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
6 * Copyright 2021,2023 Cerebras Systems
8 * Use of this software is governed by the MIT license
10 * Written by Sven Verdoolaege, K.U.Leuven, Departement
11 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
12 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
13 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
14 * B.P. 105 - 78153 Le Chesnay, France
15 * and Cerebras Systems, 1237 E Arques Ave, Sunnyvale, CA, USA
18 #include <isl_ctx_private.h>
19 #include <isl_map_private.h>
20 #include "isl_equalities.h"
24 #include <isl_space_private.h>
25 #include <isl_mat_private.h>
26 #include <isl_vec_private.h>
28 #include <bset_to_bmap.c>
29 #include <bset_from_bmap.c>
30 #include <set_to_map.c>
31 #include <set_from_map.c>
33 /* Mark "bmap" as having one or more inequality constraints modified.
34 * If "equivalent" is set, then this modification was done based
35 * on an equality constraint already available in "bmap".
37 * Any modification may result in the constraints no longer being sorted and
38 * may also undo the effect of reduce_coefficients.
40 * A modification that uses extra information may also result
41 * in the modified constraint(s) becoming redundant or
42 * turning into an implicit equality constraint.
44 static __isl_give isl_basic_map
*isl_basic_map_modify_inequality(
45 __isl_take isl_basic_map
*bmap
, int equivalent
)
49 ISL_F_CLR(bmap
, ISL_BASIC_MAP_SORTED
);
50 ISL_F_CLR(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
53 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
54 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
58 static void swap_equality(__isl_keep isl_basic_map
*bmap
, int a
, int b
)
60 isl_int
*t
= bmap
->eq
[a
];
61 bmap
->eq
[a
] = bmap
->eq
[b
];
65 static void swap_inequality(__isl_keep isl_basic_map
*bmap
, int a
, int b
)
68 isl_int
*t
= bmap
->ineq
[a
];
69 bmap
->ineq
[a
] = bmap
->ineq
[b
];
74 /* Scale down the inequality constraint "ineq" of length "len"
76 * All the coefficients, except the constant term,
77 * are assumed to be multiples of "f".
79 * If the factor is 0 or 1, then no scaling needs to be performed.
81 * If scaling is performed then take into account that the constraint
82 * is modified (not simply based on an equality constraint).
84 static __isl_give isl_basic_map
*scale_down_inequality(
85 __isl_take isl_basic_map
*bmap
, int ineq
, isl_int f
, unsigned len
)
90 if (isl_int_is_zero(f
) || isl_int_is_one(f
))
93 isl_int_fdiv_q(bmap
->ineq
[ineq
][0], bmap
->ineq
[ineq
][0], f
);
94 isl_seq_scale_down(bmap
->ineq
[ineq
] + 1, bmap
->ineq
[ineq
] + 1, f
, len
);
96 bmap
= isl_basic_map_modify_inequality(bmap
, 0);
101 __isl_give isl_basic_map
*isl_basic_map_normalize_constraints(
102 __isl_take isl_basic_map
*bmap
)
106 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
109 return isl_basic_map_free(bmap
);
112 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
113 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
114 if (isl_int_is_zero(gcd
)) {
115 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
116 bmap
= isl_basic_map_set_to_empty(bmap
);
119 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
123 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
124 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
125 if (isl_int_is_one(gcd
))
127 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
128 bmap
= isl_basic_map_set_to_empty(bmap
);
131 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
134 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
135 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
136 if (isl_int_is_zero(gcd
)) {
137 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
138 bmap
= isl_basic_map_set_to_empty(bmap
);
141 if (isl_basic_map_drop_inequality(bmap
, i
) < 0)
145 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
146 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
147 bmap
= scale_down_inequality(bmap
, i
, gcd
, total
);
156 isl_basic_map_free(bmap
);
160 __isl_give isl_basic_set
*isl_basic_set_normalize_constraints(
161 __isl_take isl_basic_set
*bset
)
163 isl_basic_map
*bmap
= bset_to_bmap(bset
);
164 return bset_from_bmap(isl_basic_map_normalize_constraints(bmap
));
167 /* Reduce the coefficient of the variable at position "pos"
168 * in integer division "div", such that it lies in the half-open
169 * interval (1/2,1/2], extracting any excess value from this integer division.
170 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
171 * corresponds to the constant term.
173 * That is, the integer division is of the form
175 * floor((... + (c * d + r) * x_pos + ...)/d)
177 * with -d < 2 * r <= d.
180 * floor((... + r * x_pos + ...)/d) + c * x_pos
182 * If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d).
183 * Otherwise, c = floor((c * d + r)/d) + 1.
185 * This is the same normalization that is performed by isl_aff_floor.
187 static __isl_give isl_basic_map
*reduce_coefficient_in_div(
188 __isl_take isl_basic_map
*bmap
, int div
, int pos
)
194 isl_int_fdiv_r(shift
, bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
195 isl_int_mul_ui(shift
, shift
, 2);
196 add_one
= isl_int_gt(shift
, bmap
->div
[div
][0]);
197 isl_int_fdiv_q(shift
, bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
199 isl_int_add_ui(shift
, shift
, 1);
200 isl_int_neg(shift
, shift
);
201 bmap
= isl_basic_map_shift_div(bmap
, div
, pos
, shift
);
202 isl_int_clear(shift
);
207 /* Does the coefficient of the variable at position "pos"
208 * in integer division "div" need to be reduced?
209 * That is, does it lie outside the half-open interval (1/2,1/2]?
210 * The coefficient c/d lies outside this interval if abs(2 * c) >= d and
213 static isl_bool
needs_reduction(__isl_keep isl_basic_map
*bmap
, int div
,
218 if (isl_int_is_zero(bmap
->div
[div
][1 + pos
]))
219 return isl_bool_false
;
221 isl_int_mul_ui(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][1 + pos
], 2);
222 r
= isl_int_abs_ge(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]) &&
223 !isl_int_eq(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
224 isl_int_divexact_ui(bmap
->div
[div
][1 + pos
],
225 bmap
->div
[div
][1 + pos
], 2);
230 /* Reduce the coefficients (including the constant term) of
231 * integer division "div", if needed.
232 * In particular, make sure all coefficients lie in
233 * the half-open interval (1/2,1/2].
235 static __isl_give isl_basic_map
*reduce_div_coefficients_of_div(
236 __isl_take isl_basic_map
*bmap
, int div
)
241 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
243 return isl_basic_map_free(bmap
);
244 for (i
= 0; i
< 1 + total
; ++i
) {
247 reduce
= needs_reduction(bmap
, div
, i
);
249 return isl_basic_map_free(bmap
);
252 bmap
= reduce_coefficient_in_div(bmap
, div
, i
);
260 /* Reduce the coefficients (including the constant term) of
261 * the known integer divisions, if needed
262 * In particular, make sure all coefficients lie in
263 * the half-open interval (1/2,1/2].
265 static __isl_give isl_basic_map
*reduce_div_coefficients(
266 __isl_take isl_basic_map
*bmap
)
272 if (bmap
->n_div
== 0)
275 for (i
= 0; i
< bmap
->n_div
; ++i
) {
276 if (isl_int_is_zero(bmap
->div
[i
][0]))
278 bmap
= reduce_div_coefficients_of_div(bmap
, i
);
286 /* Remove any common factor in numerator and denominator of the div expression,
287 * not taking into account the constant term.
288 * That is, if the div is of the form
290 * floor((a + m f(x))/(m d))
294 * floor((floor(a/m) + f(x))/d)
296 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
297 * and can therefore not influence the result of the floor.
299 static __isl_give isl_basic_map
*normalize_div_expression(
300 __isl_take isl_basic_map
*bmap
, int div
)
302 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
303 isl_ctx
*ctx
= bmap
->ctx
;
306 return isl_basic_map_free(bmap
);
307 if (isl_int_is_zero(bmap
->div
[div
][0]))
309 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
310 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
311 if (isl_int_is_one(ctx
->normalize_gcd
))
313 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
315 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
317 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
318 ctx
->normalize_gcd
, total
);
323 /* Remove any common factor in numerator and denominator of a div expression,
324 * not taking into account the constant term.
325 * That is, look for any div of the form
327 * floor((a + m f(x))/(m d))
331 * floor((floor(a/m) + f(x))/d)
333 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
334 * and can therefore not influence the result of the floor.
336 static __isl_give isl_basic_map
*normalize_div_expressions(
337 __isl_take isl_basic_map
*bmap
)
343 if (bmap
->n_div
== 0)
346 for (i
= 0; i
< bmap
->n_div
; ++i
)
347 bmap
= normalize_div_expression(bmap
, i
);
352 /* Some progress has been made.
353 * Set *progress if "progress" is not NULL.
355 static void mark_progress(int *progress
)
361 /* Eliminate the variable at position "pos" from the constraints of "bmap"
362 * using the equality constraint "eq".
363 * If "keep_divs" is set, then try and preserve
364 * the integer division expressions. In this case, these expressions
365 * are assumed to have been ordered.
366 * If "equivalent" is set, then the elimination is performed
367 * using an equality constraint of "bmap", meaning that the meaning
368 * of the constraints is preserved.
370 static __isl_give isl_basic_map
*eliminate_var_using_equality(
371 __isl_take isl_basic_map
*bmap
,
372 unsigned pos
, isl_int
*eq
, int keep_divs
, int equivalent
, int *progress
)
380 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
381 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
382 if (total
< 0 || v_div
< 0)
383 return isl_basic_map_free(bmap
);
384 ctx
= isl_basic_map_get_ctx(bmap
);
385 last_div
= isl_seq_last_non_zero(eq
+ 1 + v_div
, bmap
->n_div
);
386 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
387 if (bmap
->eq
[k
] == eq
)
389 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
391 mark_progress(progress
);
392 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
393 isl_seq_normalize(ctx
, bmap
->eq
[k
], 1 + total
);
396 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
397 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
399 mark_progress(progress
);
400 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
401 isl_seq_gcd(bmap
->ineq
[k
], 1 + total
, &ctx
->normalize_gcd
);
402 bmap
= scale_down_inequality(bmap
, k
, ctx
->normalize_gcd
,
404 bmap
= isl_basic_map_modify_inequality(bmap
, equivalent
);
409 for (k
= 0; k
< bmap
->n_div
; ++k
) {
410 if (isl_int_is_zero(bmap
->div
[k
][0]))
412 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
414 mark_progress(progress
);
415 /* We need to be careful about circular definitions,
416 * so for now we just remove the definition of div k
417 * if the equality contains any divs.
418 * If keep_divs is set, then the divs have been ordered
419 * and we can keep the definition as long as the result
422 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
423 isl_seq_elim(bmap
->div
[k
]+1, eq
,
424 1+pos
, 1+total
, &bmap
->div
[k
][0]);
425 bmap
= normalize_div_expression(bmap
, k
);
429 isl_seq_clr(bmap
->div
[k
], 1 + total
);
435 /* Eliminate and remove the local variable at position "pos" of "bmap"
436 * using the equality constraint "eq".
437 * If "keep_divs" is set, then try and preserve
438 * the integer division expressions. In this case, these expressions
439 * are assumed to have been ordered.
440 * If "equivalent" is set, then the elimination is performed
441 * using an equality constraint of "bmap", meaning that the meaning
442 * of the constraints is preserved.
444 static __isl_give isl_basic_map
*eliminate_div(__isl_take isl_basic_map
*bmap
,
445 isl_int
*eq
, unsigned div
, int keep_divs
, int equivalent
)
450 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
452 return isl_basic_map_free(bmap
);
454 bmap
= eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
,
457 bmap
= isl_basic_map_drop_div(bmap
, div
);
462 /* Check if elimination of div "div" using equality "eq" would not
463 * result in a div depending on a later div.
465 static isl_bool
ok_to_eliminate_div(__isl_keep isl_basic_map
*bmap
, isl_int
*eq
,
473 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
475 return isl_bool_error
;
478 last_div
= isl_seq_last_non_zero(eq
+ 1 + v_div
, bmap
->n_div
);
479 if (last_div
< 0 || last_div
<= div
)
480 return isl_bool_true
;
482 for (k
= 0; k
<= last_div
; ++k
) {
483 if (isl_int_is_zero(bmap
->div
[k
][0]))
485 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
486 return isl_bool_false
;
489 return isl_bool_true
;
492 /* Eliminate divs based on equalities
494 static __isl_give isl_basic_map
*eliminate_divs_eq(
495 __isl_take isl_basic_map
*bmap
, int *progress
)
502 bmap
= isl_basic_map_order_divs(bmap
);
507 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
509 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
510 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
513 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
514 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
516 ok
= ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
);
518 return isl_basic_map_free(bmap
);
522 mark_progress(progress
);
523 bmap
= eliminate_div(bmap
, bmap
->eq
[i
], d
, 1, 1);
524 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
525 return isl_basic_map_free(bmap
);
530 return eliminate_divs_eq(bmap
, progress
);
534 /* Eliminate divs based on inequalities
536 static __isl_give isl_basic_map
*eliminate_divs_ineq(
537 __isl_take isl_basic_map
*bmap
, int *progress
)
548 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
550 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
551 for (i
= 0; i
< bmap
->n_eq
; ++i
)
552 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
556 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
557 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
559 if (i
< bmap
->n_ineq
)
561 mark_progress(progress
);
562 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
563 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
565 bmap
= isl_basic_map_drop_div(bmap
, d
);
572 /* Does the equality constraint at position "eq" in "bmap" involve
573 * any local variables in the range [first, first + n)
574 * that are not marked as having an explicit representation?
576 static isl_bool
bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map
*bmap
,
577 int eq
, unsigned first
, unsigned n
)
583 return isl_bool_error
;
585 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
586 for (i
= 0; i
< n
; ++i
) {
589 if (isl_int_is_zero(bmap
->eq
[eq
][o_div
+ first
+ i
]))
591 unknown
= isl_basic_map_div_is_marked_unknown(bmap
, first
+ i
);
593 return isl_bool_error
;
595 return isl_bool_true
;
598 return isl_bool_false
;
601 /* The last local variable involved in the equality constraint
602 * at position "eq" in "bmap" is the local variable at position "div".
603 * It can therefore be used to extract an explicit representation
605 * Do so unless the local variable already has an explicit representation or
606 * the explicit representation would involve any other local variables
607 * that in turn do not have an explicit representation.
608 * An equality constraint involving local variables without an explicit
609 * representation can be used in isl_basic_map_drop_redundant_divs
610 * to separate out an independent local variable. Introducing
611 * an explicit representation here would block this transformation,
612 * while the partial explicit representation in itself is not very useful.
613 * Set *progress if anything is changed.
615 * The equality constraint is of the form
619 * with n a positive number. The explicit representation derived from
624 static __isl_give isl_basic_map
*set_div_from_eq(__isl_take isl_basic_map
*bmap
,
625 int div
, int eq
, int *progress
)
634 if (!isl_int_is_zero(bmap
->div
[div
][0]))
637 involves
= bmap_eq_involves_unknown_divs(bmap
, eq
, 0, div
);
639 return isl_basic_map_free(bmap
);
643 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
645 return isl_basic_map_free(bmap
);
646 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
647 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->eq
[eq
], 1 + total
);
648 isl_int_set_si(bmap
->div
[div
][1 + o_div
+ div
], 0);
649 isl_int_set(bmap
->div
[div
][0], bmap
->eq
[eq
][o_div
+ div
]);
650 mark_progress(progress
);
655 /* Perform fangcheng (Gaussian elimination) on the equality
656 * constraints of "bmap".
657 * That is, put them into row-echelon form, starting from the last column
658 * backward and use them to eliminate the corresponding coefficients
659 * from all constraints.
661 * If "progress" is not NULL, then it gets set if the elimination
662 * results in any changes.
663 * The elimination process may result in some equality constraints
664 * getting interchanged or removed.
665 * If "swap" or "drop" are not NULL, then they get called when
666 * two equality constraints get interchanged or
667 * when a number of final equality constraints get removed.
668 * As a special case, if the input turns out to be empty,
669 * then drop gets called with the number of removed equality
670 * constraints set to the total number of equality constraints.
671 * If "swap" or "drop" are not NULL, then the local variables (if any)
672 * are assumed to be in a valid order.
674 __isl_give isl_basic_map
*isl_basic_map_gauss5(__isl_take isl_basic_map
*bmap
,
676 isl_stat (*swap
)(unsigned a
, unsigned b
, void *user
),
677 isl_stat (*drop
)(unsigned n
, void *user
), void *user
)
687 bmap
= isl_basic_map_order_divs(bmap
);
689 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
691 return isl_basic_map_free(bmap
);
693 total_var
= total
- bmap
->n_div
;
695 last_var
= total
- 1;
696 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
697 for (; last_var
>= 0; --last_var
) {
698 for (k
= done
; k
< bmap
->n_eq
; ++k
)
699 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
707 swap_equality(bmap
, k
, done
);
708 if (swap
&& swap(k
, done
, user
) < 0)
709 return isl_basic_map_free(bmap
);
711 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
712 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
714 bmap
= eliminate_var_using_equality(bmap
, last_var
,
715 bmap
->eq
[done
], 1, 1, progress
);
717 if (last_var
>= total_var
)
718 bmap
= set_div_from_eq(bmap
, last_var
- total_var
,
723 if (done
== bmap
->n_eq
)
725 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
726 if (isl_int_is_zero(bmap
->eq
[k
][0]))
728 if (drop
&& drop(bmap
->n_eq
, user
) < 0)
729 return isl_basic_map_free(bmap
);
730 return isl_basic_map_set_to_empty(bmap
);
732 n_drop
= bmap
->n_eq
- done
;
733 bmap
= isl_basic_map_free_equality(bmap
, n_drop
);
734 if (drop
&& drop(n_drop
, user
) < 0)
735 return isl_basic_map_free(bmap
);
739 __isl_give isl_basic_map
*isl_basic_map_gauss(__isl_take isl_basic_map
*bmap
,
742 return isl_basic_map_gauss5(bmap
, progress
, NULL
, NULL
, NULL
);
745 __isl_give isl_basic_set
*isl_basic_set_gauss(
746 __isl_take isl_basic_set
*bset
, int *progress
)
748 return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset
),
753 static unsigned int round_up(unsigned int v
)
764 /* Hash table of inequalities in a basic map.
765 * "index" is an array of addresses of inequalities in the basic map, some
766 * of which are NULL. The inequalities are hashed on the coefficients
767 * except the constant term.
768 * "size" is the number of elements in the array and is always a power of two
769 * "bits" is the number of bits need to represent an index into the array.
770 * "total" is the total dimension of the basic map.
772 struct isl_constraint_index
{
779 /* Fill in the "ci" data structure for holding the inequalities of "bmap".
781 static isl_stat
create_constraint_index(struct isl_constraint_index
*ci
,
782 __isl_keep isl_basic_map
*bmap
)
788 return isl_stat_error
;
789 ci
->total
= isl_basic_map_dim(bmap
, isl_dim_all
);
791 return isl_stat_error
;
792 if (bmap
->n_ineq
== 0)
794 ci
->size
= round_up(4 * (bmap
->n_ineq
+ 1) / 3 - 1);
795 ci
->bits
= ffs(ci
->size
) - 1;
796 ctx
= isl_basic_map_get_ctx(bmap
);
797 ci
->index
= isl_calloc_array(ctx
, isl_int
**, ci
->size
);
799 return isl_stat_error
;
804 /* Free the memory allocated by create_constraint_index.
806 static void constraint_index_free(struct isl_constraint_index
*ci
)
811 /* Return the position in ci->index that contains the address of
812 * an inequality that is equal to *ineq up to the constant term,
813 * provided this address is not identical to "ineq".
814 * If there is no such inequality, then return the position where
815 * such an inequality should be inserted.
817 static int hash_index_ineq(struct isl_constraint_index
*ci
, isl_int
**ineq
)
820 uint32_t hash
= isl_seq_get_hash_bits((*ineq
) + 1, ci
->total
, ci
->bits
);
821 for (h
= hash
; ci
->index
[h
]; h
= (h
+1) % ci
->size
)
822 if (ineq
!= ci
->index
[h
] &&
823 isl_seq_eq((*ineq
) + 1, ci
->index
[h
][0]+1, ci
->total
))
828 /* Return the position in ci->index that contains the address of
829 * an inequality that is equal to the k'th inequality of "bmap"
830 * up to the constant term, provided it does not point to the very
832 * If there is no such inequality, then return the position where
833 * such an inequality should be inserted.
835 static int hash_index(struct isl_constraint_index
*ci
,
836 __isl_keep isl_basic_map
*bmap
, int k
)
838 return hash_index_ineq(ci
, &bmap
->ineq
[k
]);
841 static int set_hash_index(struct isl_constraint_index
*ci
,
842 __isl_keep isl_basic_set
*bset
, int k
)
844 return hash_index(ci
, bset
, k
);
847 /* Fill in the "ci" data structure with the inequalities of "bset".
