2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012-2013 Ecole Normale Superieure
4 * Copyright 2014-2015 INRIA Rocquencourt
5 * Copyright 2016 Sven Verdoolaege
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
12 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
13 * B.P. 105 - 78153 Le Chesnay, France
16 #include <isl_ctx_private.h>
17 #include <isl_map_private.h>
18 #include "isl_equalities.h"
22 #include <isl_space_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_vec_private.h>
26 #include <bset_to_bmap.c>
27 #include <bset_from_bmap.c>
28 #include <set_to_map.c>
29 #include <set_from_map.c>
31 /* Mark "bmap" as having one or more inequality constraints modified.
32 * If "equivalent" is set, then this modification was done based
33 * on an equality constraint already available in "bmap".
35 * Any modification may result in the constraints no longer being sorted and
36 * may also undo the effect of reduce_coefficients.
38 * A modification that uses extra information may also result
39 * in the modified constraint(s) becoming redundant or
40 * turning into an implicit equality constraint.
42 static __isl_give isl_basic_map
*isl_basic_map_modify_inequality(
43 __isl_take isl_basic_map
*bmap
, int equivalent
)
47 ISL_F_CLR(bmap
, ISL_BASIC_MAP_SORTED
);
48 ISL_F_CLR(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
51 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
52 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
56 static void swap_equality(__isl_keep isl_basic_map
*bmap
, int a
, int b
)
58 isl_int
*t
= bmap
->eq
[a
];
59 bmap
->eq
[a
] = bmap
->eq
[b
];
63 static void swap_inequality(__isl_keep isl_basic_map
*bmap
, int a
, int b
)
66 isl_int
*t
= bmap
->ineq
[a
];
67 bmap
->ineq
[a
] = bmap
->ineq
[b
];
72 /* Scale down the inequality constraint "ineq" of length "len"
74 * All the coefficients, except the constant term,
75 * are assumed to be multiples of "f".
77 * If the factor is 0 or 1, then no scaling needs to be performed.
79 * If scaling is performed then take into account that the constraint
80 * is modified (not simply based on an equality constraint).
82 static __isl_give isl_basic_map
*scale_down_inequality(
83 __isl_take isl_basic_map
*bmap
, int ineq
, isl_int f
, unsigned len
)
88 if (isl_int_is_zero(f
) || isl_int_is_one(f
))
91 isl_int_fdiv_q(bmap
->ineq
[ineq
][0], bmap
->ineq
[ineq
][0], f
);
92 isl_seq_scale_down(bmap
->ineq
[ineq
] + 1, bmap
->ineq
[ineq
] + 1, f
, len
);
94 bmap
= isl_basic_map_modify_inequality(bmap
, 0);
99 __isl_give isl_basic_map
*isl_basic_map_normalize_constraints(
100 __isl_take isl_basic_map
*bmap
)
104 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
107 return isl_basic_map_free(bmap
);
110 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
111 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
112 if (isl_int_is_zero(gcd
)) {
113 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
114 bmap
= isl_basic_map_set_to_empty(bmap
);
117 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
121 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
122 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
123 if (isl_int_is_one(gcd
))
125 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
126 bmap
= isl_basic_map_set_to_empty(bmap
);
129 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
132 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
133 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
134 if (isl_int_is_zero(gcd
)) {
135 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
136 bmap
= isl_basic_map_set_to_empty(bmap
);
139 if (isl_basic_map_drop_inequality(bmap
, i
) < 0)
143 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
144 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
145 bmap
= scale_down_inequality(bmap
, i
, gcd
, total
);
154 isl_basic_map_free(bmap
);
158 __isl_give isl_basic_set
*isl_basic_set_normalize_constraints(
159 __isl_take isl_basic_set
*bset
)
161 isl_basic_map
*bmap
= bset_to_bmap(bset
);
162 return bset_from_bmap(isl_basic_map_normalize_constraints(bmap
));
165 /* Reduce the coefficient of the variable at position "pos"
166 * in integer division "div", such that it lies in the half-open
167 * interval (1/2,1/2], extracting any excess value from this integer division.
168 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
169 * corresponds to the constant term.
171 * That is, the integer division is of the form
173 * floor((... + (c * d + r) * x_pos + ...)/d)
175 * with -d < 2 * r <= d.
178 * floor((... + r * x_pos + ...)/d) + c * x_pos
180 * If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d).
181 * Otherwise, c = floor((c * d + r)/d) + 1.
183 * This is the same normalization that is performed by isl_aff_floor.
185 static __isl_give isl_basic_map
*reduce_coefficient_in_div(
186 __isl_take isl_basic_map
*bmap
, int div
, int pos
)
192 isl_int_fdiv_r(shift
, bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
193 isl_int_mul_ui(shift
, shift
, 2);
194 add_one
= isl_int_gt(shift
, bmap
->div
[div
][0]);
195 isl_int_fdiv_q(shift
, bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
197 isl_int_add_ui(shift
, shift
, 1);
198 isl_int_neg(shift
, shift
);
199 bmap
= isl_basic_map_shift_div(bmap
, div
, pos
, shift
);
200 isl_int_clear(shift
);
205 /* Does the coefficient of the variable at position "pos"
206 * in integer division "div" need to be reduced?
207 * That is, does it lie outside the half-open interval (1/2,1/2]?
208 * The coefficient c/d lies outside this interval if abs(2 * c) >= d and
211 static isl_bool
needs_reduction(__isl_keep isl_basic_map
*bmap
, int div
,
216 if (isl_int_is_zero(bmap
->div
[div
][1 + pos
]))
217 return isl_bool_false
;
219 isl_int_mul_ui(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][1 + pos
], 2);
220 r
= isl_int_abs_ge(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]) &&
221 !isl_int_eq(bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
222 isl_int_divexact_ui(bmap
->div
[div
][1 + pos
],
223 bmap
->div
[div
][1 + pos
], 2);
228 /* Reduce the coefficients (including the constant term) of
229 * integer division "div", if needed.
230 * In particular, make sure all coefficients lie in
231 * the half-open interval (1/2,1/2].
233 static __isl_give isl_basic_map
*reduce_div_coefficients_of_div(
234 __isl_take isl_basic_map
*bmap
, int div
)
239 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
241 return isl_basic_map_free(bmap
);
242 for (i
= 0; i
< 1 + total
; ++i
) {
245 reduce
= needs_reduction(bmap
, div
, i
);
247 return isl_basic_map_free(bmap
);
250 bmap
= reduce_coefficient_in_div(bmap
, div
, i
);
258 /* Reduce the coefficients (including the constant term) of
259 * the known integer divisions, if needed
260 * In particular, make sure all coefficients lie in
261 * the half-open interval (1/2,1/2].
263 static __isl_give isl_basic_map
*reduce_div_coefficients(
264 __isl_take isl_basic_map
*bmap
)
270 if (bmap
->n_div
== 0)
273 for (i
= 0; i
< bmap
->n_div
; ++i
) {
274 if (isl_int_is_zero(bmap
->div
[i
][0]))
276 bmap
= reduce_div_coefficients_of_div(bmap
, i
);
284 /* Remove any common factor in numerator and denominator of the div expression,
285 * not taking into account the constant term.
286 * That is, if the div is of the form
288 * floor((a + m f(x))/(m d))
292 * floor((floor(a/m) + f(x))/d)
294 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
295 * and can therefore not influence the result of the floor.
297 static __isl_give isl_basic_map
*normalize_div_expression(
298 __isl_take isl_basic_map
*bmap
, int div
)
300 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
301 isl_ctx
*ctx
= bmap
->ctx
;
304 return isl_basic_map_free(bmap
);
305 if (isl_int_is_zero(bmap
->div
[div
][0]))
307 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
308 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
309 if (isl_int_is_one(ctx
->normalize_gcd
))
311 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
313 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
315 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
316 ctx
->normalize_gcd
, total
);
321 /* Remove any common factor in numerator and denominator of a div expression,
322 * not taking into account the constant term.
323 * That is, look for any div of the form
325 * floor((a + m f(x))/(m d))
329 * floor((floor(a/m) + f(x))/d)
331 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
332 * and can therefore not influence the result of the floor.
334 static __isl_give isl_basic_map
*normalize_div_expressions(
335 __isl_take isl_basic_map
*bmap
)
341 if (bmap
->n_div
== 0)
344 for (i
= 0; i
< bmap
->n_div
; ++i
)
345 bmap
= normalize_div_expression(bmap
, i
);
350 /* Eliminate the variable at position "pos" from the constraints of "bmap"
351 * using the equality constraint "eq".
352 * If "keep_divs" is set, then try and preserve
353 * the integer division expressions. In this case, these expressions
354 * are assumed to have been ordered.
355 * If "equivalent" is set, then the elimination is performed
356 * using an equality constraint of "bmap", meaning that the meaning
357 * of the constraints is preserved.
359 static __isl_give isl_basic_map
*eliminate_var_using_equality(
360 __isl_take isl_basic_map
*bmap
,
361 unsigned pos
, isl_int
*eq
, int keep_divs
, int equivalent
, int *progress
)
369 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
370 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
371 if (total
< 0 || v_div
< 0)
372 return isl_basic_map_free(bmap
);
373 ctx
= isl_basic_map_get_ctx(bmap
);
374 last_div
= isl_seq_last_non_zero(eq
+ 1 + v_div
, bmap
->n_div
);
375 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
376 if (bmap
->eq
[k
] == eq
)
378 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
382 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
383 isl_seq_normalize(ctx
, bmap
->eq
[k
], 1 + total
);
386 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
387 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
391 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
392 isl_seq_gcd(bmap
->ineq
[k
], 1 + total
, &ctx
->normalize_gcd
);
393 bmap
= scale_down_inequality(bmap
, k
, ctx
->normalize_gcd
,
395 bmap
= isl_basic_map_modify_inequality(bmap
, equivalent
);
400 for (k
= 0; k
< bmap
->n_div
; ++k
) {
401 if (isl_int_is_zero(bmap
->div
[k
][0]))
403 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
407 /* We need to be careful about circular definitions,
408 * so for now we just remove the definition of div k
409 * if the equality contains any divs.
410 * If keep_divs is set, then the divs have been ordered
411 * and we can keep the definition as long as the result
414 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
415 isl_seq_elim(bmap
->div
[k
]+1, eq
,
416 1+pos
, 1+total
, &bmap
->div
[k
][0]);
417 bmap
= normalize_div_expression(bmap
, k
);
421 isl_seq_clr(bmap
->div
[k
], 1 + total
);
427 /* Eliminate and remove the local variable at position "pos" of "bmap"
428 * using the equality constraint "eq".
429 * If "keep_divs" is set, then try and preserve
430 * the integer division expressions. In this case, these expressions
431 * are assumed to have been ordered.
432 * If "equivalent" is set, then the elimination is performed
433 * using an equality constraint of "bmap", meaning that the meaning
434 * of the constraints is preserved.
436 static __isl_give isl_basic_map
*eliminate_div(__isl_take isl_basic_map
*bmap
,
437 isl_int
*eq
, unsigned div
, int keep_divs
, int equivalent
)
442 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
444 return isl_basic_map_free(bmap
);
446 bmap
= eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
,
449 bmap
= isl_basic_map_drop_div(bmap
, div
);
454 /* Check if elimination of div "div" using equality "eq" would not
455 * result in a div depending on a later div.
457 static isl_bool
ok_to_eliminate_div(__isl_keep isl_basic_map
*bmap
, isl_int
*eq
,
465 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
467 return isl_bool_error
;
470 last_div
= isl_seq_last_non_zero(eq
+ 1 + v_div
, bmap
->n_div
);
471 if (last_div
< 0 || last_div
<= div
)
472 return isl_bool_true
;
474 for (k
= 0; k
<= last_div
; ++k
) {
475 if (isl_int_is_zero(bmap
->div
[k
][0]))
477 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
478 return isl_bool_false
;
481 return isl_bool_true
;
484 /* Eliminate divs based on equalities
486 static __isl_give isl_basic_map
*eliminate_divs_eq(
487 __isl_take isl_basic_map
*bmap
, int *progress
)
494 bmap
= isl_basic_map_order_divs(bmap
);
499 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
501 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
502 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
505 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
506 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
508 ok
= ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
);
510 return isl_basic_map_free(bmap
);
515 bmap
= eliminate_div(bmap
, bmap
->eq
[i
], d
, 1, 1);
516 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
517 return isl_basic_map_free(bmap
);
522 return eliminate_divs_eq(bmap
, progress
);
526 /* Eliminate divs based on inequalities
528 static __isl_give isl_basic_map
*eliminate_divs_ineq(
529 __isl_take isl_basic_map
*bmap
, int *progress
)
540 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
542 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
543 for (i
= 0; i
< bmap
->n_eq
; ++i
)
544 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
548 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
549 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
551 if (i
< bmap
->n_ineq
)
554 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
555 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
557 bmap
= isl_basic_map_drop_div(bmap
, d
);
564 /* Does the equality constraint at position "eq" in "bmap" involve
565 * any local variables in the range [first, first + n)
566 * that are not marked as having an explicit representation?
568 static isl_bool
bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map
*bmap
,
569 int eq
, unsigned first
, unsigned n
)
575 return isl_bool_error
;
577 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
578 for (i
= 0; i
< n
; ++i
) {
581 if (isl_int_is_zero(bmap
->eq
[eq
][o_div
+ first
+ i
]))
583 unknown
= isl_basic_map_div_is_marked_unknown(bmap
, first
+ i
);
585 return isl_bool_error
;
587 return isl_bool_true
;
590 return isl_bool_false
;
593 /* The last local variable involved in the equality constraint
594 * at position "eq" in "bmap" is the local variable at position "div".
595 * It can therefore be used to extract an explicit representation
597 * Do so unless the local variable already has an explicit representation or
598 * the explicit representation would involve any other local variables
599 * that in turn do not have an explicit representation.
600 * An equality constraint involving local variables without an explicit
601 * representation can be used in isl_basic_map_drop_redundant_divs
602 * to separate out an independent local variable. Introducing
603 * an explicit representation here would block this transformation,
604 * while the partial explicit representation in itself is not very useful.
605 * Set *progress if anything is changed.
607 * The equality constraint is of the form
611 * with n a positive number. The explicit representation derived from
616 static __isl_give isl_basic_map
*set_div_from_eq(__isl_take isl_basic_map
*bmap
,
617 int div
, int eq
, int *progress
)
626 if (!isl_int_is_zero(bmap
->div
[div
][0]))
629 involves
= bmap_eq_involves_unknown_divs(bmap
, eq
, 0, div
);
631 return isl_basic_map_free(bmap
);
635 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
637 return isl_basic_map_free(bmap
);
638 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
639 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->eq
[eq
], 1 + total
);
640 isl_int_set_si(bmap
->div
[div
][1 + o_div
+ div
], 0);
641 isl_int_set(bmap
->div
[div
][0], bmap
->eq
[eq
][o_div
+ div
]);
648 /* Perform fangcheng (Gaussian elimination) on the equality
649 * constraints of "bmap".
650 * That is, put them into row-echelon form, starting from the last column
651 * backward and use them to eliminate the corresponding coefficients
652 * from all constraints.
654 * If "progress" is not NULL, then it gets set if the elimination
655 * results in any changes.
656 * The elimination process may result in some equality constraints
657 * getting interchanged or removed.
658 * If "swap" or "drop" are not NULL, then they get called when
659 * two equality constraints get interchanged or
660 * when a number of final equality constraints get removed.
661 * As a special case, if the input turns out to be empty,
662 * then drop gets called with the number of removed equality
663 * constraints set to the total number of equality constraints.
664 * If "swap" or "drop" are not NULL, then the local variables (if any)
665 * are assumed to be in a valid order.
667 __isl_give isl_basic_map
*isl_basic_map_gauss5(__isl_take isl_basic_map
*bmap
,
669 isl_stat (*swap
)(unsigned a
, unsigned b
, void *user
),
670 isl_stat (*drop
)(unsigned n
, void *user
), void *user
)
680 bmap
= isl_basic_map_order_divs(bmap
);
682 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
684 return isl_basic_map_free(bmap
);
686 total_var
= total
- bmap
->n_div
;
688 last_var
= total
- 1;
689 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
690 for (; last_var
>= 0; --last_var
) {
691 for (k
= done
; k
< bmap
->n_eq
; ++k
)
692 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
700 swap_equality(bmap
, k
, done
);
701 if (swap
&& swap(k
, done
, user
) < 0)
702 return isl_basic_map_free(bmap
);
704 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
705 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
707 bmap
= eliminate_var_using_equality(bmap
, last_var
,
708 bmap
->eq
[done
], 1, 1, progress
);
710 if (last_var
>= total_var
)
711 bmap
= set_div_from_eq(bmap
, last_var
- total_var
,
716 if (done
== bmap
->n_eq
)
718 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
719 if (isl_int_is_zero(bmap
->eq
[k
][0]))
721 if (drop
&& drop(bmap
->n_eq
, user
) < 0)
722 return isl_basic_map_free(bmap
);
723 return isl_basic_map_set_to_empty(bmap
);
725 n_drop
= bmap
->n_eq
- done
;
726 bmap
= isl_basic_map_free_equality(bmap
, n_drop
);
727 if (drop
&& drop(n_drop
, user
) < 0)
728 return isl_basic_map_free(bmap
);
732 __isl_give isl_basic_map
*isl_basic_map_gauss(__isl_take isl_basic_map
*bmap
,
735 return isl_basic_map_gauss5(bmap
, progress
, NULL
, NULL
, NULL
);
738 __isl_give isl_basic_set
*isl_basic_set_gauss(
739 __isl_take isl_basic_set
*bset
, int *progress
)
741 return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset
),
746 static unsigned int round_up(unsigned int v
)
757 /* Hash table of inequalities in a basic map.
758 * "index" is an array of addresses of inequalities in the basic map, some
759 * of which are NULL. The inequalities are hashed on the coefficients
760 * except the constant term.
761 * "size" is the number of elements in the array and is always a power of two
762 * "bits" is the number of bits need to represent an index into the array.
763 * "total" is the total dimension of the basic map.
765 struct isl_constraint_index
{
772 /* Fill in the "ci" data structure for holding the inequalities of "bmap".
774 static isl_stat
create_constraint_index(struct isl_constraint_index
*ci
,
775 __isl_keep isl_basic_map
*bmap
)
781 return isl_stat_error
;
782 ci
->total
= isl_basic_map_dim(bmap
, isl_dim_all
);
784 return isl_stat_error
;
785 if (bmap
->n_ineq
== 0)
787 ci
->size
= round_up(4 * (bmap
->n_ineq
+ 1) / 3 - 1);
788 ci
->bits
= ffs(ci
->size
) - 1;
789 ctx
= isl_basic_map_get_ctx(bmap
);
790 ci
->index
= isl_calloc_array(ctx
, isl_int
**, ci
->size
);
792 return isl_stat_error
;
797 /* Free the memory allocated by create_constraint_index.
799 static void constraint_index_free(struct isl_constraint_index
*ci
)
804 /* Return the position in ci->index that contains the address of
805 * an inequality that is equal to *ineq up to the constant term,
806 * provided this address is not identical to "ineq".
807 * If there is no such inequality, then return the position where
808 * such an inequality should be inserted.
