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_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl_lp_private.h>
17 #include <isl_union_map_private.h>
18 #include <isl_constraint_private.h>
19 #include <isl_polynomial_private.h>
20 #include <isl_point_private.h>
21 #include <isl_space_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_vec_private.h>
24 #include <isl_range.h>
25 #include <isl_local.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_val_private.h>
29 #include <isl_config.h>
32 #define EL_BASE pw_qpolynomial
34 #include <isl_list_templ.c>
36 static unsigned pos(__isl_keep isl_space
*space
, enum isl_dim_type type
)
39 case isl_dim_param
: return 0;
40 case isl_dim_in
: return space
->nparam
;
41 case isl_dim_out
: return space
->nparam
+ space
->n_in
;
46 isl_bool
isl_poly_is_cst(__isl_keep isl_poly
*poly
)
49 return isl_bool_error
;
51 return isl_bool_ok(poly
->var
< 0);
54 __isl_keep isl_poly_cst
*isl_poly_as_cst(__isl_keep isl_poly
*poly
)
59 isl_assert(poly
->ctx
, poly
->var
< 0, return NULL
);
61 return (isl_poly_cst
*) poly
;
64 __isl_keep isl_poly_rec
*isl_poly_as_rec(__isl_keep isl_poly
*poly
)
69 isl_assert(poly
->ctx
, poly
->var
>= 0, return NULL
);
71 return (isl_poly_rec
*) poly
;
74 /* Compare two polynomials.
76 * Return -1 if "poly1" is "smaller" than "poly2", 1 if "poly1" is "greater"
77 * than "poly2" and 0 if they are equal.
79 static int isl_poly_plain_cmp(__isl_keep isl_poly
*poly1
,
80 __isl_keep isl_poly
*poly2
)
84 isl_poly_rec
*rec1
, *rec2
;
88 is_cst1
= isl_poly_is_cst(poly1
);
93 if (poly1
->var
!= poly2
->var
)
94 return poly1
->var
- poly2
->var
;
97 isl_poly_cst
*cst1
, *cst2
;
100 cst1
= isl_poly_as_cst(poly1
);
101 cst2
= isl_poly_as_cst(poly2
);
104 cmp
= isl_int_cmp(cst1
->n
, cst2
->n
);
107 return isl_int_cmp(cst1
->d
, cst2
->d
);
110 rec1
= isl_poly_as_rec(poly1
);
111 rec2
= isl_poly_as_rec(poly2
);
115 if (rec1
->n
!= rec2
->n
)
116 return rec1
->n
- rec2
->n
;
118 for (i
= 0; i
< rec1
->n
; ++i
) {
119 int cmp
= isl_poly_plain_cmp(rec1
->p
[i
], rec2
->p
[i
]);
127 isl_bool
isl_poly_is_equal(__isl_keep isl_poly
*poly1
,
128 __isl_keep isl_poly
*poly2
)
132 isl_poly_rec
*rec1
, *rec2
;
134 is_cst1
= isl_poly_is_cst(poly1
);
135 if (is_cst1
< 0 || !poly2
)
136 return isl_bool_error
;
138 return isl_bool_true
;
139 if (poly1
->var
!= poly2
->var
)
140 return isl_bool_false
;
142 isl_poly_cst
*cst1
, *cst2
;
144 cst1
= isl_poly_as_cst(poly1
);
145 cst2
= isl_poly_as_cst(poly2
);
147 return isl_bool_error
;
148 r
= isl_int_eq(cst1
->n
, cst2
->n
) &&
149 isl_int_eq(cst1
->d
, cst2
->d
);
150 return isl_bool_ok(r
);
153 rec1
= isl_poly_as_rec(poly1
);
154 rec2
= isl_poly_as_rec(poly2
);
156 return isl_bool_error
;
158 if (rec1
->n
!= rec2
->n
)
159 return isl_bool_false
;
161 for (i
= 0; i
< rec1
->n
; ++i
) {
162 isl_bool eq
= isl_poly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
167 return isl_bool_true
;
170 isl_bool
isl_poly_is_zero(__isl_keep isl_poly
*poly
)
175 is_cst
= isl_poly_is_cst(poly
);
176 if (is_cst
< 0 || !is_cst
)
179 cst
= isl_poly_as_cst(poly
);
181 return isl_bool_error
;
183 return isl_bool_ok(isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
));
186 int isl_poly_sgn(__isl_keep isl_poly
*poly
)
191 is_cst
= isl_poly_is_cst(poly
);
192 if (is_cst
< 0 || !is_cst
)
195 cst
= isl_poly_as_cst(poly
);
199 return isl_int_sgn(cst
->n
);
202 isl_bool
isl_poly_is_nan(__isl_keep isl_poly
*poly
)
207 is_cst
= isl_poly_is_cst(poly
);
208 if (is_cst
< 0 || !is_cst
)
211 cst
= isl_poly_as_cst(poly
);
213 return isl_bool_error
;
215 return isl_bool_ok(isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
));
218 isl_bool
isl_poly_is_infty(__isl_keep isl_poly
*poly
)
223 is_cst
= isl_poly_is_cst(poly
);
224 if (is_cst
< 0 || !is_cst
)
227 cst
= isl_poly_as_cst(poly
);
229 return isl_bool_error
;
231 return isl_bool_ok(isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
));
234 isl_bool
isl_poly_is_neginfty(__isl_keep isl_poly
*poly
)
239 is_cst
= isl_poly_is_cst(poly
);
240 if (is_cst
< 0 || !is_cst
)
243 cst
= isl_poly_as_cst(poly
);
245 return isl_bool_error
;
247 return isl_bool_ok(isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
));
250 isl_bool
isl_poly_is_one(__isl_keep isl_poly
*poly
)
256 is_cst
= isl_poly_is_cst(poly
);
257 if (is_cst
< 0 || !is_cst
)
260 cst
= isl_poly_as_cst(poly
);
262 return isl_bool_error
;
264 r
= isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
265 return isl_bool_ok(r
);
268 isl_bool
isl_poly_is_negone(__isl_keep isl_poly
*poly
)
273 is_cst
= isl_poly_is_cst(poly
);
274 if (is_cst
< 0 || !is_cst
)
277 cst
= isl_poly_as_cst(poly
);
279 return isl_bool_error
;
281 return isl_bool_ok(isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
));
284 __isl_give isl_poly_cst
*isl_poly_cst_alloc(isl_ctx
*ctx
)
288 cst
= isl_alloc_type(ctx
, struct isl_poly_cst
);
297 isl_int_init(cst
->n
);
298 isl_int_init(cst
->d
);
303 __isl_give isl_poly
*isl_poly_zero(isl_ctx
*ctx
)
307 cst
= isl_poly_cst_alloc(ctx
);
311 isl_int_set_si(cst
->n
, 0);
312 isl_int_set_si(cst
->d
, 1);
317 __isl_give isl_poly
*isl_poly_one(isl_ctx
*ctx
)
321 cst
= isl_poly_cst_alloc(ctx
);
325 isl_int_set_si(cst
->n
, 1);
326 isl_int_set_si(cst
->d
, 1);
331 __isl_give isl_poly
*isl_poly_infty(isl_ctx
*ctx
)
335 cst
= isl_poly_cst_alloc(ctx
);
339 isl_int_set_si(cst
->n
, 1);
340 isl_int_set_si(cst
->d
, 0);
345 __isl_give isl_poly
*isl_poly_neginfty(isl_ctx
*ctx
)
349 cst
= isl_poly_cst_alloc(ctx
);
353 isl_int_set_si(cst
->n
, -1);
354 isl_int_set_si(cst
->d
, 0);
359 __isl_give isl_poly
*isl_poly_nan(isl_ctx
*ctx
)
363 cst
= isl_poly_cst_alloc(ctx
);
367 isl_int_set_si(cst
->n
, 0);
368 isl_int_set_si(cst
->d
, 0);
373 __isl_give isl_poly
*isl_poly_rat_cst(isl_ctx
*ctx
, isl_int n
, isl_int d
)
377 cst
= isl_poly_cst_alloc(ctx
);
381 isl_int_set(cst
->n
, n
);
382 isl_int_set(cst
->d
, d
);
387 __isl_give isl_poly_rec
*isl_poly_alloc_rec(isl_ctx
*ctx
, int var
, int size
)
391 isl_assert(ctx
, var
>= 0, return NULL
);
392 isl_assert(ctx
, size
>= 0, return NULL
);
393 rec
= isl_calloc(ctx
, struct isl_poly_rec
,
394 sizeof(struct isl_poly_rec
) +
395 size
* sizeof(struct isl_poly
*));
410 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
411 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
)
413 qp
= isl_qpolynomial_cow(qp
);
417 isl_space_free(qp
->dim
);
422 isl_qpolynomial_free(qp
);
423 isl_space_free(space
);
427 /* Reset the space of "qp". This function is called from isl_pw_templ.c
428 * and doesn't know if the space of an element object is represented
429 * directly or through its domain. It therefore passes along both.
431 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
432 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
433 __isl_take isl_space
*domain
)
435 isl_space_free(space
);
436 return isl_qpolynomial_reset_domain_space(qp
, domain
);
439 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
441 return qp
? qp
->dim
->ctx
: NULL
;
444 /* Return the domain space of "qp".
446 static __isl_keep isl_space
*isl_qpolynomial_peek_domain_space(
447 __isl_keep isl_qpolynomial
*qp
)
449 return qp
? qp
->dim
: NULL
;
452 /* Return a copy of the domain space of "qp".
454 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
455 __isl_keep isl_qpolynomial
*qp
)
457 return isl_space_copy(isl_qpolynomial_peek_domain_space(qp
));
461 #define TYPE isl_qpolynomial
463 #define PEEK_SPACE peek_domain_space
466 #include "isl_type_has_equal_space_bin_templ.c"
468 #include "isl_type_check_equal_space_templ.c"
472 /* Return a copy of the local space on which "qp" is defined.
474 static __isl_give isl_local_space
*isl_qpolynomial_get_domain_local_space(
475 __isl_keep isl_qpolynomial
*qp
)
482 space
= isl_qpolynomial_get_domain_space(qp
);
483 return isl_local_space_alloc_div(space
, isl_mat_copy(qp
->div
));
486 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
491 space
= isl_space_copy(qp
->dim
);
492 space
= isl_space_from_domain(space
);
493 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
497 /* Return the number of variables of the given type in the domain of "qp".
499 isl_size
isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial
*qp
,
500 enum isl_dim_type type
)
505 space
= isl_qpolynomial_peek_domain_space(qp
);
508 return isl_size_error
;
509 if (type
== isl_dim_div
)
510 return qp
->div
->n_row
;
511 dim
= isl_space_dim(space
, type
);
513 return isl_size_error
;
514 if (type
== isl_dim_all
) {
517 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
519 return isl_size_error
;
525 /* Given the type of a dimension of an isl_qpolynomial,
526 * return the type of the corresponding dimension in its domain.
527 * This function is only called for "type" equal to isl_dim_in or
530 static enum isl_dim_type
domain_type(enum isl_dim_type type
)
532 return type
== isl_dim_in
? isl_dim_set
: type
;
535 /* Externally, an isl_qpolynomial has a map space, but internally, the
536 * ls field corresponds to the domain of that space.
538 isl_size
isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
539 enum isl_dim_type type
)
542 return isl_size_error
;
543 if (type
== isl_dim_out
)
545 type
= domain_type(type
);
546 return isl_qpolynomial_domain_dim(qp
, type
);
549 /* Return the offset of the first variable of type "type" within
550 * the variables of the domain of "qp".
552 static isl_size
isl_qpolynomial_domain_var_offset(
553 __isl_keep isl_qpolynomial
*qp
, enum isl_dim_type type
)
557 space
= isl_qpolynomial_peek_domain_space(qp
);
559 return isl_size_error
;
563 case isl_dim_set
: return isl_space_offset(space
, type
);
564 case isl_dim_div
: return isl_space_dim(space
, isl_dim_all
);
567 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
568 "invalid dimension type", return isl_size_error
);
572 /* Return the offset of the first coefficient of type "type" in
573 * the domain of "qp".