849 static isl_stat
setup_constraint_index(struct isl_constraint_index
*ci
,
850 __isl_keep isl_basic_set
*bset
)
854 if (create_constraint_index(ci
, bset
) < 0)
855 return isl_stat_error
;
857 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
858 h
= set_hash_index(ci
, bset
, k
);
859 ci
->index
[h
] = &bset
->ineq
[k
];
865 /* Is the inequality ineq (obviously) redundant with respect
866 * to the constraints in "ci"?
868 * Look for an inequality in "ci" with the same coefficients and then
869 * check if the contant term of "ineq" is greater than or equal
870 * to the constant term of that inequality. If so, "ineq" is clearly
873 * Note that hash_index_ineq ignores a stored constraint if it has
874 * the same address as the passed inequality. It is ok to pass
875 * the address of a local variable here since it will never be
876 * the same as the address of a constraint in "ci".
878 static isl_bool
constraint_index_is_redundant(struct isl_constraint_index
*ci
,
883 h
= hash_index_ineq(ci
, &ineq
);
885 return isl_bool_false
;
886 return isl_int_ge(ineq
[0], (*ci
->index
[h
])[0]);
889 /* If we can eliminate more than one div, then we need to make
890 * sure we do it from last div to first div, in order not to
891 * change the position of the other divs that still need to
894 static __isl_give isl_basic_map
*remove_duplicate_divs(
895 __isl_take isl_basic_map
*bmap
, int *progress
)
907 bmap
= isl_basic_map_order_divs(bmap
);
908 if (!bmap
|| bmap
->n_div
<= 1)
911 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
913 return isl_basic_map_free(bmap
);
914 total
= v_div
+ bmap
->n_div
;
917 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
918 if (!isl_int_is_zero(bmap
->div
[k
][0]))
923 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
926 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
927 bits
= ffs(size
) - 1;
928 index
= isl_calloc_array(ctx
, int, size
);
929 if (!elim_for
|| !index
)
931 eq
= isl_blk_alloc(ctx
, 1+total
);
932 if (isl_blk_is_error(eq
))
935 isl_seq_clr(eq
.data
, 1+total
);
936 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
937 for (--k
; k
>= 0; --k
) {
940 if (isl_int_is_zero(bmap
->div
[k
][0]))
943 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
944 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
945 if (isl_seq_eq(bmap
->div
[k
],
946 bmap
->div
[index
[h
]-1], 2+total
))
949 mark_progress(progress
);
955 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
959 isl_int_set_si(eq
.data
[1 + v_div
+ k
], -1);
960 isl_int_set_si(eq
.data
[1 + v_div
+ l
], 1);
961 bmap
= eliminate_div(bmap
, eq
.data
, l
, 1, 0);
964 isl_int_set_si(eq
.data
[1 + v_div
+ k
], 0);
965 isl_int_set_si(eq
.data
[1 + v_div
+ l
], 0);
968 isl_blk_free(ctx
, eq
);
975 /* Is the local variable at position "div" of "bmap"
976 * an integral integer division?
978 static isl_bool
is_known_integral_div(__isl_keep isl_basic_map
*bmap
, int div
)
982 unknown
= isl_basic_map_div_is_marked_unknown(bmap
, div
);
983 if (unknown
< 0 || unknown
)
984 return isl_bool_not(unknown
);
985 return isl_basic_map_div_is_integral(bmap
, div
);
988 /* Eliminate local variable "div" from "bmap", given
989 * that it represents an integer division with denominator 1.
991 * Construct an equality constraint that equates the local variable
992 * to the argument of the integer division and use that to eliminate
993 * the local variable.
995 static __isl_give isl_basic_map
*eliminate_integral_div(
996 __isl_take isl_basic_map
*bmap
, int div
)
998 isl_size total
, v_div
;
1001 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1002 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1003 if (v_div
< 0 || total
< 0)
1004 return isl_basic_map_free(bmap
);
1005 v
= isl_vec_alloc(isl_basic_map_get_ctx(bmap
), 1 + total
);
1007 return isl_basic_map_free(bmap
);
1008 isl_seq_cpy(v
->el
, bmap
->div
[div
] + 1, 1 + total
);
1009 isl_int_set_si(v
->el
[1 + v_div
+ div
], -1);
1010 bmap
= eliminate_div(bmap
, v
->el
, div
, 1, 0);
1016 /* Eliminate all integer divisions with denominator 1.
1018 static __isl_give isl_basic_map
*eliminate_integral_divs(
1019 __isl_take isl_basic_map
*bmap
, int *progress
)
1024 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1026 return isl_basic_map_free(bmap
);
1028 for (i
= 0; i
< n_div
; ++i
) {
1031 eliminate
= is_known_integral_div(bmap
, i
);
1033 return isl_basic_map_free(bmap
);
1037 bmap
= eliminate_integral_div(bmap
, i
);
1038 mark_progress(progress
);
1046 static int n_pure_div_eq(__isl_keep isl_basic_map
*bmap
)
1051 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1054 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
1055 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
1059 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + v_div
, j
) != -1)
1065 /* Normalize divs that appear in equalities.
1067 * In particular, we assume that bmap contains some equalities
1072 * and we want to replace the set of e_i by a minimal set and
1073 * such that the new e_i have a canonical representation in terms
1075 * If any of the equalities involves more than one divs, then
1076 * we currently simply bail out.
1078 * Let us first additionally assume that all equalities involve
1079 * a div. The equalities then express modulo constraints on the
1080 * remaining variables and we can use "parameter compression"
1081 * to find a minimal set of constraints. The result is a transformation
1083 * x = T(x') = x_0 + G x'
1085 * with G a lower-triangular matrix with all elements below the diagonal
1086 * non-negative and smaller than the diagonal element on the same row.
1087 * We first normalize x_0 by making the same property hold in the affine
1089 * The rows i of G with a 1 on the diagonal do not impose any modulo
1090 * constraint and simply express x_i = x'_i.
1091 * For each of the remaining rows i, we introduce a div and a corresponding
1092 * equality. In particular
1094 * g_ii e_j = x_i - g_i(x')
1096 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
1097 * corresponding div (if g_kk != 1).
1099 * If there are any equalities not involving any div, then we
1100 * first apply a variable compression on the variables x:
1102 * x = C x'' x'' = C_2 x
1104 * and perform the above parameter compression on A C instead of on A.
1105 * The resulting compression is then of the form
1107 * x'' = T(x') = x_0 + G x'
1109 * and in constructing the new divs and the corresponding equalities,
1110 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
1111 * by the corresponding row from C_2.
1113 static __isl_give isl_basic_map
*normalize_divs(__isl_take isl_basic_map
*bmap
,
1121 struct isl_mat
*T
= NULL
;
1122 struct isl_mat
*C
= NULL
;
1123 struct isl_mat
*C2
= NULL
;
1126 int dropped
, needed
;
1131 if (bmap
->n_div
== 0)
1134 if (bmap
->n_eq
== 0)
1137 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
1140 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1141 div_eq
= n_pure_div_eq(bmap
);
1142 if (v_div
< 0 || div_eq
< 0)
1143 return isl_basic_map_free(bmap
);
1147 if (div_eq
< bmap
->n_eq
) {
1148 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
1149 bmap
->n_eq
- div_eq
, 0, 1 + v_div
);
1150 C
= isl_mat_variable_compression(B
, &C2
);
1153 if (C
->n_col
== 0) {
1154 bmap
= isl_basic_map_set_to_empty(bmap
);
1161 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
1164 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
1165 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
1167 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + v_div
+ j
]);
1169 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + v_div
);
1172 B
= isl_mat_product(B
, C
);
1176 T
= isl_mat_parameter_compression(B
, d
);
1179 if (T
->n_col
== 0) {
1180 bmap
= isl_basic_map_set_to_empty(bmap
);
1186 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
1187 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
1188 if (isl_int_is_zero(v
))
1190 isl_mat_col_submul(T
, 0, v
, 1 + i
);
1193 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
1196 /* We have to be careful because dropping equalities may reorder them */
1198 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
1199 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1200 if (!isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
1202 if (i
< bmap
->n_eq
) {
1203 bmap
= isl_basic_map_drop_div(bmap
, j
);
1204 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
1211 for (i
= 1; i
< T
->n_row
; ++i
) {
1212 if (isl_int_is_one(T
->row
[i
][i
]))
1217 if (needed
> dropped
) {
1218 bmap
= isl_basic_map_extend(bmap
, needed
, needed
, 0);
1222 for (i
= 1; i
< T
->n_row
; ++i
) {
1223 if (isl_int_is_one(T
->row
[i
][i
]))
1225 k
= isl_basic_map_alloc_div(bmap
);
1226 pos
[i
] = 1 + v_div
+ k
;
1227 isl_seq_clr(bmap
->div
[k
] + 1, 1 + v_div
+ bmap
->n_div
);
1228 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
1230 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + v_div
);
1232 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
1233 for (j
= 0; j
< i
; ++j
) {
1234 if (isl_int_is_zero(T
->row
[i
][j
]))
1236 if (pos
[j
] < T
->n_row
&& C2
)
1237 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
1238 C2
->row
[pos
[j
]], 1 + v_div
);
1240 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
1243 j
= isl_basic_map_alloc_equality(bmap
);
1244 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+v_div
+bmap
->n_div
);
1245 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
1251 mark_progress(progress
);
1253 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
1261 isl_basic_map_free(bmap
);
1265 static __isl_give isl_basic_map
*set_div_from_lower_bound(
1266 __isl_take isl_basic_map
*bmap
, int div
, int ineq
)
1268 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1270 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1271 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1272 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1273 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1274 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1279 /* Check whether it is ok to define a div based on an inequality.
1280 * To avoid the introduction of circular definitions of divs, we
1281 * do not allow such a definition if the resulting expression would refer to
1282 * any other undefined divs or if any known div is defined in
1283 * terms of the unknown div.
1285 static isl_bool
ok_to_set_div_from_bound(__isl_keep isl_basic_map
*bmap
,
1289 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1291 /* Not defined in terms of unknown divs */
1292 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1295 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1297 if (isl_int_is_zero(bmap
->div
[j
][0]))
1298 return isl_bool_false
;
1301 /* No other div defined in terms of this one => avoid loops */
1302 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1305 if (isl_int_is_zero(bmap
->div
[j
][0]))
1307 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1308 return isl_bool_false
;
1311 return isl_bool_true
;
1314 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1315 * be a better expression than the current one?
1317 * If we do not have any expression yet, then any expression would be better.
1318 * Otherwise we check if the last variable involved in the inequality
1319 * (disregarding the div that it would define) is in an earlier position
1320 * than the last variable involved in the current div expression.
1322 static isl_bool
better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1325 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1329 if (isl_int_is_zero(bmap
->div
[div
][0]))
1330 return isl_bool_true
;
1332 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1333 bmap
->n_div
- (div
+ 1)) >= 0)
1334 return isl_bool_false
;
1336 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1337 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1338 total
+ bmap
->n_div
);
1340 return last_ineq
< last_div
;
1343 /* Is the sequence of "len" coefficients "ineq" equal to "res"
1344 * plus some non-trivial coefficients that are all a multiple of some number
1345 * greater than "sum"?
1346 * If so, this factor is stored in "gcd".
1348 * The current implementation requires the coefficients
1349 * in "res" to appear directly in "ineq", so that "gcd"
1350 * is the gcd of the remaining coefficients.
1351 * The same assumption is used in has_nested_unit_div.
1353 static int is_residue(isl_int
*res
, isl_int
*ineq
, isl_int sum
, unsigned len
,
1358 isl_int_set_si(*gcd
, 0);
1359 for (j
= 0; j
< len
; ++j
) {
1360 if (!isl_int_is_zero(res
[1 + j
])) {
1361 if (isl_int_eq(res
[1 + j
], ineq
[1 + j
]))
1365 if (!isl_int_is_zero(ineq
[1 + j
])) {
1366 isl_int_gcd(*gcd
, *gcd
, ineq
[1 + j
]);
1367 if (isl_int_le(*gcd
, sum
))
1372 return !isl_int_is_zero(*gcd
);
1377 * (cst - cst2) mod n + sum
1379 * greater than or equal to n?
1381 static int residue_exceeded(isl_int cst
, isl_int cst2
, isl_int n
, isl_int sum
)
1387 isl_int_sub(t
, cst
, cst2
);
1388 isl_int_fdiv_r(t
, t
, n
);
1389 isl_int_add(t
, t
, sum
);
1390 exceeded
= isl_int_ge(t
, n
);
1396 /* Given two constraints "k" and "l" that are opposite to each other,
1397 * except for the constant term, with "sum" the sum of these constant terms,
1398 * check if they can be used to simplify any integer division expression.
1400 * In particular, let "k" and "l" be of the form
1409 * Note that the same constraint holds for "k" and "l" interchanged, i.e.,
1411 * 0 <= -f(x) + c <= c
1413 * That is, the reasoning below holds for both "f(x)" and "-f(x) + c".
1415 * If there is an integer division definition of the form
1417 * floor((f(x) + n h(x) + c')/(n * m))
1423 * then it is equal to
1425 * floor((h(x) + floor(c'/n))/m)
1429 * floor((f(x) + n h(x) + c')/(n * m))
1430 * = floor((f(x) + c' % n + n (h(x) + floor(c'/n)))/(n * m))
1434 * 0 <= f(x) + c' % n < n
1436 * Note that h(x) may be equal to zero, in which case the denominator
1437 * of the integer division can be used as n (and m = 1).
1439 static __isl_give isl_basic_map
*check_for_residues_in_divs(
1440 __isl_take isl_basic_map
*bmap
, int k
, int l
, isl_int sum
,
1446 isl_size n_div
, total
;
1448 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1449 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1450 if (n_div
< 0 || total
< 0)
1451 return isl_basic_map_free(bmap
);
1453 ctx
= isl_basic_map_get_ctx(bmap
);
1454 p
= isl_seq_last_non_zero(bmap
->ineq
[k
] + 1, total
);
1455 for (i
= 0; i
< n_div
; ++i
) {
1459 unknown
= isl_basic_map_div_is_marked_unknown(bmap
, i
);
1461 return isl_basic_map_free(bmap
);
1464 if (isl_int_le(bmap
->div
[i
][0], sum
))
1466 if (isl_int_eq(bmap
->div
[i
][2 + p
], bmap
->ineq
[k
][1 + p
]))
1468 else if (isl_int_eq(bmap
->div
[i
][2 + p
], bmap
->ineq
[l
][1 + p
]))
1473 if (isl_seq_eq(bmap
->div
[i
] + 2, bmap
->ineq
[c
] + 1, total
))
1474 isl_int_set(ctx
->normalize_gcd
, bmap
->div
[i
][0]);
1475 else if (!is_residue(bmap
->ineq
[c
], bmap
->div
[i
] + 1, sum
,
1476 total
, &ctx
->normalize_gcd
))
1479 if (residue_exceeded(bmap
->div
[i
][1], bmap
->ineq
[c
][0],
1480 ctx
->normalize_gcd
, sum
))
1483 if (!isl_int_is_divisible_by(bmap
->div
[i
][0],
1484 ctx
->normalize_gcd
))
1487 isl_seq_sub(bmap
->div
[i
] + 1, bmap
->ineq
[c
], 1 + total
);
1488 mark_progress(progress
);
1494 /* Is inequality "ineq" of "bmap" a constraint defining an integer division?
1495 * "v_div" is the position of the first local variable.
1496 * "n_div" is the number of local variables.
1498 * A constraint defining an integer division must involve some local variable
1499 * and could only possibly define the last local variable involved since
1500 * it can only be defined in terms of earlier variables.
1502 static isl_bool
is_div_constraint(__isl_keep isl_basic_map
*bmap
, int ineq
,
1503 unsigned v_div
, unsigned n_div
)
1507 last
= isl_seq_last_non_zero(bmap
->ineq
[ineq
] + 1 + v_div
, n_div
);
1509 return isl_bool_false
;
1510 return isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[ineq
], last
);
1513 /* Does the inequality constraint "ineq" of "bmap" involve nested integer
1514 * divisions with unit coefficient after removing the coefficients
1515 * of inequality constraint "base"?
1516 * "v_div" is the position of the first local variable.
1517 * "n_div" is the number of local variables.
1518 * "n" is the factor with which the constraint will be scaled down.
1520 * Use the same simplifying assumption as "is_residue" that
1521 * the coefficients in "base" appear directly in "ineq".
1522 * Look for an integer division involving nested integer divisions
1523 * that does not appear in "base" and does appear in "ineq"
1524 * with a coefficient equal to "n" (up to a change of sign).
1526 static isl_bool
has_nested_unit_div(__isl_keep isl_basic_map
*bmap
,
1527 int base
, int ineq
, unsigned v_div
, unsigned n_div
, isl_int n
)
1531 for (j
= 0; j
< n_div
; ++j
) {
1534 if (!isl_int_is_zero(bmap
->ineq
[base
][1 + v_div
+ j
]))
1536 if (!isl_int_abs_eq(bmap
->ineq
[ineq
][1 + v_div
+ j
], n
))
1538 nested
= isl_basic_map_div_expr_involves_vars(bmap
, j
,
1540 if (nested
< 0 || nested
)
1544 return isl_bool_false
;
1547 /* Given two constraints "k" and "l" that are opposite to each other,
1548 * except for the constant term, with "sum" the sum of these constant terms,
1549 * check if they can be used to simplify other constraints.
1550 * Only do this for integer basic maps.
1552 * In particular, let "k" and "l" be of the form
1561 * Note that the same constraint holds for "k" and "l" interchanged, i.e.,
1563 * 0 <= -f(x) + c <= c
1565 * That is, the reasoning below holds for both "f(x)" and "-f(x) + c".
1567 * If there is some other constraint
1573 * g(x) - f(x) = n h(x) + c'
1579 * in particular, for the constant term,
1581 * (g(x) - f(x)) mod n + c < n
1583 * then this other constraint is equivalent to
1587 * (given "k" and "l") since
1589 * 0 <= f(x) + c' < n
1591 * Note that the constraint does not necessarily need to be scaled down here
1592 * since it would otherwise also be scaled down
1593 * by isl_basic_map_normalize_constraints, but since the scaling factor
1594 * is already known here, it might as well be done immediately.
1595 * Also note that the current implementation only checks for constraints
1596 * where the coefficients of f(x) appear directly in g(x), while it would
1597 * be sufficient for the differences with the corresponding coefficients
1598 * in g(x) to be multiples of n.
1600 * Similarly, if there is an integer division definition of the form
1602 * floor((f(x) + n h(x) + c')/(n * m))
1608 * then it is equal to
1610 * floor((h(x) + floor(c'/n))/m)
1613 * Do not apply any simplification to constraint(s) defining integer divisions.
1614 * Such constraints would first be simplified to be of the form
1618 * and then the integer division definition would be plugged into
1619 * this constraint, resulting in the original constraint and
1620 * causing an infinite loop.
1621 * Simplifying the integer division definitions as well mitigates
1622 * some (possibly all) of this effect, but it is too fragile to rely on
1623 * for avoiding infinite loops.
1625 * If any nested integer divisions are involved, then a similar effect
1626 * may be obtained even on constraints that do not (obviously)
1627 * define an integer division through multiple steps of such substitutions.
1628 * Any constraint that would result in an integer division with nested
1629 * integer divisions and a unit coefficient is therefore also left untouched.
1631 static __isl_give isl_basic_map
*check_for_residues(
1632 __isl_take isl_basic_map
*bmap
, int k
, int l
, isl_int sum
,
1639 isl_size n_ineq
, total
, v_div
, n_div
;
1641 rat
= isl_basic_map_is_rational(bmap
);
1642 n_ineq
= isl_basic_map_n_inequality(bmap
);
1643 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1644 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1645 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1646 if (rat
< 0 || n_ineq
< 0 || total
< 0 || v_div
< 0 || n_div
< 0)
1647 return isl_basic_map_free(bmap
);
1651 bmap
= check_for_residues_in_divs(bmap
, k
, l
, sum
, progress
);
1655 ctx
= isl_basic_map_get_ctx(bmap
);
1656 p
= isl_seq_last_non_zero(bmap
->ineq
[k
] + 1, total
);
1657 for (i
= 0; i
< n_ineq
; ++i
) {
1661 if (i
== k
|| i
== l
)
1663 if (isl_int_is_zero(bmap
->ineq
[i
][1 + p
]))
1665 skip
= is_div_constraint(bmap
, i
, v_div
, n_div
);
1667 return isl_basic_map_free(bmap
);
1670 if (isl_int_eq(bmap
->ineq
[i
][1 + p
], bmap
->ineq
[k
][1 + p
]))
1672 else if (isl_int_eq(bmap
->ineq
[i
][1 + p
], bmap
->ineq
[l
][1 + p
]))
1677 if (!is_residue(bmap
->ineq
[c
], bmap
->ineq
[i
], sum
, total
,
1678 &ctx
->normalize_gcd
))
1681 skip
= has_nested_unit_div(bmap
, c
, i
, v_div
, n_div
,
1682 ctx
->normalize_gcd
);
1684 return isl_basic_map_free(bmap
);
1687 if (residue_exceeded(bmap
->ineq
[i
][0], bmap
->ineq
[c
][0],
1688 ctx
->normalize_gcd
, sum
))
1691 isl_seq_sub(bmap
->ineq
[i
], bmap
->ineq
[c
], 1 + total
);
1692 bmap
= scale_down_inequality(bmap
, i
, ctx
->normalize_gcd
,
1696 mark_progress(progress
);
1702 /* Given two constraints "k" and "l" that are opposite to each other,
1703 * except for the constant term, check if we can use them
1704 * to obtain an expression for one of the hitherto unknown divs or
1705 * a "better" expression for a div for which we already have an expression.
