1 #include "isl_equalities.h"
3 #include "isl_map_private.h"
6 static void swap_equality(struct isl_basic_map
*bmap
, int a
, int b
)
8 isl_int
*t
= bmap
->eq
[a
];
9 bmap
->eq
[a
] = bmap
->eq
[b
];
13 static void swap_inequality(struct isl_basic_map
*bmap
, int a
, int b
)
16 isl_int
*t
= bmap
->ineq
[a
];
17 bmap
->ineq
[a
] = bmap
->ineq
[b
];
22 static void set_swap_inequality(struct isl_basic_set
*bset
, int a
, int b
)
24 swap_inequality((struct isl_basic_map
*)bset
, a
, b
);
27 static void constraint_drop_vars(isl_int
*c
, unsigned n
, unsigned rem
)
29 isl_seq_cpy(c
, c
+ n
, rem
);
30 isl_seq_clr(c
+ rem
, n
);
33 /* Drop n dimensions starting at first.
35 * In principle, this frees up some extra variables as the number
36 * of columns remains constant, but we would have to extend
37 * the div array too as the number of rows in this array is assumed
38 * to be equal to extra.
40 struct isl_basic_set
*isl_basic_set_drop_dims(
41 struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
48 isl_assert(bset
->ctx
, first
+ n
<= bset
->dim
->n_out
, goto error
);
53 bset
= isl_basic_set_cow(bset
);
57 for (i
= 0; i
< bset
->n_eq
; ++i
)
58 constraint_drop_vars(bset
->eq
[i
]+1+bset
->dim
->nparam
+first
, n
,
59 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
61 for (i
= 0; i
< bset
->n_ineq
; ++i
)
62 constraint_drop_vars(bset
->ineq
[i
]+1+bset
->dim
->nparam
+first
, n
,
63 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
65 for (i
= 0; i
< bset
->n_div
; ++i
)
66 constraint_drop_vars(bset
->div
[i
]+1+1+bset
->dim
->nparam
+first
, n
,
67 (bset
->dim
->n_out
-first
-n
)+bset
->extra
);
69 bset
->dim
= isl_dim_drop_outputs(bset
->dim
, first
, n
);
73 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
74 bset
= isl_basic_set_simplify(bset
);
75 return isl_basic_set_finalize(bset
);
77 isl_basic_set_free(bset
);
81 struct isl_set
*isl_set_drop_dims(
82 struct isl_set
*set
, unsigned first
, unsigned n
)
89 isl_assert(set
->ctx
, first
+ n
<= set
->dim
->n_out
, goto error
);
93 set
= isl_set_cow(set
);
96 set
->dim
= isl_dim_drop_outputs(set
->dim
, first
, n
);
100 for (i
= 0; i
< set
->n
; ++i
) {
101 set
->p
[i
] = isl_basic_set_drop_dims(set
->p
[i
], first
, n
);
106 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
113 /* Move "n" divs starting at "first" to the end of the list of divs.
115 static struct isl_basic_map
*move_divs_last(struct isl_basic_map
*bmap
,
116 unsigned first
, unsigned n
)
121 if (first
+ n
== bmap
->n_div
)
124 div
= isl_alloc_array(bmap
->ctx
, isl_int
*, n
);
127 for (i
= 0; i
< n
; ++i
)
128 div
[i
] = bmap
->div
[first
+ i
];
129 for (i
= 0; i
< bmap
->n_div
- first
- n
; ++i
)
130 bmap
->div
[first
+ i
] = bmap
->div
[first
+ n
+ i
];
131 for (i
= 0; i
< n
; ++i
)
132 bmap
->div
[bmap
->n_div
- n
+ i
] = div
[i
];
136 isl_basic_map_free(bmap
);
140 /* Drop "n" dimensions of type "type" starting at "first".
142 * In principle, this frees up some extra variables as the number
143 * of columns remains constant, but we would have to extend
144 * the div array too as the number of rows in this array is assumed
145 * to be equal to extra.
147 struct isl_basic_map
*isl_basic_map_drop(struct isl_basic_map
*bmap
,
148 enum isl_dim_type type
, unsigned first
, unsigned n
)
158 dim
= isl_basic_map_dim(bmap
, type
);
159 isl_assert(bmap
->ctx
, first
+ n
<= dim
, goto error
);
164 bmap
= isl_basic_map_cow(bmap
);
168 offset
= isl_basic_map_offset(bmap
, type
) + first
;
169 left
= isl_basic_map_total_dim(bmap
) - (offset
- 1) - n
;
170 for (i
= 0; i
< bmap
->n_eq
; ++i
)
171 constraint_drop_vars(bmap
->eq
[i
]+offset
, n
, left
);
173 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
174 constraint_drop_vars(bmap
->ineq
[i
]+offset
, n
, left
);
176 for (i
= 0; i
< bmap
->n_div
; ++i
)
177 constraint_drop_vars(bmap
->div
[i
]+1+offset
, n
, left
);
179 if (type
== isl_dim_div
) {
180 bmap
= move_divs_last(bmap
, first
, n
);
183 isl_basic_map_free_div(bmap
, n
);
185 bmap
->dim
= isl_dim_drop(bmap
->dim
, type
, first
, n
);
189 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
190 bmap
= isl_basic_map_simplify(bmap
);
191 return isl_basic_map_finalize(bmap
);
193 isl_basic_map_free(bmap
);
197 struct isl_basic_map
*isl_basic_map_drop_inputs(
198 struct isl_basic_map
*bmap
, unsigned first
, unsigned n
)
200 return isl_basic_map_drop(bmap
, isl_dim_in
, first
, n
);
203 struct isl_map
*isl_map_drop(struct isl_map
*map
,
204 enum isl_dim_type type
, unsigned first
, unsigned n
)
211 isl_assert(map
->ctx
, first
+ n
<= isl_map_dim(map
, type
), goto error
);
215 map
= isl_map_cow(map
);
218 map
->dim
= isl_dim_drop(map
->dim
, type
, first
, n
);
222 for (i
= 0; i
< map
->n
; ++i
) {
223 map
->p
[i
] = isl_basic_map_drop(map
->p
[i
], type
, first
, n
);
227 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
235 struct isl_map
*isl_map_drop_inputs(
236 struct isl_map
*map
, unsigned first
, unsigned n
)
238 return isl_map_drop(map
, isl_dim_in
, first
, n
);
242 * We don't cow, as the div is assumed to be redundant.
244 static struct isl_basic_map
*isl_basic_map_drop_div(
245 struct isl_basic_map
*bmap
, unsigned div
)
253 pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
255 isl_assert(bmap
->ctx
, div
< bmap
->n_div
, goto error
);
257 for (i
= 0; i
< bmap
->n_eq
; ++i
)
258 constraint_drop_vars(bmap
->eq
[i
]+pos
, 1, bmap
->extra
-div
-1);
260 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
261 if (!isl_int_is_zero(bmap
->ineq
[i
][pos
])) {
262 isl_basic_map_drop_inequality(bmap
, i
);
266 constraint_drop_vars(bmap
->ineq
[i
]+pos
, 1, bmap
->extra
-div
-1);
269 for (i
= 0; i
< bmap
->n_div
; ++i
)
270 constraint_drop_vars(bmap
->div
[i
]+1+pos
, 1, bmap
->extra
-div
-1);
272 if (div
!= bmap
->n_div
- 1) {
274 isl_int
*t
= bmap
->div
[div
];
276 for (j
= div
; j
< bmap
->n_div
- 1; ++j
)
277 bmap
->div
[j
] = bmap
->div
[j
+1];
279 bmap
->div
[bmap
->n_div
- 1] = t
;
281 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
282 isl_basic_map_free_div(bmap
, 1);
286 isl_basic_map_free(bmap
);
290 struct isl_basic_map
*isl_basic_map_normalize_constraints(
291 struct isl_basic_map
*bmap
)
295 unsigned total
= isl_basic_map_total_dim(bmap
);
298 for (i
= bmap
->n_eq
- 1; i
>= 0; --i
) {
299 isl_seq_gcd(bmap
->eq
[i
]+1, total
, &gcd
);
300 if (isl_int_is_zero(gcd
)) {
301 if (!isl_int_is_zero(bmap
->eq
[i
][0])) {
302 bmap
= isl_basic_map_set_to_empty(bmap
);
305 isl_basic_map_drop_equality(bmap
, i
);
308 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
309 isl_int_gcd(gcd
, gcd
, bmap
->eq
[i
][0]);
310 if (isl_int_is_one(gcd
))
312 if (!isl_int_is_divisible_by(bmap
->eq
[i
][0], gcd
)) {
313 bmap
= isl_basic_map_set_to_empty(bmap
);
316 isl_seq_scale_down(bmap
->eq
[i
], bmap
->eq
[i
], gcd
, 1+total
);
319 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
320 isl_seq_gcd(bmap
->ineq
[i
]+1, total
, &gcd
);
321 if (isl_int_is_zero(gcd
)) {
322 if (isl_int_is_neg(bmap
->ineq
[i
][0])) {
323 bmap
= isl_basic_map_set_to_empty(bmap
);
326 isl_basic_map_drop_inequality(bmap
, i
);
329 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
330 isl_int_gcd(gcd
, gcd
, bmap
->ineq
[i
][0]);
331 if (isl_int_is_one(gcd
))
333 isl_int_fdiv_q(bmap
->ineq
[i
][0], bmap
->ineq
[i
][0], gcd
);
334 isl_seq_scale_down(bmap
->ineq
[i
]+1, bmap
->ineq
[i
]+1, gcd
, total
);
341 struct isl_basic_set
*isl_basic_set_normalize_constraints(
342 struct isl_basic_set
*bset
)
344 (struct isl_basic_set
*)isl_basic_map_normalize_constraints(
345 (struct isl_basic_map
*)bset
);
348 static void eliminate_div(struct isl_basic_map
*bmap
, isl_int
*eq
, unsigned div
)
351 unsigned pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
353 len
= 1 + isl_basic_map_total_dim(bmap
);
355 for (i
= 0; i
< bmap
->n_eq
; ++i
)
356 if (bmap
->eq
[i
] != eq
)
357 isl_seq_elim(bmap
->eq
[i
], eq
, pos
, len
, NULL
);
359 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
360 isl_seq_elim(bmap
->ineq
[i
], eq
, pos
, len
, NULL
);
362 /* We need to be careful about circular definitions,
363 * so for now we just remove the definitions of other divs that
364 * depend on this div and (possibly) recompute them later.
