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 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
739 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
740 bits
= ffs(size
) - 1;
741 index
= isl_calloc_array(ctx
, int, size
);
744 eq
= isl_blk_alloc(ctx
, 1+total
);
745 if (isl_blk_is_error(eq
))
748 isl_seq_clr(eq
.data
, 1+total
);
749 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
750 for (--k
; k
>= 0; --k
) {
753 if (isl_int_is_zero(bmap
->div
[k
][0]))
756 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
757 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
758 if (isl_seq_eq(bmap
->div
[k
],
759 bmap
->div
[index
[h
]-1], 2+total
))
768 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
772 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
773 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
774 eliminate_div(bmap
, eq
.data
, l
, 1);
775 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
776 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
779 isl_blk_free(ctx
, eq
);
786 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
791 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
792 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
793 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
797 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
803 /* Normalize divs that appear in equalities.
805 * In particular, we assume that bmap contains some equalities
810 * and we want to replace the set of e_i by a minimal set and
811 * such that the new e_i have a canonical representation in terms
813 * If any of the equalities involves more than one divs, then
814 * we currently simply bail out.
816 * Let us first additionally assume that all equalities involve
817 * a div. The equalities then express modulo constraints on the
818 * remaining variables and we can use "parameter compression"
819 * to find a minimal set of constraints. The result is a transformation
821 * x = T(x') = x_0 + G x'
823 * with G a lower-triangular matrix with all elements below the diagonal
824 * non-negative and smaller than the diagonal element on the same row.
825 * We first normalize x_0 by making the same property hold in the affine
827 * The rows i of G with a 1 on the diagonal do not impose any modulo
828 * constraint and simply express x_i = x'_i.
829 * For each of the remaining rows i, we introduce a div and a corresponding
830 * equality. In particular
832 * g_ii e_j = x_i - g_i(x')
834 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
835 * corresponding div (if g_kk != 1).
837 * If there are any equalities not involving any div, then we
838 * first apply a variable compression on the variables x:
840 * x = C x'' x'' = C_2 x
842 * and perform the above parameter compression on A C instead of on A.
843 * The resulting compression is then of the form
845 * x'' = T(x') = x_0 + G x'
847 * and in constructing the new divs and the corresponding equalities,
848 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
849 * by the corresponding row from C_2.
851 static struct isl_basic_map
*normalize_divs(
852 struct isl_basic_map
*bmap
, int *progress
)
859 struct isl_mat
*T
= NULL
;
860 struct isl_mat
*C
= NULL
;
861 struct isl_mat
*C2
= NULL
;
869 if (bmap
->n_div
== 0)
875 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
878 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
879 div_eq
= n_pure_div_eq(bmap
);
883 if (div_eq
< bmap
->n_eq
) {
884 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
885 bmap
->n_eq
- div_eq
, 0, 1 + total
);
886 C
= isl_mat_variable_compression(B
, &C2
);
890 bmap
= isl_basic_map_set_to_empty(bmap
);
897 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
900 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
901 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
903 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
905 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
908 B
= isl_mat_product(B
, C
);
912 T
= isl_mat_parameter_compression(B
, d
);
916 bmap
= isl_basic_map_set_to_empty(bmap
);
922 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
923 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
924 if (isl_int_is_zero(v
))
926 isl_mat_col_submul(T
, 0, v
, 1 + i
);
929 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
932 /* We have to be careful because dropping equalities may reorder them */
934 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
935 for (i
= 0; i
< bmap
->n_eq
; ++i
)
936 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
938 if (i
< bmap
->n_eq
) {
939 bmap
= isl_basic_map_drop_div(bmap
, j
);
940 isl_basic_map_drop_equality(bmap
, i
);
946 for (i
= 1; i
< T
->n_row
; ++i
) {
947 if (isl_int_is_one(T
->row
[i
][i
]))
952 if (needed
> dropped
) {
953 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
958 for (i
= 1; i
< T
->n_row
; ++i
) {
959 if (isl_int_is_one(T
->row
[i
][i
]))
961 k
= isl_basic_map_alloc_div(bmap
);
962 pos
[i
] = 1 + total
+ k
;
963 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
964 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
966 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
968 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
969 for (j
= 0; j
< i
; ++j
) {
970 if (isl_int_is_zero(T
->row
[i
][j
]))
972 if (pos
[j
] < T
->n_row
&& C2
)
973 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
974 C2
->row
[pos
[j
]], 1 + total
);
976 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
979 j
= isl_basic_map_alloc_equality(bmap
);
980 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
981 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
990 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
1000 static struct isl_basic_map
*set_div_from_lower_bound(
1001 struct isl_basic_map
*bmap
, int div
, int ineq
)
1003 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1005 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1006 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1007 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1008 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1009 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1014 /* Check whether it is ok to define a div based on an inequality.
1015 * To avoid the introduction of circular definitions of divs, we
1016 * do not allow such a definition if the resulting expression would refer to
1017 * any other undefined divs or if any known div is defined in
1018 * terms of the unknown div.
1020 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
1024 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1026 /* Not defined in terms of unknown divs */
1027 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1030 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1032 if (isl_int_is_zero(bmap
->div
[j
][0]))
1036 /* No other div defined in terms of this one => avoid loops */
1037 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1040 if (isl_int_is_zero(bmap
->div
[j
][0]))
1042 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1049 /* Would an expression for div "div" based on inequality "ineq" of "bmap"
1050 * be a better expression than the current one?
1052 * If we do not have any expression yet, then any expression would be better.
1053 * Otherwise we check if the last variable involved in the inequality
1054 * (disregarding the div that it would define) is in an earlier position
1055 * than the last variable involved in the current div expression.
1057 static int better_div_constraint(__isl_keep isl_basic_map
*bmap
,
1060 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1064 if (isl_int_is_zero(bmap
->div
[div
][0]))
1067 if (isl_seq_last_non_zero(bmap
->ineq
[ineq
] + total
+ div
+ 1,
1068 bmap
->n_div
- (div
+ 1)) >= 0)
1071 last_ineq
= isl_seq_last_non_zero(bmap
->ineq
[ineq
], total
+ div
);
1072 last_div
= isl_seq_last_non_zero(bmap
->div
[div
] + 1,
1073 total
+ bmap
->n_div
);
1075 return last_ineq
< last_div
;
1078 /* Given two constraints "k" and "l" that are opposite to each other,
1079 * except for the constant term, check if we can use them
1080 * to obtain an expression for one of the hitherto unknown divs or
1081 * a "better" expression for a div for which we already have an expression.