810 static int hash_index_ineq(struct isl_constraint_index
*ci
, isl_int
**ineq
)
813 uint32_t hash
= isl_seq_get_hash_bits((*ineq
) + 1, ci
->total
, ci
->bits
);
814 for (h
= hash
; ci
->index
[h
]; h
= (h
+1) % ci
->size
)
815 if (ineq
!= ci
->index
[h
] &&
816 isl_seq_eq((*ineq
) + 1, ci
->index
[h
][0]+1, ci
->total
))
821 /* Return the position in ci->index that contains the address of
822 * an inequality that is equal to the k'th inequality of "bmap"
823 * up to the constant term, provided it does not point to the very
825 * If there is no such inequality, then return the position where
826 * such an inequality should be inserted.
828 static int hash_index(struct isl_constraint_index
*ci
,
829 __isl_keep isl_basic_map
*bmap
, int k
)
831 return hash_index_ineq(ci
, &bmap
->ineq
[k
]);
834 static int set_hash_index(struct isl_constraint_index
*ci
,
835 __isl_keep isl_basic_set
*bset
, int k
)
837 return hash_index(ci
, bset
, k
);
840 /* Fill in the "ci" data structure with the inequalities of "bset".
842 static isl_stat
setup_constraint_index(struct isl_constraint_index
*ci
,
843 __isl_keep isl_basic_set
*bset
)
847 if (create_constraint_index(ci
, bset
) < 0)
848 return isl_stat_error
;
850 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
851 h
= set_hash_index(ci
, bset
, k
);
852 ci
->index
[h
] = &bset
->ineq
[k
];
858 /* Is the inequality ineq (obviously) redundant with respect
859 * to the constraints in "ci"?
861 * Look for an inequality in "ci" with the same coefficients and then
862 * check if the contant term of "ineq" is greater than or equal
863 * to the constant term of that inequality. If so, "ineq" is clearly
866 * Note that hash_index_ineq ignores a stored constraint if it has
867 * the same address as the passed inequality. It is ok to pass
868 * the address of a local variable here since it will never be
869 * the same as the address of a constraint in "ci".
871 static isl_bool
constraint_index_is_redundant(struct isl_constraint_index
*ci
,
876 h
= hash_index_ineq(ci
, &ineq
);
878 return isl_bool_false
;
879 return isl_int_ge(ineq
[0], (*ci
->index
[h
])[0]);
882 /* If we can eliminate more than one div, then we need to make
883 * sure we do it from last div to first div, in order not to
884 * change the position of the other divs that still need to
887 static __isl_give isl_basic_map
*remove_duplicate_divs(
888 __isl_take isl_basic_map
*bmap
, int *progress
)
900 bmap
= isl_basic_map_order_divs(bmap
);
901 if (!bmap
|| bmap
->n_div
<= 1)
904 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
906 return isl_basic_map_free(bmap
);
907 total
= v_div
+ bmap
->n_div
;
910 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
911 if (!isl_int_is_zero(bmap
->div
[k
][0]))
916 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
919 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
920 bits
= ffs(size
) - 1;
921 index
= isl_calloc_array(ctx
, int, size
);
922 if (!elim_for
|| !index
)
924 eq
= isl_blk_alloc(ctx
, 1+total
);
925 if (isl_blk_is_error(eq
))
928 isl_seq_clr(eq
.data
, 1+total
);
929 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
930 for (--k
; k
>= 0; --k
) {
933 if (isl_int_is_zero(bmap
->div
[k
][0]))
936 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
937 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
938 if (isl_seq_eq(bmap
->div
[k
],
939 bmap
->div
[index
[h
]-1], 2+total
))
948 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
952 isl_int_set_si(eq
.data
[1 + v_div
+ k
], -1);
953 isl_int_set_si(eq
.data
[1 + v_div
+ l
], 1);
954 bmap
= eliminate_div(bmap
, eq
.data
, l
, 1, 0);
957 isl_int_set_si(eq
.data
[1 + v_div
+ k
], 0);
958 isl_int_set_si(eq
.data
[1 + v_div
+ l
], 0);
961 isl_blk_free(ctx
, eq
);
968 static int n_pure_div_eq(__isl_keep isl_basic_map
*bmap
)
973 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
976 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
977 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
981 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + v_div
, j
) != -1)
987 /* Normalize divs that appear in equalities.
989 * In particular, we assume that bmap contains some equalities
994 * and we want to replace the set of e_i by a minimal set and
995 * such that the new e_i have a canonical representation in terms
997 * If any of the equalities involves more than one divs, then
998 * we currently simply bail out.
1000 * Let us first additionally assume that all equalities involve
1001 * a div. The equalities then express modulo constraints on the
1002 * remaining variables and we can use "parameter compression"
1003 * to find a minimal set of constraints. The result is a transformation
1005 * x = T(x') = x_0 + G x'
1007 * with G a lower-triangular matrix with all elements below the diagonal
1008 * non-negative and smaller than the diagonal element on the same row.
1009 * We first normalize x_0 by making the same property hold in the affine
1011 * The rows i of G with a 1 on the diagonal do not impose any modulo
1012 * constraint and simply express x_i = x'_i.
1013 * For each of the remaining rows i, we introduce a div and a corresponding
1014 * equality. In particular
1016 * g_ii e_j = x_i - g_i(x')
1018 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
1019 * corresponding div (if g_kk != 1).
1021 * If there are any equalities not involving any div, then we
1022 * first apply a variable compression on the variables x:
1024 * x = C x'' x'' = C_2 x
1026 * and perform the above parameter compression on A C instead of on A.
1027 * The resulting compression is then of the form
1029 * x'' = T(x') = x_0 + G x'
1031 * and in constructing the new divs and the corresponding equalities,
1032 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
1033 * by the corresponding row from C_2.
1035 static __isl_give isl_basic_map
*normalize_divs(__isl_take isl_basic_map
*bmap
,
1043 struct isl_mat
*T
= NULL
;
1044 struct isl_mat
*C
= NULL
;
1045 struct isl_mat
*C2
= NULL
;
1048 int dropped
, needed
;
1053 if (bmap
->n_div
== 0)
1056 if (bmap
->n_eq
== 0)
1059 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
1062 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1063 div_eq
= n_pure_div_eq(bmap
);
1064 if (v_div
< 0 || div_eq
< 0)
1065 return isl_basic_map_free(bmap
);
1069 if (div_eq
< bmap
->n_eq
) {
1070 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
1071 bmap
->n_eq
- div_eq
, 0, 1 + v_div
);
1072 C
= isl_mat_variable_compression(B
, &C2
);
1075 if (C
->n_col
== 0) {
1076 bmap
= isl_basic_map_set_to_empty(bmap
);
1083 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
1086 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
1087 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
1089 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + v_div
+ j
]);
1091 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + v_div
);
1094 B
= isl_mat_product(B
, C
);
1098 T
= isl_mat_parameter_compression(B
, d
);
1101 if (T
->n_col
== 0) {
1102 bmap
= isl_basic_map_set_to_empty(bmap
);
1108 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
1109 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
1110 if (isl_int_is_zero(v
))
1112 isl_mat_col_submul(T
, 0, v
, 1 + i
);
1115 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
1118 /* We have to be careful because dropping equalities may reorder them */
1120 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
1121 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1122 if (!isl_int_is_zero(bmap
->eq
[i
][1 + v_div
+ j
]))
1124 if (i
< bmap
->n_eq
) {
1125 bmap
= isl_basic_map_drop_div(bmap
, j
);
1126 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
1133 for (i
= 1; i
< T
->n_row
; ++i
) {
1134 if (isl_int_is_one(T
->row
[i
][i
]))
1139 if (needed
> dropped
) {
1140 bmap
= isl_basic_map_extend(bmap
, needed
, needed
, 0);
1144 for (i
= 1; i
< T
->n_row
; ++i
) {
1145 if (isl_int_is_one(T
->row
[i
][i
]))
1147 k
= isl_basic_map_alloc_div(bmap
);
1148 pos
[i
] = 1 + v_div
+ k
;
1149 isl_seq_clr(bmap
->div
[k
] + 1, 1 + v_div
+ bmap
->n_div
);
1150 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
1152 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + v_div
);
1154 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
1155 for (j
= 0; j
< i
; ++j
) {
1156 if (isl_int_is_zero(T
->row
[i
][j
]))
1158 if (pos
[j
] < T
->n_row
&& C2
)
1159 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
1160 C2
->row
[pos
[j
]], 1 + v_div
);
1162 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
1165 j
= isl_basic_map_alloc_equality(bmap
);
1166 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+v_div
+bmap
->n_div
);
1167 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
1176 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
1184 isl_basic_map_free(bmap
);
1188 static __isl_give isl_basic_map
*set_div_from_lower_bound(
1189 __isl_take isl_basic_map
*bmap
, int div
, int ineq
)
1191 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1193 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1194 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1195 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1196 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1197 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1202 /* Check whether it is ok to define a div based on an inequality.
1203 * To avoid the introduction of circular definitions of divs, we
1204 * do not allow such a definition if the resulting expression would refer to
1205 * any other undefined divs or if any known div is defined in
1206 * terms of the unknown div.
1208 static isl_bool
ok_to_set_div_from_bound(__isl_keep isl_basic_map
*bmap
,
1212 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1214 /* Not defined in terms of unknown divs */
1215 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1218 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1220 if (isl_int_is_zero(bmap
->div
[j
][0]))
1221 return isl_bool_false
;
1224 /* No other div defined in terms of this one => avoid loops */
1225 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1228 if (isl_int_is_zero(bmap
->div
[j
][0]))
1230 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1231 return isl_bool_false
;
1234 return isl_bool_true
;
1237 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1238 * be a better expression than the current one?
1240 * If we do not have any expression yet, then any expression would be better.
1241 * Otherwise we check if the last variable involved in the inequality
1242 * (disregarding the div that it would define) is in an earlier position
1243 * than the last variable involved in the current div expression.
1245 static isl_bool
better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1248 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1252 if (isl_int_is_zero(bmap
->div
[div
][0]))
1253 return isl_bool_true
;
1255 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1256 bmap
->n_div
- (div
+ 1)) >= 0)
1257 return isl_bool_false
;
1259 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1260 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1261 total
+ bmap
->n_div
);
1263 return last_ineq
< last_div
;
1266 /* Given two constraints "k" and "l" that are opposite to each other,
1267 * except for the constant term, check if we can use them
1268 * to obtain an expression for one of the hitherto unknown divs or
1269 * a "better" expression for a div for which we already have an expression.
1270 * "sum" is the sum of the constant terms of the constraints.
1271 * If this sum is strictly smaller than the coefficient of one
1272 * of the divs, then this pair can be used to define the div.
1273 * To avoid the introduction of circular definitions of divs, we
1274 * do not use the pair if the resulting expression would refer to
1275 * any other undefined divs or if any known div is defined in
1276 * terms of the unknown div.
1278 static __isl_give isl_basic_map
*check_for_div_constraints(
1279 __isl_take isl_basic_map
*bmap
, int k
, int l
, isl_int sum
,
1283 unsigned total
= isl_basic_map_offset(bmap
, isl_dim_div
);
1285 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1288 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1290 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1292 set_div
= better_div_constraint(bmap
, i
, k
);
1293 if (set_div
>= 0 && set_div
)
1294 set_div
= ok_to_set_div_from_bound(bmap
, i
, k
);
1296 return isl_basic_map_free(bmap
);
1299 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1300 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1302 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1310 __isl_give isl_basic_map
*isl_basic_map_remove_duplicate_constraints(
1311 __isl_take isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1313 struct isl_constraint_index ci
;
1315 isl_size total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1318 if (total
< 0 || bmap
->n_ineq
<= 1)
1321 if (create_constraint_index(&ci
, bmap
) < 0)
1324 h
= isl_seq_get_hash_bits(bmap
->ineq
[0] + 1, total
, ci
.bits
);
1325 ci
.index
[h
] = &bmap
->ineq
[0];
1326 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1327 h
= hash_index(&ci
, bmap
, k
);
1329 ci
.index
[h
] = &bmap
->ineq
[k
];
1332 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1333 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1334 swap_inequality(bmap
, k
, l
);
1335 isl_basic_map_drop_inequality(bmap
, k
);
1339 for (k
= 0; bmap
&& k
< bmap
->n_ineq
-1; ++k
) {
1340 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1341 h
= hash_index(&ci
, bmap
, k
);
1342 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1345 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1346 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1347 if (isl_int_is_pos(sum
)) {
1349 bmap
= check_for_div_constraints(bmap
, k
, l
,
1353 if (isl_int_is_zero(sum
)) {
1354 /* We need to break out of the loop after these
1355 * changes since the contents of the hash
1356 * will no longer be valid.
1357 * Plus, we probably we want to regauss first.
1361 isl_basic_map_drop_inequality(bmap
, l
);
1362 isl_basic_map_inequality_to_equality(bmap
, k
);
1364 bmap
= isl_basic_map_set_to_empty(bmap
);
1369 constraint_index_free(&ci
);
1373 /* Detect all pairs of inequalities that form an equality.
1375 * isl_basic_map_remove_duplicate_constraints detects at most one such pair.
1376 * Call it repeatedly while it is making progress.
1378 __isl_give isl_basic_map
*isl_basic_map_detect_inequality_pairs(
1379 __isl_take isl_basic_map
*bmap
, int *progress
)
1385 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1387 if (progress
&& duplicate
)
1389 } while (duplicate
);
1394 /* Given a known integer division "div" that is not integral
1395 * (with denominator 1), eliminate it from the constraints in "bmap"
1396 * where it appears with a (positive or negative) unit coefficient.
1397 * If "progress" is not NULL, then it gets set if the elimination
1398 * results in any changes.
1402 * floor(e/m) + f >= 0
1410 * -floor(e/m) + f >= 0
1414 * -e + m f + m - 1 >= 0
1416 * The first conversion is valid because floor(e/m) >= -f is equivalent
1417 * to e/m >= -f because -f is an integral expression.
1418 * The second conversion follows from the fact that
1420 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1423 * Note that one of the div constraints may have been eliminated
1424 * due to being redundant with respect to the constraint that is
1425 * being modified by this function. The modified constraint may
1426 * no longer imply this div constraint, so we add it back to make
1427 * sure we do not lose any information.
1429 static __isl_give isl_basic_map
*eliminate_unit_div(
1430 __isl_take isl_basic_map
*bmap
, int div
, int *progress
)
1433 isl_size v_div
, dim
;
1436 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1437 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
1438 if (v_div
< 0 || dim
< 0)
1439 return isl_basic_map_free(bmap
);
1441 ctx
= isl_basic_map_get_ctx(bmap
);
1443 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1446 if (!isl_int_is_one(bmap
->ineq
[j
][1 + v_div
+ div
]) &&
1447 !isl_int_is_negone(bmap
->ineq
[j
][1 + v_div
+ div
]))
1453 s
= isl_int_sgn(bmap
->ineq
[j
][1 + v_div
+ div
]);
1454 isl_int_set_si(bmap
->ineq
[j
][1 + v_div
+ div
], 0);
1456 isl_seq_combine(bmap
->ineq
[j
],
1457 ctx
->negone
, bmap
->div
[div
] + 1,
1458 bmap
->div
[div
][0], bmap
->ineq
[j
], 1 + dim
);
1460 isl_seq_combine(bmap
->ineq
[j
],
1461 ctx
->one
, bmap
->div
[div
] + 1,
1462 bmap
->div
[div
][0], bmap
->ineq
[j
], 1 + dim
);
1464 isl_int_add(bmap
->ineq
[j
][0],
1465 bmap
->ineq
[j
][0], bmap
->div
[div
][0]);
1466 isl_int_sub_ui(bmap
->ineq
[j
][0],
1467 bmap
->ineq
[j
][0], 1);
1470 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
1471 bmap
= isl_basic_map_add_div_constraint(bmap
, div
, s
);
1479 /* Eliminate selected known divs from constraints where they appear with
1480 * a (positive or negative) unit coefficient.
1481 * In particular, only handle those for which "select" returns isl_bool_true.
1482 * If "progress" is not NULL, then it gets set if the elimination
1483 * results in any changes.
1485 * We skip integral divs, i.e., those with denominator 1, as we would
1486 * risk eliminating the div from the div constraints. We do not need
1487 * to handle those divs here anyway since the div constraints will turn
1488 * out to form an equality and this equality can then be used to eliminate
1489 * the div from all constraints.
1491 static __isl_give isl_basic_map
*eliminate_selected_unit_divs(
1492 __isl_take isl_basic_map
*bmap
,
1493 isl_bool (*select
)(__isl_keep isl_basic_map
*bmap
, int div
),
1499 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1501 return isl_basic_map_free(bmap
);
1503 for (i
= 0; i
< n_div
; ++i
) {
1507 skip
= isl_basic_map_div_is_marked_unknown(bmap
, i
);
1508 if (skip
>= 0 && !skip
)
1509 skip
= isl_basic_map_div_is_integral(bmap
, i
);
1511 return isl_basic_map_free(bmap
);
1514 selected
= select(bmap
, i
);
1516 return isl_basic_map_free(bmap
);
1519 bmap
= eliminate_unit_div(bmap
, i
, progress
);
1527 /* eliminate_selected_unit_divs callback that selects every
1530 static isl_bool
is_any_div(__isl_keep isl_basic_map
*bmap
, int div
)
1532 return isl_bool_true
;
1535 /* Eliminate known divs from constraints where they appear with
1536 * a (positive or negative) unit coefficient.
1537 * If "progress" is not NULL, then it gets set if the elimination
1538 * results in any changes.
1540 static __isl_give isl_basic_map
*eliminate_unit_divs(
1541 __isl_take isl_basic_map
*bmap
, int *progress
)
1543 return eliminate_selected_unit_divs(bmap
, &is_any_div
, progress
);
1546 /* eliminate_selected_unit_divs callback that selects
1547 * integer divisions that only appear with
1548 * a (positive or negative) unit coefficient
1549 * (outside their div constraints).
1551 static isl_bool
is_pure_unit_div(__isl_keep isl_basic_map
*bmap
, int div
)
1554 isl_size v_div
, n_ineq
;
1556 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1557 n_ineq
= isl_basic_map_n_inequality(bmap
);
1558 if (v_div
< 0 || n_ineq
< 0)
1559 return isl_bool_error
;
1561 for (i
= 0; i
< n_ineq
; ++i
) {
1564 if (isl_int_is_zero(bmap
->ineq
[i
][1 + v_div
+ div
]))
1566 skip
= isl_basic_map_is_div_constraint(bmap
,
1567 bmap
->ineq
[i
], div
);
1569 return isl_bool_error
;
1572 if (!isl_int_is_one(bmap
->ineq
[i
][1 + v_div
+ div
]) &&
1573 !isl_int_is_negone(bmap
->ineq
[i
][1 + v_div
+ div
]))
1574 return isl_bool_false
;
1577 return isl_bool_true
;
1580 /* Eliminate known divs from constraints where they appear with
1581 * a (positive or negative) unit coefficient,
1582 * but only if they do not appear in any other constraints
1583 * (other than the div constraints).