366 for (i
= 0; i
< bmap
->n_div
; ++i
)
367 if (!isl_int_is_zero(bmap
->div
[i
][0]) &&
368 !isl_int_is_zero(bmap
->div
[i
][1 + pos
]))
369 isl_seq_clr(bmap
->div
[i
], 1 + len
);
371 isl_basic_map_drop_div(bmap
, div
);
374 /* Elimininate divs based on equalities
376 static struct isl_basic_map
*eliminate_divs_eq(
377 struct isl_basic_map
*bmap
, int *progress
)
387 off
= 1 + isl_dim_total(bmap
->dim
);
389 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
390 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
391 if (!isl_int_is_one(bmap
->eq
[i
][off
+ d
]) &&
392 !isl_int_is_negone(bmap
->eq
[i
][off
+ d
]))
396 eliminate_div(bmap
, bmap
->eq
[i
], d
);
397 isl_basic_map_drop_equality(bmap
, i
);
402 return eliminate_divs_eq(bmap
, progress
);
406 /* Elimininate divs based on inequalities
408 static struct isl_basic_map
*eliminate_divs_ineq(
409 struct isl_basic_map
*bmap
, int *progress
)
420 off
= 1 + isl_dim_total(bmap
->dim
);
422 for (d
= bmap
->n_div
- 1; d
>= 0 ; --d
) {
423 for (i
= 0; i
< bmap
->n_eq
; ++i
)
424 if (!isl_int_is_zero(bmap
->eq
[i
][off
+ d
]))
428 for (i
= 0; i
< bmap
->n_ineq
; ++i
)
429 if (isl_int_abs_gt(bmap
->ineq
[i
][off
+ d
], ctx
->one
))
431 if (i
< bmap
->n_ineq
)
434 bmap
= isl_basic_map_eliminate_vars(bmap
, (off
-1)+d
, 1);
435 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
437 bmap
= isl_basic_map_drop_div(bmap
, d
);
444 static void eliminate_var_using_equality(struct isl_basic_map
*bmap
,
445 unsigned pos
, isl_int
*eq
, int *progress
)
451 total
= isl_basic_map_total_dim(bmap
);
453 isl_seq_first_non_zero(eq
+ 1 + isl_dim_total(bmap
->dim
),
455 for (k
= 0; k
< bmap
->n_eq
; ++k
) {
456 if (bmap
->eq
[k
] == eq
)
458 if (isl_int_is_zero(bmap
->eq
[k
][1+pos
]))
462 isl_seq_elim(bmap
->eq
[k
], eq
, 1+pos
, 1+total
, NULL
);
465 for (k
= 0; k
< bmap
->n_ineq
; ++k
) {
466 if (isl_int_is_zero(bmap
->ineq
[k
][1+pos
]))
470 isl_seq_elim(bmap
->ineq
[k
], eq
, 1+pos
, 1+total
, NULL
);
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.
486 isl_seq_clr(bmap
->div
[k
], 1 + total
);
488 isl_seq_elim(bmap
->div
[k
]+1, eq
,
489 1+pos
, 1+total
, &bmap
->div
[k
][0]);
490 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
494 struct isl_basic_map
*isl_basic_map_gauss(
495 struct isl_basic_map
*bmap
, int *progress
)
506 total
= isl_basic_map_total_dim(bmap
);
507 total_var
= total
- bmap
->n_div
;
509 last_var
= total
- 1;
510 for (done
= 0; done
< bmap
->n_eq
; ++done
) {
511 for (; last_var
>= 0; --last_var
) {
512 for (k
= done
; k
< bmap
->n_eq
; ++k
)
513 if (!isl_int_is_zero(bmap
->eq
[k
][1+last_var
]))
521 swap_equality(bmap
, k
, done
);
522 if (isl_int_is_neg(bmap
->eq
[done
][1+last_var
]))
523 isl_seq_neg(bmap
->eq
[done
], bmap
->eq
[done
], 1+total
);
525 eliminate_var_using_equality(bmap
, last_var
, bmap
->eq
[done
],
528 if (last_var
>= total_var
&&
529 isl_int_is_zero(bmap
->div
[last_var
- total_var
][0])) {
530 unsigned div
= last_var
- total_var
;
531 isl_seq_neg(bmap
->div
[div
]+1, bmap
->eq
[done
], 1+total
);
532 isl_int_set_si(bmap
->div
[div
][1+1+last_var
], 0);
533 isl_int_set(bmap
->div
[div
][0],
534 bmap
->eq
[done
][1+last_var
]);
535 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
538 if (done
== bmap
->n_eq
)
540 for (k
= done
; k
< bmap
->n_eq
; ++k
) {
541 if (isl_int_is_zero(bmap
->eq
[k
][0]))
543 return isl_basic_map_set_to_empty(bmap
);
545 isl_basic_map_free_equality(bmap
, bmap
->n_eq
-done
);
549 struct isl_basic_set
*isl_basic_set_gauss(
550 struct isl_basic_set
*bset
, int *progress
)
552 return (struct isl_basic_set
*)isl_basic_map_gauss(
553 (struct isl_basic_map
*)bset
, progress
);
557 static unsigned int round_up(unsigned int v
)
568 static int hash_index(isl_int
***index
, unsigned int size
, int bits
,
569 struct isl_basic_map
*bmap
, int k
)
572 unsigned total
= isl_basic_map_total_dim(bmap
);
573 uint32_t hash
= isl_seq_get_hash_bits(bmap
->ineq
[k
]+1, total
, bits
);
574 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
575 if (&bmap
->ineq
[k
] != index
[h
] &&
576 isl_seq_eq(bmap
->ineq
[k
]+1, index
[h
][0]+1, total
))
581 static int set_hash_index(isl_int
***index
, unsigned int size
, int bits
,
582 struct isl_basic_set
*bset
, int k
)
584 return hash_index(index
, size
, bits
, (struct isl_basic_map
*)bset
, k
);
587 /* If we can eliminate more than one div, then we need to make
588 * sure we do it from last div to first div, in order not to
589 * change the position of the other divs that still need to
592 static struct isl_basic_map
*remove_duplicate_divs(
593 struct isl_basic_map
*bmap
, int *progress
)
601 unsigned total_var
= isl_dim_total(bmap
->dim
);
602 unsigned total
= total_var
+ bmap
->n_div
;
605 if (bmap
->n_div
<= 1)
609 for (k
= bmap
->n_div
- 1; k
>= 0; --k
)
610 if (!isl_int_is_zero(bmap
->div
[k
][0]))
615 elim_for
= isl_calloc_array(ctx
, int, bmap
->n_div
);
616 size
= round_up(4 * bmap
->n_div
/ 3 - 1);
617 bits
= ffs(size
) - 1;
618 index
= isl_calloc_array(ctx
, int, size
);
621 eq
= isl_blk_alloc(ctx
, 1+total
);
622 if (isl_blk_is_error(eq
))
625 isl_seq_clr(eq
.data
, 1+total
);
626 index
[isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
)] = k
+ 1;
627 for (--k
; k
>= 0; --k
) {
630 if (isl_int_is_zero(bmap
->div
[k
][0]))
633 hash
= isl_seq_get_hash_bits(bmap
->div
[k
], 2+total
, bits
);
634 for (h
= hash
; index
[h
]; h
= (h
+1) % size
)
635 if (isl_seq_eq(bmap
->div
[k
],
636 bmap
->div
[index
[h
]-1], 2+total
))
645 for (l
= bmap
->n_div
- 1; l
>= 0; --l
) {
649 isl_int_set_si(eq
.data
[1+total_var
+k
], -1);
650 isl_int_set_si(eq
.data
[1+total_var
+l
], 1);
651 eliminate_div(bmap
, eq
.data
, l
);
652 isl_int_set_si(eq
.data
[1+total_var
+k
], 0);
653 isl_int_set_si(eq
.data
[1+total_var
+l
], 0);
656 isl_blk_free(ctx
, eq
);
663 static int n_pure_div_eq(struct isl_basic_map
*bmap
)
668 total
= isl_dim_total(bmap
->dim
);
669 for (i
= 0, j
= bmap
->n_div
-1; i
< bmap
->n_eq
; ++i
) {
670 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
674 if (isl_seq_first_non_zero(bmap
->eq
[i
] + 1 + total
, j
) != -1)
680 /* Normalize divs that appear in equalities.
