2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012-2013 Ecole Normale Superieure
4 * Copyright 2014 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.
770 struct isl_constraint_index
{
776 /* Fill in the "ci" data structure for holding the inequalities of "bmap".
778 static isl_stat
create_constraint_index(struct isl_constraint_index
*ci
,
779 __isl_keep isl_basic_map
*bmap
)
785 return isl_stat_error
;
786 if (bmap
->n_ineq
== 0)
788 ci
->size
= round_up(4 * (bmap
->n_ineq
+ 1) / 3 - 1);
789 ci
->bits
= ffs(ci
->size
) - 1;
790 ctx
= isl_basic_map_get_ctx(bmap
);
791 ci
->index
= isl_calloc_array(ctx
, isl_int
**, ci
->size
);
793 return isl_stat_error
;
798 /* Free the memory allocated by create_constraint_index.
800 static void constraint_index_free(struct isl_constraint_index
*ci
)
805 static int hash_index(struct isl_constraint_index
*ci
,
806 struct isl_basic_map
*bmap
, int k
)
809 unsigned total
= isl_basic_map_total_dim(bmap
);
810 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, ci
->bits
);
811 for (h
= hash
; ci
->index
[h
]; h
= (h
+1) % ci
->size
)
812 if (&bmap
->ineq
[k
] != ci
->index
[h
] &&
813 isl_seq_eq(bmap
->ineq
[k
]+1, ci
->index
[h
][0]+1, total
))
818 static int set_hash_index(struct isl_constraint_index
*ci
,
819 struct isl_basic_set
*bset
, int k
)
821 return hash_index(ci
, bset
, k
);
824 /* Fill in the "ci" data structure with the inequalities of "bset".
826 static isl_stat
setup_constraint_index(struct isl_constraint_index
*ci
,
827 __isl_keep isl_basic_set
*bset
)
831 if (create_constraint_index(ci
, bset
) < 0)
832 return isl_stat_error
;
834 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
835 h
= set_hash_index(ci
, bset
, k
);
836 ci
->index
[h
] = &bset
->ineq
[k
];
842 /* If we can eliminate more than one div, then we need to make
843 * sure we do it from last div to first div, in order not to
844 * change the position of the other divs that still need to
847 static struct isl_basic_map
*remove_duplicate_divs(
848 struct isl_basic_map
*bmap
, int *progress
)
860 bmap
= isl_basic_map_order_divs(bmap
);
861 if (!bmap
|| bmap
->n_div
<= 1)
864 total_var
= isl_space_dim(bmap
->dim
, isl_dim_all
);
865 total
= total_var
+ bmap
->n_div
;
868 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
869 if (!isl_int_is_zero(bmap
->div
[k
][0]))
874 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
877 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
878 bits
= ffs(size
) - 1;
879 index
= isl_calloc_array(ctx
, int, size
);
880 if (!elim_for
|| !index
)
882 eq
= isl_blk_alloc(ctx
, 1+total
);
883 if (isl_blk_is_error(eq
))
886 isl_seq_clr(eq
.data
, 1+total
);
887 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
888 for (--k
; k
>= 0; --k
) {
891 if (isl_int_is_zero(bmap
->div
[k
][0]))
894 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
895 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
896 if (isl_seq_eq(bmap
->div
[k
],
897 bmap
->div
[index
[h
]-1], 2+total
))
906 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
910 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
911 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
912 bmap
= eliminate_div(bmap
, eq
.data
, l
, 1);
915 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
916 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
919 isl_blk_free(ctx
, eq
);
926 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
931 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
932 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
933 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
937 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
943 /* Normalize divs that appear in equalities.
945 * In particular, we assume that bmap contains some equalities
950 * and we want to replace the set of e_i by a minimal set and
951 * such that the new e_i have a canonical representation in terms
953 * If any of the equalities involves more than one divs, then
954 * we currently simply bail out.
956 * Let us first additionally assume that all equalities involve
957 * a div. The equalities then express modulo constraints on the
958 * remaining variables and we can use "parameter compression"
959 * to find a minimal set of constraints. The result is a transformation
961 * x = T(x') = x_0 + G x'
963 * with G a lower-triangular matrix with all elements below the diagonal
964 * non-negative and smaller than the diagonal element on the same row.
965 * We first normalize x_0 by making the same property hold in the affine
967 * The rows i of G with a 1 on the diagonal do not impose any modulo
968 * constraint and simply express x_i = x'_i.
969 * For each of the remaining rows i, we introduce a div and a corresponding
970 * equality. In particular
972 * g_ii e_j = x_i - g_i(x')
974 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
975 * corresponding div (if g_kk != 1).
977 * If there are any equalities not involving any div, then we
978 * first apply a variable compression on the variables x:
980 * x = C x'' x'' = C_2 x
982 * and perform the above parameter compression on A C instead of on A.
983 * The resulting compression is then of the form
985 * x'' = T(x') = x_0 + G x'
987 * and in constructing the new divs and the corresponding equalities,
988 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
989 * by the corresponding row from C_2.
991 static struct isl_basic_map
*normalize_divs(
992 struct isl_basic_map
*bmap
, int *progress
)
999 struct isl_mat
*T
= NULL
;
1000 struct isl_mat
*C
= NULL
;
1001 struct isl_mat
*C2
= NULL
;
1004 int dropped
, needed
;
1009 if (bmap
->n_div
== 0)
1012 if (bmap
->n_eq
== 0)
1015 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
1018 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1019 div_eq
= n_pure_div_eq(bmap
);
1023 if (div_eq
< bmap
->n_eq
) {
1024 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
1025 bmap
->n_eq
- div_eq
, 0, 1 + total
);
1026 C
= isl_mat_variable_compression(B
, &C2
);
1029 if (C
->n_col
== 0) {
1030 bmap
= isl_basic_map_set_to_empty(bmap
);
1037 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
1040 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
1041 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
1043 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
1045 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
1048 B
= isl_mat_product(B
, C
);
1052 T
= isl_mat_parameter_compression(B
, d
);
1055 if (T
->n_col
== 0) {
1056 bmap
= isl_basic_map_set_to_empty(bmap
);
1062 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
1063 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
1064 if (isl_int_is_zero(v
))
1066 isl_mat_col_submul(T
, 0, v
, 1 + i
);
1069 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
1072 /* We have to be careful because dropping equalities may reorder them */
1074 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
1075 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1076 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
1078 if (i
< bmap
->n_eq
) {
1079 bmap
= isl_basic_map_drop_div(bmap
, j
);
1080 isl_basic_map_drop_equality(bmap
, i
);
1086 for (i
= 1; i
< T
->n_row
; ++i
) {
1087 if (isl_int_is_one(T
->row
[i
][i
]))
1092 if (needed
> dropped
) {
1093 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
1098 for (i
= 1; i
< T
->n_row
; ++i
) {
1099 if (isl_int_is_one(T
->row
[i
][i
]))
1101 k
= isl_basic_map_alloc_div(bmap
);
1102 pos
[i
] = 1 + total
+ k
;
1103 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
1104 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
1106 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
1108 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
1109 for (j
= 0; j
< i
; ++j
) {
1110 if (isl_int_is_zero(T
->row
[i
][j
]))
1112 if (pos
[j
] < T
->n_row
&& C2
)
1113 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
1114 C2
->row
[pos
[j
]], 1 + total
);
1116 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
1119 j
= isl_basic_map_alloc_equality(bmap
);
1120 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
1121 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
1130 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
1140 static struct isl_basic_map
*set_div_from_lower_bound(
1141 struct isl_basic_map
*bmap
, int div
, int ineq
)
1143 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1145 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1146 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1147 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1148 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1149 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1154 /* Check whether it is ok to define a div based on an inequality.
1155 * To avoid the introduction of circular definitions of divs, we
1156 * do not allow such a definition if the resulting expression would refer to
1157 * any other undefined divs or if any known div is defined in
1158 * terms of the unknown div.
