2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
11 #include <isl_union_map_private.h>
12 #include <isl_polynomial_private.h>
13 #include <isl_point_private.h>
14 #include <isl_dim_private.h>
15 #include <isl_map_private.h>
18 #include <isl_mat_private.h>
20 static __isl_give isl_qpolynomial_fold
*qpolynomial_fold_alloc(
21 enum isl_fold type
, __isl_take isl_dim
*dim
, int n
)
23 isl_qpolynomial_fold
*fold
;
28 isl_assert(dim
->ctx
, n
>= 0, goto error
);
29 fold
= isl_calloc(dim
->ctx
, struct isl_qpolynomial_fold
,
30 sizeof(struct isl_qpolynomial_fold
) +
31 (n
- 1) * sizeof(struct isl_qpolynomial
*));
47 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_reset_dim(
48 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_dim
*dim
)
52 fold
= isl_qpolynomial_fold_cow(fold
);
56 for (i
= 0; i
< fold
->n
; ++i
) {
57 fold
->qp
[i
] = isl_qpolynomial_reset_dim(fold
->qp
[i
],
63 isl_dim_free(fold
->dim
);
68 isl_qpolynomial_fold_free(fold
);
73 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold
*fold
,
74 enum isl_dim_type type
, unsigned first
, unsigned n
)
80 if (fold
->n
== 0 || n
== 0)
83 for (i
= 0; i
< fold
->n
; ++i
) {
84 int involves
= isl_qpolynomial_involves_dims(fold
->qp
[i
],
86 if (involves
< 0 || involves
)
92 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_drop_dims(
93 __isl_take isl_qpolynomial_fold
*fold
,
94 enum isl_dim_type type
, unsigned first
, unsigned n
)
103 fold
= isl_qpolynomial_fold_cow(fold
);
106 fold
->dim
= isl_dim_drop(fold
->dim
, type
, first
, n
);
110 for (i
= 0; i
< fold
->n
; ++i
) {
111 fold
->qp
[i
] = isl_qpolynomial_drop_dims(fold
->qp
[i
],
119 isl_qpolynomial_fold_free(fold
);
123 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_insert_dims(
124 __isl_take isl_qpolynomial_fold
*fold
,
125 enum isl_dim_type type
, unsigned first
, unsigned n
)
131 if (n
== 0 && !isl_dim_is_named_or_nested(fold
->dim
, type
))
134 fold
= isl_qpolynomial_fold_cow(fold
);
137 fold
->dim
= isl_dim_insert(fold
->dim
, type
, first
, n
);
141 for (i
= 0; i
< fold
->n
; ++i
) {
142 fold
->qp
[i
] = isl_qpolynomial_insert_dims(fold
->qp
[i
],
150 isl_qpolynomial_fold_free(fold
);
154 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial
*qp
)
156 struct isl_upoly_cst
*cst
;
158 cst
= isl_upoly_as_cst(qp
->upoly
);
162 return isl_int_sgn(cst
->n
) < 0 ? -1 : 1;
165 static int isl_qpolynomial_aff_sign(__isl_keep isl_set
*set
,
166 __isl_keep isl_qpolynomial
*qp
)
168 enum isl_lp_result res
;
173 aff
= isl_qpolynomial_extract_affine(qp
);
179 res
= isl_set_solve_lp(set
, 0, aff
->el
+ 1, aff
->el
[0],
181 if (res
== isl_lp_error
)
183 if (res
== isl_lp_empty
||
184 (res
== isl_lp_ok
&& !isl_int_is_neg(opt
))) {
189 res
= isl_set_solve_lp(set
, 1, aff
->el
+ 1, aff
->el
[0],
191 if (res
== isl_lp_ok
&& !isl_int_is_pos(opt
))
200 /* Determine, if possible, the sign of the quasipolynomial "qp" on
203 * If qp is a constant, then the problem is trivial.
204 * If qp is linear, then we check if the minimum of the corresponding
205 * affine constraint is non-negative or if the maximum is non-positive.
207 * Otherwise, we check if the outermost variable "v" has a lower bound "l"
208 * in "set". If so, we write qp(v,v') as
210 * q(v,v') * (v - l) + r(v')
212 * if q(v,v') and r(v') have the same known sign, then the original
213 * quasipolynomial has the same sign as well.
