set(bset
, bmap
);
3107 n_ineq
= bset
->n_ineq
;
3108 eq
= isl_basic_set_copy(bset
);
3109 eq
= isl_basic_set_cow(eq
);
3110 if (isl_basic_set_free_inequality(eq
, n_ineq
) < 0)
3111 eq
= isl_basic_set_free(eq
);
3112 if (isl_basic_set_free_equality(bset
, n_eq
) < 0)
3113 bset
= isl_basic_set_free(bset
);
3115 eq_bmap
= isl_basic_map_overlying_set(eq
, isl_basic_map_copy(bmap
));
3116 eq_bmap
= gist_strides(eq_bmap
, context
);
3117 eq_bmap
= isl_basic_map_remove_shifted_constraints(eq_bmap
, context
);
3118 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
3119 bmap
= isl_basic_map_intersect(bmap
, eq_bmap
);
3120 bmap
= isl_basic_map_remove_redundancies(bmap
);
3124 isl_basic_map_free(bmap
);
3125 isl_basic_map_free(context
);
3130 * Assumes context has no implicit divs.
3132 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
3133 __isl_take isl_basic_map
*context
)
3137 if (!map
|| !context
)
3140 if (isl_basic_map_plain_is_empty(context
)) {
3141 isl_space
*space
= isl_map_get_space(map
);
3143 isl_basic_map_free(context
);
3144 return isl_map_universe(space
);
3147 context
= isl_basic_map_remove_redundancies(context
);
3148 map
= isl_map_cow(map
);
3149 if (!map
|| !context
)
3151 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
3152 map
= isl_map_compute_divs(map
);
3155 for (i
= map
->n
- 1; i
>= 0; --i
) {
3156 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
3157 isl_basic_map_copy(context
));
3160 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
3161 isl_basic_map_free(map
->p
[i
]);
3162 if (i
!= map
->n
- 1)
3163 map
->p
[i
] = map
->p
[map
->n
- 1];
3167 isl_basic_map_free(context
);
3168 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3172 isl_basic_map_free(context
);
3176 /* Drop all inequalities from "bmap" that also appear in "context".
3177 * "context" is assumed to have only known local variables and
3178 * the initial local variables of "bmap" are assumed to be the same
3179 * as those of "context".
3180 * The constraints of both "bmap" and "context" are assumed
3181 * to have been sorted using isl_basic_map_sort_constraints.
3183 * Run through the inequality constraints of "bmap" and "context"
3185 * If a constraint of "bmap" involves variables not in "context",
3186 * then it cannot appear in "context".
3187 * If a matching constraint is found, it is removed from "bmap".
3189 static __isl_give isl_basic_map
*drop_inequalities(
3190 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_map
*context
)
3193 unsigned total
, extra
;
3195 if (!bmap
|| !context
)
3196 return isl_basic_map_free(bmap
);
3198 total
= isl_basic_map_total_dim(context
);
3199 extra
= isl_basic_map_total_dim(bmap
) - total
;
3201 i1
= bmap
->n_ineq
- 1;
3202 i2
= context
->n_ineq
- 1;
3203 while (bmap
&& i1
>= 0 && i2
>= 0) {
3206 if (isl_seq_first_non_zero(bmap
->ineq
[i1
] + 1 + total
,
3211 cmp
= isl_basic_map_constraint_cmp(context
, bmap
->ineq
[i1
],
3221 if (isl_int_eq(bmap
->ineq
[i1
][0], context
->ineq
[i2
][0])) {
3222 bmap
= isl_basic_map_cow(bmap
);
3223 if (isl_basic_map_drop_inequality(bmap
, i1
) < 0)
3224 bmap
= isl_basic_map_free(bmap
);
3233 /* Drop all equalities from "bmap" that also appear in "context".
3234 * "context" is assumed to have only known local variables and
3235 * the initial local variables of "bmap" are assumed to be the same
3236 * as those of "context".
3238 * Run through the equality constraints of "bmap" and "context"
3240 * If a constraint of "bmap" involves variables not in "context",
3241 * then it cannot appear in "context".
3242 * If a matching constraint is found, it is removed from "bmap".
3244 static __isl_give isl_basic_map
*drop_equalities(
3245 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_map
*context
)
3248 unsigned total
, extra
;
3250 if (!bmap
|| !context
)
3251 return isl_basic_map_free(bmap
);
3253 total
= isl_basic_map_total_dim(context
);
3254 extra
= isl_basic_map_total_dim(bmap
) - total
;
3256 i1
= bmap
->n_eq
- 1;
3257 i2
= context
->n_eq
- 1;
3259 while (bmap
&& i1
>= 0 && i2
>= 0) {
3262 if (isl_seq_first_non_zero(bmap
->eq
[i1
] + 1 + total
,
3265 last1
= isl_seq_last_non_zero(bmap
->eq
[i1
] + 1, total
);
3266 last2
= isl_seq_last_non_zero(context
->eq
[i2
] + 1, total
);
3267 if (last1
> last2
) {
3271 if (last1
< last2
) {
3275 if (isl_seq_eq(bmap
->eq
[i1
], context
->eq
[i2
], 1 + total
)) {
3276 bmap
= isl_basic_map_cow(bmap
);
3277 if (isl_basic_map_drop_equality(bmap
, i1
) < 0)
3278 bmap
= isl_basic_map_free(bmap
);
3287 /* Remove the constraints in "context" from "bmap".
3288 * "context" is assumed to have explicit representations
3289 * for all local variables.
3291 * First align the divs of "bmap" to those of "context" and
3292 * sort the constraints. Then drop all constraints from "bmap"
3293 * that appear in "context".
3295 __isl_give isl_basic_map
*isl_basic_map_plain_gist(
3296 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
3298 isl_bool done
, known
;
3300 done
= isl_basic_map_plain_is_universe(context
);
3301 if (done
== isl_bool_false
)
3302 done
= isl_basic_map_plain_is_universe(bmap
);
3303 if (done
== isl_bool_false
)
3304 done
= isl_basic_map_plain_is_empty(context
);
3305 if (done
== isl_bool_false
)
3306 done
= isl_basic_map_plain_is_empty(bmap
);
3310 isl_basic_map_free(context
);
3313 known
= isl_basic_map_divs_known(context
);
3317 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
3318 "context has unknown divs", goto error
);
3320 bmap
= isl_basic_map_align_divs(bmap
, context
);
3321 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3322 bmap
= isl_basic_map_sort_constraints(bmap
);
3323 context
= isl_basic_map_sort_constraints(context
);
3325 bmap
= drop_inequalities(bmap
, context
);
3326 bmap
= drop_equalities(bmap
, context
);
3328 isl_basic_map_free(context
);
3329 bmap
= isl_basic_map_finalize(bmap
);
3332 isl_basic_map_free(bmap
);
3333 isl_basic_map_free(context
);
3337 /* Replace "map" by the disjunct at position "pos" and free "context".
3339 static __isl_give isl_map
*replace_by_disjunct(__isl_take isl_map
*map
,
3340 int pos
, __isl_take isl_basic_map
*context
)
3342 isl_basic_map
*bmap
;
3344 bmap
= isl_basic_map_copy(map
->p
[pos
]);
3346 isl_basic_map_free(context
);
3347 return isl_map_from_basic_map(bmap
);
3350 /* Remove the constraints in "context" from "map".
3351 * If any of the disjuncts in the result turns out to be the universe,
3352 * then return this universe.
3353 * "context" is assumed to have explicit representations
3354 * for all local variables.