1160 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
1164 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1166 /* Not defined in terms of unknown divs */
1167 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1170 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1172 if (isl_int_is_zero(bmap
->div
[j
][0]))
1176 /* No other div defined in terms of this one => avoid loops */
1177 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1180 if (isl_int_is_zero(bmap
->div
[j
][0]))
1182 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1189 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1190 * be a better expression than the current one?
1192 * If we do not have any expression yet, then any expression would be better.
1193 * Otherwise we check if the last variable involved in the inequality
1194 * (disregarding the div that it would define) is in an earlier position
1195 * than the last variable involved in the current div expression.
1197 static int better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1200 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1204 if (isl_int_is_zero(bmap
->div
[div
][0]))
1207 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1208 bmap
->n_div
- (div
+ 1)) >= 0)
1211 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1212 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1213 total
+ bmap
->n_div
);
1215 return last_ineq
< last_div
;
1218 /* Given two constraints "k" and "l" that are opposite to each other,
1219 * except for the constant term, check if we can use them
1220 * to obtain an expression for one of the hitherto unknown divs or
1221 * a "better" expression for a div for which we already have an expression.
1222 * "sum" is the sum of the constant terms of the constraints.
1223 * If this sum is strictly smaller than the coefficient of one
1224 * of the divs, then this pair can be used define the div.
1225 * To avoid the introduction of circular definitions of divs, we
1226 * do not use the pair if the resulting expression would refer to
1227 * any other undefined divs or if any known div is defined in
1228 * terms of the unknown div.
1230 static struct isl_basic_map
*check_for_div_constraints(
1231 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
1234 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1236 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1237 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1239 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1241 if (!better_div_constraint(bmap
, i
, k
))
1243 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1245 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1246 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1248 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1256 __isl_give isl_basic_map
*isl_basic_map_remove_duplicate_constraints(
1257 __isl_take isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1259 struct isl_constraint_index ci
;
1261 unsigned total
= isl_basic_map_total_dim(bmap
);
1264 if (!bmap
|| bmap
->n_ineq
<= 1)
1267 if (create_constraint_index(&ci
, bmap
) < 0)
1270 h
= isl_seq_get_hash_bits(bmap
->ineq
[0] + 1, total
, ci
.bits
);
1271 ci
.index
[h
] = &bmap
->ineq
[0];
1272 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1273 h
= hash_index(&ci
, bmap
, k
);
1275 ci
.index
[h
] = &bmap
->ineq
[k
];
1280 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1281 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1282 swap_inequality(bmap
, k
, l
);
1283 isl_basic_map_drop_inequality(bmap
, k
);
1287 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1288 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1289 h
= hash_index(&ci
, bmap
, k
);
1290 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1293 l
= ci
.index
[h
] - &bmap
->ineq
[0];
1294 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1295 if (isl_int_is_pos(sum
)) {
1297 bmap
= check_for_div_constraints(bmap
, k
, l
,
1301 if (isl_int_is_zero(sum
)) {
1302 /* We need to break out of the loop after these
1303 * changes since the contents of the hash
1304 * will no longer be valid.
1305 * Plus, we probably we want to regauss first.
1309 isl_basic_map_drop_inequality(bmap
, l
);
1310 isl_basic_map_inequality_to_equality(bmap
, k
);
1312 bmap
= isl_basic_map_set_to_empty(bmap
);
1317 constraint_index_free(&ci
);
1321 /* Detect all pairs of inequalities that form an equality.
1323 * isl_basic_map_remove_duplicate_constraints detects at most one such pair.
1324 * Call it repeatedly while it is making progress.
1326 __isl_give isl_basic_map
*isl_basic_map_detect_inequality_pairs(
1327 __isl_take isl_basic_map
*bmap
, int *progress
)
1333 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1335 if (progress
&& duplicate
)
1337 } while (duplicate
);
1342 /* Eliminate knowns divs from constraints where they appear with
1343 * a (positive or negative) unit coefficient.
1347 * floor(e/m) + f >= 0
1355 * -floor(e/m) + f >= 0
1359 * -e + m f + m - 1 >= 0
1361 * The first conversion is valid because floor(e/m) >= -f is equivalent
1362 * to e/m >= -f because -f is an integral expression.
1363 * The second conversion follows from the fact that
1365 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1368 * Note that one of the div constraints may have been eliminated
1369 * due to being redundant with respect to the constraint that is
1370 * being modified by this function. The modified constraint may
1371 * no longer imply this div constraint, so we add it back to make
1372 * sure we do not lose any information.
1374 * We skip integral divs, i.e., those with denominator 1, as we would
1375 * risk eliminating the div from the div constraints. We do not need
1376 * to handle those divs here anyway since the div constraints will turn
1377 * out to form an equality and this equality can then be use to eliminate
1378 * the div from all constraints.
1380 static __isl_give isl_basic_map
*eliminate_unit_divs(
1381 __isl_take isl_basic_map
*bmap
, int *progress
)
1390 ctx
= isl_basic_map_get_ctx(bmap
);
1391 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1393 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1394 if (isl_int_is_zero(bmap
->div
[i
][0]))
1396 if (isl_int_is_one(bmap
->div
[i
][0]))
1398 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1401 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1402 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1407 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1408 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1410 isl_seq_combine(bmap
->ineq
[j
],
1411 ctx
->negone
, bmap
->div
[i
] + 1,
1412 bmap
->div
[i
][0], bmap
->ineq
[j
],
1413 total
+ bmap
->n_div
);
1415 isl_seq_combine(bmap
->ineq
[j
],
1416 ctx
->one
, bmap
->div
[i
] + 1,
1417 bmap
->div
[i
][0], bmap
->ineq
[j
],
1418 total
+ bmap
->n_div
);
1420 isl_int_add(bmap
->ineq
[j
][0],
1421 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1422 isl_int_sub_ui(bmap
->ineq
[j
][0],
1423 bmap
->ineq
[j
][0], 1);
1426 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
1427 if (isl_basic_map_add_div_constraint(bmap
, i
, s
) < 0)
1428 return isl_basic_map_free(bmap
);
1435 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1444 if (isl_basic_map_plain_is_empty(bmap
))
1446 bmap
= isl_basic_map_normalize_constraints(bmap
);
1447 bmap
= remove_independent_vars_from_divs(bmap
);
1448 bmap
= normalize_div_expressions(bmap
);
1449 bmap
= remove_duplicate_divs(bmap
, &progress
);
1450 bmap
= eliminate_unit_divs(bmap
, &progress
);
1451 bmap
= eliminate_divs_eq(bmap
, &progress
);
1452 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1453 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1454 /* requires equalities in normal form */
1455 bmap
= normalize_divs(bmap
, &progress
);
1456 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1458 if (bmap
&& progress
)
1459 ISL_F_CLR(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
1464 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1466 return (struct isl_basic_set
*)
1467 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1471 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1472 isl_int
*constraint
, unsigned div
)
1479 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1481 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1483 isl_int_sub(bmap
->div
[div
][1],
1484 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1485 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1486 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1487 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1488 isl_int_add(bmap
->div
[div
][1],
1489 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1492 if (isl_seq_first_non_zero(constraint
+pos
+1,
1493 bmap
->n_div
-div
-1) != -1)
1495 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1496 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1498 if (isl_seq_first_non_zero(constraint
+pos
+1,
1499 bmap
->n_div
-div
-1) != -1)
1507 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1508 isl_int
*constraint
, unsigned div
)
1510 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1514 /* If the only constraints a div d=floor(f/m)
1515 * appears in are its two defining constraints
1518 * -(f - (m - 1)) + m d >= 0
1520 * then it can safely be removed.
1522 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1525 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1527 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1528 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1531 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1532 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1534 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1538 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1539 if (isl_int_is_zero(bmap
->div
[i
][0]))
1541 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1549 * Remove divs that don't occur in any of the constraints or other divs.
