2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2012 Ecole Normale Superieure
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include "isl_equalities.h"
19 #include <isl_space_private.h>
20 #include <isl_mat_private.h>
22 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
24 isl_int
*t
= bmap
->eq
[a
];
25 bmap
->eq
[a
] = bmap
->eq
[b
];
29 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
32 isl_int
*t
= bmap
->ineq
[a
];
33 bmap
->ineq
[a
] = bmap
->ineq
[b
];
38 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
40 isl_seq_cpy(c
, c
+ n
, rem
);
41 isl_seq_clr(c
+ rem
, n
);
44 /* Drop n dimensions starting at first.
46 * In principle, this frees up some extra variables as the number
47 * of columns remains constant, but we would have to extend
48 * the div array too as the number of rows in this array is assumed
49 * to be equal to extra.
51 struct isl_basic_set
*isl_basic_set_drop_dims(
52 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
59 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
61 if (n
== 0 && !isl_space_get_tuple_name(bset
->dim
, isl_dim_set
))
64 bset
= isl_basic_set_cow(bset
);
68 for (i
= 0; i
< bset
->n_eq
; ++i
)
69 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
70 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
72 for (i
= 0; i
< bset
->n_ineq
; ++i
)
73 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
74 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
76 for (i
= 0; i
< bset
->n_div
; ++i
)
77 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
78 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
80 bset
->dim
= isl_space_drop_outputs(bset
->dim
, first
, n
);
84 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
85 bset
= isl_basic_set_simplify(bset
);
86 return isl_basic_set_finalize(bset
);
88 isl_basic_set_free(bset
);
92 struct isl_set
*isl_set_drop_dims(
93 struct isl_set
*set
, unsigned first
, unsigned n
)
100 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
102 if (n
== 0 && !isl_space_get_tuple_name(set
->dim
, isl_dim_set
))
104 set
= isl_set_cow(set
);
107 set
->dim
= isl_space_drop_outputs(set
->dim
, first
, n
);
111 for (i
= 0; i
< set
->n
; ++i
) {
112 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
117 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
124 /* Move "n" divs starting at "first" to the end of the list of divs.
126 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
127 unsigned first
, unsigned n
)
132 if (first
+ n
== bmap
->n_div
)
135 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
138 for (i
= 0; i
< n
; ++i
)
139 div
[i
] = bmap
->div
[first
+ i
];
140 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
141 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
142 for (i
= 0; i
< n
; ++i
)
143 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
147 isl_basic_map_free(bmap
);
151 /* Drop "n" dimensions of type "type" starting at "first".
153 * In principle, this frees up some extra variables as the number
154 * of columns remains constant, but we would have to extend
155 * the div array too as the number of rows in this array is assumed
156 * to be equal to extra.
158 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
159 enum isl_dim_type type
, unsigned first
, unsigned n
)
169 dim
= isl_basic_map_dim(bmap
, type
);
170 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
172 if (n
== 0 && !isl_space_is_named_or_nested(bmap
->dim
, type
))
175 bmap
= isl_basic_map_cow(bmap
);
179 offset
= isl_basic_map_offset(bmap
, type
) + first
;
180 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
181 for (i
= 0; i
< bmap
->n_eq
; ++i
)
182 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
184 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
185 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
187 for (i
= 0; i
< bmap
->n_div
; ++i
)
188 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
190 if (type
== isl_dim_div
) {
191 bmap
= move_divs_last(bmap
, first
, n
);
194 isl_basic_map_free_div(bmap
, n
);
196 bmap
->dim
= isl_space_drop_dims(bmap
->dim
, type
, first
, n
);
200 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
201 bmap
= isl_basic_map_simplify(bmap
);
202 return isl_basic_map_finalize(bmap
);
204 isl_basic_map_free(bmap
);
208 __isl_give isl_basic_set
*isl_basic_set_drop(__isl_take isl_basic_set
*bset
,
209 enum isl_dim_type type
, unsigned first
, unsigned n
)
211 return (isl_basic_set
*)isl_basic_map_drop((isl_basic_map
*)bset
,
215 struct isl_basic_map
*isl_basic_map_drop_inputs(
216 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
218 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
221 struct isl_map
*isl_map_drop(struct isl_map
*map
,
222 enum isl_dim_type type
, unsigned first
, unsigned n
)
229 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
231 if (n
== 0 && !isl_space_get_tuple_name(map
->dim
, type
))
233 map
= isl_map_cow(map
);
236 map
->dim
= isl_space_drop_dims(map
->dim
, type
, first
, n
);
240 for (i
= 0; i
< map
->n
; ++i
) {
241 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
245 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
253 struct isl_set
*isl_set_drop(struct isl_set
*set
,
254 enum isl_dim_type type
, unsigned first
, unsigned n
)
256 return (isl_set
*)isl_map_drop((isl_map
*)set
, type
, first
, n
);
259 struct isl_map
*isl_map_drop_inputs(
260 struct isl_map
*map
, unsigned first
, unsigned n
)
262 return isl_map_drop(map
, isl_dim_in
, first
, n
);
266 * We don't cow, as the div is assumed to be redundant.
268 static struct isl_basic_map
*isl_basic_map_drop_div(
269 struct isl_basic_map
*bmap
, unsigned div
)
277 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
279 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
281 for (i
= 0; i
< bmap
->n_eq
; ++i
)
282 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
284 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
285 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
286 isl_basic_map_drop_inequality(bmap
, i
);
290 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
293 for (i
= 0; i
< bmap
->n_div
; ++i
)
294 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
296 if (div
!= bmap
->n_div
- 1) {
298 isl_int
*t
= bmap
->div
[div
];
300 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
301 bmap
->div
[j
] = bmap
->div
[j
+1];
303 bmap
->div
[bmap
->n_div
- 1] = t
;
305 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
306 isl_basic_map_free_div(bmap
, 1);
310 isl_basic_map_free(bmap
);
314 struct isl_basic_map
*isl_basic_map_normalize_constraints(
315 struct isl_basic_map
*bmap
)
319 unsigned total
= isl_basic_map_total_dim(bmap
);
325 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
326 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
327 if (isl_int_is_zero(gcd
)) {
328 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
329 bmap
= isl_basic_map_set_to_empty(bmap
);
332 isl_basic_map_drop_equality(bmap
, i
);
335 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
336 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
337 if (isl_int_is_one(gcd
))
339 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
340 bmap
= isl_basic_map_set_to_empty(bmap
);
343 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
346 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
347 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
348 if (isl_int_is_zero(gcd
)) {
349 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
350 bmap
= isl_basic_map_set_to_empty(bmap
);
353 isl_basic_map_drop_inequality(bmap
, i
);
356 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
357 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
358 if (isl_int_is_one(gcd
))
360 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
361 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
368 struct isl_basic_set
*isl_basic_set_normalize_constraints(
369 struct isl_basic_set
*bset
)
371 return (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
372 (struct isl_basic_map
*)bset
);
375 /* Remove any common factor in numerator and denominator of the div expression,
376 * not taking into account the constant term.
377 * That is, if the div is of the form
379 * floor((a + m f(x))/(m d))
383 * floor((floor(a/m) + f(x))/d)
385 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
386 * and can therefore not influence the result of the floor.
