2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012 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
16 #include <isl_ctx_private.h>
17 #include <isl_map_private.h>
18 #include "isl_equalities.h"
22 #include <isl_space_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_vec_private.h>
26 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
28 isl_int
*t
= bmap
->eq
[a
];
29 bmap
->eq
[a
] = bmap
->eq
[b
];
33 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
36 isl_int
*t
= bmap
->ineq
[a
];
37 bmap
->ineq
[a
] = bmap
->ineq
[b
];
42 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
44 isl_seq_cpy(c
, c
+ n
, rem
);
45 isl_seq_clr(c
+ rem
, n
);
48 /* Drop n dimensions starting at first.
50 * In principle, this frees up some extra variables as the number
51 * of columns remains constant, but we would have to extend
52 * the div array too as the number of rows in this array is assumed
53 * to be equal to extra.
55 struct isl_basic_set
*isl_basic_set_drop_dims(
56 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
63 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
65 if (n
== 0 && !isl_space_get_tuple_name(bset
->dim
, isl_dim_set
))
68 bset
= isl_basic_set_cow(bset
);
72 for (i
= 0; i
< bset
->n_eq
; ++i
)
73 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
74 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
76 for (i
= 0; i
< bset
->n_ineq
; ++i
)
77 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
78 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
80 for (i
= 0; i
< bset
->n_div
; ++i
)
81 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
82 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
84 bset
->dim
= isl_space_drop_outputs(bset
->dim
, first
, n
);
88 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
89 bset
= isl_basic_set_simplify(bset
);
90 return isl_basic_set_finalize(bset
);
92 isl_basic_set_free(bset
);
96 struct isl_set
*isl_set_drop_dims(
97 struct isl_set
*set
, unsigned first
, unsigned n
)
104 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
106 if (n
== 0 && !isl_space_get_tuple_name(set
->dim
, isl_dim_set
))
108 set
= isl_set_cow(set
);
111 set
->dim
= isl_space_drop_outputs(set
->dim
, first
, n
);
115 for (i
= 0; i
< set
->n
; ++i
) {
116 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
121 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
128 /* Move "n" divs starting at "first" to the end of the list of divs.
130 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
131 unsigned first
, unsigned n
)
136 if (first
+ n
== bmap
->n_div
)
139 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
142 for (i
= 0; i
< n
; ++i
)
143 div
[i
] = bmap
->div
[first
+ i
];
144 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
145 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
146 for (i
= 0; i
< n
; ++i
)
147 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
151 isl_basic_map_free(bmap
);
155 /* Drop "n" dimensions of type "type" starting at "first".
157 * In principle, this frees up some extra variables as the number
158 * of columns remains constant, but we would have to extend
159 * the div array too as the number of rows in this array is assumed
160 * to be equal to extra.
162 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
163 enum isl_dim_type type
, unsigned first
, unsigned n
)
173 dim
= isl_basic_map_dim(bmap
, type
);
174 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
176 if (n
== 0 && !isl_space_is_named_or_nested(bmap
->dim
, type
))
179 bmap
= isl_basic_map_cow(bmap
);
183 offset
= isl_basic_map_offset(bmap
, type
) + first
;
184 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
185 for (i
= 0; i
< bmap
->n_eq
; ++i
)
186 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
188 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
189 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
191 for (i
= 0; i
< bmap
->n_div
; ++i
)
192 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
194 if (type
== isl_dim_div
) {
195 bmap
= move_divs_last(bmap
, first
, n
);
198 isl_basic_map_free_div(bmap
, n
);
200 bmap
->dim
= isl_space_drop_dims(bmap
->dim
, type
, first
, n
);
204 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
205 bmap
= isl_basic_map_simplify(bmap
);
206 return isl_basic_map_finalize(bmap
);
208 isl_basic_map_free(bmap
);
212 __isl_give isl_basic_set
*isl_basic_set_drop(__isl_take isl_basic_set
*bset
,
213 enum isl_dim_type type
, unsigned first
, unsigned n
)
215 return (isl_basic_set
*)isl_basic_map_drop((isl_basic_map
*)bset
,
219 struct isl_basic_map
*isl_basic_map_drop_inputs(
220 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
222 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
225 struct isl_map
*isl_map_drop(struct isl_map
*map
,
226 enum isl_dim_type type
, unsigned first
, unsigned n
)
233 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
235 if (n
== 0 && !isl_space_get_tuple_name(map
->dim
, type
))
237 map
= isl_map_cow(map
);
240 map
->dim
= isl_space_drop_dims(map
->dim
, type
, first
, n
);
244 for (i
= 0; i
< map
->n
; ++i
) {
245 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
249 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
257 struct isl_set
*isl_set_drop(struct isl_set
*set
,
258 enum isl_dim_type type
, unsigned first
, unsigned n
)
260 return (isl_set
*)isl_map_drop((isl_map
*)set
, type
, first
, n
);
263 struct isl_map
*isl_map_drop_inputs(
264 struct isl_map
*map
, unsigned first
, unsigned n
)
266 return isl_map_drop(map
, isl_dim_in
, first
, n
);
270 * We don't cow, as the div is assumed to be redundant.
272 static struct isl_basic_map
*isl_basic_map_drop_div(
273 struct isl_basic_map
*bmap
, unsigned div
)
281 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
283 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
285 for (i
= 0; i
< bmap
->n_eq
; ++i
)
286 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
288 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
289 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
290 isl_basic_map_drop_inequality(bmap
, i
);
294 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
297 for (i
= 0; i
< bmap
->n_div
; ++i
)
298 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
300 if (div
!= bmap
->n_div
- 1) {
302 isl_int
*t
= bmap
->div
[div
];
304 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
305 bmap
->div
[j
] = bmap
->div
[j
+1];
307 bmap
->div
[bmap
->n_div
- 1] = t
;
309 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
310 isl_basic_map_free_div(bmap
, 1);
314 isl_basic_map_free(bmap
);
318 struct isl_basic_map
*isl_basic_map_normalize_constraints(
319 struct isl_basic_map
*bmap
)
323 unsigned total
= isl_basic_map_total_dim(bmap
);
329 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
330 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
331 if (isl_int_is_zero(gcd
)) {
332 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
333 bmap
= isl_basic_map_set_to_empty(bmap
);
336 isl_basic_map_drop_equality(bmap
, i
);
339 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
340 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
341 if (isl_int_is_one(gcd
))
343 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
344 bmap
= isl_basic_map_set_to_empty(bmap
);
347 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
350 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
351 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
352 if (isl_int_is_zero(gcd
)) {
353 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
354 bmap
= isl_basic_map_set_to_empty(bmap
);
357 isl_basic_map_drop_inequality(bmap
, i
);
360 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
361 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
362 if (isl_int_is_one(gcd
))
364 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
365 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
372 struct isl_basic_set
*isl_basic_set_normalize_constraints(
373 struct isl_basic_set
*bset
)
375 return (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
376 (struct isl_basic_map
*)bset
);
379 /* Remove any common factor in numerator and denominator of the div expression,
380 * not taking into account the constant term.
381 * That is, if the div is of the form
383 * floor((a + m f(x))/(m d))
387 * floor((floor(a/m) + f(x))/d)
389 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
390 * and can therefore not influence the result of the floor.
392 static void normalize_div_expression(__isl_keep isl_basic_map
*bmap
, int div
)
394 unsigned total
= isl_basic_map_total_dim(bmap
);
395 isl_ctx
*ctx
= bmap
->ctx
;
397 if (isl_int_is_zero(bmap
->div
[div
][0]))
399 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
400 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
401 if (isl_int_is_one(ctx
->normalize_gcd
))
403 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
405 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
407 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
408 ctx
->normalize_gcd
, total
);
411 /* Remove any common factor in numerator and denominator of a div expression,
412 * not taking into account the constant term.
413 * That is, look for any div of the form
415 * floor((a + m f(x))/(m d))
419 * floor((floor(a/m) + f(x))/d)
421 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
422 * and can therefore not influence the result of the floor.
424 static __isl_give isl_basic_map
*normalize_div_expressions(
425 __isl_take isl_basic_map
*bmap
)
431 if (bmap
->n_div
== 0)
434 for (i
= 0; i
< bmap
->n_div
; ++i
)
435 normalize_div_expression(bmap
, i
);
440 /* Assumes divs have been ordered if keep_divs is set.