1706 * "sum" is the sum of the constant terms of the constraints.
1707 * If this sum is strictly smaller than the coefficient of one
1708 * of the divs, then this pair can be used to define the div.
1709 * To avoid the introduction of circular definitions of divs, we
1710 * do not use the pair if the resulting expression would refer to
1711 * any other undefined divs or if any known div is defined in
1712 * terms of the unknown div.
1714 static __isl_give isl_basic_map
*check_for_div_constraints(
1715 __isl_take isl_basic_map
*bmap
, int k
, int l
, isl_int sum
,
1719 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1721 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1724 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1726 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1728 set_div
= better_div_constraint(bmap
, i
, k
);
1729 if (set_div
>= 0 && set_div
)
1730 set_div
= ok_to_set_div_from_bound(bmap
, i
, k
);
1732 return isl_basic_map_free(bmap
);
1735 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1736 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1738 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1739 mark_progress(progress
);
1745 /* Look for pairs of constraints that have equal or opposite coefficients.
1746 * For each pair of constraints with equal coefficients, only keep
1747 * the one which imposes the most stringent constraint, i.e.,
1748 * the one with the smallest constant term.
1749 * For each pair of constraints with opposite coefficients,
1750 * consider the sum of the constant terms.
1751 * If the sum is smaller than zero, then the constraints conflict.
1752 * If the sum is equal to zero, then the constraints form
1753 * an equality constraint.
1754 * If the sum is greater than zero, then check whether this pair
1755 * can be used to simplify any other constraints and/or,
1756 * if "detect_divs" is set, whether a (better) integer division definition
1757 * can be read off from the pair.
1759 __isl_give isl_basic_map
*isl_basic_map_remove_duplicate_constraints(
1760 __isl_take isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1762 struct isl_constraint_index ci
;
1764 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1767 if (total
< 0 || bmap
->n_ineq
<= 1)
1770 if (create_constraint_index(&ci
, bmap
) < 0)
1773 h
= isl_seq_get_hash_bits(bmap
->ineq
[0] + 1, total
, ci
.bits
);
1774 ci
.index
[h
] = &bmap
->ineq
[0];
1775 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1776 h
= hash_index(&ci
, bmap
, k
);
1778 ci
.index
[h
] = &bmap
->ineq
[k
];
1781 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1782 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1783 swap_inequality(bmap
, k
, l
);
1784 isl_basic_map_drop_inequality(bmap
, k
);
1788 for (k
= 0; bmap
&& k
< bmap
->n_ineq
-1; ++k
) {
1789 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1790 h
= hash_index(&ci
, bmap
, k
);
1791 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1794 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1795 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1796 if (isl_int_is_pos(sum
)) {
1799 bmap
= check_for_residues(bmap
, k
, l
, sum
, &residue
);
1801 bmap
= check_for_div_constraints(bmap
, k
, l
,
1805 mark_progress(progress
);
1808 if (isl_int_is_zero(sum
)) {
1809 /* We need to break out of the loop after these
1810 * changes since the contents of the hash
1811 * will no longer be valid.
1812 * Plus, we probably we want to regauss first.
1814 mark_progress(progress
);
1815 isl_basic_map_drop_inequality(bmap
, l
);
1816 isl_basic_map_inequality_to_equality(bmap
, k
);
1818 bmap
= isl_basic_map_set_to_empty(bmap
);
1823 constraint_index_free(&ci
);
1827 /* Detect all pairs of inequalities that form an equality.
1829 * isl_basic_map_remove_duplicate_constraints detects at most one such pair.
1830 * Call it repeatedly while it is making progress.
1832 __isl_give isl_basic_map
*isl_basic_map_detect_inequality_pairs(
1833 __isl_take isl_basic_map
*bmap
, int *progress
)
1839 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1842 mark_progress(progress
);
1843 } while (duplicate
);
1848 /* Given a known integer division "div" that is not integral
1849 * (with denominator 1), eliminate it from the constraints in "bmap"
1850 * where it appears with a (positive or negative) unit coefficient.
1851 * If "progress" is not NULL, then it gets set if the elimination
1852 * results in any changes.
1856 * floor(e/m) + f >= 0
1864 * -floor(e/m) + f >= 0
1868 * -e + m f + m - 1 >= 0
1870 * The first conversion is valid because floor(e/m) >= -f is equivalent
1871 * to e/m >= -f because -f is an integral expression.
1872 * The second conversion follows from the fact that
1874 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1877 * Note that one of the div constraints may have been eliminated
1878 * due to being redundant with respect to the constraint that is
1879 * being modified by this function. The modified constraint may
1880 * no longer imply this div constraint, so we add it back to make
1881 * sure we do not lose any information.
1883 static __isl_give isl_basic_map
*eliminate_unit_div(
1884 __isl_take isl_basic_map
*bmap
, int div
, int *progress
)
1887 isl_size v_div
, dim
;
1890 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1891 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
1892 if (v_div
< 0 || dim
< 0)
1893 return isl_basic_map_free(bmap
);
1895 ctx
= isl_basic_map_get_ctx(bmap
);
1897 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1900 if (!isl_int_is_one(bmap
->ineq
[j
][1 + v_div
+ div
]) &&
1901 !isl_int_is_negone(bmap
->ineq
[j
][1 + v_div
+ div
]))
1904 mark_progress(progress
);
1906 s
= isl_int_sgn(bmap
->ineq
[j
][1 + v_div
+ div
]);
1907 isl_int_set_si(bmap
->ineq
[j
][1 + v_div
+ div
], 0);
1909 isl_seq_combine(bmap
->ineq
[j
],
1910 ctx
->negone
, bmap
->div
[div
] + 1,
1911 bmap
->div
[div
][0], bmap
->ineq
[j
], 1 + dim
);
1913 isl_seq_combine(bmap
->ineq
[j
],
1914 ctx
->one
, bmap
->div
[div
] + 1,
1915 bmap
->div
[div
][0], bmap
->ineq
[j
], 1 + dim
);
1917 isl_int_add(bmap
->ineq
[j
][0],
1918 bmap
->ineq
[j
][0], bmap
->div
[div
][0]);
1919 isl_int_sub_ui(bmap
->ineq
[j
][0],
1920 bmap
->ineq
[j
][0], 1);
1923 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
1924 bmap
= isl_basic_map_add_div_constraint(bmap
, div
, s
);
1932 /* Eliminate selected known divs from constraints where they appear with
1933 * a (positive or negative) unit coefficient.
1934 * In particular, only handle those for which "select" returns isl_bool_true.
1935 * If "progress" is not NULL, then it gets set if the elimination
1936 * results in any changes.
1938 * We skip integral divs, i.e., those with denominator 1, as we would
1939 * risk eliminating the div from the div constraints.
1940 * They are eliminated in eliminate_integral_divs instead.
1942 static __isl_give isl_basic_map
*eliminate_selected_unit_divs(
1943 __isl_take isl_basic_map
*bmap
,
1944 isl_bool (*select
)(__isl_keep isl_basic_map
*bmap
, int div
),
1950 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1952 return isl_basic_map_free(bmap
);
1954 for (i
= 0; i
< n_div
; ++i
) {
1958 skip
= isl_basic_map_div_is_marked_unknown(bmap
, i
);
1959 if (skip
>= 0 && !skip
)
1960 skip
= isl_basic_map_div_is_integral(bmap
, i
);
1962 return isl_basic_map_free(bmap
);
1965 selected
= select(bmap
, i
);
1967 return isl_basic_map_free(bmap
);
1970 bmap
= eliminate_unit_div(bmap
, i
, progress
);
1978 /* eliminate_selected_unit_divs callback that selects every
1981 static isl_bool
is_any_div(__isl_keep isl_basic_map
*bmap
, int div
)
1983 return isl_bool_true
;
1986 /* Eliminate known divs from constraints where they appear with
1987 * a (positive or negative) unit coefficient.
1988 * If "progress" is not NULL, then it gets set if the elimination
1989 * results in any changes.
1991 static __isl_give isl_basic_map
*eliminate_unit_divs(
1992 __isl_take isl_basic_map
*bmap
, int *progress
)
1994 return eliminate_selected_unit_divs(bmap
, &is_any_div
, progress
);
1997 /* eliminate_selected_unit_divs callback that selects
1998 * integer divisions that only appear with
1999 * a (positive or negative) unit coefficient
2000 * (outside their div constraints).
2002 static isl_bool
is_pure_unit_div(__isl_keep isl_basic_map
*bmap
, int div
)
2005 isl_size v_div
, n_ineq
;
2007 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
2008 n_ineq
= isl_basic_map_n_inequality(bmap
);
2009 if (v_div
< 0 || n_ineq
< 0)
2010 return isl_bool_error
;
2012 for (i
= 0; i
< n_ineq
; ++i
) {
2015 if (isl_int_is_zero(bmap
->ineq
[i
][1 + v_div
+ div
]))
2017 skip
= isl_basic_map_is_div_constraint(bmap
,
2018 bmap
->ineq
[i
], div
);
2020 return isl_bool_error
;
2023 if (!isl_int_is_one(bmap
->ineq
[i
][1 + v_div
+ div
]) &&
2024 !isl_int_is_negone(bmap
->ineq
[i
][1 + v_div
+ div
]))
2025 return isl_bool_false
;
2028 return isl_bool_true
;
2031 /* Eliminate known divs from constraints where they appear with
2032 * a (positive or negative) unit coefficient,
2033 * but only if they do not appear in any other constraints
2034 * (other than the div constraints).
2036 __isl_give isl_basic_map
*isl_basic_map_eliminate_pure_unit_divs(
2037 __isl_take isl_basic_map
*bmap
)
2039 return eliminate_selected_unit_divs(bmap
, &is_pure_unit_div
, NULL
);
2042 __isl_give isl_basic_map
*isl_basic_map_simplify(__isl_take isl_basic_map
*bmap
)
2051 empty
= isl_basic_map_plain_is_empty(bmap
);
2053 return isl_basic_map_free(bmap
);
2056 bmap
= isl_basic_map_normalize_constraints(bmap
);
2057 bmap
= reduce_div_coefficients(bmap
);
2058 bmap
= normalize_div_expressions(bmap
);
2059 bmap
= remove_duplicate_divs(bmap
, &progress
);
2060 bmap
= eliminate_unit_divs(bmap
, &progress
);
2061 bmap
= eliminate_divs_eq(bmap
, &progress
);
2062 bmap
= eliminate_divs_ineq(bmap
, &progress
);
2063 bmap
= eliminate_integral_divs(bmap
, &progress
);
2064 bmap
= isl_basic_map_gauss(bmap
, &progress
);
2065 /* requires equalities in normal form */
2066 bmap
= normalize_divs(bmap
, &progress
);
2067 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
2073 __isl_give isl_basic_set
*isl_basic_set_simplify(
2074 __isl_take isl_basic_set
*bset
)
2076 return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset
)));
2080 isl_bool
isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
2081 isl_int
*constraint
, unsigned div
)
2086 return isl_bool_error
;
2088 pos
= isl_basic_map_offset(bmap
, isl_dim_div
) + div
;
2090 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
2092 isl_int_sub(bmap
->div
[div
][1],
2093 bmap
->div
[div
][1], bmap
->div
[div
][0]);
2094 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
2095 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
2096 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
2097 isl_int_add(bmap
->div
[div
][1],
2098 bmap
->div
[div
][1], bmap
->div
[div
][0]);
2100 return isl_bool_false
;
2101 if (isl_seq_first_non_zero(constraint
+pos
+1,
2102 bmap
->n_div
-div
-1) != -1)
2103 return isl_bool_false
;
2104 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
2105 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
2106 return isl_bool_false
;
2107 if (isl_seq_first_non_zero(constraint
+pos
+1,
2108 bmap
->n_div
-div
-1) != -1)
2109 return isl_bool_false
;
2111 return isl_bool_false
;
2113 return isl_bool_true
;
2116 /* If the only constraints a div d=floor(f/m)
2117 * appears in are its two defining constraints
2120 * -(f - (m - 1)) + m d >= 0
2122 * then it can safely be removed.
2124 static isl_bool
div_is_redundant(__isl_keep isl_basic_map
*bmap
, int div
)
2128 isl_size v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
2129 unsigned pos
= 1 + v_div
+ div
;
2132 return isl_bool_error
;
2134 for (i
= 0; i
< bmap
->n_eq
; ++i
)
2135 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
2136 return isl_bool_false
;
2138 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2141 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
2143 red
= isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
);
2144 if (red
< 0 || !red
)
2148 involves
= isl_basic_map_any_div_involves_vars(bmap
, v_div
+ div
, 1);
2149 if (involves
< 0 || involves
)
2150 return isl_bool_not(involves
);
2152 return isl_bool_true
;
2156 * Remove divs that don't occur in any of the constraints or other divs.
2157 * These can arise when dropping constraints from a basic map or
2158 * when the divs of a basic map have been temporarily aligned
2159 * with the divs of another basic map.
2161 static __isl_give isl_basic_map
*remove_redundant_divs(
2162 __isl_take isl_basic_map
*bmap
)
2167 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
2169 return isl_basic_map_free(bmap
);
2171 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
2174 redundant
= div_is_redundant(bmap
, i
);
2176 return isl_basic_map_free(bmap
);
2179 bmap
= isl_basic_map_drop_constraints_involving(bmap
,
2181 bmap
= isl_basic_map_drop_div(bmap
, i
);
2186 /* Mark "bmap" as final, without checking for obviously redundant
2187 * integer divisions. This function should be used when "bmap"
2188 * is known not to involve any such integer divisions.
2190 __isl_give isl_basic_map
*isl_basic_map_mark_final(
2191 __isl_take isl_basic_map
*bmap
)
2195 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
2199 /* Mark "bmap" as final, after removing obviously redundant integer divisions.
2201 __isl_give isl_basic_map
*isl_basic_map_finalize(__isl_take isl_basic_map
*bmap
)
2203 bmap
= remove_redundant_divs(bmap
);
2204 bmap
= isl_basic_map_mark_final(bmap
);
2208 __isl_give isl_basic_set
*isl_basic_set_finalize(
2209 __isl_take isl_basic_set
*bset
)
2211 return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset
)));
2214 /* Remove definition of any div that is defined in terms of the given variable.
2215 * The div itself is not removed. Functions such as
2216 * eliminate_divs_ineq depend on the other divs remaining in place.
2218 static __isl_give isl_basic_map
*remove_dependent_vars(
2219 __isl_take isl_basic_map
*bmap
, int pos
)
2226 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2227 if (isl_int_is_zero(bmap
->div
[i
][0]))
2229 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
2231 bmap
= isl_basic_map_mark_div_unknown(bmap
, i
);
2238 /* Eliminate the specified variables from the constraints using
2239 * Fourier-Motzkin. The variables themselves are not removed.
2241 __isl_give isl_basic_map
*isl_basic_map_eliminate_vars(
2242 __isl_take isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
2251 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2253 return isl_basic_map_free(bmap
);
2255 bmap
= isl_basic_map_cow(bmap
);
2256 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
2257 bmap
= remove_dependent_vars(bmap
, d
);
2261 for (d
= pos
+ n
- 1;
2262 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
2263 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
2264 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
2265 int n_lower
, n_upper
;
2268 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2269 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
2271 bmap
= eliminate_var_using_equality(bmap
, d
,
2272 bmap
->eq
[i
], 0, 1, NULL
);
2273 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
2274 return isl_basic_map_free(bmap
);
2282 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2283 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
2285 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
2288 bmap
= isl_basic_map_extend_constraints(bmap
,
2289 0, n_lower
* n_upper
);
2292 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2294 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
2297 for (j
= 0; j
< i
; ++j
) {
2298 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
2301 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
2302 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
2304 k
= isl_basic_map_alloc_inequality(bmap
);
2307 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
2309 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
2310 1+d
, 1+total
, NULL
);
2312 isl_basic_map_drop_inequality(bmap
, i
);
2315 if (n_lower
> 0 && n_upper
> 0) {
2316 bmap
= isl_basic_map_normalize_constraints(bmap
);
2317 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
2319 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2320 bmap
= isl_basic_map_remove_redundancies(bmap
);
2324 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2329 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2332 isl_basic_map_free(bmap
);
2336 __isl_give isl_basic_set
*isl_basic_set_eliminate_vars(
2337 __isl_take isl_basic_set
*bset
, unsigned pos
, unsigned n
)
2339 return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset
),
2343 /* Eliminate the specified n dimensions starting at first from the
2344 * constraints, without removing the dimensions from the space.
2345 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
2346 * Otherwise, they are projected out and the original space is restored.
2348 __isl_give isl_basic_map
*isl_basic_map_eliminate(
2349 __isl_take isl_basic_map
*bmap
,
2350 enum isl_dim_type type
, unsigned first
, unsigned n
)
2359 if (isl_basic_map_check_range(bmap
, type
, first
, n
) < 0)
2360 return isl_basic_map_free(bmap
);
2362 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
2363 first
+= isl_basic_map_offset(bmap
, type
) - 1;
2364 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
2365 return isl_basic_map_finalize(bmap
);
2368 space
= isl_basic_map_get_space(bmap
);
2369 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
2370 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
2371 bmap
= isl_basic_map_reset_space(bmap
, space
);
2375 __isl_give isl_basic_set
*isl_basic_set_eliminate(
2376 __isl_take isl_basic_set
*bset
,
2377 enum isl_dim_type type
, unsigned first
, unsigned n
)
2379 return isl_basic_map_eliminate(bset
, type
, first
, n
);
2382 /* Remove all constraints from "bmap" that reference any unknown local
2383 * variables (directly or indirectly).
2385 * Dropping all constraints on a local variable will make it redundant,
2386 * so it will get removed implicitly by
2387 * isl_basic_map_drop_constraints_involving_dims. Some other local
2388 * variables may also end up becoming redundant if they only appear
2389 * in constraints together with the unknown local variable.
2390 * Therefore, start over after calling
2391 * isl_basic_map_drop_constraints_involving_dims.
2393 __isl_give isl_basic_map
*isl_basic_map_drop_constraints_involving_unknown_divs(
2394 __isl_take isl_basic_map
*bmap
)
2400 known
= isl_basic_map_divs_known(bmap
);
2402 return isl_basic_map_free(bmap
);
2406 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2408 return isl_basic_map_free(bmap
);
2409 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
) - 1;
2411 for (i
= 0; i
< n_div
; ++i
) {
2412 known
= isl_basic_map_div_is_known(bmap
, i
);
2414 return isl_basic_map_free(bmap
);
2417 bmap
= remove_dependent_vars(bmap
, o_div
+ i
);
2418 bmap
= isl_basic_map_drop_constraints_involving_dims(bmap
,
2420 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2422 return isl_basic_map_free(bmap
);
2429 /* Remove all constraints from "bset" that reference any unknown local
2430 * variables (directly or indirectly).
2432 __isl_give isl_basic_set
*isl_basic_set_drop_constraints_involving_unknown_divs(
2433 __isl_take isl_basic_set
*bset
)
2435 isl_basic_map
*bmap
;
2437 bmap
= bset_to_bmap(bset
);
2438 bmap
= isl_basic_map_drop_constraints_involving_unknown_divs(bmap
);
2439 return bset_from_bmap(bmap
);
2442 /* Remove all constraints from "map" that reference any unknown local
2443 * variables (directly or indirectly).
2445 * Since constraints may get dropped from the basic maps,
2446 * they may no longer be disjoint from each other.
2448 __isl_give isl_map
*isl_map_drop_constraints_involving_unknown_divs(
2449 __isl_take isl_map
*map
)
2454 known
= isl_map_divs_known(map
);
2456 return isl_map_free(map
);
2460 map
= isl_map_cow(map
);
2464 for (i
= 0; i
< map
->n
; ++i
) {
2466 isl_basic_map_drop_constraints_involving_unknown_divs(
2469 return isl_map_free(map
);
2473 ISL_F_CLR(map
, ISL_MAP_DISJOINT
);
2478 /* Don't assume equalities are in order, because align_divs
2479 * may have changed the order of the divs.