682 * In particular, we assume that bmap contains some equalities
687 * and we want to replace the set of e_i by a minimal set and
688 * such that the new e_i have a canonical representation in terms
690 * If any of the equalities involves more than one divs, then
691 * we currently simply bail out.
693 * Let us first additionally assume that all equalities involve
694 * a div. The equalities then express modulo constraints on the
695 * remaining variables and we can use "parameter compression"
696 * to find a minimal set of constraints. The result is a transformation
698 * x = T(x') = x_0 + G x'
700 * with G a lower-triangular matrix with all elements below the diagonal
701 * non-negative and smaller than the diagonal element on the same row.
702 * We first normalize x_0 by making the same property hold in the affine
704 * The rows i of G with a 1 on the diagonal do not impose any modulo
705 * constraint and simply express x_i = x'_i.
706 * For each of the remaining rows i, we introduce a div and a corresponding
707 * equality. In particular
709 * g_ii e_j = x_i - g_i(x')
711 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
712 * corresponding div (if g_kk != 1).
714 * If there are any equalities not involving any div, then we
715 * first apply a variable compression on the variables x:
717 * x = C x'' x'' = C_2 x
719 * and perform the above parameter compression on A C instead of on A.
720 * The resulting compression is then of the form
722 * x'' = T(x') = x_0 + G x'
724 * and in constructing the new divs and the corresponding equalities,
725 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
726 * by the corresponding row from C_2.
728 static struct isl_basic_map
*normalize_divs(
729 struct isl_basic_map
*bmap
, int *progress
)
736 struct isl_mat
*T
= NULL
;
737 struct isl_mat
*C
= NULL
;
738 struct isl_mat
*C2
= NULL
;
746 if (bmap
->n_div
== 0)
752 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
))
755 total
= isl_dim_total(bmap
->dim
);
756 div_eq
= n_pure_div_eq(bmap
);
760 if (div_eq
< bmap
->n_eq
) {
761 B
= isl_mat_sub_alloc(bmap
->ctx
, bmap
->eq
, div_eq
,
762 bmap
->n_eq
- div_eq
, 0, 1 + total
);
763 C
= isl_mat_variable_compression(B
, &C2
);
767 bmap
= isl_basic_map_set_to_empty(bmap
);
774 d
= isl_vec_alloc(bmap
->ctx
, div_eq
);
777 for (i
= 0, j
= bmap
->n_div
-1; i
< div_eq
; ++i
) {
778 while (j
>= 0 && isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
780 isl_int_set(d
->block
.data
[i
], bmap
->eq
[i
][1 + total
+ j
]);
782 B
= isl_mat_sub_alloc(bmap
->ctx
, bmap
->eq
, 0, div_eq
, 0, 1 + total
);
785 B
= isl_mat_product(B
, C
);
789 T
= isl_mat_parameter_compression(B
, d
);
793 bmap
= isl_basic_map_set_to_empty(bmap
);
799 for (i
= 0; i
< T
->n_row
- 1; ++i
) {
800 isl_int_fdiv_q(v
, T
->row
[1 + i
][0], T
->row
[1 + i
][1 + i
]);
801 if (isl_int_is_zero(v
))
803 isl_mat_col_submul(T
, 0, v
, 1 + i
);
806 pos
= isl_alloc_array(bmap
->ctx
, int, T
->n_row
);
807 /* We have to be careful because dropping equalities may reorder them */
809 for (j
= bmap
->n_div
- 1; j
>= 0; --j
) {
810 for (i
= 0; i
< bmap
->n_eq
; ++i
)
811 if (!isl_int_is_zero(bmap
->eq
[i
][1 + total
+ j
]))
813 if (i
< bmap
->n_eq
) {
814 bmap
= isl_basic_map_drop_div(bmap
, j
);
815 isl_basic_map_drop_equality(bmap
, i
);
821 for (i
= 1; i
< T
->n_row
; ++i
) {
822 if (isl_int_is_one(T
->row
[i
][i
]))
827 if (needed
> dropped
) {
828 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
),
833 for (i
= 1; i
< T
->n_row
; ++i
) {
834 if (isl_int_is_one(T
->row
[i
][i
]))
836 k
= isl_basic_map_alloc_div(bmap
);
837 pos
[i
] = 1 + total
+ k
;
838 isl_seq_clr(bmap
->div
[k
] + 1, 1 + total
+ bmap
->n_div
);
839 isl_int_set(bmap
->div
[k
][0], T
->row
[i
][i
]);
841 isl_seq_cpy(bmap
->div
[k
] + 1, C2
->row
[i
], 1 + total
);
843 isl_int_set_si(bmap
->div
[k
][1 + i
], 1);
844 for (j
= 0; j
< i
; ++j
) {
845 if (isl_int_is_zero(T
->row
[i
][j
]))
847 if (pos
[j
] < T
->n_row
&& C2
)
848 isl_seq_submul(bmap
->div
[k
] + 1, T
->row
[i
][j
],
849 C2
->row
[pos
[j
]], 1 + total
);
851 isl_int_neg(bmap
->div
[k
][1 + pos
[j
]],
854 j
= isl_basic_map_alloc_equality(bmap
);
855 isl_seq_neg(bmap
->eq
[j
], bmap
->div
[k
]+1, 1+total
+bmap
->n_div
);
856 isl_int_set(bmap
->eq
[j
][pos
[i
]], bmap
->div
[k
][0]);
865 ISL_F_SET(bmap
, ISL_BASIC_MAP_NORMALIZED_DIVS
);
875 static struct isl_basic_map
*set_div_from_lower_bound(
876 struct isl_basic_map
*bmap
, int div
, int ineq
)
878 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
880 isl_seq_neg(bmap
->div
[div
] + 1, bmap
->ineq
[ineq
], total
+ bmap
->n_div
);
881 isl_int_set(bmap
->div
[div
][0], bmap
->ineq
[ineq
][total
+ div
]);
882 isl_int_add(bmap
->div
[div
][1], bmap
->div
[div
][1], bmap
->div
[div
][0]);
883 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
884 isl_int_set_si(bmap
->div
[div
][1 + total
+ div
], 0);
889 /* Check whether it is ok to define a div based on an inequality.
890 * To avoid the introduction of circular definitions of divs, we
891 * do not allow such a definition if the resulting expression would refer to
892 * any other undefined divs or if any known div is defined in
893 * terms of the unknown div.
895 static int ok_to_set_div_from_bound(struct isl_basic_map
*bmap
,
899 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
901 /* Not defined in terms of unknown divs */
902 for (j
= 0; j
< bmap
->n_div
; ++j
) {
905 if (isl_int_is_zero(bmap
->ineq
[ineq
][total
+ j
]))
907 if (isl_int_is_zero(bmap
->div
[j
][0]))
911 /* No other div defined in terms of this one => avoid loops */
912 for (j
= 0; j
< bmap
->n_div
; ++j
) {
915 if (isl_int_is_zero(bmap
->div
[j
][0]))
917 if (!isl_int_is_zero(bmap
->div
[j
][1 + total
+ div
]))
924 /* Given two constraints "k" and "l" that are opposite to each other,
925 * except for the constant term, check if we can use them
926 * to obtain an expression for one of the hitherto unknown divs.