388 static void normalize_div_expression(__isl_keep isl_basic_map
*bmap
, int div
)
390 unsigned total
= isl_basic_map_total_dim(bmap
);
391 isl_ctx
*ctx
= bmap
->ctx
;
393 if (isl_int_is_zero(bmap
->div
[div
][0]))
395 isl_seq_gcd(bmap
->div
[div
] + 2, total
, &ctx
->normalize_gcd
);
396 isl_int_gcd(ctx
->normalize_gcd
, ctx
->normalize_gcd
, bmap
->div
[div
][0]);
397 if (isl_int_is_one(ctx
->normalize_gcd
))
399 isl_int_fdiv_q(bmap
->div
[div
][1], bmap
->div
[div
][1],
401 isl_int_divexact(bmap
->div
[div
][0], bmap
->div
[div
][0],
403 isl_seq_scale_down(bmap
->div
[div
] + 2, bmap
->div
[div
] + 2,
404 ctx
->normalize_gcd
, total
);
407 /* Remove any common factor in numerator and denominator of a div expression,
408 * not taking into account the constant term.
409 * That is, look for any div of the form
411 * floor((a + m f(x))/(m d))
415 * floor((floor(a/m) + f(x))/d)
417 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
418 * and can therefore not influence the result of the floor.
420 static __isl_give isl_basic_map
*normalize_div_expressions(
421 __isl_take isl_basic_map
*bmap
)
427 if (bmap
->n_div
== 0)
430 for (i
= 0; i
< bmap
->n_div
; ++i
)
431 normalize_div_expression(bmap
, i
);
436 /* Assumes divs have been ordered if keep_divs is set.
438 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
439 unsigned pos
, isl_int
*eq
, int keep_divs
, int *progress
)
442 unsigned space_total
;
446 total
= isl_basic_map_total_dim(bmap
);
447 space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
448 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
449 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
450 if (bmap
->eq
[k
] == eq
)
452 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
456 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
457 isl_seq_normalize(bmap
->ctx
, bmap
->eq
[k
], 1 + total
);
460 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
461 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
465 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
466 isl_seq_normalize(bmap
->ctx
, bmap
->ineq
[k
], 1 + total
);
467 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
470 for (k
= 0; k
< bmap
->n_div
; ++k
) {
471 if (isl_int_is_zero(bmap
->div
[k
][0]))
473 if (isl_int_is_zero(bmap
->div
[k
][1+1+pos
]))
477 /* We need to be careful about circular definitions,
478 * so for now we just remove the definition of div k
479 * if the equality contains any divs.
480 * If keep_divs is set, then the divs have been ordered
481 * and we can keep the definition as long as the result
484 if (last_div
== -1 || (keep_divs
&& last_div
< k
)) {
485 isl_seq_elim(bmap
->div
[k
]+1, eq
,
486 1+pos
, 1+total
, &bmap
->div
[k
][0]);
487 normalize_div_expression(bmap
, k
);
489 isl_seq_clr(bmap
->div
[k
], 1 + total
);
490 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
494 /* Assumes divs have been ordered if keep_divs is set.
496 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
497 unsigned div
, int keep_divs
)
499 unsigned pos
= isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
501 eliminate_var_using_equality(bmap
, pos
, eq
, keep_divs
, NULL
);
503 isl_basic_map_drop_div(bmap
, div
);
506 /* Check if elimination of div "div" using equality "eq" would not
507 * result in a div depending on a later div.
509 static int ok_to_eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
,
514 unsigned space_total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
515 unsigned pos
= space_total
+ div
;
517 last_div
= isl_seq_last_non_zero(eq
+ 1 + space_total
, bmap
->n_div
);
518 if (last_div
< 0 || last_div
<= div
)
521 for (k
= 0; k
<= last_div
; ++k
) {
522 if (isl_int_is_zero(bmap
->div
[k
][0]))
524 if (!isl_int_is_zero(bmap
->div
[k
][1 + 1 + pos
]))
531 /* Elimininate divs based on equalities
533 static struct isl_basic_map
*eliminate_divs_eq(
534 struct isl_basic_map
*bmap
, int *progress
)
541 bmap
= isl_basic_map_order_divs(bmap
);
546 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
548 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
549 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
550 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
551 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
553 if (!ok_to_eliminate_div(bmap
, bmap
->eq
[i
], d
))
557 eliminate_div(bmap
, bmap
->eq
[i
], d
, 1);
558 isl_basic_map_drop_equality(bmap
, i
);
563 return eliminate_divs_eq(bmap
, progress
);
567 /* Elimininate divs based on inequalities
569 static struct isl_basic_map
*eliminate_divs_ineq(
570 struct isl_basic_map
*bmap
, int *progress
)
581 off
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
583 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
584 for (i
= 0; i
< bmap
->n_eq
; ++i
)
585 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
589 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
590 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
592 if (i
< bmap
->n_ineq
)
595 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
596 if (!bmap
|| ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
598 bmap
= isl_basic_map_drop_div(bmap
, d
);
605 struct isl_basic_map
*isl_basic_map_gauss(
606 struct isl_basic_map
*bmap
, int *progress
)
614 bmap
= isl_basic_map_order_divs(bmap
);
619 total
= isl_basic_map_total_dim(bmap
);
620 total_var
= total
- bmap
->n_div
;
622 last_var
= total
- 1;
623 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
624 for (; last_var
>= 0; --last_var
) {
625 for (k
= done
; k
< bmap
->n_eq
; ++k
)
626 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
634 swap_equality(bmap
, k
, done
);
635 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
636 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
638 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
], 1,
641 if (last_var
>= total_var
&&
642 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
643 unsigned div
= last_var
- total_var
;
644 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
645 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
646 isl_int_set(bmap
->div
[div
][0],
647 bmap
->eq
[done
][1+last_var
]);
648 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
651 if (done
== bmap
->n_eq
)
653 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
654 if (isl_int_is_zero(bmap
->eq
[k
][0]))
656 return isl_basic_map_set_to_empty(bmap
);
658 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
662 struct isl_basic_set
*isl_basic_set_gauss(
663 struct isl_basic_set
*bset
, int *progress
)
665 return (struct isl_basic_set
*)isl_basic_map_gauss(
666 (struct isl_basic_map
*)bset
, progress
);
670 static unsigned int round_up(unsigned int v
)
681 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
682 struct isl_basic_map
*bmap
, int k
)
685 unsigned total
= isl_basic_map_total_dim(bmap
);
686 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
687 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
688 if (&bmap
->ineq
[k
] != index
[h
] &&
689 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
694 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
695 struct isl_basic_set
*bset
, int k
)
697 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
700 /* If we can eliminate more than one div, then we need to make
701 * sure we do it from last div to first div, in order not to
702 * change the position of the other divs that still need to
705 static struct isl_basic_map
*remove_duplicate_divs(
706 struct isl_basic_map
*bmap
, int *progress
)
718 bmap
= isl_basic_map_order_divs(bmap
);
719 if (!bmap
|| bmap
->n_div
<= 1)
722 total_var
= isl_space_dim(bmap
->dim
, isl_dim_all
);
723 total
= total_var
+ bmap
->n_div
;
726 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
727 if (!isl_int_is_zero(bmap
->div
[k
][0]))
732 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
733 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
734 bits
= ffs(size
) - 1;
735 index
= isl_calloc_array(ctx
, int, size
);
738 eq
= isl_blk_alloc(ctx
, 1+total
);
739 if (isl_blk_is_error(eq
))
742 isl_seq_clr(eq
.data
, 1+total
);
743 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
744 for (--k
; k
>= 0; --k
) {
747 if (isl_int_is_zero(bmap
->div
[k
][0]))
750 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
751 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
752 if (isl_seq_eq(bmap
->div
[k
],
753 bmap
->div
[index
[h
]-1], 2+total
))
762 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
766 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
767 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
768 eliminate_div(bmap
, eq
.data
, l
, 1);
769 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
770 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
773 isl_blk_free(ctx
, eq
);
780 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
785 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
786 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
787 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
791 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
797 /* Normalize divs that appear in equalities.