3356 __isl_give isl_map
*isl_map_plain_gist_basic_map(__isl_take isl_map
*map
,
3357 __isl_take isl_basic_map
*context
)
3360 isl_bool univ
, known
;
3362 univ
= isl_basic_map_plain_is_universe(context
);
3366 isl_basic_map_free(context
);
3369 known
= isl_basic_map_divs_known(context
);
3373 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
3374 "context has unknown divs", goto error
);
3376 map
= isl_map_cow(map
);
3379 for (i
= 0; i
< map
->n
; ++i
) {
3380 map
->p
[i
] = isl_basic_map_plain_gist(map
->p
[i
],
3381 isl_basic_map_copy(context
));
3382 univ
= isl_basic_map_plain_is_universe(map
->p
[i
]);
3385 if (univ
&& map
->n
> 1)
3386 return replace_by_disjunct(map
, i
, context
);
3389 isl_basic_map_free(context
);
3390 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3392 ISL_F_CLR(map
, ISL_MAP_DISJOINT
);
3396 isl_basic_map_free(context
);
3400 /* Remove the constraints in "context" from "set".
3401 * If any of the disjuncts in the result turns out to be the universe,
3402 * then return this universe.
3403 * "context" is assumed to have explicit representations
3404 * for all local variables.
3406 __isl_give isl_set
*isl_set_plain_gist_basic_set(__isl_take isl_set
*set
,
3407 __isl_take isl_basic_set
*context
)
3409 return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set
),
3410 bset_to_bmap(context
)));
3413 /* Remove the constraints in "context" from "map".
3414 * If any of the disjuncts in the result turns out to be the universe,
3415 * then return this universe.
3416 * "context" is assumed to consist of a single disjunct and
3417 * to have explicit representations for all local variables.
3419 __isl_give isl_map
*isl_map_plain_gist(__isl_take isl_map
*map
,
3420 __isl_take isl_map
*context
)
3422 isl_basic_map
*hull
;
3424 hull
= isl_map_unshifted_simple_hull(context
);
3425 return isl_map_plain_gist_basic_map(map
, hull
);
3428 /* Replace "map" by a universe map in the same space and free "drop".
3430 static __isl_give isl_map
*replace_by_universe(__isl_take isl_map
*map
,
3431 __isl_take isl_map
*drop
)
3435 res
= isl_map_universe(isl_map_get_space(map
));
3441 /* Return a map that has the same intersection with "context" as "map"
3442 * and that is as "simple" as possible.
3444 * If "map" is already the universe, then we cannot make it any simpler.
3445 * Similarly, if "context" is the universe, then we cannot exploit it
3447 * If "map" and "context" are identical to each other, then we can
3448 * return the corresponding universe.
3450 * If either "map" or "context" consists of multiple disjuncts,
3451 * then check if "context" happens to be a subset of "map",
3452 * in which case all constraints can be removed.
3453 * In case of multiple disjuncts, the standard procedure
3454 * may not be able to detect that all constraints can be removed.
3456 * If none of these cases apply, we have to work a bit harder.
3457 * During this computation, we make use of a single disjunct context,
3458 * so if the original context consists of more than one disjunct
3459 * then we need to approximate the context by a single disjunct set.
3460 * Simply taking the simple hull may drop constraints that are
3461 * only implicitly available in each disjunct. We therefore also
3462 * look for constraints among those defining "map" that are valid
3463 * for the context. These can then be used to simplify away
3464 * the corresponding constraints in "map".
3466 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
3467 __isl_take isl_map
*context
)
3471 int single_disjunct_map
, single_disjunct_context
;
3473 isl_basic_map
*hull
;
3475 is_universe
= isl_map_plain_is_universe(map
);
3476 if (is_universe
>= 0 && !is_universe
)
3477 is_universe
= isl_map_plain_is_universe(context
);
3478 if (is_universe
< 0)
3481 isl_map_free(context
);
3485 equal
= isl_map_plain_is_equal(map
, context
);
3489 return replace_by_universe(map
, context
);
3491 single_disjunct_map
= isl_map_n_basic_map(map
) == 1;
3492 single_disjunct_context
= isl_map_n_basic_map(context
) == 1;
3493 if (!single_disjunct_map
|| !single_disjunct_context
) {
3494 subset
= isl_map_is_subset(context
, map
);
3498 return replace_by_universe(map
, context
);
3501 context
= isl_map_compute_divs(context
);
3504 if (single_disjunct_context
) {
3505 hull
= isl_map_simple_hull(context
);
3510 ctx
= isl_map_get_ctx(map
);
3511 list
= isl_map_list_alloc(ctx
, 2);
3512 list
= isl_map_list_add(list
, isl_map_copy(context
));
3513 list
= isl_map_list_add(list
, isl_map_copy(map
));
3514 hull
= isl_map_unshifted_simple_hull_from_map_list(context
,
3517 return isl_map_gist_basic_map(map
, hull
);
3520 isl_map_free(context
);
3524 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
3525 __isl_take isl_map
*context
)
3527 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
3530 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
3531 struct isl_basic_set
*context
)
3533 return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset
),
3534 bset_to_bmap(context
)));
3537 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
3538 __isl_take isl_basic_set
*context
)
3540 return set_from_map(isl_map_gist_basic_map(set_to_map(set
),
3541 bset_to_bmap(context
)));
3544 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
3545 __isl_take isl_basic_set
*context
)
3547 isl_space
*space
= isl_set_get_space(set
);
3548 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
3549 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
3550 return isl_set_gist_basic_set(set
, dom_context
);
3553 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
3554 __isl_take isl_set
*context
)
3556 return set_from_map(isl_map_gist(set_to_map(set
), set_to_map(context
)));
3559 /* Compute the gist of "bmap" with respect to the constraints "context"
3562 __isl_give isl_basic_map
*isl_basic_map_gist_domain(
3563 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*context
)
3565 isl_space
*space
= isl_basic_map_get_space(bmap
);
3566 isl_basic_map
*bmap_context
= isl_basic_map_universe(space
);
3568 bmap_context
= isl_basic_map_intersect_domain(bmap_context
, context
);
3569 return isl_basic_map_gist(bmap
, bmap_context
);
3572 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
3573 __isl_take isl_set
*context
)
3575 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3576 map_context
= isl_map_intersect_domain(map_context
, context
);
3577 return isl_map_gist(map
, map_context
);
3580 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
3581 __isl_take isl_set
*context
)
3583 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3584 map_context
= isl_map_intersect_range(map_context
, context
);
3585 return isl_map_gist(map
, map_context
);
3588 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
3589 __isl_take isl_set
*context
)
3591 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3592 map_context
= isl_map_intersect_params(map_context
, context
);
3593 return isl_map_gist(map
, map_context
);
3596 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
3597 __isl_take isl_set
*context
)
3599 return isl_map_gist_params(set
, context
);
3602 /* Quick check to see if two basic maps are disjoint.
3603 * In particular, we reduce the equalities and inequalities of
3604 * one basic map in the context of the equalities of the other
3605 * basic map and check if we get a contradiction.
3607 isl_bool
isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
3608 __isl_keep isl_basic_map
*bmap2
)
3610 struct isl_vec
*v
= NULL
;
3615 if (!bmap1
|| !bmap2
)
3616 return isl_bool_error
;
3617 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
3618 return isl_bool_error
);
3619 if (bmap1
->n_div
|| bmap2
->n_div
)
3620 return isl_bool_false
;
3621 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
3622 return isl_bool_false
;
3624 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
3626 return isl_bool_false
;
3627 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
3630 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
3633 compute_elimination_index(bmap1
, elim
);
3634 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
3636 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
3638 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
3639 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3642 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
3644 reduced
= reduced_using_equalities(v
->block
.data
,
3645 bmap2
->ineq
[i
], bmap1
, elim
);
3646 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
3647 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3650 compute_elimination_index(bmap2
, elim
);
3651 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
3653 reduced
= reduced_using_equalities(v
->block
.data
,
3654 bmap1
->ineq
[i
], bmap2
, elim
);
3655 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
3656 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3661 return isl_bool_false
;
3665 return isl_bool_true
;
3669 return isl_bool_error
;
3672 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
3673 __isl_keep isl_basic_set
*bset2
)
3675 return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1
),
3676 bset_to_bmap(bset2
));
3679 /* Does "test" hold for all pairs of basic maps in "map1" and "map2"?
