2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012-2013 Ecole Normale Superieure
4 * Copyright 2014-2015 INRIA Rocquencourt
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
11 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
12 * B.P. 105 - 78153 Le Chesnay, France
15 #include <isl_ctx_private.h>
16 #include <isl_map_private.h>
17 #include "isl_equalities.h"
21 #include <isl_space_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_vec_private.h>
25 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
27 isl_int
*t
= bmap
->eq
[a
];
28 bmap
->eq
[a
] = bmap
->eq
[b
];
32 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
35 isl_int
*t
= bmap
->ineq
[a
];
36 bmap
->ineq
[a
] = bmap
->ineq
[b
];
41 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
43 isl_seq_cpy(c
, c
+ n
, rem
);
44 isl_seq_clr(c
+ rem
, n
);
47 /* Drop n dimensions starting at first.
49 * In principle, this frees up some extra variables as the number
50 * of columns remains constant, but we would have to extend
51 * the div array too as the number of rows in this array is assumed
52 * to be equal to extra.
54 struct isl_basic_set
*isl_basic_set_drop_dims(
55 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
62 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
64 if (n
== 0 && !isl_space_get_tuple_name(bset
->dim
, isl_dim_set
))
67 bset
= isl_basic_set_cow(bset
);
71 for (i
= 0; i
< bset
->n_eq
; ++i
)
72 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
73 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
75 for (i
= 0; i
< bset
->n_ineq
; ++i
)
76 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
77 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
79 for (i
= 0; i
< bset
->n_div
; ++i
)
80 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
81 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
83 bset
->dim
= isl_space_drop_outputs(bset
->dim
, first
, n
);
87 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
88 bset
= isl_basic_set_simplify(bset
);
89 return isl_basic_set_finalize(bset
);
91 isl_basic_set_free(bset
);
95 struct isl_set
*isl_set_drop_dims(
96 struct isl_set
*set
, unsigned first
, unsigned n
)
103 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
105 if (n
== 0 && !isl_space_get_tuple_name(set
->dim
, isl_dim_set
))
107 set
= isl_set_cow(set
);
110 set
->dim
= isl_space_drop_outputs(set
->dim
, first
, n
);
114 for (i
= 0; i
< set
->n
; ++i
) {
115 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
120 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
127 /* Move "n" divs starting at "first" to the end of the list of divs.
129 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
130 unsigned first
, unsigned n
)
135 if (first
+ n
== bmap
->n_div
)
138 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
141 for (i
= 0; i
< n
; ++i
)
142 div
[i
] = bmap
->div
[first
+ i
];
143 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
144 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
145 for (i
= 0; i
< n
; ++i
)
146 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
150 isl_basic_map_free(bmap
);
154 /* Drop "n" dimensions of type "type" starting at "first".
156 * In principle, this frees up some extra variables as the number
157 * of columns remains constant, but we would have to extend
158 * the div array too as the number of rows in this array is assumed
159 * to be equal to extra.
161 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
162 enum isl_dim_type type
, unsigned first
, unsigned n
)
172 dim
= isl_basic_map_dim(bmap
, type
);
173 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
175 if (n
== 0 && !isl_space_is_named_or_nested(bmap
->dim
, type
))
178 bmap
= isl_basic_map_cow(bmap
);
182 offset
= isl_basic_map_offset(bmap
, type
) + first
;
183 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
184 for (i
= 0; i
< bmap
->n_eq
; ++i
)
185 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
187 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
188 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
190 for (i
= 0; i
< bmap
->n_div
; ++i
)
191 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
193 if (type
== isl_dim_div
) {
194 bmap
= move_divs_last(bmap
, first
, n
);
197 isl_basic_map_free_div(bmap
, n
);
199 bmap
->dim
= isl_space_drop_dims(bmap
->dim
, type
, first
, n
);
203 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
204 bmap
= isl_basic_map_simplify(bmap
);
205 return isl_basic_map_finalize(bmap
);
207 isl_basic_map_free(bmap
);
211 __isl_give isl_basic_set
*isl_basic_set_drop(__isl_take isl_basic_set
*bset
,
212 enum isl_dim_type type
, unsigned first
, unsigned n
)
214 return (isl_basic_set
*)isl_basic_map_drop((isl_basic_map
*)bset
,
218 struct isl_basic_map
*isl_basic_map_drop_inputs(
219 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
221 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
224 struct isl_map
*isl_map_drop(struct isl_map
*map
,
225 enum isl_dim_type type
, unsigned first
, unsigned n
)
232 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
234 if (n
== 0 && !isl_space_get_tuple_name(map
->dim
, type
))
236 map
= isl_map_cow(map
);
239 map
->dim
= isl_space_drop_dims(map
->dim
, type
, first
, n
);
243 for (i
= 0; i
< map
->n
; ++i
) {
244 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
248 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
256 struct isl_set
*isl_set_drop(struct isl_set
*set
,
257 enum isl_dim_type type
, unsigned first
, unsigned n
)
259 return (isl_set
*)isl_map_drop((isl_map
*)set
, type
, first
, n
);
262 struct isl_map
*isl_map_drop_inputs(
263 struct isl_map
*map
, unsigned first
, unsigned n
)
265 return isl_map_drop(map
, isl_dim_in
, first
, n
);
269 * We don't cow, as the div is assumed to be redundant.
271 static struct isl_basic_map
*isl_basic_map_drop_div(
272 struct isl_basic_map
*bmap
, unsigned div
)
280 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
282 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
284 for (i
= 0; i
< bmap
->n_eq
; ++i
)
285 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
287 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
288 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
289 isl_basic_map_drop_inequality(bmap
, i
);
293 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
296 for (i
= 0; i
< bmap
->n_div
; ++i
)
297 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
299 if (div
!= bmap
->n_div
- 1) {
301 isl_int
*t
= bmap
->div
[div
];
303 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
304 bmap
->div
[j
] = bmap
->div
[j
+1];
306 bmap
->div
[bmap
->n_div
- 1] = t
;
308 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
309 isl_basic_map_free_div(bmap
, 1);
313 isl_basic_map_free(bmap
);
317 struct isl_basic_map
*isl_basic_map_normalize_constraints(
318 struct isl_basic_map
*bmap
)
322 unsigned total
= isl_basic_map_total_dim(bmap
);
328 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
329 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
330 if (isl_int_is_zero(gcd
)) {
331 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
332 bmap
= isl_basic_map_set_to_empty(bmap
);
335 isl_basic_map_drop_equality(bmap
, i
);
338 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
339 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
340 if (isl_int_is_one(gcd
))
342 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
343 bmap
= isl_basic_map_set_to_empty(bmap
);
346 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
349 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
350 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
351 if (isl_int_is_zero(gcd
)) {
352 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
353 bmap
= isl_basic_map_set_to_empty(bmap
);
356 isl_basic_map_drop_inequality(bmap
, i
);
359 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
360 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
361 if (isl_int_is_one(gcd
))
363 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
364 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
371 struct isl_basic_set
*isl_basic_set_normalize_constraints(
372 struct isl_basic_set
*bset
)
374 return (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
375 (struct isl_basic_map
*)bset
);
378 /* Assuming the variable at position "pos" has an integer coefficient
379 * in integer division "div", extract it from this integer division.
380 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
381 * corresponds to the constant term.
383 * That is, the integer division is of the form
385 * floor((... + c * d * x_pos + ...)/d)
389 * floor((... + 0 * x_pos + ...)/d) + c * x_pos
391 static __isl_give isl_basic_map
*remove_var_from_div(
392 __isl_take isl_basic_map
*bmap
, int div
, int pos
)
397 isl_int_divexact(shift
, bmap
->div
[div
][1 + pos
], bmap
->div
[div
][0]);
398 isl_int_neg(shift
, shift
);
399 bmap
= isl_basic_map_shift_div(bmap
, div
, pos
, shift
);
400 isl_int_clear(shift
);
405 /* Check if integer division "div" has any integral coefficient
406 * (or constant term). If so, extract them from the integer division.
408 static __isl_give isl_basic_map
*remove_independent_vars_from_div(
409 __isl_take isl_basic_map
*bmap
, int div
)
412 unsigned total
= 1 + isl_basic_map_total_dim(bmap
);
414 for (i
= 0; i
< total
; ++i
) {
415 if (isl_int_is_zero(bmap
->div
[div
][1 + i
]))
417 if (!isl_int_is_divisible_by(bmap
->div
[div
][1 + i
],
420 bmap
= remove_var_from_div(bmap
, div
, i
);
428 /* Check if any known integer division has any integral coefficient
429 * (or constant term). If so, extract them from the integer division.
431 static __isl_give isl_basic_map
*remove_independent_vars_from_divs(
432 __isl_take isl_basic_map
*bmap
)
438 if (bmap
->n_div
== 0)
441 for (i
= 0; i
< bmap
->n_div
; ++i
) {
442 if (isl_int_is_zero(bmap
->div
[i
][0]))
444 bmap
= remove_independent_vars_from_div(bmap
, i
);
452 /* Remove any common factor in numerator and denominator of the div expression,
453 * not taking into account the constant term.
454 * That is, if the div is of the form
456 * floor((a + m f(x))/(m d))
460 * floor((floor(a/m) + f(x))/d)
462 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
463 * and can therefore not influence the result of the floor.
465 static void normalize_div_expression(__isl_keep isl_basic_map
*bmap
, int div
)
467 unsigned total
= isl_basic_map_total_dim(bmap
);
468 isl_ctx
*ctx
= bmap
->ctx
;
470 if (isl_int_is_zero(bmap
->div
[div
][0]))
472 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
473 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
474 if (isl_int_is_one(ctx
->normalize_gcd
))
476 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
478 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
480 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
481 ctx
->normalize_gcd
, total
);
484 /* Remove any common factor in numerator and denominator of a div expression,
485 * not taking into account the constant term.
486 * That is, look for any div of the form
488 * floor((a + m f(x))/(m d))
492 * floor((floor(a/m) + f(x))/d)
494 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
495 * and can therefore not influence the result of the floor.
497 static __isl_give isl_basic_map
*normalize_div_expressions(
498 __isl_take isl_basic_map
*bmap
)
504 if (bmap
->n_div
== 0)
507 for (i
= 0; i
< bmap
->n_div
; ++i
)
508 normalize_div_expression(bmap
, i
);
513 /* Assumes divs have been ordered if keep_divs is set.
515 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
516 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
519 unsigned space_total
;
523 total
= isl_basic_map_total_dim(bmap
);
524 space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
525 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
526 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
527 if (bmap
->eq
[k
] == eq
)
529 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
533 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
534 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
537 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
538 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
542 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
543 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
544 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
547 for (k
= 0; k
< bmap
->n_div
; ++k
) {
548 if (isl_int_is_zero(bmap
->div
[k
][0]))
550 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
554 /* We need to be careful about circular definitions,
555 * so for now we just remove the definition of div k
556 * if the equality contains any divs.