1082 * "sum" is the sum of the constant terms of the constraints.
1083 * If this sum is strictly smaller than the coefficient of one
1084 * of the divs, then this pair can be used define the div.
1085 * To avoid the introduction of circular definitions of divs, we
1086 * do not use the pair if the resulting expression would refer to
1087 * any other undefined divs or if any known div is defined in
1088 * terms of the unknown div.
1090 static struct isl_basic_map
*check_for_div_constraints(
1091 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
1094 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1096 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1097 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1099 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1101 if (!better_div_constraint(bmap
, i
, k
))
1103 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1105 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1106 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1108 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1116 __isl_give isl_basic_map
*isl_basic_map_remove_duplicate_constraints(
1117 __isl_take isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1123 unsigned total
= isl_basic_map_total_dim(bmap
);
1127 if (!bmap
|| bmap
->n_ineq
<= 1)
1130 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
1131 bits
= ffs(size
) - 1;
1132 ctx
= isl_basic_map_get_ctx(bmap
);
1133 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1137 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
1138 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1139 h
= hash_index(index
, size
, bits
, bmap
, k
);
1141 index
[h
] = &bmap
->ineq
[k
];
1146 l
= index
[h
] - &bmap
->ineq
[0];
1147 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1148 swap_inequality(bmap
, k
, l
);
1149 isl_basic_map_drop_inequality(bmap
, k
);
1153 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1154 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1155 h
= hash_index(index
, size
, bits
, bmap
, k
);
1156 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1159 l
= index
[h
] - &bmap
->ineq
[0];
1160 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1161 if (isl_int_is_pos(sum
)) {
1163 bmap
= check_for_div_constraints(bmap
, k
, l
,
1167 if (isl_int_is_zero(sum
)) {
1168 /* We need to break out of the loop after these
1169 * changes since the contents of the hash
1170 * will no longer be valid.
1171 * Plus, we probably we want to regauss first.
1175 isl_basic_map_drop_inequality(bmap
, l
);
1176 isl_basic_map_inequality_to_equality(bmap
, k
);
1178 bmap
= isl_basic_map_set_to_empty(bmap
);
1188 /* Eliminate knowns divs from constraints where they appear with
1189 * a (positive or negative) unit coefficient.
1193 * floor(e/m) + f >= 0
1201 * -floor(e/m) + f >= 0
1205 * -e + m f + m - 1 >= 0
1207 * The first conversion is valid because floor(e/m) >= -f is equivalent
1208 * to e/m >= -f because -f is an integral expression.
1209 * The second conversion follows from the fact that
1211 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1214 * Note that one of the div constraints may have been eliminated
1215 * due to being redundant with respect to the constraint that is
1216 * being modified by this function. The modified constraint may
1217 * no longer imply this div constraint, so we add it back to make
1218 * sure we do not lose any information.
1220 * We skip integral divs, i.e., those with denominator 1, as we would
1221 * risk eliminating the div from the div constraints. We do not need
1222 * to handle those divs here anyway since the div constraints will turn
1223 * out to form an equality and this equality can then be use to eliminate
1224 * the div from all constraints.
1226 static __isl_give isl_basic_map
*eliminate_unit_divs(
1227 __isl_take isl_basic_map
*bmap
, int *progress
)
1236 ctx
= isl_basic_map_get_ctx(bmap
);
1237 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1239 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1240 if (isl_int_is_zero(bmap
->div
[i
][0]))
1242 if (isl_int_is_one(bmap
->div
[i
][0]))
1244 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1247 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1248 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1253 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1254 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1256 isl_seq_combine(bmap
->ineq
[j
],
1257 ctx
->negone
, bmap
->div
[i
] + 1,
1258 bmap
->div
[i
][0], bmap
->ineq
[j
],
1259 total
+ bmap
->n_div
);
1261 isl_seq_combine(bmap
->ineq
[j
],
1262 ctx
->one
, bmap
->div
[i
] + 1,
1263 bmap
->div
[i
][0], bmap
->ineq
[j
],
1264 total
+ bmap
->n_div
);
1266 isl_int_add(bmap
->ineq
[j
][0],
1267 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1268 isl_int_sub_ui(bmap
->ineq
[j
][0],
1269 bmap
->ineq
[j
][0], 1);
1272 bmap
= isl_basic_map_extend_constraints(bmap
, 0, 1);
1273 if (isl_basic_map_add_div_constraint(bmap
, i
, s
) < 0)
1274 return isl_basic_map_free(bmap
);
1281 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1290 if (isl_basic_map_plain_is_empty(bmap
))
1292 bmap
= isl_basic_map_normalize_constraints(bmap
);
1293 bmap
= normalize_div_expressions(bmap
);
1294 bmap
= remove_duplicate_divs(bmap
, &progress
);
1295 bmap
= eliminate_unit_divs(bmap
, &progress
);
1296 bmap
= eliminate_divs_eq(bmap
, &progress
);
1297 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1298 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1299 /* requires equalities in normal form */
1300 bmap
= normalize_divs(bmap
, &progress
);
1301 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1307 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1309 return (struct isl_basic_set
*)
1310 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1314 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1315 isl_int
*constraint
, unsigned div
)
1322 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1324 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1326 isl_int_sub(bmap
->div
[div
][1],
1327 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1328 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1329 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1330 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1331 isl_int_add(bmap
->div
[div
][1],
1332 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1335 if (isl_seq_first_non_zero(constraint
+pos
+1,
1336 bmap
->n_div
-div
-1) != -1)
1338 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1339 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1341 if (isl_seq_first_non_zero(constraint
+pos
+1,
1342 bmap
->n_div
-div
-1) != -1)
1350 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1351 isl_int
*constraint
, unsigned div
)
1353 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1357 /* If the only constraints a div d=floor(f/m)
1358 * appears in are its two defining constraints
1361 * -(f - (m - 1)) + m d >= 0
1363 * then it can safely be removed.
1365 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1368 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1370 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1371 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1374 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1375 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1377 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1381 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1382 if (isl_int_is_zero(bmap
->div
[i
][0]))
1384 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1392 * Remove divs that don't occur in any of the constraints or other divs.