3681 static isl_bool
all_pairs(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
,
3682 isl_bool (*test
)(__isl_keep isl_basic_map
*bmap1
,
3683 __isl_keep isl_basic_map
*bmap2
))
3688 return isl_bool_error
;
3690 for (i
= 0; i
< map1
->n
; ++i
) {
3691 for (j
= 0; j
< map2
->n
; ++j
) {
3692 isl_bool d
= test(map1
->p
[i
], map2
->p
[j
]);
3693 if (d
!= isl_bool_true
)
3698 return isl_bool_true
;
3701 /* Are "map1" and "map2" obviously disjoint, based on information
3702 * that can be derived without looking at the individual basic maps?
3704 * In particular, if one of them is empty or if they live in different spaces
3705 * (ignoring parameters), then they are clearly disjoint.
3707 static isl_bool
isl_map_plain_is_disjoint_global(__isl_keep isl_map
*map1
,
3708 __isl_keep isl_map
*map2
)
3714 return isl_bool_error
;
3716 disjoint
= isl_map_plain_is_empty(map1
);
3717 if (disjoint
< 0 || disjoint
)
3720 disjoint
= isl_map_plain_is_empty(map2
);
3721 if (disjoint
< 0 || disjoint
)
3724 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_in
,
3725 map2
->dim
, isl_dim_in
);
3726 if (match
< 0 || !match
)
3727 return match
< 0 ? isl_bool_error
: isl_bool_true
;
3729 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_out
,
3730 map2
->dim
, isl_dim_out
);
3731 if (match
< 0 || !match
)
3732 return match
< 0 ? isl_bool_error
: isl_bool_true
;
3734 return isl_bool_false
;
3737 /* Are "map1" and "map2" obviously disjoint?
3739 * If one of them is empty or if they live in different spaces (ignoring
3740 * parameters), then they are clearly disjoint.
3741 * This is checked by isl_map_plain_is_disjoint_global.
3743 * If they have different parameters, then we skip any further tests.
3745 * If they are obviously equal, but not obviously empty, then we will
3746 * not be able to detect if they are disjoint.
3748 * Otherwise we check if each basic map in "map1" is obviously disjoint
3749 * from each basic map in "map2".
3751 isl_bool
isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
3752 __isl_keep isl_map
*map2
)
3758 disjoint
= isl_map_plain_is_disjoint_global(map1
, map2
);
3759 if (disjoint
< 0 || disjoint
)
3762 match
= isl_map_has_equal_params(map1
, map2
);
3763 if (match
< 0 || !match
)
3764 return match
< 0 ? isl_bool_error
: isl_bool_false
;
3766 intersect
= isl_map_plain_is_equal(map1
, map2
);
3767 if (intersect
< 0 || intersect
)
3768 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3770 return all_pairs(map1
, map2
, &isl_basic_map_plain_is_disjoint
);
3773 /* Are "map1" and "map2" disjoint?
3774 * The parameters are assumed to have been aligned.
3776 * In particular, check whether all pairs of basic maps are disjoint.
3778 static isl_bool
isl_map_is_disjoint_aligned(__isl_keep isl_map
*map1
,
3779 __isl_keep isl_map
*map2
)
3781 return all_pairs(map1
, map2
, &isl_basic_map_is_disjoint
);
3784 /* Are "map1" and "map2" disjoint?
3786 * They are disjoint if they are "obviously disjoint" or if one of them
3787 * is empty. Otherwise, they are not disjoint if one of them is universal.
3788 * If the two inputs are (obviously) equal and not empty, then they are
3790 * If none of these cases apply, then check if all pairs of basic maps
3791 * are disjoint after aligning the parameters.
3793 isl_bool
isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
3798 disjoint
= isl_map_plain_is_disjoint_global(map1
, map2
);
3799 if (disjoint
< 0 || disjoint
)
3802 disjoint
= isl_map_is_empty(map1
);
3803 if (disjoint
< 0 || disjoint
)
3806 disjoint
= isl_map_is_empty(map2
);
3807 if (disjoint
< 0 || disjoint
)
3810 intersect
= isl_map_plain_is_universe(map1
);
3811 if (intersect
< 0 || intersect
)
3812 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3814 intersect
= isl_map_plain_is_universe(map2
);
3815 if (intersect
< 0 || intersect
)
3816 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3818 intersect
= isl_map_plain_is_equal(map1
, map2
);
3819 if (intersect
< 0 || intersect
)
3820 return isl_bool_not(intersect
);
3822 return isl_map_align_params_map_map_and_test(map1
, map2
,
3823 &isl_map_is_disjoint_aligned
);
3826 /* Are "bmap1" and "bmap2" disjoint?
3828 * They are disjoint if they are "obviously disjoint" or if one of them
3829 * is empty. Otherwise, they are not disjoint if one of them is universal.
3830 * If none of these cases apply, we compute the intersection and see if
3831 * the result is empty.
3833 isl_bool
isl_basic_map_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
3834 __isl_keep isl_basic_map
*bmap2
)
3838 isl_basic_map
*test
;
3840 disjoint
= isl_basic_map_plain_is_disjoint(bmap1
, bmap2
);
3841 if (disjoint
< 0 || disjoint
)
3844 disjoint
= isl_basic_map_is_empty(bmap1
);
3845 if (disjoint
< 0 || disjoint
)
3848 disjoint
= isl_basic_map_is_empty(bmap2
);
3849 if (disjoint
< 0 || disjoint
)
3852 intersect
= isl_basic_map_plain_is_universe(bmap1
);
3853 if (intersect
< 0 || intersect
)
3854 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3856 intersect
= isl_basic_map_plain_is_universe(bmap2
);
3857 if (intersect
< 0 || intersect
)
3858 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3860 test
= isl_basic_map_intersect(isl_basic_map_copy(bmap1
),
3861 isl_basic_map_copy(bmap2
));
3862 disjoint
= isl_basic_map_is_empty(test
);
3863 isl_basic_map_free(test
);
3868 /* Are "bset1" and "bset2" disjoint?
3870 isl_bool
isl_basic_set_is_disjoint(__isl_keep isl_basic_set
*bset1
,
3871 __isl_keep isl_basic_set
*bset2
)
3873 return isl_basic_map_is_disjoint(bset1
, bset2
);
3876 isl_bool
isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
3877 __isl_keep isl_set
*set2
)
3879 return isl_map_plain_is_disjoint(set_to_map(set1
), set_to_map(set2
));
3882 /* Are "set1" and "set2" disjoint?
3884 isl_bool
isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
3886 return isl_map_is_disjoint(set1
, set2
);
3889 /* Is "v" equal to 0, 1 or -1?
3891 static int is_zero_or_one(isl_int v
)
3893 return isl_int_is_zero(v
) || isl_int_is_one(v
) || isl_int_is_negone(v
);
3896 /* Are the "n" coefficients starting at "first" of inequality constraints
3897 * "i" and "j" of "bmap" opposite to each other?
3899 static int is_opposite_part(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
3902 return isl_seq_is_neg(bmap
->ineq
[i
] + first
, bmap
->ineq
[j
] + first
, n
);
3905 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
3906 * apart from the constant term?
3908 static isl_bool
is_opposite(__isl_keep isl_basic_map
*bmap
, int i
, int j
)
3912 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3913 return is_opposite_part(bmap
, i
, j
, 1, total
);
3916 /* Check if we can combine a given div with lower bound l and upper
3917 * bound u with some other div and if so return that other div.
3918 * Otherwise, return a position beyond the integer divisions.
3919 * Return -1 on error.
