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>
19 static __isl_give isl_qpolynomial_fold
*qpolynomial_fold_alloc(
20 enum isl_fold type
, __isl_take isl_dim
*dim
, int n
)
22 isl_qpolynomial_fold
*fold
;
27 isl_assert(dim
->ctx
, n
>= 0, goto error
);
28 fold
= isl_calloc(dim
->ctx
, struct isl_qpolynomial_fold
,
29 sizeof(struct isl_qpolynomial_fold
) +
30 (n
- 1) * sizeof(struct isl_qpolynomial
*));
46 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold
*fold
,
47 enum isl_dim_type type
, unsigned first
, unsigned n
)
53 if (fold
->n
== 0 || n
== 0)
56 for (i
= 0; i
< fold
->n
; ++i
) {
57 int involves
= isl_qpolynomial_involves_dims(fold
->qp
[i
],
59 if (involves
< 0 || involves
)
65 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_drop_dims(
66 __isl_take isl_qpolynomial_fold
*fold
,
67 enum isl_dim_type type
, unsigned first
, unsigned n
)
76 fold
= isl_qpolynomial_fold_cow(fold
);
79 fold
->dim
= isl_dim_drop(fold
->dim
, type
, first
, n
);
83 for (i
= 0; i
< fold
->n
; ++i
) {
84 fold
->qp
[i
] = isl_qpolynomial_drop_dims(fold
->qp
[i
],
92 isl_qpolynomial_fold_free(fold
);
96 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial
*qp
)
98 struct isl_upoly_cst
*cst
;
100 cst
= isl_upoly_as_cst(qp
->upoly
);
104 return isl_int_sgn(cst
->n
) < 0 ? -1 : 1;
107 static int isl_qpolynomial_aff_sign(__isl_keep isl_set
*set
,
108 __isl_keep isl_qpolynomial
*qp
)
110 enum isl_lp_result res
;
115 aff
= isl_qpolynomial_extract_affine(qp
);
121 res
= isl_set_solve_lp(set
, 0, aff
->el
+ 1, aff
->el
[0],
123 if (res
== isl_lp_error
)
125 if (res
== isl_lp_empty
||
126 (res
== isl_lp_ok
&& !isl_int_is_neg(opt
))) {
131 res
= isl_set_solve_lp(set
, 1, aff
->el
+ 1, aff
->el
[0],
133 if (res
== isl_lp_ok
&& !isl_int_is_pos(opt
))
142 /* Determine, if possible, the sign of the quasipolynomial "qp" on
145 * If qp is a constant, then the problem is trivial.
146 * If qp is linear, then we check if the minimum of the corresponding
147 * affine constraint is non-negative or if the maximum is non-positive.
149 * Otherwise, we check if the outermost variable "v" has a lower bound "l"
150 * in "set". If so, we write qp(v,v') as
152 * q(v,v') * (v - l) + r(v')
154 * if q(v,v') and r(v') have the same known sign, then the original
155 * quasipolynomial has the same sign as well.