220 static int isl_qpolynomial_sign(__isl_keep isl_set
*set
,
221 __isl_keep isl_qpolynomial
*qp
)
226 struct isl_upoly_rec
*rec
;
229 enum isl_lp_result res
;
232 is
= isl_qpolynomial_is_cst(qp
, NULL
, NULL
);
236 return isl_qpolynomial_cst_sign(qp
);
238 is
= isl_qpolynomial_is_affine(qp
);
242 return isl_qpolynomial_aff_sign(set
, qp
);
244 if (qp
->div
->n_row
> 0)
247 rec
= isl_upoly_as_rec(qp
->upoly
);
251 d
= isl_dim_total(qp
->dim
);
252 v
= isl_vec_alloc(set
->ctx
, 2 + d
);
256 isl_seq_clr(v
->el
+ 1, 1 + d
);
257 isl_int_set_si(v
->el
[0], 1);
258 isl_int_set_si(v
->el
[2 + qp
->upoly
->var
], 1);
262 res
= isl_set_solve_lp(set
, 0, v
->el
+ 1, v
->el
[0], &l
, NULL
, NULL
);
263 if (res
== isl_lp_ok
) {
264 isl_qpolynomial
*min
;
265 isl_qpolynomial
*base
;
266 isl_qpolynomial
*r
, *q
;
269 min
= isl_qpolynomial_cst(isl_dim_copy(qp
->dim
), l
);
270 base
= isl_qpolynomial_pow(isl_dim_copy(qp
->dim
),
273 r
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), 0,
274 isl_upoly_copy(rec
->p
[rec
->n
- 1]));
275 q
= isl_qpolynomial_copy(r
);
277 for (i
= rec
->n
- 2; i
>= 0; --i
) {
278 r
= isl_qpolynomial_mul(r
, isl_qpolynomial_copy(min
));
279 t
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), 0,
280 isl_upoly_copy(rec
->p
[i
]));
281 r
= isl_qpolynomial_add(r
, t
);
284 q
= isl_qpolynomial_mul(q
, isl_qpolynomial_copy(base
));
285 q
= isl_qpolynomial_add(q
, isl_qpolynomial_copy(r
));
288 if (isl_qpolynomial_is_zero(q
))
289 sgn
= isl_qpolynomial_sign(set
, r
);
290 else if (isl_qpolynomial_is_zero(r
))
291 sgn
= isl_qpolynomial_sign(set
, q
);
294 sgn_r
= isl_qpolynomial_sign(set
, r
);
295 sgn_q
= isl_qpolynomial_sign(set
, q
);
300 isl_qpolynomial_free(min
);
301 isl_qpolynomial_free(base
);
302 isl_qpolynomial_free(q
);
303 isl_qpolynomial_free(r
);
313 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_fold_on_domain(
314 __isl_keep isl_set
*set
,
315 __isl_take isl_qpolynomial_fold
*fold1
,
316 __isl_take isl_qpolynomial_fold
*fold2
)
320 struct isl_qpolynomial_fold
*res
= NULL
;
323 if (!fold1
|| !fold2
)
326 isl_assert(fold1
->dim
->ctx
, fold1
->type
== fold2
->type
, goto error
);
327 isl_assert(fold1
->dim
->ctx
, isl_dim_equal(fold1
->dim
, fold2
->dim
),
330 better
= fold1
->type
== isl_fold_max
? -1 : 1;
332 if (isl_qpolynomial_fold_is_empty(fold1
)) {
333 isl_qpolynomial_fold_free(fold1
);
337 if (isl_qpolynomial_fold_is_empty(fold2
)) {
338 isl_qpolynomial_fold_free(fold2
);
342 res
= qpolynomial_fold_alloc(fold1
->type
, isl_dim_copy(fold1
->dim
),
343 fold1
->n
+ fold2
->n
);
347 for (i
= 0; i
< fold1
->n
; ++i
) {
348 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold1
->qp
[i
]);
349 if (!res
->qp
[res
->n
])
355 for (i
= 0; i
< fold2
->n
; ++i
) {
356 for (j
= n1
- 1; j
>= 0; --j
) {
359 d
= isl_qpolynomial_sub(
360 isl_qpolynomial_copy(res
->qp
[j
]),
361 isl_qpolynomial_copy(fold2
->qp
[i
]));
362 sgn
= isl_qpolynomial_sign(set
, d
);
363 isl_qpolynomial_free(d
);
368 isl_qpolynomial_free(res
->qp
[j
]);
370 res
->qp
[j
] = res
->qp
[n1
- 1];
372 if (n1
!= res
->n
- 1)
373 res
->qp
[n1
] = res
->qp
[res
->n
- 1];
378 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold2
->qp
[i
]);
379 if (!res
->qp
[res
->n
])
384 isl_qpolynomial_fold_free(fold1
);
385 isl_qpolynomial_fold_free(fold2
);
389 isl_qpolynomial_fold_free(res
);
390 isl_qpolynomial_fold_free(fold1
);
391 isl_qpolynomial_fold_free(fold2
);