3921 * We first check that
3922 * - the bounds are opposites of each other (except for the constant
3924 * - the bounds do not reference any other div
3925 * - no div is defined in terms of this div
3927 * Let m be the size of the range allowed on the div by the bounds.
3928 * That is, the bounds are of the form
3930 * e <= a <= e + m - 1
3932 * with e some expression in the other variables.
3933 * We look for another div b such that no third div is defined in terms
3934 * of this second div b and such that in any constraint that contains
3935 * a (except for the given lower and upper bound), also contains b
3936 * with a coefficient that is m times that of b.
3937 * That is, all constraints (except for the lower and upper bound)
3940 * e + f (a + m b) >= 0
3942 * Furthermore, in the constraints that only contain b, the coefficient
3943 * of b should be equal to 1 or -1.
3944 * If so, we return b so that "a + m b" can be replaced by
3945 * a single div "c = a + m b".
3947 static int div_find_coalesce(__isl_keep isl_basic_map
*bmap
, int *pairs
,
3948 unsigned div
, unsigned l
, unsigned u
)
3956 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3959 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
3962 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + v_div
, div
) != -1)
3964 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + v_div
+ div
+ 1,
3965 n_div
- div
- 1) != -1)
3967 opp
= is_opposite(bmap
, l
, u
);
3968 if (opp
< 0 || !opp
)
3969 return opp
< 0 ? -1 : n_div
;
3971 for (i
= 0; i
< n_div
; ++i
) {
3972 if (isl_int_is_zero(bmap
->div
[i
][0]))
3974 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + v_div
+ div
]))
3978 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3979 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
3980 isl_int_sub(bmap
->ineq
[l
][0],
3981 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3982 bmap
= isl_basic_map_copy(bmap
);
3983 bmap
= isl_basic_map_set_to_empty(bmap
);
3984 isl_basic_map_free(bmap
);
3987 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
3989 for (i
= 0; i
< n_div
; ++i
) {
3994 for (j
= 0; j
< n_div
; ++j
) {
3995 if (isl_int_is_zero(bmap
->div
[j
][0]))
3997 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + v_div
+ i
]))
4002 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
4004 if (j
== l
|| j
== u
)
4006 if (isl_int_is_zero(bmap
->ineq
[j
][1 + v_div
+ div
])) {
4007 if (is_zero_or_one(bmap
->ineq
[j
][1 + v_div
+ i
]))
4011 if (isl_int_is_zero(bmap
->ineq
[j
][1 + v_div
+ i
]))
4013 isl_int_mul(bmap
->ineq
[j
][1 + v_div
+ div
],
4014 bmap
->ineq
[j
][1 + v_div
+ div
],
4016 valid
= isl_int_eq(bmap
->ineq
[j
][1 + v_div
+ div
],
4017 bmap
->ineq
[j
][1 + v_div
+ i
]);
4018 isl_int_divexact(bmap
->ineq
[j
][1 + v_div
+ div
],
4019 bmap
->ineq
[j
][1 + v_div
+ div
],
4024 if (j
< bmap
->n_ineq
)
4029 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
4030 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4034 /* Internal data structure used during the construction and/or evaluation of
4035 * an inequality that ensures that a pair of bounds always allows
4036 * for an integer value.
4038 * "tab" is the tableau in which the inequality is evaluated. It may
4039 * be NULL until it is actually needed.
4040 * "v" contains the inequality coefficients.
4041 * "g", "fl" and "fu" are temporary scalars used during the construction and
4044 struct test_ineq_data
{
4045 struct isl_tab
*tab
;
4052 /* Free all the memory allocated by the fields of "data".
4054 static void test_ineq_data_clear(struct test_ineq_data
*data
)
4056 isl_tab_free(data
->tab
);
4057 isl_vec_free(data
->v
);
4058 isl_int_clear(data
->g
);
4059 isl_int_clear(data
->fl
);
4060 isl_int_clear(data
->fu
);
4063 /* Is the inequality stored in data->v satisfied by "bmap"?
4064 * That is, does it only attain non-negative values?
4065 * data->tab is a tableau corresponding to "bmap".
4067 static isl_bool
test_ineq_is_satisfied(__isl_keep isl_basic_map
*bmap
,
4068 struct test_ineq_data
*data
)
4071 enum isl_lp_result res
;
4073 ctx
= isl_basic_map_get_ctx(bmap
);
4075 data
->tab
= isl_tab_from_basic_map(bmap
, 0);
4076 res
= isl_tab_min(data
->tab
, data
->v
->el
, ctx
->one
, &data
->g
, NULL
, 0);
4077 if (res
== isl_lp_error
)
4078 return isl_bool_error
;
4079 return res
== isl_lp_ok
&& isl_int_is_nonneg(data
->g
);
4082 /* Given a lower and an upper bound on div i, do they always allow
4083 * for an integer value of the given div?
4084 * Determine this property by constructing an inequality
4085 * such that the property is guaranteed when the inequality is nonnegative.
4086 * The lower bound is inequality l, while the upper bound is inequality u.
4087 * The constructed inequality is stored in data->v.
4089 * Let the upper bound be
4093 * and the lower bound
4097 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
4100 * - f_u e_l <= f_u f_l g a <= f_l e_u
4102 * Since all variables are integer valued, this is equivalent to
4104 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
4106 * If this interval is at least f_u f_l g, then it contains at least
4107 * one integer value for a.
4108 * That is, the test constraint is
4110 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
4114 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0
4116 * If the coefficients of f_l e_u + f_u e_l have a common divisor g',
4117 * then the constraint can be scaled down by a factor g',
4118 * with the constant term replaced by
4119 * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g').
4120 * Note that the result of applying Fourier-Motzkin to this pair
4123 * f_l e_u + f_u e_l >= 0
4125 * If the constant term of the scaled down version of this constraint,
4126 * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant
4127 * term of the scaled down test constraint, then the test constraint
4128 * is known to hold and no explicit evaluation is required.
4129 * This is essentially the Omega test.
4131 * If the test constraint consists of only a constant term, then
4132 * it is sufficient to look at the sign of this constant term.
4134 static isl_bool
int_between_bounds(__isl_keep isl_basic_map
*bmap
, int i
,
4135 int l
, int u
, struct test_ineq_data
*data
)
4137 unsigned offset
, n_div
;
4138 offset
= isl_basic_map_offset(bmap
, isl_dim_div
);
4139 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4141 isl_int_gcd(data
->g
,
4142 bmap
->ineq
[l
][offset
+ i
], bmap
->ineq
[u
][offset
+ i
]);
4143 isl_int_divexact(data
->fl
, bmap
->ineq
[l
][offset
+ i
], data
->g
);
4144 isl_int_divexact(data
->fu
, bmap
->ineq
[u
][offset
+ i
], data
->g
);
4145 isl_int_neg(data
->fu
, data
->fu
);
4146 isl_seq_combine(data
->v
->el
, data
->fl
, bmap
->ineq
[u
],
4147 data
->fu
, bmap
->ineq
[l
], offset
+ n_div
);
4148 isl_int_mul(data
->g
, data
->g
, data
->fl
);
4149 isl_int_mul(data
->g
, data
->g
, data
->fu
);
4150 isl_int_sub(data
->g
, data
->g
, data
->fl
);
4151 isl_int_sub(data
->g
, data
->g
, data
->fu
);
4152 isl_int_add_ui(data
->g
, data
->g
, 1);
4153 isl_int_sub(data
->fl
, data
->v
->el
[0], data
->g
);
4155 isl_seq_gcd(data
->v
->el
+ 1, offset
- 1 + n_div
, &data
->g
);
4156 if (isl_int_is_zero(data
->g
))
4157 return isl_int_is_nonneg(data
->fl
);
4158 if (isl_int_is_one(data
->g
)) {
4159 isl_int_set(data
->v
->el
[0], data
->fl
);
4160 return test_ineq_is_satisfied(bmap
, data
);
4162 isl_int_fdiv_q(data
->fl
, data
->fl
, data
->g
);
4163 isl_int_fdiv_q(data
->v
->el
[0], data
->v
->el
[0], data
->g
);
4164 if (isl_int_eq(data
->fl
, data
->v
->el
[0]))
4165 return isl_bool_true
;
4166 isl_int_set(data
->v
->el
[0], data
->fl
);
4167 isl_seq_scale_down(data
->v
->el
+ 1, data
->v
->el
+ 1, data
->g
,
4168 offset
- 1 + n_div
);
4170 return test_ineq_is_satisfied(bmap
, data
);
4173 /* Remove more kinds of divs that are not strictly needed.