1393 * These can arise when dropping constraints from a basic map or
1394 * when the divs of a basic map have been temporarily aligned
1395 * with the divs of another basic map.
1397 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1404 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1405 if (!div_is_redundant(bmap
, i
))
1407 bmap
= isl_basic_map_drop_div(bmap
, i
);
1412 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1414 bmap
= remove_redundant_divs(bmap
);
1417 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1421 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1423 return (struct isl_basic_set
*)
1424 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1427 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1433 for (i
= 0; i
< set
->n
; ++i
) {
1434 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1444 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1450 for (i
= 0; i
< map
->n
; ++i
) {
1451 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1455 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1463 /* Remove definition of any div that is defined in terms of the given variable.
1464 * The div itself is not removed. Functions such as
1465 * eliminate_divs_ineq depend on the other divs remaining in place.
1467 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1475 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1476 if (isl_int_is_zero(bmap
->div
[i
][0]))
1478 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1480 isl_int_set_si(bmap
->div
[i
][0], 0);
1485 /* Eliminate the specified variables from the constraints using
1486 * Fourier-Motzkin. The variables themselves are not removed.
1488 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1489 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1500 total
= isl_basic_map_total_dim(bmap
);
1502 bmap
= isl_basic_map_cow(bmap
);
1503 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1504 bmap
= remove_dependent_vars(bmap
, d
);
1508 for (d
= pos
+ n
- 1;
1509 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1510 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1511 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1512 int n_lower
, n_upper
;
1515 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1516 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1518 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1519 isl_basic_map_drop_equality(bmap
, i
);
1527 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1528 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1530 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1533 bmap
= isl_basic_map_extend_constraints(bmap
,
1534 0, n_lower
* n_upper
);
1537 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1539 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1542 for (j
= 0; j
< i
; ++j
) {
1543 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1546 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1547 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1549 k
= isl_basic_map_alloc_inequality(bmap
);
1552 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1554 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1555 1+d
, 1+total
, NULL
);
1557 isl_basic_map_drop_inequality(bmap
, i
);
1560 if (n_lower
> 0 && n_upper
> 0) {
1561 bmap
= isl_basic_map_normalize_constraints(bmap
);
1562 bmap
= isl_basic_map_remove_duplicate_constraints(bmap
,
1564 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1565 bmap
= isl_basic_map_remove_redundancies(bmap
);
1569 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1573 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1575 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1578 isl_basic_map_free(bmap
);
1582 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1583 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1585 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1586 (struct isl_basic_map
*)bset
, pos
, n
);
1589 /* Eliminate the specified n dimensions starting at first from the
1590 * constraints, without removing the dimensions from the space.
1591 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1592 * Otherwise, they are projected out and the original space is restored.
1594 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1595 __isl_take isl_basic_map
*bmap
,
1596 enum isl_dim_type type
, unsigned first
, unsigned n
)
1605 if (first
+ n
> isl_basic_map_dim(bmap
, type
) || first
+ n
< first
)
1606 isl_die(bmap
->ctx
, isl_error_invalid
,
1607 "index out of bounds", goto error
);
1609 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1610 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1611 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1612 return isl_basic_map_finalize(bmap
);
1615 space
= isl_basic_map_get_space(bmap
);
1616 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1617 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1618 bmap
= isl_basic_map_reset_space(bmap
, space
);
1621 isl_basic_map_free(bmap
);
1625 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1626 __isl_take isl_basic_set
*bset
,
1627 enum isl_dim_type type
, unsigned first
, unsigned n
)
1629 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1632 /* Don't assume equalities are in order, because align_divs
1633 * may have changed the order of the divs.
1635 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1640 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1641 for (d
= 0; d
< total
; ++d
)
1643 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1644 for (d
= total
- 1; d
>= 0; --d
) {
1645 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1653 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1655 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1658 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1659 struct isl_basic_map
*bmap
, int *elim
)
1665 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1666 for (d
= total
- 1; d
>= 0; --d
) {
1667 if (isl_int_is_zero(src
[1+d
]))
1672 isl_seq_cpy(dst
, src
, 1 + total
);
1675 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1680 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1681 struct isl_basic_set
*bset
, int *elim
)
1683 return reduced_using_equalities(dst
, src
,
1684 (struct isl_basic_map
*)bset
, elim
);
1687 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1688 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1693 if (!bset
|| !context
)
1696 if (context
->n_eq
== 0) {
1697 isl_basic_set_free(context
);
1701 bset
= isl_basic_set_cow(bset
);
1705 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1708 set_compute_elimination_index(context
, elim
);
1709 for (i
= 0; i
< bset
->n_eq
; ++i
)
1710 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1712 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1713 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1715 isl_basic_set_free(context
);
1717 bset
= isl_basic_set_simplify(bset
);
1718 bset
= isl_basic_set_finalize(bset
);
1721 isl_basic_set_free(bset
);
1722 isl_basic_set_free(context
);
1726 static struct isl_basic_set
*remove_shifted_constraints(
1727 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1738 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1739 bits
= ffs(size
) - 1;
1740 ctx
= isl_basic_set_get_ctx(bset
);
1741 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1745 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1746 h
= set_hash_index(index
, size
, bits
, context
, k
);
1747 index
[h
] = &context
->ineq
[k
];
1749 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1750 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1753 l
= index
[h
] - &context
->ineq
[0];
1754 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1756 bset
= isl_basic_set_cow(bset
);
1759 isl_basic_set_drop_inequality(bset
, k
);
1769 /* Does the (linear part of a) constraint "c" involve any of the "len"
1770 * "relevant" dimensions?
1772 static int is_related(isl_int
*c
, int len
, int *relevant
)
1776 for (i
= 0; i
< len
; ++i
) {
1779 if (!isl_int_is_zero(c
[i
]))
1786 /* Drop constraints from "bset" that do not involve any of
1787 * the dimensions marked "relevant".
1789 static __isl_give isl_basic_set
*drop_unrelated_constraints(
1790 __isl_take isl_basic_set
*bset
, int *relevant
)
1794 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1795 for (i
= 0; i
< dim
; ++i
)
1801 for (i
= bset
->n_eq
- 1; i
>= 0; --i
)
1802 if (!is_related(bset
->eq
[i
] + 1, dim
, relevant
))
1803 isl_basic_set_drop_equality(bset
, i
);
1805 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
)
1806 if (!is_related(bset
->ineq
[i
] + 1, dim
, relevant
))
1807 isl_basic_set_drop_inequality(bset
, i
);
1812 /* Update the groups in "group" based on the (linear part of a) constraint "c".