2481 static void compute_elimination_index(__isl_keep isl_basic_map
*bmap
, int *elim
,
2486 for (d
= 0; d
< len
; ++d
)
2488 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2489 for (d
= len
- 1; d
>= 0; --d
) {
2490 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
2498 static void set_compute_elimination_index(__isl_keep isl_basic_set
*bset
,
2499 int *elim
, unsigned len
)
2501 compute_elimination_index(bset_to_bmap(bset
), elim
, len
);
2504 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
2505 __isl_keep isl_basic_map
*bmap
, int *elim
, unsigned total
)
2510 for (d
= total
- 1; d
>= 0; --d
) {
2511 if (isl_int_is_zero(src
[1+d
]))
2516 isl_seq_cpy(dst
, src
, 1 + total
);
2519 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
2524 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
2525 __isl_keep isl_basic_set
*bset
, int *elim
, unsigned total
)
2527 return reduced_using_equalities(dst
, src
,
2528 bset_to_bmap(bset
), elim
, total
);
2531 static __isl_give isl_basic_set
*isl_basic_set_reduce_using_equalities(
2532 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
2538 if (!bset
|| !context
)
2541 if (context
->n_eq
== 0) {
2542 isl_basic_set_free(context
);
2546 bset
= isl_basic_set_cow(bset
);
2547 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2551 elim
= isl_alloc_array(bset
->ctx
, int, dim
);
2554 set_compute_elimination_index(context
, elim
, dim
);
2555 for (i
= 0; i
< bset
->n_eq
; ++i
)
2556 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
2557 context
, elim
, dim
);
2558 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2559 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
2560 context
, elim
, dim
);
2561 isl_basic_set_free(context
);
2563 bset
= isl_basic_set_simplify(bset
);
2564 bset
= isl_basic_set_finalize(bset
);
2567 isl_basic_set_free(bset
);
2568 isl_basic_set_free(context
);
2572 /* For each inequality in "ineq" that is a shifted (more relaxed)
2573 * copy of an inequality in "context", mark the corresponding entry
2575 * If an inequality only has a non-negative constant term, then
2578 static isl_stat
mark_shifted_constraints(__isl_keep isl_mat
*ineq
,
2579 __isl_keep isl_basic_set
*context
, int *row
)
2581 struct isl_constraint_index ci
;
2582 isl_size n_ineq
, cols
;
2586 if (!ineq
|| !context
)
2587 return isl_stat_error
;
2588 if (context
->n_ineq
== 0)
2590 if (setup_constraint_index(&ci
, context
) < 0)
2591 return isl_stat_error
;
2593 n_ineq
= isl_mat_rows(ineq
);
2594 cols
= isl_mat_cols(ineq
);
2595 if (n_ineq
< 0 || cols
< 0)
2596 return isl_stat_error
;
2598 for (k
= 0; k
< n_ineq
; ++k
) {
2602 l
= isl_seq_first_non_zero(ineq
->row
[k
] + 1, total
);
2603 if (l
< 0 && isl_int_is_nonneg(ineq
->row
[k
][0])) {
2607 redundant
= constraint_index_is_redundant(&ci
, ineq
->row
[k
]);
2614 constraint_index_free(&ci
);
2617 constraint_index_free(&ci
);
2618 return isl_stat_error
;
2621 static __isl_give isl_basic_set
*remove_shifted_constraints(
2622 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*context
)
2624 struct isl_constraint_index ci
;
2627 if (!bset
|| !context
)
2630 if (context
->n_ineq
== 0)
2632 if (setup_constraint_index(&ci
, context
) < 0)
2635 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
2638 redundant
= constraint_index_is_redundant(&ci
, bset
->ineq
[k
]);
2643 bset
= isl_basic_set_cow(bset
);
2646 isl_basic_set_drop_inequality(bset
, k
);
2649 constraint_index_free(&ci
);
2652 constraint_index_free(&ci
);
2656 /* Remove constraints from "bmap" that are identical to constraints
2657 * in "context" or that are more relaxed (greater constant term).
2659 * We perform the test for shifted copies on the pure constraints
2660 * in remove_shifted_constraints.
2662 static __isl_give isl_basic_map
*isl_basic_map_remove_shifted_constraints(
2663 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
2665 isl_basic_set
*bset
, *bset_context
;
2667 if (!bmap
|| !context
)
2670 if (bmap
->n_ineq
== 0 || context
->n_ineq
== 0) {
2671 isl_basic_map_free(context
);
2675 context
= isl_basic_map_drop_constraints_involving_unknown_divs(
2677 context
= isl_basic_map_remove_unknown_divs(context
);
2679 context
= isl_basic_map_order_divs(context
);
2680 bmap
= isl_basic_map_align_divs(bmap
, context
);
2681 context
= isl_basic_map_align_divs(context
, bmap
);
2683 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
2684 bset_context
= isl_basic_map_underlying_set(context
);
2685 bset
= remove_shifted_constraints(bset
, bset_context
);
2686 isl_basic_set_free(bset_context
);
2688 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
2692 isl_basic_map_free(bmap
);
2693 isl_basic_map_free(context
);
2697 /* Does the (linear part of a) constraint "c" involve any of the "len"
2698 * "relevant" dimensions?
2700 static int is_related(isl_int
*c
, int len
, int *relevant
)
2704 for (i
= 0; i
< len
; ++i
) {
2707 if (!isl_int_is_zero(c
[i
]))
2714 /* Drop constraints from "bmap" that do not involve any of
2715 * the dimensions marked "relevant".
2717 static __isl_give isl_basic_map
*drop_unrelated_constraints(
2718 __isl_take isl_basic_map
*bmap
, int *relevant
)
2723 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
2725 return isl_basic_map_free(bmap
);
2726 for (i
= 0; i
< dim
; ++i
)
2732 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
)
2733 if (!is_related(bmap
->eq
[i
] + 1, dim
, relevant
)) {
2734 bmap
= isl_basic_map_cow(bmap
);
2735 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
2736 return isl_basic_map_free(bmap
);
2739 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
)
2740 if (!is_related(bmap
->ineq
[i
] + 1, dim
, relevant
)) {
2741 bmap
= isl_basic_map_cow(bmap
);
2742 if (isl_basic_map_drop_inequality(bmap
, i
) < 0)
2743 return isl_basic_map_free(bmap
);
2749 /* Update the groups in "group" based on the (linear part of a) constraint "c".
2751 * In particular, for any variable involved in the constraint,
2752 * find the actual group id from before and replace the group
2753 * of the corresponding variable by the minimal group of all
2754 * the variables involved in the constraint considered so far
2755 * (if this minimum is smaller) or replace the minimum by this group
2756 * (if the minimum is larger).
2758 * At the end, all the variables in "c" will (indirectly) point
2759 * to the minimal of the groups that they referred to originally.
2761 static void update_groups(int dim
, int *group
, isl_int
*c
)
2766 for (j
= 0; j
< dim
; ++j
) {
2767 if (isl_int_is_zero(c
[j
]))
2769 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
2770 group
[j
] = group
[group
[j
]];
2771 if (group
[j
] == min
)
2773 if (group
[j
] < min
) {
2774 if (min
>= 0 && min
< dim
)
2775 group
[min
] = group
[j
];
2778 group
[group
[j
]] = min
;
2782 /* Allocate an array of groups of variables, one for each variable
2783 * in "context", initialized to zero.
2785 static int *alloc_groups(__isl_keep isl_basic_set
*context
)
2790 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2793 ctx
= isl_basic_set_get_ctx(context
);
2794 return isl_calloc_array(ctx
, int, dim
);
2797 /* Drop constraints from "bmap" that only involve variables that are
2798 * not related to any of the variables marked with a "-1" in "group".
2800 * We construct groups of variables that collect variables that
2801 * (indirectly) appear in some common constraint of "bmap".
2802 * Each group is identified by the first variable in the group,
2803 * except for the special group of variables that was already identified
2804 * in the input as -1 (or are related to those variables).
2805 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
2806 * otherwise the group of i is the group of group[i].
2808 * We first initialize groups for the remaining variables.
2809 * Then we iterate over the constraints of "bmap" and update the
2810 * group of the variables in the constraint by the smallest group.
2811 * Finally, we resolve indirect references to groups by running over
2814 * After computing the groups, we drop constraints that do not involve
2815 * any variables in the -1 group.
2817 __isl_give isl_basic_map
*isl_basic_map_drop_unrelated_constraints(
2818 __isl_take isl_basic_map
*bmap
, __isl_take
int *group
)
2824 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
2826 return isl_basic_map_free(bmap
);
2829 for (i
= 0; i
< dim
; ++i
)
2831 last
= group
[i
] = i
;
2837 for (i
= 0; i
< bmap
->n_eq
; ++i
)
2838 update_groups(dim
, group
, bmap
->eq
[i
] + 1);
2839 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
2840 update_groups(dim
, group
, bmap
->ineq
[i
] + 1);
2842 for (i
= 0; i
< dim
; ++i
)
2844 group
[i
] = group
[group
[i
]];
2846 for (i
= 0; i
< dim
; ++i
)
2847 group
[i
] = group
[i
] == -1;
2849 bmap
= drop_unrelated_constraints(bmap
, group
);
2855 /* Drop constraints from "context" that are irrelevant for computing
2856 * the gist of "bset".
2858 * In particular, drop constraints in variables that are not related
2859 * to any of the variables involved in the constraints of "bset"
2860 * in the sense that there is no sequence of constraints that connects them.
2862 * We first mark all variables that appear in "bset" as belonging
2863 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2865 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
2866 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
2872 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2873 if (!context
|| dim
< 0)
2874 return isl_basic_set_free(context
);
2876 group
= alloc_groups(context
);
2879 return isl_basic_set_free(context
);
2881 for (i
= 0; i
< dim
; ++i
) {
2882 for (j
= 0; j
< bset
->n_eq
; ++j
)
2883 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
2885 if (j
< bset
->n_eq
) {
2889 for (j
= 0; j
< bset
->n_ineq
; ++j
)
2890 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
2892 if (j
< bset
->n_ineq
)
2896 return isl_basic_map_drop_unrelated_constraints(context
, group
);
2899 /* Drop constraints from "context" that are irrelevant for computing
2900 * the gist of the inequalities "ineq".
2901 * Inequalities in "ineq" for which the corresponding element of row
2902 * is set to -1 have already been marked for removal and should be ignored.
2904 * In particular, drop constraints in variables that are not related
2905 * to any of the variables involved in "ineq"
2906 * in the sense that there is no sequence of constraints that connects them.
2908 * We first mark all variables that appear in "bset" as belonging
2909 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2911 static __isl_give isl_basic_set
*drop_irrelevant_constraints_marked(
2912 __isl_take isl_basic_set
*context
, __isl_keep isl_mat
*ineq
, int *row
)
2919 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2920 n
= isl_mat_rows(ineq
);
2921 if (dim
< 0 || n
< 0)
2922 return isl_basic_set_free(context
);
2924 group
= alloc_groups(context
);
2927 return isl_basic_set_free(context
);
2929 for (i
= 0; i
< dim
; ++i
) {
2930 for (j
= 0; j
< n
; ++j
) {
2933 if (!isl_int_is_zero(ineq
->row
[j
][1 + i
]))
2940 return isl_basic_map_drop_unrelated_constraints(context
, group
);
2943 /* Do all "n" entries of "row" contain a negative value?
2945 static int all_neg(int *row
, int n
)
2949 for (i
= 0; i
< n
; ++i
)
2956 /* Update the inequalities in "bset" based on the information in "row"
2959 * In particular, the array "row" contains either -1, meaning that
2960 * the corresponding inequality of "bset" is redundant, or the index
2961 * of an inequality in "tab".
2963 * If the row entry is -1, then drop the inequality.
2964 * Otherwise, if the constraint is marked redundant in the tableau,
2965 * then drop the inequality. Similarly, if it is marked as an equality
2966 * in the tableau, then turn the inequality into an equality and
2967 * perform Gaussian elimination.
2969 static __isl_give isl_basic_set
*update_ineq(__isl_take isl_basic_set
*bset
,
2970 __isl_keep
int *row
, struct isl_tab
*tab
)
2975 int found_equality
= 0;
2979 if (tab
&& tab
->empty
)
2980 return isl_basic_set_set_to_empty(bset
);
2982 n_ineq
= bset
->n_ineq
;
2983 for (i
= n_ineq
- 1; i
>= 0; --i
) {
2985 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2986 return isl_basic_set_free(bset
);
2992 if (isl_tab_is_equality(tab
, n_eq
+ row
[i
])) {
2993 isl_basic_map_inequality_to_equality(bset
, i
);
2995 } else if (isl_tab_is_redundant(tab
, n_eq
+ row
[i
])) {
2996 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2997 return isl_basic_set_free(bset
);
3002 bset
= isl_basic_set_gauss(bset
, NULL
);
3003 bset
= isl_basic_set_finalize(bset
);
3007 /* Update the inequalities in "bset" based on the information in "row"
3008 * and "tab" and free all arguments (other than "bset").
3010 static __isl_give isl_basic_set
*update_ineq_free(
3011 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*ineq
,
3012 __isl_take isl_basic_set
*context
, __isl_take
int *row
,
3013 struct isl_tab
*tab
)
3016 isl_basic_set_free(context
);
3018 bset
= update_ineq(bset
, row
, tab
);
3025 /* Remove all information from bset that is redundant in the context
3027 * "ineq" contains the (possibly transformed) inequalities of "bset",
3028 * in the same order.
3029 * The (explicit) equalities of "bset" are assumed to have been taken
3030 * into account by the transformation such that only the inequalities
3032 * "context" is assumed not to be empty.
3034 * "row" keeps track of the constraint index of a "bset" inequality in "tab".
3035 * A value of -1 means that the inequality is obviously redundant and may
3036 * not even appear in "tab".
3038 * We first mark the inequalities of "bset"
3039 * that are obviously redundant with respect to some inequality in "context".
3040 * Then we remove those constraints from "context" that have become
3041 * irrelevant for computing the gist of "bset".
3042 * Note that this removal of constraints cannot be replaced by
3043 * a factorization because factors in "bset" may still be connected
3044 * to each other through constraints in "context".
3046 * If there are any inequalities left, we construct a tableau for
3047 * the context and then add the inequalities of "bset".
3048 * Before adding these inequalities, we freeze all constraints such that
3049 * they won't be considered redundant in terms of the constraints of "bset".
3050 * Then we detect all redundant constraints (among the
3051 * constraints that weren't frozen), first by checking for redundancy in the
3052 * the tableau and then by checking if replacing a constraint by its negation
3053 * would lead to an empty set. This last step is fairly expensive
3054 * and could be optimized by more reuse of the tableau.
3055 * Finally, we update bset according to the results.
3057 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
3058 __isl_take isl_mat
*ineq
, __isl_take isl_basic_set
*context
)
3063 isl_basic_set
*combined
= NULL
;
3064 struct isl_tab
*tab
= NULL
;
3065 unsigned n_eq
, context_ineq
;
3067 if (!bset
|| !ineq
|| !context
)
3070 if (bset
->n_ineq
== 0 || isl_basic_set_plain_is_universe(context
)) {
3071 isl_basic_set_free(context
);
3076 ctx
= isl_basic_set_get_ctx(context
);
3077 row
= isl_calloc_array(ctx
, int, bset
->n_ineq
);
3081 if (mark_shifted_constraints(ineq
, context
, row
) < 0)
3083 if (all_neg(row
, bset
->n_ineq
))
3084 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
3086 context
= drop_irrelevant_constraints_marked(context
, ineq
, row
);
3089 if (isl_basic_set_plain_is_universe(context
))
3090 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
3092 n_eq
= context
->n_eq
;
3093 context_ineq
= context
->n_ineq
;
3094 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
3095 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
3096 tab
= isl_tab_from_basic_set(combined
, 0);
3097 for (i
= 0; i
< context_ineq
; ++i
)
3098 if (isl_tab_freeze_constraint(tab
, n_eq
+ i
) < 0)
3100 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
3103 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
3106 combined
= isl_basic_set_add_ineq(combined
, ineq
->row
[i
]);
3107 if (isl_tab_add_ineq(tab
, ineq
->row
[i
]) < 0)
3111 if (isl_tab_detect_implicit_equalities(tab
) < 0)
3113 if (isl_tab_detect_redundant(tab
) < 0)
3115 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
3116 isl_basic_set
*test
;
3122 if (tab
->con
[n_eq
+ r
].is_redundant
)
3124 test
= isl_basic_set_dup(combined
);
3125 test
= isl_inequality_negate(test
, r
);
3126 test
= isl_basic_set_update_from_tab(test
, tab
);
3127 is_empty
= isl_basic_set_is_empty(test
);
3128 isl_basic_set_free(test
);
3132 tab
->con
[n_eq
+ r
].is_redundant
= 1;
3134 bset
= update_ineq_free(bset
, ineq
, context
, row
, tab
);
3136 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
3137 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
3140 isl_basic_set_free(combined
);
3146 isl_basic_set_free(combined
);
3147 isl_basic_set_free(context
);
3148 isl_basic_set_free(bset
);
3152 /* Extract the inequalities of "bset" as an isl_mat.
3154 static __isl_give isl_mat
*extract_ineq(__isl_keep isl_basic_set
*bset
)
3160 total
= isl_basic_set_dim(bset
, isl_dim_all
);
3164 ctx
= isl_basic_set_get_ctx(bset
);
3165 ineq
= isl_mat_sub_alloc6(ctx
, bset
->ineq
, 0, bset
->n_ineq
,
3171 /* Remove all information from "bset" that is redundant in the context
3172 * of "context", for the case where both "bset" and "context" are
3175 static __isl_give isl_basic_set
*uset_gist_uncompressed(
3176 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
3180 ineq
= extract_ineq(bset
);
3181 return uset_gist_full(bset
, ineq
, context
);
3184 /* Replace "bset" by an empty basic set in the same space.
3186 static __isl_give isl_basic_set
*replace_by_empty(
3187 __isl_take isl_basic_set
*bset
)
3191 space
= isl_basic_set_get_space(bset
);
3192 isl_basic_set_free(bset
);
3193 return isl_basic_set_empty(space
);
3196 /* Remove all information from "bset" that is redundant in the context
3197 * of "context", for the case where the combined equalities of
3198 * "bset" and "context" allow for a compression that can be obtained
3199 * by preapplication of "T".
3200 * If the compression of "context" is empty, meaning that "bset" and
3201 * "context" do not intersect, then return the empty set.
3203 * "bset" itself is not transformed by "T". Instead, the inequalities
3204 * are extracted from "bset" and those are transformed by "T".
3205 * uset_gist_full then determines which of the transformed inequalities
3206 * are redundant with respect to the transformed "context" and removes
3207 * the corresponding inequalities from "bset".
3209 * After preapplying "T" to the inequalities, any common factor is
3210 * removed from the coefficients. If this results in a tightening
3211 * of the constant term, then the same tightening is applied to
3212 * the corresponding untransformed inequality in "bset".
3213 * That is, if after plugging in T, a constraint f(x) >= 0 is of the form
3217 * with 0 <= r < g, then it is equivalent to
3221 * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
3222 * subspace compressed by T since the latter would be transformed to
3226 static __isl_give isl_basic_set
*uset_gist_compressed(
3227 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
,
3228 __isl_take isl_mat
*T
)
3233 isl_size n_row
, n_col
;
3236 ineq
= extract_ineq(bset
);
3237 ineq
= isl_mat_product(ineq
, isl_mat_copy(T
));
3238 context
= isl_basic_set_preimage(context
, T
);
3240 if (!ineq
|| !context
)
3242 if (isl_basic_set_plain_is_empty(context
)) {
3244 isl_basic_set_free(context
);
3245 return replace_by_empty(bset
);
3248 ctx
= isl_mat_get_ctx(ineq
);
3249 n_row
= isl_mat_rows(ineq
);
3250 n_col
= isl_mat_cols(ineq
);
3251 if (n_row
< 0 || n_col
< 0)
3254 for (i
= 0; i
< n_row
; ++i
) {
3255 isl_seq_gcd(ineq
->row
[i
] + 1, n_col
- 1, &ctx
->normalize_gcd
);
3256 if (isl_int_is_zero(ctx
->normalize_gcd
))
3258 if (isl_int_is_one(ctx
->normalize_gcd
))
3260 isl_seq_scale_down(ineq
->row
[i
] + 1, ineq
->row
[i
] + 1,
3261 ctx
->normalize_gcd
, n_col
- 1);
3262 isl_int_fdiv_r(rem
, ineq
->row
[i
][0], ctx
->normalize_gcd
);
3263 isl_int_fdiv_q(ineq
->row
[i
][0],
3264 ineq
->row
[i
][0], ctx
->normalize_gcd
);
3265 if (isl_int_is_zero(rem
))
3267 bset
= isl_basic_set_cow(bset
);
3270 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], rem
);
3274 return uset_gist_full(bset
, ineq
, context
);
3277 isl_basic_set_free(context
);
3278 isl_basic_set_free(bset
);
3282 /* Project "bset" onto the variables that are involved in "template".