799 * In particular, we assume that bmap contains some equalities
804 * and we want to replace the set of e_i by a minimal set and
805 * such that the new e_i have a canonical representation in terms
807 * If any of the equalities involves more than one divs, then
808 * we currently simply bail out.
810 * Let us first additionally assume that all equalities involve
811 * a div. The equalities then express modulo constraints on the
812 * remaining variables and we can use "parameter compression"
813 * to find a minimal set of constraints. The result is a transformation
815 * x = T(x') = x_0 + G x'
817 * with G a lower-triangular matrix with all elements below the diagonal
818 * non-negative and smaller than the diagonal element on the same row.
819 * We first normalize x_0 by making the same property hold in the affine
821 * The rows i of G with a 1 on the diagonal do not impose any modulo
822 * constraint and simply express x_i = x'_i.
823 * For each of the remaining rows i, we introduce a div and a corresponding
824 * equality. In particular
826 * g_ii e_j = x_i - g_i(x')
828 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
829 * corresponding div (if g_kk != 1).
831 * If there are any equalities not involving any div, then we
832 * first apply a variable compression on the variables x:
834 * x = C x'' x'' = C_2 x
836 * and perform the above parameter compression on A C instead of on A.
837 * The resulting compression is then of the form
839 * x'' = T(x') = x_0 + G x'
841 * and in constructing the new divs and the corresponding equalities,
842 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
843 * by the corresponding row from C_2.
845 static struct isl_basic_map
*normalize_divs(
846 struct isl_basic_map
*bmap
, int *progress
)
853 struct isl_mat
*T
= NULL
;
854 struct isl_mat
*C
= NULL
;
855 struct isl_mat
*C2
= NULL
;
863 if (bmap
->n_div
== 0)
869 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
872 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
873 div_eq
= n_pure_div_eq(bmap
);
877 if (div_eq
< bmap
->n_eq
) {
878 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, div_eq
,
879 bmap
->n_eq
- div_eq
, 0, 1 + total
);
880 C
= isl_mat_variable_compression(B
, &C2
);
884 bmap
= isl_basic_map_set_to_empty(bmap
);
891 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
894 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
895 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
897 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
899 B
= isl_mat_sub_alloc6(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
902 B
= isl_mat_product(B
, C
);
906 T
= isl_mat_parameter_compression(B
, d
);
910 bmap
= isl_basic_map_set_to_empty(bmap
);
916 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
917 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
918 if (isl_int_is_zero(v
))
920 isl_mat_col_submul(T
, 0, v
, 1 + i
);
923 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
926 /* We have to be careful because dropping equalities may reorder them */
928 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
929 for (i
= 0; i
< bmap
->n_eq
; ++i
)
930 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
932 if (i
< bmap
->n_eq
) {
933 bmap
= isl_basic_map_drop_div(bmap
, j
);
934 isl_basic_map_drop_equality(bmap
, i
);
940 for (i
= 1; i
< T
->n_row
; ++i
) {
941 if (isl_int_is_one(T
->row
[i
][i
]))
946 if (needed
> dropped
) {
947 bmap
= isl_basic_map_extend_space(bmap
, isl_space_copy(bmap
->dim
),
952 for (i
= 1; i
< T
->n_row
; ++i
) {
953 if (isl_int_is_one(T
->row
[i
][i
]))
955 k
= isl_basic_map_alloc_div(bmap
);
956 pos
[i
] = 1 + total
+ k
;
957 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
958 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
960 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
962 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
963 for (j
= 0; j
< i
; ++j
) {
964 if (isl_int_is_zero(T
->row
[i
][j
]))
966 if (pos
[j
] < T
->n_row
&& C2
)
967 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
968 C2
->row
[pos
[j
]], 1 + total
);
970 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
973 j
= isl_basic_map_alloc_equality(bmap
);
974 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
975 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
984 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
994 static struct isl_basic_map
*set_div_from_lower_bound(
995 struct isl_basic_map
*bmap
, int div
, int ineq
)
997 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
999 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
1000 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
1001 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
1002 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1003 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
1008 /* Check whether it is ok to define a div based on an inequality.
1009 * To avoid the introduction of circular definitions of divs, we
1010 * do not allow such a definition if the resulting expression would refer to
1011 * any other undefined divs or if any known div is defined in
1012 * terms of the unknown div.
1014 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
1018 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1020 /* Not defined in terms of unknown divs */
1021 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1024 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
1026 if (isl_int_is_zero(bmap
->div
[j
][0]))
1030 /* No other div defined in terms of this one => avoid loops */
1031 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1034 if (isl_int_is_zero(bmap
->div
[j
][0]))
1036 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
1043 /* Given two constraints "k" and "l" that are opposite to each other,
1044 * except for the constant term, check if we can use them
1045 * to obtain an expression for one of the hitherto unknown divs.
1046 * "sum" is the sum of the constant terms of the constraints.
1047 * If this sum is strictly smaller than the coefficient of one
1048 * of the divs, then this pair can be used define the div.
1049 * To avoid the introduction of circular definitions of divs, we
1050 * do not use the pair if the resulting expression would refer to
1051 * any other undefined divs or if any known div is defined in
1052 * terms of the unknown div.
1054 static struct isl_basic_map
*check_for_div_constraints(
1055 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
1058 unsigned total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1060 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1061 if (!isl_int_is_zero(bmap
->div
[i
][0]))
1063 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
1065 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
1067 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
1069 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
1070 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
1072 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
1080 static struct isl_basic_map
*remove_duplicate_constraints(
1081 struct isl_basic_map
*bmap
, int *progress
, int detect_divs
)
1087 unsigned total
= isl_basic_map_total_dim(bmap
);
1091 if (!bmap
|| bmap
->n_ineq
<= 1)
1094 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
1095 bits
= ffs(size
) - 1;
1096 ctx
= isl_basic_map_get_ctx(bmap
);
1097 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1101 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
1102 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
1103 h
= hash_index(index
, size
, bits
, bmap
, k
);
1105 index
[h
] = &bmap
->ineq
[k
];
1110 l
= index
[h
] - &bmap
->ineq
[0];
1111 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
1112 swap_inequality(bmap
, k
, l
);
1113 isl_basic_map_drop_inequality(bmap
, k
);
1117 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
1118 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1119 h
= hash_index(index
, size
, bits
, bmap
, k
);
1120 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1123 l
= index
[h
] - &bmap
->ineq
[0];
1124 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1125 if (isl_int_is_pos(sum
)) {
1127 bmap
= check_for_div_constraints(bmap
, k
, l
,
1131 if (isl_int_is_zero(sum
)) {
1132 /* We need to break out of the loop after these
1133 * changes since the contents of the hash
1134 * will no longer be valid.