4174 * In particular, if all pairs of lower and upper bounds on a div
4175 * are such that they allow at least one integer value of the div,
4176 * then we can eliminate the div using Fourier-Motzkin without
4177 * introducing any spurious solutions.
4179 * If at least one of the two constraints has a unit coefficient for the div,
4180 * then the presence of such a value is guaranteed so there is no need to check.
4181 * In particular, the value attained by the bound with unit coefficient
4182 * can serve as this intermediate value.
4184 static __isl_give isl_basic_map
*drop_more_redundant_divs(
4185 __isl_take isl_basic_map
*bmap
, __isl_take
int *pairs
, int n
)
4188 struct test_ineq_data data
= { NULL
, NULL
};
4189 unsigned off
, n_div
;
4192 isl_int_init(data
.g
);
4193 isl_int_init(data
.fl
);
4194 isl_int_init(data
.fu
);
4199 ctx
= isl_basic_map_get_ctx(bmap
);
4200 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
4201 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4202 data
.v
= isl_vec_alloc(ctx
, off
+ n_div
);
4211 for (i
= 0; i
< n_div
; ++i
) {
4214 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
4220 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
4221 if (!isl_int_is_pos(bmap
->ineq
[l
][off
+ i
]))
4223 if (isl_int_is_one(bmap
->ineq
[l
][off
+ i
]))
4225 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
4226 if (!isl_int_is_neg(bmap
->ineq
[u
][off
+ i
]))
4228 if (isl_int_is_negone(bmap
->ineq
[u
][off
+ i
]))
4230 has_int
= int_between_bounds(bmap
, i
, l
, u
,
4234 if (data
.tab
&& data
.tab
->empty
)
4239 if (u
< bmap
->n_ineq
)
4242 if (data
.tab
&& data
.tab
->empty
) {
4243 bmap
= isl_basic_map_set_to_empty(bmap
);
4246 if (l
== bmap
->n_ineq
) {
4254 test_ineq_data_clear(&data
);
4261 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
4262 return isl_basic_map_drop_redundant_divs(bmap
);
4265 isl_basic_map_free(bmap
);
4266 test_ineq_data_clear(&data
);
4270 /* Given a pair of divs div1 and div2 such that, except for the lower bound l
4271 * and the upper bound u, div1 always occurs together with div2 in the form
4272 * (div1 + m div2), where m is the constant range on the variable div1
4273 * allowed by l and u, replace the pair div1 and div2 by a single
4274 * div that is equal to div1 + m div2.
4276 * The new div will appear in the location that contains div2.
4277 * We need to modify all constraints that contain
4278 * div2 = (div - div1) / m
4279 * The coefficient of div2 is known to be equal to 1 or -1.
4280 * (If a constraint does not contain div2, it will also not contain div1.)
4281 * If the constraint also contains div1, then we know they appear
4282 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
4283 * i.e., the coefficient of div is f.
4285 * Otherwise, we first need to introduce div1 into the constraint.
4294 * A lower bound on div2
4298 * can be replaced by
4300 * m div2 + div1 + m t + f >= 0
4306 * can be replaced by
4308 * -(m div2 + div1) + m t + f' >= 0
4310 * These constraint are those that we would obtain from eliminating
4311 * div1 using Fourier-Motzkin.
4313 * After all constraints have been modified, we drop the lower and upper
4314 * bound and then drop div1.
4315 * Since the new div is only placed in the same location that used
4316 * to store div2, but otherwise has a different meaning, any possible
4317 * explicit representation of the original div2 is removed.
4319 static __isl_give isl_basic_map
*coalesce_divs(__isl_take isl_basic_map
*bmap
,
4320 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
4328 ctx
= isl_basic_map_get_ctx(bmap
);
4330 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
4332 return isl_basic_map_free(bmap
);
4333 total
= 1 + v_div
+ bmap
->n_div
;
4336 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4337 isl_int_add_ui(m
, m
, 1);
4339 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4340 if (i
== l
|| i
== u
)
4342 if (isl_int_is_zero(bmap
->ineq
[i
][1 + v_div
+ div2
]))
4344 if (isl_int_is_zero(bmap
->ineq
[i
][1 + v_div
+ div1
])) {
4345 if (isl_int_is_pos(bmap
->ineq
[i
][1 + v_div
+ div2
]))
4346 isl_seq_combine(bmap
->ineq
[i
], m
, bmap
->ineq
[i
],
4347 ctx
->one
, bmap
->ineq
[l
], total
);
4349 isl_seq_combine(bmap
->ineq
[i
], m
, bmap
->ineq
[i
],
4350 ctx
->one
, bmap
->ineq
[u
], total
);
4352 isl_int_set(bmap
->ineq
[i
][1 + v_div
+ div2
],
4353 bmap
->ineq
[i
][1 + v_div
+ div1
]);
4354 isl_int_set_si(bmap
->ineq
[i
][1 + v_div
+ div1
], 0);
4359 isl_basic_map_drop_inequality(bmap
, l
);
4360 isl_basic_map_drop_inequality(bmap
, u
);
4362 isl_basic_map_drop_inequality(bmap
, u
);
4363 isl_basic_map_drop_inequality(bmap
, l
);
4365 bmap
= isl_basic_map_mark_div_unknown(bmap
, div2
);
4366 bmap
= isl_basic_map_drop_div(bmap
, div1
);
4370 /* First check if we can coalesce any pair of divs and
4371 * then continue with dropping more redundant divs.
4373 * We loop over all pairs of lower and upper bounds on a div
4374 * with coefficient 1 and -1, respectively, check if there
4375 * is any other div "c" with which we can coalesce the div
4376 * and if so, perform the coalescing.
4378 static __isl_give isl_basic_map
*coalesce_or_drop_more_redundant_divs(
4379 __isl_take isl_basic_map
*bmap
, int *pairs
, int n
)
4385 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
4387 return isl_basic_map_free(bmap
);
4389 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4390 for (i
= 0; i
< n_div
; ++i
) {
4393 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
4394 if (!isl_int_is_one(bmap
->ineq
[l
][1 + v_div
+ i
]))
4396 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
4399 if (!isl_int_is_negone(bmap
->ineq
[u
][1+v_div
+i
]))
4401 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
4407 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
4408 return isl_basic_map_drop_redundant_divs(bmap
);
4413 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
4418 return drop_more_redundant_divs(bmap
, pairs
, n
);
4421 isl_basic_map_free(bmap
);
4425 /* Are the "n" coefficients starting at "first" of inequality constraints
4426 * "i" and "j" of "bmap" equal to each other?
4428 static int is_parallel_part(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4431 return isl_seq_eq(bmap
->ineq
[i
] + first
, bmap
->ineq
[j
] + first
, n
);
4434 /* Are inequality constraints "i" and "j" of "bmap" equal to each other,
4435 * apart from the constant term and the coefficient at position "pos"?
4437 static isl_bool
is_parallel_except(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4442 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4443 return is_parallel_part(bmap
, i
, j
, 1, pos
- 1) &&
4444 is_parallel_part(bmap
, i
, j
, pos
+ 1, total
- pos
);
4447 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4448 * apart from the constant term and the coefficient at position "pos"?
