2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_map_private.h>
13 #include <isl_union_map_private.h>
14 #include <isl_polynomial_private.h>
15 #include <isl_point_private.h>
16 #include <isl_space_private.h>
19 #include <isl_mat_private.h>
20 #include <isl_val_private.h>
21 #include <isl_config.h>
23 enum isl_fold
isl_fold_type_negate(enum isl_fold type
)
34 isl_die(NULL
, isl_error_internal
, "unhandled isl_fold type", abort());
37 static __isl_give isl_qpolynomial_fold
*qpolynomial_fold_alloc(
38 enum isl_fold type
, __isl_take isl_space
*dim
, int n
)
40 isl_qpolynomial_fold
*fold
;
45 isl_assert(dim
->ctx
, n
>= 0, goto error
);
46 fold
= isl_calloc(dim
->ctx
, struct isl_qpolynomial_fold
,
47 sizeof(struct isl_qpolynomial_fold
) +
48 (n
- 1) * sizeof(struct isl_qpolynomial
*));
64 isl_ctx
*isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold
*fold
)
66 return fold
? fold
->dim
->ctx
: NULL
;
69 __isl_give isl_space
*isl_qpolynomial_fold_get_domain_space(
70 __isl_keep isl_qpolynomial_fold
*fold
)
72 return fold
? isl_space_copy(fold
->dim
) : NULL
;
75 __isl_give isl_space
*isl_qpolynomial_fold_get_space(
76 __isl_keep isl_qpolynomial_fold
*fold
)
81 space
= isl_space_copy(fold
->dim
);
82 space
= isl_space_from_domain(space
);
83 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
87 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_reset_domain_space(
88 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_space
*dim
)
92 fold
= isl_qpolynomial_fold_cow(fold
);
96 for (i
= 0; i
< fold
->n
; ++i
) {
97 fold
->qp
[i
] = isl_qpolynomial_reset_domain_space(fold
->qp
[i
],
103 isl_space_free(fold
->dim
);
108 isl_qpolynomial_fold_free(fold
);
113 /* Reset the space of "fold". This function is called from isl_pw_templ.c
114 * and doesn't know if the space of an element object is represented
115 * directly or through its domain. It therefore passes along both.
117 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_reset_space_and_domain(
118 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_space
*space
,
119 __isl_take isl_space
*domain
)
121 isl_space_free(space
);
122 return isl_qpolynomial_fold_reset_domain_space(fold
, domain
);
125 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold
*fold
,
126 enum isl_dim_type type
, unsigned first
, unsigned n
)
132 if (fold
->n
== 0 || n
== 0)
135 for (i
= 0; i
< fold
->n
; ++i
) {
136 int involves
= isl_qpolynomial_involves_dims(fold
->qp
[i
],
138 if (involves
< 0 || involves
)
144 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_set_dim_name(
145 __isl_take isl_qpolynomial_fold
*fold
,
146 enum isl_dim_type type
, unsigned pos
, const char *s
)
150 fold
= isl_qpolynomial_fold_cow(fold
);
153 fold
->dim
= isl_space_set_dim_name(fold
->dim
, type
, pos
, s
);
157 for (i
= 0; i
< fold
->n
; ++i
) {
158 fold
->qp
[i
] = isl_qpolynomial_set_dim_name(fold
->qp
[i
],
166 isl_qpolynomial_fold_free(fold
);
170 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_drop_dims(
171 __isl_take isl_qpolynomial_fold
*fold
,
172 enum isl_dim_type type
, unsigned first
, unsigned n
)
175 enum isl_dim_type set_type
;
182 set_type
= type
== isl_dim_in
? isl_dim_set
: type
;
184 fold
= isl_qpolynomial_fold_cow(fold
);
187 fold
->dim
= isl_space_drop_dims(fold
->dim
, set_type
, first
, n
);
191 for (i
= 0; i
< fold
->n
; ++i
) {
192 fold
->qp
[i
] = isl_qpolynomial_drop_dims(fold
->qp
[i
],
200 isl_qpolynomial_fold_free(fold
);
204 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_insert_dims(
205 __isl_take isl_qpolynomial_fold
*fold
,
206 enum isl_dim_type type
, unsigned first
, unsigned n
)
212 if (n
== 0 && !isl_space_is_named_or_nested(fold
->dim
, type
))
215 fold
= isl_qpolynomial_fold_cow(fold
);
218 fold
->dim
= isl_space_insert_dims(fold
->dim
, type
, first
, n
);
222 for (i
= 0; i
< fold
->n
; ++i
) {
223 fold
->qp
[i
] = isl_qpolynomial_insert_dims(fold
->qp
[i
],
231 isl_qpolynomial_fold_free(fold
);
235 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial
*qp
)
237 struct isl_upoly_cst
*cst
;
239 cst
= isl_upoly_as_cst(qp
->upoly
);
243 return isl_int_sgn(cst
->n
) < 0 ? -1 : 1;
246 static int isl_qpolynomial_aff_sign(__isl_keep isl_set
*set
,
247 __isl_keep isl_qpolynomial
*qp
)
249 enum isl_lp_result res
;
254 aff
= isl_qpolynomial_extract_affine(qp
);
260 res
= isl_set_solve_lp(set
, 0, aff
->el
+ 1, aff
->el
[0],
262 if (res
== isl_lp_error
)
264 if (res
== isl_lp_empty
||
265 (res
== isl_lp_ok
&& !isl_int_is_neg(opt
))) {
270 res
= isl_set_solve_lp(set
, 1, aff
->el
+ 1, aff
->el
[0],
272 if (res
== isl_lp_ok
&& !isl_int_is_pos(opt
))
281 /* Determine, if possible, the sign of the quasipolynomial "qp" on
284 * If qp is a constant, then the problem is trivial.
