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_set_dim_name(
93 __isl_take isl_qpolynomial_fold
*fold
,
94 enum isl_dim_type type
, unsigned pos
, const char *s
)
98 fold
= isl_qpolynomial_fold_cow(fold
);
101 fold
->dim
= isl_dim_set_name(fold
->dim
, type
, pos
, s
);
105 for (i
= 0; i
< fold
->n
; ++i
) {
106 fold
->qp
[i
] = isl_qpolynomial_set_dim_name(fold
->qp
[i
],
114 isl_qpolynomial_fold_free(fold
);
118 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_drop_dims(
119 __isl_take isl_qpolynomial_fold
*fold
,
120 enum isl_dim_type type
, unsigned first
, unsigned n
)
129 fold
= isl_qpolynomial_fold_cow(fold
);
132 fold
->dim
= isl_dim_drop(fold
->dim
, type
, first
, n
);
136 for (i
= 0; i
< fold
->n
; ++i
) {
137 fold
->qp
[i
] = isl_qpolynomial_drop_dims(fold
->qp
[i
],
145 isl_qpolynomial_fold_free(fold
);
149 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_insert_dims(
150 __isl_take isl_qpolynomial_fold
*fold
,
151 enum isl_dim_type type
, unsigned first
, unsigned n
)
157 if (n
== 0 && !isl_dim_is_named_or_nested(fold
->dim
, type
))
160 fold
= isl_qpolynomial_fold_cow(fold
);
163 fold
->dim
= isl_dim_insert(fold
->dim
, type
, first
, n
);
167 for (i
= 0; i
< fold
->n
; ++i
) {
168 fold
->qp
[i
] = isl_qpolynomial_insert_dims(fold
->qp
[i
],
176 isl_qpolynomial_fold_free(fold
);
180 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial
*qp
)
182 struct isl_upoly_cst
*cst
;
184 cst
= isl_upoly_as_cst(qp
->upoly
);
188 return isl_int_sgn(cst
->n
) < 0 ? -1 : 1;
191 static int isl_qpolynomial_aff_sign(__isl_keep isl_set
*set
,
192 __isl_keep isl_qpolynomial
*qp
)
194 enum isl_lp_result res
;
199 aff
= isl_qpolynomial_extract_affine(qp
);
205 res
= isl_set_solve_lp(set
, 0, aff
->el
+ 1, aff
->el
[0],
207 if (res
== isl_lp_error
)
209 if (res
== isl_lp_empty
||
210 (res
== isl_lp_ok
&& !isl_int_is_neg(opt
))) {
215 res
= isl_set_solve_lp(set
, 1, aff
->el
+ 1, aff
->el
[0],
217 if (res
== isl_lp_ok
&& !isl_int_is_pos(opt
))
226 /* Determine, if possible, the sign of the quasipolynomial "qp" on
229 * If qp is a constant, then the problem is trivial.
230 * If qp is linear, then we check if the minimum of the corresponding
231 * affine constraint is non-negative or if the maximum is non-positive.
233 * Otherwise, we check if the outermost variable "v" has a lower bound "l"
234 * in "set". If so, we write qp(v,v') as
236 * q(v,v') * (v - l) + r(v')
238 * if q(v,v') and r(v') have the same known sign, then the original
239 * quasipolynomial has the same sign as well.