575 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
576 enum isl_dim_type type
)
584 return 1 + isl_qpolynomial_domain_var_offset(qp
, type
);
590 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
592 return qp
? isl_poly_is_zero(qp
->poly
) : isl_bool_error
;
595 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
597 return qp
? isl_poly_is_one(qp
->poly
) : isl_bool_error
;
600 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
602 return qp
? isl_poly_is_nan(qp
->poly
) : isl_bool_error
;
605 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
607 return qp
? isl_poly_is_infty(qp
->poly
) : isl_bool_error
;
610 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
612 return qp
? isl_poly_is_neginfty(qp
->poly
) : isl_bool_error
;
615 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
617 return qp
? isl_poly_sgn(qp
->poly
) : 0;
620 static void poly_free_cst(__isl_take isl_poly_cst
*cst
)
622 isl_int_clear(cst
->n
);
623 isl_int_clear(cst
->d
);
626 static void poly_free_rec(__isl_take isl_poly_rec
*rec
)
630 for (i
= 0; i
< rec
->n
; ++i
)
631 isl_poly_free(rec
->p
[i
]);
634 __isl_give isl_poly
*isl_poly_copy(__isl_keep isl_poly
*poly
)
643 __isl_give isl_poly
*isl_poly_dup_cst(__isl_keep isl_poly
*poly
)
648 cst
= isl_poly_as_cst(poly
);
652 dup
= isl_poly_as_cst(isl_poly_zero(poly
->ctx
));
655 isl_int_set(dup
->n
, cst
->n
);
656 isl_int_set(dup
->d
, cst
->d
);
661 __isl_give isl_poly
*isl_poly_dup_rec(__isl_keep isl_poly
*poly
)
667 rec
= isl_poly_as_rec(poly
);
671 dup
= isl_poly_alloc_rec(poly
->ctx
, poly
->var
, rec
->n
);
675 for (i
= 0; i
< rec
->n
; ++i
) {
676 dup
->p
[i
] = isl_poly_copy(rec
->p
[i
]);
684 isl_poly_free(&dup
->poly
);
688 __isl_give isl_poly
*isl_poly_dup(__isl_keep isl_poly
*poly
)
692 is_cst
= isl_poly_is_cst(poly
);
696 return isl_poly_dup_cst(poly
);
698 return isl_poly_dup_rec(poly
);
701 __isl_give isl_poly
*isl_poly_cow(__isl_take isl_poly
*poly
)
709 return isl_poly_dup(poly
);
712 __isl_null isl_poly
*isl_poly_free(__isl_take isl_poly
*poly
)
721 poly_free_cst((isl_poly_cst
*) poly
);
723 poly_free_rec((isl_poly_rec
*) poly
);
725 isl_ctx_deref(poly
->ctx
);
730 static void isl_poly_cst_reduce(__isl_keep isl_poly_cst
*cst
)
735 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
736 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
737 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
738 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
743 __isl_give isl_poly
*isl_poly_sum_cst(__isl_take isl_poly
*poly1
,
744 __isl_take isl_poly
*poly2
)
749 poly1
= isl_poly_cow(poly1
);
750 if (!poly1
|| !poly2
)
753 cst1
= isl_poly_as_cst(poly1
);
754 cst2
= isl_poly_as_cst(poly2
);
756 if (isl_int_eq(cst1
->d
, cst2
->d
))
757 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
759 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
760 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
761 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
764 isl_poly_cst_reduce(cst1
);
766 isl_poly_free(poly2
);
769 isl_poly_free(poly1
);
770 isl_poly_free(poly2
);
774 static __isl_give isl_poly
*replace_by_zero(__isl_take isl_poly
*poly
)
782 return isl_poly_zero(ctx
);
785 static __isl_give isl_poly
*replace_by_constant_term(__isl_take isl_poly
*poly
)
793 rec
= isl_poly_as_rec(poly
);
796 cst
= isl_poly_copy(rec
->p
[0]);
804 __isl_give isl_poly
*isl_poly_sum(__isl_take isl_poly
*poly1
,
805 __isl_take isl_poly
*poly2
)
808 isl_bool is_zero
, is_nan
, is_cst
;
809 isl_poly_rec
*rec1
, *rec2
;
811 if (!poly1
|| !poly2
)
814 is_nan
= isl_poly_is_nan(poly1
);
818 isl_poly_free(poly2
);
822 is_nan
= isl_poly_is_nan(poly2
);
826 isl_poly_free(poly1
);
830 is_zero
= isl_poly_is_zero(poly1
);
834 isl_poly_free(poly1
);
838 is_zero
= isl_poly_is_zero(poly2
);
842 isl_poly_free(poly2
);
846 if (poly1
->var
< poly2
->var
)
847 return isl_poly_sum(poly2
, poly1
);
849 if (poly2
->var
< poly1
->var
) {
853 is_infty
= isl_poly_is_infty(poly2
);
854 if (is_infty
>= 0 && !is_infty
)
855 is_infty
= isl_poly_is_neginfty(poly2
);
859 isl_poly_free(poly1
);
862 poly1
= isl_poly_cow(poly1
);
863 rec
= isl_poly_as_rec(poly1
);
866 rec
->p
[0] = isl_poly_sum(rec
->p
[0], poly2
);
868 poly1
= replace_by_constant_term(poly1
);
872 is_cst
= isl_poly_is_cst(poly1
);
876 return isl_poly_sum_cst(poly1
, poly2
);
878 rec1
= isl_poly_as_rec(poly1
);
879 rec2
= isl_poly_as_rec(poly2
);
883 if (rec1
->n
< rec2
->n
)
884 return isl_poly_sum(poly2
, poly1
);
886 poly1
= isl_poly_cow(poly1
);
887 rec1
= isl_poly_as_rec(poly1
);
891 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
894 rec1
->p
[i
] = isl_poly_sum(rec1
->p
[i
],
895 isl_poly_copy(rec2
->p
[i
]));
898 if (i
!= rec1
->n
- 1)
900 is_zero
= isl_poly_is_zero(rec1
->p
[i
]);
904 isl_poly_free(rec1
->p
[i
]);
910 poly1
= replace_by_zero(poly1
);
911 else if (rec1
->n
== 1)
912 poly1
= replace_by_constant_term(poly1
);
914 isl_poly_free(poly2
);
918 isl_poly_free(poly1
);
919 isl_poly_free(poly2
);
923 __isl_give isl_poly
*isl_poly_cst_add_isl_int(__isl_take isl_poly
*poly
,
928 poly
= isl_poly_cow(poly
);
932 cst
= isl_poly_as_cst(poly
);
934 isl_int_addmul(cst
->n
, cst
->d
, v
);
939 __isl_give isl_poly
*isl_poly_add_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
944 is_cst
= isl_poly_is_cst(poly
);
946 return isl_poly_free(poly
);
948 return isl_poly_cst_add_isl_int(poly
, v
);
950 poly
= isl_poly_cow(poly
);
951 rec
= isl_poly_as_rec(poly
);
955 rec
->p
[0] = isl_poly_add_isl_int(rec
->p
[0], v
);
965 __isl_give isl_poly
*isl_poly_cst_mul_isl_int(__isl_take isl_poly
*poly
,
971 is_zero
= isl_poly_is_zero(poly
);
973 return isl_poly_free(poly
);
977 poly
= isl_poly_cow(poly
);
981 cst
= isl_poly_as_cst(poly
);
983 isl_int_mul(cst
->n
, cst
->n
, v
);
988 __isl_give isl_poly
*isl_poly_mul_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
994 is_cst
= isl_poly_is_cst(poly
);
996 return isl_poly_free(poly
);
998 return isl_poly_cst_mul_isl_int(poly
, v
);
1000 poly
= isl_poly_cow(poly
);
1001 rec
= isl_poly_as_rec(poly
);
1005 for (i
= 0; i
< rec
->n
; ++i
) {
1006 rec
->p
[i
] = isl_poly_mul_isl_int(rec
->p
[i
], v
);
1013 isl_poly_free(poly
);
1017 /* Multiply the constant polynomial "poly" by "v".
1019 static __isl_give isl_poly
*isl_poly_cst_scale_val(__isl_take isl_poly
*poly
,
1020 __isl_keep isl_val
*v
)
1025 is_zero
= isl_poly_is_zero(poly
);
1027 return isl_poly_free(poly
);
1031 poly
= isl_poly_cow(poly
);
1035 cst
= isl_poly_as_cst(poly
);
1037 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
1038 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
1039 isl_poly_cst_reduce(cst
);
1044 /* Multiply the polynomial "poly" by "v".
1046 static __isl_give isl_poly
*isl_poly_scale_val(__isl_take isl_poly
*poly
,
1047 __isl_keep isl_val
*v
)
1053 is_cst
= isl_poly_is_cst(poly
);
1055 return isl_poly_free(poly
);
1057 return isl_poly_cst_scale_val(poly
, v
);
1059 poly
= isl_poly_cow(poly
);
1060 rec
= isl_poly_as_rec(poly
);
1064 for (i
= 0; i
< rec
->n
; ++i
) {
1065 rec
->p
[i
] = isl_poly_scale_val(rec
->p
[i
], v
);
1072 isl_poly_free(poly
);
1076 __isl_give isl_poly
*isl_poly_mul_cst(__isl_take isl_poly
*poly1
,
1077 __isl_take isl_poly
*poly2
)
1082 poly1
= isl_poly_cow(poly1
);
1083 if (!poly1
|| !poly2
)
1086 cst1
= isl_poly_as_cst(poly1
);
1087 cst2
= isl_poly_as_cst(poly2
);
1089 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
1090 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
1092 isl_poly_cst_reduce(cst1
);
1094 isl_poly_free(poly2
);
1097 isl_poly_free(poly1
);
1098 isl_poly_free(poly2
);
1102 __isl_give isl_poly
*isl_poly_mul_rec(__isl_take isl_poly
*poly1
,
1103 __isl_take isl_poly
*poly2
)
1107 isl_poly_rec
*res
= NULL
;
1111 rec1
= isl_poly_as_rec(poly1
);
1112 rec2
= isl_poly_as_rec(poly2
);
1115 size
= rec1
->n
+ rec2
->n
- 1;
1116 res
= isl_poly_alloc_rec(poly1
->ctx
, poly1
->var
, size
);
1120 for (i
= 0; i
< rec1
->n
; ++i
) {
1121 res
->p
[i
] = isl_poly_mul(isl_poly_copy(rec2
->p
[0]),
1122 isl_poly_copy(rec1
->p
[i
]));
1127 for (; i
< size
; ++i
) {
1128 res
->p
[i
] = isl_poly_zero(poly1
->ctx
);
1133 for (i
= 0; i
< rec1
->n
; ++i
) {
1134 for (j
= 1; j
< rec2
->n
; ++j
) {
1136 poly
= isl_poly_mul(isl_poly_copy(rec2
->p
[j
]),
1137 isl_poly_copy(rec1
->p
[i
]));
1138 res
->p
[i
+ j
] = isl_poly_sum(res
->p
[i
+ j
], poly
);
1144 isl_poly_free(poly1
);
1145 isl_poly_free(poly2
);
1149 isl_poly_free(poly1
);
1150 isl_poly_free(poly2
);
1151 isl_poly_free(&res
->poly
);
1155 __isl_give isl_poly
*isl_poly_mul(__isl_take isl_poly
*poly1
,
1156 __isl_take isl_poly
*poly2
)
1158 isl_bool is_zero
, is_nan
, is_one
, is_cst
;
1160 if (!poly1
|| !poly2
)
1163 is_nan
= isl_poly_is_nan(poly1
);
1167 isl_poly_free(poly2
);
1171 is_nan
= isl_poly_is_nan(poly2
);
1175 isl_poly_free(poly1
);
1179 is_zero
= isl_poly_is_zero(poly1
);
1183 isl_poly_free(poly2
);
1187 is_zero
= isl_poly_is_zero(poly2
);
1191 isl_poly_free(poly1
);
1195 is_one
= isl_poly_is_one(poly1
);
1199 isl_poly_free(poly1
);
1203 is_one
= isl_poly_is_one(poly2
);
1207 isl_poly_free(poly2
);
1211 if (poly1
->var
< poly2
->var
)
1212 return isl_poly_mul(poly2
, poly1
);
1214 if (poly2
->var
< poly1
->var
) {
1219 is_infty
= isl_poly_is_infty(poly2
);
1220 if (is_infty
>= 0 && !is_infty
)
1221 is_infty
= isl_poly_is_neginfty(poly2
);
1225 isl_ctx
*ctx
= poly1
->ctx
;
1226 isl_poly_free(poly1
);
1227 isl_poly_free(poly2
);
1228 return isl_poly_nan(ctx
);
1230 poly1
= isl_poly_cow(poly1
);
1231 rec
= isl_poly_as_rec(poly1
);
1235 for (i
= 0; i
< rec
->n
; ++i
) {
1236 rec
->p
[i
] = isl_poly_mul(rec
->p
[i
],
1237 isl_poly_copy(poly2
));
1241 isl_poly_free(poly2
);
1245 is_cst
= isl_poly_is_cst(poly1
);
1249 return isl_poly_mul_cst(poly1
, poly2
);
1251 return isl_poly_mul_rec(poly1
, poly2
);
1253 isl_poly_free(poly1
);
1254 isl_poly_free(poly2
);
1258 __isl_give isl_poly
*isl_poly_pow(__isl_take isl_poly
*poly
, unsigned power
)
1268 res
= isl_poly_copy(poly
);
1270 res
= isl_poly_one(poly
->ctx
);
1272 while (power
>>= 1) {
1273 poly
= isl_poly_mul(poly
, isl_poly_copy(poly
));
1275 res
= isl_poly_mul(res
, isl_poly_copy(poly
));
1278 isl_poly_free(poly
);
1282 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*space
,
1283 unsigned n_div
, __isl_take isl_poly
*poly
)
1285 struct isl_qpolynomial
*qp
= NULL
;
1288 total
= isl_space_dim(space
, isl_dim_all
);
1289 if (total
< 0 || !poly
)
1292 if (!isl_space_is_set(space
))
1293 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
1294 "domain of polynomial should be a set", goto error
);
1296 qp
= isl_calloc_type(space
->ctx
, struct isl_qpolynomial
);
1301 qp
->div
= isl_mat_alloc(space
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1310 isl_space_free(space
);
1311 isl_poly_free(poly
);
1312 isl_qpolynomial_free(qp
);
1316 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1325 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1327 struct isl_qpolynomial
*dup
;
1332 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1333 isl_poly_copy(qp
->poly
));
1336 isl_mat_free(dup
->div
);
1337 dup
->div
= isl_mat_copy(qp
->div
);
1343 isl_qpolynomial_free(dup
);
1347 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1355 return isl_qpolynomial_dup(qp
);
1358 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1359 __isl_take isl_qpolynomial
*qp
)
1367 isl_space_free(qp
->dim
);
1368 isl_mat_free(qp
->div
);
1369 isl_poly_free(qp
->poly
);
1375 __isl_give isl_poly
*isl_poly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1381 rec
= isl_poly_alloc_rec(ctx
, pos
, 1 + power
);
1384 for (i
= 0; i
< 1 + power
; ++i
) {
1385 rec
->p
[i
] = isl_poly_zero(ctx
);
1390 cst
= isl_poly_as_cst(rec
->p
[power
]);
1391 isl_int_set_si(cst
->n
, 1);
1395 isl_poly_free(&rec
->poly
);
1399 /* r array maps original positions to new positions.