1585 __isl_give isl_basic_map
*isl_basic_map_eliminate_pure_unit_divs(
1586 __isl_take isl_basic_map
*bmap
)
1588 return eliminate_selected_unit_divs(bmap
, &is_pure_unit_div
, NULL
);
1591 __isl_give isl_basic_map
*isl_basic_map_simplify(__isl_take isl_basic_map
*bmap
)
1600 empty
= isl_basic_map_plain_is_empty(bmap
);
1602 return isl_basic_map_free(bmap
);
1605 bmap
= isl_basic_map_normalize_constraints(bmap
);
1606 bmap
= reduce_div_coefficients(bmap
);
1607 bmap
= normalize_div_expressions(bmap
);
1608 bmap
= remove_duplicate_divs(bmap
, &progress
);
1609 bmap
= eliminate_unit_divs(bmap
, &progress
);
1610 bmap
= eliminate_divs_eq(bmap
, &progress
);
1611 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1612 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1613 /* requires equalities in normal form */
1614 bmap
= normalize_divs(bmap
, &progress
);
1615 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1621 __isl_give isl_basic_set
*isl_basic_set_simplify(
1622 __isl_take isl_basic_set
*bset
)
1624 return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset
)));
1628 isl_bool
isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1629 isl_int
*constraint
, unsigned div
)
1634 return isl_bool_error
;
1636 pos
= isl_basic_map_offset(bmap
, isl_dim_div
) + div
;
1638 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1640 isl_int_sub(bmap
->div
[div
][1],
1641 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1642 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1643 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1644 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1645 isl_int_add(bmap
->div
[div
][1],
1646 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1648 return isl_bool_false
;
1649 if (isl_seq_first_non_zero(constraint
+pos
+1,
1650 bmap
->n_div
-div
-1) != -1)
1651 return isl_bool_false
;
1652 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1653 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1654 return isl_bool_false
;
1655 if (isl_seq_first_non_zero(constraint
+pos
+1,
1656 bmap
->n_div
-div
-1) != -1)
1657 return isl_bool_false
;
1659 return isl_bool_false
;
1661 return isl_bool_true
;
1664 /* If the only constraints a div d=floor(f/m)
1665 * appears in are its two defining constraints
1668 * -(f - (m - 1)) + m d >= 0
1670 * then it can safely be removed.
1672 static isl_bool
div_is_redundant(__isl_keep isl_basic_map
*bmap
, int div
)
1675 isl_size v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1676 unsigned pos
= 1 + v_div
+ div
;
1679 return isl_bool_error
;
1681 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1682 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1683 return isl_bool_false
;
1685 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1688 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1690 red
= isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
);
1691 if (red
< 0 || !red
)
1695 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1696 if (isl_int_is_zero(bmap
->div
[i
][0]))
1698 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1699 return isl_bool_false
;
1702 return isl_bool_true
;
1706 * Remove divs that don't occur in any of the constraints or other divs.
1707 * These can arise when dropping constraints from a basic map or
1708 * when the divs of a basic map have been temporarily aligned
1709 * with the divs of another basic map.
1711 static __isl_give isl_basic_map
*remove_redundant_divs(
1712 __isl_take isl_basic_map
*bmap
)
1717 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
1719 return isl_basic_map_free(bmap
);
1721 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1724 redundant
= div_is_redundant(bmap
, i
);
1726 return isl_basic_map_free(bmap
);
1729 bmap
= isl_basic_map_drop_constraints_involving(bmap
,
1731 bmap
= isl_basic_map_drop_div(bmap
, i
);
1736 /* Mark "bmap" as final, without checking for obviously redundant
1737 * integer divisions. This function should be used when "bmap"
1738 * is known not to involve any such integer divisions.
1740 __isl_give isl_basic_map
*isl_basic_map_mark_final(
1741 __isl_take isl_basic_map
*bmap
)
1745 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1749 /* Mark "bmap" as final, after removing obviously redundant integer divisions.
1751 __isl_give isl_basic_map
*isl_basic_map_finalize(__isl_take isl_basic_map
*bmap
)
1753 bmap
= remove_redundant_divs(bmap
);
1754 bmap
= isl_basic_map_mark_final(bmap
);
1758 __isl_give isl_basic_set
*isl_basic_set_finalize(
1759 __isl_take isl_basic_set
*bset
)
1761 return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset
)));
1764 /* Remove definition of any div that is defined in terms of the given variable.
1765 * The div itself is not removed. Functions such as
1766 * eliminate_divs_ineq depend on the other divs remaining in place.
1768 static __isl_give isl_basic_map
*remove_dependent_vars(
1769 __isl_take isl_basic_map
*bmap
, int pos
)
1776 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1777 if (isl_int_is_zero(bmap
->div
[i
][0]))
1779 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1781 bmap
= isl_basic_map_mark_div_unknown(bmap
, i
);
1788 /* Eliminate the specified variables from the constraints using
1789 * Fourier-Motzkin. The variables themselves are not removed.
1791 __isl_give isl_basic_map
*isl_basic_map_eliminate_vars(
1792 __isl_take isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1801 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
1803 return isl_basic_map_free(bmap
);
1805 bmap
= isl_basic_map_cow(bmap
);
1806 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1807 bmap
= remove_dependent_vars(bmap
, d
);
1811 for (d
= pos
+ n
- 1;
1812 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1813 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1814 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1815 int n_lower
, n_upper
;
1818 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1819 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1821 bmap
= eliminate_var_using_equality(bmap
, d
,
1822 bmap
->eq
[i
], 0, 1, NULL
);
1823 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
1824 return isl_basic_map_free(bmap
);
1832 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1833 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1835 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1838 bmap
= isl_basic_map_extend_constraints(bmap
,
1839 0, n_lower
* n_upper
);
1842 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1844 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1847 for (j
= 0; j
< i
; ++j
) {
1848 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1851 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1852 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1854 k
= isl_basic_map_alloc_inequality(bmap
);
1857 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1859 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1860 1+d
, 1+total
, NULL
);
1862 isl_basic_map_drop_inequality(bmap
, i
);
1865 if (n_lower
> 0 && n_upper
> 0) {
1866 bmap
= isl_basic_map_normalize_constraints(bmap
);
1867 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1869 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1870 bmap
= isl_basic_map_remove_redundancies(bmap
);
1874 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1879 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1882 isl_basic_map_free(bmap
);
1886 __isl_give isl_basic_set
*isl_basic_set_eliminate_vars(
1887 __isl_take isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1889 return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset
),
1893 /* Eliminate the specified n dimensions starting at first from the
1894 * constraints, without removing the dimensions from the space.
1895 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1896 * Otherwise, they are projected out and the original space is restored.
1898 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1899 __isl_take isl_basic_map
*bmap
,
1900 enum isl_dim_type type
, unsigned first
, unsigned n
)
1909 if (isl_basic_map_check_range(bmap
, type
, first
, n
) < 0)
1910 return isl_basic_map_free(bmap
);
1912 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1913 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1914 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1915 return isl_basic_map_finalize(bmap
);
1918 space
= isl_basic_map_get_space(bmap
);
1919 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1920 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1921 bmap
= isl_basic_map_reset_space(bmap
, space
);
1925 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1926 __isl_take isl_basic_set
*bset
,
1927 enum isl_dim_type type
, unsigned first
, unsigned n
)
1929 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1932 /* Remove all constraints from "bmap" that reference any unknown local
1933 * variables (directly or indirectly).
1935 * Dropping all constraints on a local variable will make it redundant,
1936 * so it will get removed implicitly by
1937 * isl_basic_map_drop_constraints_involving_dims. Some other local
1938 * variables may also end up becoming redundant if they only appear
1939 * in constraints together with the unknown local variable.
1940 * Therefore, start over after calling
1941 * isl_basic_map_drop_constraints_involving_dims.
1943 __isl_give isl_basic_map
*isl_basic_map_drop_constraints_involving_unknown_divs(
1944 __isl_take isl_basic_map
*bmap
)
1950 known
= isl_basic_map_divs_known(bmap
);
1952 return isl_basic_map_free(bmap
);
1956 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1958 return isl_basic_map_free(bmap
);
1959 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
) - 1;
1961 for (i
= 0; i
< n_div
; ++i
) {
1962 known
= isl_basic_map_div_is_known(bmap
, i
);
1964 return isl_basic_map_free(bmap
);
1967 bmap
= remove_dependent_vars(bmap
, o_div
+ i
);
1968 bmap
= isl_basic_map_drop_constraints_involving_dims(bmap
,
1970 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
1972 return isl_basic_map_free(bmap
);
1979 /* Remove all constraints from "bset" that reference any unknown local
1980 * variables (directly or indirectly).
1982 __isl_give isl_basic_set
*isl_basic_set_drop_constraints_involving_unknown_divs(
1983 __isl_take isl_basic_set
*bset
)
1985 isl_basic_map
*bmap
;
1987 bmap
= bset_to_bmap(bset
);
1988 bmap
= isl_basic_map_drop_constraints_involving_unknown_divs(bmap
);
1989 return bset_from_bmap(bmap
);
1992 /* Remove all constraints from "map" that reference any unknown local
1993 * variables (directly or indirectly).
1995 * Since constraints may get dropped from the basic maps,
1996 * they may no longer be disjoint from each other.
1998 __isl_give isl_map
*isl_map_drop_constraints_involving_unknown_divs(
1999 __isl_take isl_map
*map
)
2004 known
= isl_map_divs_known(map
);
2006 return isl_map_free(map
);
2010 map
= isl_map_cow(map
);
2014 for (i
= 0; i
< map
->n
; ++i
) {
2016 isl_basic_map_drop_constraints_involving_unknown_divs(
2019 return isl_map_free(map
);
2023 ISL_F_CLR(map
, ISL_MAP_DISJOINT
);
2028 /* Don't assume equalities are in order, because align_divs
2029 * may have changed the order of the divs.
2031 static void compute_elimination_index(__isl_keep isl_basic_map
*bmap
, int *elim
,
2036 for (d
= 0; d
< len
; ++d
)
2038 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2039 for (d
= len
- 1; d
>= 0; --d
) {
2040 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
2048 static void set_compute_elimination_index(__isl_keep isl_basic_set
*bset
,
2049 int *elim
, unsigned len
)
2051 compute_elimination_index(bset_to_bmap(bset
), elim
, len
);
2054 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
2055 __isl_keep isl_basic_map
*bmap
, int *elim
, unsigned total
)
2060 for (d
= total
- 1; d
>= 0; --d
) {
2061 if (isl_int_is_zero(src
[1+d
]))
2066 isl_seq_cpy(dst
, src
, 1 + total
);
2069 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
2074 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
2075 __isl_keep isl_basic_set
*bset
, int *elim
, unsigned total
)
2077 return reduced_using_equalities(dst
, src
,
2078 bset_to_bmap(bset
), elim
, total
);
2081 static __isl_give isl_basic_set
*isl_basic_set_reduce_using_equalities(
2082 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
2088 if (!bset
|| !context
)
2091 if (context
->n_eq
== 0) {
2092 isl_basic_set_free(context
);
2096 bset
= isl_basic_set_cow(bset
);
2097 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2101 elim
= isl_alloc_array(bset
->ctx
, int, dim
);
2104 set_compute_elimination_index(context
, elim
, dim
);
2105 for (i
= 0; i
< bset
->n_eq
; ++i
)
2106 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
2107 context
, elim
, dim
);
2108 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2109 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
2110 context
, elim
, dim
);
2111 isl_basic_set_free(context
);
2113 bset
= isl_basic_set_simplify(bset
);
2114 bset
= isl_basic_set_finalize(bset
);
2117 isl_basic_set_free(bset
);
2118 isl_basic_set_free(context
);
2122 /* For each inequality in "ineq" that is a shifted (more relaxed)
2123 * copy of an inequality in "context", mark the corresponding entry
2125 * If an inequality only has a non-negative constant term, then
2128 static isl_stat
mark_shifted_constraints(__isl_keep isl_mat
*ineq
,
2129 __isl_keep isl_basic_set
*context
, int *row
)
2131 struct isl_constraint_index ci
;
2132 isl_size n_ineq
, cols
;
2136 if (!ineq
|| !context
)
2137 return isl_stat_error
;
2138 if (context
->n_ineq
== 0)
2140 if (setup_constraint_index(&ci
, context
) < 0)
2141 return isl_stat_error
;
2143 n_ineq
= isl_mat_rows(ineq
);
2144 cols
= isl_mat_cols(ineq
);
2145 if (n_ineq
< 0 || cols
< 0)
2146 return isl_stat_error
;
2148 for (k
= 0; k
< n_ineq
; ++k
) {
2152 l
= isl_seq_first_non_zero(ineq
->row
[k
] + 1, total
);
2153 if (l
< 0 && isl_int_is_nonneg(ineq
->row
[k
][0])) {
2157 redundant
= constraint_index_is_redundant(&ci
, ineq
->row
[k
]);
2164 constraint_index_free(&ci
);
2167 constraint_index_free(&ci
);
2168 return isl_stat_error
;
2171 static __isl_give isl_basic_set
*remove_shifted_constraints(
2172 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*context
)
2174 struct isl_constraint_index ci
;
2177 if (!bset
|| !context
)
2180 if (context
->n_ineq
== 0)
2182 if (setup_constraint_index(&ci
, context
) < 0)
2185 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
2188 redundant
= constraint_index_is_redundant(&ci
, bset
->ineq
[k
]);
2193 bset
= isl_basic_set_cow(bset
);
2196 isl_basic_set_drop_inequality(bset
, k
);
2199 constraint_index_free(&ci
);
2202 constraint_index_free(&ci
);
2206 /* Remove constraints from "bmap" that are identical to constraints
2207 * in "context" or that are more relaxed (greater constant term).
2209 * We perform the test for shifted copies on the pure constraints
2210 * in remove_shifted_constraints.
2212 static __isl_give isl_basic_map
*isl_basic_map_remove_shifted_constraints(
2213 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
2215 isl_basic_set
*bset
, *bset_context
;
2217 if (!bmap
|| !context
)
2220 if (bmap
->n_ineq
== 0 || context
->n_ineq
== 0) {
2221 isl_basic_map_free(context
);
2225 bmap
= isl_basic_map_order_divs(bmap
);
2226 context
= isl_basic_map_align_divs(context
, bmap
);
2227 bmap
= isl_basic_map_align_divs(bmap
, context
);
2229 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
2230 bset_context
= isl_basic_map_underlying_set(context
);
2231 bset
= remove_shifted_constraints(bset
, bset_context
);
2232 isl_basic_set_free(bset_context
);
2234 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
2238 isl_basic_map_free(bmap
);
2239 isl_basic_map_free(context
);
2243 /* Does the (linear part of a) constraint "c" involve any of the "len"
2244 * "relevant" dimensions?
2246 static int is_related(isl_int
*c
, int len
, int *relevant
)
2250 for (i
= 0; i
< len
; ++i
) {
2253 if (!isl_int_is_zero(c
[i
]))
2260 /* Drop constraints from "bmap" that do not involve any of
2261 * the dimensions marked "relevant".
2263 static __isl_give isl_basic_map
*drop_unrelated_constraints(
2264 __isl_take isl_basic_map
*bmap
, int *relevant
)
2269 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
2271 return isl_basic_map_free(bmap
);
2272 for (i
= 0; i
< dim
; ++i
)
2278 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
)
2279 if (!is_related(bmap
->eq
[i
] + 1, dim
, relevant
)) {
2280 bmap
= isl_basic_map_cow(bmap
);
2281 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
2282 return isl_basic_map_free(bmap
);
2285 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
)
2286 if (!is_related(bmap
->ineq
[i
] + 1, dim
, relevant
)) {
2287 bmap
= isl_basic_map_cow(bmap
);
2288 if (isl_basic_map_drop_inequality(bmap
, i
) < 0)
2289 return isl_basic_map_free(bmap
);
2295 /* Update the groups in "group" based on the (linear part of a) constraint "c".
2297 * In particular, for any variable involved in the constraint,
2298 * find the actual group id from before and replace the group
2299 * of the corresponding variable by the minimal group of all
2300 * the variables involved in the constraint considered so far
2301 * (if this minimum is smaller) or replace the minimum by this group
2302 * (if the minimum is larger).
2304 * At the end, all the variables in "c" will (indirectly) point
2305 * to the minimal of the groups that they referred to originally.
2307 static void update_groups(int dim
, int *group
, isl_int
*c
)
2312 for (j
= 0; j
< dim
; ++j
) {
2313 if (isl_int_is_zero(c
[j
]))
2315 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
2316 group
[j
] = group
[group
[j
]];
2317 if (group
[j
] == min
)
2319 if (group
[j
] < min
) {
2320 if (min
>= 0 && min
< dim
)
2321 group
[min
] = group
[j
];
2324 group
[group
[j
]] = min
;
2328 /* Allocate an array of groups of variables, one for each variable
2329 * in "context", initialized to zero.
2331 static int *alloc_groups(__isl_keep isl_basic_set
*context
)
2336 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2339 ctx
= isl_basic_set_get_ctx(context
);
2340 return isl_calloc_array(ctx
, int, dim
);
2343 /* Drop constraints from "bmap" that only involve variables that are
2344 * not related to any of the variables marked with a "-1" in "group".
2346 * We construct groups of variables that collect variables that
2347 * (indirectly) appear in some common constraint of "bmap".
2348 * Each group is identified by the first variable in the group,
2349 * except for the special group of variables that was already identified
2350 * in the input as -1 (or are related to those variables).
2351 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
2352 * otherwise the group of i is the group of group[i].
2354 * We first initialize groups for the remaining variables.
2355 * Then we iterate over the constraints of "bmap" and update the
2356 * group of the variables in the constraint by the smallest group.
2357 * Finally, we resolve indirect references to groups by running over
2360 * After computing the groups, we drop constraints that do not involve
2361 * any variables in the -1 group.
2363 __isl_give isl_basic_map
*isl_basic_map_drop_unrelated_constraints(
2364 __isl_take isl_basic_map
*bmap
, __isl_take
int *group
)
2370 dim
= isl_basic_map_dim(bmap
, isl_dim_all
);
2372 return isl_basic_map_free(bmap
);
2375 for (i
= 0; i
< dim
; ++i
)
2377 last
= group
[i
] = i
;
2383 for (i
= 0; i
< bmap
->n_eq
; ++i
)
2384 update_groups(dim
, group
, bmap
->eq
[i
] + 1);
2385 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
2386 update_groups(dim
, group
, bmap
->ineq
[i
] + 1);
2388 for (i
= 0; i
< dim
; ++i
)
2390 group
[i
] = group
[group
[i
]];
2392 for (i
= 0; i
< dim
; ++i
)
2393 group
[i
] = group
[i
] == -1;
2395 bmap
= drop_unrelated_constraints(bmap
, group
);
2401 /* Drop constraints from "context" that are irrelevant for computing
2402 * the gist of "bset".
2404 * In particular, drop constraints in variables that are not related
2405 * to any of the variables involved in the constraints of "bset"
2406 * in the sense that there is no sequence of constraints that connects them.