4450 static isl_bool
is_opposite_except(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4455 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4456 return is_opposite_part(bmap
, i
, j
, 1, pos
- 1) &&
4457 is_opposite_part(bmap
, i
, j
, pos
+ 1, total
- pos
);
4460 /* Restart isl_basic_map_drop_redundant_divs after "bmap" has
4461 * been modified, simplying it if "simplify" is set.
4462 * Free the temporary data structure "pairs" that was associated
4463 * to the old version of "bmap".
4465 static __isl_give isl_basic_map
*drop_redundant_divs_again(
4466 __isl_take isl_basic_map
*bmap
, __isl_take
int *pairs
, int simplify
)
4469 bmap
= isl_basic_map_simplify(bmap
);
4471 return isl_basic_map_drop_redundant_divs(bmap
);
4474 /* Is "div" the single unknown existentially quantified variable
4475 * in inequality constraint "ineq" of "bmap"?
4476 * "div" is known to have a non-zero coefficient in "ineq".
4478 static isl_bool
single_unknown(__isl_keep isl_basic_map
*bmap
, int ineq
,
4482 unsigned n_div
, o_div
;
4485 known
= isl_basic_map_div_is_known(bmap
, div
);
4486 if (known
< 0 || known
)
4487 return isl_bool_not(known
);
4488 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4490 return isl_bool_true
;
4491 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4492 for (i
= 0; i
< n_div
; ++i
) {
4497 if (isl_int_is_zero(bmap
->ineq
[ineq
][o_div
+ i
]))
4499 known
= isl_basic_map_div_is_known(bmap
, i
);
4500 if (known
< 0 || !known
)
4504 return isl_bool_true
;
4507 /* Does integer division "div" have coefficient 1 in inequality constraint
4510 static isl_bool
has_coef_one(__isl_keep isl_basic_map
*bmap
, int div
, int ineq
)
4514 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4515 if (isl_int_is_one(bmap
->ineq
[ineq
][o_div
+ div
]))
4516 return isl_bool_true
;
4518 return isl_bool_false
;
4521 /* Turn inequality constraint "ineq" of "bmap" into an equality and
4522 * then try and drop redundant divs again,
4523 * freeing the temporary data structure "pairs" that was associated
4524 * to the old version of "bmap".
4526 static __isl_give isl_basic_map
*set_eq_and_try_again(
4527 __isl_take isl_basic_map
*bmap
, int ineq
, __isl_take
int *pairs
)
4529 bmap
= isl_basic_map_cow(bmap
);
4530 isl_basic_map_inequality_to_equality(bmap
, ineq
);
4531 return drop_redundant_divs_again(bmap
, pairs
, 1);
4534 /* Drop the integer division at position "div", along with the two
4535 * inequality constraints "ineq1" and "ineq2" in which it appears
4536 * from "bmap" and then try and drop redundant divs again,
4537 * freeing the temporary data structure "pairs" that was associated
4538 * to the old version of "bmap".
4540 static __isl_give isl_basic_map
*drop_div_and_try_again(
4541 __isl_take isl_basic_map
*bmap
, int div
, int ineq1
, int ineq2
,
4542 __isl_take
int *pairs
)
4544 if (ineq1
> ineq2
) {
4545 isl_basic_map_drop_inequality(bmap
, ineq1
);
4546 isl_basic_map_drop_inequality(bmap
, ineq2
);
4548 isl_basic_map_drop_inequality(bmap
, ineq2
);
4549 isl_basic_map_drop_inequality(bmap
, ineq1
);
4551 bmap
= isl_basic_map_drop_div(bmap
, div
);
4552 return drop_redundant_divs_again(bmap
, pairs
, 0);
4555 /* Given two inequality constraints
4557 * f(x) + n d + c >= 0, (ineq)
4559 * with d the variable at position "pos", and
4561 * f(x) + c0 >= 0, (lower)
4563 * compute the maximal value of the lower bound ceil((-f(x) - c)/n)
4564 * determined by the first constraint.
4571 static void lower_bound_from_parallel(__isl_keep isl_basic_map
*bmap
,
4572 int ineq
, int lower
, int pos
, isl_int
*l
)
4574 isl_int_neg(*l
, bmap
->ineq
[ineq
][0]);
4575 isl_int_add(*l
, *l
, bmap
->ineq
[lower
][0]);
4576 isl_int_cdiv_q(*l
, *l
, bmap
->ineq
[ineq
][pos
]);
4579 /* Given two inequality constraints
4581 * f(x) + n d + c >= 0, (ineq)
4583 * with d the variable at position "pos", and
4585 * -f(x) - c0 >= 0, (upper)
4587 * compute the minimal value of the lower bound ceil((-f(x) - c)/n)
4588 * determined by the first constraint.
4595 static void lower_bound_from_opposite(__isl_keep isl_basic_map
*bmap
,
4596 int ineq
, int upper
, int pos
, isl_int
*u
)
4598 isl_int_neg(*u
, bmap
->ineq
[ineq
][0]);
4599 isl_int_sub(*u
, *u
, bmap
->ineq
[upper
][0]);
4600 isl_int_cdiv_q(*u
, *u
, bmap
->ineq
[ineq
][pos
]);
4603 /* Given a lower bound constraint "ineq" on "div" in "bmap",
4604 * does the corresponding lower bound have a fixed value in "bmap"?
4606 * In particular, "ineq" is of the form
4608 * f(x) + n d + c >= 0
4610 * with n > 0, c the constant term and
4611 * d the existentially quantified variable "div".
4612 * That is, the lower bound is
4614 * ceil((-f(x) - c)/n)
4616 * Look for a pair of constraints
4621 * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value.
4622 * That is, check that
4624 * ceil((-c1 - c)/n) = ceil((c0 - c)/n)
4626 * If so, return the index of inequality f(x) + c0 >= 0.
4627 * Otherwise, return bmap->n_ineq.
4628 * Return -1 on error.
4630 static int lower_bound_is_cst(__isl_keep isl_basic_map
*bmap
, int div
, int ineq
)
4633 int lower
= -1, upper
= -1;
4638 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4639 for (i
= 0; i
< bmap
->n_ineq
&& (lower
< 0 || upper
< 0); ++i
) {
4644 if (!isl_int_is_zero(bmap
->ineq
[i
][o_div
+ div
]))
4646 par
= isl_bool_false
;
4648 par
= is_parallel_except(bmap
, ineq
, i
, o_div
+ div
);
4655 opp
= isl_bool_false
;
4657 opp
= is_opposite_except(bmap
, ineq
, i
, o_div
+ div
);
4664 if (lower
< 0 || upper
< 0)
4665 return bmap
->n_ineq
;
4670 lower_bound_from_parallel(bmap
, ineq
, lower
, o_div
+ div
, &l
);
4671 lower_bound_from_opposite(bmap
, ineq
, upper
, o_div
+ div
, &u
);
4673 equal
= isl_int_eq(l
, u
);
4678 return equal
? lower
: bmap
->n_ineq
;
4681 /* Given a lower bound constraint "ineq" on the existentially quantified
4682 * variable "div", such that the corresponding lower bound has
4683 * a fixed value in "bmap", assign this fixed value to the variable and
4684 * then try and drop redundant divs again,
4685 * freeing the temporary data structure "pairs" that was associated
4686 * to the old version of "bmap".
4687 * "lower" determines the constant value for the lower bound.
4689 * In particular, "ineq" is of the form
4691 * f(x) + n d + c >= 0,
4693 * while "lower" is of the form
4697 * The lower bound is ceil((-f(x) - c)/n) and its constant value
4698 * is ceil((c0 - c)/n).