1401 static __isl_give isl_poly
*reorder(__isl_take isl_poly
*poly
, int *r
)
1409 is_cst
= isl_poly_is_cst(poly
);
1411 return isl_poly_free(poly
);
1415 rec
= isl_poly_as_rec(poly
);
1419 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
1421 base
= isl_poly_var_pow(poly
->ctx
, r
[poly
->var
], 1);
1422 res
= reorder(isl_poly_copy(rec
->p
[rec
->n
- 1]), r
);
1424 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1425 res
= isl_poly_mul(res
, isl_poly_copy(base
));
1426 res
= isl_poly_sum(res
, reorder(isl_poly_copy(rec
->p
[i
]), r
));
1429 isl_poly_free(base
);
1430 isl_poly_free(poly
);
1434 isl_poly_free(poly
);
1438 static isl_bool
compatible_divs(__isl_keep isl_mat
*div1
,
1439 __isl_keep isl_mat
*div2
)
1444 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1445 div1
->n_col
>= div2
->n_col
,
1446 return isl_bool_error
);
1448 if (div1
->n_row
== div2
->n_row
)
1449 return isl_mat_is_equal(div1
, div2
);
1451 n_row
= div1
->n_row
;
1452 n_col
= div1
->n_col
;
1453 div1
->n_row
= div2
->n_row
;
1454 div1
->n_col
= div2
->n_col
;
1456 equal
= isl_mat_is_equal(div1
, div2
);
1458 div1
->n_row
= n_row
;
1459 div1
->n_col
= n_col
;
1464 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1468 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1469 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1474 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1477 struct isl_div_sort_info
{
1482 static int div_sort_cmp(const void *p1
, const void *p2
)
1484 const struct isl_div_sort_info
*i1
, *i2
;
1485 i1
= (const struct isl_div_sort_info
*) p1
;
1486 i2
= (const struct isl_div_sort_info
*) p2
;
1488 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1491 /* Sort divs and remove duplicates.
1493 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1498 struct isl_div_sort_info
*array
= NULL
;
1499 int *pos
= NULL
, *at
= NULL
;
1500 int *reordering
= NULL
;
1505 if (qp
->div
->n_row
<= 1)
1508 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
1510 return isl_qpolynomial_free(qp
);
1512 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1514 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1515 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1516 len
= qp
->div
->n_col
- 2;
1517 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1518 if (!array
|| !pos
|| !at
|| !reordering
)
1521 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1522 array
[i
].div
= qp
->div
;
1528 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1531 for (i
= 0; i
< div_pos
; ++i
)
1534 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1535 if (pos
[array
[i
].row
] == i
)
1537 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1538 pos
[at
[i
]] = pos
[array
[i
].row
];
1539 at
[pos
[array
[i
].row
]] = at
[i
];
1540 at
[i
] = array
[i
].row
;
1541 pos
[array
[i
].row
] = i
;
1545 for (i
= 0; i
< len
- div_pos
; ++i
) {
1547 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1548 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1549 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1550 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1551 2 + div_pos
+ i
- skip
);
1552 qp
->div
= isl_mat_drop_cols(qp
->div
,
1553 2 + div_pos
+ i
- skip
, 1);
1556 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1559 qp
->poly
= reorder(qp
->poly
, reordering
);
1561 if (!qp
->poly
|| !qp
->div
)
1575 isl_qpolynomial_free(qp
);
1579 static __isl_give isl_poly
*expand(__isl_take isl_poly
*poly
, int *exp
,
1586 is_cst
= isl_poly_is_cst(poly
);
1588 return isl_poly_free(poly
);
1592 if (poly
->var
< first
)
1595 if (exp
[poly
->var
- first
] == poly
->var
- first
)
1598 poly
= isl_poly_cow(poly
);
1602 poly
->var
= exp
[poly
->var
- first
] + first
;
1604 rec
= isl_poly_as_rec(poly
);
1608 for (i
= 0; i
< rec
->n
; ++i
) {
1609 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1616 isl_poly_free(poly
);
1620 static __isl_give isl_qpolynomial
*with_merged_divs(
1621 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1622 __isl_take isl_qpolynomial
*qp2
),
1623 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1627 isl_mat
*div
= NULL
;
1630 qp1
= isl_qpolynomial_cow(qp1
);
1631 qp2
= isl_qpolynomial_cow(qp2
);
1636 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1637 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1639 n_div1
= qp1
->div
->n_row
;
1640 n_div2
= qp2
->div
->n_row
;
1641 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1642 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1643 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1646 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1650 isl_mat_free(qp1
->div
);
1651 qp1
->div
= isl_mat_copy(div
);
1652 isl_mat_free(qp2
->div
);
1653 qp2
->div
= isl_mat_copy(div
);
1655 qp1
->poly
= expand(qp1
->poly
, exp1
, div
->n_col
- div
->n_row
- 2);
1656 qp2
->poly
= expand(qp2
->poly
, exp2
, div
->n_col
- div
->n_row
- 2);
1658 if (!qp1
->poly
|| !qp2
->poly
)
1665 return fn(qp1
, qp2
);
1670 isl_qpolynomial_free(qp1
);
1671 isl_qpolynomial_free(qp2
);
1675 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1676 __isl_take isl_qpolynomial
*qp2
)
1678 isl_bool compatible
;
1680 qp1
= isl_qpolynomial_cow(qp1
);
1682 if (isl_qpolynomial_check_equal_space(qp1
, qp2
) < 0)
1685 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1686 return isl_qpolynomial_add(qp2
, qp1
);
1688 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1692 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1694 qp1
->poly
= isl_poly_sum(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1698 isl_qpolynomial_free(qp2
);
1702 isl_qpolynomial_free(qp1
);
1703 isl_qpolynomial_free(qp2
);
1707 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1708 __isl_keep isl_set
*dom
,
1709 __isl_take isl_qpolynomial
*qp1
,
1710 __isl_take isl_qpolynomial
*qp2
)
1712 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1713 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1717 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1718 __isl_take isl_qpolynomial
*qp2
)
1720 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1723 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1724 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1726 if (isl_int_is_zero(v
))
1729 qp
= isl_qpolynomial_cow(qp
);
1733 qp
->poly
= isl_poly_add_isl_int(qp
->poly
, v
);
1739 isl_qpolynomial_free(qp
);
1744 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1749 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1752 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1753 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1755 if (isl_int_is_one(v
))
1758 if (qp
&& isl_int_is_zero(v
)) {
1759 isl_qpolynomial
*zero
;
1760 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1761 isl_qpolynomial_free(qp
);
1765 qp
= isl_qpolynomial_cow(qp
);
1769 qp
->poly
= isl_poly_mul_isl_int(qp
->poly
, v
);
1775 isl_qpolynomial_free(qp
);
1779 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1780 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1782 return isl_qpolynomial_mul_isl_int(qp
, v
);
1785 /* Multiply "qp" by "v".
1787 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1788 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1793 if (!isl_val_is_rat(v
))
1794 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1795 "expecting rational factor", goto error
);
1797 if (isl_val_is_one(v
)) {
1802 if (isl_val_is_zero(v
)) {
1805 space
= isl_qpolynomial_get_domain_space(qp
);
1806 isl_qpolynomial_free(qp
);
1808 return isl_qpolynomial_zero_on_domain(space
);
1811 qp
= isl_qpolynomial_cow(qp
);
1815 qp
->poly
= isl_poly_scale_val(qp
->poly
, v
);
1817 qp
= isl_qpolynomial_free(qp
);
1823 isl_qpolynomial_free(qp
);
1827 /* Divide "qp" by "v".
1829 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1830 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1835 if (!isl_val_is_rat(v
))
1836 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1837 "expecting rational factor", goto error
);
1838 if (isl_val_is_zero(v
))
1839 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1840 "cannot scale down by zero", goto error
);
1842 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1845 isl_qpolynomial_free(qp
);
1849 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1850 __isl_take isl_qpolynomial
*qp2
)
1852 isl_bool compatible
;
1854 qp1
= isl_qpolynomial_cow(qp1
);
1856 if (isl_qpolynomial_check_equal_space(qp1
, qp2
) < 0)
1859 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1860 return isl_qpolynomial_mul(qp2
, qp1
);
1862 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1866 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1868 qp1
->poly
= isl_poly_mul(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1872 isl_qpolynomial_free(qp2
);
1876 isl_qpolynomial_free(qp1
);
1877 isl_qpolynomial_free(qp2
);
1881 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1884 qp
= isl_qpolynomial_cow(qp
);
1889 qp
->poly
= isl_poly_pow(qp
->poly
, power
);
1895 isl_qpolynomial_free(qp
);
1899 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1900 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1907 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1911 for (i
= 0; i
< pwqp
->n
; ++i
) {
1912 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1914 return isl_pw_qpolynomial_free(pwqp
);
1920 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1921 __isl_take isl_space
*domain
)
1925 return isl_qpolynomial_alloc(domain
, 0, isl_poly_zero(domain
->ctx
));
1928 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1929 __isl_take isl_space
*domain
)
1933 return isl_qpolynomial_alloc(domain
, 0, isl_poly_one(domain
->ctx
));
1936 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1937 __isl_take isl_space
*domain
)
1941 return isl_qpolynomial_alloc(domain
, 0, isl_poly_infty(domain
->ctx
));
1944 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1945 __isl_take isl_space
*domain
)
1949 return isl_qpolynomial_alloc(domain
, 0, isl_poly_neginfty(domain
->ctx
));
1952 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1953 __isl_take isl_space
*domain
)
1957 return isl_qpolynomial_alloc(domain
, 0, isl_poly_nan(domain
->ctx
));
1960 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1961 __isl_take isl_space
*domain
,
1964 struct isl_qpolynomial
*qp
;
1967 qp
= isl_qpolynomial_zero_on_domain(domain
);
1971 cst
= isl_poly_as_cst(qp
->poly
);
1972 isl_int_set(cst
->n
, v
);
1977 isl_bool
isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1978 isl_int
*n
, isl_int
*d
)
1984 return isl_bool_error
;
1986 is_cst
= isl_poly_is_cst(qp
->poly
);
1987 if (is_cst
< 0 || !is_cst
)
1990 cst
= isl_poly_as_cst(qp
->poly
);
1992 return isl_bool_error
;
1995 isl_int_set(*n
, cst
->n
);
1997 isl_int_set(*d
, cst
->d
);
1999 return isl_bool_true
;
2002 /* Return the constant term of "poly".
2004 static __isl_give isl_val
*isl_poly_get_constant_val(__isl_keep isl_poly
*poly
)
2012 while ((is_cst
= isl_poly_is_cst(poly
)) == isl_bool_false
) {
2015 rec
= isl_poly_as_rec(poly
);
2023 cst
= isl_poly_as_cst(poly
);
2026 return isl_val_rat_from_isl_int(cst
->poly
.ctx
, cst
->n
, cst
->d
);
2029 /* Return the constant term of "qp".