246 static int isl_qpolynomial_sign(__isl_keep isl_set
*set
,
247 __isl_keep isl_qpolynomial
*qp
)
252 struct isl_upoly_rec
*rec
;
255 enum isl_lp_result res
;
258 is
= isl_qpolynomial_is_cst(qp
, NULL
, NULL
);
262 return isl_qpolynomial_cst_sign(qp
);
264 is
= isl_qpolynomial_is_affine(qp
);
268 return isl_qpolynomial_aff_sign(set
, qp
);
270 if (qp
->div
->n_row
> 0)
273 rec
= isl_upoly_as_rec(qp
->upoly
);
277 d
= isl_dim_total(qp
->dim
);
278 v
= isl_vec_alloc(set
->ctx
, 2 + d
);
282 isl_seq_clr(v
->el
+ 1, 1 + d
);
283 isl_int_set_si(v
->el
[0], 1);
284 isl_int_set_si(v
->el
[2 + qp
->upoly
->var
], 1);
288 res
= isl_set_solve_lp(set
, 0, v
->el
+ 1, v
->el
[0], &l
, NULL
, NULL
);
289 if (res
== isl_lp_ok
) {
290 isl_qpolynomial
*min
;
291 isl_qpolynomial
*base
;
292 isl_qpolynomial
*r
, *q
;
295 min
= isl_qpolynomial_cst(isl_dim_copy(qp
->dim
), l
);
296 base
= isl_qpolynomial_pow(isl_dim_copy(qp
->dim
),
299 r
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), 0,
300 isl_upoly_copy(rec
->p
[rec
->n
- 1]));
301 q
= isl_qpolynomial_copy(r
);
303 for (i
= rec
->n
- 2; i
>= 0; --i
) {
304 r
= isl_qpolynomial_mul(r
, isl_qpolynomial_copy(min
));
305 t
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), 0,
306 isl_upoly_copy(rec
->p
[i
]));
307 r
= isl_qpolynomial_add(r
, t
);
310 q
= isl_qpolynomial_mul(q
, isl_qpolynomial_copy(base
));
311 q
= isl_qpolynomial_add(q
, isl_qpolynomial_copy(r
));
314 if (isl_qpolynomial_is_zero(q
))
315 sgn
= isl_qpolynomial_sign(set
, r
);
316 else if (isl_qpolynomial_is_zero(r
))
317 sgn
= isl_qpolynomial_sign(set
, q
);
320 sgn_r
= isl_qpolynomial_sign(set
, r
);
321 sgn_q
= isl_qpolynomial_sign(set
, q
);
326 isl_qpolynomial_free(min
);
327 isl_qpolynomial_free(base
);
328 isl_qpolynomial_free(q
);
329 isl_qpolynomial_free(r
);
339 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_fold_on_domain(
340 __isl_keep isl_set
*set
,
341 __isl_take isl_qpolynomial_fold
*fold1
,
342 __isl_take isl_qpolynomial_fold
*fold2
)
346 struct isl_qpolynomial_fold
*res
= NULL
;
349 if (!fold1
|| !fold2
)
352 isl_assert(fold1
->dim
->ctx
, fold1
->type
== fold2
->type
, goto error
);
353 isl_assert(fold1
->dim
->ctx
, isl_dim_equal(fold1
->dim
, fold2
->dim
),
356 better
= fold1
->type
== isl_fold_max
? -1 : 1;
358 if (isl_qpolynomial_fold_is_empty(fold1
)) {
359 isl_qpolynomial_fold_free(fold1
);
363 if (isl_qpolynomial_fold_is_empty(fold2
)) {
364 isl_qpolynomial_fold_free(fold2
);
368 res
= qpolynomial_fold_alloc(fold1
->type
, isl_dim_copy(fold1
->dim
),
369 fold1
->n
+ fold2
->n
);
373 for (i
= 0; i
< fold1
->n
; ++i
) {
374 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold1
->qp
[i
]);
375 if (!res
->qp
[res
->n
])
381 for (i
= 0; i
< fold2
->n
; ++i
) {
382 for (j
= n1
- 1; j
>= 0; --j
) {
385 d
= isl_qpolynomial_sub(
386 isl_qpolynomial_copy(res
->qp
[j
]),
387 isl_qpolynomial_copy(fold2
->qp
[i
]));
388 sgn
= isl_qpolynomial_sign(set
, d
);
389 isl_qpolynomial_free(d
);
394 isl_qpolynomial_free(res
->qp
[j
]);
396 res
->qp
[j
] = res
->qp
[n1
- 1];
398 if (n1
!= res
->n
- 1)
399 res
->qp
[n1
] = res
->qp
[res
->n
- 1];
404 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold2
->qp
[i
]);
405 if (!res
->qp
[res
->n
])
410 isl_qpolynomial_fold_free(fold1
);
411 isl_qpolynomial_fold_free(fold2
);
415 isl_qpolynomial_fold_free(res
);
416 isl_qpolynomial_fold_free(fold1
);
417 isl_qpolynomial_fold_free(fold2
);
421 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_add_qpolynomial(
422 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_qpolynomial
*qp
)
429 if (isl_qpolynomial_is_zero(qp
)) {