395 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_add_qpolynomial(
396 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_qpolynomial
*qp
)
403 if (isl_qpolynomial_is_zero(qp
)) {
404 isl_qpolynomial_free(qp
);
408 fold
= isl_qpolynomial_fold_cow(fold
);
412 for (i
= 0; i
< fold
->n
; ++i
) {
413 fold
->qp
[i
] = isl_qpolynomial_add(fold
->qp
[i
],
414 isl_qpolynomial_copy(qp
));
419 isl_qpolynomial_free(qp
);
422 isl_qpolynomial_fold_free(fold
);
423 isl_qpolynomial_free(qp
);
427 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_add_on_domain(
428 __isl_keep isl_set
*dom
,
429 __isl_take isl_qpolynomial_fold
*fold1
,
430 __isl_take isl_qpolynomial_fold
*fold2
)
433 isl_qpolynomial_fold
*res
= NULL
;
435 if (!fold1
|| !fold2
)
438 if (isl_qpolynomial_fold_is_empty(fold1
)) {
439 isl_qpolynomial_fold_free(fold1
);
443 if (isl_qpolynomial_fold_is_empty(fold2
)) {
444 isl_qpolynomial_fold_free(fold2
);
448 if (fold1
->n
== 1 && fold2
->n
!= 1)
449 return isl_qpolynomial_fold_add_on_domain(dom
, fold2
, fold1
);
452 res
= isl_qpolynomial_fold_add_qpolynomial(fold1
,
453 isl_qpolynomial_copy(fold2
->qp
[0]));
454 isl_qpolynomial_fold_free(fold2
);
458 res
= isl_qpolynomial_fold_add_qpolynomial(
459 isl_qpolynomial_fold_copy(fold1
),
460 isl_qpolynomial_copy(fold2
->qp
[0]));
462 for (i
= 1; i
< fold2
->n
; ++i
) {
463 isl_qpolynomial_fold
*res_i
;
464 res_i
= isl_qpolynomial_fold_add_qpolynomial(
465 isl_qpolynomial_fold_copy(fold1
),
466 isl_qpolynomial_copy(fold2
->qp
[i
]));
467 res
= isl_qpolynomial_fold_fold_on_domain(dom
, res
, res_i
);
470 isl_qpolynomial_fold_free(fold1
);
471 isl_qpolynomial_fold_free(fold2
);
474 isl_qpolynomial_fold_free(res
);
475 isl_qpolynomial_fold_free(fold1
);
476 isl_qpolynomial_fold_free(fold2
);
480 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_substitute_equalities(
481 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_basic_set
*eq
)
488 fold
= isl_qpolynomial_fold_cow(fold
);
492 for (i
= 0; i
< fold
->n
; ++i
) {
493 fold
->qp
[i
] = isl_qpolynomial_substitute_equalities(fold
->qp
[i
],
494 isl_basic_set_copy(eq
));
499 isl_basic_set_free(eq
);
502 isl_basic_set_free(eq
);
503 isl_qpolynomial_fold_free(fold
);
510 #define PW isl_pw_qpolynomial_fold
512 #define EL isl_qpolynomial_fold
514 #define IS_ZERO is_empty
518 #include <isl_pw_templ.c>
521 #define UNION isl_union_pw_qpolynomial_fold
523 #define PART isl_pw_qpolynomial_fold
525 #define PARTS pw_qpolynomial_fold
527 #include <isl_union_templ.c>
529 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_empty(enum isl_fold type
,
530 __isl_take isl_dim
*dim
)
532 return qpolynomial_fold_alloc(type
, dim
, 0);
535 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_alloc(
536 enum isl_fold type
, __isl_take isl_qpolynomial
*qp
)
538 isl_qpolynomial_fold
*fold
;
543 fold
= qpolynomial_fold_alloc(type
, isl_dim_copy(qp
->dim
), 1);
552 isl_qpolynomial_fold_free(fold
);
553 isl_qpolynomial_free(qp
);
557 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_copy(
558 __isl_keep isl_qpolynomial_fold
*fold
)
567 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_dup(
568 __isl_keep isl_qpolynomial_fold
*fold
)
571 isl_qpolynomial_fold
*dup
;
575 dup
= qpolynomial_fold_alloc(fold
->type
,
576 isl_dim_copy(fold
->dim
), fold
->n
);
581 for (i
= 0; i
< fold
->n
; ++i
) {
582 dup
->qp
[i
] = isl_qpolynomial_copy(fold
->qp
[i
]);
589 isl_qpolynomial_fold_free(dup