557 * If keep_divs is set, then the divs have been ordered
558 * and we can keep the definition as long as the result
561 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
562 isl_seq_elim(bmap
->div
[k
]+1, eq
,
563 1+pos
, 1+total
, &bmap
->div
[k
][0]);
564 normalize_div_expression(bmap
, k
);
566 isl_seq_clr(bmap
->div
[k
], 1 + total
);
567 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
571 /* Assumes divs have been ordered if keep_divs is set.
573 static __isl_give isl_basic_map
*eliminate_div(__isl_take isl_basic_map
*bmap
,
574 isl_int
*eq
, unsigned div
, int keep_divs
)
576 unsigned pos
= isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
578 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
580 bmap
= isl_basic_map_drop_div(bmap
, div
);
585 /* Check if elimination of div "div" using equality "eq" would not
586 * result in a div depending on a later div.
588 static int ok_to_eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
593 unsigned space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
594 unsigned pos
= space_total
+ div
;
596 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
597 if (last_div
< 0 || last_div
<= div
)
600 for (k
= 0; k
<= last_div
; ++k
) {
601 if (isl_int_is_zero(bmap
->div
[k
][0]))
603 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
610 /* Elimininate divs based on equalities
612 static struct isl_basic_map
*eliminate_divs_eq(
613 struct isl_basic_map
*bmap
, int *progress
)
620 bmap
= isl_basic_map_order_divs(bmap
);
625 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
627 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
628 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
629 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
630 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
632 if (!ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
))
636 bmap
= eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
637 if (isl_basic_map_drop_equality(bmap
, i
) < 0)
638 return isl_basic_map_free(bmap
);
643 return eliminate_divs_eq(bmap
, progress
);
647 /* Elimininate divs based on inequalities
649 static struct isl_basic_map
*eliminate_divs_ineq(
650 struct isl_basic_map
*bmap
, int *progress
)
661 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
663 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
664 for (i
= 0; i
< bmap
->n_eq
; ++i
)
665 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
669 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
670 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
672 if (i
< bmap
->n_ineq
)
675 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
676 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
678 bmap
= isl_basic_map_drop_div(bmap
, d
);
685 struct isl_basic_map
*isl_basic_map_gauss(
686 struct isl_basic_map
*bmap
, int *progress
)
694 bmap
= isl_basic_map_order_divs(bmap
);
699 total
= isl_basic_map_total_dim(bmap
);
700 total_var
= total
- bmap
->n_div
;
702 last_var
= total
- 1;
703 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
704 for (; last_var
>= 0; --last_var
) {
705 for (k
= done
; k
< bmap
->n_eq
; ++k
)
706 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
714 swap_equality(bmap
, k
, done
);
715 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
716 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
718 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
721 if (last_var
>= total_var
&&
722 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
723 unsigned div
= last_var
- total_var
;
724 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
725 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
726 isl_int_set(bmap
->div
[div
][0],
727 bmap
->eq
[done
][1+last_var
]);
730 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
733 if (done
== bmap
->n_eq
)
735 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
736 if (isl_int_is_zero(bmap
->eq
[k
][0]))
738 return isl_basic_map_set_to_empty(bmap
);
740 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
744 struct isl_basic_set
*isl_basic_set_gauss(
745 struct isl_basic_set
*bset
, int *progress
)
747 return (struct isl_basic_set
*)isl_basic_map_gauss(
748 (struct isl_basic_map
*)bset
, progress
);
752 static unsigned int round_up(unsigned int v
)
763 /* Hash table of inequalities in a basic map.
764 * "index" is an array of addresses of inequalities in the basic map, some
765 * of which are NULL. The inequalities are hashed on the coefficients
766 * except the constant term.
767 * "size" is the number of elements in the array and is always a power of two
768 * "bits" is the number of bits need to represent an index into the array.
769 * "total" is the total dimension of the basic map.
771 struct isl_constraint_index
{
778 /* Fill in the "ci" data structure for holding the inequalities of "bmap".
780 static isl_stat
create_constraint_index(struct isl_constraint_index
*ci
,
781 __isl_keep isl_basic_map
*bmap
)
787 return isl_stat_error
;
788 ci
->total
= isl_basic_set_total_dim(bmap
);
789 if (bmap
->n_ineq
== 0)
791 ci
->size
= round_up(4 * (bmap
->n_ineq
+ 1) / 3 - 1);
792 ci
->bits
= ffs(ci
->size
) - 1;
793 ctx
= isl_basic_map_get_ctx(bmap
);
794 ci
->index
= isl_calloc_array(ctx
, isl_int
**, ci
->size
);
796 return isl_stat_error
;
801 /* Free the memory allocated by create_constraint_index.
803 static void constraint_index_free(struct isl_constraint_index
*ci
)
808 /* Return the position in ci->index that contains the address of
809 * an inequality that is equal to *ineq up to the constant term,
810 * provided this address is not identical to "ineq".
811 * If there is no such inequality, then return the position where
812 * such an inequality should be inserted.
814 static int hash_index_ineq(struct isl_constraint_index
*ci
, isl_int
**ineq
)
817 uint32_t hash
= isl_seq_get_hash_bits((*ineq
) + 1, ci
->total
, ci
->bits
);
818 for (h
= hash
; ci
->index
[h
]; h
= (h
+1) % ci
->size
)
819 if (ineq
!= ci
->index
[h
] &&
820 isl_seq_eq((*ineq
) + 1, ci
->index
[h
][0]+1, ci
->total
))
825 /* Return the position in ci->index that contains the address of
826 * an inequality that is equal to the k'th inequality of "bmap"
827 * up to the constant term, provided it does not point to the very
829 * If there is no such inequality, then return the position where
830 * such an inequality should be inserted.
832 static int hash_index(struct isl_constraint_index
*ci
,
833 __isl_keep isl_basic_map
*bmap
, int k
)
835 return hash_index_ineq(ci
, &bmap
->ineq
[k
]);
838 static int set_hash_index(struct isl_constraint_index
*ci
,
839 struct isl_basic_set
*bset
, int k
)
841 return hash_index(ci
, bset
, k
);
844 /* Fill in the "ci" data structure with the inequalities of "bset".
846 static isl_stat
setup_constraint_index(struct isl_constraint_index
*ci
,
847 __isl_keep isl_basic_set
*bset
)
851 if (create_constraint_index(ci
, bset
) < 0)
852 return isl_stat_error
;
854 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
855 h
= set_hash_index(ci
, bset
, k
);
856 ci
->index
[h
] = &bset
->ineq
[k
];
862 /* Is the inequality ineq (obviously) redundant with respect
863 * to the constraints in "ci"?
865 * Look for an inequality in "ci" with the same coefficients and then
866 * check if the contant term of "ineq" is greater than or equal
867 * to the constant term of that inequality. If so, "ineq" is clearly
870 * Note that hash_index_ineq ignores a stored constraint if it has
871 * the same address as the passed inequality. It is ok to pass
872 * the address of a local variable here since it will never be
873 * the same as the address of a constraint in "ci".
875 static isl_bool
constraint_index_is_redundant(struct isl_constraint_index
*ci
,
880 h
= hash_index_ineq(ci
, &ineq
);
882 return isl_bool_false
;
883 return isl_int_ge(ineq
[0], (*ci
->index
[h
])[0]);
886 /* If we can eliminate more than one div, then we need to make
887 * sure we do it from last div to first div, in order not to
888 * change the position of the other divs that still need to
891 static struct isl_basic_map
*remove_duplicate_divs(
892 struct isl_basic_map
*bmap
, int *progress
)
904 bmap
= isl_basic_map_order_divs(bmap
);
905 if (!bmap
|| bmap
->n_div
<= 1)
908 total_var
= isl_space_dim(bmap
->dim
, isl_dim_all
);
909 total
= total_var
+ bmap
->n_div
;
912 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
913 if (!isl_int_is_zero(bmap
->div
[k
][0]))
918 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
921 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
922 bits
= ffs(size
) - 1;
923 index
= isl_calloc_array(ctx
, int, size
);
924 if (!elim_for
|| !index
)
926 eq
= isl_blk_alloc(ctx
, 1+total
);
927 if (isl_blk_is_error(eq
))
930 isl_seq_clr(eq
.data
, 1+total
);
931 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
932 for (--k
; k
>= 0; --k
) {
935 if (isl_int_is_zero(bmap
->div
[k
][0]))
938 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
939 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
940 if (isl_seq_eq(bmap
->div
[k
],
941 bmap
->div
[index
[h
]-1], 2+total
))
950 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
954 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
955 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
956 bmap
= eliminate_div(bmap
, eq
.data
, l
, 1);
959 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
960 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
963 isl_blk_free(ctx
, eq
);
970 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
975 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
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 + total
+ j
]))
981 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, 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 struct isl_basic_map
*normalize_divs(
1036 struct isl_basic_map
*bmap
, int *progress
)
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 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1063 div_eq
= n_pure_div_eq(bmap
);
1067 if (div_eq
< bmap
->n_eq
) {
1068 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
1069 bmap
->n_eq
- div_eq
, 0, 1 + total
);
1070 C
= isl_mat_variable_compression(B
, &C2
);
1073 if (C
->n_col
== 0) {
1074 bmap
= isl_basic_map_set_to_empty(bmap
);
1081 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
1084 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
1085 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
1087 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
1089 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
1092 B
= isl_mat_product(B
, C
);
1096 T
= isl_mat_parameter_compression(B
, d
);
1099 if (T
->n_col
== 0) {
1100 bmap
= isl_basic_map_set_to_empty(bmap
);
1106 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
1107 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
1108 if (isl_int_is_zero(v
))
1110 isl_mat_col_submul(T
, 0, v
, 1 + i
);
1113 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
1116 /* We have to be careful because dropping equalities may reorder them */
1118 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
1119 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1120 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
1122 if (i
< bmap
->n_eq
) {
1123 bmap
= isl_basic_map_drop_div(bmap
, j
);
1124 isl_basic_map_drop_equality(bmap
, i
);
1130 for (i
= 1; i
< T
->n_row
; ++i
) {
1131 if (isl_int_is_one(T
->row
[i
][i
]))
1136 if (needed
> dropped
) {
1137 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
1142 for (i
= 1; i
< T
->n_row
; ++i
) {
1143 if (isl_int_is_one(T
->row
[i
][i
]))
1145 k
= isl_basic_map_alloc_div(bmap
);
1146 pos
[i
] = 1 + total
+ k
;
1147 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
1148 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
1150 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
1152 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
1153 for (j
= 0; j
< i
; ++j
) {
1154 if (isl_int_is_zero(T
->row
[i
][j
]))
1156 if (pos
[j
] < T
->n_row
&& C2
)
1157 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
1158 C2
->row
[pos
[j
]], 1 + total
);
1160 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
1163 j
= isl_basic_map_alloc_equality(bmap
);
1164 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
1165 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
1174 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
1184 static struct isl_basic_map
*set_div_from_lower_bound(
1185 struct isl_basic_map
*bmap
, int div
, int ineq
)
1187 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1189 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1190 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1191 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1192 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1193 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1198 /* Check whether it is ok to define a div based on an inequality.
