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 void normalize_div_expression(__isl_keep isl_basic_map
*bmap
, int div
)
239 unsigned total
= isl_basic_map_total_dim(bmap
);
240 isl_ctx
*ctx
= bmap
->ctx
;
242 if (isl_int_is_zero(bmap
->div
[div
][0]))
244 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
245 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
246 if (isl_int_is_one(ctx
->normalize_gcd
))
248 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
250 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
252 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
253 ctx
->normalize_gcd
, total
);
256 /* Remove any common factor in numerator and denominator of a div expression,
257 * not taking into account the constant term.
258 * That is, look for any div of the form
260 * floor((a + m f(x))/(m d))
264 * floor((floor(a/m) + f(x))/d)
266 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
267 * and can therefore not influence the result of the floor.
269 static __isl_give isl_basic_map
*normalize_div_expressions(
270 __isl_take isl_basic_map
*bmap
)
276 if (bmap
->n_div
== 0)
279 for (i
= 0; i
< bmap
->n_div
; ++i
)
280 normalize_div_expression(bmap
, i
);
285 /* Assumes divs have been ordered if keep_divs is set.
287 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
288 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
291 unsigned space_total
;
295 total
= isl_basic_map_total_dim(bmap
);
296 space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
297 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
298 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
299 if (bmap
->eq
[k
] == eq
)
301 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
305 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
306 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
309 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
310 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
314 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
315 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
316 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
317 ISL_F_CLR(bmap
, ISL_BASIC_MAP_SORTED
);
320 for (k
= 0; k
< bmap
->n_div
; ++k
) {
321 if (isl_int_is_zero(bmap
->div
[k
][0]))
323 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
327 /* We need to be careful about circular definitions,
328 * so for now we just remove the definition of div k
329 * if the equality contains any divs.
330 * If keep_divs is set, then the divs have been ordered
331 * and we can keep the definition as long as the result
334 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
335 isl_seq_elim(bmap
->div
[k
]+1, eq
,
336 1+pos
, 1+total
, &bmap
->div
[k
][0]);
337 normalize_div_expression(bmap
, k
);
339 isl_seq_clr(bmap
->div
[k
], 1 + total
);
343 /* Assumes divs have been ordered if keep_divs is set.
345 static __isl_give isl_basic_map
*eliminate_div(__isl_take isl_basic_map
*bmap
,
346 isl_int
*eq
, unsigned div
, int keep_divs
)
348 unsigned pos
= isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
350 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
352 bmap
= isl_basic_map_drop_div(bmap
, div
);
357 /* Check if elimination of div "div" using equality "eq" would not
358 * result in a div depending on a later div.
360 static isl_bool
ok_to_eliminate_div(__isl_keep isl_basic_map
*bmap
, isl_int
*eq
,
365 unsigned space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
366 unsigned pos
= space_total
+ div
;
368 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
369 if (last_div
< 0 || last_div
<= div
)
370 return isl_bool_true
;
372 for (k
= 0; k
<= last_div
; ++k
) {
373 if (isl_int_is_zero(bmap
->div
[k
][0]))
375 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
376 return isl_bool_false
;
379 return isl_bool_true
;
382 /* Eliminate divs based on equalities
384 static __isl_give isl_basic_map
*eliminate_divs_eq(
385 __isl_take isl_basic_map
*bmap
, int *progress
)
392 bmap
= isl_basic_map_order_divs(bmap
);
397 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
399 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
400 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
403 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
404 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
406 ok
= ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
);
408 return isl_basic_map_free(bmap
);
413 bmap
= eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
414 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
415 return isl_basic_map_free(bmap
);
420 return eliminate_divs_eq(bmap
, progress
);
424 /* Eliminate divs based on inequalities
426 static __isl_give isl_basic_map
*eliminate_divs_ineq(
427 __isl_take isl_basic_map
*bmap
, int *progress
)
438 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
440 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
441 for (i
= 0; i
< bmap
->n_eq
; ++i
)
442 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
446 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
447 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
449 if (i
< bmap
->n_ineq
)
452 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
453 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
455 bmap
= isl_basic_map_drop_div(bmap
, d
);
462 /* Does the equality constraint at position "eq" in "bmap" involve
463 * any local variables in the range [first, first + n)
464 * that are not marked as having an explicit representation?
466 static isl_bool
bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map
*bmap
,
467 int eq
, unsigned first
, unsigned n
)
473 return isl_bool_error
;
475 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
476 for (i
= 0; i
< n
; ++i
) {
479 if (isl_int_is_zero(bmap
->eq
[eq
][o_div
+ first
+ i
]))
481 unknown
= isl_basic_map_div_is_marked_unknown(bmap
, first
+ i
);
483 return isl_bool_error
;
485 return isl_bool_true
;
488 return isl_bool_false
;
491 /* The last local variable involved in the equality constraint
492 * at position "eq" in "bmap" is the local variable at position "div".
493 * It can therefore be used to extract an explicit representation
495 * Do so unless the local variable already has an explicit representation or
496 * the explicit representation would involve any other local variables
497 * that in turn do not have an explicit representation.
498 * An equality constraint involving local variables without an explicit
499 * representation can be used in isl_basic_map_drop_redundant_divs
500 * to separate out an independent local variable. Introducing
501 * an explicit representation here would block this transformation,
502 * while the partial explicit representation in itself is not very useful.
503 * Set *progress if anything is changed.
505 * The equality constraint is of the form
509 * with n a positive number. The explicit representation derived from
514 static __isl_give isl_basic_map
*set_div_from_eq(__isl_take isl_basic_map
*bmap
,
515 int div
, int eq
, int *progress
)
517 unsigned total
, o_div
;
523 if (!isl_int_is_zero(bmap
->div
[div
][0]))
526 involves
= bmap_eq_involves_unknown_divs(bmap
, eq
, 0, div
);
528 return isl_basic_map_free(bmap
);
532 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
533 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
534 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->eq
[eq
], 1 + total
);
535 isl_int_set_si(bmap
->div
[div
][1 + o_div
+ div
], 0);
536 isl_int_set(bmap
->div
[div
][0], bmap
->eq
[eq
][o_div
+ div
]);
543 __isl_give isl_basic_map
*isl_basic_map_gauss(__isl_take isl_basic_map
*bmap
,
552 bmap
= isl_basic_map_order_divs(bmap
);
557 total
= isl_basic_map_total_dim(bmap
);
558 total_var
= total
- bmap
->n_div
;
560 last_var
= total
- 1;
561 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
562 for (; last_var
>= 0; --last_var
) {
563 for (k
= done
; k
< bmap
->n_eq
; ++k
)
564 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
572 swap_equality(bmap
, k
, done
);
573 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
574 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
576 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
579 if (last_var
>= total_var
)
580 bmap
= set_div_from_eq(bmap
, last_var
- total_var
,
585 if (done
== bmap
->n_eq
)
587 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
588 if (isl_int_is_zero(bmap
->eq
[k
][0]))
590 return isl_basic_map_set_to_empty(bmap
);
592 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
596 __isl_give isl_basic_set
*isl_basic_set_gauss(
597 __isl_take isl_basic_set
*bset
, int *progress
)
599 return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset
),
604 static unsigned int round_up(unsigned int v
)
615 /* Hash table of inequalities in a basic map.
616 * "index" is an array of addresses of inequalities in the basic map, some
617 * of which are NULL. The inequalities are hashed on the coefficients
618 * except the constant term.
619 * "size" is the number of elements in the array and is always a power of two
620 * "bits" is the number of bits need to represent an index into the array.
621 * "total" is the total dimension of the basic map.
623 struct isl_constraint_index
{
630 /* Fill in the "ci" data structure for holding the inequalities of "bmap".
632 static isl_stat
create_constraint_index(struct isl_constraint_index
*ci
,
633 __isl_keep isl_basic_map
*bmap
)
639 return isl_stat_error
;
640 ci
->total
= isl_basic_set_total_dim(bmap
);
641 if (bmap
->n_ineq
== 0)
643 ci
->size
= round_up(4 * (bmap
->n_ineq
+ 1) / 3 - 1);
644 ci
->bits
= ffs(ci
->size
) - 1;
645 ctx
= isl_basic_map_get_ctx(bmap
);
646 ci
->index
= isl_calloc_array(ctx
, isl_int
**, ci
->size
);
648 return isl_stat_error
;
653 /* Free the memory allocated by create_constraint_index.
655 static void constraint_index_free(struct isl_constraint_index
*ci
)
660 /* Return the position in ci->index that contains the address of
661 * an inequality that is equal to *ineq up to the constant term,
662 * provided this address is not identical to "ineq".
663 * If there is no such inequality, then return the position where
664 * such an inequality should be inserted.
666 static int hash_index_ineq(struct isl_constraint_index
*ci
, isl_int
**ineq
)
669 uint32_t hash
= isl_seq_get_hash_bits((*ineq
) + 1, ci
->total
, ci
->bits
);
670 for (h
= hash
; ci
->index
[h
]; h
= (h
+1) % ci
->size
)
671 if (ineq
!= ci
->index
[h
] &&
672 isl_seq_eq((*ineq
) + 1, ci
->index
[h
][0]+1, ci
->total
))
677 /* Return the position in ci->index that contains the address of
678 * an inequality that is equal to the k'th inequality of "bmap"
679 * up to the constant term, provided it does not point to the very
681 * If there is no such inequality, then return the position where
682 * such an inequality should be inserted.
684 static int hash_index(struct isl_constraint_index
*ci
,
685 __isl_keep isl_basic_map
*bmap
, int k
)
687 return hash_index_ineq(ci
, &bmap
->ineq
[k
]);
690 static int set_hash_index(struct isl_constraint_index
*ci
,
691 __isl_keep isl_basic_set
*bset
, int k
)
693 return hash_index(ci
, bset
, k
);
696 /* Fill in the "ci" data structure with the inequalities of "bset".
698 static isl_stat
setup_constraint_index(struct isl_constraint_index
*ci
,
699 __isl_keep isl_basic_set
*bset
)
703 if (create_constraint_index(ci
, bset
) < 0)
704 return isl_stat_error
;
706 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
707 h
= set_hash_index(ci
, bset
, k
);
708 ci
->index
[h
] = &bset
->ineq
[k
];
714 /* Is the inequality ineq (obviously) redundant with respect
715 * to the constraints in "ci"?
717 * Look for an inequality in "ci" with the same coefficients and then
718 * check if the contant term of "ineq" is greater than or equal
719 * to the constant term of that inequality. If so, "ineq" is clearly
722 * Note that hash_index_ineq ignores a stored constraint if it has
723 * the same address as the passed inequality. It is ok to pass
724 * the address of a local variable here since it will never be
725 * the same as the address of a constraint in "ci".
727 static isl_bool
constraint_index_is_redundant(struct isl_constraint_index
*ci
,
732 h
= hash_index_ineq(ci
, &ineq
);
734 return isl_bool_false
;
735 return isl_int_ge(ineq
[0], (*ci
->index
[h
])[0]);
738 /* If we can eliminate more than one div, then we need to make
739 * sure we do it from last div to first div, in order not to
740 * change the position of the other divs that still need to
743 static __isl_give isl_basic_map
*remove_duplicate_divs(
744 __isl_take isl_basic_map
*bmap
, int *progress
)
756 bmap
= isl_basic_map_order_divs(bmap
);
757 if (!bmap
|| bmap
->n_div
<= 1)
760 total_var
= isl_space_dim(bmap
->dim
, isl_dim_all
);
761 total
= total_var
+ bmap
->n_div
;
764 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
765 if (!isl_int_is_zero(bmap
->div
[k
][0]))
770 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
773 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
774 bits
= ffs(size
) - 1;
775 index
= isl_calloc_array(ctx
, int, size
);
776 if (!elim_for
|| !index
)
778 eq
= isl_blk_alloc(ctx
, 1+total
);
779 if (isl_blk_is_error(eq
))
782 isl_seq_clr(eq
.data
, 1+total
);
783 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
784 for (--k
; k
>= 0; --k
) {
787 if (isl_int_is_zero(bmap
->div
[k
][0]))
790 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
791 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
792 if (isl_seq_eq(bmap
->div
[k
],
793 bmap
->div
[index
[h
]-1], 2+total
))
802 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
806 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
807 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
808 bmap
= eliminate_div(bmap
, eq
.data
, l
, 1);
811 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
812 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
815 isl_blk_free(ctx
, eq
);
822 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
827 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
828 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
829 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
833 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
839 /* Normalize divs that appear in equalities.
841 * In particular, we assume that bmap contains some equalities
846 * and we want to replace the set of e_i by a minimal set and
847 * such that the new e_i have a canonical representation in terms
849 * If any of the equalities involves more than one divs, then
850 * we currently simply bail out.
852 * Let us first additionally assume that all equalities involve
853 * a div. The equalities then express modulo constraints on the
854 * remaining variables and we can use "parameter compression"
855 * to find a minimal set of constraints. The result is a transformation
857 * x = T(x') = x_0 + G x'
859 * with G a lower-triangular matrix with all elements below the diagonal
860 * non-negative and smaller than the diagonal element on the same row.
861 * We first normalize x_0 by making the same property hold in the affine
863 * The rows i of G with a 1 on the diagonal do not impose any modulo
864 * constraint and simply express x_i = x'_i.
865 * For each of the remaining rows i, we introduce a div and a corresponding
866 * equality. In particular
868 * g_ii e_j = x_i - g_i(x')
870 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
871 * corresponding div (if g_kk != 1).
873 * If there are any equalities not involving any div, then we
874 * first apply a variable compression on the variables x:
876 * x = C x'' x'' = C_2 x
878 * and perform the above parameter compression on A C instead of on A.
879 * The resulting compression is then of the form
881 * x'' = T(x') = x_0 + G x'
883 * and in constructing the new divs and the corresponding equalities,
884 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
885 * by the corresponding row from C_2.
887 static __isl_give isl_basic_map
*normalize_divs(__isl_take isl_basic_map
*bmap
,
895 struct isl_mat
*T
= NULL
;
896 struct isl_mat
*C
= NULL
;
897 struct isl_mat
*C2
= NULL
;
905 if (bmap
->n_div
== 0)
911 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
914 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
915 div_eq
= n_pure_div_eq(bmap
);
919 if (div_eq
< bmap
->n_eq
) {
920 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
921 bmap
->n_eq
- div_eq
, 0, 1 + total
);
922 C
= isl_mat_variable_compression(B
, &C2
);
926 bmap
= isl_basic_map_set_to_empty(bmap
);
933 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
936 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
937 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
939 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
941 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
944 B
= isl_mat_product(B
, C
);
948 T
= isl_mat_parameter_compression(B
, d
);
952 bmap
= isl_basic_map_set_to_empty(bmap
);
958 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
959 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
960 if (isl_int_is_zero(v
))
962 isl_mat_col_submul(T
, 0, v
, 1 + i
);
965 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
968 /* We have to be careful because dropping equalities may reorder them */
970 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
971 for (i
= 0; i
< bmap
->n_eq
; ++i
)
972 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
974 if (i
< bmap
->n_eq
) {
975 bmap
= isl_basic_map_drop_div(bmap
, j
);
976 isl_basic_map_drop_equality(bmap
, i
);
982 for (i
= 1; i
< T
->n_row
; ++i
) {
983 if (isl_int_is_one(T
->row
[i
][i
]))
988 if (needed
> dropped
) {
989 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
994 for (i
= 1; i
< T
->n_row
; ++i
) {
995 if (isl_int_is_one(T
->row
[i
][i
]))
997 k
= isl_basic_map_alloc_div(bmap
);
998 pos
[i
] = 1 + total
+ k
;
999 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
1000 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
1002 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
1004 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
1005 for (j
= 0; j
< i
; ++j
) {
1006 if (isl_int_is_zero(T
->row
[i
][j
]))
1008 if (pos
[j
] < T
->n_row
&& C2
)
1009 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
1010 C2
->row
[pos
[j
]], 1 + total
);
1012 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
1015 j
= isl_basic_map_alloc_equality(bmap
);
1016 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
1017 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
1026 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
1037 static __isl_give isl_basic_map
*set_div_from_lower_bound(
1038 __isl_take isl_basic_map
*bmap
, int div
, int ineq
)
1040 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1042 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1043 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1044 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1045 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1046 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1051 /* Check whether it is ok to define a div based on an inequality.