1550 * These can arise when dropping constraints from a basic map or
1551 * when the divs of a basic map have been temporarily aligned
1552 * with the divs of another basic map.
1554 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1561 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1562 if (!div_is_redundant(bmap
, i
))
1564 bmap
= isl_basic_map_drop_div(bmap
, i
);
1569 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1571 bmap
= remove_redundant_divs(bmap
);
1574 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1578 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1580 return (struct isl_basic_set
*)
1581 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1584 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1590 for (i
= 0; i
< set
->n
; ++i
) {
1591 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1601 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1607 for (i
= 0; i
< map
->n
; ++i
) {
1608 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1612 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1620 /* Remove definition of any div that is defined in terms of the given variable.
1621 * The div itself is not removed. Functions such as
1622 * eliminate_divs_ineq depend on the other divs remaining in place.
1624 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1632 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1633 if (isl_int_is_zero(bmap
->div
[i
][0]))
1635 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1637 isl_int_set_si(bmap
->div
[i
][0], 0);
1642 /* Eliminate the specified variables from the constraints using
1643 * Fourier-Motzkin. The variables themselves are not removed.
1645 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1646 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1657 total
= isl_basic_map_total_dim(bmap
);
1659 bmap
= isl_basic_map_cow(bmap
);
1660 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1661 bmap
= remove_dependent_vars(bmap
, d
);
1665 for (d
= pos
+ n
- 1;
1666 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1667 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1668 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1669 int n_lower
, n_upper
;
1672 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1673 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1675 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1676 isl_basic_map_drop_equality(bmap
, i
);
1684 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1685 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1687 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1690 bmap
= isl_basic_map_extend_constraints(bmap
,
1691 0, n_lower
* n_upper
);
1694 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1696 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1699 for (j
= 0; j
< i
; ++j
) {
1700 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1703 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1704 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1706 k
= isl_basic_map_alloc_inequality(bmap
);
1709 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1711 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1712 1+d
, 1+total
, NULL
);
1714 isl_basic_map_drop_inequality(bmap
, i
);
1717 if (n_lower
> 0 && n_upper
> 0) {
1718 bmap
= isl_basic_map_normalize_constraints(bmap
);
1719 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1721 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1722 bmap
= isl_basic_map_remove_redundancies(bmap
);
1726 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1730 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1732 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1735 isl_basic_map_free(bmap
);
1739 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1740 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1742 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1743 (struct isl_basic_map
*)bset
, pos
, n
);
1746 /* Eliminate the specified n dimensions starting at first from the
1747 * constraints, without removing the dimensions from the space.
1748 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1749 * Otherwise, they are projected out and the original space is restored.
1751 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1752 __isl_take isl_basic_map
*bmap
,
1753 enum isl_dim_type type
, unsigned first
, unsigned n
)
1762 if (first
+ n
> isl_basic_map_dim(bmap
, type
) || first
+ n
< first
)
1763 isl_die(bmap
->ctx
, isl_error_invalid
,
1764 "index out of bounds", goto error
);
1766 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1767 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1768 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1769 return isl_basic_map_finalize(bmap
);
1772 space
= isl_basic_map_get_space(bmap
);
1773 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1774 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1775 bmap
= isl_basic_map_reset_space(bmap
, space
);
1778 isl_basic_map_free(bmap
);
1782 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1783 __isl_take isl_basic_set
*bset
,
1784 enum isl_dim_type type
, unsigned first
, unsigned n
)
1786 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1789 /* Don't assume equalities are in order, because align_divs
1790 * may have changed the order of the divs.
1792 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1797 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1798 for (d
= 0; d
< total
; ++d
)
1800 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1801 for (d
= total
- 1; d
>= 0; --d
) {
1802 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1810 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1812 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1815 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1816 struct isl_basic_map
*bmap
, int *elim
)
1822 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1823 for (d
= total
- 1; d
>= 0; --d
) {
1824 if (isl_int_is_zero(src
[1+d
]))
1829 isl_seq_cpy(dst
, src
, 1 + total
);
1832 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1837 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1838 struct isl_basic_set
*bset
, int *elim
)
1840 return reduced_using_equalities(dst
, src
,
1841 (struct isl_basic_map
*)bset
, elim
);
1844 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1845 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1850 if (!bset
|| !context
)
1853 if (context
->n_eq
== 0) {
1854 isl_basic_set_free(context
);
1858 bset
= isl_basic_set_cow(bset
);
1862 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1865 set_compute_elimination_index(context
, elim
);
1866 for (i
= 0; i
< bset
->n_eq
; ++i
)
1867 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1869 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1870 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1872 isl_basic_set_free(context
);
1874 bset
= isl_basic_set_simplify(bset
);
1875 bset
= isl_basic_set_finalize(bset
);
1878 isl_basic_set_free(bset
);
1879 isl_basic_set_free(context
);
1883 static struct isl_basic_set
*remove_shifted_constraints(
1884 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1886 struct isl_constraint_index ci
;
1889 if (!bset
|| !context
)
1892 if (context
->n_ineq
== 0)
1894 if (setup_constraint_index(&ci
, context
) < 0)
1897 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1898 h
= set_hash_index(&ci
, bset
, k
);
1901 l
= ci
.index
[h
] - &context
->ineq
[0];
1902 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1904 bset
= isl_basic_set_cow(bset
);
1907 isl_basic_set_drop_inequality(bset
, k
);
1910 constraint_index_free(&ci
);
1913 constraint_index_free(&ci
);
1917 /* Remove constraints from "bmap" that are identical to constraints
1918 * in "context" or that are more relaxed (greater constant term).
1920 * We perform the test for shifted copies on the pure constraints
1921 * in remove_shifted_constraints.
1923 static __isl_give isl_basic_map
*isl_basic_map_remove_shifted_constraints(
1924 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
1926 isl_basic_set
*bset
, *bset_context
;
1928 if (!bmap
|| !context
)
1931 if (bmap
->n_ineq
== 0 || context
->n_ineq
== 0) {
1932 isl_basic_map_free(context
);
1936 context
= isl_basic_map_align_divs(context
, bmap
);
1937 bmap
= isl_basic_map_align_divs(bmap
, context
);
1939 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
1940 bset_context
= isl_basic_map_underlying_set(context
);
1941 bset
= remove_shifted_constraints(bset
, bset_context
);
1942 isl_basic_set_free(bset_context
);
1944 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
1948 isl_basic_map_free(bmap
);
1949 isl_basic_map_free(context
);
1953 /* Does the (linear part of a) constraint "c" involve any of the "len"
1954 * "relevant" dimensions?
1956 static int is_related(isl_int
*c
, int len
, int *relevant
)
1960 for (i
= 0; i
< len
; ++i
) {
1963 if (!isl_int_is_zero(c
[i
]))
1970 /* Drop constraints from "bset" that do not involve any of
1971 * the dimensions marked "relevant".
1973 static __isl_give isl_basic_set
*drop_unrelated_constraints(
1974 __isl_take isl_basic_set
*bset
, int *relevant
)
1978 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1979 for (i
= 0; i
< dim
; ++i
)
1985 for (i
= bset
->n_eq
- 1; i
>= 0; --i
)
1986 if (!is_related(bset
->eq
[i
] + 1, dim
, relevant
))
1987 isl_basic_set_drop_equality(bset
, i
);
1989 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
)
1990 if (!is_related(bset
->ineq
[i
] + 1, dim
, relevant
))
1991 isl_basic_set_drop_inequality(bset
, i
);
1996 /* Update the groups in "group" based on the (linear part of a) constraint "c".
1998 * In particular, for any variable involved in the constraint,
1999 * find the actual group id from before and replace the group
2000 * of the corresponding variable by the minimal group of all
2001 * the variables involved in the constraint considered so far
2002 * (if this minimum is smaller) or replace the minimum by this group
2003 * (if the minimum is larger).