1135 * Plus, we probably we want to regauss first.
1139 isl_basic_map_drop_inequality(bmap
, l
);
1140 isl_basic_map_inequality_to_equality(bmap
, k
);
1142 bmap
= isl_basic_map_set_to_empty(bmap
);
1152 /* Eliminate knowns divs from constraints where they appear with
1153 * a (positive or negative) unit coefficient.
1157 * floor(e/m) + f >= 0
1165 * -floor(e/m) + f >= 0
1169 * -e + m f + m - 1 >= 0
1171 * The first conversion is valid because floor(e/m) >= -f is equivalent
1172 * to e/m >= -f because -f is an integral expression.
1173 * The second conversion follows from the fact that
1175 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1178 * We skip integral divs, i.e., those with denominator 1, as we would
1179 * risk eliminating the div from the div constraints. We do not need
1180 * to handle those divs here anyway since the div constraints will turn
1181 * out to form an equality and this equality can then be use to eliminate
1182 * the div from all constraints.
1184 static __isl_give isl_basic_map
*eliminate_unit_divs(
1185 __isl_take isl_basic_map
*bmap
, int *progress
)
1194 ctx
= isl_basic_map_get_ctx(bmap
);
1195 total
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
);
1197 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1198 if (isl_int_is_zero(bmap
->div
[i
][0]))
1200 if (isl_int_is_one(bmap
->div
[i
][0]))
1202 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1205 if (!isl_int_is_one(bmap
->ineq
[j
][total
+ i
]) &&
1206 !isl_int_is_negone(bmap
->ineq
[j
][total
+ i
]))
1211 s
= isl_int_sgn(bmap
->ineq
[j
][total
+ i
]);
1212 isl_int_set_si(bmap
->ineq
[j
][total
+ i
], 0);
1214 isl_seq_combine(bmap
->ineq
[j
],
1215 ctx
->negone
, bmap
->div
[i
] + 1,
1216 bmap
->div
[i
][0], bmap
->ineq
[j
],
1217 total
+ bmap
->n_div
);
1219 isl_seq_combine(bmap
->ineq
[j
],
1220 ctx
->one
, bmap
->div
[i
] + 1,
1221 bmap
->div
[i
][0], bmap
->ineq
[j
],
1222 total
+ bmap
->n_div
);
1224 isl_int_add(bmap
->ineq
[j
][0],
1225 bmap
->ineq
[j
][0], bmap
->div
[i
][0]);
1226 isl_int_sub_ui(bmap
->ineq
[j
][0],
1227 bmap
->ineq
[j
][0], 1);
1235 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1242 bmap
= isl_basic_map_normalize_constraints(bmap
);
1243 bmap
= normalize_div_expressions(bmap
);
1244 bmap
= remove_duplicate_divs(bmap
, &progress
);
1245 bmap
= eliminate_unit_divs(bmap
, &progress
);
1246 bmap
= eliminate_divs_eq(bmap
, &progress
);
1247 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1248 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1249 /* requires equalities in normal form */
1250 bmap
= normalize_divs(bmap
, &progress
);
1251 bmap
= remove_duplicate_constraints(bmap
, &progress
, 1);
1256 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1258 return (struct isl_basic_set
*)
1259 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1263 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map
*bmap
,
1264 isl_int
*constraint
, unsigned div
)
1271 pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1273 if (isl_int_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1275 isl_int_sub(bmap
->div
[div
][1],
1276 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1277 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1278 neg
= isl_seq_is_neg(constraint
, bmap
->div
[div
]+1, pos
);
1279 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1280 isl_int_add(bmap
->div
[div
][1],
1281 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1284 if (isl_seq_first_non_zero(constraint
+pos
+1,
1285 bmap
->n_div
-div
-1) != -1)
1287 } else if (isl_int_abs_eq(constraint
[pos
], bmap
->div
[div
][0])) {
1288 if (!isl_seq_eq(constraint
, bmap
->div
[div
]+1, pos
))
1290 if (isl_seq_first_non_zero(constraint
+pos
+1,
1291 bmap
->n_div
-div
-1) != -1)
1299 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set
*bset
,
1300 isl_int
*constraint
, unsigned div
)
1302 return isl_basic_map_is_div_constraint(bset
, constraint
, div
);
1306 /* If the only constraints a div d=floor(f/m)
1307 * appears in are its two defining constraints
1310 * -(f - (m - 1)) + m d >= 0
1312 * then it can safely be removed.
1314 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1317 unsigned pos
= 1 + isl_space_dim(bmap
->dim
, isl_dim_all
) + div
;
1319 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1320 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1323 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1324 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1326 if (!isl_basic_map_is_div_constraint(bmap
, bmap
->ineq
[i
], div
))
1330 for (i
= 0; i
< bmap
->n_div
; ++i
)
1331 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1338 * Remove divs that don't occur in any of the constraints or other divs.
1339 * These can arise when dropping some of the variables in a quast
1340 * returned by piplib.
1342 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1349 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1350 if (!div_is_redundant(bmap
, i
))
1352 bmap
= isl_basic_map_drop_div(bmap
, i
);
1357 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1359 bmap
= remove_redundant_divs(bmap
);
1362 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1366 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1368 return (struct isl_basic_set
*)
1369 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1372 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1378 for (i
= 0; i
< set
->n
; ++i
) {
1379 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1389 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1395 for (i
= 0; i
< map
->n
; ++i
) {
1396 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1400 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1408 /* Remove definition of any div that is defined in terms of the given variable.
1409 * The div itself is not removed. Functions such as
1410 * eliminate_divs_ineq depend on the other divs remaining in place.
1412 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1417 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1418 if (isl_int_is_zero(bmap
->div
[i
][0]))
1420 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1422 isl_int_set_si(bmap
->div
[i
][0], 0);
1427 /* Eliminate the specified variables from the constraints using
1428 * Fourier-Motzkin. The variables themselves are not removed.
1430 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1431 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1442 total
= isl_basic_map_total_dim(bmap
);
1444 bmap
= isl_basic_map_cow(bmap
);
1445 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1446 bmap
= remove_dependent_vars(bmap
, d
);
1448 for (d
= pos
+ n
- 1;
1449 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1450 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1451 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1452 int n_lower
, n_upper
;
1455 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1456 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1458 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], 0, NULL
);
1459 isl_basic_map_drop_equality(bmap
, i
);
1467 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1468 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1470 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1473 bmap
= isl_basic_map_extend_constraints(bmap
,
1474 0, n_lower
* n_upper
);
1477 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1479 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1482 for (j
= 0; j
< i
; ++j
) {
1483 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1486 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1487 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1489 k
= isl_basic_map_alloc_inequality(bmap
);
1492 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1494 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1495 1+d
, 1+total
, NULL
);
1497 isl_basic_map_drop_inequality(bmap
, i
);
1500 if (n_lower
> 0 && n_upper
> 0) {
1501 bmap
= isl_basic_map_normalize_constraints(bmap
);
1502 bmap
= remove_duplicate_constraints(bmap
, NULL
, 0);
1503 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1504 bmap
= isl_basic_map_remove_redundancies(bmap
);
1508 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1512 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1514 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1517 isl_basic_map_free(bmap
);
1521 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1522 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1524 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1525 (struct isl_basic_map
*)bset
, pos
, n
);
1528 /* Eliminate the specified n dimensions starting at first from the
1529 * constraints, without removing the dimensions from the space.