1814 * In particular, for any variable involved in the constraint,
1815 * find the actual group id from before and replace the group
1816 * of the corresponding variable by the minimal group of all
1817 * the variables involved in the constraint considered so far
1818 * (if this minimum is smaller) or replace the minimum by this group
1819 * (if the minimum is larger).
1821 * At the end, all the variables in "c" will (indirectly) point
1822 * to the minimal of the groups that they referred to originally.
1824 static void update_groups(int dim
, int *group
, isl_int
*c
)
1829 for (j
= 0; j
< dim
; ++j
) {
1830 if (isl_int_is_zero(c
[j
]))
1832 while (group
[j
] >= 0 && group
[group
[j
]] != group
[j
])
1833 group
[j
] = group
[group
[j
]];
1834 if (group
[j
] == min
)
1836 if (group
[j
] < min
) {
1837 if (min
>= 0 && min
< dim
)
1838 group
[min
] = group
[j
];
1841 group
[group
[j
]] = min
;
1845 /* Drop constraints from "context" that are irrelevant for computing
1846 * the gist of "bset".
1848 * In particular, drop constraints in variables that are not related
1849 * to any of the variables involved in the constraints of "bset"
1850 * in the sense that there is no sequence of constraints that connects them.
1852 * We construct groups of variables that collect variables that
1853 * (indirectly) appear in some common constraint of "context".
1854 * Each group is identified by the first variable in the group,
1855 * except for the special group of variables that appear in "bset"
1856 * (or are related to those variables), which is identified by -1.
1857 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
1858 * otherwise the group of i is the group of group[i].
1860 * We first initialize the -1 group with the variables that appear in "bset".
1861 * Then we initialize groups for the remaining variables.
1862 * Then we iterate over the constraints of "context" and update the
1863 * group of the variables in the constraint by the smallest group.
1864 * Finally, we resolve indirect references to groups by running over
1867 * After computing the groups, we drop constraints that do not involve
1868 * any variables in the -1 group.
1870 static __isl_give isl_basic_set
*drop_irrelevant_constraints(
1871 __isl_take isl_basic_set
*context
, __isl_keep isl_basic_set
*bset
)
1879 if (!context
|| !bset
)
1880 return isl_basic_set_free(context
);
1882 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
1883 ctx
= isl_basic_set_get_ctx(bset
);
1884 group
= isl_calloc_array(ctx
, int, dim
);
1889 for (i
= 0; i
< dim
; ++i
) {
1890 for (j
= 0; j
< bset
->n_eq
; ++j
)
1891 if (!isl_int_is_zero(bset
->eq
[j
][1 + i
]))
1893 if (j
< bset
->n_eq
) {
1897 for (j
= 0; j
< bset
->n_ineq
; ++j
)
1898 if (!isl_int_is_zero(bset
->ineq
[j
][1 + i
]))
1900 if (j
< bset
->n_ineq
)
1905 for (i
= 0; i
< dim
; ++i
)
1907 last
= group
[i
] = i
;
1913 for (i
= 0; i
< context
->n_eq
; ++i
)
1914 update_groups(dim
, group
, context
->eq
[i
] + 1);
1915 for (i
= 0; i
< context
->n_ineq
; ++i
)
1916 update_groups(dim
, group
, context
->ineq
[i
] + 1);
1918 for (i
= 0; i
< dim
; ++i
)
1920 group
[i
] = group
[group
[i
]];
1922 for (i
= 0; i
< dim
; ++i
)
1923 group
[i
] = group
[i
] == -1;
1925 context
= drop_unrelated_constraints(context
, group
);
1931 return isl_basic_set_free(context
);
1934 /* Remove all information from bset that is redundant in the context
1935 * of context. Both bset and context are assumed to be full-dimensional.
1937 * We first remove the inequalities from "bset"
1938 * that are obviously redundant with respect to some inequality in "context".
1939 * Then we remove those constraints from "context" that have become
1940 * irrelevant for computing the gist of "bset".
1941 * Note that this removal of constraints cannot be replaced by
1942 * a factorization because factors in "bset" may still be connected
1943 * to each other through constraints in "context".
1945 * If there are any inequalities left, we construct a tableau for
1946 * the context and then add the inequalities of "bset".
1947 * Before adding these inequalities, we freeze all constraints such that
1948 * they won't be considered redundant in terms of the constraints of "bset".
1949 * Then we detect all redundant constraints (among the
1950 * constraints that weren't frozen), first by checking for redundancy in the
1951 * the tableau and then by checking if replacing a constraint by its negation
1952 * would lead to an empty set. This last step is fairly expensive
1953 * and could be optimized by more reuse of the tableau.
1954 * Finally, we update bset according to the results.
1956 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1957 __isl_take isl_basic_set
*context
)
1960 isl_basic_set
*combined
= NULL
;
1961 struct isl_tab
*tab
= NULL
;
1962 unsigned context_ineq
;
1965 if (!bset
|| !context
)
1968 if (isl_basic_set_is_universe(bset
)) {
1969 isl_basic_set_free(context
);
1973 if (isl_basic_set_is_universe(context
)) {
1974 isl_basic_set_free(context
);
1978 bset
= remove_shifted_constraints(bset
, context
);
1981 if (bset
->n_ineq
== 0)
1984 context
= drop_irrelevant_constraints(context
, bset
);
1987 if (isl_basic_set_is_universe(context
)) {
1988 isl_basic_set_free(context
);
1992 context_ineq
= context
->n_ineq
;
1993 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1994 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
1995 tab
= isl_tab_from_basic_set(combined
, 0);
1996 for (i
= 0; i
< context_ineq
; ++i
)
1997 if (isl_tab_freeze_constraint(tab
, i
) < 0)
1999 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
2001 for (i
= 0; i
< bset
->n_ineq
; ++i
)
2002 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
2004 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
2008 if (isl_tab_detect_redundant(tab
) < 0)
2010 total
= isl_basic_set_total_dim(bset
);
2011 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
2013 if (tab
->con
[i
].is_redundant
)
2015 tab
->con
[i
].is_redundant
= 1;
2016 combined
= isl_basic_set_dup(bset
);
2017 combined
= isl_basic_set_update_from_tab(combined
, tab
);
2018 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
2019 k
= isl_basic_set_alloc_inequality(combined
);
2022 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
2023 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
2024 is_empty
= isl_basic_set_is_empty(combined
);
2027 isl_basic_set_free(combined
);
2030 tab
->con
[i
].is_redundant
= 0;
2032 for (i
= 0; i
< context_ineq
; ++i
)
2033 tab
->con
[i
].is_redundant
= 1;
2034 bset
= isl_basic_set_update_from_tab(bset
, tab
);
2036 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2037 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2042 bset
= isl_basic_set_simplify(bset
);
2043 bset
= isl_basic_set_finalize(bset
);
2044 isl_basic_set_free(context
);
2048 isl_basic_set_free(combined
);
2049 isl_basic_set_free(context
);
2050 isl_basic_set_free(bset
);
2054 /* Remove all information from bset that is redundant in the context
2055 * of context. In particular, equalities that are linear combinations
2056 * of those in context are removed. Then the inequalities that are
2057 * redundant in the context of the equalities and inequalities of
2058 * context are removed.