1052 * To avoid the introduction of circular definitions of divs, we
1053 * do not allow such a definition if the resulting expression would refer to
1054 * any other undefined divs or if any known div is defined in
1055 * terms of the unknown div.
1057 static isl_bool
ok_to_set_div_from_bound(__isl_keep isl_basic_map
*bmap
,
1061 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1063 /* Not defined in terms of unknown divs */
1064 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1067 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1069 if (isl_int_is_zero(bmap
->div
[j
][0]))
1070 return isl_bool_false
;
1073 /* No other div defined in terms of this one => avoid loops */
1074 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1077 if (isl_int_is_zero(bmap
->div
[j
][0]))
1079 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1080 return isl_bool_false
;
1083 return isl_bool_true
;
1086 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1087 * be a better expression than the current one?
1089 * If we do not have any expression yet, then any expression would be better.
1090 * Otherwise we check if the last variable involved in the inequality
1091 * (disregarding the div that it would define) is in an earlier position
1092 * than the last variable involved in the current div expression.
1094 static isl_bool
better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1097 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1101 if (isl_int_is_zero(bmap
->div
[div
][0]))
1102 return isl_bool_true
;
1104 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1105 bmap
->n_div
- (div
+ 1)) >= 0)
1106 return isl_bool_false
;
1108 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1109 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1110 total
+ bmap
->n_div
);
1112 return last_ineq
< last_div
;
1115 /* Given two constraints "k" and "l" that are opposite to each other,
1116 * except for the constant term, check if we can use them
1117 * to obtain an expression for one of the hitherto unknown divs or
1118 * a "better" expression for a div for which we already have an expression.
1119 * "sum" is the sum of the constant terms of the constraints.
1120 * If this sum is strictly smaller than the coefficient of one
1121 * of the divs, then this pair can be used define the div.
1122 * To avoid the introduction of circular definitions of divs, we
1123 * do not use the pair if the resulting expression would refer to
1124 * any other undefined divs or if any known div is defined in
1125 * terms of the unknown div.
1127 static __isl_give isl_basic_map
*check_for_div_constraints(
1128 __isl_take isl_basic_map
*bmap
, int k
, int l
, isl_int sum
,
1132 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1134 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1137 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1139 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1141 set_div
= better_div_constraint(bmap
, i
, k
);
1142 if (set_div
>= 0 && set_div
)
1143 set_div
= ok_to_set_div_from_bound(bmap
, i
, k
);
1145 return isl_basic_map_free(bmap
);
1148 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1149 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1151 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1159 __isl_give isl_basic_map
*isl_basic_map_remove_duplicate_constraints(
1160 __isl_take isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1162 struct isl_constraint_index ci
;
1164 unsigned total
= isl_basic_map_total_dim(bmap
);
1167 if (!bmap
|| bmap
->n_ineq
<= 1)
1170 if (create_constraint_index(&ci
, bmap
) < 0)
1173 h
= isl_seq_get_hash_bits(bmap
->ineq
[0] + 1, total
, ci
.bits
);
1174 ci
.index
[h
] = &bmap
->ineq
[0];
1175 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1176 h
= hash_index(&ci
, bmap
, k
);
1178 ci
.index
[h
] = &bmap
->ineq
[k
];
1183 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1184 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1185 swap_inequality(bmap
, k
, l
);
1186 isl_basic_map_drop_inequality(bmap
, k
);
1190 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1191 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1192 h
= hash_index(&ci
, bmap
, k
);
1193 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1196 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1197 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1198 if (isl_int_is_pos(sum
)) {
1200 bmap
= check_for_div_constraints(bmap
, k
, l
,
1204 if (isl_int_is_zero(sum
)) {
1205 /* We need to break out of the loop after these
1206 * changes since the contents of the hash
1207 * will no longer be valid.
1208 * Plus, we probably we want to regauss first.
1212 isl_basic_map_drop_inequality(bmap
, l
);
1213 isl_basic_map_inequality_to_equality(bmap
, k
);
1215 bmap
= isl_basic_map_set_to_empty(bmap
);
1220 constraint_index_free(&ci
);
1224 /* Detect all pairs of inequalities that form an equality.
1226 * isl_basic_map_remove_duplicate_constraints detects at most one such pair.
1227 * Call it repeatedly while it is making progress.
1229 __isl_give isl_basic_map
*isl_basic_map_detect_inequality_pairs(
1230 __isl_take isl_basic_map
*bmap
, int *progress
)
1236 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1238 if (progress
&& duplicate
)
1240 } while (duplicate
);
1245 /* Eliminate knowns divs from constraints where they appear with
1246 * a (positive or negative) unit coefficient.
1250 * floor(e/m) + f >= 0
1258 * -floor(e/m) + f >= 0
1262 * -e + m f + m - 1 >= 0
1264 * The first conversion is valid because floor(e/m) >= -f is equivalent
1265 * to e/m >= -f because -f is an integral expression.
1266 * The second conversion follows from the fact that
1268 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1271 * Note that one of the div constraints may have been eliminated
1272 * due to being redundant with respect to the constraint that is
1273 * being modified by this function. The modified constraint may
1274 * no longer imply this div constraint, so we add it back to make
1275 * sure we do not lose any information.
1277 * We skip integral divs, i.e., those with denominator 1, as we would
1278 * risk eliminating the div from the div constraints. We do not need
1279 * to handle those divs here anyway since the div constraints will turn
1280 * out to form an equality and this equality can then be used to eliminate
1281 * the div from all constraints.
1283 static __isl_give isl_basic_map
*eliminate_unit_divs(
1284 __isl_take isl_basic_map
*bmap
, int *progress
)
1293 ctx
= isl_basic_map_get_ctx(bmap
);
1294 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1296 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1297 if (isl_int_is_zero(bmap
->div
[i
][0]))
1299 if (isl_int_is_one(bmap
->div
[i
][0]))
1301 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1304 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1305 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1310 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1311 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1313 isl_seq_combine(bmap
->ineq
[j
],
1314 ctx
->negone
, bmap
->div
[i
] + 1,
1315 bmap
->div
[i
][0], bmap
->ineq
[j
],
1316 total
+ bmap
->n_div
);
1318 isl_seq_combine(bmap
->ineq
[j
],
1319 ctx
->one
, bmap
->div
[i
] + 1,
1320 bmap
->div
[i
][0], bmap
->ineq
[j
],
1321 total
+ bmap
->n_div
);
1323 isl_int_add(bmap
->ineq
[j
][0],
1324 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1325 isl_int_sub_ui(bmap
->ineq
[j
][0],
1326 bmap
->ineq
[j
][0], 1);
1329 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
1330 if (isl_basic_map_add_div_constraint(bmap
, i
, s
) < 0)
1331 return isl_basic_map_free(bmap
);
1338 __isl_give isl_basic_map
*isl_basic_map_simplify(__isl_take isl_basic_map
*bmap
)
1347 empty
= isl_basic_map_plain_is_empty(bmap
);
1349 return isl_basic_map_free(bmap
);
1352 bmap
= isl_basic_map_normalize_constraints(bmap
);
1353 bmap
= reduce_div_coefficients(bmap
);
1354 bmap
= normalize_div_expressions(bmap
);
1355 bmap
= remove_duplicate_divs(bmap
, &progress
);
1356 bmap
= eliminate_unit_divs(bmap
, &progress
);
1357 bmap
= eliminate_divs_eq(bmap
, &progress
);
1358 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1359 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1360 /* requires equalities in normal form */
1361 bmap
= normalize_divs(bmap
, &progress
);
1362 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1364 if (bmap
&& progress
)
1365 ISL_F_CLR(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
1370 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1372 return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset
)));
1376 isl_bool
isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1377 isl_int
*constraint
, unsigned div
)
1382 return isl_bool_error
;
1384 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1386 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1388 isl_int_sub(bmap
->div
[div
][1],
1389 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1390 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1391 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1392 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1393 isl_int_add(bmap
->div
[div
][1],
1394 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1396 return isl_bool_false
;
1397 if (isl_seq_first_non_zero(constraint
+pos
+1,
1398 bmap
->n_div
-div
-1) != -1)
1399 return isl_bool_false
;
1400 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1401 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1402 return isl_bool_false
;
1403 if (isl_seq_first_non_zero(constraint
+pos
+1,
1404 bmap
->n_div
-div
-1) != -1)
1405 return isl_bool_false
;
1407 return isl_bool_false
;
1409 return isl_bool_true
;
1412 isl_bool
isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1413 isl_int
*constraint
, unsigned div
)
1415 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1419 /* If the only constraints a div d=floor(f/m)
1420 * appears in are its two defining constraints
1423 * -(f - (m - 1)) + m d >= 0
1425 * then it can safely be removed.
1427 static isl_bool
div_is_redundant(__isl_keep isl_basic_map
*bmap
, int div
)
1430 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1432 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1433 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1434 return isl_bool_false
;
1436 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1439 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1441 red
= isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
);
1442 if (red
< 0 || !red
)
1446 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1447 if (isl_int_is_zero(bmap
->div
[i
][0]))
1449 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1450 return isl_bool_false
;
1453 return isl_bool_true
;
1457 * Remove divs that don't occur in any of the constraints or other divs.
1458 * These can arise when dropping constraints from a basic map or
1459 * when the divs of a basic map have been temporarily aligned
1460 * with the divs of another basic map.
1462 static __isl_give isl_basic_map
*remove_redundant_divs(
1463 __isl_take isl_basic_map
*bmap
)
1468 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1470 return isl_basic_map_free(bmap
);
1472 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1475 redundant
= div_is_redundant(bmap
, i
);
1477 return isl_basic_map_free(bmap
);
1480 bmap
= isl_basic_map_drop_constraints_involving(bmap
,
1482 bmap
= isl_basic_map_drop_div(bmap
, i
);
1487 /* Mark "bmap" as final, without checking for obviously redundant
1488 * integer divisions. This function should be used when "bmap"
1489 * is known not to involve any such integer divisions.
1491 __isl_give isl_basic_map
*isl_basic_map_mark_final(
1492 __isl_take isl_basic_map
*bmap
)
1496 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1500 /* Mark "bmap" as final, after removing obviously redundant integer divisions.
1502 __isl_give isl_basic_map
*isl_basic_map_finalize(__isl_take isl_basic_map
*bmap
)
1504 bmap
= remove_redundant_divs(bmap
);
1505 bmap
= isl_basic_map_mark_final(bmap
);
1509 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1511 return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset
)));
1514 /* Remove definition of any div that is defined in terms of the given variable.
1515 * The div itself is not removed. Functions such as
1516 * eliminate_divs_ineq depend on the other divs remaining in place.
1518 static __isl_give isl_basic_map
*remove_dependent_vars(
1519 __isl_take isl_basic_map
*bmap
, int pos
)
1526 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1527 if (isl_int_is_zero(bmap
->div
[i
][0]))
1529 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1531 bmap
= isl_basic_map_mark_div_unknown(bmap
, i
);
1538 /* Eliminate the specified variables from the constraints using
1539 * Fourier-Motzkin. The variables themselves are not removed.
1541 __isl_give isl_basic_map
*isl_basic_map_eliminate_vars(
1542 __isl_take isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1553 total
= isl_basic_map_total_dim(bmap
);
1555 bmap
= isl_basic_map_cow(bmap
);
1556 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1557 bmap
= remove_dependent_vars(bmap
, d
);
1561 for (d
= pos
+ n
- 1;
1562 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1563 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1564 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1565 int n_lower
, n_upper
;
1568 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1569 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1571 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1572 isl_basic_map_drop_equality(bmap
, i
);
1580 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1581 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1583 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1586 bmap
= isl_basic_map_extend_constraints(bmap
,
1587 0, n_lower
* n_upper
);
1590 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1592 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1595 for (j
= 0; j
< i
; ++j
) {
1596 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1599 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1600 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1602 k
= isl_basic_map_alloc_inequality(bmap
);
1605 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1607 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1608 1+d
, 1+total
, NULL
);
1610 isl_basic_map_drop_inequality(bmap
, i
);
1613 if (n_lower
> 0 && n_upper
> 0) {
1614 bmap
= isl_basic_map_normalize_constraints(bmap
);
1615 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1617 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1618 bmap
= isl_basic_map_remove_redundancies(bmap
);
1622 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1627 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1630 isl_basic_map_free(bmap
);
1634 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1635 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1637 return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset
),
1641 /* Eliminate the specified n dimensions starting at first from the
1642 * constraints, without removing the dimensions from the space.
1643 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1644 * Otherwise, they are projected out and the original space is restored.
1646 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1647 __isl_take isl_basic_map
*bmap
,
1648 enum isl_dim_type type
, unsigned first
, unsigned n
)
1657 if (isl_basic_map_check_range(bmap
, type
, first
, n
) < 0)
1658 return isl_basic_map_free(bmap
);
1660 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1661 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1662 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1663 return isl_basic_map_finalize(bmap
);
1666 space
= isl_basic_map_get_space(bmap
);
1667 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1668 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1669 bmap
= isl_basic_map_reset_space(bmap
, space
);
1673 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1674 __isl_take isl_basic_set
*bset
,
1675 enum isl_dim_type type
, unsigned first
, unsigned n
)
1677 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1680 /* Remove all constraints from "bmap" that reference any unknown local
1681 * variables (directly or indirectly).
1683 * Dropping all constraints on a local variable will make it redundant,
1684 * so it will get removed implicitly by
1685 * isl_basic_map_drop_constraints_involving_dims. Some other local
1686 * variables may also end up becoming redundant if they only appear
1687 * in constraints together with the unknown local variable.
1688 * Therefore, start over after calling
1689 * isl_basic_map_drop_constraints_involving_dims.
1691 __isl_give isl_basic_map
*isl_basic_map_drop_constraint_involving_unknown_divs(
1692 __isl_take isl_basic_map
*bmap
)
1695 int i
, n_div
, o_div
;
1697 known
= isl_basic_map_divs_known(bmap
);
1699 return isl_basic_map_free(bmap
);
1703 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1704 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
) - 1;
1706 for (i
= 0; i
< n_div
; ++i
) {
1707 known
= isl_basic_map_div_is_known(bmap
, i
);
1709 return isl_basic_map_free(bmap
);
1712 bmap
= remove_dependent_vars(bmap
, o_div
+ i
);
1713 bmap
= isl_basic_map_drop_constraints_involving_dims(bmap
,
1717 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1724 /* Remove all constraints from "map" that reference any unknown local
1725 * variables (directly or indirectly).
1727 * Since constraints may get dropped from the basic maps,
1728 * they may no longer be disjoint from each other.
1730 __isl_give isl_map
*isl_map_drop_constraint_involving_unknown_divs(
1731 __isl_take isl_map
*map
)
1736 known
= isl_map_divs_known(map
);
1738 return isl_map_free(map
);
1742 map
= isl_map_cow(map
);
1746 for (i
= 0; i
< map
->n
; ++i
) {
1748 isl_basic_map_drop_constraint_involving_unknown_divs(
1751 return isl_map_free(map
);
1755 ISL_F_CLR(map
, ISL_MAP_DISJOINT
);
1760 /* Don't assume equalities are in order, because align_divs
1761 * may have changed the order of the divs.