);
593 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_cow(
594 __isl_take isl_qpolynomial_fold
*fold
)
602 return isl_qpolynomial_fold_dup(fold
);
605 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold
*fold
)
614 for (i
= 0; i
< fold
->n
; ++i
)
615 isl_qpolynomial_free(fold
->qp
[i
]);
616 isl_dim_free(fold
->dim
);
620 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold
*fold
)
628 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_fold(
629 __isl_take isl_qpolynomial_fold
*fold1
,
630 __isl_take isl_qpolynomial_fold
*fold2
)
633 struct isl_qpolynomial_fold
*res
= NULL
;
635 if (!fold1
|| !fold2
)
638 isl_assert(fold1
->dim
->ctx
, fold1
->type
== fold2
->type
, goto error
);
639 isl_assert(fold1
->dim
->ctx
, isl_dim_equal(fold1
->dim
, fold2
->dim
),
642 if (isl_qpolynomial_fold_is_empty(fold1
)) {
643 isl_qpolynomial_fold_free(fold1
);
647 if (isl_qpolynomial_fold_is_empty(fold2
)) {
648 isl_qpolynomial_fold_free(fold2
);
652 res
= qpolynomial_fold_alloc(fold1
->type
, isl_dim_copy(fold1
->dim
),
653 fold1
->n
+ fold2
->n
);
657 for (i
= 0; i
< fold1
->n
; ++i
) {
658 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold1
->qp
[i
]);
659 if (!res
->qp
[res
->n
])
664 for (i
= 0; i
< fold2
->n
; ++i
) {
665 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold2
->qp
[i
]);
666 if (!res
->qp
[res
->n
])
671 isl_qpolynomial_fold_free(fold1
);
672 isl_qpolynomial_fold_free(fold2
);
676 isl_qpolynomial_fold_free(res
);
677 isl_qpolynomial_fold_free(fold1
);
678 isl_qpolynomial_fold_free(fold2
);
682 __isl_give isl_pw_qpolynomial_fold
*isl_pw_qpolynomial_fold_fold(
683 __isl_take isl_pw_qpolynomial_fold
*pw1
,
684 __isl_take isl_pw_qpolynomial_fold
*pw2
)
687 struct isl_pw_qpolynomial_fold
*res
;
693 isl_assert(pw1
->dim
->ctx
, isl_dim_equal(pw1
->dim
, pw2
->dim
), goto error
);
695 if (isl_pw_qpolynomial_fold_is_zero(pw1
)) {
696 isl_pw_qpolynomial_fold_free(pw1
);
700 if (isl_pw_qpolynomial_fold_is_zero(pw2
)) {
701 isl_pw_qpolynomial_fold_free(pw2
);
705 if (pw1
->type
!= pw2
->type
)
706 isl_die(set
->ctx
, isl_error_invalid
, "fold types don't match",
709 n
= (pw1
->n
+ 1) * (pw2
->n
+ 1);
710 res
= isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pw1
->dim
),
713 for (i
= 0; i
< pw1
->n
; ++i
) {
714 set
= isl_set_copy(pw1
->p
[i
].set
);
715 for (j
= 0; j
< pw2
->n
; ++j
) {
716 struct isl_set
*common
;
717 isl_qpolynomial_fold
*sum
;
718 set
= isl_set_subtract(set
,
719 isl_set_copy(pw2
->p
[j
].set
));
720 common
= isl_set_intersect(isl_set_copy(pw1
->p
[i
].set
),
721 isl_set_copy(pw2
->p
[j
].set
));
722 if (isl_set_fast_is_empty(common
)) {
723 isl_set_free(common
);
727 sum
= isl_qpolynomial_fold_fold_on_domain(common
,
728 isl_qpolynomial_fold_copy(pw1
->p
[i
].fold
),
729 isl_qpolynomial_fold_copy(pw2
->p
[j
].fold
));
731 res
= isl_pw_qpolynomial_fold_add_piece(res
, common
, sum
);
733 res
= isl_pw_qpolynomial_fold_add_piece(res
, set
,
734 isl_qpolynomial_fold_copy(pw1
->p
[i
].fold
));
737 for (j
= 0; j
< pw2
->n
; ++j
) {
738 set
= isl_set_copy(pw2
->p
[j
].set
);
739 for (i
= 0; i
< pw1
->n
; ++i
)
740 set
= isl_set_subtract(set
, isl_set_copy(pw1
->p
[i
].set
));
741 res
= isl_pw_qpolynomial_fold_add_piece(res
, set
,
742 isl_qpolynomial_fold_copy(pw2
->p
[j
].fold
));
745 isl_pw_qpolynomial_fold_free(pw1
);
746 isl_pw_qpolynomial_fold_free(pw2
);
750 isl_pw_qpolynomial_fold_free(pw1
);