1199 * To avoid the introduction of circular definitions of divs, we
1200 * do not allow such a definition if the resulting expression would refer to
1201 * any other undefined divs or if any known div is defined in
1202 * terms of the unknown div.
1204 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
1208 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1210 /* Not defined in terms of unknown divs */
1211 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1214 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1216 if (isl_int_is_zero(bmap
->div
[j
][0]))
1220 /* No other div defined in terms of this one => avoid loops */
1221 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1224 if (isl_int_is_zero(bmap
->div
[j
][0]))
1226 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1233 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1234 * be a better expression than the current one?
1236 * If we do not have any expression yet, then any expression would be better.
1237 * Otherwise we check if the last variable involved in the inequality
1238 * (disregarding the div that it would define) is in an earlier position
1239 * than the last variable involved in the current div expression.
1241 static int better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1244 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1248 if (isl_int_is_zero(bmap
->div
[div
][0]))
1251 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1252 bmap
->n_div
- (div
+ 1)) >= 0)
1255 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1256 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1257 total
+ bmap
->n_div
);
1259 return last_ineq
< last_div
;
1262 /* Given two constraints "k" and "l" that are opposite to each other,
1263 * except for the constant term, check if we can use them
1264 * to obtain an expression for one of the hitherto unknown divs or
1265 * a "better" expression for a div for which we already have an expression.
1266 * "sum" is the sum of the constant terms of the constraints.
1267 * If this sum is strictly smaller than the coefficient of one
1268 * of the divs, then this pair can be used define the div.
1269 * To avoid the introduction of circular definitions of divs, we
1270 * do not use the pair if the resulting expression would refer to
1271 * any other undefined divs or if any known div is defined in
1272 * terms of the unknown div.
1274 static struct isl_basic_map
*check_for_div_constraints(
1275 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
1278 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1280 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1281 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1283 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1285 if (!better_div_constraint(bmap
, i
, k
))
1287 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1289 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1290 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1292 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1300 __isl_give isl_basic_map
*isl_basic_map_remove_duplicate_constraints(
1301 __isl_take isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1303 struct isl_constraint_index ci
;
1305 unsigned total
= isl_basic_map_total_dim(bmap
);
1308 if (!bmap
|| bmap
->n_ineq
<= 1)
1311 if (create_constraint_index(&ci
, bmap
) < 0)
1314 h
= isl_seq_get_hash_bits(bmap
->ineq
[0] + 1, total
, ci
.bits
);
1315 ci
.index
[h
] = &bmap
->ineq
[0];
1316 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1317 h
= hash_index(&ci
, bmap
, k
);
1319 ci
.index
[h
] = &bmap
->ineq
[k
];
1324 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1325 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1326 swap_inequality(bmap
, k
, l
);
1327 isl_basic_map_drop_inequality(bmap
, k
);
1331 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1332 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1333 h
= hash_index(&ci
, bmap
, k
);
1334 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1337 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1338 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1339 if (isl_int_is_pos(sum
)) {
1341 bmap
= check_for_div_constraints(bmap
, k
, l
,
1345 if (isl_int_is_zero(sum
)) {
1346 /* We need to break out of the loop after these
1347 * changes since the contents of the hash
1348 * will no longer be valid.
1349 * Plus, we probably we want to regauss first.
1353 isl_basic_map_drop_inequality(bmap
, l
);
1354 isl_basic_map_inequality_to_equality(bmap
, k
);
1356 bmap
= isl_basic_map_set_to_empty(bmap
);
1361 constraint_index_free(&ci
);
1365 /* Detect all pairs of inequalities that form an equality.
1367 * isl_basic_map_remove_duplicate_constraints detects at most one such pair.
1368 * Call it repeatedly while it is making progress.
1370 __isl_give isl_basic_map
*isl_basic_map_detect_inequality_pairs(
1371 __isl_take isl_basic_map
*bmap
, int *progress
)
1377 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1379 if (progress
&& duplicate
)
1381 } while (duplicate
);
1386 /* Eliminate knowns divs from constraints where they appear with
1387 * a (positive or negative) unit coefficient.
1391 * floor(e/m) + f >= 0
1399 * -floor(e/m) + f >= 0
1403 * -e + m f + m - 1 >= 0
1405 * The first conversion is valid because floor(e/m) >= -f is equivalent
1406 * to e/m >= -f because -f is an integral expression.
1407 * The second conversion follows from the fact that
1409 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1412 * Note that one of the div constraints may have been eliminated
1413 * due to being redundant with respect to the constraint that is
1414 * being modified by this function. The modified constraint may
1415 * no longer imply this div constraint, so we add it back to make
1416 * sure we do not lose any information.
1418 * We skip integral divs, i.e., those with denominator 1, as we would
1419 * risk eliminating the div from the div constraints. We do not need
1420 * to handle those divs here anyway since the div constraints will turn
1421 * out to form an equality and this equality can then be use to eliminate
1422 * the div from all constraints.
1424 static __isl_give isl_basic_map
*eliminate_unit_divs(
1425 __isl_take isl_basic_map
*bmap
, int *progress
)
1434 ctx
= isl_basic_map_get_ctx(bmap
);
1435 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1437 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1438 if (isl_int_is_zero(bmap
->div
[i
][0]))
1440 if (isl_int_is_one(bmap
->div
[i
][0]))
1442 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1445 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1446 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1451 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1452 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1454 isl_seq_combine(bmap
->ineq
[j
],
1455 ctx
->negone
, bmap
->div
[i
] + 1,
1456 bmap
->div
[i
][0], bmap
->ineq
[j
],
1457 total
+ bmap
->n_div
);
1459 isl_seq_combine(bmap
->ineq
[j
],
1460 ctx
->one
, bmap
->div
[i
] + 1,
1461 bmap
->div
[i
][0], bmap
->ineq
[j
],
1462 total
+ bmap
->n_div
);
1464 isl_int_add(bmap
->ineq
[j
][0],
1465 bmap
->ineq
[j
][0], bmap
->div
[i
][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 if (isl_basic_map_add_div_constraint(bmap
, i
, s
) < 0)
1472 return isl_basic_map_free(bmap
);
1479 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1488 if (isl_basic_map_plain_is_empty(bmap
))
1490 bmap
= isl_basic_map_normalize_constraints(bmap
);
1491 bmap
= remove_independent_vars_from_divs(bmap
);
1492 bmap
= normalize_div_expressions(bmap
);
1493 bmap
= remove_duplicate_divs(bmap
, &progress
);
1494 bmap
= eliminate_unit_divs(bmap
, &progress
);
1495 bmap
= eliminate_divs_eq(bmap
, &progress
);
1496 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1497 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1498 /* requires equalities in normal form */
1499 bmap
= normalize_divs(bmap
, &progress
);
1500 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1502 if (bmap
&& progress
)
1503 ISL_F_CLR(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
1508 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1510 return (struct isl_basic_set
*)
1511 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1515 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1516 isl_int
*constraint
, unsigned div
)
1523 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1525 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1527 isl_int_sub(bmap
->div
[div
][1],
1528 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1529 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1530 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1531 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1532 isl_int_add(bmap
->div
[div
][1],
1533 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1536 if (isl_seq_first_non_zero(constraint
+pos
+1,
1537 bmap
->n_div
-div
-1) != -1)
1539 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1540 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1542 if (isl_seq_first_non_zero(constraint
+pos
+1,
1543 bmap
->n_div
-div
-1) != -1)
1551 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1552 isl_int
*constraint
, unsigned div
)
1554 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1558 /* If the only constraints a div d=floor(f/m)
1559 * appears in are its two defining constraints
1562 * -(f - (m - 1)) + m d >= 0
1564 * then it can safely be removed.
1566 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1569 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1571 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1572 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1575 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1576 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1578 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1582 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1583 if (isl_int_is_zero(bmap
->div
[i
][0]))
1585 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1593 * Remove divs that don't occur in any of the constraints or other divs.
1594 * These can arise when dropping constraints from a basic map or
1595 * when the divs of a basic map have been temporarily aligned
1596 * with the divs of another basic map.
1598 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1605 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1606 if (!div_is_redundant(bmap
, i
))
1608 bmap
= isl_basic_map_drop_div(bmap
, i
);
1613 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1615 bmap
= remove_redundant_divs(bmap
);
1618 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1622 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1624 return (struct isl_basic_set
*)
1625 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1628 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1634 for (i
= 0; i
< set
->n
; ++i
) {
1635 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1645 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1651 for (i
= 0; i
< map
->n
; ++i
) {
1652 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1656 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1664 /* Remove definition of any div that is defined in terms of the given variable.
1665 * The div itself is not removed. Functions such as
1666 * eliminate_divs_ineq depend on the other divs remaining in place.
1668 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1676 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1677 if (isl_int_is_zero(bmap
->div
[i
][0]))
1679 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1681 isl_int_set_si(bmap
->div
[i
][0], 0);
1686 /* Eliminate the specified variables from the constraints using
1687 * Fourier-Motzkin. The variables themselves are not removed.
1689 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1690 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1701 total
= isl_basic_map_total_dim(bmap
);
1703 bmap
= isl_basic_map_cow(bmap
);
1704 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1705 bmap
= remove_dependent_vars(bmap
, d
);
1709 for (d
= pos
+ n
- 1;
1710 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1711 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1712 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1713 int n_lower
, n_upper
;
1716 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1717 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1719 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1720 isl_basic_map_drop_equality(bmap
, i
);
1728 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1729 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1731 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1734 bmap
= isl_basic_map_extend_constraints(bmap
,
1735 0, n_lower
* n_upper
);
1738 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1740 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1743 for (j
= 0; j
< i
; ++j
) {
1744 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1747 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1748 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1750 k
= isl_basic_map_alloc_inequality(bmap
);
1753 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1755 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1756 1+d
, 1+total
, NULL
);
1758 isl_basic_map_drop_inequality(bmap
, i
);
1761 if (n_lower
> 0 && n_upper
> 0) {
1762 bmap
= isl_basic_map_normalize_constraints(bmap
);
1763 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1765 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1766 bmap
= isl_basic_map_remove_redundancies(bmap
);
1770 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1774 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1776 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1779 isl_basic_map_free(bmap
);
1783 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1784 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1786 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1787 (struct isl_basic_map
*)bset
, pos
, n
);
1790 /* Eliminate the specified n dimensions starting at first from the
1791 * constraints, without removing the dimensions from the space.
1792 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1793 * Otherwise, they are projected out and the original space is restored.