2031 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
2032 __isl_keep isl_qpolynomial
*qp
)
2037 return isl_poly_get_constant_val(qp
->poly
);
2040 isl_bool
isl_poly_is_affine(__isl_keep isl_poly
*poly
)
2046 return isl_bool_error
;
2049 return isl_bool_true
;
2051 rec
= isl_poly_as_rec(poly
);
2053 return isl_bool_error
;
2056 return isl_bool_false
;
2058 isl_assert(poly
->ctx
, rec
->n
> 1, return isl_bool_error
);
2060 is_cst
= isl_poly_is_cst(rec
->p
[1]);
2061 if (is_cst
< 0 || !is_cst
)
2064 return isl_poly_is_affine(rec
->p
[0]);
2067 isl_bool
isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
2070 return isl_bool_error
;
2072 if (qp
->div
->n_row
> 0)
2073 return isl_bool_false
;
2075 return isl_poly_is_affine(qp
->poly
);
2078 static void update_coeff(__isl_keep isl_vec
*aff
,
2079 __isl_keep isl_poly_cst
*cst
, int pos
)
2084 if (isl_int_is_zero(cst
->n
))
2089 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
2090 isl_int_divexact(f
, cst
->d
, gcd
);
2091 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
2092 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
2093 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
2098 int isl_poly_update_affine(__isl_keep isl_poly
*poly
, __isl_keep isl_vec
*aff
)
2106 if (poly
->var
< 0) {
2109 cst
= isl_poly_as_cst(poly
);
2112 update_coeff(aff
, cst
, 0);
2116 rec
= isl_poly_as_rec(poly
);
2119 isl_assert(poly
->ctx
, rec
->n
== 2, return -1);
2121 cst
= isl_poly_as_cst(rec
->p
[1]);
2124 update_coeff(aff
, cst
, 1 + poly
->var
);
2126 return isl_poly_update_affine(rec
->p
[0], aff
);
2129 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
2130 __isl_keep isl_qpolynomial
*qp
)
2135 d
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2139 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
);
2143 isl_seq_clr(aff
->el
+ 1, 1 + d
);
2144 isl_int_set_si(aff
->el
[0], 1);
2146 if (isl_poly_update_affine(qp
->poly
, aff
) < 0)
2155 /* Compare two quasi-polynomials.
2157 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
2158 * than "qp2" and 0 if they are equal.
2160 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
2161 __isl_keep isl_qpolynomial
*qp2
)
2172 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
2176 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
2180 return isl_poly_plain_cmp(qp1
->poly
, qp2
->poly
);
2183 /* Is "qp1" obviously equal to "qp2"?
2185 * NaN is not equal to anything, not even to another NaN.
2187 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2188 __isl_keep isl_qpolynomial
*qp2
)
2193 return isl_bool_error
;
2195 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2196 return isl_bool_false
;
2198 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2199 if (equal
< 0 || !equal
)
2202 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2203 if (equal
< 0 || !equal
)
2206 return isl_poly_is_equal(qp1
->poly
, qp2
->poly
);
2209 static isl_stat
poly_update_den(__isl_keep isl_poly
*poly
, isl_int
*d
)
2215 is_cst
= isl_poly_is_cst(poly
);
2217 return isl_stat_error
;
2220 cst
= isl_poly_as_cst(poly
);
2222 return isl_stat_error
;
2223 isl_int_lcm(*d
, *d
, cst
->d
);
2227 rec
= isl_poly_as_rec(poly
);
2229 return isl_stat_error
;
2231 for (i
= 0; i
< rec
->n
; ++i
)
2232 poly_update_den(rec
->p
[i
], d
);
2237 __isl_give isl_val
*isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
)
2243 d
= isl_val_one(isl_qpolynomial_get_ctx(qp
));
2246 if (poly_update_den(qp
->poly
, &d
->n
) < 0)
2247 return isl_val_free(d
);
2251 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2252 __isl_take isl_space
*domain
, int pos
, int power
)
2254 struct isl_ctx
*ctx
;
2261 return isl_qpolynomial_alloc(domain
, 0,
2262 isl_poly_var_pow(ctx
, pos
, power
));
2265 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(
2266 __isl_take isl_space
*domain
, enum isl_dim_type type
, unsigned pos
)
2268 if (isl_space_check_is_set(domain
) < 0)
2270 if (isl_space_check_range(domain
, type
, pos
, 1) < 0)
2273 pos
+= isl_space_offset(domain
, type
);
2275 return isl_qpolynomial_var_pow_on_domain(domain
, pos
, 1);
2277 isl_space_free(domain
);
2281 __isl_give isl_poly
*isl_poly_subs(__isl_take isl_poly
*poly
,
2282 unsigned first
, unsigned n
, __isl_keep isl_poly
**subs
)
2287 isl_poly
*base
, *res
;
2289 is_cst
= isl_poly_is_cst(poly
);
2291 return isl_poly_free(poly
);
2295 if (poly
->var
< first
)
2298 rec
= isl_poly_as_rec(poly
);
2302 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
2304 if (poly
->var
>= first
+ n
)
2305 base
= isl_poly_var_pow(poly
->ctx
, poly
->var
, 1);
2307 base
= isl_poly_copy(subs
[poly
->var
- first
]);
2309 res
= isl_poly_subs(isl_poly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2310 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2312 t
= isl_poly_subs(isl_poly_copy(rec
->p
[i
]), first
, n
, subs
);
2313 res
= isl_poly_mul(res
, isl_poly_copy(base
));
2314 res
= isl_poly_sum(res
, t
);
2317 isl_poly_free(base
);
2318 isl_poly_free(poly
);
2322 isl_poly_free(poly
);
2326 __isl_give isl_poly
*isl_poly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2327 isl_int denom
, unsigned len
)
2332 isl_assert(ctx
, len
>= 1, return NULL
);
2334 poly
= isl_poly_rat_cst(ctx
, f
[0], denom
);
2335 for (i
= 0; i
< len
- 1; ++i
) {
2339 if (isl_int_is_zero(f
[1 + i
]))
2342 c
= isl_poly_rat_cst(ctx
, f
[1 + i
], denom
);
2343 t
= isl_poly_var_pow(ctx
, i
, 1);
2344 t
= isl_poly_mul(c
, t
);
2345 poly
= isl_poly_sum(poly
, t
);
2351 /* Remove common factor of non-constant terms and denominator.
2353 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2355 isl_ctx
*ctx
= qp
->div
->ctx
;
2356 unsigned total
= qp
->div
->n_col
- 2;
2358 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2359 isl_int_gcd(ctx
->normalize_gcd
,
2360 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2361 if (isl_int_is_one(ctx
->normalize_gcd
))
2364 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2365 ctx
->normalize_gcd
, total
);
2366 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2367 ctx
->normalize_gcd
);
2368 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2369 ctx
->normalize_gcd
);
2372 /* Replace the integer division identified by "div" by the polynomial "s".
2373 * The integer division is assumed not to appear in the definition
2374 * of any other integer divisions.
2376 static __isl_give isl_qpolynomial
*substitute_div(
2377 __isl_take isl_qpolynomial
*qp
, int div
, __isl_take isl_poly
*s
)
2387 qp
= isl_qpolynomial_cow(qp
);
2391 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2394 qp
->poly
= isl_poly_subs(qp
->poly
, div_pos
+ div
, 1, &s
);
2398 ctx
= isl_qpolynomial_get_ctx(qp
);
2399 reordering
= isl_alloc_array(ctx
, int, div_pos
+ qp
->div
->n_row
);
2402 for (i
= 0; i
< div_pos
+ div
; ++i
)
2404 for (i
= div_pos
+ div
+ 1; i
< div_pos
+ qp
->div
->n_row
; ++i
)
2405 reordering
[i
] = i
- 1;
2406 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2407 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + div_pos
+ div
, 1);
2408 qp
->poly
= reorder(qp
->poly
, reordering
);
2411 if (!qp
->poly
|| !qp
->div
)
2417 isl_qpolynomial_free(qp
);
2422 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2423 * divisions because d is equal to 1 by their definition, i.e., e.
2425 static __isl_give isl_qpolynomial
*substitute_non_divs(
2426 __isl_take isl_qpolynomial
*qp
)
2432 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2434 return isl_qpolynomial_free(qp
);
2436 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2437 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2439 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2440 if (isl_int_is_zero(qp
->div
->row
[j
][2 + div_pos
+ i
]))
2442 isl_seq_combine(qp
->div
->row
[j
] + 1,
2443 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2444 qp
->div
->row
[j
][2 + div_pos
+ i
],
2445 qp
->div
->row
[i
] + 1, 1 + div_pos
+ i
);
2446 isl_int_set_si(qp
->div
->row
[j
][2 + div_pos
+ i
], 0);
2447 normalize_div(qp
, j
);
2449 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2450 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2451 qp
= substitute_div(qp
, i
, s
);
2458 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2459 * with d the denominator. When replacing the coefficient e of x by
2460 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2461 * inside the division, so we need to add floor(e/d) * x outside.
2462 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2463 * to adjust the coefficient of x in each later div that depends on the
2464 * current div "div" and also in the affine expressions in the rows of "mat"
2465 * (if they too depend on "div").
2467 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2468 __isl_keep isl_mat
**mat
)
2472 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2475 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2476 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2477 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2479 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2480 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2481 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2482 *mat
= isl_mat_col_addmul(*mat
, i
, v
, 1 + total
+ div
);
2483 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2484 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2486 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2487 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2493 /* Check if the last non-zero coefficient is bigger that half of the
2494 * denominator. If so, we will invert the div to further reduce the number
2495 * of distinct divs that may appear.
2496 * If the last non-zero coefficient is exactly half the denominator,
2497 * then we continue looking for earlier coefficients that are bigger
2498 * than half the denominator.
2500 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2505 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2506 if (isl_int_is_zero(div
->row
[row
][i
]))
2508 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2509 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2510 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2520 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2521 * We only invert the coefficients of e (and the coefficient of q in
2522 * later divs and in the rows of "mat"). After calling this function, the
2523 * coefficients of e should be reduced again.
2525 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2526 __isl_keep isl_mat
**mat
)
2528 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2530 isl_seq_neg(qp
->div
->row
[div
] + 1,
2531 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2532 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2533 isl_int_add(qp
->div
->row
[div
][1],
2534 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2535 *mat
= isl_mat_col_neg(*mat
, 1 + total
+ div
);
2536 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2537 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2540 /* Reduce all divs of "qp" to have coefficients
2541 * in the interval [0, d-1], with d the denominator and such that the
2542 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2543 * The modifications to the integer divisions need to be reflected
2544 * in the factors of the polynomial that refer to the original
2545 * integer divisions. To this end, the modifications are collected
2546 * as a set of affine expressions and then plugged into the polynomial.
2548 * After the reduction, some divs may have become redundant or identical,
2549 * so we call substitute_non_divs and sort_divs. If these functions
2550 * eliminate divs or merge two or more divs into one, the coefficients
2551 * of the enclosing divs may have to be reduced again, so we call
2552 * ourselves recursively if the number of divs decreases.