1530 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1531 * Otherwise, they are projected out and the original space is restored.
1533 __isl_give isl_basic_map
*isl_basic_map_eliminate(
1534 __isl_take isl_basic_map
*bmap
,
1535 enum isl_dim_type type
, unsigned first
, unsigned n
)
1544 if (first
+ n
> isl_basic_map_dim(bmap
, type
) || first
+ n
< first
)
1545 isl_die(bmap
->ctx
, isl_error_invalid
,
1546 "index out of bounds", goto error
);
1548 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
)) {
1549 first
+= isl_basic_map_offset(bmap
, type
) - 1;
1550 bmap
= isl_basic_map_eliminate_vars(bmap
, first
, n
);
1551 return isl_basic_map_finalize(bmap
);
1554 space
= isl_basic_map_get_space(bmap
);
1555 bmap
= isl_basic_map_project_out(bmap
, type
, first
, n
);
1556 bmap
= isl_basic_map_insert_dims(bmap
, type
, first
, n
);
1557 bmap
= isl_basic_map_reset_space(bmap
, space
);
1560 isl_basic_map_free(bmap
);
1564 __isl_give isl_basic_set
*isl_basic_set_eliminate(
1565 __isl_take isl_basic_set
*bset
,
1566 enum isl_dim_type type
, unsigned first
, unsigned n
)
1568 return isl_basic_map_eliminate(bset
, type
, first
, n
);
1571 /* Don't assume equalities are in order, because align_divs
1572 * may have changed the order of the divs.
1574 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1579 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1580 for (d
= 0; d
< total
; ++d
)
1582 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1583 for (d
= total
- 1; d
>= 0; --d
) {
1584 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1592 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1594 compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1597 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1598 struct isl_basic_map
*bmap
, int *elim
)
1604 total
= isl_space_dim(bmap
->dim
, isl_dim_all
);
1605 for (d
= total
- 1; d
>= 0; --d
) {
1606 if (isl_int_is_zero(src
[1+d
]))
1611 isl_seq_cpy(dst
, src
, 1 + total
);
1614 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1619 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1620 struct isl_basic_set
*bset
, int *elim
)
1622 return reduced_using_equalities(dst
, src
,
1623 (struct isl_basic_map
*)bset
, elim
);
1626 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1627 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1632 if (!bset
|| !context
)
1635 if (context
->n_eq
== 0) {
1636 isl_basic_set_free(context
);
1640 bset
= isl_basic_set_cow(bset
);
1644 elim
= isl_alloc_array(bset
->ctx
, int, isl_basic_set_n_dim(bset
));
1647 set_compute_elimination_index(context
, elim
);
1648 for (i
= 0; i
< bset
->n_eq
; ++i
)
1649 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1651 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1652 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1654 isl_basic_set_free(context
);
1656 bset
= isl_basic_set_simplify(bset
);
1657 bset
= isl_basic_set_finalize(bset
);
1660 isl_basic_set_free(bset
);
1661 isl_basic_set_free(context
);
1665 static struct isl_basic_set
*remove_shifted_constraints(
1666 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1677 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1678 bits
= ffs(size
) - 1;
1679 ctx
= isl_basic_set_get_ctx(bset
);
1680 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1684 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1685 h
= set_hash_index(index
, size
, bits
, context
, k
);
1686 index
[h
] = &context
->ineq
[k
];
1688 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1689 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1692 l
= index
[h
] - &context
->ineq
[0];
1693 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1695 bset
= isl_basic_set_cow(bset
);
1698 isl_basic_set_drop_inequality(bset
, k
);
1708 /* Remove all information from bset that is redundant in the context
1709 * of context. Both bset and context are assumed to be full-dimensional.
1711 * We first * remove the inequalities from "bset"
1712 * that are obviously redundant with respect to some inequality in "context".
1714 * If there are any inequalities left, we construct a tableau for
1715 * the context and then add the inequalities of "bset".
1716 * Before adding these inequalities, we freeze all constraints such that
1717 * they won't be considered redundant in terms of the constraints of "bset".
1718 * Then we detect all redundant constraints (among the
1719 * constraints that weren't frozen), first by checking for redundancy in the
1720 * the tableau and then by checking if replacing a constraint by its negation
1721 * would lead to an empty set. This last step is fairly expensive
1722 * and could be optimized by more reuse of the tableau.
1723 * Finally, we update bset according to the results.
1725 static __isl_give isl_basic_set
*uset_gist_full(__isl_take isl_basic_set
*bset
,
1726 __isl_take isl_basic_set
*context
)
1729 isl_basic_set
*combined
= NULL
;
1730 struct isl_tab
*tab
= NULL
;
1731 unsigned context_ineq
;
1734 if (!bset
|| !context
)
1737 if (isl_basic_set_is_universe(bset
)) {
1738 isl_basic_set_free(context
);
1742 if (isl_basic_set_is_universe(context
)) {
1743 isl_basic_set_free(context
);
1747 bset
= remove_shifted_constraints(bset
, context
);
1750 if (bset
->n_ineq
== 0)
1753 context_ineq
= context
->n_ineq
;
1754 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1755 combined
= isl_basic_set_extend_constraints(combined
, 0, bset
->n_ineq
);
1756 tab
= isl_tab_from_basic_set(combined
, 0);
1757 for (i
= 0; i
< context_ineq
; ++i
)
1758 if (isl_tab_freeze_constraint(tab
, i
) < 0)
1760 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1761 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1762 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
1764 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1768 if (isl_tab_detect_redundant(tab
) < 0)
1770 total
= isl_basic_set_total_dim(bset
);
1771 for (i
= context_ineq
; i
< bset
->n_ineq
; ++i
) {
1773 if (tab
->con
[i
].is_redundant
)
1775 tab
->con
[i
].is_redundant
= 1;
1776 combined
= isl_basic_set_dup(bset
);
1777 combined
= isl_basic_set_update_from_tab(combined
, tab
);
1778 combined
= isl_basic_set_extend_constraints(combined
, 0, 1);
1779 k
= isl_basic_set_alloc_inequality(combined
);
1782 isl_seq_neg(combined
->ineq
[k
], bset
->ineq
[i
], 1 + total
);
1783 isl_int_sub_ui(combined
->ineq
[k
][0], combined
->ineq
[k
][0], 1);
1784 is_empty
= isl_basic_set_is_empty(combined
);
1787 isl_basic_set_free(combined
);
1790 tab
->con
[i
].is_redundant
= 0;
1792 for (i
= 0; i
< context_ineq
; ++i
)
1793 tab
->con
[i
].is_redundant
= 1;
1794 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1796 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1797 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1802 bset
= isl_basic_set_simplify(bset
);
1803 bset
= isl_basic_set_finalize(bset
);
1804 isl_basic_set_free(context
);
1808 isl_basic_set_free(combined
);
1809 isl_basic_set_free(context
);
1810 isl_basic_set_free(bset
);
1814 /* Remove all information from bset that is redundant in the context
1815 * of context. In particular, equalities that are linear combinations
1816 * of those in context are removed. Then the inequalities that are
1817 * redundant in the context of the equalities and inequalities of
1818 * context are removed.