2408 * We first mark all variables that appear in "bset" as belonging
2409 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2411 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
2412 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
2418 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2419 if (!context
|| dim
< 0)
2420 return isl_basic_set_free(context
);
2422 group
= alloc_groups(context
);
2425 return isl_basic_set_free(context
);
2427 for (i
= 0; i
< dim
; ++i
) {
2428 for (j
= 0; j
< bset
->n_eq
; ++j
)
2429 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
2431 if (j
< bset
->n_eq
) {
2435 for (j
= 0; j
< bset
->n_ineq
; ++j
)
2436 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
2438 if (j
< bset
->n_ineq
)
2442 return isl_basic_map_drop_unrelated_constraints(context
, group
);
2445 /* Drop constraints from "context" that are irrelevant for computing
2446 * the gist of the inequalities "ineq".
2447 * Inequalities in "ineq" for which the corresponding element of row
2448 * is set to -1 have already been marked for removal and should be ignored.
2450 * In particular, drop constraints in variables that are not related
2451 * to any of the variables involved in "ineq"
2452 * in the sense that there is no sequence of constraints that connects them.
2454 * We first mark all variables that appear in "bset" as belonging
2455 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2457 static __isl_give isl_basic_set
*drop_irrelevant_constraints_marked(
2458 __isl_take isl_basic_set
*context
, __isl_keep isl_mat
*ineq
, int *row
)
2465 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2466 n
= isl_mat_rows(ineq
);
2467 if (dim
< 0 || n
< 0)
2468 return isl_basic_set_free(context
);
2470 group
= alloc_groups(context
);
2473 return isl_basic_set_free(context
);
2475 for (i
= 0; i
< dim
; ++i
) {
2476 for (j
= 0; j
< n
; ++j
) {
2479 if (!isl_int_is_zero(ineq
->row
[j
][1 + i
]))
2486 return isl_basic_map_drop_unrelated_constraints(context
, group
);
2489 /* Do all "n" entries of "row" contain a negative value?
2491 static int all_neg(int *row
, int n
)
2495 for (i
= 0; i
< n
; ++i
)
2502 /* Update the inequalities in "bset" based on the information in "row"
2505 * In particular, the array "row" contains either -1, meaning that
2506 * the corresponding inequality of "bset" is redundant, or the index
2507 * of an inequality in "tab".
2509 * If the row entry is -1, then drop the inequality.
2510 * Otherwise, if the constraint is marked redundant in the tableau,
2511 * then drop the inequality. Similarly, if it is marked as an equality
2512 * in the tableau, then turn the inequality into an equality and
2513 * perform Gaussian elimination.
2515 static __isl_give isl_basic_set
*update_ineq(__isl_take isl_basic_set
*bset
,
2516 __isl_keep
int *row
, struct isl_tab
*tab
)
2521 int found_equality
= 0;
2525 if (tab
&& tab
->empty
)
2526 return isl_basic_set_set_to_empty(bset
);
2528 n_ineq
= bset
->n_ineq
;
2529 for (i
= n_ineq
- 1; i
>= 0; --i
) {
2531 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2532 return isl_basic_set_free(bset
);
2538 if (isl_tab_is_equality(tab
, n_eq
+ row
[i
])) {
2539 isl_basic_map_inequality_to_equality(bset
, i
);
2541 } else if (isl_tab_is_redundant(tab
, n_eq
+ row
[i
])) {
2542 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2543 return isl_basic_set_free(bset
);
2548 bset
= isl_basic_set_gauss(bset
, NULL
);
2549 bset
= isl_basic_set_finalize(bset
);
2553 /* Update the inequalities in "bset" based on the information in "row"
2554 * and "tab" and free all arguments (other than "bset").
2556 static __isl_give isl_basic_set
*update_ineq_free(
2557 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*ineq
,
2558 __isl_take isl_basic_set
*context
, __isl_take
int *row
,
2559 struct isl_tab
*tab
)
2562 isl_basic_set_free(context
);
2564 bset
= update_ineq(bset
, row
, tab
);
2571 /* Remove all information from bset that is redundant in the context
2573 * "ineq" contains the (possibly transformed) inequalities of "bset",
2574 * in the same order.
2575 * The (explicit) equalities of "bset" are assumed to have been taken
2576 * into account by the transformation such that only the inequalities
2578 * "context" is assumed not to be empty.
2580 * "row" keeps track of the constraint index of a "bset" inequality in "tab".
2581 * A value of -1 means that the inequality is obviously redundant and may
2582 * not even appear in "tab".
2584 * We first mark the inequalities of "bset"
2585 * that are obviously redundant with respect to some inequality in "context".
2586 * Then we remove those constraints from "context" that have become
2587 * irrelevant for computing the gist of "bset".
2588 * Note that this removal of constraints cannot be replaced by
2589 * a factorization because factors in "bset" may still be connected
2590 * to each other through constraints in "context".
2592 * If there are any inequalities left, we construct a tableau for
2593 * the context and then add the inequalities of "bset".
2594 * Before adding these inequalities, we freeze all constraints such that
2595 * they won't be considered redundant in terms of the constraints of "bset".
2596 * Then we detect all redundant constraints (among the
2597 * constraints that weren't frozen), first by checking for redundancy in the
2598 * the tableau and then by checking if replacing a constraint by its negation
2599 * would lead to an empty set. This last step is fairly expensive
2600 * and could be optimized by more reuse of the tableau.
2601 * Finally, we update bset according to the results.
2603 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
2604 __isl_take isl_mat
*ineq
, __isl_take isl_basic_set
*context
)
2609 isl_basic_set
*combined
= NULL
;
2610 struct isl_tab
*tab
= NULL
;
2611 unsigned n_eq
, context_ineq
;
2613 if (!bset
|| !ineq
|| !context
)
2616 if (bset
->n_ineq
== 0 || isl_basic_set_plain_is_universe(context
)) {
2617 isl_basic_set_free(context
);
2622 ctx
= isl_basic_set_get_ctx(context
);
2623 row
= isl_calloc_array(ctx
, int, bset
->n_ineq
);
2627 if (mark_shifted_constraints(ineq
, context
, row
) < 0)
2629 if (all_neg(row
, bset
->n_ineq
))
2630 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
2632 context
= drop_irrelevant_constraints_marked(context
, ineq
, row
);
2635 if (isl_basic_set_plain_is_universe(context
))
2636 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
2638 n_eq
= context
->n_eq
;
2639 context_ineq
= context
->n_ineq
;
2640 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
2641 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
2642 tab
= isl_tab_from_basic_set(combined
, 0);
2643 for (i
= 0; i
< context_ineq
; ++i
)
2644 if (isl_tab_freeze_constraint(tab
, n_eq
+ i
) < 0)
2646 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
2649 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2652 combined
= isl_basic_set_add_ineq(combined
, ineq
->row
[i
]);
2653 if (isl_tab_add_ineq(tab
, ineq
->row
[i
]) < 0)
2657 if (isl_tab_detect_implicit_equalities(tab
) < 0)
2659 if (isl_tab_detect_redundant(tab
) < 0)
2661 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
2662 isl_basic_set
*test
;
2668 if (tab
->con
[n_eq
+ r
].is_redundant
)
2670 test
= isl_basic_set_dup(combined
);
2671 test
= isl_inequality_negate(test
, r
);
2672 test
= isl_basic_set_update_from_tab(test
, tab
);
2673 is_empty
= isl_basic_set_is_empty(test
);
2674 isl_basic_set_free(test
);
2678 tab
->con
[n_eq
+ r
].is_redundant
= 1;
2680 bset
= update_ineq_free(bset
, ineq
, context
, row
, tab
);
2682 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2683 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2686 isl_basic_set_free(combined
);
2692 isl_basic_set_free(combined
);
2693 isl_basic_set_free(context
);
2694 isl_basic_set_free(bset
);
2698 /* Extract the inequalities of "bset" as an isl_mat.
2700 static __isl_give isl_mat
*extract_ineq(__isl_keep isl_basic_set
*bset
)
2706 total
= isl_basic_set_dim(bset
, isl_dim_all
);
2710 ctx
= isl_basic_set_get_ctx(bset
);
2711 ineq
= isl_mat_sub_alloc6(ctx
, bset
->ineq
, 0, bset
->n_ineq
,
2717 /* Remove all information from "bset" that is redundant in the context
2718 * of "context", for the case where both "bset" and "context" are
2721 static __isl_give isl_basic_set
*uset_gist_uncompressed(
2722 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
2726 ineq
= extract_ineq(bset
);
2727 return uset_gist_full(bset
, ineq
, context
);
2730 /* Replace "bset" by an empty basic set in the same space.
2732 static __isl_give isl_basic_set
*replace_by_empty(
2733 __isl_take isl_basic_set
*bset
)
2737 space
= isl_basic_set_get_space(bset
);
2738 isl_basic_set_free(bset
);
2739 return isl_basic_set_empty(space
);
2742 /* Remove all information from "bset" that is redundant in the context
2743 * of "context", for the case where the combined equalities of
2744 * "bset" and "context" allow for a compression that can be obtained
2745 * by preapplication of "T".
2746 * If the compression of "context" is empty, meaning that "bset" and
2747 * "context" do not intersect, then return the empty set.
2749 * "bset" itself is not transformed by "T". Instead, the inequalities
2750 * are extracted from "bset" and those are transformed by "T".
2751 * uset_gist_full then determines which of the transformed inequalities
2752 * are redundant with respect to the transformed "context" and removes
2753 * the corresponding inequalities from "bset".
2755 * After preapplying "T" to the inequalities, any common factor is
2756 * removed from the coefficients. If this results in a tightening
2757 * of the constant term, then the same tightening is applied to
2758 * the corresponding untransformed inequality in "bset".
2759 * That is, if after plugging in T, a constraint f(x) >= 0 is of the form
2763 * with 0 <= r < g, then it is equivalent to
2767 * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
2768 * subspace compressed by T since the latter would be transformed to
2772 static __isl_give isl_basic_set
*uset_gist_compressed(
2773 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
,
2774 __isl_take isl_mat
*T
)
2779 isl_size n_row
, n_col
;
2782 ineq
= extract_ineq(bset
);
2783 ineq
= isl_mat_product(ineq
, isl_mat_copy(T
));
2784 context
= isl_basic_set_preimage(context
, T
);
2786 if (!ineq
|| !context
)
2788 if (isl_basic_set_plain_is_empty(context
)) {
2790 isl_basic_set_free(context
);
2791 return replace_by_empty(bset
);
2794 ctx
= isl_mat_get_ctx(ineq
);
2795 n_row
= isl_mat_rows(ineq
);
2796 n_col
= isl_mat_cols(ineq
);
2797 if (n_row
< 0 || n_col
< 0)
2800 for (i
= 0; i
< n_row
; ++i
) {
2801 isl_seq_gcd(ineq
->row
[i
] + 1, n_col
- 1, &ctx
->normalize_gcd
);
2802 if (isl_int_is_zero(ctx
->normalize_gcd
))
2804 if (isl_int_is_one(ctx
->normalize_gcd
))
2806 isl_seq_scale_down(ineq
->row
[i
] + 1, ineq
->row
[i
] + 1,
2807 ctx
->normalize_gcd
, n_col
- 1);
2808 isl_int_fdiv_r(rem
, ineq
->row
[i
][0], ctx
->normalize_gcd
);
2809 isl_int_fdiv_q(ineq
->row
[i
][0],
2810 ineq
->row
[i
][0], ctx
->normalize_gcd
);
2811 if (isl_int_is_zero(rem
))
2813 bset
= isl_basic_set_cow(bset
);
2816 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], rem
);
2820 return uset_gist_full(bset
, ineq
, context
);
2823 isl_basic_set_free(context
);
2824 isl_basic_set_free(bset
);
2828 /* Project "bset" onto the variables that are involved in "template".
2830 static __isl_give isl_basic_set
*project_onto_involved(
2831 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*template)
2836 n
= isl_basic_set_dim(template, isl_dim_set
);
2837 if (n
< 0 || !template)
2838 return isl_basic_set_free(bset
);
2840 for (i
= 0; i
< n
; ++i
) {
2843 involved
= isl_basic_set_involves_dims(template,
2846 return isl_basic_set_free(bset
);
2849 bset
= isl_basic_set_eliminate_vars(bset
, i
, 1);
2855 /* Remove all information from bset that is redundant in the context
2856 * of context. In particular, equalities that are linear combinations
2857 * of those in context are removed. Then the inequalities that are
2858 * redundant in the context of the equalities and inequalities of
2859 * context are removed.
2861 * First of all, we drop those constraints from "context"
2862 * that are irrelevant for computing the gist of "bset".
2863 * Alternatively, we could factorize the intersection of "context" and "bset".
2865 * We first compute the intersection of the integer affine hulls
2866 * of "bset" and "context",
2867 * compute the gist inside this intersection and then reduce
2868 * the constraints with respect to the equalities of the context
2869 * that only involve variables already involved in the input.
2870 * If the intersection of the affine hulls turns out to be empty,
2871 * then return the empty set.
2873 * If two constraints are mutually redundant, then uset_gist_full
2874 * will remove the second of those constraints. We therefore first
2875 * sort the constraints so that constraints not involving existentially
2876 * quantified variables are given precedence over those that do.
2877 * We have to perform this sorting before the variable compression,
2878 * because that may effect the order of the variables.
2880 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2881 __isl_take isl_basic_set
*context
)
2886 isl_basic_set
*aff_context
;
2889 total
= isl_basic_set_dim(bset
, isl_dim_all
);
2890 if (total
< 0 || !context
)
2893 context
= drop_irrelevant_constraints(context
, bset
);
2895 bset
= isl_basic_set_detect_equalities(bset
);
2896 aff
= isl_basic_set_copy(bset
);
2897 aff
= isl_basic_set_plain_affine_hull(aff
);
2898 context
= isl_basic_set_detect_equalities(context
);
2899 aff_context
= isl_basic_set_copy(context
);
2900 aff_context
= isl_basic_set_plain_affine_hull(aff_context
);
2901 aff
= isl_basic_set_intersect(aff
, aff_context
);
2904 if (isl_basic_set_plain_is_empty(aff
)) {
2905 isl_basic_set_free(bset
);
2906 isl_basic_set_free(context
);
2909 bset
= isl_basic_set_sort_constraints(bset
);
2910 if (aff
->n_eq
== 0) {
2911 isl_basic_set_free(aff
);
2912 return uset_gist_uncompressed(bset
, context
);
2914 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2915 eq
= isl_mat_cow(eq
);
2916 T
= isl_mat_variable_compression(eq
, NULL
);
2917 isl_basic_set_free(aff
);
2918 if (T
&& T
->n_col
== 0) {
2920 isl_basic_set_free(context
);
2921 return replace_by_empty(bset
);
2924 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2925 aff_context
= project_onto_involved(aff_context
, bset
);
2927 bset
= uset_gist_compressed(bset
, context
, T
);
2928 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2931 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2932 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2937 isl_basic_set_free(bset
);
2938 isl_basic_set_free(context
);
2942 /* Return the number of equality constraints in "bmap" that involve
2943 * local variables. This function assumes that Gaussian elimination
2944 * has been applied to the equality constraints.
2946 static int n_div_eq(__isl_keep isl_basic_map
*bmap
)
2949 isl_size total
, n_div
;
2954 if (bmap
->n_eq
== 0)
2957 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2958 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2959 if (total
< 0 || n_div
< 0)
2963 for (i
= 0; i
< bmap
->n_eq
; ++i
)
2964 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
,
2971 /* Construct a basic map in "space" defined by the equality constraints in "eq".
2972 * The constraints are assumed not to involve any local variables.
2974 static __isl_give isl_basic_map
*basic_map_from_equalities(
2975 __isl_take isl_space
*space
, __isl_take isl_mat
*eq
)
2979 isl_basic_map
*bmap
= NULL
;
2981 total
= isl_space_dim(space
, isl_dim_all
);
2982 if (total
< 0 || !eq
)
2985 if (1 + total
!= eq
->n_col
)
2986 isl_die(isl_space_get_ctx(space
), isl_error_internal
,
2987 "unexpected number of columns", goto error
);
2989 bmap
= isl_basic_map_alloc_space(isl_space_copy(space
),
2991 for (i
= 0; i
< eq
->n_row
; ++i
) {
2992 k
= isl_basic_map_alloc_equality(bmap
);
2995 isl_seq_cpy(bmap
->eq
[k
], eq
->row
[i
], eq
->n_col
);
2998 isl_space_free(space
);
3002 isl_space_free(space
);
3004 isl_basic_map_free(bmap
);
3008 /* Construct and return a variable compression based on the equality
3009 * constraints in "bmap1" and "bmap2" that do not involve the local variables.
3010 * "n1" is the number of (initial) equality constraints in "bmap1"
3011 * that do involve local variables.
3012 * "n2" is the number of (initial) equality constraints in "bmap2"
3013 * that do involve local variables.
3014 * "total" is the total number of other variables.
3015 * This function assumes that Gaussian elimination
3016 * has been applied to the equality constraints in both "bmap1" and "bmap2"
3017 * such that the equality constraints not involving local variables
3018 * are those that start at "n1" or "n2".
3020 * If either of "bmap1" and "bmap2" does not have such equality constraints,
3021 * then simply compute the compression based on the equality constraints
3022 * in the other basic map.
3023 * Otherwise, combine the equality constraints from both into a new
3024 * basic map such that Gaussian elimination can be applied to this combination
3025 * and then construct a variable compression from the resulting
3026 * equality constraints.
3028 static __isl_give isl_mat
*combined_variable_compression(
3029 __isl_keep isl_basic_map
*bmap1
, int n1
,
3030 __isl_keep isl_basic_map
*bmap2
, int n2
, int total
)
3033 isl_mat
*E1
, *E2
, *V
;
3034 isl_basic_map
*bmap
;
3036 ctx
= isl_basic_map_get_ctx(bmap1
);
3037 if (bmap1
->n_eq
== n1
) {
3038 E2
= isl_mat_sub_alloc6(ctx
, bmap2
->eq
,
3039 n2
, bmap2
->n_eq
- n2
, 0, 1 + total
);
3040 return isl_mat_variable_compression(E2
, NULL
);
3042 if (bmap2
->n_eq
== n2
) {
3043 E1
= isl_mat_sub_alloc6(ctx
, bmap1
->eq
,
3044 n1
, bmap1
->n_eq
- n1
, 0, 1 + total
);
3045 return isl_mat_variable_compression(E1
, NULL
);
3047 E1
= isl_mat_sub_alloc6(ctx
, bmap1
->eq
,
3048 n1
, bmap1
->n_eq
- n1
, 0, 1 + total
);
3049 E2
= isl_mat_sub_alloc6(ctx
, bmap2
->eq
,
3050 n2
, bmap2
->n_eq
- n2
, 0, 1 + total
);
3051 E1
= isl_mat_concat(E1
, E2
);
3052 bmap
= basic_map_from_equalities(isl_basic_map_get_space(bmap1
), E1
);
3053 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3056 E1
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
, 0, 1 + total
);
3057 V
= isl_mat_variable_compression(E1
, NULL
);
3058 isl_basic_map_free(bmap
);
3063 /* Extract the stride constraints from "bmap", compressed
3064 * with respect to both the stride constraints in "context" and
3065 * the remaining equality constraints in both "bmap" and "context".
3066 * "bmap_n_eq" is the number of (initial) stride constraints in "bmap".
3067 * "context_n_eq" is the number of (initial) stride constraints in "context".