430 isl_qpolynomial_free(qp
);
434 fold
= isl_qpolynomial_fold_cow(fold
);
438 for (i
= 0; i
< fold
->n
; ++i
) {
439 fold
->qp
[i
] = isl_qpolynomial_add(fold
->qp
[i
],
440 isl_qpolynomial_copy(qp
));
445 isl_qpolynomial_free(qp
);
448 isl_qpolynomial_fold_free(fold
);
449 isl_qpolynomial_free(qp
);
453 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_add_on_domain(
454 __isl_keep isl_set
*dom
,
455 __isl_take isl_qpolynomial_fold
*fold1
,
456 __isl_take isl_qpolynomial_fold
*fold2
)
459 isl_qpolynomial_fold
*res
= NULL
;
461 if (!fold1
|| !fold2
)
464 if (isl_qpolynomial_fold_is_empty(fold1
)) {
465 isl_qpolynomial_fold_free(fold1
);
469 if (isl_qpolynomial_fold_is_empty(fold2
)) {
470 isl_qpolynomial_fold_free(fold2
);
474 if (fold1
->n
== 1 && fold2
->n
!= 1)
475 return isl_qpolynomial_fold_add_on_domain(dom
, fold2
, fold1
);
478 res
= isl_qpolynomial_fold_add_qpolynomial(fold1
,
479 isl_qpolynomial_copy(fold2
->qp
[0]));
480 isl_qpolynomial_fold_free(fold2
);
484 res
= isl_qpolynomial_fold_add_qpolynomial(
485 isl_qpolynomial_fold_copy(fold1
),
486 isl_qpolynomial_copy(fold2
->qp
[0]));
488 for (i
= 1; i
< fold2
->n
; ++i
) {
489 isl_qpolynomial_fold
*res_i
;
490 res_i
= isl_qpolynomial_fold_add_qpolynomial(
491 isl_qpolynomial_fold_copy(fold1
),
492 isl_qpolynomial_copy(fold2
->qp
[i
]));
493 res
= isl_qpolynomial_fold_fold_on_domain(dom
, res
, res_i
);
496 isl_qpolynomial_fold_free(fold1
);
497 isl_qpolynomial_fold_free(fold2
);
500 isl_qpolynomial_fold_free(res
);
501 isl_qpolynomial_fold_free(fold1
);
502 isl_qpolynomial_fold_free(fold2
);
506 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_substitute_equalities(
507 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_basic_set
*eq
)
514 fold
= isl_qpolynomial_fold_cow(fold
);
518 for (i
= 0; i
< fold
->n
; ++i
) {
519 fold
->qp
[i
] = isl_qpolynomial_substitute_equalities(fold
->qp
[i
],
520 isl_basic_set_copy(eq
));
525 isl_basic_set_free(eq
);
528 isl_basic_set_free(eq
);
529 isl_qpolynomial_fold_free(fold
);
536 #define PW isl_pw_qpolynomial_fold
538 #define EL isl_qpolynomial_fold
540 #define IS_ZERO is_empty
544 #include <isl_pw_templ.c>
547 #define UNION isl_union_pw_qpolynomial_fold
549 #define PART isl_pw_qpolynomial_fold
551 #define PARTS pw_qpolynomial_fold
553 #include <isl_union_templ.c>
555 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_empty(enum isl_fold type
,
556 __isl_take isl_dim
*dim
)
558 return qpolynomial_fold_alloc(type
, dim
, 0);
561 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_alloc(
562 enum isl_fold type
, __isl_take isl_qpolynomial
*qp
)
564 isl_qpolynomial_fold
*fold
;
569 fold
= qpolynomial_fold_alloc(type
, isl_dim_copy(qp
->dim
), 1);
578 isl_qpolynomial_fold_free(fold
);
579 isl_qpolynomial_free(qp
);
583 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_copy(
584 __isl_keep isl_qpolynomial_fold
*fold
)
593 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_dup(
594 __isl_keep isl_qpolynomial_fold
*fold
)
597 isl_qpolynomial_fold
*dup
;
601 dup
= qpolynomial_fold_alloc(fold
->type
,
602 isl_dim_copy(fold
->dim
), fold
->n
);
607 for (i
= 0; i
< fold
->n
; ++i
) {
608 dup
->qp
[i
] = isl_qpolynomial_copy(fold
->qp
[i
]);
615 isl_qpolynomial_fold_free(dup
);
619 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_cow(
620 __isl_take isl_qpolynomial_fold
*fold
)
628 return isl_qpolynomial_fold_dup(fold
);
631 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold
*fold
)
640 for (i
= 0; i
< fold
->n
; ++i
)
641 isl_qpolynomial_free(fold
->qp
[i
]);
642 isl_dim_free(fold
->dim
);
646 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold
*fold
)
654 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_fold(
655 __isl_take isl_qpolynomial_fold
*fold1
,
656 __isl_take isl_qpolynomial_fold
*fold2
)
659 struct isl_qpolynomial_fold
*res
= NULL
;
661 if (!fold1
|| !fold2
)
664 isl_assert(fold1
->dim
->ctx
, fold1
->type
== fold2
->type
, goto error
);
665 isl_assert(fold1
->dim
->ctx
, isl_dim_equal(fold1
->dim
, fold2
->dim
),
668 if (isl_qpolynomial_fold_is_empty(fold1
)) {
669 isl_qpolynomial_fold_free(fold1
);
673 if (isl_qpolynomial_fold_is_empty(fold2
)) {
674 isl_qpolynomial_fold_free(fold2
);
678 res
= qpolynomial_fold_alloc(fold1
->type
, isl_dim_copy(fold1
->dim
),
679 fold1
->n
+ fold2
->n
);
683 for (i
= 0; i
< fold1
->n
; ++i
) {
684 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold1
->qp
[i
]);
685 if (!res
->qp
[res
->n
])
690 for (i
= 0; i
< fold2
->n
; ++i
) {
691 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold2
->qp
[i
]);
692 if (!res
->qp
[res
->n
])
697 isl_qpolynomial_fold_free(fold1
);
698 isl_qpolynomial_fold_free(fold2
);
702 isl_qpolynomial_fold_free(res
);
703 isl_qpolynomial_fold_free(fold1
);
704 isl_qpolynomial_fold_free(fold2
);
708 __isl_give isl_pw_qpolynomial_fold
*isl_pw_qpolynomial_fold_fold(
709 __isl_take isl_pw_qpolynomial_fold
*pw1
,
710 __isl_take isl_pw_qpolynomial_fold
*pw2
)
713 struct isl_pw_qpolynomial_fold
*res
;
719 isl_assert(pw1
->dim
->ctx
, isl_dim_equal(pw1
->dim
, pw2
->dim
), goto error
);
721 if (isl_pw_qpolynomial_fold_is_zero(pw1
)) {
722 isl_pw_qpolynomial_fold_free(pw1
);
726 if (isl_pw_qpolynomial_fold_is_zero(pw2
)) {
727 isl_pw_qpolynomial_fold_free(pw2
);
731 if (pw1
->type
!= pw2
->type
)
732 isl_die(set
->ctx
, isl_error_invalid
, "fold types don't match",
735 n
= (pw1
->n
+ 1) * (pw2
->n
+ 1);
736 res
= isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pw1
->dim
),
739 for (i
= 0; i
< pw1
->n
; ++i
) {
740 set
= isl_set_copy(pw1
->p
[i
].set
);
741 for (j
= 0; j
< pw2
->n
; ++j
) {
742 struct isl_set
*common
;
743 isl_qpolynomial_fold
*sum
;
744 set
= isl_set_subtract(set
,
745 isl_set_copy(pw2
->p
[j
].set
));
746 common
= isl_set_intersect(isl_set_copy(pw1
->p
[i
].set
),
747 isl_set_copy(pw2
->p
[j
].set
));
748 if (isl_set_fast_is_empty(common
)) {
749 isl_set_free(common
);
753 sum
= isl_qpolynomial_fold_fold_on_domain(common
,
754 isl_qpolynomial_fold_copy(pw1
->p
[i
].fold
),
755 isl_qpolynomial_fold_copy(pw2
->p
[j
].fold
));
757 res
= isl_pw_qpolynomial_fold_add_piece(res
, common
, sum
);
759 res
= isl_pw_qpolynomial_fold_add_piece(res
, set
,
760 isl_qpolynomial_fold_copy(pw1
->p
[i
].fold
));
763 for (j
= 0; j
< pw2
->n
; ++j
) {
764 set
= isl_set_copy(pw2
->p
[j
].set
);
765 for (i
= 0; i
< pw1
->n
; ++i
)
766 set
= isl_set_subtract(set
, isl_set_copy(pw1
->p
[i
].set
));
767 res
= isl_pw_qpolynomial_fold_add_piece(res
, set
,
768 isl_qpolynomial_fold_copy(pw2
->p
[j
].fold
));
771 isl_pw_qpolynomial_fold_free(pw1
);
772 isl_pw_qpolynomial_fold_free(pw2
);
776 isl_pw_qpolynomial_fold_free(pw1
);
777 isl_pw_qpolynomial_fold_free(pw2
);
781 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
782 __isl_take isl_union_pw_qpolynomial_fold
*u
,
783 __isl_take isl_pw_qpolynomial_fold
*part
)
786 struct isl_hash_table_entry
*entry
;
788 u
= isl_union_pw_qpolynomial_fold_cow(u
);
793 isl_assert(u
->dim
->ctx
, isl_dim_match(part
->dim
, isl_dim_param
, u
->dim
,
794 isl_dim_param
), goto error
);
796 hash
= isl_dim_get_hash(part
->dim
);
797 entry
= isl_hash_table_find(u
->dim
->ctx
, &u
->table
, hash
,
798 &has_dim
, part
->dim
, 1);
805 entry
->data
= isl_pw_qpolynomial_fold_fold(entry