2060 * First of all, we drop those constraints from "context"
2061 * that are irrelevant for computing the gist of "bset".
2062 * Alternatively, we could factorize the intersection of "context" and "bset".
2064 * We first compute the integer affine hull of the intersection,
2065 * compute the gist inside this affine hull and then add back
2066 * those equalities that are not implied by the context.
2068 * If two constraints are mutually redundant, then uset_gist_full
2069 * will remove the second of those constraints. We therefore first
2070 * sort the constraints so that constraints not involving existentially
2071 * quantified variables are given precedence over those that do.
2072 * We have to perform this sorting before the variable compression,
2073 * because that may effect the order of the variables.
2075 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
2076 __isl_take isl_basic_set
*context
)
2081 isl_basic_set
*aff_context
;
2084 if (!bset
|| !context
)
2087 context
= drop_irrelevant_constraints(context
, bset
);
2089 aff
= isl_basic_set_copy(bset
);
2090 aff
= isl_basic_set_intersect(aff
, isl_basic_set_copy(context
));
2091 aff
= isl_basic_set_affine_hull(aff
);
2094 if (isl_basic_set_plain_is_empty(aff
)) {
2095 isl_basic_set_free(bset
);
2096 isl_basic_set_free(context
);
2099 bset
= isl_basic_set_sort_constraints(bset
);
2100 if (aff
->n_eq
== 0) {
2101 isl_basic_set_free(aff
);
2102 return uset_gist_full(bset
, context
);
2104 total
= isl_basic_set_total_dim(bset
);
2105 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
2106 eq
= isl_mat_cow(eq
);
2107 T
= isl_mat_variable_compression(eq
, &T2
);
2108 if (T
&& T
->n_col
== 0) {
2111 isl_basic_set_free(context
);
2112 isl_basic_set_free(aff
);
2113 return isl_basic_set_set_to_empty(bset
);
2116 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
2118 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
2119 context
= isl_basic_set_preimage(context
, T
);
2121 bset
= uset_gist_full(bset
, context
);
2122 bset
= isl_basic_set_preimage(bset
, T2
);
2123 bset
= isl_basic_set_intersect(bset
, aff
);
2124 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
2127 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
2128 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
2133 isl_basic_set_free(bset
);
2134 isl_basic_set_free(context
);
2138 /* Normalize the divs in "bmap" in the context of the equalities in "context".
2139 * We simply add the equalities in context to bmap and then do a regular
2140 * div normalizations. Better results can be obtained by normalizing
2141 * only the divs in bmap than do not also appear in context.
2142 * We need to be careful to reduce the divs using the equalities
2143 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
2144 * spurious constraints.
2146 static struct isl_basic_map
*normalize_divs_in_context(
2147 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
2150 unsigned total_context
;
2153 div_eq
= n_pure_div_eq(bmap
);
2157 if (context
->n_div
> 0)
2158 bmap
= isl_basic_map_align_divs(bmap
, context
);
2160 total_context
= isl_basic_map_total_dim(context
);
2161 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
2162 for (i
= 0; i
< context
->n_eq
; ++i
) {
2164 k
= isl_basic_map_alloc_equality(bmap
);
2166 return isl_basic_map_free(bmap
);
2167 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
2168 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
2169 isl_basic_map_total_dim(bmap
) - total_context
);
2171 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2172 bmap
= normalize_divs(bmap
, NULL
);
2173 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2177 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
2178 struct isl_basic_map
*context
)
2180 struct isl_basic_set
*bset
;
2182 if (!bmap
|| !context
)
2185 if (isl_basic_map_is_universe(bmap
)) {
2186 isl_basic_map_free(context
);
2189 if (isl_basic_map_plain_is_empty(context
)) {
2190 isl_basic_map_free(bmap
);
2193 if (isl_basic_map_plain_is_empty(bmap
)) {
2194 isl_basic_map_free(context
);
2198 bmap
= isl_basic_map_remove_redundancies(bmap
);
2199 context
= isl_basic_map_remove_redundancies(context
);
2204 bmap
= normalize_divs_in_context(bmap
, context
);
2206 context
= isl_basic_map_align_divs(context
, bmap
);
2207 bmap
= isl_basic_map_align_divs(bmap
, context
);
2209 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
2210 isl_basic_map_underlying_set(context
));
2212 return isl_basic_map_overlying_set(bset
, bmap
);
2214 isl_basic_map_free(bmap
);
2215 isl_basic_map_free(context
);
2220 * Assumes context has no implicit divs.
2222 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
2223 __isl_take isl_basic_map
*context
)
2227 if (!map
|| !context
)
2230 if (isl_basic_map_plain_is_empty(context
)) {
2232 return isl_map_from_basic_map(context
);
2235 context
= isl_basic_map_remove_redundancies(context
);
2236 map
= isl_map_cow(map
);
2237 if (!map
|| !context
)
2239 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
2240 map
= isl_map_compute_divs(map
);
2243 for (i
= map
->n
- 1; i
>= 0; --i
) {
2244 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
2245 isl_basic_map_copy(context
));
2248 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
2249 isl_basic_map_free(map
->p
[i
]);
2250 if (i
!= map
->n
- 1)
2251 map
->p
[i
] = map
->p
[map
->n
- 1];
2255 isl_basic_map_free(context
);
2256 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2260 isl_basic_map_free(context
);
2264 /* Return a map that has the same intersection with "context" as "map"
2265 * and that is as "simple" as possible.