2005 * At the end, all the variables in "c" will (indirectly) point
2006 * to the minimal of the groups that they referred to originally.
2008 static void update_groups(int dim
, int *group
, isl_int
*c
)
2013 for (j
= 0; j
< dim
; ++j
) {
2014 if (isl_int_is_zero(c
[j
]))
2016 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
2017 group
[j
] = group
[group
[j
]];
2018 if (group
[j
] == min
)
2020 if (group
[j
] < min
) {
2021 if (min
>= 0 && min
< dim
)
2022 group
[min
] = group
[j
];
2025 group
[group
[j
]] = min
;
2029 /* Drop constraints from "context" that are irrelevant for computing
2030 * the gist of "bset".
2032 * In particular, drop constraints in variables that are not related
2033 * to any of the variables involved in the constraints of "bset"
2034 * in the sense that there is no sequence of constraints that connects them.
2036 * We construct groups of variables that collect variables that
2037 * (indirectly) appear in some common constraint of "context".
2038 * Each group is identified by the first variable in the group,
2039 * except for the special group of variables that appear in "bset"
2040 * (or are related to those variables), which is identified by -1.
2041 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
2042 * otherwise the group of i is the group of group[i].
2044 * We first initialize the -1 group with the variables that appear in "bset".
2045 * Then we initialize groups for the remaining variables.
2046 * Then we iterate over the constraints of "context" and update the
2047 * group of the variables in the constraint by the smallest group.
2048 * Finally, we resolve indirect references to groups by running over
2051 * After computing the groups, we drop constraints that do not involve
2052 * any variables in the -1 group.
2054 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
2055 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
2063 if (!context
|| !bset
)
2064 return isl_basic_set_free(context
);
2066 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2067 ctx
= isl_basic_set_get_ctx(bset
);
2068 group
= isl_calloc_array(ctx
, int, dim
);
2073 for (i
= 0; i
< dim
; ++i
) {
2074 for (j
= 0; j
< bset
->n_eq
; ++j
)
2075 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
2077 if (j
< bset
->n_eq
) {
2081 for (j
= 0; j
< bset
->n_ineq
; ++j
)
2082 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
2084 if (j
< bset
->n_ineq
)
2089 for (i
= 0; i
< dim
; ++i
)
2091 last
= group
[i
] = i
;
2097 for (i
= 0; i
< context
->n_eq
; ++i
)
2098 update_groups(dim
, group
, context
->eq
[i
] + 1);
2099 for (i
= 0; i
< context
->n_ineq
; ++i
)
2100 update_groups(dim
, group
, context
->ineq
[i
] + 1);
2102 for (i
= 0; i
< dim
; ++i
)
2104 group
[i
] = group
[group
[i
]];
2106 for (i
= 0; i
< dim
; ++i
)
2107 group
[i
] = group
[i
] == -1;
2109 context
= drop_unrelated_constraints(context
, group
);
2115 return isl_basic_set_free(context
);
2118 /* Remove all information from bset that is redundant in the context
2119 * of context. Both bset and context are assumed to be full-dimensional.
2121 * We first remove the inequalities from "bset"
2122 * that are obviously redundant with respect to some inequality in "context".
2123 * Then we remove those constraints from "context" that have become
2124 * irrelevant for computing the gist of "bset".
2125 * Note that this removal of constraints cannot be replaced by
2126 * a factorization because factors in "bset" may still be connected
2127 * to each other through constraints in "context".
2129 * If there are any inequalities left, we construct a tableau for
2130 * the context and then add the inequalities of "bset".
2131 * Before adding these inequalities, we freeze all constraints such that
2132 * they won't be considered redundant in terms of the constraints of "bset".
2133 * Then we detect all redundant constraints (among the
2134 * constraints that weren't frozen), first by checking for redundancy in the
2135 * the tableau and then by checking if replacing a constraint by its negation
2136 * would lead to an empty set. This last step is fairly expensive
2137 * and could be optimized by more reuse of the tableau.
2138 * Finally, we update bset according to the results.
2140 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
2141 __isl_take isl_basic_set
*context
)
2144 isl_basic_set
*combined
= NULL
;
2145 struct isl_tab
*tab
= NULL
;
2146 unsigned context_ineq
;
2149 if (!bset
|| !context
)
2152 if (isl_basic_set_is_universe(bset
)) {
2153 isl_basic_set_free(context
);
2157 if (isl_basic_set_is_universe(context
)) {
2158 isl_basic_set_free(context
);
2162 bset
= remove_shifted_constraints(bset
, context
);
2165 if (bset
->n_ineq
== 0)
2168 context
= drop_irrelevant_constraints(context
, bset
);
2171 if (isl_basic_set_is_universe(context
)) {
2172 isl_basic_set_free(context
);
2176 context_ineq
= context
->n_ineq
;
2177 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
2178 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
2179 tab
= isl_tab_from_basic_set(combined
, 0);
2180 for (i
= 0; i
< context_ineq
; ++i
)
2181 if (isl_tab_freeze_constraint(tab
, i
) < 0)
2183 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
2185 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2186 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
2188 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
2192 if (isl_tab_detect_redundant(tab
) < 0)
2194 total
= isl_basic_set_total_dim(bset
);
2195 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
2197 if (tab
->con
[i
].is_redundant
)
2199 tab
->con
[i
].is_redundant
= 1;
2200 combined
= isl_basic_set_dup(bset
);
2201 combined
= isl_basic_set_update_from_tab(combined
, tab
);
2202 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
2203 k
= isl_basic_set_alloc_inequality(combined
);
2206 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
2207 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
2208 is_empty
= isl_basic_set_is_empty(combined
);
2211 isl_basic_set_free(combined
);
2214 tab
->con
[i
].is_redundant
= 0;
2216 for (i
= 0; i
< context_ineq
; ++i
)
2217 tab
->con
[i
].is_redundant
= 1;
2218 bset
= isl_basic_set_update_from_tab(bset
, tab
);
2220 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2221 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2226 bset
= isl_basic_set_finalize(bset
);
2227 isl_basic_set_free(context
);
2231 isl_basic_set_free(combined
);
2232 isl_basic_set_free(context
);
2233 isl_basic_set_free(bset
);
2237 /* Remove all information from bset that is redundant in the context
2238 * of context. In particular, equalities that are linear combinations
2239 * of those in context are removed. Then the inequalities that are
2240 * redundant in the context of the equalities and inequalities of
2241 * context are removed.
2243 * First of all, we drop those constraints from "context"
2244 * that are irrelevant for computing the gist of "bset".
2245 * Alternatively, we could factorize the intersection of "context" and "bset".
2247 * We first compute the integer affine hull of the intersection,
2248 * compute the gist inside this affine hull and then add back
2249 * those equalities that are not implied by the context.
2251 * If two constraints are mutually redundant, then uset_gist_full
2252 * will remove the second of those constraints. We therefore first
2253 * sort the constraints so that constraints not involving existentially
2254 * quantified variables are given precedence over those that do.
2255 * We have to perform this sorting before the variable compression,
2256 * because that may effect the order of the variables.