927 * "sum" is the sum of the constant terms of the constraints.
928 * If this sum is strictly smaller than the coefficient of one
929 * of the divs, then this pair can be used define the div.
930 * To avoid the introduction of circular definitions of divs, we
931 * do not use the pair if the resulting expression would refer to
932 * any other undefined divs or if any known div is defined in
933 * terms of the unknown div.
935 static struct isl_basic_map
*check_for_div_constraints(
936 struct isl_basic_map
*bmap
, int k
, int l
, isl_int sum
, int *progress
)
939 unsigned total
= 1 + isl_dim_total(bmap
->dim
);
941 for (i
= 0; i
< bmap
->n_div
; ++i
) {
942 if (!isl_int_is_zero(bmap
->div
[i
][0]))
944 if (isl_int_is_zero(bmap
->ineq
[k
][total
+ i
]))
946 if (isl_int_abs_ge(sum
, bmap
->ineq
[k
][total
+ i
]))
948 if (!ok_to_set_div_from_bound(bmap
, i
, k
))
950 if (isl_int_is_pos(bmap
->ineq
[k
][total
+ i
]))
951 bmap
= set_div_from_lower_bound(bmap
, i
, k
);
953 bmap
= set_div_from_lower_bound(bmap
, i
, l
);
961 static struct isl_basic_map
*remove_duplicate_constraints(
962 struct isl_basic_map
*bmap
, int *progress
)
968 unsigned total
= isl_basic_map_total_dim(bmap
);
971 if (bmap
->n_ineq
<= 1)
974 size
= round_up(4 * (bmap
->n_ineq
+1) / 3 - 1);
975 bits
= ffs(size
) - 1;
976 index
= isl_calloc_array(ctx
, isl_int
**, size
);
980 index
[isl_seq_get_hash_bits(bmap
->ineq
[0]+1, total
, bits
)] = &bmap
->ineq
[0];
981 for (k
= 1; k
< bmap
->n_ineq
; ++k
) {
982 h
= hash_index(index
, size
, bits
, bmap
, k
);
984 index
[h
] = &bmap
->ineq
[k
];
989 l
= index
[h
] - &bmap
->ineq
[0];
990 if (isl_int_lt(bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]))
991 swap_inequality(bmap
, k
, l
);
992 isl_basic_map_drop_inequality(bmap
, k
);
996 for (k
= 0; k
< bmap
->n_ineq
-1; ++k
) {
997 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
998 h
= hash_index(index
, size
, bits
, bmap
, k
);
999 isl_seq_neg(bmap
->ineq
[k
]+1, bmap
->ineq
[k
]+1, total
);
1002 l
= index
[h
] - &bmap
->ineq
[0];
1003 isl_int_add(sum
, bmap
->ineq
[k
][0], bmap
->ineq
[l
][0]);
1004 if (isl_int_is_pos(sum
)) {
1005 bmap
= check_for_div_constraints(bmap
, k
, l
, sum
,
1009 if (isl_int_is_zero(sum
)) {
1010 /* We need to break out of the loop after these
1011 * changes since the contents of the hash
1012 * will no longer be valid.
1013 * Plus, we probably we want to regauss first.
1015 isl_basic_map_drop_inequality(bmap
, l
);
1016 isl_basic_map_inequality_to_equality(bmap
, k
);
1018 bmap
= isl_basic_map_set_to_empty(bmap
);
1028 struct isl_basic_map
*isl_basic_map_simplify(struct isl_basic_map
*bmap
)
1035 bmap
= isl_basic_map_normalize_constraints(bmap
);
1036 bmap
= remove_duplicate_divs(bmap
, &progress
);
1037 bmap
= eliminate_divs_eq(bmap
, &progress
);
1038 bmap
= eliminate_divs_ineq(bmap
, &progress
);
1039 bmap
= isl_basic_map_gauss(bmap
, &progress
);
1040 /* requires equalities in normal form */
1041 bmap
= normalize_divs(bmap
, &progress
);
1042 bmap
= remove_duplicate_constraints(bmap
, &progress
);
1047 struct isl_basic_set
*isl_basic_set_simplify(struct isl_basic_set
*bset
)
1049 return (struct isl_basic_set
*)
1050 isl_basic_map_simplify((struct isl_basic_map
*)bset
);
1054 /* If the only constraints a div d=floor(f/m)
1055 * appears in are its two defining constraints
1058 * -(f - (m - 1)) + m d >= 0
1060 * then it can safely be removed.
1062 static int div_is_redundant(struct isl_basic_map
*bmap
, int div
)
1065 unsigned pos
= 1 + isl_dim_total(bmap
->dim
) + div
;
1067 for (i
= 0; i
< bmap
->n_eq
; ++i
)
1068 if (!isl_int_is_zero(bmap
->eq
[i
][pos
]))
1071 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1072 if (isl_int_is_zero(bmap
->ineq
[i
][pos
]))
1074 if (isl_int_eq(bmap
->ineq
[i
][pos
], bmap
->div
[div
][0])) {
1076 isl_int_sub(bmap
->div
[div
][1],
1077 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1078 isl_int_add_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1079 neg
= isl_seq_is_neg(bmap
->ineq
[i
], bmap
->div
[div
]+1, pos
);
1080 isl_int_sub_ui(bmap
->div
[div
][1], bmap
->div
[div
][1], 1);
1081 isl_int_add(bmap
->div
[div
][1],
1082 bmap
->div
[div
][1], bmap
->div
[div
][0]);
1085 if (isl_seq_first_non_zero(bmap
->ineq
[i
]+pos
+1,
1086 bmap
->n_div
-div
-1) != -1)
1088 } else if (isl_int_abs_eq(bmap
->ineq
[i
][pos
], bmap
->div
[div
][0])) {
1089 if (!isl_seq_eq(bmap
->ineq
[i
], bmap
->div
[div
]+1, pos
))
1091 if (isl_seq_first_non_zero(bmap
->ineq
[i
]+pos
+1,
1092 bmap
->n_div
-div
-1) != -1)
1098 for (i
= 0; i
< bmap
->n_div
; ++i
)
1099 if (!isl_int_is_zero(bmap
->div
[i
][1+pos
]))
1106 * Remove divs that don't occur in any of the constraints or other divs.
1107 * These can arise when dropping some of the variables in a quast
1108 * returned by piplib.
1110 static struct isl_basic_map
*remove_redundant_divs(struct isl_basic_map
*bmap
)
1117 for (i
= bmap
->n_div
-1; i
>= 0; --i
) {
1118 if (!div_is_redundant(bmap
, i
))
1120 bmap
= isl_basic_map_drop_div(bmap
, i
);
1125 struct isl_basic_map
*isl_basic_map_finalize(struct isl_basic_map
*bmap
)
1127 bmap
= remove_redundant_divs(bmap
);
1130 ISL_F_SET(bmap
, ISL_BASIC_SET_FINAL
);
1134 struct isl_basic_set
*isl_basic_set_finalize(struct isl_basic_set
*bset
)
1136 return (struct isl_basic_set
*)
1137 isl_basic_map_finalize((struct isl_basic_map
*)bset
);
1140 struct isl_set
*isl_set_finalize(struct isl_set
*set
)
1146 for (i
= 0; i
< set
->n
; ++i
) {
1147 set
->p
[i
] = isl_basic_set_finalize(set
->p
[i
]);
1157 struct isl_map
*isl_map_finalize(struct isl_map
*map
)
1163 for (i
= 0; i
< map
->n
; ++i
) {
1164 map
->p
[i
] = isl_basic_map_finalize(map
->p
[i
]);
1168 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1176 /* Remove definition of any div that is defined in terms of the given variable.
1177 * The div itself is not removed. Functions such as
1178 * eliminate_divs_ineq depend on the other divs remaining in place.
1180 static struct isl_basic_map
*remove_dependent_vars(struct isl_basic_map
*bmap
,
1184 unsigned dim
= isl_dim_total(bmap
->dim
);
1186 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1187 if (isl_int_is_zero(bmap
->div
[i
][0]))
1189 if (isl_int_is_zero(bmap
->div
[i
][1+1+pos
]))
1191 isl_int_set_si(bmap
->div
[i
][0], 0);
1196 /* Eliminate the specified variables from the constraints using
1197 * Fourier-Motzkin. The variables themselves are not removed.