4700 static __isl_give isl_basic_map
*fix_cst_lower(__isl_take isl_basic_map
*bmap
,
4701 int div
, int ineq
, int lower
, int *pairs
)
4708 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4709 lower_bound_from_parallel(bmap
, ineq
, lower
, o_div
+ div
, &c
);
4710 bmap
= isl_basic_map_fix(bmap
, isl_dim_div
, div
, c
);
4715 return isl_basic_map_drop_redundant_divs(bmap
);
4718 /* Remove divs that are not strictly needed based on the inequality
4720 * In particular, if a div only occurs positively (or negatively)
4721 * in constraints, then it can simply be dropped.
4722 * Also, if a div occurs in only two constraints and if moreover
4723 * those two constraints are opposite to each other, except for the constant
4724 * term and if the sum of the constant terms is such that for any value
4725 * of the other values, there is always at least one integer value of the
4726 * div, i.e., if one plus this sum is greater than or equal to
4727 * the (absolute value) of the coefficient of the div in the constraints,
4728 * then we can also simply drop the div.
4730 * If an existentially quantified variable does not have an explicit
4731 * representation, appears in only a single lower bound that does not
4732 * involve any other such existentially quantified variables and appears
4733 * in this lower bound with coefficient 1,
4734 * then fix the variable to the value of the lower bound. That is,
4735 * turn the inequality into an equality.
4736 * If for any value of the other variables, there is any value
4737 * for the existentially quantified variable satisfying the constraints,
4738 * then this lower bound also satisfies the constraints.
4739 * It is therefore safe to pick this lower bound.
4741 * The same reasoning holds even if the coefficient is not one.
4742 * However, fixing the variable to the value of the lower bound may
4743 * in general introduce an extra integer division, in which case
4744 * it may be better to pick another value.
4745 * If this integer division has a known constant value, then plugging
4746 * in this constant value removes the existentially quantified variable
4747 * completely. In particular, if the lower bound is of the form
4748 * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and
4749 * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n),
4750 * then the existentially quantified variable can be assigned this
4753 * We skip divs that appear in equalities or in the definition of other divs.
4754 * Divs that appear in the definition of other divs usually occur in at least
4755 * 4 constraints, but the constraints may have been simplified.
4757 * If any divs are left after these simple checks then we move on
4758 * to more complicated cases in drop_more_redundant_divs.
4760 static __isl_give isl_basic_map
*isl_basic_map_drop_redundant_divs_ineq(
4761 __isl_take isl_basic_map
*bmap
)
4771 if (bmap
->n_div
== 0)
4774 off
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
4776 return isl_basic_map_free(bmap
);
4777 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
4781 n_ineq
= isl_basic_map_n_inequality(bmap
);
4782 for (i
= 0; i
< bmap
->n_div
; ++i
) {
4784 int last_pos
, last_neg
;
4787 isl_bool opp
, set_div
;
4789 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
4790 for (j
= i
; j
< bmap
->n_div
; ++j
)
4791 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
4793 if (j
< bmap
->n_div
)
4795 for (j
= 0; j
< bmap
->n_eq
; ++j
)
4796 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
4802 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
4803 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
4807 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
4812 pairs
[i
] = pos
* neg
;
4813 if (pairs
[i
] == 0) {
4814 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
4815 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
4816 isl_basic_map_drop_inequality(bmap
, j
);
4817 bmap
= isl_basic_map_drop_div(bmap
, i
);
4818 return drop_redundant_divs_again(bmap
, pairs
, 0);
4821 opp
= isl_bool_false
;
4823 opp
= is_opposite(bmap
, last_pos
, last_neg
);
4828 isl_bool single
, one
;
4832 single
= single_unknown(bmap
, last_pos
, i
);
4837 one
= has_coef_one(bmap
, i
, last_pos
);
4841 return set_eq_and_try_again(bmap
, last_pos
,
4843 lower
= lower_bound_is_cst(bmap
, i
, last_pos
);
4847 return fix_cst_lower(bmap
, i
, last_pos
, lower
,
4852 isl_int_add(bmap
->ineq
[last_pos
][0],
4853 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
4854 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
4855 bmap
->ineq
[last_pos
][0], 1);
4856 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
4857 bmap
->ineq
[last_pos
][1+off
+i
]);
4858 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
4859 bmap
->ineq
[last_pos
][0], 1);
4860 isl_int_sub(bmap
->ineq
[last_pos
][0],
4861 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
4863 return drop_div_and_try_again(bmap
, i
,
4864 last_pos
, last_neg
, pairs
);
4866 set_div
= isl_bool_false
;
4868 set_div
= ok_to_set_div_from_bound(bmap
, i
, last_pos
);
4870 return isl_basic_map_free(bmap
);
4872 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
4873 return drop_redundant_divs_again(bmap
, pairs
, 1);
4880 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
4886 isl_basic_map_free(bmap
);
4890 /* Consider the coefficients at "c" as a row vector and replace
4891 * them with their product with "T". "T" is assumed to be a square matrix.
4893 static isl_stat
preimage(isl_int
*c
, __isl_keep isl_mat
*T
)
4900 return isl_stat_error
;
4901 n
= isl_mat_rows(T
);
4902 if (isl_seq_first_non_zero(c
, n
) == -1)
4904 ctx
= isl_mat_get_ctx(T
);
4905 v
= isl_vec_alloc(ctx
, n
);
4907 return isl_stat_error
;
4908 isl_seq_swp_or_cpy(v
->el
, c
, n
);
4909 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
4911 return isl_stat_error
;
4912 isl_seq_swp_or_cpy(c
, v
->el
, n
);
4918 /* Plug in T for the variables in "bmap" starting at "pos".
4919 * T is a linear unimodular matrix, i.e., without constant term.
4921 static __isl_give isl_basic_map
*isl_basic_map_preimage_vars(
4922 __isl_take isl_basic_map
*bmap
, unsigned pos
, __isl_take isl_mat
*T
)
4927 bmap
= isl_basic_map_cow(bmap
);
4931 n
= isl_mat_cols(T
);
4932 if (n
!= isl_mat_rows(T
))
4933 isl_die(isl_mat_get_ctx(T
), isl_error_invalid
,
4934 "expecting square matrix", goto error
);
4936 if (isl_basic_map_check_range(bmap
, isl_dim_all
, pos
, n
) < 0)
4939 for (i
= 0; i
< bmap
->n_eq
; ++i
)
4940 if (preimage(bmap
->eq
[i
] + 1 + pos
, T
) < 0)
4942 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
4943 if (preimage(bmap
->ineq
[i
] + 1 + pos
, T
) < 0)
4945 for (i
= 0; i
< bmap
->n_div
; ++i
) {
4946 if (isl_basic_map_div_is_marked_unknown(bmap
, i
))
4948 if (preimage(bmap
->div
[i
] + 1 + 1 + pos
, T
) < 0)
4955 isl_basic_map_free(bmap
);
4960 /* Remove divs that are not strictly needed.
4962 * First look for an equality constraint involving two or more
4963 * existentially quantified variables without an explicit
4964 * representation. Replace the combination that appears
4965 * in the equality constraint by a single existentially quantified
4966 * variable such that the equality can be used to derive
4967 * an explicit representation for the variable.
4968 * If there are no more such equality constraints, then continue
4969 * with isl_basic_map_drop_redundant_divs_ineq.
4971 * In particular, if the equality constraint is of the form
4973 * f(x) + \sum_i c_i a_i = 0
4975 * with a_i existentially quantified variable without explicit
4976 * representation, then apply a transformation on the existentially
4977 * quantified variables to turn the constraint into
4981 * with g the gcd of the c_i.
4982 * In order to easily identify which existentially quantified variables
4983 * have a complete explicit representation, i.e., without being defined
4984 * in terms of other existentially quantified variables without
4985 * an explicit representation, the existentially quantified variables
4988 * The variable transformation is computed by extending the row
4989 * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation
4991 * [a_1'] [c_1/g ... c_n/g] [ a_1 ]
4996 * with [c_1/g ... c_n/g] representing the first row of U.