751 isl_pw_qpolynomial_fold_free(pw2
);
755 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
756 __isl_take isl_union_pw_qpolynomial_fold
*u
,
757 __isl_take isl_pw_qpolynomial_fold
*part
)
760 struct isl_hash_table_entry
*entry
;
762 u
= isl_union_pw_qpolynomial_fold_cow(u
);
767 isl_assert(u
->dim
->ctx
, isl_dim_match(part
->dim
, isl_dim_param
, u
->dim
,
768 isl_dim_param
), goto error
);
770 hash
= isl_dim_get_hash(part
->dim
);
771 entry
= isl_hash_table_find(u
->dim
->ctx
, &u
->table
, hash
,
772 &has_dim
, part
->dim
, 1);
779 entry
->data
= isl_pw_qpolynomial_fold_fold(entry
->data
,
780 isl_pw_qpolynomial_fold_copy(part
));
783 isl_pw_qpolynomial_fold_free(part
);
788 isl_pw_qpolynomial_fold_free(part
);
789 isl_union_pw_qpolynomial_fold_free(u
);
793 static int fold_part(__isl_take isl_pw_qpolynomial_fold
*part
, void *user
)
795 isl_union_pw_qpolynomial_fold
**u
;
796 u
= (isl_union_pw_qpolynomial_fold
**)user
;
798 *u
= isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u
, part
);
803 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_fold(
804 __isl_take isl_union_pw_qpolynomial_fold
*u1
,
805 __isl_take isl_union_pw_qpolynomial_fold
*u2
)
807 u1
= isl_union_pw_qpolynomial_fold_cow(u1
);
812 if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2
,
813 &fold_part
, &u1
) < 0)
816 isl_union_pw_qpolynomial_fold_free(u2
);
820 isl_union_pw_qpolynomial_fold_free(u1
);
821 isl_union_pw_qpolynomial_fold_free(u2
);
825 __isl_give isl_pw_qpolynomial_fold
*isl_pw_qpolynomial_fold_from_pw_qpolynomial(
826 enum isl_fold type
, __isl_take isl_pw_qpolynomial
*pwqp
)
829 isl_pw_qpolynomial_fold
*pwf
;
834 pwf
= isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pwqp
->dim
), type
,
837 for (i
= 0; i
< pwqp
->n
; ++i
)
838 pwf
= isl_pw_qpolynomial_fold_add_piece(pwf
,
839 isl_set_copy(pwqp
->p
[i
].set
),
840 isl_qpolynomial_fold_alloc(type
,
841 isl_qpolynomial_copy(pwqp
->p
[i
].qp
)));
843 isl_pw_qpolynomial_free(pwqp
);
848 int isl_qpolynomial_fold_is_equal(__isl_keep isl_qpolynomial_fold
*fold1
,
849 __isl_keep isl_qpolynomial_fold
*fold2
)
853 if (!fold1
|| !fold2
)
856 if (fold1
->n
!= fold2
->n
)
859 /* We probably want to sort the qps first... */
860 for (i
= 0; i
< fold1
->n
; ++i
) {
861 int eq
= isl_qpolynomial_is_equal(fold1
->qp
[i
], fold2
->qp
[i
]);
869 __isl_give isl_qpolynomial
*isl_qpolynomial_fold_eval(
870 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_point
*pnt
)
876 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, fold
->dim
), goto error
);
877 isl_assert(pnt
->dim
->ctx
,
878 fold
->type
== isl_fold_max
|| fold
->type
== isl_fold_min
,
882 qp
= isl_qpolynomial_zero(isl_dim_copy(fold
->dim
));
885 qp
= isl_qpolynomial_eval(isl_qpolynomial_copy(fold
->qp
[0]),
886 isl_point_copy(pnt
));
887 for (i
= 1; i
< fold
->n
; ++i
) {
888 isl_qpolynomial
*qp_i
;
889 qp_i
= isl_qpolynomial_eval(
890 isl_qpolynomial_copy(fold
->qp
[i
]),
891 isl_point_copy(pnt
));
892 if (fold
->type
== isl_fold_max
)
893 qp
= isl_qpolynomial_max_cst(qp
, qp_i
);
895 qp
= isl_qpolynomial_min_cst(qp
, qp_i
);
898 isl_qpolynomial_fold_free(fold
);
903 isl_qpolynomial_fold_free(fold
);
908 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold
*pwf
)
913 for (i
= 0; i
< pwf
->n
; ++i
)
914 n
+= pwf
->p
[i
].fold
->n
;
919 __isl_give isl_qpolynomial
*isl_qpolynomial_fold_opt_on_domain(
920 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_set
*set
, int max