1199 struct isl_basic_map
*isl_basic_map_eliminate_vars(
1200 struct isl_basic_map
*bmap
, unsigned pos
, unsigned n
)
1210 total
= isl_basic_map_total_dim(bmap
);
1212 bmap
= isl_basic_map_cow(bmap
);
1213 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
)
1214 bmap
= remove_dependent_vars(bmap
, d
);
1216 for (d
= pos
+ n
- 1;
1217 d
>= 0 && d
>= total
- bmap
->n_div
&& d
>= pos
; --d
)
1218 isl_seq_clr(bmap
->div
[d
-(total
-bmap
->n_div
)], 2+total
);
1219 for (d
= pos
+ n
- 1; d
>= 0 && d
>= pos
; --d
) {
1220 int n_lower
, n_upper
;
1223 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1224 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1226 eliminate_var_using_equality(bmap
, d
, bmap
->eq
[i
], NULL
);
1227 isl_basic_map_drop_equality(bmap
, i
);
1234 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1235 if (isl_int_is_pos(bmap
->ineq
[i
][1+d
]))
1237 else if (isl_int_is_neg(bmap
->ineq
[i
][1+d
]))
1240 bmap
= isl_basic_map_extend_constraints(bmap
,
1241 0, n_lower
* n_upper
);
1242 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1244 if (isl_int_is_zero(bmap
->ineq
[i
][1+d
]))
1247 for (j
= 0; j
< i
; ++j
) {
1248 if (isl_int_is_zero(bmap
->ineq
[j
][1+d
]))
1251 if (isl_int_sgn(bmap
->ineq
[i
][1+d
]) ==
1252 isl_int_sgn(bmap
->ineq
[j
][1+d
]))
1254 k
= isl_basic_map_alloc_inequality(bmap
);
1257 isl_seq_cpy(bmap
->ineq
[k
], bmap
->ineq
[i
],
1259 isl_seq_elim(bmap
->ineq
[k
], bmap
->ineq
[j
],
1260 1+d
, 1+total
, NULL
);
1262 isl_basic_map_drop_inequality(bmap
, i
);
1265 if (n_lower
> 0 && n_upper
> 0) {
1266 bmap
= isl_basic_map_normalize_constraints(bmap
);
1267 bmap
= remove_duplicate_constraints(bmap
, NULL
);
1268 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1269 bmap
= isl_basic_map_convex_hull(bmap
);
1272 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1276 ISL_F_CLR(bmap
, ISL_BASIC_MAP_NORMALIZED
);
1279 isl_basic_map_free(bmap
);
1283 struct isl_basic_set
*isl_basic_set_eliminate_vars(
1284 struct isl_basic_set
*bset
, unsigned pos
, unsigned n
)
1286 return (struct isl_basic_set
*)isl_basic_map_eliminate_vars(
1287 (struct isl_basic_map
*)bset
, pos
, n
);
1290 /* Don't assume equalities are in order, because align_divs
1291 * may have changed the order of the divs.
1293 static void compute_elimination_index(struct isl_basic_map
*bmap
, int *elim
)
1298 total
= isl_dim_total(bmap
->dim
);
1299 for (d
= 0; d
< total
; ++d
)
1301 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1302 for (d
= total
- 1; d
>= 0; --d
) {
1303 if (isl_int_is_zero(bmap
->eq
[i
][1+d
]))
1311 static void set_compute_elimination_index(struct isl_basic_set
*bset
, int *elim
)
1313 return compute_elimination_index((struct isl_basic_map
*)bset
, elim
);
1316 static int reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1317 struct isl_basic_map
*bmap
, int *elim
)
1323 total
= isl_dim_total(bmap
->dim
);
1324 for (d
= total
- 1; d
>= 0; --d
) {
1325 if (isl_int_is_zero(src
[1+d
]))
1330 isl_seq_cpy(dst
, src
, 1 + total
);
1333 isl_seq_elim(dst
, bmap
->eq
[elim
[d
]], 1 + d
, 1 + total
, NULL
);
1338 static int set_reduced_using_equalities(isl_int
*dst
, isl_int
*src
,
1339 struct isl_basic_set
*bset
, int *elim
)
1341 return reduced_using_equalities(dst
, src
,
1342 (struct isl_basic_map
*)bset
, elim
);
1345 static struct isl_basic_set
*isl_basic_set_reduce_using_equalities(
1346 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1351 if (!bset
|| !context
)
1354 bset
= isl_basic_set_cow(bset
);
1358 elim
= isl_alloc_array(ctx
, int, isl_basic_set_n_dim(bset
));
1361 set_compute_elimination_index(context
, elim
);
1362 for (i
= 0; i
< bset
->n_eq
; ++i
)
1363 set_reduced_using_equalities(bset
->eq
[i
], bset
->eq
[i
],
1365 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1366 set_reduced_using_equalities(bset
->ineq
[i
], bset
->ineq
[i
],
1368 isl_basic_set_free(context
);
1370 bset
= isl_basic_set_simplify(bset
);
1371 bset
= isl_basic_set_finalize(bset
);
1374 isl_basic_set_free(bset
);
1375 isl_basic_set_free(context
);
1379 static struct isl_basic_set
*remove_shifted_constraints(
1380 struct isl_basic_set
*bset
, struct isl_basic_set
*context
)
1390 size
= round_up(4 * (context
->n_ineq
+1) / 3 - 1);
1391 bits
= ffs(size
) - 1;
1392 index
= isl_calloc_array(ctx
, isl_int
**, size
);
1396 for (k
= 0; k
< context
->n_ineq
; ++k
) {
1397 h
= set_hash_index(index
, size
, bits
, context
, k
);
1398 index
[h
] = &context
->ineq
[k
];
1400 for (k
= 0; k
< bset
->n_ineq
; ++k
) {
1401 h
= set_hash_index(index
, size
, bits
, bset
, k
);
1404 l
= index
[h
] - &context
->ineq
[0];
1405 if (isl_int_lt(bset
->ineq
[k
][0], context
->ineq
[l
][0]))
1407 bset
= isl_basic_set_cow(bset
);
1410 isl_basic_set_drop_inequality(bset
, k
);
1420 /* Tighten (decrease) the constant terms of the inequalities based
1421 * on the equalities, without removing any integer points.
1422 * For example, if there is an equality
1430 * then we want to replace the inequality by
1434 * We do this by computing a variable compression and translating
1435 * the constraints to the compressed space.
1436 * If any constraint has coefficients (except the contant term)
1437 * with a common factor "f", then we can replace the constant term "c"
1444 * f * floor(c/f) - c = -fract(c/f)
1446 * and we can add the same value to the original constraint.
1448 * In the example, the compressed space only contains "j",
1449 * and the inequality translates to
1453 * We add -fract(-1/3) = -2 to the original constraint to obtain
1457 static struct isl_basic_set
*normalize_constraints_in_compressed_space(
1458 struct isl_basic_set
*bset
)
1462 struct isl_mat
*B
, *C
;
1468 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
))
1474 bset
= isl_basic_set_cow(bset
);
1478 total
= isl_basic_set_total_dim(bset
);
1479 B
= isl_mat_sub_alloc(bset
->ctx
, bset
->eq
, 0, bset
->n_eq
, 0, 1 + total
);
1480 C
= isl_mat_variable_compression(B
, NULL
);
1483 if (C
->n_col
== 0) {
1485 return isl_basic_set_set_to_empty(bset
);
1487 B
= isl_mat_sub_alloc(bset
->ctx
, bset
->ineq
,
1488 0, bset
->n_ineq
, 0, 1 + total
);
1489 C
= isl_mat_product(B
, C
);
1494 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1495 isl_seq_gcd(C
->row
[i
] + 1, C
->n_col
- 1, &gcd
);
1496 if (isl_int_is_one(gcd
))
1498 isl_int_fdiv_r(C
->row
[i
][0], C
->row
[i
][0], gcd
);
1499 isl_int_sub(bset
->ineq
[i
][0], bset
->ineq
[i
][0], C
->row
[i
][0]);
1508 /* Remove all information from bset that is redundant in the context
1509 * of context. In particular, equalities that are linear combinations
1510 * of those in context are removed. Then the inequalities that are
1511 * redundant in the context of the equalities and inequalities of
1512 * context are removed.
1514 * We first simplify the constraints of "bset" in the context of the
1515 * equalities of "context".
1516 * Then we simplify the inequalities of the context in the context
1517 * of the equalities of bset and remove the inequalities from "bset"
1518 * that are obviously redundant with respect to some inequality in "context".
1520 * If there are any inequalities left, we construct a tableau for
1521 * the context and then add the inequalities of "bset".
1522 * Before adding these equalities, we freeze all constraints such that
1523 * they won't be considered redundant in terms of the constraints of "bset".