162 static int isl_qpolynomial_sign(__isl_keep isl_set
*set
,
163 __isl_keep isl_qpolynomial
*qp
)
168 struct isl_upoly_rec
*rec
;
171 enum isl_lp_result res
;
174 is
= isl_qpolynomial_is_cst(qp
, NULL
, NULL
);
178 return isl_qpolynomial_cst_sign(qp
);
180 is
= isl_qpolynomial_is_affine(qp
);
184 return isl_qpolynomial_aff_sign(set
, qp
);
186 if (qp
->div
->n_row
> 0)
189 rec
= isl_upoly_as_rec(qp
->upoly
);
193 d
= isl_dim_total(qp
->dim
);
194 v
= isl_vec_alloc(set
->ctx
, 2 + d
);
198 isl_seq_clr(v
->el
+ 1, 1 + d
);
199 isl_int_set_si(v
->el
[0], 1);
200 isl_int_set_si(v
->el
[2 + qp
->upoly
->var
], 1);
204 res
= isl_set_solve_lp(set
, 0, v
->el
+ 1, v
->el
[0], &l
, NULL
, NULL
);
205 if (res
== isl_lp_ok
) {
206 isl_qpolynomial
*min
;
207 isl_qpolynomial
*base
;
208 isl_qpolynomial
*r
, *q
;
211 min
= isl_qpolynomial_cst(isl_dim_copy(qp
->dim
), l
);
212 base
= isl_qpolynomial_pow(isl_dim_copy(qp
->dim
),
215 r
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), 0,
216 isl_upoly_copy(rec
->p
[rec
->n
- 1]));
217 q
= isl_qpolynomial_copy(r
);
219 for (i
= rec
->n
- 2; i
>= 0; --i
) {
220 r
= isl_qpolynomial_mul(r
, isl_qpolynomial_copy(min
));
221 t
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), 0,
222 isl_upoly_copy(rec
->p
[i
]));
223 r
= isl_qpolynomial_add(r
, t
);
226 q
= isl_qpolynomial_mul(q
, isl_qpolynomial_copy(base
));
227 q
= isl_qpolynomial_add(q
, isl_qpolynomial_copy(r
));
230 if (isl_qpolynomial_is_zero(q
))
231 sgn
= isl_qpolynomial_sign(set
, r
);
232 else if (isl_qpolynomial_is_zero(r
))
233 sgn
= isl_qpolynomial_sign(set
, q
);
236 sgn_r
= isl_qpolynomial_sign(set
, r
);
237 sgn_q
= isl_qpolynomial_sign(set
, q
);
242 isl_qpolynomial_free(min
);
243 isl_qpolynomial_free(base
);
244 isl_qpolynomial_free(q
);
245 isl_qpolynomial_free(r
);
255 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_fold_on_domain(
256 __isl_keep isl_set
*set
,
257 __isl_take isl_qpolynomial_fold
*fold1
,
258 __isl_take isl_qpolynomial_fold
*fold2
)
262 struct isl_qpolynomial_fold
*res
= NULL
;
265 if (!fold1
|| !fold2
)
268 isl_assert(fold1
->dim
->ctx
, fold1
->type
== fold2
->type
, goto error
);
269 isl_assert(fold1
->dim
->ctx
, isl_dim_equal(fold1
->dim
, fold2
->dim
),
272 better
= fold1
->type
== isl_fold_max
? -1 : 1;
274 if (isl_qpolynomial_fold_is_empty(fold1
)) {
275 isl_qpolynomial_fold_free(fold1
);
279 if (isl_qpolynomial_fold_is_empty(fold2
)) {
280 isl_qpolynomial_fold_free(fold2
);
284 res
= qpolynomial_fold_alloc(fold1
->type
, isl_dim_copy(fold1
->dim
),
285 fold1
->n
+ fold2
->n
);
289 for (i
= 0; i
< fold1
->n
; ++i
) {
290 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold1
->qp
[i
]);
291 if (!res
->qp
[res
->n
])
297 for (i
= 0; i
< fold2
->n
; ++i
) {
298 for (j
= n1
- 1; j
>= 0; --j
) {
301 d
= isl_qpolynomial_sub(
302 isl_qpolynomial_copy(res
->qp
[j
]),
303 isl_qpolynomial_copy(fold2
->qp
[i
]));
304 sgn
= isl_qpolynomial_sign(set
, d
);
305 isl_qpolynomial_free(d
);
310 isl_qpolynomial_free(res