1795 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1796 __isl_take isl_basic_map
*bmap
,
1797 enum isl_dim_type type
, unsigned first
, unsigned n
)
1806 if (first
+ n
> isl_basic_map_dim(bmap
, type
) || first
+ n
< first
)
1807 isl_die(bmap
->ctx
, isl_error_invalid
,
1808 "index out of bounds", goto error
);
1810 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1811 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1812 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1813 return isl_basic_map_finalize(bmap
);
1816 space
= isl_basic_map_get_space(bmap
);
1817 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1818 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1819 bmap
= isl_basic_map_reset_space(bmap
, space
);
1822 isl_basic_map_free(bmap
);
1826 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1827 __isl_take isl_basic_set
*bset
,
1828 enum isl_dim_type type
, unsigned first
, unsigned n
)
1830 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1833 /* Don't assume equalities are in order, because align_divs
1834 * may have changed the order of the divs.
1836 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1841 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1842 for (d
= 0; d
< total
; ++d
)
1844 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1845 for (d
= total
- 1; d
>= 0; --d
) {
1846 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1854 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1856 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1859 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1860 struct isl_basic_map
*bmap
, int *elim
)
1866 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1867 for (d
= total
- 1; d
>= 0; --d
) {
1868 if (isl_int_is_zero(src
[1+d
]))
1873 isl_seq_cpy(dst
, src
, 1 + total
);
1876 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1881 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1882 struct isl_basic_set
*bset
, int *elim
)
1884 return reduced_using_equalities(dst
, src
,
1885 (struct isl_basic_map
*)bset
, elim
);
1888 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1889 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1894 if (!bset
|| !context
)
1897 if (context
->n_eq
== 0) {
1898 isl_basic_set_free(context
);
1902 bset
= isl_basic_set_cow(bset
);
1906 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1909 set_compute_elimination_index(context
, elim
);
1910 for (i
= 0; i
< bset
->n_eq
; ++i
)
1911 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1913 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1914 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1916 isl_basic_set_free(context
);
1918 bset
= isl_basic_set_simplify(bset
);
1919 bset
= isl_basic_set_finalize(bset
);
1922 isl_basic_set_free(bset
);
1923 isl_basic_set_free(context
);
1927 /* For each inequality in "ineq" that is a shifted (more relaxed)
1928 * copy of an inequality in "context", mark the corresponding entry
1930 * If an inequality only has a non-negative constant term, then
1933 static isl_stat
mark_shifted_constraints(__isl_keep isl_mat
*ineq
,
1934 __isl_keep isl_basic_set
*context
, int *row
)
1936 struct isl_constraint_index ci
;
1941 if (!ineq
|| !context
)
1942 return isl_stat_error
;
1943 if (context
->n_ineq
== 0)
1945 if (setup_constraint_index(&ci
, context
) < 0)
1946 return isl_stat_error
;
1948 n_ineq
= isl_mat_rows(ineq
);
1949 total
= isl_mat_cols(ineq
) - 1;
1950 for (k
= 0; k
< n_ineq
; ++k
) {
1954 l
= isl_seq_first_non_zero(ineq
->row
[k
] + 1, total
);
1955 if (l
< 0 && isl_int_is_nonneg(ineq
->row
[k
][0])) {
1959 redundant
= constraint_index_is_redundant(&ci
, ineq
->row
[k
]);
1966 constraint_index_free(&ci
);
1969 constraint_index_free(&ci
);
1970 return isl_stat_error
;
1973 static struct isl_basic_set
*remove_shifted_constraints(
1974 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1976 struct isl_constraint_index ci
;
1979 if (!bset
|| !context
)
1982 if (context
->n_ineq
== 0)
1984 if (setup_constraint_index(&ci
, context
) < 0)
1987 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1990 redundant
= constraint_index_is_redundant(&ci
, bset
->ineq
[k
]);
1995 bset
= isl_basic_set_cow(bset
);
1998 isl_basic_set_drop_inequality(bset
, k
);
2001 constraint_index_free(&ci
);
2004 constraint_index_free(&ci
);
2008 /* Remove constraints from "bmap" that are identical to constraints
2009 * in "context" or that are more relaxed (greater constant term).
2011 * We perform the test for shifted copies on the pure constraints
2012 * in remove_shifted_constraints.
2014 static __isl_give isl_basic_map
*isl_basic_map_remove_shifted_constraints(
2015 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
2017 isl_basic_set
*bset
, *bset_context
;
2019 if (!bmap
|| !context
)
2022 if (bmap
->n_ineq
== 0 || context
->n_ineq
== 0) {
2023 isl_basic_map_free(context
);
2027 context
= isl_basic_map_align_divs(context
, bmap
);
2028 bmap
= isl_basic_map_align_divs(bmap
, context
);
2030 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
2031 bset_context
= isl_basic_map_underlying_set(context
);
2032 bset
= remove_shifted_constraints(bset
, bset_context
);
2033 isl_basic_set_free(bset_context
);
2035 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
2039 isl_basic_map_free(bmap
);
2040 isl_basic_map_free(context
);
2044 /* Does the (linear part of a) constraint "c" involve any of the "len"
2045 * "relevant" dimensions?
2047 static int is_related(isl_int
*c
, int len
, int *relevant
)
2051 for (i
= 0; i
< len
; ++i
) {
2054 if (!isl_int_is_zero(c
[i
]))
2061 /* Drop constraints from "bset" that do not involve any of
2062 * the dimensions marked "relevant".
2064 static __isl_give isl_basic_set
*drop_unrelated_constraints(
2065 __isl_take isl_basic_set
*bset
, int *relevant
)
2069 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2070 for (i
= 0; i
< dim
; ++i
)
2076 for (i
= bset
->n_eq
- 1; i
>= 0; --i
)
2077 if (!is_related(bset
->eq
[i
] + 1, dim
, relevant
))
2078 isl_basic_set_drop_equality(bset
, i
);
2080 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
)
2081 if (!is_related(bset
->ineq
[i
] + 1, dim
, relevant
))
2082 isl_basic_set_drop_inequality(bset
, i
);
2087 /* Update the groups in "group" based on the (linear part of a) constraint "c".
2089 * In particular, for any variable involved in the constraint,
2090 * find the actual group id from before and replace the group
2091 * of the corresponding variable by the minimal group of all
2092 * the variables involved in the constraint considered so far
2093 * (if this minimum is smaller) or replace the minimum by this group
2094 * (if the minimum is larger).
2096 * At the end, all the variables in "c" will (indirectly) point
2097 * to the minimal of the groups that they referred to originally.
2099 static void update_groups(int dim
, int *group
, isl_int
*c
)
2104 for (j
= 0; j
< dim
; ++j
) {
2105 if (isl_int_is_zero(c
[j
]))
2107 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
2108 group
[j
] = group
[group
[j
]];
2109 if (group
[j
] == min
)
2111 if (group
[j
] < min
) {
2112 if (min
>= 0 && min
< dim
)
2113 group
[min
] = group
[j
];
2116 group
[group
[j
]] = min
;
2120 /* Allocate an array of groups of variables, one for each variable
2121 * in "context", initialized to zero.
2123 static int *alloc_groups(__isl_keep isl_basic_set
*context
)
2128 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2129 ctx
= isl_basic_set_get_ctx(context
);
2130 return isl_calloc_array(ctx
, int, dim
);
2133 /* Drop constraints from "context" that only involve variables that are
2134 * not related to any of the variables marked with a "-1" in "group".
2136 * We construct groups of variables that collect variables that
2137 * (indirectly) appear in some common constraint of "context".
2138 * Each group is identified by the first variable in the group,
2139 * except for the special group of variables that was already identified
2140 * in the input as -1 (or are related to those variables).
2141 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
2142 * otherwise the group of i is the group of group[i].
2144 * We first initialize groups for the remaining variables.
2145 * Then we iterate over the constraints of "context" and update the
2146 * group of the variables in the constraint by the smallest group.
2147 * Finally, we resolve indirect references to groups by running over
2150 * After computing the groups, we drop constraints that do not involve
2151 * any variables in the -1 group.
2153 static __isl_give isl_basic_set
*group_and_drop_irrelevant_constraints(
2154 __isl_take isl_basic_set
*context
, __isl_take
int *group
)
2160 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2163 for (i
= 0; i
< dim
; ++i
)
2165 last
= group
[i
] = i
;
2171 for (i
= 0; i
< context
->n_eq
; ++i
)
2172 update_groups(dim
, group
, context
->eq
[i
] + 1);
2173 for (i
= 0; i
< context
->n_ineq
; ++i
)
2174 update_groups(dim
, group
, context
->ineq
[i
] + 1);
2176 for (i
= 0; i
< dim
; ++i
)
2178 group
[i
] = group
[group
[i
]];
2180 for (i
= 0; i
< dim
; ++i
)
2181 group
[i
] = group
[i
] == -1;
2183 context
= drop_unrelated_constraints(context
, group
);
2189 /* Drop constraints from "context" that are irrelevant for computing
2190 * the gist of "bset".
2192 * In particular, drop constraints in variables that are not related
2193 * to any of the variables involved in the constraints of "bset"
2194 * in the sense that there is no sequence of constraints that connects them.
2196 * We first mark all variables that appear in "bset" as belonging
2197 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2199 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
2200 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
2206 if (!context
|| !bset
)
2207 return isl_basic_set_free(context
);
2209 group
= alloc_groups(context
);
2212 return isl_basic_set_free(context
);
2214 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2215 for (i
= 0; i
< dim
; ++i
) {
2216 for (j
= 0; j
< bset
->n_eq
; ++j
)
2217 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
2219 if (j
< bset
->n_eq
) {
2223 for (j
= 0; j
< bset
->n_ineq
; ++j
)
2224 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
2226 if (j
< bset
->n_ineq
)
2230 return group_and_drop_irrelevant_constraints(context
, group
);
2233 /* Drop constraints from "context" that are irrelevant for computing
2234 * the gist of the inequalities "ineq".
2235 * Inequalities in "ineq" for which the corresponding element of row
2236 * is set to -1 have already been marked for removal and should be ignored.
2238 * In particular, drop constraints in variables that are not related
2239 * to any of the variables involved in "ineq"
2240 * in the sense that there is no sequence of constraints that connects them.
2242 * We first mark all variables that appear in "bset" as belonging
2243 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2245 static __isl_give isl_basic_set
*drop_irrelevant_constraints_marked(
2246 __isl_take isl_basic_set
*context
, __isl_keep isl_mat
*ineq
, int *row
)
2252 if (!context
|| !ineq
)
2253 return isl_basic_set_free(context
);
2255 group
= alloc_groups(context
);
2258 return isl_basic_set_free(context
);
2260 dim
= isl_basic_set_dim(context
, isl_dim_set
);
2261 n
= isl_mat_rows(ineq
);
2262 for (i
= 0; i
< dim
; ++i
) {
2263 for (j
= 0; j
< n
; ++j
) {
2266 if (!isl_int_is_zero(ineq
->row
[j
][1 + i
]))
2273 return group_and_drop_irrelevant_constraints(context
, group
);
2276 /* Do all "n" entries of "row" contain a negative value?