1524 * Then we detect all equalities and redundant constraints (among the
1525 * constraints that weren't frozen) and update bset according to the results.
1526 * We have to be careful here because we don't want any of the context
1527 * constraints to remain and because we haven't added the equalities of "bset"
1528 * to the tableau so we temporarily have to pretend that there were no
1531 static struct isl_basic_set
*uset_gist(struct isl_basic_set
*bset
,
1532 struct isl_basic_set
*context
)
1535 struct isl_tab
*tab
;
1536 unsigned context_ineq
;
1537 struct isl_basic_set
*combined
= NULL
;
1539 if (!context
|| !bset
)
1542 if (context
->n_eq
> 0)
1543 bset
= isl_basic_set_reduce_using_equalities(bset
,
1544 isl_basic_set_copy(context
));
1547 if (isl_basic_set_fast_is_empty(bset
))
1552 if (bset
->n_eq
> 0) {
1553 struct isl_basic_set
*affine_hull
;
1554 affine_hull
= isl_basic_set_copy(bset
);
1555 affine_hull
= isl_basic_set_cow(affine_hull
);
1558 isl_basic_set_free_inequality(affine_hull
, affine_hull
->n_ineq
);
1559 context
= isl_basic_set_intersect(context
, affine_hull
);
1560 context
= isl_basic_set_gauss(context
, NULL
);
1561 context
= normalize_constraints_in_compressed_space(context
);
1565 if (ISL_F_ISSET(context
, ISL_BASIC_SET_EMPTY
)) {
1566 isl_basic_set_free(bset
);
1569 if (!context
->n_ineq
)
1571 bset
= remove_shifted_constraints(bset
, context
);
1574 isl_basic_set_free_equality(context
, context
->n_eq
);
1575 context_ineq
= context
->n_ineq
;
1576 combined
= isl_basic_set_cow(isl_basic_set_copy(context
));
1577 combined
= isl_basic_set_extend_constraints(combined
,
1578 bset
->n_eq
, bset
->n_ineq
);
1579 tab
= isl_tab_from_basic_set(combined
);
1582 for (i
= 0; i
< context_ineq
; ++i
)
1583 tab
->con
[i
].frozen
= 1;
1584 tab
= isl_tab_extend(tab
, bset
->n_ineq
);
1587 for (i
= 0; i
< bset
->n_ineq
; ++i
)
1588 tab
= isl_tab_add_ineq(tab
, bset
->ineq
[i
]);
1589 bset
= isl_basic_set_add_constraints(combined
, bset
, 0);
1590 tab
= isl_tab_detect_equalities(tab
);
1591 tab
= isl_tab_detect_redundant(tab
);
1594 for (i
= 0; i
< context_ineq
; ++i
) {
1595 tab
->con
[i
].is_zero
= 0;
1596 tab
->con
[i
].is_redundant
= 1;
1598 bset
= isl_basic_set_update_from_tab(bset
, tab
);
1600 ISL_F_SET(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1601 ISL_F_SET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1603 bset
= isl_basic_set_simplify(bset
);
1604 bset
= isl_basic_set_finalize(bset
);
1605 isl_basic_set_free(context
);
1608 isl_basic_set_free(combined
);
1610 isl_basic_set_free(bset
);
1611 isl_basic_set_free(context
);
1615 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1616 * We simply add the equalities in context to bmap and then do a regular
1617 * div normalizations. Better results can be obtained by normalizing
1618 * only the divs in bmap than do not also appear in context.
1619 * We need to be careful to reduce the divs using the equalities
1620 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1621 * spurious constraints.
1623 static struct isl_basic_map
*normalize_divs_in_context(
1624 struct isl_basic_map
*bmap
, struct isl_basic_map
*context
)
1627 unsigned total_context
;
1630 div_eq
= n_pure_div_eq(bmap
);
1634 if (context
->n_div
> 0)
1635 bmap
= isl_basic_map_align_divs(bmap
, context
);
1637 total_context
= isl_basic_map_total_dim(context
);
1638 bmap
= isl_basic_map_extend_constraints(bmap
, context
->n_eq
, 0);
1639 for (i
= 0; i
< context
->n_eq
; ++i
) {
1641 k
= isl_basic_map_alloc_equality(bmap
);
1642 isl_seq_cpy(bmap
->eq
[k
], context
->eq
[i
], 1 + total_context
);
1643 isl_seq_clr(bmap
->eq
[k
] + 1 + total_context
,
1644 isl_basic_map_total_dim(bmap
) - total_context
);
1646 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1647 bmap
= normalize_divs(bmap
, NULL
);
1648 bmap
= isl_basic_map_gauss(bmap
, NULL
);
1652 struct isl_basic_map
*isl_basic_map_gist(struct isl_basic_map
*bmap
,
1653 struct isl_basic_map
*context
)
1655 struct isl_basic_set
*bset
;
1657 if (!bmap
|| !context
)
1660 if (isl_basic_map_is_universe(context
)) {
1661 isl_basic_map_free(context
);
1664 if (isl_basic_map_is_universe(bmap
)) {
1665 isl_basic_map_free(context
);
1668 if (isl_basic_map_fast_is_empty(context
)) {
1669 struct isl_dim
*dim
= isl_dim_copy(bmap
->dim
);
1670 isl_basic_map_free(context
);
1671 isl_basic_map_free(bmap
);
1672 return isl_basic_map_universe(dim
);
1674 if (isl_basic_map_fast_is_empty(bmap
)) {
1675 isl_basic_map_free(context
);
1679 bmap
= isl_basic_map_convex_hull(bmap
);
1680 context
= isl_basic_map_convex_hull(context
);
1683 bmap
= normalize_divs_in_context(bmap
, context
);
1685 context
= isl_basic_map_align_divs(context
, bmap
);
1686 bmap
= isl_basic_map_align_divs(bmap
, context
);
1688 bset
= uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap
)),
1689 isl_basic_map_underlying_set(context
));
1691 return isl_basic_map_overlying_set(bset
, bmap
);
1693 isl_basic_map_free(bmap
);
1694 isl_basic_map_free(context
);
1699 * Assumes context has no implicit divs.
1701 struct isl_map
*isl_map_gist(struct isl_map
*map
, struct isl_basic_map
*context
)
1705 if (!map
|| !context
)
1708 if (isl_basic_map_is_universe(context
)) {
1709 isl_basic_map_free(context
);
1712 if (isl_basic_map_fast_is_empty(context
)) {
1713 struct isl_dim
*dim
= isl_dim_copy(map
->dim
);
1714 isl_basic_map_free(context
);
1716 return isl_map_universe(dim
);
1719 context
= isl_basic_map_convex_hull(context
);
1720 map
= isl_map_cow(map
);
1721 if (!map
|| !context
)
1723 isl_assert(map
->ctx
, isl_dim_equal(map
->dim
, context
->dim
), goto error
);
1724 map
= isl_map_compute_divs(map
);
1725 for (i
= 0; i
< map
->n
; ++i
)
1726 context
= isl_basic_map_align_divs(context
, map
->p
[i
]);
1727 for (i
= 0; i
< map
->n
; ++i
) {
1728 map
->p
[i
] = isl_basic_map_gist(map
->p
[i
],
1729 isl_basic_map_copy(context
));
1733 isl_basic_map_free(context
);
1734 ISL_F_CLR(map
, ISL_MAP_NORMALIZED
);
1738 isl_basic_map_free(context
);
1742 struct isl_basic_set
*isl_basic_set_gist(struct isl_basic_set
*bset
,
1743 struct isl_basic_set
*context
)
1745 return (struct isl_basic_set
*)isl_basic_map_gist(
1746 (struct isl_basic_map
*)bset
, (struct isl_basic_map
*)context
);
1749 struct isl_set
*isl_set_gist(struct isl_set
*set
, struct isl_basic_set
*context
)
1751 return (struct isl_set
*)isl_map_gist((struct isl_map
*)set
,
1752 (struct isl_basic_map
*)context
);
1755 /* Quick check to see if two basic maps are disjoint.
1756 * In particular, we reduce the equalities and inequalities of
1757 * one basic map in the context of the equalities of the other
1758 * basic map and check if we get a contradiction.