->data
,
806 isl_pw_qpolynomial_fold_copy(part
));
809 isl_pw_qpolynomial_fold_free(part
);
814 isl_pw_qpolynomial_fold_free(part
);
815 isl_union_pw_qpolynomial_fold_free(u
);
819 static int fold_part(__isl_take isl_pw_qpolynomial_fold
*part
, void *user
)
821 isl_union_pw_qpolynomial_fold
**u
;
822 u
= (isl_union_pw_qpolynomial_fold
**)user
;
824 *u
= isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u
, part
);
829 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_fold(
830 __isl_take isl_union_pw_qpolynomial_fold
*u1
,
831 __isl_take isl_union_pw_qpolynomial_fold
*u2
)
833 u1
= isl_union_pw_qpolynomial_fold_cow(u1
);
838 if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2
,
839 &fold_part
, &u1
) < 0)
842 isl_union_pw_qpolynomial_fold_free(u2
);
846 isl_union_pw_qpolynomial_fold_free(u1
);
847 isl_union_pw_qpolynomial_fold_free(u2
);
851 __isl_give isl_pw_qpolynomial_fold
*isl_pw_qpolynomial_fold_from_pw_qpolynomial(
852 enum isl_fold type
, __isl_take isl_pw_qpolynomial
*pwqp
)
855 isl_pw_qpolynomial_fold
*pwf
;
860 pwf
= isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pwqp
->dim
), type
,
863 for (i
= 0; i
< pwqp
->n
; ++i
)
864 pwf
= isl_pw_qpolynomial_fold_add_piece(pwf
,
865 isl_set_copy(pwqp
->p
[i
].set
),
866 isl_qpolynomial_fold_alloc(type
,
867 isl_qpolynomial_copy(pwqp
->p
[i
].qp
)));
869 isl_pw_qpolynomial_free(pwqp
);
874 int isl_qpolynomial_fold_is_equal(__isl_keep isl_qpolynomial_fold
*fold1
,
875 __isl_keep isl_qpolynomial_fold
*fold2
)
879 if (!fold1
|| !fold2
)
882 if (fold1
->n
!= fold2
->n
)
885 /* We probably want to sort the qps first... */
886 for (i
= 0; i
< fold1
->n
; ++i
) {
887 int eq
= isl_qpolynomial_is_equal(fold1
->qp
[i
], fold2
->qp
[i
]);
895 __isl_give isl_qpolynomial
*isl_qpolynomial_fold_eval(
896 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_point
*pnt
)
902 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, fold
->dim
), goto error
);
903 isl_assert(pnt
->dim
->ctx
,
904 fold
->type
== isl_fold_max
|| fold
->type
== isl_fold_min
,
908 qp
= isl_qpolynomial_zero(isl_dim_copy(fold
->dim
));
911 qp
= isl_qpolynomial_eval(isl_qpolynomial_copy(fold
->qp
[0]),
912 isl_point_copy(pnt
));
913 for (i
= 1; i
< fold
->n
; ++i
) {
914 isl_qpolynomial
*qp_i
;
915 qp_i
= isl_qpolynomial_eval(
916 isl_qpolynomial_copy(fold
->qp
[i
]),
917 isl_point_copy(pnt
));
918 if (fold
->type
== isl_fold_max
)
919 qp
= isl_qpolynomial_max_cst(qp
, qp_i
);
921 qp
= isl_qpolynomial_min_cst(qp
, qp_i
);
924 isl_qpolynomial_fold_free(fold
);
929 isl_qpolynomial_fold_free(fold
);
934 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold
*pwf
)
939 for (i
= 0; i
< pwf
->n
; ++i
)
940 n
+= pwf
->p
[i
].fold
->n
;
945 __isl_give isl_qpolynomial
*isl_qpolynomial_fold_opt_on_domain(
946 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_set
*set
, int max
)
949 isl_qpolynomial
*opt
;
955 isl_dim
*dim
= isl_dim_copy(fold
->dim
);
957 isl_qpolynomial_fold_free(fold
);
958 return isl_qpolynomial_zero(dim
);
961 opt
= isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold
->qp
[0]),
962 isl_set_copy(set
), max
);
963 for (i
= 1; i
< fold
->n
; ++i
) {
964 isl_qpolynomial
*opt_i
;
965 opt_i
= isl_qpolynomial_opt_on_domain(
966 isl_qpolynomial_copy(fold
->qp
[i
]),
967 isl_set_copy(set
), max
);
969 opt
= isl_qpolynomial_max_cst(opt
, opt_i
);
971 opt
= isl_qpolynomial_min_cst(opt
, opt_i
);
975 isl_qpolynomial_fold_free(fold
);
980 isl_qpolynomial_fold_free(fold
);
984 /* Check whether for each quasi-polynomial in "fold2" there is
985 * a quasi-polynomial in "fold1" that dominates it on "set".