3284 static __isl_give isl_basic_set
*project_onto_involved(
3285 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*template)
3290 n
= isl_basic_set_dim(template, isl_dim_set
);
3291 if (n
< 0 || !template)
3292 return isl_basic_set_free(bset
);
3294 for (i
= 0; i
< n
; ++i
) {
3297 involved
= isl_basic_set_involves_dims(template,
3300 return isl_basic_set_free(bset
);
3303 bset
= isl_basic_set_eliminate_vars(bset
, i
, 1);
3309 /* Remove all information from bset that is redundant in the context
3310 * of context. In particular, equalities that are linear combinations
3311 * of those in context are removed. Then the inequalities that are
3312 * redundant in the context of the equalities and inequalities of
3313 * context are removed.
3315 * First of all, we drop those constraints from "context"
3316 * that are irrelevant for computing the gist of "bset".
3317 * Alternatively, we could factorize the intersection of "context" and "bset".
3319 * We first compute the intersection of the integer affine hulls
3320 * of "bset" and "context",
3321 * compute the gist inside this intersection and then reduce
3322 * the constraints with respect to the equalities of the context
3323 * that only involve variables already involved in the input.
3324 * If the intersection of the affine hulls turns out to be empty,
3325 * then return the empty set.
3327 * If two constraints are mutually redundant, then uset_gist_full
3328 * will remove the second of those constraints. We therefore first
3329 * sort the constraints so that constraints not involving existentially
3330 * quantified variables are given precedence over those that do.
3331 * We have to perform this sorting before the variable compression,
3332 * because that may effect the order of the variables.
3334 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
3335 __isl_take isl_basic_set
*context
)
3340 isl_basic_set
*aff_context
;
3343 total
= isl_basic_set_dim(bset
, isl_dim_all
);
3344 if (total
< 0 || !context
)
3347 context
= drop_irrelevant_constraints(context
, bset
);
3349 bset
= isl_basic_set_detect_equalities(bset
);
3350 aff
= isl_basic_set_copy(bset
);
3351 aff
= isl_basic_set_plain_affine_hull(aff
);
3352 context
= isl_basic_set_detect_equalities(context
);
3353 aff_context
= isl_basic_set_copy(context
);
3354 aff_context
= isl_basic_set_plain_affine_hull(aff_context
);
3355 aff
= isl_basic_set_intersect(aff
, aff_context
);
3358 if (isl_basic_set_plain_is_empty(aff
)) {
3359 isl_basic_set_free(bset
);
3360 isl_basic_set_free(context
);
3363 bset
= isl_basic_set_sort_constraints(bset
);
3364 if (aff
->n_eq
== 0) {
3365 isl_basic_set_free(aff
);
3366 return uset_gist_uncompressed(bset
, context
);
3368 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
3369 eq
= isl_mat_cow(eq
);
3370 T
= isl_mat_variable_compression(eq
, NULL
);
3371 isl_basic_set_free(aff
);
3372 if (T
&& T
->n_col
== 0) {
3374 isl_basic_set_free(context
);
3375 return replace_by_empty(bset
);
3378 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
3379 aff_context
= project_onto_involved(aff_context
, bset
);
3381 bset
= uset_gist_compressed(bset
, context
, T
);
3382 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
3385 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
3386 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
3391 isl_basic_set_free(bset
);
3392 isl_basic_set_free(context
);
3396 /* Return the number of equality constraints in "bmap" that involve
3397 * local variables. This function assumes that Gaussian elimination
3398 * has been applied to the equality constraints.
3400 static int n_div_eq(__isl_keep isl_basic_map
*bmap
)
3403 isl_size total
, n_div
;
3408 if (bmap
->n_eq
== 0)
3411 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3412 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3413 if (total
< 0 || n_div
< 0)
3417 for (i
= 0; i
< bmap
->n_eq
; ++i
)
3418 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
,
3425 /* Construct a basic map in "space" defined by the equality constraints in "eq".
3426 * The constraints are assumed not to involve any local variables.
3428 static __isl_give isl_basic_map
*basic_map_from_equalities(
3429 __isl_take isl_space
*space
, __isl_take isl_mat
*eq
)
3433 isl_basic_map
*bmap
= NULL
;
3435 total
= isl_space_dim(space
, isl_dim_all
);
3436 if (total
< 0 || !eq
)
3439 if (1 + total
!= eq
->n_col
)
3440 isl_die(isl_space_get_ctx(space
), isl_error_internal
,
3441 "unexpected number of columns", goto error
);
3443 bmap
= isl_basic_map_alloc_space(isl_space_copy(space
),
3445 for (i
= 0; i
< eq
->n_row
; ++i
) {
3446 k
= isl_basic_map_alloc_equality(bmap
);
3449 isl_seq_cpy(bmap
->eq
[k
], eq
->row
[i
], eq
->n_col
);
3452 isl_space_free(space
);
3456 isl_space_free(space
);
3458 isl_basic_map_free(bmap
);
3462 /* Construct and return a variable compression based on the equality
3463 * constraints in "bmap1" and "bmap2" that do not involve the local variables.
3464 * "n1" is the number of (initial) equality constraints in "bmap1"
3465 * that do involve local variables.
3466 * "n2" is the number of (initial) equality constraints in "bmap2"
3467 * that do involve local variables.
3468 * "total" is the total number of other variables.
3469 * This function assumes that Gaussian elimination
3470 * has been applied to the equality constraints in both "bmap1" and "bmap2"
3471 * such that the equality constraints not involving local variables
3472 * are those that start at "n1" or "n2".
3474 * If either of "bmap1" and "bmap2" does not have such equality constraints,
3475 * then simply compute the compression based on the equality constraints
3476 * in the other basic map.
3477 * Otherwise, combine the equality constraints from both into a new
3478 * basic map such that Gaussian elimination can be applied to this combination
3479 * and then construct a variable compression from the resulting
3480 * equality constraints.
3482 static __isl_give isl_mat
*combined_variable_compression(
3483 __isl_keep isl_basic_map
*bmap1
, int n1
,
3484 __isl_keep isl_basic_map
*bmap2
, int n2
, int total
)
3487 isl_mat
*E1
, *E2
, *V
;
3488 isl_basic_map
*bmap
;
3490 ctx
= isl_basic_map_get_ctx(bmap1
);
3491 if (bmap1
->n_eq
== n1
) {
3492 E2
= isl_mat_sub_alloc6(ctx
, bmap2
->eq
,
3493 n2
, bmap2
->n_eq
- n2
, 0, 1 + total
);
3494 return isl_mat_variable_compression(E2
, NULL
);
3496 if (bmap2
->n_eq
== n2
) {
3497 E1
= isl_mat_sub_alloc6(ctx
, bmap1
->eq
,
3498 n1
, bmap1
->n_eq
- n1
, 0, 1 + total
);
3499 return isl_mat_variable_compression(E1
, NULL
);
3501 E1
= isl_mat_sub_alloc6(ctx
, bmap1
->eq
,
3502 n1
, bmap1
->n_eq
- n1
, 0, 1 + total
);
3503 E2
= isl_mat_sub_alloc6(ctx
, bmap2
->eq
,
3504 n2
, bmap2
->n_eq
- n2
, 0, 1 + total
);
3505 E1
= isl_mat_concat(E1
, E2
);
3506 bmap
= basic_map_from_equalities(isl_basic_map_get_space(bmap1
), E1
);
3507 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3510 E1
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
, 0, 1 + total
);
3511 V
= isl_mat_variable_compression(E1
, NULL
);
3512 isl_basic_map_free(bmap
);
3517 /* Extract the stride constraints from "bmap", compressed
3518 * with respect to both the stride constraints in "context" and
3519 * the remaining equality constraints in both "bmap" and "context".
3520 * "bmap_n_eq" is the number of (initial) stride constraints in "bmap".
3521 * "context_n_eq" is the number of (initial) stride constraints in "context".
3523 * Let x be all variables in "bmap" (and "context") other than the local
3524 * variables. First compute a variable compression
3528 * based on the non-stride equality constraints in "bmap" and "context".
3529 * Consider the stride constraints of "context",
3533 * with y the local variables and plug in the variable compression,
3536 * A(V x') + B(y) = 0
3538 * Use these constraints to compute a parameter compression on x'
3542 * Now consider the stride constraints of "bmap"
3546 * and plug in x = V*T x''.
3547 * That is, return A = [C*V*T D].
3549 static __isl_give isl_mat
*extract_compressed_stride_constraints(
3550 __isl_keep isl_basic_map
*bmap
, int bmap_n_eq
,
3551 __isl_keep isl_basic_map
*context
, int context_n_eq
)
3553 isl_size total
, n_div
;
3555 isl_mat
*A
, *B
, *T
, *V
;
3557 total
= isl_basic_map_dim(context
, isl_dim_all
);
3558 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
3559 if (total
< 0 || n_div
< 0)
3563 ctx
= isl_basic_map_get_ctx(bmap
);
3565 V
= combined_variable_compression(bmap
, bmap_n_eq
,
3566 context
, context_n_eq
, total
);
3568 A
= isl_mat_sub_alloc6(ctx
, context
->eq
, 0, context_n_eq
, 0, 1 + total
);
3569 B
= isl_mat_sub_alloc6(ctx
, context
->eq
,
3570 0, context_n_eq
, 1 + total
, n_div
);
3571 A
= isl_mat_product(A
, isl_mat_copy(V
));
3572 T
= isl_mat_parameter_compression_ext(A
, B
);
3573 T
= isl_mat_product(V
, T
);
3575 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3577 T
= isl_mat_free(T
);
3579 T
= isl_mat_diagonal(T
, isl_mat_identity(ctx
, n_div
));
3581 A
= isl_mat_sub_alloc6(ctx
, bmap
->eq
,
3582 0, bmap_n_eq
, 0, 1 + total
+ n_div
);
3583 A
= isl_mat_product(A
, T
);
3588 /* Remove the prime factors from *g that have an exponent that
3589 * is strictly smaller than the exponent in "c".
3590 * All exponents in *g are known to be smaller than or equal
3593 * That is, if *g is equal to
3595 * p_1^{e_1} p_2^{e_2} ... p_n^{e_n}
3597 * and "c" is equal to
3599 * p_1^{f_1} p_2^{f_2} ... p_n^{f_n}
3603 * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ...
3604 * p_n^{e_n * (e_n = f_n)}
3606 * If e_i = f_i, then c / *g does not have any p_i factors and therefore
3607 * neither does the gcd of *g and c / *g.
3608 * If e_i < f_i, then the gcd of *g and c / *g has a positive
3609 * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors.
3610 * Dividing *g by this gcd therefore strictly reduces the exponent
3611 * of the prime factors that need to be removed, while leaving the
3612 * other prime factors untouched.
3613 * Repeating this process until gcd(*g, c / *g) = 1 therefore
3614 * removes all undesired factors, without removing any others.
3616 static void remove_incomplete_powers(isl_int
*g
, isl_int c
)
3622 isl_int_divexact(t
, c
, *g
);
3623 isl_int_gcd(t
, t
, *g
);
3624 if (isl_int_is_one(t
))
3626 isl_int_divexact(*g
, *g
, t
);
3631 /* Reduce the "n" stride constraints in "bmap" based on a copy "A"
3632 * of the same stride constraints in a compressed space that exploits
3633 * all equalities in the context and the other equalities in "bmap".
3635 * If the stride constraints of "bmap" are of the form
3639 * then A is of the form
3643 * If any of these constraints involves only a single local variable y,
3644 * then the constraint appears as
3654 * Let g be the gcd of m and the coefficients of h.
3655 * Then, in particular, g is a divisor of the coefficients of h and
3659 * is known to be a multiple of g.
3660 * If some prime factor in m appears with the same exponent in g,
3661 * then it can be removed from m because f(x) is already known
3662 * to be a multiple of g and therefore in particular of this power
3663 * of the prime factors.
3664 * Prime factors that appear with a smaller exponent in g cannot
3665 * be removed from m.
3666 * Let g' be the divisor of g containing all prime factors that
3667 * appear with the same exponent in m and g, then
3671 * can be replaced by
3673 * f(x) + m/g' y_i' = 0
3675 * Note that (if g' != 1) this changes the explicit representation
3676 * of y_i to that of y_i', so the integer division at position i
3677 * is marked unknown and later recomputed by a call to
3678 * isl_basic_map_gauss.
3680 static __isl_give isl_basic_map
*reduce_stride_constraints(
3681 __isl_take isl_basic_map
*bmap
, int n
, __isl_keep isl_mat
*A
)
3684 isl_size total
, n_div
;
3688 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3689 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3690 if (total
< 0 || n_div
< 0 || !A
)
3691 return isl_basic_map_free(bmap
);
3695 for (i
= 0; i
< n
; ++i
) {
3698 div
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, n_div
);
3700 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
3701 "equality constraints modified unexpectedly",
3703 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
+ div
+ 1,
3704 n_div
- div
- 1) != -1)
3706 if (isl_mat_row_gcd(A
, i
, &gcd
) < 0)
3708 if (isl_int_is_one(gcd
))
3710 remove_incomplete_powers(&gcd
, bmap
->eq
[i
][1 + total
+ div
]);
3711 if (isl_int_is_one(gcd
))
3713 isl_int_divexact(bmap
->eq
[i
][1 + total
+ div
],
3714 bmap
->eq
[i
][1 + total
+ div
], gcd
);
3715 bmap
= isl_basic_map_mark_div_unknown(bmap
, div
);
3723 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3728 isl_basic_map_free(bmap
);
3732 /* Simplify the stride constraints in "bmap" based on
3733 * the remaining equality constraints in "bmap" and all equality
3734 * constraints in "context".
3735 * Only do this if both "bmap" and "context" have stride constraints.
3737 * First extract a copy of the stride constraints in "bmap" in a compressed
3738 * space exploiting all the other equality constraints and then
3739 * use this compressed copy to simplify the original stride constraints.
3741 static __isl_give isl_basic_map
*gist_strides(__isl_take isl_basic_map
*bmap
,
3742 __isl_keep isl_basic_map
*context
)
3744 int bmap_n_eq
, context_n_eq
;
3747 if (!bmap
|| !context
)
3748 return isl_basic_map_free(bmap
);
3750 bmap_n_eq
= n_div_eq(bmap
);
3751 context_n_eq
= n_div_eq(context
);
3753 if (bmap_n_eq
< 0 || context_n_eq
< 0)
3754 return isl_basic_map_free(bmap
);
3755 if (bmap_n_eq
== 0 || context_n_eq
== 0)
3758 A
= extract_compressed_stride_constraints(bmap
, bmap_n_eq
,
3759 context
, context_n_eq
);
3760 bmap
= reduce_stride_constraints(bmap
, bmap_n_eq
, A
);
3767 /* Return a basic map that has the same intersection with "context" as "bmap"
3768 * and that is as "simple" as possible.
3770 * The core computation is performed on the pure constraints.
3771 * When we add back the meaning of the integer divisions, we need
3772 * to (re)introduce the div constraints. If we happen to have
3773 * discovered that some of these integer divisions are equal to
3774 * some affine combination of other variables, then these div
3775 * constraints may end up getting simplified in terms of the equalities,
3776 * resulting in extra inequalities on the other variables that
3777 * may have been removed already or that may not even have been
3778 * part of the input. We try and remove those constraints of
3779 * this form that are most obviously redundant with respect to
3780 * the context. We also remove those div constraints that are
3781 * redundant with respect to the other constraints in the result.
3783 * The stride constraints among the equality constraints in "bmap" are
3784 * also simplified with respecting to the other equality constraints
3785 * in "bmap" and with respect to all equality constraints in "context".
3787 __isl_give isl_basic_map
*isl_basic_map_gist(__isl_take isl_basic_map
*bmap
,
3788 __isl_take isl_basic_map
*context
)
3790 isl_basic_set
*bset
, *eq
;
3791 isl_basic_map
*eq_bmap
;
3792 isl_size total
, n_div
, n_div_bmap
;
3793 unsigned extra
, n_eq
, n_ineq
;
3795 if (!bmap
|| !context
)
3798 if (isl_basic_map_plain_is_universe(bmap
)) {
3799 isl_basic_map_free(context
);
3802 if (isl_basic_map_plain_is_empty(context
)) {
3803 isl_space
*space
= isl_basic_map_get_space(bmap
);
3804 isl_basic_map_free(bmap
);
3805 isl_basic_map_free(context
);
3806 return isl_basic_map_universe(space
);
3808 if (isl_basic_map_plain_is_empty(bmap
)) {
3809 isl_basic_map_free(context
);
3813 bmap
= isl_basic_map_remove_redundancies(bmap
);
3814 context
= isl_basic_map_remove_redundancies(context
);
3815 bmap
= isl_basic_map_order_divs(bmap
);
3816 context
= isl_basic_map_align_divs(context
, bmap
);
3818 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
3819 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3820 n_div_bmap
= isl_basic_map_dim(bmap
, isl_dim_div
);
3821 if (n_div
< 0 || total
< 0 || n_div_bmap
< 0)
3823 extra
= n_div
- n_div_bmap
;
3825 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
3826 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, extra
);
3827 bset
= uset_gist(bset
,
3828 isl_basic_map_underlying_set(isl_basic_map_copy(context
)));
3829 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, total
, extra
);
3831 if (!bset
|| bset
->n_eq
== 0 || n_div
== 0 ||
3832 isl_basic_set_plain_is_empty(bset
)) {
3833 isl_basic_map_free(context
);
3834 return isl_basic_map_overlying_set(bset
, bmap
);
3838 n_ineq
= bset
->n_ineq
;
3839 eq
= isl_basic_set_copy(bset
);
3840 eq
= isl_basic_set_cow(eq
);
3841 eq
= isl_basic_set_free_inequality(eq
, n_ineq
);
3842 bset
= isl_basic_set_free_equality(bset
, n_eq
);
3844 eq_bmap
= isl_basic_map_overlying_set(eq
, isl_basic_map_copy(bmap
));
3845 eq_bmap
= gist_strides(eq_bmap
, context
);
3846 eq_bmap
= isl_basic_map_remove_shifted_constraints(eq_bmap
, context
);
3847 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
3848 bmap
= isl_basic_map_intersect(bmap
, eq_bmap
);
3849 bmap
= isl_basic_map_remove_redundancies(bmap
);
3853 isl_basic_map_free(bmap
);
3854 isl_basic_map_free(context
);
3859 * Assumes context has no implicit divs.
3861 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
3862 __isl_take isl_basic_map
*context
)
3866 if (!map
|| !context
)
3869 if (isl_basic_map_plain_is_empty(context
)) {
3870 isl_space
*space
= isl_map_get_space(map
);
3872 isl_basic_map_free(context
);
3873 return isl_map_universe(space
);
3876 context
= isl_basic_map_remove_redundancies(context
);
3877 map
= isl_map_cow(map
);
3878 if (isl_map_basic_map_check_equal_space(map
, context
) < 0)
3880 map
= isl_map_compute_divs(map
);
3883 for (i
= map
->n
- 1; i
>= 0; --i
) {
3884 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
3885 isl_basic_map_copy(context
));
3888 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
3889 isl_basic_map_free(map
->p
[i
]);
3890 if (i
!= map
->n
- 1)
3891 map
->p
[i
] = map
->p
[map
->n
- 1];
3895 isl_basic_map_free(context
);
3896 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3900 isl_basic_map_free(context
);
3904 /* Drop all inequalities from "bmap" that also appear in "context".
3905 * "context" is assumed to have only known local variables and
3906 * the initial local variables of "bmap" are assumed to be the same
3907 * as those of "context".
3908 * The constraints of both "bmap" and "context" are assumed
3909 * to have been sorted using isl_basic_map_sort_constraints.
3911 * Run through the inequality constraints of "bmap" and "context"
3913 * If a constraint of "bmap" involves variables not in "context",
3914 * then it cannot appear in "context".
3915 * If a matching constraint is found, it is removed from "bmap".
3917 static __isl_give isl_basic_map
*drop_inequalities(
3918 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_map
*context
)
3921 isl_size total
, bmap_total
;
3924 total
= isl_basic_map_dim(context
, isl_dim_all
);
3925 bmap_total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3926 if (total
< 0 || bmap_total
< 0)
3927 return isl_basic_map_free(bmap
);
3929 extra
= bmap_total
- total
;
3931 i1
= bmap
->n_ineq
- 1;
3932 i2
= context
->n_ineq
- 1;
3933 while (bmap
&& i1
>= 0 && i2
>= 0) {
3936 if (isl_seq_first_non_zero(bmap
->ineq
[i1
] + 1 + total
,
3941 cmp
= isl_basic_map_constraint_cmp(context
, bmap
->ineq
[i1
],
3951 if (isl_int_eq(bmap
->ineq
[i1
][0], context
->ineq
[i2
][0])) {
3952 bmap
= isl_basic_map_cow(bmap
);
3953 if (isl_basic_map_drop_inequality(bmap
, i1
) < 0)
3954 bmap
= isl_basic_map_free(bmap
);
3963 /* Drop all equalities from "bmap" that also appear in "context".
3964 * "context" is assumed to have only known local variables and
3965 * the initial local variables of "bmap" are assumed to be the same
3966 * as those of "context".
3968 * Run through the equality constraints of "bmap" and "context"
3970 * If a constraint of "bmap" involves variables not in "context",
3971 * then it cannot appear in "context".