442 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
443 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
446 unsigned space_total
;
450 total
= isl_basic_map_total_dim(bmap
);
451 space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
452 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
453 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
454 if (bmap
->eq
[k
] == eq
)
456 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
460 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
461 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
464 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
465 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
469 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
470 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
471 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
474 for (k
= 0; k
< bmap
->n_div
; ++k
) {
475 if (isl_int_is_zero(bmap
->div
[k
][0]))
477 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
481 /* We need to be careful about circular definitions,
482 * so for now we just remove the definition of div k
483 * if the equality contains any divs.
484 * If keep_divs is set, then the divs have been ordered
485 * and we can keep the definition as long as the result
488 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
489 isl_seq_elim(bmap
->div
[k
]+1, eq
,
490 1+pos
, 1+total
, &bmap
->div
[k
][0]);
491 normalize_div_expression(bmap
, k
);
493 isl_seq_clr(bmap
->div
[k
], 1 + total
);
494 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
498 /* Assumes divs have been ordered if keep_divs is set.
500 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
501 unsigned div
, int keep_divs
)
503 unsigned pos
= isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
505 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
507 isl_basic_map_drop_div(bmap
, div
);
510 /* Check if elimination of div "div" using equality "eq" would not
511 * result in a div depending on a later div.
513 static int ok_to_eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
518 unsigned space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
519 unsigned pos
= space_total
+ div
;
521 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
522 if (last_div
< 0 || last_div
<= div
)
525 for (k
= 0; k
<= last_div
; ++k
) {
526 if (isl_int_is_zero(bmap
->div
[k
][0]))
528 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
535 /* Elimininate divs based on equalities
537 static struct isl_basic_map
*eliminate_divs_eq(
538 struct isl_basic_map
*bmap
, int *progress
)
545 bmap
= isl_basic_map_order_divs(bmap
);
550 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
552 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
553 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
554 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
555 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
557 if (!ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
))
561 eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
562 isl_basic_map_drop_equality(bmap
, i
);
567 return eliminate_divs_eq(bmap
, progress
);
571 /* Elimininate divs based on inequalities
573 static struct isl_basic_map
*eliminate_divs_ineq(
574 struct isl_basic_map
*bmap
, int *progress
)
585 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
587 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
588 for (i
= 0; i
< bmap
->n_eq
; ++i
)
589 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
593 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
594 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
596 if (i
< bmap
->n_ineq
)
599 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
600 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
602 bmap
= isl_basic_map_drop_div(bmap
, d
);
609 struct isl_basic_map
*isl_basic_map_gauss(
610 struct isl_basic_map
*bmap
, int *progress
)
618 bmap
= isl_basic_map_order_divs(bmap
);
623 total
= isl_basic_map_total_dim(bmap
);
624 total_var
= total
- bmap
->n_div
;
626 last_var
= total
- 1;
627 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
628 for (; last_var
>= 0; --last_var
) {
629 for (k
= done
; k
< bmap
->n_eq
; ++k
)
630 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
638 swap_equality(bmap
, k
, done
);
639 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
640 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
642 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
645 if (last_var
>= total_var
&&
646 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
647 unsigned div
= last_var
- total_var
;
648 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
649 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
650 isl_int_set(bmap
->div
[div
][0],
651 bmap
->eq
[done
][1+last_var
]);
654 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
657 if (done
== bmap
->n_eq
)
659 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
660 if (isl_int_is_zero(bmap
->eq
[k
][0]))
662 return isl_basic_map_set_to_empty(bmap
);
664 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
668 struct isl_basic_set
*isl_basic_set_gauss(
669 struct isl_basic_set
*bset
, int *progress
)
671 return (struct isl_basic_set
*)isl_basic_map_gauss(
672 (struct isl_basic_map
*)bset
, progress
);
676 static unsigned int round_up(unsigned int v
)
687 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
688 struct isl_basic_map
*bmap
, int k
)
691 unsigned total
= isl_basic_map_total_dim(bmap
);
692 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
693 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
694 if (&bmap
->ineq
[k
] != index
[h
] &&
695 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
700 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
701 struct isl_basic_set
*bset
, int k
)
703 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
706 /* If we can eliminate more than one div, then we need to make
707 * sure we do it from last div to first div, in order not to
708 * change the position of the other divs that still need to
711 static struct isl_basic_map
*remove_duplicate_divs(
712 struct isl_basic_map
*bmap
, int *progress
)
724 bmap
= isl_basic_map_order_divs(bmap
);
725 if (!bmap
|| bmap
->n_div
<= 1)
728 total_var
= isl_space_dim(bmap
->dim
, isl_dim_all
);
729 total
= total_var
+ bmap
->n_div
;
732 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
733 if (!isl_int_is_zero(bmap
->div
[k
][0]))
738 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
741 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
742 bits
= ffs(size
) - 1;
743 index
= isl_calloc_array(ctx
, int, size
);
744 if (!elim_for
|| !index
)
746 eq
= isl_blk_alloc(ctx
, 1+total
);
747 if (isl_blk_is_error(eq
))
750 isl_seq_clr(eq
.data
, 1+total
);
751 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
752 for (--k
; k
>= 0; --k
) {
755 if (isl_int_is_zero(bmap
->div
[k
][0]))
758 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
759 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
760 if (isl_seq_eq(bmap
->div
[k
],
761 bmap
->div
[index
[h
]-1], 2+total
))
770 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
774 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
775 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
776 eliminate_div(bmap
, eq
.data
, l
, 1);
777 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
778 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
781 isl_blk_free(ctx
, eq
);
788 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
793 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
794 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
795 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
799 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
805 /* Normalize divs that appear in equalities.
807 * In particular, we assume that bmap contains some equalities
812 * and we want to replace the set of e_i by a minimal set and
813 * such that the new e_i have a canonical representation in terms
815 * If any of the equalities involves more than one divs, then
816 * we currently simply bail out.
818 * Let us first additionally assume that all equalities involve
819 * a div. The equalities then express modulo constraints on the
820 * remaining variables and we can use "parameter compression"
821 * to find a minimal set of constraints. The result is a transformation
823 * x = T(x') = x_0 + G x'
825 * with G a lower-triangular matrix with all elements below the diagonal
826 * non-negative and smaller than the diagonal element on the same row.
827 * We first normalize x_0 by making the same property hold in the affine
829 * The rows i of G with a 1 on the diagonal do not impose any modulo
830 * constraint and simply express x_i = x'_i.
831 * For each of the remaining rows i, we introduce a div and a corresponding
832 * equality. In particular
834 * g_ii e_j = x_i - g_i(x')
836 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
837 * corresponding div (if g_kk != 1).
839 * If there are any equalities not involving any div, then we
840 * first apply a variable compression on the variables x:
842 * x = C x'' x'' = C_2 x
844 * and perform the above parameter compression on A C instead of on A.
845 * The resulting compression is then of the form
847 * x'' = T(x') = x_0 + G x'
849 * and in constructing the new divs and the corresponding equalities,
850 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
851 * by the corresponding row from C_2.