987 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set
*set
,
988 __isl_keep isl_qpolynomial_fold
*fold1
,
989 __isl_keep isl_qpolynomial_fold
*fold2
)
994 if (!set
|| !fold1
|| !fold2
)
997 covers
= fold1
->type
== isl_fold_max
? 1 : -1;
999 for (i
= 0; i
< fold2
->n
; ++i
) {
1000 for (j
= 0; j
< fold1
->n
; ++j
) {
1004 d
= isl_qpolynomial_sub(
1005 isl_qpolynomial_copy(fold1
->qp
[j
]),
1006 isl_qpolynomial_copy(fold2
->qp
[i
]));
1007 sgn
= isl_qpolynomial_sign(set
, d
);
1008 isl_qpolynomial_free(d
);
1019 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1020 * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1023 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold
*pwf1
,
1024 __isl_keep isl_pw_qpolynomial_fold
*pwf2
)
1027 isl_set
*dom1
, *dom2
;
1038 dom1
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1
));
1039 dom2
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2
));
1040 is_subset
= isl_set_is_subset(dom2
, dom1
);
1044 if (is_subset
< 0 || !is_subset
)
1047 for (i
= 0; i
< pwf2
->n
; ++i
) {
1048 for (j
= 0; j
< pwf1
->n
; ++j
) {
1053 common
= isl_set_intersect(isl_set_copy(pwf1
->p
[j
].set
),
1054 isl_set_copy(pwf2
->p
[i
].set
));
1055 is_empty
= isl_set_is_empty(common
);
1056 if (is_empty
< 0 || is_empty
) {
1057 isl_set_free(common
);
1062 covers
= qpolynomial_fold_covers_on_domain(common
,
1063 pwf1
->p
[j
].fold
, pwf2
->p
[i
].fold
);
1064 isl_set_free(common
);
1065 if (covers
< 0 || !covers
)
1073 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_morph(
1074 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_morph
*morph
)
1079 if (!fold
|| !morph
)
1082 ctx
= fold
->dim
->ctx
;
1083 isl_assert(ctx
, isl_dim_equal(fold
->dim
, morph
->dom
->dim
), goto error
);
1085 fold
= isl_qpolynomial_fold_cow(fold
);
1089 isl_dim_free(fold
->dim
);
1090 fold
->dim
= isl_dim_copy(morph
->ran
->dim
);
1094 for (i
= 0; i
< fold
->n
; ++i
) {
1095 fold
->qp
[i
] = isl_qpolynomial_morph(fold
->qp
[i
],
1096 isl_morph_copy(morph
));
1101 isl_morph_free(morph
);
1105 isl_qpolynomial_fold_free(fold
);
1106 isl_morph_free(morph
);
1110 enum isl_fold
isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold
*fold
)
1113 return isl_fold_list
;
1117 enum isl_fold
isl_union_pw_qpolynomial_fold_get_type(
1118 __isl_keep isl_union_pw_qpolynomial_fold
*upwf
)
1121 return isl_fold_list
;
1125 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_lift(
1126 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_dim
*dim
)
1134 if (isl_dim_equal(fold
->dim
, dim
)) {
1139 fold
= isl_qpolynomial_fold_cow(fold
);
1143 isl_dim_free(fold
->dim
);
1144 fold
->dim
= isl_dim_copy(dim
);
1148 for (i
= 0; i
< fold
->n
; ++i
) {
1149 fold
->qp
[i
] = isl_qpolynomial_lift(fold
->qp
[i
],
1159 isl_qpolynomial_fold_free(fold
);
1164 int isl_qpolynomial_fold_foreach_qpolynomial(
1165 __isl_keep isl_qpolynomial_fold
*fold
,
1166 int (*fn
)(__isl_take isl_qpolynomial
*qp
, void *user
), void *user
)
1173 for (i
= 0; i
< fold
->n
; ++i
)
1174 if (fn(isl_qpolynomial_copy(fold
->qp
[i
]), user
) < 0)
1180 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_move_dims(
1181 __isl_take isl_qpolynomial_fold
*fold
,
1182 enum isl_dim_type dst_type
, unsigned dst_pos
,
1183 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
1190 fold
= isl_qpolynomial_fold_cow(fold
);
1194 fold
->dim
= isl_dim_move(fold
->dim
, dst_type
, dst_pos
,
1195 src_type
, src_pos
, n
);
1199 for (i
= 0; i
< fold
->n
; ++i
) {
1200 fold
->qp
[i
] = isl_qpolynomial_move_dims(fold
->qp
[i
],
1201 dst_type
, dst_pos
, src_type
, src_pos
, n
);
1208 isl_qpolynomial_fold_free(fold
);
1212 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1213 * in fold->qp[k] by subs[i].