1763 static void compute_elimination_index(__isl_keep isl_basic_map
*bmap
, int *elim
)
1768 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1769 for (d
= 0; d
< total
; ++d
)
1771 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1772 for (d
= total
- 1; d
>= 0; --d
) {
1773 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1781 static void set_compute_elimination_index(__isl_keep isl_basic_set
*bset
,
1784 compute_elimination_index(bset_to_bmap(bset
), elim
);
1787 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1788 __isl_keep isl_basic_map
*bmap
, int *elim
)
1794 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1795 for (d
= total
- 1; d
>= 0; --d
) {
1796 if (isl_int_is_zero(src
[1+d
]))
1801 isl_seq_cpy(dst
, src
, 1 + total
);
1804 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1809 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1810 __isl_keep isl_basic_set
*bset
, int *elim
)
1812 return reduced_using_equalities(dst
, src
,
1813 bset_to_bmap(bset
), elim
);
1816 static __isl_give isl_basic_set
*isl_basic_set_reduce_using_equalities(
1817 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
1822 if (!bset
|| !context
)
1825 if (context
->n_eq
== 0) {
1826 isl_basic_set_free(context
);
1830 bset
= isl_basic_set_cow(bset
);
1834 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1837 set_compute_elimination_index(context
, elim
);
1838 for (i
= 0; i
< bset
->n_eq
; ++i
)
1839 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1841 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1842 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1844 isl_basic_set_free(context
);
1846 bset
= isl_basic_set_simplify(bset
);
1847 bset
= isl_basic_set_finalize(bset
);
1850 isl_basic_set_free(bset
);
1851 isl_basic_set_free(context
);
1855 /* For each inequality in "ineq" that is a shifted (more relaxed)
1856 * copy of an inequality in "context", mark the corresponding entry
1858 * If an inequality only has a non-negative constant term, then
1861 static isl_stat
mark_shifted_constraints(__isl_keep isl_mat
*ineq
,
1862 __isl_keep isl_basic_set
*context
, int *row
)
1864 struct isl_constraint_index ci
;
1869 if (!ineq
|| !context
)
1870 return isl_stat_error
;
1871 if (context
->n_ineq
== 0)
1873 if (setup_constraint_index(&ci
, context
) < 0)
1874 return isl_stat_error
;
1876 n_ineq
= isl_mat_rows(ineq
);
1877 total
= isl_mat_cols(ineq
) - 1;
1878 for (k
= 0; k
< n_ineq
; ++k
) {
1882 l
= isl_seq_first_non_zero(ineq
->row
[k
] + 1, total
);
1883 if (l
< 0 && isl_int_is_nonneg(ineq
->row
[k
][0])) {
1887 redundant
= constraint_index_is_redundant(&ci
, ineq
->row
[k
]);
1894 constraint_index_free(&ci
);
1897 constraint_index_free(&ci
);
1898 return isl_stat_error
;
1901 static __isl_give isl_basic_set
*remove_shifted_constraints(
1902 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*context
)
1904 struct isl_constraint_index ci
;
1907 if (!bset
|| !context
)
1910 if (context
->n_ineq
== 0)
1912 if (setup_constraint_index(&ci
, context
) < 0)
1915 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1918 redundant
= constraint_index_is_redundant(&ci
, bset
->ineq
[k
]);
1923 bset
= isl_basic_set_cow(bset
);
1926 isl_basic_set_drop_inequality(bset
, k
);
1929 constraint_index_free(&ci
);
1932 constraint_index_free(&ci
);
1936 /* Remove constraints from "bmap" that are identical to constraints
1937 * in "context" or that are more relaxed (greater constant term).
1939 * We perform the test for shifted copies on the pure constraints
1940 * in remove_shifted_constraints.
1942 static __isl_give isl_basic_map
*isl_basic_map_remove_shifted_constraints(
1943 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
1945 isl_basic_set
*bset
, *bset_context
;
1947 if (!bmap
|| !context
)
1950 if (bmap
->n_ineq
== 0 || context
->n_ineq
== 0) {
1951 isl_basic_map_free(context
);
1955 context
= isl_basic_map_align_divs(context
, bmap
);
1956 bmap
= isl_basic_map_align_divs(bmap
, context
);
1958 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
1959 bset_context
= isl_basic_map_underlying_set(context
);
1960 bset
= remove_shifted_constraints(bset
, bset_context
);
1961 isl_basic_set_free(bset_context
);
1963 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
1967 isl_basic_map_free(bmap
);
1968 isl_basic_map_free(context
);
1972 /* Does the (linear part of a) constraint "c" involve any of the "len"
1973 * "relevant" dimensions?
1975 static int is_related(isl_int
*c
, int len
, int *relevant
)
1979 for (i
= 0; i
< len
; ++i
) {
1982 if (!isl_int_is_zero(c
[i
]))
1989 /* Drop constraints from "bmap" that do not involve any of
1990 * the dimensions marked "relevant".
1992 static __isl_give isl_basic_map
*drop_unrelated_constraints(
1993 __isl_take isl_basic_map
*bmap
, int *relevant
)
1997 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
1998 for (i
= 0; i
< dim
; ++i
)
2004 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
)
2005 if (!is_related(bmap
->eq
[i
] + 1, dim
, relevant
)) {
2006 bmap
= isl_basic_map_cow(bmap
);
2007 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
2008 return isl_basic_map_free(bmap
);
2011 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
)
2012 if (!is_related(bmap
->ineq
[i
] + 1, dim
, relevant
)) {
2013 bmap
= isl_basic_map_cow(bmap
);
2014 if (isl_basic_map_drop_inequality(bmap
, i
) < 0)
2015 return isl_basic_map_free(bmap
);
2021 /* Update the groups in "group" based on the (linear part of a) constraint "c".
2023 * In particular, for any variable involved in the constraint,
2024 * find the actual group id from before and replace the group
2025 * of the corresponding variable by the minimal group of all
2026 * the variables involved in the constraint considered so far
2027 * (if this minimum is smaller) or replace the minimum by this group
2028 * (if the minimum is larger).
2030 * At the end, all the variables in "c" will (indirectly) point
2031 * to the minimal of the groups that they referred to originally.
2033 static void update_groups(int dim
, int *group
, isl_int
*c
)
2038 for (j
= 0; j
< dim
; ++j
) {
2039 if (isl_int_is_zero(c
[j
]))
2041 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
2042 group
[j
] = group
[group
[j
]];
2043 if (group
[j
] == min
)
2045 if (group
[j
] < min
) {
2046 if (min
>= 0 && min
< dim
)
2047 group
[min
] = group
[j
];
2050 group
[group
[j
]] = min
;
2054 /* Allocate an array of groups of variables, one for each variable
2055 * in "context", initialized to zero.
2057 static int *alloc_groups(__isl_keep isl_basic_set
*context
)
2062 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2063 ctx
= isl_basic_set_get_ctx(context
);
2064 return isl_calloc_array(ctx
, int, dim
);
2067 /* Drop constraints from "bmap" that only involve variables that are
2068 * not related to any of the variables marked with a "-1" in "group".
2070 * We construct groups of variables that collect variables that
2071 * (indirectly) appear in some common constraint of "bmap".
2072 * Each group is identified by the first variable in the group,
2073 * except for the special group of variables that was already identified
2074 * in the input as -1 (or are related to those variables).
2075 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
2076 * otherwise the group of i is the group of group[i].
2078 * We first initialize groups for the remaining variables.
2079 * Then we iterate over the constraints of "bmap" and update the
2080 * group of the variables in the constraint by the smallest group.
2081 * Finally, we resolve indirect references to groups by running over
2084 * After computing the groups, we drop constraints that do not involve
2085 * any variables in the -1 group.
2087 __isl_give isl_basic_map
*isl_basic_map_drop_unrelated_constraints(
2088 __isl_take isl_basic_map
*bmap
, __isl_take
int *group
)
2097 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
2100 for (i
= 0; i
< dim
; ++i
)
2102 last
= group
[i
] = i
;
2108 for (i
= 0; i
< bmap
->n_eq
; ++i
)
2109 update_groups(dim
, group
, bmap
->eq
[i
] + 1);
2110 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
2111 update_groups(dim
, group
, bmap
->ineq
[i
] + 1);
2113 for (i
= 0; i
< dim
; ++i
)
2115 group
[i
] = group
[group
[i
]];
2117 for (i
= 0; i
< dim
; ++i
)
2118 group
[i
] = group
[i
] == -1;
2120 bmap
= drop_unrelated_constraints(bmap
, group
);
2126 /* Drop constraints from "context" that are irrelevant for computing
2127 * the gist of "bset".
2129 * In particular, drop constraints in variables that are not related
2130 * to any of the variables involved in the constraints of "bset"
2131 * in the sense that there is no sequence of constraints that connects them.
2133 * We first mark all variables that appear in "bset" as belonging
2134 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2136 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
2137 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
2143 if (!context
|| !bset
)
2144 return isl_basic_set_free(context
);
2146 group
= alloc_groups(context
);
2149 return isl_basic_set_free(context
);
2151 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2152 for (i
= 0; i
< dim
; ++i
) {
2153 for (j
= 0; j
< bset
->n_eq
; ++j
)
2154 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
2156 if (j
< bset
->n_eq
) {
2160 for (j
= 0; j
< bset
->n_ineq
; ++j
)
2161 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
2163 if (j
< bset
->n_ineq
)
2167 return isl_basic_map_drop_unrelated_constraints(context
, group
);
2170 /* Drop constraints from "context" that are irrelevant for computing
2171 * the gist of the inequalities "ineq".
2172 * Inequalities in "ineq" for which the corresponding element of row
2173 * is set to -1 have already been marked for removal and should be ignored.
2175 * In particular, drop constraints in variables that are not related
2176 * to any of the variables involved in "ineq"
2177 * in the sense that there is no sequence of constraints that connects them.
2179 * We first mark all variables that appear in "bset" as belonging
2180 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2182 static __isl_give isl_basic_set
*drop_irrelevant_constraints_marked(
2183 __isl_take isl_basic_set
*context
, __isl_keep isl_mat
*ineq
, int *row
)
2189 if (!context
|| !ineq
)
2190 return isl_basic_set_free(context
);
2192 group
= alloc_groups(context
);
2195 return isl_basic_set_free(context
);
2197 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2198 n
= isl_mat_rows(ineq
);
2199 for (i
= 0; i
< dim
; ++i
) {
2200 for (j
= 0; j
< n
; ++j
) {
2203 if (!isl_int_is_zero(ineq
->row
[j
][1 + i
]))
2210 return isl_basic_map_drop_unrelated_constraints(context
, group
);
2213 /* Do all "n" entries of "row" contain a negative value?
2215 static int all_neg(int *row
, int n
)
2219 for (i
= 0; i
< n
; ++i
)
2226 /* Update the inequalities in "bset" based on the information in "row"
2229 * In particular, the array "row" contains either -1, meaning that
2230 * the corresponding inequality of "bset" is redundant, or the index
2231 * of an inequality in "tab".
2233 * If the row entry is -1, then drop the inequality.
2234 * Otherwise, if the constraint is marked redundant in the tableau,
2235 * then drop the inequality. Similarly, if it is marked as an equality
2236 * in the tableau, then turn the inequality into an equality and
2237 * perform Gaussian elimination.
2239 static __isl_give isl_basic_set
*update_ineq(__isl_take isl_basic_set
*bset
,
2240 __isl_keep
int *row
, struct isl_tab
*tab
)
2245 int found_equality
= 0;
2249 if (tab
&& tab
->empty
)
2250 return isl_basic_set_set_to_empty(bset
);
2252 n_ineq
= bset
->n_ineq
;
2253 for (i
= n_ineq
- 1; i
>= 0; --i
) {
2255 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2256 return isl_basic_set_free(bset
);
2262 if (isl_tab_is_equality(tab
, n_eq
+ row
[i
])) {
2263 isl_basic_map_inequality_to_equality(bset
, i
);
2265 } else if (isl_tab_is_redundant(tab
, n_eq
+ row
[i
])) {
2266 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2267 return isl_basic_set_free(bset
);
2272 bset
= isl_basic_set_gauss(bset
, NULL
);
2273 bset
= isl_basic_set_finalize(bset
);
2277 /* Update the inequalities in "bset" based on the information in "row"
2278 * and "tab" and free all arguments (other than "bset").
2280 static __isl_give isl_basic_set
*update_ineq_free(
2281 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*ineq
,
2282 __isl_take isl_basic_set
*context
, __isl_take
int *row
,
2283 struct isl_tab
*tab
)
2286 isl_basic_set_free(context
);
2288 bset
= update_ineq(bset
, row
, tab
);
2295 /* Remove all information from bset that is redundant in the context
2297 * "ineq" contains the (possibly transformed) inequalities of "bset",
2298 * in the same order.
2299 * The (explicit) equalities of "bset" are assumed to have been taken
2300 * into account by the transformation such that only the inequalities
2302 * "context" is assumed not to be empty.
2304 * "row" keeps track of the constraint index of a "bset" inequality in "tab".
2305 * A value of -1 means that the inequality is obviously redundant and may
2306 * not even appear in "tab".
2308 * We first mark the inequalities of "bset"
2309 * that are obviously redundant with respect to some inequality in "context".
2310 * Then we remove those constraints from "context" that have become
2311 * irrelevant for computing the gist of "bset".
2312 * Note that this removal of constraints cannot be replaced by
2313 * a factorization because factors in "bset" may still be connected
2314 * to each other through constraints in "context".
2316 * If there are any inequalities left, we construct a tableau for
2317 * the context and then add the inequalities of "bset".
2318 * Before adding these inequalities, we freeze all constraints such that
2319 * they won't be considered redundant in terms of the constraints of "bset".
2320 * Then we detect all redundant constraints (among the
2321 * constraints that weren't frozen), first by checking for redundancy in the
2322 * the tableau and then by checking if replacing a constraint by its negation
2323 * would lead to an empty set. This last step is fairly expensive
2324 * and could be optimized by more reuse of the tableau.
2325 * Finally, we update bset according to the results.
2327 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
2328 __isl_take isl_mat
*ineq
, __isl_take isl_basic_set
*context
)
2333 isl_basic_set
*combined
= NULL
;
2334 struct isl_tab
*tab
= NULL
;
2335 unsigned n_eq
, context_ineq
;
2337 if (!bset
|| !ineq
|| !context
)
2340 if (bset
->n_ineq
== 0 || isl_basic_set_plain_is_universe(context
)) {
2341 isl_basic_set_free(context
);
2346 ctx
= isl_basic_set_get_ctx(context
);
2347 row
= isl_calloc_array(ctx
, int, bset
->n_ineq
);
2351 if (mark_shifted_constraints(ineq
, context
, row
) < 0)
2353 if (all_neg(row
, bset
->n_ineq
))
2354 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
2356 context
= drop_irrelevant_constraints_marked(context
, ineq
, row
);
2359 if (isl_basic_set_plain_is_universe(context
))
2360 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
2362 n_eq
= context
->n_eq
;
2363 context_ineq
= context
->n_ineq
;
2364 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
2365 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
2366 tab
= isl_tab_from_basic_set(combined
, 0);
2367 for (i
= 0; i
< context_ineq
; ++i
)
2368 if (isl_tab_freeze_constraint(tab
, n_eq
+ i
) < 0)
2370 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
2373 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2376 combined
= isl_basic_set_add_ineq(combined
, ineq
->row
[i
]);
2377 if (isl_tab_add_ineq(tab
, ineq
->row
[i
]) < 0)
2381 if (isl_tab_detect_implicit_equalities(tab
) < 0)
2383 if (isl_tab_detect_redundant(tab
) < 0)
2385 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
2386 isl_basic_set
*test
;
2392 if (tab
->con
[n_eq
+ r
].is_redundant
)
2394 test
= isl_basic_set_dup(combined
);
2395 test
= isl_inequality_negate(test
, r
);
2396 test
= isl_basic_set_update_from_tab(test
, tab
);
2397 is_empty
= isl_basic_set_is_empty(test
);
2398 isl_basic_set_free(test
);
2402 tab
->con
[n_eq
+ r
].is_redundant
= 1;
2404 bset
= update_ineq_free(bset
, ineq
, context
, row
, tab
);
2406 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2407 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2410 isl_basic_set_free(combined
);
2416 isl_basic_set_free(combined
);
2417 isl_basic_set_free(context
);
2418 isl_basic_set_free(bset
);
2422 /* Extract the inequalities of "bset" as an isl_mat.