3069 * Let x be all variables in "bmap" (and "context") other than the local
3070 * variables. First compute a variable compression
3074 * based on the non-stride equality constraints in "bmap" and "context".
3075 * Consider the stride constraints of "context",
3079 * with y the local variables and plug in the variable compression,
3082 * A(V x') + B(y) = 0
3084 * Use these constraints to compute a parameter compression on x'
3088 * Now consider the stride constraints of "bmap"
3092 * and plug in x = V*T x''.
3093 * That is, return A = [C*V*T D].
3095 static __isl_give isl_mat
*extract_compressed_stride_constraints(
3096 __isl_keep isl_basic_map
*bmap
, int bmap_n_eq
,
3097 __isl_keep isl_basic_map
*context
, int context_n_eq
)
3099 isl_size total
, n_div
;
3101 isl_mat
*A
, *B
, *T
, *V
;
3103 total
= isl_basic_map_dim(context
, isl_dim_all
);
3104 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
3105 if (total
< 0 || n_div
< 0)
3109 ctx
= isl_basic_map_get_ctx(bmap
);
3111 V
= combined_variable_compression(bmap
, bmap_n_eq
,
3112 context
, context_n_eq
, total
);
3114 A
= isl_mat_sub_alloc6(ctx
, context
->eq
, 0, context_n_eq
, 0, 1 + total
);
3115 B
= isl_mat_sub_alloc6(ctx
, context
->eq
,
3116 0, context_n_eq
, 1 + total
, n_div
);
3117 A
= isl_mat_product(A
, isl_mat_copy(V
));
3118 T
= isl_mat_parameter_compression_ext(A
, B
);
3119 T
= isl_mat_product(V
, T
);
3121 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3123 T
= isl_mat_free(T
);
3125 T
= isl_mat_diagonal(T
, isl_mat_identity(ctx
, n_div
));
3127 A
= isl_mat_sub_alloc6(ctx
, bmap
->eq
,
3128 0, bmap_n_eq
, 0, 1 + total
+ n_div
);
3129 A
= isl_mat_product(A
, T
);
3134 /* Remove the prime factors from *g that have an exponent that
3135 * is strictly smaller than the exponent in "c".
3136 * All exponents in *g are known to be smaller than or equal
3139 * That is, if *g is equal to
3141 * p_1^{e_1} p_2^{e_2} ... p_n^{e_n}
3143 * and "c" is equal to
3145 * p_1^{f_1} p_2^{f_2} ... p_n^{f_n}
3149 * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ...
3150 * p_n^{e_n * (e_n = f_n)}
3152 * If e_i = f_i, then c / *g does not have any p_i factors and therefore
3153 * neither does the gcd of *g and c / *g.
3154 * If e_i < f_i, then the gcd of *g and c / *g has a positive
3155 * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors.
3156 * Dividing *g by this gcd therefore strictly reduces the exponent
3157 * of the prime factors that need to be removed, while leaving the
3158 * other prime factors untouched.
3159 * Repeating this process until gcd(*g, c / *g) = 1 therefore
3160 * removes all undesired factors, without removing any others.
3162 static void remove_incomplete_powers(isl_int
*g
, isl_int c
)
3168 isl_int_divexact(t
, c
, *g
);
3169 isl_int_gcd(t
, t
, *g
);
3170 if (isl_int_is_one(t
))
3172 isl_int_divexact(*g
, *g
, t
);
3177 /* Reduce the "n" stride constraints in "bmap" based on a copy "A"
3178 * of the same stride constraints in a compressed space that exploits
3179 * all equalities in the context and the other equalities in "bmap".
3181 * If the stride constraints of "bmap" are of the form
3185 * then A is of the form
3189 * If any of these constraints involves only a single local variable y,
3190 * then the constraint appears as
3200 * Let g be the gcd of m and the coefficients of h.
3201 * Then, in particular, g is a divisor of the coefficients of h and
3205 * is known to be a multiple of g.
3206 * If some prime factor in m appears with the same exponent in g,
3207 * then it can be removed from m because f(x) is already known
3208 * to be a multiple of g and therefore in particular of this power
3209 * of the prime factors.
3210 * Prime factors that appear with a smaller exponent in g cannot
3211 * be removed from m.
3212 * Let g' be the divisor of g containing all prime factors that
3213 * appear with the same exponent in m and g, then
3217 * can be replaced by
3219 * f(x) + m/g' y_i' = 0
3221 * Note that (if g' != 1) this changes the explicit representation
3222 * of y_i to that of y_i', so the integer division at position i
3223 * is marked unknown and later recomputed by a call to
3224 * isl_basic_map_gauss.
3226 static __isl_give isl_basic_map
*reduce_stride_constraints(
3227 __isl_take isl_basic_map
*bmap
, int n
, __isl_keep isl_mat
*A
)
3230 isl_size total
, n_div
;
3234 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3235 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
3236 if (total
< 0 || n_div
< 0 || !A
)
3237 return isl_basic_map_free(bmap
);
3241 for (i
= 0; i
< n
; ++i
) {
3244 div
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, n_div
);
3246 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
3247 "equality constraints modified unexpectedly",
3249 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
+ div
+ 1,
3250 n_div
- div
- 1) != -1)
3252 if (isl_mat_row_gcd(A
, i
, &gcd
) < 0)
3254 if (isl_int_is_one(gcd
))
3256 remove_incomplete_powers(&gcd
, bmap
->eq
[i
][1 + total
+ div
]);
3257 if (isl_int_is_one(gcd
))
3259 isl_int_divexact(bmap
->eq
[i
][1 + total
+ div
],
3260 bmap
->eq
[i
][1 + total
+ div
], gcd
);
3261 bmap
= isl_basic_map_mark_div_unknown(bmap
, div
);
3269 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3274 isl_basic_map_free(bmap
);
3278 /* Simplify the stride constraints in "bmap" based on
3279 * the remaining equality constraints in "bmap" and all equality
3280 * constraints in "context".
3281 * Only do this if both "bmap" and "context" have stride constraints.
3283 * First extract a copy of the stride constraints in "bmap" in a compressed
3284 * space exploiting all the other equality constraints and then
3285 * use this compressed copy to simplify the original stride constraints.
3287 static __isl_give isl_basic_map
*gist_strides(__isl_take isl_basic_map
*bmap
,
3288 __isl_keep isl_basic_map
*context
)
3290 int bmap_n_eq
, context_n_eq
;
3293 if (!bmap
|| !context
)
3294 return isl_basic_map_free(bmap
);
3296 bmap_n_eq
= n_div_eq(bmap
);
3297 context_n_eq
= n_div_eq(context
);
3299 if (bmap_n_eq
< 0 || context_n_eq
< 0)
3300 return isl_basic_map_free(bmap
);
3301 if (bmap_n_eq
== 0 || context_n_eq
== 0)
3304 A
= extract_compressed_stride_constraints(bmap
, bmap_n_eq
,
3305 context
, context_n_eq
);
3306 bmap
= reduce_stride_constraints(bmap
, bmap_n_eq
, A
);
3313 /* Return a basic map that has the same intersection with "context" as "bmap"
3314 * and that is as "simple" as possible.
3316 * The core computation is performed on the pure constraints.
3317 * When we add back the meaning of the integer divisions, we need
3318 * to (re)introduce the div constraints. If we happen to have
3319 * discovered that some of these integer divisions are equal to
3320 * some affine combination of other variables, then these div
3321 * constraints may end up getting simplified in terms of the equalities,
3322 * resulting in extra inequalities on the other variables that
3323 * may have been removed already or that may not even have been
3324 * part of the input. We try and remove those constraints of
3325 * this form that are most obviously redundant with respect to
3326 * the context. We also remove those div constraints that are
3327 * redundant with respect to the other constraints in the result.
3329 * The stride constraints among the equality constraints in "bmap" are
3330 * also simplified with respecting to the other equality constraints
3331 * in "bmap" and with respect to all equality constraints in "context".
3333 __isl_give isl_basic_map
*isl_basic_map_gist(__isl_take isl_basic_map
*bmap
,
3334 __isl_take isl_basic_map
*context
)
3336 isl_basic_set
*bset
, *eq
;
3337 isl_basic_map
*eq_bmap
;
3338 isl_size total
, n_div
, n_div_bmap
;
3339 unsigned extra
, n_eq
, n_ineq
;
3341 if (!bmap
|| !context
)
3344 if (isl_basic_map_plain_is_universe(bmap
)) {
3345 isl_basic_map_free(context
);
3348 if (isl_basic_map_plain_is_empty(context
)) {
3349 isl_space
*space
= isl_basic_map_get_space(bmap
);
3350 isl_basic_map_free(bmap
);
3351 isl_basic_map_free(context
);
3352 return isl_basic_map_universe(space
);
3354 if (isl_basic_map_plain_is_empty(bmap
)) {
3355 isl_basic_map_free(context
);
3359 bmap
= isl_basic_map_remove_redundancies(bmap
);
3360 context
= isl_basic_map_remove_redundancies(context
);
3361 bmap
= isl_basic_map_order_divs(bmap
);
3362 context
= isl_basic_map_align_divs(context
, bmap
);
3364 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
3365 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3366 n_div_bmap
= isl_basic_map_dim(bmap
, isl_dim_div
);
3367 if (n_div
< 0 || total
< 0 || n_div_bmap
< 0)
3369 extra
= n_div
- n_div_bmap
;
3371 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
3372 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, extra
);
3373 bset
= uset_gist(bset
,
3374 isl_basic_map_underlying_set(isl_basic_map_copy(context
)));
3375 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, total
, extra
);
3377 if (!bset
|| bset
->n_eq
== 0 || n_div
== 0 ||
3378 isl_basic_set_plain_is_empty(bset
)) {
3379 isl_basic_map_free(context
);
3380 return isl_basic_map_overlying_set(bset
, bmap
);
3384 n_ineq
= bset
->n_ineq
;
3385 eq
= isl_basic_set_copy(bset
);
3386 eq
= isl_basic_set_cow(eq
);
3387 eq
= isl_basic_set_free_inequality(eq
, n_ineq
);
3388 bset
= isl_basic_set_free_equality(bset
, n_eq
);
3390 eq_bmap
= isl_basic_map_overlying_set(eq
, isl_basic_map_copy(bmap
));
3391 eq_bmap
= gist_strides(eq_bmap
, context
);
3392 eq_bmap
= isl_basic_map_remove_shifted_constraints(eq_bmap
, context
);
3393 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
3394 bmap
= isl_basic_map_intersect(bmap
, eq_bmap
);
3395 bmap
= isl_basic_map_remove_redundancies(bmap
);
3399 isl_basic_map_free(bmap
);
3400 isl_basic_map_free(context
);
3405 * Assumes context has no implicit divs.
3407 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
3408 __isl_take isl_basic_map
*context
)
3412 if (!map
|| !context
)
3415 if (isl_basic_map_plain_is_empty(context
)) {
3416 isl_space
*space
= isl_map_get_space(map
);
3418 isl_basic_map_free(context
);
3419 return isl_map_universe(space
);
3422 context
= isl_basic_map_remove_redundancies(context
);
3423 map
= isl_map_cow(map
);
3424 if (isl_map_basic_map_check_equal_space(map
, context
) < 0)
3426 map
= isl_map_compute_divs(map
);
3429 for (i
= map
->n
- 1; i
>= 0; --i
) {
3430 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
3431 isl_basic_map_copy(context
));
3434 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
3435 isl_basic_map_free(map
->p
[i
]);
3436 if (i
!= map
->n
- 1)
3437 map
->p
[i
] = map
->p
[map
->n
- 1];
3441 isl_basic_map_free(context
);
3442 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3446 isl_basic_map_free(context
);
3450 /* Drop all inequalities from "bmap" that also appear in "context".
3451 * "context" is assumed to have only known local variables and
3452 * the initial local variables of "bmap" are assumed to be the same
3453 * as those of "context".
3454 * The constraints of both "bmap" and "context" are assumed
3455 * to have been sorted using isl_basic_map_sort_constraints.
3457 * Run through the inequality constraints of "bmap" and "context"
3459 * If a constraint of "bmap" involves variables not in "context",
3460 * then it cannot appear in "context".
3461 * If a matching constraint is found, it is removed from "bmap".
3463 static __isl_give isl_basic_map
*drop_inequalities(
3464 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_map
*context
)
3467 isl_size total
, bmap_total
;
3470 total
= isl_basic_map_dim(context
, isl_dim_all
);
3471 bmap_total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3472 if (total
< 0 || bmap_total
< 0)
3473 return isl_basic_map_free(bmap
);
3475 extra
= bmap_total
- total
;
3477 i1
= bmap
->n_ineq
- 1;
3478 i2
= context
->n_ineq
- 1;
3479 while (bmap
&& i1
>= 0 && i2
>= 0) {
3482 if (isl_seq_first_non_zero(bmap
->ineq
[i1
] + 1 + total
,
3487 cmp
= isl_basic_map_constraint_cmp(context
, bmap
->ineq
[i1
],
3497 if (isl_int_eq(bmap
->ineq
[i1
][0], context
->ineq
[i2
][0])) {
3498 bmap
= isl_basic_map_cow(bmap
);
3499 if (isl_basic_map_drop_inequality(bmap
, i1
) < 0)
3500 bmap
= isl_basic_map_free(bmap
);
3509 /* Drop all equalities from "bmap" that also appear in "context".
3510 * "context" is assumed to have only known local variables and
3511 * the initial local variables of "bmap" are assumed to be the same
3512 * as those of "context".
3514 * Run through the equality constraints of "bmap" and "context"
3516 * If a constraint of "bmap" involves variables not in "context",
3517 * then it cannot appear in "context".
3518 * If a matching constraint is found, it is removed from "bmap".
3520 static __isl_give isl_basic_map
*drop_equalities(
3521 __isl_take isl_basic_map
*bmap
, __isl_keep isl_basic_map
*context
)
3524 isl_size total
, bmap_total
;
3527 total
= isl_basic_map_dim(context
, isl_dim_all
);
3528 bmap_total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3529 if (total
< 0 || bmap_total
< 0)
3530 return isl_basic_map_free(bmap
);
3532 extra
= bmap_total
- total
;
3534 i1
= bmap
->n_eq
- 1;
3535 i2
= context
->n_eq
- 1;
3537 while (bmap
&& i1
>= 0 && i2
>= 0) {
3540 if (isl_seq_first_non_zero(bmap
->eq
[i1
] + 1 + total
,
3543 last1
= isl_seq_last_non_zero(bmap
->eq
[i1
] + 1, total
);
3544 last2
= isl_seq_last_non_zero(context
->eq
[i2
] + 1, total
);
3545 if (last1
> last2
) {
3549 if (last1
< last2
) {
3553 if (isl_seq_eq(bmap
->eq
[i1
], context
->eq
[i2
], 1 + total
)) {
3554 bmap
= isl_basic_map_cow(bmap
);
3555 if (isl_basic_map_drop_equality(bmap
, i1
) < 0)
3556 bmap
= isl_basic_map_free(bmap
);
3565 /* Remove the constraints in "context" from "bmap".
3566 * "context" is assumed to have explicit representations
3567 * for all local variables.
3569 * First align the divs of "bmap" to those of "context" and
3570 * sort the constraints. Then drop all constraints from "bmap"
3571 * that appear in "context".
3573 __isl_give isl_basic_map
*isl_basic_map_plain_gist(
3574 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
3576 isl_bool done
, known
;
3578 done
= isl_basic_map_plain_is_universe(context
);
3579 if (done
== isl_bool_false
)
3580 done
= isl_basic_map_plain_is_universe(bmap
);
3581 if (done
== isl_bool_false
)
3582 done
= isl_basic_map_plain_is_empty(context
);
3583 if (done
== isl_bool_false
)
3584 done
= isl_basic_map_plain_is_empty(bmap
);
3588 isl_basic_map_free(context
);
3591 known
= isl_basic_map_divs_known(context
);
3595 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
3596 "context has unknown divs", goto error
);
3598 context
= isl_basic_map_order_divs(context
);
3599 bmap
= isl_basic_map_align_divs(bmap
, context
);
3600 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3601 bmap
= isl_basic_map_sort_constraints(bmap
);
3602 context
= isl_basic_map_sort_constraints(context
);
3604 bmap
= drop_inequalities(bmap
, context
);
3605 bmap
= drop_equalities(bmap
, context
);
3607 isl_basic_map_free(context
);
3608 bmap
= isl_basic_map_finalize(bmap
);
3611 isl_basic_map_free(bmap
);
3612 isl_basic_map_free(context
);
3616 /* Replace "map" by the disjunct at position "pos" and free "context".
3618 static __isl_give isl_map
*replace_by_disjunct(__isl_take isl_map
*map
,
3619 int pos
, __isl_take isl_basic_map
*context
)
3621 isl_basic_map
*bmap
;
3623 bmap
= isl_basic_map_copy(map
->p
[pos
]);
3625 isl_basic_map_free(context
);
3626 return isl_map_from_basic_map(bmap
);
3629 /* Remove the constraints in "context" from "map".
3630 * If any of the disjuncts in the result turns out to be the universe,
3631 * then return this universe.
3632 * "context" is assumed to have explicit representations
3633 * for all local variables.
3635 __isl_give isl_map
*isl_map_plain_gist_basic_map(__isl_take isl_map
*map
,
3636 __isl_take isl_basic_map
*context
)
3639 isl_bool univ
, known
;
3641 univ
= isl_basic_map_plain_is_universe(context
);
3645 isl_basic_map_free(context
);
3648 known
= isl_basic_map_divs_known(context
);
3652 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
3653 "context has unknown divs", goto error
);
3655 map
= isl_map_cow(map
);
3658 for (i
= 0; i
< map
->n
; ++i
) {
3659 map
->p
[i
] = isl_basic_map_plain_gist(map
->p
[i
],
3660 isl_basic_map_copy(context
));
3661 univ
= isl_basic_map_plain_is_universe(map
->p
[i
]);
3664 if (univ
&& map
->n
> 1)
3665 return replace_by_disjunct(map
, i
, context
);
3668 isl_basic_map_free(context
);
3669 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3671 ISL_F_CLR(map
, ISL_MAP_DISJOINT
);
3675 isl_basic_map_free(context
);
3679 /* Remove the constraints in "context" from "set".
3680 * If any of the disjuncts in the result turns out to be the universe,
3681 * then return this universe.
3682 * "context" is assumed to have explicit representations
3683 * for all local variables.
3685 __isl_give isl_set
*isl_set_plain_gist_basic_set(__isl_take isl_set
*set
,
3686 __isl_take isl_basic_set
*context
)
3688 return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set
),
3689 bset_to_bmap(context
)));
3692 /* Remove the constraints in "context" from "map".
3693 * If any of the disjuncts in the result turns out to be the universe,
3694 * then return this universe.
3695 * "context" is assumed to consist of a single disjunct and
3696 * to have explicit representations for all local variables.
3698 __isl_give isl_map
*isl_map_plain_gist(__isl_take isl_map
*map
,
3699 __isl_take isl_map
*context
)
3701 isl_basic_map
*hull
;
3703 hull
= isl_map_unshifted_simple_hull(context
);
3704 return isl_map_plain_gist_basic_map(map
, hull
);
3707 /* Replace "map" by a universe map in the same space and free "drop".