1215 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_substitute(
1216 __isl_take isl_qpolynomial_fold
*fold
,
1217 enum isl_dim_type type
, unsigned first
, unsigned n
,
1218 __isl_keep isl_qpolynomial
**subs
)
1225 fold
= isl_qpolynomial_fold_cow(fold
);
1229 for (i
= 0; i
< fold
->n
; ++i
) {
1230 fold
->qp
[i
] = isl_qpolynomial_substitute(fold
->qp
[i
],
1231 type
, first
, n
, subs
);
1238 isl_qpolynomial_fold_free(fold
);
1242 static int add_pwqp(__isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
1245 isl_pw_qpolynomial_fold
*pwf
;
1246 isl_union_pw_qpolynomial_fold
**upwf
;
1248 struct isl_hash_table_entry
*entry
;
1250 upwf
= (isl_union_pw_qpolynomial_fold
**)user
;
1252 ctx
= pwqp
->dim
->ctx
;
1253 hash
= isl_dim_get_hash(pwqp
->dim
);
1254 entry
= isl_hash_table_find(ctx
, &(*upwf
)->table
,
1255 hash
, &has_dim
, pwqp
->dim
, 1);
1259 pwf
= isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf
)->type
, pwqp
);
1263 entry
->data
= isl_pw_qpolynomial_fold_add(entry
->data
, pwf
);
1266 if (isl_pw_qpolynomial_fold_is_zero(entry
->data
)) {
1267 isl_pw_qpolynomial_fold_free(entry
->data
);
1268 isl_hash_table_remove(ctx
, &(*upwf
)->table
, entry
);
1274 isl_pw_qpolynomial_free(pwqp
);
1278 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1279 __isl_take isl_union_pw_qpolynomial_fold
*upwf
,
1280 __isl_take isl_union_pw_qpolynomial
*upwqp
)
1282 upwf
= isl_union_pw_qpolynomial_fold_align_params(upwf
,
1283 isl_union_pw_qpolynomial_get_dim(upwqp
));
1284 upwqp
= isl_union_pw_qpolynomial_align_params(upwqp
,
1285 isl_union_pw_qpolynomial_fold_get_dim(upwf
));
1287 upwf
= isl_union_pw_qpolynomial_fold_cow(upwf
);
1288 if (!upwf
|| !upwqp
)
1291 if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp
, &add_pwqp
,
1295 isl_union_pw_qpolynomial_free(upwqp
);
1299 isl_union_pw_qpolynomial_fold_free(upwf
);
1300 isl_union_pw_qpolynomial_free(upwqp
);
1304 static int compatible_range(__isl_keep isl_dim
*dim1
, __isl_keep isl_dim
*dim2
)
1307 m
= isl_dim_match(dim1
, isl_dim_param
, dim2
, isl_dim_param
);
1310 return isl_dim_tuple_match(dim1
, isl_dim_out
, dim2
, isl_dim_set
);
1313 /* Compute the intersection of the range of the map and the domain
1314 * of the piecewise quasipolynomial reduction and then compute a bound
1315 * on the associated quasipolynomial reduction over all elements
1316 * in this intersection.