2278 static int all_neg(int *row
, int n
)
2282 for (i
= 0; i
< n
; ++i
)
2289 /* Update the inequalities in "bset" based on the information in "row"
2292 * In particular, the array "row" contains either -1, meaning that
2293 * the corresponding inequality of "bset" is redundant, or the index
2294 * of an inequality in "tab".
2296 * If the row entry is -1, then drop the inequality.
2297 * Otherwise, if the constraint is marked redundant in the tableau,
2298 * then drop the inequality. Similarly, if it is marked as an equality
2299 * in the tableau, then turn the inequality into an equality and
2300 * perform Gaussian elimination.
2302 static __isl_give isl_basic_set
*update_ineq(__isl_take isl_basic_set
*bset
,
2303 __isl_keep
int *row
, struct isl_tab
*tab
)
2308 int found_equality
= 0;
2312 if (tab
&& tab
->empty
)
2313 return isl_basic_set_set_to_empty(bset
);
2315 n_ineq
= bset
->n_ineq
;
2316 for (i
= n_ineq
- 1; i
>= 0; --i
) {
2318 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2319 return isl_basic_set_free(bset
);
2325 if (isl_tab_is_equality(tab
, n_eq
+ row
[i
])) {
2326 isl_basic_map_inequality_to_equality(bset
, i
);
2328 } else if (isl_tab_is_redundant(tab
, n_eq
+ row
[i
])) {
2329 if (isl_basic_set_drop_inequality(bset
, i
) < 0)
2330 return isl_basic_set_free(bset
);
2335 bset
= isl_basic_set_gauss(bset
, NULL
);
2336 bset
= isl_basic_set_finalize(bset
);
2340 /* Update the inequalities in "bset" based on the information in "row"
2341 * and "tab" and free all arguments (other than "bset").
2343 static __isl_give isl_basic_set
*update_ineq_free(
2344 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*ineq
,
2345 __isl_take isl_basic_set
*context
, __isl_take
int *row
,
2346 struct isl_tab
*tab
)
2349 isl_basic_set_free(context
);
2351 bset
= update_ineq(bset
, row
, tab
);
2358 /* Remove all information from bset that is redundant in the context
2360 * "ineq" contains the (possibly transformed) inequalities of "bset",
2361 * in the same order.
2362 * The (explicit) equalities of "bset" are assumed to have been taken
2363 * into account by the transformation such that only the inequalities
2365 * "context" is assumed not to be empty.
2367 * "row" keeps track of the constraint index of a "bset" inequality in "tab".
2368 * A value of -1 means that the inequality is obviously redundant and may
2369 * not even appear in "tab".
2371 * We first mark the inequalities of "bset"
2372 * that are obviously redundant with respect to some inequality in "context".
2373 * Then we remove those constraints from "context" that have become
2374 * irrelevant for computing the gist of "bset".
2375 * Note that this removal of constraints cannot be replaced by
2376 * a factorization because factors in "bset" may still be connected
2377 * to each other through constraints in "context".
2379 * If there are any inequalities left, we construct a tableau for
2380 * the context and then add the inequalities of "bset".
2381 * Before adding these inequalities, we freeze all constraints such that
2382 * they won't be considered redundant in terms of the constraints of "bset".
2383 * Then we detect all redundant constraints (among the
2384 * constraints that weren't frozen), first by checking for redundancy in the
2385 * the tableau and then by checking if replacing a constraint by its negation
2386 * would lead to an empty set. This last step is fairly expensive
2387 * and could be optimized by more reuse of the tableau.
2388 * Finally, we update bset according to the results.
2390 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
2391 __isl_take isl_mat
*ineq
, __isl_take isl_basic_set
*context
)
2396 isl_basic_set
*combined
= NULL
;
2397 struct isl_tab
*tab
= NULL
;
2398 unsigned n_eq
, context_ineq
;
2401 if (!bset
|| !ineq
|| !context
)
2404 if (bset
->n_ineq
== 0 || isl_basic_set_is_universe(context
)) {
2405 isl_basic_set_free(context
);
2410 ctx
= isl_basic_set_get_ctx(context
);
2411 row
= isl_calloc_array(ctx
, int, bset
->n_ineq
);
2415 if (mark_shifted_constraints(ineq
, context
, row
) < 0)
2417 if (all_neg(row
, bset
->n_ineq
))
2418 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
2420 context
= drop_irrelevant_constraints_marked(context
, ineq
, row
);
2423 if (isl_basic_set_is_universe(context
))
2424 return update_ineq_free(bset
, ineq
, context
, row
, NULL
);
2426 n_eq
= context
->n_eq
;
2427 context_ineq
= context
->n_ineq
;
2428 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
2429 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
2430 tab
= isl_tab_from_basic_set(combined
, 0);
2431 for (i
= 0; i
< context_ineq
; ++i
)
2432 if (isl_tab_freeze_constraint(tab
, n_eq
+ i
) < 0)
2434 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
2437 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2440 combined
= isl_basic_set_add_ineq(combined
, ineq
->row
[i
]);
2441 if (isl_tab_add_ineq(tab
, ineq
->row
[i
]) < 0)
2445 if (isl_tab_detect_implicit_equalities(tab
) < 0)
2447 if (isl_tab_detect_redundant(tab
) < 0)
2449 total
= isl_basic_set_total_dim(bset
);
2450 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
2451 isl_basic_set
*test
;
2457 if (tab
->con
[n_eq
+ r
].is_redundant
)
2459 test
= isl_basic_set_dup(combined
);
2460 if (isl_inequality_negate(test
, r
) < 0)
2461 test
= isl_basic_set_free(test
);
2462 test
= isl_basic_set_update_from_tab(test
, tab
);
2463 is_empty
= isl_basic_set_is_empty(test
);
2464 isl_basic_set_free(test
);
2468 tab
->con
[n_eq
+ r
].is_redundant
= 1;
2470 bset
= update_ineq_free(bset
, ineq
, context
, row
, tab
);
2472 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2473 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2476 isl_basic_set_free(combined
);
2482 isl_basic_set_free(combined
);
2483 isl_basic_set_free(context
);
2484 isl_basic_set_free(bset
);
2488 /* Extract the inequalities of "bset" as an isl_mat.
2490 static __isl_give isl_mat
*extract_ineq(__isl_keep isl_basic_set
*bset
)
2499 ctx
= isl_basic_set_get_ctx(bset
);
2500 total
= isl_basic_set_total_dim(bset
);
2501 ineq
= isl_mat_sub_alloc6(ctx
, bset
->ineq
, 0, bset
->n_ineq
,
2507 /* Remove all information from "bset" that is redundant in the context
2508 * of "context", for the case where both "bset" and "context" are
2511 static __isl_give isl_basic_set
*uset_gist_uncompressed(
2512 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
)
2516 ineq
= extract_ineq(bset
);
2517 return uset_gist_full(bset
, ineq
, context
);
2520 /* Remove all information from "bset" that is redundant in the context
2521 * of "context", for the case where the combined equalities of
2522 * "bset" and "context" allow for a compression that can be obtained
2523 * by preapplication of "T".
2525 * "bset" itself is not transformed by "T". Instead, the inequalities
2526 * are extracted from "bset" and those are transformed by "T".
2527 * uset_gist_full then determines which of the transformed inequalities
2528 * are redundant with respect to the transformed "context" and removes
2529 * the corresponding inequalities from "bset".
2531 * After preapplying "T" to the inequalities, any common factor is
2532 * removed from the coefficients. If this results in a tightening
2533 * of the constant term, then the same tightening is applied to
2534 * the corresponding untransformed inequality in "bset".
2535 * That is, if after plugging in T, a constraint f(x) >= 0 is of the form
2539 * with 0 <= r < g, then it is equivalent to
2543 * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
2544 * subspace compressed by T since the latter would be transformed to
2548 static __isl_give isl_basic_set
*uset_gist_compressed(
2549 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*context
,
2550 __isl_take isl_mat
*T
)
2554 int i
, n_row
, n_col
;
2557 ineq
= extract_ineq(bset
);
2558 ineq
= isl_mat_product(ineq
, isl_mat_copy(T
));
2559 context
= isl_basic_set_preimage(context
, T
);
2561 if (!ineq
|| !context
)
2563 if (isl_basic_set_plain_is_empty(context
)) {
2565 isl_basic_set_free(context
);
2566 return isl_basic_set_set_to_empty(bset
);
2569 ctx
= isl_mat_get_ctx(ineq
);
2570 n_row
= isl_mat_rows(ineq
);
2571 n_col
= isl_mat_cols(ineq
);
2573 for (i
= 0; i
< n_row
; ++i
) {
2574 isl_seq_gcd(ineq
->row
[i
] + 1, n_col
- 1, &ctx
->normalize_gcd
);
2575 if (isl_int_is_zero(ctx
->normalize_gcd
))
2577 if (isl_int_is_one(ctx
->normalize_gcd
))
2579 isl_seq_scale_down(ineq
->row
[i
] + 1, ineq
->row
[i
] + 1,
2580 ctx
->normalize_gcd
, n_col
- 1);
2581 isl_int_fdiv_r(rem
, ineq
->row
[i
][0], ctx
->normalize_gcd
);
2582 isl_int_fdiv_q(ineq
->row
[i
][0],
2583 ineq
->row
[i
][0], ctx
->normalize_gcd
);
2584 if (isl_int_is_zero(rem
))
2586 bset
= isl_basic_set_cow(bset
);
2589 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], rem
);
2593 return uset_gist_full(bset
, ineq
, context
);
2596 isl_basic_set_free(context
);
2597 isl_basic_set_free(bset
);
2601 /* Project "bset" onto the variables that are involved in "template".
2603 static __isl_give isl_basic_set
*project_onto_involved(
2604 __isl_take isl_basic_set
*bset
, __isl_keep isl_basic_set
*template)
2608 if (!bset
|| !template)
2609 return isl_basic_set_free(bset
);
2611 n
= isl_basic_set_dim(template, isl_dim_set
);
2613 for (i
= 0; i
< n
; ++i
) {
2616 involved
= isl_basic_set_involves_dims(template,
2619 return isl_basic_set_free(bset
);
2622 bset
= isl_basic_set_eliminate_vars(bset
, i
, 1);
2628 /* Remove all information from bset that is redundant in the context
2629 * of context. In particular, equalities that are linear combinations
2630 * of those in context are removed. Then the inequalities that are
2631 * redundant in the context of the equalities and inequalities of
2632 * context are removed.
2634 * First of all, we drop those constraints from "context"
2635 * that are irrelevant for computing the gist of "bset".
2636 * Alternatively, we could factorize the intersection of "context" and "bset".
2638 * We first compute the intersection of the integer affine hulls
2639 * of "bset" and "context",
2640 * compute the gist inside this intersection and then reduce
2641 * the constraints with respect to the equalities of the context
2642 * that only involve variables already involved in the input.