285 * If qp is linear, then we check if the minimum of the corresponding
286 * affine constraint is non-negative or if the maximum is non-positive.
288 * Otherwise, we check if the outermost variable "v" has a lower bound "l"
289 * in "set". If so, we write qp(v,v') as
291 * q(v,v') * (v - l) + r(v')
293 * if q(v,v') and r(v') have the same known sign, then the original
294 * quasipolynomial has the same sign as well.
301 static int isl_qpolynomial_sign(__isl_keep isl_set
*set
,
302 __isl_keep isl_qpolynomial
*qp
)
307 struct isl_upoly_rec
*rec
;
310 enum isl_lp_result res
;
313 is
= isl_qpolynomial_is_cst(qp
, NULL
, NULL
);
317 return isl_qpolynomial_cst_sign(qp
);
319 is
= isl_qpolynomial_is_affine(qp
);
323 return isl_qpolynomial_aff_sign(set
, qp
);
325 if (qp
->div
->n_row
> 0)
328 rec
= isl_upoly_as_rec(qp
->upoly
);
332 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
333 v
= isl_vec_alloc(set
->ctx
, 2 + d
);
337 isl_seq_clr(v
->el
+ 1, 1 + d
);
338 isl_int_set_si(v
->el
[0], 1);
339 isl_int_set_si(v
->el
[2 + qp
->upoly
->var
], 1);
343 res
= isl_set_solve_lp(set
, 0, v
->el
+ 1, v
->el
[0], &l
, NULL
, NULL
);
344 if (res
== isl_lp_ok
) {
345 isl_qpolynomial
*min
;
346 isl_qpolynomial
*base
;
347 isl_qpolynomial
*r
, *q
;
350 min
= isl_qpolynomial_cst_on_domain(isl_space_copy(qp
->dim
), l
);
351 base
= isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp
->dim
),
354 r
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), 0,
355 isl_upoly_copy(rec
->p
[rec
->n
- 1]));
356 q
= isl_qpolynomial_copy(r
);
358 for (i
= rec
->n
- 2; i
>= 0; --i
) {
359 r
= isl_qpolynomial_mul(r
, isl_qpolynomial_copy(min
));
360 t
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), 0,
361 isl_upoly_copy(rec
->p
[i
]));
362 r
= isl_qpolynomial_add(r
, t
);
365 q
= isl_qpolynomial_mul(q
, isl_qpolynomial_copy(base
));
366 q
= isl_qpolynomial_add(q
, isl_qpolynomial_copy(r
));
369 if (isl_qpolynomial_is_zero(q
))
370 sgn
= isl_qpolynomial_sign(set
, r
);
371 else if (isl_qpolynomial_is_zero(r
))
372 sgn
= isl_qpolynomial_sign(set
, q
);
375 sgn_r
= isl_qpolynomial_sign(set
, r
);
376 sgn_q
= isl_qpolynomial_sign(set
, q
);
381 isl_qpolynomial_free(min
);
382 isl_qpolynomial_free(base
);
383 isl_qpolynomial_free(q
);
384 isl_qpolynomial_free(r
);
394 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_fold_on_domain(
395 __isl_keep isl_set
*set
,
396 __isl_take isl_qpolynomial_fold
*fold1
,
397 __isl_take isl_qpolynomial_fold
*fold2
)
401 struct isl_qpolynomial_fold
*res
= NULL
;
404 if (!fold1
|| !fold2
)
407 isl_assert(fold1
->dim
->ctx
, fold1
->type
== fold2
->type
, goto error
);
408 isl_assert(fold1
->dim
->ctx
, isl_space_is_equal(fold1
->dim
, fold2
->dim
),
411 better
= fold1
->type
== isl_fold_max
? -1 : 1;
413 if (isl_qpolynomial_fold_is_empty(fold1
)) {
414 isl_qpolynomial_fold_free(fold1
);
418 if (isl_qpolynomial_fold_is_empty(fold2
)) {
419 isl_qpolynomial_fold_free(fold2
);
423 res
= qpolynomial_fold_alloc(fold1
->type
, isl_space_copy(fold1
->dim
),
424 fold1
->n
+ fold2
->n
);
428 for (i
= 0; i
< fold1
->n
; ++i
) {
429 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold1
->qp
[i
]);
430 if (!res
->qp
[res
->n
])
436 for (i
= 0; i
< fold2
->n
; ++i
) {
437 for (j
= n1
- 1; j
>= 0; --j
) {
440 d
= isl_qpolynomial_sub(
441 isl_qpolynomial_copy(res
->qp
[j
]),
442 isl_qpolynomial_copy(fold2
->qp
[i
]));
443 sgn
= isl_qpolynomial_sign(set
, d
);
444 isl_qpolynomial_free(d
);
449 isl_qpolynomial_free(res
->qp
[j
]);
451 res
->qp
[j
] = res
->qp
[n1
- 1];
453 if (n1
!= res
->n
- 1)
454 res
->qp
[n1
] = res
->qp
[res
->n
- 1];
459 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold2
->qp
[i
]);
460 if (!res
->qp
[res
->n
])
465 isl_qpolynomial_fold_free(fold1
);
466 isl_qpolynomial_fold_free(fold2
);
470 isl_qpolynomial_fold_free(res
);
471 isl_qpolynomial_fold_free(fold1
);
472 isl_qpolynomial_fold_free(fold2
);
476 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_add_qpolynomial(
477 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_qpolynomial
*qp
)