1820 * We first compute the integer affine hull of the intersection,
1821 * compute the gist inside this affine hull and then add back
1822 * those equalities that are not implied by the context.
1824 * If two constraints are mutually redundant, then uset_gist_full
1825 * will remove the second of those constraints. We therefore first
1826 * sort the constraints so that constraints not involving existentially
1827 * quantified variables are given precedence over those that do.
1828 * We have to perform this sorting before the variable compression,
1829 * because that may effect the order of the variables.
1831 static __isl_give isl_basic_set
*uset_gist(__isl_take isl_basic_set
*bset
,
1832 __isl_take isl_basic_set
*context
)
1837 isl_basic_set
*aff_context
;
1840 if (!bset
|| !context
)
1843 bset
= isl_basic_set_intersect(bset
, isl_basic_set_copy(context
));
1844 if (isl_basic_set_plain_is_empty(bset
)) {
1845 isl_basic_set_free(context
);
1848 bset
= isl_basic_set_sort_constraints(bset
);
1849 aff
= isl_basic_set_affine_hull(isl_basic_set_copy(bset
));
1852 if (isl_basic_set_plain_is_empty(aff
)) {
1853 isl_basic_set_free(aff
);
1854 isl_basic_set_free(context
);
1857 if (aff
->n_eq
== 0) {
1858 isl_basic_set_free(aff
);
1859 return uset_gist_full(bset
, context
);
1861 total
= isl_basic_set_total_dim(bset
);
1862 eq
= isl_mat_sub_alloc6(bset
->ctx
, aff
->eq
, 0, aff
->n_eq
, 0, 1 + total
);
1863 eq
= isl_mat_cow(eq
);
1864 T
= isl_mat_variable_compression(eq
, &T2
);
1865 if (T
&& T
->n_col
== 0) {
1868 isl_basic_set_free(context
);
1869 isl_basic_set_free(aff
);
1870 return isl_basic_set_set_to_empty(bset
);
1873 aff_context
= isl_basic_set_affine_hull(isl_basic_set_copy(context
));
1875 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(T
));
1876 context
= isl_basic_set_preimage(context
, T
);
1878 bset
= uset_gist_full(bset
, context
);
1879 bset
= isl_basic_set_preimage(bset
, T2
);
1880 bset
= isl_basic_set_intersect(bset
, aff
);
1881 bset
= isl_basic_set_reduce_using_equalities(bset
, aff_context
);
1884 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1885 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1890 isl_basic_set_free(bset
);
1891 isl_basic_set_free(context
);
1895 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1896 * We simply add the equalities in context to bmap and then do a regular
1897 * div normalizations. Better results can be obtained by normalizing
1898 * only the divs in bmap than do not also appear in context.
1899 * We need to be careful to reduce the divs using the equalities
1900 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1901 * spurious constraints.
1903 static struct isl_basic_map
*normalize_divs_in_context(
1904 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
1907 unsigned total_context
;
1910 div_eq
= n_pure_div_eq(bmap
);
1914 if (context
->n_div
> 0)
1915 bmap
= isl_basic_map_align_divs(bmap
, context
);
1917 total_context
= isl_basic_map_total_dim(context
);
1918 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
1919 for (i
= 0; i
< context
->n_eq
; ++i
) {
1921 k
= isl_basic_map_alloc_equality(bmap
);
1922 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
1923 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
1924 isl_basic_map_total_dim(bmap
) - total_context
);
1926 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1927 bmap
= normalize_divs(bmap
, NULL
);
1928 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1932 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
1933 struct isl_basic_map
*context
)
1935 struct isl_basic_set
*bset
;
1937 if (!bmap
|| !context
)
1940 if (isl_basic_map_is_universe(bmap
)) {
1941 isl_basic_map_free(context
);
1944 if (isl_basic_map_plain_is_empty(context
)) {
1945 isl_basic_map_free(bmap
);
1948 if (isl_basic_map_plain_is_empty(bmap
)) {
1949 isl_basic_map_free(context
);
1953 bmap
= isl_basic_map_remove_redundancies(bmap
);
1954 context
= isl_basic_map_remove_redundancies(context
);
1957 bmap
= normalize_divs_in_context(bmap
, context
);
1959 context
= isl_basic_map_align_divs(context
, bmap
);
1960 bmap
= isl_basic_map_align_divs(bmap
, context
);
1962 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
1963 isl_basic_map_underlying_set(context
));
1965 return isl_basic_map_overlying_set(bset
, bmap
);
1967 isl_basic_map_free(bmap
);
1968 isl_basic_map_free(context
);
1973 * Assumes context has no implicit divs.
1975 __isl_give isl_map
*isl_map_gist_basic_map(__isl_take isl_map
*map
,
1976 __isl_take isl_basic_map
*context
)
1980 if (!map
|| !context
)
1983 if (isl_basic_map_plain_is_empty(context
)) {
1985 return isl_map_from_basic_map(context
);
1988 context
= isl_basic_map_remove_redundancies(context
);
1989 map
= isl_map_cow(map
);
1990 if (!map
|| !context
)
1992 isl_assert(map
->ctx
, isl_space_is_equal(map
->dim
, context
->dim
), goto error
);
1993 map
= isl_map_compute_divs(map
);
1994 for (i
= 0; i
< map
->n
; ++i
)
1995 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
1996 for (i
= map
->n
- 1; i
>= 0; --i
) {
1997 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
1998 isl_basic_map_copy(context
));
2001 if (isl_basic_map_plain_is_empty(map
->p
[i
])) {
2002 isl_basic_map_free(map
->p
[i
]);
2003 if (i
!= map
->n
- 1)
2004 map
->p
[i
] = map
->p
[map
->n
- 1];
2008 isl_basic_map_free(context
);
2009 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2013 isl_basic_map_free(context
);
2017 static __isl_give isl_map
*map_gist(__isl_take isl_map
*map
,
2018 __isl_take isl_map
*context
)
2020 context
= isl_map_compute_divs(context
);
2021 return isl_map_gist_basic_map(map
, isl_map_simple_hull(context
));
2024 __isl_give isl_map
*isl_map_gist(__isl_take isl_map
*map
,
2025 __isl_take isl_map
*context
)
2027 return isl_map_align_params_map_map_and(map
, context
, &map_gist
);
2030 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
2031 struct isl_basic_set
*context
)
2033 return (struct isl_basic_set
*)isl_basic_map_gist(
2034 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
2037 __isl_give isl_set
*isl_set_gist_basic_set(__isl_take isl_set
*set
,
2038 __isl_take isl_basic_set
*context
)
2040 return (struct isl_set
*)isl_map_gist_basic_map((struct isl_map
*)set
,
2041 (struct isl_basic_map
*)context
);
2044 __isl_give isl_set
*isl_set_gist_params_basic_set(__isl_take isl_set
*set
,
2045 __isl_take isl_basic_set
*context
)
2047 isl_space
*space
= isl_set_get_space(set
);
2048 isl_basic_set
*dom_context
= isl_basic_set_universe(space
);
2049 dom_context
= isl_basic_set_intersect_params(dom_context
, context
);
2050 return isl_set_gist_basic_set(set
, dom_context
);
2053 __isl_give isl_set
*isl_set_gist(__isl_take isl_set
*set
,
2054 __isl_take isl_set
*context
)
2056 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
2057 (struct isl_map
*)context
);
2060 __isl_give isl_map
*isl_map_gist_domain(__isl_take isl_map
*map
,
2061 __isl_take isl_set
*context
)
2063 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2064 map_context
= isl_map_intersect_domain(map_context
, context
);
2065 return isl_map_gist(map
, map_context
);
2068 __isl_give isl_map
*isl_map_gist_range(__isl_take isl_map
*map
,
2069 __isl_take isl_set
*context
)
2071 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2072 map_context
= isl_map_intersect_range(map_context
, context
);
2073 return isl_map_gist(map
, map_context
);
2076 __isl_give isl_map
*isl_map_gist_params(__isl_take isl_map
*map
,
2077 __isl_take isl_set
*context
)
2079 isl_map
*map_context
= isl_map_universe(isl_map_get_space(map
));
2080 map_context
= isl_map_intersect_params(map_context
, context
);
2081 return isl_map_gist(map
, map_context
);
2084 __isl_give isl_set
*isl_set_gist_params(__isl_take isl_set
*set
,
2085 __isl_take isl_set
*context
)
2087 return isl_map_gist_params(set
, context
);
2090 /* Quick check to see if two basic maps are disjoint.