2554 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2561 isl_size n_div
, total
, new_n_div
;
2563 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2564 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2565 o_div
= isl_qpolynomial_domain_offset(qp
, isl_dim_div
);
2566 if (total
< 0 || n_div
< 0)
2567 return isl_qpolynomial_free(qp
);
2568 ctx
= isl_qpolynomial_get_ctx(qp
);
2569 mat
= isl_mat_zero(ctx
, n_div
, 1 + total
);
2571 for (i
= 0; i
< n_div
; ++i
)
2572 mat
= isl_mat_set_element_si(mat
, i
, o_div
+ i
, 1);
2574 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2575 normalize_div(qp
, i
);
2576 reduce_div(qp
, i
, &mat
);
2577 if (needs_invert(qp
->div
, i
)) {
2578 invert_div(qp
, i
, &mat
);
2579 reduce_div(qp
, i
, &mat
);
2585 s
= isl_alloc_array(ctx
, struct isl_poly
*, n_div
);
2588 for (i
= 0; i
< n_div
; ++i
)
2589 s
[i
] = isl_poly_from_affine(ctx
, mat
->row
[i
], ctx
->one
,
2591 qp
->poly
= isl_poly_subs(qp
->poly
, o_div
- 1, n_div
, s
);
2592 for (i
= 0; i
< n_div
; ++i
)
2593 isl_poly_free(s
[i
]);
2600 qp
= substitute_non_divs(qp
);
2602 new_n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2604 return isl_qpolynomial_free(qp
);
2605 if (new_n_div
< n_div
)
2606 return reduce_divs(qp
);
2610 isl_qpolynomial_free(qp
);
2615 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2616 __isl_take isl_space
*domain
, const isl_int n
, const isl_int d
)
2618 struct isl_qpolynomial
*qp
;
2621 qp
= isl_qpolynomial_zero_on_domain(domain
);
2625 cst
= isl_poly_as_cst(qp
->poly
);
2626 isl_int_set(cst
->n
, n
);
2627 isl_int_set(cst
->d
, d
);
2632 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2634 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2635 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2637 isl_qpolynomial
*qp
;
2640 qp
= isl_qpolynomial_zero_on_domain(domain
);
2644 cst
= isl_poly_as_cst(qp
->poly
);
2645 isl_int_set(cst
->n
, val
->n
);
2646 isl_int_set(cst
->d
, val
->d
);
2652 isl_qpolynomial_free(qp
);
2656 static isl_stat
poly_set_active(__isl_keep isl_poly
*poly
, int *active
, int d
)
2662 is_cst
= isl_poly_is_cst(poly
);
2664 return isl_stat_error
;
2669 active
[poly
->var
] = 1;
2671 rec
= isl_poly_as_rec(poly
);
2672 for (i
= 0; i
< rec
->n
; ++i
)
2673 if (poly_set_active(rec
->p
[i
], active
, d
) < 0)
2674 return isl_stat_error
;
2679 static isl_stat
set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2685 space
= isl_qpolynomial_peek_domain_space(qp
);
2686 d
= isl_space_dim(space
, isl_dim_all
);
2687 if (d
< 0 || !active
)
2688 return isl_stat_error
;
2690 for (i
= 0; i
< d
; ++i
)
2691 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2692 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2698 return poly_set_active(qp
->poly
, active
, d
);
2702 #define TYPE isl_qpolynomial
2704 #include "check_type_range_templ.c"
2706 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2707 enum isl_dim_type type
, unsigned first
, unsigned n
)
2711 isl_bool involves
= isl_bool_false
;
2717 return isl_bool_error
;
2719 return isl_bool_false
;
2721 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2722 return isl_bool_error
;
2723 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2724 type
== isl_dim_in
, return isl_bool_error
);
2726 space
= isl_qpolynomial_peek_domain_space(qp
);
2727 d
= isl_space_dim(space
, isl_dim_all
);
2729 return isl_bool_error
;
2730 active
= isl_calloc_array(qp
->dim
->ctx
, int, d
);
2731 if (set_active(qp
, active
) < 0)
2734 offset
= isl_qpolynomial_domain_var_offset(qp
, domain_type(type
));
2738 for (i
= 0; i
< n
; ++i
)
2739 if (active
[first
+ i
]) {
2740 involves
= isl_bool_true
;
2749 return isl_bool_error
;
2752 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2753 * of the divs that do appear in the quasi-polynomial.
2755 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2756 __isl_take isl_qpolynomial
*qp
)
2763 int *reordering
= NULL
;
2770 if (qp
->div
->n_row
== 0)
2773 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2775 return isl_qpolynomial_free(qp
);
2776 len
= qp
->div
->n_col
- 2;
2777 ctx
= isl_qpolynomial_get_ctx(qp
);
2778 active
= isl_calloc_array(ctx
, int, len
);
2782 if (poly_set_active(qp
->poly
, active
, len
) < 0)
2785 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2786 if (!active
[div_pos
+ i
]) {
2790 for (j
= 0; j
< i
; ++j
) {
2791 if (isl_int_is_zero(qp
->div
->row
[i
][2 + div_pos
+ j
]))
2793 active
[div_pos
+ j
] = 1;
2803 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2807 for (i
= 0; i
< div_pos
; ++i
)
2811 n_div
= qp
->div
->n_row
;
2812 for (i
= 0; i
< n_div
; ++i
) {
2813 if (!active
[div_pos
+ i
]) {
2814 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2815 qp
->div
= isl_mat_drop_cols(qp
->div
,
2816 2 + div_pos
+ i
- skip
, 1);
2819 reordering
[div_pos
+ i
] = div_pos
+ i
- skip
;
2822 qp
->poly
= reorder(qp
->poly
, reordering
);
2824 if (!qp
->poly
|| !qp
->div
)
2834 isl_qpolynomial_free(qp
);
2838 __isl_give isl_poly
*isl_poly_drop(__isl_take isl_poly
*poly
,
2839 unsigned first
, unsigned n
)
2846 if (n
== 0 || poly
->var
< 0 || poly
->var
< first
)
2848 if (poly
->var
< first
+ n
) {
2849 poly
= replace_by_constant_term(poly
);
2850 return isl_poly_drop(poly
, first
, n
);
2852 poly
= isl_poly_cow(poly
);
2856 rec
= isl_poly_as_rec(poly
);
2860 for (i
= 0; i
< rec
->n
; ++i
) {
2861 rec
->p
[i
] = isl_poly_drop(rec
->p
[i
], first
, n
);
2868 isl_poly_free(poly
);
2872 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2873 __isl_take isl_qpolynomial
*qp
,
2874 enum isl_dim_type type
, unsigned pos
, const char *s
)
2876 qp
= isl_qpolynomial_cow(qp
);
2879 if (type
== isl_dim_out
)
2880 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2881 "cannot set name of output/set dimension",
2882 return isl_qpolynomial_free(qp
));
2883 type
= domain_type(type
);
2884 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2889 isl_qpolynomial_free(qp
);
2893 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2894 __isl_take isl_qpolynomial
*qp
,
2895 enum isl_dim_type type
, unsigned first
, unsigned n
)
2901 if (type
== isl_dim_out
)
2902 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2903 "cannot drop output/set dimension",
2905 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2906 return isl_qpolynomial_free(qp
);
2907 type
= domain_type(type
);
2908 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2911 qp
= isl_qpolynomial_cow(qp
);
2915 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2916 type
== isl_dim_set
, goto error
);
2918 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2922 offset
= isl_qpolynomial_domain_var_offset(qp
, type
);
2927 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2931 qp
->poly
= isl_poly_drop(qp
->poly
, first
, n
);
2937 isl_qpolynomial_free(qp
);
2941 /* Project the domain of the quasi-polynomial onto its parameter space.
2942 * The quasi-polynomial may not involve any of the domain dimensions.
2944 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2945 __isl_take isl_qpolynomial
*qp
)
2951 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2953 return isl_qpolynomial_free(qp
);
2954 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2956 return isl_qpolynomial_free(qp
);
2958 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2959 "polynomial involves some of the domain dimensions",
2960 return isl_qpolynomial_free(qp
));
2961 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2962 space
= isl_qpolynomial_get_domain_space(qp
);
2963 space
= isl_space_params(space
);
2964 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2968 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2969 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2979 if (eq
->n_eq
== 0) {
2980 isl_basic_set_free(eq
);
2984 qp
= isl_qpolynomial_cow(qp
);
2987 qp
->div
= isl_mat_cow(qp
->div
);
2991 total
= isl_basic_set_offset(eq
, isl_dim_div
);
2993 isl_int_init(denom
);
2994 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2995 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2996 if (j
< 0 || j
== 0 || j
>= total
)
2999 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
3000 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
3002 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
3003 &qp
->div
->row
[k
][0]);
3004 normalize_div(qp
, k
);
3007 if (isl_int_is_pos(eq
->eq
[i
][j
]))
3008 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
3009 isl_int_abs(denom
, eq
->eq
[i
][j
]);
3010 isl_int_set_si(eq
->eq
[i
][j
], 0);
3012 poly
= isl_poly_from_affine(qp
->dim
->ctx
,
3013 eq
->eq
[i
], denom
, total
);
3014 qp
->poly
= isl_poly_subs(qp
->poly
, j
- 1, 1, &poly
);
3015 isl_poly_free(poly
);
3017 isl_int_clear(denom
);
3022 isl_basic_set_free(eq
);
3024 qp
= substitute_non_divs(qp
);
3029 isl_basic_set_free(eq
);
3030 isl_qpolynomial_free(qp
);
3034 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
3036 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
3037 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
3041 if (qp
->div
->n_row
> 0)
3042 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
3043 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
3045 isl_basic_set_free(eq
);
3046 isl_qpolynomial_free(qp
);
3050 /* Look for equalities among the variables shared by context and qp
3051 * and the integer divisions of qp, if any.
3052 * The equalities are then used to eliminate variables and/or integer
3053 * divisions from qp.
3055 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
3056 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
3058 isl_local_space
*ls
;
3061 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3062 context
= isl_local_space_lift_set(ls
, context
);
3064 aff
= isl_set_affine_hull(context
);
3065 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
3068 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
3069 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
3071 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
3072 isl_set
*dom_context
= isl_set_universe(space
);
3073 dom_context
= isl_set_intersect_params(dom_context
, context
);
3074 return isl_qpolynomial_gist(qp
, dom_context
);
3077 /* Return a zero isl_qpolynomial in the given space.
3079 * This is a helper function for isl_pw_*_as_* that ensures a uniform
3080 * interface over all piecewise types.
3082 static __isl_give isl_qpolynomial
*isl_qpolynomial_zero_in_space(
3083 __isl_take isl_space
*space
)
3085 return isl_qpolynomial_zero_on_domain(isl_space_domain(space
));
3088 #define isl_qpolynomial_involves_nan isl_qpolynomial_is_nan
3091 #define PW isl_pw_qpolynomial
3093 #define BASE qpolynomial
3095 #define EL_IS_ZERO is_zero
3099 #define IS_ZERO is_zero
3102 #undef DEFAULT_IS_ZERO
3103 #define DEFAULT_IS_ZERO 1
3105 #include <isl_pw_templ.c>
3106 #include <isl_pw_eval.c>
3107 #include <isl_pw_insert_dims_templ.c>
3108 #include <isl_pw_lift_templ.c>
3109 #include <isl_pw_morph_templ.c>
3110 #include <isl_pw_move_dims_templ.c>
3111 #include <isl_pw_neg_templ.c>
3112 #include <isl_pw_opt_templ.c>
3113 #include <isl_pw_sub_templ.c>
3116 #define BASE pw_qpolynomial
3118 #include <isl_union_single.c>
3119 #include <isl_union_eval.c>
3120 #include <isl_union_neg.c>
3122 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
3130 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
3133 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
3136 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
3137 __isl_take isl_pw_qpolynomial
*pwqp1
,
3138 __isl_take isl_pw_qpolynomial
*pwqp2
)
3140 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
3143 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
3144 __isl_take isl_pw_qpolynomial
*pwqp1
,
3145 __isl_take isl_pw_qpolynomial
*pwqp2
)
3148 struct isl_pw_qpolynomial
*res
;
3150 if (!pwqp1
|| !pwqp2
)
3153 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
3156 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
3157 isl_pw_qpolynomial_free(pwqp2
);
3161 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
3162 isl_pw_qpolynomial_free(pwqp1
);
3166 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
3167 isl_pw_qpolynomial_free(pwqp1
);
3171 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
3172 isl_pw_qpolynomial_free(pwqp2
);
3176 n
= pwqp1
->n
* pwqp2
->n
;
3177 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3179 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3180 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3181 struct isl_set
*common
;
3182 struct isl_qpolynomial
*prod
;
3183 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3184 isl_set_copy(pwqp2
->p
[j
].set
));
3185 if (isl_set_plain_is_empty(common
)) {
3186 isl_set_free(common
);
3190 prod
= isl_qpolynomial_mul(
3191 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3192 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3194 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3198 isl_pw_qpolynomial_free(pwqp1
);
3199 isl_pw_qpolynomial_free(pwqp2
);
3203 isl_pw_qpolynomial_free(pwqp1
);
3204 isl_pw_qpolynomial_free(pwqp2
);
3208 __isl_give isl_val
*isl_poly_eval(__isl_take isl_poly
*poly
,
3209 __isl_take isl_vec
*vec
)
3217 is_cst
= isl_poly_is_cst(poly
);
3222 res
= isl_poly_get_constant_val(poly
);
3223 isl_poly_free(poly
);
3227 rec
= isl_poly_as_rec(poly
);
3231 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
3233 base
= isl_val_rat_from_isl_int(poly
->ctx
,
3234 vec
->el
[1 + poly
->var
], vec
->el
[0]);
3236 res
= isl_poly_eval(isl_poly_copy(rec
->p
[rec
->n
- 1]),
3239 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3240 res
= isl_val_mul(res
, isl_val_copy(base
));
3241 res
= isl_val_add(res
, isl_poly_eval(isl_poly_copy(rec
->p
[i
]),
3242 isl_vec_copy(vec
)));
3246 isl_poly_free(poly
);
3250 isl_poly_free(poly
);
3255 /* Evaluate "qp" in the void point "pnt".
3256 * In particular, return the value NaN.