2258 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2259 __isl_take isl_basic_set
*context
)
2264 isl_basic_set
*aff_context
;
2267 if (!bset
|| !context
)
2270 context
= drop_irrelevant_constraints(context
, bset
);
2272 aff
= isl_basic_set_copy(bset
);
2273 aff
= isl_basic_set_intersect(aff
, isl_basic_set_copy(context
));
2274 aff
= isl_basic_set_affine_hull(aff
);
2277 if (isl_basic_set_plain_is_empty(aff
)) {
2278 isl_basic_set_free(bset
);
2279 isl_basic_set_free(context
);
2282 bset
= isl_basic_set_sort_constraints(bset
);
2283 if (aff
->n_eq
== 0) {
2284 isl_basic_set_free(aff
);
2285 return uset_gist_full(bset
, context
);
2287 total
= isl_basic_set_total_dim(bset
);
2288 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2289 eq
= isl_mat_cow(eq
);
2290 T
= isl_mat_variable_compression(eq
, &T2
);
2291 if (T
&& T
->n_col
== 0) {
2294 isl_basic_set_free(context
);
2295 isl_basic_set_free(aff
);
2296 return isl_basic_set_set_to_empty(bset
);
2299 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2301 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
2302 context
= isl_basic_set_preimage(context
, T
);
2304 bset
= uset_gist_full(bset
, context
);
2305 bset
= isl_basic_set_preimage(bset
, T2
);
2306 bset
= isl_basic_set_intersect(bset
, aff
);
2307 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2310 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2311 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2316 isl_basic_set_free(bset
);
2317 isl_basic_set_free(context
);
2321 /* Return a basic map that has the same intersection with "context" as "bmap"
2322 * and that is as "simple" as possible.
2324 * The core computation is performed on the pure constraints.
2325 * When we add back the meaning of the integer divisions, we need
2326 * to (re)introduce the div constraints. If we happen to have
2327 * discovered that some of these integer divisions are equal to
2328 * some affine combination of other variables, then these div
2329 * constraints may end up getting simplified in terms of the equalities,
2330 * resulting in extra inequalities on the other variables that
2331 * may have been removed already or that may not even have been
2332 * part of the input. We try and remove those constraints of
2333 * this form that are most obviously redundant with respect to
2334 * the context. We also remove those div constraints that are
2335 * redundant with respect to the other constraints in the result.
2337 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
2338 struct isl_basic_map
*context
)
2340 isl_basic_set
*bset
, *eq
;
2341 isl_basic_map
*eq_bmap
;
2342 unsigned n_div
, n_eq
, n_ineq
;
2344 if (!bmap
|| !context
)
2347 if (isl_basic_map_is_universe(bmap
)) {
2348 isl_basic_map_free(context
);
2351 if (isl_basic_map_plain_is_empty(context
)) {
2352 isl_space
*space
= isl_basic_map_get_space(bmap
);
2353 isl_basic_map_free(bmap
);
2354 isl_basic_map_free(context
);
2355 return isl_basic_map_universe(space
);
2357 if (isl_basic_map_plain_is_empty(bmap
)) {
2358 isl_basic_map_free(context
);
2362 bmap
= isl_basic_map_remove_redundancies(bmap
);
2363 context
= isl_basic_map_remove_redundancies(context
);
2367 context
= isl_basic_map_align_divs(context
, bmap
);
2368 bmap
= isl_basic_map_align_divs(bmap
, context
);
2369 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2371 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
2372 isl_basic_map_underlying_set(isl_basic_map_copy(context
)));
2374 if (!bset
|| bset
->n_eq
== 0 || n_div
== 0 ||
2375 isl_basic_set_plain_is_empty(bset
)) {
2376 isl_basic_map_free(context
);
2377 return isl_basic_map_overlying_set(bset
, bmap
);
2381 n_ineq
= bset
->n_ineq
;
2382 eq
= isl_basic_set_copy(bset
);
2383 eq
= isl_basic_set_cow(eq
);
2384 if (isl_basic_set_free_inequality(eq
, n_ineq
) < 0)
2385 eq
= isl_basic_set_free(eq
);
2386 if (isl_basic_set_free_equality(bset
, n_eq
) < 0)
2387 bset
= isl_basic_set_free(bset
);
2389 eq_bmap
= isl_basic_map_overlying_set(eq
, isl_basic_map_copy(bmap
));
2390 eq_bmap
= isl_basic_map_remove_shifted_constraints(eq_bmap
, context
);
2391 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
2392 bmap
= isl_basic_map_intersect(bmap
, eq_bmap
);
2393 bmap
= isl_basic_map_remove_redundancies(bmap
);
2397 isl_basic_map_free(bmap
);
2398 isl_basic_map_free(context
);
2403 * Assumes context has no implicit divs.
2405 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
2406 __isl_take isl_basic_map
*context
)
2410 if (!map
|| !context
)
2413 if (isl_basic_map_plain_is_empty(context
)) {
2414 isl_space
*space
= isl_map_get_space(map
);
2416 isl_basic_map_free(context
);
2417 return isl_map_universe(space
);
2420 context
= isl_basic_map_remove_redundancies(context
);
2421 map
= isl_map_cow(map
);
2422 if (!map
|| !context
)
2424 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
2425 map
= isl_map_compute_divs(map
);
2428 for (i
= map
->n
- 1; i
>= 0; --i
) {
2429 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
2430 isl_basic_map_copy(context
));
2433 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
2434 isl_basic_map_free(map
->p
[i
]);
2435 if (i
!= map
->n
- 1)
2436 map
->p
[i
] = map
->p
[map
->n
- 1];
2440 isl_basic_map_free(context
);
2441 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2445 isl_basic_map_free(context
);
2449 /* Return a map that has the same intersection with "context" as "map"
2450 * and that is as "simple" as possible.
2452 * If "map" is already the universe, then we cannot make it any simpler.
2453 * Similarly, if "context" is the universe, then we cannot exploit it
2455 * If "map" and "context" are identical to each other, then we can
2456 * return the corresponding universe.
2458 * If none of these cases apply, we have to work a bit harder.
2459 * During this computation, we make use of a single disjunct context,
2460 * so if the original context consists of more than one disjunct
2461 * then we need to approximate the context by a single disjunct set.
2462 * Simply taking the simple hull may drop constraints that are
2463 * only implicitly available in each disjunct. We therefore also
2464 * look for constraints among those defining "map" that are valid
2465 * for the context. These can then be used to simplify away
2466 * the corresponding constraints in "map".
2468 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
2469 __isl_take isl_map
*context
)
2473 isl_basic_map
*hull
;
2475 is_universe
= isl_map_plain_is_universe(map
);
2476 if (is_universe
>= 0 && !is_universe
)
2477 is_universe
= isl_map_plain_is_universe(context
);
2478 if (is_universe
< 0)
2481 isl_map_free(context
);
2485 equal
= isl_map_plain_is_equal(map
, context
);
2489 isl_map
*res
= isl_map_universe(isl_map_get_space(map
));
2491 isl_map_free(context
);
2495 context
= isl_map_compute_divs(context
);
2498 if (isl_map_n_basic_map(context
) == 1) {
2499 hull
= isl_map_simple_hull(context
);
2504 ctx
= isl_map_get_ctx(map
);
2505 list
= isl_map_list_alloc(ctx
, 2);
2506 list
= isl_map_list_add(list
, isl_map_copy(context
));
2507 list
= isl_map_list_add(list
, isl_map_copy(map
));
2508 hull
= isl_map_unshifted_simple_hull_from_map_list(context
,
2511 return isl_map_gist_basic_map(map
, hull
);
2514 isl_map_free(context
);
2518 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
2519 __isl_take isl_map
*context
)
2521 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2524 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2525 struct isl_basic_set
*context
)
2527 return (struct isl_basic_set
*)isl_basic_map_gist(
2528 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2531 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2532 __isl_take isl_basic_set
*context
)
2534 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2535 (struct isl_basic_map
*)context
);
2538 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2539 __isl_take isl_basic_set
*context
)
2541 isl_space
*space
= isl_set_get_space(set
);
2542 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2543 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2544 return isl_set_gist_basic_set(set
, dom_context
);
2547 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2548 __isl_take isl_set
*context
)
2550 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2551 (struct isl_map
*)context
);
2554 /* Compute the gist of "bmap" with respect to the constraints "context"
2557 __isl_give isl_basic_map
*isl_basic_map_gist_domain(
2558 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_set
*context
)
2560 isl_space
*space
= isl_basic_map_get_space(bmap
);
2561 isl_basic_map
*bmap_context
= isl_basic_map_universe(space
);
2563 bmap_context
= isl_basic_map_intersect_domain(bmap_context
, context
);
2564 return isl_basic_map_gist(bmap
, bmap_context
);
2567 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2568 __isl_take isl_set
*context
)
2570 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2571 map_context
= isl_map_intersect_domain(map_context
, context
);
2572 return isl_map_gist(map
, map_context
);
2575 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2576 __isl_take isl_set
*context
)
2578 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2579 map_context
= isl_map_intersect_range(map_context
, context
);
2580 return isl_map_gist(map
, map_context
);
2583 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2584 __isl_take isl_set
*context
)
2586 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2587 map_context
= isl_map_intersect_params(map_context
, context
);
2588 return isl_map_gist(map
, map_context
);
2591 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2592 __isl_take isl_set
*context
)
2594 return isl_map_gist_params(set
, context
);
2597 /* Quick check to see if two basic maps are disjoint.