853 static struct isl_basic_map
*normalize_divs(
854 struct isl_basic_map
*bmap
, int *progress
)
861 struct isl_mat
*T
= NULL
;
862 struct isl_mat
*C
= NULL
;
863 struct isl_mat
*C2
= NULL
;
871 if (bmap
->n_div
== 0)
877 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
880 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
881 div_eq
= n_pure_div_eq(bmap
);
885 if (div_eq
< bmap
->n_eq
) {
886 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
887 bmap
->n_eq
- div_eq
, 0, 1 + total
);
888 C
= isl_mat_variable_compression(B
, &C2
);
892 bmap
= isl_basic_map_set_to_empty(bmap
);
899 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
902 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
903 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
905 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
907 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
910 B
= isl_mat_product(B
, C
);
914 T
= isl_mat_parameter_compression(B
, d
);
918 bmap
= isl_basic_map_set_to_empty(bmap
);
924 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
925 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
926 if (isl_int_is_zero(v
))
928 isl_mat_col_submul(T
, 0, v
, 1 + i
);
931 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
934 /* We have to be careful because dropping equalities may reorder them */
936 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
937 for (i
= 0; i
< bmap
->n_eq
; ++i
)
938 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
940 if (i
< bmap
->n_eq
) {
941 bmap
= isl_basic_map_drop_div(bmap
, j
);
942 isl_basic_map_drop_equality(bmap
, i
);
948 for (i
= 1; i
< T
->n_row
; ++i
) {
949 if (isl_int_is_one(T
->row
[i
][i
]))
954 if (needed
> dropped
) {
955 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
960 for (i
= 1; i
< T
->n_row
; ++i
) {
961 if (isl_int_is_one(T
->row
[i
][i
]))
963 k
= isl_basic_map_alloc_div(bmap
);
964 pos
[i
] = 1 + total
+ k
;
965 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
966 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
968 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
970 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
971 for (j
= 0; j
< i
; ++j
) {
972 if (isl_int_is_zero(T
->row
[i
][j
]))
974 if (pos
[j
] < T
->n_row
&& C2
)
975 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
976 C2
->row
[pos
[j
]], 1 + total
);
978 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
981 j
= isl_basic_map_alloc_equality(bmap
);
982 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
983 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
992 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
1002 static struct isl_basic_map
*set_div_from_lower_bound(
1003 struct isl_basic_map
*bmap
, int div
, int ineq
)
1005 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1007 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1008 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1009 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1010 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1011 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1016 /* Check whether it is ok to define a div based on an inequality.
1017 * To avoid the introduction of circular definitions of divs, we
1018 * do not allow such a definition if the resulting expression would refer to
1019 * any other undefined divs or if any known div is defined in
1020 * terms of the unknown div.
1022 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
1026 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1028 /* Not defined in terms of unknown divs */
1029 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1032 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1034 if (isl_int_is_zero(bmap
->div
[j
][0]))
1038 /* No other div defined in terms of this one => avoid loops */
1039 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1042 if (isl_int_is_zero(bmap
->div
[j
][0]))
1044 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1051 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1052 * be a better expression than the current one?
1054 * If we do not have any expression yet, then any expression would be better.
1055 * Otherwise we check if the last variable involved in the inequality
1056 * (disregarding the div that it would define) is in an earlier position
1057 * than the last variable involved in the current div expression.
1059 static int better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1062 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1066 if (isl_int_is_zero(bmap
->div
[div
][0]))
1069 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1070 bmap
->n_div
- (div
+ 1)) >= 0)
1073 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1074 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1075 total
+ bmap
->n_div
);
1077 return last_ineq
< last_div
;
1080 /* Given two constraints "k" and "l" that are opposite to each other,
1081 * except for the constant term, check if we can use them
1082 * to obtain an expression for one of the hitherto unknown divs or
1083 * a "better" expression for a div for which we already have an expression.
1084 * "sum" is the sum of the constant terms of the constraints.
1085 * If this sum is strictly smaller than the coefficient of one
1086 * of the divs, then this pair can be used define the div.
1087 * To avoid the introduction of circular definitions of divs, we
1088 * do not use the pair if the resulting expression would refer to
1089 * any other undefined divs or if any known div is defined in
1090 * terms of the unknown div.
1092 static struct isl_basic_map
*check_for_div_constraints(
1093 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
1096 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1098 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1099 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1101 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1103 if (!better_div_constraint(bmap
, i
, k
))
1105 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1107 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1108 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1110 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1118 __isl_give isl_basic_map
*isl_basic_map_remove_duplicate_constraints(
1119 __isl_take isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1125 unsigned total
= isl_basic_map_total_dim(bmap
);
1129 if (!bmap
|| bmap
->n_ineq
<= 1)
1132 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
1135 bits
= ffs(size
) - 1;
1136 ctx
= isl_basic_map_get_ctx(bmap
);
1137 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1141 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
1142 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1143 h
= hash_index(index
, size
, bits
, bmap
, k
);
1145 index
[h
] = &bmap
->ineq
[k
];
1150 l
= index
[h
] - &bmap
->ineq
[0];
1151 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1152 swap_inequality(bmap
, k
, l
);
1153 isl_basic_map_drop_inequality(bmap
, k
);
1157 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1158 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1159 h
= hash_index(index
, size
, bits
, bmap
, k
);
1160 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1163 l
= index
[h
] - &bmap
->ineq
[0];
1164 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1165 if (isl_int_is_pos(sum
)) {
1167 bmap
= check_for_div_constraints(bmap
, k
, l
,
1171 if (isl_int_is_zero(sum
)) {
1172 /* We need to break out of the loop after these
1173 * changes since the contents of the hash
1174 * will no longer be valid.
1175 * Plus, we probably we want to regauss first.
1179 isl_basic_map_drop_inequality(bmap
, l
);
1180 isl_basic_map_inequality_to_equality(bmap
, k
);
1182 bmap
= isl_basic_map_set_to_empty(bmap
);
1192 /* Eliminate knowns divs from constraints where they appear with
1193 * a (positive or negative) unit coefficient.
1197 * floor(e/m) + f >= 0
1205 * -floor(e/m) + f >= 0
1209 * -e + m f + m - 1 >= 0
1211 * The first conversion is valid because floor(e/m) >= -f is equivalent
1212 * to e/m >= -f because -f is an integral expression.
1213 * The second conversion follows from the fact that
1215 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1218 * Note that one of the div constraints may have been eliminated
1219 * due to being redundant with respect to the constraint that is
1220 * being modified by this function. The modified constraint may
1221 * no longer imply this div constraint, so we add it back to make
1222 * sure we do not lose any information.
1224 * We skip integral divs, i.e., those with denominator 1, as we would
1225 * risk eliminating the div from the div constraints. We do not need
1226 * to handle those divs here anyway since the div constraints will turn
1227 * out to form an equality and this equality can then be use to eliminate
1228 * the div from all constraints.
1230 static __isl_give isl_basic_map
*eliminate_unit_divs(
1231 __isl_take isl_basic_map
*bmap
, int *progress
)
1240 ctx
= isl_basic_map_get_ctx(bmap
);
1241 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1243 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1244 if (isl_int_is_zero(bmap
->div
[i
][0]))
1246 if (isl_int_is_one(bmap
->div
[i
][0]))
1248 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1251 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1252 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1257 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1258 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1260 isl_seq_combine(bmap
->ineq
[j
],
1261 ctx
->negone
, bmap
->div
[i
] + 1,
1262 bmap
->div
[i
][0], bmap
->ineq
[j
],
1263 total
+ bmap
->n_div
);
1265 isl_seq_combine(bmap
->ineq
[j
],
1266 ctx
->one
, bmap
->div
[i
] + 1,
1267 bmap
->div
[i
][0], bmap
->ineq
[j
],
1268 total
+ bmap
->n_div
);
1270 isl_int_add(bmap
->ineq
[j
][0],
1271 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1272 isl_int_sub_ui(bmap
->ineq
[j
][0],
1273 bmap
->ineq
[j
][0], 1);
1276 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
1277 if (isl_basic_map_add_div_constraint(bmap
, i
, s
) < 0)
1278 return isl_basic_map_free(bmap
);
1285 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1294 if (isl_basic_map_plain_is_empty(bmap
))
1296 bmap
= isl_basic_map_normalize_constraints(bmap
);
1297 bmap
= normalize_div_expressions(bmap
);
1298 bmap
= remove_duplicate_divs(bmap
, &progress
);
1299 bmap
= eliminate_unit_divs(bmap
, &progress
);
1300 bmap
= eliminate_divs_eq(bmap
, &progress
);
1301 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1302 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1303 /* requires equalities in normal form */
1304 bmap
= normalize_divs(bmap
, &progress
);
1305 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1311 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1313 return (struct isl_basic_set
*)
1314 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1318 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1319 isl_int
*constraint
, unsigned div
)
1326 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1328 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1330 isl_int_sub(bmap
->div
[div
][1],
1331 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1332 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1333 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1334 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1335 isl_int_add(bmap
->div
[div
][1],
1336 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1339 if (isl_seq_first_non_zero(constraint
+pos
+1,
1340 bmap
->n_div
-div
-1) != -1)
1342 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1343 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1345 if (isl_seq_first_non_zero(constraint
+pos
+1,
1346 bmap
->n_div
-div
-1) != -1)
1354 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1355 isl_int
*constraint
, unsigned div
)
1357 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1361 /* If the only constraints a div d=floor(f/m)
1362 * appears in are its two defining constraints
1365 * -(f - (m - 1)) + m d >= 0
1367 * then it can safely be removed.