2424 static __isl_give isl_mat
*extract_ineq(__isl_keep isl_basic_set
*bset
)
2433 ctx
= isl_basic_set_get_ctx(bset
);
2434 total
= isl_basic_set_total_dim(bset
);
2435 ineq
= isl_mat_sub_alloc6(ctx
, bset
->ineq
, 0, bset
->n_ineq
,
2441 /* Remove all information from "bset" that is redundant in the context
2442 * of "context", for the case where both "bset" and "context" are
2445 static __isl_give isl_basic_set
*uset_gist_uncompressed(
2446 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
2450 ineq
= extract_ineq(bset
);
2451 return uset_gist_full(bset
, ineq
, context
);
2454 /* Remove all information from "bset" that is redundant in the context
2455 * of "context", for the case where the combined equalities of
2456 * "bset" and "context" allow for a compression that can be obtained
2457 * by preapplication of "T".
2459 * "bset" itself is not transformed by "T". Instead, the inequalities
2460 * are extracted from "bset" and those are transformed by "T".
2461 * uset_gist_full then determines which of the transformed inequalities
2462 * are redundant with respect to the transformed "context" and removes
2463 * the corresponding inequalities from "bset".
2465 * After preapplying "T" to the inequalities, any common factor is
2466 * removed from the coefficients. If this results in a tightening
2467 * of the constant term, then the same tightening is applied to
2468 * the corresponding untransformed inequality in "bset".
2469 * That is, if after plugging in T, a constraint f(x) >= 0 is of the form
2473 * with 0 <= r < g, then it is equivalent to
2477 * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
2478 * subspace compressed by T since the latter would be transformed to
2482 static __isl_give isl_basic_set
*uset_gist_compressed(
2483 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
,
2484 __isl_take isl_mat
*T
)
2488 int i
, n_row
, n_col
;
2491 ineq
= extract_ineq(bset
);
2492 ineq
= isl_mat_product(ineq
, isl_mat_copy(T
));
2493 context
= isl_basic_set_preimage(context
, T
);
2495 if (!ineq
|| !context
)
2497 if (isl_basic_set_plain_is_empty(context
)) {
2499 isl_basic_set_free(context
);
2500 return isl_basic_set_set_to_empty(bset
);
2503 ctx
= isl_mat_get_ctx(ineq
);
2504 n_row
= isl_mat_rows(ineq
);
2505 n_col
= isl_mat_cols(ineq
);
2507 for (i
= 0; i
< n_row
; ++i
) {
2508 isl_seq_gcd(ineq
->row
[i
] + 1, n_col
- 1, &ctx
->normalize_gcd
);
2509 if (isl_int_is_zero(ctx
->normalize_gcd
))
2511 if (isl_int_is_one(ctx
->normalize_gcd
))
2513 isl_seq_scale_down(ineq
->row
[i
] + 1, ineq
->row
[i
] + 1,
2514 ctx
->normalize_gcd
, n_col
- 1);
2515 isl_int_fdiv_r(rem
, ineq
->row
[i
][0], ctx
->normalize_gcd
);
2516 isl_int_fdiv_q(ineq
->row
[i
][0],
2517 ineq
->row
[i
][0], ctx
->normalize_gcd
);
2518 if (isl_int_is_zero(rem
))
2520 bset
= isl_basic_set_cow(bset
);
2523 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], rem
);
2527 return uset_gist_full(bset
, ineq
, context
);
2530 isl_basic_set_free(context
);
2531 isl_basic_set_free(bset
);
2535 /* Project "bset" onto the variables that are involved in "template".
2537 static __isl_give isl_basic_set
*project_onto_involved(
2538 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*template)
2542 if (!bset
|| !template)
2543 return isl_basic_set_free(bset
);
2545 n
= isl_basic_set_dim(template, isl_dim_set
);
2547 for (i
= 0; i
< n
; ++i
) {
2550 involved
= isl_basic_set_involves_dims(template,
2553 return isl_basic_set_free(bset
);
2556 bset
= isl_basic_set_eliminate_vars(bset
, i
, 1);
2562 /* Remove all information from bset that is redundant in the context
2563 * of context. In particular, equalities that are linear combinations
2564 * of those in context are removed. Then the inequalities that are
2565 * redundant in the context of the equalities and inequalities of
2566 * context are removed.
2568 * First of all, we drop those constraints from "context"
2569 * that are irrelevant for computing the gist of "bset".
2570 * Alternatively, we could factorize the intersection of "context" and "bset".
2572 * We first compute the intersection of the integer affine hulls
2573 * of "bset" and "context",
2574 * compute the gist inside this intersection and then reduce
2575 * the constraints with respect to the equalities of the context
2576 * that only involve variables already involved in the input.
2578 * If two constraints are mutually redundant, then uset_gist_full
2579 * will remove the second of those constraints. We therefore first
2580 * sort the constraints so that constraints not involving existentially
2581 * quantified variables are given precedence over those that do.
2582 * We have to perform this sorting before the variable compression,
2583 * because that may effect the order of the variables.
2585 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2586 __isl_take isl_basic_set
*context
)
2591 isl_basic_set
*aff_context
;
2594 if (!bset
|| !context
)
2597 context
= drop_irrelevant_constraints(context
, bset
);
2599 bset
= isl_basic_set_detect_equalities(bset
);
2600 aff
= isl_basic_set_copy(bset
);
2601 aff
= isl_basic_set_plain_affine_hull(aff
);
2602 context
= isl_basic_set_detect_equalities(context
);
2603 aff_context
= isl_basic_set_copy(context
);
2604 aff_context
= isl_basic_set_plain_affine_hull(aff_context
);
2605 aff
= isl_basic_set_intersect(aff
, aff_context
);
2608 if (isl_basic_set_plain_is_empty(aff
)) {
2609 isl_basic_set_free(bset
);
2610 isl_basic_set_free(context
);
2613 bset
= isl_basic_set_sort_constraints(bset
);
2614 if (aff
->n_eq
== 0) {
2615 isl_basic_set_free(aff
);
2616 return uset_gist_uncompressed(bset
, context
);
2618 total
= isl_basic_set_total_dim(bset
);
2619 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2620 eq
= isl_mat_cow(eq
);
2621 T
= isl_mat_variable_compression(eq
, NULL
);
2622 isl_basic_set_free(aff
);
2623 if (T
&& T
->n_col
== 0) {
2625 isl_basic_set_free(context
);
2626 return isl_basic_set_set_to_empty(bset
);
2629 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2630 aff_context
= project_onto_involved(aff_context
, bset
);
2632 bset
= uset_gist_compressed(bset
, context
, T
);
2633 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2636 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2637 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2642 isl_basic_set_free(bset
);
2643 isl_basic_set_free(context
);
2647 /* Return the number of equality constraints in "bmap" that involve
2648 * local variables. This function assumes that Gaussian elimination
2649 * has been applied to the equality constraints.
2651 static int n_div_eq(__isl_keep isl_basic_map
*bmap
)
2659 if (bmap
->n_eq
== 0)
2662 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2663 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2666 for (i
= 0; i
< bmap
->n_eq
; ++i
)
2667 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
,
2674 /* Construct a basic map in "space" defined by the equality constraints in "eq".
2675 * The constraints are assumed not to involve any local variables.
2677 static __isl_give isl_basic_map
*basic_map_from_equalities(
2678 __isl_take isl_space
*space
, __isl_take isl_mat
*eq
)
2681 isl_basic_map
*bmap
= NULL
;
2686 if (1 + isl_space_dim(space
, isl_dim_all
) != eq
->n_col
)
2687 isl_die(isl_space_get_ctx(space
), isl_error_internal
,
2688 "unexpected number of columns", goto error
);
2690 bmap
= isl_basic_map_alloc_space(isl_space_copy(space
),
2692 for (i
= 0; i
< eq
->n_row
; ++i
) {
2693 k
= isl_basic_map_alloc_equality(bmap
);
2696 isl_seq_cpy(bmap
->eq
[k
], eq
->row
[i
], eq
->n_col
);
2699 isl_space_free(space
);
2703 isl_space_free(space
);
2705 isl_basic_map_free(bmap
);
2709 /* Construct and return a variable compression based on the equality
2710 * constraints in "bmap1" and "bmap2" that do not involve the local variables.
2711 * "n1" is the number of (initial) equality constraints in "bmap1"
2712 * that do involve local variables.
2713 * "n2" is the number of (initial) equality constraints in "bmap2"
2714 * that do involve local variables.
2715 * "total" is the total number of other variables.
2716 * This function assumes that Gaussian elimination
2717 * has been applied to the equality constraints in both "bmap1" and "bmap2"
2718 * such that the equality constraints not involving local variables
2719 * are those that start at "n1" or "n2".
2721 * If either of "bmap1" and "bmap2" does not have such equality constraints,
2722 * then simply compute the compression based on the equality constraints
2723 * in the other basic map.
2724 * Otherwise, combine the equality constraints from both into a new
2725 * basic map such that Gaussian elimination can be applied to this combination
2726 * and then construct a variable compression from the resulting
2727 * equality constraints.
2729 static __isl_give isl_mat
*combined_variable_compression(
2730 __isl_keep isl_basic_map
*bmap1
, int n1
,
2731 __isl_keep isl_basic_map
*bmap2
, int n2
, int total
)
2734 isl_mat
*E1
, *E2
, *V
;
2735 isl_basic_map
*bmap
;
2737 ctx
= isl_basic_map_get_ctx(bmap1
);
2738 if (bmap1
->n_eq
== n1
) {
2739 E2
= isl_mat_sub_alloc6(ctx
, bmap2
->eq
,
2740 n2
, bmap2
->n_eq
- n2
, 0, 1 + total
);
2741 return isl_mat_variable_compression(E2
, NULL
);
2743 if (bmap2
->n_eq
== n2
) {
2744 E1
= isl_mat_sub_alloc6(ctx
, bmap1
->eq
,
2745 n1
, bmap1
->n_eq
- n1
, 0, 1 + total
);
2746 return isl_mat_variable_compression(E1
, NULL
);
2748 E1
= isl_mat_sub_alloc6(ctx
, bmap1
->eq
,
2749 n1
, bmap1
->n_eq
- n1
, 0, 1 + total
);
2750 E2
= isl_mat_sub_alloc6(ctx
, bmap2
->eq
,
2751 n2
, bmap2
->n_eq
- n2
, 0, 1 + total
);
2752 E1
= isl_mat_concat(E1
, E2
);
2753 bmap
= basic_map_from_equalities(isl_basic_map_get_space(bmap1
), E1
);
2754 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2757 E1
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
, 0, 1 + total
);
2758 V
= isl_mat_variable_compression(E1
, NULL
);
2759 isl_basic_map_free(bmap
);
2764 /* Extract the stride constraints from "bmap", compressed
2765 * with respect to both the stride constraints in "context" and
2766 * the remaining equality constraints in both "bmap" and "context".
2767 * "bmap_n_eq" is the number of (initial) stride constraints in "bmap".
2768 * "context_n_eq" is the number of (initial) stride constraints in "context".
2770 * Let x be all variables in "bmap" (and "context") other than the local
2771 * variables. First compute a variable compression
2775 * based on the non-stride equality constraints in "bmap" and "context".
2776 * Consider the stride constraints of "context",
2780 * with y the local variables and plug in the variable compression,
2783 * A(V x') + B(y) = 0
2785 * Use these constraints to compute a parameter compression on x'
2789 * Now consider the stride constraints of "bmap"
2793 * and plug in x = V*T x''.
2794 * That is, return A = [C*V*T D].
2796 static __isl_give isl_mat
*extract_compressed_stride_constraints(
2797 __isl_keep isl_basic_map
*bmap
, int bmap_n_eq
,
2798 __isl_keep isl_basic_map
*context
, int context_n_eq
)
2802 isl_mat
*A
, *B
, *T
, *V
;
2804 total
= isl_basic_map_dim(context
, isl_dim_all
);
2805 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
2808 ctx
= isl_basic_map_get_ctx(bmap
);
2810 V
= combined_variable_compression(bmap
, bmap_n_eq
,
2811 context
, context_n_eq
, total
);
2813 A
= isl_mat_sub_alloc6(ctx
, context
->eq
, 0, context_n_eq
, 0, 1 + total
);
2814 B
= isl_mat_sub_alloc6(ctx
, context
->eq
,
2815 0, context_n_eq
, 1 + total
, n_div
);
2816 A
= isl_mat_product(A
, isl_mat_copy(V
));
2817 T
= isl_mat_parameter_compression_ext(A
, B
);
2818 T
= isl_mat_product(V
, T
);
2820 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2821 T
= isl_mat_diagonal(T
, isl_mat_identity(ctx
, n_div
));
2823 A
= isl_mat_sub_alloc6(ctx
, bmap
->eq
,
2824 0, bmap_n_eq
, 0, 1 + total
+ n_div
);
2825 A
= isl_mat_product(A
, T
);
2830 /* Remove the prime factors from *g that have an exponent that
2831 * is strictly smaller than the exponent in "c".
2832 * All exponents in *g are known to be smaller than or equal
2835 * That is, if *g is equal to
2837 * p_1^{e_1} p_2^{e_2} ... p_n^{e_n}
2839 * and "c" is equal to
2841 * p_1^{f_1} p_2^{f_2} ... p_n^{f_n}
2845 * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ...
2846 * p_n^{e_n * (e_n = f_n)}
2848 * If e_i = f_i, then c / *g does not have any p_i factors and therefore
2849 * neither does the gcd of *g and c / *g.
2850 * If e_i < f_i, then the gcd of *g and c / *g has a positive
2851 * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors.
2852 * Dividing *g by this gcd therefore strictly reduces the exponent
2853 * of the prime factors that need to be removed, while leaving the
2854 * other prime factors untouched.
2855 * Repeating this process until gcd(*g, c / *g) = 1 therefore
2856 * removes all undesired factors, without removing any others.
2858 static void remove_incomplete_powers(isl_int
*g
, isl_int c
)
2864 isl_int_divexact(t
, c
, *g
);
2865 isl_int_gcd(t
, t
, *g
);
2866 if (isl_int_is_one(t
))
2868 isl_int_divexact(*g
, *g
, t
);
2873 /* Reduce the "n" stride constraints in "bmap" based on a copy "A"
2874 * of the same stride constraints in a compressed space that exploits
2875 * all equalities in the context and the other equalities in "bmap".
2877 * If the stride constraints of "bmap" are of the form
2881 * then A is of the form
2885 * If any of these constraints involves only a single local variable y,
2886 * then the constraint appears as
2896 * Let g be the gcd of m and the coefficients of h.
2897 * Then, in particular, g is a divisor of the coefficients of h and
2901 * is known to be a multiple of g.
2902 * If some prime factor in m appears with the same exponent in g,
2903 * then it can be removed from m because f(x) is already known
2904 * to be a multiple of g and therefore in particular of this power
2905 * of the prime factors.
2906 * Prime factors that appear with a smaller exponent in g cannot
2907 * be removed from m.
2908 * Let g' be the divisor of g containing all prime factors that
2909 * appear with the same exponent in m and g, then
2913 * can be replaced by
2915 * f(x) + m/g' y_i' = 0
2917 * Note that (if g' != 1) this changes the explicit representation
2918 * of y_i to that of y_i', so the integer division at position i
2919 * is marked unknown and later recomputed by a call to
2920 * isl_basic_map_gauss.
2922 static __isl_give isl_basic_map
*reduce_stride_constraints(
2923 __isl_take isl_basic_map
*bmap
, int n
, __isl_keep isl_mat
*A
)
2931 return isl_basic_map_free(bmap
);
2933 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2934 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2938 for (i
= 0; i
< n
; ++i
) {
2941 div
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, n_div
);
2943 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
2944 "equality constraints modified unexpectedly",
2946 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
+ div
+ 1,
2947 n_div
- div
- 1) != -1)
2949 if (isl_mat_row_gcd(A
, i
, &gcd
) < 0)
2951 if (isl_int_is_one(gcd
))
2953 remove_incomplete_powers(&gcd
, bmap
->eq
[i
][1 + total
+ div
]);
2954 if (isl_int_is_one(gcd
))
2956 isl_int_divexact(bmap
->eq
[i
][1 + total
+ div
],
2957 bmap
->eq
[i
][1 + total
+ div
], gcd
);
2958 bmap
= isl_basic_map_mark_div_unknown(bmap
, div
);
2966 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2971 isl_basic_map_free(bmap
);
2975 /* Simplify the stride constraints in "bmap" based on
2976 * the remaining equality constraints in "bmap" and all equality
2977 * constraints in "context".