484 if (isl_qpolynomial_is_zero(qp
)) {
485 isl_qpolynomial_free(qp
);
489 fold
= isl_qpolynomial_fold_cow(fold
);
493 for (i
= 0; i
< fold
->n
; ++i
) {
494 fold
->qp
[i
] = isl_qpolynomial_add(fold
->qp
[i
],
495 isl_qpolynomial_copy(qp
));
500 isl_qpolynomial_free(qp
);
503 isl_qpolynomial_fold_free(fold
);
504 isl_qpolynomial_free(qp
);
508 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_add_on_domain(
509 __isl_keep isl_set
*dom
,
510 __isl_take isl_qpolynomial_fold
*fold1
,
511 __isl_take isl_qpolynomial_fold
*fold2
)
514 isl_qpolynomial_fold
*res
= NULL
;
516 if (!fold1
|| !fold2
)
519 if (isl_qpolynomial_fold_is_empty(fold1
)) {
520 isl_qpolynomial_fold_free(fold1
);
524 if (isl_qpolynomial_fold_is_empty(fold2
)) {
525 isl_qpolynomial_fold_free(fold2
);
529 if (fold1
->n
== 1 && fold2
->n
!= 1)
530 return isl_qpolynomial_fold_add_on_domain(dom
, fold2
, fold1
);
533 res
= isl_qpolynomial_fold_add_qpolynomial(fold1
,
534 isl_qpolynomial_copy(fold2
->qp
[0]));
535 isl_qpolynomial_fold_free(fold2
);
539 res
= isl_qpolynomial_fold_add_qpolynomial(
540 isl_qpolynomial_fold_copy(fold1
),
541 isl_qpolynomial_copy(fold2
->qp
[0]));
543 for (i
= 1; i
< fold2
->n
; ++i
) {
544 isl_qpolynomial_fold
*res_i
;
545 res_i
= isl_qpolynomial_fold_add_qpolynomial(
546 isl_qpolynomial_fold_copy(fold1
),
547 isl_qpolynomial_copy(fold2
->qp
[i
]));
548 res
= isl_qpolynomial_fold_fold_on_domain(dom
, res
, res_i
);
551 isl_qpolynomial_fold_free(fold1
);
552 isl_qpolynomial_fold_free(fold2
);
555 isl_qpolynomial_fold_free(res
);
556 isl_qpolynomial_fold_free(fold1
);
557 isl_qpolynomial_fold_free(fold2
);
561 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_substitute_equalities(
562 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_basic_set
*eq
)
569 fold
= isl_qpolynomial_fold_cow(fold
);
573 for (i
= 0; i
< fold
->n
; ++i
) {
574 fold
->qp
[i
] = isl_qpolynomial_substitute_equalities(fold
->qp
[i
],
575 isl_basic_set_copy(eq
));
580 isl_basic_set_free(eq
);
583 isl_basic_set_free(eq
);
584 isl_qpolynomial_fold_free(fold
);
588 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_gist(
589 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_set
*context
)
593 if (!fold
|| !context
)
596 fold
= isl_qpolynomial_fold_cow(fold
);
600 for (i
= 0; i
< fold
->n
; ++i
) {
601 fold
->qp
[i
] = isl_qpolynomial_gist(fold
->qp
[i
],
602 isl_set_copy(context
));
607 isl_set_free(context
);
610 isl_set_free(context
);
611 isl_qpolynomial_fold_free(fold
);
615 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_gist_params(
616 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_set
*context
)
618 isl_space
*space
= isl_qpolynomial_fold_get_domain_space(fold
);
619 isl_set
*dom_context
= isl_set_universe(space
);
620 dom_context
= isl_set_intersect_params(dom_context
, context
);
621 return isl_qpolynomial_fold_gist(fold
, dom_context
);
627 #define PW isl_pw_qpolynomial_fold
629 #define EL isl_qpolynomial_fold
631 #define EL_IS_ZERO is_empty
635 #define IS_ZERO is_zero
638 #undef DEFAULT_IS_ZERO
639 #define DEFAULT_IS_ZERO 1
644 #include <isl_pw_templ.c>
647 #define UNION isl_union_pw_qpolynomial_fold
649 #define PART isl_pw_qpolynomial_fold
651 #define PARTS pw_qpolynomial_fold
656 #include <isl_union_templ.c>
658 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_empty(enum isl_fold type
,
659 __isl_take isl_space
*dim
)
661 return qpolynomial_fold_alloc(type
, dim
, 0);
664 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_alloc(
665 enum isl_fold type
, __isl_take isl_qpolynomial
*qp
)
667 isl_qpolynomial_fold
*fold
;
672 fold
= qpolynomial_fold_alloc(type
, isl_space_copy(qp
->dim
), 1);
681 isl_qpolynomial_fold_free(fold
);
682 isl_qpolynomial_free(qp
);
686 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_copy(
687 __isl_keep isl_qpolynomial_fold
*fold
)
696 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_dup(
697 __isl_keep isl_qpolynomial_fold
*fold
)
700 isl_qpolynomial_fold
*dup
;
704 dup
= qpolynomial_fold_alloc(fold
->type
,
705 isl_space_copy(fold
->dim
), fold
->n
);