->qp
[j
]);
312 res
->qp
[j
] = res
->qp
[n1
- 1];
314 if (n1
!= res
->n
- 1)
315 res
->qp
[n1
] = res
->qp
[res
->n
- 1];
320 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold2
->qp
[i
]);
321 if (!res
->qp
[res
->n
])
326 isl_qpolynomial_fold_free(fold1
);
327 isl_qpolynomial_fold_free(fold2
);
331 isl_qpolynomial_fold_free(res
);
332 isl_qpolynomial_fold_free(fold1
);
333 isl_qpolynomial_fold_free(fold2
);
338 #define PW isl_pw_qpolynomial_fold
340 #define EL isl_qpolynomial_fold
342 #define IS_ZERO is_empty
346 #define ADD(d,e1,e2) isl_qpolynomial_fold_fold_on_domain(d,e1,e2)
348 #include <isl_pw_templ.c>
351 #define UNION isl_union_pw_qpolynomial_fold
353 #define PART isl_pw_qpolynomial_fold
355 #define PARTS pw_qpolynomial_fold
357 #include <isl_union_templ.c>
359 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_empty(enum isl_fold type
,
360 __isl_take isl_dim
*dim
)
362 return qpolynomial_fold_alloc(type
, dim
, 0);
365 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_alloc(
366 enum isl_fold type
, __isl_take isl_qpolynomial
*qp
)
368 isl_qpolynomial_fold
*fold
;
373 fold
= qpolynomial_fold_alloc(type
, isl_dim_copy(qp
->dim
), 1);
382 isl_qpolynomial_fold_free(fold
);
383 isl_qpolynomial_free(qp
);
387 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_copy(
388 __isl_keep isl_qpolynomial_fold
*fold
)
397 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_dup(
398 __isl_keep isl_qpolynomial_fold
*fold
)
401 isl_qpolynomial_fold
*dup
;
405 dup
= qpolynomial_fold_alloc(fold
->type
,
406 isl_dim_copy(fold
->dim
), fold
->n
);
411 for (i
= 0; i
< fold
->n
; ++i
) {
412 dup
->qp
[i
] = isl_qpolynomial_copy(fold
->qp
[i
]);
419 isl_qpolynomial_fold_free(dup
);
423 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_cow(
424 __isl_take isl_qpolynomial_fold
*fold
)
432 return isl_qpolynomial_fold_dup(fold
);
435 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold
*fold
)
444 for (i
= 0; i
< fold
->n
; ++i
)
445 isl_qpolynomial_free(fold
->qp
[i
]);
446 isl_dim_free(fold
->dim
);
450 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold
*fold
)
458 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_fold(
459 __isl_take isl_qpolynomial_fold
*fold1
,
460 __isl_take isl_qpolynomial_fold
*fold2
)
463 struct isl_qpolynomial_fold
*res
= NULL
;
465 if (!fold1
|| !fold2
)
468 isl_assert(fold1
->dim
->ctx
, fold1
->type
== fold2
->type
, goto error
);
469 isl_assert(fold1
->dim
->ctx
, isl_dim_equal(fold1
->dim
, fold2
->dim
),
472 if (isl_qpolynomial_fold_is_empty(fold1
)) {
473 isl_qpolynomial_fold_free(fold1
);
477 if (isl_qpolynomial_fold_is_empty(fold2
)) {
478 isl_qpolynomial_fold_free(fold2
);
482 res
= qpolynomial_fold_alloc(fold1
->type
, isl_dim_copy(fold1
->dim
),
483 fold1
->n
+ fold2
->n
);
487 for (i
= 0; i
< fold1
->n
; ++i
) {
488 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold1
->qp
[i
]);
489 if (!res
->qp
[res
->n
])
494 for (i
= 0; i
< fold2
->n
; ++i
) {
495 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold2