2978 * Only do this if both "bmap" and "context" have stride constraints.
2980 * First extract a copy of the stride constraints in "bmap" in a compressed
2981 * space exploiting all the other equality constraints and then
2982 * use this compressed copy to simplify the original stride constraints.
2984 static __isl_give isl_basic_map
*gist_strides(__isl_take isl_basic_map
*bmap
,
2985 __isl_keep isl_basic_map
*context
)
2987 int bmap_n_eq
, context_n_eq
;
2990 if (!bmap
|| !context
)
2991 return isl_basic_map_free(bmap
);
2993 bmap_n_eq
= n_div_eq(bmap
);
2994 context_n_eq
= n_div_eq(context
);
2996 if (bmap_n_eq
< 0 || context_n_eq
< 0)
2997 return isl_basic_map_free(bmap
);
2998 if (bmap_n_eq
== 0 || context_n_eq
== 0)
3001 A
= extract_compressed_stride_constraints(bmap
, bmap_n_eq
,
3002 context
, context_n_eq
);
3003 bmap
= reduce_stride_constraints(bmap
, bmap_n_eq
, A
);
3010 /* Return a basic map that has the same intersection with "context" as "bmap"
3011 * and that is as "simple" as possible.
3013 * The core computation is performed on the pure constraints.
3014 * When we add back the meaning of the integer divisions, we need
3015 * to (re)introduce the div constraints. If we happen to have
3016 * discovered that some of these integer divisions are equal to
3017 * some affine combination of other variables, then these div
3018 * constraints may end up getting simplified in terms of the equalities,
3019 * resulting in extra inequalities on the other variables that
3020 * may have been removed already or that may not even have been
3021 * part of the input. We try and remove those constraints of
3022 * this form that are most obviously redundant with respect to
3023 * the context. We also remove those div constraints that are
3024 * redundant with respect to the other constraints in the result.
3026 * The stride constraints among the equality constraints in "bmap" are
3027 * also simplified with respecting to the other equality constraints
3028 * in "bmap" and with respect to all equality constraints in "context".
3030 __isl_give isl_basic_map
*isl_basic_map_gist(__isl_take isl_basic_map
*bmap
,
3031 __isl_take isl_basic_map
*context
)
3033 isl_basic_set
*bset
, *eq
;
3034 isl_basic_map
*eq_bmap
;
3035 unsigned total
, n_div
, extra
, n_eq
, n_ineq
;
3037 if (!bmap
|| !context
)
3040 if (isl_basic_map_plain_is_universe(bmap
)) {
3041 isl_basic_map_free(context
);
3044 if (isl_basic_map_plain_is_empty(context
)) {
3045 isl_space
*space
= isl_basic_map_get_space(bmap
);
3046 isl_basic_map_free(bmap
);
3047 isl_basic_map_free(context
);
3048 return isl_basic_map_universe(space
);
3050 if (isl_basic_map_plain_is_empty(bmap
)) {
3051 isl_basic_map_free(context
);
3055 bmap
= isl_basic_map_remove_redundancies(bmap
);
3056 context
= isl_basic_map_remove_redundancies(context
);
3057 context
= isl_basic_map_align_divs(context
, bmap
);
3061 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
3062 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3063 extra
= n_div
- isl_basic_map_dim(bmap
, isl_dim_div
);
3065 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
3066 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, extra
);
3067 bset
= uset_gist(bset
,
3068 isl_basic_map_underlying_set(isl_basic_map_copy(context
)));
3069 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, total
, extra
);
3071 if (!bset
|| bset
->n_eq
== 0 || n_div
== 0 ||
3072 isl_basic_set_plain_is_empty(bset
)) {
3073 isl_basic_map_free(context
);
3074 return isl_basic_map_overlying_set(bset
, bmap
);
3078 n_ineq
= bset
->n_ineq
;
3079 eq
= isl_basic_set_copy(bset
);
3080 eq
= isl_basic_set_cow(eq
);
3081 if (isl_basic_set_free_inequality(eq
, n_ineq
) < 0)
3082 eq
= isl_basic_set_free(eq
);
3083 if (isl_basic_set_free_equality(bset
, n_eq
) < 0)
3084 bset
= isl_basic_set_free(bset
);
3086 eq_bmap
= isl_basic_map_overlying_set(eq
, isl_basic_map_copy(bmap
));
3087 eq_bmap
= gist_strides(eq_bmap
, context
);
3088 eq_bmap
= isl_basic_map_remove_shifted_constraints(eq_bmap
, context
);
3089 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
3090 bmap
= isl_basic_map_intersect(bmap
, eq_bmap
);
3091 bmap
= isl_basic_map_remove_redundancies(bmap
);
3095 isl_basic_map_free(bmap
);
3096 isl_basic_map_free(context
);
3101 * Assumes context has no implicit divs.
3103 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
3104 __isl_take isl_basic_map
*context
)
3108 if (!map
|| !context
)
3111 if (isl_basic_map_plain_is_empty(context
)) {
3112 isl_space
*space
= isl_map_get_space(map
);
3114 isl_basic_map_free(context
);
3115 return isl_map_universe(space
);
3118 context
= isl_basic_map_remove_redundancies(context
);
3119 map
= isl_map_cow(map
);
3120 if (!map
|| !context
)
3122 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
3123 map
= isl_map_compute_divs(map
);
3126 for (i
= map
->n
- 1; i
>= 0; --i
) {
3127 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
3128 isl_basic_map_copy(context
));
3131 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
3132 isl_basic_map_free(map
->p
[i
]);
3133 if (i
!= map
->n
- 1)
3134 map
->p
[i
] = map
->p
[map
->n
- 1];
3138 isl_basic_map_free(context
);
3139 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3143 isl_basic_map_free(context
);
3147 /* Drop all inequalities from "bmap" that also appear in "context".
3148 * "context" is assumed to have only known local variables and
3149 * the initial local variables of "bmap" are assumed to be the same
3150 * as those of "context".
3151 * The constraints of both "bmap" and "context" are assumed
3152 * to have been sorted using isl_basic_map_sort_constraints.
3154 * Run through the inequality constraints of "bmap" and "context"
3156 * If a constraint of "bmap" involves variables not in "context",
3157 * then it cannot appear in "context".
3158 * If a matching constraint is found, it is removed from "bmap".
3160 static __isl_give isl_basic_map
*drop_inequalities(
3161 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_map
*context
)
3164 unsigned total
, extra
;
3166 if (!bmap
|| !context
)
3167 return isl_basic_map_free(bmap
);
3169 total
= isl_basic_map_total_dim(context
);
3170 extra
= isl_basic_map_total_dim(bmap
) - total
;
3172 i1
= bmap
->n_ineq
- 1;
3173 i2
= context
->n_ineq
- 1;
3174 while (bmap
&& i1
>= 0 && i2
>= 0) {
3177 if (isl_seq_first_non_zero(bmap
->ineq
[i1
] + 1 + total
,
3182 cmp
= isl_basic_map_constraint_cmp(context
, bmap
->ineq
[i1
],
3192 if (isl_int_eq(bmap
->ineq
[i1
][0], context
->ineq
[i2
][0])) {
3193 bmap
= isl_basic_map_cow(bmap
);
3194 if (isl_basic_map_drop_inequality(bmap
, i1
) < 0)
3195 bmap
= isl_basic_map_free(bmap
);
3204 /* Drop all equalities from "bmap" that also appear in "context".
3205 * "context" is assumed to have only known local variables and
3206 * the initial local variables of "bmap" are assumed to be the same
3207 * as those of "context".
3209 * Run through the equality constraints of "bmap" and "context"
3211 * If a constraint of "bmap" involves variables not in "context",
3212 * then it cannot appear in "context".
3213 * If a matching constraint is found, it is removed from "bmap".
3215 static __isl_give isl_basic_map
*drop_equalities(
3216 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_map
*context
)
3219 unsigned total
, extra
;
3221 if (!bmap
|| !context
)
3222 return isl_basic_map_free(bmap
);
3224 total
= isl_basic_map_total_dim(context
);
3225 extra
= isl_basic_map_total_dim(bmap
) - total
;
3227 i1
= bmap
->n_eq
- 1;
3228 i2
= context
->n_eq
- 1;
3230 while (bmap
&& i1
>= 0 && i2
>= 0) {
3233 if (isl_seq_first_non_zero(bmap
->eq
[i1
] + 1 + total
,
3236 last1
= isl_seq_last_non_zero(bmap
->eq
[i1
] + 1, total
);
3237 last2
= isl_seq_last_non_zero(context
->eq
[i2
] + 1, total
);
3238 if (last1
> last2
) {
3242 if (last1
< last2
) {
3246 if (isl_seq_eq(bmap
->eq
[i1
], context
->eq
[i2
], 1 + total
)) {
3247 bmap
= isl_basic_map_cow(bmap
);
3248 if (isl_basic_map_drop_equality(bmap
, i1
) < 0)
3249 bmap
= isl_basic_map_free(bmap
);
3258 /* Remove the constraints in "context" from "bmap".
3259 * "context" is assumed to have explicit representations
3260 * for all local variables.
3262 * First align the divs of "bmap" to those of "context" and
3263 * sort the constraints. Then drop all constraints from "bmap"
3264 * that appear in "context".
3266 __isl_give isl_basic_map
*isl_basic_map_plain_gist(
3267 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
3269 isl_bool done
, known
;
3271 done
= isl_basic_map_plain_is_universe(context
);
3272 if (done
== isl_bool_false
)
3273 done
= isl_basic_map_plain_is_universe(bmap
);
3274 if (done
== isl_bool_false
)
3275 done
= isl_basic_map_plain_is_empty(context
);
3276 if (done
== isl_bool_false
)
3277 done
= isl_basic_map_plain_is_empty(bmap
);
3281 isl_basic_map_free(context
);
3284 known
= isl_basic_map_divs_known(context
);
3288 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
3289 "context has unknown divs", goto error
);
3291 bmap
= isl_basic_map_align_divs(bmap
, context
);
3292 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3293 bmap
= isl_basic_map_sort_constraints(bmap
);
3294 context
= isl_basic_map_sort_constraints(context
);
3296 bmap
= drop_inequalities(bmap
, context
);
3297 bmap
= drop_equalities(bmap
, context
);
3299 isl_basic_map_free(context
);
3300 bmap
= isl_basic_map_finalize(bmap
);
3303 isl_basic_map_free(bmap
);
3304 isl_basic_map_free(context
);
3308 /* Replace "map" by the disjunct at position "pos" and free "context".
3310 static __isl_give isl_map
*replace_by_disjunct(__isl_take isl_map
*map
,
3311 int pos
, __isl_take isl_basic_map
*context
)
3313 isl_basic_map
*bmap
;
3315 bmap
= isl_basic_map_copy(map
->p
[pos
]);
3317 isl_basic_map_free(context
);
3318 return isl_map_from_basic_map(bmap
);
3321 /* Remove the constraints in "context" from "map".
3322 * If any of the disjuncts in the result turns out to be the universe,
3323 * then return this universe.
3324 * "context" is assumed to have explicit representations
3325 * for all local variables.
3327 __isl_give isl_map
*isl_map_plain_gist_basic_map(__isl_take isl_map
*map
,
3328 __isl_take isl_basic_map
*context
)
3331 isl_bool univ
, known
;
3333 univ
= isl_basic_map_plain_is_universe(context
);
3337 isl_basic_map_free(context
);
3340 known
= isl_basic_map_divs_known(context
);
3344 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
3345 "context has unknown divs", goto error
);
3347 map
= isl_map_cow(map
);
3350 for (i
= 0; i
< map
->n
; ++i
) {
3351 map
->p
[i
] = isl_basic_map_plain_gist(map
->p
[i
],
3352 isl_basic_map_copy(context
));
3353 univ
= isl_basic_map_plain_is_universe(map
->p
[i
]);
3356 if (univ
&& map
->n
> 1)
3357 return replace_by_disjunct(map
, i
, context
);
3360 isl_basic_map_free(context
);
3361 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3363 ISL_F_CLR(map
, ISL_MAP_DISJOINT
);
3367 isl_basic_map_free(context
);
3371 /* Remove the constraints in "context" from "set".
3372 * If any of the disjuncts in the result turns out to be the universe,
3373 * then return this universe.
3374 * "context" is assumed to have explicit representations
3375 * for all local variables.
3377 __isl_give isl_set
*isl_set_plain_gist_basic_set(__isl_take isl_set
*set
,
3378 __isl_take isl_basic_set
*context
)
3380 return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set
),
3381 bset_to_bmap(context
)));
3384 /* Remove the constraints in "context" from "map".
3385 * If any of the disjuncts in the result turns out to be the universe,
3386 * then return this universe.
3387 * "context" is assumed to consist of a single disjunct and
3388 * to have explicit representations for all local variables.
3390 __isl_give isl_map
*isl_map_plain_gist(__isl_take isl_map
*map
,
3391 __isl_take isl_map
*context
)
3393 isl_basic_map
*hull
;
3395 hull
= isl_map_unshifted_simple_hull(context
);
3396 return isl_map_plain_gist_basic_map(map
, hull
);
3399 /* Replace "map" by a universe map in the same space and free "drop".
3401 static __isl_give isl_map
*replace_by_universe(__isl_take isl_map
*map
,
3402 __isl_take isl_map
*drop
)
3406 res
= isl_map_universe(isl_map_get_space(map
));
3412 /* Return a map that has the same intersection with "context" as "map"
3413 * and that is as "simple" as possible.
3415 * If "map" is already the universe, then we cannot make it any simpler.
3416 * Similarly, if "context" is the universe, then we cannot exploit it
3418 * If "map" and "context" are identical to each other, then we can
3419 * return the corresponding universe.
3421 * If either "map" or "context" consists of multiple disjuncts,
3422 * then check if "context" happens to be a subset of "map",
3423 * in which case all constraints can be removed.
3424 * In case of multiple disjuncts, the standard procedure
3425 * may not be able to detect that all constraints can be removed.
3427 * If none of these cases apply, we have to work a bit harder.
3428 * During this computation, we make use of a single disjunct context,
3429 * so if the original context consists of more than one disjunct
3430 * then we need to approximate the context by a single disjunct set.
3431 * Simply taking the simple hull may drop constraints that are
3432 * only implicitly available in each disjunct. We therefore also
3433 * look for constraints among those defining "map" that are valid
3434 * for the context. These can then be used to simplify away
3435 * the corresponding constraints in "map".