2091 * In particular, we reduce the equalities and inequalities of
2092 * one basic map in the context of the equalities of the other
2093 * basic map and check if we get a contradiction.
2095 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map
*bmap1
,
2096 __isl_keep isl_basic_map
*bmap2
)
2098 struct isl_vec
*v
= NULL
;
2103 if (!bmap1
|| !bmap2
)
2105 isl_assert(bmap1
->ctx
, isl_space_is_equal(bmap1
->dim
, bmap2
->dim
),
2107 if (bmap1
->n_div
|| bmap2
->n_div
)
2109 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
2112 total
= isl_space_dim(bmap1
->dim
, isl_dim_all
);
2115 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
2118 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
2121 compute_elimination_index(bmap1
, elim
);
2122 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
2124 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
2126 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
2127 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2130 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
2132 reduced
= reduced_using_equalities(v
->block
.data
,
2133 bmap2
->ineq
[i
], bmap1
, elim
);
2134 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2135 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2138 compute_elimination_index(bmap2
, elim
);
2139 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
2141 reduced
= reduced_using_equalities(v
->block
.data
,
2142 bmap1
->ineq
[i
], bmap2
, elim
);
2143 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
2144 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
2160 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set
*bset1
,
2161 __isl_keep isl_basic_set
*bset2
)
2163 return isl_basic_map_plain_is_disjoint((struct isl_basic_map
*)bset1
,
2164 (struct isl_basic_map
*)bset2
);
2167 int isl_map_plain_is_disjoint(__isl_keep isl_map
*map1
,
2168 __isl_keep isl_map
*map2
)
2175 if (isl_map_plain_is_equal(map1
, map2
))
2178 for (i
= 0; i
< map1
->n
; ++i
) {
2179 for (j
= 0; j
< map2
->n
; ++j
) {
2180 int d
= isl_basic_map_plain_is_disjoint(map1
->p
[i
],
2189 int isl_set_plain_is_disjoint(__isl_keep isl_set
*set1
,
2190 __isl_keep isl_set
*set2
)
2192 return isl_map_plain_is_disjoint((struct isl_map
*)set1
,
2193 (struct isl_map
*)set2
);
2196 int isl_set_fast_is_disjoint(__isl_keep isl_set
*set1
, __isl_keep isl_set
*set2
)
2198 return isl_set_plain_is_disjoint(set1
, set2
);
2201 /* Check if we can combine a given div with lower bound l and upper
2202 * bound u with some other div and if so return that other div.
2203 * Otherwise return -1.
2205 * We first check that
2206 * - the bounds are opposites of each other (except for the constant
2208 * - the bounds do not reference any other div
2209 * - no div is defined in terms of this div
2211 * Let m be the size of the range allowed on the div by the bounds.
2212 * That is, the bounds are of the form
2214 * e <= a <= e + m - 1
2216 * with e some expression in the other variables.
2217 * We look for another div b such that no third div is defined in terms
2218 * of this second div b and such that in any constraint that contains
2219 * a (except for the given lower and upper bound), also contains b
2220 * with a coefficient that is m times that of b.
2221 * That is, all constraints (execpt for the lower and upper bound)
2224 * e + f (a + m b) >= 0
2226 * If so, we return b so that "a + m b" can be replaced by
2227 * a single div "c = a + m b".
2229 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
2230 unsigned div
, unsigned l
, unsigned u
)
2236 if (bmap
->n_div
<= 1)
2238 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2239 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
2241 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
2242 bmap
->n_div
- div
- 1) != -1)
2244 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
2248 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2249 if (isl_int_is_zero(bmap
->div
[i
][0]))
2251 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
2255 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2256 if (isl_int_is_neg(bmap
->ineq
[l
][0])) {
2257 isl_int_sub(bmap
->ineq
[l
][0],
2258 bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2259 bmap
= isl_basic_map_copy(bmap
);
2260 bmap
= isl_basic_map_set_to_empty(bmap
);
2261 isl_basic_map_free(bmap
);
2264 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2265 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2270 for (j
= 0; j
< bmap
->n_div
; ++j
) {
2271 if (isl_int_is_zero(bmap
->div
[j
][0]))
2273 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
2276 if (j
< bmap
->n_div
)
2278 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2280 if (j
== l
|| j
== u
)
2282 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
2284 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
2286 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
2287 bmap
->ineq
[j
][1 + dim
+ div
],
2289 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
2290 bmap
->ineq
[j
][1 + dim
+ i
]);
2291 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
2292 bmap
->ineq
[j
][1 + dim
+ div
],
2297 if (j
< bmap
->n_ineq
)
2302 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
2303 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2307 /* Given a lower and an upper bound on div i, construct an inequality
2308 * that when nonnegative ensures that this pair of bounds always allows
2309 * for an integer value of the given div.
2310 * The lower bound is inequality l, while the upper bound is inequality u.
2311 * The constructed inequality is stored in ineq.
2312 * g, fl, fu are temporary scalars.
2314 * Let the upper bound be
2318 * and the lower bound
2322 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2325 * - f_u e_l <= f_u f_l g a <= f_l e_u
2327 * Since all variables are integer valued, this is equivalent to
2329 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2331 * If this interval is at least f_u f_l g, then it contains at least
2332 * one integer value for a.
2333 * That is, the test constraint is
2335 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2337 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
2338 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
2341 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2343 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
2344 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
2345 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
2346 isl_int_neg(fu
, fu
);
2347 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
2348 1 + dim
+ bmap
->n_div
);
2349 isl_int_add(ineq
[0], ineq
[0], fl
);
2350 isl_int_add(ineq
[0], ineq
[0], fu
);
2351 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2352 isl_int_mul(g
, g
, fl
);
2353 isl_int_mul(g
, g
, fu
);
2354 isl_int_sub(ineq
[0], ineq
[0], g
);
2357 /* Remove more kinds of divs that are not strictly needed.
2358 * In particular, if all pairs of lower and upper bounds on a div
2359 * are such that they allow at least one integer value of the div,
2360 * the we can eliminate the div using Fourier-Motzkin without
2361 * introducing any spurious solutions.