1369 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1372 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1374 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1375 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1378 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1379 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1381 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1385 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1386 if (isl_int_is_zero(bmap
->div
[i
][0]))
1388 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1396 * Remove divs that don't occur in any of the constraints or other divs.
1397 * These can arise when dropping constraints from a basic map or
1398 * when the divs of a basic map have been temporarily aligned
1399 * with the divs of another basic map.
1401 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1408 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1409 if (!div_is_redundant(bmap
, i
))
1411 bmap
= isl_basic_map_drop_div(bmap
, i
);
1416 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1418 bmap
= remove_redundant_divs(bmap
);
1421 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1425 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1427 return (struct isl_basic_set
*)
1428 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1431 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1437 for (i
= 0; i
< set
->n
; ++i
) {
1438 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1448 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1454 for (i
= 0; i
< map
->n
; ++i
) {
1455 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1459 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1467 /* Remove definition of any div that is defined in terms of the given variable.
1468 * The div itself is not removed. Functions such as
1469 * eliminate_divs_ineq depend on the other divs remaining in place.
1471 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1479 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1480 if (isl_int_is_zero(bmap
->div
[i
][0]))
1482 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1484 isl_int_set_si(bmap
->div
[i
][0], 0);
1489 /* Eliminate the specified variables from the constraints using
1490 * Fourier-Motzkin. The variables themselves are not removed.
1492 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1493 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1504 total
= isl_basic_map_total_dim(bmap
);
1506 bmap
= isl_basic_map_cow(bmap
);
1507 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1508 bmap
= remove_dependent_vars(bmap
, d
);
1512 for (d
= pos
+ n
- 1;
1513 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1514 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1515 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1516 int n_lower
, n_upper
;
1519 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1520 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1522 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1523 isl_basic_map_drop_equality(bmap
, i
);
1531 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1532 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1534 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1537 bmap
= isl_basic_map_extend_constraints(bmap
,
1538 0, n_lower
* n_upper
);
1541 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1543 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1546 for (j
= 0; j
< i
; ++j
) {
1547 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1550 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1551 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1553 k
= isl_basic_map_alloc_inequality(bmap
);
1556 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1558 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1559 1+d
, 1+total
, NULL
);
1561 isl_basic_map_drop_inequality(bmap
, i
);
1564 if (n_lower
> 0 && n_upper
> 0) {
1565 bmap
= isl_basic_map_normalize_constraints(bmap
);
1566 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1568 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1569 bmap
= isl_basic_map_remove_redundancies(bmap
);
1573 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1577 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1579 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1582 isl_basic_map_free(bmap
);
1586 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1587 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1589 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1590 (struct isl_basic_map
*)bset
, pos
, n
);
1593 /* Eliminate the specified n dimensions starting at first from the
1594 * constraints, without removing the dimensions from the space.
1595 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1596 * Otherwise, they are projected out and the original space is restored.
1598 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1599 __isl_take isl_basic_map
*bmap
,
1600 enum isl_dim_type type
, unsigned first
, unsigned n
)
1609 if (first
+ n
> isl_basic_map_dim(bmap
, type
) || first
+ n
< first
)
1610 isl_die(bmap
->ctx
, isl_error_invalid
,
1611 "index out of bounds", goto error
);
1613 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1614 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1615 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1616 return isl_basic_map_finalize(bmap
);
1619 space
= isl_basic_map_get_space(bmap
);
1620 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1621 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1622 bmap
= isl_basic_map_reset_space(bmap
, space
);
1625 isl_basic_map_free(bmap
);
1629 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1630 __isl_take isl_basic_set
*bset
,
1631 enum isl_dim_type type
, unsigned first
, unsigned n
)
1633 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1636 /* Don't assume equalities are in order, because align_divs
1637 * may have changed the order of the divs.
1639 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1644 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1645 for (d
= 0; d
< total
; ++d
)
1647 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1648 for (d
= total
- 1; d
>= 0; --d
) {
1649 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1657 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1659 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1662 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1663 struct isl_basic_map
*bmap
, int *elim
)
1669 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1670 for (d
= total
- 1; d
>= 0; --d
) {
1671 if (isl_int_is_zero(src
[1+d
]))
1676 isl_seq_cpy(dst
, src
, 1 + total
);
1679 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1684 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1685 struct isl_basic_set
*bset
, int *elim
)
1687 return reduced_using_equalities(dst
, src
,
1688 (struct isl_basic_map
*)bset
, elim
);
1691 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1692 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1697 if (!bset
|| !context
)
1700 if (context
->n_eq
== 0) {
1701 isl_basic_set_free(context
);
1705 bset
= isl_basic_set_cow(bset
);
1709 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1712 set_compute_elimination_index(context
, elim
);
1713 for (i
= 0; i
< bset
->n_eq
; ++i
)
1714 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1716 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1717 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1719 isl_basic_set_free(context
);
1721 bset
= isl_basic_set_simplify(bset
);
1722 bset
= isl_basic_set_finalize(bset
);
1725 isl_basic_set_free(bset
);
1726 isl_basic_set_free(context
);
1730 static struct isl_basic_set
*remove_shifted_constraints(
1731 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1739 if (!bset
|| !context
)
1742 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1745 bits
= ffs(size
) - 1;
1746 ctx
= isl_basic_set_get_ctx(bset
);
1747 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1751 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1752 h
= set_hash_index(index
, size
, bits
, context
, k
);
1753 index
[h
] = &context
->ineq
[k
];
1755 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1756 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1759 l
= index
[h
] - &context
->ineq
[0];
1760 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1762 bset
= isl_basic_set_cow(bset
);
1765 isl_basic_set_drop_inequality(bset
, k
);
1775 /* Remove constraints from "bmap" that are identical to constraints
1776 * in "context" or that are more relaxed (greater constant term).
1778 * We perform the test for shifted copies on the pure constraints
1779 * in remove_shifted_constraints.
1781 static __isl_give isl_basic_map
*isl_basic_map_remove_shifted_constraints(
1782 __isl_take isl_basic_map
*bmap
, __isl_take isl_basic_map
*context
)
1784 isl_basic_set
*bset
, *bset_context
;
1786 if (!bmap
|| !context
)
1789 if (bmap
->n_ineq
== 0 || context
->n_ineq
== 0) {
1790 isl_basic_map_free(context
);
1794 context
= isl_basic_map_align_divs(context
, bmap
);
1795 bmap
= isl_basic_map_align_divs(bmap
, context
);
1797 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
1798 bset_context
= isl_basic_map_underlying_set(context
);
1799 bset
= remove_shifted_constraints(bset
, bset_context
);
1800 isl_basic_set_free(bset_context
);
1802 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
1806 isl_basic_map_free(bmap
);
1807 isl_basic_map_free(context
);
1811 /* Does the (linear part of a) constraint "c" involve any of the "len"
1812 * "relevant" dimensions?
1814 static int is_related(isl_int
*c
, int len
, int *relevant
)
1818 for (i
= 0; i
< len
; ++i
) {
1821 if (!isl_int_is_zero(c
[i
]))
1828 /* Drop constraints from "bset" that do not involve any of
1829 * the dimensions marked "relevant".
1831 static __isl_give isl_basic_set
*drop_unrelated_constraints(
1832 __isl_take isl_basic_set
*bset
, int *relevant
)
1836 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1837 for (i
= 0; i
< dim
; ++i
)
1843 for (i
= bset
->n_eq
- 1; i
>= 0; --i
)
1844 if (!is_related(bset
->eq
[i
] + 1, dim
, relevant
))
1845 isl_basic_set_drop_equality(bset
, i
);
1847 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
)
1848 if (!is_related(bset
->ineq
[i
] + 1, dim
, relevant
))
1849 isl_basic_set_drop_inequality(bset
, i
);
1854 /* Update the groups in "group" based on the (linear part of a) constraint "c".
1856 * In particular, for any variable involved in the constraint,
1857 * find the actual group id from before and replace the group
1858 * of the corresponding variable by the minimal group of all
1859 * the variables involved in the constraint considered so far
1860 * (if this minimum is smaller) or replace the minimum by this group
1861 * (if the minimum is larger).