->qp
[i
]);
496 if (!res
->qp
[res
->n
])
501 isl_qpolynomial_fold_free(fold1
);
502 isl_qpolynomial_fold_free(fold2
);
506 isl_qpolynomial_fold_free(res
);
507 isl_qpolynomial_fold_free(fold1
);
508 isl_qpolynomial_fold_free(fold2
);
512 __isl_give isl_pw_qpolynomial_fold
*isl_pw_qpolynomial_fold_from_pw_qpolynomial(
513 enum isl_fold type
, __isl_take isl_pw_qpolynomial
*pwqp
)
516 isl_pw_qpolynomial_fold
*pwf
;
521 pwf
= isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pwqp
->dim
), pwqp
->n
);
523 for (i
= 0; i
< pwqp
->n
; ++i
)
524 pwf
= isl_pw_qpolynomial_fold_add_piece(pwf
,
525 isl_set_copy(pwqp
->p
[i
].set
),
526 isl_qpolynomial_fold_alloc(type
,
527 isl_qpolynomial_copy(pwqp
->p
[i
].qp
)));
529 isl_pw_qpolynomial_free(pwqp
);
534 int isl_qpolynomial_fold_is_equal(__isl_keep isl_qpolynomial_fold
*fold1
,
535 __isl_keep isl_qpolynomial_fold
*fold2
)
539 if (!fold1
|| !fold2
)
542 if (fold1
->n
!= fold2
->n
)
545 /* We probably want to sort the qps first... */
546 for (i
= 0; i
< fold1
->n
; ++i
) {
547 int eq
= isl_qpolynomial_is_equal(fold1
->qp
[i
], fold2
->qp
[i
]);
555 __isl_give isl_qpolynomial
*isl_qpolynomial_fold_eval(
556 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_point
*pnt
)
562 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, fold
->dim
), goto error
);
563 isl_assert(pnt
->dim
->ctx
,
564 fold
->type
== isl_fold_max
|| fold
->type
== isl_fold_min
,
568 qp
= isl_qpolynomial_zero(isl_dim_copy(fold
->dim
));
571 qp
= isl_qpolynomial_eval(isl_qpolynomial_copy(fold
->qp
[0]),
572 isl_point_copy(pnt
));
573 for (i
= 1; i
< fold
->n
; ++i
) {
574 isl_qpolynomial
*qp_i
;
575 qp_i
= isl_qpolynomial_eval(
576 isl_qpolynomial_copy(fold
->qp
[i
]),
577 isl_point_copy(pnt
));
578 if (fold
->type
== isl_fold_max
)
579 qp
= isl_qpolynomial_max_cst(qp
, qp_i
);
581 qp
= isl_qpolynomial_min_cst(qp
, qp_i
);
584 isl_qpolynomial_fold_free(fold
);
589 isl_qpolynomial_fold_free(fold
);
594 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold
*pwf
)
599 for (i
= 0; i
< pwf
->n
; ++i
)
600 n
+= pwf
->p
[i
].fold
->n
;
605 __isl_give isl_qpolynomial
*isl_qpolynomial_fold_opt_on_domain(
606 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_set
*set
, int max
)
609 isl_qpolynomial
*opt
;
615 isl_dim
*dim
= isl_dim_copy(fold
->dim
);
617 isl_qpolynomial_fold_free(fold
);
618 return isl_qpolynomial_zero(dim
);
621 opt
= isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold
->qp
[0]),
622 isl_set_copy(set
), max
);
623 for (i
= 1; i
< fold
->n
; ++i
) {
624 isl_qpolynomial
*opt_i
;
625 opt_i
= isl_qpolynomial_opt_on_domain(
626 isl_qpolynomial_copy(fold
->qp
[i
]),
627 isl_set_copy(set
), max
);
629 opt
= isl_qpolynomial_max_cst(opt
, opt_i
);
631 opt
= isl_qpolynomial_min_cst(opt
, opt_i
);
635 isl_qpolynomial_fold_free(fold
);
640 isl_qpolynomial_fold_free(fold
);
644 /* Check whether for each quasi-polynomial in "fold2" there is
645 * a quasi-polynomial in "fold1" that dominates it on "set".