1760 int isl_basic_map_fast_is_disjoint(struct isl_basic_map
*bmap1
,
1761 struct isl_basic_map
*bmap2
)
1763 struct isl_vec
*v
= NULL
;
1768 if (!bmap1
|| !bmap2
)
1770 isl_assert(bmap1
->ctx
, isl_dim_equal(bmap1
->dim
, bmap2
->dim
),
1772 if (bmap1
->n_div
|| bmap2
->n_div
)
1774 if (!bmap1
->n_eq
&& !bmap2
->n_eq
)
1777 total
= isl_dim_total(bmap1
->dim
);
1780 v
= isl_vec_alloc(bmap1
->ctx
, 1 + total
);
1783 elim
= isl_alloc_array(bmap1
->ctx
, int, total
);
1786 compute_elimination_index(bmap1
, elim
);
1787 for (i
= 0; i
< bmap2
->n_eq
; ++i
) {
1789 reduced
= reduced_using_equalities(v
->block
.data
, bmap2
->eq
[i
],
1791 if (reduced
&& !isl_int_is_zero(v
->block
.data
[0]) &&
1792 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1795 for (i
= 0; i
< bmap2
->n_ineq
; ++i
) {
1797 reduced
= reduced_using_equalities(v
->block
.data
,
1798 bmap2
->ineq
[i
], bmap1
, elim
);
1799 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1800 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1803 compute_elimination_index(bmap2
, elim
);
1804 for (i
= 0; i
< bmap1
->n_ineq
; ++i
) {
1806 reduced
= reduced_using_equalities(v
->block
.data
,
1807 bmap1
->ineq
[i
], bmap2
, elim
);
1808 if (reduced
&& isl_int_is_neg(v
->block
.data
[0]) &&
1809 isl_seq_first_non_zero(v
->block
.data
+ 1, total
) == -1)
1825 int isl_basic_set_fast_is_disjoint(struct isl_basic_set
*bset1
,
1826 struct isl_basic_set
*bset2
)
1828 return isl_basic_map_fast_is_disjoint((struct isl_basic_map
*)bset1
,
1829 (struct isl_basic_map
*)bset2
);
1832 int isl_map_fast_is_disjoint(struct isl_map
*map1
, struct isl_map
*map2
)
1839 if (isl_map_fast_is_equal(map1
, map2
))
1842 for (i
= 0; i
< map1
->n
; ++i
) {
1843 for (j
= 0; j
< map2
->n
; ++j
) {
1844 int d
= isl_basic_map_fast_is_disjoint(map1
->p
[i
],
1853 int isl_set_fast_is_disjoint(struct isl_set
*set1
, struct isl_set
*set2
)
1855 return isl_map_fast_is_disjoint((struct isl_map
*)set1
,
1856 (struct isl_map
*)set2
);
1859 /* Check if we can combine a given div with lower bound l and upper
1860 * bound u with some other div and if so return that other div.
1861 * Otherwise return -1.
1863 * We first check that
1864 * - the bounds are opposites of each other (expect for the constant
1866 * - the bounds do not reference any other div
1867 * - no div is defined in terms of this div
1869 * Let m be the size of the range allowed on the div by the bounds.
1870 * That is, the bounds are of the form
1872 * e <= a <= e + m - 1
1874 * with e some expression in the other variables.
1875 * We look for another div b such that no third div is defined in terms
1876 * of this second div b and such that in any constraint that contains
1877 * a (except for the given lower and upper bound), also contains b
1878 * with a coefficient that is m times that of b.
1879 * That is, all constraints (execpt for the lower and upper bound)
1882 * e + f (a + m b) >= 0
1884 * If so, we return b so that "a + m b" can be replaced by
1885 * a single div "c = a + m b".
1887 static int div_find_coalesce(struct isl_basic_map
*bmap
, int *pairs
,
1888 unsigned div
, unsigned l
, unsigned u
)
1894 if (bmap
->n_div
<= 1)
1896 dim
= isl_dim_total(bmap
->dim
);
1897 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
, div
) != -1)
1899 if (isl_seq_first_non_zero(bmap
->ineq
[l
] + 1 + dim
+ div
+ 1,
1900 bmap
->n_div
- div
- 1) != -1)
1902 if (!isl_seq_is_neg(bmap
->ineq
[l
] + 1, bmap
->ineq
[u
] + 1,
1906 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1907 if (isl_int_is_zero(bmap
->div
[i
][0]))
1909 if (!isl_int_is_zero(bmap
->div
[i
][1 + 1 + dim
+ div
]))
1913 isl_int_add(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
1914 isl_int_add_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
1915 for (i
= 0; i
< bmap
->n_div
; ++i
) {
1920 for (j
= 0; j
< bmap
->n_div
; ++j
) {
1921 if (isl_int_is_zero(bmap
->div
[j
][0]))
1923 if (!isl_int_is_zero(bmap
->div
[j
][1 + 1 + dim
+ i
]))
1926 if (j
< bmap
->n_div
)
1928 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
1930 if (j
== l
|| j
== u
)
1932 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ div
]))
1934 if (isl_int_is_zero(bmap
->ineq
[j
][1 + dim
+ i
]))
1936 isl_int_mul(bmap
->ineq
[j
][1 + dim
+ div
],
1937 bmap
->ineq
[j
][1 + dim
+ div
],
1939 valid
= isl_int_eq(bmap
->ineq
[j
][1 + dim
+ div
],
1940 bmap
->ineq
[j
][1 + dim
+ i
]);
1941 isl_int_divexact(bmap
->ineq
[j
][1 + dim
+ div
],
1942 bmap
->ineq
[j
][1 + dim
+ div
],
1947 if (j
< bmap
->n_ineq
)
1952 isl_int_sub_ui(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], 1);
1953 isl_int_sub(bmap
->ineq
[l
][0], bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
1957 /* Given a lower and an upper bound on div i, construct an inequality
1958 * that when nonnegative ensures that this pair of bounds always allows
1959 * for an integer value of the given div.
1960 * The lower bound is inequality l, while the upper bound is inequality u.
1961 * The constructed inequality is stored in ineq.
1962 * g, fl, fu are temporary scalars.
1964 * Let the upper bound be
1968 * and the lower bound
1972 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1975 * - f_u e_l <= f_u f_l g a <= f_l e_u
1977 * Since all variables are integer valued, this is equivalent to
1979 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1981 * If this interval is at least f_u f_l g, then it contains at least
1982 * one integer value for a.
1983 * That is, the test constraint is
1985 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
1987 static void construct_test_ineq(struct isl_basic_map
*bmap
, int i
,
1988 int l
, int u
, isl_int
*ineq
, isl_int g
, isl_int fl
, isl_int fu
)
1991 dim
= isl_dim_total(bmap
->dim
);
1993 isl_int_gcd(g
, bmap
->ineq
[l
][1 + dim
+ i
], bmap
->ineq
[u
][1 + dim
+ i
]);
1994 isl_int_divexact(fl
, bmap
->ineq
[l
][1 + dim
+ i
], g
);
1995 isl_int_divexact(fu
, bmap
->ineq
[u
][1 + dim
+ i
], g
);
1996 isl_int_neg(fu
, fu
);
1997 isl_seq_combine(ineq
, fl
, bmap
->ineq
[u
], fu
, bmap
->ineq
[l
],
1998 1 + dim
+ bmap
->n_div
);
1999 isl_int_add(ineq
[0], ineq
[0], fl
);
2000 isl_int_add(ineq
[0], ineq
[0], fu
);
2001 isl_int_sub_ui(ineq
[0], ineq
[0], 1);
2002 isl_int_mul(g
, g
, fl
);
2003 isl_int_mul(g
, g
, fu
);
2004 isl_int_sub(ineq
[0], ineq
[0], g
);
2007 /* Remove more kinds of divs that are not strictly needed.
2008 * In particular, if all pairs of lower and upper bounds on a div
2009 * are such that they allow at least one integer value of the div,
2010 * the we can eliminate the div using Fourier-Motzkin without
2011 * introducing any spurious solutions.
2013 static struct isl_basic_map
*drop_more_redundant_divs(
2014 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2016 struct isl_tab
*tab
= NULL
;
2017 struct isl_vec
*vec
= NULL
;
2029 dim
= isl_dim_total(bmap
->dim
);
2030 vec
= isl_vec_alloc(bmap
->ctx
, 1 + dim
+ bmap
->n_div
);
2034 tab
= isl_tab_from_basic_map(bmap
);
2039 enum isl_lp_result res
;
2041 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2044 if (best
>= 0 && pairs
[best
] <= pairs
[i
])
2050 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2051 if (!isl_int_is_pos(bmap
->ineq
[l
][1 + dim
+ i
]))
2053 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2054 if (!isl_int_is_neg(bmap
->ineq
[u
][1 + dim
+ i
]))
2056 construct_test_ineq(bmap
, i
, l
, u
,
2057 vec
->el
, g
, fl
, fu
);
2058 res
= isl_tab_min(tab
, vec
->el
,
2059 bmap
->ctx
->one
, &g
, NULL
, 0);
2060 if (res
== isl_lp_error
)
2062 if (res
== isl_lp_empty
) {
2063 bmap
= isl_basic_map_set_to_empty(bmap
);
2066 if (res
!= isl_lp_ok
|| isl_int_is_neg(g
))
2069 if (u
< bmap
->n_ineq
)
2072 if (l
== bmap
->n_ineq
) {
2092 bmap
= isl_basic_map_remove(bmap
, isl_dim_div
, remove
, 1);
2093 return isl_basic_map_drop_redundant_divs(bmap
);
2096 isl_basic_map_free(bmap
);
2105 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2106 * and the upper bound u, div1 always occurs together with div2 in the form
2107 * (div1 + m div2), where m is the constant range on the variable div1
2108 * allowed by l and u, replace the pair div1 and div2 by a single
2109 * div that is equal to div1 + m div2.