710 for (i
= 0; i
< fold
->n
; ++i
) {
711 dup
->qp
[i
] = isl_qpolynomial_copy(fold
->qp
[i
]);
718 isl_qpolynomial_fold_free(dup
);
722 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_cow(
723 __isl_take isl_qpolynomial_fold
*fold
)
731 return isl_qpolynomial_fold_dup(fold
);
734 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold
*fold
)
743 for (i
= 0; i
< fold
->n
; ++i
)
744 isl_qpolynomial_free(fold
->qp
[i
]);
745 isl_space_free(fold
->dim
);
749 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold
*fold
)
757 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_fold(
758 __isl_take isl_qpolynomial_fold
*fold1
,
759 __isl_take isl_qpolynomial_fold
*fold2
)
762 struct isl_qpolynomial_fold
*res
= NULL
;
764 if (!fold1
|| !fold2
)
767 isl_assert(fold1
->dim
->ctx
, fold1
->type
== fold2
->type
, goto error
);
768 isl_assert(fold1
->dim
->ctx
, isl_space_is_equal(fold1
->dim
, fold2
->dim
),
771 if (isl_qpolynomial_fold_is_empty(fold1
)) {
772 isl_qpolynomial_fold_free(fold1
);
776 if (isl_qpolynomial_fold_is_empty(fold2
)) {
777 isl_qpolynomial_fold_free(fold2
);
781 res
= qpolynomial_fold_alloc(fold1
->type
, isl_space_copy(fold1
->dim
),
782 fold1
->n
+ fold2
->n
);
786 for (i
= 0; i
< fold1
->n
; ++i
) {
787 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold1
->qp
[i
]);
788 if (!res
->qp
[res
->n
])
793 for (i
= 0; i
< fold2
->n
; ++i
) {
794 res
->qp
[res
->n
] = isl_qpolynomial_copy(fold2
->qp
[i
]);
795 if (!res
->qp
[res
->n
])
800 isl_qpolynomial_fold_free(fold1
);
801 isl_qpolynomial_fold_free(fold2
);
805 isl_qpolynomial_fold_free(res
);
806 isl_qpolynomial_fold_free(fold1
);
807 isl_qpolynomial_fold_free(fold2
);
811 __isl_give isl_pw_qpolynomial_fold
*isl_pw_qpolynomial_fold_fold(
812 __isl_take isl_pw_qpolynomial_fold
*pw1
,
813 __isl_take isl_pw_qpolynomial_fold
*pw2
)
816 struct isl_pw_qpolynomial_fold
*res
;
822 isl_assert(pw1
->dim
->ctx
, isl_space_is_equal(pw1
->dim
, pw2
->dim
), goto error
);
824 if (isl_pw_qpolynomial_fold_is_zero(pw1
)) {
825 isl_pw_qpolynomial_fold_free(pw1
);
829 if (isl_pw_qpolynomial_fold_is_zero(pw2
)) {
830 isl_pw_qpolynomial_fold_free(pw2
);
834 if (pw1
->type
!= pw2
->type
)
835 isl_die(pw1
->dim
->ctx
, isl_error_invalid
,
836 "fold types don't match", goto error
);
838 n
= (pw1
->n
+ 1) * (pw2
->n
+ 1);
839 res
= isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1
->dim
),
842 for (i
= 0; i
< pw1
->n
; ++i
) {
843 set
= isl_set_copy(pw1
->p
[i
].set
);
844 for (j
= 0; j
< pw2
->n
; ++j
) {
845 struct isl_set
*common
;
846 isl_qpolynomial_fold
*sum
;
847 set
= isl_set_subtract(set
,
848 isl_set_copy(pw2
->p
[j
].set
));
849 common
= isl_set_intersect(isl_set_copy(pw1
->p
[i
].set
),
850 isl_set_copy(pw2
->p
[j
].set
));
851 if (isl_set_plain_is_empty(common
)) {
852 isl_set_free(common
);
856 sum
= isl_qpolynomial_fold_fold_on_domain(common
,
857 isl_qpolynomial_fold_copy(pw1
->p
[i
].fold
),
858 isl_qpolynomial_fold_copy(pw2
->p
[j
].fold
));
860 res
= isl_pw_qpolynomial_fold_add_piece(res
, common
, sum
);
862 res
= isl_pw_qpolynomial_fold_add_piece(res
, set
,
863 isl_qpolynomial_fold_copy(pw1
->p
[i
].fold
));
866 for (j
= 0; j
< pw2
->n
; ++j
) {
867 set
= isl_set_copy(pw2
->p
[j
].set
);
868 for (i
= 0; i
< pw1
->n
; ++i
)
869 set
= isl_set_subtract(set
, isl_set_copy(pw1
->p
[i
].set
));
870 res
= isl_pw_qpolynomial_fold_add_piece(res
, set
,
871 isl_qpolynomial_fold_copy(pw2
->p
[j
].fold
));
874 isl_pw_qpolynomial_fold_free(pw1
);
875 isl_pw_qpolynomial_fold_free(pw2
);
879 isl_pw_qpolynomial_fold_free(pw1
);
880 isl_pw_qpolynomial_fold_free(pw2
);
884 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
885 __isl_take isl_union_pw_qpolynomial_fold
*u
,
886 __isl_take isl_pw_qpolynomial_fold
*part
)
889 struct isl_hash_table_entry
*entry
;
891 u
= isl_union_pw_qpolynomial_fold_cow(u
);
896 isl_assert(u
->dim
->ctx
, isl_space_match(part
->dim
, isl_dim_param
, u
->dim
,
897 isl_dim_param
), goto error
);
899 hash
= isl_space_get_hash(part
->dim
);
900 entry
= isl_hash_table_find(u
->dim
->ctx
, &u