3972 * If a matching constraint is found, it is removed from "bmap".
3974 static __isl_give isl_basic_map
*drop_equalities(
3975 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_map
*context
)
3978 isl_size total
, bmap_total
;
3981 total
= isl_basic_map_dim(context
, isl_dim_all
);
3982 bmap_total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3983 if (total
< 0 || bmap_total
< 0)
3984 return isl_basic_map_free(bmap
);
3986 extra
= bmap_total
- total
;
3988 i1
= bmap
->n_eq
- 1;
3989 i2
= context
->n_eq
- 1;
3991 while (bmap
&& i1
>= 0 && i2
>= 0) {
3994 if (isl_seq_first_non_zero(bmap
->eq
[i1
] + 1 + total
,
3997 last1
= isl_seq_last_non_zero(bmap
->eq
[i1
] + 1, total
);
3998 last2
= isl_seq_last_non_zero(context
->eq
[i2
] + 1, total
);
3999 if (last1
> last2
) {
4003 if (last1
< last2
) {
4007 if (isl_seq_eq(bmap
->eq
[i1
], context
->eq
[i2
], 1 + total
)) {
4008 bmap
= isl_basic_map_cow(bmap
);
4009 if (isl_basic_map_drop_equality(bmap
, i1
) < 0)
4010 bmap
= isl_basic_map_free(bmap
);
4019 /* Remove the constraints in "context" from "bmap".
4020 * "context" is assumed to have explicit representations
4021 * for all local variables.
4023 * First align the divs of "bmap" to those of "context" and
4024 * sort the constraints. Then drop all constraints from "bmap"
4025 * that appear in "context".
4027 __isl_give isl_basic_map
*isl_basic_map_plain_gist(
4028 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
4030 isl_bool done
, known
;
4032 done
= isl_basic_map_plain_is_universe(context
);
4033 if (done
== isl_bool_false
)
4034 done
= isl_basic_map_plain_is_universe(bmap
);
4035 if (done
== isl_bool_false
)
4036 done
= isl_basic_map_plain_is_empty(context
);
4037 if (done
== isl_bool_false
)
4038 done
= isl_basic_map_plain_is_empty(bmap
);
4042 isl_basic_map_free(context
);
4045 known
= isl_basic_map_divs_known(context
);
4049 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
4050 "context has unknown divs", goto error
);
4052 context
= isl_basic_map_order_divs(context
);
4053 bmap
= isl_basic_map_align_divs(bmap
, context
);
4054 bmap
= isl_basic_map_gauss(bmap
, NULL
);
4055 bmap
= isl_basic_map_sort_constraints(bmap
);
4056 context
= isl_basic_map_sort_constraints(context
);
4058 bmap
= drop_inequalities(bmap
, context
);
4059 bmap
= drop_equalities(bmap
, context
);
4061 isl_basic_map_free(context
);
4062 bmap
= isl_basic_map_finalize(bmap
);
4065 isl_basic_map_free(bmap
);
4066 isl_basic_map_free(context
);
4070 /* Replace "map" by the disjunct at position "pos" and free "context".
4072 static __isl_give isl_map
*replace_by_disjunct(__isl_take isl_map
*map
,
4073 int pos
, __isl_take isl_basic_map
*context
)
4075 isl_basic_map
*bmap
;
4077 bmap
= isl_basic_map_copy(map
->p
[pos
]);
4079 isl_basic_map_free(context
);
4080 return isl_map_from_basic_map(bmap
);
4083 /* Remove the constraints in "context" from "map".
4084 * If any of the disjuncts in the result turns out to be the universe,
4085 * then return this universe.
4086 * "context" is assumed to have explicit representations
4087 * for all local variables.
4089 __isl_give isl_map
*isl_map_plain_gist_basic_map(__isl_take isl_map
*map
,
4090 __isl_take isl_basic_map
*context
)
4093 isl_bool univ
, known
;
4095 univ
= isl_basic_map_plain_is_universe(context
);
4099 isl_basic_map_free(context
);
4102 known
= isl_basic_map_divs_known(context
);
4106 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
4107 "context has unknown divs", goto error
);
4109 map
= isl_map_cow(map
);
4112 for (i
= 0; i
< map
->n
; ++i
) {
4113 map
->p
[i
] = isl_basic_map_plain_gist(map
->p
[i
],
4114 isl_basic_map_copy(context
));
4115 univ
= isl_basic_map_plain_is_universe(map
->p
[i
]);
4118 if (univ
&& map
->n
> 1)
4119 return replace_by_disjunct(map
, i
, context
);
4122 isl_basic_map_free(context
);
4123 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
4125 ISL_F_CLR(map
, ISL_MAP_DISJOINT
);
4129 isl_basic_map_free(context
);
4133 /* Remove the constraints in "context" from "set".
4134 * If any of the disjuncts in the result turns out to be the universe,
4135 * then return this universe.
4136 * "context" is assumed to have explicit representations
4137 * for all local variables.
4139 __isl_give isl_set
*isl_set_plain_gist_basic_set(__isl_take isl_set
*set
,
4140 __isl_take isl_basic_set
*context
)
4142 return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set
),
4143 bset_to_bmap(context
)));
4146 /* Remove the constraints in "context" from "map".
4147 * If any of the disjuncts in the result turns out to be the universe,
4148 * then return this universe.
4149 * "context" is assumed to consist of a single disjunct and
4150 * to have explicit representations for all local variables.
4152 __isl_give isl_map
*isl_map_plain_gist(__isl_take isl_map
*map
,
4153 __isl_take isl_map
*context
)
4155 isl_basic_map
*hull
;
4157 hull
= isl_map_unshifted_simple_hull(context
);
4158 return isl_map_plain_gist_basic_map(map
, hull
);
4161 /* Replace "map" by a universe map in the same space and free "drop".
4163 static __isl_give isl_map
*replace_by_universe(__isl_take isl_map
*map
,
4164 __isl_take isl_map
*drop
)
4168 res
= isl_map_universe(isl_map_get_space(map
));
4174 /* Return a map that has the same intersection with "context" as "map"
4175 * and that is as "simple" as possible.
4177 * If "map" is already the universe, then we cannot make it any simpler.
4178 * Similarly, if "context" is the universe, then we cannot exploit it
4180 * If "map" and "context" are identical to each other, then we can
4181 * return the corresponding universe.
4183 * If either "map" or "context" consists of multiple disjuncts,
4184 * then check if "context" happens to be a subset of "map",
4185 * in which case all constraints can be removed.
4186 * In case of multiple disjuncts, the standard procedure
4187 * may not be able to detect that all constraints can be removed.
4189 * If none of these cases apply, we have to work a bit harder.
4190 * During this computation, we make use of a single disjunct context,
4191 * so if the original context consists of more than one disjunct
4192 * then we need to approximate the context by a single disjunct set.
4193 * Simply taking the simple hull may drop constraints that are
4194 * only implicitly available in each disjunct. We therefore also
4195 * look for constraints among those defining "map" that are valid
4196 * for the context. These can then be used to simplify away
4197 * the corresponding constraints in "map".
4199 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
4200 __isl_take isl_map
*context
)
4204 isl_size n_disjunct_map
, n_disjunct_context
;
4206 isl_basic_map
*hull
;
4208 is_universe
= isl_map_plain_is_universe(map
);
4209 if (is_universe
>= 0 && !is_universe
)
4210 is_universe
= isl_map_plain_is_universe(context
);
4211 if (is_universe
< 0)
4214 isl_map_free(context
);
4218 isl_map_align_params_bin(&map
, &context
);
4219 equal
= isl_map_plain_is_equal(map
, context
);
4223 return replace_by_universe(map
, context
);
4225 n_disjunct_map
= isl_map_n_basic_map(map
);
4226 n_disjunct_context
= isl_map_n_basic_map(context
);
4227 if (n_disjunct_map
< 0 || n_disjunct_context
< 0)
4229 if (n_disjunct_map
!= 1 || n_disjunct_context
!= 1) {
4230 subset
= isl_map_is_subset(context
, map
);
4234 return replace_by_universe(map
, context
);
4237 context
= isl_map_compute_divs(context
);
4240 if (n_disjunct_context
== 1) {
4241 hull
= isl_map_simple_hull(context
);
4246 ctx
= isl_map_get_ctx(map
);
4247 list
= isl_map_list_alloc(ctx
, 2);
4248 list
= isl_map_list_add(list
, isl_map_copy(context
));
4249 list
= isl_map_list_add(list
, isl_map_copy(map
));
4250 hull
= isl_map_unshifted_simple_hull_from_map_list(context
,
4253 return isl_map_gist_basic_map(map
, hull
);
4256 isl_map_free(context
);
4260 __isl_give isl_basic_set
*isl_basic_set_gist(__isl_take isl_basic_set
*bset
,
4261 __isl_take isl_basic_set
*context
)
4263 return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset
),
4264 bset_to_bmap(context
)));
4267 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
4268 __isl_take isl_basic_set
*context
)
4270 return set_from_map(isl_map_gist_basic_map(set_to_map(set
),
4271 bset_to_bmap(context
)));
4274 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
4275 __isl_take isl_basic_set
*context
)
4277 isl_space
*space
= isl_set_get_space(set
);
4278 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
4279 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
4280 return isl_set_gist_basic_set(set
, dom_context
);
4283 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
4284 __isl_take isl_set
*context
)
4286 return set_from_map(isl_map_gist(set_to_map(set
), set_to_map(context
)));
4289 /* Compute the gist of "bmap" with respect to the constraints "context"
4292 __isl_give isl_basic_map
*isl_basic_map_gist_domain(
4293 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*context
)
4295 isl_space
*space
= isl_basic_map_get_space(bmap
);
4296 isl_basic_map
*bmap_context
= isl_basic_map_universe(space
);
4298 bmap_context
= isl_basic_map_intersect_domain(bmap_context
, context
);
4299 return isl_basic_map_gist(bmap
, bmap_context
);
4302 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
4303 __isl_take isl_set
*context
)
4305 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
4306 map_context
= isl_map_intersect_domain(map_context
, context
);
4307 return isl_map_gist(map
, map_context
);
4310 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
4311 __isl_take isl_set
*context
)
4313 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
4314 map_context
= isl_map_intersect_range(map_context
, context
);
4315 return isl_map_gist(map
, map_context
);
4318 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
4319 __isl_take isl_set
*context
)
4321 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
4322 map_context
= isl_map_intersect_params(map_context
, context
);
4323 return isl_map_gist(map
, map_context
);
4326 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
4327 __isl_take isl_set
*context
)
4329 return isl_map_gist_params(set
, context
);
4332 /* Quick check to see if two basic maps are disjoint.
4333 * In particular, we reduce the equalities and inequalities of
4334 * one basic map in the context of the equalities of the other
4335 * basic map and check if we get a contradiction.
4337 isl_bool
isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
4338 __isl_keep isl_basic_map
*bmap2
)
4340 struct isl_vec
*v
= NULL
;
4345 if (isl_basic_map_check_equal_space(bmap1
, bmap2
) < 0)
4346 return isl_bool_error
;
4347 if (bmap1
->n_div
|| bmap2
->n_div
)
4348 return isl_bool_false
;
4349 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
4350 return isl_bool_false
;
4352 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
4354 return isl_bool_error
;
4356 return isl_bool_false
;
4357 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
4360 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
4363 compute_elimination_index(bmap1
, elim
, total
);
4364 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
4366 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
4367 bmap1
, elim
, total
);
4368 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
4369 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
4372 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
4374 reduced
= reduced_using_equalities(v
->block
.data
,
4375 bmap2
->ineq
[i
], bmap1
, elim
, total
);
4376 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
4377 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
4380 compute_elimination_index(bmap2
, elim
, total
);
4381 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
4383 reduced
= reduced_using_equalities(v
->block
.data
,
4384 bmap1
->ineq
[i
], bmap2
, elim
, total
);
4385 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
4386 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
4391 return isl_bool_false
;
4395 return isl_bool_true
;
4399 return isl_bool_error
;
4402 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
4403 __isl_keep isl_basic_set
*bset2
)
4405 return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1
),
4406 bset_to_bmap(bset2
));
4409 /* Does "test" hold for all pairs of basic maps in "map1" and "map2"?
4411 static isl_bool
all_pairs(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
,
4412 isl_bool (*test
)(__isl_keep isl_basic_map
*bmap1
,
4413 __isl_keep isl_basic_map
*bmap2
))
4418 return isl_bool_error
;
4420 for (i
= 0; i
< map1
->n
; ++i
) {
4421 for (j
= 0; j
< map2
->n
; ++j
) {
4422 isl_bool d
= test(map1
->p
[i
], map2
->p
[j
]);
4423 if (d
!= isl_bool_true
)
4428 return isl_bool_true
;
4431 /* Are "map1" and "map2" obviously disjoint, based on information
4432 * that can be derived without looking at the individual basic maps?
4434 * In particular, if one of them is empty or if they live in different spaces
4435 * (ignoring parameters), then they are clearly disjoint.
4437 static isl_bool
isl_map_plain_is_disjoint_global(__isl_keep isl_map
*map1
,
4438 __isl_keep isl_map
*map2
)
4444 return isl_bool_error
;
4446 disjoint
= isl_map_plain_is_empty(map1
);
4447 if (disjoint
< 0 || disjoint
)
4450 disjoint
= isl_map_plain_is_empty(map2
);
4451 if (disjoint
< 0 || disjoint
)
4454 match
= isl_map_tuple_is_equal(map1
, isl_dim_in
, map2
, isl_dim_in
);
4455 if (match
< 0 || !match
)
4456 return match
< 0 ? isl_bool_error
: isl_bool_true
;
4458 match
= isl_map_tuple_is_equal(map1
, isl_dim_out
, map2
, isl_dim_out
);
4459 if (match
< 0 || !match
)
4460 return match
< 0 ? isl_bool_error
: isl_bool_true
;
4462 return isl_bool_false
;
4465 /* Are "map1" and "map2" obviously disjoint?
4467 * If one of them is empty or if they live in different spaces (ignoring
4468 * parameters), then they are clearly disjoint.
4469 * This is checked by isl_map_plain_is_disjoint_global.
4471 * If they have different parameters, then we skip any further tests.
4473 * If they are obviously equal, but not obviously empty, then we will
4474 * not be able to detect if they are disjoint.
4476 * Otherwise we check if each basic map in "map1" is obviously disjoint
4477 * from each basic map in "map2".
4479 isl_bool
isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
4480 __isl_keep isl_map
*map2
)
4486 disjoint
= isl_map_plain_is_disjoint_global(map1
, map2
);
4487 if (disjoint
< 0 || disjoint
)
4490 match
= isl_map_has_equal_params(map1
, map2
);
4491 if (match
< 0 || !match
)
4492 return match
< 0 ? isl_bool_error
: isl_bool_false
;
4494 intersect
= isl_map_plain_is_equal(map1
, map2
);
4495 if (intersect
< 0 || intersect
)
4496 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
4498 return all_pairs(map1
, map2
, &isl_basic_map_plain_is_disjoint
);
4501 /* Are "map1" and "map2" disjoint?
4502 * The parameters are assumed to have been aligned.
4504 * In particular, check whether all pairs of basic maps are disjoint.
4506 static isl_bool
isl_map_is_disjoint_aligned(__isl_keep isl_map
*map1
,
4507 __isl_keep isl_map
*map2
)
4509 return all_pairs(map1
, map2
, &isl_basic_map_is_disjoint
);
4512 /* Are "map1" and "map2" disjoint?
4514 * They are disjoint if they are "obviously disjoint" or if one of them
4515 * is empty. Otherwise, they are not disjoint if one of them is universal.
4516 * If the two inputs are (obviously) equal and not empty, then they are
4518 * If none of these cases apply, then check if all pairs of basic maps
4519 * are disjoint after aligning the parameters.
4521 isl_bool
isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
4526 disjoint
= isl_map_plain_is_disjoint_global(map1
, map2
);
4527 if (disjoint
< 0 || disjoint
)
4530 disjoint
= isl_map_is_empty(map1
);
4531 if (disjoint
< 0 || disjoint
)
4534 disjoint
= isl_map_is_empty(map2
);
4535 if (disjoint
< 0 || disjoint
)
4538 intersect
= isl_map_plain_is_universe(map1
);
4539 if (intersect
< 0 || intersect
)
4540 return isl_bool_not(intersect
);
4542 intersect
= isl_map_plain_is_universe(map2
);
4543 if (intersect
< 0 || intersect
)
4544 return isl_bool_not(intersect
);
4546 intersect
= isl_map_plain_is_equal(map1
, map2
);
4547 if (intersect
< 0 || intersect
)
4548 return isl_bool_not(intersect
);
4550 return isl_map_align_params_map_map_and_test(map1
, map2
,
4551 &isl_map_is_disjoint_aligned
);
4554 /* Are "bmap1" and "bmap2" disjoint?
4556 * They are disjoint if they are "obviously disjoint" or if one of them
4557 * is empty. Otherwise, they are not disjoint if one of them is universal.
4558 * If none of these cases apply, we compute the intersection and see if
4559 * the result is empty.
4561 isl_bool
isl_basic_map_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
4562 __isl_keep isl_basic_map
*bmap2
)
4566 isl_basic_map
*test
;
4568 disjoint
= isl_basic_map_plain_is_disjoint(bmap1
, bmap2
);
4569 if (disjoint
< 0 || disjoint
)
4572 disjoint
= isl_basic_map_is_empty(bmap1
);
4573 if (disjoint
< 0 || disjoint
)
4576 disjoint
= isl_basic_map_is_empty(bmap2
);
4577 if (disjoint
< 0 || disjoint
)
4580 intersect
= isl_basic_map_plain_is_universe(bmap1
);
4581 if (intersect
< 0 || intersect
)
4582 return isl_bool_not(intersect
);
4584 intersect
= isl_basic_map_plain_is_universe(bmap2
);
4585 if (intersect
< 0 || intersect
)
4586 return isl_bool_not(intersect
);
4588 test
= isl_basic_map_intersect(isl_basic_map_copy(bmap1
),
4589 isl_basic_map_copy(bmap2
));
4590 disjoint
= isl_basic_map_is_empty(test
);
4591 isl_basic_map_free(test
);
4596 /* Are "bset1" and "bset2" disjoint?
4598 isl_bool
isl_basic_set_is_disjoint(__isl_keep isl_basic_set
*bset1
,
4599 __isl_keep isl_basic_set
*bset2
)
4601 return isl_basic_map_is_disjoint(bset1
, bset2
);
4604 isl_bool
isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
4605 __isl_keep isl_set
*set2
)
4607 return isl_map_plain_is_disjoint(set_to_map(set1
), set_to_map(set2
));
4610 /* Are "set1" and "set2" disjoint?
4612 isl_bool
isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
4614 return isl_map_is_disjoint(set1
, set2
);
4617 /* Is "v" equal to 0, 1 or -1?
4619 static int is_zero_or_one(isl_int v
)
4621 return isl_int_is_zero(v
) || isl_int_is_one(v
) || isl_int_is_negone(v
);
4624 /* Are the "n" coefficients starting at "first" of inequality constraints
4625 * "i" and "j" of "bmap" opposite to each other?
4627 static int is_opposite_part(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4630 return isl_seq_is_neg(bmap
->ineq
[i
] + first
, bmap
->ineq
[j
] + first
, n
);
4633 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4634 * apart from the constant term?
4636 static isl_bool
is_opposite(__isl_keep isl_basic_map
*bmap
, int i
, int j
)
4640 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4642 return isl_bool_error
;
4643 return is_opposite_part(bmap
, i
, j
, 1, total
);
4646 /* Check if we can combine a given div with lower bound l and upper
4647 * bound u with some other div and if so return that other div.
4648 * Otherwise, return a position beyond the integer divisions.
4649 * Return isl_size_error on error.
4651 * We first check that
4652 * - the bounds are opposites of each other (except for the constant
4654 * - the bounds do not reference any other div
4655 * - no div is defined in terms of this div
4657 * Let m be the size of the range allowed on the div by the bounds.
4658 * That is, the bounds are of the form
4660 * e <= a <= e + m - 1
4662 * with e some expression in the other variables.
4663 * We look for another div b such that no third div is defined in terms
4664 * of this second div b and such that in any constraint that contains
4665 * a (except for the given lower and upper bound), also contains b
4666 * with a coefficient that is m times that of b.
4667 * That is, all constraints (except for the lower and upper bound)
4670 * e + f (a + m b) >= 0
4672 * Furthermore, in the constraints that only contain b, the coefficient
4673 * of b should be equal to 1 or -1.
4674 * If so, we return b so that "a + m b" can be replaced by
4675 * a single div "c = a + m b".