1318 * We first introduce some unconstrained dimensions in the
1319 * piecewise quasipolynomial, intersect the resulting domain
1320 * with the wrapped map and the compute the sum.
1322 __isl_give isl_pw_qpolynomial_fold
*isl_map_apply_pw_qpolynomial_fold(
1323 __isl_take isl_map
*map
, __isl_take isl_pw_qpolynomial_fold
*pwf
,
1333 ctx
= isl_map_get_ctx(map
);
1337 map_dim
= isl_map_get_dim(map
);
1338 pwf_dim
= isl_pw_qpolynomial_fold_get_dim(pwf
);
1339 ok
= compatible_range(map_dim
, pwf_dim
);
1340 isl_dim_free(map_dim
);
1341 isl_dim_free(pwf_dim
);
1343 isl_die(ctx
, isl_error_invalid
, "incompatible dimensions",
1346 n_in
= isl_map_dim(map
, isl_dim_in
);
1347 pwf
= isl_pw_qpolynomial_fold_insert_dims(pwf
, isl_dim_set
, 0, n_in
);
1349 dom
= isl_map_wrap(map
);
1350 pwf
= isl_pw_qpolynomial_fold_reset_dim(pwf
, isl_set_get_dim(dom
));
1352 pwf
= isl_pw_qpolynomial_fold_intersect_domain(pwf
, dom
);
1353 pwf
= isl_pw_qpolynomial_fold_bound(pwf
, tight
);
1358 isl_pw_qpolynomial_fold_free(pwf
);
1362 struct isl_apply_fold_data
{
1363 isl_union_pw_qpolynomial_fold
*upwf
;
1364 isl_union_pw_qpolynomial_fold
*res
;
1369 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold
*pwf
,
1374 struct isl_apply_fold_data
*data
= user
;
1377 map_dim
= isl_map_get_dim(data
->map
);
1378 pwf_dim
= isl_pw_qpolynomial_fold_get_dim(pwf
);
1379 ok
= compatible_range(map_dim
, pwf_dim
);
1380 isl_dim_free(map_dim
);
1381 isl_dim_free(pwf_dim
);
1384 pwf
= isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data
->map
),
1385 pwf
, data
->tight
? &data
->tight
: NULL
);
1386 data
->res
= isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1389 isl_pw_qpolynomial_fold_free(pwf
);
1394 static int map_apply(__isl_take isl_map
*map
, void *user
)
1396 struct isl_apply_fold_data
*data
= user
;
1400 r
= isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1401 data
->upwf
, &pw_qpolynomial_fold_apply
, data
);
1407 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_map_apply_union_pw_qpolynomial_fold(
1408 __isl_take isl_union_map
*umap
,
1409 __isl_take isl_union_pw_qpolynomial_fold
*upwf
, int *tight
)
1413 struct isl_apply_fold_data data
;
1415 upwf
= isl_union_pw_qpolynomial_fold_align_params(upwf
,
1416 isl_union_map_get_dim(umap
));
1417 umap
= isl_union_map_align_params(umap
,
1418 isl_union_pw_qpolynomial_fold_get_dim(upwf
));
1421 data
.tight
= tight
? 1 : 0;
1422 dim
= isl_union_pw_qpolynomial_fold_get_dim(upwf
);
1423 type
= isl_union_pw_qpolynomial_fold_get_type(upwf
);
1424 data
.res
= isl_union_pw_qpolynomial_fold_zero(dim
, type
);
1425 if (isl_union_map_foreach_map(umap
, &map_apply
, &data
) < 0)
1428 isl_union_map_free(umap
);
1429 isl_union_pw_qpolynomial_fold_free(upwf
);
1432 *tight
= data
.tight
;
1436 isl_union_map_free(umap
);
1437 isl_union_pw_qpolynomial_fold_free(upwf
);
1438 isl_union_pw_qpolynomial_fold_free(data
.res
);
1442 /* Reorder the dimension of "fold" according to the given reordering.
1444 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_realign(
1445 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_reordering
*r
)
1449 fold
= isl_qpolynomial_fold_cow(fold
);
1453 for (i
= 0; i
< fold
->n
; ++i
) {
1454 fold
->qp
[i
] = isl_qpolynomial_realign(fold
->qp
[i
],
1455 isl_reordering_copy(r
));
1460 fold
= isl_qpolynomial_fold_reset_dim(fold
, isl_dim_copy(r
->dim
));
1462 isl_reordering_free(r
);
1466 isl_qpolynomial_fold_free(fold
);
1467 isl_reordering_free(r
);