3437 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
3438 __isl_take isl_map
*context
)
3442 int single_disjunct_map
, single_disjunct_context
;
3444 isl_basic_map
*hull
;
3446 is_universe
= isl_map_plain_is_universe(map
);
3447 if (is_universe
>= 0 && !is_universe
)
3448 is_universe
= isl_map_plain_is_universe(context
);
3449 if (is_universe
< 0)
3452 isl_map_free(context
);
3456 equal
= isl_map_plain_is_equal(map
, context
);
3460 return replace_by_universe(map
, context
);
3462 single_disjunct_map
= isl_map_n_basic_map(map
) == 1;
3463 single_disjunct_context
= isl_map_n_basic_map(context
) == 1;
3464 if (!single_disjunct_map
|| !single_disjunct_context
) {
3465 subset
= isl_map_is_subset(context
, map
);
3469 return replace_by_universe(map
, context
);
3472 context
= isl_map_compute_divs(context
);
3475 if (single_disjunct_context
) {
3476 hull
= isl_map_simple_hull(context
);
3481 ctx
= isl_map_get_ctx(map
);
3482 list
= isl_map_list_alloc(ctx
, 2);
3483 list
= isl_map_list_add(list
, isl_map_copy(context
));
3484 list
= isl_map_list_add(list
, isl_map_copy(map
));
3485 hull
= isl_map_unshifted_simple_hull_from_map_list(context
,
3488 return isl_map_gist_basic_map(map
, hull
);
3491 isl_map_free(context
);
3495 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
3496 __isl_take isl_map
*context
)
3498 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
3501 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
3502 struct isl_basic_set
*context
)
3504 return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset
),
3505 bset_to_bmap(context
)));
3508 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
3509 __isl_take isl_basic_set
*context
)
3511 return set_from_map(isl_map_gist_basic_map(set_to_map(set
),
3512 bset_to_bmap(context
)));
3515 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
3516 __isl_take isl_basic_set
*context
)
3518 isl_space
*space
= isl_set_get_space(set
);
3519 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
3520 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
3521 return isl_set_gist_basic_set(set
, dom_context
);
3524 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
3525 __isl_take isl_set
*context
)
3527 return set_from_map(isl_map_gist(set_to_map(set
), set_to_map(context
)));
3530 /* Compute the gist of "bmap" with respect to the constraints "context"
3533 __isl_give isl_basic_map
*isl_basic_map_gist_domain(
3534 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*context
)
3536 isl_space
*space
= isl_basic_map_get_space(bmap
);
3537 isl_basic_map
*bmap_context
= isl_basic_map_universe(space
);
3539 bmap_context
= isl_basic_map_intersect_domain(bmap_context
, context
);
3540 return isl_basic_map_gist(bmap
, bmap_context
);
3543 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
3544 __isl_take isl_set
*context
)
3546 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3547 map_context
= isl_map_intersect_domain(map_context
, context
);
3548 return isl_map_gist(map
, map_context
);
3551 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
3552 __isl_take isl_set
*context
)
3554 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3555 map_context
= isl_map_intersect_range(map_context
, context
);
3556 return isl_map_gist(map
, map_context
);
3559 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
3560 __isl_take isl_set
*context
)
3562 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3563 map_context
= isl_map_intersect_params(map_context
, context
);
3564 return isl_map_gist(map
, map_context
);
3567 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
3568 __isl_take isl_set
*context
)
3570 return isl_map_gist_params(set
, context
);
3573 /* Quick check to see if two basic maps are disjoint.
3574 * In particular, we reduce the equalities and inequalities of
3575 * one basic map in the context of the equalities of the other
3576 * basic map and check if we get a contradiction.
3578 isl_bool
isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
3579 __isl_keep isl_basic_map
*bmap2
)
3581 struct isl_vec
*v
= NULL
;
3586 if (!bmap1
|| !bmap2
)
3587 return isl_bool_error
;
3588 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
3589 return isl_bool_error
);
3590 if (bmap1
->n_div
|| bmap2
->n_div
)
3591 return isl_bool_false
;
3592 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
3593 return isl_bool_false
;
3595 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
3597 return isl_bool_false
;
3598 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
3601 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
3604 compute_elimination_index(bmap1
, elim
);
3605 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
3607 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
3609 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
3610 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3613 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
3615 reduced
= reduced_using_equalities(v
->block
.data
,
3616 bmap2
->ineq
[i
], bmap1
, elim
);
3617 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
3618 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3621 compute_elimination_index(bmap2
, elim
);
3622 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
3624 reduced
= reduced_using_equalities(v
->block
.data
,
3625 bmap1
->ineq
[i
], bmap2
, elim
);
3626 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
3627 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3632 return isl_bool_false
;
3636 return isl_bool_true
;
3640 return isl_bool_error
;
3643 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
3644 __isl_keep isl_basic_set
*bset2
)
3646 return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1
),
3647 bset_to_bmap(bset2
));
3650 /* Does "test" hold for all pairs of basic maps in "map1" and "map2"?
3652 static isl_bool
all_pairs(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
,
3653 isl_bool (*test
)(__isl_keep isl_basic_map
*bmap1
,
3654 __isl_keep isl_basic_map
*bmap2
))
3659 return isl_bool_error
;
3661 for (i
= 0; i
< map1
->n
; ++i
) {
3662 for (j
= 0; j
< map2
->n
; ++j
) {
3663 isl_bool d
= test(map1
->p
[i
], map2
->p
[j
]);
3664 if (d
!= isl_bool_true
)
3669 return isl_bool_true
;
3672 /* Are "map1" and "map2" obviously disjoint, based on information
3673 * that can be derived without looking at the individual basic maps?
3675 * In particular, if one of them is empty or if they live in different spaces
3676 * (ignoring parameters), then they are clearly disjoint.
3678 static isl_bool
isl_map_plain_is_disjoint_global(__isl_keep isl_map
*map1
,
3679 __isl_keep isl_map
*map2
)
3685 return isl_bool_error
;
3687 disjoint
= isl_map_plain_is_empty(map1
);
3688 if (disjoint
< 0 || disjoint
)
3691 disjoint
= isl_map_plain_is_empty(map2
);
3692 if (disjoint
< 0 || disjoint
)
3695 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_in
,
3696 map2
->dim
, isl_dim_in
);
3697 if (match
< 0 || !match
)
3698 return match
< 0 ? isl_bool_error
: isl_bool_true
;
3700 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_out
,
3701 map2
->dim
, isl_dim_out
);
3702 if (match
< 0 || !match
)
3703 return match
< 0 ? isl_bool_error
: isl_bool_true
;
3705 return isl_bool_false
;
3708 /* Are "map1" and "map2" obviously disjoint?
3710 * If one of them is empty or if they live in different spaces (ignoring
3711 * parameters), then they are clearly disjoint.
3712 * This is checked by isl_map_plain_is_disjoint_global.
3714 * If they have different parameters, then we skip any further tests.
3716 * If they are obviously equal, but not obviously empty, then we will
3717 * not be able to detect if they are disjoint.
3719 * Otherwise we check if each basic map in "map1" is obviously disjoint
3720 * from each basic map in "map2".
3722 isl_bool
isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
3723 __isl_keep isl_map
*map2
)
3729 disjoint
= isl_map_plain_is_disjoint_global(map1
, map2
);
3730 if (disjoint
< 0 || disjoint
)
3733 match
= isl_map_has_equal_params(map1
, map2
);
3734 if (match
< 0 || !match
)
3735 return match
< 0 ? isl_bool_error
: isl_bool_false
;
3737 intersect
= isl_map_plain_is_equal(map1
, map2
);
3738 if (intersect
< 0 || intersect
)
3739 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3741 return all_pairs(map1
, map2
, &isl_basic_map_plain_is_disjoint
);
3744 /* Are "map1" and "map2" disjoint?
3745 * The parameters are assumed to have been aligned.
3747 * In particular, check whether all pairs of basic maps are disjoint.
3749 static isl_bool
isl_map_is_disjoint_aligned(__isl_keep isl_map
*map1
,
3750 __isl_keep isl_map
*map2
)
3752 return all_pairs(map1
, map2
, &isl_basic_map_is_disjoint
);
3755 /* Are "map1" and "map2" disjoint?
3757 * They are disjoint if they are "obviously disjoint" or if one of them
3758 * is empty. Otherwise, they are not disjoint if one of them is universal.
3759 * If the two inputs are (obviously) equal and not empty, then they are
3761 * If none of these cases apply, then check if all pairs of basic maps
3762 * are disjoint after aligning the parameters.
3764 isl_bool
isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
3769 disjoint
= isl_map_plain_is_disjoint_global(map1
, map2
);
3770 if (disjoint
< 0 || disjoint
)
3773 disjoint
= isl_map_is_empty(map1
);
3774 if (disjoint
< 0 || disjoint
)
3777 disjoint
= isl_map_is_empty(map2
);
3778 if (disjoint
< 0 || disjoint
)
3781 intersect
= isl_map_plain_is_universe(map1
);
3782 if (intersect
< 0 || intersect
)
3783 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3785 intersect
= isl_map_plain_is_universe(map2
);
3786 if (intersect
< 0 || intersect
)
3787 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3789 intersect
= isl_map_plain_is_equal(map1
, map2
);
3790 if (intersect
< 0 || intersect
)
3791 return isl_bool_not(intersect
);
3793 return isl_map_align_params_map_map_and_test(map1
, map2
,
3794 &isl_map_is_disjoint_aligned
);
3797 /* Are "bmap1" and "bmap2" disjoint?
3799 * They are disjoint if they are "obviously disjoint" or if one of them
3800 * is empty. Otherwise, they are not disjoint if one of them is universal.
3801 * If none of these cases apply, we compute the intersection and see if
3802 * the result is empty.
3804 isl_bool
isl_basic_map_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
3805 __isl_keep isl_basic_map
*bmap2
)
3809 isl_basic_map
*test
;
3811 disjoint
= isl_basic_map_plain_is_disjoint(bmap1
, bmap2
);
3812 if (disjoint
< 0 || disjoint
)
3815 disjoint
= isl_basic_map_is_empty(bmap1
);
3816 if (disjoint
< 0 || disjoint
)
3819 disjoint
= isl_basic_map_is_empty(bmap2
);
3820 if (disjoint
< 0 || disjoint
)
3823 intersect
= isl_basic_map_plain_is_universe(bmap1
);
3824 if (intersect
< 0 || intersect
)
3825 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3827 intersect
= isl_basic_map_plain_is_universe(bmap2
);
3828 if (intersect
< 0 || intersect
)
3829 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3831 test
= isl_basic_map_intersect(isl_basic_map_copy(bmap1
),
3832 isl_basic_map_copy(bmap2
));
3833 disjoint
= isl_basic_map_is_empty(test
);
3834 isl_basic_map_free(test
);
3839 /* Are "bset1" and "bset2" disjoint?
3841 isl_bool
isl_basic_set_is_disjoint(__isl_keep isl_basic_set
*bset1
,
3842 __isl_keep isl_basic_set
*bset2
)
3844 return isl_basic_map_is_disjoint(bset1
, bset2
);
3847 isl_bool
isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
3848 __isl_keep isl_set
*set2
)
3850 return isl_map_plain_is_disjoint(set_to_map(set1
), set_to_map(set2
));
3853 /* Are "set1" and "set2" disjoint?
3855 isl_bool
isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
3857 return isl_map_is_disjoint(set1
, set2
);
3860 /* Is "v" equal to 0, 1 or -1?
3862 static int is_zero_or_one(isl_int v
)
3864 return isl_int_is_zero(v
) || isl_int_is_one(v
) || isl_int_is_negone(v
);
3867 /* Check if we can combine a given div with lower bound l and upper
3868 * bound u with some other div and if so return that other div.
3869 * Otherwise return -1.
3871 * We first check that
3872 * - the bounds are opposites of each other (except for the constant
3874 * - the bounds do not reference any other div
3875 * - no div is defined in terms of this div
3877 * Let m be the size of the range allowed on the div by the bounds.
3878 * That is, the bounds are of the form
3880 * e <= a <= e + m - 1
3882 * with e some expression in the other variables.
3883 * We look for another div b such that no third div is defined in terms
3884 * of this second div b and such that in any constraint that contains
3885 * a (except for the given lower and upper bound), also contains b
3886 * with a coefficient that is m times that of b.
3887 * That is, all constraints (except for the lower and upper bound)
3890 * e + f (a + m b) >= 0
3892 * Furthermore, in the constraints that only contain b, the coefficient
3893 * of b should be equal to 1 or -1.
3894 * If so, we return b so that "a + m b" can be replaced by
3895 * a single div "c = a + m b".
3897 static int div_find_coalesce(__isl_keep isl_basic_map
*bmap
, int *pairs
,
3898 unsigned div
, unsigned l
, unsigned u
)
3904 if (bmap
->n_div
<= 1)
3906 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3907 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
3909 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
3910 bmap
->n_div
- div
- 1) != -1)
3912 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
3916 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3917 if (isl_int_is_zero(bmap
->div
[i
][0]))
3919 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
3923 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3924 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
3925 isl_int_sub(bmap
->ineq
[l
][0],
3926 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3927 bmap
= isl_basic_map_copy(bmap
);
3928 bmap
= isl_basic_map_set_to_empty(bmap
);
3929 isl_basic_map_free(bmap
);
3932 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
3933 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3938 for (j
= 0; j
< bmap
->n_div
; ++j
) {
3939 if (isl_int_is_zero(bmap
->div
[j
][0]))
3941 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
3944 if (j
< bmap
->n_div
)
3946 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
3948 if (j
== l
|| j
== u
)
3950 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
])) {
3951 if (is_zero_or_one(bmap
->ineq
[j
][1 + dim
+ i
]))
3955 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
3957 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
3958 bmap
->ineq
[j
][1 + dim
+ div
],
3960 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
3961 bmap
->ineq
[j
][1 + dim
+ i
]);
3962 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
3963 bmap
->ineq
[j
][1 + dim
+ div
],
3968 if (j
< bmap
->n_ineq
)
3973 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
3974 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3978 /* Internal data structure used during the construction and/or evaluation of
3979 * an inequality that ensures that a pair of bounds always allows
3980 * for an integer value.
3982 * "tab" is the tableau in which the inequality is evaluated. It may
3983 * be NULL until it is actually needed.
3984 * "v" contains the inequality coefficients.
3985 * "g", "fl" and "fu" are temporary scalars used during the construction and
3988 struct test_ineq_data
{
3989 struct isl_tab
*tab
;
3996 /* Free all the memory allocated by the fields of "data".
3998 static void test_ineq_data_clear(struct test_ineq_data
*data
)
4000 isl_tab_free(data
->tab
);
4001 isl_vec_free(data
->v
);
4002 isl_int_clear(data
->g
);
4003 isl_int_clear(data
->fl
);
4004 isl_int_clear(data
->fu
);
4007 /* Is the inequality stored in data->v satisfied by "bmap"?
4008 * That is, does it only attain non-negative values?
4009 * data->tab is a tableau corresponding to "bmap".
4011 static isl_bool
test_ineq_is_satisfied(__isl_keep isl_basic_map
*bmap
,
4012 struct test_ineq_data
*data
)
4015 enum isl_lp_result res
;
4017 ctx
= isl_basic_map_get_ctx(bmap
);
4019 data
->tab
= isl_tab_from_basic_map(bmap
, 0);
4020 res
= isl_tab_min(data
->tab
, data
->v
->el
, ctx
->one
, &data
->g
, NULL
, 0);
4021 if (res
== isl_lp_error
)
4022 return isl_bool_error
;
4023 return res
== isl_lp_ok
&& isl_int_is_nonneg(data
->g
);
4026 /* Given a lower and an upper bound on div i, do they always allow
4027 * for an integer value of the given div?
4028 * Determine this property by constructing an inequality
4029 * such that the property is guaranteed when the inequality is nonnegative.
4030 * The lower bound is inequality l, while the upper bound is inequality u.
4031 * The constructed inequality is stored in data->v.
4033 * Let the upper bound be
4037 * and the lower bound
4041 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
4044 * - f_u e_l <= f_u f_l g a <= f_l e_u
4046 * Since all variables are integer valued, this is equivalent to
4048 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
4050 * If this interval is at least f_u f_l g, then it contains at least
4051 * one integer value for a.
4052 * That is, the test constraint is
4054 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
4058 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0
4060 * If the coefficients of f_l e_u + f_u e_l have a common divisor g',
4061 * then the constraint can be scaled down by a factor g',
4062 * with the constant term replaced by
4063 * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g').
4064 * Note that the result of applying Fourier-Motzkin to this pair
4067 * f_l e_u + f_u e_l >= 0
4069 * If the constant term of the scaled down version of this constraint,
4070 * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant
4071 * term of the scaled down test constraint, then the test constraint
4072 * is known to hold and no explicit evaluation is required.
4073 * This is essentially the Omega test.
4075 * If the test constraint consists of only a constant term, then
4076 * it is sufficient to look at the sign of this constant term.