3258 static __isl_give isl_val
*eval_void(__isl_take isl_qpolynomial
*qp
,
3259 __isl_take isl_point
*pnt
)
3263 ctx
= isl_point_get_ctx(pnt
);
3264 isl_qpolynomial_free(qp
);
3265 isl_point_free(pnt
);
3266 return isl_val_nan(ctx
);
3269 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3270 __isl_take isl_point
*pnt
)
3278 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3279 is_void
= isl_point_is_void(pnt
);
3283 return eval_void(qp
, pnt
);
3285 ext
= isl_local_extend_point_vec(qp
->div
, isl_vec_copy(pnt
->vec
));
3287 v
= isl_poly_eval(isl_poly_copy(qp
->poly
), ext
);
3289 isl_qpolynomial_free(qp
);
3290 isl_point_free(pnt
);
3294 isl_qpolynomial_free(qp
);
3295 isl_point_free(pnt
);
3299 int isl_poly_cmp(__isl_keep isl_poly_cst
*cst1
, __isl_keep isl_poly_cst
*cst2
)
3304 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3305 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3306 cmp
= isl_int_sgn(t
);
3311 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3312 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3313 unsigned first
, unsigned n
)
3321 if (type
== isl_dim_out
)
3322 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3323 "cannot insert output/set dimensions",
3325 if (isl_qpolynomial_check_range(qp
, type
, first
, 0) < 0)
3326 return isl_qpolynomial_free(qp
);
3327 type
= domain_type(type
);
3328 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3331 qp
= isl_qpolynomial_cow(qp
);
3335 g_pos
= pos(qp
->dim
, type
) + first
;
3337 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3341 total
= qp
->div
->n_col
- 2;
3342 if (total
> g_pos
) {
3344 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3347 for (i
= 0; i
< total
- g_pos
; ++i
)
3349 qp
->poly
= expand(qp
->poly
, exp
, g_pos
);
3355 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3361 isl_qpolynomial_free(qp
);
3365 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3366 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3370 pos
= isl_qpolynomial_dim(qp
, type
);
3372 return isl_qpolynomial_free(qp
);
3374 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3377 static int *reordering_move(isl_ctx
*ctx
,
3378 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3383 reordering
= isl_alloc_array(ctx
, int, len
);
3388 for (i
= 0; i
< dst
; ++i
)
3390 for (i
= 0; i
< n
; ++i
)
3391 reordering
[src
+ i
] = dst
+ i
;
3392 for (i
= 0; i
< src
- dst
; ++i
)
3393 reordering
[dst
+ i
] = dst
+ n
+ i
;
3394 for (i
= 0; i
< len
- src
- n
; ++i
)
3395 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3397 for (i
= 0; i
< src
; ++i
)
3399 for (i
= 0; i
< n
; ++i
)
3400 reordering
[src
+ i
] = dst
+ i
;
3401 for (i
= 0; i
< dst
- src
; ++i
)
3402 reordering
[src
+ n
+ i
] = src
+ i
;
3403 for (i
= 0; i
< len
- dst
- n
; ++i
)
3404 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3410 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3411 __isl_take isl_qpolynomial
*qp
,
3412 enum isl_dim_type dst_type
, unsigned dst_pos
,
3413 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3422 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3423 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3424 "cannot move output/set dimension",
3426 if (isl_qpolynomial_check_range(qp
, src_type
, src_pos
, n
) < 0)
3427 return isl_qpolynomial_free(qp
);
3428 if (dst_type
== isl_dim_in
)
3429 dst_type
= isl_dim_set
;
3430 if (src_type
== isl_dim_in
)
3431 src_type
= isl_dim_set
;
3434 !isl_space_is_named_or_nested(qp
->dim
, src_type
) &&
3435 !isl_space_is_named_or_nested(qp
->dim
, dst_type
))
3438 qp
= isl_qpolynomial_cow(qp
);
3442 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3443 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3444 if (dst_type
> src_type
)
3447 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3454 reordering
= reordering_move(qp
->dim
->ctx
,
3455 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3459 qp
->poly
= reorder(qp
->poly
, reordering
);
3464 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3470 isl_qpolynomial_free(qp
);
3474 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(
3475 __isl_take isl_space
*space
, isl_int
*f
, isl_int denom
)
3480 space
= isl_space_domain(space
);
3484 d
= isl_space_dim(space
, isl_dim_all
);
3485 poly
= d
< 0 ? NULL
: isl_poly_from_affine(space
->ctx
, f
, denom
, 1 + d
);
3487 return isl_qpolynomial_alloc(space
, 0, poly
);
3490 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3494 isl_qpolynomial
*qp
;
3499 ctx
= isl_aff_get_ctx(aff
);
3500 poly
= isl_poly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3503 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3504 aff
->ls
->div
->n_row
, poly
);
3508 isl_mat_free(qp
->div
);
3509 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3510 qp
->div
= isl_mat_cow(qp
->div
);
3515 qp
= reduce_divs(qp
);
3516 qp
= remove_redundant_divs(qp
);
3520 return isl_qpolynomial_free(qp
);
3523 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3524 __isl_take isl_pw_aff
*pwaff
)
3527 isl_pw_qpolynomial
*pwqp
;
3532 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3535 for (i
= 0; i
< pwaff
->n
; ++i
) {
3537 isl_qpolynomial
*qp
;
3539 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3540 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3541 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3544 isl_pw_aff_free(pwaff
);
3548 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3549 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3553 aff
= isl_constraint_get_bound(c
, type
, pos
);
3554 isl_constraint_free(c
);
3555 return isl_qpolynomial_from_aff(aff
);
3558 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3559 * in "qp" by subs[i].
3561 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3562 __isl_take isl_qpolynomial
*qp
,
3563 enum isl_dim_type type
, unsigned first
, unsigned n
,
3564 __isl_keep isl_qpolynomial
**subs
)
3572 qp
= isl_qpolynomial_cow(qp
);
3576 if (type
== isl_dim_out
)
3577 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3578 "cannot substitute output/set dimension",
3580 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
3581 return isl_qpolynomial_free(qp
);
3582 type
= domain_type(type
);
3584 for (i
= 0; i
< n
; ++i
)
3588 for (i
= 0; i
< n
; ++i
)
3589 if (isl_qpolynomial_check_equal_space(qp
, subs
[i
]) < 0)
3592 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3593 for (i
= 0; i
< n
; ++i
)
3594 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3596 first
+= pos(qp
->dim
, type
);
3598 polys
= isl_alloc_array(qp
->dim
->ctx
, struct isl_poly
*, n
);
3601 for (i
= 0; i
< n
; ++i
)
3602 polys
[i
] = subs
[i
]->poly
;
3604 qp
->poly
= isl_poly_subs(qp
->poly
, first
, n
, polys
);
3613 isl_qpolynomial_free(qp
);
3617 /* Extend "bset" with extra set dimensions for each integer division
3618 * in "qp" and then call "fn" with the extended bset and the polynomial
3619 * that results from replacing each of the integer divisions by the
3620 * corresponding extra set dimension.
3622 isl_stat
isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3623 __isl_keep isl_basic_set
*bset
,
3624 isl_stat (*fn
)(__isl_take isl_basic_set
*bset
,
3625 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3628 isl_local_space
*ls
;
3629 isl_qpolynomial
*poly
;
3632 return isl_stat_error
;
3633 if (qp
->div
->n_row
== 0)
3634 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3637 space
= isl_space_copy(qp
->dim
);
3638 space
= isl_space_add_dims(space
, isl_dim_set
, qp
->div
->n_row
);
3639 poly
= isl_qpolynomial_alloc(space
, 0, isl_poly_copy(qp
->poly
));
3640 bset
= isl_basic_set_copy(bset
);
3641 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3642 bset
= isl_local_space_lift_basic_set(ls
, bset
);
3644 return fn(bset
, poly
, user
);
3647 /* Return total degree in variables first (inclusive) up to last (exclusive).
3649 int isl_poly_degree(__isl_keep isl_poly
*poly
, int first
, int last
)
3653 isl_bool is_zero
, is_cst
;
3656 is_zero
= isl_poly_is_zero(poly
);
3661 is_cst
= isl_poly_is_cst(poly
);
3664 if (is_cst
|| poly
->var
< first
)
3667 rec
= isl_poly_as_rec(poly
);
3671 for (i
= 0; i
< rec
->n
; ++i
) {
3674 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3679 d
= isl_poly_degree(rec
->p
[i
], first
, last
);
3680 if (poly
->var
< last
)
3689 /* Return total degree in set variables.
3691 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3699 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3700 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3703 return isl_poly_degree(poly
->poly
, ovar
, ovar
+ nvar
);
3706 __isl_give isl_poly
*isl_poly_coeff(__isl_keep isl_poly
*poly
,
3707 unsigned pos
, int deg
)
3713 is_cst
= isl_poly_is_cst(poly
);
3716 if (is_cst
|| poly
->var
< pos
) {
3718 return isl_poly_copy(poly
);
3720 return isl_poly_zero(poly
->ctx
);
3723 rec
= isl_poly_as_rec(poly
);
3727 if (poly
->var
== pos
) {
3729 return isl_poly_copy(rec
->p
[deg
]);
3731 return isl_poly_zero(poly
->ctx
);
3734 poly
= isl_poly_copy(poly
);
3735 poly
= isl_poly_cow(poly
);
3736 rec
= isl_poly_as_rec(poly
);
3740 for (i
= 0; i
< rec
->n
; ++i
) {
3742 t
= isl_poly_coeff(rec
->p
[i
], pos
, deg
);
3745 isl_poly_free(rec
->p
[i
]);
3751 isl_poly_free(poly
);
3755 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3757 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3758 __isl_keep isl_qpolynomial
*qp
,
3759 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3768 if (type
== isl_dim_out
)
3769 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3770 "output/set dimension does not have a coefficient",
3772 if (isl_qpolynomial_check_range(qp
, type
, t_pos
, 1) < 0)
3774 type
= domain_type(type
);
3776 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3777 poly
= isl_poly_coeff(qp
->poly
, g_pos
, deg
);
3779 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
),
3780 qp
->div
->n_row
, poly
);
3783 isl_mat_free(c
->div
);
3784 c
->div
= isl_mat_copy(qp
->div
);
3789 isl_qpolynomial_free(c
);
3793 /* Homogenize the polynomial in the variables first (inclusive) up to
3794 * last (exclusive) by inserting powers of variable first.
3795 * Variable first is assumed not to appear in the input.
3797 __isl_give isl_poly
*isl_poly_homogenize(__isl_take isl_poly
*poly
, int deg
,
3798 int target
, int first
, int last
)
3801 isl_bool is_zero
, is_cst
;
3804 is_zero
= isl_poly_is_zero(poly
);
3806 return isl_poly_free(poly
);
3811 is_cst
= isl_poly_is_cst(poly
);
3813 return isl_poly_free(poly
);
3814 if (is_cst
|| poly
->var
< first
) {
3817 hom
= isl_poly_var_pow(poly
->ctx
, first
, target
- deg
);
3820 rec
= isl_poly_as_rec(hom
);
3821 rec
->p
[target
- deg
] = isl_poly_mul(rec
->p
[target
- deg
], poly
);
3826 poly
= isl_poly_cow(poly
);
3827 rec
= isl_poly_as_rec(poly
);
3831 for (i
= 0; i
< rec
->n
; ++i
) {
3832 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3834 return isl_poly_free(poly
);
3837 rec
->p
[i
] = isl_poly_homogenize(rec
->p
[i
],
3838 poly
->var
< last
? deg
+ i
: i
, target
,
3846 isl_poly_free(poly
);
3850 /* Homogenize the polynomial in the set variables by introducing
3851 * powers of an extra set variable at position 0.
3853 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3854 __isl_take isl_qpolynomial
*poly
)
3858 int deg
= isl_qpolynomial_degree(poly
);
3863 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3864 poly
= isl_qpolynomial_cow(poly
);
3868 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3869 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3871 return isl_qpolynomial_free(poly
);
3872 poly
->poly
= isl_poly_homogenize(poly
->poly
, 0, deg
, ovar
, ovar
+ nvar
);
3878 isl_qpolynomial_free(poly
);
3882 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*space
,
3883 __isl_take isl_mat
*div
)
3889 d
= isl_space_dim(space
, isl_dim_all
);
3895 term
= isl_calloc(space
->ctx
, struct isl_term
,
3896 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3903 isl_int_init(term
->n
);
3904 isl_int_init(term
->d
);
3908 isl_space_free(space
);
3913 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3922 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3928 total
= isl_term_dim(term
, isl_dim_all
);
3932 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3936 isl_int_set(dup
->n
, term
->n
);
3937 isl_int_set(dup
->d
, term
->d
);
3939 for (i
= 0; i
< total
; ++i
)
3940 dup
->pow
[i
] = term
->pow
[i
];
3945 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3953 return isl_term_dup(term
);
3956 __isl_null isl_term
*isl_term_free(__isl_take isl_term
*term
)
3961 if (--term
->ref
> 0)
3964 isl_space_free(term
->dim
);
3965 isl_mat_free(term
->div
);
3966 isl_int_clear(term
->n
);
3967 isl_int_clear(term
->d
);
3973 isl_size
isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3978 return isl_size_error
;
3983 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3984 case isl_dim_div
: return term
->div
->n_row
;
3985 case isl_dim_all
: dim
= isl_space_dim(term
->dim
, isl_dim_all
);
3987 return isl_size_error
;
3988 return dim
+ term
->div
->n_row
;
3989 default: return isl_size_error
;
3993 /* Return the space of "term".