->table
, hash
,
901 &has_dim
, part
->dim
, 1);
908 entry
->data
= isl_pw_qpolynomial_fold_fold(entry
->data
,
909 isl_pw_qpolynomial_fold_copy(part
));
912 isl_pw_qpolynomial_fold_free(part
);
917 isl_pw_qpolynomial_fold_free(part
);
918 isl_union_pw_qpolynomial_fold_free(u
);
922 static int fold_part(__isl_take isl_pw_qpolynomial_fold
*part
, void *user
)
924 isl_union_pw_qpolynomial_fold
**u
;
925 u
= (isl_union_pw_qpolynomial_fold
**)user
;
927 *u
= isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u
, part
);
932 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_fold(
933 __isl_take isl_union_pw_qpolynomial_fold
*u1
,
934 __isl_take isl_union_pw_qpolynomial_fold
*u2
)
936 u1
= isl_union_pw_qpolynomial_fold_cow(u1
);
941 if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2
,
942 &fold_part
, &u1
) < 0)
945 isl_union_pw_qpolynomial_fold_free(u2
);
949 isl_union_pw_qpolynomial_fold_free(u1
);
950 isl_union_pw_qpolynomial_fold_free(u2
);
954 __isl_give isl_pw_qpolynomial_fold
*isl_pw_qpolynomial_fold_from_pw_qpolynomial(
955 enum isl_fold type
, __isl_take isl_pw_qpolynomial
*pwqp
)
958 isl_pw_qpolynomial_fold
*pwf
;
963 pwf
= isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp
->dim
),
966 for (i
= 0; i
< pwqp
->n
; ++i
)
967 pwf
= isl_pw_qpolynomial_fold_add_piece(pwf
,
968 isl_set_copy(pwqp
->p
[i
].set
),
969 isl_qpolynomial_fold_alloc(type
,
970 isl_qpolynomial_copy(pwqp
->p
[i
].qp
)));
972 isl_pw_qpolynomial_free(pwqp
);
977 __isl_give isl_pw_qpolynomial_fold
*isl_pw_qpolynomial_fold_add(
978 __isl_take isl_pw_qpolynomial_fold
*pwf1
,
979 __isl_take isl_pw_qpolynomial_fold
*pwf2
)
981 return isl_pw_qpolynomial_fold_union_add_(pwf1
, pwf2
);
984 int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold
*fold1
,
985 __isl_keep isl_qpolynomial_fold
*fold2
)
989 if (!fold1
|| !fold2
)
992 if (fold1
->n
!= fold2
->n
)
995 /* We probably want to sort the qps first... */
996 for (i
= 0; i
< fold1
->n
; ++i
) {
997 int eq
= isl_qpolynomial_plain_is_equal(fold1
->qp
[i
], fold2
->qp
[i
]);
1005 __isl_give isl_qpolynomial
*isl_qpolynomial_fold_eval(
1006 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_point
*pnt
)
1008 isl_qpolynomial
*qp
;
1012 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, fold
->dim
), goto error
);
1013 isl_assert(pnt
->dim
->ctx
,
1014 fold
->type
== isl_fold_max
|| fold
->type
== isl_fold_min
,
1018 qp
= isl_qpolynomial_zero_on_domain(isl_space_copy(fold
->dim
));
1021 qp
= isl_qpolynomial_eval(isl_qpolynomial_copy(fold
->qp
[0]),
1022 isl_point_copy(pnt
));
1023 for (i
= 1; i
< fold
->n
; ++i
) {
1024 isl_qpolynomial
*qp_i
;
1025 qp_i
= isl_qpolynomial_eval(
1026 isl_qpolynomial_copy(fold
->qp
[i
]),
1027 isl_point_copy(pnt
));
1028 if (fold
->type
== isl_fold_max
)
1029 qp
= isl_qpolynomial_max_cst(qp
, qp_i
);
1031 qp
= isl_qpolynomial_min_cst(qp
, qp_i
);
1034 isl_qpolynomial_fold_free(fold
);
1035 isl_point_free(pnt
);
1039 isl_qpolynomial_fold_free(fold
);
1040 isl_point_free(pnt
);
1044 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold
*pwf
)
1049 for (i
= 0; i
< pwf
->n
; ++i
)
1050 n
+= pwf
->p
[i
].fold
->n
;
1055 __isl_give isl_qpolynomial
*isl_qpolynomial_fold_opt_on_domain(
1056 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_set
*set
, int max
)
1059 isl_qpolynomial
*opt
;
1065 isl_space
*dim
= isl_space_copy(fold
->dim
);
1067 isl_qpolynomial_fold_free(fold
);
1068 return isl_qpolynomial_zero_on_domain(dim
);
1071 opt
= isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold
->qp
[0]),
1072 isl_set_copy(set
), max
);
1073 for (i
= 1; i
< fold
->n
; ++i
) {
1074 isl_qpolynomial
*opt_i
;
1075 opt_i
= isl_qpolynomial_opt_on_domain(
1076 isl_qpolynomial_copy(fold
->qp
[i
]),
1077 isl_set_copy(set
), max
);
1079 opt
= isl_qpolynomial_max_cst(opt
, opt_i
);
1081 opt
= isl_qpolynomial_min_cst(opt
, opt_i
);
1085 isl_qpolynomial_fold_free(fold
);
1090 isl_qpolynomial_fold_free(fold
);
1094 /* Check whether for each quasi-polynomial in "fold2" there is
1095 * a quasi-polynomial in "fold1" that dominates it on "set".