4078 static isl_bool
int_between_bounds(__isl_keep isl_basic_map
*bmap
, int i
,
4079 int l
, int u
, struct test_ineq_data
*data
)
4081 unsigned offset
, n_div
;
4082 offset
= isl_basic_map_offset(bmap
, isl_dim_div
);
4083 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4085 isl_int_gcd(data
->g
,
4086 bmap
->ineq
[l
][offset
+ i
], bmap
->ineq
[u
][offset
+ i
]);
4087 isl_int_divexact(data
->fl
, bmap
->ineq
[l
][offset
+ i
], data
->g
);
4088 isl_int_divexact(data
->fu
, bmap
->ineq
[u
][offset
+ i
], data
->g
);
4089 isl_int_neg(data
->fu
, data
->fu
);
4090 isl_seq_combine(data
->v
->el
, data
->fl
, bmap
->ineq
[u
],
4091 data
->fu
, bmap
->ineq
[l
], offset
+ n_div
);
4092 isl_int_mul(data
->g
, data
->g
, data
->fl
);
4093 isl_int_mul(data
->g
, data
->g
, data
->fu
);
4094 isl_int_sub(data
->g
, data
->g
, data
->fl
);
4095 isl_int_sub(data
->g
, data
->g
, data
->fu
);
4096 isl_int_add_ui(data
->g
, data
->g
, 1);
4097 isl_int_sub(data
->fl
, data
->v
->el
[0], data
->g
);
4099 isl_seq_gcd(data
->v
->el
+ 1, offset
- 1 + n_div
, &data
->g
);
4100 if (isl_int_is_zero(data
->g
))
4101 return isl_int_is_nonneg(data
->fl
);
4102 if (isl_int_is_one(data
->g
)) {
4103 isl_int_set(data
->v
->el
[0], data
->fl
);
4104 return test_ineq_is_satisfied(bmap
, data
);
4106 isl_int_fdiv_q(data
->fl
, data
->fl
, data
->g
);
4107 isl_int_fdiv_q(data
->v
->el
[0], data
->v
->el
[0], data
->g
);
4108 if (isl_int_eq(data
->fl
, data
->v
->el
[0]))
4109 return isl_bool_true
;
4110 isl_int_set(data
->v
->el
[0], data
->fl
);
4111 isl_seq_scale_down(data
->v
->el
+ 1, data
->v
->el
+ 1, data
->g
,
4112 offset
- 1 + n_div
);
4114 return test_ineq_is_satisfied(bmap
, data
);
4117 /* Remove more kinds of divs that are not strictly needed.
4118 * In particular, if all pairs of lower and upper bounds on a div
4119 * are such that they allow at least one integer value of the div,
4120 * then we can eliminate the div using Fourier-Motzkin without
4121 * introducing any spurious solutions.
4123 * If at least one of the two constraints has a unit coefficient for the div,
4124 * then the presence of such a value is guaranteed so there is no need to check.
4125 * In particular, the value attained by the bound with unit coefficient
4126 * can serve as this intermediate value.
4128 static __isl_give isl_basic_map
*drop_more_redundant_divs(
4129 __isl_take isl_basic_map
*bmap
, __isl_take
int *pairs
, int n
)
4132 struct test_ineq_data data
= { NULL
, NULL
};
4133 unsigned off
, n_div
;
4136 isl_int_init(data
.g
);
4137 isl_int_init(data
.fl
);
4138 isl_int_init(data
.fu
);
4143 ctx
= isl_basic_map_get_ctx(bmap
);
4144 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
4145 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4146 data
.v
= isl_vec_alloc(ctx
, off
+ n_div
);
4155 for (i
= 0; i
< n_div
; ++i
) {
4158 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
4164 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
4165 if (!isl_int_is_pos(bmap
->ineq
[l
][off
+ i
]))
4167 if (isl_int_is_one(bmap
->ineq
[l
][off
+ i
]))
4169 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
4170 if (!isl_int_is_neg(bmap
->ineq
[u
][off
+ i
]))
4172 if (isl_int_is_negone(bmap
->ineq
[u
][off
+ i
]))
4174 has_int
= int_between_bounds(bmap
, i
, l
, u
,
4178 if (data
.tab
&& data
.tab
->empty
)
4183 if (u
< bmap
->n_ineq
)
4186 if (data
.tab
&& data
.tab
->empty
) {
4187 bmap
= isl_basic_map_set_to_empty(bmap
);
4190 if (l
== bmap
->n_ineq
) {
4198 test_ineq_data_clear(&data
);
4205 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
4206 return isl_basic_map_drop_redundant_divs(bmap
);
4209 isl_basic_map_free(bmap
);
4210 test_ineq_data_clear(&data
);
4214 /* Given a pair of divs div1 and div2 such that, except for the lower bound l
4215 * and the upper bound u, div1 always occurs together with div2 in the form
4216 * (div1 + m div2), where m is the constant range on the variable div1
4217 * allowed by l and u, replace the pair div1 and div2 by a single
4218 * div that is equal to div1 + m div2.
4220 * The new div will appear in the location that contains div2.
4221 * We need to modify all constraints that contain
4222 * div2 = (div - div1) / m
4223 * The coefficient of div2 is known to be equal to 1 or -1.
4224 * (If a constraint does not contain div2, it will also not contain div1.)
4225 * If the constraint also contains div1, then we know they appear
4226 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
4227 * i.e., the coefficient of div is f.
4229 * Otherwise, we first need to introduce div1 into the constraint.
4238 * A lower bound on div2
4242 * can be replaced by
4244 * m div2 + div1 + m t + f >= 0
4250 * can be replaced by
4252 * -(m div2 + div1) + m t + f' >= 0
4254 * These constraint are those that we would obtain from eliminating
4255 * div1 using Fourier-Motzkin.
4257 * After all constraints have been modified, we drop the lower and upper
4258 * bound and then drop div1.
4259 * Since the new div is only placed in the same location that used
4260 * to store div2, but otherwise has a different meaning, any possible
4261 * explicit representation of the original div2 is removed.
4263 static __isl_give isl_basic_map
*coalesce_divs(__isl_take isl_basic_map
*bmap
,
4264 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
4268 unsigned dim
, total
;
4271 ctx
= isl_basic_map_get_ctx(bmap
);
4273 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
4274 total
= 1 + dim
+ bmap
->n_div
;
4277 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4278 isl_int_add_ui(m
, m
, 1);
4280 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4281 if (i
== l
|| i
== u
)
4283 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
4285 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
4286 if (isl_int_is_pos(bmap
->ineq
[i
][1 + dim
+ div2
]))
4287 isl_seq_combine(bmap
->ineq
[i
], m
, bmap
->ineq
[i
],
4288 ctx
->one
, bmap
->ineq
[l
], total
);
4290 isl_seq_combine(bmap
->ineq
[i
], m
, bmap
->ineq
[i
],
4291 ctx
->one
, bmap
->ineq
[u
], total
);
4293 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
4294 bmap
->ineq
[i
][1 + dim
+ div1
]);
4295 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
4300 isl_basic_map_drop_inequality(bmap
, l
);
4301 isl_basic_map_drop_inequality(bmap
, u
);
4303 isl_basic_map_drop_inequality(bmap
, u
);
4304 isl_basic_map_drop_inequality(bmap
, l
);
4306 bmap
= isl_basic_map_mark_div_unknown(bmap
, div2
);
4307 bmap
= isl_basic_map_drop_div(bmap
, div1
);
4311 /* First check if we can coalesce any pair of divs and
4312 * then continue with dropping more redundant divs.
4314 * We loop over all pairs of lower and upper bounds on a div
4315 * with coefficient 1 and -1, respectively, check if there
4316 * is any other div "c" with which we can coalesce the div
4317 * and if so, perform the coalescing.
4319 static __isl_give isl_basic_map
*coalesce_or_drop_more_redundant_divs(
4320 __isl_take isl_basic_map
*bmap
, int *pairs
, int n
)
4325 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
4327 for (i
= 0; i
< bmap
->n_div
; ++i
) {
4330 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
4331 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
4333 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
4336 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
4338 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
4342 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
4343 return isl_basic_map_drop_redundant_divs(bmap
);
4348 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
4353 return drop_more_redundant_divs(bmap
, pairs
, n
);
4356 /* Are the "n" coefficients starting at "first" of inequality constraints
4357 * "i" and "j" of "bmap" equal to each other?
4359 static int is_parallel_part(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4362 return isl_seq_eq(bmap
->ineq
[i
] + first
, bmap
->ineq
[j
] + first
, n
);
4365 /* Are the "n" coefficients starting at "first" of inequality constraints
4366 * "i" and "j" of "bmap" opposite to each other?
4368 static int is_opposite_part(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4371 return isl_seq_is_neg(bmap
->ineq
[i
] + first
, bmap
->ineq
[j
] + first
, n
);
4374 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4375 * apart from the constant term?
4377 static isl_bool
is_opposite(__isl_keep isl_basic_map
*bmap
, int i
, int j
)
4381 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4382 return is_opposite_part(bmap
, i
, j
, 1, total
);
4385 /* Are inequality constraints "i" and "j" of "bmap" equal to each other,
4386 * apart from the constant term and the coefficient at position "pos"?
4388 static int is_parallel_except(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4393 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4394 return is_parallel_part(bmap
, i
, j
, 1, pos
- 1) &&
4395 is_parallel_part(bmap
, i
, j
, pos
+ 1, total
- pos
);
4398 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4399 * apart from the constant term and the coefficient at position "pos"?
4401 static int is_opposite_except(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4406 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4407 return is_opposite_part(bmap
, i
, j
, 1, pos
- 1) &&
4408 is_opposite_part(bmap
, i
, j
, pos
+ 1, total
- pos
);
4411 /* Restart isl_basic_map_drop_redundant_divs after "bmap" has
4412 * been modified, simplying it if "simplify" is set.
4413 * Free the temporary data structure "pairs" that was associated
4414 * to the old version of "bmap".
4416 static __isl_give isl_basic_map
*drop_redundant_divs_again(
4417 __isl_take isl_basic_map
*bmap
, __isl_take
int *pairs
, int simplify
)
4420 bmap
= isl_basic_map_simplify(bmap
);
4422 return isl_basic_map_drop_redundant_divs(bmap
);
4425 /* Is "div" the single unknown existentially quantified variable
4426 * in inequality constraint "ineq" of "bmap"?
4427 * "div" is known to have a non-zero coefficient in "ineq".
4429 static isl_bool
single_unknown(__isl_keep isl_basic_map
*bmap
, int ineq
,
4433 unsigned n_div
, o_div
;
4436 known
= isl_basic_map_div_is_known(bmap
, div
);
4437 if (known
< 0 || known
)
4438 return isl_bool_not(known
);
4439 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4441 return isl_bool_true
;
4442 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4443 for (i
= 0; i
< n_div
; ++i
) {
4448 if (isl_int_is_zero(bmap
->ineq
[ineq
][o_div
+ i
]))
4450 known
= isl_basic_map_div_is_known(bmap
, i
);
4451 if (known
< 0 || !known
)
4455 return isl_bool_true
;
4458 /* Does integer division "div" have coefficient 1 in inequality constraint
4461 static isl_bool
has_coef_one(__isl_keep isl_basic_map
*bmap
, int div
, int ineq
)
4465 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4466 if (isl_int_is_one(bmap
->ineq
[ineq
][o_div
+ div
]))
4467 return isl_bool_true
;
4469 return isl_bool_false
;
4472 /* Turn inequality constraint "ineq" of "bmap" into an equality and
4473 * then try and drop redundant divs again,
4474 * freeing the temporary data structure "pairs" that was associated
4475 * to the old version of "bmap".
4477 static __isl_give isl_basic_map
*set_eq_and_try_again(
4478 __isl_take isl_basic_map
*bmap
, int ineq
, __isl_take
int *pairs
)
4480 bmap
= isl_basic_map_cow(bmap
);
4481 isl_basic_map_inequality_to_equality(bmap
, ineq
);
4482 return drop_redundant_divs_again(bmap
, pairs
, 1);
4485 /* Drop the integer division at position "div", along with the two
4486 * inequality constraints "ineq1" and "ineq2" in which it appears
4487 * from "bmap" and then try and drop redundant divs again,
4488 * freeing the temporary data structure "pairs" that was associated
4489 * to the old version of "bmap".
4491 static __isl_give isl_basic_map
*drop_div_and_try_again(
4492 __isl_take isl_basic_map
*bmap
, int div
, int ineq1
, int ineq2
,
4493 __isl_take
int *pairs
)
4495 if (ineq1
> ineq2
) {
4496 isl_basic_map_drop_inequality(bmap
, ineq1
);
4497 isl_basic_map_drop_inequality(bmap
, ineq2
);
4499 isl_basic_map_drop_inequality(bmap
, ineq2
);
4500 isl_basic_map_drop_inequality(bmap
, ineq1
);
4502 bmap
= isl_basic_map_drop_div(bmap
, div
);
4503 return drop_redundant_divs_again(bmap
, pairs
, 0);
4506 /* Given two inequality constraints
4508 * f(x) + n d + c >= 0, (ineq)
4510 * with d the variable at position "pos", and
4512 * f(x) + c0 >= 0, (lower)
4514 * compute the maximal value of the lower bound ceil((-f(x) - c)/n)
4515 * determined by the first constraint.
4522 static void lower_bound_from_parallel(__isl_keep isl_basic_map
*bmap
,
4523 int ineq
, int lower
, int pos
, isl_int
*l
)
4525 isl_int_neg(*l
, bmap
->ineq
[ineq
][0]);
4526 isl_int_add(*l
, *l
, bmap
->ineq
[lower
][0]);
4527 isl_int_cdiv_q(*l
, *l
, bmap
->ineq
[ineq
][pos
]);
4530 /* Given two inequality constraints
4532 * f(x) + n d + c >= 0, (ineq)
4534 * with d the variable at position "pos", and
4536 * -f(x) - c0 >= 0, (upper)
4538 * compute the minimal value of the lower bound ceil((-f(x) - c)/n)
4539 * determined by the first constraint.
4546 static void lower_bound_from_opposite(__isl_keep isl_basic_map
*bmap
,
4547 int ineq
, int upper
, int pos
, isl_int
*u
)
4549 isl_int_neg(*u
, bmap
->ineq
[ineq
][0]);
4550 isl_int_sub(*u
, *u
, bmap
->ineq
[upper
][0]);
4551 isl_int_cdiv_q(*u
, *u
, bmap
->ineq
[ineq
][pos
]);
4554 /* Given a lower bound constraint "ineq" on "div" in "bmap",
4555 * does the corresponding lower bound have a fixed value in "bmap"?
4557 * In particular, "ineq" is of the form
4559 * f(x) + n d + c >= 0
4561 * with n > 0, c the constant term and
4562 * d the existentially quantified variable "div".
4563 * That is, the lower bound is
4565 * ceil((-f(x) - c)/n)
4567 * Look for a pair of constraints
4572 * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value.
4573 * That is, check that
4575 * ceil((-c1 - c)/n) = ceil((c0 - c)/n)
4577 * If so, return the index of inequality f(x) + c0 >= 0.
4578 * Otherwise, return -1.
4580 static int lower_bound_is_cst(__isl_keep isl_basic_map
*bmap
, int div
, int ineq
)
4583 int lower
= -1, upper
= -1;
4588 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4589 for (i
= 0; i
< bmap
->n_ineq
&& (lower
< 0 || upper
< 0); ++i
) {
4592 if (!isl_int_is_zero(bmap
->ineq
[i
][o_div
+ div
]))
4595 is_parallel_except(bmap
, ineq
, i
, o_div
+ div
)) {
4600 is_opposite_except(bmap
, ineq
, i
, o_div
+ div
)) {
4605 if (lower
< 0 || upper
< 0)
4611 lower_bound_from_parallel(bmap
, ineq
, lower
, o_div
+ div
, &l
);
4612 lower_bound_from_opposite(bmap
, ineq
, upper
, o_div
+ div
, &u
);
4614 equal
= isl_int_eq(l
, u
);
4619 return equal
? lower
: -1;
4622 /* Given a lower bound constraint "ineq" on the existentially quantified
4623 * variable "div", such that the corresponding lower bound has
4624 * a fixed value in "bmap", assign this fixed value to the variable and
4625 * then try and drop redundant divs again,
4626 * freeing the temporary data structure "pairs" that was associated
4627 * to the old version of "bmap".