1863 * At the end, all the variables in "c" will (indirectly) point
1864 * to the minimal of the groups that they referred to originally.
1866 static void update_groups(int dim
, int *group
, isl_int
*c
)
1871 for (j
= 0; j
< dim
; ++j
) {
1872 if (isl_int_is_zero(c
[j
]))
1874 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
1875 group
[j
] = group
[group
[j
]];
1876 if (group
[j
] == min
)
1878 if (group
[j
] < min
) {
1879 if (min
>= 0 && min
< dim
)
1880 group
[min
] = group
[j
];
1883 group
[group
[j
]] = min
;
1887 /* Drop constraints from "context" that are irrelevant for computing
1888 * the gist of "bset".
1890 * In particular, drop constraints in variables that are not related
1891 * to any of the variables involved in the constraints of "bset"
1892 * in the sense that there is no sequence of constraints that connects them.
1894 * We construct groups of variables that collect variables that
1895 * (indirectly) appear in some common constraint of "context".
1896 * Each group is identified by the first variable in the group,
1897 * except for the special group of variables that appear in "bset"
1898 * (or are related to those variables), which is identified by -1.
1899 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
1900 * otherwise the group of i is the group of group[i].
1902 * We first initialize the -1 group with the variables that appear in "bset".
1903 * Then we initialize groups for the remaining variables.
1904 * Then we iterate over the constraints of "context" and update the
1905 * group of the variables in the constraint by the smallest group.
1906 * Finally, we resolve indirect references to groups by running over
1909 * After computing the groups, we drop constraints that do not involve
1910 * any variables in the -1 group.
1912 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
1913 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
1921 if (!context
|| !bset
)
1922 return isl_basic_set_free(context
);
1924 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1925 ctx
= isl_basic_set_get_ctx(bset
);
1926 group
= isl_calloc_array(ctx
, int, dim
);
1931 for (i
= 0; i
< dim
; ++i
) {
1932 for (j
= 0; j
< bset
->n_eq
; ++j
)
1933 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
1935 if (j
< bset
->n_eq
) {
1939 for (j
= 0; j
< bset
->n_ineq
; ++j
)
1940 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
1942 if (j
< bset
->n_ineq
)
1947 for (i
= 0; i
< dim
; ++i
)
1949 last
= group
[i
] = i
;
1955 for (i
= 0; i
< context
->n_eq
; ++i
)
1956 update_groups(dim
, group
, context
->eq
[i
] + 1);
1957 for (i
= 0; i
< context
->n_ineq
; ++i
)
1958 update_groups(dim
, group
, context
->ineq
[i
] + 1);
1960 for (i
= 0; i
< dim
; ++i
)
1962 group
[i
] = group
[group
[i
]];
1964 for (i
= 0; i
< dim
; ++i
)
1965 group
[i
] = group
[i
] == -1;
1967 context
= drop_unrelated_constraints(context
, group
);
1973 return isl_basic_set_free(context
);
1976 /* Remove all information from bset that is redundant in the context
1977 * of context. Both bset and context are assumed to be full-dimensional.
1979 * We first remove the inequalities from "bset"
1980 * that are obviously redundant with respect to some inequality in "context".
1981 * Then we remove those constraints from "context" that have become
1982 * irrelevant for computing the gist of "bset".
1983 * Note that this removal of constraints cannot be replaced by
1984 * a factorization because factors in "bset" may still be connected
1985 * to each other through constraints in "context".
1987 * If there are any inequalities left, we construct a tableau for
1988 * the context and then add the inequalities of "bset".
1989 * Before adding these inequalities, we freeze all constraints such that
1990 * they won't be considered redundant in terms of the constraints of "bset".
1991 * Then we detect all redundant constraints (among the
1992 * constraints that weren't frozen), first by checking for redundancy in the
1993 * the tableau and then by checking if replacing a constraint by its negation
1994 * would lead to an empty set. This last step is fairly expensive
1995 * and could be optimized by more reuse of the tableau.
1996 * Finally, we update bset according to the results.
1998 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1999 __isl_take isl_basic_set
*context
)
2002 isl_basic_set
*combined
= NULL
;
2003 struct isl_tab
*tab
= NULL
;
2004 unsigned context_ineq
;
2007 if (!bset
|| !context
)
2010 if (isl_basic_set_is_universe(bset
)) {
2011 isl_basic_set_free(context
);
2015 if (isl_basic_set_is_universe(context
)) {
2016 isl_basic_set_free(context
);
2020 bset
= remove_shifted_constraints(bset
, context
);
2023 if (bset
->n_ineq
== 0)
2026 context
= drop_irrelevant_constraints(context
, bset
);
2029 if (isl_basic_set_is_universe(context
)) {
2030 isl_basic_set_free(context
);
2034 context_ineq
= context
->n_ineq
;
2035 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
2036 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
2037 tab
= isl_tab_from_basic_set(combined
, 0);
2038 for (i
= 0; i
< context_ineq
; ++i
)
2039 if (isl_tab_freeze_constraint(tab
, i
) < 0)
2041 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
2043 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2044 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
2046 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
2050 if (isl_tab_detect_redundant(tab
) < 0)
2052 total
= isl_basic_set_total_dim(bset
);
2053 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
2055 if (tab
->con
[i
].is_redundant
)
2057 tab
->con
[i
].is_redundant
= 1;
2058 combined
= isl_basic_set_dup(bset
);
2059 combined
= isl_basic_set_update_from_tab(combined
, tab
);
2060 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
2061 k
= isl_basic_set_alloc_inequality(combined
);
2064 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
2065 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
2066 is_empty
= isl_basic_set_is_empty(combined
);
2069 isl_basic_set_free(combined
);
2072 tab
->con
[i
].is_redundant
= 0;
2074 for (i
= 0; i
< context_ineq
; ++i
)
2075 tab
->con
[i
].is_redundant
= 1;
2076 bset
= isl_basic_set_update_from_tab(bset
, tab
);
2078 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2079 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2084 bset
= isl_basic_set_simplify(bset
);
2085 bset
= isl_basic_set_finalize(bset
);
2086 isl_basic_set_free(context
);
2090 isl_basic_set_free(combined
);
2091 isl_basic_set_free(context
);
2092 isl_basic_set_free(bset
);
2096 /* Remove all information from bset that is redundant in the context
2097 * of context. In particular, equalities that are linear combinations
2098 * of those in context are removed. Then the inequalities that are
2099 * redundant in the context of the equalities and inequalities of
2100 * context are removed.
2102 * First of all, we drop those constraints from "context"
2103 * that are irrelevant for computing the gist of "bset".
2104 * Alternatively, we could factorize the intersection of "context" and "bset".
2106 * We first compute the integer affine hull of the intersection,
2107 * compute the gist inside this affine hull and then add back
2108 * those equalities that are not implied by the context.
2110 * If two constraints are mutually redundant, then uset_gist_full
2111 * will remove the second of those constraints. We therefore first
2112 * sort the constraints so that constraints not involving existentially
2113 * quantified variables are given precedence over those that do.
2114 * We have to perform this sorting before the variable compression,
2115 * because that may effect the order of the variables.
2117 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2118 __isl_take isl_basic_set
*context
)
2123 isl_basic_set
*aff_context
;
2126 if (!bset
|| !context
)
2129 context
= drop_irrelevant_constraints(context
, bset
);
2131 aff
= isl_basic_set_copy(bset
);
2132 aff
= isl_basic_set_intersect(aff
, isl_basic_set_copy(context
));
2133 aff
= isl_basic_set_affine_hull(aff
);
2136 if (isl_basic_set_plain_is_empty(aff
)) {
2137 isl_basic_set_free(bset
);
2138 isl_basic_set_free(context
);
2141 bset
= isl_basic_set_sort_constraints(bset
);
2142 if (aff
->n_eq
== 0) {
2143 isl_basic_set_free(aff
);
2144 return uset_gist_full(bset
, context
);
2146 total
= isl_basic_set_total_dim(bset
);
2147 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2148 eq
= isl_mat_cow(eq
);
2149 T
= isl_mat_variable_compression(eq
, &T2
);
2150 if (T
&& T
->n_col
== 0) {
2153 isl_basic_set_free(context
);
2154 isl_basic_set_free(aff
);
2155 return isl_basic_set_set_to_empty(bset
);
2158 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2160 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
2161 context
= isl_basic_set_preimage(context
, T
);
2163 bset
= uset_gist_full(bset
, context
);
2164 bset
= isl_basic_set_preimage(bset
, T2
);
2165 bset
= isl_basic_set_intersect(bset
, aff
);
2166 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2169 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2170 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2175 isl_basic_set_free(bset
);
2176 isl_basic_set_free(context
);
2180 /* Normalize the divs in "bmap" in the context of the equalities in "context".