2363 static struct isl_basic_map
*drop_more_redundant_divs(
2364 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2366 struct isl_tab
*tab
= NULL
;
2367 struct isl_vec
*vec
= NULL
;
2379 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2380 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2384 tab
= isl_tab_from_basic_map(bmap
, 0);
2389 enum isl_lp_result res
;
2391 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2394 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2400 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2401 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2403 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2404 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2406 construct_test_ineq(bmap
, i
, l
, u
,
2407 vec
->el
, g
, fl
, fu
);
2408 res
= isl_tab_min(tab
, vec
->el
,
2409 bmap
->ctx
->one
, &g
, NULL
, 0);
2410 if (res
== isl_lp_error
)
2412 if (res
== isl_lp_empty
) {
2413 bmap
= isl_basic_map_set_to_empty(bmap
);
2416 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2419 if (u
< bmap
->n_ineq
)
2422 if (l
== bmap
->n_ineq
) {
2442 bmap
= isl_basic_map_remove_dims(bmap
, isl_dim_div
, remove
, 1);
2443 return isl_basic_map_drop_redundant_divs(bmap
);
2446 isl_basic_map_free(bmap
);
2455 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2456 * and the upper bound u, div1 always occurs together with div2 in the form
2457 * (div1 + m div2), where m is the constant range on the variable div1
2458 * allowed by l and u, replace the pair div1 and div2 by a single
2459 * div that is equal to div1 + m div2.
2461 * The new div will appear in the location that contains div2.
2462 * We need to modify all constraints that contain
2463 * div2 = (div - div1) / m
2464 * (If a constraint does not contain div2, it will also not contain div1.)
2465 * If the constraint also contains div1, then we know they appear
2466 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2467 * i.e., the coefficient of div is f.
2469 * Otherwise, we first need to introduce div1 into the constraint.
2478 * A lower bound on div2
2482 * can be replaced by
2484 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2486 * with g = gcd(m,n).
2491 * can be replaced by
2493 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2495 * These constraint are those that we would obtain from eliminating
2496 * div1 using Fourier-Motzkin.
2498 * After all constraints have been modified, we drop the lower and upper
2499 * bound and then drop div1.
2501 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2502 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2507 unsigned dim
, total
;
2510 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2511 total
= 1 + dim
+ bmap
->n_div
;
2516 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2517 isl_int_add_ui(m
, m
, 1);
2519 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2520 if (i
== l
|| i
== u
)
2522 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2524 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2525 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2526 isl_int_divexact(a
, m
, b
);
2527 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2528 if (isl_int_is_pos(b
)) {
2529 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2530 b
, bmap
->ineq
[l
], total
);
2533 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2534 b
, bmap
->ineq
[u
], total
);
2537 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2538 bmap
->ineq
[i
][1 + dim
+ div1
]);
2539 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2546 isl_basic_map_drop_inequality(bmap
, l
);
2547 isl_basic_map_drop_inequality(bmap
, u
);
2549 isl_basic_map_drop_inequality(bmap
, u
);
2550 isl_basic_map_drop_inequality(bmap
, l
);
2552 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2556 /* First check if we can coalesce any pair of divs and
2557 * then continue with dropping more redundant divs.
2559 * We loop over all pairs of lower and upper bounds on a div
2560 * with coefficient 1 and -1, respectively, check if there
2561 * is any other div "c" with which we can coalesce the div
2562 * and if so, perform the coalescing.
2564 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2565 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2570 dim
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2572 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2575 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2576 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2578 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2581 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2583 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2587 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2588 return isl_basic_map_drop_redundant_divs(bmap
);
2593 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
2596 return drop_more_redundant_divs(bmap
, pairs
, n
);
2599 /* Remove divs that are not strictly needed.
2600 * In particular, if a div only occurs positively (or negatively)
2601 * in constraints, then it can simply be dropped.
2602 * Also, if a div occurs in only two constraints and if moreover
2603 * those two constraints are opposite to each other, except for the constant
2604 * term and if the sum of the constant terms is such that for any value
2605 * of the other values, there is always at least one integer value of the
2606 * div, i.e., if one plus this sum is greater than or equal to
2607 * the (absolute value) of the coefficent of the div in the constraints,
2608 * then we can also simply drop the div.
2610 * We skip divs that appear in equalities or in the definition of other divs.
2611 * Divs that appear in the definition of other divs usually occur in at least
2612 * 4 constraints, but the constraints may have been simplified.
2614 * If any divs are left after these simple checks then we move on
2615 * to more complicated cases in drop_more_redundant_divs.
2617 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2618 struct isl_basic_map
*bmap
)
2628 off
= isl_space_dim(bmap
->dim
, isl_dim_all
);
2629 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2633 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2635 int last_pos
, last_neg
;
2639 defined
= !isl_int_is_zero(bmap
->div
[i
][0]);
2640 for (j
= i
; j
< bmap
->n_div
; ++j
)
2641 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + off
+ i
]))
2643 if (j
< bmap
->n_div
)
2645 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2646 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2652 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2653 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2657 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2662 pairs
[i
] = pos
* neg
;
2663 if (pairs
[i
] == 0) {
2664 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2665 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2666 isl_basic_map_drop_inequality(bmap
, j
);
2667 bmap
= isl_basic_map_drop_div(bmap
, i
);
2669 return isl_basic_map_drop_redundant_divs(bmap
);
2673 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2674 bmap
->ineq
[last_neg
] + 1,
2678 isl_int_add(bmap
->ineq
[last_pos
][0],
2679 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2680 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2681 bmap
->ineq
[last_pos
][0], 1);
2682 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2683 bmap
->ineq
[last_pos
][1+off
+i
]);
2684 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2685 bmap
->ineq
[last_pos
][0], 1);
2686 isl_int_sub(bmap
->ineq
[last_pos
][0],
2687 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2690 !ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
2695 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
2696 bmap
= isl_basic_map_simplify(bmap
);
2698 return isl_basic_map_drop_redundant_divs(bmap
);
2700 if (last_pos
> last_neg
) {
2701 isl_basic_map_drop_inequality(bmap
, last_pos
);
2702 isl_basic_map_drop_inequality(bmap
, last_neg
);
2704 isl_basic_map_drop_inequality(bmap
, last_neg
);
2705 isl_basic_map_drop_inequality(bmap
, last_pos
);
2707 bmap
= isl_basic_map_drop_div(bmap
, i
);
2709 return isl_basic_map_drop_redundant_divs(bmap
);
2713 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
2719 isl_basic_map_free(bmap
);
2723 struct isl_basic_set
*isl_basic_set_drop_redundant_divs(
2724 struct isl_basic_set
*bset
)
2726 return (struct isl_basic_set
*)
2727 isl_basic_map_drop_redundant_divs((struct isl_basic_map
*)bset
);
2730 struct isl_map
*isl_map_drop_redundant_divs(struct isl_map
*map
)
2736 for (i
= 0; i
< map
->n
; ++i
) {
2737 map
->p
[i
] = isl_basic_map_drop_redundant_divs(map
->p
[i
]);
2741 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
2748 struct isl_set
*isl_set_drop_redundant_divs(struct isl_set
*set
)
2750 return (struct isl_set
*)
2751 isl_map_drop_redundant_divs((struct isl_map
*)set
);