)
923 isl_qpolynomial
*opt
;
929 isl_dim
*dim
= isl_dim_copy(fold
->dim
);
931 isl_qpolynomial_fold_free(fold
);
932 return isl_qpolynomial_zero(dim
);
935 opt
= isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold
->qp
[0]),
936 isl_set_copy(set
), max
);
937 for (i
= 1; i
< fold
->n
; ++i
) {
938 isl_qpolynomial
*opt_i
;
939 opt_i
= isl_qpolynomial_opt_on_domain(
940 isl_qpolynomial_copy(fold
->qp
[i
]),
941 isl_set_copy(set
), max
);
943 opt
= isl_qpolynomial_max_cst(opt
, opt_i
);
945 opt
= isl_qpolynomial_min_cst(opt
, opt_i
);
949 isl_qpolynomial_fold_free(fold
);
954 isl_qpolynomial_fold_free(fold
);
958 /* Check whether for each quasi-polynomial in "fold2" there is
959 * a quasi-polynomial in "fold1" that dominates it on "set".
961 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set
*set
,
962 __isl_keep isl_qpolynomial_fold
*fold1
,
963 __isl_keep isl_qpolynomial_fold
*fold2
)
968 if (!set
|| !fold1
|| !fold2
)
971 covers
= fold1
->type
== isl_fold_max
? 1 : -1;
973 for (i
= 0; i
< fold2
->n
; ++i
) {
974 for (j
= 0; j
< fold1
->n
; ++j
) {
978 d
= isl_qpolynomial_sub(
979 isl_qpolynomial_copy(fold1
->qp
[j
]),
980 isl_qpolynomial_copy(fold2
->qp
[i
]));
981 sgn
= isl_qpolynomial_sign(set
, d
);
982 isl_qpolynomial_free(d
);
993 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
994 * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
997 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold
*pwf1
,
998 __isl_keep isl_pw_qpolynomial_fold
*pwf2
)
1001 isl_set
*dom1
, *dom2
;
1012 dom1
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1
));
1013 dom2
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2
));
1014 is_subset
= isl_set_is_subset(dom2
, dom1
);
1018 if (is_subset
< 0 || !is_subset
)
1021 for (i
= 0; i
< pwf2
->n
; ++i
) {
1022 for (j
= 0; j
< pwf1
->n
; ++j
) {
1027 common
= isl_set_intersect(isl_set_copy(pwf1
->p
[j
].set
),
1028 isl_set_copy(pwf2
->p
[i
].set
));
1029 is_empty
= isl_set_is_empty(common
);
1030 if (is_empty
< 0 || is_empty
) {
1031 isl_set_free(common
);
1036 covers
= qpolynomial_fold_covers_on_domain(common
,
1037 pwf1
->p
[j
].fold
, pwf2
->p
[i
].fold
);
1038 isl_set_free(common
);
1039 if (covers
< 0 || !covers
)
1047 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_morph(
1048 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_morph
*morph
)
1053 if (!fold
|| !morph
)
1056 ctx
= fold
->dim
->ctx
;
1057 isl_assert(ctx
, isl_dim_equal(fold
->dim
, morph
->dom
->dim
), goto error
);
1059 fold
= isl_qpolynomial_fold_cow(fold
);
1063 isl_dim_free(fold
->dim
);
1064 fold
->dim
= isl_dim_copy(morph
->ran
->dim
);
1068 for (i
= 0; i
< fold
->n
; ++i
) {
1069 fold
->qp
[i
] = isl_qpolynomial_morph(fold
->qp
[i
],
1070 isl_morph_copy(morph
));
1075 isl_morph_free(morph
);
1079 isl_qpolynomial_fold_free(fold
);
1080 isl_morph_free(morph
);
1084 enum isl_fold
isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold
*fold
)
1087 return isl_fold_list
;
1091 enum isl_fold
isl_union_pw_qpolynomial_fold_get_type(
1092 __isl_keep isl_union_pw_qpolynomial_fold
*upwf
)
1095 return isl_fold_list
;
1099 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_lift(
1100 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_dim
*dim
)
1108 if (isl_dim_equal(fold
->dim
, dim
)) {
1113 fold
= isl_qpolynomial_fold_cow(fold
);
1117 isl_dim_free(fold
->dim
);
1118 fold
->dim
= isl_dim_copy(dim
);
1122 for (i
= 0; i