2644 * If two constraints are mutually redundant, then uset_gist_full
2645 * will remove the second of those constraints. We therefore first
2646 * sort the constraints so that constraints not involving existentially
2647 * quantified variables are given precedence over those that do.
2648 * We have to perform this sorting before the variable compression,
2649 * because that may effect the order of the variables.
2651 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2652 __isl_take isl_basic_set
*context
)
2657 isl_basic_set
*aff_context
;
2660 if (!bset
|| !context
)
2663 context
= drop_irrelevant_constraints(context
, bset
);
2665 bset
= isl_basic_set_detect_equalities(bset
);
2666 aff
= isl_basic_set_copy(bset
);
2667 aff
= isl_basic_set_plain_affine_hull(aff
);
2668 context
= isl_basic_set_detect_equalities(context
);
2669 aff_context
= isl_basic_set_copy(context
);
2670 aff_context
= isl_basic_set_plain_affine_hull(aff_context
);
2671 aff
= isl_basic_set_intersect(aff
, aff_context
);
2674 if (isl_basic_set_plain_is_empty(aff
)) {
2675 isl_basic_set_free(bset
);
2676 isl_basic_set_free(context
);
2679 bset
= isl_basic_set_sort_constraints(bset
);
2680 if (aff
->n_eq
== 0) {
2681 isl_basic_set_free(aff
);
2682 return uset_gist_uncompressed(bset
, context
);
2684 total
= isl_basic_set_total_dim(bset
);
2685 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2686 eq
= isl_mat_cow(eq
);
2687 T
= isl_mat_variable_compression(eq
, NULL
);
2688 isl_basic_set_free(aff
);
2689 if (T
&& T
->n_col
== 0) {
2691 isl_basic_set_free(context
);
2692 return isl_basic_set_set_to_empty(bset
);
2695 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2696 aff_context
= project_onto_involved(aff_context
, bset
);
2698 bset
= uset_gist_compressed(bset
, context
, T
);
2699 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2702 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2703 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2708 isl_basic_set_free(bset
);
2709 isl_basic_set_free(context
);
2713 /* Return a basic map that has the same intersection with "context" as "bmap"
2714 * and that is as "simple" as possible.
2716 * The core computation is performed on the pure constraints.
2717 * When we add back the meaning of the integer divisions, we need
2718 * to (re)introduce the div constraints. If we happen to have
2719 * discovered that some of these integer divisions are equal to
2720 * some affine combination of other variables, then these div
2721 * constraints may end up getting simplified in terms of the equalities,
2722 * resulting in extra inequalities on the other variables that
2723 * may have been removed already or that may not even have been
2724 * part of the input. We try and remove those constraints of
2725 * this form that are most obviously redundant with respect to
2726 * the context. We also remove those div constraints that are
2727 * redundant with respect to the other constraints in the result.
2729 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
2730 struct isl_basic_map
*context
)
2732 isl_basic_set
*bset
, *eq
;
2733 isl_basic_map
*eq_bmap
;
2734 unsigned total
, n_div
, extra
, n_eq
, n_ineq
;
2736 if (!bmap
|| !context
)
2739 if (isl_basic_map_is_universe(bmap
)) {
2740 isl_basic_map_free(context
);
2743 if (isl_basic_map_plain_is_empty(context
)) {
2744 isl_space
*space
= isl_basic_map_get_space(bmap
);
2745 isl_basic_map_free(bmap
);
2746 isl_basic_map_free(context
);
2747 return isl_basic_map_universe(space
);
2749 if (isl_basic_map_plain_is_empty(bmap
)) {
2750 isl_basic_map_free(context
);
2754 bmap
= isl_basic_map_remove_redundancies(bmap
);
2755 context
= isl_basic_map_remove_redundancies(context
);
2759 context
= isl_basic_map_align_divs(context
, bmap
);
2760 n_div
= isl_basic_map_dim(context
, isl_dim_div
);
2761 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2762 extra
= n_div
- isl_basic_map_dim(bmap
, isl_dim_div
);
2764 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
2765 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, extra
);
2766 bset
= uset_gist(bset
,
2767 isl_basic_map_underlying_set(isl_basic_map_copy(context
)));
2768 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, total
, extra
);
2770 if (!bset
|| bset
->n_eq
== 0 || n_div
== 0 ||
2771 isl_basic_set_plain_is_empty(bset
)) {
2772 isl_basic_map_free(context
);
2773 return isl_basic_map_overlying_set(bset
, bmap
);
2777 n_ineq
= bset
->n_ineq
;
2778 eq
= isl_basic_set_copy(bset
);
2779 eq
= isl_basic_set_cow(eq
);
2780 if (isl_basic_set_free_inequality(eq
, n_ineq
) < 0)
2781 eq
= isl_basic_set_free(eq
);
2782 if (isl_basic_set_free_equality(bset
, n_eq
) < 0)
2783 bset
= isl_basic_set_free(bset
);
2785 eq_bmap
= isl_basic_map_overlying_set(eq
, isl_basic_map_copy(bmap
));
2786 eq_bmap
= isl_basic_map_remove_shifted_constraints(eq_bmap
, context
);
2787 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
2788 bmap
= isl_basic_map_intersect(bmap
, eq_bmap
);
2789 bmap
= isl_basic_map_remove_redundancies(bmap
);
2793 isl_basic_map_free(bmap
);
2794 isl_basic_map_free(context
);
2799 * Assumes context has no implicit divs.
2801 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
2802 __isl_take isl_basic_map
*context
)
2806 if (!map
|| !context
)
2809 if (isl_basic_map_plain_is_empty(context
)) {
2810 isl_space
*space
= isl_map_get_space(map
);
2812 isl_basic_map_free(context
);
2813 return isl_map_universe(space
);
2816 context
= isl_basic_map_remove_redundancies(context
);
2817 map
= isl_map_cow(map
);
2818 if (!map
|| !context
)
2820 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
2821 map
= isl_map_compute_divs(map
);
2824 for (i
= map
->n
- 1; i
>= 0; --i
) {
2825 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
2826 isl_basic_map_copy(context
));
2829 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
2830 isl_basic_map_free(map
->p
[i
]);
2831 if (i
!= map
->n
- 1)
2832 map
->p
[i
] = map
->p
[map
->n
- 1];
2836 isl_basic_map_free(context
);
2837 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2841 isl_basic_map_free(context
);
2845 /* Return a map that has the same intersection with "context" as "map"
2846 * and that is as "simple" as possible.
2848 * If "map" is already the universe, then we cannot make it any simpler.
2849 * Similarly, if "context" is the universe, then we cannot exploit it
2851 * If "map" and "context" are identical to each other, then we can
2852 * return the corresponding universe.
2854 * If none of these cases apply, we have to work a bit harder.
2855 * During this computation, we make use of a single disjunct context,
2856 * so if the original context consists of more than one disjunct
2857 * then we need to approximate the context by a single disjunct set.
2858 * Simply taking the simple hull may drop constraints that are
2859 * only implicitly available in each disjunct. We therefore also
2860 * look for constraints among those defining "map" that are valid
2861 * for the context. These can then be used to simplify away
2862 * the corresponding constraints in "map".
2864 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
2865 __isl_take isl_map
*context
)
2869 isl_basic_map
*hull
;
2871 is_universe
= isl_map_plain_is_universe(map
);
2872 if (is_universe
>= 0 && !is_universe
)
2873 is_universe
= isl_map_plain_is_universe(context
);
2874 if (is_universe
< 0)
2877 isl_map_free(context
);
2881 equal
= isl_map_plain_is_equal(map
, context
);
2885 isl_map
*res
= isl_map_universe(isl_map_get_space(map
));
2887 isl_map_free(context
);
2891 context
= isl_map_compute_divs(context
);
2894 if (isl_map_n_basic_map(context
) == 1) {
2895 hull
= isl_map_simple_hull(context
);
2900 ctx
= isl_map_get_ctx(map
);
2901 list
= isl_map_list_alloc(ctx
, 2);
2902 list
= isl_map_list_add(list
, isl_map_copy(context
));
2903 list
= isl_map_list_add(list
, isl_map_copy(map
));
2904 hull
= isl_map_unshifted_simple_hull_from_map_list(context
,
2907 return isl_map_gist_basic_map(map
, hull
);
2910 isl_map_free(context
);
2914 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
2915 __isl_take isl_map
*context
)
2917 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2920 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2921 struct isl_basic_set
*context
)
2923 return (struct isl_basic_set
*)isl_basic_map_gist(
2924 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2927 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2928 __isl_take isl_basic_set
*context
)
2930 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2931 (struct isl_basic_map
*)context
);
2934 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2935 __isl_take isl_basic_set
*context
)
2937 isl_space
*space
= isl_set_get_space(set
);
2938 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2939 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2940 return isl_set_gist_basic_set(set
, dom_context
);
2943 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2944 __isl_take isl_set
*context
)
2946 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2947 (struct isl_map
*)context
);
2950 /* Compute the gist of "bmap" with respect to the constraints "context"
2953 __isl_give isl_basic_map
*isl_basic_map_gist_domain(
2954 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*context
)
2956 isl_space
*space
= isl_basic_map_get_space(bmap
);
2957 isl_basic_map
*bmap_context
= isl_basic_map_universe(space
);
2959 bmap_context
= isl_basic_map_intersect_domain(bmap_context
, context
);
2960 return isl_basic_map_gist(bmap
, bmap_context
);
2963 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2964 __isl_take isl_set
*context
)
2966 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2967 map_context
= isl_map_intersect_domain(map_context
, context
);
2968 return isl_map_gist(map
, map_context
);
2971 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2972 __isl_take isl_set
*context
)
2974 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2975 map_context
= isl_map_intersect_range(map_context
, context
);
2976 return isl_map_gist(map
, map_context
);
2979 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2980 __isl_take isl_set
*context
)
2982 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2983 map_context
= isl_map_intersect_params(map_context
, context
);
2984 return isl_map_gist(map
, map_context
);
2987 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2988 __isl_take isl_set
*context
)
2990 return isl_map_gist_params(set
, context
);
2993 /* Quick check to see if two basic maps are disjoint.
2994 * In particular, we reduce the equalities and inequalities of
2995 * one basic map in the context of the equalities of the other
2996 * basic map and check if we get a contradiction.