4997 * The inverse of U is then plugged into the original constraints.
4998 * The call to isl_basic_map_simplify makes sure the explicit
4999 * representation for a_1' is extracted from the equality constraint.
5001 __isl_give isl_basic_map
*isl_basic_map_drop_redundant_divs(
5002 __isl_take isl_basic_map
*bmap
)
5006 unsigned o_div
, n_div
;
5013 if (isl_basic_map_divs_known(bmap
))
5014 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5015 if (bmap
->n_eq
== 0)
5016 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5017 bmap
= isl_basic_map_sort_divs(bmap
);
5021 first
= isl_basic_map_first_unknown_div(bmap
);
5023 return isl_basic_map_free(bmap
);
5025 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
5026 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
5028 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5029 l
= isl_seq_first_non_zero(bmap
->eq
[i
] + o_div
+ first
,
5034 if (isl_seq_first_non_zero(bmap
->eq
[i
] + o_div
+ l
+ 1,
5035 n_div
- (l
+ 1)) == -1)
5039 if (i
>= bmap
->n_eq
)
5040 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5042 ctx
= isl_basic_map_get_ctx(bmap
);
5043 T
= isl_mat_alloc(ctx
, n_div
- l
, n_div
- l
);
5045 return isl_basic_map_free(bmap
);
5046 isl_seq_cpy(T
->row
[0], bmap
->eq
[i
] + o_div
+ l
, n_div
- l
);
5047 T
= isl_mat_normalize_row(T
, 0);
5048 T
= isl_mat_unimodular_complete(T
, 1);
5049 T
= isl_mat_right_inverse(T
);
5051 for (i
= l
; i
< n_div
; ++i
)
5052 bmap
= isl_basic_map_mark_div_unknown(bmap
, i
);
5053 bmap
= isl_basic_map_preimage_vars(bmap
, o_div
- 1 + l
, T
);
5054 bmap
= isl_basic_map_simplify(bmap
);
5056 return isl_basic_map_drop_redundant_divs(bmap
);
5059 /* Does "bmap" satisfy any equality that involves more than 2 variables
5060 * and/or has coefficients different from -1 and 1?
5062 static isl_bool
has_multiple_var_equality(__isl_keep isl_basic_map
*bmap
)
5067 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5069 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5072 j
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1, total
);
5075 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
5076 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
5077 return isl_bool_true
;
5080 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
5084 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
5085 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
5086 return isl_bool_true
;
5089 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
5091 return isl_bool_true
;
5094 return isl_bool_false
;
5097 /* Remove any common factor g from the constraint coefficients in "v".
5098 * The constant term is stored in the first position and is replaced
5099 * by floor(c/g). If any common factor is removed and if this results
5100 * in a tightening of the constraint, then set *tightened.
5102 static __isl_give isl_vec
*normalize_constraint(__isl_take isl_vec
*v
,
5109 ctx
= isl_vec_get_ctx(v
);
5110 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
5111 if (isl_int_is_zero(ctx
->normalize_gcd
))
5113 if (isl_int_is_one(ctx
->normalize_gcd
))
5118 if (tightened
&& !isl_int_is_divisible_by(v
->el
[0], ctx
->normalize_gcd
))
5120 isl_int_fdiv_q(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
5121 isl_seq_scale_down(v
->el
+ 1, v
->el
+ 1, ctx
->normalize_gcd
,
5126 /* If "bmap" is an integer set that satisfies any equality involving
5127 * more than 2 variables and/or has coefficients different from -1 and 1,
5128 * then use variable compression to reduce the coefficients by removing
5129 * any (hidden) common factor.
5130 * In particular, apply the variable compression to each constraint,
5131 * factor out any common factor in the non-constant coefficients and
5132 * then apply the inverse of the compression.
5133 * At the end, we mark the basic map as having reduced constants.
5134 * If this flag is still set on the next invocation of this function,
5135 * then we skip the computation.
5137 * Removing a common factor may result in a tightening of some of
5138 * the constraints. If this happens, then we may end up with two
5139 * opposite inequalities that can be replaced by an equality.
5140 * We therefore call isl_basic_map_detect_inequality_pairs,
5141 * which checks for such pairs of inequalities as well as eliminate_divs_eq
5142 * and isl_basic_map_gauss if such a pair was found.
5144 * Note that this function may leave the result in an inconsistent state.
5145 * In particular, the constraints may not be gaussed.
5146 * Unfortunately, isl_map_coalesce actually depends on this inconsistent state
5147 * for some of the test cases to pass successfully.
5148 * Any potential modification of the representation is therefore only
5149 * performed on a single copy of the basic map.
5151 __isl_give isl_basic_map
*isl_basic_map_reduce_coefficients(
5152 __isl_take isl_basic_map
*bmap
)
5158 isl_mat
*eq
, *T
, *T2
;
5164 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
))
5166 if (isl_basic_map_is_rational(bmap
))
5168 if (bmap
->n_eq
== 0)
5170 multi
= has_multiple_var_equality(bmap
);
5172 return isl_basic_map_free(bmap
);
5176 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5177 ctx
= isl_basic_map_get_ctx(bmap
);
5178 v
= isl_vec_alloc(ctx
, 1 + total
);
5180 return isl_basic_map_free(bmap
);
5182 eq
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
, 0, 1 + total
);
5183 T
= isl_mat_variable_compression(eq
, &T2
);
5186 if (T
->n_col
== 0) {
5190 return isl_basic_map_set_to_empty(bmap
);
5193 bmap
= isl_basic_map_cow(bmap
);
5198 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
5199 isl_seq_cpy(v
->el
, bmap
->ineq
[i
], 1 + total
);
5200 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
5201 v
= normalize_constraint(v
, &tightened
);
5202 v
= isl_vec_mat_product(v
, isl_mat_copy(T2
));
5205 isl_seq_cpy(bmap
->ineq
[i
], v
->el
, 1 + total
);
5212 ISL_F_SET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
5217 bmap
= isl_basic_map_detect_inequality_pairs(bmap
, &progress
);
5219 bmap
= eliminate_divs_eq(bmap
, &progress
);
5220 bmap
= isl_basic_map_gauss(bmap
, NULL
);
5229 return isl_basic_map_free(bmap
);
5232 /* Shift the integer division at position "div" of "bmap"
5233 * by "shift" times the variable at position "pos".
5234 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
5235 * corresponds to the constant term.
5237 * That is, if the integer division has the form
5241 * then replace it by
5243 * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
5245 __isl_give isl_basic_map
*isl_basic_map_shift_div(
5246 __isl_take isl_basic_map
*bmap
, int div
, int pos
, isl_int shift
)
5251 if (isl_int_is_zero(shift
))
5256 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5257 total
-= isl_basic_map_dim(bmap
, isl_dim_div
);
5259 isl_int_addmul(bmap
->div
[div
][1 + pos
], shift
, bmap
->div
[div
][0]);
5261 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5262 if (isl_int_is_zero(bmap
->eq
[i
][1 + total
+ div
]))
5264 isl_int_submul(bmap
->eq
[i
][pos
],
5265 shift
, bmap
->eq
[i
][1 + total
+ div
]);
5267 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
5268 if (isl_int_is_zero(bmap
->ineq
[i
][1 + total
+ div
]))
5270 isl_int_submul(bmap
->ineq
[i
][pos
],
5271 shift
, bmap
->ineq
[i
][1 + total
+ div
]);
5273 for (i
= 0; i
< bmap
->n_div
; ++i
) {
5274 if (isl_int_is_zero(bmap
->div
[i
][0]))
5276 if (isl_int_is_zero(bmap
->div
[i
][1 + 1 + total
+ div
]))
5278 isl_int_submul(bmap
->div
[i
][1 + pos
],
5279 shift
, bmap
->div
[i
][1 + 1 + total
+ div
]);