3709 static __isl_give isl_map
*replace_by_universe(__isl_take isl_map
*map
,
3710 __isl_take isl_map
*drop
)
3714 res
= isl_map_universe(isl_map_get_space(map
));
3720 /* Return a map that has the same intersection with "context" as "map"
3721 * and that is as "simple" as possible.
3723 * If "map" is already the universe, then we cannot make it any simpler.
3724 * Similarly, if "context" is the universe, then we cannot exploit it
3726 * If "map" and "context" are identical to each other, then we can
3727 * return the corresponding universe.
3729 * If either "map" or "context" consists of multiple disjuncts,
3730 * then check if "context" happens to be a subset of "map",
3731 * in which case all constraints can be removed.
3732 * In case of multiple disjuncts, the standard procedure
3733 * may not be able to detect that all constraints can be removed.
3735 * If none of these cases apply, we have to work a bit harder.
3736 * During this computation, we make use of a single disjunct context,
3737 * so if the original context consists of more than one disjunct
3738 * then we need to approximate the context by a single disjunct set.
3739 * Simply taking the simple hull may drop constraints that are
3740 * only implicitly available in each disjunct. We therefore also
3741 * look for constraints among those defining "map" that are valid
3742 * for the context. These can then be used to simplify away
3743 * the corresponding constraints in "map".
3745 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
3746 __isl_take isl_map
*context
)
3750 isl_size n_disjunct_map
, n_disjunct_context
;
3752 isl_basic_map
*hull
;
3754 is_universe
= isl_map_plain_is_universe(map
);
3755 if (is_universe
>= 0 && !is_universe
)
3756 is_universe
= isl_map_plain_is_universe(context
);
3757 if (is_universe
< 0)
3760 isl_map_free(context
);
3764 isl_map_align_params_bin(&map
, &context
);
3765 equal
= isl_map_plain_is_equal(map
, context
);
3769 return replace_by_universe(map
, context
);
3771 n_disjunct_map
= isl_map_n_basic_map(map
);
3772 n_disjunct_context
= isl_map_n_basic_map(context
);
3773 if (n_disjunct_map
< 0 || n_disjunct_context
< 0)
3775 if (n_disjunct_map
!= 1 || n_disjunct_context
!= 1) {
3776 subset
= isl_map_is_subset(context
, map
);
3780 return replace_by_universe(map
, context
);
3783 context
= isl_map_compute_divs(context
);
3786 if (n_disjunct_context
== 1) {
3787 hull
= isl_map_simple_hull(context
);
3792 ctx
= isl_map_get_ctx(map
);
3793 list
= isl_map_list_alloc(ctx
, 2);
3794 list
= isl_map_list_add(list
, isl_map_copy(context
));
3795 list
= isl_map_list_add(list
, isl_map_copy(map
));
3796 hull
= isl_map_unshifted_simple_hull_from_map_list(context
,
3799 return isl_map_gist_basic_map(map
, hull
);
3802 isl_map_free(context
);
3806 __isl_give isl_basic_set
*isl_basic_set_gist(__isl_take isl_basic_set
*bset
,
3807 __isl_take isl_basic_set
*context
)
3809 return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset
),
3810 bset_to_bmap(context
)));
3813 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
3814 __isl_take isl_basic_set
*context
)
3816 return set_from_map(isl_map_gist_basic_map(set_to_map(set
),
3817 bset_to_bmap(context
)));
3820 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
3821 __isl_take isl_basic_set
*context
)
3823 isl_space
*space
= isl_set_get_space(set
);
3824 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
3825 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
3826 return isl_set_gist_basic_set(set
, dom_context
);
3829 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
3830 __isl_take isl_set
*context
)
3832 return set_from_map(isl_map_gist(set_to_map(set
), set_to_map(context
)));
3835 /* Compute the gist of "bmap" with respect to the constraints "context"
3838 __isl_give isl_basic_map
*isl_basic_map_gist_domain(
3839 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*context
)
3841 isl_space
*space
= isl_basic_map_get_space(bmap
);
3842 isl_basic_map
*bmap_context
= isl_basic_map_universe(space
);
3844 bmap_context
= isl_basic_map_intersect_domain(bmap_context
, context
);
3845 return isl_basic_map_gist(bmap
, bmap_context
);
3848 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
3849 __isl_take isl_set
*context
)
3851 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3852 map_context
= isl_map_intersect_domain(map_context
, context
);
3853 return isl_map_gist(map
, map_context
);
3856 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
3857 __isl_take isl_set
*context
)
3859 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3860 map_context
= isl_map_intersect_range(map_context
, context
);
3861 return isl_map_gist(map
, map_context
);
3864 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
3865 __isl_take isl_set
*context
)
3867 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
3868 map_context
= isl_map_intersect_params(map_context
, context
);
3869 return isl_map_gist(map
, map_context
);
3872 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
3873 __isl_take isl_set
*context
)
3875 return isl_map_gist_params(set
, context
);
3878 /* Quick check to see if two basic maps are disjoint.
3879 * In particular, we reduce the equalities and inequalities of
3880 * one basic map in the context of the equalities of the other
3881 * basic map and check if we get a contradiction.
3883 isl_bool
isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
3884 __isl_keep isl_basic_map
*bmap2
)
3886 struct isl_vec
*v
= NULL
;
3891 if (isl_basic_map_check_equal_space(bmap1
, bmap2
) < 0)
3892 return isl_bool_error
;
3893 if (bmap1
->n_div
|| bmap2
->n_div
)
3894 return isl_bool_false
;
3895 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
3896 return isl_bool_false
;
3898 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
3900 return isl_bool_error
;
3902 return isl_bool_false
;
3903 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
3906 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
3909 compute_elimination_index(bmap1
, elim
, total
);
3910 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
3912 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
3913 bmap1
, elim
, total
);
3914 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
3915 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3918 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
3920 reduced
= reduced_using_equalities(v
->block
.data
,
3921 bmap2
->ineq
[i
], bmap1
, elim
, total
);
3922 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
3923 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3926 compute_elimination_index(bmap2
, elim
, total
);
3927 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
3929 reduced
= reduced_using_equalities(v
->block
.data
,
3930 bmap1
->ineq
[i
], bmap2
, elim
, total
);
3931 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
3932 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3937 return isl_bool_false
;
3941 return isl_bool_true
;
3945 return isl_bool_error
;
3948 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
3949 __isl_keep isl_basic_set
*bset2
)
3951 return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1
),
3952 bset_to_bmap(bset2
));
3955 /* Does "test" hold for all pairs of basic maps in "map1" and "map2"?
3957 static isl_bool
all_pairs(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
,
3958 isl_bool (*test
)(__isl_keep isl_basic_map
*bmap1
,
3959 __isl_keep isl_basic_map
*bmap2
))
3964 return isl_bool_error
;
3966 for (i
= 0; i
< map1
->n
; ++i
) {
3967 for (j
= 0; j
< map2
->n
; ++j
) {
3968 isl_bool d
= test(map1
->p
[i
], map2
->p
[j
]);
3969 if (d
!= isl_bool_true
)
3974 return isl_bool_true
;
3977 /* Are "map1" and "map2" obviously disjoint, based on information
3978 * that can be derived without looking at the individual basic maps?
3980 * In particular, if one of them is empty or if they live in different spaces
3981 * (ignoring parameters), then they are clearly disjoint.
3983 static isl_bool
isl_map_plain_is_disjoint_global(__isl_keep isl_map
*map1
,
3984 __isl_keep isl_map
*map2
)
3990 return isl_bool_error
;
3992 disjoint
= isl_map_plain_is_empty(map1
);
3993 if (disjoint
< 0 || disjoint
)
3996 disjoint
= isl_map_plain_is_empty(map2
);
3997 if (disjoint
< 0 || disjoint
)
4000 match
= isl_map_tuple_is_equal(map1
, isl_dim_in
, map2
, isl_dim_in
);
4001 if (match
< 0 || !match
)
4002 return match
< 0 ? isl_bool_error
: isl_bool_true
;
4004 match
= isl_map_tuple_is_equal(map1
, isl_dim_out
, map2
, isl_dim_out
);
4005 if (match
< 0 || !match
)
4006 return match
< 0 ? isl_bool_error
: isl_bool_true
;
4008 return isl_bool_false
;
4011 /* Are "map1" and "map2" obviously disjoint?
4013 * If one of them is empty or if they live in different spaces (ignoring
4014 * parameters), then they are clearly disjoint.
4015 * This is checked by isl_map_plain_is_disjoint_global.
4017 * If they have different parameters, then we skip any further tests.
4019 * If they are obviously equal, but not obviously empty, then we will
4020 * not be able to detect if they are disjoint.
4022 * Otherwise we check if each basic map in "map1" is obviously disjoint
4023 * from each basic map in "map2".
4025 isl_bool
isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
4026 __isl_keep isl_map
*map2
)
4032 disjoint
= isl_map_plain_is_disjoint_global(map1
, map2
);
4033 if (disjoint
< 0 || disjoint
)
4036 match
= isl_map_has_equal_params(map1
, map2
);
4037 if (match
< 0 || !match
)
4038 return match
< 0 ? isl_bool_error
: isl_bool_false
;
4040 intersect
= isl_map_plain_is_equal(map1
, map2
);
4041 if (intersect
< 0 || intersect
)
4042 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
4044 return all_pairs(map1
, map2
, &isl_basic_map_plain_is_disjoint
);
4047 /* Are "map1" and "map2" disjoint?
4048 * The parameters are assumed to have been aligned.
4050 * In particular, check whether all pairs of basic maps are disjoint.
4052 static isl_bool
isl_map_is_disjoint_aligned(__isl_keep isl_map
*map1
,
4053 __isl_keep isl_map
*map2
)
4055 return all_pairs(map1
, map2
, &isl_basic_map_is_disjoint
);
4058 /* Are "map1" and "map2" disjoint?
4060 * They are disjoint if they are "obviously disjoint" or if one of them
4061 * is empty. Otherwise, they are not disjoint if one of them is universal.
4062 * If the two inputs are (obviously) equal and not empty, then they are
4064 * If none of these cases apply, then check if all pairs of basic maps
4065 * are disjoint after aligning the parameters.
4067 isl_bool
isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
4072 disjoint
= isl_map_plain_is_disjoint_global(map1
, map2
);
4073 if (disjoint
< 0 || disjoint
)
4076 disjoint
= isl_map_is_empty(map1
);
4077 if (disjoint
< 0 || disjoint
)
4080 disjoint
= isl_map_is_empty(map2
);
4081 if (disjoint
< 0 || disjoint
)
4084 intersect
= isl_map_plain_is_universe(map1
);
4085 if (intersect
< 0 || intersect
)
4086 return isl_bool_not(intersect
);
4088 intersect
= isl_map_plain_is_universe(map2
);
4089 if (intersect
< 0 || intersect
)
4090 return isl_bool_not(intersect
);
4092 intersect
= isl_map_plain_is_equal(map1
, map2
);
4093 if (intersect
< 0 || intersect
)
4094 return isl_bool_not(intersect
);
4096 return isl_map_align_params_map_map_and_test(map1
, map2
,
4097 &isl_map_is_disjoint_aligned
);
4100 /* Are "bmap1" and "bmap2" disjoint?
4102 * They are disjoint if they are "obviously disjoint" or if one of them
4103 * is empty. Otherwise, they are not disjoint if one of them is universal.
4104 * If none of these cases apply, we compute the intersection and see if
4105 * the result is empty.
4107 isl_bool
isl_basic_map_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
4108 __isl_keep isl_basic_map
*bmap2
)
4112 isl_basic_map
*test
;
4114 disjoint
= isl_basic_map_plain_is_disjoint(bmap1
, bmap2
);
4115 if (disjoint
< 0 || disjoint
)
4118 disjoint
= isl_basic_map_is_empty(bmap1
);
4119 if (disjoint
< 0 || disjoint
)
4122 disjoint
= isl_basic_map_is_empty(bmap2
);
4123 if (disjoint
< 0 || disjoint
)
4126 intersect
= isl_basic_map_plain_is_universe(bmap1
);
4127 if (intersect
< 0 || intersect
)
4128 return isl_bool_not(intersect
);
4130 intersect
= isl_basic_map_plain_is_universe(bmap2
);
4131 if (intersect
< 0 || intersect
)
4132 return isl_bool_not(intersect
);
4134 test
= isl_basic_map_intersect(isl_basic_map_copy(bmap1
),
4135 isl_basic_map_copy(bmap2
));
4136 disjoint
= isl_basic_map_is_empty(test
);
4137 isl_basic_map_free(test
);
4142 /* Are "bset1" and "bset2" disjoint?
4144 isl_bool
isl_basic_set_is_disjoint(__isl_keep isl_basic_set
*bset1
,
4145 __isl_keep isl_basic_set
*bset2
)
4147 return isl_basic_map_is_disjoint(bset1
, bset2
);
4150 isl_bool
isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
4151 __isl_keep isl_set
*set2
)
4153 return isl_map_plain_is_disjoint(set_to_map(set1
), set_to_map(set2
));
4156 /* Are "set1" and "set2" disjoint?
4158 isl_bool
isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
4160 return isl_map_is_disjoint(set1
, set2
);
4163 /* Is "v" equal to 0, 1 or -1?
4165 static int is_zero_or_one(isl_int v
)
4167 return isl_int_is_zero(v
) || isl_int_is_one(v
) || isl_int_is_negone(v
);
4170 /* Are the "n" coefficients starting at "first" of inequality constraints
4171 * "i" and "j" of "bmap" opposite to each other?
4173 static int is_opposite_part(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4176 return isl_seq_is_neg(bmap
->ineq
[i
] + first
, bmap
->ineq
[j
] + first
, n
);
4179 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4180 * apart from the constant term?
4182 static isl_bool
is_opposite(__isl_keep isl_basic_map
*bmap
, int i
, int j
)
4186 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4188 return isl_bool_error
;
4189 return is_opposite_part(bmap
, i
, j
, 1, total
);
4192 /* Check if we can combine a given div with lower bound l and upper
4193 * bound u with some other div and if so return that other div.
4194 * Otherwise, return a position beyond the integer divisions.
4195 * Return -1 on error.
4197 * We first check that
4198 * - the bounds are opposites of each other (except for the constant
4200 * - the bounds do not reference any other div
4201 * - no div is defined in terms of this div
4203 * Let m be the size of the range allowed on the div by the bounds.
4204 * That is, the bounds are of the form
4206 * e <= a <= e + m - 1
4208 * with e some expression in the other variables.
4209 * We look for another div b such that no third div is defined in terms
4210 * of this second div b and such that in any constraint that contains
4211 * a (except for the given lower and upper bound), also contains b
4212 * with a coefficient that is m times that of b.
4213 * That is, all constraints (except for the lower and upper bound)
4216 * e + f (a + m b) >= 0
4218 * Furthermore, in the constraints that only contain b, the coefficient
4219 * of b should be equal to 1 or -1.
4220 * If so, we return b so that "a + m b" can be replaced by
4221 * a single div "c = a + m b".
4223 static int div_find_coalesce(__isl_keep isl_basic_map
*bmap
, int *pairs
,
4224 unsigned div
, unsigned l
, unsigned u
)
4232 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4235 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
4238 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + v_div
, div
) != -1)
4240 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + v_div
+ div
+ 1,
4241 n_div
- div
- 1) != -1)
4243 opp
= is_opposite(bmap
, l
, u
);
4244 if (opp
< 0 || !opp
)
4245 return opp
< 0 ? -1 : n_div
;
4247 for (i
= 0; i
< n_div
; ++i
) {
4248 if (isl_int_is_zero(bmap
->div
[i
][0]))
4250 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + v_div
+ div
]))
4254 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4255 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
4256 isl_int_sub(bmap
->ineq
[l
][0],
4257 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4258 bmap
= isl_basic_map_copy(bmap
);
4259 bmap
= isl_basic_map_set_to_empty(bmap
);
4260 isl_basic_map_free(bmap
);
4263 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
4265 for (i
= 0; i
< n_div
; ++i
) {
4270 for (j
= 0; j
< n_div
; ++j
) {
4271 if (isl_int_is_zero(bmap
->div
[j
][0]))
4273 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + v_div
+ i
]))
4278 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
4280 if (j
== l
|| j
== u
)
4282 if (isl_int_is_zero(bmap
->ineq
[j
][1 + v_div
+ div
])) {
4283 if (is_zero_or_one(bmap
->ineq
[j
][1 + v_div
+ i
]))
4287 if (isl_int_is_zero(bmap
->ineq
[j
][1 + v_div
+ i
]))
4289 isl_int_mul(bmap
->ineq
[j
][1 + v_div
+ div
],
4290 bmap
->ineq
[j
][1 + v_div
+ div
],
4292 valid
= isl_int_eq(bmap
->ineq
[j
][1 + v_div
+ div
],
4293 bmap
->ineq
[j
][1 + v_div
+ i
]);
4294 isl_int_divexact(bmap
->ineq
[j
][1 + v_div
+ div
],
4295 bmap
->ineq
[j
][1 + v_div
+ div
],
4300 if (j
< bmap
->n_ineq
)
4305 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
4306 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4310 /* Internal data structure used during the construction and/or evaluation of
4311 * an inequality that ensures that a pair of bounds always allows
4312 * for an integer value.
4314 * "tab" is the tableau in which the inequality is evaluated. It may
4315 * be NULL until it is actually needed.
4316 * "v" contains the inequality coefficients.
4317 * "g", "fl" and "fu" are temporary scalars used during the construction and
4320 struct test_ineq_data
{
4321 struct isl_tab
*tab
;
4328 /* Free all the memory allocated by the fields of "data".
4330 static void test_ineq_data_clear(struct test_ineq_data
*data
)
4332 isl_tab_free(data
->tab
);
4333 isl_vec_free(data
->v
);
4334 isl_int_clear(data
->g
);
4335 isl_int_clear(data
->fl
);
4336 isl_int_clear(data
->fu
);
4339 /* Is the inequality stored in data->v satisfied by "bmap"?
4340 * That is, does it only attain non-negative values?
4341 * data->tab is a tableau corresponding to "bmap".
4343 static isl_bool
test_ineq_is_satisfied(__isl_keep isl_basic_map
*bmap
,
4344 struct test_ineq_data
*data
)
4347 enum isl_lp_result res
;
4349 ctx
= isl_basic_map_get_ctx(bmap
);
4351 data
->tab
= isl_tab_from_basic_map(bmap
, 0);
4352 res
= isl_tab_min(data
->tab
, data
->v
->el
, ctx
->one
, &data
->g
, NULL
, 0);
4353 if (res
== isl_lp_error
)
4354 return isl_bool_error
;
4355 return res
== isl_lp_ok
&& isl_int_is_nonneg(data
->g
);
4358 /* Given a lower and an upper bound on div i, do they always allow
4359 * for an integer value of the given div?
4360 * Determine this property by constructing an inequality
4361 * such that the property is guaranteed when the inequality is nonnegative.
4362 * The lower bound is inequality l, while the upper bound is inequality u.
4363 * The constructed inequality is stored in data->v.
4365 * Let the upper bound be
4369 * and the lower bound
4373 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
4376 * - f_u e_l <= f_u f_l g a <= f_l e_u
4378 * Since all variables are integer valued, this is equivalent to
4380 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
4382 * If this interval is at least f_u f_l g, then it contains at least
4383 * one integer value for a.