3995 static __isl_keep isl_space
*isl_term_peek_space(__isl_keep isl_term
*term
)
3997 return term
? term
->dim
: NULL
;
4000 /* Return the offset of the first variable of type "type" within
4001 * the variables of "term".
4003 static isl_size
isl_term_offset(__isl_keep isl_term
*term
,
4004 enum isl_dim_type type
)
4008 space
= isl_term_peek_space(term
);
4010 return isl_size_error
;
4014 case isl_dim_set
: return isl_space_offset(space
, type
);
4015 case isl_dim_div
: return isl_space_dim(space
, isl_dim_all
);
4017 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
4018 "invalid dimension type", return isl_size_error
);
4022 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
4024 return term
? term
->dim
->ctx
: NULL
;
4027 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
4031 isl_int_set(*n
, term
->n
);
4034 /* Return the coefficient of the term "term".
4036 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
4041 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
4046 #define TYPE isl_term
4048 #include "check_type_range_templ.c"
4050 isl_size
isl_term_get_exp(__isl_keep isl_term
*term
,
4051 enum isl_dim_type type
, unsigned pos
)
4055 if (isl_term_check_range(term
, type
, pos
, 1) < 0)
4056 return isl_size_error
;
4057 offset
= isl_term_offset(term
, type
);
4059 return isl_size_error
;
4061 return term
->pow
[offset
+ pos
];
4064 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
4066 isl_local_space
*ls
;
4069 if (isl_term_check_range(term
, isl_dim_div
, pos
, 1) < 0)
4072 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
4073 isl_mat_copy(term
->div
));
4074 aff
= isl_aff_alloc(ls
);
4078 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
4080 aff
= isl_aff_normalize(aff
);
4085 __isl_give isl_term
*isl_poly_foreach_term(__isl_keep isl_poly
*poly
,
4086 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
4087 __isl_take isl_term
*term
, void *user
)
4090 isl_bool is_zero
, is_bad
, is_cst
;
4093 is_zero
= isl_poly_is_zero(poly
);
4094 if (is_zero
< 0 || !term
)
4100 is_cst
= isl_poly_is_cst(poly
);
4101 is_bad
= isl_poly_is_nan(poly
);
4102 if (is_bad
>= 0 && !is_bad
)
4103 is_bad
= isl_poly_is_infty(poly
);
4104 if (is_bad
>= 0 && !is_bad
)
4105 is_bad
= isl_poly_is_neginfty(poly
);
4106 if (is_cst
< 0 || is_bad
< 0)
4107 return isl_term_free(term
);
4109 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
4110 "cannot handle NaN/infty polynomial",
4111 return isl_term_free(term
));
4115 cst
= isl_poly_as_cst(poly
);
4118 term
= isl_term_cow(term
);
4121 isl_int_set(term
->n
, cst
->n
);
4122 isl_int_set(term
->d
, cst
->d
);
4123 if (fn(isl_term_copy(term
), user
) < 0)
4128 rec
= isl_poly_as_rec(poly
);
4132 for (i
= 0; i
< rec
->n
; ++i
) {
4133 term
= isl_term_cow(term
);
4136 term
->pow
[poly
->var
] = i
;
4137 term
= isl_poly_foreach_term(rec
->p
[i
], fn
, term
, user
);
4141 term
= isl_term_cow(term
);
4144 term
->pow
[poly
->var
] = 0;
4148 isl_term_free(term
);
4152 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
4153 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
4158 return isl_stat_error
;
4160 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
4162 return isl_stat_error
;
4164 term
= isl_poly_foreach_term(qp
->poly
, fn
, term
, user
);
4166 isl_term_free(term
);
4168 return term
? isl_stat_ok
: isl_stat_error
;
4171 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
4174 isl_qpolynomial
*qp
;
4178 n
= isl_term_dim(term
, isl_dim_all
);
4180 term
= isl_term_free(term
);
4184 poly
= isl_poly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
4185 for (i
= 0; i
< n
; ++i
) {
4188 poly
= isl_poly_mul(poly
,
4189 isl_poly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
4192 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
),
4193 term
->div
->n_row
, poly
);
4196 isl_mat_free(qp
->div
);
4197 qp
->div
= isl_mat_copy(term
->div
);
4201 isl_term_free(term
);
4204 isl_qpolynomial_free(qp
);
4205 isl_term_free(term
);
4209 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
4210 __isl_take isl_space
*space
)
4214 isl_size total
, d_set
, d_qp
;
4219 if (isl_space_is_equal(qp
->dim
, space
)) {
4220 isl_space_free(space
);
4224 qp
= isl_qpolynomial_cow(qp
);
4228 d_set
= isl_space_dim(space
, isl_dim_set
);
4229 d_qp
= isl_qpolynomial_domain_dim(qp
, isl_dim_set
);
4230 extra
= d_set
- d_qp
;
4231 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4232 if (d_set
< 0 || d_qp
< 0 || total
< 0)
4234 if (qp
->div
->n_row
) {
4237 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
4240 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4242 qp
->poly
= expand(qp
->poly
, exp
, total
);
4247 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4250 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4251 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4253 isl_space_free(qp
->dim
);
4258 isl_space_free(space
);
4259 isl_qpolynomial_free(qp
);
4263 /* For each parameter or variable that does not appear in qp,
4264 * first eliminate the variable from all constraints and then set it to zero.
4266 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4267 __isl_keep isl_qpolynomial
*qp
)
4275 d
= isl_set_dim(set
, isl_dim_all
);
4279 active
= isl_calloc_array(set
->ctx
, int, d
);
4280 if (set_active(qp
, active
) < 0)
4283 for (i
= 0; i
< d
; ++i
)
4292 nparam
= isl_set_dim(set
, isl_dim_param
);
4293 nvar
= isl_set_dim(set
, isl_dim_set
);
4294 if (nparam
< 0 || nvar
< 0)
4296 for (i
= 0; i
< nparam
; ++i
) {
4299 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4300 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4302 for (i
= 0; i
< nvar
; ++i
) {
4303 if (active
[nparam
+ i
])
4305 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4306 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4318 struct isl_opt_data
{
4319 isl_qpolynomial
*qp
;
4325 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4327 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4330 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4334 } else if (data
->max
) {
4335 data
->opt
= isl_val_max(data
->opt
, val
);
4337 data
->opt
= isl_val_min(data
->opt
, val
);
4343 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4344 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4346 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4352 is_cst
= isl_poly_is_cst(qp
->poly
);
4357 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4358 isl_qpolynomial_free(qp
);
4362 set
= fix_inactive(set
, qp
);
4365 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4369 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4372 isl_qpolynomial_free(qp
);
4376 isl_qpolynomial_free(qp
);
4377 isl_val_free(data
.opt
);
4381 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4382 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4388 isl_mat
*mat
, *diag
;
4390 qp
= isl_qpolynomial_cow(qp
);
4395 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4397 n_sub
= morph
->inv
->n_row
- 1;
4398 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4399 n_sub
+= qp
->div
->n_row
;
4400 subs
= isl_calloc_array(ctx
, struct isl_poly
*, n_sub
);
4404 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4405 subs
[i
] = isl_poly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4406 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4407 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4408 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4409 subs
[morph
->inv
->n_row
- 1 + i
] =
4410 isl_poly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4412 qp
->poly
= isl_poly_subs(qp
->poly
, 0, n_sub
, subs
);
4414 for (i
= 0; i
< n_sub
; ++i
)
4415 isl_poly_free(subs
[i
]);
4418 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4419 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4420 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4421 mat
= isl_mat_diagonal(mat
, diag
);
4422 qp
->div
= isl_mat_product(qp
->div
, mat
);
4423 isl_space_free(qp
->dim
);
4424 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4426 if (!qp
->poly
|| !qp
->div
|| !qp
->dim
)
4429 isl_morph_free(morph
);
4433 isl_qpolynomial_free(qp
);
4434 isl_morph_free(morph
);
4438 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4439 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4440 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4442 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4443 &isl_pw_qpolynomial_mul
);
4446 /* Reorder the dimension of "qp" according to the given reordering.
4448 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4449 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4453 qp
= isl_qpolynomial_cow(qp
);
4457 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4461 qp
->div
= isl_local_reorder(qp
->div
, isl_reordering_copy(r
));
4465 qp
->poly
= reorder(qp
->poly
, r
->pos
);
4469 space
= isl_reordering_get_space(r
);
4470 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
4472 isl_reordering_free(r
);
4475 isl_qpolynomial_free(qp
);
4476 isl_reordering_free(r
);
4480 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4481 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4483 isl_bool equal_params
;
4488 equal_params
= isl_space_has_equal_params(qp
->dim
, model
);
4489 if (equal_params
< 0)
4491 if (!equal_params
) {
4492 isl_reordering
*exp
;
4494 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4495 exp
= isl_reordering_extend_space(exp
,
4496 isl_qpolynomial_get_domain_space(qp
));
4497 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4500 isl_space_free(model
);
4503 isl_space_free(model
);
4504 isl_qpolynomial_free(qp
);
4508 struct isl_split_periods_data
{
4510 isl_pw_qpolynomial
*res
;
4513 /* Create a slice where the integer division "div" has the fixed value "v".
4514 * In particular, if "div" refers to floor(f/m), then create a slice
4516 * m v <= f <= m v + (m - 1)
4521 * -f + m v + (m - 1) >= 0
4523 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*space
,
4524 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4527 isl_basic_set
*bset
= NULL
;
4530 total
= isl_space_dim(space
, isl_dim_all
);
4531 if (total
< 0 || !qp
)
4534 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0, 0, 2);
4536 k
= isl_basic_set_alloc_inequality(bset
);
4539 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4540 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4542 k
= isl_basic_set_alloc_inequality(bset
);
4545 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4546 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4547 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4548 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4550 isl_space_free(space
);
4551 return isl_set_from_basic_set(bset
);
4553 isl_basic_set_free(bset
);
4554 isl_space_free(space
);
4558 static isl_stat
split_periods(__isl_take isl_set
*set
,
4559 __isl_take isl_qpolynomial
*qp
, void *user
);
4561 /* Create a slice of the domain "set" such that integer division "div"
4562 * has the fixed value "v" and add the results to data->res,
4563 * replacing the integer division by "v" in "qp".
4565 static isl_stat
set_div(__isl_take isl_set
*set
,
4566 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4567 struct isl_split_periods_data
*data
)
4574 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4575 set
= isl_set_intersect(set
, slice
);
4577 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4581 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4582 if (isl_int_is_zero(qp
->div
->row
[i
][2 + div_pos
+ div
]))
4584 isl_int_addmul(qp
->div
->row
[i
][1],
4585 qp
->div
->row
[i
][2 + div_pos
+ div
], v
);
4586 isl_int_set_si(qp
->div
->row
[i
][2 + div_pos
+ div
], 0);
4589 cst
= isl_poly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4590 qp
= substitute_div(qp
, div
, cst
);
4592 return split_periods(set
, qp
, data
);
4595 isl_qpolynomial_free(qp
);
4596 return isl_stat_error
;
4599 /* Split the domain "set" such that integer division "div"
4600 * has a fixed value (ranging from "min" to "max") on each slice
4601 * and add the results to data->res.
4603 static isl_stat
split_div(__isl_take isl_set
*set
,
4604 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4605 struct isl_split_periods_data
*data
)
4607 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4608 isl_set
*set_i
= isl_set_copy(set
);
4609 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4611 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4615 isl_qpolynomial_free(qp
);
4619 isl_qpolynomial_free(qp
);
4620 return isl_stat_error
;
4623 /* If "qp" refers to any integer division
4624 * that can only attain "max_periods" distinct values on "set"
4625 * then split the domain along those distinct values.