< fold
->n
; ++i
) {
1123 fold
->qp
[i
] = isl_qpolynomial_lift(fold
->qp
[i
],
1133 isl_qpolynomial_fold_free(fold
);
1138 int isl_qpolynomial_fold_foreach_qpolynomial(
1139 __isl_keep isl_qpolynomial_fold
*fold
,
1140 int (*fn
)(__isl_take isl_qpolynomial
*qp
, void *user
), void *user
)
1147 for (i
= 0; i
< fold
->n
; ++i
)
1148 if (fn(isl_qpolynomial_copy(fold
->qp
[i
]), user
) < 0)
1154 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_move_dims(
1155 __isl_take isl_qpolynomial_fold
*fold
,
1156 enum isl_dim_type dst_type
, unsigned dst_pos
,
1157 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
1164 fold
= isl_qpolynomial_fold_cow(fold
);
1168 fold
->dim
= isl_dim_move(fold
->dim
, dst_type
, dst_pos
,
1169 src_type
, src_pos
, n
);
1173 for (i
= 0; i
< fold
->n
; ++i
) {
1174 fold
->qp
[i
] = isl_qpolynomial_move_dims(fold
->qp
[i
],
1175 dst_type
, dst_pos
, src_type
, src_pos
, n
);
1182 isl_qpolynomial_fold_free(fold
);
1186 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1187 * in fold->qp[k] by subs[i].
1189 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_substitute(
1190 __isl_take isl_qpolynomial_fold
*fold
,
1191 enum isl_dim_type type
, unsigned first
, unsigned n
,
1192 __isl_keep isl_qpolynomial
**subs
)
1199 fold
= isl_qpolynomial_fold_cow(fold
);
1203 for (i
= 0; i
< fold
->n
; ++i
) {
1204 fold
->qp
[i
] = isl_qpolynomial_substitute(fold
->qp
[i
],
1205 type
, first
, n
, subs
);
1212 isl_qpolynomial_fold_free(fold
);
1216 static int add_pwqp(__isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
1219 isl_pw_qpolynomial_fold
*pwf
;
1220 isl_union_pw_qpolynomial_fold
**upwf
;
1222 struct isl_hash_table_entry
*entry
;
1224 upwf
= (isl_union_pw_qpolynomial_fold
**)user
;
1226 ctx
= pwqp
->dim
->ctx
;
1227 hash
= isl_dim_get_hash(pwqp
->dim
);
1228 entry
= isl_hash_table_find(ctx
, &(*upwf
)->table
,
1229 hash
, &has_dim
, pwqp
->dim
, 1);
1233 pwf
= isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf
)->type
, pwqp
);
1237 entry
->data
= isl_pw_qpolynomial_fold_add(entry
->data
, pwf
);
1240 if (isl_pw_qpolynomial_fold_is_zero(entry
->data
)) {
1241 isl_pw_qpolynomial_fold_free(entry
->data
);
1242 isl_hash_table_remove(ctx
, &(*upwf
)->table
, entry
);
1248 isl_pw_qpolynomial_free(pwqp
);
1252 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1253 __isl_take isl_union_pw_qpolynomial_fold
*upwf
,
1254 __isl_take isl_union_pw_qpolynomial
*upwqp
)
1256 upwf
= isl_union_pw_qpolynomial_fold_align_params(upwf
,
1257 isl_union_pw_qpolynomial_get_dim(upwqp
));
1258 upwqp
= isl_union_pw_qpolynomial_align_params(upwqp
,
1259 isl_union_pw_qpolynomial_fold_get_dim(upwf
));
1261 upwf
= isl_union_pw_qpolynomial_fold_cow(upwf
);
1262 if (!upwf
|| !upwqp
)
1265 if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp
, &add_pwqp
,
1269 isl_union_pw_qpolynomial_free(upwqp
);
1273 isl_union_pw_qpolynomial_fold_free(upwf
);
1274 isl_union_pw_qpolynomial_free(upwqp
);
1278 static int compatible_range(__isl_keep isl_dim
*dim1
, __isl_keep isl_dim
*dim2
)
1281 m
= isl_dim_match(dim1
, isl_dim_param
, dim2
, isl_dim_param
);
1284 return isl_dim_tuple_match(dim1
, isl_dim_out
, dim2
, isl_dim_set
);
1287 /* Compute the intersection of the range of the map and the domain
1288 * of the piecewise quasipolynomial reduction and then compute a bound
1289 * on the associated quasipolynomial reduction over all elements
1290 * in this intersection.