4677 static isl_size
div_find_coalesce(__isl_keep isl_basic_map
*bmap
, int *pairs
,
4678 unsigned div
, unsigned l
, unsigned u
)
4684 isl_bool involves
, opp
;
4686 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4689 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
4691 return isl_size_error
;
4692 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + v_div
, div
) != -1)
4694 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + v_div
+ div
+ 1,
4695 n_div
- div
- 1) != -1)
4697 opp
= is_opposite(bmap
, l
, u
);
4698 if (opp
< 0 || !opp
)
4699 return opp
< 0 ? isl_size_error
: n_div
;
4701 involves
= isl_basic_map_any_div_involves_vars(bmap
, v_div
+ div
, 1);
4702 if (involves
< 0 || involves
)
4703 return involves
< 0 ? isl_size_error
: n_div
;
4705 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4706 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
4707 isl_int_sub(bmap
->ineq
[l
][0],
4708 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4709 bmap
= isl_basic_map_copy(bmap
);
4710 bmap
= isl_basic_map_set_to_empty(bmap
);
4711 isl_basic_map_free(bmap
);
4714 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
4716 for (i
= 0; i
< n_div
; ++i
) {
4721 involves
= isl_basic_map_any_div_involves_vars(bmap
,
4727 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
4729 if (j
== l
|| j
== u
)
4731 if (isl_int_is_zero(bmap
->ineq
[j
][1 + v_div
+ div
])) {
4732 if (is_zero_or_one(bmap
->ineq
[j
][1 + v_div
+ i
]))
4736 if (isl_int_is_zero(bmap
->ineq
[j
][1 + v_div
+ i
]))
4738 isl_int_mul(bmap
->ineq
[j
][1 + v_div
+ div
],
4739 bmap
->ineq
[j
][1 + v_div
+ div
],
4741 valid
= isl_int_eq(bmap
->ineq
[j
][1 + v_div
+ div
],
4742 bmap
->ineq
[j
][1 + v_div
+ i
]);
4743 isl_int_divexact(bmap
->ineq
[j
][1 + v_div
+ div
],
4744 bmap
->ineq
[j
][1 + v_div
+ div
],
4749 if (j
< bmap
->n_ineq
)
4755 error
: coalesce
= isl_size_error
;
4756 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
4757 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4761 /* Internal data structure used during the construction and/or evaluation of
4762 * an inequality that ensures that a pair of bounds always allows
4763 * for an integer value.
4765 * "tab" is the tableau in which the inequality is evaluated. It may
4766 * be NULL until it is actually needed.
4767 * "v" contains the inequality coefficients.
4768 * "g", "fl" and "fu" are temporary scalars used during the construction and
4771 struct test_ineq_data
{
4772 struct isl_tab
*tab
;
4779 /* Free all the memory allocated by the fields of "data".
4781 static void test_ineq_data_clear(struct test_ineq_data
*data
)
4783 isl_tab_free(data
->tab
);
4784 isl_vec_free(data
->v
);
4785 isl_int_clear(data
->g
);
4786 isl_int_clear(data
->fl
);
4787 isl_int_clear(data
->fu
);
4790 /* Is the inequality stored in data->v satisfied by "bmap"?
4791 * That is, does it only attain non-negative values?
4792 * data->tab is a tableau corresponding to "bmap".
4794 static isl_bool
test_ineq_is_satisfied(__isl_keep isl_basic_map
*bmap
,
4795 struct test_ineq_data
*data
)
4798 enum isl_lp_result res
;
4800 ctx
= isl_basic_map_get_ctx(bmap
);
4802 data
->tab
= isl_tab_from_basic_map(bmap
, 0);
4803 res
= isl_tab_min(data
->tab
, data
->v
->el
, ctx
->one
, &data
->g
, NULL
, 0);
4804 if (res
== isl_lp_error
)
4805 return isl_bool_error
;
4806 return res
== isl_lp_ok
&& isl_int_is_nonneg(data
->g
);
4809 /* Given a lower and an upper bound on div i, do they always allow
4810 * for an integer value of the given div?
4811 * Determine this property by constructing an inequality
4812 * such that the property is guaranteed when the inequality is nonnegative.
4813 * The lower bound is inequality l, while the upper bound is inequality u.
4814 * The constructed inequality is stored in data->v.
4816 * Let the upper bound be
4820 * and the lower bound
4824 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
4827 * - f_u e_l <= f_u f_l g a <= f_l e_u
4829 * Since all variables are integer valued, this is equivalent to
4831 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
4833 * If this interval is at least f_u f_l g, then it contains at least
4834 * one integer value for a.
4835 * That is, the test constraint is
4837 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
4841 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0
4843 * If the coefficients of f_l e_u + f_u e_l have a common divisor g',
4844 * then the constraint can be scaled down by a factor g',
4845 * with the constant term replaced by
4846 * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g').
4847 * Note that the result of applying Fourier-Motzkin to this pair
4850 * f_l e_u + f_u e_l >= 0
4852 * If the constant term of the scaled down version of this constraint,
4853 * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant
4854 * term of the scaled down test constraint, then the test constraint
4855 * is known to hold and no explicit evaluation is required.
4856 * This is essentially the Omega test.
4858 * If the test constraint consists of only a constant term, then
4859 * it is sufficient to look at the sign of this constant term.
4861 static isl_bool
int_between_bounds(__isl_keep isl_basic_map
*bmap
, int i
,
4862 int l
, int u
, struct test_ineq_data
*data
)
4867 offset
= isl_basic_map_offset(bmap
, isl_dim_div
);
4868 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4870 return isl_bool_error
;
4872 isl_int_gcd(data
->g
,
4873 bmap
->ineq
[l
][offset
+ i
], bmap
->ineq
[u
][offset
+ i
]);
4874 isl_int_divexact(data
->fl
, bmap
->ineq
[l
][offset
+ i
], data
->g
);
4875 isl_int_divexact(data
->fu
, bmap
->ineq
[u
][offset
+ i
], data
->g
);
4876 isl_int_neg(data
->fu
, data
->fu
);
4877 isl_seq_combine(data
->v
->el
, data
->fl
, bmap
->ineq
[u
],
4878 data
->fu
, bmap
->ineq
[l
], offset
+ n_div
);
4879 isl_int_mul(data
->g
, data
->g
, data
->fl
);
4880 isl_int_mul(data
->g
, data
->g
, data
->fu
);
4881 isl_int_sub(data
->g
, data
->g
, data
->fl
);
4882 isl_int_sub(data
->g
, data
->g
, data
->fu
);
4883 isl_int_add_ui(data
->g
, data
->g
, 1);
4884 isl_int_sub(data
->fl
, data
->v
->el
[0], data
->g
);
4886 isl_seq_gcd(data
->v
->el
+ 1, offset
- 1 + n_div
, &data
->g
);
4887 if (isl_int_is_zero(data
->g
))
4888 return isl_int_is_nonneg(data
->fl
);
4889 if (isl_int_is_one(data
->g
)) {
4890 isl_int_set(data
->v
->el
[0], data
->fl
);
4891 return test_ineq_is_satisfied(bmap
, data
);
4893 isl_int_fdiv_q(data
->fl
, data
->fl
, data
->g
);
4894 isl_int_fdiv_q(data
->v
->el
[0], data
->v
->el
[0], data
->g
);
4895 if (isl_int_eq(data
->fl
, data
->v
->el
[0]))
4896 return isl_bool_true
;
4897 isl_int_set(data
->v
->el
[0], data
->fl
);
4898 isl_seq_scale_down(data
->v
->el
+ 1, data
->v
->el
+ 1, data
->g
,
4899 offset
- 1 + n_div
);
4901 return test_ineq_is_satisfied(bmap
, data
);
4904 /* Remove more kinds of divs that are not strictly needed.
4905 * In particular, if all pairs of lower and upper bounds on a div
4906 * are such that they allow at least one integer value of the div,
4907 * then we can eliminate the div using Fourier-Motzkin without
4908 * introducing any spurious solutions.
4910 * If at least one of the two constraints has a unit coefficient for the div,
4911 * then the presence of such a value is guaranteed so there is no need to check.
4912 * In particular, the value attained by the bound with unit coefficient
4913 * can serve as this intermediate value.
4915 static __isl_give isl_basic_map
*drop_more_redundant_divs(
4916 __isl_take isl_basic_map
*bmap
, __isl_take
int *pairs
, int n
)
4919 struct test_ineq_data data
= { NULL
, NULL
};
4924 isl_int_init(data
.g
);
4925 isl_int_init(data
.fl
);
4926 isl_int_init(data
.fu
);
4928 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4932 ctx
= isl_basic_map_get_ctx(bmap
);
4933 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
4934 data
.v
= isl_vec_alloc(ctx
, off
+ n_div
);
4943 for (i
= 0; i
< n_div
; ++i
) {
4946 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
4952 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
4953 if (!isl_int_is_pos(bmap
->ineq
[l
][off
+ i
]))
4955 if (isl_int_is_one(bmap
->ineq
[l
][off
+ i
]))
4957 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
4958 if (!isl_int_is_neg(bmap
->ineq
[u
][off
+ i
]))
4960 if (isl_int_is_negone(bmap
->ineq
[u
][off
+ i
]))
4962 has_int
= int_between_bounds(bmap
, i
, l
, u
,
4966 if (data
.tab
&& data
.tab
->empty
)
4971 if (u
< bmap
->n_ineq
)
4974 if (data
.tab
&& data
.tab
->empty
) {
4975 bmap
= isl_basic_map_set_to_empty(bmap
);
4978 if (l
== bmap
->n_ineq
) {
4986 test_ineq_data_clear(&data
);
4993 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
4994 return isl_basic_map_drop_redundant_divs(bmap
);
4997 isl_basic_map_free(bmap
);
4998 test_ineq_data_clear(&data
);
5002 /* Given a pair of divs div1 and div2 such that, except for the lower bound l
5003 * and the upper bound u, div1 always occurs together with div2 in the form
5004 * (div1 + m div2), where m is the constant range on the variable div1
5005 * allowed by l and u, replace the pair div1 and div2 by a single
5006 * div that is equal to div1 + m div2.
5008 * The new div will appear in the location that contains div2.
5009 * We need to modify all constraints that contain
5010 * div2 = (div - div1) / m
5011 * The coefficient of div2 is known to be equal to 1 or -1.
5012 * (If a constraint does not contain div2, it will also not contain div1.)
5013 * If the constraint also contains div1, then we know they appear
5014 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
5015 * i.e., the coefficient of div is f.
5017 * Otherwise, we first need to introduce div1 into the constraint.
5026 * A lower bound on div2
5030 * can be replaced by
5032 * m div2 + div1 + m t + f >= 0
5038 * can be replaced by
5040 * -(m div2 + div1) + m t + f' >= 0
5042 * These constraint are those that we would obtain from eliminating
5043 * div1 using Fourier-Motzkin.
5045 * After all constraints have been modified, we drop the lower and upper
5046 * bound and then drop div1.
5047 * Since the new div is only placed in the same location that used
5048 * to store div2, but otherwise has a different meaning, any possible
5049 * explicit representation of the original div2 is removed.
5051 static __isl_give isl_basic_map
*coalesce_divs(__isl_take isl_basic_map
*bmap
,
5052 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
5060 ctx
= isl_basic_map_get_ctx(bmap
);
5062 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
5064 return isl_basic_map_free(bmap
);
5065 total
= 1 + v_div
+ bmap
->n_div
;
5068 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
5069 isl_int_add_ui(m
, m
, 1);
5071 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
5072 if (i
== l
|| i
== u
)
5074 if (isl_int_is_zero(bmap
->ineq
[i
][1 + v_div
+ div2
]))
5076 if (isl_int_is_zero(bmap
->ineq
[i
][1 + v_div
+ div1
])) {
5077 if (isl_int_is_pos(bmap
->ineq
[i
][1 + v_div
+ div2
]))
5078 isl_seq_combine(bmap
->ineq
[i
], m
, bmap
->ineq
[i
],
5079 ctx
->one
, bmap
->ineq
[l
], total
);
5081 isl_seq_combine(bmap
->ineq
[i
], m
, bmap
->ineq
[i
],
5082 ctx
->one
, bmap
->ineq
[u
], total
);
5084 isl_int_set(bmap
->ineq
[i
][1 + v_div
+ div2
],
5085 bmap
->ineq
[i
][1 + v_div
+ div1
]);
5086 isl_int_set_si(bmap
->ineq
[i
][1 + v_div
+ div1
], 0);
5091 isl_basic_map_drop_inequality(bmap
, l
);
5092 isl_basic_map_drop_inequality(bmap
, u
);
5094 isl_basic_map_drop_inequality(bmap
, u
);
5095 isl_basic_map_drop_inequality(bmap
, l
);
5097 bmap
= isl_basic_map_mark_div_unknown(bmap
, div2
);
5098 bmap
= isl_basic_map_drop_div(bmap
, div1
);
5102 /* First check if we can coalesce any pair of divs and
5103 * then continue with dropping more redundant divs.
5105 * We loop over all pairs of lower and upper bounds on a div
5106 * with coefficient 1 and -1, respectively, check if there
5107 * is any other div "c" with which we can coalesce the div
5108 * and if so, perform the coalescing.
5110 static __isl_give isl_basic_map
*coalesce_or_drop_more_redundant_divs(
5111 __isl_take isl_basic_map
*bmap
, int *pairs
, int n
)
5117 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
5118 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
5119 if (v_div
< 0 || n_div
< 0)
5120 return isl_basic_map_free(bmap
);
5122 for (i
= 0; i
< n_div
; ++i
) {
5125 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
5126 if (!isl_int_is_one(bmap
->ineq
[l
][1 + v_div
+ i
]))
5128 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
5131 if (!isl_int_is_negone(bmap
->ineq
[u
][1+v_div
+i
]))
5133 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
5139 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
5140 return isl_basic_map_drop_redundant_divs(bmap
);
5145 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
5150 return drop_more_redundant_divs(bmap
, pairs
, n
);
5153 isl_basic_map_free(bmap
);
5157 /* Are the "n" coefficients starting at "first" of inequality constraints
5158 * "i" and "j" of "bmap" equal to each other?
5160 static int is_parallel_part(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
5163 return isl_seq_eq(bmap
->ineq
[i
] + first
, bmap
->ineq
[j
] + first
, n
);
5166 /* Are inequality constraints "i" and "j" of "bmap" equal to each other,
5167 * apart from the constant term and the coefficient at position "pos"?
5169 static isl_bool
is_parallel_except(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
5174 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5176 return isl_bool_error
;
5177 return is_parallel_part(bmap
, i
, j
, 1, pos
- 1) &&
5178 is_parallel_part(bmap
, i
, j
, pos
+ 1, total
- pos
);
5181 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
5182 * apart from the constant term and the coefficient at position "pos"?
5184 static isl_bool
is_opposite_except(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
5189 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5191 return isl_bool_error
;
5192 return is_opposite_part(bmap
, i
, j
, 1, pos
- 1) &&
5193 is_opposite_part(bmap
, i
, j
, pos
+ 1, total
- pos
);
5196 /* Restart isl_basic_map_drop_redundant_divs after "bmap" has
5197 * been modified, simplying it if "simplify" is set.
5198 * Free the temporary data structure "pairs" that was associated
5199 * to the old version of "bmap".
5201 static __isl_give isl_basic_map
*drop_redundant_divs_again(
5202 __isl_take isl_basic_map
*bmap
, __isl_take
int *pairs
, int simplify
)
5205 bmap
= isl_basic_map_simplify(bmap
);
5207 return isl_basic_map_drop_redundant_divs(bmap
);
5210 /* Is "div" the single unknown existentially quantified variable
5211 * in inequality constraint "ineq" of "bmap"?
5212 * "div" is known to have a non-zero coefficient in "ineq".
5214 static isl_bool
single_unknown(__isl_keep isl_basic_map
*bmap
, int ineq
,
5222 known
= isl_basic_map_div_is_known(bmap
, div
);
5223 if (known
< 0 || known
)
5224 return isl_bool_not(known
);
5225 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
5227 return isl_bool_error
;
5229 return isl_bool_true
;
5230 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
5231 for (i
= 0; i
< n_div
; ++i
) {
5236 if (isl_int_is_zero(bmap
->ineq
[ineq
][o_div
+ i
]))
5238 known
= isl_basic_map_div_is_known(bmap
, i
);
5239 if (known
< 0 || !known
)
5243 return isl_bool_true
;
5246 /* Does integer division "div" have coefficient 1 in inequality constraint
5249 static isl_bool
has_coef_one(__isl_keep isl_basic_map
*bmap
, int div
, int ineq
)
5253 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
5254 if (isl_int_is_one(bmap
->ineq
[ineq
][o_div
+ div
]))
5255 return isl_bool_true
;
5257 return isl_bool_false
;
5260 /* Turn inequality constraint "ineq" of "bmap" into an equality and
5261 * then try and drop redundant divs again,
5262 * freeing the temporary data structure "pairs" that was associated
5263 * to the old version of "bmap".
5265 static __isl_give isl_basic_map
*set_eq_and_try_again(
5266 __isl_take isl_basic_map
*bmap
, int ineq
, __isl_take
int *pairs
)
5268 bmap
= isl_basic_map_cow(bmap
);
5269 isl_basic_map_inequality_to_equality(bmap
, ineq
);
5270 return drop_redundant_divs_again(bmap
, pairs
, 1);
5273 /* Drop the integer division at position "div", along with the two
5274 * inequality constraints "ineq1" and "ineq2" in which it appears
5275 * from "bmap" and then try and drop redundant divs again,
5276 * freeing the temporary data structure "pairs" that was associated
5277 * to the old version of "bmap".
5279 static __isl_give isl_basic_map
*drop_div_and_try_again(
5280 __isl_take isl_basic_map
*bmap
, int div
, int ineq1
, int ineq2
,
5281 __isl_take
int *pairs
)
5283 if (ineq1
> ineq2
) {
5284 isl_basic_map_drop_inequality(bmap
, ineq1
);
5285 isl_basic_map_drop_inequality(bmap
, ineq2
);
5287 isl_basic_map_drop_inequality(bmap
, ineq2
);
5288 isl_basic_map_drop_inequality(bmap
, ineq1
);
5290 bmap
= isl_basic_map_drop_div(bmap
, div
);
5291 return drop_redundant_divs_again(bmap
, pairs
, 0);
5294 /* Given two inequality constraints
5296 * f(x) + n d + c >= 0, (ineq)
5298 * with d the variable at position "pos", and
5300 * f(x) + c0 >= 0, (lower)
5302 * compute the maximal value of the lower bound ceil((-f(x) - c)/n)
5303 * determined by the first constraint.
5310 static void lower_bound_from_parallel(__isl_keep isl_basic_map
*bmap
,
5311 int ineq
, int lower
, int pos
, isl_int
*l
)
5313 isl_int_neg(*l
, bmap
->ineq
[ineq
][0]);
5314 isl_int_add(*l
, *l
, bmap
->ineq
[lower
][0]);
5315 isl_int_cdiv_q(*l
, *l
, bmap
->ineq
[ineq
][pos
]);
5318 /* Given two inequality constraints
5320 * f(x) + n d + c >= 0, (ineq)
5322 * with d the variable at position "pos", and
5324 * -f(x) - c0 >= 0, (upper)
5326 * compute the minimal value of the lower bound ceil((-f(x) - c)/n)
5327 * determined by the first constraint.
5334 static void lower_bound_from_opposite(__isl_keep isl_basic_map
*bmap
,
5335 int ineq
, int upper
, int pos
, isl_int
*u
)
5337 isl_int_neg(*u
, bmap
->ineq
[ineq
][0]);
5338 isl_int_sub(*u
, *u
, bmap
->ineq
[upper
][0]);
5339 isl_int_cdiv_q(*u
, *u
, bmap
->ineq
[ineq
][pos
]);
5342 /* Given a lower bound constraint "ineq" on "div" in "bmap",
5343 * does the corresponding lower bound have a fixed value in "bmap"?
5345 * In particular, "ineq" is of the form
5347 * f(x) + n d + c >= 0
5349 * with n > 0, c the constant term and
5350 * d the existentially quantified variable "div".
5351 * That is, the lower bound is
5353 * ceil((-f(x) - c)/n)
5355 * Look for a pair of constraints
5360 * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value.
5361 * That is, check that
5363 * ceil((-c1 - c)/n) = ceil((c0 - c)/n)
5365 * If so, return the index of inequality f(x) + c0 >= 0.
5366 * Otherwise, return bmap->n_ineq.
5367 * Return -1 on error.
5369 static int lower_bound_is_cst(__isl_keep isl_basic_map
*bmap
, int div
, int ineq
)
5372 int lower
= -1, upper
= -1;
5377 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
5378 for (i
= 0; i
< bmap
->n_ineq
&& (lower
< 0 || upper
< 0); ++i
) {
5383 if (!isl_int_is_zero(bmap
->ineq
[i
][o_div
+ div
]))
5385 par
= isl_bool_false
;
5387 par
= is_parallel_except(bmap
, ineq
, i
, o_div
+ div
);
5394 opp
= isl_bool_false
;
5396 opp
= is_opposite_except(bmap
, ineq
, i
, o_div
+ div
);
5403 if (lower
< 0 || upper
< 0)
5404 return bmap
->n_ineq
;
5409 lower_bound_from_parallel(bmap
, ineq
, lower
, o_div
+ div
, &l
);
5410 lower_bound_from_opposite(bmap
, ineq
, upper
, o_div
+ div
, &u
);
5412 equal
= isl_int_eq(l
, u
);
5417 return equal
? lower
: bmap
->n_ineq
;
5420 /* Given a lower bound constraint "ineq" on the existentially quantified
5421 * variable "div", such that the corresponding lower bound has
5422 * a fixed value in "bmap", assign this fixed value to the variable and
5423 * then try and drop redundant divs again,
5424 * freeing the temporary data structure "pairs" that was associated
5425 * to the old version of "bmap".