4384 * That is, the test constraint is
4386 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
4390 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0
4392 * If the coefficients of f_l e_u + f_u e_l have a common divisor g',
4393 * then the constraint can be scaled down by a factor g',
4394 * with the constant term replaced by
4395 * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g').
4396 * Note that the result of applying Fourier-Motzkin to this pair
4399 * f_l e_u + f_u e_l >= 0
4401 * If the constant term of the scaled down version of this constraint,
4402 * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant
4403 * term of the scaled down test constraint, then the test constraint
4404 * is known to hold and no explicit evaluation is required.
4405 * This is essentially the Omega test.
4407 * If the test constraint consists of only a constant term, then
4408 * it is sufficient to look at the sign of this constant term.
4410 static isl_bool
int_between_bounds(__isl_keep isl_basic_map
*bmap
, int i
,
4411 int l
, int u
, struct test_ineq_data
*data
)
4416 offset
= isl_basic_map_offset(bmap
, isl_dim_div
);
4417 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4419 return isl_bool_error
;
4421 isl_int_gcd(data
->g
,
4422 bmap
->ineq
[l
][offset
+ i
], bmap
->ineq
[u
][offset
+ i
]);
4423 isl_int_divexact(data
->fl
, bmap
->ineq
[l
][offset
+ i
], data
->g
);
4424 isl_int_divexact(data
->fu
, bmap
->ineq
[u
][offset
+ i
], data
->g
);
4425 isl_int_neg(data
->fu
, data
->fu
);
4426 isl_seq_combine(data
->v
->el
, data
->fl
, bmap
->ineq
[u
],
4427 data
->fu
, bmap
->ineq
[l
], offset
+ n_div
);
4428 isl_int_mul(data
->g
, data
->g
, data
->fl
);
4429 isl_int_mul(data
->g
, data
->g
, data
->fu
);
4430 isl_int_sub(data
->g
, data
->g
, data
->fl
);
4431 isl_int_sub(data
->g
, data
->g
, data
->fu
);
4432 isl_int_add_ui(data
->g
, data
->g
, 1);
4433 isl_int_sub(data
->fl
, data
->v
->el
[0], data
->g
);
4435 isl_seq_gcd(data
->v
->el
+ 1, offset
- 1 + n_div
, &data
->g
);
4436 if (isl_int_is_zero(data
->g
))
4437 return isl_int_is_nonneg(data
->fl
);
4438 if (isl_int_is_one(data
->g
)) {
4439 isl_int_set(data
->v
->el
[0], data
->fl
);
4440 return test_ineq_is_satisfied(bmap
, data
);
4442 isl_int_fdiv_q(data
->fl
, data
->fl
, data
->g
);
4443 isl_int_fdiv_q(data
->v
->el
[0], data
->v
->el
[0], data
->g
);
4444 if (isl_int_eq(data
->fl
, data
->v
->el
[0]))
4445 return isl_bool_true
;
4446 isl_int_set(data
->v
->el
[0], data
->fl
);
4447 isl_seq_scale_down(data
->v
->el
+ 1, data
->v
->el
+ 1, data
->g
,
4448 offset
- 1 + n_div
);
4450 return test_ineq_is_satisfied(bmap
, data
);
4453 /* Remove more kinds of divs that are not strictly needed.
4454 * In particular, if all pairs of lower and upper bounds on a div
4455 * are such that they allow at least one integer value of the div,
4456 * then we can eliminate the div using Fourier-Motzkin without
4457 * introducing any spurious solutions.
4459 * If at least one of the two constraints has a unit coefficient for the div,
4460 * then the presence of such a value is guaranteed so there is no need to check.
4461 * In particular, the value attained by the bound with unit coefficient
4462 * can serve as this intermediate value.
4464 static __isl_give isl_basic_map
*drop_more_redundant_divs(
4465 __isl_take isl_basic_map
*bmap
, __isl_take
int *pairs
, int n
)
4468 struct test_ineq_data data
= { NULL
, NULL
};
4473 isl_int_init(data
.g
);
4474 isl_int_init(data
.fl
);
4475 isl_int_init(data
.fu
);
4477 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4481 ctx
= isl_basic_map_get_ctx(bmap
);
4482 off
= isl_basic_map_offset(bmap
, isl_dim_div
);
4483 data
.v
= isl_vec_alloc(ctx
, off
+ n_div
);
4492 for (i
= 0; i
< n_div
; ++i
) {
4495 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
4501 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
4502 if (!isl_int_is_pos(bmap
->ineq
[l
][off
+ i
]))
4504 if (isl_int_is_one(bmap
->ineq
[l
][off
+ i
]))
4506 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
4507 if (!isl_int_is_neg(bmap
->ineq
[u
][off
+ i
]))
4509 if (isl_int_is_negone(bmap
->ineq
[u
][off
+ i
]))
4511 has_int
= int_between_bounds(bmap
, i
, l
, u
,
4515 if (data
.tab
&& data
.tab
->empty
)
4520 if (u
< bmap
->n_ineq
)
4523 if (data
.tab
&& data
.tab
->empty
) {
4524 bmap
= isl_basic_map_set_to_empty(bmap
);
4527 if (l
== bmap
->n_ineq
) {
4535 test_ineq_data_clear(&data
);
4542 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
4543 return isl_basic_map_drop_redundant_divs(bmap
);
4546 isl_basic_map_free(bmap
);
4547 test_ineq_data_clear(&data
);
4551 /* Given a pair of divs div1 and div2 such that, except for the lower bound l
4552 * and the upper bound u, div1 always occurs together with div2 in the form
4553 * (div1 + m div2), where m is the constant range on the variable div1
4554 * allowed by l and u, replace the pair div1 and div2 by a single
4555 * div that is equal to div1 + m div2.
4557 * The new div will appear in the location that contains div2.
4558 * We need to modify all constraints that contain
4559 * div2 = (div - div1) / m
4560 * The coefficient of div2 is known to be equal to 1 or -1.
4561 * (If a constraint does not contain div2, it will also not contain div1.)
4562 * If the constraint also contains div1, then we know they appear
4563 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
4564 * i.e., the coefficient of div is f.
4566 * Otherwise, we first need to introduce div1 into the constraint.
4575 * A lower bound on div2
4579 * can be replaced by
4581 * m div2 + div1 + m t + f >= 0
4587 * can be replaced by
4589 * -(m div2 + div1) + m t + f' >= 0
4591 * These constraint are those that we would obtain from eliminating
4592 * div1 using Fourier-Motzkin.
4594 * After all constraints have been modified, we drop the lower and upper
4595 * bound and then drop div1.
4596 * Since the new div is only placed in the same location that used
4597 * to store div2, but otherwise has a different meaning, any possible
4598 * explicit representation of the original div2 is removed.
4600 static __isl_give isl_basic_map
*coalesce_divs(__isl_take isl_basic_map
*bmap
,
4601 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
4609 ctx
= isl_basic_map_get_ctx(bmap
);
4611 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
4613 return isl_basic_map_free(bmap
);
4614 total
= 1 + v_div
+ bmap
->n_div
;
4617 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
4618 isl_int_add_ui(m
, m
, 1);
4620 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
4621 if (i
== l
|| i
== u
)
4623 if (isl_int_is_zero(bmap
->ineq
[i
][1 + v_div
+ div2
]))
4625 if (isl_int_is_zero(bmap
->ineq
[i
][1 + v_div
+ div1
])) {
4626 if (isl_int_is_pos(bmap
->ineq
[i
][1 + v_div
+ div2
]))
4627 isl_seq_combine(bmap
->ineq
[i
], m
, bmap
->ineq
[i
],
4628 ctx
->one
, bmap
->ineq
[l
], total
);
4630 isl_seq_combine(bmap
->ineq
[i
], m
, bmap
->ineq
[i
],
4631 ctx
->one
, bmap
->ineq
[u
], total
);
4633 isl_int_set(bmap
->ineq
[i
][1 + v_div
+ div2
],
4634 bmap
->ineq
[i
][1 + v_div
+ div1
]);
4635 isl_int_set_si(bmap
->ineq
[i
][1 + v_div
+ div1
], 0);
4640 isl_basic_map_drop_inequality(bmap
, l
);
4641 isl_basic_map_drop_inequality(bmap
, u
);
4643 isl_basic_map_drop_inequality(bmap
, u
);
4644 isl_basic_map_drop_inequality(bmap
, l
);
4646 bmap
= isl_basic_map_mark_div_unknown(bmap
, div2
);
4647 bmap
= isl_basic_map_drop_div(bmap
, div1
);
4651 /* First check if we can coalesce any pair of divs and
4652 * then continue with dropping more redundant divs.
4654 * We loop over all pairs of lower and upper bounds on a div
4655 * with coefficient 1 and -1, respectively, check if there
4656 * is any other div "c" with which we can coalesce the div
4657 * and if so, perform the coalescing.
4659 static __isl_give isl_basic_map
*coalesce_or_drop_more_redundant_divs(
4660 __isl_take isl_basic_map
*bmap
, int *pairs
, int n
)
4666 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
4667 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4668 if (v_div
< 0 || n_div
< 0)
4669 return isl_basic_map_free(bmap
);
4671 for (i
= 0; i
< n_div
; ++i
) {
4674 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
4675 if (!isl_int_is_one(bmap
->ineq
[l
][1 + v_div
+ i
]))
4677 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
4680 if (!isl_int_is_negone(bmap
->ineq
[u
][1+v_div
+i
]))
4682 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
4688 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
4689 return isl_basic_map_drop_redundant_divs(bmap
);
4694 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
4699 return drop_more_redundant_divs(bmap
, pairs
, n
);
4702 isl_basic_map_free(bmap
);
4706 /* Are the "n" coefficients starting at "first" of inequality constraints
4707 * "i" and "j" of "bmap" equal to each other?
4709 static int is_parallel_part(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4712 return isl_seq_eq(bmap
->ineq
[i
] + first
, bmap
->ineq
[j
] + first
, n
);
4715 /* Are inequality constraints "i" and "j" of "bmap" equal to each other,
4716 * apart from the constant term and the coefficient at position "pos"?
4718 static isl_bool
is_parallel_except(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4723 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4725 return isl_bool_error
;
4726 return is_parallel_part(bmap
, i
, j
, 1, pos
- 1) &&
4727 is_parallel_part(bmap
, i
, j
, pos
+ 1, total
- pos
);
4730 /* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4731 * apart from the constant term and the coefficient at position "pos"?
4733 static isl_bool
is_opposite_except(__isl_keep isl_basic_map
*bmap
, int i
, int j
,
4738 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
4740 return isl_bool_error
;
4741 return is_opposite_part(bmap
, i
, j
, 1, pos
- 1) &&
4742 is_opposite_part(bmap
, i
, j
, pos
+ 1, total
- pos
);
4745 /* Restart isl_basic_map_drop_redundant_divs after "bmap" has
4746 * been modified, simplying it if "simplify" is set.
4747 * Free the temporary data structure "pairs" that was associated
4748 * to the old version of "bmap".
4750 static __isl_give isl_basic_map
*drop_redundant_divs_again(
4751 __isl_take isl_basic_map
*bmap
, __isl_take
int *pairs
, int simplify
)
4754 bmap
= isl_basic_map_simplify(bmap
);
4756 return isl_basic_map_drop_redundant_divs(bmap
);
4759 /* Is "div" the single unknown existentially quantified variable
4760 * in inequality constraint "ineq" of "bmap"?
4761 * "div" is known to have a non-zero coefficient in "ineq".
4763 static isl_bool
single_unknown(__isl_keep isl_basic_map
*bmap
, int ineq
,
4771 known
= isl_basic_map_div_is_known(bmap
, div
);
4772 if (known
< 0 || known
)
4773 return isl_bool_not(known
);
4774 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4776 return isl_bool_error
;
4778 return isl_bool_true
;
4779 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4780 for (i
= 0; i
< n_div
; ++i
) {
4785 if (isl_int_is_zero(bmap
->ineq
[ineq
][o_div
+ i
]))
4787 known
= isl_basic_map_div_is_known(bmap
, i
);
4788 if (known
< 0 || !known
)
4792 return isl_bool_true
;
4795 /* Does integer division "div" have coefficient 1 in inequality constraint
4798 static isl_bool
has_coef_one(__isl_keep isl_basic_map
*bmap
, int div
, int ineq
)
4802 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4803 if (isl_int_is_one(bmap
->ineq
[ineq
][o_div
+ div
]))
4804 return isl_bool_true
;
4806 return isl_bool_false
;
4809 /* Turn inequality constraint "ineq" of "bmap" into an equality and
4810 * then try and drop redundant divs again,
4811 * freeing the temporary data structure "pairs" that was associated
4812 * to the old version of "bmap".
4814 static __isl_give isl_basic_map
*set_eq_and_try_again(
4815 __isl_take isl_basic_map
*bmap
, int ineq
, __isl_take
int *pairs
)
4817 bmap
= isl_basic_map_cow(bmap
);
4818 isl_basic_map_inequality_to_equality(bmap
, ineq
);
4819 return drop_redundant_divs_again(bmap
, pairs
, 1);
4822 /* Drop the integer division at position "div", along with the two
4823 * inequality constraints "ineq1" and "ineq2" in which it appears
4824 * from "bmap" and then try and drop redundant divs again,
4825 * freeing the temporary data structure "pairs" that was associated
4826 * to the old version of "bmap".
4828 static __isl_give isl_basic_map
*drop_div_and_try_again(
4829 __isl_take isl_basic_map
*bmap
, int div
, int ineq1
, int ineq2
,
4830 __isl_take
int *pairs
)
4832 if (ineq1
> ineq2
) {
4833 isl_basic_map_drop_inequality(bmap
, ineq1
);
4834 isl_basic_map_drop_inequality(bmap
, ineq2
);
4836 isl_basic_map_drop_inequality(bmap
, ineq2
);
4837 isl_basic_map_drop_inequality(bmap
, ineq1
);
4839 bmap
= isl_basic_map_drop_div(bmap
, div
);
4840 return drop_redundant_divs_again(bmap
, pairs
, 0);
4843 /* Given two inequality constraints
4845 * f(x) + n d + c >= 0, (ineq)
4847 * with d the variable at position "pos", and
4849 * f(x) + c0 >= 0, (lower)
4851 * compute the maximal value of the lower bound ceil((-f(x) - c)/n)
4852 * determined by the first constraint.
4859 static void lower_bound_from_parallel(__isl_keep isl_basic_map
*bmap
,
4860 int ineq
, int lower
, int pos
, isl_int
*l
)
4862 isl_int_neg(*l
, bmap
->ineq
[ineq
][0]);
4863 isl_int_add(*l
, *l
, bmap
->ineq
[lower
][0]);
4864 isl_int_cdiv_q(*l
, *l
, bmap
->ineq
[ineq
][pos
]);
4867 /* Given two inequality constraints
4869 * f(x) + n d + c >= 0, (ineq)
4871 * with d the variable at position "pos", and
4873 * -f(x) - c0 >= 0, (upper)
4875 * compute the minimal value of the lower bound ceil((-f(x) - c)/n)
4876 * determined by the first constraint.
4883 static void lower_bound_from_opposite(__isl_keep isl_basic_map
*bmap
,
4884 int ineq
, int upper
, int pos
, isl_int
*u
)
4886 isl_int_neg(*u
, bmap
->ineq
[ineq
][0]);
4887 isl_int_sub(*u
, *u
, bmap
->ineq
[upper
][0]);
4888 isl_int_cdiv_q(*u
, *u
, bmap
->ineq
[ineq
][pos
]);
4891 /* Given a lower bound constraint "ineq" on "div" in "bmap",
4892 * does the corresponding lower bound have a fixed value in "bmap"?
4894 * In particular, "ineq" is of the form
4896 * f(x) + n d + c >= 0
4898 * with n > 0, c the constant term and
4899 * d the existentially quantified variable "div".
4900 * That is, the lower bound is
4902 * ceil((-f(x) - c)/n)
4904 * Look for a pair of constraints
4909 * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value.
4910 * That is, check that
4912 * ceil((-c1 - c)/n) = ceil((c0 - c)/n)
4914 * If so, return the index of inequality f(x) + c0 >= 0.
4915 * Otherwise, return bmap->n_ineq.
4916 * Return -1 on error.
4918 static int lower_bound_is_cst(__isl_keep isl_basic_map
*bmap
, int div
, int ineq
)
4921 int lower
= -1, upper
= -1;
4926 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4927 for (i
= 0; i
< bmap
->n_ineq
&& (lower
< 0 || upper
< 0); ++i
) {
4932 if (!isl_int_is_zero(bmap
->ineq
[i
][o_div
+ div
]))
4934 par
= isl_bool_false
;
4936 par
= is_parallel_except(bmap
, ineq
, i
, o_div
+ div
);
4943 opp
= isl_bool_false
;
4945 opp
= is_opposite_except(bmap
, ineq
, i
, o_div
+ div
);
4952 if (lower
< 0 || upper
< 0)
4953 return bmap
->n_ineq
;
4958 lower_bound_from_parallel(bmap
, ineq
, lower
, o_div
+ div
, &l
);
4959 lower_bound_from_opposite(bmap
, ineq
, upper
, o_div
+ div
, &u
);
4961 equal
= isl_int_eq(l
, u
);
4966 return equal
? lower
: bmap
->n_ineq
;
4969 /* Given a lower bound constraint "ineq" on the existentially quantified
4970 * variable "div", such that the corresponding lower bound has
4971 * a fixed value in "bmap", assign this fixed value to the variable and
4972 * then try and drop redundant divs again,
4973 * freeing the temporary data structure "pairs" that was associated
4974 * to the old version of "bmap".
4975 * "lower" determines the constant value for the lower bound.
4977 * In particular, "ineq" is of the form
4979 * f(x) + n d + c >= 0,
4981 * while "lower" is of the form
4985 * The lower bound is ceil((-f(x) - c)/n) and its constant value
4986 * is ceil((c0 - c)/n).
4988 static __isl_give isl_basic_map
*fix_cst_lower(__isl_take isl_basic_map
*bmap
,
4989 int div
, int ineq
, int lower
, int *pairs
)
4996 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
4997 lower_bound_from_parallel(bmap
, ineq
, lower
, o_div
+ div
, &c
);
4998 bmap
= isl_basic_map_fix(bmap
, isl_dim_div
, div
, c
);
5003 return isl_basic_map_drop_redundant_divs(bmap
);
5006 /* Do any of the integer divisions of "bmap" involve integer division "div"?
5008 * The integer division "div" could only ever appear in any later
5009 * integer division (with an explicit representation).
5011 static isl_bool
any_div_involves_div(__isl_keep isl_basic_map
*bmap
, int div
)
5014 isl_size v_div
, n_div
;
5016 v_div
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
5017 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
5018 if (v_div
< 0 || n_div
< 0)
5019 return isl_bool_error
;
5021 for (i
= div
+ 1; i
< n_div
; ++i
) {
5024 unknown
= isl_basic_map_div_is_marked_unknown(bmap
, i
);
5026 return isl_bool_error
;
5029 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + v_div
+ div
]))
5030 return isl_bool_true
;
5033 return isl_bool_false
;
5036 /* Remove divs that are not strictly needed based on the inequality
5038 * In particular, if a div only occurs positively (or negatively)
5039 * in constraints, then it can simply be dropped.