1097 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set
*set
,
1098 __isl_keep isl_qpolynomial_fold
*fold1
,
1099 __isl_keep isl_qpolynomial_fold
*fold2
)
1104 if (!set
|| !fold1
|| !fold2
)
1107 covers
= fold1
->type
== isl_fold_max
? 1 : -1;
1109 for (i
= 0; i
< fold2
->n
; ++i
) {
1110 for (j
= 0; j
< fold1
->n
; ++j
) {
1114 d
= isl_qpolynomial_sub(
1115 isl_qpolynomial_copy(fold1
->qp
[j
]),
1116 isl_qpolynomial_copy(fold2
->qp
[i
]));
1117 sgn
= isl_qpolynomial_sign(set
, d
);
1118 isl_qpolynomial_free(d
);
1129 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1130 * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1133 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold
*pwf1
,
1134 __isl_keep isl_pw_qpolynomial_fold
*pwf2
)
1137 isl_set
*dom1
, *dom2
;
1148 dom1
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1
));
1149 dom2
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2
));
1150 is_subset
= isl_set_is_subset(dom2
, dom1
);
1154 if (is_subset
< 0 || !is_subset
)
1157 for (i
= 0; i
< pwf2
->n
; ++i
) {
1158 for (j
= 0; j
< pwf1
->n
; ++j
) {
1163 common
= isl_set_intersect(isl_set_copy(pwf1
->p
[j
].set
),
1164 isl_set_copy(pwf2
->p
[i
].set
));
1165 is_empty
= isl_set_is_empty(common
);
1166 if (is_empty
< 0 || is_empty
) {
1167 isl_set_free(common
);
1172 covers
= qpolynomial_fold_covers_on_domain(common
,
1173 pwf1
->p
[j
].fold
, pwf2
->p
[i
].fold
);
1174 isl_set_free(common
);
1175 if (covers
< 0 || !covers
)
1183 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_morph_domain(
1184 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_morph
*morph
)
1189 if (!fold
|| !morph
)
1192 ctx
= fold
->dim
->ctx
;
1193 isl_assert(ctx
, isl_space_is_equal(fold
->dim
, morph
->dom
->dim
), goto error
);
1195 fold
= isl_qpolynomial_fold_cow(fold
);
1199 isl_space_free(fold
->dim
);
1200 fold
->dim
= isl_space_copy(morph
->ran
->dim
);
1204 for (i
= 0; i
< fold
->n
; ++i
) {
1205 fold
->qp
[i
] = isl_qpolynomial_morph_domain(fold
->qp
[i
],
1206 isl_morph_copy(morph
));
1211 isl_morph_free(morph
);
1215 isl_qpolynomial_fold_free(fold
);
1216 isl_morph_free(morph
);
1220 enum isl_fold
isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold
*fold
)
1223 return isl_fold_list
;
1227 enum isl_fold
isl_union_pw_qpolynomial_fold_get_type(
1228 __isl_keep isl_union_pw_qpolynomial_fold
*upwf
)
1231 return isl_fold_list
;
1235 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_lift(
1236 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_space
*dim
)
1243 if (isl_space_is_equal(fold
->dim
, dim
)) {
1244 isl_space_free(dim
);
1248 fold
= isl_qpolynomial_fold_cow(fold
);
1252 isl_space_free(fold
->dim
);
1253 fold
->dim
= isl_space_copy(dim
);
1257 for (i
= 0; i
< fold
->n
; ++i
) {
1258 fold
->qp
[i
] = isl_qpolynomial_lift(fold
->qp
[i
],
1259 isl_space_copy(dim
));
1264 isl_space_free(dim
);
1268 isl_qpolynomial_fold_free(fold
);
1269 isl_space_free(dim
);
1273 int isl_qpolynomial_fold_foreach_qpolynomial(
1274 __isl_keep isl_qpolynomial_fold
*fold
,
1275 int (*fn
)(__isl_take isl_qpolynomial
*qp
, void *user
), void *user
)
1282 for (i
= 0; i
< fold
->n
; ++i
)
1283 if (fn(isl_qpolynomial_copy(fold
->qp
[i
]), user
) < 0)
1289 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_move_dims(
1290 __isl_take isl_qpolynomial_fold
*fold
,
1291 enum isl_dim_type dst_type
, unsigned dst_pos
,
1292 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
1299 fold
= isl_qpolynomial_fold_cow(fold
);
1303 fold
->dim
= isl_space_move_dims(fold
->dim
, dst_type
, dst_pos
,
1304 src_type
, src_pos
, n
);
1308 for (i
= 0; i
< fold
->n
; ++i
) {
1309 fold
->qp
[i
] = isl_qpolynomial_move_dims(fold
->qp
[i
],
1310 dst_type
, dst_pos
, src_type
, src_pos
, n
);
1317 isl_qpolynomial_fold_free(fold
);
1321 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1322 * in fold->qp[k] by subs[i].