2598 * In particular, we reduce the equalities and inequalities of
2599 * one basic map in the context of the equalities of the other
2600 * basic map and check if we get a contradiction.
2602 isl_bool
isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2603 __isl_keep isl_basic_map
*bmap2
)
2605 struct isl_vec
*v
= NULL
;
2610 if (!bmap1
|| !bmap2
)
2611 return isl_bool_error
;
2612 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
2613 return isl_bool_error
);
2614 if (bmap1
->n_div
|| bmap2
->n_div
)
2615 return isl_bool_false
;
2616 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
2617 return isl_bool_false
;
2619 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
2621 return isl_bool_false
;
2622 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
2625 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
2628 compute_elimination_index(bmap1
, elim
);
2629 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
2631 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
2633 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
2634 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2637 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
2639 reduced
= reduced_using_equalities(v
->block
.data
,
2640 bmap2
->ineq
[i
], bmap1
, elim
);
2641 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2642 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2645 compute_elimination_index(bmap2
, elim
);
2646 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
2648 reduced
= reduced_using_equalities(v
->block
.data
,
2649 bmap1
->ineq
[i
], bmap2
, elim
);
2650 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2651 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2656 return isl_bool_false
;
2660 return isl_bool_true
;
2664 return isl_bool_error
;
2667 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2668 __isl_keep isl_basic_set
*bset2
)
2670 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
2671 (struct isl_basic_map
*)bset2
);
2674 /* Are "map1" and "map2" obviously disjoint?
2676 * If one of them is empty or if they live in different spaces (ignoring
2677 * parameters), then they are clearly disjoint.
2679 * If they have different parameters, then we skip any further tests.
2681 * If they are obviously equal, but not obviously empty, then we will
2682 * not be able to detect if they are disjoint.
2684 * Otherwise we check if each basic map in "map1" is obviously disjoint
2685 * from each basic map in "map2".
2687 isl_bool
isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
2688 __isl_keep isl_map
*map2
)
2696 return isl_bool_error
;
2698 disjoint
= isl_map_plain_is_empty(map1
);
2699 if (disjoint
< 0 || disjoint
)
2702 disjoint
= isl_map_plain_is_empty(map2
);
2703 if (disjoint
< 0 || disjoint
)
2706 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_in
,
2707 map2
->dim
, isl_dim_in
);
2708 if (match
< 0 || !match
)
2709 return match
< 0 ? isl_bool_error
: isl_bool_true
;
2711 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_out
,
2712 map2
->dim
, isl_dim_out
);
2713 if (match
< 0 || !match
)
2714 return match
< 0 ? isl_bool_error
: isl_bool_true
;
2716 match
= isl_space_match(map1
->dim
, isl_dim_param
,
2717 map2
->dim
, isl_dim_param
);
2718 if (match
< 0 || !match
)
2719 return match
< 0 ? isl_bool_error
: isl_bool_false
;
2721 intersect
= isl_map_plain_is_equal(map1
, map2
);
2722 if (intersect
< 0 || intersect
)
2723 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
2725 for (i
= 0; i
< map1
->n
; ++i
) {
2726 for (j
= 0; j
< map2
->n
; ++j
) {
2727 isl_bool d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
2729 if (d
!= isl_bool_true
)
2733 return isl_bool_true
;
2736 /* Are "map1" and "map2" disjoint?
2738 * They are disjoint if they are "obviously disjoint" or if one of them
2739 * is empty. Otherwise, they are not disjoint if one of them is universal.
2740 * If none of these cases apply, we compute the intersection and see if
2741 * the result is empty.
2743 isl_bool
isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
2749 disjoint
= isl_map_plain_is_disjoint(map1
, map2
);
2750 if (disjoint
< 0 || disjoint
)
2753 disjoint
= isl_map_is_empty(map1
);
2754 if (disjoint
< 0 || disjoint
)
2757 disjoint
= isl_map_is_empty(map2
);
2758 if (disjoint
< 0 || disjoint
)
2761 intersect
= isl_map_plain_is_universe(map1
);
2762 if (intersect
< 0 || intersect
)
2763 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
2765 intersect
= isl_map_plain_is_universe(map2
);
2766 if (intersect
< 0 || intersect
)
2767 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
2769 test
= isl_map_intersect(isl_map_copy(map1
), isl_map_copy(map2
));
2770 disjoint
= isl_map_is_empty(test
);
2776 /* Are "bmap1" and "bmap2" disjoint?
2778 * They are disjoint if they are "obviously disjoint" or if one of them
2779 * is empty. Otherwise, they are not disjoint if one of them is universal.
2780 * If none of these cases apply, we compute the intersection and see if
2781 * the result is empty.
2783 isl_bool
isl_basic_map_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2784 __isl_keep isl_basic_map
*bmap2
)
2788 isl_basic_map
*test
;
2790 disjoint
= isl_basic_map_plain_is_disjoint(bmap1
, bmap2
);
2791 if (disjoint
< 0 || disjoint
)
2794 disjoint
= isl_basic_map_is_empty(bmap1
);
2795 if (disjoint
< 0 || disjoint
)
2798 disjoint
= isl_basic_map_is_empty(bmap2
);
2799 if (disjoint
< 0 || disjoint
)
2802 intersect
= isl_basic_map_is_universe(bmap1
);
2803 if (intersect
< 0 || intersect
)
2804 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
2806 intersect
= isl_basic_map_is_universe(bmap2
);
2807 if (intersect
< 0 || intersect
)
2808 return intersect
< 0 ? isl_bool_error
: isl_bool_false
;
2810 test
= isl_basic_map_intersect(isl_basic_map_copy(bmap1
),
2811 isl_basic_map_copy(bmap2
));
2812 disjoint
= isl_basic_map_is_empty(test
);
2813 isl_basic_map_free(test
);
2818 /* Are "bset1" and "bset2" disjoint?
2820 isl_bool
isl_basic_set_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2821 __isl_keep isl_basic_set
*bset2
)
2823 return isl_basic_map_is_disjoint(bset1
, bset2
);
2826 isl_bool
isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
2827 __isl_keep isl_set
*set2
)
2829 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
2830 (struct isl_map
*)set2
);
2833 /* Are "set1" and "set2" disjoint?
2835 isl_bool
isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2837 return isl_map_is_disjoint(set1
, set2
);
2840 /* Check if we can combine a given div with lower bound l and upper
2841 * bound u with some other div and if so return that other div.
2842 * Otherwise return -1.
2844 * We first check that
2845 * - the bounds are opposites of each other (except for the constant
2847 * - the bounds do not reference any other div
2848 * - no div is defined in terms of this div
2850 * Let m be the size of the range allowed on the div by the bounds.
2851 * That is, the bounds are of the form
2853 * e <= a <= e + m - 1
2855 * with e some expression in the other variables.
2856 * We look for another div b such that no third div is defined in terms
2857 * of this second div b and such that in any constraint that contains
2858 * a (except for the given lower and upper bound), also contains b
2859 * with a coefficient that is m times that of b.