2181 * We simply add the equalities in context to bmap and then do a regular
2182 * div normalizations. Better results can be obtained by normalizing
2183 * only the divs in bmap than do not also appear in context.
2184 * We need to be careful to reduce the divs using the equalities
2185 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
2186 * spurious constraints.
2188 static struct isl_basic_map
*normalize_divs_in_context(
2189 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
2192 unsigned total_context
;
2195 div_eq
= n_pure_div_eq(bmap
);
2199 bmap
= isl_basic_map_cow(bmap
);
2200 if (context
->n_div
> 0)
2201 bmap
= isl_basic_map_align_divs(bmap
, context
);
2203 total_context
= isl_basic_map_total_dim(context
);
2204 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
2205 for (i
= 0; i
< context
->n_eq
; ++i
) {
2207 k
= isl_basic_map_alloc_equality(bmap
);
2209 return isl_basic_map_free(bmap
);
2210 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
2211 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
2212 isl_basic_map_total_dim(bmap
) - total_context
);
2214 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2215 bmap
= normalize_divs(bmap
, NULL
);
2216 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2220 /* Return a basic map that has the same intersection with "context" as "bmap"
2221 * and that is as "simple" as possible.
2223 * The core computation is performed on the pure constraints.
2224 * When we add back the meaning of the integer divisions, we need
2225 * to (re)introduce the div constraints. If we happen to have
2226 * discovered that some of these integer divisions are equal to
2227 * some affine combination of other variables, then these div
2228 * constraints may end up getting simplified in terms of the equalities,
2229 * resulting in extra inequalities on the other variables that
2230 * may have been removed already or that may not even have been
2231 * part of the input. We try and remove those constraints of
2232 * this form that are most obviously redundant with respect to
2233 * the context. We also remove those div constraints that are
2234 * redundant with respect to the other constraints in the result.
2236 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
2237 struct isl_basic_map
*context
)
2239 isl_basic_set
*bset
, *eq
;
2240 isl_basic_map
*eq_bmap
;
2241 unsigned n_div
, n_eq
, n_ineq
;
2243 if (!bmap
|| !context
)
2246 if (isl_basic_map_is_universe(bmap
)) {
2247 isl_basic_map_free(context
);
2250 if (isl_basic_map_plain_is_empty(context
)) {
2251 isl_space
*space
= isl_basic_map_get_space(bmap
);
2252 isl_basic_map_free(bmap
);
2253 isl_basic_map_free(context
);
2254 return isl_basic_map_universe(space
);
2256 if (isl_basic_map_plain_is_empty(bmap
)) {
2257 isl_basic_map_free(context
);
2261 bmap
= isl_basic_map_remove_redundancies(bmap
);
2262 context
= isl_basic_map_remove_redundancies(context
);
2267 bmap
= normalize_divs_in_context(bmap
, context
);
2269 context
= isl_basic_map_align_divs(context
, bmap
);
2270 bmap
= isl_basic_map_align_divs(bmap
, context
);
2271 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
2273 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
2274 isl_basic_map_underlying_set(isl_basic_map_copy(context
)));
2276 if (!bset
|| bset
->n_eq
== 0 || n_div
== 0 ||
2277 isl_basic_set_plain_is_empty(bset
)) {
2278 isl_basic_map_free(context
);
2279 return isl_basic_map_overlying_set(bset
, bmap
);
2283 n_ineq
= bset
->n_ineq
;
2284 eq
= isl_basic_set_copy(bset
);
2285 eq
= isl_basic_set_cow(eq
);
2286 if (isl_basic_set_free_inequality(eq
, n_ineq
) < 0)
2287 eq
= isl_basic_set_free(eq
);
2288 if (isl_basic_set_free_equality(bset
, n_eq
) < 0)
2289 bset
= isl_basic_set_free(bset
);
2291 eq_bmap
= isl_basic_map_overlying_set(eq
, isl_basic_map_copy(bmap
));
2292 eq_bmap
= isl_basic_map_remove_shifted_constraints(eq_bmap
, context
);
2293 bmap
= isl_basic_map_overlying_set(bset
, bmap
);
2294 bmap
= isl_basic_map_intersect(bmap
, eq_bmap
);
2295 bmap
= isl_basic_map_remove_redundancies(bmap
);
2299 isl_basic_map_free(bmap
);
2300 isl_basic_map_free(context
);
2305 * Assumes context has no implicit divs.
2307 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
2308 __isl_take isl_basic_map
*context
)
2312 if (!map
|| !context
)
2315 if (isl_basic_map_plain_is_empty(context
)) {
2316 isl_space
*space
= isl_map_get_space(map
);
2318 isl_basic_map_free(context
);
2319 return isl_map_universe(space
);
2322 context
= isl_basic_map_remove_redundancies(context
);
2323 map
= isl_map_cow(map
);
2324 if (!map
|| !context
)
2326 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
2327 map
= isl_map_compute_divs(map
);
2330 for (i
= map
->n
- 1; i
>= 0; --i
) {
2331 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
2332 isl_basic_map_copy(context
));
2335 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
2336 isl_basic_map_free(map
->p
[i
]);
2337 if (i
!= map
->n
- 1)
2338 map
->p
[i
] = map
->p
[map
->n
- 1];
2342 isl_basic_map_free(context
);
2343 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2347 isl_basic_map_free(context
);
2351 /* Return a map that has the same intersection with "context" as "map"
2352 * and that is as "simple" as possible.
2354 * If "map" is already the universe, then we cannot make it any simpler.
2355 * Similarly, if "context" is the universe, then we cannot exploit it
2357 * If "map" and "context" are identical to each other, then we can
2358 * return the corresponding universe.
2360 * If none of these cases apply, we have to work a bit harder.
2362 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
2363 __isl_take isl_map
*context
)
2368 is_universe
= isl_map_plain_is_universe(map
);
2369 if (is_universe
>= 0 && !is_universe
)
2370 is_universe
= isl_map_plain_is_universe(context
);
2371 if (is_universe
< 0)
2374 isl_map_free(context
);
2378 equal
= isl_map_plain_is_equal(map
, context
);
2382 isl_map
*res
= isl_map_universe(isl_map_get_space(map
));
2384 isl_map_free(context
);
2388 context
= isl_map_compute_divs(context
);
2389 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
2392 isl_map_free(context
);
2396 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
2397 __isl_take isl_map
*context
)
2399 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2402 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2403 struct isl_basic_set
*context
)
2405 return (struct isl_basic_set
*)isl_basic_map_gist(
2406 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2409 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2410 __isl_take isl_basic_set
*context
)
2412 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2413 (struct isl_basic_map
*)context
);
2416 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2417 __isl_take isl_basic_set
*context
)
2419 isl_space
*space
= isl_set_get_space(set
);
2420 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2421 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2422 return isl_set_gist_basic_set(set
, dom_context
);
2425 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2426 __isl_take isl_set
*context
)
2428 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2429 (struct isl_map
*)context
);
2432 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2433 __isl_take isl_set
*context
)
2435 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2436 map_context
= isl_map_intersect_domain(map_context
, context
);
2437 return isl_map_gist(map
, map_context
);
2440 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2441 __isl_take isl_set
*context
)
2443 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2444 map_context
= isl_map_intersect_range(map_context
, context
);
2445 return isl_map_gist(map
, map_context
);
2448 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2449 __isl_take isl_set
*context
)
2451 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2452 map_context
= isl_map_intersect_params(map_context
, context
);
2453 return isl_map_gist(map
, map_context
);
2456 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2457 __isl_take isl_set
*context
)
2459 return isl_map_gist_params(set
, context
);
2462 /* Quick check to see if two basic maps are disjoint.