2998 isl_bool
isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2999 __isl_keep isl_basic_map
*bmap2
)
3001 struct isl_vec
*v
= NULL
;
3006 if (!bmap1
|| !bmap2
)
3007 return isl_bool_error
;
3008 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
3009 return isl_bool_error
);
3010 if (bmap1
->n_div
|| bmap2
->n_div
)
3011 return isl_bool_false
;
3012 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
3013 return isl_bool_false
;
3015 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
3017 return isl_bool_false
;
3018 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
3021 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
3024 compute_elimination_index(bmap1
, elim
);
3025 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
3027 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
3029 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
3030 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3033 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
3035 reduced
= reduced_using_equalities(v
->block
.data
,
3036 bmap2
->ineq
[i
], bmap1
, elim
);
3037 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
3038 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3041 compute_elimination_index(bmap2
, elim
);
3042 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
3044 reduced
= reduced_using_equalities(v
->block
.data
,
3045 bmap1
->ineq
[i
], bmap2
, elim
);
3046 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
3047 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
3052 return isl_bool_false
;
3056 return isl_bool_true
;
3060 return isl_bool_error
;
3063 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
3064 __isl_keep isl_basic_set
*bset2
)
3066 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
3067 (struct isl_basic_map
*)bset2
);
3070 /* Are "map1" and "map2" obviously disjoint?
3072 * If one of them is empty or if they live in different spaces (ignoring
3073 * parameters), then they are clearly disjoint.
3075 * If they have different parameters, then we skip any further tests.
3077 * If they are obviously equal, but not obviously empty, then we will
3078 * not be able to detect if they are disjoint.
3080 * Otherwise we check if each basic map in "map1" is obviously disjoint
3081 * from each basic map in "map2".
3083 isl_bool
isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
3084 __isl_keep isl_map
*map2
)
3092 return isl_bool_error
;
3094 disjoint
= isl_map_plain_is_empty(map1
);
3095 if (disjoint
< 0 || disjoint
)
3098 disjoint
= isl_map_plain_is_empty(map2
);
3099 if (disjoint
< 0 || disjoint
)
3102 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_in
,
3103 map2
->dim
, isl_dim_in
);
3104 if (match
< 0 || !match
)
3105 return match
< 0 ? isl_bool_error
: isl_bool_true
;
3107 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_out
,
3108 map2
->dim
, isl_dim_out
);
3109 if (match
< 0 || !match
)
3110 return match
< 0 ? isl_bool_error
: isl_bool_true
;
3112 match
= isl_space_match(map1
->dim
, isl_dim_param
,
3113 map2
->dim
, isl_dim_param
);
3114 if (match
< 0 || !match
)
3115 return match
< 0 ? isl_bool_error
: isl_bool_false
;
3117 intersect
= isl_map_plain_is_equal(map1
, map2
);
3118 if (intersect
< 0 || intersect
)
3119 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3121 for (i
= 0; i
< map1
->n
; ++i
) {
3122 for (j
= 0; j
< map2
->n
; ++j
) {
3123 isl_bool d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
3125 if (d
!= isl_bool_true
)
3129 return isl_bool_true
;
3132 /* Are "map1" and "map2" disjoint?
3134 * They are disjoint if they are "obviously disjoint" or if one of them
3135 * is empty. Otherwise, they are not disjoint if one of them is universal.
3136 * If none of these cases apply, we compute the intersection and see if
3137 * the result is empty.
3139 isl_bool
isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
3145 disjoint
= isl_map_plain_is_disjoint(map1
, map2
);
3146 if (disjoint
< 0 || disjoint
)
3149 disjoint
= isl_map_is_empty(map1
);
3150 if (disjoint
< 0 || disjoint
)
3153 disjoint
= isl_map_is_empty(map2
);
3154 if (disjoint
< 0 || disjoint
)
3157 intersect
= isl_map_plain_is_universe(map1
);
3158 if (intersect
< 0 || intersect
)
3159 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3161 intersect
= isl_map_plain_is_universe(map2
);
3162 if (intersect
< 0 || intersect
)
3163 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3165 test
= isl_map_intersect(isl_map_copy(map1
), isl_map_copy(map2
));
3166 disjoint
= isl_map_is_empty(test
);
3172 /* Are "bmap1" and "bmap2" disjoint?
3174 * They are disjoint if they are "obviously disjoint" or if one of them
3175 * is empty. Otherwise, they are not disjoint if one of them is universal.
3176 * If none of these cases apply, we compute the intersection and see if
3177 * the result is empty.
3179 isl_bool
isl_basic_map_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
3180 __isl_keep isl_basic_map
*bmap2
)
3184 isl_basic_map
*test
;
3186 disjoint
= isl_basic_map_plain_is_disjoint(bmap1
, bmap2
);
3187 if (disjoint
< 0 || disjoint
)
3190 disjoint
= isl_basic_map_is_empty(bmap1
);
3191 if (disjoint
< 0 || disjoint
)
3194 disjoint
= isl_basic_map_is_empty(bmap2
);
3195 if (disjoint
< 0 || disjoint
)
3198 intersect
= isl_basic_map_is_universe(bmap1
);
3199 if (intersect
< 0 || intersect
)
3200 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3202 intersect
= isl_basic_map_is_universe(bmap2
);
3203 if (intersect
< 0 || intersect
)
3204 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
3206 test
= isl_basic_map_intersect(isl_basic_map_copy(bmap1
),
3207 isl_basic_map_copy(bmap2
));
3208 disjoint
= isl_basic_map_is_empty(test
);
3209 isl_basic_map_free(test
);
3214 /* Are "bset1" and "bset2" disjoint?
3216 isl_bool
isl_basic_set_is_disjoint(__isl_keep isl_basic_set
*bset1
,
3217 __isl_keep isl_basic_set
*bset2
)
3219 return isl_basic_map_is_disjoint(bset1
, bset2
);
3222 isl_bool
isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
3223 __isl_keep isl_set
*set2
)
3225 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
3226 (struct isl_map
*)set2
);
3229 /* Are "set1" and "set2" disjoint?
3231 isl_bool
isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
3233 return isl_map_is_disjoint(set1
, set2
);
3236 /* Check if we can combine a given div with lower bound l and upper
3237 * bound u with some other div and if so return that other div.
3238 * Otherwise return -1.
3240 * We first check that
3241 * - the bounds are opposites of each other (except for the constant
3243 * - the bounds do not reference any other div
3244 * - no div is defined in terms of this div
3246 * Let m be the size of the range allowed on the div by the bounds.
3247 * That is, the bounds are of the form
3249 * e <= a <= e + m - 1
3251 * with e some expression in the other variables.
3252 * We look for another div b such that no third div is defined in terms
3253 * of this second div b and such that in any constraint that contains
3254 * a (except for the given lower and upper bound), also contains b
3255 * with a coefficient that is m times that of b.
3256 * That is, all constraints (execpt for the lower and upper bound)
3259 * e + f (a + m b) >= 0
3261 * If so, we return b so that "a + m b" can be replaced by
3262 * a single div "c = a + m b".
3264 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
3265 unsigned div
, unsigned l
, unsigned u
)
3271 if (bmap
->n_div
<= 1)
3273 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3274 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
3276 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
3277 bmap
->n_div
- div
- 1) != -1)
3279 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
3283 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3284 if (isl_int_is_zero(bmap
->div
[i
][0]))
3286 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
3290 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3291 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
3292 isl_int_sub(bmap
->ineq
[l
][0],
3293 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3294 bmap
= isl_basic_map_copy(bmap
);
3295 bmap
= isl_basic_map_set_to_empty(bmap
);
3296 isl_basic_map_free(bmap
);
3299 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
3300 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3305 for (j
= 0; j
< bmap
->n_div
; ++j
) {
3306 if (isl_int_is_zero(bmap
->div
[j
][0]))
3308 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
3311 if (j
< bmap
->n_div
)
3313 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
3315 if (j
== l
|| j
== u
)
3317 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
3319 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
3321 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
3322 bmap
->ineq
[j
][1 + dim
+ div
],
3324 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
3325 bmap
->ineq
[j
][1 + dim
+ i
]);
3326 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
3327 bmap
->ineq
[j
][1 + dim
+ div
],
3332 if (j
< bmap
->n_ineq
)
3337 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
3338 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3342 /* Given a lower and an upper bound on div i, construct an inequality
3343 * that when nonnegative ensures that this pair of bounds always allows
3344 * for an integer value of the given div.
3345 * The lower bound is inequality l, while the upper bound is inequality u.
3346 * The constructed inequality is stored in ineq.
3347 * g, fl, fu are temporary scalars.
3349 * Let the upper bound be
3353 * and the lower bound
3357 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
3360 * - f_u e_l <= f_u f_l g a <= f_l e_u
3362 * Since all variables are integer valued, this is equivalent to
3364 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
3366 * If this interval is at least f_u f_l g, then it contains at least
3367 * one integer value for a.
3368 * That is, the test constraint is
3370 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
3372 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
3373 int l
, int u
, isl_int
*ineq
, isl_int
*g
, isl_int
*fl
, isl_int
*fu
)
3376 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3378 isl_int_gcd(*g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
3379 isl_int_divexact(*fl
, bmap
->ineq
[l
][1 + dim
+ i
], *g
);
3380 isl_int_divexact(*fu
, bmap
->ineq
[u
][1 + dim
+ i
], *g
);
3381 isl_int_neg(*fu
, *fu
);
3382 isl_seq_combine(ineq
, *fl
, bmap
->ineq
[u
], *fu
, bmap
->ineq
[l
],
3383 1 + dim
+ bmap
->n_div
);
3384 isl_int_add(ineq
[0], ineq
[0], *fl
);
3385 isl_int_add(ineq
[0], ineq
[0], *fu
);
3386 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
3387 isl_int_mul(*g
, *g
, *fl
);
3388 isl_int_mul(*g
, *g
, *fu
);
3389 isl_int_sub(ineq
[0], ineq
[0], *g
);
3392 /* Remove more kinds of divs that are not strictly needed.
3393 * In particular, if all pairs of lower and upper bounds on a div
3394 * are such that they allow at least one integer value of the div,
3395 * the we can eliminate the div using Fourier-Motzkin without
3396 * introducing any spurious solutions.
3398 static struct isl_basic_map
*drop_more_redundant_divs(
3399 struct isl_basic_map
*bmap
, int *pairs
, int n
)
3401 struct isl_tab
*tab
= NULL
;
3402 struct isl_vec
*vec
= NULL
;
3414 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3415 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
3419 tab
= isl_tab_from_basic_map(bmap
, 0);
3424 enum isl_lp_result res
;
3426 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3429 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
3435 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
3436 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
3438 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
3439 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
3441 construct_test_ineq(bmap
, i
, l
, u
,
3442 vec
->el
, &g
, &fl
, &fu
);
3443 res
= isl_tab_min(tab
, vec
->el
,
3444 bmap
->ctx
->one
, &g
, NULL
, 0);
3445 if (res
== isl_lp_error
)
3447 if (res
== isl_lp_empty
) {
3448 bmap
= isl_basic_map_set_to_empty(bmap
);
3451 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
3454 if (u
< bmap
->n_ineq
)
3457 if (l
== bmap
->n_ineq
) {
3477 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
3478 return isl_basic_map_drop_redundant_divs(bmap
);
3481 isl_basic_map_free(bmap
);
3490 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
3491 * and the upper bound u, div1 always occurs together with div2 in the form
3492 * (div1 + m div2), where m is the constant range on the variable div1
3493 * allowed by l and u, replace the pair div1 and div2 by a single
3494 * div that is equal to div1 + m div2.