2860 * That is, all constraints (execpt for the lower and upper bound)
2863 * e + f (a + m b) >= 0
2865 * If so, we return b so that "a + m b" can be replaced by
2866 * a single div "c = a + m b".
2868 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2869 unsigned div
, unsigned l
, unsigned u
)
2875 if (bmap
->n_div
<= 1)
2877 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2878 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2880 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2881 bmap
->n_div
- div
- 1) != -1)
2883 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2887 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2888 if (isl_int_is_zero(bmap
->div
[i
][0]))
2890 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2894 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2895 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2896 isl_int_sub(bmap
->ineq
[l
][0],
2897 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2898 bmap
= isl_basic_map_copy(bmap
);
2899 bmap
= isl_basic_map_set_to_empty(bmap
);
2900 isl_basic_map_free(bmap
);
2903 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2904 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2909 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2910 if (isl_int_is_zero(bmap
->div
[j
][0]))
2912 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2915 if (j
< bmap
->n_div
)
2917 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2919 if (j
== l
|| j
== u
)
2921 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2923 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2925 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2926 bmap
->ineq
[j
][1 + dim
+ div
],
2928 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2929 bmap
->ineq
[j
][1 + dim
+ i
]);
2930 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2931 bmap
->ineq
[j
][1 + dim
+ div
],
2936 if (j
< bmap
->n_ineq
)
2941 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2942 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2946 /* Given a lower and an upper bound on div i, construct an inequality
2947 * that when nonnegative ensures that this pair of bounds always allows
2948 * for an integer value of the given div.
2949 * The lower bound is inequality l, while the upper bound is inequality u.
2950 * The constructed inequality is stored in ineq.
2951 * g, fl, fu are temporary scalars.
2953 * Let the upper bound be
2957 * and the lower bound
2961 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2964 * - f_u e_l <= f_u f_l g a <= f_l e_u
2966 * Since all variables are integer valued, this is equivalent to
2968 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2970 * If this interval is at least f_u f_l g, then it contains at least
2971 * one integer value for a.
2972 * That is, the test constraint is
2974 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2976 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2977 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2980 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2982 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2983 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2984 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2985 isl_int_neg(fu
, fu
);
2986 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2987 1 + dim
+ bmap
->n_div
);
2988 isl_int_add(ineq
[0], ineq
[0], fl
);
2989 isl_int_add(ineq
[0], ineq
[0], fu
);
2990 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2991 isl_int_mul(g
, g
, fl
);
2992 isl_int_mul(g
, g
, fu
);
2993 isl_int_sub(ineq
[0], ineq
[0], g
);
2996 /* Remove more kinds of divs that are not strictly needed.
2997 * In particular, if all pairs of lower and upper bounds on a div
2998 * are such that they allow at least one integer value of the div,
2999 * the we can eliminate the div using Fourier-Motzkin without
3000 * introducing any spurious solutions.
3002 static struct isl_basic_map
*drop_more_redundant_divs(
3003 struct isl_basic_map
*bmap
, int *pairs
, int n
)
3005 struct isl_tab
*tab
= NULL
;
3006 struct isl_vec
*vec
= NULL
;
3018 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3019 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
3023 tab
= isl_tab_from_basic_map(bmap
, 0);
3028 enum isl_lp_result res
;
3030 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3033 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
3039 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
3040 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
3042 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
3043 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
3045 construct_test_ineq(bmap
, i
, l
, u
,
3046 vec
->el
, g
, fl
, fu
);
3047 res
= isl_tab_min(tab
, vec
->el
,
3048 bmap
->ctx
->one
, &g
, NULL
, 0);
3049 if (res
== isl_lp_error
)
3051 if (res
== isl_lp_empty
) {
3052 bmap
= isl_basic_map_set_to_empty(bmap
);
3055 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
3058 if (u
< bmap
->n_ineq
)
3061 if (l
== bmap
->n_ineq
) {
3081 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
3082 return isl_basic_map_drop_redundant_divs(bmap
);
3085 isl_basic_map_free(bmap
);
3094 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
3095 * and the upper bound u, div1 always occurs together with div2 in the form
3096 * (div1 + m div2), where m is the constant range on the variable div1
3097 * allowed by l and u, replace the pair div1 and div2 by a single
3098 * div that is equal to div1 + m div2.
3100 * The new div will appear in the location that contains div2.
3101 * We need to modify all constraints that contain
3102 * div2 = (div - div1) / m
3103 * (If a constraint does not contain div2, it will also not contain div1.)
3104 * If the constraint also contains div1, then we know they appear
3105 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
3106 * i.e., the coefficient of div is f.
3108 * Otherwise, we first need to introduce div1 into the constraint.
3117 * A lower bound on div2
3121 * can be replaced by
3123 * (n * (m div 2 + div1) + m t + n f)/g >= 0
3125 * with g = gcd(m,n).
3130 * can be replaced by
3132 * (-n * (m div2 + div1) + m t + n f')/g >= 0
3134 * These constraint are those that we would obtain from eliminating
3135 * div1 using Fourier-Motzkin.
3137 * After all constraints have been modified, we drop the lower and upper
3138 * bound and then drop div1.
3140 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
3141 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
3146 unsigned dim
, total
;
3149 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3150 total
= 1 + dim
+ bmap
->n_div
;
3155 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3156 isl_int_add_ui(m
, m
, 1);
3158 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
3159 if (i
== l
|| i
== u
)
3161 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
3163 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
3164 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
3165 isl_int_divexact(a
, m
, b
);
3166 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
3167 if (isl_int_is_pos(b
)) {
3168 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
3169 b
, bmap
->ineq
[l
], total
);
3172 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
3173 b
, bmap
->ineq
[u
], total
);
3176 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
3177 bmap
->ineq
[i
][1 + dim
+ div1
]);
3178 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
3185 isl_basic_map_drop_inequality(bmap
, l
);
3186 isl_basic_map_drop_inequality(bmap
, u
);
3188 isl_basic_map_drop_inequality(bmap
, u
);
3189 isl_basic_map_drop_inequality(bmap
, l
);
3191 bmap
= isl_basic_map_drop_div(bmap
, div1
);
3195 /* First check if we can coalesce any pair of divs and
3196 * then continue with dropping more redundant divs.
3198 * We loop over all pairs of lower and upper bounds on a div
3199 * with coefficient 1 and -1, respectively, check if there
3200 * is any other div "c" with which we can coalesce the div
3201 * and if so, perform the coalescing.
3203 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
3204 struct isl_basic_map
*bmap
, int *pairs
, int n
)
3209 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3211 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3214 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
3215 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
3217 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
3220 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
3222 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
3226 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
3227 return isl_basic_map_drop_redundant_divs(bmap
);
3232 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
3235 return drop_more_redundant_divs(bmap
, pairs
, n
);
3238 /* Remove divs that are not strictly needed.
3239 * In particular, if a div only occurs positively (or negatively)
3240 * in constraints, then it can simply be dropped.
3241 * Also, if a div occurs in only two constraints and if moreover
3242 * those two constraints are opposite to each other, except for the constant
3243 * term and if the sum of the constant terms is such that for any value
3244 * of the other values, there is always at least one integer value of the
3245 * div, i.e., if one plus this sum is greater than or equal to
3246 * the (absolute value) of the coefficent of the div in the constraints,
3247 * then we can also simply drop the div.
3249 * We skip divs that appear in equalities or in the definition of other divs.
3250 * Divs that appear in the definition of other divs usually occur in at least
3251 * 4 constraints, but the constraints may have been simplified.
3253 * If any divs are left after these simple checks then we move on
3254 * to more complicated cases in drop_more_redundant_divs.