2111 * The new div will appear in the location that contains div2.
2112 * We need to modify all constraints that contain
2113 * div2 = (div - div1) / m
2114 * (If a constraint does not contain div2, it will also not contain div1.)
2115 * If the constraint also contains div1, then we know they appear
2116 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2117 * i.e., the coefficient of div is f.
2119 * Otherwise, we first need to introduce div1 into the constraint.
2128 * A lower bound on div2
2132 * can be replaced by
2134 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2136 * with g = gcd(m,n).
2141 * can be replaced by
2143 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2145 * These constraint are those that we would obtain from eliminating
2146 * div1 using Fourier-Motzkin.
2148 * After all constraints have been modified, we drop the lower and upper
2149 * bound and then drop div1.
2151 static struct isl_basic_map
*coalesce_divs(struct isl_basic_map
*bmap
,
2152 unsigned div1
, unsigned div2
, unsigned l
, unsigned u
)
2157 unsigned dim
, total
;
2160 dim
= isl_dim_total(bmap
->dim
);
2161 total
= 1 + dim
+ bmap
->n_div
;
2166 isl_int_add(m
, bmap
->ineq
[l
][0], bmap
->ineq
[u
][0]);
2167 isl_int_add_ui(m
, m
, 1);
2169 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2170 if (i
== l
|| i
== u
)
2172 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div2
]))
2174 if (isl_int_is_zero(bmap
->ineq
[i
][1 + dim
+ div1
])) {
2175 isl_int_gcd(b
, m
, bmap
->ineq
[i
][1 + dim
+ div2
]);
2176 isl_int_divexact(a
, m
, b
);
2177 isl_int_divexact(b
, bmap
->ineq
[i
][1 + dim
+ div2
], b
);
2178 if (isl_int_is_pos(b
)) {
2179 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2180 b
, bmap
->ineq
[l
], total
);
2183 isl_seq_combine(bmap
->ineq
[i
], a
, bmap
->ineq
[i
],
2184 b
, bmap
->ineq
[u
], total
);
2187 isl_int_set(bmap
->ineq
[i
][1 + dim
+ div2
],
2188 bmap
->ineq
[i
][1 + dim
+ div1
]);
2189 isl_int_set_si(bmap
->ineq
[i
][1 + dim
+ div1
], 0);
2196 isl_basic_map_drop_inequality(bmap
, l
);
2197 isl_basic_map_drop_inequality(bmap
, u
);
2199 isl_basic_map_drop_inequality(bmap
, u
);
2200 isl_basic_map_drop_inequality(bmap
, l
);
2202 bmap
= isl_basic_map_drop_div(bmap
, div1
);
2206 /* First check if we can coalesce any pair of divs and
2207 * then continue with dropping more redundant divs.
2209 * We loop over all pairs of lower and upper bounds on a div
2210 * with coefficient 1 and -1, respectively, check if there
2211 * is any other div "c" with which we can coalesce the div
2212 * and if so, perform the coalescing.
2214 static struct isl_basic_map
*coalesce_or_drop_more_redundant_divs(
2215 struct isl_basic_map
*bmap
, int *pairs
, int n
)
2220 dim
= isl_dim_total(bmap
->dim
);
2222 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2225 for (l
= 0; l
< bmap
->n_ineq
; ++l
) {
2226 if (!isl_int_is_one(bmap
->ineq
[l
][1 + dim
+ i
]))
2228 for (u
= 0; u
< bmap
->n_ineq
; ++u
) {
2231 if (!isl_int_is_negone(bmap
->ineq
[u
][1+dim
+i
]))
2233 c
= div_find_coalesce(bmap
, pairs
, i
, l
, u
);
2237 bmap
= coalesce_divs(bmap
, i
, c
, l
, u
);
2238 return isl_basic_map_drop_redundant_divs(bmap
);
2243 return drop_more_redundant_divs(bmap
, pairs
, n
);
2246 /* Remove divs that are not strictly needed.
2247 * In particular, if a div only occurs positively (or negatively)
2248 * in constraints, then it can simply be dropped.
2249 * Also, if a div occurs only occurs in two constraints and if moreover
2250 * those two constraints are opposite to each other, except for the constant
2251 * term and if the sum of the constant terms is such that for any value
2252 * of the other values, there is always at least one integer value of the
2253 * div, i.e., if one plus this sum is greater than or equal to
2254 * the (absolute value) of the coefficent of the div in the constraints,
2255 * then we can also simply drop the div.
2257 * If any divs are left after these simple checks then we move on
2258 * to more complicated cases in drop_more_redundant_divs.
2260 struct isl_basic_map
*isl_basic_map_drop_redundant_divs(
2261 struct isl_basic_map
*bmap
)
2271 off
= isl_dim_total(bmap
->dim
);
2272 pairs
= isl_calloc_array(bmap
->ctx
, int, bmap
->n_div
);
2276 for (i
= 0; i
< bmap
->n_div
; ++i
) {
2278 int last_pos
, last_neg
;
2281 if (!isl_int_is_zero(bmap
->div
[i
][0]))
2283 for (j
= 0; j
< bmap
->n_eq
; ++j
)
2284 if (!isl_int_is_zero(bmap
->eq
[j
][1 + off
+ i
]))
2290 for (j
= 0; j
< bmap
->n_ineq
; ++j
) {
2291 if (isl_int_is_pos(bmap
->ineq
[j
][1 + off
+ i
])) {
2295 if (isl_int_is_neg(bmap
->ineq
[j
][1 + off
+ i
])) {
2300 pairs
[i
] = pos
* neg
;
2301 if (pairs
[i
] == 0) {
2302 for (j
= bmap
->n_ineq
- 1; j
>= 0; --j
)
2303 if (!isl_int_is_zero(bmap
->ineq
[j
][1+off
+i
]))
2304 isl_basic_map_drop_inequality(bmap
, j
);
2305 bmap
= isl_basic_map_drop_div(bmap
, i
);
2307 return isl_basic_map_drop_redundant_divs(bmap
);
2311 if (!isl_seq_is_neg(bmap
->ineq
[last_pos
] + 1,
2312 bmap
->ineq
[last_neg
] + 1,
2316 isl_int_add(bmap
->ineq
[last_pos
][0],
2317 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2318 isl_int_add_ui(bmap
->ineq
[last_pos
][0],
2319 bmap
->ineq
[last_pos
][0], 1);
2320 redundant
= isl_int_ge(bmap
->ineq
[last_pos
][0],
2321 bmap
->ineq
[last_pos
][1+off
+i
]);
2322 isl_int_sub_ui(bmap
->ineq
[last_pos
][0],
2323 bmap
->ineq
[last_pos
][0], 1);
2324 isl_int_sub(bmap
->ineq
[last_pos
][0],
2325 bmap
->ineq
[last_pos
][0], bmap
->ineq
[last_neg
][0]);
2327 if (!ok_to_set_div_from_bound(bmap
, i
, last_pos
)) {
2332 bmap
= set_div_from_lower_bound(bmap
, i
, last_pos
);
2333 bmap
= isl_basic_map_simplify(bmap
);
2335 return isl_basic_map_drop_redundant_divs(bmap
);
2337 if (last_pos
> last_neg
) {
2338 isl_basic_map_drop_inequality(bmap
, last_pos
);
2339 isl_basic_map_drop_inequality(bmap
, last_neg
);
2341 isl_basic_map_drop_inequality(bmap
, last_neg
);
2342 isl_basic_map_drop_inequality(bmap
, last_pos
);
2344 bmap
= isl_basic_map_drop_div(bmap
, i
);
2346 return isl_basic_map_drop_redundant_divs(bmap
);
2350 return coalesce_or_drop_more_redundant_divs(bmap
, pairs
, n
);
2356 isl_basic_map_free(bmap
);