3496 * The new div will appear in the location that contains div2.
3497 * We need to modify all constraints that contain
3498 * div2 = (div - div1) / m
3499 * (If a constraint does not contain div2, it will also not contain div1.)
3500 * If the constraint also contains div1, then we know they appear
3501 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
3502 * i.e., the coefficient of div is f.
3504 * Otherwise, we first need to introduce div1 into the constraint.
3513 * A lower bound on div2
3517 * can be replaced by
3519 * (n * (m div 2 + div1) + m t + n f)/g >= 0
3521 * with g = gcd(m,n).
3526 * can be replaced by
3528 * (-n * (m div2 + div1) + m t + n f')/g >= 0
3530 * These constraint are those that we would obtain from eliminating
3531 * div1 using Fourier-Motzkin.
3533 * After all constraints have been modified, we drop the lower and upper
3534 * bound and then drop div1.
3536 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
3537 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
3542 unsigned dim
, total
;
3545 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3546 total
= 1 + dim
+ bmap
->n_div
;
3551 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3552 isl_int_add_ui(m
, m
, 1);
3554 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
3555 if (i
== l
|| i
== u
)
3557 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
3559 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
3560 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
3561 isl_int_divexact(a
, m
, b
);
3562 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
3563 if (isl_int_is_pos(b
)) {
3564 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
3565 b
, bmap
->ineq
[l
], total
);
3568 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
3569 b
, bmap
->ineq
[u
], total
);
3572 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
3573 bmap
->ineq
[i
][1 + dim
+ div1
]);
3574 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
3581 isl_basic_map_drop_inequality(bmap
, l
);
3582 isl_basic_map_drop_inequality(bmap
, u
);
3584 isl_basic_map_drop_inequality(bmap
, u
);
3585 isl_basic_map_drop_inequality(bmap
, l
);
3587 bmap
= isl_basic_map_drop_div(bmap
, div1
);
3591 /* First check if we can coalesce any pair of divs and
3592 * then continue with dropping more redundant divs.
3594 * We loop over all pairs of lower and upper bounds on a div
3595 * with coefficient 1 and -1, respectively, check if there
3596 * is any other div "c" with which we can coalesce the div
3597 * and if so, perform the coalescing.
3599 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
3600 struct isl_basic_map
*bmap
, int *pairs
, int n
)
3605 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3607 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3610 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
3611 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
3613 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
3616 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
3618 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
3622 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
3623 return isl_basic_map_drop_redundant_divs(bmap
);
3628 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
3631 return drop_more_redundant_divs(bmap
, pairs
, n
);
3634 /* Remove divs that are not strictly needed.
3635 * In particular, if a div only occurs positively (or negatively)
3636 * in constraints, then it can simply be dropped.
3637 * Also, if a div occurs in only two constraints and if moreover
3638 * those two constraints are opposite to each other, except for the constant
3639 * term and if the sum of the constant terms is such that for any value
3640 * of the other values, there is always at least one integer value of the
3641 * div, i.e., if one plus this sum is greater than or equal to
3642 * the (absolute value) of the coefficent of the div in the constraints,
3643 * then we can also simply drop the div.
3645 * We skip divs that appear in equalities or in the definition of other divs.
3646 * Divs that appear in the definition of other divs usually occur in at least
3647 * 4 constraints, but the constraints may have been simplified.
3649 * If any divs are left after these simple checks then we move on
3650 * to more complicated cases in drop_more_redundant_divs.
3652 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
3653 struct isl_basic_map
*bmap
)
3662 if (bmap
->n_div
== 0)
3665 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3666 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
3670 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3672 int last_pos
, last_neg
;
3676 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
3677 for (j
= i
; j
< bmap
->n_div
; ++j
)
3678 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
3680 if (j
< bmap
->n_div
)
3682 for (j
= 0; j
< bmap
->n_eq
; ++j
)
3683 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
3689 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
3690 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
3694 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
3699 pairs
[i
] = pos
* neg
;
3700 if (pairs
[i
] == 0) {
3701 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
3702 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
3703 isl_basic_map_drop_inequality(bmap
, j
);
3704 bmap
= isl_basic_map_drop_div(bmap
, i
);
3706 return isl_basic_map_drop_redundant_divs(bmap
);
3710 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
3711 bmap
->ineq
[last_neg
] + 1,
3715 isl_int_add(bmap
->ineq
[last_pos
][0],
3716 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3717 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
3718 bmap
->ineq
[last_pos
][0], 1);
3719 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
3720 bmap
->ineq
[last_pos
][1+off
+i
]);
3721 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
3722 bmap
->ineq
[last_pos
][0], 1);
3723 isl_int_sub(bmap
->ineq
[last_pos
][0],
3724 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3727 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
3732 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
3733 bmap
= isl_basic_map_simplify(bmap
);
3735 return isl_basic_map_drop_redundant_divs(bmap
);
3737 if (last_pos
> last_neg
) {
3738 isl_basic_map_drop_inequality(bmap
, last_pos
);
3739 isl_basic_map_drop_inequality(bmap
, last_neg
);
3741 isl_basic_map_drop_inequality(bmap
, last_neg
);
3742 isl_basic_map_drop_inequality(bmap
, last_pos
);
3744 bmap
= isl_basic_map_drop_div(bmap
, i
);
3746 return isl_basic_map_drop_redundant_divs(bmap
);
3750 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
3756 isl_basic_map_free(bmap
);
3760 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
3761 struct isl_basic_set
*bset
)
3763 return (struct isl_basic_set
*)
3764 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
3767 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
3773 for (i
= 0; i
< map
->n
; ++i
) {
3774 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
3778 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3785 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
3787 return (struct isl_set
*)
3788 isl_map_drop_redundant_divs((struct isl_map
*)set
);
3791 /* Does "bmap" satisfy any equality that involves more than 2 variables
3792 * and/or has coefficients different from -1 and 1?
3794 static int has_multiple_var_equality(__isl_keep isl_basic_map
*bmap
)
3799 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3801 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
3804 j
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1, total
);
3807 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
3808 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
3812 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
3816 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
3817 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
3821 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
3829 /* Remove any common factor g from the constraint coefficients in "v".
3830 * The constant term is stored in the first position and is replaced
3831 * by floor(c/g). If any common factor is removed and if this results
3832 * in a tightening of the constraint, then set *tightened.
3834 static __isl_give isl_vec
*normalize_constraint(__isl_take isl_vec
*v
,
3841 ctx
= isl_vec_get_ctx(v
);
3842 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
3843 if (isl_int_is_zero(ctx
->normalize_gcd
))
3845 if (isl_int_is_one(ctx
->normalize_gcd
))
3850 if (tightened
&& !isl_int_is_divisible_by(v
->el
[0], ctx
->normalize_gcd
))
3852 isl_int_fdiv_q(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
3853 isl_seq_scale_down(v
->el
+ 1, v
->el
+ 1, ctx
->normalize_gcd
,
3858 /* If "bmap" is an integer set that satisfies any equality involving
3859 * more than 2 variables and/or has coefficients different from -1 and 1,
3860 * then use variable compression to reduce the coefficients by removing
3861 * any (hidden) common factor.
3862 * In particular, apply the variable compression to each constraint,
3863 * factor out any common factor in the non-constant coefficients and
3864 * then apply the inverse of the compression.
3865 * At the end, we mark the basic map as having reduced constants.
3866 * If this flag is still set on the next invocation of this function,
3867 * then we skip the computation.
3869 * Removing a common factor may result in a tightening of some of
3870 * the constraints. If this happens, then we may end up with two
3871 * opposite inequalities that can be replaced by an equality.
3872 * We therefore call isl_basic_map_detect_inequality_pairs,
3873 * which checks for such pairs of inequalities as well as eliminate_divs_eq
3874 * and isl_basic_map_gauss if such a pair was found.
3876 __isl_give isl_basic_map
*isl_basic_map_reduce_coefficients(
3877 __isl_take isl_basic_map
*bmap
)
3882 isl_mat
*eq
, *T
, *T2
;
3888 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
))
3890 if (isl_basic_map_is_rational(bmap
))
3892 if (bmap
->n_eq
== 0)
3894 if (!has_multiple_var_equality(bmap
))
3897 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3898 ctx
= isl_basic_map_get_ctx(bmap
);
3899 v
= isl_vec_alloc(ctx
, 1 + total
);
3901 return isl_basic_map_free(bmap
);
3903 eq
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
, 0, 1 + total
);
3904 T
= isl_mat_variable_compression(eq
, &T2
);
3907 if (T
->n_col
== 0) {
3911 return isl_basic_map_set_to_empty(bmap
);
3915 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
3916 isl_seq_cpy(v
->el
, bmap
->ineq
[i
], 1 + total
);
3917 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
3918 v
= normalize_constraint(v
, &tightened
);
3919 v
= isl_vec_mat_product(v
, isl_mat_copy(T2
));
3922 isl_seq_cpy(bmap
->ineq
[i
], v
->el
, 1 + total
);
3929 ISL_F_SET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
3934 bmap
= isl_basic_map_detect_inequality_pairs(bmap
, &progress
);
3936 bmap
= eliminate_divs_eq(bmap
, &progress
);
3937 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3946 return isl_basic_map_free(bmap
);
3949 /* Shift the integer division at position "div" of "bmap"
3950 * by "shift" times the variable at position "pos".
3951 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
3952 * corresponds to the constant term.
3954 * That is, if the integer division has the form
3958 * then replace it by
3960 * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
3962 __isl_give isl_basic_map
*isl_basic_map_shift_div(
3963 __isl_take isl_basic_map
*bmap
, int div
, int pos
, isl_int shift
)
3971 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3972 total
-= isl_basic_map_dim(bmap
, isl_dim_div
);
3974 isl_int_addmul(bmap
->div
[div
][1 + pos
], shift
, bmap
->div
[div
][0]);
3976 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
3977 if (isl_int_is_zero(bmap
->eq
[i
][1 + total
+ div
]))
3979 isl_int_submul(bmap
->eq
[i
][pos
],
3980 shift
, bmap
->eq
[i
][1 + total
+ div
]);
3982 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
3983 if (isl_int_is_zero(bmap
->ineq
[i
][1 + total
+ div
]))
3985 isl_int_submul(bmap
->ineq
[i
][pos
],
3986 shift
, bmap
->ineq
[i
][1 + total
+ div
]);
3988 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3989 if (isl_int_is_zero(bmap
->div
[i
][0]))
3991 if (isl_int_is_zero(bmap
->div
[i
][1 + 1 + total
+ div
]))
3993 isl_int_submul(bmap
->div
[i
][1 + pos
],
3994 shift
, bmap
->div
[i
][1 + 1 + total
+ div
]);