2463 * In particular, we reduce the equalities and inequalities of
2464 * one basic map in the context of the equalities of the other
2465 * basic map and check if we get a contradiction.
2467 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2468 __isl_keep isl_basic_map
*bmap2
)
2470 struct isl_vec
*v
= NULL
;
2475 if (!bmap1
|| !bmap2
)
2477 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
2479 if (bmap1
->n_div
|| bmap2
->n_div
)
2481 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
2484 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
2487 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
2490 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
2493 compute_elimination_index(bmap1
, elim
);
2494 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
2496 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
2498 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
2499 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2502 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
2504 reduced
= reduced_using_equalities(v
->block
.data
,
2505 bmap2
->ineq
[i
], bmap1
, elim
);
2506 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2507 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2510 compute_elimination_index(bmap2
, elim
);
2511 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
2513 reduced
= reduced_using_equalities(v
->block
.data
,
2514 bmap1
->ineq
[i
], bmap2
, elim
);
2515 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2516 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2532 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2533 __isl_keep isl_basic_set
*bset2
)
2535 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
2536 (struct isl_basic_map
*)bset2
);
2539 /* Are "map1" and "map2" obviously disjoint?
2541 * If one of them is empty or if they live in different spaces (ignoring
2542 * parameters), then they are clearly disjoint.
2544 * If they have different parameters, then we skip any further tests.
2546 * If they are obviously equal, but not obviously empty, then we will
2547 * not be able to detect if they are disjoint.
2549 * Otherwise we check if each basic map in "map1" is obviously disjoint
2550 * from each basic map in "map2".
2552 int isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
2553 __isl_keep isl_map
*map2
)
2563 disjoint
= isl_map_plain_is_empty(map1
);
2564 if (disjoint
< 0 || disjoint
)
2567 disjoint
= isl_map_plain_is_empty(map2
);
2568 if (disjoint
< 0 || disjoint
)
2571 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_in
,
2572 map2
->dim
, isl_dim_in
);
2573 if (match
< 0 || !match
)
2574 return match
< 0 ? -1 : 1;
2576 match
= isl_space_tuple_is_equal(map1
->dim
, isl_dim_out
,
2577 map2
->dim
, isl_dim_out
);
2578 if (match
< 0 || !match
)
2579 return match
< 0 ? -1 : 1;
2581 match
= isl_space_match(map1
->dim
, isl_dim_param
,
2582 map2
->dim
, isl_dim_param
);
2583 if (match
< 0 || !match
)
2584 return match
< 0 ? -1 : 0;
2586 intersect
= isl_map_plain_is_equal(map1
, map2
);
2587 if (intersect
< 0 || intersect
)
2588 return intersect
< 0 ? -1 : 0;
2590 for (i
= 0; i
< map1
->n
; ++i
) {
2591 for (j
= 0; j
< map2
->n
; ++j
) {
2592 int d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
2601 /* Are "map1" and "map2" disjoint?
2603 * They are disjoint if they are "obviously disjoint" or if one of them
2604 * is empty. Otherwise, they are not disjoint if one of them is universal.
2605 * If none of these cases apply, we compute the intersection and see if
2606 * the result is empty.
2608 int isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
2614 disjoint
= isl_map_plain_is_disjoint(map1
, map2
);
2615 if (disjoint
< 0 || disjoint
)
2618 disjoint
= isl_map_is_empty(map1
);
2619 if (disjoint
< 0 || disjoint
)
2622 disjoint
= isl_map_is_empty(map2
);
2623 if (disjoint
< 0 || disjoint
)
2626 intersect
= isl_map_plain_is_universe(map1
);
2627 if (intersect
< 0 || intersect
)
2628 return intersect
< 0 ? -1 : 0;
2630 intersect
= isl_map_plain_is_universe(map2
);
2631 if (intersect
< 0 || intersect
)
2632 return intersect
< 0 ? -1 : 0;
2634 test
= isl_map_intersect(isl_map_copy(map1
), isl_map_copy(map2
));
2635 disjoint
= isl_map_is_empty(test
);
2641 /* Are "bmap1" and "bmap2" disjoint?
2643 * They are disjoint if they are "obviously disjoint" or if one of them
2644 * is empty. Otherwise, they are not disjoint if one of them is universal.
2645 * If none of these cases apply, we compute the intersection and see if
2646 * the result is empty.
2648 int isl_basic_map_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2649 __isl_keep isl_basic_map
*bmap2
)
2653 isl_basic_map
*test
;
2655 disjoint
= isl_basic_map_plain_is_disjoint(bmap1
, bmap2
);
2656 if (disjoint
< 0 || disjoint
)
2659 disjoint
= isl_basic_map_is_empty(bmap1
);
2660 if (disjoint
< 0 || disjoint
)
2663 disjoint
= isl_basic_map_is_empty(bmap2
);
2664 if (disjoint
< 0 || disjoint
)
2667 intersect
= isl_basic_map_is_universe(bmap1
);
2668 if (intersect
< 0 || intersect
)
2669 return intersect
< 0 ? -1 : 0;
2671 intersect
= isl_basic_map_is_universe(bmap2
);
2672 if (intersect
< 0 || intersect
)
2673 return intersect
< 0 ? -1 : 0;
2675 test
= isl_basic_map_intersect(isl_basic_map_copy(bmap1
),
2676 isl_basic_map_copy(bmap2
));
2677 disjoint
= isl_basic_map_is_empty(test
);
2678 isl_basic_map_free(test
);
2683 /* Are "bset1" and "bset2" disjoint?
2685 int isl_basic_set_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2686 __isl_keep isl_basic_set
*bset2
)
2688 return isl_basic_map_is_disjoint(bset1
, bset2
);
2691 int isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
2692 __isl_keep isl_set
*set2
)
2694 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
2695 (struct isl_map
*)set2
);
2698 /* Are "set1" and "set2" disjoint?
2700 int isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2702 return isl_map_is_disjoint(set1
, set2
);
2705 int isl_set_fast_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2707 return isl_set_plain_is_disjoint(set1
, set2
);
2710 /* Check if we can combine a given div with lower bound l and upper
2711 * bound u with some other div and if so return that other div.
2712 * Otherwise return -1.
2714 * We first check that
2715 * - the bounds are opposites of each other (except for the constant
2717 * - the bounds do not reference any other div
2718 * - no div is defined in terms of this div
2720 * Let m be the size of the range allowed on the div by the bounds.
2721 * That is, the bounds are of the form
2723 * e <= a <= e + m - 1
2725 * with e some expression in the other variables.
2726 * We look for another div b such that no third div is defined in terms
2727 * of this second div b and such that in any constraint that contains
2728 * a (except for the given lower and upper bound), also contains b
2729 * with a coefficient that is m times that of b.
2730 * That is, all constraints (execpt for the lower and upper bound)
2733 * e + f (a + m b) >= 0
2735 * If so, we return b so that "a + m b" can be replaced by
2736 * a single div "c = a + m b".
2738 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2739 unsigned div
, unsigned l
, unsigned u
)
2745 if (bmap
->n_div
<= 1)
2747 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2748 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2750 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2751 bmap
->n_div
- div
- 1) != -1)
2753 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2757 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2758 if (isl_int_is_zero(bmap
->div
[i
][0]))
2760 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2764 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2765 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2766 isl_int_sub(bmap
->ineq
[l
][0],
2767 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2768 bmap
= isl_basic_map_copy(bmap
);
2769 bmap
= isl_basic_map_set_to_empty(bmap
);
2770 isl_basic_map_free(bmap
);
2773 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2774 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2779 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2780 if (isl_int_is_zero(bmap
->div
[j
][0]))
2782 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2785 if (j
< bmap
->n_div
)
2787 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2789 if (j
== l
|| j
== u
)
2791 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2793 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2795 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2796 bmap
->ineq
[j
][1 + dim
+ div
],
2798 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2799 bmap
->ineq
[j
][1 + dim
+ i
]);
2800 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2801 bmap
->ineq
[j
][1 + dim
+ div
],
2806 if (j
< bmap
->n_ineq
)
2811 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2812 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2816 /* Given a lower and an upper bound on div i, construct an inequality
2817 * that when nonnegative ensures that this pair of bounds always allows
2818 * for an integer value of the given div.