4628 * "lower" determines the constant value for the lower bound.
4630 * In particular, "ineq" is of the form
4632 * f(x) + n d + c >= 0,
4634 * while "lower" is of the form
4638 * The lower bound is ceil((-f(x) - c)/n) and its constant value
4639 * is ceil((c0 - c)/n).
4641 static __isl_give isl_basic_map
*fix_cst_lower(__isl_take isl_basic_map
*bmap
,
4642 int div
, int ineq
, int lower
, int *pairs
)
4649 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4650 lower_bound_from_parallel(bmap
, ineq
, lower
, o_div
+ div
, &c
);
4651 bmap
= isl_basic_map_fix(bmap
, isl_dim_div
, div
, c
);
4656 return isl_basic_map_drop_redundant_divs(bmap
);
4659 /* Remove divs that are not strictly needed based on the inequality
4661 * In particular, if a div only occurs positively (or negatively)
4662 * in constraints, then it can simply be dropped.
4663 * Also, if a div occurs in only two constraints and if moreover
4664 * those two constraints are opposite to each other, except for the constant
4665 * term and if the sum of the constant terms is such that for any value
4666 * of the other values, there is always at least one integer value of the
4667 * div, i.e., if one plus this sum is greater than or equal to
4668 * the (absolute value) of the coefficient of the div in the constraints,
4669 * then we can also simply drop the div.
4671 * If an existentially quantified variable does not have an explicit
4672 * representation, appears in only a single lower bound that does not
4673 * involve any other such existentially quantified variables and appears
4674 * in this lower bound with coefficient 1,
4675 * then fix the variable to the value of the lower bound. That is,
4676 * turn the inequality into an equality.
4677 * If for any value of the other variables, there is any value
4678 * for the existentially quantified variable satisfying the constraints,
4679 * then this lower bound also satisfies the constraints.
4680 * It is therefore safe to pick this lower bound.
4682 * The same reasoning holds even if the coefficient is not one.
4683 * However, fixing the variable to the value of the lower bound may
4684 * in general introduce an extra integer division, in which case
4685 * it may be better to pick another value.
4686 * If this integer division has a known constant value, then plugging
4687 * in this constant value removes the existentially quantified variable
4688 * completely. In particular, if the lower bound is of the form
4689 * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and
4690 * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n),
4691 * then the existentially quantified variable can be assigned this
4694 * We skip divs that appear in equalities or in the definition of other divs.
4695 * Divs that appear in the definition of other divs usually occur in at least
4696 * 4 constraints, but the constraints may have been simplified.
4698 * If any divs are left after these simple checks then we move on
4699 * to more complicated cases in drop_more_redundant_divs.
4701 static __isl_give isl_basic_map
*isl_basic_map_drop_redundant_divs_ineq(
4702 __isl_take isl_basic_map
*bmap
)
4711 if (bmap
->n_div
== 0)
4714 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
4715 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
4719 for (i
= 0; i
< bmap
->n_div
; ++i
) {
4721 int last_pos
, last_neg
;
4724 isl_bool opp
, set_div
;
4726 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
4727 for (j
= i
; j
< bmap
->n_div
; ++j
)
4728 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
4730 if (j
< bmap
->n_div
)
4732 for (j
= 0; j
< bmap
->n_eq
; ++j
)
4733 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
4739 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
4740 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
4744 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
4749 pairs
[i
] = pos
* neg
;
4750 if (pairs
[i
] == 0) {
4751 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
4752 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
4753 isl_basic_map_drop_inequality(bmap
, j
);
4754 bmap
= isl_basic_map_drop_div(bmap
, i
);
4755 return drop_redundant_divs_again(bmap
, pairs
, 0);
4758 opp
= isl_bool_false
;
4760 opp
= is_opposite(bmap
, last_pos
, last_neg
);
4765 isl_bool single
, one
;
4769 single
= single_unknown(bmap
, last_pos
, i
);
4774 one
= has_coef_one(bmap
, i
, last_pos
);
4778 return set_eq_and_try_again(bmap
, last_pos
,
4780 lower
= lower_bound_is_cst(bmap
, i
, last_pos
);
4782 return fix_cst_lower(bmap
, i
, last_pos
, lower
,
4787 isl_int_add(bmap
->ineq
[last_pos
][0],
4788 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
4789 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
4790 bmap
->ineq
[last_pos
][0], 1);
4791 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
4792 bmap
->ineq
[last_pos
][1+off
+i
]);
4793 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
4794 bmap
->ineq
[last_pos
][0], 1);
4795 isl_int_sub(bmap
->ineq
[last_pos
][0],
4796 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
4798 return drop_div_and_try_again(bmap
, i
,
4799 last_pos
, last_neg
, pairs
);
4801 set_div
= isl_bool_false
;
4803 set_div
= ok_to_set_div_from_bound(bmap
, i
, last_pos
);
4805 return isl_basic_map_free(bmap
);
4807 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
4808 return drop_redundant_divs_again(bmap
, pairs
, 1);
4815 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
4821 isl_basic_map_free(bmap
);
4825 /* Consider the coefficients at "c" as a row vector and replace
4826 * them with their product with "T". "T" is assumed to be a square matrix.
4828 static isl_stat
preimage(isl_int
*c
, __isl_keep isl_mat
*T
)
4835 return isl_stat_error
;
4836 n
= isl_mat_rows(T
);
4837 if (isl_seq_first_non_zero(c
, n
) == -1)
4839 ctx
= isl_mat_get_ctx(T
);
4840 v
= isl_vec_alloc(ctx
, n
);
4842 return isl_stat_error
;
4843 isl_seq_swp_or_cpy(v
->el
, c
, n
);
4844 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
4846 return isl_stat_error
;
4847 isl_seq_swp_or_cpy(c
, v
->el
, n
);
4853 /* Plug in T for the variables in "bmap" starting at "pos".
4854 * T is a linear unimodular matrix, i.e., without constant term.
4856 static __isl_give isl_basic_map
*isl_basic_map_preimage_vars(
4857 __isl_take isl_basic_map
*bmap
, unsigned pos
, __isl_take isl_mat
*T
)
4862 bmap
= isl_basic_map_cow(bmap
);
4866 n
= isl_mat_cols(T
);
4867 if (n
!= isl_mat_rows(T
))
4868 isl_die(isl_mat_get_ctx(T
), isl_error_invalid
,
4869 "expecting square matrix", goto error
);
4871 if (isl_basic_map_check_range(bmap
, isl_dim_all
, pos
, n
) < 0)
4874 for (i
= 0; i
< bmap
->n_eq
; ++i
)
4875 if (preimage(bmap
->eq
[i
] + 1 + pos
, T
) < 0)
4877 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
4878 if (preimage(bmap
->ineq
[i
] + 1 + pos
, T
) < 0)
4880 for (i
= 0; i
< bmap
->n_div
; ++i
) {
4881 if (isl_basic_map_div_is_marked_unknown(bmap
, i
))
4883 if (preimage(bmap
->div
[i
] + 1 + 1 + pos
, T
) < 0)
4890 isl_basic_map_free(bmap
);
4895 /* Remove divs that are not strictly needed.
4897 * First look for an equality constraint involving two or more
4898 * existentially quantified variables without an explicit
4899 * representation. Replace the combination that appears
4900 * in the equality constraint by a single existentially quantified
4901 * variable such that the equality can be used to derive
4902 * an explicit representation for the variable.
4903 * If there are no more such equality constraints, then continue
4904 * with isl_basic_map_drop_redundant_divs_ineq.
4906 * In particular, if the equality constraint is of the form
4908 * f(x) + \sum_i c_i a_i = 0
4910 * with a_i existentially quantified variable without explicit
4911 * representation, then apply a transformation on the existentially
4912 * quantified variables to turn the constraint into
4916 * with g the gcd of the c_i.
4917 * In order to easily identify which existentially quantified variables
4918 * have a complete explicit representation, i.e., without being defined
4919 * in terms of other existentially quantified variables without
4920 * an explicit representation, the existentially quantified variables
4923 * The variable transformation is computed by extending the row
4924 * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation
4926 * [a_1'] [c_1/g ... c_n/g] [ a_1 ]
4931 * with [c_1/g ... c_n/g] representing the first row of U.
4932 * The inverse of U is then plugged into the original constraints.
4933 * The call to isl_basic_map_simplify makes sure the explicit
4934 * representation for a_1' is extracted from the equality constraint.
4936 __isl_give isl_basic_map
*isl_basic_map_drop_redundant_divs(
4937 __isl_take isl_basic_map
*bmap
)
4941 unsigned o_div
, n_div
;
4948 if (isl_basic_map_divs_known(bmap
))
4949 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
4950 if (bmap
->n_eq
== 0)
4951 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
4952 bmap
= isl_basic_map_sort_divs(bmap
);
4956 first
= isl_basic_map_first_unknown_div(bmap
);
4958 return isl_basic_map_free(bmap
);
4960 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4961 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4963 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
4964 l
= isl_seq_first_non_zero(bmap
->eq
[i
] + o_div
+ first
,
4969 if (isl_seq_first_non_zero(bmap
->eq
[i
] + o_div
+ l
+ 1,
4970 n_div
- (l
+ 1)) == -1)
4974 if (i
>= bmap
->n_eq
)
4975 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
4977 ctx
= isl_basic_map_get_ctx(bmap
);
4978 T
= isl_mat_alloc(ctx
, n_div
- l
, n_div
- l
);
4980 return isl_basic_map_free(bmap
);
4981 isl_seq_cpy(T
->row
[0], bmap
->eq
[i
] + o_div
+ l
, n_div
- l
);
4982 T
= isl_mat_normalize_row(T
, 0);
4983 T
= isl_mat_unimodular_complete(T
, 1);
4984 T
= isl_mat_right_inverse(T
);
4986 for (i
= l
; i
< n_div
; ++i
)
4987 bmap
= isl_basic_map_mark_div_unknown(bmap
, i
);
4988 bmap
= isl_basic_map_preimage_vars(bmap
, o_div
- 1 + l
, T
);
4989 bmap
= isl_basic_map_simplify(bmap
);
4991 return isl_basic_map_drop_redundant_divs(bmap
);
4994 /* Does "bmap" satisfy any equality that involves more than 2 variables
4995 * and/or has coefficients different from -1 and 1?
4997 static int has_multiple_var_equality(__isl_keep isl_basic_map
*bmap
)
5002 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5004 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5007 j
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1, total
);
5010 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
5011 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
5015 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
5019 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
5020 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
5024 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
5032 /* Remove any common factor g from the constraint coefficients in "v".
5033 * The constant term is stored in the first position and is replaced
5034 * by floor(c/g). If any common factor is removed and if this results
5035 * in a tightening of the constraint, then set *tightened.
5037 static __isl_give isl_vec
*normalize_constraint(__isl_take isl_vec
*v
,
5044 ctx
= isl_vec_get_ctx(v
);
5045 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
5046 if (isl_int_is_zero(ctx
->normalize_gcd
))
5048 if (isl_int_is_one(ctx
->normalize_gcd
))
5053 if (tightened
&& !isl_int_is_divisible_by(v
->el
[0], ctx
->normalize_gcd
))
5055 isl_int_fdiv_q(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
5056 isl_seq_scale_down(v
->el
+ 1, v
->el
+ 1, ctx
->normalize_gcd
,
5061 /* If "bmap" is an integer set that satisfies any equality involving
5062 * more than 2 variables and/or has coefficients different from -1 and 1,
5063 * then use variable compression to reduce the coefficients by removing
5064 * any (hidden) common factor.
5065 * In particular, apply the variable compression to each constraint,
5066 * factor out any common factor in the non-constant coefficients and
5067 * then apply the inverse of the compression.
5068 * At the end, we mark the basic map as having reduced constants.
5069 * If this flag is still set on the next invocation of this function,
5070 * then we skip the computation.
5072 * Removing a common factor may result in a tightening of some of
5073 * the constraints. If this happens, then we may end up with two
5074 * opposite inequalities that can be replaced by an equality.
5075 * We therefore call isl_basic_map_detect_inequality_pairs,
5076 * which checks for such pairs of inequalities as well as eliminate_divs_eq
5077 * and isl_basic_map_gauss if such a pair was found.
5079 * Note that this function may leave the result in an inconsistent state.
5080 * In particular, the constraints may not be gaussed.
5081 * Unfortunately, isl_map_coalesce actually depends on this inconsistent state
5082 * for some of the test cases to pass successfully.
5083 * Any potential modification of the representation is therefore only
5084 * performed on a single copy of the basic map.
5086 __isl_give isl_basic_map
*isl_basic_map_reduce_coefficients(
5087 __isl_take isl_basic_map
*bmap
)
5092 isl_mat
*eq
, *T
, *T2
;
5098 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
))
5100 if (isl_basic_map_is_rational(bmap
))
5102 if (bmap
->n_eq
== 0)
5104 if (!has_multiple_var_equality(bmap
))
5107 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5108 ctx
= isl_basic_map_get_ctx(bmap
);
5109 v
= isl_vec_alloc(ctx
, 1 + total
);
5111 return isl_basic_map_free(bmap
);
5113 eq
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
, 0, 1 + total
);
5114 T
= isl_mat_variable_compression(eq
, &T2
);
5117 if (T
->n_col
== 0) {
5121 return isl_basic_map_set_to_empty(bmap
);
5124 bmap
= isl_basic_map_cow(bmap
);
5129 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
5130 isl_seq_cpy(v
->el
, bmap
->ineq
[i
], 1 + total
);
5131 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
5132 v
= normalize_constraint(v
, &tightened
);
5133 v
= isl_vec_mat_product(v
, isl_mat_copy(T2
));
5136 isl_seq_cpy(bmap
->ineq
[i
], v
->el
, 1 + total
);
5143 ISL_F_SET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
5148 bmap
= isl_basic_map_detect_inequality_pairs(bmap
, &progress
);
5150 bmap
= eliminate_divs_eq(bmap
, &progress
);
5151 bmap
= isl_basic_map_gauss(bmap
, NULL
);
5160 return isl_basic_map_free(bmap
);
5163 /* Shift the integer division at position "div" of "bmap"
5164 * by "shift" times the variable at position "pos".
5165 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
5166 * corresponds to the constant term.
5168 * That is, if the integer division has the form
5172 * then replace it by
5174 * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
5176 __isl_give isl_basic_map
*isl_basic_map_shift_div(
5177 __isl_take isl_basic_map
*bmap
, int div
, int pos
, isl_int shift
)
5182 if (isl_int_is_zero(shift
))
5187 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5188 total
-= isl_basic_map_dim(bmap
, isl_dim_div
);
5190 isl_int_addmul(bmap
->div
[div
][1 + pos
], shift
, bmap
->div
[div
][0]);
5192 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5193 if (isl_int_is_zero(bmap
->eq
[i
][1 + total
+ div
]))
5195 isl_int_submul(bmap
->eq
[i
][pos
],
5196 shift
, bmap
->eq
[i
][1 + total
+ div
]);
5198 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
5199 if (isl_int_is_zero(bmap
->ineq
[i
][1 + total
+ div
]))
5201 isl_int_submul(bmap
->ineq
[i
][pos
],
5202 shift
, bmap
->ineq
[i
][1 + total
+ div
]);
5204 for (i
= 0; i
< bmap
->n_div
; ++i
) {
5205 if (isl_int_is_zero(bmap
->div
[i
][0]))
5207 if (isl_int_is_zero(bmap
->div
[i
][1 + 1 + total
+ div
]))
5209 isl_int_submul(bmap
->div
[i
][1 + pos
],
5210 shift
, bmap
->div
[i
][1 + 1 + total
+ div
]);