1324 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_substitute(
1325 __isl_take isl_qpolynomial_fold
*fold
,
1326 enum isl_dim_type type
, unsigned first
, unsigned n
,
1327 __isl_keep isl_qpolynomial
**subs
)
1334 fold
= isl_qpolynomial_fold_cow(fold
);
1338 for (i
= 0; i
< fold
->n
; ++i
) {
1339 fold
->qp
[i
] = isl_qpolynomial_substitute(fold
->qp
[i
],
1340 type
, first
, n
, subs
);
1347 isl_qpolynomial_fold_free(fold
);
1351 static int add_pwqp(__isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
1354 isl_pw_qpolynomial_fold
*pwf
;
1355 isl_union_pw_qpolynomial_fold
**upwf
;
1357 struct isl_hash_table_entry
*entry
;
1359 upwf
= (isl_union_pw_qpolynomial_fold
**)user
;
1361 ctx
= pwqp
->dim
->ctx
;
1362 hash
= isl_space_get_hash(pwqp
->dim
);
1363 entry
= isl_hash_table_find(ctx
, &(*upwf
)->table
,
1364 hash
, &has_dim
, pwqp
->dim
, 1);
1368 pwf
= isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf
)->type
, pwqp
);
1372 entry
->data
= isl_pw_qpolynomial_fold_add(entry
->data
, pwf
);
1375 if (isl_pw_qpolynomial_fold_is_zero(entry
->data
)) {
1376 isl_pw_qpolynomial_fold_free(entry
->data
);
1377 isl_hash_table_remove(ctx
, &(*upwf
)->table
, entry
);
1383 isl_pw_qpolynomial_free(pwqp
);
1387 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1388 __isl_take isl_union_pw_qpolynomial_fold
*upwf
,
1389 __isl_take isl_union_pw_qpolynomial
*upwqp
)
1391 upwf
= isl_union_pw_qpolynomial_fold_align_params(upwf
,
1392 isl_union_pw_qpolynomial_get_space(upwqp
));
1393 upwqp
= isl_union_pw_qpolynomial_align_params(upwqp
,
1394 isl_union_pw_qpolynomial_fold_get_space(upwf
));
1396 upwf
= isl_union_pw_qpolynomial_fold_cow(upwf
);
1397 if (!upwf
|| !upwqp
)
1400 if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp
, &add_pwqp
,
1404 isl_union_pw_qpolynomial_free(upwqp
);
1408 isl_union_pw_qpolynomial_fold_free(upwf
);
1409 isl_union_pw_qpolynomial_free(upwqp
);
1413 static int join_compatible(__isl_keep isl_space
*dim1
, __isl_keep isl_space
*dim2
)
1416 m
= isl_space_match(dim1
, isl_dim_param
, dim2
, isl_dim_param
);
1419 return isl_space_tuple_match(dim1
, isl_dim_out
, dim2
, isl_dim_in
);
1422 /* Compute the intersection of the range of the map and the domain
1423 * of the piecewise quasipolynomial reduction and then compute a bound
1424 * on the associated quasipolynomial reduction over all elements
1425 * in this intersection.
1427 * We first introduce some unconstrained dimensions in the
1428 * piecewise quasipolynomial, intersect the resulting domain
1429 * with the wrapped map and the compute the sum.
1431 __isl_give isl_pw_qpolynomial_fold
*isl_map_apply_pw_qpolynomial_fold(
1432 __isl_take isl_map
*map
, __isl_take isl_pw_qpolynomial_fold
*pwf
,
1442 ctx
= isl_map_get_ctx(map
);
1446 map_dim
= isl_map_get_space(map
);
1447 pwf_dim
= isl_pw_qpolynomial_fold_get_space(pwf
);
1448 ok
= join_compatible(map_dim
, pwf_dim
);
1449 isl_space_free(map_dim
);
1450 isl_space_free(pwf_dim
);
1452 isl_die(ctx
, isl_error_invalid
, "incompatible dimensions",
1455 n_in
= isl_map_dim(map
, isl_dim_in
);
1456 pwf
= isl_pw_qpolynomial_fold_insert_dims(pwf
, isl_dim_in
, 0, n_in
);
1458 dom
= isl_map_wrap(map
);
1459 pwf
= isl_pw_qpolynomial_fold_reset_domain_space(pwf
,
1460 isl_set_get_space(dom
));
1462 pwf
= isl_pw_qpolynomial_fold_intersect_domain(pwf
, dom
);
1463 pwf
= isl_pw_qpolynomial_fold_bound(pwf
, tight
);
1468 isl_pw_qpolynomial_fold_free(pwf
);
1472 __isl_give isl_pw_qpolynomial_fold
*isl_set_apply_pw_qpolynomial_fold(
1473 __isl_take isl_set
*set
, __isl_take isl_pw_qpolynomial_fold
*pwf
,
1476 return isl_map_apply_pw_qpolynomial_fold(set
, pwf
, tight
);
1479 struct isl_apply_fold_data
{
1480 isl_union_pw_qpolynomial_fold
*upwf
;
1481 isl_union_pw_qpolynomial_fold
*res
;
1486 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold
*pwf
,
1491 struct isl_apply_fold_data
*data
= user
;
1494 map_dim
= isl_map_get_space(data
->map
);
1495 pwf_dim
= isl_pw_qpolynomial_fold_get_space(pwf
);
1496 ok
= join_compatible(map_dim
, pwf_dim
);
1497 isl_space_free(map_dim