2819 * The lower bound is inequality l, while the upper bound is inequality u.
2820 * The constructed inequality is stored in ineq.
2821 * g, fl, fu are temporary scalars.
2823 * Let the upper bound be
2827 * and the lower bound
2831 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2834 * - f_u e_l <= f_u f_l g a <= f_l e_u
2836 * Since all variables are integer valued, this is equivalent to
2838 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2840 * If this interval is at least f_u f_l g, then it contains at least
2841 * one integer value for a.
2842 * That is, the test constraint is
2844 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2846 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2847 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2850 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2852 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2853 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2854 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2855 isl_int_neg(fu
, fu
);
2856 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2857 1 + dim
+ bmap
->n_div
);
2858 isl_int_add(ineq
[0], ineq
[0], fl
);
2859 isl_int_add(ineq
[0], ineq
[0], fu
);
2860 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2861 isl_int_mul(g
, g
, fl
);
2862 isl_int_mul(g
, g
, fu
);
2863 isl_int_sub(ineq
[0], ineq
[0], g
);
2866 /* Remove more kinds of divs that are not strictly needed.
2867 * In particular, if all pairs of lower and upper bounds on a div
2868 * are such that they allow at least one integer value of the div,
2869 * the we can eliminate the div using Fourier-Motzkin without
2870 * introducing any spurious solutions.
2872 static struct isl_basic_map
*drop_more_redundant_divs(
2873 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2875 struct isl_tab
*tab
= NULL
;
2876 struct isl_vec
*vec
= NULL
;
2888 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2889 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2893 tab
= isl_tab_from_basic_map(bmap
, 0);
2898 enum isl_lp_result res
;
2900 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2903 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2909 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2910 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2912 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2913 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2915 construct_test_ineq(bmap
, i
, l
, u
,
2916 vec
->el
, g
, fl
, fu
);
2917 res
= isl_tab_min(tab
, vec
->el
,
2918 bmap
->ctx
->one
, &g
, NULL
, 0);
2919 if (res
== isl_lp_error
)
2921 if (res
== isl_lp_empty
) {
2922 bmap
= isl_basic_map_set_to_empty(bmap
);
2925 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2928 if (u
< bmap
->n_ineq
)
2931 if (l
== bmap
->n_ineq
) {
2951 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
2952 return isl_basic_map_drop_redundant_divs(bmap
);
2955 isl_basic_map_free(bmap
);
2964 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2965 * and the upper bound u, div1 always occurs together with div2 in the form
2966 * (div1 + m div2), where m is the constant range on the variable div1
2967 * allowed by l and u, replace the pair div1 and div2 by a single
2968 * div that is equal to div1 + m div2.
2970 * The new div will appear in the location that contains div2.
2971 * We need to modify all constraints that contain
2972 * div2 = (div - div1) / m
2973 * (If a constraint does not contain div2, it will also not contain div1.)
2974 * If the constraint also contains div1, then we know they appear
2975 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2976 * i.e., the coefficient of div is f.
2978 * Otherwise, we first need to introduce div1 into the constraint.
2987 * A lower bound on div2
2991 * can be replaced by
2993 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2995 * with g = gcd(m,n).
3000 * can be replaced by
3002 * (-n * (m div2 + div1) + m t + n f')/g >= 0
3004 * These constraint are those that we would obtain from eliminating
3005 * div1 using Fourier-Motzkin.
3007 * After all constraints have been modified, we drop the lower and upper
3008 * bound and then drop div1.
3010 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
3011 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
3016 unsigned dim
, total
;
3019 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3020 total
= 1 + dim
+ bmap
->n_div
;
3025 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
3026 isl_int_add_ui(m
, m
, 1);
3028 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
3029 if (i
== l
|| i
== u
)
3031 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
3033 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
3034 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
3035 isl_int_divexact(a
, m
, b
);
3036 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
3037 if (isl_int_is_pos(b
)) {
3038 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
3039 b
, bmap
->ineq
[l
], total
);
3042 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
3043 b
, bmap
->ineq
[u
], total
);
3046 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
3047 bmap
->ineq
[i
][1 + dim
+ div1
]);
3048 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
3055 isl_basic_map_drop_inequality(bmap
, l
);
3056 isl_basic_map_drop_inequality(bmap
, u
);
3058 isl_basic_map_drop_inequality(bmap
, u
);
3059 isl_basic_map_drop_inequality(bmap
, l
);
3061 bmap
= isl_basic_map_drop_div(bmap
, div1
);
3065 /* First check if we can coalesce any pair of divs and
3066 * then continue with dropping more redundant divs.
3068 * We loop over all pairs of lower and upper bounds on a div
3069 * with coefficient 1 and -1, respectively, check if there
3070 * is any other div "c" with which we can coalesce the div
3071 * and if so, perform the coalescing.
3073 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
3074 struct isl_basic_map
*bmap
, int *pairs
, int n
)
3079 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3081 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3084 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
3085 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
3087 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
3090 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
3092 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
3096 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
3097 return isl_basic_map_drop_redundant_divs(bmap
);
3102 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
3105 return drop_more_redundant_divs(bmap
, pairs
, n
);
3108 /* Remove divs that are not strictly needed.
3109 * In particular, if a div only occurs positively (or negatively)
3110 * in constraints, then it can simply be dropped.
3111 * Also, if a div occurs in only two constraints and if moreover
3112 * those two constraints are opposite to each other, except for the constant
3113 * term and if the sum of the constant terms is such that for any value
3114 * of the other values, there is always at least one integer value of the
3115 * div, i.e., if one plus this sum is greater than or equal to
3116 * the (absolute value) of the coefficent of the div in the constraints,
3117 * then we can also simply drop the div.
3119 * We skip divs that appear in equalities or in the definition of other divs.
3120 * Divs that appear in the definition of other divs usually occur in at least
3121 * 4 constraints, but the constraints may have been simplified.
3123 * If any divs are left after these simple checks then we move on
3124 * to more complicated cases in drop_more_redundant_divs.
3126 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
3127 struct isl_basic_map
*bmap
)
3136 if (bmap
->n_div
== 0)
3139 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3140 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
3144 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3146 int last_pos
, last_neg
;
3150 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
3151 for (j
= i
; j
< bmap
->n_div
; ++j
)
3152 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
3154 if (j
< bmap
->n_div
)
3156 for (j
= 0; j
< bmap
->n_eq
; ++j
)
3157 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
3163 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
3164 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
3168 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
3173 pairs
[i
] = pos
* neg
;
3174 if (pairs
[i
] == 0) {
3175 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
3176 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
3177 isl_basic_map_drop_inequality(bmap
, j
);
3178 bmap
= isl_basic_map_drop_div(bmap
, i
);
3180 return isl_basic_map_drop_redundant_divs(bmap
);
3184 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
3185 bmap
->ineq
[last_neg
] + 1,
3189 isl_int_add(bmap
->ineq
[last_pos
][0],
3190 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3191 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
3192 bmap
->ineq
[last_pos
][0], 1);
3193 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
3194 bmap
->ineq
[last_pos
][1+off
+i
]);
3195 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
3196 bmap
->ineq
[last_pos
][0], 1);
3197 isl_int_sub(bmap
->ineq
[last_pos
][0],
3198 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3201 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
3206 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
3207 bmap
= isl_basic_map_simplify(bmap
);
3209 return isl_basic_map_drop_redundant_divs(bmap
);
3211 if (last_pos
> last_neg
) {
3212 isl_basic_map_drop_inequality(bmap
, last_pos
);
3213 isl_basic_map_drop_inequality(bmap
, last_neg
);
3215 isl_basic_map_drop_inequality(bmap
, last_neg
);
3216 isl_basic_map_drop_inequality(bmap
, last_pos
);
3218 bmap
= isl_basic_map_drop_div(bmap
, i
);
3220 return isl_basic_map_drop_redundant_divs(bmap
);
3224 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
3230 isl_basic_map_free(bmap
);
3234 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
3235 struct isl_basic_set
*bset
)
3237 return (struct isl_basic_set
*)
3238 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
3241 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
3247 for (i
= 0; i
< map
->n
; ++i
) {
3248 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
3252 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3259 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
3261 return (struct isl_set
*)
3262 isl_map_drop_redundant_divs((struct isl_map
*)set
);