2267 * If "map" is already the universe, then we cannot make it any simpler.
2268 * Similarly, if "context" is the universe, then we cannot exploit it
2270 * If "map" and "context" are identical to each other, then we can
2271 * return the corresponding universe.
2273 * If none of these cases apply, we have to work a bit harder.
2275 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
2276 __isl_take isl_map
*context
)
2281 is_universe
= isl_map_plain_is_universe(map
);
2282 if (is_universe
>= 0 && !is_universe
)
2283 is_universe
= isl_map_plain_is_universe(context
);
2284 if (is_universe
< 0)
2287 isl_map_free(context
);
2291 equal
= isl_map_plain_is_equal(map
, context
);
2295 isl_map
*res
= isl_map_universe(isl_map_get_space(map
));
2297 isl_map_free(context
);
2301 context
= isl_map_compute_divs(context
);
2302 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
2305 isl_map_free(context
);
2309 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
2310 __isl_take isl_map
*context
)
2312 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2315 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2316 struct isl_basic_set
*context
)
2318 return (struct isl_basic_set
*)isl_basic_map_gist(
2319 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2322 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2323 __isl_take isl_basic_set
*context
)
2325 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2326 (struct isl_basic_map
*)context
);
2329 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2330 __isl_take isl_basic_set
*context
)
2332 isl_space
*space
= isl_set_get_space(set
);
2333 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2334 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2335 return isl_set_gist_basic_set(set
, dom_context
);
2338 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2339 __isl_take isl_set
*context
)
2341 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2342 (struct isl_map
*)context
);
2345 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2346 __isl_take isl_set
*context
)
2348 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2349 map_context
= isl_map_intersect_domain(map_context
, context
);
2350 return isl_map_gist(map
, map_context
);
2353 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2354 __isl_take isl_set
*context
)
2356 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2357 map_context
= isl_map_intersect_range(map_context
, context
);
2358 return isl_map_gist(map
, map_context
);
2361 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2362 __isl_take isl_set
*context
)
2364 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2365 map_context
= isl_map_intersect_params(map_context
, context
);
2366 return isl_map_gist(map
, map_context
);
2369 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2370 __isl_take isl_set
*context
)
2372 return isl_map_gist_params(set
, context
);
2375 /* Quick check to see if two basic maps are disjoint.
2376 * In particular, we reduce the equalities and inequalities of
2377 * one basic map in the context of the equalities of the other
2378 * basic map and check if we get a contradiction.
2380 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2381 __isl_keep isl_basic_map
*bmap2
)
2383 struct isl_vec
*v
= NULL
;
2388 if (!bmap1
|| !bmap2
)
2390 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
2392 if (bmap1
->n_div
|| bmap2
->n_div
)
2394 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
2397 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
2400 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
2403 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
2406 compute_elimination_index(bmap1
, elim
);
2407 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
2409 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
2411 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
2412 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2415 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
2417 reduced
= reduced_using_equalities(v
->block
.data
,
2418 bmap2
->ineq
[i
], bmap1
, elim
);
2419 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2420 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2423 compute_elimination_index(bmap2
, elim
);
2424 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
2426 reduced
= reduced_using_equalities(v
->block
.data
,
2427 bmap1
->ineq
[i
], bmap2
, elim
);
2428 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2429 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2445 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2446 __isl_keep isl_basic_set
*bset2
)
2448 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
2449 (struct isl_basic_map
*)bset2
);
2452 /* Are "map1" and "map2" obviously disjoint?
2454 * If they have different parameters, then we skip any further tests.
2455 * In particular, the outcome of the subsequent calls to
2456 * isl_space_tuple_match may be affected by the different parameters
2459 * If one of them is empty or if they live in different spaces (assuming
2460 * they have the same parameters), then they are clearly disjoint.
2462 * If they are obviously equal, but not obviously empty, then we will
2463 * not be able to detect if they are disjoint.
2465 * Otherwise we check if each basic map in "map1" is obviously disjoint
2466 * from each basic map in "map2".
2468 int isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
2469 __isl_keep isl_map
*map2
)
2479 disjoint
= isl_map_plain_is_empty(map1
);
2480 if (disjoint
< 0 || disjoint
)
2483 disjoint
= isl_map_plain_is_empty(map2
);
2484 if (disjoint
< 0 || disjoint
)
2487 match
= isl_space_match(map1
->dim
, isl_dim_param
,
2488 map2
->dim
, isl_dim_param
);
2489 if (match
< 0 || !match
)
2490 return match
< 0 ? -1 : 0;
2492 match
= isl_space_tuple_match(map1
->dim
, isl_dim_in
,
2493 map2
->dim
, isl_dim_in
);
2494 if (match
< 0 || !match
)
2495 return match
< 0 ? -1 : 1;
2497 match
= isl_space_tuple_match(map1
->dim
, isl_dim_out
,
2498 map2
->dim
, isl_dim_out
);
2499 if (match
< 0 || !match
)
2500 return match
< 0 ? -1 : 1;
2502 intersect
= isl_map_plain_is_equal(map1
, map2
);
2503 if (intersect
< 0 || intersect
)
2504 return intersect
< 0 ? -1 : 0;
2506 for (i
= 0; i
< map1
->n
; ++i
) {
2507 for (j
= 0; j
< map2
->n
; ++j
) {
2508 int d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
2517 /* Are "map1" and "map2" disjoint?
2519 * They are disjoint if they are "obviously disjoint" or if one of them
2520 * is empty. Otherwise, they are not disjoint if one of them is universal.
2521 * If none of these cases apply, we compute the intersection and see if
2522 * the result is empty.
2524 int isl_map_is_disjoint(__isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
2530 disjoint
= isl_map_plain_is_disjoint(map1
, map2
);
2531 if (disjoint
< 0 || disjoint
)
2534 disjoint
= isl_map_is_empty(map1
);
2535 if (disjoint
< 0 || disjoint
)
2538 disjoint
= isl_map_is_empty(map2
);
2539 if (disjoint
< 0 || disjoint
)
2542 intersect
= isl_map_plain_is_universe(map1
);
2543 if (intersect
< 0 || intersect
)
2544 return intersect
< 0 ? -1 : 0;
2546 intersect
= isl_map_plain_is_universe(map2
);
2547 if (intersect
< 0 || intersect
)
2548 return intersect
< 0 ? -1 : 0;
2550 test
= isl_map_intersect(isl_map_copy(map1
), isl_map_copy(map2
));
2551 disjoint
= isl_map_is_empty(test
);
2557 /* Are "bmap1" and "bmap2" disjoint?