5426 * "lower" determines the constant value for the lower bound.
5428 * In particular, "ineq" is of the form
5430 * f(x) + n d + c >= 0,
5432 * while "lower" is of the form
5436 * The lower bound is ceil((-f(x) - c)/n) and its constant value
5437 * is ceil((c0 - c)/n).
5439 static __isl_give isl_basic_map
*fix_cst_lower(__isl_take isl_basic_map
*bmap
,
5440 int div
, int ineq
, int lower
, int *pairs
)
5447 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
5448 lower_bound_from_parallel(bmap
, ineq
, lower
, o_div
+ div
, &c
);
5449 bmap
= isl_basic_map_fix(bmap
, isl_dim_div
, div
, c
);
5454 return isl_basic_map_drop_redundant_divs(bmap
);
5457 /* Do any of the integer divisions of "bmap" involve integer division "div"?
5459 * The integer division "div" could only ever appear in any later
5460 * integer division (with an explicit representation).
5462 static isl_bool
any_div_involves_div(__isl_keep isl_basic_map
*bmap
, int div
)
5465 isl_size v_div
, n_div
;
5467 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
5468 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
5469 if (v_div
< 0 || n_div
< 0)
5470 return isl_bool_error
;
5472 for (i
= div
+ 1; i
< n_div
; ++i
) {
5475 involves
= isl_basic_map_div_expr_involves_vars(bmap
, i
,
5477 if (involves
< 0 || involves
)
5481 return isl_bool_false
;
5484 /* Remove divs that are not strictly needed based on the inequality
5486 * In particular, if a div only occurs positively (or negatively)
5487 * in constraints, then it can simply be dropped.
5488 * Also, if a div occurs in only two constraints and if moreover
5489 * those two constraints are opposite to each other, except for the constant
5490 * term and if the sum of the constant terms is such that for any value
5491 * of the other values, there is always at least one integer value of the
5492 * div, i.e., if one plus this sum is greater than or equal to
5493 * the (absolute value) of the coefficient of the div in the constraints,
5494 * then we can also simply drop the div.
5496 * If an existentially quantified variable does not have an explicit
5497 * representation, appears in only a single lower bound that does not
5498 * involve any other such existentially quantified variables and appears
5499 * in this lower bound with coefficient 1,
5500 * then fix the variable to the value of the lower bound. That is,
5501 * turn the inequality into an equality.
5502 * If for any value of the other variables, there is any value
5503 * for the existentially quantified variable satisfying the constraints,
5504 * then this lower bound also satisfies the constraints.
5505 * It is therefore safe to pick this lower bound.
5507 * The same reasoning holds even if the coefficient is not one.
5508 * However, fixing the variable to the value of the lower bound may
5509 * in general introduce an extra integer division, in which case
5510 * it may be better to pick another value.
5511 * If this integer division has a known constant value, then plugging
5512 * in this constant value removes the existentially quantified variable
5513 * completely. In particular, if the lower bound is of the form
5514 * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and
5515 * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n),
5516 * then the existentially quantified variable can be assigned this
5519 * We skip divs that appear in equalities or in the definition of other divs.
5520 * Divs that appear in the definition of other divs usually occur in at least
5521 * 4 constraints, but the constraints may have been simplified.
5523 * If any divs are left after these simple checks then we move on
5524 * to more complicated cases in drop_more_redundant_divs.
5526 static __isl_give isl_basic_map
*isl_basic_map_drop_redundant_divs_ineq(
5527 __isl_take isl_basic_map
*bmap
)
5537 if (bmap
->n_div
== 0)
5540 off
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
5542 return isl_basic_map_free(bmap
);
5543 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
5547 n_ineq
= isl_basic_map_n_inequality(bmap
);
5550 for (i
= 0; i
< bmap
->n_div
; ++i
) {
5552 int last_pos
, last_neg
;
5555 isl_bool involves
, opp
, set_div
;
5557 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
5558 involves
= any_div_involves_div(bmap
, i
);
5563 for (j
= 0; j
< bmap
->n_eq
; ++j
)
5564 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
5570 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
5571 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
5575 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
5580 pairs
[i
] = pos
* neg
;
5581 if (pairs
[i
] == 0) {
5582 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
5583 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
5584 isl_basic_map_drop_inequality(bmap
, j
);
5585 bmap
= isl_basic_map_drop_div(bmap
, i
);
5586 return drop_redundant_divs_again(bmap
, pairs
, 0);
5589 opp
= isl_bool_false
;
5591 opp
= is_opposite(bmap
, last_pos
, last_neg
);
5596 isl_bool single
, one
;
5600 single
= single_unknown(bmap
, last_pos
, i
);
5605 one
= has_coef_one(bmap
, i
, last_pos
);
5609 return set_eq_and_try_again(bmap
, last_pos
,
5611 lower
= lower_bound_is_cst(bmap
, i
, last_pos
);
5615 return fix_cst_lower(bmap
, i
, last_pos
, lower
,
5620 isl_int_add(bmap
->ineq
[last_pos
][0],
5621 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
5622 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
5623 bmap
->ineq
[last_pos
][0], 1);
5624 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
5625 bmap
->ineq
[last_pos
][1+off
+i
]);
5626 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
5627 bmap
->ineq
[last_pos
][0], 1);
5628 isl_int_sub(bmap
->ineq
[last_pos
][0],
5629 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
5631 return drop_div_and_try_again(bmap
, i
,
5632 last_pos
, last_neg
, pairs
);
5634 set_div
= isl_bool_false
;
5636 set_div
= ok_to_set_div_from_bound(bmap
, i
, last_pos
);
5638 return isl_basic_map_free(bmap
);
5640 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
5641 return drop_redundant_divs_again(bmap
, pairs
, 1);
5648 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
5654 isl_basic_map_free(bmap
);
5658 /* Consider the coefficients at "c" as a row vector and replace
5659 * them with their product with "T". "T" is assumed to be a square matrix.
5661 static isl_stat
preimage(isl_int
*c
, __isl_keep isl_mat
*T
)
5667 n
= isl_mat_rows(T
);
5669 return isl_stat_error
;
5670 if (isl_seq_first_non_zero(c
, n
) == -1)
5672 ctx
= isl_mat_get_ctx(T
);
5673 v
= isl_vec_alloc(ctx
, n
);
5675 return isl_stat_error
;
5676 isl_seq_swp_or_cpy(v
->el
, c
, n
);
5677 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
5679 return isl_stat_error
;
5680 isl_seq_swp_or_cpy(c
, v
->el
, n
);
5686 /* Plug in T for the variables in "bmap" starting at "pos".
5687 * T is a linear unimodular matrix, i.e., without constant term.
5689 static __isl_give isl_basic_map
*isl_basic_map_preimage_vars(
5690 __isl_take isl_basic_map
*bmap
, unsigned pos
, __isl_take isl_mat
*T
)
5693 isl_size n_row
, n_col
;
5695 bmap
= isl_basic_map_cow(bmap
);
5696 n_row
= isl_mat_rows(T
);
5697 n_col
= isl_mat_cols(T
);
5698 if (!bmap
|| n_row
< 0 || n_col
< 0)
5702 isl_die(isl_mat_get_ctx(T
), isl_error_invalid
,
5703 "expecting square matrix", goto error
);
5705 if (isl_basic_map_check_range(bmap
, isl_dim_all
, pos
, n_col
) < 0)
5708 for (i
= 0; i
< bmap
->n_eq
; ++i
)
5709 if (preimage(bmap
->eq
[i
] + 1 + pos
, T
) < 0)
5711 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
5712 if (preimage(bmap
->ineq
[i
] + 1 + pos
, T
) < 0)
5714 for (i
= 0; i
< bmap
->n_div
; ++i
) {
5715 if (isl_basic_map_div_is_marked_unknown(bmap
, i
))
5717 if (preimage(bmap
->div
[i
] + 1 + 1 + pos
, T
) < 0)
5724 isl_basic_map_free(bmap
);
5729 /* Remove divs that are not strictly needed.
5731 * First look for an equality constraint involving two or more
5732 * existentially quantified variables without an explicit
5733 * representation. Replace the combination that appears
5734 * in the equality constraint by a single existentially quantified
5735 * variable such that the equality can be used to derive
5736 * an explicit representation for the variable.
5737 * If there are no more such equality constraints, then continue
5738 * with isl_basic_map_drop_redundant_divs_ineq.
5740 * In particular, if the equality constraint is of the form
5742 * f(x) + \sum_i c_i a_i = 0
5744 * with a_i existentially quantified variable without explicit
5745 * representation, then apply a transformation on the existentially
5746 * quantified variables to turn the constraint into
5750 * with g the gcd of the c_i.
5751 * In order to easily identify which existentially quantified variables
5752 * have a complete explicit representation, i.e., without being defined
5753 * in terms of other existentially quantified variables without
5754 * an explicit representation, the existentially quantified variables
5757 * The variable transformation is computed by extending the row
5758 * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation
5760 * [a_1'] [c_1/g ... c_n/g] [ a_1 ]
5765 * with [c_1/g ... c_n/g] representing the first row of U.
5766 * The inverse of U is then plugged into the original constraints.
5767 * The call to isl_basic_map_simplify makes sure the explicit
5768 * representation for a_1' is extracted from the equality constraint.
5770 __isl_give isl_basic_map
*isl_basic_map_drop_redundant_divs(
5771 __isl_take isl_basic_map
*bmap
)
5783 if (isl_basic_map_divs_known(bmap
))
5784 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5785 if (bmap
->n_eq
== 0)
5786 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5787 bmap
= isl_basic_map_sort_divs(bmap
);
5791 first
= isl_basic_map_first_unknown_div(bmap
);
5793 return isl_basic_map_free(bmap
);
5795 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
5796 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
5798 return isl_basic_map_free(bmap
);
5800 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5801 l
= isl_seq_first_non_zero(bmap
->eq
[i
] + o_div
+ first
,
5806 if (isl_seq_first_non_zero(bmap
->eq
[i
] + o_div
+ l
+ 1,
5807 n_div
- (l
+ 1)) == -1)
5811 if (i
>= bmap
->n_eq
)
5812 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5814 ctx
= isl_basic_map_get_ctx(bmap
);
5815 T
= isl_mat_alloc(ctx
, n_div
- l
, n_div
- l
);
5817 return isl_basic_map_free(bmap
);
5818 isl_seq_cpy(T
->row
[0], bmap
->eq
[i
] + o_div
+ l
, n_div
- l
);
5819 T
= isl_mat_normalize_row(T
, 0);
5820 T
= isl_mat_unimodular_complete(T
, 1);
5821 T
= isl_mat_right_inverse(T
);
5823 for (i
= l
; i
< n_div
; ++i
)
5824 bmap
= isl_basic_map_mark_div_unknown(bmap
, i
);
5825 bmap
= isl_basic_map_preimage_vars(bmap
, o_div
- 1 + l
, T
);
5826 bmap
= isl_basic_map_simplify(bmap
);
5828 return isl_basic_map_drop_redundant_divs(bmap
);
5831 /* Does "bmap" satisfy any equality that involves more than 2 variables
5832 * and/or has coefficients different from -1 and 1?
5834 static isl_bool
has_multiple_var_equality(__isl_keep isl_basic_map
*bmap
)
5839 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5841 return isl_bool_error
;
5843 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5846 j
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1, total
);
5849 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
5850 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
5851 return isl_bool_true
;
5854 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
5858 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
5859 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
5860 return isl_bool_true
;
5863 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
5865 return isl_bool_true
;
5868 return isl_bool_false
;
5871 /* Remove any common factor g from the constraint coefficients in "v".
5872 * The constant term is stored in the first position and is replaced
5873 * by floor(c/g). If any common factor is removed and if this results
5874 * in a tightening of the constraint, then set *tightened.
5876 static __isl_give isl_vec
*normalize_constraint(__isl_take isl_vec
*v
,
5883 ctx
= isl_vec_get_ctx(v
);
5884 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
5885 if (isl_int_is_zero(ctx
->normalize_gcd
))
5887 if (isl_int_is_one(ctx
->normalize_gcd
))
5892 if (tightened
&& !isl_int_is_divisible_by(v
->el
[0], ctx
->normalize_gcd
))
5894 isl_int_fdiv_q(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
5895 isl_seq_scale_down(v
->el
+ 1, v
->el
+ 1, ctx
->normalize_gcd
,
5900 /* Internal representation used by isl_basic_map_reduce_coefficients.
5902 * "total" is the total dimensionality of the original basic map.
5903 * "v" is a temporary vector of size 1 + total that can be used
5904 * to store constraint coefficients.
5905 * "T" is the variable compression.
5906 * "T2" is the inverse transformation.
5907 * "tightened" is set if any constant term got tightened
5908 * while reducing the coefficients.
5910 struct isl_reduce_coefficients_data
{
5918 /* Free all memory allocated in "data".
5920 static void isl_reduce_coefficients_data_clear(
5921 struct isl_reduce_coefficients_data
*data
)
5923 data
->T
= isl_mat_free(data
->T
);
5924 data
->T2
= isl_mat_free(data
->T2
);
5925 data
->v
= isl_vec_free(data
->v
);
5928 /* Initialize "data" for "bmap", freeing all allocated memory
5929 * if anything goes wrong.
5931 * In particular, construct a variable compression
5932 * from the equality constraints of "bmap" and
5933 * allocate a temporary vector.
5935 static isl_stat
isl_reduce_coefficients_data_init(
5936 __isl_keep isl_basic_map
*bmap
,
5937 struct isl_reduce_coefficients_data
*data
)
5945 data
->tightened
= 0;
5947 data
->total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5948 if (data
->total
< 0)
5949 return isl_stat_error
;
5950 ctx
= isl_basic_map_get_ctx(bmap
);
5951 data
->v
= isl_vec_alloc(ctx
, 1 + data
->total
);
5953 return isl_stat_error
;
5955 eq
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
,
5956 0, 1 + data
->total
);
5957 data
->T
= isl_mat_variable_compression(eq
, &data
->T2
);
5958 if (!data
->T
|| !data
->T2
)
5963 isl_reduce_coefficients_data_clear(data
);
5964 return isl_stat_error
;
5967 /* Reduce the coefficients of "bmap" by applying the variable compression
5969 * In particular, apply the variable compression to each constraint,
5970 * factor out any common factor in the non-constant coefficients and
5971 * then apply the inverse of the compression.
5973 * Only apply the reduction on a single copy of the basic map
5974 * since the reduction may leave the result in an inconsistent state.
5975 * In particular, the constraints may not be gaussed.
5977 static __isl_give isl_basic_map
*reduce_coefficients(
5978 __isl_take isl_basic_map
*bmap
,
5979 struct isl_reduce_coefficients_data
*data
)
5984 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5986 return isl_basic_map_free(bmap
);
5987 if (total
!= data
->total
)
5988 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
5989 "total dimensionality changed unexpectedly",
5990 return isl_basic_map_free(bmap
));
5992 bmap
= isl_basic_map_cow(bmap
);
5996 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
5997 isl_seq_cpy(data
->v
->el
, bmap
->ineq
[i
], 1 + data
->total
);
5998 data
->v
= isl_vec_mat_product(data
->v
, isl_mat_copy(data
->T
));
5999 data
->v
= normalize_constraint(data
->v
, &data
->tightened
);
6000 data
->v
= isl_vec_mat_product(data
->v
, isl_mat_copy(data
->T2
));
6002 return isl_basic_map_free(bmap
);
6003 isl_seq_cpy(bmap
->ineq
[i
], data
->v
->el
, 1 + data
->total
);
6006 ISL_F_SET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
6011 /* If "bmap" is an integer set that satisfies any equality involving
6012 * more than 2 variables and/or has coefficients different from -1 and 1,
6013 * then use variable compression to reduce the coefficients by removing
6014 * any (hidden) common factor.
6015 * In particular, apply the variable compression to each constraint,
6016 * factor out any common factor in the non-constant coefficients and
6017 * then apply the inverse of the compression.
6018 * At the end, we mark the basic map as having reduced constants.
6019 * If this flag is still set on the next invocation of this function,
6020 * then we skip the computation.
6022 * Removing a common factor may result in a tightening of some of
6023 * the constraints. If this happens, then we may end up with two
6024 * opposite inequalities that can be replaced by an equality.
6025 * We therefore call isl_basic_map_detect_inequality_pairs,
6026 * which checks for such pairs of inequalities as well as eliminate_divs_eq
6027 * and isl_basic_map_gauss if such a pair was found.
6028 * This call to isl_basic_map_gauss may undo much of the effect
6029 * of the reduction on which isl_map_coalesce depends.
6030 * In particular, constraints in terms of (compressed) local variables
6031 * get reformulated in terms of the set variables again.
6032 * The reduction is therefore applied again afterwards.
6033 * This has to be done before the call to eliminate_divs_eq, however,
6034 * since that may remove some local variables, while
6035 * the data used during the reduction is formulated in terms
6036 * of the original variables.
6038 * Tightening may also result in some other constraints becoming
6039 * (rationally) redundant with respect to the tightened constraint
6040 * (in combination with other constraints). The basic map may
6041 * therefore no longer be assumed to have no redundant constraints.
6043 * Note that this function may leave the result in an inconsistent state.
6044 * In particular, the constraints may not be gaussed.
6045 * Unfortunately, isl_map_coalesce actually depends on this inconsistent state
6046 * for some of the test cases to pass successfully.
6047 * Any potential modification of the representation is therefore only
6048 * performed on a single copy of the basic map.
6050 __isl_give isl_basic_map
*isl_basic_map_reduce_coefficients(
6051 __isl_take isl_basic_map
*bmap
)
6053 struct isl_reduce_coefficients_data data
;
6058 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
))
6060 if (isl_basic_map_is_rational(bmap
))
6062 if (bmap
->n_eq
== 0)
6064 multi
= has_multiple_var_equality(bmap
);
6066 return isl_basic_map_free(bmap
);
6070 if (isl_reduce_coefficients_data_init(bmap
, &data
) < 0)
6071 return isl_basic_map_free(bmap
);
6073 if (data
.T
->n_col
== 0) {
6074 isl_reduce_coefficients_data_clear(&data
);
6075 return isl_basic_map_set_to_empty(bmap
);
6078 bmap
= reduce_coefficients(bmap
, &data
);
6082 if (data
.tightened
) {
6085 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
6086 bmap
= isl_basic_map_detect_inequality_pairs(bmap
, &progress
);
6088 bmap
= isl_basic_map_gauss(bmap
, NULL
);
6089 bmap
= reduce_coefficients(bmap
, &data
);
6090 bmap
= eliminate_divs_eq(bmap
, &progress
);
6094 isl_reduce_coefficients_data_clear(&data
);
6098 isl_reduce_coefficients_data_clear(&data
);
6099 return isl_basic_map_free(bmap
);
6102 /* Shift the integer division at position "div" of "bmap"
6103 * by "shift" times the variable at position "pos".
6104 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
6105 * corresponds to the constant term.
6107 * That is, if the integer division has the form
6111 * then replace it by
6113 * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
6115 __isl_give isl_basic_map
*isl_basic_map_shift_div(
6116 __isl_take isl_basic_map
*bmap
, int div
, int pos
, isl_int shift
)
6119 isl_size total
, n_div
;
6121 if (isl_int_is_zero(shift
))
6123 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
6124 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
6126 if (total
< 0 || n_div
< 0)
6127 return isl_basic_map_free(bmap
);
6129 isl_int_addmul(bmap
->div
[div
][1 + pos
], shift
, bmap
->div
[div
][0]);
6131 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
6132 if (isl_int_is_zero(bmap
->eq
[i
][1 + total
+ div
]))
6134 isl_int_submul(bmap
->eq
[i
][pos
],
6135 shift
, bmap
->eq
[i
][1 + total
+ div
]);
6137 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
6138 if (isl_int_is_zero(bmap
->ineq
[i
][1 + total
+ div
]))
6140 isl_int_submul(bmap
->ineq
[i
][pos
],
6141 shift
, bmap
->ineq
[i
][1 + total
+ div
]);
6143 for (i
= 0; i
< bmap
->n_div
; ++i
) {
6144 if (isl_int_is_zero(bmap
->div
[i
][0]))
6146 if (isl_int_is_zero(bmap
->div
[i
][1 + 1 + total
+ div
]))
6148 isl_int_submul(bmap
->div
[i
][1 + pos
],
6149 shift
, bmap
->div
[i
][1 + 1 + total
+ div
]);