1292 * We first introduce some unconstrained dimensions in the
1293 * piecewise quasipolynomial, intersect the resulting domain
1294 * with the wrapped map and the compute the sum.
1296 __isl_give isl_pw_qpolynomial_fold
*isl_map_apply_pw_qpolynomial_fold(
1297 __isl_take isl_map
*map
, __isl_take isl_pw_qpolynomial_fold
*pwf
,
1307 ctx
= isl_map_get_ctx(map
);
1311 map_dim
= isl_map_get_dim(map
);
1312 pwf_dim
= isl_pw_qpolynomial_fold_get_dim(pwf
);
1313 ok
= compatible_range(map_dim
, pwf_dim
);
1314 isl_dim_free(map_dim
);
1315 isl_dim_free(pwf_dim
);
1317 isl_die(ctx
, isl_error_invalid
, "incompatible dimensions",
1320 n_in
= isl_map_dim(map
, isl_dim_in
);
1321 pwf
= isl_pw_qpolynomial_fold_insert_dims(pwf
, isl_dim_set
, 0, n_in
);
1323 dom
= isl_map_wrap(map
);
1324 pwf
= isl_pw_qpolynomial_fold_reset_dim(pwf
, isl_set_get_dim(dom
));
1326 pwf
= isl_pw_qpolynomial_fold_intersect_domain(pwf
, dom
);
1327 pwf
= isl_pw_qpolynomial_fold_bound(pwf
, tight
);
1332 isl_pw_qpolynomial_fold_free(pwf
);
1336 struct isl_apply_fold_data
{
1337 isl_union_pw_qpolynomial_fold
*upwf
;
1338 isl_union_pw_qpolynomial_fold
*res
;
1343 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold
*pwf
,
1348 struct isl_apply_fold_data
*data
= user
;
1351 map_dim
= isl_map_get_dim(data
->map
);
1352 pwf_dim
= isl_pw_qpolynomial_fold_get_dim(pwf
);
1353 ok
= compatible_range(map_dim
, pwf_dim
);
1354 isl_dim_free(map_dim
);
1355 isl_dim_free(pwf_dim
);
1358 pwf
= isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data
->map
),
1359 pwf
, data
->tight
? &data
->tight
: NULL
);
1360 data
->res
= isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1363 isl_pw_qpolynomial_fold_free(pwf
);
1368 static int map_apply(__isl_take isl_map
*map
, void *user
)
1370 struct isl_apply_fold_data
*data
= user
;
1374 r
= isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1375 data
->upwf
, &pw_qpolynomial_fold_apply
, data
);
1381 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_map_apply_union_pw_qpolynomial_fold(
1382 __isl_take isl_union_map
*umap
,
1383 __isl_take isl_union_pw_qpolynomial_fold
*upwf
, int *tight
)
1387 struct isl_apply_fold_data data
;
1389 upwf
= isl_union_pw_qpolynomial_fold_align_params(upwf
,
1390 isl_union_map_get_dim(umap
));
1391 umap
= isl_union_map_align_params(umap
,
1392 isl_union_pw_qpolynomial_fold_get_dim(upwf
));
1395 data
.tight
= tight
? 1 : 0;
1396 dim
= isl_union_pw_qpolynomial_fold_get_dim(upwf
);
1397 type
= isl_union_pw_qpolynomial_fold_get_type(upwf
);
1398 data
.res
= isl_union_pw_qpolynomial_fold_zero(dim
, type
);
1399 if (isl_union_map_foreach_map(umap
, &map_apply
, &data
) < 0)
1402 isl_union_map_free(umap
);
1403 isl_union_pw_qpolynomial_fold_free(upwf
);
1406 *tight
= data
.tight
;
1410 isl_union_map_free(umap
);
1411 isl_union_pw_qpolynomial_fold_free(upwf
);
1412 isl_union_pw_qpolynomial_fold_free(data
.res
);
1416 /* Reorder the dimension of "fold" according to the given reordering.
1418 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_realign(
1419 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_reordering
*r
)
1423 fold
= isl_qpolynomial_fold_cow(fold
);
1427 for (i
= 0; i
< fold
->n
; ++i
) {
1428 fold
->qp
[i
] = isl_qpolynomial_realign(fold
->qp
[i
],
1429 isl_reordering_copy(r
));
1434 fold
= isl_qpolynomial_fold_reset_dim(fold
, isl_dim_copy(r
->dim
));
1436 isl_reordering_free(r
);
1440 isl_qpolynomial_fold_free(fold
);
1441 isl_reordering_free(r
);