2559 * They are disjoint if they are "obviously disjoint" or if one of them
2560 * is empty. Otherwise, they are not disjoint if one of them is universal.
2561 * If none of these cases apply, we compute the intersection and see if
2562 * the result is empty.
2564 int isl_basic_map_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2565 __isl_keep isl_basic_map
*bmap2
)
2569 isl_basic_map
*test
;
2571 disjoint
= isl_basic_map_plain_is_disjoint(bmap1
, bmap2
);
2572 if (disjoint
< 0 || disjoint
)
2575 disjoint
= isl_basic_map_is_empty(bmap1
);
2576 if (disjoint
< 0 || disjoint
)
2579 disjoint
= isl_basic_map_is_empty(bmap2
);
2580 if (disjoint
< 0 || disjoint
)
2583 intersect
= isl_basic_map_is_universe(bmap1
);
2584 if (intersect
< 0 || intersect
)
2585 return intersect
< 0 ? -1 : 0;
2587 intersect
= isl_basic_map_is_universe(bmap2
);
2588 if (intersect
< 0 || intersect
)
2589 return intersect
< 0 ? -1 : 0;
2591 test
= isl_basic_map_intersect(isl_basic_map_copy(bmap1
),
2592 isl_basic_map_copy(bmap2
));
2593 disjoint
= isl_basic_map_is_empty(test
);
2594 isl_basic_map_free(test
);
2599 /* Are "bset1" and "bset2" disjoint?
2601 int isl_basic_set_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2602 __isl_keep isl_basic_set
*bset2
)
2604 return isl_basic_map_is_disjoint(bset1
, bset2
);
2607 int isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
2608 __isl_keep isl_set
*set2
)
2610 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
2611 (struct isl_map
*)set2
);
2614 /* Are "set1" and "set2" disjoint?
2616 int isl_set_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2618 return isl_map_is_disjoint(set1
, set2
);
2621 int isl_set_fast_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2623 return isl_set_plain_is_disjoint(set1
, set2
);
2626 /* Check if we can combine a given div with lower bound l and upper
2627 * bound u with some other div and if so return that other div.
2628 * Otherwise return -1.
2630 * We first check that
2631 * - the bounds are opposites of each other (except for the constant
2633 * - the bounds do not reference any other div
2634 * - no div is defined in terms of this div
2636 * Let m be the size of the range allowed on the div by the bounds.
2637 * That is, the bounds are of the form
2639 * e <= a <= e + m - 1
2641 * with e some expression in the other variables.
2642 * We look for another div b such that no third div is defined in terms
2643 * of this second div b and such that in any constraint that contains
2644 * a (except for the given lower and upper bound), also contains b
2645 * with a coefficient that is m times that of b.
2646 * That is, all constraints (execpt for the lower and upper bound)
2649 * e + f (a + m b) >= 0
2651 * If so, we return b so that "a + m b" can be replaced by
2652 * a single div "c = a + m b".
2654 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2655 unsigned div
, unsigned l
, unsigned u
)
2661 if (bmap
->n_div
<= 1)
2663 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2664 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2666 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2667 bmap
->n_div
- div
- 1) != -1)
2669 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2673 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2674 if (isl_int_is_zero(bmap
->div
[i
][0]))
2676 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2680 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2681 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2682 isl_int_sub(bmap
->ineq
[l
][0],
2683 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2684 bmap
= isl_basic_map_copy(bmap
);
2685 bmap
= isl_basic_map_set_to_empty(bmap
);
2686 isl_basic_map_free(bmap
);
2689 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2690 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2695 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2696 if (isl_int_is_zero(bmap
->div
[j
][0]))
2698 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2701 if (j
< bmap
->n_div
)
2703 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2705 if (j
== l
|| j
== u
)
2707 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2709 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2711 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2712 bmap
->ineq
[j
][1 + dim
+ div
],
2714 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2715 bmap
->ineq
[j
][1 + dim
+ i
]);
2716 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2717 bmap
->ineq
[j
][1 + dim
+ div
],
2722 if (j
< bmap
->n_ineq
)
2727 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2728 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2732 /* Given a lower and an upper bound on div i, construct an inequality
2733 * that when nonnegative ensures that this pair of bounds always allows
2734 * for an integer value of the given div.
2735 * The lower bound is inequality l, while the upper bound is inequality u.
2736 * The constructed inequality is stored in ineq.
2737 * g, fl, fu are temporary scalars.
2739 * Let the upper bound be
2743 * and the lower bound
2747 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2750 * - f_u e_l <= f_u f_l g a <= f_l e_u
2752 * Since all variables are integer valued, this is equivalent to
2754 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2756 * If this interval is at least f_u f_l g, then it contains at least
2757 * one integer value for a.
2758 * That is, the test constraint is
2760 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2762 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2763 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2766 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2768 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2769 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2770 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2771 isl_int_neg(fu
, fu
);
2772 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2773 1 + dim
+ bmap
->n_div
);
2774 isl_int_add(ineq
[0], ineq
[0], fl
);
2775 isl_int_add(ineq
[0], ineq
[0], fu
);
2776 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2777 isl_int_mul(g
, g
, fl
);
2778 isl_int_mul(g
, g
, fu
);
2779 isl_int_sub(ineq
[0], ineq
[0], g
);
2782 /* Remove more kinds of divs that are not strictly needed.
2783 * In particular, if all pairs of lower and upper bounds on a div
2784 * are such that they allow at least one integer value of the div,
2785 * the we can eliminate the div using Fourier-Motzkin without
2786 * introducing any spurious solutions.