5040 * Also, if a div occurs in only two constraints and if moreover
5041 * those two constraints are opposite to each other, except for the constant
5042 * term and if the sum of the constant terms is such that for any value
5043 * of the other values, there is always at least one integer value of the
5044 * div, i.e., if one plus this sum is greater than or equal to
5045 * the (absolute value) of the coefficient of the div in the constraints,
5046 * then we can also simply drop the div.
5048 * If an existentially quantified variable does not have an explicit
5049 * representation, appears in only a single lower bound that does not
5050 * involve any other such existentially quantified variables and appears
5051 * in this lower bound with coefficient 1,
5052 * then fix the variable to the value of the lower bound. That is,
5053 * turn the inequality into an equality.
5054 * If for any value of the other variables, there is any value
5055 * for the existentially quantified variable satisfying the constraints,
5056 * then this lower bound also satisfies the constraints.
5057 * It is therefore safe to pick this lower bound.
5059 * The same reasoning holds even if the coefficient is not one.
5060 * However, fixing the variable to the value of the lower bound may
5061 * in general introduce an extra integer division, in which case
5062 * it may be better to pick another value.
5063 * If this integer division has a known constant value, then plugging
5064 * in this constant value removes the existentially quantified variable
5065 * completely. In particular, if the lower bound is of the form
5066 * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and
5067 * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n),
5068 * then the existentially quantified variable can be assigned this
5071 * We skip divs that appear in equalities or in the definition of other divs.
5072 * Divs that appear in the definition of other divs usually occur in at least
5073 * 4 constraints, but the constraints may have been simplified.
5075 * If any divs are left after these simple checks then we move on
5076 * to more complicated cases in drop_more_redundant_divs.
5078 static __isl_give isl_basic_map
*isl_basic_map_drop_redundant_divs_ineq(
5079 __isl_take isl_basic_map
*bmap
)
5089 if (bmap
->n_div
== 0)
5092 off
= isl_basic_map_var_offset(bmap
, isl_dim_div
);
5094 return isl_basic_map_free(bmap
);
5095 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
5099 n_ineq
= isl_basic_map_n_inequality(bmap
);
5102 for (i
= 0; i
< bmap
->n_div
; ++i
) {
5104 int last_pos
, last_neg
;
5107 isl_bool involves
, opp
, set_div
;
5109 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
5110 involves
= any_div_involves_div(bmap
, i
);
5115 for (j
= 0; j
< bmap
->n_eq
; ++j
)
5116 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
5122 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
5123 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
5127 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
5132 pairs
[i
] = pos
* neg
;
5133 if (pairs
[i
] == 0) {
5134 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
5135 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
5136 isl_basic_map_drop_inequality(bmap
, j
);
5137 bmap
= isl_basic_map_drop_div(bmap
, i
);
5138 return drop_redundant_divs_again(bmap
, pairs
, 0);
5141 opp
= isl_bool_false
;
5143 opp
= is_opposite(bmap
, last_pos
, last_neg
);
5148 isl_bool single
, one
;
5152 single
= single_unknown(bmap
, last_pos
, i
);
5157 one
= has_coef_one(bmap
, i
, last_pos
);
5161 return set_eq_and_try_again(bmap
, last_pos
,
5163 lower
= lower_bound_is_cst(bmap
, i
, last_pos
);
5167 return fix_cst_lower(bmap
, i
, last_pos
, lower
,
5172 isl_int_add(bmap
->ineq
[last_pos
][0],
5173 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
5174 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
5175 bmap
->ineq
[last_pos
][0], 1);
5176 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
5177 bmap
->ineq
[last_pos
][1+off
+i
]);
5178 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
5179 bmap
->ineq
[last_pos
][0], 1);
5180 isl_int_sub(bmap
->ineq
[last_pos
][0],
5181 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
5183 return drop_div_and_try_again(bmap
, i
,
5184 last_pos
, last_neg
, pairs
);
5186 set_div
= isl_bool_false
;
5188 set_div
= ok_to_set_div_from_bound(bmap
, i
, last_pos
);
5190 return isl_basic_map_free(bmap
);
5192 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
5193 return drop_redundant_divs_again(bmap
, pairs
, 1);
5200 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
5206 isl_basic_map_free(bmap
);
5210 /* Consider the coefficients at "c" as a row vector and replace
5211 * them with their product with "T". "T" is assumed to be a square matrix.
5213 static isl_stat
preimage(isl_int
*c
, __isl_keep isl_mat
*T
)
5219 n
= isl_mat_rows(T
);
5221 return isl_stat_error
;
5222 if (isl_seq_first_non_zero(c
, n
) == -1)
5224 ctx
= isl_mat_get_ctx(T
);
5225 v
= isl_vec_alloc(ctx
, n
);
5227 return isl_stat_error
;
5228 isl_seq_swp_or_cpy(v
->el
, c
, n
);
5229 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
5231 return isl_stat_error
;
5232 isl_seq_swp_or_cpy(c
, v
->el
, n
);
5238 /* Plug in T for the variables in "bmap" starting at "pos".
5239 * T is a linear unimodular matrix, i.e., without constant term.
5241 static __isl_give isl_basic_map
*isl_basic_map_preimage_vars(
5242 __isl_take isl_basic_map
*bmap
, unsigned pos
, __isl_take isl_mat
*T
)
5245 isl_size n_row
, n_col
;
5247 bmap
= isl_basic_map_cow(bmap
);
5248 n_row
= isl_mat_rows(T
);
5249 n_col
= isl_mat_cols(T
);
5250 if (!bmap
|| n_row
< 0 || n_col
< 0)
5254 isl_die(isl_mat_get_ctx(T
), isl_error_invalid
,
5255 "expecting square matrix", goto error
);
5257 if (isl_basic_map_check_range(bmap
, isl_dim_all
, pos
, n_col
) < 0)
5260 for (i
= 0; i
< bmap
->n_eq
; ++i
)
5261 if (preimage(bmap
->eq
[i
] + 1 + pos
, T
) < 0)
5263 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
5264 if (preimage(bmap
->ineq
[i
] + 1 + pos
, T
) < 0)
5266 for (i
= 0; i
< bmap
->n_div
; ++i
) {
5267 if (isl_basic_map_div_is_marked_unknown(bmap
, i
))
5269 if (preimage(bmap
->div
[i
] + 1 + 1 + pos
, T
) < 0)
5276 isl_basic_map_free(bmap
);
5281 /* Remove divs that are not strictly needed.
5283 * First look for an equality constraint involving two or more
5284 * existentially quantified variables without an explicit
5285 * representation. Replace the combination that appears
5286 * in the equality constraint by a single existentially quantified
5287 * variable such that the equality can be used to derive
5288 * an explicit representation for the variable.
5289 * If there are no more such equality constraints, then continue
5290 * with isl_basic_map_drop_redundant_divs_ineq.
5292 * In particular, if the equality constraint is of the form
5294 * f(x) + \sum_i c_i a_i = 0
5296 * with a_i existentially quantified variable without explicit
5297 * representation, then apply a transformation on the existentially
5298 * quantified variables to turn the constraint into
5302 * with g the gcd of the c_i.
5303 * In order to easily identify which existentially quantified variables
5304 * have a complete explicit representation, i.e., without being defined
5305 * in terms of other existentially quantified variables without
5306 * an explicit representation, the existentially quantified variables
5309 * The variable transformation is computed by extending the row
5310 * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation
5312 * [a_1'] [c_1/g ... c_n/g] [ a_1 ]
5317 * with [c_1/g ... c_n/g] representing the first row of U.
5318 * The inverse of U is then plugged into the original constraints.
5319 * The call to isl_basic_map_simplify makes sure the explicit
5320 * representation for a_1' is extracted from the equality constraint.
5322 __isl_give isl_basic_map
*isl_basic_map_drop_redundant_divs(
5323 __isl_take isl_basic_map
*bmap
)
5335 if (isl_basic_map_divs_known(bmap
))
5336 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5337 if (bmap
->n_eq
== 0)
5338 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5339 bmap
= isl_basic_map_sort_divs(bmap
);
5343 first
= isl_basic_map_first_unknown_div(bmap
);
5345 return isl_basic_map_free(bmap
);
5347 o_div
= isl_basic_map_offset(bmap
, isl_dim_div
);
5348 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
5350 return isl_basic_map_free(bmap
);
5352 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5353 l
= isl_seq_first_non_zero(bmap
->eq
[i
] + o_div
+ first
,
5358 if (isl_seq_first_non_zero(bmap
->eq
[i
] + o_div
+ l
+ 1,
5359 n_div
- (l
+ 1)) == -1)
5363 if (i
>= bmap
->n_eq
)
5364 return isl_basic_map_drop_redundant_divs_ineq(bmap
);
5366 ctx
= isl_basic_map_get_ctx(bmap
);
5367 T
= isl_mat_alloc(ctx
, n_div
- l
, n_div
- l
);
5369 return isl_basic_map_free(bmap
);
5370 isl_seq_cpy(T
->row
[0], bmap
->eq
[i
] + o_div
+ l
, n_div
- l
);
5371 T
= isl_mat_normalize_row(T
, 0);
5372 T
= isl_mat_unimodular_complete(T
, 1);
5373 T
= isl_mat_right_inverse(T
);
5375 for (i
= l
; i
< n_div
; ++i
)
5376 bmap
= isl_basic_map_mark_div_unknown(bmap
, i
);
5377 bmap
= isl_basic_map_preimage_vars(bmap
, o_div
- 1 + l
, T
);
5378 bmap
= isl_basic_map_simplify(bmap
);
5380 return isl_basic_map_drop_redundant_divs(bmap
);
5383 /* Does "bmap" satisfy any equality that involves more than 2 variables
5384 * and/or has coefficients different from -1 and 1?
5386 static isl_bool
has_multiple_var_equality(__isl_keep isl_basic_map
*bmap
)
5391 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5393 return isl_bool_error
;
5395 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5398 j
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1, total
);
5401 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
5402 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
5403 return isl_bool_true
;
5406 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
5410 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
5411 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
5412 return isl_bool_true
;
5415 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
5417 return isl_bool_true
;
5420 return isl_bool_false
;
5423 /* Remove any common factor g from the constraint coefficients in "v".
5424 * The constant term is stored in the first position and is replaced
5425 * by floor(c/g). If any common factor is removed and if this results
5426 * in a tightening of the constraint, then set *tightened.
5428 static __isl_give isl_vec
*normalize_constraint(__isl_take isl_vec
*v
,
5435 ctx
= isl_vec_get_ctx(v
);
5436 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
5437 if (isl_int_is_zero(ctx
->normalize_gcd
))
5439 if (isl_int_is_one(ctx
->normalize_gcd
))
5444 if (tightened
&& !isl_int_is_divisible_by(v
->el
[0], ctx
->normalize_gcd
))
5446 isl_int_fdiv_q(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
5447 isl_seq_scale_down(v
->el
+ 1, v
->el
+ 1, ctx
->normalize_gcd
,
5452 /* Internal representation used by isl_basic_map_reduce_coefficients.
5454 * "total" is the total dimensionality of the original basic map.
5455 * "v" is a temporary vector of size 1 + total that can be used
5456 * to store constraint coefficients.
5457 * "T" is the variable compression.
5458 * "T2" is the inverse transformation.
5459 * "tightened" is set if any constant term got tightened
5460 * while reducing the coefficients.
5462 struct isl_reduce_coefficients_data
{
5470 /* Free all memory allocated in "data".
5472 static void isl_reduce_coefficients_data_clear(
5473 struct isl_reduce_coefficients_data
*data
)
5475 data
->T
= isl_mat_free(data
->T
);
5476 data
->T2
= isl_mat_free(data
->T2
);
5477 data
->v
= isl_vec_free(data
->v
);
5480 /* Initialize "data" for "bmap", freeing all allocated memory
5481 * if anything goes wrong.
5483 * In particular, construct a variable compression
5484 * from the equality constraints of "bmap" and
5485 * allocate a temporary vector.
5487 static isl_stat
isl_reduce_coefficients_data_init(
5488 __isl_keep isl_basic_map
*bmap
,
5489 struct isl_reduce_coefficients_data
*data
)
5497 data
->tightened
= 0;
5499 data
->total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5500 if (data
->total
< 0)
5501 return isl_stat_error
;
5502 ctx
= isl_basic_map_get_ctx(bmap
);
5503 data
->v
= isl_vec_alloc(ctx
, 1 + data
->total
);
5505 return isl_stat_error
;
5507 eq
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
,
5508 0, 1 + data
->total
);
5509 data
->T
= isl_mat_variable_compression(eq
, &data
->T2
);
5510 if (!data
->T
|| !data
->T2
)
5515 isl_reduce_coefficients_data_clear(data
);
5516 return isl_stat_error
;
5519 /* Reduce the coefficients of "bmap" by applying the variable compression
5521 * In particular, apply the variable compression to each constraint,
5522 * factor out any common factor in the non-constant coefficients and
5523 * then apply the inverse of the compression.
5525 * Only apply the reduction on a single copy of the basic map
5526 * since the reduction may leave the result in an inconsistent state.
5527 * In particular, the constraints may not be gaussed.
5529 static __isl_give isl_basic_map
*reduce_coefficients(
5530 __isl_take isl_basic_map
*bmap
,
5531 struct isl_reduce_coefficients_data
*data
)
5536 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5538 return isl_basic_map_free(bmap
);
5539 if (total
!= data
->total
)
5540 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_internal
,
5541 "total dimensionality changed unexpectedly",
5542 return isl_basic_map_free(bmap
));
5544 bmap
= isl_basic_map_cow(bmap
);
5548 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
5549 isl_seq_cpy(data
->v
->el
, bmap
->ineq
[i
], 1 + data
->total
);
5550 data
->v
= isl_vec_mat_product(data
->v
, isl_mat_copy(data
->T
));
5551 data
->v
= normalize_constraint(data
->v
, &data
->tightened
);
5552 data
->v
= isl_vec_mat_product(data
->v
, isl_mat_copy(data
->T2
));
5554 return isl_basic_map_free(bmap
);
5555 isl_seq_cpy(bmap
->ineq
[i
], data
->v
->el
, 1 + data
->total
);
5558 ISL_F_SET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
5563 /* If "bmap" is an integer set that satisfies any equality involving
5564 * more than 2 variables and/or has coefficients different from -1 and 1,
5565 * then use variable compression to reduce the coefficients by removing
5566 * any (hidden) common factor.
5567 * In particular, apply the variable compression to each constraint,
5568 * factor out any common factor in the non-constant coefficients and
5569 * then apply the inverse of the compression.
5570 * At the end, we mark the basic map as having reduced constants.
5571 * If this flag is still set on the next invocation of this function,
5572 * then we skip the computation.
5574 * Removing a common factor may result in a tightening of some of
5575 * the constraints. If this happens, then we may end up with two
5576 * opposite inequalities that can be replaced by an equality.
5577 * We therefore call isl_basic_map_detect_inequality_pairs,
5578 * which checks for such pairs of inequalities as well as eliminate_divs_eq
5579 * and isl_basic_map_gauss if such a pair was found.
5580 * This call to isl_basic_map_gauss may undo much of the effect
5581 * of the reduction on which isl_map_coalesce depends.
5582 * In particular, constraints in terms of (compressed) local variables
5583 * get reformulated in terms of the set variables again.
5584 * The reduction is therefore applied again afterwards.
5585 * This has to be done before the call to eliminate_divs_eq, however,
5586 * since that may remove some local variables, while
5587 * the data used during the reduction is formulated in terms
5588 * of the original variables.
5590 * Tightening may also result in some other constraints becoming
5591 * (rationally) redundant with respect to the tightened constraint
5592 * (in combination with other constraints). The basic map may
5593 * therefore no longer be assumed to have no redundant constraints.
5595 * Note that this function may leave the result in an inconsistent state.
5596 * In particular, the constraints may not be gaussed.
5597 * Unfortunately, isl_map_coalesce actually depends on this inconsistent state
5598 * for some of the test cases to pass successfully.
5599 * Any potential modification of the representation is therefore only
5600 * performed on a single copy of the basic map.
5602 __isl_give isl_basic_map
*isl_basic_map_reduce_coefficients(
5603 __isl_take isl_basic_map
*bmap
)
5605 struct isl_reduce_coefficients_data data
;
5610 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
))
5612 if (isl_basic_map_is_rational(bmap
))
5614 if (bmap
->n_eq
== 0)
5616 multi
= has_multiple_var_equality(bmap
);
5618 return isl_basic_map_free(bmap
);
5622 if (isl_reduce_coefficients_data_init(bmap
, &data
) < 0)
5623 return isl_basic_map_free(bmap
);
5625 if (data
.T
->n_col
== 0) {
5626 isl_reduce_coefficients_data_clear(&data
);
5627 return isl_basic_map_set_to_empty(bmap
);
5630 bmap
= reduce_coefficients(bmap
, &data
);
5634 if (data
.tightened
) {
5637 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
5638 bmap
= isl_basic_map_detect_inequality_pairs(bmap
, &progress
);
5640 bmap
= isl_basic_map_gauss(bmap
, NULL
);
5641 bmap
= reduce_coefficients(bmap
, &data
);
5642 bmap
= eliminate_divs_eq(bmap
, &progress
);
5646 isl_reduce_coefficients_data_clear(&data
);
5650 isl_reduce_coefficients_data_clear(&data
);
5651 return isl_basic_map_free(bmap
);
5654 /* Shift the integer division at position "div" of "bmap"
5655 * by "shift" times the variable at position "pos".
5656 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
5657 * corresponds to the constant term.
5659 * That is, if the integer division has the form
5663 * then replace it by
5665 * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
5667 __isl_give isl_basic_map
*isl_basic_map_shift_div(
5668 __isl_take isl_basic_map
*bmap
, int div
, int pos
, isl_int shift
)
5671 isl_size total
, n_div
;
5673 if (isl_int_is_zero(shift
))
5675 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
5676 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
5678 if (total
< 0 || n_div
< 0)
5679 return isl_basic_map_free(bmap
);
5681 isl_int_addmul(bmap
->div
[div
][1 + pos
], shift
, bmap
->div
[div
][0]);
5683 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
5684 if (isl_int_is_zero(bmap
->eq
[i
][1 + total
+ div
]))
5686 isl_int_submul(bmap
->eq
[i
][pos
],
5687 shift
, bmap
->eq
[i
][1 + total
+ div
]);
5689 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
5690 if (isl_int_is_zero(bmap
->ineq
[i
][1 + total
+ div
]))
5692 isl_int_submul(bmap
->ineq
[i
][pos
],
5693 shift
, bmap
->ineq
[i
][1 + total
+ div
]);
5695 for (i
= 0; i
< bmap
->n_div
; ++i
) {
5696 if (isl_int_is_zero(bmap
->div
[i
][0]))
5698 if (isl_int_is_zero(bmap
->div
[i
][1 + 1 + total
+ div
]))
5700 isl_int_submul(bmap
->div
[i
][1 + pos
],
5701 shift
, bmap
->div
[i
][1 + 1 + total
+ div
]);