647 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set
*set
,
648 __isl_keep isl_qpolynomial_fold
*fold1
,
649 __isl_keep isl_qpolynomial_fold
*fold2
)
654 if (!set
|| !fold1
|| !fold2
)
657 covers
= fold1
->type
== isl_fold_max
? 1 : -1;
659 for (i
= 0; i
< fold2
->n
; ++i
) {
660 for (j
= 0; j
< fold1
->n
; ++j
) {
664 d
= isl_qpolynomial_sub(
665 isl_qpolynomial_copy(fold1
->qp
[j
]),
666 isl_qpolynomial_copy(fold2
->qp
[i
]));
667 sgn
= isl_qpolynomial_sign(set
, d
);
668 isl_qpolynomial_free(d
);
679 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
680 * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
683 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold
*pwf1
,
684 __isl_keep isl_pw_qpolynomial_fold
*pwf2
)
687 isl_set
*dom1
, *dom2
;
698 dom1
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1
));
699 dom2
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2
));
700 is_subset
= isl_set_is_subset(dom2
, dom1
);
704 if (is_subset
< 0 || !is_subset
)
707 for (i
= 0; i
< pwf2
->n
; ++i
) {
708 for (j
= 0; j
< pwf1
->n
; ++j
) {
713 common
= isl_set_intersect(isl_set_copy(pwf1
->p
[j
].set
),
714 isl_set_copy(pwf2
->p
[i
].set
));
715 is_empty
= isl_set_is_empty(common
);
716 if (is_empty
< 0 || is_empty
) {
717 isl_set_free(common
);
722 covers
= qpolynomial_fold_covers_on_domain(common
,
723 pwf1
->p
[j
].fold
, pwf2
->p
[i
].fold
);
724 isl_set_free(common
);
725 if (covers
< 0 || !covers
)
733 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_morph(
734 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_morph
*morph
)
742 ctx
= fold
->dim
->ctx
;
743 isl_assert(ctx
, isl_dim_equal(fold
->dim
, morph
->dom
->dim
), goto error
);
745 fold
= isl_qpolynomial_fold_cow(fold
);
749 isl_dim_free(fold
->dim
);
750 fold
->dim
= isl_dim_copy(morph
->ran
->dim
);
754 for (i
= 0; i
< fold
->n
; ++i
) {
755 fold
->qp
[i
] = isl_qpolynomial_morph(fold
->qp
[i
],
756 isl_morph_copy(morph
));
761 isl_morph_free(morph
);
765 isl_qpolynomial_fold_free(fold
);
766 isl_morph_free(morph
);
770 enum isl_fold
isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold
*fold
)
773 return isl_fold_list
;
777 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_lift(
778 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_dim
*dim
)
786 if (isl_dim_equal(fold
->dim
, dim
)) {
791 fold
= isl_qpolynomial_fold_cow(fold
);
795 isl_dim_free(fold
->dim
);
796 fold
->dim
= isl_dim_copy(dim
);
800 for (i
= 0; i
< fold
->n
; ++i
) {
801 fold
->qp
[i
] = isl_qpolynomial_lift(fold
->qp
[i
],
811 isl_qpolynomial_fold_free(fold
);
816 int isl_qpolynomial_fold_foreach_qpolynomial(
817 __isl_keep isl_qpolynomial_fold
*fold
,
818 int (*fn
)(__isl_take isl_qpolynomial
*qp
, void *user
), void *user
)
825 for (i
= 0; i
< fold
->n
; ++i
)
826 if (fn(isl_qpolynomial_copy(fold
->qp
[i
]), user
) < 0)
832 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_move_dims(
833 __isl_take isl_qpolynomial_fold
*fold
,
834 enum isl_dim_type dst_type
, unsigned dst_pos
,
835 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
842 fold
= isl_qpolynomial_fold_cow(fold
);
846 fold
->dim
= isl_dim_move(fold
->dim
, dst_type
, dst_pos
,
847 src_type
, src_pos
, n
);
851 for (i
= 0; i
< fold
->n
; ++i
) {
852 fold
->qp
[i
] = isl_qpolynomial_move_dims(fold
->qp
[i
],
853 dst_type
, dst_pos
, src_type
, src_pos
, n
);
860 isl_qpolynomial_fold_free(fold
);