2788 static struct isl_basic_map
*drop_more_redundant_divs(
2789 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2791 struct isl_tab
*tab
= NULL
;
2792 struct isl_vec
*vec
= NULL
;
2804 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2805 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2809 tab
= isl_tab_from_basic_map(bmap
, 0);
2814 enum isl_lp_result res
;
2816 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2819 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2825 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2826 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2828 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2829 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2831 construct_test_ineq(bmap
, i
, l
, u
,
2832 vec
->el
, g
, fl
, fu
);
2833 res
= isl_tab_min(tab
, vec
->el
,
2834 bmap
->ctx
->one
, &g
, NULL
, 0);
2835 if (res
== isl_lp_error
)
2837 if (res
== isl_lp_empty
) {
2838 bmap
= isl_basic_map_set_to_empty(bmap
);
2841 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2844 if (u
< bmap
->n_ineq
)
2847 if (l
== bmap
->n_ineq
) {
2867 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
2868 return isl_basic_map_drop_redundant_divs(bmap
);
2871 isl_basic_map_free(bmap
);
2880 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2881 * and the upper bound u, div1 always occurs together with div2 in the form
2882 * (div1 + m div2), where m is the constant range on the variable div1
2883 * allowed by l and u, replace the pair div1 and div2 by a single
2884 * div that is equal to div1 + m div2.
2886 * The new div will appear in the location that contains div2.
2887 * We need to modify all constraints that contain
2888 * div2 = (div - div1) / m
2889 * (If a constraint does not contain div2, it will also not contain div1.)
2890 * If the constraint also contains div1, then we know they appear
2891 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2892 * i.e., the coefficient of div is f.
2894 * Otherwise, we first need to introduce div1 into the constraint.
2903 * A lower bound on div2
2907 * can be replaced by
2909 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2911 * with g = gcd(m,n).
2916 * can be replaced by
2918 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2920 * These constraint are those that we would obtain from eliminating
2921 * div1 using Fourier-Motzkin.
2923 * After all constraints have been modified, we drop the lower and upper
2924 * bound and then drop div1.
2926 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2927 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2932 unsigned dim
, total
;
2935 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2936 total
= 1 + dim
+ bmap
->n_div
;
2941 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2942 isl_int_add_ui(m
, m
, 1);
2944 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2945 if (i
== l
|| i
== u
)
2947 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2949 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2950 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2951 isl_int_divexact(a
, m
, b
);
2952 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2953 if (isl_int_is_pos(b
)) {
2954 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2955 b
, bmap
->ineq
[l
], total
);
2958 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2959 b
, bmap
->ineq
[u
], total
);
2962 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2963 bmap
->ineq
[i
][1 + dim
+ div1
]);
2964 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2971 isl_basic_map_drop_inequality(bmap
, l
);
2972 isl_basic_map_drop_inequality(bmap
, u
);
2974 isl_basic_map_drop_inequality(bmap
, u
);
2975 isl_basic_map_drop_inequality(bmap
, l
);
2977 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2981 /* First check if we can coalesce any pair of divs and
2982 * then continue with dropping more redundant divs.
2984 * We loop over all pairs of lower and upper bounds on a div
2985 * with coefficient 1 and -1, respectively, check if there
2986 * is any other div "c" with which we can coalesce the div
2987 * and if so, perform the coalescing.
2989 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2990 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2995 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2997 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3000 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
3001 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
3003 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
3006 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
3008 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
3012 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
3013 return isl_basic_map_drop_redundant_divs(bmap
);
3018 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
3021 return drop_more_redundant_divs(bmap
, pairs
, n
);
3024 /* Remove divs that are not strictly needed.
3025 * In particular, if a div only occurs positively (or negatively)
3026 * in constraints, then it can simply be dropped.
3027 * Also, if a div occurs in only two constraints and if moreover
3028 * those two constraints are opposite to each other, except for the constant
3029 * term and if the sum of the constant terms is such that for any value
3030 * of the other values, there is always at least one integer value of the
3031 * div, i.e., if one plus this sum is greater than or equal to
3032 * the (absolute value) of the coefficent of the div in the constraints,
3033 * then we can also simply drop the div.
3035 * We skip divs that appear in equalities or in the definition of other divs.
3036 * Divs that appear in the definition of other divs usually occur in at least
3037 * 4 constraints, but the constraints may have been simplified.
3039 * If any divs are left after these simple checks then we move on
3040 * to more complicated cases in drop_more_redundant_divs.
3042 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
3043 struct isl_basic_map
*bmap
)
3052 if (bmap
->n_div
== 0)
3055 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
3056 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
3060 for (i
= 0; i
< bmap
->n_div
; ++i
) {
3062 int last_pos
, last_neg
;
3066 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
3067 for (j
= i
; j
< bmap
->n_div
; ++j
)
3068 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
3070 if (j
< bmap
->n_div
)
3072 for (j
= 0; j
< bmap
->n_eq
; ++j
)
3073 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
3079 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
3080 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
3084 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
3089 pairs
[i
] = pos
* neg
;
3090 if (pairs
[i
] == 0) {
3091 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
3092 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
3093 isl_basic_map_drop_inequality(bmap
, j
);
3094 bmap
= isl_basic_map_drop_div(bmap
, i
);
3096 return isl_basic_map_drop_redundant_divs(bmap
);
3100 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
3101 bmap
->ineq
[last_neg
] + 1,
3105 isl_int_add(bmap
->ineq
[last_pos
][0],
3106 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3107 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
3108 bmap
->ineq
[last_pos
][0], 1);
3109 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
3110 bmap
->ineq
[last_pos
][1+off
+i
]);
3111 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
3112 bmap
->ineq
[last_pos
][0], 1);
3113 isl_int_sub(bmap
->ineq
[last_pos
][0],
3114 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
3117 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
3122 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
3123 bmap
= isl_basic_map_simplify(bmap
);
3125 return isl_basic_map_drop_redundant_divs(bmap
);
3127 if (last_pos
> last_neg
) {
3128 isl_basic_map_drop_inequality(bmap
, last_pos
);
3129 isl_basic_map_drop_inequality(bmap
, last_neg
);
3131 isl_basic_map_drop_inequality(bmap
, last_neg
);
3132 isl_basic_map_drop_inequality(bmap
, last_pos
);
3134 bmap
= isl_basic_map_drop_div(bmap
, i
);
3136 return isl_basic_map_drop_redundant_divs(bmap
);
3140 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
3146 isl_basic_map_free(bmap
);
3150 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
3151 struct isl_basic_set
*bset
)
3153 return (struct isl_basic_set
*)
3154 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
3157 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
3163 for (i
= 0; i
< map
->n
; ++i
) {
3164 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
3168 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
3175 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
3177 return (struct isl_set
*)
3178 isl_map_drop_redundant_divs((struct isl_map
*)set
);