4626 * Add the results (or the original if no splitting occurs)
4629 static isl_stat
split_periods(__isl_take isl_set
*set
,
4630 __isl_take isl_qpolynomial
*qp
, void *user
)
4633 isl_pw_qpolynomial
*pwqp
;
4634 struct isl_split_periods_data
*data
;
4637 isl_stat r
= isl_stat_ok
;
4639 data
= (struct isl_split_periods_data
*)user
;
4644 if (qp
->div
->n_row
== 0) {
4645 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4646 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4650 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4656 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4657 enum isl_lp_result lp_res
;
4659 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + div_pos
,
4660 qp
->div
->n_row
) != -1)
4663 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4664 set
->ctx
->one
, &min
, NULL
, NULL
);
4665 if (lp_res
== isl_lp_error
)
4667 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4669 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4671 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4672 set
->ctx
->one
, &max
, NULL
, NULL
);
4673 if (lp_res
== isl_lp_error
)
4675 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4677 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4679 isl_int_sub(max
, max
, min
);
4680 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4681 isl_int_add(max
, max
, min
);
4686 if (i
< qp
->div
->n_row
) {
4687 r
= split_div(set
, qp
, i
, min
, max
, data
);
4689 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4690 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4702 isl_qpolynomial_free(qp
);
4703 return isl_stat_error
;
4706 /* If any quasi-polynomial in pwqp refers to any integer division
4707 * that can only attain "max_periods" distinct values on its domain
4708 * then split the domain along those distinct values.
4710 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4711 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4713 struct isl_split_periods_data data
;
4715 data
.max_periods
= max_periods
;
4716 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4718 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4721 isl_pw_qpolynomial_free(pwqp
);
4725 isl_pw_qpolynomial_free(data
.res
);
4726 isl_pw_qpolynomial_free(pwqp
);
4730 /* Construct a piecewise quasipolynomial that is constant on the given
4731 * domain. In particular, it is
4734 * infinity if cst == -1
4736 * If cst == -1, then explicitly check whether the domain is empty and,
4737 * if so, return 0 instead.
4739 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4740 __isl_take isl_basic_set
*bset
, int cst
)
4743 isl_qpolynomial
*qp
;
4745 if (cst
< 0 && isl_basic_set_is_empty(bset
) == isl_bool_true
)
4750 bset
= isl_basic_set_params(bset
);
4751 space
= isl_basic_set_get_space(bset
);
4753 qp
= isl_qpolynomial_infty_on_domain(space
);
4755 qp
= isl_qpolynomial_zero_on_domain(space
);
4757 qp
= isl_qpolynomial_one_on_domain(space
);
4758 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4761 /* Internal data structure for multiplicative_call_factor_pw_qpolynomial.
4762 * "fn" is the function that is called on each factor.
4763 * "pwpq" collects the results.
4765 struct isl_multiplicative_call_data_pw_qpolynomial
{
4766 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
);
4767 isl_pw_qpolynomial
*pwqp
;
4770 /* isl_factorizer_every_factor_basic_set callback that applies
4771 * data->fn to the factor "bset" and multiplies in the result
4774 static isl_bool
multiplicative_call_factor_pw_qpolynomial(
4775 __isl_keep isl_basic_set
*bset
, void *user
)
4777 struct isl_multiplicative_call_data_pw_qpolynomial
*data
= user
;
4779 bset
= isl_basic_set_copy(bset
);
4780 data
->pwqp
= isl_pw_qpolynomial_mul(data
->pwqp
, data
->fn(bset
));
4782 return isl_bool_error
;
4784 return isl_bool_true
;
4787 /* Factor bset, call fn on each of the factors and return the product.
4789 * If no factors can be found, simply call fn on the input.
4790 * Otherwise, construct the factors based on the factorizer,
4791 * call fn on each factor and compute the product.
4793 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4794 __isl_take isl_basic_set
*bset
,
4795 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4797 struct isl_multiplicative_call_data_pw_qpolynomial data
= { fn
};
4801 isl_qpolynomial
*qp
;
4804 f
= isl_basic_set_factorizer(bset
);
4807 if (f
->n_group
== 0) {
4808 isl_factorizer_free(f
);
4812 space
= isl_basic_set_get_space(bset
);
4813 space
= isl_space_params(space
);
4814 set
= isl_set_universe(isl_space_copy(space
));
4815 qp
= isl_qpolynomial_one_on_domain(space
);
4816 data
.pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4818 every
= isl_factorizer_every_factor_basic_set(f
,
4819 &multiplicative_call_factor_pw_qpolynomial
, &data
);
4821 data
.pwqp
= isl_pw_qpolynomial_free(data
.pwqp
);
4823 isl_basic_set_free(bset
);
4824 isl_factorizer_free(f
);
4828 isl_basic_set_free(bset
);
4832 /* Factor bset, call fn on each of the factors and return the product.
4833 * The function is assumed to evaluate to zero on empty domains,
4834 * to one on zero-dimensional domains and to infinity on unbounded domains
4835 * and will not be called explicitly on zero-dimensional or unbounded domains.
4837 * We first check for some special cases and remove all equalities.
4838 * Then we hand over control to compressed_multiplicative_call.
4840 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4841 __isl_take isl_basic_set
*bset
,
4842 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4847 isl_pw_qpolynomial
*pwqp
;
4852 if (isl_basic_set_plain_is_empty(bset
))
4853 return constant_on_domain(bset
, 0);
4855 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
4859 return constant_on_domain(bset
, 1);
4861 bounded
= isl_basic_set_is_bounded(bset
);
4865 return constant_on_domain(bset
, -1);
4867 if (bset
->n_eq
== 0)
4868 return compressed_multiplicative_call(bset
, fn
);
4870 morph
= isl_basic_set_full_compression(bset
);
4871 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4873 pwqp
= compressed_multiplicative_call(bset
, fn
);
4875 morph
= isl_morph_dom_params(morph
);
4876 morph
= isl_morph_ran_params(morph
);
4877 morph
= isl_morph_inverse(morph
);
4879 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4883 isl_basic_set_free(bset
);
4887 /* Drop all floors in "qp", turning each integer division [a/m] into
4888 * a rational division a/m. If "down" is set, then the integer division
4889 * is replaced by (a-(m-1))/m instead.
4891 static __isl_give isl_qpolynomial
*qp_drop_floors(
4892 __isl_take isl_qpolynomial
*qp
, int down
)
4899 if (qp
->div
->n_row
== 0)
4902 qp
= isl_qpolynomial_cow(qp
);
4906 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4908 isl_int_sub(qp
->div
->row
[i
][1],
4909 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4910 isl_int_add_ui(qp
->div
->row
[i
][1],
4911 qp
->div
->row
[i
][1], 1);
4913 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4914 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4915 qp
= substitute_div(qp
, i
, s
);
4923 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4924 * a rational division a/m.
4926 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4927 __isl_take isl_pw_qpolynomial
*pwqp
)
4934 if (isl_pw_qpolynomial_is_zero(pwqp
))
4937 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4941 for (i
= 0; i
< pwqp
->n
; ++i
) {
4942 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4949 isl_pw_qpolynomial_free(pwqp
);
4953 /* Adjust all the integer divisions in "qp" such that they are at least
4954 * one over the given orthant (identified by "signs"). This ensures
4955 * that they will still be non-negative even after subtracting (m-1)/m.
4957 * In particular, f is replaced by f' + v, changing f = [a/m]
4958 * to f' = [(a - m v)/m].
4959 * If the constant term k in a is smaller than m,
4960 * the constant term of v is set to floor(k/m) - 1.
4961 * For any other term, if the coefficient c and the variable x have
4962 * the same sign, then no changes are needed.
4963 * Otherwise, if the variable is positive (and c is negative),
4964 * then the coefficient of x in v is set to floor(c/m).
4965 * If the variable is negative (and c is positive),
4966 * then the coefficient of x in v is set to ceil(c/m).
4968 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4976 qp
= isl_qpolynomial_cow(qp
);
4977 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4979 return isl_qpolynomial_free(qp
);
4980 qp
->div
= isl_mat_cow(qp
->div
);
4984 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4986 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4987 isl_int
*row
= qp
->div
->row
[i
];
4991 if (isl_int_lt(row
[1], row
[0])) {
4992 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4993 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4994 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4996 for (j
= 0; j
< div_pos
; ++j
) {
4997 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
5000 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
5002 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
5003 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
5005 for (j
= 0; j
< i
; ++j
) {
5006 if (isl_int_sgn(row
[2 + div_pos
+ j
]) >= 0)
5008 isl_int_fdiv_q(v
->el
[1 + div_pos
+ j
],
5009 row
[2 + div_pos
+ j
], row
[0]);
5010 isl_int_submul(row
[2 + div_pos
+ j
],
5011 row
[0], v
->el
[1 + div_pos
+ j
]);
5013 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
5014 if (isl_int_is_zero(qp
->div
->row
[j
][2 + div_pos
+ i
]))
5016 isl_seq_combine(qp
->div
->row
[j
] + 1,
5017 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
5018 qp
->div
->row
[j
][2 + div_pos
+ i
], v
->el
,
5021 isl_int_set_si(v
->el
[1 + div_pos
+ i
], 1);
5022 s
= isl_poly_from_affine(qp
->dim
->ctx
, v
->el
,
5023 qp
->div
->ctx
->one
, v
->size
);
5024 qp
->poly
= isl_poly_subs(qp
->poly
, div_pos
+ i
, 1, &s
);
5034 isl_qpolynomial_free(qp
);
5038 struct isl_to_poly_data
{
5040 isl_pw_qpolynomial
*res
;
5041 isl_qpolynomial
*qp
;
5044 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
5045 * We first make all integer divisions positive and then split the
5046 * quasipolynomials into terms with sign data->sign (the direction
5047 * of the requested approximation) and terms with the opposite sign.
5048 * In the first set of terms, each integer division [a/m] is
5049 * overapproximated by a/m, while in the second it is underapproximated
5052 static isl_stat
to_polynomial_on_orthant(__isl_take isl_set
*orthant
,
5053 int *signs
, void *user
)
5055 struct isl_to_poly_data
*data
= user
;
5056 isl_pw_qpolynomial
*t
;
5057 isl_qpolynomial
*qp
, *up
, *down
;
5059 qp
= isl_qpolynomial_copy(data
->qp
);
5060 qp
= make_divs_pos(qp
, signs
);
5062 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
5063 up
= qp_drop_floors(up
, 0);
5064 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
5065 down
= qp_drop_floors(down
, 1);
5067 isl_qpolynomial_free(qp
);
5068 qp
= isl_qpolynomial_add(up
, down
);
5070 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
5071 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
5076 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
5077 * the polynomial will be an overapproximation. If "sign" is negative,
5078 * it will be an underapproximation. If "sign" is zero, the approximation
5079 * will lie somewhere in between.
5081 * In particular, is sign == 0, we simply drop the floors, turning
5082 * the integer divisions into rational divisions.
5083 * Otherwise, we split the domains into orthants, make all integer divisions
5084 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
5085 * depending on the requested sign and the sign of the term in which
5086 * the integer division appears.
5088 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
5089 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
5092 struct isl_to_poly_data data
;
5095 return pwqp_drop_floors(pwqp
);
5101 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
5103 for (i
= 0; i
< pwqp
->n
; ++i
) {
5104 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
5105 isl_pw_qpolynomial
*t
;
5106 t
= isl_pw_qpolynomial_alloc(
5107 isl_set_copy(pwqp
->p
[i
].set
),
5108 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
5109 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
5112 data
.qp
= pwqp
->p
[i
].qp
;
5113 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
5114 &to_polynomial_on_orthant
, &data
) < 0)
5118 isl_pw_qpolynomial_free(pwqp
);
5122 isl_pw_qpolynomial_free(pwqp
);
5123 isl_pw_qpolynomial_free(data
.res
);
5127 static __isl_give isl_pw_qpolynomial
*poly_entry(
5128 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
5132 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
5135 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
5136 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
5138 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
5139 &poly_entry
, &sign
);
5142 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
5143 __isl_take isl_qpolynomial
*qp
)
5147 isl_vec
*aff
= NULL
;
5148 isl_basic_map
*bmap
= NULL
;
5155 is_affine
= isl_poly_is_affine(qp
->poly
);
5159 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
5160 "input quasi-polynomial not affine", goto error
);
5161 aff
= isl_qpolynomial_extract_affine(qp
);
5164 space
= isl_qpolynomial_get_space(qp
);
5165 pos
= 1 + isl_space_offset(space
, isl_dim_out
);
5166 n_div
= qp
->div
->n_row
;
5167 bmap
= isl_basic_map_alloc_space(space
, n_div
, 1, 2 * n_div
);
5169 for (i
= 0; i
< n_div
; ++i
) {
5170 k
= isl_basic_map_alloc_div(bmap
);
5173 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
5174 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
5175 bmap
= isl_basic_map_add_div_constraints(bmap
, k
);
5177 k
= isl_basic_map_alloc_equality(bmap
);
5180 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
5181 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
5182 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
5185 isl_qpolynomial_free(qp
);
5186 bmap
= isl_basic_map_finalize(bmap
);
5190 isl_qpolynomial_free(qp
);
5191 isl_basic_map_free(bmap
);