3256 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
3257 struct isl_basic_map
*bmap
)
3266 if (bmap
->n_div
== 0)
3269 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3270 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
3274 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3276 int last_pos
, last_neg
;
3280 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
3281 for (j
= i
; j
< bmap
->n_div
; ++j
)
3282 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
3284 if (j
< bmap
->n_div
)
3286 for (j
= 0; j
< bmap
->n_eq
; ++j
)
3287 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
3293 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
3294 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
3298 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
3303 pairs
[i
] = pos
* neg
;
3304 if (pairs
[i
] == 0) {
3305 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
3306 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
3307 isl_basic_map_drop_inequality(bmap
, j
);
3308 bmap
= isl_basic_map_drop_div(bmap
, i
);
3310 return isl_basic_map_drop_redundant_divs(bmap
);
3314 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
3315 bmap
->ineq
[last_neg
] + 1,
3319 isl_int_add(bmap
->ineq
[last_pos
][0],
3320 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3321 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
3322 bmap
->ineq
[last_pos
][0], 1);
3323 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
3324 bmap
->ineq
[last_pos
][1+off
+i
]);
3325 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
3326 bmap
->ineq
[last_pos
][0], 1);
3327 isl_int_sub(bmap
->ineq
[last_pos
][0],
3328 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3331 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
3336 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
3337 bmap
= isl_basic_map_simplify(bmap
);
3339 return isl_basic_map_drop_redundant_divs(bmap
);
3341 if (last_pos
> last_neg
) {
3342 isl_basic_map_drop_inequality(bmap
, last_pos
);
3343 isl_basic_map_drop_inequality(bmap
, last_neg
);
3345 isl_basic_map_drop_inequality(bmap
, last_neg
);
3346 isl_basic_map_drop_inequality(bmap
, last_pos
);
3348 bmap
= isl_basic_map_drop_div(bmap
, i
);
3350 return isl_basic_map_drop_redundant_divs(bmap
);
3354 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
3360 isl_basic_map_free(bmap
);
3364 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
3365 struct isl_basic_set
*bset
)
3367 return (struct isl_basic_set
*)
3368 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
3371 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
3377 for (i
= 0; i
< map
->n
; ++i
) {
3378 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
3382 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3389 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
3391 return (struct isl_set
*)
3392 isl_map_drop_redundant_divs((struct isl_map
*)set
);
3395 /* Does "bmap" satisfy any equality that involves more than 2 variables
3396 * and/or has coefficients different from -1 and 1?
3398 static int has_multiple_var_equality(__isl_keep isl_basic_map
*bmap
)
3403 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3405 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
3408 j
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1, total
);
3411 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
3412 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
3416 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
3420 if (!isl_int_is_one(bmap
->eq
[i
][1 + j
]) &&
3421 !isl_int_is_negone(bmap
->eq
[i
][1 + j
]))
3425 k
= isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + j
, total
- j
);
3433 /* Remove any common factor g from the constraint coefficients in "v".
3434 * The constant term is stored in the first position and is replaced
3435 * by floor(c/g). If any common factor is removed and if this results
3436 * in a tightening of the constraint, then set *tightened.
3438 static __isl_give isl_vec
*normalize_constraint(__isl_take isl_vec
*v
,
3445 ctx
= isl_vec_get_ctx(v
);
3446 isl_seq_gcd(v
->el
+ 1, v
->size
- 1, &ctx
->normalize_gcd
);
3447 if (isl_int_is_zero(ctx
->normalize_gcd
))
3449 if (isl_int_is_one(ctx
->normalize_gcd
))
3454 if (tightened
&& !isl_int_is_divisible_by(v
->el
[0], ctx
->normalize_gcd
))
3456 isl_int_fdiv_q(v
->el
[0], v
->el
[0], ctx
->normalize_gcd
);
3457 isl_seq_scale_down(v
->el
+ 1, v
->el
+ 1, ctx
->normalize_gcd
,
3462 /* If "bmap" is an integer set that satisfies any equality involving
3463 * more than 2 variables and/or has coefficients different from -1 and 1,
3464 * then use variable compression to reduce the coefficients by removing
3465 * any (hidden) common factor.
3466 * In particular, apply the variable compression to each constraint,
3467 * factor out any common factor in the non-constant coefficients and
3468 * then apply the inverse of the compression.
3469 * At the end, we mark the basic map as having reduced constants.
3470 * If this flag is still set on the next invocation of this function,
3471 * then we skip the computation.
3473 * Removing a common factor may result in a tightening of some of
3474 * the constraints. If this happens, then we may end up with two
3475 * opposite inequalities that can be replaced by an equality.
3476 * We therefore call isl_basic_map_detect_inequality_pairs,
3477 * which checks for such pairs of inequalities as well as eliminate_divs_eq
3478 * and isl_basic_map_gauss if such a pair was found.
3480 __isl_give isl_basic_map
*isl_basic_map_reduce_coefficients(
3481 __isl_take isl_basic_map
*bmap
)
3486 isl_mat
*eq
, *T
, *T2
;
3492 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
))
3494 if (isl_basic_map_is_rational(bmap
))
3496 if (bmap
->n_eq
== 0)
3498 if (!has_multiple_var_equality(bmap
))
3501 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3502 ctx
= isl_basic_map_get_ctx(bmap
);
3503 v
= isl_vec_alloc(ctx
, 1 + total
);
3505 return isl_basic_map_free(bmap
);
3507 eq
= isl_mat_sub_alloc6(ctx
, bmap
->eq
, 0, bmap
->n_eq
, 0, 1 + total
);
3508 T
= isl_mat_variable_compression(eq
, &T2
);
3511 if (T
->n_col
== 0) {
3515 return isl_basic_map_set_to_empty(bmap
);
3519 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
3520 isl_seq_cpy(v
->el
, bmap
->ineq
[i
], 1 + total
);
3521 v
= isl_vec_mat_product(v
, isl_mat_copy(T
));
3522 v
= normalize_constraint(v
, &tightened
);
3523 v
= isl_vec_mat_product(v
, isl_mat_copy(T2
));
3526 isl_seq_cpy(bmap
->ineq
[i
], v
->el
, 1 + total
);
3533 ISL_F_SET(bmap
, ISL_BASIC_MAP_REDUCED_COEFFICIENTS
);
3538 bmap
= isl_basic_map_detect_inequality_pairs(bmap
, &progress
);
3540 bmap
= eliminate_divs_eq(bmap
, &progress
);
3541 bmap
= isl_basic_map_gauss(bmap
, NULL
);
3550 return isl_basic_map_free(bmap
);
3553 /* Shift the integer division at position "div" of "bmap"
3554 * by "shift" times the variable at position "pos".
3555 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
3556 * corresponds to the constant term.
3558 * That is, if the integer division has the form
3562 * then replace it by
3564 * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
3566 __isl_give isl_basic_map
*isl_basic_map_shift_div(
3567 __isl_take isl_basic_map
*bmap
, int div
, int pos
, isl_int shift
)
3575 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
3576 total
-= isl_basic_map_dim(bmap
, isl_dim_div
);
3578 isl_int_addmul(bmap
->div
[div
][1 + pos
], shift
, bmap
->div
[div
][0]);
3580 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
3581 if (isl_int_is_zero(bmap
->eq
[i
][1 + total
+ div
]))
3583 isl_int_submul(bmap
->eq
[i
][pos
],
3584 shift
, bmap
->eq
[i
][1 + total
+ div
]);
3586 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
3587 if (isl_int_is_zero(bmap
->ineq
[i
][1 + total
+ div
]))
3589 isl_int_submul(bmap
->ineq
[i
][pos
],
3590 shift
, bmap
->ineq
[i
][1 + total
+ div
]);
3592 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3593 if (isl_int_is_zero(bmap
->div
[i
][0]))
3595 if (isl_int_is_zero(bmap
->div
[i
][1 + 1 + total
+ div
]))
3597 isl_int_submul(bmap
->div
[i
][1 + pos
],
3598 shift
, bmap
->div
[i
][1 + 1 + total
+ div
]);