);
1498 isl_space_free(pwf_dim
);
1501 pwf
= isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data
->map
),
1502 pwf
, data
->tight
? &data
->tight
: NULL
);
1503 data
->res
= isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1506 isl_pw_qpolynomial_fold_free(pwf
);
1511 static int map_apply(__isl_take isl_map
*map
, void *user
)
1513 struct isl_apply_fold_data
*data
= user
;
1517 r
= isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1518 data
->upwf
, &pw_qpolynomial_fold_apply
, data
);
1524 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_map_apply_union_pw_qpolynomial_fold(
1525 __isl_take isl_union_map
*umap
,
1526 __isl_take isl_union_pw_qpolynomial_fold
*upwf
, int *tight
)
1530 struct isl_apply_fold_data data
;
1532 upwf
= isl_union_pw_qpolynomial_fold_align_params(upwf
,
1533 isl_union_map_get_space(umap
));
1534 umap
= isl_union_map_align_params(umap
,
1535 isl_union_pw_qpolynomial_fold_get_space(upwf
));
1538 data
.tight
= tight
? 1 : 0;
1539 dim
= isl_union_pw_qpolynomial_fold_get_space(upwf
);
1540 type
= isl_union_pw_qpolynomial_fold_get_type(upwf
);
1541 data
.res
= isl_union_pw_qpolynomial_fold_zero(dim
, type
);
1542 if (isl_union_map_foreach_map(umap
, &map_apply
, &data
) < 0)
1545 isl_union_map_free(umap
);
1546 isl_union_pw_qpolynomial_fold_free(upwf
);
1549 *tight
= data
.tight
;
1553 isl_union_map_free(umap
);
1554 isl_union_pw_qpolynomial_fold_free(upwf
);
1555 isl_union_pw_qpolynomial_fold_free(data
.res
);
1559 __isl_give isl_union_pw_qpolynomial_fold
*isl_union_set_apply_union_pw_qpolynomial_fold(
1560 __isl_take isl_union_set
*uset
,
1561 __isl_take isl_union_pw_qpolynomial_fold
*upwf
, int *tight
)
1563 return isl_union_map_apply_union_pw_qpolynomial_fold(uset
, upwf
, tight
);
1566 /* Reorder the dimension of "fold" according to the given reordering.
1568 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_realign_domain(
1569 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_reordering
*r
)
1573 fold
= isl_qpolynomial_fold_cow(fold
);
1577 for (i
= 0; i
< fold
->n
; ++i
) {
1578 fold
->qp
[i
] = isl_qpolynomial_realign_domain(fold
->qp
[i
],
1579 isl_reordering_copy(r
));
1584 fold
= isl_qpolynomial_fold_reset_domain_space(fold
,
1585 isl_space_copy(r
->dim
));
1587 isl_reordering_free(r
);
1591 isl_qpolynomial_fold_free(fold
);
1592 isl_reordering_free(r
);
1596 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_mul_isl_int(
1597 __isl_take isl_qpolynomial_fold
*fold
, isl_int v
)
1601 if (isl_int_is_one(v
))
1603 if (fold
&& isl_int_is_zero(v
)) {
1604 isl_qpolynomial_fold
*zero
;
1605 isl_space
*dim
= isl_space_copy(fold
->dim
);
1606 zero
= isl_qpolynomial_fold_empty(fold
->type
, dim
);
1607 isl_qpolynomial_fold_free(fold
);
1611 fold
= isl_qpolynomial_fold_cow(fold
);
1615 if (isl_int_is_neg(v
))
1616 fold
->type
= isl_fold_type_negate(fold
->type
);
1617 for (i
= 0; i
< fold
->n
; ++i
) {
1618 fold
->qp
[i
] = isl_qpolynomial_mul_isl_int(fold
->qp
[i
], v
);
1625 isl_qpolynomial_fold_free(fold
);
1629 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_scale(
1630 __isl_take isl_qpolynomial_fold
*fold
, isl_int v
)
1632 return isl_qpolynomial_fold_mul_isl_int(fold
, v
);
1635 /* Multiply "fold" by "v".
1637 __isl_give isl_qpolynomial_fold
*isl_qpolynomial_fold_scale_val(
1638 __isl_take isl_qpolynomial_fold
*fold
, __isl_take isl_val
*v
)
1645 if (isl_val_is_one(v
)) {
1649 if (isl_val_is_zero(v
)) {
1650 isl_qpolynomial_fold
*zero
;
1651 isl_space
*space
= isl_qpolynomial_fold_get_domain_space(fold
);
1652 zero
= isl_qpolynomial_fold_empty(fold
->type
, space
);
1653 isl_qpolynomial_fold_free(fold
);
1657 if (!isl_val_is_rat(v
))
1658 isl_die(isl_qpolynomial_fold_get_ctx(fold
), isl_error_invalid
,
1659 "expecting rational factor", goto error
);
1661 fold
= isl_qpolynomial_fold_cow(fold
);
1665 if (isl_val_is_neg(v
))
1666 fold
->type
= isl_fold_type_negate(fold
->type
);
1667 for (i
= 0; i
< fold
->n
; ++i
) {
1668 fold
->qp
[i
] = isl_qpolynomial_scale_val(fold
->qp
[i
],
1678 isl_qpolynomial_fold_free(fold
);